LMFDB - Embedded newform 475.2.e.f.201.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(26,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("475.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.e (of order $3$, degree $2$, 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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 17 x^{10} - 18 x^{9} + 109 x^{8} - 93 x^{7} + 484 x^{6} - 147 x^{5} + 1009 x^{4} + \cdots + 1 $ x^12 - 3x^11 + 17x^10 - 18x^9 + 109x^8 - 93x^7 + 484x^6 - 147x^5 + 1009x^4 - 552x^3 + 1107x^2 + 33*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			201.6
Root			$0.590804 + 1.02330i$ of defining polynomial
Character	$\chi$	$=$	475.201
Dual form			475.2.e.f.26.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.740597 - 1.28275i) q^{2} +(0.0908038 - 0.157277i) q^{3} +(-0.0969683 - 0.167954i) q^{4} +(-0.134498 - 0.232958i) q^{6} -1.30422 q^{7} +2.67513 q^{8} +(1.48351 + 2.56951i) q^{9} +4.98247 q^{11} -0.0352204 q^{12} +(0.203067 + 0.351723i) q^{13} +(-0.965899 + 1.67299i) q^{14} +(2.17513 - 3.76744i) q^{16} +(1.37510 - 2.38173i) q^{17} +4.39473 q^{18} +(-4.35785 - 0.0955054i) q^{19} +(-0.118428 + 0.205123i) q^{21} +(3.69001 - 6.39128i) q^{22} +(-3.47860 - 6.02510i) q^{23} +(0.242912 - 0.420736i) q^{24} +0.601564 q^{26} +1.08366 q^{27} +(0.126468 + 0.219048i) q^{28} +(2.00728 + 3.47672i) q^{29} -2.57321 q^{31} +(-0.546661 - 0.946844i) q^{32} +(0.452428 - 0.783628i) q^{33} +(-2.03678 - 3.52781i) q^{34} +(0.287707 - 0.498323i) q^{36} +3.71348 q^{37} +(-3.34992 + 5.51931i) q^{38} +0.0737572 q^{39} +(0.607965 - 1.05303i) q^{41} +(0.175415 + 0.303827i) q^{42} +(-1.56130 + 2.70426i) q^{43} +(-0.483142 - 0.836826i) q^{44} -10.3050 q^{46} +(3.25405 + 5.63617i) q^{47} +(-0.395020 - 0.684196i) q^{48} -5.29902 q^{49} +(-0.249728 - 0.432541i) q^{51} +(0.0393822 - 0.0682119i) q^{52} +(-3.16094 - 5.47490i) q^{53} +(0.802553 - 1.39006i) q^{54} -3.48895 q^{56} +(-0.410731 + 0.676717i) q^{57} +5.94636 q^{58} +(-5.61636 + 9.72783i) q^{59} +(-0.467072 - 0.808992i) q^{61} +(-1.90571 + 3.30079i) q^{62} +(-1.93482 - 3.35120i) q^{63} +7.08110 q^{64} +(-0.670133 - 1.16071i) q^{66} +(-2.64764 - 4.58585i) q^{67} -0.533363 q^{68} -1.26348 q^{69} +(0.817659 - 1.41623i) q^{71} +(3.96858 + 6.87378i) q^{72} +(-3.84396 + 6.65794i) q^{73} +(2.75019 - 4.76347i) q^{74} +(0.406533 + 0.741180i) q^{76} -6.49822 q^{77} +(0.0546243 - 0.0946121i) q^{78} +(7.27699 - 12.6041i) q^{79} +(-4.35213 + 7.53811i) q^{81} +(-0.900514 - 1.55974i) q^{82} -15.2643 q^{83} +0.0459350 q^{84} +(2.31260 + 4.00553i) q^{86} +0.729076 q^{87} +13.3288 q^{88} +(-7.10727 - 12.3101i) q^{89} +(-0.264844 - 0.458723i) q^{91} +(-0.674627 + 1.16849i) q^{92} +(-0.233658 + 0.404707i) q^{93} +9.63975 q^{94} -0.198556 q^{96} +(-9.14111 + 15.8329i) q^{97} +(-3.92444 + 6.79733i) q^{98} +(7.39155 + 12.8025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{6} + 4 q^{7} + 12 q^{8} - 7 q^{9} - 2 q^{11} + 14 q^{12} - 5 q^{13} + 6 q^{14} + 6 q^{16} + 3 q^{17} + 14 q^{18} - 6 q^{19} - 3 q^{21} - 9 q^{22} + 6 q^{23} - 11 q^{24}+ \cdots + 20 q^{99}+O(q^{100}) $ 12 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 + q^6 + 4 * q^7 + 12 * q^8 - 7 * q^9 - 2 * q^11 + 14 * q^12 - 5 * q^13 + 6 * q^14 + 6 * q^16 + 3 * q^17 + 14 * q^18 - 6 * q^19 - 3 * q^21 - 9 * q^22 + 6 * q^23 - 11 * q^24 + 38 * q^26 + 36 * q^27 + 4 * q^28 - 3 * q^29 - 6 * q^31 + 6 * q^32 + 18 * q^33 + q^34 - 13 * q^36 - 12 * q^37 - 18 * q^38 + 16 * q^39 - 11 * q^41 + 11 * q^42 - 13 * q^43 - 21 * q^44 - 24 * q^46 + 6 * q^47 + 19 * q^48 + 8 * q^49 + 17 * q^51 + q^52 - 18 * q^53 - 18 * q^54 + 8 * q^56 - 20 * q^57 + 10 * q^58 - 4 * q^59 - 25 * q^61 + 21 * q^62 - 43 * q^63 - 44 * q^64 - 34 * q^66 - 6 * q^67 - 2 * q^68 + 26 * q^69 - 18 * q^71 - 13 * q^72 - q^73 + 6 * q^74 + 24 * q^76 - 22 * q^77 - 72 * q^78 - 3 * q^79 - 2 * q^81 - 31 * q^82 - 46 * q^83 + 74 * q^84 - 9 * q^86 + 22 * q^87 + 22 * q^88 - 12 * q^89 + 11 * q^91 - 28 * q^92 + 13 * q^93 + 16 * q^94 - 26 * q^96 - 3 * q^97 + 22 * q^98 + 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.740597	−	1.28275i	0.523681	−	0.907043i	−0.475939	−	0.879478i	$-0.657892\pi$
$2$	0.740597	−	1.28275i	0.523681	−	0.907043i	0.999620	−	0.0275641i	$-0.00877505\pi$
$3$	0.0908038	−	0.157277i	0.0524256	−	0.0908038i	−0.838622	−	0.544714i	$-0.816638\pi$
$3$	0.0908038	−	0.157277i	0.0524256	−	0.0908038i	0.891047	+	0.453910i	$0.149971\pi$
$4$	−0.0969683	−	0.167954i	−0.0484841	−	0.0839770i
$5$		0			0
$5$		0			0
$6$	−0.134498	−	0.232958i	−0.0549086	−	0.0951045i
$7$	−1.30422			−0.492948			−0.246474	−	0.969149i	$-0.579272\pi$
$7$	−1.30422			−0.492948			−0.246474	+	0.969149i	$0.579272\pi$
$8$	2.67513			0.945802
$9$	1.48351	+	2.56951i	0.494503	+	0.856505i
$10$		0			0
$11$	4.98247			1.50227			0.751136	−	0.660147i	$-0.229506\pi$
$11$	4.98247			1.50227			0.751136	+	0.660147i	$0.229506\pi$
$12$	−0.0352204			−0.0101672
$13$	0.203067	+	0.351723i	0.0563207	+	0.0975504i	0.892811	−	0.450431i	$-0.148730\pi$
$13$	0.203067	+	0.351723i	0.0563207	+	0.0975504i	−0.836490	+	0.547982i	$0.815396\pi$
$14$	−0.965899	+	1.67299i	−0.258147	+	0.447124i
$15$		0			0
$16$	2.17513	−	3.76744i	0.543783	−	0.941859i
$17$	1.37510	−	2.38173i	0.333510	−	0.577656i	−0.649688	−	0.760201i	$-0.725100\pi$
$17$	1.37510	−	2.38173i	0.333510	−	0.577656i	0.983197	+	0.182546i	$0.0584337\pi$
$18$	4.39473			1.03585
$19$	−4.35785	−	0.0955054i	−0.999760	−	0.0219104i
$19$	−4.35785	−	0.0955054i	−0.999760	−	0.0219104i
$20$		0			0
$21$	−0.118428	+	0.205123i	−0.0258431	+	0.0447615i
$22$	3.69001	−	6.39128i	0.786712	−	1.36262i
$23$	−3.47860	−	6.02510i	−0.725337	−	1.25632i	−0.958835	−	0.283964i	$-0.908350\pi$
$23$	−3.47860	−	6.02510i	−0.725337	−	1.25632i	0.233498	−	0.972357i	$-0.424983\pi$
$24$	0.242912	−	0.420736i	0.0495842	−	0.0858824i
$25$		0			0
$26$	0.601564			0.117976
$27$	1.08366			0.208550
$28$	0.126468	+	0.219048i	0.0239001	+	0.0413963i
$29$	2.00728	+	3.47672i	0.372743	+	0.645610i	0.989986	−	0.141162i	$-0.0450839\pi$
$29$	2.00728	+	3.47672i	0.372743	+	0.645610i	−0.617243	+	0.786772i	$0.711751\pi$
$30$		0			0
$31$	−2.57321			−0.462163			−0.231081	−	0.972934i	$-0.574226\pi$
$31$	−2.57321			−0.462163			−0.231081	+	0.972934i	$0.574226\pi$
$32$	−0.546661	−	0.946844i	−0.0966369	−	0.167380i
$33$	0.452428	−	0.783628i	0.0787576	−	0.136412i
$34$	−2.03678	−	3.52781i	−0.349305	−	0.605015i
$35$		0			0
$36$	0.287707	−	0.498323i	0.0479511	−	0.0830538i
$37$	3.71348			0.610492			0.305246	−	0.952274i	$-0.401261\pi$
$37$	3.71348			0.610492			0.305246	+	0.952274i	$0.401261\pi$
$38$	−3.34992	+	5.51931i	−0.543429	+	0.895351i
$39$	0.0737572			0.0118106
$40$		0			0
$41$	0.607965	−	1.05303i	0.0949482	−	0.164455i	−0.814639	−	0.579969i	$-0.803065\pi$
$41$	0.607965	−	1.05303i	0.0949482	−	0.164455i	0.909587	+	0.415514i	$0.136398\pi$
$42$	0.175415	+	0.303827i	0.0270671	+	0.0468816i
$43$	−1.56130	+	2.70426i	−0.238097	+	0.412396i	−0.960168	−	0.279423i	$-0.909857\pi$
$43$	−1.56130	+	2.70426i	−0.238097	+	0.412396i	0.722071	+	0.691819i	$0.243190\pi$
$44$	−0.483142	−	0.836826i	−0.0728364	−	0.126156i
$45$		0			0
$46$	−10.3050			−1.51938
$47$	3.25405	+	5.63617i	0.474651	+	0.822120i	0.999579	−	0.0290269i	$-0.00924083\pi$
$47$	3.25405	+	5.63617i	0.474651	+	0.822120i	−0.524927	+	0.851147i	$0.675907\pi$
$48$	−0.395020	−	0.684196i	−0.0570163	−	0.0987551i
$49$	−5.29902			−0.757003
$50$		0			0
$51$	−0.249728	−	0.432541i	−0.0349689	−	0.0605679i
$52$	0.0393822	−	0.0682119i	0.00546132	−	0.00945929i
$53$	−3.16094	−	5.47490i	−0.434188	−	0.752036i	0.563041	−	0.826429i	$-0.309631\pi$
$53$	−3.16094	−	5.47490i	−0.434188	−	0.752036i	−0.997229	+	0.0743934i	$0.976298\pi$
$54$	0.802553	−	1.39006i	0.109214	−	0.189164i
$55$		0			0
$56$	−3.48895			−0.466231
$57$	−0.410731	+	0.676717i	−0.0544026	+	0.0896334i
$58$	5.94636			0.780795
$59$	−5.61636	+	9.72783i	−0.731188	+	1.26646i	0.225187	+	0.974315i	$0.427701\pi$
$59$	−5.61636	+	9.72783i	−0.731188	+	1.26646i	−0.956376	+	0.292140i	$0.905633\pi$
$60$		0			0
$61$	−0.467072	−	0.808992i	−0.0598024	−	0.103581i	0.834574	−	0.550896i	$-0.185714\pi$
$61$	−0.467072	−	0.808992i	−0.0598024	−	0.103581i	−0.894377	+	0.447315i	$0.852380\pi$
$62$	−1.90571	+	3.30079i	−0.242026	+	0.419201i
$63$	−1.93482	−	3.35120i	−0.243764	−	0.422212i
$64$	7.08110			0.885138
$65$		0			0
$66$	−0.670133	−	1.16071i	−0.0824877	−	0.142873i
$67$	−2.64764	−	4.58585i	−0.323461	−	0.560251i	0.657739	−	0.753246i	$-0.271513\pi$
$67$	−2.64764	−	4.58585i	−0.323461	−	0.560251i	−0.981200	+	0.192995i	$0.938180\pi$
$68$	−0.533363			−0.0646797
$69$	−1.26348			−0.152105
$70$		0			0
$71$	0.817659	−	1.41623i	0.0970383	−	0.168075i	−0.813419	−	0.581678i	$-0.802396\pi$
$71$	0.817659	−	1.41623i	0.0970383	−	0.168075i	0.910457	+	0.413603i	$0.135730\pi$
$72$	3.96858	+	6.87378i	0.467702	+	0.810083i
$73$	−3.84396	+	6.65794i	−0.449902	+	0.779252i	−0.998379	−	0.0569129i	$-0.981874\pi$
$73$	−3.84396	+	6.65794i	−0.449902	+	0.779252i	0.548478	+	0.836165i	$0.315208\pi$
$74$	2.75019	−	4.76347i	0.319703	−	0.553742i
$75$		0			0
$76$	0.406533	+	0.741180i	0.0466325	+	0.0850191i
$77$	−6.49822			−0.740541
$78$	0.0546243	−	0.0946121i	0.00618499	−	0.0107127i
$79$	7.27699	−	12.6041i	0.818725	−	1.41807i	−0.0878971	−	0.996130i	$-0.528015\pi$
$79$	7.27699	−	12.6041i	0.818725	−	1.41807i	0.906622	−	0.421944i	$-0.138652\pi$
$80$		0			0
$81$	−4.35213	+	7.53811i	−0.483570	+	0.837567i
$82$	−0.900514	−	1.55974i	−0.0994452	−	0.172244i
$83$	−15.2643			−1.67547			−0.837735	−	0.546077i	$-0.816121\pi$
$83$	−15.2643			−1.67547			−0.837735	+	0.546077i	$0.816121\pi$
$84$	0.0459350			0.00501192
$85$		0			0
$86$	2.31260	+	4.00553i	0.249374	+	0.431928i
$87$	0.729076			0.0781652
$88$	13.3288			1.42085
$89$	−7.10727	−	12.3101i	−0.753369	−	1.30487i	−0.946181	−	0.323638i	$-0.895094\pi$
$89$	−7.10727	−	12.3101i	−0.753369	−	1.30487i	0.192812	−	0.981236i	$-0.438239\pi$
$90$		0			0
$91$	−0.264844	−	0.458723i	−0.0277632	−	0.0480872i
$92$	−0.674627	+	1.16849i	−0.0703347	+	0.121823i
$93$	−0.233658	+	0.404707i	−0.0242292	+	0.0419661i
$94$	9.63975			0.994264
$95$		0			0
$96$	−0.198556			−0.0202650
$97$	−9.14111	+	15.8329i	−0.928139	+	1.60758i	−0.141707	+	0.989909i	$0.545259\pi$
$97$	−9.14111	+	15.8329i	−0.928139	+	1.60758i	−0.786433	+	0.617676i	$0.788074\pi$
$98$	−3.92444	+	6.79733i	−0.396428	+	0.686634i
$99$	7.39155	+	12.8025i	0.742878	+	1.28670i
$100$		0			0
$101$	7.99763	+	13.8523i	0.795794	+	1.37836i	0.922334	+	0.386394i	$0.126280\pi$
$101$	7.99763	+	13.8523i	0.795794	+	1.37836i	−0.126540	+	0.991962i	$0.540387\pi$
$102$	−0.739791			−0.0732502
$103$	5.30941			0.523152			0.261576	−	0.965183i	$-0.415758\pi$
$103$	5.30941			0.523152			0.261576	+	0.965183i	$0.415758\pi$
$104$	0.543232	+	0.940905i	0.0532682	+	0.0922633i
$105$		0			0
$106$	−9.36392			−0.909504
$107$	−13.0024			−1.25699			−0.628494	−	0.777814i	$-0.716329\pi$
$107$	−13.0024			−1.25699			−0.628494	+	0.777814i	$0.716329\pi$
$108$	−0.105080	−	0.182004i	−0.0101114	−	0.0175134i
$109$	4.09697	−	7.09616i	0.392418	−	0.679689i	−0.600350	−	0.799738i	$-0.704972\pi$
$109$	4.09697	−	7.09616i	0.392418	−	0.679689i	0.992768	+	0.120049i	$0.0383052\pi$
$110$		0			0
$111$	0.337198	−	0.584044i	0.0320054	−	0.0554350i
$112$	−2.83684	+	4.91355i	−0.268056	+	0.464287i
$113$	−6.54779			−0.615964			−0.307982	−	0.951392i	$-0.599654\pi$
$113$	−6.54779			−0.615964			−0.307982	+	0.951392i	$0.599654\pi$
$114$	0.563874	+	1.02804i	0.0528117	+	0.0962848i
$115$		0			0
$116$	0.389286	−	0.674263i	0.0361443	−	0.0626037i
$117$	−0.602504	+	1.04357i	−0.0557016	+	0.0964779i
$118$	8.31892	+	14.4088i	0.765819	+	1.32644i
$119$	−1.79342	+	3.10630i	−0.164403	+	0.284754i
$120$		0			0
$121$	13.8250			1.25682
$122$	−1.38365			−0.125270
$123$	−0.110411	−	0.191238i	−0.00995544	−	0.0172433i
$124$	0.249520	+	0.432181i	0.0224076	+	0.0388110i
$125$		0			0
$126$	−5.73168			−0.510619
$127$	−7.55431	−	13.0844i	−0.670336	−	1.16106i	−0.977809	−	0.209500i	$-0.932817\pi$
$127$	−7.55431	−	13.0844i	−0.670336	−	1.16106i	0.307472	−	0.951557i	$-0.400517\pi$
$128$	6.33757	−	10.9770i	0.560167	−	0.970238i
$129$	0.283545	+	0.491114i	0.0249647	+	0.0432402i
$130$		0			0
$131$	1.24679	−	2.15950i	0.108933	−	0.188677i	−0.806406	−	0.591363i	$-0.798590\pi$
$131$	1.24679	−	2.15950i	0.108933	−	0.188677i	0.915338	+	0.402686i	$0.131923\pi$
$132$	−0.175485			−0.0152740
$133$	5.68358	+	0.124560i	0.492829	+	0.0108007i
$134$	−7.84335			−0.677562
$135$		0			0
$136$	3.67856	−	6.37145i	0.315434	−	0.546348i
$137$	8.80405	+	15.2491i	0.752181	+	1.30282i	0.946764	+	0.321930i	$0.104331\pi$
$137$	8.80405	+	15.2491i	0.752181	+	1.30282i	−0.194583	+	0.980886i	$0.562335\pi$
$138$	−0.935729	+	1.62073i	−0.0796546	+	0.137966i
$139$	−1.57736	−	2.73207i	−0.133790	−	0.231731i	0.791345	−	0.611370i	$-0.209381\pi$
$139$	−1.57736	−	2.73207i	−0.133790	−	0.231731i	−0.925135	+	0.379639i	$0.876048\pi$
$140$		0			0
$141$	1.18192			0.0995356
$142$	−1.21111	−	2.09771i	−0.101634	−	0.176036i
$143$	1.01178	+	1.75245i	0.0846091	+	0.146547i
$144$	12.9073			1.07561
$145$		0			0
$146$	5.69365	+	9.86170i	0.471210	+	0.816160i
$147$	−0.481171	+	0.833413i	−0.0396863	+	0.0687388i
$148$	−0.360090	−	0.623693i	−0.0295992	−	0.0512673i
$149$	3.18694	−	5.51994i	0.261084	−	0.452211i	−0.705446	−	0.708764i	$-0.749253\pi$
$149$	3.18694	−	5.51994i	0.261084	−	0.452211i	0.966530	+	0.256552i	$0.0825866\pi$
$150$		0			0
$151$	4.96340			0.403915			0.201958	−	0.979394i	$-0.435270\pi$
$151$	4.96340			0.403915			0.201958	+	0.979394i	$0.435270\pi$
$152$	−11.6578	−	0.255489i	−0.945575	−	0.0207229i
$153$	8.15987			0.659686
$154$	−4.81257	+	8.33561i	−0.387808	+	0.671703i
$155$		0			0
$156$	−0.00715211	−	0.0123878i	−0.000572627	−	0.000991819i
$157$	1.04750	−	1.81432i	0.0835993	−	0.144798i	−0.821194	−	0.570649i	$-0.806692\pi$
$157$	1.04750	−	1.81432i	0.0835993	−	0.144798i	0.904793	+	0.425851i	$0.140025\pi$
$158$	−10.7786	−	18.6691i	−0.857502	−	1.48524i
$159$	−1.14810			−0.0910503
$160$		0			0
$161$	4.53684	+	7.85804i	0.357553	+	0.619300i
$162$	6.44635	+	11.1654i	0.506473	+	0.877237i
$163$	9.55821			0.748656			0.374328	−	0.927296i	$-0.377873\pi$
$163$	9.55821			0.748656			0.374328	+	0.927296i	$0.377873\pi$
$164$	−0.235813			−0.0184139
$165$		0			0
$166$	−11.3047	+	19.5803i	−0.877412	+	1.51972i
$167$	−8.36974	−	14.4968i	−0.647670	−	1.12180i	−0.983678	−	0.179938i	$-0.942410\pi$
$167$	−8.36974	−	14.4968i	−0.647670	−	1.12180i	0.336008	−	0.941859i	$-0.390923\pi$
$168$	−0.316810	+	0.548731i	−0.0244424	+	0.0423355i
$169$	6.41753	−	11.1155i	0.493656	−	0.855037i
$170$		0			0
$171$	−6.21951	−	11.3392i	−0.475618	−	0.867134i
$172$	0.605588			0.0461757
$173$	−6.98769	+	12.1030i	−0.531264	+	0.920177i	0.468070	+	0.883691i	$0.344950\pi$
$173$	−6.98769	+	12.1030i	−0.531264	+	0.920177i	−0.999334	+	0.0364853i	$0.988384\pi$
$174$	0.539952	−	0.935224i	0.0409336	−	0.0708992i
$175$		0			0
$176$	10.8375	−	18.7712i	0.816910	−	1.41493i
$177$	1.01997	+	1.76665i	0.0766660	+	0.132789i
$178$	−21.0545			−1.57810
$179$	−9.86133			−0.737071			−0.368535	−	0.929614i	$-0.620141\pi$
$179$	−9.86133			−0.737071			−0.368535	+	0.929614i	$0.620141\pi$
$180$		0			0
$181$	−7.38629	−	12.7934i	−0.549019	−	0.950929i	−0.998342	−	0.0575593i	$-0.981668\pi$
$181$	−7.38629	−	12.7934i	−0.549019	−	0.950929i	0.449323	−	0.893369i	$-0.351665\pi$
$182$	−0.784570			−0.0581562
$183$	−0.169648			−0.0125407
$184$	−9.30570	−	16.1179i	−0.686025	−	1.18823i
$185$		0			0
$186$	0.346092	+	0.599450i	0.0253767	+	0.0439538i
$187$	6.85138	−	11.8669i	0.501022	−	0.867796i
$188$	0.631078	−	1.09306i	0.0460261	−	0.0797196i
$189$	−1.41332			−0.102804
$190$		0			0
$191$	−20.6797			−1.49633			−0.748166	−	0.663512i	$-0.769065\pi$
$191$	−20.6797			−1.49633			−0.748166	+	0.663512i	$0.769065\pi$
$192$	0.642991	−	1.11369i	0.0464039	−	0.0803739i
$193$	−10.1391	+	17.5615i	−0.729831	+	1.26410i	0.227123	+	0.973866i	$0.427068\pi$
$193$	−10.1391	+	17.5615i	−0.729831	+	1.26410i	−0.956954	+	0.290238i	$0.906265\pi$
$194$	13.5398	+	23.4516i	0.972099	+	1.68372i
$195$		0			0
$196$	0.513837	+	0.889991i	0.0367026	+	0.0635708i
$197$	15.9172			1.13406			0.567028	−	0.823698i	$-0.308093\pi$
$197$	15.9172			1.13406			0.567028	+	0.823698i	$0.308093\pi$
$198$	21.8966			1.55613
$199$	6.61785	+	11.4625i	0.469127	+	0.812552i	0.999377	−	0.0352892i	$-0.0112352\pi$
$199$	6.61785	+	11.4625i	0.469127	+	0.812552i	−0.530250	+	0.847841i	$0.677902\pi$
$200$		0			0
$201$	−0.961665			−0.0678306
$202$	23.6921			1.66697
$203$	−2.61793	−	4.53439i	−0.183743	−	0.318252i
$204$	−0.0484314	+	0.0838856i	−0.00339087	+	0.00587317i
$205$		0			0
$206$	3.93214	−	6.81066i	0.273965	−	0.474521i
$207$	10.3211	−	17.8766i	0.717363	−	1.24251i
$208$	1.76679			0.122505
$209$	−21.7129	−	0.475853i	−1.50191	−	0.0329154i
$210$		0			0
$211$	4.88917	−	8.46829i	0.336584	−	0.582981i	−0.647204	−	0.762317i	$-0.724062\pi$
$211$	4.88917	−	8.46829i	0.336584	−	0.582981i	0.983788	+	0.179336i	$0.0573950\pi$
$212$	−0.613021	+	1.06178i	−0.0421025	+	0.0729236i
$213$	−0.148493	−	0.257198i	−0.0101746	−	0.0176229i
$214$	−9.62954	+	16.6788i	−0.658262	+	1.14014i
$215$		0			0
$216$	2.89892			0.197247
$217$	3.35603			0.227822
$218$	−6.06841	−	10.5108i	−0.411004	−	0.711880i
$219$	0.698093	+	1.20913i	0.0471727	+	0.0817056i
$220$		0			0
$221$	1.11695			0.0751340
$222$	−0.499456	−	0.865083i	−0.0335213	−	0.0580606i
$223$	12.9310	−	22.3971i	0.865923	−	1.49982i	−0.000205308	−	1.00000i	$-0.500065\pi$
$223$	12.9310	−	22.3971i	0.865923	−	1.49982i	0.866128	−	0.499822i	$-0.166601\pi$
$224$	0.712964	+	1.23489i	0.0476369	+	0.0825095i
$225$		0			0
$226$	−4.84927	+	8.39918i	−0.322569	+	0.558705i
$227$	2.28573			0.151709			0.0758545	−	0.997119i	$-0.475832\pi$
$227$	2.28573			0.151709			0.0758545	+	0.997119i	$0.475832\pi$
$228$	0.153485	+	0.00336373i	0.0101648	+	0.000222769i
$229$	−21.8805			−1.44590			−0.722952	−	0.690898i	$-0.757215\pi$
$229$	−21.8805			−1.44590			−0.722952	+	0.690898i	$0.757215\pi$
$230$		0			0
$231$	−0.590064	+	1.02202i	−0.0388233	+	0.0672440i
$232$	5.36975	+	9.30068i	0.352541	+	0.610619i
$233$	1.02692	−	1.77868i	0.0672758	−	0.116525i	−0.830425	−	0.557130i	$-0.811903\pi$
$233$	1.02692	−	1.77868i	0.0672758	−	0.116525i	0.897701	+	0.440605i	$0.145236\pi$
$234$	0.892426	+	1.54573i	0.0583397	+	0.101047i
$235$		0			0
$236$	2.17844			0.141804
$237$	−1.32156	−	2.28900i	−0.0858443	−	0.148687i
$238$	2.65641	+	4.60103i	0.172189	+	0.298241i
$239$	7.68110			0.496849			0.248425	−	0.968651i	$-0.420087\pi$
$239$	7.68110			0.496849			0.248425	+	0.968651i	$0.420087\pi$
$240$		0			0
$241$	−7.26832	−	12.5891i	−0.468194	−	0.810935i	0.531146	−	0.847280i	$-0.321762\pi$
$241$	−7.26832	−	12.5891i	−0.468194	−	0.810935i	−0.999339	+	0.0363455i	$0.988428\pi$
$242$	10.2388	−	17.7341i	0.658174	−	1.13999i
$243$	2.41586	+	4.18440i	0.154978	+	0.268429i
$244$	−0.0905823	+	0.156893i	−0.00579894	+	0.0100441i
$245$		0			0
$246$	−0.327081			−0.0208539
$247$	−0.851346	−	1.55215i	−0.0541698	−	0.0987610i
$248$	−6.88368			−0.437114
$249$	−1.38605	+	2.40072i	−0.0878376	+	0.152139i
$250$		0			0
$251$	−3.59365	−	6.22439i	−0.226829	−	0.392880i	0.730037	−	0.683407i	$-0.239503\pi$
$251$	−3.59365	−	6.22439i	−0.226829	−	0.392880i	−0.956867	+	0.290527i	$0.906169\pi$
$252$	−0.375232	+	0.649921i	−0.0236374	+	0.0409412i
$253$	−17.3320	−	30.0199i	−1.08965	−	1.88734i
$254$	−22.3788			−1.40417
$255$		0			0
$256$	−2.30606	−	3.99422i	−0.144129	−	0.249639i
$257$	4.35294	+	7.53951i	0.271529	+	0.470302i	0.969254	−	0.246064i	$-0.0791374\pi$
$257$	4.35294	+	7.53951i	0.271529	+	0.470302i	−0.697725	+	0.716366i	$0.745804\pi$
$258$	0.839970			0.0522943
$259$	−4.84318			−0.300940
$260$		0			0
$261$	−5.95565	+	10.3155i	−0.368645	+	0.638513i
$262$	−1.84674	−	3.19864i	−0.114092	−	0.197613i
$263$	−15.2616	+	26.4339i	−0.941072	+	1.62998i	−0.177639	+	0.984096i	$0.556846\pi$
$263$	−15.2616	+	26.4339i	−0.941072	+	1.62998i	−0.763432	+	0.645888i	$0.776487\pi$
$264$	1.21030	−	2.09631i	0.0744890	−	0.129019i
$265$		0			0
$266$	4.36903	−	7.19838i	0.267882	−	0.441361i
$267$	−2.58147			−0.157983
$268$	−0.513475	+	0.889365i	−0.0313655	+	0.0543266i
$269$	9.20379	−	15.9414i	0.561165	−	0.971966i	−0.436230	−	0.899835i	$-0.643687\pi$
$269$	9.20379	−	15.9414i	0.561165	−	0.971966i	0.997395	−	0.0721309i	$-0.0229800\pi$
$270$		0			0
$271$	5.73694	−	9.93668i	0.348494	−	0.603610i	−0.637488	−	0.770460i	$-0.720026\pi$
$271$	5.73694	−	9.93668i	0.348494	−	0.603610i	0.985982	+	0.166850i	$0.0533597\pi$
$272$	−5.98202	−	10.3612i	−0.362714	−	0.628238i
$273$	−0.0961953			−0.00582201
$274$	26.0810			1.57561
$275$		0			0
$276$	0.122517	+	0.212206i	0.00737468	+	0.0127733i
$277$	1.79689			0.107965			0.0539823	−	0.998542i	$-0.482809\pi$
$277$	1.79689			0.107965			0.0539823	+	0.998542i	$0.482809\pi$
$278$	−4.67276			−0.280253
$279$	−3.81739	−	6.61191i	−0.228541	−	0.395844i
$280$		0			0
$281$	7.09550	+	12.2898i	0.423282	+	0.733146i	0.996258	−	0.0864258i	$-0.0275446\pi$
$281$	7.09550	+	12.2898i	0.423282	+	0.733146i	−0.572976	+	0.819572i	$0.694211\pi$
$282$	0.875326	−	1.51611i	0.0521249	−	0.0902830i
$283$	8.95435	−	15.5094i	0.532281	−	0.921938i	−0.467009	−	0.884253i	$-0.654668\pi$
$283$	8.95435	−	15.5094i	0.532281	−	0.921938i	0.999290	−	0.0376851i	$-0.0119984\pi$
$284$	−0.317148			−0.0188193
$285$		0			0
$286$	2.99728			0.177233
$287$	−0.792918	+	1.37337i	−0.0468045	+	0.0810677i
$288$	1.62195	−	2.80930i	0.0955744	−	0.165540i
$289$	4.71823	+	8.17221i	0.277543	+	0.480718i
$290$		0			0
$291$	1.66010	+	2.87537i	0.0973166	+	0.168557i
$292$	1.49097			0.0872524
$293$	33.3088			1.94592			0.972961	−	0.230970i	$-0.0741900\pi$
$293$	33.3088			1.94592			0.972961	+	0.230970i	$0.0741900\pi$
$294$	0.712708	+	1.23445i	0.0415660	+	0.0719944i
$295$		0			0
$296$	9.93404			0.577404
$297$	5.39929			0.313299
$298$	−4.72048	−	8.17610i	−0.273450	−	0.473629i
$299$	1.41278	−	2.44700i	0.0817031	−	0.141514i
$300$		0			0
$301$	2.03628	−	3.52694i	0.117369	−	0.203289i
$302$	3.67588	−	6.36681i	0.211523	−	0.366369i
$303$	2.90486			0.166880
$304$	−9.83871	+	16.2102i	−0.564289	+	0.929719i
$305$		0			0
$306$	6.04317	−	10.4671i	0.345465	−	0.598363i
$307$	7.77854	−	13.4728i	0.443945	−	0.768935i	−0.554033	−	0.832495i	$-0.686912\pi$
$307$	7.77854	−	13.4728i	0.443945	−	0.768935i	0.997978	+	0.0635594i	$0.0202452\pi$
$308$	0.630122	+	1.09140i	0.0359045	+	0.0621884i
$309$	0.482115	−	0.835048i	0.0274266	−	0.0475042i
$310$		0			0
$311$	29.1959			1.65555			0.827773	−	0.561063i	$-0.189608\pi$
$311$	29.1959			1.65555			0.827773	+	0.561063i	$0.189608\pi$
$312$	0.197310			0.0111705
$313$	15.9440	+	27.6158i	0.901207	+	1.56094i	0.825929	+	0.563774i	$0.190651\pi$
$313$	15.9440	+	27.6158i	0.901207	+	1.56094i	0.0752782	+	0.997163i	$0.476016\pi$
$314$	−1.55155	−	2.68736i	−0.0875588	−	0.151656i
$315$		0			0
$316$	−2.82255			−0.158781
$317$	−6.78505	−	11.7520i	−0.381086	−	0.660061i	0.610131	−	0.792300i	$-0.291117\pi$
$317$	−6.78505	−	11.7520i	−0.381086	−	0.660061i	−0.991218	+	0.132239i	$0.957783\pi$
$318$	−0.850280	+	1.47273i	−0.0476813	+	0.0825865i
$319$	10.0012	+	17.3227i	0.559962	+	0.969882i
$320$		0			0
$321$	−1.18067	+	2.04498i	−0.0658984	+	0.114139i
$322$	13.4399			0.748976
$323$	−6.21993	+	10.2479i	−0.346086	+	0.570210i
$324$	1.68807			0.0937819
$325$		0			0
$326$	7.07878	−	12.2608i	0.392057	−	0.679063i
$327$	−0.744041	−	1.28872i	−0.0411456	−	0.0712662i
$328$	1.62639	−	2.81698i	0.0898022	−	0.155542i
$329$	−4.24398	−	7.35079i	−0.233978	−	0.405262i
$330$		0			0
$331$	−29.4274			−1.61747			−0.808737	−	0.588171i	$-0.799848\pi$
$331$	−29.4274			−1.61747			−0.808737	+	0.588171i	$0.799848\pi$
$332$	1.48015	+	2.56369i	0.0812337	+	0.140701i
$333$	5.50898	+	9.54183i	0.301890	+	0.522889i
$334$	−24.7944			−1.35669
$335$		0			0
$336$	0.515192	+	0.892339i	0.0281060	+	0.0486811i
$337$	−7.75588	+	13.4336i	−0.422489	+	0.731773i	−0.996182	−	0.0872973i	$-0.972177\pi$
$337$	−7.75588	+	13.4336i	−0.422489	+	0.731773i	0.573693	+	0.819071i	$0.305510\pi$
$338$	−9.50560	−	16.4642i	−0.517037	−	0.895534i
$339$	−0.594564	+	1.02982i	−0.0322923	+	0.0559319i
$340$		0			0
$341$	−12.8210			−0.694294
$342$	−19.1516	−	0.419720i	−1.03560	−	0.0226959i
$343$	16.0406			0.866110
$344$	−4.17669	+	7.23425i	−0.225192	+	0.390044i
$345$		0			0
$346$	10.3501	+	17.9269i	0.556426	+	0.963759i
$347$	−11.2938	+	19.5615i	−0.606285	+	1.05012i	0.385562	+	0.922682i	$0.374008\pi$
$347$	−11.2938	+	19.5615i	−0.606285	+	1.05012i	−0.991847	+	0.127434i	$0.959326\pi$
$348$	−0.0706973	−	0.122451i	−0.00378977	−	0.00656408i
$349$	25.4885			1.36437			0.682184	−	0.731181i	$-0.261030\pi$
$349$	25.4885			1.36437			0.682184	+	0.731181i	$0.261030\pi$
$350$		0			0
$351$	0.220055	+	0.381147i	0.0117457	+	0.0203441i
$352$	−2.72372	−	4.71762i	−0.145175	−	0.251450i
$353$	−10.2959			−0.547994			−0.273997	−	0.961730i	$-0.588346\pi$
$353$	−10.2959			−0.547994			−0.273997	+	0.961730i	$0.588346\pi$
$354$	3.02156			0.160594
$355$		0			0
$356$	−1.37836	+	2.38739i	−0.0730529	+	0.126531i
$357$	0.325699	+	0.564128i	0.0172378	+	0.0298568i
$358$	−7.30328	+	12.6496i	−0.385990	+	0.668555i
$359$	−0.991256	+	1.71691i	−0.0523165	+	0.0906148i	−0.890998	−	0.454008i	$-0.849994\pi$
$359$	−0.991256	+	1.71691i	−0.0523165	+	0.0906148i	0.838681	+	0.544623i	$0.183327\pi$
$360$		0			0
$361$	18.9818	+	0.832397i	0.999040	+	0.0438103i
$362$	−21.8811			−1.15004
$363$	1.25537	−	2.17436i	0.0658897	−	0.114124i
$364$	−0.0513629	+	0.0889631i	−0.00269215	+	0.00466294i
$365$		0			0
$366$	−0.125641	+	0.217616i	−0.00656734	+	0.0113750i
$367$	−2.63712	−	4.56763i	−0.137657	−	0.238428i	0.788953	−	0.614454i	$-0.210624\pi$
$367$	−2.63712	−	4.56763i	−0.137657	−	0.238428i	−0.926609	+	0.376026i	$0.877290\pi$
$368$	−30.2656			−1.57770
$369$	3.60769			0.187809
$370$		0			0
$371$	4.12255	+	7.14046i	0.214032	+	0.370714i
$372$	0.0906295			0.00469892
$373$	31.7192			1.64236			0.821179	−	0.570670i	$-0.193317\pi$
$373$	31.7192			1.64236			0.821179	+	0.570670i	$0.193317\pi$
$374$	−10.1482	−	17.5772i	−0.524752	−	0.908897i
$375$		0			0
$376$	8.70500	+	15.0775i	0.448926	+	0.777563i
$377$	−0.815227	+	1.41202i	−0.0419863	+	0.0727225i
$378$	−1.04670	+	1.81294i	−0.0538366	+	0.0932477i
$379$	35.5119			1.82412			0.912062	−	0.410052i	$-0.134490\pi$
$379$	35.5119			1.82412			0.912062	+	0.410052i	$0.134490\pi$
$380$		0			0
$381$	−2.74384			−0.140571
$382$	−15.3153	+	26.5269i	−0.783601	+	1.35724i
$383$	6.96509	−	12.0639i	0.355899	−	0.616436i	−0.631372	−	0.775480i	$-0.717508\pi$
$383$	6.96509	−	12.0639i	0.355899	−	0.616436i	0.987271	+	0.159044i	$0.0508412\pi$
$384$	−1.15095	−	1.99350i	−0.0587342	−	0.101731i
$385$		0			0
$386$	15.0180	+	26.0120i	0.764398	+	1.32398i
$387$	−9.26484			−0.470958
$388$	3.54559			0.180000
$389$	0.471434	+	0.816548i	0.0239027	+	0.0414006i	0.877729	−	0.479157i	$-0.159057\pi$
$389$	0.471434	+	0.816548i	0.0239027	+	0.0414006i	−0.853827	+	0.520557i	$0.825724\pi$
$390$		0			0
$391$	−19.1336			−0.967628
$392$	−14.1756			−0.715974
$393$	−0.226427	−	0.392183i	−0.0114217	−	0.0197830i
$394$	11.7883	−	20.4179i	0.593884	−	1.02864i
$395$		0			0
$396$	1.43349	−	2.48288i	0.0720356	−	0.124769i
$397$	−14.2828	+	24.7386i	−0.716834	+	1.24159i	0.245414	+	0.969418i	$0.421076\pi$
$397$	−14.2828	+	24.7386i	−0.716834	+	1.24159i	−0.962248	+	0.272174i	$0.912257\pi$
$398$	19.6047			0.982693
$399$	0.535682	−	0.882586i	0.0268176	−	0.0441846i
$400$		0			0
$401$	3.58365	−	6.20707i	0.178959	−	0.309966i	−0.762565	−	0.646911i	$-0.776060\pi$
$401$	3.58365	−	6.20707i	0.178959	−	0.309966i	0.941524	+	0.336945i	$0.109394\pi$
$402$	−0.712206	+	1.23358i	−0.0355216	+	0.0615252i
$403$	−0.522535	−	0.905058i	−0.0260293	−	0.0450841i
$404$	1.55103	−	2.68647i	0.0771668	−	0.133657i
$405$		0			0
$406$	−7.75534			−0.384891
$407$	18.5023			0.917125
$408$	−0.668055	−	1.15710i	−0.0330736	−	0.0572852i
$409$	5.26624	+	9.12140i	0.260399	+	0.451024i	0.966348	−	0.257238i	$-0.0828126\pi$
$409$	5.26624	+	9.12140i	0.260399	+	0.451024i	−0.705949	+	0.708263i	$0.749479\pi$
$410$		0			0
$411$	3.19777			0.157734
$412$	−0.514845	−	0.891737i	−0.0253646	−	0.0439327i
$413$	7.32495	−	12.6872i	0.360437	−	0.624296i
$414$	−15.2875	−	26.4787i	−0.751339	−	1.30136i
$415$		0			0
$416$	0.222018	−	0.384546i	0.0108853	−	0.0188539i
$417$	−0.572922			−0.0280561
$418$	−16.6909	+	27.4998i	−0.816379	+	1.34506i
$419$	2.52693			0.123448			0.0617242	−	0.998093i	$-0.480340\pi$
$419$	2.52693			0.123448			0.0617242	+	0.998093i	$0.480340\pi$
$420$		0			0
$421$	−7.43346	+	12.8751i	−0.362285	+	0.627495i	−0.988336	−	0.152286i	$-0.951336\pi$
$421$	−7.43346	+	12.8751i	−0.362285	+	0.627495i	0.626052	+	0.779781i	$0.284670\pi$
$422$	−7.24181	−	12.5432i	−0.352526	−	0.610592i
$423$	−9.65481	+	16.7226i	−0.469433	+	0.813082i
$424$	−8.45592	−	14.6461i	−0.410656	−	0.711276i
$425$		0			0
$426$	−0.439895			−0.0213130
$427$	0.609163	+	1.05510i	0.0294794	+	0.0510599i
$428$	1.26082	+	2.18380i	0.0609440	+	0.105558i
$429$	0.367493			0.0177427
$430$		0			0
$431$	2.09034	+	3.62057i	0.100688	+	0.174397i	0.911968	−	0.410261i	$-0.134562\pi$
$431$	2.09034	+	3.62057i	0.100688	+	0.174397i	−0.811280	+	0.584657i	$0.801229\pi$
$432$	2.35709	−	4.08261i	0.113406	−	0.196425i
$433$	−12.6527	−	21.9150i	−0.608048	−	1.05317i	−0.991562	−	0.129635i	$-0.958620\pi$
$433$	−12.6527	−	21.9150i	−0.608048	−	1.05317i	0.383514	−	0.923535i	$-0.374714\pi$
$434$	2.48546	−	4.30495i	0.119306	−	0.206644i
$435$		0			0
$436$	−1.58910			−0.0761043
$437$	14.5838	+	26.5887i	0.697637	+	1.27191i
$438$	2.06802			0.0988139
$439$	−14.4561	+	25.0386i	−0.689950	+	1.19503i	0.281904	+	0.959443i	$0.409034\pi$
$439$	−14.4561	+	25.0386i	−0.689950	+	1.19503i	−0.971854	+	0.235585i	$0.924299\pi$
$440$		0			0
$441$	−7.86114	−	13.6159i	−0.374340	−	0.648376i
$442$	0.827208	−	1.43277i	0.0393463	−	0.0681498i
$443$	−2.29432	−	3.97388i	−0.109007	−	0.188805i	0.806362	−	0.591423i	$-0.201434\pi$
$443$	−2.29432	−	3.97388i	−0.109007	−	0.188805i	−0.915368	+	0.402618i	$0.868100\pi$
$444$	−0.130790			−0.00620702
$445$		0			0
$446$	−19.1533	−	33.1745i	−0.906935	−	1.57086i
$447$	−0.578773	−	1.00246i	−0.0273750	−	0.0474149i
$448$	−9.23529			−0.436327
$449$	29.2171			1.37884			0.689420	−	0.724362i	$-0.257865\pi$
$449$	29.2171			1.37884			0.689420	+	0.724362i	$0.257865\pi$
$450$		0			0
$451$	3.02917	−	5.24668i	0.142638	−	0.247056i
$452$	0.634928	+	1.09973i	0.0298645	+	0.0517268i
$453$	0.450696	−	0.780628i	0.0211755	−	0.0366771i
$454$	1.69280	−	2.93202i	0.0794471	−	0.137606i
$455$		0			0
$456$	−1.09876	+	1.81031i	−0.0514541	+	0.0847754i
$457$	23.7113			1.10917			0.554584	−	0.832128i	$-0.312878\pi$
$457$	23.7113			1.10917			0.554584	+	0.832128i	$0.312878\pi$
$458$	−16.2046	+	28.0673i	−0.757193	+	1.31150i
$459$	1.49013	−	2.58098i	0.0695534	−	0.120470i
$460$		0			0
$461$	−17.5109	+	30.3298i	−0.815565	+	1.41260i	0.0933568	+	0.995633i	$0.470240\pi$
$461$	−17.5109	+	30.3298i	−0.815565	+	1.41260i	−0.908922	+	0.416967i	$0.863093\pi$
$462$	0.873999	+	1.51381i	0.0406621	+	0.0704289i
$463$	−20.4936			−0.952417			−0.476209	−	0.879332i	$-0.657989\pi$
$463$	−20.4936			−0.952417			−0.476209	+	0.879332i	$0.657989\pi$
$464$	17.4644			0.810765
$465$		0			0
$466$	−1.52107	−	2.63457i	−0.0704621	−	0.122044i
$467$	−9.24346			−0.427736			−0.213868	−	0.976863i	$-0.568606\pi$
$467$	−9.24346			−0.427736			−0.213868	+	0.976863i	$0.568606\pi$
$468$	0.233695			0.0108026
$469$	3.45310	+	5.98095i	0.159449	+	0.276174i
$470$		0			0
$471$	−0.190233	−	0.329494i	−0.00876549	−	0.0151823i
$472$	−15.0245	+	26.0232i	−0.691559	+	1.19782i
$473$	−7.77916	+	13.4739i	−0.357686	+	0.619530i
$474$	−3.91496			−0.179820
$475$		0			0
$476$	0.695620			0.0318837
$477$	9.37856	−	16.2441i	0.429415	−	0.743768i
$478$	5.68860	−	9.85295i	0.260191	−	0.450663i
$479$	−1.88377	−	3.26278i	−0.0860715	−	0.149080i	0.819776	−	0.572685i	$-0.194098\pi$
$479$	−1.88377	−	3.26278i	−0.0860715	−	0.149080i	−0.905847	+	0.423604i	$0.860765\pi$
$480$		0			0
$481$	0.754086	+	1.30611i	0.0343834	+	0.0595537i
$482$	−21.5316			−0.980737
$483$	1.64785			0.0749798
$484$	−1.34059	−	2.32197i	−0.0609359	−	0.105544i
$485$		0			0
$486$	7.15673			0.324636
$487$	−11.7981			−0.534621			−0.267311	−	0.963610i	$-0.586135\pi$
$487$	−11.7981			−0.534621			−0.267311	+	0.963610i	$0.586135\pi$
$488$	−1.24948	−	2.16416i	−0.0565612	−	0.0979669i
$489$	0.867922	−	1.50328i	0.0392488	−	0.0679809i
$490$		0			0
$491$	−3.91782	+	6.78586i	−0.176809	+	0.306241i	−0.940786	−	0.339002i	$-0.889911\pi$
$491$	−3.91782	+	6.78586i	−0.176809	+	0.306241i	0.763977	+	0.645243i	$0.223244\pi$
$492$	−0.0214128	+	0.0370880i	−0.000965362	+	0.00167206i
$493$	11.0408			0.497254
$494$	−2.62153	−	0.0574526i	−0.117948	−	0.00258491i
$495$		0			0
$496$	−5.59707	+	9.69442i	−0.251316	+	0.435292i
$497$	−1.06641	+	1.84707i	−0.0478348	+	0.0828523i
$498$	2.05301	+	3.55593i	0.0919978	+	0.159345i
$499$	−0.529796	+	0.917633i	−0.0237169	+	0.0410789i	−0.877640	−	0.479320i	$-0.840883\pi$
$499$	−0.529796	+	0.917633i	−0.0237169	+	0.0410789i	0.853923	+	0.520399i	$0.174217\pi$
$500$		0			0
$501$	−3.04002			−0.135818
$502$	−10.6458			−0.475145
$503$	2.68855	+	4.65671i	0.119877	+	0.207633i	0.919719	−	0.392578i	$-0.128417\pi$
$503$	2.68855	+	4.65671i	0.119877	+	0.207633i	−0.799842	+	0.600211i	$0.795083\pi$
$504$	−5.17589	−	8.96490i	−0.230552	−	0.399329i
$505$		0			0
$506$	−51.3441			−2.28253
$507$	−1.16547	−	2.01866i	−0.0517604	−	0.0896517i
$508$	−1.46506	+	2.53755i	−0.0650014	+	0.112586i
$509$	−16.9240	−	29.3132i	−0.750142	−	1.29928i	−0.947753	−	0.319004i	$-0.896652\pi$
$509$	−16.9240	−	29.3132i	−0.750142	−	1.29928i	0.197611	−	0.980280i	$-0.436682\pi$
$510$		0			0
$511$	5.01336	−	8.68339i	0.221778	−	0.384131i
$512$	18.5188			0.818423
$513$	−4.72242	−	0.103495i	−0.208500	−	0.00456942i
$514$	12.8951			0.568778
$515$		0			0
$516$	0.0549897	−	0.0952450i	0.00242079	−	0.00419293i
$517$	16.2132	+	28.0821i	0.713056	+	1.23505i
$518$	−3.58684	+	6.21260i	−0.157597	+	0.272966i
$519$	1.26902	+	2.19800i	0.0557037	+	0.0964817i
$520$		0			0
$521$	−29.5742			−1.29567			−0.647834	−	0.761782i	$-0.724325\pi$
$521$	−29.5742			−1.29567			−0.647834	+	0.761782i	$0.724325\pi$
$522$	8.82147	+	15.2792i	0.386105	+	0.668754i
$523$	−12.0223	−	20.8232i	−0.525698	−	0.910536i	−0.999552	−	0.0299323i	$-0.990471\pi$
$523$	−12.0223	−	20.8232i	−0.525698	−	0.910536i	0.473854	−	0.880604i	$-0.342863\pi$
$524$	−0.483596			−0.0211260
$525$		0			0
$526$	22.6054	+	39.1537i	0.985643	+	1.70718i
$527$	−3.53841	+	6.12871i	−0.154136	+	0.266971i
$528$	−1.96818	−	3.40899i	−0.0856540	−	0.148357i
$529$	−12.7013	+	21.9992i	−0.552228	+	0.956488i
$530$		0			0
$531$	−33.3277			−1.44630
$532$	−0.530207	−	0.966659i	−0.0229874	−	0.0419100i
$533$	0.493831			0.0213902
$534$	−1.91183	+	3.31138i	−0.0827329	+	0.143298i
$535$		0			0
$536$	−7.08279	−	12.2678i	−0.305930	−	0.529886i
$537$	−0.895447	+	1.55096i	−0.0386414	+	0.0669289i
$538$	−13.6326	−	23.6124i	−0.587743	−	1.01800i
$539$	−26.4022			−1.13722
$540$		0			0
$541$	13.0959	+	22.6827i	0.563035	+	0.975205i	0.997230	+	0.0743856i	$0.0236996\pi$
$541$	13.0959	+	22.6827i	0.563035	+	0.975205i	−0.434195	+	0.900819i	$0.642967\pi$
$542$	−8.49753	−	14.7181i	−0.365000	−	0.632199i
$543$	−2.68282			−0.115131
$544$	−3.00684			−0.128917
$545$		0			0
$546$	−0.0712420	+	0.123395i	−0.00304888	+	0.00528081i
$547$	7.46421	+	12.9284i	0.319146	+	0.552778i	0.980310	−	0.197464i	$-0.0632705\pi$
$547$	7.46421	+	12.9284i	0.319146	+	0.552778i	−0.661164	+	0.750242i	$0.729937\pi$
$548$	1.70743	−	2.95735i	0.0729377	−	0.126332i
$549$	1.38581	−	2.40029i	0.0591449	−	0.102442i
$550$		0			0
$551$	−8.41540	−	15.3427i	−0.358508	−	0.653622i
$552$	−3.37997			−0.143861
$553$	−9.49077	+	16.4385i	−0.403588	+	0.699036i
$554$	1.33077	−	2.30496i	0.0565390	−	0.0979284i
$555$		0			0
$556$	−0.305908	+	0.529848i	−0.0129734	+	0.0224706i
$557$	2.63757	+	4.56841i	0.111758	+	0.193570i	0.916479	−	0.400083i	$-0.131019\pi$
$557$	2.63757	+	4.56841i	0.111758	+	0.193570i	−0.804721	+	0.593653i	$0.797685\pi$
$558$	−11.3086			−0.478730
$559$	−1.26820			−0.0536391
$560$		0			0
$561$	−1.24426	−	2.15513i	−0.0525328	−	0.0909895i
$562$	21.0196			0.886660
$563$	17.8950			0.754186			0.377093	−	0.926175i	$-0.376924\pi$
$563$	17.8950			0.754186			0.377093	+	0.926175i	$0.376924\pi$
$564$	−0.114609	−	0.198508i	−0.00482590	−	0.00835870i
$565$		0			0
$566$	−13.2631	−	22.9724i	−0.557491	−	0.965603i
$567$	5.67612	−	9.83132i	0.238375	−	0.412877i
$568$	2.18735	−	3.78859i	0.0917790	−	0.158966i
$569$	6.81848			0.285846			0.142923	−	0.989734i	$-0.454350\pi$
$569$	6.81848			0.285846			0.142923	+	0.989734i	$0.454350\pi$
$570$		0			0
$571$	5.16915			0.216322			0.108161	−	0.994133i	$-0.465504\pi$
$571$	5.16915			0.216322			0.108161	+	0.994133i	$0.465504\pi$
$572$	0.196221	−	0.339864i	0.00820440	−	0.0142104i
$573$	−1.87780	+	3.25244i	−0.0784461	+	0.135873i
$574$	1.17447	+	2.03423i	0.0490213	+	0.0849073i
$575$		0			0
$576$	10.5049	+	18.1950i	0.437703	+	0.758125i
$577$	−28.5621			−1.18905			−0.594527	−	0.804076i	$-0.702661\pi$
$577$	−28.5621			−1.18905			−0.594527	+	0.804076i	$0.702661\pi$
$578$	13.9772			0.581376
$579$	1.84135	+	3.18930i	0.0765237	+	0.132543i
$580$		0			0
$581$	19.9079			0.825919
$582$	4.91785			0.203851
$583$	−15.7493	−	27.2786i	−0.652269	−	1.12976i
$584$	−10.2831	+	17.8108i	−0.425518	+	0.737018i
$585$		0			0
$586$	24.6684	−	42.7269i	1.01904	−	1.76503i
$587$	20.1627	−	34.9228i	0.832204	−	1.44142i	−0.0640822	−	0.997945i	$-0.520412\pi$
$587$	20.1627	−	34.9228i	0.832204	−	1.44142i	0.896286	−	0.443476i	$-0.146255\pi$
$588$	0.186633			0.00769663
$589$	11.2137	+	0.245756i	0.462052	+	0.0101262i
$590$		0			0
$591$	1.44535	−	2.50341i	0.0594536	−	0.102977i
$592$	8.07730	−	13.9903i	0.331975	−	0.574997i
$593$	13.8452	+	23.9806i	0.568555	+	0.984767i	0.996709	+	0.0810610i	$0.0258308\pi$
$593$	13.8452	+	23.9806i	0.568555	+	0.984767i	−0.428154	+	0.903706i	$0.640836\pi$
$594$	3.99870	−	6.92595i	0.164069	−	0.284175i
$595$		0			0
$596$	−1.23613			−0.0506338
$597$	2.40371			0.0983771
$598$	−2.09260	−	3.62449i	−0.0855727	−	0.148216i
$599$	1.31466	+	2.27706i	0.0537156	+	0.0930382i	0.891633	−	0.452759i	$-0.149560\pi$
$599$	1.31466	+	2.27706i	0.0537156	+	0.0930382i	−0.837917	+	0.545797i	$0.816227\pi$
$600$		0			0
$601$	27.7009			1.12994			0.564972	−	0.825110i	$-0.308887\pi$
$601$	27.7009			1.12994			0.564972	+	0.825110i	$0.308887\pi$
$602$	−3.01613	−	5.22408i	−0.122928	−	0.212918i
$603$	7.85561	−	13.6063i	0.319905	−	0.554092i
$604$	−0.481292	−	0.833622i	−0.0195835	−	0.0339196i
$605$		0			0
$606$	2.15133	−	3.72622i	0.0873919	−	0.151367i
$607$	−32.0668			−1.30155			−0.650775	−	0.759271i	$-0.725556\pi$
$607$	−32.0668			−1.30155			−0.650775	+	0.759271i	$0.725556\pi$
$608$	2.29184	+	4.17842i	0.0929463	+	0.169457i
$609$	−0.950874			−0.0385313
$610$		0			0
$611$	−1.32158	+	2.28904i	−0.0534654	+	0.0926048i
$612$	−0.791248	−	1.37048i	−0.0319843	−	0.0553985i
$613$	−6.23014	+	10.7909i	−0.251633	+	0.435841i	−0.963976	−	0.265991i	$-0.914301\pi$
$613$	−6.23014	+	10.7909i	−0.251633	+	0.435841i	0.712343	+	0.701832i	$0.247634\pi$
$614$	−11.5215	−	19.9559i	−0.464971	−	0.805354i
$615$		0			0
$616$	−17.3836			−0.700405
$617$	13.2370	+	22.9271i	0.532900	+	0.923009i	0.999262	+	0.0384155i	$0.0122311\pi$
$617$	13.2370	+	22.9271i	0.532900	+	0.923009i	−0.466362	+	0.884594i	$0.654436\pi$
$618$	−0.714106	−	1.23687i	−0.0287256	−	0.0497541i
$619$	33.3766			1.34152			0.670760	−	0.741674i	$-0.265968\pi$
$619$	33.3766			1.34152			0.670760	+	0.741674i	$0.265968\pi$
$620$		0			0
$621$	−3.76960	−	6.52914i	−0.151269	−	0.262005i
$622$	21.6224	−	37.4511i	0.866978	−	1.50165i
$623$	9.26942	+	16.0551i	0.371371	+	0.643234i
$624$	0.160431	−	0.277875i	0.00642240	−	0.0111239i
$625$		0			0
$626$	47.2323			1.88778
$627$	−2.04645	+	3.37173i	−0.0817275	+	0.134654i
$628$	−0.406296			−0.0162130
$629$	5.10638	−	8.84452i	0.203605	−	0.352654i
$630$		0			0
$631$	−20.0601	−	34.7450i	−0.798578	−	1.38318i	−0.920542	−	0.390643i	$-0.872253\pi$
$631$	−20.0601	−	34.7450i	−0.798578	−	1.38318i	0.121964	−	0.992535i	$-0.461081\pi$
$632$	19.4669	−	33.7176i	0.774351	−	1.34122i
$633$	−0.887911	−	1.53791i	−0.0352913	−	0.0611263i
$634$	−20.1000			−0.798271
$635$		0			0
$636$	0.111329	+	0.192828i	0.00441450	+	0.00764613i
$637$	−1.07606	−	1.86379i	−0.0426349	−	0.0738459i
$638$	29.6276			1.17297
$639$	4.85202			0.191943
$640$		0			0
$641$	−0.203273	+	0.352079i	−0.00802880	+	0.0139063i	−0.870012	−	0.493031i	$-0.835889\pi$
$641$	−0.203273	+	0.352079i	−0.00802880	+	0.0139063i	0.861983	+	0.506937i	$0.169222\pi$
$642$	1.74880	+	3.02901i	0.0690195	+	0.119545i
$643$	12.5848	−	21.7975i	0.496296	−	0.859610i	−0.503695	−	0.863882i	$-0.668026\pi$
$643$	12.5848	−	21.7975i	0.496296	−	0.859610i	0.999991	+	0.00427137i	$0.00135962\pi$
$644$	0.879860	−	1.52396i	0.0346713	−	0.0600525i
$645$		0			0
$646$	8.53908	+	15.5682i	0.335965	+	0.612523i
$647$	18.3604			0.721821			0.360911	−	0.932600i	$-0.382466\pi$
$647$	18.3604			0.721821			0.360911	+	0.932600i	$0.382466\pi$
$648$	−11.6425	+	20.1654i	−0.457361	+	0.792173i
$649$	−27.9834	+	48.4686i	−1.09844	+	1.90256i
$650$		0			0
$651$	0.304740	−	0.527825i	0.0119437	−	0.0206871i
$652$	−0.926843	−	1.60534i	−0.0362980	−	0.0628699i
$653$	33.0301			1.29257			0.646284	−	0.763097i	$-0.276322\pi$
$653$	33.0301			1.29257			0.646284	+	0.763097i	$0.276322\pi$
$654$	−2.20414			−0.0861886
$655$		0			0
$656$	−2.64481	−	4.58094i	−0.103262	−	0.178856i
$657$	−22.8102			−0.889911
$658$	−12.5723			−0.490120
$659$	13.2310	+	22.9167i	0.515406	+	0.892709i	0.999840	+	0.0178814i	$0.00569212\pi$
$659$	13.2310	+	22.9167i	0.515406	+	0.892709i	−0.484434	+	0.874828i	$0.660975\pi$
$660$		0			0
$661$	7.79673	+	13.5043i	0.303258	+	0.525258i	0.976872	−	0.213825i	$-0.0685924\pi$
$661$	7.79673	+	13.5043i	0.303258	+	0.525258i	−0.673614	+	0.739083i	$0.735259\pi$
$662$	−21.7938	+	37.7480i	−0.847041	+	1.46712i
$663$	0.101423	−	0.175670i	0.00393895	−	0.00682246i
$664$	−40.8339			−1.58466
$665$		0			0
$666$	16.3197			0.632377
$667$	13.9651	−	24.1882i	0.540729	−	0.936570i
$668$	−1.62320	+	2.81146i	−0.0628034	+	0.108779i
$669$	−2.34837	−	4.06749i	−0.0907931	−	0.157258i
$670$		0			0
$671$	−2.32717	−	4.03078i	−0.0898395	−	0.155607i
$672$	0.258959			0.00998958
$673$	−6.13645			−0.236543			−0.118271	−	0.992981i	$-0.537735\pi$
$673$	−6.13645			−0.236543			−0.118271	+	0.992981i	$0.537735\pi$
$674$	11.4880	+	19.8977i	0.442500	+	0.766432i
$675$		0			0
$676$	−2.48919			−0.0957379
$677$	22.2754			0.856112			0.428056	−	0.903752i	$-0.359199\pi$
$677$	22.2754			0.856112			0.428056	+	0.903752i	$0.359199\pi$
$678$	0.880665	+	1.52536i	0.0338217	+	0.0585810i
$679$	11.9220	−	20.6495i	0.457524	−	0.792455i
$680$		0			0
$681$	0.207553	−	0.359492i	0.00795344	−	0.0137758i
$682$	−9.49517	+	16.4461i	−0.363589	+	0.629754i
$683$	16.7397			0.640527			0.320264	−	0.947328i	$-0.396228\pi$
$683$	16.7397			0.640527			0.320264	+	0.947328i	$0.396228\pi$
$684$	−1.30138	+	2.14414i	−0.0497594	+	0.0819832i
$685$		0			0
$686$	11.8796	−	20.5761i	0.453566	−	0.785599i
$687$	−1.98683	+	3.44130i	−0.0758024	+	0.131294i
$688$	6.79208	+	11.7642i	0.258946	+	0.448507i
$689$	1.28377	−	2.22355i	0.0489076	−	0.0847104i
$690$		0			0
$691$	36.7557			1.39825			0.699126	−	0.714999i	$-0.253573\pi$
$691$	36.7557			1.39825			0.699126	+	0.714999i	$0.253573\pi$
$692$	2.71034			0.103032
$693$	−9.64018	−	16.6973i	−0.366200	−	0.634277i
$694$	16.7284	+	28.9744i	0.635000	+	1.09985i
$695$		0			0
$696$	1.95037			0.0739288
$697$	−1.67202	−	2.89602i	−0.0633323	−	0.109695i
$698$	18.8767	−	32.6954i	0.714494	−	1.23754i
$699$	−0.186497	−	0.323021i	−0.00705395	−	0.0122178i
$700$		0			0
$701$	−17.7053	+	30.6665i	−0.668721	+	1.15826i	0.309541	+	0.950886i	$0.399824\pi$
$701$	−17.7053	+	30.6665i	−0.668721	+	1.15826i	−0.978262	+	0.207372i	$0.933509\pi$
$702$	0.651889			0.0246040
$703$	−16.1828	−	0.354657i	−0.610345	−	0.0133761i
$704$	35.2814			1.32972
$705$		0			0
$706$	−7.62510	+	13.2071i	−0.286974	+	0.497054i
$707$	−10.4306	−	18.0664i	−0.392285	−	0.679457i
$708$	0.197810	−	0.342618i	0.00743417	−	0.0128764i
$709$	−16.9184	−	29.3036i	−0.635386	−	1.10052i	−0.986433	−	0.164163i	$-0.947508\pi$
$709$	−16.9184	−	29.3036i	−0.635386	−	1.10052i	0.351048	−	0.936358i	$-0.385826\pi$
$710$		0			0
$711$	43.1819			1.61945
$712$	−19.0129	−	32.9313i	−0.712538	−	1.23415i
$713$	8.95117	+	15.5039i	0.335224	+	0.580625i
$714$	0.964848			0.0361085
$715$		0			0
$716$	0.956237	+	1.65625i	0.0357362	+	0.0618970i
$717$	0.697474	−	1.20806i	0.0260476	−	0.0451158i
$718$	1.46824	+	2.54307i	0.0547943	+	0.0949066i
$719$	−13.4970	+	23.3775i	−0.503353	+	0.871833i	0.496640	+	0.867957i	$0.334567\pi$
$719$	−13.4970	+	23.3775i	−0.503353	+	0.871833i	−0.999992	+	0.00387581i	$0.998766\pi$
$720$		0			0
$721$	−6.92463			−0.257887
$722$	15.1256	−	23.7324i	0.562916	−	0.883229i
$723$	−2.63997			−0.0981814
$724$	−1.43247	+	2.48111i	−0.0532374	+	0.0922099i
$725$		0			0
$726$	−1.85944	−	3.22065i	−0.0690104	−	0.119529i
$727$	−10.8016	+	18.7090i	−0.400610	+	0.693878i	−0.993800	−	0.111185i	$-0.964535\pi$
$727$	−10.8016	+	18.7090i	−0.400610	+	0.693878i	0.593189	+	0.805063i	$0.297869\pi$
$728$	−0.708492	−	1.22714i	−0.0262584	−	0.0454810i
$729$	−25.2353			−0.934640
$730$		0			0
$731$	4.29388	+	7.43723i	0.158815	+	0.275076i
$732$	0.0164504	+	0.0284930i	0.000608026	+	0.00105313i
$733$	17.2551			0.637332			0.318666	−	0.947867i	$-0.396765\pi$
$733$	17.2551			0.637332			0.318666	+	0.947867i	$0.396765\pi$
$734$	−7.81217			−0.288353
$735$		0			0
$736$	−3.80322	+	6.58737i	−0.140189	+	0.242814i
$737$	−13.1918	−	22.8489i	−0.485927	−	0.841650i
$738$	2.67184	−	4.62777i	0.0983519	−	0.170350i
$739$	−2.39553	+	4.14918i	−0.0881210	+	0.152630i	−0.906717	−	0.421740i	$-0.861420\pi$
$739$	−2.39553	+	4.14918i	−0.0881210	+	0.152630i	0.818596	+	0.574370i	$0.194753\pi$
$740$		0			0
$741$	−0.321423	−	0.00704420i	−0.0118078	−	0.000258775i
$742$	12.2126			0.448338
$743$	7.24373	−	12.5465i	0.265747	−	0.460287i	−0.702012	−	0.712165i	$-0.747715\pi$
$743$	7.24373	−	12.5465i	0.265747	−	0.460287i	0.967759	+	0.251878i	$0.0810482\pi$
$744$	−0.625065	+	1.08264i	−0.0229160	+	0.0396917i
$745$		0			0
$746$	23.4912	−	40.6879i	0.860072	−	1.48969i
$747$	−22.6447	−	39.2217i	−0.828525	−	1.43505i
$748$	−2.65746			−0.0971665
$749$	16.9579			0.619630
$750$		0			0
$751$	−3.22637	−	5.58824i	−0.117732	−	0.203918i	0.801137	−	0.598482i	$-0.204229\pi$
$751$	−3.22637	−	5.58824i	−0.117732	−	0.203918i	−0.918869	+	0.394564i	$0.870896\pi$
$752$	28.3119			1.03243
$753$	−1.30527			−0.0475667
$754$	1.20751	+	2.09147i	0.0439749	+	0.0761668i
$755$		0			0
$756$	0.137047	+	0.237373i	0.00498437	+	0.00863318i
$757$	18.4795	−	32.0074i	0.671649	−	1.16333i	−0.305788	−	0.952100i	$-0.598920\pi$
$757$	18.4795	−	32.0074i	0.671649	−	1.16333i	0.977436	−	0.211230i	$-0.0677469\pi$
$758$	26.3000	−	45.5530i	0.955260	−	1.65456i
$759$	−6.29525			−0.228503
$760$		0			0
$761$	48.3893			1.75411			0.877055	−	0.480389i	$-0.159505\pi$
$761$	48.3893			1.75411			0.877055	+	0.480389i	$0.159505\pi$
$762$	−2.03208	+	3.51967i	−0.0736145	+	0.127504i
$763$	−5.34333	+	9.25493i	−0.193442	+	0.335051i
$764$	2.00528	+	3.47324i	0.0725484	+	0.125657i
$765$		0			0
$766$	−10.3167	−	17.8690i	−0.372756	−	0.645632i
$767$	−4.56200			−0.164724
$768$	−0.837598			−0.0302242
$769$	−20.7177	−	35.8841i	−0.747098	−	1.29401i	−0.949208	−	0.314649i	$-0.898113\pi$
$769$	−20.7177	−	35.8841i	−0.747098	−	1.29401i	0.202110	−	0.979363i	$-0.435220\pi$
$770$		0			0
$771$	1.58105			0.0569403
$772$	3.93270			0.141541
$773$	−19.4154	−	33.6285i	−0.698325	−	1.20953i	−0.969047	−	0.246877i	$-0.920596\pi$
$773$	−19.4154	−	33.6285i	−0.698325	−	1.20953i	0.270722	−	0.962658i	$-0.412738\pi$
$774$	−6.86151	+	11.8845i	−0.246632	+	0.427179i
$775$		0			0
$776$	−24.4537	+	42.3550i	−0.877836	+	1.52046i
$777$	−0.439779	+	0.761720i	−0.0157770	+	0.0273266i
$778$	1.39657			0.0500695
$779$	−2.74999	+	4.53087i	−0.0985287	+	0.162335i
$780$		0			0
$781$	4.07397	−	7.05632i	0.145778	−	0.252495i
$782$	−14.1703	+	24.5437i	−0.506729	+	0.877680i
$783$	2.17521	+	3.76757i	0.0777355	+	0.134642i
$784$	−11.5261	+	19.9637i	−0.411645	+	0.712990i
$785$		0			0
$786$	−0.670764			−0.0239254
$787$	51.4952			1.83561			0.917803	−	0.397037i	$-0.129962\pi$
$787$	51.4952			1.83561			0.917803	+	0.397037i	$0.129962\pi$
$788$	−1.54347	−	2.67336i	−0.0549838	−	0.0952347i
$789$	2.77163	+	4.80060i	0.0986725	+	0.170906i
$790$		0			0
$791$	8.53973			0.303638
$792$	19.7734	+	34.2485i	0.702615	+	1.21697i
$793$	0.189694	−	0.328560i	0.00673623	−	0.0116675i
$794$	21.1556	+	36.6426i	0.750785	+	1.30040i
$795$		0			0
$796$	1.28344	−	2.22299i	0.0454905	−	0.0787918i
$797$	−7.50433			−0.265817			−0.132908	−	0.991128i	$-0.542432\pi$
$797$	−7.50433			−0.265817			−0.132908	+	0.991128i	$0.542432\pi$
$798$	−0.735414	−	1.34079i	−0.0260334	−	0.0474634i
$799$	17.8985			0.633203
$800$		0			0
$801$	21.0874	−	36.5244i	0.745087	−	1.29053i
$802$	−5.30809	−	9.19387i	−0.187435	−	0.324647i
$803$	−19.1524	+	33.1730i	−0.675875	+	1.17065i
$804$	0.0932510	+	0.161515i	0.00328871	+	0.00569621i
$805$		0			0
$806$	−1.54795			−0.0545243
$807$	−1.67148	−	2.89509i	−0.0588388	−	0.101912i
$808$	21.3947	+	37.0567i	0.752663	+	1.30365i
$809$	−17.9109			−0.629714			−0.314857	−	0.949139i	$-0.601957\pi$
$809$	−17.9109			−0.629714			−0.314857	+	0.949139i	$0.601957\pi$
$810$		0			0
$811$	−2.57516	−	4.46030i	−0.0904260	−	0.156622i	0.817264	−	0.576263i	$-0.195490\pi$
$811$	−2.57516	−	4.46030i	−0.0904260	−	0.156622i	−0.907690	+	0.419640i	$0.862156\pi$
$812$	−0.507713	+	0.879385i	−0.0178172	+	0.0308604i
$813$	−1.04187	−	1.80458i	−0.0365401	−	0.0632893i
$814$	13.7028	−	23.7339i	0.480281	−	0.831871i
$815$		0			0
$816$	−2.17276			−0.0760619
$817$	7.06221	−	11.6356i	0.247075	−	0.407080i
$818$	15.6007			0.545464
$819$	0.785796	−	1.36104i	0.0274579	−	0.0475586i
$820$		0			0
$821$	0.690525	+	1.19602i	0.0240995	+	0.0417415i	0.877824	−	0.478984i	$-0.158995\pi$
$821$	0.690525	+	1.19602i	0.0240995	+	0.0417415i	−0.853724	+	0.520726i	$0.825661\pi$
$822$	2.36826	−	4.10194i	0.0826025	−	0.143072i
$823$	7.20798	+	12.4846i	0.251254	+	0.435185i	0.963871	−	0.266368i	$-0.0858236\pi$
$823$	7.20798	+	12.4846i	0.251254	+	0.435185i	−0.712617	+	0.701553i	$0.752490\pi$
$824$	14.2034			0.494798
$825$		0			0
$826$	−10.8497	−	18.7922i	−0.377509	−	0.653864i
$827$	4.73660	+	8.20404i	0.164708	+	0.285282i	0.936552	−	0.350530i	$-0.113999\pi$
$827$	4.73660	+	8.20404i	0.164708	+	0.285282i	−0.771844	+	0.635812i	$0.780665\pi$
$828$	−4.00326			−0.139123
$829$	−12.3950			−0.430497			−0.215248	−	0.976559i	$-0.569056\pi$
$829$	−12.3950			−0.430497			−0.215248	+	0.976559i	$0.569056\pi$
$830$		0			0
$831$	0.163164	−	0.282609i	0.00566011	−	0.00980359i
$832$	1.43794	+	2.49059i	0.0498516	+	0.0863455i
$833$	−7.28666	+	12.6209i	−0.252468	+	0.437287i
$834$	−0.424304	+	0.734916i	−0.0146925	+	0.0254481i
$835$		0			0
$836$	2.02554	+	3.69291i	0.0700548	+	0.127722i
$837$	−2.78848			−0.0963839
$838$	1.87144	−	3.24142i	0.0646477	−	0.111973i
$839$	−6.26491	+	10.8511i	−0.216289	+	0.374623i	−0.953670	−	0.300853i	$-0.902729\pi$
$839$	−6.26491	+	10.8511i	−0.216289	+	0.374623i	0.737382	+	0.675476i	$0.236062\pi$
$840$		0			0
$841$	6.44162	−	11.1572i	0.222125	−	0.384732i
$842$	11.0104	+	19.0706i	0.379443	+	0.657215i
$843$	2.57720			0.0887633
$844$	−1.89638			−0.0652760
$845$		0			0
$846$	14.3007	+	24.7695i	0.491667	+	0.851592i
$847$	−18.0308			−0.619547
$848$	−27.5018			−0.944416
$849$	−1.62618	−	2.81663i	−0.0558103	−	0.0966663i
$850$		0			0
$851$	−12.9177	−	22.3741i	−0.442813	−	0.766974i
$852$	−0.0287983	+	0.0498801i	−0.000986613	+	0.00170886i
$853$	1.73650	−	3.00771i	0.0594567	−	0.102982i	−0.834765	−	0.550606i	$-0.814397\pi$
$853$	1.73650	−	3.00771i	0.0594567	−	0.102982i	0.894222	+	0.447624i	$0.147730\pi$
$854$	1.80458			0.0617513
$855$		0			0
$856$	−34.7831			−1.18886
$857$	−8.33085	+	14.4295i	−0.284577	+	0.492901i	−0.972506	−	0.232876i	$-0.925186\pi$
$857$	−8.33085	+	14.4295i	−0.284577	+	0.492901i	0.687930	+	0.725777i	$0.258520\pi$
$858$	0.272164	−	0.471402i	0.00929154	−	0.0160934i
$859$	−20.4042	−	35.3412i	−0.696183	−	1.20583i	−0.969780	−	0.243981i	$-0.921547\pi$
$859$	−20.4042	−	35.3412i	−0.696183	−	1.20583i	0.273597	−	0.961844i	$-0.411787\pi$
$860$		0			0
$861$	0.144000	+	0.249415i	0.00490751	+	0.00850005i
$862$	6.19239			0.210914
$863$	−4.07050			−0.138561			−0.0692806	−	0.997597i	$-0.522070\pi$
$863$	−4.07050			−0.138561			−0.0692806	+	0.997597i	$0.522070\pi$
$864$	−0.592392	−	1.02605i	−0.0201536	−	0.0349071i
$865$		0			0
$866$	−37.4821			−1.27369
$867$	1.71373			0.0582014
$868$	−0.325428	−	0.563658i	−0.0110458	−	0.0191318i
$869$	36.2574	−	62.7996i	1.22995	−	2.13033i
$870$		0			0
$871$	1.07530	−	1.86247i	0.0364351	−	0.0631075i
$872$	10.9599	−	18.9831i	0.371150	−	0.642851i
$873$	−54.2437			−1.83587
$874$	44.9075	+	0.984178i	1.51902	+	0.0332903i
$875$		0			0
$876$	0.135386	−	0.234495i	0.00457426	−	0.00792285i
$877$	−13.2572	+	22.9621i	−0.447663	+	0.775376i	−0.998233	−	0.0594132i	$-0.981077\pi$
$877$	−13.2572	+	22.9621i	−0.447663	+	0.775376i	0.550570	+	0.834789i	$0.314410\pi$
$878$	21.4122	+	37.0871i	0.722628	+	1.25163i
$879$	3.02457	−	5.23871i	0.102016	−	0.176697i
$880$		0			0
$881$	−22.3730			−0.753766			−0.376883	−	0.926261i	$-0.623004\pi$
$881$	−22.3730			−0.753766			−0.376883	+	0.926261i	$0.623004\pi$
$882$	−23.2878			−0.784140
$883$	9.85689	+	17.0726i	0.331711	+	0.574540i	0.982847	−	0.184421i	$-0.0590408\pi$
$883$	9.85689	+	17.0726i	0.331711	+	0.574540i	−0.651137	+	0.758961i	$0.725708\pi$
$884$	−0.108308	−	0.187596i	−0.00364281	−	0.00630953i
$885$		0			0
$886$	−6.79667			−0.228339
$887$	5.71080	+	9.89139i	0.191750	+	0.332120i	0.945830	−	0.324662i	$-0.105250\pi$
$887$	5.71080	+	9.89139i	0.191750	+	0.332120i	−0.754080	+	0.656782i	$0.771917\pi$
$888$	0.902049	−	1.56239i	0.0302708	−	0.0524305i
$889$	9.85245	+	17.0649i	0.330441	+	0.572340i
$890$		0			0
$891$	−21.6844	+	37.5584i	−0.726453	+	1.25825i
$892$	−5.01558			−0.167934
$893$	−13.6424	−	24.8724i	−0.456524	−	0.832323i
$894$	−1.71455			−0.0573431
$895$		0			0
$896$	−8.26556	+	14.3164i	−0.276133	+	0.478276i
$897$	−0.256571	−	0.444395i	−0.00856667	−	0.0148379i
$898$	21.6381	−	37.4783i	0.722073	−	1.25067i
$899$	−5.16517	−	8.94634i	−0.172268	−	0.298377i
$900$		0			0
$901$	−17.3864			−0.579223
$902$	−4.48679	−	7.77135i	−0.149394	−	0.258758i
$903$	−0.369804	−	0.640519i	−0.0123063	−	0.0213151i
$904$	−17.5162			−0.582580
$905$		0			0
$906$	−0.667568	−	1.15626i	−0.0221784	−	0.0384142i
$907$	−5.36915	+	9.29964i	−0.178280	+	0.308789i	−0.941291	−	0.337595i	$-0.890387\pi$
$907$	−5.36915	+	9.29964i	−0.178280	+	0.308789i	0.763012	+	0.646385i	$0.223720\pi$
$908$	−0.221643	−	0.383897i	−0.00735548	−	0.0127401i
$909$	−23.7291	+	41.1000i	−0.787045	+	1.36320i
$910$		0			0
$911$	−27.5952			−0.914269			−0.457134	−	0.889398i	$-0.651124\pi$
$911$	−27.5952			−0.914269			−0.457134	+	0.889398i	$0.651124\pi$
$912$	1.65610	+	3.01935i	0.0548388	+	0.0999807i
$913$	−76.0538			−2.51701
$914$	17.5605	−	30.4157i	0.580850	−	1.00606i
$915$		0			0
$916$	2.12171	+	3.67492i	0.0701034	+	0.121423i
$917$	−1.62608	+	2.81646i	−0.0536980	+	0.0930077i
$918$	−2.20717	−	3.82294i	−0.0728476	−	0.126176i
$919$	−49.2639			−1.62507			−0.812533	−	0.582915i	$-0.801912\pi$
$919$	−49.2639			−1.62507			−0.812533	+	0.582915i	$0.801912\pi$
$920$		0			0
$921$	−1.41264	−	2.44677i	−0.0465482	−	0.0806238i
$922$	25.9371	+	44.9243i	0.854192	+	1.47950i
$923$	0.664160			0.0218611
$924$	0.228870			0.00752927
$925$		0			0
$926$	−15.1775	+	26.2882i	−0.498763	+	0.863883i
$927$	7.87657	+	13.6426i	0.258700	+	0.448082i
$928$	2.19461	−	3.80117i	0.0720415	−	0.124779i
$929$	−21.5374	+	37.3039i	−0.706619	+	1.22390i	0.259485	+	0.965747i	$0.416447\pi$
$929$	−21.5374	+	37.3039i	−0.706619	+	1.22390i	−0.966104	+	0.258153i	$0.916886\pi$
$930$		0			0
$931$	23.0923	+	0.506085i	0.756821	+	0.0165863i
$932$	−0.398315			−0.0130472
$933$	2.65110	−	4.59183i	0.0867930	−	0.150330i
$934$	−6.84568	+	11.8571i	−0.223998	+	0.387975i
$935$		0			0
$936$	−1.61178	+	2.79168i	−0.0526826	+	0.0912490i
$937$	−21.7222	−	37.6239i	−0.709633	−	1.22912i	−0.964993	−	0.262275i	$-0.915527\pi$
$937$	−21.7222	−	37.6239i	−0.709633	−	1.22912i	0.255360	−	0.966846i	$-0.417806\pi$
$938$	10.2294			0.334003
$939$	5.79110			0.188985
$940$		0			0
$941$	−14.6471	−	25.3694i	−0.477480	−	0.827020i	0.522186	−	0.852831i	$-0.325117\pi$
$941$	−14.6471	−	25.3694i	−0.477480	−	0.827020i	−0.999667	+	0.0258111i	$0.991783\pi$
$942$	−0.563545			−0.0183613
$943$	−8.45946			−0.275478
$944$	24.4326	+	42.3186i	0.795215	+	1.37735i
$945$		0			0
$946$	11.5224	+	19.9575i	0.374627	+	0.648873i
$947$	1.00294	−	1.73715i	0.0325913	−	0.0564498i	−0.849270	−	0.527959i	$-0.822957\pi$
$947$	1.00294	−	1.73715i	0.0325913	−	0.0564498i	0.881861	+	0.471509i	$0.156291\pi$
$948$	−0.256298	+	0.443921i	−0.00832418	+	0.0144179i
$949$	−3.12233			−0.101355
$950$		0			0
$951$	−2.46443			−0.0799148
$952$	−4.79764	+	8.30975i	−0.155492	+	0.269321i
$953$	9.61946	−	16.6614i	0.311605	−	0.539716i	−0.667105	−	0.744964i	$-0.732467\pi$
$953$	9.61946	−	16.6614i	0.311605	−	0.539716i	0.978710	+	0.205248i	$0.0658001\pi$
$954$	−13.8915	−	24.0607i	−0.449753	−	0.778995i
$955$		0			0
$956$	−0.744823	−	1.29007i	−0.0240893	−	0.0417239i
$957$	3.63260			0.117425
$958$	−5.58045			−0.180296
$959$	−11.4824	−	19.8881i	−0.370786	−	0.642220i
$960$		0			0
$961$	−24.3786			−0.786406
$962$	2.23390			0.0720237
$963$	−19.2892	−	33.4098i	−0.621585	−	1.07662i
$964$	−1.40959	+	2.44149i	−0.0453999	+	0.0786350i
$965$		0			0
$966$	1.22039	−	2.11378i	0.0392655	−	0.0680099i
$967$	−14.2071	+	24.6075i	−0.456871	+	0.791324i	−0.998794	−	0.0491047i	$-0.984363\pi$
$967$	−14.2071	+	24.6075i	−0.456871	+	0.791324i	0.541923	+	0.840428i	$0.317697\pi$
$968$	36.9838			1.18870
$969$	1.04697	+	1.90880i	0.0336334	+	0.0613196i
$970$		0			0
$971$	−8.98811	+	15.5679i	−0.288442	+	0.499597i	−0.973438	−	0.228950i	$-0.926471\pi$
$971$	−8.98811	+	15.5679i	−0.288442	+	0.499597i	0.684996	+	0.728547i	$0.259804\pi$
$972$	0.468524	−	0.811508i	0.0150279	−	0.0260291i
$973$	2.05722	+	3.56321i	0.0659515	+	0.114231i
$974$	−8.73761	+	15.1340i	−0.279971	+	0.484924i
$975$		0			0
$976$	−4.06377			−0.130078
$977$	13.2288			0.423226			0.211613	−	0.977354i	$-0.432128\pi$
$977$	13.2288			0.423226			0.211613	+	0.977354i	$0.432128\pi$
$978$	−1.28556	−	2.22666i	−0.0411077	−	0.0712006i
$979$	−35.4118	−	61.3350i	−1.13177	−	1.96027i
$980$		0			0
$981$	24.3116			0.776208
$982$	5.80305	+	10.0512i	0.185183	+	0.320746i
$983$	−24.2617	+	42.0225i	−0.773828	+	1.34031i	0.161623	+	0.986853i	$0.448327\pi$
$983$	−24.2617	+	42.0225i	−0.773828	+	1.34031i	−0.935451	+	0.353457i	$0.885006\pi$
$984$	−0.295364	−	0.511586i	−0.00941587	−	0.0163088i
$985$		0			0
$986$	8.17680	−	14.1626i	0.260403	−	0.451030i
$987$	−1.54148			−0.0490658
$988$	−0.178136	+	0.293496i	−0.00566727	+	0.00933736i
$989$	21.7246			0.690802
$990$		0			0
$991$	−20.1402	+	34.8838i	−0.639773	+	1.10812i	0.345709	+	0.938342i	$0.387638\pi$
$991$	−20.1402	+	34.8838i	−0.639773	+	1.10812i	−0.985482	+	0.169778i	$0.945695\pi$
$992$	1.40667	+	2.43643i	0.0446619	+	0.0773568i
$993$	−2.67212	+	4.62824i	−0.0847971	+	0.146873i
$994$	1.57955	+	2.73587i	0.0501004	+	0.0867764i
$995$		0			0
$996$	0.537613			0.0170349
$997$	−13.7795	−	23.8668i	−0.436401	−	0.755869i	0.561008	−	0.827811i	$-0.310414\pi$
$997$	−13.7795	−	23.8668i	−0.436401	−	0.755869i	−0.997409	+	0.0719414i	$0.977081\pi$
$998$	0.784730	+	1.35919i	0.0248402	+	0.0430245i
$999$	4.02413			0.127318

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.e.f.201.6	yes	12
5.2	odd	4		475.2.j.d.49.9		24
5.3	odd	4		475.2.j.d.49.4		24
5.4	even	2		475.2.e.h.201.1	yes	12
19.7	even	3	inner	475.2.e.f.26.6	✓	12
19.8	odd	6		9025.2.a.bs.1.6		6
19.11	even	3		9025.2.a.bz.1.1		6
95.7	odd	12		475.2.j.d.349.4		24
95.49	even	6		9025.2.a.br.1.6		6
95.64	even	6		475.2.e.h.26.1	yes	12
95.83	odd	12		475.2.j.d.349.9		24
95.84	odd	6		9025.2.a.by.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
475.2.e.f.26.6	✓	12	19.7	even	3	inner
475.2.e.f.201.6	yes	12	1.1	even	1	trivial
475.2.e.h.26.1	yes	12	95.64	even	6
475.2.e.h.201.1	yes	12	5.4	even	2
475.2.j.d.49.4		24	5.3	odd	4
475.2.j.d.49.9		24	5.2	odd	4
475.2.j.d.349.4		24	95.7	odd	12
475.2.j.d.349.9		24	95.83	odd	12
9025.2.a.br.1.6		6	95.49	even	6
9025.2.a.bs.1.6		6	19.8	odd	6
9025.2.a.by.1.1		6	95.84	odd	6
9025.2.a.bz.1.1		6	19.11	even	3

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.740597 - 1.28275i) q^{2} +(0.0908038 - 0.157277i) q^{3} +(-0.0969683 - 0.167954i) q^{4} +(-0.134498 - 0.232958i) q^{6} -1.30422 q^{7} +2.67513 q^{8} +(1.48351 + 2.56951i) q^{9} +4.98247 q^{11} -0.0352204 q^{12} +(0.203067 + 0.351723i) q^{13} +(-0.965899 + 1.67299i) q^{14} +(2.17513 - 3.76744i) q^{16} +(1.37510 - 2.38173i) q^{17} +4.39473 q^{18} +(-4.35785 - 0.0955054i) q^{19} +(-0.118428 + 0.205123i) q^{21} +(3.69001 - 6.39128i) q^{22} +(-3.47860 - 6.02510i) q^{23} +(0.242912 - 0.420736i) q^{24} +0.601564 q^{26} +1.08366 q^{27} +(0.126468 + 0.219048i) q^{28} +(2.00728 + 3.47672i) q^{29} -2.57321 q^{31} +(-0.546661 - 0.946844i) q^{32} +(0.452428 - 0.783628i) q^{33} +(-2.03678 - 3.52781i) q^{34} +(0.287707 - 0.498323i) q^{36} +3.71348 q^{37} +(-3.34992 + 5.51931i) q^{38} +0.0737572 q^{39} +(0.607965 - 1.05303i) q^{41} +(0.175415 + 0.303827i) q^{42} +(-1.56130 + 2.70426i) q^{43} +(-0.483142 - 0.836826i) q^{44} -10.3050 q^{46} +(3.25405 + 5.63617i) q^{47} +(-0.395020 - 0.684196i) q^{48} -5.29902 q^{49} +(-0.249728 - 0.432541i) q^{51} +(0.0393822 - 0.0682119i) q^{52} +(-3.16094 - 5.47490i) q^{53} +(0.802553 - 1.39006i) q^{54} -3.48895 q^{56} +(-0.410731 + 0.676717i) q^{57} +5.94636 q^{58} +(-5.61636 + 9.72783i) q^{59} +(-0.467072 - 0.808992i) q^{61} +(-1.90571 + 3.30079i) q^{62} +(-1.93482 - 3.35120i) q^{63} +7.08110 q^{64} +(-0.670133 - 1.16071i) q^{66} +(-2.64764 - 4.58585i) q^{67} -0.533363 q^{68} -1.26348 q^{69} +(0.817659 - 1.41623i) q^{71} +(3.96858 + 6.87378i) q^{72} +(-3.84396 + 6.65794i) q^{73} +(2.75019 - 4.76347i) q^{74} +(0.406533 + 0.741180i) q^{76} -6.49822 q^{77} +(0.0546243 - 0.0946121i) q^{78} +(7.27699 - 12.6041i) q^{79} +(-4.35213 + 7.53811i) q^{81} +(-0.900514 - 1.55974i) q^{82} -15.2643 q^{83} +0.0459350 q^{84} +(2.31260 + 4.00553i) q^{86} +0.729076 q^{87} +13.3288 q^{88} +(-7.10727 - 12.3101i) q^{89} +(-0.264844 - 0.458723i) q^{91} +(-0.674627 + 1.16849i) q^{92} +(-0.233658 + 0.404707i) q^{93} +9.63975 q^{94} -0.198556 q^{96} +(-9.14111 + 15.8329i) q^{97} +(-3.92444 + 6.79733i) q^{98} +(7.39155 + 12.8025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{6} + 4 q^{7} + 12 q^{8} - 7 q^{9} - 2 q^{11} + 14 q^{12} - 5 q^{13} + 6 q^{14} + 6 q^{16} + 3 q^{17} + 14 q^{18} - 6 q^{19} - 3 q^{21} - 9 q^{22} + 6 q^{23} - 11 q^{24}+ \cdots + 20 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 + q^6 + 4 * q^7 + 12 * q^8 - 7 * q^9 - 2 * q^11 + 14 * q^12 - 5 * q^13 + 6 * q^14 + 6 * q^16 + 3 * q^17 + 14 * q^18 - 6 * q^19 - 3 * q^21 - 9 * q^22 + 6 * q^23 - 11 * q^24 + 38 * q^26 + 36 * q^27 + 4 * q^28 - 3 * q^29 - 6 * q^31 + 6 * q^32 + 18 * q^33 + q^34 - 13 * q^36 - 12 * q^37 - 18 * q^38 + 16 * q^39 - 11 * q^41 + 11 * q^42 - 13 * q^43 - 21 * q^44 - 24 * q^46 + 6 * q^47 + 19 * q^48 + 8 * q^49 + 17 * q^51 + q^52 - 18 * q^53 - 18 * q^54 + 8 * q^56 - 20 * q^57 + 10 * q^58 - 4 * q^59 - 25 * q^61 + 21 * q^62 - 43 * q^63 - 44 * q^64 - 34 * q^66 - 6 * q^67 - 2 * q^68 + 26 * q^69 - 18 * q^71 - 13 * q^72 - q^73 + 6 * q^74 + 24 * q^76 - 22 * q^77 - 72 * q^78 - 3 * q^79 - 2 * q^81 - 31 * q^82 - 46 * q^83 + 74 * q^84 - 9 * q^86 + 22 * q^87 + 22 * q^88 - 12 * q^89 + 11 * q^91 - 28 * q^92 + 13 * q^93 + 16 * q^94 - 26 * q^96 - 3 * q^97 + 22 * q^98 + 20 * q^99

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