LMFDB - Embedded newform 342.2.bf.b.155.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(155,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([3, 13]))

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

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

chi := DirichletCharacter("342.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.bf (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:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			155.4
Character	$\chi$	$=$	342.155
Dual form			342.2.bf.b.203.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 + 0.342020i) q^{2} +(0.158968 - 1.72474i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.949911 + 2.60986i) q^{5} +(0.440515 + 1.67510i) q^{6} -4.55403 q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.94946 - 0.548357i) q^{9} +O(q^{10})$	\(q+(-0.939693 + 0.342020i) q^{2} +(0.158968 - 1.72474i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.949911 + 2.60986i) q^{5} +(0.440515 + 1.67510i) q^{6} -4.55403 q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.94946 - 0.548357i) q^{9} +(-1.78525 - 2.12758i) q^{10} +(-3.04312 + 1.75694i) q^{11} +(-0.986865 - 1.42341i) q^{12} +(-4.41863 + 0.779124i) q^{13} +(4.27939 - 1.55757i) q^{14} +(4.65233 - 1.22347i) q^{15} +(0.173648 - 0.984808i) q^{16} +(3.85555 - 4.59487i) q^{17} +(2.95913 - 0.493487i) q^{18} +(-1.17038 + 4.19883i) q^{19} +(2.40526 + 1.38868i) q^{20} +(-0.723946 + 7.85452i) q^{21} +(2.25868 - 2.69180i) q^{22} +(-3.19330 - 3.80563i) q^{23} +(1.41418 + 1.00004i) q^{24} +(-2.07881 + 1.74433i) q^{25} +(3.88568 - 2.24340i) q^{26} +(-1.41464 + 4.99988i) q^{27} +(-3.48859 + 2.92727i) q^{28} +(0.969438 + 5.49796i) q^{29} +(-3.95331 + 2.74087i) q^{30} +(-5.63411 - 3.25285i) q^{31} +(0.173648 + 0.984808i) q^{32} +(2.54651 + 5.52789i) q^{33} +(-2.05150 + 5.63644i) q^{34} +(-4.32592 - 11.8854i) q^{35} +(-2.61189 + 1.47581i) q^{36} +3.99276i q^{37} +(-0.336290 - 4.34591i) q^{38} +(0.641365 + 7.74485i) q^{39} +(-2.73516 - 0.482282i) q^{40} +(3.05262 + 2.56146i) q^{41} +(-2.00612 - 7.62844i) q^{42} +(-3.05103 - 2.56012i) q^{43} +(-1.20182 + 3.30198i) q^{44} +(-1.37059 - 8.21856i) q^{45} +(4.30232 + 2.48395i) q^{46} +(4.73908 - 0.835629i) q^{47} +(-1.67093 - 0.456051i) q^{48} +13.7392 q^{49} +(1.35685 - 2.35012i) q^{50} +(-7.31204 - 7.38026i) q^{51} +(-2.88406 + 3.43708i) q^{52} +(0.764024 + 4.33300i) q^{53} +(-0.380729 - 5.18219i) q^{54} +(-7.47607 - 6.27317i) q^{55} +(2.27701 - 3.94391i) q^{56} +(7.05585 + 2.68608i) q^{57} +(-2.79139 - 4.83482i) q^{58} +(-0.992697 + 5.62986i) q^{59} +(2.77747 - 3.92769i) q^{60} +(-9.13477 - 3.32478i) q^{61} +(6.40687 + 1.12970i) q^{62} +(13.4319 + 2.49724i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-6.23071 - 10.7919i) q^{65} +(-4.28359 - 4.32355i) q^{66} +(4.59687 - 12.6298i) q^{67} -5.99817i q^{68} +(-7.07135 + 4.90264i) q^{69} +(8.13007 + 9.68904i) q^{70} +(-0.450331 + 2.55396i) q^{71} +(1.94962 - 2.28013i) q^{72} +(0.318012 - 0.115747i) q^{73} +(-1.36560 - 3.75197i) q^{74} +(2.67805 + 3.86270i) q^{75} +(1.80240 + 3.96880i) q^{76} +(13.8584 - 8.00118i) q^{77} +(-3.25158 - 7.05841i) q^{78} +(3.59079 + 0.633153i) q^{79} +(2.73516 - 0.482282i) q^{80} +(8.39861 + 3.23471i) q^{81} +(-3.74460 - 1.36292i) q^{82} +13.6838i q^{83} +(4.49421 + 6.48225i) q^{84} +(15.6544 + 5.69773i) q^{85} +(3.74264 + 1.36221i) q^{86} +(9.63666 - 0.798029i) q^{87} -3.51389i q^{88} +(-0.752030 - 0.273716i) q^{89} +(4.09884 + 7.25415i) q^{90} +(20.1226 - 3.54815i) q^{91} +(-4.89242 - 0.862665i) q^{92} +(-6.50597 + 9.20027i) q^{93} +(-4.16748 + 2.40610i) q^{94} +(-12.0701 + 0.933996i) q^{95} +(1.72614 - 0.142945i) q^{96} +(-1.72071 - 4.72762i) q^{97} +(-12.9106 + 4.69908i) q^{98} +(9.93898 - 3.51332i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 9 q^{3} - 3 q^{6} - 18 q^{7} - 24 q^{8} - 3 q^{9}+O(q^{10}) $ 48 * q + 9 * q^3 - 3 * q^6 - 18 * q^7 - 24 * q^8 - 3 * q^9	$ 48 q + 9 q^{3} - 3 q^{6} - 18 q^{7} - 24 q^{8} - 3 q^{9} - 9 q^{10} - 9 q^{11} - 3 q^{12} + 6 q^{13} + 6 q^{14} + 9 q^{15} + 27 q^{17} + 9 q^{18} - 12 q^{19} - 9 q^{20} - 3 q^{21} - 9 q^{22} - 18 q^{23} - 9 q^{24} + 18 q^{25} - 18 q^{26} - 24 q^{27} + 6 q^{28} + 27 q^{30} - 36 q^{31} + 39 q^{33} + 9 q^{34} + 18 q^{35} + 9 q^{36} + 9 q^{38} + 24 q^{39} - 9 q^{40} + 36 q^{41} - 30 q^{42} - 15 q^{43} + 9 q^{44} - 9 q^{45} + 27 q^{46} - 3 q^{48} + 66 q^{49} - 3 q^{50} - 12 q^{51} - 15 q^{52} + 9 q^{55} + 9 q^{56} - 3 q^{57} - 9 q^{58} - 36 q^{59} - 21 q^{60} - 12 q^{61} + 3 q^{62} - 9 q^{63} - 24 q^{64} + 9 q^{65} - 33 q^{67} - 69 q^{69} + 18 q^{70} - 27 q^{71} + 6 q^{72} + 66 q^{73} - 39 q^{74} - 24 q^{75} - 9 q^{76} - 27 q^{77} - 6 q^{78} - 12 q^{79} + 9 q^{80} - 3 q^{81} - 9 q^{82} + 3 q^{84} - 54 q^{85} - 15 q^{86} + 63 q^{87} + 18 q^{89} + 9 q^{90} + 51 q^{91} - 18 q^{92} - 39 q^{93} + 54 q^{94} - 54 q^{95} - 3 q^{96} + 117 q^{97} - 42 q^{98} - 93 q^{99}+O(q^{100}) $ 48 * q + 9 * q^3 - 3 * q^6 - 18 * q^7 - 24 * q^8 - 3 * q^9 - 9 * q^10 - 9 * q^11 - 3 * q^12 + 6 * q^13 + 6 * q^14 + 9 * q^15 + 27 * q^17 + 9 * q^18 - 12 * q^19 - 9 * q^20 - 3 * q^21 - 9 * q^22 - 18 * q^23 - 9 * q^24 + 18 * q^25 - 18 * q^26 - 24 * q^27 + 6 * q^28 + 27 * q^30 - 36 * q^31 + 39 * q^33 + 9 * q^34 + 18 * q^35 + 9 * q^36 + 9 * q^38 + 24 * q^39 - 9 * q^40 + 36 * q^41 - 30 * q^42 - 15 * q^43 + 9 * q^44 - 9 * q^45 + 27 * q^46 - 3 * q^48 + 66 * q^49 - 3 * q^50 - 12 * q^51 - 15 * q^52 + 9 * q^55 + 9 * q^56 - 3 * q^57 - 9 * q^58 - 36 * q^59 - 21 * q^60 - 12 * q^61 + 3 * q^62 - 9 * q^63 - 24 * q^64 + 9 * q^65 - 33 * q^67 - 69 * q^69 + 18 * q^70 - 27 * q^71 + 6 * q^72 + 66 * q^73 - 39 * q^74 - 24 * q^75 - 9 * q^76 - 27 * q^77 - 6 * q^78 - 12 * q^79 + 9 * q^80 - 3 * q^81 - 9 * q^82 + 3 * q^84 - 54 * q^85 - 15 * q^86 + 63 * q^87 + 18 * q^89 + 9 * q^90 + 51 * q^91 - 18 * q^92 - 39 * q^93 + 54 * q^94 - 54 * q^95 - 3 * q^96 + 117 * q^97 - 42 * q^98 - 93 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{18}\right)$

Coefficient data

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

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

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

$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$3$	0.158968	−	1.72474i	0.0917803	−	0.995779i
$3$	0.158968	−	1.72474i	0.0917803	−	0.995779i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	0.949911	+	2.60986i	0.424813	+	1.16716i	0.948921	+	0.315513i	$0.102176\pi$
$5$	0.949911	+	2.60986i	0.424813	+	1.16716i	−0.524108	+	0.851652i	$0.675601\pi$
$6$	0.440515	+	1.67510i	0.179839	+	0.683855i
$7$	−4.55403			−1.72126			−0.860631	−	0.509230i	$-0.829930\pi$
$7$	−4.55403			−1.72126			−0.860631	+	0.509230i	$0.829930\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	−2.94946	−	0.548357i	−0.983153	−	0.182786i
$10$	−1.78525	−	2.12758i	−0.564545	−	0.672799i
$11$	−3.04312	+	1.75694i	−0.917535	+	0.529739i	−0.882848	−	0.469659i	$-0.844377\pi$
$11$	−3.04312	+	1.75694i	−0.917535	+	0.529739i	−0.0346869	+	0.999398i	$0.511043\pi$
$12$	−0.986865	−	1.42341i	−0.284883	−	0.410903i
$13$	−4.41863	+	0.779124i	−1.22551	+	0.216090i	−0.748695	−	0.662915i	$-0.769319\pi$
$13$	−4.41863	+	0.779124i	−1.22551	+	0.216090i	−0.476813	+	0.879005i	$0.658208\pi$
$14$	4.27939	−	1.55757i	1.14371	−	0.416278i
$15$	4.65233	−	1.22347i	1.20123	−	0.315897i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	3.85555	−	4.59487i	0.935108	−	1.11442i	−0.0581282	−	0.998309i	$-0.518513\pi$
$17$	3.85555	−	4.59487i	0.935108	−	1.11442i	0.993236	−	0.116109i	$-0.0370423\pi$
$18$	2.95913	−	0.493487i	0.697474	−	0.116316i
$19$	−1.17038	+	4.19883i	−0.268503	+	0.963279i
$19$	−1.17038	+	4.19883i	−0.268503	+	0.963279i
$20$	2.40526	+	1.38868i	0.537832	+	0.310518i
$21$	−0.723946	+	7.85452i	−0.157978	+	1.71400i
$22$	2.25868	−	2.69180i	0.481553	−	0.573893i
$23$	−3.19330	−	3.80563i	−0.665849	−	0.793528i	0.322364	−	0.946616i	$-0.395523\pi$
$23$	−3.19330	−	3.80563i	−0.665849	−	0.793528i	−0.988213	+	0.153088i	$0.951078\pi$
$24$	1.41418	+	1.00004i	0.288669	+	0.204132i
$25$	−2.07881	+	1.74433i	−0.415761	+	0.348865i
$26$	3.88568	−	2.24340i	0.762044	−	0.439966i
$27$	−1.41464	+	4.99988i	−0.272248	+	0.962227i
$28$	−3.48859	+	2.92727i	−0.659281	+	0.553203i
$29$	0.969438	+	5.49796i	0.180020	+	1.02094i	0.932188	+	0.361974i	$0.117897\pi$
$29$	0.969438	+	5.49796i	0.180020	+	1.02094i	−0.752168	+	0.658971i	$0.770992\pi$
$30$	−3.95331	+	2.74087i	−0.721773	+	0.500413i
$31$	−5.63411	−	3.25285i	−1.01192	−	0.584230i	−0.100164	−	0.994971i	$-0.531937\pi$
$31$	−5.63411	−	3.25285i	−1.01192	−	0.584230i	−0.911752	+	0.410741i	$0.865270\pi$
$32$	0.173648	+	0.984808i	0.0306970	+	0.174091i
$33$	2.54651	+	5.52789i	0.443291	+	0.962281i
$34$	−2.05150	+	5.63644i	−0.351829	+	0.966641i
$35$	−4.32592	−	11.8854i	−0.731214	−	2.00899i
$36$	−2.61189	+	1.47581i	−0.435316	+	0.245968i
$37$			3.99276i			0.656406i	0.944607	+	0.328203i	$0.106443\pi$
$37$			3.99276i			0.656406i	−0.944607	+	0.328203i	$0.893557\pi$
$38$	−0.336290	−	4.34591i	−0.0545534	−	0.704999i
$39$	0.641365	+	7.74485i	0.102701	+	1.24017i
$40$	−2.73516	−	0.482282i	−0.432467	−	0.0762555i
$41$	3.05262	+	2.56146i	0.476740	+	0.400032i	0.849246	−	0.527998i	$-0.177057\pi$
$41$	3.05262	+	2.56146i	0.476740	+	0.400032i	−0.372506	+	0.928030i	$0.621501\pi$
$42$	−2.00612	−	7.62844i	−0.309551	−	1.17709i
$43$	−3.05103	−	2.56012i	−0.465278	−	0.390414i	0.379791	−	0.925072i	$-0.375996\pi$
$43$	−3.05103	−	2.56012i	−0.465278	−	0.390414i	−0.845068	+	0.534658i	$0.820440\pi$
$44$	−1.20182	+	3.30198i	−0.181181	+	0.497792i
$45$	−1.37059	−	8.21856i	−0.204315	−	1.22515i
$46$	4.30232	+	2.48395i	0.634342	+	0.366238i
$47$	4.73908	−	0.835629i	0.691267	−	0.121889i	0.183031	−	0.983107i	$-0.441409\pi$
$47$	4.73908	−	0.835629i	0.691267	−	0.121889i	0.508235	+	0.861218i	$0.330298\pi$
$48$	−1.67093	−	0.456051i	−0.241178	−	0.0658253i
$49$	13.7392			1.96274
$50$	1.35685	−	2.35012i	0.191887	−	0.332358i
$51$	−7.31204	−	7.38026i	−1.02389	−	1.03344i
$52$	−2.88406	+	3.43708i	−0.399947	+	0.476638i
$53$	0.764024	+	4.33300i	0.104947	+	0.595183i	0.991242	+	0.132061i	$0.0421596\pi$
$53$	0.764024	+	4.33300i	0.104947	+	0.595183i	−0.886295	+	0.463122i	$0.846729\pi$
$54$	−0.380729	−	5.18219i	−0.0518106	−	0.705206i
$55$	−7.47607	−	6.27317i	−1.00807	−	0.845873i
$56$	2.27701	−	3.94391i	0.304279	−	0.527027i
$57$	7.05585	+	2.68608i	0.934570	+	0.355780i
$58$	−2.79139	−	4.83482i	−0.366527	−	0.634843i
$59$	−0.992697	+	5.62986i	−0.129238	+	0.732946i	0.849462	+	0.527650i	$0.176927\pi$
$59$	−0.992697	+	5.62986i	−0.129238	+	0.732946i	−0.978700	+	0.205296i	$0.934184\pi$
$60$	2.77747	−	3.92769i	0.358569	−	0.507063i
$61$	−9.13477	−	3.32478i	−1.16959	−	0.425695i	−0.317074	−	0.948401i	$-0.602700\pi$
$61$	−9.13477	−	3.32478i	−1.16959	−	0.425695i	−0.852513	+	0.522706i	$0.824923\pi$
$62$	6.40687	+	1.12970i	0.813673	+	0.143473i
$63$	13.4319	+	2.49724i	1.69226	+	0.314622i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−6.23071	−	10.7919i	−0.772824	−	1.33857i
$66$	−4.28359	−	4.32355i	−0.527273	−	0.532193i
$67$	4.59687	−	12.6298i	0.561598	−	1.54298i	−0.255697	−	0.966757i	$-0.582305\pi$
$67$	4.59687	−	12.6298i	0.561598	−	1.54298i	0.817295	−	0.576220i	$-0.195473\pi$
$68$		−	5.99817i		−	0.727385i
$69$	−7.07135	+	4.90264i	−0.851290	+	0.590208i
$70$	8.13007	+	9.68904i	0.971730	+	1.15806i
$71$	−0.450331	+	2.55396i	−0.0534445	+	0.303099i	−0.999799	−	0.0200303i	$-0.993624\pi$
$71$	−0.450331	+	2.55396i	−0.0534445	+	0.303099i	0.946355	+	0.323129i	$0.104735\pi$
$72$	1.94962	−	2.28013i	0.229765	−	0.268716i
$73$	0.318012	−	0.115747i	0.0372205	−	0.0135472i	−0.323343	−	0.946282i	$-0.604807\pi$
$73$	0.318012	−	0.115747i	0.0372205	−	0.0135472i	0.360563	+	0.932735i	$0.382584\pi$
$74$	−1.36560	−	3.75197i	−0.158748	−	0.436157i
$75$	2.67805	+	3.86270i	0.309234	+	0.446026i
$76$	1.80240	+	3.96880i	0.206749	+	0.455252i
$77$	13.8584	−	8.00118i	1.57932	−	0.911819i
$78$	−3.25158	−	7.05841i	−0.368169	−	0.799208i
$79$	3.59079	+	0.633153i	0.403995	+	0.0712353i	0.371954	−	0.928251i	$-0.378688\pi$
$79$	3.59079	+	0.633153i	0.403995	+	0.0712353i	0.0320415	+	0.999487i	$0.489799\pi$
$80$	2.73516	−	0.482282i	0.305800	−	0.0539208i
$81$	8.39861	+	3.23471i	0.933179	+	0.359413i
$82$	−3.74460	−	1.36292i	−0.413522	−	0.150510i
$83$			13.6838i			1.50199i	0.660306	+	0.750997i	$0.270427\pi$
$83$			13.6838i			1.50199i	−0.660306	+	0.750997i	$0.729573\pi$
$84$	4.49421	+	6.48225i	0.490359	+	0.707272i
$85$	15.6544	+	5.69773i	1.69796	+	0.618005i
$86$	3.74264	+	1.36221i	0.403579	+	0.146891i
$87$	9.63666	−	0.798029i	1.03316	−	0.0855577i
$88$		−	3.51389i		−	0.374582i
$89$	−0.752030	−	0.273716i	−0.0797150	−	0.0290139i	0.301855	−	0.953354i	$-0.402394\pi$
$89$	−0.752030	−	0.273716i	−0.0797150	−	0.0290139i	−0.381570	+	0.924340i	$0.624616\pi$
$90$	4.09884	+	7.25415i	0.432056	+	0.764655i
$91$	20.1226	−	3.54815i	2.10942	−	0.371947i
$92$	−4.89242	−	0.862665i	−0.510070	−	0.0899391i
$93$	−6.50597	+	9.20027i	−0.674638	+	0.954024i
$94$	−4.16748	+	2.40610i	−0.429843	+	0.248170i
$95$	−12.0701	+	0.933996i	−1.23837	+	0.0958259i
$96$	1.72614	−	0.142945i	0.176174	−	0.0145893i
$97$	−1.72071	−	4.72762i	−0.174712	−	0.480017i	0.821169	−	0.570684i	$-0.193322\pi$
$97$	−1.72071	−	4.72762i	−0.174712	−	0.480017i	−0.995881	+	0.0906679i	$0.971100\pi$
$98$	−12.9106	+	4.69908i	−1.30417	+	0.474679i
$99$	9.93898	−	3.51332i	0.998905	−	0.353102i
$100$	−0.471227	+	2.67246i	−0.0471227	+	0.267246i
$101$	−2.66395	−	3.17477i	−0.265073	−	0.315902i	0.617047	−	0.786926i	$-0.288329\pi$
$101$	−2.66395	−	3.17477i	−0.265073	−	0.315902i	−0.882120	+	0.471024i	$0.843884\pi$
$102$	9.39527	+	4.43431i	0.930270	+	0.439062i
$103$		−	2.11817i		−	0.208709i	−0.994540	−	0.104355i	$-0.966722\pi$
$103$		−	2.11817i		−	0.208709i	0.994540	−	0.104355i	$-0.0332777\pi$
$104$	1.53457	−	4.21621i	0.150477	−	0.413433i
$105$	−21.1869	+	5.57170i	−2.06763	+	0.543742i
$106$	−2.19992	−	3.81037i	−0.213675	−	0.370096i
$107$	−1.79149	−	3.10295i	−0.173190	−	0.299973i	0.766344	−	0.642431i	$-0.222074\pi$
$107$	−1.79149	−	3.10295i	−0.173190	−	0.299973i	−0.939533	+	0.342458i	$0.888741\pi$
$108$	2.13018	+	4.73944i	0.204977	+	0.456053i
$109$	−14.7786	−	2.60586i	−1.41553	−	0.249596i	−0.587021	−	0.809572i	$-0.699699\pi$
$109$	−14.7786	−	2.60586i	−1.41553	−	0.249596i	−0.828509	+	0.559976i	$0.810810\pi$
$110$	9.17075	+	3.33788i	0.874397	+	0.318255i
$111$	6.88648	+	0.634722i	0.653635	+	0.0602451i
$112$	−0.790799	+	4.48484i	−0.0747235	+	0.423778i
$113$	−4.75336	−	8.23305i	−0.447158	−	0.774500i	0.551042	−	0.834478i	$-0.314231\pi$
$113$	−4.75336	−	8.23305i	−0.447158	−	0.774500i	−0.998200	+	0.0599773i	$0.980897\pi$
$114$	−7.54902	−	0.110848i	−0.707031	−	0.0103819i
$115$	6.89879	−	11.9491i	0.643316	−	1.11426i
$116$	4.27665	+	3.58854i	0.397077	+	0.333187i
$117$	13.4598	+	0.124996i	1.24436	+	0.0115559i
$118$	−0.992697	−	5.62986i	−0.0913851	−	0.518271i
$119$	−17.5583	+	20.9252i	−1.60957	+	1.91821i
$120$	−1.26661	+	4.64077i	−0.115626	+	0.423643i
$121$	0.673711	−	1.16690i	0.0612464	−	0.106082i
$122$	9.72102			0.880099
$123$	4.90312	−	4.85779i	0.442099	−	0.438013i
$124$	−6.40687	+	1.12970i	−0.575354	+	0.101450i
$125$	5.49917	+	3.17494i	0.491860	+	0.283976i
$126$	−13.4760	+	2.24735i	−1.20054	+	0.200210i
$127$	−5.29051	+	14.5356i	−0.469457	+	1.28982i	0.448727	+	0.893669i	$0.351877\pi$
$127$	−5.29051	+	14.5356i	−0.469457	+	1.28982i	−0.918184	+	0.396154i	$0.870345\pi$
$128$	0.766044	+	0.642788i	0.0677094	+	0.0568149i
$129$	−4.90055	+	4.85526i	−0.431470	+	0.427481i
$130$	9.54600	+	8.01004i	0.837239	+	0.702527i
$131$	−1.76331	−	0.310919i	−0.154061	−	0.0271651i	0.0960857	−	0.995373i	$-0.469368\pi$
$131$	−1.76331	−	0.310919i	−0.154061	−	0.0271651i	−0.250147	+	0.968208i	$0.580479\pi$
$132$	5.50400	+	2.59774i	0.479062	+	0.226104i
$133$	5.32994	−	19.1216i	0.462164	−	1.65805i
$134$			13.4404i			1.16107i
$135$	−14.3928	+	1.05742i	−1.23873	+	0.0910080i
$136$	2.05150	+	5.63644i	0.175914	+	0.483320i
$137$	6.78821	−	18.6504i	0.579956	−	1.59342i	−0.208299	−	0.978065i	$-0.566793\pi$
$137$	6.78821	−	18.6504i	0.579956	−	1.59342i	0.788254	−	0.615350i	$-0.210985\pi$
$138$	4.96809	−	7.02552i	0.422912	−	0.598052i
$139$	−1.30828	−	7.41963i	−0.110967	−	0.629325i	−0.988668	−	0.150117i	$-0.952035\pi$
$139$	−1.30828	−	7.41963i	−0.110967	−	0.629325i	0.877701	−	0.479208i	$-0.159076\pi$
$140$	−10.9536	−	6.32407i	−0.925750	−	0.534482i
$141$	−0.687879	−	8.30653i	−0.0579298	−	0.699536i
$142$	−0.450331	−	2.55396i	−0.0377910	−	0.214323i
$143$	12.0775	−	10.1343i	1.00997	−	0.847469i
$144$	−1.05219	+	2.80943i	−0.0876829	+	0.234119i
$145$	−13.4280	+	7.75266i	−1.11514	+	0.643824i
$146$	−0.259246	+	0.217533i	−0.0214554	+	0.0180032i
$147$	2.18409	−	23.6965i	0.180141	−	1.95446i
$148$	2.56650	+	3.05863i	0.210965	+	0.251418i
$149$	−1.22568	+	1.46070i	−0.100411	+	0.119665i	−0.813910	−	0.580991i	$-0.802665\pi$
$149$	−1.22568	+	1.46070i	−0.100411	+	0.119665i	0.713499	+	0.700657i	$0.247110\pi$
$150$	−3.83766	−	2.71380i	−0.313344	−	0.221581i
$151$	−9.47172	−	5.46850i	−0.770797	−	0.445020i	0.0623617	−	0.998054i	$-0.480137\pi$
$151$	−9.47172	−	5.46850i	−0.770797	−	0.445020i	−0.833159	+	0.553034i	$0.813470\pi$
$152$	−3.05111	−	3.11300i	−0.247478	−	0.252497i
$153$	−13.8914	+	11.4381i	−1.12305	+	0.924719i
$154$	−10.2861	+	12.2585i	−0.828879	+	0.987820i
$155$	3.13759	−	17.7941i	0.252017	−	1.42926i
$156$	5.46960	+	5.52063i	0.437919	+	0.442004i
$157$	−13.2753	+	4.83180i	−1.05948	+	0.385620i	−0.812233	−	0.583333i	$-0.801748\pi$
$157$	−13.2753	+	4.83180i	−1.05948	+	0.385620i	−0.247248	+	0.968952i	$0.579526\pi$
$158$	−3.59079	+	0.633153i	−0.285668	+	0.0503709i
$159$	7.59475	−	0.628935i	0.602303	−	0.0498778i
$160$	−2.40526	+	1.38868i	−0.190152	+	0.109785i
$161$	14.5424	+	17.3309i	1.14610	+	1.36587i
$162$	−8.99845	−	0.167144i	−0.706985	−	0.0131321i
$163$	6.31589	−	10.9394i	0.494699	−	0.856844i	−0.505282	−	0.862954i	$-0.668612\pi$
$163$	6.31589	−	10.9394i	0.494699	−	0.856844i	0.999981	+	0.00611028i	$0.00194497\pi$
$164$	3.98492			0.311170
$165$	−12.0080	+	11.8970i	−0.934824	+	0.926183i
$166$	−4.68014	−	12.8586i	−0.363249	−	0.998019i
$167$	−0.0857640	+	0.0719645i	−0.00663662	+	0.00556878i	−0.646100	−	0.763253i	$-0.723601\pi$
$167$	−0.0857640	+	0.0719645i	−0.00663662	+	0.00556878i	0.639463	+	0.768822i	$0.279157\pi$
$168$	−6.44024	−	4.55421i	−0.496875	−	0.351365i
$169$	6.70125	−	2.43906i	0.515481	−	0.187620i
$170$	−16.6590			−1.27769
$171$	5.75445	−	11.7425i	0.440053	−	0.897972i
$172$	−3.98284			−0.303688
$173$	−21.0947	+	7.67783i	−1.60380	+	0.583735i	−0.980200	−	0.198011i	$-0.936552\pi$
$173$	−21.0947	+	7.67783i	−1.60380	+	0.583735i	−0.623598	+	0.781745i	$0.714330\pi$
$174$	−8.78255	+	4.04583i	−0.665804	+	0.306714i
$175$	9.46695	−	7.94371i	0.715634	−	0.600488i
$176$	1.20182	+	3.30198i	0.0905907	+	0.248896i
$177$	9.55224	+	2.60711i	0.717991	+	0.195963i
$178$	0.800293			0.0599845
$179$	−9.91972	+	17.1815i	−0.741435	+	1.28420i	0.210407	+	0.977614i	$0.432521\pi$
$179$	−9.91972	+	17.1815i	−0.741435	+	1.28420i	−0.951842	+	0.306589i	$0.900812\pi$
$180$	−6.33272	−	5.41478i	−0.472013	−	0.403594i
$181$	15.0512	+	17.9374i	1.11875	+	1.33327i	0.936759	+	0.349974i	$0.113810\pi$
$181$	15.0512	+	17.9374i	1.11875	+	1.33327i	0.181991	+	0.983300i	$0.441746\pi$
$182$	−17.6955	+	10.2165i	−1.31168	+	0.757297i
$183$	−7.18652	+	15.2266i	−0.531243	+	1.12558i
$184$	4.89242	−	0.862665i	0.360674	−	0.0635965i
$185$	−10.4205	+	3.79277i	−0.766133	+	0.278850i
$186$	2.96693	−	10.8706i	0.217546	−	0.797071i
$187$	−3.65997	+	20.7567i	−0.267643	+	1.51788i
$188$	3.09322	−	3.68635i	0.225596	−	0.268855i
$189$	6.44233	−	22.7696i	0.468611	−	1.65624i
$190$	11.0228	−	5.00589i	0.799675	−	0.363166i
$191$	8.88897	+	5.13205i	0.643183	+	0.371342i	0.785840	−	0.618430i	$-0.212231\pi$
$191$	8.88897	+	5.13205i	0.643183	+	0.371342i	−0.142656	+	0.989772i	$0.545564\pi$
$192$	−1.57315	+	0.724700i	−0.113533	+	0.0523007i
$193$	−13.0866	+	15.5961i	−0.941997	+	1.12263i	0.0502979	+	0.998734i	$0.483983\pi$
$193$	−13.0866	+	15.5961i	−0.941997	+	1.12263i	−0.992295	+	0.123895i	$0.960462\pi$
$194$	3.23388	+	3.85399i	0.232179	+	0.276700i
$195$	−19.6037	+	9.03078i	−1.40385	+	0.646708i
$196$	10.5248	−	8.83138i	0.751773	−	0.630813i
$197$	−2.98538	+	1.72361i	−0.212700	+	0.122802i	−0.602565	−	0.798070i	$-0.705855\pi$
$197$	−2.98538	+	1.72361i	−0.212700	+	0.122802i	0.389866	+	0.920872i	$0.372521\pi$
$198$	−8.13796	+	6.70077i	−0.578340	+	0.476203i
$199$	7.32937	−	6.15007i	0.519566	−	0.435967i	−0.344915	−	0.938634i	$-0.612092\pi$
$199$	7.32937	−	6.15007i	0.519566	−	0.435967i	0.864480	+	0.502667i	$0.167648\pi$
$200$	−0.471227	−	2.67246i	−0.0333208	−	0.188972i
$201$	−21.0524	−	9.93615i	−1.48492	−	0.700842i
$202$	3.58913	+	2.07219i	0.252530	+	0.145798i
$203$	−4.41485	−	25.0379i	−0.309862	−	1.75731i
$204$	−10.3453	−	0.953518i	−0.724315	−	0.0667596i
$205$	−3.78532	+	10.4001i	−0.264378	+	0.726372i
$206$	0.724456	+	1.99043i	0.0504753	+	0.138680i
$207$	7.33166	+	12.9756i	0.509585	+	0.901867i
$208$			4.48679i			0.311103i
$209$	−3.81552	−	14.8338i	−0.263925	−	1.02608i
$210$	18.0035	−	12.4820i	1.24236	−	0.861341i
$211$	18.2033	+	3.20973i	1.25317	+	0.220967i	0.760549	−	0.649280i	$-0.224930\pi$
$211$	18.2033	+	3.20973i	1.25317	+	0.220967i	0.492616	+	0.870247i	$0.336041\pi$
$212$	3.37047	+	2.82816i	0.231485	+	0.194239i
$213$	4.33332	+	1.18270i	0.296914	+	0.0810374i
$214$	2.74472	+	2.30309i	0.187625	+	0.157436i
$215$	3.78334	−	10.3946i	0.258022	−	0.708908i
$216$	−3.62270	−	3.72506i	−0.246493	−	0.253458i
$217$	25.6579	+	14.8136i	1.74177	+	1.00561i
$218$	14.7786	−	2.60586i	1.00093	−	0.176491i
$219$	−0.149080	−	0.566889i	−0.0100739	−	0.0383068i
$220$	−9.75931			−0.657973
$221$	−13.4563	+	23.3070i	−0.905167	+	1.56780i
$222$	−6.68826	+	1.75887i	−0.448886	+	0.118048i
$223$	−9.59496	+	11.4348i	−0.642526	+	0.765733i	−0.984767	−	0.173880i	$-0.944370\pi$
$223$	−9.59496	+	11.4348i	−0.642526	+	0.765733i	0.342241	+	0.939612i	$0.388814\pi$
$224$	−0.790799	−	4.48484i	−0.0528375	−	0.299656i
$225$	7.08787	−	4.00489i	0.472525	−	0.266993i
$226$	7.28256	+	6.11080i	0.484429	+	0.406484i
$227$	−0.516420	+	0.894466i	−0.0342760	+	0.0593678i	−0.882655	−	0.470022i	$-0.844246\pi$
$227$	−0.516420	+	0.894466i	−0.0342760	+	0.0593678i	0.848379	+	0.529390i	$0.177579\pi$
$228$	7.13167	−	2.47775i	0.472306	−	0.164093i
$229$	0.642134	+	1.11221i	0.0424334	+	0.0734968i	0.886462	−	0.462801i	$-0.153156\pi$
$229$	0.642134	+	1.11221i	0.0424334	+	0.0734968i	−0.844029	+	0.536298i	$0.819822\pi$
$230$	−2.39593	+	13.5880i	−0.157983	+	0.895964i
$231$	−11.5969	−	25.1742i	−0.763020	−	1.65634i
$232$	−5.24609	−	1.90942i	−0.344423	−	0.125360i
$233$	−5.91507	−	1.04299i	−0.387509	−	0.0683283i	−0.0235004	−	0.999724i	$-0.507481\pi$
$233$	−5.91507	−	1.04299i	−0.387509	−	0.0683283i	−0.364009	+	0.931396i	$0.618592\pi$
$234$	−12.6908	+	4.48607i	−0.829625	+	0.293263i
$235$	6.68258	+	11.5746i	0.435923	+	0.755042i
$236$	2.85836	+	4.95082i	0.186063	+	0.322271i
$237$	1.66285	−	6.09253i	0.108013	−	0.395752i
$238$	9.34257	−	25.6685i	0.605589	−	1.66384i
$239$			29.5412i			1.91086i	0.295215	+	0.955431i	$0.404609\pi$
$239$			29.5412i			1.91086i	−0.295215	+	0.955431i	$0.595391\pi$
$240$	−0.397009	−	4.79411i	−0.0256268	−	0.309458i
$241$	11.2965	+	13.4626i	0.727669	+	0.867202i	0.995352	−	0.0963052i	$-0.0307025\pi$
$241$	11.2965	+	13.4626i	0.727669	+	0.867202i	−0.267683	+	0.963507i	$0.586258\pi$
$242$	−0.233977	+	1.32695i	−0.0150406	+	0.0852996i
$243$	6.91415	−	13.9712i	0.443543	−	0.896253i
$244$	−9.13477	+	3.32478i	−0.584794	+	0.212847i
$245$	13.0510	+	35.8573i	0.833798	+	2.29084i
$246$	−2.94596	+	6.24180i	−0.187827	+	0.397963i
$247$	1.90006	−	19.4650i	0.120898	−	1.23853i
$248$	5.63411	−	3.25285i	0.357766	−	0.206556i
$249$	23.6010	+	2.17529i	1.49565	+	0.137853i
$250$	−6.25342	−	1.10265i	−0.395501	−	0.0697375i
$251$	−12.8706	+	2.26944i	−0.812387	+	0.143246i	−0.564383	−	0.825513i	$-0.690886\pi$
$251$	−12.8706	+	2.26944i	−0.812387	+	0.143246i	−0.248004	+	0.968759i	$0.579775\pi$
$252$	11.8946	−	6.72088i	0.749292	−	0.423376i
$253$	16.4039	+	5.97052i	1.03130	+	0.375363i
$254$		−	15.4684i		−	0.970575i
$255$	12.3156	−	26.0940i	0.771236	−	1.63407i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	−4.46140	−	1.62382i	−0.278294	−	0.101291i	0.199102	−	0.979979i	$-0.436197\pi$
$257$	−4.46140	−	1.62382i	−0.278294	−	0.101291i	−0.477397	+	0.878688i	$0.658420\pi$
$258$	2.94442	−	6.23854i	0.183312	−	0.388394i
$259$		−	18.1832i		−	1.12985i
$260$	−11.7099	−	4.26205i	−0.726217	−	0.264321i
$261$	0.155528	−	16.7476i	0.00962695	−	1.03665i
$262$	1.76331	−	0.310919i	0.108938	−	0.0192086i
$263$	11.9008	+	2.09843i	0.733835	+	0.129395i	0.528063	−	0.849205i	$-0.322918\pi$
$263$	11.9008	+	2.09843i	0.733835	+	0.129395i	0.205772	+	0.978600i	$0.434029\pi$
$264$	−6.06055	−	0.558596i	−0.373001	−	0.0343792i
$265$	−10.5828	+	6.10995i	−0.650093	+	0.375331i
$266$	1.53147	+	19.7914i	0.0939007	+	1.21349i
$267$	−0.591638	+	1.25354i	−0.0362077	+	0.0767156i
$268$	−4.59687	−	12.6298i	−0.280799	−	0.771488i
$269$	0.373826	−	0.136062i	0.0227926	−	0.00829582i	−0.330599	−	0.943771i	$-0.607251\pi$
$269$	0.373826	−	0.136062i	0.0227926	−	0.00829582i	0.353391	+	0.935476i	$0.385028\pi$
$270$	13.1631	−	5.91626i	0.801081	−	0.360052i
$271$	3.03455	−	17.2098i	0.184336	−	1.04542i	−0.742470	−	0.669880i	$-0.766346\pi$
$271$	3.03455	−	17.2098i	0.184336	−	1.04542i	0.926806	−	0.375542i	$-0.122543\pi$
$272$	−3.85555	−	4.59487i	−0.233777	−	0.278605i
$273$	−2.92079	−	35.2703i	−0.176775	−	2.13465i
$274$			19.8474i			1.19902i
$275$	3.26137	−	8.96054i	0.196668	−	0.540341i
$276$	−2.26561	+	8.30101i	−0.136374	+	0.499662i
$277$	−5.69208	−	9.85898i	−0.342004	−	0.592368i	0.642801	−	0.766033i	$-0.277772\pi$
$277$	−5.69208	−	9.85898i	−0.342004	−	0.592368i	−0.984805	+	0.173665i	$0.944439\pi$
$278$	3.76704	+	6.52471i	0.225932	+	0.391326i
$279$	14.8338	+	12.6837i	0.888079	+	0.759351i
$280$	12.4560	+	2.19633i	0.744388	+	0.131256i
$281$	3.23930	+	1.17901i	0.193240	+	0.0703337i	0.436828	−	0.899545i	$-0.356102\pi$
$281$	3.23930	+	1.17901i	0.193240	+	0.0703337i	−0.243587	+	0.969879i	$0.578324\pi$
$282$	3.48739	+	7.57032i	0.207671	+	0.450806i
$283$	−3.54166	+	20.0858i	−0.210530	+	1.19397i	0.677967	+	0.735092i	$0.262861\pi$
$283$	−3.54166	+	20.0858i	−0.210530	+	1.19397i	−0.888497	+	0.458882i	$0.848250\pi$
$284$	1.29668	+	2.24591i	0.0769437	+	0.133270i
$285$	−0.307864	+	20.9663i	−0.0182363	+	1.24194i
$286$	−7.88305	+	13.6538i	−0.466135	+	0.807369i
$287$	−13.9017	−	11.6649i	−0.820594	−	0.688560i
$288$	0.0278586	−	2.99987i	0.00164158	−	0.176769i
$289$	−3.29550	−	18.6897i	−0.193853	−	1.09940i
$290$	9.96663	−	11.8778i	0.585261	−	0.697487i
$291$	−8.42745	+	2.21624i	−0.494026	+	0.129918i
$292$	0.169211	−	0.293082i	0.00990232	−	0.0171513i
$293$	12.7209			0.743161			0.371580	−	0.928401i	$-0.378816\pi$
$293$	12.7209			0.743161			0.371580	+	0.928401i	$0.378816\pi$
$294$	6.05231	+	23.0145i	0.352978	+	1.34223i
$295$	−15.6361	+	2.75707i	−0.910370	+	0.160523i
$296$	−3.45783	−	1.99638i	−0.200982	−	0.116037i
$297$	−4.47958	−	17.7007i	−0.259932	−	1.02710i
$298$	0.652168	−	1.79182i	0.0377791	−	0.103797i
$299$	17.0751	+	14.3277i	0.987476	+	0.828591i
$300$	4.53439	+	1.23758i	0.261793	+	0.0714518i
$301$	13.8945	+	11.6589i	0.800864	+	0.672005i
$302$	10.7708	+	1.89919i	0.619792	+	0.109286i
$303$	−5.89914	+	4.08994i	−0.338897	+	0.234961i
$304$	3.93181	+	1.88172i	0.225505	+	0.107924i
$305$		−	26.9987i		−	1.54594i
$306$	9.14158	−	15.4995i	0.522589	−	0.886046i
$307$	1.12185	+	3.08226i	0.0640275	+	0.175914i	0.967581	−	0.252562i	$-0.0812730\pi$
$307$	1.12185	+	3.08226i	0.0640275	+	0.175914i	−0.903553	+	0.428476i	$0.859051\pi$
$308$	5.47313	−	15.0373i	0.311860	−	0.856830i
$309$	−3.65329	−	0.336721i	−0.207828	−	0.0191554i
$310$	3.13759	+	17.7941i	0.178203	+	1.01064i
$311$	−10.4797	−	6.05044i	−0.594248	−	0.343089i	0.172528	−	0.985005i	$-0.444807\pi$
$311$	−10.4797	−	6.05044i	−0.594248	−	0.343089i	−0.766775	+	0.641916i	$0.778140\pi$
$312$	−7.02791	−	3.31698i	−0.397877	−	0.187787i
$313$	−2.56015	−	14.5193i	−0.144708	−	0.820681i	−0.967601	−	0.252484i	$-0.918752\pi$
$313$	−2.56015	−	14.5193i	−0.144708	−	0.820681i	0.822893	−	0.568197i	$-0.192359\pi$
$314$	10.8221	−	9.08081i	0.610726	−	0.512460i
$315$	6.24169	+	37.4276i	0.351680	+	2.10880i
$316$	3.15769	−	1.82309i	0.177634	−	0.102557i
$317$	−13.6394	+	11.4448i	−0.766066	+	0.642806i	−0.939698	−	0.342005i	$-0.888894\pi$
$317$	−13.6394	+	11.4448i	−0.766066	+	0.642806i	0.173632	+	0.984811i	$0.444450\pi$
$318$	−6.92162	+	3.18856i	−0.388145	+	0.178806i
$319$	−12.6097	−	15.0277i	−0.706009	−	0.841388i
$320$	1.78525	−	2.12758i	0.0997984	−	0.118935i
$321$	−5.63657	+	2.59658i	−0.314602	+	0.144927i
$322$	−19.5929	−	11.3120i	−1.09187	−	0.630391i
$323$	14.7806	+	21.5665i	0.822416	+	1.19999i
$324$	8.51294	−	2.92059i	0.472941	−	0.162255i
$325$	7.82643	−	9.32718i	0.434132	−	0.517379i
$326$	−2.19349	+	12.4399i	−0.121486	+	0.688981i
$327$	−6.84375	+	25.0749i	−0.378460	+	1.38665i
$328$	−3.74460	+	1.36292i	−0.206761	+	0.0752548i
$329$	−21.5819	+	3.80548i	−1.18985	+	0.209803i
$330$	7.21484	−	15.2866i	0.397164	−	0.841497i
$331$	−9.02081	+	5.20817i	−0.495829	+	0.286267i	−0.726989	−	0.686649i	$-0.759081\pi$
$331$	−9.02081	+	5.20817i	−0.495829	+	0.286267i	0.231161	+	0.972916i	$0.425748\pi$
$332$	8.79578	+	10.4824i	0.482731	+	0.575297i
$333$	2.18946	−	11.7765i	0.119982	−	0.645347i
$334$	0.0559785	−	0.0969576i	0.00306301	−	0.00530528i
$335$	37.3286			2.03948
$336$	7.60948	+	2.07687i	0.415131	+	0.113303i
$337$	−4.73328	−	13.0046i	−0.257838	−	0.708404i	−0.999300	−	0.0374092i	$-0.988089\pi$
$337$	−4.73328	−	13.0046i	−0.257838	−	0.708404i	0.741462	−	0.670995i	$-0.234133\pi$
$338$	−5.46291	+	4.58393i	−0.297143	+	0.249333i
$339$	−14.9555	+	6.88951i	−0.812272	+	0.374187i
$340$	15.6544	−	5.69773i	0.848978	−	0.309003i
$341$	22.8603			1.23796
$342$	−1.39124	+	13.0025i	−0.0752295	+	0.703094i
$343$	−30.6905			−1.65713
$344$	3.74264	−	1.36221i	0.201790	−	0.0734454i
$345$	−19.5123	−	13.7981i	−1.05051	−	0.742867i
$346$	17.1965	−	14.4296i	0.924491	−	0.775740i
$347$	−6.86992	−	18.8750i	−0.368797	−	1.01326i	−0.975820	−	0.218577i	$-0.929859\pi$
$347$	−6.86992	−	18.8750i	−0.368797	−	1.01326i	0.607023	−	0.794684i	$-0.292364\pi$
$348$	6.86914	−	6.80565i	0.368225	−	0.364821i
$349$	3.57017			0.191107			0.0955533	−	0.995424i	$-0.469538\pi$
$349$	3.57017			0.191107			0.0955533	+	0.995424i	$0.469538\pi$
$350$	−6.17911	+	10.7025i	−0.330287	+	0.572075i
$351$	2.35526	−	23.1948i	0.125715	−	1.23805i
$352$	−2.25868	−	2.69180i	−0.120388	−	0.143473i
$353$	8.76118	−	5.05827i	0.466311	−	0.269225i	−0.248383	−	0.968662i	$-0.579899\pi$
$353$	8.76118	−	5.05827i	0.466311	−	0.269225i	0.714694	+	0.699437i	$0.246566\pi$
$354$	−9.86786	+	0.817175i	−0.524471	+	0.0434324i
$355$	−7.09324	+	1.25073i	−0.376470	+	0.0663818i
$356$	−0.752030	+	0.273716i	−0.0398575	+	0.0145069i
$357$	33.2992	+	33.6099i	1.76238	+	1.77883i
$358$	3.44508	−	19.5380i	0.182078	−	1.03262i
$359$	−10.4407	+	12.4428i	−0.551041	+	0.656705i	−0.967625	−	0.252392i	$-0.918783\pi$
$359$	−10.4407	+	12.4428i	−0.551041	+	0.656705i	0.416584	+	0.909097i	$0.363227\pi$
$360$	7.80277	+	2.92232i	0.411242	+	0.154020i
$361$	−16.2604	−	9.82845i	−0.855812	−	0.517287i
$362$	−20.2785	−	11.7078i	−1.06581	−	0.615348i
$363$	−1.90550	−	1.34748i	−0.100013	−	0.0707241i
$364$	13.1341	−	15.6526i	0.688413	−	0.820418i
$365$	0.604167	+	0.720018i	0.0316235	+	0.0376875i
$366$	1.54533	−	16.7662i	0.0807758	−	0.876385i
$367$	6.13515	−	5.14801i	0.320252	−	0.268724i	−0.468462	−	0.883484i	$-0.655192\pi$
$367$	6.13515	−	5.14801i	0.320252	−	0.268724i	0.788714	+	0.614760i	$0.210747\pi$
$368$	−4.30232	+	2.48395i	−0.224274	+	0.129485i
$369$	−7.59899	−	9.22884i	−0.395588	−	0.480434i
$370$	8.49490	−	7.12807i	0.441629	−	0.370571i
$371$	−3.47939	−	19.7326i	−0.180641	−	1.02447i
$372$	0.929958	+	11.2298i	0.0482161	+	0.582237i
$373$	8.86201	+	5.11648i	0.458857	+	0.264921i	0.711564	−	0.702622i	$-0.247987\pi$
$373$	8.86201	+	5.11648i	0.458857	+	0.264921i	−0.252706	+	0.967543i	$0.581321\pi$
$374$	−3.65997	−	20.7567i	−0.189252	−	1.07330i
$375$	6.35015	−	8.97992i	0.327920	−	0.463721i
$376$	−1.64587	+	4.52198i	−0.0848791	+	0.233203i
$377$	−8.56718	−	23.5381i	−0.441232	−	1.21227i
$378$	1.73385	+	23.5998i	0.0891796	+	1.21384i
$379$			11.0032i			0.565195i	0.959239	+	0.282598i	$0.0911961\pi$
$379$			11.0032i			0.565195i	−0.959239	+	0.282598i	$0.908804\pi$
$380$	−8.64589	+	8.47400i	−0.443525	+	0.434707i
$381$	24.2290	+	11.4354i	1.24129	+	0.585856i
$382$	−10.1082	−	1.78234i	−0.517179	−	0.0911926i
$383$	4.02279	+	3.37552i	0.205555	+	0.172481i	0.739754	−	0.672878i	$-0.234942\pi$
$383$	4.02279	+	3.37552i	0.205555	+	0.172481i	−0.534198	+	0.845359i	$0.679386\pi$
$384$	1.23042	−	1.21904i	0.0627895	−	0.0622091i
$385$	34.0462	+	28.5682i	1.73516	+	1.45597i
$386$	6.96326	−	19.1314i	0.354421	−	0.973763i
$387$	7.59502	+	9.22401i	0.386077	+	0.468883i
$388$	−4.35699	−	2.51551i	−0.221193	−	0.127706i
$389$	12.0595	−	2.12642i	0.611441	−	0.107814i	0.140652	−	0.990059i	$-0.455080\pi$
$389$	12.0595	−	2.12642i	0.611441	−	0.107814i	0.470789	+	0.882246i	$0.343969\pi$
$390$	15.3328	−	15.1910i	0.776404	−	0.769227i
$391$	−29.7983			−1.50696
$392$	−6.86959	+	11.8985i	−0.346967	+	0.600964i
$393$	−0.816564	+	2.99182i	−0.0411902	+	0.150917i
$394$	2.21583	−	2.64072i	0.111632	−	0.133038i
$395$	1.75849	+	9.97289i	0.0884792	+	0.501790i
$396$	5.35538	−	9.08001i	0.269118	−	0.456288i
$397$	−22.4320	−	18.8227i	−1.12583	−	0.944682i	−0.126944	−	0.991910i	$-0.540517\pi$
$397$	−22.4320	−	18.8227i	−1.12583	−	0.944682i	−0.998884	+	0.0472281i	$0.984961\pi$
$398$	−4.78391	+	8.28597i	−0.239796	+	0.415338i
$399$	−32.1325	−	12.2325i	−1.60864	−	0.612390i
$400$	1.35685	+	2.35012i	0.0678423	+	0.117506i
$401$	−1.98166	+	11.2385i	−0.0989591	+	0.561225i	0.894503	+	0.447062i	$0.147530\pi$
$401$	−1.98166	+	11.2385i	−0.0989591	+	0.561225i	−0.993462	+	0.114163i	$0.963581\pi$
$402$	23.1811	+	2.13659i	1.15617	+	0.106563i
$403$	27.4294	+	9.98349i	1.36636	+	0.497313i
$404$	−4.08141	−	0.719663i	−0.203058	−	0.0358046i
$405$	−0.464219	+	24.9919i	−0.0230672	+	1.24186i
$406$	12.7121	+	22.0179i	0.630889	+	1.09273i
$407$	−7.01506	−	12.1504i	−0.347724	−	0.602275i
$408$	10.0475	−	2.64228i	0.497426	−	0.130812i
$409$	−5.23164	+	14.3738i	−0.258688	+	0.710739i	0.740561	+	0.671989i	$0.234560\pi$
$409$	−5.23164	+	14.3738i	−0.258688	+	0.710739i	−0.999249	+	0.0387500i	$0.987662\pi$
$410$		−	11.0675i		−	0.546586i
$411$	−31.0881	−	14.6727i	−1.53346	−	0.723752i
$412$	−1.36153	−	1.62261i	−0.0670779	−	0.0799403i
$413$	4.52077	−	25.6386i	0.222453	−	1.26159i
$414$	−11.3274	−	9.68550i	−0.556712	−	0.476016i
$415$	−35.7128	+	12.9984i	−1.75307	+	0.638066i
$416$	−1.53457	−	4.21621i	−0.0752387	−	0.206717i
$417$	−13.0049	+	1.07696i	−0.636853	+	0.0527390i
$418$	8.65889	+	12.6343i	0.423520	+	0.617962i
$419$	−17.7308	+	10.2369i	−0.866207	+	0.500105i	−0.866086	−	0.499895i	$-0.833372\pi$
$419$	−17.7308	+	10.2369i	−0.866207	+	0.500105i	−0.000121226		1.00000i	$0.500039\pi$
$420$	−12.6487	+	17.8868i	−0.617192	+	0.872787i
$421$	−4.34770	−	0.766616i	−0.211894	−	0.0373626i	0.0666935	−	0.997774i	$-0.478755\pi$
$421$	−4.34770	−	0.766616i	−0.211894	−	0.0373626i	−0.278587	+	0.960411i	$0.589866\pi$
$422$	−18.2033	+	3.20973i	−0.886122	+	0.156247i
$423$	−14.4360	−	0.134061i	−0.701900	−	0.00651827i
$424$	−4.13450	−	1.50483i	−0.200789	−	0.0730812i
$425$			16.2772i			0.789559i
$426$	−4.47650	+	0.370707i	−0.216887	+	0.0179608i
$427$	41.6000	+	15.1412i	2.01317	+	0.732732i
$428$	−3.36689	−	1.22545i	−0.162745	−	0.0592343i
$429$	−15.5590	−	22.4416i	−0.751196	−	1.08349i
$430$			11.0617i			0.533444i
$431$	−7.85158	−	2.85774i	−0.378197	−	0.137652i	0.145925	−	0.989296i	$-0.453384\pi$
$431$	−7.85158	−	2.85774i	−0.378197	−	0.137652i	−0.524122	+	0.851643i	$0.675606\pi$
$432$	4.67827	+	2.26137i	0.225083	+	0.108800i
$433$	17.3071	−	3.05171i	0.831728	−	0.146656i	0.258458	−	0.966023i	$-0.416786\pi$
$433$	17.3071	−	3.05171i	0.831728	−	0.146656i	0.573270	+	0.819367i	$0.305675\pi$
$434$	−29.1771	−	5.14471i	−1.40054	−	0.246954i
$435$	11.2367	+	24.3922i	0.538759	+	1.16952i
$436$	−12.9961	+	7.50327i	−0.622398	+	0.359342i
$437$	19.7166	−	8.95411i	0.943171	−	0.428333i
$438$	0.333977	+	0.481713i	0.0159580	+	0.0230171i
$439$	−0.961769	−	2.64244i	−0.0459027	−	0.126117i	0.914623	−	0.404308i	$-0.132487\pi$
$439$	−0.961769	−	2.64244i	−0.0459027	−	0.126117i	−0.960526	+	0.278191i	$0.910265\pi$
$440$	9.17075	−	3.33788i	0.437199	−	0.159127i
$441$	−40.5232	−	7.53399i	−1.92967	−	0.358761i
$442$	4.67332	−	26.5037i	0.222287	−	1.26065i
$443$	23.4085	+	27.8971i	1.11217	+	1.32543i	0.940313	+	0.340310i	$0.110532\pi$
$443$	23.4085	+	27.8971i	1.11217	+	1.32543i	0.171856	+	0.985122i	$0.445023\pi$
$444$	5.68334	−	3.94032i	0.269719	−	0.186999i
$445$		−	2.22270i		−	0.105366i
$446$	5.10537	−	14.0269i	0.241746	−	0.664193i
$447$	2.32449	+	2.34618i	0.109945	+	0.110970i
$448$	2.27701	+	3.94391i	0.107579	+	0.186332i
$449$	−9.43888	−	16.3486i	−0.445448	−	0.771539i	0.552635	−	0.833423i	$-0.313622\pi$
$449$	−9.43888	−	16.3486i	−0.445448	−	0.771539i	−0.998083	+	0.0618842i	$0.980289\pi$
$450$	−5.29067	+	6.18756i	−0.249404	+	0.291684i
$451$	−13.7898	−	2.43152i	−0.649338	−	0.114496i
$452$	−8.93339	−	3.25149i	−0.420191	−	0.152937i
$453$	−10.9374	+	15.4669i	−0.513886	+	0.726700i
$454$	0.179351	−	1.01715i	0.00841736	−	0.0477372i
$455$	28.3748	+	49.1466i	1.33023	+	2.30403i
$456$	−5.85414	+	4.76750i	−0.274145	+	0.223259i
$457$	−16.6018	+	28.7552i	−0.776601	+	1.34511i	0.157289	+	0.987553i	$0.449725\pi$
$457$	−16.6018	+	28.7552i	−0.776601	+	1.34511i	−0.933890	+	0.357560i	$0.883609\pi$
$458$	−0.983807	−	0.825512i	−0.0459703	−	0.0385736i
$459$	17.5195	+	25.7774i	0.817742	+	1.20318i
$460$	−2.39593	−	13.5880i	−0.111711	−	0.633542i
$461$	17.2415	−	20.5477i	0.803018	−	0.957000i	−0.196706	−	0.980462i	$-0.563025\pi$
$461$	17.2415	−	20.5477i	0.803018	−	0.957000i	0.999725	+	0.0234626i	$0.00746905\pi$
$462$	19.5076	+	19.6896i	0.907575	+	0.916043i
$463$	1.98591	−	3.43970i	0.0922931	−	0.159856i	−0.816183	−	0.577794i	$-0.803914\pi$
$463$	1.98591	−	3.43970i	0.0922931	−	0.159856i	0.908476	+	0.417938i	$0.137247\pi$
$464$	5.58277			0.259174
$465$	−30.1915	−	8.24023i	−1.40010	−	0.382131i
$466$	5.91507	−	1.04299i	0.274010	−	0.0483154i
$467$	19.8788	+	11.4770i	0.919883	+	0.531094i	0.883598	−	0.468247i	$-0.155114\pi$
$467$	19.8788	+	11.4770i	0.919883	+	0.531094i	0.0362849	+	0.999341i	$0.488448\pi$
$468$	10.3912	−	8.55604i	0.480331	−	0.395503i
$469$	−20.9343	+	57.5165i	−0.966656	+	2.65587i
$470$	−10.2383	−	8.59096i	−0.472258	−	0.396271i
$471$	6.22326	+	23.6645i	0.286753	+	1.09040i
$472$	−4.37926	−	3.67463i	−0.201572	−	0.169139i
$473$	13.7826	+	2.43025i	0.633726	+	0.111743i
$474$	0.521203	+	6.29383i	0.0239397	+	0.289085i
$475$	−4.89115	−	10.7701i	−0.224421	−	0.494166i
$476$			27.3158i			1.25202i
$477$	0.122573	−	13.1989i	0.00561225	−	0.604338i
$478$	−10.1037	−	27.7596i	−0.462132	−	1.26970i
$479$	4.17751	−	11.4776i	0.190875	−	0.524426i	−0.806930	−	0.590648i	$-0.798872\pi$
$479$	4.17751	−	11.4776i	0.190875	−	0.524426i	0.997805	+	0.0662220i	$0.0210946\pi$
$480$	2.01275	+	4.36920i	0.0918689	+	0.199426i
$481$	−3.11085	−	17.6425i	−0.141843	−	0.804430i
$482$	−15.2197	−	8.78708i	−0.693237	−	0.400241i
$483$	32.2031	−	22.3268i	1.46529	−	1.01590i
$484$	−0.233977	−	1.32695i	−0.0106353	−	0.0603159i
$485$	10.7039	−	8.98163i	0.486038	−	0.407835i
$486$	−1.71875	+	15.4934i	−0.0779639	+	0.702796i
$487$	34.2538	−	19.7764i	1.55219	−	0.896156i	0.554224	−	0.832368i	$-0.313015\pi$
$487$	34.2538	−	19.7764i	1.55219	−	0.896156i	0.997963	−	0.0637882i	$-0.0203182\pi$
$488$	7.44673	−	6.24855i	0.337098	−	0.282859i
$489$	−17.8637	−	12.6323i	−0.807824	−	0.571252i
$490$	−24.5279	−	29.2312i	−1.10806	−	1.32053i
$491$	23.5873	−	28.1103i	1.06448	−	1.26860i	0.102721	−	0.994710i	$-0.467245\pi$
$491$	23.5873	−	28.1103i	1.06448	−	1.26860i	0.961761	−	0.273890i	$-0.0883104\pi$
$492$	0.633475	−	6.87295i	0.0285593	−	0.309856i
$493$	29.0001	+	16.7432i	1.30610	+	0.754076i
$494$	4.87194	+	18.9409i	0.219199	+	0.852193i
$495$	18.6104	+	22.6020i	0.836476	+	1.01588i
$496$	−4.18179	+	4.98366i	−0.187768	+	0.223773i
$497$	2.05082	−	11.6308i	0.0919920	−	0.521712i
$498$	−22.9217	+	6.02792i	−1.02715	+	0.270118i
$499$	−27.9822	+	10.1847i	−1.25266	+	0.455930i	−0.881298	−	0.472560i	$-0.843330\pi$
$499$	−27.9822	+	10.1847i	−1.25266	+	0.455930i	−0.371358	+	0.928490i	$0.621108\pi$
$500$	6.25342	−	1.10265i	0.279661	−	0.0493119i
$501$	0.110486	+	0.159361i	0.00493617	+	0.00711971i
$502$	11.3182	−	6.53459i	0.505158	−	0.291653i
$503$	−19.7200	−	23.5014i	−0.879272	−	1.04788i	−0.998486	−	0.0550071i	$-0.982482\pi$
$503$	−19.7200	−	23.5014i	−0.879272	−	1.04788i	0.119214	−	0.992869i	$-0.461963\pi$
$504$	−8.87863	+	10.3838i	−0.395486	+	0.462530i
$505$	5.75519	−	9.96828i	0.256103	−	0.443583i
$506$	−17.4566			−0.776041
$507$	−3.14145	−	11.9457i	−0.139517	−	0.530525i
$508$	5.29051	+	14.5356i	0.234728	+	0.644911i
$509$	18.2990	−	15.3547i	0.811087	−	0.680583i	−0.139780	−	0.990183i	$-0.544639\pi$
$509$	18.2990	−	15.3547i	0.811087	−	0.680583i	0.950867	+	0.309600i	$0.100195\pi$
$510$	−2.64826	+	28.7325i	−0.117267	+	1.27230i
$511$	−1.44824	+	0.527116i	−0.0640663	+	0.0233182i
$512$	1.00000			0.0441942
$513$	−19.3380	−	11.7916i	−0.853793	−	0.520612i
$514$	4.74772			0.209413
$515$	5.52812	−	2.01207i	0.243598	−	0.0886624i
$516$	−0.633144	+	6.86936i	−0.0278726	+	0.302407i
$517$	−12.9534	+	10.8692i	−0.569692	+	0.478028i
$518$	6.21900	+	17.0866i	0.273247	+	0.750741i
$519$	9.88888	+	37.6033i	0.434074	+	1.65060i
$520$	12.4614			0.546469
$521$	9.96078	−	17.2526i	0.436390	−	0.755849i	−0.561018	−	0.827803i	$-0.689590\pi$
$521$	9.96078	−	17.2526i	0.436390	−	0.755849i	0.997408	+	0.0719544i	$0.0229236\pi$
$522$	5.58186	+	15.7908i	0.244312	+	0.691144i
$523$	−11.3128	−	13.4820i	−0.494672	−	0.589527i	0.459727	−	0.888060i	$-0.347947\pi$
$523$	−11.3128	−	13.4820i	−0.494672	−	0.589527i	−0.954399	+	0.298533i	$0.903503\pi$
$524$	−1.55063	+	0.895255i	−0.0677395	+	0.0391094i
$525$	−12.1959	−	17.5908i	−0.532273	−	0.767727i
$526$	−11.9008	+	2.09843i	−0.518900	+	0.0914961i
$527$	−36.6690	+	13.3464i	−1.59733	+	0.581380i
$528$	5.88610	−	1.54792i	0.256160	−	0.0673646i
$529$	−0.291719	+	1.65442i	−0.0126834	+	0.0719312i
$530$	7.85481	−	9.36099i	0.341191	−	0.406616i
$531$	6.01510	−	16.0607i	0.261033	−	0.696975i
$532$	−8.20817	−	18.0740i	−0.355869	−	0.783609i
$533$	−15.4841	−	8.93975i	−0.670691	−	0.387224i
$534$	0.127221	−	1.38030i	0.00550539	−	0.0597313i
$535$	6.39650	−	7.62305i	0.276545	−	0.329573i
$536$	8.63930	+	10.2959i	0.373161	+	0.444716i
$537$	28.0566	+	19.8402i	1.21073	+	0.856170i
$538$	−0.304746	+	0.255712i	−0.0131385	+	0.0110245i
$539$	−41.8100	+	24.1390i	−1.80088	+	1.03974i
$540$	−10.3458	+	10.0615i	−0.445212	+	0.432979i
$541$	−0.332577	+	0.279065i	−0.0142986	+	0.0119980i	−0.649909	−	0.760012i	$-0.725193\pi$
$541$	−0.332577	+	0.279065i	−0.0142986	+	0.0119980i	0.635610	+	0.772010i	$0.280749\pi$
$542$	3.03455	+	17.2098i	0.130345	+	0.739225i
$543$	33.3300	−	23.1080i	1.43033	−	0.991660i
$544$	5.19457	+	2.99909i	0.222715	+	0.128585i
$545$	−7.23739	−	41.0453i	−0.310016	−	1.75819i
$546$	14.8078	+	32.1442i	0.633715	+	1.37565i
$547$	−13.2706	+	36.4607i	−0.567410	+	1.55895i	0.241123	+	0.970495i	$0.422484\pi$
$547$	−13.2706	+	36.4607i	−0.567410	+	1.55895i	−0.808533	+	0.588451i	$0.799738\pi$
$548$	−6.78821	−	18.6504i	−0.289978	−	0.796708i
$549$	25.1194	+	14.8154i	1.07207	+	0.632307i
$550$			9.53561i			0.406600i
$551$	−24.2196	−	2.36418i	−1.03179	−	0.100717i
$552$	−0.710135	−	8.57529i	−0.0302254	−	0.364988i
$553$	−16.3526	−	2.88340i	−0.695381	−	0.122615i
$554$	8.72078	+	7.31760i	0.370510	+	0.310895i
$555$	4.88500	+	18.5757i	0.207357	+	0.788493i
$556$	−5.77145	−	4.84282i	−0.244764	−	0.205381i
$557$	−6.45523	+	17.7356i	−0.273517	+	0.751481i	0.724544	+	0.689229i	$0.242051\pi$
$557$	−6.45523	+	17.7356i	−0.273517	+	0.751481i	−0.998060	+	0.0622522i	$0.980172\pi$
$558$	−18.2773	−	6.84527i	−0.773741	−	0.289783i
$559$	15.4760	+	8.93508i	0.654566	+	0.377914i
$560$	−12.4560	+	2.19633i	−0.526362	+	0.0928118i
$561$	35.2181	+	9.61215i	1.48691	+	0.405825i
$562$	−3.44719			−0.145411
$563$	−8.88616	+	15.3913i	−0.374507	+	0.648665i	−0.990253	−	0.139279i	$-0.955521\pi$
$563$	−8.88616	+	15.3913i	−0.374507	+	0.648665i	0.615746	+	0.787945i	$0.288855\pi$
$564$	−5.86628	−	5.92101i	−0.247015	−	0.249320i
$565$	16.9718	−	20.2262i	0.714011	−	0.850925i
$566$	−3.54166	−	20.0858i	−0.148867	−	0.844267i
$567$	−38.2475	−	14.7310i	−1.60624	−	0.618643i
$568$	−1.98663	−	1.66698i	−0.0833570	−	0.0699448i
$569$	−14.6293	+	25.3388i	−0.613294	+	1.06226i	0.377387	+	0.926056i	$0.376823\pi$
$569$	−14.6293	+	25.3388i	−0.613294	+	1.06226i	−0.990681	+	0.136201i	$0.956511\pi$
$570$	−6.88160	−	19.8072i	−0.288238	−	0.829631i
$571$	−18.8406	−	32.6329i	−0.788456	−	1.36565i	−0.926912	−	0.375278i	$-0.877547\pi$
$571$	−18.8406	−	32.6329i	−0.788456	−	1.36565i	0.138456	−	0.990369i	$-0.455786\pi$
$572$	2.73775	−	15.5266i	0.114471	−	0.649199i
$573$	10.2645	−	14.5153i	0.428806	−	0.606387i
$574$	17.0530	+	6.20679i	0.711779	+	0.259066i
$575$	13.2765	+	2.34101i	0.553669	+	0.0976267i
$576$	0.999838	+	2.82848i	0.0416599	+	0.117854i
$577$	−8.86266	−	15.3506i	−0.368957	−	0.639053i	0.620446	−	0.784250i	$-0.286952\pi$
$577$	−8.86266	−	15.3506i	−0.368957	−	0.639053i	−0.989403	+	0.145197i	$0.953618\pi$
$578$	9.48903	+	16.4355i	0.394691	+	0.683626i
$579$	24.8188	+	25.0503i	1.03143	+	1.04106i
$580$	−5.30313	+	14.5702i	−0.220201	+	0.604996i
$581$		−	62.3165i		−	2.58532i
$582$	7.16121	−	4.96494i	0.296842	−	0.205803i
$583$	−9.93785	−	11.8435i	−0.411584	−	0.490506i
$584$	−0.0587663	+	0.333280i	−0.00243177	+	0.0137912i
$585$	12.4594	+	35.2469i	0.515132	+	1.45728i
$586$	−11.9537	+	4.35079i	−0.493803	+	0.179730i
$587$	−7.10993	−	19.5344i	−0.293458	−	0.806269i	−0.995554	−	0.0941875i	$-0.969975\pi$
$587$	−7.10993	−	19.5344i	−0.293458	−	0.806269i	0.702096	−	0.712082i	$-0.252248\pi$
$588$	−13.5587	−	19.5565i	−0.559152	−	0.806497i
$589$	20.2522	−	19.8496i	0.834479	−	0.817889i
$590$	13.7502	−	7.93867i	0.566086	−	0.326830i
$591$	2.49820	+	5.42300i	0.102762	+	0.223073i
$592$	3.93210	+	0.693336i	0.161608	+	0.0284959i
$593$	16.5879	−	2.92489i	0.681183	−	0.120111i	0.177659	−	0.984092i	$-0.443148\pi$
$593$	16.5879	−	2.92489i	0.681183	−	0.120111i	0.503524	+	0.863981i	$0.332036\pi$
$594$	10.2634	+	15.1011i	0.421113	+	0.619605i
$595$	−71.2905	−	25.9476i	−2.92263	−	1.06375i
$596$			1.90681i			0.0781061i
$597$	−9.44215	−	13.6189i	−0.386441	−	0.557386i
$598$	−20.9457	−	7.62360i	−0.856532	−	0.311752i
$599$	20.5630	+	7.48431i	0.840180	+	0.305801i	0.726030	−	0.687663i	$-0.241363\pi$
$599$	20.5630	+	7.48431i	0.840180	+	0.305801i	0.114150	+	0.993463i	$0.463585\pi$
$600$	−4.68422	+	0.387908i	−0.191232	+	0.0158363i
$601$		−	13.7260i		−	0.559897i	−0.960015	−	0.279948i	$-0.909683\pi$
$601$		−	13.7260i		−	0.559897i	0.960015	−	0.279948i	$-0.0903174\pi$
$602$	−17.0441	−	6.20354i	−0.694666	−	0.252838i
$603$	−20.4839	+	34.7304i	−0.834170	+	1.41433i
$604$	−10.7708	+	1.89919i	−0.438259	+	0.0772769i
$605$	3.68541	+	0.649837i	0.149833	+	0.0264196i
$606$	4.14454	−	5.86091i	0.168360	−	0.238083i
$607$	29.7920	−	17.2004i	1.20922	−	0.698144i	0.246631	−	0.969109i	$-0.420676\pi$
$607$	29.7920	−	17.2004i	1.20922	−	0.698144i	0.962589	+	0.270966i	$0.0873430\pi$
$608$	−4.33828	−	0.423478i	−0.175940	−	0.0171743i
$609$	−43.8856	+	3.63425i	−1.77833	+	0.147267i
$610$	9.23410	+	25.3705i	0.373878	+	1.02722i
$611$	−20.2892	+	7.38467i	−0.820813	+	0.298752i
$612$	−3.28914	+	17.6914i	−0.132956	+	0.715131i
$613$	−4.13702	+	23.4622i	−0.167093	+	0.947629i	0.779788	+	0.626044i	$0.215327\pi$
$613$	−4.13702	+	23.4622i	−0.167093	+	0.947629i	−0.946881	+	0.321585i	$0.895784\pi$
$614$	−2.10839	−	2.51268i	−0.0850878	−	0.101404i
$615$	17.3357	+	8.18197i	0.699042	+	0.329929i
$616$			16.0024i			0.644753i
$617$	−3.58682	+	9.85472i	−0.144400	+	0.396736i	−0.990716	−	0.135945i	$-0.956593\pi$
$617$	−3.58682	+	9.85472i	−0.144400	+	0.396736i	0.846316	+	0.532681i	$0.178815\pi$
$618$	3.54814	−	0.933084i	0.142727	−	0.0375342i
$619$	15.6201	+	27.0548i	0.627824	+	1.08742i	0.987988	+	0.154533i	$0.0493874\pi$
$619$	15.6201	+	27.0548i	0.627824	+	1.08742i	−0.360164	+	0.932889i	$0.617279\pi$
$620$	−9.03432	−	15.6479i	−0.362827	−	0.628435i
$621$	23.5450	−	10.5825i	0.944830	−	0.424661i
$622$	11.9170	+	2.10130i	0.477830	+	0.0842543i
$623$	3.42476	+	1.24651i	0.137210	+	0.0499405i
$624$	7.73856	+	0.713257i	0.309790	+	0.0285531i
$625$	−5.41858	+	30.7303i	−0.216743	+	1.22921i
$626$	7.37165	+	12.7681i	0.294631	+	0.510315i
$627$	−26.1911	+	4.22268i	−1.04597	+	0.168637i
$628$	−7.06362	+	12.2345i	−0.281869	+	0.488212i
$629$	18.3462	+	15.3943i	0.731511	+	0.613810i
$630$	−18.6663	−	33.0356i	−0.743681	−	1.31617i
$631$	0.526346	+	2.98506i	0.0209535	+	0.118833i	0.993490	−	0.113915i	$-0.0363392\pi$
$631$	0.526346	+	2.98506i	0.0209535	+	0.118833i	−0.972537	+	0.232748i	$0.925228\pi$
$632$	−2.34372	+	2.79314i	−0.0932282	+	0.111105i
$633$	8.42969	−	30.8857i	0.335050	−	1.22760i
$634$	8.90250	−	15.4196i	0.353563	−	0.612390i
$635$	−42.9613			−1.70487
$636$	5.41364	−	5.36360i	0.214665	−	0.212681i
$637$	−60.7084	+	10.7045i	−2.40535	+	0.424129i
$638$	16.9890	+	9.80862i	0.672602	+	0.388327i
$639$	2.72871	−	7.28585i	0.107946	−	0.288224i
$640$	−0.949911	+	2.60986i	−0.0375485	+	0.103164i
$641$	1.27265	+	1.06788i	0.0502665	+	0.0421786i	0.667575	−	0.744543i	$-0.267332\pi$
$641$	1.27265	+	1.06788i	0.0502665	+	0.0421786i	−0.617308	+	0.786721i	$0.711777\pi$
$642$	4.40856	−	4.36781i	0.173992	−	0.172384i
$643$	−29.0493	−	24.3752i	−1.14559	−	0.961265i	−0.145983	−	0.989287i	$-0.546635\pi$
$643$	−29.0493	−	24.3752i	−1.14559	−	0.961265i	−0.999607	+	0.0280222i	$0.991079\pi$
$644$	22.2802	+	3.92860i	0.877963	+	0.154809i
$645$	−17.3266	−	8.17769i	−0.682235	−	0.321996i
$646$	−21.2654	−	15.2107i	−0.836678	−	0.598455i
$647$		−	29.4256i		−	1.15684i	−0.815739	−	0.578421i	$-0.803669\pi$
$647$		−	29.4256i		−	1.15684i	0.815739	−	0.578421i	$-0.196331\pi$
$648$	−7.00065	+	5.65605i	−0.275011	+	0.222191i
$649$	−6.87047	−	18.8765i	−0.269689	−	0.740965i
$650$	−4.16436	+	11.4415i	−0.163340	+	0.448772i
$651$	29.6284	−	41.8983i	1.16123	−	1.64212i
$652$	−2.19349	−	12.4399i	−0.0859036	−	0.487183i
$653$	16.1478	+	9.32294i	0.631912	+	0.364835i	0.781492	−	0.623915i	$-0.214459\pi$
$653$	16.1478	+	9.32294i	0.631912	+	0.364835i	−0.149580	+	0.988750i	$0.547792\pi$
$654$	−2.14511	−	25.9034i	−0.0838805	−	1.01290i
$655$	−0.863531	−	4.89733i	−0.0337410	−	0.191355i
$656$	3.05262	−	2.56146i	0.119185	−	0.100008i
$657$	−1.00144	+	0.167007i	−0.0390697	+	0.00651555i
$658$	18.9788	−	10.9574i	0.739872	−	0.427165i
$659$	−15.1316	+	12.6970i	−0.589445	+	0.494603i	−0.888033	−	0.459779i	$-0.847929\pi$
$659$	−15.1316	+	12.6970i	−0.589445	+	0.494603i	0.298589	+	0.954382i	$0.403484\pi$
$660$	−1.55142	+	16.8323i	−0.0603889	+	0.655196i
$661$	−0.209192	−	0.249305i	−0.00813662	−	0.00969685i	0.761961	−	0.647623i	$-0.224237\pi$
$661$	−0.209192	−	0.249305i	−0.00813662	−	0.00969685i	−0.770097	+	0.637926i	$0.779792\pi$
$662$	6.69549	−	7.97938i	0.260228	−	0.310127i
$663$	38.0593	+	26.9137i	1.47810	+	1.04524i
$664$	−11.8505	−	6.84191i	−0.459890	−	0.265517i
$665$	54.9677	−	4.25344i	2.13156	−	0.164941i
$666$	1.97037	+	11.8151i	0.0763505	+	0.457826i
$667$	17.8275	−	21.2459i	0.690282	−	0.822646i
$668$	−0.0194411	+	0.110256i	−0.000752200	+	0.00426594i
$669$	18.1968	+	18.3666i	0.703530	+	0.710093i
$670$	−35.0774	+	12.7671i	−1.35516	+	0.493238i
$671$	33.6396	−	5.93157i	1.29864	−	0.228986i
$672$	−7.86090	+	0.650976i	−0.303241	+	0.0251119i
$673$	−19.4250	+	11.2150i	−0.748778	+	0.432307i	−0.825252	−	0.564764i	$-0.808967\pi$
$673$	−19.4250	+	11.2150i	−0.748778	+	0.432307i	0.0764741	+	0.997072i	$0.475634\pi$
$674$	8.89565	+	10.6014i	0.342648	+	0.408352i
$675$	−5.78065	−	12.8614i	−0.222497	−	0.495035i
$676$	3.56566	−	6.17591i	0.137141	−	0.237535i
$677$	−28.5905			−1.09882			−0.549412	−	0.835552i	$-0.685148\pi$
$677$	−28.5905			−1.09882			−0.549412	+	0.835552i	$0.685148\pi$
$678$	11.6972	−	11.5891i	0.449229	−	0.445077i
$679$	7.83617	+	21.5297i	0.300725	+	0.826234i
$680$	−12.7616	+	10.7082i	−0.489384	+	0.410642i
$681$	1.46063	+	1.03288i	0.0559714	+	0.0395802i
$682$	−21.4817	+	7.81870i	−0.822576	+	0.299393i
$683$	−7.91544			−0.302876			−0.151438	−	0.988467i	$-0.548390\pi$
$683$	−7.91544			−0.302876			−0.151438	+	0.988467i	$0.548390\pi$
$684$	−3.13977	−	12.6942i	−0.120052	−	0.485374i
$685$	55.1232			2.10615
$686$	28.8396	−	10.4968i	1.10110	−	0.400768i
$687$	2.02035	−	0.930709i	0.0770812	−	0.0355088i
$688$	−3.05103	+	2.56012i	−0.116319	+	0.0976036i
$689$	−6.75188	−	18.5506i	−0.257226	−	0.706723i
$690$	23.0548	+	6.29240i	0.877683	+	0.239548i
$691$	30.2861			1.15214			0.576068	−	0.817402i	$-0.304586\pi$
$691$	30.2861			1.15214			0.576068	+	0.817402i	$0.304586\pi$
$692$	−11.2242	+	19.4409i	−0.426681	+	0.739034i
$693$	−45.2624	+	15.9998i	−1.71938	+	0.607781i
$694$	12.9112	+	15.3870i	0.490104	+	0.584083i
$695$	18.1214	−	10.4624i	0.687385	−	0.396862i
$696$	−4.12721	+	8.74460i	−0.156442	+	0.331463i
$697$	23.5391	−	4.15058i	0.891607	−	0.157214i
$698$	−3.35486	+	1.22107i	−0.126983	+	0.0462181i
$699$	−2.73919	+	10.0362i	−0.103606	+	0.379602i
$700$	2.14598	−	12.1705i	0.0811106	−	0.460001i
$701$	27.1889	−	32.4025i	1.02691	−	1.22382i	0.0526007	−	0.998616i	$-0.483249\pi$
$701$	27.1889	−	32.4025i	1.02691	−	1.22382i	0.974310	−	0.225209i	$-0.0723066\pi$
$702$	5.71986	+	22.6015i	0.215882	+	0.853040i
$703$	−16.7649	−	4.67304i	−0.632302	−	0.176247i
$704$	3.04312	+	1.75694i	0.114692	+	0.0662174i
$705$	21.0254	−	9.68573i	0.791864	−	0.364786i
$706$	−6.50279	+	7.74972i	−0.244736	+	0.291665i
$707$	12.1317	+	14.4580i	0.456260	+	0.543749i
$708$	8.99326	−	4.14290i	0.337988	−	0.155700i
$709$	3.55284	−	2.98119i	0.133430	−	0.111961i	−0.573630	−	0.819114i	$-0.694465\pi$
$709$	3.55284	−	2.98119i	0.133430	−	0.111961i	0.707060	+	0.707153i	$0.250021\pi$
$710$	6.23769	−	3.60133i	0.234096	−	0.135156i
$711$	−10.2437	−	3.83649i	−0.384168	−	0.143880i
$712$	0.613060	−	0.514418i	0.0229754	−	0.0192786i
$713$	5.61225	+	31.8286i	0.210180	+	1.19199i
$714$	−42.7863	−	20.1940i	−1.60124	−	0.755741i
$715$	37.9215	+	21.8940i	1.41819	+	0.818790i
$716$	3.44508	+	19.5380i	0.128749	+	0.730171i
$717$	50.9509	+	4.69611i	1.90280	+	0.175379i
$718$	5.55540	−	15.2633i	0.207326	−	0.569623i
$719$	12.2505	+	33.6580i	0.456867	+	1.25523i	0.927805	+	0.373065i	$0.121693\pi$
$719$	12.2505	+	33.6580i	0.456867	+	1.25523i	−0.470938	+	0.882166i	$0.656084\pi$
$720$	−8.33170	−	0.0773732i	−0.310504	−	0.00288353i
$721$			9.64620i			0.359243i
$722$	18.6413	+	3.67433i	0.693759	+	0.136744i
$723$	25.0153	−	17.3433i	0.930327	−	0.645005i
$724$	23.0598	+	4.06607i	0.857012	+	0.151114i
$725$	−11.6055	−	9.73817i	−0.431018	−	0.361667i
$726$	2.25145	+	0.614493i	0.0835592	+	0.0228060i
$727$	−26.6188	−	22.3358i	−0.987237	−	0.828390i	−0.00207176	−	0.999998i	$-0.500659\pi$
$727$	−26.6188	−	22.3358i	−0.987237	−	0.828390i	−0.985165	+	0.171608i	$0.945104\pi$
$728$	−6.98850	+	19.2007i	−0.259011	+	0.711627i
$729$	−22.9976	−	14.1461i	−0.851762	−	0.523929i
$730$	−0.813992	−	0.469958i	−0.0301272	−	0.0173939i
$731$	−23.5268	+	4.14841i	−0.870170	+	0.153434i
$732$	4.28225	+	16.2836i	0.158277	+	0.601860i
$733$	36.3830			1.34383			0.671917	−	0.740626i	$-0.265471\pi$
$733$	36.3830			1.34383			0.671917	+	0.740626i	$0.265471\pi$
$734$	−4.00444	+	6.93589i	−0.147807	+	0.256008i
$735$	63.9193	−	16.8094i	2.35770	−	0.620025i
$736$	3.19330	−	3.80563i	0.117707	−	0.140277i
$737$	8.20105	+	46.5104i	0.302089	+	1.71323i
$738$	10.2972	+	6.07326i	0.379044	+	0.223560i
$739$	−18.5516	−	15.5666i	−0.682431	−	0.572628i	0.234284	−	0.972168i	$-0.424725\pi$
$739$	−18.5516	−	15.5666i	−0.682431	−	0.572628i	−0.916716	+	0.399540i	$0.869170\pi$
$740$	−5.54465	+	9.60362i	−0.203825	+	0.353036i
$741$	−33.2700	−	6.37142i	−1.22220	−	0.234060i
$742$	10.0185	+	17.3526i	0.367791	+	0.637032i
$743$	−3.82457	+	21.6902i	−0.140310	+	0.795737i	0.830704	+	0.556714i	$0.187938\pi$
$743$	−3.82457	+	21.6902i	−0.140310	+	0.795737i	−0.971014	+	0.239023i	$0.923173\pi$
$744$	−4.71468	−	10.2345i	−0.172849	−	0.375214i
$745$	−4.97651	−	1.81130i	−0.182325	−	0.0663610i
$746$	−10.0775	−	1.77694i	−0.368964	−	0.0650582i
$747$	7.50362	−	40.3598i	0.274543	−	1.47669i
$748$	10.5385	+	18.2531i	0.385324	+	0.667401i
$749$	8.15848	+	14.1309i	0.298104	+	0.516332i
$750$	−2.89587	+	10.6102i	−0.105742	+	0.387431i
$751$	−10.7904	+	29.6463i	−0.393746	+	1.08181i	0.571532	+	0.820580i	$0.306349\pi$
$751$	−10.7904	+	29.6463i	−0.393746	+	1.08181i	−0.965277	+	0.261227i	$0.915873\pi$
$752$		−	4.81219i		−	0.175483i
$753$	1.86817	+	22.5593i	0.0680800	+	0.822105i
$754$	16.1010	+	19.1885i	0.586365	+	0.698802i
$755$	5.27472	−	29.9144i	0.191967	−	1.08870i
$756$	−9.70090	−	21.5836i	−0.352818	−	0.784987i
$757$	−24.3846	+	8.87526i	−0.886272	+	0.322577i	−0.744738	−	0.667357i	$-0.767426\pi$
$757$	−24.3846	+	8.87526i	−0.886272	+	0.322577i	−0.141534	+	0.989933i	$0.545203\pi$
$758$	−3.76331	−	10.3396i	−0.136689	−	0.375551i
$759$	12.9053	−	27.3433i	0.468432	−	0.992498i
$760$	5.22620	−	10.9200i	0.189574	−	0.396111i
$761$	8.53894	−	4.92996i	0.309536	−	0.178711i	−0.337183	−	0.941439i	$-0.609474\pi$
$761$	8.53894	−	4.92996i	0.309536	−	0.178711i	0.646719	+	0.762728i	$0.276141\pi$
$762$	−26.6790	−	2.45899i	−0.966478	−	0.0890796i
$763$	67.3020	+	11.8672i	2.43650	+	0.429620i
$764$	10.1082	−	1.78234i	0.365701	−	0.0644829i
$765$	−43.0475	−	25.3894i	−1.55639	−	0.917956i
$766$	−4.93469	−	1.79608i	−0.178297	−	0.0648950i
$767$		−	25.6497i		−	0.926158i
$768$	−0.739277	+	1.56636i	−0.0266764	+	0.0565210i
$769$	−46.4093	−	16.8916i	−1.67356	−	0.609127i	−0.681158	−	0.732137i	$-0.738523\pi$
$769$	−46.4093	−	16.8916i	−1.67356	−	0.609127i	−0.992406	+	0.123009i	$0.960745\pi$
$770$	−41.7639	−	15.2008i	−1.50507	−	0.547799i
$771$	−3.50988	+	7.43662i	−0.126405	+	0.267823i
$772$			20.3592i			0.732744i
$773$	−31.5469	−	11.4821i	−1.13466	−	0.412984i	−0.294680	−	0.955596i	$-0.595213\pi$
$773$	−31.5469	−	11.4821i	−1.13466	−	0.412984i	−0.839983	+	0.542613i	$0.817435\pi$
$774$	−10.2918	−	6.07009i	−0.369931	−	0.218185i
$775$	17.3863	−	3.06567i	0.624533	−	0.110122i
$776$	4.95459	+	0.873628i	0.177859	+	0.0313614i
$777$	−31.3612	−	2.89054i	−1.12508	−	0.103698i
$778$	−10.6049	+	6.12277i	−0.380206	+	0.219512i
$779$	−14.3279	+	9.81959i	−0.513349	+	0.351823i
$780$	−9.21244	+	19.5190i	−0.329858	+	0.698892i
$781$	−3.11675	−	8.56320i	−0.111526	−	0.306415i
$782$	28.0012	−	10.1916i	1.00132	−	0.364451i
$783$	−28.8605	−	2.93058i	−1.03139	−	0.104730i
$784$	2.38578	−	13.5305i	0.0852066	−	0.483231i
$785$	−25.2206	−	30.0568i	−0.900163	−	1.07277i
$786$	−0.255944	−	3.09068i	−0.00912924	−	0.110241i
$787$			8.53097i			0.304096i	0.988373	+	0.152048i	$0.0485868\pi$
$787$			8.53097i			0.304096i	−0.988373	+	0.152048i	$0.951413\pi$
$788$	−1.17902	+	3.23933i	−0.0420008	+	0.115396i
$789$	5.51110	−	20.1922i	0.196200	−	0.718862i
$790$	−5.06337	−	8.77001i	−0.180147	−	0.312023i
$791$	21.6469	+	37.4936i	0.769676	+	1.33312i
$792$	−1.92687	+	10.3641i	−0.0684683	+	0.368271i
$793$	42.9536	+	7.57387i	1.52533	+	0.268956i
$794$	27.5169	+	10.0153i	0.976537	+	0.355431i
$795$	8.85576	+	19.2238i	0.314082	+	0.681797i
$796$	1.66143	−	9.42246i	0.0588880	−	0.333970i
$797$	−8.36493	−	14.4885i	−0.296301	−	0.513209i	0.678986	−	0.734152i	$-0.262420\pi$
$797$	−8.36493	−	14.4885i	−0.296301	−	0.513209i	−0.975287	+	0.220943i	$0.929087\pi$
$798$	34.3785	+	0.504805i	1.21698	+	0.0178699i
$799$	14.4322	−	24.9973i	0.510574	−	0.884340i
$800$	−2.07881	−	1.74433i	−0.0734969	−	0.0616713i
$801$	2.06799	+	1.21970i	0.0730687	+	0.0430958i
$802$	−1.98166	−	11.2385i	−0.0699747	−	0.396846i
$803$	−0.764388	+	0.910962i	−0.0269747	+	0.0321472i
$804$	−22.5139	+	5.92068i	−0.794004	+	0.208806i
$805$	−31.4173	+	54.4164i	−1.10731	+	1.91793i
$806$	−29.1898			−1.02817
$807$	−0.175244	−	0.666382i	−0.00616890	−	0.0234578i
$808$	4.08141	−	0.719663i	0.143583	−	0.0253176i
$809$	25.2866	+	14.5992i	0.889030	+	0.513282i	0.873625	−	0.486600i	$-0.161763\pi$
$809$	25.2866	+	14.5992i	0.889030	+	0.513282i	0.0154047	+	0.999881i	$0.495096\pi$
$810$	−8.11150	−	23.6434i	−0.285009	−	0.830746i
$811$	3.99798	−	10.9844i	0.140388	−	0.385713i	−0.849495	−	0.527596i	$-0.823093\pi$
$811$	3.99798	−	10.9844i	0.140388	−	0.385713i	0.989883	+	0.141883i	$0.0453157\pi$
$812$	−19.4760	−	16.3423i	−0.683473	−	0.573502i
$813$	−29.2001	−	7.96963i	−1.02409	−	0.279507i
$814$	10.7477	+	9.01839i	0.376707	+	0.316094i
$815$	34.5499	+	6.09209i	1.21023	+	0.213397i
$816$	−8.53786	+	5.91939i	−0.298885	+	0.207220i
$817$	14.3204	−	9.81446i	0.501006	−	0.343364i
$818$		−	15.2963i		−	0.534822i
$819$	−61.2963	−	0.569235i	−2.14187	−	0.0198907i
$820$	3.78532	+	10.4001i	0.132189	+	0.363186i
$821$	5.91596	−	16.2540i	0.206468	−	0.567268i	−0.792631	−	0.609702i	$-0.791289\pi$
$821$	5.91596	−	16.2540i	0.206468	−	0.567268i	0.999099	+	0.0424344i	$0.0135114\pi$
$822$	34.2316	+	3.15510i	1.19396	+	0.110047i
$823$	2.18060	+	12.3668i	0.0760109	+	0.431079i	0.998937	+	0.0461015i	$0.0146798\pi$
$823$	2.18060	+	12.3668i	0.0760109	+	0.431079i	−0.922926	+	0.384978i	$0.874209\pi$
$824$	1.83439	+	1.05908i	0.0639039	+	0.0368949i
$825$	−14.9362	−	7.04946i	−0.520010	−	0.245431i
$826$	4.52077	+	25.6386i	0.157298	+	0.892080i
$827$	5.17698	−	4.34400i	0.180021	−	0.151056i	−0.548324	−	0.836266i	$-0.684734\pi$
$827$	5.17698	−	4.34400i	0.180021	−	0.151056i	0.728346	+	0.685210i	$0.240290\pi$
$828$	13.9569	+	5.22719i	0.485037	+	0.181657i
$829$	35.2357	−	20.3433i	1.22379	−	0.706553i	0.258063	−	0.966128i	$-0.416916\pi$
$829$	35.2357	−	20.3433i	1.22379	−	0.706553i	0.965723	+	0.259575i	$0.0835826\pi$
$830$	29.1133	−	24.4290i	1.01054	−	0.847943i
$831$	−17.9090	+	8.25010i	−0.621257	+	0.286193i
$832$	2.88406	+	3.43708i	0.0999866	+	0.119159i
$833$	52.9721	−	63.1297i	1.83538	−	2.18732i
$834$	11.8523	−	5.45995i	0.410411	−	0.189063i
$835$	−0.269285	−	0.155472i	−0.00931901	−	0.00538033i
$836$	−12.4579	−	8.91081i	−0.430864	−	0.308187i
$837$	24.2341	−	23.5682i	0.837654	−	0.814637i
$838$	13.1603	−	15.6838i	0.454615	−	0.541789i
$839$	−1.11942	+	6.34852i	−0.0386465	+	0.219175i	−0.998015	−	0.0629821i	$-0.979939\pi$
$839$	−1.11942	+	6.34852i	−0.0386465	+	0.219175i	0.959368	+	0.282157i	$0.0910500\pi$
$840$	5.76820	−	21.1342i	0.199022	−	0.729200i
$841$	−2.03662	+	0.741270i	−0.0702284	+	0.0255610i
$842$	4.34770	−	0.766616i	0.149831	−	0.0264193i
$843$	2.54843	−	5.39952i	0.0877725	−	0.185970i
$844$	16.0077	−	9.24205i	0.551007	−	0.318124i
$845$	12.7312	+	15.1724i	0.437966	+	0.521948i
$846$	13.6112	−	4.81141i	0.467963	−	0.165420i
$847$	−3.06810	+	5.31410i	−0.105421	+	0.182595i
$848$	4.39984			0.151091
$849$	34.0797	+	9.30144i	1.16961	+	0.319224i
$850$	−5.56712	−	15.2955i	−0.190951	−	0.524633i
$851$	15.1950	−	12.7501i	0.520876	−	0.437067i
$852$	4.07974	−	1.87940i	0.139770	−	0.0643873i
$853$	32.0451	−	11.6635i	1.09720	−	0.399350i	0.270919	−	0.962602i	$-0.412672\pi$
$853$	32.0451	−	11.6635i	1.09720	−	0.399350i	0.826285	+	0.563253i	$0.190450\pi$
$854$	−44.2698			−1.51488
$855$	36.1125	+	3.86396i	1.23502	+	0.132145i
$856$	3.58297			0.122464
$857$	41.1260	−	14.9687i	1.40484	−	0.511319i	0.475228	−	0.879863i	$-0.342366\pi$
$857$	41.1260	−	14.9687i	1.40484	−	0.511319i	0.929611	+	0.368543i	$0.120143\pi$
$858$	22.2962	+	15.7667i	0.761179	+	0.538268i
$859$	39.5402	−	33.1781i	1.34909	−	1.13202i	0.369904	−	0.929070i	$-0.379390\pi$
$859$	39.5402	−	33.1781i	1.34909	−	1.13202i	0.979188	−	0.202953i	$-0.0650540\pi$
$860$	−3.78334	−	10.3946i	−0.129011	−	0.354454i
$861$	−22.3289	+	22.1225i	−0.760968	+	0.753934i
$862$	8.35547			0.284589
$863$	−24.7130	+	42.8042i	−0.841241	+	1.45707i	0.0476053	+	0.998866i	$0.484841\pi$
$863$	−24.7130	+	42.8042i	−0.841241	+	1.45707i	−0.888846	+	0.458206i	$0.848492\pi$
$864$	−5.16957	−	0.524933i	−0.175872	−	0.0178586i
$865$	−40.0761	−	47.7608i	−1.36263	−	1.62392i
$866$	−15.2196	+	8.78706i	−0.517184	+	0.298597i
$867$	−32.7588	+	2.71282i	−1.11255	+	0.0921321i
$868$	29.1771	−	5.14471i	0.990335	−	0.174623i
$869$	−12.0396	+	4.38206i	−0.408416	+	0.148651i
$870$	−18.9017	−	19.0780i	−0.640827	−	0.646806i
$871$	−10.4717	+	59.3880i	−0.354820	+	2.01228i
$872$	9.64602	−	11.4957i	0.326656	−	0.389293i
$873$	2.48274	+	14.8875i	0.0840281	+	0.503865i
$874$	−15.4650	+	15.1576i	−0.523112	+	0.512713i
$875$	−25.0434	−	14.4588i	−0.846620	−	0.488796i
$876$	−0.478591	−	0.338436i	−0.0161701	−	0.0114347i
$877$	−28.4244	+	33.8749i	−0.959824	+	1.14387i	0.0297074	+	0.999559i	$0.490542\pi$
$877$	−28.4244	+	33.8749i	−0.959824	+	1.14387i	−0.989532	+	0.144316i	$0.953902\pi$
$878$	1.80753	+	2.15414i	0.0610013	+	0.0726986i
$879$	2.02221	−	21.9402i	0.0682075	−	0.740024i
$880$	−7.47607	+	6.27317i	−0.252018	+	0.211468i
$881$	−35.5711	+	20.5370i	−1.19842	+	0.691908i	−0.960203	−	0.279304i	$-0.909896\pi$
$881$	−35.5711	+	20.5370i	−1.19842	+	0.691908i	−0.238217	+	0.971212i	$0.576563\pi$
$882$	40.6561	−	6.78011i	1.36896	−	0.228298i
$883$	7.41816	−	6.22458i	0.249641	−	0.209474i	−0.509377	−	0.860544i	$-0.670124\pi$
$883$	7.41816	−	6.22458i	0.249641	−	0.209474i	0.759018	+	0.651070i	$0.225680\pi$
$884$	4.67332	+	26.5037i	0.157181	+	0.891416i
$885$	2.26958	+	27.4065i	0.0762913	+	0.921260i
$886$	−31.5381	−	18.2086i	−1.05954	−	0.611728i
$887$	0.193421	+	1.09694i	0.00649443	+	0.0368317i	0.987883	−	0.155202i	$-0.0496028\pi$
$887$	0.193421	+	1.09694i	0.00649443	+	0.0368317i	−0.981388	+	0.192034i	$0.938492\pi$
$888$	−3.99292	+	5.64650i	−0.133994	+	0.189484i
$889$	24.0931	−	66.1954i	0.808058	−	2.22012i
$890$	0.760207	+	2.08865i	0.0254822	+	0.0700118i
$891$	−31.2412	+	4.91227i	−1.04662	+	0.164567i
$892$			14.9271i			0.499797i
$893$	−2.03786	+	20.8766i	−0.0681943	+	0.698610i
$894$	−2.98675	−	1.40966i	−0.0998918	−	0.0471462i
$895$	−54.2640	−	9.56821i	−1.81385	−	0.319830i
$896$	−3.48859	−	2.92727i	−0.116546	−	0.0977934i
$897$	27.4259	−	27.1724i	0.915724	−	0.907260i
$898$	14.4612	+	12.1344i	0.482577	+	0.404930i
$899$	12.4221	−	34.1295i	0.414301	−	1.13828i
$900$	2.85533	−	7.62392i	0.0951777	−	0.254131i
$901$	22.8553	+	13.1955i	0.761419	+	0.439606i
$902$	13.7898	−	2.43152i	0.459151	−	0.0809607i
$903$	22.3173	−	22.1110i	0.742672	−	0.735807i
$904$	9.50671			0.316188
$905$	−32.5167	+	56.3205i	−1.08089	+	1.87216i
$906$	4.98783	−	18.2750i	0.165709	−	0.607146i
$907$	−15.7745	+	18.7993i	−0.523783	+	0.624220i	−0.961471	−	0.274907i	$-0.911353\pi$
$907$	−15.7745	+	18.7993i	−0.523783	+	0.624220i	0.437688	+	0.899127i	$0.355797\pi$
$908$	0.179351	+	1.01715i	0.00595197	+	0.0337553i
$909$	6.11630	+	10.8247i	0.202865	+	0.359031i
$910$	−43.4727	−	36.4780i	−1.44111	−	1.20923i
$911$	9.33916	−	16.1759i	0.309420	−	0.535932i	−0.668815	−	0.743428i	$-0.733198\pi$
$911$	9.33916	−	16.1759i	0.309420	−	0.535932i	0.978236	+	0.207497i	$0.0665317\pi$
$912$	3.87051	−	6.48222i	0.128165	−	0.214648i
$913$	−24.0417	−	41.6414i	−0.795664	−	1.37813i
$914$	5.76576	−	32.6992i	0.190714	−	1.08159i
$915$	−46.5657	−	4.29193i	−1.53942	−	0.141887i
$916$	1.20682	+	0.439246i	0.0398744	+	0.0145131i
$917$	8.03016	+	1.41593i	0.265179	+	0.0467582i
$918$	−25.2794	−	18.2308i	−0.834343	−	0.601705i
$919$	8.30357	+	14.3822i	0.273909	+	0.474425i	0.969859	−	0.243665i	$-0.0783498\pi$
$919$	8.30357	+	14.3822i	0.273909	+	0.474425i	−0.695950	+	0.718090i	$0.745017\pi$
$920$	6.89879	+	11.9491i	0.227446	+	0.393949i
$921$	5.49444	−	1.44492i	0.181048	−	0.0476118i
$922$	−9.17403	+	25.2054i	−0.302131	+	0.830097i
$923$		−	11.6359i		−	0.382999i
$924$	−25.0654	−	11.8302i	−0.824591	−	0.389184i
$925$	−6.96468	−	8.30018i	−0.228997	−	0.272908i
$926$	−0.689700	+	3.91148i	−0.0226649	+	0.128539i
$927$	−1.16151	+	6.24745i	−0.0381491	+	0.205193i
$928$	−5.24609	+	1.90942i	−0.172211	+	0.0626798i
$929$	5.95602	+	16.3640i	0.195411	+	0.536887i	0.998239	−	0.0593239i	$-0.0188945\pi$
$929$	5.95602	+	16.3640i	0.195411	+	0.536887i	−0.802828	+	0.596211i	$0.796672\pi$
$930$	31.1891	−	2.58282i	1.02273	−	0.0846941i
$931$	−16.0801	+	57.6886i	−0.527002	+	1.89067i
$932$	−5.20163	+	3.00316i	−0.170385	+	0.0983718i
$933$	−12.1014	+	17.1129i	−0.396181	+	0.560251i
$934$	−22.6054	−	3.98594i	−0.739670	−	0.130424i
$935$	−57.6487	+	10.1650i	−1.88531	+	0.332432i
$936$	−6.83815	+	11.5940i	−0.223512	+	0.378963i
$937$	−19.0298	−	6.92627i	−0.621676	−	0.226272i	0.0119284	−	0.999929i	$-0.496203\pi$
$937$	−19.0298	−	6.92627i	−0.621676	−	0.226272i	−0.633604	+	0.773657i	$0.718425\pi$
$938$		−	61.2078i		−	1.99851i
$939$	−25.4490	+	2.10748i	−0.830498	+	0.0687751i
$940$	12.5591	+	4.57115i	0.409634	+	0.149095i
$941$	14.6014	+	5.31448i	0.475992	+	0.173247i	0.568865	−	0.822431i	$-0.307383\pi$
$941$	14.6014	+	5.31448i	0.475992	+	0.173247i	−0.0928728	+	0.995678i	$0.529605\pi$
$942$	−13.9417	−	20.1089i	−0.454244	−	0.655182i
$943$		−	19.7966i		−	0.644667i
$944$	5.37195	+	1.95523i	0.174842	+	0.0636373i
$945$	65.5451	−	4.81551i	2.13218	−	0.156649i
$946$	−13.7826	+	2.43025i	−0.448112	+	0.0790142i
$947$	31.1580	+	5.49399i	1.01250	+	0.178531i	0.655197	−	0.755458i	$-0.272586\pi$
$947$	31.1580	+	5.49399i	1.01250	+	0.178531i	0.357302	+	0.933989i	$0.383697\pi$
$948$	−2.64239	−	5.73600i	−0.0858207	−	0.186297i
$949$	−1.31500	+	0.759215i	−0.0426866	+	0.0246451i
$950$	8.27976	+	8.44770i	0.268631	+	0.274080i
$951$	17.5711	+	25.3438i	0.569783	+	0.821830i
$952$	−9.34257	−	25.6685i	−0.302794	−	0.831921i
$953$	−41.1564	+	14.9797i	−1.33319	+	0.485241i	−0.907660	−	0.419705i	$-0.862133\pi$
$953$	−41.1564	+	14.9797i	−1.33319	+	0.485241i	−0.425527	+	0.904946i	$0.639911\pi$
$954$	4.39913	+	12.4449i	0.142427	+	0.402918i
$955$	−4.95019	+	28.0739i	−0.160185	+	0.908452i
$956$	18.9887	+	22.6299i	0.614139	+	0.731902i
$957$	−27.9234	+	19.3596i	−0.902635	+	0.625806i
$958$			12.2142i			0.394624i
$959$	−30.9137	+	84.9347i	−0.998255	+	2.74268i
$960$	−3.38572	−	3.41731i	−0.109274	−	0.110293i
$961$	5.66211	+	9.80707i	0.182649	+	0.316357i
$962$	8.95735	+	15.5146i	0.288796	+	0.500210i
$963$	3.58239	+	10.1344i	0.115441	+	0.326576i
$964$	17.3072	+	3.05172i	0.557427	+	0.0982893i
$965$	−53.1346	−	19.3394i	−1.71046	−	0.622558i
$966$	−22.6248	+	31.9944i	−0.727942	+	1.02940i
$967$	−7.15506	+	40.5784i	−0.230091	+	1.30491i	0.622618	+	0.782526i	$0.286069\pi$
$967$	−7.15506	+	40.5784i	−0.230091	+	1.30491i	−0.852709	+	0.522386i	$0.825042\pi$
$968$	0.673711	+	1.16690i	0.0216539	+	0.0375056i
$969$	39.5463	−	22.0643i	1.27041	−	0.708809i
$970$	−6.98646	+	12.1009i	−0.224322	+	0.388537i
$971$	0.225333	+	0.189077i	0.00723127	+	0.00606775i	0.646396	−	0.763002i	$-0.276275\pi$
$971$	0.225333	+	0.189077i	0.00723127	+	0.00606775i	−0.639165	+	0.769070i	$0.720720\pi$
$972$	−3.68397	−	15.1469i	−0.118163	−	0.485837i
$973$	5.95795	+	33.7892i	0.191003	+	1.08323i
$974$	−25.4241	+	30.2993i	−0.814641	+	0.970851i
$975$	−14.8428	−	14.9813i	−0.475350	−	0.479785i
$976$	−4.86051	+	8.41865i	−0.155581	+	0.269474i
$977$	−21.2203			−0.678897			−0.339449	−	0.940625i	$-0.610240\pi$
$977$	−21.2203			−0.678897			−0.339449	+	0.940625i	$0.610240\pi$
$978$	21.1069	+	5.76074i	0.674923	+	0.184208i
$979$	2.76942	−	0.488323i	0.0885110	−	0.0156069i
$980$	33.0463	+	19.0793i	1.05563	+	0.609465i
$981$	42.1598	+	15.7898i	1.34606	+	0.504130i
$982$	−12.5506	+	34.4824i	−0.400505	+	1.10038i
$983$	20.4611	+	17.1689i	0.652607	+	0.547602i	0.907861	−	0.419272i	$-0.137715\pi$
$983$	20.4611	+	17.1689i	0.652607	+	0.547602i	−0.255254	+	0.966874i	$0.582159\pi$
$984$	1.75542	+	6.67512i	0.0559606	+	0.212795i
$985$	−7.33422	−	6.15414i	−0.233688	−	0.196087i
$986$	−32.9777	−	5.81485i	−1.05022	−	0.185183i
$987$	3.13262	+	37.8282i	0.0997124	+	1.20408i
$988$	−11.0563	−	16.1324i	−0.351748	−	0.513239i
$989$			19.7863i			0.629167i
$990$	−25.2184	−	14.8738i	−0.801493	−	0.472720i
$991$	15.5439	+	42.7064i	0.493767	+	1.35661i	0.897208	+	0.441609i	$0.145592\pi$
$991$	15.5439	+	42.7064i	0.493767	+	1.35661i	−0.403440	+	0.915006i	$0.632186\pi$
$992$	2.22508	−	6.11337i	0.0706465	−	0.194100i
$993$	7.54872	+	16.3865i	0.239551	+	0.520010i
$994$	2.05082	+	11.6308i	0.0650481	+	0.368906i
$995$	23.0131	+	13.2866i	0.729563	+	0.421214i
$996$	19.4777	−	13.5041i	0.617174	−	0.427893i
$997$	−8.04562	−	45.6290i	−0.254807	−	1.44509i	−0.796566	−	0.604551i	$-0.793353\pi$
$997$	−8.04562	−	45.6290i	−0.254807	−	1.44509i	0.541759	−	0.840534i	$-0.317759\pi$
$998$	22.8113	−	19.1410i	0.722080	−	0.605897i
$999$	−19.9633	−	5.64833i	−0.631611	−	0.178705i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.bf.b.155.4	yes	48
9.5	odd	6		342.2.x.b.41.3	✓	48
19.13	odd	18		342.2.x.b.317.3	yes	48
171.32	even	18	inner	342.2.bf.b.203.4	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.x.b.41.3	✓	48	9.5	odd	6
342.2.x.b.317.3	yes	48	19.13	odd	18
342.2.bf.b.155.4	yes	48	1.1	even	1	trivial
342.2.bf.b.203.4	yes	48	171.32	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.bf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 + 0.342020i) q^{2} +(0.158968 - 1.72474i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.949911 + 2.60986i) q^{5} +(0.440515 + 1.67510i) q^{6} -4.55403 q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.94946 - 0.548357i) q^{9} +O(q^{10})\)	\(q+(-0.939693 + 0.342020i) q^{2} +(0.158968 - 1.72474i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.949911 + 2.60986i) q^{5} +(0.440515 + 1.67510i) q^{6} -4.55403 q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.94946 - 0.548357i) q^{9} +(-1.78525 - 2.12758i) q^{10} +(-3.04312 + 1.75694i) q^{11} +(-0.986865 - 1.42341i) q^{12} +(-4.41863 + 0.779124i) q^{13} +(4.27939 - 1.55757i) q^{14} +(4.65233 - 1.22347i) q^{15} +(0.173648 - 0.984808i) q^{16} +(3.85555 - 4.59487i) q^{17} +(2.95913 - 0.493487i) q^{18} +(-1.17038 + 4.19883i) q^{19} +(2.40526 + 1.38868i) q^{20} +(-0.723946 + 7.85452i) q^{21} +(2.25868 - 2.69180i) q^{22} +(-3.19330 - 3.80563i) q^{23} +(1.41418 + 1.00004i) q^{24} +(-2.07881 + 1.74433i) q^{25} +(3.88568 - 2.24340i) q^{26} +(-1.41464 + 4.99988i) q^{27} +(-3.48859 + 2.92727i) q^{28} +(0.969438 + 5.49796i) q^{29} +(-3.95331 + 2.74087i) q^{30} +(-5.63411 - 3.25285i) q^{31} +(0.173648 + 0.984808i) q^{32} +(2.54651 + 5.52789i) q^{33} +(-2.05150 + 5.63644i) q^{34} +(-4.32592 - 11.8854i) q^{35} +(-2.61189 + 1.47581i) q^{36} +3.99276i q^{37} +(-0.336290 - 4.34591i) q^{38} +(0.641365 + 7.74485i) q^{39} +(-2.73516 - 0.482282i) q^{40} +(3.05262 + 2.56146i) q^{41} +(-2.00612 - 7.62844i) q^{42} +(-3.05103 - 2.56012i) q^{43} +(-1.20182 + 3.30198i) q^{44} +(-1.37059 - 8.21856i) q^{45} +(4.30232 + 2.48395i) q^{46} +(4.73908 - 0.835629i) q^{47} +(-1.67093 - 0.456051i) q^{48} +13.7392 q^{49} +(1.35685 - 2.35012i) q^{50} +(-7.31204 - 7.38026i) q^{51} +(-2.88406 + 3.43708i) q^{52} +(0.764024 + 4.33300i) q^{53} +(-0.380729 - 5.18219i) q^{54} +(-7.47607 - 6.27317i) q^{55} +(2.27701 - 3.94391i) q^{56} +(7.05585 + 2.68608i) q^{57} +(-2.79139 - 4.83482i) q^{58} +(-0.992697 + 5.62986i) q^{59} +(2.77747 - 3.92769i) q^{60} +(-9.13477 - 3.32478i) q^{61} +(6.40687 + 1.12970i) q^{62} +(13.4319 + 2.49724i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-6.23071 - 10.7919i) q^{65} +(-4.28359 - 4.32355i) q^{66} +(4.59687 - 12.6298i) q^{67} -5.99817i q^{68} +(-7.07135 + 4.90264i) q^{69} +(8.13007 + 9.68904i) q^{70} +(-0.450331 + 2.55396i) q^{71} +(1.94962 - 2.28013i) q^{72} +(0.318012 - 0.115747i) q^{73} +(-1.36560 - 3.75197i) q^{74} +(2.67805 + 3.86270i) q^{75} +(1.80240 + 3.96880i) q^{76} +(13.8584 - 8.00118i) q^{77} +(-3.25158 - 7.05841i) q^{78} +(3.59079 + 0.633153i) q^{79} +(2.73516 - 0.482282i) q^{80} +(8.39861 + 3.23471i) q^{81} +(-3.74460 - 1.36292i) q^{82} +13.6838i q^{83} +(4.49421 + 6.48225i) q^{84} +(15.6544 + 5.69773i) q^{85} +(3.74264 + 1.36221i) q^{86} +(9.63666 - 0.798029i) q^{87} -3.51389i q^{88} +(-0.752030 - 0.273716i) q^{89} +(4.09884 + 7.25415i) q^{90} +(20.1226 - 3.54815i) q^{91} +(-4.89242 - 0.862665i) q^{92} +(-6.50597 + 9.20027i) q^{93} +(-4.16748 + 2.40610i) q^{94} +(-12.0701 + 0.933996i) q^{95} +(1.72614 - 0.142945i) q^{96} +(-1.72071 - 4.72762i) q^{97} +(-12.9106 + 4.69908i) q^{98} +(9.93898 - 3.51332i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 9 q^{3} - 3 q^{6} - 18 q^{7} - 24 q^{8} - 3 q^{9}+O(q^{10}) \) 48 * q + 9 * q^3 - 3 * q^6 - 18 * q^7 - 24 * q^8 - 3 * q^9	\( 48 q + 9 q^{3} - 3 q^{6} - 18 q^{7} - 24 q^{8} - 3 q^{9} - 9 q^{10} - 9 q^{11} - 3 q^{12} + 6 q^{13} + 6 q^{14} + 9 q^{15} + 27 q^{17} + 9 q^{18} - 12 q^{19} - 9 q^{20} - 3 q^{21} - 9 q^{22} - 18 q^{23} - 9 q^{24} + 18 q^{25} - 18 q^{26} - 24 q^{27} + 6 q^{28} + 27 q^{30} - 36 q^{31} + 39 q^{33} + 9 q^{34} + 18 q^{35} + 9 q^{36} + 9 q^{38} + 24 q^{39} - 9 q^{40} + 36 q^{41} - 30 q^{42} - 15 q^{43} + 9 q^{44} - 9 q^{45} + 27 q^{46} - 3 q^{48} + 66 q^{49} - 3 q^{50} - 12 q^{51} - 15 q^{52} + 9 q^{55} + 9 q^{56} - 3 q^{57} - 9 q^{58} - 36 q^{59} - 21 q^{60} - 12 q^{61} + 3 q^{62} - 9 q^{63} - 24 q^{64} + 9 q^{65} - 33 q^{67} - 69 q^{69} + 18 q^{70} - 27 q^{71} + 6 q^{72} + 66 q^{73} - 39 q^{74} - 24 q^{75} - 9 q^{76} - 27 q^{77} - 6 q^{78} - 12 q^{79} + 9 q^{80} - 3 q^{81} - 9 q^{82} + 3 q^{84} - 54 q^{85} - 15 q^{86} + 63 q^{87} + 18 q^{89} + 9 q^{90} + 51 q^{91} - 18 q^{92} - 39 q^{93} + 54 q^{94} - 54 q^{95} - 3 q^{96} + 117 q^{97} - 42 q^{98} - 93 q^{99}+O(q^{100}) \) 48 * q + 9 * q^3 - 3 * q^6 - 18 * q^7 - 24 * q^8 - 3 * q^9 - 9 * q^10 - 9 * q^11 - 3 * q^12 + 6 * q^13 + 6 * q^14 + 9 * q^15 + 27 * q^17 + 9 * q^18 - 12 * q^19 - 9 * q^20 - 3 * q^21 - 9 * q^22 - 18 * q^23 - 9 * q^24 + 18 * q^25 - 18 * q^26 - 24 * q^27 + 6 * q^28 + 27 * q^30 - 36 * q^31 + 39 * q^33 + 9 * q^34 + 18 * q^35 + 9 * q^36 + 9 * q^38 + 24 * q^39 - 9 * q^40 + 36 * q^41 - 30 * q^42 - 15 * q^43 + 9 * q^44 - 9 * q^45 + 27 * q^46 - 3 * q^48 + 66 * q^49 - 3 * q^50 - 12 * q^51 - 15 * q^52 + 9 * q^55 + 9 * q^56 - 3 * q^57 - 9 * q^58 - 36 * q^59 - 21 * q^60 - 12 * q^61 + 3 * q^62 - 9 * q^63 - 24 * q^64 + 9 * q^65 - 33 * q^67 - 69 * q^69 + 18 * q^70 - 27 * q^71 + 6 * q^72 + 66 * q^73 - 39 * q^74 - 24 * q^75 - 9 * q^76 - 27 * q^77 - 6 * q^78 - 12 * q^79 + 9 * q^80 - 3 * q^81 - 9 * q^82 + 3 * q^84 - 54 * q^85 - 15 * q^86 + 63 * q^87 + 18 * q^89 + 9 * q^90 + 51 * q^91 - 18 * q^92 - 39 * q^93 + 54 * q^94 - 54 * q^95 - 3 * q^96 + 117 * q^97 - 42 * q^98 - 93 * q^99

Introduction

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