LMFDB - Embedded newform 441.2.u.c.64.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(64,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("441.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.u (of order $7$, degree $6$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{7})$
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			64.1
Character	$\chi$	$=$	441.64
Dual form			441.2.u.c.379.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.540253 + 2.36700i) q^{2} +(-3.50889 - 1.68979i) q^{4} +(-1.42001 + 1.78063i) q^{5} +(-1.01369 - 2.44386i) q^{7} +(2.86791 - 3.59625i) q^{8} +O(q^{10})$	\(q+(-0.540253 + 2.36700i) q^{2} +(-3.50889 - 1.68979i) q^{4} +(-1.42001 + 1.78063i) q^{5} +(-1.01369 - 2.44386i) q^{7} +(2.86791 - 3.59625i) q^{8} +(-3.44760 - 4.32315i) q^{10} +(1.31000 - 5.73951i) q^{11} +(0.323592 - 1.41775i) q^{13} +(6.33226 - 1.07909i) q^{14} +(2.10648 + 2.64144i) q^{16} +(-5.81761 + 2.80161i) q^{17} +1.31823 q^{19} +(7.99154 - 3.84852i) q^{20} +(12.8777 + 6.20157i) q^{22} +(-5.45848 - 2.62867i) q^{23} +(-0.0416288 - 0.182388i) q^{25} +(3.18100 + 1.53189i) q^{26} +(-0.572700 + 10.2881i) q^{28} +(2.02588 - 0.975611i) q^{29} +5.41624 q^{31} +(0.898175 - 0.432538i) q^{32} +(-3.48845 - 15.2839i) q^{34} +(5.79106 + 1.66529i) q^{35} +(-1.83476 + 0.883574i) q^{37} +(-0.712175 + 3.12024i) q^{38} +(2.33114 + 10.2134i) q^{40} +(0.711273 - 0.891909i) q^{41} +(-5.74818 - 7.20799i) q^{43} +(-14.2952 + 17.9256i) q^{44} +(9.17101 - 11.5001i) q^{46} +(2.18128 - 9.55679i) q^{47} +(-4.94488 + 4.95461i) q^{49} +0.454202 q^{50} +(-3.53115 + 4.42792i) q^{52} +(-5.26307 - 2.53456i) q^{53} +(8.35974 + 10.4828i) q^{55} +(-11.6959 - 3.36331i) q^{56} +(1.21479 + 5.32233i) q^{58} +(3.06841 + 3.84766i) q^{59} +(-3.76100 + 1.81120i) q^{61} +(-2.92614 + 12.8203i) q^{62} +(2.04217 + 8.94731i) q^{64} +(2.06499 + 2.58942i) q^{65} -8.72541 q^{67} +25.1475 q^{68} +(-7.07039 + 12.8078i) q^{70} +(-4.42064 - 2.12887i) q^{71} +(-1.12443 - 4.92643i) q^{73} +(-1.10019 - 4.82024i) q^{74} +(-4.62551 - 2.22753i) q^{76} +(-15.3545 + 2.61659i) q^{77} -9.24302 q^{79} -7.69466 q^{80} +(1.72688 + 2.16544i) q^{82} +(-2.43259 - 10.6579i) q^{83} +(3.27241 - 14.3373i) q^{85} +(20.1668 - 9.71181i) q^{86} +(-16.8837 - 21.1715i) q^{88} +(2.48920 + 10.9059i) q^{89} +(-3.79280 + 0.646340i) q^{91} +(14.7113 + 18.4474i) q^{92} +(21.4425 + 10.3262i) q^{94} +(-1.87189 + 2.34728i) q^{95} +4.02302 q^{97} +(-9.05608 - 14.3813i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - q^{2} - 3 q^{4} - 3 q^{8}+O(q^{10}) $ 24 * q - q^2 - 3 * q^4 - 3 * q^8	$ 24 q - q^{2} - 3 q^{4} - 3 q^{8} - 30 q^{10} - 9 q^{11} + 21 q^{14} - 29 q^{16} - 5 q^{17} + 26 q^{19} + 13 q^{20} + 11 q^{22} - 4 q^{23} - 28 q^{25} + 22 q^{26} - 7 q^{28} - 6 q^{29} + 36 q^{31} - 14 q^{32} + 46 q^{34} + 7 q^{35} - 22 q^{37} + 45 q^{38} + 35 q^{40} + 11 q^{41} + 6 q^{43} - 82 q^{44} - 16 q^{46} - 29 q^{47} - 42 q^{49} + 48 q^{50} - 50 q^{52} - 28 q^{53} + 23 q^{55} - 21 q^{56} + 39 q^{58} + 15 q^{59} - 32 q^{61} + 8 q^{62} + 29 q^{64} + 21 q^{65} - 34 q^{67} + 22 q^{68} - 24 q^{71} - 15 q^{73} - 6 q^{74} + 7 q^{76} + 21 q^{77} - 34 q^{79} - 8 q^{80} + 14 q^{82} - 14 q^{83} + 20 q^{85} + 100 q^{86} - 108 q^{88} - 10 q^{89} + 84 q^{91} + 21 q^{92} + 99 q^{94} - 18 q^{95} - 64 q^{97} - 91 q^{98}+O(q^{100}) $ 24 * q - q^2 - 3 * q^4 - 3 * q^8 - 30 * q^10 - 9 * q^11 + 21 * q^14 - 29 * q^16 - 5 * q^17 + 26 * q^19 + 13 * q^20 + 11 * q^22 - 4 * q^23 - 28 * q^25 + 22 * q^26 - 7 * q^28 - 6 * q^29 + 36 * q^31 - 14 * q^32 + 46 * q^34 + 7 * q^35 - 22 * q^37 + 45 * q^38 + 35 * q^40 + 11 * q^41 + 6 * q^43 - 82 * q^44 - 16 * q^46 - 29 * q^47 - 42 * q^49 + 48 * q^50 - 50 * q^52 - 28 * q^53 + 23 * q^55 - 21 * q^56 + 39 * q^58 + 15 * q^59 - 32 * q^61 + 8 * q^62 + 29 * q^64 + 21 * q^65 - 34 * q^67 + 22 * q^68 - 24 * q^71 - 15 * q^73 - 6 * q^74 + 7 * q^76 + 21 * q^77 - 34 * q^79 - 8 * q^80 + 14 * q^82 - 14 * q^83 + 20 * q^85 + 100 * q^86 - 108 * q^88 - 10 * q^89 + 84 * q^91 + 21 * q^92 + 99 * q^94 - 18 * q^95 - 64 * q^97 - 91 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{7}\right)$	$1$

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 $

$2$	−0.540253	+	2.36700i	−0.382016	+	1.67372i	0.309139	+	0.951017i	$0.399959\pi$
$2$	−0.540253	+	2.36700i	−0.382016	+	1.67372i	−0.691155	+	0.722706i	$0.742898\pi$
$3$		0			0
$3$		0			0
$4$	−3.50889	−	1.68979i	−1.75444	−	0.844895i
$5$	−1.42001	+	1.78063i	−0.635047	+	0.796324i	−0.990374	−	0.138419i	$-0.955798\pi$
$5$	−1.42001	+	1.78063i	−0.635047	+	0.796324i	0.355327	+	0.934742i	$0.384370\pi$
$6$		0			0
$7$	−1.01369	−	2.44386i	−0.383137	−	0.923691i
$7$	−1.01369	−	2.44386i	−0.383137	−	0.923691i
$8$	2.86791	−	3.59625i	1.01396	−	1.27147i
$9$		0			0
$10$	−3.44760	−	4.32315i	−1.09023	−	1.36710i
$11$	1.31000	−	5.73951i	0.394981	−	1.73053i	−0.251736	−	0.967796i	$-0.581001\pi$
$11$	1.31000	−	5.73951i	0.394981	−	1.73053i	0.646717	−	0.762730i	$-0.276142\pi$
$12$		0			0
$13$	0.323592	−	1.41775i	0.0897483	−	0.393213i	−0.910024	−	0.414556i	$-0.863937\pi$
$13$	0.323592	−	1.41775i	0.0897483	−	0.393213i	0.999772	+	0.0213427i	$0.00679411\pi$
$14$	6.33226	−	1.07909i	1.69237	−	0.288400i
$15$		0			0
$16$	2.10648	+	2.64144i	0.526620	+	0.660361i
$17$	−5.81761	+	2.80161i	−1.41098	+	0.679491i	−0.975356	−	0.220638i	$-0.929186\pi$
$17$	−5.81761	+	2.80161i	−1.41098	+	0.679491i	−0.435622	+	0.900129i	$0.643472\pi$
$18$		0			0
$19$	1.31823			0.302422			0.151211	−	0.988502i	$-0.451683\pi$
$19$	1.31823			0.302422			0.151211	+	0.988502i	$0.451683\pi$
$20$	7.99154	−	3.84852i	1.78696	−	0.860556i
$21$		0			0
$22$	12.8777	+	6.20157i	2.74553	+	1.32218i
$23$	−5.45848	−	2.62867i	−1.13817	−	0.548115i	−0.232711	−	0.972546i	$-0.574760\pi$
$23$	−5.45848	−	2.62867i	−1.13817	−	0.548115i	−0.905460	+	0.424431i	$0.860474\pi$
$24$		0			0
$25$	−0.0416288	−	0.182388i	−0.00832575	−	0.0364775i
$26$	3.18100	+	1.53189i	0.623844	+	0.300428i
$27$		0			0
$28$	−0.572700	+	10.2881i	−0.108230	+	1.94427i
$29$	2.02588	−	0.975611i	0.376196	−	0.181166i	−0.236225	−	0.971698i	$-0.575910\pi$
$29$	2.02588	−	0.975611i	0.376196	−	0.181166i	0.612421	+	0.790532i	$0.290196\pi$
$30$		0			0
$31$	5.41624			0.972786			0.486393	−	0.873740i	$-0.338312\pi$
$31$	5.41624			0.972786			0.486393	+	0.873740i	$0.338312\pi$
$32$	0.898175	−	0.432538i	0.158776	−	0.0764627i
$33$		0			0
$34$	−3.48845	−	15.2839i	−0.598263	−	2.62116i
$35$	5.79106	+	1.66529i	0.978867	+	0.281486i
$36$		0			0
$37$	−1.83476	+	0.883574i	−0.301633	+	0.145259i	−0.578578	−	0.815627i	$-0.696392\pi$
$37$	−1.83476	+	0.883574i	−0.301633	+	0.145259i	0.276945	+	0.960886i	$0.410678\pi$
$38$	−0.712175	+	3.12024i	−0.115530	+	0.506170i
$39$		0			0
$40$	2.33114	+	10.2134i	0.368586	+	1.61488i
$41$	0.711273	−	0.891909i	0.111082	−	0.139293i	−0.723182	−	0.690657i	$-0.757321\pi$
$41$	0.711273	−	0.891909i	0.111082	−	0.139293i	0.834264	+	0.551365i	$0.185893\pi$
$42$		0			0
$43$	−5.74818	−	7.20799i	−0.876589	−	1.09921i	−0.994348	−	0.106166i	$-0.966143\pi$
$43$	−5.74818	−	7.20799i	−0.876589	−	1.09921i	0.117760	−	0.993042i	$-0.462429\pi$
$44$	−14.2952	+	17.9256i	−2.15509	+	2.70239i
$45$		0			0
$46$	9.17101	−	11.5001i	1.35219	−	1.69560i
$47$	2.18128	−	9.55679i	0.318172	−	1.39400i	−0.522584	−	0.852588i	$-0.675032\pi$
$47$	2.18128	−	9.55679i	0.318172	−	1.39400i	0.840756	−	0.541414i	$-0.182111\pi$
$48$		0			0
$49$	−4.94488	+	4.95461i	−0.706412	+	0.707801i
$50$	0.454202			0.0642338
$51$		0			0
$52$	−3.53115	+	4.42792i	−0.489682	+	0.614042i
$53$	−5.26307	−	2.53456i	−0.722938	−	0.348148i	0.0359646	−	0.999353i	$-0.488550\pi$
$53$	−5.26307	−	2.53456i	−0.722938	−	0.348148i	−0.758902	+	0.651205i	$0.774264\pi$
$54$		0			0
$55$	8.35974	+	10.4828i	1.12723	+	1.41350i
$56$	−11.6959	−	3.36331i	−1.56293	−	0.449441i
$57$		0			0
$58$	1.21479	+	5.32233i	0.159509	+	0.698856i
$59$	3.06841	+	3.84766i	0.399473	+	0.500923i	0.940364	−	0.340169i	$-0.110484\pi$
$59$	3.06841	+	3.84766i	0.399473	+	0.500923i	−0.540891	+	0.841092i	$0.681913\pi$
$60$		0			0
$61$	−3.76100	+	1.81120i	−0.481547	+	0.231901i	−0.658877	−	0.752251i	$-0.728968\pi$
$61$	−3.76100	+	1.81120i	−0.481547	+	0.231901i	0.177330	+	0.984151i	$0.443254\pi$
$62$	−2.92614	+	12.8203i	−0.371620	+	1.62817i
$63$		0			0
$64$	2.04217	+	8.94731i	0.255271	+	1.11841i
$65$	2.06499	+	2.58942i	0.256130	+	0.321177i
$66$		0			0
$67$	−8.72541			−1.06598			−0.532989	−	0.846122i	$-0.678931\pi$
$67$	−8.72541			−1.06598			−0.532989	+	0.846122i	$0.678931\pi$
$68$	25.1475			3.04958
$69$		0			0
$70$	−7.07039	+	12.8078i	−0.845073	+	1.53082i
$71$	−4.42064	−	2.12887i	−0.524634	−	0.252650i	0.152770	−	0.988262i	$-0.451181\pi$
$71$	−4.42064	−	2.12887i	−0.524634	−	0.252650i	−0.677404	+	0.735612i	$0.736895\pi$
$72$		0			0
$73$	−1.12443	−	4.92643i	−0.131604	−	0.576595i	−0.997128	−	0.0757284i	$-0.975872\pi$
$73$	−1.12443	−	4.92643i	−0.131604	−	0.576595i	0.865524	−	0.500867i	$-0.166985\pi$
$74$	−1.10019	−	4.82024i	−0.127894	−	0.560341i
$75$		0			0
$76$	−4.62551	−	2.22753i	−0.530582	−	0.255515i
$77$	−15.3545	+	2.61659i	−1.74980	+	0.298188i
$78$		0			0
$79$	−9.24302			−1.03992			−0.519961	−	0.854190i	$-0.674053\pi$
$79$	−9.24302			−1.03992			−0.519961	+	0.854190i	$0.674053\pi$
$80$	−7.69466			−0.860289
$81$		0			0
$82$	1.72688	+	2.16544i	0.190702	+	0.239133i
$83$	−2.43259	−	10.6579i	−0.267012	−	1.16986i	−0.913470	−	0.406906i	$-0.866608\pi$
$83$	−2.43259	−	10.6579i	−0.267012	−	1.16986i	0.646458	−	0.762949i	$-0.276250\pi$
$84$		0			0
$85$	3.27241	−	14.3373i	0.354942	−	1.55510i
$86$	20.1668	−	9.71181i	2.17464	−	1.04725i
$87$		0			0
$88$	−16.8837	−	21.1715i	−1.79981	−	2.25689i
$89$	2.48920	+	10.9059i	0.263855	+	1.15602i	0.917030	+	0.398818i	$0.130579\pi$
$89$	2.48920	+	10.9059i	0.263855	+	1.15602i	−0.653175	+	0.757207i	$0.726564\pi$
$90$		0			0
$91$	−3.79280	+	0.646340i	−0.397594	+	0.0677548i
$92$	14.7113	+	18.4474i	1.53376	+	1.92327i
$93$		0			0
$94$	21.4425	+	10.3262i	2.21163	+	1.06506i
$95$	−1.87189	+	2.34728i	−0.192052	+	0.240826i
$96$		0			0
$97$	4.02302			0.408476			0.204238	−	0.978921i	$-0.434528\pi$
$97$	4.02302			0.408476			0.204238	+	0.978921i	$0.434528\pi$
$98$	−9.05608	−	14.3813i	−0.914802	−	1.45273i
$99$		0			0
$100$	−0.162126	+	0.710321i	−0.0162126	+	0.0710321i
$101$	0.746457	−	0.936028i	0.0742753	−	0.0931382i	−0.743306	−	0.668952i	$-0.766743\pi$
$101$	0.746457	−	0.936028i	0.0742753	−	0.0931382i	0.817581	+	0.575814i	$0.195315\pi$
$102$		0			0
$103$	6.15500	−	7.71812i	0.606470	−	0.760489i	−0.379901	−	0.925027i	$-0.624042\pi$
$103$	6.15500	−	7.71812i	0.606470	−	0.760489i	0.986371	+	0.164538i	$0.0526133\pi$
$104$	−4.17055	−	5.22970i	−0.408956	−	0.512814i
$105$		0			0
$106$	8.84269	−	11.0884i	0.858878	−	1.07700i
$107$	−0.341166	−	1.49474i	−0.0329817	−	0.144502i	0.955756	−	0.294160i	$-0.0950399\pi$
$107$	−0.341166	−	1.49474i	−0.0329817	−	0.144502i	−0.988738	+	0.149658i	$0.952183\pi$
$108$		0			0
$109$	1.47285	−	6.45298i	0.141073	−	0.618083i	−0.854113	−	0.520087i	$-0.825900\pi$
$109$	1.47285	−	6.45298i	0.141073	−	0.618083i	0.995187	−	0.0979963i	$-0.0312433\pi$
$110$	−29.3291	+	14.1242i	−2.79642	+	1.34669i
$111$		0			0
$112$	4.32000	−	7.82553i	0.408202	−	0.739443i
$113$	−3.44490	−	15.0931i	−0.324069	−	1.41984i	−0.830240	−	0.557405i	$-0.811797\pi$
$113$	−3.44490	−	15.0931i	−0.324069	−	1.41984i	0.506172	−	0.862433i	$-0.331060\pi$
$114$		0			0
$115$	12.4318	−	5.98683i	1.15927	−	0.558274i
$116$	−8.75715			−0.813081
$117$		0			0
$118$	−10.7651	+	5.18422i	−0.991012	+	0.477246i
$119$	12.7440	+	11.3775i	1.16824	+	1.04297i
$120$		0			0
$121$	−21.3152	−	10.2648i	−1.93774	−	0.933167i
$122$	−2.25523	−	9.88080i	−0.204179	−	0.894565i
$123$		0			0
$124$	−19.0050	−	9.15232i	−1.70670	−	0.821902i
$125$	−9.87598	−	4.75602i	−0.883334	−	0.425391i
$126$		0			0
$127$	−6.09512	+	2.93526i	−0.540854	+	0.260462i	−0.684305	−	0.729196i	$-0.739894\pi$
$127$	−6.09512	+	2.93526i	−0.540854	+	0.260462i	0.143451	+	0.989657i	$0.454180\pi$
$128$	−20.2878			−1.79320
$129$		0			0
$130$	−7.24477	+	3.48890i	−0.635408	+	0.305996i
$131$	11.2496	+	14.1065i	0.982880	+	1.23249i	0.972585	+	0.232546i	$0.0747055\pi$
$131$	11.2496	+	14.1065i	0.982880	+	1.23249i	0.0102947	+	0.999947i	$0.496723\pi$
$132$		0			0
$133$	−1.33627	−	3.22156i	−0.115869	−	0.279344i
$134$	4.71393	−	20.6531i	0.407221	−	1.78415i
$135$		0			0
$136$	−6.60910	+	28.9564i	−0.566726	+	2.48299i
$137$	10.1894	+	12.7771i	0.870538	+	1.09162i	0.995047	+	0.0994019i	$0.0316930\pi$
$137$	10.1894	+	12.7771i	0.870538	+	1.09162i	−0.124509	+	0.992218i	$0.539736\pi$
$138$		0			0
$139$	−10.4556	+	13.1109i	−0.886830	+	1.11205i	0.106219	+	0.994343i	$0.466126\pi$
$139$	−10.4556	+	13.1109i	−0.886830	+	1.11205i	−0.993048	+	0.117706i	$0.962446\pi$
$140$	−17.5062	−	15.6290i	−1.47954	−	1.32089i
$141$		0			0
$142$	7.42730	−	9.31354i	0.623285	−	0.781575i
$143$	−7.71328	−	3.71452i	−0.645017	−	0.310624i
$144$		0			0
$145$	−1.13956	+	4.99272i	−0.0946350	+	0.414623i
$146$	12.2683			1.01534
$147$		0			0
$148$	7.93102			0.651926
$149$	2.69229	−	11.7957i	0.220561	−	0.966340i	−0.736496	−	0.676441i	$-0.763521\pi$
$149$	2.69229	−	11.7957i	0.220561	−	0.966340i	0.957057	−	0.289899i	$-0.0936217\pi$
$150$		0			0
$151$	13.9956	+	6.73991i	1.13894	+	0.548486i	0.905695	−	0.423931i	$-0.139350\pi$
$151$	13.9956	+	6.73991i	1.13894	+	0.548486i	0.233249	+	0.972417i	$0.425064\pi$
$152$	3.78056	−	4.74067i	0.306644	−	0.384519i
$153$		0			0
$154$	2.10182	−	37.7577i	0.169370	−	3.04260i
$155$	−7.69111	+	9.64435i	−0.617765	+	0.774653i
$156$		0			0
$157$	2.97891	+	3.73544i	0.237743	+	0.298120i	0.886362	−	0.462993i	$-0.153225\pi$
$157$	2.97891	+	3.73544i	0.237743	+	0.298120i	−0.648619	+	0.761113i	$0.724653\pi$
$158$	4.99357	−	21.8783i	0.397267	−	1.74054i
$159$		0			0
$160$	−0.505223	+	2.21353i	−0.0399414	+	0.174995i
$161$	−0.890902	+	16.0044i	−0.0702129	+	1.26132i
$162$		0			0
$163$	9.82462	+	12.3197i	0.769524	+	0.964952i	0.999967	−	0.00813372i	$-0.00258907\pi$
$163$	9.82462	+	12.3197i	0.769524	+	0.964952i	−0.230443	+	0.973086i	$0.574018\pi$
$164$	−4.00292	+	1.92770i	−0.312575	+	0.150528i
$165$		0			0
$166$	26.5415			2.06002
$167$	−20.9698	+	10.0985i	−1.62269	+	0.781447i	−0.999999	−	0.00101940i	$-0.999676\pi$
$167$	−20.9698	+	10.0985i	−1.62269	+	0.781447i	−0.622692	+	0.782467i	$0.713961\pi$
$168$		0			0
$169$	9.80729	+	4.72294i	0.754407	+	0.363303i
$170$	32.1686	+	15.4916i	2.46722	+	1.18815i
$171$		0			0
$172$	7.98971	+	35.0052i	0.609210	+	2.66912i
$173$	5.57219	+	2.68342i	0.423646	+	0.204017i	0.633545	−	0.773706i	$-0.281599\pi$
$173$	5.57219	+	2.68342i	0.423646	+	0.204017i	−0.209899	+	0.977723i	$0.567314\pi$
$174$		0			0
$175$	−0.403531	+	0.286618i	−0.0305041	+	0.0216663i
$176$	17.9201	−	8.62986i	1.35078	−	0.650500i
$177$		0			0
$178$	−27.1591			−2.03566
$179$	−7.91581	+	3.81205i	−0.591655	+	0.284926i	−0.705656	−	0.708555i	$-0.749348\pi$
$179$	−7.91581	+	3.81205i	−0.591655	+	0.284926i	0.114001	+	0.993481i	$0.463633\pi$
$180$		0			0
$181$	−0.305268	−	1.33747i	−0.0226904	−	0.0994131i	0.962315	−	0.271938i	$-0.0876646\pi$
$181$	−0.305268	−	1.33747i	−0.0226904	−	0.0994131i	−0.985005	+	0.172525i	$0.944807\pi$
$182$	0.519184	−	9.32675i	0.0384845	−	0.691345i
$183$		0			0
$184$	−25.1078	+	12.0913i	−1.85097	+	0.891380i
$185$	1.03205	−	4.52172i	0.0758780	−	0.332443i
$186$		0			0
$187$	8.45878	+	37.0603i	0.618567	+	2.71012i
$188$	−23.8028	+	29.8478i	−1.73600	+	2.17687i
$189$		0			0
$190$	−4.54472	−	5.69889i	−0.329708	−	0.413441i
$191$	8.00317	−	10.0357i	0.579089	−	0.726154i	−0.402868	−	0.915258i	$-0.631987\pi$
$191$	8.00317	−	10.0357i	0.579089	−	0.726154i	0.981957	+	0.189104i	$0.0605582\pi$
$192$		0			0
$193$	−0.324433	+	0.406826i	−0.0233532	+	0.0292840i	−0.793371	−	0.608738i	$-0.791676\pi$
$193$	−0.324433	+	0.406826i	−0.0233532	+	0.0292840i	0.770018	+	0.638022i	$0.220247\pi$
$194$	−2.17345	+	9.52250i	−0.156045	+	0.683676i
$195$		0			0
$196$	25.7233	−	9.02934i	1.83738	−	0.644953i
$197$	9.71918			0.692463			0.346232	−	0.938149i	$-0.387461\pi$
$197$	9.71918			0.692463			0.346232	+	0.938149i	$0.387461\pi$
$198$		0			0
$199$	5.96706	−	7.48246i	0.422994	−	0.530417i	−0.523979	−	0.851731i	$-0.675553\pi$
$199$	5.96706	−	7.48246i	0.422994	−	0.530417i	0.946973	+	0.321314i	$0.104124\pi$
$200$	−0.775299	−	0.373364i	−0.0548219	−	0.0264008i
$201$		0			0
$202$	1.81230	+	2.27256i	0.127513	+	0.159897i
$203$	−4.43786	−	3.96199i	−0.311477	−	0.278077i
$204$		0			0
$205$	0.578149	+	2.53303i	0.0403797	+	0.176915i
$206$	14.9436	+	18.7386i	1.04117	+	1.30558i
$207$		0			0
$208$	4.42655	−	2.13171i	0.306926	−	0.147808i
$209$	1.72688	−	7.56597i	0.119451	−	0.523349i
$210$		0			0
$211$	−3.47141	−	15.2093i	−0.238982	−	1.04705i	−0.941930	−	0.335808i	$-0.890991\pi$
$211$	−3.47141	−	15.2093i	−0.238982	−	1.04705i	0.702948	−	0.711241i	$-0.251866\pi$
$212$	14.1846	+	17.7870i	0.974204	+	1.22161i
$213$		0			0
$214$	3.72238			0.254456
$215$	20.9972			1.43200
$216$		0			0
$217$	−5.49037	−	13.2365i	−0.372711	−	0.898554i
$218$	14.4785	+	6.97248i	0.980608	+	0.472236i
$219$		0			0
$220$	−11.6197	−	50.9091i	−0.783398	−	3.43229i
$221$	2.08945	+	9.15450i	0.140552	+	0.615798i
$222$		0			0
$223$	−9.89262	−	4.76404i	−0.662459	−	0.319023i	0.0722691	−	0.997385i	$-0.476976\pi$
$223$	−9.89262	−	4.76404i	−0.662459	−	0.319023i	−0.734728	+	0.678362i	$0.762690\pi$
$224$	−1.96753	−	1.75655i	−0.131461	−	0.117365i
$225$		0			0
$226$	37.5865			2.50022
$227$	13.5133			0.896912			0.448456	−	0.893805i	$-0.351974\pi$
$227$	13.5133			0.896912			0.448456	+	0.893805i	$0.351974\pi$
$228$		0			0
$229$	7.97941	+	10.0059i	0.527294	+	0.661206i	0.972140	−	0.234401i	$-0.0753129\pi$
$229$	7.97941	+	10.0059i	0.527294	+	0.661206i	−0.444846	+	0.895607i	$0.646741\pi$
$230$	7.45453	+	32.6604i	0.491537	+	2.15356i
$231$		0			0
$232$	2.30150	−	10.0835i	0.151101	−	0.662016i
$233$	−11.5318	+	5.55343i	−0.755474	+	0.363817i	−0.771646	−	0.636052i	$-0.780566\pi$
$233$	−11.5318	+	5.55343i	−0.755474	+	0.363817i	0.0161722	+	0.999869i	$0.494852\pi$
$234$		0			0
$235$	13.9197	+	17.4548i	0.908022	+	1.13862i
$236$	−4.26495	−	18.6860i	−0.277625	−	1.21635i
$237$		0			0
$238$	−33.8154	+	24.0183i	−2.19193	+	1.55688i
$239$	−0.197715	−	0.247927i	−0.0127891	−	0.0160371i	0.775396	−	0.631476i	$-0.217550\pi$
$239$	−0.197715	−	0.247927i	−0.0127891	−	0.0160371i	−0.788185	+	0.615438i	$0.788979\pi$
$240$		0			0
$241$	−3.03317	−	1.46070i	−0.195384	−	0.0940918i	0.333634	−	0.942703i	$-0.391725\pi$
$241$	−3.03317	−	1.46070i	−0.195384	−	0.0940918i	−0.529017	+	0.848611i	$0.677439\pi$
$242$	35.8125	−	44.9074i	2.30211	−	2.88676i
$243$		0			0
$244$	16.2575			1.04078
$245$	−1.80057	−	15.8406i	−0.115034	−	1.01202i
$246$		0			0
$247$	0.426568	−	1.86892i	0.0271419	−	0.118916i
$248$	15.5333	−	19.4782i	0.986367	−	1.23686i
$249$		0			0
$250$	16.5930	−	20.8070i	1.04944	−	1.31595i
$251$	12.9043	+	16.1814i	0.814510	+	1.02136i	0.999256	+	0.0385765i	$0.0122823\pi$
$251$	12.9043	+	16.1814i	0.814510	+	1.02136i	−0.184746	+	0.982786i	$0.559146\pi$
$252$		0			0
$253$	−22.2379	+	27.8854i	−1.39808	+	1.75314i
$254$	−3.65485	−	16.0129i	−0.229326	−	1.00474i
$255$		0			0
$256$	6.87620	−	30.1266i	0.429763	−	1.88291i
$257$	−10.6014	+	5.10538i	−0.661299	+	0.318465i	−0.734258	−	0.678870i	$-0.762470\pi$
$257$	−10.6014	+	5.10538i	−0.661299	+	0.318465i	0.0729594	+	0.997335i	$0.476756\pi$
$258$		0			0
$259$	4.01920	+	3.58823i	0.249741	+	0.222962i
$260$	−2.87024	−	12.5754i	−0.178005	−	0.779891i
$261$		0			0
$262$	−39.4678	+	19.0067i	−2.43833	+	1.17424i
$263$	1.64445			0.101401			0.0507006	−	0.998714i	$-0.483855\pi$
$263$	1.64445			0.101401			0.0507006	+	0.998714i	$0.483855\pi$
$264$		0			0
$265$	11.9867	−	5.77250i	0.736338	−	0.354602i
$266$	8.34735	−	1.42249i	0.511809	−	0.0872185i
$267$		0			0
$268$	30.6165	+	14.7441i	1.87020	+	0.900640i
$269$	−2.78317	−	12.1939i	−0.169693	−	0.743474i	−0.986121	−	0.166027i	$-0.946906\pi$
$269$	−2.78317	−	12.1939i	−0.169693	−	0.743474i	0.816428	−	0.577447i	$-0.195951\pi$
$270$		0			0
$271$	−22.4429	−	10.8079i	−1.36331	−	0.656535i	−0.397936	−	0.917413i	$-0.630274\pi$
$271$	−22.4429	−	10.8079i	−1.36331	−	0.656535i	−0.965372	+	0.260878i	$0.915988\pi$
$272$	−19.6550	−	9.46535i	−1.19176	−	0.573921i
$273$		0			0
$274$	−35.7482	+	17.2154i	−2.15963	+	1.04002i
$275$	−1.10135			−0.0664138
$276$		0			0
$277$	9.19127	−	4.42628i	0.552250	−	0.265950i	−0.136880	−	0.990588i	$-0.543707\pi$
$277$	9.19127	−	4.42628i	0.552250	−	0.265950i	0.689130	+	0.724638i	$0.257993\pi$
$278$	−25.3848	−	31.8315i	−1.52248	−	1.90913i
$279$		0			0
$280$	22.5971	−	16.0502i	1.35043	−	0.959181i
$281$	0.992938	−	4.35034i	0.0592337	−	0.259520i	−0.936637	−	0.350301i	$-0.886079\pi$
$281$	0.992938	−	4.35034i	0.0592337	−	0.259520i	0.995871	+	0.0907813i	$0.0289364\pi$
$282$		0			0
$283$	−0.102220	+	0.447854i	−0.00607634	+	0.0266222i	−0.977875	−	0.209189i	$-0.932918\pi$
$283$	−0.102220	+	0.447854i	−0.00607634	+	0.0266222i	0.971799	+	0.235811i	$0.0757747\pi$
$284$	11.9142	+	14.9399i	0.706977	+	0.886521i
$285$		0			0
$286$	12.9594	−	16.2506i	0.766305	−	0.960916i
$287$	−2.90071	−	0.834136i	−0.171223	−	0.0492375i
$288$		0			0
$289$	15.3962	−	19.3063i	0.905661	−	1.13566i
$290$	−11.2021	−	5.39466i	−0.657812	−	0.316785i
$291$		0			0
$292$	−4.37915	+	19.1863i	−0.256271	+	1.12280i
$293$	−4.43947			−0.259357			−0.129678	−	0.991556i	$-0.541394\pi$
$293$	−4.43947			−0.259357			−0.129678	+	0.991556i	$0.541394\pi$
$294$		0			0
$295$	−11.2084			−0.652581
$296$	−2.08438	+	9.13227i	−0.121152	+	0.530803i
$297$		0			0
$298$	26.4659	+	12.7453i	1.53313	+	0.738316i
$299$	−5.49311	+	6.88814i	−0.317675	+	0.398352i
$300$		0			0
$301$	−11.7885	+	21.3544i	−0.679475	+	1.23085i
$302$	−23.5145	+	29.4863i	−1.35311	+	1.69675i
$303$		0			0
$304$	2.77682	+	3.48202i	0.159261	+	0.199708i
$305$	2.11556	−	9.26888i	0.121137	−	0.530735i
$306$		0			0
$307$	−6.27913	+	27.5107i	−0.358369	+	1.57012i	0.398888	+	0.917000i	$0.369396\pi$
$307$	−6.27913	+	27.5107i	−0.358369	+	1.57012i	−0.757257	+	0.653117i	$0.773461\pi$
$308$	58.2986	+	16.7645i	3.32187	+	0.955247i
$309$		0			0
$310$	−18.6730	−	23.4153i	−1.06056	−	1.32990i
$311$	14.1751	−	6.82637i	0.803796	−	0.387088i	0.0135735	−	0.999908i	$-0.495679\pi$
$311$	14.1751	−	6.82637i	0.803796	−	0.387088i	0.790222	+	0.612820i	$0.209965\pi$
$312$		0			0
$313$	10.6721			0.603223			0.301611	−	0.953431i	$-0.402476\pi$
$313$	10.6721			0.603223			0.301611	+	0.953431i	$0.402476\pi$
$314$	−10.4512	+	5.03301i	−0.589793	+	0.284029i
$315$		0			0
$316$	32.4327	+	15.6188i	1.82448	+	0.878625i
$317$	−3.62400	−	1.74522i	−0.203544	−	0.0980216i	0.329335	−	0.944213i	$-0.393176\pi$
$317$	−3.62400	−	1.74522i	−0.203544	−	0.0980216i	−0.532879	+	0.846192i	$0.678890\pi$
$318$		0			0
$319$	−2.94562	−	12.9056i	−0.164923	−	0.722574i
$320$	−18.8318	−	9.06891i	−1.05273	−	0.506967i
$321$		0			0
$322$	−37.4011	−	10.7552i	−2.08428	−	0.599363i
$323$	−7.66893	+	3.69316i	−0.426711	+	0.205493i
$324$		0			0
$325$	−0.272051			−0.0150907
$326$	−34.4685	+	16.5991i	−1.90903	+	0.919342i
$327$		0			0
$328$	−1.16766	−	5.11583i	−0.0644730	−	0.282475i
$329$	−25.5666	+	4.35686i	−1.40953	+	0.240201i
$330$		0			0
$331$	−14.6745	+	7.06687i	−0.806584	+	0.388431i	−0.791281	−	0.611452i	$-0.790586\pi$
$331$	−14.6745	+	7.06687i	−0.806584	+	0.388431i	−0.0153031	+	0.999883i	$0.504871\pi$
$332$	−9.47391	+	41.5079i	−0.519948	+	2.27804i
$333$		0			0
$334$	−12.5742	−	55.0913i	−0.688031	−	3.01446i
$335$	12.3902	−	15.5368i	0.676946	−	0.848864i
$336$		0			0
$337$	−3.27340	−	4.10472i	−0.178314	−	0.223598i	0.684640	−	0.728881i	$-0.259959\pi$
$337$	−3.27340	−	4.10472i	−0.178314	−	0.223598i	−0.862954	+	0.505283i	$0.831388\pi$
$338$	−16.4776	+	20.6623i	−0.896265	+	1.12388i
$339$		0			0
$340$	−35.7096	+	44.7784i	−1.93663	+	2.42845i
$341$	7.09531	−	31.0866i	0.384232	−	1.68343i
$342$		0			0
$343$	17.1209	+	7.06218i	0.924442	+	0.381322i
$344$	−42.4070			−2.28643
$345$		0			0
$346$	−9.36206	+	11.7397i	−0.503308	+	0.631128i
$347$	19.2789	+	9.28424i	1.03495	+	0.498404i	0.872654	−	0.488338i	$-0.162397\pi$
$347$	19.2789	+	9.28424i	1.03495	+	0.498404i	0.162293	+	0.986743i	$0.448111\pi$
$348$		0			0
$349$	−8.42534	−	10.5650i	−0.450998	−	0.565534i	0.503406	−	0.864050i	$-0.332080\pi$
$349$	−8.42534	−	10.5650i	−0.450998	−	0.565534i	−0.954405	+	0.298516i	$0.903508\pi$
$350$	−0.460418	−	1.11000i	−0.0246104	−	0.0593322i
$351$		0			0
$352$	−1.30594	−	5.72171i	−0.0696070	−	0.304968i
$353$	−4.94787	−	6.20444i	−0.263349	−	0.330229i	0.632523	−	0.774542i	$-0.282019\pi$
$353$	−4.94787	−	6.20444i	−0.263349	−	0.330229i	−0.895872	+	0.444313i	$0.853448\pi$
$354$		0			0
$355$	10.0681	−	4.84853i	0.534358	−	0.257333i
$356$	9.69437	−	42.4738i	0.513801	−	2.25111i
$357$		0			0
$358$	−4.74660	−	20.7962i	−0.250865	−	1.09911i
$359$	7.89277	+	9.89722i	0.416565	+	0.522355i	0.945199	−	0.326494i	$-0.105867\pi$
$359$	7.89277	+	9.89722i	0.416565	+	0.522355i	−0.528635	+	0.848849i	$0.677296\pi$
$360$		0			0
$361$	−17.2623			−0.908541
$362$	3.33071			0.175058
$363$		0			0
$364$	14.4007	+	4.14111i	0.754801	+	0.217053i
$365$	10.3689	+	4.99338i	0.542731	+	0.261366i
$366$		0			0
$367$	−4.76632	−	20.8826i	−0.248800	−	1.09006i	−0.932747	−	0.360532i	$-0.882595\pi$
$367$	−4.76632	−	20.8826i	−0.248800	−	1.09006i	0.683947	−	0.729531i	$-0.260262\pi$
$368$	−4.55471	−	19.9555i	−0.237431	−	1.04025i
$369$		0			0
$370$	10.1453	+	4.88574i	0.527432	+	0.253998i
$371$	−0.859007	+	15.4314i	−0.0445974	+	0.801160i
$372$		0			0
$373$	23.1797			1.20020			0.600100	−	0.799925i	$-0.295127\pi$
$373$	23.1797			1.20020			0.600100	+	0.799925i	$0.295127\pi$
$374$	−92.2918			−4.77229
$375$		0			0
$376$	−28.1129	−	35.2525i	−1.44981	−	1.81801i
$377$	−0.727615	−	3.18789i	−0.0374741	−	0.164185i
$378$		0			0
$379$	3.18904	−	13.9721i	0.163810	−	0.717699i	−0.824578	−	0.565749i	$-0.808587\pi$
$379$	3.18904	−	13.9721i	0.163810	−	0.717699i	0.988388	−	0.151951i	$-0.0485556\pi$
$380$	10.5347	−	5.07323i	0.540417	−	0.260251i
$381$		0			0
$382$	19.4307	+	24.3653i	0.994160	+	1.24664i
$383$	−0.542952	−	2.37883i	−0.0277435	−	0.121552i	0.959160	−	0.282864i	$-0.0912846\pi$
$383$	−0.542952	−	2.37883i	−0.0277435	−	0.121552i	−0.986903	+	0.161312i	$0.948427\pi$
$384$		0			0
$385$	17.1443	−	31.0563i	0.873753	−	1.58277i
$386$	−0.787682	−	0.987722i	−0.0400919	−	0.0502737i
$387$		0			0
$388$	−14.1163	−	6.79807i	−0.716648	−	0.345120i
$389$	5.90307	−	7.40221i	0.299297	−	0.375307i	−0.609329	−	0.792918i	$-0.708561\pi$
$389$	5.90307	−	7.40221i	0.299297	−	0.375307i	0.908626	+	0.417611i	$0.137132\pi$
$390$		0			0
$391$	39.1198			1.97837
$392$	3.63651	+	31.9924i	0.183671	+	1.61586i
$393$		0			0
$394$	−5.25081	+	23.0053i	−0.264532	+	1.15899i
$395$	13.1252	−	16.4584i	0.660399	−	0.828114i
$396$		0			0
$397$	−7.75397	+	9.72317i	−0.389160	+	0.487992i	−0.937363	−	0.348354i	$-0.886741\pi$
$397$	−7.75397	+	9.72317i	−0.389160	+	0.487992i	0.548203	+	0.836346i	$0.315312\pi$
$398$	14.4873	+	18.1665i	0.726181	+	0.910602i
$399$		0			0
$400$	0.394076	−	0.494156i	0.0197038	−	0.0247078i
$401$	−0.0615107	−	0.269496i	−0.00307170	−	0.0134580i	0.973369	−	0.229245i	$-0.0736256\pi$
$401$	−0.0615107	−	0.269496i	−0.00307170	−	0.0134580i	−0.976441	+	0.215787i	$0.930768\pi$
$402$		0			0
$403$	1.75265	−	7.67888i	0.0873059	−	0.382512i
$404$	−4.20092	+	2.02306i	−0.209004	+	0.100651i
$405$		0			0
$406$	11.7756	−	8.36394i	0.584414	−	0.415095i
$407$	2.66773	+	11.6881i	0.132235	+	0.579358i
$408$		0			0
$409$	28.7073	−	13.8247i	1.41949	−	0.683588i	0.442475	−	0.896781i	$-0.354100\pi$
$409$	28.7073	−	13.8247i	1.41949	−	0.683588i	0.977010	+	0.213192i	$0.0683861\pi$
$410$	−6.30804			−0.311532
$411$		0			0
$412$	−34.6392	+	16.6814i	−1.70655	+	0.821832i
$413$	6.29274	−	11.3991i	0.309646	−	0.560912i
$414$		0			0
$415$	22.4321	+	10.8027i	1.10115	+	0.530285i
$416$	−0.322589	−	1.41335i	−0.0158162	−	0.0692954i
$417$		0			0
$418$	16.9757	+	8.17507i	0.830309	+	0.399856i
$419$	6.01450	+	2.89643i	0.293828	+	0.141500i	0.574990	−	0.818160i	$-0.305006\pi$
$419$	6.01450	+	2.89643i	0.293828	+	0.141500i	−0.281163	+	0.959660i	$0.590720\pi$
$420$		0			0
$421$	−29.6405	+	14.2741i	−1.44459	+	0.695677i	−0.981646	−	0.190711i	$-0.938921\pi$
$421$	−29.6405	+	14.2741i	−1.44459	+	0.695677i	−0.462943	+	0.886388i	$0.653206\pi$
$422$	37.8758			1.84376
$423$		0			0
$424$	−24.2089	+	11.6584i	−1.17569	+	0.566182i
$425$	0.753159	+	0.944432i	0.0365336	+	0.0458117i
$426$		0			0
$427$	8.23879	+	7.35536i	0.398703	+	0.355951i
$428$	−1.32869	+	5.82138i	−0.0642248	+	0.281387i
$429$		0			0
$430$	−11.3438	+	49.7005i	−0.547047	+	2.39677i
$431$	−13.7807	−	17.2805i	−0.663793	−	0.832371i	0.329957	−	0.943996i	$-0.392966\pi$
$431$	−13.7807	−	17.2805i	−0.663793	−	0.832371i	−0.993750	+	0.111625i	$0.964394\pi$
$432$		0			0
$433$	−8.43974	+	10.5831i	−0.405588	+	0.508591i	−0.942114	−	0.335292i	$-0.891165\pi$
$433$	−8.43974	+	10.5831i	−0.405588	+	0.508591i	0.536526	+	0.843884i	$0.319736\pi$
$434$	34.2971	−	5.84464i	1.64631	−	0.280552i
$435$		0			0
$436$	−16.0722	+	20.1540i	−0.769721	+	0.965200i
$437$	−7.19551	−	3.46518i	−0.344208	−	0.165762i
$438$		0			0
$439$	7.96857	−	34.9126i	0.380319	−	1.66629i	−0.316157	−	0.948707i	$-0.602393\pi$
$439$	7.96857	−	34.9126i	0.380319	−	1.66629i	0.696476	−	0.717580i	$-0.254750\pi$
$440$	61.6737			2.94018
$441$		0			0
$442$	−22.7976			−1.08437
$443$	−3.21791	+	14.0986i	−0.152887	+	0.669844i	0.839150	+	0.543900i	$0.183053\pi$
$443$	−3.21791	+	14.0986i	−0.152887	+	0.669844i	−0.992037	+	0.125944i	$0.959804\pi$
$444$		0			0
$445$	−22.9541	−	11.0541i	−1.08813	−	0.524016i
$446$	16.6210	−	20.8421i	0.787027	−	0.986901i
$447$		0			0
$448$	19.7959	−	14.0605i	0.935266	−	0.664298i
$449$	24.7342	−	31.0158i	1.16728	−	1.46372i	0.308616	−	0.951187i	$-0.400134\pi$
$449$	24.7342	−	31.0158i	1.16728	−	1.46372i	0.858665	−	0.512537i	$-0.171294\pi$
$450$		0			0
$451$	−4.18734	−	5.25076i	−0.197174	−	0.247249i
$452$	−13.4164	+	58.7811i	−0.631054	+	2.76483i
$453$		0			0
$454$	−7.30062	+	31.9861i	−0.342635	+	1.50118i
$455$	4.23491	−	7.67139i	0.198536	−	0.359641i
$456$		0			0
$457$	−17.1293	−	21.4794i	−0.801273	−	1.00476i	−0.999696	−	0.0246477i	$-0.992154\pi$
$457$	−17.1293	−	21.4794i	−0.801273	−	1.00476i	0.198424	−	0.980116i	$-0.436418\pi$
$458$	−27.9948	+	13.4816i	−1.30811	+	0.629953i
$459$		0			0
$460$	−53.7382			−2.50555
$461$	0.463387	−	0.223155i	0.0215821	−	0.0103934i	−0.423062	−	0.906101i	$-0.639045\pi$
$461$	0.463387	−	0.223155i	0.0215821	−	0.0103934i	0.444644	+	0.895708i	$0.353330\pi$
$462$		0			0
$463$	−14.8671	−	7.15960i	−0.690931	−	0.332735i	0.0552549	−	0.998472i	$-0.482403\pi$
$463$	−14.8671	−	7.15960i	−0.690931	−	0.332735i	−0.746186	+	0.665737i	$0.768117\pi$
$464$	6.84450	+	3.29614i	0.317748	+	0.153019i
$465$		0			0
$466$	−6.91488	−	30.2961i	−0.320326	−	1.40344i
$467$	33.3270	+	16.0495i	1.54219	+	0.742680i	0.995510	−	0.0946597i	$-0.0301763\pi$
$467$	33.3270	+	16.0495i	1.54219	+	0.742680i	0.546682	+	0.837340i	$0.315891\pi$
$468$		0			0
$469$	8.84483	+	21.3237i	0.408416	+	0.984636i
$470$	−48.8356	+	23.5180i	−2.25262	+	1.08480i
$471$		0			0
$472$	22.6371			1.04196
$473$	−48.9004	+	23.5492i	−2.24844	+	1.08279i
$474$		0			0
$475$	−0.0548761	−	0.240428i	−0.00251789	−	0.0110316i
$476$	−25.4916	−	61.4569i	−1.16841	−	2.81687i
$477$		0			0
$478$	0.693660	−	0.334049i	0.0317273	−	0.0152790i
$479$	0.836185	−	3.66357i	0.0382063	−	0.167393i	−0.952226	−	0.305396i	$-0.901211\pi$
$479$	0.836185	−	3.66357i	0.0382063	−	0.167393i	0.990432	+	0.138003i	$0.0440684\pi$
$480$		0			0
$481$	0.658973	+	2.88715i	0.0300466	+	0.131643i
$482$	5.09615	−	6.39037i	0.232123	−	0.291074i
$483$		0			0
$484$	57.4470	+	72.0363i	2.61123	+	3.27438i
$485$	−5.71272	+	7.16353i	−0.259401	+	0.325279i
$486$		0			0
$487$	25.3736	−	31.8175i	1.14979	−	1.44179i	0.272288	−	0.962216i	$-0.412220\pi$
$487$	25.3736	−	31.8175i	1.14979	−	1.44179i	0.877501	−	0.479574i	$-0.159209\pi$
$488$	−4.27269	+	18.7199i	−0.193415	+	0.847408i
$489$		0			0
$490$	38.4675	+	4.29598i	1.73778	+	0.194073i
$491$	5.53326			0.249712			0.124856	−	0.992175i	$-0.460153\pi$
$491$	5.53326			0.249712			0.124856	+	0.992175i	$0.460153\pi$
$492$		0			0
$493$	−9.05248	+	11.3515i	−0.407703	+	0.511244i
$494$	4.19327	+	2.01937i	0.188664	+	0.0908559i
$495$		0			0
$496$	11.4092	+	14.3067i	0.512289	+	0.642390i
$497$	−0.721512	+	12.9614i	−0.0323642	+	0.581399i
$498$		0			0
$499$	2.87464	+	12.5946i	0.128687	+	0.563813i	0.997624	+	0.0688913i	$0.0219462\pi$
$499$	2.87464	+	12.5946i	0.128687	+	0.563813i	−0.868938	+	0.494922i	$0.835197\pi$
$500$	26.6170	+	33.3767i	1.19035	+	1.49265i
$501$		0			0
$502$	−45.2730	+	21.8023i	−2.02063	+	0.973086i
$503$	−1.66719	+	7.30446i	−0.0743365	+	0.325690i	−0.998400	−	0.0565500i	$-0.981990\pi$
$503$	−1.66719	+	7.30446i	−0.0743365	+	0.325690i	0.924063	+	0.382240i	$0.124847\pi$
$504$		0			0
$505$	0.606747	+	2.65833i	0.0269999	+	0.118294i
$506$	−53.9907	−	67.7023i	−2.40018	−	3.00973i
$507$		0			0
$508$	26.3470			1.16896
$509$	−21.9644			−0.973554			−0.486777	−	0.873526i	$-0.661827\pi$
$509$	−21.9644			−0.973554			−0.486777	+	0.873526i	$0.661827\pi$
$510$		0			0
$511$	−10.8997	+	7.74179i	−0.482174	+	0.342477i
$512$	31.0375	+	14.9469i	1.37168	+	0.660565i
$513$		0			0
$514$	−6.35699	−	27.8518i	−0.280395	−	1.22849i
$515$	5.00300	+	21.9196i	0.220459	+	0.965893i
$516$		0			0
$517$	−51.9938	−	25.0389i	−2.28668	−	1.10121i
$518$	−10.6647	+	7.57491i	−0.468581	+	0.332822i
$519$		0			0
$520$	15.2344			0.668072
$521$	5.40550			0.236819			0.118410	−	0.992965i	$-0.462220\pi$
$521$	5.40550			0.236819			0.118410	+	0.992965i	$0.462220\pi$
$522$		0			0
$523$	4.07184	+	5.10592i	0.178049	+	0.223266i	0.862845	−	0.505468i	$-0.168680\pi$
$523$	4.07184	+	5.10592i	0.178049	+	0.223266i	−0.684796	+	0.728735i	$0.740109\pi$
$524$	−15.6364	−	68.5076i	−0.683080	−	2.99277i
$525$		0			0
$526$	−0.888419	+	3.89242i	−0.0387369	+	0.169718i
$527$	−31.5096	+	15.1742i	−1.37258	+	0.661000i
$528$		0			0
$529$	8.54485	+	10.7149i	0.371515	+	0.465865i
$530$	7.18766	+	31.4912i	0.312212	+	1.36789i
$531$		0			0
$532$	−0.754948	+	13.5621i	−0.0327312	+	0.587991i
$533$	−1.03434	−	1.29702i	−0.0448023	−	0.0561803i
$534$		0			0
$535$	3.14605	+	1.51506i	0.136016	+	0.0655016i
$536$	−25.0237	+	31.3788i	−1.08086	+	1.35536i
$537$		0			0
$538$	30.3665			1.30919
$539$	21.9592	+	34.8717i	0.945849	+	1.50203i
$540$		0			0
$541$	4.46472	−	19.5612i	0.191953	−	0.841002i	−0.783605	−	0.621260i	$-0.786621\pi$
$541$	4.46472	−	19.5612i	0.191953	−	0.841002i	0.975558	−	0.219742i	$-0.0705216\pi$
$542$	37.7072	−	47.2833i	1.61966	−	2.03099i
$543$		0			0
$544$	−4.01343	+	5.03268i	−0.172074	+	0.215774i
$545$	9.39893	+	11.7859i	0.402606	+	0.504852i
$546$		0			0
$547$	23.6764	−	29.6892i	1.01233	−	1.26942i	0.0496511	−	0.998767i	$-0.484189\pi$
$547$	23.6764	−	29.6892i	1.01233	−	1.26942i	0.962677	−	0.270653i	$-0.0872395\pi$
$548$	−14.1628	−	62.0513i	−0.605005	−	2.65070i
$549$		0			0
$550$	0.595006	−	2.60689i	0.0253712	−	0.111158i
$551$	2.67057	−	1.28608i	0.113770	−	0.0547887i
$552$		0			0
$553$	9.36952	+	22.5886i	0.398433	+	0.960567i
$554$	5.51141	+	24.1471i	0.234157	+	1.02591i
$555$		0			0
$556$	58.8420	−	28.3368i	2.49546	−	1.20175i
$557$	−9.77373			−0.414126			−0.207063	−	0.978328i	$-0.566391\pi$
$557$	−9.77373			−0.414126			−0.207063	+	0.978328i	$0.566391\pi$
$558$		0			0
$559$	−12.0792	+	5.81703i	−0.510895	+	0.246034i
$560$	7.79997	+	18.8047i	0.329609	+	0.794642i
$561$		0			0
$562$	9.76083	+	4.70057i	0.411736	+	0.198282i
$563$	5.56333	+	24.3745i	0.234466	+	1.02726i	0.945887	+	0.324497i	$0.105195\pi$
$563$	5.56333	+	24.3745i	0.234466	+	1.02726i	−0.711420	+	0.702767i	$0.751948\pi$
$564$		0			0
$565$	31.7670	+	15.2982i	1.33645	+	0.643600i
$566$	−1.00485	−	0.483909i	−0.0422369	−	0.0203402i
$567$		0			0
$568$	−20.3340	+	9.79232i	−0.853194	+	0.410877i
$569$	10.9389			0.458584			0.229292	−	0.973358i	$-0.426359\pi$
$569$	10.9389			0.458584			0.229292	+	0.973358i	$0.426359\pi$
$570$		0			0
$571$	29.7566	−	14.3300i	1.24528	−	0.599693i	0.309035	−	0.951051i	$-0.399994\pi$
$571$	29.7566	−	14.3300i	1.24528	−	0.599693i	0.936241	+	0.351358i	$0.114280\pi$
$572$	20.7883	+	26.0676i	0.869201	+	1.08994i
$573$		0			0
$574$	3.54152	−	6.41533i	0.147820	−	0.267771i
$575$	−0.252206	+	1.10499i	−0.0105177	+	0.0460811i
$576$		0			0
$577$	−2.80138	+	12.2736i	−0.116623	+	0.510958i	0.882547	+	0.470224i	$0.155827\pi$
$577$	−2.80138	+	12.2736i	−0.116623	+	0.510958i	−0.999170	+	0.0407341i	$0.987030\pi$
$578$	37.3801	+	46.8732i	1.55481	+	1.94967i
$579$		0			0
$580$	12.4352	−	15.5933i	0.516345	−	0.647476i
$581$	−23.5805	+	16.7487i	−0.978283	+	0.694852i
$582$		0			0
$583$	−21.4418	+	26.8871i	−0.888027	+	1.11355i
$584$	−20.9414	−	10.0849i	−0.866563	−	0.417315i
$585$		0			0
$586$	2.39844	−	10.5082i	0.0990785	−	0.434091i
$587$	−22.1429			−0.913937			−0.456968	−	0.889483i	$-0.651065\pi$
$587$	−22.1429			−0.913937			−0.456968	+	0.889483i	$0.651065\pi$
$588$		0			0
$589$	7.13984			0.294192
$590$	6.05539	−	26.5304i	0.249297	−	1.09224i
$591$		0			0
$592$	−6.19880	−	2.98519i	−0.254769	−	0.122690i
$593$	16.9682	−	21.2775i	0.696802	−	0.873762i	−0.299978	−	0.953946i	$-0.596979\pi$
$593$	16.9682	−	21.2775i	0.696802	−	0.873762i	0.996780	+	0.0801841i	$0.0255508\pi$
$594$		0			0
$595$	−38.3556	+	6.53627i	−1.57243	+	0.267961i
$596$	−29.3792	+	36.8403i	−1.20342	+	1.50904i
$597$		0			0
$598$	−13.3366	−	16.7235i	−0.545373	−	0.683876i
$599$	8.34041	−	36.5417i	0.340780	−	1.49305i	−0.456652	−	0.889645i	$-0.650952\pi$
$599$	8.34041	−	36.5417i	0.340780	−	1.49305i	0.797432	−	0.603409i	$-0.206191\pi$
$600$		0			0
$601$	−1.21002	+	5.30145i	−0.0493578	+	0.216251i	−0.993592	−	0.113023i	$-0.963947\pi$
$601$	−1.21002	+	5.30145i	−0.0493578	+	0.216251i	0.944235	+	0.329273i	$0.106804\pi$
$602$	−44.1771	−	39.4400i	−1.80052	−	1.60746i
$603$		0			0
$604$	−37.7198	−	47.2992i	−1.53480	−	1.92458i
$605$	48.5456	−	23.3783i	1.97366	−	0.950465i
$606$		0			0
$607$	−12.3998			−0.503293			−0.251646	−	0.967819i	$-0.580972\pi$
$607$	−12.3998			−0.503293			−0.251646	+	0.967819i	$0.580972\pi$
$608$	1.18400	−	0.570183i	0.0480175	−	0.0231240i
$609$		0			0
$610$	20.7965	+	10.0151i	0.842026	+	0.405499i
$611$	−12.8433	−	6.18501i	−0.519584	−	0.250219i
$612$		0			0
$613$	2.70246	+	11.8403i	0.109151	+	0.478224i	0.999726	+	0.0233875i	$0.00744514\pi$
$613$	2.70246	+	11.8403i	0.109151	+	0.478224i	−0.890575	+	0.454836i	$0.849698\pi$
$614$	−61.7255	−	29.7254i	−2.49104	−	1.19962i
$615$		0			0
$616$	−34.6254	+	62.7227i	−1.39510	+	2.52717i
$617$	4.40470	−	2.12119i	0.177327	−	0.0853960i	−0.343114	−	0.939294i	$-0.611482\pi$
$617$	4.40470	−	2.12119i	0.177327	−	0.0853960i	0.520441	+	0.853898i	$0.325768\pi$
$618$		0			0
$619$	−19.8210			−0.796675			−0.398338	−	0.917239i	$-0.630413\pi$
$619$	−19.8210			−0.796675			−0.398338	+	0.917239i	$0.630413\pi$
$620$	43.2842	−	20.8445i	1.73833	−	0.837137i
$621$		0			0
$622$	8.49989	+	37.2404i	0.340814	+	1.49321i
$623$	24.1292	−	17.1384i	0.966717	−	0.686636i
$624$		0			0
$625$	23.3354	−	11.2378i	0.933418	−	0.449510i
$626$	−5.76563	+	25.2609i	−0.230441	+	1.00963i
$627$		0			0
$628$	−4.14056	−	18.1410i	−0.165226	−	0.723903i
$629$	8.19849	−	10.2806i	0.326895	−	0.409914i
$630$		0			0
$631$	−4.42731	−	5.55167i	−0.176248	−	0.221008i	0.685859	−	0.727735i	$-0.259427\pi$
$631$	−4.42731	−	5.55167i	−0.176248	−	0.221008i	−0.862107	+	0.506726i	$0.830855\pi$
$632$	−26.5082	+	33.2402i	−1.05444	+	1.32222i
$633$		0			0
$634$	6.08882	−	7.63514i	0.241818	−	0.303230i
$635$	3.42850	−	15.0213i	0.136056	−	0.596101i
$636$		0			0
$637$	5.42427	+	8.61388i	0.214917	+	0.341294i
$638$	32.1389			1.27239
$639$		0			0
$640$	28.8088	−	36.1251i	1.13877	−	1.42797i
$641$	4.32543	+	2.08302i	0.170844	+	0.0822743i	0.517351	−	0.855773i	$-0.326918\pi$
$641$	4.32543	+	2.08302i	0.170844	+	0.0822743i	−0.346507	+	0.938047i	$0.612632\pi$
$642$		0			0
$643$	−14.3493	−	17.9934i	−0.565879	−	0.709590i	0.413753	−	0.910389i	$-0.364218\pi$
$643$	−14.3493	−	17.9934i	−0.565879	−	0.709590i	−0.979633	+	0.200799i	$0.935646\pi$
$644$	30.1701	−	54.6521i	1.18887	−	2.15360i
$645$		0			0
$646$	−4.59856	−	20.1476i	−0.180928	−	0.792697i
$647$	−6.95053	−	8.71569i	−0.273254	−	0.342649i	0.626202	−	0.779661i	$-0.284608\pi$
$647$	−6.95053	−	8.71569i	−0.273254	−	0.342649i	−0.899456	+	0.437011i	$0.856037\pi$
$648$		0			0
$649$	26.1033	−	12.5707i	1.02464	−	0.493443i
$650$	0.146976	−	0.643944i	0.00576488	−	0.0252576i
$651$		0			0
$652$	−13.6558	−	59.8299i	−0.534802	−	2.34312i
$653$	11.1380	+	13.9666i	0.435863	+	0.546554i	0.950448	−	0.310885i	$-0.100625\pi$
$653$	11.1380	+	13.9666i	0.435863	+	0.546554i	−0.514585	+	0.857439i	$0.672054\pi$
$654$		0			0
$655$	−41.0930			−1.60564
$656$	3.85421			0.150482
$657$		0			0
$658$	3.49972	−	62.8699i	0.136433	−	2.45092i
$659$	−31.2869	−	15.0670i	−1.21876	−	0.586925i	−0.289796	−	0.957088i	$-0.593588\pi$
$659$	−31.2869	−	15.0670i	−1.21876	−	0.586925i	−0.928967	+	0.370163i	$0.879302\pi$
$660$		0			0
$661$	5.99801	+	26.2790i	0.233296	+	1.02213i	0.946885	+	0.321571i	$0.104211\pi$
$661$	5.99801	+	26.2790i	0.233296	+	1.02213i	−0.713590	+	0.700564i	$0.752932\pi$
$662$	−8.79936	−	38.5525i	−0.341997	−	1.49839i
$663$		0			0
$664$	−45.3049	−	21.8177i	−1.75817	−	0.846691i
$665$	7.63392	+	2.19524i	0.296031	+	0.0851276i
$666$		0			0
$667$	−13.6228			−0.527476
$668$	90.6450			3.50716
$669$		0			0
$670$	30.0817	+	37.7213i	1.16216	+	1.45730i
$671$	5.46848	+	23.9590i	0.211108	+	0.924925i
$672$		0			0
$673$	8.11381	−	35.5489i	0.312764	−	1.37031i	−0.537193	−	0.843459i	$-0.680515\pi$
$673$	8.11381	−	35.5489i	0.312764	−	1.37031i	0.849958	−	0.526851i	$-0.176627\pi$
$674$	11.4843	−	5.53057i	0.442360	−	0.213029i
$675$		0			0
$676$	−26.4319	−	33.1445i	−1.01661	−	1.27479i
$677$	1.55221	+	6.80069i	0.0596564	+	0.261372i	0.995957	−	0.0898268i	$-0.0286314\pi$
$677$	1.55221	+	6.80069i	0.0596564	+	0.261372i	−0.936301	+	0.351199i	$0.885774\pi$
$678$		0			0
$679$	−4.07808	−	9.83170i	−0.156502	−	0.377306i
$680$	−42.1757	−	52.8867i	−1.61736	−	2.02811i
$681$		0			0
$682$	69.7487	+	33.5892i	2.67082	+	1.28620i
$683$	7.47572	−	9.37426i	0.286051	−	0.358696i	−0.617957	−	0.786212i	$-0.712040\pi$
$683$	7.47572	−	9.37426i	0.286051	−	0.358696i	0.904008	+	0.427515i	$0.140611\pi$
$684$		0			0
$685$	−37.2203			−1.42212
$686$	−25.9658	+	36.7099i	−0.991379	+	1.40159i
$687$		0			0
$688$	6.93106	−	30.3670i	0.264244	−	1.15773i
$689$	−5.29646	+	6.64155i	−0.201779	+	0.253023i
$690$		0			0
$691$	−20.2750	+	25.4240i	−0.771297	+	0.967176i	−0.999980	−	0.00632487i	$-0.997987\pi$
$691$	−20.2750	+	25.4240i	−0.771297	+	0.967176i	0.228683	+	0.973501i	$0.426558\pi$
$692$	−15.0178	−	18.8317i	−0.570889	−	0.715872i
$693$		0			0
$694$	−32.3913	+	40.6174i	−1.22956	+	1.54182i
$695$	−8.49866	−	37.2351i	−0.322373	−	1.41241i
$696$		0			0
$697$	−1.63913	+	7.18149i	−0.0620864	+	0.272018i
$698$	29.5593	−	14.2350i	1.11884	−	0.538803i
$699$		0			0
$700$	1.90027	−	0.323829i	0.0718234	−	0.0122396i
$701$	−8.43030	−	36.9356i	−0.318408	−	1.39504i	−0.840344	−	0.542053i	$-0.817647\pi$
$701$	−8.43030	−	36.9356i	−0.318408	−	1.39504i	0.521936	−	0.852984i	$-0.325210\pi$
$702$		0			0
$703$	−2.41863	+	1.16475i	−0.0912204	+	0.0439294i
$704$	54.0284			2.03627
$705$		0			0
$706$	17.3590	−	8.35966i	0.653315	−	0.314620i
$707$	−3.04419	−	0.875397i	−0.114489	−	0.0329227i
$708$		0			0
$709$	7.55260	+	3.63714i	0.283644	+	0.136596i	0.570297	−	0.821439i	$-0.306828\pi$
$709$	7.55260	+	3.63714i	0.283644	+	0.136596i	−0.286653	+	0.958035i	$0.592543\pi$
$710$	6.03718	+	26.4506i	0.226571	+	0.992673i
$711$		0			0
$712$	46.3592	+	22.3254i	1.73738	+	0.836680i
$713$	−29.5645	−	14.2375i	−1.10720	−	0.533198i
$714$		0			0
$715$	17.5671	−	8.45987i	0.656973	−	0.316381i
$716$	34.2172			1.27876
$717$		0			0
$718$	−27.6908	+	13.3352i	−1.03341	+	0.497665i
$719$	19.0363	+	23.8707i	0.709933	+	0.890228i	0.997722	−	0.0674659i	$-0.0214914\pi$
$719$	19.0363	+	23.8707i	0.709933	+	0.890228i	−0.287788	+	0.957694i	$0.592920\pi$
$720$		0			0
$721$	−25.1012	−	7.21819i	−0.934819	−	0.268819i
$722$	9.32599	−	40.8598i	0.347078	−	1.52065i
$723$		0			0
$724$	−1.18889	+	5.20885i	−0.0441846	+	0.193586i
$725$	−0.262274	−	0.328881i	−0.00974062	−	0.0122143i
$726$		0			0
$727$	24.1265	−	30.2537i	0.894803	−	1.12205i	−0.0971282	−	0.995272i	$-0.530966\pi$
$727$	24.1265	−	30.2537i	0.894803	−	1.12205i	0.991931	−	0.126776i	$-0.0404629\pi$
$728$	−8.55302	+	15.4935i	−0.316996	+	0.574227i
$729$		0			0
$730$	−17.4211	+	21.8454i	−0.644786	+	0.808536i
$731$	53.6347	+	25.8291i	1.98375	+	0.955324i
$732$		0			0
$733$	−1.15849	+	5.07567i	−0.0427898	+	0.187474i	−0.991806	−	0.127753i	$-0.959224\pi$
$733$	−1.15849	+	5.07567i	−0.0427898	+	0.187474i	0.949016	+	0.315227i	$0.102081\pi$
$734$	52.0042			1.91951
$735$		0			0
$736$	−6.03967			−0.222625
$737$	−11.4303	+	50.0796i	−0.421042	+	1.84470i
$738$		0			0
$739$	7.87721	+	3.79347i	0.289768	+	0.139545i	0.573121	−	0.819471i	$-0.305733\pi$
$739$	7.87721	+	3.79347i	0.289768	+	0.139545i	−0.283353	+	0.959016i	$0.591447\pi$
$740$	−11.2621	+	14.1222i	−0.414004	+	0.519144i
$741$		0			0
$742$	−36.0621	−	10.3701i	−1.32388	−	0.380700i
$743$	22.1134	−	27.7294i	0.811263	−	1.01729i	−0.188119	−	0.982146i	$-0.560239\pi$
$743$	22.1134	−	27.7294i	0.811263	−	1.01729i	0.999382	−	0.0351453i	$-0.0111894\pi$
$744$		0			0
$745$	17.1807	+	21.5439i	0.629453	+	0.789309i
$746$	−12.5229	+	54.8664i	−0.458496	+	2.00880i
$747$		0			0
$748$	32.9433	−	144.334i	1.20453	−	5.27738i
$749$	−3.30711	+	2.34896i	−0.120839	+	0.0858292i
$750$		0			0
$751$	−8.63616	−	10.8294i	−0.315138	−	0.395170i	0.598884	−	0.800836i	$-0.295611\pi$
$751$	−8.63616	−	10.8294i	−0.315138	−	0.395170i	−0.914022	+	0.405666i	$0.867040\pi$
$752$	29.8385	−	14.3695i	1.08810	−	0.524001i
$753$		0			0
$754$	7.93883			0.289115
$755$	−31.8751	+	15.3503i	−1.16006	+	0.558653i
$756$		0			0
$757$	27.0892	+	13.0455i	0.984574	+	0.474146i	0.855676	−	0.517512i	$-0.173142\pi$
$757$	27.0892	+	13.0455i	0.984574	+	0.474146i	0.128898	+	0.991658i	$0.458856\pi$
$758$	31.3491	+	15.0969i	1.13865	+	0.548346i
$759$		0			0
$760$	3.07297	+	13.4636i	0.111468	+	0.488375i
$761$	−44.5587	−	21.4583i	−1.61525	−	0.777864i	−0.615305	−	0.788289i	$-0.710967\pi$
$761$	−44.5587	−	21.4583i	−1.61525	−	0.777864i	−0.999946	+	0.0104250i	$0.996682\pi$
$762$		0			0
$763$	−17.2632	+	2.94186i	−0.624969	+	0.106502i
$764$	−45.0403	+	21.6903i	−1.62950	+	0.784727i
$765$		0			0
$766$	5.92402			0.214044
$767$	6.44794	−	3.10516i	0.232822	−	0.112121i
$768$		0			0
$769$	1.74021	+	7.62438i	0.0627538	+	0.274942i	0.996564	−	0.0828266i	$-0.0263948\pi$
$769$	1.74021	+	7.62438i	0.0627538	+	0.274942i	−0.933810	+	0.357769i	$0.883538\pi$
$770$	64.2480	+	57.3588i	2.31534	+	2.06707i
$771$		0			0
$772$	1.82585	−	0.879282i	0.0657137	−	0.0316461i
$773$	−4.08369	+	17.8918i	−0.146880	+	0.643523i	0.846861	+	0.531814i	$0.178490\pi$
$773$	−4.08369	+	17.8918i	−0.146880	+	0.643523i	−0.993741	+	0.111709i	$0.964368\pi$
$774$		0			0
$775$	−0.225472	−	0.987855i	−0.00809918	−	0.0354848i
$776$	11.5377	−	14.4678i	0.414179	−	0.519364i
$777$		0			0
$778$	14.3319	+	17.9716i	0.513823	+	0.644314i
$779$	0.937619	−	1.17574i	0.0335937	−	0.0421252i
$780$		0			0
$781$	−18.0097	+	22.5835i	−0.644438	+	0.808100i
$782$	−21.1346	+	92.5967i	−0.755771	+	3.31125i
$783$		0			0
$784$	−23.5036	−	2.62484i	−0.839415	−	0.0937444i
$785$	−10.8815			−0.388378
$786$		0			0
$787$	32.4043	−	40.6337i	1.15509	−	1.44844i	0.282979	−	0.959126i	$-0.408677\pi$
$787$	32.4043	−	40.6337i	1.15509	−	1.44844i	0.872110	−	0.489310i	$-0.162751\pi$
$788$	−34.1035	−	16.4234i	−1.21489	−	0.585059i
$789$		0			0
$790$	31.8662	+	39.9590i	1.13375	+	1.42168i
$791$	−33.3933	+	23.7185i	−1.18733	+	0.843332i
$792$		0			0
$793$	1.35080	+	5.91825i	0.0479684	+	0.210163i
$794$	−18.8257	−	23.6066i	−0.668097	−	0.837768i
$795$		0			0
$796$	−33.5815	+	16.1720i	−1.19027	+	0.573202i
$797$	9.91908	−	43.4583i	0.351352	−	1.53937i	−0.422711	−	0.906264i	$-0.638922\pi$
$797$	9.91908	−	43.4583i	0.351352	−	1.53937i	0.774063	−	0.633108i	$-0.218221\pi$
$798$		0			0
$799$	14.0846	+	61.7088i	0.498279	+	2.18310i
$800$	−0.116280	−	0.145810i	−0.00411110	−	0.00515516i
$801$		0			0
$802$	0.671129			0.0236984
$803$	−29.7483			−1.04979
$804$		0			0
$805$	−27.2329	−	24.3127i	−0.959832	−	0.856911i
$806$	17.2290	+	8.29707i	0.606867	+	0.292252i
$807$		0			0
$808$	−1.22541	−	5.36889i	−0.0431099	−	0.188877i
$809$	5.50093	+	24.1011i	0.193402	+	0.847351i	0.974758	+	0.223265i	$0.0716714\pi$
$809$	5.50093	+	24.1011i	0.193402	+	0.847351i	−0.781356	+	0.624086i	$0.785471\pi$
$810$		0			0
$811$	40.8456	+	19.6702i	1.43428	+	0.690714i	0.979788	−	0.200036i	$-0.0641060\pi$
$811$	40.8456	+	19.6702i	1.43428	+	0.690714i	0.454493	+	0.890750i	$0.349820\pi$
$812$	8.87700	+	21.4012i	0.311522	+	0.751036i
$813$		0			0
$814$	−29.1070			−1.02020
$815$	−35.8879			−1.25710
$816$		0			0
$817$	−7.57740	−	9.50176i	−0.265100	−	0.332424i
$818$	17.2139	+	75.4191i	0.601871	+	2.63697i
$819$		0			0
$820$	2.25164	−	9.86508i	0.0786307	−	0.344504i
$821$	1.41462	−	0.681246i	0.0493706	−	0.0237756i	−0.409036	−	0.912518i	$-0.634135\pi$
$821$	1.41462	−	0.681246i	0.0493706	−	0.0237756i	0.458406	+	0.888743i	$0.348421\pi$
$822$		0			0
$823$	−3.00232	−	3.76479i	−0.104654	−	0.131232i	0.726746	−	0.686906i	$-0.241032\pi$
$823$	−3.00232	−	3.76479i	−0.104654	−	0.131232i	−0.831400	+	0.555674i	$0.812460\pi$
$824$	−10.1043	−	44.2698i	−0.352000	−	1.54221i
$825$		0			0
$826$	23.5820	+	21.0533i	0.820522	+	0.732538i
$827$	−13.9382	−	17.4779i	−0.484678	−	0.607767i	0.478019	−	0.878350i	$-0.341355\pi$
$827$	−13.9382	−	17.4779i	−0.484678	−	0.607767i	−0.962697	+	0.270583i	$0.912784\pi$
$828$		0			0
$829$	17.5620	+	8.45742i	0.609954	+	0.293738i	0.713247	−	0.700913i	$-0.247224\pi$
$829$	17.5620	+	8.45742i	0.609954	+	0.293738i	−0.103293	+	0.994651i	$0.532938\pi$
$830$	−37.6891	+	47.2606i	−1.30821	+	1.64044i
$831$		0			0
$832$	13.3459			0.462685
$833$	14.8865	−	42.6776i	0.515787	−	1.47869i
$834$		0			0
$835$	11.7955	−	51.6795i	0.408201	−	1.78844i
$836$	−18.8443	+	23.6300i	−0.651745	+	0.817262i
$837$		0			0
$838$	−10.1052	+	12.6715i	−0.349079	+	0.437731i
$839$	8.80466	+	11.0407i	0.303971	+	0.381167i	0.910232	−	0.414098i	$-0.135903\pi$
$839$	8.80466	+	11.0407i	0.303971	+	0.381167i	−0.606262	+	0.795265i	$0.707332\pi$
$840$		0			0
$841$	−14.9288	+	18.7202i	−0.514788	+	0.645523i
$842$	−17.7735	−	77.8707i	−0.612515	−	2.68360i
$843$		0			0
$844$	−13.5197	+	59.2335i	−0.465366	+	2.03890i
$845$	−22.3363	+	10.7566i	−0.768391	+	0.370037i
$846$		0			0
$847$	−3.47894	+	62.4965i	−0.119538	+	2.14741i
$848$	−4.39165	−	19.2411i	−0.150810	−	0.660742i
$849$		0			0
$850$	−2.64237	+	1.27250i	−0.0906325	+	0.0436463i
$851$	12.3376			0.422928
$852$		0			0
$853$	−12.6793	+	6.10601i	−0.434129	+	0.209066i	−0.638168	−	0.769897i	$-0.720307\pi$
$853$	−12.6793	+	6.10601i	−0.434129	+	0.209066i	0.204039	+	0.978963i	$0.434593\pi$
$854$	−21.8612	+	15.5275i	−0.748074	+	0.531339i
$855$		0			0
$856$	−6.35390	−	3.05988i	−0.217172	−	0.104585i
$857$	−0.139833	−	0.612650i	−0.00477661	−	0.0209277i	0.972483	−	0.232972i	$-0.0748450\pi$
$857$	−0.139833	−	0.612650i	−0.00477661	−	0.0209277i	−0.977260	+	0.212044i	$0.931988\pi$
$858$		0			0
$859$	−15.0609	−	7.25296i	−0.513872	−	0.247468i	0.158930	−	0.987290i	$-0.449195\pi$
$859$	−15.0609	−	7.25296i	−0.513872	−	0.247468i	−0.672803	+	0.739822i	$0.734910\pi$
$860$	−73.6769	−	35.4809i	−2.51236	−	1.20989i
$861$		0			0
$862$	48.3480	−	23.2831i	1.64674	−	0.793027i
$863$	2.75906			0.0939196			0.0469598	−	0.998897i	$-0.485047\pi$
$863$	2.75906			0.0939196			0.0469598	+	0.998897i	$0.485047\pi$
$864$		0			0
$865$	−12.6907	+	6.11154i	−0.431498	+	0.207799i
$866$	−20.4906	−	25.6944i	−0.696300	−	0.873132i
$867$		0			0
$868$	−3.10188	+	55.7231i	−0.105285	+	1.89136i
$869$	−12.1084	+	53.0504i	−0.410750	+	1.79961i
$870$		0			0
$871$	−2.82348	+	12.3705i	−0.0956698	+	0.419157i
$872$	−18.9825	−	23.8033i	−0.642829	−	0.806082i
$873$		0			0
$874$	12.0895	−	15.1597i	0.408932	−	0.512785i
$875$	−1.61190	+	28.9566i	−0.0544922	+	0.978911i
$876$		0			0
$877$	−12.5210	+	15.7008i	−0.422804	+	0.530180i	−0.946921	−	0.321467i	$-0.895824\pi$
$877$	−12.5210	+	15.7008i	−0.422804	+	0.530180i	0.524117	+	0.851646i	$0.324396\pi$
$878$	78.3331	+	37.7232i	2.64361	+	1.27310i
$879$		0			0
$880$	−10.0800	+	44.1636i	−0.339798	+	1.48875i
$881$	11.3028			0.380801			0.190400	−	0.981707i	$-0.439021\pi$
$881$	11.3028			0.380801			0.190400	+	0.981707i	$0.439021\pi$
$882$		0			0
$883$	41.7450			1.40483			0.702416	−	0.711767i	$-0.252105\pi$
$883$	41.7450			1.40483			0.702416	+	0.711767i	$0.252105\pi$
$884$	8.13753	−	35.6528i	0.273695	−	1.19913i
$885$		0			0
$886$	−31.6329	−	15.2336i	−1.06273	−	0.511782i
$887$	−20.6947	+	25.9503i	−0.694859	+	0.871326i	−0.996628	−	0.0820553i	$-0.973852\pi$
$887$	−20.6947	+	25.9503i	−0.694859	+	0.871326i	0.301769	+	0.953381i	$0.402423\pi$
$888$		0			0
$889$	13.3519	+	11.9202i	0.447808	+	0.399790i
$890$	38.5661	−	48.3604i	1.29274	−	1.62104i
$891$		0			0
$892$	26.6619	+	33.4329i	0.892705	+	1.11942i
$893$	2.87542	−	12.5980i	0.0962221	−	0.421577i
$894$		0			0
$895$	4.45264	−	19.5083i	0.148835	−	0.652090i
$896$	20.5654	+	49.5805i	0.687043	+	1.65637i
$897$		0			0
$898$	60.0516	+	75.3023i	2.00395	+	2.51287i
$899$	10.9726	−	5.28415i	0.365958	−	0.176236i
$900$		0			0
$901$	37.7193			1.25661
$902$	14.6908	−	7.07471i	0.489150	−	0.235562i
$903$		0			0
$904$	−64.1582	−	30.8969i	−2.13387	−	1.02762i
$905$	2.81502	+	1.35564i	0.0935744	+	0.0450631i
$906$		0			0
$907$	6.41370	+	28.1002i	0.212963	+	0.933053i	0.962541	+	0.271137i	$0.0873995\pi$
$907$	6.41370	+	28.1002i	0.212963	+	0.933053i	−0.749578	+	0.661916i	$0.769743\pi$
$908$	−47.4168	−	22.8347i	−1.57358	−	0.757797i
$909$		0			0
$910$	15.8703	+	14.1685i	0.526095	+	0.469682i
$911$	−14.5022	+	6.98390i	−0.480480	+	0.231387i	−0.658415	−	0.752655i	$-0.728773\pi$
$911$	−14.5022	+	6.98390i	−0.480480	+	0.231387i	0.177935	+	0.984042i	$0.443058\pi$
$912$		0			0
$913$	−64.3577			−2.12993
$914$	60.0959	−	28.9407i	1.98780	−	0.957272i
$915$		0			0
$916$	−11.0910	−	48.5930i	−0.366458	−	1.60556i
$917$	23.0708	−	41.7920i	0.761865	−	1.38009i
$918$		0			0
$919$	−35.7092	+	17.1966i	−1.17794	+	0.567265i	−0.917310	−	0.398174i	$-0.869644\pi$
$919$	−35.7092	+	17.1966i	−1.17794	+	0.567265i	−0.260628	+	0.965439i	$0.583930\pi$
$920$	14.1231	−	61.8774i	0.465626	−	2.04004i
$921$		0			0
$922$	0.277863	+	1.21740i	0.00915094	+	0.0400929i
$923$	−4.44869	+	5.57848i	−0.146430	+	0.183618i
$924$		0			0
$925$	0.237532	+	0.297855i	0.00781000	+	0.00979343i
$926$	24.9788	−	31.3224i	0.820853	−	1.02932i
$927$		0			0
$928$	1.39760	−	1.75254i	0.0458786	−	0.0575299i
$929$	−7.20949	+	31.5868i	−0.236536	+	1.03633i	0.707558	+	0.706655i	$0.249797\pi$
$929$	−7.20949	+	31.5868i	−0.236536	+	1.03633i	−0.944094	+	0.329676i	$0.893061\pi$
$930$		0			0
$931$	−6.51847	+	6.53129i	−0.213634	+	0.214055i
$932$	49.8479			1.63282
$933$		0			0
$934$	−55.9941	+	70.2144i	−1.83218	+	2.29749i
$935$	−78.0024	−	37.5640i	−2.55095	−	1.22847i
$936$		0			0
$937$	−7.29568	−	9.14850i	−0.238340	−	0.298868i	0.648248	−	0.761429i	$-0.275502\pi$
$937$	−7.29568	−	9.14850i	−0.238340	−	0.298868i	−0.886587	+	0.462561i	$0.846931\pi$
$938$	−55.2516	+	9.41555i	−1.80403	+	0.307429i
$939$		0			0
$940$	−19.3478	−	84.7682i	−0.631055	−	2.76483i
$941$	6.40420	+	8.03061i	0.208771	+	0.261790i	0.875182	−	0.483794i	$-0.160742\pi$
$941$	6.40420	+	8.03061i	0.208771	+	0.261790i	−0.666411	+	0.745585i	$0.732170\pi$
$942$		0			0
$943$	−6.22700	+	2.99877i	−0.202779	+	0.0976532i
$944$	−3.69984	+	16.2101i	−0.120420	+	0.527593i
$945$		0			0
$946$	−29.3224	−	128.470i	−0.953354	−	4.17692i
$947$	−12.5234	−	15.7039i	−0.406957	−	0.510308i	0.535546	−	0.844506i	$-0.320106\pi$
$947$	−12.5234	−	15.7039i	−0.406957	−	0.510308i	−0.942503	+	0.334198i	$0.891534\pi$
$948$		0			0
$949$	−7.34830			−0.238536
$950$	0.598740			0.0194257
$951$		0			0
$952$	77.4648	−	13.2010i	2.51065	−	0.427845i
$953$	4.09804	+	1.97351i	0.132748	+	0.0639283i	0.499079	−	0.866557i	$-0.333672\pi$
$953$	4.09804	+	1.97351i	0.132748	+	0.0639283i	−0.366331	+	0.930485i	$0.619386\pi$
$954$		0			0
$955$	6.50526	+	28.5014i	0.210505	+	0.922284i
$956$	0.274815	+	1.20404i	0.00888816	+	0.0389416i
$957$		0			0
$958$	8.21991	+	3.95850i	0.265573	+	0.127893i
$959$	20.8966	−	37.8534i	0.674785	−	1.22235i
$960$		0			0
$961$	−1.66429			−0.0536869
$962$	−7.18990			−0.231812
$963$		0			0
$964$	8.17478	+	10.2508i	0.263292	+	0.330157i
$965$	−0.263711	−	1.15539i	−0.00848914	−	0.0371934i
$966$		0			0
$967$	1.11978	−	4.90609i	0.0360098	−	0.157769i	−0.953726	−	0.300676i	$-0.902788\pi$
$967$	1.11978	−	4.90609i	0.0360098	−	0.157769i	0.989736	+	0.142907i	$0.0456449\pi$
$968$	−98.0450	+	47.2160i	−3.15128	+	1.51758i
$969$		0			0
$970$	−13.8698	−	17.3921i	−0.445332	−	0.558428i
$971$	−0.589473	−	2.58265i	−0.0189171	−	0.0828812i	0.964588	−	0.263760i	$-0.0849628\pi$
$971$	−0.589473	−	2.58265i	−0.0189171	−	0.0828812i	−0.983505	+	0.180879i	$0.942106\pi$
$972$		0			0
$973$	42.6398	+	12.2616i	1.36697	+	0.393090i
$974$	61.6040	+	77.2490i	1.97392	+	2.47522i
$975$		0			0
$976$	−12.7067	−	6.11921i	−0.406730	−	0.195871i
$977$	−15.7771	+	19.7839i	−0.504755	+	0.632943i	−0.967295	−	0.253656i	$-0.918367\pi$
$977$	−15.7771	+	19.7839i	−0.504755	+	0.632943i	0.462539	+	0.886599i	$0.346938\pi$
$978$		0			0
$979$	65.8554			2.10475
$980$	−20.4493	+	58.6255i	−0.653229	+	1.87272i
$981$		0			0
$982$	−2.98936	+	13.0972i	−0.0953942	+	0.417949i
$983$	−28.3910	+	35.6012i	−0.905532	+	1.13550i	0.0847467	+	0.996403i	$0.472992\pi$
$983$	−28.3910	+	35.6012i	−0.905532	+	1.13550i	−0.990279	+	0.139098i	$0.955580\pi$
$984$		0			0
$985$	−13.8013	+	17.3063i	−0.439746	+	0.551425i
$986$	−21.9783	−	27.5599i	−0.699931	−	0.877686i
$987$		0			0
$988$	−4.65485	+	5.83700i	−0.148091	+	0.185700i
$989$	12.4289	+	54.4547i	0.395217	+	1.73156i
$990$		0			0
$991$	−7.24843	+	31.7574i	−0.230254	+	1.00881i	0.719176	+	0.694828i	$0.244520\pi$
$991$	−7.24843	+	31.7574i	−0.230254	+	1.00881i	−0.949430	+	0.313980i	$0.898337\pi$
$992$	4.86474	−	2.34273i	0.154456	−	0.0743819i
$993$		0			0
$994$	−30.2899	−	8.71026i	−0.960738	−	0.276273i
$995$	4.85024	+	21.2503i	0.153763	+	0.673680i
$996$		0			0
$997$	42.4324	−	20.4344i	1.34385	−	0.647163i	0.382873	−	0.923801i	$-0.374935\pi$
$997$	42.4324	−	20.4344i	1.34385	−	0.647163i	0.960974	+	0.276638i	$0.0892203\pi$
$998$	−31.3645			−0.992827
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.u.c.64.1		24
3.2	odd	2		147.2.i.a.64.4	✓	24
49.36	even	7	inner	441.2.u.c.379.1		24
147.92	odd	14		7203.2.a.a.1.2		12
147.104	even	14		7203.2.a.b.1.2		12
147.134	odd	14		147.2.i.a.85.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.i.a.64.4	✓	24	3.2	odd	2
147.2.i.a.85.4	yes	24	147.134	odd	14
441.2.u.c.64.1		24	1.1	even	1	trivial
441.2.u.c.379.1		24	49.36	even	7	inner
7203.2.a.a.1.2		12	147.92	odd	14
7203.2.a.b.1.2		12	147.104	even	14

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.u (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.540253 + 2.36700i) q^{2} +(-3.50889 - 1.68979i) q^{4} +(-1.42001 + 1.78063i) q^{5} +(-1.01369 - 2.44386i) q^{7} +(2.86791 - 3.59625i) q^{8} +O(q^{10})\)	\(q+(-0.540253 + 2.36700i) q^{2} +(-3.50889 - 1.68979i) q^{4} +(-1.42001 + 1.78063i) q^{5} +(-1.01369 - 2.44386i) q^{7} +(2.86791 - 3.59625i) q^{8} +(-3.44760 - 4.32315i) q^{10} +(1.31000 - 5.73951i) q^{11} +(0.323592 - 1.41775i) q^{13} +(6.33226 - 1.07909i) q^{14} +(2.10648 + 2.64144i) q^{16} +(-5.81761 + 2.80161i) q^{17} +1.31823 q^{19} +(7.99154 - 3.84852i) q^{20} +(12.8777 + 6.20157i) q^{22} +(-5.45848 - 2.62867i) q^{23} +(-0.0416288 - 0.182388i) q^{25} +(3.18100 + 1.53189i) q^{26} +(-0.572700 + 10.2881i) q^{28} +(2.02588 - 0.975611i) q^{29} +5.41624 q^{31} +(0.898175 - 0.432538i) q^{32} +(-3.48845 - 15.2839i) q^{34} +(5.79106 + 1.66529i) q^{35} +(-1.83476 + 0.883574i) q^{37} +(-0.712175 + 3.12024i) q^{38} +(2.33114 + 10.2134i) q^{40} +(0.711273 - 0.891909i) q^{41} +(-5.74818 - 7.20799i) q^{43} +(-14.2952 + 17.9256i) q^{44} +(9.17101 - 11.5001i) q^{46} +(2.18128 - 9.55679i) q^{47} +(-4.94488 + 4.95461i) q^{49} +0.454202 q^{50} +(-3.53115 + 4.42792i) q^{52} +(-5.26307 - 2.53456i) q^{53} +(8.35974 + 10.4828i) q^{55} +(-11.6959 - 3.36331i) q^{56} +(1.21479 + 5.32233i) q^{58} +(3.06841 + 3.84766i) q^{59} +(-3.76100 + 1.81120i) q^{61} +(-2.92614 + 12.8203i) q^{62} +(2.04217 + 8.94731i) q^{64} +(2.06499 + 2.58942i) q^{65} -8.72541 q^{67} +25.1475 q^{68} +(-7.07039 + 12.8078i) q^{70} +(-4.42064 - 2.12887i) q^{71} +(-1.12443 - 4.92643i) q^{73} +(-1.10019 - 4.82024i) q^{74} +(-4.62551 - 2.22753i) q^{76} +(-15.3545 + 2.61659i) q^{77} -9.24302 q^{79} -7.69466 q^{80} +(1.72688 + 2.16544i) q^{82} +(-2.43259 - 10.6579i) q^{83} +(3.27241 - 14.3373i) q^{85} +(20.1668 - 9.71181i) q^{86} +(-16.8837 - 21.1715i) q^{88} +(2.48920 + 10.9059i) q^{89} +(-3.79280 + 0.646340i) q^{91} +(14.7113 + 18.4474i) q^{92} +(21.4425 + 10.3262i) q^{94} +(-1.87189 + 2.34728i) q^{95} +4.02302 q^{97} +(-9.05608 - 14.3813i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - q^{2} - 3 q^{4} - 3 q^{8}+O(q^{10}) \) 24 * q - q^2 - 3 * q^4 - 3 * q^8	\( 24 q - q^{2} - 3 q^{4} - 3 q^{8} - 30 q^{10} - 9 q^{11} + 21 q^{14} - 29 q^{16} - 5 q^{17} + 26 q^{19} + 13 q^{20} + 11 q^{22} - 4 q^{23} - 28 q^{25} + 22 q^{26} - 7 q^{28} - 6 q^{29} + 36 q^{31} - 14 q^{32} + 46 q^{34} + 7 q^{35} - 22 q^{37} + 45 q^{38} + 35 q^{40} + 11 q^{41} + 6 q^{43} - 82 q^{44} - 16 q^{46} - 29 q^{47} - 42 q^{49} + 48 q^{50} - 50 q^{52} - 28 q^{53} + 23 q^{55} - 21 q^{56} + 39 q^{58} + 15 q^{59} - 32 q^{61} + 8 q^{62} + 29 q^{64} + 21 q^{65} - 34 q^{67} + 22 q^{68} - 24 q^{71} - 15 q^{73} - 6 q^{74} + 7 q^{76} + 21 q^{77} - 34 q^{79} - 8 q^{80} + 14 q^{82} - 14 q^{83} + 20 q^{85} + 100 q^{86} - 108 q^{88} - 10 q^{89} + 84 q^{91} + 21 q^{92} + 99 q^{94} - 18 q^{95} - 64 q^{97} - 91 q^{98}+O(q^{100}) \) 24 * q - q^2 - 3 * q^4 - 3 * q^8 - 30 * q^10 - 9 * q^11 + 21 * q^14 - 29 * q^16 - 5 * q^17 + 26 * q^19 + 13 * q^20 + 11 * q^22 - 4 * q^23 - 28 * q^25 + 22 * q^26 - 7 * q^28 - 6 * q^29 + 36 * q^31 - 14 * q^32 + 46 * q^34 + 7 * q^35 - 22 * q^37 + 45 * q^38 + 35 * q^40 + 11 * q^41 + 6 * q^43 - 82 * q^44 - 16 * q^46 - 29 * q^47 - 42 * q^49 + 48 * q^50 - 50 * q^52 - 28 * q^53 + 23 * q^55 - 21 * q^56 + 39 * q^58 + 15 * q^59 - 32 * q^61 + 8 * q^62 + 29 * q^64 + 21 * q^65 - 34 * q^67 + 22 * q^68 - 24 * q^71 - 15 * q^73 - 6 * q^74 + 7 * q^76 + 21 * q^77 - 34 * q^79 - 8 * q^80 + 14 * q^82 - 14 * q^83 + 20 * q^85 + 100 * q^86 - 108 * q^88 - 10 * q^89 + 84 * q^91 + 21 * q^92 + 99 * q^94 - 18 * q^95 - 64 * q^97 - 91 * q^98

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