LMFDB - Embedded newform 130.2.m.b.49.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [130,2,Mod(49,130)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("130.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(130, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 130 = 2 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	130.m (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.03805522628$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.50027374224.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 20x^{6} + 132x^{4} + 332x^{2} + 256 $ x^8 + 20x^6 + 132x^4 + 332*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.3
Root			$1.17644i$ of defining polynomial
Character	$\chi$	$=$	130.49
Dual form			130.2.m.b.69.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(1.01883 - 0.588222i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.235468 + 2.22364i) q^{5} +(1.01883 + 0.588222i) q^{6} +(1.04346 - 1.80732i) q^{7} -1.00000 q^{8} +(-0.807991 + 1.39948i) q^{9} +(-2.04346 + 0.907896i) q^{10} +(2.59135 - 1.49612i) q^{11} +1.17644i q^{12} +(-1.51883 - 3.27004i) q^{13} +2.08692 q^{14} +(1.06809 + 2.40401i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.09135 - 0.630092i) q^{17} -1.61598 q^{18} +(-3.37028 - 1.94583i) q^{19} +(-1.80799 - 1.31574i) q^{20} -2.45514i q^{21} +(2.59135 + 1.49612i) q^{22} +(-0.778928 + 0.449714i) q^{23} +(-1.01883 + 0.588222i) q^{24} +(-4.88911 - 1.04719i) q^{25} +(2.07252 - 2.95036i) q^{26} +5.43044i q^{27} +(1.04346 + 1.80732i) q^{28} +(-0.235468 - 0.407843i) q^{29} +(-1.54789 + 2.12700i) q^{30} -0.277015i q^{31} +(0.500000 - 0.866025i) q^{32} +(1.76010 - 3.04858i) q^{33} -1.26018i q^{34} +(3.77313 + 2.74584i) q^{35} +(-0.807991 - 1.39948i) q^{36} +(-3.51883 - 6.09479i) q^{37} -3.89166i q^{38} +(-3.47094 - 2.43820i) q^{39} +(0.235468 - 2.22364i) q^{40} +(9.66804 - 5.58184i) q^{41} +(2.12621 - 1.22757i) q^{42} +(6.74056 + 3.89166i) q^{43} +2.99224i q^{44} +(-2.92168 - 2.12621i) q^{45} +(-0.778928 - 0.449714i) q^{46} -11.3189 q^{47} +(-1.01883 - 0.588222i) q^{48} +(1.32239 + 2.29044i) q^{49} +(-1.53766 - 4.75769i) q^{50} -1.48254 q^{51} +(3.59135 + 0.319674i) q^{52} +12.0148i q^{53} +(-4.70290 + 2.71522i) q^{54} +(2.71664 + 6.11451i) q^{55} +(-1.04346 + 1.80732i) q^{56} -4.57832 q^{57} +(0.235468 - 0.407843i) q^{58} +(10.7029 + 6.17932i) q^{59} +(-2.61598 - 0.277015i) q^{60} +(-3.82102 + 6.61820i) q^{61} +(0.239902 - 0.138508i) q^{62} +(1.68621 + 2.92060i) q^{63} +1.00000 q^{64} +(7.62901 - 2.60733i) q^{65} +3.52020 q^{66} +(2.00000 + 3.46410i) q^{67} +(1.09135 - 0.630092i) q^{68} +(-0.529063 + 0.916364i) q^{69} +(-0.491403 + 4.64054i) q^{70} +(4.07532 + 2.35289i) q^{71} +(0.807991 - 1.39948i) q^{72} -15.2984 q^{73} +(3.51883 - 6.09479i) q^{74} +(-5.59715 + 1.80897i) q^{75} +(3.37028 - 1.94583i) q^{76} -6.24455i q^{77} +(0.376079 - 4.22502i) q^{78} -1.63645 q^{79} +(2.04346 - 0.907896i) q^{80} +(0.770331 + 1.33425i) q^{81} +(9.66804 + 5.58184i) q^{82} +11.1943 q^{83} +(2.12621 + 1.22757i) q^{84} +(1.65807 - 2.27840i) q^{85} +7.78333i q^{86} +(-0.479805 - 0.277015i) q^{87} +(-2.59135 + 1.49612i) q^{88} +(-5.98533 + 3.45563i) q^{89} +(0.380513 - 3.59335i) q^{90} +(-7.49486 - 0.667134i) q^{91} -0.899428i q^{92} +(-0.162946 - 0.282231i) q^{93} +(-5.65944 - 9.80244i) q^{94} +(5.12041 - 7.03609i) q^{95} -1.17644i q^{96} +(1.28916 - 2.23289i) q^{97} +(-1.32239 + 2.29044i) q^{98} +4.83540i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 4 q^{4} - 3 q^{5} - 5 q^{7} - 8 q^{8} + 8 q^{9} - 3 q^{10} - 3 q^{11} - 4 q^{13} - 10 q^{14} - 10 q^{15} - 4 q^{16} + 15 q^{17} + 16 q^{18} + 9 q^{19} - 3 q^{22} + 6 q^{23} + 5 q^{25} + q^{26}+ \cdots + 15 q^{98}+O(q^{100}) $ 8 * q + 4 * q^2 - 4 * q^4 - 3 * q^5 - 5 * q^7 - 8 * q^8 + 8 * q^9 - 3 * q^10 - 3 * q^11 - 4 * q^13 - 10 * q^14 - 10 * q^15 - 4 * q^16 + 15 * q^17 + 16 * q^18 + 9 * q^19 - 3 * q^22 + 6 * q^23 + 5 * q^25 + q^26 - 5 * q^28 - 3 * q^29 - 2 * q^30 + 4 * q^32 + 10 * q^33 + 15 * q^35 + 8 * q^36 - 20 * q^37 - 30 * q^39 + 3 * q^40 + 21 * q^41 - 6 * q^42 - 18 * q^43 - 36 * q^45 + 6 * q^46 - 6 * q^47 - 15 * q^49 + 4 * q^50 - 20 * q^51 + 5 * q^52 + 18 * q^54 + 31 * q^55 + 5 * q^56 - 24 * q^57 + 3 * q^58 + 30 * q^59 + 8 * q^60 - 5 * q^61 + 6 * q^62 + 25 * q^63 + 8 * q^64 + 21 * q^65 + 20 * q^66 + 16 * q^67 - 15 * q^68 - 2 * q^69 - 18 * q^70 - 8 * q^72 - 26 * q^73 + 20 * q^74 - 24 * q^75 - 9 * q^76 - 30 * q^78 + 4 * q^79 + 3 * q^80 + 8 * q^81 + 21 * q^82 + 48 * q^83 - 6 * q^84 - 29 * q^85 - 12 * q^87 + 3 * q^88 - 39 * q^89 - 27 * q^90 + 19 * q^91 - 18 * q^93 - 3 * q^94 + 15 * q^95 + 4 * q^97 + 15 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/130\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	1.01883	−	0.588222i	0.588222	−	0.339610i	−0.176172	−	0.984359i	$-0.556372\pi$
$3$	1.01883	−	0.588222i	0.588222	−	0.339610i	0.764394	+	0.644749i	$0.223038\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.235468	+	2.22364i	−0.105305	+	0.994440i
$5$	−0.235468	+	2.22364i	−0.105305	+	0.994440i
$6$	1.01883	+	0.588222i	0.415936	+	0.240140i
$7$	1.04346	−	1.80732i	0.394390	−	0.683104i	−0.598633	−	0.801024i	$-0.704289\pi$
$7$	1.04346	−	1.80732i	0.394390	−	0.683104i	0.993023	+	0.117919i	$0.0376224\pi$
$8$	−1.00000			−0.353553
$9$	−0.807991	+	1.39948i	−0.269330	+	0.466494i
$10$	−2.04346	+	0.907896i	−0.646198	+	0.287102i
$11$	2.59135	−	1.49612i	0.781322	−	0.451096i	−0.0555766	−	0.998454i	$-0.517700\pi$
$11$	2.59135	−	1.49612i	0.781322	−	0.451096i	0.836899	+	0.547358i	$0.184366\pi$
$12$			1.17644i			0.339610i
$13$	−1.51883	−	3.27004i	−0.421248	−	0.906946i
$13$	−1.51883	−	3.27004i	−0.421248	−	0.906946i
$14$	2.08692			0.557752
$15$	1.06809	+	2.40401i	0.275779	+	0.620714i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.09135	−	0.630092i	−0.264692	−	0.152820i	0.361781	−	0.932263i	$-0.382169\pi$
$17$	−1.09135	−	0.630092i	−0.264692	−	0.152820i	−0.626473	+	0.779443i	$0.715502\pi$
$18$	−1.61598			−0.380890
$19$	−3.37028	−	1.94583i	−0.773195	−	0.446404i	0.0608181	−	0.998149i	$-0.480629\pi$
$19$	−3.37028	−	1.94583i	−0.773195	−	0.446404i	−0.834013	+	0.551744i	$0.813962\pi$
$20$	−1.80799	−	1.31574i	−0.404279	−	0.294208i
$21$		−	2.45514i		−	0.535756i
$22$	2.59135	+	1.49612i	0.552478	+	0.318973i
$23$	−0.778928	+	0.449714i	−0.162418	+	0.0937719i	−0.579006	−	0.815324i	$-0.696559\pi$
$23$	−0.778928	+	0.449714i	−0.162418	+	0.0937719i	0.416588	+	0.909095i	$0.363226\pi$
$24$	−1.01883	+	0.588222i	−0.207968	+	0.120070i
$25$	−4.88911	−	1.04719i	−0.977822	−	0.209438i
$26$	2.07252	−	2.95036i	0.406455	−	0.578614i
$27$			5.43044i			1.04509i
$28$	1.04346	+	1.80732i	0.197195	+	0.341552i
$29$	−0.235468	−	0.407843i	−0.0437254	−	0.0757346i	0.843334	−	0.537389i	$-0.180589\pi$
$29$	−0.235468	−	0.407843i	−0.0437254	−	0.0757346i	−0.887060	+	0.461654i	$0.847256\pi$
$30$	−1.54789	+	2.12700i	−0.282605	+	0.388335i
$31$		−	0.277015i		−	0.0497534i	−0.999691	−	0.0248767i	$-0.992081\pi$
$31$		−	0.277015i		−	0.0497534i	0.999691	−	0.0248767i	$-0.00791932\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	1.76010	−	3.04858i	0.306394	−	0.530689i
$34$		−	1.26018i		−	0.216120i
$35$	3.77313	+	2.74584i	0.637775	+	0.464132i
$36$	−0.807991	−	1.39948i	−0.134665	−	0.233247i
$37$	−3.51883	−	6.09479i	−0.578492	−	1.00198i	−0.995653	−	0.0931448i	$-0.970308\pi$
$37$	−3.51883	−	6.09479i	−0.578492	−	1.00198i	0.417161	−	0.908833i	$-0.363025\pi$
$38$		−	3.89166i		−	0.631311i
$39$	−3.47094	−	2.43820i	−0.555795	−	0.390425i
$40$	0.235468	−	2.22364i	0.0372308	−	0.351588i
$41$	9.66804	−	5.58184i	1.50989	−	0.871738i	0.509960	−	0.860198i	$-0.329660\pi$
$41$	9.66804	−	5.58184i	1.50989	−	0.871738i	0.999933	−	0.0115395i	$-0.00367323\pi$
$42$	2.12621	−	1.22757i	0.328082	−	0.189418i
$43$	6.74056	+	3.89166i	1.02793	+	0.593473i	0.916390	−	0.400287i	$-0.131090\pi$
$43$	6.74056	+	3.89166i	1.02793	+	0.593473i	0.111536	+	0.993760i	$0.464423\pi$
$44$			2.99224i			0.451096i
$45$	−2.92168	−	2.12621i	−0.435538	−	0.316957i
$46$	−0.778928	−	0.449714i	−0.114847	−	0.0663067i
$47$	−11.3189			−1.65103			−0.825514	−	0.564381i	$-0.809115\pi$
$47$	−11.3189			−1.65103			−0.825514	+	0.564381i	$0.809115\pi$
$48$	−1.01883	−	0.588222i	−0.147055	−	0.0849025i
$49$	1.32239	+	2.29044i	0.188912	+	0.327206i
$50$	−1.53766	−	4.75769i	−0.217458	−	0.672839i
$51$	−1.48254			−0.207597
$52$	3.59135	+	0.319674i	0.498031	+	0.0443309i
$53$			12.0148i			1.65036i	0.564868	+	0.825181i	$0.308927\pi$
$53$			12.0148i			1.65036i	−0.564868	+	0.825181i	$0.691073\pi$
$54$	−4.70290	+	2.71522i	−0.639984	+	0.369495i
$55$	2.71664	+	6.11451i	0.366311	+	0.824480i
$56$	−1.04346	+	1.80732i	−0.139438	+	0.241514i
$57$	−4.57832			−0.606413
$58$	0.235468	−	0.407843i	0.0309185	−	0.0535525i
$59$	10.7029	+	6.17932i	1.39340	+	0.804479i	0.993690	−	0.112163i	$-0.0357779\pi$
$59$	10.7029	+	6.17932i	1.39340	+	0.804479i	0.399709	+	0.916642i	$0.369111\pi$
$60$	−2.61598	−	0.277015i	−0.337722	−	0.0357625i
$61$	−3.82102	+	6.61820i	−0.489232	+	0.847374i	−0.999923	−	0.0123900i	$-0.996056\pi$
$61$	−3.82102	+	6.61820i	−0.489232	+	0.847374i	0.510692	+	0.859764i	$0.329389\pi$
$62$	0.239902	−	0.138508i	0.0304676	−	0.0175905i
$63$	1.68621	+	2.92060i	0.212442	+	0.367961i
$64$	1.00000			0.125000
$65$	7.62901	−	2.60733i	0.946262	−	0.323400i
$66$	3.52020			0.433306
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	0.961946	−	0.273241i	$-0.0880957\pi$
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	−0.717607	+	0.696449i	$0.754762\pi$
$68$	1.09135	−	0.630092i	0.132346	−	0.0764099i
$69$	−0.529063	+	0.916364i	−0.0636917	+	0.110317i
$70$	−0.491403	+	4.64054i	−0.0587339	+	0.554651i
$71$	4.07532	+	2.35289i	0.483651	+	0.279236i	0.721937	−	0.691959i	$-0.243252\pi$
$71$	4.07532	+	2.35289i	0.483651	+	0.279236i	−0.238286	+	0.971195i	$0.576585\pi$
$72$	0.807991	−	1.39948i	0.0952226	−	0.164930i
$73$	−15.2984			−1.79054			−0.895272	−	0.445520i	$-0.853019\pi$
$73$	−15.2984			−1.79054			−0.895272	+	0.445520i	$0.853019\pi$
$74$	3.51883	−	6.09479i	0.409056	−	0.708505i
$75$	−5.59715	+	1.80897i	−0.646303	+	0.208882i
$76$	3.37028	−	1.94583i	0.386598	−	0.223202i
$77$		−	6.24455i		−	0.711633i
$78$	0.376079	−	4.22502i	0.0425825	−	0.478390i
$79$	−1.63645			−0.184115			−0.0920574	−	0.995754i	$-0.529344\pi$
$79$	−1.63645			−0.184115			−0.0920574	+	0.995754i	$0.529344\pi$
$80$	2.04346	−	0.907896i	0.228466	−	0.101506i
$81$	0.770331	+	1.33425i	0.0855923	+	0.148250i
$82$	9.66804	+	5.58184i	1.06766	+	0.616412i
$83$	11.1943			1.22873			0.614367	−	0.789020i	$-0.289411\pi$
$83$	11.1943			1.22873			0.614367	+	0.789020i	$0.289411\pi$
$84$	2.12621	+	1.22757i	0.231989	+	0.133939i
$85$	1.65807	−	2.27840i	0.179843	−	0.247127i
$86$			7.78333i			0.839298i
$87$	−0.479805	−	0.277015i	−0.0514405	−	0.0296992i
$88$	−2.59135	+	1.49612i	−0.276239	+	0.159487i
$89$	−5.98533	+	3.45563i	−0.634444	+	0.366296i	−0.782471	−	0.622687i	$-0.786041\pi$
$89$	−5.98533	+	3.45563i	−0.634444	+	0.366296i	0.148027	+	0.988983i	$0.452708\pi$
$90$	0.380513	−	3.59335i	0.0401096	−	0.378773i
$91$	−7.49486	−	0.667134i	−0.785674	−	0.0699347i
$92$		−	0.899428i		−	0.0937719i
$93$	−0.162946	−	0.282231i	−0.0168968	−	0.0292660i
$94$	−5.65944	−	9.80244i	−0.583727	−	1.01104i
$95$	5.12041	−	7.03609i	0.525343	−	0.721888i
$96$		−	1.17644i		−	0.120070i
$97$	1.28916	−	2.23289i	0.130894	−	0.226716i	−0.793127	−	0.609056i	$-0.791548\pi$
$97$	1.28916	−	2.23289i	0.130894	−	0.226716i	0.924022	+	0.382340i	$0.124882\pi$
$98$	−1.32239	+	2.29044i	−0.133581	+	0.231369i
$99$			4.83540i			0.485976i
$100$	3.35145	−	3.71050i	0.335145	−	0.371050i
$101$	−0.783361	−	1.35682i	−0.0779474	−	0.135009i	0.824417	−	0.565983i	$-0.191503\pi$
$101$	−0.783361	−	1.35682i	−0.0779474	−	0.135009i	−0.902364	+	0.430974i	$0.858170\pi$
$102$	−0.741268	−	1.28391i	−0.0733965	−	0.127126i
$103$		−	0.916364i		−	0.0902920i	−0.998980	−	0.0451460i	$-0.985625\pi$
$103$		−	0.916364i		−	0.0902920i	0.998980	−	0.0451460i	$-0.0143753\pi$
$104$	1.51883	+	3.27004i	0.148934	+	0.320654i
$105$	5.45934	+	0.578108i	0.532777	+	0.0564176i
$106$	−10.4051	+	6.00741i	−1.01064	+	0.583491i
$107$	10.1345	−	5.85118i	0.979743	−	0.565655i	0.0775504	−	0.996988i	$-0.475290\pi$
$107$	10.1345	−	5.85118i	0.979743	−	0.565655i	0.902193	+	0.431334i	$0.141957\pi$
$108$	−4.70290	−	2.71522i	−0.452537	−	0.261272i
$109$		−	15.9902i		−	1.53159i	−0.643087	−	0.765793i	$-0.722347\pi$
$109$		−	15.9902i		−	1.53159i	0.643087	−	0.765793i	$-0.277653\pi$
$110$	−3.93700	+	5.40993i	−0.375378	+	0.515817i
$111$	−7.17018	−	4.13970i	−0.680563	−	0.392923i
$112$	−2.08692			−0.197195
$113$	2.40930	+	1.39101i	0.226648	+	0.130855i	0.609025	−	0.793151i	$-0.291561\pi$
$113$	2.40930	+	1.39101i	0.226648	+	0.130855i	−0.382377	+	0.924007i	$0.624894\pi$
$114$	−2.28916	−	3.96494i	−0.214400	−	0.371351i
$115$	−0.816587	−	1.83794i	−0.0761471	−	0.171389i
$116$	0.470937			0.0437254
$117$	5.80356	+	0.516588i	0.536539	+	0.0477586i
$118$			12.3586i			1.13771i
$119$	−2.27756	+	1.31495i	−0.208784	+	0.120541i
$120$	−1.06809	−	2.40401i	−0.0975027	−	0.219455i
$121$	−1.02326	+	1.77234i	−0.0930240	+	0.161122i
$122$	−7.64204			−0.691878
$123$	6.56672	−	11.3739i	0.592101	−	1.02555i
$124$	0.239902	+	0.138508i	0.0215439	+	0.0124384i
$125$	3.47980	−	10.6250i	0.311243	−	0.950330i
$126$	−1.68621	+	2.92060i	−0.150220	+	0.260188i
$127$	−7.53415	+	4.34985i	−0.668548	+	0.385986i	−0.795526	−	0.605919i	$-0.792805\pi$
$127$	−7.53415	+	4.34985i	−0.668548	+	0.385986i	0.126978	+	0.991906i	$0.459472\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	9.15664			0.806197
$130$	6.07252	+	5.30325i	0.532595	+	0.465126i
$131$	−15.8740			−1.38692			−0.693459	−	0.720496i	$-0.743914\pi$
$131$	−15.8740			−1.38692			−0.693459	+	0.720496i	$0.743914\pi$
$132$	1.76010	+	3.04858i	0.153197	+	0.265345i
$133$	−7.03350	+	4.06079i	−0.609882	+	0.352115i
$134$	−2.00000	+	3.46410i	−0.172774	+	0.299253i
$135$	−12.0753	−	1.27870i	−1.03928	−	0.110053i
$136$	1.09135	+	0.630092i	0.0935827	+	0.0540300i
$137$	−3.61155	+	6.25538i	−0.308555	+	0.534433i	−0.978047	−	0.208386i	$-0.933179\pi$
$137$	−3.61155	+	6.25538i	−0.308555	+	0.534433i	0.669491	+	0.742820i	$0.266512\pi$
$138$	−1.05813			−0.0900737
$139$	9.93700	−	17.2114i	0.842846	−	1.45985i	−0.0446337	−	0.999003i	$-0.514212\pi$
$139$	9.93700	−	17.2114i	0.842846	−	1.45985i	0.887479	−	0.460848i	$-0.152455\pi$
$140$	−4.26453	+	1.89470i	−0.360419	+	0.160132i
$141$	−11.5320	+	6.65801i	−0.971171	+	0.560706i
$142$			4.70577i			0.394900i
$143$	−8.82819	−	6.20147i	−0.738250	−	0.518593i
$144$	1.61598			0.134665
$145$	0.962340	−	0.427562i	0.0799180	−	0.0355071i
$146$	−7.64921	−	13.2488i	−0.633053	−	1.09648i
$147$	2.69457	+	1.55571i	0.222245	+	0.128313i
$148$	7.03766			0.578492
$149$	−0.851450	−	0.491585i	−0.0697535	−	0.0402722i	0.464718	−	0.885459i	$-0.346156\pi$
$149$	−0.851450	−	0.491585i	−0.0697535	−	0.0402722i	−0.534471	+	0.845187i	$0.679489\pi$
$150$	−4.36519	−	3.94279i	−0.356416	−	0.321927i
$151$			8.06034i			0.655941i	0.944688	+	0.327971i	$0.106365\pi$
$151$			8.06034i			0.655941i	−0.944688	+	0.327971i	$0.893635\pi$
$152$	3.37028	+	1.94583i	0.273366	+	0.157828i
$153$	1.76360	−	1.01822i	0.142579	−	0.0823180i
$154$	5.40794	−	3.12228i	0.435784	−	0.251600i
$155$	0.615981	+	0.0652284i	0.0494768	+	0.00523927i
$156$	3.84702	−	1.78682i	0.308008	−	0.143060i
$157$		−	2.73373i		−	0.218176i	−0.994032	−	0.109088i	$-0.965207\pi$
$157$		−	2.73373i		−	0.218176i	0.994032	−	0.109088i	$-0.0347930\pi$
$158$	−0.818224	−	1.41721i	−0.0650944	−	0.112747i
$159$	7.06738	+	12.2411i	0.560480	+	0.970779i
$160$	1.80799	+	1.31574i	0.142934	+	0.104018i
$161$			1.87703i			0.147931i
$162$	−0.770331	+	1.33425i	−0.0605229	+	0.104829i
$163$	12.2885	−	21.2842i	0.962506	−	1.66711i	0.246334	−	0.969185i	$-0.420774\pi$
$163$	12.2885	−	21.2842i	0.962506	−	1.66711i	0.716172	−	0.697924i	$-0.245893\pi$
$164$			11.1637i			0.871738i
$165$	6.36448	+	4.63166i	0.495474	+	0.360574i
$166$	5.59715	+	9.69455i	0.434423	+	0.752443i
$167$	−6.91817	−	11.9826i	−0.535344	−	0.927243i	−0.999147	−	0.0413047i	$-0.986849\pi$
$167$	−6.91817	−	11.9826i	−0.535344	−	0.927243i	0.463802	−	0.885939i	$-0.346485\pi$
$168$			2.45514i			0.189418i
$169$	−8.38631	+	9.93327i	−0.645101	+	0.764097i
$170$	2.80219	+	0.296734i	0.214918	+	0.0227584i
$171$	5.44631	−	3.14443i	0.416490	−	0.240460i
$172$	−6.74056	+	3.89166i	−0.513963	+	0.296737i
$173$	−11.4079	−	6.58638i	−0.867330	−	0.500753i	−0.000869643	−	1.00000i	$-0.500277\pi$
$173$	−11.4079	−	6.58638i	−0.867330	−	0.500753i	−0.866460	+	0.499247i	$0.833610\pi$
$174$		−	0.554031i		−	0.0420010i
$175$	−6.99420	+	7.74350i	−0.528712	+	0.585354i
$176$	−2.59135	−	1.49612i	−0.195330	−	0.112774i
$177$	14.5392			1.09284
$178$	−5.98533	−	3.45563i	−0.448620	−	0.259011i
$179$	−1.55786	−	2.69828i	−0.116440	−	0.201679i	0.801915	−	0.597438i	$-0.203815\pi$
$179$	−1.55786	−	2.69828i	−0.116440	−	0.201679i	−0.918354	+	0.395759i	$0.870481\pi$
$180$	3.30219	−	1.46714i	0.246131	−	0.109354i
$181$	7.91439			0.588272			0.294136	−	0.955764i	$-0.404968\pi$
$181$	7.91439			0.588272			0.294136	+	0.955764i	$0.404968\pi$
$182$	−3.16967	−	6.82430i	−0.234952	−	0.505851i
$183$			8.99043i			0.664592i
$184$	0.778928	−	0.449714i	0.0574233	−	0.0331534i
$185$	14.3812	−	6.38946i	1.05732	−	0.469763i
$186$	0.162946	−	0.282231i	0.0119478	−	0.0206942i
$187$	−3.77077			−0.275746
$188$	5.65944	−	9.80244i	0.412757	−	0.714916i
$189$	9.81457	+	5.66644i	0.713905	+	0.412173i
$190$	8.65364	+	0.916364i	0.627801	+	0.0664800i
$191$	−6.98046	+	12.0905i	−0.505088	+	0.874839i	0.494894	+	0.868953i	$0.335207\pi$
$191$	−6.98046	+	12.0905i	−0.505088	+	0.874839i	−0.999983	+	0.00588562i	$0.998127\pi$
$192$	1.01883	−	0.588222i	0.0735277	−	0.0424512i
$193$	6.81379	+	11.8018i	0.490467	+	0.849514i	0.999940	−	0.0109726i	$-0.00349276\pi$
$193$	6.81379	+	11.8018i	0.490467	+	0.849514i	−0.509472	+	0.860487i	$0.670159\pi$
$194$	2.57832			0.185113
$195$	6.23897	−	7.14398i	0.446782	−	0.511591i
$196$	−2.64477			−0.188912
$197$	8.86097	+	15.3477i	0.631318	+	1.09348i	0.987282	+	0.158976i	$0.0508191\pi$
$197$	8.86097	+	15.3477i	0.631318	+	1.09348i	−0.355964	+	0.934500i	$0.615848\pi$
$198$	−4.18758	+	2.41770i	−0.297598	+	0.171818i
$199$	7.18270	−	12.4408i	0.509168	−	0.881905i	−0.490775	−	0.871286i	$-0.663286\pi$
$199$	7.18270	−	12.4408i	0.509168	−	0.881905i	0.999944	−	0.0106193i	$-0.00338028\pi$
$200$	4.88911	+	1.04719i	0.345712	+	0.0740477i
$201$	4.07532	+	2.35289i	0.287451	+	0.165960i
$202$	0.783361	−	1.35682i	0.0551171	−	0.0954656i
$203$	−0.982807			−0.0689795
$204$	0.741268	−	1.28391i	0.0518991	−	0.0898919i
$205$	10.1355	+	22.8125i	0.707892	+	1.59330i
$206$	0.793595	−	0.458182i	0.0552924	−	0.0319231i
$207$		−	1.45346i		−	0.101022i
$208$	−2.07252	+	2.95036i	−0.143704	+	0.204571i
$209$	−11.6448			−0.805486
$210$	2.22901	+	5.01698i	0.153816	+	0.346204i
$211$	10.1115	+	17.5137i	0.696108	+	1.20569i	0.969806	+	0.243878i	$0.0784197\pi$
$211$	10.1115	+	17.5137i	0.696108	+	1.20569i	−0.273698	+	0.961816i	$0.588247\pi$
$212$	−10.4051	−	6.00741i	−0.714628	−	0.412591i
$213$	5.53608			0.379326
$214$	10.1345	+	5.85118i	0.692783	+	0.399978i
$215$	−10.2408	+	14.0722i	−0.698419	+	0.959715i
$216$		−	5.43044i		−	0.369495i
$217$	−0.500656	−	0.289054i	−0.0339868	−	0.0196223i
$218$	13.8479	−	7.99511i	0.937901	−	0.541497i
$219$	−15.5865	+	8.99886i	−1.05324	+	0.608086i
$220$	−6.65364	−	0.704577i	−0.448588	−	0.0475026i
$221$	−0.402849	+	4.52577i	−0.0270985	+	0.304436i
$222$		−	8.27941i		−	0.555677i
$223$	−5.57252	−	9.65189i	−0.373164	−	0.646338i	0.616887	−	0.787052i	$-0.288394\pi$
$223$	−5.57252	−	9.65189i	−0.373164	−	0.646338i	−0.990050	+	0.140714i	$0.955060\pi$
$224$	−1.04346	−	1.80732i	−0.0697190	−	0.120757i
$225$	5.41588	−	5.99609i	0.361059	−	0.399740i
$226$			2.78203i			0.185058i
$227$	−8.65364	+	14.9885i	−0.574362	+	0.994825i	0.421748	+	0.906713i	$0.361417\pi$
$227$	−8.65364	+	14.9885i	−0.574362	+	0.994825i	−0.996111	+	0.0881117i	$0.971917\pi$
$228$	2.28916	−	3.96494i	0.151603	−	0.262585i
$229$		−	9.90350i		−	0.654442i	−0.944948	−	0.327221i	$-0.893888\pi$
$229$		−	9.90350i		−	0.654442i	0.944948	−	0.327221i	$-0.106112\pi$
$230$	1.18341	−	1.62616i	0.0780319	−	0.107226i
$231$	−3.67318	−	6.36213i	−0.241677	−	0.418598i
$232$	0.235468	+	0.407843i	0.0154593	+	0.0267762i
$233$			19.1742i			1.25614i	0.778156	+	0.628070i	$0.216155\pi$
$233$			19.1742i			1.25614i	−0.778156	+	0.628070i	$0.783845\pi$
$234$	2.45440	+	5.28432i	0.160449	+	0.345447i
$235$	2.66524	−	25.1691i	0.173861	−	1.64185i
$236$	−10.7029	+	6.17932i	−0.696699	+	0.402240i
$237$	−1.66726	+	0.962594i	−0.108300	+	0.0625272i
$238$	−2.27756	−	1.31495i	−0.147632	−	0.0852356i
$239$		−	2.16448i		−	0.140009i	−0.997547	−	0.0700043i	$-0.977699\pi$
$239$		−	2.16448i		−	0.140009i	0.997547	−	0.0700043i	$-0.0223013\pi$
$240$	1.54789	−	2.12700i	0.0999161	−	0.137297i
$241$	−13.9442	−	8.05067i	−0.898223	−	0.518589i	−0.0215996	−	0.999767i	$-0.506876\pi$
$241$	−13.9442	−	8.05067i	−0.898223	−	0.518589i	−0.876623	+	0.481178i	$0.840209\pi$
$242$	−2.04653			−0.131556
$243$	−12.5390	−	7.23941i	−0.804379	−	0.464408i
$244$	−3.82102	−	6.61820i	−0.244616	−	0.423687i
$245$	−5.40449	+	2.40118i	−0.345280	+	0.153406i
$246$	13.1334			0.837358
$247$	−1.24407	+	13.9763i	−0.0791580	+	0.889293i
$248$			0.277015i			0.0175905i
$249$	11.4051	−	6.58473i	0.722768	−	0.417290i
$250$	10.9414	−	2.29891i	0.691997	−	0.145396i
$251$	9.04439	−	15.6653i	0.570877	−	0.988787i	−0.425600	−	0.904912i	$-0.639937\pi$
$251$	9.04439	−	15.6653i	0.570877	−	0.988787i	0.996476	−	0.0838757i	$-0.0267299\pi$
$252$	−3.37242			−0.212442
$253$	−1.34565	+	2.33073i	−0.0846003	+	0.146532i
$254$	−7.53415	−	4.34985i	−0.472735	−	0.272934i
$255$	0.349090	−	3.29662i	0.0218609	−	0.206442i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	8.69939	−	5.02260i	0.542653	−	0.313301i	−0.203500	−	0.979075i	$-0.565232\pi$
$257$	8.69939	−	5.02260i	0.542653	−	0.313301i	0.746154	+	0.665774i	$0.231898\pi$
$258$	4.57832	+	7.92989i	0.285034	+	0.493693i
$259$	−14.6870			−0.912607
$260$	−1.55649	+	7.91058i	−0.0965294	+	0.490594i
$261$	0.761025			0.0471063
$262$	−7.93700	−	13.7473i	−0.490350	−	0.849310i
$263$	−13.6855	+	7.90133i	−0.843884	+	0.487217i	−0.858583	−	0.512675i	$-0.828654\pi$
$263$	−13.6855	+	7.90133i	−0.843884	+	0.487217i	0.0146985	+	0.999892i	$0.495321\pi$
$264$	−1.76010	+	3.04858i	−0.108327	+	0.187627i
$265$	−26.7166	−	2.82911i	−1.64119	−	0.173791i
$266$	−7.03350	−	4.06079i	−0.431251	−	0.248983i
$267$	−4.06536	+	7.04141i	−0.248796	+	0.430927i
$268$	−4.00000			−0.244339
$269$	−3.69294	+	6.39635i	−0.225162	+	0.389993i	−0.956368	−	0.292164i	$-0.905625\pi$
$269$	−3.69294	+	6.39635i	−0.225162	+	0.389993i	0.731206	+	0.682157i	$0.238958\pi$
$270$	−4.93028	−	11.0969i	−0.300047	−	0.675335i
$271$	26.8493	−	15.5014i	1.63098	−	0.941645i	0.647184	−	0.762334i	$-0.275947\pi$
$271$	26.8493	−	15.5014i	1.63098	−	0.941645i	0.983793	−	0.179310i	$-0.0573866\pi$
$272$			1.26018i			0.0764099i
$273$	−8.02841	+	3.72894i	−0.485901	+	0.225686i
$274$	−7.22309			−0.436363
$275$	−14.2361	+	4.60104i	−0.858471	+	0.277453i
$276$	−0.529063	−	0.916364i	−0.0318459	−	0.0551586i
$277$	4.07668	+	2.35368i	0.244944	+	0.141419i	0.617447	−	0.786612i	$-0.288167\pi$
$277$	4.07668	+	2.35368i	0.244944	+	0.141419i	−0.372503	+	0.928031i	$0.621500\pi$
$278$	19.8740			1.19196
$279$	0.387678	+	0.223826i	0.0232097	+	0.0134001i
$280$	−3.77313	−	2.74584i	−0.225488	−	0.164095i
$281$		−	10.7771i		−	0.642910i	−0.946925	−	0.321455i	$-0.895828\pi$
$281$		−	10.7771i		−	0.642910i	0.946925	−	0.321455i	$-0.104172\pi$
$282$	−11.5320	−	6.65801i	−0.686721	−	0.396479i
$283$	25.2204	−	14.5610i	1.49919	−	0.865561i	0.499195	−	0.866489i	$-0.333629\pi$
$283$	25.2204	−	14.5610i	1.49919	−	0.865561i	1.00000		0.000928800i	$0.000295646\pi$
$284$	−4.07532	+	2.35289i	−0.241826	+	0.139618i
$285$	1.07805	−	10.1805i	0.0638582	−	0.603042i
$286$	0.956541	−	10.7462i	0.0565615	−	0.635434i
$287$		−	23.2977i		−	1.37522i
$288$	0.807991	+	1.39948i	0.0476113	+	0.0824652i
$289$	−7.70597	−	13.3471i	−0.453292	−	0.785125i
$290$	0.851450	+	0.619630i	0.0499988	+	0.0363859i
$291$		−	3.03325i		−	0.177812i
$292$	7.64921	−	13.2488i	0.447636	−	0.775328i
$293$	−12.7124	+	22.0186i	−0.742668	+	1.28634i	0.208609	+	0.977999i	$0.433106\pi$
$293$	−12.7124	+	22.0186i	−0.742668	+	1.28634i	−0.951277	+	0.308339i	$0.900227\pi$
$294$			3.11143i			0.181462i
$295$	−16.2608	+	22.3443i	−0.946738	+	1.30094i
$296$	3.51883	+	6.09479i	0.204528	+	0.354253i
$297$	8.12458	+	14.0722i	0.471436	+	0.816551i
$298$		−	0.983169i		−	0.0569535i
$299$	2.65364	+	1.86408i	0.153464	+	0.107803i
$300$	1.23196	−	5.75176i	0.0711274	−	0.332078i
$301$	14.0670	−	8.12158i	0.810808	−	0.468120i
$302$	−6.98046	+	4.03017i	−0.401680	+	0.231910i
$303$	−1.59622	−	0.921580i	−0.0917007	−	0.0529434i
$304$			3.89166i			0.223202i
$305$	−13.8167	−	10.0549i	−0.791144	−	0.575744i
$306$	1.76360	+	1.01822i	0.100819	+	0.0582076i
$307$	25.3305			1.44569			0.722843	−	0.691012i	$-0.242835\pi$
$307$	25.3305			1.44569			0.722843	+	0.691012i	$0.242835\pi$
$308$	5.40794	+	3.12228i	0.308146	+	0.177908i
$309$	−0.539025	−	0.933619i	−0.0306641	−	0.0531117i
$310$	0.251501	+	0.566069i	0.0142843	+	0.0321506i
$311$	−24.3495			−1.38074			−0.690368	−	0.723459i	$-0.742551\pi$
$311$	−24.3495			−1.38074			−0.690368	+	0.723459i	$0.742551\pi$
$312$	3.47094	+	2.43820i	0.196503	+	0.138036i
$313$			15.6891i			0.886802i	0.896323	+	0.443401i	$0.146228\pi$
$313$			15.6891i			0.886802i	−0.896323	+	0.443401i	$0.853772\pi$
$314$	2.36748	−	1.36687i	0.133605	−	0.0771367i
$315$	−6.89140	+	3.06181i	−0.388287	+	0.172513i
$316$	0.818224	−	1.41721i	0.0460287	−	0.0797240i
$317$	19.4607			1.09302			0.546510	−	0.837453i	$-0.315956\pi$
$317$	19.4607			1.09302			0.546510	+	0.837453i	$0.315956\pi$
$318$	−7.06738	+	12.2411i	−0.396319	+	0.686445i
$319$	−1.22036	−	0.704577i	−0.0683272	−	0.0394487i
$320$	−0.235468	+	2.22364i	−0.0131631	+	0.124305i
$321$	6.88358	−	11.9227i	0.384204	−	0.665461i
$322$	−1.62556	+	0.938516i	−0.0905888	+	0.0523015i
$323$	2.45211	+	4.24717i	0.136439	+	0.236319i
$324$	−1.54066			−0.0855923
$325$	4.00137	+	17.5781i	0.221956	+	0.975057i
$326$	24.5769			1.36119
$327$	−9.40580	−	16.2913i	−0.520142	−	0.900912i
$328$	−9.66804	+	5.58184i	−0.533828	+	0.308206i
$329$	−11.8108	+	20.4569i	−0.651150	+	1.12782i
$330$	−0.828895	+	7.82763i	−0.0456292	+	0.430897i
$331$	5.73925	+	3.31356i	0.315457	+	0.182129i	0.649366	−	0.760476i	$-0.275034\pi$
$331$	5.73925	+	3.31356i	0.315457	+	0.182129i	−0.333909	+	0.942605i	$0.608368\pi$
$332$	−5.59715	+	9.69455i	−0.307184	+	0.532058i
$333$	11.3727			0.623221
$334$	6.91817	−	11.9826i	0.378546	−	0.655660i
$335$	−8.17384	+	3.63158i	−0.446584	+	0.198415i
$336$	−2.12621	+	1.22757i	−0.115995	+	0.0669695i
$337$		−	11.0614i		−	0.602555i	−0.953537	−	0.301277i	$-0.902587\pi$
$337$		−	11.0614i		−	0.602555i	0.953537	−	0.301277i	$-0.0974130\pi$
$338$	−12.7956	−	2.29613i	−0.695990	−	0.124893i
$339$	3.27290			0.177759
$340$	1.14412	+	2.57514i	0.0620484	+	0.139656i
$341$	−0.414448	−	0.717844i	−0.0224436	−	0.0388734i
$342$	5.44631	+	3.14443i	0.294503	+	0.170031i
$343$	20.1279			1.08680
$344$	−6.74056	−	3.89166i	−0.363427	−	0.209824i
$345$	−1.91308	−	1.39222i	−0.102997	−	0.0749545i
$346$		−	13.1728i		−	0.708172i
$347$	15.3466	+	8.86035i	0.823847	+	0.475649i	0.851741	−	0.523962i	$-0.175547\pi$
$347$	15.3466	+	8.86035i	0.823847	+	0.475649i	−0.0278940	+	0.999611i	$0.508880\pi$
$348$	0.479805	−	0.277015i	0.0257202	−	0.0148496i
$349$	15.3172	−	8.84341i	0.819913	−	0.473377i	−0.0304733	−	0.999536i	$-0.509701\pi$
$349$	15.3172	−	8.84341i	0.819913	−	0.473377i	0.850387	+	0.526158i	$0.176368\pi$
$350$	−10.2032	−	2.18540i	−0.545382	−	0.116815i
$351$	17.7578	−	8.24791i	0.947839	−	0.440241i
$352$		−	2.99224i		−	0.159487i
$353$	−16.8114	−	29.1183i	−0.894783	−	1.54981i	−0.834073	−	0.551654i	$-0.813997\pi$
$353$	−16.8114	−	29.1183i	−0.894783	−	1.54981i	−0.0607098	−	0.998155i	$-0.519336\pi$
$354$	7.26962	+	12.5914i	0.386376	+	0.669223i
$355$	−6.19157	+	8.50799i	−0.328614	+	0.451557i
$356$		−	6.91127i		−	0.366296i
$357$	−1.54697	+	2.67942i	−0.0818741	+	0.141810i
$358$	1.55786	−	2.69828i	0.0823352	−	0.142609i
$359$			17.4880i			0.922981i	0.887145	+	0.461490i	$0.152685\pi$
$359$			17.4880i			0.922981i	−0.887145	+	0.461490i	$0.847315\pi$
$360$	2.92168	+	2.12621i	0.153986	+	0.112061i
$361$	−1.92748	−	3.33849i	−0.101446	−	0.175710i
$362$	3.95720	+	6.85407i	0.207986	+	0.360242i
$363$			2.40762i			0.126367i
$364$	4.32518	−	6.15717i	0.226701	−	0.322723i
$365$	3.60229	−	34.0181i	0.188553	−	1.78059i
$366$	−7.78594	+	4.49521i	−0.406978	+	0.234969i
$367$	6.37373	−	3.67988i	0.332706	−	0.192088i	−0.324336	−	0.945942i	$-0.605141\pi$
$367$	6.37373	−	3.67988i	0.332706	−	0.192088i	0.657042	+	0.753854i	$0.271807\pi$
$368$	0.778928	+	0.449714i	0.0406044	+	0.0234430i
$369$			18.0403i			0.939141i
$370$	12.7240	+	9.25973i	0.661490	+	0.481390i
$371$	21.7147	+	12.5370i	1.12737	+	0.650887i
$372$	0.325893			0.0168968
$373$	−25.2893	−	14.6008i	−1.30943	−	0.756000i	−0.327430	−	0.944875i	$-0.606183\pi$
$373$	−25.2893	−	14.6008i	−1.30943	−	0.756000i	−0.982001	+	0.188875i	$0.939516\pi$
$374$	−1.88538	−	3.26558i	−0.0974909	−	0.168859i
$375$	−2.70454	−	12.8720i	−0.139662	−	0.664706i
$376$	11.3189			0.583727
$377$	−0.976027	+	1.38944i	−0.0502680	+	0.0715596i
$378$			11.3329i			0.582901i
$379$	−13.2943	+	7.67544i	−0.682880	+	0.394261i	−0.800939	−	0.598746i	$-0.795666\pi$
$379$	−13.2943	+	7.67544i	−0.682880	+	0.394261i	0.118059	+	0.993007i	$0.462333\pi$
$380$	3.53323	+	7.95245i	0.181251	+	0.407952i
$381$	−5.11735	+	8.86350i	−0.262170	+	0.454091i
$382$	−13.9609			−0.714303
$383$	1.59622	−	2.76474i	0.0815632	−	0.141272i	−0.822358	−	0.568970i	$-0.807342\pi$
$383$	1.59622	−	2.76474i	0.0815632	−	0.141272i	0.903922	+	0.427698i	$0.140675\pi$
$384$	1.01883	+	0.588222i	0.0519919	+	0.0300176i
$385$	13.8856	+	1.47039i	0.707676	+	0.0749383i
$386$	−6.81379	+	11.8018i	−0.346813	+	0.600697i
$387$	−10.8926	+	6.28885i	−0.553703	+	0.319680i
$388$	1.28916	+	2.23289i	0.0654472	+	0.113358i
$389$	28.9316			1.46689			0.733445	−	0.679749i	$-0.237911\pi$
$389$	28.9316			1.46689			0.733445	+	0.679749i	$0.237911\pi$
$390$	9.30635	+	1.83112i	0.471246	+	0.0927224i
$391$	1.13345			0.0573208
$392$	−1.32239	−	2.29044i	−0.0667906	−	0.115685i
$393$	−16.1729	+	9.33743i	−0.815815	+	0.471011i
$394$	−8.86097	+	15.3477i	−0.446409	+	0.773204i
$395$	0.385332	−	3.63886i	0.0193881	−	0.183091i
$396$	−4.18758	−	2.41770i	−0.210434	−	0.121494i
$397$	−2.49557	+	4.32245i	−0.125249	+	0.216937i	−0.921830	−	0.387594i	$-0.873306\pi$
$397$	−2.49557	+	4.32245i	−0.125249	+	0.216937i	0.796581	+	0.604531i	$0.206640\pi$
$398$	14.3654			0.720073
$399$	−4.77729	+	8.27451i	−0.239164	+	0.414244i
$400$	1.53766	+	4.75769i	0.0768830	+	0.237884i
$401$	3.46032	−	1.99782i	0.172800	−	0.0997662i	−0.411105	−	0.911588i	$-0.634857\pi$
$401$	3.46032	−	1.99782i	0.172800	−	0.0997662i	0.583905	+	0.811822i	$0.301524\pi$
$402$			4.70577i			0.234703i
$403$	−0.905851	+	0.420739i	−0.0451236	+	0.0209585i
$404$	1.56672			0.0779474
$405$	−3.14828	+	1.39876i	−0.156439	+	0.0695050i
$406$	−0.491403	−	0.851136i	−0.0243879	−	0.0422412i
$407$	−18.2371	−	10.5292i	−0.903977	−	0.521911i
$408$	1.48254			0.0733965
$409$	2.53695	+	1.46471i	0.125444	+	0.0724252i	0.561409	−	0.827538i	$-0.310259\pi$
$409$	2.53695	+	1.46471i	0.125444	+	0.0724252i	−0.435965	+	0.899964i	$0.643593\pi$
$410$	−14.6885	+	20.1838i	−0.725413	+	0.996809i
$411$			8.49756i			0.419154i
$412$	0.793595	+	0.458182i	0.0390976	+	0.0225730i
$413$	22.3361	−	12.8957i	1.09909	−	0.634558i
$414$	1.25873	−	0.726729i	0.0618633	−	0.0357168i
$415$	−2.63591	+	24.8920i	−0.129392	+	1.22190i
$416$	−3.59135	−	0.319674i	−0.176081	−	0.0156733i
$417$		−	23.3806i		−	1.14495i
$418$	−5.82239	−	10.0847i	−0.284782	−	0.493257i
$419$	−4.85425	−	8.40780i	−0.237145	−	0.410748i	0.722749	−	0.691111i	$-0.242878\pi$
$419$	−4.85425	−	8.40780i	−0.237145	−	0.410748i	−0.959894	+	0.280363i	$0.909545\pi$
$420$	−3.23033	+	4.43887i	−0.157624	+	0.216595i
$421$			22.8217i			1.11226i	0.831094	+	0.556132i	$0.187715\pi$
$421$			22.8217i			1.11226i	−0.831094	+	0.556132i	$0.812285\pi$
$422$	−10.1115	+	17.5137i	−0.492222	+	0.852554i
$423$	9.14555	−	15.8406i	0.444672	−	0.770194i
$424$		−	12.0148i		−	0.583491i
$425$	4.67591	+	4.22345i	0.226815	+	0.204867i
$426$	2.76804	+	4.79438i	0.134112	+	0.232289i
$427$	7.97416	+	13.8116i	0.385897	+	0.668392i
$428$			11.7024i			0.565655i
$429$	−12.6423	−	1.12532i	−0.610374	−	0.0543308i
$430$	−17.3073	−	1.83273i	−0.834631	−	0.0883820i
$431$	10.0125	−	5.78073i	0.482286	−	0.278448i	−0.239082	−	0.970999i	$-0.576847\pi$
$431$	10.0125	−	5.78073i	0.482286	−	0.278448i	0.721369	+	0.692551i	$0.243513\pi$
$432$	4.70290	−	2.71522i	0.226268	−	0.130636i
$433$	−10.8821	−	6.28278i	−0.522960	−	0.301931i	0.215185	−	0.976573i	$-0.430965\pi$
$433$	−10.8821	−	6.28278i	−0.522960	−	0.301931i	−0.738145	+	0.674642i	$0.764298\pi$
$434$		−	0.578108i		−	0.0277501i
$435$	0.728960	−	1.00168i	0.0349510	−	0.0480270i
$436$	13.8479	+	7.99511i	0.663196	+	0.382897i
$437$	3.50027			0.167441
$438$	−15.5865	−	8.99886i	−0.744751	−	0.429982i
$439$	−0.905142	−	1.56775i	−0.0432001	−	0.0748247i	0.843617	−	0.536946i	$-0.180422\pi$
$439$	−0.905142	−	1.56775i	−0.0432001	−	0.0748247i	−0.886817	+	0.462121i	$0.847089\pi$
$440$	−2.71664	−	6.11451i	−0.129511	−	0.291498i
$441$	−4.27390			−0.203519
$442$	−4.12085	+	1.91401i	−0.196009	+	0.0910400i
$443$			16.7633i			0.796450i	0.917288	+	0.398225i	$0.130374\pi$
$443$			16.7633i			0.796450i	−0.917288	+	0.398225i	$0.869626\pi$
$444$	7.17018	−	4.13970i	0.340282	−	0.196462i
$445$	−6.27471	−	14.1229i	−0.297450	−	0.669489i
$446$	5.57252	−	9.65189i	0.263867	−	0.457030i
$447$	−1.15664			−0.0547073
$448$	1.04346	−	1.80732i	0.0492988	−	0.0853880i
$449$	6.13311	+	3.54095i	0.289439	+	0.167108i	0.637689	−	0.770294i	$-0.279891\pi$
$449$	6.13311	+	3.54095i	0.289439	+	0.167108i	−0.348250	+	0.937402i	$0.613224\pi$
$450$	7.90071	+	1.69224i	0.372443	+	0.0797731i
$451$	16.7022	−	28.9290i	0.786475	−	1.36222i
$452$	−2.40930	+	1.39101i	−0.113324	+	0.0654277i
$453$	4.74127	+	8.21212i	0.222764	+	0.385839i
$454$	−17.3073			−0.812271
$455$	3.24827	−	16.5087i	0.152281	−	0.773942i
$456$	4.57832			0.214400
$457$	−0.545096	−	0.944133i	−0.0254985	−	0.0441647i	0.852995	−	0.521920i	$-0.174784\pi$
$457$	−0.545096	−	0.944133i	−0.0254985	−	0.0441647i	−0.878493	+	0.477755i	$0.841451\pi$
$458$	8.57668	−	4.95175i	0.400762	−	0.231380i
$459$	3.42168	−	5.92652i	0.159710	−	0.276626i
$460$	2.00000	+	0.211787i	0.0932505	+	0.00987462i
$461$	−13.5007	−	7.79465i	−0.628791	−	0.363033i	0.151493	−	0.988458i	$-0.451592\pi$
$461$	−13.5007	−	7.79465i	−0.628791	−	0.363033i	−0.780284	+	0.625426i	$0.784925\pi$
$462$	3.67318	−	6.36213i	0.170892	−	0.295993i
$463$	19.1896			0.891817			0.445908	−	0.895079i	$-0.352881\pi$
$463$	19.1896			0.891817			0.445908	+	0.895079i	$0.352881\pi$
$464$	−0.235468	+	0.407843i	−0.0109313	+	0.0189337i
$465$	0.665949	−	0.295877i	0.0308826	−	0.0137210i
$466$	−16.6053	+	9.58708i	−0.769226	+	0.444113i
$467$			23.1857i			1.07290i	0.843931	+	0.536452i	$0.180236\pi$
$467$			23.1857i			1.07290i	−0.843931	+	0.536452i	$0.819764\pi$
$468$	−3.34916	+	4.76773i	−0.154815	+	0.220389i
$469$	8.34767			0.385460
$470$	23.1297	−	10.2764i	1.06689	−	0.474013i
$471$	−1.60804	−	2.78521i	−0.0740946	−	0.128336i
$472$	−10.7029	−	6.17932i	−0.492641	−	0.284426i
$473$	23.2895			1.07085
$474$	−1.66726	−	0.962594i	−0.0765799	−	0.0442134i
$475$	14.4400	+	13.0427i	0.662553	+	0.598441i
$476$		−	2.62990i		−	0.120541i
$477$	−16.8145	−	9.70786i	−0.769884	−	0.444493i
$478$	1.87449	−	1.08224i	0.0857374	−	0.0495005i
$479$	3.01812	−	1.74251i	0.137901	−	0.0796174i	−0.429462	−	0.903085i	$-0.641297\pi$
$479$	3.01812	−	1.74251i	0.137901	−	0.0796174i	0.567363	+	0.823467i	$0.307963\pi$
$480$	2.61598	+	0.277015i	0.119403	+	0.0126440i
$481$	−14.5857	+	20.7637i	−0.665051	+	0.946742i
$482$		−	16.1013i		−	0.733396i
$483$	1.10411	+	1.91238i	0.0502388	+	0.0870162i
$484$	−1.02326	−	1.77234i	−0.0465120	−	0.0805611i
$485$	4.66158	+	3.39240i	0.211671	+	0.154041i
$486$		−	14.4788i		−	0.656773i
$487$	1.07023	−	1.85369i	0.0484967	−	0.0839988i	−0.840758	−	0.541411i	$-0.817890\pi$
$487$	1.07023	−	1.85369i	0.0484967	−	0.0839988i	0.889255	+	0.457412i	$0.151224\pi$
$488$	3.82102	−	6.61820i	0.172969	−	0.299592i
$489$		−	28.9133i		−	1.30751i
$490$	−4.78172	−	3.47983i	−0.216016	−	0.157203i
$491$	−13.6201	−	23.5908i	−0.614668	−	1.06464i	−0.990443	−	0.137926i	$-0.955956\pi$
$491$	−13.6201	−	23.5908i	−0.614668	−	1.06464i	0.375774	−	0.926711i	$-0.377377\pi$
$492$	6.56672	+	11.3739i	0.296051	+	0.512775i
$493$			0.593468i			0.0267284i
$494$	−12.7259	+	5.91077i	−0.572565	+	0.265938i
$495$	−10.7522	−	1.13858i	−0.483274	−	0.0511755i
$496$	−0.239902	+	0.138508i	−0.0107719	+	0.00621918i
$497$	8.50486	−	4.91028i	0.381495	−	0.220256i
$498$	11.4051	+	6.58473i	0.511074	+	0.295069i
$499$		−	22.7855i		−	1.02002i	−0.860169	−	0.510010i	$-0.829642\pi$
$499$		−	22.7855i		−	1.02002i	0.860169	−	0.510010i	$-0.170358\pi$
$500$	7.46163	+	8.32611i	0.333694	+	0.372355i
$501$	−14.0969	−	8.13884i	−0.629802	−	0.363616i
$502$	18.0888			0.807341
$503$	−8.31665	−	4.80162i	−0.370821	−	0.214094i	0.302996	−	0.952992i	$-0.402013\pi$
$503$	−8.31665	−	4.80162i	−0.370821	−	0.214094i	−0.673817	+	0.738898i	$0.735346\pi$
$504$	−1.68621	−	2.92060i	−0.0751098	−	0.130094i
$505$	3.20153	−	1.42242i	0.142466	−	0.0632969i
$506$	−2.69130			−0.119643
$507$	−2.70126	+	15.0533i	−0.119967	+	0.668541i
$508$		−	8.69969i		−	0.385986i
$509$	−13.5627	+	7.83041i	−0.601155	+	0.347077i	−0.769496	−	0.638652i	$-0.779492\pi$
$509$	−13.5627	+	7.83041i	−0.601155	+	0.347077i	0.168341	+	0.985729i	$0.446159\pi$
$510$	3.02950	−	1.34599i	0.134149	−	0.0596014i
$511$	−15.9633	+	27.6492i	−0.706173	+	1.22313i
$512$	−1.00000			−0.0441942
$513$	10.5667	−	18.3021i	0.466532	−	0.808057i
$514$	8.69939	+	5.02260i	0.383714	+	0.221537i
$515$	2.03766	+	0.215775i	0.0897900	+	0.00950818i
$516$	−4.57832	+	7.92989i	−0.201549	+	0.349094i
$517$	−29.3312	+	16.9344i	−1.28998	+	0.744773i
$518$	−7.34351	−	12.7193i	−0.322655	−	0.558855i
$519$	−15.4970			−0.680243
$520$	−7.62901	+	2.60733i	−0.334554	+	0.114339i
$521$	3.26689			0.143125			0.0715625	−	0.997436i	$-0.477201\pi$
$521$	3.26689			0.143125			0.0715625	+	0.997436i	$0.477201\pi$
$522$	0.380513	+	0.659067i	0.0166546	+	0.0288466i
$523$	−13.8479	+	7.99511i	−0.605528	+	0.349602i	−0.771213	−	0.636577i	$-0.780350\pi$
$523$	−13.8479	+	7.99511i	−0.605528	+	0.349602i	0.165685	+	0.986179i	$0.447016\pi$
$524$	7.93700	−	13.7473i	0.346730	−	0.600553i
$525$	−2.57100	+	12.0035i	−0.112208	+	0.523874i
$526$	−13.6855	−	7.90133i	−0.596716	−	0.344514i
$527$	−0.174545	+	0.302321i	−0.00760331	+	0.0131693i
$528$	−3.52020			−0.153197
$529$	−11.0955	+	19.2180i	−0.482414	+	0.835565i
$530$	−10.9082	−	24.5518i	−0.473822	−	1.06646i
$531$	−17.2957	+	9.98567i	−0.750569	+	0.433341i
$532$		−	8.12158i		−	0.352115i
$533$	−32.9369	−	23.1370i	−1.42666	−	1.00217i
$534$	−8.13071			−0.351850
$535$	10.6245	+	23.9133i	0.459338	+	1.03386i
$536$	−2.00000	−	3.46410i	−0.0863868	−	0.149626i
$537$	−3.17438	−	1.83273i	−0.136985	−	0.0790881i
$538$	−7.38587			−0.318428
$539$	6.85354	+	3.95689i	0.295203	+	0.170435i
$540$	7.14504	−	9.81818i	0.307474	−	0.422507i
$541$		−	7.38554i		−	0.317529i	−0.987316	−	0.158765i	$-0.949249\pi$
$541$		−	7.38554i		−	0.317529i	0.987316	−	0.158765i	$-0.0507511\pi$
$542$	26.8493	+	15.5014i	1.15327	+	0.665843i
$543$	8.06342	−	4.65542i	0.346035	−	0.199783i
$544$	−1.09135	+	0.630092i	−0.0467913	+	0.0270150i
$545$	35.5564	+	3.76519i	1.52307	+	0.161283i
$546$	−7.24356	−	5.08833i	−0.309996	−	0.217761i
$547$			11.4488i			0.489515i	0.969584	+	0.244757i	$0.0787083\pi$
$547$			11.4488i			0.489515i	−0.969584	+	0.244757i	$0.921292\pi$
$548$	−3.61155	−	6.25538i	−0.154278	−	0.267217i
$549$	−6.17470	−	10.6949i	−0.263530	−	0.456447i
$550$	−11.1027	−	10.0283i	−0.473420	−	0.427609i
$551$			1.83273i			0.0780768i
$552$	0.529063	−	0.916364i	0.0225184	−	0.0390030i
$553$	−1.70757	+	2.95759i	−0.0726131	+	0.125770i
$554$			4.70735i			0.199996i
$555$	10.8935	−	14.9691i	0.462405	−	0.635403i
$556$	9.93700	+	17.2114i	0.421423	+	0.729926i
$557$	−9.70356	−	16.8071i	−0.411153	−	0.712138i	0.583863	−	0.811852i	$-0.301540\pi$
$557$	−9.70356	−	16.8071i	−0.411153	−	0.712138i	−0.995016	+	0.0997144i	$0.968207\pi$
$558$			0.447652i			0.0189506i
$559$	2.48813	−	27.9527i	0.105237	−	1.18227i
$560$	0.491403	−	4.64054i	0.0207656	−	0.196099i
$561$	−3.84177	+	2.21805i	−0.162200	+	0.0936461i
$562$	9.33328	−	5.38857i	0.393700	−	0.227303i
$563$	−7.70563	−	4.44885i	−0.324754	−	0.187497i	0.328756	−	0.944415i	$-0.393371\pi$
$563$	−7.70563	−	4.44885i	−0.324754	−	0.187497i	−0.653509	+	0.756918i	$0.726704\pi$
$564$		−	13.3160i		−	0.560706i
$565$	−3.66042	+	5.02988i	−0.153995	+	0.211608i
$566$	25.2204	+	14.5610i	1.06009	+	0.612044i
$567$	3.21524			0.135027
$568$	−4.07532	−	2.35289i	−0.170997	−	0.0987249i
$569$	3.44997	+	5.97552i	0.144630	+	0.250507i	0.929235	−	0.369490i	$-0.120467\pi$
$569$	3.44997	+	5.97552i	0.144630	+	0.250507i	−0.784605	+	0.619996i	$0.787134\pi$
$570$	9.35561	−	4.15664i	0.391863	−	0.174102i
$571$	−32.4491			−1.35795			−0.678975	−	0.734161i	$-0.737576\pi$
$571$	−32.4491			−1.35795			−0.678975	+	0.734161i	$0.737576\pi$
$572$	9.78473	−	4.54470i	0.409120	−	0.190023i
$573$			16.4242i			0.686132i
$574$	20.1764	−	11.6489i	0.842147	−	0.486214i
$575$	4.27920	−	1.38301i	0.178455	−	0.0576757i
$576$	−0.807991	+	1.39948i	−0.0336663	+	0.0583117i
$577$	−25.3915			−1.05706			−0.528530	−	0.848914i	$-0.677257\pi$
$577$	−25.3915			−1.05706			−0.528530	+	0.848914i	$0.677257\pi$
$578$	7.70597	−	13.3471i	0.320526	−	0.555167i
$579$	13.8842	+	8.01604i	0.577007	+	0.333135i
$580$	−0.110891	+	1.04719i	−0.00460449	+	0.0434823i
$581$	11.6808	−	20.2317i	0.484601	−	0.839354i
$582$	2.62687	−	1.51662i	0.108887	−	0.0628661i
$583$	17.9756	+	31.1346i	0.744473	+	1.28946i
$584$	15.2984			0.633053
$585$	−2.51526	+	12.7834i	−0.103993	+	0.528527i
$586$	−25.4248			−1.05029
$587$	−1.23196	−	2.13382i	−0.0508485	−	0.0880722i	0.839481	−	0.543389i	$-0.182859\pi$
$587$	−1.23196	−	2.13382i	−0.0508485	−	0.0880722i	−0.890329	+	0.455317i	$0.849526\pi$
$588$	−2.69457	+	1.55571i	−0.111122	+	0.0641565i
$589$	−0.539025	+	0.933619i	−0.0222101	+	0.0384691i
$590$	−27.4811	−	2.91007i	−1.13138	−	0.119806i
$591$	18.0556	+	10.4244i	0.742710	+	0.428804i
$592$	−3.51883	+	6.09479i	−0.144623	+	0.250494i
$593$	−40.6651			−1.66992			−0.834958	−	0.550313i	$-0.814508\pi$
$593$	−40.6651			−1.66992			−0.834958	+	0.550313i	$0.814508\pi$
$594$	−8.12458	+	14.0722i	−0.333355	+	0.577389i
$595$	−2.38768	−	5.37410i	−0.0978852	−	0.220316i
$596$	0.851450	−	0.491585i	0.0348767	−	0.0201361i
$597$		−	16.9001i		−	0.691675i
$598$	−0.287524	+	3.23016i	−0.0117577	+	0.132091i
$599$	26.1916			1.07016			0.535079	−	0.844802i	$-0.320282\pi$
$599$	26.1916			1.07016			0.535079	+	0.844802i	$0.320282\pi$
$600$	5.59715	−	1.80897i	0.228503	−	0.0738509i
$601$	6.74916	+	11.6899i	0.275304	+	0.476840i	0.970212	−	0.242259i	$-0.0778882\pi$
$601$	6.74916	+	11.6899i	0.275304	+	0.476840i	−0.694908	+	0.719099i	$0.744555\pi$
$602$	14.0670	+	8.12158i	0.573328	+	0.331011i
$603$	−6.46392			−0.263231
$604$	−6.98046	−	4.03017i	−0.284031	−	0.163985i
$605$	−3.70010	−	2.69270i	−0.150431	−	0.109474i
$606$		−	1.84316i		−	0.0748733i
$607$	8.51183	+	4.91431i	0.345485	+	0.199466i	0.662695	−	0.748890i	$-0.269413\pi$
$607$	8.51183	+	4.91431i	0.345485	+	0.199466i	−0.317210	+	0.948355i	$0.602746\pi$
$608$	−3.37028	+	1.94583i	−0.136683	+	0.0789139i
$609$	−1.00131	+	0.578108i	−0.0405752	+	0.0234261i
$610$	1.79946	−	16.9931i	0.0728580	−	0.688031i
$611$	17.1915	+	37.0132i	0.695492	+	1.49739i
$612$			2.03643i			0.0823180i
$613$	10.3086	+	17.8551i	0.416362	+	0.721161i	0.995570	−	0.0940190i	$-0.0299715\pi$
$613$	10.3086	+	17.8551i	0.416362	+	0.721161i	−0.579208	+	0.815180i	$0.696638\pi$
$614$	12.6652	+	21.9368i	0.511127	+	0.885299i
$615$	23.7451	+	17.2802i	0.957497	+	0.696805i
$616$			6.24455i			0.251600i
$617$	−8.90958	+	15.4318i	−0.358686	+	0.621262i	−0.987742	−	0.156098i	$-0.950108\pi$
$617$	−8.90958	+	15.4318i	−0.358686	+	0.621262i	0.629056	+	0.777360i	$0.283442\pi$
$618$	0.539025	−	0.933619i	0.0216828	−	0.0375557i
$619$			29.3377i			1.17918i	0.807701	+	0.589592i	$0.200711\pi$
$619$			29.3377i			1.17918i	−0.807701	+	0.589592i	$0.799289\pi$
$620$	−0.364480	+	0.500841i	−0.0146379	+	0.0201143i
$621$	−2.44214	−	4.22992i	−0.0979999	−	0.169741i
$622$	−12.1748	−	21.0873i	−0.488164	−	0.845524i
$623$			14.4232i			0.577855i
$624$	−0.376079	+	4.22502i	−0.0150552	+	0.169136i
$625$	22.8068	+	10.2397i	0.912271	+	0.409587i
$626$	−13.5872	+	7.84457i	−0.543053	+	0.313532i
$627$	−11.8640	+	6.84971i	−0.473804	+	0.273551i
$628$	2.36748	+	1.36687i	0.0944728	+	0.0545439i
$629$			8.86875i			0.353620i
$630$	−6.09730	−	4.43723i	−0.242922	−	0.176783i
$631$	−15.5662	−	8.98714i	−0.619680	−	0.357772i	0.157064	−	0.987588i	$-0.449797\pi$
$631$	−15.5662	−	8.98714i	−0.619680	−	0.357772i	−0.776744	+	0.629816i	$0.783130\pi$
$632$	1.63645			0.0650944
$633$	20.6039	+	11.8957i	0.818931	+	0.472810i
$634$	9.73033	+	16.8534i	0.386441	+	0.669335i
$635$	−7.89841	−	17.7775i	−0.313439	−	0.705477i
$636$	−14.1348			−0.560480
$637$	5.48135	−	7.80305i	0.217179	−	0.309168i
$638$		−	1.40915i		−	0.0557890i
$639$	−6.58564	+	3.80222i	−0.260524	+	0.150414i
$640$	−2.04346	+	0.907896i	−0.0807748	+	0.0358877i
$641$	−12.7805	+	22.1365i	−0.504800	+	0.874339i	0.495185	+	0.868788i	$0.335100\pi$
$641$	−12.7805	+	22.1365i	−0.504800	+	0.874339i	−0.999985	+	0.00555129i	$0.998233\pi$
$642$	13.7672			0.543347
$643$	10.9914	−	19.0376i	0.433457	−	0.750769i	−0.563712	−	0.825972i	$-0.690627\pi$
$643$	10.9914	−	19.0376i	0.433457	−	0.750769i	0.997168	+	0.0752028i	$0.0239604\pi$
$644$	−1.62556	−	0.938516i	−0.0640560	−	0.0369827i
$645$	−2.15610	+	20.3610i	−0.0848964	+	0.801715i
$646$	−2.45211	+	4.24717i	−0.0964769	+	0.167103i
$647$	26.9769	−	15.5751i	1.06057	−	0.612321i	0.134981	−	0.990848i	$-0.456903\pi$
$647$	26.9769	−	15.5751i	1.06057	−	0.612321i	0.925590	+	0.378527i	$0.123569\pi$
$648$	−0.770331	−	1.33425i	−0.0302615	−	0.0524144i
$649$	36.9800			1.45159
$650$	−13.2224	+	12.2543i	−0.518625	+	0.480654i
$651$	−0.680112			−0.0266557
$652$	12.2885	+	21.2842i	0.481253	+	0.833554i
$653$	15.4449	−	8.91711i	0.604405	−	0.348954i	−0.166367	−	0.986064i	$-0.553204\pi$
$653$	15.4449	−	8.91711i	0.604405	−	0.348954i	0.770773	+	0.637110i	$0.219870\pi$
$654$	9.40580	−	16.2913i	0.367796	−	0.637041i
$655$	3.73783	−	35.2980i	0.146049	−	1.37921i
$656$	−9.66804	−	5.58184i	−0.377473	−	0.217934i
$657$	12.3610	−	21.4098i	0.482248	−	0.835277i
$658$	−23.6216			−0.920865
$659$	9.89464	−	17.1380i	0.385440	−	0.667602i	−0.606390	−	0.795168i	$-0.707383\pi$
$659$	9.89464	−	17.1380i	0.385440	−	0.667602i	0.991830	+	0.127565i	$0.0407162\pi$
$660$	−7.19338	+	3.19597i	−0.280002	+	0.124403i
$661$	−15.7895	+	9.11607i	−0.614140	+	0.354574i	−0.774584	−	0.632471i	$-0.782041\pi$
$661$	−15.7895	+	9.11607i	−0.614140	+	0.354574i	0.160444	+	0.987045i	$0.448707\pi$
$662$			6.62711i			0.257570i
$663$	2.25172	+	4.84795i	0.0874495	+	0.188279i
$664$	−11.1943			−0.434423
$665$	−7.37355	−	16.5961i	−0.285934	−	0.643570i
$666$	5.68636	+	9.84907i	0.220342	+	0.381644i
$667$	0.366826	+	0.211787i	0.0142035	+	0.00820042i
$668$	13.8363			0.535344
$669$	−11.3549	−	6.55576i	−0.439006	−	0.253460i
$670$	−7.23196	−	5.26296i	−0.279395	−	0.203326i
$671$			22.8668i			0.882763i
$672$	−2.12621	−	1.22757i	−0.0820205	−	0.0473546i
$673$	17.1875	−	9.92322i	0.662530	−	0.382512i	−0.130710	−	0.991421i	$-0.541726\pi$
$673$	17.1875	−	9.92322i	0.662530	−	0.382512i	0.793240	+	0.608909i	$0.208392\pi$
$674$	9.57948	−	5.53072i	0.368988	−	0.213035i
$675$	5.68671	−	26.5500i	0.218882	−	1.02191i
$676$	−4.40930	−	12.2294i	−0.169589	−	0.470361i
$677$		−	4.02129i		−	0.154551i	−0.997010	−	0.0772753i	$-0.975378\pi$
$677$		−	4.02129i		−	0.154551i	0.997010	−	0.0772753i	$-0.0246220\pi$
$678$	1.63645	+	2.83441i	0.0628474	+	0.108855i
$679$	−2.69037	−	4.65986i	−0.103247	−	0.178829i
$680$	−1.65807	+	2.27840i	−0.0635843	+	0.0873727i
$681$			20.3610i			0.780237i
$682$	0.414448	−	0.717844i	0.0158700	−	0.0274877i
$683$	−5.19430	+	8.99680i	−0.198754	+	0.344253i	−0.948125	−	0.317898i	$-0.897023\pi$
$683$	−5.19430	+	8.99680i	−0.198754	+	0.344253i	0.749370	+	0.662151i	$0.230356\pi$
$684$			6.28885i			0.240460i
$685$	−13.0593	−	9.50371i	−0.498970	−	0.363118i
$686$	10.0639	+	17.4312i	0.384242	+	0.665527i
$687$	−5.82545	−	10.0900i	−0.222255	−	0.384957i
$688$		−	7.78333i		−	0.296737i
$689$	39.2889	−	18.2485i	1.49679	−	0.695211i
$690$	0.249155	−	2.35289i	0.00948518	−	0.0895729i
$691$	−24.5864	+	14.1949i	−0.935309	+	0.540001i	−0.888487	−	0.458902i	$-0.848243\pi$
$691$	−24.5864	+	14.1949i	−0.935309	+	0.540001i	−0.0468225	+	0.998903i	$0.514910\pi$
$692$	11.4079	−	6.58638i	0.433665	−	0.250376i
$693$	8.73913	+	5.04554i	0.331972	+	0.191664i
$694$			17.7207i			0.672669i
$695$	35.9320	+	26.1490i	1.36298	+	0.991888i
$696$	0.479805	+	0.277015i	0.0181869	+	0.0105002i
$697$	−14.0683			−0.532875
$698$	15.3172	+	8.84341i	0.579766	+	0.334728i
$699$	11.2787	+	19.5352i	0.426598	+	0.738889i
$700$	−3.20897	−	9.92891i	−0.121288	−	0.375277i
$701$	16.7917			0.634213			0.317106	−	0.948390i	$-0.397289\pi$
$701$	16.7917			0.634213			0.317106	+	0.948390i	$0.397289\pi$
$702$	16.0218	+	11.2547i	0.604703	+	0.424782i
$703$			27.3882i			1.03297i
$704$	2.59135	−	1.49612i	0.0976652	−	0.0563871i
$705$	−12.0896	−	27.2107i	−0.455319	−	1.02482i
$706$	16.8114	−	29.1183i	0.632707	−	1.09588i
$707$	−3.26962			−0.122967
$708$	−7.26962	+	12.5914i	−0.273209	+	0.473212i
$709$	−41.9846	−	24.2398i	−1.57676	−	0.910345i	−0.995307	−	0.0967675i	$-0.969150\pi$
$709$	−41.9846	−	24.2398i	−1.57676	−	0.910345i	−0.581457	−	0.813577i	$-0.697517\pi$
$710$	−10.4639	−	1.10806i	−0.392704	−	0.0415848i
$711$	1.32223	−	2.29018i	0.0495877	−	0.0858883i
$712$	5.98533	−	3.45563i	0.224310	−	0.129505i
$713$	0.124578	+	0.215775i	0.00466547	+	0.00808083i
$714$	−3.09393			−0.115787
$715$	15.8686	−	18.1704i	0.593451	−	0.679535i
$716$	3.11571			0.116440
$717$	−1.27319	−	2.20524i	−0.0475483	−	0.0823561i
$718$	−15.1450	+	8.74400i	−0.565208	+	0.326323i
$719$	6.14778	−	10.6483i	0.229273	−	0.397113i	−0.728320	−	0.685238i	$-0.759698\pi$
$719$	6.14778	−	10.6483i	0.229273	−	0.397113i	0.957593	+	0.288125i	$0.0930317\pi$
$720$	−0.380513	+	3.59335i	−0.0141809	+	0.133916i
$721$	−1.65617	−	0.956188i	−0.0616789	−	0.0356103i
$722$	1.92748	−	3.33849i	0.0717333	−	0.124246i
$723$	−18.9423			−0.704472
$724$	−3.95720	+	6.85407i	−0.147068	+	0.254729i
$725$	0.724141	+	2.24057i	0.0268939	+	0.0832127i
$726$	−2.08506	+	1.20381i	−0.0773839	+	0.0446776i
$727$		−	36.1491i		−	1.34070i	−0.742046	−	0.670349i	$-0.766145\pi$
$727$		−	36.1491i		−	1.34070i	0.742046	−	0.670349i	$-0.233855\pi$
$728$	7.49486	+	0.667134i	0.277778	+	0.0247256i
$729$	−21.6555			−0.802055
$730$	31.2617	−	13.8894i	1.15705	−	0.514069i
$731$	−4.90421	−	8.49435i	−0.181389	−	0.314175i
$732$	−7.78594	−	4.49521i	−0.287777	−	0.166148i
$733$	22.4789			0.830278			0.415139	−	0.909758i	$-0.363733\pi$
$733$	22.4789			0.830278			0.415139	+	0.909758i	$0.363733\pi$
$734$	6.37373	+	3.67988i	0.235259	+	0.135827i
$735$	−4.09383	+	5.62543i	−0.151003	+	0.207497i
$736$			0.899428i			0.0331534i
$737$	10.3654	+	5.98447i	0.381815	+	0.220441i
$738$	−15.6234	+	9.02015i	−0.575104	+	0.332036i
$739$	10.6967	−	6.17575i	0.393485	−	0.227179i	−0.290184	−	0.956971i	$-0.593717\pi$
$739$	10.6967	−	6.17575i	0.393485	−	0.227179i	0.683669	+	0.729792i	$0.260383\pi$
$740$	−1.65715	+	15.6492i	−0.0609179	+	0.575276i
$741$	6.95369	+	14.9713i	0.255450	+	0.549984i
$742$			25.0740i			0.920494i
$743$	11.4818	+	19.8871i	0.421227	+	0.729587i	0.996060	−	0.0886839i	$-0.0282661\pi$
$743$	11.4818	+	19.8871i	0.421227	+	0.729587i	−0.574832	+	0.818271i	$0.694933\pi$
$744$	0.162946	+	0.282231i	0.00597391	+	0.0103471i
$745$	1.29359	−	1.77756i	0.0473936	−	0.0651248i
$746$		−	29.2016i		−	1.06915i
$747$	−9.04489	+	15.6662i	−0.330935	+	0.573197i
$748$	1.88538	−	3.26558i	0.0689365	−	0.119401i
$749$		−	24.4219i		−	0.892355i
$750$	9.79519	−	8.77819i	0.357670	−	0.320534i
$751$	−16.4263	−	28.4511i	−0.599403	−	1.03820i	−0.992909	−	0.118874i	$-0.962071\pi$
$751$	−16.4263	−	28.4511i	−0.599403	−	1.03820i	0.393506	−	0.919322i	$-0.371262\pi$
$752$	5.65944	+	9.80244i	0.206379	+	0.357458i
$753$		−	21.2804i		−	0.775501i
$754$	−1.69130	−	0.150546i	−0.0615935	−	0.00548258i
$755$	−17.9233	−	1.89796i	−0.652294	−	0.0690737i
$756$	−9.81457	+	5.66644i	−0.356952	+	0.206086i
$757$	−28.6323	+	16.5309i	−1.04066	+	0.600826i	−0.920020	−	0.391871i	$-0.871828\pi$
$757$	−28.6323	+	16.5309i	−1.04066	+	0.600826i	−0.120640	+	0.992696i	$0.538495\pi$
$758$	−13.2943	−	7.67544i	−0.482869	−	0.278785i
$759$			3.16616i			0.114924i
$760$	−5.12041	+	7.03609i	−0.185737	+	0.255226i
$761$	−27.3347	−	15.7817i	−0.990882	−	0.572086i	−0.0853441	−	0.996352i	$-0.527199\pi$
$761$	−27.3347	−	15.7817i	−0.990882	−	0.572086i	−0.905538	+	0.424266i	$0.860532\pi$
$762$	−10.2347			−0.370764
$763$	−28.8995	−	16.6851i	−1.04623	−	0.604043i
$764$	−6.98046	−	12.0905i	−0.252544	−	0.437419i
$765$	1.84887	+	4.16137i	0.0668461	+	0.150455i
$766$	3.19245			0.115348
$767$	3.95074	−	44.3842i	0.142653	−	1.60262i
$768$			1.17644i			0.0424512i
$769$	−36.8445	+	21.2722i	−1.32865	+	0.767095i	−0.985090	−	0.172037i	$-0.944965\pi$
$769$	−36.8445	+	21.2722i	−1.32865	+	0.767095i	−0.343556	+	0.939132i	$0.611632\pi$
$770$	5.66940	+	12.7605i	0.204311	+	0.459856i
$771$	5.90880	−	10.2343i	0.212800	−	0.368581i
$772$	−13.6276			−0.490467
$773$	−0.533226	+	0.923574i	−0.0191788	+	0.0332187i	−0.875456	−	0.483299i	$-0.839439\pi$
$773$	−0.533226	+	0.923574i	−0.0191788	+	0.0332187i	0.856277	+	0.516517i	$0.172772\pi$
$774$	−10.8926	−	6.28885i	−0.391527	−	0.226048i
$775$	−0.290088	+	1.35436i	−0.0104203	+	0.0486500i
$776$	−1.28916	+	2.23289i	−0.0462782	+	0.0801561i
$777$	−14.9636	+	8.63922i	−0.536815	+	0.309930i
$778$	14.4658	+	25.0555i	0.518624	+	0.898283i
$779$	−43.4453			−1.55659
$780$	3.06738	+	8.97510i	0.109830	+	0.321360i
$781$	14.0808			0.503850
$782$	0.566723	+	0.981592i	0.0202660	+	0.0351017i
$783$	2.21477	−	1.27870i	0.0791494	−	0.0456969i
$784$	1.32239	−	2.29044i	0.0472281	−	0.0818015i
$785$	6.07883	+	0.643708i	0.216963	+	0.0229749i
$786$	−16.1729	−	9.33743i	−0.576869	−	0.333055i
$787$	0.0215610	−	0.0373447i	0.000768565	−	0.00133119i	−0.865641	−	0.500665i	$-0.833089\pi$
$787$	0.0215610	−	0.0373447i	0.000768565	−	0.00133119i	0.866409	+	0.499334i	$0.166422\pi$
$788$	−17.7219			−0.631318
$789$	−9.29546	+	16.1002i	−0.330927	+	0.573183i
$790$	3.34401	−	1.48572i	0.118975	−	0.0528597i
$791$	5.02802	−	2.90293i	0.178776	−	0.103216i
$792$		−	4.83540i		−	0.171818i
$793$	27.4453	+	2.44296i	0.974610	+	0.0867522i
$794$	−4.99113			−0.177129
$795$	−28.8838	+	12.8329i	−1.02440	+	0.455136i
$796$	7.18270	+	12.4408i	0.254584	+	0.440953i
$797$	29.9559	+	17.2951i	1.06109	+	0.612623i	0.925735	−	0.378174i	$-0.123448\pi$
$797$	29.9559	+	17.2951i	1.06109	+	0.612623i	0.135359	+	0.990797i	$0.456781\pi$
$798$	−9.55458			−0.338229
$799$	12.3529	+	7.13194i	0.437014	+	0.252310i
$800$	−3.35145	+	3.71050i	−0.118492	+	0.131186i
$801$		−	11.1685i		−	0.394619i
$802$	3.46032	+	1.99782i	0.122188	+	0.0705453i
$803$	−39.6436	+	22.8882i	−1.39899	+	0.807708i
$804$	−4.07532	+	2.35289i	−0.143725	+	0.0829799i
$805$	−4.17384	−	0.441982i	−0.147108	−	0.0155778i
$806$	−0.817296	−	0.574120i	−0.0287880	−	0.0202225i
$807$			8.68906i			0.305869i
$808$	0.783361	+	1.35682i	0.0275586	+	0.0477328i
$809$	−3.04046	−	5.26623i	−0.106897	−	0.185151i	0.807615	−	0.589710i	$-0.200758\pi$
$809$	−3.04046	−	5.26623i	−0.106897	−	0.185151i	−0.914512	+	0.404560i	$0.867425\pi$
$810$	−2.78550	−	2.02711i	−0.0978726	−	0.0712254i
$811$			5.47145i			0.192129i	0.995375	+	0.0960644i	$0.0306255\pi$
$811$			5.47145i			0.192129i	−0.995375	+	0.0960644i	$0.969375\pi$
$812$	0.491403	−	0.851136i	0.0172449	−	0.0298690i
$813$	18.2365	−	31.5866i	0.639584	−	1.10779i
$814$		−	21.0583i		−	0.738094i
$815$	44.4348	+	32.3368i	1.55648	+	1.13271i
$816$	0.741268	+	1.28391i	0.0259496	+	0.0449460i
$817$	−15.1450	−	26.2320i	−0.529858	−	0.917741i
$818$			2.92942i			0.102425i
$819$	6.98942	−	9.94987i	0.244230	−	0.347677i
$820$	−24.8240	−	2.62870i	−0.866891	−	0.0917981i
$821$	38.1625	−	22.0331i	1.33188	−	0.768961i	0.346291	−	0.938127i	$-0.387441\pi$
$821$	38.1625	−	22.0331i	1.33188	−	0.768961i	0.985588	+	0.169166i	$0.0541075\pi$
$822$	−7.35910	+	4.24878i	−0.256678	+	0.148193i
$823$	10.8396	+	6.25823i	0.377844	+	0.218148i	0.676880	−	0.736094i	$-0.263332\pi$
$823$	10.8396	+	6.25823i	0.377844	+	0.218148i	−0.299036	+	0.954242i	$0.596665\pi$
$824$			0.916364i			0.0319231i
$825$	−11.7978	+	13.0617i	−0.410745	+	0.454749i
$826$	22.3361	+	12.8957i	0.777171	+	0.448700i
$827$	−51.7679			−1.80015			−0.900074	−	0.435738i	$-0.856488\pi$
$827$	−51.7679			−1.80015			−0.900074	+	0.435738i	$0.856488\pi$
$828$	1.25873	+	0.726729i	0.0437440	+	0.0252556i
$829$	6.95883	+	12.0531i	0.241690	+	0.418620i	0.961196	−	0.275867i	$-0.0889649\pi$
$829$	6.95883	+	12.0531i	0.241690	+	0.418620i	−0.719506	+	0.694487i	$0.755632\pi$
$830$	−22.8751	+	10.1633i	−0.794006	+	0.352772i
$831$	5.53793			0.192109
$832$	−1.51883	−	3.27004i	−0.0526559	−	0.113368i
$833$		−	3.33290i		−	0.115478i
$834$	20.2482	−	11.6903i	0.701139	−	0.404803i
$835$	28.2740	−	12.5620i	0.978462	−	0.434725i
$836$	5.82239	−	10.0847i	0.201371	−	0.348786i
$837$	1.50432			0.0519967
$838$	4.85425	−	8.40780i	0.167687	−	0.290443i
$839$	−43.3416	−	25.0233i	−1.49632	−	0.863899i	−0.496327	−	0.868136i	$-0.665318\pi$
$839$	−43.3416	−	25.0233i	−1.49632	−	0.863899i	−0.999991	+	0.00423634i	$0.998652\pi$
$840$	−5.45934	−	0.578108i	−0.188365	−	0.0199466i
$841$	14.3891	−	24.9227i	0.496176	−	0.859402i
$842$	−19.7642	+	11.4109i	−0.681120	+	0.393245i
$843$	−6.33935	−	10.9801i	−0.218339	−	0.378174i
$844$	−20.2231			−0.696108
$845$	−20.1132	−	20.9871i	−0.691917	−	0.721977i
$846$	18.2911			0.628861
$847$	2.13547	+	3.69874i	0.0733755	+	0.127090i
$848$	10.4051	−	6.00741i	0.357314	−	0.206295i
$849$	17.1302	−	29.6703i	0.587906	−	1.01828i
$850$	−1.31966	+	6.16118i	−0.0452638	+	0.211327i
$851$	5.48183	+	3.16493i	0.187915	+	0.108493i
$852$	−2.76804	+	4.79438i	−0.0948314	+	0.164253i
$853$	−12.7392			−0.436183			−0.218092	−	0.975928i	$-0.569983\pi$
$853$	−12.7392			−0.436183			−0.218092	+	0.975928i	$0.569983\pi$
$854$	−7.97416	+	13.8116i	−0.272870	+	0.472625i
$855$	5.70963	+	12.8510i	0.195265	+	0.439495i
$856$	−10.1345	+	5.85118i	−0.346391	+	0.199989i
$857$			30.3306i			1.03607i	0.855359	+	0.518036i	$0.173337\pi$
$857$			30.3306i			1.03607i	−0.855359	+	0.518036i	$0.826663\pi$
$858$	−5.34658	−	11.5112i	−0.182529	−	0.392985i
$859$	48.7446			1.66314			0.831572	−	0.555417i	$-0.187441\pi$
$859$	48.7446			1.66314			0.831572	+	0.555417i	$0.187441\pi$
$860$	−7.06645	−	15.9049i	−0.240964	−	0.542353i
$861$	−13.7042	−	23.7364i	−0.467038	−	0.808934i
$862$	10.0125	+	5.78073i	0.341028	+	0.196893i
$863$	−17.6100			−0.599451			−0.299725	−	0.954026i	$-0.596895\pi$
$863$	−17.6100			−0.599451			−0.299725	+	0.954026i	$0.596895\pi$
$864$	4.70290	+	2.71522i	0.159996	+	0.0923737i
$865$	17.3319	−	23.8162i	0.589303	−	0.809776i
$866$		−	12.5656i		−	0.426995i
$867$	−15.7021	−	9.06563i	−0.533273	−	0.307885i
$868$	0.500656	−	0.289054i	0.0169934	−	0.00981114i
$869$	−4.24061	+	2.44832i	−0.143853	+	0.0830535i
$870$	1.23196	+	0.130457i	0.0417674	+	0.00442290i
$871$	8.29009	−	11.8015i	0.280899	−	0.399877i
$872$			15.9902i			0.541497i
$873$	2.08326	+	3.60831i	0.0705076	+	0.122123i
$874$	1.75014	+	3.03132i	0.0591992	+	0.102536i
$875$	−15.5718	−	17.3759i	−0.526423	−	0.587413i
$876$		−	17.9977i		−	0.608086i
$877$	20.9644	−	36.3115i	0.707918	−	1.22615i	−0.257709	−	0.966222i	$-0.582968\pi$
$877$	20.9644	−	36.3115i	0.707918	−	1.22615i	0.965628	−	0.259928i	$-0.0836989\pi$
$878$	0.905142	−	1.56775i	0.0305471	−	0.0529091i
$879$			29.9109i			1.00887i
$880$	3.93700	−	5.40993i	0.132716	−	0.182369i
$881$	14.9695	+	25.9280i	0.504336	+	0.873535i	0.999987	+	0.00501392i	$0.00159599\pi$
$881$	14.9695	+	25.9280i	0.504336	+	0.873535i	−0.495652	+	0.868521i	$0.665071\pi$
$882$	−2.13695	−	3.70131i	−0.0719549	−	0.124630i
$883$		−	35.3391i		−	1.18926i	−0.804001	−	0.594629i	$-0.797299\pi$
$883$		−	35.3391i		−	1.18926i	0.804001	−	0.594629i	$-0.202701\pi$
$884$	−3.71800	−	2.61176i	−0.125050	−	0.0878430i
$885$	−3.42353	+	32.3300i	−0.115081	+	1.08676i
$886$	−14.5175	+	8.38166i	−0.487724	+	0.281587i
$887$	36.8682	−	21.2859i	1.23791	−	0.714709i	0.269246	−	0.963071i	$-0.413226\pi$
$887$	36.8682	−	21.2859i	1.23791	−	0.714709i	0.968667	+	0.248362i	$0.0798922\pi$
$888$	7.17018	+	4.13970i	0.240615	+	0.138919i
$889$			18.1555i			0.608917i
$890$	9.09343	−	12.4955i	0.304812	−	0.418850i
$891$	3.99240	+	2.30501i	0.133750	+	0.0772208i
$892$	11.1450			0.373164
$893$	38.1478	+	22.0246i	1.27657	+	0.737026i
$894$	−0.578321	−	1.00168i	−0.0193420	−	0.0335013i
$895$	6.36683	−	2.82874i	0.212820	−	0.0945544i
$896$	2.08692			0.0697190
$897$	3.80010	+	0.338256i	0.126882	+	0.0112940i
$898$			7.08190i			0.236326i
$899$	−0.112979	+	0.0652284i	−0.00376806	+	0.00217549i
$900$	2.48483	+	7.68834i	0.0828276	+	0.256278i
$901$	7.57045	−	13.1124i	0.252208	−	0.436837i
$902$	33.4044			1.11224
$903$	9.55458	−	16.5490i	0.317957	−	0.550717i
$904$	−2.40930	−	1.39101i	−0.0801323	−	0.0462644i
$905$	−1.86359	+	17.5987i	−0.0619478	+	0.585002i
$906$	−4.74127	+	8.21212i	−0.157518	+	0.272829i
$907$	−12.5097	+	7.22247i	−0.415377	+	0.239818i	−0.693098	−	0.720844i	$-0.743755\pi$
$907$	−12.5097	+	7.22247i	−0.415377	+	0.239818i	0.277720	+	0.960662i	$0.410421\pi$
$908$	−8.65364	−	14.9885i	−0.287181	−	0.497412i
$909$	2.53179			0.0839743
$910$	15.9211	−	5.44129i	0.527780	−	0.180377i
$911$	−42.9419			−1.42273			−0.711364	−	0.702824i	$-0.751922\pi$
$911$	−42.9419			−1.42273			−0.711364	+	0.702824i	$0.751922\pi$
$912$	2.28916	+	3.96494i	0.0758017	+	0.131292i
$913$	29.0084	−	16.7480i	0.960037	−	0.554278i
$914$	0.545096	−	0.944133i	0.0180302	−	0.0312292i
$915$	−19.9914	−	2.11696i	−0.660897	−	0.0699846i
$916$	8.57668	+	4.95175i	0.283382	+	0.163610i
$917$	−16.5639	+	28.6895i	−0.546987	+	0.947410i
$918$	6.84336			0.225864
$919$	−20.3770	+	35.2940i	−0.672175	+	1.16424i	0.305111	+	0.952317i	$0.401307\pi$
$919$	−20.3770	+	35.2940i	−0.672175	+	1.16424i	−0.977286	+	0.211925i	$0.932027\pi$
$920$	0.816587	+	1.83794i	0.0269221	+	0.0605952i
$921$	25.8074	−	14.8999i	0.850384	−	0.490970i
$922$		−	15.5893i		−	0.513406i
$923$	1.50432	−	16.9001i	0.0495151	−	0.556273i
$924$	7.34636			0.241677
$925$	10.8215	+	33.4830i	0.355810	+	1.10091i
$926$	9.59481	+	16.6187i	0.315305	+	0.546124i
$927$	1.28243	+	0.740414i	0.0421207	+	0.0243184i
$928$	−0.470937			−0.0154593
$929$	−11.3326	−	6.54286i	−0.371809	−	0.214664i	0.302439	−	0.953169i	$-0.402199\pi$
$929$	−11.3326	−	6.54286i	−0.371809	−	0.214664i	−0.674249	+	0.738504i	$0.735532\pi$
$930$	0.589211	+	0.428790i	0.0193210	+	0.0140606i
$931$		−	10.2926i		−	0.337325i
$932$	−16.6053	−	9.58708i	−0.543925	−	0.314035i
$933$	−24.8080	+	14.3229i	−0.812178	+	0.468911i
$934$	−20.0794	+	11.5928i	−0.657017	+	0.379329i
$935$	0.887897	−	8.38482i	0.0290373	−	0.274213i
$936$	−5.80356	−	0.516588i	−0.189695	−	0.0168852i
$937$			41.0546i			1.34120i	0.741821	+	0.670598i	$0.233962\pi$
$937$			41.0546i			1.34120i	−0.741821	+	0.670598i	$0.766038\pi$
$938$	4.17384	+	7.22930i	0.136281	+	0.236045i
$939$	9.22869	+	15.9846i	0.301167	+	0.521636i
$940$	20.4644	+	14.8927i	0.667476	+	0.485746i
$941$			24.4162i			0.795945i	0.917397	+	0.397973i	$0.130286\pi$
$941$			24.4162i			0.795945i	−0.917397	+	0.397973i	$0.869714\pi$
$942$	1.60804	−	2.78521i	0.0523928	−	0.0907470i
$943$	−5.02047	+	8.69570i	−0.163489	+	0.283171i
$944$		−	12.3586i		−	0.402240i
$945$	−14.9111	+	20.4897i	−0.485059	+	0.666532i
$946$	11.6448	+	20.1693i	0.378604	+	0.655762i
$947$	2.30433	+	3.99122i	0.0748807	+	0.129697i	0.901034	−	0.433748i	$-0.142809\pi$
$947$	2.30433	+	3.99122i	0.0748807	+	0.129697i	−0.826154	+	0.563445i	$0.809476\pi$
$948$		−	1.92519i		−	0.0625272i
$949$	23.2357	+	50.0264i	0.754262	+	1.62393i
$950$	−4.07532	+	19.0268i	−0.132221	+	0.617310i
$951$	19.8271	−	11.4472i	0.642937	−	0.371200i
$952$	2.27756	−	1.31495i	0.0738162	−	0.0426178i
$953$	4.09617	+	2.36493i	0.132688	+	0.0766075i	0.564875	−	0.825177i	$-0.308925\pi$
$953$	4.09617	+	2.36493i	0.132688	+	0.0766075i	−0.432187	+	0.901784i	$0.642258\pi$
$954$		−	19.4157i		−	0.628607i
$955$	−25.2412	−	18.3689i	−0.816787	−	0.594405i
$956$	1.87449	+	1.08224i	0.0606255	+	0.0350021i
$957$	−1.65779			−0.0535887
$958$	3.01812	+	1.74251i	0.0975111	+	0.0562980i
$959$	7.53700	+	13.0545i	0.243383	+	0.421551i
$960$	1.06809	+	2.40401i	0.0344724	+	0.0775892i
$961$	30.9233			0.997525
$962$	−25.2747	−	2.24976i	−0.814889	−	0.0725352i
$963$			18.9108i			0.609392i
$964$	13.9442	−	8.05067i	0.449111	−	0.259295i
$965$	−27.8474	+	12.3724i	−0.896440	+	0.398282i
$966$	−1.10411	+	1.91238i	−0.0355242	+	0.0615297i
$967$	−23.8186			−0.765955			−0.382977	−	0.923758i	$-0.625101\pi$
$967$	−23.8186			−0.765955			−0.382977	+	0.923758i	$0.625101\pi$
$968$	1.02326	−	1.77234i	0.0328889	−	0.0569653i
$969$	4.99656	+	2.88477i	0.160513	+	0.0926720i
$970$	−0.607113	+	5.73325i	−0.0194932	+	0.184083i
$971$	15.8349	−	27.4269i	0.508167	−	0.880170i	−0.491789	−	0.870715i	$-0.663657\pi$
$971$	15.8349	−	27.4269i	0.508167	−	0.880170i	0.999955	−	0.00945572i	$-0.00300989\pi$
$972$	12.5390	−	7.23941i	0.402189	−	0.232204i
$973$	−20.7377	−	35.9188i	−0.664820	−	1.15150i
$974$	2.14046			0.0685847
$975$	14.4165	+	15.5554i	0.461698	+	0.498171i
$976$	7.64204			0.244616
$977$	13.4354	+	23.2707i	0.429835	+	0.744497i	0.996858	−	0.0792052i	$-0.0252382\pi$
$977$	13.4354	+	23.2707i	0.429835	+	0.744497i	−0.567023	+	0.823702i	$0.691905\pi$
$978$	25.0397	−	14.4567i	0.800681	−	0.462273i
$979$	−10.3401	+	17.9095i	−0.330470	+	0.572391i
$980$	0.622761	−	5.88101i	0.0198934	−	0.187862i
$981$	22.3780	+	12.9200i	0.714475	+	0.412502i
$982$	13.6201	−	23.5908i	0.434636	−	0.752812i
$983$	−8.22637			−0.262380			−0.131190	−	0.991357i	$-0.541880\pi$
$983$	−8.22637			−0.262380			−0.131190	+	0.991357i	$0.541880\pi$
$984$	−6.56672	+	11.3739i	−0.209339	+	0.362587i
$985$	−36.2141	+	16.0897i	−1.15388	+	0.512660i
$986$	−0.513958	+	0.296734i	−0.0163678	+	0.00944993i
$987$			27.7894i			0.884548i
$988$	−11.4818	−	8.06556i	−0.365286	−	0.256600i
$989$	−7.00054			−0.222604
$990$	−4.39004	−	9.88093i	−0.139525	−	0.314037i
$991$	11.1157	+	19.2530i	0.353102	+	0.611591i	0.986791	−	0.161997i	$-0.0517935\pi$
$991$	11.1157	+	19.2530i	0.353102	+	0.611591i	−0.633689	+	0.773588i	$0.718460\pi$
$992$	−0.239902	−	0.138508i	−0.00761691	−	0.00439762i
$993$	7.79642			0.247412
$994$	8.50486	+	4.91028i	0.269758	+	0.155745i
$995$	25.9725	+	18.9011i	0.823384	+	0.599206i
$996$			13.1695i			0.417290i
$997$	20.4122	+	11.7850i	0.646459	+	0.373234i	0.787098	−	0.616827i	$-0.211582\pi$
$997$	20.4122	+	11.7850i	0.646459	+	0.373234i	−0.140639	+	0.990061i	$0.544916\pi$
$998$	19.7328	−	11.3928i	0.624632	−	0.360631i
$999$	33.0974	−	19.1088i	1.04716	−	0.604576i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	130.2.m.b.49.3	yes	8
3.2	odd	2		1170.2.bj.a.829.2		8
4.3	odd	2		1040.2.df.a.49.2		8
5.2	odd	4		650.2.m.e.101.2		16
5.3	odd	4		650.2.m.e.101.7		16
5.4	even	2		130.2.m.a.49.2	✓	8
13.2	odd	12		1690.2.b.e.339.13		16
13.3	even	3		1690.2.c.e.1689.5		8
13.4	even	6		130.2.m.a.69.2	yes	8
13.10	even	6		1690.2.c.f.1689.5		8
13.11	odd	12		1690.2.b.e.339.5		16
15.14	odd	2		1170.2.bj.b.829.3		8
20.19	odd	2		1040.2.df.c.49.3		8
39.17	odd	6		1170.2.bj.b.199.3		8
52.43	odd	6		1040.2.df.c.849.3		8
65.2	even	12		8450.2.a.cr.1.5		8
65.4	even	6	inner	130.2.m.b.69.3	yes	8
65.17	odd	12		650.2.m.e.251.2		16
65.24	odd	12		1690.2.b.e.339.12		16
65.28	even	12		8450.2.a.cs.1.4		8
65.29	even	6		1690.2.c.f.1689.4		8
65.37	even	12		8450.2.a.cs.1.5		8
65.43	odd	12		650.2.m.e.251.7		16
65.49	even	6		1690.2.c.e.1689.4		8
65.54	odd	12		1690.2.b.e.339.4		16
65.63	even	12		8450.2.a.cr.1.4		8
195.134	odd	6		1170.2.bj.a.199.2		8
260.199	odd	6		1040.2.df.a.849.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.m.a.49.2	✓	8	5.4	even	2
130.2.m.a.69.2	yes	8	13.4	even	6
130.2.m.b.49.3	yes	8	1.1	even	1	trivial
130.2.m.b.69.3	yes	8	65.4	even	6	inner
650.2.m.e.101.2		16	5.2	odd	4
650.2.m.e.101.7		16	5.3	odd	4
650.2.m.e.251.2		16	65.17	odd	12
650.2.m.e.251.7		16	65.43	odd	12
1040.2.df.a.49.2		8	4.3	odd	2
1040.2.df.a.849.2		8	260.199	odd	6
1040.2.df.c.49.3		8	20.19	odd	2
1040.2.df.c.849.3		8	52.43	odd	6
1170.2.bj.a.199.2		8	195.134	odd	6
1170.2.bj.a.829.2		8	3.2	odd	2
1170.2.bj.b.199.3		8	39.17	odd	6
1170.2.bj.b.829.3		8	15.14	odd	2
1690.2.b.e.339.4		16	65.54	odd	12
1690.2.b.e.339.5		16	13.11	odd	12
1690.2.b.e.339.12		16	65.24	odd	12
1690.2.b.e.339.13		16	13.2	odd	12
1690.2.c.e.1689.4		8	65.49	even	6
1690.2.c.e.1689.5		8	13.3	even	3
1690.2.c.f.1689.4		8	65.29	even	6
1690.2.c.f.1689.5		8	13.10	even	6
8450.2.a.cr.1.4		8	65.63	even	12
8450.2.a.cr.1.5		8	65.2	even	12
8450.2.a.cs.1.4		8	65.28	even	12
8450.2.a.cs.1.5		8	65.37	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 130 = 2 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	130.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.01883 - 0.588222i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.235468 + 2.22364i) q^{5} +(1.01883 + 0.588222i) q^{6} +(1.04346 - 1.80732i) q^{7} -1.00000 q^{8} +(-0.807991 + 1.39948i) q^{9} +(-2.04346 + 0.907896i) q^{10} +(2.59135 - 1.49612i) q^{11} +1.17644i q^{12} +(-1.51883 - 3.27004i) q^{13} +2.08692 q^{14} +(1.06809 + 2.40401i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.09135 - 0.630092i) q^{17} -1.61598 q^{18} +(-3.37028 - 1.94583i) q^{19} +(-1.80799 - 1.31574i) q^{20} -2.45514i q^{21} +(2.59135 + 1.49612i) q^{22} +(-0.778928 + 0.449714i) q^{23} +(-1.01883 + 0.588222i) q^{24} +(-4.88911 - 1.04719i) q^{25} +(2.07252 - 2.95036i) q^{26} +5.43044i q^{27} +(1.04346 + 1.80732i) q^{28} +(-0.235468 - 0.407843i) q^{29} +(-1.54789 + 2.12700i) q^{30} -0.277015i q^{31} +(0.500000 - 0.866025i) q^{32} +(1.76010 - 3.04858i) q^{33} -1.26018i q^{34} +(3.77313 + 2.74584i) q^{35} +(-0.807991 - 1.39948i) q^{36} +(-3.51883 - 6.09479i) q^{37} -3.89166i q^{38} +(-3.47094 - 2.43820i) q^{39} +(0.235468 - 2.22364i) q^{40} +(9.66804 - 5.58184i) q^{41} +(2.12621 - 1.22757i) q^{42} +(6.74056 + 3.89166i) q^{43} +2.99224i q^{44} +(-2.92168 - 2.12621i) q^{45} +(-0.778928 - 0.449714i) q^{46} -11.3189 q^{47} +(-1.01883 - 0.588222i) q^{48} +(1.32239 + 2.29044i) q^{49} +(-1.53766 - 4.75769i) q^{50} -1.48254 q^{51} +(3.59135 + 0.319674i) q^{52} +12.0148i q^{53} +(-4.70290 + 2.71522i) q^{54} +(2.71664 + 6.11451i) q^{55} +(-1.04346 + 1.80732i) q^{56} -4.57832 q^{57} +(0.235468 - 0.407843i) q^{58} +(10.7029 + 6.17932i) q^{59} +(-2.61598 - 0.277015i) q^{60} +(-3.82102 + 6.61820i) q^{61} +(0.239902 - 0.138508i) q^{62} +(1.68621 + 2.92060i) q^{63} +1.00000 q^{64} +(7.62901 - 2.60733i) q^{65} +3.52020 q^{66} +(2.00000 + 3.46410i) q^{67} +(1.09135 - 0.630092i) q^{68} +(-0.529063 + 0.916364i) q^{69} +(-0.491403 + 4.64054i) q^{70} +(4.07532 + 2.35289i) q^{71} +(0.807991 - 1.39948i) q^{72} -15.2984 q^{73} +(3.51883 - 6.09479i) q^{74} +(-5.59715 + 1.80897i) q^{75} +(3.37028 - 1.94583i) q^{76} -6.24455i q^{77} +(0.376079 - 4.22502i) q^{78} -1.63645 q^{79} +(2.04346 - 0.907896i) q^{80} +(0.770331 + 1.33425i) q^{81} +(9.66804 + 5.58184i) q^{82} +11.1943 q^{83} +(2.12621 + 1.22757i) q^{84} +(1.65807 - 2.27840i) q^{85} +7.78333i q^{86} +(-0.479805 - 0.277015i) q^{87} +(-2.59135 + 1.49612i) q^{88} +(-5.98533 + 3.45563i) q^{89} +(0.380513 - 3.59335i) q^{90} +(-7.49486 - 0.667134i) q^{91} -0.899428i q^{92} +(-0.162946 - 0.282231i) q^{93} +(-5.65944 - 9.80244i) q^{94} +(5.12041 - 7.03609i) q^{95} -1.17644i q^{96} +(1.28916 - 2.23289i) q^{97} +(-1.32239 + 2.29044i) q^{98} +4.83540i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 4 q^{4} - 3 q^{5} - 5 q^{7} - 8 q^{8} + 8 q^{9} - 3 q^{10} - 3 q^{11} - 4 q^{13} - 10 q^{14} - 10 q^{15} - 4 q^{16} + 15 q^{17} + 16 q^{18} + 9 q^{19} - 3 q^{22} + 6 q^{23} + 5 q^{25} + q^{26}+ \cdots + 15 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 - 4 * q^4 - 3 * q^5 - 5 * q^7 - 8 * q^8 + 8 * q^9 - 3 * q^10 - 3 * q^11 - 4 * q^13 - 10 * q^14 - 10 * q^15 - 4 * q^16 + 15 * q^17 + 16 * q^18 + 9 * q^19 - 3 * q^22 + 6 * q^23 + 5 * q^25 + q^26 - 5 * q^28 - 3 * q^29 - 2 * q^30 + 4 * q^32 + 10 * q^33 + 15 * q^35 + 8 * q^36 - 20 * q^37 - 30 * q^39 + 3 * q^40 + 21 * q^41 - 6 * q^42 - 18 * q^43 - 36 * q^45 + 6 * q^46 - 6 * q^47 - 15 * q^49 + 4 * q^50 - 20 * q^51 + 5 * q^52 + 18 * q^54 + 31 * q^55 + 5 * q^56 - 24 * q^57 + 3 * q^58 + 30 * q^59 + 8 * q^60 - 5 * q^61 + 6 * q^62 + 25 * q^63 + 8 * q^64 + 21 * q^65 + 20 * q^66 + 16 * q^67 - 15 * q^68 - 2 * q^69 - 18 * q^70 - 8 * q^72 - 26 * q^73 + 20 * q^74 - 24 * q^75 - 9 * q^76 - 30 * q^78 + 4 * q^79 + 3 * q^80 + 8 * q^81 + 21 * q^82 + 48 * q^83 - 6 * q^84 - 29 * q^85 - 12 * q^87 + 3 * q^88 - 39 * q^89 - 27 * q^90 + 19 * q^91 - 18 * q^93 - 3 * q^94 + 15 * q^95 + 4 * q^97 + 15 * q^98

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