LMFDB - Embedded newform 189.2.ba.a.5.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(5,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5, 15]))

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

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

chi := DirichletCharacter("189.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.ba (of order $18$, degree $6$, 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			5.18
Character	$\chi$	$=$	189.5
Dual form			189.2.ba.a.38.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.77439 - 0.312873i) q^{2} +(0.626754 - 1.61468i) q^{3} +(1.17119 - 0.426279i) q^{4} +(-0.155940 + 0.884381i) q^{5} +(0.606919 - 3.06116i) q^{6} +(2.64257 - 0.129722i) q^{7} +(-1.17597 + 0.678945i) q^{8} +(-2.21436 - 2.02401i) q^{9} +O(q^{10})$	\(q+(1.77439 - 0.312873i) q^{2} +(0.626754 - 1.61468i) q^{3} +(1.17119 - 0.426279i) q^{4} +(-0.155940 + 0.884381i) q^{5} +(0.606919 - 3.06116i) q^{6} +(2.64257 - 0.129722i) q^{7} +(-1.17597 + 0.678945i) q^{8} +(-2.21436 - 2.02401i) q^{9} +1.61803i q^{10} +(-3.83262 + 0.675794i) q^{11} +(0.0457470 - 2.15827i) q^{12} +(-1.72738 + 2.05861i) q^{13} +(4.64837 - 1.05697i) q^{14} +(1.33025 + 0.806082i) q^{15} +(-3.78373 + 3.17493i) q^{16} +7.46010 q^{17} +(-4.56240 - 2.89857i) q^{18} -4.84873i q^{19} +(0.194357 + 1.10225i) q^{20} +(1.44678 - 4.34820i) q^{21} +(-6.58912 + 2.39825i) q^{22} +(-5.01423 + 5.97573i) q^{23} +(0.359234 + 2.32434i) q^{24} +(3.94065 + 1.43428i) q^{25} +(-2.42097 + 4.19324i) q^{26} +(-4.65598 + 2.30691i) q^{27} +(3.03966 - 1.27840i) q^{28} +(-3.24899 - 3.87199i) q^{29} +(2.61259 + 1.01411i) q^{30} +(0.0550233 + 0.151175i) q^{31} +(-3.97480 + 4.73698i) q^{32} +(-1.31092 + 6.61199i) q^{33} +(13.2371 - 2.33407i) q^{34} +(-0.297359 + 2.35727i) q^{35} +(-3.45623 - 1.42657i) q^{36} +(-2.45256 - 4.24796i) q^{37} +(-1.51704 - 8.60355i) q^{38} +(2.24135 + 4.07940i) q^{39} +(-0.417065 - 1.14588i) q^{40} +(2.78205 + 2.33441i) q^{41} +(1.20672 - 8.16806i) q^{42} +(5.36266 + 1.95185i) q^{43} +(-4.20065 + 2.42525i) q^{44} +(2.13530 - 1.64271i) q^{45} +(-7.02757 + 12.1721i) q^{46} +(-3.75035 - 1.36502i) q^{47} +(2.75501 + 8.09940i) q^{48} +(6.96634 - 0.685599i) q^{49} +(7.44101 + 1.31205i) q^{50} +(4.67565 - 12.0457i) q^{51} +(-1.14555 + 3.14737i) q^{52} +(-2.73831 + 1.58096i) q^{53} +(-7.53976 + 5.55010i) q^{54} -3.49487i q^{55} +(-3.01950 + 1.94671i) q^{56} +(-7.82913 - 3.03896i) q^{57} +(-6.97641 - 5.85391i) q^{58} +(-4.24780 - 3.56433i) q^{59} +(1.90160 + 0.377018i) q^{60} +(2.92051 - 8.02404i) q^{61} +(0.144931 + 0.251029i) q^{62} +(-6.11415 - 5.06134i) q^{63} +(-0.631470 + 1.09374i) q^{64} +(-1.55123 - 1.84868i) q^{65} +(-0.257373 + 12.1424i) q^{66} +(1.25577 - 7.12184i) q^{67} +(8.73721 - 3.18008i) q^{68} +(6.50618 + 11.8417i) q^{69} +(0.209894 + 4.27575i) q^{70} +(-4.65524 - 2.68770i) q^{71} +(3.97820 + 0.876742i) q^{72} +(7.96064 + 4.59608i) q^{73} +(-5.68088 - 6.77020i) q^{74} +(4.78572 - 5.46393i) q^{75} +(-2.06691 - 5.67879i) q^{76} +(-10.0403 + 2.28301i) q^{77} +(5.25337 + 6.53720i) q^{78} +(-2.02358 - 11.4763i) q^{79} +(-2.21781 - 3.84136i) q^{80} +(0.806764 + 8.96377i) q^{81} +(5.66681 + 3.27174i) q^{82} +(7.47526 - 6.27249i) q^{83} +(-0.159085 - 5.70930i) q^{84} +(-1.16333 + 6.59757i) q^{85} +(10.1261 + 1.78551i) q^{86} +(-8.28833 + 2.81927i) q^{87} +(4.04820 - 3.39685i) q^{88} -7.39610 q^{89} +(3.27490 - 3.58289i) q^{90} +(-4.29768 + 5.66410i) q^{91} +(-3.32530 + 9.13618i) q^{92} +(0.278585 + 0.00590493i) q^{93} +(-7.08167 - 1.24869i) q^{94} +(4.28812 + 0.756112i) q^{95} +(5.15747 + 9.38694i) q^{96} +(-0.434182 + 1.19291i) q^{97} +(12.1465 - 3.39610i) q^{98} +(9.85460 + 6.26080i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22} - 6 q^{23} - 9 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} + 51 q^{30} - 9 q^{31} + 3 q^{32} - 9 q^{33} - 18 q^{34} + 18 q^{35} + 3 q^{37} - 99 q^{38} - 36 q^{39} - 54 q^{40} - 45 q^{42} - 12 q^{43} - 9 q^{44} - 9 q^{45} + 3 q^{46} + 45 q^{47} - 24 q^{49} - 9 q^{50} - 48 q^{51} - 9 q^{52} - 45 q^{53} + 171 q^{54} + 3 q^{56} - 3 q^{58} + 36 q^{59} + 57 q^{60} - 9 q^{61} - 99 q^{62} - 33 q^{63} + 18 q^{64} + 69 q^{65} - 9 q^{66} - 3 q^{67} + 36 q^{68} + 108 q^{69} + 66 q^{70} + 18 q^{71} - 129 q^{72} - 9 q^{73} + 75 q^{74} + 36 q^{75} + 36 q^{76} + 15 q^{77} + 66 q^{78} - 21 q^{79} + 72 q^{80} - 33 q^{81} - 18 q^{82} - 90 q^{83} - 120 q^{84} + 9 q^{85} - 105 q^{86} - 54 q^{87} - 63 q^{88} - 18 q^{89} + 81 q^{90} + 6 q^{91} + 150 q^{92} + 21 q^{93} - 9 q^{94} + 45 q^{95} - 81 q^{96} + 27 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	1.77439	−	0.312873i	1.25468	−	0.221235i	0.493486	−	0.869754i	$-0.335722\pi$
$2$	1.77439	−	0.312873i	1.25468	−	0.221235i	0.761198	+	0.648519i	$0.224611\pi$
$3$	0.626754	−	1.61468i	0.361857	−	0.932234i
$3$	0.626754	−	1.61468i	0.361857	−	0.932234i
$4$	1.17119	−	0.426279i	0.585596	−	0.213139i
$5$	−0.155940	+	0.884381i	−0.0697386	+	0.395507i	0.929879	+	0.367865i	$0.119911\pi$
$5$	−0.155940	+	0.884381i	−0.0697386	+	0.395507i	−0.999618	+	0.0276423i	$0.991200\pi$
$6$	0.606919	−	3.06116i	0.247774	−	1.24971i
$7$	2.64257	−	0.129722i	0.998797	−	0.0490304i
$7$	2.64257	−	0.129722i	0.998797	−	0.0490304i
$8$	−1.17597	+	0.678945i	−0.415767	+	0.240043i
$9$	−2.21436	−	2.02401i	−0.738119	−	0.674670i
$10$			1.61803i			0.511665i
$11$	−3.83262	+	0.675794i	−1.15558	+	0.203759i	−0.718409	−	0.695621i	$-0.755130\pi$
$11$	−3.83262	+	0.675794i	−1.15558	+	0.203759i	−0.437168	+	0.899380i	$0.644018\pi$
$12$	0.0457470	−	2.15827i	0.0132060	−	0.623038i
$13$	−1.72738	+	2.05861i	−0.479089	+	0.570956i	−0.950408	−	0.311007i	$-0.899334\pi$
$13$	−1.72738	+	2.05861i	−0.479089	+	0.570956i	0.471318	+	0.881963i	$0.343778\pi$
$14$	4.64837	−	1.05697i	1.24233	−	0.282486i
$15$	1.33025	+	0.806082i	0.343470	+	0.208130i
$16$	−3.78373	+	3.17493i	−0.945933	+	0.793732i
$17$	7.46010			1.80934			0.904670	−	0.426112i	$-0.140117\pi$
$17$	7.46010			1.80934			0.904670	+	0.426112i	$0.140117\pi$
$18$	−4.56240	−	2.89857i	−1.07537	−	0.683200i
$19$		−	4.84873i		−	1.11238i	−0.831057	−	0.556188i	$-0.812264\pi$
$19$		−	4.84873i		−	1.11238i	0.831057	−	0.556188i	$-0.187736\pi$
$20$	0.194357	+	1.10225i	0.0434595	+	0.246471i
$21$	1.44678	−	4.34820i	0.315714	−	0.948854i
$22$	−6.58912	+	2.39825i	−1.40481	+	0.511308i
$23$	−5.01423	+	5.97573i	−1.04554	+	1.24603i	−0.0770353	+	0.997028i	$0.524545\pi$
$23$	−5.01423	+	5.97573i	−1.04554	+	1.24603i	−0.968504	+	0.248997i	$0.919899\pi$
$24$	0.359234	+	2.32434i	0.0733283	+	0.474453i
$25$	3.94065	+	1.43428i	0.788130	+	0.286856i
$26$	−2.42097	+	4.19324i	−0.474790	+	0.822361i
$27$	−4.65598	+	2.30691i	−0.896044	+	0.443966i
$28$	3.03966	−	1.27840i	0.574441	−	0.241595i
$29$	−3.24899	−	3.87199i	−0.603321	−	0.719010i	0.374786	−	0.927111i	$-0.377716\pi$
$29$	−3.24899	−	3.87199i	−0.603321	−	0.719010i	−0.978107	+	0.208101i	$0.933272\pi$
$30$	2.61259	+	1.01411i	0.476992	+	0.185149i
$31$	0.0550233	+	0.151175i	0.00988247	+	0.0271519i	0.944536	−	0.328409i	$-0.106512\pi$
$31$	0.0550233	+	0.151175i	0.00988247	+	0.0271519i	−0.934653	+	0.355560i	$0.884290\pi$
$32$	−3.97480	+	4.73698i	−0.702652	+	0.837388i
$33$	−1.31092	+	6.61199i	−0.228202	+	1.15100i
$34$	13.2371	−	2.33407i	2.27015	−	0.400289i
$35$	−0.297359	+	2.35727i	−0.0502628	+	0.398451i
$36$	−3.45623	−	1.42657i	−0.576038	−	0.237762i
$37$	−2.45256	−	4.24796i	−0.403198	−	0.698360i	0.590911	−	0.806736i	$-0.298768\pi$
$37$	−2.45256	−	4.24796i	−0.403198	−	0.698360i	−0.994110	+	0.108376i	$0.965435\pi$
$38$	−1.51704	−	8.60355i	−0.246096	−	1.39568i
$39$	2.24135	+	4.07940i	0.358903	+	0.653228i
$40$	−0.417065	−	1.14588i	−0.0659438	−	0.181179i
$41$	2.78205	+	2.33441i	0.434483	+	0.364574i	0.833640	−	0.552308i	$-0.186253\pi$
$41$	2.78205	+	2.33441i	0.434483	+	0.364574i	−0.399157	+	0.916882i	$0.630697\pi$
$42$	1.20672	−	8.16806i	0.186202	−	1.26036i
$43$	5.36266	+	1.95185i	0.817797	+	0.297654i	0.716841	−	0.697237i	$-0.245587\pi$
$43$	5.36266	+	1.95185i	0.817797	+	0.297654i	0.100957	+	0.994891i	$0.467810\pi$
$44$	−4.20065	+	2.42525i	−0.633272	+	0.365620i
$45$	2.13530	−	1.64271i	0.318312	−	0.244881i
$46$	−7.02757	+	12.1721i	−1.03616	+	1.79468i
$47$	−3.75035	−	1.36502i	−0.547045	−	0.199108i	0.0536879	−	0.998558i	$-0.482902\pi$
$47$	−3.75035	−	1.36502i	−0.547045	−	0.199108i	−0.600733	+	0.799450i	$0.705125\pi$
$48$	2.75501	+	8.09940i	0.397651	+	1.16905i
$49$	6.96634	−	0.685599i	0.995192	−	0.0979428i
$50$	7.44101	+	1.31205i	1.05232	+	0.185552i
$51$	4.67565	−	12.0457i	0.654722	−	1.68673i
$52$	−1.14555	+	3.14737i	−0.158859	+	0.436462i
$53$	−2.73831	+	1.58096i	−0.376136	+	0.217162i	−0.676136	−	0.736777i	$-0.736347\pi$
$53$	−2.73831	+	1.58096i	−0.376136	+	0.217162i	0.300000	+	0.953939i	$0.403013\pi$
$54$	−7.53976	+	5.55010i	−1.02603	+	0.755273i
$55$		−	3.49487i		−	0.471249i
$56$	−3.01950	+	1.94671i	−0.403498	+	0.260140i
$57$	−7.82913	−	3.03896i	−1.03699	−	0.402520i
$58$	−6.97641	−	5.85391i	−0.916048	−	0.768656i
$59$	−4.24780	−	3.56433i	−0.553016	−	0.464036i	0.322945	−	0.946418i	$-0.395327\pi$
$59$	−4.24780	−	3.56433i	−0.553016	−	0.464036i	−0.875961	+	0.482382i	$0.839772\pi$
$60$	1.90160	+	0.377018i	0.245495	+	0.0486728i
$61$	2.92051	−	8.02404i	0.373933	−	1.02737i	−0.599893	−	0.800080i	$-0.704790\pi$
$61$	2.92051	−	8.02404i	0.373933	−	1.02737i	0.973826	−	0.227293i	$-0.0729876\pi$
$62$	0.144931	+	0.251029i	0.0184063	+	0.0318807i
$63$	−6.11415	−	5.06134i	−0.770311	−	0.637668i
$64$	−0.631470	+	1.09374i	−0.0789338	+	0.136717i
$65$	−1.55123	−	1.84868i	−0.192406	−	0.229301i
$66$	−0.257373	+	12.1424i	−0.0316804	+	1.49463i
$67$	1.25577	−	7.12184i	0.153417	−	0.870072i	−0.806802	−	0.590822i	$-0.798803\pi$
$67$	1.25577	−	7.12184i	0.153417	−	0.870072i	0.960219	−	0.279249i	$-0.0900855\pi$
$68$	8.73721	−	3.18008i	1.05954	−	0.385642i
$69$	6.50618	+	11.8417i	0.783251	+	1.42557i
$70$	0.209894	+	4.27575i	0.0250871	+	0.511050i
$71$	−4.65524	−	2.68770i	−0.552475	−	0.318972i	0.197644	−	0.980274i	$-0.436671\pi$
$71$	−4.65524	−	2.68770i	−0.552475	−	0.318972i	−0.750120	+	0.661302i	$0.770004\pi$
$72$	3.97820	+	0.876742i	0.468836	+	0.103325i
$73$	7.96064	+	4.59608i	0.931722	+	0.537930i	0.887356	−	0.461085i	$-0.152540\pi$
$73$	7.96064	+	4.59608i	0.931722	+	0.537930i	0.0443665	+	0.999015i	$0.485873\pi$
$74$	−5.68088	−	6.77020i	−0.660388	−	0.787020i
$75$	4.78572	−	5.46393i	0.552607	−	0.630921i
$76$	−2.06691	−	5.67879i	−0.237091	−	0.651402i
$77$	−10.0403	+	2.28301i	−1.14420	+	0.260173i
$78$	5.25337	+	6.53720i	0.594827	+	0.740193i
$79$	−2.02358	−	11.4763i	−0.227670	−	1.29118i	−0.857514	−	0.514461i	$-0.827992\pi$
$79$	−2.02358	−	11.4763i	−0.227670	−	1.29118i	0.629844	−	0.776722i	$-0.283119\pi$
$80$	−2.21781	−	3.84136i	−0.247958	−	0.429477i
$81$	0.806764	+	8.96377i	0.0896405	+	0.995974i
$82$	5.66681	+	3.27174i	0.625795	+	0.361303i
$83$	7.47526	−	6.27249i	0.820517	−	0.688495i	−0.132576	−	0.991173i	$-0.542325\pi$
$83$	7.47526	−	6.27249i	0.820517	−	0.688495i	0.953093	+	0.302677i	$0.0978805\pi$
$84$	−0.159085	−	5.70930i	−0.0173576	−	0.622936i
$85$	−1.16333	+	6.59757i	−0.126181	+	0.715607i
$86$	10.1261	+	1.78551i	1.09193	+	0.192537i
$87$	−8.28833	+	2.81927i	−0.888602	+	0.302258i
$88$	4.04820	−	3.39685i	0.431540	−	0.362105i
$89$	−7.39610			−0.783985			−0.391993	−	0.919968i	$-0.628214\pi$
$89$	−7.39610			−0.783985			−0.391993	+	0.919968i	$0.628214\pi$
$90$	3.27490	−	3.58289i	0.345205	−	0.377670i
$91$	−4.29768	+	5.66410i	−0.450519	+	0.593760i
$92$	−3.32530	+	9.13618i	−0.346686	+	0.952513i
$93$	0.278585	+	0.00590493i	0.0288879	+	0.000612313i
$94$	−7.08167	−	1.24869i	−0.730419	−	0.128793i
$95$	4.28812	+	0.756112i	0.439952	+	0.0775755i
$96$	5.15747	+	9.38694i	0.526382	+	0.958051i
$97$	−0.434182	+	1.19291i	−0.0440845	+	0.121121i	−0.959781	−	0.280748i	$-0.909417\pi$
$97$	−0.434182	+	1.19291i	−0.0440845	+	0.121121i	0.915697	+	0.401870i	$0.131640\pi$
$98$	12.1465	−	3.39610i	1.22698	−	0.343058i
$99$	9.85460	+	6.26080i	0.990424	+	0.629235i
$100$	5.22666			0.522666
$101$	1.96044	−	1.64500i	0.195071	−	0.163684i	−0.540021	−	0.841652i	$-0.681584\pi$
$101$	1.96044	−	1.64500i	0.195071	−	0.163684i	0.735091	+	0.677968i	$0.237139\pi$
$102$	4.52768	−	22.8366i	0.448307	−	2.26116i
$103$	−10.3455	−	1.82420i	−1.01938	−	0.179744i	−0.361106	−	0.932525i	$-0.617601\pi$
$103$	−10.3455	−	1.82420i	−1.01938	−	0.179744i	−0.658271	+	0.752781i	$0.728712\pi$
$104$	0.633659	−	3.59366i	0.0621353	−	0.352387i
$105$	3.61985	+	1.95757i	0.353261	+	0.191039i
$106$	−4.36420	+	3.66199i	−0.423888	+	0.355684i
$107$	5.61020	+	3.23905i	0.542358	+	0.313131i	0.746034	−	0.665908i	$-0.231956\pi$
$107$	5.61020	+	3.23905i	0.542358	+	0.313131i	−0.203676	+	0.979038i	$0.565289\pi$
$108$	−4.46965	+	4.68658i	−0.430093	+	0.450967i
$109$	1.42567	+	2.46933i	0.136554	+	0.236519i	0.926190	−	0.377057i	$-0.123064\pi$
$109$	1.42567	+	2.46933i	0.136554	+	0.236519i	−0.789636	+	0.613576i	$0.789730\pi$
$110$	−1.09345	−	6.20128i	−0.104257	−	0.591269i
$111$	−8.39623	+	1.29766i	−0.796935	+	0.123169i
$112$	−9.58691	+	8.88080i	−0.905878	+	0.839156i
$113$	5.39586	+	14.8250i	0.507599	+	1.39462i	0.883706	+	0.468042i	$0.155040\pi$
$113$	5.39586	+	14.8250i	0.507599	+	1.39462i	−0.376107	+	0.926576i	$0.622737\pi$
$114$	−14.8428	−	2.94279i	−1.39015	−	0.275617i
$115$	−4.50290	−	5.36635i	−0.419897	−	0.500414i
$116$	−5.45573	−	3.14987i	−0.506552	−	0.292458i
$117$	7.99169	−	1.06227i	0.738832	−	0.0982067i
$118$	−8.65244	−	4.99549i	−0.796522	−	0.459872i
$119$	19.7138	−	0.967740i	1.80716	−	0.0887126i
$120$	−2.11162	−	0.0447582i	−0.192763	−	0.00408585i
$121$	3.89563	−	1.41789i	0.354148	−	0.128899i
$122$	2.67163	−	15.1515i	0.241878	−	1.37176i
$123$	5.51298	−	3.02900i	0.497089	−	0.273116i
$124$	0.128886	+	0.153600i	0.0115743	+	0.0137937i
$125$	−4.12801	+	7.14993i	−0.369221	+	0.639509i
$126$	−12.4325	−	7.06784i	−1.10757	−	0.629653i
$127$	−0.825343	−	1.42954i	−0.0732373	−	0.126851i	0.827081	−	0.562083i	$-0.190000\pi$
$127$	−0.825343	−	1.42954i	−0.0732373	−	0.126851i	−0.900318	+	0.435232i	$0.856666\pi$
$128$	3.45162	−	9.48325i	0.305083	−	0.838209i
$129$	6.51267	−	7.43562i	0.573408	−	0.654670i
$130$	−3.33089	−	2.79495i	−0.292138	−	0.245133i
$131$	−3.78722	−	3.17786i	−0.330891	−	0.277651i	0.462172	−	0.886790i	$-0.347070\pi$
$131$	−3.78722	−	3.17786i	−0.330891	−	0.277651i	−0.793063	+	0.609140i	$0.791515\pi$
$132$	1.28321	+	8.30272i	0.111689	+	0.722659i
$133$	−0.628988	−	12.8131i	−0.0545402	−	1.11104i
$134$		−	13.0298i		−	1.12561i
$135$	−1.31414	−	4.47740i	−0.113103	−	0.385353i
$136$	−8.77283	+	5.06500i	−0.752264	+	0.434320i
$137$	1.12888	−	3.10156i	0.0964464	−	0.264984i	−0.882082	−	0.471096i	$-0.843859\pi$
$137$	1.12888	−	3.10156i	0.0964464	−	0.264984i	0.978529	+	0.206111i	$0.0660809\pi$
$138$	15.2494	+	18.9762i	1.29812	+	1.61536i
$139$	14.5005	+	2.55683i	1.22992	+	0.216867i	0.750589	−	0.660769i	$-0.229770\pi$
$139$	14.5005	+	2.55683i	1.22992	+	0.216867i	0.479327	+	0.877637i	$0.340881\pi$
$140$	0.656588	+	2.88757i	0.0554918	+	0.244044i
$141$	−4.55461	+	5.20008i	−0.383567	+	0.437925i
$142$	−9.10113	−	3.31254i	−0.763750	−	0.277982i
$143$	5.22919	−	9.05722i	0.437287	−	0.757403i
$144$	14.8046	+	0.627884i	1.23372	+	0.0523237i
$145$	3.93096	−	2.26954i	0.326448	−	0.188475i
$146$	15.5633	+	5.66457i	1.28803	+	0.468803i
$147$	3.25917	−	11.6781i	0.268811	−	0.963193i
$148$	−4.68323	−	3.92970i	−0.384959	−	0.323019i
$149$	4.90321	+	13.4714i	0.401686	+	1.10362i	0.961452	+	0.274973i	$0.0886690\pi$
$149$	4.90321	+	13.4714i	0.401686	+	1.10362i	−0.559766	+	0.828651i	$0.689109\pi$
$150$	6.78222	−	11.1925i	0.553766	−	0.913862i
$151$	3.72945	+	21.1508i	0.303498	+	1.72122i	0.630490	+	0.776197i	$0.282854\pi$
$151$	3.72945	+	21.1508i	0.303498	+	1.72122i	−0.326992	+	0.945027i	$0.606035\pi$
$152$	3.29202	+	5.70195i	0.267018	+	0.462489i
$153$	−16.5193	−	15.0993i	−1.33551	−	1.22071i
$154$	−17.1011	+	7.19228i	−1.37805	+	0.579571i
$155$	−0.142277	+	0.0250872i	−0.0114279	+	0.00201505i
$156$	4.36401	+	3.82232i	0.349401	+	0.306031i
$157$	−7.04028	+	8.39028i	−0.561875	+	0.669617i	−0.969942	−	0.243335i	$-0.921759\pi$
$157$	−7.04028	+	8.39028i	−0.561875	+	0.669617i	0.408067	+	0.912952i	$0.366203\pi$
$158$	−7.18124	−	19.7303i	−0.571309	−	1.56966i
$159$	0.836498	+	5.41236i	0.0663386	+	0.429228i
$160$	−3.56947	−	4.25392i	−0.282191	−	0.336302i
$161$	−12.4753	+	16.4417i	−0.983189	+	1.29579i
$162$	4.23604	+	15.6528i	0.332815	+	1.22980i
$163$	−6.53530	+	11.3195i	−0.511884	+	0.886609i	0.488021	+	0.872832i	$0.337719\pi$
$163$	−6.53530	+	11.3195i	−0.511884	+	0.886609i	−0.999905	+	0.0137775i	$0.995614\pi$
$164$	4.25342	+	1.54812i	0.332136	+	0.120888i
$165$	−5.64309	−	2.19043i	−0.439314	−	0.170525i
$166$	11.3016	−	13.4687i	0.877171	−	1.04537i
$167$	11.4933	−	4.18321i	0.889377	−	0.323707i	0.143389	−	0.989666i	$-0.454200\pi$
$167$	11.4933	−	4.18321i	0.889377	−	0.323707i	0.745988	+	0.665960i	$0.231978\pi$
$168$	1.25082	+	6.09562i	0.0965027	+	0.470287i
$169$	1.00339	+	5.69049i	0.0771836	+	0.437730i
$170$			12.0707i			0.925777i
$171$	−9.81388	+	10.7368i	−0.750486	+	0.821066i
$172$	7.11273			0.542340
$173$	−7.61152	+	6.38682i	−0.578693	+	0.485581i	−0.884518	−	0.466507i	$-0.845512\pi$
$173$	−7.61152	+	6.38682i	−0.578693	+	0.485581i	0.305825	+	0.952088i	$0.401068\pi$
$174$	−13.8247	+	7.59569i	−1.04804	+	0.575828i
$175$	10.5995	+	3.27899i	0.801247	+	0.247869i
$176$	12.3560	−	14.7253i	0.931368	−	1.10996i
$177$	−8.41756	+	4.62486i	−0.632702	+	0.347626i
$178$	−13.1236	+	2.31404i	−0.983654	+	0.173445i
$179$		−	5.62434i		−	0.420383i	−0.977660	−	0.210191i	$-0.932591\pi$
$179$		−	5.62434i		−	0.420383i	0.977660	−	0.210191i	$-0.0674087\pi$
$180$	1.80060	−	2.83416i	0.134208	−	0.211246i
$181$	−4.37746	+	2.52733i	−0.325374	+	0.187855i	−0.653785	−	0.756680i	$-0.726820\pi$
$181$	−4.37746	+	2.52733i	−0.325374	+	0.187855i	0.328411	+	0.944535i	$0.393487\pi$
$182$	−5.85361	+	11.3950i	−0.433899	+	0.844651i
$183$	−11.1258	−	9.74479i	−0.822442	−	0.720355i
$184$	1.83938	−	10.4316i	0.135601	−	0.769031i
$185$	4.13927	−	1.50657i	0.304325	−	0.110765i
$186$	0.496166	−	0.0766841i	0.0363807	−	0.00562275i
$187$	−28.5917	+	5.04149i	−2.09083	+	0.368670i
$188$	−4.97426			−0.362785
$189$	−12.0045	+	6.70016i	−0.873198	+	0.487365i
$190$	7.84538			0.569164
$191$	−1.38822	+	0.244781i	−0.100448	+	0.0177118i	−0.223646	−	0.974670i	$-0.571796\pi$
$191$	−1.38822	+	0.244781i	−0.100448	+	0.0177118i	0.123198	+	0.992382i	$0.460685\pi$
$192$	1.37026	+	1.70513i	0.0988898	+	0.123057i
$193$	−14.4735	+	5.26791i	−1.04182	+	0.379193i	−0.805571	−	0.592499i	$-0.798141\pi$
$193$	−14.4735	+	5.26791i	−1.04182	+	0.379193i	−0.236252	+	0.971692i	$0.575919\pi$
$194$	−0.397181	+	2.25253i	−0.0285160	+	0.161722i
$195$	−3.95726	+	1.34606i	−0.283385	+	0.0963935i
$196$	7.86666	−	3.77257i	0.561905	−	0.269469i
$197$	11.2518	−	6.49623i	0.801658	−	0.462837i	−0.0423928	−	0.999101i	$-0.513498\pi$
$197$	11.2518	−	6.49623i	0.801658	−	0.462837i	0.844050	+	0.536264i	$0.180165\pi$
$198$	19.4448	+	8.02588i	1.38188	+	0.570375i
$199$			11.6287i			0.824340i	0.911107	+	0.412170i	$0.135229\pi$
$199$			11.6287i			0.824340i	−0.911107	+	0.412170i	$0.864771\pi$
$200$	−5.60787	+	0.988819i	−0.396536	+	0.0699201i
$201$	−10.7124	−	6.49131i	−0.755595	−	0.457862i
$202$	2.96391	−	3.53225i	0.208540	−	0.248528i
$203$	−9.08795	−	9.81054i	−0.637849	−	0.688565i
$204$	0.341277	−	16.1009i	0.0238942	−	1.12729i
$205$	−2.49834	+	2.09636i	−0.174492	+	0.146416i
$206$	−18.9278			−1.31876
$207$	23.1982	−	3.08355i	1.61239	−	0.214321i
$208$		−	13.2735i		−	0.920354i
$209$	3.27674	+	18.5833i	0.226657	+	1.28544i
$210$	7.03550	+	2.34093i	0.485496	+	0.161540i
$211$	−3.55252	+	1.29301i	−0.244565	+	0.0890146i	−0.461395	−	0.887195i	$-0.652651\pi$
$211$	−3.55252	+	1.29301i	−0.244565	+	0.0890146i	0.216829	+	0.976210i	$0.430429\pi$
$212$	−2.53315	+	3.01890i	−0.173978	+	0.207339i
$213$	−7.25746	+	5.83218i	−0.497273	+	0.399614i
$214$	10.9681	+	3.99206i	0.749764	+	0.272892i
$215$	−2.56243	+	4.43826i	−0.174756	+	0.302687i
$216$	3.90901	−	5.87401i	0.265974	−	0.399676i
$217$	0.165014	+	0.392353i	0.0112018	+	0.0266347i
$218$	3.30229	+	3.93551i	0.223659	+	0.266546i
$219$	12.4105	−	9.97324i	0.838627	−	0.673929i
$220$	−1.48979	−	4.09317i	−0.100442	−	0.275961i
$221$	−12.8864	+	15.3575i	−0.866836	+	1.03305i
$222$	−14.4922	+	4.92952i	−0.972653	+	0.330848i
$223$	9.92238	−	1.74958i	0.664451	−	0.117161i	0.168757	−	0.985658i	$-0.446025\pi$
$223$	9.92238	−	1.74958i	0.664451	−	0.117161i	0.495694	+	0.868497i	$0.334914\pi$
$224$	−9.88920	+	13.0334i	−0.660750	+	0.870832i
$225$	−5.82302	−	11.1519i	−0.388201	−	0.743462i
$226$	14.2127	+	24.6171i	0.945415	+	1.63751i
$227$	0.0868851	+	0.492750i	0.00576677	+	0.0327050i	0.987555	−	0.157272i	$-0.0502699\pi$
$227$	0.0868851	+	0.492750i	0.00576677	+	0.0327050i	−0.981789	+	0.189977i	$0.939159\pi$
$228$	−10.4649	−	0.221815i	−0.693052	−	0.0146900i
$229$	7.54187	+	20.7211i	0.498381	+	1.36929i	0.892839	+	0.450376i	$0.148710\pi$
$229$	7.54187	+	20.7211i	0.498381	+	1.36929i	−0.394458	+	0.918914i	$0.629068\pi$
$230$	−9.66889	−	8.11316i	−0.637548	−	0.534966i
$231$	−2.60648	+	17.6427i	−0.171494	+	1.16080i
$232$	6.44957	+	2.34745i	0.423435	+	0.154118i
$233$	−6.16567	+	3.55975i	−0.403926	+	0.233207i	−0.688177	−	0.725543i	$-0.741589\pi$
$233$	−6.16567	+	3.55975i	−0.403926	+	0.233207i	0.284250	+	0.958750i	$0.408255\pi$
$234$	13.8480	−	4.38527i	0.905275	−	0.286674i
$235$	1.79203	−	3.10388i	0.116899	−	0.202475i
$236$	−6.49438	−	2.36376i	−0.422748	−	0.153868i
$237$	−19.7988	−	3.92538i	−1.28607	−	0.254981i
$238$	34.6773	−	7.88508i	2.24780	−	0.511114i
$239$	−17.0760	−	3.01096i	−1.10456	−	0.194763i	−0.408505	−	0.912756i	$-0.633950\pi$
$239$	−17.0760	−	3.01096i	−1.10456	−	0.194763i	−0.696050	+	0.717993i	$0.745061\pi$
$240$	−7.59257	+	1.17346i	−0.490098	+	0.0757462i
$241$	8.22015	−	22.5847i	0.529506	−	1.45481i	−0.330148	−	0.943929i	$-0.607099\pi$
$241$	8.22015	−	22.5847i	0.529506	−	1.45481i	0.859654	−	0.510877i	$-0.170679\pi$
$242$	6.46875	−	3.73473i	0.415827	−	0.240078i
$243$	14.9792	+	4.31542i	0.960918	+	0.276834i
$244$		−	10.6426i		−	0.681325i
$245$	−0.480002	+	6.26781i	−0.0306662	+	0.400436i
$246$	8.83450	−	7.09950i	0.563267	−	0.452647i
$247$	9.98166	+	8.37561i	0.635118	+	0.532927i
$248$	−0.167345	−	0.140419i	−0.0106264	−	0.00891663i
$249$	−5.44289	−	16.0014i	−0.344929	−	1.01405i
$250$	−5.08769	+	13.9783i	−0.321774	+	0.884067i
$251$	−7.12754	−	12.3453i	−0.449886	−	0.779226i	0.548492	−	0.836156i	$-0.315202\pi$
$251$	−7.12754	−	12.3453i	−0.449886	−	0.779226i	−0.998378	+	0.0569302i	$0.981869\pi$
$252$	−9.31838	−	3.32146i	−0.587003	−	0.209232i
$253$	15.1793	−	26.2913i	0.954312	−	1.65292i
$254$	−1.91174	−	2.27833i	−0.119953	−	0.142955i
$255$	9.92382	+	6.01346i	0.621454	+	0.376577i
$256$	3.59609	−	20.3944i	0.224755	−	1.27465i
$257$	20.7228	−	7.54248i	1.29265	−	0.470487i	0.398056	−	0.917361i	$-0.369685\pi$
$257$	20.7228	−	7.54248i	1.29265	−	0.470487i	0.894597	+	0.446874i	$0.147463\pi$
$258$	9.22962	−	15.2313i	0.574611	−	0.948262i
$259$	−7.03212	−	10.9074i	−0.436954	−	0.677751i
$260$	−2.60484	−	1.50390i	−0.161545	−	0.0932682i
$261$	−0.642530	+	15.1500i	−0.0397716	+	0.937759i
$262$	−7.71428	−	4.45384i	−0.476590	−	0.275159i
$263$	9.10274	+	10.8482i	0.561299	+	0.668930i	0.969821	−	0.243819i	$-0.0784002\pi$
$263$	9.10274	+	10.8482i	0.561299	+	0.668930i	−0.408522	+	0.912748i	$0.633956\pi$
$264$	−2.94758	−	8.66552i	−0.181411	−	0.533326i
$265$	−0.971162	−	2.66825i	−0.0596580	−	0.163909i
$266$	−5.12495	−	22.5387i	−0.314231	−	1.38194i
$267$	−4.63554	+	11.9423i	−0.283690	+	0.730857i
$268$	−1.56514	−	8.87635i	−0.0956061	−	0.542209i
$269$	1.82097	+	3.15402i	0.111027	+	0.192304i	0.916184	−	0.400757i	$-0.131253\pi$
$269$	1.82097	+	3.15402i	0.111027	+	0.192304i	−0.805158	+	0.593061i	$0.797919\pi$
$270$	−3.73265	−	7.53350i	−0.227162	−	0.458474i
$271$	−23.4729	−	13.5521i	−1.42588	−	0.823232i	−0.429088	−	0.903263i	$-0.641165\pi$
$271$	−23.4729	−	13.5521i	−1.42588	−	0.823232i	−0.996792	+	0.0800305i	$0.974498\pi$
$272$	−28.2270	+	23.6853i	−1.71151	+	1.43613i
$273$	6.45211	+	10.4894i	0.390499	+	0.634845i
$274$	1.03267	−	5.85658i	0.0623861	−	0.353809i
$275$	−16.0723	−	2.83398i	−0.969195	−	0.170895i
$276$	12.6678	+	11.0954i	0.762514	+	0.667866i
$277$	−7.14943	+	5.99909i	−0.429568	+	0.360450i	−0.831789	−	0.555092i	$-0.812683\pi$
$277$	−7.14943	+	5.99909i	−0.429568	+	0.360450i	0.402221	+	0.915543i	$0.368238\pi$
$278$	26.5295			1.59113
$279$	0.184139	−	0.446124i	0.0110241	−	0.0267087i
$280$	−1.25077	−	2.97396i	−0.0747478	−	0.177728i
$281$	5.06201	−	13.9078i	0.301974	−	0.829668i	−0.692183	−	0.721722i	$-0.743351\pi$
$281$	5.06201	−	13.9078i	0.301974	−	0.829668i	0.994157	−	0.107945i	$-0.0344271\pi$
$282$	−6.45470	+	10.6520i	−0.384372	+	0.634317i
$283$	17.5190	+	3.08907i	1.04140	+	0.183626i	0.668088	−	0.744082i	$-0.267113\pi$
$283$	17.5190	+	3.08907i	1.04140	+	0.183626i	0.373307	+	0.927708i	$0.378224\pi$
$284$	−6.59789	−	1.16339i	−0.391513	−	0.0690342i
$285$	3.90848	−	6.45004i	0.231518	−	0.382067i
$286$	6.44487	−	17.7071i	0.381093	−	1.04704i
$287$	7.65457	+	5.80796i	0.451835	+	0.342833i
$288$	18.3893	−	2.44434i	1.08360	−	0.144034i
$289$	38.6531			2.27371
$290$	6.26499	−	5.25695i	0.367893	−	0.308699i
$291$	1.65403	+	1.44872i	0.0969611	+	0.0849256i
$292$	11.2826	+	1.98943i	0.660267	+	0.116423i
$293$	1.65066	−	9.36134i	0.0964324	−	0.546895i	−0.897867	−	0.440268i	$-0.854884\pi$
$293$	1.65066	−	9.36134i	0.0964324	−	0.546895i	0.994299	−	0.106628i	$-0.0340053\pi$
$294$	2.12927	−	21.7412i	0.124182	−	1.26797i
$295$	3.81462	−	3.20085i	0.222096	−	0.186361i
$296$	5.76826	+	3.33031i	0.335273	+	0.193570i
$297$	16.2856	−	11.9880i	0.944985	−	0.695614i
$298$	12.9151	+	22.3695i	0.748150	+	1.29583i
$299$	−3.64022	−	20.6447i	−0.210519	−	1.19391i
$300$	3.27583	−	8.43936i	0.189130	−	0.487247i
$301$	14.4244	+	4.46224i	0.831408	+	0.257199i
$302$	13.2350	+	36.3629i	0.761589	+	2.09245i
$303$	−1.42743	−	4.19648i	−0.0820039	−	0.241082i
$304$	15.3944	+	18.3463i	0.882927	+	1.05223i
$305$	6.64088	+	3.83412i	0.380256	+	0.219541i
$306$	−34.0360	−	21.6237i	−1.94571	−	1.23614i
$307$	−24.1263	−	13.9293i	−1.37696	−	0.794987i	−0.385166	−	0.922847i	$-0.625856\pi$
$307$	−24.1263	−	13.9293i	−1.37696	−	0.794987i	−0.991792	+	0.127860i	$0.959189\pi$
$308$	−10.7859	+	6.95380i	−0.614584	+	0.396229i
$309$	−9.42960	+	15.5614i	−0.536431	+	0.885256i
$310$	−0.244606	+	0.0890291i	−0.0138927	+	0.00505652i
$311$	−0.734417	+	4.16508i	−0.0416449	+	0.236180i	−0.998524	−	0.0543051i	$-0.982706\pi$
$311$	−0.734417	+	4.16508i	−0.0416449	+	0.236180i	0.956879	+	0.290485i	$0.0938167\pi$
$312$	−5.40544	−	3.27549i	−0.306023	−	0.185438i
$313$	−0.662036	−	0.788983i	−0.0374205	−	0.0445960i	0.747010	−	0.664813i	$-0.231489\pi$
$313$	−0.662036	−	0.788983i	−0.0374205	−	0.0445960i	−0.784430	+	0.620217i	$0.787044\pi$
$314$	−9.86712	+	17.0904i	−0.556834	+	0.964464i
$315$	5.42959	−	4.61797i	0.305923	−	0.260193i
$316$	−7.26209	−	12.5783i	−0.408525	−	0.707585i
$317$	8.67463	−	23.8334i	0.487216	−	1.33861i	−0.415975	−	0.909376i	$-0.636560\pi$
$317$	8.67463	−	23.8334i	0.487216	−	1.33861i	0.903191	−	0.429239i	$-0.141218\pi$
$318$	3.17766	+	9.34193i	0.178194	+	0.523870i
$319$	15.0688	+	12.6442i	0.843690	+	0.707940i
$320$	−0.868810	−	0.729018i	−0.0485679	−	0.0407533i
$321$	8.74623	−	7.02856i	0.488167	−	0.392296i
$322$	−16.9918	+	33.0773i	−0.946918	+	1.84332i
$323$		−	36.1720i		−	2.01267i
$324$	4.76594	+	10.1544i	0.264774	+	0.564132i
$325$	−9.75963	+	5.63473i	−0.541367	+	0.312558i
$326$	−8.05462	+	22.1299i	−0.446104	+	1.22566i
$327$	4.88072	−	0.754331i	0.269904	−	0.0417146i
$328$	−4.85653	−	0.856338i	−0.268157	−	0.0472833i
$329$	−10.0876	−	3.12065i	−0.556150	−	0.172047i
$330$	−10.6984	−	2.12111i	−0.588926	−	0.116763i
$331$	−18.6800	−	6.79897i	−1.02675	−	0.373705i	−0.226906	−	0.973917i	$-0.572861\pi$
$331$	−18.6800	−	6.79897i	−1.02675	−	0.373705i	−0.799841	+	0.600211i	$0.795083\pi$
$332$	6.08113	−	10.5328i	0.333746	−	0.578064i
$333$	−3.16707	+	14.3705i	−0.173554	+	0.787499i
$334$	19.0848	−	11.0186i	1.04427	−	0.602911i
$335$	6.10259	+	2.22116i	0.333420	+	0.121355i
$336$	8.33097	+	21.0458i	0.454492	+	1.14814i
$337$	−23.6390	−	19.8355i	−1.28770	−	1.08051i	−0.992133	−	0.125187i	$-0.960047\pi$
$337$	−23.6390	−	19.8355i	−1.28770	−	1.08051i	−0.295567	−	0.955322i	$-0.595509\pi$
$338$	3.56080	+	9.78322i	0.193682	+	0.532137i
$339$	27.3194	+	0.579067i	1.48379	+	0.0314506i
$340$	1.44992	+	8.22292i	0.0786331	+	0.445950i
$341$	−0.313046	−	0.542212i	−0.0169524	−	0.0293624i
$342$	−14.0544	+	22.1218i	−0.759975	+	1.19621i
$343$	18.3201	−	2.71543i	0.989193	−	0.146620i
$344$	−7.63150	+	1.34564i	−0.411463	+	0.0725520i
$345$	−11.4871	+	3.90734i	−0.618446	+	0.210364i
$346$	−11.5076	+	13.7142i	−0.618650	+	0.737278i
$347$	5.76541	+	15.8403i	0.309503	+	0.850353i	0.992753	+	0.120169i	$0.0383436\pi$
$347$	5.76541	+	15.8403i	0.309503	+	0.850353i	−0.683250	+	0.730184i	$0.739434\pi$
$348$	−8.50542	+	6.83504i	−0.455938	+	0.366397i
$349$	10.6801	+	12.7280i	0.571690	+	0.681314i	0.971977	−	0.235076i	$-0.0755339\pi$
$349$	10.6801	+	12.7280i	0.571690	+	0.681314i	−0.400287	+	0.916390i	$0.631089\pi$
$350$	19.8336	+	2.50192i	1.06015	+	0.133733i
$351$	3.29361	−	13.5698i	0.175800	−	0.724301i
$352$	12.0327	−	20.8412i	0.641343	−	1.11084i
$353$	22.0893	+	8.03985i	1.17570	+	0.427918i	0.854680	−	0.519156i	$-0.173754\pi$
$353$	22.0893	+	8.03985i	1.17570	+	0.427918i	0.321016	+	0.947074i	$0.395976\pi$
$354$	−13.4891	+	10.8399i	−0.716935	+	0.576137i
$355$	3.10289	−	3.69788i	0.164684	−	0.196263i
$356$	−8.66225	+	3.15280i	−0.459098	+	0.167098i
$357$	10.7931	−	32.4380i	0.571234	−	1.71680i
$358$	−1.75970	−	9.97978i	−0.0930033	−	0.527448i
$359$		−	15.6227i		−	0.824534i	−0.911063	−	0.412267i	$-0.864737\pi$
$359$		−	15.6227i		−	0.824534i	0.911063	−	0.412267i	$-0.135263\pi$
$360$	−1.39574	+	3.38153i	−0.0735617	+	0.178222i
$361$	−4.51020			−0.237379
$362$	−6.97659	+	5.85406i	−0.366682	+	0.307682i
$363$	0.152164	−	7.17885i	0.00798654	−	0.376792i
$364$	−2.61891	+	8.46576i	−0.137268	+	0.443726i
$365$	−5.30607	+	6.32352i	−0.277732	+	0.330988i
$366$	−22.7904	−	13.8101i	−1.19127	−	0.721866i
$367$	−11.3941	+	2.00909i	−0.594767	+	0.104873i	−0.462925	−	0.886397i	$-0.653200\pi$
$367$	−11.3941	+	2.00909i	−0.594767	+	0.104873i	−0.131842	+	0.991271i	$0.542089\pi$
$368$		−	38.5304i		−	2.00853i
$369$	−1.43557	−	10.8001i	−0.0747327	−	0.562232i
$370$	6.87331	−	3.96831i	0.357327	−	0.206303i
$371$	−7.03109	+	4.53303i	−0.365036	+	0.235343i
$372$	0.328793	−	0.111839i	0.0170471	−	0.00579859i
$373$	−5.63907	+	31.9808i	−0.291980	+	1.65590i	0.387249	+	0.921975i	$0.373425\pi$
$373$	−5.63907	+	31.9808i	−0.291980	+	1.65590i	−0.679229	+	0.733926i	$0.737686\pi$
$374$	−49.1555	+	17.8912i	−2.54177	+	0.925130i
$375$	8.95757	+	11.1467i	0.462567	+	0.575611i
$376$	5.33706	−	0.941068i	0.275238	−	0.0485319i
$377$	13.5832			0.699568
$378$	−19.2044	+	15.6446i	−0.987766	+	0.804671i
$379$	5.32262			0.273405			0.136702	−	0.990612i	$-0.456350\pi$
$379$	5.32262			0.273405			0.136702	+	0.990612i	$0.456350\pi$
$380$	5.34453	−	0.942385i	0.274169	−	0.0483433i
$381$	−2.82552	+	0.436694i	−0.144756	+	0.0223725i
$382$	−2.38667	+	0.868676i	−0.122112	+	0.0444453i
$383$	−0.00487891	+	0.0276697i	−0.000249301	+	0.00141386i	−0.984932	−	0.172941i	$-0.944673\pi$
$383$	−0.00487891	+	0.0276697i	−0.000249301	+	0.00141386i	0.984683	+	0.174355i	$0.0557840\pi$
$384$	−13.1491	−	11.5169i	−0.671010	−	0.587720i
$385$	−0.453363	−	9.23545i	−0.0231055	−	0.470682i
$386$	−24.0334	+	13.8757i	−1.22327	+	0.706254i
$387$	−7.92428	−	15.1762i	−0.402814	−	0.771448i
$388$			1.58220i			0.0803242i
$389$	−25.2469	+	4.45171i	−1.28007	+	0.225711i	−0.772009	−	0.635611i	$-0.780748\pi$
$389$	−25.2469	+	4.45171i	−1.28007	+	0.225711i	−0.508060	+	0.861322i	$0.669637\pi$
$390$	−6.60059	+	3.62656i	−0.334234	+	0.183638i
$391$	−37.4067	+	44.5795i	−1.89174	+	2.25448i
$392$	−7.72671	+	5.53601i	−0.390258	+	0.279611i
$393$	−7.50487	+	4.12340i	−0.378570	+	0.207998i
$394$	17.9326	−	15.0472i	0.903432	−	0.758069i
$395$	10.4650			0.526549
$396$	14.2105	+	3.13179i	0.714103	+	0.157379i
$397$			6.04507i			0.303393i	0.988427	+	0.151697i	$0.0484737\pi$
$397$			6.04507i			0.303393i	−0.988427	+	0.151697i	$0.951526\pi$
$398$	3.63832	+	20.6340i	0.182373	+	1.03429i
$399$	−21.0832	−	7.01506i	−1.05548	−	0.351192i
$400$	−19.4641	+	7.08435i	−0.973205	+	0.354218i
$401$	−11.5485	+	13.7630i	−0.576706	+	0.687291i	−0.972993	−	0.230836i	$-0.925854\pi$
$401$	−11.5485	+	13.7630i	−0.576706	+	0.687291i	0.396287	+	0.918127i	$0.370298\pi$
$402$	−21.0390	−	8.16651i	−1.04933	−	0.407308i
$403$	−0.406257	−	0.147866i	−0.0202371	−	0.00736571i
$404$	1.59482	−	2.76230i	0.0793451	−	0.137430i
$405$	−8.05319	−	0.684325i	−0.400166	−	0.0340044i
$406$	−19.1950	−	14.5644i	−0.952634	−	0.722817i
$407$	12.2705	+	14.6234i	0.608224	+	0.724854i
$408$	2.67992	+	17.3398i	0.132676	+	0.858448i
$409$	−9.02981	−	24.8092i	−0.446495	−	1.22674i	−0.935148	−	0.354257i	$-0.884734\pi$
$409$	−9.02981	−	24.8092i	−0.446495	−	1.22674i	0.488653	−	0.872478i	$-0.337488\pi$
$410$	−3.77715	+	4.50143i	−0.186540	+	0.222310i
$411$	−4.30049	−	3.76669i	−0.212128	−	0.185797i
$412$	−12.8942	+	2.27360i	−0.635253	+	0.112012i
$413$	−11.6875	−	8.86795i	−0.575103	−	0.436363i
$414$	40.1980	−	12.7295i	1.97562	−	0.625622i
$415$	4.38158	+	7.58911i	0.215083	+	0.372535i
$416$	−2.88562	−	16.3651i	−0.141479	−	0.802367i
$417$	13.2167	−	21.8111i	0.647224	−	1.06809i
$418$	11.6284	+	31.9489i	0.568766	+	1.56267i
$419$	−2.46834	−	2.07119i	−0.120586	−	0.101184i	0.580500	−	0.814260i	$-0.302857\pi$
$419$	−2.46834	−	2.07119i	−0.120586	−	0.101184i	−0.701087	+	0.713076i	$0.747301\pi$
$420$	5.07401	+	0.749618i	0.247586	+	0.0365776i
$421$	7.06763	+	2.57241i	0.344455	+	0.125371i	0.508454	−	0.861089i	$-0.330217\pi$
$421$	7.06763	+	2.57241i	0.344455	+	0.125371i	−0.163999	+	0.986461i	$0.552439\pi$
$422$	−5.89901	+	3.40580i	−0.287159	+	0.165792i
$423$	5.54182	+	10.6134i	0.269452	+	0.516041i
$424$	2.14678	−	3.71832i	0.104257	−	0.180578i
$425$	29.3977	+	10.6999i	1.42600	+	0.519020i
$426$	−11.0529	+	12.6192i	−0.535513	+	0.611404i
$427$	6.67676	−	21.5829i	0.323111	−	1.04447i
$428$	7.95135	+	1.40204i	0.384343	+	0.0677701i
$429$	−11.3471	−	14.1201i	−0.547841	−	0.681725i
$430$	−3.15814	+	8.67692i	−0.152299	+	0.418438i
$431$	12.5235	−	7.23047i	0.603238	−	0.348280i	−0.167076	−	0.985944i	$-0.553433\pi$
$431$	12.5235	−	7.23047i	0.603238	−	0.348280i	0.770314	+	0.637664i	$0.220099\pi$
$432$	10.2927	−	23.5111i	0.495207	−	1.13118i
$433$			2.90783i			0.139741i	0.997556	+	0.0698707i	$0.0222587\pi$
$433$			2.90783i			0.139741i	−0.997556	+	0.0698707i	$0.977741\pi$
$434$	0.415555	+	0.644560i	0.0199473	+	0.0309399i
$435$	−1.20083	−	7.76967i	−0.0575753	−	0.372527i
$436$	2.72236	+	2.28433i	0.130377	+	0.109400i
$437$	28.9747	+	24.3127i	1.38605	+	1.16303i
$438$	18.9008	−	21.5794i	0.903115	−	1.03110i
$439$	−12.4035	+	34.0785i	−0.591989	+	1.62648i	0.174819	+	0.984601i	$0.444066\pi$
$439$	−12.4035	+	34.0785i	−0.591989	+	1.62648i	−0.766808	+	0.641876i	$0.778156\pi$
$440$	2.37283	+	4.10986i	0.113120	+	0.195930i
$441$	−16.8136	−	12.5818i	−0.800650	−	0.599133i
$442$	−18.0607	+	31.2820i	−0.859058	+	1.48793i
$443$	−13.7969	−	16.4425i	−0.655512	−	0.781209i	0.331222	−	0.943553i	$-0.392539\pi$
$443$	−13.7969	−	16.4425i	−0.655512	−	0.781209i	−0.986734	+	0.162344i	$0.948095\pi$
$444$	−9.28043	+	5.09895i	−0.440430	+	0.241985i
$445$	1.15335	−	6.54097i	0.0546740	−	0.310072i
$446$	17.0588	−	6.20889i	0.807757	−	0.293999i
$447$	24.8251	+	0.526198i	1.17419	+	0.0248883i
$448$	−1.52682	+	2.97220i	−0.0721356	+	0.140423i
$449$	−1.81557	−	1.04822i	−0.0856820	−	0.0494685i	0.456547	−	0.889699i	$-0.349086\pi$
$449$	−1.81557	−	1.04822i	−0.0856820	−	0.0494685i	−0.542229	+	0.840231i	$0.682419\pi$
$450$	−13.8215	−	17.9660i	−0.651549	−	0.846926i
$451$	−12.2401	−	7.06682i	−0.576364	−	0.332764i
$452$	12.6392	+	15.0628i	0.594496	+	0.708493i
$453$	36.4891	+	7.23448i	1.71441	+	0.339905i
$454$	0.308337	+	0.847148i	0.0144709	+	0.0397586i
$455$	−4.33904	−	4.68404i	−0.203418	−	0.219591i
$456$	11.2701	−	1.74183i	0.527770	−	0.0815686i
$457$	4.80346	+	27.2418i	0.224696	+	1.27432i	0.863265	+	0.504751i	$0.168416\pi$
$457$	4.80346	+	27.2418i	0.224696	+	1.27432i	−0.638569	+	0.769565i	$0.720473\pi$
$458$	19.8653	+	34.4077i	0.928245	+	1.60777i
$459$	−34.7341	+	17.2098i	−1.62125	+	0.803286i
$460$	−7.56131	−	4.36553i	−0.352548	−	0.203544i
$461$	30.3564	−	25.4721i	1.41384	−	1.18635i	0.459295	−	0.888284i	$-0.348102\pi$
$461$	30.3564	−	25.4721i	1.41384	−	1.18635i	0.954545	−	0.298068i	$-0.0963423\pi$
$462$	0.895015	+	32.1206i	0.0416398	+	1.49438i
$463$	3.97186	−	22.5255i	0.184588	−	1.04685i	−0.741896	−	0.670515i	$-0.766073\pi$
$463$	3.97186	−	22.5255i	0.184588	−	1.04685i	0.926484	−	0.376335i	$-0.122816\pi$
$464$	24.5866	+	4.33528i	1.14140	+	0.201260i
$465$	−0.0486648	+	0.245454i	−0.00225678	+	0.0113827i
$466$	−9.82656	+	8.24546i	−0.455206	+	0.381964i
$467$	33.4415			1.54749			0.773743	−	0.633500i	$-0.218382\pi$
$467$	33.4415			1.54749			0.773743	+	0.633500i	$0.218382\pi$
$468$	8.90698	−	4.65081i	0.411725	−	0.214984i
$469$	2.39461	−	18.9829i	0.110573	−	0.876547i
$470$	2.20863	−	6.06817i	0.101877	−	0.279904i
$471$	9.13506	+	16.6264i	0.420921	+	0.766105i
$472$	7.41525	+	1.30751i	0.341315	+	0.0601830i
$473$	−21.8720	−	3.85663i	−1.00568	−	0.177328i
$474$	−36.3589	−	0.770669i	−1.67002	−	0.0353980i
$475$	6.95444	−	19.1072i	0.319091	−	0.876697i
$476$	22.6761	−	9.53700i	1.03936	−	0.437128i
$477$	9.26349	+	2.04155i	0.424146	+	0.0934761i
$478$	−31.2416			−1.42896
$479$	−11.4018	+	9.56726i	−0.520962	+	0.437139i	−0.864967	−	0.501829i	$-0.832661\pi$
$479$	−11.4018	+	9.56726i	−0.520962	+	0.437139i	0.344005	+	0.938968i	$0.388216\pi$
$480$	−9.10589	+	3.09737i	−0.415625	+	0.141375i
$481$	12.9814	+	2.28897i	0.591901	+	0.104368i
$482$	7.51962	−	42.6459i	0.342510	−	1.94247i
$483$	18.7291	+	30.4484i	0.852206	+	1.38545i
$484$	3.95811	−	3.32125i	0.179914	−	0.150966i
$485$	−0.987277	−	0.570005i	−0.0448299	−	0.0258826i
$486$	27.9292	+	2.97064i	1.26689	+	0.134751i
$487$	−10.9979	−	19.0489i	−0.498362	−	0.863189i	0.501636	−	0.865079i	$-0.332732\pi$
$487$	−10.9979	−	19.0489i	−0.498362	−	0.863189i	−0.999998	+	0.00188992i	$0.999398\pi$
$488$	2.01346	+	11.4189i	0.0911449	+	0.516908i
$489$	14.1813	+	17.6469i	0.641298	+	0.798021i
$490$	1.10932	+	11.2717i	0.0501139	+	0.509205i
$491$	−14.1796	−	38.9582i	−0.639918	−	1.75816i	−0.651984	−	0.758233i	$-0.726063\pi$
$491$	−14.1796	−	38.9582i	−0.639918	−	1.75816i	0.0120663	−	0.999927i	$-0.496159\pi$
$492$	5.16556	−	5.89760i	0.232881	−	0.265885i
$493$	−24.2378	−	28.8854i	−1.09161	−	1.30093i
$494$	20.3319	+	11.7386i	0.914774	+	0.528145i
$495$	−7.07366	+	7.73890i	−0.317937	+	0.347838i
$496$	−0.688163	−	0.397311i	−0.0308994	−	0.0178398i
$497$	−12.6505	−	6.49856i	−0.567450	−	0.291500i
$498$	−14.6642	−	26.6899i	−0.657120	−	1.19600i
$499$	−24.2680	+	8.83284i	−1.08639	+	0.395412i	−0.822281	−	0.569082i	$-0.807299\pi$
$499$	−24.2680	+	8.83284i	−1.08639	+	0.395412i	−0.264105	+	0.964494i	$0.585077\pi$
$500$	−1.78683	+	10.1336i	−0.0799095	+	0.453189i
$501$	0.448930	−	21.1798i	0.0200567	−	0.946243i
$502$	−16.5095	−	19.6753i	−0.736857	−	0.878152i
$503$	6.47284	−	11.2113i	0.288610	−	0.499887i	−0.684868	−	0.728667i	$-0.740140\pi$
$503$	6.47284	−	11.2113i	0.288610	−	0.499887i	0.973478	+	0.228780i	$0.0734736\pi$
$504$	10.6264	+	1.80079i	0.473338	+	0.0802136i
$505$	1.14910	+	1.99029i	0.0511341	+	0.0885669i
$506$	18.7081	−	51.4002i	0.831678	−	2.28502i
$507$	9.81717	+	1.94639i	0.435996	+	0.0864423i
$508$	−1.57601	−	1.32243i	−0.0699243	−	0.0586735i
$509$	−2.10687	−	1.76788i	−0.0933854	−	0.0783597i	0.594900	−	0.803800i	$-0.297192\pi$
$509$	−2.10687	−	1.76788i	−0.0933854	−	0.0783597i	−0.688285	+	0.725440i	$0.741636\pi$
$510$	19.4902	+	7.56533i	0.863040	+	0.334999i
$511$	21.6328	+	11.1128i	0.956977	+	0.491601i
$512$		−	17.1291i		−	0.757006i
$513$	11.1856	+	22.5756i	0.493857	+	0.996737i
$514$	34.4105	−	19.8669i	1.51778	−	0.876292i
$515$	3.22657	−	8.86493i	0.142180	−	0.390636i
$516$	4.45793	−	11.4847i	0.196250	−	0.505588i
$517$	15.2961	+	2.69712i	0.672723	+	0.118619i
$518$	−15.8904	−	17.1538i	−0.698182	−	0.753695i
$519$	5.54210	+	16.2931i	0.243271	+	0.715188i
$520$	3.07935	+	1.12079i	0.135038	+	0.0491499i
$521$	−13.5062	+	23.3935i	−0.591719	+	1.02489i	0.402281	+	0.915516i	$0.368217\pi$
$521$	−13.5062	+	23.3935i	−0.591719	+	1.02489i	−0.994001	+	0.109372i	$0.965116\pi$
$522$	3.59991	+	27.0830i	0.157564	+	1.18539i
$523$	5.83341	−	3.36792i	0.255077	−	0.147269i	−0.367010	−	0.930217i	$-0.619618\pi$
$523$	5.83341	−	3.36792i	0.255077	−	0.147269i	0.622087	+	0.782948i	$0.286285\pi$
$524$	−5.79021	−	2.10747i	−0.252947	−	0.0920650i
$525$	11.9378	−	15.0596i	0.521008	−	0.657257i
$526$	19.5459	+	16.4010i	0.852243	+	0.715117i
$527$	0.410479	+	1.12778i	0.0178808	+	0.0491270i
$528$	−16.0324	−	29.1801i	−0.697721	−	1.26990i
$529$	−6.57290	−	37.2768i	−0.285778	−	1.62073i
$530$	−2.55804	−	4.43066i	−0.111114	−	0.192456i
$531$	2.19191	+	16.4903i	0.0951210	+	0.715617i
$532$	−6.19862	−	14.7385i	−0.268744	−	0.638994i
$533$	−9.61131	+	1.69473i	−0.416312	+	0.0734070i
$534$	−4.48883	+	22.6407i	−0.194251	+	0.979757i
$535$	−3.73941	+	4.45645i	−0.161669	+	0.192669i
$536$	3.35859	+	9.22765i	0.145069	+	0.398574i
$537$	−9.08149	−	3.52508i	−0.391895	−	0.152118i
$538$	4.21792	+	5.02673i	0.181848	+	0.216718i
$539$	−26.2360	+	7.33545i	−1.13006	+	0.315960i
$540$	−3.44772	−	4.68370i	−0.148366	−	0.201554i
$541$	7.43623	−	12.8799i	0.319709	−	0.553752i	−0.660719	−	0.750634i	$-0.729748\pi$
$541$	7.43623	−	12.8799i	0.319709	−	0.553752i	0.980427	+	0.196882i	$0.0630816\pi$
$542$	−45.8903	−	16.7027i	−1.97116	−	0.717443i
$543$	1.33722	+	8.65219i	0.0573857	+	0.371301i
$544$	−29.6524	+	35.3384i	−1.27134	+	1.51512i
$545$	−2.40615	+	0.875767i	−0.103068	+	0.0375137i
$546$	14.7304	+	16.5935i	0.630403	+	0.710138i
$547$	7.58978	+	43.0438i	0.324515	+	1.84042i	0.513058	+	0.858354i	$0.328512\pi$
$547$	7.58978	+	43.0438i	0.324515	+	1.84042i	−0.188543	+	0.982065i	$0.560376\pi$
$548$		−	4.11374i		−	0.175730i
$549$	−22.7078	+	11.8570i	−0.969146	+	0.506043i
$550$	−29.4052			−1.25384
$551$	−18.7742	+	15.7535i	−0.799809	+	0.671120i
$552$	−15.6909	−	9.50808i	−0.667849	−	0.404691i
$553$	−6.83617	−	30.0644i	−0.290704	−	1.27847i
$554$	−10.8089	+	12.8816i	−0.459228	+	0.547287i
$555$	0.161681	−	7.62782i	0.00686296	−	0.323783i
$556$	18.0728	−	3.18672i	0.766456	−	0.135147i
$557$		−	26.1298i		−	1.10715i	−0.832798	−	0.553577i	$-0.813263\pi$
$557$		−	26.1298i		−	1.10715i	0.832798	−	0.553577i	$-0.186737\pi$
$558$	0.187154	−	0.849210i	0.00792288	−	0.0359499i
$559$	−13.2814	+	7.66805i	−0.561745	+	0.324324i
$560$	−6.35902	−	9.86335i	−0.268718	−	0.416803i
$561$	−9.77960	+	49.3261i	−0.412895	+	2.08255i
$562$	4.63063	−	26.2616i	0.195331	−	1.10778i
$563$	20.0729	−	7.30595i	0.845973	−	0.307909i	0.117576	−	0.993064i	$-0.462488\pi$
$563$	20.0729	−	7.30595i	0.845973	−	0.307909i	0.728397	+	0.685155i	$0.240266\pi$
$564$	−3.11764	+	8.03182i	−0.131276	+	0.338201i
$565$	−13.9524	+	2.46018i	−0.586981	+	0.103501i
$566$	32.0520			1.34725
$567$	3.29473	+	23.5827i	0.138366	+	0.990381i
$568$	7.29921			0.306268
$569$	−15.0727	+	2.65772i	−0.631879	+	0.111417i	−0.480409	−	0.877044i	$-0.659512\pi$
$569$	−15.0727	+	2.65772i	−0.631879	+	0.111417i	−0.151470	+	0.988462i	$0.548401\pi$
$570$	4.91713	−	12.6677i	0.205956	−	0.530594i
$571$	−35.6407	+	12.9722i	−1.49152	+	0.542868i	−0.953849	−	0.300288i	$-0.902917\pi$
$571$	−35.6407	+	12.9722i	−1.49152	+	0.542868i	−0.537669	+	0.843156i	$0.680695\pi$
$572$	2.26348	−	12.8368i	0.0946408	−	0.536735i
$573$	−0.474833	+	2.39495i	−0.0198364	+	0.100050i
$574$	15.3994	+	7.91068i	0.642757	+	0.330185i
$575$	−28.3302	+	16.3565i	−1.18145	+	0.682111i
$576$	3.61204	−	1.14383i	0.150502	−	0.0476594i
$577$		−	20.9397i		−	0.871730i	−0.900012	−	0.435865i	$-0.856443\pi$
$577$		−	20.9397i		−	0.871730i	0.900012	−	0.435865i	$-0.143557\pi$
$578$	68.5858	−	12.0935i	2.85279	−	0.503025i
$579$	−0.565337	+	26.6716i	−0.0234946	+	1.10844i
$580$	3.63645	−	4.33375i	0.150995	−	0.179949i
$581$	18.9402	−	17.5452i	0.785773	−	0.727898i
$582$	3.38817	+	2.05310i	0.140444	+	0.0851037i
$583$	9.42649	−	7.90976i	0.390405	−	0.327589i
$584$	−12.4819			−0.516506
$585$	−0.306776	+	7.23335i	−0.0126836	+	0.299062i
$586$		−	17.1271i		−	0.707515i
$587$	0.524168	+	2.97270i	0.0216347	+	0.122697i	0.993712	−	0.111963i	$-0.0357137\pi$
$587$	0.524168	+	2.97270i	0.0216347	+	0.122697i	−0.972078	+	0.234659i	$0.924603\pi$
$588$	−1.16102	−	15.0666i	−0.0478795	−	0.621336i
$589$	0.733008	−	0.266793i	0.0302031	−	0.0109930i
$590$	5.76718	−	6.87305i	0.237431	−	0.282959i
$591$	−3.43719	−	22.2396i	−0.141387	−	0.914813i
$592$	22.7668	+	8.28643i	0.935709	+	0.340570i
$593$	−4.67012	+	8.08888i	−0.191779	+	0.332170i	−0.945840	−	0.324634i	$-0.894759\pi$
$593$	−4.67012	+	8.08888i	−0.191779	+	0.332170i	0.754061	+	0.656804i	$0.228092\pi$
$594$	25.1463	−	26.3667i	1.03176	−	1.08184i
$595$	−2.21833	+	17.5854i	−0.0909426	+	0.720933i
$596$	11.4852	+	13.6875i	0.470452	+	0.560662i
$597$	18.7767	+	7.28837i	0.768478	+	0.298293i
$598$	−12.9184	−	35.4929i	−0.528271	−	1.45141i
$599$	−0.0277621	+	0.0330855i	−0.00113433	+	0.00135184i	−0.766611	−	0.642111i	$-0.778059\pi$
$599$	−0.0277621	+	0.0330855i	−0.00113433	+	0.00135184i	0.765477	+	0.643463i	$0.222503\pi$
$600$	−1.91814	+	9.67464i	−0.0783075	+	0.394966i
$601$	−22.8510	+	4.02924i	−0.932110	+	0.164356i	−0.619027	−	0.785370i	$-0.712473\pi$
$601$	−22.8510	+	4.02924i	−0.932110	+	0.164356i	−0.313083	+	0.949726i	$0.601362\pi$
$602$	26.9906	+	3.40475i	1.10006	+	0.138767i
$603$	−17.1954	+	13.2286i	−0.700251	+	0.538711i
$604$	13.3840	+	23.1818i	0.544588	+	0.943254i
$605$	0.646472	+	3.66632i	0.0262828	+	0.149057i
$606$	−3.84579	−	6.99960i	−0.156225	−	0.284339i
$607$	−7.20354	−	19.7916i	−0.292383	−	0.803314i	−0.995717	−	0.0924552i	$-0.970529\pi$
$607$	−7.20354	−	19.7916i	−0.292383	−	0.803314i	0.703334	−	0.710859i	$-0.251694\pi$
$608$	22.9684	+	19.2727i	0.931490	+	0.781613i
$609$	−21.5368	+	8.52530i	−0.872713	+	0.345463i
$610$	12.9831	+	4.72547i	0.525671	+	0.191329i
$611$	9.28833	−	5.36262i	0.375766	−	0.216948i
$612$	−25.7838	−	10.6424i	−1.04225	−	0.430192i
$613$	2.31304	−	4.00629i	0.0934226	−	0.161813i	−0.815527	−	0.578720i	$-0.803553\pi$
$613$	2.31304	−	4.00629i	0.0934226	−	0.161813i	0.908949	+	0.416907i	$0.136886\pi$
$614$	−47.1675	−	17.1676i	−1.90353	−	0.692827i
$615$	1.81909	+	5.34792i	0.0733529	+	0.215649i
$616$	10.2570	−	9.50154i	0.413267	−	0.382828i
$617$	6.75722	+	1.19148i	0.272036	+	0.0479672i	0.308002	−	0.951386i	$-0.400340\pi$
$617$	6.75722	+	1.19148i	0.272036	+	0.0479672i	−0.0359662	+	0.999353i	$0.511451\pi$
$618$	−11.8631	+	30.5622i	−0.477203	+	1.22939i
$619$	−4.07011	+	11.1825i	−0.163592	+	0.449464i	−0.994220	−	0.107363i	$-0.965759\pi$
$619$	−4.07011	+	11.1825i	−0.163592	+	0.449464i	0.830628	+	0.556827i	$0.187982\pi$
$620$	−0.155939	+	0.0900315i	−0.00626267	+	0.00361575i
$621$	9.56067	−	39.3903i	0.383656	−	1.58068i
$622$			7.62027i			0.305545i
$623$	−19.5447	+	0.959438i	−0.783042	+	0.0384391i
$624$	−21.4325	−	8.31925i	−0.857985	−	0.333036i
$625$	10.3827	+	8.71212i	0.415308	+	0.348485i
$626$	−1.42156	−	1.19283i	−0.0568171	−	0.0476752i
$627$	32.0598	+	6.35630i	1.28034	+	0.253846i
$628$	−4.66892	+	12.8277i	−0.186310	+	0.511883i
$629$	−18.2964	−	31.6902i	−0.729523	−	1.26357i
$630$	8.18938	−	9.89287i	0.326273	−	0.394141i
$631$	1.75818	−	3.04526i	0.0699920	−	0.121230i	−0.828906	−	0.559389i	$-0.811036\pi$
$631$	1.75818	−	3.04526i	0.0699920	−	0.121230i	0.898898	+	0.438159i	$0.144369\pi$
$632$	10.1714	+	12.1218i	0.404597	+	0.482180i
$633$	−0.138762	+	6.54657i	−0.00551530	+	0.260203i
$634$	7.93538	−	45.0038i	0.315154	−	1.78733i
$635$	1.39296	−	0.506995i	0.0552778	−	0.0201195i
$636$	3.28687	+	5.98233i	0.130333	+	0.237215i
$637$	−10.6221	+	15.5253i	−0.420865	+	0.615135i
$638$	30.6939	+	17.7212i	1.21519	+	0.701587i
$639$	4.86843	+	15.3738i	0.192592	+	0.608178i
$640$	7.84856	+	4.53137i	0.310241	+	0.179118i
$641$	0.0654360	+	0.0779836i	0.00258457	+	0.00308017i	0.767335	−	0.641246i	$-0.221582\pi$
$641$	0.0654360	+	0.0779836i	0.00258457	+	0.00308017i	−0.764751	+	0.644326i	$0.777138\pi$
$642$	13.3202	−	15.2079i	0.525706	−	0.600207i
$643$	−6.93586	−	19.0561i	−0.273524	−	0.751500i	−0.998060	−	0.0622635i	$-0.980168\pi$
$643$	−6.93586	−	19.0561i	−0.273524	−	0.751500i	0.724536	−	0.689237i	$-0.242054\pi$
$644$	−7.60217	+	24.5744i	−0.299567	+	0.968365i
$645$	5.56034	+	6.91919i	0.218938	+	0.272443i
$646$	−11.3173	−	64.1834i	−0.445272	−	2.52526i
$647$	−20.9497	−	36.2860i	−0.823619	−	1.42655i	−0.902970	−	0.429703i	$-0.858618\pi$
$647$	−20.9497	−	36.2860i	−0.823619	−	1.42655i	0.0793513	−	0.996847i	$-0.474715\pi$
$648$	−7.03463	−	9.99335i	−0.276346	−	0.392576i
$649$	18.6889	+	10.7901i	0.733605	+	0.423547i
$650$	−15.5545	+	13.0517i	−0.610096	+	0.511931i
$651$	0.736946	−	0.0205344i	0.0288832	−	0.000804808i
$652$	−2.82884	+	16.0431i	−0.110786	+	0.628297i
$653$	−2.10324	−	0.370857i	−0.0823060	−	0.0145128i	0.132343	−	0.991204i	$-0.457750\pi$
$653$	−2.10324	−	0.370857i	−0.0823060	−	0.0145128i	−0.214650	+	0.976691i	$0.568861\pi$
$654$	8.42430	−	2.86552i	0.329416	−	0.112051i
$655$	3.40101	−	2.85379i	0.132889	−	0.111507i
$656$	−17.9381			−0.700365
$657$	−8.32520	−	26.2898i	−0.324797	−	1.02566i
$658$	−18.8758	−	2.38110i	−0.735855	−	0.0928250i
$659$	−15.2227	+	41.8239i	−0.592991	+	1.62923i	0.171933	+	0.985109i	$0.444999\pi$
$659$	−15.2227	+	41.8239i	−0.592991	+	1.62923i	−0.764924	+	0.644121i	$0.777223\pi$
$660$	−7.54287	−	0.159880i	−0.293606	−	0.00622332i
$661$	36.2766	+	6.39654i	1.41099	+	0.248796i	0.826653	−	0.562712i	$-0.190242\pi$
$661$	36.2766	+	6.39654i	1.41099	+	0.248796i	0.584341	+	0.811508i	$0.301353\pi$
$662$	−35.2729	−	6.21956i	−1.37092	−	0.241730i
$663$	16.7207	+	30.4328i	0.649378	+	1.18191i
$664$	−4.53199	+	12.4515i	−0.175875	+	0.483213i
$665$	11.4298	+	1.44181i	0.443227	+	0.0559111i
$666$	−1.12347	+	26.4898i	−0.0435336	+	1.02646i
$667$	39.4291			1.52670
$668$	11.6776	−	9.79869i	0.451821	−	0.379123i
$669$	3.39388	−	17.1180i	0.131215	−	0.661819i
$670$	11.5233	+	2.03187i	0.445185	+	0.0784982i
$671$	−5.77061	+	32.7267i	−0.222772	+	1.26340i
$672$	14.8467	+	24.1366i	0.572723	+	0.931090i
$673$	−2.34203	+	1.96519i	−0.0902785	+	0.0757527i	−0.686810	−	0.726837i	$-0.740990\pi$
$673$	−2.34203	+	1.96519i	−0.0902785	+	0.0757527i	0.596531	+	0.802590i	$0.296545\pi$
$674$	−48.1509	−	27.7999i	−1.85470	−	1.07081i
$675$	−21.6564	+	2.41277i	−0.833553	+	0.0928674i
$676$	3.60089	+	6.23693i	0.138496	+	0.239882i
$677$	−4.86997	−	27.6190i	−0.187168	−	1.06148i	−0.923138	−	0.384469i	$-0.874385\pi$
$677$	−4.86997	−	27.6190i	−0.187168	−	1.06148i	0.735970	−	0.677014i	$-0.236727\pi$
$678$	48.6566	−	7.52003i	1.86864	−	0.288805i
$679$	−0.992611	+	3.20866i	−0.0380929	+	0.123137i
$680$	−3.11135	−	8.54836i	−0.119315	−	0.327815i
$681$	0.850087	+	0.168542i	0.0325754	+	0.00645854i
$682$	−0.725110	−	0.864153i	−0.0277659	−	0.0330901i
$683$	−5.74458	−	3.31663i	−0.219810	−	0.126907i	0.386052	−	0.922477i	$-0.373838\pi$
$683$	−5.74458	−	3.31663i	−0.219810	−	0.126907i	−0.605862	+	0.795570i	$0.707172\pi$
$684$	−6.91705	+	16.7583i	−0.264480	+	0.640771i
$685$	2.56693	+	1.48201i	0.0980772	+	0.0566249i
$686$	31.6575	−	10.5501i	1.20869	−	0.402805i
$687$	38.1848	+	0.809371i	1.45684	+	0.0308794i
$688$	−26.4878	+	9.64078i	−1.00984	+	0.367551i
$689$	1.47551	−	8.36805i	0.0562126	−	0.318797i
$690$	−19.1602	+	10.5272i	−0.729414	+	0.400762i
$691$	5.85721	+	6.98035i	0.222819	+	0.265545i	0.865860	−	0.500287i	$-0.166772\pi$
$691$	5.85721	+	6.98035i	0.222819	+	0.265545i	−0.643041	+	0.765832i	$0.722328\pi$
$692$	−6.19198	+	10.7248i	−0.235384	+	0.407697i
$693$	26.8536	+	15.2663i	1.02008	+	0.579917i
$694$	15.1861	+	26.3031i	0.576457	+	0.998452i
$695$	−4.52242	+	12.4252i	−0.171545	+	0.471316i
$696$	7.83267	−	8.94269i	0.296896	−	0.338972i
$697$	20.7544	+	17.4150i	0.786127	+	0.659639i
$698$	22.9329	+	19.2430i	0.868021	+	0.728356i
$699$	1.88348	+	12.1866i	0.0712399	+	0.460941i
$700$	13.8118	−	0.678013i	0.522037	−	0.0256265i
$701$			3.37952i			0.127643i	0.997961	+	0.0638214i	$0.0203288\pi$
$701$			3.37952i			0.127643i	−0.997961	+	0.0638214i	$0.979671\pi$
$702$	1.59853	−	25.1086i	0.0603327	−	0.947662i
$703$	−20.5972	+	11.8918i	−0.776839	+	0.448508i
$704$	1.68104	−	4.61862i	0.0633566	−	0.174071i
$705$	−3.88860	−	4.83891i	−0.146453	−	0.182244i
$706$	41.7105	+	7.35469i	1.56980	+	0.276798i
$707$	4.96720	−	4.60134i	0.186811	−	0.173051i
$708$	−7.88709	+	9.00482i	−0.296415	+	0.338422i
$709$	−31.1392	−	11.3337i	−1.16946	−	0.425647i	−0.316989	−	0.948429i	$-0.602672\pi$
$709$	−31.1392	−	11.3337i	−1.16946	−	0.425647i	−0.852466	+	0.522782i	$0.824894\pi$
$710$	4.34878	−	7.53231i	0.163207	−	0.282682i
$711$	−18.7472	+	29.5083i	−0.703074	+	1.10665i
$712$	8.69757	−	5.02154i	0.325955	−	0.188190i
$713$	−1.17928	−	0.429223i	−0.0441644	−	0.0160745i
$714$	9.00229	−	60.9346i	0.336902	−	2.28042i
$715$	7.19459	+	6.03698i	0.269062	+	0.225770i
$716$	−2.39754	−	6.58718i	−0.0896001	−	0.246174i
$717$	−15.5642	+	25.6851i	−0.581256	+	0.959228i
$718$	−4.88792	−	27.7208i	−0.182416	−	1.03453i
$719$	6.10517	+	10.5745i	0.227684	+	0.394361i	0.957121	−	0.289687i	$-0.0935512\pi$
$719$	6.10517	+	10.5745i	0.227684	+	0.394361i	−0.729437	+	0.684048i	$0.760218\pi$
$720$	−2.86392	+	12.9950i	−0.106732	+	0.484295i
$721$	−27.5754	−	3.47852i	−1.02696	−	0.129547i
$722$	−8.00285	+	1.41112i	−0.297835	+	0.0525164i
$723$	−31.3149	−	27.4279i	−1.16461	−	1.02006i
$724$	−4.04949	+	4.82600i	−0.150498	+	0.179357i
$725$	−7.24960	−	19.9181i	−0.269243	−	0.739740i
$726$	−1.97607	−	12.7857i	−0.0733388	−	0.474522i
$727$	6.93845	+	8.26893i	0.257333	+	0.306677i	0.879207	−	0.476440i	$-0.158073\pi$
$727$	6.93845	+	8.26893i	0.257333	+	0.306677i	−0.621874	+	0.783117i	$0.713628\pi$
$728$	1.20831	−	9.57868i	0.0447829	−	0.355010i
$729$	16.3563	−	21.4819i	0.605789	−	0.795626i
$730$	−7.43658	+	12.8805i	−0.275240	+	0.476730i
$731$	40.0060	+	14.5610i	1.47967	+	0.538557i
$732$	−17.1844	−	6.67032i	−0.635155	−	0.246542i
$733$	5.24676	−	6.25285i	0.193794	−	0.230954i	−0.660394	−	0.750919i	$-0.729611\pi$
$733$	5.24676	−	6.25285i	0.193794	−	0.230954i	0.854187	+	0.519965i	$0.174055\pi$
$734$	−19.5890	+	7.12981i	−0.723043	+	0.263166i
$735$	9.81964	+	4.70343i	0.362203	+	0.173489i
$736$	−8.37635	−	47.5047i	−0.308756	−	1.75105i
$737$			28.1439i			1.03669i
$738$	−5.92633	−	18.7145i	−0.218151	−	0.688890i
$739$	−1.55326			−0.0571375			−0.0285688	−	0.999592i	$-0.509095\pi$
$739$	−1.55326			−0.0571375			−0.0285688	+	0.999592i	$0.509095\pi$
$740$	4.20565	−	3.52896i	0.154603	−	0.129727i
$741$	19.7799	−	10.8677i	0.726634	−	0.399235i
$742$	−11.0576	+	10.2432i	−0.405939	+	0.376040i
$743$	−3.17132	+	3.77943i	−0.116344	+	0.138654i	−0.821073	−	0.570823i	$-0.806624\pi$
$743$	−3.17132	+	3.77943i	−0.116344	+	0.138654i	0.704729	+	0.709477i	$0.251069\pi$
$744$	−0.331616	+	0.182200i	−0.0121576	+	0.00667977i
$745$	−12.6785	+	2.23556i	−0.464504	+	0.0819046i
$746$			58.5107i			2.14223i
$747$	−29.2485	−	1.24047i	−1.07015	−	0.0453864i
$748$	−31.3373	+	18.0926i	−1.14580	+	0.661530i
$749$	15.2455	+	7.83164i	0.557059	+	0.286162i
$750$	19.3817	+	16.9760i	0.707721	+	0.619874i
$751$	0.323318	−	1.83363i	0.0117981	−	0.0669101i	−0.978340	−	0.207003i	$-0.933629\pi$
$751$	0.323318	−	1.83363i	0.0117981	−	0.0669101i	0.990138	+	0.140093i	$0.0447401\pi$
$752$	18.5242	−	6.74224i	0.675506	−	0.245864i
$753$	−24.4008	+	3.77122i	−0.889215	+	0.137431i
$754$	24.1018	−	4.24981i	0.877738	−	0.154769i
$755$	−19.2869			−0.701922
$756$	−11.2034	+	12.9644i	−0.407464	+	0.471512i
$757$	11.8379			0.430255			0.215128	−	0.976586i	$-0.430983\pi$
$757$	11.8379			0.430255			0.215128	+	0.976586i	$0.430983\pi$
$758$	9.44442	−	1.66531i	0.343037	−	0.0604866i
$759$	−32.9382	−	40.9878i	−1.19558	−	1.48776i
$760$	−5.55605	+	2.02224i	−0.201539	+	0.0733543i
$761$	0.859368	−	4.87372i	0.0311521	−	0.176672i	−0.965262	−	0.261284i	$-0.915854\pi$
$761$	0.859368	−	4.87372i	0.0311521	−	0.176672i	0.996414	+	0.0846121i	$0.0269651\pi$
$762$	−4.87696	+	1.65890i	−0.176673	+	0.0600955i
$763$	4.08776	+	6.34044i	0.147987	+	0.229539i
$764$	−1.52153	+	0.878456i	−0.0550470	+	0.0317814i
$765$	15.9296	−	12.2548i	0.575935	−	0.443073i
$766$			0.0506234i			0.00182910i
$767$	14.6751	−	2.58762i	0.529888	−	0.0934336i
$768$	−30.6765	−	18.5888i	−1.10694	−	0.670766i
$769$	23.5161	−	28.0254i	0.848014	−	1.01062i	−0.151740	−	0.988420i	$-0.548488\pi$
$769$	23.5161	−	28.0254i	0.848014	−	1.01062i	0.999753	−	0.0222027i	$-0.00706792\pi$
$770$	−3.69397	−	16.2455i	−0.133121	−	0.585446i
$771$	0.809437	−	38.1879i	0.0291512	−	1.37530i
$772$	−14.7056	+	12.3395i	−0.529266	+	0.444107i
$773$	−52.7239			−1.89635			−0.948174	−	0.317753i	$-0.897072\pi$
$773$	−52.7239			−1.89635			−0.948174	+	0.317753i	$0.897072\pi$
$774$	−18.8090	−	24.4492i	−0.676075	−	0.878807i
$775$			0.674647i			0.0242341i
$776$	−0.299333	−	1.69760i	−0.0107454	−	0.0609404i
$777$	−22.0193	+	4.51834i	−0.789938	+	0.162095i
$778$	−43.4051	+	15.7982i	−1.55615	+	0.566391i
$779$	11.3189	−	13.4894i	0.405543	−	0.483308i
$780$	−4.06091	+	3.26339i	−0.145404	+	0.116848i
$781$	19.6581	+	7.15496i	0.703422	+	0.256024i
$782$	−52.4264	+	90.8051i	−1.87476	+	3.24718i
$783$	24.0596	+	10.5328i	0.859818	+	0.376411i
$784$	−24.1820	+	24.7118i	−0.863644	+	0.882563i
$785$	−6.32234	−	7.53467i	−0.225654	−	0.268924i
$786$	−12.0265	+	9.66460i	−0.428970	+	0.344725i
$787$	−5.82483	−	16.0036i	−0.207633	−	0.570466i	0.791541	−	0.611116i	$-0.209279\pi$
$787$	−5.82483	−	16.0036i	−0.207633	−	0.570466i	−0.999173	+	0.0406503i	$0.987057\pi$
$788$	10.4088	−	12.4047i	0.370798	−	0.441900i
$789$	23.2215	−	7.89880i	0.826709	−	0.281205i
$790$	18.5689	−	3.27420i	0.660653	−	0.116491i
$791$	16.1821	+	38.4761i	0.575368	+	1.36805i
$792$	−15.8394	−	0.671772i	−0.562829	−	0.0238704i
$793$	11.4736	+	19.8728i	0.407438	+	0.705703i
$794$	1.89134	+	10.7263i	0.0671212	+	0.380663i
$795$	−4.91703	−	0.104222i	−0.174389	−	0.00369638i
$796$	4.95709	+	13.6195i	0.175699	+	0.482730i
$797$	−5.99875	−	5.03354i	−0.212486	−	0.178297i	0.530332	−	0.847790i	$-0.322067\pi$
$797$	−5.99875	−	5.03354i	−0.212486	−	0.178297i	−0.742819	+	0.669493i	$0.766512\pi$
$798$	−39.6048	−	5.85108i	−1.40199	−	0.207126i
$799$	−27.9780	−	10.1832i	−0.989791	−	0.360255i
$800$	−22.4575	+	12.9658i	−0.793991	+	0.458411i
$801$	16.3776	+	14.9698i	0.578675	+	0.528931i
$802$	−16.1855	+	28.0342i	−0.571531	+	0.989921i
$803$	−33.6161	−	12.2353i	−1.18629	−	0.431773i
$804$	−15.3134	−	3.03610i	−0.540061	−	0.107075i
$805$	−12.5954	−	13.5968i	−0.443928	−	0.479225i
$806$	−0.767123	−	0.135264i	−0.0270207	−	0.00476449i
$807$	6.23402	−	0.963487i	0.219448	−	0.0339163i
$808$	−1.18854	+	3.26550i	−0.0418128	+	0.114880i
$809$	22.6335	−	13.0675i	0.795752	−	0.459427i	−0.0462318	−	0.998931i	$-0.514721\pi$
$809$	22.6335	−	13.0675i	0.795752	−	0.459427i	0.841983	+	0.539503i	$0.181388\pi$
$810$	−14.5036	+	1.30537i	−0.509605	+	0.0458659i
$811$			39.0940i			1.37278i	0.727236	+	0.686388i	$0.240805\pi$
$811$			39.0940i			1.37278i	−0.727236	+	0.686388i	$0.759195\pi$
$812$	−14.8258	−	7.61601i	−0.520282	−	0.267270i
$813$	−36.5940	+	29.4074i	−1.28341	+	1.03136i
$814$	26.3479	+	22.1085i	0.923492	+	0.774902i
$815$	−8.99161	−	7.54485i	−0.314962	−	0.264285i
$816$	20.5527	+	60.4223i	0.719487	+	2.11521i
$817$	9.46398	−	26.0021i	0.331103	−	0.909698i
$818$	−23.7845	−	41.1960i	−0.831607	−	1.44039i
$819$	20.9808	−	3.84382i	0.733128	−	0.134314i
$820$	−2.03240	+	3.52023i	−0.0709746	+	0.122932i
$821$	11.0335	+	13.1492i	0.385070	+	0.458909i	0.923408	−	0.383821i	$-0.125392\pi$
$821$	11.0335	+	13.1492i	0.385070	+	0.458909i	−0.538338	+	0.842729i	$0.680947\pi$
$822$	−8.80925	−	5.33807i	−0.307258	−	0.186187i
$823$	6.60641	−	37.4668i	0.230285	−	1.30601i	−0.622034	−	0.782990i	$-0.713694\pi$
$823$	6.60641	−	37.4668i	0.230285	−	1.30601i	0.852320	−	0.523021i	$-0.175195\pi$
$824$	13.4045	−	4.87886i	0.466969	−	0.169963i
$825$	−14.6493	+	24.1753i	−0.510024	+	0.841677i
$826$	−23.5127	−	12.0785i	−0.818111	−	0.420265i
$827$	26.3724	+	15.2261i	0.917059	+	0.529464i	0.882696	−	0.469945i	$-0.155726\pi$
$827$	26.3724	+	15.2261i	0.917059	+	0.529464i	0.0343635	+	0.999409i	$0.489060\pi$
$828$	25.8551	−	13.5003i	0.898528	−	0.469169i
$829$	38.2814	+	22.1018i	1.32957	+	0.767627i	0.985233	−	0.171220i	$-0.0547708\pi$
$829$	38.2814	+	22.1018i	1.32957	+	0.767627i	0.344336	+	0.938847i	$0.388104\pi$
$830$	10.1491	+	12.0952i	0.352279	+	0.419830i
$831$	5.20564	+	15.3040i	0.180582	+	0.530889i
$832$	−1.16079	−	3.18926i	−0.0402433	−	0.110568i
$833$	51.9696	−	5.11464i	1.80064	−	0.177212i
$834$	16.6275	−	42.8366i	0.575763	−	1.48331i
$835$	1.90729	+	10.8168i	0.0660045	+	0.374330i
$836$	11.7594	+	20.3678i	0.406706	+	0.704436i
$837$	−0.604935	−	0.576935i	−0.0209096	−	0.0199418i
$838$	−5.02783	−	2.90282i	−0.173683	−	0.100276i
$839$	21.2334	−	17.8169i	0.733058	−	0.615108i	−0.197906	−	0.980221i	$-0.563414\pi$
$839$	21.2334	−	17.8169i	0.733058	−	0.615108i	0.930963	+	0.365113i	$0.118970\pi$
$840$	−5.58590	+	0.155647i	−0.192732	+	0.00537033i
$841$	0.599397	−	3.39935i	0.0206689	−	0.117219i
$842$	13.3456	+	2.35318i	0.459919	+	0.0810961i
$843$	−19.2839	−	16.8903i	−0.664173	−	0.581731i
$844$	−3.60950	+	3.02873i	−0.124244	+	0.104253i
$845$	−5.18902			−0.178508
$846$	13.1540	+	17.0984i	0.452244	+	0.587856i
$847$	10.1105	−	4.25223i	0.347402	−	0.146108i
$848$	5.34158	−	14.6759i	0.183431	−	0.503972i
$849$	15.9679	−	26.3514i	0.548018	−	0.904377i
$850$	55.5107	+	9.78803i	1.90400	+	0.335727i
$851$	37.6824	+	6.64442i	1.29173	+	0.227768i
$852$	−6.01375	+	9.92430i	−0.206028	+	0.340001i
$853$	−4.95468	+	13.6129i	−0.169645	+	0.466096i	−0.995158	−	0.0982873i	$-0.968664\pi$
$853$	−4.95468	+	13.6129i	−0.169645	+	0.466096i	0.825513	+	0.564383i	$0.190886\pi$
$854$	5.09447	−	40.3856i	0.174329	−	1.38197i
$855$	−7.96506	−	10.3535i	−0.272399	−	0.354083i
$856$	−8.79654			−0.300660
$857$	−26.4306	+	22.1779i	−0.902853	+	0.757583i	−0.970746	−	0.240109i	$-0.922817\pi$
$857$	−26.4306	+	22.1779i	−0.902853	+	0.757583i	0.0678932	+	0.997693i	$0.478372\pi$
$858$	−24.5519	−	21.5044i	−0.838189	−	0.734148i
$859$	−17.0238	−	3.00176i	−0.580845	−	0.102419i	−0.124497	−	0.992220i	$-0.539732\pi$
$859$	−17.0238	−	3.00176i	−0.580845	−	0.102419i	−0.456348	+	0.889801i	$0.650843\pi$
$860$	−1.10916	+	6.29036i	−0.0378220	+	0.214499i
$861$	14.1755	−	8.71950i	0.483100	−	0.297160i
$862$	19.9595	−	16.7480i	0.679822	−	0.570438i
$863$	−20.1511	−	11.6343i	−0.685953	−	0.396035i	0.116141	−	0.993233i	$-0.462947\pi$
$863$	−20.1511	−	11.6343i	−0.685953	−	0.396035i	−0.802094	+	0.597198i	$0.796281\pi$
$864$	7.57878	−	31.2248i	0.257835	−	1.06229i
$865$	−4.46144	−	7.72744i	−0.151694	−	0.262741i
$866$	0.909782	+	5.15963i	0.0309157	+	0.175331i
$867$	24.2260	−	62.4123i	0.822759	−	2.11963i
$868$	0.360514	+	0.389179i	0.0122367	+	0.0132096i
$869$	15.5112	+	42.6167i	0.526181	+	1.44567i
$870$	−4.56166	−	13.4107i	−0.154655	−	0.454667i
$871$	12.4919	+	14.8873i	0.423272	+	0.504436i
$872$	−3.35308	−	1.93590i	−0.113550	−	0.0655579i
$873$	3.37589	−	1.76273i	0.114257	−	0.0596594i
$874$	59.0192	+	34.0748i	1.99636	+	1.15260i
$875$	−9.98106	+	19.4297i	−0.337421	+	0.656843i
$876$	10.2837	−	16.9709i	0.347455	−	0.573394i
$877$	−45.8556	+	16.6901i	−1.54843	+	0.563584i	−0.968050	−	0.250759i	$-0.919320\pi$
$877$	−45.8556	+	16.6901i	−1.54843	+	0.563584i	−0.580385	+	0.814343i	$0.697098\pi$
$878$	−11.3465	+	64.3493i	−0.382926	+	2.17168i
$879$	−14.0810	−	8.53253i	−0.474939	−	0.287795i
$880$	11.0960	+	13.2237i	0.374045	+	0.445770i
$881$	−17.2137	+	29.8150i	−0.579944	+	1.00449i	0.415541	+	0.909575i	$0.363592\pi$
$881$	−17.2137	+	29.8150i	−0.579944	+	1.00449i	−0.995485	+	0.0949185i	$0.969741\pi$
$882$	−33.7705	−	17.0645i	−1.13711	−	0.574591i
$883$	13.6856	+	23.7041i	0.460556	+	0.797707i	0.998989	−	0.0449619i	$-0.0143166\pi$
$883$	13.6856	+	23.7041i	0.460556	+	0.797707i	−0.538432	+	0.842669i	$0.680983\pi$
$884$	−8.54593	+	23.4797i	−0.287431	+	0.789709i
$885$	−2.77750	−	8.16553i	−0.0933648	−	0.274481i
$886$	−29.6256	−	24.8588i	−0.995291	−	0.835149i
$887$	−11.6760	−	9.79736i	−0.392043	−	0.328963i	0.425366	−	0.905022i	$-0.360146\pi$
$887$	−11.6760	−	9.79736i	−0.392043	−	0.328963i	−0.817408	+	0.576059i	$0.804590\pi$
$888$	8.99265	−	7.22659i	0.301774	−	0.242508i
$889$	−2.36647	−	3.67058i	−0.0793688	−	0.123107i
$890$		−	11.9671i		−	0.401138i
$891$	−9.14967	−	33.8095i	−0.306526	−	1.13266i
$892$	10.8752	−	6.27879i	0.364128	−	0.210230i
$893$	−6.61860	+	18.1845i	−0.221483	+	0.608520i
$894$	44.2141	−	6.83344i	1.47874	−	0.228544i
$895$	4.97406	+	0.877060i	0.166264	+	0.0293169i
$896$	7.89096	−	25.5079i	0.263618	−	0.852159i
$897$	−35.6161	−	7.06139i	−1.18919	−	0.235773i
$898$	−3.54949	−	1.29191i	−0.118448	−	0.0431116i
$899$	0.406579	−	0.704215i	0.0135602	−	0.0234869i
$900$	−11.5737	−	10.5788i	−0.385790	−	0.352627i
$901$	−20.4281	+	11.7942i	−0.680558	+	0.392920i
$902$	−23.9297	−	8.70971i	−0.796773	−	0.290002i
$903$	16.2456	−	20.4940i	0.540620	−	0.681997i
$904$	−16.4107	−	13.7702i	−0.545812	−	0.457990i
$905$	−1.55250	−	4.26545i	−0.0516067	−	0.141788i
$906$	67.0094	+	1.42034i	2.22624	+	0.0471877i
$907$	1.37639	+	7.80587i	0.0457021	+	0.259190i	0.999095	−	0.0425432i	$-0.0135460\pi$
$907$	1.37639	+	7.80587i	0.0457021	+	0.259190i	−0.953392	+	0.301733i	$0.902435\pi$
$908$	0.311808	+	0.540067i	0.0103477	+	0.0179228i
$909$	−7.67061	−	0.325321i	−0.254418	−	0.0107902i
$910$	−9.16468	−	6.95376i	−0.303806	−	0.230515i
$911$	54.9032	−	9.68092i	1.81902	−	0.320743i	0.842919	−	0.538040i	$-0.180835\pi$
$911$	54.9032	−	9.68092i	1.81902	−	0.320743i	0.976106	+	0.217297i	$0.0697239\pi$
$912$	39.2718	−	13.3583i	1.30042	−	0.442337i
$913$	−24.4109	+	29.0918i	−0.807883	+	0.962798i
$914$	17.0464	+	46.8347i	0.563846	+	1.54915i
$915$	10.3531	−	8.31983i	0.342262	−	0.275045i
$916$	17.6659	+	21.0534i	0.583699	+	0.695626i
$917$	−10.4202	−	7.90642i	−0.344106	−	0.261093i
$918$	−56.2474	+	41.4043i	−1.85644	+	1.36655i
$919$	−9.01295	+	15.6109i	−0.297310	+	0.514956i	−0.975520	−	0.219913i	$-0.929423\pi$
$919$	−9.01295	+	15.6109i	−0.297310	+	0.514956i	0.678210	+	0.734868i	$0.262756\pi$
$920$	8.93871	+	3.25343i	0.294701	+	0.107262i
$921$	−37.6126	+	30.2258i	−1.23938	+	0.995976i
$922$	45.8947	−	54.6951i	1.51146	−	1.80129i
$923$	13.5743	−	4.94065i	0.446804	−	0.162623i
$924$	4.46802	+	21.7741i	0.146987	+	0.716314i
$925$	−3.57192	−	20.2574i	−0.117444	−	0.666059i
$926$		−	41.2118i		−	1.35430i
$927$	19.2165	+	24.9789i	0.631154	+	0.820415i
$928$	31.2556			1.02602
$929$	14.6804	−	12.3184i	0.481650	−	0.404152i	−0.369373	−	0.929281i	$-0.620427\pi$
$929$	14.6804	−	12.3184i	0.481650	−	0.404152i	0.851022	+	0.525129i	$0.175983\pi$
$930$	−0.00955435	+	0.450758i	−0.000313299	+	0.0147809i
$931$	−3.32429	−	33.7779i	−0.108949	−	1.10703i
$932$	−5.70373	+	6.79744i	−0.186832	+	0.222658i
$933$	6.26496	+	3.79633i	0.205106	+	0.124286i
$934$	59.3382	−	10.4629i	1.94161	−	0.342358i
$935$		−	26.0721i		−	0.852650i
$936$	−8.67674	+	6.67511i	−0.283608	+	0.218183i
$937$	5.45017	−	3.14666i	0.178049	−	0.102797i	−0.408327	−	0.912836i	$-0.633888\pi$
$937$	5.45017	−	3.14666i	0.178049	−	0.102797i	0.586376	+	0.810039i	$0.300554\pi$
$938$	−1.69026	−	34.4322i	−0.0551889	−	1.12425i
$939$	−1.68889	+	0.574475i	−0.0551147	+	0.0187473i
$940$	0.775687	−	4.39914i	0.0253001	−	0.143484i
$941$	49.5167	−	18.0226i	1.61420	−	0.587520i	0.631934	−	0.775022i	$-0.282261\pi$
$941$	49.5167	−	18.0226i	1.61420	−	0.587520i	0.982264	+	0.187502i	$0.0600392\pi$
$942$	21.4111	+	26.6437i	0.697612	+	0.868097i
$943$	−27.8996	+	4.91946i	−0.908537	+	0.160200i
$944$	27.3890			0.891436
$945$	−4.05351	−	11.6614i	−0.131861	−	0.379344i
$946$	−40.0162			−1.30104
$947$	1.09020	−	0.192231i	0.0354267	−	0.00624668i	−0.155907	−	0.987772i	$-0.549830\pi$
$947$	1.09020	−	0.192231i	0.0354267	−	0.00624668i	0.191333	+	0.981525i	$0.438719\pi$
$948$	−24.8614	+	3.84242i	−0.807462	+	0.124796i
$949$	−23.2126	+	8.44869i	−0.753513	+	0.274256i
$950$	6.36178	−	36.0794i	0.206403	−	1.17057i
$951$	−33.0463	−	28.9444i	−1.07160	−	0.938586i
$952$	−22.5258	+	14.5226i	−0.730065	+	0.470681i
$953$	−1.04062	+	0.600799i	−0.0337088	+	0.0194618i	−0.516760	−	0.856130i	$-0.672862\pi$
$953$	−1.04062	+	0.600799i	−0.0337088	+	0.0194618i	0.483051	+	0.875592i	$0.339529\pi$
$954$	17.0758	+	0.724209i	0.552850	+	0.0234471i
$955$		−	1.26589i		−	0.0409632i
$956$	−21.2828	+	3.75273i	−0.688335	+	0.121372i
$957$	29.8607	−	16.4064i	0.965260	−	0.530343i
$958$	−17.2380	+	20.5434i	−0.556933	+	0.663727i
$959$	2.58079	−	8.34254i	0.0833382	−	0.269395i
$960$	−1.72166	+	0.945931i	−0.0555663	+	0.0305298i
$961$	23.7276	−	19.9098i	0.765405	−	0.642251i
$962$	23.7503			0.765739
$963$	−5.86712	−	18.5275i	−0.189065	−	0.597041i
$964$		−	29.9550i		−	0.964787i
$965$	−2.40184	−	13.6215i	−0.0773181	−	0.438493i
$966$	42.7593	+	48.1676i	1.37576	+	1.54977i
$967$	31.5203	−	11.4724i	1.01362	−	0.368929i	0.218801	−	0.975770i	$-0.429786\pi$
$967$	31.5203	−	11.4724i	1.01362	−	0.368929i	0.794824	+	0.606841i	$0.207563\pi$
$968$	−3.61846	+	4.31231i	−0.116302	+	0.138603i
$969$	−58.4061	−	22.6710i	−1.87628	−	0.728297i
$970$	−1.93015	−	0.702519i	−0.0619735	−	0.0225565i
$971$	−9.48429	+	16.4273i	−0.304365	+	0.527176i	−0.977120	−	0.212690i	$-0.931778\pi$
$971$	−9.48429	+	16.4273i	−0.304365	+	0.527176i	0.672755	+	0.739866i	$0.265111\pi$
$972$	19.3831	−	1.33115i	0.621713	−	0.0426966i
$973$	38.6502	+	4.87556i	1.23907	+	0.156303i
$974$	−25.4745	−	30.3593i	−0.816255	−	0.972775i
$975$	2.98137	+	19.2902i	0.0954801	+	0.617782i
$976$	14.4253	+	39.6332i	0.461743	+	1.26863i
$977$	−7.71135	+	9.19003i	−0.246708	+	0.294015i	−0.875160	−	0.483833i	$-0.839244\pi$
$977$	−7.71135	+	9.19003i	−0.246708	+	0.294015i	0.628452	+	0.777848i	$0.283689\pi$
$978$	30.6843	+	26.8756i	0.981177	+	0.859387i
$979$	28.3464	−	4.99824i	0.905955	−	0.159744i
$980$	2.10966	+	7.54542i	0.0673907	+	0.241030i
$981$	1.84101	−	8.35356i	0.0587790	−	0.266709i
$982$	−37.3492	−	64.6907i	−1.19186	−	2.06436i
$983$	1.06435	+	6.03623i	0.0339475	+	0.192526i	0.997065	−	0.0765537i	$-0.0243917\pi$
$983$	1.06435	+	6.03623i	0.0339475	+	0.192526i	−0.963118	+	0.269079i	$0.913281\pi$
$984$	−4.42656	+	7.30501i	−0.141114	+	0.232875i
$985$	3.99053	+	10.9639i	0.127149	+	0.349339i
$986$	−52.0448	−	43.6707i	−1.65744	−	1.39076i
$987$	−11.3613	+	14.3324i	−0.361634	+	0.456205i
$988$	15.2608	+	5.55447i	0.485510	+	0.176711i
$989$	−38.5533	+	22.2588i	−1.22592	+	0.707787i
$990$	−10.1302	+	15.9450i	−0.321957	+	0.506766i
$991$	−7.91453	+	13.7084i	−0.251413	+	0.435460i	−0.963915	−	0.266210i	$-0.914229\pi$
$991$	−7.91453	+	13.7084i	−0.251413	+	0.435460i	0.712502	+	0.701670i	$0.247562\pi$
$992$	−0.934821	−	0.340247i	−0.0296806	−	0.0108029i
$993$	−22.6859	+	25.9009i	−0.719916	+	0.821941i
$994$	−24.4801	−	7.57300i	−0.776461	−	0.240201i
$995$	−10.2842	−	1.81339i	−0.326032	−	0.0574883i
$996$	−13.1957	−	16.4206i	−0.418123	−	0.520305i
$997$	11.2427	−	30.8891i	0.356061	−	0.978269i	−0.624322	−	0.781167i	$-0.714625\pi$
$997$	11.2427	−	30.8891i	0.356061	−	0.978269i	0.980383	−	0.197102i	$-0.0631530\pi$
$998$	−40.2974	+	23.2657i	−1.27559	+	0.736464i
$999$	21.2187	+	14.1206i	0.671332	+	0.446755i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.ba.a.5.18	✓	132
3.2	odd	2		567.2.ba.a.530.5		132
7.3	odd	6		189.2.bd.a.59.5	yes	132
21.17	even	6		567.2.bd.a.206.18		132
27.11	odd	18		189.2.bd.a.173.5	yes	132
27.16	even	9		567.2.bd.a.278.18		132
189.38	even	18	inner	189.2.ba.a.38.18	yes	132
189.178	odd	18		567.2.ba.a.521.5		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.5.18	✓	132	1.1	even	1	trivial
189.2.ba.a.38.18	yes	132	189.38	even	18	inner
189.2.bd.a.59.5	yes	132	7.3	odd	6
189.2.bd.a.173.5	yes	132	27.11	odd	18
567.2.ba.a.521.5		132	189.178	odd	18
567.2.ba.a.530.5		132	3.2	odd	2
567.2.bd.a.206.18		132	21.17	even	6
567.2.bd.a.278.18		132	27.16	even	9

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.ba (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.77439 - 0.312873i) q^{2} +(0.626754 - 1.61468i) q^{3} +(1.17119 - 0.426279i) q^{4} +(-0.155940 + 0.884381i) q^{5} +(0.606919 - 3.06116i) q^{6} +(2.64257 - 0.129722i) q^{7} +(-1.17597 + 0.678945i) q^{8} +(-2.21436 - 2.02401i) q^{9} +O(q^{10})\)	\(q+(1.77439 - 0.312873i) q^{2} +(0.626754 - 1.61468i) q^{3} +(1.17119 - 0.426279i) q^{4} +(-0.155940 + 0.884381i) q^{5} +(0.606919 - 3.06116i) q^{6} +(2.64257 - 0.129722i) q^{7} +(-1.17597 + 0.678945i) q^{8} +(-2.21436 - 2.02401i) q^{9} +1.61803i q^{10} +(-3.83262 + 0.675794i) q^{11} +(0.0457470 - 2.15827i) q^{12} +(-1.72738 + 2.05861i) q^{13} +(4.64837 - 1.05697i) q^{14} +(1.33025 + 0.806082i) q^{15} +(-3.78373 + 3.17493i) q^{16} +7.46010 q^{17} +(-4.56240 - 2.89857i) q^{18} -4.84873i q^{19} +(0.194357 + 1.10225i) q^{20} +(1.44678 - 4.34820i) q^{21} +(-6.58912 + 2.39825i) q^{22} +(-5.01423 + 5.97573i) q^{23} +(0.359234 + 2.32434i) q^{24} +(3.94065 + 1.43428i) q^{25} +(-2.42097 + 4.19324i) q^{26} +(-4.65598 + 2.30691i) q^{27} +(3.03966 - 1.27840i) q^{28} +(-3.24899 - 3.87199i) q^{29} +(2.61259 + 1.01411i) q^{30} +(0.0550233 + 0.151175i) q^{31} +(-3.97480 + 4.73698i) q^{32} +(-1.31092 + 6.61199i) q^{33} +(13.2371 - 2.33407i) q^{34} +(-0.297359 + 2.35727i) q^{35} +(-3.45623 - 1.42657i) q^{36} +(-2.45256 - 4.24796i) q^{37} +(-1.51704 - 8.60355i) q^{38} +(2.24135 + 4.07940i) q^{39} +(-0.417065 - 1.14588i) q^{40} +(2.78205 + 2.33441i) q^{41} +(1.20672 - 8.16806i) q^{42} +(5.36266 + 1.95185i) q^{43} +(-4.20065 + 2.42525i) q^{44} +(2.13530 - 1.64271i) q^{45} +(-7.02757 + 12.1721i) q^{46} +(-3.75035 - 1.36502i) q^{47} +(2.75501 + 8.09940i) q^{48} +(6.96634 - 0.685599i) q^{49} +(7.44101 + 1.31205i) q^{50} +(4.67565 - 12.0457i) q^{51} +(-1.14555 + 3.14737i) q^{52} +(-2.73831 + 1.58096i) q^{53} +(-7.53976 + 5.55010i) q^{54} -3.49487i q^{55} +(-3.01950 + 1.94671i) q^{56} +(-7.82913 - 3.03896i) q^{57} +(-6.97641 - 5.85391i) q^{58} +(-4.24780 - 3.56433i) q^{59} +(1.90160 + 0.377018i) q^{60} +(2.92051 - 8.02404i) q^{61} +(0.144931 + 0.251029i) q^{62} +(-6.11415 - 5.06134i) q^{63} +(-0.631470 + 1.09374i) q^{64} +(-1.55123 - 1.84868i) q^{65} +(-0.257373 + 12.1424i) q^{66} +(1.25577 - 7.12184i) q^{67} +(8.73721 - 3.18008i) q^{68} +(6.50618 + 11.8417i) q^{69} +(0.209894 + 4.27575i) q^{70} +(-4.65524 - 2.68770i) q^{71} +(3.97820 + 0.876742i) q^{72} +(7.96064 + 4.59608i) q^{73} +(-5.68088 - 6.77020i) q^{74} +(4.78572 - 5.46393i) q^{75} +(-2.06691 - 5.67879i) q^{76} +(-10.0403 + 2.28301i) q^{77} +(5.25337 + 6.53720i) q^{78} +(-2.02358 - 11.4763i) q^{79} +(-2.21781 - 3.84136i) q^{80} +(0.806764 + 8.96377i) q^{81} +(5.66681 + 3.27174i) q^{82} +(7.47526 - 6.27249i) q^{83} +(-0.159085 - 5.70930i) q^{84} +(-1.16333 + 6.59757i) q^{85} +(10.1261 + 1.78551i) q^{86} +(-8.28833 + 2.81927i) q^{87} +(4.04820 - 3.39685i) q^{88} -7.39610 q^{89} +(3.27490 - 3.58289i) q^{90} +(-4.29768 + 5.66410i) q^{91} +(-3.32530 + 9.13618i) q^{92} +(0.278585 + 0.00590493i) q^{93} +(-7.08167 - 1.24869i) q^{94} +(4.28812 + 0.756112i) q^{95} +(5.15747 + 9.38694i) q^{96} +(-0.434182 + 1.19291i) q^{97} +(12.1465 - 3.39610i) q^{98} +(9.85460 + 6.26080i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22} - 6 q^{23} - 9 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} + 51 q^{30} - 9 q^{31} + 3 q^{32} - 9 q^{33} - 18 q^{34} + 18 q^{35} + 3 q^{37} - 99 q^{38} - 36 q^{39} - 54 q^{40} - 45 q^{42} - 12 q^{43} - 9 q^{44} - 9 q^{45} + 3 q^{46} + 45 q^{47} - 24 q^{49} - 9 q^{50} - 48 q^{51} - 9 q^{52} - 45 q^{53} + 171 q^{54} + 3 q^{56} - 3 q^{58} + 36 q^{59} + 57 q^{60} - 9 q^{61} - 99 q^{62} - 33 q^{63} + 18 q^{64} + 69 q^{65} - 9 q^{66} - 3 q^{67} + 36 q^{68} + 108 q^{69} + 66 q^{70} + 18 q^{71} - 129 q^{72} - 9 q^{73} + 75 q^{74} + 36 q^{75} + 36 q^{76} + 15 q^{77} + 66 q^{78} - 21 q^{79} + 72 q^{80} - 33 q^{81} - 18 q^{82} - 90 q^{83} - 120 q^{84} + 9 q^{85} - 105 q^{86} - 54 q^{87} - 63 q^{88} - 18 q^{89} + 81 q^{90} + 6 q^{91} + 150 q^{92} + 21 q^{93} - 9 q^{94} + 45 q^{95} - 81 q^{96} + 27 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more