LMFDB - Embedded newform 378.2.u.a.211.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(43,378)]

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([4, 0]))

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

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

chi := DirichletCharacter("378.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.u (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:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			211.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	378.211
Dual form			378.2.u.a.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 - 0.642788i) q^{2} +(1.11334 + 1.32683i) q^{3} +(0.173648 - 0.984808i) q^{4} +(2.37939 - 0.866025i) q^{5} +(1.70574 + 0.300767i) q^{6} +(0.173648 + 0.984808i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.520945 + 2.95442i) q^{9} +O(q^{10})$	\(q+(0.766044 - 0.642788i) q^{2} +(1.11334 + 1.32683i) q^{3} +(0.173648 - 0.984808i) q^{4} +(2.37939 - 0.866025i) q^{5} +(1.70574 + 0.300767i) q^{6} +(0.173648 + 0.984808i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.520945 + 2.95442i) q^{9} +(1.26604 - 2.19285i) q^{10} +(-0.286989 - 0.104455i) q^{11} +(1.50000 - 0.866025i) q^{12} +(-1.43969 - 1.20805i) q^{13} +(0.766044 + 0.642788i) q^{14} +(3.79813 + 2.19285i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-0.592396 + 1.02606i) q^{17} +(1.50000 + 2.59808i) q^{18} +(-2.31908 - 4.01676i) q^{19} +(-0.439693 - 2.49362i) q^{20} +(-1.11334 + 1.32683i) q^{21} +(-0.286989 + 0.104455i) q^{22} +(-0.215537 + 1.22237i) q^{23} +(0.592396 - 1.62760i) q^{24} +(1.08125 - 0.907278i) q^{25} -1.87939 q^{26} +(-4.50000 + 2.59808i) q^{27} +1.00000 q^{28} +(2.14543 - 1.80023i) q^{29} +(4.31908 - 0.761570i) q^{30} +(-0.847296 + 4.80526i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(-0.180922 - 0.497079i) q^{33} +(0.205737 + 1.16679i) q^{34} +(1.26604 + 2.19285i) q^{35} +(2.81908 + 1.02606i) q^{36} +(5.41147 - 9.37295i) q^{37} +(-4.35844 - 1.58634i) q^{38} -3.25519i q^{39} +(-1.93969 - 1.62760i) q^{40} +(-2.69459 - 2.26103i) q^{41} +1.73205i q^{42} +(4.04576 + 1.47254i) q^{43} +(-0.152704 + 0.264490i) q^{44} +(1.31908 + 7.48086i) q^{45} +(0.620615 + 1.07494i) q^{46} +(1.59967 + 9.07218i) q^{47} +(-0.592396 - 1.62760i) q^{48} +(-0.939693 + 0.342020i) q^{49} +(0.245100 - 1.39003i) q^{50} +(-2.02094 + 0.356347i) q^{51} +(-1.43969 + 1.20805i) q^{52} -11.4192 q^{53} +(-1.77719 + 4.88279i) q^{54} -0.773318 q^{55} +(0.766044 - 0.642788i) q^{56} +(2.74763 - 7.54904i) q^{57} +(0.486329 - 2.75811i) q^{58} +(-5.01114 + 1.82391i) q^{59} +(2.81908 - 3.35965i) q^{60} +(-1.96064 - 11.1193i) q^{61} +(2.43969 + 4.22567i) q^{62} -3.00000 q^{63} +(-0.500000 + 0.866025i) q^{64} +(-4.47178 - 1.62760i) q^{65} +(-0.458111 - 0.264490i) q^{66} +(-8.10014 - 6.79682i) q^{67} +(0.907604 + 0.761570i) q^{68} +(-1.86184 + 1.07494i) q^{69} +(2.37939 + 0.866025i) q^{70} +(-6.76991 + 11.7258i) q^{71} +(2.81908 - 1.02606i) q^{72} +(-0.163848 - 0.283793i) q^{73} +(-1.87939 - 10.6585i) q^{74} +(2.40760 + 0.424525i) q^{75} +(-4.35844 + 1.58634i) q^{76} +(0.0530334 - 0.300767i) q^{77} +(-2.09240 - 2.49362i) q^{78} +(9.60607 - 8.06045i) q^{79} -2.53209 q^{80} +(-8.45723 - 3.07818i) q^{81} -3.51754 q^{82} +(-1.18479 + 0.994159i) q^{83} +(1.11334 + 1.32683i) q^{84} +(-0.520945 + 2.95442i) q^{85} +(4.04576 - 1.47254i) q^{86} +(4.77719 + 0.842347i) q^{87} +(0.0530334 + 0.300767i) q^{88} +(1.89646 + 3.28476i) q^{89} +(5.81908 + 4.88279i) q^{90} +(0.939693 - 1.62760i) q^{91} +(1.16637 + 0.424525i) q^{92} +(-7.31908 + 4.22567i) q^{93} +(7.05690 + 5.92145i) q^{94} +(-8.99660 - 7.54904i) q^{95} +(-1.50000 - 0.866025i) q^{96} +(3.65910 + 1.33180i) q^{97} +(-0.500000 + 0.866025i) q^{98} +(0.458111 - 0.793471i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{5} - 3 q^{8}+O(q^{10}) $ 6 * q + 3 * q^5 - 3 * q^8	$ 6 q + 3 q^{5} - 3 q^{8} + 3 q^{10} + 6 q^{11} + 9 q^{12} - 3 q^{13} + 9 q^{15} + 9 q^{18} + 3 q^{19} + 3 q^{20} + 6 q^{22} + 6 q^{23} + 9 q^{25} - 27 q^{27} + 6 q^{28} - 3 q^{29} + 9 q^{30} - 3 q^{31} - 18 q^{33} - 9 q^{34} + 3 q^{35} + 12 q^{37} - 18 q^{38} - 6 q^{40} - 12 q^{41} - 6 q^{43} - 3 q^{44} - 9 q^{45} + 15 q^{46} + 24 q^{47} - 9 q^{51} - 3 q^{52} - 18 q^{55} + 24 q^{58} - 24 q^{59} - 3 q^{61} + 9 q^{62} - 18 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 3 q^{67} + 9 q^{68} - 45 q^{69} + 3 q^{70} - 12 q^{71} + 3 q^{73} + 18 q^{75} - 18 q^{76} - 12 q^{77} - 9 q^{78} + 33 q^{79} - 6 q^{80} + 24 q^{82} - 6 q^{86} + 18 q^{87} - 12 q^{88} + 21 q^{89} + 18 q^{90} - 12 q^{92} - 27 q^{93} + 6 q^{94} - 12 q^{95} - 9 q^{96} - 15 q^{97} - 3 q^{98} + 9 q^{99}+O(q^{100}) $ 6 * q + 3 * q^5 - 3 * q^8 + 3 * q^10 + 6 * q^11 + 9 * q^12 - 3 * q^13 + 9 * q^15 + 9 * q^18 + 3 * q^19 + 3 * q^20 + 6 * q^22 + 6 * q^23 + 9 * q^25 - 27 * q^27 + 6 * q^28 - 3 * q^29 + 9 * q^30 - 3 * q^31 - 18 * q^33 - 9 * q^34 + 3 * q^35 + 12 * q^37 - 18 * q^38 - 6 * q^40 - 12 * q^41 - 6 * q^43 - 3 * q^44 - 9 * q^45 + 15 * q^46 + 24 * q^47 - 9 * q^51 - 3 * q^52 - 18 * q^55 + 24 * q^58 - 24 * q^59 - 3 * q^61 + 9 * q^62 - 18 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 3 * q^67 + 9 * q^68 - 45 * q^69 + 3 * q^70 - 12 * q^71 + 3 * q^73 + 18 * q^75 - 18 * q^76 - 12 * q^77 - 9 * q^78 + 33 * q^79 - 6 * q^80 + 24 * q^82 - 6 * q^86 + 18 * q^87 - 12 * q^88 + 21 * q^89 + 18 * q^90 - 12 * q^92 - 27 * q^93 + 6 * q^94 - 12 * q^95 - 9 * q^96 - 15 * q^97 - 3 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$3$	1.11334	+	1.32683i	0.642788	+	0.766044i
$3$	1.11334	+	1.32683i	0.642788	+	0.766044i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	2.37939	−	0.866025i	1.06409	−	0.387298i	0.250129	−	0.968213i	$-0.419527\pi$
$5$	2.37939	−	0.866025i	1.06409	−	0.387298i	0.813965	+	0.580914i	$0.197305\pi$
$6$	1.70574	+	0.300767i	0.696364	+	0.122788i
$7$	0.173648	+	0.984808i	0.0656328	+	0.372222i
$7$	0.173648	+	0.984808i	0.0656328	+	0.372222i
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−0.520945	+	2.95442i	−0.173648	+	0.984808i
$10$	1.26604	−	2.19285i	0.400358	−	0.693441i
$11$	−0.286989	−	0.104455i	−0.0865304	−	0.0314945i	0.298392	−	0.954443i	$-0.403550\pi$
$11$	−0.286989	−	0.104455i	−0.0865304	−	0.0314945i	−0.384923	+	0.922949i	$0.625772\pi$
$12$	1.50000	−	0.866025i	0.433013	−	0.250000i
$13$	−1.43969	−	1.20805i	−0.399299	−	0.335052i	0.420924	−	0.907096i	$-0.361706\pi$
$13$	−1.43969	−	1.20805i	−0.399299	−	0.335052i	−0.820223	+	0.572044i	$0.806150\pi$
$14$	0.766044	+	0.642788i	0.204734	+	0.171792i
$15$	3.79813	+	2.19285i	0.980674	+	0.566192i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	−0.592396	+	1.02606i	−0.143677	+	0.248856i	−0.928879	−	0.370384i	$-0.879226\pi$
$17$	−0.592396	+	1.02606i	−0.143677	+	0.248856i	0.785201	+	0.619240i	$0.212559\pi$
$18$	1.50000	+	2.59808i	0.353553	+	0.612372i
$19$	−2.31908	−	4.01676i	−0.532033	−	0.921508i	−0.999301	−	0.0373922i	$-0.988095\pi$
$19$	−2.31908	−	4.01676i	−0.532033	−	0.921508i	0.467268	−	0.884116i	$-0.345238\pi$
$20$	−0.439693	−	2.49362i	−0.0983183	−	0.557591i
$21$	−1.11334	+	1.32683i	−0.242951	+	0.289538i
$22$	−0.286989	+	0.104455i	−0.0611863	+	0.0222700i
$23$	−0.215537	+	1.22237i	−0.0449426	+	0.254882i	−0.998998	−	0.0447469i	$-0.985752\pi$
$23$	−0.215537	+	1.22237i	−0.0449426	+	0.254882i	0.954056	+	0.299629i	$0.0968630\pi$
$24$	0.592396	−	1.62760i	0.120922	−	0.332232i
$25$	1.08125	−	0.907278i	0.216250	−	0.181456i
$26$	−1.87939			−0.368578
$27$	−4.50000	+	2.59808i	−0.866025	+	0.500000i
$28$	1.00000			0.188982
$29$	2.14543	−	1.80023i	0.398396	−	0.334294i	−0.421477	−	0.906839i	$-0.638488\pi$
$29$	2.14543	−	1.80023i	0.398396	−	0.334294i	0.819873	+	0.572545i	$0.194044\pi$
$30$	4.31908	−	0.761570i	0.788552	−	0.139043i
$31$	−0.847296	+	4.80526i	−0.152179	+	0.863050i	0.809141	+	0.587615i	$0.199933\pi$
$31$	−0.847296	+	4.80526i	−0.152179	+	0.863050i	−0.961320	+	0.275435i	$0.911178\pi$
$32$	−0.939693	+	0.342020i	−0.166116	+	0.0604612i
$33$	−0.180922	−	0.497079i	−0.0314945	−	0.0865304i
$34$	0.205737	+	1.16679i	0.0352836	+	0.200103i
$35$	1.26604	+	2.19285i	0.214001	+	0.370660i
$36$	2.81908	+	1.02606i	0.469846	+	0.171010i
$37$	5.41147	−	9.37295i	0.889641	−	1.54090i	0.0493405	−	0.998782i	$-0.484288\pi$
$37$	5.41147	−	9.37295i	0.889641	−	1.54090i	0.840300	−	0.542121i	$-0.182379\pi$
$38$	−4.35844	−	1.58634i	−0.707032	−	0.257339i
$39$		−	3.25519i		−	0.521248i
$40$	−1.93969	−	1.62760i	−0.306692	−	0.257345i
$41$	−2.69459	−	2.26103i	−0.420825	−	0.353114i	0.407652	−	0.913137i	$-0.366348\pi$
$41$	−2.69459	−	2.26103i	−0.420825	−	0.353114i	−0.828477	+	0.560024i	$0.810792\pi$
$42$			1.73205i			0.267261i
$43$	4.04576	+	1.47254i	0.616973	+	0.224560i	0.631551	−	0.775334i	$-0.282419\pi$
$43$	4.04576	+	1.47254i	0.616973	+	0.224560i	−0.0145788	+	0.999894i	$0.504641\pi$
$44$	−0.152704	+	0.264490i	−0.0230209	+	0.0398734i
$45$	1.31908	+	7.48086i	0.196637	+	1.11518i
$46$	0.620615	+	1.07494i	0.0915047	+	0.158491i
$47$	1.59967	+	9.07218i	0.233336	+	1.32331i	0.846090	+	0.533040i	$0.178950\pi$
$47$	1.59967	+	9.07218i	0.233336	+	1.32331i	−0.612754	+	0.790274i	$0.709938\pi$
$48$	−0.592396	−	1.62760i	−0.0855050	−	0.234923i
$49$	−0.939693	+	0.342020i	−0.134242	+	0.0488600i
$50$	0.245100	−	1.39003i	0.0346624	−	0.196580i
$51$	−2.02094	+	0.356347i	−0.282989	+	0.0498986i
$52$	−1.43969	+	1.20805i	−0.199649	+	0.167526i
$53$	−11.4192			−1.56855			−0.784275	−	0.620413i	$-0.786965\pi$
$53$	−11.4192			−1.56855			−0.784275	+	0.620413i	$0.786965\pi$
$54$	−1.77719	+	4.88279i	−0.241845	+	0.664463i
$55$	−0.773318			−0.104274
$56$	0.766044	−	0.642788i	0.102367	−	0.0858961i
$57$	2.74763	−	7.54904i	0.363932	−	0.999895i
$58$	0.486329	−	2.75811i	0.0638582	−	0.362158i
$59$	−5.01114	+	1.82391i	−0.652395	+	0.237453i	−0.646950	−	0.762533i	$-0.723956\pi$
$59$	−5.01114	+	1.82391i	−0.652395	+	0.237453i	−0.00544570	+	0.999985i	$0.501733\pi$
$60$	2.81908	−	3.35965i	0.363941	−	0.433728i
$61$	−1.96064	−	11.1193i	−0.251034	−	1.42368i	−0.806052	−	0.591845i	$-0.798400\pi$
$61$	−1.96064	−	11.1193i	−0.251034	−	1.42368i	0.555018	−	0.831839i	$-0.312711\pi$
$62$	2.43969	+	4.22567i	0.309841	+	0.536661i
$63$	−3.00000			−0.377964
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−4.47178	−	1.62760i	−0.554656	−	0.201878i
$66$	−0.458111	−	0.264490i	−0.0563896	−	0.0325565i
$67$	−8.10014	−	6.79682i	−0.989589	−	0.830364i	−0.00408103	−	0.999992i	$-0.501299\pi$
$67$	−8.10014	−	6.79682i	−0.989589	−	0.830364i	−0.985508	+	0.169628i	$0.945743\pi$
$68$	0.907604	+	0.761570i	0.110063	+	0.0923539i
$69$	−1.86184	+	1.07494i	−0.224140	+	0.129407i
$70$	2.37939	+	0.866025i	0.284391	+	0.103510i
$71$	−6.76991	+	11.7258i	−0.803441	+	1.39160i	0.113897	+	0.993493i	$0.463666\pi$
$71$	−6.76991	+	11.7258i	−0.803441	+	1.39160i	−0.917338	+	0.398108i	$0.869667\pi$
$72$	2.81908	−	1.02606i	0.332232	−	0.120922i
$73$	−0.163848	−	0.283793i	−0.0191770	−	0.0332155i	0.856278	−	0.516516i	$-0.172771\pi$
$73$	−0.163848	−	0.283793i	−0.0191770	−	0.0332155i	−0.875455	+	0.483300i	$0.839438\pi$
$74$	−1.87939	−	10.6585i	−0.218474	−	1.23903i
$75$	2.40760	+	0.424525i	0.278006	+	0.0490200i
$76$	−4.35844	+	1.58634i	−0.499947	+	0.181966i
$77$	0.0530334	−	0.300767i	0.00604372	−	0.0342756i
$78$	−2.09240	−	2.49362i	−0.236917	−	0.282347i
$79$	9.60607	−	8.06045i	1.08077	−	0.906871i	0.0847827	−	0.996399i	$-0.472980\pi$
$79$	9.60607	−	8.06045i	1.08077	−	0.906871i	0.995984	+	0.0895283i	$0.0285360\pi$
$80$	−2.53209			−0.283096
$81$	−8.45723	−	3.07818i	−0.939693	−	0.342020i
$82$	−3.51754			−0.388447
$83$	−1.18479	+	0.994159i	−0.130048	+	0.109123i	−0.705492	−	0.708718i	$-0.749274\pi$
$83$	−1.18479	+	0.994159i	−0.130048	+	0.109123i	0.575444	+	0.817841i	$0.304829\pi$
$84$	1.11334	+	1.32683i	0.121475	+	0.144769i
$85$	−0.520945	+	2.95442i	−0.0565044	+	0.320452i
$86$	4.04576	−	1.47254i	0.436265	−	0.158788i
$87$	4.77719	+	0.842347i	0.512168	+	0.0903091i
$88$	0.0530334	+	0.300767i	0.00565338	+	0.0320619i
$89$	1.89646	+	3.28476i	0.201024	+	0.348184i	0.948859	−	0.315701i	$-0.102240\pi$
$89$	1.89646	+	3.28476i	0.201024	+	0.348184i	−0.747834	+	0.663885i	$0.768906\pi$
$90$	5.81908	+	4.88279i	0.613385	+	0.514691i
$91$	0.939693	−	1.62760i	0.0985066	−	0.170618i
$92$	1.16637	+	0.424525i	0.121603	+	0.0442598i
$93$	−7.31908	+	4.22567i	−0.758953	+	0.438182i
$94$	7.05690	+	5.92145i	0.727864	+	0.610750i
$95$	−8.99660	−	7.54904i	−0.923031	−	0.774515i
$96$	−1.50000	−	0.866025i	−0.153093	−	0.0883883i
$97$	3.65910	+	1.33180i	0.371525	+	0.135224i	0.521033	−	0.853536i	$-0.325547\pi$
$97$	3.65910	+	1.33180i	0.371525	+	0.135224i	−0.149508	+	0.988761i	$0.547769\pi$
$98$	−0.500000	+	0.866025i	−0.0505076	+	0.0874818i
$99$	0.458111	−	0.793471i	0.0460419	−	0.0797469i
$100$	−0.705737	−	1.22237i	−0.0705737	−	0.122237i
$101$	2.68479	+	15.2262i	0.267147	+	1.51507i	0.762851	+	0.646574i	$0.223799\pi$
$101$	2.68479	+	15.2262i	0.267147	+	1.51507i	−0.495705	+	0.868491i	$0.665090\pi$
$102$	−1.31908	+	1.57202i	−0.130608	+	0.155653i
$103$	−12.6630	+	4.60894i	−1.24772	+	0.454133i	−0.879630	−	0.475658i	$-0.842210\pi$
$103$	−12.6630	+	4.60894i	−1.24772	+	0.454133i	−0.368089	+	0.929791i	$0.619988\pi$
$104$	−0.326352	+	1.85083i	−0.0320014	+	0.181489i
$105$	−1.50000	+	4.12122i	−0.146385	+	0.402190i
$106$	−8.74763	+	7.34013i	−0.849645	+	0.712936i
$107$	7.61587			0.736254			0.368127	−	0.929776i	$-0.379999\pi$
$107$	7.61587			0.736254			0.368127	+	0.929776i	$0.379999\pi$
$108$	1.77719	+	4.88279i	0.171010	+	0.469846i
$109$	5.93582			0.568549			0.284274	−	0.958743i	$-0.408247\pi$
$109$	5.93582			0.568549			0.284274	+	0.958743i	$0.408247\pi$
$110$	−0.592396	+	0.497079i	−0.0564828	+	0.0473947i
$111$	18.4611	−	3.25519i	1.75225	−	0.308969i
$112$	0.173648	−	0.984808i	0.0164082	−	0.0930556i
$113$	10.4153	−	3.79088i	0.979793	−	0.356616i	0.198033	−	0.980195i	$-0.436545\pi$
$113$	10.4153	−	3.79088i	0.979793	−	0.356616i	0.781760	+	0.623580i	$0.214322\pi$
$114$	−2.74763	−	7.54904i	−0.257339	−	0.707032i
$115$	0.545759	+	3.09516i	0.0508923	+	0.288625i
$116$	−1.40033	−	2.42544i	−0.130017	−	0.225197i
$117$	4.31908	−	3.62414i	0.399299	−	0.335052i
$118$	−2.66637	+	4.61830i	−0.245460	+	0.425149i
$119$	−1.11334	−	0.405223i	−0.102060	−	0.0371467i
$120$		−	4.38571i		−	0.400358i
$121$	−8.35504	−	7.01071i	−0.759549	−	0.637337i
$122$	−8.64930	−	7.25762i	−0.783071	−	0.657074i
$123$		−	6.09256i		−	0.549348i
$124$	4.58512	+	1.66885i	0.411756	+	0.149867i
$125$	−4.54323	+	7.86911i	−0.406359	+	0.703835i
$126$	−2.29813	+	1.92836i	−0.204734	+	0.171792i
$127$	6.21301	+	10.7613i	0.551316	+	0.954907i	0.998180	+	0.0603049i	$0.0192073\pi$
$127$	6.21301	+	10.7613i	0.551316	+	0.954907i	−0.446864	+	0.894602i	$0.647459\pi$
$128$	0.173648	+	0.984808i	0.0153485	+	0.0870455i
$129$	2.55051	+	7.00746i	0.224560	+	0.616973i
$130$	−4.47178	+	1.62760i	−0.392201	+	0.142750i
$131$	−0.592396	+	3.35965i	−0.0517579	+	0.293534i	−0.999689	−	0.0249421i	$-0.992060\pi$
$131$	−0.592396	+	3.35965i	−0.0517579	+	0.293534i	0.947931	+	0.318476i	$0.103171\pi$
$132$	−0.520945	+	0.0918566i	−0.0453424	+	0.00799509i
$133$	3.55303	−	2.98135i	0.308087	−	0.258516i
$134$	−10.5740			−0.913453
$135$	−8.45723	+	10.0789i	−0.727883	+	0.867457i
$136$	1.18479			0.101595
$137$	14.4042	−	12.0866i	1.23063	−	1.03262i	0.232436	−	0.972612i	$-0.425330\pi$
$137$	14.4042	−	12.0866i	1.23063	−	1.03262i	0.998198	−	0.0600128i	$-0.0191142\pi$
$138$	−0.735300	+	2.02022i	−0.0625929	+	0.171972i
$139$	0.112159	−	0.636084i	0.00951318	−	0.0539519i	−0.979682	−	0.200559i	$-0.935724\pi$
$139$	0.112159	−	0.636084i	0.00951318	−	0.0539519i	0.989195	+	0.146607i	$0.0468353\pi$
$140$	2.37939	−	0.866025i	0.201095	−	0.0731925i
$141$	−10.2562	+	12.2229i	−0.863732	+	1.02936i
$142$	2.35117	+	13.3341i	0.197306	+	1.11898i
$143$	0.286989	+	0.497079i	0.0239992	+	0.0415679i
$144$	1.50000	−	2.59808i	0.125000	−	0.216506i
$145$	3.54576	−	6.14144i	0.294459	−	0.510018i
$146$	−0.307934	−	0.112079i	−0.0254848	−	0.00927569i
$147$	−1.50000	−	0.866025i	−0.123718	−	0.0714286i
$148$	−8.29086	−	6.95686i	−0.681504	−	0.571850i
$149$	−15.3498	−	12.8800i	−1.25751	−	1.05517i	−0.995943	−	0.0899869i	$-0.971317\pi$
$149$	−15.3498	−	12.8800i	−1.25751	−	1.05517i	−0.261564	−	0.965186i	$-0.584238\pi$
$150$	2.11721	−	1.22237i	0.172870	−	0.0998063i
$151$	19.5719	+	7.12360i	1.59274	+	0.579710i	0.977924	−	0.208961i	$-0.0670080\pi$
$151$	19.5719	+	7.12360i	1.59274	+	0.579710i	0.614816	+	0.788671i	$0.289230\pi$
$152$	−2.31908	+	4.01676i	−0.188102	+	0.325802i
$153$	−2.72281	−	2.28471i	−0.220126	−	0.184708i
$154$	−0.152704	−	0.264490i	−0.0123052	−	0.0213132i
$155$	2.14543	+	12.1673i	0.172325	+	0.977304i
$156$	−3.20574	−	0.565258i	−0.256664	−	0.0452569i
$157$	0.229208	−	0.0834248i	0.0182928	−	0.00665803i	−0.332858	−	0.942977i	$-0.608013\pi$
$157$	0.229208	−	0.0834248i	0.0182928	−	0.00665803i	0.351150	+	0.936319i	$0.385791\pi$
$158$	2.17752	−	12.3493i	0.173234	−	0.982459i
$159$	−12.7135	−	15.1513i	−1.00824	−	1.20158i
$160$	−1.93969	+	1.62760i	−0.153346	+	0.128673i
$161$	−1.24123			−0.0978226
$162$	−8.45723	+	3.07818i	−0.664463	+	0.241845i
$163$	7.49525			0.587073			0.293537	−	0.955948i	$-0.405168\pi$
$163$	7.49525			0.587073			0.293537	+	0.955948i	$0.405168\pi$
$164$	−2.69459	+	2.26103i	−0.210412	+	0.176557i
$165$	−0.860967	−	1.02606i	−0.0670262	−	0.0798787i
$166$	−0.268571	+	1.52314i	−0.0208451	+	0.118219i
$167$	8.46926	−	3.08256i	0.655371	−	0.238535i	0.00713425	−	0.999975i	$-0.497729\pi$
$167$	8.46926	−	3.08256i	0.655371	−	0.238535i	0.648236	+	0.761439i	$0.275507\pi$
$168$	1.70574	+	0.300767i	0.131600	+	0.0232047i
$169$	−1.64409	−	9.32407i	−0.126468	−	0.717236i
$170$	1.50000	+	2.59808i	0.115045	+	0.199263i
$171$	13.0753	−	4.75903i	0.999895	−	0.363932i
$172$	2.15270	−	3.72859i	0.164142	−	0.284302i
$173$	10.6775	+	3.88630i	0.811797	+	0.295470i	0.714366	−	0.699772i	$-0.246715\pi$
$173$	10.6775	+	3.88630i	0.811797	+	0.295470i	0.0974309	+	0.995242i	$0.468938\pi$
$174$	4.20099	−	2.42544i	0.318476	−	0.183872i
$175$	1.08125	+	0.907278i	0.0817350	+	0.0685838i
$176$	0.233956	+	0.196312i	0.0176351	+	0.0147976i
$177$	−7.99912	−	4.61830i	−0.601251	−	0.347132i
$178$	3.56418	+	1.29725i	0.267146	+	0.0972333i
$179$	2.77584	−	4.80790i	0.207476	−	0.359360i	−0.743443	−	0.668800i	$-0.766808\pi$
$179$	2.77584	−	4.80790i	0.207476	−	0.359360i	0.950919	+	0.309440i	$0.100142\pi$
$180$	7.59627			0.566192
$181$	6.48680	+	11.2355i	0.482160	+	0.835125i	0.999790	−	0.0204790i	$-0.00651914\pi$
$181$	6.48680	+	11.2355i	0.482160	+	0.835125i	−0.517631	+	0.855604i	$0.673186\pi$
$182$	−0.326352	−	1.85083i	−0.0241908	−	0.137193i
$183$	12.5706	−	14.9810i	0.929244	−	1.10743i
$184$	1.16637	−	0.424525i	0.0859862	−	0.0312964i
$185$	4.75877	−	26.9883i	0.349872	−	1.98422i
$186$	−2.89053	+	7.94166i	−0.211944	+	0.582311i
$187$	0.277189	−	0.232589i	0.0202701	−	0.0170086i
$188$	9.21213			0.671864
$189$	−3.34002	−	3.98048i	−0.242951	−	0.289538i
$190$	−11.7442			−0.852015
$191$	2.10741	−	1.76833i	0.152487	−	0.127952i	−0.563353	−	0.826217i	$-0.690489\pi$
$191$	2.10741	−	1.76833i	0.152487	−	0.127952i	0.715839	+	0.698265i	$0.246044\pi$
$192$	−1.70574	+	0.300767i	−0.123101	+	0.0217060i
$193$	−0.503870	+	2.85759i	−0.0362694	+	0.205694i	−0.997557	−	0.0698517i	$-0.977747\pi$
$193$	−0.503870	+	2.85759i	−0.0362694	+	0.205694i	0.961288	+	0.275546i	$0.0888585\pi$
$194$	3.65910	−	1.33180i	0.262708	−	0.0956179i
$195$	−2.81908	−	7.74535i	−0.201878	−	0.554656i
$196$	0.173648	+	0.984808i	0.0124034	+	0.0703434i
$197$	5.56670	+	9.64181i	0.396611	+	0.686951i	0.993305	−	0.115518i	$-0.0368528\pi$
$197$	5.56670	+	9.64181i	0.396611	+	0.686951i	−0.596694	+	0.802469i	$0.703519\pi$
$198$	−0.159100	−	0.902302i	−0.0113068	−	0.0641238i
$199$	12.2062	−	21.1418i	0.865275	−	1.49870i	−0.00149916	−	0.999999i	$-0.500477\pi$
$199$	12.2062	−	21.1418i	0.865275	−	1.49870i	0.866774	−	0.498701i	$-0.166189\pi$
$200$	−1.32635	−	0.482753i	−0.0937872	−	0.0341358i
$201$		−	18.3147i		−	1.29182i
$202$	11.8439	+	9.93821i	0.833333	+	0.699250i
$203$	2.14543	+	1.80023i	0.150580	+	0.126351i
$204$			2.05212i			0.143677i
$205$	−8.36959	−	3.04628i	−0.584557	−	0.212761i
$206$	−6.73783	+	11.6703i	−0.469447	+	0.813105i
$207$	−3.49912	−	1.27358i	−0.243206	−	0.0885197i
$208$	0.939693	+	1.62760i	0.0651560	+	0.112853i
$209$	0.245977	+	1.39501i	0.0170146	+	0.0964946i
$210$	1.50000	+	4.12122i	0.103510	+	0.284391i
$211$	10.7258	−	3.90387i	0.738395	−	0.268754i	0.0546809	−	0.998504i	$-0.482586\pi$
$211$	10.7258	−	3.90387i	0.738395	−	0.268754i	0.683714	+	0.729750i	$0.260364\pi$
$212$	−1.98293	+	11.2457i	−0.136188	+	0.772360i
$213$	−23.0954	+	4.07234i	−1.58247	+	0.279032i
$214$	5.83409	−	4.89538i	0.398810	−	0.334642i
$215$	10.9017			0.743488
$216$	4.50000	+	2.59808i	0.306186	+	0.176777i
$217$	−4.87939			−0.331234
$218$	4.54710	−	3.81547i	0.307969	−	0.258416i
$219$	0.194126	−	0.533356i	0.0131178	−	0.0360409i
$220$	−0.134285	+	0.761570i	−0.00905352	+	0.0513450i
$221$	2.09240	−	0.761570i	0.140750	−	0.0512287i
$222$	12.0496	−	14.3602i	0.808718	−	0.963793i
$223$	4.12361	+	23.3861i	0.276137	+	1.56605i	0.735326	+	0.677713i	$0.237029\pi$
$223$	4.12361	+	23.3861i	0.276137	+	1.56605i	−0.459189	+	0.888339i	$0.651860\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$	2.11721	+	3.66712i	0.141147	+	0.244474i
$226$	5.54189	−	9.59883i	0.368641	−	0.638505i
$227$	13.7208	+	4.99395i	0.910678	+	0.331460i	0.754524	−	0.656273i	$-0.227868\pi$
$227$	13.7208	+	4.99395i	0.910678	+	0.331460i	0.156155	+	0.987733i	$0.450090\pi$
$228$	−6.95723	−	4.01676i	−0.460754	−	0.266016i
$229$	−14.6591	−	12.3004i	−0.968701	−	0.812836i	0.0136459	−	0.999907i	$-0.495656\pi$
$229$	−14.6591	−	12.3004i	−0.968701	−	0.812836i	−0.982346	+	0.187071i	$0.940101\pi$
$230$	2.40760	+	2.02022i	0.158753	+	0.133209i
$231$	0.458111	−	0.264490i	0.0301415	−	0.0174022i
$232$	−2.63176	−	0.957882i	−0.172783	−	0.0628880i
$233$	9.65183	−	16.7175i	0.632312	−	1.09520i	−0.354766	−	0.934955i	$-0.615439\pi$
$233$	9.65183	−	16.7175i	0.632312	−	1.09520i	0.987078	−	0.160242i	$-0.0512273\pi$
$234$	0.979055	−	5.55250i	0.0640029	−	0.362978i
$235$	11.6630	+	20.2009i	0.760808	+	1.31776i
$236$	0.926022	+	5.25173i	0.0602789	+	0.341859i
$237$	21.3897	+	3.77157i	1.38941	+	0.244990i
$238$	−1.11334	+	0.405223i	−0.0721672	+	0.0262667i
$239$	−1.67412	+	9.49438i	−0.108289	+	0.614140i	0.881566	+	0.472061i	$0.156490\pi$
$239$	−1.67412	+	9.49438i	−0.108289	+	0.614140i	−0.989855	+	0.142079i	$0.954621\pi$
$240$	−2.81908	−	3.35965i	−0.181971	−	0.216864i
$241$	−18.9119	+	15.8690i	−1.21823	+	1.02221i	−0.219310	+	0.975655i	$0.570380\pi$
$241$	−18.9119	+	15.8690i	−1.21823	+	1.02221i	−0.998916	+	0.0465570i	$0.985175\pi$
$242$	−10.9067			−0.701111
$243$	−5.33157	−	14.6484i	−0.342020	−	0.939693i
$244$	−11.2909			−0.722823
$245$	−1.93969	+	1.62760i	−0.123922	+	0.103983i
$246$	−3.91622	−	4.66717i	−0.249689	−	0.297568i
$247$	−1.51367	+	8.58445i	−0.0963126	+	0.546216i
$248$	4.58512	−	1.66885i	0.291156	−	0.105972i
$249$	−2.63816	−	0.465178i	−0.167186	−	0.0294795i
$250$	1.57785	+	8.94842i	0.0997919	+	0.565948i
$251$	−2.65657	−	4.60132i	−0.167681	−	0.290433i	0.769923	−	0.638137i	$-0.220295\pi$
$251$	−2.65657	−	4.60132i	−0.167681	−	0.290433i	−0.937604	+	0.347704i	$0.886961\pi$
$252$	−0.520945	+	2.95442i	−0.0328164	+	0.186111i
$253$	0.189540	−	0.328293i	0.0119163	−	0.0206396i
$254$	11.6766	+	4.24995i	0.732658	+	0.266666i
$255$	−4.50000	+	2.59808i	−0.281801	+	0.162698i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	6.74691	+	5.66133i	0.420861	+	0.353144i	0.828490	−	0.560003i	$-0.189200\pi$
$257$	6.74691	+	5.66133i	0.420861	+	0.353144i	−0.407630	+	0.913147i	$0.633645\pi$
$258$	6.45811	+	3.72859i	0.402064	+	0.232132i
$259$	10.1702	+	3.70167i	0.631948	+	0.230010i
$260$	−2.37939	+	4.12122i	−0.147563	+	0.255587i
$261$	4.20099	+	7.27633i	0.260035	+	0.450393i
$262$	1.70574	+	2.95442i	0.105381	+	0.182525i
$263$	0.950837	+	5.39246i	0.0586311	+	0.332514i	0.999988	−	0.00489894i	$-0.00155939\pi$
$263$	0.950837	+	5.39246i	0.0586311	+	0.332514i	−0.941357	+	0.337413i	$0.890448\pi$
$264$	−0.340022	+	0.405223i	−0.0209269	+	0.0249397i
$265$	−27.1707	+	9.88933i	−1.66908	+	0.607497i
$266$	0.805407	−	4.56769i	0.0493827	−	0.280063i
$267$	−2.24691	+	6.17334i	−0.137509	+	0.377802i
$268$	−8.10014	+	6.79682i	−0.494795	+	0.415182i
$269$	14.0942			0.859339			0.429669	−	0.902986i	$-0.358630\pi$
$269$	14.0942			0.859339			0.429669	+	0.902986i	$0.358630\pi$
$270$			13.1571i			0.800717i
$271$	−30.6013			−1.85890			−0.929449	−	0.368951i	$-0.879717\pi$
$271$	−30.6013			−1.85890			−0.929449	+	0.368951i	$0.879717\pi$
$272$	0.907604	−	0.761570i	0.0550316	−	0.0461770i
$273$	3.20574	−	0.565258i	0.194020	−	0.0342110i
$274$	3.26517	−	18.5177i	0.197256	−	1.11869i
$275$	−0.405078	+	0.147436i	−0.0244271	+	0.00889073i
$276$	0.735300	+	2.02022i	0.0442598	+	0.121603i
$277$	−2.46657	−	13.9886i	−0.148202	−	0.840493i	−0.964741	−	0.263203i	$-0.915221\pi$
$277$	−2.46657	−	13.9886i	−0.148202	−	0.840493i	0.816539	−	0.577290i	$-0.195890\pi$
$278$	−0.322948	−	0.559363i	−0.0193691	−	0.0335484i
$279$	−13.7554	−	5.00654i	−0.823512	−	0.299734i
$280$	1.26604	−	2.19285i	0.0756606	−	0.131048i
$281$	25.6805	+	9.34694i	1.53197	+	0.557592i	0.964103	−	0.265528i	$-0.0855463\pi$
$281$	25.6805	+	9.34694i	1.53197	+	0.557592i	0.567868	+	0.823120i	$0.307768\pi$
$282$			15.9559i			0.950159i
$283$	15.1382	+	12.7024i	0.899870	+	0.755081i	0.970165	−	0.242446i	$-0.0779496\pi$
$283$	15.1382	+	12.7024i	0.899870	+	0.755081i	−0.0702950	+	0.997526i	$0.522394\pi$
$284$	10.3721	+	8.70323i	0.615472	+	0.516442i
$285$		−	20.3416i		−	1.20493i
$286$	0.539363	+	0.196312i	0.0318932	+	0.0116082i
$287$	1.75877	−	3.04628i	0.103817	−	0.179816i
$288$	−0.520945	−	2.95442i	−0.0306970	−	0.174091i
$289$	7.79813	+	13.5068i	0.458714	+	0.794515i
$290$	−1.23143	−	6.98378i	−0.0723120	−	0.410102i
$291$	2.30675	+	6.33775i	0.135224	+	0.371525i
$292$	−0.307934	+	0.112079i	−0.0180204	+	0.00655891i
$293$	−1.89528	+	10.7487i	−0.110723	+	0.627943i	0.878056	+	0.478558i	$0.158840\pi$
$293$	−1.89528	+	10.7487i	−0.110723	+	0.627943i	−0.988779	+	0.149385i	$0.952271\pi$
$294$	−1.70574	+	0.300767i	−0.0994806	+	0.0175411i
$295$	−10.3439	+	8.67956i	−0.602245	+	0.505343i
$296$	−10.8229			−0.629071
$297$	1.56283	−	0.275570i	0.0906848	−	0.0159902i
$298$	−20.0378			−1.16076
$299$	1.78699	−	1.49946i	0.103344	−	0.0867161i
$300$	0.836152	−	2.29731i	0.0482753	−	0.132635i
$301$	−0.747626	+	4.24000i	−0.0430925	+	0.244389i
$302$	19.5719	−	7.12360i	1.12624	−	0.409917i
$303$	−17.2135	+	20.5142i	−0.988888	+	1.17851i
$304$	0.805407	+	4.56769i	0.0461933	+	0.261975i
$305$	−14.2947	−	24.7592i	−0.818514	−	1.41771i
$306$	−3.55438			−0.203190
$307$	10.4820	−	18.1554i	0.598242	−	1.03619i	−0.394838	−	0.918751i	$-0.629199\pi$
$307$	10.4820	−	18.1554i	0.598242	−	1.03619i	0.993081	−	0.117435i	$-0.0374672\pi$
$308$	−0.286989	−	0.104455i	−0.0163527	−	0.00595190i
$309$	−20.2135	−	11.6703i	−1.14990	−	0.663898i
$310$	9.46451	+	7.94166i	0.537548	+	0.451056i
$311$	−13.9363	−	11.6939i	−0.790254	−	0.663102i	0.155554	−	0.987827i	$-0.450284\pi$
$311$	−13.9363	−	11.6939i	−0.790254	−	0.663102i	−0.945808	+	0.324725i	$0.894728\pi$
$312$	−2.81908	+	1.62760i	−0.159599	+	0.0921444i
$313$	−16.8824	−	6.14468i	−0.954248	−	0.347318i	−0.182471	−	0.983211i	$-0.558410\pi$
$313$	−16.8824	−	6.14468i	−0.954248	−	0.347318i	−0.771777	+	0.635893i	$0.780632\pi$
$314$	0.121959	−	0.211239i	0.00688254	−	0.0119209i
$315$	−7.13816	+	2.59808i	−0.402190	+	0.146385i
$316$	−6.26991	−	10.8598i	−0.352710	−	0.610912i
$317$	−2.85369	−	16.1841i	−0.160279	−	0.908989i	−0.953799	−	0.300445i	$-0.902865\pi$
$317$	−2.85369	−	16.1841i	−0.160279	−	0.908989i	0.793520	−	0.608544i	$-0.208246\pi$
$318$	−19.4782	−	3.43453i	−1.09228	−	0.192599i
$319$	−0.803758	+	0.292544i	−0.0450018	+	0.0163793i
$320$	−0.439693	+	2.49362i	−0.0245796	+	0.139398i
$321$	8.47906	+	10.1049i	0.473255	+	0.564003i
$322$	−0.950837	+	0.797847i	−0.0529881	+	0.0444623i
$323$	5.49525			0.305764
$324$	−4.50000	+	7.79423i	−0.250000	+	0.433013i
$325$	−2.65270			−0.147146
$326$	5.74170	−	4.81786i	0.318003	−	0.266836i
$327$	6.60859	+	7.87581i	0.365456	+	0.435534i
$328$	−0.610815	+	3.46410i	−0.0337266	+	0.191273i
$329$	−8.65657	+	3.15074i	−0.477252	+	0.173706i
$330$	−1.31908	−	0.232589i	−0.0726128	−	0.0128036i
$331$	1.18345	+	6.71167i	0.0650482	+	0.368907i	0.999904	+	0.0138782i	$0.00441772\pi$
$331$	1.18345	+	6.71167i	0.0650482	+	0.368907i	−0.934855	+	0.355028i	$0.884471\pi$
$332$	0.773318	+	1.33943i	0.0424414	+	0.0735106i
$333$	24.8726	+	20.8706i	1.36301	+	1.14370i
$334$	4.50640	−	7.80531i	0.246579	−	0.427087i
$335$	−25.1596	−	9.15733i	−1.37461	−	0.500319i
$336$	1.50000	−	0.866025i	0.0818317	−	0.0472456i
$337$	−1.80335	−	1.51319i	−0.0982346	−	0.0824286i	0.592348	−	0.805682i	$-0.298201\pi$
$337$	−1.80335	−	1.51319i	−0.0982346	−	0.0824286i	−0.690582	+	0.723254i	$0.742646\pi$
$338$	−7.25284	−	6.08586i	−0.394503	−	0.331027i
$339$	16.6257	+	9.59883i	0.902982	+	0.521337i
$340$	2.81908	+	1.02606i	0.152886	+	0.0556459i
$341$	0.745100	−	1.29055i	0.0403494	−	0.0698872i
$342$	6.95723	−	12.0503i	0.376204	−	0.651605i
$343$	−0.500000	−	0.866025i	−0.0269975	−	0.0467610i
$344$	−0.747626	−	4.24000i	−0.0403093	−	0.228605i
$345$	−3.49912	+	4.17009i	−0.188386	+	0.224510i
$346$	10.6775	−	3.88630i	0.574027	−	0.208929i
$347$	−1.60947	+	9.12776i	−0.0864009	+	0.490004i	0.910645	+	0.413191i	$0.135586\pi$
$347$	−1.60947	+	9.12776i	−0.0864009	+	0.490004i	−0.997045	+	0.0768133i	$0.975525\pi$
$348$	1.65910	−	4.55834i	0.0889371	−	0.244353i
$349$	−7.23577	+	6.07153i	−0.387322	+	0.325001i	−0.815569	−	0.578660i	$-0.803576\pi$
$349$	−7.23577	+	6.07153i	−0.387322	+	0.325001i	0.428247	+	0.903662i	$0.359131\pi$
$350$	1.41147			0.0754465
$351$	9.61721	+	1.69577i	0.513329	+	0.0905137i
$352$	0.305407			0.0162783
$353$	14.6250	−	12.2718i	0.778408	−	0.653162i	−0.164439	−	0.986387i	$-0.552582\pi$
$353$	14.6250	−	12.2718i	0.778408	−	0.653162i	0.942847	+	0.333226i	$0.108137\pi$
$354$	−9.09627	+	1.60392i	−0.483461	+	0.0852472i
$355$	−5.95336	+	33.7632i	−0.315972	+	1.79196i
$356$	3.56418	−	1.29725i	0.188901	−	0.0687544i
$357$	−0.701867	−	1.92836i	−0.0371467	−	0.102060i
$358$	−0.964041	−	5.46735i	−0.0509511	−	0.288958i
$359$	3.12449	+	5.41177i	0.164904	+	0.285622i	0.936621	−	0.350344i	$-0.113935\pi$
$359$	3.12449	+	5.41177i	0.164904	+	0.285622i	−0.771717	+	0.635966i	$0.780602\pi$
$360$	5.81908	−	4.88279i	0.306692	−	0.257345i
$361$	−1.25624	+	2.17588i	−0.0661181	+	0.114520i
$362$	12.1912	+	4.43723i	0.640755	+	0.233216i
$363$		−	18.8910i		−	0.991521i
$364$	−1.43969	−	1.20805i	−0.0754604	−	0.0633188i
$365$	−0.635630	−	0.533356i	−0.0332704	−	0.0279172i
$366$		−	19.5563i		−	1.02223i
$367$	−24.0043	−	8.73686i	−1.25302	−	0.456061i	−0.371596	−	0.928394i	$-0.621189\pi$
$367$	−24.0043	−	8.73686i	−1.25302	−	0.456061i	−0.881420	+	0.472334i	$0.843412\pi$
$368$	0.620615	−	1.07494i	0.0323518	−	0.0560349i
$369$	8.08378	−	6.78310i	0.420825	−	0.353114i
$370$	−13.7023	−	23.7331i	−0.712350	−	1.23383i
$371$	−1.98293	−	11.2457i	−0.102948	−	0.583849i
$372$	2.89053	+	7.94166i	0.149867	+	0.411756i
$373$	4.09879	−	1.49184i	0.212227	−	0.0772445i	−0.233719	−	0.972304i	$-0.575089\pi$
$373$	4.09879	−	1.49184i	0.212227	−	0.0772445i	0.445946	+	0.895060i	$0.352867\pi$
$374$	0.0628336	−	0.356347i	0.00324905	−	0.0184263i
$375$	−15.4991	+	2.73291i	−0.800371	+	0.141127i
$376$	7.05690	−	5.92145i	0.363932	−	0.305375i
$377$	−5.26352			−0.271085
$378$	−5.11721	−	0.902302i	−0.263201	−	0.0464094i
$379$	−10.4115			−0.534802			−0.267401	−	0.963585i	$-0.586165\pi$
$379$	−10.4115			−0.534802			−0.267401	+	0.963585i	$0.586165\pi$
$380$	−8.99660	+	7.54904i	−0.461516	+	0.387258i
$381$	−7.36113	+	20.2245i	−0.377122	+	1.03613i
$382$	0.477711	−	2.70924i	0.0244418	−	0.138617i
$383$	−32.5869	+	11.8607i	−1.66511	+	0.606052i	−0.991154	−	0.132715i	$-0.957630\pi$
$383$	−32.5869	+	11.8607i	−1.66511	+	0.606052i	−0.673960	+	0.738768i	$0.735408\pi$
$384$	−1.11334	+	1.32683i	−0.0568149	+	0.0677094i
$385$	−0.134285	−	0.761570i	−0.00684381	−	0.0388132i
$386$	1.45084	+	2.51292i	0.0738457	+	0.127904i
$387$	−6.45811	+	11.1858i	−0.328284	+	0.568605i
$388$	1.94697	−	3.37225i	0.0988423	−	0.171200i
$389$	20.6758	+	7.52536i	1.04830	+	0.381551i	0.808022	−	0.589152i	$-0.200538\pi$
$389$	20.6758	+	7.52536i	1.04830	+	0.381551i	0.240281	+	0.970703i	$0.422760\pi$
$390$	−7.13816	−	4.12122i	−0.361455	−	0.208686i
$391$	−1.12654	−	0.945283i	−0.0569718	−	0.0478050i
$392$	0.766044	+	0.642788i	0.0386911	+	0.0324657i
$393$	−5.11721	+	2.95442i	−0.258129	+	0.149031i
$394$	10.4620	+	3.80785i	0.527067	+	0.191837i
$395$	15.8760	−	27.4980i	0.798807	−	1.38357i
$396$	−0.701867	−	0.588936i	−0.0352701	−	0.0295952i
$397$	−10.3032	−	17.8456i	−0.517102	−	0.895647i	−0.999803	−	0.0198617i	$-0.993677\pi$
$397$	−10.3032	−	17.8456i	−0.517102	−	0.895647i	0.482701	−	0.875785i	$-0.339656\pi$
$398$	−4.23917	−	24.0415i	−0.212490	−	1.20509i
$399$	7.91147	+	1.39501i	0.396069	+	0.0698377i
$400$	−1.32635	+	0.482753i	−0.0663176	+	0.0241376i
$401$	−5.05257	+	28.6545i	−0.252313	+	1.43094i	0.550563	+	0.834793i	$0.314413\pi$
$401$	−5.05257	+	28.6545i	−0.252313	+	1.43094i	−0.802876	+	0.596145i	$0.796698\pi$
$402$	−11.7724	−	14.0298i	−0.587156	−	0.699745i
$403$	7.02481	−	5.89452i	0.349931	−	0.293627i
$404$	15.4611			0.769219
$405$	−22.7888			−1.13238
$406$	2.80066			0.138994
$407$	−2.53209	+	2.12467i	−0.125511	+	0.105316i
$408$	1.31908	+	1.57202i	0.0653041	+	0.0778264i
$409$	2.04142	−	11.5775i	0.100942	−	0.572470i	−0.891822	−	0.452386i	$-0.850573\pi$
$409$	2.04142	−	11.5775i	0.100942	−	0.572470i	0.992764	−	0.120083i	$-0.0383161\pi$
$410$	−8.36959	+	3.04628i	−0.413344	+	0.150445i
$411$	32.0736	+	5.65544i	1.58207	+	0.278962i
$412$	2.34002	+	13.2709i	0.115285	+	0.653812i
$413$	−2.66637	−	4.61830i	−0.131204	−	0.227251i
$414$	−3.49912	+	1.27358i	−0.171972	+	0.0625929i
$415$	−1.95811	+	3.39155i	−0.0961199	+	0.166485i
$416$	1.76604	+	0.642788i	0.0865875	+	0.0315153i
$417$	0.968845	−	0.559363i	0.0474445	−	0.0273921i
$418$	1.08512	+	0.910526i	0.0530751	+	0.0445353i
$419$	−15.2554	−	12.8008i	−0.745273	−	0.625359i	0.188975	−	0.981982i	$-0.439484\pi$
$419$	−15.2554	−	12.8008i	−0.745273	−	0.625359i	−0.934248	+	0.356623i	$0.883928\pi$
$420$	3.79813	+	2.19285i	0.185330	+	0.107000i
$421$	−10.6985	−	3.89392i	−0.521411	−	0.189778i	0.0678881	−	0.997693i	$-0.478374\pi$
$421$	−10.6985	−	3.89392i	−0.521411	−	0.189778i	−0.589299	+	0.807915i	$0.700596\pi$
$422$	5.70708	−	9.88495i	0.277816	−	0.481192i
$423$	−27.6364			−1.34373
$424$	5.70961	+	9.88933i	0.277283	+	0.480268i
$425$	0.290393	+	1.64690i	0.0140861	+	0.0798863i
$426$	−15.0744	+	17.9650i	−0.730359	+	0.870408i
$427$	10.6099	−	3.86170i	0.513451	−	0.186881i
$428$	1.32248	−	7.50016i	0.0639246	−	0.362534i
$429$	−0.340022	+	0.934204i	−0.0164164	+	0.0451038i
$430$	8.35117	−	7.00746i	0.402729	−	0.337930i
$431$	−28.5398			−1.37472			−0.687358	−	0.726319i	$-0.741229\pi$
$431$	−28.5398			−1.37472			−0.687358	+	0.726319i	$0.741229\pi$
$432$	5.11721	−	0.902302i	0.246202	−	0.0434120i
$433$	−12.4388			−0.597771			−0.298886	−	0.954289i	$-0.596615\pi$
$433$	−12.4388			−0.597771			−0.298886	+	0.954289i	$0.596615\pi$
$434$	−3.73783	+	3.13641i	−0.179421	+	0.150552i
$435$	12.0963	−	2.13290i	0.579972	−	0.102265i
$436$	1.03074	−	5.84564i	0.0493637	−	0.279956i
$437$	5.40983	−	1.96902i	0.258787	−	0.0941908i
$438$	−0.194126	−	0.533356i	−0.00927569	−	0.0254848i
$439$	6.32651	+	35.8794i	0.301948	+	1.71243i	0.637533	+	0.770423i	$0.279955\pi$
$439$	6.32651	+	35.8794i	0.301948	+	1.71243i	−0.335585	+	0.942010i	$0.608934\pi$
$440$	0.386659	+	0.669713i	0.0184333	+	0.0319273i
$441$	−0.520945	−	2.95442i	−0.0248069	−	0.140687i
$442$	1.11334	−	1.92836i	0.0529562	−	0.0917229i
$443$	−21.2738	−	7.74302i	−1.01075	−	0.367882i	−0.217028	−	0.976165i	$-0.569636\pi$
$443$	−21.2738	−	7.74302i	−1.01075	−	0.367882i	−0.793720	+	0.608283i	$0.791859\pi$
$444$		−	18.7459i		−	0.889641i
$445$	7.35710	+	6.17334i	0.348760	+	0.292644i
$446$	18.1912	+	15.2642i	0.861378	+	0.722782i
$447$		−	34.7064i		−	1.64156i
$448$	−0.939693	−	0.342020i	−0.0443963	−	0.0161589i
$449$	−14.7408	+	25.5318i	−0.695662	+	1.20492i	0.274295	+	0.961646i	$0.411556\pi$
$449$	−14.7408	+	25.5318i	−0.695662	+	1.20492i	−0.969957	+	0.243277i	$0.921778\pi$
$450$	3.97906	+	1.44826i	0.187574	+	0.0682715i
$451$	0.537141	+	0.930356i	0.0252930	+	0.0438088i
$452$	−1.92468	−	10.9154i	−0.0905292	−	0.513417i
$453$	12.3384	+	33.8996i	0.579710	+	1.59274i
$454$	13.7208	−	4.99395i	0.643947	−	0.234377i
$455$	0.826352	−	4.68647i	0.0387400	−	0.219705i
$456$	−7.91147	+	1.39501i	−0.370489	+	0.0653272i
$457$	16.2561	−	13.6405i	0.760427	−	0.638074i	−0.177811	−	0.984065i	$-0.556901\pi$
$457$	16.2561	−	13.6405i	0.760427	−	0.638074i	0.938238	+	0.345990i	$0.112457\pi$
$458$	−19.1361			−0.894171
$459$		−	6.15636i		−	0.287354i
$460$	3.14290			0.146539
$461$	−21.2041	+	17.7924i	−0.987575	+	0.828674i	−0.985215	−	0.171323i	$-0.945196\pi$
$461$	−21.2041	+	17.7924i	−0.987575	+	0.828674i	−0.00236055	+	0.999997i	$0.500751\pi$
$462$	0.180922	−	0.497079i	0.00841726	−	0.0231262i
$463$	4.97400	−	28.2090i	0.231162	−	1.31098i	−0.619387	−	0.785086i	$-0.712619\pi$
$463$	4.97400	−	28.2090i	0.231162	−	1.31098i	0.850549	−	0.525896i	$-0.176270\pi$
$464$	−2.63176	+	0.957882i	−0.122176	+	0.0444686i
$465$	−13.7554	+	16.3930i	−0.637890	+	0.760208i
$466$	−3.35204	−	19.0104i	−0.155280	−	0.880639i
$467$	−4.31908	−	7.48086i	−0.199863	−	0.346173i	0.748621	−	0.662998i	$-0.230716\pi$
$467$	−4.31908	−	7.48086i	−0.199863	−	0.346173i	−0.948484	+	0.316825i	$0.897383\pi$
$468$	−2.81908	−	4.88279i	−0.130312	−	0.225707i
$469$	5.28699	−	9.15733i	0.244130	−	0.422846i
$470$	21.9192	+	7.97794i	1.01106	+	0.367995i
$471$	0.365877	+	0.211239i	0.0168587	+	0.00973338i
$472$	4.08512	+	3.42782i	0.188033	+	0.157778i
$473$	−1.00727	−	0.845203i	−0.0463145	−	0.0388625i
$474$	18.8097	−	10.8598i	0.863960	−	0.498808i
$475$	−6.15183	−	2.23908i	−0.282265	−	0.102736i
$476$	−0.592396	+	1.02606i	−0.0271524	+	0.0470294i
$477$	5.94878	−	33.7372i	0.272376	−	1.54472i
$478$	4.82042	+	8.34922i	0.220481	+	0.381884i
$479$	4.58647	+	26.0111i	0.209561	+	1.18848i	0.890099	+	0.455767i	$0.150635\pi$
$479$	4.58647	+	26.0111i	0.209561	+	1.18848i	−0.680538	+	0.732713i	$0.738254\pi$
$480$	−4.31908	−	0.761570i	−0.197138	−	0.0347608i
$481$	−19.1138	+	6.95686i	−0.871515	+	0.317205i
$482$	−4.28699	+	24.3127i	−0.195267	+	1.10741i
$483$	−1.38191	−	1.64690i	−0.0628791	−	0.0749365i
$484$	−8.35504	+	7.01071i	−0.379774	+	0.318669i
$485$	9.85978			0.447710
$486$	−13.5000	−	7.79423i	−0.612372	−	0.353553i
$487$	17.0993			0.774841			0.387421	−	0.921903i	$-0.373366\pi$
$487$	17.0993			0.774841			0.387421	+	0.921903i	$0.373366\pi$
$488$	−8.64930	+	7.25762i	−0.391535	+	0.328537i
$489$	8.34477	+	9.94491i	0.377364	+	0.449724i
$490$	−0.439693	+	2.49362i	−0.0198633	+	0.112650i
$491$	−9.21853	+	3.35527i	−0.416026	+	0.151421i	−0.541548	−	0.840670i	$-0.682162\pi$
$491$	−9.21853	+	3.35527i	−0.416026	+	0.151421i	0.125522	+	0.992091i	$0.459939\pi$
$492$	−6.00000	−	1.05796i	−0.270501	−	0.0476966i
$493$	0.576199	+	3.26779i	0.0259507	+	0.147174i
$494$	4.35844	+	7.54904i	0.196096	+	0.339647i
$495$	0.402856	−	2.28471i	0.0181070	−	0.102690i
$496$	2.43969	−	4.22567i	0.109545	−	0.189738i
$497$	−12.7233	−	4.63089i	−0.570717	−	0.207724i
$498$	−2.31996	+	1.33943i	−0.103960	+	0.0600211i
$499$	5.09808	+	4.27780i	0.228221	+	0.191500i	0.749727	−	0.661748i	$-0.230185\pi$
$499$	5.09808	+	4.27780i	0.228221	+	0.191500i	−0.521505	+	0.853248i	$0.674629\pi$
$500$	6.96064	+	5.84067i	0.311289	+	0.261203i
$501$	13.5192	+	7.80531i	0.603993	+	0.348715i
$502$	−4.99273	−	1.81720i	−0.222836	−	0.0811058i
$503$	7.98932	−	13.8379i	0.356226	−	0.617002i	−0.631101	−	0.775701i	$-0.717397\pi$
$503$	7.98932	−	13.8379i	0.356226	−	0.617002i	0.987327	+	0.158699i	$0.0507299\pi$
$504$	1.50000	+	2.59808i	0.0668153	+	0.115728i
$505$	19.5744	+	33.9039i	0.871051	+	1.50871i
$506$	−0.0658266	−	0.373321i	−0.00292635	−	0.0165962i
$507$	10.5410	−	12.5623i	0.468143	−	0.557911i
$508$	11.6766	−	4.24995i	0.518067	−	0.188561i
$509$	−7.33750	+	41.6130i	−0.325229	+	1.84446i	0.182834	+	0.983144i	$0.441473\pi$
$509$	−7.33750	+	41.6130i	−0.325229	+	1.84446i	−0.508062	+	0.861320i	$0.669638\pi$
$510$	−1.77719	+	4.88279i	−0.0786952	+	0.216213i
$511$	0.251030	−	0.210639i	0.0111049	−	0.00931812i
$512$	1.00000			0.0441942
$513$	20.8717	+	12.0503i	0.921508	+	0.532033i
$514$	8.80747			0.388481
$515$	−26.1386	+	21.9329i	−1.15181	+	0.966479i
$516$	7.34389	−	1.29493i	0.323297	−	0.0570060i
$517$	0.488551	−	2.77071i	0.0214864	−	0.121856i
$518$	10.1702	−	3.70167i	0.446855	−	0.162642i
$519$	6.73127	+	18.4940i	0.295470	+	0.811797i
$520$	0.826352	+	4.68647i	0.0362379	+	0.205515i
$521$	−6.67705	−	11.5650i	−0.292527	−	0.506672i	0.681880	−	0.731464i	$-0.261163\pi$
$521$	−6.67705	−	11.5650i	−0.292527	−	0.506672i	−0.974407	+	0.224793i	$0.927829\pi$
$522$	7.89528	+	2.87365i	0.345567	+	0.125776i
$523$	−4.58260	+	7.93729i	−0.200383	+	0.347073i	−0.948652	−	0.316322i	$-0.897552\pi$
$523$	−4.58260	+	7.93729i	−0.200383	+	0.347073i	0.748269	+	0.663396i	$0.230885\pi$
$524$	3.20574	+	1.16679i	0.140043	+	0.0509716i
$525$			2.44474i			0.106697i
$526$	4.19459	+	3.51968i	0.182893	+	0.153465i
$527$	−4.42855	−	3.71599i	−0.192911	−	0.161871i
$528$			0.528981i			0.0230209i
$529$	20.1652	+	7.33953i	0.876747	+	0.319110i
$530$	−14.4572	+	25.0407i	−0.627982	+	1.08770i
$531$	−2.77807	−	15.7552i	−0.120558	−	0.683717i
$532$	−2.31908	−	4.01676i	−0.100545	−	0.174149i
$533$	1.14796	+	6.51038i	0.0497235	+	0.281996i
$534$	2.24691	+	6.17334i	0.0972333	+	0.267146i
$535$	18.1211	−	6.59553i	0.783443	−	0.285150i
$536$	−1.83615	+	10.4133i	−0.0793097	+	0.449788i
$537$	9.46972	−	1.66977i	0.408649	−	0.0720558i
$538$	10.7968	−	9.05958i	0.465483	−	0.390586i
$539$	0.305407			0.0131548
$540$	8.45723	+	10.0789i	0.363941	+	0.433728i
$541$	−12.0401			−0.517646			−0.258823	−	0.965925i	$-0.583335\pi$
$541$	−12.0401			−0.517646			−0.258823	+	0.965925i	$0.583335\pi$
$542$	−23.4420	+	19.6701i	−1.00692	+	0.844905i
$543$	−7.68551	+	21.1158i	−0.329817	+	0.906164i
$544$	0.205737	−	1.16679i	0.00882090	−	0.0500258i
$545$	14.1236	−	5.14057i	0.604989	−	0.220198i
$546$	2.09240	−	2.49362i	0.0895463	−	0.106717i
$547$	−5.97209	−	33.8694i	−0.255348	−	1.44815i	−0.795178	−	0.606376i	$-0.792623\pi$
$547$	−5.97209	−	33.8694i	−0.255348	−	1.44815i	0.539830	−	0.841774i	$-0.318489\pi$
$548$	−9.40167	−	16.2842i	−0.401620	−	0.695626i
$549$	33.8726			1.44565
$550$	−0.215537	+	0.373321i	−0.00919054	+	0.0159185i
$551$	−12.2065	−	4.44281i	−0.520015	−	0.189270i
$552$	1.86184	+	1.07494i	0.0792454	+	0.0457523i
$553$	9.60607	+	8.06045i	0.408492	+	0.342765i
$554$	−10.8812	−	9.13041i	−0.462298	−	0.387914i
$555$	41.1070	−	23.7331i	1.74489	−	1.00742i
$556$	−0.606944	−	0.220910i	−0.0257402	−	0.00936865i
$557$	2.87551	−	4.98054i	0.121839	−	0.211032i	−0.798654	−	0.601791i	$-0.794454\pi$
$557$	2.87551	−	4.98054i	0.121839	−	0.211032i	0.920493	+	0.390759i	$0.127787\pi$
$558$	−13.7554	+	5.00654i	−0.582311	+	0.211944i
$559$	−4.04576	−	7.00746i	−0.171117	−	0.296384i
$560$	−0.439693	−	2.49362i	−0.0185804	−	0.105375i
$561$	0.617211	+	0.108831i	0.0260587	+	0.00459485i
$562$	25.6805	−	9.34694i	1.08327	−	0.394277i
$563$	7.79039	−	44.1815i	0.328326	−	1.86203i	−0.156864	−	0.987620i	$-0.550139\pi$
$563$	7.79039	−	44.1815i	0.328326	−	1.86203i	0.485190	−	0.874409i	$-0.338750\pi$
$564$	10.2562	+	12.2229i	0.431866	+	0.514678i
$565$	21.4991	−	18.0399i	0.904475	−	0.758945i
$566$	19.7615			0.830636
$567$	1.56283	−	8.86327i	0.0656328	−	0.372222i
$568$	13.5398			0.568119
$569$	17.8255	−	14.9573i	0.747283	−	0.627045i	−0.187500	−	0.982265i	$-0.560038\pi$
$569$	17.8255	−	14.9573i	0.747283	−	0.627045i	0.934783	+	0.355220i	$0.115594\pi$
$570$	−13.0753	−	15.5826i	−0.547665	−	0.652682i
$571$	4.12361	−	23.3861i	0.172568	−	0.978680i	−0.768346	−	0.640034i	$-0.778920\pi$
$571$	4.12361	−	23.3861i	0.172568	−	0.978680i	0.940914	−	0.338645i	$-0.109969\pi$
$572$	0.539363	−	0.196312i	0.0225519	−	0.00820822i
$573$	4.69253	+	0.827420i	0.196033	+	0.0345660i
$574$	−0.610815	−	3.46410i	−0.0254949	−	0.144589i
$575$	0.875982	+	1.51724i	0.0365310	+	0.0632735i
$576$	−2.29813	−	1.92836i	−0.0957556	−	0.0803485i
$577$	−5.41875	+	9.38555i	−0.225585	+	0.390725i	−0.956495	−	0.291749i	$-0.905763\pi$
$577$	−5.41875	+	9.38555i	−0.225585	+	0.390725i	0.730909	+	0.682474i	$0.239096\pi$
$578$	14.6557	+	5.33424i	0.609597	+	0.221875i
$579$	−4.35251	+	2.51292i	−0.180884	+	0.104434i
$580$	−5.43242	−	4.55834i	−0.225569	−	0.189275i
$581$	−1.18479	−	0.994159i	−0.0491535	−	0.0412447i
$582$	5.84090	+	3.37225i	0.242113	+	0.139784i
$583$	3.27719	+	1.19280i	0.135727	+	0.0494007i
$584$	−0.163848	+	0.283793i	−0.00678008	+	0.0117434i
$585$	7.13816	−	12.3636i	0.295126	−	0.511174i
$586$	5.45723	+	9.45221i	0.225436	+	0.390467i
$587$	0.271974	+	1.54244i	0.0112256	+	0.0636634i	0.989906	−	0.141726i	$-0.0452651\pi$
$587$	0.271974	+	1.54244i	0.0112256	+	0.0636634i	−0.978680	+	0.205389i	$0.934154\pi$
$588$	−1.11334	+	1.32683i	−0.0459134	+	0.0547175i
$589$	21.2665	−	7.74038i	0.876271	−	0.318937i
$590$	−2.34477	+	13.2979i	−0.0965327	+	0.547464i
$591$	−6.59539	+	18.1207i	−0.271298	+	0.745385i
$592$	−8.29086	+	6.95686i	−0.340752	+	0.285925i
$593$	44.1634			1.81358			0.906788	−	0.421588i	$-0.138527\pi$
$593$	44.1634			1.81358			0.906788	+	0.421588i	$0.138527\pi$
$594$	1.02007	−	1.21567i	0.0418539	−	0.0498795i
$595$	−3.00000			−0.122988
$596$	−15.3498	+	12.8800i	−0.628753	+	0.527587i
$597$	41.6411	−	7.34246i	1.70426	−	0.300507i
$598$	0.405078	−	2.29731i	0.0165649	−	0.0939439i
$599$	−28.4736	+	10.3635i	−1.16340	+	0.423443i	−0.850311	−	0.526281i	$-0.823586\pi$
$599$	−28.4736	+	10.3635i	−1.16340	+	0.423443i	−0.313089	+	0.949724i	$0.601364\pi$
$600$	−0.836152	−	2.29731i	−0.0341358	−	0.0937872i
$601$	−6.22849	−	35.3235i	−0.254066	−	1.44088i	−0.798460	−	0.602048i	$-0.794352\pi$
$601$	−6.22849	−	35.3235i	−0.254066	−	1.44088i	0.544395	−	0.838829i	$-0.316759\pi$
$602$	2.15270	+	3.72859i	0.0877377	+	0.151966i
$603$	24.3004	−	20.3905i	0.989589	−	0.830364i
$604$	10.4140	−	18.0376i	0.423740	−	0.733939i
$605$	−25.9513	−	9.44550i	−1.05507	−	0.384014i
$606$			26.7794i			1.08784i
$607$	−7.85916	−	6.59461i	−0.318993	−	0.267667i	0.469204	−	0.883090i	$-0.344541\pi$
$607$	−7.85916	−	6.59461i	−0.318993	−	0.267667i	−0.788197	+	0.615423i	$0.788985\pi$
$608$	3.55303	+	2.98135i	0.144095	+	0.120910i
$609$			4.85088i			0.196568i
$610$	−26.8653	−	9.77817i	−1.08774	−	0.395907i
$611$	8.65657	−	14.9936i	0.350208	−	0.606577i
$612$	−2.72281	+	2.28471i	−0.110063	+	0.0923539i
$613$	18.2713	+	31.6467i	0.737969	+	1.27820i	0.953408	+	0.301683i	$0.0975484\pi$
$613$	18.2713	+	31.6467i	0.737969	+	1.27820i	−0.215439	+	0.976517i	$0.569118\pi$
$614$	−3.64038	−	20.6456i	−0.146914	−	0.833189i
$615$	−5.27631	−	14.4965i	−0.212761	−	0.584557i
$616$	−0.286989	+	0.104455i	−0.0115631	+	0.00420863i
$617$	5.91694	−	33.5566i	0.238207	−	1.35094i	−0.597547	−	0.801834i	$-0.703858\pi$
$617$	5.91694	−	33.5566i	0.238207	−	1.35094i	0.835754	−	0.549105i	$-0.185031\pi$
$618$	−22.9859	+	4.05304i	−0.924629	+	0.163037i
$619$	31.0371	−	26.0433i	1.24749	−	1.04677i	0.250588	−	0.968094i	$-0.419376\pi$
$619$	31.0371	−	26.0433i	1.24749	−	1.04677i	0.996900	−	0.0786728i	$-0.0250682\pi$
$620$	12.3550			0.496190
$621$	−2.20590	−	6.06066i	−0.0885197	−	0.243206i
$622$	−18.1925			−0.729454
$623$	−2.90554	+	2.43804i	−0.116408	+	0.0976781i
$624$	−1.11334	+	3.05888i	−0.0445693	+	0.122453i
$625$	−5.22075	+	29.6084i	−0.208830	+	1.18433i
$626$	−16.8824	+	6.14468i	−0.674756	+	0.245591i
$627$	−1.57708	+	1.87949i	−0.0629824	+	0.0750595i
$628$	−0.0423559	−	0.240212i	−0.00169018	−	0.00958551i
$629$	6.41147	+	11.1050i	0.255642	+	0.442785i
$630$	−3.79813	+	6.57856i	−0.151321	+	0.262096i
$631$	−8.83140	+	15.2964i	−0.351573	+	0.608942i	−0.986525	−	0.163609i	$-0.947686\pi$
$631$	−8.83140	+	15.2964i	−0.351573	+	0.608942i	0.634953	+	0.772551i	$0.281020\pi$
$632$	−11.7836	−	4.28887i	−0.468726	−	0.170602i
$633$	17.1212	+	9.88495i	0.680508	+	0.392892i
$634$	−12.5890	−	10.5634i	−0.499973	−	0.419527i
$635$	24.1027	+	20.2245i	0.956485	+	0.802586i
$636$	−17.1288	+	9.88933i	−0.679202	+	0.392137i
$637$	1.76604	+	0.642788i	0.0699732	+	0.0254682i
$638$	−0.427671	+	0.740748i	−0.0169317	+	0.0293265i
$639$	−31.1163	−	26.1097i	−1.23094	−	1.03288i
$640$	1.26604	+	2.19285i	0.0500448	+	0.0866801i
$641$	2.46884	+	14.0015i	0.0975135	+	0.553027i	0.993948	+	0.109851i	$0.0350372\pi$
$641$	2.46884	+	14.0015i	0.0975135	+	0.553027i	−0.896435	+	0.443176i	$0.853852\pi$
$642$	12.9907	+	2.29061i	0.512701	+	0.0904030i
$643$	0.654925	−	0.238373i	0.0258277	−	0.00940052i	−0.329074	−	0.944304i	$-0.606737\pi$
$643$	0.654925	−	0.238373i	0.0258277	−	0.00940052i	0.354902	+	0.934904i	$0.384514\pi$
$644$	−0.215537	+	1.22237i	−0.00849336	+	0.0481682i
$645$	12.1373	+	14.4646i	0.477905	+	0.569545i
$646$	4.20961	−	3.53228i	0.165625	−	0.138976i
$647$	−36.5499			−1.43693			−0.718463	−	0.695565i	$-0.755154\pi$
$647$	−36.5499			−1.43693			−0.718463	+	0.695565i	$0.755154\pi$
$648$	1.56283	+	8.86327i	0.0613939	+	0.348182i
$649$	1.62866			0.0639305
$650$	−2.03209	+	1.70513i	−0.0797051	+	0.0668805i
$651$	−5.43242	−	6.47410i	−0.212913	−	0.253740i
$652$	1.30154	−	7.38138i	0.0509721	−	0.289077i
$653$	41.5565	−	15.1253i	1.62623	−	0.591900i	0.641676	−	0.766976i	$-0.278239\pi$
$653$	41.5565	−	15.1253i	1.62623	−	0.591900i	0.984555	+	0.175076i	$0.0560171\pi$
$654$	10.1250	+	1.78530i	0.395917	+	0.0698108i
$655$	1.50000	+	8.50692i	0.0586098	+	0.332393i
$656$	1.75877	+	3.04628i	0.0686685	+	0.118937i
$657$	0.923801	−	0.336236i	0.0360409	−	0.0131178i
$658$	−4.60607	+	7.97794i	−0.179563	+	0.311013i
$659$	−34.2396	−	12.4622i	−1.33379	−	0.485459i	−0.425937	−	0.904753i	$-0.640055\pi$
$659$	−34.2396	−	12.4622i	−1.33379	−	0.485459i	−0.907850	+	0.419294i	$0.862278\pi$
$660$	−1.15998	+	0.669713i	−0.0451521	+	0.0260686i
$661$	1.38919	+	1.16566i	0.0540331	+	0.0453391i	0.669404	−	0.742898i	$-0.266549\pi$
$661$	1.38919	+	1.16566i	0.0540331	+	0.0453391i	−0.615371	+	0.788237i	$0.710994\pi$
$662$	5.22075	+	4.38073i	0.202910	+	0.170262i
$663$	3.34002	+	1.92836i	0.129716	+	0.0748914i
$664$	1.45336	+	0.528981i	0.0564014	+	0.0205284i
$665$	5.87211	−	10.1708i	0.227711	−	0.394407i
$666$	32.4688			1.25814
$667$	1.73813	+	3.01053i	0.0673007	+	0.116568i
$668$	−1.56506	−	8.87587i	−0.0605538	−	0.343418i
$669$	−26.4384	+	31.5081i	−1.02217	+	1.21817i
$670$	−25.1596	+	9.15733i	−0.971999	+	0.353779i
$671$	−0.598793	+	3.39592i	−0.0231161	+	0.131098i
$672$	0.592396	−	1.62760i	0.0228522	−	0.0627859i
$673$	−28.4243	+	23.8508i	−1.09567	+	0.919380i	−0.997127	−	0.0757518i	$-0.975864\pi$
$673$	−28.4243	+	23.8508i	−1.09567	+	0.919380i	−0.0985483	+	0.995132i	$0.531420\pi$
$674$	−2.35410			−0.0906767
$675$	−2.50846	+	6.89193i	−0.0965505	+	0.265270i
$676$	−9.46791			−0.364150
$677$	6.79813	−	5.70431i	0.261273	−	0.219234i	−0.502735	−	0.864440i	$-0.667673\pi$
$677$	6.79813	−	5.70431i	0.261273	−	0.219234i	0.764009	+	0.645206i	$0.223228\pi$
$678$	18.9060	−	3.33364i	0.726081	−	0.128028i
$679$	−0.676174	+	3.83478i	−0.0259492	+	0.147165i
$680$	2.81908	−	1.02606i	0.108107	−	0.0393476i
$681$	8.64977	+	23.7650i	0.331460	+	0.910678i
$682$	−0.258770	−	1.46756i	−0.00990883	−	0.0561958i
$683$	5.08899	+	8.81439i	0.194725	+	0.337273i	0.946810	−	0.321792i	$-0.104285\pi$
$683$	5.08899	+	8.81439i	0.194725	+	0.337273i	−0.752085	+	0.659066i	$0.770952\pi$
$684$	−2.41622	−	13.7031i	−0.0923866	−	0.523950i
$685$	23.8059	−	41.2330i	0.909576	−	1.57543i
$686$	−0.939693	−	0.342020i	−0.0358776	−	0.0130584i
$687$		−	33.1447i		−	1.26455i
$688$	−3.29813	−	2.76746i	−0.125740	−	0.105509i
$689$	16.4402	+	13.7949i	0.626320	+	0.525545i
$690$			5.44367i			0.207237i
$691$	2.15910	+	0.785848i	0.0821360	+	0.0298951i	0.382761	−	0.923847i	$-0.374973\pi$
$691$	2.15910	+	0.785848i	0.0821360	+	0.0298951i	−0.300625	+	0.953742i	$0.597195\pi$
$692$	5.68139	−	9.84045i	0.215974	−	0.374078i
$693$	0.860967	+	0.313366i	0.0327054	+	0.0119038i
$694$	4.63429	+	8.02682i	0.175915	+	0.304694i
$695$	−0.283996	−	1.61062i	−0.0107726	−	0.0610943i
$696$	−1.65910	−	4.55834i	−0.0628880	−	0.172783i
$697$	3.91622	−	1.42539i	0.148337	−	0.0539904i
$698$	−1.64022	+	9.30212i	−0.0620831	+	0.352091i
$699$	32.9270	−	5.80591i	1.24541	−	0.219600i
$700$	1.08125	−	0.907278i	0.0408675	−	0.0342919i
$701$	−23.1566			−0.874614			−0.437307	−	0.899312i	$-0.644068\pi$
$701$	−23.1566			−0.874614			−0.437307	+	0.899312i	$0.644068\pi$
$702$	8.45723	−	4.88279i	0.319198	−	0.184289i
$703$	−50.1985			−1.89327
$704$	0.233956	−	0.196312i	0.00881753	−	0.00739879i
$705$	−13.8182	+	37.9652i	−0.520424	+	1.42985i
$706$	3.31521	−	18.8015i	0.124769	−	0.707603i
$707$	−14.5287	+	5.28801i	−0.546407	+	0.198876i
$708$	−5.93717	+	7.07564i	−0.223132	+	0.265919i
$709$	−6.40760	−	36.3393i	−0.240643	−	1.36475i	−0.830398	−	0.557170i	$-0.811887\pi$
$709$	−6.40760	−	36.3393i	−0.240643	−	1.36475i	0.589756	−	0.807582i	$-0.299224\pi$
$710$	17.1420	+	29.6909i	0.643329	+	1.11428i
$711$	18.8097	+	32.5794i	0.705421	+	1.22182i
$712$	1.89646	−	3.28476i	0.0710728	−	0.123102i
$713$	−5.69119	−	2.07142i	−0.213137	−	0.0775754i
$714$	−1.77719	−	1.02606i	−0.0665096	−	0.0383993i
$715$	1.11334	+	0.934204i	0.0416366	+	0.0349372i
$716$	−4.25284	−	3.56856i	−0.158936	−	0.133363i
$717$	−14.4613	+	8.34922i	−0.540066	+	0.311807i
$718$	5.87211	+	2.13727i	0.219145	+	0.0797623i
$719$	13.6425	−	23.6295i	0.508779	−	0.881231i	−0.491169	−	0.871064i	$-0.663430\pi$
$719$	13.6425	−	23.6295i	0.508779	−	0.881231i	0.999948	−	0.0101671i	$-0.00323635\pi$
$720$	1.31908	−	7.48086i	0.0491591	−	0.278795i
$721$	−6.73783	−	11.6703i	−0.250930	−	0.434623i
$722$	0.436289	+	2.47432i	0.0162370	+	0.0920846i
$723$	−42.1109	−	7.42528i	−1.56612	−	0.276149i
$724$	12.1912	−	4.43723i	0.453082	−	0.164908i
$725$	0.686441	−	3.89300i	0.0254938	−	0.144582i
$726$	−12.1429	−	14.4713i	−0.450665	−	0.537082i
$727$	−1.40348	+	1.17766i	−0.0520524	+	0.0436771i	−0.668443	−	0.743764i	$-0.733039\pi$
$727$	−1.40348	+	1.17766i	−0.0520524	+	0.0436771i	0.616390	+	0.787441i	$0.288594\pi$
$728$	−1.87939			−0.0696547
$729$	13.5000	−	23.3827i	0.500000	−	0.866025i
$730$	−0.829755			−0.0307106
$731$	−3.90760	+	3.27887i	−0.144528	+	0.121273i
$732$	−12.5706	−	14.9810i	−0.464622	−	0.553715i
$733$	1.16204	−	6.59024i	0.0429208	−	0.243416i	−0.955798	−	0.294025i	$-0.905005\pi$
$733$	1.16204	−	6.59024i	0.0429208	−	0.243416i	0.998719	+	0.0506090i	$0.0161162\pi$
$734$	−24.0043	+	8.73686i	−0.886016	+	0.322484i
$735$	−4.31908	−	0.761570i	−0.159312	−	0.0280909i
$736$	−0.215537	−	1.22237i	−0.00794481	−	0.0450572i
$737$	1.61468	+	2.79672i	0.0594777	+	0.103018i
$738$	1.83244	−	10.3923i	0.0674532	−	0.382546i
$739$	−14.1348	+	24.4821i	−0.519955	+	0.900589i	0.479776	+	0.877391i	$0.340718\pi$
$739$	−14.1348	+	24.4821i	−0.519955	+	0.900589i	−0.999731	+	0.0231977i	$0.992615\pi$
$740$	−25.7520	−	9.37295i	−0.946661	−	0.344556i
$741$	−13.0753	+	7.54904i	−0.480334	+	0.277321i
$742$	−8.74763	−	7.34013i	−0.321135	−	0.269465i
$743$	−32.7893	−	27.5135i	−1.20292	−	1.00937i	−0.999542	−	0.0302711i	$-0.990363\pi$
$743$	−32.7893	−	27.5135i	−1.20292	−	1.00937i	−0.203380	−	0.979100i	$-0.565193\pi$
$744$	7.31908	+	4.22567i	0.268330	+	0.154921i
$745$	−47.6776	−	17.3532i	−1.74677	−	0.635773i
$746$	2.18092	−	3.77747i	0.0798492	−	0.138303i
$747$	−2.31996	−	4.01828i	−0.0848827	−	0.147021i
$748$	−0.180922	−	0.313366i	−0.00661517	−	0.0114578i
$749$	1.32248	+	7.50016i	0.0483224	+	0.274050i
$750$	−10.1163	+	12.0562i	−0.369396	+	0.440229i
$751$	−29.6177	+	10.7800i	−1.08076	+	0.393366i	−0.820192	−	0.572088i	$-0.806133\pi$
$751$	−29.6177	+	10.7800i	−1.08076	+	0.393366i	−0.260572	+	0.965454i	$0.583911\pi$
$752$	1.59967	−	9.07218i	0.0583340	−	0.330828i
$753$	3.14749	−	8.64766i	0.114701	−	0.315138i
$754$	−4.03209	+	3.38332i	−0.146840	+	0.123213i
$755$	52.7383			1.91935
$756$	−4.50000	+	2.59808i	−0.163663	+	0.0944911i
$757$	−15.0966			−0.548694			−0.274347	−	0.961631i	$-0.588462\pi$
$757$	−15.0966			−0.548694			−0.274347	+	0.961631i	$0.588462\pi$
$758$	−7.97565	+	6.69237i	−0.289689	+	0.243078i
$759$	0.646612	−	0.114015i	0.0234705	−	0.00413849i
$760$	−2.03936	+	11.5658i	−0.0739755	+	0.419536i
$761$	−25.5158	+	9.28699i	−0.924947	+	0.336653i	−0.760205	−	0.649684i	$-0.774901\pi$
$761$	−25.5158	+	9.28699i	−0.924947	+	0.336653i	−0.164742	+	0.986337i	$0.552679\pi$
$762$	7.36113	+	20.2245i	0.266666	+	0.732658i
$763$	1.03074	+	5.84564i	0.0373155	+	0.211627i
$764$	−1.37551	−	2.38246i	−0.0497644	−	0.0861944i
$765$	−8.45723	−	3.07818i	−0.305772	−	0.111292i
$766$	−17.3391	+

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.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{2} +(1.11334 + 1.32683i) q^{3} +(0.173648 - 0.984808i) q^{4} +(2.37939 - 0.866025i) q^{5} +(1.70574 + 0.300767i) q^{6} +(0.173648 + 0.984808i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.520945 + 2.95442i) q^{9} +O(q^{10})\)	\(q+(0.766044 - 0.642788i) q^{2} +(1.11334 + 1.32683i) q^{3} +(0.173648 - 0.984808i) q^{4} +(2.37939 - 0.866025i) q^{5} +(1.70574 + 0.300767i) q^{6} +(0.173648 + 0.984808i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.520945 + 2.95442i) q^{9} +(1.26604 - 2.19285i) q^{10} +(-0.286989 - 0.104455i) q^{11} +(1.50000 - 0.866025i) q^{12} +(-1.43969 - 1.20805i) q^{13} +(0.766044 + 0.642788i) q^{14} +(3.79813 + 2.19285i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-0.592396 + 1.02606i) q^{17} +(1.50000 + 2.59808i) q^{18} +(-2.31908 - 4.01676i) q^{19} +(-0.439693 - 2.49362i) q^{20} +(-1.11334 + 1.32683i) q^{21} +(-0.286989 + 0.104455i) q^{22} +(-0.215537 + 1.22237i) q^{23} +(0.592396 - 1.62760i) q^{24} +(1.08125 - 0.907278i) q^{25} -1.87939 q^{26} +(-4.50000 + 2.59808i) q^{27} +1.00000 q^{28} +(2.14543 - 1.80023i) q^{29} +(4.31908 - 0.761570i) q^{30} +(-0.847296 + 4.80526i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(-0.180922 - 0.497079i) q^{33} +(0.205737 + 1.16679i) q^{34} +(1.26604 + 2.19285i) q^{35} +(2.81908 + 1.02606i) q^{36} +(5.41147 - 9.37295i) q^{37} +(-4.35844 - 1.58634i) q^{38} -3.25519i q^{39} +(-1.93969 - 1.62760i) q^{40} +(-2.69459 - 2.26103i) q^{41} +1.73205i q^{42} +(4.04576 + 1.47254i) q^{43} +(-0.152704 + 0.264490i) q^{44} +(1.31908 + 7.48086i) q^{45} +(0.620615 + 1.07494i) q^{46} +(1.59967 + 9.07218i) q^{47} +(-0.592396 - 1.62760i) q^{48} +(-0.939693 + 0.342020i) q^{49} +(0.245100 - 1.39003i) q^{50} +(-2.02094 + 0.356347i) q^{51} +(-1.43969 + 1.20805i) q^{52} -11.4192 q^{53} +(-1.77719 + 4.88279i) q^{54} -0.773318 q^{55} +(0.766044 - 0.642788i) q^{56} +(2.74763 - 7.54904i) q^{57} +(0.486329 - 2.75811i) q^{58} +(-5.01114 + 1.82391i) q^{59} +(2.81908 - 3.35965i) q^{60} +(-1.96064 - 11.1193i) q^{61} +(2.43969 + 4.22567i) q^{62} -3.00000 q^{63} +(-0.500000 + 0.866025i) q^{64} +(-4.47178 - 1.62760i) q^{65} +(-0.458111 - 0.264490i) q^{66} +(-8.10014 - 6.79682i) q^{67} +(0.907604 + 0.761570i) q^{68} +(-1.86184 + 1.07494i) q^{69} +(2.37939 + 0.866025i) q^{70} +(-6.76991 + 11.7258i) q^{71} +(2.81908 - 1.02606i) q^{72} +(-0.163848 - 0.283793i) q^{73} +(-1.87939 - 10.6585i) q^{74} +(2.40760 + 0.424525i) q^{75} +(-4.35844 + 1.58634i) q^{76} +(0.0530334 - 0.300767i) q^{77} +(-2.09240 - 2.49362i) q^{78} +(9.60607 - 8.06045i) q^{79} -2.53209 q^{80} +(-8.45723 - 3.07818i) q^{81} -3.51754 q^{82} +(-1.18479 + 0.994159i) q^{83} +(1.11334 + 1.32683i) q^{84} +(-0.520945 + 2.95442i) q^{85} +(4.04576 - 1.47254i) q^{86} +(4.77719 + 0.842347i) q^{87} +(0.0530334 + 0.300767i) q^{88} +(1.89646 + 3.28476i) q^{89} +(5.81908 + 4.88279i) q^{90} +(0.939693 - 1.62760i) q^{91} +(1.16637 + 0.424525i) q^{92} +(-7.31908 + 4.22567i) q^{93} +(7.05690 + 5.92145i) q^{94} +(-8.99660 - 7.54904i) q^{95} +(-1.50000 - 0.866025i) q^{96} +(3.65910 + 1.33180i) q^{97} +(-0.500000 + 0.866025i) q^{98} +(0.458111 - 0.793471i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{5} - 3 q^{8}+O(q^{10}) \) 6 * q + 3 * q^5 - 3 * q^8	\( 6 q + 3 q^{5} - 3 q^{8} + 3 q^{10} + 6 q^{11} + 9 q^{12} - 3 q^{13} + 9 q^{15} + 9 q^{18} + 3 q^{19} + 3 q^{20} + 6 q^{22} + 6 q^{23} + 9 q^{25} - 27 q^{27} + 6 q^{28} - 3 q^{29} + 9 q^{30} - 3 q^{31} - 18 q^{33} - 9 q^{34} + 3 q^{35} + 12 q^{37} - 18 q^{38} - 6 q^{40} - 12 q^{41} - 6 q^{43} - 3 q^{44} - 9 q^{45} + 15 q^{46} + 24 q^{47} - 9 q^{51} - 3 q^{52} - 18 q^{55} + 24 q^{58} - 24 q^{59} - 3 q^{61} + 9 q^{62} - 18 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 3 q^{67} + 9 q^{68} - 45 q^{69} + 3 q^{70} - 12 q^{71} + 3 q^{73} + 18 q^{75} - 18 q^{76} - 12 q^{77} - 9 q^{78} + 33 q^{79} - 6 q^{80} + 24 q^{82} - 6 q^{86} + 18 q^{87} - 12 q^{88} + 21 q^{89} + 18 q^{90} - 12 q^{92} - 27 q^{93} + 6 q^{94} - 12 q^{95} - 9 q^{96} - 15 q^{97} - 3 q^{98} + 9 q^{99}+O(q^{100}) \) 6 * q + 3 * q^5 - 3 * q^8 + 3 * q^10 + 6 * q^11 + 9 * q^12 - 3 * q^13 + 9 * q^15 + 9 * q^18 + 3 * q^19 + 3 * q^20 + 6 * q^22 + 6 * q^23 + 9 * q^25 - 27 * q^27 + 6 * q^28 - 3 * q^29 + 9 * q^30 - 3 * q^31 - 18 * q^33 - 9 * q^34 + 3 * q^35 + 12 * q^37 - 18 * q^38 - 6 * q^40 - 12 * q^41 - 6 * q^43 - 3 * q^44 - 9 * q^45 + 15 * q^46 + 24 * q^47 - 9 * q^51 - 3 * q^52 - 18 * q^55 + 24 * q^58 - 24 * q^59 - 3 * q^61 + 9 * q^62 - 18 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 3 * q^67 + 9 * q^68 - 45 * q^69 + 3 * q^70 - 12 * q^71 + 3 * q^73 + 18 * q^75 - 18 * q^76 - 12 * q^77 - 9 * q^78 + 33 * q^79 - 6 * q^80 + 24 * q^82 - 6 * q^86 + 18 * q^87 - 12 * q^88 + 21 * q^89 + 18 * q^90 - 12 * q^92 - 27 * q^93 + 6 * q^94 - 12 * q^95 - 9 * q^96 - 15 * q^97 - 3 * q^98 + 9 * q^99

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