LMFDB - Embedded newform 729.2.e.j.163.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(82,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.e (of order $9$, degree $6$, not 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:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
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} + 18x^{10} + 105x^{8} + 266x^{6} + 306x^{4} + 132x^{2} + 1 $ x^12 + 18x^10 + 105x^8 + 266x^6 + 306x^4 + 132*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			163.1
Root			$1.91182i$ of defining polynomial
Character	$\chi$	$=$	729.163
Dual form			729.2.e.j.568.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.30957 + 0.840614i) q^{2} +(3.09538 - 2.59733i) q^{4} +(0.534882 + 3.03347i) q^{5} +(-2.03666 - 1.70896i) q^{7} +(-2.50784 + 4.34371i) q^{8} +O(q^{10})$	\(q+(-2.30957 + 0.840614i) q^{2} +(3.09538 - 2.59733i) q^{4} +(0.534882 + 3.03347i) q^{5} +(-2.03666 - 1.70896i) q^{7} +(-2.50784 + 4.34371i) q^{8} +(-3.78532 - 6.55636i) q^{10} +(0.596367 - 3.38217i) q^{11} +(3.14229 + 1.14370i) q^{13} +(6.14037 + 2.23491i) q^{14} +(0.737316 - 4.18153i) q^{16} +(1.28641 + 2.22813i) q^{17} +(1.04838 - 1.81585i) q^{19} +(9.53458 + 8.00046i) q^{20} +(1.46574 + 8.31265i) q^{22} +(-0.409408 + 0.343534i) q^{23} +(-4.21736 + 1.53499i) q^{25} -8.21874 q^{26} -10.7430 q^{28} +(2.37826 - 0.865617i) q^{29} +(5.90980 - 4.95891i) q^{31} +(0.0702390 + 0.398345i) q^{32} +(-4.84404 - 4.06463i) q^{34} +(4.09470 - 7.09222i) q^{35} +(5.14783 + 8.91631i) q^{37} +(-0.894879 + 5.07511i) q^{38} +(-14.5179 - 5.28408i) q^{40} +(-4.59040 - 1.67077i) q^{41} +(0.476055 - 2.69984i) q^{43} +(-6.93862 - 12.0180i) q^{44} +(0.656775 - 1.13757i) q^{46} +(4.33428 + 3.63689i) q^{47} +(0.0118968 + 0.0674701i) q^{49} +(8.44994 - 7.09034i) q^{50} +(12.6971 - 4.62138i) q^{52} -6.42657 q^{53} +10.5787 q^{55} +(12.5308 - 4.56085i) q^{56} +(-4.76511 + 3.99840i) q^{58} +(-0.287379 - 1.62981i) q^{59} +(11.0098 + 9.23828i) q^{61} +(-9.48056 + 16.4208i) q^{62} +(3.74896 + 6.49338i) q^{64} +(-1.78862 + 10.1438i) q^{65} +(5.52444 + 2.01073i) q^{67} +(9.76910 + 3.55566i) q^{68} +(-3.49516 + 19.8220i) q^{70} +(7.40813 + 12.8313i) q^{71} +(-0.940699 + 1.62934i) q^{73} +(-19.3844 - 16.2655i) q^{74} +(-1.47123 - 8.34374i) q^{76} +(-6.99457 + 5.86915i) q^{77} +(-16.1566 + 5.88052i) q^{79} +13.0789 q^{80} +12.0063 q^{82} +(3.72944 - 1.35740i) q^{83} +(-6.07087 + 5.09406i) q^{85} +(1.17004 + 6.63564i) q^{86} +(13.1955 + 11.0724i) q^{88} +(2.54940 - 4.41569i) q^{89} +(-4.44523 - 7.69937i) q^{91} +(-0.375001 + 2.12674i) q^{92} +(-13.0675 - 4.75619i) q^{94} +(6.06908 + 2.20897i) q^{95} +(-1.84621 + 10.4704i) q^{97} +(-0.0841927 - 0.145826i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} + 6 q^{4} + 6 q^{5} - 3 q^{7} + 6 q^{8}+O(q^{10}) $ 12 * q - 6 * q^2 + 6 * q^4 + 6 * q^5 - 3 * q^7 + 6 * q^8	$ 12 q - 6 q^{2} + 6 q^{4} + 6 q^{5} - 3 q^{7} + 6 q^{8} - 6 q^{10} + 12 q^{11} - 3 q^{13} + 15 q^{14} - 36 q^{16} - 9 q^{17} - 12 q^{19} + 42 q^{20} + 6 q^{22} + 6 q^{23} + 6 q^{25} - 48 q^{26} + 6 q^{28} + 12 q^{29} + 6 q^{31} + 54 q^{32} - 9 q^{34} + 30 q^{35} - 3 q^{37} + 42 q^{38} - 57 q^{40} + 24 q^{41} + 6 q^{43} - 33 q^{44} + 3 q^{46} + 21 q^{47} + 33 q^{49} + 21 q^{50} + 45 q^{52} + 18 q^{53} + 30 q^{55} + 3 q^{56} + 33 q^{58} + 15 q^{59} + 33 q^{61} - 30 q^{62} - 6 q^{64} - 6 q^{65} + 42 q^{67} - 18 q^{68} + 24 q^{70} - 12 q^{73} - 3 q^{74} - 87 q^{76} - 57 q^{77} - 48 q^{79} + 42 q^{80} - 42 q^{82} + 12 q^{83} - 36 q^{85} - 30 q^{86} + 30 q^{88} - 9 q^{89} - 18 q^{91} - 48 q^{92} + 33 q^{94} + 30 q^{95} - 3 q^{97} + 18 q^{98}+O(q^{100}) $ 12 * q - 6 * q^2 + 6 * q^4 + 6 * q^5 - 3 * q^7 + 6 * q^8 - 6 * q^10 + 12 * q^11 - 3 * q^13 + 15 * q^14 - 36 * q^16 - 9 * q^17 - 12 * q^19 + 42 * q^20 + 6 * q^22 + 6 * q^23 + 6 * q^25 - 48 * q^26 + 6 * q^28 + 12 * q^29 + 6 * q^31 + 54 * q^32 - 9 * q^34 + 30 * q^35 - 3 * q^37 + 42 * q^38 - 57 * q^40 + 24 * q^41 + 6 * q^43 - 33 * q^44 + 3 * q^46 + 21 * q^47 + 33 * q^49 + 21 * q^50 + 45 * q^52 + 18 * q^53 + 30 * q^55 + 3 * q^56 + 33 * q^58 + 15 * q^59 + 33 * q^61 - 30 * q^62 - 6 * q^64 - 6 * q^65 + 42 * q^67 - 18 * q^68 + 24 * q^70 - 12 * q^73 - 3 * q^74 - 87 * q^76 - 57 * q^77 - 48 * q^79 + 42 * q^80 - 42 * q^82 + 12 * q^83 - 36 * q^85 - 30 * q^86 + 30 * q^88 - 9 * q^89 - 18 * q^91 - 48 * q^92 + 33 * q^94 + 30 * q^95 - 3 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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 $

$2$	−2.30957	+	0.840614i	−1.63311	+	0.594404i	−0.985815	−	0.167836i	$-0.946322\pi$
$2$	−2.30957	+	0.840614i	−1.63311	+	0.594404i	−0.647295	+	0.762239i	$0.724100\pi$
$3$		0			0
$3$		0			0
$4$	3.09538	−	2.59733i	1.54769	−	1.29867i
$5$	0.534882	+	3.03347i	0.239207	+	1.35661i	0.833571	+	0.552412i	$0.186292\pi$
$5$	0.534882	+	3.03347i	0.239207	+	1.35661i	−0.594365	+	0.804196i	$0.702596\pi$
$6$		0			0
$7$	−2.03666	−	1.70896i	−0.769784	−	0.645926i	0.170870	−	0.985294i	$-0.445342\pi$
$7$	−2.03666	−	1.70896i	−0.769784	−	0.645926i	−0.940654	+	0.339368i	$0.889787\pi$
$8$	−2.50784	+	4.34371i	−0.886656	+	1.53573i
$9$		0			0
$10$	−3.78532	−	6.55636i	−1.19702	−	2.07330i
$11$	0.596367	−	3.38217i	0.179811	−	1.01976i	−0.752631	−	0.658443i	$-0.771216\pi$
$11$	0.596367	−	3.38217i	0.179811	−	1.01976i	0.932442	−	0.361319i	$-0.117673\pi$
$12$		0			0
$13$	3.14229	+	1.14370i	0.871515	+	0.317205i	0.738780	−	0.673946i	$-0.235402\pi$
$13$	3.14229	+	1.14370i	0.871515	+	0.317205i	0.132734	+	0.991152i	$0.457624\pi$
$14$	6.14037	+	2.23491i	1.64108	+	0.597305i
$15$		0			0
$16$	0.737316	−	4.18153i	0.184329	−	1.04538i
$17$	1.28641	+	2.22813i	0.312000	+	0.540400i	0.978795	−	0.204841i	$-0.0656678\pi$
$17$	1.28641	+	2.22813i	0.312000	+	0.540400i	−0.666795	+	0.745241i	$0.732334\pi$
$18$		0			0
$19$	1.04838	−	1.81585i	0.240515	−	0.416585i	−0.720346	−	0.693615i	$-0.756017\pi$
$19$	1.04838	−	1.81585i	0.240515	−	0.416585i	0.960861	+	0.277030i	$0.0893503\pi$
$20$	9.53458	+	8.00046i	2.13200	+	1.78896i
$21$		0			0
$22$	1.46574	+	8.31265i	0.312498	+	1.77226i
$23$	−0.409408	+	0.343534i	−0.0853674	+	0.0716318i	−0.684473	−	0.729038i	$-0.739968\pi$
$23$	−0.409408	+	0.343534i	−0.0853674	+	0.0716318i	0.599105	+	0.800670i	$0.295523\pi$
$24$		0			0
$25$	−4.21736	+	1.53499i	−0.843472	+	0.306999i
$26$	−8.21874			−1.61183
$27$		0			0
$28$	−10.7430			−2.03023
$29$	2.37826	−	0.865617i	0.441632	−	0.160741i	−0.111627	−	0.993750i	$-0.535606\pi$
$29$	2.37826	−	0.865617i	0.441632	−	0.160741i	0.553259	+	0.833009i	$0.313384\pi$
$30$		0			0
$31$	5.90980	−	4.95891i	1.06143	−	0.890647i	0.0671832	−	0.997741i	$-0.478599\pi$
$31$	5.90980	−	4.95891i	1.06143	−	0.890647i	0.994249	+	0.107093i	$0.0341544\pi$
$32$	0.0702390	+	0.398345i	0.0124166	+	0.0704182i
$33$		0			0
$34$	−4.84404	−	4.06463i	−0.830746	−	0.697079i
$35$	4.09470	−	7.09222i	0.692130	−	1.19880i
$36$		0			0
$37$	5.14783	+	8.91631i	0.846298	+	1.46583i	0.884489	+	0.466561i	$0.154507\pi$
$37$	5.14783	+	8.91631i	0.846298	+	1.46583i	−0.0381907	+	0.999270i	$0.512159\pi$
$38$	−0.894879	+	5.07511i	−0.145169	+	0.823292i
$39$		0			0
$40$	−14.5179	−	5.28408i	−2.29548	−	0.835487i
$41$	−4.59040	−	1.67077i	−0.716901	−	0.260931i	−0.0422913	−	0.999105i	$-0.513466\pi$
$41$	−4.59040	−	1.67077i	−0.716901	−	0.260931i	−0.674610	+	0.738175i	$0.735688\pi$
$42$		0			0
$43$	0.476055	−	2.69984i	0.0725977	−	0.411722i	−0.926752	−	0.375673i	$-0.877412\pi$
$43$	0.476055	−	2.69984i	0.0725977	−	0.411722i	0.999350	−	0.0360490i	$-0.0114772\pi$
$44$	−6.93862	−	12.0180i	−1.04604	−	1.81179i
$45$		0			0
$46$	0.656775	−	1.13757i	0.0968363	−	0.167725i
$47$	4.33428	+	3.63689i	0.632219	+	0.530495i	0.901618	−	0.432534i	$-0.142380\pi$
$47$	4.33428	+	3.63689i	0.632219	+	0.530495i	−0.269398	+	0.963029i	$0.586825\pi$
$48$		0			0
$49$	0.0118968	+	0.0674701i	0.00169954	+	0.00963858i
$50$	8.44994	−	7.09034i	1.19500	−	1.00273i
$51$		0			0
$52$	12.6971	−	4.62138i	1.76078	−	0.640871i
$53$	−6.42657			−0.882758			−0.441379	−	0.897321i	$-0.645511\pi$
$53$	−6.42657			−0.882758			−0.441379	+	0.897321i	$0.645511\pi$
$54$		0			0
$55$	10.5787			1.42643
$56$	12.5308	−	4.56085i	1.67450	−	0.609469i
$57$		0			0
$58$	−4.76511	+	3.99840i	−0.625689	+	0.525015i
$59$	−0.287379	−	1.62981i	−0.0374136	−	0.212183i	0.960370	−	0.278729i	$-0.0899131\pi$
$59$	−0.287379	−	1.62981i	−0.0374136	−	0.212183i	−0.997783	+	0.0665462i	$0.978802\pi$
$60$		0			0
$61$	11.0098	+	9.23828i	1.40965	+	1.18284i	0.956617	+	0.291349i	$0.0941039\pi$
$61$	11.0098	+	9.23828i	1.40965	+	1.18284i	0.453037	+	0.891492i	$0.350341\pi$
$62$	−9.48056	+	16.4208i	−1.20403	+	2.08544i
$63$		0			0
$64$	3.74896	+	6.49338i	0.468620	+	0.811673i
$65$	−1.78862	+	10.1438i	−0.221851	+	1.25818i
$66$		0			0
$67$	5.52444	+	2.01073i	0.674917	+	0.245650i	0.656664	−	0.754184i	$-0.271967\pi$
$67$	5.52444	+	2.01073i	0.674917	+	0.245650i	0.0182537	+	0.999833i	$0.494189\pi$
$68$	9.76910	+	3.55566i	1.18468	+	0.431187i
$69$		0			0
$70$	−3.49516	+	19.8220i	−0.417751	+	2.36918i
$71$	7.40813	+	12.8313i	0.879184	+	1.52279i	0.852238	+	0.523154i	$0.175245\pi$
$71$	7.40813	+	12.8313i	0.879184	+	1.52279i	0.0269456	+	0.999637i	$0.491422\pi$
$72$		0			0
$73$	−0.940699	+	1.62934i	−0.110101	+	0.190700i	−0.915811	−	0.401610i	$-0.868451\pi$
$73$	−0.940699	+	1.62934i	−0.110101	+	0.190700i	0.805710	+	0.592310i	$0.201784\pi$
$74$	−19.3844	−	16.2655i	−2.25339	−	1.89082i
$75$		0			0
$76$	−1.47123	−	8.34374i	−0.168761	−	0.957092i
$77$	−6.99457	+	5.86915i	−0.797106	+	0.668851i
$78$		0			0
$79$	−16.1566	+	5.88052i	−1.81776	+	0.661610i	−0.822013	+	0.569469i	$0.807149\pi$
$79$	−16.1566	+	5.88052i	−1.81776	+	0.661610i	−0.995746	+	0.0921413i	$0.970629\pi$
$80$	13.0789			1.46227
$81$		0			0
$82$	12.0063			1.32588
$83$	3.72944	−	1.35740i	0.409359	−	0.148994i	−0.129129	−	0.991628i	$-0.541218\pi$
$83$	3.72944	−	1.35740i	0.409359	−	0.148994i	0.538488	+	0.842633i	$0.318996\pi$
$84$		0			0
$85$	−6.07087	+	5.09406i	−0.658478	+	0.552529i
$86$	1.17004	+	6.63564i	0.126169	+	0.715539i
$87$		0			0
$88$	13.1955	+	11.0724i	1.40665	+	1.18032i
$89$	2.54940	−	4.41569i	0.270236	−	0.468062i	−0.698686	−	0.715428i	$-0.746232\pi$
$89$	2.54940	−	4.41569i	0.270236	−	0.468062i	0.968922	+	0.247366i	$0.0795651\pi$
$90$		0			0
$91$	−4.44523	−	7.69937i	−0.465987	−	0.807113i
$92$	−0.375001	+	2.12674i	−0.0390965	+	0.221727i
$93$		0			0
$94$	−13.0675	−	4.75619i	−1.34781	−	0.490563i
$95$	6.06908	+	2.20897i	0.622675	+	0.226635i
$96$		0			0
$97$	−1.84621	+	10.4704i	−0.187454	+	1.06310i	0.735308	+	0.677733i	$0.237037\pi$
$97$	−1.84621	+	10.4704i	−0.187454	+	1.06310i	−0.922762	+	0.385371i	$0.874074\pi$
$98$	−0.0841927	−	0.145826i	−0.00850475	−	0.0147307i
$99$		0			0
$100$	−9.06744	+	15.7053i	−0.906744	+	1.57053i
$101$	−4.33435	−	3.63695i	−0.431284	−	0.361890i	0.401152	−	0.916011i	$-0.368610\pi$
$101$	−4.33435	−	3.63695i	−0.431284	−	0.361890i	−0.832436	+	0.554121i	$0.813054\pi$
$102$		0			0
$103$	1.80083	+	10.2130i	0.177441	+	1.00632i	0.935289	+	0.353885i	$0.115140\pi$
$103$	1.80083	+	10.2130i	0.177441	+	1.00632i	−0.757848	+	0.652431i	$0.773749\pi$
$104$	−12.8483	+	10.7810i	−1.25988	+	1.05716i
$105$		0			0
$106$	14.8426	−	5.40227i	1.44164	−	0.524714i
$107$	14.2457			1.37719			0.688594	−	0.725147i	$-0.258228\pi$
$107$	14.2457			1.37719			0.688594	+	0.725147i	$0.258228\pi$
$108$		0			0
$109$	5.76064			0.551769			0.275884	−	0.961191i	$-0.411029\pi$
$109$	5.76064			0.551769			0.275884	+	0.961191i	$0.411029\pi$
$110$	−24.4321	+	8.89257i	−2.32951	+	0.847874i
$111$		0			0
$112$	−8.64771	+	7.25629i	−0.817132	+	0.685655i
$113$	1.98249	+	11.2432i	0.186497	+	1.05768i	0.924017	+	0.382351i	$0.124885\pi$
$113$	1.98249	+	11.2432i	0.186497	+	1.05768i	−0.737520	+	0.675325i	$0.764003\pi$
$114$		0			0
$115$	−1.26108	−	1.05818i	−0.117597	−	0.0986753i
$116$	5.11333	−	8.85654i	0.474761	−	0.822309i
$117$		0			0
$118$	2.03376	+	3.52257i	0.187223	+	0.324279i
$119$	1.18780	−	6.73635i	0.108885	−	0.617520i
$120$		0			0
$121$	−0.746770	−	0.271802i	−0.0678882	−	0.0247093i
$122$	−33.1936	−	12.0815i	−3.00520	−	1.09381i
$123$		0			0
$124$	5.41314	−	30.6994i	0.486114	−	2.75689i
$125$	0.788517	+	1.36575i	0.0705271	+	0.122157i
$126$		0			0
$127$	−1.29510	+	2.24317i	−0.114921	+	0.199049i	−0.917748	−	0.397163i	$-0.869995\pi$
$127$	−1.29510	+	2.24317i	−0.114921	+	0.199049i	0.802827	+	0.596212i	$0.203328\pi$
$128$	−14.7366	−	12.3655i	−1.30254	−	1.09296i
$129$		0			0
$130$	−4.39606	−	24.9313i	−0.385560	−	2.18662i
$131$	3.37901	−	2.83533i	0.295226	−	0.247724i	−0.483128	−	0.875550i	$-0.660499\pi$
$131$	3.37901	−	2.83533i	0.295226	−	0.247724i	0.778354	+	0.627826i	$0.216055\pi$
$132$		0			0
$133$	−5.23841	+	1.90662i	−0.454227	+	0.165325i
$134$	−14.4493			−1.24823
$135$		0			0
$136$	−12.9044			−1.10655
$137$	17.0720	−	6.21371i	1.45856	−	0.530873i	0.513594	−	0.858033i	$-0.328314\pi$
$137$	17.0720	−	6.21371i	1.45856	−	0.530873i	0.944969	+	0.327160i	$0.106092\pi$
$138$		0			0
$139$	1.49987	−	1.25854i	0.127217	−	0.106748i	−0.576959	−	0.816773i	$-0.695761\pi$
$139$	1.49987	−	1.25854i	0.127217	−	0.106748i	0.704177	+	0.710025i	$0.251316\pi$
$140$	−5.74621	−	32.5884i	−0.485644	−	2.75422i
$141$		0			0
$142$	−27.8957	−	23.4073i	−2.34096	−	1.96430i
$143$	5.74214	−	9.94568i	0.480182	−	0.831700i
$144$		0			0
$145$	3.89791	+	6.75138i	0.323704	+	0.560671i
$146$	0.802963	−	4.55383i	0.0664537	−	0.376878i
$147$		0			0
$148$	39.0931	+	14.2287i	3.21343	+	1.16959i
$149$	6.87403	+	2.50194i	0.563142	+	0.204967i	0.607876	−	0.794032i	$-0.292022\pi$
$149$	6.87403	+	2.50194i	0.563142	+	0.204967i	−0.0447337	+	0.998999i	$0.514244\pi$
$150$		0			0
$151$	0.842365	−	4.77729i	0.0685507	−	0.388770i	−0.931158	−	0.364617i	$-0.881200\pi$
$151$	0.842365	−	4.77729i	0.0685507	−	0.388770i	0.999708	−	0.0241532i	$-0.00768897\pi$
$152$	5.25835	+	9.10773i	0.426508	+	0.738734i
$153$		0			0
$154$	11.2208	−	19.4349i	0.904194	−	1.56611i
$155$	18.2038	+	15.2748i	1.46216	+	1.22690i
$156$		0			0
$157$	0.256427	+	1.45427i	0.0204651	+	0.116063i	0.993329	−	0.115315i	$-0.0367877\pi$
$157$	0.256427	+	1.45427i	0.0204651	+	0.116063i	−0.972864	+	0.231378i	$0.925677\pi$
$158$	32.3715	−	27.1629i	2.57534	−	2.16096i
$159$		0			0
$160$	−1.17080	+	0.426136i	−0.0925597	+	0.0336890i
$161$	1.42091			0.111983
$162$		0			0
$163$	−17.2536			−1.35141			−0.675703	−	0.737174i	$-0.736160\pi$
$163$	−17.2536			−1.35141			−0.675703	+	0.737174i	$0.736160\pi$
$164$	−18.5486	+	6.75113i	−1.44840	+	0.527175i
$165$		0			0
$166$	−7.47233	+	6.27003i	−0.579965	+	0.486649i
$167$	−1.18782	−	6.73644i	−0.0919160	−	0.521282i	−0.995649	−	0.0931847i	$-0.970295\pi$
$167$	−1.18782	−	6.73644i	−0.0919160	−	0.521282i	0.903733	−	0.428097i	$-0.140816\pi$
$168$		0			0
$169$	−1.39264	−	1.16856i	−0.107126	−	0.0898893i
$170$	9.73894	−	16.8683i	0.746942	−	1.29374i
$171$		0			0
$172$	−5.53881	−	9.59350i	−0.422330	−	0.731497i
$173$	4.16189	−	23.6033i	0.316423	−	1.79452i	−0.247705	−	0.968835i	$-0.579676\pi$
$173$	4.16189	−	23.6033i	0.316423	−	1.79452i	0.564128	−	0.825687i	$-0.309212\pi$
$174$		0			0
$175$	11.2126	+	4.08104i	0.847589	+	0.308497i
$176$	−13.7029	−	4.98745i	−1.03290	−	0.375943i
$177$		0			0
$178$	−2.17612	+	12.3414i	−0.163107	+	0.925026i
$179$	−10.2861	−	17.8161i	−0.768820	−	1.33163i	−0.938203	−	0.346084i	$-0.887511\pi$
$179$	−10.2861	−	17.8161i	−0.768820	−	1.33163i	0.169384	−	0.985550i	$-0.445822\pi$
$180$		0			0
$181$	7.73507	−	13.3975i	0.574943	−	0.995830i	−0.421105	−	0.907012i	$-0.638358\pi$
$181$	7.73507	−	13.3975i	0.574943	−	0.995830i	0.996048	−	0.0888184i	$-0.0283091\pi$
$182$	16.7388	+	14.0455i	1.24076	+	1.04112i
$183$		0			0
$184$	−0.465482	−	2.63988i	−0.0343158	−	0.194614i
$185$	−24.2938	+	20.3849i	−1.78612	+	1.49873i
$186$		0			0
$187$	8.30306	−	3.02207i	0.607180	−	0.220995i
$188$	22.8624			1.66741
$189$		0			0
$190$	−15.8738			−1.15161
$191$	−10.2904	+	3.74541i	−0.744589	+	0.271008i	−0.686327	−	0.727293i	$-0.740778\pi$
$191$	−10.2904	+	3.74541i	−0.744589	+	0.271008i	−0.0582623	+	0.998301i	$0.518556\pi$
$192$		0			0
$193$	0.877007	−	0.735896i	0.0631284	−	0.0529710i	−0.610678	−	0.791879i	$-0.709103\pi$
$193$	0.877007	−	0.735896i	0.0631284	−	0.0529710i	0.673806	+	0.738908i	$0.264658\pi$
$194$	−4.53759	−	25.7339i	−0.325780	−	1.84759i
$195$		0			0
$196$	0.212067	+	0.177946i	0.0151477	+	0.0127104i
$197$	−2.52097	+	4.36645i	−0.179612	+	0.311097i	−0.941748	−	0.336320i	$-0.890818\pi$
$197$	−2.52097	+	4.36645i	−0.179612	+	0.311097i	0.762136	+	0.647417i	$0.224151\pi$
$198$		0			0
$199$	−6.86291	−	11.8869i	−0.486499	−	0.842640i	0.513381	−	0.858161i	$-0.328393\pi$
$199$	−6.86291	−	11.8869i	−0.486499	−	0.842640i	−0.999880	+	0.0155206i	$0.995059\pi$
$200$	3.90890	−	22.1685i	0.276401	−	1.56755i
$201$		0			0
$202$	13.0677	+	4.75627i	0.919443	+	0.334650i
$203$	−6.32301	−	2.30139i	−0.443788	−	0.161526i
$204$		0			0
$205$	2.61290	−	14.8185i	0.182493	−	1.03497i
$206$	−12.7443	−	22.0738i	−0.887938	−	1.53795i
$207$		0			0
$208$	7.09927	−	12.2963i	0.492246	−	0.852595i
$209$	−5.51629	−	4.62871i	−0.381569	−	0.320175i
$210$		0			0
$211$	−1.01326	−	5.74648i	−0.0697557	−	0.395604i	−0.999616	−	0.0276926i	$-0.991184\pi$
$211$	−1.01326	−	5.74648i	−0.0697557	−	0.395604i	0.929861	−	0.367912i	$-0.119927\pi$
$212$	−19.8927	+	16.6919i	−1.36623	+	1.14641i
$213$		0			0
$214$	−32.9015	+	11.9752i	−2.24910	+	0.818605i
$215$	8.44451			0.575911
$216$		0			0
$217$	−20.5108			−1.39237
$218$	−13.3046	+	4.84247i	−0.901099	+	0.327973i
$219$		0			0
$220$	32.7450	−	27.4763i	2.20767	−	1.85245i
$221$	1.49396	+	8.47269i	0.100495	+	0.569934i
$222$		0			0
$223$	6.68656	+	5.61069i	0.447765	+	0.375719i	0.838606	−	0.544739i	$-0.183371\pi$
$223$	6.68656	+	5.61069i	0.447765	+	0.375719i	−0.390841	+	0.920458i	$0.627816\pi$
$224$	0.537703	−	0.931329i	0.0359268	−	0.0622270i
$225$		0			0
$226$	−14.0299	−	24.3005i	−0.933256	−	1.61645i
$227$	−4.21662	+	23.9136i	−0.279867	+	1.58720i	0.443199	+	0.896423i	$0.353843\pi$
$227$	−4.21662	+	23.9136i	−0.279867	+	1.58720i	−0.723066	+	0.690779i	$0.757268\pi$
$228$		0			0
$229$	−17.0568	−	6.20815i	−1.12714	−	0.410246i	−0.289888	−	0.957060i	$-0.593618\pi$
$229$	−17.0568	−	6.20815i	−1.12714	−	0.410246i	−0.837254	+	0.546814i	$0.815840\pi$
$230$	3.80207	+	1.38384i	0.250701	+	0.0912478i
$231$		0			0
$232$	−2.20432	+	12.5013i	−0.144721	+	0.820751i
$233$	5.26900	+	9.12617i	0.345183	+	0.597875i	0.985387	−	0.170330i	$-0.0544834\pi$
$233$	5.26900	+	9.12617i	0.345183	+	0.597875i	−0.640204	+	0.768205i	$0.721150\pi$
$234$		0			0
$235$	−8.71406	+	15.0932i	−0.568442	+	0.984571i
$236$	−5.12270	−	4.29845i	−0.333459	−	0.279805i
$237$		0			0
$238$	2.91936	+	16.5565i	0.189234	+	1.07320i
$239$	7.30546	−	6.13001i	0.472551	−	0.396517i	−0.375173	−	0.926955i	$-0.622417\pi$
$239$	7.30546	−	6.13001i	0.472551	−	0.396517i	0.847724	+	0.530437i	$0.177972\pi$
$240$		0			0
$241$	6.61288	−	2.40689i	0.425973	−	0.155042i	−0.120133	−	0.992758i	$-0.538332\pi$
$241$	6.61288	−	2.40689i	0.425973	−	0.155042i	0.546106	+	0.837716i	$0.316110\pi$
$242$	1.95320			0.125556
$243$		0			0
$244$	58.0742			3.71782
$245$	−0.198305	+	0.0721771i	−0.0126692	+	0.00461122i
$246$		0			0
$247$	5.37111	−	4.50689i	0.341755	−	0.286767i
$248$	6.71923	+	38.1066i	0.426671	+	2.41977i
$249$		0			0
$250$	−2.96920	−	2.49146i	−0.187789	−	0.157574i
$251$	−7.79350	+	13.4987i	−0.491921	+	0.852033i	−0.999957	−	0.00930331i	$-0.997039\pi$
$251$	−7.79350	+	13.4987i	−0.491921	+	0.852033i	0.508035	+	0.861336i	$0.330372\pi$
$252$		0			0
$253$	0.917731	+	1.58956i	0.0576973	+	0.0999346i
$254$	1.10547	−	6.26944i	0.0693634	−	0.393379i
$255$		0			0
$256$	30.3383	+	11.0422i	1.89614	+	0.690140i
$257$	−11.4546	−	4.16915i	−0.714521	−	0.260064i	−0.0409230	−	0.999162i	$-0.513030\pi$
$257$	−11.4546	−	4.16915i	−0.714521	−	0.260064i	−0.673598	+	0.739098i	$0.735252\pi$
$258$		0			0
$259$	4.75323	−	26.9569i	0.295351	−	1.67502i
$260$	20.8103	+	36.0445i	1.29060	+	2.23538i
$261$		0			0
$262$	−5.42064	+	9.38882i	−0.334888	+	0.580043i
$263$	−5.27777	−	4.42857i	−0.325441	−	0.273077i	0.465398	−	0.885101i	$-0.345911\pi$
$263$	−5.27777	−	4.42857i	−0.325441	−	0.273077i	−0.790839	+	0.612024i	$0.790356\pi$
$264$		0			0
$265$	−3.43746	−	19.4948i	−0.211161	−	1.19756i
$266$	10.4957	−	8.80695i	0.643534	−	0.539989i
$267$		0			0
$268$	22.3228	−	8.12482i	1.36358	−	0.496302i
$269$	7.05875			0.430380			0.215190	−	0.976572i	$-0.430963\pi$
$269$	7.05875			0.430380			0.215190	+	0.976572i	$0.430963\pi$
$270$		0			0
$271$	23.7575			1.44316			0.721581	−	0.692330i	$-0.243416\pi$
$271$	23.7575			1.44316			0.721581	+	0.692330i	$0.243416\pi$
$272$	10.2655	−	3.73632i	0.622435	−	0.226548i
$273$		0			0
$274$	−34.2057	+	28.7020i	−2.06644	+	1.73395i
$275$	2.67651	+	15.1792i	0.161399	+	0.915342i
$276$		0			0
$277$	−0.0800238	−	0.0671480i	−0.00480817	−	0.00403453i	0.640380	−	0.768058i	$-0.278777\pi$
$277$	−0.0800238	−	0.0671480i	−0.00480817	−	0.00403453i	−0.645189	+	0.764023i	$0.723221\pi$
$278$	−2.40611	+	4.16750i	−0.144309	+	0.249950i
$279$		0			0
$280$	20.5377	+	35.5723i	1.22736	+	2.12585i
$281$	1.41561	−	8.02835i	0.0844485	−	0.478931i	−0.913026	−	0.407902i	$-0.866261\pi$
$281$	1.41561	−	8.02835i	0.0844485	−	0.478931i	0.997474	−	0.0710292i	$-0.0226283\pi$
$282$		0			0
$283$	−22.1918	−	8.07714i	−1.31916	−	0.480136i	−0.415973	−	0.909377i	$-0.636559\pi$
$283$	−22.1918	−	8.07714i	−1.31916	−	0.480136i	−0.903190	+	0.429240i	$0.858781\pi$
$284$	56.2580	+	20.4762i	3.33830	+	1.21504i
$285$		0			0
$286$	−4.90139	+	27.7971i	−0.289825	+	1.64368i
$287$	6.49380	+	11.2476i	0.383317	+	0.663925i
$288$		0			0
$289$	5.19030	−	8.98987i	0.305312	−	0.528816i
$290$	−14.6778	−	12.3161i	−0.861909	−	0.723227i
$291$		0			0
$292$	1.32011	+	7.48673i	0.0772537	+	0.438127i
$293$	16.5663	−	13.9008i	0.967813	−	0.812091i	−0.0143935	−	0.999896i	$-0.504582\pi$
$293$	16.5663	−	13.9008i	0.967813	−	0.812091i	0.982206	+	0.187805i	$0.0601373\pi$
$294$		0			0
$295$	4.79025	−	1.74351i	0.278899	−	0.101511i
$296$	−51.6398			−3.00150
$297$		0			0
$298$	−17.9792			−1.04151
$299$	−1.67938	+	0.611244i	−0.0971210	+	0.0353491i
$300$		0			0
$301$	−5.58348	+	4.68509i	−0.321826	+	0.270044i
$302$	2.07036	+	11.7416i	0.119136	+	0.675651i
$303$		0			0
$304$	−6.82004	−	5.72269i	−0.391156	−	0.328219i
$305$	−22.1351	+	38.3391i	−1.26745	+	2.19529i
$306$		0			0
$307$	−8.17997	−	14.1681i	−0.466855	−	0.808617i	0.532428	−	0.846475i	$-0.321280\pi$
$307$	−8.17997	−	14.1681i	−0.466855	−	0.808617i	−0.999283	+	0.0378581i	$0.987946\pi$
$308$	−6.40674	+	36.3344i	−0.365058	+	2.07035i
$309$		0			0
$310$	−54.8829	−	19.9758i	−3.11714	−	1.13455i
$311$	−7.28719	−	2.65232i	−0.413218	−	0.150399i	0.127041	−	0.991897i	$-0.459452\pi$
$311$	−7.28719	−	2.65232i	−0.413218	−	0.150399i	−0.540260	+	0.841498i	$0.681674\pi$
$312$		0			0
$313$	2.67732	−	15.1838i	0.151331	−	0.858240i	−0.810733	−	0.585416i	$-0.800931\pi$
$313$	2.67732	−	15.1838i	0.151331	−	0.858240i	0.962064	−	0.272824i	$-0.0879577\pi$
$314$	−1.81471	−	3.14317i	−0.102410	−	0.177380i
$315$		0			0
$316$	−34.7371	+	60.1664i	−1.95412	+	3.38463i
$317$	−6.61572	−	5.55125i	−0.371576	−	0.311789i	0.437809	−	0.899068i	$-0.355755\pi$
$317$	−6.61572	−	5.55125i	−0.371576	−	0.311789i	−0.809385	+	0.587279i	$0.800199\pi$
$318$		0			0
$319$	−1.50934	−	8.55990i	−0.0845069	−	0.479262i
$320$	−17.6922	+	14.8455i	−0.989025	+	0.829890i
$321$		0			0
$322$	−3.28168	+	1.19444i	−0.182881	+	0.0665633i
$323$	5.39459			0.300163
$324$		0			0
$325$	−15.0077			−0.832480
$326$	39.8483	−	14.5036i	2.20700	−	0.803281i
$327$		0			0
$328$	18.7693	−	15.7494i	1.03636	−	0.869612i
$329$	−2.61214	−	14.8142i	−0.144012	−	0.816733i
$330$		0			0
$331$	15.7380	+	13.2058i	0.865039	+	0.725854i	0.963048	−	0.269331i	$-0.0868027\pi$
$331$	15.7380	+	13.2058i	0.865039	+	0.725854i	−0.0980081	+	0.995186i	$0.531247\pi$
$332$	8.01839	−	13.8883i	0.440066	−	0.762217i
$333$		0			0
$334$	8.40609	+	14.5598i	0.459961	+	0.796675i
$335$	−3.14456	+	17.8337i	−0.171806	+	0.974359i
$336$		0			0
$337$	−15.0146	−	5.46487i	−0.817897	−	0.297690i	−0.101015	−	0.994885i	$-0.532209\pi$
$337$	−15.0146	−	5.46487i	−0.817897	−	0.297690i	−0.716882	+	0.697195i	$0.754431\pi$
$338$	4.19869	+	1.52820i	0.228379	+	0.0831231i
$339$		0			0
$340$	−5.56067	+	31.5361i	−0.301569	+	1.71029i
$341$	−13.2475	−	22.9453i	−0.717390	−	1.24256i
$342$		0			0
$343$	−9.21426	+	15.9596i	−0.497523	+	0.861736i
$344$	10.5335	+	8.83861i	0.567926	+	0.476546i
$345$		0			0
$346$	10.2291	+	58.0118i	0.549917	+	3.11874i
$347$	7.51051	−	6.30207i	0.403185	−	0.338313i	−0.418538	−	0.908199i	$-0.637457\pi$
$347$	7.51051	−	6.30207i	0.403185	−	0.338313i	0.821723	+	0.569887i	$0.193013\pi$
$348$		0			0
$349$	8.86598	−	3.22695i	0.474585	−	0.172735i	−0.0936433	−	0.995606i	$-0.529851\pi$
$349$	8.86598	−	3.22695i	0.474585	−	0.172735i	0.568228	+	0.822871i	$0.307629\pi$
$350$	−29.3267			−1.56758
$351$		0			0
$352$	1.38916			0.0740424
$353$	−3.18101	+	1.15779i	−0.169308	+	0.0616232i	−0.425284	−	0.905060i	$-0.639826\pi$
$353$	−3.18101	+	1.15779i	−0.169308	+	0.0616232i	0.255975	+	0.966683i	$0.417603\pi$
$354$		0			0
$355$	−34.9607	+	29.3355i	−1.85552	+	1.55697i
$356$	−3.57765	−	20.2899i	−0.189615	−	1.07536i
$357$		0			0
$358$	38.7329	+	32.5007i	2.04710	+	1.71772i
$359$	17.6137	−	30.5078i	0.929614	−	1.61014i	0.145646	−	0.989337i	$-0.453474\pi$
$359$	17.6137	−	30.5078i	0.929614	−	1.61014i	0.783968	−	0.620801i	$-0.213193\pi$
$360$		0			0
$361$	7.30179	+	12.6471i	0.384305	+	0.665636i
$362$	−6.60251	+	37.4447i	−0.347020	+	1.96805i
$363$		0			0
$364$	−33.7575	−	12.2867i	−1.76937	−	0.643999i
$365$	−5.44571	−	1.98208i	−0.285041	−	0.103747i
$366$		0			0
$367$	−5.47781	+	31.0662i	−0.285939	+	1.62164i	0.415972	+	0.909377i	$0.363441\pi$
$367$	−5.47781	+	31.0662i	−0.285939	+	1.62164i	−0.701911	+	0.712264i	$0.747670\pi$
$368$	1.13463	+	1.96524i	0.0591469	+	0.102445i
$369$		0			0
$370$	38.9724	−	67.5021i	2.02608	−	3.50927i
$371$	13.0887	+	10.9827i	0.679533	+	0.570196i
$372$		0			0
$373$	2.50788	+	14.2229i	0.129853	+	0.736434i	0.978306	+	0.207163i	$0.0664232\pi$
$373$	2.50788	+	14.2229i	0.129853	+	0.736434i	−0.848453	+	0.529270i	$0.822466\pi$
$374$	−16.6361	+	13.9593i	−0.860231	+	0.721820i
$375$		0			0
$376$	−26.6673	+	9.70609i	−1.37526	+	0.500553i
$377$	8.46320			0.435877
$378$		0			0
$379$	1.00099			0.0514176			0.0257088	−	0.999669i	$-0.491816\pi$
$379$	1.00099			0.0514176			0.0257088	+	0.999669i	$0.491816\pi$
$380$	24.5235	−	8.92583i	1.25803	−	0.457885i
$381$		0			0
$382$	20.6180	−	17.3006i	1.05491	−	0.885173i
$383$	−0.714969	−	4.05479i	−0.0365332	−	0.207190i	0.961077	−	0.276280i	$-0.0891016\pi$
$383$	−0.714969	−	4.05479i	−0.0365332	−	0.207190i	−0.997610	+	0.0690897i	$0.977991\pi$
$384$		0			0
$385$	−21.5451	−	18.0785i	−1.09804	−	0.921366i
$386$	−1.40690	+	2.43683i	−0.0716094	+	0.124031i
$387$		0			0
$388$	21.4803	+	37.2049i	1.09050	+	1.88879i
$389$	2.69501	−	15.2841i	0.136642	−	0.774936i	−0.837060	−	0.547111i	$-0.815727\pi$
$389$	2.69501	−	15.2841i	0.136642	−	0.774936i	0.973702	−	0.227825i	$-0.0731614\pi$
$390$		0			0
$391$	−1.29210	−	0.470287i	−0.0653445	−	0.0237834i
$392$	−0.322906	−	0.117528i	−0.0163092	−	0.00593606i
$393$		0			0
$394$	2.15186	−	12.2038i	0.108409	−	0.614818i
$395$	−26.4802	−	45.8651i	−1.33237	−	2.30772i
$396$		0			0
$397$	0.774463	−	1.34141i	0.0388692	−	0.0673234i	−0.845936	−	0.533284i	$-0.820958\pi$
$397$	0.774463	−	1.34141i	0.0388692	−	0.0673234i	0.884806	+	0.465960i	$0.154291\pi$
$398$	25.8426	+	21.6845i	1.29537	+	1.08695i
$399$		0			0
$400$	3.30909	+	18.7668i	0.165454	+	0.938339i
$401$	−6.08805	+	5.10848i	−0.304022	+	0.255105i	−0.782016	−	0.623258i	$-0.785809\pi$
$401$	−6.08805	+	5.10848i	−0.304022	+	0.255105i	0.477994	+	0.878363i	$0.341364\pi$
$402$		0			0
$403$	24.2418	−	8.82331i	1.20757	−	0.439520i
$404$	−22.8628			−1.13747
$405$		0			0
$406$	16.5380			0.820766
$407$	33.2264	−	12.0934i	1.64697	−	0.599449i
$408$		0			0
$409$	20.2660	−	17.0052i	1.00209	−	0.840853i	0.0148172	−	0.999890i	$-0.495283\pi$
$409$	20.2660	−	17.0052i	1.00209	−	0.840853i	0.987273	+	0.159037i	$0.0508389\pi$
$410$	6.42196	+	36.4208i	0.317158	+	1.79869i
$411$		0			0
$412$	32.1007	+	26.9357i	1.58149	+	1.32703i
$413$	−2.19998	+	3.81048i	−0.108254	+	0.187501i
$414$		0			0
$415$	6.11245	+	10.5871i	0.300048	+	0.519699i
$416$	−0.234876	+	1.33205i	−0.0115158	+	0.0653091i
$417$		0			0
$418$	16.6312	+	6.05326i	0.813458	+	0.296074i
$419$	36.0278	+	13.1130i	1.76007	+	0.640614i	0.999958	−	0.00917341i	$-0.00292003\pi$
$419$	36.0278	+	13.1130i	1.76007	+	0.640614i	0.760116	+	0.649788i	$0.225142\pi$
$420$		0			0
$421$	1.27536	−	7.23292i	0.0621572	−	0.352511i	−0.937828	−	0.347100i	$-0.887167\pi$
$421$	1.27536	−	7.23292i	0.0621572	−	0.352511i	0.999985	−	0.00541096i	$-0.00172237\pi$
$422$	7.17076	+	12.4201i	0.349067	+	0.604602i
$423$		0			0
$424$	16.1168	−	27.9152i	0.782702	−	1.35568i
$425$	−8.84541	−	7.42218i	−0.429065	−	0.360028i
$426$		0			0
$427$	−6.63526	−	37.6304i	−0.321103	−	1.82106i
$428$	44.0959	−	37.0009i	2.13146	−	1.78851i
$429$		0			0
$430$	−19.5032	+	7.09857i	−0.940526	+	0.342323i
$431$	15.8463			0.763289			0.381644	−	0.924309i	$-0.375358\pi$
$431$	15.8463			0.763289			0.381644	+	0.924309i	$0.375358\pi$
$432$		0			0
$433$	−23.8507			−1.14619			−0.573097	−	0.819488i	$-0.694258\pi$
$433$	−23.8507			−1.14619			−0.573097	+	0.819488i	$0.694258\pi$
$434$	47.3711	−	17.2417i	2.27389	−	0.827627i
$435$		0			0
$436$	17.8313	−	14.9623i	0.853967	−	0.716563i
$437$	0.194591	+	1.10358i	0.00930853	+	0.0527913i
$438$		0			0
$439$	−16.4469	−	13.8006i	−0.784969	−	0.658667i	0.159526	−	0.987194i	$-0.449003\pi$
$439$	−16.4469	−	13.8006i	−0.784969	−	0.658667i	−0.944495	+	0.328527i	$0.893448\pi$
$440$	−26.5296	+	45.9507i	−1.26475	+	2.19061i
$441$		0			0
$442$	−10.5727	−	18.3124i	−0.502890	−	0.871031i
$443$	−5.47824	+	31.0686i	−0.260279	+	1.47612i	0.521871	+	0.853025i	$0.325234\pi$
$443$	−5.47824	+	31.0686i	−0.260279	+	1.47612i	−0.782150	+	0.623091i	$0.785877\pi$
$444$		0			0
$445$	14.7585	+	5.37164i	0.699618	+	0.254640i
$446$	−20.1595	−	7.33745i	−0.954578	−	0.347438i
$447$		0			0
$448$	3.46158	−	19.6316i	0.163544	−	0.927506i
$449$	10.3949	+	18.0045i	0.490565	+	0.849684i	0.999941	−	0.0108605i	$-0.00345708\pi$
$449$	10.3949	+	18.0045i	0.490565	+	0.849684i	−0.509376	+	0.860544i	$0.670124\pi$
$450$		0			0
$451$	−8.38839	+	14.5291i	−0.394994	+	0.684149i
$452$	35.3390	+	29.6529i	1.66221	+	1.39476i
$453$		0			0
$454$	−10.3636	−	58.7746i	−0.486386	−	2.75843i
$455$	20.9781	−	17.6027i	0.983469	−	0.825228i
$456$		0			0
$457$	16.3767	−	5.96064i	0.766070	−	0.278827i	0.0707185	−	0.997496i	$-0.477471\pi$
$457$	16.3767	−	5.96064i	0.766070	−	0.278827i	0.695352	+	0.718670i	$0.255249\pi$
$458$	44.6124			2.08460
$459$		0			0
$460$	−6.65196			−0.310149
$461$	−29.1347	+	10.6042i	−1.35694	+	0.493885i	−0.915106	−	0.403214i	$-0.867893\pi$
$461$	−29.1347	+	10.6042i	−1.35694	+	0.493885i	−0.441831	+	0.897098i	$0.645671\pi$
$462$		0			0
$463$	4.97006	−	4.17037i	0.230978	−	0.193814i	−0.519952	−	0.854196i	$-0.674050\pi$
$463$	4.97006	−	4.17037i	0.230978	−	0.193814i	0.750930	+	0.660382i	$0.229606\pi$
$464$	−1.86607	−	10.5830i	−0.0866300	−	0.491303i
$465$		0			0
$466$	−19.8407	−	16.6483i	−0.919102	−	0.771218i
$467$	0.971950	−	1.68347i	0.0449765	−	0.0779016i	−0.842661	−	0.538445i	$-0.819012\pi$
$467$	0.971950	−	1.68347i	0.0449765	−	0.0779016i	0.887637	+	0.460543i	$0.152345\pi$
$468$		0			0
$469$	−7.81513	−	13.5362i	−0.360869	−	0.625044i
$470$	7.43816	−	42.1839i	0.343097	−	1.94580i
$471$		0			0
$472$	7.80011	+	2.83901i	0.359029	+	0.130676i
$473$	−8.84740	−	3.22019i	−0.406804	−	0.148065i
$474$		0			0
$475$	−1.63408	+	9.26735i	−0.0749769	+	0.425215i
$476$	−13.8198	−	23.9367i	−0.633431	−	1.09713i
$477$		0			0
$478$	−11.7195	+	20.2987i	−0.536036	+	0.928442i
$479$	−1.01837	−	0.854516i	−0.0465306	−	0.0390438i	0.619226	−	0.785213i	$-0.287447\pi$
$479$	−1.01837	−	0.854516i	−0.0465306	−	0.0390438i	−0.665756	+	0.746169i	$0.731891\pi$
$480$		0			0
$481$	5.97840	+	33.9052i	0.272592	+	1.54594i
$482$	−13.2496	+	11.1178i	−0.603504	+	0.506400i
$483$		0			0
$484$	−3.01750	+	1.09828i	−0.137159	+	0.0499217i
$485$	−32.7490			−1.48705
$486$		0			0
$487$	21.2040			0.960844			0.480422	−	0.877037i	$-0.340484\pi$
$487$	21.2040			0.960844			0.480422	+	0.877037i	$0.340484\pi$
$488$	−67.7391	+	24.6550i	−3.06640	+	1.11608i
$489$		0			0
$490$	0.397325	−	0.333396i	0.0179493	−	0.0150613i
$491$	−4.69026	−	26.5998i	−0.211669	−	1.20043i	−0.886595	−	0.462547i	$-0.846936\pi$
$491$	−4.69026	−	26.5998i	−0.211669	−	1.20043i	0.674926	−	0.737885i	$-0.264175\pi$
$492$		0			0
$493$	4.98812	+	4.18553i	0.224654	+	0.188507i
$494$	−8.61638	+	14.9240i	−0.387669	+	0.671463i
$495$		0			0
$496$	−16.3784	−	28.3683i	−0.735414	−	1.27377i
$497$	6.84027	−	38.7931i	0.306828	−	1.74011i
$498$		0			0
$499$	−14.1320	−	5.14361i	−0.632633	−	0.230260i	0.00574369	−	0.999984i	$-0.498172\pi$
$499$	−14.1320	−	5.14361i	−0.632633	−	0.230260i	−0.638377	+	0.769724i	$0.720394\pi$
$500$	5.98807	+	2.17948i	0.267794	+	0.0974692i
$501$		0			0
$502$	6.65239	−	37.7276i	0.296911	−	1.68386i
$503$	2.30325	+	3.98934i	0.102697	+	0.177876i	0.912795	−	0.408418i	$-0.133920\pi$
$503$	2.30325	+	3.98934i	0.102697	+	0.177876i	−0.810098	+	0.586294i	$0.800586\pi$
$504$		0			0
$505$	8.71420	−	15.0934i	0.387777	−	0.671649i
$506$	−3.45577	−	2.89973i	−0.153628	−	0.128909i
$507$		0			0
$508$	1.81745	+	10.3073i	0.0806363	+	0.457311i
$509$	−22.8256	+	19.1529i	−1.01173	+	0.848938i	−0.988565	−	0.150793i	$-0.951817\pi$
$509$	−22.8256	+	19.1529i	−1.01173	+	0.848938i	−0.0231600	+	0.999732i	$0.507373\pi$
$510$		0			0
$511$	4.70035	−	1.71079i	0.207931	−	0.0756808i
$512$	−40.8760			−1.80648
$513$		0			0
$514$	29.9599			1.32147
$515$	−30.0175	+	10.9255i	−1.32273	+	0.481435i
$516$		0			0
$517$	14.8854	−	12.4903i	0.654658	−	0.549324i
$518$	11.6824	+	66.2544i	0.513297	+	2.91105i
$519$		0			0
$520$	−39.5760	−	33.2082i	−1.73552	−	1.45628i
$521$	−5.88104	+	10.1863i	−0.257653	+	0.446268i	−0.965613	−	0.259985i	$-0.916283\pi$
$521$	−5.88104	+	10.1863i	−0.257653	+	0.446268i	0.707960	+	0.706253i	$0.249616\pi$
$522$		0			0
$523$	−14.6926	−	25.4484i	−0.642464	−	1.11278i	−0.984881	−	0.173232i	$-0.944579\pi$
$523$	−14.6926	−	25.4484i	−0.642464	−	1.11278i	0.342417	−	0.939548i	$-0.388754\pi$
$524$	3.09503	−	17.5528i	0.135207	−	0.766798i
$525$		0			0
$526$	15.9121	+	5.79152i	0.693799	+	0.252522i
$527$	18.6515	+	6.78859i	0.812473	+	0.295716i
$528$		0			0
$529$	−3.94431	+	22.3693i	−0.171492	+	0.972578i
$530$	24.3266	+	42.1350i	1.05668	+	1.83023i
$531$		0			0
$532$	−11.2627	+	19.5076i	−0.488301	+	0.845761i
$533$	−12.5135	−	10.5001i	−0.542021	−	0.454810i
$534$		0			0
$535$	7.61979	+	43.2140i	0.329432	+	1.86830i
$536$	−22.5884	+	18.9539i	−0.975672	+	0.818686i
$537$		0			0
$538$	−16.3027	+	5.93368i	−0.702858	+	0.255819i
$539$	0.235290			0.0101347
$540$		0			0
$541$	−22.9116			−0.985046			−0.492523	−	0.870300i	$-0.663925\pi$
$541$	−22.9116			−0.985046			−0.492523	+	0.870300i	$0.663925\pi$
$542$	−54.8694	+	19.9708i	−2.35684	+	0.857821i
$543$		0			0
$544$	−0.797207	+	0.668936i	−0.0341800	+	0.0286804i
$545$	3.08126	+	17.4747i	0.131987	+	0.748534i
$546$		0			0
$547$	−10.5390	−	8.84328i	−0.450615	−	0.378111i	0.389049	−	0.921217i	$-0.372804\pi$
$547$	−10.5390	−	8.84328i	−0.450615	−	0.378111i	−0.839664	+	0.543106i	$0.817248\pi$
$548$	36.7053	−	63.5755i	1.56797	−	2.71581i
$549$		0			0
$550$	−18.9414	−	32.8075i	−0.807665	−	1.39892i
$551$	0.921496	−	5.22606i	0.0392571	−	0.222638i
$552$		0			0
$553$	42.9550	+	15.6343i	1.82663	+	0.664840i
$554$	0.241266	+	0.0878136i	0.0102504	+	0.00373084i
$555$		0			0
$556$	1.37382	−	7.79133i	0.0582630	−	0.330426i
$557$	10.9520	+	18.9695i	0.464053	+	0.803763i	0.999158	−	0.0410224i	$-0.0130615\pi$
$557$	10.9520	+	18.9695i	0.464053	+	0.803763i	−0.535106	+	0.844785i	$0.679728\pi$
$558$		0			0
$559$	4.58371	−	7.93922i	0.193870	−	0.335793i
$560$	−26.6372	−	22.3513i	−1.12563	−	0.944514i
$561$		0			0
$562$	3.47928	+	19.7320i	0.146765	+	0.832344i
$563$	−11.1601	+	9.36440i	−0.470341	+	0.394663i	−0.846919	−	0.531722i	$-0.821545\pi$
$563$	−11.1601	+	9.36440i	−0.470341	+	0.394663i	0.376578	+	0.926385i	$0.377101\pi$
$564$		0			0
$565$	−33.0456	+	12.0276i	−1.39024	+	0.506006i
$566$	58.0431			2.43973
$567$		0			0
$568$	−74.3137			−3.11813
$569$	−21.0087	+	7.64655i	−0.880732	+	0.320560i	−0.742505	−	0.669840i	$-0.766363\pi$
$569$	−21.0087	+	7.64655i	−0.880732	+	0.320560i	−0.138227	+	0.990401i	$0.544140\pi$
$570$		0			0
$571$	−11.8171	+	9.91573i	−0.494531	+	0.414961i	−0.855647	−	0.517560i	$-0.826840\pi$
$571$	−11.8171	+	9.91573i	−0.494531	+	0.414961i	0.361116	+	0.932521i	$0.382396\pi$
$572$	−8.05812	−	45.6999i	−0.336927	−	1.91081i
$573$		0			0
$574$	−24.4528	−	20.5183i	−1.02064	−	0.856417i
$575$	1.19930	−	2.07724i	0.0500142	−	0.0866271i
$576$		0			0
$577$	−16.4040	−	28.4126i	−0.682909	−	1.18283i	−0.974089	−	0.226165i	$-0.927381\pi$
$577$	−16.4040	−	28.4126i	−0.682909	−	1.18283i	0.291180	−	0.956668i	$-0.405952\pi$
$578$	−4.43035	+	25.1257i	−0.184278	+	1.04509i
$579$		0			0
$580$	29.6011	+	10.7739i	1.22912	+	0.447362i
$581$	−9.91533	−	3.60889i	−0.411357	−	0.149722i
$582$		0			0
$583$	−3.83260	+	21.7357i	−0.158730	+	0.900202i
$584$	−4.71825	−	8.17225i	−0.195242	−	0.338170i
$585$		0			0
$586$	−26.5758	+	46.0306i	−1.09784	+	1.90151i
$587$	−23.1608	−	19.4342i	−0.955948	−	0.802136i	0.0243412	−	0.999704i	$-0.492251\pi$
$587$	−23.1608	−	19.4342i	−0.955948	−	0.802136i	−0.980289	+	0.197568i	$0.936696\pi$
$588$		0			0
$589$	−2.80892	−	15.9302i	−0.115739	−	0.656391i
$590$	−9.59779	+	8.05350i	−0.395135	+	0.331557i
$591$		0			0
$592$	41.0793	−	14.9517i	1.68835	−	0.614509i
$593$	−41.1023			−1.68787			−0.843935	−	0.536446i	$-0.819766\pi$
$593$	−41.1023			−1.68787			−0.843935	+	0.536446i	$0.819766\pi$
$594$		0			0
$595$	21.0698			0.863778
$596$	27.7761	−	10.1097i	1.13775	−	0.414108i
$597$		0			0
$598$	3.36482	−	2.82342i	0.137598	−	0.115458i
$599$	−6.34693	−	35.9952i	−0.259329	−	1.47073i	−0.784712	−	0.619860i	$-0.787189\pi$
$599$	−6.34693	−	35.9952i	−0.259329	−	1.47073i	0.525384	−	0.850865i	$-0.323922\pi$
$600$		0			0
$601$	3.02266	+	2.53631i	0.123297	+	0.103458i	0.702351	−	0.711831i	$-0.252134\pi$
$601$	3.02266	+	2.53631i	0.123297	+	0.103458i	−0.579054	+	0.815289i	$0.696578\pi$
$602$	8.95706	−	15.5141i	0.365062	−	0.632307i
$603$		0			0
$604$	−9.80076	−	16.9754i	−0.398787	−	0.690720i
$605$	0.425069	−	2.41068i	0.0172815	−	0.0980082i
$606$		0			0
$607$	−9.40775	−	3.42414i	−0.381849	−	0.138982i	0.143962	−	0.989583i	$-0.454016\pi$
$607$	−9.40775	−	3.42414i	−0.381849	−	0.138982i	−0.525811	+	0.850602i	$0.676238\pi$
$608$	0.796973	+	0.290074i	0.0323215	+	0.0117641i
$609$		0			0
$610$	18.8941	−	107.154i	0.765000	−	4.33853i
$611$	9.46005	+	16.3853i	0.382712	+	0.662877i
$612$		0			0
$613$	9.37838	−	16.2438i	0.378789	−	0.656082i	−0.612097	−	0.790783i	$-0.709674\pi$
$613$	9.37838	−	16.2438i	0.378789	−	0.656082i	0.990886	+	0.134700i	$0.0430072\pi$
$614$	30.8021	+	25.8460i	1.24307	+	1.04306i
$615$		0			0
$616$	−7.95257	−	45.1013i	−0.320418	−	1.81718i
$617$	17.6267	−	14.7906i	0.709626	−	0.595447i	−0.214869	−	0.976643i	$-0.568932\pi$
$617$	17.6267	−	14.7906i	0.709626	−	0.595447i	0.924494	+	0.381196i	$0.124488\pi$
$618$		0			0
$619$	−6.96690	+	2.53574i	−0.280023	+	0.101920i	−0.478214	−	0.878243i	$-0.658716\pi$
$619$	−6.96690	+	2.53574i	−0.280023	+	0.101920i	0.198191	+	0.980163i	$0.436493\pi$
$620$	96.0211			3.85630
$621$		0			0
$622$	19.0598			0.764229
$623$	−12.7385	+	4.63643i	−0.510356	+	0.185754i
$624$		0			0
$625$	−20.9113	+	17.5467i	−0.836452	+	0.701867i
$626$	6.58028	+	37.3186i	0.263001	+	1.49155i
$627$		0			0
$628$	4.57095	+	3.83549i	0.182401	+	0.153053i
$629$	−13.2444	+	22.9400i	−0.528090	+	0.914679i
$630$		0			0
$631$	15.4962	+	26.8402i	0.616894	+	1.06849i	0.990049	+	0.140723i	$0.0449426\pi$
$631$	15.4962	+	26.8402i	0.616894	+	1.06849i	−0.373155	+	0.927769i	$0.621724\pi$
$632$	14.9749	−	84.9269i	0.595670	−	3.37821i
$633$		0			0
$634$	19.9459	+	7.25971i	0.792153	+	0.288320i
$635$	−7.49732	−	2.72880i	−0.297522	−	0.108289i
$636$		0			0
$637$	−0.0397824	+	0.225617i	−0.00157623	+	0.00893927i
$638$	10.6815	+	18.5009i	0.422884	+	0.732457i
$639$		0			0
$640$	29.6279	−	51.3171i	1.17115	−	2.02849i
$641$	27.0767	+	22.7201i	1.06947	+	0.897388i	0.995004	−	0.0998358i	$-0.0318317\pi$
$641$	27.0767	+	22.7201i	1.06947	+	0.897388i	0.0744616	+	0.997224i	$0.476276\pi$
$642$		0			0
$643$	−3.42103	−	19.4016i	−0.134912	−	0.765126i	−0.974921	−	0.222552i	$-0.928561\pi$
$643$	−3.42103	−	19.4016i	−0.134912	−	0.765126i	0.840008	−	0.542573i	$-0.182550\pi$
$644$	4.39825	−	3.69057i	0.173315	−	0.145429i
$645$		0			0
$646$	−12.4592	+	4.53476i	−0.490199	+	0.178418i
$647$	−46.8317			−1.84114			−0.920572	−	0.390572i	$-0.872277\pi$
$647$	−46.8317			−1.84114			−0.920572	+	0.390572i	$0.872277\pi$
$648$		0			0
$649$	−5.68366			−0.223103
$650$	34.6614	−	12.6157i	1.35953	−	0.494829i
$651$		0			0
$652$	−53.4064	+	44.8133i	−2.09156	+	1.75502i
$653$	−3.00875	−	17.0635i	−0.117742	−	0.667746i	−0.985356	−	0.170509i	$-0.945459\pi$
$653$	−3.00875	−	17.0635i	−0.117742	−	0.667746i	0.867615	−	0.497237i	$-0.165652\pi$
$654$		0			0
$655$	10.4082	+	8.73355i	0.406684	+	0.341248i
$656$	−10.3709	+	17.9630i	−0.404918	+	0.701338i
$657$		0			0
$658$	18.4859	+	32.0186i	0.720657	+	1.24821i
$659$	−7.59436	+	43.0698i	−0.295834	+	1.67776i	0.367957	+	0.929843i	$0.380057\pi$
$659$	−7.59436	+	43.0698i	−0.295834	+	1.67776i	−0.663792	+	0.747917i	$0.731054\pi$
$660$		0			0
$661$	8.53885	+	3.10789i	0.332123	+	0.120883i	0.502699	−	0.864462i	$-0.332341\pi$
$661$	8.53885	+	3.10789i	0.332123	+	0.120883i	−0.170576	+	0.985345i	$0.554563\pi$
$662$	−47.4489	−	17.2700i	−1.84416	−	0.671218i
$663$		0			0
$664$	−3.45667	+	19.6037i	−0.134145	+	0.760773i
$665$	−8.58561	−	14.8707i	−0.332936	−	0.576661i
$666$		0			0
$667$	−0.676311	+	1.17140i	−0.0261868	+	0.0453570i
$668$	−21.1735	−	17.7667i	−0.819228	−	0.687414i
$669$		0			0
$670$	−7.72867	−	43.8315i	−0.298585	−	1.69336i
$671$	37.8112	−	31.7274i	1.45969	−	1.22482i
$672$		0			0
$673$	−7.04458	+	2.56402i	−0.271549	+	0.0988356i	−0.474205	−	0.880414i	$-0.657265\pi$
$673$	−7.04458	+	2.56402i	−0.271549	+	0.0988356i	0.202657	+	0.979250i	$0.435042\pi$
$674$	39.2711			1.51266
$675$		0			0
$676$	−7.34587			−0.282534
$677$	14.4361	−	5.25430i	0.554823	−	0.201939i	−0.0493648	−	0.998781i	$-0.515720\pi$
$677$	14.4361	−	5.25430i	0.554823	−	0.201939i	0.604188	+	0.796842i	$0.293497\pi$
$678$		0			0
$679$	21.6535	−	18.1694i	0.830985	−	0.697279i
$680$	−6.90235	−	39.1452i	−0.264693	−	1.50115i
$681$		0			0
$682$	49.8840	+	41.8576i	1.91016	+	1.60281i
$683$	3.31079	−	5.73445i	0.126684	−	0.219423i	−0.795706	−	0.605683i	$-0.792900\pi$
$683$	3.31079	−	5.73445i	0.126684	−	0.219423i	0.922390	+	0.386260i	$0.126233\pi$
$684$		0			0
$685$	27.9806	+	48.4639i	1.06908	+	1.85171i
$686$	7.86512	−	44.6053i	0.300292	−	1.70304i
$687$		0			0
$688$	−10.9385	−	3.98127i	−0.417025	−	0.151785i
$689$	−20.1942	−	7.35008i	−0.769336	−	0.280016i
$690$		0			0
$691$	−3.23973	+	18.3734i	−0.123245	+	0.698958i	0.859090	+	0.511825i	$0.171030\pi$
$691$	−3.23973	+	18.3734i	−0.123245	+	0.698958i	−0.982335	+	0.187132i	$0.940081\pi$
$692$	−48.4228	−	83.8708i	−1.84076	−	3.18829i
$693$		0			0
$694$	−12.0484	+	20.8685i	−0.457352	+	0.792157i
$695$	4.62000	+	3.87664i	0.175247	+	0.147049i
$696$		0			0
$697$	−2.18245	−	12.3773i	−0.0826662	−	0.468823i
$698$	−17.7639	+	14.9057i	−0.672375	+	0.564190i
$699$		0			0
$700$	45.3069	−	16.4904i	1.71244	−	0.623277i
$701$	−24.8903			−0.940092			−0.470046	−	0.882642i	$-0.655763\pi$
$701$	−24.8903			−0.940092			−0.470046	+	0.882642i	$0.655763\pi$
$702$		0			0
$703$	21.5876			0.814190
$704$	24.1975	−	8.80715i	0.911976	−	0.331932i
$705$		0			0
$706$	6.37350	−	5.34801i	0.239870	−	0.201275i
$707$	2.61219	+	14.8144i	0.0982413	+	0.557154i
$708$		0			0
$709$	−20.0541	−	16.8274i	−0.753147	−	0.631965i	0.183186	−	0.983078i	$-0.441359\pi$
$709$	−20.0541	−	16.8274i	−0.753147	−	0.631965i	−0.936333	+	0.351113i	$0.885803\pi$
$710$	56.0843	−	97.1409i	2.10481	−	3.64563i
$711$		0			0
$712$	12.7870	+	22.1477i	0.479212	+	0.830020i
$713$	−0.715965	+	4.06044i	−0.0268131	+	0.152065i
$714$		0			0
$715$	33.2413	+	12.0988i	1.24315	+	0.452471i
$716$	−78.1136	−	28.4310i	−2.91924	−	1.06252i
$717$		0			0
$718$	−15.0347	+	85.2660i	−0.561090	+	3.18210i
$719$	10.5145	+	18.2117i	0.392125	+	0.679181i	0.992730	−	0.120365i	$-0.0384066\pi$
$719$	10.5145	+	18.2117i	0.392125	+	0.679181i	−0.600604	+	0.799546i	$0.705073\pi$
$720$		0			0
$721$	13.7859	−	23.8779i	0.513414	−	0.889259i
$722$	−27.4953	−	23.0713i	−1.02327	−	0.858624i
$723$		0			0
$724$	−10.8549	−	61.5609i	−0.403417	−	2.28789i
$725$	−8.70127	+	7.30123i	−0.323157	+	0.271161i
$726$		0			0
$727$	−38.8992	+	14.1582i	−1.44269	+	0.525097i	−0.940540	−	0.339683i	$-0.889680\pi$
$727$	−38.8992	+	14.1582i	−1.44269	+	0.525097i	−0.502152	+	0.864779i	$0.667458\pi$
$728$	44.5918			1.65268
$729$		0			0
$730$	14.2434			0.527171
$731$	6.62799	−	2.41239i	0.245145	−	0.0892254i
$732$		0			0
$733$	25.7596	−	21.6148i	0.951451	−	0.798362i	−0.0280903	−	0.999605i	$-0.508943\pi$
$733$	25.7596	−	21.6148i	0.951451	−	0.798362i	0.979541	+	0.201243i	$0.0644982\pi$
$734$	−13.4633	−	76.3541i	−0.496939	−	2.81828i
$735$		0			0
$736$	−0.165602	−	0.138956i	−0.00610416	−	0.00512200i
$737$	10.0952	−	17.4854i	0.371862	−	0.644084i
$738$		0			0
$739$	6.47268	+	11.2110i	0.238101	+	0.412403i	0.960169	−	0.279418i	$-0.0901417\pi$
$739$	6.47268	+	11.2110i	0.238101	+	0.412403i	−0.722068	+	0.691822i	$0.756808\pi$
$740$	−22.2522	+	126.198i	−0.818005	+	4.63914i
$741$		0			0
$742$	−39.4615	−	14.3628i	−1.44868	−	0.527276i
$743$	−0.0826264	−	0.0300735i	−0.00303127	−	0.00110329i	0.340504	−	0.940243i	$-0.389402\pi$
$743$	−0.0826264	−	0.0300735i	−0.00303127	−	0.00110329i	−0.343535	+	0.939140i	$0.611625\pi$
$744$		0			0
$745$	−3.91276	+	22.1904i	−0.143353	+	0.812993i
$746$	−17.7481	−	30.7406i	−0.649803	−	1.12549i
$747$		0			0
$748$	17.8518	−	30.9202i	0.652727	−	1.13056i
$749$	−29.0137	−	24.3454i	−1.06014	−	0.889561i
$750$		0			0
$751$	8.66435	+	49.1380i	0.316167	+	1.79307i	0.565601	+	0.824679i	$0.308644\pi$
$751$	8.66435	+	49.1380i	0.316167	+	1.79307i	−0.249434	+	0.968392i	$0.580245\pi$
$752$	18.4035	−	15.4424i	0.671106	−	0.563125i
$753$		0			0
$754$	−19.5463	+	7.11428i	−0.711835	+	0.259087i
$755$	14.9423			0.543806
$756$		0			0
$757$	−11.8679			−0.431348			−0.215674	−	0.976465i	$-0.569195\pi$
$757$	−11.8679			−0.431348			−0.215674	+	0.976465i	$0.569195\pi$
$758$	−2.31186	+	0.841448i	−0.0839705	+	0.0305628i
$759$		0			0
$760$	−24.8154	+	20.8226i	−0.900149	+	0.755315i
$761$	−0.658179	−	3.73272i	−0.0238590	−	0.135311i	0.970552	−	0.240893i	$-0.0774404\pi$
$761$	−0.658179	−	3.73272i	−0.0238590	−	0.135311i	−0.994411	+	0.105582i	$0.966329\pi$
$762$		0			0
$763$	−11.7324	−	9.84469i	−0.424743	−	0.356402i
$764$	−22.1247	+	38.3211i	−0.800444	+	1.38641i
$765$		0			0
$766$	5.05978	+	8.76379i	0.182817	+	0.316649i
$767$	0.960983	−	5.45000i	0.0346991	−	0.196788i
$768$		0			0
$769$	−5.89140	−	2.14430i	−0.212449	−	0.0773253i	0.233603	−	0.972332i	$-0.424948\pi$
$769$	−5.89140	−	2.14430i	−0.212449	−	0.0773253i	−0.446053	+	0.895007i	$0.647171\pi$
$770$	64.9570	+	23.6424i	2.34089	+	0.852013i
$771$		0			0
$772$	0.803302	−	4.55575i	0.0289115	−	0.163965i
$773$	−0.647678	−	1.12181i	−0.0232954	−	0.0403487i	0.854143	−	0.520039i	$-0.174082\pi$
$773$	−0.647678	−	1.12181i	−0.0232954	−	0.0403487i	−0.877438	+	0.479690i	$0.840749\pi$
$774$		0			0
$775$	−17.3119	+	29.9850i	−0.621861	+	1.07709i
$776$	−40.8502	−	34.2774i	−1.46644	−	1.23049i
$777$		0			0
$778$	6.62376	+	37.5652i	0.237473	+	1.34678i
$779$	−7.84636	+	6.58388i	−0.281125	+	0.235892i
$780$		0			0
$781$	47.8154	−	17.4034i	1.71097	−	0.622742i
$782$	3.37953			0.120852
$783$		0			0
$784$	0.290900			0.0103893
$785$	−4.27432	+	1.55572i	−0.152557	+	0.0555262i
$786$		0			0
$787$	−9.49299	+	7.96557i	−0.338389	+	0.283942i	−0.796108	−	0.605155i	$-0.793111\pi$
$787$	−9.49299	+	7.96557i	−0.338389	+	0.283942i	0.457719	+	0.889097i	$0.348667\pi$
$788$	3.53776	+	20.0636i	0.126027	+	0.714737i
$789$		0			0
$790$	99.7127	+	83.6689i	3.54762	+	2.97681i
$791$	15.1766	−	26.2866i	0.539618	−	0.934645i
$792$		0			0
$793$	24.0300	+	41.6212i	0.853331	+	1.47801i
$794$	−0.661067	+	3.74910i	−0.0234604	+	0.133051i
$795$		0			0
$796$	−52.1175	−	18.9692i	−1.84726	−	0.672346i
$797$	22.9122	+	8.33937i	0.811593	+	0.295396i	0.714282	−	0.699858i	$-0.246753\pi$
$797$	22.9122	+	8.33937i	0.811593	+	0.295396i	0.0973115	+	0.995254i	$0.468976\pi$
$798$		0			0
$799$	−2.52780	+	14.3358i	−0.0894270	+	0.507166i
$800$	−0.907681	−	1.57215i	−0.0320914	−	0.0555839i
$801$		0			0
$802$	9.76649	−	16.9161i	0.344867	−	0.597327i
$803$	4.94969	+	4.15328i	0.174671	+	0.146566i
$804$		0			0
$805$	0.760019	+	4.31028i	0.0267871	+	0.151917i
$806$	−48.5711	+	40.7560i	−1.71085	+	1.43557i
$807$		0			0
$808$	26.6677	−	9.70625i	0.938167	−	0.341465i
$809$	−24.1156			−0.847861			−0.423930	−	0.905695i	$-0.639350\pi$
$809$	−24.1156			−0.847861			−0.423930	+	0.905695i	$0.639350\pi$
$810$		0			0
$811$	48.1121			1.68944			0.844721	−	0.535206i	$-0.179766\pi$
$811$	48.1121			1.68944			0.844721	+	0.535206i	$0.179766\pi$
$812$	−25.5496	+	9.29928i	−0.896614	+	0.326341i
$813$		0			0
$814$	−66.5727	+	55.8611i	−2.33337	+	1.95793i
$815$	−9.22864	−	52.3382i	−0.323265	−	1.83333i
$816$		0			0
$817$	−4.40342	−	3.69491i	−0.154056	−	0.129268i
$818$	−32.5109	+	56.3105i	−1.13672	+	1.96885i
$819$		0			0
$820$	−30.4006	−	52.6554i	−1.06164	−	1.83881i
$821$	2.94140	−	16.6815i	0.102655	−	0.582188i	−0.889475	−	0.456983i	$-0.848930\pi$
$821$	2.94140	−	16.6815i	0.102655	−	0.582188i	0.992131	−	0.125205i	$-0.0399589\pi$
$822$		0			0
$823$	−10.8590	−	3.95236i	−0.378522	−	0.137771i	0.145750	−	0.989321i	$-0.453440\pi$
$823$	−10.8590	−	3.95236i	−0.378522	−	0.137771i	−0.524272	+	0.851551i	$0.675663\pi$
$824$	−48.8784	−	17.7903i	−1.70276	−	0.619754i
$825$		0			0
$826$	1.87786	−	10.6499i	0.0653392	−	0.370557i
$827$	−5.11869	−	8.86582i	−0.177994	−	0.308295i	0.763199	−	0.646163i	$-0.223627\pi$
$827$	−5.11869	−	8.86582i	−0.177994	−	0.308295i	−0.941193	+	0.337868i	$0.890294\pi$
$828$		0			0
$829$	−4.67622	+	8.09945i	−0.162412	+	0.281306i	−0.935733	−	0.352709i	$-0.885261\pi$
$829$	−4.67622	+	8.09945i	−0.162412	+	0.281306i	0.773321	+	0.634014i	$0.218594\pi$
$830$	−23.0167	−	19.3133i	−0.798923	−	0.670376i
$831$		0			0
$832$	4.35383	+	24.6918i	0.150942	+	0.856034i
$833$	−0.135028	+	0.113302i	−0.00467843	+	0.00392567i
$834$		0			0
$835$	19.7994	−	7.20640i	0.685188	−	0.249388i
$836$	−29.0973			−1.00635
$837$		0			0
$838$	−94.2316			−3.25518
$839$	11.1308	−	4.05127i	0.384277	−	0.139865i	−0.142656	−	0.989772i	$-0.545564\pi$
$839$	11.1308	−	4.05127i	0.384277	−	0.139865i	0.526933	+	0.849907i	$0.323342\pi$
$840$		0			0
$841$	−17.3084	+	14.5235i	−0.596843	+	0.500811i
$842$	3.13456	+	17.7770i	0.108024	+	0.612635i
$843$		0			0
$844$	−18.0619	−	15.1558i	−0.621718	−	0.521683i
$845$	2.79989	−	4.84956i	0.0963193	−	0.166830i
$846$		0			0
$847$	1.05642	+	1.82977i	0.0362989	+	0.0628715i
$848$	−4.73842	+	26.8729i	−0.162718	+	0.922819i
$849$		0			0
$850$	26.6682	+	9.70644i	0.914713	+	0.332928i
$851$	−5.17062	−	1.88195i	−0.177246	−	0.0645124i
$852$		0			0
$853$	−6.47209	+	36.7051i	−0.221600	+	1.25676i	0.647479	+	0.762084i	$0.275823\pi$
$853$	−6.47209	+	36.7051i	−0.221600	+	1.25676i	−0.869079	+	0.494673i	$0.835288\pi$
$854$	46.9572	+	81.3322i	1.60684	+	2.78313i
$855$		0			0
$856$	−35.7261	+	61.8793i	−1.22109	+	2.11499i
$857$	−31.7386	−	26.6319i	−1.08417	−	0.909728i	−0.0879107	−	0.996128i	$-0.528019\pi$
$857$	−31.7386	−	26.6319i	−1.08417	−	0.909728i	−0.996260	+	0.0864008i	$0.972463\pi$
$858$		0			0
$859$	−1.60772	−	9.11785i	−0.0548548	−	0.311097i	0.945018	−	0.327017i	$-0.106043\pi$
$859$	−1.60772	−	9.11785i	−0.0548548	−	0.311097i	−0.999873	+	0.0159199i	$0.994932\pi$
$860$	26.1390	−	21.9332i	0.891331	−	0.747915i
$861$		0			0
$862$	−36.5981	+	13.3206i	−1.24653	+	0.453702i
$863$	51.4748			1.75222			0.876110	−	0.482110i	$-0.160130\pi$
$863$	51.4748			1.75222			0.876110	+	0.482110i	$0.160130\pi$
$864$		0			0
$865$	73.8258			2.51015
$866$	55.0849	−	20.0493i	1.87186	−	0.681301i
$867$		0			0
$868$	−63.4887	+	53.2734i	−2.15495	+	1.80822i
$869$	10.2536	+	58.1512i	0.347831	+	1.97265i
$870$		0			0
$871$	15.0597	+	12.6366i	0.510279	+	0.428175i
$872$	−14.4468	+	25.0225i	−0.489229	+	0.847370i
$873$		0			0
$874$	−1.37710	−	2.38521i	−0.0465812	−	0.0806810i
$875$	0.728074	−	4.12911i	0.0246134	−	0.139589i
$876$		0			0
$877$	23.3974	+	8.51597i	0.790075	+	0.287564i	0.705367	−	0.708842i	$-0.250782\pi$
$877$	23.3974	+	8.51597i	0.790075	+	0.287564i	0.0847080	+	0.996406i	$0.473004\pi$
$878$	49.5862	+	18.0479i	1.67345	+	0.609088i
$879$		0			0
$880$	7.79982	−	44.2350i	0.262932	−	1.49116i
$881$	0.716807	+	1.24155i	0.0241498	+	0.0418287i	0.877848	−	0.478940i	$-0.158979\pi$
$881$	0.716807	+	1.24155i	0.0241498	+	0.0418287i	−0.853698	+	0.520769i	$0.825645\pi$
$882$		0			0
$883$	−13.1023	+	22.6939i	−0.440928	+	0.763709i	−0.997759	−	0.0669168i	$-0.978684\pi$
$883$	−13.1023	+	22.6939i	−0.440928	+	0.763709i	0.556831	+	0.830626i	$0.312017\pi$
$884$	26.6307	+	22.3458i	0.895689	+	0.751572i
$885$		0			0
$886$	−13.4644	−	76.3602i	−0.452344	−	2.56537i
$887$	33.2253	−	27.8793i	1.11560	−	0.936097i	0.117223	−	0.993106i	$-0.462601\pi$
$887$	33.2253	−	27.8793i	1.11560	−	0.936097i	0.998374	+	0.0570089i	$0.0181563\pi$
$888$		0			0
$889$	6.47116	−	2.35531i	0.217036	−	0.0789945i
$890$	−38.6011			−1.29391
$891$		0			0
$892$	35.2702			1.18093
$893$	11.1480	−	4.05755i	0.373054	−	0.135781i
$894$		0			0
$895$	48.5426	−	40.7320i	1.62260	−	1.36152i
$896$	8.88132	+	50.3685i	0.296704	+	1.68269i
$897$		0			0
$898$	−39.1425	−	32.8444i	−1.30620	−	1.09603i
$899$	9.76254	−	16.9092i	0.325599	−	0.563954i
$900$		0			0
$901$	−8.26720	−	14.3192i	−0.275420	−	0.477042i
$902$	7.16017	−	40.6074i	0.238408	−	1.35208i
$903$		0			0
$904$	−53.8092	−	19.5849i	−1.78967	−	0.651385i
$905$	44.7783	+	16.2980i	1.48848	+	0.541763i
$906$		0			0
$907$	4.14529	−	23.5091i	0.137642	−	0.780607i	−0.835341	−	0.549732i	$-0.814730\pi$
$907$	4.14529	−	23.5091i	0.137642	−	0.780607i	0.972983	−	0.230875i	$-0.0741589\pi$
$908$	49.0595	+	84.9736i	1.62810	+	2.81995i
$909$		0			0
$910$	−33.6532	+	58.2891i	−1.11559	+	1.93227i
$911$	3.30971	+	2.77718i	0.109656	+	0.0920120i	0.695967	−	0.718074i	$-0.254976\pi$
$911$	3.30971	+	2.77718i	0.109656	+	0.0920120i	−0.586311	+	0.810086i	$0.699420\pi$
$912$		0			0
$913$	−2.36685	−	13.4231i	−0.0783314	−	0.444239i
$914$	−32.8125	+	27.5330i	−1.08534	+	0.910710i
$915$		0			0
$916$	−68.9217	+	25.0855i	−2.27724	+	0.828847i
$917$	−11.7273			−0.387271
$918$		0			0
$919$	3.56151			0.117483			0.0587417	−	0.998273i	$-0.481291\pi$
$919$	3.56151			0.117483			0.0587417	+	0.998273i	$0.481291\pi$
$920$	7.75900	−	2.82405i	0.255807	−	0.0931060i
$921$		0			0
$922$	58.3745	−	48.9820i	1.92246	−	1.61314i
$923$	8.60339	+	48.7923i	0.283184	+	1.60602i
$924$		0			0
$925$	−35.3967	−	29.7014i	−1.16384	−	0.976575i
$926$	−7.97301	+	13.8097i	−0.262009	+	0.453813i
$927$		0			0
$928$	0.511861	+	0.886570i	0.0168027	+	0.0291031i
$929$	−5.78696	+	32.8195i	−0.189864	+	1.07677i	0.729681	+	0.683788i	$0.239669\pi$
$929$	−5.78696	+	32.8195i	−0.189864	+	1.07677i	−0.919545	+	0.392985i	$0.871443\pi$
$930$		0			0
$931$	0.134988	+	0.0491316i	0.00442405	+	0.00161022i
$932$	40.0132	+	14.5636i	1.31068	+	0.477047i
$933$		0			0
$934$	−0.829639	+	4.70511i	−0.0271466	+	0.153956i
$935$	13.6085	+	23.5706i	0.445045	+	0.770841i
$936$		0			0
$937$	−13.0297	+	22.5681i	−0.425661	+	0.737267i	−0.996482	−	0.0838079i	$-0.973292\pi$
$937$	−13.0297	+	22.5681i	−0.425661	+	0.737267i	0.570821	+	0.821075i	$0.306625\pi$
$938$	29.4283	+	24.6933i	0.960867	+	0.806263i
$939$		0			0
$940$	12.2287	+	69.3524i	0.398856	+	2.26203i
$941$	−18.3801	+	15.4228i	−0.599175	+	0.502768i	−0.891180	−	0.453649i	$-0.850122\pi$
$941$	−18.3801	+	15.4228i	−0.599175	+	0.502768i	0.292005	+	0.956417i	$0.405677\pi$
$942$		0			0
$943$	2.45331	−	0.892933i	0.0798909	−	0.0290779i
$944$	−7.02697			−0.228708
$945$		0			0
$946$	23.1406			0.752366
$947$	−28.0824	+	10.2212i	−0.912556	+	0.332143i	−0.755273	−	0.655410i	$-0.772496\pi$
$947$	−28.0824	+	10.2212i	−0.912556	+	0.332143i	−0.157283	+	0.987554i	$0.550273\pi$
$948$		0			0
$949$	−4.81943	+	4.04398i	−0.156445	+	0.131273i
$950$	−4.01623	−	22.7772i	−0.130304	−	0.738990i
$951$		0			0
$952$	26.2819	+	22.0531i	0.851802	+	0.714747i
$953$	5.09669	−	8.82773i	0.165098	−	0.285958i	−0.771592	−	0.636118i	$-0.780539\pi$
$953$	5.09669	−	8.82773i	0.165098	−	0.285958i	0.936690	+	0.350159i	$0.113873\pi$
$954$		0			0
$955$	−16.8657	−	29.2123i	−0.545763	−	0.945289i
$956$	6.69150	−	37.9494i	0.216419	−	1.22737i
$957$		0			0
$958$	3.07032	+	1.11750i	0.0991974	+	0.0361049i
$959$	−45.3889	−	16.5202i	−1.46568	−	0.533465i
$960$		0			0
$961$	4.95186	−	28.0834i	0.159737	−	0.905916i
$962$	−42.3087	−	73.2808i	−1.36409	−	2.36267i
$963$		0			0
$964$	14.2179	−	24.6261i	0.457927	−	0.793152i
$965$	2.70141	+	2.26675i	0.0869615	+	0.0729694i
$966$		0			0
$967$	−3.25879	−	18.4815i	−0.104796	−	0.594325i	−0.991302	−	0.131608i	$-0.957986\pi$
$967$	−3.25879	−	18.4815i	−0.104796	−	0.594325i	0.886506	−	0.462717i	$-0.153125\pi$
$968$	3.05341	−	2.56211i	0.0981403	−	0.0823495i
$969$		0			0
$970$	75.6360	−	27.5292i	2.42852	−	0.883910i
$971$	−51.9535			−1.66727			−0.833633	−	0.552319i	$-0.813743\pi$
$971$	−51.9535			−1.66727			−0.833633	+	0.552319i	$0.813743\pi$
$972$		0			0
$973$	−5.20552			−0.166881
$974$	−48.9720	+	17.8244i	−1.56916	+	0.571129i
$975$		0			0
$976$	46.7478	−	39.2260i	1.49636	−	1.25559i
$977$	5.65817	+	32.0891i	0.181021	+	1.02662i	0.930962	+	0.365116i	$0.118971\pi$
$977$	5.65817	+	32.0891i	0.181021	+	1.02662i	−0.749941	+	0.661504i	$0.769918\pi$
$978$		0			0
$979$	−13.4142	−	11.2559i	−0.428720	−	0.359739i
$980$	−0.426361	+	0.738479i	−0.0136196	+	0.0235898i
$981$		0			0
$982$	33.1926	+	57.4913i	1.05922	+	1.83462i
$983$	6.09148	−	34.5465i	0.194288	−	1.10186i	−0.719141	−	0.694865i	$-0.755464\pi$
$983$	6.09148	−	34.5465i	0.194288	−	1.10186i	0.913429	−	0.406998i	$-0.133425\pi$
$984$		0			0
$985$	−14.5939	−	5.31175i	−0.465001	−	0.169246i
$986$	−15.0388	−	5.47368i	−0.478933	−	0.174317i
$987$		0			0
$988$	4.91971	−	27.9011i	0.156517	−	0.887652i
$989$	0.732587	+	1.26888i	0.0232949	+	0.0403479i
$990$		0			0
$991$	27.3818	−	47.4266i	0.869810	−	1.50656i	0.00762014	−	0.999971i	$-0.497574\pi$
$991$	27.3818	−	47.4266i	0.869810	−	1.50656i	0.862190	−	0.506585i	$-0.169092\pi$
$992$	2.39046	+	2.00583i	0.0758972	+	0.0636853i
$993$		0			0
$994$	16.8119	+	95.3452i	0.533242	+	3.02417i
$995$	32.3877	−	27.1765i	1.02676	−	0.861553i
$996$		0			0
$997$	−47.2948	+	17.2139i	−1.49784	+	0.545169i	−0.955501	−	0.294989i	$-0.904684\pi$
$997$	−47.2948	+	17.2139i	−1.49784	+	0.545169i	−0.542340	+	0.840159i	$0.682462\pi$
$998$	36.9625			1.17003
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.e.j.163.1		12
3.2	odd	2		729.2.e.u.163.2		12
9.2	odd	6		729.2.e.l.406.1		12
9.4	even	3		729.2.e.t.649.2		12
9.5	odd	6		729.2.e.k.649.1		12
9.7	even	3		729.2.e.s.406.2		12
27.2	odd	18		729.2.a.e.1.1	yes	6
27.4	even	9	inner	729.2.e.j.568.1		12
27.5	odd	18		729.2.e.k.82.1		12
27.7	even	9		729.2.c.d.487.1		12
27.11	odd	18		729.2.c.a.244.6		12
27.13	even	9		729.2.e.s.325.2		12
27.14	odd	18		729.2.e.l.325.1		12
27.16	even	9		729.2.c.d.244.1		12
27.20	odd	18		729.2.c.a.487.6		12
27.22	even	9		729.2.e.t.82.2		12
27.23	odd	18		729.2.e.u.568.2		12
27.25	even	9		729.2.a.b.1.6	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
729.2.a.b.1.6	✓	6	27.25	even	9
729.2.a.e.1.1	yes	6	27.2	odd	18
729.2.c.a.244.6		12	27.11	odd	18
729.2.c.a.487.6		12	27.20	odd	18
729.2.c.d.244.1		12	27.16	even	9
729.2.c.d.487.1		12	27.7	even	9
729.2.e.j.163.1		12	1.1	even	1	trivial
729.2.e.j.568.1		12	27.4	even	9	inner
729.2.e.k.82.1		12	27.5	odd	18
729.2.e.k.649.1		12	9.5	odd	6
729.2.e.l.325.1		12	27.14	odd	18
729.2.e.l.406.1		12	9.2	odd	6
729.2.e.s.325.2		12	27.13	even	9
729.2.e.s.406.2		12	9.7	even	3
729.2.e.t.82.2		12	27.22	even	9
729.2.e.t.649.2		12	9.4	even	3
729.2.e.u.163.2		12	3.2	odd	2
729.2.e.u.568.2		12	27.23	odd	18

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.30957 + 0.840614i) q^{2} +(3.09538 - 2.59733i) q^{4} +(0.534882 + 3.03347i) q^{5} +(-2.03666 - 1.70896i) q^{7} +(-2.50784 + 4.34371i) q^{8} +O(q^{10})\)	\(q+(-2.30957 + 0.840614i) q^{2} +(3.09538 - 2.59733i) q^{4} +(0.534882 + 3.03347i) q^{5} +(-2.03666 - 1.70896i) q^{7} +(-2.50784 + 4.34371i) q^{8} +(-3.78532 - 6.55636i) q^{10} +(0.596367 - 3.38217i) q^{11} +(3.14229 + 1.14370i) q^{13} +(6.14037 + 2.23491i) q^{14} +(0.737316 - 4.18153i) q^{16} +(1.28641 + 2.22813i) q^{17} +(1.04838 - 1.81585i) q^{19} +(9.53458 + 8.00046i) q^{20} +(1.46574 + 8.31265i) q^{22} +(-0.409408 + 0.343534i) q^{23} +(-4.21736 + 1.53499i) q^{25} -8.21874 q^{26} -10.7430 q^{28} +(2.37826 - 0.865617i) q^{29} +(5.90980 - 4.95891i) q^{31} +(0.0702390 + 0.398345i) q^{32} +(-4.84404 - 4.06463i) q^{34} +(4.09470 - 7.09222i) q^{35} +(5.14783 + 8.91631i) q^{37} +(-0.894879 + 5.07511i) q^{38} +(-14.5179 - 5.28408i) q^{40} +(-4.59040 - 1.67077i) q^{41} +(0.476055 - 2.69984i) q^{43} +(-6.93862 - 12.0180i) q^{44} +(0.656775 - 1.13757i) q^{46} +(4.33428 + 3.63689i) q^{47} +(0.0118968 + 0.0674701i) q^{49} +(8.44994 - 7.09034i) q^{50} +(12.6971 - 4.62138i) q^{52} -6.42657 q^{53} +10.5787 q^{55} +(12.5308 - 4.56085i) q^{56} +(-4.76511 + 3.99840i) q^{58} +(-0.287379 - 1.62981i) q^{59} +(11.0098 + 9.23828i) q^{61} +(-9.48056 + 16.4208i) q^{62} +(3.74896 + 6.49338i) q^{64} +(-1.78862 + 10.1438i) q^{65} +(5.52444 + 2.01073i) q^{67} +(9.76910 + 3.55566i) q^{68} +(-3.49516 + 19.8220i) q^{70} +(7.40813 + 12.8313i) q^{71} +(-0.940699 + 1.62934i) q^{73} +(-19.3844 - 16.2655i) q^{74} +(-1.47123 - 8.34374i) q^{76} +(-6.99457 + 5.86915i) q^{77} +(-16.1566 + 5.88052i) q^{79} +13.0789 q^{80} +12.0063 q^{82} +(3.72944 - 1.35740i) q^{83} +(-6.07087 + 5.09406i) q^{85} +(1.17004 + 6.63564i) q^{86} +(13.1955 + 11.0724i) q^{88} +(2.54940 - 4.41569i) q^{89} +(-4.44523 - 7.69937i) q^{91} +(-0.375001 + 2.12674i) q^{92} +(-13.0675 - 4.75619i) q^{94} +(6.06908 + 2.20897i) q^{95} +(-1.84621 + 10.4704i) q^{97} +(-0.0841927 - 0.145826i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} + 6 q^{4} + 6 q^{5} - 3 q^{7} + 6 q^{8}+O(q^{10}) \) 12 * q - 6 * q^2 + 6 * q^4 + 6 * q^5 - 3 * q^7 + 6 * q^8	\( 12 q - 6 q^{2} + 6 q^{4} + 6 q^{5} - 3 q^{7} + 6 q^{8} - 6 q^{10} + 12 q^{11} - 3 q^{13} + 15 q^{14} - 36 q^{16} - 9 q^{17} - 12 q^{19} + 42 q^{20} + 6 q^{22} + 6 q^{23} + 6 q^{25} - 48 q^{26} + 6 q^{28} + 12 q^{29} + 6 q^{31} + 54 q^{32} - 9 q^{34} + 30 q^{35} - 3 q^{37} + 42 q^{38} - 57 q^{40} + 24 q^{41} + 6 q^{43} - 33 q^{44} + 3 q^{46} + 21 q^{47} + 33 q^{49} + 21 q^{50} + 45 q^{52} + 18 q^{53} + 30 q^{55} + 3 q^{56} + 33 q^{58} + 15 q^{59} + 33 q^{61} - 30 q^{62} - 6 q^{64} - 6 q^{65} + 42 q^{67} - 18 q^{68} + 24 q^{70} - 12 q^{73} - 3 q^{74} - 87 q^{76} - 57 q^{77} - 48 q^{79} + 42 q^{80} - 42 q^{82} + 12 q^{83} - 36 q^{85} - 30 q^{86} + 30 q^{88} - 9 q^{89} - 18 q^{91} - 48 q^{92} + 33 q^{94} + 30 q^{95} - 3 q^{97} + 18 q^{98}+O(q^{100}) \) 12 * q - 6 * q^2 + 6 * q^4 + 6 * q^5 - 3 * q^7 + 6 * q^8 - 6 * q^10 + 12 * q^11 - 3 * q^13 + 15 * q^14 - 36 * q^16 - 9 * q^17 - 12 * q^19 + 42 * q^20 + 6 * q^22 + 6 * q^23 + 6 * q^25 - 48 * q^26 + 6 * q^28 + 12 * q^29 + 6 * q^31 + 54 * q^32 - 9 * q^34 + 30 * q^35 - 3 * q^37 + 42 * q^38 - 57 * q^40 + 24 * q^41 + 6 * q^43 - 33 * q^44 + 3 * q^46 + 21 * q^47 + 33 * q^49 + 21 * q^50 + 45 * q^52 + 18 * q^53 + 30 * q^55 + 3 * q^56 + 33 * q^58 + 15 * q^59 + 33 * q^61 - 30 * q^62 - 6 * q^64 - 6 * q^65 + 42 * q^67 - 18 * q^68 + 24 * q^70 - 12 * q^73 - 3 * q^74 - 87 * q^76 - 57 * q^77 - 48 * q^79 + 42 * q^80 - 42 * q^82 + 12 * q^83 - 36 * q^85 - 30 * q^86 + 30 * q^88 - 9 * q^89 - 18 * q^91 - 48 * q^92 + 33 * q^94 + 30 * q^95 - 3 * q^97 + 18 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more