LMFDB - Embedded newform 475.2.e.h.26.1

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			26.1
Root			$0.590804 - 1.02330i$ of defining polynomial
Character	$\chi$	$=$	475.26
Dual form			475.2.e.h.201.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.740597 - 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 $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

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

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	−0.999620	−	0.0275641i	$-0.991225\pi$
$2$	−0.740597	−	1.28275i	−0.523681	−	0.907043i	0.475939	−	0.879478i	$-0.342108\pi$
$3$	−0.0908038	−	0.157277i	−0.0524256	−	0.0908038i	0.838622	−	0.544714i	$-0.183362\pi$
$3$	−0.0908038	−	0.157277i	−0.0524256	−	0.0908038i	−0.891047	+	0.453910i	$0.850029\pi$
$4$	−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	$-0.420728\pi$
$7$	1.30422			0.492948			0.246474	+	0.969149i	$0.420728\pi$
$8$	−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	$-0.851270\pi$
$13$	−0.203067	+	0.351723i	−0.0563207	+	0.0975504i	0.836490	+	0.547982i	$0.184604\pi$
$14$	−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	$-0.274900\pi$
$17$	−1.37510	−	2.38173i	−0.333510	−	0.577656i	−0.983197	+	0.182546i	$0.941566\pi$
$18$	−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	−0.233498	−	0.972357i	$-0.575017\pi$
$23$	3.47860	−	6.02510i	0.725337	−	1.25632i	0.958835	−	0.283964i	$-0.0916495\pi$
$24$	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	−0.617243	−	0.786772i	$-0.711751\pi$
$29$	2.00728	−	3.47672i	0.372743	−	0.645610i	0.989986	+	0.141162i	$0.0450839\pi$
$30$		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	$-0.598739\pi$
$37$	−3.71348			−0.610492			−0.305246	+	0.952274i	$0.598739\pi$
$38$	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	0.909587	−	0.415514i	$-0.136398\pi$
$41$	0.607965	+	1.05303i	0.0949482	+	0.164455i	−0.814639	+	0.579969i	$0.803065\pi$
$42$	−0.175415	+	0.303827i	−0.0270671	+	0.0468816i
$43$	1.56130	+	2.70426i	0.238097	+	0.412396i	0.960168	−	0.279423i	$-0.0901431\pi$
$43$	1.56130	+	2.70426i	0.238097	+	0.412396i	−0.722071	+	0.691819i	$0.756810\pi$
$44$	−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	$-0.990759\pi$
$47$	−3.25405	+	5.63617i	−0.474651	+	0.822120i	0.524927	+	0.851147i	$0.324093\pi$
$48$	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	$-0.690369\pi$
$53$	3.16094	−	5.47490i	0.434188	−	0.752036i	0.997229	+	0.0743934i	$0.0237020\pi$
$54$	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	−0.956376	−	0.292140i	$-0.905633\pi$
$59$	−5.61636	−	9.72783i	−0.731188	−	1.26646i	0.225187	−	0.974315i	$-0.427701\pi$
$60$		0			0
$61$	−0.467072	+	0.808992i	−0.0598024	+	0.103581i	−0.894377	−	0.447315i	$-0.852380\pi$
$61$	−0.467072	+	0.808992i	−0.0598024	+	0.103581i	0.834574	+	0.550896i	$0.185714\pi$
$62$	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	$-0.728487\pi$
$67$	2.64764	−	4.58585i	0.323461	−	0.560251i	0.981200	+	0.192995i	$0.0618202\pi$
$68$	0.533363			0.0646797
$69$	−1.26348			−0.152105
$70$		0			0
$71$	0.817659	+	1.41623i	0.0970383	+	0.168075i	0.910457	−	0.413603i	$-0.135730\pi$
$71$	0.817659	+	1.41623i	0.0970383	+	0.168075i	−0.813419	+	0.581678i	$0.802396\pi$
$72$	−3.96858	+	6.87378i	−0.467702	+	0.810083i
$73$	3.84396	+	6.65794i	0.449902	+	0.779252i	0.998379	−	0.0569129i	$-0.0181257\pi$
$73$	3.84396	+	6.65794i	0.449902	+	0.779252i	−0.548478	+	0.836165i	$0.684792\pi$
$74$	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	0.906622	+	0.421944i	$0.138652\pi$
$79$	7.27699	+	12.6041i	0.818725	+	1.41807i	−0.0878971	+	0.996130i	$0.528015\pi$
$80$		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	$-0.183879\pi$
$83$	15.2643			1.67547			0.837735	+	0.546077i	$0.183879\pi$
$84$	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	0.192812	+	0.981236i	$0.438239\pi$
$89$	−7.10727	+	12.3101i	−0.753369	+	1.30487i	−0.946181	+	0.323638i	$0.895094\pi$
$90$		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	0.786433	+	0.617676i	$0.211926\pi$
$97$	9.14111	+	15.8329i	0.928139	+	1.60758i	0.141707	+	0.989909i	$0.454741\pi$
$98$	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	−0.126540	−	0.991962i	$-0.540387\pi$
$101$	7.99763	−	13.8523i	0.795794	−	1.37836i	0.922334	−	0.386394i	$-0.126280\pi$
$102$	0.739791			0.0732502
$103$	−5.30941			−0.523152			−0.261576	−	0.965183i	$-0.584242\pi$
$103$	−5.30941			−0.523152			−0.261576	+	0.965183i	$0.584242\pi$
$104$	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	$-0.283671\pi$
$107$	13.0024			1.25699			0.628494	+	0.777814i	$0.283671\pi$
$108$	0.105080	−	0.182004i	0.0101114	−	0.0175134i
$109$	4.09697	+	7.09616i	0.392418	+	0.679689i	0.992768	−	0.120049i	$-0.0383052\pi$
$109$	4.09697	+	7.09616i	0.392418	+	0.679689i	−0.600350	+	0.799738i	$0.704972\pi$
$110$		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	$-0.400346\pi$
$113$	6.54779			0.615964			0.307982	+	0.951392i	$0.400346\pi$
$114$	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	−0.307472	−	0.951557i	$-0.599483\pi$
$127$	7.55431	−	13.0844i	0.670336	−	1.16106i	0.977809	−	0.209500i	$-0.0671835\pi$
$128$	−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	0.915338	−	0.402686i	$-0.131923\pi$
$131$	1.24679	+	2.15950i	0.108933	+	0.188677i	−0.806406	+	0.591363i	$0.798590\pi$
$132$	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	0.194583	+	0.980886i	$0.437665\pi$
$137$	−8.80405	+	15.2491i	−0.752181	+	1.30282i	−0.946764	+	0.321930i	$0.895669\pi$
$138$	0.935729	+	1.62073i	0.0796546	+	0.137966i
$139$	−1.57736	+	2.73207i	−0.133790	+	0.231731i	−0.925135	−	0.379639i	$-0.876048\pi$
$139$	−1.57736	+	2.73207i	−0.133790	+	0.231731i	0.791345	+	0.611370i	$0.209381\pi$
$140$		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	0.966530	−	0.256552i	$-0.0825866\pi$
$149$	3.18694	+	5.51994i	0.261084	+	0.452211i	−0.705446	+	0.708764i	$0.749253\pi$
$150$		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	$-0.193308\pi$
$157$	−1.04750	−	1.81432i	−0.0835993	−	0.144798i	−0.904793	+	0.425851i	$0.859975\pi$
$158$	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	$-0.622127\pi$
$163$	−9.55821			−0.748656			−0.374328	+	0.927296i	$0.622127\pi$
$164$	−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	−0.336008	−	0.941859i	$-0.609077\pi$
$167$	8.36974	−	14.4968i	0.647670	−	1.12180i	0.983678	−	0.179938i	$-0.0575897\pi$
$168$	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	0.999334	+	0.0364853i	$0.0116162\pi$
$173$	6.98769	+	12.1030i	0.531264	+	0.920177i	−0.468070	+	0.883691i	$0.655050\pi$
$174$	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	0.449323	+	0.893369i	$0.351665\pi$
$181$	−7.38629	+	12.7934i	−0.549019	+	0.950929i	−0.998342	+	0.0575593i	$0.981668\pi$
$182$	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	0.956954	+	0.290238i	$0.0937346\pi$
$193$	10.1391	+	17.5615i	0.729831	+	1.26410i	−0.227123	+	0.973866i	$0.572932\pi$
$194$	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	$-0.691907\pi$
$197$	−15.9172			−1.13406			−0.567028	+	0.823698i	$0.691907\pi$
$198$	−21.8966			−1.55613
$199$	6.61785	−	11.4625i	0.469127	−	0.812552i	−0.530250	−	0.847841i	$-0.677902\pi$
$199$	6.61785	−	11.4625i	0.469127	−	0.812552i	0.999377	+	0.0352892i	$0.0112352\pi$
$200$		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	0.983788	−	0.179336i	$-0.0573950\pi$
$211$	4.88917	+	8.46829i	0.336584	+	0.582981i	−0.647204	+	0.762317i	$0.724062\pi$
$212$	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	−0.866128	−	0.499822i	$-0.833399\pi$
$223$	−12.9310	−	22.3971i	−0.865923	−	1.49982i	0.000205308	−	1.00000i	$-0.499935\pi$
$224$	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	$-0.524168\pi$
$227$	−2.28573			−0.151709			−0.0758545	+	0.997119i	$0.524168\pi$
$228$	−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	$-0.188097\pi$
$233$	−1.02692	−	1.77868i	−0.0672758	−	0.116525i	−0.897701	+	0.440605i	$0.854764\pi$
$234$	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	−0.999339	−	0.0363455i	$-0.988428\pi$
$241$	−7.26832	+	12.5891i	−0.468194	+	0.810935i	0.531146	+	0.847280i	$0.321762\pi$
$242$	−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	−0.956867	−	0.290527i	$-0.906169\pi$
$251$	−3.59365	+	6.22439i	−0.226829	+	0.392880i	0.730037	+	0.683407i	$0.239503\pi$
$252$	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	$-0.920863\pi$
$257$	−4.35294	+	7.53951i	−0.271529	+	0.470302i	0.697725	+	0.716366i	$0.254196\pi$
$258$	−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	0.763432	+	0.645888i	$0.223513\pi$
$263$	15.2616	+	26.4339i	0.941072	+	1.62998i	0.177639	+	0.984096i	$0.443154\pi$
$264$	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	0.997395	+	0.0721309i	$0.0229800\pi$
$269$	9.20379	+	15.9414i	0.561165	+	0.971966i	−0.436230	+	0.899835i	$0.643687\pi$
$270$		0			0
$271$	5.73694	+	9.93668i	0.348494	+	0.603610i	0.985982	−	0.166850i	$-0.0533597\pi$
$271$	5.73694	+	9.93668i	0.348494	+	0.603610i	−0.637488	+	0.770460i	$0.720026\pi$
$272$	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	$-0.517191\pi$
$277$	−1.79689			−0.107965			−0.0539823	+	0.998542i	$0.517191\pi$
$278$	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	−0.572976	−	0.819572i	$-0.694211\pi$
$281$	7.09550	−	12.2898i	0.423282	−	0.733146i	0.996258	+	0.0864258i	$0.0275446\pi$
$282$	−0.875326	−	1.51611i	−0.0521249	−	0.0902830i
$283$	−8.95435	−	15.5094i	−0.532281	−	0.921938i	−0.999290	−	0.0376851i	$-0.988002\pi$
$283$	−8.95435	−	15.5094i	−0.532281	−	0.921938i	0.467009	−	0.884253i	$-0.345332\pi$
$284$	−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	$-0.925810\pi$
$293$	−33.3088			−1.94592			−0.972961	+	0.230970i	$0.925810\pi$
$294$	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	$-0.313088\pi$
$307$	−7.77854	−	13.4728i	−0.443945	−	0.768935i	−0.997978	+	0.0635594i	$0.979755\pi$
$308$	−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	−0.0752782	+	0.997163i	$0.523984\pi$
$313$	−15.9440	+	27.6158i	−0.901207	+	1.56094i	−0.825929	+	0.563774i	$0.809349\pi$
$314$	−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	$-0.708883\pi$
$317$	6.78505	−	11.7520i	0.381086	−	0.660061i	0.991218	+	0.132239i	$0.0422167\pi$
$318$	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	$-0.0278230\pi$
$337$	7.75588	+	13.4336i	0.422489	+	0.731773i	−0.573693	+	0.819071i	$0.694490\pi$
$338$	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	0.991847	+	0.127434i	$0.0406742\pi$
$347$	11.2938	+	19.5615i	0.606285	+	1.05012i	−0.385562	+	0.922682i	$0.625992\pi$
$348$	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	$-0.411654\pi$
$353$	10.2959			0.547994			0.273997	+	0.961730i	$0.411654\pi$
$354$	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	0.838681	−	0.544623i	$-0.183327\pi$
$359$	−0.991256	−	1.71691i	−0.0523165	−	0.0906148i	−0.890998	+	0.454008i	$0.849994\pi$
$360$		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	$-0.789376\pi$
$367$	2.63712	−	4.56763i	0.137657	−	0.238428i	0.926609	+	0.376026i	$0.122710\pi$
$368$	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	$-0.806683\pi$
$373$	−31.7192			−1.64236			−0.821179	+	0.570670i	$0.806683\pi$
$374$	−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	$-0.282492\pi$
$383$	−6.96509	−	12.0639i	−0.355899	−	0.616436i	−0.987271	+	0.159044i	$0.949159\pi$
$384$	−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	−0.853827	−	0.520557i	$-0.825724\pi$
$389$	0.471434	−	0.816548i	0.0239027	−	0.0414006i	0.877729	+	0.479157i	$0.159057\pi$
$390$		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	0.962248	+	0.272174i	$0.0877428\pi$
$397$	14.2828	+	24.7386i	0.716834	+	1.24159i	−0.245414	+	0.969418i	$0.578924\pi$
$398$	−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	0.941524	−	0.336945i	$-0.109394\pi$
$401$	3.58365	+	6.20707i	0.178959	+	0.309966i	−0.762565	+	0.646911i	$0.776060\pi$
$402$	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	−0.705949	−	0.708263i	$-0.749479\pi$
$409$	5.26624	−	9.12140i	0.260399	−	0.451024i	0.966348	+	0.257238i	$0.0828126\pi$
$410$		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	0.626052	−	0.779781i	$-0.284670\pi$
$421$	−7.43346	−	12.8751i	−0.362285	−	0.627495i	−0.988336	+	0.152286i	$0.951336\pi$
$422$	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	−0.811280	−	0.584657i	$-0.801229\pi$
$431$	2.09034	−	3.62057i	0.100688	−	0.174397i	0.911968	+	0.410261i	$0.134562\pi$
$432$	−2.35709	−	4.08261i	−0.113406	−	0.196425i
$433$	12.6527	−	21.9150i	0.608048	−	1.05317i	−0.383514	−	0.923535i	$-0.625286\pi$
$433$	12.6527	−	21.9150i	0.608048	−	1.05317i	0.991562	−	0.129635i	$-0.0413804\pi$
$434$	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	−0.971854	−	0.235585i	$-0.924299\pi$
$439$	−14.4561	−	25.0386i	−0.689950	−	1.19503i	0.281904	−	0.959443i	$-0.409034\pi$
$440$		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	$-0.798566\pi$
$443$	2.29432	−	3.97388i	0.109007	−	0.188805i	0.915368	+	0.402618i	$0.131900\pi$
$444$	−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	$-0.687122\pi$
$457$	−23.7113			−1.10917			−0.554584	+	0.832128i	$0.687122\pi$
$458$	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	−0.908922	−	0.416967i	$-0.863093\pi$
$461$	−17.5109	−	30.3298i	−0.815565	−	1.41260i	0.0933568	−	0.995633i	$-0.470240\pi$
$462$	−0.873999	+	1.51381i	−0.0406621	+	0.0704289i
$463$	20.4936			0.952417			0.476209	−	0.879332i	$-0.342011\pi$
$463$	20.4936			0.952417			0.476209	+	0.879332i	$0.342011\pi$
$464$	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	$-0.431394\pi$
$467$	9.24346			0.427736			0.213868	+	0.976863i	$0.431394\pi$
$468$	−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	−0.905847	−	0.423604i	$-0.860765\pi$
$479$	−1.88377	+	3.26278i	−0.0860715	+	0.149080i	0.819776	+	0.572685i	$0.194098\pi$
$480$		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	$-0.413865\pi$
$487$	11.7981			0.534621			0.267311	+	0.963610i	$0.413865\pi$
$488$	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	0.763977	−	0.645243i	$-0.223244\pi$
$491$	−3.91782	−	6.78586i	−0.176809	−	0.306241i	−0.940786	+	0.339002i	$0.889911\pi$
$492$	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	0.853923	−	0.520399i	$-0.174217\pi$
$499$	−0.529796	−	0.917633i	−0.0237169	−	0.0410789i	−0.877640	+	0.479320i	$0.840883\pi$
$500$		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	$-0.871583\pi$
$503$	−2.68855	+	4.65671i	−0.119877	+	0.207633i	0.799842	+	0.600211i	$0.204917\pi$
$504$	−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	0.197611	+	0.980280i	$0.436682\pi$
$509$	−16.9240	+	29.3132i	−0.750142	+	1.29928i	−0.947753	+	0.319004i	$0.896652\pi$
$510$		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	−0.473854	−	0.880604i	$-0.657137\pi$
$523$	12.0223	−	20.8232i	0.525698	−	0.910536i	0.999552	−	0.0299323i	$-0.00952918\pi$
$524$	−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	−0.434195	−	0.900819i	$-0.642967\pi$
$541$	13.0959	−	22.6827i	0.563035	−	0.975205i	0.997230	−	0.0743856i	$-0.0236996\pi$
$542$	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	$-0.936730\pi$
$547$	−7.46421	+	12.9284i	−0.319146	+	0.552778i	0.661164	+	0.750242i	$0.270063\pi$
$548$	−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	$-0.868981\pi$
$557$	−2.63757	+	4.56841i	−0.111758	+	0.193570i	0.804721	+	0.593653i	$0.202315\pi$
$558$	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	$-0.623076\pi$
$563$	−17.8950			−0.754186			−0.377093	+	0.926175i	$0.623076\pi$
$564$	−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	$-0.297339\pi$
$577$	28.5621			1.18905			0.594527	+	0.804076i	$0.297339\pi$
$578$	−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	−0.896286	−	0.443476i	$-0.853745\pi$
$587$	−20.1627	−	34.9228i	−0.832204	−	1.44142i	0.0640822	−	0.997945i	$-0.479588\pi$
$588$	−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	0.428154	+	0.903706i	$0.359164\pi$
$593$	−13.8452	+	23.9806i	−0.568555	+	0.984767i	−0.996709	+	0.0810610i	$0.974169\pi$
$594$	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	−0.837917	−	0.545797i	$-0.816227\pi$
$599$	1.31466	−	2.27706i	0.0537156	−	0.0930382i	0.891633	+	0.452759i	$0.149560\pi$
$600$		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	$-0.274444\pi$
$607$	32.0668			1.30155			0.650775	+	0.759271i	$0.274444\pi$
$608$	−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	$-0.0856991\pi$
$613$	6.23014	+	10.7909i	0.251633	+	0.435841i	−0.712343	+	0.701832i	$0.752366\pi$
$614$	−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	0.466362	+	0.884594i	$0.345564\pi$
$617$	−13.2370	+	22.9271i	−0.532900	+	0.923009i	−0.999262	+	0.0384155i	$0.987769\pi$
$618$	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	0.121964	+	0.992535i	$0.461081\pi$
$631$	−20.0601	+	34.7450i	−0.798578	+	1.38318i	−0.920542	+	0.390643i	$0.872253\pi$
$632$	−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	0.861983	−	0.506937i	$-0.169222\pi$
$641$	−0.203273	−	0.352079i	−0.00802880	−	0.0139063i	−0.870012	+	0.493031i	$0.835889\pi$
$642$	−1.74880	+	3.02901i	−0.0690195	+	0.119545i
$643$	−12.5848	−	21.7975i	−0.496296	−	0.859610i	0.503695	−	0.863882i	$-0.331974\pi$
$643$	−12.5848	−	21.7975i	−0.496296	−	0.859610i	−0.999991	+	0.00427137i	$0.998640\pi$
$644$	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	$-0.617534\pi$
$647$	−18.3604			−0.721821			−0.360911	+	0.932600i	$0.617534\pi$
$648$	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	$-0.723678\pi$
$653$	−33.0301			−1.29257			−0.646284	+	0.763097i	$0.723678\pi$
$654$	−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	−0.484434	−	0.874828i	$-0.660975\pi$
$659$	13.2310	−	22.9167i	0.515406	−	0.892709i	0.999840	−	0.0178814i	$-0.00569212\pi$
$660$		0			0
$661$	7.79673	−	13.5043i	0.303258	−	0.525258i	−0.673614	−	0.739083i	$-0.735259\pi$
$661$	7.79673	−	13.5043i	0.303258	−	0.525258i	0.976872	+	0.213825i	$0.0685924\pi$
$662$	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	$-0.462265\pi$
$673$	6.13645			0.236543			0.118271	+	0.992981i	$0.462265\pi$
$674$	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	$-0.640801\pi$
$677$	−22.2754			−0.856112			−0.428056	+	0.903752i	$0.640801\pi$
$678$	−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	$-0.603772\pi$
$683$	−16.7397			−0.640527			−0.320264	+	0.947328i	$0.603772\pi$
$684$	−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	−0.978262	−	0.207372i	$-0.933509\pi$
$701$	−17.7053	−	30.6665i	−0.668721	−	1.15826i	0.309541	−	0.950886i	$-0.399824\pi$
$702$	−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	0.351048	+	0.936358i	$0.385826\pi$
$709$	−16.9184	+	29.3036i	−0.635386	+	1.10052i	−0.986433	+	0.164163i	$0.947508\pi$
$710$		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	−0.999992	−	0.00387581i	$-0.998766\pi$
$719$	−13.4970	−	23.3775i	−0.503353	−	0.871833i	0.496640	−	0.867957i	$-0.334567\pi$
$720$		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	$-0.0354648\pi$
$727$	10.8016	+	18.7090i	0.400610	+	0.693878i	−0.593189	+	0.805063i	$0.702131\pi$
$728$	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	$-0.603235\pi$
$733$	−17.2551			−0.637332			−0.318666	+	0.947867i	$0.603235\pi$
$734$	−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	0.818596	−	0.574370i	$-0.194753\pi$
$739$	−2.39553	−	4.14918i	−0.0881210	−	0.152630i	−0.906717	+	0.421740i	$0.861420\pi$
$740$		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	$-0.252285\pi$
$743$	−7.24373	−	12.5465i	−0.265747	−	0.460287i	−0.967759	+	0.251878i	$0.918952\pi$
$744$	−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	−0.918869	−	0.394564i	$-0.870896\pi$
$751$	−3.22637	+	5.58824i	−0.117732	+	0.203918i	0.801137	+	0.598482i	$0.204229\pi$
$752$	−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	−0.977436	−	0.211230i	$-0.932253\pi$
$757$	−18.4795	−	32.0074i	−0.671649	−	1.16333i	0.305788	−	0.952100i	$-0.401080\pi$
$758$	−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	0.202110	+	0.979363i	$0.435220\pi$
$769$	−20.7177	+	35.8841i	−0.747098	+	1.29401i	−0.949208	+	0.314649i	$0.898113\pi$
$770$		0			0
$771$	1.58105			0.0569403
$772$	−3.93270			−0.141541
$773$	19.4154	−	33.6285i	0.698325	−	1.20953i	−0.270722	−	0.962658i	$-0.587262\pi$
$773$	19.4154	−	33.6285i	0.698325	−	1.20953i	0.969047	−	0.246877i	$-0.0794044\pi$
$774$	−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	$-0.870038\pi$
$787$	−51.4952			−1.83561			−0.917803	+	0.397037i	$0.870038\pi$
$788$	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	$-0.457568\pi$
$797$	7.50433			0.265817			0.132908	+	0.991128i	$0.457568\pi$
$798$	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	−0.907690	−	0.419640i	$-0.862156\pi$
$811$	−2.57516	+	4.46030i	−0.0904260	+	0.156622i	0.817264	+	0.576263i	$0.195490\pi$
$812$	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	−0.853724	−	0.520726i	$-0.825661\pi$
$821$	0.690525	−	1.19602i	0.0240995	−	0.0417415i	0.877824	+	0.478984i	$0.158995\pi$
$822$	−2.36826	−	4.10194i	−0.0826025	−	0.143072i
$823$	−7.20798	+	12.4846i	−0.251254	+	0.435185i	−0.963871	−	0.266368i	$-0.914176\pi$
$823$	−7.20798	+	12.4846i	−0.251254	+	0.435185i	0.712617	+	0.701553i	$0.247510\pi$
$824$	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	$-0.886001\pi$
$827$	−4.73660	+	8.20404i	−0.164708	+	0.285282i	0.771844	+	0.635812i	$0.219335\pi$
$828$	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	0.737382	−	0.675476i	$-0.236062\pi$
$839$	−6.26491	−	10.8511i	−0.216289	−	0.374623i	−0.953670	+	0.300853i	$0.902729\pi$
$840$		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	$-0.185603\pi$
$853$	−1.73650	−	3.00771i	−0.0594567	−	0.102982i	−0.894222	+	0.447624i	$0.852270\pi$
$854$	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	$-0.0748137\pi$
$857$	8.33085	+	14.4295i	0.284577	+	0.492901i	−0.687930	+	0.725777i	$0.741480\pi$
$858$	−0.272164	−	0.471402i	−0.00929154	−	0.0160934i
$859$	−20.4042	+	35.3412i	−0.696183	+	1.20583i	0.273597	+	0.961844i	$0.411787\pi$
$859$	−20.4042	+	35.3412i	−0.696183	+	1.20583i	−0.969780	+	0.243981i	$0.921547\pi$
$860$		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	$-0.477930\pi$
$863$	4.07050			0.138561			0.0692806	+	0.997597i	$0.477930\pi$
$864$	−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	$-0.0189229\pi$
$877$	13.2572	+	22.9621i	0.447663	+	0.775376i	−0.550570	+	0.834789i	$0.685590\pi$
$878$	−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	$-0.940959\pi$
$883$	−9.85689	+	17.0726i	−0.331711	+	0.574540i	0.651137	+	0.758961i	$0.274292\pi$
$884$	−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	$-0.894750\pi$
$887$	−5.71080	+	9.89139i	−0.191750	+	0.332120i	0.754080	+	0.656782i	$0.228083\pi$
$888$	−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	$-0.109613\pi$
$907$	5.36915	+	9.29964i	0.178280	+	0.308789i	−0.763012	+	0.646385i	$0.776280\pi$
$908$	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	−0.966104	−	0.258153i	$-0.916886\pi$
$929$	−21.5374	−	37.3039i	−0.706619	−	1.22390i	0.259485	−	0.965747i	$-0.416447\pi$
$930$		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	−0.255360	−	0.966846i	$-0.582194\pi$
$937$	21.7222	−	37.6239i	0.709633	−	1.22912i	0.964993	−	0.262275i	$-0.0844726\pi$
$938$	−10.2294			−0.334003
$939$	5.79110			0.188985
$940$		0			0
$941$	−14.6471	+	25.3694i	−0.477480	+	0.827020i	−0.999667	−	0.0258111i	$-0.991783\pi$
$941$	−14.6471	+	25.3694i	−0.477480	+	0.827020i	0.522186	+	0.852831i	$0.325117\pi$
$942$	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	$-0.177043\pi$
$947$	−1.00294	−	1.73715i	−0.0325913	−	0.0564498i	−0.881861	+	0.471509i	$0.843709\pi$
$948$	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	$-0.267533\pi$
$953$	−9.61946	−	16.6614i	−0.311605	−	0.539716i	−0.978710	+	0.205248i	$0.934200\pi$
$954$	−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	$-0.0156368\pi$
$967$	14.2071	+	24.6075i	0.456871	+	0.791324i	−0.541923	+	0.840428i	$0.682303\pi$
$968$	−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	0.684996	−	0.728547i	$-0.259804\pi$
$971$	−8.98811	−	15.5679i	−0.288442	−	0.499597i	−0.973438	+	0.228950i	$0.926471\pi$
$972$	−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	$-0.567872\pi$
$977$	−13.2288			−0.423226			−0.211613	+	0.977354i	$0.567872\pi$
$978$	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	0.935451	+	0.353457i	$0.114994\pi$
$983$	24.2617	+	42.0225i	0.773828	+	1.34031i	−0.161623	+	0.986853i	$0.551673\pi$
$984$	−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	−0.985482	−	0.169778i	$-0.945695\pi$
$991$	−20.1402	−	34.8838i	−0.639773	−	1.10812i	0.345709	−	0.938342i	$-0.387638\pi$
$992$	−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	$-0.689586\pi$
$997$	13.7795	−	23.8668i	0.436401	−	0.755869i	0.997409	+	0.0719414i	$0.0229195\pi$
$998$	−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.h.26.1	yes	12
5.2	odd	4		475.2.j.d.349.9		24
5.3	odd	4		475.2.j.d.349.4		24
5.4	even	2		475.2.e.f.26.6	✓	12
19.7	even	3		9025.2.a.br.1.6		6
19.11	even	3	inner	475.2.e.h.201.1	yes	12
19.12	odd	6		9025.2.a.by.1.1		6
95.49	even	6		475.2.e.f.201.6	yes	12
95.64	even	6		9025.2.a.bz.1.1		6
95.68	odd	12		475.2.j.d.49.9		24
95.69	odd	6		9025.2.a.bs.1.6		6
95.87	odd	12		475.2.j.d.49.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
475.2.e.f.26.6	✓	12	5.4	even	2
475.2.e.f.201.6	yes	12	95.49	even	6
475.2.e.h.26.1	yes	12	1.1	even	1	trivial
475.2.e.h.201.1	yes	12	19.11	even	3	inner
475.2.j.d.49.4		24	95.87	odd	12
475.2.j.d.49.9		24	95.68	odd	12
475.2.j.d.349.4		24	5.3	odd	4
475.2.j.d.349.9		24	5.2	odd	4
9025.2.a.br.1.6		6	19.7	even	3
9025.2.a.bs.1.6		6	95.69	odd	6
9025.2.a.by.1.1		6	19.12	odd	6
9025.2.a.bz.1.1		6	95.64	even	6

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more