LMFDB - Embedded newform 495.2.n.a.181.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("495.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

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

Embedding invariants

Embedding label			181.1
Root			$1.69513 - 1.23158i$ of defining polynomial
Character	$\chi$	$=$	495.181
Dual form			495.2.n.a.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.338464 - 1.04169i) q^{2} +(0.647481 - 0.470423i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(0.570387 - 0.414410i) q^{7} +(-2.48141 - 1.80285i) q^{8} +O(q^{10})$	\(q+(-0.338464 - 1.04169i) q^{2} +(0.647481 - 0.470423i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(0.570387 - 0.414410i) q^{7} +(-2.48141 - 1.80285i) q^{8} +1.09529 q^{10} +(-3.31118 - 0.189896i) q^{11} +(-1.45650 - 4.48264i) q^{13} +(-0.624741 - 0.453901i) q^{14} +(-0.543502 + 1.67273i) q^{16} +(2.40431 - 7.39971i) q^{17} +(0.970553 + 0.705148i) q^{19} +(0.247316 + 0.761160i) q^{20} +(0.922906 + 3.51349i) q^{22} +6.89318 q^{23} +(-0.809017 - 0.587785i) q^{25} +(-4.17653 + 3.03443i) q^{26} +(0.174367 - 0.536646i) q^{28} +(1.07389 - 0.780229i) q^{29} +(-2.37364 - 7.30532i) q^{31} -4.20796 q^{32} -8.52195 q^{34} +(0.217868 + 0.670530i) q^{35} +(-6.82618 + 4.95951i) q^{37} +(0.406045 - 1.24968i) q^{38} +(2.48141 - 1.80285i) q^{40} +(-0.188421 - 0.136896i) q^{41} +7.32892 q^{43} +(-2.23326 + 1.43470i) q^{44} +(-2.33310 - 7.18053i) q^{46} +(6.73287 + 4.89171i) q^{47} +(-2.00951 + 6.18465i) q^{49} +(-0.338464 + 1.04169i) q^{50} +(-3.05179 - 2.21726i) q^{52} +(-2.10852 - 6.48936i) q^{53} +(1.20381 - 3.09044i) q^{55} -2.16248 q^{56} +(-1.17623 - 0.854580i) q^{58} +(-2.86401 + 2.08083i) q^{59} +(-3.35959 + 10.3397i) q^{61} +(-6.80645 + 4.94518i) q^{62} +(2.51125 + 7.72883i) q^{64} +4.71333 q^{65} -2.04036 q^{67} +(-1.92424 - 5.92222i) q^{68} +(0.624741 - 0.453901i) q^{70} +(-0.207204 + 0.637709i) q^{71} +(4.04859 - 2.94147i) q^{73} +(7.47668 + 5.43212i) q^{74} +0.960132 q^{76} +(-1.96735 + 1.26387i) q^{77} +(0.704642 + 2.16867i) q^{79} +(-1.42291 - 1.03380i) q^{80} +(-0.0788288 + 0.242610i) q^{82} +(0.652022 - 2.00672i) q^{83} +(6.29457 + 4.57327i) q^{85} +(-2.48058 - 7.63443i) q^{86} +(7.87404 + 6.44077i) q^{88} +3.34722 q^{89} +(-2.68842 - 1.95325i) q^{91} +(4.46321 - 3.24271i) q^{92} +(2.81680 - 8.66921i) q^{94} +(-0.970553 + 0.705148i) q^{95} +(1.02664 + 3.15968i) q^{97} +7.12261 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.338464	−	1.04169i	−0.239331	−	0.736584i	−0.996517	−	0.0833853i	$-0.973427\pi$
$2$	−0.338464	−	1.04169i	−0.239331	−	0.736584i	0.757187	−	0.653198i	$-0.226573\pi$
$3$		0			0
$3$		0			0
$4$	0.647481	−	0.470423i	0.323741	−	0.235211i
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$6$		0			0
$7$	0.570387	−	0.414410i	0.215586	−	0.156632i	−0.474751	−	0.880120i	$-0.657462\pi$
$7$	0.570387	−	0.414410i	0.215586	−	0.156632i	0.690337	+	0.723487i	$0.257462\pi$
$8$	−2.48141	−	1.80285i	−0.877309	−	0.637403i
$9$		0			0
$10$	1.09529			0.346362
$11$	−3.31118	−	0.189896i	−0.998360	−	0.0572559i
$11$	−3.31118	−	0.189896i	−0.998360	−	0.0572559i
$12$		0			0
$13$	−1.45650	−	4.48264i	−0.403960	−	1.24326i	−0.921761	−	0.387760i	$-0.873249\pi$
$13$	−1.45650	−	4.48264i	−0.403960	−	1.24326i	0.517801	−	0.855501i	$-0.326751\pi$
$14$	−0.624741	−	0.453901i	−0.166969	−	0.121310i
$15$		0			0
$16$	−0.543502	+	1.67273i	−0.135875	+	0.418181i
$17$	2.40431	−	7.39971i	0.583131	−	1.79469i	−0.0235184	−	0.999723i	$-0.507487\pi$
$17$	2.40431	−	7.39971i	0.583131	−	1.79469i	0.606649	−	0.794969i	$-0.292513\pi$
$18$		0			0
$19$	0.970553	+	0.705148i	0.222660	+	0.161772i	0.693523	−	0.720434i	$-0.256057\pi$
$19$	0.970553	+	0.705148i	0.222660	+	0.161772i	−0.470863	+	0.882206i	$0.656057\pi$
$20$	0.247316	+	0.761160i	0.0553015	+	0.170201i
$21$		0			0
$22$	0.922906	+	3.51349i	0.196764	+	0.749078i
$23$	6.89318			1.43733			0.718664	−	0.695358i	$-0.244754\pi$
$23$	6.89318			1.43733			0.718664	+	0.695358i	$0.244754\pi$
$24$		0			0
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$	−4.17653	+	3.03443i	−0.819086	+	0.595101i
$27$		0			0
$28$	0.174367	−	0.536646i	0.0329522	−	0.101417i
$29$	1.07389	−	0.780229i	0.199417	−	0.144885i	−0.483596	−	0.875292i	$-0.660669\pi$
$29$	1.07389	−	0.780229i	0.199417	−	0.144885i	0.683013	+	0.730407i	$0.260669\pi$
$30$		0			0
$31$	−2.37364	−	7.30532i	−0.426318	−	1.31207i	−0.901726	−	0.432308i	$-0.857699\pi$
$31$	−2.37364	−	7.30532i	−0.426318	−	1.31207i	0.475408	−	0.879766i	$-0.342301\pi$
$32$	−4.20796			−0.743869
$33$		0			0
$34$	−8.52195			−1.46150
$35$	0.217868	+	0.670530i	0.0368265	+	0.113340i
$36$		0			0
$37$	−6.82618	+	4.95951i	−1.12222	+	0.815339i	−0.984544	−	0.175139i	$-0.943963\pi$
$37$	−6.82618	+	4.95951i	−1.12222	+	0.815339i	−0.137674	+	0.990478i	$0.543963\pi$
$38$	0.406045	−	1.24968i	0.0658692	−	0.202725i
$39$		0			0
$40$	2.48141	−	1.80285i	0.392345	−	0.285055i
$41$	−0.188421	−	0.136896i	−0.0294264	−	0.0213795i	0.572975	−	0.819573i	$-0.305789\pi$
$41$	−0.188421	−	0.136896i	−0.0294264	−	0.0213795i	−0.602401	+	0.798193i	$0.705789\pi$
$42$		0			0
$43$	7.32892			1.11765			0.558825	−	0.829286i	$-0.311252\pi$
$43$	7.32892			1.11765			0.558825	+	0.829286i	$0.311252\pi$
$44$	−2.23326	+	1.43470i	−0.336677	+	0.216289i
$45$		0			0
$46$	−2.33310	−	7.18053i	−0.343996	−	1.05871i
$47$	6.73287	+	4.89171i	0.982090	+	0.713530i	0.958175	−	0.286184i	$-0.0923869\pi$
$47$	6.73287	+	4.89171i	0.982090	+	0.713530i	0.0239149	+	0.999714i	$0.492387\pi$
$48$		0			0
$49$	−2.00951	+	6.18465i	−0.287073	+	0.883521i
$50$	−0.338464	+	1.04169i	−0.0478661	+	0.147317i
$51$		0			0
$52$	−3.05179	−	2.21726i	−0.423207	−	0.307478i
$53$	−2.10852	−	6.48936i	−0.289628	−	0.891382i	−0.984973	−	0.172707i	$-0.944749\pi$
$53$	−2.10852	−	6.48936i	−0.289628	−	0.891382i	0.695346	−	0.718675i	$-0.255251\pi$
$54$		0			0
$55$	1.20381	−	3.09044i	0.162322	−	0.416715i
$56$	−2.16248			−0.288974
$57$		0			0
$58$	−1.17623	−	0.854580i	−0.154446	−	0.112212i
$59$	−2.86401	+	2.08083i	−0.372862	+	0.270900i	−0.758397	−	0.651793i	$-0.774017\pi$
$59$	−2.86401	+	2.08083i	−0.372862	+	0.270900i	0.385534	+	0.922693i	$0.374017\pi$
$60$		0			0
$61$	−3.35959	+	10.3397i	−0.430151	+	1.32387i	0.467824	+	0.883822i	$0.345038\pi$
$61$	−3.35959	+	10.3397i	−0.430151	+	1.32387i	−0.897975	+	0.440047i	$0.854962\pi$
$62$	−6.80645	+	4.94518i	−0.864421	+	0.628038i
$63$		0			0
$64$	2.51125	+	7.72883i	0.313906	+	0.966103i
$65$	4.71333			0.584616
$66$		0			0
$67$	−2.04036			−0.249269			−0.124635	−	0.992203i	$-0.539776\pi$
$67$	−2.04036			−0.249269			−0.124635	+	0.992203i	$0.539776\pi$
$68$	−1.92424	−	5.92222i	−0.233349	−	0.718174i
$69$		0			0
$70$	0.624741	−	0.453901i	0.0746709	−	0.0542516i
$71$	−0.207204	+	0.637709i	−0.0245906	+	0.0756821i	−0.962599	−	0.270931i	$-0.912668\pi$
$71$	−0.207204	+	0.637709i	−0.0245906	+	0.0756821i	0.938008	+	0.346613i	$0.112668\pi$
$72$		0			0
$73$	4.04859	−	2.94147i	0.473852	−	0.344273i	−0.325089	−	0.945684i	$-0.605394\pi$
$73$	4.04859	−	2.94147i	0.473852	−	0.344273i	0.798941	+	0.601410i	$0.205394\pi$
$74$	7.47668	+	5.43212i	0.869146	+	0.631472i
$75$		0			0
$76$	0.960132			0.110135
$77$	−1.96735	+	1.26387i	−0.224200	+	0.144032i
$78$		0			0
$79$	0.704642	+	2.16867i	0.0792784	+	0.243994i	0.982839	−	0.184467i	$-0.0590559\pi$
$79$	0.704642	+	2.16867i	0.0792784	+	0.243994i	−0.903560	+	0.428461i	$0.859056\pi$
$80$	−1.42291	−	1.03380i	−0.159086	−	0.115583i
$81$		0			0
$82$	−0.0788288	+	0.242610i	−0.00870518	+	0.0267918i
$83$	0.652022	−	2.00672i	0.0715687	−	0.220266i	−0.908874	−	0.417071i	$-0.863057\pi$
$83$	0.652022	−	2.00672i	0.0715687	−	0.220266i	0.980443	+	0.196805i	$0.0630566\pi$
$84$		0			0
$85$	6.29457	+	4.57327i	0.682742	+	0.496041i
$86$	−2.48058	−	7.63443i	−0.267488	−	0.823242i
$87$		0			0
$88$	7.87404	+	6.44077i	0.839375	+	0.686588i
$89$	3.34722			0.354805			0.177402	−	0.984138i	$-0.443231\pi$
$89$	3.34722			0.354805			0.177402	+	0.984138i	$0.443231\pi$
$90$		0			0
$91$	−2.68842	−	1.95325i	−0.281823	−	0.204756i
$92$	4.46321	−	3.24271i	0.465321	−	0.338076i
$93$		0			0
$94$	2.81680	−	8.66921i	0.290530	−	0.894160i
$95$	−0.970553	+	0.705148i	−0.0995766	+	0.0723466i
$96$		0			0
$97$	1.02664	+	3.15968i	0.104240	+	0.320817i	0.989551	−	0.144182i	$-0.0460550\pi$
$97$	1.02664	+	3.15968i	0.104240	+	0.320817i	−0.885312	+	0.464998i	$0.846055\pi$
$98$	7.12261			0.719492
$99$		0			0
$100$	−0.800331			−0.0800331
$101$	5.84715	+	17.9957i	0.581813	+	1.79064i	0.611708	+	0.791084i	$0.290483\pi$
$101$	5.84715	+	17.9957i	0.581813	+	1.79064i	−0.0298945	+	0.999553i	$0.509517\pi$
$102$		0			0
$103$	14.6403	−	10.6368i	1.44255	−	1.04807i	0.455049	−	0.890467i	$-0.349622\pi$
$103$	14.6403	−	10.6368i	1.44255	−	1.04807i	0.987502	−	0.157608i	$-0.0503782\pi$
$104$	−4.46735	+	13.7491i	−0.438060	+	1.34821i
$105$		0			0
$106$	−6.04622	+	4.39283i	−0.587261	+	0.426670i
$107$	−4.95074	−	3.59692i	−0.478606	−	0.347727i	0.322180	−	0.946678i	$-0.395584\pi$
$107$	−4.95074	−	3.59692i	−0.478606	−	0.347727i	−0.800786	+	0.598951i	$0.795584\pi$
$108$		0			0
$109$	9.03128			0.865039			0.432520	−	0.901625i	$-0.357625\pi$
$109$	9.03128			0.865039			0.432520	+	0.901625i	$0.357625\pi$
$110$	−3.62672	−	0.207992i	−0.345794	−	0.0198313i
$111$		0			0
$112$	0.383189	+	1.17933i	0.0362079	+	0.111437i
$113$	3.16879	+	2.30226i	0.298095	+	0.216579i	0.726771	−	0.686879i	$-0.241020\pi$
$113$	3.16879	+	2.30226i	0.298095	+	0.216579i	−0.428676	+	0.903458i	$0.641020\pi$
$114$		0			0
$115$	−2.13011	+	6.55580i	−0.198634	+	0.611332i
$116$	0.328288	−	1.01037i	0.0304808	−	0.0938103i
$117$		0			0
$118$	3.13693	+	2.27912i	0.288778	+	0.209810i
$119$	−1.69513	−	5.21707i	−0.155392	−	0.478248i
$120$		0			0
$121$	10.9279	+	1.25756i	0.993444	+	0.114324i
$122$	11.9079			1.07809
$123$		0			0
$124$	−4.97348	−	3.61344i	−0.446631	−	0.324497i
$125$	0.809017	−	0.587785i	0.0723607	−	0.0525731i
$126$		0			0
$127$	3.35825	−	10.3356i	0.297996	−	0.917138i	−0.684202	−	0.729292i	$-0.739849\pi$
$127$	3.35825	−	10.3356i	0.297996	−	0.917138i	0.982199	−	0.187846i	$-0.0601506\pi$
$128$	0.392424	−	0.285113i	0.0346857	−	0.0252006i
$129$		0			0
$130$	−1.59529	−	4.90981i	−0.139917	−	0.430619i
$131$	11.7094			1.02305			0.511526	−	0.859268i	$-0.329080\pi$
$131$	11.7094			1.02305			0.511526	+	0.859268i	$0.329080\pi$
$132$		0			0
$133$	0.845811			0.0733411
$134$	0.690588	+	2.12541i	0.0596577	+	0.183608i
$135$		0			0
$136$	−19.3066	+	14.0271i	−1.65553	+	1.20281i
$137$	−6.31328	+	19.4303i	−0.539380	+	1.66004i	0.194611	+	0.980881i	$0.437656\pi$
$137$	−6.31328	+	19.4303i	−0.539380	+	1.66004i	−0.733990	+	0.679160i	$0.762344\pi$
$138$		0			0
$139$	6.61048	−	4.80280i	0.560694	−	0.407368i	−0.271019	−	0.962574i	$-0.587361\pi$
$139$	6.61048	−	4.80280i	0.560694	−	0.407368i	0.831713	+	0.555206i	$0.187361\pi$
$140$	0.456498	+	0.331666i	0.0385812	+	0.0280309i
$141$		0			0
$142$	0.734424			0.0616315
$143$	3.97150	+	15.1194i	0.332113	+	1.26435i
$144$		0			0
$145$	0.410191	+	1.26244i	0.0340645	+	0.104840i
$146$	−4.43440	−	3.22178i	−0.366993	−	0.266636i
$147$		0			0
$148$	−2.08676	+	6.42238i	−0.171531	+	0.527917i
$149$	2.96723	−	9.13221i	0.243085	−	0.748140i	−0.752860	−	0.658181i	$-0.771326\pi$
$149$	2.96723	−	9.13221i	0.243085	−	0.748140i	0.995945	−	0.0899592i	$-0.0286737\pi$
$150$		0			0
$151$	−5.58850	−	4.06028i	−0.454785	−	0.330421i	0.336697	−	0.941613i	$-0.390690\pi$
$151$	−5.58850	−	4.06028i	−0.454785	−	0.330421i	−0.791482	+	0.611192i	$0.790690\pi$
$152$	−1.13706	−	3.49951i	−0.0922278	−	0.283848i
$153$		0			0
$154$	1.98244	+	1.62159i	0.159750	+	0.130671i
$155$	7.68126			0.616974
$156$		0			0
$157$	−9.18388	−	6.67248i	−0.732953	−	0.532522i	0.157543	−	0.987512i	$-0.449643\pi$
$157$	−9.18388	−	6.67248i	−0.732953	−	0.532522i	−0.890496	+	0.454990i	$0.849643\pi$
$158$	2.02057	−	1.46803i	0.160748	−	0.116790i
$159$		0			0
$160$	1.30033	−	4.00201i	0.102800	−	0.316386i
$161$	3.93178	−	2.85661i	0.309868	−	0.225132i
$162$		0			0
$163$	−0.553922	−	1.70480i	−0.0433865	−	0.133530i	0.927017	−	0.375020i	$-0.122364\pi$
$163$	−0.553922	−	1.70480i	−0.0433865	−	0.133530i	−0.970403	+	0.241490i	$0.922364\pi$
$164$	−0.186398			−0.0145552
$165$		0			0
$166$	−2.31106			−0.179373
$167$	−1.86167	−	5.72964i	−0.144060	−	0.443373i	0.852829	−	0.522191i	$-0.174885\pi$
$167$	−1.86167	−	5.72964i	−0.144060	−	0.443373i	−0.996889	+	0.0788186i	$0.974885\pi$
$168$		0			0
$169$	−7.45546	+	5.41671i	−0.573497	+	0.416670i
$170$	2.63343	−	8.10486i	0.201975	−	0.621614i
$171$		0			0
$172$	4.74534	−	3.44769i	0.361829	−	0.262884i
$173$	3.38715	+	2.46091i	0.257520	+	0.187099i	0.709053	−	0.705155i	$-0.249123\pi$
$173$	3.38715	+	2.46091i	0.257520	+	0.187099i	−0.451533	+	0.892254i	$0.649123\pi$
$174$		0			0
$175$	−0.705037			−0.0532958
$176$	2.11728	−	5.43549i	0.159596	−	0.409716i
$177$		0			0
$178$	−1.13292	−	3.48676i	−0.0849156	−	0.261343i
$179$	3.92507	+	2.85173i	0.293374	+	0.213148i	0.724730	−	0.689033i	$-0.241965\pi$
$179$	3.92507	+	2.85173i	0.293374	+	0.213148i	−0.431356	+	0.902182i	$0.641965\pi$
$180$		0			0
$181$	−7.13450	+	21.9577i	−0.530303	+	1.63211i	0.223281	+	0.974754i	$0.428323\pi$
$181$	−7.13450	+	21.9577i	−0.530303	+	1.63211i	−0.753584	+	0.657351i	$0.771677\pi$
$182$	−1.12474	+	3.46160i	−0.0833714	+	0.256591i
$183$		0			0
$184$	−17.1048	−	12.4273i	−1.26098	−	0.916156i
$185$	−2.60737	−	8.02466i	−0.191698	−	0.589985i
$186$		0			0
$187$	−9.36629	+	24.0452i	−0.684931	+	1.75836i
$188$	6.66058			0.485773
$189$		0			0
$190$	1.06304	+	0.772344i	0.0771211	+	0.0560317i
$191$	5.03670	−	3.65938i	0.364443	−	0.264783i	−0.390460	−	0.920620i	$-0.627684\pi$
$191$	5.03670	−	3.65938i	0.364443	−	0.264783i	0.754903	+	0.655837i	$0.227684\pi$
$192$		0			0
$193$	5.89815	−	18.1526i	0.424558	−	1.30666i	−0.478858	−	0.877892i	$-0.658949\pi$
$193$	5.89815	−	18.1526i	0.424558	−	1.30666i	0.903417	−	0.428764i	$-0.141051\pi$
$194$	2.94391	−	2.13888i	0.211361	−	0.153562i
$195$		0			0
$196$	1.60828	+	4.94977i	0.114877	+	0.353555i
$197$	−6.80056			−0.484520			−0.242260	−	0.970211i	$-0.577889\pi$
$197$	−6.80056			−0.484520			−0.242260	+	0.970211i	$0.577889\pi$
$198$		0			0
$199$	21.2972			1.50972			0.754860	−	0.655886i	$-0.227705\pi$
$199$	21.2972			1.50972			0.754860	+	0.655886i	$0.227705\pi$
$200$	0.947813	+	2.91707i	0.0670205	+	0.206268i
$201$		0			0
$202$	16.7668	−	12.1818i	1.17971	−	0.857108i
$203$	0.289200	−	0.890065i	0.0202978	−	0.0624703i
$204$		0			0
$205$	0.188421	−	0.136896i	0.0131599	−	0.00956122i
$206$	−16.0354	−	11.6504i	−1.11724	−	0.811723i
$207$		0			0
$208$	8.28984			0.574797
$209$	−3.07977	−	2.51918i	−0.213032	−	0.174255i
$210$		0			0
$211$	−2.74739	−	8.45559i	−0.189138	−	0.582107i	0.810857	−	0.585244i	$-0.199001\pi$
$211$	−2.74739	−	8.45559i	−0.189138	−	0.582107i	−0.999995	+	0.00313734i	$0.999001\pi$
$212$	−4.41797	−	3.20984i	−0.303427	−	0.220453i
$213$		0			0
$214$	−2.07121	+	6.37454i	−0.141585	+	0.435755i
$215$	−2.26476	+	6.97021i	−0.154455	+	0.475365i
$216$		0			0
$217$	−4.38129	−	3.18320i	−0.297422	−	0.216089i
$218$	−3.05677	−	9.40776i	−0.207030	−	0.637174i
$219$		0			0
$220$	−0.674367	−	2.56731i	−0.0454658	−	0.173088i
$221$	−36.6721			−2.46683
$222$		0			0
$223$	−4.38261	−	3.18415i	−0.293481	−	0.213226i	0.431295	−	0.902211i	$-0.358057\pi$
$223$	−4.38261	−	3.18415i	−0.293481	−	0.213226i	−0.724776	+	0.688985i	$0.758057\pi$
$224$	−2.40017	+	1.74382i	−0.160368	+	0.116514i
$225$		0			0
$226$	1.32571	−	4.08012i	0.0881850	−	0.271406i
$227$	−6.82682	+	4.95998i	−0.453112	+	0.329205i	−0.790823	−	0.612045i	$-0.790347\pi$
$227$	−6.82682	+	4.95998i	−0.453112	+	0.329205i	0.337711	+	0.941250i	$0.390347\pi$
$228$		0			0
$229$	−3.46262	−	10.6569i	−0.228817	−	0.704225i	−0.997882	−	0.0650545i	$-0.979278\pi$
$229$	−3.46262	−	10.6569i	−0.228817	−	0.704225i	0.769065	−	0.639170i	$-0.220722\pi$
$230$	7.55006			0.497836
$231$		0			0
$232$	−4.07140			−0.267300
$233$	−1.80459	−	5.55397i	−0.118223	−	0.363852i	0.874383	−	0.485237i	$-0.161267\pi$
$233$	−1.80459	−	5.55397i	−0.118223	−	0.363852i	−0.992606	+	0.121384i	$0.961267\pi$
$234$		0			0
$235$	−6.73287	+	4.89171i	−0.439204	+	0.319100i
$236$	−0.875526	+	2.69459i	−0.0569919	+	0.175403i
$237$		0			0
$238$	−4.86081	+	3.53158i	−0.315079	+	0.228919i
$239$	−13.3699	−	9.71382i	−0.864829	−	0.628335i	0.0643656	−	0.997926i	$-0.479498\pi$
$239$	−13.3699	−	9.71382i	−0.864829	−	0.628335i	−0.929194	+	0.369592i	$0.879498\pi$
$240$		0			0
$241$	−3.29180			−0.212043			−0.106022	−	0.994364i	$-0.533811\pi$
$241$	−3.29180			−0.212043			−0.106022	+	0.994364i	$0.533811\pi$
$242$	−2.38871	−	11.8091i	−0.153552	−	0.759115i
$243$		0			0
$244$	2.68878	+	8.27522i	0.172132	+	0.529767i
$245$	−5.26097	−	3.82232i	−0.336111	−	0.244199i
$246$		0			0
$247$	1.74732	−	5.37769i	0.111179	−	0.342174i
$248$	−7.28040	+	22.4068i	−0.462306	+	1.42283i
$249$		0			0
$250$	−0.886111	−	0.643798i	−0.0560426	−	0.0407173i
$251$	2.28652	+	7.03719i	0.144324	+	0.444183i	0.996923	−	0.0783815i	$-0.0249752\pi$
$251$	2.28652	+	7.03719i	0.144324	+	0.444183i	−0.852600	+	0.522565i	$0.824975\pi$
$252$		0			0
$253$	−22.8246	−	1.30899i	−1.43497	−	0.0822955i
$254$	−11.9031			−0.746869
$255$		0			0
$256$	12.7192	+	9.24107i	0.794953	+	0.577567i
$257$	−15.1279	+	10.9911i	−0.943653	+	0.685604i	−0.949297	−	0.314380i	$-0.898203\pi$
$257$	−15.1279	+	10.9911i	−0.943653	+	0.685604i	0.00564422	+	0.999984i	$0.498203\pi$
$258$		0			0
$259$	−1.83829	+	5.65768i	−0.114226	+	0.351551i
$260$	3.05179	−	2.21726i	0.189264	−	0.137508i
$261$		0			0
$262$	−3.96321	−	12.1975i	−0.244848	−	0.753564i
$263$	−3.99020			−0.246046			−0.123023	−	0.992404i	$-0.539259\pi$
$263$	−3.99020			−0.246046			−0.123023	+	0.992404i	$0.539259\pi$
$264$		0			0
$265$	6.82332			0.419153
$266$	−0.286277	−	0.881070i	−0.0175528	−	0.0540219i
$267$		0			0
$268$	−1.32109	+	0.959830i	−0.0806986	+	0.0586309i
$269$	3.92915	−	12.0927i	0.239564	−	0.737303i	−0.756919	−	0.653509i	$-0.773296\pi$
$269$	3.92915	−	12.0927i	0.239564	−	0.737303i	0.996483	−	0.0837941i	$-0.0267038\pi$
$270$		0			0
$271$	−19.2773	+	14.0057i	−1.17101	+	0.850788i	−0.991129	−	0.132900i	$-0.957571\pi$
$271$	−19.2773	+	14.0057i	−1.17101	+	0.850788i	−0.179880	+	0.983689i	$0.557571\pi$
$272$	11.0709	+	8.04351i	0.671274	+	0.487709i
$273$		0			0
$274$	22.3771			1.35185
$275$	2.56719	+	2.09989i	0.154807	+	0.126628i
$276$		0			0
$277$	2.29059	+	7.04973i	0.137628	+	0.423577i	0.995990	−	0.0894691i	$-0.0285170\pi$
$277$	2.29059	+	7.04973i	0.137628	+	0.423577i	−0.858361	+	0.513046i	$0.828517\pi$
$278$	−7.24042	−	5.26047i	−0.434252	−	0.315502i
$279$		0			0
$280$	0.668243	−	2.05664i	0.0399352	−	0.122908i
$281$	8.98667	−	27.6581i	0.536100	−	1.64994i	−0.205161	−	0.978728i	$-0.565772\pi$
$281$	8.98667	−	27.6581i	0.536100	−	1.64994i	0.741261	−	0.671217i	$-0.234228\pi$
$282$		0			0
$283$	17.5337	+	12.7390i	1.04227	+	0.757256i	0.970728	−	0.240182i	$-0.0772070\pi$
$283$	17.5337	+	12.7390i	1.04227	+	0.757256i	0.0715451	+	0.997437i	$0.477207\pi$
$284$	0.165832	+	0.510378i	0.00984031	+	0.0302854i
$285$		0			0
$286$	14.4055	−	9.25445i	0.851815	−	0.547227i
$287$	−0.164204			−0.00969265
$288$		0			0
$289$	−35.2217	−	25.5901i	−2.07186	−	1.50530i
$290$	1.17623	−	0.854580i	0.0690705	−	0.0501827i
$291$		0			0
$292$	1.23765	−	3.80910i	0.0724281	−	0.222911i
$293$	−6.80561	+	4.94456i	−0.397588	+	0.288865i	−0.768558	−	0.639780i	$-0.779025\pi$
$293$	−6.80561	+	4.94456i	−0.397588	+	0.288865i	0.370970	+	0.928645i	$0.379025\pi$
$294$		0			0
$295$	−1.09395	−	3.36685i	−0.0636925	−	0.196025i
$296$	25.8798			1.50423
$297$		0			0
$298$	−10.5172			−0.609245
$299$	−10.0399	−	30.8997i	−0.580623	−	1.78697i
$300$		0			0
$301$	4.18032	−	3.03718i	0.240950	−	0.175060i
$302$	−2.33803	+	7.19572i	−0.134539	+	0.414067i
$303$		0			0
$304$	−1.70702	+	1.24022i	−0.0979041	+	0.0711315i
$305$	−8.79551	−	6.39031i	−0.503630	−	0.365908i
$306$		0			0
$307$	23.7431			1.35509			0.677545	−	0.735481i	$-0.263044\pi$
$307$	23.7431			1.35509			0.677545	+	0.735481i	$0.263044\pi$
$308$	−0.679268	+	1.74382i	−0.0387049	+	0.0993635i
$309$		0			0
$310$	−2.59983	−	8.00147i	−0.147661	−	0.454453i
$311$	18.6455	+	13.5467i	1.05729	+	0.768164i	0.973585	−	0.228326i	$-0.0733253\pi$
$311$	18.6455	+	13.5467i	1.05729	+	0.768164i	0.0837029	+	0.996491i	$0.473325\pi$
$312$		0			0
$313$	−5.36571	+	16.5140i	−0.303288	+	0.933424i	0.677023	+	0.735962i	$0.263270\pi$
$313$	−5.36571	+	16.5140i	−0.303288	+	0.933424i	−0.980311	+	0.197462i	$0.936730\pi$
$314$	−3.84221	+	11.8251i	−0.216829	+	0.667330i
$315$		0			0
$316$	1.47643	+	1.07269i	0.0830558	+	0.0603436i
$317$	1.90075	+	5.84990i	0.106757	+	0.328563i	0.990139	−	0.140090i	$-0.0447393\pi$
$317$	1.90075	+	5.84990i	0.106757	+	0.328563i	−0.883382	+	0.468654i	$0.844739\pi$
$318$		0			0
$319$	−3.70402	+	2.37955i	−0.207385	+	0.133229i
$320$	−8.12657			−0.454289
$321$		0			0
$322$	−4.30645	−	3.12882i	−0.239989	−	0.174362i
$323$	7.55140	−	5.48641i	0.420171	−	0.305272i
$324$		0			0
$325$	−1.45650	+	4.48264i	−0.0807920	+	0.248652i
$326$	−1.58838	+	1.15403i	−0.0879722	+	0.0639156i
$327$		0			0
$328$	0.220747	+	0.679388i	0.0121887	+	0.0375129i
$329$	5.86752			0.323487
$330$		0			0
$331$	19.4191			1.06737			0.533685	−	0.845683i	$-0.320807\pi$
$331$	19.4191			1.06737			0.533685	+	0.845683i	$0.320807\pi$
$332$	−0.521833	−	1.60604i	−0.0286393	−	0.0881428i
$333$		0			0
$334$	−5.33837	+	3.87856i	−0.292103	+	0.212225i
$335$	0.630505	−	1.94049i	0.0344481	−	0.106021i
$336$		0			0
$337$	−25.6352	+	18.6250i	−1.39644	+	1.01457i	−0.401312	+	0.915941i	$0.631446\pi$
$337$	−25.6352	+	18.6250i	−1.39644	+	1.01457i	−0.995124	+	0.0986291i	$0.968554\pi$
$338$	8.16593	+	5.93289i	0.444168	+	0.322707i
$339$		0			0
$340$	6.22699			0.337706
$341$	6.47231	+	24.6400i	0.350495	+	1.33433i
$342$		0			0
$343$	2.94186	+	9.05412i	0.158846	+	0.488876i
$344$	−18.1860	−	13.2129i	−0.980524	−	0.712392i
$345$		0			0
$346$	1.41706	−	4.36127i	0.0761818	−	0.234463i
$347$	8.63499	−	26.5758i	0.463551	−	1.42666i	−0.397246	−	0.917712i	$-0.630034\pi$
$347$	8.63499	−	26.5758i	0.463551	−	1.42666i	0.860796	−	0.508950i	$-0.169966\pi$
$348$		0			0
$349$	0.552827	+	0.401652i	0.0295921	+	0.0214999i	0.602483	−	0.798132i	$-0.294178\pi$
$349$	0.552827	+	0.401652i	0.0295921	+	0.0214999i	−0.572891	+	0.819632i	$0.694178\pi$
$350$	0.238630	+	0.734428i	0.0127553	+	0.0392568i
$351$		0			0
$352$	13.9333	+	0.799077i	0.742649	+	0.0425909i
$353$	−1.55900			−0.0829769			−0.0414885	−	0.999139i	$-0.513210\pi$
$353$	−1.55900			−0.0829769			−0.0414885	+	0.999139i	$0.513210\pi$
$354$		0			0
$355$	−0.542467	−	0.394126i	−0.0287912	−	0.0209180i
$356$	2.16726	−	1.57461i	0.114865	−	0.0834542i
$357$		0			0
$358$	1.64211	−	5.05390i	0.0867884	−	0.267107i
$359$	12.8151	−	9.31073i	0.676356	−	0.491402i	−0.195791	−	0.980646i	$-0.562727\pi$
$359$	12.8151	−	9.31073i	0.676356	−	0.491402i	0.872147	+	0.489244i	$0.162727\pi$
$360$		0			0
$361$	−5.42658	−	16.7013i	−0.285610	−	0.879016i
$362$	25.2878			1.32910
$363$		0			0
$364$	−2.65956			−0.139399
$365$	1.54642	+	4.75940i	0.0809435	+	0.249119i
$366$		0			0
$367$	−12.7308	+	9.24947i	−0.664542	+	0.482818i	−0.868194	−	0.496225i	$-0.834719\pi$
$367$	−12.7308	+	9.24947i	−0.664542	+	0.482818i	0.203652	+	0.979043i	$0.434719\pi$
$368$	−3.74645	+	11.5304i	−0.195297	+	0.601064i
$369$		0			0
$370$	−7.47668	+	5.43212i	−0.388694	+	0.282403i
$371$	−3.89193	−	2.82765i	−0.202059	−	0.146804i
$372$		0			0
$373$	−5.27703			−0.273234			−0.136617	−	0.990624i	$-0.543623\pi$
$373$	−5.27703			−0.273234			−0.136617	+	0.990624i	$0.543623\pi$
$374$	28.2177	+	1.61829i	1.45910	+	0.0836797i
$375$		0			0
$376$	−7.88796	−	24.2767i	−0.406791	−	1.25197i
$377$	−5.06161	−	3.67748i	−0.260686	−	0.189400i
$378$		0			0
$379$	10.3549	−	31.8692i	0.531897	−	1.63701i	−0.218363	−	0.975868i	$-0.570072\pi$
$379$	10.3549	−	31.8692i	0.531897	−	1.63701i	0.750260	−	0.661143i	$-0.229928\pi$
$380$	−0.296697	+	0.913140i	−0.0152202	+	0.0468431i
$381$		0			0
$382$	−5.51667	−	4.00810i	−0.282257	−	0.205072i
$383$	6.25212	+	19.2420i	0.319468	+	0.983222i	0.973876	+	0.227080i	$0.0729180\pi$
$383$	6.25212	+	19.2420i	0.319468	+	0.983222i	−0.654408	+	0.756142i	$0.727082\pi$
$384$		0			0
$385$	−0.594071	−	2.26162i	−0.0302767	−	0.115263i
$386$	−20.9057			−1.06407
$387$		0			0
$388$	2.15112	+	1.56288i	0.109206	+	0.0793430i
$389$	−22.3069	+	16.2069i	−1.13101	+	0.821724i	−0.985841	−	0.167684i	$-0.946371\pi$
$389$	−22.3069	+	16.2069i	−1.13101	+	0.821724i	−0.145165	+	0.989408i	$0.546371\pi$
$390$		0			0
$391$	16.5733	−	51.0075i	0.838150	−	2.57956i
$392$	16.1364	−	11.7238i	0.815011	−	0.592140i
$393$		0			0
$394$	2.30175	+	7.08406i	0.115960	+	0.356890i
$395$	−2.28027			−0.114733
$396$		0			0
$397$	11.7601			0.590222			0.295111	−	0.955463i	$-0.404643\pi$
$397$	11.7601			0.590222			0.295111	+	0.955463i	$0.404643\pi$
$398$	−7.20835	−	22.1850i	−0.361322	−	1.11204i
$399$		0			0
$400$	1.42291	−	1.03380i	0.0711453	−	0.0516901i
$401$	2.38687	−	7.34602i	0.119194	−	0.366843i	−0.873604	−	0.486637i	$-0.838223\pi$
$401$	2.38687	−	7.34602i	0.119194	−	0.366843i	0.992799	+	0.119794i	$0.0382235\pi$
$402$		0			0
$403$	−29.2899	+	21.2804i	−1.45903	+	1.06005i
$404$	12.2515	+	8.90124i	0.609535	+	0.442853i
$405$		0			0
$406$	−1.02505			−0.0508725
$407$	23.5445	−	15.1256i	1.16706	−	0.749748i
$408$		0			0
$409$	5.17322	+	15.9215i	0.255799	+	0.787269i	0.993671	+	0.112328i	$0.0358307\pi$
$409$	5.17322	+	15.9215i	0.255799	+	0.787269i	−0.737872	+	0.674941i	$0.764169\pi$
$410$	−0.206376	−	0.149941i	−0.0101922	−	0.00740507i
$411$		0			0
$412$	4.47553	−	13.7743i	0.220493	−	0.678609i
$413$	−0.771279	+	2.37375i	−0.0379521	+	0.116805i
$414$		0			0
$415$	1.70702	+	1.24022i	0.0837941	+	0.0608800i
$416$	6.12889	+	18.8628i	0.300493	+	0.924824i
$417$		0			0
$418$	−1.58180	+	4.06081i	−0.0773684	+	0.198621i
$419$	38.0968			1.86115			0.930576	−	0.366100i	$-0.119307\pi$
$419$	38.0968			1.86115			0.930576	+	0.366100i	$0.119307\pi$
$420$		0			0
$421$	18.3350	+	13.3212i	0.893594	+	0.649234i	0.936813	−	0.349831i	$-0.113761\pi$
$421$	18.3350	+	13.3212i	0.893594	+	0.649234i	−0.0432184	+	0.999066i	$0.513761\pi$
$422$	−7.87818	+	5.72383i	−0.383504	+	0.278632i
$423$		0			0
$424$	−6.46722	+	19.9041i	−0.314076	+	0.966627i
$425$	−6.29457	+	4.57327i	−0.305331	+	0.221836i
$426$		0			0
$427$	2.36863	+	7.28990i	0.114626	+	0.352783i
$428$	−4.89758			−0.236734
$429$		0			0
$430$	8.02732			0.387112
$431$	10.4994	+	32.3137i	0.505736	+	1.55650i	0.799529	+	0.600627i	$0.205082\pi$
$431$	10.4994	+	32.3137i	0.505736	+	1.55650i	−0.293793	+	0.955869i	$0.594918\pi$
$432$		0			0
$433$	29.6709	−	21.5572i	1.42589	−	1.03597i	0.435131	−	0.900367i	$-0.356702\pi$
$433$	29.6709	−	21.5572i	1.42589	−	1.03597i	0.990763	−	0.135605i	$-0.0432978\pi$
$434$	−1.83298	+	5.64133i	−0.0879858	+	0.270793i
$435$		0			0
$436$	5.84758	−	4.24852i	0.280048	−	0.203467i
$437$	6.69019	+	4.86071i	0.320035	+	0.232519i
$438$		0			0
$439$	1.05012			0.0501193			0.0250596	−	0.999686i	$-0.492022\pi$
$439$	1.05012			0.0501193			0.0250596	+	0.999686i	$0.492022\pi$
$440$	−8.55874	+	5.49835i	−0.408022	+	0.262123i
$441$		0			0
$442$	12.4122	+	38.2008i	0.590388	+	1.81703i
$443$	−24.6917	−	17.9396i	−1.17314	−	0.852334i	−0.181756	−	0.983344i	$-0.558178\pi$
$443$	−24.6917	−	17.9396i	−1.17314	−	0.852334i	−0.991381	+	0.131009i	$0.958178\pi$
$444$		0			0
$445$	−1.03435	+	3.18340i	−0.0490328	+	0.150908i
$446$	−1.83353	+	5.64302i	−0.0868201	+	0.267205i
$447$		0			0
$448$	4.63529	+	3.36773i	0.218997	+	0.159111i
$449$	11.3006	+	34.7796i	0.533308	+	1.64135i	0.747277	+	0.664513i	$0.231361\pi$
$449$	11.3006	+	34.7796i	0.533308	+	1.64135i	−0.213969	+	0.976840i	$0.568639\pi$
$450$		0			0
$451$	0.597901	+	0.489068i	0.0281540	+	0.0230293i
$452$	3.13477			0.147447
$453$		0			0
$454$	7.47738	+	5.43263i	0.350931	+	0.254966i
$455$	2.68842	−	1.95325i	0.126035	−	0.0915699i
$456$		0			0
$457$	−0.736724	+	2.26740i	−0.0344625	+	0.106065i	−0.966808	−	0.255504i	$-0.917759\pi$
$457$	−0.736724	+	2.26740i	−0.0344625	+	0.106065i	0.932346	+	0.361568i	$0.117759\pi$
$458$	−9.92913	+	7.21393i	−0.463958	+	0.337085i
$459$		0			0
$460$	1.70479	+	5.24681i	0.0794864	+	0.244634i
$461$	−28.5962			−1.33186			−0.665929	−	0.746015i	$-0.731965\pi$
$461$	−28.5962			−1.33186			−0.665929	+	0.746015i	$0.731965\pi$
$462$		0			0
$463$	−30.5806			−1.42120			−0.710600	−	0.703596i	$-0.751577\pi$
$463$	−30.5806			−1.42120			−0.710600	+	0.703596i	$0.751577\pi$
$464$	0.721447	+	2.22038i	0.0334923	+	0.103079i
$465$		0			0
$466$	−5.17470	+	3.75964i	−0.239713	+	0.174162i
$467$	1.15640	−	3.55903i	0.0535118	−	0.164692i	−0.920729	−	0.390203i	$-0.872405\pi$
$467$	1.15640	−	3.55903i	0.0535118	−	0.164692i	0.974241	+	0.225510i	$0.0724049\pi$
$468$		0			0
$469$	−1.16379	+	0.845545i	−0.0537389	+	0.0390436i
$470$	7.37447	+	5.35786i	0.340159	+	0.247140i
$471$		0			0
$472$	10.8582			0.499788
$473$	−24.2674	−	1.39174i	−1.11582	−	0.0639920i
$474$		0			0
$475$	−0.370718	−	1.14095i	−0.0170097	−	0.0523505i
$476$	−3.55179	−	2.58053i	−0.162796	−	0.118278i
$477$		0			0
$478$	−5.59351	+	17.2151i	−0.255841	+	0.787398i
$479$	0.292006	−	0.898702i	0.0133421	−	0.0410627i	−0.944164	−	0.329476i	$-0.893128\pi$
$479$	0.292006	−	0.898702i	0.0133421	−	0.0410627i	0.957506	+	0.288414i	$0.0931278\pi$
$480$		0			0
$481$	32.1740	+	23.3758i	1.46701	+	1.06584i
$482$	1.11416	+	3.42902i	0.0507484	+	0.156188i
$483$		0			0
$484$	7.66719	−	4.32647i	0.348508	−	0.196658i
$485$	−3.32228			−0.150857
$486$		0			0
$487$	10.8306	+	7.86887i	0.490780	+	0.356573i	0.805484	−	0.592617i	$-0.201905\pi$
$487$	10.8306	+	7.86887i	0.490780	+	0.356573i	−0.314704	+	0.949190i	$0.601905\pi$
$488$	26.9775	−	19.6003i	1.22121	−	0.887263i
$489$		0			0
$490$	−2.20101	+	6.77401i	−0.0994314	+	0.306018i
$491$	−2.25625	+	1.63926i	−0.101823	+	0.0739787i	−0.637532	−	0.770424i	$-0.720045\pi$
$491$	−2.25625	+	1.63926i	−0.101823	+	0.0739787i	0.535709	+	0.844403i	$0.320045\pi$
$492$		0			0
$493$	−3.19149	−	9.82241i	−0.143738	−	0.442379i
$494$	−6.19327			−0.278648
$495$		0			0
$496$	13.5099			0.606611
$497$	0.146087	+	0.449608i	0.00655288	+	0.0201677i
$498$		0			0
$499$	−14.3835	+	10.4503i	−0.643896	+	0.467818i	−0.861187	−	0.508289i	$-0.830278\pi$
$499$	−14.3835	+	10.4503i	−0.643896	+	0.467818i	0.217290	+	0.976107i	$0.430278\pi$
$500$	0.247316	−	0.761160i	0.0110603	−	0.0340401i
$501$		0			0
$502$	6.55664	−	4.76368i	0.292637	−	0.212613i
$503$	20.8596	+	15.1554i	0.930081	+	0.675744i	0.946013	−	0.324129i	$-0.105071\pi$
$503$	20.8596	+	15.1554i	0.930081	+	0.675744i	−0.0159313	+	0.999873i	$0.505071\pi$
$504$		0			0
$505$	−18.9218			−0.842008
$506$	6.36175	+	24.2191i	0.282814	+	1.07667i
$507$		0			0
$508$	−2.68771	−	8.27192i	−0.119248	−	0.367007i
$509$	−22.8386	−	16.5932i	−1.01231	−	0.735483i	−0.0476138	−	0.998866i	$-0.515162\pi$
$509$	−22.8386	−	16.5932i	−1.01231	−	0.735483i	−0.964691	+	0.263383i	$0.915162\pi$
$510$		0			0
$511$	1.09029	−	3.35556i	0.0482314	−	0.148441i
$512$	5.62107	−	17.2999i	0.248419	−	0.764554i
$513$		0			0
$514$	16.5695	+	12.0385i	0.730850	+	0.530993i
$515$	5.59209	+	17.2107i	0.246417	+	0.758394i
$516$		0			0
$517$	−21.3648	−	17.4759i	−0.939625	−	0.768590i
$518$	6.51573			0.286285
$519$		0			0
$520$	−11.6957	−	8.49741i	−0.512889	−	0.372636i
$521$	9.46183	−	6.87442i	0.414530	−	0.301174i	−0.360903	−	0.932603i	$-0.617531\pi$
$521$	9.46183	−	6.87442i	0.414530	−	0.301174i	0.775433	+	0.631429i	$0.217531\pi$
$522$		0			0
$523$	−6.08365	+	18.7236i	−0.266019	+	0.818724i	0.725437	+	0.688288i	$0.241638\pi$
$523$	−6.08365	+	18.7236i	−0.266019	+	0.818724i	−0.991457	+	0.130436i	$0.958362\pi$
$524$	7.58160	−	5.50836i	0.331204	−	0.240634i
$525$		0			0
$526$	1.35054	+	4.15654i	0.0588863	+	0.181234i
$527$	−59.7642			−2.60337
$528$		0			0
$529$	24.5159			1.06591
$530$	−2.30945	−	7.10776i	−0.100316	−	0.308741i
$531$		0			0
$532$	0.547647	−	0.397889i	0.0237435	−	0.0172507i
$533$	−0.339220	+	1.04401i	−0.0146933	+	0.0452212i
$534$		0			0
$535$	4.95074	−	3.59692i	0.214039	−	0.155508i
$536$	5.06295	+	3.67845i	0.218686	+	0.158885i
$537$		0			0
$538$	−13.9266			−0.600420
$539$	7.82831	−	20.0969i	0.337189	−	0.865635i
$540$		0			0
$541$	−1.68443	−	5.18413i	−0.0724191	−	0.222883i	0.908295	−	0.418330i	$-0.137384\pi$
$541$	−1.68443	−	5.18413i	−0.0724191	−	0.222883i	−0.980714	+	0.195447i	$0.937384\pi$
$542$	21.1143	+	15.3404i	0.906935	+	0.658927i
$543$		0			0
$544$	−10.1172	+	31.1377i	−0.433773	+	1.33502i
$545$	−2.79082	+	8.58925i	−0.119545	+	0.367923i
$546$		0			0
$547$	−10.3467	−	7.51731i	−0.442393	−	0.321417i	0.344192	−	0.938899i	$-0.388153\pi$
$547$	−10.3467	−	7.51731i	−0.442393	−	0.321417i	−0.786585	+	0.617482i	$0.788153\pi$
$548$	5.05271	+	15.5507i	0.215841	+	0.664291i
$549$		0			0
$550$	1.31853	−	3.38494i	0.0562223	−	0.144334i
$551$	1.59245			0.0678405
$552$		0			0
$553$	1.30064	+	0.944967i	0.0553087	+	0.0401841i
$554$	6.56832	−	4.77216i	0.279061	−	0.202750i
$555$		0			0
$556$	2.02082	−	6.21944i	0.0857018	−	0.263763i
$557$	−0.286771	+	0.208351i	−0.0121509	+	0.00882812i	−0.593844	−	0.804580i	$-0.702390\pi$
$557$	−0.286771	+	0.208351i	−0.0121509	+	0.00882812i	0.581693	+	0.813408i	$0.302390\pi$
$558$		0			0
$559$	−10.6746	−	32.8529i	−0.451486	−	1.38953i
$560$	−1.24002			−0.0524006
$561$		0			0
$562$	−31.8528			−1.34363
$563$	−10.8409	−	33.3648i	−0.456888	−	1.40616i	−0.868904	−	0.494981i	$-0.835175\pi$
$563$	−10.8409	−	33.3648i	−0.456888	−	1.40616i	0.412015	−	0.911177i	$-0.364825\pi$
$564$		0			0
$565$	−3.16879	+	2.30226i	−0.133312	+	0.0968569i
$566$	7.33551	−	22.5764i	0.308334	−	0.948956i
$567$		0			0
$568$	1.66385	−	1.20886i	0.0698135	−	0.0507225i
$569$	−13.2015	−	9.59145i	−0.553436	−	0.402094i	0.275615	−	0.961268i	$-0.411119\pi$
$569$	−13.2015	−	9.59145i	−0.553436	−	0.402094i	−0.829051	+	0.559174i	$0.811119\pi$
$570$		0			0
$571$	−14.4160			−0.603291			−0.301645	−	0.953420i	$-0.597536\pi$
$571$	−14.4160			−0.603291			−0.301645	+	0.953420i	$0.597536\pi$
$572$	9.68400	+	7.92127i	0.404908	+	0.331205i
$573$		0			0
$574$	0.0555772	+	0.171049i	0.00231975	+	0.00713945i
$575$	−5.57670	−	4.05171i	−0.232564	−	0.168968i
$576$		0			0
$577$	2.75292	−	8.47261i	0.114605	−	0.352719i	−0.877259	−	0.480017i	$-0.840630\pi$
$577$	2.75292	−	8.47261i	0.114605	−	0.352719i	0.991865	+	0.127298i	$0.0406304\pi$
$578$	−14.7355	+	45.3513i	−0.612917	+	1.88636i
$579$		0			0
$580$	0.859470	+	0.624442i	0.0356876	+	0.0259285i
$581$	−0.459700	−	1.41481i	−0.0190716	−	0.0586962i
$582$		0			0
$583$	5.74939	+	21.8879i	0.238116	+	0.906503i
$584$	−15.3492			−0.635155
$585$		0			0
$586$	7.45414	+	5.41575i	0.307928	+	0.223723i
$587$	−11.1655	+	8.11225i	−0.460851	+	0.334828i	−0.793865	−	0.608094i	$-0.791934\pi$
$587$	−11.1655	+	8.11225i	−0.460851	+	0.334828i	0.333014	+	0.942922i	$0.391934\pi$
$588$		0			0
$589$	2.84758	−	8.76396i	0.117333	−	0.361113i
$590$	−3.13693	+	2.27912i	−0.129146	+	0.0938297i
$591$		0			0
$592$	−4.58586	−	14.1138i	−0.188478	−	0.580075i
$593$	16.4676			0.676242			0.338121	−	0.941103i	$-0.390209\pi$
$593$	16.4676			0.676242			0.338121	+	0.941103i	$0.390209\pi$
$594$		0			0
$595$	5.48555			0.224886
$596$	−2.37477	−	7.30879i	−0.0972744	−	0.299380i
$597$		0			0
$598$	−28.7896	+	20.9169i	−1.17729	+	0.855354i
$599$	−11.6994	+	36.0069i	−0.478023	+	1.47120i	0.363814	+	0.931472i	$0.381475\pi$
$599$	−11.6994	+	36.0069i	−0.478023	+	1.47120i	−0.841837	+	0.539732i	$0.818525\pi$
$600$		0			0
$601$	−1.26563	+	0.919535i	−0.0516262	+	0.0375086i	−0.613299	−	0.789851i	$-0.710158\pi$
$601$	−1.26563	+	0.919535i	−0.0516262	+	0.0375086i	0.561673	+	0.827359i	$0.310158\pi$
$602$	−4.57868	−	3.32660i	−0.186613	−	0.135582i
$603$		0			0
$604$	−5.52850			−0.224951
$605$	−4.57291	+	10.0044i	−0.185915	+	0.406738i
$606$		0			0
$607$	5.82568	+	17.9296i	0.236457	+	0.727740i	0.996925	+	0.0783641i	$0.0249697\pi$
$607$	5.82568	+	17.9296i	0.236457	+	0.727740i	−0.760468	+	0.649376i	$0.775030\pi$
$608$	−4.08405	−	2.96723i	−0.165630	−	0.120337i
$609$		0			0
$610$	−3.67974	+	11.3251i	−0.148988	+	0.458538i
$611$	12.1214	−	37.3058i	0.490379	−	1.50923i
$612$		0			0
$613$	−26.4306	−	19.2030i	−1.06752	−	0.775601i	−0.0920574	−	0.995754i	$-0.529344\pi$
$613$	−26.4306	−	19.2030i	−1.06752	−	0.775601i	−0.975465	+	0.220153i	$0.929344\pi$
$614$	−8.03619	−	24.7329i	−0.324314	−	0.998137i
$615$		0			0
$616$	7.16037	+	0.410647i	0.288499	+	0.0165454i
$617$	33.6559			1.35493			0.677467	−	0.735553i	$-0.263078\pi$
$617$	33.6559			1.35493			0.677467	+	0.735553i	$0.263078\pi$
$618$		0			0
$619$	7.23262	+	5.25480i	0.290703	+	0.211208i	0.723572	−	0.690248i	$-0.242499\pi$
$619$	7.23262	+	5.25480i	0.290703	+	0.211208i	−0.432869	+	0.901457i	$0.642499\pi$
$620$	4.97348	−	3.61344i	0.199740	−	0.145119i
$621$		0			0
$622$	7.80061	−	24.0078i	0.312776	−	0.962626i
$623$	1.90921	−	1.38712i	0.0764910	−	0.0555739i
$624$		0			0
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$	19.0185			0.760131
$627$		0			0
$628$	−9.08528			−0.362542
$629$	20.2867	+	62.4360i	0.808883	+	2.48949i
$630$		0			0
$631$	15.5798	−	11.3194i	0.620224	−	0.450619i	−0.232776	−	0.972530i	$-0.574781\pi$
$631$	15.5798	−	11.3194i	0.620224	−	0.450619i	0.853000	+	0.521912i	$0.174781\pi$
$632$	2.16127	−	6.65170i	0.0859706	−	0.264590i
$633$		0			0
$634$	5.45043	−	3.95997i	0.216464	−	0.157270i
$635$	8.79201	+	6.38777i	0.348900	+	0.253491i
$636$		0			0
$637$	30.6504			1.21441
$638$	3.73243	+	3.05303i	0.147768	+	0.120871i
$639$		0			0
$640$	0.149893	+	0.461322i	0.00592502	+	0.0182354i
$641$	−12.0485	−	8.75375i	−0.475887	−	0.345752i	0.323844	−	0.946110i	$-0.395025\pi$
$641$	−12.0485	−	8.75375i	−0.475887	−	0.345752i	−0.799731	+	0.600358i	$0.795025\pi$
$642$		0			0
$643$	10.9143	−	33.5907i	0.430417	−	1.32469i	−0.467295	−	0.884102i	$-0.654771\pi$
$643$	10.9143	−	33.5907i	0.430417	−	1.32469i	0.897711	−	0.440584i	$-0.145229\pi$
$644$	1.20194	−	3.69920i	0.0473632	−	0.145769i
$645$		0			0
$646$	−8.27100	−	6.00923i	−0.325418	−	0.236430i
$647$	−9.62366	−	29.6186i	−0.378345	−	1.16443i	−0.941194	−	0.337867i	$-0.890295\pi$
$647$	−9.62366	−	29.6186i	−0.378345	−	1.16443i	0.562849	−	0.826560i	$-0.309705\pi$
$648$		0			0
$649$	9.87841	−	6.34613i	0.387761	−	0.249107i
$650$	5.16248			0.202489
$651$		0			0
$652$	−1.16063	−	0.843246i	−0.0454537	−	0.0330241i
$653$	4.08953	−	2.97122i	0.160036	−	0.116273i	−0.504885	−	0.863186i	$-0.668465\pi$
$653$	4.08953	−	2.97122i	0.160036	−	0.116273i	0.664921	+	0.746914i	$0.268465\pi$
$654$		0			0
$655$	−3.61839	+	11.1363i	−0.141382	+	0.435130i
$656$	0.331396	−	0.240774i	0.0129389	−	0.00940063i
$657$		0			0
$658$	−1.98595	−	6.11211i	−0.0774202	−	0.238275i
$659$	14.4486			0.562837			0.281419	−	0.959585i	$-0.409195\pi$
$659$	14.4486			0.562837			0.281419	+	0.959585i	$0.409195\pi$
$660$		0			0
$661$	14.8696			0.578361			0.289181	−	0.957275i	$-0.406617\pi$
$661$	14.8696			0.578361			0.289181	+	0.957275i	$0.406617\pi$
$662$	−6.57267	−	20.2286i	−0.255454	−	0.786207i
$663$		0			0
$664$	−5.23573	+	3.80398i	−0.203186	+	0.147623i
$665$	−0.261370	+	0.804414i	−0.0101355	+	0.0311938i
$666$		0			0
$667$	7.40254	−	5.37826i	0.286627	−	0.208247i
$668$	−3.90075	−	2.83406i	−0.150925	−	0.109653i
$669$		0			0
$670$	−2.23479			−0.0863375
$671$	13.0877	−	33.5988i	0.505245	−	1.29707i
$672$		0			0
$673$	−12.8598	−	39.5785i	−0.495710	−	1.52564i	−0.815848	−	0.578267i	$-0.803729\pi$
$673$	−12.8598	−	39.5785i	−0.495710	−	1.52564i	0.320138	−	0.947371i	$-0.396271\pi$
$674$	28.0780	+	20.3999i	1.08153	+	0.785774i
$675$		0			0
$676$	−2.27913	+	7.01444i	−0.0876588	+	0.269786i
$677$	−13.6699	+	42.0715i	−0.525376	+	1.61694i	0.238195	+	0.971217i	$0.423444\pi$
$677$	−13.6699	+	42.0715i	−0.525376	+	1.61694i	−0.763571	+	0.645724i	$0.776556\pi$
$678$		0			0
$679$	1.89499	+	1.37679i	0.0727229	+	0.0528363i
$680$	−7.37447	−	22.6963i	−0.282798	−	0.870363i
$681$		0			0
$682$	23.4765	−	15.0819i	0.898962	−	0.577515i
$683$	−24.5318			−0.938683			−0.469342	−	0.883017i	$-0.655509\pi$
$683$	−24.5318			−0.938683			−0.469342	+	0.883017i	$0.655509\pi$
$684$		0			0
$685$	−16.5284	−	12.0086i	−0.631517	−	0.458824i
$686$	8.43584	−	6.12899i	0.322082	−	0.234006i
$687$		0			0
$688$	−3.98328	+	12.2593i	−0.151861	+	0.467380i
$689$	−26.0184	+	18.9035i	−0.991222	+	0.720165i
$690$		0			0
$691$	7.34440	+	22.6037i	0.279394	+	0.859887i	0.988023	+	0.154306i	$0.0493141\pi$
$691$	7.34440	+	22.6037i	0.279394	+	0.859887i	−0.708629	+	0.705581i	$0.750686\pi$
$692$	3.35078			0.127378
$693$		0			0
$694$	−30.6063			−1.16180
$695$	2.52498	+	7.77109i	0.0957779	+	0.294774i
$696$		0			0
$697$	−1.46601	+	1.06512i	−0.0555292	+	0.0403443i
$698$	0.231283	−	0.711817i	0.00875420	−	0.0269427i
$699$		0			0
$700$	−0.456498	+	0.331666i	−0.0172540	+	0.0125358i
$701$	−26.4499	−	19.2170i	−0.998999	−	0.725816i	−0.0371259	−	0.999311i	$-0.511820\pi$
$701$	−26.4499	−	19.2170i	−0.998999	−	0.725816i	−0.961873	+	0.273495i	$0.911820\pi$
$702$		0			0
$703$	−10.1224			−0.381772
$704$	−6.84753	−	26.0684i	−0.258076	−	0.982491i
$705$		0			0
$706$	0.527664	+	1.62398i	0.0198589	+	0.0611194i
$707$	10.7927	+	7.84138i	0.405903	+	0.294905i
$708$		0			0
$709$	7.36278	−	22.6603i	0.276515	−	0.851025i	−0.712300	−	0.701875i	$-0.752346\pi$
$709$	7.36278	−	22.6603i	0.276515	−	0.851025i	0.988815	−	0.149150i	$-0.0476537\pi$
$710$	−0.226949	+	0.698478i	−0.00851726	+	0.0262134i
$711$		0			0
$712$	−8.30582	−	6.03453i	−0.311274	−	0.226154i
$713$	−16.3619	−	50.3568i	−0.612759	−	1.88588i
$714$		0			0
$715$	−15.6067	−	0.895044i	−0.583657	−	0.0334728i
$716$	3.88293			0.145112
$717$		0			0
$718$	−14.0363	−	10.1980i	−0.523831	−	0.380586i
$719$	−2.30311	+	1.67331i	−0.0858914	+	0.0624038i	−0.629902	−	0.776674i	$-0.716905\pi$
$719$	−2.30311	+	1.67331i	−0.0858914	+	0.0624038i	0.544011	+	0.839078i	$0.316905\pi$
$720$		0			0
$721$	3.94263	−	12.1342i	0.146831	−	0.451900i
$722$	−15.5608	+	11.3056i	−0.579114	+	0.420751i
$723$		0			0
$724$	5.70996	+	17.5735i	0.212209	+	0.653112i
$725$	−1.32741			−0.0492986
$726$		0			0
$727$	−13.5192			−0.501399			−0.250700	−	0.968065i	$-0.580661\pi$
$727$	−13.5192			−0.501399			−0.250700	+	0.968065i	$0.580661\pi$
$728$	3.14965	+	9.69362i	0.116734	+	0.359270i
$729$		0			0
$730$	4.43440	−	3.22178i	0.164124	−	0.119243i
$731$	17.6210	−	54.2318i	0.651736	−	2.00584i
$732$		0			0
$733$	−26.5643	+	19.3001i	−0.981174	+	0.712864i	−0.957971	−	0.286866i	$-0.907386\pi$
$733$	−26.5643	+	19.3001i	−0.981174	+	0.712864i	−0.0232030	+	0.999731i	$0.507386\pi$
$734$	13.9440	+	10.1309i	0.514681	+	0.373938i
$735$		0			0
$736$	−29.0062			−1.06918
$737$	6.75599	+	0.387456i	0.248860	+	0.0142721i
$738$		0			0
$739$	15.7267	+	48.4018i	0.578516	+	1.78049i	0.623882	+	0.781519i	$0.285555\pi$
$739$	15.7267	+	48.4018i	0.578516	+	1.78049i	−0.0453660	+	0.998970i	$0.514445\pi$
$740$	−5.46321	−	3.96925i	−0.200831	−	0.145913i
$741$		0			0
$742$	−1.62825	+	5.01123i	−0.0597749	+	0.183968i
$743$	4.78528	−	14.7276i	0.175555	−	0.540302i	−0.824104	−	0.566439i	$-0.808321\pi$
$743$	4.78528	−	14.7276i	0.175555	−	0.540302i	0.999658	+	0.0261370i	$0.00832063\pi$
$744$		0			0
$745$	7.76832	+	5.64402i	0.284609	+	0.206781i
$746$	1.78609	+	5.49702i	0.0653933	+	0.201260i
$747$		0			0
$748$	5.24692	+	19.9750i	0.191846	+	0.730357i
$749$	−4.31444			−0.157646
$750$		0			0
$751$	−8.94571	−	6.49944i	−0.326434	−	0.237168i	0.412482	−	0.910966i	$-0.364662\pi$
$751$	−8.94571	−	6.49944i	−0.326434	−	0.237168i	−0.738916	+	0.673798i	$0.764662\pi$
$752$	−11.8418	+	8.60359i	−0.431827	+	0.313740i
$753$		0			0
$754$	−2.11760	+	6.51731i	−0.0771185	+	0.237346i
$755$	5.58850	−	4.06028i	0.203386	−	0.147769i
$756$		0			0
$757$	2.78203	+	8.56219i	0.101114	+	0.311198i	0.988799	−	0.149254i	$-0.0476872\pi$
$757$	2.78203	+	8.56219i	0.101114	+	0.311198i	−0.887684	+	0.460452i	$0.847687\pi$
$758$	−36.7025			−1.33309
$759$		0			0
$760$	3.67961			0.133473
$761$	−2.56374	−	7.89038i	−0.0929355	−	0.286026i	0.893775	−	0.448516i	$-0.148047\pi$
$761$	−2.56374	−	7.89038i	−0.0929355	−	0.286026i	−0.986710	+	0.162490i	$0.948047\pi$
$762$		0			0
$763$	5.15132	−	3.74265i	0.186490	−	0.135493i
$764$	1.53972	−	4.73876i	0.0557050	−	0.171442i
$765$		0			0
$766$	17.9281	−	13.0255i	0.647767	−	0.470630i
$767$	13.4990	+	9.80761i	0.487421	+	0.354132i
$768$		0			0
$769$	2.89088			0.104248			0.0521239	−	0.998641i	$-0.483401\pi$
$769$	2.89088			0.104248			0.0521239	+	0.998641i	$0.483401\pi$
$770$	−2.15483	+	1.38431i	−0.0776546	+	0.0498872i
$771$		0			0
$772$	−4.72047	−	14.5281i	−0.169894	−	0.522879i
$773$	−22.5293	−	16.3685i	−0.810322	−	0.588734i	0.103602	−	0.994619i	$-0.466963\pi$
$773$	−22.5293	−	16.3685i	−0.810322	−	0.588734i	−0.913924	+	0.405885i	$0.866963\pi$
$774$		0			0
$775$	−2.37364	+	7.30532i	−0.0852637	+	0.262415i
$776$	3.14890	−	9.69132i	0.113039	−	0.347898i
$777$		0			0
$778$	24.4326	+	17.7513i	0.875952	+	0.636417i
$779$	−0.0863407	−	0.265729i	−0.00309348	−	0.00952074i
$780$		0			0
$781$	0.807189	−	2.07222i	0.0288835	−	0.0741500i
$782$	−58.7433			−2.10066
$783$		0			0
$784$	−9.25304	−	6.72273i	−0.330466	−	0.240098i
$785$	9.18388	−	6.67248i	0.327787	−	0.238151i
$786$		0			0
$787$	−7.67461	+	23.6200i	−0.273570	+	0.841963i	0.716024	+	0.698076i	$0.245960\pi$
$787$	−7.67461	+	23.6200i	−0.273570	+	0.841963i	−0.989594	+	0.143887i	$0.954040\pi$
$788$	−4.40324	+	3.19914i	−0.156859	+	0.113965i
$789$		0			0
$790$	0.771790	+	2.37533i	0.0274591	+	0.0845103i
$791$	2.76152			0.0981883
$792$		0			0
$793$	51.2426			1.81968
$794$	−3.98037	−	12.2503i	−0.141258	−	0.434748i
$795$		0			0
$796$	13.7896	−	10.0187i	0.488758	−	0.355103i
$797$	0.868668	−	2.67348i	0.0307698	−	0.0946997i	−0.934492	−	0.355984i	$-0.884146\pi$
$797$	0.868668	−	2.67348i	0.0307698	−	0.0946997i	0.965262	+	0.261284i	$0.0841459\pi$
$798$		0			0
$799$	52.3852	−	38.0600i	1.85325	−	1.34647i
$800$	3.40431	+	2.47338i	0.120361	+	0.0874471i
$801$		0			0
$802$	−8.46012			−0.298737
$803$	−13.9642	+	8.97095i	−0.492786	+	0.316578i
$804$		0			0
$805$	1.50181	+	4.62208i	0.0529317	+	0.162907i
$806$	32.0811	+	23.3083i	1.13001	+	0.820998i
$807$		0			0
$808$	17.9343	−	55.1961i	0.630926	−	1.94179i
$809$	−3.60825	+	11.1051i	−0.126859	+	0.390433i	−0.994235	−	0.107220i	$-0.965805\pi$
$809$	−3.60825	+	11.1051i	−0.126859	+	0.390433i	0.867376	+	0.497654i	$0.165805\pi$
$810$		0			0
$811$	−19.4722	−	14.1474i	−0.683761	−	0.496782i	0.190842	−	0.981621i	$-0.438878\pi$
$811$	−19.4722	−	14.1474i	−0.683761	−	0.496782i	−0.874603	+	0.484839i	$0.838878\pi$
$812$	−0.231455	−	0.712347i	−0.00812250	−	0.0249985i
$813$		0			0
$814$	−23.7251	−	19.4066i	−0.831565	−	0.680199i
$815$	1.79253			0.0627895
$816$		0			0
$817$	7.11310	+	5.16797i	0.248856	+	0.180804i
$818$	14.8343	−	10.7777i	0.518669	−	0.376835i
$819$		0			0
$820$	0.0576002	−	0.177275i	0.00201148	−	0.00619071i
$821$	3.92827	−	2.85406i	0.137098	−	0.0996073i	−0.517123	−	0.855911i	$-0.672997\pi$
$821$	3.92827	−	2.85406i	0.137098	−	0.0996073i	0.654220	+	0.756304i	$0.272997\pi$
$822$		0			0
$823$	8.05300	+	24.7846i	0.280710	+	0.863937i	0.987652	+	0.156665i	$0.0500743\pi$
$823$	8.05300	+	24.7846i	0.280710	+	0.863937i	−0.706942	+	0.707272i	$0.749926\pi$
$824$	−55.5050			−1.93361
$825$		0			0
$826$	2.73376			0.0951195
$827$	5.03212	+	15.4873i	0.174984	+	0.538546i	0.999633	−	0.0270996i	$-0.00862714\pi$
$827$	5.03212	+	15.4873i	0.174984	+	0.538546i	−0.824649	+	0.565645i	$0.808627\pi$
$828$		0			0
$829$	8.10161	−	5.88616i	0.281380	−	0.204435i	−0.438139	−	0.898907i	$-0.644362\pi$
$829$	8.10161	−	5.88616i	0.281380	−	0.204435i	0.719519	+	0.694472i	$0.244362\pi$
$830$	0.714156	−	2.19795i	0.0247887	−	0.0762918i
$831$		0			0
$832$	30.9879	−	22.5140i	1.07431	−	0.780534i
$833$	40.9331	+	29.7396i	1.41825	+	1.03042i
$834$		0			0
$835$	6.02450			0.208486
$836$	−3.17917	−	0.182326i	−0.109954	−	0.00630587i
$837$		0			0
$838$	−12.8944	−	39.6849i	−0.445430	−	1.37089i
$839$	9.50855	+	6.90837i	0.328272	+	0.238503i	0.739697	−	0.672940i	$-0.234969\pi$
$839$	9.50855	+	6.90837i	0.328272	+	0.238503i	−0.411425	+	0.911444i	$0.634969\pi$
$840$		0			0
$841$	−8.41700	+	25.9049i	−0.290242	+	0.893271i
$842$	7.67073	−	23.6081i	0.264351	−	0.813588i
$843$		0			0
$844$	−5.75659	−	4.18240i	−0.198150	−	0.143964i
$845$	−2.84773	−	8.76442i	−0.0979650	−	0.301505i
$846$		0			0
$847$	6.75427	−	3.81133i	0.232079	−	0.130959i
$848$	12.0009			0.412113
$849$		0			0
$850$	6.89440	+	5.00908i	0.236476	+	0.171810i
$851$	−47.0541	+	34.1868i	−1.61299	+	1.17191i
$852$		0			0
$853$	−14.1021	+	43.4018i	−0.482847	+	1.48605i	0.352229	+	0.935914i	$0.385424\pi$
$853$	−14.1021	+	43.4018i	−0.482847	+	1.48605i	−0.835076	+	0.550135i	$0.814576\pi$
$854$	6.79210	−	4.93475i	0.232421	−	0.168864i
$855$		0			0
$856$	5.80009	+	17.8508i	0.198243	+	0.610129i
$857$	8.41558			0.287471			0.143735	−	0.989616i	$-0.454089\pi$
$857$	8.41558			0.287471			0.143735	+	0.989616i	$0.454089\pi$
$858$		0			0
$859$	−45.3009			−1.54565			−0.772823	−	0.634622i	$-0.781156\pi$
$859$	−45.3009			−1.54565			−0.772823	+	0.634622i	$0.781156\pi$
$860$	1.81256	+	5.57848i	0.0618077	+	0.190225i
$861$		0			0
$862$	30.1071	−	21.8741i	1.02545	−	0.745034i
$863$	3.72644	−	11.4688i	0.126849	−	0.390402i	−0.867384	−	0.497639i	$-0.834200\pi$
$863$	3.72644	−	11.4688i	0.126849	−	0.390402i	0.994233	+	0.107237i	$0.0342003\pi$
$864$		0			0
$865$	−3.38715	+	2.46091i	−0.115166	+	0.0836733i
$866$	−32.4984	−	23.6115i	−1.10434	−	0.802350i
$867$		0			0
$868$	−4.33425			−0.147114
$869$	−1.92138	−	7.31466i	−0.0651783	−	0.248133i
$870$		0			0
$871$	2.97178	+	9.14618i	0.100695	+	0.309907i
$872$	−22.4103	−	16.2820i	−0.758907	−	0.551378i
$873$		0			0
$874$	2.79894	−	8.61426i	0.0946757	−	0.291382i
$875$	0.217868	−	0.670530i	0.00736530	−	0.0226681i
$876$		0			0
$877$	17.1058	+	12.4281i	0.577621	+	0.419666i	0.837866	−	0.545876i	$-0.183803\pi$
$877$	17.1058	+	12.4281i	0.577621	+	0.419666i	−0.260245	+	0.965543i	$0.583803\pi$
$878$	−0.355427	−	1.09389i	−0.0119951	−	0.0369170i
$879$		0			0
$880$	4.51519	+	3.69331i	0.152207	+	0.124501i
$881$	13.1669			0.443605			0.221803	−	0.975092i	$-0.428806\pi$
$881$	13.1669			0.443605			0.221803	+	0.975092i	$0.428806\pi$
$882$		0			0
$883$	28.1293	+	20.4371i	0.946627	+	0.687765i	0.950007	−	0.312230i	$-0.101076\pi$
$883$	28.1293	+	20.4371i	0.946627	+	0.687765i	−0.00337992	+	0.999994i	$0.501076\pi$
$884$	−23.7445	+	17.2514i	−0.798614	+	0.580227i
$885$		0			0
$886$	−10.3301	+	31.7929i	−0.347048	+	1.06810i
$887$	−16.9542	+	12.3179i	−0.569266	+	0.413596i	−0.834838	−	0.550495i	$-0.814439\pi$
$887$	−16.9542	+	12.3179i	−0.569266	+	0.413596i	0.265573	+	0.964091i	$0.414439\pi$
$888$		0			0
$889$	−2.36769	−	7.28700i	−0.0794097	−	0.244398i
$890$	3.66619			0.122891
$891$		0			0
$892$	−4.33555			−0.145165
$893$	3.08522	+	9.49533i	0.103243	+	0.317749i
$894$		0			0
$895$	−3.92507	+	2.85173i	−0.131201	+	0.0953229i
$896$	0.105680	−	0.325249i	0.00353052	−	0.0108658i
$897$		0			0
$898$	32.4046	−	23.5433i	1.08136	−	0.785652i
$899$	−8.24886	−	5.99314i	−0.275115	−	0.199883i
$900$		0			0
$901$	−53.0889			−1.76865
$902$	0.307087	−	0.788357i	0.0102249	−	0.0262494i
$903$		0			0
$904$	−3.71243	−	11.4257i	−0.123474	−	0.380013i
$905$	−18.6784	−	13.5706i	−0.620890	−	0.451103i
$906$		0			0
$907$	8.10886	−	24.9565i	0.269250	−	0.828667i	−0.721433	−	0.692484i	$-0.756516\pi$
$907$	8.10886	−	24.9565i	0.269250	−	0.828667i	0.990684	−	0.136183i	$-0.0434836\pi$
$908$	−2.08695	+	6.42299i	−0.0692580	+	0.213154i
$909$		0			0
$910$	−2.94461	−	2.13939i	−0.0976129	−	0.0709199i
$911$	12.2556	+	37.7188i	0.406045	+	1.24968i	0.920019	+	0.391873i	$0.128173\pi$
$911$	12.2556	+	37.7188i	0.406045	+	1.24968i	−0.513974	+	0.857806i	$0.671827\pi$
$912$		0			0
$913$	−2.54003	+	6.52079i	−0.0840628	+	0.215807i
$914$	2.61128			0.0863734
$915$		0			0
$916$	−7.25521	−	5.27122i	−0.239719	−	0.174166i
$917$	6.67887	−	4.85249i	0.220556	−	0.160243i
$918$		0			0
$919$	4.62777	−	14.2428i	0.152656	−	0.469827i	−0.845260	−	0.534356i	$-0.820554\pi$
$919$	4.62777	−	14.2428i	0.152656	−	0.469827i	0.997916	+	0.0645285i	$0.0205543\pi$
$920$	17.1048	−	12.4273i	0.563928	−	0.409717i
$921$		0			0
$922$	9.67881	+	29.7883i	0.318754	+	0.981025i
$923$	3.16041			0.104026
$924$		0			0
$925$	8.43763			0.277427
$926$	10.3504	+	31.8554i	0.340137	+	1.04683i
$927$		0			0
$928$	−4.51890	+	3.28317i	−0.148340	+	0.107775i
$929$	15.3415	−	47.2162i	0.503338	−	1.54911i	−0.300210	−	0.953873i	$-0.597057\pi$
$929$	15.3415	−	47.2162i	0.503338	−	1.54911i	0.803547	−	0.595241i	$-0.202943\pi$
$930$		0			0
$931$	−6.31143	+	4.58552i	−0.206849	+	0.150284i
$932$	−3.78115	−	2.74717i	−0.123856	−	0.0899865i
$933$		0			0
$934$	−4.09880			−0.134117
$935$	−19.9740	−	16.3383i	−0.653220	−	0.534318i
$936$		0			0
$937$	−16.7770	−	51.6342i	−0.548079	−	1.68682i	−0.713553	−	0.700601i	$-0.752915\pi$
$937$	−16.7770	−	51.6342i	−0.548079	−	1.68682i	0.165474	−	0.986214i	$-0.447085\pi$
$938$	1.27469	+	0.926120i	0.0416203	+	0.0302389i
$939$		0			0
$940$	−2.05823	+	6.33459i	−0.0671321	+	0.206611i
$941$	−2.05826	+	6.33466i	−0.0670972	+	0.206504i	−0.978984	−	0.203938i	$-0.934626\pi$
$941$	−2.05826	+	6.33466i	−0.0670972	+	0.206504i	0.911886	+	0.410442i	$0.134626\pi$
$942$		0			0
$943$	−1.29882	−	0.943648i	−0.0422954	−	0.0307294i
$944$	−1.92406	−	5.92164i	−0.0626227	−	0.192733i
$945$		0			0
$946$	6.76390	+	25.7501i	0.219913	+	0.837207i
$947$	42.6250			1.38513			0.692563	−	0.721358i	$-0.256482\pi$
$947$	42.6250			1.38513			0.692563	+	0.721358i	$0.256482\pi$
$948$		0			0
$949$	−19.0823	−	13.8641i	−0.619439	−	0.450049i
$950$	−1.06304	+	0.772344i	−0.0344896	+	0.0250581i
$951$		0			0
$952$	−5.19927	+	16.0017i	−0.168509	+	0.518619i
$953$	−13.5542	+	9.84772i	−0.439064	+	0.318999i	−0.785263	−	0.619162i	$-0.787472\pi$
$953$	−13.5542	+	9.84772i	−0.439064	+	0.318999i	0.346199	+	0.938161i	$0.387472\pi$
$954$		0			0
$955$	1.92385	+	5.92100i	0.0622543	+	0.191599i
$956$	−13.2264			−0.427772
$957$		0			0
$958$	−1.03500			−0.0334393
$959$	4.45110	+	13.6991i	0.143733	+	0.442366i
$960$		0			0
$961$	−22.6539	+	16.4590i	−0.730772	+	0.530937i
$962$	13.4605	−	41.4271i	0.433984	−	1.33566i
$963$		0			0
$964$	−2.13138	+	1.54854i	−0.0686470	+	0.0498750i
$965$	15.4416	+	11.2190i	0.497082	+	0.361151i
$966$		0			0
$967$	−50.1233			−1.61186			−0.805928	−	0.592014i	$-0.798333\pi$
$967$	−50.1233			−1.61186			−0.805928	+	0.592014i	$0.798333\pi$
$968$	−24.8493	−	22.8218i	−0.798687	−	0.733521i
$969$		0			0
$970$	1.12447	+	3.46078i	0.0361047	+	0.111119i
$971$	32.4602	+	23.5837i	1.04170	+	0.756837i	0.970616	−	0.240633i	$-0.0773551\pi$
$971$	32.4602	+	23.5837i	1.04170	+	0.756837i	0.0710811	+	0.997471i	$0.477355\pi$
$972$		0			0
$973$	1.78020	−	5.47890i	0.0570707	−	0.175646i
$974$	4.53113	−	13.9454i	0.145187	−	0.446839i
$975$		0			0
$976$	−15.4696	−	11.2393i	−0.495170	−	0.359762i
$977$	7.46838	+	22.9853i	0.238935	+	0.735365i	0.996575	+	0.0826930i	$0.0263521\pi$
$977$	7.46838	+	22.9853i	0.238935	+	0.735365i	−0.757640	+	0.652672i	$0.773648\pi$
$978$		0			0
$979$	−11.0833	−	0.635626i	−0.354223	−	0.0203147i
$980$	−5.20449			−0.166251
$981$		0			0
$982$	2.47125	+	1.79547i	0.0788608	+	0.0572958i
$983$	18.8518	−	13.6966i	0.601278	−	0.436854i	−0.245055	−	0.969509i	$-0.578806\pi$
$983$	18.8518	−	13.6966i	0.601278	−	0.436854i	0.846332	+	0.532656i	$0.178806\pi$
$984$		0			0
$985$	2.10149	−	6.46772i	0.0669590	−	0.206079i
$986$	−9.15166	+	6.64907i	−0.291448	+	0.211750i
$987$		0			0
$988$	−1.39843	−	4.30393i	−0.0444900	−	0.136926i
$989$	50.5195			1.60643
$990$		0			0
$991$	−54.0689			−1.71756			−0.858778	−	0.512348i	$-0.828776\pi$
$991$	−54.0689			−1.71756			−0.858778	+	0.512348i	$0.828776\pi$
$992$	9.98818	+	30.7405i	0.317125	+	0.976011i
$993$		0			0
$994$	0.418906	−	0.304353i	0.0132869	−	0.00965348i
$995$	−6.58121	+	20.2549i	−0.208638	+	0.642122i
$996$		0			0
$997$	−41.0260	+	29.8071i	−1.29931	+	0.944001i	−0.999949	−	0.0101405i	$-0.996772\pi$
$997$	−41.0260	+	29.8071i	−1.29931	+	0.944001i	−0.299357	+	0.954141i	$0.596772\pi$
$998$	15.7542	+	11.4461i	0.498691	+	0.362320i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.n.a.181.1		8
3.2	odd	2		165.2.m.d.16.2	✓	8
11.3	even	5		5445.2.a.bt.1.1		4
11.8	odd	10		5445.2.a.bf.1.4		4
11.9	even	5	inner	495.2.n.a.361.1		8
15.2	even	4		825.2.bx.f.49.2		16
15.8	even	4		825.2.bx.f.49.3		16
15.14	odd	2		825.2.n.g.676.1		8
33.8	even	10		1815.2.a.w.1.1		4
33.14	odd	10		1815.2.a.p.1.4		4
33.20	odd	10		165.2.m.d.31.2	yes	8
165.14	odd	10		9075.2.a.di.1.1		4
165.53	even	20		825.2.bx.f.724.2		16
165.74	even	10		9075.2.a.cm.1.4		4
165.119	odd	10		825.2.n.g.526.1		8
165.152	even	20		825.2.bx.f.724.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.m.d.16.2	✓	8	3.2	odd	2
165.2.m.d.31.2	yes	8	33.20	odd	10
495.2.n.a.181.1		8	1.1	even	1	trivial
495.2.n.a.361.1		8	11.9	even	5	inner
825.2.n.g.526.1		8	165.119	odd	10
825.2.n.g.676.1		8	15.14	odd	2
825.2.bx.f.49.2		16	15.2	even	4
825.2.bx.f.49.3		16	15.8	even	4
825.2.bx.f.724.2		16	165.53	even	20
825.2.bx.f.724.3		16	165.152	even	20
1815.2.a.p.1.4		4	33.14	odd	10
1815.2.a.w.1.1		4	33.8	even	10
5445.2.a.bf.1.4		4	11.8	odd	10
5445.2.a.bt.1.1		4	11.3	even	5
9075.2.a.cm.1.4		4	165.74	even	10
9075.2.a.di.1.1		4	165.14	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)

\(f(q)\)	\(=\)	\(q+(-0.338464 - 1.04169i) q^{2} +(0.647481 - 0.470423i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(0.570387 - 0.414410i) q^{7} +(-2.48141 - 1.80285i) q^{8} +O(q^{10})\)	\(q+(-0.338464 - 1.04169i) q^{2} +(0.647481 - 0.470423i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(0.570387 - 0.414410i) q^{7} +(-2.48141 - 1.80285i) q^{8} +1.09529 q^{10} +(-3.31118 - 0.189896i) q^{11} +(-1.45650 - 4.48264i) q^{13} +(-0.624741 - 0.453901i) q^{14} +(-0.543502 + 1.67273i) q^{16} +(2.40431 - 7.39971i) q^{17} +(0.970553 + 0.705148i) q^{19} +(0.247316 + 0.761160i) q^{20} +(0.922906 + 3.51349i) q^{22} +6.89318 q^{23} +(-0.809017 - 0.587785i) q^{25} +(-4.17653 + 3.03443i) q^{26} +(0.174367 - 0.536646i) q^{28} +(1.07389 - 0.780229i) q^{29} +(-2.37364 - 7.30532i) q^{31} -4.20796 q^{32} -8.52195 q^{34} +(0.217868 + 0.670530i) q^{35} +(-6.82618 + 4.95951i) q^{37} +(0.406045 - 1.24968i) q^{38} +(2.48141 - 1.80285i) q^{40} +(-0.188421 - 0.136896i) q^{41} +7.32892 q^{43} +(-2.23326 + 1.43470i) q^{44} +(-2.33310 - 7.18053i) q^{46} +(6.73287 + 4.89171i) q^{47} +(-2.00951 + 6.18465i) q^{49} +(-0.338464 + 1.04169i) q^{50} +(-3.05179 - 2.21726i) q^{52} +(-2.10852 - 6.48936i) q^{53} +(1.20381 - 3.09044i) q^{55} -2.16248 q^{56} +(-1.17623 - 0.854580i) q^{58} +(-2.86401 + 2.08083i) q^{59} +(-3.35959 + 10.3397i) q^{61} +(-6.80645 + 4.94518i) q^{62} +(2.51125 + 7.72883i) q^{64} +4.71333 q^{65} -2.04036 q^{67} +(-1.92424 - 5.92222i) q^{68} +(0.624741 - 0.453901i) q^{70} +(-0.207204 + 0.637709i) q^{71} +(4.04859 - 2.94147i) q^{73} +(7.47668 + 5.43212i) q^{74} +0.960132 q^{76} +(-1.96735 + 1.26387i) q^{77} +(0.704642 + 2.16867i) q^{79} +(-1.42291 - 1.03380i) q^{80} +(-0.0788288 + 0.242610i) q^{82} +(0.652022 - 2.00672i) q^{83} +(6.29457 + 4.57327i) q^{85} +(-2.48058 - 7.63443i) q^{86} +(7.87404 + 6.44077i) q^{88} +3.34722 q^{89} +(-2.68842 - 1.95325i) q^{91} +(4.46321 - 3.24271i) q^{92} +(2.81680 - 8.66921i) q^{94} +(-0.970553 + 0.705148i) q^{95} +(1.02664 + 3.15968i) q^{97} +7.12261 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 2 q^{4} + 2 q^{5} + 3 q^{7} + q^{8}+O(q^{10}) \) 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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