LMFDB - Embedded newform 495.2.n.d.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			$-0.227943 + 0.701538i$ of defining polynomial
Character	$\chi$	$=$	495.361
Dual form			495.2.n.d.181.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.359123 + 1.10527i) q^{2} +(0.525387 + 0.381716i) q^{4} +(0.309017 + 0.951057i) q^{5} +(3.46813 + 2.51974i) q^{7} +(-2.49097 + 1.80980i) q^{8} +O(q^{10})$	\(q+(-0.359123 + 1.10527i) q^{2} +(0.525387 + 0.381716i) q^{4} +(0.309017 + 0.951057i) q^{5} +(3.46813 + 2.51974i) q^{7} +(-2.49097 + 1.80980i) q^{8} -1.16215 q^{10} +(3.15911 + 1.00996i) q^{11} +(1.59676 - 4.91433i) q^{13} +(-4.03048 + 2.92831i) q^{14} +(-0.704384 - 2.16787i) q^{16} +(-1.54508 - 4.75528i) q^{17} +(-4.53048 + 3.29158i) q^{19} +(-0.200680 + 0.617629i) q^{20} +(-2.25079 + 3.12896i) q^{22} +0.219819 q^{23} +(-0.809017 + 0.587785i) q^{25} +(4.85822 + 3.52970i) q^{26} +(0.860283 + 2.64768i) q^{28} +(5.19262 + 3.77266i) q^{29} +(-0.874813 + 2.69240i) q^{31} -3.50898 q^{32} +5.81074 q^{34} +(-1.32471 + 4.07703i) q^{35} +(-3.17784 - 2.30883i) q^{37} +(-2.01108 - 6.18947i) q^{38} +(-2.49097 - 1.80980i) q^{40} +(4.74165 - 3.44501i) q^{41} -8.90173 q^{43} +(1.27424 + 1.73650i) q^{44} +(-0.0789420 + 0.242959i) q^{46} +(-0.192447 + 0.139821i) q^{47} +(3.51569 + 10.8202i) q^{49} +(-0.359123 - 1.10527i) q^{50} +(2.71480 - 1.97242i) q^{52} +(-0.783885 + 2.41255i) q^{53} +(0.0156899 + 3.31659i) q^{55} -13.1992 q^{56} +(-6.03459 + 4.38439i) q^{58} +(-6.36725 - 4.62608i) q^{59} +(-1.50123 - 4.62030i) q^{61} +(-2.66165 - 1.93381i) q^{62} +(2.66892 - 8.21410i) q^{64} +5.16724 q^{65} +12.1280 q^{67} +(1.00340 - 3.08815i) q^{68} +(-4.03048 - 2.92831i) q^{70} +(3.08459 + 9.49339i) q^{71} +(-11.7813 - 8.55964i) q^{73} +(3.69311 - 2.68320i) q^{74} -3.63670 q^{76} +(8.41136 + 11.4628i) q^{77} +(2.47274 - 7.61030i) q^{79} +(1.84410 - 1.33982i) q^{80} +(2.10482 + 6.47797i) q^{82} +(-3.87908 - 11.9386i) q^{83} +(4.04508 - 2.93893i) q^{85} +(3.19682 - 9.83880i) q^{86} +(-9.69707 + 3.20157i) q^{88} +2.56545 q^{89} +(17.9206 - 13.0201i) q^{91} +(0.115490 + 0.0839083i) q^{92} +(-0.0854274 - 0.262919i) q^{94} +(-4.53048 - 3.29158i) q^{95} +(0.621738 - 1.91351i) q^{97} -13.2218 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.359123	+	1.10527i	−0.253938	+	0.781542i	0.740098	+	0.672499i	$0.234779\pi$
$2$	−0.359123	+	1.10527i	−0.253938	+	0.781542i	−0.994037	+	0.109044i	$0.965221\pi$
$3$		0			0
$3$		0			0
$4$	0.525387	+	0.381716i	0.262693	+	0.190858i
$5$	0.309017	+	0.951057i	0.138197	+	0.425325i
$5$	0.309017	+	0.951057i	0.138197	+	0.425325i
$6$		0			0
$7$	3.46813	+	2.51974i	1.31083	+	0.952373i	0.999998	+	0.00190785i	$0.000607288\pi$
$7$	3.46813	+	2.51974i	1.31083	+	0.952373i	0.310831	+	0.950465i	$0.399393\pi$
$8$	−2.49097	+	1.80980i	−0.880691	+	0.639860i
$9$		0			0
$10$	−1.16215			−0.367503
$11$	3.15911	+	1.00996i	0.952508	+	0.304514i
$11$	3.15911	+	1.00996i	0.952508	+	0.304514i
$12$		0			0
$13$	1.59676	−	4.91433i	0.442863	−	1.36299i	−0.441948	−	0.897040i	$-0.645713\pi$
$13$	1.59676	−	4.91433i	0.442863	−	1.36299i	0.884811	−	0.465950i	$-0.154287\pi$
$14$	−4.03048	+	2.92831i	−1.07719	+	0.782624i
$15$		0			0
$16$	−0.704384	−	2.16787i	−0.176096	−	0.541968i
$17$	−1.54508	−	4.75528i	−0.374738	−	1.15333i	−0.943655	−	0.330930i	$-0.892637\pi$
$17$	−1.54508	−	4.75528i	−0.374738	−	1.15333i	0.568917	−	0.822395i	$-0.307363\pi$
$18$		0			0
$19$	−4.53048	+	3.29158i	−1.03936	+	0.755141i	−0.970161	−	0.242462i	$-0.922045\pi$
$19$	−4.53048	+	3.29158i	−1.03936	+	0.755141i	−0.0692013	+	0.997603i	$0.522045\pi$
$20$	−0.200680	+	0.617629i	−0.0448734	+	0.138106i
$21$		0			0
$22$	−2.25079	+	3.12896i	−0.479869	+	0.667097i
$23$	0.219819			0.0458354			0.0229177	−	0.999737i	$-0.492704\pi$
$23$	0.219819			0.0458354			0.0229177	+	0.999737i	$0.492704\pi$
$24$		0			0
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$	4.85822	+	3.52970i	0.952775	+	0.692232i
$27$		0			0
$28$	0.860283	+	2.64768i	0.162578	+	0.500364i
$29$	5.19262	+	3.77266i	0.964246	+	0.700566i	0.954133	−	0.299383i	$-0.0967809\pi$
$29$	5.19262	+	3.77266i	0.964246	+	0.700566i	0.0101128	+	0.999949i	$0.496781\pi$
$30$		0			0
$31$	−0.874813	+	2.69240i	−0.157121	+	0.483569i	−0.998370	−	0.0570796i	$-0.981821\pi$
$31$	−0.874813	+	2.69240i	−0.157121	+	0.483569i	0.841249	+	0.540649i	$0.181821\pi$
$32$	−3.50898			−0.620306
$33$		0			0
$34$	5.81074			0.996533
$35$	−1.32471	+	4.07703i	−0.223916	+	0.689144i
$36$		0			0
$37$	−3.17784	−	2.30883i	−0.522433	−	0.379570i	0.295087	−	0.955471i	$-0.404652\pi$
$37$	−3.17784	−	2.30883i	−0.522433	−	0.379570i	−0.817520	+	0.575901i	$0.804652\pi$
$38$	−2.01108	−	6.18947i	−0.326240	−	1.00406i
$39$		0			0
$40$	−2.49097	−	1.80980i	−0.393857	−	0.286154i
$41$	4.74165	−	3.44501i	0.740521	−	0.538020i	−0.152353	−	0.988326i	$-0.548685\pi$
$41$	4.74165	−	3.44501i	0.740521	−	0.538020i	0.892874	+	0.450306i	$0.148685\pi$
$42$		0			0
$43$	−8.90173			−1.35750			−0.678751	−	0.734369i	$-0.737478\pi$
$43$	−8.90173			−1.35750			−0.678751	+	0.734369i	$0.737478\pi$
$44$	1.27424	+	1.73650i	0.192099	+	0.261788i
$45$		0			0
$46$	−0.0789420	+	0.242959i	−0.0116394	+	0.0358223i
$47$	−0.192447	+	0.139821i	−0.0280713	+	0.0203950i	−0.601732	−	0.798698i	$-0.705523\pi$
$47$	−0.192447	+	0.139821i	−0.0280713	+	0.0203950i	0.573661	+	0.819093i	$0.305523\pi$
$48$		0			0
$49$	3.51569	+	10.8202i	0.502241	+	1.54574i
$50$	−0.359123	−	1.10527i	−0.0507877	−	0.156308i
$51$		0			0
$52$	2.71480	−	1.97242i	0.376475	−	0.273525i
$53$	−0.783885	+	2.41255i	−0.107675	+	0.331389i	−0.990349	−	0.138596i	$-0.955741\pi$
$53$	−0.783885	+	2.41255i	−0.107675	+	0.331389i	0.882674	+	0.469986i	$0.155741\pi$
$54$		0			0
$55$	0.0156899	+	3.31659i	0.00211563	+	0.447209i
$56$	−13.1992			−1.76382
$57$		0			0
$58$	−6.03459	+	4.38439i	−0.792381	+	0.575698i
$59$	−6.36725	−	4.62608i	−0.828945	−	0.602264i	0.0903156	−	0.995913i	$-0.471212\pi$
$59$	−6.36725	−	4.62608i	−0.828945	−	0.602264i	−0.919261	+	0.393649i	$0.871212\pi$
$60$		0			0
$61$	−1.50123	−	4.62030i	−0.192212	−	0.591569i	−0.999998	−	0.00209225i	$-0.999334\pi$
$61$	−1.50123	−	4.62030i	−0.192212	−	0.591569i	0.807785	−	0.589477i	$-0.200666\pi$
$62$	−2.66165	−	1.93381i	−0.338031	−	0.245594i
$63$		0			0
$64$	2.66892	−	8.21410i	0.333615	−	1.02676i
$65$	5.16724			0.640917
$66$		0			0
$67$	12.1280			1.48167			0.740834	−	0.671688i	$-0.234431\pi$
$67$	12.1280			1.48167			0.740834	+	0.671688i	$0.234431\pi$
$68$	1.00340	−	3.08815i	0.121680	−	0.374493i
$69$		0			0
$70$	−4.03048	−	2.92831i	−0.481734	−	0.350000i
$71$	3.08459	+	9.49339i	0.366073	+	1.12666i	0.949306	+	0.314353i	$0.101788\pi$
$71$	3.08459	+	9.49339i	0.366073	+	1.12666i	−0.583233	+	0.812305i	$0.698212\pi$
$72$		0			0
$73$	−11.7813	−	8.55964i	−1.37890	−	1.00183i	−0.996982	−	0.0776335i	$-0.975264\pi$
$73$	−11.7813	−	8.55964i	−1.37890	−	1.00183i	−0.381918	−	0.924196i	$-0.624736\pi$
$74$	3.69311	−	2.68320i	0.429316	−	0.311916i
$75$		0			0
$76$	−3.63670			−0.417158
$77$	8.41136	+	11.4628i	0.958564	+	1.30631i
$78$		0			0
$79$	2.47274	−	7.61030i	0.278205	−	0.856226i	−0.710149	−	0.704051i	$-0.751372\pi$
$79$	2.47274	−	7.61030i	0.278205	−	0.856226i	0.988354	−	0.152174i	$-0.0486275\pi$
$80$	1.84410	−	1.33982i	0.206177	−	0.149796i
$81$		0			0
$82$	2.10482	+	6.47797i	0.232439	+	0.715373i
$83$	−3.87908	−	11.9386i	−0.425784	−	1.31043i	−0.902242	−	0.431231i	$-0.858079\pi$
$83$	−3.87908	−	11.9386i	−0.425784	−	1.31043i	0.476458	−	0.879197i	$-0.341921\pi$
$84$		0			0
$85$	4.04508	−	2.93893i	0.438751	−	0.318771i
$86$	3.19682	−	9.83880i	0.344722	−	1.06094i
$87$		0			0
$88$	−9.69707	+	3.20157i	−1.03371	+	0.341288i
$89$	2.56545			0.271937			0.135969	−	0.990713i	$-0.456585\pi$
$89$	2.56545			0.271937			0.135969	+	0.990713i	$0.456585\pi$
$90$		0			0
$91$	17.9206	−	13.0201i	1.87859	−	1.36488i
$92$	0.115490	+	0.0839083i	0.0120407	+	0.00874805i
$93$		0			0
$94$	−0.0854274	−	0.262919i	−0.00881116	−	0.0271180i
$95$	−4.53048	−	3.29158i	−0.464817	−	0.337709i
$96$		0			0
$97$	0.621738	−	1.91351i	0.0631279	−	0.194288i	−0.914518	−	0.404545i	$-0.867430\pi$
$97$	0.621738	−	1.91351i	0.0631279	−	0.194288i	0.977646	+	0.210257i	$0.0674300\pi$
$98$	−13.2218			−1.33560
$99$		0			0
$100$	−0.649414			−0.0649414
$101$	2.34385	−	7.21362i	0.233221	−	0.717782i	−0.764131	−	0.645061i	$-0.776832\pi$
$101$	2.34385	−	7.21362i	0.233221	−	0.717782i	0.997352	−	0.0727205i	$-0.0231681\pi$
$102$		0			0
$103$	13.6469	+	9.91508i	1.34467	+	0.976962i	0.999258	+	0.0385116i	$0.0122617\pi$
$103$	13.6469	+	9.91508i	1.34467	+	0.976962i	0.345414	+	0.938450i	$0.387738\pi$
$104$	4.91645	+	15.1313i	0.482098	+	1.48374i
$105$		0			0
$106$	−2.38500	−	1.73281i	−0.231652	−	0.168305i
$107$	6.27928	−	4.56216i	0.607041	−	0.441041i	−0.241330	−	0.970443i	$-0.577584\pi$
$107$	6.27928	−	4.56216i	0.607041	−	0.441041i	0.848371	+	0.529402i	$0.177584\pi$
$108$		0			0
$109$	4.45671			0.426876			0.213438	−	0.976957i	$-0.431534\pi$
$109$	4.45671			0.426876			0.213438	+	0.976957i	$0.431534\pi$
$110$	−3.67135	−	1.17372i	−0.350050	−	0.111910i
$111$		0			0
$112$	3.01958	−	9.29332i	0.285324	−	0.878136i
$113$	−6.23952	+	4.53327i	−0.586964	+	0.426455i	−0.841228	−	0.540680i	$-0.818167\pi$
$113$	−6.23952	+	4.53327i	−0.586964	+	0.426455i	0.254264	+	0.967135i	$0.418167\pi$
$114$		0			0
$115$	0.0679277	+	0.209060i	0.00633429	+	0.0194950i
$116$	1.28805	+	3.96421i	0.119593	+	0.368068i
$117$		0			0
$118$	7.39968	−	5.37618i	0.681196	−	0.494918i
$119$	6.62353	−	20.3851i	0.607178	−	1.86870i
$120$		0			0
$121$	8.95996	+	6.38115i	0.814542	+	0.580105i
$122$	5.64579			0.511146
$123$		0			0
$124$	−1.48735	+	1.08062i	−0.133568	+	0.0970426i
$125$	−0.809017	−	0.587785i	−0.0723607	−	0.0525731i
$126$		0			0
$127$	0.473149	+	1.45620i	0.0419852	+	0.129217i	0.969852	−	0.243695i	$-0.0783594\pi$
$127$	0.473149	+	1.45620i	0.0419852	+	0.129217i	−0.927867	+	0.372912i	$0.878359\pi$
$128$	2.44266	+	1.77470i	0.215903	+	0.156863i
$129$		0			0
$130$	−1.85567	+	5.71118i	−0.162753	+	0.500903i
$131$	−2.66108			−0.232500			−0.116250	−	0.993220i	$-0.537087\pi$
$131$	−2.66108			−0.232500			−0.116250	+	0.993220i	$0.537087\pi$
$132$		0			0
$133$	−24.0062			−2.08160
$134$	−4.35544	+	13.4047i	−0.376252	+	1.15799i
$135$		0			0
$136$	12.4549	+	9.04898i	1.06799	+	0.775944i
$137$	−3.16911	−	9.75352i	−0.270756	−	0.833300i	−0.990311	−	0.138865i	$-0.955655\pi$
$137$	−3.16911	−	9.75352i	−0.270756	−	0.833300i	0.719556	−	0.694435i	$-0.244345\pi$
$138$		0			0
$139$	4.28381	+	3.11237i	0.363348	+	0.263987i	0.754447	−	0.656361i	$-0.227905\pi$
$139$	4.28381	+	3.11237i	0.363348	+	0.263987i	−0.391099	+	0.920348i	$0.627905\pi$
$140$	−2.25225	+	1.63636i	−0.190350	+	0.138297i
$141$		0			0
$142$	−11.6005			−0.973491
$143$	10.0076	−	13.9123i	0.836880	−	1.16340i
$144$		0			0
$145$	−1.98341	+	6.10429i	−0.164713	+	0.506934i
$146$	13.6916	−	9.94756i	1.13313	−	0.823266i
$147$		0			0
$148$	−0.788275	−	2.42606i	−0.0647958	−	0.199421i
$149$	−1.17068	−	3.60300i	−0.0959062	−	0.295169i	0.891583	−	0.452858i	$-0.149596\pi$
$149$	−1.17068	−	3.60300i	−0.0959062	−	0.295169i	−0.987489	+	0.157689i	$0.949596\pi$
$150$		0			0
$151$	4.78939	−	3.47969i	0.389755	−	0.283173i	−0.375600	−	0.926782i	$-0.622563\pi$
$151$	4.78939	−	3.47969i	0.389755	−	0.283173i	0.765355	+	0.643608i	$0.222563\pi$
$152$	5.32819	−	16.3985i	0.432173	−	1.33009i
$153$		0			0
$154$	−15.6902	+	5.18024i	−1.26435	+	0.417436i
$155$	−2.83095			−0.227388
$156$		0			0
$157$	6.01026	−	4.36671i	0.479671	−	0.348501i	−0.321528	−	0.946900i	$-0.604196\pi$
$157$	6.01026	−	4.36671i	0.479671	−	0.348501i	0.801198	+	0.598399i	$0.204196\pi$
$158$	7.52340	+	5.46607i	0.598530	+	0.434857i
$159$		0			0
$160$	−1.08433	−	3.33724i	−0.0857242	−	0.263832i
$161$	0.762360	+	0.553887i	0.0600824	+	0.0436524i
$162$		0			0
$163$	1.64424	−	5.06044i	0.128786	−	0.396364i	−0.865785	−	0.500415i	$-0.833181\pi$
$163$	1.64424	−	5.06044i	0.128786	−	0.396364i	0.994572	+	0.104051i	$0.0331807\pi$
$164$	3.80621			0.297215
$165$		0			0
$166$	14.5884			1.13228
$167$	0.609193	−	1.87490i	0.0471407	−	0.145084i	−0.924716	−	0.380659i	$-0.875697\pi$
$167$	0.609193	−	1.87490i	0.0471407	−	0.145084i	0.971856	+	0.235575i	$0.0756972\pi$
$168$		0			0
$169$	−11.0838	−	8.05285i	−0.852599	−	0.619450i
$170$	1.79562	+	5.52634i	0.137717	+	0.423851i
$171$		0			0
$172$	−4.67685	−	3.39793i	−0.356607	−	0.259090i
$173$	−1.59784	+	1.16090i	−0.121482	+	0.0882617i	−0.646867	−	0.762603i	$-0.723921\pi$
$173$	−1.59784	+	1.16090i	−0.121482	+	0.0882617i	0.525385	+	0.850864i	$0.323921\pi$
$174$		0			0
$175$	−4.28684			−0.324055
$176$	−0.0357642	−	7.55994i	−0.00269583	−	0.569852i
$177$		0			0
$178$	−0.921313	+	2.83551i	−0.0690553	+	0.212530i
$179$	−1.63676	+	1.18918i	−0.122337	+	0.0888832i	−0.647271	−	0.762260i	$-0.724090\pi$
$179$	−1.63676	+	1.18918i	−0.122337	+	0.0888832i	0.524934	+	0.851143i	$0.324090\pi$
$180$		0			0
$181$	6.22299	+	19.1524i	0.462551	+	1.42359i	0.862036	+	0.506846i	$0.169189\pi$
$181$	6.22299	+	19.1524i	0.462551	+	1.42359i	−0.399485	+	0.916740i	$0.630811\pi$
$182$	7.95498	+	24.4829i	0.589662	+	1.81479i
$183$		0			0
$184$	−0.547562	+	0.397827i	−0.0403668	+	0.0293282i
$185$	1.21383	−	3.73577i	0.0892422	−	0.274659i
$186$		0			0
$187$	−0.0784497	−	16.5829i	−0.00573681	−	1.21266i
$188$	−0.154481			−0.0112667
$189$		0			0
$190$	5.26508	−	3.82530i	0.381969	−	0.277517i
$191$	10.2463	+	7.44439i	0.741398	+	0.538657i	0.893149	−	0.449762i	$-0.148491\pi$
$191$	10.2463	+	7.44439i	0.741398	+	0.538657i	−0.151751	+	0.988419i	$0.548491\pi$
$192$		0			0
$193$	−4.30526	−	13.2502i	−0.309900	−	0.953773i	−0.977803	−	0.209525i	$-0.932808\pi$
$193$	−4.30526	−	13.2502i	−0.309900	−	0.953773i	0.667904	−	0.744248i	$-0.267192\pi$
$194$	1.89166	+	1.37437i	0.135813	+	0.0986743i
$195$		0			0
$196$	−2.28314	+	7.02678i	−0.163081	+	0.501913i
$197$	−14.6060			−1.04064			−0.520319	−	0.853972i	$-0.674187\pi$
$197$	−14.6060			−1.04064			−0.520319	+	0.853972i	$0.674187\pi$
$198$		0			0
$199$	−11.8748			−0.841784			−0.420892	−	0.907111i	$-0.638283\pi$
$199$	−11.8748			−0.841784			−0.420892	+	0.907111i	$0.638283\pi$
$200$	0.951466	−	2.92831i	0.0672788	−	0.207063i
$201$		0			0
$202$	7.13125	+	5.18115i	0.501753	+	0.364545i
$203$	8.50254	+	26.1681i	0.596762	+	1.83664i
$204$		0			0
$205$	4.74165	+	3.44501i	0.331171	+	0.240610i
$206$	−15.8597	+	11.5228i	−1.10500	+	0.802830i
$207$		0			0
$208$	−11.7784			−0.816683
$209$	−17.6366	+	5.82288i	−1.21995	+	0.402777i
$210$		0			0
$211$	−6.90710	+	21.2579i	−0.475504	+	1.46345i	0.369772	+	0.929122i	$0.379436\pi$
$211$	−6.90710	+	21.2579i	−0.475504	+	1.46345i	−0.845277	+	0.534329i	$0.820564\pi$
$212$	−1.33275	+	0.968301i	−0.0915338	+	0.0665032i
$213$		0			0
$214$	2.78738	+	8.57866i	0.190541	+	0.586425i
$215$	−2.75079	−	8.46605i	−0.187602	−	0.577380i
$216$		0			0
$217$	−9.81811	+	7.13328i	−0.666497	+	0.484238i
$218$	−1.60051	+	4.92586i	−0.108400	+	0.333621i
$219$		0			0
$220$	−1.25775	+	1.74848i	−0.0847976	+	0.117883i
$221$	−25.8362			−1.73793
$222$		0			0
$223$	15.4994	−	11.2610i	1.03792	−	0.754091i	0.0680388	−	0.997683i	$-0.478326\pi$
$223$	15.4994	−	11.2610i	1.03792	−	0.754091i	0.969878	+	0.243592i	$0.0783258\pi$
$224$	−12.1696	−	8.84173i	−0.813115	−	0.590763i
$225$		0			0
$226$	−2.76973	−	8.52434i	−0.184239	−	0.567031i
$227$	12.4394	+	9.03772i	0.825629	+	0.599855i	0.918319	−	0.395840i	$-0.129547\pi$
$227$	12.4394	+	9.03772i	0.825629	+	0.599855i	−0.0926901	+	0.995695i	$0.529547\pi$
$228$		0			0
$229$	2.75064	−	8.46560i	0.181767	−	0.559422i	−0.818110	−	0.575061i	$-0.804978\pi$
$229$	2.75064	−	8.46560i	0.181767	−	0.559422i	0.999878	+	0.0156388i	$0.00497820\pi$
$230$	−0.255462			−0.0168447
$231$		0			0
$232$	−19.7624			−1.29747
$233$	−7.05677	+	21.7185i	−0.462304	+	1.42283i	0.400037	+	0.916499i	$0.368997\pi$
$233$	−7.05677	+	21.7185i	−0.462304	+	1.42283i	−0.862342	+	0.506327i	$0.831003\pi$
$234$		0			0
$235$	−0.192447	−	0.139821i	−0.0125539	−	0.00912092i
$236$	−1.57942	−	4.86096i	−0.102812	−	0.316422i
$237$		0			0
$238$	20.1524	+	14.6416i	1.30628	+	0.949071i
$239$	13.6405	−	9.91037i	0.882327	−	0.641048i	−0.0515388	−	0.998671i	$-0.516413\pi$
$239$	13.6405	−	9.91037i	0.882327	−	0.641048i	0.933866	+	0.357623i	$0.116413\pi$
$240$		0			0
$241$	−11.9607			−0.770459			−0.385229	−	0.922821i	$-0.625878\pi$
$241$	−11.9607			−0.770459			−0.385229	+	0.922821i	$0.625878\pi$
$242$	−10.2706	+	7.61154i	−0.660220	+	0.489288i
$243$		0			0
$244$	0.974917	−	3.00049i	0.0624127	−	0.192087i
$245$	−9.20420	+	6.68724i	−0.588034	+	0.427232i
$246$		0			0
$247$	8.94184	+	27.5201i	0.568955	+	1.75106i
$248$	−2.69356	−	8.28992i	−0.171041	−	0.526410i
$249$		0			0
$250$	0.940197	−	0.683093i	0.0594633	−	0.0432026i
$251$	−4.94533	+	15.2201i	−0.312146	+	0.960687i	0.664767	+	0.747051i	$0.268531\pi$
$251$	−4.94533	+	15.2201i	−0.312146	+	0.960687i	−0.976913	+	0.213637i	$0.931469\pi$
$252$		0			0
$253$	0.694432	+	0.222008i	0.0436586	+	0.0139575i
$254$	−1.77941			−0.111650
$255$		0			0
$256$	11.1359	−	8.09073i	0.695996	−	0.505671i
$257$	4.42893	+	3.21780i	0.276269	+	0.200721i	0.717288	−	0.696776i	$-0.245383\pi$
$257$	4.42893	+	3.21780i	0.276269	+	0.200721i	−0.441019	+	0.897498i	$0.645383\pi$
$258$		0			0
$259$	−5.20348	−	16.0147i	−0.323328	−	0.995103i
$260$	2.71480	+	1.97242i	0.168365	+	0.122324i
$261$		0			0
$262$	0.955657	−	2.94121i	0.0590407	−	0.181709i
$263$	−11.9841			−0.738971			−0.369486	−	0.929236i	$-0.620466\pi$
$263$	−11.9841			−0.738971			−0.369486	+	0.929236i	$0.620466\pi$
$264$		0			0
$265$	−2.53671			−0.155829
$266$	8.62119	−	26.5333i	0.528599	−	1.62686i
$267$		0			0
$268$	6.37188	+	4.62944i	0.389224	+	0.282788i
$269$	−4.21700	−	12.9786i	−0.257115	−	0.791318i	−0.993406	−	0.114653i	$-0.963424\pi$
$269$	−4.21700	−	12.9786i	−0.257115	−	0.791318i	0.736291	−	0.676665i	$-0.236576\pi$
$270$		0			0
$271$	−9.57702	−	6.95812i	−0.581763	−	0.422675i	0.257596	−	0.966253i	$-0.417070\pi$
$271$	−9.57702	−	6.95812i	−0.581763	−	0.422675i	−0.839359	+	0.543577i	$0.817070\pi$
$272$	−9.22050	+	6.69909i	−0.559075	+	0.406192i
$273$		0			0
$274$	11.9184			0.720014
$275$	−3.14941	+	1.03980i	−0.189917	+	0.0627025i
$276$		0			0
$277$	3.17170	−	9.76148i	0.190569	−	0.586511i	−0.809431	−	0.587215i	$-0.800224\pi$
$277$	3.17170	−	9.76148i	0.190569	−	0.586511i	1.00000		0.000704561i	$0.000224269\pi$
$278$	−4.97841	+	3.61703i	−0.298585	+	0.216935i
$279$		0			0
$280$	−4.07878	−	12.5532i	−0.243754	−	0.750198i
$281$	0.908167	+	2.79505i	0.0541767	+	0.166739i	0.974484	−	0.224458i	$-0.0720612\pi$
$281$	0.908167	+	2.79505i	0.0541767	+	0.166739i	−0.920307	+	0.391197i	$0.872061\pi$
$282$		0			0
$283$	−17.6592	+	12.8301i	−1.04973	+	0.762673i	−0.972161	−	0.234314i	$-0.924716\pi$
$283$	−17.6592	+	12.8301i	−1.04973	+	0.762673i	−0.0775682	+	0.996987i	$0.524716\pi$
$284$	−2.00318	+	6.16514i	−0.118867	+	0.365834i
$285$		0			0
$286$	11.7828	+	16.0573i	0.696731	+	0.949490i
$287$	25.1252			1.48309
$288$		0			0
$289$	−6.47214	+	4.70228i	−0.380714	+	0.276605i
$290$	−6.03459	−	4.38439i	−0.354363	−	0.257460i
$291$		0			0
$292$	−2.92241	−	8.99424i	−0.171021	−	0.526348i
$293$	−20.0365	−	14.5574i	−1.17055	−	0.850452i	−0.179473	−	0.983763i	$-0.557439\pi$
$293$	−20.0365	−	14.5574i	−1.17055	−	0.850452i	−0.991074	+	0.133311i	$0.957439\pi$
$294$		0			0
$295$	2.43207	−	7.48515i	0.141601	−	0.435802i
$296$	12.0944			0.702974
$297$		0			0
$298$	4.40269			0.255041
$299$	0.350999	−	1.08026i	0.0202988	−	0.0624732i
$300$		0			0
$301$	−30.8723	−	22.4301i	−1.77945	−	1.29285i
$302$	2.12601	+	6.54319i	0.122338	+	0.376518i
$303$		0			0
$304$	10.3269	+	7.50295i	0.592289	+	0.430323i
$305$	3.93026	−	2.85550i	0.225046	−	0.163506i
$306$		0			0
$307$	−4.94023			−0.281954			−0.140977	−	0.990013i	$-0.545024\pi$
$307$	−4.94023			−0.281954			−0.140977	+	0.990013i	$0.545024\pi$
$308$	0.0436798	+	9.23316i	0.00248889	+	0.526108i
$309$		0			0
$310$	1.01666	−	3.12896i	0.0577425	−	0.177713i
$311$	−11.1722	+	8.11707i	−0.633517	+	0.460277i	−0.857617	−	0.514289i	$-0.828056\pi$
$311$	−11.1722	+	8.11707i	−0.633517	+	0.460277i	0.224100	+	0.974566i	$0.428056\pi$
$312$		0			0
$313$	−1.25750	−	3.87017i	−0.0710779	−	0.218755i	0.909207	−	0.416344i	$-0.136689\pi$
$313$	−1.25750	−	3.87017i	−0.0710779	−	0.218755i	−0.980285	+	0.197589i	$0.936689\pi$
$314$	2.66796	+	8.21113i	0.150562	+	0.463381i
$315$		0			0
$316$	4.20412	−	3.05447i	0.236500	−	0.171827i
$317$	−7.97880	+	24.5562i	−0.448134	+	1.37921i	0.430876	+	0.902411i	$0.358205\pi$
$317$	−7.97880	+	24.5562i	−0.448134	+	1.37921i	−0.879010	+	0.476803i	$0.841795\pi$
$318$		0			0
$319$	12.5938	+	17.1626i	0.705119	+	0.960921i
$320$	8.63682			0.482813
$321$		0			0
$322$	−0.885974	+	0.643698i	−0.0493734	+	0.0358719i
$323$	22.6524	+	16.4579i	1.26041	+	0.915743i
$324$		0			0
$325$	1.59676	+	4.91433i	0.0885725	+	0.272598i
$326$	5.00265	+	3.63464i	0.277071	+	0.201304i
$327$		0			0
$328$	−5.57654	+	17.1628i	−0.307913	+	0.947659i
$329$	−1.01974			−0.0562203
$330$		0			0
$331$	−3.35008			−0.184137			−0.0920684	−	0.995753i	$-0.529348\pi$
$331$	−3.35008			−0.184137			−0.0920684	+	0.995753i	$0.529348\pi$
$332$	2.51913	−	7.75307i	0.138255	−	0.425505i
$333$		0			0
$334$	1.85349	+	1.34664i	0.101419	+	0.0736850i
$335$	3.74775	+	11.5344i	0.204761	+	0.630191i
$336$		0			0
$337$	22.1669	+	16.1052i	1.20751	+	0.877307i	0.995002	−	0.0998530i	$-0.0318372\pi$
$337$	22.1669	+	16.1052i	1.20751	+	0.877307i	0.212507	+	0.977160i	$0.431837\pi$
$338$	12.8810	−	9.35859i	0.700634	−	0.509040i
$339$		0			0
$340$	3.24707			0.176097
$341$	−5.48285	+	7.62206i	−0.296913	+	0.412758i
$342$		0			0
$343$	−5.79826	+	17.8452i	−0.313076	+	0.963550i
$344$	22.1739	−	16.1103i	1.19554	−	0.868610i
$345$		0			0
$346$	−0.709284	−	2.18295i	−0.0381313	−	0.117356i
$347$	−4.89065	−	15.0519i	−0.262544	−	0.808027i	−0.992249	−	0.124265i	$-0.960343\pi$
$347$	−4.89065	−	15.0519i	−0.262544	−	0.808027i	0.729705	−	0.683762i	$-0.239657\pi$
$348$		0			0
$349$	2.96043	−	2.15088i	0.158468	−	0.115134i	−0.505725	−	0.862695i	$-0.668775\pi$
$349$	2.96043	−	2.15088i	0.158468	−	0.115134i	0.664194	+	0.747561i	$0.268775\pi$
$350$	1.53950	−	4.73811i	0.0822900	−	0.253263i
$351$		0			0
$352$	−11.0853	−	3.54393i	−0.590846	−	0.188892i
$353$	27.4937			1.46334			0.731671	−	0.681658i	$-0.238741\pi$
$353$	27.4937			1.46334			0.731671	+	0.681658i	$0.238741\pi$
$354$		0			0
$355$	−8.07556	+	5.86724i	−0.428606	+	0.311401i
$356$	1.34785	+	0.979273i	0.0714361	+	0.0519014i
$357$		0			0
$358$	−0.726559	−	2.23612i	−0.0383998	−	0.118183i
$359$	0.387309	+	0.281397i	0.0204414	+	0.0148515i	0.597959	−	0.801527i	$-0.295979\pi$
$359$	0.387309	+	0.281397i	0.0204414	+	0.0148515i	−0.577518	+	0.816378i	$0.695979\pi$
$360$		0			0
$361$	3.81936	−	11.7548i	0.201019	−	0.618673i
$362$	−23.4033			−1.23005
$363$		0			0
$364$	14.3852			0.753992
$365$	4.50007	−	13.8498i	0.235544	−	0.724931i
$366$		0			0
$367$	20.5961	+	14.9639i	1.07511	+	0.781111i	0.976823	−	0.214047i	$-0.0686645\pi$
$367$	20.5961	+	14.9639i	1.07511	+	0.781111i	0.0982843	+	0.995158i	$0.468665\pi$
$368$	−0.154837	−	0.476539i	−0.00807143	−	0.0248413i
$369$		0			0
$370$	3.69311	+	2.68320i	0.191996	+	0.139493i
$371$	−8.79762	+	6.39184i	−0.456750	+	0.331848i
$372$		0			0
$373$	−2.75967			−0.142890			−0.0714451	−	0.997445i	$-0.522761\pi$
$373$	−2.75967			−0.142890			−0.0714451	+	0.997445i	$0.522761\pi$
$374$	18.3568	+	5.86861i	0.949205	+	0.303459i
$375$		0			0
$376$	0.226333	−	0.696580i	0.0116722	−	0.0359234i
$377$	26.8315	−	19.4942i	1.38189	−	1.00400i
$378$		0			0
$379$	−6.69130	−	20.5937i	−0.343709	−	1.05783i	−0.962271	−	0.272092i	$-0.912284\pi$
$379$	−6.69130	−	20.5937i	−0.343709	−	1.05783i	0.618562	−	0.785736i	$-0.287716\pi$
$380$	−1.12380	−	3.45871i	−0.0576499	−	0.177428i
$381$		0			0
$382$	−11.9077	+	8.65148i	−0.609253	+	0.442648i
$383$	−5.01518	+	15.4351i	−0.256264	+	0.788699i	0.737314	+	0.675550i	$0.236094\pi$
$383$	−5.01518	+	15.4351i	−0.256264	+	0.788699i	−0.993578	+	0.113149i	$0.963906\pi$
$384$		0			0
$385$	−8.30253	+	11.5419i	−0.423136	+	0.588229i
$386$	16.1912			0.824109
$387$		0			0
$388$	1.05707	−	0.768007i	0.0536647	−	0.0389897i
$389$	−13.1802	−	9.57598i	−0.668263	−	0.485522i	0.201180	−	0.979554i	$-0.435522\pi$
$389$	−13.1802	−	9.57598i	−0.668263	−	0.485522i	−0.869443	+	0.494033i	$0.835522\pi$
$390$		0			0
$391$	−0.339639	−	1.04530i	−0.0171763	−	0.0528631i
$392$	−28.3398	−	20.5901i	−1.43138	−	1.03996i
$393$		0			0
$394$	5.24537	−	16.1436i	0.264258	−	0.813302i
$395$	8.00194			0.402621
$396$		0			0
$397$	−19.9673			−1.00213			−0.501064	−	0.865410i	$-0.667058\pi$
$397$	−19.9673			−1.00213			−0.501064	+	0.865410i	$0.667058\pi$
$398$	4.26453	−	13.1249i	0.213761	−	0.657890i
$399$		0			0
$400$	1.84410	+	1.33982i	0.0922050	+	0.0669909i
$401$	8.44448	+	25.9894i	0.421697	+	1.29785i	0.906122	+	0.423017i	$0.139029\pi$
$401$	8.44448	+	25.9894i	0.421697	+	1.29785i	−0.484425	+	0.874833i	$0.660971\pi$
$402$		0			0
$403$	11.8345	+	8.59825i	0.589517	+	0.428309i
$404$	3.98498	−	2.89526i	0.198260	−	0.144044i
$405$		0			0
$406$	−31.9763			−1.58696
$407$	−7.70731	−	10.5034i	−0.382037	−	0.520632i
$408$		0			0
$409$	7.70626	−	23.7174i	0.381050	−	1.17275i	−0.558255	−	0.829669i	$-0.688529\pi$
$409$	7.70626	−	23.7174i	0.381050	−	1.17275i	0.939305	−	0.343082i	$-0.111471\pi$
$410$	−5.51049	+	4.00361i	−0.272144	+	0.197724i
$411$		0			0
$412$	3.38518	+	10.4185i	0.166776	+	0.513283i
$413$	−10.4259	−	32.0876i	−0.513025	−	1.57893i
$414$		0			0
$415$	10.1556	−	7.37844i	0.498517	−	0.362193i
$416$	−5.60301	+	17.2443i	−0.274710	+	0.845471i
$417$		0			0
$418$	−0.102110	−	21.5843i	−0.00499437	−	1.05572i
$419$	−16.8256			−0.821986			−0.410993	−	0.911639i	$-0.634818\pi$
$419$	−16.8256			−0.821986			−0.410993	+	0.911639i	$0.634818\pi$
$420$		0			0
$421$	−19.0933	+	13.8721i	−0.930551	+	0.676085i	−0.946128	−	0.323793i	$-0.895042\pi$
$421$	−19.0933	+	13.8721i	−0.930551	+	0.676085i	0.0155763	+	0.999879i	$0.495042\pi$
$422$	−21.0151	−	15.2684i	−1.02300	−	0.743253i
$423$		0			0
$424$	−2.41359	−	7.42826i	−0.117214	−	0.360748i
$425$	4.04508	+	2.93893i	0.196215	+	0.142559i
$426$		0			0
$427$	6.43552	−	19.8065i	0.311437	−	0.958504i
$428$	5.04050			0.243642
$429$		0			0
$430$	10.3451			0.498886
$431$	11.6362	−	35.8126i	0.560497	−	1.72503i	−0.120469	−	0.992717i	$-0.538440\pi$
$431$	11.6362	−	35.8126i	0.560497	−	1.72503i	0.680966	−	0.732315i	$-0.261560\pi$
$432$		0			0
$433$	25.0594	+	18.2068i	1.20428	+	0.874961i	0.994699	−	0.102831i	$-0.0327900\pi$
$433$	25.0594	+	18.2068i	1.20428	+	0.874961i	0.209581	+	0.977791i	$0.432790\pi$
$434$	−4.35827	−	13.4134i	−0.209204	−	0.643862i
$435$		0			0
$436$	2.34150	+	1.70120i	0.112137	+	0.0814726i
$437$	−0.995884	+	0.723552i	−0.0476396	+	0.0346122i
$438$		0			0
$439$	−28.2131			−1.34654			−0.673268	−	0.739399i	$-0.735110\pi$
$439$	−28.2131			−1.34654			−0.673268	+	0.739399i	$0.735110\pi$
$440$	−6.04143	−	8.23313i	−0.288014	−	0.392499i
$441$		0			0
$442$	9.27837	−	28.5559i	0.441327	−	1.35827i
$443$	11.8456	−	8.60636i	0.562803	−	0.408900i	−0.269681	−	0.962950i	$-0.586918\pi$
$443$	11.8456	−	8.60636i	0.562803	−	0.408900i	0.832484	+	0.554050i	$0.186918\pi$
$444$		0			0
$445$	0.792768	+	2.43989i	0.0375808	+	0.115662i
$446$	6.88019	+	21.1751i	0.325787	+	1.00267i
$447$		0			0
$448$	29.9536	−	21.7626i	1.41517	−	1.02818i
$449$	−3.70749	+	11.4105i	−0.174967	+	0.538493i	−0.999632	−	0.0271282i	$-0.991364\pi$
$449$	−3.70749	+	11.4105i	−0.174967	+	0.538493i	0.824665	+	0.565622i	$0.191364\pi$
$450$		0			0
$451$	18.4587	−	6.09429i	0.869187	−	0.286969i
$452$	−5.00858			−0.235584
$453$		0			0
$454$	−14.4564	+	10.5032i	−0.678471	+	0.492938i
$455$	17.9206	+	13.0201i	0.840132	+	0.610392i
$456$		0			0
$457$	3.10367	+	9.55211i	0.145183	+	0.446829i	0.997035	−	0.0769553i	$-0.0245199\pi$
$457$	3.10367	+	9.55211i	0.145183	+	0.446829i	−0.851851	+	0.523784i	$0.824520\pi$
$458$	8.36893	+	6.08039i	0.391055	+	0.284118i
$459$		0			0
$460$	−0.0441132	+	0.135767i	−0.00205679	+	0.00633015i
$461$	13.4491			0.626386			0.313193	−	0.949689i	$-0.398601\pi$
$461$	13.4491			0.626386			0.313193	+	0.949689i	$0.398601\pi$
$462$		0			0
$463$	18.7836			0.872946			0.436473	−	0.899717i	$-0.356227\pi$
$463$	18.7836			0.872946			0.436473	+	0.899717i	$0.356227\pi$
$464$	4.52104	−	13.9143i	0.209884	−	0.645957i
$465$		0			0
$466$	−21.4705	−	15.5992i	−0.994602	−	0.722620i
$467$	−8.20470	−	25.2515i	−0.379668	−	1.16850i	−0.940275	−	0.340416i	$-0.889432\pi$
$467$	−8.20470	−	25.2515i	−0.379668	−	1.16850i	0.560607	−	0.828082i	$-0.310568\pi$
$468$		0			0
$469$	42.0614	+	30.5594i	1.94221	+	1.41110i
$470$	0.223652	−	0.162493i	0.0103163	−	0.00749522i
$471$		0			0
$472$	24.2329			1.11541
$473$	−28.1216	−	8.99039i	−1.29303	−	0.413379i
$474$		0			0
$475$	1.73049	−	5.32589i	0.0794002	−	0.244369i
$476$	11.2613	−	8.18178i	0.516159	−	0.375011i
$477$		0			0
$478$	6.05501	+	18.6354i	0.276950	+	0.852363i
$479$	−3.33214	−	10.2553i	−0.152249	−	0.468575i	0.845623	−	0.533781i	$-0.179229\pi$
$479$	−3.33214	−	10.2553i	−0.152249	−	0.468575i	−0.997872	+	0.0652062i	$0.979229\pi$
$480$		0			0
$481$	−16.4206	+	11.9303i	−0.748716	+	0.543974i
$482$	4.29538	−	13.2198i	0.195649	−	0.602146i
$483$		0			0
$484$	2.27166	+	6.77273i	0.103257	+	0.307851i
$485$	2.01199			0.0913596
$486$		0			0
$487$	−5.51018	+	4.00338i	−0.249690	+	0.181410i	−0.705589	−	0.708621i	$-0.749318\pi$
$487$	−5.51018	+	4.00338i	−0.249690	+	0.181410i	0.455899	+	0.890031i	$0.349318\pi$
$488$	12.1013	+	8.79212i	0.547801	+	0.398001i
$489$		0			0
$490$	−4.08575	−	12.5746i	−0.184575	−	0.568064i
$491$	21.1116	+	15.3385i	0.952754	+	0.692216i	0.951457	−	0.307783i	$-0.0995871\pi$
$491$	21.1116	+	15.3385i	0.952754	+	0.692216i	0.00129727	+	0.999999i	$0.499587\pi$
$492$		0			0
$493$	9.91703	−	30.5215i	0.446640	−	1.37462i
$494$	−33.6283			−1.51301
$495$		0			0
$496$	6.45297			0.289747
$497$	−13.2231	+	40.6967i	−0.593139	+	1.82549i
$498$		0			0
$499$	−15.6815	−	11.3933i	−0.702000	−	0.510033i	0.178583	−	0.983925i	$-0.442849\pi$
$499$	−15.6815	−	11.3933i	−0.702000	−	0.510033i	−0.880583	+	0.473892i	$0.842849\pi$
$500$	−0.200680	−	0.617629i	−0.00897468	−	0.0276212i
$501$		0			0
$502$	−15.0464	−	10.9318i	−0.671552	−	0.487911i
$503$	15.2437	−	11.0752i	0.679683	−	0.493819i	−0.193570	−	0.981087i	$-0.562007\pi$
$503$	15.2437	−	11.0752i	0.679683	−	0.493819i	0.873253	+	0.487268i	$0.162007\pi$
$504$		0			0
$505$	7.58484			0.337521
$506$	−0.494765	+	0.687805i	−0.0219950	+	0.0305767i
$507$		0			0
$508$	−0.307270	+	0.945678i	−0.0136329	+	0.0419577i
$509$	−4.16741	+	3.02780i	−0.184717	+	0.134205i	−0.676301	−	0.736625i	$-0.736418\pi$
$509$	−4.16741	+	3.02780i	−0.184717	+	0.134205i	0.491584	+	0.870830i	$0.336418\pi$
$510$		0			0
$511$	−19.2911	−	59.3718i	−0.853387	−	2.62645i
$512$	6.80928	+	20.9568i	0.300930	+	0.926168i
$513$		0			0
$514$	−5.14707	+	3.73956i	−0.227027	+	0.164945i
$515$	−5.21267	+	16.0429i	−0.229698	+	0.706936i
$516$		0			0
$517$	−0.749175	+	0.247346i	−0.0329487	+	0.0108783i
$518$	19.5692			0.859820
$519$		0			0
$520$	−12.8714	+	9.35164i	−0.564450	+	0.410097i
$521$	−33.5759	−	24.3944i	−1.47099	−	1.06874i	−0.980326	−	0.197387i	$-0.936754\pi$
$521$	−33.5759	−	24.3944i	−1.47099	−	1.06874i	−0.490663	−	0.871349i	$-0.663246\pi$
$522$		0			0
$523$	−2.13926	−	6.58397i	−0.0935434	−	0.287897i	0.893328	−	0.449405i	$-0.148364\pi$
$523$	−2.13926	−	6.58397i	−0.0935434	−	0.287897i	−0.986871	+	0.161508i	$0.948364\pi$
$524$	−1.39810	−	1.01578i	−0.0610762	−	0.0443745i
$525$		0			0
$526$	4.30377	−	13.2456i	0.187653	−	0.577537i
$527$	14.1548			0.616592
$528$		0			0
$529$	−22.9517			−0.997899
$530$	0.910990	−	2.80374i	0.0395709	−	0.121787i
$531$		0			0
$532$	−12.6125	−	9.16355i	−0.546823	−	0.397290i
$533$	−9.35863	−	28.8029i	−0.405367	−	1.24759i
$534$		0			0
$535$	6.27928	+	4.56216i	0.271477	+	0.197239i
$536$	−30.2104	+	21.9492i	−1.30489	+	0.948059i
$537$		0			0
$538$	15.8592			0.683740
$539$	0.178505	+	37.7329i	0.00768874	+	1.62527i
$540$		0			0
$541$	−8.78173	+	27.0274i	−0.377556	+	1.16200i	0.564182	+	0.825651i	$0.309192\pi$
$541$	−8.78173	+	27.0274i	−0.377556	+	1.16200i	−0.941738	+	0.336348i	$0.890808\pi$
$542$	11.1299	−	8.08635i	0.478071	−	0.347339i
$543$		0			0
$544$	5.42167	+	16.6862i	0.232452	+	0.715415i
$545$	1.37720	+	4.23858i	0.0589928	+	0.181561i
$546$		0			0
$547$	−20.9205	+	15.1996i	−0.894496	+	0.649889i	−0.937046	−	0.349205i	$-0.886452\pi$
$547$	−20.9205	+	15.1996i	−0.894496	+	0.649889i	0.0425503	+	0.999094i	$0.486452\pi$
$548$	2.05807	−	6.33407i	0.0879162	−	0.270578i
$549$		0			0
$550$	−0.0182340	−	3.85436i	−0.000777501	−	0.164351i
$551$	−35.9431			−1.53123
$552$		0			0
$553$	27.7518	−	20.1628i	1.18012	−	0.857411i
$554$	9.65002	+	7.01115i	0.409990	+	0.297875i
$555$		0			0
$556$	1.06262	+	3.27039i	0.0450649	+	0.138696i
$557$	−6.52399	−	4.73996i	−0.276430	−	0.200838i	0.440929	−	0.897542i	$-0.354649\pi$
$557$	−6.52399	−	4.73996i	−0.276430	−	0.200838i	−0.717359	+	0.696704i	$0.754649\pi$
$558$		0			0
$559$	−14.2140	+	43.7461i	−0.601186	+	1.85026i
$560$	9.77157			0.412924
$561$		0			0
$562$	−3.41542			−0.144071
$563$	−9.16284	+	28.2003i	−0.386168	+	1.18850i	0.549462	+	0.835519i	$0.314833\pi$
$563$	−9.16284	+	28.2003i	−0.386168	+	1.18850i	−0.935630	+	0.352983i	$0.885167\pi$
$564$		0			0
$565$	−6.23952	−	4.53327i	−0.262498	−	0.190716i
$566$	−7.83892	−	24.1257i	−0.329494	−	1.01408i
$567$		0			0
$568$	−24.8647	−	18.0653i	−1.04330	−	0.758002i
$569$	−34.0618	+	24.7473i	−1.42794	+	1.03746i	−0.437548	+	0.899195i	$0.644153\pi$
$569$	−34.0618	+	24.7473i	−1.42794	+	1.03746i	−0.990395	+	0.138266i	$0.955847\pi$
$570$		0			0
$571$	−26.6823			−1.11662			−0.558311	−	0.829632i	$-0.688550\pi$
$571$	−26.6823			−1.11662			−0.558311	+	0.829632i	$0.688550\pi$
$572$	10.5684	−	3.48924i	0.441887	−	0.145893i
$573$		0			0
$574$	−9.02304	+	27.7700i	−0.376614	+	1.15910i
$575$	−0.177837	+	0.129206i	−0.00741632	+	0.00538827i
$576$		0			0
$577$	−1.02228	−	3.14627i	−0.0425582	−	0.130981i	0.927520	−	0.373774i	$-0.121936\pi$
$577$	−1.02228	−	3.14627i	−0.0425582	−	0.130981i	−0.970078	+	0.242793i	$0.921936\pi$
$578$	−2.87299	−	8.84214i	−0.119500	−	0.367785i
$579$		0			0
$580$	−3.37216	+	2.45002i	−0.140021	+	0.101731i
$581$	16.6290	−	51.1788i	0.689887	−	2.12325i
$582$		0			0
$583$	−4.91296	+	6.82982i	−0.203474	+	0.282862i
$584$	44.8381			1.85542
$585$		0			0
$586$	23.2854	−	16.9178i	0.961911	−	0.698869i
$587$	−6.89906	−	5.01246i	−0.284755	−	0.206886i	0.436234	−	0.899833i	$-0.356312\pi$
$587$	−6.89906	−	5.01246i	−0.284755	−	0.206886i	−0.720989	+	0.692947i	$0.756312\pi$
$588$		0			0
$589$	−4.89893	−	15.0774i	−0.201857	−	0.621252i
$590$	7.39968	+	5.37618i	0.304640	+	0.221334i
$591$		0			0
$592$	−2.76684	+	8.51544i	−0.113716	+	0.349983i
$593$	23.4343			0.962333			0.481167	−	0.876629i	$-0.340213\pi$
$593$	23.4343			0.962333			0.481167	+	0.876629i	$0.340213\pi$
$594$		0			0
$595$	21.4342			0.878717
$596$	0.760259	−	2.33984i	0.0311414	−	0.0958434i
$597$		0			0
$598$	1.06793	+	0.775895i	0.0436708	+	0.0317287i
$599$	−5.82017	−	17.9126i	−0.237805	−	0.731890i	−0.996737	−	0.0807194i	$-0.974278\pi$
$599$	−5.82017	−	17.9126i	−0.237805	−	0.731890i	0.758931	−	0.651171i	$-0.225722\pi$
$600$		0			0
$601$	30.4664	+	22.1351i	1.24275	+	0.902911i	0.997778	−	0.0666198i	$-0.0212214\pi$
$601$	30.4664	+	22.1351i	1.24275	+	0.902911i	0.244971	+	0.969530i	$0.421221\pi$
$602$	35.8782	−	26.0670i	1.46229	−	1.06241i
$603$		0			0
$604$	3.84453			0.156432
$605$	−3.30005	+	10.4933i	−0.134166	+	0.426614i
$606$		0			0
$607$	−9.07520	+	27.9306i	−0.368351	+	1.13367i	0.579505	+	0.814969i	$0.303246\pi$
$607$	−9.07520	+	27.9306i	−0.368351	+	1.13367i	−0.947856	+	0.318699i	$0.896754\pi$
$608$	15.8973	−	11.5501i	0.644723	−	0.468418i
$609$		0			0
$610$	1.74465	+	5.36947i	0.0706387	+	0.217403i
$611$	0.379834	+	1.16901i	0.0153665	+	0.0472931i
$612$		0			0
$613$	10.4453	−	7.58894i	0.421881	−	0.306515i	−0.356513	−	0.934290i	$-0.616035\pi$
$613$	10.4453	−	7.58894i	0.421881	−	0.306515i	0.778394	+	0.627776i	$0.216035\pi$
$614$	1.77415	−	5.46027i	0.0715989	−	0.220359i
$615$		0			0
$616$	−41.6978	−	13.3307i	−1.68005	−	0.537109i
$617$	−41.6041			−1.67492			−0.837459	−	0.546500i	$-0.815960\pi$
$617$	−41.6041			−1.67492			−0.837459	+	0.546500i	$0.815960\pi$
$618$		0			0
$619$	−3.45545	+	2.51053i	−0.138886	+	0.100907i	−0.655059	−	0.755578i	$-0.727356\pi$
$619$	−3.45545	+	2.51053i	−0.138886	+	0.100907i	0.516173	+	0.856484i	$0.327356\pi$
$620$	−1.48735	−	1.08062i	−0.0597333	−	0.0433988i
$621$		0			0
$622$	−4.95935	−	15.2633i	−0.198852	−	0.612002i
$623$	8.89731	+	6.46427i	0.356463	+	0.258986i
$624$		0			0
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$	4.72918			0.189016
$627$		0			0
$628$	4.82455			0.192521
$629$	−6.06913	+	18.6789i	−0.241992	+	0.744775i
$630$		0			0
$631$	22.2892	+	16.1941i	0.887319	+	0.644675i	0.935178	−	0.354179i	$-0.115240\pi$
$631$	22.2892	+	16.1941i	0.887319	+	0.644675i	−0.0478586	+	0.998854i	$0.515240\pi$
$632$	7.61358	+	23.4322i	0.302852	+	0.932082i
$633$		0			0
$634$	−24.2758	−	17.6374i	−0.964116	−	0.700471i
$635$	−1.23872	+	0.899983i	−0.0491571	+	0.0357147i
$636$		0			0
$637$	58.7877			2.32925
$638$	−23.4920	+	7.75607i	−0.930057	+	0.307066i
$639$		0			0
$640$	−0.933014	+	2.87152i	−0.0368806	+	0.113507i
$641$	7.41712	−	5.38885i	0.292958	−	0.212847i	−0.431591	−	0.902069i	$-0.642048\pi$
$641$	7.41712	−	5.38885i	0.292958	−	0.212847i	0.724550	+	0.689222i	$0.242048\pi$
$642$		0			0
$643$	−1.05346	−	3.24223i	−0.0415446	−	0.127861i	0.928133	−	0.372249i	$-0.121413\pi$
$643$	−1.05346	−	3.24223i	−0.0415446	−	0.127861i	−0.969678	+	0.244387i	$0.921413\pi$
$644$	0.189106	+	0.582010i	0.00745184	+	0.0229344i
$645$		0			0
$646$	−26.3254	+	19.1265i	−1.03576	+	0.752523i
$647$	−6.90986	+	21.2663i	−0.271654	+	0.836066i	0.718431	+	0.695598i	$0.244861\pi$
$647$	−6.90986	+	21.2663i	−0.271654	+	0.836066i	−0.990085	+	0.140468i	$0.955139\pi$
$648$		0			0
$649$	−15.4427	−	21.0450i	−0.606179	−	0.826087i
$650$	−6.00509			−0.235539
$651$		0			0
$652$	2.79551	−	2.03106i	0.109481	−	0.0795423i
$653$	−11.9699	−	8.69667i	−0.468420	−	0.340327i	0.328405	−	0.944537i	$-0.393489\pi$
$653$	−11.9699	−	8.69667i	−0.468420	−	0.340327i	−0.796825	+	0.604210i	$0.793489\pi$
$654$		0			0
$655$	−0.822320	−	2.53084i	−0.0321307	−	0.0988882i
$656$	−10.8083	−	7.85267i	−0.421992	−	0.306595i
$657$		0			0
$658$	0.366214	−	1.12709i	0.0142765	−	0.0439385i
$659$	47.4724			1.84926			0.924631	−	0.380864i	$-0.124373\pi$
$659$	47.4724			1.84926			0.924631	+	0.380864i	$0.124373\pi$
$660$		0			0
$661$	−21.6525			−0.842184			−0.421092	−	0.907018i	$-0.638353\pi$
$661$	−21.6525			−0.842184			−0.421092	+	0.907018i	$0.638353\pi$
$662$	1.20309	−	3.70273i	0.0467594	−	0.143911i
$663$		0			0
$664$	31.2690	+	22.7183i	1.21347	+	0.881641i
$665$	−7.41833	−	22.8313i	−0.287670	−	0.885358i
$666$		0			0
$667$	1.14144	+	0.829302i	0.0441966	+	0.0321107i
$668$	1.03574	−	0.752510i	0.0400740	−	0.0291155i
$669$		0			0
$670$	−14.0945			−0.544518
$671$	−0.0762228	−	16.1122i	−0.00294255	−	0.622005i
$672$		0			0
$673$	−11.8639	+	36.5133i	−0.457319	+	1.40748i	0.411072	+	0.911603i	$0.365154\pi$
$673$	−11.8639	+	36.5133i	−0.457319	+	1.40748i	−0.868391	+	0.495880i	$0.834846\pi$
$674$	−25.7612	+	18.7166i	−0.992285	+	0.720937i
$675$		0			0
$676$	−2.74938	−	8.46172i	−0.105745	−	0.325451i
$677$	7.08677	+	21.8108i	0.272367	+	0.838259i	0.989904	+	0.141739i	$0.0452693\pi$
$677$	7.08677	+	21.8108i	0.272367	+	0.838259i	−0.717537	+	0.696520i	$0.754731\pi$
$678$		0			0
$679$	6.97782	−	5.06969i	0.267784	−	0.194557i
$680$	−4.75733	+	14.6416i	−0.182435	+	0.561478i
$681$		0			0
$682$	−6.45540	−	8.79727i	−0.247190	−	0.336865i
$683$	−25.9084			−0.991359			−0.495680	−	0.868505i	$-0.665081\pi$
$683$	−25.9084			−0.991359			−0.495680	+	0.868505i	$0.665081\pi$
$684$		0			0
$685$	8.29684	−	6.02801i	0.317006	−	0.230318i
$686$	−17.6414	−	12.8173i	−0.673553	−	0.489365i
$687$		0			0
$688$	6.27024	+	19.2978i	0.239050	+	0.735722i
$689$	10.6044	+	7.70454i	0.403995	+	0.293520i
$690$		0			0
$691$	4.57824	−	14.0904i	0.174165	−	0.536023i	−0.825430	−	0.564505i	$-0.809067\pi$
$691$	4.57824	−	14.0904i	0.174165	−	0.536023i	0.999594	+	0.0284814i	$0.00906715\pi$
$692$	−1.28262			−0.0487579
$693$		0			0
$694$	18.3927			0.698177
$695$	−1.63627	+	5.03592i	−0.0620672	+	0.191023i
$696$		0			0
$697$	−23.7082	−	17.2250i	−0.898014	−	0.652445i
$698$	1.31414	+	4.04450i	0.0497409	+	0.153087i
$699$		0			0
$700$	−2.25225	−	1.63636i	−0.0851271	−	0.0618484i
$701$	4.45471	−	3.23653i	0.168252	−	0.122242i	−0.500473	−	0.865752i	$-0.666840\pi$
$701$	4.45471	−	3.23653i	0.168252	−	0.122242i	0.668725	+	0.743510i	$0.266840\pi$
$702$		0			0
$703$	21.9968			0.829626
$704$	16.7273	−	23.2538i	0.630435	−	0.876409i
$705$		0			0
$706$	−9.87362	+	30.3879i	−0.371599	+	1.14366i
$707$	26.3052	−	19.1119i	0.989309	−	0.718775i
$708$		0			0
$709$	−5.53161	−	17.0245i	−0.207744	−	0.639370i	−0.999590	−	0.0286488i	$-0.990880\pi$
$709$	−5.53161	−	17.0245i	−0.207744	−	0.639370i	0.791846	−	0.610721i	$-0.209120\pi$
$710$	−3.58475	−	11.0327i	−0.134533	−	0.414050i
$711$		0			0
$712$	−6.39046	+	4.64294i	−0.239493	+	0.174002i
$713$	−0.192300	+	0.591840i	−0.00720171	+	0.0221646i
$714$		0			0
$715$	16.3239	+	5.21870i	0.610478	+	0.195168i
$716$	−1.31386			−0.0491012
$717$		0			0
$718$	−0.450110	+	0.327024i	−0.0167980	+	0.0122044i
$719$	26.3673	+	19.1570i	0.983334	+	0.714434i	0.958451	−	0.285256i	$-0.0920786\pi$
$719$	26.3673	+	19.1570i	0.983334	+	0.714434i	0.0248831	+	0.999690i	$0.492079\pi$
$720$		0			0
$721$	22.3459	+	68.7735i	0.832204	+	2.56126i
$722$	11.6206	+	8.44284i	0.432473	+	0.314210i
$723$		0			0
$724$	−4.04130	+	12.4378i	−0.150194	+	0.462248i
$725$	−6.41843			−0.238375
$726$		0			0
$727$	−43.0199			−1.59552			−0.797759	−	0.602976i	$-0.793982\pi$
$727$	−43.0199			−1.59552			−0.797759	+	0.602976i	$0.793982\pi$
$728$	−21.0760	+	64.8654i	−0.781130	+	2.40407i
$729$		0			0
$730$	13.6916	+	9.94756i	0.506750	+	0.368176i
$731$	13.7539	+	42.3302i	0.508708	+	1.56564i
$732$		0			0
$733$	−32.9323	−	23.9267i	−1.21638	−	0.883755i	−0.220589	−	0.975367i	$-0.570798\pi$
$733$	−32.9323	−	23.9267i	−1.21638	−	0.883755i	−0.995795	+	0.0916123i	$0.970798\pi$
$734$	−23.9357	+	17.3903i	−0.883483	+	0.641888i
$735$		0			0
$736$	−0.771340			−0.0284320
$737$	38.3136	+	12.2488i	1.41130	+	0.451189i
$738$		0			0
$739$	11.7810	−	36.2581i	0.433370	−	1.33377i	−0.461379	−	0.887203i	$-0.652645\pi$
$739$	11.7810	−	36.2581i	0.433370	−	1.33377i	0.894748	−	0.446571i	$-0.147355\pi$
$740$	2.06373	−	1.49939i	0.0758643	−	0.0551186i
$741$		0			0
$742$	−3.90527	−	12.0192i	−0.143367	−	0.441238i
$743$	5.57409	+	17.1553i	0.204493	+	0.629366i	0.999734	+	0.0230717i	$0.00734459\pi$
$743$	5.57409	+	17.1553i	0.204493	+	0.629366i	−0.795240	+	0.606294i	$0.792655\pi$
$744$		0			0
$745$	3.06489	−	2.22677i	0.112289	−	0.0815827i
$746$	0.991061	−	3.05017i	0.0362853	−	0.111675i
$747$		0			0
$748$	6.28875	−	8.74240i	0.229940	−	0.319654i
$749$	33.2728			1.21576
$750$		0			0
$751$	14.1861	−	10.3068i	0.517657	−	0.376100i	−0.298064	−	0.954546i	$-0.596341\pi$
$751$	14.1861	−	10.3068i	0.517657	−	0.376100i	0.815720	+	0.578446i	$0.196341\pi$
$752$	0.438670	+	0.318713i	0.0159967	+	0.0116223i
$753$		0			0
$754$	11.9105	+	36.6568i	0.433756	+	1.33496i
$755$	4.78939	+	3.47969i	0.174304	+	0.126639i
$756$		0			0
$757$	−8.02236	+	24.6903i	−0.291578	+	0.897383i	0.692772	+	0.721157i	$0.256389\pi$
$757$	−8.02236	+	24.6903i	−0.291578	+	0.897383i	−0.984350	+	0.176227i	$0.943611\pi$
$758$	25.1646			0.914019
$759$		0			0
$760$	17.2424			0.625447
$761$	−8.65430	+	26.6352i	−0.313718	+	0.965525i	0.662561	+	0.749008i	$0.269470\pi$
$761$	−8.65430	+	26.6352i	−0.313718	+	0.965525i	−0.976279	+	0.216517i	$0.930530\pi$
$762$		0			0
$763$	15.4564	+	11.2298i	0.559561	+	0.406545i
$764$	2.54164	+	7.82237i	0.0919534	+	0.283003i
$765$		0			0
$766$	−15.2589	−	11.0862i	−0.551326	−	0.400562i
$767$	−32.9011	+	23.9040i	−1.18799	+	0.863124i
$768$		0			0
$769$	22.9537			0.827732			0.413866	−	0.910338i	$-0.364178\pi$
$769$	22.9537			0.827732			0.413866	+	0.910338i	$0.364178\pi$
$770$	−9.77524	−	13.3215i	−0.352275	−	0.480073i
$771$		0			0
$772$	2.79590	−	8.60489i	0.100627	−	0.309697i
$773$	−19.0347	+	13.8295i	−0.684631	+	0.497414i	−0.874891	−	0.484320i	$-0.839067\pi$
$773$	−19.0347	+	13.8295i	−0.684631	+	0.497414i	0.190259	+	0.981734i	$0.439067\pi$
$774$		0			0
$775$	−0.874813	−	2.69240i	−0.0314242	−	0.0967138i
$776$	1.91434	+	5.89172i	0.0687207	+	0.211500i
$777$		0			0
$778$	15.3173	−	11.1287i	0.549153	−	0.398983i
$779$	−10.1424	+	31.2151i	−0.363389	+	1.11840i
$780$		0			0
$781$	0.156616	+	33.1060i	0.00560416	+	1.18463i
$782$	1.27731			0.0456765
$783$		0			0
$784$	20.9804	−	15.2431i	0.749298	−	0.544397i
$785$	6.01026	+	4.36671i	0.214515	+	0.155854i
$786$		0			0
$787$	−7.80964	−	24.0356i	−0.278384	−	0.856777i	−0.988304	−	0.152495i	$-0.951269\pi$
$787$	−7.80964	−	24.0356i	−0.278384	−	0.856777i	0.709921	−	0.704282i	$-0.248731\pi$
$788$	−7.67383	−	5.57536i	−0.273369	−	0.198614i
$789$		0			0
$790$	−2.87368	+	8.84429i	−0.102241	+	0.314666i
$791$	−33.0621			−1.17555
$792$		0			0
$793$	−25.1028			−0.891427
$794$	7.17071	−	22.0692i	0.254479	−	0.783205i
$795$		0			0
$796$	−6.23888	−	4.53281i	−0.221131	−	0.160661i
$797$	−2.67499	−	8.23277i	−0.0947530	−	0.291620i	0.892436	−	0.451173i	$-0.148994\pi$
$797$	−2.67499	−	8.23277i	−0.0947530	−	0.291620i	−0.987189	+	0.159554i	$0.948994\pi$
$798$		0			0
$799$	0.962236	+	0.699105i	0.0340414	+	0.0247326i
$800$	2.83882	−	2.06253i	0.100368	−	0.0729213i
$801$		0			0
$802$	−31.7579			−1.12141
$803$	−28.5736	−	38.9395i	−1.00834	−	1.37415i
$804$		0			0
$805$	−0.291195	+	0.896208i	−0.0102633	+	0.0315872i
$806$	−13.7534	+	9.99243i	−0.484443	+	0.351968i
$807$		0			0
$808$	7.21672	+	22.2108i	0.253883	+	0.781373i
$809$	3.15582	+	9.71261i	0.110953	+	0.341477i	0.991081	−	0.133258i	$-0.0425438\pi$
$809$	3.15582	+	9.71261i	0.110953	+	0.341477i	−0.880129	+	0.474735i	$0.842544\pi$
$810$		0			0
$811$	38.5273	−	27.9917i	1.35288	−	0.982923i	0.354015	−	0.935240i	$-0.384816\pi$
$811$	38.5273	−	27.9917i	1.35288	−	0.982923i	0.998862	−	0.0476835i	$-0.0151839\pi$
$812$	−5.52167	+	16.9940i	−0.193773	+	0.596371i
$813$		0			0
$814$	14.3769	−	4.74664i	0.503910	−	0.166370i
$815$	5.32086			0.186381
$816$		0			0
$817$	40.3291	−	29.3008i	1.41094	−	1.02510i
$818$	23.4466	+	17.0350i	0.819792	+	0.595613i
$819$		0			0
$820$	1.17618	+	3.61993i	0.0410742	+	0.126413i
$821$	−38.4767	−	27.9550i	−1.34285	−	0.975635i	−0.999334	−	0.0364868i	$-0.988383\pi$
$821$	−38.4767	−	27.9550i	−1.34285	−	0.975635i	−0.343512	−	0.939148i	$-0.611617\pi$
$822$		0			0
$823$	−7.64384	+	23.5253i	−0.266448	+	0.820041i	0.724909	+	0.688845i	$0.241882\pi$
$823$	−7.64384	+	23.5253i	−0.266448	+	0.820041i	−0.991356	+	0.131196i	$0.958118\pi$
$824$	−51.9384			−1.80936
$825$		0			0
$826$	39.2096			1.36428
$827$	0.482580	−	1.48523i	0.0167810	−	0.0516465i	−0.942315	−	0.334726i	$-0.891356\pi$
$827$	0.482580	−	1.48523i	0.0167810	−	0.0516465i	0.959096	+	0.283080i	$0.0913561\pi$
$828$		0			0
$829$	−34.1365	−	24.8016i	−1.18561	−	0.861396i	−0.192817	−	0.981235i	$-0.561762\pi$
$829$	−34.1365	−	24.8016i	−1.18561	−	0.861396i	−0.992793	+	0.119839i	$0.961762\pi$
$830$	4.50806	+	13.8744i	0.156477	+	0.481587i
$831$		0			0
$832$	−36.1052	−	26.2320i	−1.25172	−	0.909430i
$833$	46.0210	−	33.4362i	1.59453	−	1.15850i
$834$		0			0
$835$	1.97139			0.0682227
$836$	−11.4887	−	3.67292i	−0.397346	−	0.127031i
$837$		0			0
$838$	6.04247	−	18.5968i	0.208734	−	0.642416i
$839$	−5.09236	+	3.69982i	−0.175808	+	0.127732i	−0.672209	−	0.740361i	$-0.734654\pi$
$839$	−5.09236	+	3.69982i	−0.175808	+	0.127732i	0.496401	+	0.868093i	$0.334654\pi$
$840$		0			0
$841$	3.76886	+	11.5994i	0.129961	+	0.399978i
$842$	−8.47554	−	26.0850i	−0.292086	−	0.898949i
$843$		0			0
$844$	−11.7434	+	8.53205i	−0.404223	+	0.293685i
$845$	4.23363	−	13.0298i	0.145641	−	0.448238i
$846$		0			0
$847$	14.9954	+	44.7074i	0.515249	+	1.53617i
$848$	5.78225			0.198563
$849$		0			0
$850$	−4.70098	+	3.41546i	−0.161242	+	0.117149i
$851$	−0.698548	−	0.507525i	−0.0239459	−	0.0173977i
$852$		0			0
$853$	−2.24692	−	6.91532i	−0.0769332	−	0.236776i	0.905193	−	0.425002i	$-0.139726\pi$
$853$	−2.24692	−	6.91532i	−0.0769332	−	0.236776i	−0.982126	+	0.188225i	$0.939726\pi$
$854$	19.5803	+	14.2259i	0.670025	+	0.486802i
$855$		0			0
$856$	−7.38491	+	22.7284i	−0.252411	+	0.776841i
$857$	−39.8590			−1.36156			−0.680779	−	0.732489i	$-0.738359\pi$
$857$	−39.8590			−1.36156			−0.680779	+	0.732489i	$0.738359\pi$
$858$		0			0
$859$	13.5278			0.461564			0.230782	−	0.973006i	$-0.425872\pi$
$859$	13.5278			0.461564			0.230782	+	0.973006i	$0.425872\pi$
$860$	1.78640	−	5.49797i	0.0609157	−	0.187479i
$861$		0			0
$862$	35.4037	+	25.7223i	1.20585	+	0.876104i
$863$	−15.5472	−	47.8493i	−0.529232	−	1.62881i	−0.755792	−	0.654812i	$-0.772748\pi$
$863$	−15.5472	−	47.8493i	−0.529232	−	1.62881i	0.226560	−	0.973997i	$-0.427252\pi$
$864$		0			0
$865$	−1.59784	−	1.16090i	−0.0543283	−	0.0394718i
$866$	−29.1228	+	21.1589i	−0.989632	+	0.719010i
$867$		0			0
$868$	−7.88119			−0.267505
$869$	15.4977	−	21.5444i	0.525725	−	0.730844i
$870$		0			0
$871$	19.3655	−	59.6009i	0.656175	−	2.01950i
$872$	−11.1015	+	8.06574i	−0.375946	+	0.273140i
$873$		0			0
$874$	−0.442073	−	1.36056i	−0.0149534	−	0.0460217i
$875$	−1.32471	−	4.07703i	−0.0447833	−	0.137829i
$876$		0			0
$877$	0.976773	−	0.709667i	0.0329833	−	0.0239638i	−0.571171	−	0.820831i	$-0.693511\pi$
$877$	0.976773	−	0.709667i	0.0329833	−	0.0239638i	0.604155	+	0.796867i	$0.293511\pi$
$878$	10.1320	−	31.1830i	0.341937	−	1.05237i
$879$		0			0
$880$	7.17888	−	2.37016i	0.242000	−	0.0798982i
$881$	−1.91816			−0.0646245			−0.0323123	−	0.999478i	$-0.510287\pi$
$881$	−1.91816			−0.0646245			−0.0323123	+	0.999478i	$0.510287\pi$
$882$		0			0
$883$	−46.9950	+	34.1439i	−1.58151	+	1.14903i	−0.666566	+	0.745446i	$0.732237\pi$
$883$	−46.9950	+	34.1439i	−1.58151	+	1.14903i	−0.914941	+	0.403587i	$0.867763\pi$
$884$	−13.5740	−	9.86208i	−0.456543	−	0.331698i
$885$		0			0
$886$	5.25828	+	16.1833i	0.176656	+	0.543690i
$887$	24.4668	+	17.7762i	0.821516	+	0.596866i	0.917146	−	0.398551i	$-0.130487\pi$
$887$	24.4668	+	17.7762i	0.821516	+	0.596866i	−0.0956306	+	0.995417i	$0.530487\pi$
$888$		0			0
$889$	−2.02832	+	6.24251i	−0.0680275	+	0.209367i
$890$	−2.98143			−0.0999378
$891$		0			0
$892$	12.4417			0.416578
$893$	0.411644	−	1.26691i	0.0137752	−	0.0423956i
$894$		0			0
$895$	−1.63676	−	1.18918i	−0.0547109	−	0.0397498i
$896$	3.99968	+	12.3098i	0.133620	+	0.411240i
$897$		0			0
$898$	−11.2802	−	8.19553i	−0.376425	−	0.273488i
$899$	−14.7001	+	10.6802i	−0.490275	+	0.356206i
$900$		0			0
$901$	12.6835			0.422550
$902$	0.106870	+	22.5904i	0.00355837	+	0.752179i
$903$		0			0
$904$	7.33815	−	22.5845i	0.244063	−	0.751149i
$905$	−16.2920	+	11.8368i	−0.541564	+	0.393469i
$906$		0			0
$907$	−9.87830	−	30.4023i	−0.328004	−	1.00949i	−0.970066	−	0.242839i	$-0.921921\pi$
$907$	−9.87830	−	30.4023i	−0.328004	−	1.00949i	0.642063	−	0.766652i	$-0.278079\pi$
$908$	3.08563	+	9.49660i	0.102400	+	0.315156i
$909$		0			0
$910$	−20.8264	+	15.1313i	−0.690389	+	0.501597i
$911$	16.0211	−	49.3079i	0.530803	−	1.63364i	−0.221745	−	0.975105i	$-0.571175\pi$
$911$	16.0211	−	49.3079i	0.530803	−	1.63364i	0.752547	−	0.658538i	$-0.228825\pi$
$912$		0			0
$913$	−0.196955	−	41.6330i	−0.00651826	−	1.37785i
$914$	−11.6722			−0.386083
$915$		0			0
$916$	4.67660	−	3.39775i	0.154519	−	0.112265i
$917$	−9.22898	−	6.70525i	−0.304768	−	0.221427i
$918$		0			0
$919$	−10.5710	−	32.5341i	−0.348704	−	1.07320i	−0.959571	−	0.281468i	$-0.909179\pi$
$919$	−10.5710	−	32.5341i	−0.348704	−	1.07320i	0.610866	−	0.791734i	$-0.290821\pi$
$920$	−0.547562	−	0.397827i	−0.0180526	−	0.0131160i
$921$		0			0
$922$	−4.82988	+	14.8648i	−0.159064	+	0.489547i
$923$	51.5790			1.69774
$924$		0			0
$925$	3.92802			0.129153
$926$	−6.74561	+	20.7609i	−0.221675	+	0.682244i
$927$		0			0
$928$	−18.2208	−	13.2382i	−0.598127	−	0.434565i
$929$	−5.66990	−	17.4502i	−0.186023	−	0.572521i	0.813941	−	0.580947i	$-0.197318\pi$
$929$	−5.66990	−	17.4502i	−0.186023	−	0.572521i	−0.999964	+	0.00842624i	$0.997318\pi$
$930$		0			0
$931$	−51.5433	−	37.4484i	−1.68926	−	1.22732i
$932$	−11.9978	+	8.71693i	−0.393002	+	0.285533i
$933$		0			0
$934$	30.8561			1.00964
$935$	15.7471	−	5.19902i	0.514984	−	0.170026i
$936$		0			0
$937$	1.04576	−	3.21852i	0.0341635	−	0.105144i	−0.932521	−	0.361117i	$-0.882396\pi$
$937$	1.04576	−	3.21852i	0.0341635	−	0.105144i	0.966684	+	0.255972i	$0.0823956\pi$
$938$	−48.8815	+	35.5145i	−1.59604	+	1.15959i
$939$		0			0
$940$	−0.0477373	−	0.146920i	−0.00155702	−	0.00479201i
$941$	10.8465	+	33.3822i	0.353587	+	1.08823i	0.956824	+	0.290668i	$0.0938774\pi$
$941$	10.8465	+	33.3822i	0.353587	+	1.08823i	−0.603237	+	0.797562i	$0.706123\pi$
$942$		0			0
$943$	1.04230	−	0.757278i	0.0339421	−	0.0246604i
$944$	−5.54375	+	17.0619i	−0.180434	+	0.555318i
$945$		0			0
$946$	20.0359	−	27.8532i	0.651423	−	0.905585i
$947$	39.0512			1.26899			0.634497	−	0.772925i	$-0.281207\pi$
$947$	39.0512			1.26899			0.634497	+	0.772925i	$0.281207\pi$
$948$		0			0
$949$	−60.8769	+	44.2297i	−1.97615	+	1.43576i
$950$	5.26508	+	3.82530i	0.170822	+	0.124109i
$951$		0			0
$952$	20.3939	+	62.7660i	0.660971	+	2.03426i
$953$	19.9652	+	14.5055i	0.646735	+	0.469881i	0.862158	−	0.506640i	$-0.169113\pi$
$953$	19.9652	+	14.5055i	0.646735	+	0.469881i	−0.215422	+	0.976521i	$0.569113\pi$
$954$		0			0
$955$	−3.91375	+	12.0453i	−0.126646	+	0.389776i
$956$	10.9495			0.354131
$957$		0			0
$958$	12.5315			0.404873
$959$	13.5855	−	41.8118i	0.438698	−	1.35017i
$960$		0			0
$961$	18.5958	+	13.5107i	0.599865	+	0.435827i
$962$	−7.28913	−	22.4336i	−0.235011	−	0.723290i
$963$		0			0
$964$	−6.28401	−	4.56560i	−0.202394	−	0.147048i
$965$	11.2713	−	8.18910i	0.362837	−	0.263616i
$966$		0			0
$967$	1.20724			0.0388222			0.0194111	−	0.999812i	$-0.493821\pi$
$967$	1.20724			0.0388222			0.0194111	+	0.999812i	$0.493821\pi$
$968$	−33.8676	+	0.320445i	−1.08855	+	0.0102995i
$969$		0			0
$970$	−0.722551	+	2.22378i	−0.0231997	+	0.0714014i
$971$	40.7599	−	29.6138i	1.30805	−	0.950353i	0.308049	−	0.951370i	$-0.400324\pi$
$971$	40.7599	−	29.6138i	1.30805	−	0.950353i	0.999999	+	0.00101751i	$0.000323883\pi$
$972$		0			0
$973$	7.01442	+	21.5882i	0.224872	+	0.692085i
$974$	−2.44597	−	7.52793i	−0.0783740	−	0.241210i
$975$		0			0
$976$	−8.95877	+	6.50893i	−0.286763	+	0.208346i
$977$	1.81804	−	5.59535i	0.0581642	−	0.179011i	−0.917753	−	0.397151i	$-0.869999\pi$
$977$	1.81804	−	5.59535i	0.0581642	−	0.179011i	0.975917	+	0.218140i	$0.0699989\pi$
$978$		0			0
$979$	8.10454	+	2.59100i	0.259022	+	0.0828088i
$980$	−7.38839			−0.236013
$981$		0			0
$982$	−24.5348	+	17.8256i	−0.782937	+	0.568837i
$983$	29.5210	+	21.4482i	0.941573	+	0.684093i	0.948799	−	0.315881i	$-0.102300\pi$
$983$	29.5210	+	21.4482i	0.941573	+	0.684093i	−0.00722580	+	0.999974i	$0.502300\pi$
$984$		0			0
$985$	−4.51352	−	13.8912i	−0.143813	−	0.442610i
$986$	30.1730	+	21.9219i	0.960903	+	0.698137i
$987$		0			0
$988$	−5.80695	+	17.8720i	−0.184744	+	0.568583i
$989$	−1.95677			−0.0622216
$990$		0			0
$991$	−36.8404			−1.17027			−0.585137	−	0.810934i	$-0.698959\pi$
$991$	−36.8404			−1.17027			−0.585137	+	0.810934i	$0.698959\pi$
$992$	3.06970	−	9.44757i	0.0974631	−	0.299961i
$993$		0			0
$994$	−40.2320	−	29.2302i	−1.27608	−	0.927127i
$995$	−3.66952	−	11.2936i	−0.116332	−	0.358032i
$996$		0			0
$997$	−28.2099	−	20.4957i	−0.893417	−	0.649105i	0.0433498	−	0.999060i	$-0.486197\pi$
$997$	−28.2099	−	20.4957i	−0.893417	−	0.649105i	−0.936767	+	0.349955i	$0.886197\pi$
$998$	18.2242	−	13.2406i	0.576877	−	0.419125i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.n.d.361.2		8
3.2	odd	2		165.2.m.a.31.1	yes	8
11.4	even	5		5445.2.a.be.1.3		4
11.5	even	5	inner	495.2.n.d.181.2		8
11.7	odd	10		5445.2.a.bv.1.2		4
15.2	even	4		825.2.bx.h.724.3		16
15.8	even	4		825.2.bx.h.724.2		16
15.14	odd	2		825.2.n.k.526.2		8
33.5	odd	10		165.2.m.a.16.1	✓	8
33.26	odd	10		1815.2.a.x.1.2		4
33.29	even	10		1815.2.a.o.1.3		4
165.29	even	10		9075.2.a.dj.1.2		4
165.38	even	20		825.2.bx.h.49.3		16
165.59	odd	10		9075.2.a.cl.1.3		4
165.104	odd	10		825.2.n.k.676.2		8
165.137	even	20		825.2.bx.h.49.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.m.a.16.1	✓	8	33.5	odd	10
165.2.m.a.31.1	yes	8	3.2	odd	2
495.2.n.d.181.2		8	11.5	even	5	inner
495.2.n.d.361.2		8	1.1	even	1	trivial
825.2.n.k.526.2		8	15.14	odd	2
825.2.n.k.676.2		8	165.104	odd	10
825.2.bx.h.49.2		16	165.137	even	20
825.2.bx.h.49.3		16	165.38	even	20
825.2.bx.h.724.2		16	15.8	even	4
825.2.bx.h.724.3		16	15.2	even	4
1815.2.a.o.1.3		4	33.29	even	10
1815.2.a.x.1.2		4	33.26	odd	10
5445.2.a.be.1.3		4	11.4	even	5
5445.2.a.bv.1.2		4	11.7	odd	10
9075.2.a.cl.1.3		4	165.59	odd	10
9075.2.a.dj.1.2		4	165.29	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)

\(f(q)\)	\(=\)	\(q+(-0.359123 + 1.10527i) q^{2} +(0.525387 + 0.381716i) q^{4} +(0.309017 + 0.951057i) q^{5} +(3.46813 + 2.51974i) q^{7} +(-2.49097 + 1.80980i) q^{8} +O(q^{10})\)	\(q+(-0.359123 + 1.10527i) q^{2} +(0.525387 + 0.381716i) q^{4} +(0.309017 + 0.951057i) q^{5} +(3.46813 + 2.51974i) q^{7} +(-2.49097 + 1.80980i) q^{8} -1.16215 q^{10} +(3.15911 + 1.00996i) q^{11} +(1.59676 - 4.91433i) q^{13} +(-4.03048 + 2.92831i) q^{14} +(-0.704384 - 2.16787i) q^{16} +(-1.54508 - 4.75528i) q^{17} +(-4.53048 + 3.29158i) q^{19} +(-0.200680 + 0.617629i) q^{20} +(-2.25079 + 3.12896i) q^{22} +0.219819 q^{23} +(-0.809017 + 0.587785i) q^{25} +(4.85822 + 3.52970i) q^{26} +(0.860283 + 2.64768i) q^{28} +(5.19262 + 3.77266i) q^{29} +(-0.874813 + 2.69240i) q^{31} -3.50898 q^{32} +5.81074 q^{34} +(-1.32471 + 4.07703i) q^{35} +(-3.17784 - 2.30883i) q^{37} +(-2.01108 - 6.18947i) q^{38} +(-2.49097 - 1.80980i) q^{40} +(4.74165 - 3.44501i) q^{41} -8.90173 q^{43} +(1.27424 + 1.73650i) q^{44} +(-0.0789420 + 0.242959i) q^{46} +(-0.192447 + 0.139821i) q^{47} +(3.51569 + 10.8202i) q^{49} +(-0.359123 - 1.10527i) q^{50} +(2.71480 - 1.97242i) q^{52} +(-0.783885 + 2.41255i) q^{53} +(0.0156899 + 3.31659i) q^{55} -13.1992 q^{56} +(-6.03459 + 4.38439i) q^{58} +(-6.36725 - 4.62608i) q^{59} +(-1.50123 - 4.62030i) q^{61} +(-2.66165 - 1.93381i) q^{62} +(2.66892 - 8.21410i) q^{64} +5.16724 q^{65} +12.1280 q^{67} +(1.00340 - 3.08815i) q^{68} +(-4.03048 - 2.92831i) q^{70} +(3.08459 + 9.49339i) q^{71} +(-11.7813 - 8.55964i) q^{73} +(3.69311 - 2.68320i) q^{74} -3.63670 q^{76} +(8.41136 + 11.4628i) q^{77} +(2.47274 - 7.61030i) q^{79} +(1.84410 - 1.33982i) q^{80} +(2.10482 + 6.47797i) q^{82} +(-3.87908 - 11.9386i) q^{83} +(4.04508 - 2.93893i) q^{85} +(3.19682 - 9.83880i) q^{86} +(-9.69707 + 3.20157i) q^{88} +2.56545 q^{89} +(17.9206 - 13.0201i) q^{91} +(0.115490 + 0.0839083i) q^{92} +(-0.0854274 - 0.262919i) q^{94} +(-4.53048 - 3.29158i) q^{95} +(0.621738 - 1.91351i) q^{97} -13.2218 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{4} - 2 q^{5} + q^{7} - 5 q^{8}+O(q^{10}) \) 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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