LMFDB - Embedded newform 867.2.h.d.757.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [867,2,Mod(688,867)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(867, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("867.688");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 867 = 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	867.h (of order $8$, degree $4$, not 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:	$6.92302985525$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{8})$
Coefficient field:	$\Q(\zeta_{16})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 51)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			757.2
Root			$0.382683 + 0.923880i$ of defining polynomial
Character	$\chi$	$=$	867.757
Dual form			867.2.h.d.733.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(0.923880 + 0.382683i) q^{3} +1.00000i q^{4} +(-0.923880 + 0.382683i) q^{6} +(-1.53073 - 3.69552i) q^{7} +(-2.12132 - 2.12132i) q^{8} +(0.707107 + 0.707107i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.923880 + 0.382683i) q^{3} +1.00000i q^{4} +(-0.923880 + 0.382683i) q^{6} +(-1.53073 - 3.69552i) q^{7} +(-2.12132 - 2.12132i) q^{8} +(0.707107 + 0.707107i) q^{9} +(3.69552 - 1.53073i) q^{11} +(-0.382683 + 0.923880i) q^{12} +2.00000i q^{13} +(3.69552 + 1.53073i) q^{14} +1.00000 q^{16} -1.00000 q^{18} +(2.82843 - 2.82843i) q^{19} -4.00000i q^{21} +(-1.53073 + 3.69552i) q^{22} +(3.69552 - 1.53073i) q^{23} +(-1.14805 - 2.77164i) q^{24} +(3.53553 + 3.53553i) q^{25} +(-1.41421 - 1.41421i) q^{26} +(0.382683 + 0.923880i) q^{27} +(3.69552 - 1.53073i) q^{28} +(3.69552 + 1.53073i) q^{31} +(3.53553 - 3.53553i) q^{32} +4.00000 q^{33} +(-0.707107 + 0.707107i) q^{36} +(7.39104 + 3.06147i) q^{37} +4.00000i q^{38} +(-0.765367 + 1.84776i) q^{39} +(-3.06147 - 7.39104i) q^{41} +(2.82843 + 2.82843i) q^{42} +(2.82843 + 2.82843i) q^{43} +(1.53073 + 3.69552i) q^{44} +(-1.53073 + 3.69552i) q^{46} -8.00000i q^{47} +(0.923880 + 0.382683i) q^{48} +(-6.36396 + 6.36396i) q^{49} -5.00000 q^{50} -2.00000 q^{52} +(-4.24264 + 4.24264i) q^{53} +(-0.923880 - 0.382683i) q^{54} +(-4.59220 + 11.0866i) q^{56} +(3.69552 - 1.53073i) q^{57} +(-8.48528 - 8.48528i) q^{59} +(3.06147 + 7.39104i) q^{61} +(-3.69552 + 1.53073i) q^{62} +(1.53073 - 3.69552i) q^{63} +7.00000i q^{64} +(-2.82843 + 2.82843i) q^{66} -12.0000 q^{67} +4.00000 q^{69} +(11.0866 + 4.59220i) q^{71} -3.00000i q^{72} +(-7.39104 + 3.06147i) q^{74} +(1.91342 + 4.61940i) q^{75} +(2.82843 + 2.82843i) q^{76} +(-11.3137 - 11.3137i) q^{77} +(-0.765367 - 1.84776i) q^{78} +(-3.69552 + 1.53073i) q^{79} +1.00000i q^{81} +(7.39104 + 3.06147i) q^{82} +(8.48528 - 8.48528i) q^{83} +4.00000 q^{84} -4.00000 q^{86} +(-11.0866 - 4.59220i) q^{88} +10.0000i q^{89} +(7.39104 - 3.06147i) q^{91} +(1.53073 + 3.69552i) q^{92} +(2.82843 + 2.82843i) q^{93} +(5.65685 + 5.65685i) q^{94} +(4.61940 - 1.91342i) q^{96} +(6.12293 - 14.7821i) q^{97} -9.00000i q^{98} +(3.69552 + 1.53073i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q + 8 q^{16} - 8 q^{18} + 32 q^{33} - 40 q^{50} - 16 q^{52} - 96 q^{67} + 32 q^{69} + 32 q^{84} - 32 q^{86}+O(q^{100}) $ 8 * q + 8 * q^16 - 8 * q^18 + 32 * q^33 - 40 * q^50 - 16 * q^52 - 96 * q^67 + 32 * q^69 + 32 * q^84 - 32 * q^86

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$1$	$e\left(\frac{1}{8}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i	−0.911438	−	0.411438i	$-0.865027\pi$
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i	0.411438	+	0.911438i	$0.365027\pi$
$3$	0.923880	+	0.382683i	0.533402	+	0.220942i
$3$	0.923880	+	0.382683i	0.533402	+	0.220942i
$4$			1.00000i			0.500000i
$5$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$5$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$6$	−0.923880	+	0.382683i	−0.377172	+	0.156230i
$7$	−1.53073	−	3.69552i	−0.578563	−	1.39677i	−0.894103	−	0.447862i	$-0.852186\pi$
$7$	−1.53073	−	3.69552i	−0.578563	−	1.39677i	0.315540	−	0.948912i	$-0.397814\pi$
$8$	−2.12132	−	2.12132i	−0.750000	−	0.750000i
$9$	0.707107	+	0.707107i	0.235702	+	0.235702i
$10$		0			0
$11$	3.69552	−	1.53073i	1.11424	−	0.461534i	0.251845	−	0.967768i	$-0.418963\pi$
$11$	3.69552	−	1.53073i	1.11424	−	0.461534i	0.862396	+	0.506234i	$0.168963\pi$
$12$	−0.382683	+	0.923880i	−0.110471	+	0.266701i
$13$			2.00000i			0.554700i	0.960769	+	0.277350i	$0.0894562\pi$
$13$			2.00000i			0.554700i	−0.960769	+	0.277350i	$0.910544\pi$
$14$	3.69552	+	1.53073i	0.987669	+	0.409106i
$15$		0			0
$16$	1.00000			0.250000
$17$		0			0
$17$		0			0
$18$	−1.00000			−0.235702
$19$	2.82843	−	2.82843i	0.648886	−	0.648886i	−0.303838	−	0.952724i	$-0.598268\pi$
$19$	2.82843	−	2.82843i	0.648886	−	0.648886i	0.952724	+	0.303838i	$0.0982682\pi$
$20$		0			0
$21$		−	4.00000i		−	0.872872i
$22$	−1.53073	+	3.69552i	−0.326354	+	0.787887i
$23$	3.69552	−	1.53073i	0.770569	−	0.319180i	0.0374660	−	0.999298i	$-0.488071\pi$
$23$	3.69552	−	1.53073i	0.770569	−	0.319180i	0.733103	+	0.680118i	$0.238071\pi$
$24$	−1.14805	−	2.77164i	−0.234345	−	0.565758i
$25$	3.53553	+	3.53553i	0.707107	+	0.707107i
$26$	−1.41421	−	1.41421i	−0.277350	−	0.277350i
$27$	0.382683	+	0.923880i	0.0736475	+	0.177801i
$28$	3.69552	−	1.53073i	0.698387	−	0.289281i
$29$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$29$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$30$		0			0
$31$	3.69552	+	1.53073i	0.663735	+	0.274928i	0.689009	−	0.724753i	$-0.258046\pi$
$31$	3.69552	+	1.53073i	0.663735	+	0.274928i	−0.0252745	+	0.999681i	$0.508046\pi$
$32$	3.53553	−	3.53553i	0.625000	−	0.625000i
$33$	4.00000			0.696311
$34$		0			0
$35$		0			0
$36$	−0.707107	+	0.707107i	−0.117851	+	0.117851i
$37$	7.39104	+	3.06147i	1.21508	+	0.503302i	0.895842	−	0.444373i	$-0.146573\pi$
$37$	7.39104	+	3.06147i	1.21508	+	0.503302i	0.319237	+	0.947675i	$0.396573\pi$
$38$			4.00000i			0.648886i
$39$	−0.765367	+	1.84776i	−0.122557	+	0.295878i
$40$		0			0
$41$	−3.06147	−	7.39104i	−0.478121	−	1.15429i	−0.960489	−	0.278317i	$-0.910223\pi$
$41$	−3.06147	−	7.39104i	−0.478121	−	1.15429i	0.482368	−	0.875969i	$-0.339777\pi$
$42$	2.82843	+	2.82843i	0.436436	+	0.436436i
$43$	2.82843	+	2.82843i	0.431331	+	0.431331i	0.889081	−	0.457750i	$-0.151344\pi$
$43$	2.82843	+	2.82843i	0.431331	+	0.431331i	−0.457750	+	0.889081i	$0.651344\pi$
$44$	1.53073	+	3.69552i	0.230767	+	0.557120i
$45$		0			0
$46$	−1.53073	+	3.69552i	−0.225694	+	0.544874i
$47$		−	8.00000i		−	1.16692i	−0.812142	−	0.583460i	$-0.801699\pi$
$47$		−	8.00000i		−	1.16692i	0.812142	−	0.583460i	$-0.198301\pi$
$48$	0.923880	+	0.382683i	0.133351	+	0.0552356i
$49$	−6.36396	+	6.36396i	−0.909137	+	0.909137i
$50$	−5.00000			−0.707107
$51$		0			0
$52$	−2.00000			−0.277350
$53$	−4.24264	+	4.24264i	−0.582772	+	0.582772i	−0.935664	−	0.352892i	$-0.885198\pi$
$53$	−4.24264	+	4.24264i	−0.582772	+	0.582772i	0.352892	+	0.935664i	$0.385198\pi$
$54$	−0.923880	−	0.382683i	−0.125724	−	0.0520766i
$55$		0			0
$56$	−4.59220	+	11.0866i	−0.613659	+	1.48150i
$57$	3.69552	−	1.53073i	0.489483	−	0.202751i
$58$		0			0
$59$	−8.48528	−	8.48528i	−1.10469	−	1.10469i	−0.993837	−	0.110853i	$-0.964642\pi$
$59$	−8.48528	−	8.48528i	−1.10469	−	1.10469i	−0.110853	−	0.993837i	$-0.535358\pi$
$60$		0			0
$61$	3.06147	+	7.39104i	0.391981	+	0.946325i	0.989508	+	0.144477i	$0.0461499\pi$
$61$	3.06147	+	7.39104i	0.391981	+	0.946325i	−0.597527	+	0.801848i	$0.703850\pi$
$62$	−3.69552	+	1.53073i	−0.469331	+	0.194403i
$63$	1.53073	−	3.69552i	0.192854	−	0.465592i
$64$			7.00000i			0.875000i
$65$		0			0
$66$	−2.82843	+	2.82843i	−0.348155	+	0.348155i
$67$	−12.0000			−1.46603			−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000			−1.46603			−0.733017	+	0.680211i	$0.761888\pi$
$68$		0			0
$69$	4.00000			0.481543
$70$		0			0
$71$	11.0866	+	4.59220i	1.31573	+	0.544994i	0.926552	−	0.376168i	$-0.122758\pi$
$71$	11.0866	+	4.59220i	1.31573	+	0.544994i	0.389180	+	0.921162i	$0.372758\pi$
$72$		−	3.00000i		−	0.353553i
$73$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$73$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$74$	−7.39104	+	3.06147i	−0.859191	+	0.355888i
$75$	1.91342	+	4.61940i	0.220942	+	0.533402i
$76$	2.82843	+	2.82843i	0.324443	+	0.324443i
$77$	−11.3137	−	11.3137i	−1.28932	−	1.28932i
$78$	−0.765367	−	1.84776i	−0.0866607	−	0.209218i
$79$	−3.69552	+	1.53073i	−0.415778	+	0.172221i	−0.580759	−	0.814076i	$-0.697244\pi$
$79$	−3.69552	+	1.53073i	−0.415778	+	0.172221i	0.164980	+	0.986297i	$0.447244\pi$
$80$		0			0
$81$			1.00000i			0.111111i
$82$	7.39104	+	3.06147i	0.816203	+	0.338083i
$83$	8.48528	−	8.48528i	0.931381	−	0.931381i	−0.0664117	−	0.997792i	$-0.521155\pi$
$83$	8.48528	−	8.48528i	0.931381	−	0.931381i	0.997792	+	0.0664117i	$0.0211551\pi$
$84$	4.00000			0.436436
$85$		0			0
$86$	−4.00000			−0.431331
$87$		0			0
$88$	−11.0866	−	4.59220i	−1.18183	−	0.489530i
$89$			10.0000i			1.06000i	0.847998	+	0.529999i	$0.177808\pi$
$89$			10.0000i			1.06000i	−0.847998	+	0.529999i	$0.822192\pi$
$90$		0			0
$91$	7.39104	−	3.06147i	0.774791	−	0.320929i
$92$	1.53073	+	3.69552i	0.159590	+	0.385284i
$93$	2.82843	+	2.82843i	0.293294	+	0.293294i
$94$	5.65685	+	5.65685i	0.583460	+	0.583460i
$95$		0			0
$96$	4.61940	−	1.91342i	0.471465	−	0.195287i
$97$	6.12293	−	14.7821i	0.621690	−	1.50089i	−0.228028	−	0.973655i	$-0.573228\pi$
$97$	6.12293	−	14.7821i	0.621690	−	1.50089i	0.849718	−	0.527238i	$-0.176772\pi$
$98$		−	9.00000i		−	0.909137i
$99$	3.69552	+	1.53073i	0.371414	+	0.153845i
$100$	−3.53553	+	3.53553i	−0.353553	+	0.353553i
$101$	6.00000			0.597022			0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000			0.597022			0.298511	+	0.954406i	$0.403510\pi$
$102$		0			0
$103$		0			0			−	1.00000i	$-0.5\pi$
$103$		0			0				1.00000i	$0.5\pi$
$104$	4.24264	−	4.24264i	0.416025	−	0.416025i
$105$		0			0
$106$		−	6.00000i		−	0.582772i
$107$	4.59220	−	11.0866i	0.443945	−	1.07178i	−0.530608	−	0.847618i	$-0.678036\pi$
$107$	4.59220	−	11.0866i	0.443945	−	1.07178i	0.974552	−	0.224160i	$-0.0719638\pi$
$108$	−0.923880	+	0.382683i	−0.0889003	+	0.0368237i
$109$	3.06147	+	7.39104i	0.293235	+	0.707933i	1.00000		0.000483966i	$0.000154051\pi$
$109$	3.06147	+	7.39104i	0.293235	+	0.707933i	−0.706764	+	0.707449i	$0.749846\pi$
$110$		0			0
$111$	5.65685	+	5.65685i	0.536925	+	0.536925i
$112$	−1.53073	−	3.69552i	−0.144641	−	0.349194i
$113$	−7.39104	+	3.06147i	−0.695290	+	0.287999i	−0.702202	−	0.711977i	$-0.747800\pi$
$113$	−7.39104	+	3.06147i	−0.695290	+	0.287999i	0.00691210	+	0.999976i	$0.497800\pi$
$114$	−1.53073	+	3.69552i	−0.143366	+	0.346117i
$115$		0			0
$116$		0			0
$117$	−1.41421	+	1.41421i	−0.130744	+	0.130744i
$118$	12.0000			1.10469
$119$		0			0
$120$		0			0
$121$	3.53553	−	3.53553i	0.321412	−	0.321412i
$122$	−7.39104	−	3.06147i	−0.669153	−	0.277172i
$123$		−	8.00000i		−	0.721336i
$124$	−1.53073	+	3.69552i	−0.137464	+	0.331867i
$125$		0			0
$126$	1.53073	+	3.69552i	0.136369	+	0.329223i
$127$	5.65685	+	5.65685i	0.501965	+	0.501965i	0.912048	−	0.410083i	$-0.134500\pi$
$127$	5.65685	+	5.65685i	0.501965	+	0.501965i	−0.410083	+	0.912048i	$0.634500\pi$
$128$	2.12132	+	2.12132i	0.187500	+	0.187500i
$129$	1.53073	+	3.69552i	0.134774	+	0.325372i
$130$		0			0
$131$	1.53073	−	3.69552i	0.133741	−	0.322879i	−0.842795	−	0.538235i	$-0.819091\pi$
$131$	1.53073	−	3.69552i	0.133741	−	0.322879i	0.976536	+	0.215356i	$0.0690912\pi$
$132$			4.00000i			0.348155i
$133$	−14.7821	−	6.12293i	−1.28177	−	0.530926i
$134$	8.48528	−	8.48528i	0.733017	−	0.733017i
$135$		0			0
$136$		0			0
$137$	−10.0000			−0.854358			−0.427179	−	0.904167i	$-0.640493\pi$
$137$	−10.0000			−0.854358			−0.427179	+	0.904167i	$0.640493\pi$
$138$	−2.82843	+	2.82843i	−0.240772	+	0.240772i
$139$	3.69552	+	1.53073i	0.313450	+	0.129835i	0.533862	−	0.845572i	$-0.320740\pi$
$139$	3.69552	+	1.53073i	0.313450	+	0.129835i	−0.220412	+	0.975407i	$0.570740\pi$
$140$		0			0
$141$	3.06147	−	7.39104i	0.257822	−	0.622438i
$142$	−11.0866	+	4.59220i	−0.930363	+	0.385369i
$143$	3.06147	+	7.39104i	0.256013	+	0.618070i
$144$	0.707107	+	0.707107i	0.0589256	+	0.0589256i
$145$		0			0
$146$		0			0
$147$	−8.31492	+	3.44415i	−0.685803	+	0.284069i
$148$	−3.06147	+	7.39104i	−0.251651	+	0.607539i
$149$			6.00000i			0.491539i	0.969328	+	0.245770i	$0.0790407\pi$
$149$			6.00000i			0.491539i	−0.969328	+	0.245770i	$0.920959\pi$
$150$	−4.61940	−	1.91342i	−0.377172	−	0.156230i
$151$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$151$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$152$	−12.0000			−0.973329
$153$		0			0
$154$	16.0000			1.28932
$155$		0			0
$156$	−1.84776	−	0.765367i	−0.147939	−	0.0612784i
$157$			2.00000i			0.159617i	0.996810	+	0.0798087i	$0.0254309\pi$
$157$			2.00000i			0.159617i	−0.996810	+	0.0798087i	$0.974569\pi$
$158$	1.53073	−	3.69552i	0.121779	−	0.294000i
$159$	−5.54328	+	2.29610i	−0.439610	+	0.182093i
$160$		0			0
$161$	−11.3137	−	11.3137i	−0.891645	−	0.891645i
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	−7.65367	−	18.4776i	−0.599482	−	1.44728i	−0.874111	−	0.485726i	$-0.838555\pi$
$163$	−7.65367	−	18.4776i	−0.599482	−	1.44728i	0.274629	−	0.961550i	$-0.411445\pi$
$164$	7.39104	−	3.06147i	0.577143	−	0.239060i
$165$		0			0
$166$			12.0000i			0.931381i
$167$	−11.0866	−	4.59220i	−0.857903	−	0.355355i	−0.0900162	−	0.995940i	$-0.528692\pi$
$167$	−11.0866	−	4.59220i	−0.857903	−	0.355355i	−0.767887	+	0.640585i	$0.778692\pi$
$168$	−8.48528	+	8.48528i	−0.654654	+	0.654654i
$169$	9.00000			0.692308
$170$		0			0
$171$	4.00000			0.305888
$172$	−2.82843	+	2.82843i	−0.215666	+	0.215666i
$173$	−14.7821	−	6.12293i	−1.12386	−	0.465518i	−0.258171	−	0.966099i	$-0.583120\pi$
$173$	−14.7821	−	6.12293i	−1.12386	−	0.465518i	−0.865690	+	0.500581i	$0.833120\pi$
$174$		0			0
$175$	7.65367	−	18.4776i	0.578563	−	1.39677i
$176$	3.69552	−	1.53073i	0.278560	−	0.115383i
$177$	−4.59220	−	11.0866i	−0.345171	−	0.833316i
$178$	−7.07107	−	7.07107i	−0.529999	−	0.529999i
$179$	−2.82843	−	2.82843i	−0.211407	−	0.211407i	0.593458	−	0.804865i	$-0.297762\pi$
$179$	−2.82843	−	2.82843i	−0.211407	−	0.211407i	−0.804865	+	0.593458i	$0.797762\pi$
$180$		0			0
$181$	−7.39104	+	3.06147i	−0.549371	+	0.227557i	−0.640064	−	0.768322i	$-0.721092\pi$
$181$	−7.39104	+	3.06147i	−0.549371	+	0.227557i	0.0906923	+	0.995879i	$0.471092\pi$
$182$	−3.06147	+	7.39104i	−0.226931	+	0.547860i
$183$			8.00000i			0.591377i
$184$	−11.0866	−	4.59220i	−0.817312	−	0.338542i
$185$		0			0
$186$	−4.00000			−0.293294
$187$		0			0
$188$	8.00000			0.583460
$189$	2.82843	−	2.82843i	0.205738	−	0.205738i
$190$		0			0
$191$			8.00000i			0.578860i	0.957199	+	0.289430i	$0.0934657\pi$
$191$			8.00000i			0.578860i	−0.957199	+	0.289430i	$0.906534\pi$
$192$	−2.67878	+	6.46716i	−0.193325	+	0.466727i
$193$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$193$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$194$	6.12293	+	14.7821i	0.439601	+	1.06129i
$195$		0			0
$196$	−6.36396	−	6.36396i	−0.454569	−	0.454569i
$197$	−6.12293	−	14.7821i	−0.436241	−	1.05318i	−0.977236	−	0.212153i	$-0.931952\pi$
$197$	−6.12293	−	14.7821i	−0.436241	−	1.05318i	0.540995	−	0.841026i	$-0.318048\pi$
$198$	−3.69552	+	1.53073i	−0.262629	+	0.108785i
$199$	−7.65367	+	18.4776i	−0.542554	+	1.30984i	0.380361	+	0.924838i	$0.375800\pi$
$199$	−7.65367	+	18.4776i	−0.542554	+	1.30984i	−0.922915	+	0.385004i	$0.874200\pi$
$200$		−	15.0000i		−	1.06066i
$201$	−11.0866	−	4.59220i	−0.781985	−	0.323909i
$202$	−4.24264	+	4.24264i	−0.298511	+	0.298511i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	3.69552	+	1.53073i	0.256856	+	0.106393i
$208$			2.00000i			0.138675i
$209$	6.12293	−	14.7821i	0.423532	−	1.02250i
$210$		0			0
$211$	1.53073	+	3.69552i	0.105380	+	0.254410i	0.967771	−	0.251834i	$-0.0810336\pi$
$211$	1.53073	+	3.69552i	0.105380	+	0.254410i	−0.862390	+	0.506244i	$0.831034\pi$
$212$	−4.24264	−	4.24264i	−0.291386	−	0.291386i
$213$	8.48528	+	8.48528i	0.581402	+	0.581402i
$214$	4.59220	+	11.0866i	0.313916	+	0.757861i
$215$		0			0
$216$	1.14805	−	2.77164i	0.0781149	−	0.188586i
$217$		−	16.0000i		−	1.08615i
$218$	−7.39104	−	3.06147i	−0.500584	−	0.207349i
$219$		0			0
$220$		0			0
$221$		0			0
$222$	−8.00000			−0.536925
$223$	−11.3137	+	11.3137i	−0.757622	+	0.757622i	−0.975889	−	0.218267i	$-0.929960\pi$
$223$	−11.3137	+	11.3137i	−0.757622	+	0.757622i	0.218267	+	0.975889i	$0.429960\pi$
$224$	−18.4776	−	7.65367i	−1.23459	−	0.511382i
$225$			5.00000i			0.333333i
$226$	3.06147	−	7.39104i	0.203646	−	0.491644i
$227$	11.0866	−	4.59220i	0.735840	−	0.304795i	0.0168909	−	0.999857i	$-0.494623\pi$
$227$	11.0866	−	4.59220i	0.735840	−	0.304795i	0.718950	+	0.695062i	$0.244623\pi$
$228$	1.53073	+	3.69552i	0.101375	+	0.244742i
$229$	7.07107	+	7.07107i	0.467269	+	0.467269i	0.901029	−	0.433759i	$-0.142813\pi$
$229$	7.07107	+	7.07107i	0.467269	+	0.467269i	−0.433759	+	0.901029i	$0.642813\pi$
$230$		0			0
$231$	−6.12293	−	14.7821i	−0.402860	−	0.972589i
$232$		0			0
$233$	3.06147	−	7.39104i	0.200563	−	0.484203i	−0.791313	−	0.611412i	$-0.790602\pi$
$233$	3.06147	−	7.39104i	0.200563	−	0.484203i	0.991876	+	0.127209i	$0.0406019\pi$
$234$		−	2.00000i		−	0.130744i
$235$		0			0
$236$	8.48528	−	8.48528i	0.552345	−	0.552345i
$237$	−4.00000			−0.259828
$238$		0			0
$239$	−8.00000			−0.517477			−0.258738	−	0.965947i	$-0.583307\pi$
$239$	−8.00000			−0.517477			−0.258738	+	0.965947i	$0.583307\pi$
$240$		0			0
$241$	−14.7821	−	6.12293i	−0.952197	−	0.394413i	−0.148141	−	0.988966i	$-0.547329\pi$
$241$	−14.7821	−	6.12293i	−0.952197	−	0.394413i	−0.804056	+	0.594553i	$0.797329\pi$
$242$			5.00000i			0.321412i
$243$	−0.382683	+	0.923880i	−0.0245492	+	0.0592669i
$244$	−7.39104	+	3.06147i	−0.473163	+	0.195990i
$245$		0			0
$246$	5.65685	+	5.65685i	0.360668	+	0.360668i
$247$	5.65685	+	5.65685i	0.359937	+	0.359937i
$248$	−4.59220	−	11.0866i	−0.291605	−	0.703997i
$249$	11.0866	−	4.59220i	0.702582	−	0.291019i
$250$		0			0
$251$			12.0000i			0.757433i	0.925513	+	0.378717i	$0.123635\pi$
$251$			12.0000i			0.757433i	−0.925513	+	0.378717i	$0.876365\pi$
$252$	3.69552	+	1.53073i	0.232796	+	0.0964272i
$253$	11.3137	−	11.3137i	0.711287	−	0.711287i
$254$	−8.00000			−0.501965
$255$		0			0
$256$	−17.0000			−1.06250
$257$	1.41421	−	1.41421i	0.0882162	−	0.0882162i	−0.661622	−	0.749838i	$-0.730131\pi$
$257$	1.41421	−	1.41421i	0.0882162	−	0.0882162i	0.749838	+	0.661622i	$0.230131\pi$
$258$	−3.69552	−	1.53073i	−0.230073	−	0.0952993i
$259$		−	32.0000i		−	1.98838i
$260$		0			0
$261$		0			0
$262$	1.53073	+	3.69552i	0.0945690	+	0.228310i
$263$	16.9706	+	16.9706i	1.04645	+	1.04645i	0.998867	+	0.0475824i	$0.0151517\pi$
$263$	16.9706	+	16.9706i	1.04645	+	1.04645i	0.0475824	+	0.998867i	$0.484848\pi$
$264$	−8.48528	−	8.48528i	−0.522233	−	0.522233i
$265$		0			0
$266$	14.7821	−	6.12293i	0.906347	−	0.375421i
$267$	−3.82683	+	9.23880i	−0.234198	+	0.565405i
$268$		−	12.0000i		−	0.733017i
$269$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$269$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$270$		0			0
$271$		0			0			−	1.00000i	$-0.5\pi$
$271$		0			0				1.00000i	$0.5\pi$
$272$		0			0
$273$	8.00000			0.484182
$274$	7.07107	−	7.07107i	0.427179	−	0.427179i
$275$	18.4776	+	7.65367i	1.11424	+	0.461534i
$276$			4.00000i			0.240772i
$277$	3.06147	−	7.39104i	0.183946	−	0.444084i	−0.804827	−	0.593509i	$-0.797742\pi$
$277$	3.06147	−	7.39104i	0.183946	−	0.444084i	0.988773	+	0.149425i	$0.0477421\pi$
$278$	−3.69552	+	1.53073i	−0.221642	+	0.0918073i
$279$	1.53073	+	3.69552i	0.0916426	+	0.221245i
$280$		0			0
$281$	−7.07107	−	7.07107i	−0.421825	−	0.421825i	0.464007	−	0.885832i	$-0.346411\pi$
$281$	−7.07107	−	7.07107i	−0.421825	−	0.421825i	−0.885832	+	0.464007i	$0.846411\pi$
$282$	3.06147	+	7.39104i	0.182308	+	0.440130i
$283$	3.69552	−	1.53073i	0.219676	−	0.0909927i	−0.270131	−	0.962823i	$-0.587067\pi$
$283$	3.69552	−	1.53073i	0.219676	−	0.0909927i	0.489807	+	0.871831i	$0.337067\pi$
$284$	−4.59220	+	11.0866i	−0.272497	+	0.657866i
$285$		0			0
$286$	−7.39104	−	3.06147i	−0.437041	−	0.181028i
$287$	−22.6274	+	22.6274i	−1.33565	+	1.33565i
$288$	5.00000			0.294628
$289$		0			0
$290$		0			0
$291$	11.3137	−	11.3137i	0.663221	−	0.663221i
$292$		0			0
$293$			10.0000i			0.584206i	0.956387	+	0.292103i	$0.0943550\pi$
$293$			10.0000i			0.584206i	−0.956387	+	0.292103i	$0.905645\pi$
$294$	3.44415	−	8.31492i	0.200867	−	0.484936i
$295$		0			0
$296$	−9.18440	−	22.1731i	−0.533833	−	1.28879i
$297$	2.82843	+	2.82843i	0.164122	+	0.164122i
$298$	−4.24264	−	4.24264i	−0.245770	−	0.245770i
$299$	3.06147	+	7.39104i	0.177049	+	0.427435i
$300$	−4.61940	+	1.91342i	−0.266701	+	0.110471i
$301$	6.12293	−	14.7821i	0.352920	−	0.852024i
$302$		0			0
$303$	5.54328	+	2.29610i	0.318453	+	0.131908i
$304$	2.82843	−	2.82843i	0.162221	−	0.162221i
$305$		0			0
$306$		0			0
$307$	−12.0000			−0.684876			−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000			−0.684876			−0.342438	+	0.939540i	$0.611253\pi$
$308$	11.3137	−	11.3137i	0.644658	−	0.644658i
$309$		0			0
$310$		0			0
$311$	−4.59220	+	11.0866i	−0.260400	+	0.628661i	−0.998963	−	0.0455232i	$-0.985505\pi$
$311$	−4.59220	+	11.0866i	−0.260400	+	0.628661i	0.738563	+	0.674184i	$0.235505\pi$
$312$	5.54328	−	2.29610i	0.313826	−	0.129991i
$313$	−6.12293	−	14.7821i	−0.346089	−	0.835532i	−0.997074	−	0.0764418i	$-0.975644\pi$
$313$	−6.12293	−	14.7821i	−0.346089	−	0.835532i	0.650985	−	0.759090i	$-0.274356\pi$
$314$	−1.41421	−	1.41421i	−0.0798087	−	0.0798087i
$315$		0			0
$316$	−1.53073	−	3.69552i	−0.0861105	−	0.207889i
$317$	−29.5641	+	12.2459i	−1.66049	+	0.687797i	−0.998115	−	0.0613775i	$-0.980451\pi$
$317$	−29.5641	+	12.2459i	−1.66049	+	0.687797i	−0.662373	+	0.749174i	$0.730451\pi$
$318$	2.29610	−	5.54328i	0.128759	−	0.310852i
$319$		0			0
$320$		0			0
$321$	8.48528	−	8.48528i	0.473602	−	0.473602i
$322$	16.0000			0.891645
$323$		0			0
$324$	−1.00000			−0.0555556
$325$	−7.07107	+	7.07107i	−0.392232	+	0.392232i
$326$	18.4776	+	7.65367i	1.02338	+	0.423898i
$327$			8.00000i			0.442401i
$328$	−9.18440	+	22.1731i	−0.507124	+	1.22431i
$329$	−29.5641	+	12.2459i	−1.62992	+	0.675137i
$330$		0			0
$331$	−14.1421	−	14.1421i	−0.777322	−	0.777322i	0.202053	−	0.979375i	$-0.435239\pi$
$331$	−14.1421	−	14.1421i	−0.777322	−	0.777322i	−0.979375	+	0.202053i	$0.935239\pi$
$332$	8.48528	+	8.48528i	0.465690	+	0.465690i
$333$	3.06147	+	7.39104i	0.167767	+	0.405026i
$334$	11.0866	−	4.59220i	0.606629	−	0.251274i
$335$		0			0
$336$		−	4.00000i		−	0.218218i
$337$	14.7821	+	6.12293i	0.805231	+	0.333538i	0.747049	−	0.664769i	$-0.231470\pi$
$337$	14.7821	+	6.12293i	0.805231	+	0.333538i	0.0581814	+	0.998306i	$0.481470\pi$
$338$	−6.36396	+	6.36396i	−0.346154	+	0.346154i
$339$	−8.00000			−0.434500
$340$		0			0
$341$	16.0000			0.866449
$342$	−2.82843	+	2.82843i	−0.152944	+	0.152944i
$343$	7.39104	+	3.06147i	0.399078	+	0.165304i
$344$		−	12.0000i		−	0.646997i
$345$		0			0
$346$	14.7821	−	6.12293i	0.794689	−	0.329171i
$347$	1.53073	+	3.69552i	0.0821741	+	0.198386i	0.959626	−	0.281278i	$-0.0907585\pi$
$347$	1.53073	+	3.69552i	0.0821741	+	0.198386i	−0.877452	+	0.479664i	$0.840758\pi$
$348$		0			0
$349$	1.41421	+	1.41421i	0.0757011	+	0.0757011i	0.743944	−	0.668242i	$-0.232953\pi$
$349$	1.41421	+	1.41421i	0.0757011	+	0.0757011i	−0.668242	+	0.743944i	$0.732953\pi$
$350$	7.65367	+	18.4776i	0.409106	+	0.987669i
$351$	−1.84776	+	0.765367i	−0.0986261	+	0.0408523i
$352$	7.65367	−	18.4776i	0.407942	−	0.984859i
$353$			18.0000i			0.958043i	0.877803	+	0.479022i	$0.159008\pi$
$353$			18.0000i			0.958043i	−0.877803	+	0.479022i	$0.840992\pi$
$354$	11.0866	+	4.59220i	0.589244	+	0.244073i
$355$		0			0
$356$	−10.0000			−0.529999
$357$		0			0
$358$	4.00000			0.211407
$359$	−22.6274	+	22.6274i	−1.19423	+	1.19423i	−0.218361	+	0.975868i	$0.570071\pi$
$359$	−22.6274	+	22.6274i	−1.19423	+	1.19423i	−0.975868	+	0.218361i	$0.929929\pi$
$360$		0			0
$361$			3.00000i			0.157895i
$362$	3.06147	−	7.39104i	0.160907	−	0.388464i
$363$	4.61940	−	1.91342i	0.242455	−	0.100428i
$364$	3.06147	+	7.39104i	0.160464	+	0.387396i
$365$		0			0
$366$	−5.65685	−	5.65685i	−0.295689	−	0.295689i
$367$	−4.59220	−	11.0866i	−0.239711	−	0.578713i	0.757542	−	0.652787i	$-0.226400\pi$
$367$	−4.59220	−	11.0866i	−0.239711	−	0.578713i	−0.997253	+	0.0740732i	$0.976400\pi$
$368$	3.69552	−	1.53073i	0.192642	−	0.0797950i
$369$	3.06147	−	7.39104i	0.159374	−	0.384762i
$370$		0			0
$371$	22.1731	+	9.18440i	1.15117	+	0.476830i
$372$	−2.82843	+	2.82843i	−0.146647	+	0.146647i
$373$	−26.0000			−1.34623			−0.673114	−	0.739538i	$-0.735044\pi$
$373$	−26.0000			−1.34623			−0.673114	+	0.739538i	$0.735044\pi$
$374$		0			0
$375$		0			0
$376$	−16.9706	+	16.9706i	−0.875190	+	0.875190i
$377$		0			0
$378$			4.00000i			0.205738i
$379$	−7.65367	+	18.4776i	−0.393143	+	0.949130i	0.596109	+	0.802904i	$0.296713\pi$
$379$	−7.65367	+	18.4776i	−0.393143	+	0.949130i	−0.989251	+	0.146226i	$0.953287\pi$
$380$		0			0
$381$	3.06147	+	7.39104i	0.156844	+	0.378654i
$382$	−5.65685	−	5.65685i	−0.289430	−	0.289430i
$383$	11.3137	+	11.3137i	0.578103	+	0.578103i	0.934380	−	0.356277i	$-0.115954\pi$
$383$	11.3137	+	11.3137i	0.578103	+	0.578103i	−0.356277	+	0.934380i	$0.615954\pi$
$384$	1.14805	+	2.77164i	0.0585862	+	0.141440i
$385$		0			0
$386$		0			0
$387$			4.00000i			0.203331i
$388$	14.7821	+	6.12293i	0.750446	+	0.310845i
$389$	−4.24264	+	4.24264i	−0.215110	+	0.215110i	−0.806434	−	0.591324i	$-0.798606\pi$
$389$	−4.24264	+	4.24264i	−0.215110	+	0.215110i	0.591324	+	0.806434i	$0.298606\pi$
$390$		0			0
$391$		0			0
$392$	27.0000			1.36371
$393$	2.82843	−	2.82843i	0.142675	−	0.142675i
$394$	14.7821	+	6.12293i	0.744710	+	0.308469i
$395$		0			0
$396$	−1.53073	+	3.69552i	−0.0769223	+	0.185707i
$397$	7.39104	−	3.06147i	0.370945	−	0.153651i	−0.189420	−	0.981896i	$-0.560661\pi$
$397$	7.39104	−	3.06147i	0.370945	−	0.153651i	0.560365	+	0.828246i	$0.310661\pi$
$398$	−7.65367	−	18.4776i	−0.383644	−	0.926198i
$399$	−11.3137	−	11.3137i	−0.566394	−	0.566394i
$400$	3.53553	+	3.53553i	0.176777	+	0.176777i
$401$	9.18440	+	22.1731i	0.458647	+	1.10727i	0.968945	+	0.247275i	$0.0795350\pi$
$401$	9.18440	+	22.1731i	0.458647	+	1.10727i	−0.510298	+	0.859997i	$0.670465\pi$
$402$	11.0866	−	4.59220i	0.552947	−	0.229038i
$403$	−3.06147	+	7.39104i	−0.152503	+	0.368174i
$404$			6.00000i			0.298511i
$405$		0			0
$406$		0			0
$407$	32.0000			1.58618
$408$		0			0
$409$	10.0000			0.494468			0.247234	−	0.968956i	$-0.420478\pi$
$409$	10.0000			0.494468			0.247234	+	0.968956i	$0.420478\pi$
$410$		0			0
$411$	−9.23880	−	3.82683i	−0.455716	−	0.188764i
$412$		0			0
$413$	−18.3688	+	44.3462i	−0.903870	+	2.18213i
$414$	−3.69552	+	1.53073i	−0.181625	+	0.0752315i
$415$		0			0
$416$	7.07107	+	7.07107i	0.346688	+	0.346688i
$417$	2.82843	+	2.82843i	0.138509	+	0.138509i
$418$	6.12293	+	14.7821i	0.299483	+	0.723015i
$419$	3.69552	−	1.53073i	0.180538	−	0.0747812i	−0.290583	−	0.956850i	$-0.593849\pi$
$419$	3.69552	−	1.53073i	0.180538	−	0.0747812i	0.471121	+	0.882068i	$0.343849\pi$
$420$		0			0
$421$		−	22.0000i		−	1.07221i	−0.844150	−	0.536107i	$-0.819894\pi$
$421$		−	22.0000i		−	1.07221i	0.844150	−	0.536107i	$-0.180106\pi$
$422$	−3.69552	−	1.53073i	−0.179895	−	0.0745150i
$423$	5.65685	−	5.65685i	0.275046	−	0.275046i
$424$	18.0000			0.874157
$425$		0			0
$426$	−12.0000			−0.581402
$427$	22.6274	−	22.6274i	1.09502	−	1.09502i
$428$	11.0866	+	4.59220i	0.535889	+	0.221972i
$429$			8.00000i			0.386244i
$430$		0			0
$431$	18.4776	−	7.65367i	0.890034	−	0.368664i	0.109654	−	0.993970i	$-0.465026\pi$
$431$	18.4776	−	7.65367i	0.890034	−	0.368664i	0.780380	+	0.625306i	$0.215026\pi$
$432$	0.382683	+	0.923880i	0.0184119	+	0.0444502i
$433$	−1.41421	−	1.41421i	−0.0679628	−	0.0679628i	0.672308	−	0.740271i	$-0.265303\pi$
$433$	−1.41421	−	1.41421i	−0.0679628	−	0.0679628i	−0.740271	+	0.672308i	$0.765303\pi$
$434$	11.3137	+	11.3137i	0.543075	+	0.543075i
$435$		0			0
$436$	−7.39104	+	3.06147i	−0.353966	+	0.146618i
$437$	6.12293	−	14.7821i	0.292900	−	0.707122i
$438$		0			0
$439$	33.2597	+	13.7766i	1.58740	+	0.657521i	0.989563	−	0.144099i	$-0.0460283\pi$
$439$	33.2597	+	13.7766i	1.58740	+	0.657521i	0.597834	+	0.801620i	$0.296028\pi$
$440$		0			0
$441$	−9.00000			−0.428571
$442$		0			0
$443$	−20.0000			−0.950229			−0.475114	−	0.879924i	$-0.657593\pi$
$443$	−20.0000			−0.950229			−0.475114	+	0.879924i	$0.657593\pi$
$444$	−5.65685	+	5.65685i	−0.268462	+	0.268462i
$445$		0			0
$446$		−	16.0000i		−	0.757622i
$447$	−2.29610	+	5.54328i	−0.108602	+	0.262188i
$448$	25.8686	−	10.7151i	1.22218	−	0.506243i
$449$	3.06147	+	7.39104i	0.144480	+	0.348805i	0.979509	−	0.201401i	$-0.0645494\pi$
$449$	3.06147	+	7.39104i	0.144480	+	0.348805i	−0.835029	+	0.550205i	$0.814549\pi$
$450$	−3.53553	−	3.53553i	−0.166667	−	0.166667i
$451$	−22.6274	−	22.6274i	−1.06548	−	1.06548i
$452$	−3.06147	−	7.39104i	−0.143999	−	0.347645i
$453$		0			0
$454$	−4.59220	+	11.0866i	−0.215523	+	0.520318i
$455$		0			0
$456$	−11.0866	−	4.59220i	−0.519175	−	0.215050i
$457$	26.8701	−	26.8701i	1.25693	−	1.25693i	0.304376	−	0.952552i	$-0.401552\pi$
$457$	26.8701	−	26.8701i	1.25693	−	1.25693i	0.952552	−	0.304376i	$-0.0984481\pi$
$458$	−10.0000			−0.467269
$459$		0			0
$460$		0			0
$461$	24.0416	−	24.0416i	1.11973	−	1.11973i	0.127950	−	0.991781i	$-0.459160\pi$
$461$	24.0416	−	24.0416i	1.11973	−	1.11973i	0.991781	−	0.127950i	$-0.0408396\pi$
$462$	14.7821	+	6.12293i	0.687724	+	0.284865i
$463$			40.0000i			1.85896i	0.368875	+	0.929479i	$0.379743\pi$
$463$			40.0000i			1.85896i	−0.368875	+	0.929479i	$0.620257\pi$
$464$		0			0
$465$		0			0
$466$	3.06147	+	7.39104i	0.141820	+	0.342383i
$467$	2.82843	+	2.82843i	0.130884	+	0.130884i	0.769514	−	0.638630i	$-0.220499\pi$
$467$	2.82843	+	2.82843i	0.130884	+	0.130884i	−0.638630	+	0.769514i	$0.720499\pi$
$468$	−1.41421	−	1.41421i	−0.0653720	−	0.0653720i
$469$	18.3688	+	44.3462i	0.848193	+	2.04772i
$470$		0			0
$471$	−0.765367	+	1.84776i	−0.0352662	+	0.0851402i
$472$			36.0000i			1.65703i
$473$	14.7821	+	6.12293i	0.679680	+	0.281533i
$474$	2.82843	−	2.82843i	0.129914	−	0.129914i
$475$	20.0000			0.917663
$476$		0			0
$477$	−6.00000			−0.274721
$478$	5.65685	−	5.65685i	0.258738	−	0.258738i
$479$	11.0866	+	4.59220i	0.506558	+	0.209823i	0.621301	−	0.783572i	$-0.286605\pi$
$479$	11.0866	+	4.59220i	0.506558	+	0.209823i	−0.114743	+	0.993395i	$0.536605\pi$
$480$		0			0
$481$	−6.12293	+	14.7821i	−0.279182	+	0.674004i
$482$	14.7821	−	6.12293i	0.673305	−	0.278892i
$483$	−6.12293	−	14.7821i	−0.278603	−	0.672608i
$484$	3.53553	+	3.53553i	0.160706	+	0.160706i
$485$		0			0
$486$	−0.382683	−	0.923880i	−0.0173589	−	0.0419080i
$487$	−3.69552	+	1.53073i	−0.167460	+	0.0693642i	−0.464839	−	0.885395i	$-0.653888\pi$
$487$	−3.69552	+	1.53073i	−0.167460	+	0.0693642i	0.297379	+	0.954760i	$0.403888\pi$
$488$	9.18440	−	22.1731i	0.415758	−	1.00373i
$489$		−	20.0000i		−	0.904431i
$490$		0			0
$491$	−14.1421	+	14.1421i	−0.638226	+	0.638226i	−0.950118	−	0.311892i	$-0.899037\pi$
$491$	−14.1421	+	14.1421i	−0.638226	+	0.638226i	0.311892	+	0.950118i	$0.399037\pi$
$492$	8.00000			0.360668
$493$		0			0
$494$	−8.00000			−0.359937
$495$		0			0
$496$	3.69552	+	1.53073i	0.165934	+	0.0687320i
$497$		−	48.0000i		−	2.15309i
$498$	−4.59220	+	11.0866i	−0.205781	+	0.496800i
$499$	−33.2597	+	13.7766i	−1.48891	+	0.616725i	−0.971079	−	0.238759i	$-0.923259\pi$
$499$	−33.2597	+	13.7766i	−1.48891	+	0.616725i	−0.517828	+	0.855485i	$0.673259\pi$
$500$		0			0
$501$	−8.48528	−	8.48528i	−0.379094	−	0.379094i
$502$	−8.48528	−	8.48528i	−0.378717	−	0.378717i
$503$	−4.59220	−	11.0866i	−0.204756	−	0.494325i	0.787826	−	0.615897i	$-0.211206\pi$
$503$	−4.59220	−	11.0866i	−0.204756	−	0.494325i	−0.992583	+	0.121572i	$0.961206\pi$
$504$	−11.0866	+	4.59220i	−0.493834	+	0.204553i
$505$		0			0
$506$			16.0000i			0.711287i
$507$	8.31492	+	3.44415i	0.369278	+	0.152960i
$508$	−5.65685	+	5.65685i	−0.250982	+	0.250982i
$509$	18.0000			0.797836			0.398918	−	0.916987i	$-0.369386\pi$
$509$	18.0000			0.797836			0.398918	+	0.916987i	$0.369386\pi$
$510$		0			0
$511$		0			0
$512$	7.77817	−	7.77817i	0.343750	−	0.343750i
$513$	3.69552	+	1.53073i	0.163161	+	0.0675835i
$514$			2.00000i			0.0882162i
$515$		0			0
$516$	−3.69552	+	1.53073i	−0.162686	+	0.0673868i
$517$	−12.2459	−	29.5641i	−0.538573	−	1.30023i
$518$	22.6274	+	22.6274i	0.994192	+	0.994192i
$519$	−11.3137	−	11.3137i	−0.496617	−	0.496617i
$520$		0			0
$521$	22.1731	−	9.18440i	0.971422	−	0.402376i	0.160180	−	0.987088i	$-0.448792\pi$
$521$	22.1731	−	9.18440i	0.971422	−	0.402376i	0.811241	+	0.584712i	$0.198792\pi$
$522$		0			0
$523$		−	12.0000i		−	0.524723i	−0.964970	−	0.262362i	$-0.915499\pi$
$523$		−	12.0000i		−	0.524723i	0.964970	−	0.262362i	$-0.0845013\pi$
$524$	3.69552	+	1.53073i	0.161439	+	0.0668704i
$525$	14.1421	−	14.1421i	0.617213	−	0.617213i
$526$	−24.0000			−1.04645
$527$		0			0
$528$	4.00000			0.174078
$529$	−4.94975	+	4.94975i	−0.215206	+	0.215206i
$530$		0			0
$531$		−	12.0000i		−	0.520756i
$532$	6.12293	−	14.7821i	0.265463	−	0.640884i
$533$	14.7821	−	6.12293i	0.640283	−	0.265214i
$534$	−3.82683	−	9.23880i	−0.165603	−	0.399802i
$535$		0			0
$536$	25.4558	+	25.4558i	1.09952	+	1.09952i
$537$	−1.53073	−	3.69552i	−0.0660560	−	0.159473i
$538$		0			0
$539$	−13.7766	+	33.2597i	−0.593400	+	1.43260i
$540$		0			0
$541$	−36.9552	−	15.3073i	−1.58883	−	0.658114i	−0.599047	−	0.800714i	$-0.704454\pi$
$541$	−36.9552	−	15.3073i	−1.58883	−	0.658114i	−0.989780	+	0.142600i	$0.954454\pi$
$542$		0			0
$543$	−8.00000			−0.343313
$544$		0			0
$545$		0			0
$546$	−5.65685	+	5.65685i	−0.242091	+	0.242091i
$547$	33.2597	+	13.7766i	1.42208	+	0.589045i	0.955382	−	0.295372i	$-0.0954435\pi$
$547$	33.2597	+	13.7766i	1.42208	+	0.589045i	0.466698	+	0.884417i	$0.345443\pi$
$548$		−	10.0000i		−	0.427179i
$549$	−3.06147	+	7.39104i	−0.130660	+	0.315442i
$550$	−18.4776	+	7.65367i	−0.787887	+	0.326354i
$551$		0			0
$552$	−8.48528	−	8.48528i	−0.361158	−	0.361158i
$553$	11.3137	+	11.3137i	0.481108	+	0.481108i
$554$	3.06147	+	7.39104i	0.130069	+	0.314015i
$555$		0			0
$556$	−1.53073	+	3.69552i	−0.0649176	+	0.156725i
$557$			18.0000i			0.762684i	0.924434	+	0.381342i	$0.124538\pi$
$557$			18.0000i			0.762684i	−0.924434	+	0.381342i	$0.875462\pi$
$558$	−3.69552	−	1.53073i	−0.156444	−	0.0648011i
$559$	−5.65685	+	5.65685i	−0.239259	+	0.239259i
$560$		0			0
$561$		0			0
$562$	10.0000			0.421825
$563$	−31.1127	+	31.1127i	−1.31124	+	1.31124i	−0.390745	+	0.920499i	$0.627783\pi$
$563$	−31.1127	+	31.1127i	−1.31124	+	1.31124i	−0.920499	+	0.390745i	$0.872217\pi$
$564$	7.39104	+	3.06147i	0.311219	+	0.128911i
$565$		0			0
$566$	−1.53073	+	3.69552i	−0.0643415	+	0.155334i
$567$	3.69552	−	1.53073i	0.155197	−	0.0642848i
$568$	−13.7766	−	33.2597i	−0.578053	−	1.39554i
$569$	18.3848	+	18.3848i	0.770730	+	0.770730i	0.978234	−	0.207504i	$-0.0665341\pi$
$569$	18.3848	+	18.3848i	0.770730	+	0.770730i	−0.207504	+	0.978234i	$0.566534\pi$
$570$		0			0
$571$	−7.65367	−	18.4776i	−0.320296	−	0.773263i	−0.999236	−	0.0390697i	$-0.987561\pi$
$571$	−7.65367	−	18.4776i	−0.320296	−	0.773263i	0.678940	−	0.734193i	$-0.262439\pi$
$572$	−7.39104	+	3.06147i	−0.309035	+	0.128006i
$573$	−3.06147	+	7.39104i	−0.127895	+	0.308765i
$574$		−	32.0000i		−	1.33565i
$575$	18.4776	+	7.65367i	0.770569	+	0.319180i
$576$	−4.94975	+	4.94975i	−0.206239	+	0.206239i
$577$	−30.0000			−1.24892			−0.624458	−	0.781058i	$-0.714680\pi$
$577$	−30.0000			−1.24892			−0.624458	+	0.781058i	$0.714680\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−44.3462	−	18.3688i	−1.83979	−	0.762066i
$582$			16.0000i			0.663221i
$583$	−9.18440	+	22.1731i	−0.380379	+	0.918316i
$584$		0			0
$585$		0			0
$586$	−7.07107	−	7.07107i	−0.292103	−	0.292103i
$587$	−8.48528	−	8.48528i	−0.350225	−	0.350225i	0.509968	−	0.860193i	$-0.329657\pi$
$587$	−8.48528	−	8.48528i	−0.350225	−	0.350225i	−0.860193	+	0.509968i	$0.829657\pi$
$588$	−3.44415	−	8.31492i	−0.142034	−	0.342901i
$589$	14.7821	−	6.12293i	0.609085	−	0.252291i
$590$		0			0
$591$		−	16.0000i		−	0.658152i
$592$	7.39104	+	3.06147i	0.303770	+	0.125826i
$593$	−32.5269	+	32.5269i	−1.33572	+	1.33572i	−0.435561	+	0.900159i	$0.643450\pi$
$593$	−32.5269	+	32.5269i	−1.33572	+	1.33572i	−0.900159	+	0.435561i	$0.856550\pi$
$594$	−4.00000			−0.164122
$595$		0			0
$596$	−6.00000			−0.245770
$597$	−14.1421	+	14.1421i	−0.578799	+	0.578799i
$598$	−7.39104	−	3.06147i	−0.302242	−	0.125193i
$599$			8.00000i			0.326871i	0.986554	+	0.163436i	$0.0522576\pi$
$599$			8.00000i			0.326871i	−0.986554	+	0.163436i	$0.947742\pi$
$600$	5.74025	−	13.8582i	0.234345	−	0.565758i
$601$	−14.7821	+	6.12293i	−0.602973	+	0.249760i	−0.663221	−	0.748424i	$-0.730811\pi$
$601$	−14.7821	+	6.12293i	−0.602973	+	0.249760i	0.0602475	+	0.998183i	$0.480811\pi$
$602$	6.12293	+	14.7821i	0.249552	+	0.602472i
$603$	−8.48528	−	8.48528i	−0.345547	−	0.345547i
$604$		0			0
$605$		0			0
$606$	−5.54328	+	2.29610i	−0.225180	+	0.0932727i
$607$	−1.53073	+	3.69552i	−0.0621306	+	0.149996i	−0.951896	−	0.306422i	$-0.900868\pi$
$607$	−1.53073	+	3.69552i	−0.0621306	+	0.149996i	0.889765	+	0.456419i	$0.150868\pi$
$608$		−	20.0000i		−	0.811107i
$609$		0			0
$610$		0			0
$611$	16.0000			0.647291
$612$		0			0
$613$	6.00000			0.242338			0.121169	−	0.992632i	$-0.461336\pi$
$613$	6.00000			0.242338			0.121169	+	0.992632i	$0.461336\pi$
$614$	8.48528	−	8.48528i	0.342438	−	0.342438i
$615$		0			0
$616$			48.0000i			1.93398i
$617$	9.18440	−	22.1731i	0.369750	−	0.892656i	−0.624041	−	0.781392i	$-0.714510\pi$
$617$	9.18440	−	22.1731i	0.369750	−	0.892656i	0.993791	−	0.111264i	$-0.0354899\pi$
$618$		0			0
$619$	13.7766	+	33.2597i	0.553728	+	1.33682i	0.914659	+	0.404226i	$0.132459\pi$
$619$	13.7766	+	33.2597i	0.553728	+	1.33682i	−0.360931	+	0.932593i	$0.617541\pi$
$620$		0			0
$621$	2.82843	+	2.82843i	0.113501	+	0.113501i
$622$	−4.59220	−	11.0866i	−0.184130	−	0.444530i
$623$	36.9552	−	15.3073i	1.48058	−	0.613276i
$624$	−0.765367	+	1.84776i	−0.0306392	+	0.0739696i
$625$			25.0000i			1.00000i
$626$	14.7821	+	6.12293i	0.590810	+	0.244722i
$627$	11.3137	−	11.3137i	0.451826	−	0.451826i
$628$	−2.00000			−0.0798087
$629$		0			0
$630$		0			0
$631$	5.65685	−	5.65685i	0.225196	−	0.225196i	−0.585486	−	0.810682i	$-0.699096\pi$
$631$	5.65685	−	5.65685i	0.225196	−	0.225196i	0.810682	+	0.585486i	$0.199096\pi$
$632$	11.0866	+	4.59220i	0.440999	+	0.182668i
$633$			4.00000i			0.158986i
$634$	12.2459	−	29.5641i	0.486346	−	1.17414i
$635$		0			0
$636$	−2.29610	−	5.54328i	−0.0910463	−	0.219805i
$637$	−12.7279	−	12.7279i	−0.504299	−	0.504299i
$638$		0			0
$639$	4.59220	+	11.0866i	0.181665	+	0.438577i
$640$		0			0
$641$	3.06147	−	7.39104i	0.120921	−	0.291928i	−0.851816	−	0.523841i	$-0.824498\pi$
$641$	3.06147	−	7.39104i	0.120921	−	0.291928i	0.972737	+	0.231913i	$0.0744985\pi$
$642$			12.0000i			0.473602i
$643$	−3.69552	−	1.53073i	−0.145737	−	0.0603662i	0.308623	−	0.951185i	$-0.400132\pi$
$643$	−3.69552	−	1.53073i	−0.145737	−	0.0603662i	−0.454360	+	0.890818i	$0.650132\pi$
$644$	11.3137	−	11.3137i	0.445823	−	0.445823i
$645$		0			0
$646$		0			0
$647$	32.0000			1.25805			0.629025	−	0.777385i	$-0.283454\pi$
$647$	32.0000			1.25805			0.629025	+	0.777385i	$0.283454\pi$
$648$	2.12132	−	2.12132i	0.0833333	−	0.0833333i
$649$	−44.3462	−	18.3688i	−1.74074	−	0.721039i
$650$		−	10.0000i		−	0.392232i
$651$	6.12293	−	14.7821i	0.239977	−	0.579355i
$652$	18.4776	−	7.65367i	0.723638	−	0.299741i
$653$	−12.2459	−	29.5641i	−0.479218	−	1.15693i	−0.959976	−	0.280081i	$-0.909639\pi$
$653$	−12.2459	−	29.5641i	−0.479218	−	1.15693i	0.480758	−	0.876853i	$-0.340361\pi$
$654$	−5.65685	−	5.65685i	−0.221201	−	0.221201i
$655$		0			0
$656$	−3.06147	−	7.39104i	−0.119530	−	0.288571i
$657$		0			0
$658$	12.2459	−	29.5641i	0.477394	−	1.15253i
$659$		−	4.00000i		−	0.155818i	−0.996960	−	0.0779089i	$-0.975176\pi$
$659$		−	4.00000i		−	0.155818i	0.996960	−	0.0779089i	$-0.0248243\pi$
$660$		0			0
$661$	−29.6985	+	29.6985i	−1.15514	+	1.15514i	−0.169629	+	0.985508i	$0.554257\pi$
$661$	−29.6985	+	29.6985i	−1.15514	+	1.15514i	−0.985508	+	0.169629i	$0.945743\pi$
$662$	20.0000			0.777322
$663$		0			0
$664$	−36.0000			−1.39707
$665$		0			0
$666$	−7.39104	−	3.06147i	−0.286397	−	0.118629i
$667$		0			0
$668$	4.59220	−	11.0866i	0.177678	−	0.428952i
$669$	−14.7821	+	6.12293i	−0.571508	+	0.236726i
$670$		0			0
$671$	22.6274	+	22.6274i	0.873522	+	0.873522i
$672$	−14.1421	−	14.1421i	−0.545545	−	0.545545i
$673$	−12.2459	−	29.5641i	−0.472044	−	1.13961i	−0.963259	−	0.268576i	$-0.913447\pi$
$673$	−12.2459	−	29.5641i	−0.472044	−	1.13961i	0.491215	−	0.871038i	$-0.336553\pi$
$674$	−14.7821	+	6.12293i	−0.569384	+	0.235847i
$675$	−1.91342	+	4.61940i	−0.0736475	+	0.177801i
$676$			9.00000i			0.346154i
$677$	−44.3462	−	18.3688i	−1.70436	−	0.705971i	−0.704371	−	0.709832i	$-0.748771\pi$
$677$	−44.3462	−	18.3688i	−1.70436	−	0.705971i	−0.999993	+	0.00386145i	$0.998771\pi$
$678$	5.65685	−	5.65685i	0.217250	−	0.217250i
$679$	−64.0000			−2.45609
$680$		0			0
$681$	12.0000			0.459841
$682$	−11.3137	+	11.3137i	−0.433224	+	0.433224i
$683$	−11.0866	−	4.59220i	−0.424215	−	0.175716i	0.160354	−	0.987060i	$-0.448736\pi$
$683$	−11.0866	−	4.59220i	−0.424215	−	0.175716i	−0.584569	+	0.811344i	$0.698736\pi$
$684$			4.00000i			0.152944i
$685$		0			0
$686$	−7.39104	+	3.06147i	−0.282191	+	0.116887i
$687$	3.82683	+	9.23880i	0.146003	+	0.352482i
$688$	2.82843	+	2.82843i	0.107833	+	0.107833i
$689$	−8.48528	−	8.48528i	−0.323263	−	0.323263i
$690$		0			0
$691$	18.4776	−	7.65367i	0.702921	−	0.291159i	−0.00245092	−	0.999997i	$-0.500780\pi$
$691$	18.4776	−	7.65367i	0.702921	−	0.291159i	0.705372	+	0.708838i	$0.250780\pi$
$692$	6.12293	−	14.7821i	0.232759	−	0.561930i
$693$		−	16.0000i		−	0.607790i
$694$	−3.69552	−	1.53073i	−0.140280	−	0.0581059i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	−2.00000			−0.0757011
$699$	5.65685	−	5.65685i	0.213962	−	0.213962i
$700$	18.4776	+	7.65367i	0.698387	+	0.289281i
$701$		−	34.0000i		−	1.28416i	−0.766637	−	0.642081i	$-0.778071\pi$
$701$		−	34.0000i		−	1.28416i	0.766637	−	0.642081i	$-0.221929\pi$
$702$	0.765367	−	1.84776i	0.0288869	−	0.0697392i
$703$	29.5641	−	12.2459i	1.11503	−	0.461862i
$704$	10.7151	+	25.8686i	0.403842	+	0.974961i
$705$		0			0
$706$	−12.7279	−	12.7279i	−0.479022	−	0.479022i
$707$	−9.18440	−	22.1731i	−0.345415	−	0.833906i
$708$	11.0866	−	4.59220i	0.416658	−	0.172585i
$709$	−15.3073	+	36.9552i	−0.574879	+	1.38788i	0.322478	+	0.946577i	$0.395484\pi$
$709$	−15.3073	+	36.9552i	−0.574879	+	1.38788i	−0.897358	+	0.441304i	$0.854516\pi$
$710$		0			0
$711$	−3.69552	−	1.53073i	−0.138593	−	0.0574070i
$712$	21.2132	−	21.2132i	0.794998	−	0.794998i
$713$	16.0000			0.599205
$714$		0			0
$715$		0			0
$716$	2.82843	−	2.82843i	0.105703	−	0.105703i
$717$	−7.39104	−	3.06147i	−0.276023	−	0.114333i
$718$		−	32.0000i		−	1.19423i
$719$	13.7766	−	33.2597i	0.513781	−	1.24038i	−0.427887	−	0.903832i	$-0.640742\pi$
$719$	13.7766	−	33.2597i	0.513781	−	1.24038i	0.941668	−	0.336544i	$-0.109258\pi$
$720$		0			0
$721$		0			0
$722$	−2.12132	−	2.12132i	−0.0789474	−	0.0789474i
$723$	−11.3137	−	11.3137i	−0.420761	−	0.420761i
$724$	−3.06147	−	7.39104i	−0.113779	−	0.274686i
$725$		0			0
$726$	−1.91342	+	4.61940i	−0.0710136	+	0.171442i
$727$			8.00000i			0.296704i	0.988935	+	0.148352i	$0.0473968\pi$
$727$			8.00000i			0.296704i	−0.988935	+	0.148352i	$0.952603\pi$
$728$	−22.1731	−	9.18440i	−0.821790	−	0.340397i
$729$	−0.707107	+	0.707107i	−0.0261891	+	0.0261891i
$730$		0			0
$731$		0			0
$732$	−8.00000			−0.295689
$733$	24.0416	−	24.0416i	0.887998	−	0.887998i	−0.106333	−	0.994331i	$-0.533911\pi$
$733$	24.0416	−	24.0416i	0.887998	−	0.887998i	0.994331	+	0.106333i	$0.0339109\pi$
$734$	11.0866	+	4.59220i	0.409212	+	0.169501i
$735$		0			0
$736$	7.65367	−	18.4776i	0.282118	−	0.681093i
$737$	−44.3462	+	18.3688i	−1.63351	+	0.676624i
$738$	3.06147	+	7.39104i	0.112694	+	0.272068i
$739$	−2.82843	−	2.82843i	−0.104045	−	0.104045i	0.653168	−	0.757213i	$-0.273440\pi$
$739$	−2.82843	−	2.82843i	−0.104045	−	0.104045i	−0.757213	+	0.653168i	$0.773440\pi$
$740$		0			0
$741$	3.06147	+	7.39104i	0.112466	+	0.271517i
$742$	−22.1731	+	9.18440i	−0.814000	+	0.337170i
$743$	−13.7766	+	33.2597i	−0.505415	+	1.22018i	0.441083	+	0.897467i	$0.354595\pi$
$743$	−13.7766	+	33.2597i	−0.505415	+	1.22018i	−0.946497	+	0.322712i	$0.895405\pi$
$744$		−	12.0000i		−	0.439941i
$745$		0			0
$746$	18.3848	−	18.3848i	0.673114	−	0.673114i
$747$	12.0000			0.439057
$748$		0			0
$749$	−48.0000			−1.75388
$750$		0			0
$751$	−18.4776	−	7.65367i	−0.674257	−	0.279286i	0.0191669	−	0.999816i	$-0.493899\pi$
$751$	−18.4776	−	7.65367i	−0.674257	−	0.279286i	−0.693424	+	0.720530i	$0.743899\pi$
$752$		−	8.00000i		−	0.291730i
$753$	−4.59220	+	11.0866i	−0.167349	+	0.404017i
$754$		0			0
$755$		0			0
$756$	2.82843	+	2.82843i	0.102869	+	0.102869i
$757$	26.8701	+	26.8701i	0.976609	+	0.976609i	0.999733	−	0.0231238i	$-0.00736118\pi$
$757$	26.8701	+	26.8701i	0.976609	+	0.976609i	−0.0231238	+	0.999733i	$0.507361\pi$
$758$	−7.65367	−	18.4776i	−0.277994	−	0.671136i
$759$	14.7821	−	6.12293i	0.536555	−	0.222248i
$760$		0			0
$761$			6.00000i			0.217500i	0.994069	+	0.108750i	$0.0346848\pi$
$761$			6.00000i			0.217500i	−0.994069	+	0.108750i	$0.965315\pi$
$762$	−7.39104	−	3.06147i	−0.267749	−	0.110905i
$763$	22.6274	−	22.6274i	0.819167	−	0.819167i
$764$	−8.00000			−0.289430
$765$		0			0
$766$	−16.0000			−0.578103
$767$	16.9706	−	16.9706i	0.612772	−	0.612772i
$768$	−15.7060	−	6.50562i	−0.566740	−	0.234751i
$769$			34.0000i			1.22607i	0.790055	+	0.613036i	$0.210052\pi$
$769$			34.0000i			1.22607i	−0.790055	+	0.613036i	$0.789948\pi$
$770$		0			0
$771$	1.84776	−	0.765367i	0.0665454	−	0.0275640i
$772$		0			0
$773$	−4.24264	−	4.24264i	−0.152597	−	0.152597i	0.626680	−	0.779277i	$-0.284413\pi$
$773$	−4.24264	−	4.24264i	−0.152597	−	0.152597i	−0.779277	+	0.626680i	$0.784413\pi$
$774$	−2.82843	−	2.82843i	−0.101666	−	0.101666i
$775$	7.65367	+	18.4776i	0.274928	+	0.663735i
$776$	−44.3462	+	18.3688i	−1.59194	+	0.659402i
$777$	12.2459	−	29.5641i	0.439318	−	1.06061i
$778$		−	6.00000i		−	0.215110i
$779$	−29.5641	−	12.2459i	−1.05925	−	0.438754i
$780$		0			0
$781$	48.0000			1.71758
$782$		0			0
$783$		0			0
$784$	−6.36396	+	6.36396i	−0.227284	+	0.227284i
$785$		0			0
$786$			4.00000i			0.142675i
$787$	4.59220	−	11.0866i	0.163694	−	0.395193i	−0.820654	−	0.571425i	$-0.806391\pi$
$787$	4.59220	−	11.0866i	0.163694	−	0.395193i	0.984349	+	0.176232i	$0.0563909\pi$
$788$	14.7821	−	6.12293i	0.526590	−	0.218121i
$789$	9.18440	+	22.1731i	0.326973	+	0.789384i
$790$		0			0
$791$	22.6274	+	22.6274i	0.804538	+	0.804538i
$792$	−4.59220	−	11.0866i	−0.163177	−	0.393944i
$793$	−14.7821	+	6.12293i	−0.524927	+	0.217432i
$794$	−3.06147	+	7.39104i	−0.108647	+	0.262298i
$795$		0			0
$796$	−18.4776	−	7.65367i	−0.654921	−	0.271277i
$797$	−12.7279	+	12.7279i	−0.450846	+	0.450846i	−0.895635	−	0.444789i	$-0.853279\pi$
$797$	−12.7279	+	12.7279i	−0.450846	+	0.450846i	0.444789	+	0.895635i	$0.353279\pi$
$798$	16.0000			0.566394
$799$		0			0
$800$	25.0000			0.883883
$801$	−7.07107	+	7.07107i	−0.249844	+	0.249844i
$802$	−22.1731	−	9.18440i	−0.782960	−	0.324313i
$803$		0			0
$804$	4.59220	−	11.0866i	0.161954	−	0.390993i
$805$		0			0
$806$	−3.06147	−	7.39104i	−0.107836	−	0.260338i
$807$		0			0
$808$	−12.7279	−	12.7279i	−0.447767	−	0.447767i
$809$	15.3073	+	36.9552i	0.538177	+	1.29927i	0.925994	+	0.377538i	$0.123229\pi$
$809$	15.3073	+	36.9552i	0.538177	+	1.29927i	−0.387817	+	0.921737i	$0.626771\pi$
$810$		0			0
$811$	1.53073	−	3.69552i	0.0537513	−	0.129767i	−0.894723	−	0.446622i	$-0.852627\pi$
$811$	1.53073	−	3.69552i	0.0537513	−	0.129767i	0.948474	+	0.316855i	$0.102627\pi$
$812$		0			0
$813$		0			0
$814$	−22.6274	+	22.6274i	−0.793091	+	0.793091i
$815$		0			0
$816$		0			0
$817$	16.0000			0.559769
$818$	−7.07107	+	7.07107i	−0.247234	+	0.247234i
$819$	7.39104	+	3.06147i	0.258264	+	0.106976i
$820$		0			0
$821$	−12.2459	+	29.5641i	−0.427384	+	1.03180i	0.552730	+	0.833360i	$0.313586\pi$
$821$	−12.2459	+	29.5641i	−0.427384	+	1.03180i	−0.980114	+	0.198435i	$0.936414\pi$
$822$	9.23880	−	3.82683i	0.322240	−	0.133476i
$823$	16.8381	+	40.6507i	0.586938	+	1.41699i	0.886415	+	0.462891i	$0.153188\pi$
$823$	16.8381	+	40.6507i	0.586938	+	1.41699i	−0.299477	+	0.954104i	$0.596812\pi$
$824$		0			0
$825$	14.1421	+	14.1421i	0.492366	+	0.492366i
$826$	−18.3688	−	44.3462i	−0.639132	−	1.54300i
$827$	−11.0866	+	4.59220i	−0.385517	+	0.159686i	−0.567020	−	0.823704i	$-0.691904\pi$
$827$	−11.0866	+	4.59220i	−0.385517	+	0.159686i	0.181503	+	0.983390i	$0.441904\pi$
$828$	−1.53073	+	3.69552i	−0.0531967	+	0.128428i
$829$		−	2.00000i		−	0.0694629i	−0.999397	−	0.0347314i	$-0.988942\pi$
$829$		−	2.00000i		−	0.0694629i	0.999397	−	0.0347314i	$-0.0110576\pi$
$830$		0			0
$831$	5.65685	−	5.65685i	0.196234	−	0.196234i
$832$	−14.0000			−0.485363
$833$		0			0
$834$	−4.00000			−0.138509
$835$		0			0
$836$	14.7821	+	6.12293i	0.511249	+	0.211766i
$837$			4.00000i			0.138260i
$838$	−1.53073	+	3.69552i	−0.0528783	+	0.127660i
$839$	−40.6507	+	16.8381i	−1.40342	+	0.581315i	−0.950636	−	0.310307i	$-0.899568\pi$
$839$	−40.6507	+	16.8381i	−1.40342	+	0.581315i	−0.452782	+	0.891622i	$0.649568\pi$
$840$		0			0
$841$	20.5061	+	20.5061i	0.707107	+	0.707107i
$842$	15.5563	+	15.5563i	0.536107	+	0.536107i
$843$	−3.82683	−	9.23880i	−0.131803	−	0.318201i
$844$	−3.69552	+	1.53073i	−0.127205	+	0.0526900i
$845$		0			0
$846$			8.00000i			0.275046i
$847$	−18.4776	−	7.65367i	−0.634898	−	0.262983i
$848$	−4.24264	+	4.24264i	−0.145693	+	0.145693i
$849$	4.00000			0.137280
$850$		0			0
$851$	32.0000			1.09695
$852$	−8.48528	+	8.48528i	−0.290701	+	0.290701i
$853$	−22.1731	−	9.18440i	−0.759193	−	0.314468i	−0.0307066	−	0.999528i	$-0.509776\pi$
$853$	−22.1731	−	9.18440i	−0.759193	−	0.314468i	−0.728486	+	0.685060i	$0.759776\pi$
$854$			32.0000i			1.09502i
$855$		0			0
$856$	−33.2597	+	13.7766i	−1.13679	+	0.470875i
$857$	3.06147	+	7.39104i	0.104578	+	0.252473i	0.967503	−	0.252858i	$-0.0813705\pi$
$857$	3.06147	+	7.39104i	0.104578	+	0.252473i	−0.862926	+	0.505331i	$0.831370\pi$
$858$	−5.65685	−	5.65685i	−0.193122	−	0.193122i
$859$	2.82843	+	2.82843i	0.0965047	+	0.0965047i	0.753711	−	0.657206i	$-0.228262\pi$
$859$	2.82843	+	2.82843i	0.0965047	+	0.0965047i	−0.657206	+	0.753711i	$0.728262\pi$
$860$		0			0
$861$	−29.5641	+	12.2459i	−1.00754	+	0.417338i
$862$	−7.65367	+	18.4776i	−0.260685	+	0.629349i
$863$		0			0		1.00000			$0$
$863$		0			0		−1.00000			$\pi$
$864$	4.61940	+	1.91342i	0.157155	+	0.0650958i
$865$		0			0
$866$	2.00000			0.0679628
$867$		0			0
$868$	16.0000			0.543075
$869$	−11.3137	+	11.3137i	−0.383791	+	0.383791i
$870$		0			0
$871$		−	24.0000i		−	0.813209i
$872$	9.18440	−	22.1731i	0.311023	−	0.750876i
$873$	14.7821	−	6.12293i	0.500297	−	0.207230i
$874$	6.12293	+	14.7821i	0.207111	+	0.500011i
$875$		0			0
$876$		0			0
$877$	15.3073	+	36.9552i	0.516892	+	1.24789i	0.939803	+	0.341717i	$0.111008\pi$
$877$	15.3073	+	36.9552i	0.516892	+	1.24789i	−0.422911	+	0.906171i	$0.638992\pi$
$878$	−33.2597	+	13.7766i	−1.12246	+	0.464938i
$879$	−3.82683	+	9.23880i	−0.129076	+	0.311617i
$880$		0			0
$881$	−22.1731	−	9.18440i	−0.747031	−	0.309430i	−0.0235015	−	0.999724i	$-0.507481\pi$
$881$	−22.1731	−	9.18440i	−0.747031	−	0.309430i	−0.723530	+	0.690293i	$0.757481\pi$
$882$	6.36396	−	6.36396i	0.214286	−	0.214286i
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$		0			0
$885$		0			0
$886$	14.1421	−	14.1421i	0.475114	−	0.475114i
$887$	−3.69552	−	1.53073i	−0.124083	−	0.0513970i	0.319778	−	0.947493i	$-0.396392\pi$
$887$	−3.69552	−	1.53073i	−0.124083	−	0.0513970i	−0.443861	+	0.896096i	$0.646392\pi$
$888$		−	24.0000i		−	0.805387i
$889$	12.2459	−	29.5641i	0.410713	−	0.991550i
$890$		0			0
$891$	1.53073	+	3.69552i	0.0512815	+	0.123805i
$892$	−11.3137	−	11.3137i	−0.378811	−	0.378811i
$893$	−22.6274	−	22.6274i	−0.757198	−	0.757198i
$894$	−2.29610	−	5.54328i	−0.0767931	−	0.185395i
$895$		0			0
$896$	4.59220	−	11.0866i	0.153415	−	0.370376i
$897$			8.00000i			0.267112i
$898$	−7.39104	−	3.06147i	−0.246642	−	0.102162i
$899$		0			0
$900$	−5.00000			−0.166667
$901$		0			0
$902$	32.0000			1.06548
$903$	11.3137	−	11.3137i	0.376497	−	0.376497i
$904$	22.1731	+	9.18440i	0.737467	+	0.305469i
$905$		0			0
$906$		0			0
$907$	25.8686	−	10.7151i	0.858954	−	0.355790i	0.0906554	−	0.995882i	$-0.471104\pi$
$907$	25.8686	−	10.7151i	0.858954	−	0.355790i	0.768298	+	0.640092i	$0.221104\pi$
$908$	4.59220	+	11.0866i	0.152398	+	0.367920i
$909$	4.24264	+	4.24264i	0.140720	+	0.140720i
$910$		0			0
$911$	−10.7151	−	25.8686i	−0.355008	−	0.857066i	−0.995986	−	0.0895065i	$-0.971471\pi$
$911$	−10.7151	−	25.8686i	−0.355008	−	0.857066i	0.640978	−	0.767559i	$-0.278529\pi$
$912$	3.69552	−	1.53073i	0.122371	−	0.0506877i
$913$	18.3688	−	44.3462i	0.607919	−	1.46765i
$914$			38.0000i			1.25693i
$915$		0			0
$916$	−7.07107	+	7.07107i	−0.233635	+	0.233635i
$917$	−16.0000			−0.528367
$918$		0			0
$919$	24.0000			0.791687			0.395843	−	0.918318i	$-0.370452\pi$
$919$	24.0000			0.791687			0.395843	+	0.918318i	$0.370452\pi$
$920$		0			0
$921$	−11.0866	−	4.59220i	−0.365314	−	0.151318i
$922$			34.0000i			1.11973i
$923$	−9.18440	+	22.1731i	−0.302308	+	0.729837i
$924$	14.7821	−	6.12293i	0.486294	−	0.201430i
$925$	15.3073	+	36.9552i	0.503302	+	1.21508i
$926$	−28.2843	−	28.2843i	−0.929479	−	0.929479i
$927$		0			0
$928$		0			0
$929$	22.1731	−	9.18440i	0.727476	−	0.301330i	0.0119617	−	0.999928i	$-0.496192\pi$
$929$	22.1731	−	9.18440i	0.727476	−	0.301330i	0.715514	+	0.698598i	$0.246192\pi$
$930$		0			0
$931$			36.0000i			1.17985i
$932$	7.39104	+	3.06147i	0.242101	+	0.100282i
$933$	−8.48528	+	8.48528i	−0.277796	+	0.277796i
$934$	−4.00000			−0.130884
$935$		0			0
$936$	6.00000			0.196116
$937$	−18.3848	+	18.3848i	−0.600604	+	0.600604i	−0.940473	−	0.339869i	$-0.889617\pi$
$937$	−18.3848	+	18.3848i	−0.600604	+	0.600604i	0.339869	+	0.940473i	$0.389617\pi$
$938$	−44.3462	−	18.3688i	−1.44796	−	0.599763i
$939$		−	16.0000i		−	0.522140i
$940$		0			0
$941$	44.3462	−	18.3688i	1.44565	−	0.598806i	0.484486	−	0.874799i	$-0.339007\pi$
$941$	44.3462	−	18.3688i	1.44565	−	0.598806i	0.961160	+	0.275993i	$0.0890067\pi$
$942$	−0.765367	−	1.84776i	−0.0249370	−	0.0602032i
$943$	−22.6274	−	22.6274i	−0.736850	−	0.736850i
$944$	−8.48528	−	8.48528i	−0.276172	−	0.276172i
$945$		0			0
$946$	−14.7821	+	6.12293i	−0.480607	+	0.199074i
$947$	−4.59220	+	11.0866i	−0.149226	+	0.360265i	−0.980762	−	0.195207i	$-0.937462\pi$
$947$	−4.59220	+	11.0866i	−0.149226	+	0.360265i	0.831536	+	0.555471i	$0.187462\pi$
$948$		−	4.00000i		−	0.129914i
$949$		0			0
$950$	−14.1421	+	14.1421i	−0.458831	+	0.458831i
$951$	−32.0000			−1.03767
$952$		0			0
$953$	−42.0000			−1.36051			−0.680257	−	0.732974i	$-0.738132\pi$
$953$	−42.0000			−1.36051			−0.680257	+	0.732974i	$0.738132\pi$
$954$	4.24264	−	4.24264i	0.137361	−	0.137361i
$955$		0			0
$956$		−	8.00000i		−	0.258738i
$957$		0			0
$958$	−11.0866	+	4.59220i	−0.358190	+	0.148367i
$959$	15.3073	+	36.9552i	0.494300	+	1.19335i
$960$		0			0
$961$	−10.6066	−	10.6066i	−0.342148	−	0.342148i
$962$	−6.12293	−	14.7821i	−0.197411	−	0.476593i
$963$	11.0866	−	4.59220i	0.357259	−	0.147982i
$964$	6.12293	−	14.7821i	0.197206	−	0.476098i
$965$		0			0
$966$	14.7821	+	6.12293i	0.475605	+	0.197002i
$967$	16.9706	−	16.9706i	0.545737	−	0.545737i	−0.379468	−	0.925205i	$-0.623893\pi$
$967$	16.9706	−	16.9706i	0.545737	−	0.545737i	0.925205	+	0.379468i	$0.123893\pi$
$968$	−15.0000			−0.482118
$969$		0			0
$970$		0			0
$971$	−25.4558	+	25.4558i	−0.816917	+	0.816917i	−0.985660	−	0.168743i	$-0.946029\pi$
$971$	−25.4558	+	25.4558i	−0.816917	+	0.816917i	0.168743	+	0.985660i	$0.446029\pi$
$972$	−0.923880	−	0.382683i	−0.0296334	−	0.0122746i
$973$		−	16.0000i		−	0.512936i
$974$	1.53073	−	3.69552i	0.0490479	−	0.118412i
$975$	−9.23880	+	3.82683i	−0.295878	+	0.122557i
$976$	3.06147	+	7.39104i	0.0979952	+	0.236581i
$977$	−32.5269	−	32.5269i	−1.04063	−	1.04063i	−0.999139	−	0.0414892i	$-0.986790\pi$
$977$	−32.5269	−	32.5269i	−1.04063	−	1.04063i	−0.0414892	−	0.999139i	$-0.513210\pi$
$978$	14.1421	+	14.1421i	0.452216	+	0.452216i
$979$	15.3073	+	36.9552i	0.489225	+	1.18109i
$980$		0			0
$981$	−3.06147	+	7.39104i	−0.0977451	+	0.235978i
$982$		−	20.0000i		−	0.638226i
$983$	18.4776	+	7.65367i	0.589344	+	0.244114i	0.657368	−	0.753570i	$-0.271670\pi$
$983$	18.4776	+	7.65367i	0.589344	+	0.244114i	−0.0680246	+	0.997684i	$0.521670\pi$
$984$	−16.9706	+	16.9706i	−0.541002	+	0.541002i
$985$		0			0
$986$		0			0
$987$	−32.0000			−1.01857
$988$	−5.65685	+	5.65685i	−0.179969	+	0.179969i
$989$	14.7821	+	6.12293i	0.470043	+	0.194698i
$990$		0			0
$991$	−4.59220	+	11.0866i	−0.145876	+	0.352176i	−0.979881	−	0.199580i	$-0.936042\pi$
$991$	−4.59220	+	11.0866i	−0.145876	+	0.352176i	0.834005	+	0.551756i	$0.186042\pi$
$992$	18.4776	−	7.65367i	0.586664	−	0.243004i
$993$	−7.65367	−	18.4776i	−0.242882	−	0.586369i
$994$	33.9411	+	33.9411i	1.07655	+	1.07655i
$995$		0			0
$996$	4.59220	+	11.0866i	0.145509	+	0.351291i
$997$	7.39104	−	3.06147i	0.234076	−	0.0969576i	−0.262562	−	0.964915i	$-0.584567\pi$
$997$	7.39104	−	3.06147i	0.234076	−	0.0969576i	0.496639	+	0.867957i	$0.334567\pi$
$998$	13.7766	−	33.2597i	0.436091	−	1.05282i
$999$			8.00000i			0.253109i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.h.d.757.2		8
17.2	even	8	inner	867.2.h.d.733.2		8
17.3	odd	16		867.2.e.d.829.2		4
17.4	even	4	inner	867.2.h.d.688.2		8
17.5	odd	16		867.2.e.d.616.1		4
17.6	odd	16		867.2.a.b.1.1		1
17.7	odd	16		51.2.d.b.16.1	✓	2
17.8	even	8	inner	867.2.h.d.712.1		8
17.9	even	8	inner	867.2.h.d.712.2		8
17.10	odd	16		51.2.d.b.16.2	yes	2
17.11	odd	16		867.2.a.a.1.1		1
17.12	odd	16		867.2.e.d.616.2		4
17.13	even	4	inner	867.2.h.d.688.1		8
17.14	odd	16		867.2.e.d.829.1		4
17.15	even	8	inner	867.2.h.d.733.1		8
17.16	even	2	inner	867.2.h.d.757.1		8
51.11	even	16		2601.2.a.i.1.1		1
51.23	even	16		2601.2.a.j.1.1		1
51.41	even	16		153.2.d.a.118.2		2
51.44	even	16		153.2.d.a.118.1		2
68.7	even	16		816.2.c.c.577.2		2
68.27	even	16		816.2.c.c.577.1		2
85.7	even	16		1275.2.d.b.424.2		2
85.24	odd	16		1275.2.g.a.526.2		2
85.27	even	16		1275.2.d.d.424.2		2
85.44	odd	16		1275.2.g.a.526.1		2
85.58	even	16		1275.2.d.d.424.1		2
85.78	even	16		1275.2.d.b.424.1		2
136.27	even	16		3264.2.c.d.577.2		2
136.61	odd	16		3264.2.c.e.577.1		2
136.75	even	16		3264.2.c.d.577.1		2
136.109	odd	16		3264.2.c.e.577.2		2
204.95	odd	16		2448.2.c.j.577.2		2
204.143	odd	16		2448.2.c.j.577.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.d.b.16.1	✓	2	17.7	odd	16
51.2.d.b.16.2	yes	2	17.10	odd	16
153.2.d.a.118.1		2	51.44	even	16
153.2.d.a.118.2		2	51.41	even	16
816.2.c.c.577.1		2	68.27	even	16
816.2.c.c.577.2		2	68.7	even	16
867.2.a.a.1.1		1	17.11	odd	16
867.2.a.b.1.1		1	17.6	odd	16
867.2.e.d.616.1		4	17.5	odd	16
867.2.e.d.616.2		4	17.12	odd	16
867.2.e.d.829.1		4	17.14	odd	16
867.2.e.d.829.2		4	17.3	odd	16
867.2.h.d.688.1		8	17.13	even	4	inner
867.2.h.d.688.2		8	17.4	even	4	inner
867.2.h.d.712.1		8	17.8	even	8	inner
867.2.h.d.712.2		8	17.9	even	8	inner
867.2.h.d.733.1		8	17.15	even	8	inner
867.2.h.d.733.2		8	17.2	even	8	inner
867.2.h.d.757.1		8	17.16	even	2	inner
867.2.h.d.757.2		8	1.1	even	1	trivial
1275.2.d.b.424.1		2	85.78	even	16
1275.2.d.b.424.2		2	85.7	even	16
1275.2.d.d.424.1		2	85.58	even	16
1275.2.d.d.424.2		2	85.27	even	16
1275.2.g.a.526.1		2	85.44	odd	16
1275.2.g.a.526.2		2	85.24	odd	16
2448.2.c.j.577.1		2	204.143	odd	16
2448.2.c.j.577.2		2	204.95	odd	16
2601.2.a.i.1.1		1	51.11	even	16
2601.2.a.j.1.1		1	51.23	even	16
3264.2.c.d.577.1		2	136.75	even	16
3264.2.c.d.577.2		2	136.27	even	16
3264.2.c.e.577.1		2	136.61	odd	16
3264.2.c.e.577.2		2	136.109	odd	16

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:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	867.h (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.923880 + 0.382683i) q^{3} +1.00000i q^{4} +(-0.923880 + 0.382683i) q^{6} +(-1.53073 - 3.69552i) q^{7} +(-2.12132 - 2.12132i) q^{8} +(0.707107 + 0.707107i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.923880 + 0.382683i) q^{3} +1.00000i q^{4} +(-0.923880 + 0.382683i) q^{6} +(-1.53073 - 3.69552i) q^{7} +(-2.12132 - 2.12132i) q^{8} +(0.707107 + 0.707107i) q^{9} +(3.69552 - 1.53073i) q^{11} +(-0.382683 + 0.923880i) q^{12} +2.00000i q^{13} +(3.69552 + 1.53073i) q^{14} +1.00000 q^{16} -1.00000 q^{18} +(2.82843 - 2.82843i) q^{19} -4.00000i q^{21} +(-1.53073 + 3.69552i) q^{22} +(3.69552 - 1.53073i) q^{23} +(-1.14805 - 2.77164i) q^{24} +(3.53553 + 3.53553i) q^{25} +(-1.41421 - 1.41421i) q^{26} +(0.382683 + 0.923880i) q^{27} +(3.69552 - 1.53073i) q^{28} +(3.69552 + 1.53073i) q^{31} +(3.53553 - 3.53553i) q^{32} +4.00000 q^{33} +(-0.707107 + 0.707107i) q^{36} +(7.39104 + 3.06147i) q^{37} +4.00000i q^{38} +(-0.765367 + 1.84776i) q^{39} +(-3.06147 - 7.39104i) q^{41} +(2.82843 + 2.82843i) q^{42} +(2.82843 + 2.82843i) q^{43} +(1.53073 + 3.69552i) q^{44} +(-1.53073 + 3.69552i) q^{46} -8.00000i q^{47} +(0.923880 + 0.382683i) q^{48} +(-6.36396 + 6.36396i) q^{49} -5.00000 q^{50} -2.00000 q^{52} +(-4.24264 + 4.24264i) q^{53} +(-0.923880 - 0.382683i) q^{54} +(-4.59220 + 11.0866i) q^{56} +(3.69552 - 1.53073i) q^{57} +(-8.48528 - 8.48528i) q^{59} +(3.06147 + 7.39104i) q^{61} +(-3.69552 + 1.53073i) q^{62} +(1.53073 - 3.69552i) q^{63} +7.00000i q^{64} +(-2.82843 + 2.82843i) q^{66} -12.0000 q^{67} +4.00000 q^{69} +(11.0866 + 4.59220i) q^{71} -3.00000i q^{72} +(-7.39104 + 3.06147i) q^{74} +(1.91342 + 4.61940i) q^{75} +(2.82843 + 2.82843i) q^{76} +(-11.3137 - 11.3137i) q^{77} +(-0.765367 - 1.84776i) q^{78} +(-3.69552 + 1.53073i) q^{79} +1.00000i q^{81} +(7.39104 + 3.06147i) q^{82} +(8.48528 - 8.48528i) q^{83} +4.00000 q^{84} -4.00000 q^{86} +(-11.0866 - 4.59220i) q^{88} +10.0000i q^{89} +(7.39104 - 3.06147i) q^{91} +(1.53073 + 3.69552i) q^{92} +(2.82843 + 2.82843i) q^{93} +(5.65685 + 5.65685i) q^{94} +(4.61940 - 1.91342i) q^{96} +(6.12293 - 14.7821i) q^{97} -9.00000i q^{98} +(3.69552 + 1.53073i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q + 8 q^{16} - 8 q^{18} + 32 q^{33} - 40 q^{50} - 16 q^{52} - 96 q^{67} + 32 q^{69} + 32 q^{84} - 32 q^{86}+O(q^{100}) \) 8 * q + 8 * q^16 - 8 * q^18 + 32 * q^33 - 40 * q^50 - 16 * q^52 - 96 * q^67 + 32 * q^69 + 32 * q^84 - 32 * q^86

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