LMFDB - Embedded newform 54.2.e.a.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [54,2,Mod(7,54)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(54, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("54.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 54 = 2 \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	54.e (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:	$0.431192170915$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			13.1
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	54.13
Dual form			54.2.e.a.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 - 0.984808i) q^{2} +(-0.592396 - 1.62760i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.673648 - 0.565258i) q^{5} +(-1.50000 + 0.866025i) q^{6} +(3.31908 + 1.20805i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.29813 + 1.92836i) q^{9} +O(q^{10})$	\(q+(-0.173648 - 0.984808i) q^{2} +(-0.592396 - 1.62760i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.673648 - 0.565258i) q^{5} +(-1.50000 + 0.866025i) q^{6} +(3.31908 + 1.20805i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.29813 + 1.92836i) q^{9} +(-0.439693 + 0.761570i) q^{10} +(2.73783 - 2.29731i) q^{11} +(1.11334 + 1.32683i) q^{12} +(-0.641559 + 3.63846i) q^{13} +(0.613341 - 3.47843i) q^{14} +(-0.520945 + 1.43128i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-3.12449 + 5.41177i) q^{17} +(2.29813 + 1.92836i) q^{18} +(-2.08512 - 3.61154i) q^{19} +(0.826352 + 0.300767i) q^{20} -6.11776i q^{21} +(-2.73783 - 2.29731i) q^{22} +(-1.93969 + 0.705990i) q^{23} +(1.11334 - 1.32683i) q^{24} +(-0.733956 - 4.16247i) q^{25} +3.69459 q^{26} +(4.50000 + 2.59808i) q^{27} -3.53209 q^{28} +(0.0282185 + 0.160035i) q^{29} +(1.50000 + 0.264490i) q^{30} +(-1.53936 + 0.560282i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(-5.36097 - 3.09516i) q^{33} +(5.87211 + 2.13727i) q^{34} +(-1.55303 - 2.68993i) q^{35} +(1.50000 - 2.59808i) q^{36} +(3.85844 - 6.68302i) q^{37} +(-3.19459 + 2.68058i) q^{38} +(6.30200 - 1.11121i) q^{39} +(0.152704 - 0.866025i) q^{40} +(-1.33750 + 7.58532i) q^{41} +(-6.02481 + 1.06234i) q^{42} +(-8.29086 + 6.95686i) q^{43} +(-1.78699 + 3.09516i) q^{44} +2.63816 q^{45} +(1.03209 + 1.78763i) q^{46} +(6.02481 + 2.19285i) q^{47} +(-1.50000 - 0.866025i) q^{48} +(4.19459 + 3.51968i) q^{49} +(-3.97178 + 1.44561i) q^{50} +(10.6591 + 1.87949i) q^{51} +(-0.641559 - 3.63846i) q^{52} +0.716881 q^{53} +(1.77719 - 4.88279i) q^{54} -3.14290 q^{55} +(0.613341 + 3.47843i) q^{56} +(-4.64290 + 5.53320i) q^{57} +(0.152704 - 0.0555796i) q^{58} +(-5.35117 - 4.49016i) q^{59} -1.52314i q^{60} +(1.19207 + 0.433877i) q^{61} +(0.819078 + 1.41868i) q^{62} +(-9.95723 + 3.62414i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(2.48886 - 2.08840i) q^{65} +(-2.11721 + 5.81699i) q^{66} +(0.624485 - 3.54163i) q^{67} +(1.08512 - 6.15403i) q^{68} +(2.29813 + 2.73881i) q^{69} +(-2.37939 + 1.99654i) q^{70} +(6.76991 - 11.7258i) q^{71} +(-2.81908 - 1.02606i) q^{72} +(1.16385 + 2.01584i) q^{73} +(-7.25150 - 2.63933i) q^{74} +(-6.34002 + 3.66041i) q^{75} +(3.19459 + 2.68058i) q^{76} +(11.8623 - 4.31753i) q^{77} +(-2.18866 - 6.01330i) q^{78} +(-1.14930 - 6.51800i) q^{79} -0.879385 q^{80} +(1.56283 - 8.86327i) q^{81} +7.70233 q^{82} +(-0.773318 - 4.38571i) q^{83} +(2.09240 + 5.74881i) q^{84} +(5.16385 - 1.87949i) q^{85} +(8.29086 + 6.95686i) q^{86} +(0.243756 - 0.140732i) q^{87} +(3.35844 + 1.22237i) q^{88} +(-4.62449 - 8.00984i) q^{89} +(-0.458111 - 2.59808i) q^{90} +(-6.52481 + 11.3013i) q^{91} +(1.58125 - 1.32683i) q^{92} +(1.82383 + 2.17355i) q^{93} +(1.11334 - 6.31407i) q^{94} +(-0.636812 + 3.61154i) q^{95} +(-0.592396 + 1.62760i) q^{96} +(-8.64930 + 7.25762i) q^{97} +(2.73783 - 4.74205i) q^{98} +(-1.86184 + 10.5590i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{5} - 9 q^{6} + 3 q^{7} + 3 q^{8}+O(q^{10}) $ 6 * q - 3 * q^5 - 9 * q^6 + 3 * q^7 + 3 * q^8	$ 6 q - 3 q^{5} - 9 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{10} - 3 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{17} + 9 q^{19} + 6 q^{20} + 3 q^{22} - 6 q^{23} - 9 q^{25} + 18 q^{26} + 27 q^{27} - 12 q^{28} + 15 q^{29} + 9 q^{30} - 18 q^{31} - 9 q^{33} + 6 q^{34} + 3 q^{35} + 9 q^{36} + 15 q^{37} - 15 q^{38} + 3 q^{40} - 3 q^{41} - 9 q^{42} - 18 q^{43} - 3 q^{44} - 18 q^{45} - 3 q^{46} + 9 q^{47} - 9 q^{48} + 21 q^{49} - 9 q^{50} + 27 q^{51} - 12 q^{52} - 12 q^{53} - 18 q^{55} - 3 q^{56} - 27 q^{57} + 3 q^{58} - 6 q^{59} + 18 q^{61} - 12 q^{62} - 9 q^{63} - 3 q^{64} + 21 q^{65} + 18 q^{66} - 9 q^{67} - 15 q^{68} - 3 q^{70} + 12 q^{71} + 3 q^{73} - 3 q^{74} - 18 q^{75} + 15 q^{76} + 39 q^{77} + 18 q^{78} + 33 q^{79} + 6 q^{80} - 6 q^{82} - 18 q^{83} + 9 q^{84} + 27 q^{85} + 18 q^{86} + 9 q^{87} + 12 q^{88} - 15 q^{89} - 9 q^{90} - 12 q^{91} + 12 q^{92} + 27 q^{93} + 21 q^{95} - 12 q^{97} - 3 q^{98} - 45 q^{99}+O(q^{100}) $ 6 * q - 3 * q^5 - 9 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^10 - 3 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^17 + 9 * q^19 + 6 * q^20 + 3 * q^22 - 6 * q^23 - 9 * q^25 + 18 * q^26 + 27 * q^27 - 12 * q^28 + 15 * q^29 + 9 * q^30 - 18 * q^31 - 9 * q^33 + 6 * q^34 + 3 * q^35 + 9 * q^36 + 15 * q^37 - 15 * q^38 + 3 * q^40 - 3 * q^41 - 9 * q^42 - 18 * q^43 - 3 * q^44 - 18 * q^45 - 3 * q^46 + 9 * q^47 - 9 * q^48 + 21 * q^49 - 9 * q^50 + 27 * q^51 - 12 * q^52 - 12 * q^53 - 18 * q^55 - 3 * q^56 - 27 * q^57 + 3 * q^58 - 6 * q^59 + 18 * q^61 - 12 * q^62 - 9 * q^63 - 3 * q^64 + 21 * q^65 + 18 * q^66 - 9 * q^67 - 15 * q^68 - 3 * q^70 + 12 * q^71 + 3 * q^73 - 3 * q^74 - 18 * q^75 + 15 * q^76 + 39 * q^77 + 18 * q^78 + 33 * q^79 + 6 * q^80 - 6 * q^82 - 18 * q^83 + 9 * q^84 + 27 * q^85 + 18 * q^86 + 9 * q^87 + 12 * q^88 - 15 * q^89 - 9 * q^90 - 12 * q^91 + 12 * q^92 + 27 * q^93 + 21 * q^95 - 12 * q^97 - 3 * q^98 - 45 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

Coefficient data

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

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

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

$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$3$	−0.592396	−	1.62760i	−0.342020	−	0.939693i
$3$	−0.592396	−	1.62760i	−0.342020	−	0.939693i
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	−0.673648	−	0.565258i	−0.301265	−	0.252791i	0.479606	−	0.877484i	$-0.340780\pi$
$5$	−0.673648	−	0.565258i	−0.301265	−	0.252791i	−0.780870	+	0.624693i	$0.785224\pi$
$6$	−1.50000	+	0.866025i	−0.612372	+	0.353553i
$7$	3.31908	+	1.20805i	1.25449	+	0.456598i	0.881918	−	0.471403i	$-0.156252\pi$
$7$	3.31908	+	1.20805i	1.25449	+	0.456598i	0.372576	+	0.928002i	$0.378475\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−2.29813	+	1.92836i	−0.766044	+	0.642788i
$10$	−0.439693	+	0.761570i	−0.139043	+	0.240830i
$11$	2.73783	−	2.29731i	0.825486	−	0.692665i	−0.128764	−	0.991675i	$-0.541101\pi$
$11$	2.73783	−	2.29731i	0.825486	−	0.692665i	0.954250	+	0.299011i	$0.0966566\pi$
$12$	1.11334	+	1.32683i	0.321394	+	0.383022i
$13$	−0.641559	+	3.63846i	−0.177937	+	1.00913i	0.756763	+	0.653689i	$0.226780\pi$
$13$	−0.641559	+	3.63846i	−0.177937	+	1.00913i	−0.934700	+	0.355439i	$0.884331\pi$
$14$	0.613341	−	3.47843i	0.163922	−	0.929649i
$15$	−0.520945	+	1.43128i	−0.134507	+	0.369556i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−3.12449	+	5.41177i	−0.757799	+	1.31255i	0.186172	+	0.982517i	$0.440392\pi$
$17$	−3.12449	+	5.41177i	−0.757799	+	1.31255i	−0.943971	+	0.330029i	$0.892941\pi$
$18$	2.29813	+	1.92836i	0.541675	+	0.454519i
$19$	−2.08512	−	3.61154i	−0.478360	−	0.828544i	0.521332	−	0.853354i	$-0.325435\pi$
$19$	−2.08512	−	3.61154i	−0.478360	−	0.828544i	−0.999692	+	0.0248102i	$0.992102\pi$
$20$	0.826352	+	0.300767i	0.184778	+	0.0672537i
$21$		−	6.11776i		−	1.33500i
$22$	−2.73783	−	2.29731i	−0.583706	−	0.489788i
$23$	−1.93969	+	0.705990i	−0.404454	+	0.147209i	−0.536233	−	0.844070i	$-0.680153\pi$
$23$	−1.93969	+	0.705990i	−0.404454	+	0.147209i	0.131779	+	0.991279i	$0.457931\pi$
$24$	1.11334	−	1.32683i	0.227260	−	0.270838i
$25$	−0.733956	−	4.16247i	−0.146791	−	0.832494i
$26$	3.69459			0.724569
$27$	4.50000	+	2.59808i	0.866025	+	0.500000i
$28$	−3.53209			−0.667502
$29$	0.0282185	+	0.160035i	0.00524004	+	0.0297178i	0.987316	−	0.158770i	$-0.0507527\pi$
$29$	0.0282185	+	0.160035i	0.00524004	+	0.0297178i	−0.982076	+	0.188487i	$0.939642\pi$
$30$	1.50000	+	0.264490i	0.273861	+	0.0482891i
$31$	−1.53936	+	0.560282i	−0.276478	+	0.100630i	−0.476538	−	0.879154i	$-0.658108\pi$
$31$	−1.53936	+	0.560282i	−0.276478	+	0.100630i	0.200060	+	0.979784i	$0.435886\pi$
$32$	−0.766044	−	0.642788i	−0.135419	−	0.113630i
$33$	−5.36097	−	3.09516i	−0.933225	−	0.538797i
$34$	5.87211	+	2.13727i	1.00706	+	0.366539i
$35$	−1.55303	−	2.68993i	−0.262511	−	0.454682i
$36$	1.50000	−	2.59808i	0.250000	−	0.433013i
$37$	3.85844	−	6.68302i	0.634324	−	1.09868i	−0.352334	−	0.935874i	$-0.614612\pi$
$37$	3.85844	−	6.68302i	0.634324	−	1.09868i	0.986658	−	0.162807i	$-0.0520547\pi$
$38$	−3.19459	+	2.68058i	−0.518231	+	0.434848i
$39$	6.30200	−	1.11121i	1.00913	−	0.177937i
$40$	0.152704	−	0.866025i	0.0241446	−	0.136931i
$41$	−1.33750	+	7.58532i	−0.208882	+	1.18463i	0.682331	+	0.731043i	$0.260966\pi$
$41$	−1.33750	+	7.58532i	−0.208882	+	1.18463i	−0.891213	+	0.453585i	$0.850145\pi$
$42$	−6.02481	+	1.06234i	−0.929649	+	0.163922i
$43$	−8.29086	+	6.95686i	−1.26434	+	1.06091i	−0.269139	+	0.963101i	$0.586739\pi$
$43$	−8.29086	+	6.95686i	−1.26434	+	1.06091i	−0.995205	+	0.0978094i	$0.968816\pi$
$44$	−1.78699	+	3.09516i	−0.269399	+	0.466612i
$45$	2.63816			0.393273
$46$	1.03209	+	1.78763i	0.152173	+	0.263572i
$47$	6.02481	+	2.19285i	0.878810	+	0.319861i	0.741729	−	0.670699i	$-0.234006\pi$
$47$	6.02481	+	2.19285i	0.878810	+	0.319861i	0.137080	+	0.990560i	$0.456228\pi$
$48$	−1.50000	−	0.866025i	−0.216506	−	0.125000i
$49$	4.19459	+	3.51968i	0.599228	+	0.502812i
$50$	−3.97178	+	1.44561i	−0.561695	+	0.204440i
$51$	10.6591	+	1.87949i	1.49257	+	0.263181i
$52$	−0.641559	−	3.63846i	−0.0889683	−	0.504564i
$53$	0.716881			0.0984712			0.0492356	−	0.998787i	$-0.484321\pi$
$53$	0.716881			0.0984712			0.0492356	+	0.998787i	$0.484321\pi$
$54$	1.77719	−	4.88279i	0.241845	−	0.664463i
$55$	−3.14290			−0.423789
$56$	0.613341	+	3.47843i	0.0819611	+	0.464825i
$57$	−4.64290	+	5.53320i	−0.614968	+	0.732890i
$58$	0.152704	−	0.0555796i	0.0200510	−	0.00729796i
$59$	−5.35117	−	4.49016i	−0.696663	−	0.584569i	0.224159	−	0.974552i	$-0.428036\pi$
$59$	−5.35117	−	4.49016i	−0.696663	−	0.584569i	−0.920822	+	0.389983i	$0.872481\pi$
$60$		−	1.52314i		−	0.196637i
$61$	1.19207	+	0.433877i	0.152628	+	0.0555522i	0.417205	−	0.908813i	$-0.363010\pi$
$61$	1.19207	+	0.433877i	0.152628	+	0.0555522i	−0.264576	+	0.964365i	$0.585232\pi$
$62$	0.819078	+	1.41868i	0.104023	+	0.180173i
$63$	−9.95723	+	3.62414i	−1.25449	+	0.456598i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	2.48886	−	2.08840i	0.308705	−	0.259034i
$66$	−2.11721	+	5.81699i	−0.260611	+	0.716022i
$67$	0.624485	−	3.54163i	0.0762930	−	0.432679i	−0.922605	−	0.385746i	$-0.873944\pi$
$67$	0.624485	−	3.54163i	0.0762930	−	0.432679i	0.998898	−	0.0469331i	$-0.0149448\pi$
$68$	1.08512	−	6.15403i	0.131590	−	0.746286i
$69$	2.29813	+	2.73881i	0.276663	+	0.329714i
$70$	−2.37939	+	1.99654i	−0.284391	+	0.238632i
$71$	6.76991	−	11.7258i	0.803441	−	1.39160i	−0.113897	−	0.993493i	$-0.536334\pi$
$71$	6.76991	−	11.7258i	0.803441	−	1.39160i	0.917338	−	0.398108i	$-0.130333\pi$
$72$	−2.81908	−	1.02606i	−0.332232	−	0.120922i
$73$	1.16385	+	2.01584i	0.136218	+	0.235937i	0.926062	−	0.377371i	$-0.123172\pi$
$73$	1.16385	+	2.01584i	0.136218	+	0.235937i	−0.789844	+	0.613308i	$0.789839\pi$
$74$	−7.25150	−	2.63933i	−0.842969	−	0.306816i
$75$	−6.34002	+	3.66041i	−0.732083	+	0.422668i
$76$	3.19459	+	2.68058i	0.366445	+	0.307484i
$77$	11.8623	−	4.31753i	1.35184	−	0.492028i
$78$	−2.18866	−	6.01330i	−0.247817	−	0.680872i
$79$	−1.14930	−	6.51800i	−0.129306	−	0.733333i	−0.978656	−	0.205503i	$-0.934117\pi$
$79$	−1.14930	−	6.51800i	−0.129306	−	0.733333i	0.849350	−	0.527830i	$-0.176994\pi$
$80$	−0.879385			−0.0983183
$81$	1.56283	−	8.86327i	0.173648	−	0.984808i
$82$	7.70233			0.850580
$83$	−0.773318	−	4.38571i	−0.0848827	−	0.481394i	−0.997382	−	0.0723151i	$-0.976961\pi$
$83$	−0.773318	−	4.38571i	−0.0848827	−	0.481394i	0.912499	−	0.409079i	$-0.134150\pi$
$84$	2.09240	+	5.74881i	0.228299	+	0.627247i
$85$	5.16385	−	1.87949i	0.560098	−	0.203859i
$86$	8.29086	+	6.95686i	0.894026	+	0.750177i
$87$	0.243756	−	0.140732i	0.0261334	−	0.0150881i
$88$	3.35844	+	1.22237i	0.358011	+	0.130305i
$89$	−4.62449	−	8.00984i	−0.490194	−	0.849042i	0.509742	−	0.860327i	$-0.329741\pi$
$89$	−4.62449	−	8.00984i	−0.490194	−	0.849042i	−0.999936	+	0.0112857i	$0.996408\pi$
$90$	−0.458111	−	2.59808i	−0.0482891	−	0.273861i
$91$	−6.52481	+	11.3013i	−0.683986	+	1.18470i
$92$	1.58125	−	1.32683i	0.164857	−	0.138331i
$93$	1.82383	+	2.17355i	0.189122	+	0.225387i
$94$	1.11334	−	6.31407i	0.114832	−	0.651247i
$95$	−0.636812	+	3.61154i	−0.0653355	+	0.370536i
$96$	−0.592396	+	1.62760i	−0.0604612	+	0.166116i
$97$	−8.64930	+	7.25762i	−0.878203	+	0.736900i	−0.965809	−	0.259255i	$-0.916523\pi$
$97$	−8.64930	+	7.25762i	−0.878203	+	0.736900i	0.0876055	+	0.996155i	$0.472079\pi$
$98$	2.73783	−	4.74205i	0.276562	−	0.479020i
$99$	−1.86184	+	10.5590i	−0.187122	+	1.06122i
$100$	2.11334	+	3.66041i	0.211334	+	0.366041i
$101$	−8.80928	−	3.20631i	−0.876556	−	0.319040i	−0.135737	−	0.990745i	$-0.543340\pi$
$101$	−8.80928	−	3.20631i	−0.876556	−	0.319040i	−0.740819	+	0.671705i	$0.765562\pi$
$102$		−	10.8235i		−	1.07169i
$103$	−2.47178	−	2.07407i	−0.243552	−	0.204364i	0.512838	−	0.858485i	$-0.328594\pi$
$103$	−2.47178	−	2.07407i	−0.243552	−	0.204364i	−0.756390	+	0.654121i	$0.773039\pi$
$104$	−3.47178	+	1.26363i	−0.340436	+	0.123909i
$105$	−3.45811	+	4.12122i	−0.337477	+	0.402190i
$106$	−0.124485	−	0.705990i	−0.0120911	−	0.0685718i
$107$	−2.28312			−0.220717			−0.110359	−	0.993892i	$-0.535200\pi$
$107$	−2.28312			−0.220717			−0.110359	+	0.993892i	$0.535200\pi$
$108$	−5.11721	−	0.902302i	−0.492404	−	0.0868241i
$109$	10.4192			0.997980			0.498990	−	0.866608i	$-0.333704\pi$
$109$	10.4192			0.997980			0.498990	+	0.866608i	$0.333704\pi$
$110$	0.545759	+	3.09516i	0.0520361	+	0.295112i
$111$	−13.1630	−	2.32099i	−1.24937	−	0.220298i
$112$	3.31908	−	1.20805i	0.313623	−	0.114150i
$113$	8.52869	+	7.15642i	0.802311	+	0.673219i	0.948759	−	0.315999i	$-0.102340\pi$
$113$	8.52869	+	7.15642i	0.802311	+	0.673219i	−0.146448	+	0.989218i	$0.546784\pi$
$114$	6.25537	+	3.61154i	0.585869	+	0.338252i
$115$	1.70574	+	0.620838i	0.159061	+	0.0578934i
$116$	−0.0812519	−	0.140732i	−0.00754405	−	0.0130667i
$117$	−5.54189	−	9.59883i	−0.512348	−	0.887412i
$118$	−3.49273	+	6.04958i	−0.321531	+	0.556909i
$119$	−16.9081	+	14.1876i	−1.54996	+	1.30057i
$120$	−1.50000	+	0.264490i	−0.136931	+	0.0241446i
$121$	0.307934	−	1.74638i	0.0279940	−	0.158762i
$122$	0.220285	−	1.24930i	0.0199437	−	0.113106i
$123$	13.1382	−	2.31661i	1.18463	−	0.208882i
$124$	1.25490	−	1.05299i	0.112693	−	0.0945610i
$125$	−4.05690	+	7.02676i	−0.362861	+	0.628493i
$126$	5.29813	+	9.17664i	0.471995	+	0.817520i
$127$	4.95336	+	8.57948i	0.439540	+	0.761305i	0.997654	−	0.0684588i	$-0.0218082\pi$
$127$	4.95336	+	8.57948i	0.439540	+	0.761305i	−0.558114	+	0.829764i	$0.688475\pi$
$128$	0.939693	+	0.342020i	0.0830579	+	0.0302306i
$129$	16.2344	+	9.37295i	1.42936	+	0.825242i
$130$	−2.48886	−	2.08840i	−0.218287	−	0.183165i
$131$	8.48545	−	3.08845i	0.741377	−	0.269839i	0.0564046	−	0.998408i	$-0.482036\pi$
$131$	8.48545	−	3.08845i	0.741377	−	0.269839i	0.684973	+	0.728569i	$0.259814\pi$
$132$	6.09627	+	1.07494i	0.530612	+	0.0935612i
$133$	−2.55778	−	14.5059i	−0.221788	−	1.25782i
$134$	−3.59627			−0.310670
$135$	−1.56283	−	4.29385i	−0.134507	−	0.369556i
$136$	−6.24897			−0.535845
$137$	0.352044	+	1.99654i	0.0300772	+	0.170576i	0.996146	−	0.0877077i	$-0.0279542\pi$
$137$	0.352044	+	1.99654i	0.0300772	+	0.170576i	−0.966069	+	0.258284i	$0.916843\pi$
$138$	2.29813	−	2.73881i	0.195630	−	0.233143i
$139$	−0.155230	+	0.0564991i	−0.0131664	+	0.00479219i	−0.348595	−	0.937273i	$-0.613341\pi$
$139$	−0.155230	+	0.0564991i	−0.0131664	+	0.00479219i	0.335429	+	0.942066i	$0.391119\pi$
$140$	2.37939	+	1.99654i	0.201095	+	0.168739i
$141$		−	11.1050i		−	0.935210i
$142$	−12.7233	−	4.63089i	−1.06771	−	0.388616i
$143$	6.60220	+	11.4353i	0.552103	+	0.956271i
$144$	−0.520945	+	2.95442i	−0.0434120	+	0.246202i
$145$	0.0714517	−	0.123758i	0.00593374	−	0.0102775i
$146$	1.78312	−	1.49621i	0.147572	−	0.123828i
$147$	3.24376	−	8.91215i	0.267540	−	0.735061i
$148$	−1.34002	+	7.59964i	−0.110149	+	0.624687i
$149$	−1.00727	+	5.71253i	−0.0825191	+	0.467989i	0.915345	+	0.402670i	$0.131918\pi$
$149$	−1.00727	+	5.71253i	−0.0825191	+	0.467989i	−0.997864	+	0.0653193i	$0.979193\pi$
$150$	4.70574	+	5.60808i	0.384222	+	0.457898i
$151$	10.7626	−	9.03093i	0.875851	−	0.734926i	−0.0894705	−	0.995989i	$-0.528517\pi$
$151$	10.7626	−	9.03093i	0.875851	−	0.734926i	0.965322	+	0.261063i	$0.0840730\pi$
$152$	2.08512	−	3.61154i	0.169126	−	0.292934i
$153$	−3.25537	−	18.4621i	−0.263181	−	1.49257i
$154$	−6.31180	−	10.9324i	−0.508620	−	0.880955i
$155$	1.35369	+	0.492704i	0.108731	+	0.0395749i
$156$	−5.54189	+	3.19961i	−0.443706	+	0.256174i
$157$	−3.65657	−	3.06823i	−0.291826	−	0.244871i	0.485106	−	0.874455i	$-0.338781\pi$
$157$	−3.65657	−	3.06823i	−0.291826	−	0.244871i	−0.776933	+	0.629584i	$0.783225\pi$
$158$	−6.21941	+	2.26368i	−0.494790	+	0.180089i
$159$	−0.424678	−	1.16679i	−0.0336791	−	0.0925327i
$160$	0.152704	+	0.866025i	0.0120723	+	0.0684653i
$161$	−7.29086			−0.574600
$162$	−9.00000			−0.707107
$163$	−10.7169			−0.839411			−0.419705	−	0.907660i	$-0.637867\pi$
$163$	−10.7169			−0.839411			−0.419705	+	0.907660i	$0.637867\pi$
$164$	−1.33750	−	7.58532i	−0.104441	−	0.592314i
$165$	1.86184	+	5.11538i	0.144944	+	0.398231i
$166$	−4.18479	+	1.52314i	−0.324803	+	0.118219i
$167$	−9.88120	−	8.29131i	−0.764630	−	0.641601i	0.174698	−	0.984622i	$-0.444105\pi$
$167$	−9.88120	−	8.29131i	−0.764630	−	0.641601i	−0.939328	+	0.343021i	$0.888550\pi$
$168$	5.29813	−	3.05888i	0.408760	−	0.235998i
$169$	−0.610815	−	0.222318i	−0.0469857	−	0.0171014i
$170$	−2.74763	−	4.75903i	−0.210733	−	0.365001i
$171$	11.7562	+	4.27892i	0.899022	+	0.327217i
$172$	5.41147	−	9.37295i	0.412621	−	0.714681i
$173$	9.86097	−	8.27433i	0.749715	−	0.629086i	−0.185712	−	0.982604i	$-0.559459\pi$
$173$	9.86097	−	8.27433i	0.749715	−	0.629086i	0.935428	+	0.353518i	$0.115015\pi$
$174$	−0.180922	−	0.215615i	−0.0137157	−	0.0163457i
$175$	2.59240	−	14.7022i	0.195967	−	1.11138i
$176$	0.620615	−	3.51968i	0.0467806	−	0.265306i
$177$	−4.13816	+	11.3695i	−0.311043	+	0.854583i
$178$	−7.08512	+	5.94512i	−0.531052	+	0.445606i
$179$	4.48158	−	7.76233i	0.334969	−	0.580184i	−0.648510	−	0.761206i	$-0.724607\pi$
$179$	4.48158	−	7.76233i	0.334969	−	0.580184i	0.983479	+	0.181023i	$0.0579408\pi$
$180$	−2.47906	+	0.902302i	−0.184778	+	0.0672537i
$181$	0.992726	+	1.71945i	0.0737887	+	0.127806i	0.900559	−	0.434734i	$-0.143158\pi$
$181$	0.992726	+	1.71945i	0.0737887	+	0.127806i	−0.826770	+	0.562540i	$0.809824\pi$
$182$	12.2626	+	4.46324i	0.908967	+	0.330837i
$183$		−	2.19723i		−	0.162424i
$184$	−1.58125	−	1.32683i	−0.116571	−	0.0978151i
$185$	−6.37686	+	2.32099i	−0.468836	+	0.170642i
$186$	1.82383	−	2.17355i	0.133729	−	0.159372i
$187$	3.87820	+	21.9944i	0.283602	+	1.60839i
$188$	−6.41147			−0.467605
$189$	11.7973	+	14.0594i	0.858124	+	1.02267i
$190$	3.66725			0.266050
$191$	2.27853	+	12.9222i	0.164869	+	0.935018i	0.949200	+	0.314675i	$0.101895\pi$
$191$	2.27853	+	12.9222i	0.164869	+	0.935018i	−0.784331	+	0.620343i	$0.786993\pi$
$192$	1.70574	+	0.300767i	0.123101	+	0.0217060i
$193$	−5.40895	+	1.96870i	−0.389345	+	0.141710i	−0.529273	−	0.848452i	$-0.677535\pi$
$193$	−5.40895	+	1.96870i	−0.389345	+	0.141710i	0.139928	+	0.990162i	$0.455313\pi$
$194$	8.64930	+	7.25762i	0.620984	+	0.521067i
$195$	−4.87346	−	2.81369i	−0.348995	−	0.201493i
$196$	−5.14543	−	1.87278i	−0.367531	−	0.133770i
$197$	13.3405	+	23.1064i	0.950471	+	1.64626i	0.744409	+	0.667724i	$0.232731\pi$
$197$	13.3405	+	23.1064i	0.950471	+	1.64626i	0.206062	+	0.978539i	$0.433935\pi$
$198$	10.7219			0.761975
$199$	5.32160	−	9.21729i	0.377239	−	0.653396i	−0.613421	−	0.789756i	$-0.710207\pi$
$199$	5.32160	−	9.21729i	0.377239	−	0.653396i	0.990659	+	0.136360i	$0.0435404\pi$
$200$	3.23783	−	2.71686i	0.228949	−	0.192111i
$201$	−6.13429	+	1.08164i	−0.432679	+	0.0762930i
$202$	−1.62789	+	9.23222i	−0.114538	+	0.649576i
$203$	−0.0996702	+	0.565258i	−0.00699548	+	0.0396733i
$204$	−10.6591	+	1.87949i	−0.746286	+	0.131590i
$205$	5.18866	−	4.35381i	0.362392	−	0.304083i
$206$	−1.61334	+	2.79439i	−0.112407	+	0.194694i
$207$	3.09627	−	5.36289i	0.215205	−	0.372747i
$208$	1.84730	+	3.19961i	0.128087	+	0.221853i
$209$	−14.0055	−	5.09759i	−0.968782	−	0.352608i
$210$	4.65910	+	2.68993i	0.321508	+	0.185623i
$211$	−4.09105	−	3.43280i	−0.281640	−	0.236324i	0.491014	−	0.871152i	$-0.336626\pi$
$211$	−4.09105	−	3.43280i	−0.281640	−	0.236324i	−0.772653	+	0.634828i	$0.781071\pi$
$212$	−0.673648	+	0.245188i	−0.0462663	+	0.0168396i
$213$	−23.0954	−	4.07234i	−1.58247	−	0.279032i
$214$	0.396459	+	2.24843i	0.0271014	+	0.153700i
$215$	9.51754			0.649091
$216$			5.19615i			0.353553i
$217$	−5.78611			−0.392787
$218$	−1.80928	−	10.2609i	−0.122540	−	0.694957i
$219$	2.59152	−	3.08845i	0.175119	−	0.208698i
$220$	2.95336	−	1.07494i	0.199116	−	0.0724722i
$221$	−17.6860	−	14.8403i	−1.18969	−	0.998266i
$222$			13.3660i			0.897069i
$223$	17.9008	+	6.51536i	1.19873	+	0.436301i	0.862779	−	0.505580i	$-0.168722\pi$
$223$	17.9008	+	6.51536i	1.19873	+	0.436301i	0.335947	+	0.941881i	$0.390944\pi$
$224$	−1.76604	−	3.05888i	−0.117999	−	0.204380i
$225$	9.71348	+	8.15058i	0.647565	+	0.543372i
$226$	5.56670	−	9.64181i	0.370292	−	0.641364i
$227$	−2.65136	+	2.22475i	−0.175977	+	0.147662i	−0.726522	−	0.687143i	$-0.758864\pi$
$227$	−2.65136	+	2.22475i	−0.175977	+	0.147662i	0.550545	+	0.834806i	$0.314420\pi$
$228$	2.47044	−	6.78747i	0.163609	−	0.449511i
$229$	−5.02528	+	28.4998i	−0.332080	+	1.88332i	0.122272	+	0.992497i	$0.460982\pi$
$229$	−5.02528	+	28.4998i	−0.332080	+	1.88332i	−0.454352	+	0.890822i	$0.650129\pi$
$230$	0.315207	−	1.78763i	0.0207842	−	0.117873i
$231$	−14.0544	−	16.7494i	−0.924710	−	1.10203i
$232$	−0.124485	+	0.104455i	−0.00817285	+	0.00685784i
$233$	3.33022	−	5.76811i	0.218170	−	0.377882i	−0.736078	−	0.676896i	$-0.763325\pi$
$233$	3.33022	−	5.76811i	0.218170	−	0.377882i	0.954249	+	0.299015i	$0.0966579\pi$
$234$	−8.49067	+	7.12452i	−0.555052	+	0.465744i
$235$	−2.81908	−	4.88279i	−0.183896	−	0.318518i
$236$	6.56418	+	2.38917i	0.427292	+	0.155521i
$237$	−9.92783	+	5.73184i	−0.644882	+	0.372323i
$238$	16.9081	+	14.1876i	1.09599	+	0.919643i
$239$	−7.31908	+	2.66393i	−0.473432	+	0.172315i	−0.567706	−	0.823231i	$-0.692169\pi$
$239$	−7.31908	+	2.66393i	−0.473432	+	0.172315i	0.0942745	+	0.995546i	$0.469947\pi$
$240$	0.520945	+	1.43128i	0.0336268	+	0.0923889i
$241$	3.80200	+	21.5622i	0.244909	+	1.38895i	0.820705	+	0.571352i	$0.193581\pi$
$241$	3.80200	+	21.5622i	0.244909	+	1.38895i	−0.575796	+	0.817593i	$0.695308\pi$
$242$	−1.77332			−0.113993
$243$	−15.3516	+	2.70691i	−0.984808	+	0.173648i
$244$	−1.26857			−0.0812119
$245$	−0.836152	−	4.74205i	−0.0534198	−	0.302959i
$246$	−4.56283	−	12.5363i	−0.290916	−	0.799284i
$247$	14.4782	−	5.26963i	0.921224	−	0.335298i
$248$	−1.25490	−	1.05299i	−0.0796862	−	0.0668647i
$249$	−6.68004	+	3.85673i	−0.423331	+	0.244410i
$250$	7.62449	+	2.77509i	0.482215	+	0.175512i
$251$	−8.04236	−	13.9298i	−0.507629	−	0.879239i	−0.999961	−	0.00883173i	$-0.997189\pi$
$251$	−8.04236	−	13.9298i	−0.507629	−	0.879239i	0.492332	−	0.870407i	$-0.336145\pi$
$252$	8.11721	−	6.81115i	0.511336	−	0.429062i
$253$	−3.68866	+	6.38895i	−0.231904	+	0.401670i
$254$	7.58899	−	6.36792i	0.476176	−	0.399559i
$255$	−6.11809	−	7.29125i	−0.383130	−	0.456596i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	4.49138	−	25.4719i	0.280165	−	1.58889i	−0.441898	−	0.897065i	$-0.645695\pi$
$257$	4.49138	−	25.4719i	0.280165	−	1.58889i	0.722063	−	0.691828i	$-0.243194\pi$
$258$	6.41147	−	17.6154i	0.399161	−	1.09669i
$259$	20.8799	−	17.5203i	1.29741	−	1.08866i
$260$	−1.62449	+	2.81369i	−0.100746	+	0.174498i
$261$	−0.373455	−	0.313366i	−0.0231163	−	0.0193969i
$262$	−4.51501	−	7.82023i	−0.278939	−	0.483136i
$263$	29.5967	+	10.7723i	1.82501	+	0.664250i	0.994180	+	0.107727i	$0.0343574\pi$
$263$	29.5967	+	10.7723i	1.82501	+	0.664250i	0.830832	+	0.556523i	$0.187865\pi$
$264$		−	6.19031i		−	0.380987i
$265$	−0.482926	−	0.405223i	−0.0296659	−	0.0248926i
$266$	−13.8414	+	5.03785i	−0.848669	+	0.308890i
$267$	−10.2973	+	12.2718i	−0.630182	+	0.751021i
$268$	0.624485	+	3.54163i	0.0381465	+	0.216340i
$269$	−4.60906			−0.281019			−0.140510	−	0.990079i	$-0.544874\pi$
$269$	−4.60906			−0.281019			−0.140510	+	0.990079i	$0.544874\pi$
$270$	−3.95723	+	2.28471i	−0.240830	+	0.139043i
$271$	−1.31820			−0.0800750			−0.0400375	−	0.999198i	$-0.512748\pi$
$271$	−1.31820			−0.0800750			−0.0400375	+	0.999198i	$0.512748\pi$
$272$	1.08512	+	6.15403i	0.0657952	+	0.373143i
$273$	22.2592	+	3.92490i	1.34719	+	0.237546i
$274$	1.90508	−	0.693392i	0.115090	−	0.0418893i
$275$	−11.5719	−	9.70999i	−0.697813	−	0.585535i
$276$	−3.09627	−	1.78763i	−0.186373	−	0.107603i
$277$	−28.9624	−	10.5415i	−1.74018	−	0.633375i	−0.740916	−	0.671598i	$-0.765608\pi$
$277$	−28.9624	−	10.5415i	−1.74018	−	0.633375i	−0.999269	+	0.0382227i	$0.987830\pi$
$278$	0.0825961	+	0.143061i	0.00495378	+	0.00858021i
$279$	2.45723	−	4.25605i	0.147111	−	0.254803i
$280$	1.55303	−	2.68993i	0.0928115	−	0.160754i
$281$	16.4172	−	13.7756i	0.979365	−	0.821785i	−0.00462815	−	0.999989i	$-0.501473\pi$
$281$	16.4172	−	13.7756i	0.979365	−	0.821785i	0.983994	+	0.178204i	$0.0570287\pi$
$282$	−10.9363	+	1.92836i	−0.651247	+	0.114832i
$283$	−0.307934	+	1.74638i	−0.0183047	+	0.103811i	−0.992591	−	0.121501i	$-0.961229\pi$
$283$	−0.307934	+	1.74638i	−0.0183047	+	0.103811i	0.974287	+	0.225313i	$0.0723403\pi$
$284$	−2.35117	+	13.3341i	−0.139516	+	0.791235i
$285$	6.25537	−	1.10299i	0.370536	−	0.0653355i
$286$	10.1152	−	8.48762i	0.598121	−	0.501884i
$287$	−13.6027	+	23.5605i	−0.802940	+	1.39073i
$288$	3.00000			0.176777
$289$	−11.0248	−	19.0955i	−0.648519	−	1.12327i
$290$	−0.134285	−	0.0488759i	−0.00788551	−	0.00287009i
$291$	16.9363	+	9.77817i	0.992823	+	0.573207i
$292$	−1.78312	−	1.49621i	−0.104349	−	0.0875593i
$293$	29.0920	−	10.5886i	1.69957	−	0.618594i	0.703795	−	0.710403i	$-0.251487\pi$
$293$	29.0920	−	10.5886i	1.69957	−	0.618594i	0.995777	+	0.0918092i	$0.0292650\pi$
$294$	−9.34002	−	1.64690i	−0.544721	−	0.0960490i
$295$	1.06670	+	6.04958i	0.0621059	+	0.352220i
$296$	7.71688			0.448535
$297$	18.2888	−	3.22481i	1.06122	−	0.187122i
$298$	5.80066			0.336023
$299$	−1.32429	−	7.51044i	−0.0765858	−	0.434340i
$300$	4.70574	−	5.60808i	0.271686	−	0.323783i
$301$	−35.9222	+	13.0746i	−2.07052	+	0.753608i
$302$	−10.7626	−	9.03093i	−0.619320	−	0.519672i
$303$			16.2373i			0.932811i
$304$	−3.91875	−	1.42631i	−0.224756	−	0.0818044i
$305$	−0.557781	−	0.966105i	−0.0319385	−	0.0553190i
$306$	−17.6163	+	6.41182i	−1.00706	+	0.366539i
$307$	−4.26857	+	7.39338i	−0.243620	+	0.421963i	−0.961743	−	0.273954i	$-0.911668\pi$
$307$	−4.26857	+	7.39338i	−0.243620	+	0.421963i	0.718123	+	0.695917i	$0.245002\pi$
$308$	−9.67024	+	8.11430i	−0.551013	+	0.462355i
$309$	−1.91147	+	5.25173i	−0.108740	+	0.298761i
$310$	0.250152	−	1.41868i	0.0142077	−	0.0805759i
$311$	−3.12789	+	17.7391i	−0.177366	+	1.00589i	0.758011	+	0.652242i	$0.226171\pi$
$311$	−3.12789	+	17.7391i	−0.177366	+	1.00589i	−0.935377	+	0.353652i	$0.884940\pi$
$312$	4.11334	+	4.90209i	0.232872	+	0.277526i
$313$	13.1800	−	11.0594i	0.744980	−	0.625113i	−0.189190	−	0.981941i	$-0.560586\pi$
$313$	13.1800	−	11.0594i	0.744980	−	0.625113i	0.934170	+	0.356828i	$0.116142\pi$
$314$	−2.38666	+	4.13381i	−0.134687	+	0.233285i
$315$	8.75624	+	3.18701i	0.493358	+	0.179568i
$316$	3.30928	+	5.73184i	0.186161	+	0.322441i
$317$	−23.4094	−	8.52033i	−1.31480	−	0.478549i	−0.413014	−	0.910725i	$-0.635524\pi$
$317$	−23.4094	−	8.52033i	−1.31480	−	0.478549i	−0.901790	+	0.432175i	$0.857746\pi$
$318$	−1.07532	+	0.620838i	−0.0603011	+	0.0348148i
$319$	0.444907	+	0.373321i	0.0249100	+	0.0209020i
$320$	0.826352	−	0.300767i	0.0461945	−	0.0168134i
$321$	1.35251	+	3.71599i	0.0754898	+	0.207407i
$322$	1.26604	+	7.18009i	0.0705539	+	0.400131i
$323$	26.0597			1.45000
$324$	1.56283	+	8.86327i	0.0868241	+	0.492404i
$325$	15.6159			0.866212
$326$	1.86097	+	10.5541i	0.103069	+	0.584536i
$327$	−6.17230	−	16.9583i	−0.341329	−	0.937794i
$328$	−7.23783	+	2.63435i	−0.399642	+	0.145458i
$329$	17.3478	+	14.5565i	0.956413	+	0.802526i
$330$	4.71436	−	2.72183i	0.259517	−	0.149832i
$331$	−8.32547	−	3.03022i	−0.457609	−	0.166556i	0.102922	−	0.994689i	$-0.467181\pi$
$331$	−8.32547	−	3.03022i	−0.457609	−	0.166556i	−0.560531	+	0.828133i	$0.689403\pi$
$332$	2.22668	+	3.85673i	0.122205	+	0.211665i
$333$	4.02007	+	22.7989i	0.220298	+	1.24937i
$334$	−6.44949	+	11.1708i	−0.352901	+	0.611242i
$335$	−2.42262	+	2.03282i	−0.132362	+	0.111065i
$336$	−3.93242	−	4.68647i	−0.214531	−	0.255668i
$337$	3.65910	−	20.7518i	0.199324	−	1.13042i	−0.706801	−	0.707412i	$-0.749862\pi$
$337$	3.65910	−	20.7518i	0.199324	−	1.13042i	0.906125	−	0.423010i	$-0.139026\pi$
$338$	−0.112874	+	0.640140i	−0.00613953	+	0.0348190i
$339$	6.59539	−	18.1207i	0.358212	−	0.984180i
$340$	−4.20961	+	3.53228i	−0.228298	+	0.191565i
$341$	−2.92737	+	5.07035i	−0.158526	+	0.274575i
$342$	2.17247	−	12.3207i	0.117474	−	0.666225i
$343$	−2.69207	−	4.66280i	−0.145358	−	0.251767i
$344$	−10.1702	−	3.70167i	−0.548343	−	0.199580i
$345$		−	3.14403i		−	0.169269i
$346$	−9.86097	−	8.27433i	−0.530129	−	0.444831i
$347$	−20.7754	+	7.56164i	−1.11528	+	0.405930i	−0.832929	−	0.553380i	$-0.813338\pi$
$347$	−20.7754	+	7.56164i	−1.11528	+	0.405930i	−0.282355	+	0.959310i	$0.591116\pi$
$348$	−0.180922	+	0.215615i	−0.00969844	+	0.0115582i
$349$	0.381911	+	2.16593i	0.0204433	+	0.115939i	0.993322	−	0.115377i	$-0.0368077\pi$
$349$	0.381911	+	2.16593i	0.0204433	+	0.115939i	−0.972878	+	0.231317i	$0.925697\pi$
$350$	−14.9290			−0.797989
$351$	−12.3400	+	14.7063i	−0.658662	+	0.784962i
$352$	−3.57398			−0.190494
$353$	0.826352	+	4.68647i	0.0439823	+	0.249436i	0.998870	−	0.0475321i	$-0.0151356\pi$
$353$	0.826352	+	4.68647i	0.0439823	+	0.249436i	−0.954887	+	0.296968i	$0.904025\pi$
$354$	11.9153	+	2.10100i	0.633293	+	0.111667i
$355$	−11.1887	+	4.07234i	−0.593833	+	0.216137i
$356$	7.08512	+	5.94512i	0.375511	+	0.315091i
$357$	33.1079	+	19.1148i	1.75225	+	1.01166i
$358$	−8.42262	−	3.06558i	−0.445149	−	0.162021i
$359$	1.30288	+	2.25666i	0.0687634	+	0.119102i	0.898357	−	0.439266i	$-0.144761\pi$
$359$	1.30288	+	2.25666i	0.0687634	+	0.119102i	−0.829594	+	0.558367i	$0.811428\pi$
$360$	1.31908	+	2.28471i	0.0695215	+	0.120415i
$361$	0.804530	−	1.39349i	0.0423437	−	0.0733414i
$362$	1.52094	−	1.27622i	0.0799391	−	0.0670768i
$363$	−3.02481	+	0.533356i	−0.158762	+	0.0279940i
$364$	2.26604	−	12.8514i	0.118773	−	0.673595i
$365$	0.355448	−	2.01584i	0.0186050	−	0.105514i
$366$	−2.16385	+	0.381545i	−0.113106	+	0.0199437i
$367$	−10.9042	+	9.14971i	−0.569195	+	0.477611i	−0.881379	−	0.472411i	$-0.843384\pi$
$367$	−10.9042	+	9.14971i	−0.569195	+	0.477611i	0.312184	+	0.950022i	$0.398939\pi$
$368$	−1.03209	+	1.78763i	−0.0538014	+	0.0931867i
$369$	−11.5535	−	20.0112i	−0.601451	−	1.04174i
$370$	3.39306	+	5.87695i	0.176397	+	0.305528i
$371$	2.37939	+	0.866025i	0.123532	+	0.0449618i
$372$	−2.45723	−	1.41868i	−0.127402	−	0.0735554i
$373$	−1.76810	−	1.48362i	−0.0915489	−	0.0768187i	0.595865	−	0.803085i	$-0.296810\pi$
$373$	−1.76810	−	1.48362i	−0.0915489	−	0.0768187i	−0.687413	+	0.726266i	$0.741254\pi$
$374$	20.9868	−	7.63857i	1.08520	−	0.394981i
$375$	13.8400	+	2.44037i	0.714696	+	0.126020i
$376$	1.11334	+	6.31407i	0.0574162	+	0.325623i
$377$	−0.600385			−0.0309214
$378$	11.7973	−	14.0594i	0.606785	−	0.723139i
$379$	−6.02734			−0.309604			−0.154802	−	0.987946i	$-0.549474\pi$
$379$	−6.02734			−0.309604			−0.154802	+	0.987946i	$0.549474\pi$
$380$	−0.636812	−	3.61154i	−0.0326677	−	0.185268i
$381$	11.0296	−	13.1445i	0.565062	−	0.673414i
$382$	12.3302	−	4.48783i	0.630869	−	0.229618i
$383$	16.3007	+	13.6779i	0.832925	+	0.698907i	0.955960	−	0.293495i	$-0.0948185\pi$
$383$	16.3007	+	13.6779i	0.832925	+	0.698907i	−0.123036	+	0.992402i	$0.539263\pi$
$384$		−	1.73205i		−	0.0883883i
$385$	−10.4315	−	3.79677i	−0.531641	−	0.193501i
$386$	2.87804	+	4.98491i	0.146488	+	0.253725i
$387$	5.63816	−	31.9756i	0.286604	−	1.62541i
$388$	5.64543	−	9.77817i	0.286603	−	0.496411i
$389$	−15.8248	+	13.2785i	−0.802347	+	0.673249i	−0.948768	−	0.315973i	$-0.897669\pi$
$389$	−15.8248	+	13.2785i	−0.802347	+	0.673249i	0.146421	+	0.989222i	$0.453225\pi$
$390$	−1.92468	+	5.28801i	−0.0974599	+	0.267769i
$391$	2.23989	−	12.7030i	0.113276	−	0.642419i
$392$	−0.950837	+	5.39246i	−0.0480245	+	0.272361i
$393$	−10.0535	−	11.9813i	−0.507132	−	0.604376i
$394$	20.4388	−	17.1502i	1.02969	−	0.864015i
$395$	−2.91013	+	5.04049i	−0.146425	+	0.253615i
$396$	−1.86184	−	10.5590i	−0.0935612	−	0.530612i
$397$	12.2638	+	21.2416i	0.615504	+	1.06608i	0.990296	+	0.138975i	$0.0443807\pi$
$397$	12.2638	+	21.2416i	0.615504	+	1.06608i	−0.374792	+	0.927109i	$0.622286\pi$
$398$	−10.0013	−	3.64019i	−0.501322	−	0.182466i
$399$	−22.0945	+	12.7563i	−1.10611	+	0.638612i
$400$	−3.23783	−	2.71686i	−0.161891	−	0.135843i
$401$	−13.7433	+	5.00217i	−0.686310	+	0.249796i	−0.661554	−	0.749897i	$-0.730103\pi$
$401$	−13.7433	+	5.00217i	−0.686310	+	0.249796i	−0.0247555	+	0.999694i	$0.507881\pi$
$402$	2.13041	+	5.85327i	0.106255	+	0.291934i
$403$	−1.05097	−	5.96037i	−0.0523527	−	0.296907i
$404$	9.37464			0.466406
$405$	−6.06283	+	5.08732i	−0.301265	+	0.252791i
$406$	0.573978			0.0284860
$407$	−4.78921	−	27.1610i	−0.237392	−	1.34632i
$408$	3.70187	+	10.1708i	0.183270	+	0.503529i
$409$	33.9479	−	12.3560i	1.67862	−	0.610966i	0.685497	−	0.728076i	$-0.259585\pi$
$409$	33.9479	−	12.3560i	1.67862	−	0.610966i	0.993119	+	0.117110i	$0.0373629\pi$
$410$	−5.18866	−	4.35381i	−0.256250	−	0.215019i
$411$	3.04101	−	1.75573i	0.150002	−	0.0866037i
$412$	3.03209	+	1.10359i	0.149380	+	0.0543700i
$413$	−12.3366	−	21.3677i	−0.607045	−	1.05143i
$414$	−5.81908	−	2.11797i	−0.285992	−	0.104093i
$415$	−1.95811	+	3.39155i	−0.0961199	+	0.166485i
$416$	2.83022	−	2.37484i	0.138763	−	0.116436i
$417$	0.183915	+	0.219182i	0.00900637	+	0.0107334i
$418$	−2.58812	+	14.6779i	−0.126589	+	0.717921i
$419$	3.42309	−	19.4133i	0.167229	−	0.948401i	−0.779508	−	0.626392i	$-0.784531\pi$
$419$	3.42309	−	19.4133i	0.167229	−	0.948401i	0.946737	−	0.322009i	$-0.104358\pi$
$420$	1.84002	−	5.05542i	0.0897839	−	0.246679i
$421$	2.63041	−	2.20718i	0.128199	−	0.107571i	−0.576434	−	0.817144i	$-0.695556\pi$
$421$	2.63041	−	2.20718i	0.128199	−	0.107571i	0.704633	+	0.709572i	$0.251112\pi$
$422$	−2.67024	+	4.62500i	−0.129985	+	0.225141i
$423$	−18.0744	+	6.57856i	−0.878810	+	0.319861i
$424$	0.358441	+	0.620838i	0.0174074	+	0.0301505i
$425$	24.8195	+	9.03358i	1.20392	+	0.438193i
$426$			23.4517i			1.13624i
$427$	3.43242	+	2.88014i	0.166106	+	0.139380i
$428$	2.14543	−	0.780873i	0.103703	−	0.0377449i
$429$	14.7010	−	17.5200i	0.709770	−	0.845871i
$430$	−1.65270	−	9.37295i	−0.0797004	−	0.452004i
$431$	−28.7151			−1.38316			−0.691579	−	0.722300i	$-0.743085\pi$
$431$	−28.7151			−1.38316			−0.691579	+	0.722300i	$0.743085\pi$
$432$	5.11721	−	0.902302i	0.246202	−	0.0434120i
$433$	−14.1179			−0.678464			−0.339232	−	0.940703i	$-0.610167\pi$
$433$	−14.1179			−0.678464			−0.339232	+	0.940703i	$0.610167\pi$
$434$	1.00475	+	5.69821i	0.0482294	+	0.273523i
$435$	−0.243756	−	0.0429807i	−0.0116872	−	0.00206077i
$436$	−9.79086	+	3.56358i	−0.468897	+	0.170665i
$437$	6.59421	+	5.53320i	0.315444	+	0.264689i
$438$	−3.49154	−	2.01584i	−0.166832	−	0.0963207i
$439$	−14.5842	−	5.30823i	−0.696068	−	0.253348i	−0.0303369	−	0.999540i	$-0.509658\pi$
$439$	−14.5842	−	5.30823i	−0.696068	−	0.253348i	−0.665731	+	0.746192i	$0.731880\pi$
$440$	−1.57145	−	2.72183i	−0.0749160	−	0.129758i
$441$	−16.4270			−0.782236
$442$	−11.5437	+	19.9943i	−0.549078	+	0.951031i
$443$	−27.3897	+	22.9826i	−1.30132	+	1.09194i	−0.311407	+	0.950277i	$0.600800\pi$
$443$	−27.3897	+	22.9826i	−1.30132	+	1.09194i	−0.989915	+	0.141662i	$0.954755\pi$
$444$	13.1630	−	2.32099i	0.624687	−	0.110149i
$445$	−1.41235	+	8.00984i	−0.0669519	+	0.379703i
$446$	3.30793	−	18.7602i	0.156635	−	0.888322i
$447$	9.89440	−	1.74465i	0.467989	−	0.0825191i
$448$	−2.70574	+	2.27038i	−0.127834	+	0.107266i
$449$	12.8564	−	22.2679i	0.606730	−	1.05089i	−0.385045	−	0.922898i	$-0.625814\pi$
$449$	12.8564	−	22.2679i	0.606730	−	1.05089i	0.991775	−	0.127990i	$-0.0408525\pi$
$450$	6.34002	−	10.9812i	0.298872	−	0.517661i
$451$	13.7640	+	23.8399i	0.648121	+	1.12258i
$452$	−10.4620	−	3.80785i	−0.492090	−	0.179106i
$453$	−21.0744	−	12.1673i	−0.990164	−	0.571671i
$454$	2.65136	+	2.22475i	0.124434	+	0.104413i
$455$	10.7836	−	3.92490i	0.505542	−	0.184002i
$456$	−7.11334	−	1.25427i	−0.333113	−	0.0587368i
$457$	0.352921	+	2.00152i	0.0165090	+	0.0936270i	0.991949	−	0.126638i	$-0.0404188\pi$
$457$	0.352921	+	2.00152i	0.0165090	+	0.0936270i	−0.975440	+	0.220265i	$0.929308\pi$
$458$	28.9394			1.35225
$459$	−28.1204	+	16.2353i	−1.31255	+	0.757799i
$460$	−1.81521			−0.0846345
$461$	3.74628	+	21.2462i	0.174482	+	0.989535i	0.938740	+	0.344625i	$0.111994\pi$
$461$	3.74628	+	21.2462i	0.174482	+	0.989535i	−0.764259	+	0.644910i	$0.776895\pi$
$462$	−14.0544	+	16.7494i	−0.653869	+	0.779251i
$463$	20.2986	−	7.38809i	0.943356	−	0.343353i	0.175866	−	0.984414i	$-0.443728\pi$
$463$	20.2986	−	7.38809i	0.943356	−	0.343353i	0.767490	+	0.641061i	$0.221505\pi$
$464$	0.124485	+	0.104455i	0.00577908	+	0.00484922i
$465$		−	2.49514i		−	0.115709i
$466$	−6.25877	−	2.27801i	−0.289932	−	0.105527i
$467$	−12.2622	−	21.2387i	−0.567426	−	0.982810i	−0.996819	−	0.0796928i	$-0.974606\pi$
$467$	−12.2622	−	21.2387i	−0.567426	−	0.982810i	0.429394	−	0.903117i	$-0.358727\pi$
$468$	8.49067	+	7.12452i	0.392481	+	0.329331i
$469$	6.35117	−	11.0005i	0.293270	−	0.507958i
$470$	−4.31908	+	3.62414i	−0.199224	+	0.167169i
$471$	−2.82770	+	7.76903i	−0.130293	+	0.357978i
$472$	1.21301	−	6.87933i	0.0558334	−	0.316647i
$473$	−6.71688	+	38.0933i	−0.308843	+	1.75153i
$474$	7.36871	+	8.78168i	0.338456	+	0.403356i
$475$	−13.5025	+	11.3300i	−0.619538	+	0.519854i
$476$	11.0360	−	19.1148i	0.505832	−	0.876127i
$477$	−1.64749	+	1.38241i	−0.0754333	+	0.0632961i
$478$	3.89440	+	6.74530i	0.178126	+	0.308523i
$479$	−13.4620	−	4.89976i	−0.615094	−	0.223876i	0.0156369	−	0.999878i	$-0.495022\pi$
$479$	−13.4620	−	4.89976i	−0.615094	−	0.223876i	−0.630730	+	0.776002i	$0.717245\pi$
$480$	1.31908	−	0.761570i	0.0602074	−	0.0347608i
$481$	21.8405	+	18.3263i	0.995841	+	0.835609i
$482$	20.5744	−	7.48849i	0.937140	−	0.341091i
$483$	4.31908	+	11.8666i	0.196525	+	0.539948i
$484$	0.307934	+	1.74638i	0.0139970	+	0.0793808i
$485$	9.92902			0.450853
$486$	5.33157	+	14.6484i	0.241845	+	0.664463i
$487$	32.3114			1.46417			0.732084	−	0.681214i	$-0.238548\pi$
$487$	32.3114			1.46417			0.732084	+	0.681214i	$0.238548\pi$
$488$	0.220285	+	1.24930i	0.00997183	+	0.0565531i
$489$	6.34864	+	17.4427i	0.287095	+	0.788788i
$490$	−4.52481	+	1.64690i	−0.204410	+	0.0743993i
$491$	24.8576	+	20.8580i	1.12181	+	0.941307i	0.998694	−	0.0510857i	$-0.0162682\pi$
$491$	24.8576	+	20.8580i	1.12181	+	0.941307i	0.123112	+	0.992393i	$0.460713\pi$
$492$	−11.5535	+	6.67042i	−0.520872	+	0.300726i
$493$	−0.954241	−	0.347315i	−0.0429768	−	0.0156423i
$494$	−7.70368	−	13.3432i	−0.346605	−	0.600337i
$495$	7.22281	−	6.06066i	0.324641	−	0.272406i
$496$	−0.819078	+	1.41868i	−0.0367777	+	0.0637008i
$497$	36.6352	−	30.7406i	1.64331	−	1.37890i
$498$	4.95811	+	5.90885i	0.222178	+	0.264782i
$499$	−4.31180	+	24.4535i	−0.193023	+	1.09469i	0.722184	+	0.691702i	$0.243139\pi$
$499$	−4.31180	+	24.4535i	−0.193023	+	1.09469i	−0.915206	+	0.402985i	$0.867973\pi$
$500$	1.40895	−	7.99054i	0.0630101	−	0.357348i
$501$	−7.64131	+	20.9943i	−0.341389	+	0.937957i
$502$	−12.3216	+	10.3391i	−0.549940	+	0.461455i
$503$	7.46198	−	12.9245i	0.332713	−	0.576276i	−0.650330	−	0.759652i	$-0.725369\pi$
$503$	7.46198	−	12.9245i	0.332713	−	0.576276i	0.983043	+	0.183376i	$0.0587025\pi$
$504$	−8.11721	−	6.81115i	−0.361569	−	0.303393i
$505$	4.12196	+	7.13944i	0.183425	+	0.317701i
$506$	6.93242	+	2.52319i	0.308184	+	0.112170i
$507$			1.12586i			0.0500012i
$508$	−7.58899	−	6.36792i	−0.336707	−	0.282531i
$509$	−14.4595	+	5.26281i	−0.640904	+	0.233270i	−0.641970	−	0.766729i	$-0.721883\pi$
$509$	−14.4595	+	5.26281i	−0.640904	+	0.233270i	0.00106632	+	0.999999i	$0.499661\pi$
$510$	−6.11809	+	7.29125i	−0.270914	+	0.322862i
$511$	1.42767	+	8.09672i	0.0631564	+	0.358178i
$512$	−1.00000			−0.0441942
$513$		−	21.6692i		−	0.956720i
$514$	−25.8648			−1.14085
$515$	0.492726	+	2.79439i	0.0217121	+	0.123135i
$516$	−18.4611	−	3.25519i	−0.812705	−	0.143302i
$517$	21.5326	−	7.83721i	0.947001	−	0.344680i
$518$	−20.8799	−	17.5203i	−0.917408	−	0.769797i
$519$	−19.3089	−	11.1480i	−0.847565	−	0.489342i
$520$	3.05303	+	1.11121i	0.133884	+	0.0487299i
$521$	−6.69207	−	11.5910i	−0.293185	−	0.507811i	0.681376	−	0.731933i	$-0.261382\pi$
$521$	−6.69207	−	11.5910i	−0.293185	−	0.507811i	−0.974561	+	0.224122i	$0.928048\pi$
$522$	−0.243756	+	0.422197i	−0.0106689	+	0.0184791i
$523$	12.4402	−	21.5470i	0.543970	−	0.942184i	−0.454701	−	0.890644i	$-0.650254\pi$
$523$	12.4402	−	21.5470i	0.543970	−	0.942184i	0.998671	−	0.0515397i	$-0.0164129\pi$
$524$	−6.91740	+	5.80439i	−0.302188	+	0.253566i
$525$	−25.4650	+	4.49016i	−1.11138	+	0.195967i
$526$	5.46926	−	31.0177i	0.238471	−	1.35244i
$527$	1.77760	−	10.0813i	0.0774334	−	0.439147i
$528$	−6.09627	+	1.07494i	−0.265306	+	0.0467806i
$529$	−14.3550	+	12.0453i	−0.624132	+	0.523709i
$530$	−0.315207	+	0.545955i	−0.0136917	+	0.0237148i
$531$	20.9564			0.909428
$532$	7.36484	+	12.7563i	0.319306	+	0.553055i
$533$	−26.7408	−	9.73286i	−1.15827	−	0.421577i
$534$	13.8735	+	8.00984i	0.600363	+	0.346620i
$535$	1.53802	+	1.29055i	0.0664943	+	0.0557954i
$536$	3.37939	−	1.23000i	0.145967	−	0.0531277i
$537$	−15.2888	−	2.69583i	−0.659760	−	0.116334i
$538$	0.800355	+	4.53904i	0.0345057	+	0.195692i
$539$	19.5699			0.842934
$540$	2.93717	+	3.50038i	0.126396	+	0.150632i
$541$	−9.09421			−0.390991			−0.195495	−	0.980705i	$-0.562631\pi$
$541$	−9.09421			−0.390991			−0.195495	+	0.980705i	$0.562631\pi$
$542$	0.228903	+	1.29817i	0.00983223	+	0.0557614i
$543$	2.21048	−	2.63435i	0.0948610	−	0.113051i
$544$	5.87211	−	2.13727i	0.251765	−	0.0916349i
$545$	−7.01889	−	5.88954i	−0.300656	−	0.252280i
$546$		−	22.6026i		−	0.967303i
$547$	−20.8701	−	7.59608i	−0.892339	−	0.324785i	−0.145160	−	0.989408i	$-0.546370\pi$
$547$	−20.8701	−	7.59608i	−0.892339	−	0.324785i	−0.747179	+	0.664623i	$0.768592\pi$
$548$	−1.01367	−	1.75573i	−0.0433019	−	0.0750010i
$549$	−3.57620	+	1.30163i	−0.152628	+	0.0555522i
$550$	−7.55303	+	13.0822i	−0.322062	+	0.557828i
$551$	0.519134	−	0.435605i	0.0221158	−	0.0185574i
$552$	−1.22281	+	3.35965i	−0.0520463	+	0.142996i
$553$	4.05943	−	23.0222i	0.172625	−	0.979002i
$554$	−5.35204	+	30.3530i	−0.227387	+	1.28957i
$555$	7.55525	+	9.00400i	0.320703	+	0.382199i
$556$	0.126545	−	0.106183i	0.00536668	−	0.00450318i
$557$	1.35369	−	2.34466i	0.0573578	−	0.0993466i	−0.835921	−	0.548850i	$-0.815066\pi$
$557$	1.35369	−	2.34466i	0.0573578	−	0.0993466i	0.893279	+	0.449504i	$0.148399\pi$
$558$	−4.61809	−	1.68085i	−0.195499	−	0.0711559i
$559$	−19.9932	−	34.6292i	−0.845622	−	1.46466i
$560$	−2.91875	−	1.06234i	−0.123340	−	0.0448919i
$561$	33.5005	−	19.3415i	1.41439	−	0.816600i
$562$	−16.4172	−	13.7756i	−0.692516	−	0.581090i
$563$	−6.60859	+	2.40533i	−0.278519	+	0.101373i	−0.477503	−	0.878630i	$-0.658458\pi$
$563$	−6.60859	+	2.40533i	−0.278519	+	0.101373i	0.198984	+	0.980003i	$0.436236\pi$
$564$	3.79813	+	10.4353i	0.159930	+	0.439405i
$565$	−1.70011	−	9.64181i	−0.0715242	−	0.405634i
$566$	1.77332			0.0745381
$567$	15.8944	−	27.5299i	0.667502	−	1.15615i
$568$	13.5398			0.568119
$569$	4.34507	+	24.6421i	0.182155	+	1.03305i	0.929556	+	0.368680i	$0.120190\pi$
$569$	4.34507	+	24.6421i	0.182155	+	1.03305i	−0.747401	+	0.664373i	$0.768699\pi$
$570$	−2.17247	−	5.96880i	−0.0909946	−	0.250006i
$571$	−6.43242	+	2.34121i	−0.269188	+	0.0979765i	−0.473088	−	0.881015i	$-0.656861\pi$
$571$	−6.43242	+	2.34121i	−0.269188	+	0.0979765i	0.203899	+	0.978992i	$0.434638\pi$
$572$	−10.1152	−	8.48762i	−0.422936	−	0.354885i
$573$	19.6823	−	11.3636i	0.822241	−	0.474721i
$574$	25.5646	+	9.30477i	1.06705	+	0.388374i
$575$	4.36231	+	7.55574i	0.181921	+	0.315096i
$576$	−0.520945	−	2.95442i	−0.0217060	−	0.123101i
$577$	−2.10014	+	3.63754i	−0.0874298	+	0.151433i	−0.906424	−	0.422369i	$-0.861199\pi$
$577$	−2.10014	+	3.63754i	−0.0874298	+	0.151433i	0.818994	+	0.573802i	$0.194532\pi$
$578$	−16.8910	+	14.1732i	−0.702573	+	0.589529i
$579$	6.40848	+	7.63733i	0.266327	+	0.317397i
$580$	−0.0248149	+	0.140732i	−0.00103038	+	0.00584360i
$581$	2.73143	−	15.4907i	0.113319	−	0.642663i
$582$	6.68866	−	18.3770i	0.277254	−	0.761749i
$583$	1.96270	−	1.64690i	0.0812866	−	0.0682075i
$584$	−1.16385	+	2.01584i	−0.0481604	+	0.0834162i
$585$	−1.69253	+	9.59883i	−0.0699776	+	0.396863i
$586$	−15.4795	−	26.8113i	−0.639453	−	1.10757i
$587$	34.3491	+	12.5021i	1.41774	+	0.516015i	0.933391	−	0.358860i	$-0.116835\pi$
$587$	34.3491	+	12.5021i	1.41774	+	0.516015i	0.484348	+	0.874875i	$0.339057\pi$
$588$			9.48411i			0.391118i
$589$	5.23324	+	4.39121i	0.215632	+	0.180937i
$590$	5.77244	−	2.10100i	0.237648	−	0.0864967i
$591$	29.7050	−	35.4011i	1.22190	−	1.45621i
$592$	−1.34002	−	7.59964i	−0.0550746	−	0.312343i
$593$	−45.0660			−1.85064			−0.925320	−	0.379186i	$-0.876204\pi$
$593$	−45.0660			−1.85064			−0.925320	+	0.379186i	$0.876204\pi$
$594$	−6.35163	−	17.4510i	−0.260611	−	0.716022i
$595$	19.4097			0.795721
$596$	−1.00727	−	5.71253i	−0.0412595	−	0.233995i
$597$	−18.1545	−	3.20113i	−0.743015	−	0.131014i
$598$	−7.16637	+	2.60835i	−0.293055	+	0.106663i
$599$	12.4531	+	10.4494i	0.508820	+	0.426951i	0.860714	−	0.509089i	$-0.170018\pi$
$599$	12.4531	+	10.4494i	0.508820	+	0.426951i	−0.351893	+	0.936040i	$0.614462\pi$
$600$	−6.34002	−	3.66041i	−0.258830	−	0.149436i
$601$	39.0057	+	14.1969i	1.59107	+	0.579104i	0.977574	−	0.210590i	$-0.0675386\pi$
$601$	39.0057	+	14.1969i	1.59107	+	0.579104i	0.613501	+	0.789694i	$0.289761\pi$
$602$	19.1138	+	33.1061i	0.779021	+	1.34930i
$603$	5.39440	+	9.34337i	0.219677	+	0.380492i
$604$	−7.02481	+	12.1673i	−0.285836	+	0.495082i
$605$	−1.19459	+	1.00238i	−0.0485671	+	0.0407526i
$606$	15.9907	−	2.81959i	0.649576	−	0.114538i
$607$	−7.34565	+	41.6592i	−0.298151	+	1.69090i	0.355963	+	0.934500i	$0.384153\pi$
$607$	−7.34565	+	41.6592i	−0.298151	+	1.69090i	−0.654114	+	0.756396i	$0.726958\pi$
$608$	−0.724155	+	4.10689i	−0.0293684	+	0.166556i
$609$	0.979055	−	0.172634i	0.0396733	−	0.00699548i
$610$	−0.854570	+	0.717070i	−0.0346005	+	0.0290333i
$611$	−11.8439	+	20.5142i	−0.479153	+	0.829917i
$612$	9.37346	+	16.2353i	0.378899	+	0.656273i
$613$	−9.50686	−	16.4664i	−0.383979	−	0.665070i	0.607648	−	0.794206i	$-0.292113\pi$
$613$	−9.50686	−	16.4664i	−0.383979	−	0.665070i	−0.991627	+	0.129136i	$0.958780\pi$
$614$	8.02229	+	2.91987i	0.323753	+	0.117837i
$615$	−10.1600	−	5.86587i	−0.409690	−	0.236535i
$616$	9.67024	+	8.11430i	0.389625	+	0.326934i
$617$	−34.7550	+	12.6498i	−1.39918	+	0.509261i	−0.927935	−	0.372741i	$-0.878418\pi$
$617$	−34.7550	+	12.6498i	−1.39918	+	0.509261i	−0.471246	+	0.882002i	$0.656196\pi$
$618$	5.50387	+	0.970481i	0.221398	+	0.0390385i
$619$	−5.29648	−	30.0379i	−0.212884	−	1.20732i	−0.884541	−	0.466462i	$-0.845529\pi$
$619$	−5.29648	−	30.0379i	−0.212884	−	1.20732i	0.671658	−	0.740862i	$-0.265583\pi$
$620$	−1.44057			−0.0578547
$621$	−10.5628	−	1.86251i	−0.423872	−	0.0747401i
$622$	18.0128			0.722247
$623$	−5.67277	−	32.1719i	−0.227275	−	1.28894i
$624$	4.11334	−	4.90209i	0.164665	−	0.196241i
$625$	−13.1540	+	4.78768i	−0.526162	+	0.191507i
$626$	−13.1800	−	11.0594i	−0.526781	−	0.442021i
$627$			25.8151i			1.03096i
$628$	4.48545	+	1.63257i	0.178989	+	0.0651467i
$629$	24.1113	+	41.7620i	0.961380	+	1.66516i
$630$	1.61809	−	9.17664i	0.0644662	−	0.365606i
$631$	−6.86349	+	11.8879i	−0.273231	+	0.473251i	−0.969687	−	0.244349i	$-0.921426\pi$
$631$	−6.86349	+	11.8879i	−0.273231	+	0.473251i	0.696456	+	0.717599i	$0.254759\pi$
$632$	5.07011	−	4.25433i	0.201678	−	0.169228i
$633$	−3.16369	+	8.69216i	−0.125745	+	0.345482i
$634$	−4.32588	+	24.5333i	−0.171803	+	0.974342i
$635$	1.51279	−	8.57948i	0.0600334	−	0.340466i
$636$	0.798133	+	0.951178i	0.0316480	+	0.0377167i
$637$	−15.4973	+	13.0038i	−0.614026	+	0.515229i
$638$	0.290393	−	0.502975i	0.0114968	−	0.0199130i
$639$	7.05350	+	40.0024i	0.279032	+	1.58247i
$640$	−0.439693	−	0.761570i	−0.0173804	−	0.0301037i
$641$	−4.01367	−	1.46086i	−0.158530	−	0.0577004i	0.261536	−	0.965194i	$-0.415771\pi$
$641$	−4.01367	−	1.46086i	−0.158530	−	0.0577004i	−0.420066	+	0.907493i	$0.637993\pi$
$642$	3.42468	−	1.97724i	0.135161	−	0.0780354i
$643$	−16.1511	−	13.5524i	−0.636938	−	0.534454i	0.266138	−	0.963935i	$-0.414252\pi$
$643$	−16.1511	−	13.5524i	−0.636938	−	0.534454i	−0.903076	+	0.429481i	$0.858697\pi$
$644$	6.85117	−	2.49362i	0.269974	−	0.0982624i
$645$	−5.63816	−	15.4907i	−0.222002	−	0.609946i
$646$	−4.52523	−	25.6638i	−0.178043	−	1.00973i
$647$	−27.4023			−1.07730			−0.538648	−	0.842531i	$-0.681065\pi$
$647$	−27.4023			−1.07730			−0.538648	+	0.842531i	$0.681065\pi$
$648$	8.45723	−	3.07818i	0.332232	−	0.120922i
$649$	−24.9659			−0.979995
$650$	−2.71167	−	15.3786i	−0.106360	−	0.603199i
$651$	3.42767	+	9.41745i	0.134341	+	0.369099i
$652$	10.0706	−	3.66539i	0.394394	−	0.143548i
$653$	3.61540	+	3.03368i	0.141482	+	0.118717i	0.710782	−	0.703413i	$-0.248341\pi$
$653$	3.61540	+	3.03368i	0.141482	+	0.118717i	−0.569300	+	0.822130i	$0.692786\pi$
$654$	−15.6288	+	9.02330i	−0.611135	+	0.352839i
$655$	−7.46198	−	2.71594i	−0.291564	−	0.106121i
$656$	3.85117	+	6.67042i	0.150363	+	0.260436i
$657$	−6.56196	−	2.38836i	−0.256006	−	0.0931787i
$658$	11.3229	−	19.6119i	0.441414	−	0.764552i
$659$	16.1099	−	13.5178i	0.627554	−	0.526580i	−0.272614	−	0.962124i	$-0.587888\pi$
$659$	16.1099	−	13.5178i	0.627554	−	0.526580i	0.900168	+	0.435543i	$0.143444\pi$
$660$	−3.49912	−	4.17009i	−0.136203	−	0.162321i
$661$	4.40184	−	24.9641i	0.171212	−	0.970989i	−0.771215	−	0.636575i	$-0.780351\pi$
$661$	4.40184	−	24.9641i	0.171212	−	0.970989i	0.942426	−	0.334414i	$-0.108538\pi$
$662$	−1.53849	+	8.72518i	−0.0597949	+	0.339114i
$663$	−13.6769	+	37.5769i	−0.531166	+	1.45937i
$664$	3.41147	−	2.86257i	0.132391	−	0.111089i
$665$	−6.47653	+	11.2177i	−0.251149	+	0.435003i
$666$	21.7545	−	7.91799i	0.842969	−	0.306816i
$667$	−0.167718	−	0.290497i	−0.00649408	−	0.0112481i
$668$	12.1211	+	4.41171i	0.468979	+	0.170694i
$669$		−	32.9949i		−	1.27566i
$670$	2.42262	+	2.03282i	0.0935939	+	0.0785346i
$671$	4.26042	−	1.55067i	0.164472	−	0.0598628i
$672$	−3.93242	+	4.68647i	−0.151696	+	0.180785i
$673$	2.47090	+	14.0132i	0.0952464	+	0.540169i	0.994672	+	0.103094i	$0.0328743\pi$
$673$	2.47090	+	14.0132i	0.0952464	+	0.540169i	−0.899425	+	0.437075i	$0.856015\pi$
$674$	−21.0719			−0.811660
$675$	7.51161	−	20.6380i	0.289122	−	0.794356i
$676$	0.650015			0.0250006
$677$	8.07878	+	45.8170i	0.310493	+	1.76089i	0.596450	+	0.802650i	$0.296577\pi$
$677$	8.07878	+	45.8170i	0.310493	+	1.76089i	−0.285958	+	0.958242i	$0.592312\pi$
$678$	−18.9907	−	3.34857i	−0.729332	−	0.128601i
$679$	−37.4752	+	13.6399i	−1.43817	+	0.523450i
$680$	4.20961	+	3.53228i	0.161431	+	0.135457i
$681$	5.19166	+	2.99740i	0.198945	+	0.114861i
$682$	5.50165	+	2.00244i	0.210669	+	0.0766773i
$683$	5.10101	+	8.83522i	0.195185	+	0.338070i	0.946961	−	0.321348i	$-0.104136\pi$
$683$	5.10101	+	8.83522i	0.195185	+	0.338070i	−0.751776	+	0.659418i	$0.770803\pi$
$684$	−12.5107			−0.478360
$685$	0.891407	−	1.54396i	0.0340589	−	0.0589918i
$686$	−4.12449	+	3.46085i	−0.157474	+	0.132136i
$687$	49.3631	−	8.70404i	1.88332	−	0.332080i
$688$	−1.87939	+	10.6585i	−0.0716509	+	0.406352i
$689$	−0.459922	+	2.60835i	−0.0175216	+	0.0993701i
$690$	−3.09627	+	0.545955i	−0.117873	+	0.0207842i
$691$	−0.269915	+	0.226485i	−0.0102680	+	0.00861591i	−0.647907	−	0.761719i	$-0.724356\pi$
$691$	−0.269915	+	0.226485i	−0.0102680	+	0.00861591i	0.637639	+	0.770335i	$0.279911\pi$
$692$	−6.43629	+	11.1480i	−0.244671	+	0.423783i
$693$	−18.9354	+	32.7971i	−0.719297	+	1.24586i
$694$	11.0544	+	19.1467i	0.419618	+	0.726800i
$695$	0.136507	+	0.0496844i	0.00517800	+	0.00188464i
$696$	0.243756	+	0.140732i	0.00923954	+	0.00533445i
$697$	−36.8710	−	30.9384i	−1.39659	−	1.17188i
$698$	2.06670	−	0.752219i	0.0782259	−	0.0284719i
$699$	−11.3610	−	2.00324i	−0.429711	−	0.0757697i
$700$	2.59240	+	14.7022i	0.0979834	+	0.555691i
$701$	39.9358			1.50836			0.754178	−	0.656671i	$-0.228036\pi$
$701$	39.9358			1.50836			0.754178	+	0.656671i	$0.228036\pi$
$702$	16.6257	+	9.59883i	0.627495	+	0.362285i
$703$	−32.1813			−1.21374
$704$	0.620615	+	3.51968i	0.0233903	+	0.132653i
$705$	−6.27719	+	7.48086i	−0.236413	+	0.281746i
$706$	4.47178	−	1.62760i	0.168298	−	0.0612554i
$707$	−25.3653	−	21.2840i	−0.953960	−	0.800468i
$708$		−	12.0992i		−	0.454714i
$709$	46.2789	+	16.8441i	1.73804	+	0.632595i	0.999150	−	0.0412304i	$-0.0131278\pi$
$709$	46.2789	+	16.8441i	1.73804	+	0.632595i	0.738891	+	0.673825i	$0.235350\pi$
$710$	5.95336	+	10.3115i	0.223426	+	0.386985i
$711$	15.2103	+	12.7630i	0.570432	+	0.478649i
$712$	4.62449	−	8.00984i	0.173310	−	0.300182i
$713$	2.59034	−	2.17355i	0.0970089	−	0.0814001i
$714$	13.0753	−	35.9242i	0.489332	−	1.34443i
$715$	2.01636	−	11.4353i	0.0754075	−	0.427657i
$716$	−1.55644	+	8.82699i	−0.0581668	+	0.329880i
$717$	8.67159	+	10.3344i	0.323846	+	0.385945i
$718$	1.99613	−	1.67495i	0.0744949	−	0.0625086i
$719$	25.8050	−	44.6956i	0.962364	−	1.66686i	0.245828	−	0.969314i	$-0.420940\pi$
$719$	25.8050	−	44.6956i	0.962364	−	1.66686i	0.716536	−	0.697550i	$-0.245726\pi$
$720$	2.02094	−	1.69577i	0.0753162	−	0.0631978i
$721$	−5.69846	−	9.87003i	−0.212222	−	0.367579i
$722$	−1.51202	−	0.550331i	−0.0562716	−	0.0204812i
$723$	32.8423	−	18.9615i	1.22142	−	0.705186i
$724$	−1.52094	−	1.27622i	−0.0565255	−	0.0474305i
$725$	0.645430	−	0.234917i	0.0239707	−	0.00872461i
$726$	1.05051	+	2.88624i	0.0389880	+	0.107119i
$727$	−4.79932	−	27.2183i	−0.177997	−	1.00947i	−0.934628	−	0.355628i	$-0.884267\pi$
$727$	−4.79932	−	27.2183i	−0.177997	−	1.00947i	0.756631	−	0.653842i	$-0.226844\pi$
$728$	−13.0496			−0.483651
$729$	13.5000	+	23.3827i	0.500000	+	0.866025i
$730$	−2.04694			−0.0757607
$731$	−11.7442	−	66.6048i	−0.434376	−	2.46347i
$732$	0.751497	+	2.06472i	0.0277761	+	0.0763142i
$733$	−25.9072	+	9.42945i	−0.956904	+	0.348285i	−0.772820	−	0.634626i	$-0.781154\pi$
$733$	−25.9072	+	9.42945i	−0.956904	+	0.348285i	−0.184084	+	0.982910i	$0.558932\pi$
$734$	10.9042	+	9.14971i	0.402481	+	0.337722i
$735$	−7.22281	+	4.17009i	−0.266417	+	0.153816i
$736$	1.93969	+	0.705990i	0.0714980	+	0.0260232i
$737$	−6.42649	−	11.1310i	−0.236723	−	0.410016i
$738$	−17.7010	+	14.8529i	−0.651582	+	0.546743i
$739$	2.01320	−	3.48697i	0.0740569	−	0.128270i	−0.826619	−	0.562762i	$-0.809739\pi$
$739$	2.01320	−	3.48697i	0.0740569	−	0.128270i	0.900676	+	0.434492i	$0.143072\pi$
$740$	5.19846	−	4.36203i	0.191099	−	0.160351i
$741$	−17.1536	−	20.4429i	−0.630155	−	0.750989i
$742$	0.439693	−	2.49362i	0.0161416	−	0.0915437i
$743$	5.04979	−	28.6388i	0.185259	−	1.05066i	−0.740363	−	0.672207i	$-0.765347\pi$
$743$	5.04979	−	28.6388i	0.185259	−	1.05066i	0.925622	−	0.378449i	$-0.123542\pi$
$744$	−0.970437	+	2.66625i	−0.0355780	+	0.0977496i
$745$	3.90760	−	3.27887i	0.143164	−	0.120128i
$746$	−1.15405	+	1.99887i	−0.0422527	+	0.0731838i
$747$	10.2344	+	8.58770i	0.374458	+	0.314208i
$748$	−11.1668	−	19.3415i	−0.408300	−	0.707197i
$749$	−7.57785	−	2.75811i	−0.276889	−	0.100779i
$750$		−	14.0535i		−	0.513162i
$751$	31.1962	+	26.1768i	1.13837	+	0.955203i	0.999384	−	0.0350914i	$-0.0111722\pi$
$751$	31.1962	+	26.1768i	1.13837	+	0.955203i	0.138983	+	0.990295i	$0.455617\pi$
$752$	6.02481	−	2.19285i	0.219702	−	0.0799651i
$753$	−17.9078	+	21.3416i	−0.652595	+	0.777733i
$754$	0.104256	+	0.591264i	0.00379677	+	0.0215326i
$755$	−12.3550			−0.449646
$756$	−15.8944	−	9.17664i	−0.578074	−	0.333751i
$757$	32.9486			1.19754			0.598769	−	0.800922i	$-0.295657\pi$
$757$	32.9486			1.19754			0.598769	+	0.800922i	$0.295657\pi$
$758$	1.04664	+	5.93577i	0.0380156	+	0.215597i
$759$	12.5838	+	2.21886i	0.456762	+	0.0805395i
$760$	−3.44609	+	1.25427i	−0.125003	+	0.0454973i
$761$	−0.773318	−	0.648891i	−0.0280328	−	0.0235223i	0.628664	−	0.777677i	$-0.283602\pi$
$761$	−0.773318	−	0.648891i	−0.0280328	−	0.0235223i	−0.656696	+	0.754155i	$0.728047\pi$
$762$	−14.8601	−	8.57948i	−0.538324	−	0.310802i
$763$	34.5822	+	12.5869i	1.25196	+	0.455676i
$764$	−6.56077	−	11.3636i	−0.237360	−	0.411120i
$765$	−8.24288	+	14.2771i	−0.298022	+	0.516189i

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:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	54.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 - 0.984808i) q^{2} +(-0.592396 - 1.62760i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.673648 - 0.565258i) q^{5} +(-1.50000 + 0.866025i) q^{6} +(3.31908 + 1.20805i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.29813 + 1.92836i) q^{9} +O(q^{10})\)	\(q+(-0.173648 - 0.984808i) q^{2} +(-0.592396 - 1.62760i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.673648 - 0.565258i) q^{5} +(-1.50000 + 0.866025i) q^{6} +(3.31908 + 1.20805i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.29813 + 1.92836i) q^{9} +(-0.439693 + 0.761570i) q^{10} +(2.73783 - 2.29731i) q^{11} +(1.11334 + 1.32683i) q^{12} +(-0.641559 + 3.63846i) q^{13} +(0.613341 - 3.47843i) q^{14} +(-0.520945 + 1.43128i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-3.12449 + 5.41177i) q^{17} +(2.29813 + 1.92836i) q^{18} +(-2.08512 - 3.61154i) q^{19} +(0.826352 + 0.300767i) q^{20} -6.11776i q^{21} +(-2.73783 - 2.29731i) q^{22} +(-1.93969 + 0.705990i) q^{23} +(1.11334 - 1.32683i) q^{24} +(-0.733956 - 4.16247i) q^{25} +3.69459 q^{26} +(4.50000 + 2.59808i) q^{27} -3.53209 q^{28} +(0.0282185 + 0.160035i) q^{29} +(1.50000 + 0.264490i) q^{30} +(-1.53936 + 0.560282i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(-5.36097 - 3.09516i) q^{33} +(5.87211 + 2.13727i) q^{34} +(-1.55303 - 2.68993i) q^{35} +(1.50000 - 2.59808i) q^{36} +(3.85844 - 6.68302i) q^{37} +(-3.19459 + 2.68058i) q^{38} +(6.30200 - 1.11121i) q^{39} +(0.152704 - 0.866025i) q^{40} +(-1.33750 + 7.58532i) q^{41} +(-6.02481 + 1.06234i) q^{42} +(-8.29086 + 6.95686i) q^{43} +(-1.78699 + 3.09516i) q^{44} +2.63816 q^{45} +(1.03209 + 1.78763i) q^{46} +(6.02481 + 2.19285i) q^{47} +(-1.50000 - 0.866025i) q^{48} +(4.19459 + 3.51968i) q^{49} +(-3.97178 + 1.44561i) q^{50} +(10.6591 + 1.87949i) q^{51} +(-0.641559 - 3.63846i) q^{52} +0.716881 q^{53} +(1.77719 - 4.88279i) q^{54} -3.14290 q^{55} +(0.613341 + 3.47843i) q^{56} +(-4.64290 + 5.53320i) q^{57} +(0.152704 - 0.0555796i) q^{58} +(-5.35117 - 4.49016i) q^{59} -1.52314i q^{60} +(1.19207 + 0.433877i) q^{61} +(0.819078 + 1.41868i) q^{62} +(-9.95723 + 3.62414i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(2.48886 - 2.08840i) q^{65} +(-2.11721 + 5.81699i) q^{66} +(0.624485 - 3.54163i) q^{67} +(1.08512 - 6.15403i) q^{68} +(2.29813 + 2.73881i) q^{69} +(-2.37939 + 1.99654i) q^{70} +(6.76991 - 11.7258i) q^{71} +(-2.81908 - 1.02606i) q^{72} +(1.16385 + 2.01584i) q^{73} +(-7.25150 - 2.63933i) q^{74} +(-6.34002 + 3.66041i) q^{75} +(3.19459 + 2.68058i) q^{76} +(11.8623 - 4.31753i) q^{77} +(-2.18866 - 6.01330i) q^{78} +(-1.14930 - 6.51800i) q^{79} -0.879385 q^{80} +(1.56283 - 8.86327i) q^{81} +7.70233 q^{82} +(-0.773318 - 4.38571i) q^{83} +(2.09240 + 5.74881i) q^{84} +(5.16385 - 1.87949i) q^{85} +(8.29086 + 6.95686i) q^{86} +(0.243756 - 0.140732i) q^{87} +(3.35844 + 1.22237i) q^{88} +(-4.62449 - 8.00984i) q^{89} +(-0.458111 - 2.59808i) q^{90} +(-6.52481 + 11.3013i) q^{91} +(1.58125 - 1.32683i) q^{92} +(1.82383 + 2.17355i) q^{93} +(1.11334 - 6.31407i) q^{94} +(-0.636812 + 3.61154i) q^{95} +(-0.592396 + 1.62760i) q^{96} +(-8.64930 + 7.25762i) q^{97} +(2.73783 - 4.74205i) q^{98} +(-1.86184 + 10.5590i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{5} - 9 q^{6} + 3 q^{7} + 3 q^{8}+O(q^{10}) \) 6 * q - 3 * q^5 - 9 * q^6 + 3 * q^7 + 3 * q^8	\( 6 q - 3 q^{5} - 9 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{10} - 3 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{17} + 9 q^{19} + 6 q^{20} + 3 q^{22} - 6 q^{23} - 9 q^{25} + 18 q^{26} + 27 q^{27} - 12 q^{28} + 15 q^{29} + 9 q^{30} - 18 q^{31} - 9 q^{33} + 6 q^{34} + 3 q^{35} + 9 q^{36} + 15 q^{37} - 15 q^{38} + 3 q^{40} - 3 q^{41} - 9 q^{42} - 18 q^{43} - 3 q^{44} - 18 q^{45} - 3 q^{46} + 9 q^{47} - 9 q^{48} + 21 q^{49} - 9 q^{50} + 27 q^{51} - 12 q^{52} - 12 q^{53} - 18 q^{55} - 3 q^{56} - 27 q^{57} + 3 q^{58} - 6 q^{59} + 18 q^{61} - 12 q^{62} - 9 q^{63} - 3 q^{64} + 21 q^{65} + 18 q^{66} - 9 q^{67} - 15 q^{68} - 3 q^{70} + 12 q^{71} + 3 q^{73} - 3 q^{74} - 18 q^{75} + 15 q^{76} + 39 q^{77} + 18 q^{78} + 33 q^{79} + 6 q^{80} - 6 q^{82} - 18 q^{83} + 9 q^{84} + 27 q^{85} + 18 q^{86} + 9 q^{87} + 12 q^{88} - 15 q^{89} - 9 q^{90} - 12 q^{91} + 12 q^{92} + 27 q^{93} + 21 q^{95} - 12 q^{97} - 3 q^{98} - 45 q^{99}+O(q^{100}) \) 6 * q - 3 * q^5 - 9 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^10 - 3 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^17 + 9 * q^19 + 6 * q^20 + 3 * q^22 - 6 * q^23 - 9 * q^25 + 18 * q^26 + 27 * q^27 - 12 * q^28 + 15 * q^29 + 9 * q^30 - 18 * q^31 - 9 * q^33 + 6 * q^34 + 3 * q^35 + 9 * q^36 + 15 * q^37 - 15 * q^38 + 3 * q^40 - 3 * q^41 - 9 * q^42 - 18 * q^43 - 3 * q^44 - 18 * q^45 - 3 * q^46 + 9 * q^47 - 9 * q^48 + 21 * q^49 - 9 * q^50 + 27 * q^51 - 12 * q^52 - 12 * q^53 - 18 * q^55 - 3 * q^56 - 27 * q^57 + 3 * q^58 - 6 * q^59 + 18 * q^61 - 12 * q^62 - 9 * q^63 - 3 * q^64 + 21 * q^65 + 18 * q^66 - 9 * q^67 - 15 * q^68 - 3 * q^70 + 12 * q^71 + 3 * q^73 - 3 * q^74 - 18 * q^75 + 15 * q^76 + 39 * q^77 + 18 * q^78 + 33 * q^79 + 6 * q^80 - 6 * q^82 - 18 * q^83 + 9 * q^84 + 27 * q^85 + 18 * q^86 + 9 * q^87 + 12 * q^88 - 15 * q^89 - 9 * q^90 - 12 * q^91 + 12 * q^92 + 27 * q^93 + 21 * q^95 - 12 * q^97 - 3 * q^98 - 45 * q^99

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