LMFDB - Embedded newform 825.2.k.c.518.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(518,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("825.518");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.k (of order $4$, 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:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			518.1
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	825.518
Dual form			825.2.k.c.782.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70711 - 1.70711i) q^{2} +(1.41421 + 1.00000i) q^{3} +3.82843i q^{4} +(-0.707107 - 4.12132i) q^{6} +(0.585786 - 0.585786i) q^{7} +(3.12132 - 3.12132i) q^{8} +(1.00000 + 2.82843i) q^{9} +O(q^{10})$	\(q+(-1.70711 - 1.70711i) q^{2} +(1.41421 + 1.00000i) q^{3} +3.82843i q^{4} +(-0.707107 - 4.12132i) q^{6} +(0.585786 - 0.585786i) q^{7} +(3.12132 - 3.12132i) q^{8} +(1.00000 + 2.82843i) q^{9} -1.00000i q^{11} +(-3.82843 + 5.41421i) q^{12} +(2.00000 + 2.00000i) q^{13} -2.00000 q^{14} -3.00000 q^{16} +(2.82843 + 2.82843i) q^{17} +(3.12132 - 6.53553i) q^{18} -2.82843i q^{19} +(1.41421 - 0.242641i) q^{21} +(-1.70711 + 1.70711i) q^{22} +(-5.24264 + 5.24264i) q^{23} +(7.53553 - 1.29289i) q^{24} -6.82843i q^{26} +(-1.41421 + 5.00000i) q^{27} +(2.24264 + 2.24264i) q^{28} +4.82843 q^{29} -8.82843 q^{31} +(-1.12132 - 1.12132i) q^{32} +(1.00000 - 1.41421i) q^{33} -9.65685i q^{34} +(-10.8284 + 3.82843i) q^{36} +(5.82843 - 5.82843i) q^{37} +(-4.82843 + 4.82843i) q^{38} +(0.828427 + 4.82843i) q^{39} +3.65685i q^{41} +(-2.82843 - 2.00000i) q^{42} +(8.24264 + 8.24264i) q^{43} +3.82843 q^{44} +17.8995 q^{46} +(1.24264 + 1.24264i) q^{47} +(-4.24264 - 3.00000i) q^{48} +6.31371i q^{49} +(1.17157 + 6.82843i) q^{51} +(-7.65685 + 7.65685i) q^{52} +(1.00000 - 1.00000i) q^{53} +(10.9497 - 6.12132i) q^{54} -3.65685i q^{56} +(2.82843 - 4.00000i) q^{57} +(-8.24264 - 8.24264i) q^{58} +4.00000 q^{59} +10.4853 q^{61} +(15.0711 + 15.0711i) q^{62} +(2.24264 + 1.07107i) q^{63} +9.82843i q^{64} +(-4.12132 + 0.707107i) q^{66} +(3.58579 - 3.58579i) q^{67} +(-10.8284 + 10.8284i) q^{68} +(-12.6569 + 2.17157i) q^{69} +14.4853i q^{71} +(11.9497 + 5.70711i) q^{72} -19.8995 q^{74} +10.8284 q^{76} +(-0.585786 - 0.585786i) q^{77} +(6.82843 - 9.65685i) q^{78} -5.17157i q^{79} +(-7.00000 + 5.65685i) q^{81} +(6.24264 - 6.24264i) q^{82} +(5.07107 - 5.07107i) q^{83} +(0.928932 + 5.41421i) q^{84} -28.1421i q^{86} +(6.82843 + 4.82843i) q^{87} +(-3.12132 - 3.12132i) q^{88} -1.65685 q^{89} +2.34315 q^{91} +(-20.0711 - 20.0711i) q^{92} +(-12.4853 - 8.82843i) q^{93} -4.24264i q^{94} +(-0.464466 - 2.70711i) q^{96} +(0.656854 - 0.656854i) q^{97} +(10.7782 - 10.7782i) q^{98} +(2.82843 - 1.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 8 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 8 * q^7 + 4 * q^8 + 4 * q^9	$ 4 q - 4 q^{2} + 8 q^{7} + 4 q^{8} + 4 q^{9} - 4 q^{12} + 8 q^{13} - 8 q^{14} - 12 q^{16} + 4 q^{18} - 4 q^{22} - 4 q^{23} + 16 q^{24} - 8 q^{28} + 8 q^{29} - 24 q^{31} + 4 q^{32} + 4 q^{33} - 32 q^{36} + 12 q^{37} - 8 q^{38} - 8 q^{39} + 16 q^{43} + 4 q^{44} + 32 q^{46} - 12 q^{47} + 16 q^{51} - 8 q^{52} + 4 q^{53} + 24 q^{54} - 16 q^{58} + 16 q^{59} + 8 q^{61} + 32 q^{62} - 8 q^{63} - 8 q^{66} + 20 q^{67} - 32 q^{68} - 28 q^{69} + 28 q^{72} - 40 q^{74} + 32 q^{76} - 8 q^{77} + 16 q^{78} - 28 q^{81} + 8 q^{82} - 8 q^{83} + 32 q^{84} + 16 q^{87} - 4 q^{88} + 16 q^{89} + 32 q^{91} - 52 q^{92} - 16 q^{93} - 16 q^{96} - 20 q^{97} + 12 q^{98}+O(q^{100}) $ 4 * q - 4 * q^2 + 8 * q^7 + 4 * q^8 + 4 * q^9 - 4 * q^12 + 8 * q^13 - 8 * q^14 - 12 * q^16 + 4 * q^18 - 4 * q^22 - 4 * q^23 + 16 * q^24 - 8 * q^28 + 8 * q^29 - 24 * q^31 + 4 * q^32 + 4 * q^33 - 32 * q^36 + 12 * q^37 - 8 * q^38 - 8 * q^39 + 16 * q^43 + 4 * q^44 + 32 * q^46 - 12 * q^47 + 16 * q^51 - 8 * q^52 + 4 * q^53 + 24 * q^54 - 16 * q^58 + 16 * q^59 + 8 * q^61 + 32 * q^62 - 8 * q^63 - 8 * q^66 + 20 * q^67 - 32 * q^68 - 28 * q^69 + 28 * q^72 - 40 * q^74 + 32 * q^76 - 8 * q^77 + 16 * q^78 - 28 * q^81 + 8 * q^82 - 8 * q^83 + 32 * q^84 + 16 * q^87 - 4 * q^88 + 16 * q^89 + 32 * q^91 - 52 * q^92 - 16 * q^93 - 16 * q^96 - 20 * q^97 + 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.70711	−	1.70711i	−1.20711	−	1.20711i	−0.971960	−	0.235147i	$-0.924443\pi$
$2$	−1.70711	−	1.70711i	−1.20711	−	1.20711i	−0.235147	−	0.971960i	$-0.575557\pi$
$3$	1.41421	+	1.00000i	0.816497	+	0.577350i
$3$	1.41421	+	1.00000i	0.816497	+	0.577350i
$4$			3.82843i			1.91421i
$5$		0			0
$5$		0			0
$6$	−0.707107	−	4.12132i	−0.288675	−	1.68252i
$7$	0.585786	−	0.585786i	0.221406	−	0.221406i	−0.587684	−	0.809091i	$-0.699960\pi$
$7$	0.585786	−	0.585786i	0.221406	−	0.221406i	0.809091	+	0.587684i	$0.199960\pi$
$8$	3.12132	−	3.12132i	1.10355	−	1.10355i
$9$	1.00000	+	2.82843i	0.333333	+	0.942809i
$10$		0			0
$11$		−	1.00000i		−	0.301511i
$11$		−	1.00000i		−	0.301511i
$12$	−3.82843	+	5.41421i	−1.10517	+	1.56295i
$13$	2.00000	+	2.00000i	0.554700	+	0.554700i	0.927794	−	0.373094i	$-0.121703\pi$
$13$	2.00000	+	2.00000i	0.554700	+	0.554700i	−0.373094	+	0.927794i	$0.621703\pi$
$14$	−2.00000			−0.534522
$15$		0			0
$16$	−3.00000			−0.750000
$17$	2.82843	+	2.82843i	0.685994	+	0.685994i	0.961344	−	0.275350i	$-0.0887937\pi$
$17$	2.82843	+	2.82843i	0.685994	+	0.685994i	−0.275350	+	0.961344i	$0.588794\pi$
$18$	3.12132	−	6.53553i	0.735702	−	1.54044i
$19$		−	2.82843i		−	0.648886i	−0.945905	−	0.324443i	$-0.894823\pi$
$19$		−	2.82843i		−	0.648886i	0.945905	−	0.324443i	$-0.105177\pi$
$20$		0			0
$21$	1.41421	−	0.242641i	0.308607	−	0.0529485i
$22$	−1.70711	+	1.70711i	−0.363956	+	0.363956i
$23$	−5.24264	+	5.24264i	−1.09317	+	1.09317i	−0.0979775	+	0.995189i	$0.531237\pi$
$23$	−5.24264	+	5.24264i	−1.09317	+	1.09317i	−0.995189	+	0.0979775i	$0.968763\pi$
$24$	7.53553	−	1.29289i	1.53818	−	0.263911i
$25$		0			0
$26$		−	6.82843i		−	1.33916i
$27$	−1.41421	+	5.00000i	−0.272166	+	0.962250i
$28$	2.24264	+	2.24264i	0.423819	+	0.423819i
$29$	4.82843			0.896616			0.448308	−	0.893879i	$-0.352027\pi$
$29$	4.82843			0.896616			0.448308	+	0.893879i	$0.352027\pi$
$30$		0			0
$31$	−8.82843			−1.58563			−0.792816	−	0.609461i	$-0.791386\pi$
$31$	−8.82843			−1.58563			−0.792816	+	0.609461i	$0.791386\pi$
$32$	−1.12132	−	1.12132i	−0.198223	−	0.198223i
$33$	1.00000	−	1.41421i	0.174078	−	0.246183i
$34$		−	9.65685i		−	1.65614i
$35$		0			0
$36$	−10.8284	+	3.82843i	−1.80474	+	0.638071i
$37$	5.82843	−	5.82843i	0.958188	−	0.958188i	−0.0409727	−	0.999160i	$-0.513046\pi$
$37$	5.82843	−	5.82843i	0.958188	−	0.958188i	0.999160	+	0.0409727i	$0.0130457\pi$
$38$	−4.82843	+	4.82843i	−0.783274	+	0.783274i
$39$	0.828427	+	4.82843i	0.132655	+	0.773167i
$40$		0			0
$41$			3.65685i			0.571105i	0.958363	+	0.285552i	$0.0921770\pi$
$41$			3.65685i			0.571105i	−0.958363	+	0.285552i	$0.907823\pi$
$42$	−2.82843	−	2.00000i	−0.436436	−	0.308607i
$43$	8.24264	+	8.24264i	1.25699	+	1.25699i	0.952522	+	0.304469i	$0.0984788\pi$
$43$	8.24264	+	8.24264i	1.25699	+	1.25699i	0.304469	+	0.952522i	$0.401521\pi$
$44$	3.82843			0.577157
$45$		0			0
$46$	17.8995			2.63914
$47$	1.24264	+	1.24264i	0.181258	+	0.181258i	0.791904	−	0.610646i	$-0.209090\pi$
$47$	1.24264	+	1.24264i	0.181258	+	0.181258i	−0.610646	+	0.791904i	$0.709090\pi$
$48$	−4.24264	−	3.00000i	−0.612372	−	0.433013i
$49$			6.31371i			0.901958i
$50$		0			0
$51$	1.17157	+	6.82843i	0.164053	+	0.956171i
$52$	−7.65685	+	7.65685i	−1.06181	+	1.06181i
$53$	1.00000	−	1.00000i	0.137361	−	0.137361i	−0.635083	−	0.772444i	$-0.719034\pi$
$53$	1.00000	−	1.00000i	0.137361	−	0.137361i	0.772444	+	0.635083i	$0.219034\pi$
$54$	10.9497	−	6.12132i	1.49007	−	0.833006i
$55$		0			0
$56$		−	3.65685i		−	0.488668i
$57$	2.82843	−	4.00000i	0.374634	−	0.529813i
$58$	−8.24264	−	8.24264i	−1.08231	−	1.08231i
$59$	4.00000			0.520756			0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000			0.520756			0.260378	+	0.965507i	$0.416153\pi$
$60$		0			0
$61$	10.4853			1.34250			0.671251	−	0.741230i	$-0.265757\pi$
$61$	10.4853			1.34250			0.671251	+	0.741230i	$0.265757\pi$
$62$	15.0711	+	15.0711i	1.91403	+	1.91403i
$63$	2.24264	+	1.07107i	0.282546	+	0.134942i
$64$			9.82843i			1.22855i
$65$		0			0
$66$	−4.12132	+	0.707107i	−0.507299	+	0.0870388i
$67$	3.58579	−	3.58579i	0.438074	−	0.438074i	−0.453290	−	0.891363i	$-0.649750\pi$
$67$	3.58579	−	3.58579i	0.438074	−	0.438074i	0.891363	+	0.453290i	$0.149750\pi$
$68$	−10.8284	+	10.8284i	−1.31314	+	1.31314i
$69$	−12.6569	+	2.17157i	−1.52371	+	0.261427i
$70$		0			0
$71$			14.4853i			1.71909i	0.511063	+	0.859543i	$0.329252\pi$
$71$			14.4853i			1.71909i	−0.511063	+	0.859543i	$0.670748\pi$
$72$	11.9497	+	5.70711i	1.40829	+	0.672589i
$73$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$73$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$74$	−19.8995			−2.31327
$75$		0			0
$76$	10.8284			1.24211
$77$	−0.585786	−	0.585786i	−0.0667566	−	0.0667566i
$78$	6.82843	−	9.65685i	0.773167	−	1.09342i
$79$		−	5.17157i		−	0.581847i	−0.956746	−	0.290924i	$-0.906037\pi$
$79$		−	5.17157i		−	0.581847i	0.956746	−	0.290924i	$-0.0939626\pi$
$80$		0			0
$81$	−7.00000	+	5.65685i	−0.777778	+	0.628539i
$82$	6.24264	−	6.24264i	0.689384	−	0.689384i
$83$	5.07107	−	5.07107i	0.556622	−	0.556622i	−0.371722	−	0.928344i	$-0.621233\pi$
$83$	5.07107	−	5.07107i	0.556622	−	0.556622i	0.928344	+	0.371722i	$0.121233\pi$
$84$	0.928932	+	5.41421i	0.101355	+	0.590739i
$85$		0			0
$86$		−	28.1421i		−	3.03464i
$87$	6.82843	+	4.82843i	0.732084	+	0.517662i
$88$	−3.12132	−	3.12132i	−0.332734	−	0.332734i
$89$	−1.65685			−0.175626			−0.0878131	−	0.996137i	$-0.527988\pi$
$89$	−1.65685			−0.175626			−0.0878131	+	0.996137i	$0.527988\pi$
$90$		0			0
$91$	2.34315			0.245628
$92$	−20.0711	−	20.0711i	−2.09255	−	2.09255i
$93$	−12.4853	−	8.82843i	−1.29466	−	0.915465i
$94$		−	4.24264i		−	0.437595i
$95$		0			0
$96$	−0.464466	−	2.70711i	−0.0474044	−	0.276293i
$97$	0.656854	−	0.656854i	0.0666934	−	0.0666934i	−0.672973	−	0.739667i	$-0.734983\pi$
$97$	0.656854	−	0.656854i	0.0666934	−	0.0666934i	0.739667	+	0.672973i	$0.234983\pi$
$98$	10.7782	−	10.7782i	1.08876	−	1.08876i
$99$	2.82843	−	1.00000i	0.284268	−	0.100504i
$100$		0			0
$101$		−	12.8284i		−	1.27648i	−0.769839	−	0.638238i	$-0.779664\pi$
$101$		−	12.8284i		−	1.27648i	0.769839	−	0.638238i	$-0.220336\pi$
$102$	9.65685	−	13.6569i	0.956171	−	1.35223i
$103$	3.58579	+	3.58579i	0.353318	+	0.353318i	0.861343	−	0.508025i	$-0.169624\pi$
$103$	3.58579	+	3.58579i	0.353318	+	0.353318i	−0.508025	+	0.861343i	$0.669624\pi$
$104$	12.4853			1.22428
$105$		0			0
$106$	−3.41421			−0.331618
$107$	−8.24264	−	8.24264i	−0.796846	−	0.796846i	0.185751	−	0.982597i	$-0.440528\pi$
$107$	−8.24264	−	8.24264i	−0.796846	−	0.796846i	−0.982597	+	0.185751i	$0.940528\pi$
$108$	−19.1421	−	5.41421i	−1.84195	−	0.520983i
$109$		−	8.82843i		−	0.845610i	−0.906221	−	0.422805i	$-0.861046\pi$
$109$		−	8.82843i		−	0.845610i	0.906221	−	0.422805i	$-0.138954\pi$
$110$		0			0
$111$	14.0711	−	2.41421i	1.33557	−	0.229147i
$112$	−1.75736	+	1.75736i	−0.166055	+	0.166055i
$113$	−0.171573	+	0.171573i	−0.0161402	+	0.0161402i	−0.715131	−	0.698991i	$-0.753633\pi$
$113$	−0.171573	+	0.171573i	−0.0161402	+	0.0161402i	0.698991	+	0.715131i	$0.253633\pi$
$114$	−11.6569	+	2.00000i	−1.09176	+	0.187317i
$115$		0			0
$116$			18.4853i			1.71632i
$117$	−3.65685	+	7.65685i	−0.338076	+	0.707876i
$118$	−6.82843	−	6.82843i	−0.628608	−	0.628608i
$119$	3.31371			0.303767
$120$		0			0
$121$	−1.00000			−0.0909091
$122$	−17.8995	−	17.8995i	−1.62054	−	1.62054i
$123$	−3.65685	+	5.17157i	−0.329727	+	0.466305i
$124$		−	33.7990i		−	3.03524i
$125$		0			0
$126$	−2.00000	−	5.65685i	−0.178174	−	0.503953i
$127$	1.41421	−	1.41421i	0.125491	−	0.125491i	−0.641572	−	0.767063i	$-0.721717\pi$
$127$	1.41421	−	1.41421i	0.125491	−	0.125491i	0.767063	+	0.641572i	$0.221717\pi$
$128$	14.5355	−	14.5355i	1.28477	−	1.28477i
$129$	3.41421	+	19.8995i	0.300605	+	1.75205i
$130$		0			0
$131$			1.17157i			0.102361i	0.998689	+	0.0511804i	$0.0162983\pi$
$131$			1.17157i			0.102361i	−0.998689	+	0.0511804i	$0.983702\pi$
$132$	5.41421	+	3.82843i	0.471247	+	0.333222i
$133$	−1.65685	−	1.65685i	−0.143667	−	0.143667i
$134$	−12.2426			−1.05760
$135$		0			0
$136$	17.6569			1.51406
$137$	5.82843	+	5.82843i	0.497956	+	0.497956i	0.910801	−	0.412845i	$-0.135465\pi$
$137$	5.82843	+	5.82843i	0.497956	+	0.497956i	−0.412845	+	0.910801i	$0.635465\pi$
$138$	25.3137	+	17.8995i	2.15485	+	1.52371i
$139$			6.34315i			0.538019i	0.963138	+	0.269009i	$0.0866962\pi$
$139$			6.34315i			0.538019i	−0.963138	+	0.269009i	$0.913304\pi$
$140$		0			0
$141$	0.514719	+	3.00000i	0.0433471	+	0.252646i
$142$	24.7279	−	24.7279i	2.07512	−	2.07512i
$143$	2.00000	−	2.00000i	0.167248	−	0.167248i
$144$	−3.00000	−	8.48528i	−0.250000	−	0.707107i
$145$		0			0
$146$		0			0
$147$	−6.31371	+	8.92893i	−0.520746	+	0.736446i
$148$	22.3137	+	22.3137i	1.83418	+	1.83418i
$149$	10.0000			0.819232			0.409616	−	0.912258i	$-0.365663\pi$
$149$	10.0000			0.819232			0.409616	+	0.912258i	$0.365663\pi$
$150$		0			0
$151$	−18.1421			−1.47639			−0.738193	−	0.674590i	$-0.764321\pi$
$151$	−18.1421			−1.47639			−0.738193	+	0.674590i	$0.764321\pi$
$152$	−8.82843	−	8.82843i	−0.716080	−	0.716080i
$153$	−5.17157	+	10.8284i	−0.418097	+	0.875426i
$154$			2.00000i			0.161165i
$155$		0			0
$156$	−18.4853	+	3.17157i	−1.48001	+	0.253929i
$157$	−7.48528	+	7.48528i	−0.597390	+	0.597390i	−0.939617	−	0.342227i	$-0.888819\pi$
$157$	−7.48528	+	7.48528i	−0.597390	+	0.597390i	0.342227	+	0.939617i	$0.388819\pi$
$158$	−8.82843	+	8.82843i	−0.702352	+	0.702352i
$159$	2.41421	−	0.414214i	0.191460	−	0.0328493i
$160$		0			0
$161$			6.14214i			0.484068i
$162$	21.6066	+	2.29289i	1.69757	+	0.180147i
$163$	−6.41421	−	6.41421i	−0.502400	−	0.502400i	0.409783	−	0.912183i	$-0.365604\pi$
$163$	−6.41421	−	6.41421i	−0.502400	−	0.502400i	−0.912183	+	0.409783i	$0.865604\pi$
$164$	−14.0000			−1.09322
$165$		0			0
$166$	−17.3137			−1.34380
$167$	−10.7279	−	10.7279i	−0.830152	−	0.830152i	0.157386	−	0.987537i	$-0.449693\pi$
$167$	−10.7279	−	10.7279i	−0.830152	−	0.830152i	−0.987537	+	0.157386i	$0.949693\pi$
$168$	3.65685	−	5.17157i	0.282132	−	0.398996i
$169$		−	5.00000i		−	0.384615i
$170$		0			0
$171$	8.00000	−	2.82843i	0.611775	−	0.216295i
$172$	−31.5563	+	31.5563i	−2.40615	+	2.40615i
$173$	−8.48528	+	8.48528i	−0.645124	+	0.645124i	−0.951811	−	0.306687i	$-0.900780\pi$
$173$	−8.48528	+	8.48528i	−0.645124	+	0.645124i	0.306687	+	0.951811i	$0.400780\pi$
$174$	−3.41421	−	19.8995i	−0.258831	−	1.50858i
$175$		0			0
$176$			3.00000i			0.226134i
$177$	5.65685	+	4.00000i	0.425195	+	0.300658i
$178$	2.82843	+	2.82843i	0.212000	+	0.212000i
$179$	4.14214			0.309598			0.154799	−	0.987946i	$-0.450527\pi$
$179$	4.14214			0.309598			0.154799	+	0.987946i	$0.450527\pi$
$180$		0			0
$181$	−5.65685			−0.420471			−0.210235	−	0.977651i	$-0.567423\pi$
$181$	−5.65685			−0.420471			−0.210235	+	0.977651i	$0.567423\pi$
$182$	−4.00000	−	4.00000i	−0.296500	−	0.296500i
$183$	14.8284	+	10.4853i	1.09615	+	0.775094i
$184$			32.7279i			2.41273i
$185$		0			0
$186$	6.24264	+	36.3848i	0.457733	+	2.66786i
$187$	2.82843	−	2.82843i	0.206835	−	0.206835i
$188$	−4.75736	+	4.75736i	−0.346966	+	0.346966i
$189$	2.10051	+	3.75736i	0.152789	+	0.273308i
$190$		0			0
$191$		−	11.3137i		−	0.818631i	−0.912393	−	0.409316i	$-0.865768\pi$
$191$		−	11.3137i		−	0.818631i	0.912393	−	0.409316i	$-0.134232\pi$
$192$	−9.82843	+	13.8995i	−0.709306	+	1.00311i
$193$	−8.00000	−	8.00000i	−0.575853	−	0.575853i	0.357905	−	0.933758i	$-0.383491\pi$
$193$	−8.00000	−	8.00000i	−0.575853	−	0.575853i	−0.933758	+	0.357905i	$0.883491\pi$
$194$	−2.24264			−0.161012
$195$		0			0
$196$	−24.1716			−1.72654
$197$	14.1421	+	14.1421i	1.00759	+	1.00759i	0.999971	+	0.00761443i	$0.00242377\pi$
$197$	14.1421	+	14.1421i	1.00759	+	1.00759i	0.00761443	+	0.999971i	$0.497576\pi$
$198$	−6.53553	−	3.12132i	−0.464460	−	0.221823i
$199$		−	2.48528i		−	0.176177i	−0.996113	−	0.0880885i	$-0.971924\pi$
$199$		−	2.48528i		−	0.176177i	0.996113	−	0.0880885i	$-0.0280758\pi$
$200$		0			0
$201$	8.65685	−	1.48528i	0.610607	−	0.104764i
$202$	−21.8995	+	21.8995i	−1.54084	+	1.54084i
$203$	2.82843	−	2.82843i	0.198517	−	0.198517i
$204$	−26.1421	+	4.48528i	−1.83032	+	0.314033i
$205$		0			0
$206$		−	12.2426i		−	0.852985i
$207$	−20.0711	−	9.58579i	−1.39504	−	0.666258i
$208$	−6.00000	−	6.00000i	−0.416025	−	0.416025i
$209$	−2.82843			−0.195646
$210$		0			0
$211$	12.4853			0.859522			0.429761	−	0.902943i	$-0.358598\pi$
$211$	12.4853			0.859522			0.429761	+	0.902943i	$0.358598\pi$
$212$	3.82843	+	3.82843i	0.262937	+	0.262937i
$213$	−14.4853	+	20.4853i	−0.992515	+	1.40363i
$214$			28.1421i			1.92376i
$215$		0			0
$216$	11.1924	+	20.0208i	0.761546	+	1.36224i
$217$	−5.17157	+	5.17157i	−0.351069	+	0.351069i
$218$	−15.0711	+	15.0711i	−1.02074	+	1.02074i
$219$		0			0
$220$		0			0
$221$			11.3137i			0.761042i
$222$	−28.1421	−	19.8995i	−1.88878	−	1.33557i
$223$	−14.5563	−	14.5563i	−0.974765	−	0.974765i	0.0249241	−	0.999689i	$-0.492066\pi$
$223$	−14.5563	−	14.5563i	−0.974765	−	0.974765i	−0.999689	+	0.0249241i	$0.992066\pi$
$224$	−1.31371			−0.0877758
$225$		0			0
$226$	0.585786			0.0389659
$227$	1.75736	+	1.75736i	0.116640	+	0.116640i	0.763018	−	0.646378i	$-0.223717\pi$
$227$	1.75736	+	1.75736i	0.116640	+	0.116640i	−0.646378	+	0.763018i	$0.723717\pi$
$228$	15.3137	+	10.8284i	1.01418	+	0.717130i
$229$		−	1.65685i		−	0.109488i	−0.998500	−	0.0547440i	$-0.982566\pi$
$229$		−	1.65685i		−	0.109488i	0.998500	−	0.0547440i	$-0.0174343\pi$
$230$		0			0
$231$	−0.242641	−	1.41421i	−0.0159646	−	0.0930484i
$232$	15.0711	−	15.0711i	0.989464	−	0.989464i
$233$	8.34315	−	8.34315i	0.546578	−	0.546578i	−0.378872	−	0.925449i	$-0.623688\pi$
$233$	8.34315	−	8.34315i	0.546578	−	0.546578i	0.925449	+	0.378872i	$0.123688\pi$
$234$	19.3137	−	6.82843i	1.26258	−	0.446388i
$235$		0			0
$236$			15.3137i			0.996838i
$237$	5.17157	−	7.31371i	0.335930	−	0.475076i
$238$	−5.65685	−	5.65685i	−0.366679	−	0.366679i
$239$	−15.7990			−1.02195			−0.510976	−	0.859595i	$-0.670716\pi$
$239$	−15.7990			−1.02195			−0.510976	+	0.859595i	$0.670716\pi$
$240$		0			0
$241$	−28.1421			−1.81279			−0.906397	−	0.422427i	$-0.861178\pi$
$241$	−28.1421			−1.81279			−0.906397	+	0.422427i	$0.861178\pi$
$242$	1.70711	+	1.70711i	0.109737	+	0.109737i
$243$	−15.5563	+	1.00000i	−0.997940	+	0.0641500i
$244$			40.1421i			2.56984i
$245$		0			0
$246$	15.0711	−	2.58579i	0.960896	−	0.164864i
$247$	5.65685	−	5.65685i	0.359937	−	0.359937i
$248$	−27.5563	+	27.5563i	−1.74983	+	1.74983i
$249$	12.2426	−	2.10051i	0.775846	−	0.133114i
$250$		0			0
$251$			12.1421i			0.766405i	0.923664	+	0.383202i	$0.125179\pi$
$251$			12.1421i			0.766405i	−0.923664	+	0.383202i	$0.874821\pi$
$252$	−4.10051	+	8.58579i	−0.258308	+	0.540854i
$253$	5.24264	+	5.24264i	0.329602	+	0.329602i
$254$	−4.82843			−0.302962
$255$		0			0
$256$	−29.9706			−1.87316
$257$	3.82843	+	3.82843i	0.238811	+	0.238811i	0.816358	−	0.577547i	$-0.195990\pi$
$257$	3.82843	+	3.82843i	0.238811	+	0.238811i	−0.577547	+	0.816358i	$0.695990\pi$
$258$	28.1421	−	39.7990i	1.75205	−	2.47778i
$259$		−	6.82843i		−	0.424298i
$260$		0			0
$261$	4.82843	+	13.6569i	0.298872	+	0.845338i
$262$	2.00000	−	2.00000i	0.123560	−	0.123560i
$263$	−10.2426	+	10.2426i	−0.631588	+	0.631588i	−0.948466	−	0.316878i	$-0.897365\pi$
$263$	−10.2426	+	10.2426i	−0.631588	+	0.631588i	0.316878	+	0.948466i	$0.397365\pi$
$264$	−1.29289	−	7.53553i	−0.0795721	−	0.463780i
$265$		0			0
$266$			5.65685i			0.346844i
$267$	−2.34315	−	1.65685i	−0.143398	−	0.101398i
$268$	13.7279	+	13.7279i	0.838566	+	0.838566i
$269$	14.0000			0.853595			0.426798	−	0.904347i	$-0.359642\pi$
$269$	14.0000			0.853595			0.426798	+	0.904347i	$0.359642\pi$
$270$		0			0
$271$	−8.48528			−0.515444			−0.257722	−	0.966219i	$-0.582972\pi$
$271$	−8.48528			−0.515444			−0.257722	+	0.966219i	$0.582972\pi$
$272$	−8.48528	−	8.48528i	−0.514496	−	0.514496i
$273$	3.31371	+	2.34315i	0.200555	+	0.141814i
$274$		−	19.8995i		−	1.20217i
$275$		0			0
$276$	−8.31371	−	48.4558i	−0.500426	−	2.91670i
$277$	1.51472	−	1.51472i	0.0910106	−	0.0910106i	−0.660136	−	0.751146i	$-0.729501\pi$
$277$	1.51472	−	1.51472i	0.0910106	−	0.0910106i	0.751146	+	0.660136i	$0.229501\pi$
$278$	10.8284	−	10.8284i	0.649446	−	0.649446i
$279$	−8.82843	−	24.9706i	−0.528544	−	1.49495i
$280$		0			0
$281$		−	16.6274i		−	0.991909i	−0.868349	−	0.495954i	$-0.834818\pi$
$281$		−	16.6274i		−	0.991909i	0.868349	−	0.495954i	$-0.165182\pi$
$282$	4.24264	−	6.00000i	0.252646	−	0.357295i
$283$	0.928932	+	0.928932i	0.0552193	+	0.0552193i	0.734177	−	0.678958i	$-0.237568\pi$
$283$	0.928932	+	0.928932i	0.0552193	+	0.0552193i	−0.678958	+	0.734177i	$0.737568\pi$
$284$	−55.4558			−3.29070
$285$		0			0
$286$	−6.82843			−0.403773
$287$	2.14214	+	2.14214i	0.126446	+	0.126446i
$288$	2.05025	−	4.29289i	0.120812	−	0.252961i
$289$		−	1.00000i		−	0.0588235i
$290$		0			0
$291$	1.58579	−	0.272078i	0.0929604	−	0.0159495i
$292$		0			0
$293$	7.65685	−	7.65685i	0.447318	−	0.447318i	−0.447144	−	0.894462i	$-0.647559\pi$
$293$	7.65685	−	7.65685i	0.447318	−	0.447318i	0.894462	+	0.447144i	$0.147559\pi$
$294$	26.0208	−	4.46447i	1.51756	−	0.260373i
$295$		0			0
$296$		−	36.3848i		−	2.11482i
$297$	5.00000	+	1.41421i	0.290129	+	0.0820610i
$298$	−17.0711	−	17.0711i	−0.988900	−	0.988900i
$299$	−20.9706			−1.21276
$300$		0			0
$301$	9.65685			0.556612
$302$	30.9706	+	30.9706i	1.78216	+	1.78216i
$303$	12.8284	−	18.1421i	0.736974	−	1.04224i
$304$			8.48528i			0.486664i
$305$		0			0
$306$	27.3137	−	9.65685i	1.56142	−	0.552046i
$307$	−7.89949	+	7.89949i	−0.450848	+	0.450848i	−0.895636	−	0.444788i	$-0.853279\pi$
$307$	−7.89949	+	7.89949i	−0.450848	+	0.450848i	0.444788	+	0.895636i	$0.353279\pi$
$308$	2.24264	−	2.24264i	0.127786	−	0.127786i
$309$	1.48528	+	8.65685i	0.0844947	+	0.492471i
$310$		0			0
$311$		−	0.142136i		−	0.00805977i	−0.999992	−	0.00402989i	$-0.998717\pi$
$311$		−	0.142136i		−	0.00805977i	0.999992	−	0.00402989i	$-0.00128276\pi$
$312$	17.6569	+	12.4853i	0.999623	+	0.706840i
$313$	−1.34315	−	1.34315i	−0.0759191	−	0.0759191i	0.668128	−	0.744047i	$-0.267096\pi$
$313$	−1.34315	−	1.34315i	−0.0759191	−	0.0759191i	−0.744047	+	0.668128i	$0.767096\pi$
$314$	25.5563			1.44223
$315$		0			0
$316$	19.7990			1.11378
$317$	−20.3137	−	20.3137i	−1.14093	−	1.14093i	−0.988280	−	0.152651i	$-0.951219\pi$
$317$	−20.3137	−	20.3137i	−1.14093	−	1.14093i	−0.152651	−	0.988280i	$-0.548781\pi$
$318$	−4.82843	−	3.41421i	−0.270765	−	0.191460i
$319$		−	4.82843i		−	0.270340i
$320$		0			0
$321$	−3.41421	−	19.8995i	−0.190563	−	1.11068i
$322$	10.4853	−	10.4853i	0.584322	−	0.584322i
$323$	8.00000	−	8.00000i	0.445132	−	0.445132i
$324$	−21.6569	−	26.7990i	−1.20316	−	1.48883i
$325$		0			0
$326$			21.8995i			1.21290i
$327$	8.82843	−	12.4853i	0.488213	−	0.690438i
$328$	11.4142	+	11.4142i	0.630245	+	0.630245i
$329$	1.45584			0.0802633
$330$		0			0
$331$	10.4853			0.576323			0.288162	−	0.957582i	$-0.406956\pi$
$331$	10.4853			0.576323			0.288162	+	0.957582i	$0.406956\pi$
$332$	19.4142	+	19.4142i	1.06549	+	1.06549i
$333$	22.3137	+	10.6569i	1.22278	+	0.583992i
$334$			36.6274i			2.00416i
$335$		0			0
$336$	−4.24264	+	0.727922i	−0.231455	+	0.0397114i
$337$	5.17157	−	5.17157i	0.281714	−	0.281714i	−0.552079	−	0.833792i	$-0.686165\pi$
$337$	5.17157	−	5.17157i	0.281714	−	0.281714i	0.833792	+	0.552079i	$0.186165\pi$
$338$	−8.53553	+	8.53553i	−0.464272	+	0.464272i
$339$	−0.414214	+	0.0710678i	−0.0224970	+	0.00385987i
$340$		0			0
$341$			8.82843i			0.478086i
$342$	−18.4853	−	8.82843i	−0.999570	−	0.477387i
$343$	7.79899	+	7.79899i	0.421106	+	0.421106i
$344$	51.4558			2.77431
$345$		0			0
$346$	28.9706			1.55747
$347$	−17.8995	−	17.8995i	−0.960895	−	0.960895i	0.0383684	−	0.999264i	$-0.487784\pi$
$347$	−17.8995	−	17.8995i	−0.960895	−	0.960895i	−0.999264	+	0.0383684i	$0.987784\pi$
$348$	−18.4853	+	26.1421i	−0.990915	+	1.40137i
$349$		−	30.0000i		−	1.60586i	−0.596071	−	0.802932i	$-0.703272\pi$
$349$		−	30.0000i		−	1.60586i	0.596071	−	0.802932i	$-0.296728\pi$
$350$		0			0
$351$	−12.8284	+	7.17157i	−0.684731	+	0.382790i
$352$	−1.12132	+	1.12132i	−0.0597666	+	0.0597666i
$353$	2.17157	−	2.17157i	0.115581	−	0.115581i	−0.646951	−	0.762532i	$-0.723956\pi$
$353$	2.17157	−	2.17157i	0.115581	−	0.115581i	0.762532	+	0.646951i	$0.223956\pi$
$354$	−2.82843	−	16.4853i	−0.150329	−	0.876183i
$355$		0			0
$356$		−	6.34315i		−	0.336186i
$357$	4.68629	+	3.31371i	0.248025	+	0.175380i
$358$	−7.07107	−	7.07107i	−0.373718	−	0.373718i
$359$	−6.14214			−0.324170			−0.162085	−	0.986777i	$-0.551822\pi$
$359$	−6.14214			−0.324170			−0.162085	+	0.986777i	$0.551822\pi$
$360$		0			0
$361$	11.0000			0.578947
$362$	9.65685	+	9.65685i	0.507553	+	0.507553i
$363$	−1.41421	−	1.00000i	−0.0742270	−	0.0524864i
$364$			8.97056i			0.470185i
$365$		0			0
$366$	−7.41421	−	43.2132i	−0.387547	−	2.25879i
$367$	20.8995	−	20.8995i	1.09094	−	1.09094i	0.0955170	−	0.995428i	$-0.469550\pi$
$367$	20.8995	−	20.8995i	1.09094	−	1.09094i	0.995428	−	0.0955170i	$-0.0304504\pi$
$368$	15.7279	−	15.7279i	0.819875	−	0.819875i
$369$	−10.3431	+	3.65685i	−0.538443	+	0.190368i
$370$		0			0
$371$		−	1.17157i		−	0.0608250i
$372$	33.7990	−	47.7990i	1.75240	−	2.47826i
$373$	−20.4853	−	20.4853i	−1.06069	−	1.06069i	−0.998035	−	0.0626522i	$-0.980044\pi$
$373$	−20.4853	−	20.4853i	−1.06069	−	1.06069i	−0.0626522	−	0.998035i	$-0.519956\pi$
$374$	−9.65685			−0.499344
$375$		0			0
$376$	7.75736			0.400055
$377$	9.65685	+	9.65685i	0.497353	+	0.497353i
$378$	2.82843	−	10.0000i	0.145479	−	0.514344i
$379$		−	0.142136i		−	0.00730102i	−0.999993	−	0.00365051i	$-0.998838\pi$
$379$		−	0.142136i		−	0.00730102i	0.999993	−	0.00365051i	$-0.00116200\pi$
$380$		0			0
$381$	3.41421	−	0.585786i	0.174915	−	0.0300107i
$382$	−19.3137	+	19.3137i	−0.988175	+	0.988175i
$383$	8.07107	−	8.07107i	0.412412	−	0.412412i	−0.470166	−	0.882578i	$-0.655806\pi$
$383$	8.07107	−	8.07107i	0.412412	−	0.412412i	0.882578	+	0.470166i	$0.155806\pi$
$384$	35.0919	−	6.02082i	1.79078	−	0.307248i
$385$		0			0
$386$			27.3137i			1.39023i
$387$	−15.0711	+	31.5563i	−0.766105	+	1.60410i
$388$	2.51472	+	2.51472i	0.127665	+	0.127665i
$389$	−5.31371			−0.269416			−0.134708	−	0.990885i	$-0.543010\pi$
$389$	−5.31371			−0.269416			−0.134708	+	0.990885i	$0.543010\pi$
$390$		0			0
$391$	−29.6569			−1.49981
$392$	19.7071	+	19.7071i	0.995359	+	0.995359i
$393$	−1.17157	+	1.65685i	−0.0590980	+	0.0835772i
$394$		−	48.2843i		−	2.43253i
$395$		0			0
$396$	3.82843	+	10.8284i	0.192386	+	0.544149i
$397$	−11.8284	+	11.8284i	−0.593652	+	0.593652i	−0.938616	−	0.344964i	$-0.887891\pi$
$397$	−11.8284	+	11.8284i	−0.593652	+	0.593652i	0.344964	+	0.938616i	$0.387891\pi$
$398$	−4.24264	+	4.24264i	−0.212664	+	0.212664i
$399$	−0.686292	−	4.00000i	−0.0343575	−	0.200250i
$400$		0			0
$401$			24.3431i			1.21564i	0.794075	+	0.607819i	$0.207956\pi$
$401$			24.3431i			1.21564i	−0.794075	+	0.607819i	$0.792044\pi$
$402$	−17.3137	−	12.2426i	−0.863529	−	0.610607i
$403$	−17.6569	−	17.6569i	−0.879551	−	0.879551i
$404$	49.1127			2.44345
$405$		0			0
$406$	−9.65685			−0.479262
$407$	−5.82843	−	5.82843i	−0.288904	−	0.288904i
$408$	24.9706	+	17.6569i	1.23623	+	0.874145i
$409$		−	1.51472i		−	0.0748980i	−0.999299	−	0.0374490i	$-0.988077\pi$
$409$		−	1.51472i		−	0.0748980i	0.999299	−	0.0374490i	$-0.0119232\pi$
$410$		0			0
$411$	2.41421	+	14.0711i	0.119084	+	0.694075i
$412$	−13.7279	+	13.7279i	−0.676326	+	0.676326i
$413$	2.34315	−	2.34315i	0.115299	−	0.115299i
$414$	17.8995	+	50.6274i	0.879712	+	2.48820i
$415$		0			0
$416$		−	4.48528i		−	0.219909i
$417$	−6.34315	+	8.97056i	−0.310625	+	0.439290i
$418$	4.82843	+	4.82843i	0.236166	+	0.236166i
$419$	35.4558			1.73213			0.866066	−	0.499930i	$-0.166641\pi$
$419$	35.4558			1.73213			0.866066	+	0.499930i	$0.166641\pi$
$420$		0			0
$421$	−4.00000			−0.194948			−0.0974740	−	0.995238i	$-0.531076\pi$
$421$	−4.00000			−0.194948			−0.0974740	+	0.995238i	$0.531076\pi$
$422$	−21.3137	−	21.3137i	−1.03754	−	1.03754i
$423$	−2.27208	+	4.75736i	−0.110472	+	0.231311i
$424$		−	6.24264i		−	0.303169i
$425$		0			0
$426$	59.6985	−	10.2426i	2.89240	−	0.496258i
$427$	6.14214	−	6.14214i	0.297239	−	0.297239i
$428$	31.5563	−	31.5563i	1.52533	−	1.52533i
$429$	4.82843	−	0.828427i	0.233119	−	0.0399968i
$430$		0			0
$431$		−	17.6569i		−	0.850501i	−0.905076	−	0.425250i	$-0.860186\pi$
$431$		−	17.6569i		−	0.850501i	0.905076	−	0.425250i	$-0.139814\pi$
$432$	4.24264	−	15.0000i	0.204124	−	0.721688i
$433$	−22.3137	−	22.3137i	−1.07233	−	1.07233i	−0.997172	−	0.0751567i	$-0.976054\pi$
$433$	−22.3137	−	22.3137i	−1.07233	−	1.07233i	−0.0751567	−	0.997172i	$-0.523946\pi$
$434$	17.6569			0.847556
$435$		0			0
$436$	33.7990			1.61868
$437$	14.8284	+	14.8284i	0.709340	+	0.709340i
$438$		0			0
$439$			15.3137i			0.730883i	0.930834	+	0.365442i	$0.119082\pi$
$439$			15.3137i			0.730883i	−0.930834	+	0.365442i	$0.880918\pi$
$440$		0			0
$441$	−17.8579	+	6.31371i	−0.850374	+	0.300653i
$442$	19.3137	−	19.3137i	0.918659	−	0.918659i
$443$	−29.2426	+	29.2426i	−1.38936	+	1.38936i	−0.562696	+	0.826664i	$0.690236\pi$
$443$	−29.2426	+	29.2426i	−1.38936	+	1.38936i	−0.826664	+	0.562696i	$0.809764\pi$
$444$	9.24264	+	53.8701i	0.438636	+	2.55656i
$445$		0			0
$446$			49.6985i			2.35329i
$447$	14.1421	+	10.0000i	0.668900	+	0.472984i
$448$	5.75736	+	5.75736i	0.272010	+	0.272010i
$449$	36.9706			1.74475			0.872374	−	0.488838i	$-0.162579\pi$
$449$	36.9706			1.74475			0.872374	+	0.488838i	$0.162579\pi$
$450$		0			0
$451$	3.65685			0.172195
$452$	−0.656854	−	0.656854i	−0.0308958	−	0.0308958i
$453$	−25.6569	−	18.1421i	−1.20546	−	0.852392i
$454$		−	6.00000i		−	0.281594i
$455$		0			0
$456$	−3.65685	−	21.3137i	−0.171248	−	0.998106i
$457$	−10.4853	+	10.4853i	−0.490481	+	0.490481i	−0.908458	−	0.417977i	$-0.862739\pi$
$457$	−10.4853	+	10.4853i	−0.490481	+	0.490481i	0.417977	+	0.908458i	$0.362739\pi$
$458$	−2.82843	+	2.82843i	−0.132164	+	0.132164i
$459$	−18.1421	+	10.1421i	−0.846802	+	0.473394i
$460$		0			0
$461$		−	30.4853i		−	1.41984i	−0.704282	−	0.709921i	$-0.748731\pi$
$461$		−	30.4853i		−	1.41984i	0.704282	−	0.709921i	$-0.251269\pi$
$462$	−2.00000	+	2.82843i	−0.0930484	+	0.131590i
$463$	13.7279	+	13.7279i	0.637991	+	0.637991i	0.950059	−	0.312069i	$-0.101022\pi$
$463$	13.7279	+	13.7279i	0.637991	+	0.637991i	−0.312069	+	0.950059i	$0.601022\pi$
$464$	−14.4853			−0.672462
$465$		0			0
$466$	−28.4853			−1.31956
$467$	2.41421	+	2.41421i	0.111716	+	0.111716i	0.760755	−	0.649039i	$-0.224829\pi$
$467$	2.41421	+	2.41421i	0.111716	+	0.111716i	−0.649039	+	0.760755i	$0.724829\pi$
$468$	−29.3137	−	14.0000i	−1.35503	−	0.647150i
$469$		−	4.20101i		−	0.193985i
$470$		0			0
$471$	−18.0711	+	3.10051i	−0.832671	+	0.142864i
$472$	12.4853	−	12.4853i	0.574682	−	0.574682i
$473$	8.24264	−	8.24264i	0.378997	−	0.378997i
$474$	−21.3137	+	3.65685i	−0.978971	+	0.167965i
$475$		0			0
$476$			12.6863i			0.581475i
$477$	3.82843	+	1.82843i	0.175292	+	0.0837179i
$478$	26.9706	+	26.9706i	1.23360	+	1.23360i
$479$	1.85786			0.0848880			0.0424440	−	0.999099i	$-0.486486\pi$
$479$	1.85786			0.0848880			0.0424440	+	0.999099i	$0.486486\pi$
$480$		0			0
$481$	23.3137			1.06301
$482$	48.0416	+	48.0416i	2.18824	+	2.18824i
$483$	−6.14214	+	8.68629i	−0.279477	+	0.395240i
$484$		−	3.82843i		−	0.174019i
$485$		0			0
$486$	28.2635	+	24.8492i	1.28206	+	1.12718i
$487$	13.7279	−	13.7279i	0.622072	−	0.622072i	−0.323989	−	0.946061i	$-0.605024\pi$
$487$	13.7279	−	13.7279i	0.622072	−	0.622072i	0.946061	+	0.323989i	$0.105024\pi$
$488$	32.7279	−	32.7279i	1.48152	−	1.48152i
$489$	−2.65685	−	15.4853i	−0.120147	−	0.700269i
$490$		0			0
$491$		−	20.0000i		−	0.902587i	−0.892375	−	0.451294i	$-0.850963\pi$
$491$		−	20.0000i		−	0.902587i	0.892375	−	0.451294i	$-0.149037\pi$
$492$	−19.7990	−	14.0000i	−0.892607	−	0.631169i
$493$	13.6569	+	13.6569i	0.615074	+	0.615074i
$494$	−19.3137			−0.868965
$495$		0			0
$496$	26.4853			1.18922
$497$	8.48528	+	8.48528i	0.380617	+	0.380617i
$498$	−24.4853	−	17.3137i	−1.09721	−	0.775846i
$499$			19.1716i			0.858237i	0.903248	+	0.429119i	$0.141176\pi$
$499$			19.1716i			0.858237i	−0.903248	+	0.429119i	$0.858824\pi$
$500$		0			0
$501$	−4.44365	−	25.8995i	−0.198528	−	1.15710i
$502$	20.7279	−	20.7279i	0.925132	−	0.925132i
$503$	15.0711	−	15.0711i	0.671986	−	0.671986i	−0.286188	−	0.958174i	$-0.592388\pi$
$503$	15.0711	−	15.0711i	0.671986	−	0.671986i	0.958174	+	0.286188i	$0.0923881\pi$
$504$	10.3431	−	3.65685i	0.460720	−	0.162889i
$505$		0			0
$506$		−	17.8995i		−	0.795730i
$507$	5.00000	−	7.07107i	0.222058	−	0.314037i
$508$	5.41421	+	5.41421i	0.240217	+	0.240217i
$509$	−24.3431			−1.07899			−0.539495	−	0.841988i	$-0.681385\pi$
$509$	−24.3431			−1.07899			−0.539495	+	0.841988i	$0.681385\pi$
$510$		0			0
$511$		0			0
$512$	22.0919	+	22.0919i	0.976333	+	0.976333i
$513$	14.1421	+	4.00000i	0.624391	+	0.176604i
$514$		−	13.0711i		−	0.576540i
$515$		0			0
$516$	−76.1838	+	13.0711i	−3.35380	+	0.575422i
$517$	1.24264	−	1.24264i	0.0546513	−	0.0546513i
$518$	−11.6569	+	11.6569i	−0.512173	+	0.512173i
$519$	−20.4853	+	3.51472i	−0.899204	+	0.154279i
$520$		0			0
$521$		−	16.3431i		−	0.716006i	−0.933720	−	0.358003i	$-0.883458\pi$
$521$		−	16.3431i		−	0.716006i	0.933720	−	0.358003i	$-0.116542\pi$
$522$	15.0711	−	31.5563i	0.659643	−	1.38118i
$523$	−15.2132	−	15.2132i	−0.665227	−	0.665227i	0.291380	−	0.956607i	$-0.405885\pi$
$523$	−15.2132	−	15.2132i	−0.665227	−	0.665227i	−0.956607	+	0.291380i	$0.905885\pi$
$524$	−4.48528			−0.195940
$525$		0			0
$526$	34.9706			1.52479
$527$	−24.9706	−	24.9706i	−1.08773	−	1.08773i
$528$	−3.00000	+	4.24264i	−0.130558	+	0.184637i
$529$		−	31.9706i		−	1.39002i
$530$		0			0
$531$	4.00000	+	11.3137i	0.173585	+	0.490973i
$532$	6.34315	−	6.34315i	0.275010	−	0.275010i
$533$	−7.31371	+	7.31371i	−0.316792	+	0.316792i
$534$	1.17157	+	6.82843i	0.0506989	+	0.295495i
$535$		0			0
$536$		−	22.3848i		−	0.966875i
$537$	5.85786	+	4.14214i	0.252786	+	0.178746i
$538$	−23.8995	−	23.8995i	−1.03038	−	1.03038i
$539$	6.31371			0.271951
$540$		0			0
$541$	−33.3137			−1.43227			−0.716134	−	0.697963i	$-0.754090\pi$
$541$	−33.3137			−1.43227			−0.716134	+	0.697963i	$0.754090\pi$
$542$	14.4853	+	14.4853i	0.622196	+	0.622196i
$543$	−8.00000	−	5.65685i	−0.343313	−	0.242759i
$544$		−	6.34315i		−	0.271960i
$545$		0			0
$546$	−1.65685	−	9.65685i	−0.0709068	−	0.413275i
$547$	−21.8995	+	21.8995i	−0.936355	+	0.936355i	−0.998092	−	0.0617376i	$-0.980336\pi$
$547$	−21.8995	+	21.8995i	−0.936355	+	0.936355i	0.0617376	+	0.998092i	$0.480336\pi$
$548$	−22.3137	+	22.3137i	−0.953194	+	0.953194i
$549$	10.4853	+	29.6569i	0.447501	+	1.26572i
$550$		0			0
$551$		−	13.6569i		−	0.581802i
$552$	−32.7279	+	46.2843i	−1.39299	+	1.96999i
$553$	−3.02944	−	3.02944i	−0.128825	−	0.128825i
$554$	−5.17157			−0.219719
$555$		0			0
$556$	−24.2843			−1.02988
$557$	−24.9706	−	24.9706i	−1.05804	−	1.05804i	−0.998209	−	0.0598280i	$-0.980945\pi$
$557$	−24.9706	−	24.9706i	−1.05804	−	1.05804i	−0.0598280	−	0.998209i	$-0.519055\pi$
$558$	−27.5563	+	57.6985i	−1.16655	+	2.44257i
$559$			32.9706i			1.39451i
$560$		0			0
$561$	6.82843	−	1.17157i	0.288296	−	0.0494638i
$562$	−28.3848	+	28.3848i	−1.19734	+	1.19734i
$563$	9.89949	−	9.89949i	0.417214	−	0.417214i	−0.467028	−	0.884242i	$-0.654675\pi$
$563$	9.89949	−	9.89949i	0.417214	−	0.417214i	0.884242	+	0.467028i	$0.154675\pi$
$564$	−11.4853	+	1.97056i	−0.483618	+	0.0829757i
$565$		0			0
$566$		−	3.17157i		−	0.133311i
$567$	−0.786797	+	7.41421i	−0.0330423	+	0.311368i
$568$	45.2132	+	45.2132i	1.89710	+	1.89710i
$569$	39.6569			1.66250			0.831251	−	0.555897i	$-0.187625\pi$
$569$	39.6569			1.66250			0.831251	+	0.555897i	$0.187625\pi$
$570$		0			0
$571$	18.3431			0.767637			0.383818	−	0.923409i	$-0.374609\pi$
$571$	18.3431			0.767637			0.383818	+	0.923409i	$0.374609\pi$
$572$	7.65685	+	7.65685i	0.320149	+	0.320149i
$573$	11.3137	−	16.0000i	0.472637	−	0.668410i
$574$		−	7.31371i		−	0.305268i
$575$		0			0
$576$	−27.7990	+	9.82843i	−1.15829	+	0.409518i
$577$	−17.0000	+	17.0000i	−0.707719	+	0.707719i	−0.966055	−	0.258336i	$-0.916826\pi$
$577$	−17.0000	+	17.0000i	−0.707719	+	0.707719i	0.258336	+	0.966055i	$0.416826\pi$
$578$	−1.70711	+	1.70711i	−0.0710063	+	0.0710063i
$579$	−3.31371	−	19.3137i	−0.137713	−	0.802650i
$580$		0			0
$581$		−	5.94113i		−	0.246479i
$582$	−3.17157	−	2.24264i	−0.131466	−	0.0929604i
$583$	−1.00000	−	1.00000i	−0.0414158	−	0.0414158i
$584$		0			0
$585$		0			0
$586$	−26.1421			−1.07992
$587$	2.41421	+	2.41421i	0.0996453	+	0.0996453i	0.755172	−	0.655527i	$-0.227553\pi$
$587$	2.41421	+	2.41421i	0.0996453	+	0.0996453i	−0.655527	+	0.755172i	$0.727553\pi$
$588$	−34.1838	−	24.1716i	−1.40971	−	0.996819i
$589$			24.9706i			1.02889i
$590$		0			0
$591$	5.85786	+	34.1421i	0.240960	+	1.40442i
$592$	−17.4853	+	17.4853i	−0.718641	+	0.718641i
$593$	34.1421	−	34.1421i	1.40205	−	1.40205i	0.608481	−	0.793568i	$-0.291779\pi$
$593$	34.1421	−	34.1421i	1.40205	−	1.40205i	0.793568	−	0.608481i	$-0.208221\pi$
$594$	−6.12132	−	10.9497i	−0.251161	−	0.449274i
$595$		0			0
$596$			38.2843i			1.56818i
$597$	2.48528	−	3.51472i	0.101716	−	0.143848i
$598$	35.7990	+	35.7990i	1.46393	+	1.46393i
$599$	−47.4558			−1.93899			−0.969497	−	0.245105i	$-0.921178\pi$
$599$	−47.4558			−1.93899			−0.969497	+	0.245105i	$0.921178\pi$
$600$		0			0
$601$	23.4558			0.956784			0.478392	−	0.878146i	$-0.341220\pi$
$601$	23.4558			0.956784			0.478392	+	0.878146i	$0.341220\pi$
$602$	−16.4853	−	16.4853i	−0.671890	−	0.671890i
$603$	13.7279	+	6.55635i	0.559044	+	0.266995i
$604$		−	69.4558i		−	2.82612i
$605$		0			0
$606$	−52.8701	+	9.07107i	−2.14770	+	0.368487i
$607$	2.10051	−	2.10051i	0.0852569	−	0.0852569i	−0.663192	−	0.748449i	$-0.730799\pi$
$607$	2.10051	−	2.10051i	0.0852569	−	0.0852569i	0.748449	+	0.663192i	$0.230799\pi$
$608$	−3.17157	+	3.17157i	−0.128624	+	0.128624i
$609$	6.82843	−	1.17157i	0.276702	−	0.0474745i
$610$		0			0
$611$			4.97056i			0.201087i
$612$	−41.4558	−	19.7990i	−1.67575	−	0.800327i
$613$	16.0000	+	16.0000i	0.646234	+	0.646234i	0.952081	−	0.305847i	$-0.0989395\pi$
$613$	16.0000	+	16.0000i	0.646234	+	0.646234i	−0.305847	+	0.952081i	$0.598940\pi$
$614$	26.9706			1.08844
$615$		0			0
$616$	−3.65685			−0.147339
$617$	24.1716	+	24.1716i	0.973111	+	0.973111i	0.999648	−	0.0265370i	$-0.00844797\pi$
$617$	24.1716	+	24.1716i	0.973111	+	0.973111i	−0.0265370	+	0.999648i	$0.508448\pi$
$618$	12.2426	−	17.3137i	0.492471	−	0.696459i
$619$		−	23.3137i		−	0.937057i	−0.883448	−	0.468529i	$-0.844784\pi$
$619$		−	23.3137i		−	0.937057i	0.883448	−	0.468529i	$-0.155216\pi$
$620$		0			0
$621$	−18.7990	−	33.6274i	−0.754377	−	1.34942i
$622$	−0.242641	+	0.242641i	−0.00972901	+	0.00972901i
$623$	−0.970563	+	0.970563i	−0.0388848	+	0.0388848i
$624$	−2.48528	−	14.4853i	−0.0994909	−	0.579875i
$625$		0			0
$626$			4.58579i			0.183285i
$627$	−4.00000	−	2.82843i	−0.159745	−	0.112956i
$628$	−28.6569	−	28.6569i	−1.14353	−	1.14353i
$629$	32.9706			1.31462
$630$		0			0
$631$	16.9706			0.675587			0.337794	−	0.941220i	$-0.390319\pi$
$631$	16.9706			0.675587			0.337794	+	0.941220i	$0.390319\pi$
$632$	−16.1421	−	16.1421i	−0.642100	−	0.642100i
$633$	17.6569	+	12.4853i	0.701797	+	0.496245i
$634$			69.3553i			2.75445i
$635$		0			0
$636$	1.58579	+	9.24264i	0.0628805	+	0.366495i
$637$	−12.6274	+	12.6274i	−0.500316	+	0.500316i
$638$	−8.24264	+	8.24264i	−0.326329	+	0.326329i
$639$	−40.9706	+	14.4853i	−1.62077	+	0.573029i
$640$		0			0
$641$			12.6274i			0.498753i	0.968407	+	0.249376i	$0.0802257\pi$
$641$			12.6274i			0.498753i	−0.968407	+	0.249376i	$0.919774\pi$
$642$	−28.1421	+	39.7990i	−1.11068	+	1.57074i
$643$	0.757359	+	0.757359i	0.0298673	+	0.0298673i	0.721883	−	0.692015i	$-0.243277\pi$
$643$	0.757359	+	0.757359i	0.0298673	+	0.0298673i	−0.692015	+	0.721883i	$0.743277\pi$
$644$	−23.5147			−0.926610
$645$		0			0
$646$	−27.3137			−1.07464
$647$	−13.7279	−	13.7279i	−0.539700	−	0.539700i	0.383741	−	0.923441i	$-0.374636\pi$
$647$	−13.7279	−	13.7279i	−0.539700	−	0.539700i	−0.923441	+	0.383741i	$0.874636\pi$
$648$	−4.19239	+	39.5061i	−0.164693	+	1.55195i
$649$		−	4.00000i		−	0.157014i
$650$		0			0
$651$	−12.4853	+	2.14214i	−0.489337	+	0.0839569i
$652$	24.5563	−	24.5563i	0.961701	−	0.961701i
$653$	−2.65685	+	2.65685i	−0.103971	+	0.103971i	−0.757179	−	0.653208i	$-0.773423\pi$
$653$	−2.65685	+	2.65685i	−0.103971	+	0.103971i	0.653208	+	0.757179i	$0.273423\pi$
$654$	−36.3848	+	6.24264i	−1.42276	+	0.244107i
$655$		0			0
$656$		−	10.9706i		−	0.428329i
$657$		0			0
$658$	−2.48528	−	2.48528i	−0.0968864	−	0.0968864i
$659$	−8.97056			−0.349444			−0.174722	−	0.984618i	$-0.555903\pi$
$659$	−8.97056			−0.349444			−0.174722	+	0.984618i	$0.555903\pi$
$660$		0			0
$661$	14.0000			0.544537			0.272268	−	0.962221i	$-0.412226\pi$
$661$	14.0000			0.544537			0.272268	+	0.962221i	$0.412226\pi$
$662$	−17.8995	−	17.8995i	−0.695684	−	0.695684i
$663$	−11.3137	+	16.0000i	−0.439388	+	0.621389i
$664$		−	31.6569i		−	1.22852i
$665$		0			0
$666$	−19.8995	−	56.2843i	−0.771090	−	2.18097i
$667$	−25.3137	+	25.3137i	−0.980151	+	0.980151i
$668$	41.0711	−	41.0711i	1.58909	−	1.58909i
$669$	−6.02944	−	35.1421i	−0.233112	−	1.35867i
$670$		0			0
$671$		−	10.4853i		−	0.404780i
$672$	−1.85786	−	1.31371i	−0.0716687	−	0.0506774i
$673$	33.6569	+	33.6569i	1.29738	+	1.29738i	0.930120	+	0.367257i	$0.119703\pi$
$673$	33.6569	+	33.6569i	1.29738	+	1.29738i	0.367257	+	0.930120i	$0.380297\pi$
$674$	−17.6569			−0.680117
$675$		0			0
$676$	19.1421			0.736236
$677$	8.34315	+	8.34315i	0.320653	+	0.320653i	0.849018	−	0.528365i	$-0.177195\pi$
$677$	8.34315	+	8.34315i	0.320653	+	0.320653i	−0.528365	+	0.849018i	$0.677195\pi$
$678$	0.828427	+	0.585786i	0.0318156	+	0.0224970i
$679$		−	0.769553i		−	0.0295327i
$680$		0			0
$681$	0.727922	+	4.24264i	0.0278940	+	0.162578i
$682$	15.0711	−	15.0711i	0.577101	−	0.577101i
$683$	−17.7279	+	17.7279i	−0.678340	+	0.678340i	−0.959624	−	0.281284i	$-0.909240\pi$
$683$	−17.7279	+	17.7279i	−0.678340	+	0.678340i	0.281284	+	0.959624i	$0.409240\pi$
$684$	10.8284	+	30.6274i	0.414035	+	1.17107i
$685$		0			0
$686$		−	26.6274i		−	1.01664i
$687$	1.65685	−	2.34315i	0.0632129	−	0.0893966i
$688$	−24.7279	−	24.7279i	−0.942743	−	0.942743i
$689$	4.00000			0.152388
$690$		0			0
$691$	20.0000			0.760836			0.380418	−	0.924815i	$-0.375780\pi$
$691$	20.0000			0.760836			0.380418	+	0.924815i	$0.375780\pi$
$692$	−32.4853	−	32.4853i	−1.23491	−	1.23491i
$693$	1.07107	−	2.24264i	0.0406865	−	0.0851909i
$694$			61.1127i			2.31981i
$695$		0			0
$696$	36.3848	−	6.24264i	1.37916	−	0.236627i
$697$	−10.3431	+	10.3431i	−0.391775	+	0.391775i
$698$	−51.2132	+	51.2132i	−1.93845	+	1.93845i
$699$	20.1421	−	3.45584i	0.761846	−	0.130712i
$700$		0			0
$701$		−	21.3137i		−	0.805008i	−0.915418	−	0.402504i	$-0.868140\pi$
$701$		−	21.3137i		−	0.805008i	0.915418	−	0.402504i	$-0.131860\pi$
$702$	34.1421	+	9.65685i	1.28861	+	0.364474i
$703$	−16.4853	−	16.4853i	−0.621754	−	0.621754i
$704$	9.82843			0.370423
$705$		0			0
$706$	−7.41421			−0.279038
$707$	−7.51472	−	7.51472i	−0.282620	−	0.282620i
$708$	−15.3137	+	21.6569i	−0.575524	+	0.813914i
$709$			6.68629i			0.251109i	0.992087	+	0.125554i	$0.0400710\pi$
$709$			6.68629i			0.251109i	−0.992087	+	0.125554i	$0.959929\pi$
$710$		0			0
$711$	14.6274	−	5.17157i	0.548571	−	0.193949i
$712$	−5.17157	+	5.17157i	−0.193813	+	0.193813i
$713$	46.2843	−	46.2843i	1.73336	−	1.73336i
$714$	−2.34315	−	13.6569i	−0.0876900	−	0.511095i
$715$		0			0
$716$			15.8579i			0.592636i
$717$	−22.3431	−	15.7990i	−0.834420	−	0.590024i
$718$	10.4853	+	10.4853i	0.391307	+	0.391307i
$719$	−50.7696			−1.89338			−0.946692	−	0.322139i	$-0.895598\pi$
$719$	−50.7696			−1.89338			−0.946692	+	0.322139i	$0.895598\pi$
$720$		0			0
$721$	4.20101			0.156454
$722$	−18.7782	−	18.7782i	−0.698851	−	0.698851i
$723$	−39.7990	−	28.1421i	−1.48014	−	1.04662i
$724$		−	21.6569i		−	0.804871i
$725$		0			0
$726$	0.707107	+	4.12132i	0.0262432	+	0.152957i
$727$	22.2132	−	22.2132i	0.823842	−	0.823842i	−0.162815	−	0.986657i	$-0.552057\pi$
$727$	22.2132	−	22.2132i	0.823842	−	0.823842i	0.986657	+	0.162815i	$0.0520572\pi$
$728$	7.31371	−	7.31371i	0.271064	−	0.271064i
$729$	−23.0000	−	14.1421i	−0.851852	−	0.523783i
$730$		0			0
$731$			46.6274i			1.72458i
$732$	−40.1421	+	56.7696i	−1.48370	+	2.09826i
$733$	35.7990	+	35.7990i	1.32227	+	1.32227i	0.911938	+	0.410328i	$0.134586\pi$
$733$	35.7990	+	35.7990i	1.32227	+	1.32227i	0.410328	+	0.911938i	$0.365414\pi$
$734$	−71.3553			−2.63377
$735$		0			0
$736$	11.7574			0.433382
$737$	−3.58579	−	3.58579i	−0.132084	−	0.132084i
$738$	23.8995	+	11.4142i	0.879753	+	0.420163i
$739$			30.6274i			1.12665i	0.826236	+	0.563324i	$0.190478\pi$
$739$			30.6274i			1.12665i	−0.826236	+	0.563324i	$0.809522\pi$
$740$		0			0
$741$	13.6569	−	2.34315i	0.501697	−	0.0860776i
$742$	−2.00000	+	2.00000i	−0.0734223	+	0.0734223i
$743$	22.0416	−	22.0416i	0.808629	−	0.808629i	−0.175797	−	0.984426i	$-0.556250\pi$
$743$	22.0416	−	22.0416i	0.808629	−	0.808629i	0.984426	+	0.175797i	$0.0562504\pi$
$744$	−66.5269	+	11.4142i	−2.43899	+	0.418465i
$745$		0			0
$746$			69.9411i			2.56073i
$747$	19.4142	+	9.27208i	0.710329	+	0.339248i
$748$	10.8284	+	10.8284i	0.395927	+	0.395927i
$749$	−9.65685			−0.352854
$750$		0			0
$751$	−1.37258			−0.0500863			−0.0250431	−	0.999686i	$-0.507972\pi$
$751$	−1.37258			−0.0500863			−0.0250431	+	0.999686i	$0.507972\pi$
$752$	−3.72792	−	3.72792i	−0.135943	−	0.135943i
$753$	−12.1421	+	17.1716i	−0.442484	+	0.625767i
$754$		−	32.9706i		−	1.20072i
$755$		0			0
$756$	−14.3848	+	8.04163i	−0.523169	+	0.292471i
$757$	−5.82843	+	5.82843i	−0.211838	+	0.211838i	−0.805048	−	0.593210i	$-0.797860\pi$
$757$	−5.82843	+	5.82843i	−0.211838	+	0.211838i	0.593210	+	0.805048i	$0.297860\pi$
$758$	−0.242641	+	0.242641i	−0.00881311	+	0.00881311i
$759$	2.17157	+	12.6569i	0.0788231	+	0.459415i
$760$		0			0
$761$			18.4853i			0.670091i	0.942202	+	0.335045i	$0.108752\pi$
$761$			18.4853i			0.670091i	−0.942202	+	0.335045i	$0.891248\pi$
$762$	−6.82843	−	4.82843i	−0.247368	−	0.174915i
$763$	−5.17157	−	5.17157i	−0.187224	−	0.187224i
$764$	43.3137			1.56703
$765$		0			0
$766$	−27.5563			−0.995651
$767$	8.00000	+	8.00000i	0.288863	+	0.288863i
$768$	−42.3848	−	29.9706i	−1.52943	−	1.08147i
$769$			7.37258i			0.265862i	0.991125	+	0.132931i	$0.0424389\pi$
$769$			7.37258i			0.265862i	−0.991125	+	0.132931i	$0.957561\pi$
$770$		0			0
$771$	1.58579	+	9.24264i	0.0571107	+	0.332866i
$772$	30.6274	−	30.6274i	1.10230	−	1.10230i
$773$	−0.656854	+	0.656854i	−0.0236254	+	0.0236254i	−0.718821	−	0.695195i	$-0.755318\pi$
$773$	−0.656854	+	0.656854i	−0.0236254	+	0.0236254i	0.695195	+	0.718821i	$0.255318\pi$
$774$	79.5980	−	28.1421i	2.86109	−	1.01155i
$775$		0			0
$776$		−	4.10051i		−	0.147200i
$777$	6.82843	−	9.65685i	0.244968	−	0.346438i
$778$	9.07107	+	9.07107i	0.325214	+	0.325214i
$779$	10.3431			0.370582
$780$		0			0
$781$	14.4853			0.518324
$782$	50.6274	+	50.6274i	1.81043	+	1.81043i
$783$	−6.82843	+	24.1421i	−0.244028	+	0.862770i
$784$		−	18.9411i		−	0.676469i
$785$		0			0
$786$	4.82843	−	0.828427i	0.172224	−	0.0295490i
$787$	31.4142	−	31.4142i	1.11980	−	1.11980i	0.128025	−	0.991771i	$-0.459136\pi$
$787$	31.4142	−	31.4142i	1.11980	−	1.11980i	0.991771	−	0.128025i	$-0.0408637\pi$
$788$	−54.1421	+	54.1421i	−1.92873	+	1.92873i
$789$	−24.7279	+	4.24264i	−0.880337	+	0.151042i
$790$		0			0
$791$			0.201010i			0.00714710i
$792$	5.70711	−	11.9497i	0.202793	−	0.424616i
$793$	20.9706	+	20.9706i	0.744687	+	0.744687i
$794$	40.3848			1.43320
$795$		0			0
$796$	9.51472			0.337240
$797$	−7.97056	−	7.97056i	−0.282332	−	0.282332i	0.551707	−	0.834038i	$-0.313977\pi$
$797$	−7.97056	−	7.97056i	−0.282332	−	0.282332i	−0.834038	+	0.551707i	$0.813977\pi$
$798$	−5.65685	+	8.00000i	−0.200250	+	0.283197i
$799$			7.02944i			0.248684i
$800$		0			0
$801$	−1.65685	−	4.68629i	−0.0585421	−	0.165582i
$802$	41.5563	−	41.5563i	1.46741	−	1.46741i
$803$		0			0
$804$	5.68629	+	33.1421i	0.200540	+	1.16883i
$805$		0			0
$806$			60.2843i			2.12342i
$807$	19.7990	+	14.0000i	0.696957	+	0.492823i
$808$	−40.0416	−	40.0416i	−1.40866	−	1.40866i
$809$	44.1421			1.55195			0.775977	−	0.630761i	$-0.217257\pi$
$809$	44.1421			1.55195			0.775977	+	0.630761i	$0.217257\pi$
$810$		0			0
$811$	−30.3431			−1.06549			−0.532746	−	0.846275i	$-0.678840\pi$
$811$	−30.3431			−1.06549			−0.532746	+	0.846275i	$0.678840\pi$
$812$	10.8284	+	10.8284i	0.380003	+	0.380003i
$813$	−12.0000	−	8.48528i	−0.420858	−	0.297592i
$814$			19.8995i			0.697477i
$815$		0			0
$816$	−3.51472	−	20.4853i	−0.123040	−	0.717128i
$817$	23.3137	−	23.3137i	0.815643	−	0.815643i
$818$	−2.58579	+	2.58579i	−0.0904099	+	0.0904099i
$819$	2.34315	+	6.62742i	0.0818761	+	0.231581i
$820$		0			0
$821$		−	11.6569i		−	0.406827i	−0.979093	−	0.203414i	$-0.934796\pi$
$821$		−	11.6569i		−	0.406827i	0.979093	−	0.203414i	$-0.0652036\pi$
$822$	19.8995	−	28.1421i	0.694075	−	0.981570i
$823$	15.5858	+	15.5858i	0.543286	+	0.543286i	0.924491	−	0.381204i	$-0.124491\pi$
$823$	15.5858	+	15.5858i	0.543286	+	0.543286i	−0.381204	+	0.924491i	$0.624491\pi$
$824$	22.3848			0.779811
$825$		0			0
$826$	−8.00000			−0.278356
$827$	20.0416	+	20.0416i	0.696916	+	0.696916i	0.963744	−	0.266828i	$-0.0859757\pi$
$827$	20.0416	+	20.0416i	0.696916	+	0.696916i	−0.266828	+	0.963744i	$0.585976\pi$
$828$	36.6985	−	76.8406i	1.27536	−	2.67040i
$829$			22.9706i			0.797801i	0.916994	+	0.398900i	$0.130608\pi$
$829$			22.9706i			0.797801i	−0.916994	+	0.398900i	$0.869392\pi$
$830$		0			0
$831$	3.65685	−	0.627417i	0.126855	−	0.0217649i
$832$	−19.6569	+	19.6569i	−0.681479	+	0.681479i
$833$	−17.8579	+	17.8579i	−0.618738	+	0.618738i
$834$	26.1421	−	4.48528i	0.905228	−	0.155313i
$835$		0			0
$836$		−	10.8284i		−	0.374509i
$837$	12.4853	−	44.1421i	0.431554	−	1.52578i
$838$	−60.5269	−	60.5269i	−2.09087	−	2.09087i
$839$	10.3431			0.357085			0.178543	−	0.983932i	$-0.442862\pi$
$839$	10.3431			0.357085			0.178543	+	0.983932i	$0.442862\pi$
$840$		0			0
$841$	−5.68629			−0.196079
$842$	6.82843	+	6.82843i	0.235323	+	0.235323i
$843$	16.6274	−	23.5147i	0.572679	−	0.809890i
$844$			47.7990i			1.64531i
$845$		0			0
$846$	12.0000	−	4.24264i	0.412568	−	0.145865i
$847$	−0.585786	+	0.585786i	−0.0201279	+	0.0201279i
$848$	−3.00000	+	3.00000i	−0.103020	+	0.103020i
$849$	0.384776	+	2.24264i	0.0132055	+	0.0769672i
$850$		0			0
$851$			61.1127i			2.09492i
$852$	−78.4264	−	55.4558i	−2.68684	−	1.89989i
$853$	10.1421	+	10.1421i	0.347260	+	0.347260i	0.859088	−	0.511828i	$-0.171031\pi$
$853$	10.1421	+	10.1421i	0.347260	+	0.347260i	−0.511828	+	0.859088i	$0.671031\pi$
$854$	−20.9706			−0.717598
$855$		0			0
$856$	−51.4558			−1.75872
$857$	0.485281	+	0.485281i	0.0165769	+	0.0165769i	0.715347	−	0.698770i	$-0.246269\pi$
$857$	0.485281	+	0.485281i	0.0165769	+	0.0165769i	−0.698770	+	0.715347i	$0.746269\pi$
$858$	−9.65685	−	6.82843i	−0.329680	−	0.233119i
$859$		−	36.0000i		−	1.22830i	−0.789188	−	0.614152i	$-0.789498\pi$
$859$		−	36.0000i		−	1.22830i	0.789188	−	0.614152i	$-0.210502\pi$
$860$		0			0
$861$	0.887302	+	5.17157i	0.0302392	+	0.176247i
$862$	−30.1421	+	30.1421i	−1.02665	+	1.02665i
$863$	−18.5563	+	18.5563i	−0.631665	+	0.631665i	−0.948486	−	0.316820i	$-0.897385\pi$
$863$	−18.5563	+	18.5563i	−0.631665	+	0.631665i	0.316820	+	0.948486i	$0.397385\pi$
$864$	7.19239	−	4.02082i	0.244690	−	0.136791i
$865$		0			0
$866$			76.1838i			2.58883i
$867$	1.00000	−	1.41421i	0.0339618	−	0.0480292i
$868$	−19.7990	−	19.7990i	−0.672022	−	0.672022i
$869$	−5.17157			−0.175434
$870$		0			0
$871$	14.3431			0.485999
$872$	−27.5563	−	27.5563i	−0.933176	−	0.933176i
$873$	2.51472	+	1.20101i	0.0851103	+	0.0406480i
$874$		−	50.6274i		−	1.71250i
$875$		0			0
$876$		0			0
$877$	38.6274	−	38.6274i	1.30436	−	1.30436i	0.378930	−	0.925425i	$-0.376292\pi$
$877$	38.6274	−	38.6274i	1.30436	−	1.30436i	0.925425	−	0.378930i	$-0.123708\pi$
$878$	26.1421	−	26.1421i	0.882254	−	0.882254i
$879$	18.4853	−	3.17157i	0.623493	−	0.106974i
$880$		0			0
$881$		−	20.9706i		−	0.706516i	−0.935526	−	0.353258i	$-0.885074\pi$
$881$		−	20.9706i		−	0.706516i	0.935526	−	0.353258i	$-0.114926\pi$
$882$	41.2635	+	19.7071i	1.38941	+	0.663573i
$883$	6.41421	+	6.41421i	0.215855	+	0.215855i	0.806749	−	0.590894i	$-0.201225\pi$
$883$	6.41421	+	6.41421i	0.215855	+	0.215855i	−0.590894	+	0.806749i	$0.701225\pi$
$884$	−43.3137			−1.45680
$885$		0			0
$886$	99.8406			3.35421
$887$	−18.2426	−	18.2426i	−0.612528	−	0.612528i	0.331076	−	0.943604i	$-0.392588\pi$
$887$	−18.2426	−	18.2426i	−0.612528	−	0.612528i	−0.943604	+	0.331076i	$0.892588\pi$
$888$	36.3848	−	51.4558i	1.22099	−	1.72675i
$889$		−	1.65685i		−	0.0555691i
$890$		0			0
$891$	5.65685	+	7.00000i	0.189512	+	0.234509i
$892$	55.7279	−	55.7279i	1.86591	−	1.86591i
$893$	3.51472	−	3.51472i	0.117616	−	0.117616i
$894$	−7.07107	−	41.2132i	−0.236492	−	1.37838i
$895$		0			0
$896$		−	17.0294i		−	0.568914i
$897$	−29.6569	−	20.9706i	−0.990214	−	0.700187i
$898$	−63.1127	−	63.1127i	−2.10610	−	2.10610i
$899$	−42.6274			−1.42170
$900$		0			0
$901$	5.65685			0.188457
$902$	−6.24264	−	6.24264i	−0.207857	−	0.207857i
$903$	13.6569	+	9.65685i	0.454472	+	0.321360i
$904$			1.07107i			0.0356232i
$905$		0			0
$906$	12.8284	+	74.7696i	0.426196	+	2.48405i
$907$	19.0416	−	19.0416i	0.632267	−	0.632267i	−0.316369	−	0.948636i	$-0.602464\pi$
$907$	19.0416	−	19.0416i	0.632267	−	0.632267i	0.948636	+	0.316369i	$0.102464\pi$
$908$	−6.72792	+	6.72792i	−0.223274	+	0.223274i
$909$	36.2843	−	12.8284i	1.20347	−	0.425492i
$910$		0			0
$911$		−	56.0000i		−	1.85536i	−0.373373	−	0.927681i	$-0.621799\pi$
$911$		−	56.0000i		−	1.85536i	0.373373	−	0.927681i	$-0.378201\pi$
$912$	−8.48528	+	12.0000i	−0.280976	+	0.397360i
$913$	−5.07107	−	5.07107i	−0.167828	−	0.167828i
$914$	35.7990			1.18413
$915$		0			0
$916$	6.34315			0.209583
$917$	0.686292	+	0.686292i	0.0226633	+	0.0226633i
$918$	48.2843	+	13.6569i	1.59362	+	0.450743i
$919$		−	30.6274i		−	1.01031i	−0.863030	−	0.505153i	$-0.831436\pi$
$919$		−	30.6274i		−	1.01031i	0.863030	−	0.505153i	$-0.168564\pi$
$920$		0			0
$921$	−19.0711	+	3.27208i	−0.628413	+	0.107819i
$922$	−52.0416	+	52.0416i	−1.71390	+	1.71390i
$923$	−28.9706	+	28.9706i	−0.953578	+	0.953578i
$924$	5.41421	−	0.928932i	0.178115	−	0.0305596i
$925$		0			0
$926$		−	46.8701i		−	1.54025i
$927$	−6.55635	+	13.7279i	−0.215339	+	0.450884i
$928$	−5.41421	−	5.41421i	−0.177730	−	0.177730i
$929$	−18.0000			−0.590561			−0.295280	−	0.955411i	$-0.595413\pi$
$929$	−18.0000			−0.590561			−0.295280	+	0.955411i	$0.595413\pi$
$930$		0			0
$931$	17.8579			0.585268
$932$	31.9411	+	31.9411i	1.04627	+	1.04627i
$933$	0.142136	−	0.201010i	0.00465331	−	0.00658078i
$934$		−	8.24264i		−	0.269707i
$935$		0			0
$936$	12.4853	+	35.3137i	0.408094	+	1.15426i
$937$	−22.9706	+	22.9706i	−0.750416	+	0.750416i	−0.974557	−	0.224141i	$-0.928042\pi$
$937$	−22.9706	+	22.9706i	−0.750416	+	0.750416i	0.224141	+	0.974557i	$0.428042\pi$
$938$	−7.17157	+	7.17157i	−0.234160	+	0.234160i
$939$	−0.556349	−	3.24264i	−0.0181558	−	0.105820i
$940$		0			0
$941$		−	25.1127i		−	0.818651i	−0.912389	−	0.409325i	$-0.865764\pi$
$941$		−	25.1127i		−	0.818651i	0.912389	−	0.409325i	$-0.134236\pi$
$942$	36.1421	+	25.5563i	1.17757	+	0.832671i
$943$	−19.1716	−	19.1716i	−0.624312	−	0.624312i
$944$	−12.0000			−0.390567
$945$		0			0
$946$	−28.1421			−0.914980
$947$	−8.75736	−	8.75736i	−0.284576	−	0.284576i	0.550355	−	0.834931i	$-0.314492\pi$
$947$	−8.75736	−	8.75736i	−0.284576	−	0.284576i	−0.834931	+	0.550355i	$0.814492\pi$
$948$	28.0000	+	19.7990i	0.909398	+	0.643041i
$949$		0			0
$950$		0			0
$951$	−8.41421	−	49.0416i	−0.272850	−	1.59028i
$952$	10.3431	−	10.3431i	0.335223	−	0.335223i
$953$	−33.7990	+	33.7990i	−1.09486	+	1.09486i	−0.0998546	+	0.995002i	$0.531838\pi$
$953$	−33.7990	+	33.7990i	−1.09486	+	1.09486i	−0.995002	+	0.0998546i	$0.968162\pi$
$954$	−3.41421	−	9.65685i	−0.110539	−	0.312652i
$955$		0			0
$956$		−	60.4853i		−	1.95623i
$957$	4.82843	−	6.82843i	0.156081	−	0.220732i
$958$	−3.17157	−	3.17157i	−0.102469	−	0.102469i
$959$	6.82843			0.220501
$960$		0			0
$961$	46.9411			1.51423
$962$	−39.7990	−	39.7990i	−1.28317	−	1.28317i
$963$	15.0711	−	31.5563i	0.485658	−	1.01689i
$964$		−	107.740i		−	3.47008i
$965$		0			0
$966$	25.3137	−	4.34315i	0.814455	−	0.139738i
$967$	−1.61522	+	1.61522i	−0.0519421	+	0.0519421i	−0.732601	−	0.680659i	$-0.761694\pi$
$967$	−1.61522	+	1.61522i	−0.0519421	+	0.0519421i	0.680659	+	0.732601i	$0.261694\pi$
$968$	−3.12132	+	3.12132i	−0.100323	+	0.100323i
$969$	19.3137	−	3.31371i	0.620446	−	0.106452i
$970$		0			0
$971$		−	20.0000i		−	0.641831i	−0.947108	−	0.320915i	$-0.896010\pi$
$971$		−	20.0000i		−	0.641831i	0.947108	−	0.320915i	$-0.103990\pi$
$972$	−3.82843	−	59.5563i	−0.122797	−	1.91027i
$973$	3.71573	+	3.71573i	0.119121	+	0.119121i
$974$	−46.8701			−1.50181
$975$		0			0
$976$	−31.4558			−1.00688
$977$	24.1127	+	24.1127i	0.771434	+	0.771434i	0.978357	−	0.206924i	$-0.0663451\pi$
$977$	24.1127	+	24.1127i	0.771434	+	0.771434i	−0.206924	+	0.978357i	$0.566345\pi$
$978$	−21.8995	+	30.9706i	−0.700269	+	0.990329i
$979$			1.65685i			0.0529533i
$980$		0			0
$981$	24.9706	−	8.82843i	0.797249	−	0.281870i
$982$	−34.1421	+	34.1421i	−1.08952	+	1.08952i
$983$	−1.72792	+	1.72792i	−0.0551122	+	0.0551122i	−0.734126	−	0.679014i	$-0.762408\pi$
$983$	−1.72792	+	1.72792i	−0.0551122	+	0.0551122i	0.679014	+	0.734126i	$0.262408\pi$
$984$	4.72792	+	27.5563i	0.150721	+	0.878464i
$985$		0			0
$986$		−	46.6274i		−	1.48492i
$987$	2.05887	+	1.45584i	0.0655347	+	0.0463400i
$988$	21.6569	+	21.6569i	0.688996	+	0.688996i
$989$	−86.4264			−2.74820
$990$		0			0
$991$	19.1716			0.609005			0.304503	−	0.952512i	$-0.401510\pi$
$991$	19.1716			0.609005			0.304503	+	0.952512i	$0.401510\pi$
$992$	9.89949	+	9.89949i	0.314309	+	0.314309i
$993$	14.8284	+	10.4853i	0.470566	+	0.332740i
$994$		−	28.9706i		−	0.918890i
$995$		0			0
$996$	8.04163	+	46.8701i	0.254809	+	1.48513i
$997$	36.7696	−	36.7696i	1.16450	−	1.16450i	0.181025	−	0.983479i	$-0.442059\pi$
$997$	36.7696	−	36.7696i	1.16450	−	1.16450i	0.983479	−	0.181025i	$-0.0579415\pi$
$998$	32.7279	−	32.7279i	1.03598	−	1.03598i
$999$	20.8995	+	37.3848i	0.661231	+	1.18280i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.k.c.518.1		4
3.2	odd	2		825.2.k.f.518.2		4
5.2	odd	4		825.2.k.f.782.2		4
5.3	odd	4		165.2.k.a.122.1	yes	4
5.4	even	2		165.2.k.b.23.2	yes	4
15.2	even	4	inner	825.2.k.c.782.1		4
15.8	even	4		165.2.k.b.122.2	yes	4
15.14	odd	2		165.2.k.a.23.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.k.a.23.1	✓	4	15.14	odd	2
165.2.k.a.122.1	yes	4	5.3	odd	4
165.2.k.b.23.2	yes	4	5.4	even	2
165.2.k.b.122.2	yes	4	15.8	even	4
825.2.k.c.518.1		4	1.1	even	1	trivial
825.2.k.c.782.1		4	15.2	even	4	inner
825.2.k.f.518.2		4	3.2	odd	2
825.2.k.f.782.2		4	5.2	odd	4

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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.70711 - 1.70711i) q^{2} +(1.41421 + 1.00000i) q^{3} +3.82843i q^{4} +(-0.707107 - 4.12132i) q^{6} +(0.585786 - 0.585786i) q^{7} +(3.12132 - 3.12132i) q^{8} +(1.00000 + 2.82843i) q^{9} +O(q^{10})\)	\(q+(-1.70711 - 1.70711i) q^{2} +(1.41421 + 1.00000i) q^{3} +3.82843i q^{4} +(-0.707107 - 4.12132i) q^{6} +(0.585786 - 0.585786i) q^{7} +(3.12132 - 3.12132i) q^{8} +(1.00000 + 2.82843i) q^{9} -1.00000i q^{11} +(-3.82843 + 5.41421i) q^{12} +(2.00000 + 2.00000i) q^{13} -2.00000 q^{14} -3.00000 q^{16} +(2.82843 + 2.82843i) q^{17} +(3.12132 - 6.53553i) q^{18} -2.82843i q^{19} +(1.41421 - 0.242641i) q^{21} +(-1.70711 + 1.70711i) q^{22} +(-5.24264 + 5.24264i) q^{23} +(7.53553 - 1.29289i) q^{24} -6.82843i q^{26} +(-1.41421 + 5.00000i) q^{27} +(2.24264 + 2.24264i) q^{28} +4.82843 q^{29} -8.82843 q^{31} +(-1.12132 - 1.12132i) q^{32} +(1.00000 - 1.41421i) q^{33} -9.65685i q^{34} +(-10.8284 + 3.82843i) q^{36} +(5.82843 - 5.82843i) q^{37} +(-4.82843 + 4.82843i) q^{38} +(0.828427 + 4.82843i) q^{39} +3.65685i q^{41} +(-2.82843 - 2.00000i) q^{42} +(8.24264 + 8.24264i) q^{43} +3.82843 q^{44} +17.8995 q^{46} +(1.24264 + 1.24264i) q^{47} +(-4.24264 - 3.00000i) q^{48} +6.31371i q^{49} +(1.17157 + 6.82843i) q^{51} +(-7.65685 + 7.65685i) q^{52} +(1.00000 - 1.00000i) q^{53} +(10.9497 - 6.12132i) q^{54} -3.65685i q^{56} +(2.82843 - 4.00000i) q^{57} +(-8.24264 - 8.24264i) q^{58} +4.00000 q^{59} +10.4853 q^{61} +(15.0711 + 15.0711i) q^{62} +(2.24264 + 1.07107i) q^{63} +9.82843i q^{64} +(-4.12132 + 0.707107i) q^{66} +(3.58579 - 3.58579i) q^{67} +(-10.8284 + 10.8284i) q^{68} +(-12.6569 + 2.17157i) q^{69} +14.4853i q^{71} +(11.9497 + 5.70711i) q^{72} -19.8995 q^{74} +10.8284 q^{76} +(-0.585786 - 0.585786i) q^{77} +(6.82843 - 9.65685i) q^{78} -5.17157i q^{79} +(-7.00000 + 5.65685i) q^{81} +(6.24264 - 6.24264i) q^{82} +(5.07107 - 5.07107i) q^{83} +(0.928932 + 5.41421i) q^{84} -28.1421i q^{86} +(6.82843 + 4.82843i) q^{87} +(-3.12132 - 3.12132i) q^{88} -1.65685 q^{89} +2.34315 q^{91} +(-20.0711 - 20.0711i) q^{92} +(-12.4853 - 8.82843i) q^{93} -4.24264i q^{94} +(-0.464466 - 2.70711i) q^{96} +(0.656854 - 0.656854i) q^{97} +(10.7782 - 10.7782i) q^{98} +(2.82843 - 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 8 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 8 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} + 8 q^{7} + 4 q^{8} + 4 q^{9} - 4 q^{12} + 8 q^{13} - 8 q^{14} - 12 q^{16} + 4 q^{18} - 4 q^{22} - 4 q^{23} + 16 q^{24} - 8 q^{28} + 8 q^{29} - 24 q^{31} + 4 q^{32} + 4 q^{33} - 32 q^{36} + 12 q^{37} - 8 q^{38} - 8 q^{39} + 16 q^{43} + 4 q^{44} + 32 q^{46} - 12 q^{47} + 16 q^{51} - 8 q^{52} + 4 q^{53} + 24 q^{54} - 16 q^{58} + 16 q^{59} + 8 q^{61} + 32 q^{62} - 8 q^{63} - 8 q^{66} + 20 q^{67} - 32 q^{68} - 28 q^{69} + 28 q^{72} - 40 q^{74} + 32 q^{76} - 8 q^{77} + 16 q^{78} - 28 q^{81} + 8 q^{82} - 8 q^{83} + 32 q^{84} + 16 q^{87} - 4 q^{88} + 16 q^{89} + 32 q^{91} - 52 q^{92} - 16 q^{93} - 16 q^{96} - 20 q^{97} + 12 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 + 8 * q^7 + 4 * q^8 + 4 * q^9 - 4 * q^12 + 8 * q^13 - 8 * q^14 - 12 * q^16 + 4 * q^18 - 4 * q^22 - 4 * q^23 + 16 * q^24 - 8 * q^28 + 8 * q^29 - 24 * q^31 + 4 * q^32 + 4 * q^33 - 32 * q^36 + 12 * q^37 - 8 * q^38 - 8 * q^39 + 16 * q^43 + 4 * q^44 + 32 * q^46 - 12 * q^47 + 16 * q^51 - 8 * q^52 + 4 * q^53 + 24 * q^54 - 16 * q^58 + 16 * q^59 + 8 * q^61 + 32 * q^62 - 8 * q^63 - 8 * q^66 + 20 * q^67 - 32 * q^68 - 28 * q^69 + 28 * q^72 - 40 * q^74 + 32 * q^76 - 8 * q^77 + 16 * q^78 - 28 * q^81 + 8 * q^82 - 8 * q^83 + 32 * q^84 + 16 * q^87 - 4 * q^88 + 16 * q^89 + 32 * q^91 - 52 * q^92 - 16 * q^93 - 16 * q^96 - 20 * q^97 + 12 * q^98

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