LMFDB - Embedded newform 378.2.u.e.169.2

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:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			169.2
Character	$\chi$	$=$	378.169
Dual form			378.2.u.e.85.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 - 0.342020i) q^{2} +(-1.33644 - 1.10178i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.619299 - 3.51222i) q^{5} +(-1.63268 - 0.578248i) q^{6} +(0.766044 + 0.642788i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.572147 + 2.94494i) q^{9} +O(q^{10})$	\(q+(0.939693 - 0.342020i) q^{2} +(-1.33644 - 1.10178i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.619299 - 3.51222i) q^{5} +(-1.63268 - 0.578248i) q^{6} +(0.766044 + 0.642788i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.572147 + 2.94494i) q^{9} +(-1.78320 - 3.08859i) q^{10} +(0.0584572 - 0.331527i) q^{11} +(-1.73199 + 0.0150326i) q^{12} +(-4.08396 - 1.48644i) q^{13} +(0.939693 + 0.342020i) q^{14} +(-3.04205 + 5.37621i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-1.39140 - 2.40998i) q^{17} +(1.54487 + 2.57165i) q^{18} +(-2.27154 + 3.93443i) q^{19} +(-2.73202 - 2.29244i) q^{20} +(-0.315560 - 1.70306i) q^{21} +(-0.0584572 - 0.331527i) q^{22} +(6.51434 - 5.46618i) q^{23} +(-1.62239 + 0.606500i) q^{24} +(-7.25369 + 2.64013i) q^{25} -4.34606 q^{26} +(2.48004 - 4.56611i) q^{27} +1.00000 q^{28} +(-5.34649 + 1.94596i) q^{29} +(-1.01982 + 6.09242i) q^{30} +(4.31346 - 3.61942i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(-0.443396 + 0.378659i) q^{33} +(-2.13175 - 1.78875i) q^{34} +(1.78320 - 3.08859i) q^{35} +(2.33126 + 1.88818i) q^{36} +(2.41310 + 4.17961i) q^{37} +(-0.788899 + 4.47407i) q^{38} +(3.82023 + 6.48618i) q^{39} +(-3.35132 - 1.21978i) q^{40} +(5.32774 + 1.93914i) q^{41} +(-0.879011 - 1.49243i) q^{42} +(2.04239 - 11.5830i) q^{43} +(-0.168321 - 0.291540i) q^{44} +(9.98893 - 3.83330i) q^{45} +(4.25194 - 7.36457i) q^{46} +(7.48488 + 6.28056i) q^{47} +(-1.31712 + 1.12481i) q^{48} +(0.173648 + 0.984808i) q^{49} +(-5.91326 + 4.96182i) q^{50} +(-0.795747 + 4.75381i) q^{51} +(-4.08396 + 1.48644i) q^{52} +4.98092 q^{53} +(0.768772 - 5.13897i) q^{54} -1.20060 q^{55} +(0.939693 - 0.342020i) q^{56} +(7.37067 - 2.75538i) q^{57} +(-4.35850 + 3.65722i) q^{58} +(-1.93133 - 10.9531i) q^{59} +(1.12541 + 6.07380i) q^{60} +(5.50111 + 4.61598i) q^{61} +(2.81541 - 4.87643i) q^{62} +(-1.45468 + 2.62372i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-2.69151 + 15.2643i) q^{65} +(-0.287147 + 0.507474i) q^{66} +(-2.23965 - 0.815165i) q^{67} +(-2.61498 - 0.951774i) q^{68} +(-14.7286 + 0.127835i) q^{69} +(0.619299 - 3.51222i) q^{70} +(2.40629 + 4.16781i) q^{71} +(2.83646 + 0.976974i) q^{72} +(-1.04583 + 1.81143i) q^{73} +(3.69708 + 3.10222i) q^{74} +(12.6030 + 4.46362i) q^{75} +(0.788899 + 4.47407i) q^{76} +(0.257883 - 0.216389i) q^{77} +(5.80825 + 4.78841i) q^{78} +(-5.47927 + 1.99429i) q^{79} -3.56640 q^{80} +(-8.34529 + 3.36988i) q^{81} +5.66966 q^{82} +(1.01209 - 0.368370i) q^{83} +(-1.33644 - 1.10178i) q^{84} +(-7.60267 + 6.37940i) q^{85} +(-2.04239 - 11.5830i) q^{86} +(9.28930 + 3.29001i) q^{87} +(-0.257883 - 0.216389i) q^{88} +(7.81214 - 13.5310i) q^{89} +(8.07546 - 7.01854i) q^{90} +(-2.17303 - 3.76380i) q^{91} +(1.47668 - 8.37468i) q^{92} +(-9.75249 + 0.0846459i) q^{93} +(9.18156 + 3.34182i) q^{94} +(15.2253 + 5.54157i) q^{95} +(-0.852974 + 1.50746i) q^{96} +(-0.519971 + 2.94890i) q^{97} +(0.500000 + 0.866025i) q^{98} +(1.00977 - 0.0175298i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 3 q^{3} + 3 q^{5} + 6 q^{6} + 18 q^{8} + 3 q^{9}+O(q^{10}) $ 36 * q + 3 * q^3 + 3 * q^5 + 6 * q^6 + 18 * q^8 + 3 * q^9	$ 36 q + 3 q^{3} + 3 q^{5} + 6 q^{6} + 18 q^{8} + 3 q^{9} - 3 q^{10} + 9 q^{13} - 6 q^{15} + 6 q^{18} - 15 q^{19} - 6 q^{20} + 3 q^{21} - 3 q^{24} - 3 q^{25} - 18 q^{26} - 30 q^{27} + 36 q^{28} - 6 q^{29} - 9 q^{30} + 60 q^{33} + 9 q^{34} + 3 q^{35} - 27 q^{37} + 15 q^{38} + 6 q^{39} - 3 q^{40} - 9 q^{41} - 6 q^{43} + 9 q^{44} + 42 q^{45} - 9 q^{46} + 36 q^{47} + 3 q^{48} - 15 q^{50} - 36 q^{51} + 9 q^{52} - 42 q^{53} - 27 q^{54} + 30 q^{55} - 18 q^{57} - 21 q^{58} + 12 q^{59} + 24 q^{60} + 3 q^{61} + 18 q^{62} + 12 q^{63} - 18 q^{64} - 84 q^{65} + 18 q^{66} - 69 q^{67} + 9 q^{68} - 48 q^{69} - 3 q^{70} + 12 q^{71} + 6 q^{72} - 12 q^{73} + 9 q^{75} - 15 q^{76} + 9 q^{77} - 48 q^{78} - 51 q^{79} - 6 q^{80} - 69 q^{81} + 15 q^{83} + 3 q^{84} - 12 q^{85} + 6 q^{86} + 84 q^{87} - 9 q^{88} - 3 q^{89} + 6 q^{90} - 9 q^{91} + 18 q^{92} - 21 q^{93} + 9 q^{94} - 75 q^{95} - 42 q^{97} + 18 q^{98} + 39 q^{99}+O(q^{100}) $ 36 * q + 3 * q^3 + 3 * q^5 + 6 * q^6 + 18 * q^8 + 3 * q^9 - 3 * q^10 + 9 * q^13 - 6 * q^15 + 6 * q^18 - 15 * q^19 - 6 * q^20 + 3 * q^21 - 3 * q^24 - 3 * q^25 - 18 * q^26 - 30 * q^27 + 36 * q^28 - 6 * q^29 - 9 * q^30 + 60 * q^33 + 9 * q^34 + 3 * q^35 - 27 * q^37 + 15 * q^38 + 6 * q^39 - 3 * q^40 - 9 * q^41 - 6 * q^43 + 9 * q^44 + 42 * q^45 - 9 * q^46 + 36 * q^47 + 3 * q^48 - 15 * q^50 - 36 * q^51 + 9 * q^52 - 42 * q^53 - 27 * q^54 + 30 * q^55 - 18 * q^57 - 21 * q^58 + 12 * q^59 + 24 * q^60 + 3 * q^61 + 18 * q^62 + 12 * q^63 - 18 * q^64 - 84 * q^65 + 18 * q^66 - 69 * q^67 + 9 * q^68 - 48 * q^69 - 3 * q^70 + 12 * q^71 + 6 * q^72 - 12 * q^73 + 9 * q^75 - 15 * q^76 + 9 * q^77 - 48 * q^78 - 51 * q^79 - 6 * q^80 - 69 * q^81 + 15 * q^83 + 3 * q^84 - 12 * q^85 + 6 * q^86 + 84 * q^87 - 9 * q^88 - 3 * q^89 + 6 * q^90 - 9 * q^91 + 18 * q^92 - 21 * q^93 + 9 * q^94 - 75 * q^95 - 42 * q^97 + 18 * q^98 + 39 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$1$

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 $

$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$3$	−1.33644	−	1.10178i	−0.771594	−	0.636115i
$3$	−1.33644	−	1.10178i	−0.771594	−	0.636115i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	−0.619299	−	3.51222i	−0.276959	−	1.57071i	−0.732670	−	0.680584i	$-0.761726\pi$
$5$	−0.619299	−	3.51222i	−0.276959	−	1.57071i	0.455711	−	0.890128i	$-0.349385\pi$
$6$	−1.63268	−	0.578248i	−0.666537	−	0.236069i
$7$	0.766044	+	0.642788i	0.289538	+	0.242951i
$7$	0.766044	+	0.642788i	0.289538	+	0.242951i
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	0.572147	+	2.94494i	0.190716	+	0.981645i
$10$	−1.78320	−	3.08859i	−0.563898	−	0.976699i
$11$	0.0584572	−	0.331527i	0.0176255	−	0.0999593i	−0.974726	−	0.223404i	$-0.928283\pi$
$11$	0.0584572	−	0.331527i	0.0176255	−	0.0999593i	0.992351	+	0.123445i	$0.0393942\pi$
$12$	−1.73199	+	0.0150326i	−0.499981	+	0.00433954i
$13$	−4.08396	−	1.48644i	−1.13269	−	0.412264i	−0.293419	−	0.955984i	$-0.594793\pi$
$13$	−4.08396	−	1.48644i	−1.13269	−	0.412264i	−0.839267	+	0.543720i	$0.817015\pi$
$14$	0.939693	+	0.342020i	0.251143	+	0.0914087i
$15$	−3.04205	+	5.37621i	−0.785453	+	1.38813i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−1.39140	−	2.40998i	−0.337464	−	0.584505i	0.646491	−	0.762922i	$-0.276236\pi$
$17$	−1.39140	−	2.40998i	−0.337464	−	0.584505i	−0.983955	+	0.178417i	$0.942902\pi$
$18$	1.54487	+	2.57165i	0.364129	+	0.606143i
$19$	−2.27154	+	3.93443i	−0.521128	+	0.902620i	0.478570	+	0.878049i	$0.341155\pi$
$19$	−2.27154	+	3.93443i	−0.521128	+	0.902620i	−0.999698	+	0.0245705i	$0.992178\pi$
$20$	−2.73202	−	2.29244i	−0.610899	−	0.512605i
$21$	−0.315560	−	1.70306i	−0.0688609	−	0.371639i
$22$	−0.0584572	−	0.331527i	−0.0124631	−	0.0706819i
$23$	6.51434	−	5.46618i	1.35833	−	1.13978i	0.381842	−	0.924228i	$-0.375290\pi$
$23$	6.51434	−	5.46618i	1.35833	−	1.13978i	0.976493	−	0.215550i	$-0.0691545\pi$
$24$	−1.62239	+	0.606500i	−0.331170	+	0.123801i
$25$	−7.25369	+	2.64013i	−1.45074	+	0.528025i
$26$	−4.34606			−0.852332
$27$	2.48004	−	4.56611i	0.477284	−	0.878749i
$28$	1.00000			0.188982
$29$	−5.34649	+	1.94596i	−0.992819	+	0.361357i	−0.786811	−	0.617194i	$-0.788269\pi$
$29$	−5.34649	+	1.94596i	−0.992819	+	0.361357i	−0.206008	+	0.978550i	$0.566047\pi$
$30$	−1.01982	+	6.09242i	−0.186193	+	1.11232i
$31$	4.31346	−	3.61942i	0.774720	−	0.650067i	−0.167193	−	0.985924i	$-0.553470\pi$
$31$	4.31346	−	3.61942i	0.774720	−	0.650067i	0.941913	+	0.335857i	$0.109026\pi$
$32$	−0.173648	−	0.984808i	−0.0306970	−	0.174091i
$33$	−0.443396	+	0.378659i	−0.0771853	+	0.0659162i
$34$	−2.13175	−	1.78875i	−0.365592	−	0.306768i
$35$	1.78320	−	3.08859i	0.301416	−	0.522068i
$36$	2.33126	+	1.88818i	0.388543	+	0.314697i
$37$	2.41310	+	4.17961i	0.396711	+	0.687123i	0.993318	−	0.115410i	$-0.0368183\pi$
$37$	2.41310	+	4.17961i	0.396711	+	0.687123i	−0.596607	+	0.802533i	$0.703485\pi$
$38$	−0.788899	+	4.47407i	−0.127976	+	0.725789i
$39$	3.82023	+	6.48618i	0.611727	+	1.03862i
$40$	−3.35132	−	1.21978i	−0.529890	−	0.192864i
$41$	5.32774	+	1.93914i	0.832053	+	0.302843i	0.722701	−	0.691161i	$-0.242900\pi$
$41$	5.32774	+	1.93914i	0.832053	+	0.302843i	0.109352	+	0.994003i	$0.465123\pi$
$42$	−0.879011	−	1.49243i	−0.135634	−	0.230287i
$43$	2.04239	−	11.5830i	0.311462	−	1.76639i	−0.279946	−	0.960016i	$-0.590316\pi$
$43$	2.04239	−	11.5830i	0.311462	−	1.76639i	0.591408	−	0.806373i	$-0.298572\pi$
$44$	−0.168321	−	0.291540i	−0.0253753	−	0.0439514i
$45$	9.98893	−	3.83330i	1.48906	−	0.571435i
$46$	4.25194	−	7.36457i	0.626914	−	1.08585i
$47$	7.48488	+	6.28056i	1.09178	+	0.916114i	0.996845	−	0.0793695i	$-0.0252907\pi$
$47$	7.48488	+	6.28056i	1.09178	+	0.916114i	0.0949366	+	0.995483i	$0.469735\pi$
$48$	−1.31712	+	1.12481i	−0.190109	+	0.162353i
$49$	0.173648	+	0.984808i	0.0248069	+	0.140687i
$50$	−5.91326	+	4.96182i	−0.836262	+	0.701707i
$51$	−0.795747	+	4.75381i	−0.111427	+	0.665667i
$52$	−4.08396	+	1.48644i	−0.566343	+	0.206132i
$53$	4.98092			0.684182			0.342091	−	0.939667i	$-0.388865\pi$
$53$	4.98092			0.684182			0.342091	+	0.939667i	$0.388865\pi$
$54$	0.768772	−	5.13897i	0.104617	−	0.699325i
$55$	−1.20060			−0.161889
$56$	0.939693	−	0.342020i	0.125572	−	0.0457044i
$57$	7.37067	−	2.75538i	0.976269	−	0.364959i
$58$	−4.35850	+	3.65722i	−0.572299	+	0.480216i
$59$	−1.93133	−	10.9531i	−0.251438	−	1.42597i	−0.805054	−	0.593202i	$-0.797864\pi$
$59$	−1.93133	−	10.9531i	−0.251438	−	1.42597i	0.553616	−	0.832772i	$-0.313248\pi$
$60$	1.12541	+	6.07380i	0.145290	+	0.784125i
$61$	5.50111	+	4.61598i	0.704345	+	0.591016i	0.923006	−	0.384785i	$-0.125724\pi$
$61$	5.50111	+	4.61598i	0.704345	+	0.591016i	−0.218661	+	0.975801i	$0.570169\pi$
$62$	2.81541	−	4.87643i	0.357557	−	0.619307i
$63$	−1.45468	+	2.62372i	−0.183272	+	0.330558i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−2.69151	+	15.2643i	−0.333841	+	1.89330i
$66$	−0.287147	+	0.507474i	−0.0353453	+	0.0624657i
$67$	−2.23965	−	0.815165i	−0.273617	−	0.0995883i	0.201568	−	0.979475i	$-0.435396\pi$
$67$	−2.23965	−	0.815165i	−0.273617	−	0.0995883i	−0.475184	+	0.879886i	$0.657619\pi$
$68$	−2.61498	−	0.951774i	−0.317113	−	0.115420i
$69$	−14.7286	+	0.127835i	−1.77311	+	0.0153896i
$70$	0.619299	−	3.51222i	0.0740204	−	0.419791i
$71$	2.40629	+	4.16781i	0.285574	+	0.494628i	0.972748	−	0.231864i	$-0.0744825\pi$
$71$	2.40629	+	4.16781i	0.285574	+	0.494628i	−0.687174	+	0.726492i	$0.741149\pi$
$72$	2.83646	+	0.976974i	0.334280	+	0.115137i
$73$	−1.04583	+	1.81143i	−0.122405	+	0.212012i	−0.920716	−	0.390234i	$-0.872394\pi$
$73$	−1.04583	+	1.81143i	−0.122405	+	0.212012i	0.798311	+	0.602246i	$0.205727\pi$
$74$	3.69708	+	3.10222i	0.429777	+	0.360625i
$75$	12.6030	+	4.46362i	1.45527	+	0.515415i
$76$	0.788899	+	4.47407i	0.0904929	+	0.513211i
$77$	0.257883	−	0.216389i	0.0293884	−	0.0246598i
$78$	5.80825	+	4.78841i	0.657655	+	0.542181i
$79$	−5.47927	+	1.99429i	−0.616466	+	0.224375i	−0.631330	−	0.775514i	$-0.717491\pi$
$79$	−5.47927	+	1.99429i	−0.616466	+	0.224375i	0.0148640	+	0.999890i	$0.495268\pi$
$80$	−3.56640			−0.398736
$81$	−8.34529	+	3.36988i	−0.927255	+	0.374431i
$82$	5.66966			0.626109
$83$	1.01209	−	0.368370i	0.111091	−	0.0404339i	−0.285877	−	0.958266i	$-0.592285\pi$
$83$	1.01209	−	0.368370i	0.111091	−	0.0404339i	0.396968	+	0.917833i	$0.370063\pi$
$84$	−1.33644	−	1.10178i	−0.145818	−	0.120214i
$85$	−7.60267	+	6.37940i	−0.824625	+	0.691943i
$86$	−2.04239	−	11.5830i	−0.220237	−	1.24903i
$87$	9.28930	+	3.29001i	0.995918	+	0.352726i
$88$	−0.257883	−	0.216389i	−0.0274904	−	0.0230672i
$89$	7.81214	−	13.5310i	0.828085	−	1.43429i	−0.0714531	−	0.997444i	$-0.522764\pi$
$89$	7.81214	−	13.5310i	0.828085	−	1.43429i	0.899538	−	0.436842i	$-0.143903\pi$
$90$	8.07546	−	7.01854i	0.851228	−	0.739819i
$91$	−2.17303	−	3.76380i	−0.227795	−	0.394553i
$92$	1.47668	−	8.37468i	0.153955	−	0.873121i
$93$	−9.75249	+	0.0846459i	−1.01129	+	0.00877737i
$94$	9.18156	+	3.34182i	0.947006	+	0.344682i
$95$	15.2253	+	5.54157i	1.56209	+	0.568553i
$96$	−0.852974	+	1.50746i	−0.0870563	+	0.153854i
$97$	−0.519971	+	2.94890i	−0.0527950	+	0.299416i	−0.999760	−	0.0219222i	$-0.993021\pi$
$97$	−0.519971	+	2.94890i	−0.0527950	+	0.299416i	0.946965	+	0.321338i	$0.104132\pi$
$98$	0.500000	+	0.866025i	0.0505076	+	0.0874818i
$99$	1.00977	−	0.0175298i	0.101486	−	0.00176181i
$100$	−3.85961	+	6.68504i	−0.385961	+	0.668504i
$101$	−4.04051	−	3.39039i	−0.402046	−	0.337357i	0.419238	−	0.907876i	$-0.362297\pi$
$101$	−4.04051	−	3.39039i	−0.402046	−	0.337357i	−0.821284	+	0.570520i	$0.806742\pi$
$102$	0.878141	+	4.73928i	0.0869490	+	0.469259i
$103$	3.47286	+	19.6955i	0.342191	+	1.94066i	0.339340	+	0.940664i	$0.389796\pi$
$103$	3.47286	+	19.6955i	0.342191	+	1.94066i	0.00285061	+	0.999996i	$0.499093\pi$
$104$	−3.32927	+	2.79359i	−0.326462	+	0.273934i
$105$	−5.78610	+	2.16302i	−0.564666	+	0.211089i
$106$	4.68054	−	1.70358i	0.454614	−	0.165466i
$107$	17.5300			1.69469			0.847344	−	0.531044i	$-0.178200\pi$
$107$	17.5300			1.69469			0.847344	+	0.531044i	$0.178200\pi$
$108$	−1.03522	−	5.09199i	−0.0996142	−	0.489977i
$109$	−8.48319			−0.812543			−0.406271	−	0.913752i	$-0.633171\pi$
$109$	−8.48319			−0.812543			−0.406271	+	0.913752i	$0.633171\pi$
$110$	−1.12819	+	0.410629i	−0.107569	+	0.0391520i
$111$	1.38006	−	8.24451i	0.130989	−	0.782534i
$112$	0.766044	−	0.642788i	0.0723844	−	0.0607377i
$113$	−1.10404	−	6.26130i	−0.103859	−	0.589014i	−0.991670	−	0.128805i	$-0.958886\pi$
$113$	−1.10404	−	6.26130i	−0.103859	−	0.589014i	0.887811	−	0.460209i	$-0.152225\pi$
$114$	5.98377	−	5.11013i	0.560431	−	0.478607i
$115$	−23.2328	−	19.4946i	−2.16647	−	1.81788i
$116$	−2.84481	+	4.92736i	−0.264134	+	0.457494i
$117$	2.04084	−	12.8775i	0.188676	−	1.19052i
$118$	−5.56104	−	9.63201i	−0.511935	−	0.886698i
$119$	0.483228	−	2.74052i	0.0442975	−	0.251223i
$120$	3.13491	+	5.32259i	0.286177	+	0.485884i
$121$	10.2301	+	3.72346i	0.930011	+	0.338496i
$122$	6.74811	+	2.45611i	0.610945	+	0.222366i
$123$	−4.98370	−	8.46156i	−0.449365	−	0.762953i
$124$	0.977781	−	5.54527i	0.0878073	−	0.497980i
$125$	4.84891	+	8.39855i	0.433700	+	0.751190i
$126$	−0.469585	+	2.96302i	−0.0418339	+	0.263967i
$127$	7.11841	−	12.3294i	0.631656	−	1.09406i	−0.355557	−	0.934655i	$-0.615709\pi$
$127$	7.11841	−	12.3294i	0.631656	−	1.09406i	0.987213	−	0.159406i	$-0.0509580\pi$
$128$	−0.766044	−	0.642788i	−0.0677094	−	0.0568149i
$129$	−15.4915	+	13.2297i	−1.36395	+	1.16481i
$130$	2.69151	+	15.2643i	0.236061	+	1.33877i
$131$	−5.46457	+	4.58532i	−0.477442	+	0.400621i	−0.849500	−	0.527588i	$-0.823097\pi$
$131$	−5.46457	+	4.58532i	−0.477442	+	0.400621i	0.372058	+	0.928209i	$0.378652\pi$
$132$	−0.0962633	+	0.575079i	−0.00837865	+	0.0500542i
$133$	−4.26910	+	1.55383i	−0.370178	+	0.134734i
$134$	−2.38338			−0.205893
$135$	−17.5731	−	5.88265i	−1.51245	−	0.506298i
$136$	−2.78280			−0.238623
$137$	−12.0694	+	4.39289i	−1.03116	+	0.375310i	−0.801521	−	0.597967i	$-0.795975\pi$
$137$	−12.0694	+	4.39289i	−1.03116	+	0.375310i	−0.229635	+	0.973277i	$0.573753\pi$
$138$	−13.7966	+	5.15760i	−1.17445	+	0.439044i
$139$	2.25314	−	1.89061i	0.191109	−	0.160359i	−0.542213	−	0.840241i	$-0.682413\pi$
$139$	2.25314	−	1.89061i	0.191109	−	0.160359i	0.733322	+	0.679882i	$0.237969\pi$
$140$	−0.619299	−	3.51222i	−0.0523403	−	0.296837i
$141$	−3.08328	−	16.6403i	−0.259659	−	1.40137i
$142$	3.68665	+	3.09346i	0.309376	+	0.259598i
$143$	−0.731532	+	1.26705i	−0.0611738	+	0.105956i
$144$	2.99955	−	0.0520725i	0.249962	−	0.00433938i
$145$	10.1457	+	17.5729i	0.842557	+	1.45935i
$146$	−0.363212	+	2.05988i	−0.0300597	+	0.170477i
$147$	0.852974	−	1.50746i	0.0703521	−	0.124333i
$148$	4.53514	+	1.65066i	0.372786	+	0.135683i
$149$	−5.49954	−	2.00167i	−0.450540	−	0.163983i	0.106777	−	0.994283i	$-0.465947\pi$
$149$	−5.49954	−	2.00167i	−0.450540	−	0.163983i	−0.557317	+	0.830300i	$0.688169\pi$
$150$	13.3696	−	0.116040i	1.09162	−	0.00947462i
$151$	0.803840	−	4.55880i	0.0654155	−	0.370990i	−0.934473	−	0.356035i	$-0.884128\pi$
$151$	0.803840	−	4.55880i	0.0654155	−	0.370990i	0.999888	−	0.0149550i	$-0.00476050\pi$
$152$	2.27154	+	3.93443i	0.184246	+	0.319124i
$153$	6.30114	−	5.47645i	0.509417	−	0.442744i
$154$	0.168321	−	0.291540i	0.0135637	−	0.0234930i
$155$	−15.3835	−	12.9083i	−1.23563	−	1.03682i
$156$	7.09570	+	2.51310i	0.568111	+	0.201209i
$157$	−0.642720	−	3.64504i	−0.0512946	−	0.290906i	0.948360	−	0.317197i	$-0.102742\pi$
$157$	−0.642720	−	3.64504i	−0.0512946	−	0.290906i	−0.999654	+	0.0262906i	$0.991630\pi$
$158$	−4.46674	+	3.74804i	−0.355355	+	0.298178i
$159$	−6.65671	−	5.48790i	−0.527911	−	0.435219i
$160$	−3.35132	+	1.21978i	−0.264945	+	0.0964322i
$161$	8.50387			0.670199
$162$	−6.68945	+	6.02091i	−0.525573	+	0.473047i
$163$	0.368801			0.0288867			0.0144434	−	0.999896i	$-0.495402\pi$
$163$	0.368801			0.0288867			0.0144434	+	0.999896i	$0.495402\pi$
$164$	5.32774	−	1.93914i	0.416026	−	0.151421i
$165$	1.60453	+	1.32280i	0.124912	+	0.102980i
$166$	0.825062	−	0.692309i	0.0640372	−	0.0537336i
$167$	1.07715	+	6.10879i	0.0833520	+	0.472713i	0.997700	+	0.0677835i	$0.0215927\pi$
$167$	1.07715	+	6.10879i	0.0833520	+	0.472713i	−0.914348	+	0.404929i	$0.867296\pi$
$168$	−1.63268	−	0.578248i	−0.125964	−	0.0446128i
$169$	4.51064	+	3.78488i	0.346972	+	0.291144i
$170$	−4.96229	+	8.59494i	−0.380590	+	0.659202i
$171$	−12.8863	−	4.43848i	−0.985440	−	0.339419i
$172$	−5.88084	−	10.1859i	−0.448409	−	0.776668i
$173$	−1.69144	+	9.59262i	−0.128598	+	0.729314i	0.850508	+	0.525962i	$0.176295\pi$
$173$	−1.69144	+	9.59262i	−0.128598	+	0.729314i	−0.979106	+	0.203352i	$0.934817\pi$
$174$	9.85434	−	0.0855298i	0.747056	−	0.00648400i
$175$	−7.25369	−	2.64013i	−0.548327	−	0.199575i
$176$	−0.316340	−	0.115138i	−0.0238450	−	0.00867887i
$177$	−9.48685	+	16.7661i	−0.713075	+	1.26022i
$178$	2.71313	−	15.3869i	0.203358	−	1.15330i
$179$	10.0877	+	17.4724i	0.753990	+	1.30595i	0.945875	+	0.324532i	$0.105207\pi$
$179$	10.0877	+	17.4724i	0.753990	+	1.30595i	−0.191885	+	0.981417i	$0.561460\pi$
$180$	5.18796	−	9.35724i	0.386688	−	0.697448i
$181$	−4.63805	+	8.03333i	−0.344743	+	0.597113i	−0.985307	−	0.170792i	$-0.945367\pi$
$181$	−4.63805	+	8.03333i	−0.344743	+	0.597113i	0.640564	+	0.767905i	$0.278701\pi$
$182$	−3.32927	−	2.79359i	−0.246782	−	0.207075i
$183$	−2.26610	−	12.2300i	−0.167515	−	0.904069i
$184$	−1.47668	−	8.37468i	−0.108862	−	0.617389i
$185$	13.1853	−	11.0638i	0.969400	−	0.813423i
$186$	−9.13540	+	3.41509i	−0.669840	+	0.250407i
$187$	−0.880310	+	0.320407i	−0.0643747	+	0.0234305i
$188$	9.77082			0.712610
$189$	4.83486	−	1.90371i	0.351685	−	0.138474i
$190$	16.2025			1.17545
$191$	−9.43784	+	3.43509i	−0.682898	+	0.248555i	−0.660091	−	0.751185i	$-0.729482\pi$
$191$	−9.43784	+	3.43509i	−0.682898	+	0.248555i	−0.0228066	+	0.999740i	$0.507260\pi$
$192$	−0.285952	+	1.70828i	−0.0206368	+	0.123285i
$193$	−17.5906	+	14.7603i	−1.26620	+	1.06247i	−0.271209	+	0.962521i	$0.587423\pi$
$193$	−17.5906	+	14.7603i	−1.26620	+	1.06247i	−0.994993	+	0.0999485i	$0.968132\pi$
$194$	0.519971	+	2.94890i	0.0373317	+	0.211719i
$195$	20.4150	−	17.4344i	1.46195	−	1.24850i
$196$	0.766044	+	0.642788i	0.0547175	+	0.0459134i
$197$	4.27917	−	7.41174i	0.304878	−	0.528065i	−0.672356	−	0.740228i	$-0.734718\pi$
$197$	4.27917	−	7.41174i	0.304878	−	0.528065i	0.977234	+	0.212163i	$0.0680509\pi$
$198$	0.942881	−	0.361835i	0.0670076	−	0.0257145i
$199$	6.00531	+	10.4015i	0.425705	+	0.737343i	0.996486	−	0.0837593i	$-0.0266927\pi$
$199$	6.00531	+	10.4015i	0.425705	+	0.737343i	−0.570781	+	0.821103i	$0.693359\pi$
$200$	−1.34043	+	7.60194i	−0.0947826	+	0.537539i
$201$	2.09502	+	3.55703i	0.147771	+	0.250893i
$202$	−4.95642	−	1.80399i	−0.348733	−	0.126928i
$203$	−5.34649	−	1.94596i	−0.375250	−	0.136580i
$204$	2.44611	+	4.15313i	0.171262	+	0.290777i
$205$	3.51122	−	19.9131i	0.245234	−	1.39079i
$206$	9.99969	+	17.3200i	0.696711	+	1.20674i
$207$	19.8247	+	16.0569i	1.37791	+	1.11603i
$208$	−2.17303	+	3.76380i	−0.150672	+	0.260972i
$209$	1.17158	+	0.983075i	0.0810401	+	0.0680007i
$210$	−4.69736	+	4.01154i	−0.324149	+	0.276823i
$211$	2.24278	+	12.7195i	0.154400	+	0.875644i	0.959333	+	0.282278i	$0.0910901\pi$
$211$	2.24278	+	12.7195i	0.154400	+	0.875644i	−0.804933	+	0.593366i	$0.797799\pi$
$212$	3.81561	−	3.20168i	0.262057	−	0.219892i
$213$	1.37616	−	8.22124i	0.0942933	−	0.563310i
$214$	16.4728	−	5.99561i	1.12606	−	0.409851i
$215$	−41.9468			−2.86075
$216$	−2.71435	−	4.43083i	−0.184688	−	0.301480i
$217$	5.63082			0.382245
$218$	−7.97160	+	2.90142i	−0.539905	+	0.196509i
$219$	3.39349	−	1.26859i	0.229311	−	0.0857233i
$220$	−0.919712	+	0.771730i	−0.0620070	+	0.0520301i
$221$	2.10014	+	11.9105i	0.141271	+	0.801185i
$222$	−1.52296	−	8.21931i	−0.102214	−	0.551644i
$223$	−0.529822	−	0.444574i	−0.0354795	−	0.0297709i	0.624875	−	0.780724i	$-0.285150\pi$
$223$	−0.529822	−	0.444574i	−0.0354795	−	0.0297709i	−0.660355	+	0.750954i	$0.729594\pi$
$224$	0.500000	−	0.866025i	0.0334077	−	0.0578638i
$225$	−11.9252	−	19.8511i	−0.795012	−	1.32341i
$226$	−3.17895	−	5.50610i	−0.211460	−	0.366260i
$227$	−0.459864	+	2.60802i	−0.0305222	+	0.173100i	−0.996258	−	0.0864261i	$-0.972455\pi$
$227$	−0.459864	+	2.60802i	−0.0305222	+	0.173100i	0.965736	+	0.259526i	$0.0835665\pi$
$228$	3.87514	−	6.84852i	0.256637	−	0.453554i
$229$	5.84291	+	2.12665i	0.386111	+	0.140533i	0.527780	−	0.849381i	$-0.323025\pi$
$229$	5.84291	+	2.12665i	0.386111	+	0.140533i	−0.141669	+	0.989914i	$0.545247\pi$
$230$	−28.4992	−	10.3729i	−1.87918	−	0.683966i
$231$	−0.583059	+	0.00506060i	−0.0383624	+	0.000332963i
$232$	−0.987992	+	5.60318i	−0.0648649	+	0.367867i
$233$	−12.7091	−	22.0127i	−0.832598	−	1.44210i	−0.895971	−	0.444112i	$-0.853519\pi$
$233$	−12.7091	−	22.0127i	−0.832598	−	1.44210i	0.0633731	−	0.997990i	$-0.479814\pi$
$234$	−2.48659	−	12.7989i	−0.162553	−	0.836688i
$235$	17.4233	−	30.1781i	1.13657	−	1.96860i
$236$	−8.52001	−	7.14914i	−0.554605	−	0.465369i
$237$	9.52000	+	3.37172i	0.618390	+	0.219017i
$238$	−0.483228	−	2.74052i	−0.0313230	−	0.177642i
$239$	−5.60615	+	4.70412i	−0.362631	+	0.304284i	−0.805839	−	0.592135i	$-0.798285\pi$
$239$	−5.60615	+	4.70412i	−0.362631	+	0.304284i	0.443207	+	0.896419i	$0.353841\pi$
$240$	4.76628	+	3.92940i	0.307662	+	0.253642i
$241$	−24.1120	+	8.77606i	−1.55319	+	0.565316i	−0.969164	−	0.246418i	$-0.920747\pi$
$241$	−24.1120	+	8.77606i	−1.55319	+	0.565316i	−0.584028	+	0.811733i	$0.698524\pi$
$242$	10.8867			0.699822
$243$	14.8659	+	4.69107i	0.953646	+	0.300932i
$244$	7.18119			0.459729
$245$	3.35132	−	1.21978i	0.214108	−	0.0779289i
$246$	−7.57717	−	6.24674i	−0.483102	−	0.398277i
$247$	15.1252	−	12.6915i	0.962392	−	0.807543i
$248$	−0.977781	−	5.54527i	−0.0620892	−	0.352125i
$249$	−1.75846	−	0.622797i	−0.111438	−	0.0394682i
$250$	7.42896	+	6.23364i	0.469849	+	0.394250i
$251$	−5.93216	+	10.2748i	−0.374434	+	0.648539i	−0.990242	−	0.139357i	$-0.955496\pi$
$251$	−5.93216	+	10.2748i	−0.374434	+	0.648539i	0.615808	+	0.787896i	$0.288830\pi$
$252$	0.572147	+	2.94494i	0.0360419	+	0.185514i
$253$	−1.43138	−	2.47922i	−0.0899900	−	0.155867i
$254$	2.47220	−	14.0205i	0.155119	−	0.879726i
$255$	17.1892	−	0.149192i	1.07643	−	0.00934279i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	−17.7949	−	6.47683i	−1.11002	−	0.404013i	−0.279018	−	0.960286i	$-0.590009\pi$
$257$	−17.7949	−	6.47683i	−1.11002	−	0.404013i	−0.831000	+	0.556273i	$0.812231\pi$
$258$	−10.0324	+	17.7302i	−0.624590	+	1.10384i
$259$	−0.838060	+	4.75287i	−0.0520745	+	0.295329i
$260$	7.74989	+	13.4232i	0.480628	+	0.832472i
$261$	−8.78973	−	14.6317i	−0.544070	−	0.905680i
$262$	−3.56675	+	6.17779i	−0.220354	+	0.381665i
$263$	1.35018	+	1.13294i	0.0832558	+	0.0698599i	0.683466	−	0.729983i	$-0.260472\pi$
$263$	1.35018	+	1.13294i	0.0832558	+	0.0698599i	−0.600210	+	0.799843i	$0.704916\pi$
$264$	0.106231	+	0.573322i	0.00653805	+	0.0352855i
$265$	−3.08468	−	17.4941i	−0.189490	−	1.07465i
$266$	−3.48021	+	2.92024i	−0.213385	+	0.179051i
$267$	−25.3487	+	9.47613i	−1.55132	+	0.579930i
$268$	−2.23965	+	0.815165i	−0.136808	+	0.0497941i
$269$	−30.4647			−1.85747			−0.928734	−	0.370748i	$-0.879101\pi$
$269$	−30.4647			−1.85747			−0.928734	+	0.370748i	$0.879101\pi$
$270$	−18.5253	+	0.482462i	−1.12741	+	0.0293617i
$271$	8.56982			0.520579			0.260290	−	0.965531i	$-0.416182\pi$
$271$	8.56982			0.520579			0.260290	+	0.965531i	$0.416182\pi$
$272$	−2.61498	+	0.951774i	−0.158556	+	0.0577098i
$273$	−1.24276	+	7.42430i	−0.0752155	+	0.449339i
$274$	−9.83904	+	8.25593i	−0.594398	+	0.498759i
$275$	0.451244	+	2.55913i	0.0272110	+	0.154321i
$276$	−11.2006	+	9.56528i	−0.674196	+	0.575762i
$277$	17.5005	+	14.6847i	1.05151	+	0.882318i	0.993251	−	0.115984i	$-0.0370020\pi$
$277$	17.5005	+	14.6847i	1.05151	+	0.882318i	0.0582547	+	0.998302i	$0.481446\pi$
$278$	1.47063	−	2.54721i	0.0882025	−	0.152771i
$279$	13.1269	+	10.6320i	0.785887	+	0.636522i
$280$	−1.78320	−	3.08859i	−0.106567	−	0.184579i
$281$	1.94480	−	11.0295i	0.116017	−	0.657964i	−0.870225	−	0.492654i	$-0.836027\pi$
$281$	1.94480	−	11.0295i	0.116017	−	0.657964i	0.986242	−	0.165309i	$-0.0528622\pi$
$282$	−8.58866	−	14.5822i	−0.511447	−	0.868359i
$283$	20.9660	+	7.63100i	1.24630	+	0.453616i	0.879150	−	0.476546i	$-0.158111\pi$
$283$	20.9660	+	7.63100i	1.24630	+	0.453616i	0.367150	+	0.930162i	$0.380334\pi$
$284$	4.52234	+	1.64600i	0.268352	+	0.0976720i
$285$	−14.2422	−	24.1810i	−0.843632	−	1.43236i
$286$	−0.254058	+	1.44084i	−0.0150228	+	0.0851985i
$287$	2.83483	+	4.91007i	0.167335	+	0.289832i
$288$	2.80084	−	1.07484i	0.165041	−	0.0633354i
$289$	4.62801	−	8.01595i	0.272236	−	0.471527i
$290$	15.5442	+	13.0431i	0.912785	+	0.765918i
$291$	3.94396	−	3.36814i	0.231199	−	0.197444i
$292$	0.363212	+	2.05988i	0.0212554	+	0.120545i
$293$	−6.95706	+	5.83767i	−0.406436	+	0.341040i	−0.822975	−	0.568078i	$-0.807687\pi$
$293$	−6.95706	+	5.83767i	−0.406436	+	0.341040i	0.416539	+	0.909118i	$0.363243\pi$
$294$	0.285952	−	1.70828i	0.0166771	−	0.0996291i
$295$	−37.2737	+	13.5665i	−2.17016	+	0.789872i
$296$	4.82619			0.280517
$297$	−1.36882	−	1.08912i	−0.0794267	−	0.0631974i
$298$	−5.85249			−0.339026
$299$	−34.7295	+	12.6405i	−2.00846	+	0.731018i
$300$	12.5236	−	4.68170i	0.723050	−	0.270298i
$301$	9.00996	−	7.56026i	0.519326	−	0.435766i
$302$	−0.803840	−	4.55880i	−0.0462558	−	0.262330i
$303$	1.66443	+	8.98282i	0.0956188	+	0.516050i
$304$	3.48021	+	2.92024i	0.199604	+	0.167487i
$305$	12.8055	−	22.1798i	0.733241	−	1.27001i
$306$	4.04808	−	7.30129i	0.231413	−	0.417387i
$307$	14.2851	+	24.7425i	0.815294	+	1.41213i	0.909116	+	0.416542i	$0.136758\pi$
$307$	14.2851	+	24.7425i	0.815294	+	1.41213i	−0.0938218	+	0.995589i	$0.529908\pi$
$308$	0.0584572	−	0.331527i	0.00333091	−	0.0188905i
$309$	17.0590	−	30.1483i	0.970450	−	1.71507i
$310$	−18.8707	−	6.86836i	−1.07178	−	0.390097i
$311$	−5.83427	−	2.12350i	−0.330831	−	0.120413i	0.171264	−	0.985225i	$-0.445215\pi$
$311$	−5.83427	−	2.12350i	−0.330831	−	0.120413i	−0.502095	+	0.864813i	$0.667437\pi$
$312$	7.52731	−	0.0653326i	0.426150	−	0.00369873i
$313$	−2.28786	+	12.9751i	−0.129318	+	0.733397i	0.849332	+	0.527860i	$0.177005\pi$
$313$	−2.28786	+	12.9751i	−0.129318	+	0.733397i	−0.978649	+	0.205537i	$0.934106\pi$
$314$	−1.85064	−	3.20540i	−0.104438	−	0.180891i
$315$	10.1160	+	3.48428i	0.569970	+	0.196317i
$316$	−2.91546	+	5.04972i	−0.164007	+	0.284069i
$317$	18.0455	+	15.1419i	1.01353	+	0.850456i	0.988801	−	0.149238i	$-0.0476821\pi$
$317$	18.0455	+	15.1419i	1.01353	+	0.850456i	0.0247328	+	0.999694i	$0.492127\pi$
$318$	−8.13223	−	2.88021i	−0.456033	−	0.161514i
$319$	0.332599	+	1.88627i	0.0186220	+	0.105611i
$320$	−2.73202	+	2.29244i	−0.152725	+	0.128151i
$321$	−23.4278	−	19.3142i	−1.30761	−	1.07802i
$322$	7.99103	−	2.90850i	0.445322	−	0.162084i
$323$	12.6425			0.703448
$324$	−4.22675	+	7.94573i	−0.234820	+	0.441429i
$325$	33.5482			1.86092
$326$	0.346560	−	0.126137i	0.0191942	−	0.00698610i
$327$	11.3373	+	9.34664i	0.626953	+	0.516870i
$328$	4.34321	−	3.64439i	0.239814	−	0.201228i
$329$	1.69668	+	9.62238i	0.0935412	+	0.530499i
$330$	1.96019	+	0.694244i	0.107905	+	0.0382169i
$331$	4.63193	+	3.88665i	0.254594	+	0.213630i	0.761147	−	0.648579i	$-0.224636\pi$
$331$	4.63193	+	3.88665i	0.254594	+	0.213630i	−0.506554	+	0.862208i	$0.669081\pi$
$332$	0.538521	−	0.932746i	0.0295552	−	0.0511911i
$333$	−10.9280	+	9.49777i	−0.598852	+	0.520474i
$334$	3.10152	+	5.37198i	0.169707	+	0.293942i
$335$	−1.47603	+	8.37097i	−0.0806440	+	0.457355i
$336$	−1.73199	+	0.0150326i	−0.0944876	+	0.000820096i
$337$	26.7032	+	9.71915i	1.45461	+	0.529436i	0.943876	−	0.330301i	$-0.107150\pi$
$337$	26.7032	+	9.71915i	1.45461	+	0.529436i	0.510738	+	0.859737i	$0.329372\pi$
$338$	5.53312	+	2.01389i	0.300962	+	0.109541i
$339$	−5.42312	+	9.58427i	−0.294543	+	0.520546i
$340$	−1.72339	+	9.77380i	−0.0934637	+	0.530059i
$341$	−0.947784	−	1.64161i	−0.0513254	−	0.0888982i
$342$	−13.6272	+	0.236570i	−0.736875	+	0.0127922i
$343$	−0.500000	+	0.866025i	−0.0269975	+	0.0467610i
$344$	−9.00996	−	7.56026i	−0.485785	−	0.407622i
$345$	9.57038	+	51.6508i	0.515252	+	2.78079i
$346$	1.69144	+	9.59262i	0.0909323	+	0.515703i
$347$	19.2010	−	16.1116i	1.03077	−	0.864915i	0.0398237	−	0.999207i	$-0.487320\pi$
$347$	19.2010	−	16.1116i	1.03077	−	0.864915i	0.990942	+	0.134292i	$0.0428759\pi$
$348$	9.23080	−	3.45075i	0.494823	−	0.184980i
$349$	14.4922	−	5.27473i	0.775750	−	0.282350i	0.0763509	−	0.997081i	$-0.475673\pi$
$349$	14.4922	−	5.27473i	0.775750	−	0.282350i	0.699399	+	0.714731i	$0.253451\pi$
$350$	−7.71922			−0.412609
$351$	−16.9156	+	14.9614i	−0.902890	+	0.798580i
$352$	−0.336642			−0.0179431
$353$	24.2854	−	8.83916i	1.29258	−	0.470461i	0.398008	−	0.917382i	$-0.369702\pi$
$353$	24.2854	−	8.83916i	1.29258	−	0.470461i	0.894574	+	0.446921i	$0.147479\pi$
$354$	−3.18038	+	18.9997i	−0.169035	+	1.00982i
$355$	13.1481	−	11.0325i	0.697826	−	0.585546i
$356$	−2.71313	−	15.3869i	−0.143795	−	0.815505i
$357$	−3.66527	+	3.13013i	−0.193987	+	0.165664i
$358$	15.4553	+	12.9685i	0.816836	+	0.685406i
$359$	−2.44711	+	4.23851i	−0.129153	+	0.223700i	−0.923349	−	0.383962i	$-0.874559\pi$
$359$	−2.44711	+	4.23851i	−0.129153	+	0.223700i	0.794195	+	0.607662i	$0.207893\pi$
$360$	1.67473	−	10.5673i	0.0882659	−	0.556947i
$361$	−0.819817	−	1.41997i	−0.0431483	−	0.0747350i
$362$	−1.61078	+	9.13517i	−0.0846605	+	0.480134i
$363$	−9.56951	−	16.2476i	−0.502269	−	0.852776i
$364$	−4.08396	−	1.48644i	−0.214058	−	0.0779106i
$365$	7.00981	+	2.55136i	0.366910	+	0.133544i
$366$	−6.31235	−	10.7174i	−0.329952	−	0.560208i
$367$	3.60498	−	20.4449i	0.188179	−	1.06721i	−0.733624	−	0.679555i	$-0.762173\pi$
$367$	3.60498	−	20.4449i	0.188179	−	1.06721i	0.921803	−	0.387659i	$-0.126716\pi$
$368$	−4.25194	−	7.36457i	−0.221647	−	0.383905i
$369$	−2.66239	+	16.7993i	−0.138598	+	0.874538i
$370$	8.60607	−	14.9062i	0.447408	−	0.774934i
$371$	3.81561	+	3.20168i	0.198097	+	0.166223i
$372$	−7.41644	+	6.33363i	−0.384524	+	0.328383i
$373$	−3.57291	−	20.2630i	−0.184998	−	1.04918i	−0.925958	−	0.377627i	$-0.876740\pi$
$373$	−3.57291	−	20.2630i	−0.184998	−	1.04918i	0.740960	−	0.671549i	$-0.234371\pi$
$374$	−0.717635	+	0.602168i	−0.0371080	+	0.0311373i
$375$	2.77311	−	16.5666i	0.143203	−	0.855496i
$376$	9.18156	−	3.34182i	0.473503	−	0.172341i
$377$	24.7274			1.27353
$378$	3.89218	−	3.44252i	0.200192	−	0.177064i
$379$	24.5175			1.25938			0.629689	−	0.776848i	$-0.283183\pi$
$379$	24.5175			1.25938			0.629689	+	0.776848i	$0.283183\pi$
$380$	15.2253	−	5.54157i	0.781043	−	0.284277i
$381$	−23.0977	+	8.63463i	−1.18333	+	0.442365i
$382$	−7.69379	+	6.45586i	−0.393649	+	0.330311i
$383$	−0.812701	−	4.60906i	−0.0415271	−	0.235512i	0.956979	−	0.290158i	$-0.0937079\pi$
$383$	−0.812701	−	4.60906i	−0.0415271	−	0.235512i	−0.998506	+	0.0546464i	$0.982597\pi$
$384$	0.315560	+	1.70306i	0.0161034	+	0.0869090i
$385$	−0.919712	−	0.771730i	−0.0468729	−	0.0393310i
$386$	−11.4815	+	19.8865i	−0.584391	+	1.01220i
$387$	35.2797	−	0.612460i	1.79337	−	0.0311331i
$388$	1.49720	+	2.59322i	0.0760086	+	0.131651i
$389$	−0.426769	+	2.42033i	−0.0216381	+	0.122716i	−0.993713	−	0.111953i	$-0.964289\pi$
$389$	−0.426769	+	2.42033i	−0.0216381	+	0.122716i	0.972075	+	0.234669i	$0.0754005\pi$
$390$	13.2209	−	23.3653i	0.669467	−	1.18315i
$391$	−22.2374	−	8.09376i	−1.12459	−	0.409319i
$392$	0.939693	+	0.342020i	0.0474616	+	0.0172746i
$393$	12.3551	−	0.107235i	0.623233	−	0.00540929i
$394$	1.48614	−	8.42832i	0.0748706	−	0.424613i
$395$	10.3977	+	18.0093i	0.523165	+	0.906148i
$396$	0.762263	−	0.662498i	0.0383052	−	0.0332918i
$397$	8.64883	−	14.9802i	0.434072	−	0.751835i	−0.563147	−	0.826357i	$-0.690410\pi$
$397$	8.64883	−	14.9802i	0.434072	−	0.751835i	0.997219	+	0.0745216i	$0.0237430\pi$
$398$	9.20067	+	7.72028i	0.461188	+	0.386983i
$399$	7.41739	+	2.62703i	0.371334	+	0.131516i
$400$	1.34043	+	7.60194i	0.0670214	+	0.380097i
$401$	23.6379	−	19.8346i	1.18042	−	0.990491i	0.180445	−	0.983585i	$-0.442246\pi$
$401$	23.6379	−	19.8346i	1.18042	−	0.990491i	0.999976	−	0.00690553i	$-0.00219811\pi$
$402$	3.18525	+	2.62597i	0.158866	+	0.130972i
$403$	−22.9960	+	8.36987i	−1.14551	+	0.416933i
$404$	−5.27451			−0.262417
$405$	17.0040	+	27.2235i	0.844934	+	1.35275i
$406$	−5.68962			−0.282371
$407$	1.52672	−	0.555680i	0.0756765	−	0.0275440i
$408$	3.71905	+	3.06604i	0.184120	+	0.151792i
$409$	−1.90334	+	1.59709i	−0.0941139	+	0.0789710i	−0.688631	−	0.725112i	$-0.741788\pi$
$409$	−1.90334	+	1.59709i	−0.0941139	+	0.0789710i	0.594517	+	0.804083i	$0.297343\pi$
$410$	−3.51122	−	19.9131i	−0.173407	−	0.983438i
$411$	20.9700	+	7.42699i	1.03437	+	0.366346i
$412$	15.3204	+	12.8554i	0.754783	+	0.633338i
$413$	5.56104	−	9.63201i	0.273641	−	0.473960i
$414$	24.1209	+	8.30806i	1.18548	+	0.408319i
$415$	−1.92058	−	3.32654i	−0.0942776	−	0.163294i
$416$	−0.754685	+	4.28003i	−0.0370015	+	0.209846i
$417$	−5.09422	+	0.0442148i	−0.249465	+	0.00216521i
$418$	1.43716	+	0.523083i	0.0702937	+	0.0255848i
$419$	−17.1197	−	6.23108i	−0.836354	−	0.304408i	−0.111890	−	0.993721i	$-0.535690\pi$
$419$	−17.1197	−	6.23108i	−0.836354	−	0.304408i	−0.724464	+	0.689313i	$0.757913\pi$
$420$	−3.04205	+	5.37621i	−0.148437	+	0.262332i
$421$	−5.82937	+	33.0600i	−0.284106	+	1.61125i	0.424356	+	0.905496i	$0.360501\pi$
$421$	−5.82937	+	33.0600i	−0.284106	+	1.61125i	−0.708462	+	0.705749i	$0.750610\pi$
$422$	6.45784	+	11.1853i	0.314363	+	0.544492i
$423$	−14.2134	+	25.6359i	−0.691079	+	1.24646i
$424$	2.49046	−	4.31361i	0.120947	−	0.209487i
$425$	16.4554	+	13.8077i	0.798206	+	0.669774i
$426$	−1.51866	−	8.19611i	−0.0735792	−	0.397103i
$427$	1.24700	+	7.07209i	0.0603466	+	0.342242i
$428$	13.4288	−	11.2681i	0.649103	−	0.544662i
$429$	2.37366	−	0.887349i	0.114602	−	0.0428416i
$430$	−39.4171	+	14.3467i	−1.90086	+	0.691857i
$431$	−39.2240			−1.88936			−0.944678	−	0.328000i	$-0.893625\pi$
$431$	−39.2240			−1.88936			−0.944678	+	0.328000i	$0.893625\pi$
$432$	−4.06609	−	3.23526i	−0.195630	−	0.155657i
$433$	−19.5808			−0.940993			−0.470496	−	0.882402i	$-0.655925\pi$
$433$	−19.5808			−0.940993			−0.470496	+	0.882402i	$0.655925\pi$
$434$	5.29124	−	1.92585i	0.253988	−	0.0924439i
$435$	5.80238	−	34.6636i	0.278203	−	1.66199i
$436$	−6.49850	+	5.45289i	−0.311222	+	0.261146i
$437$	6.70869	+	38.0469i	0.320920	+	1.82003i
$438$	2.75495	−	2.35273i	0.131637	−	0.112418i
$439$	28.6672	+	24.0546i	1.36821	+	1.14806i	0.973350	+	0.229324i	$0.0736515\pi$
$439$	28.6672	+	24.0546i	1.36821	+	1.14806i	0.394860	+	0.918741i	$0.370793\pi$
$440$	−0.600300	+	1.03975i	−0.0286182	+	0.0495681i
$441$	−2.80084	+	1.07484i	−0.133373	+	0.0511828i
$442$	6.04711	+	10.4739i	0.287631	+	0.498192i
$443$	−1.98920	+	11.2813i	−0.0945095	+	0.535990i	0.900387	+	0.435090i	$0.143283\pi$
$443$	−1.98920	+	11.2813i	−0.0945095	+	0.535990i	−0.994897	+	0.100900i	$0.967828\pi$
$444$	−4.24228	−	7.20274i	−0.201330	−	0.341827i
$445$	−52.3620	−	19.0582i	−2.48220	−	0.903445i
$446$	−0.649923	−	0.236553i	−0.0307748	−	0.0112011i
$447$	5.14440	+	8.73441i	0.243322	+	0.413124i
$448$	0.173648	−	0.984808i	0.00820411	−	0.0465278i
$449$	−1.99933	−	3.46293i	−0.0943540	−	0.163426i	0.814985	−	0.579482i	$-0.196745\pi$
$449$	−1.99933	−	3.46293i	−0.0943540	−	0.163426i	−0.909339	+	0.416056i	$0.863412\pi$
$450$	−17.9955	−	14.5753i	−0.848316	−	0.687086i
$451$	0.954322	−	1.65293i	0.0449373	−	0.0778336i
$452$	−4.87043	−	4.08678i	−0.229086	−	0.192226i
$453$	−6.09709	+	5.20691i	−0.286467	+	0.244642i
$454$	0.459864	+	2.60802i	0.0215825	+	0.122400i
$455$	−11.8735	+	9.96307i	−0.556639	+	0.467076i
$456$	1.29910	−	7.76088i	0.0608361	−	0.363436i
$457$	6.49373	−	2.36353i	0.303764	−	0.110561i	−0.185641	−	0.982618i	$-0.559436\pi$
$457$	6.49373	−	2.36353i	0.303764	−	0.110561i	0.489405	+	0.872057i	$0.337214\pi$
$458$	6.21790			0.290543
$459$	−14.4550	+	0.376457i	−0.674699	+	0.0175715i
$460$	−30.3282			−1.41406
$461$	−32.3619	+	11.7788i	−1.50725	+	0.548592i	−0.957925	−	0.287019i	$-0.907336\pi$
$461$	−32.3619	+	11.7788i	−1.50725	+	0.548592i	−0.549320	+	0.835612i	$0.685113\pi$
$462$	−0.546165	+	0.204173i	−0.0254099	+	0.00949900i
$463$	−0.418157	+	0.350875i	−0.0194334	+	0.0163065i	−0.652453	−	0.757830i	$-0.726260\pi$
$463$	−0.418157	+	0.350875i	−0.0194334	+	0.0163065i	0.633019	+	0.774136i	$0.281815\pi$
$464$	0.987992	+	5.60318i	0.0458664	+	0.260121i
$465$	6.33701	+	34.2005i	0.293872	+	1.58601i
$466$	−19.4714	−	16.3385i	−0.901995	−	0.756864i
$467$	1.56578	−	2.71201i	0.0724558	−	0.125497i	−0.827521	−	0.561434i	$-0.810250\pi$
$467$	1.56578	−	2.71201i	0.0724558	−	0.125497i	0.899977	+	0.435937i	$0.143583\pi$
$468$	−6.71410	−	11.1765i	−0.310359	−	0.516635i
$469$	−1.19169	−	2.06407i	−0.0550272	−	0.0953099i
$470$	6.05106	−	34.3173i	0.279114	−	1.58294i
$471$	−3.15709	+	5.57952i	−0.145471	+	0.257091i
$472$	−10.4513	−	3.80398i	−0.481062	−	0.175092i
$473$	−3.72068	−	1.35422i	−0.171077	−	0.0622670i
$474$	10.0991	−	0.0876539i	0.463865	−	0.00402608i
$475$	6.08968	−	34.5363i	0.279414	−	1.58463i
$476$	−1.39140	−	2.40998i	−0.0637747	−	0.110461i
$477$	2.84982	+	14.6685i	0.130484	+	0.671624i
$478$	−3.65915	+	6.33784i	−0.167366	+	0.289886i
$479$	−11.0880	−	9.30397i	−0.506625	−	0.425109i	0.353314	−	0.935505i	$-0.385055\pi$
$479$	−11.0880	−	9.30397i	−0.506625	−	0.425109i	−0.859940	+	0.510395i	$0.829499\pi$
$480$	5.82278	+	2.06226i	0.265772	+	0.0941290i
$481$	−3.64226	−	20.6563i	−0.166073	−	0.941845i
$482$	−19.6563	+	16.4936i	−0.895320	+	0.751263i
$483$	−11.3649	−	9.36942i	−0.517122	−	0.426324i
$484$	10.2301	−	3.72346i	0.465006	−	0.169248i
$485$	10.6792			0.484918
$486$	15.5738	−	0.676264i	0.706441	−	0.0306759i
$487$	−16.8756			−0.764708			−0.382354	−	0.924016i	$-0.624887\pi$
$487$	−16.8756			−0.764708			−0.382354	+	0.924016i	$0.624887\pi$
$488$	6.74811	−	2.45611i	0.305473	−	0.111183i
$489$	−0.492881	−	0.406339i	−0.0222888	−	0.0183753i
$490$	2.73202	−	2.29244i	0.123420	−	0.103562i
$491$	3.61755	+	20.5161i	0.163258	+	0.925881i	0.950843	+	0.309675i	$0.100220\pi$
$491$	3.61755	+	20.5161i	0.163258	+	0.925881i	−0.787585	+	0.616206i	$0.788669\pi$
$492$	−9.25672	−	3.27847i	−0.417325	−	0.147805i
$493$	12.1288	+	10.1773i	0.546256	+	0.458363i
$494$	9.87226	−	17.0993i	0.444174	−	0.769332i
$495$	−0.686920	−	3.53569i	−0.0308748	−	0.158917i
$496$	−2.81541	−	4.87643i	−0.126416	−	0.218958i
$497$	−0.835695	+	4.73946i	−0.0374860	+	0.212594i
$498$	−1.86542	+	0.0161907i	−0.0835915	+	0.000725525i
$499$	−12.2297	−	4.45125i	−0.547477	−	0.199265i	0.0534480	−	0.998571i	$-0.482979\pi$
$499$	−12.2297	−	4.45125i	−0.547477	−	0.199265i	−0.600925	+	0.799305i	$0.705201\pi$
$500$	9.11297	+	3.31685i	0.407544	+	0.148334i
$501$	5.29103	−	9.35082i	0.236386	−	0.417764i
$502$	−2.06022	+	11.6841i	−0.0919520	+	0.521485i
$503$	−10.7390	−	18.6004i	−0.478827	−	0.829353i	0.520878	−	0.853631i	$-0.325605\pi$
$503$	−10.7390	−	18.6004i	−0.478827	−	0.829353i	−0.999705	+	0.0242783i	$0.992271\pi$
$504$	1.54487	+	2.57165i	0.0688140	+	0.114550i
$505$	−9.40551	+	16.2908i	−0.418540	+	0.724932i
$506$	−2.19300	−	1.84015i	−0.0974907	−	0.0818044i
$507$	−1.85809	−	10.0280i	−0.0825206	−	0.445359i
$508$	−2.47220	−	14.0205i	−0.109686	−	0.622060i
$509$	0.452114	−	0.379369i	0.0200396	−	0.0168152i	−0.632713	−	0.774387i	$-0.718059\pi$
$509$	0.452114	−	0.379369i	0.0200396	−	0.0168152i	0.652752	+	0.757571i	$0.273614\pi$
$510$	16.1016	−	6.01926i	0.712989	−	0.266537i
$511$	−1.96551	+	0.715389i	−0.0869492	+	0.0316469i
$512$	−1.00000			−0.0441942
$513$	12.3315	+	20.1297i	0.544450	+	0.888746i
$514$	−18.9370			−0.835274
$515$	67.0243	−	24.3949i	2.95345	−	1.07497i
$516$	−3.36327	+	20.0923i	−0.148060	+	0.884513i
$517$	2.51972	−	2.11430i	0.110817	−	0.0929867i
$518$	0.838060	+	4.75287i	0.0368222	+	0.208829i
$519$	12.8295	−	10.9564i	0.563153	−	0.480931i
$520$	11.8735	+	9.96307i	0.520689	+	0.436910i
$521$	10.6238	−	18.4010i	0.465439	−	0.806164i	−0.533782	−	0.845622i	$-0.679230\pi$
$521$	10.6238	−	18.4010i	0.465439	−	0.806164i	0.999221	+	0.0394581i	$0.0125632\pi$
$522$	−13.2640	−	10.7430i	−0.580549	−	0.470210i
$523$	−11.5529	−	20.0103i	−0.505175	−	0.874988i	−0.999982	−	0.00598553i	$-0.998095\pi$
$523$	−11.5529	−	20.0103i	−0.505175	−	0.874988i	0.494807	−	0.869003i	$-0.335239\pi$
$524$	−1.23872	+	7.02512i	−0.0541137	+	0.306894i
$525$	6.78528	+	11.5204i	0.296134	+	0.502790i
$526$	1.65624	+	0.602824i	0.0722157	+	0.0262844i
$527$	−14.7245	−	5.35926i	−0.641407	−	0.233453i
$528$	0.295912	+	0.502413i	0.0128779	+	0.0218647i
$529$	8.56360	−	48.5666i	0.372331	−	2.11159i
$530$	−8.88198	−	15.3840i	−0.385809	−	0.668240i
$531$	31.1512	−	11.9544i	1.35185	−	0.518778i
$532$	−2.27154	+	3.93443i	−0.0984839	+	0.170579i
$533$	−18.8759	−	15.8387i	−0.817604	−	0.686051i
$534$	−20.5790	+	17.5744i	−0.890539	+	0.760519i
$535$	−10.8563	−	61.5692i	−0.469359	−	2.66187i
$536$	−1.82578	+	1.53201i	−0.0788616	+	0.0661727i
$537$	5.76919	−	34.4653i	0.248959	−	1.48729i
$538$	−28.6275	+	10.4195i	−1.23422	+	0.449219i
$539$	0.336642			0.0145002
$540$	−17.2431	+	6.78939i	−0.742023	+	0.292169i
$541$	−23.3036			−1.00190			−0.500949	−	0.865477i	$-0.667016\pi$
$541$	−23.3036			−1.00190			−0.500949	+	0.865477i	$0.667016\pi$
$542$	8.05299	−	2.93105i	0.345906	−	0.125899i
$543$	15.0495	−	5.62595i	0.645834	−	0.241433i
$544$	−2.13175	+	1.78875i	−0.0913980	+	0.0766920i
$545$	5.25363	+	29.7948i	0.225041	+	1.27627i
$546$	1.37144	+	7.40161i	0.0586924	+	0.316760i
$547$	−33.0413	−	27.7249i	−1.41274	−	1.18543i	−0.955095	−	0.296301i	$-0.904247\pi$
$547$	−33.0413	−	27.7249i	−1.41274	−	1.18543i	−0.457650	−	0.889133i	$-0.651309\pi$
$548$	−6.42198	+	11.1232i	−0.274333	+	0.475159i
$549$	−10.4463	+	18.8414i	−0.445838	+	0.804133i
$550$	1.29931	+	2.25046i	0.0554026	+	0.0959600i
$551$	4.48853	−	25.4557i	0.191218	−	1.08445i
$552$	−7.25358	+	12.8192i	−0.308733	+	0.545623i
$553$	−5.47927	−	1.99429i	−0.233002	−	0.0848059i
$554$	21.4676	+	7.81357i	0.912071	+	0.331967i
$555$	−29.8112	+	0.258743i	−1.26541	+	0.0109830i
$556$	0.510745	−	2.89658i	0.0216604	−	0.122842i
$557$	−2.34745	−	4.06590i	−0.0994645	−	0.172278i	0.811999	−	0.583659i	$-0.198380\pi$
$557$	−2.34745	−	4.06590i	−0.0994645	−	0.172278i	−0.911463	+	0.411382i	$0.865046\pi$
$558$	15.9716	+	5.50116i	0.676132	+	0.232883i
$559$	−25.5585	+	44.2685i	−1.08101	+	1.87236i
$560$	−2.73202	−	2.29244i	−0.115449	−	0.0968732i
$561$	1.52950	+	0.541706i	0.0645756	+	0.0228709i
$562$	−1.94480	−	11.0295i	−0.0820362	−	0.465251i
$563$	9.52275	−	7.99053i	0.401336	−	0.336761i	−0.419674	−	0.907675i	$-0.637856\pi$
$563$	9.52275	−	7.99053i	0.401336	−	0.336761i	0.821010	+	0.570914i	$0.193411\pi$
$564$	−13.0581	−	10.7653i	−0.549846	−	0.453302i
$565$	−21.3073	+	7.75524i	−0.896407	+	0.326265i
$566$	22.3116			0.937825
$567$	−8.55898	−	2.78278i	−0.359443	−	0.116866i
$568$	4.81257			0.201931
$569$	13.2899	−	4.83714i	0.557143	−	0.202783i	−0.0480745	−	0.998844i	$-0.515308\pi$
$569$	13.2899	−	4.83714i	0.557143	−	0.202783i	0.605217	+	0.796060i	$0.293086\pi$
$570$	−21.6536	−	17.8516i	−0.906971	−	0.747722i
$571$	10.1801	−	8.54216i	0.426026	−	0.357478i	−0.404424	−	0.914572i	$-0.632528\pi$
$571$	10.1801	−	8.54216i	0.426026	−	0.357478i	0.830450	+	0.557093i	$0.188083\pi$
$572$	0.254058	+	1.44084i	0.0106227	+	0.0602444i
$573$	16.3978	+	5.80765i	0.685029	+	0.242618i
$574$	4.34321	+	3.64439i	0.181282	+	0.152114i
$575$	−32.8216	+	56.8487i	−1.36876	+	2.37075i
$576$	2.26432	−	1.96796i	0.0943465	−	0.0819984i
$577$	−9.21653	−	15.9635i	−0.383689	−	0.664569i	0.607897	−	0.794016i	$-0.292013\pi$
$577$	−9.21653	−	15.9635i	−0.383689	−	0.664569i	−0.991586	+	0.129446i	$0.958680\pi$
$578$	1.60729	−	9.11540i	0.0668545	−	0.379151i
$579$	39.7715	−	0.345193i	1.65285	−	0.0143457i
$580$	19.0677	+	6.94009i	0.791745	+	0.288172i
$581$	1.01209	+	0.368370i	0.0419885	+	0.0152826i
$582$	2.55414	−	4.51393i	0.105872	−	0.187108i
$583$	0.291171	−	1.65131i	0.0120591	−	0.0683904i
$584$	1.04583	+	1.81143i	0.0432767	+	0.0749574i
$585$	−46.4924	+	0.807113i	−1.92222	+	0.0333700i
$586$	−4.54090	+	7.86507i	−0.187583	+	0.324903i
$587$	−13.6548	−	11.4577i	−0.563594	−	0.472911i	0.315919	−	0.948786i	$-0.397687\pi$
$587$	−13.6548	−	11.4577i	−0.563594	−	0.472911i	−0.879513	+	0.475875i	$0.842132\pi$
$588$	−0.315560	−	1.70306i	−0.0130135	−	0.0702331i
$589$	4.44214	+	25.1927i	0.183035	+	1.03805i
$590$	−30.3858	+	25.4967i	−1.25096	+	1.04968i
$591$	−13.8850	+	5.19063i	−0.571152	+	0.213514i
$592$	4.53514	−	1.65066i	0.186393	−	0.0678415i
$593$	21.2186			0.871343			0.435671	−	0.900106i	$-0.356511\pi$
$593$	21.2186			0.871343			0.435671	+	0.900106i	$0.356511\pi$
$594$	−1.65877	−	0.555279i	−0.0680601	−	0.0227834i
$595$	−9.92458			−0.406868
$596$	−5.49954	+	2.00167i	−0.225270	+	0.0819916i
$597$	3.43446	−	20.5175i	0.140563	−	0.839727i
$598$	−28.3117	+	23.7563i	−1.15775	+	0.971469i
$599$	3.47751	+	19.7219i	0.142087	+	0.805816i	0.969660	+	0.244458i	$0.0786099\pi$
$599$	3.47751	+	19.7219i	0.142087	+	0.805816i	−0.827573	+	0.561358i	$0.810279\pi$
$600$	10.1671	−	8.68269i	0.415070	−	0.354469i
$601$	33.0352	+	27.7198i	1.34754	+	1.13072i	0.979621	+	0.200857i	$0.0643725\pi$
$601$	33.0352	+	27.7198i	1.34754	+	1.13072i	0.367914	+	0.929860i	$0.380072\pi$
$602$	5.88084	−	10.1859i	0.239685	−	0.415146i
$603$	1.11920	−	7.06202i	0.0455774	−	0.287588i
$604$	−2.31456	−	4.00894i	−0.0941783	−	0.163122i
$605$	6.74211	−	38.2364i	0.274106	−	1.55453i
$606$	4.63636	+	7.87183i	0.188339	+	0.319771i
$607$	6.17111	+	2.24610i	0.250478	+	0.0911664i	0.464208	−	0.885726i	$-0.346339\pi$
$607$	6.17111	+	2.24610i	0.250478	+	0.0911664i	−0.213730	+	0.976893i	$0.568561\pi$
$608$	4.26910	+	1.55383i	0.173135	+	0.0630160i
$609$	5.00124	+	8.49134i	0.202661	+	0.344087i
$610$	4.44730	−	25.2219i	0.180066	−	1.02121i
$611$	−21.2323	−	36.7754i	−0.858966	−	1.48777i
$612$	1.30676	−	8.24549i	0.0528226	−	0.333304i
$613$	−1.93248	+	3.34716i	−0.0780522	+	0.135190i	−0.902409	−	0.430879i	$-0.858203\pi$
$613$	−1.93248	+	3.34716i	−0.0780522	+	0.135190i	0.824357	+	0.566070i	$0.191537\pi$
$614$	21.8861	+	18.3646i	0.883250	+	0.741134i
$615$	−26.6324	+	22.7441i	−1.07392	+	0.917129i
$616$	−0.0584572	−	0.331527i	−0.00235531	−	0.0133576i
$617$	21.5209	−	18.0582i	0.866399	−	0.726995i	−0.0969378	−	0.995290i	$-0.530905\pi$
$617$	21.5209	−	18.0582i	0.866399	−	0.726995i	0.963337	+	0.268296i	$0.0864604\pi$
$618$	5.71886	−	34.1646i	0.230046	−	1.37430i
$619$	31.4445	−	11.4449i	1.26386	−	0.460008i	0.378799	−	0.925479i	$-0.376337\pi$
$619$	31.4445	−	11.4449i	1.26386	−	0.460008i	0.885063	+	0.465471i	$0.154115\pi$
$620$	−20.0818			−0.806503
$621$	−8.80339	−	43.3016i	−0.353268	−	1.73763i
$622$	−6.20870			−0.248946
$623$	14.6820	−	5.34382i	0.588223	−	0.214096i
$624$	7.05101	−	2.63588i	0.282266	−	0.105520i
$625$	−3.07167	+	2.57744i	−0.122867	+	0.103098i
$626$	2.28786	+	12.9751i	0.0914414	+	0.518590i
$627$	−0.482616	−	2.60465i	−0.0192738	−	0.104020i
$628$	−2.83534	−	2.37913i	−0.113142	−	0.0949378i
$629$	6.71517	−	11.6310i	0.267751	−	0.463759i
$630$	10.6976	−	0.185712i	0.426202	−	0.00739892i
$631$	−17.6533	−	30.5764i	−0.702767	−	1.21723i	−0.967491	−	0.252904i	$-0.918614\pi$
$631$	−17.6533	−	30.5764i	−0.702767	−	1.21723i	0.264725	−	0.964324i	$-0.414719\pi$
$632$	−1.01253	+	5.74233i	−0.0402762	+	0.228418i
$633$	11.0167	−	19.4699i	0.437876	−	0.773858i
$634$	22.1360	+	8.05686i	0.879134	+	0.319979i
$635$	−47.7121	−	17.3658i	−1.89340	−	0.689141i
$636$	−8.62689	+	0.0748763i	−0.342078	+	0.00296904i
$637$	0.754685	−	4.28003i	0.0299017	−	0.169581i
$638$	0.957682	+	1.65875i	0.0379150	+	0.0656707i
$639$	−10.8972	+	9.47096i	−0.431086	+	0.374666i
$640$	−1.78320	+	3.08859i	−0.0704872	+	0.122087i
$641$	−20.1879	−	16.9397i	−0.797374	−	0.669076i	0.150185	−	0.988658i	$-0.452013\pi$
$641$	−20.1879	−	16.9397i	−0.797374	−	0.669076i	−0.947559	+	0.319582i	$0.896458\pi$
$642$	−28.6208	−	10.1367i	−1.12957	−	0.400063i
$643$	2.24935	+	12.7567i	0.0887055	+	0.503074i	0.996495	+	0.0836486i	$0.0266573\pi$
$643$	2.24935	+	12.7567i	0.0887055	+	0.503074i	−0.907790	+	0.419425i	$0.862232\pi$
$644$	6.51434	−	5.46618i	0.256701	−	0.215398i
$645$	56.0595	+	46.2163i	2.20734	+	1.81977i
$646$	11.8801	−	4.32399i	0.467415	−	0.170125i
$647$	3.55685			0.139834			0.0699170	−	0.997553i	$-0.477727\pi$
$647$	3.55685			0.139834			0.0699170	+	0.997553i	$0.477727\pi$
$648$	−1.25425	+	8.91217i	−0.0492716	+	0.350103i
$649$	−3.74416			−0.146971
$650$	31.5250	−	11.4741i	1.23651	−	0.450053i
$651$	−7.52525	−	6.20394i	−0.294938	−	0.243152i
$652$	0.282518	−	0.237061i	0.0110643	−	0.00928401i
$653$	−1.38222	−	7.83898i	−0.0540906	−	0.306763i	0.945745	−	0.324911i	$-0.105334\pi$
$653$	−1.38222	−	7.83898i	−0.0540906	−	0.306763i	−0.999835	+	0.0181476i	$0.994223\pi$
$654$	13.8503	+	4.90539i	0.541590	+	0.191816i
$655$	19.4889	+	16.3531i	0.761493	+	0.638968i
$656$	2.83483	−	4.91007i	0.110682	−	0.191706i
$657$	−5.93291	−	2.04349i	−0.231465	−	0.0797243i
$658$	4.88541	+	8.46178i	0.190453	+	0.329874i
$659$	−2.45406	+	13.9177i	−0.0955965	+	0.542155i	0.898966	+	0.438018i	$0.144319\pi$
$659$	−2.45406	+	13.9177i	−0.0955965	+	0.542155i	−0.994563	+	0.104137i	$0.966792\pi$
$660$	2.07942	−	0.0180481i	0.0809413	−	0.000702523i
$661$	43.8565	+	15.9625i	1.70582	+	0.620868i	0.996467	−	0.0839831i	$-0.0267642\pi$
$661$	43.8565	+	15.9625i	1.70582	+	0.620868i	0.709355	+	0.704852i	$0.248986\pi$
$662$	5.68190	+	2.06804i	0.220833	+	0.0803768i
$663$	10.3160	−	18.2315i	0.400642	−	0.708054i
$664$	0.187026	−	1.06068i	0.00725803	−	0.0411623i
$665$	8.10123	+	14.0317i	0.314152	+	0.544128i
$666$	−7.02056	+	12.6626i	−0.272041	+	0.490665i
$667$	−24.1919	+	41.9016i	−0.936714	+	1.62244i
$668$	4.75180	+	3.98723i	0.183853	+	0.154271i
$669$	0.218252	+	1.17790i	0.00843812	+	0.0455401i
$670$	1.47603	+	8.37097i	0.0570239	+	0.323399i
$671$	1.85190	−	1.55393i	0.0714919	−	0.0599889i
$672$	−1.62239	+	0.606500i	−0.0625852	+	0.0233962i
$673$	−23.7513	+	8.64476i	−0.915544	+	0.333231i	−0.756464	−	0.654035i	$-0.773075\pi$
$673$	−23.7513	+	8.64476i	−0.915544	+	0.333231i	−0.159080	+	0.987266i	$0.550853\pi$
$674$	28.4169			1.09458
$675$	−5.93432	+	39.6688i	−0.228412	+	1.52685i
$676$	5.88822			0.226470
$677$	−14.7102	+	5.35406i	−0.565357	+	0.205773i	−0.608857	−	0.793280i	$-0.708372\pi$
$677$	−14.7102	+	5.35406i	−0.565357	+	0.205773i	0.0434995	+	0.999053i	$0.486149\pi$
$678$	−1.81805	+	10.8611i	−0.0698219	+	0.417118i
$679$	−2.29384	+	1.92476i	−0.0880294	+	0.0738654i
$680$	1.72339	+	9.77380i	0.0660888	+	0.374808i
$681$	3.48805	−	2.97879i	0.133662	−	0.114148i
$682$	−1.45209	−	1.21845i	−0.0556034	−	0.0466568i
$683$	5.34781	−	9.26268i	0.204628	−	0.354427i	−0.745386	−	0.666633i	$-0.767735\pi$
$683$	5.34781	−	9.26268i	0.204628	−	0.354427i	0.950014	+	0.312207i	$0.101068\pi$
$684$	−12.7245	+	4.88308i	−0.486532	+	0.186709i
$685$	22.9033	+	39.6697i	0.875092	+	1.51570i
$686$	−0.173648	+	0.984808i	−0.00662992	+	0.0376001i
$687$	−5.46560	−	9.27976i	−0.208526	−	0.354045i
$688$	−11.0524	−	4.02273i	−0.421367	−	0.153365i
$689$	−20.3419	−	7.40384i	−0.774964	−	0.282064i
$690$	26.6588	+	45.2627i	1.01488	+	1.72312i
$691$	3.18482	−	18.0620i	0.121156	−	0.687112i	−0.862360	−	0.506295i	$-0.831015\pi$
$691$	3.18482	−	18.0620i	0.121156	−	0.687112i	0.983517	−	0.180817i	$-0.0578742\pi$
$692$	4.87030	+	8.43561i	0.185141	+	0.320674i
$693$	0.784799	+	0.635641i	0.0298120	+	0.0241460i
$694$	12.5326	−	21.7071i	0.475730	−	0.823989i
$695$	−8.03559	−	6.74266i	−0.304807	−	0.255764i
$696$	7.49389	−	6.39977i	0.284055	−	0.242583i
$697$	−2.73974	−	15.5378i	−0.103775	−	0.588538i
$698$	11.8142	−	9.91326i	0.447173	−	0.375222i
$699$	−7.26836	+	43.4213i	−0.274915	+	1.64235i
$700$	−7.25369	+	2.64013i	−0.274164	+	0.0997874i
$701$	−10.2198			−0.385998			−0.192999	−	0.981199i	$-0.561821\pi$
$701$	−10.2198			−0.385998			−0.192999	+	0.981199i	$0.561821\pi$
$702$	−10.7784	+	19.8446i	−0.406804	+	0.748986i
$703$	−21.9258			−0.826948
$704$	−0.316340	+	0.115138i	−0.0119225	+	0.00433944i
$705$	−56.5349	+	21.1345i	−2.12923	+	0.795971i
$706$	19.7976	−	16.6122i	0.745094	−	0.625208i
$707$	−0.915910	−	5.19438i	−0.0344463	−	0.195355i
$708$	3.50969	+	18.9416i	0.131902	+	0.711869i
$709$	−4.59649	−	3.85691i	−0.172625	−	0.144849i	0.552382	−	0.833591i	$-0.313719\pi$
$709$	−4.59649	−	3.85691i	−0.172625	−	0.144849i	−0.725007	+	0.688742i	$0.758163\pi$
$710$	8.58178	−	14.8641i	0.322069	−	0.557839i
$711$	−9.00801	−	14.9951i	−0.337827	−	0.562359i
$712$	−7.81214	−	13.5310i	−0.292772	−	0.507097i
$713$	8.31493	−	47.1563i	0.311396	−	1.76602i
$714$	−2.37366	+	4.19496i	−0.0888319	+	0.156992i
$715$	4.90320	+	1.78462i	0.183369	+	0.0667409i
$716$	18.9587	+	6.90039i	0.708519	+	0.257880i
$717$	12.6752	−	0.110013i	0.473364	−	0.00410852i
$718$	−0.849871	+	4.81986i	−0.0317169	+	0.179876i
$719$	0.0508780	+	0.0881233i	0.00189743	+	0.00328644i	0.866973	−	0.498356i	$-0.166063\pi$
$719$	0.0508780	+	0.0881233i	0.00189743	+	0.00328644i	−0.865075	+	0.501642i	$0.832729\pi$
$720$	−2.04051	−	10.5028i	−0.0760452	−	0.391417i
$721$	−9.99969	+	17.3200i	−0.372408	+	0.645029i
$722$	−1.25603	−	1.05394i	−0.0467447	−	0.0392235i
$723$	41.8936	+	14.8375i	1.55804	+	0.551814i
$724$	1.61078	+	9.13517i	0.0598640	+	0.339506i
$725$	33.6442	−	28.2309i	1.24952	−	1.04847i
$726$	−14.5494	−	11.9948i	−0.539979	−	0.445167i
$727$	−15.1482	+	5.51350i	−0.561816	+	0.204484i	−0.607289	−	0.794481i	$-0.707743\pi$
$727$	−15.1482	+	5.51350i	−0.561816	+	0.204484i	0.0454725	+	0.998966i	$0.485521\pi$
$728$	−4.34606			−0.161076
$729$	−14.6988	−	22.6483i	−0.544400	−	0.838826i
$730$	7.45969			0.276095
$731$	−30.7565	+	11.1944i	−1.13757	+	0.414042i
$732$	−9.59723	−	7.91211i	−0.354724	−	0.292440i
$733$	−12.0932	+	10.1474i	−0.446672	+	0.374802i	−0.838199	−	0.545364i	$-0.816391\pi$
$733$	−12.0932	+	10.1474i	−0.446672	+	0.374802i	0.391527	+	0.920167i	$0.371947\pi$
$734$	−3.60498	−	20.4449i	−0.133062	−	0.754634i
$735$	−5.82278	−	2.06226i	−0.214776	−	0.0760678i
$736$	−6.51434	−	5.46618i	−0.240122	−	0.201486i
$737$	−0.401173	+	0.694852i	−0.0147774	+	0.0255952i
$738$	3.24388	+	16.6968i	0.119409	+	0.614617i
$739$	−12.4010	−	21.4792i	−0.456179	−	0.790126i	0.542576	−	0.840007i	$-0.317449\pi$
$739$	−12.4010	−	21.4792i	−0.456179	−	0.790126i	−0.998755	+	0.0498809i	$0.984116\pi$
$740$	2.98886	−	16.9507i	0.109873	−	0.623118i
$741$	−34.1972	+	0.296812i	−1.25627	+	0.0109036i
$742$	4.68054	+	1.70358i	0.171828	+	0.0625402i
$743$	18.1197	+	6.59504i	0.664749	+	0.241949i	0.652285	−	0.757974i	$-0.273810\pi$
$743$	18.1197	+	6.59504i	0.664749	+	0.241949i	0.0124634	+	0.999922i	$0.496033\pi$
$744$	−4.80294	+	8.48823i	−0.176084	+	0.311194i
$745$	−3.62444	+	20.5552i	−0.132789	+	0.753085i
$746$	−10.2878	−	17.8189i	−0.376662	−	0.652398i
$747$	1.66389	+	2.76977i	0.0608785	+	0.101341i
$748$	−0.468403	+	0.811298i	−0.0171265	+	0.0296640i
$749$	13.4288	+	11.2681i	0.490676	+	0.411726i
$750$	−3.06025	−	16.5160i	−0.111744	−	0.603079i
$751$	2.04781	+	11.6137i	0.0747256	+	0.423790i	0.999104	+	0.0423138i	$0.0134729\pi$
$751$	2.04781	+	11.6137i	0.0747256	+	0.423790i	−0.924379	+	0.381476i	$0.875416\pi$
$752$	7.48488	−	6.28056i	0.272945	−	0.229028i
$753$	19.2486	−	7.19571i	0.701457	−	0.262226i
$754$	23.2362	−	8.45728i	0.846212	−	0.307996i
$755$	−16.5093			−0.600836
$756$	2.48004	−	4.56611i	0.0901982	−	0.166068i
$757$	12.1253			0.440702			0.220351	−	0.975421i	$-0.429280\pi$
$757$	12.1253			0.440702			0.220351	+	0.975421i	$0.429280\pi$
$758$	23.0389	−	8.38546i	0.836809	−	0.304574i
$759$	−0.818611	+	4.89040i	−0.0297137	+	0.177510i
$760$	12.4118	−	10.4147i	0.450224	−	0.377783i
$761$	3.33110	+	18.8916i	0.120752	+	0.684820i	0.983740	+	0.179596i	$0.0574791\pi$
$761$	3.33110	+	18.8916i	0.120752	+	0.684820i	−0.862988	+	0.505224i	$0.831410\pi$
$762$	−18.7515	+	16.0138i	−0.679296	+	0.580118i
$763$	−6.49850	−	5.45289i	−0.235262	−	0.197408i
$764$	−5.02177	+	8.69796i	−0.181681	+	0.314681i
$765$	−23.1368	−	18.7394i	−0.836512	−	0.677525i
$766$	−2.34008	−	4.05314i	−0.0845505	−	0.146446i
$767$	−8.39367	+	47.6029i	−0.303078	+	1.71884i
$768$	0.879011	+	1.49243i	0.0317186	+	0.0538533i
$769$	−1.49850	−	0.545411i	−0.0540375	−	0.0196680i	0.314860	−	0.949138i	$-0.398042\pi$
$769$	−1.49850	−	0.545411i	−0.0540375	−	0.0196680i	−0.368897	+	0.929470i	$0.620265\pi$
$770$	−1.12819	−	0.410629i	−0.0406573	−	0.0147980i
$771$	16.6458	+	28.2621i	0.599484	+	1.01783i
$772$	−3.98747	+	22.6141i	−0.143512	+	0.813899i
$773$	17.8604	+	30.9351i	0.642393	+	1.11266i	0.984897	+	0.173141i	$0.0553915\pi$
$773$	17.8604	+	30.9351i	0.642393	+	1.11266i	−0.342504	+	0.939516i	$0.611275\pi$
$774$	32.9426	−	12.6419i	1.18410	−	0.454403i
$775$	−21.7327	+	37.6422i	−0.780663	+	1.35215i
$776$	2.29384	+	1.92476i	0.0823440	+	0.0690948i
$777$	6.35665	−	5.42857i	0.228044	−	0.194749i
$778$	0.426769	+	2.42033i	0.0153004	+	0.0867730i
$779$	−19.7316	+	16.5568i	−0.706958	+	0.593208i
$780$	4.43219	−	26.4780i	0.158698	−	0.948065i
$781$	1.52241	−	0.554111i	0.0544761	−	0.0198277i
$782$	−23.6646			−0.846243
$783$	−4.37402	+	29.2388i	−0.156315	+	1.04491i
$784$	1.00000			0.0357143
$785$	−12.4042	+	4.51475i	−0.442724	+	0.161138i
$786$	11.5733	−	4.32646i	0.412807	−	0.154320i
$787$	−10.9702	+	9.20506i	−0.391044	+	0.328125i	−0.817020	−	0.576610i	$-0.804375\pi$
$787$	−10.9702	+	9.20506i	−0.391044	+	0.328125i	0.425976	+	0.904735i	$0.359931\pi$
$788$	−1.48614	−	8.42832i	−0.0529415	−	0.300246i
$789$	−0.556187	−	3.00171i	−0.0198008	−	0.106864i
$790$	15.9302	+	13.3670i	0.566771	+	0.475577i
$791$	3.17895	−	5.50610i	0.113030	−	0.195774i
$792$	0.489705	−	0.883254i	0.0174009	−	0.0313851i
$793$	−15.6049	−	27.0285i	−0.554147	−	0.959812i
$794$	3.00371	−	17.0349i	0.106598	−	0.604545i
$795$	−15.1522	+	26.7785i	−0.537393	+	0.949734i
$796$	11.2863	+	4.10788i	0.400032	+	0.145600i
$797$	30.9840	+	11.2773i	1.09751	+	0.399461i	0.826398	−	0.563087i	$-0.190386\pi$
$797$	30.9840	+	11.2773i	1.09751	+	0.399461i	0.271112	+	0.962548i	$0.412609\pi$
$798$	7.86856	−	0.0682944i	0.278544	−	0.00241760i
$799$	4.72153	−	26.7771i	0.167036	−	0.947307i
$800$	3.85961	+	6.68504i	0.136458	+	0.236352i
$801$	44.3177	+	15.2645i	1.56589	+	0.539345i
$802$	15.4285	−	26.7230i	0.544801	−	0.943623i
$803$	0.539402	+	0.452612i	0.0190351	+	0.0159723i
$804$	3.89129	+	1.37819i	0.137235	+	0.0486049i
$805$	−5.26644	−	29.8675i	−0.185618	−	1.05269i
$806$	−18.7465	+	15.7302i	−0.660318	+	0.554073i
$807$	40.7143	+	33.5655i	1.43321	+	1.18156i
$808$	−4.95642	+	1.80399i	−0.174366	+	0.0634641i
$809$	−39.3837			−1.38466			−0.692328	−	0.721583i	$-0.743415\pi$
$809$	−39.3837			−1.38466			−0.692328	+	0.721583i	$0.743415\pi$
$810$	25.2895	+	19.7661i	0.888583	+	0.694509i
$811$	−35.1227			−1.23332			−0.616662	−	0.787228i	$-0.711516\pi$
$811$	−35.1227			−1.23332			−0.616662	+	0.787228i	$0.711516\pi$
$812$	−5.34649	+	1.94596i	−0.187625	+	0.0682900i
$813$	−11.4531	−	9.44208i	−0.401676	−	0.331148i
$814$	1.24459	−	1.04434i	0.0436229	−	0.0366040i
$815$	−0.228398	−	1.29531i	−0.00800044	−	0.0453727i
$816$	4.54341	+	1.60915i	0.159051	+	0.0563315i
$817$	40.9330	+	34.3469i	1.43207	+	1.20165i
$818$	−1.24231	+	2.15175i	−0.0434365	+	0.0752342i
$819$	9.84085	−	8.55288i	0.343867	−	0.298862i
$820$	−10.1101	−	17.5113i	−0.353061	−	0.611520i
$821$	−4.91933	+	27.8989i	−0.171686	+	0.973679i	0.770214	+	0.637786i	$0.220149\pi$
$821$	−4.91933	+	27.8989i	−0.171686	+	0.973679i	−0.941900	+	0.335894i	$0.890962\pi$
$822$	22.2455	−	0.193078i	0.775902	−	0.00673437i
$823$	17.1853	+	6.25493i	0.599041	+	0.218033i	0.623701	−	0.781663i	$-0.285628\pi$
$823$	17.1853	+	6.25493i	0.599041	+	0.218033i	−0.0246604	+	0.999696i	$0.507850\pi$
$824$	18.7933	+	6.84019i	0.654695	+	0.238289i
$825$	2.21655	−	3.91730i	0.0771703	−	0.136383i
$826$	1.93133	−	10.9531i	0.0671995	−	0.381108i
$827$	−14.3366	−	24.8318i	−0.498534	−	0.863486i	0.501465	−	0.865178i	$-0.332795\pi$
$827$	−14.3366	−	24.8318i	−0.498534	−	0.863486i	−0.999999	+	0.00169197i	$0.999461\pi$
$828$	25.5078	−	0.442818i	0.886456	−	0.0153890i
$829$	28.0160	−	48.5252i	0.973037	−	1.68535i	0.286771	−	0.957999i	$-0.407418\pi$
$829$	28.0160	−	48.5252i	0.973037	−	1.68535i	0.686266	−	0.727350i	$-0.259248\pi$
$830$	−2.94250	−	2.46905i	−0.102136	−	0.0857020i
$831$	−7.20908	−	38.9070i	−0.250080	−	1.34967i
$832$	0.754685	+	4.28003i	0.0261640	+	0.148383i
$833$	2.13175	−	1.78875i	0.0738607	−	0.0619765i
$834$	−4.77188	+	1.78387i	−0.165237	+	0.0617705i
$835$	20.7884	−	7.56634i	0.719411	−	0.261844i
$836$	1.52939			0.0528951
$837$	−5.82914	−	28.6720i	−0.201485	−	0.991051i
$838$	−18.2184			−0.629346
$839$	51.5382	−	18.7584i	1.77930	−	0.647611i	0.779522	−	0.626375i	$-0.215462\pi$
$839$	51.5382	−	18.7584i	1.77930	−	0.647611i	0.999775	−	0.0212354i	$-0.00675994\pi$
$840$	−1.01982	+	6.09242i	−0.0351871	+	0.210209i
$841$	2.58294	−	2.16734i	0.0890668	−	0.0747359i
$842$	5.82937	+	33.0600i	0.200893	+	1.13932i
$843$	−14.7512	+	12.5975i	−0.508058	+	0.433881i
$844$	9.89399	+	8.30204i	0.340565	+	0.285768i
$845$	10.4999	−	18.1863i	0.361207	−	0.625628i
$846$	−4.58823	+	28.9511i	−0.157746	+	0.995360i
$847$	5.44334	+	9.42813i	0.187035	+	0.323955i
$848$	0.864928	−	4.90525i	0.0297018	−	0.168447i
$849$	−19.6121	−	33.2984i	−0.673086	−	1.14280i
$850$	20.1856	+	7.34695i	0.692359	+	0.251998i
$851$	38.5662	+	14.0370i	1.32203	+	0.481181i
$852$	−4.23031	−	7.18242i	−0.144928	−	0.246066i
$853$	−6.37863	+	36.1750i	−0.218400	+	1.23861i	0.656507	+	0.754320i	$0.272033\pi$
$853$	−6.37863	+	36.1750i	−0.218400	+	1.23861i	−0.874908	+	0.484290i	$0.839078\pi$
$854$	3.59059	+	6.21909i	0.122868	+	0.212813i
$855$	−7.60843	+	48.0082i	−0.260203	+	1.64185i
$856$	8.76499	−	15.1814i	0.299581	−	0.518890i
$857$	−41.5852	−	34.8941i	−1.42052	−	1.19196i	−0.951060	−	0.309008i	$-0.900003\pi$
$857$	−41.5852	−	34.8941i	−1.42052	−	1.19196i	−0.469463	−	0.882952i	$-0.655552\pi$
$858$	1.92702	−	1.64568i	0.0657875	−	0.0561825i
$859$	−8.06098	−	45.7161i	−0.275037	−	1.55981i	−0.738844	−	0.673877i	$-0.764628\pi$
$859$	−8.06098	−	45.7161i	−0.275037	−	1.55981i	0.463806	−	0.885937i	$-0.346483\pi$
$860$	−32.1331	+	26.9629i	−1.09573	+	0.919427i
$861$	1.62125	−	9.68539i	0.0552521	−	0.330077i
$862$	−36.8585	+	13.4154i	−1.25541	+	0.456931i
$863$	32.8629			1.11867			0.559333	−	0.828943i	$-0.311058\pi$
$863$	32.8629			1.11867			0.559333	+	0.828943i	$0.311058\pi$
$864$	−4.92740	−	1.64946i	−0.167634	−	0.0561159i
$865$	34.7389			1.18116
$866$	−18.3999	+	6.69703i	−0.625255	+	0.227574i
$867$	−15.0169	+	5.61378i	−0.510001	+	0.190654i
$868$	4.31346	−	3.61942i	0.146408	−	0.122851i
$869$	0.340859	+	1.93311i	0.0115629	+	0.0655762i
$870$	−6.40318	−	34.5576i	−0.217088	−	1.17161i
$871$	7.93494	+	6.65820i	0.268865	+	0.225605i
$872$	−4.24160	+	7.34666i	−0.143639	+	0.248789i
$873$	−8.98182	+	0.155926i	−0.303989	+	0.00527728i
$874$	19.3169	+	33.4579i	0.653404	+	1.13173i
$875$	−1.68401	+	9.55048i	−0.0569299	+	0.322865i
$876$	1.78413	−	3.15309i	0.0602801	−	0.106533i
$877$	21.9432	+	7.98668i	0.740970	+	0.269691i	0.684801	−	0.728730i	$-0.259889\pi$
$877$	21.9432	+	7.98668i	0.740970	+	0.269691i	0.0561692	+	0.998421i	$0.482111\pi$
$878$	35.1655	+	12.7992i	1.18678	+	0.431952i
$879$	15.7295	−	0.136523i	0.530544	−	0.00460481i
$880$	−0.208482	+	1.18236i	−0.00702792	+	0.0398573i
$881$	−13.9316	−	24.1302i	−0.469368	−	0.812968i	0.530019	−	0.847986i	$-0.322185\pi$
$881$	−13.9316	−	24.1302i	−0.469368	−	0.812968i	−0.999387	+	0.0350172i	$0.988851\pi$
$882$	−2.26432	+	1.96796i	−0.0762435	+	0.0662647i
$883$	10.5455	−	18.2653i	0.354883	−	0.614675i	−0.632215	−	0.774793i	$-0.717854\pi$
$883$	10.5455	−	18.2653i	0.354883	−	0.614675i	0.987098	+	0.160118i	$0.0511875\pi$
$884$	9.26470	+	7.77401i	0.311606	+	0.261468i
$885$	64.7614	+	22.9367i	2.17693	+	0.771008i
$886$	1.98920	+	11.2813i	0.0668283	+	0.379002i
$887$	−32.5383	+	27.3029i	−1.09253	+	0.916741i	−0.996900	−	0.0786758i	$-0.974931\pi$
$887$	−32.5383	+	27.3029i	−1.09253	+	0.916741i	−0.0956294	+	0.995417i	$0.530486\pi$
$888$	−6.44992	−	5.31742i	−0.216445	−	0.178441i
$889$	13.3782	−	4.86928i	0.448691	−	0.163310i
$890$	−55.7225			−1.86782
$891$	0.629363	+	2.96369i	0.0210845	+	0.0992873i
$892$	−0.691634			−0.0231576
$893$	−41.7126	+	15.1822i	−1.39586	+	0.508052i
$894$	7.82150	+	6.44817i	0.261590	+	0.215659i
$895$	55.1196	−	46.2509i	1.84245	−	1.54600i
$896$	−0.173648	−	0.984808i	−0.00580118	−	0.0329001i
$897$	60.3409	+	21.3711i	2.01473	+	0.713559i
$898$	−3.06314	−	2.57028i	−0.102218	−	0.0857715i
$899$	−16.0186	+	27.7450i	−0.534251	+	0.925349i
$900$	−21.8953	−	7.54147i	−0.729842	−	0.251382i
$901$	−6.93046	−	12.0039i	−0.230887	−	0.399908i
$902$	0.331433	−	1.87965i	0.0110355	−	0.0625854i
$903$	−20.3710	+	0.176809i	−0.677906	+	0.00588382i
$904$	−5.97447	−	2.17453i	−0.198708	−	0.0723237i
$905$	31.0872	+	11.3148i	1.03337	+	0.376117i
$906$	−3.94853	+	6.97822i	−0.131181	+	0.231836i
$907$	3.30024	−	18.7166i	0.109583	−	0.621475i	−0.879708	−	0.475515i	$-0.842262\pi$
$907$	3.30024	−	18.7166i	0.109583	−	0.621475i	0.989290	−	0.145960i	$-0.0466271\pi$
$908$	1.32413	+	2.29345i	0.0439427	+	0.0761109i
$909$	7.67272	−	13.8389i	0.254488	−	0.459006i
$910$	−7.74989	+	13.4232i	−0.256906	+	0.444975i
$911$	32.0358	+	26.8812i	1.06139	+	0.890614i	0.994245	−	0.107129i	$-0.0341658\pi$
$911$	32.0358	+	26.8812i	1.06139	+	0.890614i	0.0671472	+	0.997743i	$0.478610\pi$
$912$	−1.43362	−	7.73716i	−0.0474718	−	0.256203i
$913$	−0.0629609	−	0.357069i	−0.00208370	−	0.0118173i
$914$	5.29374	−	4.44198i	0.175101	−	0.146927i
$915$	−41.5511	+	15.5331i	−1.37364	+	0.513508i
$916$	5.84291	−	2.12665i	0.193055	−	0.0702664i
$917$	−7.13349			−0.235569
$918$	−13.4545	+	5.29764i	−0.444063	+	0.174848i
$919$	−40.5987			−1.33923			−0.669614	−	0.742709i	$-0.733540\pi$
$919$	−40.5987			−1.33923			−0.669614	+	0.742709i	$0.733540\pi$
$920$	−28.4992	+	10.3729i	−0.939591	+	0.341983i
$921$	8.16971	−	48.8060i	0.269201	−	1.60821i
$922$	−26.3817	+	22.1369i	−0.868834	+	0.729039i
$923$	−3.63198	−	20.5980i	−0.119548	−	0.677990i
$924$	−0.443396	+	0.378659i	−0.0145867	+	0.0124570i
$925$	−28.5386	−	23.9467i	−0.938342	−	0.787362i
$926$	−0.272932	+	0.472733i	−0.00896911	+	0.0155350i
$927$	−56.0151	+	21.4961i	−1.83978	+	0.706024i
$928$	2.84481	+	4.92736i	0.0933855	+	0.161748i
$929$	−1.78832	+	10.1421i	−0.0586729	+	0.332751i	−0.999989	−	0.00477674i	$-0.998480\pi$
$929$	−1.78832	+	10.1421i	−0.0586729	+	0.332751i	0.941316	+	0.337528i	$0.109591\pi$
$930$	17.6521	+	29.9706i	0.578835	+	0.982773i
$931$	−4.26910	−	1.55383i	−0.139914	−	0.0509246i
$932$	−23.8852	−	8.69351i	−0.782386	−	0.284765i
$933$	5.45752	+	9.26603i	0.178671	+	0.303356i
$934$	0.543790	−	3.08399i	0.0177934	−	0.100911i
$935$	1.67051	+	2.89342i	0.0546317	+	0.0946248i
$936$	−10.1318	−	8.20615i	−0.331168	−	0.268226i
$937$	5.26629	−	9.12148i	0.172042	−	0.297986i	−0.767091	−	0.641538i	$-0.778297\pi$
$937$	5.26629	−	9.12148i	0.172042	−	0.297986i	0.939134	+	0.343552i	$0.111630\pi$
$938$	−1.82578	−	1.53201i	−0.0596138	−	0.0500219i
$939$	17.3534	−	14.8197i	0.566305	−	0.483624i
$940$	−6.05106	−	34.3173i	−0.197364	−	1.11931i
$941$	−33.3955	+	28.0221i	−1.08866	+	0.913495i	−0.996611	−	0.0822591i	$-0.973787\pi$
$941$	−33.3955	+	28.0221i	−1.08866	+	0.913495i	−0.0920503	+	0.995754i	$0.529342\pi$
$942$	−1.05839	+	6.32283i	−0.0344841	+	0.206009i
$943$	45.3064	−	16.4902i	1.47538	−	0.536994i
$944$	−11.1221			−0.361993
$945$	−9.68047	−	15.8021i	−0.314906	−	0.514043i
$946$	−3.95947			−0.128733
$947$	3.54124	−	1.28890i	0.115075	−	0.0418838i	−0.283841	−	0.958871i	$-0.591609\pi$
$947$	3.54124	−	1.28890i	0.115075	−	0.0418838i	0.398916	+	0.916988i	$0.369387\pi$
$948$	9.46004	−	3.53645i	0.307248	−	0.114859i
$949$	6.96370	−	5.84323i	0.226051	−	0.189679i
$950$	−6.08968	−	34.5363i	−0.197575	−	1.12051i
$951$	−7.43355	−	40.1185i	−0.241049	−	1.30093i
$952$	−2.13175	−	1.78875i	−0.0690904	−	0.0579737i
$953$	−27.9217	+	48.3617i	−0.904471	+	1.56659i	−0.0828463	+	0.996562i	$0.526401\pi$
$953$	−27.9217	+	48.3617i	−0.904471	+	1.56659i	−0.821625	+	0.570028i	$0.806932\pi$
$954$	7.69488	+	12.8092i	0.249131	+	0.414713i
$955$	17.9096	+	31.0204i	0.579542	+	1.00380i
$956$	−1.27081	+	7.20712i	−0.0411009	+	0.233095i
$957$	1.63376	−	2.88733i	0.0528118	−	0.0933342i
$958$	−13.6015	−	4.95054i	−0.439444	−	0.159945i
$959$	−12.0694	−	4.39289i	−0.389740	−	0.141854i
$960$	6.17696	−	0.0536123i	0.199360	−	0.00173033i
$961$	0.122614	−	0.695380i	0.00395530	−	0.0224316i
$962$	−10.4875	−	18.1648i	−0.338129	−	0.585657i
$963$	10.0297	+	51.6247i	0.323204	+	1.66358i
$964$	−12.8297	+	22.2218i	−0.413218	+	0.715715i
$965$	62.7352	+	52.6411i	2.01952	+	1.69458i
$966$	−13.8841	−	4.91735i	−0.446712	−	0.158213i
$967$	4.29734	+	24.3714i	0.138193	+	0.783732i	0.972583	+	0.232557i	$0.0747093\pi$
$967$	4.29734	+	24.3714i	0.138193	+	0.783732i	−0.834390	+	0.551175i	$0.814180\pi$
$968$	8.33967	−	6.99782i	0.268047	−	0.224918i
$969$	−16.8960	−	13.9293i	−0.542776	−	0.447473i
$970$	10.0352	−	3.65250i	0.322210	−	0.117275i
$971$	52.0410			1.67007			0.835037	−	0.550194i	$-0.185446\pi$
$971$	52.0410			1.67007			0.835037	+	0.550194i	$0.185446\pi$
$972$	14.4033	−	5.96203i	0.461985	−	0.191232i
$973$	2.94126			0.0942925
$974$	−15.8579	+	5.77181i	−0.508120	+	0.184941i
$975$	−44.8351	−	36.9628i	−1.43587	−	1.18376i
$976$	5.50111	−	4.61598i	0.176086	−	0.147754i
$977$	−3.41259	−	19.3538i	−0.109179	−	0.619182i	−0.989469	−	0.144747i	$-0.953763\pi$
$977$	−3.41259	−	19.3538i	−0.109179	−	0.619182i	0.880290	−	0.474436i	$-0.157348\pi$
$978$	−0.602132	−	0.213258i	−0.0192541	−	0.00681925i
$979$	−4.02923	−	3.38092i	−0.128775	−	0.108055i
$980$	1.78320	−	3.08859i	0.0569623	−	0.0986615i
$981$	−4.85364	−	24.9825i	−0.154965	−	0.797629i
$982$	10.4163	+	18.0416i	0.332398	+	0.575731i
$983$	4.30795	−	24.4316i	0.137402	−	0.779247i	−0.835754	−	0.549103i	$-0.814969\pi$
$983$	4.30795	−	24.4316i	0.137402	−	0.779247i	0.973157	−	0.230144i	$-0.0739196\pi$
$984$	−9.81977	+	0.0852298i	−0.313043	+	0.00271703i
$985$	−28.6817	−	10.4393i	−0.913876	−	0.332624i
$986$	14.8782	+	5.41523i	0.473819	+	0.172456i
$987$	8.33425	−	14.7291i	0.265282	−	0.468833i
$988$	3.42860	−	19.4446i	0.109078	−	0.618614i
$989$	−50.0099	−	86.6196i	−1.59022	−	2.75434i
$990$	−1.85477	−	3.08752i	−0.0589485	−	0.0981278i
$991$	−23.2237	+	40.2247i	−0.737726	+	1.27778i	0.215790	+	0.976440i	$0.430767\pi$
$991$	−23.2237	+	40.2247i	−0.737726	+	1.27778i	−0.953517	+	0.301340i	$0.902566\pi$
$992$	−4.31346	−	3.61942i	−0.136952	−	0.114917i
$993$	−1.90805	−	10.2977i	−0.0605502	−	0.326786i
$994$	0.835695	+	4.73946i	0.0265066	+	0.150327i
$995$	32.8133	−	27.5336i	1.04025	−	0.872874i
$996$	−1.74738	+	0.653226i	−0.0553680	+	0.0206983i
$997$	13.9673	−	5.08370i	0.442350	−	0.161002i	−0.111236	−	0.993794i	$-0.535481\pi$
$997$	13.9673	−	5.08370i	0.442350	−	0.161002i	0.553586	+	0.832792i	$0.313259\pi$
$998$	−13.0146			−0.411970
$999$	25.0691	−	0.652887i	0.793152	−	0.0206564i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.u.e.169.2	yes	36
27.4	even	9	inner	378.2.u.e.85.2	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.u.e.85.2	✓	36	27.4	even	9	inner
378.2.u.e.169.2	yes	36	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{2} +(-1.33644 - 1.10178i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.619299 - 3.51222i) q^{5} +(-1.63268 - 0.578248i) q^{6} +(0.766044 + 0.642788i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.572147 + 2.94494i) q^{9} +O(q^{10})\)	\(q+(0.939693 - 0.342020i) q^{2} +(-1.33644 - 1.10178i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.619299 - 3.51222i) q^{5} +(-1.63268 - 0.578248i) q^{6} +(0.766044 + 0.642788i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.572147 + 2.94494i) q^{9} +(-1.78320 - 3.08859i) q^{10} +(0.0584572 - 0.331527i) q^{11} +(-1.73199 + 0.0150326i) q^{12} +(-4.08396 - 1.48644i) q^{13} +(0.939693 + 0.342020i) q^{14} +(-3.04205 + 5.37621i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-1.39140 - 2.40998i) q^{17} +(1.54487 + 2.57165i) q^{18} +(-2.27154 + 3.93443i) q^{19} +(-2.73202 - 2.29244i) q^{20} +(-0.315560 - 1.70306i) q^{21} +(-0.0584572 - 0.331527i) q^{22} +(6.51434 - 5.46618i) q^{23} +(-1.62239 + 0.606500i) q^{24} +(-7.25369 + 2.64013i) q^{25} -4.34606 q^{26} +(2.48004 - 4.56611i) q^{27} +1.00000 q^{28} +(-5.34649 + 1.94596i) q^{29} +(-1.01982 + 6.09242i) q^{30} +(4.31346 - 3.61942i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(-0.443396 + 0.378659i) q^{33} +(-2.13175 - 1.78875i) q^{34} +(1.78320 - 3.08859i) q^{35} +(2.33126 + 1.88818i) q^{36} +(2.41310 + 4.17961i) q^{37} +(-0.788899 + 4.47407i) q^{38} +(3.82023 + 6.48618i) q^{39} +(-3.35132 - 1.21978i) q^{40} +(5.32774 + 1.93914i) q^{41} +(-0.879011 - 1.49243i) q^{42} +(2.04239 - 11.5830i) q^{43} +(-0.168321 - 0.291540i) q^{44} +(9.98893 - 3.83330i) q^{45} +(4.25194 - 7.36457i) q^{46} +(7.48488 + 6.28056i) q^{47} +(-1.31712 + 1.12481i) q^{48} +(0.173648 + 0.984808i) q^{49} +(-5.91326 + 4.96182i) q^{50} +(-0.795747 + 4.75381i) q^{51} +(-4.08396 + 1.48644i) q^{52} +4.98092 q^{53} +(0.768772 - 5.13897i) q^{54} -1.20060 q^{55} +(0.939693 - 0.342020i) q^{56} +(7.37067 - 2.75538i) q^{57} +(-4.35850 + 3.65722i) q^{58} +(-1.93133 - 10.9531i) q^{59} +(1.12541 + 6.07380i) q^{60} +(5.50111 + 4.61598i) q^{61} +(2.81541 - 4.87643i) q^{62} +(-1.45468 + 2.62372i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-2.69151 + 15.2643i) q^{65} +(-0.287147 + 0.507474i) q^{66} +(-2.23965 - 0.815165i) q^{67} +(-2.61498 - 0.951774i) q^{68} +(-14.7286 + 0.127835i) q^{69} +(0.619299 - 3.51222i) q^{70} +(2.40629 + 4.16781i) q^{71} +(2.83646 + 0.976974i) q^{72} +(-1.04583 + 1.81143i) q^{73} +(3.69708 + 3.10222i) q^{74} +(12.6030 + 4.46362i) q^{75} +(0.788899 + 4.47407i) q^{76} +(0.257883 - 0.216389i) q^{77} +(5.80825 + 4.78841i) q^{78} +(-5.47927 + 1.99429i) q^{79} -3.56640 q^{80} +(-8.34529 + 3.36988i) q^{81} +5.66966 q^{82} +(1.01209 - 0.368370i) q^{83} +(-1.33644 - 1.10178i) q^{84} +(-7.60267 + 6.37940i) q^{85} +(-2.04239 - 11.5830i) q^{86} +(9.28930 + 3.29001i) q^{87} +(-0.257883 - 0.216389i) q^{88} +(7.81214 - 13.5310i) q^{89} +(8.07546 - 7.01854i) q^{90} +(-2.17303 - 3.76380i) q^{91} +(1.47668 - 8.37468i) q^{92} +(-9.75249 + 0.0846459i) q^{93} +(9.18156 + 3.34182i) q^{94} +(15.2253 + 5.54157i) q^{95} +(-0.852974 + 1.50746i) q^{96} +(-0.519971 + 2.94890i) q^{97} +(0.500000 + 0.866025i) q^{98} +(1.00977 - 0.0175298i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{3} + 3 q^{5} + 6 q^{6} + 18 q^{8} + 3 q^{9}+O(q^{10}) \) 36 * q + 3 * q^3 + 3 * q^5 + 6 * q^6 + 18 * q^8 + 3 * q^9	\( 36 q + 3 q^{3} + 3 q^{5} + 6 q^{6} + 18 q^{8} + 3 q^{9} - 3 q^{10} + 9 q^{13} - 6 q^{15} + 6 q^{18} - 15 q^{19} - 6 q^{20} + 3 q^{21} - 3 q^{24} - 3 q^{25} - 18 q^{26} - 30 q^{27} + 36 q^{28} - 6 q^{29} - 9 q^{30} + 60 q^{33} + 9 q^{34} + 3 q^{35} - 27 q^{37} + 15 q^{38} + 6 q^{39} - 3 q^{40} - 9 q^{41} - 6 q^{43} + 9 q^{44} + 42 q^{45} - 9 q^{46} + 36 q^{47} + 3 q^{48} - 15 q^{50} - 36 q^{51} + 9 q^{52} - 42 q^{53} - 27 q^{54} + 30 q^{55} - 18 q^{57} - 21 q^{58} + 12 q^{59} + 24 q^{60} + 3 q^{61} + 18 q^{62} + 12 q^{63} - 18 q^{64} - 84 q^{65} + 18 q^{66} - 69 q^{67} + 9 q^{68} - 48 q^{69} - 3 q^{70} + 12 q^{71} + 6 q^{72} - 12 q^{73} + 9 q^{75} - 15 q^{76} + 9 q^{77} - 48 q^{78} - 51 q^{79} - 6 q^{80} - 69 q^{81} + 15 q^{83} + 3 q^{84} - 12 q^{85} + 6 q^{86} + 84 q^{87} - 9 q^{88} - 3 q^{89} + 6 q^{90} - 9 q^{91} + 18 q^{92} - 21 q^{93} + 9 q^{94} - 75 q^{95} - 42 q^{97} + 18 q^{98} + 39 q^{99}+O(q^{100}) \) 36 * q + 3 * q^3 + 3 * q^5 + 6 * q^6 + 18 * q^8 + 3 * q^9 - 3 * q^10 + 9 * q^13 - 6 * q^15 + 6 * q^18 - 15 * q^19 - 6 * q^20 + 3 * q^21 - 3 * q^24 - 3 * q^25 - 18 * q^26 - 30 * q^27 + 36 * q^28 - 6 * q^29 - 9 * q^30 + 60 * q^33 + 9 * q^34 + 3 * q^35 - 27 * q^37 + 15 * q^38 + 6 * q^39 - 3 * q^40 - 9 * q^41 - 6 * q^43 + 9 * q^44 + 42 * q^45 - 9 * q^46 + 36 * q^47 + 3 * q^48 - 15 * q^50 - 36 * q^51 + 9 * q^52 - 42 * q^53 - 27 * q^54 + 30 * q^55 - 18 * q^57 - 21 * q^58 + 12 * q^59 + 24 * q^60 + 3 * q^61 + 18 * q^62 + 12 * q^63 - 18 * q^64 - 84 * q^65 + 18 * q^66 - 69 * q^67 + 9 * q^68 - 48 * q^69 - 3 * q^70 + 12 * q^71 + 6 * q^72 - 12 * q^73 + 9 * q^75 - 15 * q^76 + 9 * q^77 - 48 * q^78 - 51 * q^79 - 6 * q^80 - 69 * q^81 + 15 * q^83 + 3 * q^84 - 12 * q^85 + 6 * q^86 + 84 * q^87 - 9 * q^88 - 3 * q^89 + 6 * q^90 - 9 * q^91 + 18 * q^92 - 21 * q^93 + 9 * q^94 - 75 * q^95 - 42 * q^97 + 18 * q^98 + 39 * q^99

Introduction

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