LMFDB - Embedded newform 495.2.n.d.181.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [495,2,Mod(91,495)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(495, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("495.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.n (of order $5$, degree $4$, 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:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.13140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			181.1
Root			$0.418926 + 1.28932i$ of defining polynomial
Character	$\chi$	$=$	495.181
Dual form			495.2.n.d.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.758911 - 2.33569i) q^{2} +(-3.26145 + 2.36959i) q^{4} +(0.309017 - 0.951057i) q^{5} +(-2.65911 + 1.93196i) q^{7} +(4.03606 + 2.93237i) q^{8} +O(q^{10})$	\(q+(-0.758911 - 2.33569i) q^{2} +(-3.26145 + 2.36959i) q^{4} +(0.309017 - 0.951057i) q^{5} +(-2.65911 + 1.93196i) q^{7} +(4.03606 + 2.93237i) q^{8} -2.45589 q^{10} +(-2.96813 - 1.47994i) q^{11} +(-0.0967635 - 0.297808i) q^{13} +(6.53048 + 4.74467i) q^{14} +(1.29455 - 3.98423i) q^{16} +(-1.54508 + 4.75528i) q^{17} +(6.03048 + 4.38140i) q^{19} +(1.24576 + 3.83407i) q^{20} +(-1.20413 + 8.05576i) q^{22} -1.07392 q^{23} +(-0.809017 - 0.587785i) q^{25} +(-0.622150 + 0.452019i) q^{26} +(4.09463 - 12.6020i) q^{28} +(-4.07459 + 2.96036i) q^{29} +(1.06580 + 3.28018i) q^{31} -0.310680 q^{32} +12.2794 q^{34} +(1.01569 + 3.12597i) q^{35} +(-2.13118 + 1.54839i) q^{37} +(5.65698 - 17.4104i) q^{38} +(4.03606 - 2.93237i) q^{40} +(8.77557 + 6.37583i) q^{41} -5.51468 q^{43} +(13.1873 - 2.20648i) q^{44} +(0.815010 + 2.50834i) q^{46} +(-9.70674 - 7.05236i) q^{47} +(1.17529 - 3.61718i) q^{49} +(-0.758911 + 2.33569i) q^{50} +(1.02127 + 0.741996i) q^{52} +(-1.52513 - 4.69387i) q^{53} +(-2.32471 + 2.36553i) q^{55} -16.3975 q^{56} +(10.0067 + 7.27031i) q^{58} +(-7.41391 + 5.38652i) q^{59} +(2.83811 - 8.73480i) q^{61} +(6.85264 - 4.97873i) q^{62} +(-2.35333 - 7.24280i) q^{64} -0.313133 q^{65} -15.2739 q^{67} +(-6.22882 - 19.1704i) q^{68} +(6.53048 - 4.74467i) q^{70} +(-0.949335 + 2.92175i) q^{71} +(7.00018 - 5.08592i) q^{73} +(5.23394 + 3.80268i) q^{74} -30.0502 q^{76} +(10.7518 - 1.79898i) q^{77} +(1.67316 + 5.14946i) q^{79} +(-3.38919 - 2.46239i) q^{80} +(8.23206 - 25.3357i) q^{82} +(-5.02011 + 15.4503i) q^{83} +(4.04508 + 2.93893i) q^{85} +(4.18515 + 12.8806i) q^{86} +(-7.63981 - 14.6768i) q^{88} -1.62118 q^{89} +(0.832656 + 0.604960i) q^{91} +(3.50254 - 2.54475i) q^{92} +(-9.10556 + 28.0240i) q^{94} +(6.03048 - 4.38140i) q^{95} +(0.0692451 + 0.213115i) q^{97} -9.34054 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{4} - 2 q^{5} + q^{7} - 5 q^{8}+O(q^{10}) $ 8 * q - 2 * q^4 - 2 * q^5 + q^7 - 5 * q^8	$ 8 q - 2 q^{4} - 2 q^{5} + q^{7} - 5 q^{8} - 10 q^{10} + 3 q^{11} + 6 q^{13} + 10 q^{14} - 20 q^{16} + 10 q^{17} + 6 q^{19} - 7 q^{20} - 25 q^{22} + 10 q^{23} - 2 q^{25} + 8 q^{26} + 31 q^{28} + 3 q^{31} - 60 q^{32} + 50 q^{34} + q^{35} - 19 q^{37} + 28 q^{38} - 5 q^{40} + 25 q^{41} - 4 q^{43} - 7 q^{44} - 6 q^{46} - 15 q^{47} + 21 q^{49} + 6 q^{52} - 7 q^{53} - 7 q^{55} - 20 q^{56} - 2 q^{58} - 35 q^{59} + 21 q^{61} + 19 q^{62} - 77 q^{64} + 6 q^{65} - 26 q^{67} + 35 q^{68} + 10 q^{70} - 25 q^{71} + q^{73} + 29 q^{74} - 14 q^{76} + 61 q^{77} + 30 q^{79} + 5 q^{80} + 57 q^{82} - 11 q^{83} + 10 q^{85} + 34 q^{86} - 85 q^{88} - 32 q^{89} + 37 q^{91} + 10 q^{92} - 39 q^{94} + 6 q^{95} + 5 q^{97} - 50 q^{98}+O(q^{100}) $ 8 * q - 2 * q^4 - 2 * q^5 + q^7 - 5 * q^8 - 10 * q^10 + 3 * q^11 + 6 * q^13 + 10 * q^14 - 20 * q^16 + 10 * q^17 + 6 * q^19 - 7 * q^20 - 25 * q^22 + 10 * q^23 - 2 * q^25 + 8 * q^26 + 31 * q^28 + 3 * q^31 - 60 * q^32 + 50 * q^34 + q^35 - 19 * q^37 + 28 * q^38 - 5 * q^40 + 25 * q^41 - 4 * q^43 - 7 * q^44 - 6 * q^46 - 15 * q^47 + 21 * q^49 + 6 * q^52 - 7 * q^53 - 7 * q^55 - 20 * q^56 - 2 * q^58 - 35 * q^59 + 21 * q^61 + 19 * q^62 - 77 * q^64 + 6 * q^65 - 26 * q^67 + 35 * q^68 + 10 * q^70 - 25 * q^71 + q^73 + 29 * q^74 - 14 * q^76 + 61 * q^77 + 30 * q^79 + 5 * q^80 + 57 * q^82 - 11 * q^83 + 10 * q^85 + 34 * q^86 - 85 * q^88 - 32 * q^89 + 37 * q^91 + 10 * q^92 - 39 * q^94 + 6 * q^95 + 5 * q^97 - 50 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$1$

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 $

$2$	−0.758911	−	2.33569i	−0.536631	−	1.65158i	−0.740098	−	0.672499i	$-0.765221\pi$
$2$	−0.758911	−	2.33569i	−0.536631	−	1.65158i	0.203468	−	0.979082i	$-0.434779\pi$
$3$		0			0
$3$		0			0
$4$	−3.26145	+	2.36959i	−1.63073	+	1.18479i
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i
$6$		0			0
$7$	−2.65911	+	1.93196i	−1.00505	+	0.730211i	−0.963165	−	0.268911i	$-0.913336\pi$
$7$	−2.65911	+	1.93196i	−1.00505	+	0.730211i	−0.0418845	+	0.999122i	$0.513336\pi$
$8$	4.03606	+	2.93237i	1.42696	+	1.03675i
$9$		0			0
$10$	−2.45589			−0.776620
$11$	−2.96813	−	1.47994i	−0.894924	−	0.446218i
$11$	−2.96813	−	1.47994i	−0.894924	−	0.446218i
$12$		0			0
$13$	−0.0967635	−	0.297808i	−0.0268374	−	0.0825970i	0.936741	−	0.350024i	$-0.113827\pi$
$13$	−0.0967635	−	0.297808i	−0.0268374	−	0.0825970i	−0.963578	+	0.267427i	$0.913827\pi$
$14$	6.53048	+	4.74467i	1.74534	+	1.26807i
$15$		0			0
$16$	1.29455	−	3.98423i	0.323638	−	0.996057i
$17$	−1.54508	+	4.75528i	−0.374738	+	1.15333i	0.568917	+	0.822395i	$0.307363\pi$
$17$	−1.54508	+	4.75528i	−0.374738	+	1.15333i	−0.943655	+	0.330930i	$0.892637\pi$
$18$		0			0
$19$	6.03048	+	4.38140i	1.38349	+	1.00516i	0.996545	+	0.0830568i	$0.0264683\pi$
$19$	6.03048	+	4.38140i	1.38349	+	1.00516i	0.386941	+	0.922104i	$0.373532\pi$
$20$	1.24576	+	3.83407i	0.278561	+	0.857324i
$21$		0			0
$22$	−1.20413	+	8.05576i	−0.256721	+	1.71749i
$23$	−1.07392			−0.223928			−0.111964	−	0.993712i	$-0.535714\pi$
$23$	−1.07392			−0.223928			−0.111964	+	0.993712i	$0.535714\pi$
$24$		0			0
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$	−0.622150	+	0.452019i	−0.122014	+	0.0886482i
$27$		0			0
$28$	4.09463	−	12.6020i	0.773813	−	2.38155i
$29$	−4.07459	+	2.96036i	−0.756632	+	0.549725i	−0.897875	−	0.440250i	$-0.854890\pi$
$29$	−4.07459	+	2.96036i	−0.756632	+	0.549725i	0.141243	+	0.989975i	$0.454890\pi$
$30$		0			0
$31$	1.06580	+	3.28018i	0.191423	+	0.589138i	1.00000		0.000748050i	$0.000238112\pi$
$31$	1.06580	+	3.28018i	0.191423	+	0.589138i	−0.808577	+	0.588390i	$0.799762\pi$
$32$	−0.310680			−0.0549210
$33$		0			0
$34$	12.2794			2.10591
$35$	1.01569	+	3.12597i	0.171683	+	0.528386i
$36$		0			0
$37$	−2.13118	+	1.54839i	−0.350364	+	0.254554i	−0.749022	−	0.662546i	$-0.769476\pi$
$37$	−2.13118	+	1.54839i	−0.350364	+	0.254554i	0.398658	+	0.917100i	$0.369476\pi$
$38$	5.65698	−	17.4104i	0.917683	−	2.82434i
$39$		0			0
$40$	4.03606	−	2.93237i	0.638156	−	0.463648i
$41$	8.77557	+	6.37583i	1.37051	+	0.995737i	0.997697	+	0.0678321i	$0.0216082\pi$
$41$	8.77557	+	6.37583i	1.37051	+	0.995737i	0.372817	+	0.927905i	$0.378392\pi$
$42$		0			0
$43$	−5.51468			−0.840980			−0.420490	−	0.907297i	$-0.638142\pi$
$43$	−5.51468			−0.840980			−0.420490	+	0.907297i	$0.638142\pi$
$44$	13.1873	−	2.20648i	1.98805	−	0.332640i
$45$		0			0
$46$	0.815010	+	2.50834i	0.120167	+	0.369835i
$47$	−9.70674	−	7.05236i	−1.41587	−	1.02869i	−0.992435	−	0.122767i	$-0.960823\pi$
$47$	−9.70674	−	7.05236i	−1.41587	−	1.02869i	−0.423438	−	0.905925i	$-0.639177\pi$
$48$		0			0
$49$	1.17529	−	3.61718i	0.167899	−	0.516740i
$50$	−0.758911	+	2.33569i	−0.107326	+	0.330316i
$51$		0			0
$52$	1.02127	+	0.741996i	0.141625	+	0.102896i
$53$	−1.52513	−	4.69387i	−0.209493	−	0.644753i	−0.999499	−	0.0316539i	$-0.989923\pi$
$53$	−1.52513	−	4.69387i	−0.209493	−	0.644753i	0.790006	−	0.613099i	$-0.210077\pi$
$54$		0			0
$55$	−2.32471	+	2.36553i	−0.313463	+	0.318968i
$56$	−16.3975			−2.19121
$57$		0			0
$58$	10.0067	+	7.27031i	1.31395	+	0.954639i
$59$	−7.41391	+	5.38652i	−0.965208	+	0.701265i	−0.954354	−	0.298676i	$-0.903455\pi$
$59$	−7.41391	+	5.38652i	−0.965208	+	0.701265i	−0.0108537	+	0.999941i	$0.503455\pi$
$60$		0			0
$61$	2.83811	−	8.73480i	0.363382	−	1.11838i	−0.587605	−	0.809148i	$-0.699929\pi$
$61$	2.83811	−	8.73480i	0.363382	−	1.11838i	0.950988	−	0.309229i	$-0.100071\pi$
$62$	6.85264	−	4.97873i	0.870286	−	0.632300i
$63$		0			0
$64$	−2.35333	−	7.24280i	−0.294166	−	0.905350i
$65$	−0.313133			−0.0388394
$66$		0			0
$67$	−15.2739			−1.86600			−0.933000	−	0.359876i	$-0.882819\pi$
$67$	−15.2739			−1.86600			−0.933000	+	0.359876i	$0.882819\pi$
$68$	−6.22882	−	19.1704i	−0.755356	−	2.32475i
$69$		0			0
$70$	6.53048	−	4.74467i	0.780541	−	0.567096i
$71$	−0.949335	+	2.92175i	−0.112665	+	0.346748i	−0.991453	−	0.130465i	$-0.958353\pi$
$71$	−0.949335	+	2.92175i	−0.112665	+	0.346748i	0.878788	+	0.477213i	$0.158353\pi$
$72$		0			0
$73$	7.00018	−	5.08592i	0.819309	−	0.595262i	−0.0972058	−	0.995264i	$-0.530991\pi$
$73$	7.00018	−	5.08592i	0.819309	−	0.595262i	0.916514	+	0.400002i	$0.130991\pi$
$74$	5.23394	+	3.80268i	0.608433	+	0.442052i
$75$		0			0
$76$	−30.0502			−3.44700
$77$	10.7518	−	1.79898i	1.22528	−	0.205012i
$78$		0			0
$79$	1.67316	+	5.14946i	0.188245	+	0.579360i	0.999989	−	0.00465401i	$-0.00148142\pi$
$79$	1.67316	+	5.14946i	0.188245	+	0.579360i	−0.811744	+	0.584014i	$0.801481\pi$
$80$	−3.38919	−	2.46239i	−0.378922	−	0.275303i
$81$		0			0
$82$	8.23206	−	25.3357i	0.909079	−	2.79786i
$83$	−5.02011	+	15.4503i	−0.551029	+	1.69589i	0.155178	+	0.987887i	$0.450405\pi$
$83$	−5.02011	+	15.4503i	−0.551029	+	1.69589i	−0.706207	+	0.708006i	$0.749595\pi$
$84$		0			0
$85$	4.04508	+	2.93893i	0.438751	+	0.318771i
$86$	4.18515	+	12.8806i	0.451296	+	1.38895i
$87$		0			0
$88$	−7.63981	−	14.6768i	−0.814406	−	1.56455i
$89$	−1.62118			−0.171845			−0.0859223	−	0.996302i	$-0.527384\pi$
$89$	−1.62118			−0.171845			−0.0859223	+	0.996302i	$0.527384\pi$
$90$		0			0
$91$	0.832656	+	0.604960i	0.0872861	+	0.0634171i
$92$	3.50254	−	2.54475i	0.365165	−	0.265308i
$93$		0			0
$94$	−9.10556	+	28.0240i	−0.939166	+	2.89046i
$95$	6.03048	−	4.38140i	0.618714	−	0.449522i
$96$		0			0
$97$	0.0692451	+	0.213115i	0.00703078	+	0.0216385i	0.954510	−	0.298178i	$-0.0963788\pi$
$97$	0.0692451	+	0.213115i	0.00703078	+	0.0216385i	−0.947480	+	0.319816i	$0.896379\pi$
$98$	−9.34054			−0.943537
$99$		0			0
$100$	4.03138			0.403138
$101$	0.156154	+	0.480593i	0.0155379	+	0.0478208i	0.958525	−	0.285009i	$-0.0919966\pi$
$101$	0.156154	+	0.480593i	0.0155379	+	0.0478208i	−0.942987	+	0.332830i	$0.891997\pi$
$102$		0			0
$103$	5.17930	−	3.76298i	0.510332	−	0.370778i	−0.302618	−	0.953112i	$-0.597861\pi$
$103$	5.17930	−	3.76298i	0.510332	−	0.370778i	0.812949	+	0.582334i	$0.197861\pi$
$104$	0.482738	−	1.48571i	0.0473363	−	0.145686i
$105$		0			0
$106$	−9.80598	+	7.12446i	−0.952441	+	0.691989i
$107$	1.69286	+	1.22993i	0.163655	+	0.118902i	0.666598	−	0.745417i	$-0.267750\pi$
$107$	1.69286	+	1.22993i	0.163655	+	0.118902i	−0.502943	+	0.864319i	$0.667750\pi$
$108$		0			0
$109$	−6.69278			−0.641052			−0.320526	−	0.947240i	$-0.603860\pi$
$109$	−6.69278			−0.641052			−0.320526	+	0.947240i	$0.603860\pi$
$110$	7.28939	+	3.63456i	0.695016	+	0.346542i
$111$		0			0
$112$	4.25499	+	13.0955i	0.402059	+	1.23741i
$113$	−8.73262	−	6.34462i	−0.821496	−	0.596852i	0.0956448	−	0.995416i	$-0.469509\pi$
$113$	−8.73262	−	6.34462i	−0.821496	−	0.596852i	−0.917141	+	0.398564i	$0.869509\pi$
$114$		0			0
$115$	−0.331860	+	1.02136i	−0.0309461	+	0.0952423i
$116$	6.27426	−	19.3102i	0.582550	−	1.79290i
$117$		0			0
$118$	18.2077	+	13.2287i	1.67616	+	1.21780i
$119$	−5.07845	−	15.6299i	−0.465541	−	1.43279i
$120$		0			0
$121$	6.61956	+	8.78529i	0.601779	+	0.798663i
$122$	−22.5556			−2.04209
$123$		0			0
$124$	−11.2487	−	8.17267i	−1.01017	−	0.733928i
$125$	−0.809017	+	0.587785i	−0.0723607	+	0.0525731i
$126$		0			0
$127$	−5.25430	+	16.1711i	−0.466244	+	1.43495i	0.391167	+	0.920320i	$0.372071\pi$
$127$	−5.25430	+	16.1711i	−0.466244	+	1.43495i	−0.857411	+	0.514632i	$0.827929\pi$
$128$	−15.6336	+	11.3585i	−1.38183	+	1.00396i
$129$		0			0
$130$	0.237640	+	0.731382i	0.0208424	+	0.0641464i
$131$	0.0430508			0.00376136			0.00188068	−	0.999998i	$-0.499401\pi$
$131$	0.0430508			0.00376136			0.00188068	+	0.999998i	$0.499401\pi$
$132$		0			0
$133$	−24.5004			−2.12445
$134$	11.5915	+	35.6750i	1.00135	+	3.08185i
$135$		0			0
$136$	−20.1803	+	14.6618i	−1.73044	+	1.25724i
$137$	−2.27516	+	7.00222i	−0.194380	+	0.598240i	0.805603	+	0.592455i	$0.201841\pi$
$137$	−2.27516	+	7.00222i	−0.194380	+	0.598240i	−0.999983	+	0.00578480i	$0.998159\pi$
$138$		0			0
$139$	−10.7109	+	7.78189i	−0.908483	+	0.660052i	−0.940631	−	0.339432i	$-0.889765\pi$
$139$	−10.7109	+	7.78189i	−0.908483	+	0.660052i	0.0321478	+	0.999483i	$0.489765\pi$
$140$	−10.7199	−	7.78845i	−0.905996	−	0.658244i
$141$		0			0
$142$	7.54476			0.633142
$143$	−0.153530	+	1.02713i	−0.0128388	+	0.0858933i
$144$		0			0
$145$	1.55635	+	4.78997i	0.129248	+	0.397785i
$146$	−17.1916	−	12.4905i	−1.42279	−	1.03372i
$147$		0			0
$148$	3.28170	−	10.1000i	0.269754	−	0.830217i
$149$	1.81658	−	5.59087i	0.148820	−	0.458022i	−0.848662	−	0.528935i	$-0.822591\pi$
$149$	1.81658	−	5.59087i	0.148820	−	0.458022i	0.997482	+	0.0709136i	$0.0225915\pi$
$150$		0			0
$151$	−6.17135	−	4.48375i	−0.502217	−	0.364882i	0.307646	−	0.951501i	$-0.400459\pi$
$151$	−6.17135	−	4.48375i	−0.502217	−	0.364882i	−0.809863	+	0.586619i	$0.800459\pi$
$152$	11.4915	+	35.3671i	0.932082	+	2.86865i
$153$		0			0
$154$	−12.3615	−	23.7475i	−0.996116	−	1.91363i
$155$	3.44899			0.277029
$156$		0			0
$157$	8.19795	+	5.95616i	0.654267	+	0.475353i	0.864722	−	0.502250i	$-0.167494\pi$
$157$	8.19795	+	5.95616i	0.654267	+	0.475353i	−0.210455	+	0.977604i	$0.567494\pi$
$158$	10.7578	−	7.81596i	0.855841	−	0.621805i
$159$		0			0
$160$	−0.0960054	+	0.295474i	−0.00758989	+	0.0233593i
$161$	2.85567	−	2.07477i	0.225059	−	0.163515i
$162$		0			0
$163$	−1.55407	−	4.78292i	−0.121724	−	0.374627i	0.871566	−	0.490278i	$-0.163105\pi$
$163$	−1.55407	−	4.78292i	−0.121724	−	0.374627i	−0.993290	+	0.115651i	$0.963105\pi$
$164$	−43.7292			−3.41468
$165$		0			0
$166$	39.8969			3.09660
$167$	−1.78953	−	5.50761i	−0.138478	−	0.426192i	0.857637	−	0.514256i	$-0.171932\pi$
$167$	−1.78953	−	5.50761i	−0.138478	−	0.426192i	−0.996115	+	0.0880642i	$0.971932\pi$
$168$		0			0
$169$	10.4379	−	7.58357i	0.802915	−	0.583352i
$170$	3.79455	−	11.6784i	0.291029	−	0.895695i
$171$		0			0
$172$	17.9859	−	13.0675i	1.37141	−	0.996387i
$173$	12.9970	+	9.44290i	0.988146	+	0.717930i	0.959514	−	0.281660i	$-0.0908850\pi$
$173$	12.9970	+	9.44290i	0.988146	+	0.717930i	0.0286316	+	0.999590i	$0.490885\pi$
$174$		0			0
$175$	3.28684			0.248462
$176$	−9.73881	+	9.90983i	−0.734090	+	0.746982i
$177$		0			0
$178$	1.23033	+	3.78657i	0.0922171	+	0.283815i
$179$	−6.71734	−	4.88043i	−0.502078	−	0.364781i	0.307732	−	0.951473i	$-0.400430\pi$
$179$	−6.71734	−	4.88043i	−0.502078	−	0.364781i	−0.809810	+	0.586692i	$0.800430\pi$
$180$		0			0
$181$	−1.99756	+	6.14787i	−0.148478	+	0.456968i	−0.997442	−	0.0714830i	$-0.977227\pi$
$181$	−1.99756	+	6.14787i	−0.148478	+	0.456968i	0.848964	+	0.528451i	$0.177227\pi$
$182$	0.781086	−	2.40394i	0.0578980	−	0.178192i
$183$		0			0
$184$	−4.33440	−	3.14913i	−0.319536	−	0.232157i
$185$	0.814038	+	2.50535i	0.0598493	+	0.184197i
$186$		0			0
$187$	11.6235	−	11.8277i	0.849997	−	0.864924i
$188$	48.3693			3.52769
$189$		0			0
$190$	−14.8102	−	10.7602i	−1.07444	−	0.780628i
$191$	12.4340	−	9.03384i	0.899694	−	0.653666i	−0.0386935	−	0.999251i	$-0.512320\pi$
$191$	12.4340	−	9.03384i	0.899694	−	0.653666i	0.938387	+	0.345585i	$0.112320\pi$
$192$		0			0
$193$	4.86757	−	14.9808i	0.350375	−	1.07834i	−0.608267	−	0.793732i	$-0.708135\pi$
$193$	4.86757	−	14.9808i	0.350375	−	1.07834i	0.958643	−	0.284612i	$-0.0918648\pi$
$194$	0.445218	−	0.323470i	0.0319648	−	0.0232238i
$195$		0			0
$196$	4.73805	+	14.5822i	0.338432	+	1.04159i
$197$	−16.3940			−1.16802			−0.584010	−	0.811746i	$-0.698517\pi$
$197$	−16.3940			−1.16802			−0.584010	+	0.811746i	$0.698517\pi$
$198$		0			0
$199$	6.96500			0.493736			0.246868	−	0.969049i	$-0.420599\pi$
$199$	6.96500			0.493736			0.246868	+	0.969049i	$0.420599\pi$
$200$	−1.54164	−	4.74467i	−0.109010	−	0.335499i
$201$		0			0
$202$	1.00401	−	0.729455i	0.0706418	−	0.0513242i
$203$	5.11549	−	15.7439i	0.359037	−	1.10500i
$204$		0			0
$205$	8.77557	−	6.37583i	0.612913	−	0.445307i
$206$	−12.7198	−	9.24146i	−0.886229	−	0.643883i
$207$		0			0
$208$	−1.31180			−0.0909569
$209$	−11.4150	−	21.9293i	−0.789594	−	1.51688i
$210$		0			0
$211$	−6.16585	−	18.9765i	−0.424475	−	1.30640i	−0.903496	−	0.428596i	$-0.859008\pi$
$211$	−6.16585	−	18.9765i	−0.424475	−	1.30640i	0.479022	−	0.877803i	$-0.340992\pi$
$212$	16.0967	+	11.6949i	1.10552	+	0.803211i
$213$		0			0
$214$	1.58801	−	4.88740i	0.108554	−	0.334096i
$215$	−1.70413	+	5.24477i	−0.116221	+	0.357690i
$216$		0			0
$217$	−9.17124	−	6.66330i	−0.622585	−	0.452334i
$218$	5.07922	+	15.6322i	0.344008	+	1.05875i
$219$		0			0
$220$	1.97660	−	13.2237i	0.133262	−	0.891539i
$221$	1.56567			0.105318
$222$		0			0
$223$	16.2990	+	11.8419i	1.09146	+	0.792992i	0.979645	−	0.200737i	$-0.0643336\pi$
$223$	16.2990	+	11.8419i	1.09146	+	0.792992i	0.111815	+	0.993729i	$0.464334\pi$
$224$	0.826133	−	0.600220i	0.0551983	−	0.0401039i
$225$		0			0
$226$	−8.19177	+	25.2117i	−0.544908	+	1.67706i
$227$	0.431964	−	0.313840i	0.0286705	−	0.0208303i	−0.573358	−	0.819305i	$-0.694359\pi$
$227$	0.431964	−	0.313840i	0.0286705	−	0.0208303i	0.602028	+	0.798475i	$0.294359\pi$
$228$		0			0
$229$	−6.85803	−	21.1068i	−0.453191	−	1.39478i	−0.873245	−	0.487281i	$-0.837989\pi$
$229$	−6.85803	−	21.1068i	−0.453191	−	1.39478i	0.420054	−	0.907499i	$-0.362011\pi$
$230$	2.63743			0.173907
$231$		0			0
$232$	−25.1261			−1.64961
$233$	1.41087	+	4.34221i	0.0924291	+	0.284467i	0.986575	−	0.163308i	$-0.0522164\pi$
$233$	1.41087	+	4.34221i	0.0924291	+	0.284467i	−0.894146	+	0.447775i	$0.852216\pi$
$234$		0			0
$235$	−9.70674	+	7.05236i	−0.633198	+	0.460045i
$236$	11.4163	−	35.1358i	0.743138	−	2.28714i
$237$		0			0
$238$	−32.6524	+	23.7233i	−2.11654	+	1.53776i
$239$	−4.74126	−	3.44473i	−0.306687	−	0.222821i	0.423787	−	0.905762i	$-0.360701\pi$
$239$	−4.74126	−	3.44473i	−0.306687	−	0.222821i	−0.730474	+	0.682941i	$0.760701\pi$
$240$		0			0
$241$	9.96074			0.641628			0.320814	−	0.947142i	$-0.396044\pi$
$241$	9.96074			0.641628			0.320814	+	0.947142i	$0.396044\pi$
$242$	15.4960	−	22.1285i	0.996123	−	1.42247i
$243$		0			0
$244$	11.4415	+	35.2133i	0.732466	+	2.25430i
$245$	−3.07696	−	2.23554i	−0.196580	−	0.142823i
$246$		0			0
$247$	0.721283	−	2.21988i	0.0458941	−	0.141248i
$248$	−5.31709	+	16.3643i	−0.337635	+	1.03913i
$249$		0			0
$250$	1.98685	+	1.44353i	0.125660	+	0.0912971i
$251$	5.21584	+	16.0527i	0.329221	+	1.01324i	0.969499	+	0.245094i	$0.0788189\pi$
$251$	5.21584	+	16.0527i	0.329221	+	1.01324i	−0.640279	+	0.768143i	$0.721181\pi$
$252$		0			0
$253$	3.18753	+	1.58934i	0.200399	+	0.0999207i
$254$	41.7581			2.62014
$255$		0			0
$256$	26.0723	+	18.9426i	1.62952	+	1.18391i
$257$	9.01534	−	6.55003i	0.562362	−	0.408580i	−0.269961	−	0.962871i	$-0.587011\pi$
$257$	9.01534	−	6.55003i	0.562362	−	0.408580i	0.832323	+	0.554292i	$0.187011\pi$
$258$		0			0
$259$	2.67561	−	8.23470i	0.166255	−	0.511679i
$260$	1.02127	−	0.741996i	0.0633365	−	0.0460167i
$261$		0			0
$262$	−0.0326717	−	0.100553i	−0.00201846	−	0.00621220i
$263$	26.8726			1.65704			0.828519	−	0.559961i	$-0.189184\pi$
$263$	26.8726			1.65704			0.828519	+	0.559961i	$0.189184\pi$
$264$		0			0
$265$	−4.93543			−0.303181
$266$	18.5936	+	57.2252i	1.14005	+	3.50870i
$267$		0			0
$268$	49.8150	−	36.1927i	3.04294	−	2.21082i
$269$	3.10961	−	9.57038i	0.189596	−	0.583516i	−0.810401	−	0.585875i	$-0.800751\pi$
$269$	3.10961	−	9.57038i	0.189596	−	0.583516i	0.999997	+	0.00235886i	$0.000750850\pi$
$270$		0			0
$271$	−8.53037	+	6.19767i	−0.518183	+	0.376482i	−0.815919	−	0.578166i	$-0.803768\pi$
$271$	−8.53037	+	6.19767i	−0.518183	+	0.376482i	0.297736	+	0.954648i	$0.403768\pi$
$272$	16.9459	+	12.3119i	1.02750	+	0.746521i
$273$		0			0
$274$	18.0816			1.09235
$275$	1.53138	+	2.94192i	0.0923457	+	0.177404i
$276$		0			0
$277$	−5.54302	−	17.0597i	−0.333048	−	1.02502i	−0.967676	−	0.252198i	$-0.918847\pi$
$277$	−5.54302	−	17.0597i	−0.333048	−	1.02502i	0.634628	−	0.772818i	$-0.281153\pi$
$278$	26.3047	+	19.1114i	1.57765	+	1.14623i
$279$		0			0
$280$	−5.06711	+	15.5950i	−0.302818	+	0.931978i
$281$	−2.29013	+	7.04830i	−0.136618	+	0.420467i	−0.995838	−	0.0911392i	$-0.970949\pi$
$281$	−2.29013	+	7.04830i	−0.136618	+	0.420467i	0.859220	+	0.511606i	$0.170949\pi$
$282$		0			0
$283$	−4.35804	−	3.16630i	−0.259059	−	0.188217i	0.450673	−	0.892689i	$-0.351184\pi$
$283$	−4.35804	−	3.16630i	−0.259059	−	0.188217i	−0.709732	+	0.704472i	$0.751184\pi$
$284$	−3.82713	−	11.7787i	−0.227098	−	0.698937i
$285$		0			0
$286$	2.51558	−	0.420905i	0.148749	−	0.0248886i
$287$	−35.6530			−2.10453
$288$		0			0
$289$	−6.47214	−	4.70228i	−0.380714	−	0.276605i
$290$	10.0067	−	7.27031i	0.587615	−	0.426927i
$291$		0			0
$292$	−10.7792	+	33.1750i	−0.630806	+	1.94142i
$293$	−1.40774	+	1.02278i	−0.0822409	+	0.0597515i	−0.628146	−	0.778096i	$-0.716186\pi$
$293$	−1.40774	+	1.02278i	−0.0822409	+	0.0597515i	0.545905	+	0.837847i	$0.316186\pi$
$294$		0			0
$295$	2.83186	+	8.71557i	0.164877	+	0.507440i
$296$	−13.1420			−0.763864
$297$		0			0
$298$	−14.4371			−0.836321
$299$	0.103916	+	0.319822i	0.00600964	+	0.0184958i
$300$		0			0
$301$	14.6641	−	10.6541i	0.845227	−	0.614093i
$302$	−5.78913	+	17.8171i	−0.333127	+	1.02526i
$303$		0			0
$304$	25.2633	−	18.3548i	1.44895	−	1.05272i
$305$	−7.43026	−	5.39840i	−0.425456	−	0.309112i
$306$		0			0
$307$	21.3566			1.21889			0.609444	−	0.792829i	$-0.291393\pi$
$307$	21.3566			1.21889			0.609444	+	0.792829i	$0.291393\pi$
$308$	−30.8035	+	31.3445i	−1.75519	+	1.78602i
$309$		0			0
$310$	−2.61747	−	8.05576i	−0.148663	−	0.457536i
$311$	26.5435	+	19.2850i	1.50514	+	1.09355i	0.968275	+	0.249886i	$0.0803933\pi$
$311$	26.5435	+	19.2850i	1.50514	+	1.09355i	0.536870	+	0.843665i	$0.319607\pi$
$312$		0			0
$313$	−1.06874	+	3.28925i	−0.0604089	+	0.185919i	−0.976707	−	0.214578i	$-0.931163\pi$
$313$	−1.06874	+	3.28925i	−0.0604089	+	0.185919i	0.916298	+	0.400497i	$0.131163\pi$
$314$	7.69021	−	23.6680i	0.433984	−	1.33566i
$315$		0			0
$316$	−17.6590	−	12.8300i	−0.993398	−	0.721746i
$317$	0.888626	+	2.73491i	0.0499102	+	0.153608i	0.972905	−	0.231204i	$-0.0742664\pi$
$317$	0.888626	+	2.73491i	0.0499102	+	0.153608i	−0.922995	+	0.384812i	$0.874266\pi$
$318$		0			0
$319$	16.4751	−	2.75659i	0.922426	−	0.154340i
$320$	−7.61553			−0.425721
$321$		0			0
$322$	−7.01321	−	5.09540i	−0.390831	−	0.283955i
$323$	−30.1524	+	21.9070i	−1.67772	+	1.21894i
$324$		0			0
$325$	−0.0967635	+	0.297808i	−0.00536748	+	0.0165194i
$326$	−9.99201	+	7.25962i	−0.553406	+	0.402073i
$327$		0			0
$328$	16.7224	+	51.4664i	0.923342	+	2.84176i
$329$	39.4362			2.17419
$330$		0			0
$331$	−14.1221			−0.776219			−0.388109	−	0.921613i	$-0.626872\pi$
$331$	−14.1221			−0.776219			−0.388109	+	0.921613i	$0.626872\pi$
$332$	−20.2380	−	62.2861i	−1.11070	−	3.41839i
$333$		0			0
$334$	−11.5060	+	8.35958i	−0.629579	+	0.457416i
$335$	−4.71989	+	14.5263i	−0.257875	+	0.793657i
$336$		0			0
$337$	−12.9030	+	9.37457i	−0.702870	+	0.510665i	−0.880866	−	0.473366i	$-0.843039\pi$
$337$	−12.9030	+	9.37457i	−0.702870	+	0.510665i	0.177995	+	0.984031i	$0.443039\pi$
$338$	−25.6343	−	18.6244i	−1.39432	−	1.01303i
$339$		0			0
$340$	−20.1569			−1.09316
$341$	1.69105	−	11.3133i	0.0915755	−	0.612650i
$342$		0			0
$343$	−3.24683	−	9.99271i	−0.175312	−	0.539555i
$344$	−22.2575	−	16.1711i	−1.20005	−	0.871885i
$345$		0			0
$346$	12.1921	−	37.5233i	0.655449	−	2.01727i
$347$	−9.17166	+	28.2275i	−0.492360	+	1.51533i	0.328670	+	0.944445i	$0.393400\pi$
$347$	−9.17166	+	28.2275i	−0.492360	+	1.51533i	−0.821030	+	0.570884i	$0.806600\pi$
$348$		0			0
$349$	−25.6408	−	18.6291i	−1.37252	−	0.997194i	−0.997536	−	0.0701620i	$-0.977648\pi$
$349$	−25.6408	−	18.6291i	−1.37252	−	0.997194i	−0.374984	−	0.927031i	$-0.622352\pi$
$350$	−2.49442	−	7.67703i	−0.133332	−	0.410355i
$351$		0			0
$352$	0.922138	+	0.459787i	0.0491501	+	0.0245067i
$353$	−1.20189			−0.0639703			−0.0319852	−	0.999488i	$-0.510183\pi$
$353$	−1.20189			−0.0639703			−0.0319852	+	0.999488i	$0.510183\pi$
$354$		0			0
$355$	2.48539	+	1.80574i	0.131911	+	0.0958388i
$356$	5.28740	−	3.84152i	0.280232	−	0.203600i
$357$		0			0
$358$	−6.30130	+	19.3934i	−0.333034	+	1.02497i
$359$	−9.43239	+	6.85304i	−0.497823	+	0.361689i	−0.808185	−	0.588929i	$-0.799550\pi$
$359$	−9.43239	+	6.85304i	−0.497823	+	0.361689i	0.310362	+	0.950618i	$0.399550\pi$
$360$		0			0
$361$	11.2987	+	34.7737i	0.594667	+	1.83020i
$362$	15.8755			0.834396
$363$		0			0
$364$	−4.14918			−0.217476
$365$	−2.67383	−	8.22920i	−0.139955	−	0.430736i
$366$		0			0
$367$	−12.9330	+	9.39636i	−0.675096	+	0.490486i	−0.871727	−	0.489991i	$-0.837000\pi$
$367$	−12.9330	+	9.39636i	−0.675096	+	0.490486i	0.196631	+	0.980478i	$0.437000\pi$
$368$	−1.39025	+	4.27874i	−0.0724717	+	0.223045i
$369$		0			0
$370$	5.23394	−	3.80268i	0.272099	−	0.197692i
$371$	13.1239	+	9.53504i	0.681357	+	0.495035i
$372$		0			0
$373$	0.321975			0.0166712			0.00833561	−	0.999965i	$-0.497347\pi$
$373$	0.321975			0.0166712			0.00833561	+	0.999965i	$0.497347\pi$
$374$	−36.4469	−	18.1728i	−1.88463	−	0.939693i
$375$		0			0
$376$	−18.4968	−	56.9274i	−0.953902	−	2.93581i
$377$	1.27589	+	0.926988i	0.0657117	+	0.0477423i
$378$		0			0
$379$	3.52819	−	10.8586i	0.181231	−	0.557771i	−0.818632	−	0.574318i	$-0.805267\pi$
$379$	3.52819	−	10.8586i	0.181231	−	0.557771i	0.999863	+	0.0165471i	$0.00526734\pi$
$380$	−9.28603	+	28.5795i	−0.476363	+	1.46610i
$381$		0			0
$382$	−30.5365	−	22.1861i	−1.56239	−	1.13514i
$383$	−8.76597	−	26.9789i	−0.447920	−	1.37856i	−0.879249	−	0.476362i	$-0.841955\pi$
$383$	−8.76597	−	26.9789i	−0.447920	−	1.37856i	0.431329	−	0.902195i	$-0.358045\pi$
$384$		0			0
$385$	1.61155	−	10.7814i	0.0821321	−	0.549473i
$386$	−38.6846			−1.96899
$387$		0			0
$388$	−0.730833	−	0.530981i	−0.0371024	−	0.0269565i
$389$	12.2810	−	8.92269i	0.622673	−	0.452398i	−0.231181	−	0.972911i	$-0.574259\pi$
$389$	12.2810	−	8.92269i	0.622673	−	0.452398i	0.853854	+	0.520513i	$0.174259\pi$
$390$		0			0
$391$	1.65930	−	5.10680i	0.0839143	−	0.258262i
$392$	15.3504	−	11.1528i	0.775315	−	0.563299i
$393$		0			0
$394$	12.4415	+	38.2911i	0.626796	+	1.92908i
$395$	5.41446			0.272431
$396$		0			0
$397$	5.22461			0.262216			0.131108	−	0.991368i	$-0.458147\pi$
$397$	5.22461			0.262216			0.131108	+	0.991368i	$0.458147\pi$
$398$	−5.28581	−	16.2681i	−0.264954	−	0.815444i
$399$		0			0
$400$	−3.38919	+	2.46239i	−0.169459	+	0.123119i
$401$	−4.32644	+	13.3154i	−0.216052	+	0.664941i	0.783025	+	0.621990i	$0.213676\pi$
$401$	−4.32644	+	13.3154i	−0.216052	+	0.664941i	−0.999077	+	0.0429502i	$0.986324\pi$
$402$		0			0
$403$	0.873733	−	0.634804i	0.0435238	−	0.0316219i
$404$	−1.64810	−	1.19741i	−0.0819959	−	0.0595735i
$405$		0			0
$406$	−40.6549			−2.01767
$407$	8.61714	−	1.44181i	0.427136	−	0.0714680i
$408$		0			0
$409$	10.2937	+	31.6809i	0.508993	+	1.56652i	0.793953	+	0.607979i	$0.208020\pi$
$409$	10.2937	+	31.6809i	0.508993	+	1.56652i	−0.284960	+	0.958539i	$0.591980\pi$
$410$	−21.5518	−	15.6583i	−1.06437	−	0.773309i
$411$		0			0
$412$	−7.97535	+	24.5456i	−0.392917	+	1.20927i
$413$	9.30787	−	28.6467i	0.458011	−	1.40961i
$414$		0			0
$415$	13.1428	+	9.54882i	0.645156	+	0.468733i
$416$	0.0300625	+	0.0925229i	0.00147394	+	0.00453631i
$417$		0			0
$418$	−42.5569	+	43.3043i	−2.08153	+	2.11808i
$419$	5.28460			0.258170			0.129085	−	0.991634i	$-0.458796\pi$
$419$	5.28460			0.258170			0.129085	+	0.991634i	$0.458796\pi$
$420$		0			0
$421$	24.9023	+	18.0926i	1.21367	+	0.881780i	0.995558	−	0.0941452i	$-0.0300118\pi$
$421$	24.9023	+	18.0926i	1.21367	+	0.881780i	0.218107	+	0.975925i	$0.430012\pi$
$422$	−39.6439	+	28.8030i	−1.92984	+	1.40211i
$423$		0			0
$424$	7.60864	−	23.4170i	0.369508	−	1.13723i
$425$	4.04508	−	2.93893i	0.196215	−	0.142559i
$426$		0			0
$427$	9.32841	+	28.7099i	0.451433	+	1.38937i
$428$	−8.43562			−0.407751
$429$		0			0
$430$	13.5434			0.653122
$431$	−3.81656	−	11.7462i	−0.183837	−	0.565793i	0.816089	−	0.577926i	$-0.196138\pi$
$431$	−3.81656	−	11.7462i	−0.183837	−	0.565793i	−0.999926	+	0.0121333i	$0.996138\pi$
$432$		0			0
$433$	−1.14304	+	0.830465i	−0.0549308	+	0.0399096i	−0.614912	−	0.788596i	$-0.710808\pi$
$433$	−1.14304	+	0.830465i	−0.0549308	+	0.0399096i	0.559981	+	0.828505i	$0.310808\pi$
$434$	−8.60323	+	26.4780i	−0.412968	+	1.27098i
$435$		0			0
$436$	21.8282	−	15.8591i	1.04538	−	0.759514i
$437$	−6.47625	−	4.70527i	−0.309801	−	0.225084i
$438$		0			0
$439$	−7.58532			−0.362028			−0.181014	−	0.983481i	$-0.557938\pi$
$439$	−7.58532			−0.362028			−0.181014	+	0.983481i	$0.557938\pi$
$440$	−16.3192	+	2.73052i	−0.777990	+	0.130173i
$441$		0			0
$442$	−1.18820	−	3.65691i	−0.0565170	−	0.173941i
$443$	8.95274	+	6.50455i	0.425358	+	0.309040i	0.779790	−	0.626041i	$-0.215326\pi$
$443$	8.95274	+	6.50455i	0.425358	+	0.309040i	−0.354432	+	0.935082i	$0.615326\pi$
$444$		0			0
$445$	−0.500972	+	1.54183i	−0.0237483	+	0.0730899i
$446$	15.2895	−	47.0562i	0.723979	−	2.22818i
$447$		0			0
$448$	20.2505	+	14.7129i	0.956748	+	0.695118i
$449$	−1.95563	−	6.01882i	−0.0922920	−	0.284045i	0.894247	−	0.447575i	$-0.147712\pi$
$449$	−1.95563	−	6.01882i	−0.0922920	−	0.284045i	−0.986538	+	0.163529i	$0.947712\pi$
$450$		0			0
$451$	−16.6112	−	31.9116i	−0.782190	−	1.50266i
$452$	43.5152			2.04678
$453$		0			0
$454$	−1.06085	−	0.770756i	−0.0497884	−	0.0361734i
$455$	0.832656	−	0.604960i	0.0390355	−	0.0283610i
$456$		0			0
$457$	−0.0585832	+	0.180300i	−0.00274040	+	0.00843410i	−0.952417	−	0.304797i	$-0.901411\pi$
$457$	−0.0585832	+	0.180300i	−0.00274040	+	0.00843410i	0.949677	+	0.313231i	$0.101411\pi$
$458$	−44.0944	+	32.0364i	−2.06039	+	1.49696i
$459$		0			0
$460$	−1.33785	−	4.11749i	−0.0623777	−	0.191979i
$461$	26.6198			1.23981			0.619904	−	0.784678i	$-0.287172\pi$
$461$	26.6198			1.23981			0.619904	+	0.784678i	$0.287172\pi$
$462$		0			0
$463$	20.9935			0.975652			0.487826	−	0.872941i	$-0.337790\pi$
$463$	20.9935			0.975652			0.487826	+	0.872941i	$0.337790\pi$
$464$	6.51998	+	20.0664i	0.302682	+	0.931561i
$465$		0			0
$466$	9.07131	−	6.59070i	0.420221	−	0.305308i
$467$	−2.44120	+	7.51324i	−0.112965	+	0.347671i	−0.991517	−	0.129976i	$-0.958510\pi$
$467$	−2.44120	+	7.51324i	−0.112965	+	0.347671i	0.878552	+	0.477647i	$0.158510\pi$
$468$		0			0
$469$	40.6149	−	29.5085i	1.87542	−	1.36257i
$470$	23.8387	+	17.3198i	1.09960	+	0.798903i
$471$		0			0
$472$	−45.7182			−2.10435
$473$	16.3683	+	8.16138i	0.752614	+	0.375261i
$474$		0			0
$475$	−2.30344	−	7.08925i	−0.105689	−	0.325277i
$476$	53.5994	+	38.9423i	2.45673	+	1.78492i
$477$		0			0
$478$	−4.44762	+	13.6884i	−0.203429	+	0.626091i
$479$	−12.3523	+	38.0164i	−0.564389	+	1.73701i	0.105369	+	0.994433i	$0.466398\pi$
$479$	−12.3523	+	38.0164i	−0.564389	+	1.73701i	−0.669758	+	0.742579i	$0.733602\pi$
$480$		0			0
$481$	0.667344	+	0.484854i	0.0304282	+	0.0221074i
$482$	−7.55931	−	23.2652i	−0.344317	−	1.05970i
$483$		0			0
$484$	−42.4069	−	12.9672i	−1.92759	−	0.589419i
$485$	0.224082			0.0101750
$486$		0			0
$487$	8.03804	+	5.83998i	0.364238	+	0.264635i	0.754818	−	0.655935i	$-0.227725\pi$
$487$	8.03804	+	5.83998i	0.364238	+	0.264635i	−0.390579	+	0.920569i	$0.627725\pi$
$488$	37.0684	−	26.9318i	1.67801	−	1.21914i
$489$		0			0
$490$	−2.88639	+	8.88338i	−0.130394	+	0.401310i
$491$	4.02364	−	2.92335i	0.181584	−	0.131929i	−0.493280	−	0.869871i	$-0.664202\pi$
$491$	4.02364	−	2.92335i	0.181584	−	0.131929i	0.674864	+	0.737942i	$0.264202\pi$
$492$		0			0
$493$	−7.78177	−	23.9498i	−0.350473	−	1.07865i
$494$	−5.73234			−0.257910
$495$		0			0
$496$	14.4487			0.648767
$497$	−3.12031	−	9.60333i	−0.139965	−	0.430768i
$498$		0			0
$499$	−35.4153	+	25.7307i	−1.58541	+	1.15186i	−0.675256	+	0.737584i	$0.735967\pi$
$499$	−35.4153	+	25.7307i	−1.58541	+	1.15186i	−0.910149	+	0.414281i	$0.864033\pi$
$500$	1.24576	−	3.83407i	0.0557123	−	0.171465i
$501$		0			0
$502$	33.5357	−	24.3651i	1.49677	−	1.08747i
$503$	5.08254	+	3.69268i	0.226619	+	0.164648i	0.695301	−	0.718718i	$-0.255271\pi$
$503$	5.08254	+	3.69268i	0.226619	+	0.164648i	−0.468682	+	0.883367i	$0.655271\pi$
$504$		0			0
$505$	0.505326			0.0224867
$506$	1.29314	−	8.65125i	0.0574870	−	0.384595i
$507$		0			0
$508$	−21.1821	−	65.1918i	−0.939803	−	2.89242i
$509$	20.0945	+	14.5995i	0.890671	+	0.647111i	0.936053	−	0.351859i	$-0.114450\pi$
$509$	20.0945	+	14.5995i	0.890671	+	0.647111i	−0.0453816	+	0.998970i	$0.514450\pi$
$510$		0			0
$511$	−8.78845	+	27.0481i	−0.388778	+	1.19654i
$512$	12.5144	−	38.5155i	0.553066	−	1.70216i
$513$		0			0
$514$	−22.1407	−	16.0861i	−0.976583	−	0.709529i
$515$	−1.97832	−	6.08863i	−0.0871751	−	0.268297i
$516$		0			0
$517$	18.3738	+	35.2977i	0.808078	+	1.55239i
$518$	−21.2642			−0.934296
$519$		0			0
$520$	−1.26382	−	0.918222i	−0.0554223	−	0.0402667i
$521$	−5.62161	+	4.08434i	−0.246287	+	0.178938i	−0.704080	−	0.710121i	$-0.748640\pi$
$521$	−5.62161	+	4.08434i	−0.246287	+	0.178938i	0.457792	+	0.889059i	$0.348640\pi$
$522$		0			0
$523$	−8.26650	+	25.4417i	−0.361469	+	1.11249i	0.590694	+	0.806896i	$0.298854\pi$
$523$	−8.26650	+	25.4417i	−0.361469	+	1.11249i	−0.952163	+	0.305591i	$0.901146\pi$
$524$	−0.140408	+	0.102013i	−0.00613376	+	0.00445644i
$525$		0			0
$526$	−20.3939	−	62.7661i	−0.889218	−	2.73673i
$527$	−17.2449			−0.751202
$528$		0			0
$529$	−21.8467			−0.949856
$530$	3.74555	+	11.5276i	0.162696	+	0.500728i
$531$		0			0
$532$	79.9069	−	58.0557i	3.46440	−	2.51704i
$533$	1.04961	−	3.23038i	0.0454638	−	0.139923i
$534$		0			0
$535$	1.69286	−	1.22993i	0.0731887	−	0.0531747i
$536$	−61.6462	−	44.7886i	−2.66271	−	1.93457i
$537$		0			0
$538$	−24.7133			−1.06547
$539$	−8.84162	+	8.99689i	−0.380836	+	0.387524i
$540$		0			0
$541$	4.48336	+	13.7984i	0.192755	+	0.593237i	0.999995	+	0.00301536i	$0.000959822\pi$
$541$	4.48336	+	13.7984i	0.192755	+	0.593237i	−0.807241	+	0.590222i	$0.799040\pi$
$542$	20.9496	+	15.2208i	0.899863	+	0.653789i
$543$		0			0
$544$	0.480027	−	1.47737i	0.0205810	−	0.0633418i
$545$	−2.06818	+	6.36521i	−0.0885912	+	0.272656i
$546$		0			0
$547$	21.6287	+	15.7142i	0.924777	+	0.671890i	0.944708	−	0.327912i	$-0.106345\pi$
$547$	21.6287	+	15.7142i	0.924777	+	0.671890i	−0.0199316	+	0.999801i	$0.506345\pi$
$548$	−9.17203	−	28.2286i	−0.391810	−	1.20587i
$549$		0			0
$550$	5.70922	−	5.80948i	0.243442	−	0.247717i
$551$	−37.5422			−1.59935
$552$		0			0
$553$	−14.3977	−	10.4605i	−0.612251	−	0.444826i
$554$	−35.6394	+	25.8935i	−1.51417	+	1.10011i
$555$		0			0
$556$	16.4931	−	50.7606i	0.699464	−	2.15273i
$557$	13.9510	−	10.1360i	0.591125	−	0.429477i	−0.251593	−	0.967833i	$-0.580954\pi$
$557$	13.9510	−	10.1360i	0.591125	−	0.429477i	0.842718	+	0.538356i	$0.180954\pi$
$558$		0			0
$559$	0.533620	+	1.64231i	0.0225697	+	0.0694624i
$560$	13.7694			0.581865
$561$		0			0
$562$	18.2006			0.767748
$563$	0.257075	+	0.791197i	0.0108344	+	0.0333450i	0.956328	−	0.292297i	$-0.0944196\pi$
$563$	0.257075	+	0.791197i	0.0108344	+	0.0333450i	−0.945493	+	0.325642i	$0.894420\pi$
$564$		0			0
$565$	−8.73262	+	6.34462i	−0.367384	+	0.266920i
$566$	−4.08813	+	12.5820i	−0.171837	+	0.528860i
$567$		0			0
$568$	−12.3992	+	9.00855i	−0.520259	+	0.377991i
$569$	9.38141	+	6.81599i	0.393289	+	0.285741i	0.766802	−	0.641884i	$-0.221847\pi$
$569$	9.38141	+	6.81599i	0.393289	+	0.285741i	−0.373513	+	0.927625i	$0.621847\pi$
$570$		0			0
$571$	21.8414			0.914034			0.457017	−	0.889458i	$-0.348918\pi$
$571$	21.8414			0.914034			0.457017	+	0.889458i	$0.348918\pi$
$572$	−1.93315	−	3.71376i	−0.0808292	−	0.155280i
$573$		0			0
$574$	27.0575	+	83.2744i	1.12936	+	3.47580i
$575$	0.868820	+	0.631235i	0.0362323	+	0.0263243i
$576$		0			0
$577$	3.01164	−	9.26888i	0.125376	−	0.385868i	−0.868593	−	0.495526i	$-0.834975\pi$
$577$	3.01164	−	9.26888i	0.125376	−	0.385868i	0.993969	+	0.109657i	$0.0349754\pi$
$578$	−6.07129	+	18.6855i	−0.252532	+	0.777214i
$579$		0			0
$580$	−16.4262	−	11.9343i	−0.682061	−	0.495547i
$581$	−16.5003	−	50.7827i	−0.684548	−	2.10682i
$582$		0			0
$583$	−2.41986	+	16.1891i	−0.100220	+	0.670485i
$584$	43.1669			1.78626
$585$		0			0
$586$	3.45724	+	2.51183i	0.142817	+	0.103763i
$587$	18.5622	−	13.4862i	0.766143	−	0.556635i	−0.134645	−	0.990894i	$-0.542990\pi$
$587$	18.5622	−	13.4862i	0.766143	−	0.556635i	0.900788	+	0.434258i	$0.142990\pi$
$588$		0			0
$589$	−7.94453	+	24.4507i	−0.327349	+	1.00748i
$590$	18.2077	−	13.2287i	0.749600	−	0.544616i
$591$		0			0
$592$	3.41022	+	10.4956i	0.140159	+	0.431366i
$593$	−28.7819			−1.18193			−0.590965	−	0.806697i	$-0.701253\pi$
$593$	−28.7819			−1.18193			−0.590965	+	0.806697i	$0.701253\pi$
$594$		0			0
$595$	−16.4342			−0.673737
$596$	7.32333	+	22.5389i	0.299975	+	0.923229i
$597$		0			0
$598$	0.668140	−	0.485432i	0.0273223	−	0.0198508i
$599$	9.02179	−	27.7662i	0.368620	−	1.13450i	−0.579062	−	0.815283i	$-0.696581\pi$
$599$	9.02179	−	27.7662i	0.368620	−	1.13450i	0.947683	−	0.319214i	$-0.103419\pi$
$600$		0			0
$601$	5.40494	−	3.92692i	0.220472	−	0.160182i	−0.472067	−	0.881563i	$-0.656492\pi$
$601$	5.40494	−	3.92692i	0.220472	−	0.160182i	0.692539	+	0.721380i	$0.256492\pi$
$602$	−36.0135	−	26.1653i	−1.46780	−	1.06642i
$603$		0			0
$604$	30.7522			1.25129
$605$	10.4009	−	3.58078i	0.422855	−	0.145579i
$606$		0			0
$607$	−13.1674	−	40.5252i	−0.534450	−	1.64487i	−0.744834	−	0.667250i	$-0.767471\pi$
$607$	−13.1674	−	40.5252i	−0.534450	−	1.64487i	0.210384	−	0.977619i	$-0.432529\pi$
$608$	−1.87355	−	1.36121i	−0.0759824	−	0.0552044i
$609$		0			0
$610$	−6.97007	+	21.4517i	−0.282210	+	0.868553i
$611$	−1.16099	+	3.57315i	−0.0469685	+	0.144554i
$612$		0			0
$613$	4.71783	+	3.42771i	0.190552	+	0.138444i	0.678971	−	0.734165i	$-0.262426\pi$
$613$	4.71783	+	3.42771i	0.190552	+	0.138444i	−0.488419	+	0.872609i	$0.662426\pi$
$614$	−16.2078	−	49.8824i	−0.654093	−	2.01309i
$615$		0			0
$616$	48.6699	+	24.2673i	1.96097	+	0.977758i
$617$	33.6386			1.35424			0.677119	−	0.735874i	$-0.263228\pi$
$617$	33.6386			1.35424			0.677119	+	0.735874i	$0.263228\pi$
$618$		0			0
$619$	−34.4331	−	25.0171i	−1.38398	−	1.00552i	−0.996495	−	0.0836477i	$-0.973343\pi$
$619$	−34.4331	−	25.0171i	−1.38398	−	1.00552i	−0.387488	−	0.921875i	$-0.626657\pi$
$620$	−11.2487	+	8.17267i	−0.451760	+	0.328223i
$621$		0			0
$622$	24.8996	−	76.6329i	0.998381	−	3.07270i
$623$	4.31089	−	3.13205i	0.172712	−	0.125483i
$624$		0			0
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$	8.49374			0.339478
$627$		0			0
$628$	−40.8509			−1.63013
$629$	−4.07019	−	12.5268i	−0.162289	−	0.499475i
$630$		0			0
$631$	7.20016	−	5.23122i	0.286634	−	0.208252i	−0.435172	−	0.900347i	$-0.643312\pi$
$631$	7.20016	−	5.23122i	0.286634	−	0.208252i	0.721806	+	0.692096i	$0.243312\pi$
$632$	−8.34713	+	25.6898i	−0.332031	+	1.02189i
$633$		0			0
$634$	5.71351	−	4.15111i	0.226912	−	0.164862i
$635$	13.7559	+	9.99428i	0.545888	+	0.396611i
$636$		0			0
$637$	−1.19095			−0.0471871
$638$	−18.9416	−	36.3886i	−0.749906	−	1.44064i
$639$		0			0
$640$	5.97152	+	18.3785i	0.236045	+	0.726472i
$641$	−4.99007	−	3.62549i	−0.197096	−	0.143198i	0.484860	−	0.874592i	$-0.338870\pi$
$641$	−4.99007	−	3.62549i	−0.197096	−	0.143198i	−0.681956	+	0.731393i	$0.738870\pi$
$642$		0			0
$643$	1.34526	−	4.14029i	0.0530519	−	0.163277i	−0.921020	−	0.389515i	$-0.872643\pi$
$643$	1.34526	−	4.14029i	0.0530519	−	0.163277i	0.974072	+	0.226238i	$0.0726427\pi$
$644$	−4.39731	+	13.5335i	−0.173278	+	0.533296i
$645$		0			0
$646$	74.0508	+	53.8011i	2.91349	+	2.11677i
$647$	−4.16967	−	12.8329i	−0.163927	−	0.504514i	0.835029	−	0.550206i	$-0.185451\pi$
$647$	−4.16967	−	12.8329i	−0.163927	−	0.504514i	−0.998956	+	0.0456916i	$0.985451\pi$
$648$		0			0
$649$	29.9771	−	5.01575i	1.17671	−	0.196885i
$650$	0.769020			0.0301635
$651$		0			0
$652$	16.4021	+	11.9168i	0.642354	+	0.466697i
$653$	22.2060	−	16.1336i	0.868988	−	0.631357i	−0.0613270	−	0.998118i	$-0.519533\pi$
$653$	22.2060	−	16.1336i	0.868988	−	0.631357i	0.930315	+	0.366761i	$0.119533\pi$
$654$		0			0
$655$	0.0133034	−	0.0409437i	0.000519808	−	0.00159980i
$656$	36.7632	−	26.7100i	1.43536	−	1.04285i
$657$		0			0
$658$	−29.9285	−	92.1105i	−1.16674	−	3.59084i
$659$	18.7768			0.731441			0.365721	−	0.930725i	$-0.380823\pi$
$659$	18.7768			0.731441			0.365721	+	0.930725i	$0.380823\pi$
$660$		0			0
$661$	−21.6525			−0.842184			−0.421092	−	0.907018i	$-0.638353\pi$
$661$	−21.6525			−0.842184			−0.421092	+	0.907018i	$0.638353\pi$
$662$	10.7174	+	32.9847i	0.416543	+	1.28199i
$663$		0			0
$664$	−65.5674	+	47.6375i	−2.54451	+	1.84869i
$665$	−7.57103	+	23.3012i	−0.293592	+	0.903583i
$666$		0			0
$667$	4.37578	−	3.17919i	0.169431	−	0.123099i
$668$	18.8872	+	13.7224i	0.730769	+	0.530935i
$669$		0			0
$670$	37.5109			1.44917
$671$	−21.3508	+	21.7258i	−0.824240	+	0.838714i
$672$		0			0
$673$	7.20076	+	22.1617i	0.277569	+	0.854269i	0.988528	+	0.151036i	$0.0482609\pi$
$673$	7.20076	+	22.1617i	0.277569	+	0.854269i	−0.710959	+	0.703233i	$0.751739\pi$
$674$	31.6883	+	23.0229i	1.22059	+	0.886808i
$675$		0			0
$676$	−16.0728	+	49.4670i	−0.618184	+	1.90258i
$677$	−10.2843	+	31.6519i	−0.395259	+	1.21648i	0.533501	+	0.845800i	$0.320876\pi$
$677$	−10.2843	+	31.6519i	−0.395259	+	1.21648i	−0.928760	+	0.370683i	$0.879124\pi$
$678$		0			0
$679$	−0.595859	−	0.432917i	−0.0228670	−	0.0166138i
$680$	7.70818	+	23.7233i	0.295595	+	0.909749i
$681$		0			0
$682$	−27.7077	+	4.63603i	−1.06098	+	0.177523i
$683$	−16.9244			−0.647593			−0.323796	−	0.946127i	$-0.604959\pi$
$683$	−16.9244			−0.647593			−0.323796	+	0.946127i	$0.604959\pi$
$684$		0			0
$685$	5.95645	+	4.32761i	0.227584	+	0.165350i
$686$	−20.8758	+	15.1671i	−0.797041	+	0.579084i
$687$		0			0
$688$	−7.13905	+	21.9717i	−0.272174	+	0.837664i
$689$	−1.25029	+	0.908392i	−0.0476324	+	0.0346070i
$690$		0			0
$691$	−14.9668	−	46.0630i	−0.569363	−	1.75232i	−0.654617	−	0.755961i	$-0.727170\pi$
$691$	−14.9668	−	46.0630i	−0.569363	−	1.75232i	0.0852532	−	0.996359i	$-0.472830\pi$
$692$	−64.7650			−2.46200
$693$		0			0
$694$	72.8910			2.76690
$695$	4.09118	+	12.5914i	0.155187	+	0.477618i
$696$		0			0
$697$	−43.8779	+	31.8791i	−1.66199	+	1.20751i
$698$	−24.0527	+	74.0267i	−0.910409	+	2.80195i
$699$		0			0
$700$	−10.7199	+	7.78845i	−0.405174	+	0.294376i
$701$	−36.7424	−	26.6949i	−1.38774	−	1.00825i	−0.996109	−	0.0881330i	$-0.971910\pi$
$701$	−36.7424	−	26.6949i	−1.38774	−	1.00825i	−0.391634	−	0.920121i	$-0.628090\pi$
$702$		0			0
$703$	−19.6361			−0.740591
$704$	−3.73392	+	24.9803i	−0.140727	+	0.941482i
$705$		0			0
$706$	0.912130	+	2.80725i	0.0343285	+	0.105652i
$707$	−1.34372	−	0.976267i	−0.0505357	−	0.0367163i
$708$		0			0
$709$	−0.545405	+	1.67858i	−0.0204831	+	0.0630406i	−0.960776	−	0.277327i	$-0.910551\pi$
$709$	−0.545405	+	1.67858i	−0.0204831	+	0.0630406i	0.940292	+	0.340368i	$0.110551\pi$
$710$	2.33146	−	7.17549i	0.0874981	−	0.269291i
$711$		0			0
$712$	−6.54317	−	4.75389i	−0.245216	−	0.178160i
$713$	−1.14458	−	3.52266i	−0.0428649	−	0.131925i
$714$		0			0
$715$	0.929420	+	0.463418i	0.0347583	+	0.0173309i
$716$	33.4729			1.25094
$717$		0			0
$718$	23.1649	+	16.8303i	0.864506	+	0.628100i
$719$	−2.66974	+	1.93968i	−0.0995645	+	0.0723379i	−0.636454	−	0.771315i	$-0.719599\pi$
$719$	−2.66974	+	1.93968i	−0.0995645	+	0.0723379i	0.536889	+	0.843653i	$0.319599\pi$
$720$		0			0
$721$	−6.50241	+	20.0124i	−0.242163	+	0.745300i
$722$	72.6459	−	52.7803i	2.70360	−	1.96428i
$723$		0			0
$724$	−8.05294	−	24.7844i	−0.299285	−	0.921105i
$725$	5.03647			0.187050
$726$		0			0
$727$	11.7838			0.437037			0.218519	−	0.975833i	$-0.429878\pi$
$727$	11.7838			0.437037			0.218519	+	0.975833i	$0.429878\pi$
$728$	1.58668	+	4.88331i	0.0588064	+	0.180987i
$729$		0			0
$730$	−17.1916	+	12.4905i	−0.636291	+	0.462293i
$731$	8.52064	−	26.2238i	0.315147	−	0.969924i
$732$		0			0
$733$	−4.63654	+	3.36865i	−0.171255	+	0.124424i	−0.670111	−	0.742261i	$-0.733754\pi$
$733$	−4.63654	+	3.36865i	−0.171255	+	0.124424i	0.498856	+	0.866685i	$0.333754\pi$
$734$	31.7619	+	23.0764i	1.17235	+	0.851765i
$735$		0			0
$736$	0.333646			0.0122983
$737$	45.3348	+	22.6044i	1.66993	+	0.832643i
$738$		0			0
$739$	−6.50638	−	20.0246i	−0.239341	−	0.736616i	−0.996516	−	0.0834038i	$-0.973421\pi$
$739$	−6.50638	−	20.0246i	−0.239341	−	0.736616i	0.757175	−	0.653212i	$-0.226579\pi$
$740$	−8.59160	−	6.24216i	−0.315833	−	0.229466i
$741$		0			0
$742$	12.3110	−	37.8895i	0.451952	−	1.39097i
$743$	−4.05686	+	12.4857i	−0.148832	+	0.458058i	−0.997484	−	0.0708942i	$-0.977415\pi$
$743$	−4.05686	+	12.4857i	−0.148832	+	0.458058i	0.848652	+	0.528952i	$0.177415\pi$
$744$		0			0
$745$	−4.75587	−	3.45534i	−0.174242	−	0.126594i
$746$	−0.244350	−	0.752032i	−0.00894629	−	0.0275339i
$747$		0			0
$748$	−9.88299	+	66.1183i	−0.361358	+	2.41753i
$749$	−6.87768			−0.251305
$750$		0			0
$751$	−20.7311	−	15.0621i	−0.756490	−	0.549622i	0.141342	−	0.989961i	$-0.454858\pi$
$751$	−20.7311	−	15.0621i	−0.756490	−	0.549622i	−0.897832	+	0.440339i	$0.854858\pi$
$752$	−40.6641	+	29.5442i	−1.48287	+	1.07737i
$753$		0			0
$754$	1.19687	−	3.68358i	0.0435874	−	0.134148i
$755$	−6.17135	+	4.48375i	−0.224598	+	0.163180i
$756$		0			0
$757$	9.64039	+	29.6701i	0.350386	+	1.07838i	0.958637	+	0.284632i	$0.0918715\pi$
$757$	9.64039	+	29.6701i	0.350386	+	1.07838i	−0.608251	+	0.793745i	$0.708129\pi$
$758$	−28.0400			−1.01846
$759$		0			0
$760$	37.1872			1.34892
$761$	−3.51539	−	10.8193i	−0.127433	−	0.392198i	0.866904	−	0.498476i	$-0.166107\pi$
$761$	−3.51539	−	10.8193i	−0.127433	−	0.392198i	−0.994336	+	0.106278i	$0.966107\pi$
$762$		0			0
$763$	17.7968	−	12.9302i	0.644289	−	0.468103i
$764$	−19.1465	+	58.9269i	−0.692697	+	2.13190i
$765$		0			0
$766$	−56.3617	+	40.9491i	−2.03643	+	1.47955i
$767$	2.32154	+	1.68670i	0.0838260	+	0.0609032i
$768$		0			0
$769$	10.3938			0.374811			0.187405	−	0.982283i	$-0.439992\pi$
$769$	10.3938			0.374811			0.187405	+	0.982283i	$0.439992\pi$
$770$	−26.4051	+	4.41808i	−0.951574	+	0.159217i
$771$		0			0
$772$	19.6230	+	60.3935i	0.706248	+	2.17361i
$773$	11.3544	+	8.24944i	0.408389	+	0.296712i	0.772949	−	0.634468i	$-0.218781\pi$
$773$	11.3544	+	8.24944i	0.408389	+	0.296712i	−0.364560	+	0.931180i	$0.618781\pi$
$774$		0			0
$775$	1.06580	−	3.28018i	0.0382845	−	0.117828i
$776$	−0.345453	+	1.06319i	−0.0124010	+	0.0381665i
$777$		0			0
$778$	−30.1608	−	21.9131i	−1.08132	−	0.785623i
$779$	24.9858	+	76.8985i	0.895211	+	2.75518i
$780$		0			0
$781$	7.14176	−	7.26717i	0.255552	−	0.260040i
$782$	−13.1871			−0.471571
$783$		0			0
$784$	−12.8902	−	9.36527i	−0.460364	−	0.334474i
$785$	8.19795	−	5.95616i	0.292597	−	0.212584i
$786$		0			0
$787$	−4.26988	+	13.1414i	−0.152205	+	0.468439i	−0.997867	−	0.0652802i	$-0.979206\pi$
$787$	−4.26988	+	13.1414i	−0.152205	+	0.468439i	0.845662	+	0.533719i	$0.179206\pi$
$788$	53.4681	−	38.8469i	1.90472	−	1.38386i
$789$		0			0
$790$	−4.10910	−	12.6465i	−0.146195	−	0.449942i
$791$	35.4785			1.26147
$792$		0			0
$793$	−2.87591			−0.102127
$794$	−3.96502	−	12.2031i	−0.140713	−	0.433070i
$795$		0			0
$796$	−22.7160	+	16.5042i	−0.805149	+	0.584975i
$797$	1.66435	−	5.12233i	0.0589541	−	0.181442i	−0.917243	−	0.398329i	$-0.869590\pi$
$797$	1.66435	−	5.12233i	0.0589541	−	0.181442i	0.976197	+	0.216887i	$0.0695902\pi$
$798$		0			0
$799$	48.5337	−	35.2618i	1.71700	−	1.24747i
$800$	0.251345	+	0.182613i	0.00888640	+	0.00645635i
$801$		0			0
$802$	34.3840			1.21414
$803$	−28.3043	+	4.73585i	−0.998836	+	0.167124i
$804$		0			0
$805$	−1.09077	−	3.35705i	−0.0384446	−	0.118320i
$806$	−2.14579	−	1.55901i	−0.0755822	−	0.0549137i
$807$		0			0
$808$	−0.779028	+	2.39760i	−0.0274061	+	0.0843473i
$809$	−7.34680	+	22.6111i	−0.258300	+	0.794965i	0.734862	+	0.678217i	$0.237247\pi$
$809$	−7.34680	+	22.6111i	−0.258300	+	0.794965i	−0.993162	+	0.116748i	$0.962753\pi$
$810$		0			0
$811$	−7.65601	−	5.56242i	−0.268839	−	0.195323i	0.445196	−	0.895433i	$-0.353134\pi$
$811$	−7.65601	−	5.56242i	−0.268839	−	0.195323i	−0.714035	+	0.700110i	$0.753134\pi$
$812$	20.6225	+	63.4695i	0.723707	+	2.22734i
$813$		0			0
$814$	−9.90726	−	19.0327i	−0.347249	−	0.667097i
$815$	−5.02906			−0.176160
$816$		0			0
$817$	−33.2561	−	24.1620i	−1.16348	−	0.845321i
$818$	66.1846	−	48.0859i	2.31409	−	1.68128i
$819$		0			0
$820$	−13.5131	+	41.5889i	−0.471897	+	1.45235i
$821$	−8.42906	+	6.12407i	−0.294176	+	0.213731i	−0.725077	−	0.688668i	$-0.758196\pi$
$821$	−8.42906	+	6.12407i	−0.294176	+	0.213731i	0.430901	+	0.902399i	$0.358196\pi$
$822$		0			0
$823$	7.52581	+	23.1620i	0.262333	+	0.807378i	0.992296	+	0.123891i	$0.0395374\pi$
$823$	7.52581	+	23.1620i	0.262333	+	0.807378i	−0.729963	+	0.683487i	$0.760463\pi$
$824$	31.9384			1.11263
$825$		0			0
$826$	−73.9736			−2.57387
$827$	6.79857	+	20.9239i	0.236410	+	0.727594i	0.996931	+	0.0782813i	$0.0249432\pi$
$827$	6.79857	+	20.9239i	0.236410	+	0.727594i	−0.760522	+	0.649312i	$0.775057\pi$
$828$		0			0
$829$	−2.45366	+	1.78269i	−0.0852191	+	0.0619153i	−0.629579	−	0.776936i	$-0.716773\pi$
$829$	−2.45366	+	1.78269i	−0.0852191	+	0.0619153i	0.544360	+	0.838852i	$0.316773\pi$
$830$	12.3288	−	37.9442i	0.427940	−	1.31706i
$831$		0			0
$832$	−1.92924	+	1.40168i	−0.0668845	+	0.0485945i
$833$	15.3848	+	11.1777i	0.533051	+	0.387284i
$834$		0			0
$835$	−5.79105			−0.200408
$836$	89.1929	+	44.4725i	3.08480	+	1.53811i
$837$		0			0
$838$	−4.01054	−	12.3432i	−0.138542	−	0.426388i
$839$	−39.2683	−	28.5301i	−1.35569	−	0.984968i	−0.998706	−	0.0508591i	$-0.983804\pi$
$839$	−39.2683	−	28.5301i	−1.35569	−	0.984968i	−0.356987	−	0.934109i	$-0.616196\pi$
$840$		0			0
$841$	−1.12296	+	3.45613i	−0.0387229	+	0.119177i
$842$	23.3600	−	71.8947i	0.805039	−	2.47766i
$843$		0			0
$844$	65.0762	+	47.2806i	2.24001	+	1.62747i
$845$	−3.98692	−	12.2705i	−0.137154	−	0.422117i
$846$		0			0
$847$	−34.5750	−	10.5723i	−1.18801	−	0.363270i
$848$	−20.6758			−0.710011
$849$		0			0
$850$	−9.93427	−	7.21767i	−0.340743	−	0.247564i
$851$	2.28872	−	1.66285i	0.0784563	−	0.0570018i
$852$		0			0
$853$	−3.63504	+	11.1875i	−0.124461	+	0.383053i	−0.993803	−	0.111160i	$-0.964544\pi$
$853$	−3.63504	+	11.1875i	−0.124461	+	0.383053i	0.869341	+	0.494213i	$0.164544\pi$
$854$	59.9779	−	43.5765i	2.05240	−	1.49116i
$855$		0			0
$856$	3.22586	+	9.92817i	0.110258	+	0.339338i
$857$	−1.61311			−0.0551026			−0.0275513	−	0.999620i	$-0.508771\pi$
$857$	−1.61311			−0.0551026			−0.0275513	+	0.999620i	$0.508771\pi$
$858$		0			0
$859$	47.3263			1.61475			0.807376	−	0.590038i	$-0.200887\pi$
$859$	47.3263			1.61475			0.807376	+	0.590038i	$0.200887\pi$
$860$	−6.86999	−	21.1437i	−0.234265	−	0.720993i
$861$		0			0
$862$	−24.5389	+	17.8286i	−0.835799	+	0.607244i
$863$	3.08162	−	9.48425i	0.104900	−	0.322848i	−0.884807	−	0.465957i	$-0.845710\pi$
$863$	3.08162	−	9.48425i	0.104900	−	0.322848i	0.989707	+	0.143109i	$0.0457101\pi$
$864$		0			0
$865$	12.9970	−	9.44290i	0.441912	−	0.321068i
$866$	2.80717	+	2.03953i	0.0953915	+	0.0693060i
$867$		0			0
$868$	45.7009			1.55119
$869$	2.65473	−	17.7604i	0.0900555	−	0.602482i
$870$		0			0
$871$	1.47795	+	4.54867i	0.0500786	+	0.154126i
$872$	−27.0124	−	19.6257i	−0.914756	−	0.664609i
$873$		0			0
$874$	−6.07515	+	18.6974i	−0.205495	+	0.632448i
$875$	1.01569	−	3.12597i	0.0343366	−	0.105677i
$876$		0			0
$877$	−21.0391	−	15.2858i	−0.710439	−	0.516164i	0.172876	−	0.984944i	$-0.444694\pi$
$877$	−21.0391	−	15.2858i	−0.710439	−	0.516164i	−0.883315	+	0.468779i	$0.844694\pi$
$878$	5.75658	+	17.7169i	0.194275	+	0.597918i
$879$		0			0
$880$	6.41535	+	12.3245i	0.216262	+	0.415458i
$881$	−10.4081			−0.350657			−0.175329	−	0.984510i	$-0.556099\pi$
$881$	−10.4081			−0.350657			−0.175329	+	0.984510i	$0.556099\pi$
$882$		0			0
$883$	43.4671	+	31.5807i	1.46279	+	1.06278i	0.982626	+	0.185595i	$0.0594211\pi$
$883$	43.4671	+	31.5807i	1.46279	+	1.06278i	0.480159	+	0.877181i	$0.340579\pi$
$884$	−5.10635	+	3.70998i	−0.171745	+	0.124780i
$885$		0			0
$886$	8.39826	−	25.8472i	0.282145	−	0.868353i
$887$	−32.8660	+	23.8786i	−1.10353	+	0.801763i	−0.981633	−	0.190779i	$-0.938899\pi$
$887$	−32.8660	+	23.8786i	−1.10353	+	0.801763i	−0.121900	+	0.992542i	$0.538899\pi$
$888$		0			0
$889$	−17.2701	−	53.1518i	−0.579219	−	1.78265i
$890$	3.98143			0.133458
$891$		0			0
$892$	−81.2188			−2.71941
$893$	−27.6371	−	85.0582i	−0.924839	−	2.84636i
$894$		0			0
$895$	−6.71734	+	4.88043i	−0.224536	+	0.163135i
$896$	19.6274	−	60.4071i	0.655707	−	2.01806i
$897$		0			0
$898$	−12.5739	+	9.13549i	−0.419597	+	0.304855i
$899$	−14.0532	−	10.2103i	−0.468701	−	0.340531i
$900$		0			0
$901$	24.6772			0.822115
$902$	−61.9290	+	63.0166i	−2.06201	+	2.09822i
$903$		0			0
$904$	−16.6406	−	51.2145i	−0.553458	−	1.70337i
$905$	5.22969	+	3.79959i	0.173841	+	0.126303i
$906$		0			0
$907$	−5.99708	+	18.4571i	−0.199130	+	0.612859i	0.800774	+	0.598967i	$0.204422\pi$
$907$	−5.99708	+	18.4571i	−0.199130	+	0.612859i	−0.999904	+	0.0138917i	$0.995578\pi$
$908$	−0.665160	+	2.04715i	−0.0220741	+	0.0679371i
$909$		0			0
$910$	−2.04491	−	1.48571i	−0.0677881	−	0.0492509i
$911$	−3.31290	−	10.1960i	−0.109761	−	0.337810i	0.881057	−	0.473010i	$-0.156832\pi$
$911$	−3.31290	−	10.1960i	−0.109761	−	0.337810i	−0.990818	+	0.135200i	$0.956832\pi$
$912$		0			0
$913$	37.7658	−	38.4290i	1.24987	−	1.27182i
$914$	0.465585			0.0154002
$915$		0			0
$916$	72.3816	+	52.5883i	2.39156	+	1.73757i
$917$	−0.114477	+	0.0831723i	−0.00378036	+	0.00274659i
$918$		0			0
$919$	−7.14787	+	21.9989i	−0.235787	+	0.725676i	0.761230	+	0.648483i	$0.224596\pi$
$919$	−7.14787	+	21.9989i	−0.235787	+	0.725676i	−0.997016	+	0.0771939i	$0.975404\pi$
$920$	−4.33440	+	3.14913i	−0.142901	+	0.103824i
$921$		0			0
$922$	−20.2020	−	62.1755i	−0.665319	−	2.04764i
$923$	0.961981			0.0316640
$924$		0			0
$925$	2.63428			0.0866147
$926$	−15.9322	−	49.0343i	−0.523565	−	1.61137i
$927$		0			0
$928$	1.26589	−	0.919725i	0.0415550	−	0.0301915i
$929$	−8.10467	+	24.9436i	−0.265906	+	0.818374i	0.725578	+	0.688140i	$0.241573\pi$
$929$	−8.10467	+	24.9436i	−0.265906	+	0.818374i	−0.991483	+	0.130233i	$0.958427\pi$
$930$		0			0
$931$	22.9359	−	16.6639i	0.751693	−	0.546137i
$932$	−14.8907	−	10.8187i	−0.487762	−	0.354380i
$933$		0			0
$934$	19.4012			0.634828
$935$	−7.65690	−	14.7096i	−0.250407	−	0.481055i
$936$		0			0
$937$	7.23133	+	22.2557i	0.236237	+	0.727063i	0.996955	+	0.0779804i	$0.0248472\pi$
$937$	7.23133	+	22.2557i	0.236237	+	0.727063i	−0.760718	+	0.649083i	$0.775153\pi$
$938$	−99.7456	−	72.4694i	−3.25681	−	2.36621i
$939$		0			0
$940$	14.9469	−	46.0019i	0.487515	−	1.50042i
$941$	3.38952	−	10.4319i	0.110495	−	0.340069i	−0.880486	−	0.474073i	$-0.842783\pi$
$941$	3.38952	−	10.4319i	0.110495	−	0.340069i	0.990981	+	0.134004i	$0.0427833\pi$
$942$		0			0
$943$	−9.42427	−	6.84713i	−0.306896	−	0.222973i
$944$	11.8634	+	36.5118i	0.386121	+	1.18836i
$945$		0			0
$946$	6.64038	−	44.4249i	0.215897	−	1.44438i
$947$	13.3652			0.434310			0.217155	−	0.976137i	$-0.430322\pi$
$947$	13.3652			0.434310			0.217155	+	0.976137i	$0.430322\pi$
$948$		0			0
$949$	−2.19199	−	1.59257i	−0.0711550	−	0.0516971i
$950$	−14.8102	+	10.7602i	−0.480505	+	0.349107i
$951$		0			0
$952$	25.3356	−	77.9749i	0.821130	−	2.52718i
$953$	−17.6562	+	12.8280i	−0.571939	+	0.415538i	−0.835809	−	0.549020i	$-0.815001\pi$
$953$	−17.6562	+	12.8280i	−0.571939	+	0.415538i	0.263870	+	0.964558i	$0.415001\pi$
$954$		0			0
$955$	−4.74937	−	14.6171i	−0.153686	−	0.472997i
$956$	23.6260			0.764120
$957$		0			0
$958$	98.1686			3.17168
$959$	−7.47809	−	23.0152i	−0.241480	−	0.743199i
$960$		0			0
$961$	15.4558	−	11.2293i	0.498576	−	0.362236i
$962$	0.626012	−	1.92667i	0.0201834	−	0.0621182i
$963$		0			0
$964$	−32.4865	+	23.6028i	−1.04632	+	0.760196i
$965$	−12.7435	−	9.25867i	−0.410227	−	0.298047i
$966$		0			0
$967$	16.6600			0.535750			0.267875	−	0.963454i	$-0.413679\pi$
$967$	16.6600			0.535750			0.267875	+	0.963454i	$0.413679\pi$
$968$	0.955240	+	54.8689i	0.0307026	+	1.76355i
$969$		0			0
$970$	−0.170058	−	0.523385i	−0.00546024	−	0.0168049i
$971$	8.98271	+	6.52632i	0.288269	+	0.209440i	0.722516	−	0.691354i	$-0.242986\pi$
$971$	8.98271	+	6.52632i	0.288269	+	0.209440i	−0.434247	+	0.900794i	$0.642986\pi$
$972$		0			0
$973$	13.4471	−	41.3858i	0.431093	−	1.32677i
$974$	7.54021	−	23.2064i	0.241604	−	0.743580i
$975$		0			0
$976$	−31.1273	−	22.6153i	−0.996362	−	0.723899i
$977$	−5.81397	−	17.8936i	−0.186005	−	0.572466i	0.813959	−	0.580923i	$-0.197308\pi$
$977$	−5.81397	−	17.8936i	−0.186005	−	0.572466i	−0.999964	+	0.00845665i	$0.997308\pi$
$978$		0			0
$979$	4.81187	+	2.39924i	0.153788	+	0.0766802i
$980$	15.3327			0.489784
$981$		0			0
$982$	−9.88160	−	7.17940i	−0.315335	−	0.229104i
$983$	−1.11521	+	0.810250i	−0.0355698	+	0.0258430i	−0.605428	−	0.795900i	$-0.706998\pi$
$983$	−1.11521	+	0.810250i	−0.0355698	+	0.0258430i	0.569858	+	0.821743i	$0.306998\pi$
$984$		0			0
$985$	−5.06601	+	15.5916i	−0.161416	+	0.496789i
$986$	−50.0336	+	36.3516i	−1.59340	+	1.15767i
$987$		0			0
$988$	2.90777	+	8.94918i	0.0925083	+	0.284711i
$989$	5.92233			0.188319
$990$		0			0
$991$	−46.3186			−1.47136			−0.735680	−	0.677329i	$-0.763137\pi$
$991$	−46.3186			−1.47136			−0.735680	+	0.677329i	$0.763137\pi$
$992$	−0.331122	−	1.01909i	−0.0105131	−	0.0323561i
$993$		0			0
$994$	−20.0623	+	14.5761i	−0.636339	+	0.462327i
$995$	2.15230	−	6.62411i	0.0682326	−	0.209998i
$996$		0			0
$997$	−11.7688	+	8.55054i	−0.372722	+	0.270798i	−0.758339	−	0.651861i	$-0.773989\pi$
$997$	−11.7688	+	8.55054i	−0.372722	+	0.270798i	0.385617	+	0.922659i	$0.373989\pi$
$998$	86.9759	+	63.1917i	2.75317	+	2.00030i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.n.d.181.1		8
3.2	odd	2		165.2.m.a.16.2	✓	8
11.3	even	5		5445.2.a.be.1.2		4
11.8	odd	10		5445.2.a.bv.1.3		4
11.9	even	5	inner	495.2.n.d.361.1		8
15.2	even	4		825.2.bx.h.49.1		16
15.8	even	4		825.2.bx.h.49.4		16
15.14	odd	2		825.2.n.k.676.1		8
33.8	even	10		1815.2.a.o.1.2		4
33.14	odd	10		1815.2.a.x.1.3		4
33.20	odd	10		165.2.m.a.31.2	yes	8
165.14	odd	10		9075.2.a.cl.1.2		4
165.53	even	20		825.2.bx.h.724.1		16
165.74	even	10		9075.2.a.dj.1.3		4
165.119	odd	10		825.2.n.k.526.1		8
165.152	even	20		825.2.bx.h.724.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.m.a.16.2	✓	8	3.2	odd	2
165.2.m.a.31.2	yes	8	33.20	odd	10
495.2.n.d.181.1		8	1.1	even	1	trivial
495.2.n.d.361.1		8	11.9	even	5	inner
825.2.n.k.526.1		8	165.119	odd	10
825.2.n.k.676.1		8	15.14	odd	2
825.2.bx.h.49.1		16	15.2	even	4
825.2.bx.h.49.4		16	15.8	even	4
825.2.bx.h.724.1		16	165.53	even	20
825.2.bx.h.724.4		16	165.152	even	20
1815.2.a.o.1.2		4	33.8	even	10
1815.2.a.x.1.3		4	33.14	odd	10
5445.2.a.be.1.2		4	11.3	even	5
5445.2.a.bv.1.3		4	11.8	odd	10
9075.2.a.cl.1.2		4	165.14	odd	10
9075.2.a.dj.1.3		4	165.74	even	10

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:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.758911 - 2.33569i) q^{2} +(-3.26145 + 2.36959i) q^{4} +(0.309017 - 0.951057i) q^{5} +(-2.65911 + 1.93196i) q^{7} +(4.03606 + 2.93237i) q^{8} +O(q^{10})\)	\(q+(-0.758911 - 2.33569i) q^{2} +(-3.26145 + 2.36959i) q^{4} +(0.309017 - 0.951057i) q^{5} +(-2.65911 + 1.93196i) q^{7} +(4.03606 + 2.93237i) q^{8} -2.45589 q^{10} +(-2.96813 - 1.47994i) q^{11} +(-0.0967635 - 0.297808i) q^{13} +(6.53048 + 4.74467i) q^{14} +(1.29455 - 3.98423i) q^{16} +(-1.54508 + 4.75528i) q^{17} +(6.03048 + 4.38140i) q^{19} +(1.24576 + 3.83407i) q^{20} +(-1.20413 + 8.05576i) q^{22} -1.07392 q^{23} +(-0.809017 - 0.587785i) q^{25} +(-0.622150 + 0.452019i) q^{26} +(4.09463 - 12.6020i) q^{28} +(-4.07459 + 2.96036i) q^{29} +(1.06580 + 3.28018i) q^{31} -0.310680 q^{32} +12.2794 q^{34} +(1.01569 + 3.12597i) q^{35} +(-2.13118 + 1.54839i) q^{37} +(5.65698 - 17.4104i) q^{38} +(4.03606 - 2.93237i) q^{40} +(8.77557 + 6.37583i) q^{41} -5.51468 q^{43} +(13.1873 - 2.20648i) q^{44} +(0.815010 + 2.50834i) q^{46} +(-9.70674 - 7.05236i) q^{47} +(1.17529 - 3.61718i) q^{49} +(-0.758911 + 2.33569i) q^{50} +(1.02127 + 0.741996i) q^{52} +(-1.52513 - 4.69387i) q^{53} +(-2.32471 + 2.36553i) q^{55} -16.3975 q^{56} +(10.0067 + 7.27031i) q^{58} +(-7.41391 + 5.38652i) q^{59} +(2.83811 - 8.73480i) q^{61} +(6.85264 - 4.97873i) q^{62} +(-2.35333 - 7.24280i) q^{64} -0.313133 q^{65} -15.2739 q^{67} +(-6.22882 - 19.1704i) q^{68} +(6.53048 - 4.74467i) q^{70} +(-0.949335 + 2.92175i) q^{71} +(7.00018 - 5.08592i) q^{73} +(5.23394 + 3.80268i) q^{74} -30.0502 q^{76} +(10.7518 - 1.79898i) q^{77} +(1.67316 + 5.14946i) q^{79} +(-3.38919 - 2.46239i) q^{80} +(8.23206 - 25.3357i) q^{82} +(-5.02011 + 15.4503i) q^{83} +(4.04508 + 2.93893i) q^{85} +(4.18515 + 12.8806i) q^{86} +(-7.63981 - 14.6768i) q^{88} -1.62118 q^{89} +(0.832656 + 0.604960i) q^{91} +(3.50254 - 2.54475i) q^{92} +(-9.10556 + 28.0240i) q^{94} +(6.03048 - 4.38140i) q^{95} +(0.0692451 + 0.213115i) q^{97} -9.34054 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{4} - 2 q^{5} + q^{7} - 5 q^{8}+O(q^{10}) \) 8 * q - 2 * q^4 - 2 * q^5 + q^7 - 5 * q^8	\( 8 q - 2 q^{4} - 2 q^{5} + q^{7} - 5 q^{8} - 10 q^{10} + 3 q^{11} + 6 q^{13} + 10 q^{14} - 20 q^{16} + 10 q^{17} + 6 q^{19} - 7 q^{20} - 25 q^{22} + 10 q^{23} - 2 q^{25} + 8 q^{26} + 31 q^{28} + 3 q^{31} - 60 q^{32} + 50 q^{34} + q^{35} - 19 q^{37} + 28 q^{38} - 5 q^{40} + 25 q^{41} - 4 q^{43} - 7 q^{44} - 6 q^{46} - 15 q^{47} + 21 q^{49} + 6 q^{52} - 7 q^{53} - 7 q^{55} - 20 q^{56} - 2 q^{58} - 35 q^{59} + 21 q^{61} + 19 q^{62} - 77 q^{64} + 6 q^{65} - 26 q^{67} + 35 q^{68} + 10 q^{70} - 25 q^{71} + q^{73} + 29 q^{74} - 14 q^{76} + 61 q^{77} + 30 q^{79} + 5 q^{80} + 57 q^{82} - 11 q^{83} + 10 q^{85} + 34 q^{86} - 85 q^{88} - 32 q^{89} + 37 q^{91} + 10 q^{92} - 39 q^{94} + 6 q^{95} + 5 q^{97} - 50 q^{98}+O(q^{100}) \) 8 * q - 2 * q^4 - 2 * q^5 + q^7 - 5 * q^8 - 10 * q^10 + 3 * q^11 + 6 * q^13 + 10 * q^14 - 20 * q^16 + 10 * q^17 + 6 * q^19 - 7 * q^20 - 25 * q^22 + 10 * q^23 - 2 * q^25 + 8 * q^26 + 31 * q^28 + 3 * q^31 - 60 * q^32 + 50 * q^34 + q^35 - 19 * q^37 + 28 * q^38 - 5 * q^40 + 25 * q^41 - 4 * q^43 - 7 * q^44 - 6 * q^46 - 15 * q^47 + 21 * q^49 + 6 * q^52 - 7 * q^53 - 7 * q^55 - 20 * q^56 - 2 * q^58 - 35 * q^59 + 21 * q^61 + 19 * q^62 - 77 * q^64 + 6 * q^65 - 26 * q^67 + 35 * q^68 + 10 * q^70 - 25 * q^71 + q^73 + 29 * q^74 - 14 * q^76 + 61 * q^77 + 30 * q^79 + 5 * q^80 + 57 * q^82 - 11 * q^83 + 10 * q^85 + 34 * q^86 - 85 * q^88 - 32 * q^89 + 37 * q^91 + 10 * q^92 - 39 * q^94 + 6 * q^95 + 5 * q^97 - 50 * q^98

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