LMFDB - Embedded newform 87.2.g.a.82.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [87,2,Mod(7,87)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(87, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("87.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 87 = 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	87.g (of order $7$, 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:	$0.694698497585$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} + 18 x^{16} - 37 x^{15} + 71 x^{14} - 83 x^{13} + 225 x^{12} - 237 x^{11} + 485 x^{10} + \cdots + 64 $ x^18 - 6x^17 + 18x^16 - 37x^15 + 71x^14 - 83x^13 + 225x^12 - 237x^11 + 485x^10 - 319x^9 + 1092x^8 - 1080x^7 + 1833x^6 - 4032x^5 + 6004x^4 - 4480x^3 + 3200x^2 - 576*x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			82.1
Root			$0.491931 - 2.15529i$ of defining polynomial
Character	$\chi$	$=$	87.82
Dual form			87.2.g.a.52.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.754870 - 0.946578i) q^{2} +(-0.222521 - 0.974928i) q^{3} +(0.118862 - 0.520769i) q^{4} +(1.12131 + 1.40607i) q^{5} +(-0.754870 + 0.946578i) q^{6} +(-0.951706 - 4.16970i) q^{7} +(-2.76431 + 1.33122i) q^{8} +(-0.900969 + 0.433884i) q^{9} +O(q^{10})$	\(q+(-0.754870 - 0.946578i) q^{2} +(-0.222521 - 0.974928i) q^{3} +(0.118862 - 0.520769i) q^{4} +(1.12131 + 1.40607i) q^{5} +(-0.754870 + 0.946578i) q^{6} +(-0.951706 - 4.16970i) q^{7} +(-2.76431 + 1.33122i) q^{8} +(-0.900969 + 0.433884i) q^{9} +(0.484517 - 2.12281i) q^{10} +(-0.951656 - 0.458293i) q^{11} -0.534161 q^{12} +(4.75885 + 2.29174i) q^{13} +(-3.22853 + 4.04845i) q^{14} +(1.12131 - 1.40607i) q^{15} +(2.38428 + 1.14821i) q^{16} +5.61769 q^{17} +(1.09082 + 0.525311i) q^{18} +(-1.42675 + 6.25099i) q^{19} +(0.865520 - 0.416812i) q^{20} +(-3.85338 + 1.85569i) q^{21} +(0.284567 + 1.24677i) q^{22} +(1.27587 - 1.59988i) q^{23} +(1.91296 + 2.39878i) q^{24} +(0.392890 - 1.72136i) q^{25} +(-1.42300 - 6.23459i) q^{26} +(0.623490 + 0.781831i) q^{27} -2.28457 q^{28} +(-4.54927 + 2.88169i) q^{29} -2.17740 q^{30} +(2.38467 + 2.99028i) q^{31} +(0.652504 + 2.85881i) q^{32} +(-0.235040 + 1.02978i) q^{33} +(-4.24063 - 5.31758i) q^{34} +(4.79575 - 6.01368i) q^{35} +(0.118862 + 0.520769i) q^{36} +(0.315606 - 0.151988i) q^{37} +(6.99406 - 3.36816i) q^{38} +(1.17534 - 5.14950i) q^{39} +(-4.97144 - 2.39412i) q^{40} -3.62240 q^{41} +(4.66536 + 2.24672i) q^{42} +(1.09049 - 1.36743i) q^{43} +(-0.351781 + 0.441119i) q^{44} +(-1.62033 - 0.780312i) q^{45} -2.47753 q^{46} +(-6.28881 - 3.02853i) q^{47} +(0.588868 - 2.58000i) q^{48} +(-10.1739 + 4.89947i) q^{49} +(-1.92598 + 0.927505i) q^{50} +(-1.25005 - 5.47684i) q^{51} +(1.75911 - 2.20586i) q^{52} +(-4.87488 - 6.11290i) q^{53} +(0.269410 - 1.18036i) q^{54} +(-0.422703 - 1.85198i) q^{55} +(8.18161 + 10.2594i) q^{56} +6.41175 q^{57} +(6.16185 + 2.13093i) q^{58} +0.382668 q^{59} +(-0.598958 - 0.751070i) q^{60} +(1.21640 + 5.32939i) q^{61} +(1.03041 - 4.51454i) q^{62} +(2.66662 + 3.34384i) q^{63} +(5.51347 - 6.91367i) q^{64} +(2.11377 + 9.26104i) q^{65} +(1.15219 - 0.554864i) q^{66} +(-7.03806 + 3.38935i) q^{67} +(0.667730 - 2.92552i) q^{68} +(-1.84368 - 0.887869i) q^{69} -9.31258 q^{70} +(14.0654 + 6.77356i) q^{71} +(1.91296 - 2.39878i) q^{72} +(-1.58547 + 1.98811i) q^{73} +(-0.382110 - 0.184015i) q^{74} -1.76563 q^{75} +(3.08574 + 1.48601i) q^{76} +(-1.00525 + 4.40428i) q^{77} +(-5.76163 + 2.77465i) q^{78} +(-9.25113 + 4.45511i) q^{79} +(1.05904 + 4.63996i) q^{80} +(0.623490 - 0.781831i) q^{81} +(2.73445 + 3.42889i) q^{82} +(-0.338541 + 1.48324i) q^{83} +(0.508365 + 2.22729i) q^{84} +(6.29915 + 7.89888i) q^{85} -2.11755 q^{86} +(3.82175 + 3.79397i) q^{87} +3.24076 q^{88} +(-11.1881 - 14.0295i) q^{89} +(0.484517 + 2.12281i) q^{90} +(5.02684 - 22.0240i) q^{91} +(-0.681518 - 0.854597i) q^{92} +(2.38467 - 2.99028i) q^{93} +(1.88050 + 8.23899i) q^{94} +(-10.3892 + 5.00316i) q^{95} +(2.64194 - 1.27229i) q^{96} +(1.51530 - 6.63895i) q^{97} +(12.3177 + 5.93188i) q^{98} +1.05626 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 4 q^{2} - 3 q^{3} - 6 q^{4} - q^{5} - 4 q^{6} - 4 q^{7} - 15 q^{8} - 3 q^{9}+O(q^{10}) $ 18 * q - 4 * q^2 - 3 * q^3 - 6 * q^4 - q^5 - 4 * q^6 - 4 * q^7 - 15 * q^8 - 3 * q^9	\( 18 q - 4 q^{2} - 3 q^{3} - 6 q^{4} - q^{5} - 4 q^{6} - 4 q^{7} - 15 q^{8} - 3 q^{9} - 14 q^{10} + 26 q^{11} + 22 q^{12} + 9 q^{13} - 10 q^{14} - q^{15} - 14 q^{16} + 4 q^{17} - 4 q^{18} - 10 q^{19} - q^{20} - 4 q^{21} - 8 q^{22} - 8 q^{23} - 8 q^{24} + 16 q^{25} + 5 q^{26} - 3 q^{27} + 80 q^{28} + 8 q^{29} - 12 q^{31} + 9 q^{32} - 16 q^{33} - 22 q^{34} + 9 q^{35} - 6 q^{36} - 16 q^{37} - 32 q^{38} + 2 q^{39} + 33 q^{40} + 24 q^{41} - 3 q^{42} - 31 q^{43} - 52 q^{44} + 6 q^{45} - 44 q^{46} + 5 q^{47} - 47 q^{49} - 7 q^{50} + 11 q^{51} + 80 q^{52} + 5 q^{53} + 3 q^{54} - 17 q^{55} + 45 q^{56} + 18 q^{57} + 54 q^{58} - 32 q^{59} + 27 q^{60} - 28 q^{61} + 69 q^{62} + 3 q^{63} - 75 q^{64} + 22 q^{65} + 34 q^{66} + 6 q^{67} + 38 q^{68} + 20 q^{69} - 12 q^{70} + 46 q^{71} - 8 q^{72} - q^{73} - 35 q^{74} + 2 q^{75} - 45 q^{76} - 36 q^{77} - 51 q^{78} - 15 q^{79} - 86 q^{80} - 3 q^{81} + 47 q^{82} - 16 q^{83} - 25 q^{84} + 19 q^{85} + 116 q^{86} + 43 q^{87} + 54 q^{88} - 72 q^{89} - 14 q^{90} - 47 q^{91} - 121 q^{92} - 12 q^{93} - 22 q^{94} - 72 q^{95} - 12 q^{96} + 43 q^{97} + 31 q^{98} - 2 q^{99}+O(q^{100}) \) 18 * q - 4 * q^2 - 3 * q^3 - 6 * q^4 - q^5 - 4 * q^6 - 4 * q^7 - 15 * q^8 - 3 * q^9 - 14 * q^10 + 26 * q^11 + 22 * q^12 + 9 * q^13 - 10 * q^14 - q^15 - 14 * q^16 + 4 * q^17 - 4 * q^18 - 10 * q^19 - q^20 - 4 * q^21 - 8 * q^22 - 8 * q^23 - 8 * q^24 + 16 * q^25 + 5 * q^26 - 3 * q^27 + 80 * q^28 + 8 * q^29 - 12 * q^31 + 9 * q^32 - 16 * q^33 - 22 * q^34 + 9 * q^35 - 6 * q^36 - 16 * q^37 - 32 * q^38 + 2 * q^39 + 33 * q^40 + 24 * q^41 - 3 * q^42 - 31 * q^43 - 52 * q^44 + 6 * q^45 - 44 * q^46 + 5 * q^47 - 47 * q^49 - 7 * q^50 + 11 * q^51 + 80 * q^52 + 5 * q^53 + 3 * q^54 - 17 * q^55 + 45 * q^56 + 18 * q^57 + 54 * q^58 - 32 * q^59 + 27 * q^60 - 28 * q^61 + 69 * q^62 + 3 * q^63 - 75 * q^64 + 22 * q^65 + 34 * q^66 + 6 * q^67 + 38 * q^68 + 20 * q^69 - 12 * q^70 + 46 * q^71 - 8 * q^72 - q^73 - 35 * q^74 + 2 * q^75 - 45 * q^76 - 36 * q^77 - 51 * q^78 - 15 * q^79 - 86 * q^80 - 3 * q^81 + 47 * q^82 - 16 * q^83 - 25 * q^84 + 19 * q^85 + 116 * q^86 + 43 * q^87 + 54 * q^88 - 72 * q^89 - 14 * q^90 - 47 * q^91 - 121 * q^92 - 12 * q^93 - 22 * q^94 - 72 * q^95 - 12 * q^96 + 43 * q^97 + 31 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$e\left(\frac{2}{7}\right)$	$1$

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 $

$2$	−0.754870	−	0.946578i	−0.533774	−	0.669331i	0.439696	−	0.898147i	$-0.355086\pi$
$2$	−0.754870	−	0.946578i	−0.533774	−	0.669331i	−0.973470	+	0.228815i	$0.926515\pi$
$3$	−0.222521	−	0.974928i	−0.128473	−	0.562875i
$3$	−0.222521	−	0.974928i	−0.128473	−	0.562875i
$4$	0.118862	−	0.520769i	0.0594310	−	0.260384i
$5$	1.12131	+	1.40607i	0.501463	+	0.628815i	0.966559	−	0.256445i	$-0.0825514\pi$
$5$	1.12131	+	1.40607i	0.501463	+	0.628815i	−0.465095	+	0.885261i	$0.653980\pi$
$6$	−0.754870	+	0.946578i	−0.308175	+	0.386439i
$7$	−0.951706	−	4.16970i	−0.359711	−	1.57600i	−0.753913	−	0.656974i	$-0.771836\pi$
$7$	−0.951706	−	4.16970i	−0.359711	−	1.57600i	0.394202	−	0.919024i	$-0.371021\pi$
$8$	−2.76431	+	1.33122i	−0.977332	+	0.470658i
$9$	−0.900969	+	0.433884i	−0.300323	+	0.144628i
$10$	0.484517	−	2.12281i	0.153218	−	0.671290i
$11$	−0.951656	−	0.458293i	−0.286935	−	0.138181i	0.284880	−	0.958563i	$-0.408046\pi$
$11$	−0.951656	−	0.458293i	−0.286935	−	0.138181i	−0.571815	+	0.820383i	$0.693761\pi$
$12$	−0.534161			−0.154199
$13$	4.75885	+	2.29174i	1.31987	+	0.635615i	0.955321	−	0.295570i	$-0.0955096\pi$
$13$	4.75885	+	2.29174i	1.31987	+	0.635615i	0.364547	+	0.931185i	$0.381224\pi$
$14$	−3.22853	+	4.04845i	−0.862860	+	1.08199i
$15$	1.12131	−	1.40607i	0.289520	−	0.363047i
$16$	2.38428	+	1.14821i	0.596069	+	0.287052i
$17$	5.61769			1.36249			0.681245	−	0.732056i	$-0.261439\pi$
$17$	5.61769			1.36249			0.681245	+	0.732056i	$0.261439\pi$
$18$	1.09082	+	0.525311i	0.257109	+	0.123817i
$19$	−1.42675	+	6.25099i	−0.327319	+	1.43408i	0.496902	+	0.867807i	$0.334471\pi$
$19$	−1.42675	+	6.25099i	−0.327319	+	1.43408i	−0.824220	+	0.566269i	$0.808386\pi$
$20$	0.865520	−	0.416812i	0.193536	−	0.0932021i
$21$	−3.85338	+	1.85569i	−0.840877	+	0.404945i
$22$	0.284567	+	1.24677i	0.0606698	+	0.265812i
$23$	1.27587	−	1.59988i	0.266036	−	0.333599i	−0.630813	−	0.775935i	$-0.717279\pi$
$23$	1.27587	−	1.59988i	0.266036	−	0.333599i	0.896850	+	0.442336i	$0.145850\pi$
$24$	1.91296	+	2.39878i	0.390482	+	0.489649i
$25$	0.392890	−	1.72136i	0.0785779	−	0.344272i
$26$	−1.42300	−	6.23459i	−0.279074	−	1.22270i
$27$	0.623490	+	0.781831i	0.119991	+	0.150464i
$28$	−2.28457			−0.431743
$29$	−4.54927	+	2.88169i	−0.844778	+	0.535117i
$29$	−4.54927	+	2.88169i	−0.844778	+	0.535117i
$30$	−2.17740			−0.397537
$31$	2.38467	+	2.99028i	0.428299	+	0.537069i	0.948417	−	0.317025i	$-0.102684\pi$
$31$	2.38467	+	2.99028i	0.428299	+	0.537069i	−0.520119	+	0.854094i	$0.674112\pi$
$32$	0.652504	+	2.85881i	0.115348	+	0.505371i
$33$	−0.235040	+	1.02978i	−0.0409151	+	0.179261i
$34$	−4.24063	−	5.31758i	−0.727261	−	0.911957i
$35$	4.79575	−	6.01368i	0.810629	−	1.01650i
$36$	0.118862	+	0.520769i	0.0198103	+	0.0867948i
$37$	0.315606	−	0.151988i	0.0518854	−	0.0249867i	−0.407761	−	0.913089i	$-0.633690\pi$
$37$	0.315606	−	0.151988i	0.0518854	−	0.0249867i	0.459647	+	0.888102i	$0.347976\pi$
$38$	6.99406	−	3.36816i	1.13459	−	0.546388i
$39$	1.17534	−	5.14950i	0.188205	−	0.824579i
$40$	−4.97144	−	2.39412i	−0.786053	−	0.378543i
$41$	−3.62240			−0.565725			−0.282862	−	0.959161i	$-0.591284\pi$
$41$	−3.62240			−0.565725			−0.282862	+	0.959161i	$0.591284\pi$
$42$	4.66536	+	2.24672i	0.719880	+	0.346676i
$43$	1.09049	−	1.36743i	0.166298	−	0.208530i	−0.691699	−	0.722186i	$-0.743138\pi$
$43$	1.09049	−	1.36743i	0.166298	−	0.208530i	0.857997	+	0.513655i	$0.171709\pi$
$44$	−0.351781	+	0.441119i	−0.0530329	+	0.0665012i
$45$	−1.62033	−	0.780312i	−0.241545	−	0.116322i
$46$	−2.47753			−0.365292
$47$	−6.28881	−	3.02853i	−0.917317	−	0.441756i	−0.0852043	−	0.996363i	$-0.527154\pi$
$47$	−6.28881	−	3.02853i	−0.917317	−	0.441756i	−0.832112	+	0.554607i	$0.812869\pi$
$48$	0.588868	−	2.58000i	0.0849958	−	0.372391i
$49$	−10.1739	+	4.89947i	−1.45341	+	0.699924i
$50$	−1.92598	+	0.927505i	−0.272375	+	0.131169i
$51$	−1.25005	−	5.47684i	−0.175042	−	0.766911i
$52$	1.75911	−	2.20586i	0.243945	−	0.305898i
$53$	−4.87488	−	6.11290i	−0.669616	−	0.839672i	0.324736	−	0.945805i	$-0.394724\pi$
$53$	−4.87488	−	6.11290i	−0.669616	−	0.839672i	−0.994352	+	0.106133i	$0.966153\pi$
$54$	0.269410	−	1.18036i	0.0366621	−	0.160627i
$55$	−0.422703	−	1.85198i	−0.0569973	−	0.249722i
$56$	8.18161	+	10.2594i	1.09331	+	1.37097i
$57$	6.41175			0.849257
$58$	6.16185	+	2.13093i	0.809091	+	0.279805i
$59$	0.382668			0.0498191			0.0249096	−	0.999690i	$-0.492070\pi$
$59$	0.382668			0.0498191			0.0249096	+	0.999690i	$0.492070\pi$
$60$	−0.598958	−	0.751070i	−0.0773252	−	0.0969627i
$61$	1.21640	+	5.32939i	0.155744	+	0.682358i	0.991152	+	0.132729i	$0.0423740\pi$
$61$	1.21640	+	5.32939i	0.155744	+	0.682358i	−0.835409	+	0.549629i	$0.814769\pi$
$62$	1.03041	−	4.51454i	0.130863	−	0.573347i
$63$	2.66662	+	3.34384i	0.335963	+	0.421284i
$64$	5.51347	−	6.91367i	0.689184	−	0.864209i
$65$	2.11377	+	9.26104i	0.262181	+	1.14869i
$66$	1.15219	−	0.554864i	0.141824	−	0.0682990i
$67$	−7.03806	+	3.38935i	−0.859836	+	0.414075i	−0.811219	−	0.584742i	$-0.801196\pi$
$67$	−7.03806	+	3.38935i	−0.859836	+	0.414075i	−0.0486169	+	0.998818i	$0.515481\pi$
$68$	0.667730	−	2.92552i	0.0809742	−	0.354771i
$69$	−1.84368	−	0.887869i	−0.221953	−	0.106887i
$70$	−9.31258			−1.11307
$71$	14.0654	+	6.77356i	1.66926	+	0.803874i	0.998038	+	0.0626189i	$0.0199452\pi$
$71$	14.0654	+	6.77356i	1.66926	+	0.803874i	0.671224	+	0.741255i	$0.265769\pi$
$72$	1.91296	−	2.39878i	0.225445	−	0.282699i
$73$	−1.58547	+	1.98811i	−0.185565	+	0.232691i	−0.865909	−	0.500202i	$-0.833259\pi$
$73$	−1.58547	+	1.98811i	−0.185565	+	0.232691i	0.680344	+	0.732893i	$0.261830\pi$
$74$	−0.382110	−	0.184015i	−0.0444194	−	0.0213913i
$75$	−1.76563			−0.203877
$76$	3.08574	+	1.48601i	0.353958	+	0.170457i
$77$	−1.00525	+	4.40428i	−0.114559	+	0.501914i
$78$	−5.76163	+	2.77465i	−0.652376	+	0.314168i
$79$	−9.25113	+	4.45511i	−1.04083	+	0.501239i	−0.874599	−	0.484847i	$-0.838875\pi$
$79$	−9.25113	+	4.45511i	−1.04083	+	0.501239i	−0.166235	+	0.986086i	$0.553161\pi$
$80$	1.05904	+	4.63996i	0.118404	+	0.518764i
$81$	0.623490	−	0.781831i	0.0692766	−	0.0868702i
$82$	2.73445	+	3.42889i	0.301969	+	0.378657i
$83$	−0.338541	+	1.48324i	−0.0371597	+	0.162807i	−0.990103	−	0.140340i	$-0.955180\pi$
$83$	−0.338541	+	1.48324i	−0.0371597	+	0.162807i	0.952944	+	0.303148i	$0.0980375\pi$
$84$	0.508365	+	2.22729i	0.0554672	+	0.243017i
$85$	6.29915	+	7.89888i	0.683239	+	0.856754i
$86$	−2.11755			−0.228341
$87$	3.82175	+	3.79397i	0.409735	+	0.406756i
$88$	3.24076			0.345467
$89$	−11.1881	−	14.0295i	−1.18594	−	1.48712i	−0.834587	−	0.550876i	$-0.814294\pi$
$89$	−11.1881	−	14.0295i	−1.18594	−	1.48712i	−0.351351	−	0.936244i	$-0.614278\pi$
$90$	0.484517	+	2.12281i	0.0510725	+	0.223763i
$91$	5.02684	−	22.0240i	0.526956	−	2.30875i
$92$	−0.681518	−	0.854597i	−0.0710532	−	0.0890979i
$93$	2.38467	−	2.99028i	0.247278	−	0.310077i
$94$	1.88050	+	8.23899i	0.193958	+	0.849787i
$95$	−10.3892	+	5.00316i	−1.06591	+	0.513314i
$96$	2.64194	−	1.27229i	0.269641	−	0.129852i
$97$	1.51530	−	6.63895i	0.153855	−	0.674083i	−0.837888	−	0.545842i	$-0.816210\pi$
$97$	1.51530	−	6.63895i	0.153855	−	0.674083i	0.991743	−	0.128241i	$-0.0409331\pi$
$98$	12.3177	+	5.93188i	1.24427	+	0.599210i
$99$	1.05626			0.106158
$100$	−0.849732	−	0.409209i	−0.0849732	−	0.0409209i
$101$	2.94644	−	3.69472i	0.293182	−	0.367639i	−0.613324	−	0.789831i	$-0.710168\pi$
$101$	2.94644	−	3.69472i	0.293182	−	0.367639i	0.906506	+	0.422193i	$0.138739\pi$
$102$	−4.24063	+	5.31758i	−0.419885	+	0.526519i
$103$	−3.14881	−	1.51639i	−0.310261	−	0.149414i	0.272273	−	0.962220i	$-0.412225\pi$
$103$	−3.14881	−	1.51639i	−0.310261	−	0.149414i	−0.582534	+	0.812806i	$0.697939\pi$
$104$	−16.2058			−1.58911
$105$	−6.93006	−	3.33734i	−0.676304	−	0.325691i
$106$	−2.10644	+	9.22890i	−0.204595	+	0.896390i
$107$	4.43449	−	2.13554i	0.428699	−	0.206450i	−0.207076	−	0.978325i	$-0.566395\pi$
$107$	4.43449	−	2.13554i	0.428699	−	0.206450i	0.635775	+	0.771874i	$0.280681\pi$
$108$	0.481263	−	0.231764i	0.0463095	−	0.0223015i
$109$	3.31215	+	14.5115i	0.317246	+	1.38995i	0.842360	+	0.538915i	$0.181166\pi$
$109$	3.31215	+	14.5115i	0.317246	+	1.38995i	−0.525114	+	0.851032i	$0.675977\pi$
$110$	−1.43396	+	1.79813i	−0.136723	+	0.171445i
$111$	−0.218406	−	0.273873i	−0.0207302	−	0.0259949i
$112$	2.51855	−	11.0345i	0.237980	−	1.04266i
$113$	1.41140	+	6.18375i	0.132773	+	0.581718i	0.996916	+	0.0784718i	$0.0250041\pi$
$113$	1.41140	+	6.18375i	0.132773	+	0.581718i	−0.864143	+	0.503246i	$0.832139\pi$
$114$	−4.84004	−	6.06922i	−0.453311	−	0.568434i
$115$	3.68019			0.343180
$116$	0.959961	+	2.71164i	0.0891301	+	0.251770i
$117$	−5.28193			−0.488314
$118$	−0.288865	−	0.362225i	−0.0265922	−	0.0333455i
$119$	−5.34639	−	23.4241i	−0.490103	−	2.14728i
$120$	−1.22784	+	5.37953i	−0.112086	+	0.491082i
$121$	−6.16277	−	7.72787i	−0.560252	−	0.702534i
$122$	4.12646	−	5.17441i	0.373592	−	0.468469i
$123$	0.806061	+	3.53158i	0.0726801	+	0.318432i
$124$	1.84069	−	0.886429i	0.165299	−	0.0796037i
$125$	10.9626	−	5.27930i	0.980523	−	0.472195i
$126$	1.15225	−	5.04833i	0.102650	−	0.449741i
$127$	4.02345	+	1.93759i	0.357023	+	0.171933i	0.603794	−	0.797141i	$-0.293655\pi$
$127$	4.02345	+	1.93759i	0.357023	+	0.171933i	−0.246770	+	0.969074i	$0.579369\pi$
$128$	−4.84163			−0.427944
$129$	−1.57580	−	0.758864i	−0.138741	−	0.0668143i
$130$	7.17067	−	8.99173i	0.628909	−	0.788627i
$131$	0.00620961	−	0.00778660i	0.000542536	−	0.000680318i	−0.781560	−	0.623830i	$-0.785576\pi$
$131$	0.00620961	−	0.00778660i	0.000542536	−	0.000680318i	0.782103	+	0.623150i	$0.214147\pi$
$132$	0.508338	+	0.244803i	0.0442451	+	0.0213073i
$133$	27.4226			2.37784
$134$	8.52111	+	4.10355i	0.736112	+	0.354493i
$135$	−0.400190	+	1.75334i	−0.0344428	+	0.150904i
$136$	−15.5290	+	7.47839i	−1.33160	+	0.641267i
$137$	−11.0039	+	5.29921i	−0.940129	+	0.452742i	−0.840215	−	0.542254i	$-0.817571\pi$
$137$	−11.0039	+	5.29921i	−0.940129	+	0.452742i	−0.0999140	+	0.994996i	$0.531857\pi$
$138$	0.551302	+	2.41541i	0.0469299	+	0.205613i
$139$	3.08354	−	3.86663i	0.261542	−	0.327964i	−0.633670	−	0.773603i	$-0.718452\pi$
$139$	3.08354	−	3.86663i	0.261542	−	0.327964i	0.895212	+	0.445640i	$0.147024\pi$
$140$	−2.56170	−	3.21227i	−0.216503	−	0.271487i
$141$	−1.55321	+	6.80504i	−0.130804	+	0.573088i
$142$	−4.20589	−	18.4272i	−0.352950	−	1.54638i
$143$	−3.47850	−	4.36190i	−0.290887	−	0.364760i
$144$	−2.64635			−0.220529
$145$	−9.15299	−	3.16534i	−0.760115	−	0.262868i
$146$	3.07873			0.254797
$147$	7.04053	+	8.82854i	0.580693	+	0.728166i
$148$	−0.0416370	−	0.182424i	−0.00342254	−	0.0149951i
$149$	−3.11840	+	13.6626i	−0.255470	+	1.11929i	0.670566	+	0.741850i	$0.266051\pi$
$149$	−3.11840	+	13.6626i	−0.255470	+	1.11929i	−0.926036	+	0.377436i	$0.876806\pi$
$150$	1.33282	+	1.67131i	0.108824	+	0.136462i
$151$	1.82927	−	2.29383i	0.148864	−	0.186669i	−0.701809	−	0.712366i	$-0.747624\pi$
$151$	1.82927	−	2.29383i	0.148864	−	0.186669i	0.850672	+	0.525697i	$0.176195\pi$
$152$	−4.37749	−	19.1790i	−0.355061	−	1.55562i
$153$	−5.06136	+	2.43742i	−0.409187	+	0.197054i
$154$	4.92782	−	2.37311i	0.397095	−	0.191231i
$155$	−1.53061	+	6.70603i	−0.122941	+	0.538641i
$156$	−2.54199	−	1.22416i	−0.203522	−	0.0980112i
$157$	16.1919			1.29226			0.646128	−	0.763229i	$-0.276387\pi$
$157$	16.1919			1.29226			0.646128	+	0.763229i	$0.276387\pi$
$158$	11.2005	+	5.39388i	0.891065	+	0.429114i
$159$	−4.87488	+	6.11290i	−0.386603	+	0.484785i
$160$	−3.28804	+	4.12307i	−0.259942	+	0.325957i
$161$	−7.88529	−	3.79735i	−0.621448	−	0.299273i
$162$	−1.21072			−0.0951230
$163$	−12.2292	−	5.88927i	−0.957865	−	0.461284i	−0.111428	−	0.993772i	$-0.535543\pi$
$163$	−12.2292	−	5.88927i	−0.957865	−	0.461284i	−0.846437	+	0.532489i	$0.821257\pi$
$164$	−0.430567	+	1.88644i	−0.0336216	+	0.147306i
$165$	−1.71149	+	0.824211i	−0.133239	+	0.0641647i
$166$	1.65956	−	0.799202i	0.128807	−	0.0620301i
$167$	3.64080	+	15.9514i	0.281734	+	1.23436i	0.895569	+	0.444922i	$0.146769\pi$
$167$	3.64080	+	15.9514i	0.281734	+	1.23436i	−0.613836	+	0.789434i	$0.710374\pi$
$168$	8.18161	−	10.2594i	0.631225	−	0.791531i
$169$	9.28921	+	11.6483i	0.714555	+	0.896024i
$170$	2.72186	−	11.9253i	0.208757	−	0.914626i
$171$	−1.42675	−	6.25099i	−0.109106	−	0.478025i
$172$	−0.582495	−	0.730426i	−0.0444149	−	0.0556945i
$173$	−4.46374			−0.339372			−0.169686	−	0.985498i	$-0.554275\pi$
$173$	−4.46374			−0.339372			−0.169686	+	0.985498i	$0.554275\pi$
$174$	0.706362	−	6.48154i	0.0535491	−	0.491364i
$175$	−7.55148			−0.570838
$176$	−1.74280	−	2.18540i	−0.131368	−	0.164730i
$177$	−0.0851516	−	0.373074i	−0.00640039	−	0.0280419i
$178$	−4.83439	+	21.1808i	−0.362353	+	1.58757i
$179$	2.12026	+	2.65872i	0.158476	+	0.198722i	0.854730	−	0.519073i	$-0.173723\pi$
$179$	2.12026	+	2.65872i	0.158476	+	0.198722i	−0.696254	+	0.717795i	$0.745151\pi$
$180$	−0.598958	+	0.751070i	−0.0446437	+	0.0559815i
$181$	−1.47339	−	6.45532i	−0.109516	−	0.479820i	−0.999706	−	0.0242319i	$-0.992286\pi$
$181$	−1.47339	−	6.45532i	−0.109516	−	0.479820i	0.890190	−	0.455589i	$-0.150571\pi$
$182$	−24.6421	+	11.8670i	−1.82659	+	0.879640i
$183$	4.92510	−	2.37180i	0.364074	−	0.175329i
$184$	−1.39709	+	6.12104i	−0.102995	+	0.451249i
$185$	0.567598	+	0.273341i	0.0417306	+	0.0200964i
$186$	−4.63064			−0.339535
$187$	−5.34610	−	2.57455i	−0.390946	−	0.188270i
$188$	−2.32466	+	2.91504i	−0.169544	+	0.212601i
$189$	2.66662	−	3.34384i	0.193968	−	0.243228i
$190$	12.5784	+	6.05742i	0.912531	+	0.439452i
$191$	17.6196			1.27491			0.637454	−	0.770489i	$-0.279988\pi$
$191$	17.6196			1.27491			0.637454	+	0.770489i	$0.279988\pi$
$192$	−7.96720	−	3.83680i	−0.574983	−	0.276897i
$193$	2.98147	−	13.0627i	0.214611	−	0.940273i	−0.746776	−	0.665075i	$-0.768399\pi$
$193$	2.98147	−	13.0627i	0.214611	−	0.940273i	0.961388	−	0.275198i	$-0.0887434\pi$
$194$	−7.42813	+	3.57720i	−0.533309	+	0.256828i
$195$	8.55849	−	4.12155i	0.612886	−	0.295150i
$196$	1.34221	+	5.88059i	0.0958719	+	0.420042i
$197$	−5.11558	+	6.41474i	−0.364470	+	0.457031i	−0.929926	−	0.367748i	$-0.880129\pi$
$197$	−5.11558	+	6.41474i	−0.364470	+	0.457031i	0.565455	+	0.824779i	$0.308700\pi$
$198$	−0.797338	−	0.999830i	−0.0566643	−	0.0710548i
$199$	−5.45073	+	23.8812i	−0.386392	+	1.69290i	0.290551	+	0.956860i	$0.406162\pi$
$199$	−5.45073	+	23.8812i	−0.386392	+	1.69290i	−0.676943	+	0.736036i	$0.736696\pi$
$200$	1.20545	+	5.28141i	0.0852379	+	0.373452i
$201$	4.87049	+	6.10740i	0.343538	+	0.430783i
$202$	−5.72153			−0.402565
$203$	16.3454	+	16.2266i	1.14722	+	1.13888i
$204$	−3.00075			−0.210095
$205$	−4.06182	−	5.09337i	−0.283690	−	0.355736i
$206$	0.941565	+	4.12527i	0.0656019	+	0.287421i
$207$	−0.455351	+	1.99502i	−0.0316491	+	0.138664i
$208$	8.71503	+	10.9283i	0.604278	+	0.757741i
$209$	4.22256	−	5.29492i	0.292081	−	0.366258i
$210$	2.07224	+	9.07909i	0.142998	+	0.626517i
$211$	1.99243	−	0.959502i	0.137164	−	0.0660549i	−0.364043	−	0.931382i	$-0.618604\pi$
$211$	1.99243	−	0.959502i	0.137164	−	0.0660549i	0.501207	+	0.865327i	$0.332890\pi$
$212$	−3.76285	+	1.81209i	−0.258433	+	0.124455i
$213$	3.47388	−	15.2201i	0.238026	−	1.04286i
$214$	−5.36892	−	2.58554i	−0.367012	−	0.176744i
$215$	3.14547			0.214519
$216$	−2.76431	−	1.33122i	−0.188088	−	0.0905782i
$217$	10.1990	−	12.7892i	0.692356	−	0.868187i
$218$	11.2360	−	14.0895i	0.760997	−	0.954260i
$219$	2.29107	+	1.10332i	0.154816	+	0.0745554i
$220$	−1.01470			−0.0684110
$221$	26.7337	+	12.8743i	1.79831	+	0.866018i
$222$	−0.0943735	+	0.413477i	−0.00633393	+	0.0277508i
$223$	−2.43655	+	1.17338i	−0.163164	+	0.0785755i	−0.513683	−	0.857980i	$-0.671719\pi$
$223$	−2.43655	+	1.17338i	−0.163164	+	0.0785755i	0.350519	+	0.936555i	$0.386005\pi$
$224$	11.2994	−	5.44149i	0.754971	−	0.363575i
$225$	0.392890	+	1.72136i	0.0261926	+	0.114757i
$226$	4.78798	−	6.00393i	0.318491	−	0.399376i
$227$	8.99231	+	11.2760i	0.596840	+	0.748414i	0.984882	−	0.173228i	$-0.0554197\pi$
$227$	8.99231	+	11.2760i	0.596840	+	0.748414i	−0.388041	+	0.921642i	$0.626848\pi$
$228$	0.762114	−	3.33904i	0.0504722	−	0.221133i
$229$	−5.72917	−	25.1011i	−0.378594	−	1.65873i	−0.701779	−	0.712394i	$-0.747611\pi$
$229$	−5.72917	−	25.1011i	−0.378594	−	1.65873i	0.323185	−	0.946336i	$-0.395246\pi$
$230$	−2.77807	−	3.48359i	−0.183180	−	0.229701i
$231$	4.51754			0.297232
$232$	8.73942	−	14.0220i	0.573771	−	0.920589i
$233$	−22.6039			−1.48083			−0.740417	−	0.672148i	$-0.765372\pi$
$233$	−22.6039			−1.48083			−0.740417	+	0.672148i	$0.765372\pi$
$234$	3.98717	+	4.99975i	0.260649	+	0.326844i
$235$	−2.79334	−	12.2384i	−0.182218	−	0.798347i
$236$	0.0454847	−	0.199282i	0.00296080	−	0.0129721i
$237$	6.40198	+	8.02783i	0.415853	+	0.521464i
$238$	−18.1369	+	22.7429i	−1.17564	+	1.47420i
$239$	−5.21218	−	22.8361i	−0.337148	−	1.47714i	−0.804968	−	0.593318i	$-0.797818\pi$
$239$	−5.21218	−	22.8361i	−0.337148	−	1.47714i	0.467820	−	0.883824i	$-0.345040\pi$
$240$	4.28797	−	2.06498i	0.276787	−	0.133294i
$241$	−20.1661	+	9.71147i	−1.29901	+	0.625570i	−0.950205	−	0.311625i	$-0.899127\pi$
$241$	−20.1661	+	9.71147i	−1.29901	+	0.625570i	−0.348805	+	0.937195i	$0.613413\pi$
$242$	−2.66294	+	11.6671i	−0.171180	+	0.749989i
$243$	−0.900969	−	0.433884i	−0.0577972	−	0.0278337i
$244$	2.91996			0.186932
$245$	−18.2970	−	8.81138i	−1.16895	−	0.562939i
$246$	2.73445	−	3.42889i	0.174342	−	0.218618i
$247$	−21.1153	+	26.4778i	−1.34354	+	1.68474i
$248$	−10.5727	−	5.09154i	−0.671366	−	0.323313i
$249$	1.52139			0.0964141
$250$	−13.2726	−	6.39175i	−0.839433	−	0.404250i
$251$	1.32618	−	5.81039i	0.0837079	−	0.366748i	−0.915673	−	0.401924i	$-0.868342\pi$
$251$	1.32618	−	5.81039i	0.0837079	−	0.366748i	0.999381	+	0.0351751i	$0.0111989\pi$
$252$	2.05833	−	0.991238i	0.129662	−	0.0624421i
$253$	−1.94740	+	0.937819i	−0.122432	+	0.0589602i
$254$	−1.20310	−	5.27114i	−0.0754894	−	0.330741i
$255$	6.29915	−	7.89888i	0.394468	−	0.494647i
$256$	−7.37214	−	9.24437i	−0.460759	−	0.577773i
$257$	3.35390	−	14.6944i	0.209211	−	0.916612i	−0.755883	−	0.654707i	$-0.772792\pi$
$257$	3.35390	−	14.6944i	0.209211	−	0.916612i	0.965094	−	0.261905i	$-0.0843508\pi$
$258$	0.471199	+	2.06446i	0.0293356	+	0.128528i
$259$	−0.934109	−	1.17134i	−0.0580427	−	0.0727832i
$260$	5.07411			0.314683
$261$	2.84843	−	4.57017i	0.176313	−	0.282886i
$262$	−0.0120581			−0.000744950
$263$	−11.6750	−	14.6400i	−0.719911	−	0.902740i	0.278422	−	0.960459i	$-0.410189\pi$
$263$	−11.6750	−	14.6400i	−0.719911	−	0.902740i	−0.998333	+	0.0577193i	$0.981617\pi$
$264$	−0.721138	−	3.15951i	−0.0443830	−	0.194454i
$265$	3.12896	−	13.7089i	0.192210	−	0.842129i
$266$	−20.7005	−	25.9576i	−1.26923	−	1.59156i
$267$	−11.1881	+	14.0295i	−0.684702	+	0.858589i
$268$	0.928510	+	4.06807i	0.0567178	+	0.248497i
$269$	20.8357	−	10.0340i	1.27038	−	0.611781i	0.327477	−	0.944859i	$-0.393802\pi$
$269$	20.8357	−	10.0340i	1.27038	−	0.611781i	0.942899	+	0.333078i	$0.108087\pi$
$270$	1.96177	−	0.944738i	0.119389	−	0.0574949i
$271$	−4.75012	+	20.8116i	−0.288549	+	1.26422i	0.597967	+	0.801521i	$0.295975\pi$
$271$	−4.75012	+	20.8116i	−0.288549	+	1.26422i	−0.886517	+	0.462697i	$0.846882\pi$
$272$	13.3941	+	6.45027i	0.812138	+	0.391105i
$273$	−22.5904			−1.36723
$274$	13.3227	+	6.41585i	0.804851	+	0.387596i
$275$	−1.16278	+	1.45809i	−0.0701185	+	0.0879258i
$276$	−0.681518	+	0.854597i	−0.0410226	+	0.0514407i
$277$	7.49769	+	3.61070i	0.450493	+	0.216946i	0.645352	−	0.763885i	$-0.276711\pi$
$277$	7.49769	+	3.61070i	0.450493	+	0.216946i	−0.194859	+	0.980831i	$0.562425\pi$
$278$	−5.98774			−0.359121
$279$	−3.44594	−	1.65948i	−0.206303	−	0.0993503i
$280$	−5.25140	+	23.0079i	−0.313831	+	1.37498i
$281$	26.0562	−	12.5480i	1.55438	−	0.748552i	0.557709	−	0.830037i	$-0.311681\pi$
$281$	26.0562	−	12.5480i	1.55438	−	0.748552i	0.996675	+	0.0814850i	$0.0259663\pi$
$282$	7.61397	−	3.66670i	0.453405	−	0.218349i
$283$	−6.67116	−	29.2282i	−0.396559	−	1.73744i	−0.640785	−	0.767721i	$-0.721391\pi$
$283$	−6.67116	−	29.2282i	−0.396559	−	1.73744i	0.244226	−	0.969718i	$-0.421466\pi$
$284$	5.19931	−	6.51973i	0.308522	−	0.386875i
$285$	7.18953	+	9.01539i	0.425871	+	0.534026i
$286$	−1.50306	+	6.58534i	−0.0888778	+	0.389399i
$287$	3.44747	+	15.1043i	0.203497	+	0.891581i
$288$	−1.82828	−	2.29259i	−0.107732	−	0.135092i
$289$	14.5584			0.856378
$290$	3.91308	+	11.0534i	0.229784	+	0.649081i
$291$	−6.80968			−0.399191
$292$	0.846895	+	1.06197i	0.0495608	+	0.0621473i
$293$	−1.94796	−	8.53458i	−0.113801	−	0.498595i	−0.999416	−	0.0341747i	$-0.989120\pi$
$293$	−1.94796	−	8.53458i	−0.113801	−	0.498595i	0.885615	−	0.464421i	$-0.153737\pi$
$294$	3.04221	−	13.3288i	0.177426	−	0.777352i
$295$	0.429088	+	0.538059i	0.0249825	+	0.0313270i
$296$	−0.670105	+	0.840285i	−0.0389490	+	0.0488405i
$297$	−0.235040	−	1.02978i	−0.0136384	−	0.0597536i
$298$	15.2867	−	7.36170i	0.885536	−	0.426452i
$299$	9.73818	−	4.68966i	0.563173	−	0.271210i
$300$	−0.209867	+	0.919485i	−0.0121166	+	0.0530865i
$301$	−6.73958	−	3.24561i	−0.388463	−	0.187074i
$302$	−3.55215			−0.204403
$303$	−4.25773	−	2.05042i	−0.244600	−	0.117793i
$304$	−10.5792	+	13.2659i	−0.606759	+	0.760852i
$305$	−6.12956	+	7.68622i	−0.350977	+	0.440112i
$306$	6.12788	+	2.95103i	0.350308	+	0.168699i
$307$	−33.9161			−1.93570			−0.967848	−	0.251536i	$-0.919064\pi$
$307$	−33.9161			−1.93570			−0.967848	+	0.251536i	$0.919064\pi$
$308$	2.17412	+	1.04700i	0.123882	+	0.0596585i
$309$	−0.777691	+	3.40729i	−0.0442413	+	0.193834i
$310$	7.50319	−	3.61334i	0.426152	−	0.205224i
$311$	−7.32104	+	3.52563i	−0.415138	+	0.199920i	−0.629781	−	0.776773i	$-0.716855\pi$
$311$	−7.32104	+	3.52563i	−0.415138	+	0.199920i	0.214643	+	0.976693i	$0.431141\pi$
$312$	3.60612	+	15.7995i	0.204157	+	0.894468i
$313$	1.57580	−	1.97599i	0.0890693	−	0.111689i	−0.735300	−	0.677742i	$-0.762959\pi$
$313$	1.57580	−	1.97599i	0.0890693	−	0.111689i	0.824369	+	0.566053i	$0.191530\pi$
$314$	−12.2228	−	15.3269i	−0.689773	−	0.864948i
$315$	−1.71158	+	7.49893i	−0.0964367	+	0.422517i
$316$	1.22047	+	5.34724i	0.0686570	+	0.300806i
$317$	10.3738	+	13.0083i	0.582651	+	0.730621i	0.982562	−	0.185933i	$-0.0595306\pi$
$317$	10.3738	+	13.0083i	0.582651	+	0.730621i	−0.399912	+	0.916554i	$0.630959\pi$
$318$	9.46624			0.530840
$319$	5.65000	−	0.657481i	0.316339	−	0.0368119i
$320$	15.9034			0.889028
$321$	−3.06876	−	3.84811i	−0.171282	−	0.214780i
$322$	2.35788	+	10.3305i	0.131399	+	0.575699i
$323$	−8.01503	+	35.1161i	−0.445968	+	1.95391i
$324$	−0.333044	−	0.417624i	−0.0185025	−	0.0232013i
$325$	5.81462	−	7.29130i	0.322537	−	0.404449i
$326$	3.65681	+	16.0215i	0.202532	+	0.887350i
$327$	13.4106	−	6.45821i	0.741609	−	0.357140i
$328$	10.0135	−	4.82223i	0.552901	−	0.266263i
$329$	−6.64296	+	29.1047i	−0.366238	+	1.60459i
$330$	2.07213	+	0.997887i	0.114067	+	0.0549319i
$331$	12.9286			0.710619			0.355309	−	0.934749i	$-0.384375\pi$
$331$	12.9286			0.710619			0.355309	+	0.934749i	$0.384375\pi$
$332$	0.732188	+	0.352603i	0.0401840	+	0.0193516i
$333$	−0.218406	+	0.273873i	−0.0119686	+	0.0150081i
$334$	12.3509	−	15.4875i	0.675811	−	0.847440i
$335$	−12.6575	−	6.09553i	−0.691553	−	0.333034i
$336$	−11.3182			−0.617461
$337$	5.01185	+	2.41358i	0.273013	+	0.131476i	0.565381	−	0.824830i	$-0.308729\pi$
$337$	5.01185	+	2.41358i	0.273013	+	0.131476i	−0.292368	+	0.956306i	$0.594443\pi$
$338$	4.01387	−	17.5859i	0.218326	−	0.956548i
$339$	5.71464	−	2.75203i	0.310377	−	0.149470i
$340$	4.86222	−	2.34152i	0.263691	−	0.126987i
$341$	−0.898957	−	3.93859i	−0.0486813	−	0.213286i
$342$	−4.84004	+	6.06922i	−0.261719	+	0.328186i
$343$	11.4455	+	14.3522i	0.617998	+	0.774945i
$344$	−1.19409	+	5.23167i	−0.0643813	+	0.282073i
$345$	−0.818920	−	3.58792i	−0.0440891	−	0.193167i
$346$	3.36955	+	4.22528i	0.181148	+	0.227152i
$347$	−8.78686			−0.471703			−0.235852	−	0.971789i	$-0.575788\pi$
$347$	−8.78686			−0.471703			−0.235852	+	0.971789i	$0.575788\pi$
$348$	2.43004	−	1.53929i	0.130264	−	0.0825146i
$349$	15.1943			0.813332			0.406666	−	0.913577i	$-0.366691\pi$
$349$	15.1943			0.813332			0.406666	+	0.913577i	$0.366691\pi$
$350$	5.70039	+	7.14806i	0.304698	+	0.382080i
$351$	1.17534	+	5.14950i	0.0627350	+	0.274860i
$352$	0.689213	−	3.01964i	0.0367352	−	0.160947i
$353$	−7.71052	−	9.66868i	−0.410389	−	0.514612i	0.533083	−	0.846063i	$-0.321033\pi$
$353$	−7.71052	−	9.66868i	−0.410389	−	0.514612i	−0.943473	+	0.331451i	$0.892462\pi$
$354$	−0.288865	+	0.362225i	−0.0153530	+	0.0192520i
$355$	6.24754	+	27.3723i	0.331585	+	1.45277i
$356$	−8.63595	+	4.15885i	−0.457704	+	0.220419i
$357$	−21.6471	+	10.4247i	−1.14569	+	0.551733i
$358$	0.916165	−	4.01398i	0.0484208	−	0.212146i
$359$	14.4303	+	6.94924i	0.761600	+	0.366767i	0.774024	−	0.633156i	$-0.218241\pi$
$359$	14.4303	+	6.94924i	0.761600	+	0.366767i	−0.0124248	+	0.999923i	$0.503955\pi$
$360$	5.51788			0.290818
$361$	−19.9209	−	9.59340i	−1.04847	−	0.504916i
$362$	−4.99825	+	6.26761i	−0.262702	+	0.329418i
$363$	−6.16277	+	7.72787i	−0.323462	+	0.405608i
$364$	−10.8719	−	5.23565i	−0.569844	−	0.274422i
$365$	−4.57323			−0.239374
$366$	−5.96290	−	2.87158i	−0.311686	−	0.150100i
$367$	4.94990	−	21.6869i	0.258383	−	1.13205i	−0.664597	−	0.747202i	$-0.731397\pi$
$367$	4.94990	−	21.6869i	0.258383	−	1.13205i	0.922980	−	0.384847i	$-0.125746\pi$
$368$	4.87902	−	2.34961i	0.254336	−	0.122482i
$369$	3.26367	−	1.57170i	0.169900	−	0.0818196i
$370$	−0.169725	−	0.743612i	−0.00882356	−	0.0386585i
$371$	−20.8495	+	26.1445i	−1.08245	+	1.35735i
$372$	−1.27380	−	1.59729i	−0.0660433	−	0.0828156i
$373$	−1.54213	+	6.75653i	−0.0798487	+	0.349840i	−0.999032	−	0.0439901i	$-0.985993\pi$
$373$	−1.54213	+	6.75653i	−0.0798487	+	0.349840i	0.919183	+	0.393830i	$0.128850\pi$
$374$	1.59861	+	7.00395i	0.0826620	+	0.362166i
$375$	−7.58634	−	9.51297i	−0.391757	−	0.491248i
$376$	21.4159			1.10444
$377$	−28.2534	+	3.28780i	−1.45512	+	0.169330i
$378$	−5.17816			−0.266336
$379$	−4.85604	−	6.08928i	−0.249438	−	0.312785i	0.641311	−	0.767281i	$-0.278391\pi$
$379$	−4.85604	−	6.08928i	−0.249438	−	0.312785i	−0.890749	+	0.454496i	$0.849819\pi$
$380$	1.37061	+	6.00505i	0.0703110	+	0.308052i
$381$	0.993710	−	4.35373i	0.0509093	−	0.223048i
$382$	−13.3005	−	16.6783i	−0.680512	−	0.853335i
$383$	15.8756	−	19.9074i	0.811206	−	1.01722i	−0.188178	−	0.982135i	$-0.560258\pi$
$383$	15.8756	−	19.9074i	0.811206	−	1.01722i	0.999384	−	0.0350856i	$-0.0111704\pi$
$384$	1.07736	+	4.72024i	0.0549790	+	0.240879i
$385$	−7.31993	+	3.52509i	−0.373058	+	0.179655i
$386$	−14.6155	+	7.03844i	−0.743908	+	0.358247i
$387$	−0.389190	+	1.70515i	−0.0197836	+	0.0866778i
$388$	−3.27725	−	1.57824i	−0.166377	−	0.0801229i
$389$	10.9838			0.556902			0.278451	−	0.960450i	$-0.410179\pi$
$389$	10.9838			0.556902			0.278451	+	0.960450i	$0.410179\pi$
$390$	−10.3619	−	4.99004i	−0.524696	−	0.252680i
$391$	7.16741	−	8.98765i	0.362472	−	0.454525i
$392$	21.6014	−	27.0873i	1.09104	−	1.36812i
$393$	−0.00897314	−	0.00432124i	−0.000452635	−	0.000217978i
$394$	9.93365			0.500450
$395$	−16.6376	−	8.01223i	−0.837127	−	0.403139i
$396$	0.125549	−	0.550066i	0.00630908	−	0.0276419i
$397$	−4.59536	+	2.21301i	−0.230635	+	0.111068i	−0.545632	−	0.838025i	$-0.683711\pi$
$397$	−4.59536	+	2.21301i	−0.230635	+	0.111068i	0.314998	+	0.949092i	$0.397996\pi$
$398$	26.7200	−	12.8677i	1.33935	−	0.644999i
$399$	−6.10210	−	26.7351i	−0.305487	−	1.33843i
$400$	2.91324	−	3.65309i	0.145662	−	0.182654i
$401$	−12.1843	−	15.2786i	−0.608455	−	0.762979i	0.378214	−	0.925718i	$-0.376538\pi$
$401$	−12.1843	−	15.2786i	−0.608455	−	0.762979i	−0.986669	+	0.162740i	$0.947967\pi$
$402$	2.10454	−	9.22059i	0.104965	−	0.459881i
$403$	4.49533	+	19.6953i	0.223928	+	0.981093i
$404$	−1.57388	−	1.97358i	−0.0783033	−	0.0981892i
$405$	1.79844			0.0893650
$406$	3.02106	−	27.7211i	0.149933	−	1.37577i
$407$	−0.370004			−0.0183404
$408$	10.7464	+	13.4756i	0.532028	+	0.667142i
$409$	3.98856	+	17.4750i	0.197221	+	0.864083i	0.972581	+	0.232564i	$0.0747114\pi$
$409$	3.98856	+	17.4750i	0.197221	+	0.864083i	−0.775360	+	0.631520i	$0.782431\pi$
$410$	−1.75512	+	7.68966i	−0.0866790	+	0.379765i
$411$	7.61495	+	9.54885i	0.375618	+	0.471010i
$412$	−1.16396	+	1.45956i	−0.0573442	+	0.0719074i
$413$	−0.364188	−	1.59561i	−0.0179205	−	0.0785148i
$414$	2.23218	−	1.07496i	0.109705	−	0.0528314i
$415$	−2.46516	+	1.18716i	−0.121010	+	0.0582753i
$416$	−3.44648	+	15.1000i	−0.168978	+	0.740339i
$417$	−4.45584	−	2.14582i	−0.218204	−	0.105081i
$418$	−8.19954			−0.401053
$419$	−3.36801	−	1.62195i	−0.164538	−	0.0792373i	0.349802	−	0.936824i	$-0.386249\pi$
$419$	−3.36801	−	1.62195i	−0.164538	−	0.0792373i	−0.514340	+	0.857586i	$0.671963\pi$
$420$	−2.56170	+	3.21227i	−0.124998	+	0.156743i
$421$	5.16735	−	6.47965i	0.251841	−	0.315799i	−0.639800	−	0.768541i	$-0.720983\pi$
$421$	5.16735	−	6.47965i	0.251841	−	0.315799i	0.891641	+	0.452742i	$0.149554\pi$
$422$	−2.41227	−	1.16169i	−0.117427	−	0.0565500i
$423$	6.98005			0.339382
$424$	21.6133	+	10.4084i	1.04964	+	0.505478i
$425$	2.20713	−	9.67008i	0.107062	−	0.469068i
$426$	−17.0293	+	8.20087i	−0.825072	+	0.397334i
$427$	21.0643	−	10.1440i	1.01937	−	0.490904i
$428$	−0.585029	−	2.56318i	−0.0282785	−	0.123896i
$429$	−3.47850	+	4.36190i	−0.167943	+	0.210594i
$430$	−2.37442	−	2.97743i	−0.114505	−	0.143584i
$431$	−4.25670	+	18.6498i	−0.205038	+	0.898330i	0.762776	+	0.646663i	$0.223836\pi$
$431$	−4.25670	+	18.6498i	−0.205038	+	0.898330i	−0.967814	+	0.251667i	$0.919021\pi$
$432$	0.588868	+	2.58000i	0.0283319	+	0.124130i
$433$	−10.0699	−	12.6273i	−0.483929	−	0.606828i	0.478591	−	0.878038i	$-0.341148\pi$
$433$	−10.0699	−	12.6273i	−0.483929	−	0.606828i	−0.962520	+	0.271210i	$0.912576\pi$
$434$	−19.8049			−0.950667
$435$	−1.04925	+	9.62787i	−0.0503077	+	0.461621i
$436$	7.95081			0.380775
$437$	8.18053	+	10.2581i	0.391328	+	0.490710i
$438$	−0.685081	−	3.00154i	−0.0327344	−	0.143419i
$439$	−0.660522	+	2.89393i	−0.0315250	+	0.138120i	−0.988241	−	0.152902i	$-0.951138\pi$
$439$	−0.660522	+	2.89393i	−0.0315250	+	0.138120i	0.956716	+	0.291022i	$0.0939953\pi$
$440$	3.63389	+	4.55675i	0.173239	+	0.217235i
$441$	7.04053	−	8.82854i	0.335263	−	0.420407i
$442$	−7.99400	−	35.0240i	−0.380236	−	1.66592i
$443$	−9.45260	+	4.55213i	−0.449107	+	0.216278i	−0.644745	−	0.764398i	$-0.723036\pi$
$443$	−9.45260	+	4.55213i	−0.449107	+	0.216278i	0.195638	+	0.980676i	$0.437322\pi$
$444$	−0.168585	+	0.0811861i	−0.00800068	+	0.00385292i
$445$	7.18114	−	31.4626i	0.340419	−	1.49147i
$446$	2.94998	+	1.42064i	0.139686	+	0.0672691i
$447$	14.0140			0.662839
$448$	−34.0751	−	16.4097i	−1.60990	−	0.775287i
$449$	−2.74538	+	3.44260i	−0.129563	+	0.162466i	−0.842381	−	0.538882i	$-0.818847\pi$
$449$	−2.74538	+	3.44260i	−0.129563	+	0.162466i	0.712819	+	0.701348i	$0.247418\pi$
$450$	1.33282	−	1.67131i	0.0628298	−	0.0787861i
$451$	3.44728	+	1.66012i	0.162326	+	0.0781721i
$452$	3.38807			0.159361
$453$	−2.64337	−	1.27298i	−0.124196	−	0.0598097i
$454$	3.88558	−	17.0238i	0.182359	−	0.798968i
$455$	36.6040	−	17.6276i	1.71602	−	0.826394i
$456$	−17.7241	+	8.53547i	−0.830006	+	0.399710i
$457$	−2.52528	−	11.0640i	−0.118127	−	0.517550i	−0.999021	−	0.0442360i	$-0.985915\pi$
$457$	−2.52528	−	11.0640i	−0.118127	−	0.517550i	0.880894	−	0.473314i	$-0.156943\pi$
$458$	−19.4354	+	24.3712i	−0.908156	+	1.13879i
$459$	3.50257	+	4.39209i	0.163486	+	0.205005i
$460$	0.437435	−	1.91653i	0.0203955	−	0.0893586i
$461$	−4.38570	−	19.2150i	−0.204262	−	0.894932i	−0.968306	−	0.249767i	$-0.919646\pi$
$461$	−4.38570	−	19.2150i	−0.204262	−	0.894932i	0.764044	−	0.645165i	$-0.223211\pi$
$462$	−3.41016	−	4.27620i	−0.158655	−	0.198947i
$463$	0.753315			0.0350095			0.0175048	−	0.999847i	$-0.494428\pi$
$463$	0.753315			0.0350095			0.0175048	+	0.999847i	$0.494428\pi$
$464$	−14.1555	+	1.64725i	−0.657153	+	0.0764718i
$465$	6.87849			0.318982
$466$	17.0631	+	21.3964i	0.790431	+	0.991169i
$467$	−2.32424	−	10.1832i	−0.107553	−	0.471221i	−0.999806	−	0.0196852i	$-0.993734\pi$
$467$	−2.32424	−	10.1832i	−0.107553	−	0.471221i	0.892253	−	0.451535i	$-0.149124\pi$
$468$	−0.627821	+	2.75066i	−0.0290210	+	0.127149i
$469$	20.8307	+	26.1209i	0.961874	+	1.20615i
$470$	−9.47601	+	11.8825i	−0.437096	+	0.548101i
$471$	−3.60304	−	15.7860i	−0.166020	−	0.727379i
$472$	−1.05781	+	0.509416i	−0.0486898	+	0.0234478i
$473$	−1.66445	+	0.801556i	−0.0765314	+	0.0368556i
$474$	2.76630	−	12.1199i	0.127060	−	0.556688i
$475$	10.1997	+	4.91190i	0.467993	+	0.225374i
$476$	−12.8340			−0.588246
$477$	7.04440	+	3.39240i	0.322541	+	0.155328i
$478$	−17.6816	+	22.1720i	−0.808737	+	1.01412i
$479$	−8.71517	+	10.9285i	−0.398206	+	0.499335i	−0.939999	−	0.341177i	$-0.889174\pi$
$479$	−8.71517	+	10.9285i	−0.398206	+	0.499335i	0.541793	+	0.840512i	$0.317746\pi$
$480$	4.75135	+	2.28813i	0.216869	+	0.104438i
$481$	1.85024			0.0843637
$482$	24.4154	+	11.7578i	1.11209	+	0.535555i
$483$	−1.94750	+	8.53258i	−0.0886145	+	0.388246i
$484$	−4.75695	+	2.29083i	−0.216225	+	0.104129i
$485$	11.0340	−	5.31367i	0.501026	−	0.241282i
$486$	0.269410	+	1.18036i	0.0122207	+	0.0535424i
$487$	−0.910473	+	1.14170i	−0.0412575	+	0.0517352i	−0.802032	−	0.597281i	$-0.796248\pi$
$487$	−0.910473	+	1.14170i	−0.0412575	+	0.0517352i	0.760775	+	0.649016i	$0.224819\pi$
$488$	−10.4571	−	13.1128i	−0.473371	−	0.593589i
$489$	−3.02036	+	13.2331i	−0.136586	+	0.598420i
$490$	5.47123	+	23.9710i	0.247165	+	1.08290i
$491$	−7.57677	−	9.50097i	−0.341935	−	0.428773i	0.580896	−	0.813978i	$-0.302702\pi$
$491$	−7.57677	−	9.50097i	−0.341935	−	0.428773i	−0.922831	+	0.385205i	$0.874131\pi$
$492$	1.93495			0.0872342
$493$	−25.5564	+	16.1885i	−1.15100	+	0.729091i
$494$	41.0027			1.84480
$495$	1.18439	+	1.48518i	0.0532343	+	0.0667537i
$496$	2.25225	+	9.86774i	0.101129	+	0.443075i
$497$	14.8575	−	65.0951i	0.666451	−	2.91991i
$498$	−1.14845	−	1.44011i	−0.0514633	−	0.0645330i
$499$	−22.4256	+	28.1208i	−1.00391	+	1.25886i	−0.0381883	+	0.999271i	$0.512159\pi$
$499$	−22.4256	+	28.1208i	−1.00391	+	1.25886i	−0.965719	+	0.259589i	$0.916413\pi$
$500$	−1.44626	−	6.33648i	−0.0646787	−	0.283376i
$501$	14.7413	−	7.09904i	0.658593	−	0.317162i
$502$	−6.50108	+	3.13075i	−0.290157	+	0.139732i
$503$	3.19420	−	13.9947i	0.142422	−	0.623993i	−0.852446	−	0.522815i	$-0.824882\pi$
$503$	3.19420	−	13.9947i	0.142422	−	0.623993i	0.994868	−	0.101178i	$-0.0322612\pi$
$504$	−11.8228	−	5.69355i	−0.526628	−	0.253611i
$505$	8.49892			0.378197
$506$	2.35775	+	1.13543i	0.104815	+	0.0504762i
$507$	9.28921	−	11.6483i	0.412549	−	0.517319i
$508$	1.48727	−	1.86498i	0.0659871	−	0.0827452i
$509$	27.9345	+	13.4525i	1.23817	+	0.596273i	0.934316	−	0.356445i	$-0.116011\pi$
$509$	27.9345	+	13.4525i	1.23817	+	0.596273i	0.303857	+	0.952718i	$0.401725\pi$
$510$	−12.2319			−0.541640
$511$	9.79873	+	4.71882i	0.433470	+	0.208748i
$512$	−5.34023	+	23.3971i	−0.236007	+	1.03401i
$513$	−5.77679	+	2.78195i	−0.255051	+	0.122826i
$514$	−16.4412	+	7.91765i	−0.725189	+	0.349232i
$515$	−1.39863	−	6.12779i	−0.0616309	−	0.270023i
$516$	−0.582495	+	0.730426i	−0.0256429	+	0.0321552i
$517$	4.59682	+	5.76423i	0.202168	+	0.253511i
$518$	−0.403629	+	1.76841i	−0.0177344	+	0.0776996i
$519$	0.993276	+	4.35182i	0.0436000	+	0.191024i
$520$	−18.1716	−	22.7865i	−0.796879	−	0.999254i
$521$	−14.9084			−0.653150			−0.326575	−	0.945171i	$-0.605895\pi$
$521$	−14.9084			−0.653150			−0.326575	+	0.945171i	$0.605895\pi$
$522$	−6.47622	+	0.753627i	−0.283456	+	0.0329853i
$523$	−12.9505			−0.566284			−0.283142	−	0.959078i	$-0.591377\pi$
$523$	−12.9505			−0.566284			−0.283142	+	0.959078i	$0.591377\pi$
$524$	−0.00331693	−	0.00415930i	−0.000144901	−	0.000181700i
$525$	1.68036	+	7.36215i	0.0733370	+	0.321310i
$526$	−5.04477	+	22.1026i	−0.219962	+	0.963718i
$527$	13.3963	+	16.7984i	0.583552	+	0.731751i
$528$	−1.74280	+	2.18540i	−0.0758454	+	0.0951072i
$529$	4.18618	+	18.3409i	0.182008	+	0.797429i
$530$	−15.3385	+	7.38662i	−0.666260	+	0.320854i
$531$	−0.344772	+	0.166033i	−0.0149618	+	0.00720524i
$532$	3.25951	−	14.2808i	0.141318	−	0.619153i
$533$	−17.2385	−	8.30162i	−0.746682	−	0.359583i
$534$	21.7256			0.940157
$535$	7.97515	+	3.84063i	0.344796	+	0.166045i
$536$	14.9434	−	18.7385i	0.645457	−	0.809378i
$537$	2.12026	−	2.65872i	0.0914960	−	0.114732i
$538$	−25.2262	−	12.1483i	−1.08758	−	0.523750i
$539$	11.9274			0.513750
$540$	0.865520	+	0.416812i	0.0372461	+	0.0179368i
$541$	−2.41951	+	10.6006i	−0.104023	+	0.455754i	0.895911	+	0.444234i	$0.146524\pi$
$541$	−2.41951	+	10.6006i	−0.104023	+	0.455754i	−0.999934	+	0.0115201i	$0.996333\pi$
$542$	23.2856	−	11.2137i	1.00020	−	0.481671i
$543$	−5.96562	+	2.87289i	−0.256009	+	0.123287i
$544$	3.66557	+	16.0599i	0.157160	+	0.688562i
$545$	−16.6903	+	20.9289i	−0.714932	+	0.896497i
$546$	17.0528	+	21.3836i	0.729794	+	0.915133i
$547$	5.14692	−	22.5501i	0.220066	−	0.964174i	−0.737361	−	0.675499i	$-0.763928\pi$
$547$	5.14692	−	22.5501i	0.220066	−	0.964174i	0.957427	−	0.288675i	$-0.0932147\pi$
$548$	1.45171	+	6.36038i	0.0620142	+	0.271702i
$549$	−3.40827	−	4.27384i	−0.145462	−	0.182403i
$550$	2.25794			0.0962790
$551$	−11.5228	−	32.5489i	−0.490887	−	1.38663i
$552$	6.27846			0.267229
$553$	27.3808	+	34.3345i	1.16435	+	1.46005i
$554$	−2.24198	−	9.82275i	−0.0952526	−	0.417329i
$555$	0.140185	−	0.614191i	0.00595052	−	0.0260709i
$556$	−1.64711	−	2.06541i	−0.0698529	−	0.0875928i
$557$	−26.8909	+	33.7201i	−1.13940	+	1.42877i	−0.252029	+	0.967720i	$0.581098\pi$
$557$	−26.8909	+	33.7201i	−1.13940	+	1.42877i	−0.887375	+	0.461048i	$0.847474\pi$
$558$	1.03041	+	4.51454i	0.0436209	+	0.191116i
$559$	8.32325	−	4.00826i	0.352036	−	0.169532i
$560$	18.3393	−	8.83176i	0.774979	−	0.373210i
$561$	−1.32038	+	5.78496i	−0.0557464	+	0.244241i
$562$	−31.5467	−	15.1921i	−1.33072	−	0.640840i
$563$	34.1036			1.43729			0.718647	−	0.695375i	$-0.244762\pi$
$563$	34.1036			1.43729			0.718647	+	0.695375i	$0.244762\pi$
$564$	3.35924	+	1.61772i	0.141449	+	0.0681185i
$565$	−7.11219	+	8.91841i	−0.299212	+	0.375200i
$566$	−22.6309	+	28.3783i	−0.951250	+	1.19283i
$567$	−3.85338	−	1.85569i	−0.161827	−	0.0779317i
$568$	−47.8984			−2.00977
$569$	17.1914	+	8.27893i	0.720700	+	0.347071i	0.758019	−	0.652233i	$-0.226167\pi$
$569$	17.1914	+	8.27893i	0.720700	+	0.347071i	−0.0373190	+	0.999303i	$0.511882\pi$
$570$	3.10660	−	13.6109i	0.130121	−	0.570098i
$571$	5.91613	−	2.84906i	0.247582	−	0.119229i	−0.305978	−	0.952039i	$-0.598983\pi$
$571$	5.91613	−	2.84906i	0.247582	−	0.119229i	0.553560	+	0.832809i	$0.313269\pi$
$572$	−2.68500	+	1.29303i	−0.112266	+	0.0540642i
$573$	−3.92072	−	17.1778i	−0.163791	−	0.717613i
$574$	11.6950	−	14.6651i	0.488141	−	0.612110i
$575$	−2.25271	−	2.82480i	−0.0939444	−	0.117803i
$576$	−1.96773	+	8.62121i	−0.0819890	+	0.359217i
$577$	4.57508	+	20.0447i	0.190463	+	0.834474i	0.976366	+	0.216124i	$0.0693415\pi$
$577$	4.57508	+	20.0447i	0.190463	+	0.834474i	−0.785903	+	0.618350i	$0.787801\pi$
$578$	−10.9897	−	13.7807i	−0.457112	−	0.573200i
$579$	−13.3986			−0.556828
$580$	−2.73636	+	4.39036i	−0.113621	+	0.182300i
$581$	6.50687			0.269951
$582$	5.14043	+	6.44589i	0.213078	+	0.267191i
$583$	1.83770	+	8.05150i	0.0761098	+	0.333459i
$584$	1.73611	−	7.60637i	0.0718406	−	0.314754i
$585$	−5.92266	−	7.42678i	−0.244872	−	0.307059i
$586$	−6.60818	+	8.28640i	−0.272981	+	0.342308i
$587$	2.15654	+	9.44844i	0.0890101	+	0.389979i	0.999735	−	0.0230356i	$-0.00733309\pi$
$587$	2.15654	+	9.44844i	0.0890101	+	0.389979i	−0.910725	+	0.413014i	$0.864476\pi$
$588$	5.43448	−	2.61711i	0.224114	−	0.107928i
$589$	−22.0945	+	10.6402i	−0.910389	+	0.438420i
$590$	0.185409	−	0.812330i	0.00763317	−	0.0334431i
$591$	7.39223	+	3.55991i	0.304076	+	0.146435i
$592$	0.927007			0.0380997
$593$	11.8757	+	5.71902i	0.487675	+	0.234852i	0.661529	−	0.749919i	$-0.269908\pi$
$593$	11.8757	+	5.71902i	0.487675	+	0.234852i	−0.173854	+	0.984771i	$0.555622\pi$
$594$	−0.797338	+	0.999830i	−0.0327152	+	0.0410235i
$595$	26.9410	−	33.7830i	1.10447	−	1.38497i
$596$	6.74441	+	3.24794i	0.276262	+	0.133041i
$597$	24.4954			1.00253
$598$	−11.7902	−	5.67786i	−0.482137	−	0.232185i
$599$	3.21314	−	14.0777i	0.131285	−	0.575198i	−0.865900	−	0.500218i	$-0.833253\pi$
$599$	3.21314	−	14.0777i	0.131285	−	0.575198i	0.997185	−	0.0749808i	$-0.0238895\pi$
$600$	4.88075	−	2.35045i	0.199256	−	0.0959566i
$601$	−4.40415	+	2.12093i	−0.179649	+	0.0865143i	−0.521546	−	0.853223i	$-0.674645\pi$
$601$	−4.40415	+	2.12093i	−0.179649	+	0.0865143i	0.341898	+	0.939737i	$0.388930\pi$
$602$	2.01529	+	8.82955i	0.0821369	+	0.359865i
$603$	4.87049	−	6.10740i	0.198342	−	0.248713i
$604$	−0.977124	−	1.22527i	−0.0397586	−	0.0498557i
$605$	3.95560	−	17.3306i	0.160818	−	0.704590i
$606$	1.27316	+	5.57808i	0.0517186	+	0.226594i
$607$	−7.82778	−	9.81573i	−0.317720	−	0.398408i	0.597168	−	0.802116i	$-0.296293\pi$
$607$	−7.82778	−	9.81573i	−0.317720	−	0.398408i	−0.914888	+	0.403708i	$0.867721\pi$
$608$	−18.8014			−0.762496
$609$	12.1825	−	19.5463i	0.493661	−	0.792056i
$610$	11.9026			0.481923
$611$	−22.9869	−	28.8246i	−0.929950	−	1.16612i
$612$	0.667730	+	2.92552i	0.0269914	+	0.118257i
$613$	−0.778292	+	3.40992i	−0.0314349	+	0.137725i	−0.988210	−	0.153102i	$-0.951074\pi$
$613$	−0.778292	+	3.40992i	−0.0314349	+	0.137725i	0.956775	+	0.290828i	$0.0939307\pi$
$614$	25.6023	+	32.1042i	1.03322	+	1.29562i
$615$	−4.06182	+	5.09337i	−0.163789	+	0.205384i
$616$	−3.08426	−	13.5130i	−0.124268	−	0.544455i
$617$	24.5871	−	11.8405i	0.989838	−	0.476681i	0.132360	−	0.991202i	$-0.457745\pi$
$617$	24.5871	−	11.8405i	0.989838	−	0.476681i	0.857478	+	0.514521i	$0.172030\pi$
$618$	3.81232	−	1.83592i	0.153354	−	0.0738514i
$619$	5.68340	−	24.9006i	0.228435	−	1.00084i	−0.722481	−	0.691391i	$-0.756998\pi$
$619$	5.68340	−	24.9006i	0.228435	−	1.00084i	0.950916	−	0.309449i	$-0.100145\pi$
$620$	3.31036	+	1.59419i	0.132947	+	0.0640240i
$621$	2.04633			0.0821164
$622$	8.86372	+	4.26854i	0.355403	+	0.171153i
$623$	−47.8508	+	60.0030i	−1.91710	+	2.40397i
$624$	8.71503	−	10.9283i	0.348880	−	0.437482i
$625$	11.7616	+	5.66409i	0.470464	+	0.226564i
$626$	−3.05995			−0.122300
$627$	−6.10178	−	2.93846i	−0.243682	−	0.117351i
$628$	1.92461	−	8.43225i	0.0768002	−	0.336484i
$629$	1.77298	−	0.853821i	0.0706933	−	0.0340441i
$630$	8.39035	−	4.04058i	0.334279	−	0.160980i
$631$	−4.62745	−	20.2742i	−0.184216	−	0.807102i	−0.979594	−	0.200988i	$-0.935585\pi$
$631$	−4.62745	−	20.2742i	−0.184216	−	0.807102i	0.795378	−	0.606114i	$-0.207272\pi$
$632$	19.6423	−	24.6306i	0.781328	−	0.979754i
$633$	−1.37880	−	1.72896i	−0.0548025	−	0.0687201i
$634$	4.48252	−	19.6392i	0.178024	−	0.779973i
$635$	1.78712	+	7.82990i	0.0709198	+	0.310720i
$636$	2.60397	+	3.26528i	0.103254	+	0.129477i
$637$	−59.6442			−2.36319
$638$	−4.88737	−	4.85185i	−0.193493	−	0.192086i
$639$	−15.6115			−0.617580
$640$	−5.42895	−	6.80769i	−0.214598	−	0.269097i
$641$	3.14628	+	13.7848i	0.124271	+	0.544466i	0.998284	+	0.0585631i	$0.0186519\pi$
$641$	3.14628	+	13.7848i	0.124271	+	0.544466i	−0.874013	+	0.485903i	$0.838491\pi$
$642$	−1.32601	+	5.80965i	−0.0523336	+	0.229288i
$643$	22.1303	+	27.7505i	0.872734	+	1.09437i	0.994800	+	0.101852i	$0.0324768\pi$
$643$	22.1303	+	27.7505i	0.872734	+	1.09437i	−0.122066	+	0.992522i	$0.538952\pi$
$644$	−2.91481	+	3.65505i	−0.114859	+	0.144029i
$645$	−0.699933	−	3.06661i	−0.0275598	−	0.120747i
$646$	39.2905	−	18.9213i	1.54586	−	0.744448i
$647$	18.0758	−	8.70484i	0.710633	−	0.342223i	−0.0434016	−	0.999058i	$-0.513819\pi$
$647$	18.0758	−	8.70484i	0.710633	−	0.342223i	0.754034	+	0.656835i	$0.228105\pi$
$648$	−0.682729	+	2.99123i	−0.0268201	+	0.117507i
$649$	−0.364168	−	0.175374i	−0.0142948	−	0.00688404i
$650$	−11.2911			−0.442872
$651$	−14.7380	−	7.09747i	−0.577630	−	0.278172i
$652$	−4.52054	+	5.66858i	−0.177038	+	0.221999i
$653$	8.32587	−	10.4403i	0.325816	−	0.408561i	−0.591764	−	0.806111i	$-0.701568\pi$
$653$	8.32587	−	10.4403i	0.325816	−	0.408561i	0.917580	+	0.397550i	$0.130140\pi$
$654$	−16.2365	−	7.81907i	−0.634896	−	0.305750i
$655$	0.0179114			0.000699856
$656$	−8.63682	−	4.15927i	−0.337211	−	0.162392i
$657$	0.565847	−	2.47914i	0.0220758	−	0.0967203i
$658$	32.5644	−	15.6822i	1.26949	−	0.611356i
$659$	−10.2522	+	4.93720i	−0.399369	+	0.192326i	−0.622778	−	0.782399i	$-0.713996\pi$
$659$	−10.2522	+	4.93720i	−0.399369	+	0.192326i	0.223408	+	0.974725i	$0.428282\pi$
$660$	0.225792	+	0.989259i	0.00878893	+	0.0385068i
$661$	−23.0877	+	28.9510i	−0.898007	+	1.12606i	0.0934495	+	0.995624i	$0.470211\pi$
$661$	−23.0877	+	28.9510i	−0.898007	+	1.12606i	−0.991456	+	0.130441i	$0.958361\pi$
$662$	−9.75940	−	12.2379i	−0.379310	−	0.475640i
$663$	6.60269	−	28.9283i	0.256427	−	1.12348i
$664$	−1.03870	−	4.55082i	−0.0403092	−	0.176606i
$665$	30.7491	+	38.5582i	1.19240	+	1.49522i
$666$	0.424110			0.0164339
$667$	−1.19388	+	10.9550i	−0.0462271	+	0.424178i
$668$	8.73974			0.338151
$669$	1.68615	+	2.11436i	0.0651903	+	0.0817460i
$670$	3.78488	+	16.5826i	0.146223	+	0.640643i
$671$	1.28483	−	5.62921i	0.0496003	−	0.217313i
$672$	−7.81941	−	9.80523i	−0.301640	−	0.378245i
$673$	23.2210	−	29.1182i	0.895103	−	1.12242i	−0.0967842	−	0.995305i	$-0.530856\pi$
$673$	23.2210	−	29.1182i	0.895103	−	1.12242i	0.991888	−	0.127119i	$-0.0405729\pi$
$674$	−1.49866	−	6.56604i	−0.0577261	−	0.252915i
$675$	1.59078	−	0.766078i	0.0612291	−	0.0294864i
$676$	7.17021	−	3.45299i	0.275777	−	0.132807i
$677$	−9.99898	+	43.8084i	−0.384292	+	1.68369i	0.299564	+	0.954076i	$0.403159\pi$
$677$	−9.99898	+	43.8084i	−0.384292	+	1.68369i	−0.683856	+	0.729617i	$0.739698\pi$
$678$	−6.91882	−	3.33193i	−0.265716	−	0.127962i
$679$	−29.1245			−1.11770
$680$	−27.9280	−	13.4494i	−1.07099	−	0.515761i
$681$	8.99231	−	11.2760i	0.344586	−	0.432097i
$682$	−3.04958	+	3.82406i	−0.116775	+	0.146431i
$683$	−20.3639	−	9.80672i	−0.779201	−	0.375244i	0.00161933	−	0.999999i	$-0.499485\pi$
$683$	−20.3639	−	9.80672i	−0.779201	−	0.375244i	−0.780821	+	0.624755i	$0.785199\pi$
$684$	−3.42491			−0.130955
$685$	−19.7898	−	9.53029i	−0.756131	−	0.364134i
$686$	4.94560	−	21.6681i	0.188824	−	0.827291i
$687$	−23.1969	+	11.1711i	−0.885019	+	0.426202i
$688$	4.17011	−	2.00822i	0.158984	−	0.0765626i
$689$	−9.18962	−	40.2623i	−0.350097	−	1.53387i
$690$	−2.77807	+	3.48359i	−0.105759	+	0.132618i
$691$	−24.2367	−	30.3919i	−0.922009	−	1.15616i	−0.987391	−	0.158302i	$-0.949398\pi$
$691$	−24.2367	−	30.3919i	−0.922009	−	1.15616i	0.0653818	−	0.997860i	$-0.479173\pi$
$692$	−0.530569	+	2.32458i	−0.0201692	+	0.0883671i
$693$	−1.00525	−	4.40428i	−0.0381862	−	0.167305i
$694$	6.63294	+	8.31744i	0.251783	+	0.315726i
$695$	8.89436			0.337382
$696$	−15.6151	−	5.40012i	−0.591890	−	0.204691i
$697$	−20.3495			−0.770794
$698$	−11.4697	−	14.3826i	−0.434135	−	0.544388i
$699$	5.02985	+	22.0372i	0.190246	+	0.833524i
$700$	−0.897584	+	3.93257i	−0.0339255	+	0.148637i
$701$	−24.5921	−	30.8375i	−0.928831	−	1.16472i	−0.986066	−	0.166357i	$-0.946800\pi$
$701$	−24.5921	−	30.8375i	−0.928831	−	1.16472i	0.0572342	−	0.998361i	$-0.481772\pi$
$702$	3.98717	−	4.99975i	0.150486	−	0.188704i
$703$	0.499785	+	2.18970i	0.0188498	+	0.0825862i
$704$	−8.41541	+	4.05265i	−0.317168	+	0.152740i
$705$	−11.3100	+	5.44661i	−0.425960	+	0.205131i
$706$	−3.33172	+	14.5972i	−0.125391	+	0.549373i
$707$	−18.2100	−	8.76949i	−0.684859	−	0.329811i
$708$	−0.204406			−0.00768207
$709$	3.67038	+	1.76756i	0.137844	+	0.0663823i	0.501534	−	0.865138i	$-0.332769\pi$
$709$	3.67038	+	1.76756i	0.137844	+	0.0663823i	−0.363690	+	0.931520i	$0.618483\pi$
$710$	21.1939	−	26.5763i	0.795393	−	0.997391i
$711$	6.40198	−	8.02783i	0.240093	−	0.301067i
$712$	49.6038	+	23.8879i	1.85898	+	0.895238i
$713$	7.82661			0.293109
$714$	26.2085	+	12.6214i	0.980829	+	0.472343i
$715$	2.23269	−	9.78204i	0.0834978	−	0.365828i
$716$	1.63660	−	0.788144i	0.0611625	−	0.0294543i
$717$	−21.1037	+	10.1630i	−0.788132	+	0.379544i
$718$	−4.31497	−	18.9051i	−0.161033	−	0.705533i
$719$	−11.4911	+	14.4094i	−0.428546	+	0.537380i	−0.948484	−	0.316824i	$-0.897384\pi$
$719$	−11.4911	+	14.4094i	−0.428546	+	0.537380i	0.519938	+	0.854204i	$0.325955\pi$
$720$	−2.96737	−	3.72096i	−0.110587	−	0.138672i
$721$	−3.32613	+	14.5727i	−0.123872	+	0.542717i
$722$	5.95680	+	26.0985i	0.221689	+	0.971284i
$723$	13.9554	+	17.4995i	0.519005	+	0.650812i
$724$	−3.53686			−0.131446
$725$	3.17308	+	8.96313i	0.117845	+	0.332882i
$726$	11.9671			0.444142
$727$	10.9828	+	13.7720i	0.407330	+	0.510775i	0.942608	−	0.333900i	$-0.108365\pi$
$727$	10.9828	+	13.7720i	0.407330	+	0.510775i	−0.535279	+	0.844675i	$0.679793\pi$
$728$	15.4231	+	67.5732i	0.571619	+	2.50443i
$729$	−0.222521	+	0.974928i	−0.00824152	+	0.0361084i
$730$	3.45219	+	4.32891i	0.127771	+	0.160220i
$731$	6.12601	−	7.68177i	0.226579	−	0.284121i
$732$	−0.649753	−	2.84675i	−0.0240156	−	0.105219i
$733$	7.41249	−	3.56967i	0.273786	−	0.131849i	−0.291953	−	0.956433i	$-0.594305\pi$
$733$	7.41249	−	3.56967i	0.273786	−	0.131849i	0.565739	+	0.824584i	$0.308591\pi$
$734$	−24.2649	+	11.6854i	−0.895634	+	0.431315i
$735$	−4.51899	+	19.7990i	−0.166686	+	0.730297i
$736$	5.40627	+	2.60352i	0.199278	+	0.0959671i
$737$	8.25113			0.303934
$738$	−3.95139	−	1.90289i	−0.145453	−	0.0700463i
$739$	22.3350	−	28.0072i	0.821607	−	1.03026i	−0.177329	−	0.984152i	$-0.556746\pi$
$739$	22.3350	−	28.0072i	0.821607	−	1.03026i	0.998936	−	0.0461112i	$-0.0146829\pi$
$740$	0.209813	−	0.263097i	0.00771288	−	0.00967165i
$741$	30.5126	+	14.6941i	1.12091	+	0.539800i
$742$	40.4864			1.48630
$743$	−8.37415	−	4.03278i	−0.307218	−	0.147948i	0.273922	−	0.961752i	$-0.411679\pi$
$743$	−8.37415	−	4.03278i	−0.307218	−	0.147948i	−0.581140	+	0.813803i	$0.697393\pi$
$744$	−2.61124	+	11.4406i	−0.0957326	+	0.419432i
$745$	−22.7073	+	10.9353i	−0.831933	+	0.400638i
$746$	7.55969	−	3.64056i	0.276780	−	0.133290i
$747$	−0.338541	−	1.48324i	−0.0123866	−	0.0542691i
$748$	−1.97619	+	2.47807i	−0.0722568	+	0.0906071i
$749$	−13.1249	−	16.4581i	−0.479573	−	0.601366i
$750$	−3.27806	+	14.3621i	−0.119698	+	0.524431i
$751$	9.98479	+	43.7462i	0.364350	+	1.59632i	0.742017	+	0.670381i	$0.233869\pi$
$751$	9.98479	+	43.7462i	0.364350	+	1.59632i	−0.377667	+	0.925941i	$0.623274\pi$
$752$	−11.5169	−	14.4417i	−0.419977	−	0.526635i
$753$	−5.95981			−0.217188
$754$	24.4398	+	24.2622i	0.890045	+	0.883576i
$755$	5.27646			0.192030
$756$	−1.42441	−	1.78615i	−0.0518052	−	0.0649616i
$757$	−4.81041	−	21.0758i	−0.174837	−	0.766012i	−0.983962	−	0.178376i	$-0.942916\pi$
$757$	−4.81041	−	21.0758i	−0.174837	−	0.766012i	0.809125	−	0.587636i	$-0.199941\pi$
$758$	−2.09830	+	9.19323i	−0.0762135	+	0.333913i
$759$	1.34764	+	1.68989i	0.0489163	+	0.0613392i
$760$	22.0586	−	27.6606i	0.800150	−	1.00336i
$761$	8.76193	+	38.3885i	0.317620	+	1.39158i	0.841714	+	0.539923i	$0.181547\pi$
$761$	8.76193	+	38.3885i	0.317620	+	1.39158i	−0.524094	+	0.851660i	$0.675596\pi$
$762$	−4.87126	+	2.34588i	−0.176467	+	0.0849822i
$763$	57.3563	−	27.6213i	2.07644	−	0.999959i
$764$	2.09430	−	9.17572i	0.0757691	−	0.331966i
$765$	−9.10253	−

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:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	87.g (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.754870 - 0.946578i) q^{2} +(-0.222521 - 0.974928i) q^{3} +(0.118862 - 0.520769i) q^{4} +(1.12131 + 1.40607i) q^{5} +(-0.754870 + 0.946578i) q^{6} +(-0.951706 - 4.16970i) q^{7} +(-2.76431 + 1.33122i) q^{8} +(-0.900969 + 0.433884i) q^{9} +O(q^{10})\)	\(q+(-0.754870 - 0.946578i) q^{2} +(-0.222521 - 0.974928i) q^{3} +(0.118862 - 0.520769i) q^{4} +(1.12131 + 1.40607i) q^{5} +(-0.754870 + 0.946578i) q^{6} +(-0.951706 - 4.16970i) q^{7} +(-2.76431 + 1.33122i) q^{8} +(-0.900969 + 0.433884i) q^{9} +(0.484517 - 2.12281i) q^{10} +(-0.951656 - 0.458293i) q^{11} -0.534161 q^{12} +(4.75885 + 2.29174i) q^{13} +(-3.22853 + 4.04845i) q^{14} +(1.12131 - 1.40607i) q^{15} +(2.38428 + 1.14821i) q^{16} +5.61769 q^{17} +(1.09082 + 0.525311i) q^{18} +(-1.42675 + 6.25099i) q^{19} +(0.865520 - 0.416812i) q^{20} +(-3.85338 + 1.85569i) q^{21} +(0.284567 + 1.24677i) q^{22} +(1.27587 - 1.59988i) q^{23} +(1.91296 + 2.39878i) q^{24} +(0.392890 - 1.72136i) q^{25} +(-1.42300 - 6.23459i) q^{26} +(0.623490 + 0.781831i) q^{27} -2.28457 q^{28} +(-4.54927 + 2.88169i) q^{29} -2.17740 q^{30} +(2.38467 + 2.99028i) q^{31} +(0.652504 + 2.85881i) q^{32} +(-0.235040 + 1.02978i) q^{33} +(-4.24063 - 5.31758i) q^{34} +(4.79575 - 6.01368i) q^{35} +(0.118862 + 0.520769i) q^{36} +(0.315606 - 0.151988i) q^{37} +(6.99406 - 3.36816i) q^{38} +(1.17534 - 5.14950i) q^{39} +(-4.97144 - 2.39412i) q^{40} -3.62240 q^{41} +(4.66536 + 2.24672i) q^{42} +(1.09049 - 1.36743i) q^{43} +(-0.351781 + 0.441119i) q^{44} +(-1.62033 - 0.780312i) q^{45} -2.47753 q^{46} +(-6.28881 - 3.02853i) q^{47} +(0.588868 - 2.58000i) q^{48} +(-10.1739 + 4.89947i) q^{49} +(-1.92598 + 0.927505i) q^{50} +(-1.25005 - 5.47684i) q^{51} +(1.75911 - 2.20586i) q^{52} +(-4.87488 - 6.11290i) q^{53} +(0.269410 - 1.18036i) q^{54} +(-0.422703 - 1.85198i) q^{55} +(8.18161 + 10.2594i) q^{56} +6.41175 q^{57} +(6.16185 + 2.13093i) q^{58} +0.382668 q^{59} +(-0.598958 - 0.751070i) q^{60} +(1.21640 + 5.32939i) q^{61} +(1.03041 - 4.51454i) q^{62} +(2.66662 + 3.34384i) q^{63} +(5.51347 - 6.91367i) q^{64} +(2.11377 + 9.26104i) q^{65} +(1.15219 - 0.554864i) q^{66} +(-7.03806 + 3.38935i) q^{67} +(0.667730 - 2.92552i) q^{68} +(-1.84368 - 0.887869i) q^{69} -9.31258 q^{70} +(14.0654 + 6.77356i) q^{71} +(1.91296 - 2.39878i) q^{72} +(-1.58547 + 1.98811i) q^{73} +(-0.382110 - 0.184015i) q^{74} -1.76563 q^{75} +(3.08574 + 1.48601i) q^{76} +(-1.00525 + 4.40428i) q^{77} +(-5.76163 + 2.77465i) q^{78} +(-9.25113 + 4.45511i) q^{79} +(1.05904 + 4.63996i) q^{80} +(0.623490 - 0.781831i) q^{81} +(2.73445 + 3.42889i) q^{82} +(-0.338541 + 1.48324i) q^{83} +(0.508365 + 2.22729i) q^{84} +(6.29915 + 7.89888i) q^{85} -2.11755 q^{86} +(3.82175 + 3.79397i) q^{87} +3.24076 q^{88} +(-11.1881 - 14.0295i) q^{89} +(0.484517 + 2.12281i) q^{90} +(5.02684 - 22.0240i) q^{91} +(-0.681518 - 0.854597i) q^{92} +(2.38467 - 2.99028i) q^{93} +(1.88050 + 8.23899i) q^{94} +(-10.3892 + 5.00316i) q^{95} +(2.64194 - 1.27229i) q^{96} +(1.51530 - 6.63895i) q^{97} +(12.3177 + 5.93188i) q^{98} +1.05626 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 4 q^{2} - 3 q^{3} - 6 q^{4} - q^{5} - 4 q^{6} - 4 q^{7} - 15 q^{8} - 3 q^{9}+O(q^{10}) \) 18 * q - 4 * q^2 - 3 * q^3 - 6 * q^4 - q^5 - 4 * q^6 - 4 * q^7 - 15 * q^8 - 3 * q^9	\( 18 q - 4 q^{2} - 3 q^{3} - 6 q^{4} - q^{5} - 4 q^{6} - 4 q^{7} - 15 q^{8} - 3 q^{9} - 14 q^{10} + 26 q^{11} + 22 q^{12} + 9 q^{13} - 10 q^{14} - q^{15} - 14 q^{16} + 4 q^{17} - 4 q^{18} - 10 q^{19} - q^{20} - 4 q^{21} - 8 q^{22} - 8 q^{23} - 8 q^{24} + 16 q^{25} + 5 q^{26} - 3 q^{27} + 80 q^{28} + 8 q^{29} - 12 q^{31} + 9 q^{32} - 16 q^{33} - 22 q^{34} + 9 q^{35} - 6 q^{36} - 16 q^{37} - 32 q^{38} + 2 q^{39} + 33 q^{40} + 24 q^{41} - 3 q^{42} - 31 q^{43} - 52 q^{44} + 6 q^{45} - 44 q^{46} + 5 q^{47} - 47 q^{49} - 7 q^{50} + 11 q^{51} + 80 q^{52} + 5 q^{53} + 3 q^{54} - 17 q^{55} + 45 q^{56} + 18 q^{57} + 54 q^{58} - 32 q^{59} + 27 q^{60} - 28 q^{61} + 69 q^{62} + 3 q^{63} - 75 q^{64} + 22 q^{65} + 34 q^{66} + 6 q^{67} + 38 q^{68} + 20 q^{69} - 12 q^{70} + 46 q^{71} - 8 q^{72} - q^{73} - 35 q^{74} + 2 q^{75} - 45 q^{76} - 36 q^{77} - 51 q^{78} - 15 q^{79} - 86 q^{80} - 3 q^{81} + 47 q^{82} - 16 q^{83} - 25 q^{84} + 19 q^{85} + 116 q^{86} + 43 q^{87} + 54 q^{88} - 72 q^{89} - 14 q^{90} - 47 q^{91} - 121 q^{92} - 12 q^{93} - 22 q^{94} - 72 q^{95} - 12 q^{96} + 43 q^{97} + 31 q^{98} - 2 q^{99}+O(q^{100}) \) 18 * q - 4 * q^2 - 3 * q^3 - 6 * q^4 - q^5 - 4 * q^6 - 4 * q^7 - 15 * q^8 - 3 * q^9 - 14 * q^10 + 26 * q^11 + 22 * q^12 + 9 * q^13 - 10 * q^14 - q^15 - 14 * q^16 + 4 * q^17 - 4 * q^18 - 10 * q^19 - q^20 - 4 * q^21 - 8 * q^22 - 8 * q^23 - 8 * q^24 + 16 * q^25 + 5 * q^26 - 3 * q^27 + 80 * q^28 + 8 * q^29 - 12 * q^31 + 9 * q^32 - 16 * q^33 - 22 * q^34 + 9 * q^35 - 6 * q^36 - 16 * q^37 - 32 * q^38 + 2 * q^39 + 33 * q^40 + 24 * q^41 - 3 * q^42 - 31 * q^43 - 52 * q^44 + 6 * q^45 - 44 * q^46 + 5 * q^47 - 47 * q^49 - 7 * q^50 + 11 * q^51 + 80 * q^52 + 5 * q^53 + 3 * q^54 - 17 * q^55 + 45 * q^56 + 18 * q^57 + 54 * q^58 - 32 * q^59 + 27 * q^60 - 28 * q^61 + 69 * q^62 + 3 * q^63 - 75 * q^64 + 22 * q^65 + 34 * q^66 + 6 * q^67 + 38 * q^68 + 20 * q^69 - 12 * q^70 + 46 * q^71 - 8 * q^72 - q^73 - 35 * q^74 + 2 * q^75 - 45 * q^76 - 36 * q^77 - 51 * q^78 - 15 * q^79 - 86 * q^80 - 3 * q^81 + 47 * q^82 - 16 * q^83 - 25 * q^84 + 19 * q^85 + 116 * q^86 + 43 * q^87 + 54 * q^88 - 72 * q^89 - 14 * q^90 - 47 * q^91 - 121 * q^92 - 12 * q^93 - 22 * q^94 - 72 * q^95 - 12 * q^96 + 43 * q^97 + 31 * q^98 - 2 * q^99

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