LMFDB - Embedded newform 441.2.bb.e.46.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(37,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 32]))

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

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

chi := DirichletCharacter("441.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bb (of order $21$, degree $12$, 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:	$60$
Relative dimension:	$5$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			46.2
Character	$\chi$	$=$	441.46
Dual form			441.2.bb.e.163.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.489645 + 1.24760i) q^{2} +(0.149360 + 0.138586i) q^{4} +(2.98135 + 2.03265i) q^{5} +(-2.47781 - 0.927615i) q^{7} +(-2.66107 + 1.28150i) q^{8} +O(q^{10})$	\(q+(-0.489645 + 1.24760i) q^{2} +(0.149360 + 0.138586i) q^{4} +(2.98135 + 2.03265i) q^{5} +(-2.47781 - 0.927615i) q^{7} +(-2.66107 + 1.28150i) q^{8} +(-3.99573 + 2.72425i) q^{10} +(-6.22519 + 0.938296i) q^{11} +(2.32688 + 2.91781i) q^{13} +(2.37054 - 2.63710i) q^{14} +(-0.265365 - 3.54105i) q^{16} +(0.0676464 + 0.0208662i) q^{17} +(2.01698 + 3.49352i) q^{19} +(0.163598 + 0.716772i) q^{20} +(1.87752 - 8.22595i) q^{22} +(5.42692 - 1.67398i) q^{23} +(2.93009 + 7.46574i) q^{25} +(-4.77959 + 1.47431i) q^{26} +(-0.241532 - 0.481939i) q^{28} +(0.0859522 + 0.376581i) q^{29} +(0.883415 - 1.53012i) q^{31} +(-1.09694 - 0.338362i) q^{32} +(-0.0591553 + 0.0741784i) q^{34} +(-5.50170 - 7.80207i) q^{35} +(-0.999440 + 0.927345i) q^{37} +(-5.34610 + 0.805795i) q^{38} +(-10.5384 - 1.58841i) q^{40} +(-2.94534 + 1.41840i) q^{41} +(-0.767499 - 0.369608i) q^{43} +(-1.05983 - 0.722580i) q^{44} +(-0.568812 + 7.59027i) q^{46} +(-0.752434 + 1.91717i) q^{47} +(5.27906 + 4.59690i) q^{49} -10.7489 q^{50} +(-0.0568251 + 0.758278i) q^{52} +(6.98962 + 6.48542i) q^{53} +(-20.4667 - 9.85625i) q^{55} +(7.78235 - 0.706870i) q^{56} +(-0.511907 - 0.0771576i) q^{58} +(8.77092 - 5.97991i) q^{59} +(8.08726 - 7.50388i) q^{61} +(1.47641 + 1.85136i) q^{62} +(5.38726 - 6.75541i) q^{64} +(1.00635 + 13.4288i) q^{65} +(-4.81538 + 8.34049i) q^{67} +(0.00721193 + 0.0124914i) q^{68} +(12.4277 - 3.04365i) q^{70} +(3.38079 - 14.8122i) q^{71} +(0.231869 + 0.590793i) q^{73} +(-0.667581 - 1.70097i) q^{74} +(-0.182896 + 0.801318i) q^{76} +(16.2952 + 3.44966i) q^{77} +(0.140427 + 0.243226i) q^{79} +(6.40658 - 11.0965i) q^{80} +(-0.327420 - 4.36911i) q^{82} +(-1.34948 + 1.69219i) q^{83} +(0.159264 + 0.199711i) q^{85} +(0.836924 - 0.776552i) q^{86} +(15.3632 - 10.4745i) q^{88} +(-3.96210 - 0.597191i) q^{89} +(-3.05895 - 9.38822i) q^{91} +(1.04256 + 0.502069i) q^{92} +(-2.02343 - 1.87747i) q^{94} +(-1.08777 + 14.5152i) q^{95} -1.60053 q^{97} +(-8.31995 + 4.33528i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8}+O(q^{10}) $ 60 * q - q^2 + 5 * q^4 + 2 * q^5 + 5 * q^7 - 6 * q^8	$ 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8} - 34 q^{10} + 11 q^{11} - 2 q^{13} - 40 q^{14} - 31 q^{16} + 9 q^{17} - 29 q^{19} + 43 q^{20} + 9 q^{22} + 4 q^{23} + 55 q^{25} - 36 q^{26} - 57 q^{28} - 4 q^{29} - 39 q^{31} + 92 q^{32} - 36 q^{34} + 33 q^{35} - 24 q^{37} - 118 q^{38} - 35 q^{41} + 2 q^{43} - 40 q^{44} - 40 q^{46} + 5 q^{47} + 129 q^{49} + 176 q^{50} - 6 q^{52} - 26 q^{53} + 2 q^{55} - 63 q^{56} + 11 q^{58} + 41 q^{59} + 6 q^{61} - 36 q^{62} + 74 q^{64} + 51 q^{65} - 55 q^{67} + 22 q^{68} - 68 q^{70} + 66 q^{71} + 24 q^{73} - 28 q^{74} + 3 q^{76} + 34 q^{77} - 51 q^{79} + 5 q^{80} - 41 q^{82} - 30 q^{83} + 68 q^{85} - 110 q^{86} + 129 q^{88} - 75 q^{89} + 5 q^{91} + 38 q^{94} - 36 q^{95} - 168 q^{97} - 227 q^{98}+O(q^{100}) $ 60 * q - q^2 + 5 * q^4 + 2 * q^5 + 5 * q^7 - 6 * q^8 - 34 * q^10 + 11 * q^11 - 2 * q^13 - 40 * q^14 - 31 * q^16 + 9 * q^17 - 29 * q^19 + 43 * q^20 + 9 * q^22 + 4 * q^23 + 55 * q^25 - 36 * q^26 - 57 * q^28 - 4 * q^29 - 39 * q^31 + 92 * q^32 - 36 * q^34 + 33 * q^35 - 24 * q^37 - 118 * q^38 - 35 * q^41 + 2 * q^43 - 40 * q^44 - 40 * q^46 + 5 * q^47 + 129 * q^49 + 176 * q^50 - 6 * q^52 - 26 * q^53 + 2 * q^55 - 63 * q^56 + 11 * q^58 + 41 * q^59 + 6 * q^61 - 36 * q^62 + 74 * q^64 + 51 * q^65 - 55 * q^67 + 22 * q^68 - 68 * q^70 + 66 * q^71 + 24 * q^73 - 28 * q^74 + 3 * q^76 + 34 * q^77 - 51 * q^79 + 5 * q^80 - 41 * q^82 - 30 * q^83 + 68 * q^85 - 110 * q^86 + 129 * q^88 - 75 * q^89 + 5 * q^91 + 38 * q^94 - 36 * q^95 - 168 * q^97 - 227 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{11}{21}\right)$	$1$

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 $

$2$	−0.489645	+	1.24760i	−0.346232	+	0.882184i	0.646618	+	0.762814i	$0.276183\pi$
$2$	−0.489645	+	1.24760i	−0.346232	+	0.882184i	−0.992850	+	0.119370i	$0.961913\pi$
$3$		0			0
$3$		0			0
$4$	0.149360	+	0.138586i	0.0746802	+	0.0692931i
$5$	2.98135	+	2.03265i	1.33330	+	0.909030i	0.999436	−	0.0335908i	$-0.0106943\pi$
$5$	2.98135	+	2.03265i	1.33330	+	0.909030i	0.333866	+	0.942621i	$0.391647\pi$
$6$		0			0
$7$	−2.47781	−	0.927615i	−0.936523	−	0.350606i
$7$	−2.47781	−	0.927615i	−0.936523	−	0.350606i
$8$	−2.66107	+	1.28150i	−0.940829	+	0.453079i
$9$		0			0
$10$	−3.99573	+	2.72425i	−1.26356	+	0.861482i
$11$	−6.22519	+	0.938296i	−1.87696	+	0.282907i	−0.985434	−	0.170056i	$-0.945605\pi$
$11$	−6.22519	+	0.938296i	−1.87696	+	0.282907i	−0.891530	+	0.452962i	$0.850367\pi$
$12$		0			0
$13$	2.32688	+	2.91781i	0.645359	+	0.809255i	0.991662	−	0.128868i	$-0.0411343\pi$
$13$	2.32688	+	2.91781i	0.645359	+	0.809255i	−0.346302	+	0.938123i	$0.612563\pi$
$14$	2.37054	−	2.63710i	0.633552	−	0.704795i
$15$		0			0
$16$	−0.265365	−	3.54105i	−0.0663413	−	0.885263i
$17$	0.0676464	+	0.0208662i	0.0164067	+	0.00506079i	0.302948	−	0.953007i	$-0.402029\pi$
$17$	0.0676464	+	0.0208662i	0.0164067	+	0.00506079i	−0.286541	+	0.958068i	$0.592505\pi$
$18$		0			0
$19$	2.01698	+	3.49352i	0.462727	+	0.801467i	0.999096	−	0.0425166i	$-0.0135375\pi$
$19$	2.01698	+	3.49352i	0.462727	+	0.801467i	−0.536368	+	0.843984i	$0.680204\pi$
$20$	0.163598	+	0.716772i	0.0365817	+	0.160275i
$21$		0			0
$22$	1.87752	−	8.22595i	0.400288	−	1.75378i
$23$	5.42692	−	1.67398i	1.13159	−	0.349050i	0.328263	−	0.944586i	$-0.393537\pi$
$23$	5.42692	−	1.67398i	1.13159	−	0.349050i	0.803328	+	0.595537i	$0.203060\pi$
$24$		0			0
$25$	2.93009	+	7.46574i	0.586017	+	1.49315i
$26$	−4.77959	+	1.47431i	−0.937355	+	0.289136i
$27$		0			0
$28$	−0.241532	−	0.481939i	−0.0456452	−	0.0910778i
$29$	0.0859522	+	0.376581i	0.0159609	+	0.0699293i	0.982281	−	0.187413i	$-0.0600103\pi$
$29$	0.0859522	+	0.376581i	0.0159609	+	0.0699293i	−0.966320	+	0.257342i	$0.917153\pi$
$30$		0			0
$31$	0.883415	−	1.53012i	0.158666	−	0.274818i	−0.775722	−	0.631075i	$-0.782614\pi$
$31$	0.883415	−	1.53012i	0.158666	−	0.274818i	0.934388	+	0.356257i	$0.115947\pi$
$32$	−1.09694	−	0.338362i	−0.193914	−	0.0598146i
$33$		0			0
$34$	−0.0591553	+	0.0741784i	−0.0101451	+	0.0127215i
$35$	−5.50170	−	7.80207i	−0.929957	−	1.31879i
$36$		0			0
$37$	−0.999440	+	0.927345i	−0.164307	+	0.152455i	−0.758041	−	0.652207i	$-0.773843\pi$
$37$	−0.999440	+	0.927345i	−0.164307	+	0.152455i	0.593734	+	0.804661i	$0.297653\pi$
$38$	−5.34610	+	0.805795i	−0.867252	+	0.130717i
$39$		0			0
$40$	−10.5384	−	1.58841i	−1.66627	−	0.251150i
$41$	−2.94534	+	1.41840i	−0.459985	+	0.221517i	−0.649501	−	0.760360i	$-0.725022\pi$
$41$	−2.94534	+	1.41840i	−0.459985	+	0.221517i	0.189516	+	0.981878i	$0.439308\pi$
$42$		0			0
$43$	−0.767499	−	0.369608i	−0.117042	−	0.0563647i	0.374446	−	0.927249i	$-0.377833\pi$
$43$	−0.767499	−	0.369608i	−0.117042	−	0.0563647i	−0.491489	+	0.870884i	$0.663547\pi$
$44$	−1.05983	−	0.722580i	−0.159775	−	0.108933i
$45$		0			0
$46$	−0.568812	+	7.59027i	−0.0838667	+	1.11912i
$47$	−0.752434	+	1.91717i	−0.109754	+	0.279648i	−0.975189	−	0.221372i	$-0.928947\pi$
$47$	−0.752434	+	1.91717i	−0.109754	+	0.279648i	0.865436	+	0.501020i	$0.167042\pi$
$48$		0			0
$49$	5.27906	+	4.59690i	0.754152	+	0.656700i
$50$	−10.7489			−1.52013
$51$		0			0
$52$	−0.0568251	+	0.758278i	−0.00788022	+	0.105154i
$53$	6.98962	+	6.48542i	0.960098	+	0.890841i	0.994088	−	0.108581i	$-0.0346308\pi$
$53$	6.98962	+	6.48542i	0.960098	+	0.890841i	−0.0339895	+	0.999422i	$0.510821\pi$
$54$		0			0
$55$	−20.4667	−	9.85625i	−2.75973	−	1.32902i
$56$	7.78235	−	0.706870i	1.03996	−	0.0944595i
$57$		0			0
$58$	−0.511907	−	0.0771576i	−0.0672167	−	0.0101313i
$59$	8.77092	−	5.97991i	1.14188	−	0.778518i	0.163745	−	0.986503i	$-0.447643\pi$
$59$	8.77092	−	5.97991i	1.14188	−	0.778518i	0.978132	+	0.207984i	$0.0666903\pi$
$60$		0			0
$61$	8.08726	−	7.50388i	1.03547	−	0.960774i	0.0362119	−	0.999344i	$-0.488471\pi$
$61$	8.08726	−	7.50388i	1.03547	−	0.960774i	0.999256	+	0.0385705i	$0.0122804\pi$
$62$	1.47641	+	1.85136i	0.187504	+	0.235123i
$63$		0			0
$64$	5.38726	−	6.75541i	0.673407	−	0.844426i
$65$	1.00635	+	13.4288i	0.124822	+	1.66563i
$66$		0			0
$67$	−4.81538	+	8.34049i	−0.588293	+	1.01895i	0.406163	+	0.913800i	$0.366866\pi$
$67$	−4.81538	+	8.34049i	−0.588293	+	1.01895i	−0.994456	+	0.105152i	$0.966467\pi$
$68$	0.00721193	+	0.0124914i	0.000874575	+	0.00151481i
$69$		0			0
$70$	12.4277	−	3.04365i	1.48540	−	0.363786i
$71$	3.38079	−	14.8122i	0.401226	−	1.75789i	−0.221221	−	0.975224i	$-0.571004\pi$
$71$	3.38079	−	14.8122i	0.401226	−	1.75789i	0.622447	−	0.782662i	$-0.286139\pi$
$72$		0			0
$73$	0.231869	+	0.590793i	0.0271382	+	0.0691471i	0.943801	−	0.330515i	$-0.107223\pi$
$73$	0.231869	+	0.590793i	0.0271382	+	0.0691471i	−0.916662	+	0.399662i	$0.869127\pi$
$74$	−0.667581	−	1.70097i	−0.0776047	−	0.197733i
$75$		0			0
$76$	−0.182896	+	0.801318i	−0.0209796	+	0.0919175i
$77$	16.2952	+	3.44966i	1.85701	+	0.393125i
$78$		0			0
$79$	0.140427	+	0.243226i	0.0157992	+	0.0273651i	0.873817	−	0.486255i	$-0.161637\pi$
$79$	0.140427	+	0.243226i	0.0157992	+	0.0273651i	−0.858018	+	0.513620i	$0.828304\pi$
$80$	6.40658	−	11.0965i	0.716278	−	1.24063i
$81$		0			0
$82$	−0.327420	−	4.36911i	−0.0361574	−	0.482488i
$83$	−1.34948	+	1.69219i	−0.148125	+	0.185742i	−0.850358	−	0.526204i	$-0.823615\pi$
$83$	−1.34948	+	1.69219i	−0.148125	+	0.185742i	0.702234	+	0.711947i	$0.252186\pi$
$84$		0			0
$85$	0.159264	+	0.199711i	0.0172746	+	0.0216617i
$86$	0.836924	−	0.776552i	0.0902478	−	0.0837377i
$87$		0			0
$88$	15.3632	−	10.4745i	1.63772	−	1.11658i
$89$	−3.96210	−	0.597191i	−0.419982	−	0.0633021i	−0.0643482	−	0.997928i	$-0.520497\pi$
$89$	−3.96210	−	0.597191i	−0.419982	−	0.0633021i	−0.355634	+	0.934625i	$0.615735\pi$
$90$		0			0
$91$	−3.05895	−	9.38822i	−0.320665	−	0.984153i
$92$	1.04256	+	0.502069i	0.108694	+	0.0523443i
$93$		0			0
$94$	−2.02343	−	1.87747i	−0.208701	−	0.193646i
$95$	−1.08777	+	14.5152i	−0.111602	+	1.48923i
$96$		0			0
$97$	−1.60053			−0.162509			−0.0812545	−	0.996693i	$-0.525893\pi$
$97$	−1.60053			−0.162509			−0.0812545	+	0.996693i	$0.525893\pi$
$98$	−8.31995	+	4.33528i	−0.840441	+	0.437930i
$99$		0			0
$100$	−0.597009	+	1.52115i	−0.0597009	+	0.152115i
$101$	0.620049	−	8.27397i	0.0616971	−	0.823291i	−0.877426	−	0.479711i	$-0.840741\pi$
$101$	0.620049	−	8.27397i	0.0616971	−	0.823291i	0.939124	−	0.343580i	$-0.111640\pi$
$102$		0			0
$103$	4.14318	+	2.82477i	0.408239	+	0.278333i	0.749979	−	0.661462i	$-0.230064\pi$
$103$	4.14318	+	2.82477i	0.408239	+	0.278333i	−0.341739	+	0.939795i	$0.611016\pi$
$104$	−9.93115	−	4.78259i	−0.973829	−	0.468971i
$105$		0			0
$106$	−11.5136	+	5.54467i	−1.11830	+	0.538546i
$107$	15.5873	+	2.34941i	1.50688	+	0.227126i	0.849967	−	0.526837i	$-0.176622\pi$
$107$	15.5873	+	2.34941i	1.50688	+	0.227126i	0.656917	+	0.753963i	$0.271860\pi$
$108$		0			0
$109$	−1.89728	+	0.285969i	−0.181727	+	0.0273909i	−0.239275	−	0.970952i	$-0.576910\pi$
$109$	−1.89728	+	0.285969i	−0.181727	+	0.0273909i	0.0575483	+	0.998343i	$0.481672\pi$
$110$	22.3180	−	20.7081i	2.12794	−	1.97444i
$111$		0			0
$112$	−2.62721	+	9.02021i	−0.248248	+	0.852329i
$113$	−4.55328	+	5.70963i	−0.428336	+	0.537117i	−0.948428	−	0.316994i	$-0.897326\pi$
$113$	−4.55328	+	5.70963i	−0.428336	+	0.537117i	0.520091	+	0.854111i	$0.325898\pi$
$114$		0			0
$115$	19.5822	+	6.04031i	1.82605	+	0.563262i
$116$	−0.0393511	+	0.0681580i	−0.00365365	+	0.00632831i
$117$		0			0
$118$	3.16588	+	13.8706i	0.291442	+	1.27689i
$119$	−0.148259	−	0.114452i	−0.0135909	−	0.0104918i
$120$		0			0
$121$	27.3612	−	8.43982i	2.48739	−	0.767257i
$122$	5.40192	+	13.7639i	0.489067	+	1.24612i
$123$		0			0
$124$	0.344000	−	0.106110i	0.0308922	−	0.00952897i
$125$	−2.42497	+	10.6245i	−0.216896	+	0.950283i
$126$		0			0
$127$	2.92425	+	12.8120i	0.259486	+	1.13688i	0.921803	+	0.387658i	$0.126716\pi$
$127$	2.92425	+	12.8120i	0.259486	+	1.13688i	−0.662318	+	0.749223i	$0.730427\pi$
$128$	4.64223	+	8.04058i	0.410319	+	0.710693i
$129$		0			0
$130$	−17.2464	−	5.31981i	−1.51261	−	0.466579i
$131$	0.00401730	+	0.0536071i	0.000350993	+	0.00468367i	0.997377	−	0.0723881i	$-0.0230620\pi$
$131$	0.00401730	+	0.0536071i	0.000350993	+	0.00468367i	−0.997026	+	0.0770717i	$0.975443\pi$
$132$		0			0
$133$	−1.75706	−	10.5272i	−0.152356	−	0.912828i
$134$	−8.04773	−	10.0915i	−0.695218	−	0.871776i
$135$		0			0
$136$	−0.206752	+	0.0311628i	−0.0177288	+	0.00267219i
$137$	−1.66673	+	1.13635i	−0.142398	+	0.0970853i	−0.632424	−	0.774623i	$-0.717940\pi$
$137$	−1.66673	+	1.13635i	−0.142398	+	0.0970853i	0.490026	+	0.871708i	$0.336987\pi$
$138$		0			0
$139$	−16.7309	+	8.05719i	−1.41910	+	0.683402i	−0.976936	−	0.213532i	$-0.931503\pi$
$139$	−16.7309	+	8.05719i	−1.41910	+	0.683402i	−0.442163	+	0.896935i	$0.645789\pi$
$140$	0.259523	−	1.92778i	0.0219337	−	0.162927i
$141$		0			0
$142$	16.8243	+	11.4706i	1.41186	+	0.962591i
$143$	−17.2230	−	15.9806i	−1.44026	−	1.33637i
$144$		0			0
$145$	−0.509204	+	1.29743i	−0.0422871	+	0.107746i
$146$	−0.850605			−0.0703965
$147$		0			0
$148$	−0.277794			−0.0228345
$149$	1.69125	−	4.30923i	0.138552	−	0.353026i	−0.844709	−	0.535226i	$-0.820227\pi$
$149$	1.69125	−	4.30923i	0.138552	−	0.353026i	0.983262	+	0.182200i	$0.0583218\pi$
$150$		0			0
$151$	2.76393	+	2.56455i	0.224926	+	0.208700i	0.784583	−	0.620023i	$-0.212877\pi$
$151$	2.76393	+	2.56455i	0.224926	+	0.208700i	−0.559658	+	0.828724i	$0.689067\pi$
$152$	−9.84427	−	6.71171i	−0.798476	−	0.544391i
$153$		0			0
$154$	−12.2826	+	18.6407i	−0.989764	+	1.50211i
$155$	5.74397	−	2.76615i	0.461367	−	0.222183i
$156$		0			0
$157$	−2.57088	+	1.75280i	−0.205179	+	0.139888i	−0.661550	−	0.749901i	$-0.730101\pi$
$157$	−2.57088	+	1.75280i	−0.205179	+	0.139888i	0.456372	+	0.889789i	$0.349149\pi$
$158$	−0.372208	+	0.0561013i	−0.0296112	+	0.00446318i
$159$		0			0
$160$	−2.58261	−	3.23848i	−0.204173	−	0.256025i
$161$	−14.9997	−	0.886285i	−1.18214	−	0.0698490i
$162$		0			0
$163$	0.524815	+	7.00317i	0.0411067	+	0.548530i	0.979299	+	0.202417i	$0.0648797\pi$
$163$	0.524815	+	7.00317i	0.0411067	+	0.548530i	−0.938193	+	0.346113i	$0.887501\pi$
$164$	−0.636488	−	0.196331i	−0.0497014	−	0.0153308i
$165$		0			0
$166$	−1.45041	−	2.51218i	−0.112573	−	0.194983i
$167$	−0.556240	−	2.43704i	−0.0430431	−	0.188584i	0.948836	−	0.315770i	$-0.102263\pi$
$167$	−0.556240	−	2.43704i	−0.0430431	−	0.188584i	−0.991879	+	0.127186i	$0.959406\pi$
$168$		0			0
$169$	−0.206493	+	0.904704i	−0.0158841	+	0.0695926i
$170$	−0.327142	+	0.100910i	−0.0250906	+	0.00773944i
$171$		0			0
$172$	−0.0634113	−	0.161569i	−0.00483507	−	0.0123196i
$173$	−0.881378	+	0.271869i	−0.0670099	+	0.0206698i	−0.328079	−	0.944650i	$-0.606401\pi$
$173$	−0.881378	+	0.271869i	−0.0670099	+	0.0206698i	0.261069	+	0.965320i	$0.415925\pi$
$174$		0			0
$175$	−0.334859	−	21.2167i	−0.0253130	−	1.60383i
$176$	4.97450	+	21.7947i	0.374967	+	1.64284i
$177$		0			0
$178$	2.68508	−	4.65069i	0.201255	−	0.348584i
$179$	16.4861	+	5.08530i	1.23223	+	0.380093i	0.841422	−	0.540378i	$-0.181719\pi$
$179$	16.4861	+	5.08530i	1.23223	+	0.380093i	0.390810	+	0.920472i	$0.372195\pi$
$180$		0			0
$181$	8.67791	−	10.8818i	0.645024	−	0.808835i	−0.346597	−	0.938014i	$-0.612663\pi$
$181$	8.67791	−	10.8818i	0.645024	−	0.808835i	0.991621	+	0.129179i	$0.0412343\pi$
$182$	13.2105	+	0.780568i	0.979228	+	0.0578595i
$183$		0			0
$184$	−12.2962	+	11.4092i	−0.906487	+	0.841097i
$185$	−4.86465	+	0.733229i	−0.357656	+	0.0539080i
$186$		0			0
$187$	−0.440690	−	0.0664234i	−0.0322265	−	0.00485736i
$188$	−0.378077	+	0.182072i	−0.0275741	+	0.0132790i
$189$		0			0
$190$	−17.5765	−	8.46441i	−1.27513	−	0.614073i
$191$	4.45950	+	3.04043i	0.322678	+	0.219998i	0.713815	−	0.700334i	$-0.246966\pi$
$191$	4.45950	+	3.04043i	0.322678	+	0.219998i	−0.391137	+	0.920332i	$0.627918\pi$
$192$		0			0
$193$	1.78701	−	23.8460i	0.128632	−	1.71647i	−0.443467	−	0.896291i	$-0.646252\pi$
$193$	1.78701	−	23.8460i	0.128632	−	1.71647i	0.572099	−	0.820184i	$-0.306129\pi$
$194$	0.783691	−	1.99681i	0.0562657	−	0.143363i
$195$		0			0
$196$	0.151415	+	1.41820i	0.0108154	+	0.101300i
$197$	4.44869			0.316956			0.158478	−	0.987363i	$-0.449341\pi$
$197$	4.44869			0.316956			0.158478	+	0.987363i	$0.449341\pi$
$198$		0			0
$199$	1.76371	−	23.5350i	0.125026	−	1.66835i	−0.483898	−	0.875125i	$-0.660779\pi$
$199$	1.76371	−	23.5350i	0.125026	−	1.66835i	0.608924	−	0.793229i	$-0.291602\pi$
$200$	−17.3645	−	16.1119i	−1.22786	−	1.13928i
$201$		0			0
$202$	10.0190	+	4.82488i	0.704932	+	0.339478i
$203$	0.136349	−	1.01283i	0.00956984	−	0.0710864i
$204$		0			0
$205$	−11.6642	−	1.75810i	−0.814665	−	0.122791i
$206$	−5.55286	+	3.78588i	−0.386886	+	0.263775i
$207$		0			0
$208$	9.71465	−	9.01388i	0.673590	−	0.625000i
$209$	−15.8340	−	19.8553i	−1.09526	−	1.37342i
$210$		0			0
$211$	3.15920	−	3.96151i	0.217488	−	0.272722i	−0.661104	−	0.750294i	$-0.729912\pi$
$211$	3.15920	−	3.96151i	0.217488	−	0.272722i	0.878592	+	0.477572i	$0.158483\pi$
$212$	0.145183	+	1.93733i	0.00997119	+	0.133056i
$213$		0			0
$214$	−10.5634	+	18.2963i	−0.722098	+	1.25071i
$215$	−1.53690	−	2.66199i	−0.104816	−	0.181546i
$216$		0			0
$217$	−3.60829	+	2.97187i	−0.244947	+	0.201744i
$218$	0.572222	−	2.50707i	0.0387557	−	0.169800i
$219$		0			0
$220$	−1.69097	−	4.30853i	−0.114006	−	0.290481i
$221$	0.0965214	+	0.245932i	0.00649273	+	0.0165432i
$222$		0			0
$223$	4.82516	−	21.1404i	0.323116	−	1.41567i	−0.508858	−	0.860851i	$-0.669932\pi$
$223$	4.82516	−	21.1404i	0.323116	−	1.41567i	0.831974	−	0.554815i	$-0.187211\pi$
$224$	2.40415	+	1.85594i	0.160634	+	0.124005i
$225$		0			0
$226$	−4.89382	−	8.47634i	−0.325532	−	0.563838i
$227$	−9.15140	+	15.8507i	−0.607400	+	1.05205i	0.384267	+	0.923222i	$0.374454\pi$
$227$	−9.15140	+	15.8507i	−0.607400	+	1.05205i	−0.991667	+	0.128826i	$0.958879\pi$
$228$		0			0
$229$	1.55161	+	20.7048i	0.102533	+	1.36821i	0.776810	+	0.629735i	$0.216836\pi$
$229$	1.55161	+	20.7048i	0.102533	+	1.36821i	−0.674277	+	0.738479i	$0.735545\pi$
$230$	−17.1242	+	21.4731i	−1.12914	+	1.41589i
$231$		0			0
$232$	−0.711314	−	0.891959i	−0.0467000	−	0.0585600i
$233$	−7.45545	+	6.91765i	−0.488423	+	0.453190i	−0.885530	−	0.464582i	$-0.846205\pi$
$233$	−7.45545	+	6.91765i	−0.488423	+	0.453190i	0.397107	+	0.917772i	$0.370014\pi$
$234$		0			0
$235$	−6.14021	+	4.18633i	−0.400543	+	0.273086i
$236$	2.13876	+	0.322366i	0.139221	+	0.0209843i
$237$		0			0
$238$	0.215385	−	0.128926i	0.0139613	−	0.00835706i
$239$	−10.4972	−	5.05520i	−0.679010	−	0.326994i	0.0623954	−	0.998052i	$-0.480126\pi$
$239$	−10.4972	−	5.05520i	−0.679010	−	0.326994i	−0.741405	+	0.671058i	$0.765840\pi$
$240$		0			0
$241$	−13.1410	−	12.1930i	−0.846484	−	0.785423i	0.132107	−	0.991235i	$-0.457826\pi$
$241$	−13.1410	−	12.1930i	−0.846484	−	0.785423i	−0.978591	+	0.205813i	$0.934016\pi$
$242$	−2.86781	+	38.2683i	−0.184350	+	2.45998i
$243$		0			0
$244$	2.24785			0.143904
$245$	6.39484	+	24.4355i	0.408551	+	1.56113i
$246$		0			0
$247$	−5.50015	+	14.0141i	−0.349966	+	0.891699i
$248$	−0.389974	+	5.20385i	−0.0247634	+	0.330445i
$249$		0			0
$250$	−12.0677	−	8.22761i	−0.763228	−	0.520360i
$251$	13.1723	+	6.34345i	0.831429	+	0.400395i	0.800651	−	0.599131i	$-0.204487\pi$
$251$	13.1723	+	6.34345i	0.831429	+	0.400395i	0.0307783	+	0.999526i	$0.490201\pi$
$252$		0			0
$253$	−32.2129	+	15.5129i	−2.02521	+	0.975289i
$254$	−17.4160	−	2.62505i	−1.09278	−	0.164710i
$255$		0			0
$256$	4.78353	−	0.721001i	0.298970	−	0.0450625i
$257$	−2.07848	+	1.92855i	−0.129652	+	0.120299i	−0.742334	−	0.670030i	$-0.766281\pi$
$257$	−2.07848	+	1.92855i	−0.129652	+	0.120299i	0.612682	+	0.790330i	$0.290091\pi$
$258$		0			0
$259$	3.33664	−	1.37069i	0.207329	−	0.0851703i
$260$	−1.71073	+	2.14519i	−0.106095	+	0.133039i
$261$		0			0
$262$	−0.0688471	−	0.0212365i	−0.00425339	−	0.00131200i
$263$	0.753562	−	1.30521i	0.0464667	−	0.0804826i	−0.841857	−	0.539701i	$-0.818537\pi$
$263$	0.753562	−	1.30521i	0.0464667	−	0.0804826i	0.888323	+	0.459219i	$0.151871\pi$
$264$		0			0
$265$	7.65592	+	33.5428i	0.470300	+	2.06052i
$266$	13.9941	+	2.96252i	0.858032	+	0.181644i
$267$		0			0
$268$	−1.87510	+	0.578393i	−0.114540	+	0.0353310i
$269$	−0.828063	−	2.10987i	−0.0504879	−	0.128641i	0.903405	−	0.428788i	$-0.141059\pi$
$269$	−0.828063	−	2.10987i	−0.0504879	−	0.128641i	−0.953893	+	0.300147i	$0.902964\pi$
$270$		0			0
$271$	−30.0745	+	9.27677i	−1.82690	+	0.563523i	−0.826899	+	0.562351i	$0.809897\pi$
$271$	−30.0745	+	9.27677i	−1.82690	+	0.563523i	−0.999999	+	0.00117281i	$0.999627\pi$
$272$	0.0559372	−	0.245077i	0.00339169	−	0.0148600i
$273$		0			0
$274$	−0.601607	−	2.63581i	−0.0363444	−	0.159235i
$275$	−25.2454	−	43.7263i	−1.52236	−	2.63680i
$276$		0			0
$277$	7.33693	+	2.26314i	0.440833	+	0.135979i	0.507223	−	0.861815i	$-0.330672\pi$
$277$	7.33693	+	2.26314i	0.440833	+	0.135979i	−0.0663900	+	0.997794i	$0.521148\pi$
$278$	−1.85990	−	24.8186i	−0.111549	−	1.48852i
$279$		0			0
$280$	24.6388	+	13.7114i	1.47245	+	0.819412i
$281$	−12.7279	−	15.9603i	−0.759285	−	0.952114i	0.240543	−	0.970638i	$-0.422674\pi$
$281$	−12.7279	−	15.9603i	−0.759285	−	0.952114i	−0.999828	+	0.0185248i	$0.994103\pi$
$282$		0			0
$283$	−16.0033	+	2.41211i	−0.951297	+	0.143385i	−0.606315	−	0.795224i	$-0.707353\pi$
$283$	−16.0033	+	2.41211i	−0.951297	+	0.143385i	−0.344982	+	0.938609i	$0.612115\pi$
$284$	2.55772	−	1.74383i	0.151773	−	0.103477i
$285$		0			0
$286$	28.3705	−	13.6625i	1.67758	−	0.807882i
$287$	8.61372	−	0.782383i	0.508452	−	0.0461826i
$288$		0			0
$289$	−14.0419	−	9.57362i	−0.825995	−	0.563154i
$290$	−1.36934	−	1.27056i	−0.0804105	−	0.0746100i
$291$		0			0
$292$	−0.0472436	+	0.120375i	−0.00276473	+	0.00704441i
$293$	6.81892			0.398366			0.199183	−	0.979962i	$-0.436171\pi$
$293$	6.81892			0.398366			0.199183	+	0.979962i	$0.436171\pi$
$294$		0			0
$295$	38.3043			2.23016
$296$	1.47118	−	3.74851i	0.0855107	−	0.217878i
$297$		0			0
$298$	4.54807	+	4.21999i	0.263462	+	0.244457i
$299$	17.5121	+	11.9396i	1.01275	+	0.690484i
$300$		0			0
$301$	1.55886	+	1.62776i	0.0898512	+	0.0938226i
$302$	−4.55288	+	2.19255i	−0.261989	+	0.126167i
$303$		0			0
$304$	11.8355	−	8.06930i	0.678812	−	0.462806i
$305$	39.3638	−	5.93313i	2.25396	−	0.339730i
$306$		0			0
$307$	17.7544	+	22.2633i	1.01330	+	1.27063i	0.962316	+	0.271933i	$0.0876630\pi$
$307$	17.7544	+	22.2633i	1.01330	+	1.27063i	0.0509799	+	0.998700i	$0.483766\pi$
$308$	1.95578	+	2.77353i	0.111441	+	0.158037i
$309$		0			0
$310$	0.638530	+	8.52059i	0.0362661	+	0.483937i
$311$	−9.09027	−	2.80398i	−0.515462	−	0.158999i	0.0261008	−	0.999659i	$-0.491691\pi$
$311$	−9.09027	−	2.80398i	−0.515462	−	0.158999i	−0.541563	+	0.840660i	$0.682167\pi$
$312$		0			0
$313$	10.6402	+	18.4293i	0.601418	+	1.04169i	0.992607	+	0.121376i	$0.0387308\pi$
$313$	10.6402	+	18.4293i	0.601418	+	1.04169i	−0.391188	+	0.920311i	$0.627936\pi$
$314$	−0.927963	−	4.06567i	−0.0523680	−	0.229439i
$315$		0			0
$316$	−0.0127336	+	0.0557896i	−0.000716321	+	0.00313841i
$317$	−0.622234	+	0.191934i	−0.0349481	+	0.0107801i	−0.312180	−	0.950023i	$-0.601059\pi$
$317$	−0.622234	+	0.191934i	−0.0349481	+	0.0107801i	0.277232	+	0.960803i	$0.410583\pi$
$318$		0			0
$319$	−0.888412	−	2.26364i	−0.0497415	−	0.126739i
$320$	29.7927	−	9.18983i	1.66546	−	0.513727i
$321$		0			0
$322$	8.45025	−	18.2796i	0.470914	−	1.01868i
$323$	0.0635454	+	0.278411i	0.00353576	+	0.0154912i
$324$		0			0
$325$	−14.9657	+	25.9213i	−0.830146	+	1.43785i
$326$	−8.99410	−	2.77431i	−0.498137	−	0.153655i
$327$		0			0
$328$	6.02006	−	7.54892i	0.332402	−	0.416819i
$329$	3.64278	−	4.05241i	0.200833	−	0.223417i
$330$		0			0
$331$	−6.46594	+	5.99952i	−0.355400	+	0.329763i	−0.837586	−	0.546306i	$-0.816034\pi$
$331$	−6.46594	+	5.99952i	−0.355400	+	0.329763i	0.482185	+	0.876069i	$0.339843\pi$
$332$	−0.436073	+	0.0657274i	−0.0239326	+	0.00360726i
$333$		0			0
$334$	3.31281	+	0.499325i	0.181269	+	0.0273219i
$335$	−31.3097	+	15.0779i	−1.71063	+	0.823796i
$336$		0			0
$337$	−7.26495	−	3.49862i	−0.395747	−	0.190582i	0.225417	−	0.974262i	$-0.427626\pi$
$337$	−7.26495	−	3.49862i	−0.395747	−	0.190582i	−0.621164	+	0.783681i	$0.713340\pi$
$338$	−1.02760	−	0.700604i	−0.0558939	−	0.0381078i
$339$		0			0
$340$	−0.00388942	+	0.0519007i	−0.000210934	+	0.00281471i
$341$	−4.06372	+	10.3542i	−0.220063	+	0.560710i
$342$		0			0
$343$	−8.81634	−	16.2872i	−0.476038	−	0.879425i
$344$	2.51602			0.135655
$345$		0			0
$346$	0.0923798	−	1.23272i	0.00496637	−	0.0662716i
$347$	−23.1526	−	21.4825i	−1.24290	−	1.15324i	−0.982204	−	0.187817i	$-0.939859\pi$
$347$	−23.1526	−	21.4825i	−1.24290	−	1.15324i	−0.260692	−	0.965422i	$-0.583951\pi$
$348$		0			0
$349$	−9.91729	−	4.77592i	−0.530861	−	0.255649i	0.149197	−	0.988807i	$-0.452331\pi$
$349$	−9.91729	−	4.77592i	−0.530861	−	0.255649i	−0.680058	+	0.733158i	$0.738045\pi$
$350$	26.6338	+	9.97087i	1.42364	+	0.532965i
$351$		0			0
$352$	7.14617	+	1.07711i	0.380892	+	0.0574102i
$353$	20.2296	−	13.7923i	1.07672	−	0.734092i	0.111032	−	0.993817i	$-0.464584\pi$
$353$	20.2296	−	13.7923i	1.07672	−	0.734092i	0.965683	+	0.259725i	$0.0836319\pi$
$354$		0			0
$355$	40.1874	−	37.2885i	2.13293	−	1.97907i
$356$	−0.509018	−	0.638289i	−0.0269779	−	0.0338292i
$357$		0			0
$358$	−14.4168	+	18.0780i	−0.761949	+	0.955454i
$359$	1.89995	+	25.3530i	0.100275	+	1.33808i	0.789597	+	0.613625i	$0.210290\pi$
$359$	1.89995	+	25.3530i	0.100275	+	1.33808i	−0.689322	+	0.724455i	$0.742091\pi$
$360$		0			0
$361$	1.36357	−	2.36177i	0.0717667	−	0.124304i
$362$	9.32694	+	16.1547i	0.490213	+	0.849074i
$363$		0			0
$364$	0.844192	−	1.82615i	0.0442477	−	0.0957165i
$365$	−0.509593	+	2.23267i	−0.0266733	+	0.116863i
$366$		0			0
$367$	−2.40832	−	6.13631i	−0.125713	−	0.320313i	0.854136	−	0.520049i	$-0.174086\pi$
$367$	−2.40832	−	6.13631i	−0.125713	−	0.320313i	−0.979850	+	0.199737i	$0.935991\pi$
$368$	−7.36778	−	18.7728i	−0.384072	−	0.978600i
$369$		0			0
$370$	1.46718	−	6.42815i	0.0762752	−	0.334183i
$371$	−11.3030	−	22.5533i	−0.586820	−	1.17091i
$372$		0			0
$373$	−9.00494	−	15.5970i	−0.466258	−	0.807583i	0.532999	−	0.846116i	$-0.321065\pi$
$373$	−9.00494	−	15.5970i	−0.466258	−	0.807583i	−0.999257	+	0.0385329i	$0.987732\pi$
$374$	0.298652	−	0.517280i	0.0154429	−	0.0267479i
$375$		0			0
$376$	−0.454581	−	6.06596i	−0.0234432	−	0.312828i
$377$	−0.898792	+	1.12705i	−0.0462901	+	0.0580460i
$378$		0			0
$379$	−3.23956	−	4.06228i	−0.166405	−	0.208665i	0.691636	−	0.722246i	$-0.256890\pi$
$379$	−3.23956	−	4.06228i	−0.166405	−	0.208665i	−0.858041	+	0.513581i	$0.828319\pi$
$380$	−2.17408	+	2.01725i	−0.111528	+	0.103483i
$381$		0			0
$382$	−5.97681	+	4.07492i	−0.305800	+	0.208491i
$383$	−30.3766	−	4.57853i	−1.55217	−	0.233952i	−0.683726	−	0.729739i	$-0.739642\pi$
$383$	−30.3766	−	4.57853i	−1.55217	−	0.233952i	−0.868444	+	0.495787i	$0.834880\pi$
$384$		0			0
$385$	41.5698	+	43.4071i	2.11859	+	2.21223i
$386$	28.8752	+	13.9056i	1.46971	+	0.707775i
$387$		0			0
$388$	−0.239055	−	0.221811i	−0.0121362	−	0.0112607i
$389$	−1.63076	+	21.7609i	−0.0826826	+	1.10332i	0.789373	+	0.613914i	$0.210406\pi$
$389$	−1.63076	+	21.7609i	−0.0826826	+	1.10332i	−0.872055	+	0.489408i	$0.837213\pi$
$390$		0			0
$391$	0.402042			0.0203321
$392$	−19.9389	−	5.46754i	−1.00706	−	0.276152i
$393$		0			0
$394$	−2.17828	+	5.55017i	−0.109740	+	0.279613i
$395$	−0.0757327	+	1.01058i	−0.00381052	+	0.0508479i
$396$		0			0
$397$	7.99784	+	5.45283i	0.401400	+	0.273670i	0.747148	−	0.664657i	$-0.231423\pi$
$397$	7.99784	+	5.45283i	0.401400	+	0.273670i	−0.345748	+	0.938327i	$0.612375\pi$
$398$	28.4986	+	13.7242i	1.42851	+	0.687932i
$399$		0			0
$400$	25.6590	−	12.3567i	1.28295	−	0.617837i
$401$	32.1147	+	4.84052i	1.60373	+	0.241724i	0.889079	−	0.457754i	$-0.151346\pi$
$401$	32.1147	+	4.84052i	1.60373	+	0.241724i	0.714654	+	0.699478i	$0.246584\pi$
$402$		0			0
$403$	6.52020	−	0.982761i	0.324794	−	0.0489548i
$404$	1.23927	−	1.14987i	0.0616559	−	0.0572083i
$405$		0			0
$406$	1.19683	+	0.666034i	0.0593979	+	0.0330547i
$407$	5.35158	−	6.71066i	0.265268	−	0.332635i
$408$		0			0
$409$	−25.2706	−	7.79494i	−1.24955	−	0.385435i	−0.401749	−	0.915750i	$-0.631598\pi$
$409$	−25.2706	−	7.79494i	−1.24955	−	0.385435i	−0.847801	+	0.530315i	$0.822074\pi$
$410$	7.90473	−	13.6914i	0.390387	−	0.676170i
$411$		0			0
$412$	0.227352	+	0.996096i	0.0112008	+	0.0490741i
$413$	−27.2797	+	6.68104i	−1.34235	+	0.328752i
$414$		0			0
$415$	−7.46291	+	2.30200i	−0.366340	+	0.113001i
$416$	−1.56518	−	3.98800i	−0.0767391	−	0.195528i
$417$		0			0
$418$	32.5244	−	10.0324i	1.59082	−	0.490703i
$419$	7.35777	−	32.2365i	0.359451	−	1.57486i	−0.395115	−	0.918632i	$-0.629295\pi$
$419$	7.35777	−	32.2365i	0.359451	−	1.57486i	0.754566	−	0.656225i	$-0.227848\pi$
$420$		0			0
$421$	−5.63666	−	24.6958i	−0.274714	−	1.20360i	−0.904378	−	0.426732i	$-0.859665\pi$
$421$	−5.63666	−	24.6958i	−0.274714	−	1.20360i	0.629664	−	0.776867i	$-0.283192\pi$
$422$	3.39548	+	5.88114i	0.165289	+	0.286290i
$423$		0			0
$424$	−26.9109	−	8.30092i	−1.30691	−	0.403128i
$425$	0.0424286	+	0.566170i	0.00205809	+	0.0274633i
$426$		0			0
$427$	−26.9994	+	11.0913i	−1.30659	+	0.536746i
$428$	2.00253	+	2.51110i	0.0967960	+	0.121378i
$429$		0			0
$430$	4.07363	−	0.614000i	0.196448	−	0.0296097i
$431$	−6.17871	+	4.21257i	−0.297618	+	0.202912i	−0.702917	−	0.711272i	$-0.748120\pi$
$431$	−6.17871	+	4.21257i	−0.297618	+	0.202912i	0.405300	+	0.914184i	$0.367167\pi$
$432$		0			0
$433$	−10.5083	+	5.06052i	−0.504996	+	0.243193i	−0.668995	−	0.743267i	$-0.733275\pi$
$433$	−10.5083	+	5.06052i	−0.504996	+	0.243193i	0.163999	+	0.986461i	$0.447561\pi$
$434$	−1.94091	−	5.95686i	−0.0931668	−	0.285938i
$435$		0			0
$436$	−0.323010	−	0.220225i	−0.0154694	−	0.0105468i
$437$	16.7941	+	15.5826i	0.803370	+	0.745419i
$438$		0			0
$439$	−5.02634	+	12.8069i	−0.239894	+	0.611240i	−0.999221	−	0.0394694i	$-0.987433\pi$
$439$	−5.02634	+	12.8069i	−0.239894	+	0.611240i	0.759327	+	0.650710i	$0.225528\pi$
$440$	67.0940			3.19858
$441$		0			0
$442$	−0.354086			−0.0168421
$443$	−5.60071	+	14.2704i	−0.266098	+	0.678006i	−0.999999	−	0.00124988i	$-0.999602\pi$
$443$	−5.60071	+	14.2704i	−0.266098	+	0.678006i	0.733901	+	0.679256i	$0.237697\pi$
$444$		0			0
$445$	−10.5985	−	9.83401i	−0.502419	−	0.466177i
$446$	24.0121	+	16.3711i	1.13700	+	0.775196i
$447$		0			0
$448$	−19.6150	+	11.7413i	−0.926722	+	0.554724i
$449$	−4.60220	+	2.21630i	−0.217191	+	0.104594i	−0.539316	−	0.842103i	$-0.681317\pi$
$449$	−4.60220	+	2.21630i	−0.217191	+	0.104594i	0.322125	+	0.946697i	$0.395603\pi$
$450$		0			0
$451$	17.0044	−	11.5934i	0.800707	−	0.545913i
$452$	−1.47135	+	0.221771i	−0.0692067	+	0.0104312i
$453$		0			0
$454$	−15.2943	−	19.1785i	−0.717798	−	0.900090i
$455$	9.96318	−	34.2074i	0.467081	−	1.60367i
$456$		0			0
$457$	−0.887144	−	11.8381i	−0.0414988	−	0.553763i	−0.978743	−	0.205090i	$-0.934251\pi$
$457$	−0.887144	−	11.8381i	−0.0414988	−	0.553763i	0.937244	−	0.348673i	$-0.113368\pi$
$458$	−26.5910	−	8.20224i	−1.24252	−	0.383265i
$459$		0			0
$460$	2.08770	+	3.61600i	0.0973395	+	0.168597i
$461$	−4.82376	−	21.1343i	−0.224665	−	0.984321i	−0.953916	−	0.300075i	$-0.902988\pi$
$461$	−4.82376	−	21.1343i	−0.224665	−	0.984321i	0.729251	−	0.684247i	$-0.239869\pi$
$462$		0			0
$463$	−5.70812	+	25.0089i	−0.265279	+	1.16226i	0.650158	+	0.759799i	$0.274703\pi$
$463$	−5.70812	+	25.0089i	−0.265279	+	1.16226i	−0.915436	+	0.402462i	$0.868154\pi$
$464$	1.31068	−	0.404293i	0.0608470	−	0.0187688i
$465$		0			0
$466$	−4.97990	−	12.6886i	−0.230689	−	0.587787i
$467$	−9.53264	+	2.94043i	−0.441118	+	0.136067i	−0.507355	−	0.861737i	$-0.669377\pi$
$467$	−9.53264	+	2.94043i	−0.441118	+	0.136067i	0.0662373	+	0.997804i	$0.478901\pi$
$468$		0			0
$469$	19.6684	−	16.1993i	0.908200	−	0.748014i
$470$	−2.21632	−	9.71032i	−0.102231	−	0.447904i
$471$		0			0
$472$	−15.6767	+	27.1529i	−0.721580	+	1.24981i
$473$	5.12462	+	1.58074i	0.235630	+	0.0726824i
$474$		0			0
$475$	−20.1717	+	25.2946i	−0.925543	+	1.16059i
$476$	−0.00628254	−	0.0376413i	−0.000287960	−	0.00172528i
$477$		0			0
$478$	11.4468	−	10.6211i	0.523563	−	0.485796i
$479$	21.5916	−	3.25440i	0.986543	−	0.148697i	0.364098	−	0.931361i	$-0.381377\pi$
$479$	21.5916	−	3.25440i	0.986543	−	0.148697i	0.622445	+	0.782663i	$0.286139\pi$
$480$		0			0
$481$	−5.03139	−	0.758360i	−0.229412	−	0.0345782i
$482$	21.6464	−	10.4244i	0.985967	−	0.474817i
$483$		0			0
$484$	5.25633	+	2.53131i	0.238924	+	0.115060i
$485$	−4.77174	−	3.25332i	−0.216673	−	0.147725i
$486$		0			0
$487$	1.41125	−	18.8319i	0.0639499	−	0.853353i	−0.869337	−	0.494220i	$-0.835454\pi$
$487$	1.41125	−	18.8319i	0.0639499	−	0.853353i	0.933287	−	0.359132i	$-0.116927\pi$
$488$	−11.9045	+	30.3322i	−0.538891	+	1.37307i
$489$		0			0
$490$	−33.6168	−	3.98655i	−1.51865	−	0.180094i
$491$	7.07668			0.319366			0.159683	−	0.987168i	$-0.448953\pi$
$491$	7.07668			0.319366			0.159683	+	0.987168i	$0.448953\pi$
$492$		0			0
$493$	−0.00204344	+	0.0272679i	−9.20321e−5	+	0.00122808i
$494$	−14.7909	−	13.7239i	−0.665473	−	0.617469i
$495$		0			0
$496$	−5.65266	−	2.72218i	−0.253812	−	0.122229i
$497$	−22.1170	+	33.5657i	−0.992082	+	1.50563i
$498$		0			0
$499$	26.5578	+	4.00295i	1.18889	+	0.179197i	0.713550	−	0.700605i	$-0.247086\pi$
$499$	26.5578	+	4.00295i	1.18889	+	0.179197i	0.475342	+	0.879801i	$0.342324\pi$
$500$	−1.83460	+	1.25081i	−0.0820458	+	0.0559379i
$501$		0			0
$502$	−14.3638	+	13.3277i	−0.641089	+	0.594844i
$503$	16.8438	+	21.1215i	0.751028	+	0.941759i	0.999640	−	0.0268439i	$-0.00854570\pi$
$503$	16.8438	+	21.1215i	0.751028	+	0.941759i	−0.248612	+	0.968603i	$0.579974\pi$
$504$		0			0
$505$	18.6667	−	23.4073i	0.830657	−	1.04161i
$506$	−3.58095	−	47.7845i	−0.159193	−	2.12428i
$507$		0			0
$508$	−1.33880	+	2.31887i	−0.0593995	+	0.102883i
$509$	−7.82937	−	13.5609i	−0.347031	−	0.601075i	0.638690	−	0.769464i	$-0.279477\pi$
$509$	−7.82937	−	13.5609i	−0.347031	−	0.601075i	−0.985721	+	0.168389i	$0.946143\pi$
$510$		0			0
$511$	−0.0264987	−	1.67896i	−0.00117223	−	0.0742727i
$512$	−5.57469	+	24.4243i	−0.246369	+	1.07941i
$513$		0			0
$514$	−1.38833	−	3.53741i	−0.0612366	−	0.156028i
$515$	6.61050	+	16.8433i	0.291293	+	0.742204i
$516$		0			0
$517$	2.88517	−	12.6408i	0.126890	−	0.555940i
$518$	0.0762931	+	4.83393i	0.00335213	+	0.212391i
$519$		0			0
$520$	−19.8869	−	34.4452i	−0.872099	−	1.51052i
$521$	−16.1852	+	28.0335i	−0.709084	+	1.22817i	0.256113	+	0.966647i	$0.417558\pi$
$521$	−16.1852	+	28.0335i	−0.709084	+	1.22817i	−0.965197	+	0.261523i	$0.915775\pi$
$522$		0			0
$523$	−3.05616	−	40.7816i	−0.133637	−	1.78326i	−0.513378	−	0.858163i	$-0.671606\pi$
$523$	−3.05616	−	40.7816i	−0.133637	−	1.78326i	0.379741	−	0.925093i	$-0.376013\pi$
$524$	−0.00682918	+	0.00856352i	−0.000298334	+	0.000374099i
$525$		0			0
$526$	1.25939	+	1.57923i	0.0549122	+	0.0688577i
$527$	0.0916876	−	0.0850737i	0.00399397	−	0.00370587i
$528$		0			0
$529$	7.64577	−	5.21280i	0.332425	−	0.226643i
$530$	−45.5965	−	6.87257i	−1.98059	−	0.298525i
$531$		0			0
$532$	1.19650	−	1.81586i	0.0518746	−	0.0787273i
$533$	−10.9921	−	5.29350i	−0.476119	−	0.229287i
$534$		0			0
$535$	41.6958	+	38.6880i	1.80267	+	1.67263i
$536$	2.12570	−	28.3655i	0.0918163	−	1.22520i
$537$		0			0
$538$	3.03772			0.130965
$539$	−37.1764	−	23.6633i	−1.60130	−	1.01925i
$540$		0			0
$541$	−7.72213	+	19.6757i	−0.332000	+	0.845923i	0.663234	+	0.748412i	$0.269183\pi$
$541$	−7.72213	+	19.6757i	−0.332000	+	0.845923i	−0.995234	+	0.0975108i	$0.968912\pi$
$542$	3.15220	−	42.0632i	0.135399	−	1.80677i
$543$		0			0
$544$	−0.0671441	−	0.0457780i	−0.00287878	−	0.00196272i
$545$	−6.23775	−	3.00394i	−0.267196	−	0.128675i
$546$		0			0
$547$	−7.90014	+	3.80451i	−0.337786	+	0.162669i	−0.595085	−	0.803663i	$-0.702882\pi$
$547$	−7.90014	+	3.80451i	−0.337786	+	0.162669i	0.257299	+	0.966332i	$0.417167\pi$
$548$	−0.406426	−	0.0612588i	−0.0173616	−	0.00261685i
$549$		0			0
$550$	66.9141	−	10.0857i	2.85323	−	0.430055i
$551$	−1.14223	+	1.05983i	−0.0486605	+	0.0451504i
$552$		0			0
$553$	−0.122330	−	0.732930i	−0.00520201	−	0.0311674i
$554$	−6.41598	+	8.04539i	−0.272589	+	0.341816i
$555$		0			0
$556$	−3.61555	−	1.11525i	−0.153334	−	0.0472971i
$557$	9.62919	−	16.6782i	0.408002	−	0.706680i	−0.586664	−	0.809831i	$-0.699559\pi$
$557$	9.62919	−	16.6782i	0.408002	−	0.706680i	0.994666	+	0.103150i	$0.0328923\pi$
$558$		0			0
$559$	−0.707429	−	3.09945i	−0.0299211	−	0.131093i
$560$	−26.1676	+	21.5522i	−1.10578	+	0.910747i
$561$		0			0
$562$	26.1442	−	8.06443i	1.10283	−	0.340177i
$563$	−9.63275	−	24.5439i	−0.405972	−	1.03440i	−0.976956	−	0.213439i	$-0.931534\pi$
$563$	−9.63275	−	24.5439i	−0.405972	−	1.03440i	0.570984	−	0.820961i	$-0.306562\pi$
$564$		0			0
$565$	−25.1806	+	7.76719i	−1.05936	+	0.326768i
$566$	4.82660	−	21.1467i	0.202877	−	0.888863i
$567$		0			0
$568$	9.98537	+	43.7488i	0.418977	+	1.83566i
$569$	15.7697	+	27.3139i	0.661099	+	1.14506i	0.980327	+	0.197379i	$0.0632429\pi$
$569$	15.7697	+	27.3139i	0.661099	+	1.14506i	−0.319229	+	0.947678i	$0.603424\pi$
$570$		0			0
$571$	32.4957	+	10.0236i	1.35990	+	0.419475i	0.887053	−	0.461667i	$-0.152749\pi$
$571$	32.4957	+	10.0236i	1.35990	+	0.419475i	0.472851	+	0.881142i	$0.343225\pi$
$572$	−0.357742	−	4.77374i	−0.0149580	−	0.199600i
$573$		0			0
$574$	−3.24157	+	11.1295i	−0.135301	+	0.464538i
$575$	28.3989	+	35.6111i	1.18432	+	1.48508i
$576$		0			0
$577$	20.0642	−	3.02419i	0.835283	−	0.125899i	0.282546	−	0.959254i	$-0.408821\pi$
$577$	20.0642	−	3.02419i	0.835283	−	0.125899i	0.552738	+	0.833355i	$0.313583\pi$
$578$	18.8196	−	12.8310i	0.782791	−	0.533698i
$579$		0			0
$580$	−0.255861	+	0.123216i	−0.0106240	+	0.00511627i
$581$	4.91345	−	2.94113i	0.203844	−	0.122019i
$582$		0			0
$583$	−49.5969	−	33.8146i	−2.05409	−	1.40046i
$584$	−1.37412	−	1.27500i	−0.0568615	−	0.0527598i
$585$		0			0
$586$	−3.33885	+	8.50726i	−0.137927	+	0.351432i
$587$	−1.56463			−0.0645794			−0.0322897	−	0.999479i	$-0.510280\pi$
$587$	−1.56463			−0.0645794			−0.0322897	+	0.999479i	$0.510280\pi$
$588$		0			0
$589$	7.12733			0.293676
$590$	−18.7555	+	47.7883i	−0.772153	+	1.96741i
$591$		0			0
$592$	3.54899	+	3.29299i	0.145863	+	0.135341i
$593$	−7.79412	−	5.31394i	−0.320066	−	0.218217i	0.392619	−	0.919701i	$-0.371569\pi$
$593$	−7.79412	−	5.31394i	−0.320066	−	0.218217i	−0.712686	+	0.701484i	$0.752521\pi$
$594$		0			0
$595$	−0.209371	−	0.642582i	−0.00858338	−	0.0263433i
$596$	0.849805	−	0.409244i	0.0348094	−	0.0167633i
$597$		0			0
$598$	−23.4705	+	16.0019i	−0.959781	+	0.654367i
$599$	−6.65884	+	1.00366i	−0.272073	+	0.0410084i	−0.283661	−	0.958924i	$-0.591549\pi$
$599$	−6.65884	+	1.00366i	−0.272073	+	0.0410084i	0.0115888	+	0.999933i	$0.496311\pi$
$600$		0			0
$601$	−10.9938	−	13.7857i	−0.448445	−	0.562332i	0.505302	−	0.862942i	$-0.331381\pi$
$601$	−10.9938	−	13.7857i	−0.448445	−	0.562332i	−0.953747	+	0.300611i	$0.902810\pi$
$602$	−2.79408	+	1.14780i	−0.113878	+	0.0467809i
$603$		0			0
$604$	0.0574102	+	0.766085i	0.00233599	+	0.0311716i
$605$	98.7287	+	30.4538i	4.01389	+	1.23812i
$606$		0			0
$607$	0.800945	+	1.38728i	0.0325094	+	0.0563079i	0.881822	−	0.471582i	$-0.156317\pi$
$607$	0.800945	+	1.38728i	0.0325094	+	0.0563079i	−0.849313	+	0.527890i	$0.822983\pi$
$608$	−1.03044	−	4.51466i	−0.0417900	−	0.183094i
$609$		0			0
$610$	−11.8721	+	52.0152i	−0.480689	+	2.10603i
$611$	−7.34476	+	2.26556i	−0.297137	+	0.0916547i
$612$		0			0
$613$	4.78188	+	12.1840i	0.193138	+	0.492109i	0.994335	−	0.106293i	$-0.0338980\pi$
$613$	4.78188	+	12.1840i	0.193138	+	0.492109i	−0.801196	+	0.598401i	$0.795803\pi$
$614$	−36.4689	+	11.2492i	−1.47177	+	0.453980i
$615$		0			0
$616$	−47.7833	+	11.7025i	−1.92524	+	0.471509i
$617$	−1.54098	−	6.75148i	−0.0620376	−	0.271804i	0.934390	−	0.356251i	$-0.115945\pi$
$617$	−1.54098	−	6.75148i	−0.0620376	−	0.271804i	−0.996428	+	0.0844461i	$0.973088\pi$
$618$		0			0
$619$	14.1428	−	24.4960i	0.568446	−	0.984578i	−0.428274	−	0.903649i	$-0.640878\pi$
$619$	14.1428	−	24.4960i	0.568446	−	0.984578i	0.996720	−	0.0809288i	$-0.0257886\pi$
$620$	1.24127	+	0.382882i	0.0498507	+	0.0153769i
$621$		0			0
$622$	7.94924	−	9.96803i	0.318735	−	0.399682i
$623$	9.26336	+	5.15503i	0.371129	+	0.206532i
$624$		0			0
$625$	0.570332	−	0.529190i	0.0228133	−	0.0211676i
$626$	−28.2023	+	4.25081i	−1.12719	+	0.169896i
$627$		0			0
$628$	−0.626901	−	0.0944901i	−0.0250161	−	0.00377057i
$629$	−0.0869587	+	0.0418771i	−0.00346727	+	0.00166975i
$630$		0			0
$631$	31.2036	+	15.0268i	1.24219	+	0.598209i	0.935408	−	0.353569i	$-0.115032\pi$
$631$	31.2036	+	15.0268i	1.24219	+	0.598209i	0.306786	+	0.951779i	$0.400746\pi$
$632$	−0.685380	−	0.467284i	−0.0272629	−	0.0185876i
$633$		0			0
$634$	0.0652181	−	0.870276i	0.00259014	−	0.0345631i
$635$	−17.3241	+	44.1411i	−0.687486	+	1.75169i
$636$		0			0
$637$	−1.12917	+	26.0997i	−0.0447394	+	1.03411i
$638$	3.25911			0.129030
$639$		0			0
$640$	−2.50357	+	33.4078i	−0.0989623	+	1.32056i
$641$	−33.8835	−	31.4393i	−1.33832	−	1.24178i	−0.946885	−	0.321573i	$-0.895788\pi$
$641$	−33.8835	−	31.4393i	−1.33832	−	1.24178i	−0.391435	−	0.920206i	$-0.628021\pi$
$642$		0			0
$643$	−20.5414	−	9.89221i	−0.810073	−	0.390111i	−0.0174691	−	0.999847i	$-0.505561\pi$
$643$	−20.5414	−	9.89221i	−0.810073	−	0.390111i	−0.792604	+	0.609737i	$0.791275\pi$
$644$	−2.11753	−	2.21112i	−0.0834424	−	0.0871305i
$645$		0			0
$646$	−0.378459	−	0.0570435i	−0.0148903	−	0.00224434i
$647$	−3.88520	+	2.64889i	−0.152743	+	0.104139i	−0.637280	−	0.770632i	$-0.719941\pi$
$647$	−3.88520	+	2.64889i	−0.152743	+	0.104139i	0.484537	+	0.874771i	$0.338988\pi$
$648$		0			0
$649$	−48.9897	+	45.4558i	−1.92301	+	1.78430i
$650$	−25.0114	−	31.3633i	−0.981029	−	1.23017i
$651$		0			0
$652$	−0.892155	+	1.11873i	−0.0349395	+	0.0438127i
$653$	−1.81888	−	24.2713i	−0.0711784	−	0.949809i	−0.912448	−	0.409193i	$-0.865810\pi$
$653$	−1.81888	−	24.2713i	−0.0711784	−	0.949809i	0.841269	−	0.540616i	$-0.181809\pi$
$654$		0			0
$655$	−0.0969876	+	0.167988i	−0.00378962	+	0.00656381i
$656$	5.80423	+	10.0532i	0.226617	+	0.392512i
$657$		0			0
$658$	3.27210	+	6.52897i	0.127560	+	0.254526i
$659$	6.27850	−	27.5079i	0.244576	−	1.07156i	−0.692222	−	0.721685i	$-0.743368\pi$
$659$	6.27850	−	27.5079i	0.244576	−	1.07156i	0.936798	−	0.349871i	$-0.113775\pi$
$660$		0			0
$661$	14.8443	+	37.8226i	0.577375	+	1.47113i	0.859189	+	0.511659i	$0.170969\pi$
$661$	14.8443	+	37.8226i	0.577375	+	1.47113i	−0.281814	+	0.959469i	$0.590936\pi$
$662$	−4.31896	−	11.0045i	−0.167861	−	0.427703i
$663$		0			0
$664$	1.42250	−	6.23240i	0.0552039	−	0.241864i
$665$	16.1598	−	34.9569i	0.626651	−	1.35557i
$666$		0			0
$667$	1.09685	+	1.89979i	0.0424701	+	0.0735603i
$668$	0.254660	−	0.441085i	0.00985311	−	0.0170661i
$669$		0			0
$670$	−3.48055	−	46.4447i	−0.134465	−	1.79431i
$671$	−43.3038	+	54.3013i	−1.67173	+	2.09628i
$672$		0			0
$673$	17.1689	+	21.5292i	0.661814	+	0.829888i	0.993539	−	0.113488i	$-0.0362023\pi$
$673$	17.1689	+	21.5292i	0.661814	+	0.829888i	−0.331726	+	0.943376i	$0.607631\pi$
$674$	7.92211	−	7.35065i	0.305148	−	0.283136i
$675$		0			0
$676$	−0.156221	+	0.106510i	−0.00600851	+	0.00409653i
$677$	46.8415	+	7.06022i	1.80027	+	0.271346i	0.961829	−	0.273652i	$-0.0882315\pi$
$677$	46.8415	+	7.06022i	1.80027	+	0.271346i	0.838437	+	0.544998i	$0.183470\pi$
$678$		0			0
$679$	3.96580	+	1.48467i	0.152193	+	0.0569765i
$680$	−0.679743	−	0.327347i	−0.0260669	−	0.0125532i
$681$		0			0
$682$	−10.9281	−	10.1398i	−0.418457	−	0.388271i
$683$	0.986522	−	13.1642i	0.0377482	−	0.503715i	−0.946001	−	0.324165i	$-0.894917\pi$
$683$	0.986522	−	13.1642i	0.0377482	−	0.503715i	0.983749	−	0.179550i	$-0.0574642\pi$
$684$		0			0
$685$	−7.27891			−0.278113
$686$	24.6367	−	3.02429i	0.940634	−	0.115468i
$687$		0			0
$688$	−1.10513	+	2.81584i	−0.0421328	+	0.107353i
$689$	−2.65924	+	35.4851i	−0.101309	+	1.35188i
$690$		0			0
$691$	−28.7437	−	19.5971i	−1.09346	−	0.745510i	−0.124376	−	0.992235i	$-0.539693\pi$
$691$	−28.7437	−	19.5971i	−1.09346	−	0.745510i	−0.969085	+	0.246726i	$0.920645\pi$
$692$	−0.169320	−	0.0815403i	−0.00643659	−	0.00309970i
$693$		0			0
$694$	38.1380	−	18.3663i	1.44770	−	0.697175i
$695$	−66.2583	−	9.98683i	−2.51332	−	0.378822i
$696$		0			0
$697$	−0.228838	+	0.0344919i	−0.00866788	+	0.00130647i
$698$	10.8144	−	10.0343i	0.409330	−	0.379803i
$699$		0			0
$700$	2.89032	−	3.21533i	0.109244	−	0.121528i
$701$	−23.5564	+	29.5387i	−0.889711	+	1.11566i	0.102944	+	0.994687i	$0.467174\pi$
$701$	−23.5564	+	29.5387i	−0.889711	+	1.11566i	−0.992656	+	0.120975i	$0.961398\pi$
$702$		0			0
$703$	−5.25555	−	1.62112i	−0.198217	−	0.0611418i
$704$	−27.1981	+	47.1085i	−1.02507	+	1.77547i
$705$		0			0
$706$	7.30191	+	31.9918i	0.274811	+	1.20403i
$707$	−9.21142	+	19.9261i	−0.346431	+	0.749400i
$708$		0			0
$709$	14.5590	−	4.49086i	0.546776	−	0.168658i	−0.00904664	−	0.999959i	$-0.502880\pi$
$709$	14.5590	−	4.49086i	0.546776	−	0.168658i	0.555822	+	0.831301i	$0.312403\pi$
$710$	26.8434	+	68.3958i	1.00741	+	2.56685i
$711$		0			0
$712$	11.3087	−	3.48828i	0.423812	−	0.130729i
$713$	2.23283	−	9.78266i	0.0836201	−	0.366364i
$714$		0			0
$715$	−18.8648	−	82.6522i	−0.705505	−	3.09102i
$716$	1.75762	+	3.04429i	0.0656854	+	0.113771i
$717$		0			0
$718$	−32.5606	−	10.0436i	−1.21515	−	0.374825i
$719$	0.623511	+	8.32017i	0.0232530	+	0.310290i	0.996688	+	0.0813249i	$0.0259151\pi$
$719$	0.623511	+	8.32017i	0.0232530	+	0.310290i	−0.973435	+	0.228965i	$0.926466\pi$
$720$		0			0
$721$	−7.64570	−	10.8425i	−0.284741	−	0.403796i
$722$	2.27887	+	2.85761i	0.0848107	+	0.106349i
$723$		0			0
$724$	2.80420	−	0.422665i	0.104217	−	0.0157082i
$725$	−2.55961	+	1.74511i	−0.0950615	+	0.0648118i
$726$		0			0
$727$	−17.4740	+	8.41502i	−0.648074	+	0.312096i	−0.728888	−	0.684633i	$-0.759962\pi$
$727$	−17.4740	+	8.41502i	−0.648074	+	0.312096i	0.0808138	+	0.996729i	$0.474248\pi$
$728$	20.1711	+	21.0626i	0.747590	+	0.780633i
$729$		0			0
$730$	−2.53595	−	1.72898i	−0.0938598	−	0.0639925i
$731$	−0.0442063	−	0.0410174i	−0.00163503	−	0.00151708i
$732$		0			0
$733$	−11.6768	+	29.7521i	−0.431293	+	1.09892i	0.535766	+	0.844367i	$0.320023\pi$
$733$	−11.6768	+	29.7521i	−0.431293	+	1.09892i	−0.967059	+	0.254551i	$0.918072\pi$
$734$	8.83485			0.326100
$735$		0			0
$736$	−6.51944			−0.240310
$737$	22.1508	−	56.4394i	0.815936	−	2.07897i
$738$		0			0
$739$	−15.8559	−	14.7121i	−0.583269	−	0.541195i	0.332394	−	0.943141i	$-0.392144\pi$
$739$	−15.8559	−	14.7121i	−0.583269	−	0.541195i	−0.915663	+	0.401946i	$0.868334\pi$
$740$	−0.828202	−	0.564658i	−0.0304453	−	0.0207573i
$741$		0			0
$742$	33.6718	−	3.05841i	1.23613	−	0.112278i
$743$	42.8292	−	20.6254i	1.57125	−	0.756674i	0.573219	−	0.819402i	$-0.305694\pi$
$743$	42.8292	−	20.6254i	1.57125	−	0.756674i	0.998031	+	0.0627278i	$0.0199800\pi$
$744$		0			0
$745$	13.8014	−	9.40962i	0.505643	−	0.344742i
$746$	23.8680	−	3.59752i	0.873870	−	0.131715i
$747$		0			0
$748$	−0.0566163	−	0.0709946i	−0.00207010	−	0.00259582i
$749$	−36.4430	−	20.2804i	−1.33160	−	0.741031i
$750$		0			0
$751$	3.69930	+	49.3637i	0.134989	+	1.80131i	0.495558	+	0.868575i	$0.334963\pi$
$751$	3.69930	+	49.3637i	0.134989	+	1.80131i	−0.360569	+	0.932732i	$0.617418\pi$
$752$	6.98847	+	2.15566i	0.254843	+	0.0786088i
$753$		0			0
$754$	−0.966013	−	1.67318i	−0.0351801	−	0.0609338i
$755$	3.02741	+	13.2640i	0.110179	+	0.482725i
$756$		0			0
$757$	12.0409	−	52.7547i	0.437634	−	1.91740i	0.0416789	−	0.999131i	$-0.486729\pi$
$757$	12.0409	−	52.7547i	0.437634	−	1.91740i	0.395955	−	0.918270i	$-0.370413\pi$
$758$	6.65432	−	2.05258i	0.241696	−	0.0745532i
$759$		0			0
$760$	−15.7067	−	40.0199i	−0.569741	−	1.45168i
$761$	−14.1733	+	4.37188i	−0.513781	+	0.158480i	−0.540795	−	0.841155i	$-0.681876\pi$
$761$	−14.1733	+	4.37188i	−0.513781	+	0.158480i	0.0270136	+	0.999635i	$0.491400\pi$
$762$		0			0
$763$	4.96637	+	1.05137i	0.179795	+	0.0380622i
$764$	0.244710	+	1.07214i	0.00885330	+	0.0387888i
$765$		0			0
$766$	20.5859	−	35.6558i	0.743799	−	1.28830i
$767$	37.8571	+	11.6774i	1.36694	+	0.421645i
$768$		0			0
$769$	18.6323	−	23.3642i	0.671898	−	0.842534i	−0.322682	−	0.946507i	$-0.604584\pi$
$769$	18.6323	−	23.3642i	0.671898	−	0.842534i	0.994580	+	0.103974i	$0.0331558\pi$
$770$	−74.5090	+	30.6082i	−2.68512	+	1.10304i
$771$		0			0
$772$	3.57164	−	3.31400i	0.128546	−	0.119273i
$773$	−7.14748	+	1.07731i	−0.257077	+	0.0387481i	−0.276316	−	0.961067i	$-0.589114\pi$
$773$	−7.14748	+	1.07731i	−0.257077	+	0.0387481i	0.0192392	+	0.999815i	$0.493876\pi$
$774$		0			0
$775$	14.0120	+	2.11196i	0.503324	+	0.0758639i
$776$	4.25911	−	2.05108i	0.152893	−	0.0736294i
$777$		0			0
$778$	−26.3503	−	12.6897i	−0.944705	−	0.454946i
$779$	−10.8959	−	7.42870i	−0.390386	−	0.266161i
$780$		0			0
$781$	−7.14781	+	95.3809i	−0.255769	+	3.41300i
$782$	−0.196858	+	0.501586i	−0.00703962	+	0.0179367i
$783$		0			0
$784$	14.8770	−	19.9133i	0.531321	−	0.711189i
$785$	−11.2275			−0.400728
$786$		0			0
$787$	−1.04280	+	13.9152i	−0.0371717	+	0.496023i	0.947285	+	0.320393i	$0.103815\pi$
$787$	−1.04280	+	13.9152i	−0.0371717	+	0.496023i	−0.984456	+	0.175629i	$0.943804\pi$
$788$	0.664458	+	0.616527i	0.0236703	+	0.0219629i
$789$		0			0
$790$	−1.22372	−	0.589311i	−0.0435379	−	0.0209667i
$791$	16.5785	−	9.92367i	0.589463	−	0.352845i
$792$		0			0
$793$	40.7130	+	6.13649i	1.44576	+	0.217913i
$794$	−10.7190	+	7.30811i	−0.380404	+	0.259355i
$795$		0			0
$796$	3.52506	−	3.27077i	0.124942	−	0.115929i
$797$	25.5021	+	31.9786i	0.903330	+	1.13274i	0.990632	+	0.136558i	$0.0436041\pi$
$797$	25.5021	+	31.9786i	0.903330	+	1.13274i	−0.0873019	+	0.996182i	$0.527824\pi$
$798$		0			0
$799$	−0.0909035	+	0.113989i	−0.00321593	+	0.00403265i
$800$	−0.688016	−	9.18093i	−0.0243250	−	0.324595i
$801$		0			0
$802$	−21.7638	+	37.6961i	−0.768508	+	1.33109i
$803$	−1.99777	−	3.46023i	−0.0704997	−	0.122109i
$804$		0			0
$805$	−42.9178	−	33.1315i	−1.51266	−	1.16773i
$806$	−1.96649	+	8.61577i	−0.0692668	+	0.303478i
$807$		0			0
$808$	8.95312	+	22.8122i	0.314970	+	0.802530i
$809$	−10.1735	−	25.9216i	−0.357681	−	0.911356i	−0.990557	−	0.137103i	$-0.956221\pi$
$809$	−10.1735	−	25.9216i	−0.357681	−	0.911356i	0.632876	−	0.774253i	$-0.281874\pi$
$810$		0			0
$811$	5.65682	−	24.7841i	0.198638	−	0.870289i	−0.773111	−	0.634271i	$-0.781300\pi$
$811$	5.65682	−	24.7841i	0.198638	−	0.870289i	0.971749	−	0.236018i	$-0.0758425\pi$
$812$	0.160729	−	0.132380i	0.00564047	−	0.00464562i
$813$		0			0
$814$	5.75182	+	9.96245i	0.201601	+	0.349184i
$815$	−12.6703	+	21.9457i	−0.443823	+	0.768724i
$816$		0			0
$817$	−0.256800	−	3.42676i	−0.00898430	−	0.119887i
$818$	22.0986	−	27.7107i	0.772658	−	0.968883i
$819$		0			0
$820$	−1.49852	−	1.87909i	−0.0523307	−	0.0656206i
$821$	21.2142	−	19.6839i	0.740381	−	0.686973i	−0.216880	−	0.976198i	$-0.569588\pi$
$821$	21.2142	−	19.6839i	0.740381	−	0.686973i	0.957261	+	0.289225i	$0.0933976\pi$
$822$		0			0
$823$	11.0759	−	7.55144i	0.386082	−	0.263227i	−0.354688	−	0.934985i	$-0.615413\pi$
$823$	11.0759	−	7.55144i	0.386082	−	0.263227i	0.740771	+	0.671758i	$0.234461\pi$
$824$	−14.6452	−	2.20741i	−0.510190	−	0.0768988i
$825$		0			0
$826$	5.02215	−	37.3054i	0.174743	−	1.29802i
$827$	0.718822	+	0.346166i	0.0249959	+	0.0120374i	0.446340	−	0.894863i	$-0.352727\pi$
$827$	0.718822	+	0.346166i	0.0249959	+	0.0120374i	−0.421344	+	0.906901i	$0.638442\pi$
$828$		0			0
$829$	−19.4500	−	18.0470i	−0.675528	−	0.626798i	0.265905	−	0.963999i	$-0.414329\pi$
$829$	−19.4500	−	18.0470i	−0.675528	−	0.626798i	−0.941433	+	0.337201i	$0.890520\pi$
$830$	0.782210	−	10.4379i	0.0271509	−	0.362304i
$831$		0			0
$832$	32.2465			1.11795
$833$	0.261190	+	0.421118i	0.00904970	+	0.0145909i
$834$		0			0
$835$	3.29532	−	8.39633i	0.114039	−	0.290567i
$836$	0.386686	−	5.15997i	0.0133738	−	0.178461i
$837$		0			0
$838$	36.6154	+	24.9640i	1.26486	+	0.862366i
$839$	−40.8113	−	19.6537i	−1.40896	−	0.678521i	−0.434006	−	0.900910i	$-0.642900\pi$
$839$	−40.8113	−	19.6537i	−1.40896	−	0.678521i	−0.974958	+	0.222389i	$0.928615\pi$
$840$		0			0
$841$	25.9937	−	12.5179i	0.896334	−	0.431651i
$842$	33.5703	+	5.05992i	1.15691	+	0.174376i
$843$		0			0
$844$	1.02087	−	0.153871i	0.0351398	−	0.00529647i
$845$	−2.45458	+	2.27751i	−0.0844400	+	0.0783489i
$846$		0			0
$847$	−75.6248	−	4.46844i	−2.59850	−	0.153537i
$848$	21.1104	−	26.4716i	0.724935	−	0.909039i
$849$		0			0
$850$	−0.727127	−	0.224289i	−0.0249403	−	0.00769305i
$851$	−3.87152	+	6.70568i	−0.132714	+	0.229868i
$852$		0			0
$853$	−4.58823	−	20.1024i	−0.157098	−	0.688291i	−0.990716	−	0.135950i	$-0.956591\pi$
$853$	−4.58823	−	20.1024i	−0.157098	−	0.688291i	0.833618	−	0.552342i	$-0.186266\pi$
$854$	−0.617348	−	39.1151i	−0.0211252	−	1.33849i
$855$		0			0
$856$	−44.4897	+	13.7232i	−1.52063	+	0.469051i
$857$	3.25136	+	8.28434i	0.111064	+	0.282988i	0.975590	−	0.219602i	$-0.0704759\pi$
$857$	3.25136	+	8.28434i	0.111064	+	0.282988i	−0.864525	+	0.502590i	$0.832381\pi$
$858$		0			0
$859$	16.6377	−	5.13206i	0.567672	−	0.175104i	0.00238369	−	0.999997i	$-0.499241\pi$
$859$	16.6377	−	5.13206i	0.567672	−	0.175104i	0.565288	+	0.824894i	$0.308765\pi$
$860$	0.139363	−	0.610589i	0.00475224	−	0.0208209i
$861$		0			0
$862$	−2.23021	−	9.77119i	−0.0759613	−	0.332808i
$863$	−19.2424	−	33.3288i	−0.655019	−	1.13453i	−0.981889	−	0.189457i	$-0.939327\pi$
$863$	−19.2424	−	33.3288i	−0.655019	−	1.13453i	0.326870	−	0.945069i	$-0.394006\pi$
$864$		0			0
$865$	−3.18031	−	0.980997i	−0.108134	−	0.0333549i
$866$	−1.16816	−	15.5880i	−0.0396956	−	0.529700i
$867$		0			0
$868$	−0.950796	−	0.0561796i	−0.0322721	−	0.00190686i
$869$	−1.10240	−	1.38237i	−0.0373964	−	0.0468936i
$870$		0			0
$871$	−35.5408	+	5.35691i	−1.20425	+	0.181512i
$872$	4.68233	−	3.19236i	0.158564	−	0.108107i
$873$		0			0
$874$	−27.6640	+	13.3223i	−0.935748	+	0.450633i
$875$	15.8640	−	24.0760i	0.536302	−	0.813917i
$876$		0			0
$877$	17.0172	+	11.6021i	0.574629	+	0.391775i	0.815479	−	0.578787i	$-0.196474\pi$
$877$	17.0172	+	11.6021i	0.574629	+	0.391775i	−0.240850	+	0.970562i	$0.577426\pi$
$878$	−13.5167	−	12.5417i	−0.456167	−	0.423261i
$879$		0			0
$880$	−29.4703	+	75.0892i	−0.993445	+	2.53126i
$881$	−34.5649			−1.16452			−0.582260	−	0.813003i	$-0.697831\pi$
$881$	−34.5649			−1.16452			−0.582260	+	0.813003i	$0.697831\pi$
$882$		0			0
$883$	−39.8213			−1.34009			−0.670047	−	0.742319i	$-0.733726\pi$
$883$	−39.8213			−1.34009			−0.670047	+	0.742319i	$0.733726\pi$
$884$	−0.0196664	+	0.0501091i	−0.000661451	+	0.00168535i
$885$		0			0
$886$	−15.0613	−	13.9748i	−0.505994	−	0.469494i
$887$	41.1218	+	28.0364i	1.38073	+	0.941369i	0.999860	+	0.0167423i	$0.00532947\pi$
$887$	41.1218	+	28.0364i	1.38073	+	0.941369i	0.380875	+	0.924627i	$0.375623\pi$
$888$		0			0
$889$	4.63886	−	34.4582i	0.155582	−	1.15569i
$890$	17.4584	−	8.40752i	0.585207	−	0.281821i
$891$		0			0
$892$	3.65045	−	2.48884i	0.122226	−	0.0833324i
$893$	−8.21531	+	1.23826i	−0.274915	+	0.0414368i
$894$		0			0
$895$	38.8143	+	48.6717i	1.29742	+	1.62691i
$896$	−4.04399	−	24.2292i	−0.135100	−	0.809441i
$897$		0			0
$898$	−0.511605	−	6.82690i	−0.0170725	−	0.227816i
$899$	0.652145	+	0.201160i	0.0217503	+	0.00670907i
$900$		0			0
$901$	0.337497	+	0.584562i	0.0112437	+	0.0194746i
$902$	6.13777	+	26.8913i	0.204365	+	0.895383i
$903$		0			0
$904$	4.79967	−	21.0287i	0.159635	−	0.699405i
$905$	47.9908	−	14.8032i	1.59527	−	0.492075i
$906$		0			0
$907$	0.222184	+	0.566116i	0.00737751	+	0.0187976i	0.934515	−	0.355924i	$-0.115834\pi$
$907$	0.222184	+	0.566116i	0.00737751	+	0.0187976i	−0.927138	+	0.374721i	$0.877738\pi$
$908$	−3.56354	+	1.09921i	−0.118260	+	0.0364785i
$909$		0			0
$910$	37.7986	+	29.1795i	1.25301	+	0.967291i
$911$	1.68869	+	7.39862i	0.0559487	+	0.245127i	0.995167	−	0.0981920i	$-0.0313059\pi$
$911$	1.68869	+	7.39862i	0.0559487	+	0.245127i	−0.939219	+	0.343319i	$0.888449\pi$
$912$		0			0
$913$	6.81298	−	11.8004i	0.225477	−	0.390537i
$914$	15.2036	+	4.68968i	0.502889	+	0.155121i
$915$		0			0
$916$	−2.63765	+	3.30751i	−0.0871505	+	0.109283i
$917$	0.0397727	−	0.136555i	0.00131341	−	0.00450943i
$918$		0			0
$919$	25.4876	−	23.6490i	0.840757	−	0.780109i	−0.136840	−	0.990593i	$-0.543695\pi$
$919$	25.4876	−	23.6490i	0.840757	−	0.780109i	0.977597	+	0.210485i	$0.0675042\pi$
$920$	−59.8502	+	9.02096i	−1.97320	+	0.297412i
$921$		0			0
$922$	28.7290	+	4.33020i	0.946138	+	0.142607i
$923$	51.0859	−	24.6017i	1.68151	−	0.809774i
$924$		0			0
$925$	−9.85176	−	4.74436i	−0.323924	−	0.155994i
$926$	−28.4060	−	19.3669i	−0.933480	−	0.636436i
$927$		0			0
$928$	0.0331362	−	0.442171i	0.00108775	−	0.0145150i
$929$	−9.61766	+	24.5054i	−0.315545	+	0.803996i	0.681825	+	0.731516i	$0.261187\pi$
$929$	−9.61766	+	24.5054i	−0.315545	+	0.803996i	−0.997370	+	0.0724803i	$0.976909\pi$
$930$		0			0
$931$	−5.41158	+	27.7143i	−0.177357	+	0.908301i
$932$	−2.07224			−0.0678784
$933$		0			0
$934$	0.999144	−	13.3326i	0.0326930	−	0.436258i
$935$	−1.17884	−	1.09380i	−0.0385521	−	0.0357711i
$936$		0			0
$937$	30.3226	+	14.6026i	0.990595	+	0.477045i	0.857736	−	0.514090i	$-0.171870\pi$
$937$	30.3226	+	14.6026i	0.990595	+	0.477045i	0.132858	+	0.991135i	$0.457584\pi$
$938$	10.5797	+	32.4701i	0.345438	+	1.06019i
$939$		0			0
$940$	−1.49727	−	0.225677i	−0.0488356	−	0.00736078i
$941$	14.3523	−	9.78524i	0.467872	−	0.318990i	−0.306333	−	0.951924i	$-0.599102\pi$
$941$	14.3523	−	9.78524i	0.467872	−	0.318990i	0.774205	+	0.632935i	$0.218150\pi$
$942$		0			0
$943$	−13.6098	+	12.6280i	−0.443195	+	0.411225i
$944$	−23.5027	−	29.4714i	−0.764947	−	0.959214i
$945$		0			0
$946$	−4.48137	+	5.61946i	−0.145702	+	0.182704i
$947$	0.155232	+	2.07142i	0.00504436	+	0.0673122i	0.999158	−	0.0410314i	$-0.0130644\pi$
$947$	0.155232	+	2.07142i	0.00504436	+	0.0673122i	−0.994114	+	0.108344i	$0.965445\pi$
$948$		0			0
$949$	−1.18429	+	2.05125i	−0.0384437	+	0.0665865i
$950$	−21.6804	−	37.5516i	−0.703405	−	1.21833i
$951$		0			0
$952$	0.541198	+	0.114571i	0.0175403	+	0.00371325i
$953$	−3.62424	+	15.8788i	−0.117401	+	0.514365i	0.881694	+	0.471821i	$0.156403\pi$
$953$	−3.62424	+	15.8788i	−0.117401	+	0.514365i	−0.999095	+	0.0425437i	$0.986454\pi$
$954$		0			0
$955$	7.11519	+	18.1292i	0.230242	+	0.586648i
$956$	−0.867290	−	2.20982i	−0.0280502	−	0.0714706i
$957$		0			0
$958$	−6.51202	+	28.5310i	−0.210394	+	0.921796i
$959$	5.18393	−	1.26959i	0.167398	−	0.0409971i
$960$		0			0
$961$	13.9392	+	24.1433i	0.449650	+	0.778817i
$962$	3.40972	−	5.90582i	0.109934	−	0.190411i
$963$		0			0
$964$	−0.272954	−	3.64231i	−0.00879124	−	0.117311i
$965$	53.7984	−	67.4611i	1.73183	−	2.17165i
$966$		0			0
$967$	14.9597	+	18.7589i	0.481071	+	0.603244i	0.961843	−	0.273602i	$-0.0882150\pi$
$967$	14.9597	+	18.7589i	0.481071	+	0.603244i	−0.480772	+	0.876846i	$0.659644\pi$
$968$	−61.9944	+	57.5224i	−1.99258	+	1.84884i
$969$		0			0
$970$	6.39528	−	4.36023i	0.205340	−	0.139999i
$971$	40.9260	+	6.16861i	1.31338	+	0.197960i	0.768119	−	0.640307i	$-0.221193\pi$
$971$	40.9260	+	6.16861i	1.31338	+	0.197960i	0.545260	+	0.838267i	$0.316431\pi$
$972$		0			0
$973$	48.9300	−	4.44431i	1.56862	−	0.142478i
$974$	22.8035	+	10.9816i	0.730672	+	0.351873i
$975$		0			0
$976$	−28.7177	−	26.6462i	−0.919232	−	0.852923i
$977$	−4.35946	+	58.1729i	−0.139471	+	1.86112i	0.288700	+	0.957420i	$0.406777\pi$
$977$	−4.35946	+	58.1729i	−0.139471	+	1.86112i	−0.428171	+	0.903698i	$0.640842\pi$
$978$		0			0
$979$	25.2252			0.806199
$980$	−2.43128	+	4.53593i	−0.0776645	+	0.144895i
$981$		0			0
$982$	−3.46506	+	8.82884i	−0.110575	+	0.281740i
$983$	3.94672	−	52.6654i	0.125881	−	1.67976i	−0.474659	−	0.880170i	$-0.657429\pi$
$983$	3.94672	−	52.6654i	0.125881	−	1.67976i	0.600540	−	0.799595i	$-0.294952\pi$
$984$		0			0
$985$	13.2631	+	9.04264i	0.422598	+	0.288122i
$986$	−0.0330187	−	0.0159010i	−0.00105153	−	0.000506390i
$987$		0			0
$988$	−2.76367	+	1.33091i	−0.0879241	+	0.0423420i
$989$	−4.78387	−	0.721053i	−0.152118	−	0.0229282i
$990$		0			0
$991$	8.38363	−	1.26363i	0.266315	−	0.0401405i	−0.0145273	−	0.999894i	$-0.504624\pi$
$991$	8.38363	−	1.26363i	0.266315	−	0.0401405i	0.280842	+	0.959754i	$0.409386\pi$
$992$	−1.48679	+	1.37954i	−0.0472057	+	0.0438005i
$993$		0			0
$994$	−31.0470	−	44.0284i	−0.984751	−	1.39649i
$995$	53.0967	−	66.5812i	1.68328	−	2.11077i
$996$		0			0
$997$	23.3247	+	7.19472i	0.738701	+	0.227859i	0.641197	−	0.767376i	$-0.278438\pi$
$997$	23.3247	+	7.19472i	0.738701	+	0.227859i	0.0975037	+	0.995235i	$0.468914\pi$
$998$	−17.9980	+	31.1734i	−0.569716	+	0.986777i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.e.46.2		60
3.2	odd	2		147.2.m.b.46.4	yes	60
49.16	even	21	inner	441.2.bb.e.163.2		60
147.53	odd	42		7203.2.a.n.1.20		30
147.65	odd	42		147.2.m.b.16.4	✓	60
147.143	even	42		7203.2.a.m.1.20		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.m.b.16.4	✓	60	147.65	odd	42
147.2.m.b.46.4	yes	60	3.2	odd	2
441.2.bb.e.46.2		60	1.1	even	1	trivial
441.2.bb.e.163.2		60	49.16	even	21	inner
7203.2.a.m.1.20		30	147.143	even	42
7203.2.a.n.1.20		30	147.53	odd	42

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.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.489645 + 1.24760i) q^{2} +(0.149360 + 0.138586i) q^{4} +(2.98135 + 2.03265i) q^{5} +(-2.47781 - 0.927615i) q^{7} +(-2.66107 + 1.28150i) q^{8} +O(q^{10})\)	\(q+(-0.489645 + 1.24760i) q^{2} +(0.149360 + 0.138586i) q^{4} +(2.98135 + 2.03265i) q^{5} +(-2.47781 - 0.927615i) q^{7} +(-2.66107 + 1.28150i) q^{8} +(-3.99573 + 2.72425i) q^{10} +(-6.22519 + 0.938296i) q^{11} +(2.32688 + 2.91781i) q^{13} +(2.37054 - 2.63710i) q^{14} +(-0.265365 - 3.54105i) q^{16} +(0.0676464 + 0.0208662i) q^{17} +(2.01698 + 3.49352i) q^{19} +(0.163598 + 0.716772i) q^{20} +(1.87752 - 8.22595i) q^{22} +(5.42692 - 1.67398i) q^{23} +(2.93009 + 7.46574i) q^{25} +(-4.77959 + 1.47431i) q^{26} +(-0.241532 - 0.481939i) q^{28} +(0.0859522 + 0.376581i) q^{29} +(0.883415 - 1.53012i) q^{31} +(-1.09694 - 0.338362i) q^{32} +(-0.0591553 + 0.0741784i) q^{34} +(-5.50170 - 7.80207i) q^{35} +(-0.999440 + 0.927345i) q^{37} +(-5.34610 + 0.805795i) q^{38} +(-10.5384 - 1.58841i) q^{40} +(-2.94534 + 1.41840i) q^{41} +(-0.767499 - 0.369608i) q^{43} +(-1.05983 - 0.722580i) q^{44} +(-0.568812 + 7.59027i) q^{46} +(-0.752434 + 1.91717i) q^{47} +(5.27906 + 4.59690i) q^{49} -10.7489 q^{50} +(-0.0568251 + 0.758278i) q^{52} +(6.98962 + 6.48542i) q^{53} +(-20.4667 - 9.85625i) q^{55} +(7.78235 - 0.706870i) q^{56} +(-0.511907 - 0.0771576i) q^{58} +(8.77092 - 5.97991i) q^{59} +(8.08726 - 7.50388i) q^{61} +(1.47641 + 1.85136i) q^{62} +(5.38726 - 6.75541i) q^{64} +(1.00635 + 13.4288i) q^{65} +(-4.81538 + 8.34049i) q^{67} +(0.00721193 + 0.0124914i) q^{68} +(12.4277 - 3.04365i) q^{70} +(3.38079 - 14.8122i) q^{71} +(0.231869 + 0.590793i) q^{73} +(-0.667581 - 1.70097i) q^{74} +(-0.182896 + 0.801318i) q^{76} +(16.2952 + 3.44966i) q^{77} +(0.140427 + 0.243226i) q^{79} +(6.40658 - 11.0965i) q^{80} +(-0.327420 - 4.36911i) q^{82} +(-1.34948 + 1.69219i) q^{83} +(0.159264 + 0.199711i) q^{85} +(0.836924 - 0.776552i) q^{86} +(15.3632 - 10.4745i) q^{88} +(-3.96210 - 0.597191i) q^{89} +(-3.05895 - 9.38822i) q^{91} +(1.04256 + 0.502069i) q^{92} +(-2.02343 - 1.87747i) q^{94} +(-1.08777 + 14.5152i) q^{95} -1.60053 q^{97} +(-8.31995 + 4.33528i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8}+O(q^{10}) \) 60 * q - q^2 + 5 * q^4 + 2 * q^5 + 5 * q^7 - 6 * q^8	\( 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8} - 34 q^{10} + 11 q^{11} - 2 q^{13} - 40 q^{14} - 31 q^{16} + 9 q^{17} - 29 q^{19} + 43 q^{20} + 9 q^{22} + 4 q^{23} + 55 q^{25} - 36 q^{26} - 57 q^{28} - 4 q^{29} - 39 q^{31} + 92 q^{32} - 36 q^{34} + 33 q^{35} - 24 q^{37} - 118 q^{38} - 35 q^{41} + 2 q^{43} - 40 q^{44} - 40 q^{46} + 5 q^{47} + 129 q^{49} + 176 q^{50} - 6 q^{52} - 26 q^{53} + 2 q^{55} - 63 q^{56} + 11 q^{58} + 41 q^{59} + 6 q^{61} - 36 q^{62} + 74 q^{64} + 51 q^{65} - 55 q^{67} + 22 q^{68} - 68 q^{70} + 66 q^{71} + 24 q^{73} - 28 q^{74} + 3 q^{76} + 34 q^{77} - 51 q^{79} + 5 q^{80} - 41 q^{82} - 30 q^{83} + 68 q^{85} - 110 q^{86} + 129 q^{88} - 75 q^{89} + 5 q^{91} + 38 q^{94} - 36 q^{95} - 168 q^{97} - 227 q^{98}+O(q^{100}) \) 60 * q - q^2 + 5 * q^4 + 2 * q^5 + 5 * q^7 - 6 * q^8 - 34 * q^10 + 11 * q^11 - 2 * q^13 - 40 * q^14 - 31 * q^16 + 9 * q^17 - 29 * q^19 + 43 * q^20 + 9 * q^22 + 4 * q^23 + 55 * q^25 - 36 * q^26 - 57 * q^28 - 4 * q^29 - 39 * q^31 + 92 * q^32 - 36 * q^34 + 33 * q^35 - 24 * q^37 - 118 * q^38 - 35 * q^41 + 2 * q^43 - 40 * q^44 - 40 * q^46 + 5 * q^47 + 129 * q^49 + 176 * q^50 - 6 * q^52 - 26 * q^53 + 2 * q^55 - 63 * q^56 + 11 * q^58 + 41 * q^59 + 6 * q^61 - 36 * q^62 + 74 * q^64 + 51 * q^65 - 55 * q^67 + 22 * q^68 - 68 * q^70 + 66 * q^71 + 24 * q^73 - 28 * q^74 + 3 * q^76 + 34 * q^77 - 51 * q^79 + 5 * q^80 - 41 * q^82 - 30 * q^83 + 68 * q^85 - 110 * q^86 + 129 * q^88 - 75 * q^89 + 5 * q^91 + 38 * q^94 - 36 * q^95 - 168 * q^97 - 227 * q^98

Introduction

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