LMFDB - Embedded newform 147.2.o.b.101.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,2,Mod(5,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 29]))

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

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

chi := DirichletCharacter("147.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$147 = 3 \cdot 7^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	147.o (of order $42$ , degree $12$ , 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:	$1.17380090971$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			101.12
Character	$\chi$	$=$	147.101
Dual form			147.2.o.b.131.12

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.56819 + 0.615471i) q^{2} +(-1.65243 - 0.519108i) q^{3} +(0.614325 + 0.570011i) q^{4} +(2.65137 + 1.80767i) q^{5} +(-2.27184 - 1.83109i) q^{6} +(2.29514 + 1.31619i) q^{7} +(-0.849326 - 1.76364i) q^{8} +(2.46105 + 1.71558i) q^{9} +(3.04529 + 4.46662i) q^{10} +(-0.541036 - 3.58954i) q^{11} +(-0.719233 - 1.26080i) q^{12} +(-4.31240 + 3.43903i) q^{13} +(2.78914 + 3.47663i) q^{14} +(-3.44282 - 4.36340i) q^{15} +(-0.371690 - 4.95986i) q^{16} +(-4.48139 - 1.38232i) q^{17} +(2.80352 + 4.20507i) q^{18} +(0.711342 - 0.410693i) q^{19} +(0.598410 + 2.62181i) q^{20} +(-3.10931 - 3.36633i) q^{21} +(1.36081 - 5.96209i) q^{22} +(-0.734239 - 2.38034i) q^{23} +(0.487931 + 3.35519i) q^{24} +(1.93536 + 4.93123i) q^{25} +(-8.87931 + 2.73890i) q^{26} +(-3.17615 - 4.11243i) q^{27} +(0.659720 + 2.11682i) q^{28} +(-0.788916 + 0.180065i) q^{29} +(-2.71347 - 8.96161i) q^{30} +(-0.958230 - 0.553234i) q^{31} +(1.31580 - 4.26573i) q^{32} +(-0.969335 + 6.21232i) q^{33} +(-6.17691 - 4.92592i) q^{34} +(3.70601 + 7.63855i) q^{35} +(0.533989 + 2.45675i) q^{36} +(-6.79657 + 6.30630i) q^{37} +(1.36829 - 0.206237i) q^{38} +(8.91118 - 3.44415i) q^{39} +(0.936213 - 6.21137i) q^{40} +(6.13274 - 2.95337i) q^{41} +(-2.80412 - 7.19275i) q^{42} +(6.79183 + 3.27077i) q^{43} +(1.71370 - 2.51354i) q^{44} +(3.42395 + 8.99741i) q^{45} +(0.313603 - 4.18475i) q^{46} +(2.17345 - 5.53786i) q^{47} +(-1.96051 + 8.38877i) q^{48} +(3.53530 + 6.04166i) q^{49} +8.92429i q^{50} +(6.68761 + 4.61052i) q^{51} +(-4.60950 - 0.345434i) q^{52} +(4.53538 - 4.88798i) q^{53} +(-2.44974 - 8.40392i) q^{54} +(5.05422 - 10.4952i) q^{55} +(0.371967 - 5.16567i) q^{56} +(-1.38864 + 0.309379i) q^{57} +(-1.34800 - 0.203178i) q^{58} +(-9.54680 + 6.50889i) q^{59} +(0.372169 - 4.64299i) q^{60} +(2.17722 + 2.34649i) q^{61} +(-1.16219 - 1.45734i) q^{62} +(3.39043 + 7.17670i) q^{63} +(-1.51332 + 1.89764i) q^{64} +(-17.6504 + 1.32271i) q^{65} +(-5.34361 + 9.14553i) q^{66} +(-0.0184595 + 0.0319729i) q^{67} +(-1.96509 - 3.40364i) q^{68} +(-0.0223770 + 4.31450i) q^{69} +(1.11044 + 14.2597i) q^{70} +(-1.83619 - 0.419099i) q^{71} +(0.935435 - 5.79751i) q^{72} +(-0.0286487 + 0.0112438i) q^{73} +(-14.5397 + 5.70641i) q^{74} +(-0.638215 - 9.15318i) q^{75} +(0.671095 + 0.153173i) q^{76} +(3.48276 - 8.95059i) q^{77} +(16.0942 + 0.0834721i) q^{78} +(-2.78927 - 4.83116i) q^{79} +(7.98031 - 13.8223i) q^{80} +(3.11357 + 8.44427i) q^{81} +(11.4350 - 0.856938i) q^{82} +(-3.58517 + 4.49566i) q^{83} +(0.00871762 - 3.84036i) q^{84} +(-9.38301 - 11.7659i) q^{85} +(8.63784 + 9.30938i) q^{86} +(1.39710 + 0.111988i) q^{87} +(-5.87115 + 4.00288i) q^{88} +(11.3571 + 1.71181i) q^{89} +(-0.168222 + 16.2170i) q^{90} +(-14.4240 + 2.21710i) q^{91} +(0.905760 - 1.88083i) q^{92} +(1.29622 + 1.41161i) q^{93} +(6.81678 - 7.34674i) q^{94} +(2.62843 + 0.196973i) q^{95} +(-4.38865 + 6.36578i) q^{96} +6.56063i q^{97} +(1.82557 + 11.6504i) q^{98} +(4.82663 - 9.76224i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$192 q - 14 q^{3} - 44 q^{4} - 28 q^{6} - 28 q^{7} - 26 q^{9} - 28 q^{10} + 21 q^{12} - 28 q^{13} - 10 q^{15} - 20 q^{16} - 3 q^{18} - 42 q^{19} - 14 q^{21} - 34 q^{22} - 14 q^{24} - 16 q^{25} + 7 q^{27}+ \cdots - 136 q^{99}+O(q^{100})$ 192 * q - 14 * q^3 - 44 * q^4 - 28 * q^6 - 28 * q^7 - 26 * q^9 - 28 * q^10 + 21 * q^12 - 28 * q^13 - 10 * q^15 - 20 * q^16 - 3 * q^18 - 42 * q^19 - 14 * q^21 - 34 * q^22 - 14 * q^24 - 16 * q^25 + 7 * q^27 - 70 * q^28 - q^30 - 42 * q^31 - 14 * q^33 + 28 * q^34 + 10 * q^36 + 46 * q^37 + 51 * q^39 + 112 * q^40 - 28 * q^42 - 36 * q^43 - 35 * q^45 + 148 * q^46 + 28 * q^49 - 20 * q^51 - 28 * q^52 - 14 * q^54 + 182 * q^55 + 2 * q^57 + 126 * q^58 - 132 * q^60 - 168 * q^61 - 119 * q^63 - 4 * q^64 - 42 * q^66 - 26 * q^67 + 70 * q^69 + 28 * q^70 + 6 * q^72 - 28 * q^73 - 140 * q^75 - 252 * q^76 + 36 * q^78 - 10 * q^79 + 134 * q^81 + 42 * q^82 + 56 * q^84 - 76 * q^85 + 98 * q^87 - 20 * q^88 + 175 * q^90 + 178 * q^93 + 322 * q^96 - 136 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$ .

$n$	$50$	$52$
$\chi(n)$	$-1$	$e\left(\frac{1}{42}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	1.56819	+	0.615471i	1.10888	+	0.435204i	0.847909	−	0.530143i	$-0.177862\pi$
$2$	1.56819	+	0.615471i	1.10888	+	0.435204i	0.260972	+	0.965346i	$0.415957\pi$
$3$	−1.65243	−	0.519108i	−0.954031	−	0.299707i
$3$	−1.65243	−	0.519108i	−0.954031	−	0.299707i
$4$	0.614325	+	0.570011i	0.307163	+	0.285005i
$5$	2.65137	+	1.80767i	1.18573	+	0.808415i	0.985223	−	0.171278i	$-0.0547895\pi$
$5$	2.65137	+	1.80767i	1.18573	+	0.808415i	0.200504	+	0.979693i	$0.435742\pi$
$6$	−2.27184	−	1.83109i	−0.927473	−	0.747537i
$7$	2.29514	+	1.31619i	0.867480	+	0.497472i
$7$	2.29514	+	1.31619i	0.867480	+	0.497472i
$8$	−0.849326	−	1.76364i	−0.300282	−	0.623542i
$9$	2.46105	+	1.71558i	0.820351	+	0.571860i
$10$	3.04529	+	4.46662i	0.963005	+	1.41247i
$11$	−0.541036	−	3.58954i	−0.163129	−	1.08229i	−0.909181	−	0.416400i	$-0.863291\pi$
$11$	−0.541036	−	3.58954i	−0.163129	−	1.08229i	0.746053	−	0.665887i	$-0.231947\pi$
$12$	−0.719233	−	1.26080i	−0.207625	−	0.363963i
$13$	−4.31240	+	3.43903i	−1.19605	+	0.953815i	−0.999643	−	0.0267087i	$-0.991497\pi$
$13$	−4.31240	+	3.43903i	−1.19605	+	0.953815i	−0.196402	+	0.980523i	$0.562926\pi$
$14$	2.78914	+	3.47663i	0.745430	+	0.929168i
$15$	−3.44282	−	4.36340i	−0.888933	−	1.12662i
$16$	−0.371690	−	4.95986i	−0.0929225	−	1.23997i
$17$	−4.48139	−	1.38232i	−1.08690	−	0.335263i	−0.301002	−	0.953624i	$-0.597321\pi$
$17$	−4.48139	−	1.38232i	−1.08690	−	0.335263i	−0.785895	+	0.618361i	$0.787797\pi$
$18$	2.80352	+	4.20507i	0.660796	+	0.991145i
$19$	0.711342	−	0.410693i	0.163193	−	0.0942195i	−0.416179	−	0.909283i	$-0.636631\pi$
$19$	0.711342	−	0.410693i	0.163193	−	0.0942195i	0.579372	+	0.815063i	$0.303298\pi$
$20$	0.598410	+	2.62181i	0.133809	+	0.586254i
$21$	−3.10931	−	3.36633i	−0.678507	−	0.734594i
$22$	1.36081	−	5.96209i	0.290125	−	1.27112i
$23$	−0.734239	−	2.38034i	−0.153099	−	0.496336i	0.846235	−	0.532810i	$-0.178864\pi$
$23$	−0.734239	−	2.38034i	−0.153099	−	0.496336i	−0.999335	+	0.0364734i	$0.988388\pi$
$24$	0.487931	+	3.35519i	0.0995984	+	0.684875i
$25$	1.93536	+	4.93123i	0.387073	+	0.986246i
$26$	−8.87931	+	2.73890i	−1.74138	+	0.537143i
$27$	−3.17615	−	4.11243i	−0.611250	−	0.791437i
$28$	0.659720	+	2.11682i	0.124675	+	0.400041i
$29$	−0.788916	+	0.180065i	−0.146498	+	0.0334372i	−0.295141	−	0.955454i	$-0.595367\pi$
$29$	−0.788916	+	0.180065i	−0.146498	+	0.0334372i	0.148643	+	0.988891i	$0.452509\pi$
$30$	−2.71347	−	8.96161i	−0.495410	−	1.63616i
$31$	−0.958230	−	0.553234i	−0.172103	−	0.0993638i	0.411474	−	0.911421i	$-0.365014\pi$
$31$	−0.958230	−	0.553234i	−0.172103	−	0.0993638i	−0.583577	+	0.812058i	$0.698347\pi$
$32$	1.31580	−	4.26573i	0.232603	−	0.754082i
$33$	−0.969335	+	6.21232i	−0.168740	+	1.08143i
$34$	−6.17691	−	4.92592i	−1.05933	−	0.844788i
$35$	3.70601	+	7.63855i	0.626431	+	1.29115i
$36$	0.533989	+	2.45675i	0.0889981	+	0.409459i
$37$	−6.79657	+	6.30630i	−1.11735	+	1.03675i	−0.118308	+	0.992977i	$0.537747\pi$
$37$	−6.79657	+	6.30630i	−1.11735	+	1.03675i	−0.999042	+	0.0437717i	$0.986063\pi$
$38$	1.36829	−	0.206237i	0.221966	−	0.0334560i
$39$	8.91118	−	3.44415i	1.42693	−	0.551505i
$40$	0.936213	−	6.21137i	0.148028	−	0.982103i
$41$	6.13274	−	2.95337i	0.957773	−	0.461239i	0.111368	−	0.993779i	$-0.464477\pi$
$41$	6.13274	−	2.95337i	0.957773	−	0.461239i	0.846405	+	0.532540i	$0.178762\pi$
$42$	−2.80412	−	7.19275i	−0.432685	−	1.10987i
$43$	6.79183	+	3.27077i	1.03574	+	0.498788i	0.872918	−	0.487867i	$-0.162225\pi$
$43$	6.79183	+	3.27077i	1.03574	+	0.498788i	0.162826	+	0.986655i	$0.447939\pi$
$44$	1.71370	−	2.51354i	0.258351	−	0.378931i
$45$	3.42395	+	8.99741i	0.510412	+	1.34125i
$46$	0.313603	−	4.18475i	0.0462383	−	0.617007i
$47$	2.17345	−	5.53786i	0.317030	−	0.807779i	−0.680174	−	0.733051i	$-0.738096\pi$
$47$	2.17345	−	5.53786i	0.317030	−	0.807779i	0.997204	−	0.0747285i	$-0.0238090\pi$
$48$	−1.96051	+	8.38877i	−0.282975	+	1.21082i
$49$	3.53530	+	6.04166i	0.505043	+	0.863094i
$50$			8.92429i			1.26208i
$51$	6.68761	+	4.61052i	0.936452	+	0.645602i
$52$	−4.60950	−	0.345434i	−0.639223	−	0.0479031i
$53$	4.53538	−	4.88798i	0.622983	−	0.671415i	−0.340172	−	0.940363i	$-0.610485\pi$
$53$	4.53538	−	4.88798i	0.622983	−	0.671415i	0.963155	+	0.268948i	$0.0866759\pi$
$54$	−2.44974	−	8.40392i	−0.333367	−	1.14363i
$55$	5.05422	−	10.4952i	0.681511	−	1.41517i
$56$	0.371967	−	5.16567i	0.0497062	−	0.690292i
$57$	−1.38864	+	0.309379i	−0.183929	+	0.0409783i
$58$	−1.34800	−	0.203178i	−0.177001	−	0.0266786i
$59$	−9.54680	+	6.50889i	−1.24289	+	0.847386i	−0.992676	−	0.120806i	$-0.961452\pi$
$59$	−9.54680	+	6.50889i	−1.24289	+	0.847386i	−0.250211	+	0.968191i	$0.580500\pi$
$60$	0.372169	−	4.64299i	0.0480469	−	0.599408i
$61$	2.17722	+	2.34649i	0.278765	+	0.300437i	0.856878	−	0.515520i	$-0.172401\pi$
$61$	2.17722	+	2.34649i	0.278765	+	0.300437i	−0.578113	+	0.815957i	$0.696211\pi$
$62$	−1.16219	−	1.45734i	−0.147598	−	0.185082i
$63$	3.39043	+	7.17670i	0.427154	+	0.904179i
$64$	−1.51332	+	1.89764i	−0.189165	+	0.237205i
$65$	−17.6504	+	1.32271i	−2.18926	+	0.164063i
$66$	−5.34361	+	9.14553i	−0.657753	+	1.12574i
$67$	−0.0184595	+	0.0319729i	−0.00225519	+	0.00390611i	−0.867151	−	0.498046i	$-0.834051\pi$
$67$	−0.0184595	+	0.0319729i	−0.00225519	+	0.00390611i	0.864896	+	0.501952i	$0.167385\pi$
$68$	−1.96509	−	3.40364i	−0.238302	−	0.412752i
$69$	−0.0223770	+	4.31450i	−0.00269387	+	0.519405i
$70$	1.11044	+	14.2597i	0.132724	+	1.70436i
$71$	−1.83619	−	0.419099i	−0.217916	−	0.0497379i	0.112169	−	0.993689i	$-0.464220\pi$
$71$	−1.83619	−	0.419099i	−0.217916	−	0.0497379i	−0.330085	+	0.943951i	$0.607077\pi$
$72$	0.935435	−	5.79751i	0.110242	−	0.683243i
$73$	−0.0286487	+	0.0112438i	−0.00335307	+	0.00131598i	−0.367017	−	0.930214i	$-0.619621\pi$
$73$	−0.0286487	+	0.0112438i	−0.00335307	+	0.00131598i	0.363664	+	0.931530i	$0.381526\pi$
$74$	−14.5397	+	5.70641i	−1.69020	+	0.663356i
$75$	−0.638215	−	9.15318i	−0.0736947	−	1.05692i
$76$	0.671095	+	0.153173i	0.0769799	+	0.0175702i
$77$	3.48276	−	8.95059i	0.396897	−	1.02001i
$78$	16.0942	+	0.0834721i	1.82231	+	0.00945135i
$79$	−2.78927	−	4.83116i	−0.313817	−	0.543548i	0.665368	−	0.746516i	$-0.268275\pi$
$79$	−2.78927	−	4.83116i	−0.313817	−	0.543548i	−0.979185	+	0.202968i	$0.934941\pi$
$80$	7.98031	−	13.8223i	0.892226	−	1.54538i
$81$	3.11357	+	8.44427i	0.345952	+	0.938252i
$82$	11.4350	−	0.856938i	1.26279	−	0.0946330i
$83$	−3.58517	+	4.49566i	−0.393524	+	0.493463i	−0.938641	−	0.344897i	$-0.887914\pi$
$83$	−3.58517	+	4.49566i	−0.393524	+	0.493463i	0.545117	+	0.838360i	$0.316485\pi$
$84$	0.00871762	−	3.84036i	0.000951170	−	0.419018i
$85$	−9.38301	−	11.7659i	−1.01773	−	1.27619i
$86$	8.63784	+	9.30938i	0.931442	+	1.00386i
$87$	1.39710	+	0.111988i	0.149785	+	0.0120064i
$88$	−5.87115	+	4.00288i	−0.625867	+	0.426709i
$89$	11.3571	+	1.71181i	1.20385	+	0.181452i	0.720174	−	0.693793i	$-0.244062\pi$
$89$	11.3571	+	1.71181i	1.20385	+	0.181452i	0.483680	+	0.875245i	$0.339300\pi$
$90$	−0.168222	+	16.2170i	−0.0177322	+	1.70942i
$91$	−14.4240	+	2.21710i	−1.51204	+	0.232416i
$92$	0.905760	−	1.88083i	0.0944320	−	0.196090i
$93$	1.29622	+	1.41161i	0.134412	+	0.146377i
$94$	6.81678	−	7.34674i	0.703097	−	0.757758i
$95$	2.62843	+	0.196973i	0.269671	+	0.0202090i
$96$	−4.38865	+	6.36578i	−0.447915	+	0.649705i
$97$			6.56063i			0.666131i	0.942904	+	0.333066i	$0.108083\pi$
$97$			6.56063i			0.666131i	−0.942904	+	0.333066i	$0.891917\pi$
$98$	1.82557	+	11.6504i	0.184411	+	1.17687i
$99$	4.82663	−	9.76224i	0.485094	−	0.981142i
$100$	−1.62191	+	4.13256i	−0.162191	+	0.413256i
$101$	0.557919	−	7.44491i	0.0555150	−	0.740796i	−0.898105	−	0.439782i	$-0.855056\pi$
$101$	0.557919	−	7.44491i	0.0555150	−	0.740796i	0.953620	−	0.301014i	$-0.0973252\pi$
$102$	7.64982	+	11.3462i	0.757445	+	1.12344i
$103$	−0.326837	+	0.479382i	−0.0322042	+	0.0472349i	−0.842003	−	0.539472i	$-0.818624\pi$
$103$	−0.326837	+	0.479382i	−0.0322042	+	0.0472349i	0.809799	+	0.586707i	$0.199576\pi$
$104$	9.72785	+	4.68469i	0.953895	+	0.459371i
$105$	−2.15870	−	14.5460i	−0.210667	−	1.41954i
$106$	10.1208	−	4.87391i	0.983016	−	0.473396i
$107$	−1.79457	+	11.9062i	−0.173487	+	1.15101i	0.717357	+	0.696705i	$0.245352\pi$
$107$	−1.79457	+	11.9062i	−0.173487	+	1.15101i	−0.890845	+	0.454308i	$0.849887\pi$
$108$	0.392940	−	4.33681i	0.0378107	−	0.417310i
$109$	8.81313	−	1.32837i	0.844145	−	0.127234i	0.287289	−	0.957844i	$-0.407246\pi$
$109$	8.81313	−	1.32837i	0.844145	−	0.127234i	0.556855	+	0.830609i	$0.312008\pi$
$110$	14.3855	−	13.3478i	1.37160	−	1.27266i
$111$	14.5045	−	6.89256i	1.37671	−	0.654213i
$112$	5.67503	−	11.8728i	0.536240	−	1.12187i
$113$	6.50491	+	5.18749i	0.611930	+	0.487998i	0.879728	−	0.475477i	$-0.157725\pi$
$113$	6.50491	+	5.18749i	0.611930	+	0.487998i	−0.267798	+	0.963475i	$0.586296\pi$
$114$	−2.36807	−	0.369499i	−0.221790	−	0.0346068i
$115$	2.35614	−	7.63843i	0.219711	−	0.712287i
$116$	−0.587290	−	0.339072i	−0.0545285	−	0.0314821i
$117$	−16.5130	+	1.06536i	−1.52663	+	0.0984922i
$118$	−18.9773	+	4.33144i	−1.74700	+	0.398741i
$119$	−8.46600	−	9.07097i	−0.776077	−	0.831535i
$120$	−4.77140	+	9.77786i	−0.435567	+	0.892592i
$121$	−2.08078	+	0.641835i	−0.189162	+	0.0583487i
$122$	1.97011	+	5.01976i	0.178366	+	0.454468i
$123$	−11.6670	+	1.69669i	−1.05198	+	0.152985i
$124$	−0.273315	−	0.886067i	−0.0245445	−	0.0795712i
$125$	−0.212376	+	0.930480i	−0.0189955	+	0.0832246i
$126$	0.899800	+	13.3412i	0.0801606	+	1.18853i
$127$	0.360894	+	1.58118i	0.0320241	+	0.140307i	0.988413	−	0.151791i	$-0.0485039\pi$
$127$	0.360894	+	1.58118i	0.0320241	+	0.140307i	−0.956389	+	0.292098i	$0.905647\pi$
$128$	−11.2731	+	6.50852i	−0.996410	+	0.575278i
$129$	−9.52514	−	8.93041i	−0.838642	−	0.786279i
$130$	−28.4933	−	8.78903i	−2.49903	−	0.770849i
$131$	−0.773365	−	10.3198i	−0.0675692	−	0.901648i	−0.923264	−	0.384167i	$-0.874489\pi$
$131$	−0.773365	−	10.3198i	−0.0675692	−	0.901648i	0.855694	−	0.517481i	$-0.173130\pi$
$132$	−4.13658	+	3.26386i	−0.360043	+	0.284082i
$133$	2.17318	−	0.00633791i	0.188438	−	0.000549567i
$134$	−0.0486265	+	0.0387784i	−0.00420069	+	0.00334994i
$135$	−0.987214	−	16.6450i	−0.0849659	−	1.43257i
$136$	1.36823	+	9.07761i	0.117325	+	0.778399i
$137$	7.98153	+	11.7068i	0.681908	+	1.00018i	0.998664	+	0.0516683i	$0.0164539\pi$
$137$	7.98153	+	11.7068i	0.681908	+	1.00018i	−0.316756	+	0.948507i	$0.602594\pi$
$138$	−2.69054	+	6.75221i	−0.229034	+	0.574786i
$139$	−2.99108	−	6.21105i	−0.253700	−	0.526814i	0.734754	−	0.678334i	$-0.237298\pi$
$139$	−2.99108	−	6.21105i	−0.253700	−	0.526814i	−0.988454	+	0.151520i	$0.951583\pi$
$140$	−2.07736	+	6.80502i	−0.175569	+	0.575129i
$141$	−6.46622	+	8.02267i	−0.544554	+	0.675631i
$142$	−2.62156	−	1.78735i	−0.219997	−	0.149991i
$143$	14.6777	+	13.6189i	1.22741	+	1.13887i
$144$	7.59429	−	12.8441i	0.632857	−	1.07035i
$145$	−2.41720	−	0.948682i	−0.200738	−	0.0787838i
$146$	−0.0518469			−0.00429088
$147$	−2.70556	−	11.8186i	−0.223151	−	0.974784i
$148$	−7.76996			−0.638687
$149$	−1.19733	−	0.469918i	−0.0980893	−	0.0384972i	0.315789	−	0.948829i	$-0.397731\pi$
$149$	−1.19733	−	0.469918i	−0.0980893	−	0.0384972i	−0.413878	+	0.910332i	$0.635826\pi$
$150$	4.63267	−	14.7468i	0.378256	−	1.20407i
$151$	−0.632570	−	0.586939i	−0.0514778	−	0.0477645i	0.654014	−	0.756482i	$-0.273084\pi$
$151$	−0.632570	−	0.586939i	−0.0514778	−	0.0477645i	−0.705492	+	0.708718i	$0.749274\pi$
$152$	−1.32848	−	0.905741i	−0.107754	−	0.0734653i
$153$	−8.65745	−	11.0902i	−0.699913	−	0.896586i
$154$	10.9705	−	11.8927i	0.884025	−	0.958343i
$155$	−1.54055	−	3.19899i	−0.123740	−	0.256949i
$156$	7.43757	+	2.96364i	0.595482	+	0.237281i
$157$	−8.61976	−	12.6429i	−0.687932	−	1.00901i	−0.998294	−	0.0583919i	$-0.981403\pi$
$157$	−8.61976	−	12.6429i	−0.687932	−	1.00901i	0.310362	−	0.950618i	$-0.399550\pi$
$158$	−1.40068	−	9.29291i	−0.111432	−	0.739304i
$159$	−10.0318	+	5.72269i	−0.795573	+	0.453839i
$160$	11.1997	−	8.93147i	0.885415	−	0.706095i
$161$	1.44780	−	6.42961i	0.114103	−	0.506724i
$162$	−0.314520	+	15.1586i	−0.0247110	+	1.19097i
$163$	1.63031	+	21.7550i	0.127696	+	1.70398i	0.582041	+	0.813159i	$0.302254\pi$
$163$	1.63031	+	21.7550i	0.127696	+	1.70398i	−0.454345	+	0.890826i	$0.650127\pi$
$164$	5.45095	+	1.68140i	0.425648	+	0.131295i
$165$	−13.7999	+	14.7189i	−1.07432	+	1.14587i
$166$	−8.38920	+	4.84351i	−0.651128	+	0.375929i
$167$	−1.42096	−	6.22561i	−0.109957	−	0.481752i	−0.999681	−	0.0252540i	$-0.991961\pi$
$167$	−1.42096	−	6.22561i	−0.109957	−	0.481752i	0.889724	−	0.456498i	$-0.150897\pi$
$168$	−3.29619	+	8.34283i	−0.254307	+	0.643663i
$169$	3.87715	−	16.9869i	0.298242	−	1.30668i
$170$	−7.47280	−	24.2262i	−0.573138	−	1.85807i
$171$	2.45523	+	0.209625i	0.187756	+	0.0160305i
$172$	2.30802	+	5.88073i	0.175985	+	0.448402i
$173$	−8.72274	+	2.69061i	−0.663177	+	0.204563i	−0.608029	−	0.793915i	$-0.708039\pi$
$173$	−8.72274	+	2.69061i	−0.663177	+	0.204563i	−0.0551486	+	0.998478i	$0.517563\pi$
$174$	2.12200	+	1.03549i	0.160869	+	0.0785006i
$175$	−2.04850	+	13.8651i	−0.154852	+	1.04811i
$176$	−17.6025	+	4.01766i	−1.32684	+	0.302843i
$177$	19.1542	−	5.79968i	1.43972	−	0.435931i
$178$	16.7566	+	9.67445i	1.25596	+	0.725130i
$179$	−4.58220	+	14.8551i	−0.342490	+	1.11032i	0.606518	+	0.795070i	$0.292566\pi$
$179$	−4.58220	+	14.8551i	−0.342490	+	1.11032i	−0.949007	+	0.315254i	$0.897910\pi$
$180$	−3.02520	+	7.47903i	−0.225485	+	0.557454i
$181$	8.79767	+	7.01591i	0.653926	+	0.521489i	0.893313	−	0.449436i	$-0.148375\pi$
$181$	8.79767	+	7.01591i	0.653926	+	0.521489i	−0.239387	+	0.970924i	$0.576946\pi$
$182$	−23.9841	−	5.40068i	−1.77782	−	0.400325i
$183$	−2.37963	−	5.00762i	−0.175907	−	0.370174i
$184$	−3.57447	+	3.31662i	−0.263513	+	0.244505i
$185$	−29.4199	+	4.43434i	−2.16299	+	0.326019i
$186$	1.16392	+	3.01146i	0.0853429	+	0.220811i
$187$	−2.53732	+	16.8340i	−0.185547	+	1.23102i
$188$	4.49184	−	2.16316i	0.327601	−	0.157764i
$189$	−1.87696	−	13.6190i	−0.136529	−	0.990636i
$190$	4.00065	+	1.92661i	0.290238	+	0.139771i
$191$	11.8778	−	17.4216i	0.859450	−	1.26058i	−0.104507	−	0.994524i	$-0.533326\pi$
$191$	11.8778	−	17.4216i	0.859450	−	1.26058i	0.963957	−	0.266058i	$-0.0857213\pi$
$192$	3.48574	−	2.35015i	0.251561	−	0.169607i
$193$	0.690353	−	9.21212i	0.0496927	−	0.663103i	−0.915626	−	0.402030i	$-0.868305\pi$
$193$	0.690353	−	9.21212i	0.0496927	−	0.663103i	0.965319	−	0.261073i	$-0.0840763\pi$
$194$	−4.03788	+	10.2883i	−0.289903	+	0.738660i
$195$	29.8527	+	6.97677i	2.13780	+	0.499617i
$196$	−1.27199	+	5.72670i	−0.0908562	+	0.409050i
$197$			3.85561i			0.274701i	0.990523	+	0.137350i	$0.0438586\pi$
$197$			3.85561i			0.274701i	−0.990523	+	0.137350i	$0.956141\pi$
$198$	13.5775	−	12.3384i	0.964908	−	0.876855i
$199$	15.0780	+	1.12994i	1.06885	+	0.0800991i	0.597516	−	0.801857i	$-0.296154\pi$
$199$	15.0780	+	1.12994i	1.06885	+	0.0800991i	0.471332	+	0.881956i	$0.343773\pi$
$200$	7.05317	−	7.60151i	0.498735	−	0.537508i
$201$	0.0471005	−	0.0432504i	0.00332221	−	0.00305065i
$202$	5.45705	−	11.3317i	0.383957	−	0.797294i
$203$	−2.04767	−	0.625088i	−0.143718	−	0.0438726i
$204$	1.48032	+	6.64437i	0.103643	+	0.465199i
$205$	21.5989	+	3.25551i	1.50853	+	0.227374i
$206$	−0.807590	+	0.550606i	−0.0562675	+	0.0383625i
$207$	2.27667	−	7.11780i	0.158240	−	0.494721i
$208$	18.6600	+	20.1107i	1.29384	+	1.39442i
$209$	−1.85906	−	2.33119i	−0.128594	−	0.161252i
$210$	5.56738	−	24.1396i	0.384186	−	1.66579i
$211$	−1.87090	+	2.34604i	−0.128798	+	0.161508i	−0.842049	−	0.539401i	$-0.818651\pi$
$211$	−1.87090	+	2.34604i	−0.128798	+	0.161508i	0.713251	+	0.700909i	$0.247222\pi$
$212$	5.57240	−	0.417594i	0.382714	−	0.0286805i
$213$	2.81662	+	1.64571i	0.192992	+	0.112762i
$214$	−10.1421	+	17.5667i	−0.693302	+	1.20083i
$215$	12.0951	+	20.9494i	0.824882	+	1.42874i
$216$	−4.55527	+	9.09439i	−0.309947	+	0.618795i
$217$	−1.47111	−	2.53096i	−0.0998653	−	0.171813i
$218$	14.6383	+	3.34109i	0.991429	+	0.226287i
$219$	0.0531766	−	0.00370780i	0.00359334	−	0.000250550i
$220$	9.08732	−	3.56651i	0.612667	−	0.240454i
$221$	24.0794	−	9.45047i	1.61976	−	0.635707i
$222$	26.9881	−	1.88177i	1.81132	−	0.126296i
$223$	−14.6233	−	3.33767i	−0.979248	−	0.223507i	−0.297201	−	0.954815i	$-0.596053\pi$
$223$	−14.6233	−	3.33767i	−0.979248	−	0.223507i	−0.682047	+	0.731308i	$0.738910\pi$
$224$	8.63445	−	8.05859i	0.576913	−	0.538437i
$225$	−3.69688	+	15.4563i	−0.246459	+	1.03042i
$226$	7.00821	+	12.1386i	0.466179	+	0.807446i
$227$	4.43828	−	7.68733i	0.294579	−	0.510226i	−0.680308	−	0.732927i	$-0.738154\pi$
$227$	4.43828	−	7.68733i	0.294579	−	0.510226i	0.974887	+	0.222700i	$0.0714872\pi$
$228$	−1.02942	−	0.601479i	−0.0681753	−	0.0398339i
$229$	2.68231	−	0.201011i	0.177252	−	0.0132832i	0.0141915	−	0.999899i	$-0.495483\pi$
$229$	2.68231	−	0.201011i	0.177252	−	0.0132832i	0.163060	+	0.986616i	$0.447864\pi$
$230$	8.39612	−	10.5284i	0.553624	−	0.694222i
$231$	−10.4013	+	12.9823i	−0.684358	+	0.854173i
$232$	0.987617	+	1.23843i	0.0648402	+	0.0813071i
$233$	11.5784	+	12.4785i	0.758524	+	0.817494i	0.987777	−	0.155872i	$-0.0498189\pi$
$233$	11.5784	+	12.4785i	0.758524	+	0.817494i	−0.229253	+	0.973367i	$0.573628\pi$
$234$	−26.5513	−	8.49258i	−1.73571	−	0.555177i
$235$	15.7732	−	10.7540i	1.02893	−	0.701514i
$236$	−9.57498	−	1.44320i	−0.623278	−	0.0939441i
$237$	2.10118	+	9.43109i	0.136486	+	0.612615i
$238$	−7.69341	−	19.4356i	−0.498690	−	1.25982i
$239$	4.82059	−	10.0101i	0.311818	−	0.647497i	−0.684883	−	0.728653i	$-0.740147\pi$
$239$	4.82059	−	10.0101i	0.311818	−	0.647497i	0.996701	+	0.0811559i	$0.0258612\pi$
$240$	−20.3622	+	18.6978i	−1.31437	+	1.20693i
$241$	−2.14013	+	2.30651i	−0.137858	+	0.148575i	−0.798207	−	0.602384i	$-0.794218\pi$
$241$	−2.14013	+	2.30651i	−0.137858	+	0.148575i	0.660349	+	0.750959i	$0.270408\pi$
$242$	−3.65810	−	0.274136i	−0.235151	−	0.0176222i
$243$	−0.761470	−	15.5698i	−0.0488483	−	0.998806i
$244$			2.68255i			0.171732i
$245$	−1.54796	+	22.4093i	−0.0988954	+	1.43168i
$246$	−19.3405	−	4.51999i	−1.23310	−	0.288184i
$247$	−1.65521	+	4.21740i	−0.105318	+	0.268347i
$248$	−0.161858	+	2.15985i	−0.0102780	+	0.137151i
$249$	8.25798	−	5.56768i	0.523328	−	0.352837i
$250$	−0.905730	+	1.32846i	−0.0572834	+	0.0840193i
$251$	−23.9585	−	11.5378i	−1.51225	−	0.728261i	−0.520193	−	0.854049i	$-0.674140\pi$
$251$	−23.9585	−	11.5378i	−1.51225	−	0.728261i	−0.992057	+	0.125787i	$0.959854\pi$
$252$	−2.00797	+	6.34141i	−0.126490	+	0.399471i
$253$	−8.14709	+	3.92343i	−0.512203	+	0.246664i
$254$	−0.407218	+	2.70172i	−0.0255511	+	0.169521i
$255$	9.39699	+	24.3132i	0.588462	+	1.52255i
$256$	−16.8841	+	2.54487i	−1.05525	+	0.159054i
$257$	−21.5969	+	20.0390i	−1.34718	+	1.25000i	−0.405244	+	0.914209i	$0.632813\pi$
$257$	−21.5969	+	20.0390i	−1.34718	+	1.25000i	−0.941936	+	0.335792i	$0.890996\pi$
$258$	−9.44086	−	19.8671i	−0.587762	−	1.23687i
$259$	−23.8993	+	5.52825i	−1.48503	+	0.343508i
$260$	−11.5970	−	9.24834i	−0.719218	−	0.573558i
$261$	−2.25048	−	0.910299i	−0.139301	−	0.0563461i
$262$	5.13877	−	16.6595i	0.317474	−	1.02923i
$263$	−20.2016	−	11.6634i	−1.24568	−	0.719195i	−0.275437	−	0.961319i	$-0.588823\pi$
$263$	−20.2016	−	11.6634i	−1.24568	−	0.719195i	−0.970245	+	0.242124i	$0.922156\pi$
$264$	11.7796	−	3.56673i	0.724984	−	0.219517i
$265$	20.8608	−	4.76135i	1.28147	−	0.292487i
$266$	3.41186	+	1.32759i	0.209195	+	0.0813996i
$267$	−17.8783	−	8.72424i	−1.09413	−	0.533915i
$268$	−0.0295650	+	0.00911961i	−0.00180597	+	0.000557069i
$269$	−1.01672	−	2.59056i	−0.0619904	−	0.157949i	0.896522	−	0.442998i	$-0.146085\pi$
$269$	−1.01672	−	2.59056i	−0.0619904	−	0.157949i	−0.958513	+	0.285049i	$0.907990\pi$
$270$	8.69637	−	26.7102i	0.529244	−	1.62553i
$271$	1.78745	+	5.79476i	0.108580	+	0.352007i	0.993514	−	0.113709i	$-0.0362731\pi$
$271$	1.78745	+	5.79476i	0.108580	+	0.352007i	−0.884934	+	0.465716i	$0.845797\pi$
$272$	−5.19045	+	22.7409i	−0.314717	+	1.37887i
$273$	24.9855	+	3.82399i	1.51219	+	0.231438i
$274$	5.31142	+	23.2709i	0.320875	+	1.40584i
$275$	16.6537	−	9.61504i	1.00426	−	0.579809i
$276$	−2.47306	+	2.63775i	−0.148861	+	0.158774i
$277$	−21.1249	−	6.51618i	−1.26927	−	0.391519i	−0.414276	−	0.910151i	$-0.635965\pi$
$277$	−21.1249	−	6.51618i	−1.26927	−	0.391519i	−0.854998	+	0.518632i	$0.826442\pi$
$278$	−0.867880	−	11.5810i	−0.0520520	−	0.694585i
$279$	−1.40914	−	3.00546i	−0.0843628	−	0.179932i
$280$	10.3241	−	13.0237i	0.616981	−	0.778315i
$281$	9.51959	−	7.59162i	0.567891	−	0.452878i	−0.296972	−	0.954886i	$-0.595977\pi$
$281$	9.51959	−	7.59162i	0.567891	−	0.452878i	0.864863	+	0.502008i	$0.167405\pi$
$282$	−15.0780	+	8.60133i	−0.897882	+	0.512202i
$283$	−0.250059	−	1.65903i	−0.0148645	−	0.0986193i	0.980168	−	0.198167i	$-0.0634987\pi$
$283$	−0.250059	−	1.65903i	−0.0148645	−	0.0986193i	−0.995033	+	0.0995472i	$0.968261\pi$
$284$	−0.889129	−	1.30411i	−0.0527601	−	0.0773848i
$285$	−4.24104	−	1.68992i	−0.251218	−	0.100102i
$286$	14.6354	+	30.3908i	0.865411	+	1.79705i
$287$	17.9627	+	1.29345i	1.06030	+	0.0763497i
$288$	10.5565	−	8.24082i	0.622046	−	0.485595i
$289$	4.12595	+	2.81303i	0.242703	+	0.165472i
$290$	−3.20676	−	2.97544i	−0.188307	−	0.174724i
$291$	3.40568	−	10.8410i	0.199644	−	0.635510i
$292$	−0.0240087	−	0.00942271i	−0.00140500	−	0.000551422i
$293$	−18.1546			−1.06060			−0.530302	−	0.847809i	$-0.677922\pi$
$293$	−18.1546			−1.06060			−0.530302	+	0.847809i	$0.677922\pi$
$294$	3.03117	−	20.1991i	0.176782	−	1.17804i
$295$	−37.0780			−2.15876
$296$	16.8946	+	6.63063i	0.981976	+	0.385397i
$297$	−13.0433	+	13.6259i	−0.756850	+	0.790654i
$298$	−1.58843	−	1.47385i	−0.0920152	−	0.0853777i
$299$	11.3524	+	7.73994i	0.656527	+	0.447612i
$300$	4.82534	−	5.98682i	0.278591	−	0.345649i
$301$	11.2832	+	16.4462i	0.650354	+	0.947942i
$302$	−0.630749	−	1.30976i	−0.0362955	−	0.0753684i
$303$	−4.78664	+	12.0126i	−0.274985	+	0.690105i
$304$	−2.30138	−	3.37551i	−0.131993	−	0.193599i
$305$	1.53094	+	10.1571i	0.0876611	+	0.581593i
$306$	−6.75089	−	22.7199i	−0.385923	−	1.29881i
$307$	15.8808	−	12.6645i	0.906364	−	0.722801i	−0.0548824	−	0.998493i	$-0.517478\pi$
$307$	15.8808	−	12.6645i	0.906364	−	0.722801i	0.961246	+	0.275692i	$0.0889070\pi$
$308$	7.24148	−	3.51337i	0.412622	−	0.200193i
$309$	0.788927	−	0.622482i	0.0448805	−	0.0354118i
$310$	−0.447000	−	5.96480i	−0.0253879	−	0.338778i
$311$	3.77949	+	1.16582i	0.214315	+	0.0661075i	0.400054	−	0.916492i	$-0.368992\pi$
$311$	3.77949	+	1.16582i	0.214315	+	0.0661075i	−0.185738	+	0.982599i	$0.559468\pi$
$312$	−13.6427	−	12.7909i	−0.772368	−	0.724144i
$313$	22.5790	−	13.0360i	1.27624	−	0.736836i	0.300084	−	0.953913i	$-0.402985\pi$
$313$	22.5790	−	13.0360i	1.27624	−	0.736836i	0.976155	+	0.217076i	$0.0696521\pi$
$314$	−5.73614	−	25.1317i	−0.323709	−	1.41826i
$315$	−3.98384	+	25.1568i	−0.224464	+	1.41743i
$316$	1.04029	−	4.55782i	0.0585210	−	0.256397i
$317$	7.46957	+	24.2157i	0.419533	+	1.36009i	0.881076	+	0.472974i	$0.156820\pi$
$317$	7.46957	+	24.2157i	0.419533	+	1.36009i	−0.461543	+	0.887118i	$0.652704\pi$
$318$	−19.2540	+	2.80002i	−1.07971	+	0.157017i
$319$	1.07318	+	2.73442i	0.0600867	+	0.153098i
$320$	−7.44268	+	2.29576i	−0.416058	+	0.128337i
$321$	9.14599	−	18.7426i	0.510479	−	1.04611i
$322$	6.22767	−	9.19180i	0.347055	−	0.512239i
$323$	−3.75551	+	0.857171i	−0.208962	+	0.0476942i
$324$	−2.90058	+	6.96230i	−0.161143	+	0.386794i
$325$	−25.3047	−	14.6097i	−1.40365	−	0.810399i
$326$	−10.8329	+	35.1195i	−0.599981	+	1.94509i
$327$	−15.2527	−	2.37994i	−0.843474	−	0.131611i
$328$	−10.4174	−	8.30759i	−0.575204	−	0.458710i
$329$	12.2772	−	9.84947i	0.676865	−	0.543019i
$330$	−30.7000	+	14.5887i	−1.68998	+	0.803080i
$331$	9.46461	−	8.78188i	0.520222	−	0.482696i	−0.375803	−	0.926700i	$-0.622633\pi$
$331$	9.46461	−	8.78188i	0.520222	−	0.482696i	0.896025	+	0.444004i	$0.146442\pi$
$332$	−4.76504	+	0.718214i	−0.261515	+	0.0394171i
$333$	−27.5457	+	3.86007i	−1.50949	+	0.211531i
$334$	1.60335	−	10.6375i	0.0877314	−	0.582060i
$335$	−0.106739	+	0.0514030i	−0.00583180	+	0.00280845i
$336$	−15.5408	+	16.6730i	−0.847822	+	0.909585i
$337$	5.12730	+	2.46918i	0.279302	+	0.134505i	0.568291	−	0.822828i	$-0.307605\pi$
$337$	5.12730	+	2.46918i	0.279302	+	0.134505i	−0.288989	+	0.957332i	$0.593319\pi$
$338$	16.5351	−	24.2525i	0.899389	−	1.31916i
$339$	−8.05604	−	11.9487i	−0.437544	−	0.648965i
$340$	0.942480	−	12.5765i	0.0511132	−	0.682058i
$341$	−1.46742	+	3.73892i	−0.0794652	+	0.202474i
$342$	3.72126	+	1.83985i	0.201222	+	0.0994880i
$343$	0.162037	+	18.5196i	0.00874915	+	0.999962i
$344$		−	14.7563i		−	0.795607i
$345$	−7.85853	+	11.3989i	−0.423089	+	0.613695i
$346$	−15.3349	−	1.14919i	−0.824411	−	0.0617811i
$347$	0.127408	−	0.137313i	0.00683963	−	0.00737137i	−0.729623	−	0.683850i	$-0.760304\pi$
$347$	0.127408	−	0.137313i	0.00683963	−	0.00737137i	0.736462	+	0.676478i	$0.236495\pi$
$348$	0.794441	+	0.865160i	0.0425865	+	0.0463774i
$349$	4.46847	−	9.27886i	0.239191	−	0.496686i	−0.746470	−	0.665419i	$-0.768253\pi$
$349$	4.46847	−	9.27886i	0.239191	−	0.496686i	0.985662	+	0.168732i	$0.0539674\pi$
$350$	−11.7460	+	20.4825i	−0.627852	+	1.09483i
$351$	27.8396	+	6.81160i	1.48597	+	0.363576i
$352$	−16.0239	−	2.41522i	−0.854077	−	0.128731i
$353$	26.2703	−	17.9108i	1.39823	−	0.953296i	0.398887	−	0.917000i	$-0.369396\pi$
$353$	26.2703	−	17.9108i	1.39823	−	0.953296i	0.999341	−	0.0362959i	$-0.0115559\pi$
$354$	33.6071	+	2.69385i	1.78620	+	0.143177i
$355$	−4.11082	−	4.43042i	−0.218180	−	0.235142i
$356$	6.00123	+	7.52530i	0.318065	+	0.398840i
$357$	9.28066	+	19.3839i	0.491184	+	1.02591i
$358$	−16.3287	+	20.4755i	−0.862997	+	1.08216i
$359$	−27.6645	+	2.07317i	−1.46008	+	0.109418i	−0.780947	−	0.624598i	$-0.785263\pi$
$359$	−27.6645	+	2.07317i	−1.46008	+	0.109418i	−0.679132	+	0.734016i	$0.737644\pi$
$360$	12.9602	−	13.6804i	0.683061	−	0.721018i
$361$	−9.16266	+	15.8702i	−0.482245	+	0.835273i
$362$	9.47837	+	16.4170i	0.498172	+	0.862860i
$363$	3.77153	+	0.0195609i	0.197954	+	0.00102668i
$364$	−10.1248	−	6.85979i	−0.530683	−	0.359551i
$365$	−0.0962831	−	0.0219760i	−0.00503969	−	0.00115028i
$366$	−0.649673	−	9.31751i	−0.0339590	−	0.487034i
$367$	26.5962	−	10.4382i	1.38831	−	0.544872i	0.450736	−	0.892657i	$-0.351162\pi$
$367$	26.5962	−	10.4382i	1.38831	−	0.544872i	0.937574	+	0.347786i	$0.113066\pi$
$368$	−11.5333	+	4.52647i	−0.601213	+	0.235959i
$369$	20.1597	+	3.25280i	1.04947	+	0.169334i
$370$	−48.8653	−	11.1532i	−2.54039	−	0.579827i
$371$	16.8428	−	5.24916i	0.874435	−	0.272523i
$372$	−0.00832969	+	1.60604i	−0.000431874	+	0.0832695i
$373$	−18.6766	−	32.3488i	−0.967038	−	1.67496i	−0.704036	−	0.710165i	$-0.748621\pi$
$373$	−18.6766	−	32.3488i	−0.967038	−	1.67496i	−0.263003	−	0.964795i	$-0.584713\pi$
$374$	−14.3399	+	24.8374i	−0.741496	+	1.28431i
$375$	0.833956	−	1.42731i	0.0430653	−	0.0737058i
$376$	−11.6128	+	0.870257i	−0.598883	+	0.0448801i
$377$	2.78288	−	3.48962i	0.143325	−	0.179724i
$378$	5.43865	−	22.5124i	0.279734	−	1.15792i
$379$	10.3589	+	12.9896i	0.532100	+	0.667232i	0.973129	−	0.230261i	$-0.0739580\pi$
$379$	10.3589	+	12.9896i	0.532100	+	0.667232i	−0.441029	+	0.897493i	$0.645387\pi$
$380$	1.50243	+	1.61924i	0.0770732	+	0.0830651i
$381$	0.224451	−	2.80013i	0.0114990	−	0.143455i
$382$	29.3492	−	20.0100i	1.50164	−	1.02380i
$383$	−13.5679	−	2.04503i	−0.693285	−	0.104496i	−0.207059	−	0.978329i	$-0.566389\pi$
$383$	−13.5679	−	2.04503i	−0.693285	−	0.104496i	−0.486227	+	0.873833i	$0.661627\pi$
$384$	22.0066	−	4.90293i	1.12302	−	0.250202i
$385$	25.4138	−	17.4356i	1.29521	−	0.888601i
$386$	6.75240	−	14.0215i	0.343688	−	0.713676i
$387$	11.1038	+	19.7015i	0.564437	+	1.00148i
$388$	−3.73963	+	4.03036i	−0.189851	+	0.204611i
$389$	−4.43578	−	0.332416i	−0.224903	−	0.0168541i	−0.0381981	−	0.999270i	$-0.512162\pi$
$389$	−4.43578	−	0.332416i	−0.224903	−	0.0168541i	−0.186705	+	0.982416i	$0.559781\pi$
$390$	42.5208	+	29.3144i	2.15313	+	1.48439i
$391$			11.6822i			0.590794i
$392$	7.65271	−	11.3663i	0.386520	−	0.574087i
$393$	−4.07918	+	17.4543i	−0.205767	+	0.880452i
$394$	−2.37302	+	6.04635i	−0.119551	+	0.304611i
$395$	1.33777	−	17.8513i	0.0673104	−	0.898194i
$396$	8.52970	−	3.24597i	0.428634	−	0.163116i
$397$	−16.3299	+	23.9515i	−0.819572	+	1.20209i	0.157149	+	0.987575i	$0.449770\pi$
$397$	−16.3299	+	23.9515i	−0.819572	+	1.20209i	−0.976720	+	0.214516i	$0.931183\pi$
$398$	22.9497	+	11.0520i	1.15037	+	0.553987i
$399$	−3.59431	−	1.11764i	−0.179941	−	0.0559520i
$400$	23.7389	−	11.4320i	1.18694	−	0.571601i
$401$	5.16146	−	34.2440i	0.257751	−	1.71007i	−0.367819	−	0.929897i	$-0.619895\pi$
$401$	5.16146	−	34.2440i	0.257751	−	1.71007i	0.625570	−	0.780168i	$-0.284866\pi$
$402$	0.100482	−	0.0388361i	0.00501159	−	0.00193697i
$403$	6.03486	−	0.909609i	0.300618	−	0.0453108i
$404$	4.58642	−	4.25558i	0.228183	−	0.211723i
$405$	−7.00925	+	28.0172i	−0.348292	+	1.39218i
$406$	−2.82642	−	2.24054i	−0.140273	−	0.111196i
$407$	26.3139	+	20.9846i	1.30433	+	1.04017i
$408$	2.45136	−	15.7104i	0.121360	−	0.777780i
$409$	−7.10204	+	23.0242i	−0.351173	+	1.13848i	0.591934	+	0.805987i	$0.298365\pi$
$409$	−7.10204	+	23.0242i	−0.351173	+	1.13848i	−0.943107	+	0.332489i	$0.892111\pi$
$410$	31.8676	+	18.3987i	1.57383	+	0.908649i
$411$	−7.11185	−	23.4879i	−0.350802	−	1.15857i
$412$	−0.474038	+	0.108196i	−0.0233542	+	0.00533043i
$413$	−30.4781	+	2.37343i	−1.49973	+	0.116789i
$414$	7.95106	−	9.76087i	0.390773	−	0.479721i
$415$	−17.6323	+	5.43884i	−0.865535	+	0.266982i
$416$	8.99569	+	22.9206i	0.441050	+	1.12378i
$417$	1.71835	+	11.8160i	0.0841480	+	0.578633i
$418$	−1.48059	−	4.79996i	−0.0724181	−	0.234774i
$419$	−7.80200	+	34.1828i	−0.381152	+	1.66994i	0.312724	+	0.949844i	$0.398759\pi$
$419$	−7.80200	+	34.1828i	−0.381152	+	1.66994i	−0.693876	+	0.720094i	$0.744099\pi$
$420$	6.96523	−	10.1665i	0.339868	−	0.496072i
$421$	−8.27075	−	36.2365i	−0.403092	−	1.76606i	−0.614756	−	0.788717i	$-0.710745\pi$
$421$	−8.27075	−	36.2365i	−0.403092	−	1.76606i	0.211664	−	0.977342i	$-0.432112\pi$
$422$	−4.37786	+	2.52756i	−0.213111	+	0.123040i
$423$	14.8496	−	9.90024i	0.722013	−	0.481366i
$424$	−12.4727	−	3.84731i	−0.605726	−	0.186842i
$425$	−1.85656	−	24.7741i	−0.0900563	−	1.20172i
$426$	3.40412	+	4.31435i	0.164930	+	0.209031i
$427$	1.90860	+	8.25114i	0.0923637	+	0.399300i
$428$	−7.88910	+	6.29134i	−0.381334	+	0.304104i
$429$	−17.1842	−	30.1236i	−0.829660	−	1.45438i
$430$	6.07379	+	40.2969i	0.292904	+	1.94329i
$431$	−15.8579	−	23.2592i	−0.763846	−	1.12036i	−0.989270	−	0.146096i	$-0.953329\pi$
$431$	−15.8579	−	23.2592i	−0.763846	−	1.12036i	0.225425	−	0.974261i	$-0.427623\pi$
$432$	−19.2165	+	17.2818i	−0.924556	+	0.831471i
$433$	14.3402	+	29.7778i	0.689147	+	1.43103i	0.892099	+	0.451841i	$0.149232\pi$
$433$	14.3402	+	29.7778i	0.689147	+	1.43103i	−0.202951	+	0.979189i	$0.565053\pi$
$434$	−0.749252	−	4.87446i	−0.0359652	−	0.233981i
$435$	3.50179	+	2.82242i	0.167898	+	0.135325i
$436$	6.17131	+	4.20753i	0.295552	+	0.201504i
$437$	−1.49989	−	1.39169i	−0.0717493	−	0.0665736i
$438$	0.0856734	+	0.0269141i	0.00409363	+	0.00128601i
$439$	−32.5828	−	12.7878i	−1.55509	−	0.610329i	−0.576676	−	0.816973i	$-0.695651\pi$
$439$	−32.5828	−	12.7878i	−1.55509	−	0.610329i	−0.978416	+	0.206644i	$0.933746\pi$
$440$	−22.8025			−1.08707
$441$	−1.66439	+	20.9339i	−0.0792566	+	0.996854i
$442$	43.5777			2.07278
$443$	−2.36090	−	0.926585i	−0.112170	−	0.0440234i	0.308592	−	0.951194i	$-0.400142\pi$
$443$	−2.36090	−	0.926585i	−0.112170	−	0.0440234i	−0.420762	+	0.907171i	$0.638237\pi$
$444$	12.8393	+	4.03345i	0.609327	+	0.191419i
$445$	27.0175	+	25.0686i	1.28075	+	1.18837i
$446$	−20.8779	−	14.2343i	−0.988599	−	0.674015i
$447$	1.73457	+	1.39805i	0.0820424	+	0.0661256i
$448$	−5.97093	+	2.36354i	−0.282100	+	0.111667i
$449$	−15.7272	−	32.6579i	−0.742214	−	1.54122i	−0.837907	−	0.545813i	$-0.816221\pi$
$449$	−15.7272	−	32.6579i	−0.742214	−	1.54122i	0.0956929	−	0.995411i	$-0.469493\pi$
$450$	−15.3103	+	21.9631i	−0.721736	+	1.03535i
$451$	−13.9193	−	20.4158i	−0.655433	−	0.961344i
$452$	1.03921	+	6.89467i	0.0488801	+	0.324298i
$453$	0.740594	+	1.29825i	0.0347961	+	0.0609971i
$454$	11.6914	−	9.32360i	0.548706	−	0.437578i
$455$	−42.2510	−	20.1954i	−1.98076	−	0.946776i
$456$	1.72504	+	2.18630i	0.0807824	+	0.102383i
$457$	−1.32903	−	17.7347i	−0.0621696	−	0.829595i	−0.937925	−	0.346839i	$-0.887255\pi$
$457$	−1.32903	−	17.7347i	−0.0621696	−	0.829595i	0.875755	−	0.482756i	$-0.160364\pi$
$458$	4.33009	+	1.33566i	0.202332	+	0.0624111i
$459$	8.54884	+	22.8199i	0.399026	+	1.06514i
$460$	5.80143	−	3.34945i	0.270493	−	0.156169i
$461$	0.323766	+	1.41851i	0.0150793	+	0.0660666i	0.981908	−	0.189360i	$-0.0606413\pi$
$461$	0.323766	+	1.41851i	0.0150793	+	0.0660666i	−0.966828	+	0.255426i	$0.917784\pi$
$462$	−24.3015	+	13.9570i	−1.13061	+	0.649341i
$463$	−2.40420	+	10.5335i	−0.111732	+	0.489532i	0.887836	+	0.460160i	$0.152208\pi$
$463$	−2.40420	+	10.5335i	−0.111732	+	0.489532i	−0.999569	+	0.0293721i	$0.990649\pi$
$464$	1.18633	+	3.84598i	0.0550739	+	0.178545i
$465$	0.885034	+	6.08582i	0.0410425	+	0.282223i
$466$	10.4770	+	26.6949i	0.485336	+	1.23662i
$467$	−5.82385	+	1.79642i	−0.269496	+	0.0831284i	−0.426558	−	0.904460i	$-0.640274\pi$
$467$	−5.82385	+	1.79642i	−0.269496	+	0.0831284i	0.157062	+	0.987589i	$0.449798\pi$
$468$	−10.7516	−	8.75810i	−0.496993	−	0.404843i
$469$	−0.0844494	+	0.0490859i	−0.00389951	+	0.00226657i
$470$	31.3543	−	7.15641i	1.44626	−	0.330100i
$471$	7.68054	+	25.3660i	0.353901	+	1.16881i
$472$	19.5877	+	11.3090i	0.901597	+	0.520537i
$473$	8.06594	−	26.1491i	0.370872	−	1.20234i
$474$	−2.50950	+	16.0830i	−0.115265	+	0.738716i
$475$	3.40193	+	2.71295i	0.156091	+	0.124479i
$476$	−0.0303257	−	10.3982i	−0.00138998	−	0.476602i
$477$	19.5475	−	4.24877i	0.895020	−	0.194538i
$478$	13.7205	−	12.7308i	0.627562	−	0.582292i
$479$	33.1048	−	4.98975i	1.51260	−	0.227987i	0.660283	−	0.751017i	$-0.270436\pi$
$479$	33.1048	−	4.98975i	1.51260	−	0.227987i	0.852314	+	0.523030i	$0.175198\pi$
$480$	−23.1431	+	8.94478i	−1.05634	+	0.408271i
$481$	7.62203	−	50.5689i	0.347535	−	2.30574i
$482$	−4.77572	+	2.29987i	−0.217528	+	0.104756i
$483$	−5.73005	+	9.87292i	−0.260727	+	0.449233i
$484$	−1.64413	−	0.791771i	−0.0747331	−	0.0359896i
$485$	−11.8595	+	17.3946i	−0.538511	+	0.789850i
$486$	8.38866	−	24.8852i	0.380517	−	1.12882i
$487$	1.10498	−	14.7449i	0.0500715	−	0.668157i	−0.914542	−	0.404490i	$-0.867449\pi$
$487$	1.10498	−	14.7449i	0.0500715	−	0.668157i	0.964614	−	0.263667i	$-0.0849320\pi$
$488$	2.28919	−	5.83277i	0.103627	−	0.264037i
$489$	8.59923	−	36.7950i	0.388871	−	1.66393i
$490$	−16.2198	+	34.1894i	−0.732735	+	1.54452i
$491$			30.9699i			1.39765i	0.715292	+	0.698825i	$0.246294\pi$
$491$			30.9699i			1.39765i	−0.715292	+	0.698825i	$0.753706\pi$
$492$	−8.13449	−	5.60802i	−0.366731	−	0.252829i
$493$	3.78435	+	0.283598i	0.170438	+	0.0127726i
$494$	−5.19137	+	5.59497i	−0.233571	+	0.251730i
$495$	30.4441	−	17.1583i	1.36836	−	0.771210i
$496$	−2.38780	+	4.95832i	−0.107215	+	0.222635i
$497$	−3.66270	−	3.37866i	−0.164294	−	0.151554i
$498$	16.3769	−	3.64866i	0.733865	−	0.163500i
$499$	−16.7327	−	2.52205i	−0.749059	−	0.112902i	−0.236591	−	0.971609i	$-0.576030\pi$
$499$	−16.7327	−	2.52205i	−0.749059	−	0.112902i	−0.512467	+	0.858707i	$0.671268\pi$
$500$	−0.660851	+	0.450561i	−0.0295542	+	0.0201497i
$501$	−0.883736	+	11.0250i	−0.0394824	+	0.492562i
$502$	−30.4705	−	32.8393i	−1.35996	−	1.46569i
$503$	6.02722	+	7.55790i	0.268741	+	0.336990i	0.897829	−	0.440343i	$-0.145143\pi$
$503$	6.02722	+	7.55790i	0.268741	+	0.336990i	−0.629089	+	0.777333i	$0.716572\pi$
$504$	9.77756	−	12.0749i	0.435527	−	0.537857i
$505$	14.9372	−	18.7307i	0.664697	−	0.833503i
$506$	−15.1910	+	1.13841i	−0.675322	+	0.0506084i
$507$	−15.2247	+	26.0570i	−0.676155	+	1.15723i
$508$	−0.679583	+	1.17707i	−0.0301516	+	0.0522241i
$509$	−2.58739	−	4.48149i	−0.114684	−	0.198639i	0.802969	−	0.596020i	$-0.203252\pi$
$509$	−2.58739	−	4.48149i	−0.114684	−	0.198639i	−0.917653	+	0.397382i	$0.869919\pi$
$510$	−0.227745	+	43.9114i	−0.0100847	+	1.94443i
$511$	−0.0805515	−	0.0119010i	−0.00356339	−	0.000526470i
$512$	−2.66244	−	0.607685i	−0.117664	−	0.0268561i
$513$	−3.94828	−	1.62092i	−0.174321	−	0.0715654i
$514$	−46.2016	+	18.1328i	−2.03787	+	0.799804i
$515$	−1.73313	+	0.680204i	−0.0763709	+	0.0299734i
$516$	−0.761103	−	10.9156i	−0.0335057	−	0.480533i
$517$	−21.0543	−	4.80550i	−0.925966	−	0.211346i
$518$	−40.8813	−	6.03998i	−1.79622	−	0.265381i
$519$	15.8104	+	0.0820002i	0.694001	+	0.00359941i
$520$	17.3237	+	30.0056i	0.759696	+	1.31583i
$521$	−5.49327	+	9.51462i	−0.240665	+	0.416843i	−0.960904	−	0.276883i	$-0.910699\pi$
$521$	−5.49327	+	9.51462i	−0.240665	+	0.416843i	0.720239	+	0.693726i	$0.244032\pi$
$522$	−2.96893	−	2.81263i	−0.129946	−	0.123106i
$523$	14.3682	−	1.07675i	0.628277	−	0.0470828i	0.243213	−	0.969973i	$-0.421799\pi$
$523$	14.3682	−	1.07675i	0.628277	−	0.0470828i	0.385064	+	0.922890i	$0.374180\pi$
$524$	5.40732	−	6.78057i	0.236220	−	0.296210i
$525$	10.5825	−	21.8478i	0.461859	−	0.953516i
$526$	−24.5015	−	30.7239i	−1.06832	−	1.33963i
$527$	3.52945	+	3.80384i	0.153745	+	0.165698i
$528$	31.1725	+	2.49871i	1.35661	+	0.108742i
$529$	13.8766	−	9.46088i	0.603329	−	0.411343i
$530$	35.6443	+	5.37251i	1.54829	+	0.233367i
$531$	−34.6617	−	0.359553i	−1.50419	−	0.0156033i
$532$	1.33865	+	1.23484i	0.0580378	+	0.0535371i
$533$	−16.2901	+	33.8268i	−0.705604	+	1.46520i
$534$	−22.6671	−	24.6849i	−0.980901	−	1.06822i
$535$	−26.2805	+	28.3237i	−1.13621	+	1.22454i
$536$	0.0720669	+	0.00540067i	0.00311282	+	0.000233273i
$537$	15.2832	−	22.1684i	0.659518	−	0.956637i
$538$		−	4.68825i		−	0.202125i
$539$	19.7741	−	15.9589i	0.851729	−	0.687397i
$540$	8.88135	−	10.7882i	0.382193	−	0.464249i
$541$	8.58734	−	21.8802i	0.369199	−	0.940703i	−0.618703	−	0.785625i	$-0.712342\pi$
$541$	8.58734	−	21.8802i	0.369199	−	0.940703i	0.987902	−	0.155078i	$-0.0495630\pi$
$542$	−0.763443	+	10.1874i	−0.0327927	+	0.437588i
$543$	−10.8955	−	16.1603i	−0.467572	−	0.693503i
$544$	−11.7932	+	17.2975i	−0.505631	+	0.741625i
$545$	25.7681	+	12.4093i	1.10378	+	0.531554i
$546$	36.8286	+	21.3746i	1.57612	+	0.914749i
$547$	−12.0805	+	5.81765i	−0.516524	+	0.248745i	−0.673938	−	0.738788i	$-0.735399\pi$
$547$	−12.0805	+	5.81765i	−0.516524	+	0.248745i	0.157414	+	0.987533i	$0.449684\pi$
$548$	−1.76972	+	11.7413i	−0.0755986	+	0.501564i
$549$	1.33267	+	9.51002i	0.0568771	+	0.405878i
$550$	32.0341	−	4.82836i	1.36594	−	0.205882i
$551$	−0.487237	+	0.452090i	−0.0207570	+	0.0192597i
$552$	7.62825	−	3.62495i	0.324680	−	0.154288i
$553$	−0.0430447	−	14.7594i	−0.00183045	−	0.627632i
$554$	−29.1175	−	23.2204i	−1.23708	−	0.986541i
$555$	50.9163	+	7.94468i	2.16127	+	0.337233i
$556$	1.70286	−	5.52055i	0.0722176	−	0.234124i
$557$	3.96390	+	2.28856i	0.167956	+	0.0969693i	0.581622	−	0.813460i	$-0.302418\pi$
$557$	3.96390	+	2.28856i	0.167956	+	0.0969693i	−0.413666	+	0.910429i	$0.635752\pi$
$558$	−0.360028	−	5.58043i	−0.0152412	−	0.236238i
$559$	−40.5374	+	9.25239i	−1.71455	+	0.391334i
$560$	36.5086	−	21.2205i	1.54277	−	0.896729i
$561$	12.9314	−	26.4999i	0.545965	−	1.11883i
$562$	19.6010	−	6.04611i	0.826818	−	0.255040i
$563$	−9.04294	−	23.0410i	−0.381114	−	0.971063i	−0.984777	−	0.173823i	$-0.944388\pi$
$563$	−9.04294	−	23.0410i	−0.381114	−	0.971063i	0.603663	−	0.797240i	$-0.293707\pi$
$564$	−8.54537	+	1.24272i	−0.359825	+	0.0523278i
$565$	7.86962	+	25.5127i	0.331077	+	1.07333i
$566$	0.628946	−	2.75559i	0.0264366	−	0.115826i
$567$	−3.96818	+	23.4788i	−0.166648	+	0.986016i
$568$	0.820384	+	3.59434i	0.0344226	+	0.150815i
$569$	−12.8279	+	7.40619i	−0.537774	+	0.310484i	−0.744176	−	0.667983i	$-0.767158\pi$
$569$	−12.8279	+	7.40619i	−0.537774	+	0.310484i	0.206402	+	0.978467i	$0.433824\pi$
$570$	−5.61068	−	5.26036i	−0.235006	−	0.220332i
$571$	14.5545	+	4.48946i	0.609086	+	0.187878i	0.583928	−	0.811805i	$-0.301515\pi$
$571$	14.5545	+	4.48946i	0.609086	+	0.187878i	0.0251578	+	0.999683i	$0.491991\pi$
$572$	1.25396	+	16.7329i	0.0524306	+	0.699637i
$573$	−28.6710	+	22.6221i	−1.19775	+	0.945051i
$574$	27.3729	+	13.0839i	1.14252	+	0.546110i
$575$	10.3170	−	8.22754i	0.430249	−	0.343112i
$576$	−6.97992	+	2.07398i	−0.290830	+	0.0864158i
$577$	−5.30477	−	35.1949i	−0.220841	−	1.46518i	−0.774572	−	0.632486i	$-0.782035\pi$
$577$	−5.30477	−	35.1949i	−0.220841	−	1.46518i	0.553731	−	0.832695i	$-0.313203\pi$
$578$	4.73896	+	6.95078i	0.197115	+	0.289114i
$579$	−5.92285	+	14.8640i	−0.246145	+	0.617728i
$580$	−0.944190	−	1.96063i	−0.0392054	−	0.0814108i
$581$	−14.1456	+	5.59940i	−0.586858	+	0.232302i
$582$	12.0131	−	14.9047i	0.497958	−	0.617819i
$583$	−19.9994	−	13.6354i	−0.828291	−	0.564719i
$584$	0.0441620	+	0.0409764i	0.00182744	+	0.00169561i
$585$	−45.7078	−	27.0254i	−1.88978	−	1.11736i
$586$	−28.4700	−	11.1736i	−1.17608	−	0.461579i
$587$	−23.8115			−0.982805			−0.491402	−	0.870933i	$-0.663516\pi$
$587$	−23.8115			−0.982805			−0.491402	+	0.870933i	$0.663516\pi$
$588$	5.07465	−	8.80268i	0.209275	−	0.363017i
$589$	−0.908838			−0.0374480
$590$	−58.1455	−	22.8204i	−2.39381	−	0.939502i
$591$	2.00148	−	6.37113i	0.0823298	−	0.262073i
$592$	33.8046	+	31.3661i	1.38936	+	1.28914i
$593$	−3.16027	−	2.15464i	−0.129777	−	0.0884803i	0.496692	−	0.867927i	$-0.334548\pi$
$593$	−3.16027	−	2.15464i	−0.129777	−	0.0884803i	−0.626469	+	0.779447i	$0.715500\pi$
$594$	−28.8408	+	13.3403i	−1.18335	+	0.547357i
$595$	−6.04912	−	39.3542i	−0.247990	−	1.61337i
$596$	−0.467693	−	0.971175i	−0.0191575	−	0.0397809i
$597$	−24.3287	−	9.69424i	−0.995709	−	0.396759i
$598$	13.0391	+	19.1248i	0.533207	+	0.782071i
$599$	2.09529	+	13.9013i	0.0856111	+	0.567993i	0.989976	+	0.141233i	$0.0451068\pi$
$599$	2.09529	+	13.9013i	0.0856111	+	0.567993i	−0.904365	+	0.426759i	$0.859655\pi$
$600$	−15.6009	+	8.89961i	−0.636904	+	0.363325i
$601$	20.5735	−	16.4068i	0.839212	−	0.669249i	−0.106480	−	0.994315i	$-0.533958\pi$
$601$	20.5735	−	16.4068i	0.839212	−	0.669249i	0.945691	+	0.325066i	$0.105386\pi$
$602$	7.57213	+	32.7353i	0.308617	+	1.33419i
$603$	−0.100282	+	0.0470181i	−0.00408380	+	0.00191473i
$604$	−0.0540423	−	0.721144i	−0.00219895	−	0.0293429i
$605$	−6.67714	−	2.05962i	−0.271464	−	0.0837356i
$606$	−14.8998	+	15.8920i	−0.605262	+	0.645569i
$607$	0.965768	−	0.557586i	0.0391993	−	0.0226317i	−0.480272	−	0.877119i	$-0.659462\pi$
$607$	0.965768	−	0.557586i	0.0391993	−	0.0226317i	0.519472	+	0.854488i	$0.326129\pi$
$608$	−0.815921	−	3.57478i	−0.0330900	−	0.144977i
$609$	3.05914	+	2.09588i	0.123963	+	0.0849292i
$610$	−3.85059	+	16.8705i	−0.155906	+	0.683068i
$611$	9.67205	+	31.3560i	0.391289	+	1.26853i
$612$	1.00302	−	11.7478i	0.0405446	−	0.474877i
$613$	−1.78425	−	4.54619i	−0.0720651	−	0.183619i	0.890303	−	0.455369i	$-0.150493\pi$
$613$	−1.78425	−	4.54619i	−0.0720651	−	0.183619i	−0.962368	+	0.271750i	$0.912398\pi$
$614$	32.6988	−	10.0862i	1.31961	−	0.407047i
$615$	−34.0007	−	16.5916i	−1.37104	−	0.669040i
$616$	−18.7436	+	1.45963i	−0.755203	+	0.0588100i
$617$	13.2248	−	3.01846i	0.532409	−	0.121519i	0.0521392	−	0.998640i	$-0.483396\pi$
$617$	13.2248	−	3.01846i	0.532409	−	0.121519i	0.480269	+	0.877121i	$0.340539\pi$
$618$	1.62031	−	0.490611i	0.0651785	−	0.0197353i
$619$	24.0863	+	13.9062i	0.968110	+	0.558939i	0.898660	−	0.438647i	$-0.144542\pi$
$619$	24.0863	+	13.9062i	0.968110	+	0.558939i	0.0694505	+	0.997585i	$0.477875\pi$
$620$	0.877058	−	2.84335i	0.0352235	−	0.114192i
$621$	−7.45695	+	10.5798i	−0.299237	+	0.424554i
$622$	5.20945	+	4.15440i	0.208880	+	0.166576i
$623$	23.8131	+	18.8770i	0.954052	+	0.756290i
$624$	−20.3947	−	42.9180i	−0.816442	−	1.71810i
$625$	17.1713	−	15.9327i	0.686853	−	0.637307i
$626$	43.4315	−	6.54624i	1.73587	−	0.261640i
$627$	1.86183	+	4.81718i	0.0743544	+	0.192380i
$628$	1.91123	−	12.6802i	0.0762664	−	0.505995i
$629$	39.1754	−	18.8659i	1.56203	−	0.752232i
$630$	−21.7307	+	36.9989i	−0.865774	+	1.47407i
$631$	29.5709	+	14.2406i	1.17720	+	0.566910i	0.917094	−	0.398670i	$-0.130528\pi$
$631$	29.5709	+	14.2406i	1.17720	+	0.566910i	0.260106	+	0.965580i	$0.416243\pi$
$632$	−6.15144	+	9.02251i	−0.244691	+	0.358896i
$633$	4.30938	−	2.90546i	0.171283	−	0.115482i
$634$	−3.19035	+	42.5723i	−0.126705	+	1.69076i
$635$	−1.90139	+	4.84466i	−0.0754544	+	0.192255i
$636$	−9.42478	−	2.20263i	−0.373717	−	0.0873401i
$637$	−36.0231	−	13.8961i	−1.42729	−	0.550583i
$638$			4.94862i			0.195918i
$639$	−3.79997	−	4.18156i	−0.150324	−	0.165420i
$640$	−41.6544	−	3.12156i	−1.64653	−	0.123391i
$641$	−10.8486	+	11.6920i	−0.428493	+	0.461806i	−0.909983	−	0.414646i	$-0.863905\pi$
$641$	−10.8486	+	11.6920i	−0.428493	+	0.461806i	0.481490	+	0.876452i	$0.340096\pi$
$642$	25.8782	−	23.7629i	1.02133	−	0.937846i
$643$	−13.8639	+	28.7888i	−0.546741	+	1.13532i	0.426278	+	0.904592i	$0.359825\pi$
$643$	−13.8639	+	28.7888i	−0.546741	+	1.13532i	−0.973019	+	0.230727i	$0.925890\pi$
$644$	4.55437	−	3.12461i	0.179467	−	0.123127i
$645$	−9.11138	−	40.8961i	−0.358760	−	1.61028i
$646$	−6.41693	−	0.967197i	−0.252471	−	0.0380539i
$647$	−8.51907	+	5.80820i	−0.334919	+	0.228344i	−0.719088	−	0.694919i	$-0.755440\pi$
$647$	−8.51907	+	5.80820i	−0.334919	+	0.228344i	0.384169	+	0.923263i	$0.374488\pi$
$648$	12.2482	−	12.6632i	0.481156	−	0.497456i
$649$	28.5291	+	30.7471i	1.11987	+	1.20693i
$650$	−30.6909	−	38.4851i	−1.20379	−	1.50951i
$651$	1.11706	+	4.94590i	0.0437811	+	0.193845i
$652$	−11.3991	+	14.2940i	−0.446421	+	0.559795i
$653$	42.1086	−	3.15560i	1.64784	−	0.123488i	0.781819	−	0.623505i	$-0.214292\pi$
$653$	42.1086	−	3.15560i	1.64784	−	0.123488i	0.866016	+	0.500017i	$0.166673\pi$
$654$	−22.4543	−	13.1198i	−0.878034	−	0.513023i
$655$	16.6044	−	28.7597i	0.648788	−	1.12373i
$656$	−16.9278	−	29.3198i	−0.660919	−	1.14475i
$657$	−0.0897955	−	0.0214775i	−0.00350325	−	0.000837919i
$658$	25.3151	−	7.88961i	0.986886	−	0.307569i
$659$	−36.9876	−	8.44219i	−1.44083	−	0.328861i	−0.570490	−	0.821305i	$-0.693247\pi$
$659$	−36.9876	−	8.44219i	−1.44083	−	0.328861i	−0.870344	+	0.492444i	$0.836104\pi$
$660$	−16.8676	+	1.17611i	−0.656569	+	0.0457800i
$661$	12.0016	−	4.71028i	0.466809	−	0.183209i	−0.120266	−	0.992742i	$-0.538375\pi$
$661$	12.0016	−	4.71028i	0.466809	−	0.183209i	0.587075	+	0.809533i	$0.300280\pi$
$662$	20.2473	−	7.94650i	0.786935	−	0.308849i
$663$	−44.6954	+	3.11643i	−1.73582	+	0.121032i
$664$	10.9737	+	2.50468i	0.425863	+	0.0972005i
$665$	5.77334	+	3.91158i	0.223881	+	0.151685i
$666$	−45.5727	−	10.9002i	−1.76591	−	0.422375i
$667$	1.00787	+	1.74568i	0.0390249	+	0.0675930i
$668$	2.67574	−	4.63451i	0.103527	−	0.179315i
$669$	22.4314	+	13.1063i	0.867247	+	0.506720i
$670$	−0.199025	+	0.0149149i	−0.00768902	+	0.000576212i
$671$	7.24485	−	9.08476i	0.279684	−	0.350713i
$672$	−18.4511	+	8.83404i	−0.711767	+	0.340781i
$673$	22.4813	+	28.1907i	0.866591	+	1.08667i	0.995476	+	0.0950114i	$0.0302888\pi$
$673$	22.4813	+	28.1907i	0.866591	+	1.08667i	−0.128885	+	0.991660i	$0.541140\pi$
$674$	6.52090	+	7.02786i	0.251176	+	0.270703i
$675$	14.1323	−	23.6214i	0.543954	−	0.909187i
$676$	12.0645	−	8.22546i	0.464021	−	0.316364i
$677$	4.96637	+	0.748560i	0.190873	+	0.0287695i	0.243783	−	0.969830i	$-0.421612\pi$
$677$	4.96637	+	0.748560i	0.190873	+	0.0287695i	−0.0529099	+	0.998599i	$0.516850\pi$
$678$	−5.27935	−	23.6962i	−0.202752	−	0.910046i
$679$	−8.63502	+	15.0575i	−0.331382	+	0.577855i
$680$	−12.7817	+	26.5414i	−0.490154	+	1.01782i
$681$	−11.3245	+	10.3988i	−0.433956	+	0.398484i
$682$	−4.60240	+	4.96020i	−0.176235	+	0.189936i
$683$	17.9831	+	1.34765i	0.688103	+	0.0515662i	0.414193	−	0.910189i	$-0.364064\pi$
$683$	17.9831	+	1.34765i	0.688103	+	0.0515662i	0.273910	+	0.961755i	$0.411683\pi$
$684$	1.38882	+	1.52828i	0.0531029	+	0.0584354i
$685$			45.4669i			1.73720i
$686$	−11.1441	+	29.1420i	−0.425485	+	1.11265i
$687$	−4.53667	−	1.06025i	−0.173085	−	0.0404510i
$688$	13.6981	−	34.9022i	0.522236	−	1.33064i
$689$	−2.74850	+	36.6762i	−0.104710	+	1.39725i
$690$	−19.3394	+	13.0390i	−0.736238	+	0.496385i
$691$	11.9421	−	17.5159i	0.454300	−	0.666336i	−0.528938	−	0.848660i	$-0.677410\pi$
$691$	11.9421	−	17.5159i	0.454300	−	0.666336i	0.983238	+	0.182324i	$0.0583621\pi$
$692$	−6.89227	−	3.31914i	−0.262005	−	0.126175i
$693$	23.9267	−	16.0529i	0.908900	−	0.609800i
$694$	0.284313	−	0.136918i	0.0107924	−	0.00519734i
$695$	3.29707	−	21.8746i	0.125065	−	0.829753i
$696$	−0.989088	−	2.55910i	−0.0374913	−	0.0970026i
$697$	−31.5657	+	4.75776i	−1.19564	+	0.180213i
$698$	12.7183	−	11.8009i	0.481394	−	0.446669i
$699$	−12.6547	−	26.6303i	−0.478647	−	1.00725i
$700$	−9.16173	+	7.35005i	−0.346281	+	0.277806i
$701$	5.27964	+	4.21038i	0.199409	+	0.159024i	0.718104	−	0.695936i	$-0.245010\pi$
$701$	5.27964	+	4.21038i	0.199409	+	0.159024i	−0.518694	+	0.854960i	$0.673582\pi$
$702$	39.4656	+	27.8164i	1.48953	+	1.04986i
$703$	−2.24473	+	7.27724i	−0.0846616	+	0.274466i
$704$	7.63043	+	4.40543i	0.287582	+	0.166036i
$705$	−31.6467	+	9.58224i	−1.19188	+	0.360888i
$706$	52.2206	−	11.9190i	1.96535	−	0.448578i
$707$	11.0794	−	16.3528i	0.416684	−	0.615009i
$708$	15.0728	+	7.35523i	0.566471	+	0.276426i
$709$	−15.7893	+	4.87036i	−0.592980	+	0.182910i	−0.576698	−	0.816957i	$-0.695659\pi$
$709$	−15.7893	+	4.87036i	−0.592980	+	0.182910i	−0.0162820	+	0.999867i	$0.505183\pi$
$710$	−3.71978	−	9.47785i	−0.139601	−	0.355697i
$711$	1.42369	−	16.6750i	0.0533927	−	0.625360i
$712$	−6.62688	−	21.4838i	−0.248353	−	0.805141i
$713$	−0.613318	+	2.68712i	−0.0229689	+	0.100634i
$714$	2.62363	+	36.1097i	0.0981870	+	1.35137i
$715$	14.2974	+	62.6412i	0.534694	+	2.34265i
$716$	−11.2825	+	6.51398i	−0.421648	+	0.243439i
$717$	−13.1620	+	14.0385i	−0.491544	+	0.524278i
$718$	−44.6594	−	13.7756i	−1.66667	−	0.514100i
$719$	1.74372	+	23.2683i	0.0650297	+	0.867761i	0.930381	+	0.366595i	$0.119476\pi$
$719$	1.74372	+	23.2683i	0.0650297	+	0.867761i	−0.865351	+	0.501166i	$0.832905\pi$
$720$	43.3532	−	20.3266i	1.61568	−	0.757526i
$721$	−1.38109	+	0.670068i	−0.0514346	+	0.0249547i
$722$	−24.1365	+	19.2482i	−0.898267	+	0.716344i
$723$	4.73373	−	2.70039i	0.176049	−	0.100428i
$724$	1.40549	+	9.32482i	0.0522347	+	0.346554i
$725$	−2.41478	−	3.54183i	−0.0896827	−	0.131540i
$726$	5.90245	+	2.35194i	0.219060	+	0.0872887i
$727$	−2.79773	−	5.80954i	−0.103762	−	0.215464i	0.842624	−	0.538503i	$-0.181010\pi$
$727$	−2.79773	−	5.80954i	−0.103762	−	0.215464i	−0.946386	+	0.323039i	$0.895296\pi$
$728$	16.1608	+	23.5557i	0.598960	+	0.873032i
$729$	−6.82416	+	26.1234i	−0.252747	+	0.967533i
$730$	−0.137465	−	0.0937221i	−0.00508781	−	0.00346881i
$731$	−25.9155	−	24.0461i	−0.958521	−	0.889377i
$732$	1.39253	−	4.43272i	0.0514694	−	0.163838i
$733$	30.4264	+	11.9415i	1.12382	+	0.441069i	0.853183	−	0.521612i	$-0.174669\pi$
$733$	30.4264	+	11.9415i	1.12382	+	0.441069i	0.270641	+	0.962680i	$0.412764\pi$
$734$	48.1324			1.77660
$735$	14.1907	−	36.2263i	0.523434	−	1.33623i
$736$	−11.1200			−0.409889
$737$	0.124755	+	0.0489628i	0.00459542	+	0.00180357i
$738$	29.6124	+	17.5088i	1.09005	+	0.644506i
$739$	−18.7938	−	17.4381i	−0.691339	−	0.641469i	0.254134	−	0.967169i	$-0.418210\pi$
$739$	−18.7938	−	17.4381i	−0.691339	−	0.641469i	−0.945473	+	0.325700i	$0.894400\pi$
$740$	−20.6010	−	14.0455i	−0.757309	−	0.516324i
$741$	4.92440	−	6.10973i	0.180902	−	0.224447i
$742$	29.6435	+	2.13455i	1.08825	+	0.0783620i
$743$	18.0328	+	37.4455i	0.661559	+	1.37374i	0.913835	+	0.406086i	$0.133107\pi$
$743$	18.0328	+	37.4455i	0.661559	+	1.37374i	−0.252276	+	0.967655i	$0.581179\pi$
$744$	1.38866	−	3.48498i	0.0509106	−	0.127766i
$745$	−2.32511	−	3.41031i	−0.0851854	−	0.124944i
$746$	−9.37879	−	62.2242i	−0.343382	−	2.27819i
$747$	−16.5360	+	4.91342i	−0.605020	+	0.179773i
$748$	−11.1543	+	8.89526i	−0.407842	+	0.325243i
$749$	−19.7895	+	24.9643i	−0.723094	+	0.912176i
$750$	2.18627	−	1.72502i	0.0798313	−	0.0629888i
$751$	2.62322	+	35.0044i	0.0957226	+	1.27733i	0.813709	+	0.581272i	$0.197445\pi$
$751$	2.62322	+	35.0044i	0.0957226	+	1.27733i	−0.717986	+	0.696057i	$0.754936\pi$
$752$	−28.2748	−	8.72163i	−1.03108	−	0.318045i
$753$	33.6005	+	31.5025i	1.22447	+	1.14802i
$754$	6.51185	−	3.75962i	0.237148	−	0.136917i
$755$	−0.616182	−	2.69967i	−0.0224252	−	0.0982511i
$756$	6.60991	−	9.43639i	0.240400	−	0.343198i
$757$	3.06960	−	13.4488i	0.111566	−	0.488804i	−0.888013	−	0.459818i	$-0.847915\pi$
$757$	3.06960	−	13.4488i	0.111566	−	0.488804i	0.999580	−	0.0289867i	$-0.00922804\pi$
$758$	8.25000	+	26.7458i	0.299653	+	0.971452i
$759$	15.4992	−	2.25398i	0.562585	−	0.0818143i
$760$	−1.88500	−	4.80290i	−0.0683761	−	0.174220i
$761$	−19.8309	+	6.11701i	−0.718868	+	0.221742i	−0.632543	−	0.774525i	$-0.717989\pi$
$761$	−19.8309	+	6.11701i	−0.718868	+	0.221742i	−0.0863257	+	0.996267i	$0.527513\pi$
$762$	2.07538	−	4.25301i	0.0751832	−	0.154070i
$763$	21.9757	+	8.55095i	0.795574	+	0.309565i
$764$	17.2274	−	3.93203i	0.623264	−	0.142256i
$765$	−2.90671	−	45.0539i	−0.105092	−	1.62893i
$766$	−20.0184	−	11.5576i	−0.723294	−	0.417594i
$767$	18.7854	−	60.9007i	0.678300	−	2.19900i
$768$	29.2208	+	4.55945i	1.05442	+	0.164525i
$769$	30.2619	+	24.1331i	1.09127	+	0.870261i	0.992180	−	0.124817i	$-0.0398344\pi$
$769$	30.2619	+	24.1331i	1.09127	+	0.870261i	0.0990931	+	0.995078i	$0.468406\pi$
$770$	50.5849	−	11.7010i	1.82295	−	0.421674i
$771$	46.0899	−	21.9020i	1.65989	−	0.788780i
$772$	5.67511	−	5.26573i	0.204252	−	0.189518i
$773$	−5.94769	+	0.896469i	−0.213923	+	0.0322438i	−0.255129	−	0.966907i	$-0.582118\pi$
$773$	−5.94769	+	0.896469i	−0.213923	+	0.0322438i	0.0412061	+	0.999151i	$0.486880\pi$
$774$	5.28720	+	37.7298i	0.190045	+	1.35617i
$775$	0.873600	−	5.79596i	0.0313806	−	0.208197i
$776$	11.5706	−	5.57211i	0.415361	−	0.200027i
$777$	42.3617	+	3.27129i	1.51972	+	0.117357i
$778$	−6.75157	−	3.25139i	−0.242056	−	0.116568i
$779$	3.14954	−	4.61953i	0.112844	−	0.165512i
$780$	14.3624	+	21.3024i	0.514258	+	0.762747i
$781$	−0.510926	+	6.81783i	−0.0182824	+	0.243961i
$782$	−7.19006	+	18.3200i	−0.257116	+	0.655121i
$783$	3.24622	+	2.67245i	0.116010	+	0.0955055i
$784$	28.6518	−	19.7802i	1.02328	−	0.706436i
$785$		−	49.1025i		−	1.75255i
$786$	−17.1395	+	24.8611i	−0.611347	+	0.886765i
$787$	−0.371533	−	0.0278426i	−0.0132437	−	0.000992481i	0.0681066	−	0.997678i	$-0.478304\pi$
$787$	−0.371533	−	0.0278426i	−0.0132437	−	0.000992481i	−0.0813503	+	0.996686i	$0.525923\pi$
$788$	−2.19774	+	2.36860i	−0.0782912	+	0.0843779i
$789$	27.3271	+	29.7597i	0.972872	+	1.05947i
$790$	13.0848	−	27.1709i	0.465537	−	0.966697i
$791$	8.10194	+	20.4677i	0.288072	+	0.727747i
$792$	−21.3165	−	0.221120i	−0.757449	−	0.00785717i
$793$	−17.4587	−	2.63147i	−0.619976	−	0.0934464i
$794$	−40.3498	+	27.5100i	−1.43196	+	0.976295i
$795$	−36.9427	−	2.96123i	−1.31022	−	0.105024i
$796$	8.61870	+	9.28875i	0.305482	+	0.329231i
$797$	−3.35083	−	4.20180i	−0.118692	−	0.148836i	0.718936	−	0.695077i	$-0.244630\pi$
$797$	−3.35083	−	4.20180i	−0.118692	−	0.148836i	−0.837628	+	0.546241i	$0.816058\pi$
$798$	−4.94871	−	3.96487i	−0.175182	−	0.140355i
$799$	−17.3952	+	21.8129i	−0.615397	+	0.771684i
$800$	23.5819	−	1.76722i	0.833744	−	0.0624805i
$801$	25.0138	+	23.6970i	0.883818	+	0.837291i
$802$	29.1704	−	50.5246i	1.03004	−	1.78408i
$803$	0.0558599	+	0.0967522i	0.00197125	+	0.00341431i
$804$	0.0535882		0.000277933i	0.00188991		9.80195e-6i
$805$	15.4613	−	14.4301i	0.544938	−	0.508594i
$806$	10.0237	+	2.28784i	0.353069	+	0.0805856i
$807$	0.335278	+	4.80850i	0.0118023	+	0.169267i
$808$	−13.6040	+	5.33918i	−0.478588	+	0.187832i
$809$	−29.6266	+	11.6276i	−1.04162	+	0.408805i	−0.823618	−	0.567144i	$-0.808048\pi$
$809$	−29.6266	+	11.6276i	−1.04162	+	0.408805i	−0.217999	+	0.975949i	$0.569953\pi$
$810$	−28.2356	+	39.6224i	−0.992098	+	1.39219i
$811$	10.6465	+	2.43000i	0.373849	+	0.0853287i	0.405317	−	0.914176i	$-0.367161\pi$
$811$	10.6465	+	2.43000i	0.373849	+	0.0853287i	−0.0314678	+	0.999505i	$0.510018\pi$
$812$	−0.901628	−	1.55120i	−0.0316409	−	0.0544365i
$813$	0.0544751	−	10.5033i	0.00191052	−	0.368368i
$814$	28.3499	+	49.1034i	0.993662	+	1.72107i
$815$	−35.0034	+	60.6276i	−1.22611	+	2.12369i
$816$	20.3818	−	34.8833i	0.713506	−	1.22116i
$817$	6.17459	−	0.462722i	0.216022	−	0.0161886i
$818$	−25.3081	+	31.7354i	−0.884878	+	1.10960i
$819$	−39.3018	−	19.2890i	−1.37331	−	0.674014i
$820$	11.4131	+	14.3115i	0.398561	+	0.499780i
$821$	−10.8436	−	11.6867i	−0.378446	−	0.407867i	0.514891	−	0.857256i	$-0.327832\pi$
$821$	−10.8436	−	11.6867i	−0.378446	−	0.407867i	−0.893337	+	0.449388i	$0.851642\pi$
$822$	3.30334	−	41.2107i	0.115217	−	1.43739i
$823$	20.2114	−	13.7799i	0.704525	−	0.480337i	−0.157294	−	0.987552i	$-0.550277\pi$
$823$	20.2114	−	13.7799i	0.704525	−	0.480337i	0.861820	+	0.507214i	$0.169325\pi$
$824$	1.12305	+	0.169273i	0.0391233	+	0.00589689i
$825$	−32.5104	+	7.24310i	−1.13187	+	0.252172i
$826$	−49.2564	−	15.0364i	−1.71385	−	0.523183i
$827$	15.1602	−	31.4804i	0.527170	−	1.09468i	−0.452071	−	0.891982i	$-0.649315\pi$
$827$	15.1602	−	31.4804i	0.527170	−	1.09468i	0.979241	−	0.202698i	$-0.0649710\pi$
$828$	5.45584	−	3.07492i	0.189604	−	0.106861i
$829$	−16.7747	+	18.0788i	−0.582610	+	0.627904i	−0.953724	−	0.300683i	$-0.902785\pi$
$829$	−16.7747	+	18.0788i	−0.582610	+	0.627904i	0.371114	+	0.928587i	$0.378976\pi$
$830$	−30.9983	−	2.32300i	−1.07597	−	0.0806326i
$831$	31.5249	+	21.7337i	1.09359	+	0.753932i
$832$		−	13.3877i		−	0.464137i
$833$	−7.49151	−	31.9620i	−0.259565	−	1.10742i
$834$	−4.57771	+	19.5874i	−0.158513	+	0.678256i
$835$	7.48639	−	19.0750i	0.259077	−	0.660118i
$836$	0.186734	−	2.49179i	0.00645834	−	0.0861805i
$837$	0.768343	+	5.69781i	0.0265578	+	0.196945i
$838$	−33.2736	+	48.8033i	−1.14942	+	1.68588i
$839$	19.9527	+	9.60870i	0.688843	+	0.331729i	0.745350	−	0.666673i	$-0.232282\pi$
$839$	19.9527	+	9.60870i	0.688843	+	0.331729i	−0.0565076	+	0.998402i	$0.517997\pi$
$840$	−23.8205	+	16.1615i	−0.821885	+	0.557623i
$841$	−25.5381	+	12.2985i	−0.880625	+	0.424087i
$842$	9.33238	−	61.9163i	0.321615	−	2.13378i
$843$	−19.6713	+	7.60293i	−0.677517	+	0.261859i
$844$	−2.48661	+	0.374796i	−0.0855926	+	0.0129010i
$845$	40.9865	−	38.0299i	1.40998	−	1.30827i
$846$	29.3804	−	6.38599i	1.01012	−	0.219555i
$847$	−5.62045	−	1.26560i	−0.193121	−	0.0434864i
$848$	−25.9294	−	20.6780i	−0.890421	−	0.710087i
$849$	−0.448013	+	2.87125i	−0.0153758	+	0.0985409i
$850$	12.3363	−	39.9932i	0.423130	−	1.37175i
$851$	20.0015	+	11.5479i	0.685641	+	0.395855i
$852$	0.792248	+	2.61651i	0.0271420	+	0.0896401i
$853$	−6.77412	+	1.54615i	−0.231941	+	0.0529391i	−0.336912	−	0.941536i	$-0.609382\pi$
$853$	−6.77412	+	1.54615i	−0.231941	+	0.0529391i	0.104970	+	0.994475i	$0.466525\pi$
$854$	−2.08528	+	14.1141i	−0.0713566	+	0.482974i
$855$	6.13078	+	4.99404i	0.209668	+	0.170793i
$856$	22.5224	−	6.94725i	0.769800	−	0.237452i
$857$	−9.22293	−	23.4996i	−0.315049	−	0.802733i	−0.997424	−	0.0717301i	$-0.977148\pi$
$857$	−9.22293	−	23.4996i	−0.315049	−	0.802733i	0.682375	−	0.731003i	$-0.260947\pi$
$858$	−8.40793	−	57.8161i	−0.287042	−	1.97381i
$859$	−5.18207	−	16.7998i	−0.176810	−	0.573203i	−0.999985	−	0.00541629i	$-0.998276\pi$
$859$	−5.18207	−	16.7998i	−0.176810	−	0.573203i	0.823176	−	0.567787i	$-0.192200\pi$
$860$	−4.51103	+	19.7641i	−0.153825	+	0.673951i
$861$	−29.0106	−	11.4619i	−0.988679	−	0.390620i
$862$	−10.5528	−	46.2350i	−0.359431	−	1.57477i
$863$	−20.0390	+	11.5695i	−0.682136	+	0.393831i	−0.800659	−	0.599120i	$-0.795517\pi$
$863$	−20.0390	+	11.5695i	−0.682136	+	0.393831i	0.118524	+	0.992951i	$0.462184\pi$
$864$	−21.7217	+	8.13744i	−0.738987	+	0.276841i
$865$	−27.9909	−	8.63405i	−0.951719	−	0.293567i
$866$	4.16090	+	55.5234i	0.141393	+	1.88676i
$867$	−5.35758	−	6.79015i	−0.181953	−	0.230605i
$868$	0.538934	−	2.39338i	0.0182926	−	0.0812366i
$869$	−15.8325	+	12.6260i	−0.537082	+	0.428309i
$870$	3.75437	+	6.58136i	0.127285	+	0.223129i
$871$	−0.0303506	−	0.201363i	−0.00102839	−	0.00682292i
$872$	−9.82798	−	14.4150i	−0.332818	−	0.488154i
$873$	−11.2553	+	16.1461i	−0.380934	+	0.546462i
$874$	−1.49557	−	3.10558i	−0.0505883	−	0.105048i
$875$	−1.71212	+	1.85605i	−0.0578801	+	0.0627460i
$876$	0.0347813	+	0.0280335i	0.00117515	+	0.000947163i
$877$	9.26278	+	6.31526i	0.312782	+	0.213251i	0.709528	−	0.704677i	$-0.248908\pi$
$877$	9.26278	+	6.31526i	0.312782	+	0.213251i	−0.396746	+	0.917928i	$0.629861\pi$
$878$	−43.2256	−	40.1075i	−1.45879	−	1.35356i
$879$	29.9993	+	9.42421i	1.01185	+	0.317871i
$880$	−53.9334	−	21.1673i	−1.81809	−	0.713549i
$881$	−24.4719			−0.824480			−0.412240	−	0.911075i	$-0.635253\pi$
$881$	−24.4719			−0.824480			−0.412240	+	0.911075i	$0.635253\pi$
$882$	−15.4943	+	31.8041i	−0.521721	+	1.07090i
$883$	−26.4571			−0.890352			−0.445176	−	0.895443i	$-0.646859\pi$
$883$	−26.4571			−0.890352			−0.445176	+	0.895443i	$0.646859\pi$
$884$	20.1795	+	7.91986i	0.678709	+	0.266374i
$885$	61.2688	+	19.2475i	2.05953	+	0.646997i
$886$	−3.13206	−	2.90613i	−0.105224	−	0.0976334i
$887$	−16.4021	−	11.1828i	−0.550728	−	0.375480i	0.255751	−	0.966743i	$-0.417677\pi$
$887$	−16.4021	−	11.1828i	−0.550728	−	0.375480i	−0.806479	+	0.591263i	$0.798630\pi$
$888$	−24.4751	−	19.7268i	−0.821330	−	0.661986i
$889$	−1.25283	+	4.10403i	−0.0420185	+	0.137645i
$890$	26.9398	+	55.9410i	0.903023	+	1.87515i
$891$	28.6265	−	15.7449i	0.959024	−	0.527475i
$892$	−7.08095	−	10.3859i	−0.237088	−	0.347744i
$893$	−0.728296	−	4.83193i	−0.0243715	−	0.161694i
$894$	1.85968	+	3.26000i	0.0621971	+	0.109031i
$895$	−39.0023	+	31.1033i	−1.30370	+	1.03967i
$896$	−34.4397	+	0.100441i	−1.15055	+	0.00335550i
$897$	−14.7412	−	18.6828i	−0.492194	−	0.623802i
$898$	−4.56335	−	60.8937i	−0.152281	−	2.03205i
$899$	0.855581	+	0.263912i	0.0285352	+	0.00880195i
$900$	−11.0813	+	7.38793i	−0.369378	+	0.246264i
$901$	−27.0816	+	15.6356i	−0.902218	+	0.520896i
$902$	−9.26279	−	40.5829i	−0.308417	−	1.35126i
$903$	−10.1074	−	33.0334i	−0.336353	−	1.09928i
$904$	3.62410	−	15.8782i	0.120536	−	0.528101i
$905$	10.6434	+	34.5051i	0.353799	+	1.14699i
$906$	0.362360	+	2.49172i	0.0120386	+	0.0827819i
$907$	19.3190	+	49.2240i	0.641476	+	1.63445i	0.766457	+	0.642296i	$0.222018\pi$
$907$	19.3190	+	49.2240i	0.641476	+	1.63445i	−0.124981	+	0.992159i	$0.539887\pi$
$908$	7.10841	−	2.19265i	0.235901	−	0.0727658i
$909$	14.1454	−	17.3652i	0.469174	−	0.575966i
$910$	−53.8281	−	57.6746i	−1.78438	−	1.91189i
$911$	−38.2933	+	8.74020i	−1.26871	+	0.289576i	−0.803331	−	0.595533i	$-0.796941\pi$
$911$	−38.2933	+	8.74020i	−1.26871	+	0.289576i	−0.465384	+	0.885109i	$0.654084\pi$
$912$	2.05062	+	6.77245i	0.0679028	+	0.224258i
$913$	18.0771	+	10.4368i	0.598264	+	0.345408i
$914$	8.83102	−	28.6295i	0.292104	−	0.946979i
$915$	2.74286	−	17.5786i	0.0906763	−	0.581131i
$916$	1.76239	+	1.40546i	0.0582309	+	0.0464376i
$917$	11.8079	−	24.7033i	0.389930	−	0.815776i
$918$	−0.638720	+	41.0475i	−0.0210809	+	1.35477i
$919$	−29.9808	+	27.8181i	−0.988974	+	0.917634i	−0.996605	−	0.0823368i	$-0.973762\pi$
$919$	−29.9808	+	27.8181i	−0.988974	+	0.917634i	0.00763021	+	0.999971i	$0.497571\pi$
$920$	−15.4726	+	2.33212i	−0.510116	+	0.0768877i
$921$	−32.8161	+	12.6834i	−1.08133	+	0.417931i
$922$	−0.365324	+	2.42377i	−0.0120313	+	0.0798226i
$923$	9.35969	−	4.50739i	0.308078	−	0.148363i
$924$	−13.7899	+	2.04648i	−0.453653	+	0.0673244i
$925$	−44.2516	−	21.3105i	−1.45498	−	0.700684i
$926$	−10.2533	+	15.0388i	−0.336944	+	0.494206i
$927$	−1.62678	+	0.619070i	−0.0534306	+	0.0203329i
$928$	−0.269950	+	3.60223i	−0.00886154	+	0.118249i
$929$	−4.77878	+	12.1761i	−0.156787	+	0.399486i	−0.987585	−	0.157088i	$-0.949789\pi$
$929$	−4.77878	+	12.1761i	−0.156787	+	0.399486i	0.830798	+	0.556574i	$0.187885\pi$
$930$	−2.35774	+	10.0885i	−0.0773134	+	0.330814i
$931$	4.99608	+	2.84576i	0.163740	+	0.0932660i
$932$			14.2657i			0.467287i
$933$	−5.64016	−	3.88840i	−0.184651	−	0.127300i
$934$	−10.2386	−	0.767275i	−0.335017	−	0.0251060i
$935$	−37.1577	+	40.0465i	−1.21519	+	1.30966i
$936$	15.9038	+	28.2182i	0.519832	+	0.922340i
$937$	−0.254104	+	0.527653i	−0.00830122	+	0.0172377i	−0.905078	−	0.425245i	$-0.860188\pi$
$937$	−0.254104	+	0.527653i	−0.00830122	+	0.0172377i	0.896777	+	0.442483i	$0.145902\pi$
$938$	−0.162644	+	0.0250000i	−0.00531052	+	0.000816278i
$939$	−44.0772	+	9.82011i	−1.43841	+	0.320467i
$940$	15.8198	+	2.38445i	0.515985	+	0.0777722i
$941$	42.9327	−	29.2710i	1.39957	−	0.954208i	0.400282	−	0.916392i	$-0.368912\pi$
$941$	42.9327	−	29.2710i	1.39957	−	0.954208i	0.999285	−	0.0378162i	$-0.0120401\pi$
$942$	−3.56748	+	44.5060i	−0.116235	+	1.45008i
$943$	−11.5329	−	12.4296i	−0.375564	−	0.404762i
$944$	35.8317	+	44.9315i	1.16622	+	1.46240i
$945$	19.6421	−	39.5019i	0.638959	−	1.28500i
$946$	28.7430	−	36.0426i	0.934516	−	1.17185i
$947$	−41.2278	+	3.08960i	−1.33973	+	0.100399i	−0.725222	−	0.688516i	$-0.758263\pi$
$947$	−41.2278	+	3.08960i	−1.33973	+	0.100399i	−0.614504	+	0.788914i	$0.710644\pi$
$948$	−4.08501	+	6.99145i	−0.132675	+	0.227072i
$949$	0.0848769	−	0.147011i	0.00275522	−	0.00477218i
$950$	3.66515	+	6.34822i	0.118913	+	0.205963i
$951$	0.227646	−	43.8924i	0.00738193	−	1.42331i
$952$	−8.80757	+	22.6352i	−0.285455	+	0.733611i
$953$	−1.91482	−	0.437045i	−0.0620271	−	0.0141573i	0.191395	−	0.981513i	$-0.438699\pi$
$953$	−1.91482	−	0.437045i	−0.0620271	−	0.0141573i	−0.253422	+	0.967356i	$0.581556\pi$
$954$	33.2693	+	5.36805i	1.07713	+	0.173797i
$955$	62.9850	−	24.7198i	2.03815	−	0.799914i
$956$	8.66725	−	3.40165i	0.280319	−	0.110017i
$957$	−0.353898	−	5.07554i	−0.0114399	−	0.164069i
$958$	54.9858	+	12.5502i	1.77651	+	0.405477i
$959$	2.91041	+	37.3738i	0.0939821	+	1.20686i
$960$	13.4903	+	0.0699667i	0.435396	+	0.00225817i
$961$	−14.8879	−	25.7865i	−0.480254	−	0.831824i
$962$	43.0765	−	74.6107i	1.38884	−	2.40555i
$963$	−24.8425	+	26.2230i	−0.800539	+	0.845025i
$964$	−2.62947	+	0.197051i	−0.0846894	+	0.00634660i
$965$	18.4829	−	23.1768i	0.594984	−	0.746087i
$966$	−15.0623	+	11.9560i	−0.484623	+	0.384677i
$967$	−23.9727	−	30.0608i	−0.770910	−	0.966691i	0.229067	−	0.973411i	$-0.426432\pi$
$967$	−23.9727	−	30.0608i	−0.770910	−	0.966691i	−0.999977	+	0.00672000i	$0.997861\pi$
$968$	2.89923	+	3.12462i	0.0931847	+	0.100429i
$969$	6.65068	+	0.533101i	0.213651	+	0.0171257i
$970$	−29.3038	+	19.9790i	−0.940890	+	0.641488i
$971$	60.1242	+	9.06226i	1.92948	+	0.290822i	0.997438	−	0.0715369i	$-0.0227904\pi$
$971$	60.1242	+	9.06226i	1.92948	+	0.290822i	0.932039	+	0.362359i	$0.118028\pi$
$972$	8.40719	−	9.99900i	0.269661	−	0.320718i
$973$	1.30996	−	18.1920i	0.0419954	−	0.583209i
$974$	10.8079	−	22.4429i	0.346308	−	0.719116i
$975$	34.2303	+	37.2774i	1.09625	+	1.19383i
$976$	10.8290	−	11.6709i	0.346628	−	0.373576i
$977$	−18.7298	−	1.40361i	−0.599220	−	0.0449053i	−0.228332	−	0.973583i	$-0.573327\pi$
$977$	−18.7298	−	1.40361i	−0.599220	−	0.0449053i	−0.370887	+	0.928678i	$0.620946\pi$
$978$	36.1315	−	52.4091i	1.15536	−	1.67586i
$979$		−	41.6931i		−	1.33252i
$980$	−13.7245	+	12.8843i	−0.438413	+	0.411573i
$981$	23.9685	+	11.8505i	0.765255	+	0.378356i
$982$	−19.0611	+	48.5668i	−0.608263	+	1.54983i
$983$	0.860041	−	11.4765i	0.0274311	−	0.366042i	−0.966549	−	0.256482i	$-0.917437\pi$
$983$	0.860041	−	11.4765i	0.0274311	−	0.366042i	0.993980	−	0.109560i	$-0.0349443\pi$
$984$	12.9015	+	19.1355i	0.411284	+	0.610016i
$985$	−6.96968	+	10.2226i	−0.222072	+	0.325720i
$986$	5.76004	+	2.77389i	0.183437	+	0.0883387i
$987$	−25.4002	+	9.90236i	−0.808497	+	0.315196i
$988$	−3.42080	+	1.64737i	−0.108830	+	0.0524098i
$989$	2.79874	−	18.5684i	0.0889947	−	0.590441i
$990$	58.3027	−	8.17016i	1.85298	−	0.259665i
$991$	46.5637	−	7.01835i	1.47915	−	0.222945i	0.640642	−	0.767840i	$-0.278668\pi$
$991$	46.5637	−	7.01835i	1.47915	−	0.222945i	0.838504	+	0.544895i	$0.183430\pi$
$992$	−3.62079	+	3.35960i	−0.114960	+	0.106667i
$993$	−20.1984	+	9.59829i	−0.640976	+	0.304592i
$994$	−3.66435	−	7.55268i	−0.116226	−	0.239557i
$995$	37.9347	+	30.2519i	1.20261	+	0.959049i
$996$	8.24673	+	1.28677i	0.261308	+	0.0407729i
$997$	−4.45979	+	14.4583i	−0.141243	+	0.457898i	−0.998362	−	0.0572209i	$-0.981776\pi$
$997$	−4.45979	+	14.4583i	−0.141243	+	0.457898i	0.857119	+	0.515119i	$0.172252\pi$
$998$	−24.6879	−	14.2536i	−0.781481	−	0.451188i
$999$	47.5211	+	7.92069i	1.50350	+	0.250599i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.2.o.b.101.12	yes	192
3.2	odd	2	inner	147.2.o.b.101.5	✓	192
49.33	odd	42	inner	147.2.o.b.131.5	yes	192
147.131	even	42	inner	147.2.o.b.131.12	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.o.b.101.5	✓	192	3.2	odd	2	inner
147.2.o.b.101.12	yes	192	1.1	even	1	trivial
147.2.o.b.131.5	yes	192	49.33	odd	42	inner
147.2.o.b.131.12	yes	192	147.131	even	42	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

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	147.2.o.b.101.12

Level	$147$
Weight	$2$
Character	147.101
Analytic conductor	$1.174$
Analytic rank	$0$
Dimension	$192$
Inner twists	$4$