LMFDB - Embedded newform 206.2.c.a.159.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [206,2,Mod(149,206)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(206, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("206.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 206 = 2 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	206.c (of order $3$, degree $2$, 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:	$1.64491828164$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			159.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	206.159
Dual form			206.2.c.a.149.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +2.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.00000 + 1.73205i) q^{5} +(1.00000 - 1.73205i) q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +2.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.00000 + 1.73205i) q^{5} +(1.00000 - 1.73205i) q^{6} -1.00000 q^{8} +1.00000 q^{9} +2.00000 q^{10} +(-1.00000 - 1.73205i) q^{12} -2.00000 q^{13} +(2.00000 + 3.46410i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.50000 - 4.33013i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-1.00000 + 1.73205i) q^{19} +(1.00000 - 1.73205i) q^{20} -3.00000 q^{23} -2.00000 q^{24} +(0.500000 - 0.866025i) q^{25} +(-1.00000 + 1.73205i) q^{26} -4.00000 q^{27} +4.00000 q^{30} +5.00000 q^{31} +(0.500000 + 0.866025i) q^{32} -5.00000 q^{34} +(-0.500000 - 0.866025i) q^{36} +2.00000 q^{37} +(1.00000 + 1.73205i) q^{38} -4.00000 q^{39} +(-1.00000 - 1.73205i) q^{40} +(-2.50000 + 4.33013i) q^{41} +(-1.00000 + 1.73205i) q^{43} +(1.00000 + 1.73205i) q^{45} +(-1.50000 + 2.59808i) q^{46} +(2.50000 + 4.33013i) q^{47} +(-1.00000 + 1.73205i) q^{48} +(3.50000 - 6.06218i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-5.00000 - 8.66025i) q^{51} +(1.00000 + 1.73205i) q^{52} +(6.00000 + 10.3923i) q^{53} +(-2.00000 + 3.46410i) q^{54} +(-2.00000 + 3.46410i) q^{57} +(-3.00000 + 5.19615i) q^{59} +(2.00000 - 3.46410i) q^{60} -2.00000 q^{61} +(2.50000 - 4.33013i) q^{62} +1.00000 q^{64} +(-2.00000 - 3.46410i) q^{65} +(-5.00000 - 8.66025i) q^{67} +(-2.50000 + 4.33013i) q^{68} -6.00000 q^{69} +(1.50000 + 2.59808i) q^{71} -1.00000 q^{72} +7.00000 q^{73} +(1.00000 - 1.73205i) q^{74} +(1.00000 - 1.73205i) q^{75} +2.00000 q^{76} +(-2.00000 + 3.46410i) q^{78} -3.00000 q^{79} -2.00000 q^{80} -11.0000 q^{81} +(2.50000 + 4.33013i) q^{82} +(-7.00000 + 12.1244i) q^{83} +(5.00000 - 8.66025i) q^{85} +(1.00000 + 1.73205i) q^{86} +11.0000 q^{89} +2.00000 q^{90} +(1.50000 + 2.59808i) q^{92} +10.0000 q^{93} +5.00000 q^{94} -4.00000 q^{95} +(1.00000 + 1.73205i) q^{96} +(9.50000 - 16.4545i) q^{97} +(-3.50000 - 6.06218i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + 4 q^{3} - q^{4} + 2 q^{5} + 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + q^2 + 4 * q^3 - q^4 + 2 * q^5 + 2 * q^6 - 2 * q^8 + 2 * q^9	$ 2 q + q^{2} + 4 q^{3} - q^{4} + 2 q^{5} + 2 q^{6} - 2 q^{8} + 2 q^{9} + 4 q^{10} - 2 q^{12} - 4 q^{13} + 4 q^{15} - q^{16} - 5 q^{17} + q^{18} - 2 q^{19} + 2 q^{20} - 6 q^{23} - 4 q^{24} + q^{25} - 2 q^{26} - 8 q^{27} + 8 q^{30} + 10 q^{31} + q^{32} - 10 q^{34} - q^{36} + 4 q^{37} + 2 q^{38} - 8 q^{39} - 2 q^{40} - 5 q^{41} - 2 q^{43} + 2 q^{45} - 3 q^{46} + 5 q^{47} - 2 q^{48} + 7 q^{49} - q^{50} - 10 q^{51} + 2 q^{52} + 12 q^{53} - 4 q^{54} - 4 q^{57} - 6 q^{59} + 4 q^{60} - 4 q^{61} + 5 q^{62} + 2 q^{64} - 4 q^{65} - 10 q^{67} - 5 q^{68} - 12 q^{69} + 3 q^{71} - 2 q^{72} + 14 q^{73} + 2 q^{74} + 2 q^{75} + 4 q^{76} - 4 q^{78} - 6 q^{79} - 4 q^{80} - 22 q^{81} + 5 q^{82} - 14 q^{83} + 10 q^{85} + 2 q^{86} + 22 q^{89} + 4 q^{90} + 3 q^{92} + 20 q^{93} + 10 q^{94} - 8 q^{95} + 2 q^{96} + 19 q^{97} - 7 q^{98}+O(q^{100}) $ 2 * q + q^2 + 4 * q^3 - q^4 + 2 * q^5 + 2 * q^6 - 2 * q^8 + 2 * q^9 + 4 * q^10 - 2 * q^12 - 4 * q^13 + 4 * q^15 - q^16 - 5 * q^17 + q^18 - 2 * q^19 + 2 * q^20 - 6 * q^23 - 4 * q^24 + q^25 - 2 * q^26 - 8 * q^27 + 8 * q^30 + 10 * q^31 + q^32 - 10 * q^34 - q^36 + 4 * q^37 + 2 * q^38 - 8 * q^39 - 2 * q^40 - 5 * q^41 - 2 * q^43 + 2 * q^45 - 3 * q^46 + 5 * q^47 - 2 * q^48 + 7 * q^49 - q^50 - 10 * q^51 + 2 * q^52 + 12 * q^53 - 4 * q^54 - 4 * q^57 - 6 * q^59 + 4 * q^60 - 4 * q^61 + 5 * q^62 + 2 * q^64 - 4 * q^65 - 10 * q^67 - 5 * q^68 - 12 * q^69 + 3 * q^71 - 2 * q^72 + 14 * q^73 + 2 * q^74 + 2 * q^75 + 4 * q^76 - 4 * q^78 - 6 * q^79 - 4 * q^80 - 22 * q^81 + 5 * q^82 - 14 * q^83 + 10 * q^85 + 2 * q^86 + 22 * q^89 + 4 * q^90 + 3 * q^92 + 20 * q^93 + 10 * q^94 - 8 * q^95 + 2 * q^96 + 19 * q^97 - 7 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/206\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	2.00000			1.15470			0.577350	−	0.816497i	$-0.304087\pi$
$3$	2.00000			1.15470			0.577350	+	0.816497i	$0.304087\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.00000	+	1.73205i	0.447214	+	0.774597i	0.998203	−	0.0599153i	$-0.0190830\pi$
$5$	1.00000	+	1.73205i	0.447214	+	0.774597i	−0.550990	+	0.834512i	$0.685750\pi$
$6$	1.00000	−	1.73205i	0.408248	−	0.707107i
$7$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$7$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$8$	−1.00000			−0.353553
$9$	1.00000			0.333333
$10$	2.00000			0.632456
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$	−1.00000	−	1.73205i	−0.288675	−	0.500000i
$13$	−2.00000			−0.554700			−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000			−0.554700			−0.277350	+	0.960769i	$0.589456\pi$
$14$		0			0
$15$	2.00000	+	3.46410i	0.516398	+	0.894427i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.50000	−	4.33013i	−0.606339	−	1.05021i	−0.991838	−	0.127502i	$-0.959304\pi$
$17$	−2.50000	−	4.33013i	−0.606339	−	1.05021i	0.385499	−	0.922708i	$-0.374029\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	−0.957635	−	0.287984i	$-0.907015\pi$
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	0.728219	+	0.685344i	$0.240348\pi$
$20$	1.00000	−	1.73205i	0.223607	−	0.387298i
$21$		0			0
$22$		0			0
$23$	−3.00000			−0.625543			−0.312772	−	0.949828i	$-0.601257\pi$
$23$	−3.00000			−0.625543			−0.312772	+	0.949828i	$0.601257\pi$
$24$	−2.00000			−0.408248
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−1.00000	+	1.73205i	−0.196116	+	0.339683i
$27$	−4.00000			−0.769800
$28$		0			0
$29$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$29$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$30$	4.00000			0.730297
$31$	5.00000			0.898027			0.449013	−	0.893525i	$-0.351776\pi$
$31$	5.00000			0.898027			0.449013	+	0.893525i	$0.351776\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	−5.00000			−0.857493
$35$		0			0
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$	1.00000	+	1.73205i	0.162221	+	0.280976i
$39$	−4.00000			−0.640513
$40$	−1.00000	−	1.73205i	−0.158114	−	0.273861i
$41$	−2.50000	+	4.33013i	−0.390434	+	0.676252i	−0.992507	−	0.122189i	$-0.961009\pi$
$41$	−2.50000	+	4.33013i	−0.390434	+	0.676252i	0.602072	+	0.798441i	$0.294342\pi$
$42$		0			0
$43$	−1.00000	+	1.73205i	−0.152499	+	0.264135i	−0.932145	−	0.362084i	$-0.882065\pi$
$43$	−1.00000	+	1.73205i	−0.152499	+	0.264135i	0.779647	+	0.626219i	$0.215399\pi$
$44$		0			0
$45$	1.00000	+	1.73205i	0.149071	+	0.258199i
$46$	−1.50000	+	2.59808i	−0.221163	+	0.383065i
$47$	2.50000	+	4.33013i	0.364662	+	0.631614i	0.988722	−	0.149763i	$-0.0478510\pi$
$47$	2.50000	+	4.33013i	0.364662	+	0.631614i	−0.624059	+	0.781377i	$0.714518\pi$
$48$	−1.00000	+	1.73205i	−0.144338	+	0.250000i
$49$	3.50000	−	6.06218i	0.500000	−	0.866025i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	−5.00000	−	8.66025i	−0.700140	−	1.21268i
$52$	1.00000	+	1.73205i	0.138675	+	0.240192i
$53$	6.00000	+	10.3923i	0.824163	+	1.42749i	0.902557	+	0.430570i	$0.141688\pi$
$53$	6.00000	+	10.3923i	0.824163	+	1.42749i	−0.0783936	+	0.996922i	$0.524979\pi$
$54$	−2.00000	+	3.46410i	−0.272166	+	0.471405i
$55$		0			0
$56$		0			0
$57$	−2.00000	+	3.46410i	−0.264906	+	0.458831i
$58$		0			0
$59$	−3.00000	+	5.19615i	−0.390567	+	0.676481i	−0.992524	−	0.122047i	$-0.961054\pi$
$59$	−3.00000	+	5.19615i	−0.390567	+	0.676481i	0.601958	+	0.798528i	$0.294388\pi$
$60$	2.00000	−	3.46410i	0.258199	−	0.447214i
$61$	−2.00000			−0.256074			−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000			−0.256074			−0.128037	+	0.991769i	$0.540868\pi$
$62$	2.50000	−	4.33013i	0.317500	−	0.549927i
$63$		0			0
$64$	1.00000			0.125000
$65$	−2.00000	−	3.46410i	−0.248069	−	0.429669i
$66$		0			0
$67$	−5.00000	−	8.66025i	−0.610847	−	1.05802i	−0.991098	−	0.133135i	$-0.957496\pi$
$67$	−5.00000	−	8.66025i	−0.610847	−	1.05802i	0.380251	−	0.924883i	$-0.375838\pi$
$68$	−2.50000	+	4.33013i	−0.303170	+	0.525105i
$69$	−6.00000			−0.722315
$70$		0			0
$71$	1.50000	+	2.59808i	0.178017	+	0.308335i	0.941201	−	0.337846i	$-0.109698\pi$
$71$	1.50000	+	2.59808i	0.178017	+	0.308335i	−0.763184	+	0.646181i	$0.776365\pi$
$72$	−1.00000			−0.117851
$73$	7.00000			0.819288			0.409644	−	0.912245i	$-0.365653\pi$
$73$	7.00000			0.819288			0.409644	+	0.912245i	$0.365653\pi$
$74$	1.00000	−	1.73205i	0.116248	−	0.201347i
$75$	1.00000	−	1.73205i	0.115470	−	0.200000i
$76$	2.00000			0.229416
$77$		0			0
$78$	−2.00000	+	3.46410i	−0.226455	+	0.392232i
$79$	−3.00000			−0.337526			−0.168763	−	0.985657i	$-0.553977\pi$
$79$	−3.00000			−0.337526			−0.168763	+	0.985657i	$0.553977\pi$
$80$	−2.00000			−0.223607
$81$	−11.0000			−1.22222
$82$	2.50000	+	4.33013i	0.276079	+	0.478183i
$83$	−7.00000	+	12.1244i	−0.768350	+	1.33082i	0.170107	+	0.985426i	$0.445589\pi$
$83$	−7.00000	+	12.1244i	−0.768350	+	1.33082i	−0.938457	+	0.345395i	$0.887745\pi$
$84$		0			0
$85$	5.00000	−	8.66025i	0.542326	−	0.939336i
$86$	1.00000	+	1.73205i	0.107833	+	0.186772i
$87$		0			0
$88$		0			0
$89$	11.0000			1.16600			0.582999	−	0.812473i	$-0.301879\pi$
$89$	11.0000			1.16600			0.582999	+	0.812473i	$0.301879\pi$
$90$	2.00000			0.210819
$91$		0			0
$92$	1.50000	+	2.59808i	0.156386	+	0.270868i
$93$	10.0000			1.03695
$94$	5.00000			0.515711
$95$	−4.00000			−0.410391
$96$	1.00000	+	1.73205i	0.102062	+	0.176777i
$97$	9.50000	−	16.4545i	0.964579	−	1.67070i	0.253837	−	0.967247i	$-0.418307\pi$
$97$	9.50000	−	16.4545i	0.964579	−	1.67070i	0.710742	−	0.703452i	$-0.248359\pi$
$98$	−3.50000	−	6.06218i	−0.353553	−	0.612372i
$99$		0			0
$100$	−1.00000			−0.100000
$101$	9.00000	−	15.5885i	0.895533	−	1.55111i	0.0623905	−	0.998052i	$-0.480128\pi$
$101$	9.00000	−	15.5885i	0.895533	−	1.55111i	0.833143	−	0.553058i	$-0.186539\pi$
$102$	−10.0000			−0.990148
$103$	10.0000	−	1.73205i	0.985329	−	0.170664i
$103$	10.0000	−	1.73205i	0.985329	−	0.170664i
$104$	2.00000			0.196116
$105$		0			0
$106$	12.0000			1.16554
$107$	−7.00000	−	12.1244i	−0.676716	−	1.17211i	−0.975964	−	0.217931i	$-0.930069\pi$
$107$	−7.00000	−	12.1244i	−0.676716	−	1.17211i	0.299249	−	0.954175i	$-0.403264\pi$
$108$	2.00000	+	3.46410i	0.192450	+	0.333333i
$109$	5.00000	−	8.66025i	0.478913	−	0.829502i	−0.520794	−	0.853682i	$-0.674364\pi$
$109$	5.00000	−	8.66025i	0.478913	−	0.829502i	0.999708	+	0.0241802i	$0.00769755\pi$
$110$		0			0
$111$	4.00000			0.379663
$112$		0			0
$113$	−5.00000			−0.470360			−0.235180	−	0.971952i	$-0.575568\pi$
$113$	−5.00000			−0.470360			−0.235180	+	0.971952i	$0.575568\pi$
$114$	2.00000	+	3.46410i	0.187317	+	0.324443i
$115$	−3.00000	−	5.19615i	−0.279751	−	0.484544i
$116$		0			0
$117$	−2.00000			−0.184900
$118$	3.00000	+	5.19615i	0.276172	+	0.478345i
$119$		0			0
$120$	−2.00000	−	3.46410i	−0.182574	−	0.316228i
$121$	5.50000	−	9.52628i	0.500000	−	0.866025i
$122$	−1.00000	+	1.73205i	−0.0905357	+	0.156813i
$123$	−5.00000	+	8.66025i	−0.450835	+	0.780869i
$124$	−2.50000	−	4.33013i	−0.224507	−	0.388857i
$125$	12.0000			1.07331
$126$		0			0
$127$	1.00000			0.0887357			0.0443678	−	0.999015i	$-0.485873\pi$
$127$	1.00000			0.0887357			0.0443678	+	0.999015i	$0.485873\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−2.00000	+	3.46410i	−0.176090	+	0.304997i
$130$	−4.00000			−0.350823
$131$	−8.00000	+	13.8564i	−0.698963	+	1.21064i	0.269863	+	0.962899i	$0.413022\pi$
$131$	−8.00000	+	13.8564i	−0.698963	+	1.21064i	−0.968826	+	0.247741i	$0.920312\pi$
$132$		0			0
$133$		0			0
$134$	−10.0000			−0.863868
$135$	−4.00000	−	6.92820i	−0.344265	−	0.596285i
$136$	2.50000	+	4.33013i	0.214373	+	0.371305i
$137$	−3.00000			−0.256307			−0.128154	−	0.991754i	$-0.540905\pi$
$137$	−3.00000			−0.256307			−0.128154	+	0.991754i	$0.540905\pi$
$138$	−3.00000	+	5.19615i	−0.255377	+	0.442326i
$139$	−2.00000	−	3.46410i	−0.169638	−	0.293821i	0.768655	−	0.639664i	$-0.220926\pi$
$139$	−2.00000	−	3.46410i	−0.169638	−	0.293821i	−0.938293	+	0.345843i	$0.887593\pi$
$140$		0			0
$141$	5.00000	+	8.66025i	0.421076	+	0.729325i
$142$	3.00000			0.251754
$143$		0			0
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$		0			0
$146$	3.50000	−	6.06218i	0.289662	−	0.501709i
$147$	7.00000	−	12.1244i	0.577350	−	1.00000i
$148$	−1.00000	−	1.73205i	−0.0821995	−	0.142374i
$149$	−1.00000	+	1.73205i	−0.0819232	+	0.141895i	−0.904076	−	0.427372i	$-0.859440\pi$
$149$	−1.00000	+	1.73205i	−0.0819232	+	0.141895i	0.822153	+	0.569267i	$0.192773\pi$
$150$	−1.00000	−	1.73205i	−0.0816497	−	0.141421i
$151$	−1.50000	+	2.59808i	−0.122068	+	0.211428i	−0.920583	−	0.390547i	$-0.872286\pi$
$151$	−1.50000	+	2.59808i	−0.122068	+	0.211428i	0.798515	+	0.601975i	$0.205619\pi$
$152$	1.00000	−	1.73205i	0.0811107	−	0.140488i
$153$	−2.50000	−	4.33013i	−0.202113	−	0.350070i
$154$		0			0
$155$	5.00000	+	8.66025i	0.401610	+	0.695608i
$156$	2.00000	+	3.46410i	0.160128	+	0.277350i
$157$	−9.00000	+	15.5885i	−0.718278	+	1.24409i	0.243403	+	0.969925i	$0.421736\pi$
$157$	−9.00000	+	15.5885i	−0.718278	+	1.24409i	−0.961681	+	0.274169i	$0.911597\pi$
$158$	−1.50000	+	2.59808i	−0.119334	+	0.206692i
$159$	12.0000	+	20.7846i	0.951662	+	1.64833i
$160$	−1.00000	+	1.73205i	−0.0790569	+	0.136931i
$161$		0			0
$162$	−5.50000	+	9.52628i	−0.432121	+	0.748455i
$163$	−3.00000	+	5.19615i	−0.234978	+	0.406994i	−0.959266	−	0.282503i	$-0.908835\pi$
$163$	−3.00000	+	5.19615i	−0.234978	+	0.406994i	0.724288	+	0.689497i	$0.242169\pi$
$164$	5.00000			0.390434
$165$		0			0
$166$	7.00000	+	12.1244i	0.543305	+	0.941033i
$167$	−13.0000			−1.00597			−0.502985	−	0.864295i	$-0.667765\pi$
$167$	−13.0000			−1.00597			−0.502985	+	0.864295i	$0.667765\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$	−5.00000	−	8.66025i	−0.383482	−	0.664211i
$171$	−1.00000	+	1.73205i	−0.0764719	+	0.132453i
$172$	2.00000			0.152499
$173$	5.00000	+	8.66025i	0.380143	+	0.658427i	0.991082	−	0.133250i	$-0.0425415\pi$
$173$	5.00000	+	8.66025i	0.380143	+	0.658427i	−0.610939	+	0.791677i	$0.709208\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−6.00000	+	10.3923i	−0.450988	+	0.781133i
$178$	5.50000	−	9.52628i	0.412242	−	0.714025i
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$	1.00000	−	1.73205i	0.0745356	−	0.129099i
$181$	2.00000	−	3.46410i	0.148659	−	0.257485i	−0.782073	−	0.623187i	$-0.785838\pi$
$181$	2.00000	−	3.46410i	0.148659	−	0.257485i	0.930732	+	0.365702i	$0.119171\pi$
$182$		0			0
$183$	−4.00000			−0.295689
$184$	3.00000			0.221163
$185$	2.00000	+	3.46410i	0.147043	+	0.254686i
$186$	5.00000	−	8.66025i	0.366618	−	0.635001i
$187$		0			0
$188$	2.50000	−	4.33013i	0.182331	−	0.315807i
$189$		0			0
$190$	−2.00000	+	3.46410i	−0.145095	+	0.251312i
$191$	−6.00000	−	10.3923i	−0.434145	−	0.751961i	0.563081	−	0.826402i	$-0.309616\pi$
$191$	−6.00000	−	10.3923i	−0.434145	−	0.751961i	−0.997225	+	0.0744412i	$0.976283\pi$
$192$	2.00000			0.144338
$193$	−2.00000			−0.143963			−0.0719816	−	0.997406i	$-0.522932\pi$
$193$	−2.00000			−0.143963			−0.0719816	+	0.997406i	$0.522932\pi$
$194$	−9.50000	−	16.4545i	−0.682060	−	1.18136i
$195$	−4.00000	−	6.92820i	−0.286446	−	0.496139i
$196$	−7.00000			−0.500000
$197$	−8.00000			−0.569976			−0.284988	−	0.958531i	$-0.591990\pi$
$197$	−8.00000			−0.569976			−0.284988	+	0.958531i	$0.591990\pi$
$198$		0			0
$199$	11.5000	+	19.9186i	0.815213	+	1.41199i	0.909175	+	0.416415i	$0.136714\pi$
$199$	11.5000	+	19.9186i	0.815213	+	1.41199i	−0.0939612	+	0.995576i	$0.529953\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	−10.0000	−	17.3205i	−0.705346	−	1.22169i
$202$	−9.00000	−	15.5885i	−0.633238	−	1.09680i
$203$		0			0
$204$	−5.00000	+	8.66025i	−0.350070	+	0.606339i
$205$	−10.0000			−0.698430
$206$	3.50000	−	9.52628i	0.243857	−	0.663727i
$207$	−3.00000			−0.208514
$208$	1.00000	−	1.73205i	0.0693375	−	0.120096i
$209$		0			0
$210$		0			0
$211$	8.00000	+	13.8564i	0.550743	+	0.953914i	0.998221	+	0.0596196i	$0.0189888\pi$
$211$	8.00000	+	13.8564i	0.550743	+	0.953914i	−0.447478	+	0.894295i	$0.647678\pi$
$212$	6.00000	−	10.3923i	0.412082	−	0.713746i
$213$	3.00000	+	5.19615i	0.205557	+	0.356034i
$214$	−14.0000			−0.957020
$215$	−4.00000			−0.272798
$216$	4.00000			0.272166
$217$		0			0
$218$	−5.00000	−	8.66025i	−0.338643	−	0.586546i
$219$	14.0000			0.946032
$220$		0			0
$221$	5.00000	+	8.66025i	0.336336	+	0.582552i
$222$	2.00000	−	3.46410i	0.134231	−	0.232495i
$223$	4.50000	+	7.79423i	0.301342	+	0.521940i	0.976440	−	0.215788i	$-0.0692320\pi$
$223$	4.50000	+	7.79423i	0.301342	+	0.521940i	−0.675098	+	0.737728i	$0.735899\pi$
$224$		0			0
$225$	0.500000	−	0.866025i	0.0333333	−	0.0577350i
$226$	−2.50000	+	4.33013i	−0.166298	+	0.288036i
$227$	−12.0000	−	20.7846i	−0.796468	−	1.37952i	−0.921903	−	0.387421i	$-0.873366\pi$
$227$	−12.0000	−	20.7846i	−0.796468	−	1.37952i	0.125435	−	0.992102i	$-0.459967\pi$
$228$	4.00000			0.264906
$229$	4.00000			0.264327			0.132164	−	0.991228i	$-0.457808\pi$
$229$	4.00000			0.264327			0.132164	+	0.991228i	$0.457808\pi$
$230$	−6.00000			−0.395628
$231$		0			0
$232$		0			0
$233$	−18.0000			−1.17922			−0.589610	−	0.807688i	$-0.700718\pi$
$233$	−18.0000			−1.17922			−0.589610	+	0.807688i	$0.700718\pi$
$234$	−1.00000	+	1.73205i	−0.0653720	+	0.113228i
$235$	−5.00000	+	8.66025i	−0.326164	+	0.564933i
$236$	6.00000			0.390567
$237$	−6.00000			−0.389742
$238$		0			0
$239$	9.50000	+	16.4545i	0.614504	+	1.06435i	0.990471	+	0.137719i	$0.0439771\pi$
$239$	9.50000	+	16.4545i	0.614504	+	1.06435i	−0.375967	+	0.926633i	$0.622690\pi$
$240$	−4.00000			−0.258199
$241$	−1.00000	+	1.73205i	−0.0644157	+	0.111571i	−0.896435	−	0.443176i	$-0.853852\pi$
$241$	−1.00000	+	1.73205i	−0.0644157	+	0.111571i	0.832019	+	0.554747i	$0.187185\pi$
$242$	−5.50000	−	9.52628i	−0.353553	−	0.612372i
$243$	−10.0000			−0.641500
$244$	1.00000	+	1.73205i	0.0640184	+	0.110883i
$245$	14.0000			0.894427
$246$	5.00000	+	8.66025i	0.318788	+	0.552158i
$247$	2.00000	−	3.46410i	0.127257	−	0.220416i
$248$	−5.00000			−0.317500
$249$	−14.0000	+	24.2487i	−0.887214	+	1.53670i
$250$	6.00000	−	10.3923i	0.379473	−	0.657267i
$251$	8.00000	+	13.8564i	0.504956	+	0.874609i	0.999984	+	0.00573163i	$0.00182444\pi$
$251$	8.00000	+	13.8564i	0.504956	+	0.874609i	−0.495028	+	0.868877i	$0.664842\pi$
$252$		0			0
$253$		0			0
$254$	0.500000	−	0.866025i	0.0313728	−	0.0543393i
$255$	10.0000	−	17.3205i	0.626224	−	1.08465i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−7.50000	−	12.9904i	−0.467837	−	0.810318i	0.531487	−	0.847066i	$-0.321633\pi$
$257$	−7.50000	−	12.9904i	−0.467837	−	0.810318i	−0.999325	+	0.0367485i	$0.988300\pi$
$258$	2.00000	+	3.46410i	0.124515	+	0.215666i
$259$		0			0
$260$	−2.00000	+	3.46410i	−0.124035	+	0.214834i
$261$		0			0
$262$	8.00000	+	13.8564i	0.494242	+	0.856052i
$263$	4.50000	−	7.79423i	0.277482	−	0.480613i	−0.693276	−	0.720672i	$-0.743833\pi$
$263$	4.50000	−	7.79423i	0.277482	−	0.480613i	0.970758	+	0.240059i	$0.0771668\pi$
$264$		0			0
$265$	−12.0000	+	20.7846i	−0.737154	+	1.27679i
$266$		0			0
$267$	22.0000			1.34638
$268$	−5.00000	+	8.66025i	−0.305424	+	0.529009i
$269$	8.00000	+	13.8564i	0.487769	+	0.844840i	0.999901	−	0.0140665i	$-0.00447764\pi$
$269$	8.00000	+	13.8564i	0.487769	+	0.844840i	−0.512132	+	0.858906i	$0.671144\pi$
$270$	−8.00000			−0.486864
$271$	−12.0000	−	20.7846i	−0.728948	−	1.26258i	−0.957328	−	0.289003i	$-0.906676\pi$
$271$	−12.0000	−	20.7846i	−0.728948	−	1.26258i	0.228380	−	0.973572i	$-0.426657\pi$
$272$	5.00000			0.303170
$273$		0			0
$274$	−1.50000	+	2.59808i	−0.0906183	+	0.156956i
$275$		0			0
$276$	3.00000	+	5.19615i	0.180579	+	0.312772i
$277$	8.00000	+	13.8564i	0.480673	+	0.832551i	0.999754	−	0.0221745i	$-0.00705893\pi$
$277$	8.00000	+	13.8564i	0.480673	+	0.832551i	−0.519081	+	0.854725i	$0.673726\pi$
$278$	−4.00000			−0.239904
$279$	5.00000			0.299342
$280$		0			0
$281$	−7.50000	+	12.9904i	−0.447412	+	0.774941i	−0.998217	−	0.0596933i	$-0.980988\pi$
$281$	−7.50000	+	12.9904i	−0.447412	+	0.774941i	0.550804	+	0.834634i	$0.314321\pi$
$282$	10.0000			0.595491
$283$	4.00000	−	6.92820i	0.237775	−	0.411839i	−0.722300	−	0.691580i	$-0.756915\pi$
$283$	4.00000	−	6.92820i	0.237775	−	0.411839i	0.960076	+	0.279741i	$0.0902485\pi$
$284$	1.50000	−	2.59808i	0.0890086	−	0.154167i
$285$	−8.00000			−0.473879
$286$		0			0
$287$		0			0
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	−4.00000	+	6.92820i	−0.235294	+	0.407541i
$290$		0			0
$291$	19.0000	−	32.9090i	1.11380	−	1.92916i
$292$	−3.50000	−	6.06218i	−0.204822	−	0.354762i
$293$	12.0000	−	20.7846i	0.701047	−	1.21425i	−0.267052	−	0.963682i	$-0.586049\pi$
$293$	12.0000	−	20.7846i	0.701047	−	1.21425i	0.968099	−	0.250568i	$-0.0806172\pi$
$294$	−7.00000	−	12.1244i	−0.408248	−	0.707107i
$295$	−12.0000			−0.698667
$296$	−2.00000			−0.116248
$297$		0			0
$298$	1.00000	+	1.73205i	0.0579284	+	0.100335i
$299$	6.00000			0.346989
$300$	−2.00000			−0.115470
$301$		0			0
$302$	1.50000	+	2.59808i	0.0863153	+	0.149502i
$303$	18.0000	−	31.1769i	1.03407	−	1.79107i
$304$	−1.00000	−	1.73205i	−0.0573539	−	0.0993399i
$305$	−2.00000	−	3.46410i	−0.114520	−	0.198354i
$306$	−5.00000			−0.285831
$307$	15.0000	−	25.9808i	0.856095	−	1.48280i	−0.0195300	−	0.999809i	$-0.506217\pi$
$307$	15.0000	−	25.9808i	0.856095	−	1.48280i	0.875625	−	0.482991i	$-0.160450\pi$
$308$		0			0
$309$	20.0000	−	3.46410i	1.13776	−	0.197066i
$310$	10.0000			0.567962
$311$	−16.5000	+	28.5788i	−0.935629	+	1.62056i	−0.162121	+	0.986771i	$0.551833\pi$
$311$	−16.5000	+	28.5788i	−0.935629	+	1.62056i	−0.773508	+	0.633786i	$0.781500\pi$
$312$	4.00000			0.226455
$313$	−11.0000	−	19.0526i	−0.621757	−	1.07691i	−0.989158	−	0.146852i	$-0.953086\pi$
$313$	−11.0000	−	19.0526i	−0.621757	−	1.07691i	0.367402	−	0.930062i	$-0.380247\pi$
$314$	9.00000	+	15.5885i	0.507899	+	0.879708i
$315$		0			0
$316$	1.50000	+	2.59808i	0.0843816	+	0.146153i
$317$	12.0000			0.673987			0.336994	−	0.941507i	$-0.390590\pi$
$317$	12.0000			0.673987			0.336994	+	0.941507i	$0.390590\pi$
$318$	24.0000			1.34585
$319$		0			0
$320$	1.00000	+	1.73205i	0.0559017	+	0.0968246i
$321$	−14.0000	−	24.2487i	−0.781404	−	1.35343i
$322$		0			0
$323$	10.0000			0.556415
$324$	5.50000	+	9.52628i	0.305556	+	0.529238i
$325$	−1.00000	+	1.73205i	−0.0554700	+	0.0960769i
$326$	3.00000	+	5.19615i	0.166155	+	0.287788i
$327$	10.0000	−	17.3205i	0.553001	−	0.957826i
$328$	2.50000	−	4.33013i	0.138039	−	0.239091i
$329$		0			0
$330$		0			0
$331$	8.00000			0.439720			0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000			0.439720			0.219860	+	0.975531i	$0.429440\pi$
$332$	14.0000			0.768350
$333$	2.00000			0.109599
$334$	−6.50000	+	11.2583i	−0.355664	+	0.616028i
$335$	10.0000	−	17.3205i	0.546358	−	0.946320i
$336$		0			0
$337$	−3.50000	+	6.06218i	−0.190657	+	0.330228i	−0.945468	−	0.325714i	$-0.894395\pi$
$337$	−3.50000	+	6.06218i	−0.190657	+	0.330228i	0.754811	+	0.655942i	$0.227729\pi$
$338$	−4.50000	+	7.79423i	−0.244768	+	0.423950i
$339$	−10.0000			−0.543125
$340$	−10.0000			−0.542326
$341$		0			0
$342$	1.00000	+	1.73205i	0.0540738	+	0.0936586i
$343$		0			0
$344$	1.00000	−	1.73205i	0.0539164	−	0.0933859i
$345$	−6.00000	−	10.3923i	−0.323029	−	0.559503i
$346$	10.0000			0.537603
$347$	9.00000	+	15.5885i	0.483145	+	0.836832i	0.999813	−	0.0193540i	$-0.00616095\pi$
$347$	9.00000	+	15.5885i	0.483145	+	0.836832i	−0.516667	+	0.856186i	$0.672828\pi$
$348$		0			0
$349$	8.00000	+	13.8564i	0.428230	+	0.741716i	0.996716	−	0.0809766i	$-0.0258039\pi$
$349$	8.00000	+	13.8564i	0.428230	+	0.741716i	−0.568486	+	0.822693i	$0.692471\pi$
$350$		0			0
$351$	8.00000			0.427008
$352$		0			0
$353$	−7.50000	+	12.9904i	−0.399185	+	0.691408i	−0.993626	−	0.112731i	$-0.964040\pi$
$353$	−7.50000	+	12.9904i	−0.399185	+	0.691408i	0.594441	+	0.804139i	$0.297373\pi$
$354$	6.00000	+	10.3923i	0.318896	+	0.552345i
$355$	−3.00000	+	5.19615i	−0.159223	+	0.275783i
$356$	−5.50000	−	9.52628i	−0.291499	−	0.504892i
$357$		0			0
$358$		0			0
$359$	−8.00000	−	13.8564i	−0.422224	−	0.731313i	0.573933	−	0.818902i	$-0.305417\pi$
$359$	−8.00000	−	13.8564i	−0.422224	−	0.731313i	−0.996157	+	0.0875892i	$0.972084\pi$
$360$	−1.00000	−	1.73205i	−0.0527046	−	0.0912871i
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	−2.00000	−	3.46410i	−0.105118	−	0.182069i
$363$	11.0000	−	19.0526i	0.577350	−	1.00000i
$364$		0			0
$365$	7.00000	+	12.1244i	0.366397	+	0.634618i
$366$	−2.00000	+	3.46410i	−0.104542	+	0.181071i
$367$	−17.5000	−	30.3109i	−0.913493	−	1.58222i	−0.809093	−	0.587680i	$-0.800041\pi$
$367$	−17.5000	−	30.3109i	−0.913493	−	1.58222i	−0.104399	−	0.994535i	$-0.533292\pi$
$368$	1.50000	−	2.59808i	0.0781929	−	0.135434i
$369$	−2.50000	+	4.33013i	−0.130145	+	0.225417i
$370$	4.00000			0.207950
$371$		0			0
$372$	−5.00000	−	8.66025i	−0.259238	−	0.449013i
$373$	−34.0000			−1.76045			−0.880227	−	0.474554i	$-0.842610\pi$
$373$	−34.0000			−1.76045			−0.880227	+	0.474554i	$0.842610\pi$
$374$		0			0
$375$	24.0000			1.23935
$376$	−2.50000	−	4.33013i	−0.128928	−	0.223309i
$377$		0			0
$378$		0			0
$379$	18.0000	+	31.1769i	0.924598	+	1.60145i	0.792207	+	0.610253i	$0.208932\pi$
$379$	18.0000	+	31.1769i	0.924598	+	1.60145i	0.132391	+	0.991198i	$0.457734\pi$
$380$	2.00000	+	3.46410i	0.102598	+	0.177705i
$381$	2.00000			0.102463
$382$	−12.0000			−0.613973
$383$	−6.50000	+	11.2583i	−0.332134	+	0.575274i	−0.982930	−	0.183979i	$-0.941102\pi$
$383$	−6.50000	+	11.2583i	−0.332134	+	0.575274i	0.650796	+	0.759253i	$0.274435\pi$
$384$	1.00000	−	1.73205i	0.0510310	−	0.0883883i
$385$		0			0
$386$	−1.00000	+	1.73205i	−0.0508987	+	0.0881591i
$387$	−1.00000	+	1.73205i	−0.0508329	+	0.0880451i
$388$	−19.0000			−0.964579
$389$	12.0000			0.608424			0.304212	−	0.952604i	$-0.401607\pi$
$389$	12.0000			0.608424			0.304212	+	0.952604i	$0.401607\pi$
$390$	−8.00000			−0.405096
$391$	7.50000	+	12.9904i	0.379291	+	0.656952i
$392$	−3.50000	+	6.06218i	−0.176777	+	0.306186i
$393$	−16.0000	+	27.7128i	−0.807093	+	1.39793i
$394$	−4.00000	+	6.92820i	−0.201517	+	0.349038i
$395$	−3.00000	−	5.19615i	−0.150946	−	0.261447i
$396$		0			0
$397$	6.00000	+	10.3923i	0.301131	+	0.521575i	0.976392	−	0.216004i	$-0.0693024\pi$
$397$	6.00000	+	10.3923i	0.301131	+	0.521575i	−0.675261	+	0.737579i	$0.735969\pi$
$398$	23.0000			1.15289
$399$		0			0
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	−15.0000	−	25.9808i	−0.749064	−	1.29742i	−0.948272	−	0.317460i	$-0.897170\pi$
$401$	−15.0000	−	25.9808i	−0.749064	−	1.29742i	0.199207	−	0.979957i	$-0.436163\pi$
$402$	−20.0000			−0.997509
$403$	−10.0000			−0.498135
$404$	−18.0000			−0.895533
$405$	−11.0000	−	19.0526i	−0.546594	−	0.946729i
$406$		0			0
$407$		0			0
$408$	5.00000	+	8.66025i	0.247537	+	0.428746i
$409$	−19.0000			−0.939490			−0.469745	−	0.882802i	$-0.655654\pi$
$409$	−19.0000			−0.939490			−0.469745	+	0.882802i	$0.655654\pi$
$410$	−5.00000	+	8.66025i	−0.246932	+	0.427699i
$411$	−6.00000			−0.295958
$412$	−6.50000	−	7.79423i	−0.320232	−	0.383994i
$413$		0			0
$414$	−1.50000	+	2.59808i	−0.0737210	+	0.127688i
$415$	−28.0000			−1.37447
$416$	−1.00000	−	1.73205i	−0.0490290	−	0.0849208i
$417$	−4.00000	−	6.92820i	−0.195881	−	0.339276i
$418$		0			0
$419$	5.00000	+	8.66025i	0.244266	+	0.423081i	0.961925	−	0.273314i	$-0.0881197\pi$
$419$	5.00000	+	8.66025i	0.244266	+	0.423081i	−0.717659	+	0.696395i	$0.754786\pi$
$420$		0			0
$421$	−28.0000			−1.36464			−0.682318	−	0.731055i	$-0.739028\pi$
$421$	−28.0000			−1.36464			−0.682318	+	0.731055i	$0.739028\pi$
$422$	16.0000			0.778868
$423$	2.50000	+	4.33013i	0.121554	+	0.210538i
$424$	−6.00000	−	10.3923i	−0.291386	−	0.504695i
$425$	−5.00000			−0.242536
$426$	6.00000			0.290701
$427$		0			0
$428$	−7.00000	+	12.1244i	−0.338358	+	0.586053i
$429$		0			0
$430$	−2.00000	+	3.46410i	−0.0964486	+	0.167054i
$431$	−3.50000	+	6.06218i	−0.168589	+	0.292005i	−0.937924	−	0.346841i	$-0.887254\pi$
$431$	−3.50000	+	6.06218i	−0.168589	+	0.292005i	0.769335	+	0.638846i	$0.220588\pi$
$432$	2.00000	−	3.46410i	0.0962250	−	0.166667i
$433$	−17.0000	−	29.4449i	−0.816968	−	1.41503i	−0.907906	−	0.419173i	$-0.862320\pi$
$433$	−17.0000	−	29.4449i	−0.816968	−	1.41503i	0.0909384	−	0.995857i	$-0.471013\pi$
$434$		0			0
$435$		0			0
$436$	−10.0000			−0.478913
$437$	3.00000	−	5.19615i	0.143509	−	0.248566i
$438$	7.00000	−	12.1244i	0.334473	−	0.579324i
$439$	−15.0000			−0.715911			−0.357955	−	0.933739i	$-0.616526\pi$
$439$	−15.0000			−0.715911			−0.357955	+	0.933739i	$0.616526\pi$
$440$		0			0
$441$	3.50000	−	6.06218i	0.166667	−	0.288675i
$442$	10.0000			0.475651
$443$	−36.0000			−1.71041			−0.855206	−	0.518289i	$-0.826569\pi$
$443$	−36.0000			−1.71041			−0.855206	+	0.518289i	$0.826569\pi$
$444$	−2.00000	−	3.46410i	−0.0949158	−	0.164399i
$445$	11.0000	+	19.0526i	0.521450	+	0.903178i
$446$	9.00000			0.426162
$447$	−2.00000	+	3.46410i	−0.0945968	+	0.163846i
$448$		0			0
$449$	9.00000			0.424736			0.212368	−	0.977190i	$-0.431882\pi$
$449$	9.00000			0.424736			0.212368	+	0.977190i	$0.431882\pi$
$450$	−0.500000	−	0.866025i	−0.0235702	−	0.0408248i
$451$		0			0
$452$	2.50000	+	4.33013i	0.117590	+	0.203672i
$453$	−3.00000	+	5.19615i	−0.140952	+	0.244137i
$454$	−24.0000			−1.12638
$455$		0			0
$456$	2.00000	−	3.46410i	0.0936586	−	0.162221i
$457$	3.50000	+	6.06218i	0.163723	+	0.283577i	0.936201	−	0.351465i	$-0.114316\pi$
$457$	3.50000	+	6.06218i	0.163723	+	0.283577i	−0.772478	+	0.635042i	$0.780983\pi$
$458$	2.00000	−	3.46410i	0.0934539	−	0.161867i
$459$	10.0000	+	17.3205i	0.466760	+	0.808452i
$460$	−3.00000	+	5.19615i	−0.139876	+	0.242272i
$461$	12.0000	−	20.7846i	0.558896	−	0.968036i	−0.438693	−	0.898637i	$-0.644559\pi$
$461$	12.0000	−	20.7846i	0.558896	−	0.968036i	0.997589	−	0.0693989i	$-0.0221081\pi$
$462$		0			0
$463$	2.50000	+	4.33013i	0.116185	+	0.201238i	0.918253	−	0.395995i	$-0.129600\pi$
$463$	2.50000	+	4.33013i	0.116185	+	0.201238i	−0.802068	+	0.597233i	$0.796267\pi$
$464$		0			0
$465$	10.0000	+	17.3205i	0.463739	+	0.803219i
$466$	−9.00000	+	15.5885i	−0.416917	+	0.722121i
$467$	11.0000	−	19.0526i	0.509019	−	0.881647i	−0.490926	−	0.871201i	$-0.663342\pi$
$467$	11.0000	−	19.0526i	0.509019	−	0.881647i	0.999945	−	0.0104461i	$-0.00332515\pi$
$468$	1.00000	+	1.73205i	0.0462250	+	0.0800641i
$469$		0			0
$470$	5.00000	+	8.66025i	0.230633	+	0.399468i
$471$	−18.0000	+	31.1769i	−0.829396	+	1.43656i
$472$	3.00000	−	5.19615i	0.138086	−	0.239172i
$473$		0			0
$474$	−3.00000	+	5.19615i	−0.137795	+	0.238667i
$475$	1.00000	+	1.73205i	0.0458831	+	0.0794719i
$476$		0			0
$477$	6.00000	+	10.3923i	0.274721	+	0.475831i
$478$	19.0000			0.869040
$479$	−3.50000	−	6.06218i	−0.159919	−	0.276988i	0.774920	−	0.632059i	$-0.217790\pi$
$479$	−3.50000	−	6.06218i	−0.159919	−	0.276988i	−0.934839	+	0.355071i	$0.884457\pi$
$480$	−2.00000	+	3.46410i	−0.0912871	+	0.158114i
$481$	−4.00000			−0.182384
$482$	1.00000	+	1.73205i	0.0455488	+	0.0788928i
$483$		0			0
$484$	−11.0000			−0.500000
$485$	38.0000			1.72549
$486$	−5.00000	+	8.66025i	−0.226805	+	0.392837i
$487$	14.0000	−	24.2487i	0.634401	−	1.09881i	−0.352241	−	0.935909i	$-0.614580\pi$
$487$	14.0000	−	24.2487i	0.634401	−	1.09881i	0.986642	−	0.162905i	$-0.0520863\pi$
$488$	2.00000			0.0905357
$489$	−6.00000	+	10.3923i	−0.271329	+	0.469956i
$490$	7.00000	−	12.1244i	0.316228	−	0.547723i
$491$	4.00000			0.180517			0.0902587	−	0.995918i	$-0.471231\pi$
$491$	4.00000			0.180517			0.0902587	+	0.995918i	$0.471231\pi$
$492$	10.0000			0.450835
$493$		0			0
$494$	−2.00000	−	3.46410i	−0.0899843	−	0.155857i
$495$		0			0
$496$	−2.50000	+	4.33013i	−0.112253	+	0.194428i
$497$		0			0
$498$	14.0000	+	24.2487i	0.627355	+	1.08661i
$499$	−5.00000	+	8.66025i	−0.223831	+	0.387686i	−0.955968	−	0.293471i	$-0.905190\pi$
$499$	−5.00000	+	8.66025i	−0.223831	+	0.387686i	0.732137	+	0.681157i	$0.238523\pi$
$500$	−6.00000	−	10.3923i	−0.268328	−	0.464758i
$501$	−26.0000			−1.16159
$502$	16.0000			0.714115
$503$	4.50000	+	7.79423i	0.200645	+	0.347527i	0.948736	−	0.316068i	$-0.102363\pi$
$503$	4.50000	+	7.79423i	0.200645	+	0.347527i	−0.748091	+	0.663596i	$0.769030\pi$
$504$		0			0
$505$	36.0000			1.60198
$506$		0			0
$507$	−18.0000			−0.799408
$508$	−0.500000	−	0.866025i	−0.0221839	−	0.0384237i
$509$	9.00000	−	15.5885i	0.398918	−	0.690946i	−0.594675	−	0.803966i	$-0.702719\pi$
$509$	9.00000	−	15.5885i	0.398918	−	0.690946i	0.993593	+	0.113020i	$0.0360525\pi$
$510$	−10.0000	−	17.3205i	−0.442807	−	0.766965i
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	4.00000	−	6.92820i	0.176604	−	0.305888i
$514$	−15.0000			−0.661622
$515$	13.0000	+	15.5885i	0.572848	+	0.686909i
$516$	4.00000			0.176090
$517$		0			0
$518$		0			0
$519$	10.0000	+	17.3205i	0.438951	+	0.760286i
$520$	2.00000	+	3.46410i	0.0877058	+	0.151911i
$521$	5.00000	−	8.66025i	0.219054	−	0.379413i	−0.735465	−	0.677563i	$-0.763036\pi$
$521$	5.00000	−	8.66025i	0.219054	−	0.379413i	0.954519	+	0.298150i	$0.0963696\pi$
$522$		0			0
$523$	−4.00000			−0.174908			−0.0874539	−	0.996169i	$-0.527873\pi$
$523$	−4.00000			−0.174908			−0.0874539	+	0.996169i	$0.527873\pi$
$524$	16.0000			0.698963
$525$		0			0
$526$	−4.50000	−	7.79423i	−0.196209	−	0.339845i
$527$	−12.5000	−	21.6506i	−0.544509	−	0.943116i
$528$		0			0
$529$	−14.0000			−0.608696
$530$	12.0000	+	20.7846i	0.521247	+	0.902826i
$531$	−3.00000	+	5.19615i	−0.130189	+	0.225494i
$532$		0			0
$533$	5.00000	−	8.66025i	0.216574	−	0.375117i
$534$	11.0000	−	19.0526i	0.476017	−	0.824485i
$535$	14.0000	−	24.2487i	0.605273	−	1.04836i
$536$	5.00000	+	8.66025i	0.215967	+	0.374066i
$537$		0			0
$538$	16.0000			0.689809
$539$		0			0
$540$	−4.00000	+	6.92820i	−0.172133	+	0.298142i
$541$	−8.00000	+	13.8564i	−0.343947	+	0.595733i	−0.985162	−	0.171628i	$-0.945097\pi$
$541$	−8.00000	+	13.8564i	−0.343947	+	0.595733i	0.641215	+	0.767361i	$0.278431\pi$
$542$	−24.0000			−1.03089
$543$	4.00000	−	6.92820i	0.171656	−	0.297318i
$544$	2.50000	−	4.33013i	0.107187	−	0.185653i
$545$	20.0000			0.856706
$546$		0			0
$547$	−2.00000	−	3.46410i	−0.0855138	−	0.148114i	0.820096	−	0.572226i	$-0.193920\pi$
$547$	−2.00000	−	3.46410i	−0.0855138	−	0.148114i	−0.905610	+	0.424111i	$0.860587\pi$
$548$	1.50000	+	2.59808i	0.0640768	+	0.110984i
$549$	−2.00000			−0.0853579
$550$		0			0
$551$		0			0
$552$	6.00000			0.255377
$553$		0			0
$554$	16.0000			0.679775
$555$	4.00000	+	6.92820i	0.169791	+	0.294086i
$556$	−2.00000	+	3.46410i	−0.0848189	+	0.146911i
$557$	−24.0000			−1.01691			−0.508456	−	0.861088i	$-0.669784\pi$
$557$	−24.0000			−1.01691			−0.508456	+	0.861088i	$0.669784\pi$
$558$	2.50000	−	4.33013i	0.105833	−	0.183309i
$559$	2.00000	−	3.46410i	0.0845910	−	0.146516i
$560$		0			0
$561$		0			0
$562$	7.50000	+	12.9904i	0.316368	+	0.547966i
$563$	−12.0000	+	20.7846i	−0.505740	+	0.875967i	0.494238	+	0.869326i	$0.335447\pi$
$563$	−12.0000	+	20.7846i	−0.505740	+	0.875967i	−0.999978	+	0.00664037i	$0.997886\pi$
$564$	5.00000	−	8.66025i	0.210538	−	0.364662i
$565$	−5.00000	−	8.66025i	−0.210352	−	0.364340i
$566$	−4.00000	−	6.92820i	−0.168133	−	0.291214i
$567$		0			0
$568$	−1.50000	−	2.59808i	−0.0629386	−	0.109013i
$569$	17.5000	−	30.3109i	0.733638	−	1.27070i	−0.221680	−	0.975119i	$-0.571154\pi$
$569$	17.5000	−	30.3109i	0.733638	−	1.27070i	0.955318	−	0.295579i	$-0.0955126\pi$
$570$	−4.00000	+	6.92820i	−0.167542	+	0.290191i
$571$	10.0000	+	17.3205i	0.418487	+	0.724841i	0.995788	−	0.0916910i	$-0.0292272\pi$
$571$	10.0000	+	17.3205i	0.418487	+	0.724841i	−0.577301	+	0.816532i	$0.695894\pi$
$572$		0			0
$573$	−12.0000	−	20.7846i	−0.501307	−	0.868290i
$574$		0			0
$575$	−1.50000	+	2.59808i	−0.0625543	+	0.108347i
$576$	1.00000			0.0416667
$577$	8.50000	−	14.7224i	0.353860	−	0.612903i	−0.633062	−	0.774101i	$-0.718202\pi$
$577$	8.50000	−	14.7224i	0.353860	−	0.612903i	0.986922	+	0.161198i	$0.0515357\pi$
$578$	4.00000	+	6.92820i	0.166378	+	0.288175i
$579$	−4.00000			−0.166234
$580$		0			0
$581$		0			0
$582$	−19.0000	−	32.9090i	−0.787575	−	1.36412i
$583$		0			0
$584$	−7.00000			−0.289662
$585$	−2.00000	−	3.46410i	−0.0826898	−	0.143223i
$586$	−12.0000	−	20.7846i	−0.495715	−	0.858604i
$587$	30.0000			1.23823			0.619116	−	0.785299i	$-0.287491\pi$
$587$	30.0000			1.23823			0.619116	+	0.785299i	$0.287491\pi$
$588$	−14.0000			−0.577350
$589$	−5.00000	+	8.66025i	−0.206021	+	0.356840i
$590$	−6.00000	+	10.3923i	−0.247016	+	0.427844i
$591$	−16.0000			−0.658152
$592$	−1.00000	+	1.73205i	−0.0410997	+	0.0711868i
$593$	20.5000	−	35.5070i	0.841834	−	1.45810i	−0.0465084	−	0.998918i	$-0.514809\pi$
$593$	20.5000	−	35.5070i	0.841834	−	1.45810i	0.888342	−	0.459182i	$-0.151857\pi$
$594$		0			0
$595$		0			0
$596$	2.00000			0.0819232
$597$	23.0000	+	39.8372i	0.941327	+	1.63043i
$598$	3.00000	−	5.19615i	0.122679	−	0.212486i
$599$	−20.5000	+	35.5070i	−0.837607	+	1.45078i	0.0542825	+	0.998526i	$0.482713\pi$
$599$	−20.5000	+	35.5070i	−0.837607	+	1.45078i	−0.891890	+	0.452253i	$0.850620\pi$
$600$	−1.00000	+	1.73205i	−0.0408248	+	0.0707107i
$601$	18.5000	+	32.0429i	0.754631	+	1.30706i	0.945558	+	0.325455i	$0.105517\pi$
$601$	18.5000	+	32.0429i	0.754631	+	1.30706i	−0.190927	+	0.981604i	$0.561149\pi$
$602$		0			0
$603$	−5.00000	−	8.66025i	−0.203616	−	0.352673i
$604$	3.00000			0.122068
$605$	22.0000			0.894427
$606$	−18.0000	−	31.1769i	−0.731200	−	1.26648i
$607$	−4.50000	−	7.79423i	−0.182649	−	0.316358i	0.760133	−	0.649768i	$-0.225134\pi$
$607$	−4.50000	−	7.79423i	−0.182649	−	0.316358i	−0.942782	+	0.333410i	$0.891801\pi$
$608$	−2.00000			−0.0811107
$609$		0			0
$610$	−4.00000			−0.161955
$611$	−5.00000	−	8.66025i	−0.202278	−	0.350356i
$612$	−2.50000	+	4.33013i	−0.101057	+	0.175035i
$613$	−12.0000	−	20.7846i	−0.484675	−	0.839482i	0.515170	−	0.857088i	$-0.327729\pi$
$613$	−12.0000	−	20.7846i	−0.484675	−	0.839482i	−0.999845	+	0.0176058i	$0.994396\pi$
$614$	−15.0000	−	25.9808i	−0.605351	−	1.04850i
$615$	−20.0000			−0.806478
$616$		0			0
$617$	−29.0000			−1.16750			−0.583748	−	0.811935i	$-0.698414\pi$
$617$	−29.0000			−1.16750			−0.583748	+	0.811935i	$0.698414\pi$
$618$	7.00000	−	19.0526i	0.281581	−	0.766406i
$619$	46.0000			1.84890			0.924448	−	0.381308i	$-0.124526\pi$
$619$	46.0000			1.84890			0.924448	+	0.381308i	$0.124526\pi$
$620$	5.00000	−	8.66025i	0.200805	−	0.347804i
$621$	12.0000			0.481543
$622$	16.5000	+	28.5788i	0.661590	+	1.14591i
$623$		0			0
$624$	2.00000	−	3.46410i	0.0800641	−	0.138675i
$625$	9.50000	+	16.4545i	0.380000	+	0.658179i
$626$	−22.0000			−0.879297
$627$		0			0
$628$	18.0000			0.718278
$629$	−5.00000	−	8.66025i	−0.199363	−	0.345307i
$630$		0			0
$631$	−21.0000			−0.835997			−0.417998	−	0.908448i	$-0.637268\pi$
$631$	−21.0000			−0.835997			−0.417998	+	0.908448i	$0.637268\pi$
$632$	3.00000			0.119334
$633$	16.0000	+	27.7128i	0.635943	+	1.10149i
$634$	6.00000	−	10.3923i	0.238290	−	0.412731i
$635$	1.00000	+	1.73205i	0.0396838	+	0.0687343i
$636$	12.0000	−	20.7846i	0.475831	−	0.824163i
$637$	−7.00000	+	12.1244i	−0.277350	+	0.480384i
$638$		0			0
$639$	1.50000	+	2.59808i	0.0593391	+	0.102778i
$640$	2.00000			0.0790569
$641$	26.0000			1.02694			0.513469	−	0.858108i	$-0.328360\pi$
$641$	26.0000			1.02694			0.513469	+	0.858108i	$0.328360\pi$
$642$	−28.0000			−1.10507
$643$	3.00000	−	5.19615i	0.118308	−	0.204916i	−0.800789	−	0.598947i	$-0.795586\pi$
$643$	3.00000	−	5.19615i	0.118308	−	0.204916i	0.919097	+	0.394030i	$0.128920\pi$
$644$		0			0
$645$	−8.00000			−0.315000
$646$	5.00000	−	8.66025i	0.196722	−	0.340733i
$647$	−4.00000	+	6.92820i	−0.157256	+	0.272376i	−0.933878	−	0.357591i	$-0.883598\pi$
$647$	−4.00000	+	6.92820i	−0.157256	+	0.272376i	0.776622	+	0.629967i	$0.216932\pi$
$648$	11.0000			0.432121
$649$		0			0
$650$	1.00000	+	1.73205i	0.0392232	+	0.0679366i
$651$		0			0
$652$	6.00000			0.234978
$653$	−14.0000	+	24.2487i	−0.547862	+	0.948925i	0.450558	+	0.892747i	$0.351225\pi$
$653$	−14.0000	+	24.2487i	−0.547862	+	0.948925i	−0.998421	+	0.0561784i	$0.982108\pi$
$654$	−10.0000	−	17.3205i	−0.391031	−	0.677285i
$655$	−32.0000			−1.25034
$656$	−2.50000	−	4.33013i	−0.0976086	−	0.169063i
$657$	7.00000			0.273096
$658$		0			0
$659$	10.0000	−	17.3205i	0.389545	−	0.674711i	−0.602844	−	0.797859i	$-0.705966\pi$
$659$	10.0000	−	17.3205i	0.389545	−	0.674711i	0.992388	+	0.123148i	$0.0392990\pi$
$660$		0			0
$661$	−15.0000	+	25.9808i	−0.583432	+	1.01053i	0.411636	+	0.911348i	$0.364957\pi$
$661$	−15.0000	+	25.9808i	−0.583432	+	1.01053i	−0.995069	+	0.0991864i	$0.968376\pi$
$662$	4.00000	−	6.92820i	0.155464	−	0.269272i
$663$	10.0000	+	17.3205i	0.388368	+	0.672673i
$664$	7.00000	−	12.1244i	0.271653	−	0.470516i
$665$		0			0
$666$	1.00000	−	1.73205i	0.0387492	−	0.0671156i
$667$		0			0
$668$	6.50000	+	11.2583i	0.251493	+	0.435598i
$669$	9.00000	+	15.5885i	0.347960	+	0.602685i
$670$	−10.0000	−	17.3205i	−0.386334	−	0.669150i
$671$		0			0
$672$		0			0
$673$	3.50000	−	6.06218i	0.134915	−	0.233680i	−0.790650	−	0.612268i	$-0.790257\pi$
$673$	3.50000	−	6.06218i	0.134915	−	0.233680i	0.925565	+	0.378589i	$0.123591\pi$
$674$	3.50000	+	6.06218i	0.134815	+	0.233506i
$675$	−2.00000	+	3.46410i	−0.0769800	+	0.133333i
$676$	4.50000	+	7.79423i	0.173077	+	0.299778i
$677$	16.0000	−	27.7128i	0.614930	−	1.06509i	−0.375467	−	0.926836i	$-0.622518\pi$
$677$	16.0000	−	27.7128i	0.614930	−	1.06509i	0.990397	−	0.138254i	$-0.0441491\pi$
$678$	−5.00000	+	8.66025i	−0.192024	+	0.332595i
$679$		0			0
$680$	−5.00000	+	8.66025i	−0.191741	+	0.332106i
$681$	−24.0000	−	41.5692i	−0.919682	−	1.59294i
$682$		0			0
$683$	10.0000	+	17.3205i	0.382639	+	0.662751i	0.991439	−	0.130573i	$-0.0416818\pi$
$683$	10.0000	+	17.3205i	0.382639	+	0.662751i	−0.608799	+	0.793324i	$0.708349\pi$
$684$	2.00000			0.0764719
$685$	−3.00000	−	5.19615i	−0.114624	−	0.198535i
$686$		0			0
$687$	8.00000			0.305219
$688$	−1.00000	−	1.73205i	−0.0381246	−	0.0660338i
$689$	−12.0000	−	20.7846i	−0.457164	−	0.791831i
$690$	−12.0000			−0.456832
$691$	28.0000			1.06517			0.532585	−	0.846376i	$-0.321221\pi$
$691$	28.0000			1.06517			0.532585	+	0.846376i	$0.321221\pi$
$692$	5.00000	−	8.66025i	0.190071	−	0.329213i
$693$		0			0
$694$	18.0000			0.683271
$695$	4.00000	−	6.92820i	0.151729	−	0.262802i
$696$		0			0
$697$	25.0000			0.946943
$698$	16.0000			0.605609
$699$	−36.0000			−1.36165
$700$		0			0
$701$	−9.00000	+	15.5885i	−0.339925	+	0.588768i	−0.984418	−	0.175842i	$-0.943735\pi$
$701$	−9.00000	+	15.5885i	−0.339925	+	0.588768i	0.644493	+	0.764610i	$0.277068\pi$
$702$	4.00000	−	6.92820i	0.150970	−	0.261488i
$703$	−2.00000	+	3.46410i	−0.0754314	+	0.130651i
$704$		0			0
$705$	−10.0000	+	17.3205i	−0.376622	+	0.652328i
$706$	7.50000	+	12.9904i	0.282266	+	0.488899i
$707$		0			0
$708$	12.0000			0.450988
$709$	−7.00000	−	12.1244i	−0.262891	−	0.455340i	0.704118	−	0.710083i	$-0.251342\pi$
$709$	−7.00000	−	12.1244i	−0.262891	−	0.455340i	−0.967009	+	0.254743i	$0.918009\pi$
$710$	3.00000	+	5.19615i	0.112588	+	0.195008i
$711$	−3.00000			−0.112509
$712$	−11.0000			−0.412242
$713$	−15.0000			−0.561754
$714$		0			0
$715$		0			0
$716$		0			0
$717$	19.0000	+	32.9090i	0.709568	+	1.22901i
$718$	−16.0000			−0.597115
$719$	19.5000	−	33.7750i	0.727227	−	1.25959i	−0.230823	−	0.972996i	$-0.574142\pi$
$719$	19.5000	−	33.7750i	0.727227	−	1.25959i	0.958051	−	0.286599i	$-0.0925247\pi$
$720$	−2.00000			−0.0745356
$721$		0			0
$722$	15.0000			0.558242
$723$	−2.00000	+	3.46410i	−0.0743808	+	0.128831i
$724$	−4.00000			−0.148659
$725$		0			0
$726$	−11.0000	−	19.0526i	−0.408248	−	0.707107i
$727$	−20.0000	+	34.6410i	−0.741759	+	1.28476i	0.209935	+	0.977715i	$0.432675\pi$
$727$	−20.0000	+	34.6410i	−0.741759	+	1.28476i	−0.951694	+	0.307049i	$0.900659\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	14.0000			0.518163
$731$	10.0000			0.369863
$732$	2.00000	+	3.46410i	0.0739221	+	0.128037i
$733$	−9.00000	−	15.5885i	−0.332423	−	0.575773i	0.650564	−	0.759452i	$-0.274533\pi$
$733$	−9.00000	−	15.5885i	−0.332423	−	0.575773i	−0.982986	+	0.183679i	$0.941199\pi$
$734$	−35.0000			−1.29187
$735$	28.0000			1.03280
$736$	−1.50000	−	2.59808i	−0.0552907	−	0.0957664i
$737$		0			0
$738$	2.50000	+	4.33013i	0.0920263	+	0.159394i
$739$	25.0000	−	43.3013i	0.919640	−	1.59286i	0.119677	−	0.992813i	$-0.461814\pi$
$739$	25.0000	−	43.3013i	0.919640	−	1.59286i	0.799962	−	0.600050i	$-0.204853\pi$
$740$	2.00000	−	3.46410i	0.0735215	−	0.127343i
$741$	4.00000	−	6.92820i	0.146944	−	0.254514i
$742$		0			0
$743$	−36.0000			−1.32071			−0.660356	−	0.750953i	$-0.729595\pi$
$743$	−36.0000			−1.32071			−0.660356	+	0.750953i	$0.729595\pi$
$744$	−10.0000			−0.366618
$745$	−4.00000			−0.146549
$746$	−17.0000	+	29.4449i	−0.622414	+	1.07805i
$747$	−7.00000	+	12.1244i	−0.256117	+	0.443607i
$748$		0			0
$749$		0			0
$750$	12.0000	−	20.7846i	0.438178	−	0.758947i
$751$	−11.0000			−0.401396			−0.200698	−	0.979653i	$-0.564321\pi$
$751$	−11.0000			−0.401396			−0.200698	+	0.979653i	$0.564321\pi$
$752$	−5.00000			−0.182331
$753$	16.0000	+	27.7128i	0.583072	+	1.00991i
$754$		0			0
$755$	−6.00000			−0.218362
$756$		0			0
$757$	21.0000	+	36.3731i	0.763258	+	1.32200i	0.941163	+	0.337954i	$0.109735\pi$
$757$	21.0000	+	36.3731i	0.763258	+	1.32200i	−0.177905	+	0.984048i	$0.556932\pi$
$758$	36.0000			1.30758
$759$		0			0
$760$	4.00000			0.145095
$761$	−0.500000	−	0.866025i	−0.0181250	−	0.0313934i	0.856821	−	0.515615i	$-0.172436\pi$
$761$	−0.500000	−	0.866025i	−0.0181250	−	0.0313934i	−0.874946	+	0.484221i	$0.839103\pi$
$762$	1.00000	−	1.73205i	0.0362262	−	0.0627456i
$763$		0			0
$764$	−6.00000	+	10.3923i	−0.217072	+	0.375980i
$765$	5.00000	−	8.66025i	0.180775	−	0.313112i
$766$	6.50000	+	11.2583i	0.234855	+	0.406780i
$767$	6.00000	−	10.3923i	0.216647	−	0.375244i
$768$	−1.00000	−	1.73205i	−0.0360844	−	0.0625000i
$769$	−5.00000	+	8.66025i	−0.180305	+	0.312297i	−0.941984	−	0.335657i	$-0.891042\pi$
$769$	−5.00000	+	8.66025i	−0.180305	+	0.312297i	0.761680	+	0.647954i	$0.224375\pi$
$770$		0			0
$771$	−15.0000	−	25.9808i	−0.540212	−	0.935674i
$772$	1.00000	+	1.73205i	0.0359908	+	0.0623379i
$773$	18.0000	+	31.1769i	0.647415	+	1.12136i	0.983738	+	0.179609i	$0.0574833\pi$
$773$	18.0000	+	31.1769i	0.647415	+	1.12136i	−0.336323	+	0.941747i	$0.609183\pi$
$774$	1.00000	+	1.73205i	0.0359443	+	0.0622573i
$775$	2.50000	−	4.33013i	0.0898027	−	0.155543i
$776$	−9.50000	+	16.4545i	−0.341030	+	0.590682i
$777$		0			0
$778$	6.00000	−	10.3923i	0.215110	−	0.372582i
$779$	−5.00000	−	8.66025i	−0.179144	−	0.310286i
$780$	−4.00000	+	6.92820i	−0.143223	+	0.248069i
$781$		0			0
$782$	15.0000			0.536399
$783$		0			0
$784$	3.50000	+	6.06218i	0.125000	+	0.216506i
$785$	−36.0000			−1.28490
$786$	16.0000	+	27.7128i	0.570701	+	0.988483i
$787$	6.00000			0.213877			0.106938	−	0.994266i	$-0.465895\pi$
$787$	6.00000			0.213877			0.106938	+	0.994266i	$0.465895\pi$
$788$	4.00000	+	6.92820i	0.142494	+	0.246807i
$789$	9.00000	−	15.5885i	0.320408	−	0.554964i
$790$	−6.00000			−0.213470
$791$		0			0
$792$		0			0
$793$	4.00000			0.142044
$794$	12.0000			0.425864
$795$	−24.0000	+	41.5692i	−0.851192	+	1.47431i
$796$	11.5000	−	19.9186i	0.407607	−	0.705996i
$797$	−32.0000			−1.13350			−0.566749	−	0.823890i	$-0.691799\pi$
$797$	−32.0000			−1.13350			−0.566749	+	0.823890i	$0.691799\pi$
$798$		0			0
$799$	12.5000	−	21.6506i	0.442218	−	0.765944i
$800$	1.00000			0.0353553
$801$	11.0000			0.388666
$802$	−30.0000			−1.05934
$803$		0			0
$804$	−10.0000	+	17.3205i	−0.352673	+	0.610847i
$805$		0			0
$806$	−5.00000	+	8.66025i	−0.176117	+	0.305044i
$807$	16.0000	+	27.7128i	0.563227	+	0.975537i
$808$	−9.00000	+	15.5885i	−0.316619	+	0.548400i
$809$	15.0000	+	25.9808i	0.527372	+	0.913435i	0.999491	+	0.0319002i	$0.0101559\pi$
$809$	15.0000	+	25.9808i	0.527372	+	0.913435i	−0.472119	+	0.881535i	$0.656511\pi$
$810$	−22.0000			−0.773001
$811$	−34.0000			−1.19390			−0.596951	−	0.802278i	$-0.703621\pi$
$811$	−34.0000			−1.19390			−0.596951	+	0.802278i	$0.703621\pi$
$812$		0			0
$813$	−24.0000	−	41.5692i	−0.841717	−	1.45790i
$814$		0			0
$815$	−12.0000			−0.420342
$816$	10.0000			0.350070
$817$	−2.00000	−	3.46410i	−0.0699711	−	0.121194i
$818$	−9.50000	+	16.4545i	−0.332160	+	0.575317i
$819$		0			0
$820$	5.00000	+	8.66025i	0.174608	+	0.302429i
$821$	−8.00000			−0.279202			−0.139601	−	0.990208i	$-0.544582\pi$
$821$	−8.00000			−0.279202			−0.139601	+	0.990208i	$0.544582\pi$
$822$	−3.00000	+	5.19615i	−0.104637	+	0.181237i
$823$	29.0000			1.01088			0.505438	−	0.862863i	$-0.331331\pi$
$823$	29.0000			1.01088			0.505438	+	0.862863i	$0.331331\pi$
$824$	−10.0000	+	1.73205i	−0.348367	+	0.0603388i
$825$		0			0
$826$		0			0
$827$	−54.0000			−1.87776			−0.938882	−	0.344239i	$-0.888137\pi$
$827$	−54.0000			−1.87776			−0.938882	+	0.344239i	$0.888137\pi$
$828$	1.50000	+	2.59808i	0.0521286	+	0.0902894i
$829$	−23.0000	−	39.8372i	−0.798823	−	1.38360i	−0.920383	−	0.391018i	$-0.872123\pi$
$829$	−23.0000	−	39.8372i	−0.798823	−	1.38360i	0.121560	−	0.992584i	$-0.461210\pi$
$830$	−14.0000	+	24.2487i	−0.485947	+	0.841685i
$831$	16.0000	+	27.7128i	0.555034	+	0.961347i
$832$	−2.00000			−0.0693375
$833$	−35.0000			−1.21268
$834$	−8.00000			−0.277017
$835$	−13.0000	−	22.5167i	−0.449884	−	0.779221i
$836$		0			0
$837$	−20.0000			−0.691301
$838$	10.0000			0.345444
$839$	−4.50000	−	7.79423i	−0.155357	−	0.269087i	0.777832	−	0.628473i	$-0.216320\pi$
$839$	−4.50000	−	7.79423i	−0.155357	−	0.269087i	−0.933189	+	0.359386i	$0.882986\pi$
$840$		0			0
$841$	14.5000	+	25.1147i	0.500000	+	0.866025i
$842$	−14.0000	+	24.2487i	−0.482472	+	0.835666i
$843$	−15.0000	+	25.9808i	−0.516627	+	0.894825i
$844$	8.00000	−	13.8564i	0.275371	−	0.476957i
$845$	−9.00000	−	15.5885i	−0.309609	−	0.536259i
$846$	5.00000			0.171904
$847$		0			0
$848$	−12.0000			−0.412082
$849$	8.00000	−	13.8564i	0.274559	−	0.475551i
$850$	−2.50000	+	4.33013i	−0.0857493	+	0.148522i
$851$	−6.00000			−0.205677
$852$	3.00000	−	5.19615i	0.102778	−	0.178017i
$853$	27.0000	−	46.7654i	0.924462	−	1.60122i	0.132039	−	0.991245i	$-0.457848\pi$
$853$	27.0000	−	46.7654i	0.924462	−	1.60122i	0.792424	−	0.609971i	$-0.208819\pi$
$854$		0			0
$855$	−4.00000			−0.136797
$856$	7.00000	+	12.1244i	0.239255	+	0.414402i
$857$	7.50000	+	12.9904i	0.256195	+	0.443743i	0.965219	−	0.261441i	$-0.0841977\pi$
$857$	7.50000	+	12.9904i	0.256195	+	0.443743i	−0.709024	+	0.705184i	$0.750864\pi$
$858$		0			0
$859$	−8.00000	+	13.8564i	−0.272956	+	0.472774i	−0.969618	−	0.244626i	$-0.921335\pi$
$859$	−8.00000	+	13.8564i	−0.272956	+	0.472774i	0.696661	+	0.717400i	$0.254668\pi$
$860$	2.00000	+	3.46410i	0.0681994	+	0.118125i
$861$		0			0
$862$	3.50000	+	6.06218i	0.119210	+	0.206479i
$863$	−17.0000			−0.578687			−0.289343	−	0.957225i	$-0.593437\pi$
$863$	−17.0000			−0.578687			−0.289343	+	0.957225i	$0.593437\pi$
$864$	−2.00000	−	3.46410i	−0.0680414	−	0.117851i
$865$	−10.0000	+	17.3205i	−0.340010	+	0.588915i
$866$	−34.0000			−1.15537
$867$	−8.00000	+	13.8564i	−0.271694	+	0.470588i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	10.0000	+	17.3205i	0.338837	+	0.586883i
$872$	−5.00000	+	8.66025i	−0.169321	+	0.293273i
$873$	9.50000	−	16.4545i	0.321526	−	0.556900i
$874$	−3.00000	−	5.19615i	−0.101477	−	0.175762i
$875$		0			0
$876$	−7.00000	−	12.1244i	−0.236508	−	0.409644i
$877$	16.0000	+	27.7128i	0.540282	+	0.935795i	0.998888	+	0.0471555i	$0.0150156\pi$
$877$	16.0000	+	27.7128i	0.540282	+	0.935795i	−0.458606	+	0.888640i	$0.651651\pi$
$878$	−7.50000	+	12.9904i	−0.253113	+	0.438404i
$879$	24.0000	−	41.5692i	0.809500	−	1.40209i
$880$		0			0
$881$	−1.50000	+	2.59808i	−0.0505363	+	0.0875314i	−0.890187	−	0.455595i	$-0.849426\pi$
$881$	−1.50000	+	2.59808i	−0.0505363	+	0.0875314i	0.839651	+	0.543127i	$0.182760\pi$
$882$	−3.50000	−	6.06218i	−0.117851	−	0.204124i
$883$	13.0000	−	22.5167i	0.437485	−	0.757746i	−0.560010	−	0.828486i	$-0.689203\pi$
$883$	13.0000	−	22.5167i	0.437485	−	0.757746i	0.997495	+	0.0707399i	$0.0225360\pi$
$884$	5.00000	−	8.66025i	0.168168	−	0.291276i
$885$	−24.0000			−0.806751
$886$	−18.0000	+	31.1769i	−0.604722	+	1.04741i
$887$	−13.5000	−	23.3827i	−0.453286	−	0.785114i	0.545302	−	0.838240i	$-0.316415\pi$
$887$	−13.5000	−	23.3827i	−0.453286	−	0.785114i	−0.998588	+	0.0531258i	$0.983082\pi$
$888$	−4.00000			−0.134231
$889$		0			0
$890$	22.0000			0.737442
$891$		0			0
$892$	4.50000	−	7.79423i	0.150671	−	0.260970i
$893$	−10.0000			−0.334637
$894$	2.00000	+	3.46410i	0.0668900	+	0.115857i
$895$		0			0
$896$		0			0
$897$	12.0000			0.400668
$898$	4.50000	−	7.79423i	0.150167	−	0.260097i
$899$		0			0
$900$	−1.00000			−0.0333333
$901$	30.0000	−	51.9615i	0.999445	−	1.73109i
$902$		0			0
$903$		0			0
$904$	5.00000			0.166298
$905$	8.00000			0.265929
$906$	3.00000	+	5.19615i	0.0996683	+	0.172631i
$907$	−7.00000	+	12.1244i	−0.232431	+	0.402583i	−0.958523	−	0.285015i	$-0.908001\pi$
$907$	−7.00000	+	12.1244i	−0.232431	+	0.402583i	0.726092	+	0.687598i	$0.241335\pi$
$908$	−12.0000	+	20.7846i	−0.398234	+	0.689761i
$909$	9.00000	−	15.5885i	0.298511	−	0.517036i
$910$		0			0
$911$	−16.0000	+	27.7128i	−0.530104	+	0.918166i	0.469280	+	0.883050i	$0.344514\pi$
$911$	−16.0000	+	27.7128i	−0.530104	+	0.918166i	−0.999383	+	0.0351168i	$0.988820\pi$
$912$	−2.00000	−	3.46410i	−0.0662266	−	0.114708i
$913$		0			0
$914$	7.00000			0.231539
$915$	−4.00000	−	6.92820i	−0.132236	−	0.229039i
$916$	−2.00000	−	3.46410i	−0.0660819	−	0.114457i
$917$		0			0
$918$	20.0000			0.660098
$919$	25.0000			0.824674			0.412337	−	0.911031i	$-0.364713\pi$
$919$	25.0000			0.824674			0.412337	+	0.911031i	$0.364713\pi$
$920$	3.00000	+	5.19615i	0.0989071	+	0.171312i
$921$	30.0000	−	51.9615i	0.988534	−	1.71219i
$922$	−12.0000	−	20.7846i	−0.395199	−	0.684505i
$923$	−3.00000	−	5.19615i	−0.0987462	−	0.171033i
$924$		0			0
$925$	1.00000	−	1.73205i	0.0328798	−	0.0569495i
$926$	5.00000			0.164310
$927$	10.0000	−	1.73205i	0.328443	−	0.0568880i
$928$		0			0
$929$	17.5000	−	30.3109i	0.574156	−	0.994468i	−0.421976	−	0.906607i	$-0.638663\pi$
$929$	17.5000	−	30.3109i	0.574156	−	0.994468i	0.996133	−	0.0878612i	$-0.0280032\pi$
$930$	20.0000			0.655826
$931$	7.00000	+	12.1244i	0.229416	+	0.397360i
$932$	9.00000	+	15.5885i	0.294805	+	0.510617i
$933$	−33.0000	+	57.1577i	−1.08037	+	1.87126i
$934$	−11.0000	−	19.0526i	−0.359931	−	0.623419i
$935$		0			0
$936$	2.00000			0.0653720
$937$	−42.0000			−1.37208			−0.686040	−	0.727564i	$-0.740653\pi$
$937$	−42.0000			−1.37208			−0.686040	+	0.727564i	$0.740653\pi$
$938$		0			0
$939$	−22.0000	−	38.1051i	−0.717943	−	1.24351i
$940$	10.0000			0.326164
$941$	26.0000			0.847576			0.423788	−	0.905761i	$-0.360700\pi$
$941$	26.0000			0.847576			0.423788	+	0.905761i	$0.360700\pi$
$942$	18.0000	+	31.1769i	0.586472	+	1.01580i
$943$	7.50000	−	12.9904i	0.244234	−	0.423025i
$944$	−3.00000	−	5.19615i	−0.0976417	−	0.169120i
$945$		0			0
$946$		0			0
$947$	21.0000	−	36.3731i	0.682408	−	1.18197i	−0.291835	−	0.956469i	$-0.594266\pi$
$947$	21.0000	−	36.3731i	0.682408	−	1.18197i	0.974244	−	0.225497i	$-0.0724007\pi$
$948$	3.00000	+	5.19615i	0.0974355	+	0.168763i
$949$	−14.0000			−0.454459
$950$	2.00000			0.0648886
$951$	24.0000			0.778253
$952$		0			0
$953$	19.0000	−	32.9090i	0.615470	−	1.06603i	−0.374831	−	0.927093i	$-0.622299\pi$
$953$	19.0000	−	32.9090i	0.615470	−	1.06603i	0.990302	−	0.138933i	$-0.0443673\pi$
$954$	12.0000			0.388514
$955$	12.0000	−	20.7846i	0.388311	−	0.672574i
$956$	9.50000	−	16.4545i	0.307252	−	0.532176i
$957$		0			0
$958$	−7.00000			−0.226160
$959$		0			0
$960$	2.00000	+	3.46410i	0.0645497	+	0.111803i
$961$	−6.00000			−0.193548
$962$	−2.00000	+	3.46410i	−0.0644826	+	0.111687i
$963$	−7.00000	−	12.1244i	−0.225572	−	0.390702i
$964$	2.00000			0.0644157
$965$	−2.00000	−	3.46410i	−0.0643823	−	0.111513i
$966$		0			0
$967$	21.5000	+	37.2391i	0.691393	+	1.19753i	0.971381	+	0.237525i	$0.0763362\pi$
$967$	21.5000	+	37.2391i	0.691393	+	1.19753i	−0.279988	+	0.960003i	$0.590331\pi$
$968$	−5.50000	+	9.52628i	−0.176777	+	0.306186i
$969$	20.0000			0.642493
$970$	19.0000	−	32.9090i	0.610053	−	1.05664i
$971$	−13.0000	+	22.5167i	−0.417190	+	0.722594i	−0.995656	−	0.0931127i	$-0.970318\pi$
$971$	−13.0000	+	22.5167i	−0.417190	+	0.722594i	0.578466	+	0.815707i	$0.303652\pi$
$972$	5.00000	+	8.66025i	0.160375	+	0.277778i
$973$		0			0
$974$	−14.0000	−	24.2487i	−0.448589	−	0.776979i
$975$	−2.00000	+	3.46410i	−0.0640513	+	0.110940i
$976$	1.00000	−	1.73205i	0.0320092	−	0.0554416i
$977$	−1.00000	−	1.73205i	−0.0319928	−	0.0554132i	0.849586	−	0.527451i	$-0.176852\pi$
$977$	−1.00000	−	1.73205i	−0.0319928	−	0.0554132i	−0.881579	+	0.472037i	$0.843519\pi$
$978$	6.00000	+	10.3923i	0.191859	+	0.332309i
$979$		0			0
$980$	−7.00000	−	12.1244i	−0.223607	−	0.387298i
$981$	5.00000	−	8.66025i	0.159638	−	0.276501i
$982$	2.00000	−	3.46410i	0.0638226	−	0.110544i
$983$	8.00000	+	13.8564i	0.255160	+	0.441951i	0.964939	−	0.262474i	$-0.0845384\pi$
$983$	8.00000	+	13.8564i	0.255160	+	0.441951i	−0.709779	+	0.704425i	$0.751205\pi$
$984$	5.00000	−	8.66025i	0.159394	−	0.276079i
$985$	−8.00000	−	13.8564i	−0.254901	−	0.441502i
$986$		0			0
$987$		0			0
$988$	−4.00000			−0.127257
$989$	3.00000	−	5.19615i	0.0953945	−	0.165228i
$990$		0			0
$991$	4.00000			0.127064			0.0635321	−	0.997980i	$-0.479763\pi$
$991$	4.00000			0.127064			0.0635321	+	0.997980i	$0.479763\pi$
$992$	2.50000	+	4.33013i	0.0793751	+	0.137482i
$993$	16.0000			0.507745
$994$		0			0
$995$	−23.0000	+	39.8372i	−0.729149	+	1.26292i
$996$	28.0000			0.887214
$997$	26.0000	+	45.0333i	0.823428	+	1.42622i	0.903115	+	0.429400i	$0.141275\pi$
$997$	26.0000	+	45.0333i	0.823428	+	1.42622i	−0.0796863	+	0.996820i	$0.525392\pi$
$998$	5.00000	+	8.66025i	0.158272	+	0.274136i
$999$	−8.00000			−0.253109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	206.2.c.a.159.1	yes	2
3.2	odd	2		1854.2.f.b.1189.1		2
103.46	even	3	inner	206.2.c.a.149.1	✓	2
309.149	odd	6		1854.2.f.b.973.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
206.2.c.a.149.1	✓	2	103.46	even	3	inner
206.2.c.a.159.1	yes	2	1.1	even	1	trivial
1854.2.f.b.973.1		2	309.149	odd	6
1854.2.f.b.1189.1		2	3.2	odd	2

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:	\( N \)	\(=\)	\( 206 = 2 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	206.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +2.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.00000 + 1.73205i) q^{5} +(1.00000 - 1.73205i) q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +2.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.00000 + 1.73205i) q^{5} +(1.00000 - 1.73205i) q^{6} -1.00000 q^{8} +1.00000 q^{9} +2.00000 q^{10} +(-1.00000 - 1.73205i) q^{12} -2.00000 q^{13} +(2.00000 + 3.46410i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.50000 - 4.33013i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-1.00000 + 1.73205i) q^{19} +(1.00000 - 1.73205i) q^{20} -3.00000 q^{23} -2.00000 q^{24} +(0.500000 - 0.866025i) q^{25} +(-1.00000 + 1.73205i) q^{26} -4.00000 q^{27} +4.00000 q^{30} +5.00000 q^{31} +(0.500000 + 0.866025i) q^{32} -5.00000 q^{34} +(-0.500000 - 0.866025i) q^{36} +2.00000 q^{37} +(1.00000 + 1.73205i) q^{38} -4.00000 q^{39} +(-1.00000 - 1.73205i) q^{40} +(-2.50000 + 4.33013i) q^{41} +(-1.00000 + 1.73205i) q^{43} +(1.00000 + 1.73205i) q^{45} +(-1.50000 + 2.59808i) q^{46} +(2.50000 + 4.33013i) q^{47} +(-1.00000 + 1.73205i) q^{48} +(3.50000 - 6.06218i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-5.00000 - 8.66025i) q^{51} +(1.00000 + 1.73205i) q^{52} +(6.00000 + 10.3923i) q^{53} +(-2.00000 + 3.46410i) q^{54} +(-2.00000 + 3.46410i) q^{57} +(-3.00000 + 5.19615i) q^{59} +(2.00000 - 3.46410i) q^{60} -2.00000 q^{61} +(2.50000 - 4.33013i) q^{62} +1.00000 q^{64} +(-2.00000 - 3.46410i) q^{65} +(-5.00000 - 8.66025i) q^{67} +(-2.50000 + 4.33013i) q^{68} -6.00000 q^{69} +(1.50000 + 2.59808i) q^{71} -1.00000 q^{72} +7.00000 q^{73} +(1.00000 - 1.73205i) q^{74} +(1.00000 - 1.73205i) q^{75} +2.00000 q^{76} +(-2.00000 + 3.46410i) q^{78} -3.00000 q^{79} -2.00000 q^{80} -11.0000 q^{81} +(2.50000 + 4.33013i) q^{82} +(-7.00000 + 12.1244i) q^{83} +(5.00000 - 8.66025i) q^{85} +(1.00000 + 1.73205i) q^{86} +11.0000 q^{89} +2.00000 q^{90} +(1.50000 + 2.59808i) q^{92} +10.0000 q^{93} +5.00000 q^{94} -4.00000 q^{95} +(1.00000 + 1.73205i) q^{96} +(9.50000 - 16.4545i) q^{97} +(-3.50000 - 6.06218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 4 q^{3} - q^{4} + 2 q^{5} + 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + q^2 + 4 * q^3 - q^4 + 2 * q^5 + 2 * q^6 - 2 * q^8 + 2 * q^9	\( 2 q + q^{2} + 4 q^{3} - q^{4} + 2 q^{5} + 2 q^{6} - 2 q^{8} + 2 q^{9} + 4 q^{10} - 2 q^{12} - 4 q^{13} + 4 q^{15} - q^{16} - 5 q^{17} + q^{18} - 2 q^{19} + 2 q^{20} - 6 q^{23} - 4 q^{24} + q^{25} - 2 q^{26} - 8 q^{27} + 8 q^{30} + 10 q^{31} + q^{32} - 10 q^{34} - q^{36} + 4 q^{37} + 2 q^{38} - 8 q^{39} - 2 q^{40} - 5 q^{41} - 2 q^{43} + 2 q^{45} - 3 q^{46} + 5 q^{47} - 2 q^{48} + 7 q^{49} - q^{50} - 10 q^{51} + 2 q^{52} + 12 q^{53} - 4 q^{54} - 4 q^{57} - 6 q^{59} + 4 q^{60} - 4 q^{61} + 5 q^{62} + 2 q^{64} - 4 q^{65} - 10 q^{67} - 5 q^{68} - 12 q^{69} + 3 q^{71} - 2 q^{72} + 14 q^{73} + 2 q^{74} + 2 q^{75} + 4 q^{76} - 4 q^{78} - 6 q^{79} - 4 q^{80} - 22 q^{81} + 5 q^{82} - 14 q^{83} + 10 q^{85} + 2 q^{86} + 22 q^{89} + 4 q^{90} + 3 q^{92} + 20 q^{93} + 10 q^{94} - 8 q^{95} + 2 q^{96} + 19 q^{97} - 7 q^{98}+O(q^{100}) \) 2 * q + q^2 + 4 * q^3 - q^4 + 2 * q^5 + 2 * q^6 - 2 * q^8 + 2 * q^9 + 4 * q^10 - 2 * q^12 - 4 * q^13 + 4 * q^15 - q^16 - 5 * q^17 + q^18 - 2 * q^19 + 2 * q^20 - 6 * q^23 - 4 * q^24 + q^25 - 2 * q^26 - 8 * q^27 + 8 * q^30 + 10 * q^31 + q^32 - 10 * q^34 - q^36 + 4 * q^37 + 2 * q^38 - 8 * q^39 - 2 * q^40 - 5 * q^41 - 2 * q^43 + 2 * q^45 - 3 * q^46 + 5 * q^47 - 2 * q^48 + 7 * q^49 - q^50 - 10 * q^51 + 2 * q^52 + 12 * q^53 - 4 * q^54 - 4 * q^57 - 6 * q^59 + 4 * q^60 - 4 * q^61 + 5 * q^62 + 2 * q^64 - 4 * q^65 - 10 * q^67 - 5 * q^68 - 12 * q^69 + 3 * q^71 - 2 * q^72 + 14 * q^73 + 2 * q^74 + 2 * q^75 + 4 * q^76 - 4 * q^78 - 6 * q^79 - 4 * q^80 - 22 * q^81 + 5 * q^82 - 14 * q^83 + 10 * q^85 + 2 * q^86 + 22 * q^89 + 4 * q^90 + 3 * q^92 + 20 * q^93 + 10 * q^94 - 8 * q^95 + 2 * q^96 + 19 * q^97 - 7 * q^98

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