LMFDB - Embedded newform 756.2.bt.a.367.128

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(103,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 14, 15]))

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

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

chi := DirichletCharacter("756.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bt (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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$840$
Relative dimension:	$140$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			367.128
Character	$\chi$	$=$	756.367
Dual form			756.2.bt.a.103.128

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.35760 + 0.396119i) q^{2} +(0.696355 - 1.58590i) q^{3} +(1.68618 + 1.07554i) q^{4} +(0.824097 - 0.145310i) q^{5} +(1.57358 - 1.87719i) q^{6} +(2.46179 + 0.969313i) q^{7} +(1.86312 + 2.12809i) q^{8} +(-2.03018 - 2.20870i) q^{9} +O(q^{10})$	\(q+(1.35760 + 0.396119i) q^{2} +(0.696355 - 1.58590i) q^{3} +(1.68618 + 1.07554i) q^{4} +(0.824097 - 0.145310i) q^{5} +(1.57358 - 1.87719i) q^{6} +(2.46179 + 0.969313i) q^{7} +(1.86312 + 2.12809i) q^{8} +(-2.03018 - 2.20870i) q^{9} +(1.17636 + 0.129166i) q^{10} +(-0.278983 - 0.0491922i) q^{11} +(2.87989 - 1.92516i) q^{12} +(1.31006 + 1.56127i) q^{13} +(2.95818 + 2.29111i) q^{14} +(0.343415 - 1.40813i) q^{15} +(1.68641 + 3.62712i) q^{16} -4.81084i q^{17} +(-1.88127 - 3.80274i) q^{18} -8.59082 q^{19} +(1.54586 + 0.641333i) q^{20} +(3.25152 - 3.22918i) q^{21} +(-0.359262 - 0.177294i) q^{22} +(2.88728 + 3.44093i) q^{23} +(4.67234 - 1.47282i) q^{24} +(-4.04044 + 1.47060i) q^{25} +(1.16010 + 2.63853i) q^{26} +(-4.91652 + 1.68163i) q^{27} +(3.10849 + 4.28221i) q^{28} +(5.96928 + 5.00882i) q^{29} +(1.02401 - 1.77564i) q^{30} +(-3.68103 - 1.33978i) q^{31} +(0.852701 + 5.59222i) q^{32} +(-0.272285 + 0.408184i) q^{33} +(1.90566 - 6.53121i) q^{34} +(2.16961 + 0.441083i) q^{35} +(-1.04769 - 5.90782i) q^{36} +(3.74603 - 6.48831i) q^{37} +(-11.6629 - 3.40298i) q^{38} +(3.38829 - 0.990433i) q^{39} +(1.84463 + 1.48302i) q^{40} +(-2.95032 - 3.51605i) q^{41} +(5.69342 - 3.09596i) q^{42} +(-2.84340 - 7.81219i) q^{43} +(-0.417507 - 0.383005i) q^{44} +(-1.99401 - 1.52518i) q^{45} +(2.55677 + 5.81512i) q^{46} +(-0.125817 + 0.0457938i) q^{47} +(6.92661 - 0.148711i) q^{48} +(5.12086 + 4.77250i) q^{49} +(-6.06786 + 0.396000i) q^{50} +(-7.62952 - 3.35005i) q^{51} +(0.529783 + 4.04162i) q^{52} +(0.319577 - 0.553524i) q^{53} +(-7.34081 + 0.335460i) q^{54} -0.237057 q^{55} +(2.52384 + 7.04487i) q^{56} +(-5.98226 + 13.6242i) q^{57} +(6.11984 + 9.16454i) q^{58} +(5.96567 - 5.00579i) q^{59} +(2.09356 - 2.00499i) q^{60} +(0.0771396 + 0.211939i) q^{61} +(-4.46666 - 3.27702i) q^{62} +(-2.85696 - 7.40525i) q^{63} +(-1.05755 + 7.92979i) q^{64} +(1.30649 + 1.09627i) q^{65} +(-0.531345 + 0.446296i) q^{66} +(-11.0538 + 1.94908i) q^{67} +(5.17427 - 8.11194i) q^{68} +(7.46755 - 2.18284i) q^{69} +(2.77075 + 1.45824i) q^{70} +(-11.9820 + 6.91779i) q^{71} +(0.917852 - 8.43549i) q^{72} +(9.86810 - 5.69735i) q^{73} +(7.65577 - 7.32469i) q^{74} +(-0.481352 + 7.43181i) q^{75} +(-14.4857 - 9.23981i) q^{76} +(-0.639115 - 0.391523i) q^{77} +(4.99229 - 0.00244993i) q^{78} +(-7.57594 - 1.33584i) q^{79} +(1.91682 + 2.74405i) q^{80} +(-0.756743 + 8.96813i) q^{81} +(-2.61259 - 5.94208i) q^{82} +(3.79339 + 3.18303i) q^{83} +(8.95578 - 1.94783i) q^{84} +(-0.699065 - 3.96460i) q^{85} +(-0.765665 - 11.7322i) q^{86} +(12.1002 - 5.97879i) q^{87} +(-0.415093 - 0.685352i) q^{88} +0.953752i q^{89} +(-2.10293 - 2.86046i) q^{90} +(1.71174 + 5.11339i) q^{91} +(1.16760 + 8.90742i) q^{92} +(-4.68807 + 4.90479i) q^{93} +(-0.188950 + 0.0123312i) q^{94} +(-7.07967 + 1.24834i) q^{95} +(9.46250 + 2.54187i) q^{96} +(0.471632 + 1.29580i) q^{97} +(5.06163 + 8.50764i) q^{98} +(0.457734 + 0.716059i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9}+O(q^{10}) $ 840 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9	$ 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9} - 9 q^{12} - 21 q^{14} - 3 q^{16} - 3 q^{18} - 12 q^{21} - 12 q^{22} - 9 q^{24} - 6 q^{25} - 18 q^{26} - 12 q^{28} - 36 q^{29} - 39 q^{30} + 27 q^{32} - 18 q^{33} + 18 q^{34} + 18 q^{36} + 6 q^{37} - 99 q^{38} + 36 q^{40} + 9 q^{42} + 3 q^{44} - 18 q^{45} + 3 q^{46} - 12 q^{49} + 3 q^{50} - 9 q^{52} - 12 q^{53} - 135 q^{54} + 15 q^{56} - 42 q^{57} - 3 q^{58} - 33 q^{60} - 18 q^{61} - 99 q^{62} - 6 q^{64} + 18 q^{65} - 9 q^{66} - 54 q^{68} + 72 q^{69} - 36 q^{70} - 111 q^{72} - 18 q^{73} + 93 q^{74} - 36 q^{76} - 36 q^{77} + 6 q^{78} - 18 q^{80} - 30 q^{81} - 18 q^{82} + 84 q^{84} + 6 q^{85} + 135 q^{86} - 51 q^{88} + 81 q^{90} + 48 q^{92} - 6 q^{93} - 9 q^{94} - 9 q^{96} - 117 q^{98}+O(q^{100}) $ 840 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9 - 9 * q^12 - 21 * q^14 - 3 * q^16 - 3 * q^18 - 12 * q^21 - 12 * q^22 - 9 * q^24 - 6 * q^25 - 18 * q^26 - 12 * q^28 - 36 * q^29 - 39 * q^30 + 27 * q^32 - 18 * q^33 + 18 * q^34 + 18 * q^36 + 6 * q^37 - 99 * q^38 + 36 * q^40 + 9 * q^42 + 3 * q^44 - 18 * q^45 + 3 * q^46 - 12 * q^49 + 3 * q^50 - 9 * q^52 - 12 * q^53 - 135 * q^54 + 15 * q^56 - 42 * q^57 - 3 * q^58 - 33 * q^60 - 18 * q^61 - 99 * q^62 - 6 * q^64 + 18 * q^65 - 9 * q^66 - 54 * q^68 + 72 * q^69 - 36 * q^70 - 111 * q^72 - 18 * q^73 + 93 * q^74 - 36 * q^76 - 36 * q^77 + 6 * q^78 - 18 * q^80 - 30 * q^81 - 18 * q^82 + 84 * q^84 + 6 * q^85 + 135 * q^86 - 51 * q^88 + 81 * q^90 + 48 * q^92 - 6 * q^93 - 9 * q^94 - 9 * q^96 - 117 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	1.35760	+	0.396119i	0.959971	+	0.280098i
$2$	1.35760	+	0.396119i	0.959971	+	0.280098i
$3$	0.696355	−	1.58590i	0.402041	−	0.915622i
$3$	0.696355	−	1.58590i	0.402041	−	0.915622i
$4$	1.68618	+	1.07554i	0.843090	+	0.537772i
$5$	0.824097	−	0.145310i	0.368547	−	0.0649848i	0.0136925	−	0.999906i	$-0.495641\pi$
$5$	0.824097	−	0.145310i	0.368547	−	0.0649848i	0.354855	+	0.934921i	$0.384530\pi$
$6$	1.57358	−	1.87719i	0.642412	−	0.766360i
$7$	2.46179	+	0.969313i	0.930471	+	0.366366i
$7$	2.46179	+	0.969313i	0.930471	+	0.366366i
$8$	1.86312	+	2.12809i	0.658713	+	0.752394i
$9$	−2.03018	−	2.20870i	−0.676726	−	0.736235i
$10$	1.17636	+	0.129166i	0.371997	+	0.0408458i
$11$	−0.278983	−	0.0491922i	−0.0841164	−	0.0148320i	0.131432	−	0.991325i	$-0.458043\pi$
$11$	−0.278983	−	0.0491922i	−0.0841164	−	0.0148320i	−0.215548	+	0.976493i	$0.569154\pi$
$12$	2.87989	−	1.92516i	0.831353	−	0.555745i
$13$	1.31006	+	1.56127i	0.363346	+	0.433019i	0.916484	−	0.400071i	$-0.131014\pi$
$13$	1.31006	+	1.56127i	0.363346	+	0.433019i	−0.553138	+	0.833089i	$0.686570\pi$
$14$	2.95818	+	2.29111i	0.790607	+	0.612324i
$15$	0.343415	−	1.40813i	0.0886695	−	0.363576i
$16$	1.68641	+	3.62712i	0.421602	+	0.906781i
$17$		−	4.81084i		−	1.16680i	−0.812185	−	0.583400i	$-0.801722\pi$
$17$		−	4.81084i		−	1.16680i	0.812185	−	0.583400i	$-0.198278\pi$
$18$	−1.88127	−	3.80274i	−0.443420	−	0.896314i
$19$	−8.59082			−1.97087			−0.985435	−	0.170055i	$-0.945606\pi$
$19$	−8.59082			−1.97087			−0.985435	+	0.170055i	$0.945606\pi$
$20$	1.54586	+	0.641333i	0.345666	+	0.143407i
$21$	3.25152	−	3.22918i	0.709540	−	0.704665i
$22$	−0.359262	−	0.177294i	−0.0765950	−	0.0377992i
$23$	2.88728	+	3.44093i	0.602039	+	0.717483i	0.977872	−	0.209205i	$-0.0670876\pi$
$23$	2.88728	+	3.44093i	0.602039	+	0.717483i	−0.375832	+	0.926688i	$0.622643\pi$
$24$	4.67234	−	1.47282i	0.953738	−	0.300639i
$25$	−4.04044	+	1.47060i	−0.808089	+	0.294120i
$26$	1.16010	+	2.63853i	0.227514	+	0.517458i
$27$	−4.91652	+	1.68163i	−0.946184	+	0.323629i
$28$	3.10849	+	4.28221i	0.587449	+	0.809261i
$29$	5.96928	+	5.00882i	1.10847	+	0.930115i	0.997965	−	0.0637608i	$-0.0203095\pi$
$29$	5.96928	+	5.00882i	1.10847	+	0.930115i	0.110503	+	0.993876i	$0.464754\pi$
$30$	1.02401	−	1.77564i	0.186957	−	0.324187i
$31$	−3.68103	−	1.33978i	−0.661132	−	0.240632i	−0.0104068	−	0.999946i	$-0.503313\pi$
$31$	−3.68103	−	1.33978i	−0.661132	−	0.240632i	−0.650725	+	0.759314i	$0.725535\pi$
$32$	0.852701	+	5.59222i	0.150738	+	0.988574i
$33$	−0.272285	+	0.408184i	−0.0473987	+	0.0710558i
$34$	1.90566	−	6.53121i	0.326818	−	1.12009i
$35$	2.16961	+	0.441083i	0.366731	+	0.0745567i
$36$	−1.04769	−	5.90782i	−0.174615	−	0.984637i
$37$	3.74603	−	6.48831i	0.615843	−	1.06667i	−0.374392	−	0.927270i	$-0.622149\pi$
$37$	3.74603	−	6.48831i	0.615843	−	1.06667i	0.990236	−	0.139402i	$-0.0445180\pi$
$38$	−11.6629	−	3.40298i	−1.89198	−	0.552037i
$39$	3.38829	−	0.990433i	0.542561	−	0.158596i
$40$	1.84463	+	1.48302i	0.291661	+	0.234486i
$41$	−2.95032	−	3.51605i	−0.460762	−	0.549115i	0.484771	−	0.874641i	$-0.338903\pi$
$41$	−2.95032	−	3.51605i	−0.460762	−	0.549115i	−0.945533	+	0.325526i	$0.894458\pi$
$42$	5.69342	−	3.09596i	0.878513	−	0.477718i
$43$	−2.84340	−	7.81219i	−0.433615	−	1.19135i	−0.943578	−	0.331151i	$-0.892563\pi$
$43$	−2.84340	−	7.81219i	−0.433615	−	1.19135i	0.509963	−	0.860197i	$-0.329659\pi$
$44$	−0.417507	−	0.383005i	−0.0629415	−	0.0577402i
$45$	−1.99401	−	1.52518i	−0.297250	−	0.227360i
$46$	2.55677	+	5.81512i	0.376975	+	0.857393i
$47$	−0.125817	+	0.0457938i	−0.0183523	+	0.00667971i	−0.351180	−	0.936308i	$-0.614219\pi$
$47$	−0.125817	+	0.0457938i	−0.0183523	+	0.00667971i	0.332828	+	0.942988i	$0.391997\pi$
$48$	6.92661	−	0.148711i	0.999770	−	0.0214646i
$49$	5.12086	+	4.77250i	0.731552	+	0.681786i
$50$	−6.06786	+	0.396000i	−0.858124	+	0.0560028i
$51$	−7.62952	−	3.35005i	−1.06835	−	0.469101i
$52$	0.529783	+	4.04162i	0.0734677	+	0.560471i
$53$	0.319577	−	0.553524i	0.0438973	−	0.0760324i	−0.843242	−	0.537534i	$-0.819356\pi$
$53$	0.319577	−	0.553524i	0.0438973	−	0.0760324i	0.887139	+	0.461502i	$0.152689\pi$
$54$	−7.34081	+	0.335460i	−0.998957	+	0.0456504i
$55$	−0.237057			−0.0319647
$56$	2.52384	+	7.04487i	0.337262	+	0.941411i
$57$	−5.98226	+	13.6242i	−0.792370	+	1.80457i
$58$	6.11984	+	9.16454i	0.803574	+	1.20336i
$59$	5.96567	−	5.00579i	0.776664	−	0.651698i	−0.165742	−	0.986169i	$-0.553002\pi$
$59$	5.96567	−	5.00579i	0.776664	−	0.651698i	0.942406	+	0.334471i	$0.108558\pi$
$60$	2.09356	−	2.00499i	0.270278	−	0.258844i
$61$	0.0771396	+	0.211939i	0.00987672	+	0.0271361i	0.944533	−	0.328416i	$-0.106515\pi$
$61$	0.0771396	+	0.211939i	0.00987672	+	0.0271361i	−0.934656	+	0.355553i	$0.884293\pi$
$62$	−4.46666	−	3.27702i	−0.567267	−	0.416182i
$63$	−2.85696	−	7.40525i	−0.359943	−	0.932974i
$64$	−1.05755	+	7.92979i	−0.132194	+	0.991224i
$65$	1.30649	+	1.09627i	0.162050	+	0.135976i
$66$	−0.531345	+	0.446296i	−0.0654040	+	0.0549352i
$67$	−11.0538	+	1.94908i	−1.35043	+	0.238118i	−0.801624	−	0.597829i	$-0.796030\pi$
$67$	−11.0538	+	1.94908i	−1.35043	+	0.238118i	−0.548811	+	0.835947i	$0.684919\pi$
$68$	5.17427	−	8.11194i	0.627473	−	0.983717i
$69$	7.46755	−	2.18284i	0.898987	−	0.262783i
$70$	2.77075	+	1.45824i	0.331168	+	0.174293i
$71$	−11.9820	+	6.91779i	−1.42200	+	0.820991i	−0.996470	−	0.0839538i	$-0.973245\pi$
$71$	−11.9820	+	6.91779i	−1.42200	+	0.820991i	−0.425529	+	0.904945i	$0.639912\pi$
$72$	0.917852	−	8.43549i	0.108170	−	0.994132i
$73$	9.86810	−	5.69735i	1.15497	−	0.666825i	0.204880	−	0.978787i	$-0.434320\pi$
$73$	9.86810	−	5.69735i	1.15497	−	0.666825i	0.950094	+	0.311962i	$0.100986\pi$
$74$	7.65577	−	7.32469i	0.889965	−	0.851478i
$75$	−0.481352	+	7.43181i	−0.0555817	+	0.858152i
$76$	−14.4857	−	9.23981i	−1.66162	−	1.05988i
$77$	−0.639115	−	0.391523i	−0.0728340	−	0.0446181i
$78$	4.99229	−	0.00244993i	0.565266	−	0.000277400i
$79$	−7.57594	−	1.33584i	−0.852360	−	0.150294i	−0.269634	−	0.962963i	$-0.586903\pi$
$79$	−7.57594	−	1.33584i	−0.852360	−	0.150294i	−0.582726	+	0.812669i	$0.698014\pi$
$80$	1.91682	+	2.74405i	0.214307	+	0.306794i
$81$	−0.756743	+	8.96813i	−0.0840826	+	0.996459i
$82$	−2.61259	−	5.94208i	−0.288512	−	0.656193i
$83$	3.79339	+	3.18303i	0.416378	+	0.349383i	0.826783	−	0.562520i	$-0.190168\pi$
$83$	3.79339	+	3.18303i	0.416378	+	0.349383i	−0.410405	+	0.911903i	$0.634613\pi$
$84$	8.95578	−	1.94783i	0.977156	−	0.212525i
$85$	−0.699065	−	3.96460i	−0.0758243	−	0.430021i
$86$	−0.765665	−	11.7322i	−0.0825637	−	1.26511i
$87$	12.1002	−	5.97879i	1.29728	−	0.640993i
$88$	−0.415093	−	0.685352i	−0.0442491	−	0.0730588i
$89$			0.953752i			0.101098i	0.998722	+	0.0505488i	$0.0160970\pi$
$89$			0.953752i			0.101098i	−0.998722	+	0.0505488i	$0.983903\pi$
$90$	−2.10293	−	2.86046i	−0.221668	−	0.301518i
$91$	1.71174	+	5.11339i	0.179439	+	0.536029i
$92$	1.16760	+	8.90742i	0.121731	+	0.928662i
$93$	−4.68807	+	4.90479i	−0.486130	+	0.508603i
$94$	−0.188950	+	0.0123312i	−0.0194887	+	0.00127187i
$95$	−7.07967	+	1.24834i	−0.726358	+	0.128077i
$96$	9.46250	+	2.54187i	0.965762	+	0.259428i
$97$	0.471632	+	1.29580i	0.0478870	+	0.131568i	0.961331	−	0.275397i	$-0.0888092\pi$
$97$	0.471632	+	1.29580i	0.0478870	+	0.131568i	−0.913444	+	0.406965i	$0.866587\pi$
$98$	5.06163	+	8.50764i	0.511302	+	0.859401i
$99$	0.457734	+	0.716059i	0.0460040	+	0.0719666i
$100$	−8.39461	−	1.86598i	−0.839461	−	0.186598i
$101$	−5.47709	+	6.52735i	−0.544991	+	0.649495i	−0.966299	−	0.257423i	$-0.917127\pi$
$101$	−5.47709	+	6.52735i	−0.544991	+	0.649495i	0.421308	+	0.906918i	$0.361571\pi$
$102$	−9.03086	−	7.57024i	−0.894188	−	0.749565i
$103$	−0.875709	−	4.96639i	−0.0862862	−	0.489353i	−0.997072	−	0.0764733i	$-0.975634\pi$
$103$	−0.875709	−	4.96639i	−0.0862862	−	0.489353i	0.910785	−	0.412880i	$-0.135477\pi$
$104$	−0.881723	+	5.69677i	−0.0864601	+	0.558614i
$105$	2.21033	−	3.13364i	0.215706	−	0.305812i
$106$	0.653121	−	0.624876i	0.0634367	−	0.0606934i
$107$	−7.57672	+	4.37442i	−0.732469	+	0.422891i	−0.819325	−	0.573330i	$-0.805651\pi$
$107$	−7.57672	+	4.37442i	−0.732469	+	0.422891i	0.0868559	+	0.996221i	$0.472318\pi$
$108$	−10.0988	−	2.45241i	−0.971757	−	0.235983i
$109$	−8.09892	+	14.0277i	−0.775736	+	1.34361i	0.158643	+	0.987336i	$0.449288\pi$
$109$	−8.09892	+	14.0277i	−0.775736	+	1.34361i	−0.934380	+	0.356279i	$0.884045\pi$
$110$	−0.321829	−	0.0939026i	−0.0306852	−	0.00895327i
$111$	−7.68127	−	10.4590i	−0.729074	−	0.992725i
$112$	0.635766	+	10.5639i	0.0600742	+	0.998194i
$113$	13.5853	+	4.94465i	1.27800	+	0.465154i	0.889770	−	0.456409i	$-0.150865\pi$
$113$	13.5853	+	4.94465i	1.27800	+	0.465154i	0.388229	+	0.921563i	$0.373087\pi$
$114$	−13.5183	+	16.1266i	−1.26611	+	1.51039i
$115$	2.87940	+	2.41610i	0.268505	+	0.225303i
$116$	4.67807	+	14.8660i	0.434348	+	1.38027i
$117$	0.788724	−	6.06320i	0.0729176	−	0.560543i
$118$	10.0819	−	4.43277i	0.928114	−	0.408069i
$119$	4.66321	−	11.8433i	0.427476	−	1.08567i
$120$	3.63645	−	1.89269i	0.331961	−	0.172778i
$121$	−10.2612	−	3.73477i	−0.932837	−	0.339525i
$122$	0.0207720	+	0.318286i	0.00188061	+	0.0288163i
$123$	−7.63058	+	2.23050i	−0.688026	+	0.201117i
$124$	−4.76587	−	6.21822i	−0.427988	−	0.558413i
$125$	−6.73951	+	3.89106i	−0.602801	+	0.348027i
$126$	−0.945261	−	11.1851i	−0.0842106	−	0.996448i
$127$	14.4730	+	8.35602i	1.28428	+	0.741477i	0.977627	−	0.210346i	$-0.0674591\pi$
$127$	14.4730	+	8.35602i	1.28428	+	0.741477i	0.306648	+	0.951823i	$0.400792\pi$
$128$	−4.57687	+	10.3466i	−0.404542	+	0.914519i
$129$	−14.3694	−	0.930692i	−1.26515	−	0.0819429i
$130$	1.33944	+	2.00583i	0.117477	+	0.175923i
$131$	−11.9406	+	10.0194i	−1.04326	+	0.875395i	−0.992368	−	0.123309i	$-0.960649\pi$
$131$	−11.9406	+	10.0194i	−1.04326	+	0.875395i	−0.0508872	+	0.998704i	$0.516205\pi$
$132$	−0.898142	+	0.395418i	−0.0781732	+	0.0344167i
$133$	−21.1488	−	8.32719i	−1.83384	−	0.722059i
$134$	−15.7787	−	1.73253i	−1.36307	−	0.149668i
$135$	−3.80733	+	2.10024i	−0.327683	+	0.180760i
$136$	10.2379	−	8.96318i	0.877893	−	0.768586i
$137$	11.6855	−	4.25318i	0.998361	−	0.363374i	0.209409	−	0.977828i	$-0.432846\pi$
$137$	11.6855	−	4.25318i	0.998361	−	0.363374i	0.788952	+	0.614455i	$0.210624\pi$
$138$	11.0026	−	0.00539947i	0.936607	−	0.000459633i
$139$	0.511428	+	2.90045i	0.0433788	+	0.246013i	0.998785	−	0.0492816i	$-0.0156932\pi$
$139$	0.511428	+	2.90045i	0.0433788	+	0.246013i	−0.955406	+	0.295295i	$0.904582\pi$
$140$	3.18395	+	3.07726i	0.269092	+	0.260076i
$141$	−0.0149890	+	0.231423i	−0.00126231	+	0.0194893i
$142$	−19.0070	+	4.64535i	−1.59504	+	0.389829i
$143$	−0.288682	−	0.500012i	−0.0241408	−	0.0418131i
$144$	4.58754	−	11.0885i	0.382295	−	0.924040i
$145$	5.64710	+	3.26036i	0.468966	+	0.270758i
$146$	15.6538	−	3.82581i	1.29552	−	0.316626i
$147$	11.1347	−	4.79784i	0.918371	−	0.395719i
$148$	13.2950	−	6.91144i	1.09284	−	0.568117i
$149$	9.25342	+	3.36797i	0.758070	+	0.275915i	0.691997	−	0.721900i	$-0.256731\pi$
$149$	9.25342	+	3.36797i	0.758070	+	0.275915i	0.0660724	+	0.997815i	$0.478953\pi$
$150$	−3.59736	+	9.89879i	−0.293724	+	0.808233i
$151$	−3.74841	−	0.660945i	−0.305041	−	0.0537869i	0.0190325	−	0.999819i	$-0.493941\pi$
$151$	−3.74841	−	0.660945i	−0.305041	−	0.0537869i	−0.324073	+	0.946032i	$0.605053\pi$
$152$	−16.0057	−	18.2821i	−1.29824	−	1.48287i
$153$	−10.6257	+	9.76686i	−0.859038	+	0.789604i
$154$	−0.712577	−	0.784698i	−0.0574211	−	0.0632328i
$155$	−3.22821	−	0.569220i	−0.259296	−	0.0457208i
$156$	6.77853	+	1.97421i	0.542717	+	0.158064i
$157$	−4.89319	−	5.83147i	−0.390519	−	0.465402i	0.534586	−	0.845114i	$-0.320468\pi$
$157$	−4.89319	−	5.83147i	−0.390519	−	0.465402i	−0.925105	+	0.379712i	$0.876023\pi$
$158$	−9.75598	−	4.81452i	−0.776144	−	0.383022i
$159$	−0.655297	−	0.892268i	−0.0519684	−	0.0707615i
$160$	1.51532	+	4.48462i	0.119796	+	0.354541i
$161$	3.77255	+	11.2695i	0.297319	+	0.888163i
$162$	−4.57980	+	11.8754i	−0.359823	+	0.933021i
$163$	−1.01464	+	0.585801i	−0.0794726	+	0.0458835i	−0.539210	−	0.842172i	$-0.681277\pi$
$163$	−1.01464	+	0.585801i	−0.0794726	+	0.0458835i	0.459737	+	0.888055i	$0.347944\pi$
$164$	−1.19309	−	9.10189i	−0.0931650	−	0.710738i
$165$	−0.165076	+	0.375949i	−0.0128511	+	0.0292676i
$166$	3.88906	+	5.82393i	0.301850	+	0.452025i
$167$	22.3345	+	8.12908i	1.72829	+	0.629047i	0.998507	−	0.0546284i	$-0.0173974\pi$
$167$	22.3345	+	8.12908i	1.72829	+	0.629047i	0.729786	+	0.683676i	$0.239620\pi$
$168$	12.9300	+	0.903172i	0.997569	+	0.0696813i
$169$	1.53612	−	8.71178i	0.118163	−	0.670137i
$170$	0.621396	−	5.65926i	0.0476589	−	0.434046i
$171$	17.4409	+	18.9746i	1.33374	+	1.45102i
$172$	3.60787	−	16.2310i	0.275097	−	1.23760i
$173$	9.51139	−	11.3352i	0.723138	−	0.861802i	−0.271794	−	0.962355i	$-0.587617\pi$
$173$	9.51139	−	11.3352i	0.723138	−	0.861802i	0.994932	+	0.100554i	$0.0320614\pi$
$174$	18.7957	−	3.32369i	1.42490	−	0.251969i
$175$	−11.3722	−	0.296137i	−0.859658	−	0.0223859i
$176$	−0.292052	−	1.09486i	−0.0220142	−	0.0825284i
$177$	−3.78448	−	12.9468i	−0.284459	−	0.973139i
$178$	−0.377799	+	1.29482i	−0.0283172	+	0.0970507i
$179$		−	3.97055i		−	0.296773i	−0.988929	−	0.148386i	$-0.952592\pi$
$179$		−	3.97055i		−	0.296773i	0.988929	−	0.148386i	$-0.0474079\pi$
$180$	−1.72186	−	4.71638i	−0.128340	−	0.351538i
$181$	−14.2010	−	8.19897i	−1.05555	−	0.609424i	−0.131355	−	0.991335i	$-0.541933\pi$
$181$	−14.2010	−	8.19897i	−1.05555	−	0.609424i	−0.924199	+	0.381911i	$0.875266\pi$
$182$	0.298361	+	7.62001i	0.0221160	+	0.564833i
$183$	0.389832	+	0.0252491i	0.0288172	+	0.00186646i
$184$	−1.94325	+	12.5553i	−0.143258	+	0.925586i
$185$	2.14427	−	5.89134i	0.157650	−	0.433140i
$186$	−8.30742	+	4.80173i	−0.609130	+	0.352080i
$187$	−0.236656	+	1.34214i	−0.0173060	+	0.0981470i
$188$	−0.261404	−	0.0581057i	−0.0190648	−	0.00423779i
$189$	−13.7335	−	0.625824i	−0.998963	−	0.0455220i
$190$	−10.1059	−	1.10964i	−0.733157	−	0.0805018i
$191$	−9.53332	−	1.68098i	−0.689807	−	0.121632i	−0.182253	−	0.983252i	$-0.558339\pi$
$191$	−9.53332	−	1.68098i	−0.689807	−	0.121632i	−0.507554	+	0.861620i	$0.669450\pi$
$192$	11.8395	+	7.19912i	0.854439	+	0.519552i
$193$	3.86120	+	1.40536i	0.277935	+	0.101160i	0.477227	−	0.878780i	$-0.341642\pi$
$193$	3.86120	+	1.40536i	0.277935	+	0.101160i	−0.199292	+	0.979940i	$0.563864\pi$
$194$	0.127000	+	1.94600i	0.00911806	+	0.139715i
$195$	2.64836	−	1.30857i	0.189653	−	0.0937084i
$196$	3.50166	+	13.5550i	0.250119	+	0.968215i
$197$	−4.68906	+	8.12169i	−0.334082	+	0.578646i	−0.983308	−	0.181949i	$-0.941759\pi$
$197$	−4.68906	+	8.12169i	−0.334082	+	0.578646i	0.649226	+	0.760595i	$0.275093\pi$
$198$	0.337777	+	1.15344i	0.0240048	+	0.0819715i
$199$	4.68700			0.332252			0.166126	−	0.986105i	$-0.446874\pi$
$199$	4.68700			0.332252			0.166126	+	0.986105i	$0.446874\pi$
$200$	−10.6574	−	5.85852i	−0.753593	−	0.414260i
$201$	−4.60630	+	18.8875i	−0.324904	+	1.33222i
$202$	−10.0213	+	6.69197i	−0.705098	+	0.470846i
$203$	9.84003	+	18.1168i	0.690635	+	1.27155i
$204$	−9.26162	−	13.8547i	−0.648443	−	0.970022i
$205$	−2.94226	−	2.46885i	−0.205497	−	0.172432i
$206$	0.778414	−	7.08928i	0.0542347	−	0.493934i
$207$	1.73829	−	13.3628i	0.120819	−	0.928782i
$208$	−3.45363	+	7.38470i	−0.239466	+	0.512037i
$209$	2.39669	+	0.422601i	0.165783	+	0.0292319i
$210$	4.24205	−	3.37869i	0.292729	−	0.233152i
$211$	−3.45813	+	9.50112i	−0.238067	+	0.654084i	0.761912	+	0.647680i	$0.224261\pi$
$211$	−3.45813	+	9.50112i	−0.238067	+	0.654084i	−0.999979	+	0.00640397i	$0.997962\pi$
$212$	1.13421	−	0.589622i	0.0778975	−	0.0404954i
$213$	2.62725	+	23.8195i	0.180016	+	1.63208i
$214$	−12.0190	+	2.93745i	−0.821600	+	0.200800i
$215$	−3.47843	−	6.02482i	−0.237227	−	0.410890i
$216$	−12.7387	−	7.32972i	−0.866761	−	0.498724i
$217$	−7.76326	−	6.86634i	−0.527004	−	0.466117i
$218$	−16.5518	+	15.8360i	−1.12103	+	1.07255i
$219$	−2.16375	−	19.6172i	−0.146212	−	1.32561i
$220$	−0.399721	−	0.254965i	−0.0269492	−	0.0171898i
$221$	7.51102	−	6.30250i	0.505246	−	0.423952i
$222$	−6.28512	−	17.2419i	−0.421830	−	1.15720i
$223$	−0.729901	+	4.13947i	−0.0488778	+	0.277200i	−0.999445	−	0.0333200i	$-0.989392\pi$
$223$	−0.729901	+	4.13947i	−0.0488778	+	0.277200i	0.950567	+	0.310520i	$0.100503\pi$
$224$	−3.32144	+	14.5934i	−0.221923	+	0.975064i
$225$	11.4509	+	5.93856i	0.763396	+	0.395904i
$226$	16.4848	+	12.0943i	1.09655	+	0.804499i
$227$	3.61302	−	20.4904i	0.239804	−	1.36000i	−0.592451	−	0.805606i	$-0.701840\pi$
$227$	3.61302	−	20.4904i	0.239804	−	1.36000i	0.832256	−	0.554392i	$-0.187049\pi$
$228$	−24.7406	+	16.5387i	−1.63849	+	1.09530i
$229$	8.20134	−	22.5330i	0.541960	−	1.48902i	−0.302365	−	0.953192i	$-0.597776\pi$
$229$	8.20134	−	22.5330i	0.541960	−	1.48902i	0.844325	−	0.535831i	$-0.180002\pi$
$230$	2.95202	+	4.42070i	0.194651	+	0.291492i
$231$	−1.06597	+	0.740937i	−0.0701356	+	0.0487501i
$232$	0.462267	+	22.0352i	0.0303493	+	1.44668i
$233$	3.03138	−	5.25051i	0.198592	−	0.343972i	−0.749480	−	0.662027i	$-0.769696\pi$
$233$	3.03138	−	5.25051i	0.198592	−	0.343972i	0.948072	+	0.318055i	$0.103030\pi$
$234$	3.47252	−	7.91900i	0.227006	−	0.517681i
$235$	−0.0970313	+	0.0560211i	−0.00632963	+	0.00365441i
$236$	15.4431	−	2.02432i	1.00526	−	0.131772i
$237$	−7.39406	+	11.0845i	−0.480296	+	0.720015i
$238$	11.0221	−	14.2313i	0.714459	−	0.922480i
$239$	24.5125	−	4.32221i	1.58558	−	0.279580i	0.689773	−	0.724026i	$-0.257710\pi$
$239$	24.5125	−	4.32221i	1.58558	−	0.279580i	0.895806	+	0.444446i	$0.146599\pi$
$240$	5.68659	−	1.12906i	0.367067	−	0.0728806i
$241$	−2.66530	−	7.32285i	−0.171687	−	0.471706i	0.823769	−	0.566925i	$-0.191867\pi$
$241$	−2.66530	−	7.32285i	−0.171687	−	0.471706i	−0.995456	+	0.0952190i	$0.969645\pi$
$242$	−12.4512	−	9.13500i	−0.800397	−	0.587220i
$243$	13.6956	+	7.44512i	0.878575	+	0.477605i
$244$	−0.0978790	+	0.440335i	−0.00626606	+	0.0281896i
$245$	4.91358	+	3.18889i	0.313917	+	0.203730i
$246$	−11.2429	+	0.00551735i	−0.716818	+	0.000351774i
$247$	−11.2545	−	13.4126i	−0.716107	−	0.853423i
$248$	−4.00702	−	10.3297i	−0.254446	−	0.655939i
$249$	7.68952	−	3.79943i	0.487304	−	0.240779i
$250$	−10.6909	+	2.61287i	−0.676153	+	0.165253i
$251$	−7.94251	+	13.7568i	−0.501327	+	0.868324i	0.498672	+	0.866791i	$0.333821\pi$
$251$	−7.94251	+	13.7568i	−0.501327	+	0.868324i	−0.999999	+	0.00153285i	$0.999512\pi$
$252$	3.14734	−	15.5594i	0.198264	−	0.980149i
$253$	−0.636234	−	1.10199i	−0.0399997	−	0.0692815i
$254$	16.3387	+	17.0772i	1.02518	+	1.07152i
$255$	−6.77426	−	1.65212i	−0.424221	−	0.103460i
$256$	−10.3121	+	12.2336i	−0.644504	+	0.764601i
$257$	9.58297	−	26.3290i	0.597769	−	1.64236i	−0.157938	−	0.987449i	$-0.550485\pi$
$257$	9.58297	−	26.3290i	0.597769	−	1.64236i	0.755708	−	0.654909i	$-0.227293\pi$
$258$	−19.1393	−	6.95550i	−1.19156	−	0.433030i
$259$	15.5112	−	12.3418i	0.963817	−	0.766883i
$260$	1.02388	+	3.25370i	0.0634984	+	0.201786i
$261$	−1.05571	−	23.3532i	−0.0653468	−	1.44553i
$262$	−20.1795	+	8.87243i	−1.24669	+	0.548140i
$263$	18.7577	−	22.3545i	1.15665	−	1.37844i	0.243958	−	0.969786i	$-0.421554\pi$
$263$	18.7577	−	22.3545i	1.15665	−	1.37844i	0.912690	−	0.408654i	$-0.134002\pi$
$264$	−1.37595	+	0.181050i	−0.0846841	+	0.0111428i
$265$	0.182930	−	0.502595i	0.0112373	−	0.0308742i
$266$	−25.4132	−	19.6825i	−1.55818	−	1.20681i
$267$	1.51256	+	0.664150i	0.0925671	+	0.0406453i
$268$	−20.7350	−	8.60234i	−1.26659	−	0.525472i
$269$	3.74252	+	2.16075i	0.228186	+	0.131743i	0.609735	−	0.792605i	$-0.291276\pi$
$269$	3.74252	+	2.16075i	0.228186	+	0.131743i	−0.381549	+	0.924349i	$0.624609\pi$
$270$	−6.00079	+	1.34315i	−0.365196	+	0.0817414i
$271$	14.3983	+	24.9386i	0.874635	+	1.51491i	0.857151	+	0.515065i	$0.172232\pi$
$271$	14.3983	+	24.9386i	0.874635	+	1.51491i	0.0174837	+	0.999847i	$0.494434\pi$
$272$	17.4495	−	8.11302i	1.05803	−	0.491924i
$273$	9.30132	+	0.846075i	0.562942	+	0.0512068i
$274$	17.5491	−	1.14529i	1.06018	−	0.0691892i
$275$	1.19956	−	0.211514i	0.0723359	−	0.0127548i
$276$	14.9394	+	4.35102i	0.899244	+	0.261901i
$277$	−13.2152	−	11.0889i	−0.794025	−	0.666266i	0.152713	−	0.988271i	$-0.451199\pi$
$277$	−13.2152	−	11.0889i	−0.794025	−	0.666266i	−0.946738	+	0.322005i	$0.895643\pi$
$278$	−0.454607	+	4.14026i	−0.0272655	+	0.248316i
$279$	4.51396	+	10.8503i	0.270244	+	0.649590i
$280$	3.10358	+	5.43892i	0.185474	+	0.325038i
$281$	3.18857	−	1.16055i	0.190214	−	0.0692324i	−0.245157	−	0.969483i	$-0.578839\pi$
$281$	3.18857	−	1.16055i	0.190214	−	0.0692324i	0.435371	+	0.900251i	$0.356617\pi$
$282$	−0.112020	+	0.308243i	−0.00667070	+	0.0183556i
$283$	−1.76330	−	10.0002i	−0.104818	−	0.594450i	−0.991293	−	0.131674i	$-0.957965\pi$
$283$	−1.76330	−	10.0002i	−0.104818	−	0.594450i	0.886476	−	0.462776i	$-0.153146\pi$
$284$	−27.6442	−	1.22250i	−1.64038	−	0.0725421i
$285$	−2.95022	+	12.0970i	−0.174756	+	0.716562i
$286$	−0.193852	−	0.793172i	−0.0114627	−	0.0469012i
$287$	−3.85492	−	11.5156i	−0.227549	−	0.679743i
$288$	10.6204	−	13.2366i	0.625814	−	0.779972i
$289$	−6.14415			−0.361421
$290$	6.37504	+	6.66320i	0.374355	+	0.391276i
$291$	2.38343	+	0.154373i	0.139719	+	0.00904950i
$292$	22.7672	+	1.00683i	1.33235	+	0.0589201i
$293$	−15.9105	+	2.80545i	−0.929500	+	0.163896i	−0.617845	−	0.786300i	$-0.711994\pi$
$293$	−15.9105	+	2.80545i	−0.929500	+	0.163896i	−0.311654	+	0.950196i	$0.600883\pi$
$294$	17.0170	−	2.10292i	0.992451	−	0.122645i
$295$	4.18889	−	4.99213i	0.243887	−	0.290653i
$296$	20.7870	−	4.11663i	1.20822	−	0.239274i
$297$	1.45435	−	0.227291i	0.0843897	−	0.0131887i
$298$	11.2284	+	8.23782i	0.650442	+	0.477204i
$299$	−1.58970	+	9.01565i	−0.0919349	+	0.521389i
$300$	−8.80489	+	12.0137i	−0.508351	+	0.693609i
$301$	0.572580	−	21.9882i	0.0330030	−	1.26738i
$302$	−4.82704	−	2.38212i	−0.277765	−	0.137075i
$303$	6.53774	+	13.2315i	0.375583	+	0.760129i
$304$	−14.4876	−	31.1600i	−0.830922	−	1.78715i
$305$	0.0943675	+	0.163449i	0.00540347	+	0.00935908i
$306$	−18.2944	+	9.05049i	−1.04582	+	0.517382i
$307$	−11.4678	−	19.8628i	−0.654501	−	1.13363i	−0.982019	−	0.188784i	$-0.939545\pi$
$307$	−11.4678	−	19.8628i	−0.654501	−	1.13363i	0.327518	−	0.944845i	$-0.393788\pi$
$308$	−0.656563	−	1.34757i	−0.0374112	−	0.0767852i
$309$	−8.48603	−	2.06958i	−0.482753	−	0.117734i
$310$	−4.15715	−	2.05153i	−0.236110	−	0.116519i
$311$	0.252891	+	1.43422i	0.0143402	+	0.0813271i	0.991138	−	0.132837i	$-0.0424085\pi$
$311$	0.252891	+	1.43422i	0.0143402	+	0.0813271i	−0.976798	+	0.214164i	$0.931297\pi$
$312$	8.42054	+	5.36530i	0.476719	+	0.303750i
$313$	−7.70722	+	9.18511i	−0.435638	+	0.519173i	−0.938540	−	0.345170i	$-0.887821\pi$
$313$	−7.70722	+	9.18511i	−0.435638	+	0.519173i	0.502902	+	0.864343i	$0.332266\pi$
$314$	−4.33306	−	9.85511i	−0.244529	−	0.556156i
$315$	−3.43047	−	5.68750i	−0.193285	−	0.320454i
$316$	−11.3376	−	10.4007i	−0.637792	−	0.585087i
$317$	17.0928	−	6.22128i	0.960029	−	0.349422i	0.185984	−	0.982553i	$-0.440453\pi$
$317$	17.0928	−	6.22128i	0.960029	−	0.349422i	0.774045	+	0.633131i	$0.218230\pi$
$318$	−0.536190	−	1.47092i	−0.0300680	−	0.0824852i
$319$	−1.41893	−	1.69102i	−0.0794449	−	0.0946788i
$320$	0.280757	+	6.68859i	0.0156948	+	0.373903i
$321$	1.66132	+	15.0621i	0.0927259	+	0.840684i
$322$	0.657566	+	16.7939i	0.0366447	+	0.935890i
$323$			41.3290i			2.29961i
$324$	−10.9216	+	14.3080i	−0.606757	+	0.794887i
$325$	−7.58924	−	4.38165i	−0.420975	−	0.243050i
$326$	−1.60952	+	0.393370i	−0.0891433	+	0.0217867i
$327$	16.6069	+	22.6124i	0.918365	+	1.25047i
$328$	1.98568	−	12.8294i	0.109641	−	0.708384i
$329$	−0.354125	−	0.00922156i	−0.0195235	−	0.000508401i
$330$	−0.373028	+	0.445001i	−0.0205345	+	0.0244965i
$331$	4.60202	+	12.6439i	0.252950	+	0.694974i	0.999559	+	0.0297105i	$0.00945853\pi$
$331$	4.60202	+	12.6439i	0.252950	+	0.694974i	−0.746609	+	0.665263i	$0.768319\pi$
$332$	2.97284	+	9.44712i	0.163156	+	0.518478i
$333$	−21.9359	+	4.89857i	−1.20208	+	0.268440i
$334$	27.1013	+	19.8832i	1.48292	+	1.08796i
$335$	−8.82616	+	3.21246i	−0.482225	+	0.175516i
$336$	17.1960	+	6.34796i	0.938120	+	0.346309i
$337$	1.44286	−	1.21070i	0.0785974	−	0.0659511i	−0.602643	−	0.798011i	$-0.705885\pi$
$337$	1.44286	−	1.21070i	0.0785974	−	0.0659511i	0.681240	+	0.732060i	$0.261441\pi$
$338$	5.53634	−	11.2187i	0.301137	−	0.610215i
$339$	17.3019	−	18.1018i	0.939712	−	0.983153i
$340$	3.08535	−	7.43690i	0.167327	−	0.403322i
$341$	0.961035	+	0.554854i	0.0520430	+	0.0300470i
$342$	16.1617	+	32.6686i	0.873923	+	1.76652i
$343$	7.98047	+	16.7126i	0.430905	+	0.902397i
$344$	11.3274	−	20.6061i	0.610735	−	1.11101i
$345$	5.83679	−	2.88398i	0.314242	−	0.155269i
$346$	17.4028	−	11.6211i	0.935581	−	0.624756i
$347$	6.95282	−	19.1027i	0.373247	−	1.02549i	−0.600851	−	0.799361i	$-0.705171\pi$
$347$	6.95282	−	19.1027i	0.373247	−	1.02549i	0.974098	−	0.226127i	$-0.0726064\pi$
$348$	26.8337	+	2.93305i	1.43843	+	0.157228i
$349$	0.337079	−	0.401715i	0.0180434	−	0.0215033i	−0.756947	−	0.653476i	$-0.773310\pi$
$349$	0.337079	−	0.401715i	0.0180434	−	0.0215033i	0.774991	+	0.631973i	$0.217755\pi$
$350$	−15.3217	−	4.90678i	−0.818977	−	0.262279i
$351$	−9.06642	−	5.47298i	−0.483930	−	0.292126i
$352$	0.0372046	−	1.60208i	0.00198301	−	0.0853911i
$353$	6.04600	+	16.6113i	0.321796	+	0.884128i	0.990116	+	0.140254i	$0.0447918\pi$
$353$	6.04600	+	16.6113i	0.321796	+	0.884128i	−0.668319	+	0.743875i	$0.732986\pi$
$354$	−0.00936127	−	19.0757i	−0.000497546	−	1.01386i
$355$	−8.86908	+	7.44204i	−0.470722	+	0.394982i
$356$	−1.02580	+	1.60820i	−0.0543675	+	0.0852343i
$357$	−15.5351	−	15.6425i	−0.822203	−	0.827891i
$358$	1.57281	−	5.39043i	0.0831255	−	0.284893i
$359$		−	11.1765i		−	0.589873i	−0.955517	−	0.294936i	$-0.904702\pi$
$359$		−	11.1765i		−	0.589873i	0.955517	−	0.294936i	$-0.0952985\pi$
$360$	−0.469367	−	7.08504i	−0.0247378	−	0.373414i
$361$	54.8022			2.88433
$362$	−16.0316	−	16.7562i	−0.842603	−	0.880689i
$363$	−13.0684	+	13.6726i	−0.685915	+	0.717623i
$364$	−2.61337	+	10.4632i	−0.136978	+	0.548418i
$365$	7.30439	−	6.12911i	0.382329	−	0.320812i
$366$	0.519236	+	0.188698i	0.0271409	+	0.00986340i
$367$	−1.04745	+	5.94039i	−0.0546765	+	0.310086i	−0.999865	−	0.0164397i	$-0.994767\pi$
$367$	−1.04745	+	5.94039i	−0.0546765	+	0.310086i	0.945188	+	0.326526i	$0.105878\pi$
$368$	−7.61154	+	16.2753i	−0.396779	+	0.848410i
$369$	−1.77624	+	13.6546i	−0.0924674	+	0.710829i
$370$	5.24474	−	7.14872i	0.272661	−	0.371644i
$371$	1.32327	−	1.05289i	0.0687009	−	0.0546635i
$372$	−13.1802	+	3.22812i	−0.683364	+	0.167370i
$373$	4.02379	+	22.8201i	0.208344	+	1.18158i	0.892090	+	0.451858i	$0.149238\pi$
$373$	4.02379	+	22.8201i	0.208344	+	1.18158i	−0.683746	+	0.729720i	$0.739650\pi$
$374$	−0.852931	+	1.72835i	−0.0441040	+	0.0893710i
$375$	1.47775	+	13.3978i	0.0763108	+	0.691858i
$376$	−0.331866	−	0.182431i	−0.0171147	−	0.00940819i
$377$			15.8815i			0.817941i
$378$	−18.3967	−	6.28971i	−0.946226	−	0.323508i
$379$			16.8672i			0.866408i	0.901296	+	0.433204i	$0.142617\pi$
$379$			16.8672i			0.866408i	−0.901296	+	0.433204i	$0.857383\pi$
$380$	−13.2802	−	5.50958i	−0.681262	−	0.282635i
$381$	23.3302	−	17.1341i	1.19524	−	0.877807i
$382$	−12.2766	−	6.05843i	−0.628126	−	0.309976i
$383$	−5.23950	−	29.7147i	−0.267726	−	1.51835i	−0.761159	−	0.648565i	$-0.775369\pi$
$383$	−5.23950	−	29.7147i	−0.267726	−	1.51835i	0.493433	−	0.869784i	$-0.335742\pi$
$384$	13.2216	+	14.4634i	0.674711	+	0.738082i
$385$	−0.583585	−	0.229782i	−0.0297423	−	0.0117108i
$386$	4.68530	+	3.43742i	0.238475	+	0.174960i
$387$	−11.4822	+	22.1404i	−0.583672	+	1.12546i
$388$	−0.598433	+	2.69221i	−0.0303808	+	0.136676i
$389$	−0.974215	+	5.52505i	−0.0493947	+	0.280131i	−0.999494	−	0.0318174i	$-0.989871\pi$
$389$	−0.974215	+	5.52505i	−0.0493947	+	0.280131i	0.950099	+	0.311948i	$0.100982\pi$
$390$	4.11378	−	0.727451i	0.208309	−	0.0368359i
$391$	16.5537	−	13.8902i	0.837158	−	0.702459i
$392$	−0.615522	+	19.7894i	−0.0310886	+	0.999517i
$393$	7.57483	+	25.9137i	0.382100	+	1.30717i
$394$	−9.58304	+	9.16862i	−0.482787	+	0.461908i
$395$	−6.43742			−0.323902
$396$	0.00166825	+	1.69972i	8.38327e−5	+	0.0854140i
$397$			24.0198i			1.20552i	0.797923	+	0.602759i	$0.205932\pi$
$397$			24.0198i			1.20552i	−0.797923	+	0.602759i	$0.794068\pi$
$398$	6.36309	+	1.85661i	0.318953	+	0.0930633i
$399$	−27.9332	+	27.7413i	−1.39841	+	1.38880i
$400$	−12.1479	−	12.1752i	−0.607394	−	0.608758i
$401$	7.58690	−	6.36617i	0.378872	−	0.317911i	−0.433387	−	0.901208i	$-0.642682\pi$
$401$	7.58690	−	6.36617i	0.378872	−	0.317911i	0.812259	+	0.583296i	$0.198237\pi$
$402$	−13.7352	+	23.8171i	−0.685051	+	1.18789i
$403$	−2.73061	−	7.50228i	−0.136021	−	0.373715i
$404$	−16.2558	+	5.11542i	−0.808757	+	0.254502i
$405$	0.679534	+	7.50057i	0.0337663	+	0.372706i
$406$	6.18247	+	28.4933i	0.306831	+	1.41410i
$407$	−1.36425	+	1.62585i	−0.0676234	+	0.0805905i
$408$	−7.08552	−	22.4779i	−0.350785	−	1.11282i
$409$	8.44831	−	23.2115i	0.417742	−	1.14774i	−0.535238	−	0.844702i	$-0.679778\pi$
$409$	8.44831	−	23.2115i	0.417742	−	1.14774i	0.952979	−	0.303035i	$-0.0979998\pi$
$410$	−3.01647	−	4.51721i	−0.148973	−	0.223089i
$411$	1.39213	−	21.4938i	0.0686689	−	1.06021i
$412$	3.86498	−	9.31610i	0.190414	−	0.458971i
$413$	19.5384	−	6.54062i	0.961423	−	0.321843i
$414$	7.65318	−	17.4529i	0.376133	−	0.857762i
$415$	3.58865	+	2.07191i	0.176160	+	0.101706i
$416$	−7.61388	+	8.65745i	−0.373301	+	0.424466i
$417$	4.95598	+	1.20867i	0.242695	+	0.0591888i
$418$	3.08636	+	1.52310i	0.150959	+	0.0744972i
$419$	−10.7816	+	9.04680i	−0.526713	+	0.441965i	−0.866965	−	0.498370i	$-0.833932\pi$
$419$	−10.7816	+	9.04680i	−0.526713	+	0.441965i	0.340251	+	0.940335i	$0.389488\pi$
$420$	7.09739	−	2.90657i	0.346317	−	0.141826i
$421$	−1.73169	+	0.630283i	−0.0843973	+	0.0307181i	−0.383874	−	0.923386i	$-0.625410\pi$
$421$	−1.73169	+	0.630283i	−0.0843973	+	0.0307181i	0.299476	+	0.954104i	$0.403188\pi$
$422$	−8.45834	+	11.5289i	−0.411745	+	0.561220i
$423$	0.356577	+	0.184924i	0.0173373	+	0.00899130i
$424$	1.77336	−	0.351193i	0.0861221	−	0.0170555i
$425$	7.07482	+	19.4379i	0.343179	+	0.942877i
$426$	−5.86858	+	33.3781i	−0.284334	+	1.61718i
$427$	−0.0155337	+	0.596524i	−0.000751729	+	0.0288678i
$428$	−17.4806	−	0.773041i	−0.844956	−	0.0373663i
$429$	−0.993997	+	0.109636i	−0.0479906	+	0.00529328i
$430$	−2.33579	−	9.55720i	−0.112642	−	0.460889i
$431$	3.05326	+	1.76280i	0.147070	+	0.0849111i	0.571729	−	0.820442i	$-0.306273\pi$
$431$	3.05326	+	1.76280i	0.147070	+	0.0849111i	−0.424659	+	0.905353i	$0.639606\pi$
$432$	−14.3907	−	14.9969i	−0.692374	−	0.721539i
$433$			27.3460i			1.31417i	0.753819	+	0.657083i	$0.228210\pi$
$433$			27.3460i			1.31417i	−0.753819	+	0.657083i	$0.771790\pi$
$434$	−7.81955	−	12.3969i	−0.375350	−	0.595072i
$435$	9.10300	−	6.68539i	0.436455	−	0.320540i
$436$	−28.7437	+	14.9426i	−1.37657	+	0.715618i
$437$	−24.8041	−	29.5604i	−1.18654	−	1.41406i
$438$	4.83324	−	27.4896i	0.230941	−	1.31350i
$439$	19.1588	−	6.97322i	0.914398	−	0.332813i	0.158390	−	0.987377i	$-0.449370\pi$
$439$	19.1588	−	6.97322i	0.914398	−	0.332813i	0.756007	+	0.654563i	$0.227147\pi$
$440$	−0.441666	−	0.504479i	−0.0210556	−	0.0240501i
$441$	0.144764	−	20.9995i	0.00689350	−	0.999976i
$442$	12.6935	−	5.58104i	0.603770	−	0.265463i
$443$	15.4629	−	18.4280i	0.734666	−	0.875541i	−0.261302	−	0.965257i	$-0.584152\pi$
$443$	15.4629	−	18.4280i	0.734666	−	0.875541i	0.995967	+	0.0897166i	$0.0285961\pi$
$444$	−1.70287	−	25.8973i	−0.0808147	−	1.22903i
$445$	0.138590	+	0.785984i	0.00656981	+	0.0372592i
$446$	−2.63064	+	5.33064i	−0.124564	+	0.252413i
$447$	11.7849	−	12.3297i	0.557409	−	0.583176i
$448$	−10.2899	+	18.4964i	−0.486153	+	0.873874i
$449$	13.4524	+	23.3002i	0.634858	+	1.09961i	0.986545	+	0.163488i	$0.0522746\pi$
$449$	13.4524	+	23.3002i	0.634858	+	1.09961i	−0.351688	+	0.936117i	$0.614392\pi$
$450$	13.1935	+	12.5981i	0.621947	+	0.593882i
$451$	0.650125	+	1.12605i	0.0306132	+	0.0530236i
$452$	17.5891	+	22.9492i	0.827321	+	1.07944i
$453$	−3.65842	+	5.48436i	−0.171887	+	0.257678i
$454$	13.0217	−	26.3867i	0.611139	−	1.23839i
$455$	2.15367	+	3.96519i	0.100966	+	0.185891i
$456$	−40.1393	+	12.6528i	−1.87969	+	0.592520i
$457$	−1.90386	+	10.7973i	−0.0890588	+	0.505078i	0.907348	+	0.420380i	$0.138103\pi$
$457$	−1.90386	+	10.7973i	−0.0890588	+	0.505078i	−0.996407	+	0.0846972i	$0.973008\pi$
$458$	20.0599	−	27.3422i	0.937339	−	1.27762i
$459$	8.09003	+	23.6526i	0.377610	+	1.10401i
$460$	2.25656	+	7.17091i	0.105213	+	0.334345i
$461$	0.428282	−	0.510407i	0.0199471	−	0.0237720i	−0.755979	−	0.654596i	$-0.772839\pi$
$461$	0.428282	−	0.510407i	0.0199471	−	0.0237720i	0.775926	+	0.630824i	$0.217283\pi$
$462$	−1.74066	+	0.583649i	−0.0809829	+	0.0271538i
$463$	−8.05247	+	1.41987i	−0.374230	+	0.0659869i	−0.357600	−	0.933875i	$-0.616405\pi$
$463$	−8.05247	+	1.41987i	−0.374230	+	0.0659869i	−0.0166301	+	0.999862i	$0.505294\pi$
$464$	−8.10099	+	30.0982i	−0.376079	+	1.39728i
$465$	−3.15070	+	4.72324i	−0.146110	+	0.219035i
$466$	6.19524	−	5.92733i	0.286989	−	0.274578i
$467$	28.4514			1.31657			0.658287	−	0.752767i	$-0.271281\pi$
$467$	28.4514			1.31657			0.658287	+	0.752767i	$0.271281\pi$
$468$	7.85117	−	9.37534i	0.362921	−	0.433375i
$469$	−29.1014	−	5.91634i	−1.34378	−	0.273191i
$470$	−0.153921	+	0.0376185i	−0.00709985	+	0.00173521i
$471$	−12.6555	+	3.69935i	−0.583137	+	0.170457i
$472$	21.7675	+	3.36909i	1.00193	+	0.155075i
$473$	0.408962	+	2.31934i	0.0188041	+	0.106643i
$474$	−14.4290	+	12.1194i	−0.662745	+	0.556664i
$475$	34.7107	−	12.6337i	1.59264	−	0.579672i
$476$	20.6010	−	14.9544i	0.944245	−	0.685435i
$477$	−1.87137	+	0.417902i	−0.0856842	+	0.0191344i
$478$	34.9903	+	3.84199i	1.60042	+	0.175729i
$479$	−2.31784	−	1.94490i	−0.105905	−	0.0888647i	0.588298	−	0.808644i	$-0.299798\pi$
$479$	−2.31784	−	1.94490i	−0.105905	−	0.0888647i	−0.694203	+	0.719780i	$0.744243\pi$
$480$	8.16738	+	0.719744i	0.372788	+	0.0328517i
$481$	15.0375	−	2.65153i	0.685653	−	0.120899i
$482$	−0.717705	−	10.9973i	−0.0326906	−	0.500914i
$483$	20.4994	+	1.86469i	0.932756	+	0.0848462i
$484$	−13.2853	−	17.3339i	−0.603878	−	0.787904i
$485$	0.576964	+	0.999330i	0.0261986	+	0.0453772i
$486$	15.6441	+	15.5326i	0.709630	+	0.704574i
$487$	−15.4968	−	8.94709i	−0.702228	−	0.405431i	0.105949	−	0.994372i	$-0.466212\pi$
$487$	−15.4968	−	8.94709i	−0.702228	−	0.405431i	−0.808177	+	0.588940i	$0.799545\pi$
$488$	−0.307306	+	0.559029i	−0.0139111	+	0.0253061i
$489$	0.222476	+	2.01704i	0.0100607	+	0.0912139i
$490$	5.40752	+	6.27561i	0.244287	+	0.283503i
$491$	−2.25048	+	6.18315i	−0.101563	+	0.279042i	−0.980059	−	0.198708i	$-0.936325\pi$
$491$	−2.25048	+	6.18315i	−0.101563	+	0.279042i	0.878496	+	0.477750i	$0.158548\pi$
$492$	−15.2655	−	4.44601i	−0.688223	−	0.200442i
$493$	24.0966	−	28.7172i	1.08526	−	1.29336i
$494$	−9.96619	−	22.6671i	−0.448400	−	1.01984i
$495$	0.481268	+	0.523588i	0.0216314	+	0.0235335i
$496$	−1.34814	−	15.6110i	−0.0605333	−	0.700953i
$497$	−36.2027	+	5.41591i	−1.62391	+	0.242937i
$498$	11.9444	−	2.11216i	0.535239	−	0.0946480i
$499$	13.6848	−	37.5987i	0.612616	−	1.68315i	−0.111753	−	0.993736i	$-0.535647\pi$
$499$	13.6848	−	37.5987i	0.612616	−	1.68315i	0.724369	−	0.689412i	$-0.242131\pi$
$500$	−15.5490	−	0.687622i	−0.695374	−	0.0307514i
$501$	28.4447	−	29.7596i	1.27081	−	1.32956i
$502$	−16.2321	+	15.5302i	−0.724475	+	0.693145i
$503$	−1.96603	−	3.40526i	−0.0876610	−	0.151833i	0.818861	−	0.573992i	$-0.194606\pi$
$503$	−1.96603	−	3.40526i	−0.0876610	−	0.151833i	−0.906522	+	0.422159i	$0.861273\pi$
$504$	10.4362	−	19.8768i	0.464865	−	0.885381i
$505$	−3.56516	+	6.17504i	−0.158648	+	0.274786i
$506$	−0.427236	−	1.74809i	−0.0189929	−	0.0777121i
$507$	−12.7463	−	8.50263i	−0.566085	−	0.377615i
$508$	15.4169	+	29.6562i	0.684014	+	1.31578i
$509$	−13.8235	−	16.4742i	−0.612717	−	0.730207i	0.367083	−	0.930188i	$-0.380356\pi$
$509$	−13.8235	−	16.4742i	−0.612717	−	0.730207i	−0.979800	+	0.199981i	$0.935912\pi$
$510$	−8.54234	−	4.92633i	−0.378261	−	0.218142i
$511$	29.8158	−	4.46043i	1.31897	−	0.197318i
$512$	−18.8457	+	12.5236i	−0.832869	+	0.553470i
$513$	42.2369	−	14.4466i	1.86480	−	0.637831i
$514$	23.4393	−	31.9484i	1.03386	−	1.40918i
$515$	−1.44334	−	3.96554i	−0.0636011	−	0.174743i
$516$	−23.2284	−	17.0242i	−1.02257	−	0.749451i
$517$	0.0373536	−	0.00658644i	0.00164281	−	0.000289671i
$518$	25.9468	−	10.6110i	1.14004	−	0.466223i
$519$	−11.3533	−	22.9775i	−0.498354	−	1.00860i
$520$	0.101176	+	4.82281i	0.00443684	+	0.211494i
$521$	−15.1834	+	8.76611i	−0.665195	+	0.384050i	−0.794253	−	0.607587i	$-0.792138\pi$
$521$	−15.1834	+	8.76611i	−0.665195	+	0.384050i	0.129059	+	0.991637i	$0.458804\pi$
$522$	7.81740	−	32.1226i	0.342158	−	1.40597i
$523$	−5.67500	+	9.82938i	−0.248150	+	0.429809i	−0.963013	−	0.269456i	$-0.913156\pi$
$523$	−5.67500	+	9.82938i	−0.248150	+	0.429809i	0.714862	+	0.699265i	$0.246489\pi$
$524$	−30.9103	+	4.05178i	−1.35032	+	0.177003i
$525$	−8.38874	+	17.8290i	−0.366115	+	0.778122i
$526$	34.3206	−	22.9183i	1.49645	−	0.999287i
$527$	−6.44548	+	17.7088i	−0.280770	+	0.771408i
$528$	−1.93972	−	0.299247i	−0.0844154	−	0.0130231i
$529$	0.490322	−	2.78076i	0.0213184	−	0.120902i
$530$	0.447434	−	0.609864i	0.0194353	−	0.0264908i
$531$	−23.1677	−	3.01374i	−1.00539	−	0.130785i
$532$	−26.7045	−	36.7877i	−1.15779	−	1.59495i
$533$	1.62441	−	9.21249i	0.0703610	−	0.399037i
$534$	1.79037	+	1.50081i	0.0774771	+	0.0649462i
$535$	−5.60830	+	4.70592i	−0.242468	+	0.203455i
$536$	−24.7424	−	19.8921i	−1.06871	−	0.859208i
$537$	−6.29690	−	2.76491i	−0.271731	−	0.119315i
$538$	4.22496	+	4.41592i	0.182151	+	0.190384i
$539$	−1.19386	−	1.58335i	−0.0514233	−	0.0681998i
$540$	−8.67875	−	0.553561i	−0.373474	−	0.0238215i
$541$	8.35918	+	14.4785i	0.359389	+	0.622480i	0.987859	−	0.155354i	$-0.0496518\pi$
$541$	8.35918	+	14.4785i	0.359389	+	0.622480i	−0.628470	+	0.777834i	$0.716318\pi$
$542$	9.66856	+	39.5602i	0.415300	+	1.69926i
$543$	−22.8917	+	16.8121i	−0.982378	+	0.721475i
$544$	26.9032	−	4.10220i	1.15347	−	0.175881i
$545$	−4.63592	+	12.7371i	−0.198581	+	0.545597i
$546$	12.2924	+	4.83306i	0.526065	+	0.206836i
$547$	27.6868	+	4.88192i	1.18380	+	0.208736i	0.730684	−	0.682715i	$-0.239201\pi$
$547$	27.6868	+	4.88192i	1.18380	+	0.208736i	0.453116	+	0.891451i	$0.350312\pi$
$548$	24.2784	+	5.39667i	1.03712	+	0.230534i
$549$	0.311504	−	0.600654i	0.0132947	−	0.0256353i
$550$	1.71231	+	0.188014i	0.0730130	+	0.00801694i
$551$	−51.2810	−	43.0299i	−2.18465	−	1.83314i
$552$	18.5582	+	11.8247i	0.789891	+	0.503294i
$553$	−17.3556	−	10.6320i	−0.738034	−	0.452120i
$554$	−13.5485	−	20.2891i	−0.575621	−	0.862001i
$555$	−7.84992	−	7.50307i	−0.333210	−	0.318487i
$556$	−2.25721	+	5.44075i	−0.0957270	+	0.230739i
$557$	−2.42937			−0.102936			−0.0514679	−	0.998675i	$-0.516390\pi$
$557$	−2.42937			−0.102936			−0.0514679	+	0.998675i	$0.516390\pi$
$558$	1.83016	+	16.5185i	0.0774770	+	0.699283i
$559$	8.47191	−	14.6738i	0.358324	−	0.620635i
$560$	2.05898	+	8.61329i	0.0870076	+	0.363978i
$561$	1.96371	+	1.30992i	0.0829078	+	0.0553048i
$562$	4.78854	−	0.312509i	0.201992	−	0.0131824i
$563$	4.08005	+	1.48502i	0.171954	+	0.0625861i	0.426562	−	0.904458i	$-0.359724\pi$
$563$	4.08005	+	1.48502i	0.171954	+	0.0625861i	−0.254609	+	0.967044i	$0.581947\pi$
$564$	−0.274180	+	0.374099i	−0.0115451	+	0.0157524i
$565$	11.9141	+	2.10078i	0.501231	+	0.0883805i
$566$	1.56739	−	14.2748i	0.0658825	−	0.600014i
$567$	−10.5559	+	21.3442i	−0.443305	+	0.896371i
$568$	−37.0456	−	12.6100i	−1.55440	−	0.529106i
$569$	2.85677	−	16.2015i	0.119762	−	0.679204i	−0.864520	−	0.502599i	$-0.832377\pi$
$569$	2.85677	−	16.2015i	0.119762	−	0.679204i	0.984282	−	0.176605i	$-0.0565116\pi$
$570$	−8.79706	+	15.2542i	−0.368468	+	0.638930i
$571$	−0.967689	+	2.65870i	−0.0404965	+	0.111263i	−0.958293	−	0.285789i	$-0.907744\pi$
$571$	−0.967689	+	2.65870i	−0.0404965	+	0.111263i	0.917796	+	0.397052i	$0.129967\pi$
$572$	0.0510155	−	1.15360i	0.00213307	−	0.0482345i
$573$	−9.30445	+	13.9484i	−0.388699	+	0.582701i
$574$	−0.671922	−	17.1606i	−0.0280455	−	0.716269i
$575$	−16.7261	−	9.65683i	−0.697527	−	0.402717i
$576$	19.6616	−	13.7631i	0.819232	−	0.573462i
$577$			34.4277i			1.43324i	0.697463	+	0.716621i	$0.254312\pi$
$577$			34.4277i			1.43324i	−0.697463	+	0.716621i	$0.745688\pi$
$578$	−8.34133	−	2.43381i	−0.346953	−	0.101233i
$579$	4.91754	−	5.14486i	0.204366	−	0.213813i
$580$	6.01537	+	11.5713i	0.249775	+	0.480470i
$581$	6.25319	+	11.5129i	0.259426	+	0.477638i
$582$	3.17461	+	1.15370i	0.131592	+	0.0478224i
$583$	−0.116386	+	0.138703i	−0.00482020	+	0.00574449i
$584$	30.5100	+	10.3854i	1.26251	+	0.429750i
$585$	−0.231061	−	5.11127i	−0.00955322	−	0.211325i
$586$	−22.7114	−	2.49375i	−0.938200	−	0.103016i
$587$	−2.53148	+	14.3567i	−0.104485	+	0.592565i	0.886939	+	0.461886i	$0.152827\pi$
$587$	−2.53148	+	14.3567i	−0.104485	+	0.592565i	−0.991425	+	0.130679i	$0.958284\pi$
$588$	23.9353	+	3.88580i	0.987077	+	0.160248i
$589$	31.6230	+	11.5098i	1.30300	+	0.474255i
$590$	7.66433	−	5.11804i	0.315536	−	0.210706i
$591$	9.61496	+	13.0920i	0.395507	+	0.538532i
$592$	29.8512	+	2.64538i	1.22688	+	0.108725i
$593$	−1.97275	+	1.13897i	−0.0810113	+	0.0467719i	−0.539958	−	0.841692i	$-0.681560\pi$
$593$	−1.97275	+	1.13897i	−0.0810113	+	0.0467719i	0.458947	+	0.888464i	$0.348227\pi$
$594$	2.06446	+	0.267523i	0.0847058	+	0.0109766i
$595$	2.12198	−	10.4376i	0.0869927	−	0.427901i
$596$	11.9805	+	15.6315i	0.490742	+	0.640290i
$597$	3.26381	−	7.43312i	0.133579	−	0.304218i
$598$	−5.72946	+	11.6100i	−0.234295	+	0.474767i
$599$	−10.1151	−	12.0547i	−0.413292	−	0.492542i	0.518733	−	0.854936i	$-0.326404\pi$
$599$	−10.1151	−	12.0547i	−0.413292	−	0.492542i	−0.932025	+	0.362394i	$0.881960\pi$
$600$	−16.7124	+	12.8220i	−0.682281	+	0.523457i
$601$	−25.2117	−	4.44550i	−1.02840	−	0.181336i	−0.366104	−	0.930574i	$-0.619309\pi$
$601$	−25.2117	−	4.44550i	−1.02840	−	0.181336i	−0.662301	+	0.749238i	$0.730420\pi$
$602$	9.48725	−	29.6244i	0.386672	−	1.20740i
$603$	26.7461	+	20.4575i	1.08919	+	0.833096i
$604$	−5.60961	−	5.14605i	−0.228252	−	0.209390i
$605$	−8.99893	−	1.58675i	−0.365859	−	0.0645107i
$606$	3.63442	+	20.5529i	0.147638	+	0.834902i
$607$	23.7420	+	8.64137i	0.963657	+	0.350742i	0.775465	−	0.631390i	$-0.217515\pi$
$607$	23.7420	+	8.64137i	0.963657	+	0.350742i	0.188191	+	0.982132i	$0.439738\pi$
$608$	−7.32540	−	48.0417i	−0.297084	−	1.94835i
$609$	35.5836	−	2.98961i	1.44192	−	0.121145i
$610$	0.0633685	+	0.259280i	0.00256571	+	0.0104980i
$611$	−0.236325	−	0.136442i	−0.00956069	−	0.00551987i
$612$	−28.4216	+	5.04026i	−1.14887	+	0.203740i
$613$	−11.2367	−	19.4625i	−0.453845	−	0.786083i	0.544776	−	0.838582i	$-0.316615\pi$
$613$	−11.2367	−	19.4625i	−0.453845	−	0.786083i	−0.998621	+	0.0524986i	$0.983281\pi$
$614$	−7.70069	−	31.5084i	−0.310775	−	1.27158i
$615$	−5.96422	+	2.94695i	−0.240501	+	0.118832i
$616$	−0.357554	−	2.08955i	−0.0144063	−	0.0841904i
$617$	6.80316	+	38.5826i	0.273885	+	1.55328i	0.742482	+	0.669866i	$0.233649\pi$
$617$	6.80316	+	38.5826i	0.273885	+	1.55328i	−0.468597	+	0.883412i	$0.655240\pi$
$618$	−10.7009	−	6.17115i	−0.430452	−	0.248240i
$619$	6.49764	−	2.36495i	0.261162	−	0.0950553i	−0.208121	−	0.978103i	$-0.566735\pi$
$619$	6.49764	−	2.36495i	0.261162	−	0.0950553i	0.469283	+	0.883048i	$0.344512\pi$
$620$	−4.83111	−	4.43189i	−0.194022	−	0.177989i
$621$	−19.9817	−	12.0620i	−0.801838	−	0.484033i
$622$	−0.224794	+	2.04728i	−0.00901343	+	0.0820883i
$623$	−0.924485	+	2.34794i	−0.0370387	+	0.0940683i
$624$	9.30646	+	10.6195i	0.372557	+	0.425120i
$625$	11.4804	−	9.63320i	0.459216	−	0.385328i
$626$	−14.1018	+	9.41677i	−0.563619	+	0.376370i
$627$	2.33915	−	3.50664i	0.0934167	−	0.140042i
$628$	−1.97878	−	15.0958i	−0.0789620	−	0.602386i
$629$	−31.2142	−	18.0215i	−1.24459	−	0.718566i
$630$	−2.40430	−	9.08025i	−0.0957896	−	0.361766i
$631$	−9.08927	+	5.24769i	−0.361838	+	0.208907i	−0.669887	−	0.742463i	$-0.733657\pi$
$631$	−9.08927	+	5.24769i	−0.361838	+	0.208907i	0.308049	+	0.951371i	$0.400324\pi$
$632$	−11.2721	−	18.6111i	−0.448380	−	0.740311i
$633$	12.6598	+	12.1004i	0.503181	+	0.480948i
$634$	25.6697	−	1.67525i	1.01947	−	0.0665327i
$635$	13.1414	+	4.78308i	0.521501	+	0.189811i
$636$	−0.145274	−	2.20933i	−0.00576047	−	0.0876055i
$637$	−0.742516	+	14.2473i	−0.0294196	+	0.564500i
$638$	−1.25650	−	2.85780i	−0.0497455	−	0.113141i
$639$	39.6049	+	12.4203i	1.56675	+	0.491338i
$640$	−2.26832	+	9.19167i	−0.0896631	+	0.363333i
$641$	−10.9001	−	9.14631i	−0.430530	−	0.361257i	0.401622	−	0.915806i	$-0.368447\pi$
$641$	−10.9001	−	9.14631i	−0.430530	−	0.361257i	−0.832152	+	0.554548i	$0.812891\pi$
$642$	−3.71096	+	21.1064i	−0.146460	+	0.833005i
$643$	−20.9452	−	7.62342i	−0.825997	−	0.300638i	−0.105782	−	0.994389i	$-0.533735\pi$
$643$	−20.9452	−	7.62342i	−0.825997	−	0.300638i	−0.720215	+	0.693751i	$0.755957\pi$
$644$	−5.75968	+	23.0600i	−0.226963	+	0.908691i
$645$	−11.9770	+	1.32104i	−0.471594	+	0.0520160i
$646$	−16.3712	+	56.1085i	−0.644116	+	2.20756i
$647$	−2.32029	+	4.01887i	−0.0912202	+	0.157998i	−0.908025	−	0.418916i	$-0.862410\pi$
$647$	−2.32029	+	4.01887i	−0.0912202	+	0.157998i	0.816805	+	0.576914i	$0.195743\pi$
$648$	−20.4949	+	15.0983i	−0.805116	+	0.593117i
$649$	−1.91056	+	1.10306i	−0.0749962	+	0.0432991i
$650$	−8.56753	−	8.95478i	−0.336046	−	0.351236i
$651$	−16.2953	+	7.53037i	−0.638664	+	0.295138i
$652$	−2.34092	−	0.103522i	−0.0916774	−	0.00405423i
$653$	2.73896	+	15.5334i	0.107184	+	0.607870i	0.990326	+	0.138764i	$0.0443129\pi$
$653$	2.73896	+	15.5334i	0.107184	+	0.607870i	−0.883142	+	0.469107i	$0.844576\pi$
$654$	13.5884	+	37.2770i	0.531350	+	1.45765i
$655$	−8.38430	+	9.99202i	−0.327602	+	0.390420i
$656$	7.77772	−	16.6306i	0.303669	−	0.649318i
$657$	−32.6178	−	10.2291i	−1.27254	−	0.399074i
$658$	−0.477109	−	0.152795i	−0.0185996	−	0.00595656i
$659$	−8.86427	−	24.3544i	−0.345303	−	0.948712i	−0.983829	−	0.179112i	$-0.942678\pi$
$659$	−8.86427	−	24.3544i	−0.345303	−	0.948712i	0.638526	−	0.769600i	$-0.279545\pi$
$660$	−0.682698	+	0.456372i	−0.0265740	+	0.0177642i
$661$	−34.1463	+	6.02091i	−1.32814	+	0.234186i	−0.792298	−	0.610134i	$-0.791116\pi$
$661$	−34.1463	+	6.02091i	−1.32814	+	0.234186i	−0.535839	+	0.844320i	$0.680004\pi$
$662$	1.23922	+	18.9884i	0.0481636	+	0.738006i
$663$	−4.76481	−	16.3005i	−0.185050	−	0.633060i
$664$	0.293764	+	14.0031i	0.0114002	+	0.543424i
$665$	−18.6387	−	3.78927i	−0.722778	−	0.146941i
$666$	−31.7207	−	2.03889i	−1.22915	−	0.0790052i
$667$			35.0017i			1.35527i
$668$	28.9167	+	37.7288i	1.11882	+	1.45977i
$669$	6.05654	+	4.04010i	0.234159	+	0.156199i
$670$	−13.2550	+	0.865043i	−0.512084	+	0.0334195i
$671$	−0.0110949	−	0.0629221i	−0.000428312	−	0.00242908i
$672$	20.8309	+	15.4297i	0.803568	+	0.595213i
$673$	−3.27672	−	2.74949i	−0.126308	−	0.105985i	0.577445	−	0.816429i	$-0.304050\pi$
$673$	−3.27672	−	2.74949i	−0.126308	−	0.105985i	−0.703754	+	0.710444i	$0.748494\pi$
$674$	2.43841	−	1.07211i	0.0939240	−	0.0412961i
$675$	17.3919	−	14.0247i	0.669415	−	0.539813i
$676$	11.9601	−	13.0375i	0.460003	−	0.501441i
$677$	−3.68197	−	0.649231i	−0.141510	−	0.0249520i	0.102445	−	0.994739i	$-0.467334\pi$
$677$	−3.68197	−	0.649231i	−0.141510	−	0.0249520i	−0.243954	+	0.969787i	$0.578445\pi$
$678$	30.6596	−	17.7214i	1.17748	−	0.680587i
$679$	−0.0949732	+	3.64715i	−0.00364474	+	0.139965i
$680$	7.13458	−	8.87420i	0.273599	−	0.340310i
$681$	−29.9799	−	19.9985i	−1.14883	−	0.766345i
$682$	1.08492	+	1.13396i	0.0415437	+	0.0434214i
$683$	−13.2021	+	7.62222i	−0.505164	+	0.291656i	−0.730843	−	0.682545i	$-0.760873\pi$
$683$	−13.2021	+	7.62222i	−0.505164	+	0.291656i	0.225680	+	0.974202i	$0.427540\pi$
$684$	9.00050	+	50.7530i	0.344143	+	1.94059i
$685$	9.01196	−	5.20306i	0.344329	−	0.198799i
$686$	4.21413	+	25.8504i	0.160896	+	0.986971i
$687$	−30.0241	−	28.6975i	−1.14549	−	1.09488i
$688$	23.5406	−	23.4879i	0.897479	−	0.895468i
$689$	1.28287	−	0.226204i	0.0488734	−	0.00861769i
$690$	9.06645	−	1.60325i	0.345154	−	0.0610346i
$691$	−23.8179	−	19.9856i	−0.906075	−	0.760288i	0.0652929	−	0.997866i	$-0.479202\pi$
$691$	−23.8179	−	19.9856i	−0.906075	−	0.760288i	−0.971368	+	0.237579i	$0.923646\pi$
$692$	28.2295	−	8.88332i	1.07312	−	0.337693i
$693$	0.432762	+	2.20648i	0.0164393	+	0.0838172i
$694$	17.0061	−	23.1798i	0.645544	−	0.879893i
$695$	0.842933	+	2.31594i	0.0319743	+	0.0878486i
$696$	35.2677	+	14.6112i	1.33682	+	0.553837i
$697$	−16.9151	+	14.1935i	−0.640707	+	0.537617i
$698$	0.616747	−	0.411847i	0.0233442	−	0.0155886i
$699$	−6.21588	−	8.46370i	−0.235106	−	0.320126i
$700$	−18.8571	−	12.7307i	−0.712731	−	0.481174i
$701$	−46.0444			−1.73907			−0.869537	−	0.493868i	$-0.835582\pi$
$701$	−46.0444			−1.73907			−0.869537	+	0.493868i	$0.835582\pi$
$702$	−10.1407	−	11.0215i	−0.382735	−	0.415980i
$703$	−32.1815	+	55.7399i	−1.21375	+	2.10227i
$704$	0.685122	−	2.16025i	0.0258215	−	0.0814175i
$705$	0.0212757	+	0.192893i	0.000801291	+	0.00726477i
$706$	1.62805	+	24.9465i	0.0612726	+	0.938872i
$707$	−19.8105	+	10.7600i	−0.745051	+	0.404670i
$708$	7.54353	−	25.9010i	0.283503	−	0.973418i
$709$	10.4123	−	3.78978i	0.391043	−	0.142328i	−0.139013	−	0.990291i	$-0.544393\pi$
$709$	10.4123	−	3.78978i	0.391043	−	0.142328i	0.530056	+	0.847962i	$0.322171\pi$
$710$	−14.9886	+	6.59014i	−0.562513	+	0.247323i
$711$	12.4300	+	19.4450i	0.466163	+	0.729245i
$712$	−2.02967	+	1.77696i	−0.0760652	+	0.0665943i
$713$	−6.01805	−	16.5345i	−0.225378	−	0.619220i
$714$	−14.8942	−	27.3901i	−0.557401	−	1.02505i
$715$	−0.310559	−	0.370110i	−0.0116143	−	0.0138413i
$716$	4.27050	−	6.69506i	0.159596	−	0.250206i
$717$	10.2148	−	41.8842i	0.381477	−	1.56419i
$718$	4.42722	−	15.1733i	0.165222	−	0.566261i
$719$	−15.6819	+	27.1619i	−0.584837	+	1.01297i	0.410058	+	0.912059i	$0.365508\pi$
$719$	−15.6819	+	27.1619i	−0.584837	+	1.01297i	−0.994896	+	0.100909i	$0.967825\pi$
$720$	2.16930	−	9.80460i	0.0808451	−	0.365396i
$721$	2.65817	−	13.0751i	0.0989956	−	0.486941i
$722$	74.3997	+	21.7082i	2.76887	+	0.807894i
$723$	−13.4693	−	0.872395i	−0.500930	−	0.0324447i
$724$	−15.1271	−	29.0988i	−0.562195	−	1.08145i
$725$	−31.4845	−	11.4594i	−1.16931	−	0.425593i
$726$	−23.1577	+	13.3853i	−0.859464	+	0.496774i
$727$	35.1517	+	29.4958i	1.30371	+	1.09394i	0.989492	+	0.144586i	$0.0461852\pi$
$727$	35.1517	+	29.4958i	1.30371	+	1.09394i	0.314213	+	0.949352i	$0.398259\pi$
$728$	−7.69258	+	13.1696i	−0.285106	+	0.488098i
$729$	21.3443	−	16.5355i	0.790528	−	0.612426i
$730$	12.3443	−	5.42750i	0.456884	−	0.200881i
$731$	−37.5832	+	13.6792i	−1.39006	+	0.505942i
$732$	0.630170	+	0.461856i	0.0232918	+	0.0170707i
$733$	14.6853	+	17.5012i	0.542413	+	0.646423i	0.965727	−	0.259560i	$-0.0835777\pi$
$733$	14.6853	+	17.5012i	0.542413	+	0.646423i	−0.423314	+	0.905983i	$0.639133\pi$
$734$	−3.77513	+	7.64979i	−0.139342	+	0.282359i
$735$	8.47886	−	5.57187i	0.312748	−	0.205522i
$736$	−16.7804	+	19.0804i	−0.618534	+	0.703312i
$737$	3.17969			0.117126
$738$	−7.82027	+	17.8339i	−0.287868	+	0.656476i
$739$		−	34.1262i		−	1.25535i	−0.778475	−	0.627676i	$-0.784006\pi$
$739$		−	34.1262i		−	1.25535i	0.778475	−	0.627676i	$-0.215994\pi$
$740$	9.95202	−	7.62759i	0.365844	−	0.280396i
$741$	−29.1082	+	8.50863i	−1.06932	+	0.312572i
$742$	2.21355	−	0.905239i	0.0812620	−	0.0332324i
$743$	−29.4414	−	35.0869i	−1.08010	−	1.28721i	−0.955495	−	0.295006i	$-0.904678\pi$
$743$	−29.4414	−	35.0869i	−1.08010	−	1.28721i	−0.124604	−	0.992207i	$-0.539766\pi$
$744$	−19.1723	−	0.838425i	−0.702890	−	0.0307381i
$745$	8.11512	+	1.43091i	0.297315	+	0.0524246i
$746$	−3.57673	+	32.5745i	−0.130953	+	1.19264i
$747$	−0.670888	−	14.8406i	−0.0245465	−	0.542989i
$748$	−1.84258	+	2.00856i	−0.0673712	+	0.0734401i
$749$	−22.8925	+	3.42471i	−0.836474	+	0.125136i
$750$	−3.30091	+	18.7743i	−0.120532	+	0.685539i
$751$	39.8545	−	7.02743i	1.45431	−	0.256435i	0.610049	−	0.792363i	$-0.291150\pi$
$751$	39.8545	−	7.02743i	1.45431	−	0.256435i	0.844263	+	0.535929i	$0.180039\pi$
$752$	−0.378279	−	0.379128i	−0.0137944	−	0.0138254i
$753$	16.2862	+	22.1757i	0.593502	+	0.808127i
$754$	−6.29097	+	21.5608i	−0.229104	+	0.785200i
$755$	−3.18509			−0.115917
$756$	−22.4840	−	15.8262i	−0.817736	−	0.575594i
$757$	14.6804			0.533566			0.266783	−	0.963757i	$-0.414039\pi$
$757$	14.6804			0.533566			0.266783	+	0.963757i	$0.414039\pi$
$758$	−6.68140	+	22.8989i	−0.242679	+	0.831727i
$759$	−2.19069	+	0.241630i	−0.0795172	+	0.00877061i
$760$	−15.8469	−	12.7404i	−0.574826	−	0.462142i
$761$	−2.29626	+	0.404893i	−0.0832394	+	0.0146774i	−0.215113	−	0.976589i	$-0.569012\pi$
$761$	−2.29626	+	0.404893i	−0.0832394	+	0.0146774i	0.131873	+	0.991267i	$0.457901\pi$
$762$	38.4603	−	14.0198i	1.39327	−	0.507884i
$763$	−33.5352	+	26.6830i	−1.21405	+	0.965991i
$764$	−14.2669	−	13.0880i	−0.516159	−	0.473506i
$765$	−7.33739	+	9.59287i	−0.265284	+	0.346831i
$766$	4.65737	−	42.4162i	0.168278	−	1.53256i
$767$	15.6308	+	2.75613i	0.564395	+	0.0995181i
$768$	12.2205	+	24.8729i	0.440968	+	0.897523i
$769$	−8.67879	−	10.3430i	−0.312965	−	0.372977i	0.586515	−	0.809938i	$-0.300499\pi$
$769$	−8.67879	−	10.3430i	−0.312965	−	0.372977i	−0.899481	+	0.436961i	$0.856055\pi$
$770$	−0.701257	−	0.543123i	−0.0252715	−	0.0195728i
$771$	−35.0821	−	33.5320i	−1.26345	−	1.20763i
$772$	4.99915	+	6.52259i	0.179923	+	0.234753i
$773$			1.17713i			0.0423386i	0.999776	+	0.0211693i	$0.00673890\pi$
$773$			1.17713i			0.0423386i	−0.999776	+	0.0211693i	$0.993261\pi$
$774$	−24.3585	+	25.5096i	−0.875548	+	0.916923i
$775$	16.8433			0.605028
$776$	−1.87887	+	3.41791i	−0.0674475	+	0.122696i
$777$	−8.77166	−	33.1935i	−0.314681	−	1.19081i
$778$	−3.51117	+	7.11493i	−0.125882	+	0.255082i
$779$	25.3456	+	30.2057i	0.908101	+	1.08223i
$780$	5.87304	+	0.641952i	0.210288	+	0.0229856i
$781$	3.68306	−	1.34053i	0.131790	−	0.0479678i
$782$	27.9756	−	12.3002i	1.00041	−	0.439854i
$783$	−37.7710	−	14.5879i	−1.34983	−	0.521327i
$784$	−8.67459	+	26.6224i	−0.309807	+	0.950799i
$785$	−4.87983	−	4.09467i	−0.174169	−	0.146145i
$786$	0.0187371	+	38.1811i	0.000668330	+	1.36187i
$787$	−39.6569	−	14.4339i	−1.41362	−	0.514515i	−0.481428	−	0.876486i	$-0.659882\pi$
$787$	−39.6569	−	14.4339i	−1.41362	−	0.514515i	−0.932189	+	0.361971i	$0.882104\pi$
$788$	−16.6418	+	8.65133i	−0.592841	+	0.308191i
$789$	−22.3901	−	45.3146i	−0.797109	−	1.61324i
$790$	−8.73947	−	2.54998i	−0.310936	−	0.0907243i
$791$	28.6513	+	25.3411i	1.01872	+	0.901027i
$792$	−0.671025	+	2.30821i	−0.0238438	+	0.0820185i
$793$	−0.229837	+	0.398090i	−0.00816176	+	0.0141366i
$794$	−9.51468	+	32.6094i	−0.337663	+	1.15726i
$795$	−0.669684	−	0.640094i	−0.0237512	−	0.0227018i
$796$	7.90312	+	5.04108i	0.280119	+	0.178676i
$797$	−9.49270	−	11.3130i	−0.336249	−	0.400725i	0.571253	−	0.820774i	$-0.306457\pi$
$797$	−9.49270	−	11.3130i	−0.336249	−	0.400725i	−0.907502	+	0.420049i	$0.862013\pi$
$798$	−48.9111	+	26.5969i	−1.73144	+	0.941519i
$799$	0.220306	+	0.605287i	0.00779388	+	0.0214135i
$800$	−11.6692	−	21.3411i	−0.412569	−	0.754520i
$801$	2.10656	−	1.93629i	0.0744315	−	0.0684154i
$802$	12.8218	−	5.63742i	0.452753	−	0.199064i
$803$	−3.03330	+	1.10403i	−0.107043	+	0.0389603i
$804$	−28.0814	+	26.8934i	−0.990354	+	0.948457i
$805$	4.74653	+	8.73899i	0.167293	+	0.308009i
$806$	−0.735291	−	11.2668i	−0.0258995	−	0.396855i
$807$	6.03286	−	4.43064i	0.212367	−	0.155966i
$808$	−24.0953	+	0.505484i	−0.847669	+	0.0177829i
$809$	11.5634	−	20.0283i	0.406546	−	0.704159i	−0.587954	−	0.808895i	$-0.700066\pi$
$809$	11.5634	−	20.0283i	0.406546	−	0.704159i	0.994500	+	0.104736i	$0.0333996\pi$
$810$	−2.04858	+	10.4520i	−0.0719797	+	0.367245i
$811$	4.18981			0.147124			0.0735621	−	0.997291i	$-0.476563\pi$
$811$	4.18981			0.147124			0.0735621	+	0.997291i	$0.476563\pi$
$812$	−2.89337	+	41.1316i	−0.101537	+	1.44344i
$813$	49.5765	−	5.46821i	1.73873	−	0.191778i
$814$	−2.49614	+	1.66686i	−0.0874898	+	0.0584233i
$815$	−0.751037	+	0.630195i	−0.0263077	+	0.0220748i
$816$	−0.715424	−	33.3228i	−0.0250448	−	1.16653i
$817$	24.4272	+	67.1131i	0.854599	+	2.34799i
$818$	20.6640	−	28.1655i	0.722499	−	0.984785i
$819$	7.81882	−	14.1618i	0.273212	−	0.494854i
$820$	−2.30583	−	7.32747i	−0.0805229	−	0.255886i
$821$	40.7845	+	34.2222i	1.42339	+	1.19436i	0.949495	+	0.313782i	$0.101596\pi$
$821$	40.7845	+	34.2222i	1.42339	+	1.19436i	0.473893	+	0.880582i	$0.342848\pi$
$822$	10.4041	−	28.6287i	0.362884	−	0.998539i
$823$	−17.8860	+	3.15378i	−0.623466	+	0.109934i	−0.476452	−	0.879200i	$-0.658077\pi$
$823$	−17.8860	+	3.15378i	−0.623466	+	0.109934i	−0.147014	+	0.989134i	$0.546966\pi$
$824$	8.93739	−	11.1166i	0.311349	−	0.387265i
$825$	0.499876	−	2.04967i	0.0174034	−	0.0713603i
$826$	29.1163	−	1.14005i	1.01309	−	0.0396673i
$827$	−10.1949	+	5.88605i	−0.354513	+	0.204678i	−0.666671	−	0.745352i	$-0.732281\pi$
$827$	−10.1949	+	5.88605i	−0.354513	+	0.204678i	0.312158	+	0.950030i	$0.398948\pi$
$828$	17.3034	−	20.6625i	0.601335	−	0.718073i
$829$	6.47455	−	3.73808i	0.224870	−	0.129829i	−0.383333	−	0.923610i	$-0.625224\pi$
$829$	6.47455	−	3.73808i	0.224870	−	0.129829i	0.608203	+	0.793781i	$0.291891\pi$
$830$	4.05124	+	4.23436i	0.140621	+	0.146977i
$831$	−26.7884	+	13.2362i	−0.929278	+	0.459160i
$832$	−13.7660	+	8.73739i	−0.477251	+	0.302915i
$833$	22.9597	−	24.6356i	0.795507	−	0.853574i
$834$	6.24948	+	3.60405i	0.216402	+	0.124798i
$835$	19.5870	+	3.45372i	0.677836	+	0.119521i
$836$	3.58672	+	3.29033i	0.124049	+	0.113798i
$837$	20.3508	+	0.396957i	0.703428	+	0.0137209i
$838$	−18.2207	+	8.01120i	−0.629423	+	0.276742i
$839$	30.8446	+	25.8817i	1.06487	+	0.893536i	0.994578	−	0.103990i	$-0.0331610\pi$
$839$	30.8446	+	25.8817i	1.06487	+	0.893536i	0.0702964	+	0.997526i	$0.477605\pi$
$840$	10.7868	−	1.13456i	0.372180	−	0.0391460i
$841$	5.50823	+	31.2387i	0.189939	+	1.07720i
$842$	−2.60061	+	0.169721i	−0.0896231	+	0.00584897i
$843$	0.379866	−	5.86492i	0.0130833	−	0.201999i
$844$	−16.0499	+	12.3012i	−0.552460	+	0.423426i
$845$		−	7.40256i		−	0.254656i
$846$	0.410838	+	0.392300i	0.0141249	+	0.0134875i
$847$	−21.6408	−	19.1406i	−0.743587	−	0.657678i
$848$	2.54664	+	0.225680i	0.0874519	+	0.00774989i
$849$	−17.0872	−	4.16725i	−0.586432	−	0.143020i
$850$	1.90509	+	29.1915i	0.0653440	+	1.00126i
$851$	33.1416	−	5.84376i	1.13608	−	0.200322i
$852$	−21.1889	+	42.9897i	−0.725920	+	1.47280i
$853$	−5.14428	−	14.1338i	−0.176137	−	0.483932i	0.819937	−	0.572453i	$-0.194008\pi$
$853$	−5.14428	−	14.1338i	−0.176137	−	0.483932i	−0.996074	+	0.0885210i	$0.971786\pi$
$854$	−0.257383	+	0.803690i	−0.00880746	+	0.0275017i
$855$	17.1302	+	13.1025i	0.585840	+	0.448097i
$856$	−23.4255	−	7.97387i	−0.800668	−	0.272541i
$857$	−21.4984	+	25.6208i	−0.734373	+	0.875191i	−0.995942	−	0.0899934i	$-0.971315\pi$
$857$	−21.4984	+	25.6208i	−0.734373	+	0.875191i	0.261570	+	0.965185i	$0.415760\pi$
$858$	−1.39288	−	0.244898i	−0.0475523	−	0.00836069i
$859$	−0.112787	−	0.639646i	−0.00384824	−	0.0218245i	0.982823	−	0.184550i	$-0.0590827\pi$
$859$	−0.112787	−	0.639646i	−0.00384824	−	0.0218245i	−0.986671	+	0.162725i	$0.947972\pi$
$860$	0.614703	−	13.9001i	0.0209612	−	0.473991i
$861$	−20.9470	−	1.90540i	−0.713871	−	0.0649358i
$862$	3.44684	+	3.60264i	0.117400	+	0.122706i
$863$	−14.9562	+	8.63499i	−0.509117	+	0.293939i	−0.732470	−	0.680799i	$-0.761633\pi$
$863$	−14.9562	+	8.63499i	−0.509117	+	0.293939i	0.223354	+	0.974737i	$0.428299\pi$
$864$	−13.5963	−	26.0603i	−0.462557	−	0.886590i
$865$	6.19118	−	10.7234i	0.210506	−	0.364608i
$866$	−10.8323	+	37.1251i	−0.368095	+	1.26156i
$867$	−4.27851	+	9.74403i	−0.145306	+	0.330925i
$868$	−5.70520	−	19.9276i	−0.193647	−	0.676387i
$869$	2.04784	+	0.745354i	0.0694683	+	0.0252844i
$870$	15.0065	−	5.47025i	0.508767	−	0.185459i
$871$	−17.5242	−	14.7045i	−0.593784	−	0.498244i
$872$	−44.9416	+	8.90015i	−1.52192	+	0.301397i
$873$	1.90454	−	3.67240i	0.0644588	−	0.124292i
$874$	−21.9647	−	49.9567i	−0.742968	−	1.68981i
$875$	−20.3630	+	3.04629i	−0.688394	+	0.102983i
$876$	17.4508	−	35.4054i	0.589606	−	1.19624i
$877$	−50.9845	−	18.5568i	−1.72162	−	0.626620i	−0.723645	−	0.690173i	$-0.757535\pi$
$877$	−50.9845	−	18.5568i	−1.72162	−	0.626620i	−0.997978	+	0.0635530i	$0.979757\pi$
$878$	28.7722	−	1.87773i	0.971016	−	0.0633703i
$879$	−6.63017	+	27.1861i	−0.223630	+	0.916963i
$880$	−0.399774	−	0.859835i	−0.0134764	−	0.0289850i
$881$	30.6839	−	17.7154i	1.03377	−	0.596846i	0.115706	−	0.993283i	$-0.463087\pi$
$881$	30.6839	−	17.7154i	1.03377	−	0.596846i	0.918062	+	0.396437i	$0.129754\pi$
$882$	8.51483	−	28.4517i	0.286709	−	0.958018i
$883$	−24.0832	−	13.9044i	−0.810463	−	0.467921i	0.0366535	−	0.999328i	$-0.488330\pi$
$883$	−24.0832	−	13.9044i	−0.810463	−	0.467921i	−0.847117	+	0.531407i	$0.821664\pi$
$884$	19.4436	−	2.54870i	0.653957	−	0.0857221i
$885$	−5.00008	−	10.1195i	−0.168076	−	0.340162i
$886$	28.2922	−	18.8928i	0.950495	−	0.634715i
$887$	15.4345	−	12.9511i	0.518240	−	0.434855i	−0.345778	−	0.938317i	$-0.612385\pi$
$887$	15.4345	−	12.9511i	0.518240	−	0.434855i	0.864018	+	0.503461i	$0.167940\pi$
$888$	7.94659	−	35.8329i	0.266670	−	1.20247i
$889$	27.5301	+	34.5997i	0.923329	+	1.16044i
$890$	−0.123192	+	1.12195i	−0.00412941	+	0.0376080i
$891$	0.652280	−	2.46473i	0.0218522	−	0.0825715i
$892$	−5.68294	+	6.19486i	−0.190279	+	0.207419i
$893$	1.08087	−	0.393406i	0.0361701	−	0.0131648i
$894$	20.8833	−	12.0707i	0.698443	−	0.403703i
$895$	−0.576962	−	3.27211i	−0.0192857	−	0.109375i
$896$	−21.2964	+	21.0348i	−0.711464	+	0.702723i
$897$	13.1910	+	8.79921i	0.440433	+	0.293797i
$898$	9.03337	+	36.9612i	0.301448	+	1.23341i
$899$	−15.2623	−	26.4352i	−0.509028	−	0.881662i
$900$	12.9212	+	22.3295i	0.430706	+	0.744316i
$901$	−2.66291	−	1.53743i	−0.0887146	−	0.0512194i
$902$	0.436563	+	1.78626i	0.0145360	+	0.0594758i
$903$	−34.4724	−	16.2196i	−1.14717	−	0.539755i
$904$	14.7884	+	38.1233i	0.491856	+	1.26796i
$905$	−12.8944	−	4.69318i	−0.428625	−	0.156007i
$906$	−7.13914	+	5.99642i	−0.237182	+	0.199218i
$907$	−53.8985	−	9.50377i	−1.78967	−	0.315567i	−0.822324	−	0.569020i	$-0.807323\pi$
$907$	−53.8985	−	9.50377i	−1.78967	−	0.315567i	−0.967348	+	0.253452i	$0.918434\pi$
$908$	28.1306	−	30.6646i	0.933547	−	1.01764i
$909$	25.5365	−	1.15441i	0.846991	−	0.0382893i
$910$	1.35315	+	6.23627i	0.0448564	+	0.206730i
$911$	31.5609	+	5.56503i	1.04566	+	0.184378i	0.669985	−	0.742375i	$-0.266301\pi$
$911$	31.5609	+	5.56503i	1.04566	+	0.184378i	0.375673	+	0.926752i	$0.377412\pi$
$912$	−59.5052	+	1.27755i	−1.97042	+	0.0423038i
$913$	−0.901710	−	1.07462i	−0.0298422	−	0.0355646i
$914$	−6.86171	+	13.9043i	−0.226965	+	0.459915i
$915$	0.324928	−	0.0358390i	0.0107418	−	0.00118480i
$916$	38.0642	−	29.1738i	1.25768	−	0.963929i
$917$	−39.1072	+	13.0914i	−1.29143	+	0.432317i
$918$	1.61384	+	35.3154i	0.0532648	+	1.16558i
$919$	−11.9972	+	6.92658i	−0.395751	+	0.228487i	−0.684649	−	0.728873i	$-0.740044\pi$
$919$	−11.9972	+	6.92658i	−0.395751	+	0.228487i	0.288898	+	0.957360i	$0.406711\pi$
$920$	0.222984	+	10.6291i	0.00735155	+	0.350432i
$921$	−39.4861	+	4.35525i	−1.30111	+	0.143510i
$922$	0.783619	−	0.523280i	0.0258071	−	0.0172333i
$923$	−26.4977	−	9.64437i	−0.872182	−	0.317448i
$924$	−2.59433	+	0.102856i	−0.0853470	+	0.00338371i
$925$	−5.59390	+	31.7246i	−0.183926	+	1.04310i
$926$	−11.4945	−	1.26212i	−0.377733	−	0.0414757i
$927$	−9.19144	+	12.0169i	−0.301887	+	0.394685i
$928$	−22.9204	+	37.6526i	−0.752400	+	1.23601i
$929$	−25.9622	+	30.9405i	−0.851791	+	1.01513i	0.147867	+	0.989007i	$0.452759\pi$
$929$	−25.9622	+	30.9405i	−0.851791	+	1.01513i	−0.999659	+	0.0261183i	$0.991685\pi$
$930$	−6.14838	+	5.16424i	−0.201613	+	0.169342i
$931$	−43.9924	−	40.9997i	−1.44179	−	1.34371i
$932$	10.7586	−	5.59291i	0.352410	−	0.183202i
$933$	2.45063	+	0.597664i	0.0802302	+	0.0195666i
$934$	38.6258	+	11.2701i	1.26387	+	0.368770i
$935$			1.14044i			0.0372964i
$936$	14.3725	−	9.61800i	0.469781	−	0.314374i
$937$	10.9014	+	6.29393i	0.356133	+	0.205614i	0.667383	−	0.744714i	$-0.267414\pi$
$937$	10.9014	+	6.29393i	0.356133	+	0.205614i	−0.311250	+	0.950328i	$0.600748\pi$
$938$	−37.1646	−	19.5597i	−1.21347	−	0.638646i
$939$	9.19973	+	18.6190i	0.300222	+	0.607608i
$940$	−0.223865	−	0.00989996i	−0.00730169	−	0.000322901i
$941$	−5.64087	+	15.4982i	−0.183887	+	0.505225i	−0.997045	−	0.0768174i	$-0.975524\pi$
$941$	−5.64087	+	15.4982i	−0.183887	+	0.505225i	0.813158	+	0.582043i	$0.197746\pi$
$942$	−18.6466	+	0.00915070i	−0.607539	+	0.000298146i
$943$	3.58008	−	20.3036i	0.116583	−	0.661177i
$944$	28.2172	+	13.1964i	0.918390	+	0.429507i
$945$	−11.4087	+	1.47988i	−0.371123	+	0.0481404i
$946$	−0.363525	+	3.31074i	−0.0118192	+	0.107642i
$947$	4.18030	+	0.737100i	0.135841	+	0.0239525i	0.241155	−	0.970487i	$-0.422474\pi$
$947$	4.18030	+	0.737100i	0.135841	+	0.0239525i	−0.105314	+	0.994439i	$0.533585\pi$
$948$	−24.3896	+	10.7378i	−0.792137	+	0.348748i
$949$	21.8229	+	7.94290i	0.708403	+	0.257837i
$950$	52.1279	−	3.40196i	1.69125	−	0.110374i
$951$	2.03633	−	31.4398i	0.0660324	−	1.01951i
$952$	33.8917	−	12.1418i	1.09844	−	0.393517i
$953$	18.2350	−	31.5839i	0.590689	−	1.02310i	−0.403451	−	0.915001i	$-0.632190\pi$
$953$	18.2350	−	31.5839i	0.590689	−	1.02310i	0.994140	−	0.108101i	$-0.0344771\pi$
$954$	−2.70612	−	0.173939i	−0.0876139	−	0.00563149i
$955$	−8.10064			−0.262131
$956$	45.9811	+	19.0762i	1.48714	+	0.616969i
$957$	−3.66987	+	1.07274i	−0.118630	+	0.0346768i
$958$	−2.37630	−	3.55854i	−0.0767748	−	0.114971i
$959$	32.8900	+	0.856469i	1.06207	+	0.0276568i
$960$	10.8030	+	4.21238i	0.348664	+	0.135954i
$961$	−11.9925	−	10.0629i	−0.386853	−	0.324608i
$962$	21.4654	+	2.35693i	0.692071	+	0.0759905i
$963$	25.0439	+	7.85386i	0.807028	+	0.253087i
$964$	3.38188	−	15.2143i	0.108923	−	0.490019i
$965$	3.38622	+	0.597082i	0.109006	+	0.0192207i
$966$	27.0915	+	10.6517i	0.871654	+	0.342713i
$967$	5.60859	−	15.4095i	0.180360	−	0.495536i	−0.816260	−	0.577685i	$-0.803956\pi$
$967$	5.60859	−	15.4095i	0.180360	−	0.495536i	0.996620	+	0.0821493i	$0.0261784\pi$
$968$	−11.1699	−	28.7951i	−0.359015	−	0.925511i
$969$	65.5439	+	28.7797i	2.10557	+	0.924536i
$970$	0.387435	+	1.58524i	0.0124398	+	0.0508990i
$971$	−6.84699	−	11.8593i	−0.219730	−	0.380584i	0.734995	−	0.678072i	$-0.237184\pi$
$971$	−6.84699	−	11.8593i	−0.219730	−	0.380584i	−0.954725	+	0.297488i	$0.903851\pi$
$972$	15.0857	+	27.2841i	0.483875	+	0.875137i
$973$	−1.55242	+	7.63606i	−0.0497682	+	0.244801i
$974$	−17.4944	−	18.2852i	−0.560558	−	0.585895i
$975$	−12.2337	+	8.98462i	−0.391791	+	0.287738i
$976$	−0.638642	+	0.637211i	−0.0204424	+	0.0203966i
$977$	−18.0698	+	15.1623i	−0.578103	+	0.485086i	−0.884324	−	0.466875i	$-0.845380\pi$
$977$	−18.0698	+	15.1623i	−0.578103	+	0.485086i	0.306220	+	0.951961i	$0.400936\pi$
$978$	−0.496954	+	2.82647i	−0.0158908	+	0.0903807i
$979$	0.0469171	−	0.266080i	0.00149948	−	0.00850396i
$980$	4.85539	+	10.6618i	0.155100	+	0.340579i
$981$	47.4254	−	10.5907i	1.51418	−	0.338136i
$982$	−5.50453	+	7.50282i	−0.175657	+	0.239425i
$983$	8.71903	−	49.4481i	0.278094	−	1.57715i	−0.450865	−	0.892592i	$-0.648885\pi$
$983$	8.71903	−	49.4481i	0.278094	−	1.57715i	0.728959	−	0.684557i	$-0.240004\pi$
$984$	−18.9634	−	12.0829i	−0.604531	−	0.385188i
$985$	−2.68407	+	7.37443i	−0.0855216	+	0.234969i
$986$	44.0891	−	29.4415i	1.40408	−	0.937610i
$987$	−0.261221	+	0.555186i	−0.00831476	+	0.0176718i
$988$	−4.55127	−	34.7208i	−0.144795	−	1.10462i
$989$	18.6715	−	32.3399i	0.593718	−	1.02835i
$990$	0.445968	+	0.901465i	0.0141738	+	0.0286504i
$991$	−24.9959	+	14.4314i	−0.794021	+	0.458428i	−0.841376	−	0.540450i	$-0.818254\pi$
$991$	−24.9959	+	14.4314i	−0.794021	+	0.458428i	0.0473553	+	0.998878i	$0.484921\pi$
$992$	4.35355	−	21.7275i	0.138225	−	0.689850i
$993$	23.2567	+	1.50632i	0.738029	+	0.0478015i
$994$	−51.2942	−	6.98789i	−1.62695	−	0.221642i
$995$	3.86254	−	0.681070i	0.122451	−	0.0215914i
$996$	17.0524	+	1.86391i	0.540325	+	0.0590602i
$997$	−9.26616	−	25.4586i	−0.293462	−	0.806281i	−0.995554	−	0.0941943i	$-0.969973\pi$
$997$	−9.26616	−	25.4586i	−0.293462	−	0.806281i	0.702092	−	0.712087i	$-0.252250\pi$
$998$	33.4721	−	45.6233i	1.05954	−	1.44418i
$999$	−7.50649	+	38.1993i	−0.237495	+	1.20857i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bt.a.367.128	yes	840
4.3	odd	2	inner	756.2.bt.a.367.5	yes	840
7.5	odd	6		756.2.cd.a.691.59	yes	840
27.22	even	9		756.2.cd.a.535.91	yes	840
28.19	even	6		756.2.cd.a.691.91	yes	840
108.103	odd	18		756.2.cd.a.535.59	yes	840
189.103	odd	18	inner	756.2.bt.a.103.5	✓	840
756.103	even	18	inner	756.2.bt.a.103.128	yes	840

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bt.a.103.5	✓	840	189.103	odd	18	inner
756.2.bt.a.103.128	yes	840	756.103	even	18	inner
756.2.bt.a.367.5	yes	840	4.3	odd	2	inner
756.2.bt.a.367.128	yes	840	1.1	even	1	trivial
756.2.cd.a.535.59	yes	840	108.103	odd	18
756.2.cd.a.535.91	yes	840	27.22	even	9
756.2.cd.a.691.59	yes	840	7.5	odd	6
756.2.cd.a.691.91	yes	840	28.19	even	6

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bt (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.35760 + 0.396119i) q^{2} +(0.696355 - 1.58590i) q^{3} +(1.68618 + 1.07554i) q^{4} +(0.824097 - 0.145310i) q^{5} +(1.57358 - 1.87719i) q^{6} +(2.46179 + 0.969313i) q^{7} +(1.86312 + 2.12809i) q^{8} +(-2.03018 - 2.20870i) q^{9} +O(q^{10})\)	\(q+(1.35760 + 0.396119i) q^{2} +(0.696355 - 1.58590i) q^{3} +(1.68618 + 1.07554i) q^{4} +(0.824097 - 0.145310i) q^{5} +(1.57358 - 1.87719i) q^{6} +(2.46179 + 0.969313i) q^{7} +(1.86312 + 2.12809i) q^{8} +(-2.03018 - 2.20870i) q^{9} +(1.17636 + 0.129166i) q^{10} +(-0.278983 - 0.0491922i) q^{11} +(2.87989 - 1.92516i) q^{12} +(1.31006 + 1.56127i) q^{13} +(2.95818 + 2.29111i) q^{14} +(0.343415 - 1.40813i) q^{15} +(1.68641 + 3.62712i) q^{16} -4.81084i q^{17} +(-1.88127 - 3.80274i) q^{18} -8.59082 q^{19} +(1.54586 + 0.641333i) q^{20} +(3.25152 - 3.22918i) q^{21} +(-0.359262 - 0.177294i) q^{22} +(2.88728 + 3.44093i) q^{23} +(4.67234 - 1.47282i) q^{24} +(-4.04044 + 1.47060i) q^{25} +(1.16010 + 2.63853i) q^{26} +(-4.91652 + 1.68163i) q^{27} +(3.10849 + 4.28221i) q^{28} +(5.96928 + 5.00882i) q^{29} +(1.02401 - 1.77564i) q^{30} +(-3.68103 - 1.33978i) q^{31} +(0.852701 + 5.59222i) q^{32} +(-0.272285 + 0.408184i) q^{33} +(1.90566 - 6.53121i) q^{34} +(2.16961 + 0.441083i) q^{35} +(-1.04769 - 5.90782i) q^{36} +(3.74603 - 6.48831i) q^{37} +(-11.6629 - 3.40298i) q^{38} +(3.38829 - 0.990433i) q^{39} +(1.84463 + 1.48302i) q^{40} +(-2.95032 - 3.51605i) q^{41} +(5.69342 - 3.09596i) q^{42} +(-2.84340 - 7.81219i) q^{43} +(-0.417507 - 0.383005i) q^{44} +(-1.99401 - 1.52518i) q^{45} +(2.55677 + 5.81512i) q^{46} +(-0.125817 + 0.0457938i) q^{47} +(6.92661 - 0.148711i) q^{48} +(5.12086 + 4.77250i) q^{49} +(-6.06786 + 0.396000i) q^{50} +(-7.62952 - 3.35005i) q^{51} +(0.529783 + 4.04162i) q^{52} +(0.319577 - 0.553524i) q^{53} +(-7.34081 + 0.335460i) q^{54} -0.237057 q^{55} +(2.52384 + 7.04487i) q^{56} +(-5.98226 + 13.6242i) q^{57} +(6.11984 + 9.16454i) q^{58} +(5.96567 - 5.00579i) q^{59} +(2.09356 - 2.00499i) q^{60} +(0.0771396 + 0.211939i) q^{61} +(-4.46666 - 3.27702i) q^{62} +(-2.85696 - 7.40525i) q^{63} +(-1.05755 + 7.92979i) q^{64} +(1.30649 + 1.09627i) q^{65} +(-0.531345 + 0.446296i) q^{66} +(-11.0538 + 1.94908i) q^{67} +(5.17427 - 8.11194i) q^{68} +(7.46755 - 2.18284i) q^{69} +(2.77075 + 1.45824i) q^{70} +(-11.9820 + 6.91779i) q^{71} +(0.917852 - 8.43549i) q^{72} +(9.86810 - 5.69735i) q^{73} +(7.65577 - 7.32469i) q^{74} +(-0.481352 + 7.43181i) q^{75} +(-14.4857 - 9.23981i) q^{76} +(-0.639115 - 0.391523i) q^{77} +(4.99229 - 0.00244993i) q^{78} +(-7.57594 - 1.33584i) q^{79} +(1.91682 + 2.74405i) q^{80} +(-0.756743 + 8.96813i) q^{81} +(-2.61259 - 5.94208i) q^{82} +(3.79339 + 3.18303i) q^{83} +(8.95578 - 1.94783i) q^{84} +(-0.699065 - 3.96460i) q^{85} +(-0.765665 - 11.7322i) q^{86} +(12.1002 - 5.97879i) q^{87} +(-0.415093 - 0.685352i) q^{88} +0.953752i q^{89} +(-2.10293 - 2.86046i) q^{90} +(1.71174 + 5.11339i) q^{91} +(1.16760 + 8.90742i) q^{92} +(-4.68807 + 4.90479i) q^{93} +(-0.188950 + 0.0123312i) q^{94} +(-7.07967 + 1.24834i) q^{95} +(9.46250 + 2.54187i) q^{96} +(0.471632 + 1.29580i) q^{97} +(5.06163 + 8.50764i) q^{98} +(0.457734 + 0.716059i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9}+O(q^{10}) \) 840 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9	\( 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9} - 9 q^{12} - 21 q^{14} - 3 q^{16} - 3 q^{18} - 12 q^{21} - 12 q^{22} - 9 q^{24} - 6 q^{25} - 18 q^{26} - 12 q^{28} - 36 q^{29} - 39 q^{30} + 27 q^{32} - 18 q^{33} + 18 q^{34} + 18 q^{36} + 6 q^{37} - 99 q^{38} + 36 q^{40} + 9 q^{42} + 3 q^{44} - 18 q^{45} + 3 q^{46} - 12 q^{49} + 3 q^{50} - 9 q^{52} - 12 q^{53} - 135 q^{54} + 15 q^{56} - 42 q^{57} - 3 q^{58} - 33 q^{60} - 18 q^{61} - 99 q^{62} - 6 q^{64} + 18 q^{65} - 9 q^{66} - 54 q^{68} + 72 q^{69} - 36 q^{70} - 111 q^{72} - 18 q^{73} + 93 q^{74} - 36 q^{76} - 36 q^{77} + 6 q^{78} - 18 q^{80} - 30 q^{81} - 18 q^{82} + 84 q^{84} + 6 q^{85} + 135 q^{86} - 51 q^{88} + 81 q^{90} + 48 q^{92} - 6 q^{93} - 9 q^{94} - 9 q^{96} - 117 q^{98}+O(q^{100}) \) 840 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9 - 9 * q^12 - 21 * q^14 - 3 * q^16 - 3 * q^18 - 12 * q^21 - 12 * q^22 - 9 * q^24 - 6 * q^25 - 18 * q^26 - 12 * q^28 - 36 * q^29 - 39 * q^30 + 27 * q^32 - 18 * q^33 + 18 * q^34 + 18 * q^36 + 6 * q^37 - 99 * q^38 + 36 * q^40 + 9 * q^42 + 3 * q^44 - 18 * q^45 + 3 * q^46 - 12 * q^49 + 3 * q^50 - 9 * q^52 - 12 * q^53 - 135 * q^54 + 15 * q^56 - 42 * q^57 - 3 * q^58 - 33 * q^60 - 18 * q^61 - 99 * q^62 - 6 * q^64 + 18 * q^65 - 9 * q^66 - 54 * q^68 + 72 * q^69 - 36 * q^70 - 111 * q^72 - 18 * q^73 + 93 * q^74 - 36 * q^76 - 36 * q^77 + 6 * q^78 - 18 * q^80 - 30 * q^81 - 18 * q^82 + 84 * q^84 + 6 * q^85 + 135 * q^86 - 51 * q^88 + 81 * q^90 + 48 * q^92 - 6 * q^93 - 9 * q^94 - 9 * q^96 - 117 * q^98

Introduction

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