LMFDB - Embedded newform 495.2.n.a.361.2

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			361.2
Root			$-0.386111 - 0.280526i$ of defining polynomial
Character	$\chi$	$=$	495.361
Dual form			495.2.n.a.181.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.456498 - 1.40496i) q^{2} +(-0.147481 - 0.107152i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(1.85666 + 1.34895i) q^{7} +(2.17239 - 1.57833i) q^{8} +O(q^{10})$	\(q+(0.456498 - 1.40496i) q^{2} +(-0.147481 - 0.107152i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(1.85666 + 1.34895i) q^{7} +(2.17239 - 1.57833i) q^{8} -1.47726 q^{10} +(3.12020 + 1.12443i) q^{11} +(-0.661536 + 2.03600i) q^{13} +(2.74278 - 1.99274i) q^{14} +(-1.33846 - 4.11937i) q^{16} +(-0.168243 - 0.517799i) q^{17} +(1.76552 - 1.28272i) q^{19} +(-0.0563329 + 0.173375i) q^{20} +(3.00415 - 3.87045i) q^{22} -2.03908 q^{23} +(-0.809017 + 0.587785i) q^{25} +(2.55850 + 1.85886i) q^{26} +(-0.129282 - 0.397889i) q^{28} +(-8.04603 - 5.84578i) q^{29} +(2.09249 - 6.44002i) q^{31} -1.02811 q^{32} -0.804288 q^{34} +(0.709183 - 2.18264i) q^{35} +(7.13520 + 5.18403i) q^{37} +(-0.996215 - 3.06604i) q^{38} +(-2.17239 - 1.57833i) q^{40} +(-1.47470 + 1.07143i) q^{41} -0.620713 q^{43} +(-0.339687 - 0.500167i) q^{44} +(-0.930836 + 2.86482i) q^{46} +(-0.305816 + 0.222188i) q^{47} +(-0.535571 - 1.64832i) q^{49} +(0.456498 + 1.40496i) q^{50} +(0.315724 - 0.229387i) q^{52} +(-3.58246 + 11.0257i) q^{53} +(0.105203 - 3.31496i) q^{55} +6.16248 q^{56} +(-11.8861 + 8.63574i) q^{58} +(-6.53518 - 4.74808i) q^{59} +(2.69647 + 8.29887i) q^{61} +(-8.09273 - 5.87971i) q^{62} +(2.20760 - 6.79429i) q^{64} +2.14077 q^{65} -9.75802 q^{67} +(-0.0306702 + 0.0943932i) q^{68} +(-2.74278 - 1.99274i) q^{70} +(4.63426 + 14.2628i) q^{71} +(-6.35761 - 4.61907i) q^{73} +(10.5405 - 7.65815i) q^{74} -0.397826 q^{76} +(4.27637 + 6.29667i) q^{77} +(-2.85054 + 8.77306i) q^{79} +(-3.50415 + 2.54591i) q^{80} +(0.832118 + 2.56099i) q^{82} +(2.92093 + 8.98969i) q^{83} +(-0.440466 + 0.320017i) q^{85} +(-0.283354 + 0.872075i) q^{86} +(8.55302 - 2.48201i) q^{88} -0.583290 q^{89} +(-3.97470 + 2.88779i) q^{91} +(0.300726 + 0.218490i) q^{92} +(0.172561 + 0.531087i) q^{94} +(-1.76552 - 1.28272i) q^{95} +(-1.66190 + 5.11479i) q^{97} -2.56031 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 2 q^{4} + 2 q^{5} + 3 q^{7} + q^{8}+O(q^{10}) $ 8 * q - 4 * q^2 + 2 * q^4 + 2 * q^5 + 3 * q^7 + q^8	$ 8 q - 4 q^{2} + 2 q^{4} + 2 q^{5} + 3 q^{7} + q^{8} - 6 q^{10} - 3 q^{11} - 4 q^{13} + 4 q^{14} - 12 q^{16} + 2 q^{19} + 3 q^{20} + 9 q^{22} + 6 q^{23} - 2 q^{25} - 2 q^{26} - 11 q^{28} - 10 q^{29} + 19 q^{31} - 12 q^{32} - 6 q^{34} - 3 q^{35} - q^{37} + 20 q^{38} - q^{40} + 9 q^{41} - 17 q^{44} - 22 q^{46} + 19 q^{47} + q^{49} - 4 q^{50} - 2 q^{52} - 25 q^{53} + 3 q^{55} + 16 q^{56} - 12 q^{58} - 13 q^{59} + 13 q^{61} - 35 q^{62} + 39 q^{64} + 14 q^{65} + 2 q^{67} - 19 q^{68} - 4 q^{70} + 11 q^{71} - 7 q^{73} + 43 q^{74} - 38 q^{76} + 7 q^{77} - 22 q^{79} - 13 q^{80} - 35 q^{82} + 21 q^{83} + 10 q^{85} - 20 q^{86} + 59 q^{88} + 20 q^{89} - 11 q^{91} + 28 q^{92} - 35 q^{94} - 2 q^{95} + 31 q^{97} - 22 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 + 2 * q^4 + 2 * q^5 + 3 * q^7 + q^8 - 6 * q^10 - 3 * q^11 - 4 * q^13 + 4 * q^14 - 12 * q^16 + 2 * q^19 + 3 * q^20 + 9 * q^22 + 6 * q^23 - 2 * q^25 - 2 * q^26 - 11 * q^28 - 10 * q^29 + 19 * q^31 - 12 * q^32 - 6 * q^34 - 3 * q^35 - q^37 + 20 * q^38 - q^40 + 9 * q^41 - 17 * q^44 - 22 * q^46 + 19 * q^47 + q^49 - 4 * q^50 - 2 * q^52 - 25 * q^53 + 3 * q^55 + 16 * q^56 - 12 * q^58 - 13 * q^59 + 13 * q^61 - 35 * q^62 + 39 * q^64 + 14 * q^65 + 2 * q^67 - 19 * q^68 - 4 * q^70 + 11 * q^71 - 7 * q^73 + 43 * q^74 - 38 * q^76 + 7 * q^77 - 22 * q^79 - 13 * q^80 - 35 * q^82 + 21 * q^83 + 10 * q^85 - 20 * q^86 + 59 * q^88 + 20 * q^89 - 11 * q^91 + 28 * q^92 - 35 * q^94 - 2 * q^95 + 31 * q^97 - 22 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$46$	$56$	$397$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$	$1$

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 $

$2$	0.456498	−	1.40496i	0.322793	−	0.993455i	−0.649634	−	0.760247i	$-0.725078\pi$
$2$	0.456498	−	1.40496i	0.322793	−	0.993455i	0.972427	−	0.233208i	$-0.0749222\pi$
$3$		0			0
$3$		0			0
$4$	−0.147481	−	0.107152i	−0.0737407	−	0.0535758i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$6$		0			0
$7$	1.85666	+	1.34895i	0.701753	+	0.509853i	0.880503	−	0.474041i	$-0.157205\pi$
$7$	1.85666	+	1.34895i	0.701753	+	0.509853i	−0.178750	+	0.983895i	$0.557205\pi$
$8$	2.17239	−	1.57833i	0.768055	−	0.558025i
$9$		0			0
$10$	−1.47726			−0.467151
$11$	3.12020	+	1.12443i	0.940776	+	0.339029i
$11$	3.12020	+	1.12443i	0.940776	+	0.339029i
$12$		0			0
$13$	−0.661536	+	2.03600i	−0.183477	+	0.564684i	−0.999919	−	0.0127437i	$-0.995943\pi$
$13$	−0.661536	+	2.03600i	−0.183477	+	0.564684i	0.816442	+	0.577428i	$0.195943\pi$
$14$	2.74278	−	1.99274i	0.733038	−	0.532583i
$15$		0			0
$16$	−1.33846	−	4.11937i	−0.334616	−	1.02984i
$17$	−0.168243	−	0.517799i	−0.0408049	−	0.125585i	0.928579	−	0.371135i	$-0.121031\pi$
$17$	−0.168243	−	0.517799i	−0.0408049	−	0.125585i	−0.969384	+	0.245550i	$0.921031\pi$
$18$		0			0
$19$	1.76552	−	1.28272i	0.405037	−	0.294277i	−0.366553	−	0.930397i	$-0.619462\pi$
$19$	1.76552	−	1.28272i	0.405037	−	0.294277i	0.771590	+	0.636121i	$0.219462\pi$
$20$	−0.0563329	+	0.173375i	−0.0125964	+	0.0387678i
$21$		0			0
$22$	3.00415	−	3.87045i	0.640486	−	0.825183i
$23$	−2.03908			−0.425177			−0.212589	−	0.977142i	$-0.568189\pi$
$23$	−2.03908			−0.425177			−0.212589	+	0.977142i	$0.568189\pi$
$24$		0			0
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$	2.55850	+	1.85886i	0.501763	+	0.364552i
$27$		0			0
$28$	−0.129282	−	0.397889i	−0.0244320	−	0.0751939i
$29$	−8.04603	−	5.84578i	−1.49411	−	1.08553i	−0.972655	−	0.232256i	$-0.925389\pi$
$29$	−8.04603	−	5.84578i	−1.49411	−	1.08553i	−0.521455	−	0.853279i	$-0.674611\pi$
$30$		0			0
$31$	2.09249	−	6.44002i	0.375822	−	1.15666i	−0.567101	−	0.823649i	$-0.691935\pi$
$31$	2.09249	−	6.44002i	0.375822	−	1.15666i	0.942922	−	0.333012i	$-0.108065\pi$
$32$	−1.02811			−0.181746
$33$		0			0
$34$	−0.804288			−0.137934
$35$	0.709183	−	2.18264i	0.119874	−	0.368933i
$36$		0			0
$37$	7.13520	+	5.18403i	1.17302	+	0.852249i	0.991367	−	0.131114i	$-0.0418555\pi$
$37$	7.13520	+	5.18403i	1.17302	+	0.852249i	0.181652	+	0.983363i	$0.441855\pi$
$38$	−0.996215	−	3.06604i	−0.161607	−	0.497377i
$39$		0			0
$40$	−2.17239	−	1.57833i	−0.343485	−	0.249556i
$41$	−1.47470	+	1.07143i	−0.230309	+	0.167329i	−0.696955	−	0.717115i	$-0.745462\pi$
$41$	−1.47470	+	1.07143i	−0.230309	+	0.167329i	0.466646	+	0.884444i	$0.345462\pi$
$42$		0			0
$43$	−0.620713			−0.0946578			−0.0473289	−	0.998879i	$-0.515071\pi$
$43$	−0.620713			−0.0946578			−0.0473289	+	0.998879i	$0.515071\pi$
$44$	−0.339687	−	0.500167i	−0.0512098	−	0.0754030i
$45$		0			0
$46$	−0.930836	+	2.86482i	−0.137244	+	0.422394i
$47$	−0.305816	+	0.222188i	−0.0446078	+	0.0324095i	−0.609866	−	0.792505i	$-0.708777\pi$
$47$	−0.305816	+	0.222188i	−0.0446078	+	0.0324095i	0.565258	+	0.824914i	$0.308777\pi$
$48$		0			0
$49$	−0.535571	−	1.64832i	−0.0765102	−	0.235474i
$50$	0.456498	+	1.40496i	0.0645586	+	0.198691i
$51$		0			0
$52$	0.315724	−	0.229387i	0.0437831	−	0.0318103i
$53$	−3.58246	+	11.0257i	−0.492089	+	1.51449i	0.329355	+	0.944206i	$0.393169\pi$
$53$	−3.58246	+	11.0257i	−0.492089	+	1.51449i	−0.821445	+	0.570288i	$0.806831\pi$
$54$		0			0
$55$	0.105203	−	3.31496i	0.0141855	−	0.446989i
$56$	6.16248			0.823496
$57$		0			0
$58$	−11.8861	+	8.63574i	−1.56072	+	1.13393i
$59$	−6.53518	−	4.74808i	−0.850807	−	0.618148i	0.0745611	−	0.997216i	$-0.476244\pi$
$59$	−6.53518	−	4.74808i	−0.850807	−	0.618148i	−0.925369	+	0.379069i	$0.876244\pi$
$60$		0			0
$61$	2.69647	+	8.29887i	0.345247	+	1.06256i	0.961451	+	0.274975i	$0.0886697\pi$
$61$	2.69647	+	8.29887i	0.345247	+	1.06256i	−0.616204	+	0.787587i	$0.711330\pi$
$62$	−8.09273	−	5.87971i	−1.02778	−	0.746724i
$63$		0			0
$64$	2.20760	−	6.79429i	0.275950	−	0.849286i
$65$	2.14077			0.265530
$66$		0			0
$67$	−9.75802			−1.19213			−0.596066	−	0.802936i	$-0.703270\pi$
$67$	−9.75802			−1.19213			−0.596066	+	0.802936i	$0.703270\pi$
$68$	−0.0306702	+	0.0943932i	−0.00371931	+	0.0114469i
$69$		0			0
$70$	−2.74278	−	1.99274i	−0.327824	−	0.238178i
$71$	4.63426	+	14.2628i	0.549985	+	1.69268i	0.708833	+	0.705376i	$0.249222\pi$
$71$	4.63426	+	14.2628i	0.549985	+	1.69268i	−0.158848	+	0.987303i	$0.550778\pi$
$72$		0			0
$73$	−6.35761	−	4.61907i	−0.744102	−	0.540622i	0.149891	−	0.988702i	$-0.452108\pi$
$73$	−6.35761	−	4.61907i	−0.744102	−	0.540622i	−0.893993	+	0.448081i	$0.852108\pi$
$74$	10.5405	−	7.65815i	1.22531	−	0.890242i
$75$		0			0
$76$	−0.397826			−0.0456338
$77$	4.27637	+	6.29667i	0.487337	+	0.717572i
$78$		0			0
$79$	−2.85054	+	8.77306i	−0.320711	+	0.987046i	0.652629	+	0.757678i	$0.273666\pi$
$79$	−2.85054	+	8.77306i	−0.320711	+	0.987046i	−0.973340	+	0.229369i	$0.926334\pi$
$80$	−3.50415	+	2.54591i	−0.391775	+	0.284641i
$81$		0			0
$82$	0.832118	+	2.56099i	0.0918920	+	0.282815i
$83$	2.92093	+	8.98969i	0.320613	+	0.986747i	0.973382	+	0.229189i	$0.0736074\pi$
$83$	2.92093	+	8.98969i	0.320613	+	0.986747i	−0.652769	+	0.757557i	$0.726393\pi$
$84$		0			0
$85$	−0.440466	+	0.320017i	−0.0477752	+	0.0347107i
$86$	−0.283354	+	0.872075i	−0.0305549	+	0.0940383i
$87$		0			0
$88$	8.55302	−	2.48201i	0.911754	−	0.264583i
$89$	−0.583290			−0.0618287			−0.0309143	−	0.999522i	$-0.509842\pi$
$89$	−0.583290			−0.0618287			−0.0309143	+	0.999522i	$0.509842\pi$
$90$		0			0
$91$	−3.97470	+	2.88779i	−0.416662	+	0.302722i
$92$	0.300726	+	0.218490i	0.0313529	+	0.0227792i
$93$		0			0
$94$	0.172561	+	0.531087i	0.0177983	+	0.0547774i
$95$	−1.76552	−	1.28272i	−0.181138	−	0.131605i
$96$		0			0
$97$	−1.66190	+	5.11479i	−0.168740	+	0.519328i	−0.999292	−	0.0376122i	$-0.988025\pi$
$97$	−1.66190	+	5.11479i	−0.168740	+	0.519328i	0.830552	+	0.556940i	$0.188025\pi$
$98$	−2.56031			−0.258630
$99$		0			0
$100$	0.182297			0.0182297
$101$	6.03482	−	18.5733i	0.600487	−	1.84811i	0.0752256	−	0.997167i	$-0.476032\pi$
$101$	6.03482	−	18.5733i	0.600487	−	1.84811i	0.525261	−	0.850941i	$-0.323968\pi$
$102$		0			0
$103$	−10.5223	−	7.64487i	−1.03679	−	0.753271i	−0.0671325	−	0.997744i	$-0.521385\pi$
$103$	−10.5223	−	7.64487i	−1.03679	−	0.753271i	−0.969656	+	0.244473i	$0.921385\pi$
$104$	1.77637	+	5.46710i	0.174187	+	0.536093i
$105$		0			0
$106$	13.8552	+	10.0664i	1.34574	+	0.977737i
$107$	1.59663	−	1.16002i	0.154352	−	0.112144i	−0.507928	−	0.861399i	$-0.669589\pi$
$107$	1.59663	−	1.16002i	0.154352	−	0.112144i	0.662281	+	0.749256i	$0.269589\pi$
$108$		0			0
$109$	10.6212			1.01733			0.508663	−	0.860966i	$-0.330140\pi$
$109$	10.6212			1.01733			0.508663	+	0.860966i	$0.330140\pi$
$110$	−4.60935	−	1.66108i	−0.439484	−	0.158378i
$111$		0			0
$112$	3.07173	−	9.45380i	0.290251	−	0.893300i
$113$	−13.6688	+	9.93096i	−1.28585	+	0.934226i	−0.999713	−	0.0239621i	$-0.992372\pi$
$113$	−13.6688	+	9.93096i	−1.28585	+	0.934226i	−0.286139	+	0.958188i	$0.592372\pi$
$114$		0			0
$115$	0.630110	+	1.93928i	0.0587580	+	0.180839i
$116$	0.560255	+	1.72429i	0.0520184	+	0.160096i
$117$		0			0
$118$	−9.65415	+	7.01415i	−0.888737	+	0.645705i
$119$	0.386111	−	1.18833i	0.0353948	−	0.108934i
$120$		0			0
$121$	8.47131	+	7.01690i	0.770119	+	0.637900i
$122$	12.8905			1.16705
$123$		0			0
$124$	−0.998661	+	0.725569i	−0.0896824	+	0.0651581i
$125$	0.809017	+	0.587785i	0.0723607	+	0.0525731i
$126$		0			0
$127$	1.27701	+	3.93022i	0.113316	+	0.348751i	0.991592	−	0.129403i	$-0.0413061\pi$
$127$	1.27701	+	3.93022i	0.113316	+	0.348751i	−0.878276	+	0.478154i	$0.841306\pi$
$128$	−10.2014	−	7.41178i	−0.901689	−	0.655115i
$129$		0			0
$130$	0.977260	−	3.00770i	0.0857114	−	0.263792i
$131$	0.436527			0.0381395			0.0190698	−	0.999818i	$-0.493930\pi$
$131$	0.436527			0.0381395			0.0190698	+	0.999818i	$0.493930\pi$
$132$		0			0
$133$	5.00829			0.434274
$134$	−4.45452	+	13.7096i	−0.384812	+	1.18433i
$135$		0			0
$136$	−1.18275	−	0.859317i	−0.101420	−	0.0736858i
$137$	2.43131	+	7.48281i	0.207721	+	0.639300i	0.999591	+	0.0286095i	$0.00910794\pi$
$137$	2.43131	+	7.48281i	0.207721	+	0.639300i	−0.791870	+	0.610690i	$0.790892\pi$
$138$		0			0
$139$	−14.2736	−	10.3704i	−1.21067	−	0.879604i	−0.215379	−	0.976530i	$-0.569099\pi$
$139$	−14.2736	−	10.3704i	−1.21067	−	0.879604i	−0.995292	+	0.0969265i	$0.969099\pi$
$140$	−0.338464	+	0.245909i	−0.0286055	+	0.0207831i
$141$		0			0
$142$	22.1541			1.85913
$143$	−4.35346	+	5.60887i	−0.364055	+	0.469037i
$144$		0			0
$145$	−3.07331	+	9.45867i	−0.255224	+	0.785500i
$146$	−9.39184	+	6.82357i	−0.777274	+	0.564723i
$147$		0			0
$148$	−0.496833	−	1.52910i	−0.0408394	−	0.125691i
$149$	3.38687	+	10.4237i	0.277463	+	0.853943i	0.988557	+	0.150846i	$0.0481999\pi$
$149$	3.38687	+	10.4237i	0.277463	+	0.853943i	−0.711094	+	0.703097i	$0.751800\pi$
$150$		0			0
$151$	16.2065	−	11.7747i	1.31887	−	0.958214i	0.318923	−	0.947781i	$-0.396679\pi$
$151$	16.2065	−	11.7747i	1.31887	−	0.958214i	0.999946	−	0.0104337i	$-0.00332120\pi$
$152$	1.81082	−	5.57314i	0.146877	−	0.452041i
$153$		0			0
$154$	10.7987	−	3.13370i	0.870185	−	0.252520i
$155$	−6.77143			−0.543895
$156$		0			0
$157$	−7.40629	+	5.38098i	−0.591086	+	0.429449i	−0.842704	−	0.538377i	$-0.819037\pi$
$157$	−7.40629	+	5.38098i	−0.591086	+	0.429449i	0.251618	+	0.967827i	$0.419037\pi$
$158$	11.0245	+	8.00978i	0.877063	+	0.637224i
$159$		0			0
$160$	0.317703	+	0.977789i	0.0251166	+	0.0773010i
$161$	−3.78588	−	2.75060i	−0.298369	−	0.216778i
$162$		0			0
$163$	−3.50181	+	10.7775i	−0.274283	+	0.844155i	0.715126	+	0.698996i	$0.246369\pi$
$163$	−3.50181	+	10.7775i	−0.274283	+	0.844155i	−0.989408	+	0.145159i	$0.953631\pi$
$164$	0.332296			0.0259480
$165$		0			0
$166$	13.9635			1.08378
$167$	−4.66619	+	14.3611i	−0.361081	+	1.11129i	0.591318	+	0.806438i	$0.298608\pi$
$167$	−4.66619	+	14.3611i	−0.361081	+	1.11129i	−0.952399	+	0.304854i	$0.901392\pi$
$168$		0			0
$169$	6.80957	+	4.94744i	0.523813	+	0.380572i
$170$	0.248539	+	0.764923i	0.0190620	+	0.0586669i
$171$		0			0
$172$	0.0915436	+	0.0665103i	0.00698013	+	0.00507136i
$173$	14.7760	−	10.7354i	1.12340	−	0.816195i	0.138676	−	0.990338i	$-0.455715\pi$
$173$	14.7760	−	10.7354i	1.12340	−	0.816195i	0.984720	+	0.174143i	$0.0557153\pi$
$174$		0			0
$175$	−2.29496			−0.173483
$176$	0.455671	−	14.3583i	0.0343475	−	1.08230i
$177$		0			0
$178$	−0.266271	+	0.819498i	−0.0199579	+	0.0614240i
$179$	−0.425073	+	0.308833i	−0.0317714	+	0.0230833i	−0.603558	−	0.797319i	$-0.706251\pi$
$179$	−0.425073	+	0.308833i	−0.0317714	+	0.0230833i	0.571786	+	0.820403i	$0.306251\pi$
$180$		0			0
$181$	−5.47289	−	16.8438i	−0.406797	−	1.25199i	−0.919386	−	0.393358i	$-0.871313\pi$
$181$	−5.47289	−	16.8438i	−0.406797	−	1.25199i	0.512589	−	0.858634i	$-0.328687\pi$
$182$	2.24278	+	6.90255i	0.166246	+	0.511651i
$183$		0			0
$184$	−4.42967	+	3.21834i	−0.326560	+	0.237259i
$185$	2.72540	−	8.38793i	0.200376	−	0.616693i
$186$		0			0
$187$	0.0572771	−	1.80481i	0.00418852	−	0.131981i
$188$	0.0689100			0.00502578
$189$		0			0
$190$	−2.60813	+	1.89491i	−0.189213	+	0.137472i
$191$	−13.3908	−	9.72899i	−0.968925	−	0.703965i	−0.0137185	−	0.999906i	$-0.504367\pi$
$191$	−13.3908	−	9.72899i	−0.968925	−	0.703965i	−0.955206	+	0.295941i	$0.904367\pi$
$192$		0			0
$193$	−7.57191	−	23.3040i	−0.545038	−	1.67746i	−0.720899	−	0.693040i	$-0.756271\pi$
$193$	−7.57191	−	23.3040i	−0.545038	−	1.67746i	0.175860	−	0.984415i	$-0.443729\pi$
$194$	6.42741	+	4.66979i	0.461461	+	0.335271i
$195$		0			0
$196$	−0.0976331	+	0.300484i	−0.00697379	+	0.0214631i
$197$	7.50877			0.534978			0.267489	−	0.963561i	$-0.413806\pi$
$197$	7.50877			0.534978			0.267489	+	0.963561i	$0.413806\pi$
$198$		0			0
$199$	−20.0956			−1.42454			−0.712270	−	0.701906i	$-0.752333\pi$
$199$	−20.0956			−1.42454			−0.712270	+	0.701906i	$0.752333\pi$
$200$	−0.829779	+	2.55380i	−0.0586742	+	0.180581i
$201$		0			0
$202$	−23.3398	−	16.9573i	−1.64218	−	1.19311i
$203$	−7.05313	−	21.7073i	−0.495033	−	1.52355i
$204$		0			0
$205$	1.47470	+	1.07143i	0.102997	+	0.0748320i
$206$	−15.5441	+	11.2935i	−1.08301	+	0.786852i
$207$		0			0
$208$	9.27247			0.642930
$209$	6.95110	−	2.01715i	0.480817	−	0.139529i
$210$		0			0
$211$	1.67444	−	5.15339i	0.115273	−	0.354774i	−0.876731	−	0.480981i	$-0.840280\pi$
$211$	1.67444	−	5.15339i	0.115273	−	0.354774i	0.992004	+	0.126207i	$0.0402804\pi$
$212$	1.70977	−	1.24222i	0.117427	−	0.0853159i
$213$		0			0
$214$	−0.900921	−	2.77275i	−0.0615857	−	0.189541i
$215$	0.191811	+	0.590333i	0.0130814	+	0.0402604i
$216$		0			0
$217$	12.5723	−	9.13429i	0.853462	−	0.620076i
$218$	4.84856	−	14.9223i	0.328386	−	1.01067i
$219$		0			0
$220$	−0.370718	+	0.477622i	−0.0249938	+	0.0322013i
$221$	1.16554			0.0784024
$222$		0			0
$223$	−12.7076	+	9.23259i	−0.850961	+	0.618260i	−0.925411	−	0.378965i	$-0.876280\pi$
$223$	−12.7076	+	9.23259i	−0.850961	+	0.618260i	0.0744495	+	0.997225i	$0.476280\pi$
$224$	−1.90885	−	1.38686i	−0.127541	−	0.0926636i
$225$		0			0
$226$	7.71280	+	23.7375i	0.513048	+	1.57900i
$227$	−1.19040	−	0.864876i	−0.0790096	−	0.0574038i	0.547579	−	0.836754i	$-0.315549\pi$
$227$	−1.19040	−	0.864876i	−0.0790096	−	0.0574038i	−0.626589	+	0.779350i	$0.715549\pi$
$228$		0			0
$229$	−4.93656	+	15.1932i	−0.326217	+	1.00399i	0.644671	+	0.764460i	$0.276994\pi$
$229$	−4.93656	+	15.1932i	−0.326217	+	1.00399i	−0.970888	+	0.239533i	$0.923006\pi$
$230$	3.01225			0.198622
$231$		0			0
$232$	−26.7057			−1.75331
$233$	7.92263	−	24.3833i	0.519029	−	1.59741i	−0.256802	−	0.966464i	$-0.582669\pi$
$233$	7.92263	−	24.3833i	0.519029	−	1.59741i	0.775830	−	0.630942i	$-0.217331\pi$
$234$		0			0
$235$	0.305816	+	0.222188i	0.0199492	+	0.0144940i
$236$	0.455053	+	1.40051i	0.0296214	+	0.0911653i
$237$		0			0
$238$	−1.49329	−	1.08494i	−0.0967958	−	0.0703262i
$239$	−3.38336	+	2.45816i	−0.218851	+	0.159005i	−0.691809	−	0.722080i	$-0.743186\pi$
$239$	−3.38336	+	2.45816i	−0.218851	+	0.159005i	0.472958	+	0.881085i	$0.343186\pi$
$240$		0			0
$241$	−3.29180			−0.212043			−0.106022	−	0.994364i	$-0.533811\pi$
$241$	−3.29180			−0.212043			−0.106022	+	0.994364i	$0.533811\pi$
$242$	13.7256	−	8.69862i	0.882314	−	0.559169i
$243$		0			0
$244$	0.491558	−	1.51286i	0.0314688	−	0.0968510i
$245$	−1.40214	+	1.01872i	−0.0895797	+	0.0650835i
$246$		0			0
$247$	1.44367	+	4.44315i	0.0918583	+	0.282711i
$248$	−5.61879	−	17.2929i	−0.356794	−	1.09810i
$249$		0			0
$250$	1.19513	−	0.868312i	0.0755866	−	0.0549169i
$251$	2.89382	−	8.90626i	0.182656	−	0.562158i	−0.817244	−	0.576292i	$-0.804499\pi$
$251$	2.89382	−	8.90626i	0.182656	−	0.562158i	0.999900	+	0.0141339i	$0.00449912\pi$
$252$		0			0
$253$	−6.36233	−	2.29280i	−0.399996	−	0.144147i
$254$	6.10475			0.383046
$255$		0			0
$256$	−3.51104	+	2.55092i	−0.219440	+	0.159433i
$257$	−10.1705	−	7.38928i	−0.634416	−	0.460930i	0.223511	−	0.974701i	$-0.428248\pi$
$257$	−10.1705	−	7.38928i	−0.634416	−	0.460930i	−0.857927	+	0.513771i	$0.828248\pi$
$258$		0			0
$259$	6.25470	+	19.2500i	0.388648	+	1.19614i
$260$	−0.315724	−	0.229387i	−0.0195804	−	0.0142260i
$261$		0			0
$262$	0.199274	−	0.613302i	0.0123112	−	0.0378899i
$263$	−4.82946			−0.297797			−0.148899	−	0.988852i	$-0.547573\pi$
$263$	−4.82946			−0.297797			−0.148899	+	0.988852i	$0.547573\pi$
$264$		0			0
$265$	11.5931			0.712158
$266$	2.28628	−	7.03644i	0.140181	−	0.431432i
$267$		0			0
$268$	1.43913	+	1.04559i	0.0879087	+	0.0638694i
$269$	1.61594	+	4.97335i	0.0985255	+	0.303230i	0.988156	−	0.153450i	$-0.0490383\pi$
$269$	1.61594	+	4.97335i	0.0985255	+	0.303230i	−0.889631	+	0.456680i	$0.849038\pi$
$270$		0			0
$271$	−24.5383	−	17.8281i	−1.49060	−	1.08298i	−0.973944	−	0.226789i	$-0.927177\pi$
$271$	−24.5383	−	17.8281i	−1.49060	−	1.08298i	−0.516654	−	0.856194i	$-0.672823\pi$
$272$	−1.90782	+	1.38611i	−0.115678	+	0.0840453i
$273$		0			0
$274$	11.6229			0.702167
$275$	−3.18522	+	0.924324i	−0.192076	+	0.0557388i
$276$		0			0
$277$	4.93483	−	15.1878i	0.296505	−	0.912549i	−0.686206	−	0.727407i	$-0.740725\pi$
$277$	4.93483	−	15.1878i	0.296505	−	0.912549i	0.982712	−	0.185142i	$-0.0592746\pi$
$278$	−21.0858	+	15.3197i	−1.26464	+	0.918817i
$279$		0			0
$280$	−1.90431	−	5.86087i	−0.113804	−	0.350254i
$281$	0.429741	+	1.32261i	0.0256362	+	0.0789000i	0.963056	−	0.269301i	$-0.0867927\pi$
$281$	0.429741	+	1.32261i	0.0256362	+	0.0789000i	−0.937420	+	0.348201i	$0.886793\pi$
$282$		0			0
$283$	−4.75259	+	3.45296i	−0.282512	+	0.205257i	−0.720013	−	0.693961i	$-0.755864\pi$
$283$	−4.75259	+	3.45296i	−0.282512	+	0.205257i	0.437500	+	0.899218i	$0.355864\pi$
$284$	0.844811	−	2.60006i	0.0501303	−	0.154285i
$285$		0			0
$286$	5.89287	+	8.67687i	0.348453	+	0.513074i
$287$	−4.18332			−0.246934
$288$		0			0
$289$	13.5135	−	9.81812i	0.794911	−	0.577536i
$290$	11.8861	+	8.63574i	0.697974	+	0.507108i
$291$		0			0
$292$	0.442688	+	1.36246i	0.0259064	+	0.0797317i
$293$	16.1597	+	11.7407i	0.944060	+	0.685900i	0.949395	−	0.314086i	$-0.101698\pi$
$293$	16.1597	+	11.7407i	0.944060	+	0.685900i	−0.00533421	+	0.999986i	$0.501698\pi$
$294$		0			0
$295$	−2.49622	+	7.68256i	−0.145335	+	0.447296i
$296$	23.6825			1.37652
$297$		0			0
$298$	16.1910			0.937917
$299$	1.34892	−	4.15156i	0.0780102	−	0.240091i
$300$		0			0
$301$	−1.15245	−	0.837307i	−0.0664264	−	0.0482616i
$302$	−9.14475	−	28.1446i	−0.526221	−	1.61954i
$303$		0			0
$304$	−7.64709	−	5.55593i	−0.438590	−	0.318655i
$305$	7.05944	−	5.12899i	0.404223	−	0.293685i
$306$		0			0
$307$	19.4372			1.10934			0.554671	−	0.832070i	$-0.312844\pi$
$307$	19.4372			1.10934			0.554671	+	0.832070i	$0.312844\pi$
$308$	0.0440131	−	1.38686i	0.00250788	−	0.0790238i
$309$		0			0
$310$	−3.09115	+	9.51358i	−0.175565	+	0.540335i
$311$	4.87175	−	3.53954i	0.276252	−	0.200709i	−0.441029	−	0.897493i	$-0.645386\pi$
$311$	4.87175	−	3.53954i	0.276252	−	0.200709i	0.717281	+	0.696784i	$0.245386\pi$
$312$		0			0
$313$	−1.57856	−	4.85831i	−0.0892256	−	0.274608i	0.896480	−	0.443084i	$-0.146116\pi$
$313$	−1.57856	−	4.85831i	−0.0892256	−	0.274608i	−0.985706	+	0.168476i	$0.946116\pi$
$314$	4.17910	+	12.8619i	0.235840	+	0.725841i
$315$		0			0
$316$	1.36045	−	0.988424i	0.0765312	−	0.0556032i
$317$	−4.22699	+	13.0093i	−0.237411	+	0.730677i	0.759381	+	0.650646i	$0.225502\pi$
$317$	−4.22699	+	13.0093i	−0.237411	+	0.730677i	−0.996792	+	0.0800306i	$0.974498\pi$
$318$		0			0
$319$	−18.5320	−	27.2872i	−1.03760	−	1.52779i
$320$	−7.14394			−0.399358
$321$		0			0
$322$	−5.59273	+	4.06336i	−0.311671	+	0.226442i
$323$	−0.961227	−	0.698373i	−0.0534841	−	0.0388585i
$324$		0			0
$325$	−0.661536	−	2.03600i	−0.0366954	−	0.112937i
$326$	13.5433	+	9.83978i	0.750094	+	0.544975i
$327$		0			0
$328$	−1.51254	+	4.65513i	−0.0835162	+	0.257036i
$329$	−0.867517			−0.0478278
$330$		0			0
$331$	11.4695			0.630418			0.315209	−	0.949022i	$-0.397925\pi$
$331$	11.4695			0.630418			0.315209	+	0.949022i	$0.397925\pi$
$332$	0.532477	−	1.63879i	0.0292234	−	0.0899405i
$333$		0			0
$334$	18.0466	+	13.1116i	0.987465	+	0.717435i
$335$	3.01539	+	9.28043i	0.164749	+	0.507044i
$336$		0			0
$337$	−3.04517	−	2.21245i	−0.165881	−	0.120520i	0.501748	−	0.865014i	$-0.332691\pi$
$337$	−3.04517	−	2.21245i	−0.165881	−	0.120520i	−0.667629	+	0.744494i	$0.732691\pi$
$338$	10.0595	−	7.30865i	0.547165	−	0.397538i
$339$		0			0
$340$	0.0992509			0.00538264
$341$	13.7703	−	17.7413i	0.745706	−	0.960744i
$342$		0			0
$343$	6.19339	−	19.0613i	0.334412	−	1.02921i
$344$	−1.34843	+	0.979691i	−0.0727024	+	0.0528214i
$345$		0			0
$346$	−8.33754	−	25.6603i	−0.448229	−	1.37951i
$347$	0.122365	+	0.376600i	0.00656888	+	0.0202169i	0.954287	−	0.298891i	$-0.0966167\pi$
$347$	0.122365	+	0.376600i	0.00656888	+	0.0202169i	−0.947718	+	0.319108i	$0.896617\pi$
$348$		0			0
$349$	10.6554	−	7.74158i	0.570369	−	0.414398i	−0.264870	−	0.964284i	$-0.585329\pi$
$349$	10.6554	−	7.74158i	0.570369	−	0.414398i	0.835239	+	0.549887i	$0.185329\pi$
$350$	−1.04765	+	3.22433i	−0.0559991	+	0.172347i
$351$		0			0
$352$	−3.20790	−	1.15604i	−0.170982	−	0.0616170i
$353$	−11.3853			−0.605977			−0.302989	−	0.952994i	$-0.597984\pi$
$353$	−11.3853			−0.605977			−0.302989	+	0.952994i	$0.597984\pi$
$354$		0			0
$355$	12.1326	−	8.81488i	0.643934	−	0.467845i
$356$	0.0860245	+	0.0625005i	0.00455929	+	0.00331252i
$357$		0			0
$358$	0.239853	+	0.738191i	0.0126766	+	0.0390146i
$359$	−11.6241	−	8.44543i	−0.613499	−	0.445733i	0.237146	−	0.971474i	$-0.423788\pi$
$359$	−11.6241	−	8.44543i	−0.613499	−	0.445733i	−0.850645	+	0.525741i	$0.823788\pi$
$360$		0			0
$361$	−4.39965	+	13.5407i	−0.231561	+	0.712671i
$362$	−26.1632			−1.37511
$363$		0			0
$364$	0.895625			0.0469435
$365$	−2.42839	+	7.47382i	−0.127108	+	0.391197i
$366$		0			0
$367$	21.2480	+	15.4376i	1.10914	+	0.805836i	0.982528	−	0.186117i	$-0.0595903\pi$
$367$	21.2480	+	15.4376i	1.10914	+	0.805836i	0.126610	+	0.991953i	$0.459590\pi$
$368$	2.72923	+	8.39972i	0.142271	+	0.437865i
$369$		0			0
$370$	−10.5405	−	7.65815i	−0.547977	−	0.398128i
$371$	−21.5245	+	15.6384i	−1.11750	+	0.811908i
$372$		0			0
$373$	21.8951			1.13368			0.566842	−	0.823827i	$-0.308165\pi$
$373$	21.8951			1.13368			0.566842	+	0.823827i	$0.308165\pi$
$374$	−2.50954	−	0.904367i	−0.129765	−	0.0467637i
$375$		0			0
$376$	−0.313664	+	0.965358i	−0.0161760	+	0.0497845i
$377$	17.2247	−	12.5145i	0.887119	−	0.644529i
$378$		0			0
$379$	7.89836	+	24.3087i	0.405711	+	1.24865i	0.920300	+	0.391214i	$0.127945\pi$
$379$	7.89836	+	24.3087i	0.405711	+	1.24865i	−0.514588	+	0.857437i	$0.672055\pi$
$380$	0.122935	+	0.378355i	0.00630644	+	0.0194092i
$381$		0			0
$382$	−19.7817	+	14.3722i	−1.01212	+	0.735348i
$383$	−5.88737	+	18.1195i	−0.300831	+	0.925862i	0.680370	+	0.732869i	$0.261819\pi$
$383$	−5.88737	+	18.1195i	−0.300831	+	0.925862i	−0.981200	+	0.192992i	$0.938181\pi$
$384$		0			0
$385$	4.66702	−	6.01285i	0.237853	−	0.306443i
$386$	−36.1976			−1.84241
$387$		0			0
$388$	0.793157	−	0.576262i	0.0402664	−	0.0292553i
$389$	13.2618	+	9.63528i	0.672401	+	0.488528i	0.870828	−	0.491587i	$-0.163583\pi$
$389$	13.2618	+	9.63528i	0.672401	+	0.488528i	−0.198427	+	0.980116i	$0.563583\pi$
$390$		0			0
$391$	0.343061	+	1.05583i	0.0173493	+	0.0533957i
$392$	−3.76506	−	2.73548i	−0.190164	−	0.138163i
$393$		0			0
$394$	3.42774	−	10.5495i	0.172687	−	0.531476i
$395$	9.22454			0.464137
$396$		0			0
$397$	30.9826			1.55497			0.777485	−	0.628901i	$-0.216495\pi$
$397$	30.9826			1.55497			0.777485	+	0.628901i	$0.216495\pi$
$398$	−9.17361	+	28.2335i	−0.459832	+	1.41522i
$399$		0			0
$400$	3.50415	+	2.54591i	0.175207	+	0.127296i
$401$	1.96723	+	6.05453i	0.0982390	+	0.302349i	0.988084	−	0.153914i	$-0.0491878\pi$
$401$	1.96723	+	6.05453i	0.0982390	+	0.302349i	−0.889845	+	0.456262i	$0.849188\pi$
$402$		0			0
$403$	11.7276	+	8.52060i	0.584193	+	0.424441i
$404$	−2.88018	+	2.09257i	−0.143294	+	0.104109i
$405$		0			0
$406$	−33.7176			−1.67338
$407$	16.4342	+	24.1982i	0.814612	+	1.19946i
$408$		0			0
$409$	−1.93715	+	5.96193i	−0.0957858	+	0.294798i	−0.987458	−	0.157884i	$-0.949533\pi$
$409$	−1.93715	+	5.96193i	−0.0957858	+	0.294798i	0.891672	+	0.452682i	$0.149533\pi$
$410$	2.17851	−	1.58278i	0.107589	−	0.0781680i
$411$		0			0
$412$	0.732678	+	2.25495i	0.0360965	+	0.111093i
$413$	−5.72872	−	17.6312i	−0.281892	−	0.867574i
$414$		0			0
$415$	7.64709	−	5.55593i	0.375381	−	0.272730i
$416$	0.680130	−	2.09323i	0.0333461	−	0.102629i
$417$		0			0
$418$	0.339154	−	10.6868i	0.0165886	−	0.522710i
$419$	−3.90332			−0.190689			−0.0953447	−	0.995444i	$-0.530395\pi$
$419$	−3.90332			−0.190689			−0.0953447	+	0.995444i	$0.530395\pi$
$420$		0			0
$421$	−14.0539	+	10.2107i	−0.684944	+	0.497641i	−0.874994	−	0.484134i	$-0.839135\pi$
$421$	−14.0539	+	10.2107i	−0.684944	+	0.497641i	0.190050	+	0.981774i	$0.439135\pi$
$422$	−6.47592	−	4.70503i	−0.315243	−	0.229037i
$423$		0			0
$424$	9.61970	+	29.6064i	0.467174	+	1.43781i
$425$	0.440466	+	0.320017i	0.0213657	+	0.0155231i
$426$		0			0
$427$	−6.18829	+	19.0456i	−0.299473	+	0.921682i
$428$	−0.359772			−0.0173902
$429$		0			0
$430$	0.916954			0.0442194
$431$	2.17440	−	6.69212i	0.104737	−	0.322348i	−0.884931	−	0.465721i	$-0.845795\pi$
$431$	2.17440	−	6.69212i	0.104737	−	0.322348i	0.989669	+	0.143373i	$0.0457949\pi$
$432$		0			0
$433$	−2.22665	−	1.61776i	−0.107006	−	0.0777445i	0.532995	−	0.846118i	$-0.321066\pi$
$433$	−2.22665	−	1.61776i	−0.107006	−	0.0777445i	−0.640002	+	0.768374i	$0.721066\pi$
$434$	−7.09407	−	21.8333i	−0.340526	−	1.04803i
$435$		0			0
$436$	−1.56643	−	1.13808i	−0.0750184	−	0.0545041i
$437$	−3.60002	+	2.61557i	−0.172212	+	0.125120i
$438$		0			0
$439$	−2.73703			−0.130631			−0.0653157	−	0.997865i	$-0.520805\pi$
$439$	−2.73703			−0.130631			−0.0653157	+	0.997865i	$0.520805\pi$
$440$	−5.00356	−	7.36742i	−0.238535	−	0.351228i
$441$		0			0
$442$	0.532065	−	1.63753i	0.0253078	−	0.0778893i
$443$	8.98348	−	6.52688i	0.426818	−	0.310102i	−0.353557	−	0.935413i	$-0.615028\pi$
$443$	8.98348	−	6.52688i	0.426818	−	0.310102i	0.780375	+	0.625311i	$0.215028\pi$
$444$		0			0
$445$	0.180247	+	0.554742i	0.00854451	+	0.0262973i
$446$	7.17041	+	22.0683i	0.339529	+	1.04496i
$447$		0			0
$448$	13.2639	−	9.63679i	0.626660	−	0.455295i
$449$	−4.58174	+	14.1012i	−0.216226	+	0.665475i	0.782838	+	0.622225i	$0.213771\pi$
$449$	−4.58174	+	14.1012i	−0.216226	+	0.665475i	−0.999064	+	0.0432498i	$0.986229\pi$
$450$		0			0
$451$	−5.80610	+	1.68488i	−0.273399	+	0.0793380i
$452$	3.08001			0.144872
$453$		0			0
$454$	−1.75853	+	1.27765i	−0.0825319	+	0.0599629i
$455$	3.97470	+	2.88779i	0.186337	+	0.135382i
$456$		0			0
$457$	9.01788	+	27.7542i	0.421838	+	1.29829i	0.905989	+	0.423301i	$0.139129\pi$
$457$	9.01788	+	27.7542i	0.421838	+	1.29829i	−0.484151	+	0.874985i	$0.660871\pi$
$458$	19.0922	+	13.8713i	0.892122	+	0.648165i
$459$		0			0
$460$	0.114867	−	0.353525i	0.00535571	−	0.0164832i
$461$	31.1798			1.45219			0.726094	−	0.687595i	$-0.241334\pi$
$461$	31.1798			1.45219			0.726094	+	0.687595i	$0.241334\pi$
$462$		0			0
$463$	41.1642			1.91306			0.956531	−	0.291631i	$-0.0941978\pi$
$463$	41.1642			1.91306			0.956531	+	0.291631i	$0.0941978\pi$
$464$	−13.3116	+	40.9689i	−0.617976	+	1.90194i
$465$		0			0
$466$	−30.6409	−	22.2619i	−1.41941	−	1.03126i
$467$	−11.9826	−	36.8788i	−0.554490	−	1.70655i	−0.697285	−	0.716794i	$-0.745609\pi$
$467$	−11.9826	−	36.8788i	−0.554490	−	1.70655i	0.142795	−	0.989752i	$-0.454391\pi$
$468$		0			0
$469$	−18.1174	−	13.1630i	−0.836582	−	0.607812i
$470$	0.451769	−	0.328230i	0.0208386	−	0.0151401i
$471$		0			0
$472$	−21.6910			−0.998409
$473$	−1.93675	−	0.697949i	−0.0890518	−	0.0320917i
$474$		0			0
$475$	−0.674367	+	2.07549i	−0.0309421	+	0.0952299i
$476$	−0.184276	+	0.133884i	−0.00844626	+	0.00613656i
$477$		0			0
$478$	1.90911	+	5.87562i	0.0873205	+	0.268745i
$479$	−5.15675	−	15.8708i	−0.235618	−	0.725158i	−0.997039	−	0.0768997i	$-0.975498\pi$
$479$	−5.15675	−	15.8708i	−0.235618	−	0.725158i	0.761421	−	0.648258i	$-0.224502\pi$
$480$		0			0
$481$	−15.2748	+	11.0978i	−0.696473	+	0.506017i
$482$	−1.50270	+	4.62483i	−0.0684461	+	0.210655i
$483$		0			0
$484$	−0.497489	−	1.94258i	−0.0226131	−	0.0882989i
$485$	5.37801			0.244203
$486$		0			0
$487$	−2.03220	+	1.47648i	−0.0920877	+	0.0669056i	−0.632876	−	0.774253i	$-0.718126\pi$
$487$	−2.03220	+	1.47648i	−0.0920877	+	0.0669056i	0.540789	+	0.841158i	$0.318126\pi$
$488$	18.9562	+	13.7725i	0.858105	+	0.623450i
$489$		0			0
$490$	0.791178	+	2.43500i	0.0357418	+	0.110002i
$491$	−6.11508	−	4.44286i	−0.275970	−	0.200504i	0.441188	−	0.897415i	$-0.354557\pi$
$491$	−6.11508	−	4.44286i	−0.275970	−	0.200504i	−0.717158	+	0.696911i	$0.754557\pi$
$492$		0			0
$493$	−1.67325	+	5.14974i	−0.0753594	+	0.231932i
$494$	6.90147			0.310512
$495$		0			0
$496$	−29.3295			−1.31693
$497$	−10.6354	+	32.7325i	−0.477065	+	1.46825i
$498$		0			0
$499$	−13.5886	−	9.87269i	−0.608309	−	0.441962i	0.240510	−	0.970647i	$-0.422685\pi$
$499$	−13.5886	−	9.87269i	−0.608309	−	0.441962i	−0.848818	+	0.528685i	$0.822685\pi$
$500$	−0.0563329	−	0.173375i	−0.00251928	−	0.00775356i
$501$		0			0
$502$	−11.1919	−	8.13139i	−0.499519	−	0.362922i
$503$	6.17489	−	4.48632i	0.275325	−	0.200035i	−0.441551	−	0.897236i	$-0.645572\pi$
$503$	6.17489	−	4.48632i	0.275325	−	0.200035i	0.716876	+	0.697201i	$0.245572\pi$
$504$		0			0
$505$	−19.5291			−0.869032
$506$	−6.12569	+	7.89215i	−0.272320	+	0.350849i
$507$		0			0
$508$	0.232795	−	0.716469i	0.0103286	−	0.0317882i
$509$	26.6198	−	19.3404i	1.17990	−	0.857249i	0.187741	−	0.982219i	$-0.439883\pi$
$509$	26.6198	−	19.3404i	1.17990	−	0.857249i	0.992161	+	0.124970i	$0.0398834\pi$
$510$		0			0
$511$	−5.57307	−	17.1521i	−0.246538	−	0.758766i
$512$	−5.81206	−	17.8877i	−0.256859	−	0.790531i
$513$		0			0
$514$	−15.0244	+	10.9159i	−0.662699	+	0.481479i
$515$	−4.01914	+	12.3697i	−0.177105	+	0.545072i
$516$		0			0
$517$	−1.20404	+	0.349403i	−0.0529537	+	0.0153667i
$518$	29.9007			1.31376
$519$		0			0
$520$	4.65059	−	3.37885i	0.203942	−	0.148173i
$521$	0.645559	+	0.469026i	0.0282824	+	0.0205484i	0.601837	−	0.798619i	$-0.294436\pi$
$521$	0.645559	+	0.469026i	0.0282824	+	0.0205484i	−0.573554	+	0.819168i	$0.694436\pi$
$522$		0			0
$523$	1.33036	+	4.09443i	0.0581727	+	0.179037i	0.975920	−	0.218127i	$-0.0699945\pi$
$523$	1.33036	+	4.09443i	0.0581727	+	0.179037i	−0.917748	+	0.397164i	$0.869995\pi$
$524$	−0.0643796	−	0.0467745i	−0.00281244	−	0.00204336i
$525$		0			0
$526$	−2.20464	+	6.78519i	−0.0961270	+	0.295848i
$527$	−3.68668			−0.160594
$528$		0			0
$529$	−18.8422			−0.819224
$530$	5.29223	−	16.2878i	0.229880	−	0.707497i
$531$		0			0
$532$	−0.738630	−	0.536646i	−0.0320237	−	0.0232666i
$533$	−1.20586	−	3.71127i	−0.0522318	−	0.160753i
$534$		0			0
$535$	−1.59663	−	1.16002i	−0.0690285	−	0.0501521i
$536$	−21.1982	+	15.4014i	−0.915623	+	0.665239i
$537$		0			0
$538$	7.72502			0.333049
$539$	0.182331	−	5.74530i	0.00785357	−	0.247468i
$540$		0			0
$541$	−7.01720	+	21.5967i	−0.301693	+	0.928516i	0.679198	+	0.733955i	$0.262328\pi$
$541$	−7.01720	+	21.5967i	−0.301693	+	0.928516i	−0.980891	+	0.194560i	$0.937672\pi$
$542$	−36.2495	+	26.3368i	−1.55705	+	1.13126i
$543$		0			0
$544$	0.172972	+	0.532353i	0.00741611	+	0.0228245i
$545$	−3.28213	−	10.1014i	−0.140591	−	0.432695i
$546$		0			0
$547$	−26.0140	+	18.9003i	−1.11228	+	0.808117i	−0.983021	−	0.183494i	$-0.941259\pi$
$547$	−26.0140	+	18.9003i	−1.11228	+	0.808117i	−0.129257	+	0.991611i	$0.541259\pi$
$548$	0.443221	−	1.36409i	0.0189335	−	0.0582712i
$549$		0			0
$550$	−0.155412	+	4.89705i	−0.00662678	+	0.208811i
$551$	−21.7039			−0.924617
$552$		0			0
$553$	−17.1269	+	12.4434i	−0.728309	+	0.529147i
$554$	−19.0855	−	13.8665i	−0.810867	−	0.589129i
$555$		0			0
$556$	0.993889	+	3.05888i	0.0421503	+	0.129725i
$557$	30.5122	+	22.1684i	1.29284	+	0.939306i	0.999859	−	0.0168116i	$-0.00535155\pi$
$557$	30.5122	+	22.1684i	1.29284	+	0.939306i	0.292985	+	0.956117i	$0.405352\pi$
$558$		0			0
$559$	0.410623	−	1.26377i	0.0173675	−	0.0534517i
$560$	−9.94032			−0.420055
$561$		0			0
$562$	2.05438			0.0866588
$563$	−6.79438	+	20.9109i	−0.286349	+	0.881291i	0.699642	+	0.714493i	$0.253343\pi$
$563$	−6.79438	+	20.9109i	−0.286349	+	0.881291i	−0.985991	+	0.166798i	$0.946657\pi$
$564$		0			0
$565$	13.6688	+	9.93096i	0.575050	+	0.417799i
$566$	2.68171	+	8.25347i	0.112721	+	0.346919i
$567$		0			0
$568$	32.5788	+	23.6699i	1.36698	+	0.993166i
$569$	−16.5690	+	12.0381i	−0.694609	+	0.504663i	−0.878172	−	0.478345i	$-0.841237\pi$
$569$	−16.5690	+	12.0381i	−0.694609	+	0.504663i	0.183563	+	0.983008i	$0.441237\pi$
$570$		0			0
$571$	17.4373			0.729728			0.364864	−	0.931061i	$-0.381116\pi$
$571$	17.4373			0.729728			0.364864	+	0.931061i	$0.381116\pi$
$572$	1.24305	−	0.360724i	0.0519747	−	0.0150826i
$573$		0			0
$574$	−1.90968	+	5.87739i	−0.0797085	+	0.245317i
$575$	1.64965	−	1.19854i	0.0687951	−	0.0499826i
$576$		0			0
$577$	−10.2701	−	31.6082i	−0.427551	−	1.31587i	−0.900530	−	0.434794i	$-0.856821\pi$
$577$	−10.2701	−	31.6082i	−0.427551	−	1.31587i	0.472978	−	0.881074i	$-0.343179\pi$
$578$	−7.62516	−	23.4678i	−0.317165	−	0.976133i
$579$		0			0
$580$	1.46677	−	1.06567i	0.0609042	−	0.0442495i
$581$	−6.70342	+	20.6310i	−0.278105	+	0.855918i
$582$		0			0
$583$	−23.5756	+	30.3741i	−0.976403	+	1.25797i
$584$	−21.1016			−0.873192
$585$		0			0
$586$	23.8721	−	17.3441i	0.986147	−	0.716478i
$587$	−34.6222	−	25.1545i	−1.42901	−	1.03824i	−0.990200	−	0.139657i	$-0.955400\pi$
$587$	−34.6222	−	25.1545i	−1.42901	−	1.03824i	−0.438811	−	0.898580i	$-0.644600\pi$
$588$		0			0
$589$	−4.56643	−	14.0540i	−0.188156	−	0.579086i
$590$	9.65415	+	7.01415i	0.397455	+	0.288768i
$591$		0			0
$592$	11.8047	−	36.3312i	0.485171	−	1.49320i
$593$	42.6570			1.75171			0.875857	−	0.482570i	$-0.160297\pi$
$593$	42.6570			1.75171			0.875857	+	0.482570i	$0.160297\pi$
$594$		0			0
$595$	−1.24948			−0.0512238
$596$	0.617416	−	1.90021i	0.0252903	−	0.0778357i
$597$		0			0
$598$	−5.21698	−	3.79036i	−0.213338	−	0.154999i
$599$	−8.75148	−	26.9343i	−0.357576	−	1.10051i	−0.954501	−	0.298208i	$-0.903611\pi$
$599$	−8.75148	−	26.9343i	−0.357576	−	1.10051i	0.596925	−	0.802297i	$-0.296389\pi$
$600$		0			0
$601$	6.19268	+	4.49925i	0.252605	+	0.183528i	0.706880	−	0.707333i	$-0.250102\pi$
$601$	6.19268	+	4.49925i	0.252605	+	0.183528i	−0.454276	+	0.890861i	$0.650102\pi$
$602$	−1.70248	+	1.23692i	−0.0693877	+	0.0504131i
$603$		0			0
$604$	−3.65184			−0.148591
$605$	4.05569	−	10.2250i	0.164887	−	0.415707i
$606$		0			0
$607$	3.58415	−	11.0309i	0.145476	−	0.447730i	−0.851596	−	0.524199i	$-0.824365\pi$
$607$	3.58415	−	11.0309i	0.145476	−	0.447730i	0.997072	+	0.0764693i	$0.0243647\pi$
$608$	−1.81514	+	1.31878i	−0.0736137	+	0.0534835i
$609$		0			0
$610$	−3.98338	−	12.2596i	−0.161282	−	0.496376i
$611$	−0.250066	−	0.769625i	−0.0101166	−	0.0311357i
$612$		0			0
$613$	25.9757	−	18.8725i	1.04915	−	0.762251i	0.0770985	−	0.997023i	$-0.475434\pi$
$613$	25.9757	−	18.8725i	1.04915	−	0.762251i	0.972050	+	0.234772i	$0.0754344\pi$
$614$	8.87307	−	27.3085i	0.358088	−	1.10208i
$615$		0			0
$616$	19.2282	+	6.92929i	0.774725	+	0.279189i
$617$	18.7392			0.754414			0.377207	−	0.926129i	$-0.376885\pi$
$617$	18.7392			0.754414			0.377207	+	0.926129i	$0.376885\pi$
$618$		0			0
$619$	31.6002	−	22.9589i	1.27012	−	0.922796i	0.270912	−	0.962604i	$-0.412675\pi$
$619$	31.6002	−	22.9589i	1.27012	−	0.922796i	0.999207	+	0.0398085i	$0.0126748\pi$
$620$	0.998661	+	0.725569i	0.0401072	+	0.0291396i
$621$		0			0
$622$	−2.74895	−	8.46040i	−0.110223	−	0.339231i
$623$	−1.08297	−	0.786827i	−0.0433884	−	0.0315236i
$624$		0			0
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$	−7.54633			−0.301612
$627$		0			0
$628$	1.66887			0.0665952
$629$	1.48383	−	4.56677i	0.0591644	−	0.182089i
$630$		0			0
$631$	−36.4512	−	26.4833i	−1.45110	−	1.05428i	−0.985573	−	0.169249i	$-0.945866\pi$
$631$	−36.4512	−	26.4833i	−1.45110	−	1.05428i	−0.465524	−	0.885035i	$-0.654134\pi$
$632$	7.65433	+	23.5576i	0.304473	+	0.937071i
$633$		0			0
$634$	16.3479	+	11.8775i	0.649260	+	0.471715i
$635$	3.34325	−	2.42901i	0.132673	−	0.0963924i
$636$		0			0
$637$	3.71027			0.147006
$638$	−46.7972	+	13.5802i	−1.85272	+	0.537644i
$639$		0			0
$640$	−3.89660	+	11.9925i	−0.154027	+	0.474046i
$641$	20.9477	−	15.2194i	0.827384	−	0.601130i	−0.0914341	−	0.995811i	$-0.529145\pi$
$641$	20.9477	−	15.2194i	0.827384	−	0.601130i	0.918818	+	0.394682i	$0.129145\pi$
$642$		0			0
$643$	9.46770	+	29.1386i	0.373370	+	1.14911i	0.944572	+	0.328304i	$0.106477\pi$
$643$	9.46770	+	29.1386i	0.373370	+	1.14911i	−0.571202	+	0.820809i	$0.693523\pi$
$644$	0.263616	+	0.811326i	0.0103879	+	0.0319707i
$645$		0			0
$646$	−1.41998	+	1.03168i	−0.0558685	+	0.0405908i
$647$	4.66875	−	14.3689i	0.183547	−	0.564901i	−0.816373	−	0.577525i	$-0.804019\pi$
$647$	4.66875	−	14.3689i	0.183547	−	0.564901i	0.999920	+	0.0126243i	$0.00401854\pi$
$648$		0			0
$649$	−15.0522	−	22.1633i	−0.590849	−	0.869987i
$650$	−3.16248			−0.124043
$651$		0			0
$652$	1.67127	−	1.21425i	0.0654521	−	0.0475537i
$653$	−4.23543	−	3.07722i	−0.165745	−	0.120421i	0.501821	−	0.864972i	$-0.332664\pi$
$653$	−4.23543	−	3.07722i	−0.165745	−	0.120421i	−0.667566	+	0.744551i	$0.732664\pi$
$654$		0			0
$655$	−0.134894	−	0.415162i	−0.00527075	−	0.0162217i
$656$	6.38745	+	4.64075i	0.249388	+	0.181191i
$657$		0			0
$658$	−0.396020	+	1.21882i	−0.0154385	+	0.0475147i
$659$	−14.9207			−0.581229			−0.290615	−	0.956840i	$-0.593860\pi$
$659$	−14.9207			−0.581229			−0.290615	+	0.956840i	$0.593860\pi$
$660$		0			0
$661$	45.7403			1.77909			0.889545	−	0.456847i	$-0.151021\pi$
$661$	45.7403			1.77909			0.889545	+	0.456847i	$0.151021\pi$
$662$	5.23579	−	16.1141i	0.203495	−	0.626292i
$663$		0			0
$664$	20.5341	+	14.9189i	0.796878	+	0.578966i
$665$	−1.54765	−	4.76317i	−0.0600152	−	0.184708i
$666$		0			0
$667$	16.4065	+	11.9200i	0.635261	+	0.461544i
$668$	2.22699	−	1.61800i	0.0861647	−	0.0626023i
$669$		0			0
$670$	14.4151			0.556905
$671$	−0.917993	+	28.9261i	−0.0354387	+	1.11668i
$672$		0			0
$673$	6.52294	−	20.0755i	0.251441	−	0.773855i	−0.743069	−	0.669214i	$-0.766631\pi$
$673$	6.52294	−	20.0755i	0.251441	−	0.773855i	0.994510	−	0.104641i	$-0.0333693\pi$
$674$	−4.49852	+	3.26836i	−0.173276	+	0.125893i
$675$		0			0
$676$	−0.474159	−	1.45931i	−0.0182369	−	0.0561273i
$677$	13.6182	+	41.9125i	0.523390	+	1.61083i	0.767477	+	0.641077i	$0.221512\pi$
$677$	13.6182	+	41.9125i	0.523390	+	1.61083i	−0.244087	+	0.969753i	$0.578488\pi$
$678$		0			0
$679$	−9.98516	+	7.25464i	−0.383195	+	0.278408i
$680$	−0.451769	+	1.39040i	−0.0173246	+	0.0533195i
$681$		0			0
$682$	−18.6396	−	27.4456i	−0.713748	−	1.05095i
$683$	42.5318			1.62743			0.813717	−	0.581261i	$-0.197440\pi$
$683$	42.5318			1.62743			0.813717	+	0.581261i	$0.197440\pi$
$684$		0			0
$685$	6.36526	−	4.62463i	0.243204	−	0.176698i
$686$	−23.9531	−	17.4029i	−0.914532	−	0.664446i
$687$		0			0
$688$	0.830802	+	2.55694i	0.0316740	+	0.0974826i
$689$	−20.0783	−	14.5878i	−0.764924	−	0.555750i
$690$		0			0
$691$	−1.77552	+	5.46449i	−0.0675439	+	0.207879i	−0.979132	−	0.203227i	$-0.934857\pi$
$691$	−1.77552	+	5.46449i	−0.0675439	+	0.207879i	0.911588	+	0.411105i	$0.134857\pi$
$692$	−3.32949			−0.126568
$693$		0			0
$694$	0.584966			0.0222050
$695$	−5.45203	+	16.7796i	−0.206807	+	0.636487i
$696$		0			0
$697$	0.802893	+	0.583336i	0.0304117	+	0.0220954i
$698$	−6.01244	−	18.5044i	−0.227574	−	0.700401i
$699$		0			0
$700$	0.338464	+	0.245909i	0.0127928	+	0.00929448i
$701$	−0.983718	+	0.714713i	−0.0371545	+	0.0269943i	−0.606208	−	0.795307i	$-0.707310\pi$
$701$	−0.983718	+	0.714713i	−0.0371545	+	0.0269943i	0.569053	+	0.822301i	$0.307310\pi$
$702$		0			0
$703$	19.2470			0.725913
$704$	14.5279	−	18.7173i	0.547540	−	0.705433i
$705$		0			0
$706$	−5.19736	+	15.9958i	−0.195605	+	0.602011i
$707$	36.2589	−	26.3437i	1.36366	−	0.990755i
$708$		0			0
$709$	−8.16115	−	25.1174i	−0.306498	−	0.943305i	−0.979114	−	0.203313i	$-0.934829\pi$
$709$	−8.16115	−	25.1174i	−0.306498	−	0.943305i	0.672615	−	0.739992i	$-0.265171\pi$
$710$	−6.84600	−	21.0698i	−0.256926	−	0.790736i
$711$		0			0
$712$	−1.26713	+	0.920626i	−0.0474878	+	0.0345019i
$713$	−4.26675	+	13.1317i	−0.159791	+	0.491786i
$714$		0			0
$715$	6.67965	+	2.40715i	0.249805	+	0.0900224i
$716$	0.0957823			0.00357955
$717$		0			0
$718$	−17.1719	+	12.4761i	−0.640849	+	0.465604i
$719$	40.0007	+	29.0622i	1.49177	+	1.08384i	0.973518	+	0.228611i	$0.0734183\pi$
$719$	40.0007	+	29.0622i	1.49177	+	1.08384i	0.518255	+	0.855226i	$0.326582\pi$
$720$		0			0
$721$	−9.22379	−	28.3879i	−0.343512	−	1.05722i
$722$	17.0157	+	12.3627i	0.633260	+	0.460090i
$723$		0			0
$724$	−0.997692	+	3.07058i	−0.0370789	+	0.114117i
$725$	9.94544			0.369364
$726$		0			0
$727$	−39.2447			−1.45551			−0.727753	−	0.685839i	$-0.759435\pi$
$727$	−39.2447			−1.45551			−0.727753	+	0.685839i	$0.759435\pi$
$728$	−4.07670	+	12.5468i	−0.151093	+	0.465015i
$729$		0			0
$730$	9.39184	+	6.82357i	0.347608	+	0.252552i
$731$	0.104431	+	0.321404i	0.00386250	+	0.0118876i
$732$		0			0
$733$	−4.20624	−	3.05601i	−0.155361	−	0.112876i	0.507389	−	0.861717i	$-0.330611\pi$
$733$	−4.20624	−	3.05601i	−0.155361	−	0.112876i	−0.662750	+	0.748841i	$0.730611\pi$
$734$	31.3888	−	22.8053i	1.15858	−	0.841760i
$735$		0			0
$736$	2.09639			0.0772740
$737$	−30.4470	−	10.9722i	−1.12153	−	0.404167i
$738$		0			0
$739$	8.96428	−	27.5892i	0.329757	−	1.01489i	−0.639491	−	0.768799i	$-0.720855\pi$
$739$	8.96428	−	27.5892i	0.329757	−	1.01489i	0.969248	−	0.246088i	$-0.0791451\pi$
$740$	−1.30073	+	0.945033i	−0.0478156	+	0.0347401i
$741$		0			0
$742$	12.1455	+	37.3799i	0.445874	+	1.37226i
$743$	−2.62874	−	8.09042i	−0.0964390	−	0.296809i	0.891187	−	0.453636i	$-0.149873\pi$
$743$	−2.62874	−	8.09042i	−0.0964390	−	0.296809i	−0.987626	+	0.156827i	$0.949873\pi$
$744$		0			0
$745$	8.86693	−	6.44220i	0.324859	−	0.236024i
$746$	9.99506	−	30.7616i	0.365945	−	1.12626i
$747$		0			0
$748$	−0.201836	+	0.260039i	−0.00737985	+	0.00950798i
$749$	4.52922			0.165494
$750$		0			0
$751$	28.4006	−	20.6343i	1.03635	−	0.752955i	0.0667831	−	0.997768i	$-0.478726\pi$
$751$	28.4006	−	20.6343i	1.03635	−	0.752955i	0.969570	+	0.244813i	$0.0787264\pi$
$752$	1.32460	+	0.962377i	0.0483032	+	0.0350943i
$753$		0			0
$754$	−9.71928	−	29.9129i	−0.353955	−	1.08936i
$755$	−16.2065	−	11.7747i	−0.589816	−	0.428526i
$756$		0			0
$757$	−2.21972	+	6.83159i	−0.0806771	+	0.248298i	−0.983257	−	0.182224i	$-0.941671\pi$
$757$	−2.21972	+	6.83159i	−0.0806771	+	0.248298i	0.902580	+	0.430522i	$0.141671\pi$
$758$	37.7582			1.37144
$759$		0			0
$760$	−5.85995			−0.212563
$761$	13.4072	−	41.2631i	0.486011	−	1.49579i	−0.344501	−	0.938786i	$-0.611952\pi$
$761$	13.4072	−	41.2631i	0.486011	−	1.49579i	0.830512	−	0.557001i	$-0.188048\pi$
$762$		0			0
$763$	19.7200	+	14.3274i	0.713912	+	0.518687i
$764$	0.932419	+	2.86969i	0.0337337	+	0.103822i
$765$		0			0
$766$	22.7695	+	16.5430i	0.822696	+	0.597724i
$767$	13.9903	−	10.1646i	0.505162	−	0.367021i
$768$		0			0
$769$	−19.6548			−0.708771			−0.354385	−	0.935099i	$-0.615310\pi$
$769$	−19.6548			−0.708771			−0.354385	+	0.935099i	$0.615310\pi$
$770$	−6.31731	−	9.30182i	−0.227660	−	0.335214i
$771$		0			0
$772$	−1.38034	+	4.24824i	−0.0496795	+	0.152898i
$773$	−19.7691	+	14.3631i	−0.711044	+	0.516604i	−0.883510	−	0.468412i	$-0.844826\pi$
$773$	−19.7691	+	14.3631i	−0.711044	+	0.516604i	0.172466	+	0.985015i	$0.444826\pi$
$774$		0			0
$775$	2.09249	+	6.44002i	0.0751644	+	0.231332i
$776$	4.46256	+	13.7343i	0.160196	+	0.493034i
$777$		0			0
$778$	19.5912	−	14.2338i	0.702377	−	0.510307i
$779$	−1.22925	+	3.78326i	−0.0440426	+	0.135549i
$780$		0			0
$781$	−1.57770	+	49.7136i	−0.0564545	+	1.77889i
$782$	1.64001			0.0586465
$783$		0			0
$784$	−6.07319	+	4.41243i	−0.216900	+	0.157587i
$785$	7.40629	+	5.38098i	0.264342	+	0.192056i
$786$		0			0
$787$	−10.5508	−	32.4721i	−0.376096	−	1.15750i	−0.942736	−	0.333539i	$-0.891757\pi$
$787$	−10.5508	−	32.4721i	−0.376096	−	1.15750i	0.566640	−	0.823965i	$-0.308243\pi$
$788$	−1.10740	−	0.804576i	−0.0394496	−	0.0286618i
$789$		0			0
$790$	4.21099	−	12.9601i	0.149820	−	0.461099i
$791$	−38.7747			−1.37867
$792$		0			0
$793$	−18.6803			−0.663357
$794$	14.1435	−	43.5292i	0.501934	−	1.54479i
$795$		0			0
$796$	2.96373	+	2.15327i	0.105047	+	0.0763208i
$797$	0.940349	+	2.89410i	0.0333089	+	0.102514i	0.966329	−	0.257311i	$-0.0828364\pi$
$797$	0.940349	+	2.89410i	0.0333089	+	0.102514i	−0.933020	+	0.359825i	$0.882836\pi$
$798$		0			0
$799$	0.166500	+	0.120969i	0.00589035	+	0.00427959i
$800$	0.831757	−	0.604307i	0.0294071	−	0.0213655i
$801$		0			0
$802$	9.40439			0.332081
$803$	−14.6432	−	21.5611i	−0.516747	−	0.760876i
$804$		0			0
$805$	−1.44608	+	4.45057i	−0.0509676	+	0.156862i
$806$	17.3247	−	12.5871i	0.610237	−	0.443363i
$807$		0			0
$808$	−16.2048	−	49.8733i	−0.570083	−	1.75454i
$809$	3.43043	+	10.5578i	0.120607	+	0.371191i	0.993075	−	0.117480i	$-0.0374816\pi$
$809$	3.43043	+	10.5578i	0.120607	+	0.371191i	−0.872468	+	0.488672i	$0.837482\pi$
$810$		0			0
$811$	−33.4336	+	24.2909i	−1.17401	+	0.852969i	−0.991484	−	0.130231i	$-0.958428\pi$
$811$	−33.4336	+	24.2909i	−1.17401	+	0.852969i	−0.182528	+	0.983201i	$0.558428\pi$
$812$	−1.28577	+	3.95718i	−0.0451215	+	0.138870i
$813$		0			0
$814$	41.4997	−	12.0429i	1.45456	−	0.422102i
$815$	11.3321			0.396946
$816$		0			0
$817$	−1.09588	+	0.796202i	−0.0383399	+	0.0278556i
$818$	7.49195	+	5.44322i	0.261950	+	0.190318i
$819$		0			0
$820$	−0.102685	−	0.316032i	−0.00358592	−	0.0110363i
$821$	6.61681	+	4.80739i	0.230928	+	0.167779i	0.697232	−	0.716845i	$-0.254415\pi$
$821$	6.61681	+	4.80739i	0.230928	+	0.167779i	−0.466304	+	0.884625i	$0.654415\pi$
$822$		0			0
$823$	4.07819	−	12.5514i	0.142157	−	0.437513i	−0.854478	−	0.519488i	$-0.826123\pi$
$823$	4.07819	−	12.5514i	0.142157	−	0.437513i	0.996634	+	0.0819748i	$0.0261227\pi$
$824$	−34.9246			−1.21665
$825$		0			0
$826$	−27.3862			−0.952889
$827$	9.49825	−	29.2326i	0.330287	−	1.01652i	−0.638711	−	0.769447i	$-0.720532\pi$
$827$	9.49825	−	29.2326i	0.330287	−	1.01652i	0.968997	−	0.247071i	$-0.0794680\pi$
$828$		0			0
$829$	−2.98357	−	2.16769i	−0.103624	−	0.0752871i	0.534767	−	0.845000i	$-0.320399\pi$
$829$	−2.98357	−	2.16769i	−0.103624	−	0.0752871i	−0.638390	+	0.769713i	$0.720399\pi$
$830$	−4.31497	−	13.2801i	−0.149775	−	0.460959i
$831$		0			0
$832$	12.3728	+	8.98933i	0.428948	+	0.311649i
$833$	−0.763391	+	0.554636i	−0.0264499	+	0.0192170i
$834$		0			0
$835$	15.1001			0.522561
$836$	−1.24130	−	0.447329i	−0.0429312	−	0.0154712i
$837$		0			0
$838$	−1.78186	+	5.48399i	−0.0615533	+	0.189441i
$839$	35.2341	−	25.5991i	1.21642	−	0.883778i	0.220618	−	0.975360i	$-0.429192\pi$
$839$	35.2341	−	25.5991i	1.21642	−	0.883778i	0.995798	+	0.0915823i	$0.0291924\pi$
$840$		0			0
$841$	21.6039	+	66.4900i	0.744963	+	2.29276i
$842$	7.93008	+	24.4063i	0.273289	+	0.841096i
$843$		0			0
$844$	−0.799143	+	0.580611i	−0.0275076	+	0.0199855i
$845$	2.60102	−	8.00513i	0.0894779	−	0.275385i
$846$		0			0
$847$	6.26295	+	24.4554i	0.215198	+	0.840296i
$848$	50.2139			1.72435
$849$		0			0
$850$	0.650683	−	0.472749i	0.0223182	−	0.0162151i
$851$	−14.5492	−	10.5706i	−0.498741	−	0.362357i
$852$		0			0
$853$	−9.37662	−	28.8583i	−0.321049	−	0.988088i	−0.973192	−	0.229992i	$-0.926130\pi$
$853$	−9.37662	−	28.8583i	−0.321049	−	0.988088i	0.652143	−	0.758096i	$-0.273870\pi$
$854$	23.9333	+	17.3886i	0.818982	+	0.595025i
$855$		0			0
$856$	1.63761	−	5.04004i	0.0559723	−	0.172265i
$857$	−12.5402			−0.428365			−0.214182	−	0.976794i	$-0.568709\pi$
$857$	−12.5402			−0.428365			−0.214182	+	0.976794i	$0.568709\pi$
$858$		0			0
$859$	−8.67783			−0.296084			−0.148042	−	0.988981i	$-0.547297\pi$
$859$	−8.67783			−0.296084			−0.148042	+	0.988981i	$0.547297\pi$
$860$	0.0349665	−	0.107616i	0.00119235	−	0.00366967i
$861$		0			0
$862$	−8.40953	−	6.10988i	−0.286430	−	0.208103i
$863$	11.8637	+	36.5128i	0.403846	+	1.24291i	0.921855	+	0.387535i	$0.126673\pi$
$863$	11.8637	+	36.5128i	0.403846	+	1.24291i	−0.518009	+	0.855375i	$0.673327\pi$
$864$		0			0
$865$	−14.7760	−	10.7354i	−0.502398	−	0.365014i
$866$	−3.28935	+	2.38985i	−0.111777	+	0.0812104i
$867$		0			0
$868$	−2.83293			−0.0961559
$869$	−18.7590	+	24.1685i	−0.636354	+	0.819859i
$870$		0			0
$871$	6.45528	−	19.8673i	0.218729	−	0.673178i
$872$	23.0734	−	16.7638i	0.781363	−	0.567693i
$873$		0			0
$874$	2.03136	+	6.25188i	0.0687118	+	0.211473i
$875$	0.709183	+	2.18264i	0.0239747	+	0.0737867i
$876$		0			0
$877$	−25.3140	+	18.3917i	−0.854792	+	0.621043i	−0.926463	−	0.376385i	$-0.877167\pi$
$877$	−25.3140	+	18.3917i	−0.854792	+	0.621043i	0.0716708	+	0.997428i	$0.477167\pi$
$878$	−1.24945	+	3.84542i	−0.0421669	+	0.129777i
$879$		0			0
$880$	−13.7963	+	4.00358i	−0.465075	+	0.134961i
$881$	−49.2703			−1.65996			−0.829979	−	0.557795i	$-0.811647\pi$
$881$	−49.2703			−1.65996			−0.829979	+	0.557795i	$0.811647\pi$
$882$		0			0
$883$	−22.8031	+	16.5674i	−0.767385	+	0.557537i	−0.901166	−	0.433473i	$-0.857288\pi$
$883$	−22.8031	+	16.5674i	−0.767385	+	0.557537i	0.133782	+	0.991011i	$0.457288\pi$
$884$	−0.171895	−	0.124889i	−0.00578145	−	0.00420047i
$885$		0			0
$886$	−5.06905	−	15.6009i	−0.170298	−	0.524123i
$887$	−20.6253	−	14.9852i	−0.692531	−	0.503153i	0.184960	−	0.982746i	$-0.440784\pi$
$887$	−20.6253	−	14.9852i	−0.692531	−	0.503153i	−0.877491	+	0.479593i	$0.840784\pi$
$888$		0			0
$889$	−2.93068	+	9.01972i	−0.0982920	+	0.302512i
$890$	0.861672			0.0288833
$891$		0			0
$892$	2.86342			0.0958743
$893$	−0.254917	+	0.784553i	−0.00853047	+	0.0262541i
$894$		0			0
$895$	0.425073	+	0.308833i	0.0142086	+	0.0103232i
$896$	−8.94256	−	27.5224i	−0.298750	−	0.919458i
$897$		0			0
$898$	17.7200	+	12.8743i	0.591323	+	0.429621i
$899$	−54.4831	+	39.5843i	−1.81711	+	1.32021i
$900$		0			0
$901$	6.31181			0.210277
$902$	−0.283289	+	8.92648i	−0.00943248	+	0.297219i
$903$		0			0
$904$	−14.0196	+	43.1478i	−0.466284	+	1.43507i
$905$	−14.3282	+	10.4101i	−0.476286	+	0.346042i
$906$		0			0
$907$	0.766528	+	2.35913i	0.0254522	+	0.0783337i	0.962976	−	0.269588i	$-0.0868875\pi$
$907$	0.766528	+	2.35913i	0.0254522	+	0.0783337i	−0.937524	+	0.347922i	$0.886888\pi$
$908$	0.0828891	+	0.255106i	0.00275077	+	0.00846600i
$909$		0			0
$910$	5.87166	−	4.26601i	0.194644	−	0.141417i
$911$	−0.839165	+	2.58268i	−0.0278028	+	0.0855681i	−0.963995	−	0.265920i	$-0.914324\pi$
$911$	−0.839165	+	2.58268i	−0.0278028	+	0.0855681i	0.936192	+	0.351488i	$0.114324\pi$
$912$		0			0
$913$	−0.994409	+	31.3340i	−0.0329101	+	1.03700i
$914$	43.1101			1.42595
$915$		0			0
$916$	2.35602	−	1.71175i	0.0778453	−	0.0565579i
$917$	0.810484	+	0.588851i	0.0267645	+	0.0194456i
$918$		0			0
$919$	1.00091	+	3.08047i	0.0330169	+	0.101615i	0.966207	−	0.257768i	$-0.0829870\pi$
$919$	1.00091	+	3.08047i	0.0330169	+	0.101615i	−0.933190	+	0.359383i	$0.882987\pi$
$920$	4.42967	+	3.21834i	0.146042	+	0.106106i
$921$		0			0
$922$	14.2335	−	43.8063i	0.468757	−	1.44268i
$923$	−32.1047			−1.05674
$924$		0			0
$925$	−8.81959			−0.289986
$926$	18.7914	−	57.8339i	0.617523	−	1.90054i
$927$		0			0
$928$	8.27219	+	6.01010i	0.271548	+	0.197291i
$929$	−2.21938	−	6.83056i	−0.0728156	−	0.224103i	0.908025	−	0.418916i	$-0.137590\pi$
$929$	−2.21938	−	6.83056i	−0.0728156	−	0.224103i	−0.980840	+	0.194813i	$0.937590\pi$
$930$		0			0
$931$	−3.05989	−	2.22314i	−0.100284	−	0.0728606i
$932$	−3.78115	+	2.74717i	−0.123856	+	0.0899865i
$933$		0			0
$934$	−57.2832			−1.87436
$935$	−1.73418	+	0.503244i	−0.0567137	+	0.0164578i
$936$		0			0
$937$	6.27696	−	19.3185i	0.205059	−	0.631108i	−0.794652	−	0.607066i	$-0.792346\pi$
$937$	6.27696	−	19.3185i	0.205059	−	0.631108i	0.999711	−	0.0240421i	$-0.00765359\pi$
$938$	−26.7641	+	19.4452i	−0.873877	+	0.634909i
$939$		0			0
$940$	−0.0212943	−	0.0655373i	−0.000694545	−	0.00213759i
$941$	7.85663	+	24.1802i	0.256119	+	0.788253i	0.993607	+	0.112893i	$0.0360117\pi$
$941$	7.85663	+	24.1802i	0.256119	+	0.788253i	−0.737488	+	0.675360i	$0.763988\pi$
$942$		0			0
$943$	3.00702	−	2.18473i	0.0979222	−	0.0711446i
$944$	−10.8120	+	33.2760i	−0.351901	+	1.08304i
$945$		0			0
$946$	−1.86471	+	2.40244i	−0.0606270	+	0.0781099i
$947$	4.55536			0.148029			0.0740147	−	0.997257i	$-0.476419\pi$
$947$	4.55536			0.148029			0.0740147	+	0.997257i	$0.476419\pi$
$948$		0			0
$949$	13.6102	−	9.88839i	0.441806	−	0.320991i
$950$	2.60813	+	1.89491i	0.0846188	+	0.0614791i
$951$		0			0
$952$	−1.03679	−	3.19092i	−0.0336027	−	0.103418i
$953$	−33.6433	−	24.4433i	−1.08981	−	0.791797i	−0.110447	−	0.993882i	$-0.535228\pi$
$953$	−33.6433	−	24.4433i	−1.08981	−	0.791797i	−0.979368	+	0.202085i	$0.935228\pi$
$954$		0			0
$955$	−5.11483	+	15.7418i	−0.165512	+	0.509394i
$956$	0.762378			0.0246571
$957$		0			0
$958$	−24.6519			−0.796467
$959$	−5.57977	+	17.1728i	−0.180180	+	0.554538i
$960$		0			0
$961$	−12.0158	−	8.72996i	−0.387605	−	0.281612i
$962$	8.61903	+	26.5267i	0.277889	+	0.855254i
$963$		0			0
$964$	0.485479	+	0.352721i	0.0156362	+	0.0113604i
$965$	−19.8235	+	14.4026i	−0.638142	+	0.463637i
$966$		0			0
$967$	−16.2161			−0.521476			−0.260738	−	0.965410i	$-0.583966\pi$
$967$	−16.2161			−0.521476			−0.260738	+	0.965410i	$0.583966\pi$
$968$	29.4780	+	1.87290i	0.947458	+	0.0601972i
$969$		0			0
$970$	2.45505	−	7.55588i	0.0788270	−	0.242605i
$971$	−10.8979	+	7.91778i	−0.349730	+	0.254094i	−0.748756	−	0.662846i	$-0.769348\pi$
$971$	−10.8979	+	7.91778i	−0.349730	+	0.254094i	0.399026	+	0.916940i	$0.369348\pi$
$972$		0			0
$973$	−12.5122	−	38.5086i	−0.401123	−	1.23453i
$974$	1.14669	+	3.52916i	0.0367425	+	0.113082i
$975$		0			0
$976$	30.5770	−	22.2155i	0.978746	−	0.711101i
$977$	4.49311	−	13.8284i	0.143747	−	0.442409i	−0.853100	−	0.521747i	$-0.825281\pi$
$977$	4.49311	−	13.8284i	0.143747	−	0.442409i	0.996848	+	0.0793377i	$0.0252805\pi$
$978$		0			0
$979$	−1.81998	−	0.655870i	−0.0581669	−	0.0209617i
$980$	0.315947			0.0100926
$981$		0			0
$982$	−9.03356	+	6.56326i	−0.288272	+	0.209442i
$983$	−19.8968	−	14.4559i	−0.634611	−	0.461072i	0.223384	−	0.974731i	$-0.428290\pi$
$983$	−19.8968	−	14.4559i	−0.634611	−	0.461072i	−0.857994	+	0.513659i	$0.828290\pi$
$984$		0			0
$985$	−2.32034	−	7.14126i	−0.0739321	−	0.227540i
$986$	6.47132	+	4.70169i	0.206089	+	0.149732i
$987$		0			0
$988$	0.263176	−	0.809973i	0.00837275	−	0.0257687i
$989$	1.26568			0.0402463
$990$		0			0
$991$	4.43775			0.140970			0.0704848	−	0.997513i	$-0.477545\pi$
$991$	4.43775			0.140970			0.0704848	+	0.997513i	$0.477545\pi$
$992$	−2.15130	+	6.62103i	−0.0683040	+	0.210218i
$993$		0			0
$994$	41.1328	+	29.8847i	1.30465	+	0.947885i
$995$	6.20988	+	19.1121i	0.196867	+	0.605893i
$996$		0			0
$997$	−0.00847083	−	0.00615442i	−0.000268274	−	0.000194912i	0.587651	−	0.809114i	$-0.300053\pi$
$997$	−0.00847083	−	0.00615442i	−0.000268274	−	0.000194912i	−0.587919	+	0.808920i	$0.700053\pi$
$998$	−20.0739	+	14.5845i	−0.635427	+	0.461665i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.n.a.361.2		8
3.2	odd	2		165.2.m.d.31.1	yes	8
11.4	even	5		5445.2.a.bt.1.3		4
11.5	even	5	inner	495.2.n.a.181.2		8
11.7	odd	10		5445.2.a.bf.1.2		4
15.2	even	4		825.2.bx.f.724.1		16
15.8	even	4		825.2.bx.f.724.4		16
15.14	odd	2		825.2.n.g.526.2		8
33.5	odd	10		165.2.m.d.16.1	✓	8
33.26	odd	10		1815.2.a.p.1.2		4
33.29	even	10		1815.2.a.w.1.3		4
165.29	even	10		9075.2.a.cm.1.2		4
165.38	even	20		825.2.bx.f.49.1		16
165.59	odd	10		9075.2.a.di.1.3		4
165.104	odd	10		825.2.n.g.676.2		8
165.137	even	20		825.2.bx.f.49.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.m.d.16.1	✓	8	33.5	odd	10
165.2.m.d.31.1	yes	8	3.2	odd	2
495.2.n.a.181.2		8	11.5	even	5	inner
495.2.n.a.361.2		8	1.1	even	1	trivial
825.2.n.g.526.2		8	15.14	odd	2
825.2.n.g.676.2		8	165.104	odd	10
825.2.bx.f.49.1		16	165.38	even	20
825.2.bx.f.49.4		16	165.137	even	20
825.2.bx.f.724.1		16	15.2	even	4
825.2.bx.f.724.4		16	15.8	even	4
1815.2.a.p.1.2		4	33.26	odd	10
1815.2.a.w.1.3		4	33.29	even	10
5445.2.a.bf.1.2		4	11.7	odd	10
5445.2.a.bt.1.3		4	11.4	even	5
9075.2.a.cm.1.2		4	165.29	even	10
9075.2.a.di.1.3		4	165.59	odd	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)

\(f(q)\)	\(=\)	\(q+(0.456498 - 1.40496i) q^{2} +(-0.147481 - 0.107152i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(1.85666 + 1.34895i) q^{7} +(2.17239 - 1.57833i) q^{8} +O(q^{10})\)	\(q+(0.456498 - 1.40496i) q^{2} +(-0.147481 - 0.107152i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(1.85666 + 1.34895i) q^{7} +(2.17239 - 1.57833i) q^{8} -1.47726 q^{10} +(3.12020 + 1.12443i) q^{11} +(-0.661536 + 2.03600i) q^{13} +(2.74278 - 1.99274i) q^{14} +(-1.33846 - 4.11937i) q^{16} +(-0.168243 - 0.517799i) q^{17} +(1.76552 - 1.28272i) q^{19} +(-0.0563329 + 0.173375i) q^{20} +(3.00415 - 3.87045i) q^{22} -2.03908 q^{23} +(-0.809017 + 0.587785i) q^{25} +(2.55850 + 1.85886i) q^{26} +(-0.129282 - 0.397889i) q^{28} +(-8.04603 - 5.84578i) q^{29} +(2.09249 - 6.44002i) q^{31} -1.02811 q^{32} -0.804288 q^{34} +(0.709183 - 2.18264i) q^{35} +(7.13520 + 5.18403i) q^{37} +(-0.996215 - 3.06604i) q^{38} +(-2.17239 - 1.57833i) q^{40} +(-1.47470 + 1.07143i) q^{41} -0.620713 q^{43} +(-0.339687 - 0.500167i) q^{44} +(-0.930836 + 2.86482i) q^{46} +(-0.305816 + 0.222188i) q^{47} +(-0.535571 - 1.64832i) q^{49} +(0.456498 + 1.40496i) q^{50} +(0.315724 - 0.229387i) q^{52} +(-3.58246 + 11.0257i) q^{53} +(0.105203 - 3.31496i) q^{55} +6.16248 q^{56} +(-11.8861 + 8.63574i) q^{58} +(-6.53518 - 4.74808i) q^{59} +(2.69647 + 8.29887i) q^{61} +(-8.09273 - 5.87971i) q^{62} +(2.20760 - 6.79429i) q^{64} +2.14077 q^{65} -9.75802 q^{67} +(-0.0306702 + 0.0943932i) q^{68} +(-2.74278 - 1.99274i) q^{70} +(4.63426 + 14.2628i) q^{71} +(-6.35761 - 4.61907i) q^{73} +(10.5405 - 7.65815i) q^{74} -0.397826 q^{76} +(4.27637 + 6.29667i) q^{77} +(-2.85054 + 8.77306i) q^{79} +(-3.50415 + 2.54591i) q^{80} +(0.832118 + 2.56099i) q^{82} +(2.92093 + 8.98969i) q^{83} +(-0.440466 + 0.320017i) q^{85} +(-0.283354 + 0.872075i) q^{86} +(8.55302 - 2.48201i) q^{88} -0.583290 q^{89} +(-3.97470 + 2.88779i) q^{91} +(0.300726 + 0.218490i) q^{92} +(0.172561 + 0.531087i) q^{94} +(-1.76552 - 1.28272i) q^{95} +(-1.66190 + 5.11479i) q^{97} -2.56031 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 2 q^{4} + 2 q^{5} + 3 q^{7} + q^{8}+O(q^{10}) \) 8 * q - 4 * q^2 + 2 * q^4 + 2 * q^5 + 3 * q^7 + q^8	\( 8 q - 4 q^{2} + 2 q^{4} + 2 q^{5} + 3 q^{7} + q^{8} - 6 q^{10} - 3 q^{11} - 4 q^{13} + 4 q^{14} - 12 q^{16} + 2 q^{19} + 3 q^{20} + 9 q^{22} + 6 q^{23} - 2 q^{25} - 2 q^{26} - 11 q^{28} - 10 q^{29} + 19 q^{31} - 12 q^{32} - 6 q^{34} - 3 q^{35} - q^{37} + 20 q^{38} - q^{40} + 9 q^{41} - 17 q^{44} - 22 q^{46} + 19 q^{47} + q^{49} - 4 q^{50} - 2 q^{52} - 25 q^{53} + 3 q^{55} + 16 q^{56} - 12 q^{58} - 13 q^{59} + 13 q^{61} - 35 q^{62} + 39 q^{64} + 14 q^{65} + 2 q^{67} - 19 q^{68} - 4 q^{70} + 11 q^{71} - 7 q^{73} + 43 q^{74} - 38 q^{76} + 7 q^{77} - 22 q^{79} - 13 q^{80} - 35 q^{82} + 21 q^{83} + 10 q^{85} - 20 q^{86} + 59 q^{88} + 20 q^{89} - 11 q^{91} + 28 q^{92} - 35 q^{94} - 2 q^{95} + 31 q^{97} - 22 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 + 2 * q^4 + 2 * q^5 + 3 * q^7 + q^8 - 6 * q^10 - 3 * q^11 - 4 * q^13 + 4 * q^14 - 12 * q^16 + 2 * q^19 + 3 * q^20 + 9 * q^22 + 6 * q^23 - 2 * q^25 - 2 * q^26 - 11 * q^28 - 10 * q^29 + 19 * q^31 - 12 * q^32 - 6 * q^34 - 3 * q^35 - q^37 + 20 * q^38 - q^40 + 9 * q^41 - 17 * q^44 - 22 * q^46 + 19 * q^47 + q^49 - 4 * q^50 - 2 * q^52 - 25 * q^53 + 3 * q^55 + 16 * q^56 - 12 * q^58 - 13 * q^59 + 13 * q^61 - 35 * q^62 + 39 * q^64 + 14 * q^65 + 2 * q^67 - 19 * q^68 - 4 * q^70 + 11 * q^71 - 7 * q^73 + 43 * q^74 - 38 * q^76 + 7 * q^77 - 22 * q^79 - 13 * q^80 - 35 * q^82 + 21 * q^83 + 10 * q^85 - 20 * q^86 + 59 * q^88 + 20 * q^89 - 11 * q^91 + 28 * q^92 - 35 * q^94 - 2 * q^95 + 31 * q^97 - 22 * q^98

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