LMFDB - Embedded newform 1014.3.f.h.577.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,3,Mod(577,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1014.577");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1014.f (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:	$27.6294988061$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 82x^{5} + 5053x^{4} - 6736x^{3} + 6728x^{2} + 275384x + 5635876 $ x^8 - 2x^7 + 2x^6 + 82x^5 + 5053x^4 - 6736x^3 + 6728x^2 + 275384*x + 5635876
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			577.4
Root			$-4.04651 + 4.04651i$ of defining polynomial
Character	$\chi$	$=$	1014.577
Dual form			1014.3.f.h.775.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +1.73205 q^{3} -2.00000i q^{4} +(4.41254 - 4.41254i) q^{5} +(-1.73205 + 1.73205i) q^{6} +(5.77857 + 5.77857i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +1.73205 q^{3} -2.00000i q^{4} +(4.41254 - 4.41254i) q^{5} +(-1.73205 + 1.73205i) q^{6} +(5.77857 + 5.77857i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000 q^{9} +8.82508i q^{10} +(-13.5571 - 13.5571i) q^{11} -3.46410i q^{12} -11.5571 q^{14} +(7.64274 - 7.64274i) q^{15} -4.00000 q^{16} -23.0866i q^{17} +(-3.00000 + 3.00000i) q^{18} +(-0.305695 + 0.305695i) q^{19} +(-8.82508 - 8.82508i) q^{20} +(10.0088 + 10.0088i) q^{21} +27.1143 q^{22} -42.1106i q^{23} +(3.46410 + 3.46410i) q^{24} -13.9410i q^{25} +5.19615 q^{27} +(11.5571 - 11.5571i) q^{28} +6.51569 q^{29} +15.2855i q^{30} +(-17.8476 + 17.8476i) q^{31} +(4.00000 - 4.00000i) q^{32} +(-23.4816 - 23.4816i) q^{33} +(23.0866 + 23.0866i) q^{34} +50.9963 q^{35} -6.00000i q^{36} +(1.01014 + 1.01014i) q^{37} -0.611390i q^{38} +17.6502 q^{40} +(-29.5572 + 29.5572i) q^{41} -20.0175 q^{42} -59.0397i q^{43} +(-27.1143 + 27.1143i) q^{44} +(13.2376 - 13.2376i) q^{45} +(42.1106 + 42.1106i) q^{46} +(15.0543 + 15.0543i) q^{47} -6.92820 q^{48} +17.7836i q^{49} +(13.9410 + 13.9410i) q^{50} -39.9872i q^{51} +8.90794 q^{53} +(-5.19615 + 5.19615i) q^{54} -119.643 q^{55} +23.1143i q^{56} +(-0.529479 + 0.529479i) q^{57} +(-6.51569 + 6.51569i) q^{58} +(31.1999 + 31.1999i) q^{59} +(-15.2855 - 15.2855i) q^{60} -89.6053 q^{61} -35.6953i q^{62} +(17.3357 + 17.3357i) q^{63} +8.00000i q^{64} +46.9633 q^{66} +(28.0209 - 28.0209i) q^{67} -46.1732 q^{68} -72.9376i q^{69} +(-50.9963 + 50.9963i) q^{70} +(-6.27170 + 6.27170i) q^{71} +(6.00000 + 6.00000i) q^{72} +(-5.92683 - 5.92683i) q^{73} -2.02028 q^{74} -24.1466i q^{75} +(0.611390 + 0.611390i) q^{76} -156.682i q^{77} +115.826 q^{79} +(-17.6502 + 17.6502i) q^{80} +9.00000 q^{81} -59.1143i q^{82} +(-34.2340 + 34.2340i) q^{83} +(20.0175 - 20.0175i) q^{84} +(-101.871 - 101.871i) q^{85} +(59.0397 + 59.0397i) q^{86} +11.2855 q^{87} -54.2285i q^{88} +(-42.5122 - 42.5122i) q^{89} +26.4752i q^{90} -84.2211 q^{92} +(-30.9130 + 30.9130i) q^{93} -30.1085 q^{94} +2.69778i q^{95} +(6.92820 - 6.92820i) q^{96} +(94.5385 - 94.5385i) q^{97} +(-17.7836 - 17.7836i) q^{98} +(-40.6714 - 40.6714i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - 6 q^{5} - 2 q^{7} + 16 q^{8} + 24 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 - 6 * q^5 - 2 * q^7 + 16 * q^8 + 24 * q^9	$ 8 q - 8 q^{2} - 6 q^{5} - 2 q^{7} + 16 q^{8} + 24 q^{9} - 12 q^{11} + 4 q^{14} + 6 q^{15} - 32 q^{16} - 24 q^{18} - 44 q^{19} + 12 q^{20} + 18 q^{21} + 24 q^{22} - 4 q^{28} - 72 q^{29} - 94 q^{31} + 32 q^{32} - 36 q^{33} + 60 q^{34} + 408 q^{35} - 46 q^{37} - 24 q^{40} - 30 q^{41} - 36 q^{42} - 24 q^{44} - 18 q^{45} + 144 q^{46} + 300 q^{47} + 208 q^{50} + 84 q^{53} - 792 q^{55} + 24 q^{57} + 72 q^{58} - 12 q^{59} - 12 q^{60} + 180 q^{61} - 6 q^{63} + 72 q^{66} - 74 q^{67} - 120 q^{68} - 408 q^{70} + 156 q^{71} + 48 q^{72} + 16 q^{73} + 92 q^{74} + 88 q^{76} - 96 q^{79} + 24 q^{80} + 72 q^{81} + 36 q^{84} + 234 q^{85} + 168 q^{86} - 60 q^{87} + 228 q^{89} - 288 q^{92} - 198 q^{93} - 600 q^{94} + 2 q^{97} - 32 q^{98} - 36 q^{99}+O(q^{100}) $ 8 * q - 8 * q^2 - 6 * q^5 - 2 * q^7 + 16 * q^8 + 24 * q^9 - 12 * q^11 + 4 * q^14 + 6 * q^15 - 32 * q^16 - 24 * q^18 - 44 * q^19 + 12 * q^20 + 18 * q^21 + 24 * q^22 - 4 * q^28 - 72 * q^29 - 94 * q^31 + 32 * q^32 - 36 * q^33 + 60 * q^34 + 408 * q^35 - 46 * q^37 - 24 * q^40 - 30 * q^41 - 36 * q^42 - 24 * q^44 - 18 * q^45 + 144 * q^46 + 300 * q^47 + 208 * q^50 + 84 * q^53 - 792 * q^55 + 24 * q^57 + 72 * q^58 - 12 * q^59 - 12 * q^60 + 180 * q^61 - 6 * q^63 + 72 * q^66 - 74 * q^67 - 120 * q^68 - 408 * q^70 + 156 * q^71 + 48 * q^72 + 16 * q^73 + 92 * q^74 + 88 * q^76 - 96 * q^79 + 24 * q^80 + 72 * q^81 + 36 * q^84 + 234 * q^85 + 168 * q^86 - 60 * q^87 + 228 * q^89 - 288 * q^92 - 198 * q^93 - 600 * q^94 + 2 * q^97 - 32 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$3$	1.73205			0.577350
$3$	1.73205			0.577350
$4$		−	2.00000i		−	0.500000i
$5$	4.41254	−	4.41254i	0.882508	−	0.882508i	−0.111281	−	0.993789i	$-0.535495\pi$
$5$	4.41254	−	4.41254i	0.882508	−	0.882508i	0.993789	+	0.111281i	$0.0354953\pi$
$6$	−1.73205	+	1.73205i	−0.288675	+	0.288675i
$7$	5.77857	+	5.77857i	0.825509	+	0.825509i	0.986892	−	0.161383i	$-0.0515953\pi$
$7$	5.77857	+	5.77857i	0.825509	+	0.825509i	−0.161383	+	0.986892i	$0.551595\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$	3.00000			0.333333
$10$			8.82508i			0.882508i
$11$	−13.5571	−	13.5571i	−1.23247	−	1.23247i	−0.963014	−	0.269453i	$-0.913157\pi$
$11$	−13.5571	−	13.5571i	−1.23247	−	1.23247i	−0.269453	−	0.963014i	$-0.586843\pi$
$12$		−	3.46410i		−	0.288675i
$13$		0			0
$13$		0			0
$14$	−11.5571			−0.825509
$15$	7.64274	−	7.64274i	0.509516	−	0.509516i
$16$	−4.00000			−0.250000
$17$		−	23.0866i		−	1.35804i	−0.734122	−	0.679018i	$-0.762406\pi$
$17$		−	23.0866i		−	1.35804i	0.734122	−	0.679018i	$-0.237594\pi$
$18$	−3.00000	+	3.00000i	−0.166667	+	0.166667i
$19$	−0.305695	+	0.305695i	−0.0160892	+	0.0160892i	−0.715106	−	0.699016i	$-0.753621\pi$
$19$	−0.305695	+	0.305695i	−0.0160892	+	0.0160892i	0.699016	+	0.715106i	$0.253621\pi$
$20$	−8.82508	−	8.82508i	−0.441254	−	0.441254i
$21$	10.0088	+	10.0088i	0.476608	+	0.476608i
$22$	27.1143			1.23247
$23$		−	42.1106i		−	1.83089i	−0.402438	−	0.915447i	$-0.631837\pi$
$23$		−	42.1106i		−	1.83089i	0.402438	−	0.915447i	$-0.368163\pi$
$24$	3.46410	+	3.46410i	0.144338	+	0.144338i
$25$		−	13.9410i		−	0.557641i
$26$		0			0
$27$	5.19615			0.192450
$28$	11.5571	−	11.5571i	0.412755	−	0.412755i
$29$	6.51569			0.224679			0.112340	−	0.993670i	$-0.464166\pi$
$29$	6.51569			0.224679			0.112340	+	0.993670i	$0.464166\pi$
$30$			15.2855i			0.509516i
$31$	−17.8476	+	17.8476i	−0.575730	+	0.575730i	−0.933724	−	0.357994i	$-0.883461\pi$
$31$	−17.8476	+	17.8476i	−0.575730	+	0.575730i	0.357994	+	0.933724i	$0.383461\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$	−23.4816	−	23.4816i	−0.711565	−	0.711565i
$34$	23.0866	+	23.0866i	0.679018	+	0.679018i
$35$	50.9963			1.45704
$36$		−	6.00000i		−	0.166667i
$37$	1.01014	+	1.01014i	0.0273011	+	0.0273011i	0.720626	−	0.693324i	$-0.243855\pi$
$37$	1.01014	+	1.01014i	0.0273011	+	0.0273011i	−0.693324	+	0.720626i	$0.743855\pi$
$38$		−	0.611390i		−	0.0160892i
$39$		0			0
$40$	17.6502			0.441254
$41$	−29.5572	+	29.5572i	−0.720906	+	0.720906i	−0.968790	−	0.247884i	$-0.920265\pi$
$41$	−29.5572	+	29.5572i	−0.720906	+	0.720906i	0.247884	+	0.968790i	$0.420265\pi$
$42$	−20.0175			−0.476608
$43$		−	59.0397i		−	1.37302i	−0.727122	−	0.686509i	$-0.759142\pi$
$43$		−	59.0397i		−	1.37302i	0.727122	−	0.686509i	$-0.240858\pi$
$44$	−27.1143	+	27.1143i	−0.616233	+	0.616233i
$45$	13.2376	−	13.2376i	0.294169	−	0.294169i
$46$	42.1106	+	42.1106i	0.915447	+	0.915447i
$47$	15.0543	+	15.0543i	0.320303	+	0.320303i	0.848883	−	0.528580i	$-0.177275\pi$
$47$	15.0543	+	15.0543i	0.320303	+	0.320303i	−0.528580	+	0.848883i	$0.677275\pi$
$48$	−6.92820			−0.144338
$49$			17.7836i			0.362931i
$50$	13.9410	+	13.9410i	0.278820	+	0.278820i
$51$		−	39.9872i		−	0.784062i
$52$		0			0
$53$	8.90794			0.168074			0.0840372	−	0.996463i	$-0.473219\pi$
$53$	8.90794			0.168074			0.0840372	+	0.996463i	$0.473219\pi$
$54$	−5.19615	+	5.19615i	−0.0962250	+	0.0962250i
$55$	−119.643			−2.17532
$56$			23.1143i			0.412755i
$57$	−0.529479	+	0.529479i	−0.00928910	+	0.00928910i
$58$	−6.51569	+	6.51569i	−0.112340	+	0.112340i
$59$	31.1999	+	31.1999i	0.528812	+	0.528812i	0.920218	−	0.391406i	$-0.128011\pi$
$59$	31.1999	+	31.1999i	0.528812	+	0.528812i	−0.391406	+	0.920218i	$0.628011\pi$
$60$	−15.2855	−	15.2855i	−0.254758	−	0.254758i
$61$	−89.6053			−1.46894			−0.734470	−	0.678641i	$-0.762569\pi$
$61$	−89.6053			−1.46894			−0.734470	+	0.678641i	$0.762569\pi$
$62$		−	35.6953i		−	0.575730i
$63$	17.3357	+	17.3357i	0.275170	+	0.275170i
$64$			8.00000i			0.125000i
$65$		0			0
$66$	46.9633			0.711565
$67$	28.0209	−	28.0209i	0.418222	−	0.418222i	−0.466369	−	0.884590i	$-0.654438\pi$
$67$	28.0209	−	28.0209i	0.418222	−	0.418222i	0.884590	+	0.466369i	$0.154438\pi$
$68$	−46.1732			−0.679018
$69$		−	72.9376i		−	1.05707i
$70$	−50.9963	+	50.9963i	−0.728519	+	0.728519i
$71$	−6.27170	+	6.27170i	−0.0883338	+	0.0883338i	−0.749893	−	0.661559i	$-0.769895\pi$
$71$	−6.27170	+	6.27170i	−0.0883338	+	0.0883338i	0.661559	+	0.749893i	$0.269895\pi$
$72$	6.00000	+	6.00000i	0.0833333	+	0.0833333i
$73$	−5.92683	−	5.92683i	−0.0811895	−	0.0811895i	0.665346	−	0.746535i	$-0.268284\pi$
$73$	−5.92683	−	5.92683i	−0.0811895	−	0.0811895i	−0.746535	+	0.665346i	$0.768284\pi$
$74$	−2.02028			−0.0273011
$75$		−	24.1466i		−	0.321954i
$76$	0.611390	+	0.611390i	0.00804460	+	0.00804460i
$77$		−	156.682i		−	2.03483i
$78$		0			0
$79$	115.826			1.46616			0.733078	−	0.680144i	$-0.238083\pi$
$79$	115.826			1.46616			0.733078	+	0.680144i	$0.238083\pi$
$80$	−17.6502	+	17.6502i	−0.220627	+	0.220627i
$81$	9.00000			0.111111
$82$		−	59.1143i		−	0.720906i
$83$	−34.2340	+	34.2340i	−0.412458	+	0.412458i	−0.882594	−	0.470136i	$-0.844205\pi$
$83$	−34.2340	+	34.2340i	−0.412458	+	0.412458i	0.470136	+	0.882594i	$0.344205\pi$
$84$	20.0175	−	20.0175i	0.238304	−	0.238304i
$85$	−101.871	−	101.871i	−1.19848	−	1.19848i
$86$	59.0397	+	59.0397i	0.686509	+	0.686509i
$87$	11.2855			0.129718
$88$		−	54.2285i		−	0.616233i
$89$	−42.5122	−	42.5122i	−0.477666	−	0.477666i	0.426719	−	0.904384i	$-0.359669\pi$
$89$	−42.5122	−	42.5122i	−0.477666	−	0.477666i	−0.904384	+	0.426719i	$0.859669\pi$
$90$			26.4752i			0.294169i
$91$		0			0
$92$	−84.2211			−0.915447
$93$	−30.9130	+	30.9130i	−0.332398	+	0.332398i
$94$	−30.1085			−0.320303
$95$			2.69778i			0.0283977i
$96$	6.92820	−	6.92820i	0.0721688	−	0.0721688i
$97$	94.5385	−	94.5385i	0.974624	−	0.974624i	−0.0250617	−	0.999686i	$-0.507978\pi$
$97$	94.5385	−	94.5385i	0.974624	−	0.974624i	0.999686	+	0.0250617i	$0.00797824\pi$
$98$	−17.7836	−	17.7836i	−0.181466	−	0.181466i
$99$	−40.6714	−	40.6714i	−0.410822	−	0.410822i
$100$	−27.8820			−0.278820
$101$		−	38.2541i		−	0.378754i	−0.981904	−	0.189377i	$-0.939353\pi$
$101$		−	38.2541i		−	0.378754i	0.981904	−	0.189377i	$-0.0606468\pi$
$102$	39.9872	+	39.9872i	0.392031	+	0.392031i
$103$		−	65.9827i		−	0.640609i	−0.947315	−	0.320304i	$-0.896215\pi$
$103$		−	65.9827i		−	0.640609i	0.947315	−	0.320304i	$-0.103785\pi$
$104$		0			0
$105$	88.3282			0.841221
$106$	−8.90794	+	8.90794i	−0.0840372	+	0.0840372i
$107$	94.4827			0.883016			0.441508	−	0.897257i	$-0.354444\pi$
$107$	94.4827			0.883016			0.441508	+	0.897257i	$0.354444\pi$
$108$		−	10.3923i		−	0.0962250i
$109$	−100.935	+	100.935i	−0.926011	+	0.926011i	−0.997445	−	0.0714342i	$-0.977242\pi$
$109$	−100.935	+	100.935i	−0.926011	+	0.926011i	0.0714342	+	0.997445i	$0.477242\pi$
$110$	119.643	−	119.643i	1.08766	−	1.08766i
$111$	1.74962	+	1.74962i	0.0157623	+	0.0157623i
$112$	−23.1143	−	23.1143i	−0.206377	−	0.206377i
$113$	30.7018			0.271697			0.135849	−	0.990730i	$-0.456624\pi$
$113$	30.7018			0.271697			0.135849	+	0.990730i	$0.456624\pi$
$114$		−	1.05896i		−	0.00928910i
$115$	−185.815	−	185.815i	−1.61578	−	1.61578i
$116$		−	13.0314i		−	0.112340i
$117$		0			0
$118$	−62.3998			−0.528812
$119$	133.407	−	133.407i	1.12107	−	1.12107i
$120$	30.5710			0.254758
$121$			246.592i			2.03795i
$122$	89.6053	−	89.6053i	0.734470	−	0.734470i
$123$	−51.1945	+	51.1945i	−0.416215	+	0.416215i
$124$	35.6953	+	35.6953i	0.287865	+	0.287865i
$125$	48.7982	+	48.7982i	0.390385	+	0.390385i
$126$	−34.6714			−0.275170
$127$			159.188i			1.25345i	0.779241	+	0.626725i	$0.215605\pi$
$127$			159.188i			1.25345i	−0.779241	+	0.626725i	$0.784395\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$		−	102.260i		−	0.792712i
$130$		0			0
$131$	88.8918			0.678563			0.339282	−	0.940685i	$-0.389816\pi$
$131$	88.8918			0.678563			0.339282	+	0.940685i	$0.389816\pi$
$132$	−46.9633	+	46.9633i	−0.355782	+	0.355782i
$133$	−3.53295			−0.0265636
$134$			56.0417i			0.418222i
$135$	22.9282	−	22.9282i	0.169839	−	0.169839i
$136$	46.1732	−	46.1732i	0.339509	−	0.339509i
$137$	77.8172	+	77.8172i	0.568009	+	0.568009i	0.931570	−	0.363561i	$-0.118439\pi$
$137$	77.8172	+	77.8172i	0.568009	+	0.568009i	−0.363561	+	0.931570i	$0.618439\pi$
$138$	72.9376	+	72.9376i	0.528534	+	0.528534i
$139$	248.135			1.78515			0.892573	−	0.450903i	$-0.148898\pi$
$139$	248.135			1.78515			0.892573	+	0.450903i	$0.148898\pi$
$140$		−	101.993i		−	0.728519i
$141$	26.0747	+	26.0747i	0.184927	+	0.184927i
$142$		−	12.5434i		−	0.0883338i
$143$		0			0
$144$	−12.0000			−0.0833333
$145$	28.7507	−	28.7507i	0.198281	−	0.198281i
$146$	11.8537			0.0811895
$147$			30.8022i			0.209539i
$148$	2.02028	−	2.02028i	0.0136506	−	0.0136506i
$149$	97.6623	−	97.6623i	0.655452	−	0.655452i	−0.298849	−	0.954300i	$-0.596603\pi$
$149$	97.6623	−	97.6623i	0.655452	−	0.655452i	0.954300	+	0.298849i	$0.0966027\pi$
$150$	24.1466	+	24.1466i	0.160977	+	0.160977i
$151$	−19.6390	−	19.6390i	−0.130060	−	0.130060i	0.639080	−	0.769140i	$-0.279315\pi$
$151$	−19.6390	−	19.6390i	−0.130060	−	0.130060i	−0.769140	+	0.639080i	$0.779315\pi$
$152$	−1.22278			−0.00804460
$153$		−	69.2598i		−	0.452679i
$154$	156.682	+	156.682i	1.01741	+	1.01741i
$155$			157.507i			1.01617i
$156$		0			0
$157$	−121.293			−0.772569			−0.386285	−	0.922380i	$-0.626242\pi$
$157$	−121.293			−0.772569			−0.386285	+	0.922380i	$0.626242\pi$
$158$	−115.826	+	115.826i	−0.733078	+	0.733078i
$159$	15.4290			0.0970378
$160$		−	35.3003i		−	0.220627i
$161$	243.339	−	243.339i	1.51142	−	1.51142i
$162$	−9.00000	+	9.00000i	−0.0555556	+	0.0555556i
$163$	133.860	+	133.860i	0.821226	+	0.821226i	0.986284	−	0.165058i	$-0.0527810\pi$
$163$	133.860	+	133.860i	0.821226	+	0.821226i	−0.165058	+	0.986284i	$0.552781\pi$
$164$	59.1143	+	59.1143i	0.360453	+	0.360453i
$165$	−207.227			−1.25592
$166$		−	68.4679i		−	0.412458i
$167$	40.0958	+	40.0958i	0.240095	+	0.240095i	0.816889	−	0.576794i	$-0.195697\pi$
$167$	40.0958	+	40.0958i	0.240095	+	0.240095i	−0.576794	+	0.816889i	$0.695697\pi$
$168$			40.0351i			0.238304i
$169$		0			0
$170$	203.741			1.19848
$171$	−0.917084	+	0.917084i	−0.00536307	+	0.00536307i
$172$	−118.079			−0.686509
$173$		−	325.495i		−	1.88147i	−0.339141	−	0.940736i	$-0.610136\pi$
$173$		−	325.495i		−	1.88147i	0.339141	−	0.940736i	$-0.389864\pi$
$174$	−11.2855	+	11.2855i	−0.0648592	+	0.0648592i
$175$	80.5591	−	80.5591i	0.460338	−	0.460338i
$176$	54.2285	+	54.2285i	0.308117	+	0.308117i
$177$	54.0398	+	54.0398i	0.305310	+	0.305310i
$178$	85.0245			0.477666
$179$			140.895i			0.787124i	0.919298	+	0.393562i	$0.128757\pi$
$179$			140.895i			0.787124i	−0.919298	+	0.393562i	$0.871243\pi$
$180$	−26.4752	−	26.4752i	−0.147085	−	0.147085i
$181$		−	56.0814i		−	0.309842i	−0.987927	−	0.154921i	$-0.950488\pi$
$181$		−	56.0814i		−	0.309842i	0.987927	−	0.154921i	$-0.0495123\pi$
$182$		0			0
$183$	−155.201			−0.848093
$184$	84.2211	−	84.2211i	0.457724	−	0.457724i
$185$	8.91458			0.0481869
$186$		−	61.8260i		−	0.332398i
$187$	−312.988	+	312.988i	−1.67373	+	1.67373i
$188$	30.1085	−	30.1085i	0.160152	−	0.160152i
$189$	30.0263	+	30.0263i	0.158869	+	0.158869i
$190$	−2.69778	−	2.69778i	−0.0141988	−	0.0141988i
$191$	−161.233			−0.844151			−0.422076	−	0.906561i	$-0.638698\pi$
$191$	−161.233			−0.844151			−0.422076	+	0.906561i	$0.638698\pi$
$192$			13.8564i			0.0721688i
$193$	−118.657	−	118.657i	−0.614804	−	0.614804i	0.329390	−	0.944194i	$-0.393157\pi$
$193$	−118.657	−	118.657i	−0.614804	−	0.614804i	−0.944194	+	0.329390i	$0.893157\pi$
$194$			189.077i			0.974624i
$195$		0			0
$196$	35.5673			0.181466
$197$	142.975	−	142.975i	0.725760	−	0.725760i	−0.244012	−	0.969772i	$-0.578464\pi$
$197$	142.975	−	142.975i	0.725760	−	0.725760i	0.969772	+	0.244012i	$0.0784637\pi$
$198$	81.3428			0.410822
$199$			93.3316i			0.469003i	0.972116	+	0.234501i	$0.0753457\pi$
$199$			93.3316i			0.469003i	−0.972116	+	0.234501i	$0.924654\pi$
$200$	27.8820	−	27.8820i	0.139410	−	0.139410i
$201$	48.5335	−	48.5335i	0.241460	−	0.241460i
$202$	38.2541	+	38.2541i	0.189377	+	0.189377i
$203$	37.6513	+	37.6513i	0.185475	+	0.185475i
$204$	−79.9744			−0.392031
$205$			260.844i			1.27241i
$206$	65.9827	+	65.9827i	0.320304	+	0.320304i
$207$		−	126.332i		−	0.610298i
$208$		0			0
$209$	8.28869			0.0396588
$210$	−88.3282	+	88.3282i	−0.420610	+	0.420610i
$211$	316.451			1.49977			0.749885	−	0.661568i	$-0.230109\pi$
$211$	316.451			1.49977			0.749885	+	0.661568i	$0.230109\pi$
$212$		−	17.8159i		−	0.0840372i
$213$	−10.8629	+	10.8629i	−0.0509995	+	0.0509995i
$214$	−94.4827	+	94.4827i	−0.441508	+	0.441508i
$215$	−260.515	−	260.515i	−1.21170	−	1.21170i
$216$	10.3923	+	10.3923i	0.0481125	+	0.0481125i
$217$	−206.267			−0.950541
$218$		−	201.870i		−	0.926011i
$219$	−10.2656	−	10.2656i	−0.0468748	−	0.0468748i
$220$			239.286i			1.08766i
$221$		0			0
$222$	−3.49923			−0.0157623
$223$	48.2913	−	48.2913i	0.216553	−	0.216553i	−0.590491	−	0.807044i	$-0.701066\pi$
$223$	48.2913	−	48.2913i	0.216553	−	0.216553i	0.807044	+	0.590491i	$0.201066\pi$
$224$	46.2285			0.206377
$225$		−	41.8231i		−	0.185880i
$226$	−30.7018	+	30.7018i	−0.135849	+	0.135849i
$227$	−17.7936	+	17.7936i	−0.0783861	+	0.0783861i	−0.745213	−	0.666827i	$-0.767652\pi$
$227$	−17.7936	+	17.7936i	−0.0783861	+	0.0783861i	0.666827	+	0.745213i	$0.267652\pi$
$228$	1.05896	+	1.05896i	0.00464455	+	0.00464455i
$229$	−274.910	−	274.910i	−1.20048	−	1.20048i	−0.974020	−	0.226461i	$-0.927284\pi$
$229$	−274.910	−	274.910i	−1.20048	−	1.20048i	−0.226461	−	0.974020i	$-0.572716\pi$
$230$	371.629			1.61578
$231$		−	271.380i		−	1.17481i
$232$	13.0314	+	13.0314i	0.0561698	+	0.0561698i
$233$		−	401.576i		−	1.72350i	−0.507333	−	0.861750i	$-0.669369\pi$
$233$		−	401.576i		−	1.72350i	0.507333	−	0.861750i	$-0.330631\pi$
$234$		0			0
$235$	132.855			0.565341
$236$	62.3998	−	62.3998i	0.264406	−	0.264406i
$237$	200.617			0.846486
$238$			266.815i			1.12107i
$239$	305.397	−	305.397i	1.27781	−	1.27781i	0.335919	−	0.941891i	$-0.390953\pi$
$239$	305.397	−	305.397i	1.27781	−	1.27781i	0.941891	−	0.335919i	$-0.109047\pi$
$240$	−30.5710	+	30.5710i	−0.127379	+	0.127379i
$241$	−78.7032	−	78.7032i	−0.326569	−	0.326569i	0.524711	−	0.851280i	$-0.324173\pi$
$241$	−78.7032	−	78.7032i	−0.326569	−	0.326569i	−0.851280	+	0.524711i	$0.824173\pi$
$242$	−246.592	−	246.592i	−1.01897	−	1.01897i
$243$	15.5885			0.0641500
$244$			179.211i			0.734470i
$245$	78.4710	+	78.4710i	0.320290	+	0.320290i
$246$		−	102.389i		−	0.416215i
$247$		0			0
$248$	−71.3905			−0.287865
$249$	−59.2950	+	59.2950i	−0.238132	+	0.238132i
$250$	−97.5964			−0.390385
$251$			87.6429i			0.349175i	0.984642	+	0.174587i	$0.0558592\pi$
$251$			87.6429i			0.349175i	−0.984642	+	0.174587i	$0.944141\pi$
$252$	34.6714	−	34.6714i	0.137585	−	0.137585i
$253$	−570.898	+	570.898i	−2.25652	+	2.25652i
$254$	−159.188	−	159.188i	−0.626725	−	0.626725i
$255$	−176.445	−	176.445i	−0.691941	−	0.691941i
$256$	16.0000			0.0625000
$257$			175.409i			0.682525i	0.939968	+	0.341263i	$0.110855\pi$
$257$			175.409i			0.682525i	−0.939968	+	0.341263i	$0.889145\pi$
$258$	102.260	+	102.260i	0.396356	+	0.396356i
$259$			11.6743i			0.0450747i
$260$		0			0
$261$	19.5471			0.0748930
$262$	−88.8918	+	88.8918i	−0.339282	+	0.339282i
$263$	−127.364			−0.484272			−0.242136	−	0.970242i	$-0.577848\pi$
$263$	−127.364			−0.484272			−0.242136	+	0.970242i	$0.577848\pi$
$264$		−	93.9266i		−	0.355782i
$265$	39.3066	−	39.3066i	0.148327	−	0.148327i
$266$	3.53295	−	3.53295i	0.0132818	−	0.0132818i
$267$	−73.6334	−	73.6334i	−0.275780	−	0.275780i
$268$	−56.0417	−	56.0417i	−0.209111	−	0.209111i
$269$	−208.253			−0.774175			−0.387087	−	0.922043i	$-0.626519\pi$
$269$	−208.253			−0.774175			−0.387087	+	0.922043i	$0.626519\pi$
$270$			45.8565i			0.169839i
$271$	−2.67953	−	2.67953i	−0.00988757	−	0.00988757i	0.702146	−	0.712033i	$-0.252226\pi$
$271$	−2.67953	−	2.67953i	−0.00988757	−	0.00988757i	−0.712033	+	0.702146i	$0.752226\pi$
$272$			92.3464i			0.339509i
$273$		0			0
$274$	−155.634			−0.568009
$275$	−189.000	+	189.000i	−0.687274	+	0.687274i
$276$	−145.875			−0.528534
$277$			68.7460i			0.248180i	0.992271	+	0.124090i	$0.0396012\pi$
$277$			68.7460i			0.248180i	−0.992271	+	0.124090i	$0.960399\pi$
$278$	−248.135	+	248.135i	−0.892573	+	0.892573i
$279$	−53.5429	+	53.5429i	−0.191910	+	0.191910i
$280$	101.993	+	101.993i	0.364259	+	0.364259i
$281$	−19.5583	−	19.5583i	−0.0696025	−	0.0696025i	0.671449	−	0.741051i	$-0.265672\pi$
$281$	−19.5583	−	19.5583i	−0.0696025	−	0.0696025i	−0.741051	+	0.671449i	$0.765672\pi$
$282$	−52.1495			−0.184927
$283$			126.477i			0.446914i	0.974714	+	0.223457i	$0.0717343\pi$
$283$			126.477i			0.446914i	−0.974714	+	0.223457i	$0.928266\pi$
$284$	12.5434	+	12.5434i	0.0441669	+	0.0441669i
$285$			4.67269i			0.0163954i
$286$		0			0
$287$	−341.596			−1.19023
$288$	12.0000	−	12.0000i	0.0416667	−	0.0416667i
$289$	−243.992			−0.844261
$290$			57.5015i			0.198281i
$291$	163.746	−	163.746i	0.562700	−	0.562700i
$292$	−11.8537	+	11.8537i	−0.0405947	+	0.0405947i
$293$	263.480	+	263.480i	0.899248	+	0.899248i	0.995370	−	0.0961218i	$-0.0306438\pi$
$293$	263.480	+	263.480i	0.899248	+	0.899248i	−0.0961218	+	0.995370i	$0.530644\pi$
$294$	−30.8022	−	30.8022i	−0.104769	−	0.104769i
$295$	275.342			0.933362
$296$			4.04057i			0.0136506i
$297$	−70.4449	−	70.4449i	−0.237188	−	0.237188i
$298$			195.325i			0.655452i
$299$		0			0
$300$	−48.2931			−0.160977
$301$	341.165	−	341.165i	1.13344	−	1.13344i
$302$	39.2781			0.130060
$303$		−	66.2581i		−	0.218674i
$304$	1.22278	−	1.22278i	0.00402230	−	0.00402230i
$305$	−395.387	+	395.387i	−1.29635	+	1.29635i
$306$	69.2598	+	69.2598i	0.226339	+	0.226339i
$307$	259.830	+	259.830i	0.846352	+	0.846352i	0.989676	−	0.143324i	$-0.0457792\pi$
$307$	259.830	+	259.830i	0.846352	+	0.846352i	−0.143324	+	0.989676i	$0.545779\pi$
$308$	−313.363			−1.01741
$309$		−	114.285i		−	0.369856i
$310$	−157.507	−	157.507i	−0.508087	−	0.508087i
$311$			356.838i			1.14739i	0.819069	+	0.573695i	$0.194491\pi$
$311$			356.838i			1.14739i	−0.819069	+	0.573695i	$0.805509\pi$
$312$		0			0
$313$	−19.6152			−0.0626683			−0.0313342	−	0.999509i	$-0.509976\pi$
$313$	−19.6152			−0.0626683			−0.0313342	+	0.999509i	$0.509976\pi$
$314$	121.293	−	121.293i	0.386285	−	0.386285i
$315$	152.989			0.485679
$316$		−	231.653i		−	0.733078i
$317$	−139.801	+	139.801i	−0.441011	+	0.441011i	−0.892352	−	0.451341i	$-0.850946\pi$
$317$	−139.801	+	139.801i	−0.441011	+	0.441011i	0.451341	+	0.892352i	$0.350946\pi$
$318$	−15.4290	+	15.4290i	−0.0485189	+	0.0485189i
$319$	−88.3341	−	88.3341i	−0.276909	−	0.276909i
$320$	35.3003	+	35.3003i	0.110314	+	0.110314i
$321$	163.649			0.509809
$322$			486.677i			1.51142i
$323$	7.05746	+	7.05746i	0.0218497	+	0.0218497i
$324$		−	18.0000i		−	0.0555556i
$325$		0			0
$326$	−267.720			−0.821226
$327$	−174.825	+	174.825i	−0.534633	+	0.534633i
$328$	−118.229			−0.360453
$329$			173.984i			0.528827i
$330$	207.227	−	207.227i	0.627962	−	0.627962i
$331$	−194.533	+	194.533i	−0.587713	+	0.587713i	−0.937011	−	0.349299i	$-0.886420\pi$
$331$	−194.533	+	194.533i	−0.587713	+	0.587713i	0.349299	+	0.937011i	$0.386420\pi$
$332$	68.4679	+	68.4679i	0.206229	+	0.206229i
$333$	3.03043	+	3.03043i	0.00910038	+	0.00910038i
$334$	−80.1917			−0.240095
$335$		−	247.286i		−	0.738168i
$336$	−40.0351	−	40.0351i	−0.119152	−	0.119152i
$337$			625.952i			1.85743i	0.370800	+	0.928713i	$0.379084\pi$
$337$			625.952i			1.85743i	−0.370800	+	0.928713i	$0.620916\pi$
$338$		0			0
$339$	53.1771			0.156864
$340$	−203.741	+	203.741i	−0.599239	+	0.599239i
$341$	483.926			1.41914
$342$		−	1.83417i		−	0.00536307i
$343$	180.386	−	180.386i	0.525906	−	0.525906i
$344$	118.079	−	118.079i	0.343254	−	0.343254i
$345$	−321.840	−	321.840i	−0.932870	−	0.932870i
$346$	325.495	+	325.495i	0.940736	+	0.940736i
$347$	−105.688			−0.304575			−0.152288	−	0.988336i	$-0.548664\pi$
$347$	−105.688			−0.304575			−0.152288	+	0.988336i	$0.548664\pi$
$348$		−	22.5710i		−	0.0648592i
$349$	306.359	+	306.359i	0.877818	+	0.877818i	0.993309	−	0.115490i	$-0.0368440\pi$
$349$	306.359	+	306.359i	0.877818	+	0.877818i	−0.115490	+	0.993309i	$0.536844\pi$
$350$			161.118i			0.460338i
$351$		0			0
$352$	−108.457			−0.308117
$353$	−415.902	+	415.902i	−1.17819	+	1.17819i	−0.197988	+	0.980204i	$0.563441\pi$
$353$	−415.902	+	415.902i	−1.17819	+	1.17819i	−0.980204	+	0.197988i	$0.936559\pi$
$354$	−108.080			−0.305310
$355$			55.3483i			0.155911i
$356$	−85.0245	+	85.0245i	−0.238833	+	0.238833i
$357$	231.069	−	231.069i	0.647251	−	0.647251i
$358$	−140.895	−	140.895i	−0.393562	−	0.393562i
$359$	172.896	+	172.896i	0.481604	+	0.481604i	0.905644	−	0.424040i	$-0.139388\pi$
$359$	172.896	+	172.896i	0.481604	+	0.481604i	−0.424040	+	0.905644i	$0.639388\pi$
$360$	52.9505			0.147085
$361$			360.813i			0.999482i
$362$	56.0814	+	56.0814i	0.154921	+	0.154921i
$363$			427.109i			1.17661i
$364$		0			0
$365$	−52.3048			−0.143301
$366$	155.201	−	155.201i	0.424046	−	0.424046i
$367$	−345.226			−0.940669			−0.470335	−	0.882488i	$-0.655867\pi$
$367$	−345.226			−0.940669			−0.470335	+	0.882488i	$0.655867\pi$
$368$			168.442i			0.457724i
$369$	−88.6715	+	88.6715i	−0.240302	+	0.240302i
$370$	−8.91458	+	8.91458i	−0.0240935	+	0.0240935i
$371$	51.4751	+	51.4751i	0.138747	+	0.138747i
$372$	61.8260	+	61.8260i	0.166199	+	0.166199i
$373$	446.582			1.19727			0.598635	−	0.801022i	$-0.295710\pi$
$373$	446.582			1.19727			0.598635	+	0.801022i	$0.295710\pi$
$374$		−	625.976i		−	1.67373i
$375$	84.5209	+	84.5209i	0.225389	+	0.225389i
$376$			60.2170i			0.160152i
$377$		0			0
$378$	−60.0526			−0.158869
$379$	158.517	−	158.517i	0.418250	−	0.418250i	−0.466350	−	0.884600i	$-0.654431\pi$
$379$	158.517	−	158.517i	0.418250	−	0.418250i	0.884600	+	0.466350i	$0.154431\pi$
$380$	5.39556			0.0141988
$381$			275.722i			0.723679i
$382$	161.233	−	161.233i	0.422076	−	0.422076i
$383$	−201.372	+	201.372i	−0.525776	+	0.525776i	−0.919310	−	0.393534i	$-0.871252\pi$
$383$	−201.372	+	201.372i	−0.525776	+	0.525776i	0.393534	+	0.919310i	$0.371252\pi$
$384$	−13.8564	−	13.8564i	−0.0360844	−	0.0360844i
$385$	−691.364	−	691.364i	−1.79575	−	1.79575i
$386$	237.314			0.614804
$387$		−	177.119i		−	0.457672i
$388$	−189.077	−	189.077i	−0.487312	−	0.487312i
$389$			55.5965i			0.142922i	0.997443	+	0.0714608i	$0.0227661\pi$
$389$			55.5965i			0.142922i	−0.997443	+	0.0714608i	$0.977234\pi$
$390$		0			0
$391$	−972.190			−2.48642
$392$	−35.5673	+	35.5673i	−0.0907329	+	0.0907329i
$393$	153.965			0.391769
$394$			285.949i			0.725760i
$395$	511.089	−	511.089i	1.29390	−	1.29390i
$396$	−81.3428	+	81.3428i	−0.205411	+	0.205411i
$397$	−165.356	−	165.356i	−0.416514	−	0.416514i	0.467486	−	0.884000i	$-0.345160\pi$
$397$	−165.356	−	165.356i	−0.416514	−	0.416514i	−0.884000	+	0.467486i	$0.845160\pi$
$398$	−93.3316	−	93.3316i	−0.234501	−	0.234501i
$399$	−6.11926			−0.0153365
$400$			55.7641i			0.139410i
$401$	102.445	+	102.445i	0.255473	+	0.255473i	0.823210	−	0.567737i	$-0.192181\pi$
$401$	102.445	+	102.445i	0.255473	+	0.255473i	−0.567737	+	0.823210i	$0.692181\pi$
$402$			97.0671i			0.241460i
$403$		0			0
$404$	−76.5083			−0.189377
$405$	39.7129	−	39.7129i	0.0980564	−	0.0980564i
$406$	−75.3027			−0.185475
$407$		−	27.3893i		−	0.0672955i
$408$	79.9744	−	79.9744i	0.196016	−	0.196016i
$409$	487.571	−	487.571i	1.19211	−	1.19211i	0.215631	−	0.976475i	$-0.430819\pi$
$409$	487.571	−	487.571i	1.19211	−	1.19211i	0.976475	−	0.215631i	$-0.0691808\pi$
$410$	−260.844	−	260.844i	−0.636206	−	0.636206i
$411$	134.783	+	134.783i	0.327940	+	0.327940i
$412$	−131.965			−0.320304
$413$			360.581i			0.873078i
$414$	126.332	+	126.332i	0.305149	+	0.305149i
$415$			302.118i			0.727994i
$416$		0			0
$417$	429.783			1.03065
$418$	−8.28869	+	8.28869i	−0.0198294	+	0.0198294i
$419$	−70.6481			−0.168611			−0.0843056	−	0.996440i	$-0.526867\pi$
$419$	−70.6481			−0.168611			−0.0843056	+	0.996440i	$0.526867\pi$
$420$		−	176.656i		−	0.420610i
$421$	−269.923	+	269.923i	−0.641148	+	0.641148i	−0.950838	−	0.309690i	$-0.899775\pi$
$421$	−269.923	+	269.923i	−0.641148	+	0.641148i	0.309690	+	0.950838i	$0.399775\pi$
$422$	−316.451	+	316.451i	−0.749885	+	0.749885i
$423$	45.1628	+	45.1628i	0.106768	+	0.106768i
$424$	17.8159	+	17.8159i	0.0420186	+	0.0420186i
$425$	−321.851			−0.757296
$426$		−	21.7258i		−	0.0509995i
$427$	−517.790	−	517.790i	−1.21262	−	1.21262i
$428$		−	188.965i		−	0.441508i
$429$		0			0
$430$	521.030			1.21170
$431$	−458.463	+	458.463i	−1.06372	+	1.06372i	−0.0658931	+	0.997827i	$0.520990\pi$
$431$	−458.463	+	458.463i	−1.06372	+	1.06372i	−0.997827	+	0.0658931i	$0.979010\pi$
$432$	−20.7846			−0.0481125
$433$			381.184i			0.880333i	0.897916	+	0.440166i	$0.145081\pi$
$433$			381.184i			0.880333i	−0.897916	+	0.440166i	$0.854919\pi$
$434$	206.267	−	206.267i	0.475271	−	0.475271i
$435$	49.7978	−	49.7978i	0.114478	−	0.114478i
$436$	201.870	+	201.870i	0.463006	+	0.463006i
$437$	12.8730	+	12.8730i	0.0294576	+	0.0294576i
$438$	20.5311			0.0468748
$439$		−	111.422i		−	0.253809i	−0.991915	−	0.126905i	$-0.959496\pi$
$439$		−	111.422i		−	0.253809i	0.991915	−	0.126905i	$-0.0405042\pi$
$440$	−239.286	−	239.286i	−0.543831	−	0.543831i
$441$			53.3509i			0.120977i
$442$		0			0
$443$	480.157			1.08388			0.541938	−	0.840418i	$-0.317691\pi$
$443$	480.157			1.08388			0.541938	+	0.840418i	$0.317691\pi$
$444$	3.49923	−	3.49923i	0.00788116	−	0.00788116i
$445$	−375.174			−0.843087
$446$			96.5826i			0.216553i
$447$	169.156	−	169.156i	0.378425	−	0.378425i
$448$	−46.2285	+	46.2285i	−0.103189	+	0.103189i
$449$	−287.900	−	287.900i	−0.641203	−	0.641203i	0.309648	−	0.950851i	$-0.399789\pi$
$449$	−287.900	−	287.900i	−0.641203	−	0.641203i	−0.950851	+	0.309648i	$0.899789\pi$
$450$	41.8231	+	41.8231i	0.0929401	+	0.0929401i
$451$	801.421			1.77699
$452$		−	61.4036i		−	0.135849i
$453$	−34.0158	−	34.0158i	−0.0750901	−	0.0750901i
$454$		−	35.5873i		−	0.0783861i
$455$		0			0
$456$	−2.11792			−0.00464455
$457$	−14.3544	+	14.3544i	−0.0314101	+	0.0314101i	−0.722637	−	0.691227i	$-0.757070\pi$
$457$	−14.3544	+	14.3544i	−0.0314101	+	0.0314101i	0.691227	+	0.722637i	$0.257070\pi$
$458$	549.821			1.20048
$459$		−	119.962i		−	0.261354i
$460$	−371.629	+	371.629i	−0.807889	+	0.807889i
$461$	−335.073	+	335.073i	−0.726840	+	0.726840i	−0.969989	−	0.243149i	$-0.921820\pi$
$461$	−335.073	+	335.073i	−0.726840	+	0.726840i	0.243149	+	0.969989i	$0.421820\pi$
$462$	271.380	+	271.380i	0.587403	+	0.587403i
$463$	266.154	+	266.154i	0.574846	+	0.574846i	0.933479	−	0.358633i	$-0.116757\pi$
$463$	266.154	+	266.154i	0.574846	+	0.574846i	−0.358633	+	0.933479i	$0.616757\pi$
$464$	−26.0628			−0.0561698
$465$			272.810i			0.586688i
$466$	401.576	+	401.576i	0.861750	+	0.861750i
$467$		−	231.396i		−	0.495494i	−0.968825	−	0.247747i	$-0.920310\pi$
$467$		−	231.396i		−	0.495494i	0.968825	−	0.247747i	$-0.0796901\pi$
$468$		0			0
$469$	323.841			0.690492
$470$	−132.855	+	132.855i	−0.282670	+	0.282670i
$471$	−210.086			−0.446043
$472$			124.800i			0.264406i
$473$	−800.410	+	800.410i	−1.69220	+	1.69220i
$474$	−200.617	+	200.617i	−0.423243	+	0.423243i
$475$	4.26170	+	4.26170i	0.00897199	+	0.00897199i
$476$	−266.815	−	266.815i	−0.560536	−	0.560536i
$477$	26.7238			0.0560248
$478$			610.793i			1.27781i
$479$	59.3095	+	59.3095i	0.123819	+	0.123819i	0.766301	−	0.642482i	$-0.222095\pi$
$479$	59.3095	+	59.3095i	0.123819	+	0.123819i	−0.642482	+	0.766301i	$0.722095\pi$
$480$		−	61.1420i		−	0.127379i
$481$		0			0
$482$	157.406			0.326569
$483$	421.475	−	421.475i	0.872619	−	0.872619i
$484$	493.183			1.01897
$485$		−	834.310i		−	1.72023i
$486$	−15.5885	+	15.5885i	−0.0320750	+	0.0320750i
$487$	37.7991	−	37.7991i	0.0776163	−	0.0776163i	−0.667233	−	0.744849i	$-0.732521\pi$
$487$	37.7991	−	37.7991i	0.0776163	−	0.0776163i	0.744849	+	0.667233i	$0.232521\pi$
$488$	−179.211	−	179.211i	−0.367235	−	0.367235i
$489$	231.852	+	231.852i	0.474135	+	0.474135i
$490$	−156.942			−0.320290
$491$			872.594i			1.77718i	0.458705	+	0.888589i	$0.348314\pi$
$491$			872.594i			1.77718i	−0.458705	+	0.888589i	$0.651686\pi$
$492$	102.389	+	102.389i	0.208108	+	0.208108i
$493$		−	150.425i		−	0.305122i
$494$		0			0
$495$	−358.928			−0.725108
$496$	71.3905	−	71.3905i	0.143933	−	0.143933i
$497$	−72.4829			−0.145841
$498$		−	118.590i		−	0.238132i
$499$	178.607	−	178.607i	0.357929	−	0.357929i	−0.505120	−	0.863049i	$-0.668552\pi$
$499$	178.607	−	178.607i	0.357929	−	0.357929i	0.863049	+	0.505120i	$0.168552\pi$
$500$	97.5964	−	97.5964i	0.195193	−	0.195193i
$501$	69.4480	+	69.4480i	0.138619	+	0.138619i
$502$	−87.6429	−	87.6429i	−0.174587	−	0.174587i
$503$	−581.871			−1.15680			−0.578401	−	0.815753i	$-0.696323\pi$
$503$	−581.871			−1.15680			−0.578401	+	0.815753i	$0.696323\pi$
$504$			69.3428i			0.137585i
$505$	−168.798	−	168.798i	−0.334253	−	0.334253i
$506$		−	1141.80i		−	2.25652i
$507$		0			0
$508$	318.376			0.626725
$509$	−219.420	+	219.420i	−0.431081	+	0.431081i	−0.888996	−	0.457915i	$-0.848597\pi$
$509$	−219.420	+	219.420i	−0.431081	+	0.431081i	0.457915	+	0.888996i	$0.348597\pi$
$510$	352.890			0.691941
$511$		−	68.4972i		−	0.134045i
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	−1.58844	+	1.58844i	−0.00309637	+	0.00309637i
$514$	−175.409	−	175.409i	−0.341263	−	0.341263i
$515$	−291.151	−	291.151i	−0.565343	−	0.565343i
$516$	−204.520			−0.396356
$517$		−	408.185i		−	0.789526i
$518$	−11.6743	−	11.6743i	−0.0225373	−	0.0225373i
$519$		−	563.773i		−	1.08627i
$520$		0			0
$521$	400.878			0.769440			0.384720	−	0.923033i	$-0.374298\pi$
$521$	400.878			0.769440			0.384720	+	0.923033i	$0.374298\pi$
$522$	−19.5471	+	19.5471i	−0.0374465	+	0.0374465i
$523$	510.681			0.976445			0.488222	−	0.872719i	$-0.337646\pi$
$523$	510.681			0.976445			0.488222	+	0.872719i	$0.337646\pi$
$524$		−	177.784i		−	0.339282i
$525$	139.532	−	139.532i	0.265776	−	0.265776i
$526$	127.364	−	127.364i	0.242136	−	0.242136i
$527$	412.041	+	412.041i	0.781862	+	0.781862i
$528$	93.9266	+	93.9266i	0.177891	+	0.177891i
$529$	−1244.30			−2.35217
$530$			78.6133i			0.148327i
$531$	93.5997	+	93.5997i	0.176271	+	0.176271i
$532$			7.06591i			0.0132818i
$533$		0			0
$534$	147.267			0.275780
$535$	416.909	−	416.909i	0.779269	−	0.779269i
$536$	112.083			0.209111
$537$			244.038i			0.454446i
$538$	208.253	−	208.253i	0.387087	−	0.387087i
$539$	241.095	−	241.095i	0.447301	−	0.447301i
$540$	−45.8565	−	45.8565i	−0.0849194	−	0.0849194i
$541$	75.0411	+	75.0411i	0.138708	+	0.138708i	0.773051	−	0.634343i	$-0.218729\pi$
$541$	75.0411	+	75.0411i	0.138708	+	0.138708i	−0.634343	+	0.773051i	$0.718729\pi$
$542$	5.35906			0.00988757
$543$		−	97.1359i		−	0.178887i
$544$	−92.3464	−	92.3464i	−0.169754	−	0.169754i
$545$			890.761i			1.63442i
$546$		0			0
$547$	−328.719			−0.600950			−0.300475	−	0.953790i	$-0.597145\pi$
$547$	−328.719			−0.600950			−0.300475	+	0.953790i	$0.597145\pi$
$548$	155.634	−	155.634i	0.284004	−	0.284004i
$549$	−268.816			−0.489647
$550$		−	378.001i		−	0.687274i
$551$	−1.99181	+	1.99181i	−0.00361491	+	0.00361491i
$552$	145.875	−	145.875i	0.264267	−	0.264267i
$553$	669.310	+	669.310i	1.21033	+	1.21033i
$554$	−68.7460	−	68.7460i	−0.124090	−	0.124090i
$555$	15.4405			0.0278207
$556$		−	496.270i		−	0.892573i
$557$	242.429	+	242.429i	0.435241	+	0.435241i	0.890407	−	0.455165i	$-0.150420\pi$
$557$	242.429	+	242.429i	0.435241	+	0.435241i	−0.455165	+	0.890407i	$0.650420\pi$
$558$		−	107.086i		−	0.191910i
$559$		0			0
$560$	−203.985			−0.364259
$561$	−542.111	+	542.111i	−0.966331	+	0.966331i
$562$	39.1166			0.0696025
$563$		−	363.595i		−	0.645816i	−0.946430	−	0.322908i	$-0.895340\pi$
$563$		−	363.595i		−	0.645816i	0.946430	−	0.322908i	$-0.104660\pi$
$564$	52.1495	−	52.1495i	0.0924636	−	0.0924636i
$565$	135.473	−	135.473i	0.239775	−	0.239775i
$566$	−126.477	−	126.477i	−0.223457	−	0.223457i
$567$	52.0071	+	52.0071i	0.0917233	+	0.0917233i
$568$	−25.0868			−0.0441669
$569$		−	633.540i		−	1.11343i	−0.830705	−	0.556714i	$-0.812062\pi$
$569$		−	633.540i		−	1.11343i	0.830705	−	0.556714i	$-0.187938\pi$
$570$	−4.67269	−	4.67269i	−0.00819771	−	0.00819771i
$571$			54.2364i			0.0949849i	0.998872	+	0.0474925i	$0.0151230\pi$
$571$			54.2364i			0.0949849i	−0.998872	+	0.0474925i	$0.984877\pi$
$572$		0			0
$573$	−279.264			−0.487371
$574$	341.596	−	341.596i	0.595115	−	0.595115i
$575$	−587.064			−1.02098
$576$			24.0000i			0.0416667i
$577$	−704.420	+	704.420i	−1.22083	+	1.22083i	−0.253495	+	0.967337i	$0.581580\pi$
$577$	−704.420	+	704.420i	−1.22083	+	1.22083i	−0.967337	+	0.253495i	$0.918420\pi$
$578$	243.992	−	243.992i	0.422131	−	0.422131i
$579$	−205.520	−	205.520i	−0.354957	−	0.354957i
$580$	−57.5015	−	57.5015i	−0.0991405	−	0.0991405i
$581$	−395.647			−0.680975
$582$			327.491i			0.562700i
$583$	−120.766	−	120.766i	−0.207146	−	0.207146i
$584$		−	23.7073i		−	0.0405947i
$585$		0			0
$586$	−526.959			−0.899248
$587$	666.000	−	666.000i	1.13458	−	1.13458i	0.145178	−	0.989406i	$-0.453625\pi$
$587$	666.000	−	666.000i	1.13458	−	1.13458i	0.989406	−	0.145178i	$-0.0463754\pi$
$588$	61.6043			0.104769
$589$		−	10.9119i		−	0.0185261i
$590$	−275.342	+	275.342i	−0.466681	+	0.466681i
$591$	247.640	−	247.640i	0.419018	−	0.419018i
$592$	−4.04057	−	4.04057i	−0.00682528	−	0.00682528i
$593$	−457.589	−	457.589i	−0.771650	−	0.771650i	0.206745	−	0.978395i	$-0.433713\pi$
$593$	−457.589	−	457.589i	−0.771650	−	0.771650i	−0.978395	+	0.206745i	$0.933713\pi$
$594$	140.890			0.237188
$595$		−	1177.33i		−	1.97871i
$596$	−195.325	−	195.325i	−0.327726	−	0.327726i
$597$			161.655i			0.270779i
$598$		0			0
$599$	−78.9882			−0.131867			−0.0659334	−	0.997824i	$-0.521002\pi$
$599$	−78.9882			−0.131867			−0.0659334	+	0.997824i	$0.521002\pi$
$600$	48.2931	−	48.2931i	0.0804885	−	0.0804885i
$601$	−364.688			−0.606802			−0.303401	−	0.952863i	$-0.598122\pi$
$601$	−364.688			−0.606802			−0.303401	+	0.952863i	$0.598122\pi$
$602$			682.330i			1.13344i
$603$	84.0626	−	84.0626i	0.139407	−	0.139407i
$604$	−39.2781	+	39.2781i	−0.0650299	+	0.0650299i
$605$	1088.10	+	1088.10i	1.79850	+	1.79850i
$606$	66.2581	+	66.2581i	0.109337	+	0.109337i
$607$	591.021			0.973676			0.486838	−	0.873492i	$-0.338150\pi$
$607$	591.021			0.973676			0.486838	+	0.873492i	$0.338150\pi$
$608$			2.44556i			0.00402230i
$609$	65.2140	+	65.2140i	0.107084	+	0.107084i
$610$		−	790.774i		−	1.29635i
$611$		0			0
$612$	−138.520			−0.226339
$613$	−308.223	+	308.223i	−0.502810	+	0.502810i	−0.912310	−	0.409500i	$-0.865703\pi$
$613$	−308.223	+	308.223i	−0.502810	+	0.502810i	0.409500	+	0.912310i	$0.365703\pi$
$614$	−519.660			−0.846352
$615$			451.796i			0.734627i
$616$	313.363	−	313.363i	0.508706	−	0.508706i
$617$	211.441	−	211.441i	0.342693	−	0.342693i	−0.514686	−	0.857379i	$-0.672091\pi$
$617$	211.441	−	211.441i	0.342693	−	0.342693i	0.857379	+	0.514686i	$0.172091\pi$
$618$	114.285	+	114.285i	0.184928	+	0.184928i
$619$	84.5481	+	84.5481i	0.136588	+	0.136588i	0.772095	−	0.635507i	$-0.219209\pi$
$619$	84.5481	+	84.5481i	0.136588	+	0.136588i	−0.635507	+	0.772095i	$0.719209\pi$
$620$	315.014			0.508087
$621$		−	218.813i		−	0.352356i
$622$	−356.838	−	356.838i	−0.573695	−	0.573695i
$623$		−	491.319i		−	0.788635i
$624$		0			0
$625$	779.173			1.24668
$626$	19.6152	−	19.6152i	0.0313342	−	0.0313342i
$627$	14.3564			0.0228970
$628$			242.587i			0.386285i
$629$	23.3208	−	23.3208i	0.0370759	−	0.0370759i
$630$	−152.989	+	152.989i	−0.242840	+	0.242840i
$631$	−533.568	−	533.568i	−0.845591	−	0.845591i	0.143989	−	0.989579i	$-0.454007\pi$
$631$	−533.568	−	533.568i	−0.845591	−	0.845591i	−0.989579	+	0.143989i	$0.954007\pi$
$632$	231.653	+	231.653i	0.366539	+	0.366539i
$633$	548.110			0.865892
$634$		−	279.601i		−	0.441011i
$635$	702.424	+	702.424i	1.10618	+	1.10618i
$636$		−	30.8580i		−	0.0485189i
$637$		0			0
$638$	176.668			0.276909
$639$	−18.8151	+	18.8151i	−0.0294446	+	0.0294446i
$640$	−70.6006			−0.110314
$641$			377.129i			0.588345i	0.955752	+	0.294172i	$0.0950440\pi$
$641$			377.129i			0.588345i	−0.955752	+	0.294172i	$0.904956\pi$
$642$	−163.649	+	163.649i	−0.254905	+	0.254905i
$643$	854.112	−	854.112i	1.32832	−	1.32832i	0.421491	−	0.906833i	$-0.361507\pi$
$643$	854.112	−	854.112i	1.32832	−	1.32832i	0.906833	−	0.421491i	$-0.138493\pi$
$644$	−486.677	−	486.677i	−0.755710	−	0.755710i
$645$	−451.226	−	451.226i	−0.699575	−	0.699575i
$646$	−14.1149			−0.0218497
$647$		−	252.912i		−	0.390899i	−0.980714	−	0.195450i	$-0.937383\pi$
$647$		−	252.912i		−	0.390899i	0.980714	−	0.195450i	$-0.0626166\pi$
$648$	18.0000	+	18.0000i	0.0277778	+	0.0277778i
$649$		−	845.962i		−	1.30349i
$650$		0			0
$651$	−357.266			−0.548795
$652$	267.720	−	267.720i	0.410613	−	0.410613i
$653$	432.586			0.662460			0.331230	−	0.943550i	$-0.392536\pi$
$653$	432.586			0.662460			0.331230	+	0.943550i	$0.392536\pi$
$654$		−	349.650i		−	0.534633i
$655$	392.239	−	392.239i	0.598837	−	0.598837i
$656$	118.229	−	118.229i	0.180227	−	0.180227i
$657$	−17.7805	−	17.7805i	−0.0270632	−	0.0270632i
$658$	−173.984	−	173.984i	−0.264413	−	0.264413i
$659$	1208.86			1.83438			0.917190	−	0.398450i	$-0.130452\pi$
$659$	1208.86			1.83438			0.917190	+	0.398450i	$0.130452\pi$
$660$			414.455i			0.627962i
$661$	745.599	+	745.599i	1.12799	+	1.12799i	0.990504	+	0.137483i	$0.0439012\pi$
$661$	745.599	+	745.599i	1.12799	+	1.12799i	0.137483	+	0.990504i	$0.456099\pi$
$662$		−	389.066i		−	0.587713i
$663$		0			0
$664$	−136.936			−0.206229
$665$	−15.5893	+	15.5893i	−0.0234426	+	0.0234426i
$666$	−6.06085			−0.00910038
$667$		−	274.379i		−	0.411364i
$668$	80.1917	−	80.1917i	0.120047	−	0.120047i
$669$	83.6430	−	83.6430i	0.125027	−	0.125027i
$670$	247.286	+	247.286i	0.369084	+	0.369084i
$671$	1214.79	+	1214.79i	1.81042	+	1.81042i
$672$	80.0702			0.119152
$673$		−	795.027i		−	1.18132i	−0.806921	−	0.590659i	$-0.798868\pi$
$673$		−	795.027i		−	1.18132i	0.806921	−	0.590659i	$-0.201132\pi$
$674$	−625.952	−	625.952i	−0.928713	−	0.928713i
$675$		−	72.4397i		−	0.107318i
$676$		0			0
$677$	642.236			0.948649			0.474325	−	0.880350i	$-0.342692\pi$
$677$	642.236			0.948649			0.474325	+	0.880350i	$0.342692\pi$
$678$	−53.1771	+	53.1771i	−0.0784322	+	0.0784322i
$679$	1092.59			1.60912
$680$		−	407.482i		−	0.599239i
$681$	−30.8195	+	30.8195i	−0.0452562	+	0.0452562i
$682$	−483.926	+	483.926i	−0.709568	+	0.709568i
$683$	461.618	+	461.618i	0.675868	+	0.675868i	0.959062	−	0.283195i	$-0.0913942\pi$
$683$	461.618	+	461.618i	0.675868	+	0.675868i	−0.283195	+	0.959062i	$0.591394\pi$
$684$	1.83417	+	1.83417i	0.00268153	+	0.00268153i
$685$	686.743			1.00254
$686$			360.772i			0.525906i
$687$	−476.159	−	476.159i	−0.693098	−	0.693098i
$688$			236.159i			0.343254i
$689$		0			0
$690$	643.681			0.932870
$691$	−543.987	+	543.987i	−0.787246	+	0.787246i	−0.981042	−	0.193796i	$-0.937920\pi$
$691$	−543.987	+	543.987i	−0.787246	+	0.787246i	0.193796	+	0.981042i	$0.437920\pi$
$692$	−650.989			−0.940736
$693$		−	470.045i		−	0.678275i
$694$	105.688	−	105.688i	0.152288	−	0.152288i
$695$	1094.91	−	1094.91i	1.57541	−	1.57541i
$696$	22.5710	+	22.5710i	0.0324296	+	0.0324296i
$697$	682.375	+	682.375i	0.979017	+	0.979017i
$698$	−612.717			−0.877818
$699$		−	695.549i		−	0.995063i
$700$	−161.118	−	161.118i	−0.230169	−	0.230169i
$701$		−	415.401i		−	0.592584i	−0.955097	−	0.296292i	$-0.904250\pi$
$701$		−	415.401i		−	0.592584i	0.955097	−	0.296292i	$-0.0957502\pi$
$702$		0			0
$703$	−0.617590			−0.000878507
$704$	108.457	−	108.457i	0.154058	−	0.154058i
$705$	230.112			0.326400
$706$		−	831.804i		−	1.17819i
$707$	221.054	−	221.054i	0.312665	−	0.312665i
$708$	108.080	−	108.080i	0.152655	−	0.152655i
$709$	221.729	+	221.729i	0.312735	+	0.312735i	0.845968	−	0.533233i	$-0.179023\pi$
$709$	221.729	+	221.729i	0.312735	+	0.312735i	−0.533233	+	0.845968i	$0.679023\pi$
$710$	−55.3483	−	55.3483i	−0.0779553	−	0.0779553i
$711$	347.479			0.488719
$712$		−	170.049i		−	0.238833i
$713$	751.574	+	751.574i	1.05410	+	1.05410i
$714$			462.137i			0.647251i
$715$		0			0
$716$	281.790			0.393562
$717$	528.962	−	528.962i	0.737744	−	0.737744i
$718$	−345.792			−0.481604
$719$			236.834i			0.329393i	0.986344	+	0.164697i	$0.0526645\pi$
$719$			236.834i			0.329393i	−0.986344	+	0.164697i	$0.947336\pi$
$720$	−52.9505	+	52.9505i	−0.0735423	+	0.0735423i
$721$	381.285	−	381.285i	0.528829	−	0.528829i
$722$	−360.813	−	360.813i	−0.499741	−	0.499741i
$723$	−136.318	−	136.318i	−0.188545	−	0.188545i
$724$	−112.163			−0.154921
$725$		−	90.8354i		−	0.125290i
$726$	−427.109	−	427.109i	−0.588305	−	0.588305i
$727$			919.030i			1.26414i	0.774911	+	0.632070i	$0.217794\pi$
$727$			919.030i			1.26414i	−0.774911	+	0.632070i	$0.782206\pi$
$728$		0			0
$729$	27.0000			0.0370370
$730$	52.3048	−	52.3048i	0.0716503	−	0.0716503i
$731$	−1363.03			−1.86461
$732$			310.402i			0.424046i
$733$	709.566	−	709.566i	0.968030	−	0.968030i	−0.0314750	−	0.999505i	$-0.510020\pi$
$733$	709.566	−	709.566i	0.968030	−	0.968030i	0.999505	+	0.0314750i	$0.0100205\pi$
$734$	345.226	−	345.226i	0.470335	−	0.470335i
$735$	135.916	+	135.916i	0.184919	+	0.184919i
$736$	−168.442	−	168.442i	−0.228862	−	0.228862i
$737$	−759.765			−1.03089
$738$		−	177.343i		−	0.240302i
$739$	−86.9546	−	86.9546i	−0.117665	−	0.117665i	0.645822	−	0.763488i	$-0.276515\pi$
$739$	−86.9546	−	86.9546i	−0.117665	−	0.117665i	−0.763488	+	0.645822i	$0.776515\pi$
$740$		−	17.8292i		−	0.0240935i
$741$		0			0
$742$	−102.950			−0.138747
$743$	941.086	−	941.086i	1.26660	−	1.26660i	0.318771	−	0.947832i	$-0.396730\pi$
$743$	941.086	−	941.086i	1.26660	−	1.26660i	0.947832	−	0.318771i	$-0.103270\pi$
$744$	−123.652			−0.166199
$745$		−	861.877i		−	1.15688i
$746$	−446.582	+	446.582i	−0.598635	+	0.598635i
$747$	−102.702	+	102.702i	−0.137486	+	0.137486i
$748$	625.976	+	625.976i	0.836867	+	0.836867i
$749$	545.974	+	545.974i	0.728938	+	0.728938i
$750$	−169.042			−0.225389
$751$			1360.06i			1.81100i	0.424345	+	0.905501i	$0.360504\pi$
$751$			1360.06i			1.81100i	−0.424345	+	0.905501i	$0.639496\pi$
$752$	−60.2170	−	60.2170i	−0.0800758	−	0.0800758i
$753$			151.802i			0.201596i
$754$		0			0
$755$	−173.316			−0.229558
$756$	60.0526	−	60.0526i	0.0794347	−	0.0794347i
$757$	−1083.74			−1.43162			−0.715812	−	0.698293i	$-0.753943\pi$
$757$	−1083.74			−1.43162			−0.715812	+	0.698293i	$0.753943\pi$
$758$			317.034i			0.418250i
$759$	−988.825	+	988.825i	−1.30280	+	1.30280i
$760$	−5.39556	+	5.39556i	−0.00709942	+	0.00709942i
$761$	−823.963	−	823.963i	−1.08274	−	1.08274i	−0.996253	−	0.0864843i	$-0.972437\pi$
$761$	−823.963	−	823.963i	−1.08274	−	1.08274i	−0.0864843	−	0.996253i	$-0.527563\pi$
$762$	−275.722	−	275.722i	−0.361840	−	0.361840i
$763$	−1166.52			−1.52886
$764$			322.466i			0.422076i
$765$	−305.612	−	305.612i	−0.399493	−	0.399493i
$766$		−	402.745i		−	0.525776i
$767$		0			0
$768$	27.7128			0.0360844
$769$	−650.234	+	650.234i	−0.845558	+	0.845558i	−0.989575	−	0.144017i	$-0.953998\pi$
$769$	−650.234	+	650.234i	−0.845558	+	0.845558i	0.144017	+	0.989575i	$0.453998\pi$
$770$	1382.73			1.79575
$771$			303.817i			0.394056i
$772$	−237.314	+	237.314i	−0.307402	+	0.307402i
$773$	−864.830	+	864.830i	−1.11880	+	1.11880i	−0.126879	+	0.991918i	$0.540496\pi$
$773$	−864.830	+	864.830i	−1.11880	+	1.11880i	−0.991918	+	0.126879i	$0.959504\pi$
$774$	177.119	+	177.119i	0.228836	+	0.228836i
$775$	248.814	+	248.814i	0.321051	+	0.321051i
$776$	378.154			0.487312
$777$			20.2206i			0.0260239i
$778$	−55.5965	−	55.5965i	−0.0714608	−	0.0714608i
$779$		−	18.0709i		−	0.0231976i
$780$		0			0
$781$	170.053			0.217737
$782$	972.190	−	972.190i	1.24321	−	1.24321i
$783$	33.8565			0.0432395
$784$		−	71.1346i		−	0.0907329i
$785$	−535.212	+	535.212i	−0.681799	+	0.681799i
$786$	−153.965	+	153.965i	−0.195884	+	0.195884i
$787$	62.9482	+	62.9482i	0.0799850	+	0.0799850i	0.745967	−	0.665982i	$-0.231987\pi$
$787$	62.9482	+	62.9482i	0.0799850	+	0.0799850i	−0.665982	+	0.745967i	$0.731987\pi$
$788$	−285.949	−	285.949i	−0.362880	−	0.362880i
$789$	−220.600			−0.279595
$790$			1022.18i			1.29390i
$791$	177.412	+	177.412i	0.224289	+	0.224289i
$792$		−	162.686i		−	0.205411i
$793$		0			0
$794$	330.712			0.416514
$795$	68.0811	−	68.0811i	0.0856366	−	0.0856366i
$796$	186.663			0.234501
$797$		−	574.090i		−	0.720313i	−0.932892	−	0.360157i	$-0.882723\pi$
$797$		−	574.090i		−	0.720313i	0.932892	−	0.360157i	$-0.117277\pi$
$798$	6.11926	−	6.11926i	0.00766824	−	0.00766824i
$799$	347.552	−	347.552i	0.434983	−	0.434983i
$800$	−55.7641	−	55.7641i	−0.0697051	−	0.0697051i
$801$	−127.537	−	127.537i	−0.159222	−	0.159222i
$802$	−204.889			−0.255473
$803$			160.702i			0.200127i
$804$	−97.0671	−	97.0671i	−0.120730	−	0.120730i
$805$		−	2147.48i		−	2.66768i
$806$		0			0
$807$	−360.705			−0.446970
$808$	76.5083	−	76.5083i	0.0946885	−	0.0946885i
$809$	−183.580			−0.226923			−0.113461	−	0.993542i	$-0.536194\pi$
$809$	−183.580			−0.226923			−0.113461	+	0.993542i	$0.536194\pi$
$810$			79.4257i			0.0980564i
$811$	40.9644	−	40.9644i	0.0505110	−	0.0505110i	−0.681400	−	0.731911i	$-0.738629\pi$
$811$	40.9644	−	40.9644i	0.0505110	−	0.0505110i	0.731911	+	0.681400i	$0.238629\pi$
$812$	75.3027	−	75.3027i	0.0927373	−	0.0927373i
$813$	−4.64108	−	4.64108i	−0.00570859	−	0.00570859i
$814$	27.3893	+	27.3893i	0.0336477	+	0.0336477i
$815$	1181.32			1.44948
$816$			159.949i			0.196016i
$817$	18.0481	+	18.0481i	0.0220907	+	0.0220907i
$818$			975.143i			1.19211i
$819$		0			0
$820$	521.689			0.636206
$821$	−559.097	+	559.097i	−0.680995	+	0.680995i	−0.960224	−	0.279229i	$-0.909921\pi$
$821$	−559.097	+	559.097i	−0.680995	+	0.680995i	0.279229	+	0.960224i	$0.409921\pi$
$822$	−269.567			−0.327940
$823$			590.300i			0.717254i	0.933481	+	0.358627i	$0.116755\pi$
$823$			590.300i			0.717254i	−0.933481	+	0.358627i	$0.883245\pi$
$824$	131.965	−	131.965i	0.160152	−	0.160152i
$825$	−327.358	+	327.358i	−0.396798	+	0.396798i
$826$	−360.581	−	360.581i	−0.436539	−	0.436539i
$827$	−6.60106	−	6.60106i	−0.00798194	−	0.00798194i	0.703105	−	0.711086i	$-0.251797\pi$
$827$	−6.60106	−	6.60106i	−0.00798194	−	0.00798194i	−0.711086	+	0.703105i	$0.751797\pi$
$828$	−252.663			−0.305149
$829$		−	1289.33i		−	1.55528i	−0.628711	−	0.777639i	$-0.716417\pi$
$829$		−	1289.33i		−	1.55528i	0.628711	−	0.777639i	$-0.283583\pi$
$830$	−302.118	−	302.118i	−0.363997	−	0.363997i
$831$			119.071i			0.143287i
$832$		0			0
$833$	410.564			0.492874
$834$	−429.783	+	429.783i	−0.515327	+	0.515327i
$835$	353.849			0.423771
$836$		−	16.5774i		−	0.0198294i
$837$	−92.7390	+	92.7390i	−0.110799	+	0.110799i
$838$	70.6481	−	70.6481i	0.0843056	−	0.0843056i
$839$	12.6872	+	12.6872i	0.0151218	+	0.0151218i	0.714627	−	0.699505i	$-0.246596\pi$
$839$	12.6872	+	12.6872i	0.0151218	+	0.0151218i	−0.699505	+	0.714627i	$0.746596\pi$
$840$	176.656	+	176.656i	0.210305	+	0.210305i
$841$	−798.546			−0.949519
$842$		−	539.847i		−	0.641148i
$843$	−33.8760	−	33.8760i	−0.0401850	−	0.0401850i
$844$		−	632.903i		−	0.749885i
$845$		0			0
$846$	−90.3256			−0.106768
$847$	−1424.95	+	1424.95i	−1.68234	+	1.68234i
$848$	−35.6318			−0.0420186
$849$			219.064i			0.258026i
$850$	321.851	−	321.851i	0.378648	−	0.378648i
$851$	42.5377	−	42.5377i	0.0499855	−	0.0499855i
$852$	21.7258	+	21.7258i	0.0254998	+	0.0254998i
$853$	530.523	+	530.523i	0.621949	+	0.621949i	0.946030	−	0.324080i	$-0.105055\pi$
$853$	530.523	+	530.523i	0.621949	+	0.621949i	−0.324080	+	0.946030i	$0.605055\pi$
$854$	1035.58			1.21262
$855$			8.09334i			0.00946590i
$856$	188.965	+	188.965i	0.220754	+	0.220754i
$857$		−	938.561i		−	1.09517i	−0.836750	−	0.547585i	$-0.815547\pi$
$857$		−	938.561i		−	1.09517i	0.836750	−	0.547585i	$-0.184453\pi$
$858$		0			0
$859$	−30.0614			−0.0349958			−0.0174979	−	0.999847i	$-0.505570\pi$
$859$	−30.0614			−0.0349958			−0.0174979	+	0.999847i	$0.505570\pi$
$860$	−521.030	+	521.030i	−0.605849	+	0.605849i
$861$	−591.662			−0.687180
$862$		−	916.926i		−	1.06372i
$863$	32.0489	−	32.0489i	0.0371366	−	0.0371366i	−0.688295	−	0.725431i	$-0.741640\pi$
$863$	32.0489	−	32.0489i	0.0371366	−	0.0371366i	0.725431	+	0.688295i	$0.241640\pi$
$864$	20.7846	−	20.7846i	0.0240563	−	0.0240563i
$865$	−1436.26	−	1436.26i	−1.66041	−	1.66041i
$866$	−381.184	−	381.184i	−0.440166	−	0.440166i
$867$	−422.606			−0.487435
$868$			412.535i			0.475271i
$869$	−1570.27	−	1570.27i	−1.80699	−	1.80699i
$870$			99.5955i			0.114478i
$871$		0			0
$872$	−403.741			−0.463006
$873$	283.616	−	283.616i	0.324875	−	0.324875i
$874$	−25.7460			−0.0294576
$875$			563.967i			0.644534i
$876$	−20.5311	+	20.5311i	−0.0234374	+	0.0234374i
$877$	−586.534	+	586.534i	−0.668795	+	0.668795i	−0.957437	−	0.288642i	$-0.906796\pi$
$877$	−586.534	+	586.534i	−0.668795	+	0.668795i	0.288642	+	0.957437i	$0.406796\pi$
$878$	111.422	+	111.422i	0.126905	+	0.126905i
$879$	456.360	+	456.360i	0.519181	+	0.519181i
$880$	478.571			0.543831
$881$			198.181i			0.224950i	0.993655	+	0.112475i	$0.0358778\pi$
$881$			198.181i			0.224950i	−0.993655	+	0.112475i	$0.964122\pi$
$882$	−53.3509	−	53.3509i	−0.0604886	−	0.0604886i
$883$			328.692i			0.372245i	0.982527	+	0.186122i	$0.0595921\pi$
$883$			328.692i			0.372245i	−0.982527	+	0.186122i	$0.940408\pi$
$884$		0			0
$885$	476.906			0.538877
$886$	−480.157	+	480.157i	−0.541938	+	0.541938i
$887$	−548.992			−0.618931			−0.309465	−	0.950911i	$-0.600150\pi$
$887$	−548.992			−0.618931			−0.309465	+	0.950911i	$0.600150\pi$
$888$			6.99847i			0.00788116i
$889$	−919.879	+	919.879i	−1.03473	+	1.03473i
$890$	375.174	−	375.174i	0.421544	−	0.421544i
$891$	−122.014	−	122.014i	−0.136941	−	0.136941i
$892$	−96.5826	−	96.5826i	−0.108276	−	0.108276i
$893$	−9.20402			−0.0103068
$894$			338.312i			0.378425i
$895$	621.706	+	621.706i	0.694644	+	0.694644i
$896$		−	92.4570i		−	0.103189i
$897$		0			0
$898$	575.801			0.641203
$899$	−116.290	+	116.290i	−0.129354	+	0.129354i
$900$	−83.6461			−0.0929401
$901$		−	205.654i		−	0.228251i
$902$	−801.421	+	801.421i	−0.888493	+	0.888493i
$903$	590.915	−	590.915i	0.654391	−	0.654391i
$904$	61.4036	+	61.4036i	0.0679243	+	0.0679243i
$905$	−247.461	−	247.461i	−0.273438	−	0.273438i
$906$	68.0316			0.0750901
$907$		−	580.530i		−	0.640055i	−0.947408	−	0.320028i	$-0.896308\pi$
$907$		−	580.530i		−	0.640055i	0.947408	−	0.320028i	$-0.103692\pi$
$908$	35.5873	+	35.5873i	0.0391930	+	0.0391930i
$909$		−	114.762i		−	0.126251i
$910$		0			0
$911$	1086.06			1.19216			0.596081	−	0.802924i	$-0.296724\pi$
$911$	1086.06			1.19216			0.596081	+	0.802924i	$0.296724\pi$
$912$	2.11792	−	2.11792i	0.00232228	−	0.00232228i
$913$	928.229			1.01668
$914$		−	28.7088i		−	0.0314101i
$915$	−684.831	+	684.831i	−0.748449	+	0.748449i
$916$	−549.821	+	549.821i	−0.600241	+	0.600241i
$917$	513.667	+	513.667i	0.560160	+	0.560160i
$918$	119.962	+	119.962i	0.130677	+	0.130677i
$919$	240.478			0.261674			0.130837	−	0.991404i	$-0.458234\pi$
$919$	240.478			0.261674			0.130837	+	0.991404i	$0.458234\pi$
$920$		−	743.258i		−	0.807889i
$921$	450.039	+	450.039i	0.488641	+	0.488641i
$922$		−	670.147i		−	0.726840i
$923$		0			0
$924$	−542.761			−0.587403
$925$	14.0824	−	14.0824i	0.0152242	−	0.0152242i
$926$	−532.307			−0.574846
$927$		−	197.948i		−	0.213536i
$928$	26.0628	−	26.0628i	0.0280849	−	0.0280849i
$929$	20.7901	−	20.7901i	0.0223790	−	0.0223790i	−0.695829	−	0.718208i	$-0.744963\pi$
$929$	20.7901	−	20.7901i	0.0223790	−	0.0223790i	0.718208	+	0.695829i	$0.244963\pi$
$930$	−272.810	−	272.810i	−0.293344	−	0.293344i
$931$	−5.43637	−	5.43637i	−0.00583928	−	0.00583928i
$932$	−803.151			−0.861750
$933$			618.062i			0.662446i
$934$	231.396	+	231.396i	0.247747	+	0.247747i
$935$			2762.15i			2.95417i
$936$		0			0
$937$	−254.283			−0.271380			−0.135690	−	0.990751i	$-0.543325\pi$
$937$	−254.283			−0.271380			−0.135690	+	0.990751i	$0.543325\pi$
$938$	−323.841	+	323.841i	−0.345246	+	0.345246i
$939$	−33.9745			−0.0361816
$940$		−	265.710i		−	0.282670i
$941$	−237.783	+	237.783i	−0.252692	+	0.252692i	−0.822073	−	0.569382i	$-0.807183\pi$
$941$	−237.783	+	237.783i	−0.252692	+	0.252692i	0.569382	+	0.822073i	$0.307183\pi$
$942$	210.086	−	210.086i	0.223022	−	0.223022i
$943$	1244.67	+	1244.67i	1.31990	+	1.31990i
$944$	−124.800	−	124.800i	−0.132203	−	0.132203i
$945$	264.985			0.280407
$946$		−	1600.82i		−	1.69220i
$947$	−1042.24	−	1042.24i	−1.10057	−	1.10057i	−0.994341	−	0.106232i	$-0.966121\pi$
$947$	−1042.24	−	1042.24i	−1.10057	−	1.10057i	−0.106232	−	0.994341i	$-0.533879\pi$
$948$		−	401.234i		−	0.423243i
$949$		0			0
$950$	−8.52340			−0.00897199
$951$	−242.142	+	242.142i	−0.254618	+	0.254618i
$952$	533.630			0.560536
$953$		−	191.127i		−	0.200553i	−0.994960	−	0.100276i	$-0.968027\pi$
$953$		−	191.127i		−	0.200553i	0.994960	−	0.100276i	$-0.0319727\pi$
$954$	−26.7238	+	26.7238i	−0.0280124	+	0.0280124i
$955$	−711.447	+	711.447i	−0.744970	+	0.744970i
$956$	−610.793	−	610.793i	−0.638905	−	0.638905i
$957$	−152.999	−	152.999i	−0.159874	−	0.159874i
$958$	−118.619			−0.123819
$959$			899.344i			0.937793i
$960$	61.1420	+	61.1420i	0.0636895	+	0.0636895i
$961$			323.924i			0.337069i
$962$		0			0
$963$	283.448			0.294339
$964$	−157.406	+	157.406i	−0.163285	+	0.163285i
$965$	−1047.16			−1.08514
$966$			842.950i			0.872619i
$967$	748.972	−	748.972i	0.774531	−	0.774531i	−0.204364	−	0.978895i	$-0.565513\pi$
$967$	748.972	−	748.972i	0.774531	−	0.774531i	0.978895	+	0.204364i	$0.0655125\pi$
$968$	−493.183	+	493.183i	−0.509487	+	0.509487i
$969$	12.2239	+	12.2239i	0.0126149	+	0.0126149i
$970$	834.310	+	834.310i	0.860114	+	0.860114i
$971$	−145.962			−0.150321			−0.0751605	−	0.997171i	$-0.523947\pi$
$971$	−145.962			−0.150321			−0.0751605	+	0.997171i	$0.523947\pi$
$972$		−	31.1769i		−	0.0320750i
$973$	1433.87	+	1433.87i	1.47365	+	1.47365i
$974$			75.5983i			0.0776163i
$975$		0			0
$976$	358.421			0.367235
$977$	−583.667	+	583.667i	−0.597408	+	0.597408i	−0.939622	−	0.342214i	$-0.888823\pi$
$977$	−583.667	+	583.667i	−0.597408	+	0.597408i	0.342214	+	0.939622i	$0.388823\pi$
$978$	−463.704			−0.474135
$979$			1152.69i			1.17741i
$980$	156.942	−	156.942i	0.160145	−	0.160145i
$981$	−302.806	+	302.806i	−0.308670	+	0.308670i
$982$	−872.594	−	872.594i	−0.888589	−	0.888589i
$983$	−238.633	−	238.633i	−0.242760	−	0.242760i	0.575231	−	0.817991i	$-0.304912\pi$
$983$	−238.633	−	238.633i	−0.242760	−	0.242760i	−0.817991	+	0.575231i	$0.804912\pi$
$984$	−204.778			−0.208108
$985$		−	1261.76i		−	1.28098i
$986$	150.425	+	150.425i	0.152561	+	0.152561i
$987$			301.349i			0.305318i
$988$		0			0
$989$	−2486.20			−2.51385
$990$	358.928	−	358.928i	0.362554	−	0.362554i
$991$	−285.960			−0.288557			−0.144279	−	0.989537i	$-0.546086\pi$
$991$	−285.960			−0.288557			−0.144279	+	0.989537i	$0.546086\pi$
$992$			142.781i			0.143933i
$993$	−336.941	+	336.941i	−0.339316	+	0.339316i
$994$	72.4829	−	72.4829i	0.0729204	−	0.0729204i
$995$	411.829	+	411.829i	0.413899	+	0.413899i
$996$	118.590	+	118.590i	0.119066	+	0.119066i
$997$	−117.569			−0.117922			−0.0589612	−	0.998260i	$-0.518779\pi$
$997$	−117.569			−0.117922			−0.0589612	+	0.998260i	$0.518779\pi$
$998$			357.214i			0.357929i
$999$	5.24885	+	5.24885i	0.00525411	+	0.00525411i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.3.f.h.577.4		8
13.3	even	3		78.3.l.c.19.2	✓	8
13.5	odd	4		1014.3.f.j.775.3		8
13.7	odd	12		78.3.l.c.37.2	yes	8
13.8	odd	4	inner	1014.3.f.h.775.4		8
13.12	even	2		1014.3.f.j.577.3		8
39.20	even	12		234.3.bb.d.37.1		8
39.29	odd	6		234.3.bb.d.19.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.3.l.c.19.2	✓	8	13.3	even	3
78.3.l.c.37.2	yes	8	13.7	odd	12
234.3.bb.d.19.1		8	39.29	odd	6
234.3.bb.d.37.1		8	39.20	even	12
1014.3.f.h.577.4		8	1.1	even	1	trivial
1014.3.f.h.775.4		8	13.8	odd	4	inner
1014.3.f.j.577.3		8	13.12	even	2
1014.3.f.j.775.3		8	13.5	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:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1014.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +1.73205 q^{3} -2.00000i q^{4} +(4.41254 - 4.41254i) q^{5} +(-1.73205 + 1.73205i) q^{6} +(5.77857 + 5.77857i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +1.73205 q^{3} -2.00000i q^{4} +(4.41254 - 4.41254i) q^{5} +(-1.73205 + 1.73205i) q^{6} +(5.77857 + 5.77857i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000 q^{9} +8.82508i q^{10} +(-13.5571 - 13.5571i) q^{11} -3.46410i q^{12} -11.5571 q^{14} +(7.64274 - 7.64274i) q^{15} -4.00000 q^{16} -23.0866i q^{17} +(-3.00000 + 3.00000i) q^{18} +(-0.305695 + 0.305695i) q^{19} +(-8.82508 - 8.82508i) q^{20} +(10.0088 + 10.0088i) q^{21} +27.1143 q^{22} -42.1106i q^{23} +(3.46410 + 3.46410i) q^{24} -13.9410i q^{25} +5.19615 q^{27} +(11.5571 - 11.5571i) q^{28} +6.51569 q^{29} +15.2855i q^{30} +(-17.8476 + 17.8476i) q^{31} +(4.00000 - 4.00000i) q^{32} +(-23.4816 - 23.4816i) q^{33} +(23.0866 + 23.0866i) q^{34} +50.9963 q^{35} -6.00000i q^{36} +(1.01014 + 1.01014i) q^{37} -0.611390i q^{38} +17.6502 q^{40} +(-29.5572 + 29.5572i) q^{41} -20.0175 q^{42} -59.0397i q^{43} +(-27.1143 + 27.1143i) q^{44} +(13.2376 - 13.2376i) q^{45} +(42.1106 + 42.1106i) q^{46} +(15.0543 + 15.0543i) q^{47} -6.92820 q^{48} +17.7836i q^{49} +(13.9410 + 13.9410i) q^{50} -39.9872i q^{51} +8.90794 q^{53} +(-5.19615 + 5.19615i) q^{54} -119.643 q^{55} +23.1143i q^{56} +(-0.529479 + 0.529479i) q^{57} +(-6.51569 + 6.51569i) q^{58} +(31.1999 + 31.1999i) q^{59} +(-15.2855 - 15.2855i) q^{60} -89.6053 q^{61} -35.6953i q^{62} +(17.3357 + 17.3357i) q^{63} +8.00000i q^{64} +46.9633 q^{66} +(28.0209 - 28.0209i) q^{67} -46.1732 q^{68} -72.9376i q^{69} +(-50.9963 + 50.9963i) q^{70} +(-6.27170 + 6.27170i) q^{71} +(6.00000 + 6.00000i) q^{72} +(-5.92683 - 5.92683i) q^{73} -2.02028 q^{74} -24.1466i q^{75} +(0.611390 + 0.611390i) q^{76} -156.682i q^{77} +115.826 q^{79} +(-17.6502 + 17.6502i) q^{80} +9.00000 q^{81} -59.1143i q^{82} +(-34.2340 + 34.2340i) q^{83} +(20.0175 - 20.0175i) q^{84} +(-101.871 - 101.871i) q^{85} +(59.0397 + 59.0397i) q^{86} +11.2855 q^{87} -54.2285i q^{88} +(-42.5122 - 42.5122i) q^{89} +26.4752i q^{90} -84.2211 q^{92} +(-30.9130 + 30.9130i) q^{93} -30.1085 q^{94} +2.69778i q^{95} +(6.92820 - 6.92820i) q^{96} +(94.5385 - 94.5385i) q^{97} +(-17.7836 - 17.7836i) q^{98} +(-40.6714 - 40.6714i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 6 q^{5} - 2 q^{7} + 16 q^{8} + 24 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 - 6 * q^5 - 2 * q^7 + 16 * q^8 + 24 * q^9	\( 8 q - 8 q^{2} - 6 q^{5} - 2 q^{7} + 16 q^{8} + 24 q^{9} - 12 q^{11} + 4 q^{14} + 6 q^{15} - 32 q^{16} - 24 q^{18} - 44 q^{19} + 12 q^{20} + 18 q^{21} + 24 q^{22} - 4 q^{28} - 72 q^{29} - 94 q^{31} + 32 q^{32} - 36 q^{33} + 60 q^{34} + 408 q^{35} - 46 q^{37} - 24 q^{40} - 30 q^{41} - 36 q^{42} - 24 q^{44} - 18 q^{45} + 144 q^{46} + 300 q^{47} + 208 q^{50} + 84 q^{53} - 792 q^{55} + 24 q^{57} + 72 q^{58} - 12 q^{59} - 12 q^{60} + 180 q^{61} - 6 q^{63} + 72 q^{66} - 74 q^{67} - 120 q^{68} - 408 q^{70} + 156 q^{71} + 48 q^{72} + 16 q^{73} + 92 q^{74} + 88 q^{76} - 96 q^{79} + 24 q^{80} + 72 q^{81} + 36 q^{84} + 234 q^{85} + 168 q^{86} - 60 q^{87} + 228 q^{89} - 288 q^{92} - 198 q^{93} - 600 q^{94} + 2 q^{97} - 32 q^{98} - 36 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 6 * q^5 - 2 * q^7 + 16 * q^8 + 24 * q^9 - 12 * q^11 + 4 * q^14 + 6 * q^15 - 32 * q^16 - 24 * q^18 - 44 * q^19 + 12 * q^20 + 18 * q^21 + 24 * q^22 - 4 * q^28 - 72 * q^29 - 94 * q^31 + 32 * q^32 - 36 * q^33 + 60 * q^34 + 408 * q^35 - 46 * q^37 - 24 * q^40 - 30 * q^41 - 36 * q^42 - 24 * q^44 - 18 * q^45 + 144 * q^46 + 300 * q^47 + 208 * q^50 + 84 * q^53 - 792 * q^55 + 24 * q^57 + 72 * q^58 - 12 * q^59 - 12 * q^60 + 180 * q^61 - 6 * q^63 + 72 * q^66 - 74 * q^67 - 120 * q^68 - 408 * q^70 + 156 * q^71 + 48 * q^72 + 16 * q^73 + 92 * q^74 + 88 * q^76 - 96 * q^79 + 24 * q^80 + 72 * q^81 + 36 * q^84 + 234 * q^85 + 168 * q^86 - 60 * q^87 + 228 * q^89 - 288 * q^92 - 198 * q^93 - 600 * q^94 + 2 * q^97 - 32 * q^98 - 36 * q^99

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