LMFDB - Embedded newform 756.2.bt.a.103.5

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			103.5
Character	$\chi$	$=$	756.103
Dual form			756.2.bt.a.367.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41121 + 0.0920983i) q^{2} +(-0.696355 - 1.58590i) q^{3} +(1.98304 - 0.259940i) q^{4} +(0.824097 + 0.145310i) q^{5} +(1.12876 + 2.17391i) q^{6} +(-2.46179 + 0.969313i) q^{7} +(-2.77454 + 0.549465i) q^{8} +(-2.03018 + 2.20870i) q^{9} +O(q^{10})$	\(q+(-1.41121 + 0.0920983i) q^{2} +(-0.696355 - 1.58590i) q^{3} +(1.98304 - 0.259940i) q^{4} +(0.824097 + 0.145310i) q^{5} +(1.12876 + 2.17391i) q^{6} +(-2.46179 + 0.969313i) q^{7} +(-2.77454 + 0.549465i) q^{8} +(-2.03018 + 2.20870i) q^{9} +(-1.17636 - 0.129166i) q^{10} +(0.278983 - 0.0491922i) q^{11} +(-1.79314 - 2.96389i) q^{12} +(1.31006 - 1.56127i) q^{13} +(3.38484 - 1.59463i) q^{14} +(-0.343415 - 1.40813i) q^{15} +(3.86486 - 1.03094i) q^{16} +4.81084i q^{17} +(2.66159 - 3.30392i) q^{18} +8.59082 q^{19} +(1.67199 + 0.0739399i) q^{20} +(3.25152 + 3.22918i) q^{21} +(-0.389173 + 0.0951144i) q^{22} +(-2.88728 + 3.44093i) q^{23} +(2.80347 + 4.01753i) q^{24} +(-4.04044 - 1.47060i) q^{25} +(-1.70498 + 2.32394i) q^{26} +(4.91652 + 1.68163i) q^{27} +(-4.62986 + 2.56210i) q^{28} +(5.96928 - 5.00882i) q^{29} +(0.614318 + 1.95553i) q^{30} +(3.68103 - 1.33978i) q^{31} +(-5.35919 + 1.81082i) q^{32} +(-0.272285 - 0.408184i) q^{33} +(-0.443070 - 6.78911i) q^{34} +(-2.16961 + 0.441083i) q^{35} +(-3.45179 + 4.90766i) q^{36} +(3.74603 + 6.48831i) q^{37} +(-12.1235 + 0.791200i) q^{38} +(-3.38829 - 0.990433i) q^{39} +(-2.36633 + 0.0496423i) q^{40} +(-2.95032 + 3.51605i) q^{41} +(-4.88598 - 4.25760i) q^{42} +(2.84340 - 7.81219i) q^{43} +(0.540446 - 0.170069i) q^{44} +(-1.99401 + 1.52518i) q^{45} +(3.75766 - 5.12179i) q^{46} +(0.125817 + 0.0457938i) q^{47} +(-4.32629 - 5.41140i) q^{48} +(5.12086 - 4.77250i) q^{49} +(5.83736 + 1.70321i) q^{50} +(7.62952 - 3.35005i) q^{51} +(2.19206 - 3.43659i) q^{52} +(0.319577 + 0.553524i) q^{53} +(-7.09312 - 1.92033i) q^{54} +0.237057 q^{55} +(6.29775 - 4.04207i) q^{56} +(-5.98226 - 13.6242i) q^{57} +(-7.96262 + 7.61827i) q^{58} +(-5.96567 - 5.00579i) q^{59} +(-1.04703 - 2.70310i) q^{60} +(0.0771396 - 0.211939i) q^{61} +(-5.07131 + 2.22973i) q^{62} +(2.85696 - 7.40525i) q^{63} +(7.39618 - 3.04903i) q^{64} +(1.30649 - 1.09627i) q^{65} +(0.421845 + 0.550958i) q^{66} +(11.0538 + 1.94908i) q^{67} +(1.25053 + 9.54006i) q^{68} +(7.46755 + 2.18284i) q^{69} +(3.02115 - 0.822279i) q^{70} +(11.9820 + 6.91779i) q^{71} +(4.41921 - 7.24366i) q^{72} +(9.86810 + 5.69735i) q^{73} +(-5.88400 - 8.81138i) q^{74} +(0.481352 + 7.43181i) q^{75} +(17.0359 - 2.23310i) q^{76} +(-0.639115 + 0.391523i) q^{77} +(4.87282 + 1.08565i) q^{78} +(7.57594 - 1.33584i) q^{79} +(3.33483 - 0.287991i) q^{80} +(-0.756743 - 8.96813i) q^{81} +(3.83970 - 5.23361i) q^{82} +(-3.79339 + 3.18303i) q^{83} +(7.28728 + 5.55838i) q^{84} +(-0.699065 + 3.96460i) q^{85} +(-3.29316 + 11.2865i) q^{86} +(-12.1002 - 5.97879i) q^{87} +(-0.747020 + 0.289777i) q^{88} -0.953752i q^{89} +(2.67351 - 2.33600i) q^{90} +(-1.71174 + 5.11339i) q^{91} +(-4.83114 + 7.57400i) q^{92} +(-4.68807 - 4.90479i) q^{93} +(-0.181772 - 0.0530371i) q^{94} +(7.07967 + 1.24834i) q^{95} +(6.60369 + 7.23818i) q^{96} +(0.471632 - 1.29580i) q^{97} +(-6.78708 + 7.20663i) 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 $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−1.41121	+	0.0920983i	−0.997877	+	0.0651233i
$2$	−1.41121	+	0.0920983i	−0.997877	+	0.0651233i
$3$	−0.696355	−	1.58590i	−0.402041	−	0.915622i
$3$	−0.696355	−	1.58590i	−0.402041	−	0.915622i
$4$	1.98304	−	0.259940i	0.991518	−	0.129970i
$5$	0.824097	+	0.145310i	0.368547	+	0.0649848i	0.354855	−	0.934921i	$-0.384530\pi$
$5$	0.824097	+	0.145310i	0.368547	+	0.0649848i	0.0136925	+	0.999906i	$0.495641\pi$
$6$	1.12876	+	2.17391i	0.460816	+	0.887496i
$7$	−2.46179	+	0.969313i	−0.930471	+	0.366366i
$7$	−2.46179	+	0.969313i	−0.930471	+	0.366366i
$8$	−2.77454	+	0.549465i	−0.980949	+	0.194265i
$9$	−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	$-0.541957\pi$
$11$	0.278983	−	0.0491922i	0.0841164	−	0.0148320i	0.215548	+	0.976493i	$0.430846\pi$
$12$	−1.79314	−	2.96389i	−0.517634	−	0.855602i
$13$	1.31006	−	1.56127i	0.363346	−	0.433019i	−0.553138	−	0.833089i	$-0.686570\pi$
$13$	1.31006	−	1.56127i	0.363346	−	0.433019i	0.916484	+	0.400071i	$0.131014\pi$
$14$	3.38484	−	1.59463i	0.904637	−	0.426184i
$15$	−0.343415	−	1.40813i	−0.0886695	−	0.363576i
$16$	3.86486	−	1.03094i	0.966215	−	0.257736i
$17$			4.81084i			1.16680i	0.812185	+	0.583400i	$0.198278\pi$
$17$			4.81084i			1.16680i	−0.812185	+	0.583400i	$0.801722\pi$
$18$	2.66159	−	3.30392i	0.627344	−	0.778742i
$19$	8.59082			1.97087			0.985435	−	0.170055i	$-0.0543944\pi$
$19$	8.59082			1.97087			0.985435	+	0.170055i	$0.0543944\pi$
$20$	1.67199	+	0.0739399i	0.373867	+	0.0165335i
$21$	3.25152	+	3.22918i	0.709540	+	0.704665i
$22$	−0.389173	+	0.0951144i	−0.0829720	+	0.0202785i
$23$	−2.88728	+	3.44093i	−0.602039	+	0.717483i	−0.977872	−	0.209205i	$-0.932912\pi$
$23$	−2.88728	+	3.44093i	−0.602039	+	0.717483i	0.375832	+	0.926688i	$0.377357\pi$
$24$	2.80347	+	4.01753i	0.572255	+	0.820076i
$25$	−4.04044	−	1.47060i	−0.808089	−	0.294120i
$26$	−1.70498	+	2.32394i	−0.334375	+	0.455762i
$27$	4.91652	+	1.68163i	0.946184	+	0.323629i
$28$	−4.62986	+	2.56210i	−0.874962	+	0.484192i
$29$	5.96928	−	5.00882i	1.10847	−	0.930115i	0.110503	−	0.993876i	$-0.464754\pi$
$29$	5.96928	−	5.00882i	1.10847	−	0.930115i	0.997965	+	0.0637608i	$0.0203095\pi$
$30$	0.614318	+	1.95553i	0.112159	+	0.357030i
$31$	3.68103	−	1.33978i	0.661132	−	0.240632i	0.0104068	−	0.999946i	$-0.496687\pi$
$31$	3.68103	−	1.33978i	0.661132	−	0.240632i	0.650725	+	0.759314i	$0.274465\pi$
$32$	−5.35919	+	1.81082i	−0.947380	+	0.320112i
$33$	−0.272285	−	0.408184i	−0.0473987	−	0.0710558i
$34$	−0.443070	−	6.78911i	−0.0759859	−	1.16432i
$35$	−2.16961	+	0.441083i	−0.366731	+	0.0745567i
$36$	−3.45179	+	4.90766i	−0.575298	+	0.817944i
$37$	3.74603	+	6.48831i	0.615843	+	1.06667i	0.990236	+	0.139402i	$0.0445180\pi$
$37$	3.74603	+	6.48831i	0.615843	+	1.06667i	−0.374392	+	0.927270i	$0.622149\pi$
$38$	−12.1235	+	0.791200i	−1.96669	+	0.128350i
$39$	−3.38829	−	0.990433i	−0.542561	−	0.158596i
$40$	−2.36633	+	0.0496423i	−0.374150	+	0.00784913i
$41$	−2.95032	+	3.51605i	−0.460762	+	0.549115i	−0.945533	−	0.325526i	$-0.894458\pi$
$41$	−2.95032	+	3.51605i	−0.460762	+	0.549115i	0.484771	+	0.874641i	$0.338903\pi$
$42$	−4.88598	−	4.25760i	−0.753924	−	0.656962i
$43$	2.84340	−	7.81219i	0.433615	−	1.19135i	−0.509963	−	0.860197i	$-0.670341\pi$
$43$	2.84340	−	7.81219i	0.433615	−	1.19135i	0.943578	−	0.331151i	$-0.107437\pi$
$44$	0.540446	−	0.170069i	0.0814752	−	0.0256388i
$45$	−1.99401	+	1.52518i	−0.297250	+	0.227360i
$46$	3.75766	−	5.12179i	0.554036	−	0.755166i
$47$	0.125817	+	0.0457938i	0.0183523	+	0.00667971i	0.351180	−	0.936308i	$-0.385781\pi$
$47$	0.125817	+	0.0457938i	0.0183523	+	0.00667971i	−0.332828	+	0.942988i	$0.608003\pi$
$48$	−4.32629	−	5.41140i	−0.624446	−	0.781068i
$49$	5.12086	−	4.77250i	0.731552	−	0.681786i
$50$	5.83736	+	1.70321i	0.825527	+	0.240870i
$51$	7.62952	−	3.35005i	1.06835	−	0.469101i
$52$	2.19206	−	3.43659i	0.303984	−	0.476570i
$53$	0.319577	+	0.553524i	0.0438973	+	0.0760324i	0.887139	−	0.461502i	$-0.152689\pi$
$53$	0.319577	+	0.553524i	0.0438973	+	0.0760324i	−0.843242	+	0.537534i	$0.819356\pi$
$54$	−7.09312	−	1.92033i	−0.965251	−	0.261324i
$55$	0.237057			0.0319647
$56$	6.29775	−	4.04207i	0.841572	−	0.540144i
$57$	−5.98226	−	13.6242i	−0.792370	−	1.80457i
$58$	−7.96262	+	7.61827i	−1.04554	+	1.00033i
$59$	−5.96567	−	5.00579i	−0.776664	−	0.651698i	0.165742	−	0.986169i	$-0.446998\pi$
$59$	−5.96567	−	5.00579i	−0.776664	−	0.651698i	−0.942406	+	0.334471i	$0.891442\pi$
$60$	−1.04703	−	2.70310i	−0.135171	−	0.348968i
$61$	0.0771396	−	0.211939i	0.00987672	−	0.0271361i	−0.934656	−	0.355553i	$-0.884293\pi$
$61$	0.0771396	−	0.211939i	0.00987672	−	0.0271361i	0.944533	+	0.328416i	$0.106515\pi$
$62$	−5.07131	+	2.22973i	−0.644057	+	0.283177i
$63$	2.85696	−	7.40525i	0.359943	−	0.932974i
$64$	7.39618	−	3.04903i	0.924522	−	0.381129i
$65$	1.30649	−	1.09627i	0.162050	−	0.135976i
$66$	0.421845	+	0.550958i	0.0519255	+	0.0678182i
$67$	11.0538	+	1.94908i	1.35043	+	0.238118i	0.801624	−	0.597829i	$-0.203970\pi$
$67$	11.0538	+	1.94908i	1.35043	+	0.238118i	0.548811	+	0.835947i	$0.315081\pi$
$68$	1.25053	+	9.54006i	0.151649	+	1.15690i
$69$	7.46755	+	2.18284i	0.898987	+	0.262783i
$70$	3.02115	−	0.822279i	0.361097	−	0.0982811i
$71$	11.9820	+	6.91779i	1.42200	+	0.820991i	0.996470	−	0.0839538i	$-0.0267548\pi$
$71$	11.9820	+	6.91779i	1.42200	+	0.820991i	0.425529	+	0.904945i	$0.360088\pi$
$72$	4.41921	−	7.24366i	0.520809	−	0.853673i
$73$	9.86810	+	5.69735i	1.15497	+	0.666825i	0.950094	−	0.311962i	$-0.100986\pi$
$73$	9.86810	+	5.69735i	1.15497	+	0.666825i	0.204880	+	0.978787i	$0.434320\pi$
$74$	−5.88400	−	8.81138i	−0.684001	−	1.02430i
$75$	0.481352	+	7.43181i	0.0555817	+	0.858152i
$76$	17.0359	−	2.23310i	1.95415	−	0.256154i
$77$	−0.639115	+	0.391523i	−0.0728340	+	0.0446181i
$78$	4.87282	+	1.08565i	0.551738	+	0.122926i
$79$	7.57594	−	1.33584i	0.852360	−	0.150294i	0.269634	−	0.962963i	$-0.413097\pi$
$79$	7.57594	−	1.33584i	0.852360	−	0.150294i	0.582726	+	0.812669i	$0.301986\pi$
$80$	3.33483	−	0.287991i	0.372845	−	0.0321984i
$81$	−0.756743	−	8.96813i	−0.0840826	−	0.996459i
$82$	3.83970	−	5.23361i	0.424024	−	0.577955i
$83$	−3.79339	+	3.18303i	−0.416378	+	0.349383i	−0.826783	−	0.562520i	$-0.809832\pi$
$83$	−3.79339	+	3.18303i	−0.416378	+	0.349383i	0.410405	+	0.911903i	$0.365387\pi$
$84$	7.28728	+	5.55838i	0.795107	+	0.606469i
$85$	−0.699065	+	3.96460i	−0.0758243	+	0.430021i
$86$	−3.29316	+	11.2865i	−0.355110	+	1.21706i
$87$	−12.1002	−	5.97879i	−1.29728	−	0.640993i
$88$	−0.747020	+	0.289777i	−0.0796326	+	0.0308903i
$89$		−	0.953752i		−	0.101098i	−0.998722	−	0.0505488i	$-0.983903\pi$
$89$		−	0.953752i		−	0.101098i	0.998722	−	0.0505488i	$-0.0160970\pi$
$90$	2.67351	−	2.33600i	0.281812	−	0.246236i
$91$	−1.71174	+	5.11339i	−0.179439	+	0.536029i
$92$	−4.83114	+	7.57400i	−0.503681	+	0.789644i
$93$	−4.68807	−	4.90479i	−0.486130	−	0.508603i
$94$	−0.181772	−	0.0530371i	−0.0187484	−	0.00547036i
$95$	7.07967	+	1.24834i	0.726358	+	0.128077i
$96$	6.60369	+	7.23818i	0.673986	+	0.738744i
$97$	0.471632	−	1.29580i	0.0478870	−	0.131568i	−0.913444	−	0.406965i	$-0.866587\pi$
$97$	0.471632	−	1.29580i	0.0478870	−	0.131568i	0.961331	+	0.275397i	$0.0888092\pi$
$98$	−6.78708	+	7.20663i	−0.685599	+	0.727979i
$99$	−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	0.421308	−	0.906918i	$-0.361571\pi$
$101$	−5.47709	−	6.52735i	−0.544991	−	0.649495i	−0.966299	+	0.257423i	$0.917127\pi$
$102$	−10.4583	+	5.43030i	−1.03553	+	0.537679i
$103$	0.875709	−	4.96639i	0.0862862	−	0.489353i	−0.910785	−	0.412880i	$-0.864523\pi$
$103$	0.875709	−	4.96639i	0.0862862	−	0.489353i	0.997072	−	0.0764733i	$-0.0243660\pi$
$104$	−2.77696	+	5.05165i	−0.272303	+	0.495355i
$105$	2.21033	+	3.13364i	0.215706	+	0.305812i
$106$	−0.501970	−	0.751707i	−0.0487556	−	0.0730123i
$107$	7.57672	+	4.37442i	0.732469	+	0.422891i	0.819325	−	0.573330i	$-0.194349\pi$
$107$	7.57672	+	4.37442i	0.732469	+	0.422891i	−0.0868559	+	0.996221i	$0.527682\pi$
$108$	10.1868	+	2.05672i	0.980221	+	0.197908i
$109$	−8.09892	−	14.0277i	−0.775736	−	1.34361i	−0.934380	−	0.356279i	$-0.884045\pi$
$109$	−8.09892	−	14.0277i	−0.775736	−	1.34361i	0.158643	−	0.987336i	$-0.449288\pi$
$110$	−0.334537	+	0.0218325i	−0.0318969	+	0.00208165i
$111$	7.68127	−	10.4590i	0.729074	−	0.992725i
$112$	−8.51519	+	6.28423i	−0.804610	+	0.593804i
$113$	13.5853	−	4.94465i	1.27800	−	0.465154i	0.388229	−	0.921563i	$-0.373087\pi$
$113$	13.5853	−	4.94465i	1.27800	−	0.465154i	0.889770	+	0.456409i	$0.150865\pi$
$114$	9.69700	+	18.6757i	0.908207	+	1.74914i
$115$	−2.87940	+	2.41610i	−0.268505	+	0.225303i
$116$	10.5353	−	11.4843i	0.978179	−	1.06629i
$117$	0.788724	+	6.06320i	0.0729176	+	0.560543i
$118$	8.87984	+	6.51480i	0.817456	+	0.599736i
$119$	−4.66321	−	11.8433i	−0.427476	−	1.08567i
$120$	1.72654	+	3.71821i	0.157611	+	0.339425i
$121$	−10.2612	+	3.73477i	−0.932837	+	0.339525i
$122$	−0.0893411	+	0.306196i	−0.00808856	+	0.0277217i
$123$	7.63058	+	2.23050i	0.688026	+	0.201117i
$124$	6.95134	−	3.61369i	0.624249	−	0.324519i
$125$	−6.73951	−	3.89106i	−0.602801	−	0.348027i
$126$	−3.34976	+	10.7135i	−0.298421	+	0.954434i
$127$	−14.4730	+	8.35602i	−1.28428	+	0.741477i	−0.977627	−	0.210346i	$-0.932541\pi$
$127$	−14.4730	+	8.35602i	−1.28428	+	0.741477i	−0.306648	+	0.951823i	$0.599208\pi$
$128$	−10.1568	+	4.98400i	−0.897739	+	0.440528i
$129$	−14.3694	+	0.930692i	−1.26515	+	0.0819429i
$130$	−1.74276	+	1.66740i	−0.152851	+	0.146240i
$131$	11.9406	+	10.0194i	1.04326	+	0.875395i	0.992368	−	0.123309i	$-0.0393507\pi$
$131$	11.9406	+	10.0194i	1.04326	+	0.875395i	0.0508872	+	0.998704i	$0.483795\pi$
$132$	−0.646055	−	0.738666i	−0.0562318	−	0.0642927i
$133$	−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
$136$	−2.64339	−	13.3479i	−0.226669	−	1.14457i
$137$	11.6855	+	4.25318i	0.998361	+	0.363374i	0.788952	−	0.614455i	$-0.210624\pi$
$137$	11.6855	+	4.25318i	0.998361	+	0.363374i	0.209409	+	0.977828i	$0.432846\pi$
$138$	−10.7393	−	2.39270i	−0.914192	−	0.203680i
$139$	−0.511428	+	2.90045i	−0.0433788	+	0.246013i	−0.998785	−	0.0492816i	$-0.984307\pi$
$139$	−0.511428	+	2.90045i	−0.0433788	+	0.246013i	0.955406	+	0.295295i	$0.0954179\pi$
$140$	−4.18776	+	1.43865i	−0.353930	+	0.121588i
$141$	−0.0149890	−	0.231423i	−0.00126231	−	0.0194893i
$142$	−17.5462	−	8.65895i	−1.47245	−	0.726643i
$143$	0.288682	−	0.500012i	0.0241408	−	0.0418131i
$144$	−5.56932	+	10.6293i	−0.464110	+	0.885778i
$145$	5.64710	−	3.26036i	0.468966	−	0.270758i
$146$	−14.4507	−	7.13133i	−1.19595	−	0.590193i
$147$	−11.1347	−	4.79784i	−0.918371	−	0.395719i
$148$	9.11509	+	11.8928i	0.749255	+	0.977583i
$149$	9.25342	−	3.36797i	0.758070	−	0.275915i	0.0660724	−	0.997815i	$-0.478953\pi$
$149$	9.25342	−	3.36797i	0.758070	−	0.275915i	0.691997	+	0.721900i	$0.256731\pi$
$150$	−1.36375	−	10.4435i	−0.111349	−	0.852710i
$151$	3.74841	−	0.660945i	0.305041	−	0.0537869i	−0.0190325	−	0.999819i	$-0.506059\pi$
$151$	3.74841	−	0.660945i	0.305041	−	0.0537869i	0.324073	+	0.946032i	$0.394947\pi$
$152$	−23.8356	+	4.72036i	−1.93332	+	0.382871i
$153$	−10.6257	−	9.76686i	−0.859038	−	0.789604i
$154$	0.865868	−	0.611383i	0.0697737	−	0.0492666i
$155$	3.22821	−	0.569220i	0.259296	−	0.0457208i
$156$	−6.97656	−	1.08331i	−0.558572	−	0.0867342i
$157$	−4.89319	+	5.83147i	−0.390519	+	0.465402i	−0.925105	−	0.379712i	$-0.876023\pi$
$157$	−4.89319	+	5.83147i	−0.390519	+	0.465402i	0.534586	+	0.845114i	$0.320468\pi$
$158$	−10.5682	+	2.58289i	−0.840763	+	0.205484i
$159$	0.655297	−	0.892268i	0.0519684	−	0.0707615i
$160$	−4.67962	+	0.713548i	−0.369957	+	0.0564110i
$161$	3.77255	−	11.2695i	0.297319	−	0.888163i
$162$	1.89387	+	12.5862i	0.148797	+	0.988868i
$163$	1.01464	+	0.585801i	0.0794726	+	0.0458835i	0.539210	−	0.842172i	$-0.318723\pi$
$163$	1.01464	+	0.585801i	0.0794726	+	0.0458835i	−0.459737	+	0.888055i	$0.652056\pi$
$164$	−4.93662	+	7.73936i	−0.385485	+	0.604342i
$165$	−0.165076	−	0.375949i	−0.0128511	−	0.0292676i
$166$	5.06012	−	4.84129i	0.392742	−	0.375757i
$167$	−22.3345	+	8.12908i	−1.72829	+	0.629047i	−0.998507	−	0.0546284i	$-0.982603\pi$
$167$	−22.3345	+	8.12908i	−1.72829	+	0.629047i	−0.729786	+	0.683676i	$0.760380\pi$
$168$	−10.7958	−	7.17291i	−0.832914	−	0.553402i
$169$	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	0.994932	−	0.100554i	$-0.0320614\pi$
$173$	9.51139	+	11.3352i	0.723138	+	0.861802i	−0.271794	+	0.962355i	$0.587617\pi$
$174$	17.6266	+	7.32292i	1.33627	+	0.555149i
$175$	11.3722	−	0.296137i	0.859658	−	0.0223859i
$176$	1.02752	−	0.477736i	0.0774519	−	0.0360107i
$177$	−3.78448	+	12.9468i	−0.284459	+	0.973139i
$178$	0.0878390	+	1.34595i	0.00658381	+	0.100883i
$179$		−	3.97055i		−	0.296773i	−0.988929	−	0.148386i	$-0.952592\pi$
$179$		−	3.97055i		−	0.296773i	0.988929	−	0.148386i	$-0.0474079\pi$
$180$	−3.55774	+	3.54281i	−0.265178	+	0.264065i
$181$	−14.2010	+	8.19897i	−1.05555	+	0.609424i	−0.924199	−	0.381911i	$-0.875266\pi$
$181$	−14.2010	+	8.19897i	−1.05555	+	0.609424i	−0.131355	+	0.991335i	$0.541933\pi$
$182$	1.94470	−	7.37372i	0.144151	−	0.546577i
$183$	−0.389832	+	0.0252491i	−0.0288172	+	0.00186646i
$184$	6.12021	−	11.1335i	0.451188	−	0.820769i
$185$	2.14427	+	5.89134i	0.157650	+	0.433140i
$186$	7.06758	+	6.48993i	0.518220	+	0.475865i
$187$	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	$-0.441661\pi$
$191$	9.53332	−	1.68098i	0.689807	−	0.121632i	0.507554	+	0.861620i	$0.330550\pi$
$192$	−9.98583	−	9.60641i	−0.720665	−	0.693283i
$193$	3.86120	−	1.40536i	0.277935	−	0.101160i	−0.199292	−	0.979940i	$-0.563864\pi$
$193$	3.86120	−	1.40536i	0.277935	−	0.101160i	0.477227	+	0.878780i	$0.341642\pi$
$194$	−0.546232	+	1.87208i	−0.0392172	+	0.134408i
$195$	−2.64836	−	1.30857i	−0.189653	−	0.0937084i
$196$	8.91429	−	10.7952i	0.636735	−	0.771083i
$197$	−4.68906	−	8.12169i	−0.334082	−	0.578646i	0.649226	−	0.760595i	$-0.275093\pi$
$197$	−4.68906	−	8.12169i	−0.334082	−	0.578646i	−0.983308	+	0.181949i	$0.941759\pi$
$198$	0.580012	−	1.05267i	0.0412196	−	0.0748098i
$199$	−4.68700			−0.332252			−0.166126	−	0.986105i	$-0.553126\pi$
$199$	−4.68700			−0.332252			−0.166126	+	0.986105i	$0.553126\pi$
$200$	12.0184	+	1.86016i	0.849831	+	0.131533i
$201$	−4.60630	−	18.8875i	−0.324904	−	1.33222i
$202$	8.33049	+	8.70703i	0.586132	+	0.612625i
$203$	−9.84003	+	18.1168i	−0.690635	+	1.27155i
$204$	14.2588	−	8.62649i	0.998316	−	0.603975i
$205$	−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
$210$	−3.40785	−	4.21866i	−0.235164	−	0.291115i
$211$	3.45813	+	9.50112i	0.238067	+	0.654084i	0.999979	+	0.00640397i	$0.00203846\pi$
$211$	3.45813	+	9.50112i	0.238067	+	0.654084i	−0.761912	+	0.647680i	$0.775739\pi$
$212$	0.777617	+	1.01459i	0.0534069	+	0.0696821i
$213$	2.62725	−	23.8195i	0.180016	−	1.63208i
$214$	−11.0952	−	5.47543i	−0.758454	−	0.374292i
$215$	3.47843	−	6.02482i	0.237227	−	0.410890i
$216$	−14.5651	−	1.96429i	−0.991028	−	0.133653i
$217$	−7.76326	+	6.86634i	−0.527004	+	0.466117i
$218$	12.7212	+	19.0502i	0.861590	+	1.29024i
$219$	2.16375	−	19.6172i	0.146212	−	1.32561i
$220$	0.470092	−	0.0616207i	0.0316936	−	0.00415446i
$221$	7.51102	+	6.30250i	0.505246	+	0.423952i
$222$	−9.87664	+	15.4673i	−0.662877	+	1.03810i
$223$	0.729901	+	4.13947i	0.0488778	+	0.277200i	0.999445	−	0.0333200i	$-0.0106080\pi$
$223$	0.729901	+	4.13947i	0.0488778	+	0.277200i	−0.950567	+	0.310520i	$0.899497\pi$
$224$	11.4380	−	9.65261i	0.764231	−	0.644942i
$225$	11.4509	−	5.93856i	0.763396	−	0.395904i
$226$	−18.7164	+	8.22913i	−1.24499	+	0.547394i
$227$	−3.61302	−	20.4904i	−0.239804	−	1.36000i	−0.832256	−	0.554392i	$-0.812951\pi$
$227$	−3.61302	−	20.4904i	−0.239804	−	1.36000i	0.592451	−	0.805606i	$-0.298160\pi$
$228$	−15.4045	−	25.4623i	−1.02019	−	1.68628i
$229$	8.20134	+	22.5330i	0.541960	+	1.48902i	0.844325	+	0.535831i	$0.180002\pi$
$229$	8.20134	+	22.5330i	0.541960	+	1.48902i	−0.302365	+	0.953192i	$0.597776\pi$
$230$	3.84092	−	3.67482i	0.253263	−	0.242310i
$231$	1.06597	+	0.740937i	0.0701356	+	0.0487501i
$232$	−13.8099	+	17.1771i	−0.906662	+	1.12773i
$233$	3.03138	+	5.25051i	0.198592	+	0.343972i	0.948072	−	0.318055i	$-0.103030\pi$
$233$	3.03138	+	5.25051i	0.198592	+	0.343972i	−0.749480	+	0.662027i	$0.769696\pi$
$234$	−1.67147	−	8.48382i	−0.109267	−	0.554604i
$235$	0.0970313	+	0.0560211i	0.00632963	+	0.00365441i
$236$	−13.1313	−	8.37594i	−0.854777	−	0.545227i
$237$	−7.39406	−	11.0845i	−0.480296	−	0.720015i
$238$	7.67152	+	16.2839i	0.497271	+	1.05553i
$239$	−24.5125	−	4.32221i	−1.58558	−	0.279580i	−0.689773	−	0.724026i	$-0.742290\pi$
$239$	−24.5125	−	4.32221i	−1.58558	−	0.279580i	−0.895806	+	0.444446i	$0.853401\pi$
$240$	−2.77895	−	5.08817i	−0.179380	−	0.328440i
$241$	−2.66530	+	7.32285i	−0.171687	+	0.471706i	−0.995456	−	0.0952190i	$-0.969645\pi$
$241$	−2.66530	+	7.32285i	−0.171687	+	0.471706i	0.823769	+	0.566925i	$0.191867\pi$
$242$	14.1368	−	6.21560i	0.908746	−	0.399554i
$243$	−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
$246$	−10.9738	−	2.44494i	−0.699663	−	0.155884i
$247$	11.2545	−	13.4126i	0.716107	−	0.853423i
$248$	−9.47700	+	5.73988i	−0.601790	+	0.364483i
$249$	7.68952	+	3.79943i	0.487304	+	0.240779i
$250$	9.86924	+	4.87041i	0.624186	+	0.308032i
$251$	7.94251	+	13.7568i	0.501327	+	0.868324i	0.999999	+	0.00153285i	$0.000487921\pi$
$251$	7.94251	+	13.7568i	0.501327	+	0.868324i	−0.498672	+	0.866791i	$0.666179\pi$
$252$	3.74053	−	15.4275i	0.235631	−	0.971843i
$253$	−0.636234	+	1.10199i	−0.0399997	+	0.0692815i
$254$	19.6550	−	13.1251i	1.23326	−	0.823539i
$255$	6.77426	−	1.65212i	0.424221	−	0.103460i
$256$	13.8743	−	7.96890i	0.867145	−	0.498056i
$257$	9.58297	+	26.3290i	0.597769	+	1.64236i	0.755708	+	0.654909i	$0.227293\pi$
$257$	9.58297	+	26.3290i	0.597769	+	1.64236i	−0.157938	+	0.987449i	$0.550485\pi$
$258$	20.1925	−	2.63680i	1.25713	−	0.164160i
$259$	−15.5112	−	12.3418i	−0.963817	−	0.766883i
$260$	2.30585	−	2.51356i	0.143002	−	0.155884i
$261$	−1.05571	+	23.3532i	−0.0653468	+	1.44553i
$262$	−17.7735	−	13.0397i	−1.09805	−	0.805597i
$263$	−18.7577	−	22.3545i	−1.15665	−	1.37844i	−0.912690	−	0.408654i	$-0.865998\pi$
$263$	−18.7577	−	22.3545i	−1.15665	−	1.37844i	−0.243958	−	0.969786i	$-0.578446\pi$
$264$	0.979750	+	0.982914i	0.0602994	+	0.0604942i
$265$	0.182930	+	0.502595i	0.0112373	+	0.0308742i
$266$	29.0786	−	13.6992i	1.78292	−	0.839952i
$267$	−1.51256	+	0.664150i	−0.0925671	+	0.0406453i
$268$	22.4267	+	0.991771i	1.36993	+	0.0605821i
$269$	3.74252	−	2.16075i	0.228186	−	0.131743i	−0.381549	−	0.924349i	$-0.624609\pi$
$269$	3.74252	−	2.16075i	0.228186	−	0.131743i	0.609735	+	0.792605i	$0.291276\pi$
$270$	−5.56637	−	2.61324i	−0.338759	−	0.159037i
$271$	−14.3983	+	24.9386i	−0.874635	+	1.51491i	−0.0174837	+	0.999847i	$0.505566\pi$
$271$	−14.3983	+	24.9386i	−0.874635	+	1.51491i	−0.857151	+	0.515065i	$0.827768\pi$
$272$	4.95970	+	18.5932i	0.300726	+	1.12738i
$273$	9.30132	−	0.846075i	0.562942	−	0.0512068i
$274$	−16.8824	−	4.92592i	−1.01991	−	0.297586i
$275$	−1.19956	−	0.211514i	−0.0723359	−	0.0127548i
$276$	15.3758	+	2.38753i	0.925516	+	0.143713i
$277$	−13.2152	+	11.0889i	−0.794025	+	0.666266i	−0.946738	−	0.322005i	$-0.895643\pi$
$277$	−13.2152	+	11.0889i	−0.794025	+	0.666266i	0.152713	+	0.988271i	$0.451199\pi$
$278$	0.454607	−	4.14026i	0.0272655	−	0.248316i
$279$	−4.51396	+	10.8503i	−0.270244	+	0.649590i
$280$	5.77731	−	2.41593i	0.345260	−	0.144379i
$281$	3.18857	+	1.16055i	0.190214	+	0.0692324i	0.435371	−	0.900251i	$-0.356617\pi$
$281$	3.18857	+	1.16055i	0.190214	+	0.0692324i	−0.245157	+	0.969483i	$0.578839\pi$
$282$	0.0424664	+	0.325206i	0.00252884	+	0.0193657i
$283$	1.76330	−	10.0002i	0.104818	−	0.594450i	−0.886476	−	0.462776i	$-0.846854\pi$
$283$	1.76330	−	10.0002i	0.104818	−	0.594450i	0.991293	−	0.131674i	$-0.0420353\pi$
$284$	25.5589	+	10.6036i	1.51664	+	0.629210i
$285$	−2.95022	−	12.0970i	−0.174756	−	0.716562i
$286$	−0.361342	+	0.732210i	−0.0213666	+	0.0432965i
$287$	3.85492	−	11.5156i	0.227549	−	0.679743i
$288$	6.88054	−	15.5132i	0.405440	−	0.914122i
$289$	−6.14415			−0.361421
$290$	−7.66898	+	5.12114i	−0.450338	+	0.300724i
$291$	−2.38343	+	0.154373i	−0.139719	+	0.00904950i
$292$	21.0498	+	8.73293i	1.23184	+	0.511056i
$293$	−15.9105	−	2.80545i	−0.929500	−	0.163896i	−0.311654	−	0.950196i	$-0.600883\pi$
$293$	−15.9105	−	2.80545i	−0.929500	−	0.163896i	−0.617845	+	0.786300i	$0.711994\pi$
$294$	16.1552	+	5.74529i	0.942193	+	0.335072i
$295$	−4.18889	−	4.99213i	−0.243887	−	0.290653i
$296$	−13.9586	−	15.9438i	−0.811328	−	0.926714i
$297$	1.45435	+	0.227291i	0.0843897	+	0.0131887i
$298$	−12.7483	+	5.60514i	−0.738492	+	0.324697i
$299$	1.58970	+	9.01565i	0.0919349	+	0.521389i
$300$	2.88637	+	14.6124i	0.166644	+	0.843649i
$301$	0.572580	+	21.9882i	0.0330030	+	1.26738i
$302$	−5.22892	+	1.27796i	−0.300891	+	0.0735381i
$303$	−6.53774	+	13.2315i	−0.375583	+	0.760129i
$304$	33.2023	−	8.85664i	1.90428	−	0.507963i
$305$	0.0943675	−	0.163449i	0.00540347	−	0.00935908i
$306$	15.8946	+	12.8045i	0.908636	+	0.731984i
$307$	11.4678	−	19.8628i	0.654501	−	1.13363i	−0.327518	−	0.944845i	$-0.606212\pi$
$307$	11.4678	−	19.8628i	0.654501	−	1.13363i	0.982019	−	0.188784i	$-0.0604545\pi$
$308$	−1.16562	+	0.942535i	−0.0664171	+	0.0537059i
$309$	−8.48603	+	2.06958i	−0.482753	+	0.117734i
$310$	−4.50326	+	1.10060i	−0.255768	+	0.0625100i
$311$	−0.252891	+	1.43422i	−0.0143402	+	0.0813271i	−0.991138	−	0.132837i	$-0.957591\pi$
$311$	−0.252891	+	1.43422i	−0.0143402	+	0.0813271i	0.976798	+	0.214164i	$0.0687026\pi$
$312$	9.94517	+	0.886249i	0.563035	+	0.0501740i
$313$	−7.70722	−	9.18511i	−0.435638	−	0.519173i	0.502902	−	0.864343i	$-0.332266\pi$
$313$	−7.70722	−	9.18511i	−0.435638	−	0.519173i	−0.938540	+	0.345170i	$0.887821\pi$
$314$	6.36825	−	8.68009i	0.359381	−	0.489846i
$315$	3.43047	−	5.68750i	0.193285	−	0.320454i
$316$	14.6761	−	4.61832i	0.825596	−	0.259801i
$317$	17.0928	+	6.22128i	0.960029	+	0.349422i	0.774045	−	0.633131i	$-0.218230\pi$
$317$	17.0928	+	6.22128i	0.960029	+	0.349422i	0.185984	+	0.982553i	$0.440453\pi$
$318$	−0.842586	+	1.31953i	−0.0472499	+	0.0739956i
$319$	1.41893	−	1.69102i	0.0794449	−	0.0946788i
$320$	6.53822	−	1.43795i	0.365498	−	0.0803840i
$321$	1.66132	−	15.0621i	0.0927259	−	0.840684i
$322$	−4.28597	+	16.2511i	−0.238848	+	0.905640i
$323$			41.3290i			2.29961i
$324$	−3.83183	−	17.5874i	−0.212879	−	0.977079i
$325$	−7.58924	+	4.38165i	−0.420975	+	0.243050i
$326$	−1.48582	−	0.733243i	−0.0822920	−	0.0406106i
$327$	−16.6069	+	22.6124i	−0.918365	+	1.25047i
$328$	6.25383	−	11.3765i	0.345310	−	0.628163i
$329$	−0.354125	+	0.00922156i	−0.0195235	+	0.000508401i
$330$	0.267581	+	0.515341i	0.0147299	+	0.0283686i
$331$	−4.60202	+	12.6439i	−0.252950	+	0.694974i	0.746609	+	0.665263i	$0.231681\pi$
$331$	−4.60202	+	12.6439i	−0.252950	+	0.694974i	−0.999559	+	0.0297105i	$0.990541\pi$
$332$	−6.69503	+	7.29812i	−0.367437	+	0.400536i
$333$	−21.9359	−	4.89857i	−1.20208	−	0.268440i
$334$	30.7700	−	13.5288i	1.68366	−	0.740264i
$335$	8.82616	+	3.21246i	0.482225	+	0.175516i
$336$	15.8958	+	9.12821i	0.867186	+	0.497985i
$337$	1.44286	+	1.21070i	0.0785974	+	0.0659511i	0.681240	−	0.732060i	$-0.261441\pi$
$337$	1.44286	+	1.21070i	0.0785974	+	0.0659511i	−0.602643	+	0.798011i	$0.705885\pi$
$338$	−2.97013	−	12.1527i	−0.161554	−	0.661019i
$339$	−17.3019	−	18.1018i	−0.939712	−	0.983153i
$340$	−0.355713	+	8.04365i	−0.0192912	+	0.436228i
$341$	0.961035	−	0.554854i	0.0520430	−	0.0300470i
$342$	22.8653	−	28.3834i	1.23641	−	1.53480i
$343$	−7.98047	+	16.7126i	−0.430905	+	0.902397i
$344$	−3.59662	+	23.2376i	−0.193917	+	1.25289i
$345$	5.83679	+	2.88398i	0.314242	+	0.155269i
$346$	−14.4665	−	15.1204i	−0.777726	−	0.812879i
$347$	−6.95282	−	19.1027i	−0.373247	−	1.02549i	−0.974098	−	0.226127i	$-0.927394\pi$
$347$	−6.95282	−	19.1027i	−0.373247	−	1.02549i	0.600851	−	0.799361i	$-0.294829\pi$
$348$	−25.5494	−	8.71080i	−1.36959	−	0.466948i
$349$	0.337079	+	0.401715i	0.0180434	+	0.0215033i	0.774991	−	0.631973i	$-0.217755\pi$
$349$	0.337079	+	0.401715i	0.0180434	+	0.0215033i	−0.756947	+	0.653476i	$0.773310\pi$
$350$	−16.0213	+	1.46527i	−0.856376	+	0.0783222i
$351$	9.06642	−	5.47298i	0.483930	−	0.292126i
$352$	−1.40604	+	0.768819i	−0.0749423	+	0.0409782i
$353$	6.04600	−	16.6113i	0.321796	−	0.884128i	−0.668319	−	0.743875i	$-0.732986\pi$
$353$	6.04600	−	16.6113i	0.321796	−	0.884128i	0.990116	−	0.140254i	$-0.0447918\pi$
$354$	4.14832	−	18.6192i	0.220481	−	0.989598i
$355$	8.86908	+	7.44204i	0.470722	+	0.394982i
$356$	−0.247919	−	1.89132i	−0.0131397	−	0.100240i
$357$	−15.5351	+	15.6425i	−0.822203	+	0.827891i
$358$	0.365681	+	5.60328i	0.0193268	+	0.296143i
$359$		−	11.1765i		−	0.589873i	−0.955517	−	0.294936i	$-0.904702\pi$
$359$		−	11.1765i		−	0.589873i	0.955517	−	0.294936i	$-0.0952985\pi$
$360$	4.69444	−	5.32731i	0.247419	−	0.280774i
$361$	54.8022			2.88433
$362$	19.2855	−	12.8784i	1.01363	−	0.676872i
$363$	13.0684	+	13.6726i	0.685915	+	0.717623i
$364$	−2.06527	+	10.5850i	−0.108250	+	0.554804i
$365$	7.30439	+	6.12911i	0.382329	+	0.320812i
$366$	0.547810	−	0.0715346i	0.0286345	−	0.00373917i
$367$	1.04745	+	5.94039i	0.0546765	+	0.310086i	0.999865	−	0.0164397i	$-0.00523315\pi$
$367$	1.04745	+	5.94039i	0.0546765	+	0.310086i	−0.945188	+	0.326526i	$0.894122\pi$
$368$	−7.61154	+	16.2753i	−0.396779	+	0.848410i
$369$	−1.77624	−	13.6546i	−0.0924674	−	0.710829i
$370$	−3.56860	−	8.11644i	−0.185523	−	0.421953i
$371$	−1.32327	−	1.05289i	−0.0687009	−	0.0546635i
$372$	−10.5716	−	8.50775i	−0.548110	−	0.441106i
$373$	4.02379	−	22.8201i	0.208344	−	1.18158i	−0.683746	−	0.729720i	$-0.739650\pi$
$373$	4.02379	−	22.8201i	0.208344	−	1.18158i	0.892090	−	0.451858i	$-0.149238\pi$
$374$	−0.457580	−	1.87225i	−0.0236609	−	0.0968116i
$375$	−1.47775	+	13.3978i	−0.0763108	+	0.691858i
$376$	−0.374248	−	0.0579245i	−0.0193003	−	0.00298723i
$377$		−	15.8815i		−	0.817941i
$378$	19.3232	−	2.14800i	0.993878	−	0.110481i
$379$			16.8672i			0.866408i	0.901296	+	0.433204i	$0.142617\pi$
$379$			16.8672i			0.866408i	−0.901296	+	0.433204i	$0.857383\pi$
$380$	14.3637	+	0.635204i	0.736844	+	0.0325853i
$381$	23.3302	+	17.1341i	1.19524	+	0.877807i
$382$	−13.2987	+	3.25022i	−0.680422	+	0.166296i
$383$	5.23950	−	29.7147i	0.267726	−	1.51835i	−0.493433	−	0.869784i	$-0.664258\pi$
$383$	5.23950	−	29.7147i	0.267726	−	1.51835i	0.761159	−	0.648565i	$-0.224631\pi$
$384$	14.9769	+	12.6370i	0.764284	+	0.644879i
$385$	−0.583585	+	0.229782i	−0.0297423	+	0.0117108i
$386$	−5.31954	+	2.33887i	−0.270758	+	0.119046i
$387$	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	0.950099	−	0.311948i	$-0.100982\pi$
$389$	−0.974215	−	5.52505i	−0.0493947	−	0.280131i	−0.999494	+	0.0318174i	$0.989871\pi$
$390$	3.85792	+	1.60276i	0.195353	+	0.0811587i
$391$	−16.5537	−	13.8902i	−0.837158	−	0.702459i
$392$	−11.5857	+	16.0552i	−0.585168	+	0.810912i
$393$	7.57483	−	25.9137i	0.382100	−	1.30717i
$394$	7.36525	+	11.0296i	0.371056	+	0.555661i
$395$	6.43742			0.323902
$396$	−0.721570	+	1.53895i	−0.0362603	+	0.0773354i
$397$		−	24.0198i		−	1.20552i	−0.797923	−	0.602759i	$-0.794068\pi$
$397$		−	24.0198i		−	1.20552i	0.797923	−	0.602759i	$-0.205932\pi$
$398$	6.61434	−	0.431665i	0.331547	−	0.0216374i
$399$	27.9332	+	27.7413i	1.39841	+	1.38880i
$400$	−17.1319	−	1.51821i	−0.856593	−	0.0759103i
$401$	7.58690	+	6.36617i	0.378872	+	0.317911i	0.812259	−	0.583296i	$-0.198237\pi$
$401$	7.58690	+	6.36617i	0.378872	+	0.317911i	−0.433387	+	0.901208i	$0.642682\pi$
$402$	8.23997	+	26.2300i	0.410973	+	1.30823i
$403$	2.73061	−	7.50228i	0.136021	−	0.373715i
$404$	−12.5580	−	11.5202i	−0.624783	−	0.573153i
$405$	0.679534	−	7.50057i	0.0337663	−	0.372706i
$406$	12.2178	−	26.4729i	0.606361	−	1.31383i
$407$	1.36425	+	1.62585i	0.0676234	+	0.0805905i
$408$	−19.3277	+	13.4870i	−0.956864	+	0.667707i
$409$	8.44831	+	23.2115i	0.417742	+	1.14774i	0.952979	+	0.303035i	$0.0979998\pi$
$409$	8.44831	+	23.2115i	0.417742	+	1.14774i	−0.535238	+	0.844702i	$0.679778\pi$
$410$	3.92478	−	3.75505i	0.193831	−	0.185449i
$411$	−1.39213	−	21.4938i	−0.0686689	−	1.06021i
$412$	0.445596	−	10.0762i	0.0219530	−	0.496417i
$413$	19.5384	+	6.54062i	0.961423	+	0.321843i
$414$	3.68379	+	18.6977i	0.181048	+	0.918942i
$415$	−3.58865	+	2.07191i	−0.176160	+	0.101706i
$416$	−4.19368	+	10.7394i	−0.205612	+	0.526544i
$417$	4.95598	−	1.20867i	0.242695	−	0.0591888i
$418$	−3.34332	+	0.817111i	−0.163527	+	0.0399662i
$419$	10.7816	+	9.04680i	0.526713	+	0.441965i	0.866965	−	0.498370i	$-0.166068\pi$
$419$	10.7816	+	9.04680i	0.526713	+	0.441965i	−0.340251	+	0.940335i	$0.610512\pi$
$420$	5.19773	+	5.63956i	0.253623	+	0.275182i
$421$	−1.73169	−	0.630283i	−0.0843973	−	0.0307181i	0.299476	−	0.954104i	$-0.403188\pi$
$421$	−1.73169	−	0.630283i	−0.0843973	−	0.0307181i	−0.383874	+	0.923386i	$0.625410\pi$
$422$	−5.75518	−	13.0896i	−0.280158	−	0.637192i
$423$	−0.356577	+	0.184924i	−0.0173373	+	0.00899130i
$424$	−1.19082	−	1.36018i	−0.0578315	−	0.0660562i
$425$	7.07482	−	19.4379i	0.343179	−	0.942877i
$426$	−1.51387	+	33.8563i	−0.0733471	+	1.64034i
$427$	0.0155337	+	0.596524i	0.000751729	+	0.0288678i
$428$	16.1620	+	6.70513i	0.781219	+	0.324105i
$429$	−0.993997	−	0.109636i	−0.0479906	−	0.00529328i
$430$	−4.35393	+	8.82266i	−0.209965	+	0.425466i
$431$	−3.05326	+	1.76280i	−0.147070	+	0.0849111i	−0.571729	−	0.820442i	$-0.693727\pi$
$431$	−3.05326	+	1.76280i	−0.147070	+	0.0849111i	0.424659	+	0.905353i	$0.360394\pi$
$432$	20.7353	+	1.43061i	0.997628	+	0.0688303i
$433$		−	27.3460i		−	1.31417i	−0.753819	−	0.657083i	$-0.771790\pi$
$433$		−	27.3460i		−	1.31417i	0.753819	−	0.657083i	$-0.228210\pi$
$434$	10.3232	−	10.4048i	0.495530	−	0.499448i
$435$	−9.10300	−	6.68539i	−0.436455	−	0.320540i
$436$	−19.7068	−	25.7123i	−0.943786	−	1.23140i
$437$	−24.8041	+	29.5604i	−1.18654	+	1.41406i
$438$	−1.24679	+	27.8834i	−0.0595739	+	1.33232i
$439$	−19.1588	−	6.97322i	−0.914398	−	0.332813i	−0.158390	−	0.987377i	$-0.550630\pi$
$439$	−19.1588	−	6.97322i	−0.914398	−	0.332813i	−0.756007	+	0.654563i	$0.772853\pi$
$440$	−0.657724	+	0.130254i	−0.0313558	+	0.00620964i
$441$	0.144764	+	20.9995i	0.00689350	+	0.999976i
$442$	−11.1801	−	8.20240i	−0.531783	−	0.390148i
$443$	−15.4629	−	18.4280i	−0.734666	−	0.875541i	0.261302	−	0.965257i	$-0.415848\pi$
$443$	−15.4629	−	18.4280i	−0.734666	−	0.875541i	−0.995967	+	0.0897166i	$0.971404\pi$
$444$	12.5135	−	22.7373i	0.593865	−	1.07906i
$445$	0.138590	−	0.785984i	0.00656981	−	0.0372592i
$446$	−1.41128	−	5.77445i	−0.0668262	−	0.273428i
$447$	−11.7849	−	12.3297i	−0.557409	−	0.583176i
$448$	−15.2524	+	14.6753i	−0.720608	+	0.693342i
$449$	13.4524	−	23.3002i	0.634858	−	1.09961i	−0.351688	−	0.936117i	$-0.614392\pi$
$449$	13.4524	−	23.3002i	0.634858	−	1.09961i	0.986545	−	0.163488i	$-0.0522746\pi$
$450$	−15.6128	+	9.43517i	−0.735993	+	0.444778i
$451$	−0.650125	+	1.12605i	−0.0306132	+	0.0530236i
$452$	25.6549	−	13.3368i	1.20670	−	0.627310i
$453$	−3.65842	−	5.48436i	−0.171887	−	0.257678i
$454$	6.98587	+	28.5836i	0.327863	+	1.34149i
$455$	−2.15367	+	3.96519i	−0.100966	+	0.185891i
$456$	24.0841	+	34.5139i	1.12784	+	1.61626i
$457$	−1.90386	−	10.7973i	−0.0890588	−	0.505078i	−0.996407	−	0.0846972i	$-0.973008\pi$
$457$	−1.90386	−	10.7973i	−0.0890588	−	0.505078i	0.907348	−	0.420380i	$-0.138103\pi$
$458$	−13.6491	−	31.0435i	−0.637780	−	1.45057i
$459$	−8.09003	+	23.6526i	−0.377610	+	1.10401i
$460$	−5.08191	+	5.53969i	−0.236945	+	0.258289i
$461$	0.428282	+	0.510407i	0.0199471	+	0.0237720i	0.775926	−	0.630824i	$-0.217283\pi$
$461$	0.428282	+	0.510407i	0.0199471	+	0.0237720i	−0.755979	+	0.654596i	$0.772839\pi$
$462$	−1.57255	−	0.947444i	−0.0731614	−	0.0440791i
$463$	8.05247	+	1.41987i	0.374230	+	0.0659869i	0.357600	−	0.933875i	$-0.383595\pi$
$463$	8.05247	+	1.41987i	0.374230	+	0.0659869i	0.0166301	+	0.999862i	$0.494706\pi$
$464$	17.9066	−	25.5124i	0.831295	−	1.18438i
$465$	−3.15070	−	4.72324i	−0.146110	−	0.219035i
$466$	−4.76148	−	7.13039i	−0.220571	−	0.330309i
$467$	−28.4514			−1.31657			−0.658287	−	0.752767i	$-0.728719\pi$
$467$	−28.4514			−1.31657			−0.658287	+	0.752767i	$0.728719\pi$
$468$	3.14014	+	11.8185i	0.145153	+	0.546311i
$469$	−29.1014	+	5.91634i	−1.34378	+	0.273191i
$470$	−0.142091	−	0.0701212i	−0.00655418	−	0.00323445i
$471$	12.6555	+	3.69935i	0.583137	+	0.170457i
$472$	19.3025	+	10.6108i	0.888470	+	0.488404i
$473$	0.408962	−	2.31934i	0.0188041	−	0.106643i
$474$	11.4554	+	14.9616i	0.526166	+	0.687208i
$475$	−34.7107	−	12.6337i	−1.59264	−	0.579672i
$476$	−12.3259	−	22.2735i	−0.564955	−	1.02090i
$477$	−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	$-0.700202\pi$
$479$	2.31784	−	1.94490i	0.105905	−	0.0888647i	0.694203	+	0.719780i	$0.255757\pi$
$480$	4.39030	+	6.92455i	0.200389	+	0.316061i
$481$	15.0375	+	2.65153i	0.685653	+	0.120899i
$482$	3.08688	−	10.5796i	0.140603	−	0.481886i
$483$	−20.4994	+	1.86469i	−0.932756	+	0.0848462i
$484$	−19.3775	+	10.0735i	−0.880796	+	0.457886i
$485$	0.576964	−	0.999330i	0.0261986	−	0.0453772i
$486$	18.6417	−	11.7680i	0.845607	−	0.533807i
$487$	15.4968	−	8.94709i	0.702228	−	0.405431i	−0.105949	−	0.994372i	$-0.533788\pi$
$487$	15.4968	−	8.94709i	0.702228	−	0.405431i	0.808177	+	0.588940i	$0.200455\pi$
$488$	−0.0975739	+	0.630421i	−0.00441696	+	0.0285378i
$489$	0.222476	−	2.01704i	0.0100607	−	0.0912139i
$490$	−6.64041	+	4.95273i	−0.299983	+	0.223741i
$491$	2.25048	+	6.18315i	0.101563	+	0.279042i	0.980059	−	0.198708i	$-0.0636746\pi$
$491$	2.25048	+	6.18315i	0.101563	+	0.279042i	−0.878496	+	0.477750i	$0.841452\pi$
$492$	15.7115	+	2.43966i	0.708330	+	0.109988i
$493$	24.0966	+	28.7172i	1.08526	+	1.29336i
$494$	−14.6472	+	19.9645i	−0.659009	+	0.898247i
$495$	−0.481268	+	0.523588i	−0.0216314	+	0.0235335i
$496$	12.8454	−	8.97300i	0.576776	−	0.402900i
$497$	−36.2027	−	5.41591i	−1.62391	−	0.242937i
$498$	−11.2015	−	4.65360i	−0.501950	−	0.208533i
$499$	−13.6848	−	37.5987i	−0.612616	−	1.68315i	−0.724369	−	0.689412i	$-0.757869\pi$
$499$	−13.6848	−	37.5987i	−0.612616	−	1.68315i	0.111753	−	0.993736i	$-0.464353\pi$
$500$	−14.3761	−	5.96424i	−0.642921	−	0.266729i
$501$	28.4447	+	29.7596i	1.27081	+	1.32956i
$502$	−12.4755	−	18.6823i	−0.556811	−	0.833832i
$503$	1.96603	−	3.40526i	0.0876610	−	0.151833i	−0.818861	−	0.573992i	$-0.805394\pi$
$503$	1.96603	−	3.40526i	0.0876610	−	0.151833i	0.906522	+	0.422159i	$0.138727\pi$
$504$	−3.85783	+	22.1160i	−0.171841	+	0.985125i
$505$	−3.56516	−	6.17504i	−0.158648	−	0.274786i
$506$	0.796370	−	1.61374i	0.0354030	−	0.0717394i
$507$	12.7463	−	8.50263i	0.566085	−	0.377615i
$508$	−26.5285	+	20.3324i	−1.17701	+	0.902105i
$509$	−13.8235	+	16.4742i	−0.612717	+	0.730207i	−0.979800	−	0.199981i	$-0.935912\pi$
$509$	−13.8235	+	16.4742i	−0.612717	+	0.730207i	0.367083	+	0.930188i	$0.380356\pi$
$510$	−9.40776	+	2.95538i	−0.416583	+	0.130867i
$511$	−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
$514$	−15.9485	−	36.2732i	−0.703456	−	1.59994i
$515$	1.44334	−	3.96554i	0.0636011	−	0.174743i
$516$	−28.2531	+	5.58078i	−1.24377	+	0.245680i
$517$	0.0373536	+	0.00658644i	0.00164281	+	0.000289671i
$518$	23.0262	+	15.9884i	1.01171	+	0.702488i
$519$	11.3533	−	22.9775i	0.498354	−	1.00860i
$520$	−3.02254	+	3.75953i	−0.132547	+	0.164866i
$521$	−15.1834	−	8.76611i	−0.665195	−	0.384050i	0.129059	−	0.991637i	$-0.458804\pi$
$521$	−15.1834	−	8.76611i	−0.665195	−	0.384050i	−0.794253	+	0.607587i	$0.792138\pi$
$522$	−0.660959	−	33.0535i	−0.0289294	−	1.44671i
$523$	5.67500	+	9.82938i	0.248150	+	0.429809i	0.963013	−	0.269456i	$-0.0868440\pi$
$523$	5.67500	+	9.82938i	0.248150	+	0.429809i	−0.714862	+	0.699265i	$0.753511\pi$
$524$	26.2831	+	16.7649i	1.14818	+	0.732378i
$525$	−8.38874	−	17.8290i	−0.366115	−	0.778122i
$526$	28.5299	+	29.8194i	1.24396	+	1.30019i
$527$	6.44548	+	17.7088i	0.280770	+	0.771408i
$528$	−1.47316	−	1.29687i	−0.0641110	−	0.0564389i
$529$	0.490322	+	2.78076i	0.0213184	+	0.120902i
$530$	−0.304441	−	0.692421i	−0.0132241	−	0.0300768i
$531$	23.1677	−	3.01374i	1.00539	−	0.130785i
$532$	−39.7743	+	22.0106i	−1.72444	+	0.954279i
$533$	1.62441	+	9.21249i	0.0703610	+	0.399037i
$534$	2.07337	−	1.07656i	0.0897236	−	0.0465873i
$535$	5.60830	+	4.70592i	0.242468	+	0.203455i
$536$	−31.7401	+	0.665862i	−1.37097	+	0.0287609i
$537$	−6.29690	+	2.76491i	−0.271731	+	0.119315i
$538$	−5.08249	+	3.39395i	−0.219122	+	0.146324i
$539$	1.19386	−	1.58335i	0.0514233	−	0.0681998i
$540$	8.09600	+	3.17518i	0.348397	+	0.136638i
$541$	8.35918	−	14.4785i	0.359389	−	0.622480i	−0.628470	−	0.777834i	$-0.716318\pi$
$541$	8.35918	−	14.4785i	0.359389	−	0.622480i	0.987859	+	0.155354i	$0.0496518\pi$
$542$	18.0223	−	36.5197i	0.774122	−	1.56866i
$543$	22.8917	+	16.8121i	0.982378	+	0.721475i
$544$	−8.71158	−	25.7822i	−0.373506	−	1.10540i
$545$	−4.63592	−	12.7371i	−0.198581	−	0.545597i
$546$	−13.0482	+	2.05063i	−0.558412	+	0.0877587i
$547$	−27.6868	+	4.88192i	−1.18380	+	0.208736i	−0.730684	−	0.682715i	$-0.760799\pi$
$547$	−27.6868	+	4.88192i	−1.18380	+	0.208736i	−0.453116	+	0.891451i	$0.649688\pi$
$548$	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
$552$	−21.9184	−	1.95323i	−0.932910	−	0.0831349i
$553$	−17.3556	+	10.6320i	−0.738034	+	0.452120i
$554$	17.6282	−	16.8658i	0.748950	−	0.716561i
$555$	7.84992	−	7.50307i	0.333210	−	0.318487i
$556$	−0.260236	+	5.88465i	−0.0110364	+	0.249565i
$557$	−2.42937			−0.102936			−0.0514679	−	0.998675i	$-0.516390\pi$
$557$	−2.42937			−0.102936			−0.0514679	+	0.998675i	$0.516390\pi$
$558$	5.37085	−	15.7278i	0.227366	−	0.665810i
$559$	−8.47191	−	14.6738i	−0.358324	−	0.620635i
$560$	−7.93050	+	3.94147i	−0.335125	+	0.166557i
$561$	1.96371	−	1.30992i	0.0829078	−	0.0553048i
$562$	−4.60664	−	1.34411i	−0.194319	−	0.0566980i
$563$	−4.08005	+	1.48502i	−0.171954	+	0.0625861i	−0.426562	−	0.904458i	$-0.640276\pi$
$563$	−4.08005	+	1.48502i	−0.171954	+	0.0625861i	0.254609	+	0.967044i	$0.418053\pi$
$564$	−0.0898800	−	0.455024i	−0.00378463	−	0.0191599i
$565$	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	0.984282	+	0.176605i	$0.0565116\pi$
$569$	2.85677	+	16.2015i	0.119762	+	0.679204i	−0.864520	+	0.502599i	$0.832377\pi$
$570$	5.27749	+	16.7996i	0.221050	+	0.703660i
$571$	0.967689	+	2.65870i	0.0404965	+	0.111263i	0.958293	−	0.285789i	$-0.0922555\pi$
$571$	0.967689	+	2.65870i	0.0404965	+	0.111263i	−0.917796	+	0.397052i	$0.870033\pi$
$572$	0.442494	−	1.06658i	0.0185016	−	0.0445961i
$573$	−9.30445	−	13.9484i	−0.388699	−	0.582701i
$574$	−4.37954	+	16.6059i	−0.182798	+	0.693118i
$575$	16.7261	−	9.65683i	0.697527	−	0.402717i
$576$	−8.28116	+	22.5260i	−0.345048	+	0.938585i
$577$		−	34.4277i		−	1.43324i	−0.697463	−	0.716621i	$-0.745688\pi$
$577$		−	34.4277i		−	1.43324i	0.697463	−	0.716621i	$-0.254312\pi$
$578$	8.67070	−	0.565866i	0.360653	−	0.0235369i
$579$	−4.91754	−	5.14486i	−0.204366	−	0.213813i
$580$	10.3509	−	7.93331i	0.429798	−	0.329413i
$581$	6.25319	−	11.5129i	0.259426	−	0.477638i
$582$	3.34931	−	0.437363i	0.138833	−	0.0181293i
$583$	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	0.991425	+	0.130679i	$0.0417159\pi$
$587$	2.53148	+	14.3567i	0.104485	+	0.592565i	−0.886939	+	0.461886i	$0.847173\pi$
$588$	−23.3276	−	6.61994i	−0.962013	−	0.273002i
$589$	31.6230	−	11.5098i	1.30300	−	0.474255i
$590$	6.37118	+	6.65916i	0.262297	+	0.274153i
$591$	−9.61496	+	13.0920i	−0.395507	+	0.538532i
$592$	21.1670	+	21.2145i	0.869957	+	0.871910i
$593$	−1.97275	−	1.13897i	−0.0810113	−	0.0467719i	0.458947	−	0.888464i	$-0.348227\pi$
$593$	−1.97275	−	1.13897i	−0.0810113	−	0.0467719i	−0.539958	+	0.841692i	$0.681560\pi$
$594$	−2.07332	−	0.186812i	−0.0850695	−	0.00766500i
$595$	−2.12198	−	10.4376i	−0.0869927	−	0.427901i
$596$	17.4744	−	9.08414i	0.715779	−	0.372101i
$597$	3.26381	+	7.43312i	0.133579	+	0.304218i
$598$	−3.07373	−	12.5766i	−0.125694	−	0.514295i
$599$	10.1151	−	12.0547i	0.413292	−	0.492542i	−0.518733	−	0.854936i	$-0.673596\pi$
$599$	10.1151	−	12.0547i	0.413292	−	0.492542i	0.932025	+	0.362394i	$0.118040\pi$
$600$	−5.41905	−	20.3554i	−0.221232	−	0.831006i
$601$	−25.2117	+	4.44550i	−1.02840	+	0.181336i	−0.662301	−	0.749238i	$-0.730420\pi$
$601$	−25.2117	+	4.44550i	−1.02840	+	0.181336i	−0.366104	+	0.930574i	$0.619309\pi$
$602$	−2.83310	−	30.9772i	−0.115469	−	1.26254i
$603$	−26.7461	+	20.4575i	−1.08919	+	0.833096i
$604$	7.26142	−	2.28504i	0.295463	−	0.0929770i
$605$	−8.99893	+	1.58675i	−0.365859	+	0.0645107i
$606$	8.00753	−	19.2745i	0.325284	−	0.782975i
$607$	−23.7420	+	8.64137i	−0.963657	+	0.350742i	−0.775465	−	0.631390i	$-0.782485\pi$
$607$	−23.7420	+	8.64137i	−0.963657	+	0.350742i	−0.188191	+	0.982132i	$0.560262\pi$
$608$	−46.0398	+	15.5565i	−1.86716	+	0.630898i
$609$	35.5836	+	2.98961i	1.44192	+	0.121145i
$610$	−0.118119	+	0.239353i	−0.00478250	+	0.00969111i
$611$	0.236325	−	0.136442i	0.00956069	−	0.00551987i
$612$	−23.6100	−	16.6060i	−0.954376	−	0.671257i
$613$	−11.2367	+	19.4625i	−0.453845	+	0.786083i	−0.998621	−	0.0524986i	$-0.983281\pi$
$613$	−11.2367	+	19.4625i	−0.453845	+	0.786083i	0.544776	+	0.838582i	$0.316615\pi$
$614$	−14.3541	+	29.0867i	−0.579286	+	1.17385i
$615$	5.96422	+	2.94695i	0.240501	+	0.118832i
$616$	1.55813	−	1.43747i	0.0627786	−	0.0579172i
$617$	6.80316	−	38.5826i	0.273885	−	1.55328i	−0.468597	−	0.883412i	$-0.655240\pi$
$617$	6.80316	−	38.5826i	0.273885	−	1.55328i	0.742482	−	0.669866i	$-0.233649\pi$
$618$	11.7850	−	3.70217i	0.474061	−	0.148923i
$619$	−6.49764	−	2.36495i	−0.261162	−	0.0950553i	0.208121	−	0.978103i	$-0.433265\pi$
$619$	−6.49764	−	2.36495i	−0.261162	−	0.0950553i	−0.469283	+	0.883048i	$0.655488\pi$
$620$	6.25368	−	1.96792i	0.251154	−	0.0790337i
$621$	−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
$624$	−14.1164	−	0.334752i	−0.565107	−	0.0134008i
$625$	11.4804	+	9.63320i	0.459216	+	0.385328i
$626$	11.7225	+	12.2523i	0.468523	+	0.489701i
$627$	−2.33915	−	3.50664i	−0.0934167	−	0.140042i
$628$	−8.18753	+	12.8360i	−0.326718	+	0.512210i
$629$	−31.2142	+	18.0215i	−1.24459	+	0.718566i
$630$	−4.31731	+	8.34221i	−0.172006	+	0.332361i
$631$	9.08927	+	5.24769i	0.361838	+	0.208907i	0.669887	−	0.742463i	$-0.266343\pi$
$631$	9.08927	+	5.24769i	0.361838	+	0.208907i	−0.308049	+	0.951371i	$0.599676\pi$
$632$	−20.2858	+	7.86907i	−0.806925	+	0.313015i
$633$	12.6598	−	12.1004i	0.503181	−	0.480948i
$634$	−24.6946	−	7.20532i	−0.980746	−	0.286160i
$635$	−13.1414	+	4.78308i	−0.521501	+	0.189811i
$636$	1.06754	−	1.93974i	0.0423307	−	0.0769156i
$637$	−0.742516	−	14.2473i	−0.0294196	−	0.564500i
$638$	−1.84667	+	2.51706i	−0.0731105	+	0.0996515i
$639$	−39.6049	+	12.4203i	−1.56675	+	0.491338i
$640$	−9.09438	+	2.63141i	−0.359487	+	0.104016i
$641$	−10.9001	+	9.14631i	−0.430530	+	0.361257i	−0.832152	−	0.554548i	$-0.812891\pi$
$641$	−10.9001	+	9.14631i	−0.430530	+	0.361257i	0.401622	+	0.915806i	$0.368447\pi$
$642$	−0.957284	+	21.4088i	−0.0377810	+	0.844938i
$643$	20.9452	−	7.62342i	0.825997	−	0.300638i	0.105782	−	0.994389i	$-0.466265\pi$
$643$	20.9452	−	7.62342i	0.825997	−	0.300638i	0.720215	+	0.693751i	$0.244043\pi$
$644$	4.55170	−	23.3285i	0.179362	−	0.919272i
$645$	−11.9770	−	1.32104i	−0.471594	−	0.0520160i
$646$	−3.80633	−	58.3240i	−0.149758	−	2.29473i
$647$	2.32029	+	4.01887i	0.0912202	+	0.157998i	0.908025	−	0.418916i	$-0.137590\pi$
$647$	2.32029	+	4.01887i	0.0912202	+	0.157998i	−0.816805	+	0.576914i	$0.804257\pi$
$648$	7.02729	+	24.4667i	0.276058	+	0.961141i
$649$	−1.91056	−	1.10306i	−0.0749962	−	0.0432991i
$650$	10.3065	−	6.88239i	0.404253	−	0.269950i
$651$	16.2953	+	7.53037i	0.638664	+	0.295138i
$652$	2.16434	+	0.897920i	0.0847620	+	0.0351653i
$653$	2.73896	−	15.5334i	0.107184	−	0.607870i	−0.883142	−	0.469107i	$-0.844576\pi$
$653$	2.73896	−	15.5334i	0.107184	−	0.607870i	0.990326	−	0.138764i	$-0.0443129\pi$
$654$	21.3533	−	33.4404i	0.834981	−	1.30762i
$655$	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
$658$	0.498896	−	0.0456279i	0.0194490	−	0.00177876i
$659$	8.86427	−	24.3544i	0.345303	−	0.948712i	−0.638526	−	0.769600i	$-0.720455\pi$
$659$	8.86427	−	24.3544i	0.345303	−	0.948712i	0.983829	−	0.179112i	$-0.0573223\pi$
$660$	−0.425076	−	0.702611i	−0.0165460	−	0.0273491i
$661$	−34.1463	−	6.02091i	−1.32814	−	0.234186i	−0.535839	−	0.844320i	$-0.680004\pi$
$661$	−34.1463	−	6.02091i	−1.32814	−	0.234186i	−0.792298	+	0.610134i	$0.791116\pi$
$662$	5.32994	−	18.2671i	0.207154	−	0.709972i
$663$	4.76481	−	16.3005i	0.185050	−	0.633060i
$664$	8.77595	−	10.9158i	0.340573	−	0.423615i
$665$	−18.6387	+	3.78927i	−0.722778	+	0.146941i
$666$	31.4073	+	4.89266i	1.21701	+	0.189587i
$667$			35.0017i			1.35527i
$668$	−42.1770	+	21.9259i	−1.63188	+	0.848338i
$669$	6.05654	−	4.04010i	0.234159	−	0.156199i
$670$	−12.7514	−	3.72059i	−0.492631	−	0.143739i
$671$	0.0110949	−	0.0629221i	0.000428312	−	0.00242908i
$672$	−23.2730	−	11.4179i	−0.897775	−	0.440454i
$673$	−3.27672	+	2.74949i	−0.126308	+	0.105985i	−0.703754	−	0.710444i	$-0.748494\pi$
$673$	−3.27672	+	2.74949i	−0.126308	+	0.105985i	0.577445	+	0.816429i	$0.304050\pi$
$674$	−2.14768	−	1.57567i	−0.0827255	−	0.0606925i
$675$	−17.3919	−	14.0247i	−0.669415	−	0.539813i
$676$	5.31073	+	16.8765i	0.204259	+	0.649095i
$677$	−3.68197	+	0.649231i	−0.141510	+	0.0249520i	−0.243954	−	0.969787i	$-0.578445\pi$
$677$	−3.68197	+	0.649231i	−0.141510	+	0.0249520i	0.102445	+	0.994739i	$0.467334\pi$
$678$	26.0838	+	23.9519i	1.00174	+	0.919869i
$679$	0.0949732	+	3.64715i	0.00364474	+	0.139965i
$680$	−0.238821	−	11.3841i	−0.00915836	−	0.436558i
$681$	−29.9799	+	19.9985i	−1.14883	+	0.766345i
$682$	−1.30512	+	0.871526i	−0.0499757	+	0.0333725i
$683$	13.2021	+	7.62222i	0.505164	+	0.291656i	0.730843	−	0.682545i	$-0.239127\pi$
$683$	13.2021	+	7.62222i	0.505164	+	0.291656i	−0.225680	+	0.974202i	$0.572460\pi$
$684$	−29.6537	+	42.1609i	−1.13384	+	1.61206i
$685$	9.01196	+	5.20306i	0.344329	+	0.198799i
$686$	9.72292	−	24.3200i	0.371223	−	0.928544i
$687$	30.0241	−	28.6975i	1.14549	−	1.09488i
$688$	2.93545	−	33.1244i	0.111913	−	1.26286i
$689$	1.28287	+	0.226204i	0.0488734	+	0.00861769i
$690$	−8.50256	−	3.53235i	−0.323687	−	0.134474i
$691$	23.8179	−	19.9856i	0.906075	−	0.760288i	−0.0652929	−	0.997866i	$-0.520798\pi$
$691$	23.8179	−	19.9856i	0.906075	−	0.760288i	0.971368	+	0.237579i	$0.0763537\pi$
$692$	21.8079	+	20.0058i	0.829013	+	0.760506i
$693$	0.432762	−	2.20648i	0.0164393	−	0.0838172i
$694$	11.5712	+	26.3176i	0.439238	+	0.999004i
$695$	−0.842933	+	2.31594i	−0.0319743	+	0.0878486i
$696$	36.8578	+	9.93974i	1.39709	+	0.376765i
$697$	−16.9151	−	14.1935i	−0.640707	−	0.537617i
$698$	−0.512687	−	0.535861i	−0.0194055	−	0.0202826i
$699$	6.21588	−	8.46370i	0.235106	−	0.320126i
$700$	22.4745	−	3.54335i	0.849457	−	0.133926i
$701$	−46.0444			−1.73907			−0.869537	−	0.493868i	$-0.835582\pi$
$701$	−46.0444			−1.73907			−0.869537	+	0.493868i	$0.835582\pi$
$702$	−12.2906	+	8.55853i	−0.463878	+	0.323021i
$703$	32.1815	+	55.7399i	1.21375	+	2.10227i
$704$	1.91342	−	1.21446i	0.0721146	−	0.0457717i
$705$	0.0212757	−	0.192893i	0.000801291	−	0.00726477i
$706$	−7.00232	+	23.9988i	−0.263536	+	0.903208i
$707$	19.8105	+	10.7600i	0.745051	+	0.404670i
$708$	−4.13936	+	26.6577i	−0.155567	+	1.00186i
$709$	10.4123	+	3.78978i	0.391043	+	0.142328i	0.530056	−	0.847962i	$-0.322171\pi$
$709$	10.4123	+	3.78978i	0.391043	+	0.142328i	−0.139013	+	0.990291i	$0.544393\pi$
$710$	−13.2015	−	9.68546i	−0.495445	−	0.363489i
$711$	−12.4300	+	19.4450i	−0.466163	+	0.729245i
$712$	0.524054	+	2.64623i	0.0196397	+	0.0991715i
$713$	−6.01805	+	16.5345i	−0.225378	+	0.619220i
$714$	20.4826	−	23.5057i	0.766543	−	0.879678i
$715$	0.310559	−	0.370110i	0.0116143	−	0.0138413i
$716$	−1.03211	−	7.87374i	−0.0385716	−	0.294255i
$717$	10.2148	+	41.8842i	0.381477	+	1.56419i
$718$	1.02934	+	15.7724i	0.0384145	+	0.588621i
$719$	15.6819	+	27.1619i	0.584837	+	1.01297i	0.994896	+	0.100909i	$0.0321750\pi$
$719$	15.6819	+	27.1619i	0.584837	+	1.01297i	−0.410058	+	0.912059i	$0.634492\pi$
$720$	−6.13421	+	7.95032i	−0.228609	+	0.296291i
$721$	2.65817	+	13.0751i	0.0989956	+	0.486941i
$722$	−77.3375	+	5.04719i	−2.87820	+	0.187837i
$723$	13.4693	−	0.872395i	0.500930	−	0.0324447i
$724$	−26.0299	+	19.9503i	−0.967394	+	0.741446i
$725$	−31.4845	+	11.4594i	−1.16931	+	0.425593i
$726$	−19.7015	−	18.0913i	−0.731193	−	0.671431i
$727$	−35.1517	+	29.4958i	−1.30371	+	1.09394i	−0.314213	+	0.949352i	$0.601741\pi$
$727$	−35.1517	+	29.4958i	−1.30371	+	1.09394i	−0.989492	+	0.144586i	$0.953815\pi$
$728$	1.93968	−	15.1279i	0.0718891	−	0.560676i
$729$	21.3443	+	16.5355i	0.790528	+	0.612426i
$730$	−10.8725	−	7.97675i	−0.402410	−	0.295233i
$731$	37.5832	+	13.6792i	1.39006	+	0.505942i
$732$	−0.766488	+	0.151403i	−0.0283302	+	0.00559601i
$733$	14.6853	−	17.5012i	0.542413	−	0.646423i	−0.423314	−	0.905983i	$-0.639133\pi$
$733$	14.6853	−	17.5012i	0.542413	−	0.646423i	0.965727	+	0.259560i	$0.0835777\pi$
$734$	−2.02528	−	8.28668i	−0.0747543	−	0.305867i
$735$	−8.47886	−	5.57187i	−0.312748	−	0.205522i
$736$	9.24256	−	23.6689i	0.340685	−	0.872448i
$737$	3.17969			0.117126
$738$	3.76422	+	19.1059i	0.138563	+	0.703298i
$739$		−	34.1262i		−	1.25535i	−0.778475	−	0.627676i	$-0.784006\pi$
$739$		−	34.1262i		−	1.25535i	0.778475	−	0.627676i	$-0.215994\pi$
$740$	5.78356	+	11.1253i	0.212608	+	0.408976i
$741$	−29.1082	−	8.50863i	−1.06932	−	0.312572i
$742$	1.96439	+	1.36398i	0.0721149	+	0.0500734i
$743$	29.4414	−	35.0869i	1.08010	−	1.28721i	0.124604	−	0.992207i	$-0.460234\pi$
$743$	29.4414	−	35.0869i	1.08010	−	1.28721i	0.955495	−	0.295006i	$-0.0953216\pi$
$744$	15.7023	+	11.0326i	0.575673	+	0.404475i
$745$	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
$748$	0.818173	+	2.60000i	0.0299154	+	0.0950653i
$749$	−22.8925	−	3.42471i	−0.836474	−	0.125136i
$750$	0.851507	−	19.0432i	0.0310926	−	0.695359i
$751$	−39.8545	−	7.02743i	−1.45431	−	0.256435i	−0.610049	−	0.792363i	$-0.708850\pi$
$751$	−39.8545	−	7.02743i	−1.45431	−	0.256435i	−0.844263	+	0.535929i	$0.819961\pi$
$752$	0.533477	+	0.0472762i	0.0194539	+	0.00172398i
$753$	16.2862	−	22.1757i	0.593502	−	0.808127i
$754$	1.46266	+	22.4122i	0.0532670	+	0.816205i
$755$	3.18509			0.115917
$756$	−27.0713	+	4.81092i	−0.984574	+	0.174971i
$757$	14.6804			0.533566			0.266783	−	0.963757i	$-0.414039\pi$
$757$	14.6804			0.533566			0.266783	+	0.963757i	$0.414039\pi$
$758$	−1.55344	−	23.8031i	−0.0564234	−	0.864569i
$759$	2.19069	+	0.241630i	0.0795172	+	0.00877061i
$760$	−20.3288	+	0.426468i	−0.737401	+	0.0154696i
$761$	−2.29626	−	0.404893i	−0.0832394	−	0.0146774i	0.131873	−	0.991267i	$-0.457901\pi$
$761$	−2.29626	−	0.404893i	−0.0832394	−	0.0146774i	−0.215113	+	0.976589i	$0.569012\pi$
$762$	−34.5019	−	22.0312i	−1.24987	−	0.798105i
$763$	33.5352	+	26.6830i	1.21405	+	0.965991i
$764$	18.4680	−	5.81154i	0.668147	−	0.210254i
$765$	−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
$768$	−22.2994	−	16.4541i	−0.804659	−	0.593738i
$769$	−8.67879	+	10.3430i	−0.312965	+	0.372977i	−0.899481	−	0.436961i	$-0.856055\pi$
$769$	−8.67879	+	10.3430i	−0.312965	+	0.372977i	0.586515	+	0.809938i	$0.300499\pi$
$770$	0.802400	−	0.378019i	0.0289165	−	0.0136228i
$771$	35.0821	−	33.5320i	1.26345	−	1.20763i
$772$	7.29159	−	3.79057i	0.262430	−	0.136426i
$773$		−	1.17713i		−	0.0423386i	−0.999776	−	0.0211693i	$-0.993261\pi$
$773$		−	1.17713i		−	0.0423386i	0.999776	−	0.0211693i	$-0.00673890\pi$
$774$	−18.2429	−	30.1873i	−0.655727	−	1.08506i
$775$	−16.8433			−0.605028
$776$	−0.596567	+	3.85439i	−0.0214155	+	0.138365i
$777$	−8.77166	+	33.1935i	−0.314681	+	1.19081i
$778$	1.88367	+	7.70729i	0.0675329	+	0.276320i
$779$	−25.3456	+	30.2057i	−0.908101	+	1.08223i
$780$	−5.59195	−	1.90652i	−0.200224	−	0.0682644i
$781$	3.68306	+	1.34053i	0.131790	+	0.0479678i
$782$	24.6401	+	18.0775i	0.881127	+	0.646449i
$783$	37.7710	−	14.5879i	1.34983	−	0.521327i
$784$	14.8713	−	23.7244i	0.531116	−	0.847299i
$785$	−4.87983	+	4.09467i	−0.174169	+	0.146145i
$786$	−8.30309	+	37.2673i	−0.296161	+	1.32928i
$787$	39.6569	−	14.4339i	1.41362	−	0.514515i	0.481428	−	0.876486i	$-0.340118\pi$
$787$	39.6569	−	14.4339i	1.41362	−	0.514515i	0.932189	+	0.361971i	$0.117896\pi$
$788$	−11.4097	−	14.8867i	−0.406455	−	0.530318i
$789$	−22.3901	+	45.3146i	−0.797109	+	1.61324i
$790$	−9.08456	+	0.592876i	−0.323214	+	0.0210936i
$791$	−28.6513	+	25.3411i	−1.01872	+	0.901027i
$792$	0.876553	−	2.23825i	0.0311470	−	0.0795326i
$793$	−0.229837	−	0.398090i	−0.00816176	−	0.0141366i
$794$	2.21218	+	33.8970i	0.0785074	+	1.20296i
$795$	0.669684	−	0.640094i	0.0237512	−	0.0227018i
$796$	−9.29448	+	1.21834i	−0.329434	+	0.0431829i
$797$	−9.49270	+	11.3130i	−0.336249	+	0.400725i	−0.907502	−	0.420049i	$-0.862013\pi$
$797$	−9.49270	+	11.3130i	−0.336249	+	0.400725i	0.571253	+	0.820774i	$0.306457\pi$
$798$	−41.9746	−	36.5763i	−1.48589	−	1.29479i
$799$	−0.220306	+	0.605287i	−0.00779388	+	0.0214135i
$800$	24.3165	+	0.564695i	0.859718	+	0.0199650i
$801$	2.10656	+	1.93629i	0.0744315	+	0.0684154i
$802$	−11.2930	−	8.28527i	−0.398771	−	0.292563i
$803$	3.03330	+	1.10403i	0.107043	+	0.0389603i
$804$	−14.0441	−	36.2572i	−0.495297	−	1.27869i
$805$	4.74653	−	8.73899i	0.167293	−	0.308009i
$806$	−3.16252	+	10.8388i	−0.111395	+	0.381780i
$807$	−6.03286	−	4.43064i	−0.212367	−	0.155966i
$808$	18.7830	+	15.1009i	0.660783	+	0.531249i
$809$	11.5634	+	20.0283i	0.406546	+	0.704159i	0.994500	−	0.104736i	$-0.0333996\pi$
$809$	11.5634	+	20.0283i	0.406546	+	0.704159i	−0.587954	+	0.808895i	$0.700066\pi$
$810$	−0.268176	+	10.6475i	−0.00942275	+	0.374114i
$811$	−4.18981			−0.147124			−0.0735621	−	0.997291i	$-0.523437\pi$
$811$	−4.18981			−0.147124			−0.0735621	+	0.997291i	$0.523437\pi$
$812$	−14.8038	+	38.4841i	−0.519513	+	1.35053i
$813$	49.5765	+	5.46821i	1.73873	+	0.191778i
$814$	−2.07499	−	2.16878i	−0.0727282	−	0.0760155i
$815$	0.751037	+	0.630195i	0.0263077	+	0.0220748i
$816$	26.0333	−	20.8131i	0.911349	−	0.728604i
$817$	24.4272	−	67.1131i	0.854599	−	2.34799i
$818$	−14.0601	−	31.9783i	−0.491600	−	1.11810i
$819$	−7.81882	−	14.1618i	−0.273212	−	0.494854i
$820$	−5.19286	+	5.66064i	−0.181343	+	0.197678i
$821$	40.7845	−	34.2222i	1.42339	−	1.19436i	0.473893	−	0.880582i	$-0.342848\pi$
$821$	40.7845	−	34.2222i	1.42339	−	1.19436i	0.949495	−	0.313782i	$-0.101596\pi$
$822$	3.94414	+	30.2041i	0.137568	+	1.05349i
$823$	17.8860	+	3.15378i	0.623466	+	0.109934i	0.476452	−	0.879200i	$-0.341923\pi$
$823$	17.8860	+	3.15378i	0.623466	+	0.109934i	0.147014	+	0.989134i	$0.453034\pi$
$824$	0.299168	+	14.2606i	0.0104220	+	0.496793i
$825$	0.499876	+	2.04967i	0.0174034	+	0.0713603i
$826$	−28.1752	−	7.43075i	−0.980341	−	0.258549i
$827$	10.1949	+	5.88605i	0.354513	+	0.204678i	0.666671	−	0.745352i	$-0.267719\pi$
$827$	10.1949	+	5.88605i	0.354513	+	0.204678i	−0.312158	+	0.950030i	$0.601052\pi$
$828$	−6.92063	−	26.0471i	−0.240509	−	0.905201i
$829$	6.47455	+	3.73808i	0.224870	+	0.129829i	0.608203	−	0.793781i	$-0.291891\pi$
$829$	6.47455	+	3.73808i	0.224870	+	0.129829i	−0.383333	+	0.923610i	$0.625224\pi$
$830$	4.87352	−	3.25441i	0.169162	−	0.112962i
$831$	26.7884	+	13.2362i	0.929278	+	0.459160i
$832$	4.92909	−	15.5419i	0.170885	−	0.538817i
$833$	22.9597	+	24.6356i	0.795507	+	0.853574i
$834$	−6.88262	+	2.16213i	−0.238325	+	0.0748683i
$835$	−19.5870	+	3.45372i	−0.677836	+	0.119521i
$836$	4.64287	−	1.46103i	0.160577	−	0.0505308i
$837$	20.3508	−	0.396957i	0.703428	−	0.0137209i
$838$	−16.0482	−	11.7740i	−0.554378	−	0.406725i
$839$	−30.8446	+	25.8817i	−1.06487	+	0.893536i	−0.994578	−	0.103990i	$-0.966839\pi$
$839$	−30.8446	+	25.8817i	−1.06487	+	0.893536i	−0.0702964	+	0.997526i	$0.522395\pi$
$840$	−7.85449	−	7.47991i	−0.271006	−	0.258082i
$841$	5.50823	−	31.2387i	0.189939	−	1.07720i
$842$	2.50183	+	0.729977i	0.0862186	+	0.0251567i
$843$	−0.379866	−	5.86492i	−0.0130833	−	0.201999i
$844$	9.32731	+	17.9422i	0.321059	+	0.617594i
$845$			7.40256i			0.254656i
$846$	0.486174	−	0.293806i	0.0167150	−	0.0101013i
$847$	21.6408	−	19.1406i	0.743587	−	0.657678i
$848$	1.80577	+	1.80983i	0.0620105	+	0.0621498i
$849$	−17.0872	+	4.16725i	−0.586432	+	0.143020i
$850$	−8.19387	+	28.0826i	−0.281047	+	0.963225i
$851$	−33.1416	−	5.84376i	−1.13608	−	0.200322i
$852$	−0.981721	−	47.9178i	−0.0336332	−	1.64164i
$853$	−5.14428	+	14.1338i	−0.176137	+	0.483932i	−0.996074	−	0.0885210i	$-0.971786\pi$
$853$	−5.14428	+	14.1338i	−0.176137	+	0.483932i	0.819937	+	0.572453i	$0.194008\pi$
$854$	−0.0768602	−	0.840391i	−0.00263010	−	0.0287576i
$855$	−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	0.261570	−	0.965185i	$-0.415760\pi$
$857$	−21.4984	−	25.6208i	−0.734373	−	0.875191i	−0.995942	+	0.0899934i	$0.971315\pi$
$858$	1.41284	+	0.0631743i	0.0482335	+	0.00215674i
$859$	0.112787	−	0.639646i	0.00384824	−	0.0218245i	−0.982823	−	0.184550i	$-0.940917\pi$
$859$	0.112787	−	0.639646i	0.00384824	−	0.0218245i	0.986671	+	0.162725i	$0.0520284\pi$
$860$	5.33176	−	12.8516i	0.181812	−	0.438237i
$861$	−20.9470	+	1.90540i	−0.713871	+	0.0649358i
$862$	4.14644	−	2.76888i	0.141228	−	0.0943085i
$863$	14.9562	+	8.63499i	0.509117	+	0.293939i	0.732470	−	0.680799i	$-0.238367\pi$
$863$	14.9562	+	8.63499i	0.509117	+	0.293939i	−0.223354	+	0.974737i	$0.571701\pi$
$864$	−29.3937	−	0.109207i	−0.999993	−	0.00371529i
$865$	6.19118	+	10.7234i	0.210506	+	0.364608i
$866$	2.51852	+	38.5910i	0.0855828	+	1.31138i
$867$	4.27851	+	9.74403i	0.145306	+	0.330925i
$868$	−13.6100	+	15.6342i	−0.461953	+	0.530659i
$869$	2.04784	−	0.745354i	0.0694683	−	0.0252844i
$870$	13.4620	+	8.59613i	0.456403	+	0.291436i
$871$	17.5242	−	14.7045i	0.593784	−	0.498244i
$872$	30.1786	+	34.4705i	1.02198	+	1.16732i
$873$	1.90454	+	3.67240i	0.0644588	+	0.124292i
$874$	32.2814	−	44.0003i	1.09193	−	1.48833i
$875$	20.3630	+	3.04629i	0.688394	+	0.102983i
$876$	−0.808525	−	39.4641i	−0.0273175	−	1.33337i
$877$	−50.9845	+	18.5568i	−1.72162	+	0.626620i	−0.997978	−	0.0635530i	$-0.979757\pi$
$877$	−50.9845	+	18.5568i	−1.72162	+	0.626620i	−0.723645	+	0.690173i	$0.757535\pi$
$878$	27.6793	+	8.07619i	0.934130	+	0.272558i
$879$	6.63017	+	27.1861i	0.223630	+	0.916963i
$880$	0.916192	−	0.244392i	0.0308848	−	0.00823845i
$881$	30.6839	+	17.7154i	1.03377	+	0.596846i	0.918062	−	0.396437i	$-0.129754\pi$
$881$	30.6839	+	17.7154i	1.03377	+	0.596846i	0.115706	+	0.993283i	$0.463087\pi$
$882$	−2.13831	−	29.6214i	−0.0720007	−	0.997405i
$883$	24.0832	−	13.9044i	0.810463	−	0.467921i	−0.0366535	−	0.999328i	$-0.511670\pi$
$883$	24.0832	−	13.9044i	0.810463	−	0.467921i	0.847117	+	0.531407i	$0.178336\pi$
$884$	16.5329	+	10.5457i	0.556062	+	0.354689i
$885$	−5.00008	+	10.1195i	−0.168076	+	0.340162i
$886$	23.5186	+	24.5817i	0.790124	+	0.825838i
$887$	−15.4345	−	12.9511i	−0.518240	−	0.434855i	0.345778	−	0.938317i	$-0.387615\pi$
$887$	−15.4345	−	12.9511i	−0.518240	−	0.434855i	−0.864018	+	0.503461i	$0.832060\pi$
$888$	−15.5652	+	33.2396i	−0.522332	+	1.11545i
$889$	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
$892$	2.52344	+	8.01900i	0.0844909	+	0.268496i
$893$	1.08087	+	0.393406i	0.0361701	+	0.0131648i
$894$	17.7666	+	16.3145i	0.594204	+	0.545638i
$895$	0.576962	−	3.27211i	0.0192857	−	0.109375i
$896$	20.1728	−	22.1147i	0.673926	−	0.738799i
$897$	13.1910	−	8.79921i	0.440433	−	0.293797i
$898$	−16.8383	+	34.1205i	−0.561900	+	1.13862i
$899$	15.2623	−	26.4352i	0.509028	−	0.881662i
$900$	21.1640	−	14.7529i	0.705465	−	0.491764i
$901$	−2.66291	+	1.53743i	−0.0887146	+	0.0512194i
$902$	0.813756	−	1.64897i	0.0270951	−	0.0549047i
$903$	34.4724	−	16.2196i	1.14717	−	0.539755i
$904$	−34.9761	+	21.1838i	−1.16329	+	0.704563i
$905$	−12.8944	+	4.69318i	−0.428625	+	0.156007i
$906$	5.66790	+	7.40265i	0.188303	+	0.245937i
$907$	53.8985	−	9.50377i	1.78967	−	0.315567i	0.822324	−	0.569020i	$-0.192677\pi$
$907$	53.8985	−	9.50377i	1.78967	−	0.315567i	0.967348	+	0.253452i	$0.0815661\pi$
$908$	−12.4910	−	39.6941i	−0.414530	−	1.31730i
$909$	25.5365	+	1.15441i	0.846991	+	0.0382893i
$910$	2.67410	−	5.79408i	0.0886455	−	0.192072i
$911$	−31.5609	+	5.56503i	−1.04566	+	0.184378i	−0.669985	−	0.742375i	$-0.733699\pi$
$911$	−31.5609	+	5.56503i	−1.04566	+	0.184378i	−0.375673	+	0.926752i	$0.622588\pi$
$912$	−37.1664	−	46.4883i	−1.23070	−	1.53938i
$913$	−0.901710	+	1.07462i	−0.0298422	+	0.0355646i
$914$	3.68116	+	15.0620i	0.121762	+	0.498206i
$915$	−0.324928	−	0.0358390i	−0.0107418	−	0.00118480i
$916$	22.1208	+	42.5519i	0.730892	+	1.40595i
$917$	−39.1072	−	13.0914i	−1.29143	−	0.432317i
$918$	9.23839	−	34.1238i	0.304912	−	1.12625i
$919$	11.9972	+	6.92658i	0.395751	+	0.228487i	0.684649	−	0.728873i	$-0.259956\pi$
$919$	11.9972	+	6.92658i	0.395751	+	0.228487i	−0.288898	+	0.957360i	$0.593289\pi$
$920$	6.66145	−	8.28571i	0.219622	−	0.273172i
$921$	−39.4861	−	4.35525i	−1.30111	−	0.143510i
$922$	−0.651404	−	0.680848i	−0.0214529	−	0.0224225i
$923$	26.4977	−	9.64437i	0.872182	−	0.317448i
$924$	2.30645	+	1.19222i	0.0758767	+	0.0392210i
$925$	−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	−0.999659	−	0.0261183i	$-0.991685\pi$
$929$	−25.9622	−	30.9405i	−0.851791	−	1.01513i	0.147867	−	0.989007i	$-0.452759\pi$
$930$	4.88131	+	6.37532i	0.160065	+	0.209055i
$931$	43.9924	−	40.9997i	1.44179	−	1.34371i
$932$	7.37616	+	9.62397i	0.241614	+	0.315243i
$933$	2.45063	−	0.597664i	0.0802302	−	0.0195666i
$934$	40.1510	−	2.62033i	1.31378	−	0.0857397i
$935$			1.14044i			0.0372964i
$936$	−5.51987	−	16.3892i	−0.180422	−	0.535699i
$937$	10.9014	−	6.29393i	0.356133	−	0.205614i	−0.311250	−	0.950328i	$-0.600748\pi$
$937$	10.9014	−	6.29393i	0.356133	−	0.205614i	0.667383	+	0.744714i	$0.267414\pi$
$938$	40.5234	−	11.0294i	1.32313	−	0.360123i
$939$	−9.19973	+	18.6190i	−0.300222	+	0.607608i
$940$	0.206979	+	0.0858694i	0.00675090	+	0.00280075i
$941$	−5.64087	−	15.4982i	−0.183887	−	0.505225i	0.813158	−	0.582043i	$-0.197746\pi$
$941$	−5.64087	−	15.4982i	−0.183887	−	0.505225i	−0.997045	+	0.0768174i	$0.975524\pi$
$942$	−18.2004	−	4.05500i	−0.593000	−	0.132119i
$943$	−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	$-0.577526\pi$
$947$	−4.18030	+	0.737100i	−0.135841	+	0.0239525i	0.105314	+	0.994439i	$0.466415\pi$
$948$	−17.5440	−	20.0589i	−0.569803	−	0.651484i
$949$	21.8229	−	7.94290i	0.708403	−	0.257837i
$950$	50.1477	+	14.6320i	1.62701	+	0.474724i
$951$	−2.03633	−	31.4398i	−0.0660324	−	1.01951i
$952$	19.4457	+	30.2975i	0.630240	+	0.981946i
$953$	18.2350	+	31.5839i	0.590689	+	1.02310i	0.994140	+	0.108101i	$0.0344771\pi$
$953$	18.2350	+	31.5839i	0.590689	+	1.02310i	−0.403451	+	0.915001i	$0.632190\pi$
$954$	2.67939	+	0.417398i	0.0867484	+	0.0135138i
$955$	8.10064			0.262131
$956$	−49.7326	−	2.19931i	−1.60847	−	0.0711309i
$957$	−3.66987	−	1.07274i	−0.118630	−	0.0346768i
$958$	−3.09184	+	2.95813i	−0.0998928	+	0.0955729i
$959$	−32.8900	+	0.856469i	−1.06207	+	0.0276568i
$960$	−6.83338	−	9.36766i	−0.220546	−	0.302340i
$961$	−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
$966$	28.7573	−	4.51943i	0.925250	−	0.145410i
$967$	−5.60859	−	15.4095i	−0.180360	−	0.495536i	0.816260	−	0.577685i	$-0.196044\pi$
$967$	−5.60859	−	15.4095i	−0.180360	−	0.495536i	−0.996620	+	0.0821493i	$0.973822\pi$
$968$	26.4180	−	16.0005i	0.849108	−	0.514274i
$969$	65.5439	−	28.7797i	2.10557	−	0.924536i
$970$	−0.722181	+	1.46340i	−0.0231878	+	0.0469871i
$971$	6.84699	−	11.8593i	0.219730	−	0.380584i	−0.734995	−	0.678072i	$-0.762816\pi$
$971$	6.84699	−	11.8593i	0.219730	−	0.380584i	0.954725	+	0.297488i	$0.0961489\pi$
$972$	−25.2236	+	18.3240i	−0.809048	+	0.587742i
$973$	−1.55242	−	7.63606i	−0.0497682	−	0.244801i
$974$	−21.0453	+	14.0535i	−0.674334	+	0.450302i
$975$	12.2337	+	8.98462i	0.391791	+	0.287738i
$976$	0.0796368	−	0.898643i	0.00254911	−	0.0287649i
$977$	−18.0698	−	15.1623i	−0.578103	−	0.485086i	0.306220	−	0.951961i	$-0.400936\pi$
$977$	−18.0698	−	15.1623i	−0.578103	−	0.485086i	−0.884324	+	0.466875i	$0.845380\pi$
$978$	−0.128195	+	2.86696i	−0.00409922	+	0.0916754i
$979$	−0.0469171	−	0.266080i	−0.00149948	−	0.00850396i
$980$	8.91489	−	7.60091i	0.284776	−	0.242802i
$981$	47.4254	+	10.5907i	1.51418	+	0.338136i
$982$	−3.74537	−	8.51847i	−0.119519	−	0.271835i
$983$	−8.71903	−	49.4481i	−0.278094	−	1.57715i	−0.728959	−	0.684557i	$-0.759996\pi$
$983$	−8.71903	−	49.4481i	−0.278094	−	1.57715i	0.450865	−	0.892592i	$-0.351115\pi$
$984$	−22.3970	−	1.99587i	−0.713989	−	0.0636261i
$985$	−2.68407	−	7.37443i	−0.0855216	−	0.234969i
$986$	−36.6503	−	38.3068i	−1.16718	−	1.21994i
$987$	0.261221	+	0.555186i	0.00831476	+	0.0176718i
$988$	18.8316	−	29.5232i	0.599114	−	0.939257i
$989$	18.6715	+	32.3399i	0.593718	+	1.02835i
$990$	0.630949	−	0.783218i	0.0200529	−	0.0248923i
$991$	24.9959	+	14.4314i	0.794021	+	0.458428i	0.841376	−	0.540450i	$-0.181746\pi$
$991$	24.9959	+	14.4314i	0.794021	+	0.458428i	−0.0473553	+	0.998878i	$0.515079\pi$
$992$	−17.3012	+	13.8458i	−0.549314	+	0.439606i
$993$	23.2567	−	1.50632i	0.738029	−	0.0478015i
$994$	51.5884	+	4.30878i	1.63628	+	0.136666i
$995$	−3.86254	−	0.681070i	−0.122451	−	0.0215914i
$996$	16.2362	+	5.53558i	0.514465	+	0.175402i
$997$	−9.26616	+	25.4586i	−0.293462	+	0.806281i	0.702092	+	0.712087i	$0.252250\pi$
$997$	−9.26616	+	25.4586i	−0.293462	+	0.806281i	−0.995554	+	0.0941943i	$0.969973\pi$
$998$	22.7749	+	51.7994i	0.720928	+	1.63968i
$999$	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.103.5	✓	840
4.3	odd	2	inner	756.2.bt.a.103.128	yes	840
7.3	odd	6		756.2.cd.a.535.91	yes	840
27.16	even	9		756.2.cd.a.691.59	yes	840
28.3	even	6		756.2.cd.a.535.59	yes	840
108.43	odd	18		756.2.cd.a.691.91	yes	840
189.178	odd	18	inner	756.2.bt.a.367.128	yes	840
756.367	even	18	inner	756.2.bt.a.367.5	yes	840

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bt.a.103.5	✓	840	1.1	even	1	trivial
756.2.bt.a.103.128	yes	840	4.3	odd	2	inner
756.2.bt.a.367.5	yes	840	756.367	even	18	inner
756.2.bt.a.367.128	yes	840	189.178	odd	18	inner
756.2.cd.a.535.59	yes	840	28.3	even	6
756.2.cd.a.535.91	yes	840	7.3	odd	6
756.2.cd.a.691.59	yes	840	27.16	even	9
756.2.cd.a.691.91	yes	840	108.43	odd	18

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)

\(f(q)\)	\(=\)	\(q+(-1.41121 + 0.0920983i) q^{2} +(-0.696355 - 1.58590i) q^{3} +(1.98304 - 0.259940i) q^{4} +(0.824097 + 0.145310i) q^{5} +(1.12876 + 2.17391i) q^{6} +(-2.46179 + 0.969313i) q^{7} +(-2.77454 + 0.549465i) q^{8} +(-2.03018 + 2.20870i) q^{9} +O(q^{10})\)	\(q+(-1.41121 + 0.0920983i) q^{2} +(-0.696355 - 1.58590i) q^{3} +(1.98304 - 0.259940i) q^{4} +(0.824097 + 0.145310i) q^{5} +(1.12876 + 2.17391i) q^{6} +(-2.46179 + 0.969313i) q^{7} +(-2.77454 + 0.549465i) q^{8} +(-2.03018 + 2.20870i) q^{9} +(-1.17636 - 0.129166i) q^{10} +(0.278983 - 0.0491922i) q^{11} +(-1.79314 - 2.96389i) q^{12} +(1.31006 - 1.56127i) q^{13} +(3.38484 - 1.59463i) q^{14} +(-0.343415 - 1.40813i) q^{15} +(3.86486 - 1.03094i) q^{16} +4.81084i q^{17} +(2.66159 - 3.30392i) q^{18} +8.59082 q^{19} +(1.67199 + 0.0739399i) q^{20} +(3.25152 + 3.22918i) q^{21} +(-0.389173 + 0.0951144i) q^{22} +(-2.88728 + 3.44093i) q^{23} +(2.80347 + 4.01753i) q^{24} +(-4.04044 - 1.47060i) q^{25} +(-1.70498 + 2.32394i) q^{26} +(4.91652 + 1.68163i) q^{27} +(-4.62986 + 2.56210i) q^{28} +(5.96928 - 5.00882i) q^{29} +(0.614318 + 1.95553i) q^{30} +(3.68103 - 1.33978i) q^{31} +(-5.35919 + 1.81082i) q^{32} +(-0.272285 - 0.408184i) q^{33} +(-0.443070 - 6.78911i) q^{34} +(-2.16961 + 0.441083i) q^{35} +(-3.45179 + 4.90766i) q^{36} +(3.74603 + 6.48831i) q^{37} +(-12.1235 + 0.791200i) q^{38} +(-3.38829 - 0.990433i) q^{39} +(-2.36633 + 0.0496423i) q^{40} +(-2.95032 + 3.51605i) q^{41} +(-4.88598 - 4.25760i) q^{42} +(2.84340 - 7.81219i) q^{43} +(0.540446 - 0.170069i) q^{44} +(-1.99401 + 1.52518i) q^{45} +(3.75766 - 5.12179i) q^{46} +(0.125817 + 0.0457938i) q^{47} +(-4.32629 - 5.41140i) q^{48} +(5.12086 - 4.77250i) q^{49} +(5.83736 + 1.70321i) q^{50} +(7.62952 - 3.35005i) q^{51} +(2.19206 - 3.43659i) q^{52} +(0.319577 + 0.553524i) q^{53} +(-7.09312 - 1.92033i) q^{54} +0.237057 q^{55} +(6.29775 - 4.04207i) q^{56} +(-5.98226 - 13.6242i) q^{57} +(-7.96262 + 7.61827i) q^{58} +(-5.96567 - 5.00579i) q^{59} +(-1.04703 - 2.70310i) q^{60} +(0.0771396 - 0.211939i) q^{61} +(-5.07131 + 2.22973i) q^{62} +(2.85696 - 7.40525i) q^{63} +(7.39618 - 3.04903i) q^{64} +(1.30649 - 1.09627i) q^{65} +(0.421845 + 0.550958i) q^{66} +(11.0538 + 1.94908i) q^{67} +(1.25053 + 9.54006i) q^{68} +(7.46755 + 2.18284i) q^{69} +(3.02115 - 0.822279i) q^{70} +(11.9820 + 6.91779i) q^{71} +(4.41921 - 7.24366i) q^{72} +(9.86810 + 5.69735i) q^{73} +(-5.88400 - 8.81138i) q^{74} +(0.481352 + 7.43181i) q^{75} +(17.0359 - 2.23310i) q^{76} +(-0.639115 + 0.391523i) q^{77} +(4.87282 + 1.08565i) q^{78} +(7.57594 - 1.33584i) q^{79} +(3.33483 - 0.287991i) q^{80} +(-0.756743 - 8.96813i) q^{81} +(3.83970 - 5.23361i) q^{82} +(-3.79339 + 3.18303i) q^{83} +(7.28728 + 5.55838i) q^{84} +(-0.699065 + 3.96460i) q^{85} +(-3.29316 + 11.2865i) q^{86} +(-12.1002 - 5.97879i) q^{87} +(-0.747020 + 0.289777i) q^{88} -0.953752i q^{89} +(2.67351 - 2.33600i) q^{90} +(-1.71174 + 5.11339i) q^{91} +(-4.83114 + 7.57400i) q^{92} +(-4.68807 - 4.90479i) q^{93} +(-0.181772 - 0.0530371i) q^{94} +(7.07967 + 1.24834i) q^{95} +(6.60369 + 7.23818i) q^{96} +(0.471632 - 1.29580i) q^{97} +(-6.78708 + 7.20663i) 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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