LMFDB - Embedded newform 378.2.u.e.85.2

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			85.2
Character	$\chi$	$=$	378.85
Dual form			378.2.u.e.169.2

$q$-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 $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

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

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	0.455711	+	0.890128i	$0.349385\pi$
$5$	−0.619299	+	3.51222i	−0.276959	+	1.57071i	−0.732670	+	0.680584i	$0.761726\pi$
$6$	−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	0.992351	−	0.123445i	$-0.0393942\pi$
$11$	0.0584572	+	0.331527i	0.0176255	+	0.0999593i	−0.974726	+	0.223404i	$0.928283\pi$
$12$	−1.73199	−	0.0150326i	−0.499981	−	0.00433954i
$13$	−4.08396	+	1.48644i	−1.13269	+	0.412264i	−0.839267	−	0.543720i	$-0.817015\pi$
$13$	−4.08396	+	1.48644i	−1.13269	+	0.412264i	−0.293419	+	0.955984i	$0.594793\pi$
$14$	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	−0.983955	−	0.178417i	$-0.942902\pi$
$17$	−1.39140	+	2.40998i	−0.337464	+	0.584505i	0.646491	+	0.762922i	$0.276236\pi$
$18$	1.54487	−	2.57165i	0.364129	−	0.606143i
$19$	−2.27154	−	3.93443i	−0.521128	−	0.902620i	−0.999698	−	0.0245705i	$-0.992178\pi$
$19$	−2.27154	−	3.93443i	−0.521128	−	0.902620i	0.478570	−	0.878049i	$-0.341155\pi$
$20$	−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	0.976493	+	0.215550i	$0.0691545\pi$
$23$	6.51434	+	5.46618i	1.35833	+	1.13978i	0.381842	+	0.924228i	$0.375290\pi$
$24$	−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	−0.206008	−	0.978550i	$-0.566047\pi$
$29$	−5.34649	−	1.94596i	−0.992819	−	0.361357i	−0.786811	+	0.617194i	$0.788269\pi$
$30$	−1.01982	−	6.09242i	−0.186193	−	1.11232i
$31$	4.31346	+	3.61942i	0.774720	+	0.650067i	0.941913	−	0.335857i	$-0.109026\pi$
$31$	4.31346	+	3.61942i	0.774720	+	0.650067i	−0.167193	+	0.985924i	$0.553470\pi$
$32$	−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	−0.596607	−	0.802533i	$-0.703485\pi$
$37$	2.41310	−	4.17961i	0.396711	−	0.687123i	0.993318	+	0.115410i	$0.0368183\pi$
$38$	−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	0.109352	−	0.994003i	$-0.465123\pi$
$41$	5.32774	−	1.93914i	0.832053	−	0.302843i	0.722701	+	0.691161i	$0.242900\pi$
$42$	−0.879011	+	1.49243i	−0.135634	+	0.230287i
$43$	2.04239	+	11.5830i	0.311462	+	1.76639i	0.591408	+	0.806373i	$0.298572\pi$
$43$	2.04239	+	11.5830i	0.311462	+	1.76639i	−0.279946	+	0.960016i	$0.590316\pi$
$44$	−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	0.0949366	−	0.995483i	$-0.469735\pi$
$47$	7.48488	−	6.28056i	1.09178	−	0.916114i	0.996845	+	0.0793695i	$0.0252907\pi$
$48$	−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	0.553616	+	0.832772i	$0.313248\pi$
$59$	−1.93133	+	10.9531i	−0.251438	+	1.42597i	−0.805054	+	0.593202i	$0.797864\pi$
$60$	1.12541	−	6.07380i	0.145290	−	0.784125i
$61$	5.50111	−	4.61598i	0.704345	−	0.591016i	−0.218661	−	0.975801i	$-0.570169\pi$
$61$	5.50111	−	4.61598i	0.704345	−	0.591016i	0.923006	+	0.384785i	$0.125724\pi$
$62$	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	−0.475184	−	0.879886i	$-0.657619\pi$
$67$	−2.23965	+	0.815165i	−0.273617	+	0.0995883i	0.201568	+	0.979475i	$0.435396\pi$
$68$	−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	−0.687174	−	0.726492i	$-0.741149\pi$
$71$	2.40629	−	4.16781i	0.285574	−	0.494628i	0.972748	+	0.231864i	$0.0744825\pi$
$72$	2.83646	−	0.976974i	0.334280	−	0.115137i
$73$	−1.04583	−	1.81143i	−0.122405	−	0.212012i	0.798311	−	0.602246i	$-0.205727\pi$
$73$	−1.04583	−	1.81143i	−0.122405	−	0.212012i	−0.920716	+	0.390234i	$0.872394\pi$
$74$	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	0.0148640	−	0.999890i	$-0.495268\pi$
$79$	−5.47927	−	1.99429i	−0.616466	−	0.224375i	−0.631330	+	0.775514i	$0.717491\pi$
$80$	−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	0.396968	−	0.917833i	$-0.370063\pi$
$83$	1.01209	+	0.368370i	0.111091	+	0.0404339i	−0.285877	+	0.958266i	$0.592285\pi$
$84$	−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	0.899538	+	0.436842i	$0.143903\pi$
$89$	7.81214	+	13.5310i	0.828085	+	1.43429i	−0.0714531	+	0.997444i	$0.522764\pi$
$90$	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	0.946965	−	0.321338i	$-0.104132\pi$
$97$	−0.519971	−	2.94890i	−0.0527950	−	0.299416i	−0.999760	+	0.0219222i	$0.993021\pi$
$98$	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	−0.821284	−	0.570520i	$-0.806742\pi$
$101$	−4.04051	+	3.39039i	−0.402046	+	0.337357i	0.419238	+	0.907876i	$0.362297\pi$
$102$	0.878141	−	4.73928i	0.0869490	−	0.469259i
$103$	3.47286	−	19.6955i	0.342191	−	1.94066i	0.00285061	−	0.999996i	$-0.499093\pi$
$103$	3.47286	−	19.6955i	0.342191	−	1.94066i	0.339340	−	0.940664i	$-0.389796\pi$
$104$	−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	0.887811	+	0.460209i	$0.152225\pi$
$113$	−1.10404	+	6.26130i	−0.103859	+	0.589014i	−0.991670	+	0.128805i	$0.958886\pi$
$114$	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	0.987213	+	0.159406i	$0.0509580\pi$
$127$	7.11841	+	12.3294i	0.631656	+	1.09406i	−0.355557	+	0.934655i	$0.615709\pi$
$128$	−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	0.372058	−	0.928209i	$-0.378652\pi$
$131$	−5.46457	−	4.58532i	−0.477442	−	0.400621i	−0.849500	+	0.527588i	$0.823097\pi$
$132$	−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	−0.229635	−	0.973277i	$-0.573753\pi$
$137$	−12.0694	−	4.39289i	−1.03116	−	0.375310i	−0.801521	+	0.597967i	$0.795975\pi$
$138$	−13.7966	−	5.15760i	−1.17445	−	0.439044i
$139$	2.25314	+	1.89061i	0.191109	+	0.160359i	0.733322	−	0.679882i	$-0.237969\pi$
$139$	2.25314	+	1.89061i	0.191109	+	0.160359i	−0.542213	+	0.840241i	$0.682413\pi$
$140$	−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	−0.557317	−	0.830300i	$-0.688169\pi$
$149$	−5.49954	+	2.00167i	−0.450540	+	0.163983i	0.106777	+	0.994283i	$0.465947\pi$
$150$	13.3696	+	0.116040i	1.09162	+	0.00947462i
$151$	0.803840	+	4.55880i	0.0654155	+	0.370990i	0.999888	+	0.0149550i	$0.00476050\pi$
$151$	0.803840	+	4.55880i	0.0654155	+	0.370990i	−0.934473	+	0.356035i	$0.884128\pi$
$152$	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	−0.999654	−	0.0262906i	$-0.991630\pi$
$157$	−0.642720	+	3.64504i	−0.0512946	+	0.290906i	0.948360	+	0.317197i	$0.102742\pi$
$158$	−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	−0.914348	−	0.404929i	$-0.867296\pi$
$167$	1.07715	−	6.10879i	0.0833520	−	0.472713i	0.997700	−	0.0677835i	$-0.0215927\pi$
$168$	−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	−0.979106	−	0.203352i	$-0.934817\pi$
$173$	−1.69144	−	9.59262i	−0.128598	−	0.729314i	0.850508	−	0.525962i	$-0.176295\pi$
$174$	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	−0.191885	−	0.981417i	$-0.561460\pi$
$179$	10.0877	−	17.4724i	0.753990	−	1.30595i	0.945875	−	0.324532i	$-0.105207\pi$
$180$	5.18796	+	9.35724i	0.386688	+	0.697448i
$181$	−4.63805	−	8.03333i	−0.344743	−	0.597113i	0.640564	−	0.767905i	$-0.278701\pi$
$181$	−4.63805	−	8.03333i	−0.344743	−	0.597113i	−0.985307	+	0.170792i	$0.945367\pi$
$182$	−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	−0.0228066	−	0.999740i	$-0.507260\pi$
$191$	−9.43784	−	3.43509i	−0.682898	−	0.248555i	−0.660091	+	0.751185i	$0.729482\pi$
$192$	−0.285952	−	1.70828i	−0.0206368	−	0.123285i
$193$	−17.5906	−	14.7603i	−1.26620	−	1.06247i	−0.994993	−	0.0999485i	$-0.968132\pi$
$193$	−17.5906	−	14.7603i	−1.26620	−	1.06247i	−0.271209	−	0.962521i	$-0.587423\pi$
$194$	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	0.977234	−	0.212163i	$-0.0680509\pi$
$197$	4.27917	+	7.41174i	0.304878	+	0.528065i	−0.672356	+	0.740228i	$0.734718\pi$
$198$	0.942881	+	0.361835i	0.0670076	+	0.0257145i
$199$	6.00531	−	10.4015i	0.425705	−	0.737343i	−0.570781	−	0.821103i	$-0.693359\pi$
$199$	6.00531	−	10.4015i	0.425705	−	0.737343i	0.996486	+	0.0837593i	$0.0266927\pi$
$200$	−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	−0.804933	−	0.593366i	$-0.797799\pi$
$211$	2.24278	−	12.7195i	0.154400	−	0.875644i	0.959333	−	0.282278i	$-0.0910901\pi$
$212$	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	−0.660355	−	0.750954i	$-0.729594\pi$
$223$	−0.529822	+	0.444574i	−0.0354795	+	0.0297709i	0.624875	+	0.780724i	$0.285150\pi$
$224$	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	0.965736	−	0.259526i	$-0.0835665\pi$
$227$	−0.459864	−	2.60802i	−0.0305222	−	0.173100i	−0.996258	+	0.0864261i	$0.972455\pi$
$228$	3.87514	+	6.84852i	0.256637	+	0.453554i
$229$	5.84291	−	2.12665i	0.386111	−	0.140533i	−0.141669	−	0.989914i	$-0.545247\pi$
$229$	5.84291	−	2.12665i	0.386111	−	0.140533i	0.527780	+	0.849381i	$0.323025\pi$
$230$	−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	0.0633731	+	0.997990i	$0.479814\pi$
$233$	−12.7091	+	22.0127i	−0.832598	+	1.44210i	−0.895971	+	0.444112i	$0.853519\pi$
$234$	−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	0.443207	−	0.896419i	$-0.353841\pi$
$239$	−5.60615	−	4.70412i	−0.362631	−	0.304284i	−0.805839	+	0.592135i	$0.798285\pi$
$240$	4.76628	−	3.92940i	0.307662	−	0.253642i
$241$	−24.1120	−	8.77606i	−1.55319	−	0.565316i	−0.584028	−	0.811733i	$-0.698524\pi$
$241$	−24.1120	−	8.77606i	−1.55319	−	0.565316i	−0.969164	+	0.246418i	$0.920747\pi$
$242$	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	0.615808	−	0.787896i	$-0.288830\pi$
$251$	−5.93216	−	10.2748i	−0.374434	−	0.648539i	−0.990242	+	0.139357i	$0.955496\pi$
$252$	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	−0.831000	−	0.556273i	$-0.812231\pi$
$257$	−17.7949	+	6.47683i	−1.11002	+	0.404013i	−0.279018	+	0.960286i	$0.590009\pi$
$258$	−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	−0.600210	−	0.799843i	$-0.704916\pi$
$263$	1.35018	−	1.13294i	0.0832558	−	0.0698599i	0.683466	+	0.729983i	$0.260472\pi$
$264$	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	0.0582547	−	0.998302i	$-0.481446\pi$
$277$	17.5005	−	14.6847i	1.05151	−	0.882318i	0.993251	+	0.115984i	$0.0370020\pi$
$278$	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	0.986242	+	0.165309i	$0.0528622\pi$
$281$	1.94480	+	11.0295i	0.116017	+	0.657964i	−0.870225	+	0.492654i	$0.836027\pi$
$282$	−8.58866	+	14.5822i	−0.511447	+	0.868359i
$283$	20.9660	−	7.63100i	1.24630	−	0.453616i	0.367150	−	0.930162i	$-0.380334\pi$
$283$	20.9660	−	7.63100i	1.24630	−	0.453616i	0.879150	+	0.476546i	$0.158111\pi$
$284$	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	0.416539	−	0.909118i	$-0.363243\pi$
$293$	−6.95706	−	5.83767i	−0.406436	−	0.341040i	−0.822975	+	0.568078i	$0.807687\pi$
$294$	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	−0.0938218	−	0.995589i	$-0.529908\pi$
$307$	14.2851	−	24.7425i	0.815294	−	1.41213i	0.909116	−	0.416542i	$-0.136758\pi$
$308$	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	−0.502095	−	0.864813i	$-0.667437\pi$
$311$	−5.83427	+	2.12350i	−0.330831	+	0.120413i	0.171264	+	0.985225i	$0.445215\pi$
$312$	7.52731	+	0.0653326i	0.426150	+	0.00369873i
$313$	−2.28786	−	12.9751i	−0.129318	−	0.733397i	−0.978649	−	0.205537i	$-0.934106\pi$
$313$	−2.28786	−	12.9751i	−0.129318	−	0.733397i	0.849332	−	0.527860i	$-0.177005\pi$
$314$	−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	0.0247328	−	0.999694i	$-0.492127\pi$
$317$	18.0455	−	15.1419i	1.01353	−	0.850456i	0.988801	+	0.149238i	$0.0476821\pi$
$318$	−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	−0.506554	−	0.862208i	$-0.669081\pi$
$331$	4.63193	−	3.88665i	0.254594	−	0.213630i	0.761147	+	0.648579i	$0.224636\pi$
$332$	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	0.510738	−	0.859737i	$-0.329372\pi$
$337$	26.7032	−	9.71915i	1.45461	−	0.529436i	0.943876	+	0.330301i	$0.107150\pi$
$338$	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	0.990942	−	0.134292i	$-0.0428759\pi$
$347$	19.2010	+	16.1116i	1.03077	+	0.864915i	0.0398237	+	0.999207i	$0.487320\pi$
$348$	9.23080	+	3.45075i	0.494823	+	0.184980i
$349$	14.4922	+	5.27473i	0.775750	+	0.282350i	0.699399	−	0.714731i	$-0.253451\pi$
$349$	14.4922	+	5.27473i	0.775750	+	0.282350i	0.0763509	+	0.997081i	$0.475673\pi$
$350$	−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	0.894574	−	0.446921i	$-0.147479\pi$
$353$	24.2854	+	8.83916i	1.29258	+	0.470461i	0.398008	+	0.917382i	$0.369702\pi$
$354$	−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	0.794195	−	0.607662i	$-0.207893\pi$
$359$	−2.44711	−	4.23851i	−0.129153	−	0.223700i	−0.923349	+	0.383962i	$0.874559\pi$
$360$	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	0.921803	+	0.387659i	$0.126716\pi$
$367$	3.60498	+	20.4449i	0.188179	+	1.06721i	−0.733624	+	0.679555i	$0.762173\pi$
$368$	−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	0.740960	+	0.671549i	$0.234371\pi$
$373$	−3.57291	+	20.2630i	−0.184998	+	1.04918i	−0.925958	+	0.377627i	$0.876740\pi$
$374$	−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	−0.998506	−	0.0546464i	$-0.982597\pi$
$383$	−0.812701	+	4.60906i	−0.0415271	+	0.235512i	0.956979	+	0.290158i	$0.0937079\pi$
$384$	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	0.972075	−	0.234669i	$-0.0754005\pi$
$389$	−0.426769	−	2.42033i	−0.0216381	−	0.122716i	−0.993713	+	0.111953i	$0.964289\pi$
$390$	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	0.997219	−	0.0745216i	$-0.0237430\pi$
$397$	8.64883	+	14.9802i	0.434072	+	0.751835i	−0.563147	+	0.826357i	$0.690410\pi$
$398$	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	0.999976	+	0.00690553i	$0.00219811\pi$
$401$	23.6379	+	19.8346i	1.18042	+	0.990491i	0.180445	+	0.983585i	$0.442246\pi$
$402$	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	0.594517	−	0.804083i	$-0.297343\pi$
$409$	−1.90334	−	1.59709i	−0.0941139	−	0.0789710i	−0.688631	+	0.725112i	$0.741788\pi$
$410$	−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	−0.724464	−	0.689313i	$-0.757913\pi$
$419$	−17.1197	+	6.23108i	−0.836354	+	0.304408i	−0.111890	+	0.993721i	$0.535690\pi$
$420$	−3.04205	−	5.37621i	−0.148437	−	0.262332i
$421$	−5.82937	−	33.0600i	−0.284106	−	1.61125i	−0.708462	−	0.705749i	$-0.750610\pi$
$421$	−5.82937	−	33.0600i	−0.284106	−	1.61125i	0.424356	−	0.905496i	$-0.360501\pi$
$422$	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	0.394860	−	0.918741i	$-0.370793\pi$
$439$	28.6672	−	24.0546i	1.36821	−	1.14806i	0.973350	−	0.229324i	$-0.0736515\pi$
$440$	−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	−0.994897	−	0.100900i	$-0.967828\pi$
$443$	−1.98920	−	11.2813i	−0.0945095	−	0.535990i	0.900387	−	0.435090i	$-0.143283\pi$
$444$	−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	−0.909339	−	0.416056i	$-0.863412\pi$
$449$	−1.99933	+	3.46293i	−0.0943540	+	0.163426i	0.814985	+	0.579482i	$0.196745\pi$
$450$	−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	0.489405	−	0.872057i	$-0.337214\pi$
$457$	6.49373	+	2.36353i	0.303764	+	0.110561i	−0.185641	+	0.982618i	$0.559436\pi$
$458$	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	−0.549320	−	0.835612i	$-0.685113\pi$
$461$	−32.3619	−	11.7788i	−1.50725	−	0.548592i	−0.957925	+	0.287019i	$0.907336\pi$
$462$	−0.546165	−	0.204173i	−0.0254099	−	0.00949900i
$463$	−0.418157	−	0.350875i	−0.0194334	−	0.0163065i	0.633019	−	0.774136i	$-0.281815\pi$
$463$	−0.418157	−	0.350875i	−0.0194334	−	0.0163065i	−0.652453	+	0.757830i	$0.726260\pi$
$464$	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	0.899977	−	0.435937i	$-0.143583\pi$
$467$	1.56578	+	2.71201i	0.0724558	+	0.125497i	−0.827521	+	0.561434i	$0.810250\pi$
$468$	−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	−0.859940	−	0.510395i	$-0.829499\pi$
$479$	−11.0880	+	9.30397i	−0.506625	+	0.425109i	0.353314	+	0.935505i	$0.385055\pi$
$480$	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	−0.787585	−	0.616206i	$-0.788669\pi$
$491$	3.61755	−	20.5161i	0.163258	−	0.925881i	0.950843	−	0.309675i	$-0.100220\pi$
$492$	−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	−0.600925	−	0.799305i	$-0.705201\pi$
$499$	−12.2297	+	4.45125i	−0.547477	+	0.199265i	0.0534480	+	0.998571i	$0.482979\pi$
$500$	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	−0.999705	−	0.0242783i	$-0.992271\pi$
$503$	−10.7390	+	18.6004i	−0.478827	+	0.829353i	0.520878	+	0.853631i	$0.325605\pi$
$504$	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	0.652752	−	0.757571i	$-0.273614\pi$
$509$	0.452114	+	0.379369i	0.0200396	+	0.0168152i	−0.632713	+	0.774387i	$0.718059\pi$
$510$	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	0.999221	−	0.0394581i	$-0.0125632\pi$
$521$	10.6238	+	18.4010i	0.465439	+	0.806164i	−0.533782	+	0.845622i	$0.679230\pi$
$522$	−13.2640	+	10.7430i	−0.580549	+	0.470210i
$523$	−11.5529	+	20.0103i	−0.505175	+	0.874988i	0.494807	+	0.869003i	$0.335239\pi$
$523$	−11.5529	+	20.0103i	−0.505175	+	0.874988i	−0.999982	+	0.00598553i	$0.998095\pi$
$524$	−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	−0.457650	+	0.889133i	$0.651309\pi$
$547$	−33.0413	+	27.7249i	−1.41274	+	1.18543i	−0.955095	+	0.296301i	$0.904247\pi$
$548$	−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	−0.911463	−	0.411382i	$-0.865046\pi$
$557$	−2.34745	+	4.06590i	−0.0994645	+	0.172278i	0.811999	+	0.583659i	$0.198380\pi$
$558$	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	0.821010	−	0.570914i	$-0.193411\pi$
$563$	9.52275	+	7.99053i	0.401336	+	0.336761i	−0.419674	+	0.907675i	$0.637856\pi$
$564$	−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	0.605217	−	0.796060i	$-0.293086\pi$
$569$	13.2899	+	4.83714i	0.557143	+	0.202783i	−0.0480745	+	0.998844i	$0.515308\pi$
$570$	−21.6536	+	17.8516i	−0.906971	+	0.747722i
$571$	10.1801	+	8.54216i	0.426026	+	0.357478i	0.830450	−	0.557093i	$-0.188083\pi$
$571$	10.1801	+	8.54216i	0.426026	+	0.357478i	−0.404424	+	0.914572i	$0.632528\pi$
$572$	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	−0.991586	−	0.129446i	$-0.958680\pi$
$577$	−9.21653	+	15.9635i	−0.383689	+	0.664569i	0.607897	+	0.794016i	$0.292013\pi$
$578$	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	−0.879513	−	0.475875i	$-0.842132\pi$
$587$	−13.6548	+	11.4577i	−0.563594	+	0.472911i	0.315919	+	0.948786i	$0.397687\pi$
$588$	−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	−0.827573	−	0.561358i	$-0.810279\pi$
$599$	3.47751	−	19.7219i	0.142087	−	0.805816i	0.969660	−	0.244458i	$-0.0786099\pi$
$600$	10.1671	+	8.68269i	0.415070	+	0.354469i
$601$	33.0352	−	27.7198i	1.34754	−	1.13072i	0.367914	−	0.929860i	$-0.380072\pi$
$601$	33.0352	−	27.7198i	1.34754	−	1.13072i	0.979621	−	0.200857i	$-0.0643725\pi$
$602$	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	−0.213730	−	0.976893i	$-0.568561\pi$
$607$	6.17111	−	2.24610i	0.250478	−	0.0911664i	0.464208	+	0.885726i	$0.346339\pi$
$608$	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	0.824357	−	0.566070i	$-0.191537\pi$
$613$	−1.93248	−	3.34716i	−0.0780522	−	0.135190i	−0.902409	+	0.430879i	$0.858203\pi$
$614$	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	0.963337	−	0.268296i	$-0.0864604\pi$
$617$	21.5209	+	18.0582i	0.866399	+	0.726995i	−0.0969378	+	0.995290i	$0.530905\pi$
$618$	5.71886	+	34.1646i	0.230046	+	1.37430i
$619$	31.4445	+	11.4449i	1.26386	+	0.460008i	0.885063	−	0.465471i	$-0.154115\pi$
$619$	31.4445	+	11.4449i	1.26386	+	0.460008i	0.378799	+	0.925479i	$0.376337\pi$
$620$	−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	0.264725	+	0.964324i	$0.414719\pi$
$631$	−17.6533	+	30.5764i	−0.702767	+	1.21723i	−0.967491	+	0.252904i	$0.918614\pi$
$632$	−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	−0.947559	−	0.319582i	$-0.896458\pi$
$641$	−20.1879	+	16.9397i	−0.797374	+	0.669076i	0.150185	+	0.988658i	$0.452013\pi$
$642$	−28.6208	+	10.1367i	−1.12957	+	0.400063i
$643$	2.24935	−	12.7567i	0.0887055	−	0.503074i	−0.907790	−	0.419425i	$-0.862232\pi$
$643$	2.24935	−	12.7567i	0.0887055	−	0.503074i	0.996495	−	0.0836486i	$-0.0266573\pi$
$644$	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	−0.999835	−	0.0181476i	$-0.994223\pi$
$653$	−1.38222	+	7.83898i	−0.0540906	+	0.306763i	0.945745	+	0.324911i	$0.105334\pi$
$654$	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	−0.994563	−	0.104137i	$-0.966792\pi$
$659$	−2.45406	−	13.9177i	−0.0955965	−	0.542155i	0.898966	−	0.438018i	$-0.144319\pi$
$660$	2.07942	+	0.0180481i	0.0809413	+	0.000702523i
$661$	43.8565	−	15.9625i	1.70582	−	0.620868i	0.709355	−	0.704852i	$-0.248986\pi$
$661$	43.8565	−	15.9625i	1.70582	−	0.620868i	0.996467	+	0.0839831i	$0.0267642\pi$
$662$	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	−0.159080	−	0.987266i	$-0.550853\pi$
$673$	−23.7513	−	8.64476i	−0.915544	−	0.333231i	−0.756464	+	0.654035i	$0.773075\pi$
$674$	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	0.0434995	−	0.999053i	$-0.486149\pi$
$677$	−14.7102	−	5.35406i	−0.565357	−	0.205773i	−0.608857	+	0.793280i	$0.708372\pi$
$678$	−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	0.950014	−	0.312207i	$-0.101068\pi$
$683$	5.34781	+	9.26268i	0.204628	+	0.354427i	−0.745386	+	0.666633i	$0.767735\pi$
$684$	−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	0.983517	+	0.180817i	$0.0578742\pi$
$691$	3.18482	+	18.0620i	0.121156	+	0.687112i	−0.862360	+	0.506295i	$0.831015\pi$
$692$	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	−0.725007	−	0.688742i	$-0.758163\pi$
$709$	−4.59649	+	3.85691i	−0.172625	+	0.144849i	0.552382	+	0.833591i	$0.313719\pi$
$710$	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	−0.865075	−	0.501642i	$-0.832729\pi$
$719$	0.0508780	−	0.0881233i	0.00189743	−	0.00328644i	0.866973	+	0.498356i	$0.166063\pi$
$720$	−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	0.0454725	−	0.998966i	$-0.485521\pi$
$727$	−15.1482	−	5.51350i	−0.561816	−	0.204484i	−0.607289	+	0.794481i	$0.707743\pi$
$728$	−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	0.391527	−	0.920167i	$-0.371947\pi$
$733$	−12.0932	−	10.1474i	−0.446672	−	0.374802i	−0.838199	+	0.545364i	$0.816391\pi$
$734$	−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	−0.998755	−	0.0498809i	$-0.984116\pi$
$739$	−12.4010	+	21.4792i	−0.456179	+	0.790126i	0.542576	+	0.840007i	$0.317449\pi$
$740$	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	0.0124634	−	0.999922i	$-0.496033\pi$
$743$	18.1197	−	6.59504i	0.664749	−	0.241949i	0.652285	+	0.757974i	$0.273810\pi$
$744$	−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	−0.924379	−	0.381476i	$-0.875416\pi$
$751$	2.04781	−	11.6137i	0.0747256	−	0.423790i	0.999104	−	0.0423138i	$-0.0134729\pi$
$752$	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	−0.862988	−	0.505224i	$-0.831410\pi$
$761$	3.33110	−	18.8916i	0.120752	−	0.684820i	0.983740	−	0.179596i	$-0.0574791\pi$
$762$	−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	−0.368897	−	0.929470i	$-0.620265\pi$
$769$	−1.49850	+	0.545411i	−0.0540375	+	0.0196680i	0.314860	+	0.949138i	$0.398042\pi$
$770$	−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	−0.342504	−	0.939516i	$-0.611275\pi$
$773$	17.8604	−	30.9351i	0.642393	−	1.11266i	0.984897	−	0.173141i	$-0.0553915\pi$
$774$	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	0.425976	−	0.904735i	$-0.359931\pi$
$787$	−10.9702	−	9.20506i	−0.391044	−	0.328125i	−0.817020	+	0.576610i	$0.804375\pi$
$788$	−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	0.271112	−	0.962548i	$-0.412609\pi$
$797$	30.9840	−	11.2773i	1.09751	−	0.399461i	0.826398	+	0.563087i	$0.190386\pi$
$798$	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	−0.941900	−	0.335894i	$-0.890962\pi$
$821$	−4.91933	−	27.8989i	−0.171686	−	0.973679i	0.770214	−	0.637786i	$-0.220149\pi$
$822$	22.2455	+	0.193078i	0.775902	+	0.00673437i
$823$	17.1853	−	6.25493i	0.599041	−	0.218033i	−0.0246604	−	0.999696i	$-0.507850\pi$
$823$	17.1853	−	6.25493i	0.599041	−	0.218033i	0.623701	+	0.781663i	$0.285628\pi$
$824$	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	−0.999999	−	0.00169197i	$-0.999461\pi$
$827$	−14.3366	+	24.8318i	−0.498534	+	0.863486i	0.501465	+	0.865178i	$0.332795\pi$
$828$	25.5078	+	0.442818i	0.886456	+	0.0153890i
$829$	28.0160	+	48.5252i	0.973037	+	1.68535i	0.686266	+	0.727350i	$0.259248\pi$
$829$	28.0160	+	48.5252i	0.973037	+	1.68535i	0.286771	+	0.957999i	$0.407418\pi$
$830$	−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	0.999775	+	0.0212354i	$0.00675994\pi$
$839$	51.5382	+	18.7584i	1.77930	+	0.647611i	0.779522	+	0.626375i	$0.215462\pi$
$840$	−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	−0.874908	−	0.484290i	$-0.839078\pi$
$853$	−6.37863	−	36.1750i	−0.218400	−	1.23861i	0.656507	−	0.754320i	$-0.272033\pi$
$854$	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	−0.469463	+	0.882952i	$0.655552\pi$
$857$	−41.5852	+	34.8941i	−1.42052	+	1.19196i	−0.951060	+	0.309008i	$0.900003\pi$
$858$	1.92702	+	1.64568i	0.0657875	+	0.0561825i
$859$	−8.06098	+	45.7161i	−0.275037	+	1.55981i	0.463806	+	0.885937i	$0.346483\pi$
$859$	−8.06098	+	45.7161i	−0.275037	+	1.55981i	−0.738844	+	0.673877i	$0.764628\pi$
$860$	−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	0.0561692	−	0.998421i	$-0.482111\pi$
$877$	21.9432	−	7.98668i	0.740970	−	0.269691i	0.684801	+	0.728730i	$0.259889\pi$
$878$	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	−0.999387	−	0.0350172i	$-0.988851\pi$
$881$	−13.9316	+	24.1302i	−0.469368	+	0.812968i	0.530019	+	0.847986i	$0.322185\pi$
$882$	−2.26432	−	1.96796i	−0.0762435	−	0.0662647i
$883$	10.5455	+	18.2653i	0.354883	+	0.614675i	0.987098	−	0.160118i	$-0.0511875\pi$
$883$	10.5455	+	18.2653i	0.354883	+	0.614675i	−0.632215	+	0.774793i	$0.717854\pi$
$884$	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	−0.0956294	−	0.995417i	$-0.530486\pi$
$887$	−32.5383	−	27.3029i	−1.09253	−	0.916741i	−0.996900	+	0.0786758i	$0.974931\pi$
$888$	−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	0.989290	+	0.145960i	$0.0466271\pi$
$907$	3.30024	+	18.7166i	0.109583	+	0.621475i	−0.879708	+	0.475515i	$0.842262\pi$
$908$	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	0.0671472	−	0.997743i	$-0.478610\pi$
$911$	32.0358	−	26.8812i	1.06139	−	0.890614i	0.994245	+	0.107129i	$0.0341658\pi$
$912$	−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	0.941316	−	0.337528i	$-0.109591\pi$
$929$	−1.78832	−	10.1421i	−0.0586729	−	0.332751i	−0.999989	+	0.00477674i	$0.998480\pi$
$930$	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	0.939134	−	0.343552i	$-0.111630\pi$
$937$	5.26629	+	9.12148i	0.172042	+	0.297986i	−0.767091	+	0.641538i	$0.778297\pi$
$938$	−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	−0.0920503	−	0.995754i	$-0.529342\pi$
$941$	−33.3955	−	28.0221i	−1.08866	−	0.913495i	−0.996611	+	0.0822591i	$0.973787\pi$
$942$	−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	0.398916	−	0.916988i	$-0.369387\pi$
$947$	3.54124	+	1.28890i	0.115075	+	0.0418838i	−0.283841	+	0.958871i	$0.591609\pi$
$948$	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	−0.821625	−	0.570028i	$-0.806932\pi$
$953$	−27.9217	−	48.3617i	−0.904471	−	1.56659i	−0.0828463	−	0.996562i	$-0.526401\pi$
$954$	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	−0.834390	−	0.551175i	$-0.814180\pi$
$967$	4.29734	−	24.3714i	0.138193	−	0.783732i	0.972583	−	0.232557i	$-0.0747093\pi$
$968$	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	0.880290	+	0.474436i	$0.157348\pi$
$977$	−3.41259	+	19.3538i	−0.109179	+	0.619182i	−0.989469	+	0.144747i	$0.953763\pi$
$978$	−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	0.973157	+	0.230144i	$0.0739196\pi$
$983$	4.30795	+	24.4316i	0.137402	+	0.779247i	−0.835754	+	0.549103i	$0.814969\pi$
$984$	−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	−0.953517	−	0.301340i	$-0.902566\pi$
$991$	−23.2237	−	40.2247i	−0.737726	−	1.27778i	0.215790	−	0.976440i	$-0.430767\pi$
$992$	−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	0.553586	−	0.832792i	$-0.313259\pi$
$997$	13.9673	+	5.08370i	0.442350	+	0.161002i	−0.111236	+	0.993794i	$0.535481\pi$
$998$	−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.85.2	✓	36
27.7	even	9	inner	378.2.u.e.169.2	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.u.e.85.2	✓	36	1.1	even	1	trivial
378.2.u.e.169.2	yes	36	27.7	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
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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