LMFDB - Embedded newform 380.2.bj.a.207.48

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(23,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 27, 4]))

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

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

chi := DirichletCharacter("380.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bj (of order $36$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$56$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			207.48
Character	$\chi$	$=$	380.207
Dual form			380.2.bj.a.123.48

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22744 - 0.702418i) q^{2} +(0.106910 + 1.22198i) q^{3} +(1.01322 - 1.72435i) q^{4} +(-2.11456 + 0.727088i) q^{5} +(0.989567 + 1.42482i) q^{6} +(1.61039 + 0.431503i) q^{7} +(0.0324513 - 2.82824i) q^{8} +(1.47261 - 0.259661i) q^{9} +O(q^{10})$	\(q+(1.22744 - 0.702418i) q^{2} +(0.106910 + 1.22198i) q^{3} +(1.01322 - 1.72435i) q^{4} +(-2.11456 + 0.727088i) q^{5} +(0.989567 + 1.42482i) q^{6} +(1.61039 + 0.431503i) q^{7} +(0.0324513 - 2.82824i) q^{8} +(1.47261 - 0.259661i) q^{9} +(-2.08477 + 2.37776i) q^{10} +(5.01572 + 2.89583i) q^{11} +(2.21545 + 1.05379i) q^{12} +(-0.0482361 + 0.551342i) q^{13} +(2.27975 - 0.601523i) q^{14} +(-1.11456 - 2.50622i) q^{15} +(-1.94677 - 3.49429i) q^{16} +(3.11759 - 2.18296i) q^{17} +(1.62515 - 1.35311i) q^{18} +(-2.94962 + 3.20932i) q^{19} +(-0.888753 + 4.38293i) q^{20} +(-0.355123 + 2.01400i) q^{21} +(8.19057 + 0.0313250i) q^{22} +(-2.98823 - 6.40828i) q^{23} +(3.45953 - 0.262711i) q^{24} +(3.94269 - 3.07493i) q^{25} +(0.328065 + 0.710621i) q^{26} +(1.42718 + 5.32631i) q^{27} +(2.37574 - 2.33967i) q^{28} +(-5.77613 + 1.01849i) q^{29} +(-3.12846 - 2.29335i) q^{30} +(-6.23641 + 3.60059i) q^{31} +(-4.84400 - 2.92159i) q^{32} +(-3.00242 + 6.43871i) q^{33} +(2.29331 - 4.86931i) q^{34} +(-3.71900 + 0.258459i) q^{35} +(1.04433 - 2.80239i) q^{36} +(0.800371 + 0.800371i) q^{37} +(-1.36620 + 6.01111i) q^{38} -0.678887 q^{39} +(1.98776 + 6.00407i) q^{40} +(0.851443 + 0.714445i) q^{41} +(0.978778 + 2.72151i) q^{42} +(-9.66399 - 4.50639i) q^{43} +(10.0754 - 5.71475i) q^{44} +(-2.92512 + 1.61978i) q^{45} +(-8.16916 - 5.76679i) q^{46} +(-0.187828 - 0.131519i) q^{47} +(4.06183 - 2.75250i) q^{48} +(-3.65501 - 2.11022i) q^{49} +(2.67952 - 6.54371i) q^{50} +(3.00084 + 3.57626i) q^{51} +(0.901833 + 0.641806i) q^{52} +(11.6395 - 5.42758i) q^{53} +(5.49307 + 5.53525i) q^{54} +(-12.7115 - 2.47652i) q^{55} +(1.27265 - 4.54057i) q^{56} +(-4.23708 - 3.26128i) q^{57} +(-6.37445 + 5.30739i) q^{58} +(-0.103605 + 0.587574i) q^{59} +(-5.45089 - 0.617463i) q^{60} +(-9.10704 - 3.31469i) q^{61} +(-5.12570 + 8.80008i) q^{62} +(2.48352 + 0.217280i) q^{63} +(-7.99789 - 0.183560i) q^{64} +(-0.298876 - 1.20091i) q^{65} +(0.837373 + 10.0121i) q^{66} +(3.42093 + 2.39536i) q^{67} +(-0.605389 - 7.58764i) q^{68} +(7.51133 - 4.33667i) q^{69} +(-4.38330 + 2.92953i) q^{70} +(3.02668 + 8.31573i) q^{71} +(-0.686596 - 4.17332i) q^{72} +(1.23907 - 0.108404i) q^{73} +(1.54460 + 0.420213i) q^{74} +(4.17903 + 4.48916i) q^{75} +(2.54538 + 8.33793i) q^{76} +(6.82771 + 6.82771i) q^{77} +(-0.833293 + 0.476862i) q^{78} +(-2.51261 - 2.10833i) q^{79} +(6.65722 + 5.97340i) q^{80} +(-2.14063 + 0.779125i) q^{81} +(1.54693 + 0.278871i) q^{82} +(2.67629 - 9.98803i) q^{83} +(3.11303 + 2.65298i) q^{84} +(-5.00512 + 6.88276i) q^{85} +(-15.0273 + 1.25683i) q^{86} +(-1.86210 - 6.94945i) q^{87} +(8.35286 - 14.0917i) q^{88} +(-3.19797 - 3.81119i) q^{89} +(-2.45265 + 4.04285i) q^{90} +(-0.315584 + 0.867061i) q^{91} +(-14.0778 - 1.34023i) q^{92} +(-5.06660 - 7.23585i) q^{93} +(-0.322929 - 0.0294976i) q^{94} +(3.90368 - 8.93092i) q^{95} +(3.05226 - 6.23163i) q^{96} +(4.73916 - 3.31840i) q^{97} +(-5.96857 - 0.0228269i) q^{98} +(8.13814 + 2.96204i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8}+O(q^{10}) $ 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8	$ 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8} - 12 q^{10} - 6 q^{12} - 24 q^{13} - 36 q^{16} - 24 q^{17} - 24 q^{18} + 36 q^{20} - 48 q^{21} - 24 q^{22} - 24 q^{25} - 60 q^{26} - 24 q^{28} - 6 q^{30} + 18 q^{32} - 60 q^{33} + 24 q^{36} - 48 q^{37} - 114 q^{38} - 42 q^{40} - 24 q^{41} - 48 q^{42} - 12 q^{45} - 12 q^{46} - 96 q^{48} - 6 q^{50} - 12 q^{52} - 24 q^{53} - 48 q^{56} - 24 q^{57} + 120 q^{58} - 12 q^{60} - 48 q^{61} + 36 q^{62} - 12 q^{65} - 96 q^{66} - 6 q^{68} - 12 q^{70} + 120 q^{72} - 24 q^{73} - 96 q^{76} - 360 q^{77} - 126 q^{78} + 48 q^{80} - 48 q^{81} + 228 q^{82} - 24 q^{85} - 132 q^{86} - 102 q^{88} + 78 q^{90} + 108 q^{92} - 60 q^{93} - 144 q^{96} - 24 q^{97} + 18 q^{98}+O(q^{100}) $ 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8 - 12 * q^10 - 6 * q^12 - 24 * q^13 - 36 * q^16 - 24 * q^17 - 24 * q^18 + 36 * q^20 - 48 * q^21 - 24 * q^22 - 24 * q^25 - 60 * q^26 - 24 * q^28 - 6 * q^30 + 18 * q^32 - 60 * q^33 + 24 * q^36 - 48 * q^37 - 114 * q^38 - 42 * q^40 - 24 * q^41 - 48 * q^42 - 12 * q^45 - 12 * q^46 - 96 * q^48 - 6 * q^50 - 12 * q^52 - 24 * q^53 - 48 * q^56 - 24 * q^57 + 120 * q^58 - 12 * q^60 - 48 * q^61 + 36 * q^62 - 12 * q^65 - 96 * q^66 - 6 * q^68 - 12 * q^70 + 120 * q^72 - 24 * q^73 - 96 * q^76 - 360 * q^77 - 126 * q^78 + 48 * q^80 - 48 * q^81 + 228 * q^82 - 24 * q^85 - 132 * q^86 - 102 * q^88 + 78 * q^90 + 108 * q^92 - 60 * q^93 - 144 * q^96 - 24 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.22744	−	0.702418i	0.867931	−	0.496684i
$2$	1.22744	−	0.702418i	0.867931	−	0.496684i
$3$	0.106910	+	1.22198i	0.0617243	+	0.705512i	0.962510	+	0.271247i	$0.0874362\pi$
$3$	0.106910	+	1.22198i	0.0617243	+	0.705512i	−0.900785	+	0.434265i	$0.857008\pi$
$4$	1.01322	−	1.72435i	0.506610	−	0.862176i
$5$	−2.11456	+	0.727088i	−0.945658	+	0.325164i
$5$	−2.11456	+	0.727088i	−0.945658	+	0.325164i
$6$	0.989567	+	1.42482i	0.403989	+	0.581679i
$7$	1.61039	+	0.431503i	0.608670	+	0.163093i	0.549972	−	0.835183i	$-0.314638\pi$
$7$	1.61039	+	0.431503i	0.608670	+	0.163093i	0.0586983	+	0.998276i	$0.481305\pi$
$8$	0.0324513	−	2.82824i	0.0114733	−	0.999934i
$9$	1.47261	−	0.259661i	0.490870	−	0.0865537i
$10$	−2.08477	+	2.37776i	−0.659262	+	0.751913i
$11$	5.01572	+	2.89583i	1.51230	+	0.873125i	0.999897	+	0.0143773i	$0.00457661\pi$
$11$	5.01572	+	2.89583i	1.51230	+	0.873125i	0.512399	+	0.858747i	$0.328757\pi$
$12$	2.21545	+	1.05379i	0.639545	+	0.304202i
$13$	−0.0482361	+	0.551342i	−0.0133783	+	0.152915i	−0.999945	−	0.0104414i	$-0.996676\pi$
$13$	−0.0482361	+	0.551342i	−0.0133783	+	0.152915i	0.986567	+	0.163356i	$0.0522319\pi$
$14$	2.27975	−	0.601523i	0.609290	−	0.160764i
$15$	−1.11456	−	2.50622i	−0.287777	−	0.647103i
$16$	−1.94677	−	3.49429i	−0.486694	−	0.873573i
$17$	3.11759	−	2.18296i	0.756127	−	0.529446i	−0.130770	−	0.991413i	$-0.541745\pi$
$17$	3.11759	−	2.18296i	0.756127	−	0.529446i	0.886897	+	0.461967i	$0.152856\pi$
$18$	1.62515	−	1.35311i	0.383052	−	0.318930i
$19$	−2.94962	+	3.20932i	−0.676690	+	0.736268i
$19$	−2.94962	+	3.20932i	−0.676690	+	0.736268i
$20$	−0.888753	+	4.38293i	−0.198731	+	0.980054i
$21$	−0.355123	+	2.01400i	−0.0774941	+	0.439491i
$22$	8.19057	+	0.0313250i	1.74624	+	0.00667852i
$23$	−2.98823	−	6.40828i	−0.623089	−	1.33622i	−0.923937	−	0.382546i	$-0.875047\pi$
$23$	−2.98823	−	6.40828i	−0.623089	−	1.33622i	0.300848	−	0.953672i	$-0.402730\pi$
$24$	3.45953	−	0.262711i	0.706174	−	0.0536257i
$25$	3.94269	−	3.07493i	0.788537	−	0.614987i
$26$	0.328065	+	0.710621i	0.0643388	+	0.139364i
$27$	1.42718	+	5.32631i	0.274661	+	1.02505i
$28$	2.37574	−	2.33967i	0.448973	−	0.442156i
$29$	−5.77613	+	1.01849i	−1.07260	+	0.189128i	−0.681941	−	0.731407i	$-0.738864\pi$
$29$	−5.77613	+	1.01849i	−1.07260	+	0.189128i	−0.390659	+	0.920535i	$0.627753\pi$
$30$	−3.12846	−	2.29335i	−0.571176	−	0.418706i
$31$	−6.23641	+	3.60059i	−1.12009	+	0.646686i	−0.941425	−	0.337224i	$-0.890512\pi$
$31$	−6.23641	+	3.60059i	−1.12009	+	0.646686i	−0.178668	+	0.983909i	$0.557179\pi$
$32$	−4.84400	−	2.92159i	−0.856306	−	0.516468i
$33$	−3.00242	+	6.43871i	−0.522655	+	1.12084i
$34$	2.29331	−	4.86931i	0.393299	−	0.835079i
$35$	−3.71900	+	0.258459i	−0.628626	+	0.0436875i
$36$	1.04433	−	2.80239i	0.174055	−	0.467065i
$37$	0.800371	+	0.800371i	0.131580	+	0.131580i	0.769830	−	0.638249i	$-0.220341\pi$
$37$	0.800371	+	0.800371i	0.131580	+	0.131580i	−0.638249	+	0.769830i	$0.720341\pi$
$38$	−1.36620	+	6.01111i	−0.221628	+	0.975131i
$39$	−0.678887			−0.108709
$40$	1.98776	+	6.00407i	0.314292	+	0.949326i
$41$	0.851443	+	0.714445i	0.132973	+	0.111578i	0.706849	−	0.707365i	$-0.250116\pi$
$41$	0.851443	+	0.714445i	0.132973	+	0.111578i	−0.573876	+	0.818943i	$0.694561\pi$
$42$	0.978778	+	2.72151i	0.151029	+	0.419938i
$43$	−9.66399	−	4.50639i	−1.47375	−	0.687219i	−0.490826	−	0.871258i	$-0.663305\pi$
$43$	−9.66399	−	4.50639i	−1.47375	−	0.687219i	−0.982919	+	0.184039i	$0.941083\pi$
$44$	10.0754	−	5.71475i	1.51893	−	0.861532i
$45$	−2.92512	+	1.61978i	−0.436051	+	0.241463i
$46$	−8.16916	−	5.76679i	−1.20448	−	0.850267i
$47$	−0.187828	−	0.131519i	−0.0273976	−	0.0191840i	0.559797	−	0.828629i	$-0.310879\pi$
$47$	−0.187828	−	0.131519i	−0.0273976	−	0.0191840i	−0.587195	+	0.809445i	$0.699768\pi$
$48$	4.06183	−	2.75250i	0.586275	−	0.397289i
$49$	−3.65501	−	2.11022i	−0.522145	−	0.301461i
$50$	2.67952	−	6.54371i	0.378942	−	0.925420i
$51$	3.00084	+	3.57626i	0.420202	+	0.500777i
$52$	0.901833	+	0.641806i	0.125062	+	0.0890024i
$53$	11.6395	−	5.42758i	1.59881	−	0.745535i	0.600278	−	0.799791i	$-0.295057\pi$
$53$	11.6395	−	5.42758i	1.59881	−	0.745535i	0.998527	+	0.0542564i	$0.0172788\pi$
$54$	5.49307	+	5.53525i	0.747512	+	0.753252i
$55$	−12.7115	−	2.47652i	−1.71402	−	0.333934i
$56$	1.27265	−	4.54057i	0.170065	−	0.606759i
$57$	−4.23708	−	3.26128i	−0.561214	−	0.431967i
$58$	−6.37445	+	5.30739i	−0.837007	+	0.696894i
$59$	−0.103605	+	0.587574i	−0.0134882	+	0.0764956i	−0.990809	−	0.135269i	$-0.956810\pi$
$59$	−0.103605	+	0.587574i	−0.0134882	+	0.0764956i	0.977321	+	0.211765i	$0.0679211\pi$
$60$	−5.45089	−	0.617463i	−0.703707	−	0.0797141i
$61$	−9.10704	−	3.31469i	−1.16604	−	0.424403i	−0.314787	−	0.949162i	$-0.601933\pi$
$61$	−9.10704	−	3.31469i	−1.16604	−	0.424403i	−0.851251	+	0.524759i	$0.824155\pi$
$62$	−5.12570	+	8.80008i	−0.650965	+	1.11761i
$63$	2.48352	+	0.217280i	0.312895	+	0.0273747i
$64$	−7.99789	−	0.183560i	−0.999737	−	0.0229450i
$65$	−0.298876	−	1.20091i	−0.0370710	−	0.148955i
$66$	0.837373	+	10.0121i	0.103073	+	1.23240i
$67$	3.42093	+	2.39536i	0.417933	+	0.292640i	0.763566	−	0.645730i	$-0.223447\pi$
$67$	3.42093	+	2.39536i	0.417933	+	0.292640i	−0.345633	+	0.938370i	$0.612336\pi$
$68$	−0.605389	−	7.58764i	−0.0734141	−	0.920137i
$69$	7.51133	−	4.33667i	0.904258	−	0.522074i
$70$	−4.38330	+	2.92953i	−0.523905	+	0.350146i
$71$	3.02668	+	8.31573i	0.359201	+	0.986895i	0.979307	+	0.202378i	$0.0648670\pi$
$71$	3.02668	+	8.31573i	0.359201	+	0.986895i	−0.620107	+	0.784517i	$0.712911\pi$
$72$	−0.686596	−	4.17332i	−0.0809161	−	0.491831i
$73$	1.23907	−	0.108404i	0.145022	−	0.0126877i	−0.0144137	−	0.999896i	$-0.504588\pi$
$73$	1.23907	−	0.108404i	0.145022	−	0.0126877i	0.159435	+	0.987208i	$0.449033\pi$
$74$	1.54460	+	0.420213i	0.179556	+	0.0488488i
$75$	4.17903	+	4.48916i	0.482553	+	0.518363i
$76$	2.54538	+	8.33793i	0.291975	+	0.956426i
$77$	6.82771	+	6.82771i	0.778090	+	0.778090i
$78$	−0.833293	+	0.476862i	−0.0943518	+	0.0539940i
$79$	−2.51261	−	2.10833i	−0.282691	−	0.237206i	0.490405	−	0.871494i	$-0.336849\pi$
$79$	−2.51261	−	2.10833i	−0.282691	−	0.237206i	−0.773096	+	0.634288i	$0.781293\pi$
$80$	6.65722	+	5.97340i	0.744300	+	0.667846i
$81$	−2.14063	+	0.779125i	−0.237848	+	0.0865694i
$82$	1.54693	+	0.278871i	0.170830	+	0.0307961i
$83$	2.67629	−	9.98803i	0.293761	−	1.09633i	−0.648436	−	0.761269i	$-0.724577\pi$
$83$	2.67629	−	9.98803i	0.293761	−	1.09633i	0.942197	−	0.335060i	$-0.108757\pi$
$84$	3.11303	+	2.65298i	0.339659	+	0.289464i
$85$	−5.00512	+	6.88276i	−0.542881	+	0.746540i
$86$	−15.0273	+	1.25683i	−1.62044	+	0.135527i
$87$	−1.86210	−	6.94945i	−0.199638	−	0.745059i
$88$	8.35286	−	14.0917i	0.890418	−	1.50218i
$89$	−3.19797	−	3.81119i	−0.338984	−	0.403986i	0.569442	−	0.822032i	$-0.307159\pi$
$89$	−3.19797	−	3.81119i	−0.338984	−	0.403986i	−0.908426	+	0.418046i	$0.862715\pi$
$90$	−2.45265	+	4.04285i	−0.258532	+	0.426153i
$91$	−0.315584	+	0.867061i	−0.0330822	+	0.0908927i
$92$	−14.0778	−	1.34023i	−1.46772	−	0.139729i
$93$	−5.06660	−	7.23585i	−0.525382	−	0.750323i
$94$	−0.322929	−	0.0294976i	−0.0333076	−	0.00304244i
$95$	3.90368	−	8.93092i	0.400510	−	0.916293i
$96$	3.05226	−	6.23163i	0.311520	−	0.636013i
$97$	4.73916	−	3.31840i	0.481189	−	0.336932i	−0.307684	−	0.951489i	$-0.599554\pi$
$97$	4.73916	−	3.31840i	0.481189	−	0.336932i	0.788873	+	0.614556i	$0.210665\pi$
$98$	−5.96857	−	0.0228269i	−0.602917	−	0.00230587i
$99$	8.13814	+	2.96204i	0.817913	+	0.297696i
$100$	−1.30746	−	9.91416i	−0.130746	−	0.991416i
$101$	7.84814	−	6.58537i	0.780919	−	0.655269i	−0.162561	−	0.986698i	$-0.551975\pi$
$101$	7.84814	−	6.58537i	0.780919	−	0.655269i	0.943480	+	0.331430i	$0.107531\pi$
$102$	6.19539	+	2.28181i	0.613435	+	0.225933i
$103$	−9.78580	+	2.62210i	−0.964224	+	0.258363i	−0.706387	−	0.707826i	$-0.749676\pi$
$103$	−9.78580	+	2.62210i	−0.964224	+	0.258363i	−0.257837	+	0.966189i	$0.583010\pi$
$104$	1.55776	+	0.154315i	0.152751	+	0.0151318i
$105$	−0.713429	−	4.51692i	−0.0696235	−	0.440807i
$106$	10.4743	−	14.8378i	1.01736	−	1.44117i
$107$	−5.98840	−	1.60459i	−0.578921	−	0.155121i	−0.0425359	−	0.999095i	$-0.513544\pi$
$107$	−5.98840	−	1.60459i	−0.578921	−	0.155121i	−0.536385	+	0.843974i	$0.680210\pi$
$108$	10.6305	+	2.93576i	1.02292	+	0.282493i
$109$	5.07288	+	13.9376i	0.485894	+	1.33498i	0.904368	+	0.426754i	$0.140343\pi$
$109$	5.07288	+	13.9376i	0.485894	+	1.33498i	−0.418474	+	0.908229i	$0.637435\pi$
$110$	−17.3422	+	5.88903i	−1.65351	+	0.561497i
$111$	−0.892472	+	1.06361i	−0.0847097	+	0.100953i
$112$	−1.62727	−	6.46721i	−0.153763	−	0.611094i
$113$	−12.9038	+	12.9038i	−1.21389	+	1.21389i	−0.244148	+	0.969738i	$0.578508\pi$
$113$	−12.9038	+	12.9038i	−1.21389	+	1.21389i	−0.969738	+	0.244148i	$0.921492\pi$
$114$	−7.49154	−	1.02683i	−0.701647	−	0.0961716i
$115$	10.9782	+	11.3779i	1.02372	+	1.06100i
$116$	−4.09626	+	10.9920i	−0.380328	+	1.02058i
$117$	0.0721289	+	0.824437i	0.00666832	+	0.0762192i
$118$	0.285553	+	0.793986i	0.0262873	+	0.0730924i
$119$	5.96250	−	2.17017i	0.546581	−	0.198939i
$120$	−7.12436	+	3.07090i	−0.650362	+	0.280334i
$121$	11.2716	+	19.5230i	1.02469	+	1.77482i
$122$	−13.5067	+	2.32836i	−1.22283	+	0.210800i
$123$	−0.782012	+	1.11683i	−0.0705117	+	0.100701i
$124$	−0.110163	+	14.4020i	−0.00989291	+	1.29333i
$125$	−6.10128	+	9.36880i	−0.545715	+	0.837971i
$126$	3.20100	−	1.47777i	0.285168	−	0.131650i
$127$	1.15480	−	13.1995i	0.102472	−	1.17126i	−0.754642	−	0.656137i	$-0.772189\pi$
$127$	1.15480	−	13.1995i	0.102472	−	1.17126i	0.857114	−	0.515127i	$-0.172255\pi$
$128$	−9.94587	+	5.39255i	−0.879099	+	0.476639i
$129$	4.47356	−	12.2910i	0.393875	−	1.08216i
$130$	−1.21040	−	1.26411i	−0.106159	−	0.110870i
$131$	13.2679	+	2.33948i	1.15922	+	0.204402i	0.719997	−	0.693977i	$-0.244143\pi$
$131$	13.2679	+	2.33948i	1.15922	+	0.204402i	0.439222	+	0.898378i	$0.355254\pi$
$132$	8.06049	+	11.7011i	0.701576	+	1.01845i
$133$	−6.13488	+	3.89549i	−0.531961	+	0.337781i
$134$	5.88153	+	0.537241i	0.508087	+	0.0464105i
$135$	−6.89054	−	10.2251i	−0.593043	−	0.880035i
$136$	−6.07277	−	8.88814i	−0.520736	−	0.762152i
$137$	−1.64892	−	3.53612i	−0.140877	−	0.302111i	0.823192	−	0.567763i	$-0.192191\pi$
$137$	−1.64892	−	3.53612i	−0.140877	−	0.302111i	−0.964069	+	0.265651i	$0.914413\pi$
$138$	6.17356	−	10.5991i	0.525528	−	0.902255i
$139$	−17.3470	+	14.5559i	−1.47135	+	1.23461i	−0.556486	+	0.830857i	$0.687851\pi$
$139$	−17.3470	+	14.5559i	−1.47135	+	1.23461i	−0.914867	+	0.403755i	$0.867705\pi$
$140$	−3.32249	+	6.67474i	−0.280802	+	0.564118i
$141$	0.140633	−	0.243584i	0.0118434	−	0.0205134i
$142$	9.55618	+	8.08107i	0.801937	+	0.678148i
$143$	−1.83853	+	2.62569i	−0.153745	+	0.219571i
$144$	−3.77417	−	4.64023i	−0.314514	−	0.386686i
$145$	11.4734	−	6.35340i	0.952816	−	0.527621i
$146$	1.44473	−	1.00340i	0.119567	−	0.0830420i
$147$	2.18790	−	4.69197i	0.180455	−	0.386987i
$148$	2.19107	−	0.569170i	0.180105	−	0.0467854i
$149$	−4.52982	+	5.39843i	−0.371098	+	0.442257i	−0.918983	−	0.394296i	$-0.870988\pi$
$149$	−4.52982	+	5.39843i	−0.371098	+	0.442257i	0.547886	+	0.836553i	$0.315433\pi$
$150$	8.28277	+	2.57475i	0.676285	+	0.210227i
$151$			6.54299i			0.532461i	0.963909	+	0.266230i	$0.0857782\pi$
$151$			6.54299i			0.532461i	−0.963909	+	0.266230i	$0.914222\pi$
$152$	8.98101	+	8.44639i	0.728456	+	0.685093i
$153$	4.02417	−	4.02417i	0.325335	−	0.325335i
$154$	13.1765	+	3.58470i	1.06179	+	0.288864i
$155$	10.5693	−	12.1481i	0.848946	−	0.975757i
$156$	−0.687861	+	1.17064i	−0.0550730	+	0.0937261i
$157$	−10.3695	−	4.83538i	−0.827576	−	0.385905i	−0.0377888	−	0.999286i	$-0.512031\pi$
$157$	−10.3695	−	4.83538i	−0.827576	−	0.385905i	−0.789787	+	0.613381i	$0.789809\pi$
$158$	−4.56501	−	0.822949i	−0.363173	−	0.0654703i
$159$	7.87678	+	13.6430i	0.624669	+	1.08196i
$160$	12.3672	+	2.65584i	0.977709	+	0.209963i
$161$	−2.04703	−	11.6093i	−0.161328	−	0.914938i
$162$	−2.08022	+	2.45994i	−0.163438	+	0.193271i
$163$	5.88689	−	1.57739i	0.461097	−	0.123551i	−0.0207903	−	0.999784i	$-0.506618\pi$
$163$	5.88689	−	1.57739i	0.461097	−	0.123551i	0.481887	+	0.876233i	$0.339952\pi$
$164$	2.09465	−	0.744297i	0.163565	−	0.0581198i
$165$	1.66728	−	15.7980i	0.129797	−	1.22988i
$166$	−3.73079	−	14.1396i	−0.289565	−	1.09744i
$167$	11.7459	−	5.47719i	0.908922	−	0.423837i	0.0888157	−	0.996048i	$-0.471692\pi$
$167$	11.7459	−	5.47719i	0.908922	−	0.423837i	0.820107	+	0.572211i	$0.193914\pi$
$168$	5.68456	+	1.06973i	0.438573	+	0.0825314i
$169$	12.5009	+	2.20424i	0.961604	+	0.169557i
$170$	−1.30891	+	11.9639i	−0.100389	+	0.917586i
$171$	−3.51031	+	5.49198i	−0.268440	+	0.419982i
$172$	−17.5623	+	12.0982i	−1.33912	+	0.922476i
$173$	3.13549	+	4.47795i	0.238387	+	0.340452i	0.920463	−	0.390829i	$-0.127812\pi$
$173$	3.13549	+	4.47795i	0.238387	+	0.340452i	−0.682076	+	0.731281i	$0.738923\pi$
$174$	−7.16703	−	7.22206i	−0.543331	−	0.547503i
$175$	7.67611	−	3.25056i	0.580259	−	0.245720i
$176$	0.354389	−	23.1639i	0.0267131	−	1.74604i
$177$	−0.729082	−	0.0637864i	−0.0548011	−	0.00479448i
$178$	−6.60236	−	2.43170i	−0.494868	−	0.182264i
$179$	5.40615	−	9.36373i	0.404075	−	0.699878i	−0.590138	−	0.807302i	$-0.700927\pi$
$179$	5.40615	−	9.36373i	0.404075	−	0.699878i	0.994213	+	0.107424i	$0.0342602\pi$
$180$	−0.170710	+	6.68513i	−0.0127240	+	0.498280i
$181$	0.463143	+	2.62662i	0.0344252	+	0.195235i	0.997170	−	0.0751756i	$-0.0239517\pi$
$181$	0.463143	+	2.62662i	0.0344252	+	0.195235i	−0.962745	+	0.270410i	$0.912841\pi$
$182$	0.221678	+	1.28594i	0.0164319	+	0.0953201i
$183$	3.07687	−	11.4830i	0.227449	−	0.848850i
$184$	−18.2211	+	8.24347i	−1.34328	+	0.607717i
$185$	−2.27437	−	1.11049i	−0.167215	−	0.0816448i
$186$	−11.3015	−	5.32271i	−0.828669	−	0.390280i
$187$	21.9584	−	1.92112i	1.60576	−	0.140486i
$188$	−0.417096	+	0.190625i	−0.0304198	+	0.0139027i
$189$			9.19326i			0.668712i
$190$	−1.48169	−	13.7042i	−0.107493	−	0.994206i
$191$		−	19.3545i		−	1.40044i	−0.713928	−	0.700220i	$-0.753085\pi$
$191$		−	19.3545i		−	1.40044i	0.713928	−	0.700220i	$-0.246915\pi$
$192$	−0.630745	−	9.79291i	−0.0455201	−	0.706743i
$193$	−1.38754	+	0.121394i	−0.0998772	+	0.00873812i	−0.136985	−	0.990573i	$-0.543741\pi$
$193$	−1.38754	+	0.121394i	−0.0998772	+	0.00873812i	0.0371076	+	0.999311i	$0.488186\pi$
$194$	3.48614	−	7.40201i	0.250290	−	0.531433i
$195$	1.43554	−	0.493610i	0.102801	−	0.0353482i
$196$	−7.34210	+	4.16441i	−0.524436	+	0.297458i
$197$	1.77232	−	6.61438i	0.126272	−	0.471255i	−0.873609	−	0.486628i	$-0.838227\pi$
$197$	1.77232	−	6.61438i	0.126272	−	0.471255i	0.999882	+	0.0153726i	$0.00489345\pi$
$198$	12.0697	−	2.08064i	0.857754	−	0.147865i
$199$	0.122564	+	0.695095i	0.00868833	+	0.0492739i	0.988844	−	0.148957i	$-0.0475916\pi$
$199$	0.122564	+	0.695095i	0.00868833	+	0.0492739i	−0.980155	+	0.198231i	$0.936480\pi$
$200$	−8.56871	−	11.2507i	−0.605899	−	0.795541i
$201$	−2.56136	+	4.43640i	−0.180664	+	0.312920i
$202$	5.00744	−	13.5958i	0.352322	−	0.956598i
$203$	−9.74131	−	0.852254i	−0.683706	−	0.0598165i
$204$	9.20725	−	1.55097i	0.644636	−	0.108589i
$205$	−2.31989	−	0.891660i	−0.162028	−	0.0622763i
$206$	−10.1697	+	10.0922i	−0.708555	+	0.703156i
$207$	−6.06448	−	8.66097i	−0.421510	−	0.601979i
$208$	2.02045	−	0.904786i	0.140093	−	0.0627356i
$209$	−24.0881	+	7.55544i	−1.66621	+	0.522621i
$210$	−4.04846	−	5.04313i	−0.279370	−	0.348009i
$211$	1.98431	+	0.349888i	0.136606	+	0.0240872i	0.241533	−	0.970393i	$-0.422350\pi$
$211$	1.98431	+	0.349888i	0.136606	+	0.0240872i	−0.104927	+	0.994480i	$0.533461\pi$
$212$	2.43429	−	25.5699i	0.167188	−	1.75615i
$213$	−9.83810	+	4.58758i	−0.674095	+	0.314336i
$214$	−8.47749	+	2.23682i	−0.579510	+	0.152906i
$215$	23.7116	+	2.50245i	1.61712	+	0.170665i
$216$	15.1104	−	3.86356i	1.02813	−	0.262882i
$217$	−11.5967	+	3.10733i	−0.787237	+	0.210940i
$218$	16.0167	+	13.5443i	1.08479	+	0.917338i
$219$	0.264936	+	1.50253i	0.0179027	+	0.101531i
$220$	−17.1500	+	19.4099i	−1.15625	+	1.30861i
$221$	1.05318	+	1.82416i	0.0708443	+	0.122706i
$222$	−0.348360	+	1.93240i	−0.0233804	+	0.129694i
$223$	1.03034	+	0.480456i	0.0689968	+	0.0321737i	0.456810	−	0.889564i	$-0.348992\pi$
$223$	1.03034	+	0.480456i	0.0689968	+	0.0321737i	−0.387814	+	0.921738i	$0.626770\pi$
$224$	−6.54006	−	6.79509i	−0.436976	−	0.454016i
$225$	5.00760	−	5.55194i	0.333840	−	0.370130i
$226$	−6.77478	+	24.9025i	−0.450652	+	1.65649i
$227$	5.29735	−	5.29735i	0.351597	−	0.351597i	−0.509106	−	0.860704i	$-0.670024\pi$
$227$	5.29735	−	5.29735i	0.351597	−	0.351597i	0.860704	+	0.509106i	$0.170024\pi$
$228$	−9.91668	+	4.00181i	−0.656748	+	0.265027i
$229$		−	1.43513i		−	0.0948360i	−0.998875	−	0.0474180i	$-0.984901\pi$
$229$		−	1.43513i		−	0.0948360i	0.998875	−	0.0474180i	$-0.0150993\pi$
$230$	21.4671	+	6.25451i	1.41550	+	0.412410i
$231$	−7.61340	+	9.07329i	−0.500925	+	0.596979i
$232$	2.69309	+	16.3693i	0.176810	+	1.07470i
$233$	5.18962	−	11.1292i	0.339983	−	0.729097i	−0.659766	−	0.751471i	$-0.729345\pi$
$233$	5.18962	−	11.1292i	0.339983	−	0.729097i	0.999750	+	0.0223741i	$0.00712248\pi$
$234$	0.667633	+	0.961282i	0.0436445	+	0.0628410i
$235$	0.492799	+	0.141536i	0.0321467	+	0.00923280i
$236$	0.908209	+	0.773993i	0.0591194	+	0.0503827i
$237$	2.30772	−	3.29577i	0.149903	−	0.214083i
$238$	5.79424	−	6.85192i	0.375585	−	0.444144i
$239$	−7.67793	+	13.2986i	−0.496644	+	0.860213i	−0.999993	−	0.00387070i	$-0.998768\pi$
$239$	−7.67793	+	13.2986i	−0.496644	+	0.860213i	0.503348	+	0.864084i	$0.332101\pi$
$240$	−6.58767	+	8.77362i	−0.425232	+	0.566335i
$241$	19.6777	−	16.5116i	1.26755	−	1.06360i	0.272718	−	0.962094i	$-0.412077\pi$
$241$	19.6777	−	16.5116i	1.26755	−	1.06360i	0.994835	−	0.101509i	$-0.0323671\pi$
$242$	27.5486	+	16.0460i	1.77089	+	1.03147i
$243$	5.81027	+	12.4602i	0.372729	+	0.799320i
$244$	−14.9431	+	12.3452i	−0.956636	+	0.790323i
$245$	9.26305	+	1.80467i	0.591794	+	0.115296i
$246$	−0.175393	+	1.92014i	−0.0111826	+	0.122424i
$247$	−1.62715	−	1.78105i	−0.103533	−	0.113326i
$248$	9.98097	+	17.7549i	0.633792	+	1.12744i
$249$	12.4913	+	2.20256i	0.791606	+	0.139581i
$250$	−0.908150	+	15.7853i	−0.0574365	+	0.998349i
$251$	0.709917	−	1.95048i	0.0448095	−	0.123113i	−0.915269	−	0.402842i	$-0.868022\pi$
$251$	0.709917	−	1.95048i	0.0448095	−	0.123113i	0.960079	+	0.279729i	$0.0902446\pi$
$252$	2.89102	−	4.06231i	0.182117	−	0.255902i
$253$	3.56914	−	40.7955i	0.224390	−	2.56479i
$254$	−7.85409	−	17.0127i	−0.492809	−	1.06747i
$255$	−8.94570	−	5.38033i	−0.560202	−	0.336930i
$256$	−8.42014	+	13.6052i	−0.526259	+	0.850324i
$257$	−1.00593	+	1.43662i	−0.0627483	+	0.0896139i	−0.849300	−	0.527911i	$-0.822976\pi$
$257$	−1.00593	+	1.43662i	−0.0627483	+	0.0896139i	0.786552	+	0.617525i	$0.211864\pi$
$258$	−3.14239	−	18.2288i	−0.195637	−	1.13487i
$259$	0.943548	+	1.63427i	0.0586292	+	0.101549i
$260$	−2.37362	−	0.701422i	−0.147206	−	0.0435004i
$261$	−8.24153	+	2.99967i	−0.510138	+	0.185675i
$262$	17.9288	−	6.44801i	1.10765	−	0.398360i
$263$	−0.221758	−	2.53470i	−0.0136742	−	0.156297i	0.986288	−	0.165035i	$-0.0527738\pi$
$263$	−0.221758	−	2.53470i	−0.0136742	−	0.156297i	−0.999962	+	0.00873888i	$0.997218\pi$
$264$	18.1128	+	8.70052i	1.11477	+	0.535480i
$265$	−20.6660	+	19.9398i	−1.26950	+	1.22489i
$266$	−4.79394	+	9.09072i	−0.293935	+	0.557388i
$267$	4.31532	−	4.31532i	0.264093	−	0.264093i
$268$	7.59659	−	3.47186i	0.464036	−	0.212077i
$269$	13.8922	−	16.5561i	0.847023	−	1.00944i	−0.152753	−	0.988264i	$-0.548814\pi$
$269$	13.8922	−	16.5561i	0.847023	−	1.00944i	0.999776	−	0.0211781i	$-0.00674170\pi$
$270$	−15.6400	−	7.71064i	−0.951820	−	0.469255i
$271$	6.04671	+	16.6132i	0.367312	+	1.00918i	0.976380	+	0.216062i	$0.0693215\pi$
$271$	6.04671	+	16.6132i	0.367312	+	1.00918i	−0.609068	+	0.793118i	$0.708456\pi$
$272$	−13.6972	−	6.64404i	−0.830512	−	0.402854i
$273$	−1.09327	−	0.292942i	−0.0661679	−	0.0177296i
$274$	−4.50779	−	3.18215i	−0.272325	−	0.192241i
$275$	28.6799	−	4.00567i	1.72946	−	0.241551i
$276$	0.132684	−	17.3462i	0.00798661	−	1.04412i
$277$	−12.4014	+	3.32294i	−0.745127	+	0.199656i	−0.611356	−	0.791356i	$-0.709376\pi$
$277$	−12.4014	+	3.32294i	−0.745127	+	0.199656i	−0.133772	+	0.991012i	$0.542709\pi$
$278$	−11.0681	+	30.0513i	−0.663821	+	1.80236i
$279$	−8.24887	+	6.92163i	−0.493847	+	0.414387i
$280$	0.610297	+	10.5266i	0.0364722	+	0.629086i
$281$	3.25506	+	1.18475i	0.194181	+	0.0706760i	0.437280	−	0.899325i	$-0.355942\pi$
$281$	3.25506	+	1.18475i	0.194181	+	0.0706760i	−0.243099	+	0.970001i	$0.578164\pi$
$282$	0.00152127	−	0.397768i	9.05903e−5	−	0.0236867i
$283$	−6.69026	+	4.68457i	−0.397694	+	0.278469i	−0.755268	−	0.655416i	$-0.772493\pi$
$283$	−6.69026	+	4.68457i	−0.397694	+	0.278469i	0.357573	+	0.933885i	$0.383604\pi$
$284$	17.4059	+	3.20660i	1.03285	+	0.190277i
$285$	11.3308	+	3.81543i	0.671177	+	0.226007i
$286$	−0.412352	+	4.51429i	−0.0243829	+	0.266936i
$287$	1.06287	+	1.51794i	0.0627392	+	0.0896009i
$288$	−7.89195	−	3.04456i	−0.465038	−	0.179402i
$289$	−0.860282	+	2.36360i	−0.0506048	+	0.139036i
$290$	9.62019	−	15.8576i	0.564917	−	0.931188i
$291$	4.56169	+	5.43641i	0.267411	+	0.318688i
$292$	1.06852	−	2.24642i	0.0625303	−	0.131462i
$293$	5.76192	+	21.5038i	0.336615	+	1.25626i	0.902108	+	0.431510i	$0.142019\pi$
$293$	5.76192	+	21.5038i	0.336615	+	1.25626i	−0.565493	+	0.824753i	$0.691314\pi$
$294$	−0.610204	−	7.29593i	−0.0355878	−	0.425507i
$295$	−0.208139	−	1.31779i	−0.0121183	−	0.0767246i
$296$	2.28962	−	2.23767i	0.133081	−	0.130062i
$297$	−8.26573	+	30.8481i	−0.479626	+	1.78999i
$298$	−1.76813	+	9.80808i	−0.102425	+	0.568167i
$299$	3.67729	−	1.33842i	0.212663	−	0.0774031i
$300$	11.9752	−	2.65761i	0.691386	−	0.153437i
$301$	−13.6183	−	11.4271i	−0.784945	−	0.658647i
$302$	4.59591	+	8.03113i	0.264465	+	0.462140i
$303$	8.88625	+	8.88625i	0.510502	+	0.510502i
$304$	16.9565	+	4.05902i	0.972524	+	0.232801i
$305$	21.6674	+	0.387481i	1.24067	+	0.0221871i
$306$	2.11278	−	7.76608i	0.120780	−	0.443957i
$307$	−29.2809	+	2.56175i	−1.67115	+	0.146207i	−0.883030	−	0.469317i	$-0.844500\pi$
$307$	−29.2809	+	2.56175i	−1.67115	+	0.146207i	−0.788119	+	0.615523i	$0.788945\pi$
$308$	18.6913	−	4.85540i	1.06504	−	0.276662i
$309$	−4.25036	−	11.6778i	−0.241794	−	0.664324i
$310$	4.44015	−	22.3351i	0.252184	−	1.26855i
$311$	−8.34163	+	4.81604i	−0.473011	+	0.273093i	−0.717499	−	0.696559i	$-0.754713\pi$
$311$	−8.34163	+	4.81604i	−0.473011	+	0.273093i	0.244489	+	0.969652i	$0.421380\pi$
$312$	−0.0220307	+	1.92006i	−0.00124725	+	0.108702i
$313$	11.3367	+	7.93804i	0.640788	+	0.448685i	0.848277	−	0.529553i	$-0.177640\pi$
$313$	11.3367	+	7.93804i	0.640788	+	0.448685i	−0.207489	+	0.978237i	$0.566529\pi$
$314$	−16.1244	+	1.34858i	−0.909952	+	0.0761049i
$315$	−5.40953	+	1.34629i	−0.304792	+	0.0758548i
$316$	−6.18134	+	2.19643i	−0.347727	+	0.123559i
$317$	−7.38549	−	0.646146i	−0.414810	−	0.0362912i	−0.122159	−	0.992511i	$-0.538982\pi$
$317$	−7.38549	−	0.646146i	−0.414810	−	0.0362912i	−0.292651	+	0.956219i	$0.594537\pi$
$318$	19.2513	+	11.2132i	1.07956	+	0.628802i
$319$	−31.9208	−	11.6182i	−1.78722	−	0.650496i
$320$	17.0455	−	5.42702i	0.952870	−	0.303380i
$321$	1.32056	−	7.48927i	0.0737065	−	0.418010i
$322$	−10.6671	−	12.8118i	−0.594457	−	0.713974i
$323$	−2.18990	+	16.4443i	−0.121849	+	0.914983i
$324$	−0.825440	+	4.48062i	−0.0458578	+	0.248923i
$325$	1.50516	+	2.32209i	0.0834912	+	0.128806i
$326$	6.11782	−	6.07120i	0.338835	−	0.336253i
$327$	−16.4892	+	7.68904i	−0.911855	+	0.425205i
$328$	2.04825	−	2.38490i	0.113096	−	0.131684i
$329$	−0.245726	−	0.292845i	−0.0135473	−	0.0161451i
$330$	−9.05034	−	20.5623i	−0.498205	−	1.13192i
$331$	17.5888	+	10.1549i	0.966770	+	0.558165i	0.898250	−	0.439485i	$-0.144839\pi$
$331$	17.5888	+	10.1549i	0.966770	+	0.558165i	0.0685199	+	0.997650i	$0.478172\pi$
$332$	−14.5112	−	14.7349i	−0.796406	−	0.808684i
$333$	1.38646	+	0.970810i	0.0759776	+	0.0532001i
$334$	10.5701	−	14.9734i	0.578369	−	0.819309i
$335$	−8.97538	−	2.57780i	−0.490377	−	0.140841i
$336$	7.72885	−	2.67990i	0.421643	−	0.146201i
$337$	22.4252	+	10.4570i	1.22158	+	0.569632i	0.923017	−	0.384758i	$-0.125715\pi$
$337$	22.4252	+	10.4570i	1.22158	+	0.569632i	0.298562	+	0.954390i	$0.403493\pi$
$338$	16.8923	−	6.07525i	0.918822	−	0.330450i
$339$	−17.1477	−	14.3887i	−0.931338	−	0.781485i
$340$	6.79701	+	15.6043i	0.368620	+	0.846263i
$341$	−41.7068			−2.25855
$342$	−0.451035	+	9.20678i	−0.0243892	+	0.497846i
$343$	−13.2276	−	13.2276i	−0.714226	−	0.714226i
$344$	−13.0588	+	27.1859i	−0.704082	+	1.46576i
$345$	−12.7300	+	14.6315i	−0.685360	+	0.787735i
$346$	6.99402	+	3.29399i	0.376001	+	0.177086i
$347$	−10.0758	+	21.6076i	−0.540896	+	1.15996i	0.425985	+	0.904730i	$0.359928\pi$
$347$	−10.0758	+	21.6076i	−0.540896	+	1.15996i	−0.966881	+	0.255226i	$0.917850\pi$
$348$	−13.8700	−	3.83040i	−0.743510	−	0.205331i
$349$	−16.4000	+	9.46857i	−0.877874	+	0.506841i	−0.869957	−	0.493128i	$-0.835854\pi$
$349$	−16.4000	+	9.46857i	−0.877874	+	0.506841i	−0.00791745	+	0.999969i	$0.502520\pi$
$350$	7.13871	−	9.38171i	0.381580	−	0.501473i
$351$	−3.00545	+	0.529943i	−0.160419	+	0.0282863i
$352$	−15.8357	−	28.6812i	−0.844048	−	1.52871i
$353$	0.229305	+	0.855778i	0.0122047	+	0.0455485i	0.971760	−	0.235973i	$-0.0758277\pi$
$353$	0.229305	+	0.855778i	0.0122047	+	0.0455485i	−0.959555	+	0.281521i	$0.909161\pi$
$354$	−0.939709	+	0.433826i	−0.0499450	+	0.0230576i
$355$	−12.4463	−	15.3834i	−0.660583	−	0.816466i
$356$	−9.81208	+	1.65285i	−0.520039	+	0.0876009i
$357$	3.28936	+	7.05406i	0.174091	+	0.373340i
$358$	0.0584800	−	15.2908i	0.00309076	−	0.808144i
$359$	2.41084	−	13.6726i	0.127239	−	0.721611i	−0.852713	−	0.522379i	$-0.825044\pi$
$359$	2.41084	−	13.6726i	0.127239	−	0.721611i	0.979953	−	0.199231i	$-0.0638444\pi$
$360$	4.48622	+	8.32551i	0.236444	+	0.438793i
$361$	−1.59945	−	18.9326i	−0.0841816	−	0.996450i
$362$	2.41346	+	2.89869i	0.126849	+	0.152352i
$363$	−22.6518	+	15.8609i	−1.18891	+	0.832483i
$364$	1.17536	+	1.42270i	0.0616057	+	0.0745698i
$365$	−2.54125	+	1.13014i	−0.133015	+	0.0591540i
$366$	−4.28921	−	16.2560i	−0.224200	−	0.849713i
$367$	0.199792	−	2.28363i	0.0104291	−	0.119205i	−0.989196	−	0.146602i	$-0.953166\pi$
$367$	0.199792	−	2.28363i	0.0104291	−	0.119205i	0.999625	+	0.0273972i	$0.00872190\pi$
$368$	−16.5750	+	22.9172i	−0.864030	+	1.19464i
$369$	1.43936	+	0.831013i	0.0749300	+	0.0432608i
$370$	−3.57168	+	0.234498i	−0.185683	+	0.0121910i
$371$	21.0861	−	3.71805i	1.09474	−	0.193032i
$372$	−17.6107	+	1.40509i	−0.913073	+	0.0728506i
$373$	32.8959	+	8.81443i	1.70329	+	0.456394i	0.973763	−	0.227564i	$-0.0730760\pi$
$373$	32.8959	+	8.81443i	1.70329	+	0.456394i	0.729522	+	0.683958i	$0.239743\pi$
$374$	25.6033	−	17.7821i	1.32391	−	0.919488i
$375$	−12.1008	−	6.45405i	−0.624882	−	0.333286i
$376$	−0.378062	+	0.526956i	−0.0194971	+	0.0271757i
$377$	−0.282916	−	3.23375i	−0.0145709	−	0.166547i
$378$	6.45751	+	11.2842i	0.332139	+	0.580396i
$379$	−30.6173			−1.57270			−0.786351	−	0.617779i	$-0.788032\pi$
$379$	−30.6173			−1.57270			−0.786351	+	0.617779i	$0.788032\pi$
$380$	−11.4447	−	15.7803i	−0.587103	−	0.809512i
$381$	16.2530			0.832666
$382$	−13.5949	−	23.7564i	−0.695576	−	1.21548i
$383$	0.0881244	+	1.00727i	0.00450295	+	0.0514689i	0.998114	−	0.0613922i	$-0.0195540\pi$
$383$	0.0881244	+	1.00727i	0.00450295	+	0.0514689i	−0.993611	+	0.112861i	$0.963998\pi$
$384$	−7.65292	−	11.5772i	−0.390536	−	0.590795i
$385$	−19.4019	−	9.47322i	−0.988813	−	0.482800i
$386$	−1.61785	+	1.12364i	−0.0823465	+	0.0571915i
$387$	−15.4014	−	4.12680i	−0.782899	−	0.209777i
$388$	−0.920273	−	11.5342i	−0.0467198	−	0.585563i
$389$	16.6134	−	2.92939i	0.842332	−	0.148526i	0.264199	−	0.964468i	$-0.414892\pi$
$389$	16.6134	−	2.92939i	0.842332	−	0.148526i	0.578133	+	0.815942i	$0.303781\pi$
$390$	1.41532	−	1.61423i	0.0716677	−	0.0817396i
$391$	−23.3051	−	13.4552i	−1.17859	−	0.680459i
$392$	−6.08683	+	10.2688i	−0.307431	+	0.518652i
$393$	−1.44035	+	16.4632i	−0.0726559	+	0.830460i
$394$	−2.47064	−	9.36367i	−0.124469	−	0.471735i
$395$	6.84600	+	2.63130i	0.344460	+	0.132395i
$396$	13.3533	−	11.0318i	0.671029	−	0.554369i
$397$	3.65004	−	2.55579i	0.183190	−	0.128271i	−0.478384	−	0.878151i	$-0.658777\pi$
$397$	3.65004	−	2.55579i	0.183190	−	0.128271i	0.661575	+	0.749879i	$0.269889\pi$
$398$	0.638687	+	0.767096i	0.0320145	+	0.0384510i
$399$	−5.41609	−	7.08025i	−0.271144	−	0.354456i
$400$	−18.4202	−	7.79069i	−0.921012	−	0.389535i
$401$	−3.94650	+	22.3817i	−0.197079	+	1.11769i	0.712348	+	0.701826i	$0.247632\pi$
$401$	−3.94650	+	22.3817i	−0.197079	+	1.11769i	−0.909427	+	0.415864i	$0.863479\pi$
$402$	−0.0277070	+	7.24456i	−0.00138190	+	0.361326i
$403$	−1.68434	−	3.61207i	−0.0839028	−	0.179930i
$404$	−3.40361	−	20.2054i	−0.169336	−	1.00525i
$405$	3.95998	−	3.20393i	0.196773	−	0.159204i
$406$	−12.5555	+	5.79638i	−0.623120	+	0.287669i
$407$	1.69670	+	6.33217i	0.0841023	+	0.313874i
$408$	10.2119	−	8.37105i	0.505565	−	0.414429i
$409$	−7.04418	+	1.24208i	−0.348312	+	0.0614168i	−0.345067	−	0.938578i	$-0.612144\pi$
$409$	−7.04418	+	1.24208i	−0.348312	+	0.0614168i	−0.00324470	+	0.999995i	$0.501033\pi$
$410$	−3.47384	+	0.535070i	−0.171561	+	0.0264252i
$411$	4.14480	−	2.39300i	0.204448	−	0.118038i
$412$	−5.39374	+	19.5309i	−0.265731	+	0.962219i
$413$	−0.420385	+	0.901518i	−0.0206858	+	0.0443608i
$414$	−13.5274	−	6.37103i	−0.664836	−	0.313119i
$415$	1.60302	+	23.0661i	0.0786893	+	1.13227i
$416$	1.84445	−	2.52977i	0.0904315	−	0.124032i
$417$	−19.6416	−	19.6416i	−0.961852	−	0.961852i
$418$	−24.2596	+	26.1938i	−1.18658	+	1.28118i
$419$	1.83212			0.0895051			0.0447526	−	0.998998i	$-0.485750\pi$
$419$	1.83212			0.0895051			0.0447526	+	0.998998i	$0.485750\pi$
$420$	−8.51162	−	3.34643i	−0.415325	−	0.163289i
$421$	10.3866	+	8.71542i	0.506213	+	0.424764i	0.859794	−	0.510640i	$-0.170592\pi$
$421$	10.3866	+	8.71542i	0.506213	+	0.424764i	−0.353581	+	0.935404i	$0.615036\pi$
$422$	2.68139	−	0.964349i	0.130528	−	0.0469438i
$423$	−0.310748	−	0.144904i	−0.0151091	−	0.00704549i
$424$	−14.9728	−	33.0954i	−0.727142	−	1.60725i
$425$	5.57923	−	18.1931i	0.270632	−	0.882496i
$426$	−8.85328	+	12.5414i	−0.428943	+	0.607634i
$427$	−13.2356	−	9.26767i	−0.640516	−	0.448494i
$428$	−8.83443	+	8.70031i	−0.427028	+	0.420545i
$429$	−3.40511	−	1.96594i	−0.164400	−	0.0949164i
$430$	30.8623	−	13.5838i	1.48831	−	0.655071i
$431$	−7.43697	−	8.86304i	−0.358226	−	0.426918i	0.556590	−	0.830787i	$-0.312109\pi$
$431$	−7.43697	−	8.86304i	−0.358226	−	0.426918i	−0.914817	+	0.403870i	$0.867665\pi$
$432$	15.8333	−	15.3561i	0.761778	−	0.738820i
$433$	−2.87171	+	1.33910i	−0.138006	+	0.0643531i	−0.490394	−	0.871501i	$-0.663147\pi$
$433$	−2.87171	+	1.33910i	−0.138006	+	0.0643531i	0.352389	+	0.935854i	$0.385369\pi$
$434$	−12.0516	+	11.9598i	−0.578497	+	0.574089i
$435$	8.99037	+	13.3411i	0.431055	+	0.639656i
$436$	29.1733	+	5.37444i	1.39715	+	0.257389i
$437$	29.3803	+	9.31182i	1.40545	+	0.445445i
$438$	1.38059	+	1.65817i	0.0659674	+	0.0792303i
$439$	3.59523	−	20.3895i	0.171591	−	0.973140i	−0.770415	−	0.637543i	$-0.779951\pi$
$439$	3.59523	−	20.3895i	0.171591	−	0.973140i	0.942006	−	0.335597i	$-0.108938\pi$
$440$	−7.41669	+	35.8709i	−0.353577	+	1.71008i
$441$	−5.93036	−	2.15847i	−0.282398	−	0.102784i
$442$	2.57403	+	1.49927i	0.122434	+	0.0713131i
$443$	−12.7113	−	1.11210i	−0.603933	−	0.0528373i	−0.218911	−	0.975745i	$-0.570250\pi$
$443$	−12.7113	−	1.11210i	−0.603933	−	0.0528373i	−0.385022	+	0.922908i	$0.625806\pi$
$444$	0.929762	+	2.61660i	0.0441246	+	0.124178i
$445$	9.53335	+	5.73377i	0.451924	+	0.271807i
$446$	1.60216	−	0.133999i	0.0758646	−	0.00634503i
$447$	−7.08108	−	4.95822i	−0.334923	−	0.234516i
$448$	−12.8005	−	3.74672i	−0.604768	−	0.177016i
$449$	4.97461	−	2.87209i	0.234766	−	0.135542i	−0.378003	−	0.925804i	$-0.623389\pi$
$449$	4.97461	−	2.87209i	0.234766	−	0.135542i	0.612769	+	0.790262i	$0.290056\pi$
$450$	2.24675	−	10.3321i	0.105913	−	0.487060i
$451$	2.20169	+	6.04909i	0.103673	+	0.284840i
$452$	9.17630	+	35.3250i	0.431617	+	1.66155i
$453$	−7.99542	+	0.699509i	−0.375658	+	0.0328658i
$454$	2.78123	−	10.2231i	0.130529	−	0.479795i
$455$	0.0368912	−	2.06291i	0.00172948	−	0.0967105i
$456$	−9.36119	+	11.8776i	−0.438378	+	0.556221i
$457$	−12.4600	−	12.4600i	−0.582856	−	0.582856i	0.352831	−	0.935687i	$-0.385219\pi$
$457$	−12.4600	−	12.4600i	−0.582856	−	0.582856i	−0.935687	+	0.352831i	$0.885219\pi$
$458$	−1.00806	−	1.76154i	−0.0471036	−	0.0823112i
$459$	16.0765	+	13.4898i	0.750386	+	0.629649i
$460$	30.7429	−	7.40184i	1.43339	−	0.345112i
$461$	22.2402	−	8.09476i	1.03583	−	0.377011i	0.232531	−	0.972589i	$-0.425299\pi$
$461$	22.2402	−	8.09476i	1.03583	−	0.377011i	0.803297	+	0.595578i	$0.203077\pi$
$462$	−2.97175	+	16.4847i	−0.138258	+	0.766938i
$463$	−2.34547	+	8.75340i	−0.109003	+	0.406805i	−0.998769	−	0.0496132i	$-0.984201\pi$
$463$	−2.34547	+	8.75340i	−0.109003	+	0.406805i	0.889765	+	0.456418i	$0.150868\pi$
$464$	14.8037	+	18.2007i	0.687245	+	0.844947i
$465$	15.9747	+	11.6167i	0.740809	+	0.538714i
$466$	−1.44738	−	17.3057i	−0.0670486	−	0.801670i
$467$	10.1664	+	37.9417i	0.470446	+	1.75573i	0.638169	+	0.769896i	$0.279692\pi$
$467$	10.1664	+	37.9417i	0.470446	+	1.75573i	−0.167723	+	0.985834i	$0.553641\pi$
$468$	1.49470	+	0.710959i	0.0690926	+	0.0328641i
$469$	4.47543	+	5.33360i	0.206656	+	0.246283i
$470$	0.704299	−	0.172424i	0.0324869	−	0.00795331i
$471$	4.80015	−	13.1883i	0.221179	−	0.607685i
$472$	1.65844	+	0.312088i	0.0763358	+	0.0143650i
$473$	−35.4221	−	50.5881i	−1.62871	−	2.32604i
$474$	0.517586	−	5.66635i	0.0237735	−	0.260264i
$475$	−1.76100	+	21.7232i	−0.0808000	+	0.996730i
$476$	2.29918	−	12.4803i	0.105383	−	0.572033i
$477$	15.7311	−	11.0150i	0.720277	−	0.504343i
$478$	−0.0830545	+	21.7163i	−0.00379883	+	0.993281i
$479$	24.5839	+	8.94780i	1.12327	+	0.408835i	0.835843	−	0.548968i	$-0.184979\pi$
$479$	24.5839	+	8.94780i	1.12327	+	0.408835i	0.287423	+	0.957804i	$0.407202\pi$
$480$	−1.92322	+	15.3964i	−0.0877827	+	0.702746i
$481$	−0.479885	+	0.402671i	−0.0218809	+	0.0183602i
$482$	12.5552	−	34.0889i	0.571874	−	1.55271i
$483$	13.9675	−	3.74257i	0.635542	−	0.170293i
$484$	45.0852	+	0.344864i	2.04933	+	0.0156756i
$485$	−7.60846	+	10.4627i	−0.345482	+	0.475088i
$486$	15.8840	+	11.2129i	0.720513	+	0.508626i
$487$	12.0339	+	3.22446i	0.545306	+	0.146114i	0.520947	−	0.853589i	$-0.325579\pi$
$487$	12.0339	+	3.22446i	0.545306	+	0.146114i	0.0243589	+	0.999703i	$0.492246\pi$
$488$	−9.67029	+	25.6493i	−0.437753	+	1.16109i
$489$	2.55691	+	7.02504i	0.115627	+	0.317683i
$490$	12.6375	−	4.29141i	0.570903	−	0.193866i
$491$	10.9308	−	13.0268i	0.493298	−	0.587890i	−0.460755	−	0.887527i	$-0.652421\pi$
$491$	10.9308	−	13.0268i	0.493298	−	0.587890i	0.954053	+	0.299638i	$0.0968657\pi$
$492$	1.13346	+	2.48006i	0.0511002	+	0.111810i
$493$	−15.7843	+	15.7843i	−0.710889	+	0.710889i
$494$	−3.24828	−	1.04320i	−0.146147	−	0.0469357i
$495$	−19.3622	−	0.346256i	−0.870266	−	0.0155631i
$496$	24.7224	+	14.7823i	1.11007	+	0.663745i
$497$	1.28587	+	14.6976i	0.0576793	+	0.659277i
$498$	16.8795	−	6.07062i	0.756387	−	0.272031i
$499$	28.5586	−	10.3945i	1.27846	−	0.465321i	0.388537	−	0.921433i	$-0.372981\pi$
$499$	28.5586	−	10.3945i	1.27846	−	0.465321i	0.889922	+	0.456112i	$0.150758\pi$
$500$	9.97316	+	20.0134i	0.446013	+	0.895026i
$501$	7.94877	+	13.7677i	0.355125	+	0.615095i
$502$	−0.498671	−	2.89276i	−0.0222568	−	0.129110i
$503$	−4.07485	+	5.81949i	−0.181689	+	0.259478i	−0.899657	−	0.436598i	$-0.856183\pi$
$503$	−4.07485	+	5.81949i	−0.181689	+	0.259478i	0.717968	+	0.696076i	$0.245072\pi$
$504$	0.695114	−	7.01695i	0.0309628	−	0.312560i
$505$	−11.8072	+	19.6314i	−0.525413	+	0.873586i
$506$	−24.2746	−	52.5811i	−1.07914	−	2.33751i
$507$	−1.35708	+	15.5115i	−0.0602700	+	0.688889i
$508$	−21.5905	−	15.3652i	−0.957921	−	0.681722i
$509$	1.94329	−	5.33913i	0.0861346	−	0.236653i	−0.889146	−	0.457624i	$-0.848701\pi$
$509$	1.94329	−	5.33913i	0.0861346	−	0.236653i	0.975280	+	0.220971i	$0.0709227\pi$
$510$	−14.7596	−	0.320417i	−0.653564	−	0.0141883i
$511$	2.04216	+	0.360087i	0.0903397	+	0.0159293i
$512$	−0.778694	+	22.6140i	−0.0344137	+	0.999408i
$513$	−21.3035	−	11.1303i	−0.940570	−	0.491416i
$514$	−0.225615	+	2.46995i	−0.00995143	+	0.108945i
$515$	18.7861	−	12.6597i	0.827815	−	0.557853i
$516$	−16.6613	−	20.1675i	−0.733474	−	0.887824i
$517$	−0.561238	−	1.20358i	−0.0246832	−	0.0529334i
$518$	2.30609	+	1.34321i	0.101324	+	0.0590171i
$519$	−5.13676	+	4.31025i	−0.225479	+	0.189199i
$520$	−3.40617	+	0.806321i	−0.149371	+	0.0353595i
$521$	−3.21658	+	5.57128i	−0.140921	+	0.244082i	−0.927844	−	0.372969i	$-0.878340\pi$
$521$	−3.21658	+	5.57128i	−0.140921	+	0.244082i	0.786923	+	0.617052i	$0.211673\pi$
$522$	−8.00897	+	9.47092i	−0.350543	+	0.414531i
$523$	−3.03724	+	4.33763i	−0.132809	+	0.189671i	−0.880048	−	0.474884i	$-0.842490\pi$
$523$	−3.03724	+	4.33763i	−0.132809	+	0.189671i	0.747239	+	0.664555i	$0.231379\pi$
$524$	17.4774	−	20.5081i	0.763502	−	0.895899i
$525$	4.79278	+	9.03256i	0.209174	+	0.394213i
$526$	−2.05262	−	2.95543i	−0.0894983	−	0.128863i
$527$	−11.5826	+	24.8390i	−0.504547	+	1.08201i
$528$	28.3438	−	2.04339i	1.23350	−	0.0889270i
$529$	−17.3524	+	20.6798i	−0.754451	+	0.899120i
$530$	−11.3602	+	38.9911i	−0.493455	+	1.69367i
$531$			0.892170i			0.0387169i
$532$	0.501213	+	14.5257i	0.0217303	+	0.629767i
$533$	−0.434974	+	0.434974i	−0.0188408	+	0.0188408i
$534$	2.26564	−	8.32795i	0.0980438	−	0.360386i
$535$	13.8295	−	0.961105i	0.597901	−	0.0415522i
$536$	6.88567	−	9.59748i	0.297416	−	0.414548i
$537$	12.0203	+	5.60515i	0.518714	+	0.241880i
$538$	5.42257	−	30.0797i	0.233783	−	1.29683i
$539$	−12.2217	−	21.1686i	−0.526425	−	0.911795i
$540$	−24.6133	+	1.52146i	−1.05919	+	0.0654734i
$541$	−1.37147	−	7.77801i	−0.0589643	−	0.334403i	0.941028	−	0.338329i	$-0.109862\pi$
$541$	−1.37147	−	7.77801i	−0.0589643	−	0.334403i	−0.999992	+	0.00392567i	$0.998750\pi$
$542$	19.0914	+	16.1444i	0.820045	+	0.693461i
$543$	−3.16016	+	0.846764i	−0.135616	+	0.0363381i
$544$	−21.4793	+	1.46596i	−0.920919	+	0.0628523i
$545$	−20.8608	−	25.7835i	−0.893577	−	1.10444i
$546$	−1.54769	+	0.408366i	−0.0662352	+	0.0174764i
$547$	8.26839	−	3.85561i	0.353531	−	0.164854i	−0.237737	−	0.971330i	$-0.576406\pi$
$547$	8.26839	−	3.85561i	0.353531	−	0.164854i	0.591268	+	0.806475i	$0.298628\pi$
$548$	−7.76824	−	0.739548i	−0.331843	−	0.0315919i
$549$	−14.2718	−	2.51651i	−0.609107	−	0.107402i
$550$	32.3892	−	25.0620i	1.38108	−	1.06865i
$551$	13.7688	−	21.5416i	0.586569	−	0.917703i
$552$	−12.0214	−	21.3846i	−0.511665	−	0.910189i
$553$	−3.13654	−	4.47944i	−0.133379	−	0.190485i
$554$	−12.8879	+	12.7897i	−0.547553	+	0.543381i
$555$	1.11385	−	2.89796i	0.0472801	−	0.123012i
$556$	7.52311	+	44.6606i	0.319051	+	1.89403i
$557$	−20.2332	−	1.77017i	−0.857307	−	0.0750046i	−0.349979	−	0.936758i	$-0.613811\pi$
$557$	−20.2332	−	1.77017i	−0.857307	−	0.0750046i	−0.507328	+	0.861753i	$0.669367\pi$
$558$	−5.26313	+	14.2900i	−0.222806	+	0.604946i
$559$	2.95072	−	5.11079i	0.124802	−	0.216163i
$560$	8.14318	+	12.4921i	0.344112	+	0.527888i
$561$	4.69514	+	26.6275i	0.198229	+	1.12421i
$562$	4.82758	−	0.832209i	0.203639	−	0.0351046i
$563$	1.37353	−	5.12608i	0.0578873	−	0.216038i	−0.930923	−	0.365215i	$-0.880996\pi$
$563$	1.37353	−	5.12608i	0.0578873	−	0.216038i	0.988811	+	0.149176i	$0.0476622\pi$
$564$	−0.277532	−	0.489304i	−0.0116862	−	0.0206034i
$565$	17.9036	−	36.6680i	0.753209	−	1.54263i
$566$	−4.92137	+	10.4494i	−0.206860	+	0.439220i
$567$	−3.78344	+	0.331008i	−0.158890	+	0.0139010i
$568$	23.6171	−	8.29032i	0.990952	−	0.347854i
$569$			16.9427i			0.710274i	0.934814	+	0.355137i	$0.115566\pi$
$569$			16.9427i			0.710274i	−0.934814	+	0.355137i	$0.884434\pi$
$570$	16.5879	−	3.27571i	0.694789	−	0.137205i
$571$			13.0517i			0.546195i	0.961986	+	0.273098i	$0.0880482\pi$
$571$			13.0517i			0.546195i	−0.961986	+	0.273098i	$0.911952\pi$
$572$	2.66478	+	5.83067i	0.111420	+	0.243792i
$573$	23.6508	−	2.06918i	0.988027	−	0.0864411i
$574$	2.37083	+	1.11660i	0.0989567	+	0.0466059i
$575$	−31.4867	−	16.0772i	−1.31309	−	0.670466i
$576$	−11.8254	+	1.80643i	−0.492727	+	0.0752679i
$577$	7.63868	−	28.5079i	0.318002	−	1.18680i	−0.603159	−	0.797621i	$-0.706092\pi$
$577$	7.63868	−	28.5079i	0.318002	−	1.18680i	0.921162	−	0.389180i	$-0.127242\pi$
$578$	0.604293	+	3.50546i	0.0251353	+	0.145808i
$579$	−0.296682	−	1.68257i	−0.0123297	−	0.0699252i
$580$	0.669588	−	26.2216i	0.0278031	−	1.08879i
$581$	8.61973	−	14.9298i	0.357607	−	0.619393i
$582$	9.41783	+	3.46866i	0.390381	+	0.143780i
$583$	74.0977	+	6.48271i	3.06881	+	0.268486i
$584$	−0.266384	−	3.50789i	−0.0110230	−	0.145158i
$585$	−0.751958	−	1.69087i	−0.0310896	−	0.0699090i
$586$	22.1770	+	22.3473i	0.916125	+	0.923159i
$587$	−0.247484	−	0.353444i	−0.0102148	−	0.0145882i	0.814012	−	0.580848i	$-0.197279\pi$
$587$	−0.247484	−	0.353444i	−0.0102148	−	0.0145882i	−0.824227	+	0.566260i	$0.808390\pi$
$588$	−5.87378	−	8.52670i	−0.242231	−	0.351635i
$589$	6.83961	−	30.6350i	0.281821	−	1.26229i
$590$	−1.18112	−	1.47131i	−0.0486258	−	0.0605727i
$591$	8.27214	+	1.45860i	0.340270	+	0.0599988i
$592$	1.23859	−	4.35487i	0.0509056	−	0.178984i
$593$	6.59736	−	3.07640i	0.270921	−	0.126333i	−0.282411	−	0.959294i	$-0.591134\pi$
$593$	6.59736	−	3.07640i	0.270921	−	0.126333i	0.553332	+	0.832961i	$0.313356\pi$
$594$	11.5226	+	43.6702i	0.472777	+	1.79181i
$595$	−11.0301	+	8.92420i	−0.452191	+	0.365857i
$596$	4.71909	+	13.2808i	0.193302	+	0.544003i
$597$	−0.836290	+	0.224083i	−0.0342271	+	0.00917112i
$598$	3.57352	−	4.22583i	0.146132	−	0.172807i
$599$	2.01675	+	11.4376i	0.0824023	+	0.467327i	0.997887	+	0.0649739i	$0.0206964\pi$
$599$	2.01675	+	11.4376i	0.0824023	+	0.467327i	−0.915485	+	0.402353i	$0.868192\pi$
$600$	12.8320	−	11.6736i	0.523865	−	0.476574i
$601$	18.1030	+	31.3554i	0.738438	+	1.27901i	0.953198	+	0.302346i	$0.0977698\pi$
$601$	18.1030	+	31.3554i	0.738438	+	1.27901i	−0.214760	+	0.976667i	$0.568897\pi$
$602$	−24.7422	−	4.46036i	−1.00842	−	0.181791i
$603$	5.65968	+	2.63915i	0.230480	+	0.107475i
$604$	11.2824	+	6.62948i	0.459075	+	0.269750i
$605$	−38.0294	−	33.0871i	−1.54612	−	1.34518i
$606$	17.1492	+	4.66548i	0.696639	+	0.189522i
$607$	13.7429	−	13.7429i	0.557807	−	0.557807i	−0.370876	−	0.928682i	$-0.620942\pi$
$607$	13.7429	−	13.7429i	0.557807	−	0.557807i	0.928682	+	0.370876i	$0.120942\pi$
$608$	23.6643	−	6.92837i	0.959713	−	0.280982i
$609$		−	11.9948i		−	0.486055i
$610$	26.8676	−	14.7440i	1.08784	−	0.596966i
$611$	0.0815719	−	0.0972136i	0.00330005	−	0.00393284i
$612$	−2.86172	−	11.0164i	−0.115678	−	0.445314i
$613$	−18.4718	+	39.6129i	−0.746069	+	1.59995i	0.0529166	+	0.998599i	$0.483148\pi$
$613$	−18.4718	+	39.6129i	−0.746069	+	1.59995i	−0.798985	+	0.601351i	$0.794630\pi$
$614$	−34.1411	+	23.7118i	−1.37782	+	0.956930i
$615$	0.841575	−	2.93019i	0.0339356	−	0.118157i
$616$	19.5320	−	19.0888i	0.786966	−	0.769111i
$617$	20.3164	−	29.0148i	0.817907	−	1.16809i	−0.165416	−	0.986224i	$-0.552897\pi$
$617$	20.3164	−	29.0148i	0.817907	−	1.16809i	0.983323	−	0.181868i	$-0.0582145\pi$
$618$	−13.4197	−	11.3482i	−0.539820	−	0.456492i
$619$	16.4231	−	28.4456i	0.660098	−	1.14332i	−0.320491	−	0.947251i	$-0.603848\pi$
$619$	16.4231	−	28.4456i	0.660098	−	1.14332i	0.980589	−	0.196072i	$-0.0628187\pi$
$620$	−10.2385	−	30.5338i	−0.411190	−	1.22627i
$621$	29.8677	−	25.0620i	1.19855	−	1.00570i
$622$	−6.85598	+	11.7707i	−0.274900	+	0.471963i
$623$	−3.50544	−	7.51744i	−0.140442	−	0.301180i
$624$	1.32164	+	2.37223i	0.0529079	+	0.0949651i
$625$	6.08956	−	24.2470i	0.243582	−	0.969880i
$626$	19.4909	+	1.78038i	0.779014	+	0.0711581i
$627$	−11.8079	−	28.6275i	−0.471561	−	1.14327i
$628$	−18.8445	+	12.9814i	−0.751976	+	0.518013i
$629$	4.24241	+	0.748051i	0.169156	+	0.0298268i
$630$	−5.69422	+	5.45224i	−0.226863	+	0.217222i
$631$	−6.17587	+	16.9681i	−0.245857	+	0.675488i	0.753970	+	0.656909i	$0.228136\pi$
$631$	−6.17587	+	16.9681i	−0.245857	+	0.675488i	−0.999827	+	0.0185788i	$0.994086\pi$
$632$	−6.04441	+	7.03786i	−0.240434	+	0.279951i
$633$	−0.215415	+	2.46220i	−0.00856196	+	0.0978637i
$634$	−9.51911	+	4.39459i	−0.378052	+	0.174531i
$635$	7.15528	+	28.7506i	0.283948	+	1.14093i
$636$	31.5062	+	0.240996i	1.24930	+	0.00955610i
$637$	1.33976	−	1.91337i	0.0530831	−	0.0758106i
$638$	−47.3417	+	8.16106i	−1.87428	+	0.323100i
$639$	6.61639	+	11.4599i	0.261740	+	0.453347i
$640$	17.1102	−	18.6344i	0.676342	−	0.736588i
$641$	−29.5509	+	10.7556i	−1.16719	+	0.424822i	−0.851660	−	0.524094i	$-0.824404\pi$
$641$	−29.5509	+	10.7556i	−1.16719	+	0.424822i	−0.315529	+	0.948916i	$0.602182\pi$
$642$	−3.63969	−	10.1202i	−0.143647	−	0.399413i
$643$	2.89992	+	33.1462i	0.114362	+	1.30716i	0.809004	+	0.587804i	$0.200007\pi$
$643$	2.89992	+	33.1462i	0.114362	+	1.30716i	−0.694642	+	0.719356i	$0.744437\pi$
$644$	−22.0925	−	8.23293i	−0.870567	−	0.324423i
$645$	−0.522950	+	29.2427i	−0.0205911	+	1.15143i
$646$	8.86276	+	21.7226i	0.348701	+	0.854663i
$647$	2.27324	−	2.27324i	0.0893703	−	0.0893703i	−0.661008	−	0.750379i	$-0.729871\pi$
$647$	2.27324	−	2.27324i	0.0893703	−	0.0893703i	0.750379	+	0.661008i	$0.229871\pi$
$648$	2.13409	+	6.07949i	0.0838348	+	0.238825i
$649$	−2.22117	+	2.64708i	−0.0871884	+	0.103907i
$650$	3.47857	+	1.79298i	0.136441	+	0.0703263i
$651$	−5.03691	−	13.8388i	−0.197412	−	0.542385i
$652$	3.24474	−	11.7493i	0.127074	−	0.460138i
$653$	38.6454	+	10.3550i	1.51231	+	0.405223i	0.917202	−	0.398421i	$-0.130442\pi$
$653$	38.6454	+	10.3550i	1.51231	+	0.405223i	0.595110	+	0.803644i	$0.297109\pi$
$654$	−14.8386	+	21.0201i	−0.580235	+	0.821953i
$655$	−29.7567	+	4.69994i	−1.16269	+	0.183642i
$656$	0.838913	−	4.36605i	0.0327541	−	0.170466i
$657$	1.79651	−	0.481374i	0.0700886	−	0.0187802i
$658$	−0.507314	−	0.186847i	−0.0197772	−	0.00728407i
$659$	−2.07681	+	1.74265i	−0.0809010	+	0.0678840i	−0.682341	−	0.731034i	$-0.739038\pi$
$659$	−2.07681	+	1.74265i	−0.0809010	+	0.0678840i	0.601440	+	0.798918i	$0.294594\pi$
$660$	−25.5521	−	18.8818i	−0.994612	−	0.734975i
$661$	−41.9796	−	15.2793i	−1.63282	−	0.594297i	−0.647055	−	0.762443i	$-0.724000\pi$
$661$	−41.9796	−	15.2793i	−1.63282	−	0.594297i	−0.985762	+	0.168146i	$0.946222\pi$
$662$	28.7222	+	0.109849i	1.11632	+	0.00426940i
$663$	−2.11649	+	1.48198i	−0.0821977	+	0.0575555i
$664$	−28.1617	−	7.89331i	−1.09289	−	0.306320i
$665$	10.1402	−	12.6978i	0.393219	−	0.492400i
$666$	2.38371	+	0.217737i	0.0923669	+	0.00843714i
$667$	23.7872	+	33.9716i	0.921042	+	1.31538i
$668$	2.45654	−	25.8036i	0.0950464	−	0.998371i
$669$	−0.476956	+	1.31043i	−0.0184402	+	0.0506640i
$670$	−12.8274	+	3.14036i	−0.495567	+	0.121323i
$671$	−36.0796	−	42.9980i	−1.39284	−	1.65992i
$672$	7.60429	−	8.71830i	0.293342	−	0.336316i
$673$	−1.88839	−	7.04757i	−0.0727921	−	0.271664i	0.919931	−	0.392079i	$-0.128244\pi$
$673$	−1.88839	−	7.04757i	−0.0727921	−	0.271664i	−0.992724	+	0.120415i	$0.961577\pi$
$674$	34.8708	−	2.91646i	1.34317	−	0.112338i
$675$	22.0050	+	16.6115i	0.846971	+	0.639376i
$676$	16.4670	−	19.3225i	0.633345	−	0.743172i
$677$	−6.15168	+	22.9584i	−0.236428	+	0.882362i	0.741072	+	0.671426i	$0.234318\pi$
$677$	−6.15168	+	22.9584i	−0.236428	+	0.882362i	−0.977500	+	0.210936i	$0.932349\pi$
$678$	−31.1547	−	5.61635i	−1.19649	−	0.215695i
$679$	9.06380	−	3.29895i	0.347837	−	0.126602i
$680$	19.3037	+	14.3790i	0.740262	+	0.551411i
$681$	7.03961	+	5.90693i	0.269758	+	0.226354i
$682$	−51.1926	+	29.2956i	−1.96027	+	1.12179i
$683$	−16.1335	−	16.1335i	−0.617329	−	0.617329i	0.327516	−	0.944846i	$-0.393788\pi$
$683$	−16.1335	−	16.1335i	−0.617329	−	0.617329i	−0.944846	+	0.327516i	$0.893788\pi$
$684$	5.91339	+	11.6176i	0.226104	+	0.444210i
$685$	6.05781	+	6.27842i	0.231457	+	0.239886i
$686$	−25.5275	−	6.94481i	−0.974644	−	0.265154i
$687$	1.75370	−	0.153429i	0.0669080	−	0.00585369i
$688$	3.06696	+	42.5417i	0.116927	+	1.62189i
$689$	2.43101	+	6.67913i	0.0926139	+	0.254455i
$690$	−5.34786	+	26.9011i	−0.203589	+	1.02411i
$691$	30.8171	−	17.7923i	1.17234	−	0.676850i	0.218109	−	0.975924i	$-0.430011\pi$
$691$	30.8171	−	17.7923i	1.17234	−	0.676850i	0.954230	+	0.299074i	$0.0966777\pi$
$692$	10.8985	−	0.869548i	0.414299	−	0.0330553i
$693$	11.8274	+	8.28167i	0.449288	+	0.314595i
$694$	2.81013	+	33.5994i	0.106671	+	1.27542i
$695$	26.0978	−	43.3920i	0.989946	−	1.64595i
$696$	−19.7151	+	5.04095i	−0.747301	+	0.191077i
$697$	4.21406	+	0.368682i	0.159619	+	0.0139648i
$698$	−13.4792	+	23.1418i	−0.510195	+	0.875930i
$699$	14.1545	+	5.15181i	0.535372	+	0.194859i
$700$	2.17246	−	16.5298i	0.0821115	−	0.624769i
$701$	3.50902	−	19.9006i	0.132534	−	0.751636i	−0.844012	−	0.536325i	$-0.819812\pi$
$701$	3.50902	−	19.9006i	0.132534	−	0.751636i	0.976545	−	0.215311i	$-0.0690766\pi$
$702$	−3.31678	+	2.76156i	−0.125184	+	0.104228i
$703$	−4.92944	+	0.207853i	−0.185917	+	0.00783932i
$704$	−39.5836	−	24.0812i	−1.49186	−	0.907594i
$705$	−0.120270	+	0.617324i	−0.00452962	+	0.0232498i
$706$	0.882571	+	0.889348i	0.0332160	+	0.0334711i
$707$	15.4802	−	7.21852i	0.582192	−	0.271480i
$708$	−0.848710	+	1.19256i	−0.0318965	+	0.0448193i
$709$	−10.9329	−	13.0293i	−0.410592	−	0.489325i	0.520627	−	0.853784i	$-0.325698\pi$
$709$	−10.9329	−	13.0293i	−0.410592	−	0.489325i	−0.931219	+	0.364460i	$0.881254\pi$
$710$	−26.0827	−	10.1397i	−0.978867	−	0.380535i
$711$	−4.24755	−	2.45233i	−0.159296	−	0.0919694i
$712$	−10.8827	+	8.92095i	−0.407848	+	0.334327i
$713$	41.7094	+	29.2053i	1.56203	+	1.09375i
$714$	8.99239	+	6.34793i	0.336532	+	0.237565i
$715$	1.97856	−	6.88894i	0.0739940	−	0.257632i
$716$	−10.6687	−	18.8096i	−0.398710	−	0.702949i
$717$	−17.0715	−	7.96056i	−0.637546	−	0.297292i
$718$	−6.64469	−	18.4757i	−0.247978	−	0.689506i
$719$	23.1643	+	19.4371i	0.863882	+	0.724883i	0.962801	−	0.270213i	$-0.0870940\pi$
$719$	23.1643	+	19.4371i	0.863882	+	0.724883i	−0.0989189	+	0.995095i	$0.531538\pi$
$720$	11.3545	+	7.06787i	0.423159	+	0.263404i
$721$	−16.8904			−0.629032
$722$	−15.2618	−	22.1151i	−0.567985	−	0.823039i
$723$	22.2806	+	22.2806i	0.828624	+	0.828624i
$724$	4.99847	+	1.86272i	0.185767	+	0.0692273i
$725$	−19.6417	+	21.7768i	−0.729474	+	0.808770i
$726$	−16.6627	+	35.3793i	−0.618410	+	1.31305i
$727$	16.7769	−	35.9782i	0.622222	−	1.33436i	−0.302294	−	0.953215i	$-0.597752\pi$
$727$	16.7769	−	35.9782i	0.622222	−	1.33436i	0.924516	−	0.381144i	$-0.124470\pi$
$728$	2.44202	+	0.920686i	0.0905072	+	0.0341229i
$729$	−20.5234	+	11.8492i	−0.760125	+	0.438858i
$730$	−2.32541	+	3.17219i	−0.0860672	+	0.117408i
$731$	−39.9657	+	7.04703i	−1.47818	+	0.260644i
$732$	−16.6832	−	16.9404i	−0.616630	−	0.626136i
$733$	−2.20996	−	8.24767i	−0.0816266	−	0.304635i	0.913027	−	0.407898i	$-0.133738\pi$
$733$	−2.20996	−	8.24767i	−0.0816266	−	0.304635i	−0.994654	+	0.103263i	$0.967072\pi$
$734$	−1.35883	−	2.94336i	−0.0501554	−	0.108642i
$735$	−1.21496	+	11.5122i	−0.0448146	+	0.424635i
$736$	−4.24735	+	39.7721i	−0.156559	+	1.46602i
$737$	10.2219	+	21.9209i	0.376527	+	0.807465i
$738$	2.35044	+	0.00898932i	0.0865210	+	0.000330902i
$739$	2.06819	−	11.7293i	0.0760797	−	0.431469i	−0.922848	−	0.385165i	$-0.874145\pi$
$739$	2.06819	−	11.7293i	0.0760797	−	0.431469i	0.998927	−	0.0463042i	$-0.0147444\pi$
$740$	−4.21931	+	2.79664i	−0.155105	+	0.102807i
$741$	2.00246	−	2.17876i	0.0735622	−	0.0800389i
$742$	23.2703	−	19.3749i	0.854281	−	0.711277i
$743$	35.1111	−	24.5851i	1.28810	−	0.901939i	0.289628	−	0.957139i	$-0.406469\pi$
$743$	35.1111	−	24.5851i	1.28810	−	0.901939i	0.998475	+	0.0552000i	$0.0175796\pi$
$744$	−20.6291	+	14.0947i	−0.756301	+	0.516738i
$745$	5.65343	−	14.7089i	0.207126	−	0.538891i
$746$	46.5692	−	12.2875i	1.70502	−	0.449876i
$747$	1.34762	−	15.4034i	0.0493070	−	0.563581i
$748$	18.9360	−	39.8106i	0.692370	−	1.45562i
$749$	−8.95128	−	5.16802i	−0.327073	−	0.188835i
$750$	−19.3864	+	0.577855i	−0.707893	+	0.0211003i
$751$	−27.0576	+	4.77098i	−0.987344	+	0.174095i	−0.643927	−	0.765087i	$-0.722696\pi$
$751$	−27.0576	+	4.77098i	−0.987344	+	0.174095i	−0.343418	+	0.939183i	$0.611585\pi$
$752$	−0.0939057	+	0.912364i	−0.00342439	+	0.0332705i
$753$	2.45935	+	0.658981i	0.0896237	+	0.0240146i
$754$	−2.61871	−	3.77051i	−0.0953676	−	0.137314i
$755$	−4.75733	−	13.8355i	−0.173137	−	0.503526i
$756$	15.8524	+	9.31479i	0.576547	+	0.338776i
$757$	3.34768	+	38.2641i	0.121673	+	1.39073i	0.774187	+	0.632957i	$0.218159\pi$
$757$	3.34768	+	38.2641i	0.121673	+	1.39073i	−0.652514	+	0.757777i	$0.726286\pi$
$758$	−37.5809	+	21.5061i	−1.36500	+	0.781137i
$759$	50.2330			1.82334
$760$	−25.1321	−	11.3304i	−0.911637	−	0.410996i
$761$	4.91673			0.178231			0.0891157	−	0.996021i	$-0.471596\pi$
$761$	4.91673			0.178231			0.0891157	+	0.996021i	$0.471596\pi$
$762$	19.9496	−	11.4164i	0.722697	−	0.413572i
$763$	2.15520	+	24.6340i	0.0780233	+	0.891810i
$764$	−33.3739	−	19.6103i	−1.20742	−	0.709476i
$765$	−5.58341	+	11.4353i	−0.201868	+	0.413443i
$766$	0.815690	+	1.17446i	0.0294721	+	0.0424350i
$767$	−0.318956	−	0.0854641i	−0.0115169	−	0.00308593i
$768$	−17.5255	−	8.83474i	−0.632397	−	0.318796i
$769$	−18.5369	+	3.26855i	−0.668456	+	0.117867i	−0.497570	−	0.867424i	$-0.665774\pi$
$769$	−18.5369	+	3.26855i	−0.668456	+	0.117867i	−0.170886	+	0.985291i	$0.554663\pi$
$770$	−30.4688	+	2.00043i	−1.09802	+	0.0720904i
$771$	−1.86307	−	1.07564i	−0.0670968	−	0.0387384i
$772$	−1.19655	+	2.51560i	−0.0430649	+	0.0905385i
$773$	0.426780	−	4.87811i	0.0153502	−	0.175454i	−0.984649	−	0.174544i	$-0.944155\pi$
$773$	0.426780	−	4.87811i	0.0153502	−	0.175454i	1.00000		0.000909616i	$-0.000289540\pi$
$774$	−21.8031	+	5.75284i	−0.783696	+	0.206781i
$775$	−13.5166	+	33.3726i	−0.485532	+	1.19878i
$776$	−9.23144	−	13.5112i	−0.331389	−	0.485023i
$777$	−1.89618	+	1.32772i	−0.0680250	+	0.0476316i
$778$	18.3343	−	15.2652i	0.657316	−	0.547283i
$779$	−4.80432	+	0.625207i	−0.172133	+	0.0224004i
$780$	0.603363	−	2.97552i	0.0216038	−	0.106541i
$781$	−8.89994	+	50.4741i	−0.318465	+	1.80610i
$782$	−38.0568	−	0.145549i	−1.36091	−	0.00520482i
$783$	−13.6684	−	29.3119i	−0.488467	−	1.04752i
$784$	−0.258248	+	16.8798i	−0.00922313	+	0.602850i
$785$	25.4426	+	2.68514i	0.908086	+	0.0958366i
$786$	9.79612	+	21.2194i	0.349416	+	0.756869i
$787$	−12.0462	−	44.9569i	−0.429400	−	1.60254i	−0.754124	−	0.656732i	$-0.771938\pi$
$787$	−12.0462	−	44.9569i	−0.429400	−	1.60254i	0.324724	−	0.945809i	$-0.394728\pi$
$788$	−9.60977	−	9.75792i	−0.342334	−	0.347611i
$789$	3.07366	−	0.541969i	0.109425	−	0.0192946i
$790$	10.2513	−	1.57899i	0.364726	−	0.0561781i
$791$	−26.3482	+	15.2121i	−0.936833	+	0.540881i
$792$	8.64145	−	22.9205i	0.307061	−	0.814444i
$793$	2.26682	−	4.86120i	0.0804970	−	0.172626i
$794$	2.68498	−	5.70093i	0.0952863	−	0.202318i
$795$	−26.5755	−	23.1217i	−0.942537	−	0.820043i
$796$	1.32277	+	0.492940i	0.0468844	+	0.0174718i
$797$	−22.1214	−	22.1214i	−0.783581	−	0.783581i	0.196852	−	0.980433i	$-0.436928\pi$
$797$	−22.1214	−	22.1214i	−0.783581	−	0.783581i	−0.980433	+	0.196852i	$0.936928\pi$
$798$	−11.6212	−	4.88622i	−0.411387	−	0.172970i
$799$	−0.872673			−0.0308729
$800$	−28.0821	+	3.37609i	−0.992851	+	0.119363i
$801$	−5.69898	−	4.78201i	−0.201364	−	0.168964i
$802$	10.8772	+	30.2443i	0.384088	+	1.06796i
$803$	6.52872	+	3.04439i	0.230394	+	0.107434i
$804$	5.05470	+	8.91173i	0.178265	+	0.314292i
$805$	12.7695	+	23.0600i	0.450066	+	0.812760i
$806$	−4.60461	−	3.25049i	−0.162190	−	0.114494i
$807$	21.7165	+	15.2060i	0.764456	+	0.535278i
$808$	−18.3703	−	22.4101i	−0.646266	−	0.788386i
$809$	42.2631	+	24.4006i	1.48589	+	0.857880i	0.999871	−	0.0160674i	$-0.00511462\pi$
$809$	42.2631	+	24.4006i	1.48589	+	0.857880i	0.486021	+	0.873947i	$0.338448\pi$
$810$	2.61015	−	6.71419i	0.0917113	−	0.235913i
$811$	−28.2912	−	33.7161i	−0.993437	−	1.18393i	−0.982929	−	0.183987i	$-0.941099\pi$
$811$	−28.2912	−	33.7161i	−0.993437	−	1.18393i	−0.0105083	−	0.999945i	$-0.503345\pi$
$812$	−11.3397	+	15.9339i	−0.397944	+	0.559171i
$813$	−19.6546	+	9.16509i	−0.689317	+	0.321434i
$814$	6.53043	+	6.58057i	0.228891	+	0.230649i
$815$	−11.3013	+	7.61576i	−0.395866	+	0.266768i
$816$	6.65455	−	17.4480i	0.232956	−	0.610802i
$817$	42.9676	−	17.7227i	1.50325	−	0.620038i
$818$	−7.77385	+	6.47253i	−0.271806	+	0.226307i
$819$	−0.239591	+	1.35879i	−0.00837199	+	0.0474799i
$820$	−3.88809	+	3.09685i	−0.135778	+	0.108147i
$821$	−45.4821	−	16.5541i	−1.58734	−	0.577744i	−0.610554	−	0.791974i	$-0.709053\pi$
$821$	−45.4821	−	16.5541i	−1.58734	−	0.577744i	−0.976783	+	0.214231i	$0.931275\pi$
$822$	3.40661	−	5.84864i	0.118819	−	0.203995i
$823$	22.2880	+	1.94995i	0.776912	+	0.0679710i	0.468712	−	0.883351i	$-0.344718\pi$
$823$	22.2880	+	1.94995i	0.776912	+	0.0679710i	0.308199	+	0.951322i	$0.400274\pi$
$824$	7.09836	+	27.7617i	0.247283	+	0.967125i
$825$	7.96101	+	34.6181i	0.277167	+	1.20525i
$826$	0.117245	+	1.40184i	0.00407947	+	0.0487764i
$827$	−32.3673	−	22.6638i	−1.12552	−	0.788098i	−0.145969	−	0.989289i	$-0.546630\pi$
$827$	−32.3673	−	22.6638i	−1.12552	−	0.788098i	−0.979552	+	0.201191i	$0.935519\pi$
$828$	−21.0792	+	1.68183i	−0.732553	+	0.0584475i
$829$	30.4007	−	17.5518i	1.05586	−	0.609600i	0.131575	−	0.991306i	$-0.457997\pi$
$829$	30.4007	−	17.5518i	1.05586	−	0.609600i	0.924284	+	0.381706i	$0.124663\pi$
$830$	18.1697	+	27.1863i	0.630679	+	0.943651i
$831$	−5.38641	−	14.7990i	−0.186852	−	0.513373i
$832$	0.486992	−	4.40072i	0.0168834	−	0.152567i
$833$	−16.0014	+	1.39994i	−0.554415	+	0.0485050i
$834$	−37.9054	−	10.3123i	−1.31256	−	0.357085i
$835$	−20.8549	+	20.1221i	−0.721713	+	0.696354i
$836$	−11.3783	+	49.1917i	−0.393527	+	1.70133i
$837$	−28.0783	−	28.0783i	−0.970529	−	0.970529i
$838$	2.24882	−	1.28692i	0.0776843	−	0.0444558i
$839$	−11.1506	−	9.35648i	−0.384962	−	0.323022i	0.429685	−	0.902979i	$-0.358625\pi$
$839$	−11.1506	−	9.35648i	−0.384962	−	0.323022i	−0.814647	+	0.579957i	$0.803069\pi$
$840$	−12.7981	+	1.87117i	−0.441576	+	0.0645615i
$841$	5.07530	−	1.84726i	0.175010	−	0.0636986i
$842$	18.8708	+	3.40190i	0.650332	+	0.117237i
$843$	−1.09974	+	4.10429i	−0.0378771	+	0.141359i
$844$	2.61387	−	3.06714i	0.0899731	−	0.105575i
$845$	−28.0364	+	4.42823i	−0.964482	+	0.152336i
$846$	−0.483208	+	0.0404137i	−0.0166130	+	0.00138945i
$847$	9.72748	+	36.3034i	0.334240	+	1.24740i
$848$	−41.6250	−	30.1055i	−1.42941	−	1.03383i
$849$	−6.43971	−	7.67455i	−0.221010	−	0.263390i
$850$	−5.93100	−	26.2499i	−0.203432	−	0.900365i
$851$	2.73731	−	7.52069i	0.0938337	−	0.257806i
$852$	−2.05755	+	21.6126i	−0.0704904	+	0.740434i
$853$	−17.0926	−	24.4108i	−0.585241	−	0.835811i	0.411911	−	0.911224i	$-0.364861\pi$
$853$	−17.0926	−	24.4108i	−0.585241	−	0.835811i	−0.997152	+	0.0754130i	$0.975972\pi$
$854$	−22.7557	−	2.07859i	−0.778683	−	0.0711279i
$855$	3.42960	−	14.1654i	0.117290	−	0.484446i
$856$	−4.73249	+	16.8846i	−0.161753	+	0.577103i
$857$	−12.7704	+	8.94192i	−0.436228	+	0.305450i	−0.770984	−	0.636855i	$-0.780235\pi$
$857$	−12.7704	+	8.94192i	−0.436228	+	0.305450i	0.334756	+	0.942305i	$0.391346\pi$
$858$	−5.56047	−	0.0212662i	−0.189831	−	0.000726014i
$859$	−17.4959	−	6.36798i	−0.596952	−	0.217273i	0.0258325	−	0.999666i	$-0.491776\pi$
$859$	−17.4959	−	6.36798i	−0.596952	−	0.217273i	−0.622784	+	0.782394i	$0.713999\pi$
$860$	28.3401	−	38.3516i	0.966391	−	1.30778i
$861$	−1.74126	+	1.46109i	−0.0593420	+	0.0497939i
$862$	−15.3540	−	5.65499i	−0.522959	−	0.192610i
$863$	17.9535	−	4.81064i	0.611146	−	0.163756i	0.0600462	−	0.998196i	$-0.480875\pi$
$863$	17.9535	−	4.81064i	0.611146	−	0.163756i	0.551099	+	0.834440i	$0.314209\pi$
$864$	8.64800	−	29.9703i	0.294211	−	1.01961i
$865$	−9.88603	−	7.18909i	−0.336135	−	0.244436i
$866$	−2.58424	+	3.66081i	−0.0878162	+	0.124399i
$867$	−2.98026	−	0.798557i	−0.101215	−	0.0271204i
$868$	−6.39189	+	23.1452i	−0.216955	+	0.785601i
$869$	−6.49720	−	17.8509i	−0.220402	−	0.605550i
$870$	20.4062	+	10.0604i	0.691833	+	0.341079i
$871$	−1.48567	+	1.77056i	−0.0503401	+	0.0599930i
$872$	39.5836	−	13.8950i	1.34047	−	0.470545i
$873$	6.11728	−	6.11728i	0.207039	−	0.207039i
$874$	42.6034	−	9.20757i	1.44108	−	0.311451i
$875$	−13.8681	+	12.4547i	−0.468828	+	0.421046i
$876$	2.85932	+	1.06555i	0.0966076	+	0.0360015i
$877$	2.76283	+	31.5793i	0.0932942	+	1.06636i	0.888148	+	0.459557i	$0.151992\pi$
$877$	2.76283	+	31.5793i	0.0932942	+	1.06636i	−0.794854	+	0.606800i	$0.792453\pi$
$878$	−9.90905	−	27.5523i	−0.334414	−	0.929845i
$879$	−25.6612	+	9.33992i	−0.865532	+	0.315028i
$880$	16.0928	+	49.2390i	0.542489	+	1.65985i
$881$	22.8172	+	39.5205i	0.768729	+	1.33148i	0.938252	+	0.345952i	$0.112444\pi$
$881$	22.8172	+	39.5205i	0.768729	+	1.33148i	−0.169523	+	0.985526i	$0.554223\pi$
$882$	−8.79531	+	1.51619i	−0.296153	+	0.0510528i
$883$	19.0777	−	27.2458i	0.642016	−	0.916894i	−0.357841	−	0.933782i	$-0.616487\pi$
$883$	19.0777	−	27.2458i	0.642016	−	0.916894i	0.999857	+	0.0168886i	$0.00537605\pi$
$884$	4.21258	+	0.0322227i	0.141685	+	0.00108377i
$885$	1.58806	−	0.395227i	0.0533821	−	0.0132854i
$886$	−16.3835	+	7.56362i	−0.550416	+	0.254105i
$887$	−3.42057	+	39.0973i	−0.114852	+	1.31276i	0.691953	+	0.721942i	$0.256750\pi$
$887$	−3.42057	+	39.0973i	−0.114852	+	1.31276i	−0.806805	+	0.590818i	$0.798805\pi$
$888$	2.97918	+	2.55864i	0.0999746	+	0.0858624i
$889$	7.55529	−	20.7580i	0.253396	−	0.696201i
$890$	15.7291	+	0.341465i	0.527241	+	0.0114459i
$891$	−12.9930	−	2.29102i	−0.435282	−	0.0767519i
$892$	1.87244	−	1.28986i	0.0626938	−	0.0431878i
$893$	0.976109	−	0.214870i	0.0326642	−	0.00719035i
$894$	−12.1743	−	1.11205i	−0.407171	−	0.0371925i
$895$	−4.62335	+	23.7309i	−0.154542	+	0.793236i
$896$	−18.3436	+	4.39244i	−0.612818	+	0.146741i
$897$	2.02867	+	4.35049i	0.0677353	+	0.145259i
$898$	4.08862	−	7.01957i	0.136439	−	0.234246i
$899$	32.3552	−	27.1492i	1.07911	−	0.905477i
$900$	−4.49970	−	14.2602i	−0.149990	−	0.475340i
$901$	24.4389	−	42.3295i	0.814179	−	1.41020i
$902$	6.95143	+	5.87839i	0.231457	+	0.195729i
$903$	12.5078	−	17.8630i	0.416233	−	0.594443i
$904$	36.0763	+	36.9138i	1.19988	+	1.22773i
$905$	−2.88912	−	5.21738i	−0.0960377	−	0.173432i
$906$	−9.32255	+	6.47473i	−0.309721	+	0.215108i
$907$	13.8128	−	29.6217i	0.458647	−	0.983572i	−0.531952	−	0.846774i	$-0.678541\pi$
$907$	13.8128	−	29.6217i	0.458647	−	0.983572i	0.990599	−	0.136797i	$-0.0436809\pi$
$908$	−3.76711	−	14.5019i	−0.125016	−	0.481261i
$909$	9.84729	−	11.7355i	0.326614	−	0.389243i
$910$	−1.40374	−	2.55801i	−0.0465335	−	0.0847971i
$911$			33.0850i			1.09615i	0.836428	+	0.548077i	$0.184640\pi$
$911$			33.0850i			1.09615i	−0.836428	+	0.548077i	$0.815360\pi$
$912$	−3.14724	+	21.1546i	−0.104215	+	0.700497i
$913$	42.3471	−	42.3471i	1.40148	−	1.40148i
$914$	−24.0461	−	6.54180i	−0.795374	−	0.216384i
$915$	1.84296	+	26.5186i	0.0609264	+	0.876679i
$916$	−2.47467	−	1.45410i	−0.0817653	−	0.0480448i
$917$	20.3570	+	9.49261i	0.672246	+	0.313474i
$918$	29.2084	+	5.26548i	0.964020	+	0.173787i
$919$	20.6827	+	35.8236i	0.682261	+	1.18171i	0.974289	+	0.225301i	$0.0723364\pi$
$919$	20.6827	+	35.8236i	0.682261	+	1.18171i	−0.292029	+	0.956410i	$0.594330\pi$
$920$	32.5358	−	30.6796i	1.07267	−	1.01148i
$921$	−6.26082	−	35.5069i	−0.206301	−	1.16999i
$922$	21.6126	−	25.5577i	0.711773	−	0.841699i
$923$	−4.73080	+	1.26761i	−0.155716	+	0.0417240i
$924$	7.93150	+	22.3214i	0.260927	+	0.734320i
$925$	5.61670	+	0.694524i	0.184676	+	0.0228358i
$926$	3.26962	+	12.3918i	0.107446	+	0.407219i
$927$	−13.7298	+	6.40232i	−0.450947	+	0.210280i
$928$	30.9552	+	11.9419i	1.01615	+	0.392012i
$929$	−1.95873	−	0.345376i	−0.0642637	−	0.0113314i	0.141424	−	0.989949i	$-0.454832\pi$
$929$	−1.95873	−	0.345376i	−0.0642637	−	0.0113314i	−0.205688	+	0.978618i	$0.565943\pi$
$930$	27.7678	+	3.03795i	0.910542	+	0.0996183i
$931$	17.5533	−	5.50574i	0.575286	−	0.180443i
$932$	−13.9324	−	20.2250i	−0.456371	−	0.662493i
$933$	−6.77692	−	9.67845i	−0.221866	−	0.316858i
$934$	39.1296	+	39.4300i	1.28036	+	1.29019i
$935$	−45.0355	+	20.0280i	−1.47282	+	0.654986i
$936$	2.33405	−	0.177244i	0.0762907	−	0.00579339i
$937$	2.55819	+	0.223813i	0.0835724	+	0.00731164i	0.128865	−	0.991662i	$-0.458867\pi$
$937$	2.55819	+	0.223813i	0.0835724	+	0.00731164i	−0.0452928	+	0.998974i	$0.514422\pi$
$938$	9.23974	+	3.40306i	0.301688	+	0.111114i
$939$	−8.48815	+	14.7019i	−0.277000	+	0.479778i
$940$	0.743371	−	0.706352i	0.0242461	−	0.0230387i
$941$	7.08397	+	40.1752i	0.230931	+	1.30967i	0.851016	+	0.525139i	$0.175987\pi$
$941$	7.08397	+	40.1752i	0.230931	+	1.30967i	−0.620086	+	0.784534i	$0.712902\pi$
$942$	−3.37180	−	19.5596i	−0.109859	−	0.637285i
$943$	2.03406	−	7.59121i	0.0662380	−	0.247204i
$944$	2.25485	−	0.781847i	0.0733891	−	0.0254470i
$945$	−6.68431	−	19.4397i	−0.217441	−	0.632372i
$946$	−79.0125	−	37.2127i	−2.56892	−	1.20989i
$947$	−14.0724	+	1.23117i	−0.457290	+	0.0400077i	−0.313474	−	0.949597i	$-0.601493\pi$
$947$	−14.0724	+	1.23117i	−0.457290	+	0.0400077i	−0.143816	+	0.989604i	$0.545937\pi$
$948$	−3.34484	−	7.31867i	−0.108635	−	0.237699i
$949$			0.688377i			0.0223457i
$950$	13.0973	+	27.9009i	0.424931	+	0.905226i
$951$		−	9.09402i		−	0.294894i
$952$	−5.94428	−	16.9338i	−0.192655	−	0.548828i
$953$	−23.1214	+	2.02286i	−0.748976	+	0.0655269i	−0.455251	−	0.890363i	$-0.650450\pi$
$953$	−23.1214	+	2.02286i	−0.748976	+	0.0655269i	−0.293725	+	0.955890i	$0.594895\pi$
$954$	11.5718	−	24.5701i	0.374652	−	0.795486i
$955$	14.0724	+	40.9261i	0.455372	+	1.32434i
$956$	15.1520	+	26.7138i	0.490050	+	0.863987i
$957$	10.7846	−	40.2488i	0.348618	−	1.30106i
$958$	36.4603	−	6.28526i	1.17798	−	0.203067i
$959$	−1.12956	−	6.40606i	−0.0364754	−	0.206862i
$960$	8.45405	+	20.2490i	0.272853	+	0.653535i
$961$	10.4286	−	18.0628i	0.336405	−	0.582671i
$962$	−0.306186	+	0.831334i	−0.00987185	+	0.0268033i
$963$	−9.23523	−	0.807978i	−0.297601	−	0.0260367i
$964$	−8.53390	−	50.6611i	−0.274858	−	1.63168i
$965$	2.84576	−	1.26556i	0.0916083	−	0.0407397i
$966$	14.5154	−	14.4048i	0.467025	−	0.463466i
$967$	21.7674	+	31.0871i	0.699994	+	0.999694i	0.998967	+	0.0454331i	$0.0144668\pi$
$967$	21.7674	+	31.0871i	0.699994	+	0.999694i	−0.298974	+	0.954261i	$0.596644\pi$
$968$	55.5816	−	31.2453i	1.78646	−	1.00426i
$969$	−20.3287	−	0.917973i	−0.653053	−	0.0294896i
$970$	−1.98972	+	18.1867i	−0.0638862	+	0.583939i
$971$	−53.5152	−	9.43618i	−1.71738	−	0.302821i	−0.773672	−	0.633586i	$-0.781582\pi$
$971$	−53.5152	−	9.43618i	−1.71738	−	0.302821i	−0.943713	+	0.330765i	$0.892693\pi$
$972$	27.3728	+	2.60593i	0.877982	+	0.0835853i
$973$	−34.2163	+	15.9553i	−1.09693	+	0.511505i
$974$	17.0358	−	4.49496i	0.545861	−	0.144028i
$975$	−2.67664	+	2.08753i	−0.0857210	+	0.0668545i
$976$	6.14686	+	38.2756i	0.196756	+	1.22517i
$977$	−4.35739	+	1.16756i	−0.139405	+	0.0373535i	−0.327847	−	0.944731i	$-0.606323\pi$
$977$	−4.35739	+	1.16756i	−0.139405	+	0.0373535i	0.188442	+	0.982084i	$0.439656\pi$
$978$	8.07296	+	6.82680i	0.258145	+	0.218297i
$979$	−5.00357	−	28.3766i	−0.159915	−	0.906921i
$980$	12.4974	−	14.1442i	0.399214	−	0.451821i
$981$	11.0894	+	19.2075i	0.354059	+	0.613248i
$982$	4.26662	−	23.6675i	0.136153	−	0.755261i
$983$	4.43089	+	2.06616i	0.141324	+	0.0659002i	0.491994	−	0.870599i	$-0.336268\pi$
$983$	4.43089	+	2.06616i	0.141324	+	0.0659002i	−0.350670	+	0.936499i	$0.614046\pi$
$984$	3.13329	+	2.24796i	0.0998855	+	0.0716624i
$985$	1.06157	+	15.2751i	0.0338245	+	0.486705i
$986$	−8.28712	+	30.4615i	−0.263916	+	0.970091i
$987$	0.331581	−	0.331581i	0.0105543	−	0.0105543i
$988$	−4.71983	+	1.00118i	−0.150158	+	0.0318519i
$989$			75.3957i			2.39744i
$990$	−24.0092	+	13.1753i	−0.763061	+	0.418740i
$991$	37.5378	−	44.7358i	1.19243	−	1.42108i	0.309933	−	0.950758i	$-0.399693\pi$
$991$	37.5378	−	44.7358i	1.19243	−	1.42108i	0.882495	−	0.470322i	$-0.155862\pi$
$992$	40.7286	+	0.778929i	1.29314	+	0.0247310i
$993$	−10.5287	+	22.5789i	−0.334119	+	0.716520i
$994$	11.9022	+	17.1372i	0.377514	+	0.543559i
$995$	−0.764563	−	1.38070i	−0.0242383	−	0.0437712i
$996$	16.4544	−	19.3078i	0.521379	−	0.611790i
$997$	10.5991	−	15.1371i	0.335676	−	0.479395i	−0.615460	−	0.788169i	$-0.711030\pi$
$997$	10.5991	−	15.1371i	0.335676	−	0.479395i	0.951136	+	0.308773i	$0.0999184\pi$
$998$	27.7527	−	32.8187i	0.878497	−	1.03886i
$999$	−3.12075	+	5.40529i	−0.0987361	+	0.171016i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bj.a.207.48	yes	672
4.3	odd	2	inner	380.2.bj.a.207.44	yes	672
5.3	odd	4	inner	380.2.bj.a.283.19	yes	672
19.9	even	9	inner	380.2.bj.a.47.15	✓	672
20.3	even	4	inner	380.2.bj.a.283.15	yes	672
76.47	odd	18	inner	380.2.bj.a.47.19	yes	672
95.28	odd	36	inner	380.2.bj.a.123.44	yes	672
380.123	even	36	inner	380.2.bj.a.123.48	yes	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bj.a.47.15	✓	672	19.9	even	9	inner
380.2.bj.a.47.19	yes	672	76.47	odd	18	inner
380.2.bj.a.123.44	yes	672	95.28	odd	36	inner
380.2.bj.a.123.48	yes	672	380.123	even	36	inner
380.2.bj.a.207.44	yes	672	4.3	odd	2	inner
380.2.bj.a.207.48	yes	672	1.1	even	1	trivial
380.2.bj.a.283.15	yes	672	20.3	even	4	inner
380.2.bj.a.283.19	yes	672	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bj (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22744 - 0.702418i) q^{2} +(0.106910 + 1.22198i) q^{3} +(1.01322 - 1.72435i) q^{4} +(-2.11456 + 0.727088i) q^{5} +(0.989567 + 1.42482i) q^{6} +(1.61039 + 0.431503i) q^{7} +(0.0324513 - 2.82824i) q^{8} +(1.47261 - 0.259661i) q^{9} +O(q^{10})\)	\(q+(1.22744 - 0.702418i) q^{2} +(0.106910 + 1.22198i) q^{3} +(1.01322 - 1.72435i) q^{4} +(-2.11456 + 0.727088i) q^{5} +(0.989567 + 1.42482i) q^{6} +(1.61039 + 0.431503i) q^{7} +(0.0324513 - 2.82824i) q^{8} +(1.47261 - 0.259661i) q^{9} +(-2.08477 + 2.37776i) q^{10} +(5.01572 + 2.89583i) q^{11} +(2.21545 + 1.05379i) q^{12} +(-0.0482361 + 0.551342i) q^{13} +(2.27975 - 0.601523i) q^{14} +(-1.11456 - 2.50622i) q^{15} +(-1.94677 - 3.49429i) q^{16} +(3.11759 - 2.18296i) q^{17} +(1.62515 - 1.35311i) q^{18} +(-2.94962 + 3.20932i) q^{19} +(-0.888753 + 4.38293i) q^{20} +(-0.355123 + 2.01400i) q^{21} +(8.19057 + 0.0313250i) q^{22} +(-2.98823 - 6.40828i) q^{23} +(3.45953 - 0.262711i) q^{24} +(3.94269 - 3.07493i) q^{25} +(0.328065 + 0.710621i) q^{26} +(1.42718 + 5.32631i) q^{27} +(2.37574 - 2.33967i) q^{28} +(-5.77613 + 1.01849i) q^{29} +(-3.12846 - 2.29335i) q^{30} +(-6.23641 + 3.60059i) q^{31} +(-4.84400 - 2.92159i) q^{32} +(-3.00242 + 6.43871i) q^{33} +(2.29331 - 4.86931i) q^{34} +(-3.71900 + 0.258459i) q^{35} +(1.04433 - 2.80239i) q^{36} +(0.800371 + 0.800371i) q^{37} +(-1.36620 + 6.01111i) q^{38} -0.678887 q^{39} +(1.98776 + 6.00407i) q^{40} +(0.851443 + 0.714445i) q^{41} +(0.978778 + 2.72151i) q^{42} +(-9.66399 - 4.50639i) q^{43} +(10.0754 - 5.71475i) q^{44} +(-2.92512 + 1.61978i) q^{45} +(-8.16916 - 5.76679i) q^{46} +(-0.187828 - 0.131519i) q^{47} +(4.06183 - 2.75250i) q^{48} +(-3.65501 - 2.11022i) q^{49} +(2.67952 - 6.54371i) q^{50} +(3.00084 + 3.57626i) q^{51} +(0.901833 + 0.641806i) q^{52} +(11.6395 - 5.42758i) q^{53} +(5.49307 + 5.53525i) q^{54} +(-12.7115 - 2.47652i) q^{55} +(1.27265 - 4.54057i) q^{56} +(-4.23708 - 3.26128i) q^{57} +(-6.37445 + 5.30739i) q^{58} +(-0.103605 + 0.587574i) q^{59} +(-5.45089 - 0.617463i) q^{60} +(-9.10704 - 3.31469i) q^{61} +(-5.12570 + 8.80008i) q^{62} +(2.48352 + 0.217280i) q^{63} +(-7.99789 - 0.183560i) q^{64} +(-0.298876 - 1.20091i) q^{65} +(0.837373 + 10.0121i) q^{66} +(3.42093 + 2.39536i) q^{67} +(-0.605389 - 7.58764i) q^{68} +(7.51133 - 4.33667i) q^{69} +(-4.38330 + 2.92953i) q^{70} +(3.02668 + 8.31573i) q^{71} +(-0.686596 - 4.17332i) q^{72} +(1.23907 - 0.108404i) q^{73} +(1.54460 + 0.420213i) q^{74} +(4.17903 + 4.48916i) q^{75} +(2.54538 + 8.33793i) q^{76} +(6.82771 + 6.82771i) q^{77} +(-0.833293 + 0.476862i) q^{78} +(-2.51261 - 2.10833i) q^{79} +(6.65722 + 5.97340i) q^{80} +(-2.14063 + 0.779125i) q^{81} +(1.54693 + 0.278871i) q^{82} +(2.67629 - 9.98803i) q^{83} +(3.11303 + 2.65298i) q^{84} +(-5.00512 + 6.88276i) q^{85} +(-15.0273 + 1.25683i) q^{86} +(-1.86210 - 6.94945i) q^{87} +(8.35286 - 14.0917i) q^{88} +(-3.19797 - 3.81119i) q^{89} +(-2.45265 + 4.04285i) q^{90} +(-0.315584 + 0.867061i) q^{91} +(-14.0778 - 1.34023i) q^{92} +(-5.06660 - 7.23585i) q^{93} +(-0.322929 - 0.0294976i) q^{94} +(3.90368 - 8.93092i) q^{95} +(3.05226 - 6.23163i) q^{96} +(4.73916 - 3.31840i) q^{97} +(-5.96857 - 0.0228269i) q^{98} +(8.13814 + 2.96204i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8}+O(q^{10}) \) 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8	\( 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8} - 12 q^{10} - 6 q^{12} - 24 q^{13} - 36 q^{16} - 24 q^{17} - 24 q^{18} + 36 q^{20} - 48 q^{21} - 24 q^{22} - 24 q^{25} - 60 q^{26} - 24 q^{28} - 6 q^{30} + 18 q^{32} - 60 q^{33} + 24 q^{36} - 48 q^{37} - 114 q^{38} - 42 q^{40} - 24 q^{41} - 48 q^{42} - 12 q^{45} - 12 q^{46} - 96 q^{48} - 6 q^{50} - 12 q^{52} - 24 q^{53} - 48 q^{56} - 24 q^{57} + 120 q^{58} - 12 q^{60} - 48 q^{61} + 36 q^{62} - 12 q^{65} - 96 q^{66} - 6 q^{68} - 12 q^{70} + 120 q^{72} - 24 q^{73} - 96 q^{76} - 360 q^{77} - 126 q^{78} + 48 q^{80} - 48 q^{81} + 228 q^{82} - 24 q^{85} - 132 q^{86} - 102 q^{88} + 78 q^{90} + 108 q^{92} - 60 q^{93} - 144 q^{96} - 24 q^{97} + 18 q^{98}+O(q^{100}) \) 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8 - 12 * q^10 - 6 * q^12 - 24 * q^13 - 36 * q^16 - 24 * q^17 - 24 * q^18 + 36 * q^20 - 48 * q^21 - 24 * q^22 - 24 * q^25 - 60 * q^26 - 24 * q^28 - 6 * q^30 + 18 * q^32 - 60 * q^33 + 24 * q^36 - 48 * q^37 - 114 * q^38 - 42 * q^40 - 24 * q^41 - 48 * q^42 - 12 * q^45 - 12 * q^46 - 96 * q^48 - 6 * q^50 - 12 * q^52 - 24 * q^53 - 48 * q^56 - 24 * q^57 + 120 * q^58 - 12 * q^60 - 48 * q^61 + 36 * q^62 - 12 * q^65 - 96 * q^66 - 6 * q^68 - 12 * q^70 + 120 * q^72 - 24 * q^73 - 96 * q^76 - 360 * q^77 - 126 * q^78 + 48 * q^80 - 48 * q^81 + 228 * q^82 - 24 * q^85 - 132 * q^86 - 102 * q^88 + 78 * q^90 + 108 * q^92 - 60 * q^93 - 144 * q^96 - 24 * q^97 + 18 * q^98

Introduction

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