LMFDB - Embedded newform 378.2.v.a.79.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(67,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8, 12]))

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

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

chi := DirichletCharacter("378.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.v (of order $9$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			79.4
Character	$\chi$	$=$	378.79
Dual form			378.2.v.a.67.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 - 0.642788i) q^{2} +(-0.921674 + 1.46646i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.622926 + 3.53279i) q^{5} +(1.64867 - 0.530936i) q^{6} +(2.63270 - 0.262455i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.30103 - 2.70320i) q^{9} +O(q^{10})$	\(q+(-0.766044 - 0.642788i) q^{2} +(-0.921674 + 1.46646i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.622926 + 3.53279i) q^{5} +(1.64867 - 0.530936i) q^{6} +(2.63270 - 0.262455i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.30103 - 2.70320i) q^{9} +(1.79365 - 3.10668i) q^{10} +(-0.384477 + 2.18048i) q^{11} +(-1.60423 - 0.653023i) q^{12} +(0.493989 + 2.80155i) q^{13} +(-2.18547 - 1.49122i) q^{14} +(-5.75485 - 2.34258i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(1.79836 - 3.11484i) q^{17} +(-0.740936 + 2.90706i) q^{18} +(-0.812212 - 1.40679i) q^{19} +(-3.37095 + 1.22693i) q^{20} +(-2.04161 + 4.10266i) q^{21} +(1.69611 - 1.42321i) q^{22} +(-6.48380 + 5.44055i) q^{23} +(0.809158 + 1.53143i) q^{24} +(-7.39412 + 2.69124i) q^{25} +(1.42239 - 2.46364i) q^{26} +(5.16328 + 0.583554i) q^{27} +(0.715631 + 2.54713i) q^{28} +(-1.16849 + 6.62686i) q^{29} +(2.90269 + 5.49367i) q^{30} +(-1.66997 - 9.47086i) q^{31} +(0.939693 + 0.342020i) q^{32} +(-2.84323 - 2.57351i) q^{33} +(-3.37980 + 1.23015i) q^{34} +(2.56718 + 9.13730i) q^{35} +(2.43621 - 1.75067i) q^{36} +3.04443 q^{37} +(-0.282078 + 1.59974i) q^{38} +(-4.56367 - 1.85770i) q^{39} +(3.37095 + 1.22693i) q^{40} +(1.85372 + 10.5129i) q^{41} +(4.20110 - 1.83050i) q^{42} +(1.66936 + 1.40076i) q^{43} -2.21412 q^{44} +(8.73941 - 6.28018i) q^{45} +8.46400 q^{46} +(0.870558 - 4.93718i) q^{47} +(0.364530 - 1.69326i) q^{48} +(6.86224 - 1.38193i) q^{49} +(7.39412 + 2.69124i) q^{50} +(2.91031 + 5.50810i) q^{51} +(-2.67321 + 0.972969i) q^{52} +(-5.55919 - 9.62879i) q^{53} +(-3.58020 - 3.76592i) q^{54} -7.94268 q^{55} +(1.08906 - 2.41121i) q^{56} +(2.81160 + 0.105524i) q^{57} +(5.15478 - 4.32538i) q^{58} +(1.89952 + 0.691370i) q^{59} +(1.30768 - 6.07420i) q^{60} +(-0.386180 + 2.19013i) q^{61} +(-4.80848 + 8.32854i) q^{62} +(-4.13470 - 6.77527i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-9.58958 + 3.49032i) q^{65} +(0.523819 + 3.79902i) q^{66} +(-3.49657 + 2.93397i) q^{67} +(3.37980 + 1.23015i) q^{68} +(-2.00243 - 14.5227i) q^{69} +(3.90677 - 8.64972i) q^{70} +(-3.66979 - 6.35627i) q^{71} +(-2.99156 - 0.224874i) q^{72} +3.88508 q^{73} +(-2.33217 - 1.95692i) q^{74} +(2.86836 - 13.3236i) q^{75} +(1.24438 - 1.04416i) q^{76} +(-0.439937 + 5.84146i) q^{77} +(2.30187 + 4.35655i) q^{78} +(0.121652 + 0.102078i) q^{79} +(-1.79365 - 3.10668i) q^{80} +(-5.61462 + 7.03392i) q^{81} +(5.33756 - 9.24492i) q^{82} +(2.54125 - 14.4121i) q^{83} +(-4.39485 - 1.29818i) q^{84} +(12.1243 + 4.41290i) q^{85} +(-0.378414 - 2.14609i) q^{86} +(-8.64108 - 7.82136i) q^{87} +(1.69611 + 1.42321i) q^{88} +(6.94314 + 12.0259i) q^{89} +(-10.7316 - 0.806688i) q^{90} +(2.03581 + 7.24600i) q^{91} +(-6.48380 - 5.44055i) q^{92} +(15.4278 + 6.28010i) q^{93} +(-3.84044 + 3.22251i) q^{94} +(4.46395 - 3.74570i) q^{95} +(-1.36765 + 1.06279i) q^{96} +(-0.437555 - 0.367152i) q^{97} +(-6.14506 - 3.35234i) q^{98} +(6.39450 - 1.79756i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{6} - 6 q^{7} + 36 q^{8}+O(q^{10}) $ 72 * q + 3 * q^6 - 6 * q^7 + 36 * q^8	$ 72 q + 3 q^{6} - 6 q^{7} + 36 q^{8} + 6 q^{10} + 12 q^{11} + 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} + 18 q^{19} + 6 q^{22} + 12 q^{23} - 6 q^{25} - 18 q^{26} + 6 q^{27} + 3 q^{29} + 15 q^{30} - 9 q^{31} - 18 q^{33} - 9 q^{34} - 18 q^{35} - 3 q^{36} - 48 q^{39} - 6 q^{41} + 36 q^{42} - 24 q^{43} - 45 q^{45} - 27 q^{47} + 6 q^{48} + 48 q^{49} + 6 q^{50} + 15 q^{51} - 6 q^{52} - 15 q^{53} - 63 q^{54} - 72 q^{55} - 3 q^{56} + 57 q^{57} - 3 q^{58} - 30 q^{59} + 21 q^{60} + 9 q^{61} - 24 q^{62} - 21 q^{63} - 36 q^{64} + 45 q^{65} + 6 q^{67} + 9 q^{68} - 39 q^{69} + 15 q^{70} + 12 q^{71} - 60 q^{73} - 18 q^{74} + 42 q^{75} + 3 q^{77} + 6 q^{78} - 27 q^{79} - 6 q^{80} + 12 q^{81} + 33 q^{82} + 18 q^{83} - 21 q^{84} + 51 q^{85} - 12 q^{86} - 117 q^{87} + 6 q^{88} - 36 q^{89} - 69 q^{90} - 3 q^{91} + 12 q^{92} - 30 q^{93} - 27 q^{94} + 3 q^{95} + 48 q^{97} - 12 q^{98} + 90 q^{99}+O(q^{100}) $ 72 * q + 3 * q^6 - 6 * q^7 + 36 * q^8 + 6 * q^10 + 12 * q^11 + 12 * q^13 - 3 * q^14 - 6 * q^15 - 12 * q^17 + 18 * q^19 + 6 * q^22 + 12 * q^23 - 6 * q^25 - 18 * q^26 + 6 * q^27 + 3 * q^29 + 15 * q^30 - 9 * q^31 - 18 * q^33 - 9 * q^34 - 18 * q^35 - 3 * q^36 - 48 * q^39 - 6 * q^41 + 36 * q^42 - 24 * q^43 - 45 * q^45 - 27 * q^47 + 6 * q^48 + 48 * q^49 + 6 * q^50 + 15 * q^51 - 6 * q^52 - 15 * q^53 - 63 * q^54 - 72 * q^55 - 3 * q^56 + 57 * q^57 - 3 * q^58 - 30 * q^59 + 21 * q^60 + 9 * q^61 - 24 * q^62 - 21 * q^63 - 36 * q^64 + 45 * q^65 + 6 * q^67 + 9 * q^68 - 39 * q^69 + 15 * q^70 + 12 * q^71 - 60 * q^73 - 18 * q^74 + 42 * q^75 + 3 * q^77 + 6 * q^78 - 27 * q^79 - 6 * q^80 + 12 * q^81 + 33 * q^82 + 18 * q^83 - 21 * q^84 + 51 * q^85 - 12 * q^86 - 117 * q^87 + 6 * q^88 - 36 * q^89 - 69 * q^90 - 3 * q^91 + 12 * q^92 - 30 * q^93 - 27 * q^94 + 3 * q^95 + 48 * q^97 - 12 * q^98 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$3$	−0.921674	+	1.46646i	−0.532129	+	0.846663i
$3$	−0.921674	+	1.46646i	−0.532129	+	0.846663i
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	0.622926	+	3.53279i	0.278581	+	1.57991i	0.727351	+	0.686265i	$0.240751\pi$
$5$	0.622926	+	3.53279i	0.278581	+	1.57991i	−0.448770	+	0.893647i	$0.648138\pi$
$6$	1.64867	−	0.530936i	0.673066	−	0.216754i
$7$	2.63270	−	0.262455i	0.995068	−	0.0991986i
$7$	2.63270	−	0.262455i	0.995068	−	0.0991986i
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−1.30103	−	2.70320i	−0.433678	−	0.901068i
$10$	1.79365	−	3.10668i	0.567200	−	0.982420i
$11$	−0.384477	+	2.18048i	−0.115924	+	0.657439i	0.870364	+	0.492409i	$0.163883\pi$
$11$	−0.384477	+	2.18048i	−0.115924	+	0.657439i	−0.986288	+	0.165031i	$0.947228\pi$
$12$	−1.60423	−	0.653023i	−0.463102	−	0.188512i
$13$	0.493989	+	2.80155i	0.137008	+	0.777011i	0.973440	+	0.228941i	$0.0735262\pi$
$13$	0.493989	+	2.80155i	0.137008	+	0.777011i	−0.836432	+	0.548070i	$0.815363\pi$
$14$	−2.18547	−	1.49122i	−0.584091	−	0.398544i
$15$	−5.75485	−	2.34258i	−1.48590	−	0.604852i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	1.79836	−	3.11484i	0.436165	−	0.755461i	−0.561225	−	0.827664i	$-0.689670\pi$
$17$	1.79836	−	3.11484i	0.436165	−	0.755461i	0.997390	+	0.0722029i	$0.0230029\pi$
$18$	−0.740936	+	2.90706i	−0.174640	+	0.685201i
$19$	−0.812212	−	1.40679i	−0.186334	−	0.322740i	0.757691	−	0.652613i	$-0.226327\pi$
$19$	−0.812212	−	1.40679i	−0.186334	−	0.322740i	−0.944025	+	0.329873i	$0.892994\pi$
$20$	−3.37095	+	1.22693i	−0.753767	+	0.274349i
$21$	−2.04161	+	4.10266i	−0.445516	+	0.895274i
$22$	1.69611	−	1.42321i	0.361612	−	0.303429i
$23$	−6.48380	+	5.44055i	−1.35197	+	1.13443i	−0.373590	+	0.927594i	$0.621873\pi$
$23$	−6.48380	+	5.44055i	−1.35197	+	1.13443i	−0.978375	+	0.206840i	$0.933682\pi$
$24$	0.809158	+	1.53143i	0.165169	+	0.312601i
$25$	−7.39412	+	2.69124i	−1.47882	+	0.538248i
$26$	1.42239	−	2.46364i	0.278953	−	0.483160i
$27$	5.16328	+	0.583554i	0.993674	+	0.112305i
$28$	0.715631	+	2.54713i	0.135242	+	0.481362i
$29$	−1.16849	+	6.62686i	−0.216984	+	1.23058i	0.660446	+	0.750873i	$0.270367\pi$
$29$	−1.16849	+	6.62686i	−0.216984	+	1.23058i	−0.877430	+	0.479704i	$0.840744\pi$
$30$	2.90269	+	5.49367i	0.529955	+	1.00300i
$31$	−1.66997	−	9.47086i	−0.299935	−	1.70102i	−0.646436	−	0.762968i	$-0.723741\pi$
$31$	−1.66997	−	9.47086i	−0.299935	−	1.70102i	0.346501	−	0.938050i	$-0.387370\pi$
$32$	0.939693	+	0.342020i	0.166116	+	0.0604612i
$33$	−2.84323	−	2.57351i	−0.494943	−	0.447991i
$34$	−3.37980	+	1.23015i	−0.579632	+	0.210969i
$35$	2.56718	+	9.13730i	0.433932	+	1.54448i
$36$	2.43621	−	1.75067i	0.406036	−	0.291779i
$37$	3.04443			0.500502			0.250251	−	0.968181i	$-0.419487\pi$
$37$	3.04443			0.500502			0.250251	+	0.968181i	$0.419487\pi$
$38$	−0.282078	+	1.59974i	−0.0457591	+	0.259513i
$39$	−4.56367	−	1.85770i	−0.730773	−	0.297470i
$40$	3.37095	+	1.22693i	0.532994	+	0.193994i
$41$	1.85372	+	10.5129i	0.289502	+	1.64185i	0.688747	+	0.725001i	$0.258161\pi$
$41$	1.85372	+	10.5129i	0.289502	+	1.64185i	−0.399246	+	0.916844i	$0.630728\pi$
$42$	4.20110	−	1.83050i	0.648245	−	0.282452i
$43$	1.66936	+	1.40076i	0.254575	+	0.213614i	0.761140	−	0.648588i	$-0.224640\pi$
$43$	1.66936	+	1.40076i	0.254575	+	0.213614i	−0.506564	+	0.862202i	$0.669085\pi$
$44$	−2.21412			−0.333791
$45$	8.73941	−	6.28018i	1.30279	−	0.936194i
$46$	8.46400			1.24795
$47$	0.870558	−	4.93718i	0.126984	−	0.720161i	−0.853126	−	0.521705i	$-0.825296\pi$
$47$	0.870558	−	4.93718i	0.126984	−	0.720161i	0.980110	−	0.198456i	$-0.0635928\pi$
$48$	0.364530	−	1.69326i	0.0526154	−	0.244401i
$49$	6.86224	−	1.38193i	0.980319	−	0.197419i
$50$	7.39412	+	2.69124i	1.04569	+	0.380599i
$51$	2.91031	+	5.50810i	0.407525	+	0.771288i
$52$	−2.67321	+	0.972969i	−0.370708	+	0.134927i
$53$	−5.55919	−	9.62879i	−0.763613	−	1.32262i	−0.940977	−	0.338471i	$-0.890090\pi$
$53$	−5.55919	−	9.62879i	−0.763613	−	1.32262i	0.177364	−	0.984145i	$-0.443243\pi$
$54$	−3.58020	−	3.76592i	−0.487204	−	0.512477i
$55$	−7.94268			−1.07099
$56$	1.08906	−	2.41121i	0.145532	−	0.322212i
$57$	2.81160	+	0.105524i	0.372406	+	0.0139771i
$58$	5.15478	−	4.32538i	0.676856	−	0.567950i
$59$	1.89952	+	0.691370i	0.247297	+	0.0900087i	0.462695	−	0.886518i	$-0.346883\pi$
$59$	1.89952	+	0.691370i	0.247297	+	0.0900087i	−0.215398	+	0.976526i	$0.569105\pi$
$60$	1.30768	−	6.07420i	0.168820	−	0.784176i
$61$	−0.386180	+	2.19013i	−0.0494452	+	0.280418i	−0.999498	−	0.0316704i	$-0.989917\pi$
$61$	−0.386180	+	2.19013i	−0.0494452	+	0.280418i	0.950053	+	0.312088i	$0.101028\pi$
$62$	−4.80848	+	8.32854i	−0.610678	+	1.05773i
$63$	−4.13470	−	6.77527i	−0.520923	−	0.853603i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−9.58958	+	3.49032i	−1.18944	+	0.432921i
$66$	0.523819	+	3.79902i	0.0644777	+	0.467627i
$67$	−3.49657	+	2.93397i	−0.427174	+	0.358442i	−0.830884	−	0.556445i	$-0.812165\pi$
$67$	−3.49657	+	2.93397i	−0.427174	+	0.358442i	0.403710	+	0.914887i	$0.367720\pi$
$68$	3.37980	+	1.23015i	0.409861	+	0.149177i
$69$	−2.00243	−	14.5227i	−0.241064	−	1.74832i
$70$	3.90677	−	8.64972i	0.466948	−	1.03384i
$71$	−3.66979	−	6.35627i	−0.435524	−	0.754351i	0.561814	−	0.827264i	$-0.310104\pi$
$71$	−3.66979	−	6.35627i	−0.435524	−	0.754351i	−0.997338	+	0.0729132i	$0.976770\pi$
$72$	−2.99156	−	0.224874i	−0.352559	−	0.0265016i
$73$	3.88508			0.454714			0.227357	−	0.973811i	$-0.426992\pi$
$73$	3.88508			0.454714			0.227357	+	0.973811i	$0.426992\pi$
$74$	−2.33217	−	1.95692i	−0.271109	−	0.227488i
$75$	2.86836	−	13.3236i	0.331210	−	1.53848i
$76$	1.24438	−	1.04416i	0.142740	−	0.119773i
$77$	−0.439937	+	5.84146i	−0.0501355	+	0.665696i
$78$	2.30187	+	4.35655i	0.260635	+	0.493283i
$79$	0.121652	+	0.102078i	0.0136869	+	0.0114847i	0.649605	−	0.760272i	$-0.274934\pi$
$79$	0.121652	+	0.102078i	0.0136869	+	0.0114847i	−0.635919	+	0.771756i	$0.719379\pi$
$80$	−1.79365	−	3.10668i	−0.200536	−	0.347338i
$81$	−5.61462	+	7.03392i	−0.623847	+	0.781546i
$82$	5.33756	−	9.24492i	0.589435	−	1.02093i
$83$	2.54125	−	14.4121i	0.278938	−	1.58194i	−0.447230	−	0.894419i	$-0.647589\pi$
$83$	2.54125	−	14.4121i	0.278938	−	1.58194i	0.726168	−	0.687517i	$-0.241300\pi$
$84$	−4.39485	−	1.29818i	−0.479518	−	0.141643i
$85$	12.1243	+	4.41290i	1.31507	+	0.478646i
$86$	−0.378414	−	2.14609i	−0.0408054	−	0.231419i
$87$	−8.64108	−	7.82136i	−0.926421	−	0.838538i
$88$	1.69611	+	1.42321i	0.180806	+	0.151714i
$89$	6.94314	+	12.0259i	0.735972	+	1.27474i	0.954296	+	0.298864i	$0.0966077\pi$
$89$	6.94314	+	12.0259i	0.735972	+	1.27474i	−0.218324	+	0.975876i	$0.570059\pi$
$90$	−10.7316	−	0.806688i	−1.13121	−	0.0850323i
$91$	2.03581	+	7.24600i	0.213411	+	0.759587i
$92$	−6.48380	−	5.44055i	−0.675983	−	0.567217i
$93$	15.4278	+	6.28010i	1.59979	+	0.651216i
$94$	−3.84044	+	3.22251i	−0.396111	+	0.332377i
$95$	4.46395	−	3.74570i	0.457992	−	0.384301i
$96$	−1.36765	+	1.06279i	−0.139585	+	0.108471i
$97$	−0.437555	−	0.367152i	−0.0444270	−	0.0372787i	0.620304	−	0.784362i	$-0.287009\pi$
$97$	−0.437555	−	0.367152i	−0.0444270	−	0.0372787i	−0.664731	+	0.747083i	$0.731454\pi$
$98$	−6.14506	−	3.35234i	−0.620745	−	0.338637i
$99$	6.39450	−	1.79756i	0.642671	−	0.180661i
$100$	−3.93433	−	6.81445i	−0.393433	−	0.681445i
$101$	9.15880	+	7.68514i	0.911334	+	0.764700i	0.972372	−	0.233435i	$-0.0749967\pi$
$101$	9.15880	+	7.68514i	0.911334	+	0.764700i	−0.0610380	+	0.998135i	$0.519441\pi$
$102$	1.31111	−	6.09016i	0.129819	−	0.603015i
$103$	1.08510	+	6.15392i	0.106918	+	0.606364i	0.990437	+	0.137967i	$0.0440569\pi$
$103$	1.08510	+	6.15392i	0.106918	+	0.606364i	−0.883519	+	0.468396i	$0.844832\pi$
$104$	2.67321	+	0.972969i	0.262130	+	0.0954075i
$105$	−15.7656	−	4.65694i	−1.53857	−	0.454470i
$106$	−1.93069	+	10.9495i	−0.187525	+	1.06351i
$107$	4.96674	−	8.60265i	0.480153	−	0.831649i	−0.519588	−	0.854417i	$-0.673914\pi$
$107$	4.96674	−	8.60265i	0.480153	−	0.831649i	0.999741	+	0.0227676i	$0.00724779\pi$
$108$	0.321906	+	5.18617i	0.0309754	+	0.499040i
$109$	4.26967	+	7.39528i	0.408960	+	0.708340i	0.994773	−	0.102106i	$-0.0325582\pi$
$109$	4.26967	+	7.39528i	0.408960	+	0.708340i	−0.585813	+	0.810446i	$0.699225\pi$
$110$	6.08445	+	5.10546i	0.580129	+	0.486786i
$111$	−2.80598	+	4.46455i	−0.266331	+	0.423756i
$112$	−2.38417	+	1.14706i	−0.225282	+	0.108387i
$113$	1.86575	−	1.56555i	0.175515	−	0.147274i	−0.550798	−	0.834638i	$-0.685677\pi$
$113$	1.86575	−	1.56555i	0.175515	−	0.147274i	0.726313	+	0.687364i	$0.241232\pi$
$114$	−2.08598	−	1.88810i	−0.195370	−	0.176837i
$115$	−23.2593	−	19.5168i	−2.16894	−	1.81995i
$116$	−6.72909			−0.624780
$117$	6.93047	−	4.98027i	0.640722	−	0.460426i
$118$	−1.01072	−	1.75061i	−0.0930439	−	0.161157i
$119$	3.91703	−	8.67244i	0.359074	−	0.795002i
$120$	−4.90616	+	3.81255i	−0.447869	+	0.348037i
$121$	5.72995	+	2.08553i	0.520905	+	0.189594i
$122$	1.70362	−	1.42951i	0.154239	−	0.129422i
$123$	−17.1254	−	6.97110i	−1.54414	−	0.628563i
$124$	9.03699	−	3.28920i	0.811546	−	0.295379i
$125$	−5.14535	−	8.91200i	−0.460214	−	0.797114i
$126$	−1.18769	+	7.84789i	−0.105808	+	0.699146i
$127$	5.79857	−	10.0434i	0.514540	−	0.891209i	−0.485318	−	0.874338i	$-0.661296\pi$
$127$	5.79857	−	10.0434i	0.514540	−	0.891209i	0.999858	−	0.0168715i	$-0.00537064\pi$
$128$	−0.173648	+	0.984808i	−0.0153485	+	0.0870455i
$129$	−3.59278	+	1.15701i	−0.316326	+	0.101869i
$130$	9.58958	+	3.49032i	0.841062	+	0.306122i
$131$	10.4009	−	8.72743i	0.908735	−	0.762519i	−0.0631433	−	0.998004i	$-0.520113\pi$
$131$	10.4009	−	8.72743i	0.908735	−	0.762519i	0.971878	+	0.235486i	$0.0756681\pi$
$132$	2.04069	−	3.24692i	0.177620	−	0.282608i
$133$	−2.50753	−	3.49049i	−0.217430	−	0.302664i
$134$	4.56445			0.394309
$135$	1.15477	+	18.6043i	0.0993867	+	1.60120i
$136$	−1.79836	−	3.11484i	−0.154208	−	0.267096i
$137$	13.1544	−	4.78780i	1.12385	−	0.409049i	0.287797	−	0.957692i	$-0.407077\pi$
$137$	13.1544	−	4.78780i	1.12385	−	0.409049i	0.836057	+	0.548642i	$0.184855\pi$
$138$	−7.80105	+	12.4121i	−0.664069	+	1.05659i
$139$	17.5833	+	6.39980i	1.49140	+	0.542824i	0.953817	−	0.300389i	$-0.0971164\pi$
$139$	17.5833	+	6.39980i	1.49140	+	0.542824i	0.537580	+	0.843213i	$0.319339\pi$
$140$	−8.55269	+	4.11485i	−0.722835	+	0.347768i
$141$	6.43782	+	5.82711i	0.542163	+	0.490731i
$142$	−1.27451	+	7.22808i	−0.106954	+	0.606567i
$143$	−6.29865			−0.526720
$144$	2.14712	+	2.09520i	0.178927	+	0.174600i
$145$	−24.1392			−2.00465
$146$	−2.97614	−	2.49728i	−0.246307	−	0.206676i
$147$	−4.29819	+	11.3369i	−0.354509	+	0.935053i
$148$	0.528660	+	2.99818i	0.0434556	+	0.246449i
$149$	−10.7910	−	3.92759i	−0.884029	−	0.321760i	−0.140195	−	0.990124i	$-0.544773\pi$
$149$	−10.7910	−	3.92759i	−0.884029	−	0.321760i	−0.743835	+	0.668364i	$0.766995\pi$
$150$	−10.7616	+	8.36276i	−0.878678	+	0.682817i
$151$	−0.595949	+	3.37980i	−0.0484977	+	0.275044i	−0.999407	−	0.0344248i	$-0.989040\pi$
$151$	−0.595949	+	3.37980i	−0.0484977	+	0.275044i	0.950910	+	0.309469i	$0.100151\pi$
$152$	−1.62442			−0.131758
$153$	−10.7598	−	0.808806i	−0.869877	−	0.0653881i
$154$	4.09183	−	4.19203i	0.329729	−	0.337804i
$155$	32.4183	−	11.7993i	2.60390	−	0.947743i
$156$	1.03700	−	4.81693i	0.0830268	−	0.385663i
$157$	17.4323	+	6.34482i	1.39125	+	0.506372i	0.925568	−	0.378582i	$-0.123588\pi$
$157$	17.4323	+	6.34482i	1.39125	+	0.506372i	0.465678	+	0.884954i	$0.345810\pi$
$158$	−0.0275762	−	0.156392i	−0.00219384	−	0.0124419i
$159$	19.2440	+	0.722263i	1.52615	+	0.0572792i
$160$	−0.622926	+	3.53279i	−0.0492467	+	0.279292i
$161$	−15.6420	+	16.0251i	−1.23276	+	1.26295i
$162$	8.82237	−	1.77928i	0.693151	−	0.139794i
$163$	−6.60017	+	11.4318i	−0.516965	+	0.895409i	0.482841	+	0.875708i	$0.339605\pi$
$163$	−6.60017	+	11.4318i	−0.516965	+	0.895409i	−0.999806	+	0.0197014i	$0.993728\pi$
$164$	−10.0313	+	3.65111i	−0.783315	+	0.285103i
$165$	7.32056	−	11.6477i	0.569905	−	0.906769i
$166$	−11.2106	+	9.40685i	−0.870115	+	0.730113i
$167$	−1.07295	+	0.900314i	−0.0830276	+	0.0696684i	−0.683357	−	0.730085i	$-0.739481\pi$
$167$	−1.07295	+	0.900314i	−0.0830276	+	0.0696684i	0.600329	+	0.799753i	$0.295036\pi$
$168$	2.53220	+	3.81942i	0.195364	+	0.294675i
$169$	4.61133	−	1.67839i	0.354718	−	0.129107i
$170$	−6.45123	−	11.1739i	−0.494786	−	0.856995i
$171$	−2.74613	+	4.02586i	−0.210002	+	0.307865i
$172$	−1.08960	+	1.88724i	−0.0830812	+	0.143901i
$173$	4.66599	−	1.69828i	0.354748	−	0.129118i	−0.158498	−	0.987359i	$-0.550665\pi$
$173$	4.66599	−	1.69828i	0.354748	−	0.129118i	0.513246	+	0.858242i	$0.328443\pi$
$174$	1.59198	+	11.5459i	0.120688	+	0.875292i
$175$	−18.7602	+	9.02585i	−1.41814	+	0.682290i
$176$	−0.384477	−	2.18048i	−0.0289811	−	0.164360i
$177$	−2.76461	+	2.14837i	−0.207801	+	0.161481i
$178$	2.41133	−	13.6753i	0.180737	−	1.02501i
$179$	−9.73284	+	16.8578i	−0.727467	+	1.26001i	0.230484	+	0.973076i	$0.425969\pi$
$179$	−9.73284	+	16.8578i	−0.727467	+	1.26001i	−0.957951	+	0.286933i	$0.907364\pi$
$180$	7.70235	+	7.51609i	0.574099	+	0.560217i
$181$	−8.24448	+	14.2799i	−0.612807	+	1.06141i	0.377958	+	0.925823i	$0.376626\pi$
$181$	−8.24448	+	14.2799i	−0.612807	+	1.06141i	−0.990765	+	0.135590i	$0.956707\pi$
$182$	3.09812	−	6.85935i	0.229648	−	0.508449i
$183$	−2.85582	−	2.58491i	−0.211108	−	0.191082i
$184$	1.46976	+	8.33541i	0.108352	+	0.614495i
$185$	1.89646	+	10.7553i	0.139430	+	0.790749i
$186$	−7.78165	−	14.7277i	−0.570578	−	1.07988i
$187$	6.10043	+	5.11887i	0.446107	+	0.374329i
$188$	5.01334			0.365636
$189$	13.7465	+	0.181196i	0.999913	+	0.0131801i
$190$	−5.82728			−0.422755
$191$	2.70272	+	2.26785i	0.195562	+	0.164096i	0.735311	−	0.677730i	$-0.237036\pi$
$191$	2.70272	+	2.26785i	0.195562	+	0.164096i	−0.539748	+	0.841826i	$0.681481\pi$
$192$	1.73083	+	0.0649612i	0.124912	+	0.00468817i
$193$	−1.12568	−	6.38403i	−0.0810280	−	0.459533i	−0.998143	−	0.0609104i	$-0.980600\pi$
$193$	−1.12568	−	6.38403i	−0.0810280	−	0.459533i	0.917115	−	0.398622i	$-0.130511\pi$
$194$	0.0991856	+	0.562510i	0.00712111	+	0.0403858i
$195$	3.72004	−	17.2797i	0.266397	−	1.23743i
$196$	2.55255	+	6.51801i	0.182325	+	0.465572i
$197$	2.61375	−	4.52715i	0.186222	−	0.322546i	−0.757766	−	0.652527i	$-0.773709\pi$
$197$	2.61375	−	4.52715i	0.186222	−	0.322546i	0.943988	+	0.329981i	$0.107042\pi$
$198$	−6.05392	−	2.73330i	−0.430233	−	0.194247i
$199$	6.79144	−	11.7631i	0.481433	−	0.833866i	−0.518340	−	0.855174i	$-0.673450\pi$
$199$	6.79144	−	11.7631i	0.481433	−	0.833866i	0.999773	+	0.0213088i	$0.00678332\pi$
$200$	−1.36638	+	7.74911i	−0.0966175	+	0.547945i
$201$	−1.07987	−	7.83177i	−0.0761678	−	0.552410i
$202$	−2.07613	−	11.7743i	−0.146076	−	0.828438i
$203$	−1.33705	+	17.7532i	−0.0938423	+	1.24603i
$204$	−4.91905	+	3.82257i	−0.344402	+	0.267633i
$205$	−35.9853	+	13.0976i	−2.51332	+	0.914775i
$206$	3.12443	−	5.41166i	0.217689	−	0.377049i
$207$	23.1426	+	10.4487i	1.60852	+	0.726234i
$208$	−1.42239	−	2.46364i	−0.0986247	−	0.170823i
$209$	3.37976	−	1.23013i	0.233783	−	0.0850899i
$210$	9.08374	+	13.7014i	0.626838	+	0.945484i
$211$	−11.5932	+	9.72788i	−0.798112	+	0.669695i	−0.947739	−	0.319047i	$-0.896637\pi$
$211$	−11.5932	+	9.72788i	−0.798112	+	0.669695i	0.149627	+	0.988742i	$0.452193\pi$
$212$	8.51717	−	7.14675i	0.584962	−	0.490841i
$213$	12.7036	+	0.476788i	0.870436	+	0.0326690i
$214$	−9.33442	+	3.39745i	−0.638088	+	0.232245i
$215$	−3.90871	+	6.77008i	−0.266572	+	0.461716i
$216$	3.08701	−	4.17975i	0.210045	−	0.284396i
$217$	−6.88220	−	24.4957i	−0.467194	−	1.66287i
$218$	1.48284	−	8.40961i	0.100431	−	0.569570i
$219$	−3.58078	+	5.69733i	−0.241967	+	0.384990i
$220$	−1.37923	−	7.82201i	−0.0929878	−	0.527360i
$221$	9.61477	+	3.49949i	0.646759	+	0.235401i
$222$	5.01926	−	1.61640i	0.336871	−	0.108486i
$223$	3.65517	−	1.33037i	0.244768	−	0.0890883i	−0.216723	−	0.976233i	$-0.569537\pi$
$223$	3.65517	−	1.33037i	0.244768	−	0.0890883i	0.461491	+	0.887145i	$0.347315\pi$
$224$	2.56370	+	0.653810i	0.171294	+	0.0436845i
$225$	16.8950	+	16.4864i	1.12633	+	1.09909i
$226$	−2.43556			−0.162011
$227$	0.632952	−	3.58965i	0.0420105	−	0.238254i	−0.956571	−	0.291500i	$-0.905846\pi$
$227$	0.632952	−	3.58965i	0.0420105	−	0.238254i	0.998581	+	0.0532463i	$0.0169568\pi$
$228$	0.384309	+	2.78721i	0.0254515	+	0.184588i
$229$	−16.2918	−	5.92974i	−1.07659	−	0.391848i	−0.257956	−	0.966157i	$-0.583049\pi$
$229$	−16.2918	−	5.92974i	−1.07659	−	0.391848i	−0.818639	+	0.574308i	$0.805271\pi$
$230$	5.27245	+	29.9015i	0.347655	+	1.97165i
$231$	−8.16081	−	6.02907i	−0.536942	−	0.396684i
$232$	5.15478	+	4.32538i	0.338428	+	0.283975i
$233$	14.5827			0.955344			0.477672	−	0.878538i	$-0.341481\pi$
$233$	14.5827			0.955344			0.477672	+	0.878538i	$0.341481\pi$
$234$	−8.51030	−	0.639714i	−0.556336	−	0.0418194i
$235$	17.9843			1.17317
$236$	−0.351018	+	1.99072i	−0.0228493	+	0.129585i
$237$	−0.261817	+	0.0843152i	−0.0170068	+	0.00547686i
$238$	−8.57516	+	4.12566i	−0.555845	+	0.267427i
$239$	−0.222801	−	0.0810929i	−0.0144118	−	0.00524546i	0.334804	−	0.942288i	$-0.391330\pi$
$239$	−0.222801	−	0.0810929i	−0.0144118	−	0.00524546i	−0.349216	+	0.937042i	$0.613552\pi$
$240$	6.20900	+	0.233035i	0.400789	+	0.0150423i
$241$	5.97573	−	2.17499i	0.384930	−	0.140103i	−0.142304	−	0.989823i	$-0.545451\pi$
$241$	5.97573	−	2.17499i	0.384930	−	0.140103i	0.527235	+	0.849720i	$0.323229\pi$
$242$	−3.04884	−	5.28075i	−0.195987	−	0.339460i
$243$	−5.14014	−	14.7166i	−0.329740	−	0.944072i
$244$	−2.22392			−0.142372
$245$	9.15674	+	23.3820i	0.585003	+	1.49382i
$246$	8.63786	+	16.3481i	0.550730	+	1.04232i
$247$	3.53998	−	2.97039i	0.225243	−	0.189002i
$248$	−9.03699	−	3.28920i	−0.573850	−	0.208864i
$249$	18.7927	+	17.0099i	1.19094	+	1.07796i
$250$	−1.78696	+	10.1344i	−0.113017	+	0.640953i
$251$	3.41197	−	5.90971i	0.215362	−	0.373018i	−0.738023	−	0.674776i	$-0.764240\pi$
$251$	3.41197	−	5.90971i	0.215362	−	0.373018i	0.953384	+	0.301758i	$0.0975735\pi$
$252$	5.95435	−	5.24840i	0.375089	−	0.330618i
$253$	−9.37014	−	16.2296i	−0.589096	−	1.02034i
$254$	−10.8977	+	3.96646i	−0.683786	+	0.248878i
$255$	−17.6460	+	13.7127i	−1.10504	+	0.858720i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−22.4243	−	8.16176i	−1.39879	−	0.509117i	−0.470968	−	0.882150i	$-0.656095\pi$
$257$	−22.4243	−	8.16176i	−1.39879	−	0.509117i	−0.927818	+	0.373033i	$0.878318\pi$
$258$	3.49594	+	1.42307i	0.217648	+	0.0885963i
$259$	8.01508	−	0.799026i	0.498033	−	0.0496490i
$260$	−5.10251	−	8.83781i	−0.316444	−	0.548097i
$261$	19.4340	−	5.46309i	1.20293	−	0.338157i
$262$	−13.5775			−0.838819
$263$	−22.2804	−	18.6955i	−1.37387	−	1.15281i	−0.971419	−	0.237371i	$-0.923714\pi$
$263$	−22.2804	−	18.6955i	−1.37387	−	1.15281i	−0.402450	−	0.915442i	$-0.631841\pi$
$264$	−3.65034	+	1.17555i	−0.224663	+	0.0723504i
$265$	30.5536	−	25.6375i	1.87689	−	1.57490i
$266$	−0.322767	+	4.28568i	−0.0197901	+	0.262772i
$267$	−24.0348	−	0.902070i	−1.47091	−	0.0552058i
$268$	−3.49657	−	2.93397i	−0.213587	−	0.179221i
$269$	−6.95270	−	12.0424i	−0.423913	−	0.734239i	0.572405	−	0.819971i	$-0.306011\pi$
$269$	−6.95270	−	12.0424i	−0.423913	−	0.734239i	−0.996318	+	0.0857317i	$0.972677\pi$
$270$	11.0740	−	14.9940i	0.673943	−	0.912506i
$271$	−13.9492	+	24.1607i	−0.847352	+	1.46766i	0.0362113	+	0.999344i	$0.488471\pi$
$271$	−13.9492	+	24.1607i	−0.847352	+	1.46766i	−0.883563	+	0.468312i	$0.844862\pi$
$272$	−0.624563	+	3.54207i	−0.0378697	+	0.214770i
$273$	−12.5024	−	3.69301i	−0.756677	−	0.223511i
$274$	−13.1544	−	4.78780i	−0.794685	−	0.289242i
$275$	−3.02532	−	17.1574i	−0.182434	−	1.03463i
$276$	13.9543	−	4.49384i	0.839952	−	0.270497i
$277$	−14.4006	−	12.0836i	−0.865250	−	0.726031i	0.0978421	−	0.995202i	$-0.468806\pi$
$277$	−14.4006	−	12.0836i	−0.865250	−	0.726031i	−0.963092	+	0.269171i	$0.913250\pi$
$278$	−9.35588	−	16.2049i	−0.561129	−	0.971903i
$279$	−23.4290	+	16.8362i	−1.40266	+	1.00796i
$280$	9.19672	+	2.34541i	0.549609	+	0.140165i
$281$	−3.57699	−	3.00145i	−0.213385	−	0.179052i	0.529830	−	0.848104i	$-0.322256\pi$
$281$	−3.57699	−	3.00145i	−0.213385	−	0.179052i	−0.743215	+	0.669052i	$0.766700\pi$
$282$	−1.18606	−	8.60198i	−0.0706291	−	0.512240i
$283$	1.19203	−	1.00023i	0.0708587	−	0.0594575i	−0.606670	−	0.794953i	$-0.707495\pi$
$283$	1.19203	−	1.00023i	0.0708587	−	0.0594575i	0.677529	+	0.735496i	$0.263051\pi$
$284$	5.62245	−	4.71780i	0.333631	−	0.279950i
$285$	1.37863	+	9.99854i	0.0816628	+	0.592263i
$286$	4.82505	+	4.04870i	0.285311	+	0.239404i
$287$	7.63945	+	27.1909i	0.450942	+	1.60503i
$288$	−0.298022	−	2.98516i	−0.0175611	−	0.175902i
$289$	2.03183	+	3.51923i	0.119519	+	0.207014i
$290$	18.4917	+	15.5164i	1.08587	+	0.911153i
$291$	0.941698	−	0.303264i	0.0552033	−	0.0177776i
$292$	0.674637	+	3.82606i	0.0394802	+	0.223903i
$293$	−4.88736	−	1.77885i	−0.285523	−	0.103922i	0.195289	−	0.980746i	$-0.437436\pi$
$293$	−4.88736	−	1.77885i	−0.285523	−	0.103922i	−0.480811	+	0.876824i	$0.659658\pi$
$294$	10.5798	−	5.92175i	0.617028	−	0.345364i
$295$	−1.25920	+	7.14129i	−0.0733136	+	0.415782i
$296$	1.52222	−	2.63656i	0.0884770	−	0.153247i
$297$	−3.25759	+	11.0341i	−0.189025	+	0.640261i
$298$	5.74175	+	9.94500i	0.332610	+	0.576098i
$299$	−18.4449	−	15.4771i	−1.06670	−	0.895065i
$300$	13.6193	+	0.511157i	0.786312	+	0.0295117i
$301$	4.76257	+	3.24966i	0.274510	+	0.187307i
$302$	2.62901	−	2.20600i	0.151283	−	0.126941i
$303$	−19.7114	+	6.34785i	−1.13239	+	0.364674i
$304$	1.24438	+	1.04416i	0.0713701	+	0.0598866i
$305$	−7.97784			−0.456810
$306$	7.72258	+	7.53584i	0.441471	+	0.430795i
$307$	−3.18238	−	5.51205i	−0.181628	−	0.314589i	0.760807	−	0.648978i	$-0.224803\pi$
$307$	−3.18238	−	5.51205i	−0.181628	−	0.314589i	−0.942435	+	0.334389i	$0.891470\pi$
$308$	−5.82911	+	0.581105i	−0.332144	+	0.0331116i
$309$	−10.0246	−	4.08064i	−0.570280	−	0.232140i
$310$	−32.4183	−	11.7993i	−1.84124	−	0.670155i
$311$	11.3066	−	9.48735i	0.641138	−	0.537978i	−0.263230	−	0.964733i	$-0.584788\pi$
$311$	11.3066	−	9.48735i	0.641138	−	0.537978i	0.904367	+	0.426755i	$0.140343\pi$
$312$	−3.89065	+	3.02341i	−0.220265	+	0.171167i
$313$	−1.04392	+	0.379956i	−0.0590059	+	0.0214764i	−0.371354	−	0.928491i	$-0.621107\pi$
$313$	−1.04392	+	0.379956i	−0.0590059	+	0.0214764i	0.312349	+	0.949968i	$0.398884\pi$
$314$	−9.27551	−	16.0657i	−0.523447	−	0.906638i
$315$	21.3600	−	18.8275i	1.20350	−	1.06081i
$316$	−0.0794025	+	0.137529i	−0.00446674	+	0.00773662i
$317$	4.74013	−	26.8826i	0.266232	−	1.50988i	−0.499270	−	0.866446i	$-0.666399\pi$
$317$	4.74013	−	26.8826i	0.266232	−	1.50988i	0.765503	−	0.643433i	$-0.222490\pi$
$318$	−14.2775	−	12.9231i	−0.800644	−	0.724692i
$319$	−14.0005	−	5.09576i	−0.783876	−	0.285308i
$320$	2.74802	−	2.30587i	0.153619	−	0.128902i
$321$	8.03776	+	15.2124i	0.448624	+	0.849073i
$322$	22.2832	−	2.22142i	1.24179	−	0.123795i
$323$	−5.84258			−0.325090
$324$	−7.90203	−	4.30790i	−0.439001	−	0.239328i
$325$	−11.1923	−	19.3856i	−0.620835	−	1.07532i
$326$	12.4043	−	4.51478i	0.687008	−	0.250050i
$327$	−14.7802	−	0.554725i	−0.817345	−	0.0306764i
$328$	10.0313	+	3.65111i	0.553888	+	0.201599i
$329$	0.996133	−	13.2266i	0.0549186	−	0.729206i
$330$	−13.0948	+	4.21705i	−0.720847	+	0.232141i
$331$	−4.58932	+	26.0273i	−0.252252	+	1.43059i	0.550777	+	0.834652i	$0.314331\pi$
$331$	−4.58932	+	26.0273i	−0.252252	+	1.43059i	−0.803029	+	0.595939i	$0.796780\pi$
$332$	14.6345			0.803170
$333$	−3.96091	−	8.22972i	−0.217057	−	0.450986i
$334$	1.40064			0.0766396
$335$	−12.5432	−	10.5250i	−0.685310	−	0.575043i
$336$	0.515296	−	4.55351i	0.0281117	−	0.248414i
$337$	−0.424932	−	2.40991i	−0.0231475	−	0.131276i	0.971044	−	0.238900i	$-0.0767869\pi$
$337$	−0.424932	−	2.40991i	−0.0231475	−	0.131276i	−0.994192	+	0.107624i	$0.965676\pi$
$338$	−4.61133	−	1.67839i	−0.250823	−	0.0912923i
$339$	0.576209	+	4.17898i	0.0312954	+	0.226971i
$340$	−2.24049	+	12.7064i	−0.121507	+	0.689103i
$341$	21.2931			1.15309
$342$	4.69143	−	1.31881i	0.253683	−	0.0713129i
$343$	17.7035	−	5.43923i	0.955900	−	0.293691i
$344$	2.04778	−	0.745330i	0.110409	−	0.0401855i
$345$	50.0582	−	16.1207i	2.69504	−	0.867910i
$346$	−4.66599	−	1.69828i	−0.250845	−	0.0913001i
$347$	−2.30750	−	13.0865i	−0.123873	−	0.702518i	−0.981971	−	0.189032i	$-0.939465\pi$
$347$	−2.30750	−	13.0865i	−0.123873	−	0.702518i	0.858098	−	0.513486i	$-0.171646\pi$
$348$	6.20203	−	9.86797i	0.332464	−	0.528979i
$349$	1.90954	−	10.8295i	0.102215	−	0.579691i	−0.890081	−	0.455802i	$-0.849352\pi$
$349$	1.90954	−	10.8295i	0.102215	−	0.579691i	0.992296	−	0.123889i	$-0.0395365\pi$
$350$	20.1728	+	5.14461i	1.07828	+	0.274991i
$351$	0.915748	+	14.7535i	0.0488790	+	0.787482i
$352$	−1.10706	+	1.91748i	−0.0590064	+	0.102202i
$353$	14.8145	−	5.39203i	0.788496	−	0.286989i	0.0837852	−	0.996484i	$-0.473299\pi$
$353$	14.8145	−	5.39203i	0.788496	−	0.286989i	0.704711	+	0.709495i	$0.251077\pi$
$354$	3.49876	+	0.131315i	0.185957	+	0.00697929i
$355$	20.1694	−	16.9241i	1.07048	−	0.898238i
$356$	−10.6375	+	8.92593i	−0.563787	+	0.473074i
$357$	9.10760	+	13.7373i	0.482025	+	0.727058i
$358$	18.2918	−	6.65766i	0.966749	−	0.351868i
$359$	0.954843	+	1.65384i	0.0503947	+	0.0872861i	0.890122	−	0.455722i	$-0.150619\pi$
$359$	0.954843	+	1.65384i	0.0503947	+	0.0872861i	−0.839728	+	0.543008i	$0.817285\pi$
$360$	−1.06909	−	10.7086i	−0.0563460	−	0.564395i
$361$	8.18062	−	14.1693i	0.430559	−	0.745750i
$362$	15.4945	−	5.63955i	0.814375	−	0.296408i
$363$	−8.33951	+	6.48059i	−0.437711	+	0.340143i
$364$	−6.78240	+	3.26313i	−0.355495	+	0.171035i
$365$	2.42012	+	13.7252i	0.126675	+	0.718409i
$366$	0.526138	+	3.81584i	0.0275017	+	0.199457i
$367$	−3.96624	+	22.4937i	−0.207036	+	1.17416i	0.687167	+	0.726499i	$0.258854\pi$
$367$	−3.96624	+	22.4937i	−0.207036	+	1.17416i	−0.894203	+	0.447661i	$0.852257\pi$
$368$	4.23200	−	7.33004i	0.220608	−	0.382105i
$369$	26.0069	−	18.6887i	1.35386	−	0.972893i
$370$	5.46063	−	9.45809i	0.283885	−	0.491703i
$371$	−17.1628	−	23.8907i	−0.891048	−	1.24034i
$372$	−3.50567	+	16.2840i	−0.181761	+	0.844286i
$373$	4.46783	+	25.3383i	0.231335	+	1.31197i	0.850196	+	0.526467i	$0.176484\pi$
$373$	4.46783	+	25.3383i	0.231335	+	1.31197i	−0.618860	+	0.785501i	$0.712405\pi$
$374$	−1.38285	−	7.84256i	−0.0715057	−	0.405529i
$375$	17.8115	+	0.668495i	0.919780	+	0.0345210i
$376$	−3.84044	−	3.22251i	−0.198056	−	0.166188i
$377$	−19.1427			−0.985900
$378$	−10.4140	−	8.97491i	−0.535638	−	0.461619i
$379$	3.07838			0.158126			0.0790629	−	0.996870i	$-0.474807\pi$
$379$	3.07838			0.158126			0.0790629	+	0.996870i	$0.474807\pi$
$380$	4.46395	+	3.74570i	0.228996	+	0.192150i
$381$	9.38392	+	17.7602i	0.480753	+	0.909880i
$382$	−0.612658	−	3.47456i	−0.0313463	−	0.177774i
$383$	−1.00852	−	5.71962i	−0.0515331	−	0.292259i	0.948139	−	0.317855i	$-0.102963\pi$
$383$	−1.00852	−	5.71962i	−0.0515331	−	0.292259i	−0.999672	+	0.0255964i	$0.991852\pi$
$384$	−1.28414	−	1.16232i	−0.0655309	−	0.0593144i
$385$	−20.9107	+	2.08459i	−1.06571	+	0.106241i
$386$	−3.24126	+	5.61402i	−0.164976	+	0.285746i
$387$	1.61465	−	6.33507i	0.0820771	−	0.322030i
$388$	0.285594	−	0.494663i	0.0144988	−	0.0251127i
$389$	−5.75438	+	32.6347i	−0.291759	+	1.65465i	0.388332	+	0.921519i	$0.373051\pi$
$389$	−5.75438	+	32.6347i	−0.291759	+	1.65465i	−0.680091	+	0.733127i	$0.738060\pi$
$390$	−13.9569	+	10.8458i	−0.706735	+	0.549200i
$391$	5.28630	+	29.9801i	0.267339	+	1.51616i
$392$	2.23433	−	6.63383i	0.112851	−	0.335059i
$393$	3.21218	+	23.2965i	0.162033	+	1.17515i
$394$	−4.91224	+	1.78791i	−0.247475	+	0.0900736i
$395$	−0.284840	+	0.493357i	−0.0143318	+	0.0248235i
$396$	2.88064	+	5.98521i	0.144758	+	0.300768i
$397$	−0.469848	−	0.813800i	−0.0235810	−	0.0408435i	0.853994	−	0.520283i	$-0.174173\pi$
$397$	−0.469848	−	0.813800i	−0.0235810	−	0.0408435i	−0.877575	+	0.479439i	$0.840840\pi$
$398$	−12.7637	+	4.64562i	−0.639788	+	0.232864i
$399$	7.42981	−	0.460104i	0.371956	−	0.0230340i
$400$	6.02774	−	5.05787i	0.301387	−	0.252894i
$401$	1.03105	−	0.865156i	0.0514883	−	0.0432038i	−0.616680	−	0.787214i	$-0.711523\pi$
$401$	1.03105	−	0.865156i	0.0514883	−	0.0432038i	0.668169	+	0.744010i	$0.267078\pi$
$402$	−4.20694	+	6.69360i	−0.209823	+	0.333847i
$403$	25.7082	−	9.35701i	1.28062	−	0.466106i
$404$	−5.97798	+	10.3542i	−0.297416	+	0.515139i
$405$	−28.3469	−	15.4537i	−1.40857	−	0.767899i
$406$	12.4358	−	12.7403i	0.617178	−	0.632292i
$407$	−1.17052	+	6.63832i	−0.0580203	+	0.329049i
$408$	6.22531	+	0.233647i	0.308199	+	0.0115672i
$409$	−6.31542	−	35.8165i	−0.312277	−	1.77101i	−0.587097	−	0.809516i	$-0.699729\pi$
$409$	−6.31542	−	35.8165i	−0.312277	−	1.77101i	0.274820	−	0.961496i	$-0.411382\pi$
$410$	35.9853	+	13.0976i	1.77719	+	0.646843i
$411$	−5.10291	+	23.7032i	−0.251708	+	1.16919i
$412$	−5.87200	+	2.13723i	−0.289293	+	0.105294i
$413$	5.18233	+	1.32163i	0.255006	+	0.0650333i
$414$	−11.0119	−	22.8799i	−0.541208	−	1.12449i
$415$	52.4981			2.57703
$416$	−0.493989	+	2.80155i	−0.0242198	+	0.137357i
$417$	−25.5912	+	19.8868i	−1.25320	+	0.973859i
$418$	−3.37976	−	1.23013i	−0.165309	−	0.0601677i
$419$	−2.57976	−	14.6305i	−0.126029	−	0.714748i	−0.980691	−	0.195563i	$-0.937347\pi$
$419$	−2.57976	−	14.6305i	−0.126029	−	0.714748i	0.854662	−	0.519185i	$-0.173765\pi$
$420$	1.84852	−	16.3348i	0.0901983	−	0.797055i
$421$	−13.0356	−	10.9382i	−0.635317	−	0.533094i	0.267259	−	0.963625i	$-0.413882\pi$
$421$	−13.0356	−	10.9382i	−0.635317	−	0.533094i	−0.902576	+	0.430531i	$0.858326\pi$
$422$	15.1339			0.736707
$423$	−14.4788	+	4.07014i	−0.703985	+	0.197897i
$424$	−11.1184			−0.539956
$425$	−4.91447	+	27.8713i	−0.238387	+	1.35196i
$426$	−9.42505	−	8.53096i	−0.456645	−	0.413326i
$427$	−0.441885	+	5.86732i	−0.0213843	+	0.283940i
$428$	9.33442	+	3.39745i	0.451196	+	0.164222i
$429$	5.80531	−	9.23675i	0.280283	−	0.445955i
$430$	7.34597	−	2.67371i	0.354254	−	0.128938i
$431$	0.143736	+	0.248959i	0.00692354	+	0.0119919i	0.869466	−	0.493992i	$-0.164463\pi$
$431$	0.143736	+	0.248959i	0.00692354	+	0.0119919i	−0.862543	+	0.505984i	$0.831129\pi$
$432$	−5.05148	+	1.21758i	−0.243040	+	0.0585811i
$433$	20.9438			1.00649			0.503246	−	0.864143i	$-0.332139\pi$
$433$	20.9438			1.00649			0.503246	+	0.864143i	$0.332139\pi$
$434$	−10.4734	+	23.1886i	−0.502741	+	1.11309i
$435$	22.2485	−	35.3993i	1.06673	−	1.69727i
$436$	−6.54151	+	5.48898i	−0.313282	+	0.262875i
$437$	12.9199	+	4.70247i	0.618045	+	0.224950i
$438$	6.40521	−	2.06273i	0.306053	−	0.0985610i
$439$	2.35898	−	13.3784i	0.112588	−	0.638517i	−0.875329	−	0.483529i	$-0.839355\pi$
$439$	2.35898	−	13.3784i	0.112588	−	0.638517i	0.987916	−	0.154988i	$-0.0495340\pi$
$440$	−3.97134	+	6.87856i	−0.189326	+	0.327923i
$441$	−12.6636	−	16.7521i	−0.603030	−	0.797718i
$442$	−5.11591	−	8.86102i	−0.243339	−	0.421476i
$443$	26.5312	−	9.65658i	1.26054	−	0.458798i	0.376588	−	0.926381i	$-0.377097\pi$
$443$	26.5312	−	9.65658i	1.26054	−	0.458798i	0.883949	+	0.467583i	$0.154875\pi$
$444$	−4.88398	−	1.98808i	−0.231783	−	0.0943503i
$445$	−38.1599	+	32.0199i	−1.80895	+	1.51789i
$446$	−3.65517	−	1.33037i	−0.173077	−	0.0629950i
$447$	15.7054	−	12.2046i	0.742840	−	0.577257i
$448$	−1.54364	−	2.14876i	−0.0729303	−	0.101519i
$449$	1.63600	+	2.83364i	0.0772078	+	0.133728i	0.902044	−	0.431644i	$-0.142066\pi$
$449$	1.63600	+	2.83364i	0.0772078	+	0.133728i	−0.824836	+	0.565371i	$0.808733\pi$
$450$	−2.34503	−	23.4892i	−0.110546	−	1.10729i
$451$	−23.6360			−1.11297
$452$	1.86575	+	1.56555i	0.0877574	+	0.0736372i
$453$	−4.40708	−	3.98901i	−0.207063	−	0.187420i
$454$	−2.79225	+	2.34298i	−0.131047	+	0.109961i
$455$	−24.3305	+	11.7058i	−1.14063	+	0.548777i
$456$	1.49719	−	2.38216i	0.0701123	−	0.111555i
$457$	−24.0446	−	20.1758i	−1.12476	−	0.943784i	−0.125923	−	0.992040i	$-0.540189\pi$
$457$	−24.0446	−	20.1758i	−1.12476	−	0.943784i	−0.998835	+	0.0482560i	$0.984634\pi$
$458$	8.66870	+	15.0146i	0.405062	+	0.701588i
$459$	11.1031	−	15.0334i	0.518248	−	0.701698i
$460$	15.1814	−	26.2950i	0.707837	−	1.22601i
$461$	1.11842	−	6.34290i	0.0520902	−	0.295418i	−0.947622	−	0.319393i	$-0.896521\pi$
$461$	1.11842	−	6.34290i	0.0520902	−	0.295418i	0.999713	+	0.0239747i	$0.00763212\pi$
$462$	2.37613	+	9.86421i	0.110548	+	0.458924i
$463$	−36.0530	−	13.1222i	−1.67553	−	0.609841i	−0.682839	−	0.730568i	$-0.739255\pi$
$463$	−36.0530	−	13.1222i	−1.67553	−	0.609841i	−0.992686	+	0.120727i	$0.961477\pi$
$464$	−1.16849	−	6.62686i	−0.0542460	−	0.307644i
$465$	−12.5759	+	58.4154i	−0.583192	+	2.70895i
$466$	−11.1710	−	9.37358i	−0.517486	−	0.434223i
$467$	−3.09746	−	5.36496i	−0.143333	−	0.248261i	0.785417	−	0.618968i	$-0.212449\pi$
$467$	−3.09746	−	5.36496i	−0.143333	−	0.248261i	−0.928750	+	0.370707i	$0.879115\pi$
$468$	6.10807	+	5.96037i	0.282346	+	0.275518i
$469$	−8.43540	+	8.64197i	−0.389511	+	0.399049i
$470$	−13.7768	−	11.5601i	−0.635476	−	0.533227i
$471$	−25.3713	+	19.7159i	−1.16905	+	0.908462i
$472$	1.54851	−	1.29935i	0.0712758	−	0.0598075i
$473$	−3.69616	+	3.10145i	−0.169950	+	0.142605i
$474$	0.254760	+	0.103703i	0.0117015	+	0.00476325i
$475$	9.79160	+	8.21613i	0.449269	+	0.376982i
$476$	9.22087	+	2.35157i	0.422638	+	0.107784i
$477$	−18.7959	+	27.5550i	−0.860605	+	1.26166i
$478$	0.118550	+	0.205334i	0.00542234	+	0.00939177i
$479$	25.6889	+	21.5555i	1.17376	+	0.984898i	1.00000		0.000109224i	$3.47670e-5\pi$
$479$	25.6889	+	21.5555i	1.17376	+	0.984898i	0.173756	+	0.984789i	$0.444410\pi$
$480$	−4.60658	−	4.16958i	−0.210260	−	0.190314i
$481$	1.50392	+	8.52914i	0.0685727	+	0.388895i
$482$	−5.97573	−	2.17499i	−0.272187	−	0.0990679i
$483$	−9.08333	−	37.7083i	−0.413306	−	1.71579i
$484$	−1.05885	+	6.00505i	−0.0481296	+	0.272957i
$485$	1.02451	−	1.77450i	0.0465205	−	0.0805758i
$486$	−5.52209	+	14.5776i	−0.250487	+	0.661254i
$487$	7.75756	+	13.4365i	0.351528	+	0.608865i	0.986517	−	0.163656i	$-0.0523287\pi$
$487$	7.75756	+	13.4365i	0.351528	+	0.608865i	−0.634989	+	0.772521i	$0.718995\pi$
$488$	1.70362	+	1.42951i	0.0771193	+	0.0647108i
$489$	−10.6812	−	20.2153i	−0.483018	−	0.914168i
$490$	8.01520	−	23.7975i	0.362090	−	1.07506i
$491$	−17.5894	+	14.7593i	−0.793801	+	0.666078i	−0.946683	−	0.322167i	$-0.895589\pi$
$491$	−17.5894	+	14.7593i	−0.793801	+	0.666078i	0.152882	+	0.988244i	$0.451144\pi$
$492$	3.89140	−	18.0757i	0.175438	−	0.814916i
$493$	18.5403	+	15.5571i	0.835012	+	0.700658i
$494$	−4.62111			−0.207914
$495$	10.3337	+	21.4707i	0.464465	+	0.965035i
$496$	4.80848	+	8.32854i	0.215907	+	0.373962i
$497$	−11.3297	−	15.7710i	−0.508207	−	0.707426i
$498$	−3.46224	−	25.1101i	−0.155147	−	1.12521i
$499$	29.0128	+	10.5598i	1.29879	+	0.472721i	0.896602	−	0.442837i	$-0.146028\pi$
$499$	29.0128	+	10.5598i	1.29879	+	0.472721i	0.402187	+	0.915557i	$0.368250\pi$
$500$	7.88313	−	6.61473i	0.352544	−	0.295820i
$501$	−0.331366	−	2.40324i	−0.0148043	−	0.107369i
$502$	−6.41242	+	2.33393i	−0.286200	+	0.104168i
$503$	15.5416	+	26.9189i	0.692966	+	1.20025i	0.970861	+	0.239642i	$0.0770299\pi$
$503$	15.5416	+	26.9189i	0.692966	+	1.20025i	−0.277895	+	0.960611i	$0.589637\pi$
$504$	−7.93490	+	0.193123i	−0.353449	+	0.00860240i
$505$	−21.4448	+	37.1434i	−0.954279	+	1.65286i
$506$	−3.25422	+	18.4556i	−0.144668	+	0.820450i
$507$	−1.78885	+	8.30928i	−0.0794457	+	0.369028i
$508$	10.8977	+	3.96646i	0.483509	+	0.175983i
$509$	5.40896	−	4.53865i	0.239748	−	0.201172i	−0.514995	−	0.857193i	$-0.672206\pi$
$509$	5.40896	−	4.53865i	0.239748	−	0.201172i	0.754743	+	0.656021i	$0.227762\pi$
$510$	22.3320	+	0.838158i	0.988877	+	0.0371143i
$511$	10.2283	−	1.01966i	0.452471	−	0.0451070i
$512$	−1.00000			−0.0441942
$513$	−3.37274	−	7.73763i	−0.148910	−	0.341625i
$514$	11.9317	+	20.6663i	0.526285	+	0.911552i
$515$	−21.0646	+	7.66688i	−0.928216	+	0.337843i
$516$	−1.76332	−	3.33728i	−0.0776257	−	0.146916i
$517$	10.4307	+	3.79647i	0.458742	+	0.166968i
$518$	−6.65351	−	4.53991i	−0.292339	−	0.199472i
$519$	−1.81005	+	8.40776i	−0.0794525	+	0.369060i
$520$	−1.77208	+	10.0500i	−0.0777110	+	0.440721i
$521$	−7.23543			−0.316990			−0.158495	−	0.987360i	$-0.550664\pi$
$521$	−7.23543			−0.316990			−0.158495	+	0.987360i	$0.550664\pi$
$522$	−18.3989	−	8.30697i	−0.805299	−	0.363586i
$523$	−17.2665			−0.755010			−0.377505	−	0.926008i	$-0.623218\pi$
$523$	−17.2665			−0.755010			−0.377505	+	0.926008i	$0.623218\pi$
$524$	10.4009	+	8.72743i	0.454367	+	0.381259i
$525$	4.05468	−	35.8300i	0.176961	−	1.56375i
$526$	5.05056	+	28.6431i	0.220215	+	1.24890i
$527$	−32.5035	−	11.8303i	−1.41587	−	0.515336i
$528$	3.55196	+	1.44587i	0.154579	+	0.0629234i
$529$	8.44612	−	47.9003i	0.367222	−	2.08262i
$530$	−39.8848			−1.73249
$531$	−0.602430	−	6.03429i	−0.0261432	−	0.261866i
$532$	3.00204	−	3.07555i	0.130155	−	0.133342i
$533$	−28.5368	+	10.3866i	−1.23607	+	0.449892i
$534$	17.8319	+	16.1403i	0.771662	+	0.698460i
$535$	33.4853	+	12.1876i	1.44769	+	0.526918i
$536$	0.792609	+	4.49511i	0.0342355	+	0.194159i
$537$	−15.7508	−	29.8102i	−0.679698	−	1.28641i
$538$	−2.41465	+	13.6941i	−0.104103	+	0.590396i
$539$	0.374895	+	15.4943i	0.0161479	+	0.667386i
$540$	−18.1211	+	4.36783i	−0.779810	+	0.187961i
$541$	5.96279	−	10.3279i	0.256360	−	0.444029i	−0.708904	−	0.705305i	$-0.750810\pi$
$541$	5.96279	−	10.3279i	0.256360	−	0.444029i	0.965264	+	0.261276i	$0.0841433\pi$
$542$	26.2159	−	9.54179i	1.12607	−	0.409855i
$543$	−13.3422	−	25.2516i	−0.572567	−	1.08365i
$544$	2.75524	−	2.31192i	0.118130	−	0.0991228i
$545$	−23.4663	+	19.6906i	−1.00519	+	0.843451i
$546$	7.20353	+	10.8654i	0.308283	+	0.464995i
$547$	24.4309	−	8.89212i	1.04459	−	0.380199i	0.237971	−	0.971272i	$-0.423518\pi$
$547$	24.4309	−	8.89212i	1.04459	−	0.380199i	0.806618	+	0.591073i	$0.201295\pi$
$548$	6.99930	+	12.1231i	0.298995	+	0.517875i
$549$	6.42281	−	1.80551i	0.274119	−	0.0770575i
$550$	−8.71106	+	15.0880i	−0.371441	+	0.643354i
$551$	10.2717	−	3.73859i	0.437588	−	0.159269i
$552$	−13.5782	−	5.52718i	−0.577927	−	0.235253i
$553$	0.347063	+	0.236812i	0.0147586	+	0.0100703i
$554$	3.26436	+	18.5131i	0.138689	+	0.786546i
$555$	−17.5202	−	7.13184i	−0.743693	−	0.302730i
$556$	−3.24926	+	18.4275i	−0.137799	+	0.781500i
$557$	−14.7654	+	25.5745i	−0.625632	+	1.08363i	0.362787	+	0.931872i	$0.381825\pi$
$557$	−14.7654	+	25.5745i	−0.625632	+	1.08363i	−0.988418	+	0.151754i	$0.951508\pi$
$558$	28.7697	+	2.16260i	1.21792	+	0.0915503i
$559$	−3.09966	+	5.36877i	−0.131102	+	0.227075i
$560$	−5.53750	−	7.70822i	−0.234002	−	0.325732i
$561$	−13.1292	+	4.22813i	−0.554317	+	0.178512i
$562$	0.810838	+	4.59849i	0.0342031	+	0.193976i
$563$	4.13510	+	23.4513i	0.174274	+	0.988354i	0.938979	+	0.343974i	$0.111773\pi$
$563$	4.13510	+	23.4513i	0.174274	+	0.988354i	−0.764705	+	0.644380i	$0.777116\pi$
$564$	−4.62067	+	7.35189i	−0.194565	+	0.309570i
$565$	6.69298	+	5.61608i	0.281576	+	0.236270i
$566$	−1.55608			−0.0654070
$567$	−12.9355	+	19.9918i	−0.543242	+	0.839576i
$568$	−7.33959			−0.307962
$569$	−4.50387	−	3.77919i	−0.188812	−	0.158432i	0.543482	−	0.839421i	$-0.317106\pi$
$569$	−4.50387	−	3.77919i	−0.188812	−	0.158432i	−0.732294	+	0.680989i	$0.761550\pi$
$570$	5.37085	−	8.54549i	0.224960	−	0.357931i
$571$	−4.27975	−	24.2716i	−0.179102	−	1.01574i	−0.933302	−	0.359092i	$-0.883086\pi$
$571$	−4.27975	−	24.2716i	−0.179102	−	1.01574i	0.754200	−	0.656644i	$-0.228025\pi$
$572$	−1.09375	−	6.20296i	−0.0457320	−	0.259359i
$573$	−5.81676	+	1.87322i	−0.242999	+	0.0782551i
$574$	11.6258	−	25.7400i	0.485253	−	1.07437i
$575$	33.3001	−	57.6775i	1.38871	−	2.40532i
$576$	−1.69053	+	2.47833i	−0.0704386	+	0.103264i
$577$	−7.33975	+	12.7128i	−0.305558	+	0.529241i	−0.977385	−	0.211466i	$-0.932176\pi$
$577$	−7.33975	+	12.7128i	−0.305558	+	0.529241i	0.671828	+	0.740708i	$0.265510\pi$
$578$	0.705647	−	4.00192i	0.0293511	−	0.166458i
$579$	10.3995	+	4.23323i	0.432187	+	0.175927i
$580$	−4.19173	−	23.7725i	−0.174052	−	0.987098i
$581$	2.90781	−	38.6098i	0.120636	−	1.60180i
$582$	−0.916317	−	0.372998i	−0.0379826	−	0.0154613i
$583$	23.1328	−	8.41964i	0.958061	−	0.348706i
$584$	1.94254	−	3.36458i	0.0803829	−	0.139227i
$585$	21.9114	+	21.3816i	0.905926	+	0.884019i
$586$	2.60051	+	4.50422i	0.107426	+	0.186067i
$587$	18.3049	−	6.66246i	0.755526	−	0.274989i	0.0645969	−	0.997911i	$-0.479424\pi$
$587$	18.3049	−	6.66246i	0.755526	−	0.274989i	0.690929	+	0.722922i	$0.257202\pi$
$588$	−11.9111	−	2.26426i	−0.491203	−	0.0933766i
$589$	−11.9672	+	10.0416i	−0.493098	+	0.413759i
$590$	5.55494	−	4.66115i	0.228693	−	0.191896i
$591$	4.22987	+	8.00553i	0.173994	+	0.329303i
$592$	−2.86083	+	1.04126i	−0.117579	+	0.0427954i
$593$	−10.1112	+	17.5131i	−0.415217	+	0.719178i	−0.995451	−	0.0952724i	$-0.969628\pi$
$593$	−10.1112	+	17.5131i	−0.415217	+	0.719178i	0.580234	+	0.814450i	$0.302961\pi$
$594$	9.58802	−	6.35864i	0.393401	−	0.260898i
$595$	33.0780	+	8.43576i	1.35606	+	0.345832i
$596$	1.99409	−	11.3090i	0.0816810	−	0.463236i
$597$	10.9907	+	20.8012i	0.449819	+	0.851335i
$598$	4.18112	+	23.7123i	0.170979	+	0.969669i
$599$	−33.6248	−	12.2384i	−1.37387	−	0.500049i	−0.453558	−	0.891227i	$-0.649846\pi$
$599$	−33.6248	−	12.2384i	−1.37387	−	0.500049i	−0.920315	+	0.391177i	$0.872068\pi$
$600$	−10.1044	−	9.14590i	−0.412512	−	0.373380i
$601$	41.2382	−	15.0095i	1.68214	−	0.612250i	0.688541	−	0.725197i	$-0.258251\pi$
$601$	41.2382	−	15.0095i	1.68214	−	0.612250i	0.993601	+	0.112947i	$0.0360292\pi$
$602$	−1.55950	−	5.55070i	−0.0635606	−	0.226230i
$603$	12.4803	+	5.63475i	0.508237	+	0.229465i
$604$	−3.43193			−0.139643
$605$	−3.79841	+	21.5419i	−0.154427	+	0.875801i
$606$	19.1801	+	7.80752i	0.779140	+	0.317159i
$607$	−32.0297	−	11.6578i	−1.30004	−	0.473177i	−0.403033	−	0.915186i	$-0.632044\pi$
$607$	−32.0297	−	11.6578i	−1.30004	−	0.473177i	−0.897011	+	0.442008i	$0.854266\pi$
$608$	−0.282078	−	1.59974i	−0.0114398	−	0.0648782i
$609$	−24.8021	−	18.3234i	−1.00503	−	0.742502i
$610$	6.11138	+	5.12806i	0.247443	+	0.207629i
$611$	14.2618			0.576971
$612$	−1.07190	−	10.7368i	−0.0433289	−	0.434008i
$613$	−11.2820			−0.455676			−0.227838	−	0.973699i	$-0.573166\pi$
$613$	−11.2820			−0.455676			−0.227838	+	0.973699i	$0.573166\pi$
$614$	−1.10523	+	6.26807i	−0.0446035	+	0.252959i
$615$	13.9596	−	64.8428i	0.562905	−	2.61472i
$616$	4.83888	+	3.30173i	0.194964	+	0.133030i
$617$	−12.4010	−	4.51360i	−0.499246	−	0.181711i	0.0801090	−	0.996786i	$-0.474473\pi$
$617$	−12.4010	−	4.51360i	−0.499246	−	0.181711i	−0.579355	+	0.815076i	$0.696695\pi$
$618$	5.05631	+	9.56965i	0.203395	+	0.384948i
$619$	−22.0349	+	8.02006i	−0.885658	+	0.322353i	−0.744491	−	0.667632i	$-0.767308\pi$
$619$	−22.0349	+	8.02006i	−0.885658	+	0.322353i	−0.141167	+	0.989986i	$0.545086\pi$
$620$	17.2494	+	29.8769i	0.692754	+	1.19988i
$621$	−36.6525	+	24.3075i	−1.47082	+	0.975424i
$622$	−14.7597			−0.591810
$623$	21.4355	+	29.8383i	0.858794	+	1.19545i
$624$	4.92382	+	0.184800i	0.197111	+	0.00739791i
$625$	−1.85962	+	1.56041i	−0.0743848	+	0.0624163i
$626$	1.04392	+	0.379956i	0.0417234	+	0.0151861i
$627$	−1.31109	+	6.09007i	−0.0523600	+	0.243214i
$628$	−3.22135	+	18.2692i	−0.128546	+	0.729020i
$629$	5.47498	−	9.48294i	0.218302	−	0.378109i
$630$	−28.4648	+	0.692790i	−1.13407	+	0.0276014i
$631$	4.36566	+	7.56154i	0.173794	+	0.301020i	0.939743	−	0.341881i	$-0.111064\pi$
$631$	4.36566	+	7.56154i	0.173794	+	0.301020i	−0.765949	+	0.642901i	$0.777731\pi$
$632$	0.149228	−	0.0543145i	0.00593596	−	0.00216051i
$633$	−3.58040	−	25.9670i	−0.142308	−	1.03210i
$634$	−20.9110	+	17.5464i	−0.830481	+	0.696856i
$635$	39.0934	+	14.2288i	1.55137	+	0.564654i
$636$	2.63040	+	19.0771i	0.104302	+	0.756456i
$637$	7.26142	+	18.5423i	0.287708	+	0.734671i
$638$	7.44950	+	12.9029i	0.294928	+	0.510831i
$639$	−12.4078	+	18.1899i	−0.490844	+	0.719582i
$640$	−3.58729			−0.141800
$641$	−25.1631	−	21.1143i	−0.993881	−	0.833965i	−0.00775630	−	0.999970i	$-0.502469\pi$
$641$	−25.1631	−	21.1143i	−0.993881	−	0.833965i	−0.986125	+	0.166004i	$0.946913\pi$
$642$	3.62105	−	16.8199i	0.142912	−	0.663830i
$643$	12.6672	−	10.6290i	0.499545	−	0.419168i	−0.357887	−	0.933765i	$-0.616503\pi$
$643$	12.6672	−	10.6290i	0.499545	−	0.419168i	0.857432	+	0.514597i	$0.172058\pi$
$644$	−18.4978	−	12.6216i	−0.728916	−	0.497363i
$645$	−6.32553	−	11.9718i	−0.249067	−	0.471389i
$646$	4.47568	+	3.75554i	0.176093	+	0.147760i
$647$	4.75023	+	8.22764i	0.186751	+	0.323462i	0.944165	−	0.329473i	$-0.106871\pi$
$647$	4.75023	+	8.22764i	0.186751	+	0.323462i	−0.757414	+	0.652935i	$0.773538\pi$
$648$	3.28424	+	8.37937i	0.129017	+	0.329173i
$649$	−2.23784	+	3.87606i	−0.0878430	+	0.152148i
$650$	−3.88703	+	22.0444i	−0.152462	+	0.864654i
$651$	42.2652	+	12.4845i	1.65650	+	0.489307i
$652$	−12.4043	−	4.51478i	−0.485788	−	0.176812i
$653$	−2.78788	−	15.8108i	−0.109098	−	0.618726i	−0.989504	−	0.144505i	$-0.953841\pi$
$653$	−2.78788	−	15.8108i	−0.109098	−	0.618726i	0.880406	−	0.474221i	$-0.157270\pi$
$654$	10.9657	+	9.92545i	0.428792	+	0.388116i
$655$	37.3112	+	31.3078i	1.45787	+	1.22330i
$656$	−5.33756	−	9.24492i	−0.208397	−	0.360954i
$657$	−5.05462	−	10.5022i	−0.197200	−	0.409728i
$658$	−9.26498	+	9.49186i	−0.361186	+	0.370031i
$659$	−26.5624	−	22.2885i	−1.03472	−	0.868237i	−0.0433188	−	0.999061i	$-0.513793\pi$
$659$	−26.5624	−	22.2885i	−1.03472	−	0.868237i	−0.991406	+	0.130825i	$0.958238\pi$
$660$	12.7419	+	5.18675i	0.495978	+	0.201894i
$661$	23.7417	−	19.9216i	0.923445	−	0.774862i	−0.0511842	−	0.998689i	$-0.516300\pi$
$661$	23.7417	−	19.9216i	0.923445	−	0.774862i	0.974629	+	0.223827i	$0.0718551\pi$
$662$	20.2457	−	16.9881i	0.786870	−	0.660263i
$663$	−13.9936	+	10.8743i	−0.543465	+	0.422324i
$664$	−11.2106	−	9.40685i	−0.435057	−	0.365057i
$665$	10.7692	−	11.0329i	0.417611	−	0.427838i
$666$	−2.25573	+	8.85036i	−0.0874078	+	0.342944i
$667$	−28.4775	−	49.3245i	−1.10265	−	1.90985i
$668$	−1.07295	−	0.900314i	−0.0415138	−	0.0348342i
$669$	−1.41793	+	6.58634i	−0.0548204	+	0.254643i
$670$	2.84332	+	16.1253i	0.109847	+	0.622973i
$671$	−4.62706	−	1.68411i	−0.178626	−	0.0650145i
$672$	−3.32168	+	3.15697i	−0.128137	+	0.121783i
$673$	5.06620	−	28.7318i	0.195288	−	1.10753i	−0.716721	−	0.697360i	$-0.754358\pi$
$673$	5.06620	−	28.7318i	0.195288	−	1.10753i	0.912009	−	0.410171i	$-0.134531\pi$
$674$	−1.22354	+	2.11924i	−0.0471292	+	0.0816301i
$675$	−39.7484	+	9.58075i	−1.52992	+	0.368763i
$676$	2.45364	+	4.24983i	0.0943707	+	0.163455i
$677$	−26.7309	−	22.4299i	−1.02735	−	0.862051i	−0.0368189	−	0.999322i	$-0.511722\pi$
$677$	−26.7309	−	22.4299i	−1.02735	−	0.862051i	−0.990534	+	0.137271i	$0.956167\pi$
$678$	2.24479	−	3.57166i	0.0862108	−	0.137169i
$679$	−1.24831	−	0.851764i	−0.0479058	−	0.0326877i
$680$	9.88385	−	8.29354i	0.379028	−	0.318043i
$681$	4.68072	+	4.23669i	0.179366	+	0.162350i
$682$	−16.3115	−	13.6869i	−0.624598	−	0.524100i
$683$	7.25962			0.277782			0.138891	−	0.990308i	$-0.455646\pi$
$683$	7.25962			0.277782			0.138891	+	0.990308i	$0.455646\pi$
$684$	−4.44156	−	2.00533i	−0.169827	−	0.0766756i
$685$	25.1085	+	43.4892i	0.959347	+	1.66164i
$686$	−17.0580	−	7.21291i	−0.651276	−	0.275390i
$687$	23.7115	−	18.4261i	0.904651	−	0.703000i
$688$	−2.04778	−	0.745330i	−0.0780708	−	0.0284154i
$689$	24.2294	−	20.3309i	0.923066	−	0.774545i
$690$	−48.7090	−	19.8276i	−1.85432	−	0.754824i
$691$	35.1435	−	12.7912i	1.33692	−	0.486600i	0.428081	−	0.903740i	$-0.359190\pi$
$691$	35.1435	−	12.7912i	1.33692	−	0.486600i	0.908842	+	0.417140i	$0.136968\pi$
$692$	2.48272	+	4.30020i	0.0943788	+	0.163469i
$693$	16.3630	−	6.41070i	0.621580	−	0.243522i
$694$	−6.64417	+	11.5080i	−0.252209	+	0.436839i
$695$	−11.6561	+	66.1048i	−0.442139	+	2.50750i
$696$	−11.0940	+	3.57272i	−0.420518	+	0.135423i
$697$	36.0798	+	13.1320i	1.36662	+	0.497409i
$698$	−8.42387	+	7.06847i	−0.318848	+	0.267545i
$699$	−13.4405	+	21.3850i	−0.508366	+	0.808855i
$700$	−12.1464	−	16.9078i	−0.459091	−	0.639056i
$701$	−25.3690			−0.958175			−0.479088	−	0.877767i	$-0.659032\pi$
$701$	−25.3690			−0.958175			−0.479088	+	0.877767i	$0.659032\pi$
$702$	8.78184	−	11.8904i	0.331449	−	0.448776i
$703$	−2.47272	−	4.28288i	−0.0932605	−	0.161532i
$704$	2.08059	−	0.757273i	0.0784152	−	0.0285408i
$705$	−16.5757	+	26.3734i	−0.624276	+	0.993278i
$706$	−14.8145	−	5.39203i	−0.557551	−	0.202932i
$707$	26.1294	+	17.8289i	0.982696	+	0.670525i
$708$	−2.59580	−	2.34955i	−0.0975560	−	0.0883015i
$709$	5.08512	−	28.8391i	0.190976	−	1.08308i	−0.727059	−	0.686575i	$-0.759113\pi$
$709$	5.08512	−	28.8391i	0.190976	−	1.08308i	0.918034	−	0.396501i	$-0.129776\pi$
$710$	−26.3292			−0.988119
$711$	0.117664	−	0.461656i	0.00441276	−	0.0173134i
$712$	13.8863			0.520411
$713$	62.3545	+	52.3216i	2.33519	+	1.95946i
$714$	1.85337	−	16.3777i	0.0693607	−	0.612919i
$715$	−3.92360	−	22.2518i	−0.146734	−	0.832171i
$716$	−18.2918	−	6.65766i	−0.683595	−	0.248808i
$717$	0.324270	−	0.251988i	0.0121101	−	0.00941067i
$718$	0.331613	−	1.88067i	0.0123757	−	0.0701861i
$719$	6.82830			0.254653			0.127326	−	0.991861i	$-0.459360\pi$
$719$	6.82830			0.254653			0.127326	+	0.991861i	$0.459360\pi$
$720$	−6.06441	+	8.89049i	−0.226007	+	0.331329i
$721$	4.47187	+	15.9166i	0.166541	+	0.592767i
$722$	−15.3745	+	5.59588i	−0.572181	+	0.208257i
$723$	−2.31813	+	10.7678i	−0.0862123	+	0.400459i
$724$	−15.4945	−	5.63955i	−0.575850	−	0.209592i
$725$	−9.19448	−	52.1445i	−0.341474	−	1.93660i
$726$	10.5541	+	0.396113i	0.391698	+	0.0147011i
$727$	−6.67878	+	37.8773i	−0.247702	+	1.40479i	0.566429	+	0.824110i	$0.308324\pi$
$727$	−6.67878	+	37.8773i	−0.247702	+	1.40479i	−0.814132	+	0.580680i	$0.802787\pi$
$728$	7.29312	+	1.85994i	0.270301	+	0.0689340i
$729$	26.3189	+	6.02611i	0.974775	+	0.223189i
$730$	6.96846	−	12.0697i	0.257914	−	0.446720i
$731$	7.36526	−	2.68074i	0.272414	−	0.0991506i
$732$	2.04973	−	3.26130i	0.0757602	−	0.120541i
$733$	30.8929	−	25.9222i	1.14105	−	0.957459i	0.141582	−	0.989927i	$-0.454781\pi$
$733$	30.8929	−	25.9222i	1.14105	−	0.957459i	0.999473	+	0.0324678i	$0.0103366\pi$
$734$	17.4970	−	14.6817i	0.645825	−	0.541912i
$735$	−42.7284	−	8.12256i	−1.57606	−	0.299605i
$736$	−7.95356	+	2.89486i	−0.293172	+	0.106706i
$737$	−5.05311	−	8.75225i	−0.186134	−	0.322393i
$738$	−31.9353	−	2.40055i	−1.17555	−	0.0883656i
$739$	−8.16745	+	14.1464i	−0.300445	+	0.520385i	−0.976237	−	0.216707i	$-0.930468\pi$
$739$	−8.16745	+	14.1464i	−0.300445	+	0.520385i	0.675792	+	0.737092i	$0.263802\pi$
$740$	−10.2626	+	3.73529i	−0.377262	+	0.137312i
$741$	1.09327	+	7.92898i	0.0401623	+	0.291278i
$742$	−2.20918	+	29.3334i	−0.0811016	+	1.07686i
$743$	−2.57617	−	14.6102i	−0.0945104	−	0.535995i	−0.994896	−	0.100903i	$-0.967827\pi$
$743$	−2.57617	−	14.6102i	−0.0945104	−	0.535995i	0.900386	−	0.435092i	$-0.143284\pi$
$744$	13.1527	−	10.2209i	0.482200	−	0.374715i
$745$	7.15337	−	40.5688i	0.262079	−	1.48633i
$746$	12.8646	−	22.2821i	0.471006	−	0.815807i
$747$	−42.2652	+	11.8812i	−1.54640	+	0.434709i
$748$	−3.98177	+	6.89663i	−0.145588	+	0.252166i
$749$	10.8181	−	23.9518i	0.395286	−	0.875178i
$750$	−13.2147	−	11.9611i	−0.482532	−	0.436757i
$751$	3.25803	+	18.4772i	0.118887	+	0.674243i	0.984752	+	0.173965i	$0.0556579\pi$
$751$	3.25803	+	18.4772i	0.118887	+	0.674243i	−0.865865	+	0.500279i	$0.833231\pi$
$752$	0.870558	+	4.93718i	0.0317460	+	0.180040i
$753$	5.52165	+	10.4504i	0.201220	+	0.380833i
$754$	14.6642	+	12.3047i	0.534038	+	0.448111i
$755$	−12.3113			−0.448056
$756$	2.20862	+	13.5692i	0.0803266	+	0.493505i
$757$	−21.7187			−0.789379			−0.394690	−	0.918815i	$-0.629148\pi$
$757$	−21.7187			−0.789379			−0.394690	+	0.918815i	$0.629148\pi$
$758$	−2.35818	−	1.97875i	−0.0856529	−	0.0718713i
$759$	32.4363	+	1.21739i	1.17736	+	0.0441885i
$760$	−1.01190	−	5.73875i	−0.0367053	−	0.208166i
$761$	7.21511	+	40.9189i	0.261548	+	1.48331i	0.778689	+	0.627410i	$0.215885\pi$
$761$	7.21511	+	40.9189i	0.261548	+	1.48331i	−0.517142	+	0.855900i	$0.673004\pi$
$762$	4.22751	−	19.6369i	0.153146	−	0.711371i
$763$	13.1817	+	18.3490i	0.477209	+	0.664278i
$764$	−1.76408	+	3.05547i	−0.0638221	+	0.110543i
$765$	−3.84521	−	38.5159i	−0.139024	−	1.39254i
$766$	−2.90393	+	5.02975i	−0.104923	+	0.181732i
$767$	−0.998565	+	5.66314i	−0.0360561	+	0.204484i
$768$	0.236582	+	1.71582i	0.00853690	+	0.0619142i
$769$	−4.20100	−	23.8250i	−0.151492	−	0.859153i	−0.961923	−	0.273319i	$-0.911878\pi$
$769$	−4.20100	−	23.8250i	−0.151492	−	0.859153i	0.810431	−	0.585833i	$-0.199233\pi$
$770$	17.3585	+	11.8443i	0.625556	+	0.426837i
$771$	32.6368	−	25.3619i	1.17538	−	0.913386i
$772$	6.09157	−	2.21715i	0.219240	−	0.0797970i
$773$	−6.55884	+	11.3602i	−0.235905	+	0.408600i	−0.959535	−	0.281588i	$-0.909139\pi$
$773$	−6.55884	+	11.3602i	−0.235905	+	0.408600i	0.723630	+	0.690188i	$0.242472\pi$
$774$	−5.30899	+	3.81507i	−0.190828	+	0.137130i
$775$	37.8363	+	65.5344i	1.35912	+	2.35406i
$776$	−0.536740	+	0.195358i	−0.0192679	+	0.00701293i
$777$	−6.21555	+	12.4903i	−0.222982	+	0.448086i
$778$	25.3853	−	21.3008i	0.910108	−	0.763671i
$779$	13.2839	−	11.1465i	0.475945	−	0.399366i
$780$	17.6632	+	0.662930i	0.632443	+	0.0237367i
$781$	15.2707	−	5.55807i	0.546428	−	0.198883i
$782$	15.2213	−	26.3640i	0.544312	−	0.942776i
$783$	−9.90040	+	33.5345i	−0.353811	+	1.19842i
$784$	−5.97574	+	3.64561i	−0.213419	+	0.130200i
$785$	−11.5559	+	65.5369i	−0.412449	+	2.33911i
$786$	12.5140	−	19.9109i	0.446360	−	0.710197i
$787$	−4.98120	−	28.2498i	−0.177561	−	1.00700i	−0.935147	−	0.354261i	$-0.884733\pi$
$787$	−4.98120	−	28.2498i	−0.177561	−	1.00700i	0.757586	−	0.652735i	$-0.226379\pi$
$788$	4.91224	+	1.78791i	0.174991	+	0.0636917i
$789$	47.9515	−	15.4423i	1.70712	−	0.549760i
$790$	0.535323	−	0.194842i	0.0190460	−	0.00693216i
$791$	4.50107	−	4.61130i	0.160040	−	0.163959i
$792$	1.64052	−	6.43658i	0.0582933	−	0.228714i
$793$	−6.32654			−0.224662
$794$	−0.163176	+	0.925420i	−0.00579091	+	0.0328419i
$795$	9.43602	+	68.4351i	0.334661	+	2.42714i
$796$	12.7637	+	4.64562i	0.452399	+	0.164660i
$797$	2.10926	+	11.9622i	0.0747139	+	0.423723i	0.999106	+	0.0422795i	$0.0134620\pi$
$797$	2.10926	+	11.9622i	0.0747139	+	0.423723i	−0.924392	+	0.381444i	$0.875427\pi$
$798$	−5.98731	−	4.42333i	−0.211949	−	0.156584i
$799$	−13.8130	−	11.5905i	−0.488668	−	0.410041i
$800$	−7.86865			−0.278199
$801$	23.4751	−	34.4148i	0.829453	−	1.21599i
$802$	−1.34594			−0.0475269
$803$	−1.49373	+	8.47134i	−0.0527124	+	0.298947i
$804$	7.52527	−	2.42343i	0.265396	−	0.0854678i
$805$	−66.3570	−	45.2775i	−2.33878	−	1.59582i
$806$	−25.7082	−	9.35701i	−0.905532	−	0.329587i
$807$	24.0679	+	0.903311i	0.847230	+	0.0317980i
$808$	11.2349	−	4.08918i	0.395243	−	0.143857i
$809$	19.9107	+	34.4863i	0.700021	+	1.21247i	0.968458	+	0.249175i	$0.0801596\pi$
$809$	19.9107	+	34.4863i	0.700021	+	1.21247i	−0.268437	+	0.963297i	$0.586507\pi$
$810$	11.7815	+	30.0592i	0.413961	+	1.05617i
$811$	−47.8526			−1.68033			−0.840166	−	0.542329i	$-0.817543\pi$
$811$	−47.8526			−1.68033			−0.840166	+	0.542329i	$0.817543\pi$
$812$	−17.7157	+	1.76608i	−0.621699	+	0.0619773i
$813$	−22.5742	−	42.7242i	−0.791711	−	1.49840i
$814$	5.16370	−	4.33286i	0.180988	−	0.151867i
$815$	−44.4977	−	16.1958i	−1.55869	−	0.567315i
$816$	−4.61868	−	4.18053i	−0.161686	−	0.146348i
$817$	0.614704	−	3.48616i	0.0215058	−	0.121965i
$818$	−18.1845	+	31.4965i	−0.635807	+	1.10125i
$819$	16.9388	−	14.9305i	0.591888	−	0.521714i
$820$	−19.1474	−	33.1642i	−0.668655	−	1.15815i
$821$	2.82526	−	1.02831i	0.0986022	−	0.0358883i	−0.292248	−	0.956343i	$-0.594403\pi$
$821$	2.82526	−	1.02831i	0.0986022	−	0.0358883i	0.390850	+	0.920454i	$0.372181\pi$
$822$	19.1452	−	14.8776i	0.667765	−	0.518917i
$823$	26.9553	−	22.6181i	0.939601	−	0.788419i	−0.0379147	−	0.999281i	$-0.512072\pi$
$823$	26.9553	−	22.6181i	0.939601	−	0.788419i	0.977516	+	0.210862i	$0.0676271\pi$
$824$	5.87200	+	2.13723i	0.204561	+	0.0744540i
$825$	27.9491	+	11.3770i	0.973064	+	0.396098i
$826$	−3.12037	−	4.34357i	−0.108571	−	0.151132i
$827$	−0.410700	−	0.711353i	−0.0142814	−	0.0247362i	0.858796	−	0.512317i	$-0.171213\pi$
$827$	−0.410700	−	0.711353i	−0.0142814	−	0.0247362i	−0.873078	+	0.487581i	$0.837879\pi$
$828$	−6.27128	+	24.6054i	−0.217942	+	0.855096i
$829$	−14.4753			−0.502749			−0.251375	−	0.967890i	$-0.580883\pi$
$829$	−14.4753			−0.502749			−0.251375	+	0.967890i	$0.580883\pi$
$830$	−40.2158	−	33.7451i	−1.39591	−	1.17131i
$831$	30.9928	−	9.98090i	1.07513	−	0.346234i
$832$	2.17922	−	1.82858i	0.0755509	−	0.0633947i
$833$	8.03625	−	23.8600i	0.278439	−	0.826700i
$834$	32.3869	+	1.21554i	1.12147	+	0.0420906i
$835$	−3.84899	−	3.22969i	−0.133200	−	0.111768i
$836$	1.79833	+	3.11480i	0.0621966	+	0.107728i
$837$	−3.09576	−	49.8752i	−0.107005	−	1.72394i
$838$	−7.42812	+	12.8659i	−0.256600	+	0.444444i
$839$	0.519920	−	2.94861i	0.0179496	−	0.101797i	−0.974517	−	0.224315i	$-0.927986\pi$
$839$	0.519920	−	2.94861i	0.0179496	−	0.101797i	0.992466	+	0.122517i	$0.0390967\pi$
$840$	−11.9158	+	11.3250i	−0.411135	+	0.390748i
$841$	−15.2988	−	5.56832i	−0.527546	−	0.192011i
$842$	2.95493	+	16.7583i	0.101834	+	0.577528i
$843$	7.69834	−	2.47917i	0.265145	−	0.0853871i
$844$	−11.5932	−	9.72788i	−0.399056	−	0.334848i
$845$	8.80192	+	15.2454i	0.302795	+	0.524457i
$846$	13.7077	+	6.18890i	0.471279	+	0.212779i
$847$	15.6326	+	3.98673i	0.537143	+	0.136986i
$848$	8.51717	+	7.14675i	0.292481	+	0.245421i
$849$	0.368140	+	2.66995i	0.0126345	+	0.0916325i
$850$	21.6800	−	18.1917i	0.743619	−	0.623971i
$851$	−19.7395	+	16.5634i	−0.676661	+	0.567786i
$852$	1.73641	+	12.5934i	0.0594885	+	0.431443i
$853$	32.2146	+	27.0312i	1.10301	+	0.925532i	0.997624	−	0.0688994i	$-0.0219487\pi$
$853$	32.2146	+	27.0312i	1.10301	+	0.925532i	0.105383	+	0.994432i	$0.466393\pi$
$854$	4.10994	−	4.21059i	0.140639	−	0.144083i
$855$	−15.9331	−	7.19369i	−0.544902	−	0.246019i
$856$	−4.96674	−	8.60265i	−0.169760	−	0.294032i
$857$	−30.2210	−	25.3584i	−1.03233	−	0.866226i	−0.0412020	−	0.999151i	$-0.513119\pi$
$857$	−30.2210	−	25.3584i	−1.03233	−	0.866226i	−0.991126	+	0.132925i	$0.957563\pi$
$858$	−10.3844	+	3.34418i	−0.354517	+	0.114168i
$859$	1.87176	+	10.6153i	0.0638635	+	0.362188i	0.999946	+	0.0104069i	$0.00331269\pi$
$859$	1.87176	+	10.6153i	0.0638635	+	0.362188i	−0.936082	+	0.351781i	$0.885576\pi$
$860$	−7.34597	−	2.67371i	−0.250495	−	0.0911729i
$861$	−46.9156	−	13.8582i	−1.59888	−	0.472286i
$862$	0.0499191	−	0.283105i	0.00170025	−	0.00964261i
$863$	21.2282	−	36.7683i	0.722617	−	1.25161i	−0.237331	−	0.971429i	$-0.576272\pi$
$863$	21.2282	−	36.7683i	0.722617	−	1.25161i	0.959947	−	0.280180i	$-0.0903942\pi$
$864$	4.65231	+	2.31431i	0.158275	+	0.0787343i
$865$	8.90623	+	15.4261i	0.302821	+	0.524501i
$866$	−16.0438	−	13.4624i	−0.545192	−	0.457471i
$867$	−7.03351	−	0.263980i	−0.238871	−	0.00896523i
$868$	22.9284	−	11.0313i	0.778242	−	0.374426i
$869$	−0.269351	+	0.226012i	−0.00913710	+	0.00766694i
$870$	−39.7975	+	12.8164i	−1.34926	+	0.434516i
$871$	−9.94695	−	8.34648i	−0.337040	−	0.282810i
$872$	8.53934			0.289178
$873$	−0.423213	+	1.66048i	−0.0143236	+	0.0561986i
$874$	−6.87456	−	11.9071i	−0.232535	−	0.402763i
$875$	−15.8852	−	22.1122i	−0.537016	−	0.747529i
$876$	−6.23257	−	2.53705i	−0.210579	−	0.0857189i
$877$	−24.7754	−	9.01751i	−0.836606	−	0.304500i	−0.112039	−	0.993704i	$-0.535738\pi$
$877$	−24.7754	−	9.01751i	−0.836606	−	0.304500i	−0.724567	+	0.689204i	$0.757960\pi$
$878$	−10.4066	+	8.73214i	−0.351204	+	0.294696i
$879$	7.11318	−	5.52762i	0.239922	−	0.186442i
$880$	7.46368	−	2.71656i	0.251601	−	0.0915751i
$881$	−17.4217	−	30.1753i	−0.586953	−	1.01663i	−0.994629	−	0.103506i	$-0.966994\pi$
$881$	−17.4217	−	30.1753i	−0.586953	−	1.01663i	0.407676	−	0.913127i	$-0.366339\pi$
$882$	−1.06712	+	20.9729i	−0.0359319	+	0.706193i
$883$	11.9222	−	20.6499i	0.401214	−	0.694923i	−0.592658	−	0.805454i	$-0.701922\pi$
$883$	11.9222	−	20.6499i	0.401214	−	0.694923i	0.993873	+	0.110530i	$0.0352549\pi$
$884$	−1.77674	+	10.0764i	−0.0597581	+	0.338905i
$885$	−9.31188	−	8.42852i	−0.313015	−	0.283322i
$886$	−26.5312	−	9.65658i	−0.891335	−	0.324419i
$887$	−28.0551	+	23.5410i	−0.941997	+	0.790430i	−0.977932	−	0.208925i	$-0.933004\pi$
$887$	−28.0551	+	23.5410i	−0.941997	+	0.790430i	0.0359344	+	0.999354i	$0.488559\pi$
$888$	2.46343	+	4.66232i	0.0826672	+	0.156457i
$889$	12.6300	−	27.9632i	0.423595	−	0.937855i
$890$	49.8141			1.66977
$891$	−13.1786	−	14.9470i	−0.441500	−	0.500742i
$892$	1.94487	+	3.36862i	0.0651192	+	0.112790i
$893$	−7.65266	+	2.78534i	−0.256086	+	0.0932078i
$894$	−19.8760	−	0.745981i	−0.664753	−	0.0249493i
$895$	−65.6179	−	23.8829i	−2.19336	−	0.798319i
$896$	−0.198696	+	2.63828i	−0.00663798	+	0.0881387i
$897$	39.6969	−	12.7839i	1.32544	−	0.426844i
$898$	0.568178	−	3.22230i	0.0189604	−	0.107529i
$899$	64.7135			2.15831
$900$	−13.3022	+	19.5011i	−0.443406	+	0.650037i
$901$	−39.9896			−1.33225
$902$	18.1062	+	15.1929i	0.602870	+	0.505868i
$903$	−9.15504	+	3.98902i	−0.304661	+	0.132746i
$904$	−0.422931	−	2.39856i	−0.0140665	−	0.0797749i
$905$	−55.5835	−	20.2307i	−1.84766	−	0.672492i
$906$	0.811932	+	5.88857i	0.0269746	+	0.195635i
$907$	1.04919	−	5.95028i	0.0348379	−	0.197576i	−0.962421	−	0.271560i	$-0.912460\pi$
$907$	1.04919	−	5.95028i	0.0348379	−	0.197576i	0.997259	+	0.0739844i	$0.0235715\pi$
$908$	3.64503			0.120964
$909$	8.85861	−	34.7567i	0.293821	−	1.15281i
$910$	26.1626	+	6.67215i	0.867280	+	0.221179i
$911$	36.8589	−	13.4155i	1.22119	−	0.444477i	0.350618	−	0.936519i	$-0.385972\pi$
$911$	36.8589	−	13.4155i	1.22119	−	0.444477i	0.870571	+	0.492042i	$0.163749\pi$
$912$	−2.67813	+	0.862465i	−0.0886819	+	0.0285591i
$913$	30.4483	+	11.0823i	1.00769	+	0.366770i
$914$	5.45046	+	30.9111i	0.180285	+	1.02245i
$915$	7.35297	−	11.6992i	0.243082	−	0.386764i
$916$	3.01061	−	17.0740i	0.0994733	−	0.564141i
$917$	25.0920	−	25.7065i	0.828612	−	0.848903i
$918$	−18.1687	+	4.37930i	−0.599658	+	0.144538i
$919$	11.7174	−	20.2951i	0.386521	−	0.669473i	−0.605458	−	0.795877i	$-0.707010\pi$
$919$	11.7174	−	20.2951i	0.386521	−	0.669473i	0.991979	+	0.126404i	$0.0403434\pi$
$920$	−28.5317	+	10.3847i	−0.940663	+	0.342373i
$921$	11.0163	+	0.413463i	0.363001	+	0.0136241i
$922$	−4.93390	+	4.14003i	−0.162489	+	0.136345i
$923$	15.9946	−	13.4211i	0.526468	−	0.441759i
$924$	4.52037	−	9.08377i	0.148709	−	0.298834i
$925$	−22.5109	+	8.19329i	−0.740153	+	0.269394i
$926$	19.1834	+	33.2266i	0.630406	+	1.09189i
$927$	15.2235	−	10.9397i	0.500007	−	0.359307i
$928$	−3.36455	+	5.82756i	−0.110447	+	0.191299i
$929$	11.8387	−	4.30895i	0.388416	−	0.141372i	−0.140428	−	0.990091i	$-0.544848\pi$
$929$	11.8387	−	4.30895i	0.388416	−	0.141372i	0.528844	+	0.848719i	$0.322626\pi$
$930$	47.1824	−	36.6652i	1.54717	−	1.20230i
$931$	−7.51767	−	8.53132i	−0.246382	−	0.279603i
$932$	2.53226	+	14.3612i	0.0829469	+	0.470415i
$933$	3.49187	+	25.3249i	0.114319	+	0.829102i
$934$	−1.07574	+	6.10081i	−0.0351992	+	0.199625i
$935$	−14.2838	+	24.7402i	−0.467129	+	0.809091i
$936$	−0.847803	−	8.49210i	−0.0277113	−	0.277573i
$937$	7.17883	−	12.4341i	0.234522	−	0.406205i	−0.724611	−	0.689158i	$-0.757981\pi$
$937$	7.17883	−	12.4341i	0.234522	−	0.406205i	0.959134	+	0.282953i	$0.0913141\pi$
$938$	12.0168	−	1.19796i	0.392364	−	0.0391148i
$939$	0.404963	−	1.88107i	0.0132155	−	0.0613863i
$940$	3.12294	+	17.7111i	0.101859	+	0.577672i
$941$	7.71320	+	43.7438i	0.251443	+	1.42601i	0.805040	+	0.593221i	$0.202144\pi$
$941$	7.71320	+	43.7438i	0.251443	+	1.42601i	−0.553597	+	0.832785i	$0.686745\pi$
$942$	32.1087	+	1.20510i	1.04616	+	0.0392642i
$943$	−69.2153	−	58.0785i	−2.25396	−	1.89130i
$944$	−2.02143			−0.0657920
$945$	7.92295	+	48.6765i	0.257734	+	1.58345i
$946$	4.82500			0.156874
$947$	−25.4159	−	21.3264i	−0.825904	−	0.693016i	0.128442	−	0.991717i	$-0.459002\pi$
$947$	−25.4159	−	21.3264i	−0.825904	−	0.693016i	−0.954347	+	0.298701i	$0.903447\pi$
$948$	−0.128498	−	0.243198i	−0.00417343	−	0.00789870i
$949$	1.91919	+	10.8843i	0.0622995	+	0.353318i
$950$	−2.21957	−	12.5878i	−0.0720125	−	0.408403i
$951$	35.0536	+	31.7283i	1.13669	+	1.02886i
$952$	−5.55204	−	7.72847i	−0.179943	−	0.250481i
$953$	−10.8009	+	18.7078i	−0.349877	+	0.606005i	−0.986227	−	0.165395i	$-0.947110\pi$
$953$	−10.8009	+	18.7078i	−0.349877	+	0.606005i	0.636350	+	0.771400i	$0.280443\pi$
$954$	32.1105	−	9.02658i	1.03962	−	0.292246i
$955$	−6.32826	+	10.9609i	−0.204778	+	0.354685i
$956$	0.0411719	−	0.233498i	0.00133160	−	0.00755185i
$957$	20.3766	−	15.8346i	0.658683	−	0.511859i
$958$	−5.82320	−	33.0250i	−0.188139	−	1.06699i
$959$	33.3750	−	16.0573i	1.07773	−	0.518517i
$960$	0.848687	+	6.15514i	0.0273913	+	0.198656i
$961$	−57.7780	+	21.0295i	−1.86381	+	0.678370i
$962$	4.33036	−	7.50040i	0.139616	−	0.241823i
$963$	−29.7166	−	2.23378i	−0.957604	−	0.0719826i
$964$	3.17962	+	5.50726i	0.102409	+	0.177377i
$965$	21.8522	−	7.95356i	0.703448	−	0.256034i
$966$	−17.2802	+	34.7249i	−0.555981	+	1.11726i
$967$	−36.0689	+	30.2654i	−1.15990	+	0.973269i	−0.999904	−	0.0138489i	$-0.995592\pi$
$967$	−36.0689	+	30.2654i	−1.15990	+	0.973269i	−0.159993	+	0.987118i	$0.551147\pi$
$968$	4.67110	−	3.91952i	0.150135	−	0.125978i
$969$	5.38496	−	8.56794i	0.172990	−	0.275242i
$970$	−1.92544	+	0.700804i	−0.0618223	+	0.0225015i
$971$	27.4481	−	47.5416i	0.880853	−	1.52568i	0.0304582	−	0.999536i	$-0.490303\pi$
$971$	27.4481	−	47.5416i	0.880853	−	1.52568i	0.850395	−	0.526146i	$-0.176363\pi$
$972$	13.6005	−	7.61756i	0.436235	−	0.244333i
$973$	47.9713	+	12.2339i	1.53789	+	0.392202i
$974$	2.69417	−	15.2794i	0.0863268	−	0.489584i
$975$	38.7438	+	1.45412i	1.24080	+	0.0465693i
$976$	−0.386180	−	2.19013i	−0.0123613	−	0.0701044i
$977$	53.8113	+	19.5857i	1.72158	+	0.626602i	0.997974	−	0.0636160i	$-0.0202633\pi$
$977$	53.8113	+	19.5857i	1.72158	+	0.626602i	0.723601	+	0.690218i	$0.242486\pi$
$978$	−4.81192	+	22.3515i	−0.153868	+	0.714724i
$979$	−28.8917	+	10.5157i	−0.923381	+	0.336083i
$980$	−21.4367	+	13.0779i	−0.684771	+	0.417757i
$981$	14.4360	−	21.1633i	0.460905	−	0.675692i
$982$	22.9614			0.732728
$983$	−1.87437	+	10.6301i	−0.0597831	+	0.339047i	−0.999999	−	0.00153263i	$-0.999512\pi$
$983$	−1.87437	+	10.6301i	−0.0597831	+	0.339047i	0.940216	+	0.340580i	$0.110623\pi$
$984$	−14.5998	+	11.3455i	−0.465426	+	0.361680i
$985$	17.6216	+	6.41375i	0.561472	+	0.204359i
$986$	−4.20274	−	23.8349i	−0.133842	−	0.759058i
$987$	18.4782	+	13.6514i	0.588168	+	0.434529i
$988$	3.53998	+	2.97039i	0.112622	+	0.0945008i
$989$	−18.4447			−0.586508
$990$	5.88502	−	23.0899i	0.187038	−	0.733844i
$991$	−39.7060			−1.26130			−0.630652	−	0.776066i	$-0.717212\pi$
$991$	−39.7060			−1.26130			−0.630652	+	0.776066i	$0.717212\pi$
$992$	1.66997	−	9.47086i	0.0530216	−	0.300700i
$993$	−33.9383	−	30.7188i	−1.07700	−	0.974831i
$994$	−1.45835	+	19.3639i	−0.0462561	+	0.614185i
$995$	45.7872	+	16.6652i	1.45155	+	0.528322i
$996$	−13.4882	+	21.4609i	−0.427390	+	0.680015i
$997$	−23.0885	+	8.40354i	−0.731221	+	0.266143i	−0.680682	−	0.732579i	$-0.738316\pi$
$997$	−23.0885	+	8.40354i	−0.731221	+	0.266143i	−0.0505395	+	0.998722i	$0.516094\pi$
$998$	−15.4374	−	26.7383i	−0.488661	−	0.846386i
$999$	15.7193	+	1.77659i	0.497335	+	0.0562089i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.v.a.79.4	yes	72
7.4	even	3		378.2.w.b.25.12	yes	72
27.13	even	9		378.2.w.b.121.12	yes	72
189.67	even	9	inner	378.2.v.a.67.4	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.v.a.67.4	✓	72	189.67	even	9	inner
378.2.v.a.79.4	yes	72	1.1	even	1	trivial
378.2.w.b.25.12	yes	72	7.4	even	3
378.2.w.b.121.12	yes	72	27.13	even	9

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.v (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 - 0.642788i) q^{2} +(-0.921674 + 1.46646i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.622926 + 3.53279i) q^{5} +(1.64867 - 0.530936i) q^{6} +(2.63270 - 0.262455i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.30103 - 2.70320i) q^{9} +O(q^{10})\)	\(q+(-0.766044 - 0.642788i) q^{2} +(-0.921674 + 1.46646i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.622926 + 3.53279i) q^{5} +(1.64867 - 0.530936i) q^{6} +(2.63270 - 0.262455i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.30103 - 2.70320i) q^{9} +(1.79365 - 3.10668i) q^{10} +(-0.384477 + 2.18048i) q^{11} +(-1.60423 - 0.653023i) q^{12} +(0.493989 + 2.80155i) q^{13} +(-2.18547 - 1.49122i) q^{14} +(-5.75485 - 2.34258i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(1.79836 - 3.11484i) q^{17} +(-0.740936 + 2.90706i) q^{18} +(-0.812212 - 1.40679i) q^{19} +(-3.37095 + 1.22693i) q^{20} +(-2.04161 + 4.10266i) q^{21} +(1.69611 - 1.42321i) q^{22} +(-6.48380 + 5.44055i) q^{23} +(0.809158 + 1.53143i) q^{24} +(-7.39412 + 2.69124i) q^{25} +(1.42239 - 2.46364i) q^{26} +(5.16328 + 0.583554i) q^{27} +(0.715631 + 2.54713i) q^{28} +(-1.16849 + 6.62686i) q^{29} +(2.90269 + 5.49367i) q^{30} +(-1.66997 - 9.47086i) q^{31} +(0.939693 + 0.342020i) q^{32} +(-2.84323 - 2.57351i) q^{33} +(-3.37980 + 1.23015i) q^{34} +(2.56718 + 9.13730i) q^{35} +(2.43621 - 1.75067i) q^{36} +3.04443 q^{37} +(-0.282078 + 1.59974i) q^{38} +(-4.56367 - 1.85770i) q^{39} +(3.37095 + 1.22693i) q^{40} +(1.85372 + 10.5129i) q^{41} +(4.20110 - 1.83050i) q^{42} +(1.66936 + 1.40076i) q^{43} -2.21412 q^{44} +(8.73941 - 6.28018i) q^{45} +8.46400 q^{46} +(0.870558 - 4.93718i) q^{47} +(0.364530 - 1.69326i) q^{48} +(6.86224 - 1.38193i) q^{49} +(7.39412 + 2.69124i) q^{50} +(2.91031 + 5.50810i) q^{51} +(-2.67321 + 0.972969i) q^{52} +(-5.55919 - 9.62879i) q^{53} +(-3.58020 - 3.76592i) q^{54} -7.94268 q^{55} +(1.08906 - 2.41121i) q^{56} +(2.81160 + 0.105524i) q^{57} +(5.15478 - 4.32538i) q^{58} +(1.89952 + 0.691370i) q^{59} +(1.30768 - 6.07420i) q^{60} +(-0.386180 + 2.19013i) q^{61} +(-4.80848 + 8.32854i) q^{62} +(-4.13470 - 6.77527i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-9.58958 + 3.49032i) q^{65} +(0.523819 + 3.79902i) q^{66} +(-3.49657 + 2.93397i) q^{67} +(3.37980 + 1.23015i) q^{68} +(-2.00243 - 14.5227i) q^{69} +(3.90677 - 8.64972i) q^{70} +(-3.66979 - 6.35627i) q^{71} +(-2.99156 - 0.224874i) q^{72} +3.88508 q^{73} +(-2.33217 - 1.95692i) q^{74} +(2.86836 - 13.3236i) q^{75} +(1.24438 - 1.04416i) q^{76} +(-0.439937 + 5.84146i) q^{77} +(2.30187 + 4.35655i) q^{78} +(0.121652 + 0.102078i) q^{79} +(-1.79365 - 3.10668i) q^{80} +(-5.61462 + 7.03392i) q^{81} +(5.33756 - 9.24492i) q^{82} +(2.54125 - 14.4121i) q^{83} +(-4.39485 - 1.29818i) q^{84} +(12.1243 + 4.41290i) q^{85} +(-0.378414 - 2.14609i) q^{86} +(-8.64108 - 7.82136i) q^{87} +(1.69611 + 1.42321i) q^{88} +(6.94314 + 12.0259i) q^{89} +(-10.7316 - 0.806688i) q^{90} +(2.03581 + 7.24600i) q^{91} +(-6.48380 - 5.44055i) q^{92} +(15.4278 + 6.28010i) q^{93} +(-3.84044 + 3.22251i) q^{94} +(4.46395 - 3.74570i) q^{95} +(-1.36765 + 1.06279i) q^{96} +(-0.437555 - 0.367152i) q^{97} +(-6.14506 - 3.35234i) q^{98} +(6.39450 - 1.79756i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{6} - 6 q^{7} + 36 q^{8}+O(q^{10}) \) 72 * q + 3 * q^6 - 6 * q^7 + 36 * q^8	\( 72 q + 3 q^{6} - 6 q^{7} + 36 q^{8} + 6 q^{10} + 12 q^{11} + 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} + 18 q^{19} + 6 q^{22} + 12 q^{23} - 6 q^{25} - 18 q^{26} + 6 q^{27} + 3 q^{29} + 15 q^{30} - 9 q^{31} - 18 q^{33} - 9 q^{34} - 18 q^{35} - 3 q^{36} - 48 q^{39} - 6 q^{41} + 36 q^{42} - 24 q^{43} - 45 q^{45} - 27 q^{47} + 6 q^{48} + 48 q^{49} + 6 q^{50} + 15 q^{51} - 6 q^{52} - 15 q^{53} - 63 q^{54} - 72 q^{55} - 3 q^{56} + 57 q^{57} - 3 q^{58} - 30 q^{59} + 21 q^{60} + 9 q^{61} - 24 q^{62} - 21 q^{63} - 36 q^{64} + 45 q^{65} + 6 q^{67} + 9 q^{68} - 39 q^{69} + 15 q^{70} + 12 q^{71} - 60 q^{73} - 18 q^{74} + 42 q^{75} + 3 q^{77} + 6 q^{78} - 27 q^{79} - 6 q^{80} + 12 q^{81} + 33 q^{82} + 18 q^{83} - 21 q^{84} + 51 q^{85} - 12 q^{86} - 117 q^{87} + 6 q^{88} - 36 q^{89} - 69 q^{90} - 3 q^{91} + 12 q^{92} - 30 q^{93} - 27 q^{94} + 3 q^{95} + 48 q^{97} - 12 q^{98} + 90 q^{99}+O(q^{100}) \) 72 * q + 3 * q^6 - 6 * q^7 + 36 * q^8 + 6 * q^10 + 12 * q^11 + 12 * q^13 - 3 * q^14 - 6 * q^15 - 12 * q^17 + 18 * q^19 + 6 * q^22 + 12 * q^23 - 6 * q^25 - 18 * q^26 + 6 * q^27 + 3 * q^29 + 15 * q^30 - 9 * q^31 - 18 * q^33 - 9 * q^34 - 18 * q^35 - 3 * q^36 - 48 * q^39 - 6 * q^41 + 36 * q^42 - 24 * q^43 - 45 * q^45 - 27 * q^47 + 6 * q^48 + 48 * q^49 + 6 * q^50 + 15 * q^51 - 6 * q^52 - 15 * q^53 - 63 * q^54 - 72 * q^55 - 3 * q^56 + 57 * q^57 - 3 * q^58 - 30 * q^59 + 21 * q^60 + 9 * q^61 - 24 * q^62 - 21 * q^63 - 36 * q^64 + 45 * q^65 + 6 * q^67 + 9 * q^68 - 39 * q^69 + 15 * q^70 + 12 * q^71 - 60 * q^73 - 18 * q^74 + 42 * q^75 + 3 * q^77 + 6 * q^78 - 27 * q^79 - 6 * q^80 + 12 * q^81 + 33 * q^82 + 18 * q^83 - 21 * q^84 + 51 * q^85 - 12 * q^86 - 117 * q^87 + 6 * q^88 - 36 * q^89 - 69 * q^90 - 3 * q^91 + 12 * q^92 - 30 * q^93 - 27 * q^94 + 3 * q^95 + 48 * q^97 - 12 * q^98 + 90 * q^99

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