LMFDB - Embedded newform 637.2.r.g.116.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(116,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("637.116");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.r (of order $6$, degree $2$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			116.5
Character	$\chi$	$=$	637.116
Dual form			637.2.r.g.324.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31930 + 0.761698i) q^{2} +(-1.49755 + 2.59383i) q^{3} +(0.160367 - 0.277763i) q^{4} +(2.55136 - 1.47303i) q^{5} -4.56272i q^{6} -2.55819i q^{8} +(-2.98531 - 5.17071i) q^{9} +O(q^{10})$	\(q+(-1.31930 + 0.761698i) q^{2} +(-1.49755 + 2.59383i) q^{3} +(0.160367 - 0.277763i) q^{4} +(2.55136 - 1.47303i) q^{5} -4.56272i q^{6} -2.55819i q^{8} +(-2.98531 - 5.17071i) q^{9} +(-2.24401 + 3.88673i) q^{10} +(2.05342 + 1.18554i) q^{11} +(0.480314 + 0.831928i) q^{12} +(2.32734 + 2.75381i) q^{13} +8.82374i q^{15} +(2.26930 + 3.93054i) q^{16} +(2.68497 - 4.65051i) q^{17} +(7.87704 + 4.54781i) q^{18} +(4.63703 - 2.67719i) q^{19} -0.944899i q^{20} -3.61209 q^{22} +(1.39528 + 2.41670i) q^{23} +(6.63551 + 3.83101i) q^{24} +(1.83963 - 3.18634i) q^{25} +(-5.16803 - 1.86037i) q^{26} +8.89733 q^{27} +0.585818 q^{29} +(-6.72103 - 11.6412i) q^{30} +(7.21727 + 4.16690i) q^{31} +(-1.55686 - 0.898851i) q^{32} +(-6.15019 + 3.55081i) q^{33} +8.18054i q^{34} -1.91498 q^{36} +(0.585182 - 0.337855i) q^{37} +(-4.07842 + 7.06402i) q^{38} +(-10.6282 + 1.91277i) q^{39} +(-3.76829 - 6.52686i) q^{40} -11.2799i q^{41} -10.5271 q^{43} +(0.658599 - 0.380242i) q^{44} +(-15.2332 - 8.79491i) q^{45} +(-3.68159 - 2.12557i) q^{46} +(0.465700 - 0.268872i) q^{47} -13.5936 q^{48} +5.60498i q^{50} +(8.04176 + 13.9287i) q^{51} +(1.13814 - 0.204831i) q^{52} +(-3.95173 + 6.84459i) q^{53} +(-11.7382 + 6.77707i) q^{54} +6.98535 q^{55} +16.0369i q^{57} +(-0.772869 + 0.446216i) q^{58} +(5.32262 + 3.07301i) q^{59} +(2.45091 + 1.41503i) q^{60} +(1.39344 + 2.41352i) q^{61} -12.6957 q^{62} -6.33858 q^{64} +(9.99434 + 3.59772i) q^{65} +(5.40929 - 9.36917i) q^{66} +(3.64902 + 2.10676i) q^{67} +(-0.861159 - 1.49157i) q^{68} -8.35802 q^{69} -1.25151i q^{71} +(-13.2277 + 7.63699i) q^{72} +(-9.40676 - 5.43100i) q^{73} +(-0.514686 + 0.891463i) q^{74} +(5.50989 + 9.54340i) q^{75} -1.71733i q^{76} +(12.5649 - 10.6190i) q^{78} +(-3.14568 - 5.44848i) q^{79} +(11.5796 + 6.68549i) q^{80} +(-4.36825 + 7.56604i) q^{81} +(8.59184 + 14.8815i) q^{82} +1.74725i q^{83} -15.8202i q^{85} +(13.8884 - 8.01845i) q^{86} +(-0.877292 + 1.51951i) q^{87} +(3.03283 - 5.25302i) q^{88} +(8.86315 - 5.11714i) q^{89} +26.7963 q^{90} +0.895027 q^{92} +(-21.6165 + 12.4803i) q^{93} +(-0.409598 + 0.709445i) q^{94} +(7.88715 - 13.6610i) q^{95} +(4.66294 - 2.69215i) q^{96} +9.90640i q^{97} -14.1568i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 20 q^{4} - 16 q^{9}+O(q^{10}) $ 32 * q + 20 * q^4 - 16 * q^9	$ 32 q + 20 q^{4} - 16 q^{9} - 28 q^{16} - 16 q^{22} + 36 q^{23} + 44 q^{25} + 72 q^{29} + 104 q^{36} - 32 q^{39} - 72 q^{43} + 72 q^{51} - 12 q^{53} - 328 q^{64} + 24 q^{65} - 96 q^{74} + 48 q^{78} - 36 q^{79} - 16 q^{81} - 136 q^{88} + 48 q^{92} + 84 q^{95}+O(q^{100}) $ 32 * q + 20 * q^4 - 16 * q^9 - 28 * q^16 - 16 * q^22 + 36 * q^23 + 44 * q^25 + 72 * q^29 + 104 * q^36 - 32 * q^39 - 72 * q^43 + 72 * q^51 - 12 * q^53 - 328 * q^64 + 24 * q^65 - 96 * q^74 + 48 * q^78 - 36 * q^79 - 16 * q^81 - 136 * q^88 + 48 * q^92 + 84 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.31930	+	0.761698i	−0.932885	+	0.538602i	−0.887723	−	0.460378i	$-0.847714\pi$
$2$	−1.31930	+	0.761698i	−0.932885	+	0.538602i	−0.0451623	+	0.998980i	$0.514381\pi$
$3$	−1.49755	+	2.59383i	−0.864611	+	1.49755i	0.00282181	+	0.999996i	$0.499102\pi$
$3$	−1.49755	+	2.59383i	−0.864611	+	1.49755i	−0.867433	+	0.497554i	$0.834232\pi$
$4$	0.160367	−	0.277763i	0.0801833	−	0.138882i
$5$	2.55136	−	1.47303i	1.14100	−	0.658759i	0.194325	−	0.980937i	$-0.437748\pi$
$5$	2.55136	−	1.47303i	1.14100	−	0.658759i	0.946679	+	0.322178i	$0.104415\pi$
$6$		−	4.56272i		−	1.86272i
$7$		0			0
$7$		0			0
$8$		−	2.55819i		−	0.904456i
$9$	−2.98531	−	5.17071i	−0.995105	−	1.72357i
$10$	−2.24401	+	3.88673i	−0.709617	+	1.22909i
$11$	2.05342	+	1.18554i	0.619128	+	0.357454i	0.776530	−	0.630081i	$-0.216978\pi$
$11$	2.05342	+	1.18554i	0.619128	+	0.357454i	−0.157401	+	0.987535i	$0.550312\pi$
$12$	0.480314	+	0.831928i	0.138655	+	0.240157i
$13$	2.32734	+	2.75381i	0.645489	+	0.763770i
$13$	2.32734	+	2.75381i	0.645489	+	0.763770i
$14$		0			0
$15$			8.82374i			2.27828i
$16$	2.26930	+	3.93054i	0.567325	+	0.982635i
$17$	2.68497	−	4.65051i	0.651201	−	1.12791i	−0.331631	−	0.943409i	$-0.607599\pi$
$17$	2.68497	−	4.65051i	0.651201	−	1.12791i	0.982832	−	0.184504i	$-0.0590679\pi$
$18$	7.87704	+	4.54781i	1.85664	+	1.07193i
$19$	4.63703	−	2.67719i	1.06381	−	0.614189i	0.137324	−	0.990526i	$-0.456150\pi$
$19$	4.63703	−	2.67719i	1.06381	−	0.614189i	0.926483	+	0.376337i	$0.122817\pi$
$20$		−	0.944899i		−	0.211286i
$21$		0			0
$22$	−3.61209			−0.770101
$23$	1.39528	+	2.41670i	0.290936	+	0.503917i	0.974031	−	0.226413i	$-0.0726999\pi$
$23$	1.39528	+	2.41670i	0.290936	+	0.503917i	−0.683095	+	0.730330i	$0.739367\pi$
$24$	6.63551	+	3.83101i	1.35447	+	0.782002i
$25$	1.83963	−	3.18634i	0.367927	−	0.637268i
$26$	−5.16803	−	1.86037i	−1.01353	−	0.364848i
$27$	8.89733			1.71229
$28$		0			0
$29$	0.585818			0.108784			0.0543918	−	0.998520i	$-0.482678\pi$
$29$	0.585818			0.108784			0.0543918	+	0.998520i	$0.482678\pi$
$30$	−6.72103	−	11.6412i	−1.22709	−	2.12537i
$31$	7.21727	+	4.16690i	1.29626	+	0.748397i	0.979756	−	0.200194i	$-0.0641574\pi$
$31$	7.21727	+	4.16690i	1.29626	+	0.748397i	0.316505	+	0.948591i	$0.397491\pi$
$32$	−1.55686	−	0.898851i	−0.275216	−	0.158896i
$33$	−6.15019	+	3.55081i	−1.07061	+	0.618117i
$34$			8.18054i			1.40295i
$35$		0			0
$36$	−1.91498			−0.319163
$37$	0.585182	−	0.337855i	0.0962033	−	0.0555430i	−0.451127	−	0.892460i	$-0.648978\pi$
$37$	0.585182	−	0.337855i	0.0962033	−	0.0555430i	0.547330	+	0.836917i	$0.315644\pi$
$38$	−4.07842	+	7.06402i	−0.661606	+	1.14594i
$39$	−10.6282	+	1.91277i	−1.70188	+	0.306288i
$40$	−3.76829	−	6.52686i	−0.595818	−	1.03199i
$41$		−	11.2799i		−	1.76162i	−0.473473	−	0.880808i	$-0.657000\pi$
$41$		−	11.2799i		−	1.76162i	0.473473	−	0.880808i	$-0.343000\pi$
$42$		0			0
$43$	−10.5271			−1.60536			−0.802682	−	0.596408i	$-0.796594\pi$
$43$	−10.5271			−1.60536			−0.802682	+	0.596408i	$0.796594\pi$
$44$	0.658599	−	0.380242i	0.0992875	−	0.0573237i
$45$	−15.2332	−	8.79491i	−2.27084	−	1.31107i
$46$	−3.68159	−	2.12557i	−0.542821	−	0.313398i
$47$	0.465700	−	0.268872i	0.0679293	−	0.0392190i	−0.465651	−	0.884969i	$-0.654180\pi$
$47$	0.465700	−	0.268872i	0.0679293	−	0.0392190i	0.533580	+	0.845750i	$0.320846\pi$
$48$	−13.5936			−1.96206
$49$		0			0
$50$			5.60498i			0.792664i
$51$	8.04176	+	13.9287i	1.12607	+	1.95041i
$52$	1.13814	−	0.204831i	0.157831	−	0.0284049i
$53$	−3.95173	+	6.84459i	−0.542811	+	0.940177i	0.455930	+	0.890016i	$0.349307\pi$
$53$	−3.95173	+	6.84459i	−0.542811	+	0.940177i	−0.998741	+	0.0501612i	$0.984026\pi$
$54$	−11.7382	+	6.77707i	−1.59737	+	0.922243i
$55$	6.98535			0.941904
$56$		0			0
$57$			16.0369i			2.12414i
$58$	−0.772869	+	0.446216i	−0.101483	+	0.0585910i
$59$	5.32262	+	3.07301i	0.692946	+	0.400072i	0.804715	−	0.593662i	$-0.202318\pi$
$59$	5.32262	+	3.07301i	0.692946	+	0.400072i	−0.111769	+	0.993734i	$0.535652\pi$
$60$	2.45091	+	1.41503i	0.316411	+	0.182680i
$61$	1.39344	+	2.41352i	0.178412	+	0.309019i	0.941337	−	0.337468i	$-0.109571\pi$
$61$	1.39344	+	2.41352i	0.178412	+	0.309019i	−0.762925	+	0.646487i	$0.776237\pi$
$62$	−12.6957			−1.61235
$63$		0			0
$64$	−6.33858			−0.792323
$65$	9.99434	+	3.59772i	1.23965	+	0.446243i
$66$	5.40929	−	9.36917i	0.665838	−	1.15326i
$67$	3.64902	+	2.10676i	0.445799	+	0.257382i	0.706054	−	0.708158i	$-0.250473\pi$
$67$	3.64902	+	2.10676i	0.445799	+	0.257382i	−0.260255	+	0.965540i	$0.583807\pi$
$68$	−0.861159	−	1.49157i	−0.104431	−	0.180880i
$69$	−8.35802			−1.00619
$70$		0			0
$71$		−	1.25151i		−	0.148527i	−0.997239	−	0.0742637i	$-0.976339\pi$
$71$		−	1.25151i		−	0.148527i	0.997239	−	0.0742637i	$-0.0236607\pi$
$72$	−13.2277	+	7.63699i	−1.55889	+	0.900028i
$73$	−9.40676	−	5.43100i	−1.10098	−	0.635650i	−0.164501	−	0.986377i	$-0.552601\pi$
$73$	−9.40676	−	5.43100i	−1.10098	−	0.635650i	−0.936478	+	0.350727i	$0.885935\pi$
$74$	−0.514686	+	0.891463i	−0.0598311	+	0.103630i
$75$	5.50989	+	9.54340i	0.636227	+	1.10198i
$76$		−	1.71733i		−	0.196991i
$77$		0			0
$78$	12.5649	−	10.6190i	1.42269	−	1.20237i
$79$	−3.14568	−	5.44848i	−0.353917	−	0.613002i	0.633015	−	0.774139i	$-0.281817\pi$
$79$	−3.14568	−	5.44848i	−0.353917	−	0.613002i	−0.986932	+	0.161138i	$0.948484\pi$
$80$	11.5796	+	6.68549i	1.29464	+	0.747460i
$81$	−4.36825	+	7.56604i	−0.485362	+	0.840671i
$82$	8.59184	+	14.8815i	0.948810	+	1.64339i
$83$			1.74725i			0.191786i	0.995392	+	0.0958928i	$0.0305706\pi$
$83$			1.74725i			0.191786i	−0.995392	+	0.0958928i	$0.969429\pi$
$84$		0			0
$85$		−	15.8202i		−	1.71594i
$86$	13.8884	−	8.01845i	1.49762	−	0.864651i
$87$	−0.877292	+	1.51951i	−0.0940555	+	0.162909i
$88$	3.03283	−	5.25302i	0.323301	−	0.559974i
$89$	8.86315	−	5.11714i	0.939492	−	0.542416i	0.0496912	−	0.998765i	$-0.484176\pi$
$89$	8.86315	−	5.11714i	0.939492	−	0.542416i	0.889801	+	0.456348i	$0.150843\pi$
$90$	26.7963			2.82457
$91$		0			0
$92$	0.895027			0.0933130
$93$	−21.6165	+	12.4803i	−2.24152	+	1.29414i
$94$	−0.409598	+	0.709445i	−0.0422468	+	0.0731736i
$95$	7.88715	−	13.6610i	0.809205	−	1.40158i
$96$	4.66294	−	2.69215i	0.475909	−	0.274766i
$97$			9.90640i			1.00584i	0.864332	+	0.502921i	$0.167741\pi$
$97$			9.90640i			1.00584i	−0.864332	+	0.502921i	$0.832259\pi$
$98$		0			0
$99$		−	14.1568i		−	1.42282i
$100$	−0.590032	−	1.02196i	−0.0590032	−	0.102196i
$101$	−1.02539	+	1.77602i	−0.102030	+	0.176721i	−0.912521	−	0.409030i	$-0.865867\pi$
$101$	−1.02539	+	1.77602i	−0.102030	+	0.176721i	0.810491	+	0.585751i	$0.199200\pi$
$102$	−21.2190	−	12.2508i	−2.10099	−	1.21301i
$103$	−1.51481	−	2.62373i	−0.149259	−	0.258523i	0.781695	−	0.623661i	$-0.214355\pi$
$103$	−1.51481	−	2.62373i	−0.149259	−	0.258523i	−0.930954	+	0.365137i	$0.881022\pi$
$104$	7.04476	−	5.95378i	0.690796	−	0.583816i
$105$		0			0
$106$		−	12.0401i		−	1.16944i
$107$	6.21526	+	10.7652i	0.600852	+	1.04071i	0.992692	+	0.120673i	$0.0385053\pi$
$107$	6.21526	+	10.7652i	0.600852	+	1.04071i	−0.391840	+	0.920033i	$0.628161\pi$
$108$	1.42683	−	2.47135i	0.137297	−	0.237806i
$109$	−3.06384	−	1.76891i	−0.293463	−	0.169431i	0.346040	−	0.938220i	$-0.387526\pi$
$109$	−3.06384	−	1.76891i	−0.293463	−	0.169431i	−0.639502	+	0.768789i	$0.720860\pi$
$110$	−9.21576	+	5.32072i	−0.878688	+	0.507311i
$111$			2.02382i			0.192092i
$112$		0			0
$113$	10.3848			0.976921			0.488460	−	0.872586i	$-0.337559\pi$
$113$	10.3848			0.976921			0.488460	+	0.872586i	$0.337559\pi$
$114$	−12.2153	−	21.1575i	−1.14406	−	1.98158i
$115$	7.11974	+	4.11058i	0.663919	+	0.383314i
$116$	0.0939456	−	0.162719i	0.00872263	−	0.0151080i
$117$	7.29132	−	20.2550i	0.674083	−	1.87258i
$118$	−9.36283			−0.861918
$119$		0			0
$120$	22.5728			2.06060
$121$	−2.68899	−	4.65746i	−0.244453	−	0.423406i
$122$	−3.67674	−	2.12277i	−0.332876	−	0.192186i
$123$	29.2581	+	16.8921i	2.63811	+	1.52311i
$124$	2.31482	−	1.33646i	0.207877	−	0.120018i
$125$			3.89096i			0.348018i
$126$		0			0
$127$	−5.09504			−0.452112			−0.226056	−	0.974114i	$-0.572583\pi$
$127$	−5.09504			−0.452112			−0.226056	+	0.974114i	$0.572583\pi$
$128$	11.4762	−	6.62579i	1.01436	−	0.585642i
$129$	15.7648	−	27.3055i	1.38802	−	2.40411i
$130$	−15.9259	+	2.86619i	−1.39679	+	0.251382i
$131$	11.2722	+	19.5240i	0.984854	+	1.70582i	0.642583	+	0.766216i	$0.277863\pi$
$131$	11.2722	+	19.5240i	0.984854	+	1.70582i	0.342271	+	0.939601i	$0.388804\pi$
$132$			2.27773i			0.198251i
$133$		0			0
$134$	−6.41887			−0.554506
$135$	22.7003	−	13.1060i	1.95373	−	1.12799i
$136$	−11.8969	−	6.86866i	−1.02015	−	0.588983i
$137$	−0.896156	−	0.517396i	−0.0765638	−	0.0442041i	0.461229	−	0.887281i	$-0.347409\pi$
$137$	−0.896156	−	0.517396i	−0.0765638	−	0.0442041i	−0.537793	+	0.843077i	$0.680742\pi$
$138$	11.0267	−	6.36628i	0.938657	−	0.541934i
$139$	−8.49456			−0.720499			−0.360249	−	0.932856i	$-0.617308\pi$
$139$	−8.49456			−0.720499			−0.360249	+	0.932856i	$0.617308\pi$
$140$		0			0
$141$			1.61060i			0.135637i
$142$	0.953276	+	1.65112i	0.0799971	+	0.138559i
$143$	1.51425	+	8.41388i	0.126628	+	0.703604i
$144$	13.5491	−	23.4678i	1.12909	−	1.95565i
$145$	1.49463	−	0.862927i	0.124123	−	0.0716622i
$146$	16.5471			1.36945
$147$		0			0
$148$		−	0.216723i		−	0.0178145i
$149$	−3.73554	+	2.15672i	−0.306028	+	0.176685i	−0.645148	−	0.764058i	$-0.723204\pi$
$149$	−3.73554	+	2.15672i	−0.306028	+	0.176685i	0.339120	+	0.940743i	$0.389871\pi$
$150$	−14.5384	−	8.39374i	−1.18705	−	0.685346i
$151$	−10.6043	−	6.12237i	−0.862963	−	0.498232i	0.00204066	−	0.999998i	$-0.499350\pi$
$151$	−10.6043	−	6.12237i	−0.862963	−	0.498232i	−0.865003	+	0.501766i	$0.832684\pi$
$152$	−6.84875	−	11.8624i	−0.555507	−	0.962166i
$153$	−32.0619			−2.59205
$154$		0			0
$155$	24.5518			1.97205
$156$	−1.17312	+	3.25888i	−0.0939246	+	0.260919i
$157$	−11.1020	+	19.2292i	−0.886035	+	1.53466i	−0.0415118	+	0.999138i	$0.513217\pi$
$157$	−11.1020	+	19.2292i	−0.886035	+	1.53466i	−0.844523	+	0.535519i	$0.820116\pi$
$158$	8.30019	+	4.79211i	0.660327	+	0.381240i
$159$	−11.8358	−	20.5002i	−0.938642	−	1.62577i
$160$	−5.29614			−0.418697
$161$		0			0
$162$		−	13.3092i		−	1.04567i
$163$	9.84184	−	5.68219i	0.770872	−	0.445063i	−0.0623134	−	0.998057i	$-0.519848\pi$
$163$	9.84184	−	5.68219i	0.770872	−	0.445063i	0.833186	+	0.552993i	$0.186515\pi$
$164$	−3.13313	−	1.80891i	−0.244656	−	0.141252i
$165$	−10.4609	+	18.1188i	−0.814380	+	1.41055i
$166$	−1.33088	−	2.30515i	−0.103296	−	0.178914i
$167$			1.88127i			0.145577i	0.997347	+	0.0727885i	$0.0231898\pi$
$167$			1.88127i			0.145577i	−0.997347	+	0.0727885i	$0.976810\pi$
$168$		0			0
$169$	−2.16695	+	12.8181i	−0.166688	+	0.986010i
$170$	12.0502	+	20.8715i	0.924207	+	1.60077i
$171$	−27.6859	−	15.9845i	−2.11720	−	1.22236i
$172$	−1.68819	+	2.92403i	−0.128723	+	0.222955i
$173$	2.78557	+	4.82474i	0.211783	+	0.366818i	0.952273	−	0.305249i	$-0.0987398\pi$
$173$	2.78557	+	4.82474i	0.211783	+	0.366818i	−0.740490	+	0.672068i	$0.765406\pi$
$174$		−	2.67292i		−	0.202634i
$175$		0			0
$176$			10.7614i			0.811170i
$177$	−15.9418	+	9.20399i	−1.19826	+	0.691814i
$178$	−7.79543	+	13.5021i	−0.584292	+	1.01202i
$179$	−2.33071	+	4.03691i	−0.174205	+	0.301733i	−0.939886	−	0.341488i	$-0.889069\pi$
$179$	−2.33071	+	4.03691i	−0.174205	+	0.301733i	0.765681	+	0.643221i	$0.222402\pi$
$180$	−4.88580	+	2.82082i	−0.364166	+	0.210252i
$181$	12.5360			0.931794			0.465897	−	0.884839i	$-0.345732\pi$
$181$	12.5360			0.931794			0.465897	+	0.884839i	$0.345732\pi$
$182$		0			0
$183$	−8.34701			−0.617029
$184$	6.18237	−	3.56939i	0.455770	−	0.263139i
$185$	0.995340	−	1.72398i	0.0731789	−	0.126750i
$186$	19.0124	−	32.9304i	1.39406	−	2.41458i
$187$	11.0267	−	6.36628i	0.806354	−	0.465549i
$188$		−	0.172472i		−	0.0125788i
$189$		0			0
$190$			24.0305i			1.74336i
$191$	0.658818	+	1.14111i	0.0476704	+	0.0825676i	0.888876	−	0.458148i	$-0.151487\pi$
$191$	0.658818	+	1.14111i	0.0476704	+	0.0825676i	−0.841206	+	0.540715i	$0.818154\pi$
$192$	9.49234	−	16.4412i	0.685051	−	1.18654i
$193$	13.1155	+	7.57223i	0.944073	+	0.545061i	0.891235	−	0.453542i	$-0.149840\pi$
$193$	13.1155	+	7.57223i	0.944073	+	0.545061i	0.0528385	+	0.998603i	$0.483173\pi$
$194$	−7.54568	−	13.0695i	−0.541748	−	0.938336i
$195$	−24.2989	+	20.5359i	−1.74008	+	1.47061i
$196$		0			0
$197$		−	9.90571i		−	0.705753i	−0.935670	−	0.352876i	$-0.885204\pi$
$197$		−	9.90571i		−	0.705753i	0.935670	−	0.352876i	$-0.114796\pi$
$198$	10.7832	+	18.6771i	0.766331	+	1.32732i
$199$	4.28663	−	7.42466i	0.303871	−	0.526320i	−0.673138	−	0.739517i	$-0.735054\pi$
$199$	4.28663	−	7.42466i	0.303871	−	0.526320i	0.977009	+	0.213197i	$0.0683875\pi$
$200$	−8.15125	−	4.70613i	−0.576380	−	0.332773i
$201$	−10.9292	+	6.30997i	−0.770886	+	0.445071i
$202$		−	3.12413i		−	0.219813i
$203$		0			0
$204$	5.15852			0.361169
$205$	−16.6156	−	28.7790i	−1.16048	−	2.01001i
$206$	3.99697	+	2.30765i	0.278482	+	0.160782i
$207$	8.33071	−	14.4292i	0.579024	−	1.00290i
$208$	−5.54253	+	15.3969i	−0.384305	+	1.06759i
$209$	12.6957			0.878177
$210$		0			0
$211$	−1.44515			−0.0994881			−0.0497440	−	0.998762i	$-0.515841\pi$
$211$	−1.44515			−0.0994881			−0.0497440	+	0.998762i	$0.515841\pi$
$212$	1.26745	+	2.19529i	0.0870488	+	0.150773i
$213$	3.24622	+	1.87421i	0.222427	+	0.128418i
$214$	−16.3996	−	9.46830i	−1.12105	−	0.647240i
$215$	−26.8584	+	15.5067i	−1.83173	+	1.05755i
$216$		−	22.7610i		−	1.54869i
$217$		0			0
$218$	5.38950			0.365023
$219$	28.1742	−	16.2664i	1.90384	−	1.09918i
$220$	1.12022	−	1.94027i	0.0755250	−	0.130813i
$221$	19.0555	−	3.42942i	1.28181	−	0.230688i
$222$	−1.54154	−	2.67002i	−0.103461	−	0.179200i
$223$			14.9949i			1.00413i	0.864829	+	0.502067i	$0.167427\pi$
$223$			14.9949i			1.00413i	−0.864829	+	0.502067i	$0.832573\pi$
$224$		0			0
$225$	−21.9675			−1.46450
$226$	−13.7007	+	7.91008i	−0.911355	+	0.526171i
$227$	−0.989174	−	0.571100i	−0.0656538	−	0.0379052i	0.466814	−	0.884356i	$-0.345402\pi$
$227$	−0.989174	−	0.571100i	−0.0656538	−	0.0379052i	−0.532468	+	0.846450i	$0.678735\pi$
$228$	4.45446	+	2.57178i	0.295004	+	0.170320i
$229$	−5.42942	+	3.13467i	−0.358786	+	0.207145i	−0.668548	−	0.743669i	$-0.733084\pi$
$229$	−5.42942	+	3.13467i	−0.358786	+	0.207145i	0.309762	+	0.950814i	$0.399751\pi$
$230$	−12.5241			−0.825814
$231$		0			0
$232$		−	1.49863i		−	0.0983900i
$233$	−3.08347	−	5.34073i	−0.202005	−	0.349883i	0.747169	−	0.664634i	$-0.231412\pi$
$233$	−3.08347	−	5.34073i	−0.202005	−	0.349883i	−0.949174	+	0.314751i	$0.898079\pi$
$234$	5.80877	+	32.2762i	0.379731	+	2.10996i
$235$	0.792113	−	1.37198i	0.0516717	−	0.0894981i
$236$	1.70714	−	0.985618i	0.111125	−	0.0641583i
$237$	18.8433			1.22400
$238$		0			0
$239$		−	27.4589i		−	1.77617i	−0.459684	−	0.888083i	$-0.652037\pi$
$239$		−	27.4589i		−	1.77617i	0.459684	−	0.888083i	$-0.347963\pi$
$240$	−34.6821	+	20.0237i	−2.23872	+	1.29252i
$241$	−8.48166	−	4.89689i	−0.546352	−	0.315436i	0.201298	−	0.979530i	$-0.435484\pi$
$241$	−8.48166	−	4.89689i	−0.546352	−	0.315436i	−0.747649	+	0.664094i	$0.768818\pi$
$242$	7.09516	+	4.09639i	0.456094	+	0.263326i
$243$	0.262631	+	0.454890i	0.0168478	+	0.0291812i
$244$	0.893848			0.0572227
$245$		0			0
$246$	−51.4668			−3.28140
$247$	18.1644	+	6.53875i	1.15577	+	0.416051i
$248$	10.6597	−	18.4631i	0.676892	−	1.17241i
$249$	−4.53208	−	2.61660i	−0.287209	−	0.165820i
$250$	−2.96373	−	5.13334i	−0.187443	−	0.324661i
$251$	12.4945			0.788644			0.394322	−	0.918972i	$-0.370979\pi$
$251$	12.4945			0.788644			0.394322	+	0.918972i	$0.370979\pi$
$252$		0			0
$253$			6.61665i			0.415985i
$254$	6.72188	−	3.88088i	0.421768	−	0.243508i
$255$	41.0349	+	23.6915i	2.56970	+	1.48362i
$256$	−3.75511	+	6.50404i	−0.234694	+	0.406502i
$257$	−9.59645	−	16.6215i	−0.598610	−	1.03682i	−0.993026	−	0.117891i	$-0.962387\pi$
$257$	−9.59645	−	16.6215i	−0.598610	−	1.03682i	0.394416	−	0.918932i	$-0.370947\pi$
$258$			48.0321i			2.99035i
$259$		0			0
$260$	2.60207	−	2.19910i	0.161374	−	0.136383i
$261$	−1.74885	−	3.02910i	−0.108251	−	0.187496i
$262$	−29.7427	−	17.1720i	−1.83751	−	1.06089i
$263$	−14.4077	+	24.9548i	−0.888415	+	1.53878i	−0.0466659	+	0.998911i	$0.514860\pi$
$263$	−14.4077	+	24.9548i	−0.888415	+	1.53878i	−0.841749	+	0.539869i	$0.818474\pi$
$264$	9.08364	+	15.7333i	0.559060	+	0.968320i
$265$			23.2840i			1.43033i
$266$		0			0
$267$			30.6527i			1.87592i
$268$	1.17036	−	0.675710i	0.0714913	−	0.0412755i
$269$	4.07709	−	7.06173i	0.248585	−	0.430561i	−0.714549	−	0.699586i	$-0.753368\pi$
$269$	4.07709	−	7.06173i	0.248585	−	0.430561i	0.963133	+	0.269024i	$0.0867012\pi$
$270$	−19.9657	+	34.5815i	−1.21507	+	2.10457i
$271$	16.0897	−	9.28939i	0.977379	−	0.564290i	0.0759014	−	0.997115i	$-0.475817\pi$
$271$	16.0897	−	9.28939i	0.977379	−	0.564290i	0.901478	+	0.432825i	$0.142483\pi$
$272$	24.3720			1.47777
$273$		0			0
$274$	1.57640			0.0952336
$275$	7.55507	−	4.36192i	0.455588	−	0.263034i
$276$	−1.34035	+	2.32155i	−0.0806794	+	0.139741i
$277$	−8.61710	+	14.9253i	−0.517752	+	0.896772i	0.482036	+	0.876152i	$0.339898\pi$
$277$	−8.61710	+	14.9253i	−0.517752	+	0.896772i	−0.999787	+	0.0206205i	$0.993436\pi$
$278$	11.2069	−	6.47028i	0.672143	−	0.388062i
$279$		−	49.7580i		−	2.97893i
$280$		0			0
$281$			11.4691i			0.684191i	0.939665	+	0.342096i	$0.111137\pi$
$281$			11.4691i			0.684191i	−0.939665	+	0.342096i	$0.888863\pi$
$282$	−1.22679	−	2.12486i	−0.0730541	−	0.126533i
$283$	−0.727876	+	1.26072i	−0.0432678	+	0.0749420i	−0.886848	−	0.462061i	$-0.847110\pi$
$283$	−0.727876	+	1.26072i	−0.0432678	+	0.0749420i	0.843580	+	0.537003i	$0.180444\pi$
$284$	−0.347625	−	0.200701i	−0.0206277	−	0.0119094i
$285$	23.6228	+	40.9159i	1.39930	+	2.42365i
$286$	−8.40658	−	9.94702i	−0.497092	−	0.588180i
$287$		0			0
$288$			10.7334i			0.632472i
$289$	−5.91814	−	10.2505i	−0.348126	−	0.602972i
$290$	−1.31458	+	2.27692i	−0.0771947	+	0.133705i
$291$	−25.6955	−	14.8353i	−1.50630	−	0.869662i
$292$	−3.01706	+	1.74190i	−0.176560	+	0.101937i
$293$		−	30.6962i		−	1.79329i	−0.442750	−	0.896645i	$-0.645997\pi$
$293$		−	30.6962i		−	1.79329i	0.442750	−	0.896645i	$-0.354003\pi$
$294$		0			0
$295$	18.1066			1.05421
$296$	−0.864296	−	1.49700i	−0.0502362	−	0.0870116i
$297$	18.2699	+	10.5481i	1.06013	+	0.612065i
$298$	3.28553	−	5.69071i	0.190326	−	0.329654i
$299$	−3.40783	+	9.46683i	−0.197080	+	0.547481i
$300$	3.53441			0.204059
$301$		0			0
$302$	18.6536			1.07339
$303$	−3.07113	−	5.31936i	−0.176432	−	0.305589i
$304$	21.0456	+	12.1507i	1.20705	+	0.696889i
$305$	7.11036	+	4.10517i	0.407138	+	0.235061i
$306$	42.2993	−	24.4215i	2.41809	−	1.39608i
$307$		−	21.2602i		−	1.21339i	−0.794936	−	0.606693i	$-0.792496\pi$
$307$		−	21.2602i		−	1.21339i	0.794936	−	0.606693i	$-0.207504\pi$
$308$		0			0
$309$	9.07401			0.516202
$310$	−32.3912	+	18.7011i	−1.83970	+	1.06215i
$311$	−2.22324	+	3.85076i	−0.126068	+	0.218357i	−0.922150	−	0.386833i	$-0.873569\pi$
$311$	−2.22324	+	3.85076i	−0.126068	+	0.218357i	0.796082	+	0.605189i	$0.206902\pi$
$312$	4.89322	+	27.1890i	0.277024	+	1.53928i
$313$	−1.14343	−	1.98049i	−0.0646307	−	0.111944i	0.831899	−	0.554926i	$-0.187254\pi$
$313$	−1.14343	−	1.98049i	−0.0646307	−	0.111944i	−0.896530	+	0.442983i	$0.853920\pi$
$314$		−	33.8254i		−	1.90888i
$315$		0			0
$316$	−2.01785			−0.113513
$317$	−7.01555	+	4.05043i	−0.394033	+	0.227495i	−0.683906	−	0.729570i	$-0.739720\pi$
$317$	−7.01555	+	4.05043i	−0.394033	+	0.227495i	0.289873	+	0.957065i	$0.406387\pi$
$318$	31.2300	+	18.0306i	1.75129	+	1.01111i
$319$	1.20293	+	0.694511i	0.0673510	+	0.0388851i
$320$	−16.1720	+	9.33692i	−0.904043	+	0.521950i
$321$	−37.2307			−2.07801
$322$		0			0
$323$		−	28.7527i		−	1.59984i
$324$	1.40104	+	2.42668i	0.0778358	+	0.134816i
$325$	13.0560	−	2.34970i	0.724218	−	0.130338i
$326$	−8.65622	+	14.9930i	−0.479424	+	0.830386i
$327$	9.17652	−	5.29806i	0.507462	−	0.292984i
$328$	−28.8560			−1.59330
$329$		0			0
$330$		−	31.8722i		−	1.75451i
$331$	−10.2068	+	5.89288i	−0.561015	+	0.323902i	−0.753553	−	0.657388i	$-0.771661\pi$
$331$	−10.2068	+	5.89288i	−0.561015	+	0.323902i	0.192538	+	0.981290i	$0.438328\pi$
$332$	0.485322	+	0.280201i	0.0266355	+	0.0153780i
$333$	−3.49390	−	2.01720i	−0.191465	−	0.110542i
$334$	−1.43296	−	2.48196i	−0.0784080	−	0.135807i
$335$	12.4133			0.678212
$336$		0			0
$337$	−2.63045			−0.143290			−0.0716450	−	0.997430i	$-0.522825\pi$
$337$	−2.63045			−0.143290			−0.0716450	+	0.997430i	$0.522825\pi$
$338$	−6.90469	−	18.5615i	−0.375565	−	1.00961i
$339$	−15.5518	+	26.9365i	−0.844656	+	1.46299i
$340$	−4.39426	−	2.53703i	−0.238312	−	0.137590i
$341$	9.88005	+	17.1127i	0.535035	+	0.926707i
$342$	48.7014			2.63347
$343$		0			0
$344$			26.9302i			1.45198i
$345$	−21.3243	+	12.3116i	−1.14806	+	0.662835i
$346$	−7.34999	−	4.24352i	−0.395138	−	0.228133i
$347$	−2.41231	+	4.17825i	−0.129500	+	0.224300i	−0.923483	−	0.383640i	$-0.874670\pi$
$347$	−2.41231	+	4.17825i	−0.129500	+	0.224300i	0.793983	+	0.607940i	$0.208004\pi$
$348$	0.281377	+	0.487358i	0.0150834	+	0.0261252i
$349$		−	17.5231i		−	0.937991i	−0.883201	−	0.468995i	$-0.844616\pi$
$349$		−	17.5231i		−	0.937991i	0.883201	−	0.468995i	$-0.155384\pi$
$350$		0			0
$351$	20.7071	+	24.5016i	1.10527	+	1.30780i
$352$	−2.13125	−	3.69143i	−0.113596	−	0.196754i
$353$	−5.71338	−	3.29862i	−0.304092	−	0.175568i	0.340188	−	0.940358i	$-0.389509\pi$
$353$	−5.71338	−	3.29862i	−0.304092	−	0.175568i	−0.644280	+	0.764790i	$0.722843\pi$
$354$	14.0213	−	24.2856i	0.745224	−	1.29077i
$355$	−1.84352	−	3.19307i	−0.0978438	−	0.169470i
$356$		−	3.28248i		−	0.173971i
$357$		0			0
$358$		−	7.10118i		−	0.375309i
$359$	−19.9605	+	11.5242i	−1.05348	+	0.608225i	−0.923621	−	0.383308i	$-0.874785\pi$
$359$	−19.9605	+	11.5242i	−1.05348	+	0.608225i	−0.129856	+	0.991533i	$0.541452\pi$
$360$	−22.4990	+	38.9695i	−1.18580	+	2.05387i
$361$	4.83467	−	8.37389i	0.254456	−	0.440731i
$362$	−16.5387	+	9.54865i	−0.869257	+	0.501866i
$363$	16.1076			0.845428
$364$		0			0
$365$	−32.0001			−1.67496
$366$	11.0122	−	6.35790i	0.575617	−	0.332333i
$367$	−7.96588	+	13.7973i	−0.415815	+	0.720213i	−0.995514	−	0.0946179i	$-0.969837\pi$
$367$	−7.96588	+	13.7973i	−0.415815	+	0.720213i	0.579698	+	0.814831i	$0.303170\pi$
$368$	−6.33262	+	10.9684i	−0.330111	+	0.571769i
$369$	−58.3249	+	33.6739i	−3.03627	+	1.75299i
$370$			3.03259i			0.157657i
$371$		0			0
$372$			8.00568i			0.415075i
$373$	−11.7145	−	20.2901i	−0.606552	−	1.05058i	−0.991804	−	0.127768i	$-0.959219\pi$
$373$	−11.7145	−	20.2901i	−0.606552	−	1.05058i	0.385252	−	0.922811i	$-0.374115\pi$
$374$	−9.69837	+	16.7981i	−0.501491	+	0.868607i
$375$	−10.0925	−	5.82691i	−0.521174	−	0.300900i
$376$	−0.687825	−	1.19135i	−0.0354718	−	0.0614390i
$377$	1.36340	+	1.61323i	0.0702186	+	0.0830856i
$378$		0			0
$379$		−	30.1041i		−	1.54634i	−0.634196	−	0.773172i	$-0.718669\pi$
$379$		−	30.1041i		−	1.54634i	0.634196	−	0.773172i	$-0.281331\pi$
$380$	−2.52967	−	4.38152i	−0.129769	−	0.224767i
$381$	7.63008	−	13.2157i	0.390901	−	0.677060i
$382$	−1.73836	−	1.00364i	−0.0889421	−	0.0513507i
$383$	−11.1368	+	6.42986i	−0.569066	+	0.328551i	−0.756776	−	0.653674i	$-0.773227\pi$
$383$	−11.1368	+	6.42986i	−0.569066	+	0.328551i	0.187710	+	0.982224i	$0.439893\pi$
$384$			39.6898i			2.02541i
$385$		0			0
$386$	−23.0710			−1.17428
$387$	31.4266	+	54.4325i	1.59750	+	2.76696i
$388$	2.75163	+	1.58866i	0.139693	+	0.0806518i
$389$	18.4266	−	31.9158i	0.934264	−	1.61819i	0.158323	−	0.987387i	$-0.449391\pi$
$389$	18.4266	−	31.9158i	0.934264	−	1.61819i	0.775941	−	0.630806i	$-0.217275\pi$
$390$	16.4154	−	45.6014i	0.831227	−	2.30912i
$391$	14.9852			0.757833
$392$		0			0
$393$	−67.5226			−3.40606
$394$	7.54516	+	13.0686i	0.380119	+	0.658386i
$395$	−16.0515	−	9.26736i	−0.807641	−	0.466292i
$396$	−3.93225	−	2.27028i	−0.197603	−	0.114086i
$397$	17.5878	−	10.1543i	0.882707	−	0.509631i	0.0111570	−	0.999938i	$-0.496449\pi$
$397$	17.5878	−	10.1543i	0.882707	−	0.509631i	0.871550	+	0.490307i	$0.163115\pi$
$398$			13.0605i			0.654662i
$399$		0			0
$400$	16.6987			0.834935
$401$	17.0346	−	9.83495i	0.850669	−	0.491134i	−0.0102075	−	0.999948i	$-0.503249\pi$
$401$	17.0346	−	9.83495i	0.850669	−	0.491134i	0.860877	+	0.508814i	$0.169916\pi$
$402$	9.61258	−	16.6495i	0.479432	−	0.830401i
$403$	5.32223	+	29.5728i	0.265119	+	1.47313i
$404$	0.328875	+	0.569628i	0.0163621	+	0.0283401i
$405$			25.7383i			1.27895i
$406$		0			0
$407$	1.60216			0.0794162
$408$	35.6323	−	20.5723i	1.76406	−	1.01848i
$409$	−20.0705	−	11.5877i	−0.992424	−	0.572976i	−0.0864259	−	0.996258i	$-0.527545\pi$
$409$	−20.0705	−	11.5877i	−0.992424	−	0.572976i	−0.905998	+	0.423282i	$0.860878\pi$
$410$	43.8418	+	25.3121i	2.16519	+	1.25007i
$411$	2.68408	−	1.54965i	0.132396	−	0.0764387i
$412$	−0.971699			−0.0478722
$413$		0			0
$414$			25.3819i			1.24745i
$415$	2.57375	+	4.45787i	0.126341	+	0.218828i
$416$	−1.14807	−	6.37922i	−0.0562889	−	0.312767i
$417$	12.7210	−	22.0335i	0.622951	−	1.07898i
$418$	−16.7494	+	9.67025i	−0.819238	+	0.472988i
$419$	−28.6478			−1.39953			−0.699767	−	0.714371i	$-0.746713\pi$
$419$	−28.6478			−1.39953			−0.699767	+	0.714371i	$0.746713\pi$
$420$		0			0
$421$			36.3249i			1.77037i	0.465241	+	0.885184i	$0.345968\pi$
$421$			36.3249i			1.77037i	−0.465241	+	0.885184i	$0.654032\pi$
$422$	1.90658	−	1.10077i	0.0928110	−	0.0535844i
$423$	−2.78052	−	1.60533i	−0.135193	−	0.0780540i
$424$	17.5097	+	10.1093i	0.850349	+	0.490949i
$425$	−9.87873	−	17.1105i	−0.479189	−	0.829979i
$426$	−5.71031			−0.276666
$427$		0			0
$428$	3.98688			0.192713
$429$	−24.0919	−	8.67249i	−1.16317	−	0.418712i
$430$	23.6228	−	40.9159i	1.13919	−	1.97314i
$431$	6.86872	+	3.96566i	0.330855	+	0.191019i	0.656220	−	0.754569i	$-0.272154\pi$
$431$	6.86872	+	3.96566i	0.330855	+	0.191019i	−0.325366	+	0.945588i	$0.605487\pi$
$432$	20.1907	+	34.9713i	0.971425	+	1.68256i
$433$	9.60994			0.461824			0.230912	−	0.972975i	$-0.425829\pi$
$433$	9.60994			0.461824			0.230912	+	0.972975i	$0.425829\pi$
$434$		0			0
$435$			5.16911i			0.247840i
$436$	−0.982676	+	0.567348i	−0.0470616	+	0.0271711i
$437$	12.9399	+	7.47086i	0.619000	+	0.357380i
$438$	−24.7801	+	42.9205i	−1.18404	+	2.05082i
$439$	−1.73345	−	3.00243i	−0.0827332	−	0.143298i	0.821690	−	0.569935i	$-0.193032\pi$
$439$	−1.73345	−	3.00243i	−0.0827332	−	0.143298i	−0.904423	+	0.426637i	$0.859698\pi$
$440$		−	17.8698i		−	0.851910i
$441$		0			0
$442$	−22.5277	+	19.0389i	−1.07153	+	0.905590i
$443$	−1.22834	−	2.12754i	−0.0583600	−	0.101082i	0.835369	−	0.549689i	$-0.185254\pi$
$443$	−1.22834	−	2.12754i	−0.0583600	−	0.101082i	−0.893729	+	0.448607i	$0.851920\pi$
$444$	0.562142	+	0.324553i	0.0266781	+	0.0154026i
$445$	15.0754	−	26.1114i	0.714643	−	1.23780i
$446$	−11.4216	−	19.7828i	−0.540828	−	0.936741i
$447$		−	12.9192i		−	0.611056i
$448$		0			0
$449$		−	22.7487i		−	1.07358i	−0.843716	−	0.536790i	$-0.819637\pi$
$449$		−	22.7487i		−	1.07358i	0.843716	−	0.536790i	$-0.180363\pi$
$450$	28.9817	−	16.7326i	1.36621	−	0.788783i
$451$	13.3727	−	23.1622i	0.629697	−	1.09067i
$452$	1.66538	−	2.88452i	0.0783327	−	0.135676i
$453$	31.7608	−	18.3371i	1.49225	−	0.861553i
$454$	1.74002			0.0816633
$455$		0			0
$456$	41.0254			1.92119
$457$	−10.6147	+	6.12840i	−0.496535	+	0.286675i	−0.727282	−	0.686339i	$-0.759217\pi$
$457$	−10.6147	+	6.12840i	−0.496535	+	0.286675i	0.230746	+	0.973014i	$0.425883\pi$
$458$	4.77535	−	8.27115i	0.223137	−	0.386485i
$459$	23.8891	−	41.3771i	1.11505	−	1.93132i
$460$	2.28354	−	1.31840i	0.106470	−	0.0614708i
$461$			24.0650i			1.12082i	0.828216	+	0.560409i	$0.189356\pi$
$461$			24.0650i			1.12082i	−0.828216	+	0.560409i	$0.810644\pi$
$462$		0			0
$463$			19.3956i			0.901390i	0.892678	+	0.450695i	$0.148824\pi$
$463$			19.3956i			0.901390i	−0.892678	+	0.450695i	$0.851176\pi$
$464$	1.32940	+	2.30258i	0.0617156	+	0.106895i
$465$	−36.7676	+	63.6834i	−1.70506	+	2.95325i
$466$	8.13605	+	4.69735i	0.376895	+	0.217600i
$467$	−8.93912	−	15.4830i	−0.413653	−	0.716469i	0.581633	−	0.813452i	$-0.302414\pi$
$467$	−8.93912	−	15.4830i	−0.413653	−	0.716469i	−0.995286	+	0.0969829i	$0.969081\pi$
$468$	−4.45681	−	5.27349i	−0.206016	−	0.243767i
$469$		0			0
$470$			2.41340i			0.111322i
$471$	−33.2516	−	57.5934i	−1.53215	−	2.65376i
$472$	7.86135	−	13.6162i	0.361848	−	0.626739i
$473$	−21.6165	−	12.4803i	−0.993926	−	0.573843i
$474$	−24.8599	+	14.3529i	−1.14185	+	0.659249i
$475$		−	19.7002i		−	0.903906i
$476$		0			0
$477$	47.1886			2.16062
$478$	20.9153	+	36.2264i	0.956646	+	1.65696i
$479$	−17.9849	−	10.3836i	−0.821750	−	0.474437i	0.0292699	−	0.999572i	$-0.490682\pi$
$479$	−17.9849	−	10.3836i	−0.821750	−	0.474437i	−0.851019	+	0.525134i	$0.824015\pi$
$480$	7.93123	−	13.7373i	0.362010	−	0.627019i
$481$	2.29231	+	0.825175i	0.104520	+	0.0376248i
$482$	14.9198			0.679578
$483$		0			0
$484$	−1.72490			−0.0784043
$485$	14.5924	+	25.2748i	0.662608	+	1.14767i
$486$	−0.692977	−	0.400091i	−0.0314341	−	0.0181485i
$487$	−16.6266	−	9.59936i	−0.753422	−	0.434988i	0.0735069	−	0.997295i	$-0.476581\pi$
$487$	−16.6266	−	9.59936i	−0.753422	−	0.434988i	−0.826929	+	0.562306i	$0.809914\pi$
$488$	6.17422	−	3.56469i	0.279494	−	0.161366i
$489$			34.0374i			1.53923i
$490$		0			0
$491$	−7.91648			−0.357266			−0.178633	−	0.983916i	$-0.557167\pi$
$491$	−7.91648			−0.357266			−0.178633	+	0.983916i	$0.557167\pi$
$492$	9.38403	−	5.41787i	0.423065	−	0.244257i
$493$	1.57290	−	2.72435i	0.0708400	−	0.122699i
$494$	−28.9449	+	5.20922i	−1.30229	+	0.234374i
$495$	−20.8534	−	36.1192i	−0.937293	−	1.62344i
$496$			37.8237i			1.69833i
$497$		0			0
$498$	7.97222			0.357244
$499$	−33.9265	+	19.5875i	−1.51876	+	0.876856i	−0.519003	+	0.854772i	$0.673697\pi$
$499$	−33.9265	+	19.5875i	−1.51876	+	0.876856i	−0.999756	+	0.0220840i	$0.992970\pi$
$500$	1.08076	+	0.623980i	0.0483333	+	0.0279052i
$501$	−4.87970	−	2.81730i	−0.218009	−	0.125868i
$502$	−16.4839	+	9.51701i	−0.735714	+	0.424765i
$503$	16.1533			0.720239			0.360120	−	0.932906i	$-0.382736\pi$
$503$	16.1533			0.720239			0.360120	+	0.932906i	$0.382736\pi$
$504$		0			0
$505$			6.04169i			0.268852i
$506$	−5.03989	−	8.72934i	−0.224050	−	0.388067i
$507$	−30.0030	−	24.8165i	−1.33248	−	1.10214i
$508$	−0.817075	+	1.41521i	−0.0362518	+	0.0627900i
$509$	21.0597	−	12.1588i	0.933455	−	0.538930i	0.0455523	−	0.998962i	$-0.485495\pi$
$509$	21.0597	−	12.1588i	0.933455	−	0.538930i	0.887903	+	0.460032i	$0.152162\pi$
$510$	−72.1830			−3.19632
$511$		0			0
$512$			15.0621i			0.665658i
$513$	41.2571	−	23.8198i	1.82155	−	1.05167i
$514$	25.3212	+	14.6192i	1.11687	+	0.644825i
$515$	−7.72965	−	4.46272i	−0.340609	−	0.196651i
$516$	−5.05630	−	8.75777i	−0.222591	−	0.385539i
$517$	1.27503			0.0560759
$518$		0			0
$519$	−16.6861			−0.732439
$520$	9.20365	−	25.5674i	0.403607	−	1.12120i
$521$	17.2275	−	29.8389i	0.754750	−	1.30727i	−0.190748	−	0.981639i	$-0.561091\pi$
$521$	17.2275	−	29.8389i	0.754750	−	1.30727i	0.945498	−	0.325627i	$-0.105575\pi$
$522$	4.61451	+	2.66419i	0.201972	+	0.116608i
$523$	−17.3433	−	30.0394i	−0.758368	−	1.31353i	−0.943683	−	0.330852i	$-0.892664\pi$
$523$	−17.3433	−	30.0394i	−0.758368	−	1.31353i	0.185315	−	0.982679i	$-0.440670\pi$
$524$	7.23072			0.315875
$525$		0			0
$526$		−	43.8971i		−	1.91401i
$527$	38.7563	−	22.3760i	1.68825	−	0.974713i
$528$	−27.9132	−	16.1157i	−1.21477	−	0.701346i
$529$	7.60638	−	13.1746i	0.330712	−	0.572810i
$530$	−17.7354	−	30.7186i	−0.770377	−	1.33433i
$531$		−	36.6956i		−	1.59246i
$532$		0			0
$533$	31.0626	−	26.2521i	1.34547	−	1.13710i
$534$	−23.3481	−	40.4401i	−1.01037	−	1.75001i
$535$	31.7148	+	18.3105i	1.37115	+	0.791633i
$536$	5.38950	−	9.33489i	0.232791	−	0.403206i
$537$	−6.98071	−	12.0909i	−0.301240	−	0.521763i
$538$			12.4221i			0.535553i
$539$		0			0
$540$		−	8.40708i		−	0.361783i
$541$	−10.6147	+	6.12840i	−0.456362	+	0.263481i	−0.710513	−	0.703684i	$-0.751537\pi$
$541$	−10.6147	+	6.12840i	−0.456362	+	0.263481i	0.254151	+	0.967164i	$0.418204\pi$
$542$	−14.1514	+	24.5110i	−0.607855	+	1.05284i
$543$	−18.7733	+	32.5163i	−0.805639	+	1.39541i
$544$	−8.36023	+	4.82678i	−0.358442	+	0.206946i
$545$	−10.4226			−0.446456
$546$		0			0
$547$	−16.4110			−0.701686			−0.350843	−	0.936434i	$-0.614105\pi$
$547$	−16.4110			−0.701686			−0.350843	+	0.936434i	$0.614105\pi$
$548$	−0.287427	+	0.165946i	−0.0122783	+	0.00708886i
$549$	8.31973	−	14.4102i	0.355078	−	0.615012i
$550$	−6.64493	+	11.5094i	−0.283341	+	0.490760i
$551$	2.71645	−	1.56834i	0.115725	−	0.0668137i
$552$			21.3814i			0.910052i
$553$		0			0
$554$		−	26.2545i		−	1.11545i
$555$	2.98114	+	5.16349i	0.126543	+	0.219178i
$556$	−1.36224	+	2.35947i	−0.0577720	+	0.100064i
$557$	−30.8773	−	17.8270i	−1.30831	−	0.755356i	−0.326499	−	0.945197i	$-0.605869\pi$
$557$	−30.8773	−	17.8270i	−1.30831	−	0.755356i	−0.981815	+	0.189842i	$0.939202\pi$
$558$	37.9005	+	65.6456i	1.60446	+	2.77900i
$559$	−24.5001	−	28.9896i	−1.03624	−	1.22613i
$560$		0			0
$561$			38.1353i			1.61007i
$562$	−8.73601	−	15.1312i	−0.368506	−	0.638272i
$563$	5.38740	−	9.33124i	0.227052	−	0.393265i	−0.729881	−	0.683574i	$-0.760425\pi$
$563$	5.38740	−	9.33124i	0.227052	−	0.393265i	0.956933	+	0.290309i	$0.0937580\pi$
$564$	0.447364	+	0.258286i	0.0188374	+	0.0108758i
$565$	26.4954	−	15.2971i	1.11467	−	0.643555i
$566$		−	2.21769i		−	0.0932163i
$567$		0			0
$568$	−3.20161			−0.134336
$569$	10.4664	+	18.1284i	0.438775	+	0.759980i	0.997595	−	0.0693083i	$-0.0220792\pi$
$569$	10.4664	+	18.1284i	0.438775	+	0.759980i	−0.558820	+	0.829289i	$0.688746\pi$
$570$	−62.3311	−	35.9869i	−2.61076	−	1.50733i
$571$	16.1334	−	27.9438i	0.675161	−	1.16941i	−0.301261	−	0.953542i	$-0.597407\pi$
$571$	16.1334	−	27.9438i	0.675161	−	1.16941i	0.976422	−	0.215871i	$-0.0692592\pi$
$572$	2.57990	+	0.928702i	0.107871	+	0.0388310i
$573$	−3.94645			−0.164865
$574$		0			0
$575$	10.2672			0.428173
$576$	18.9227	+	32.7750i	0.788444	+	1.36562i
$577$	0.171383	+	0.0989479i	0.00713476	+	0.00411925i	0.503563	−	0.863958i	$-0.332022\pi$
$577$	0.171383	+	0.0989479i	0.00713476	+	0.00411925i	−0.496428	+	0.868078i	$0.665355\pi$
$578$	15.6156	+	9.01567i	0.649523	+	0.375002i
$579$	−39.2822	+	22.6796i	−1.63251	+	0.942532i
$580$		−	0.553539i		−	0.0229844i
$581$		0			0
$582$	45.2001			1.87361
$583$	−16.2291	+	9.36987i	−0.672140	+	0.388060i
$584$	−13.8935	+	24.0643i	−0.574918	+	0.995786i
$585$	−11.2334	−	62.4182i	−0.464446	−	2.58068i
$586$	23.3812	+	40.4975i	0.965869	+	1.67293i
$587$		−	10.1251i		−	0.417907i	−0.977926	−	0.208954i	$-0.932994\pi$
$587$		−	10.1251i		−	0.417907i	0.977926	−	0.208954i	$-0.0670058\pi$
$588$		0			0
$589$	44.6222			1.83863
$590$	−23.8880	+	13.7917i	−0.983452	+	0.567796i
$591$	25.6938	+	14.8343i	1.05690	+	0.610201i
$592$	2.65590	+	1.53339i	0.109157	+	0.0630218i
$593$	25.9240	−	14.9672i	1.06457	−	0.614631i	0.137878	−	0.990449i	$-0.455972\pi$
$593$	25.9240	−	14.9672i	1.06457	−	0.614631i	0.926693	+	0.375819i	$0.122638\pi$
$594$	−32.1380			−1.31864
$595$		0			0
$596$			1.38346i			0.0566688i
$597$	12.8389	+	22.2376i	0.525460	+	0.910124i
$598$	−2.71491	−	15.0853i	−0.111021	−	0.616885i
$599$	−13.4436	+	23.2850i	−0.549291	+	0.951399i	0.449033	+	0.893515i	$0.351769\pi$
$599$	−13.4436	+	23.2850i	−0.549291	+	0.951399i	−0.998323	+	0.0578839i	$0.981565\pi$
$600$	24.4138	−	14.0953i	0.996690	−	0.575439i
$601$	24.7432			1.00930			0.504649	−	0.863325i	$-0.331622\pi$
$601$	24.7432			1.00930			0.504649	+	0.863325i	$0.331622\pi$
$602$		0			0
$603$		−	25.1574i		−	1.02449i
$604$	−3.40114	+	1.96365i	−0.138390	+	0.0798997i
$605$	−13.7212	−	7.92192i	−0.557845	−	0.322072i
$606$	8.10348	+	4.67855i	0.329181	+	0.190053i
$607$	1.54617	+	2.67805i	0.0627573	+	0.108699i	0.895697	−	0.444665i	$-0.146677\pi$
$607$	1.54617	+	2.67805i	0.0627573	+	0.108699i	−0.832940	+	0.553364i	$0.813344\pi$
$608$	−9.62557			−0.390369
$609$		0			0
$610$	−12.5076			−0.506417
$611$	1.82427	+	0.656692i	0.0738019	+	0.0265669i
$612$	−5.14166	+	8.90562i	−0.207839	+	0.359988i
$613$	27.1590	+	15.6802i	1.09694	+	0.633319i	0.935416	−	0.353550i	$-0.115026\pi$
$613$	27.1590	+	15.6802i	1.09694	+	0.633319i	0.161525	+	0.986869i	$0.448359\pi$
$614$	16.1939	+	28.0486i	0.653531	+	1.13195i
$615$	99.5305			4.01346
$616$		0			0
$617$		−	12.5311i		−	0.504484i	−0.967664	−	0.252242i	$-0.918832\pi$
$617$		−	12.5311i		−	0.504484i	0.967664	−	0.252242i	$-0.0811678\pi$
$618$	−11.9713	+	6.91165i	−0.481558	+	0.278027i
$619$	−10.0556	−	5.80559i	−0.404167	−	0.233346i	0.284113	−	0.958791i	$-0.408301\pi$
$619$	−10.0556	−	5.80559i	−0.404167	−	0.233346i	−0.688281	+	0.725445i	$0.741634\pi$
$620$	3.93730	−	6.81960i	0.158126	−	0.273882i
$621$	12.4143	+	21.5022i	0.498168	+	0.862852i
$622$		−	6.77374i		−	0.271602i
$623$		0			0
$624$	−31.6369	−	37.4341i	−1.26649	−	1.49856i
$625$	14.9297	+	25.8589i	0.597187	+	1.03436i
$626$	3.01706	+	1.74190i	0.120586	+	0.0696204i
$627$	−19.0124	+	32.9304i	−0.759282	+	1.31511i
$628$	3.56078	+	6.16744i	0.142090	+	0.246108i
$629$		−	3.62852i		−	0.144679i
$630$		0			0
$631$		−	12.7037i		−	0.505728i	−0.967502	−	0.252864i	$-0.918628\pi$
$631$		−	12.7037i		−	0.505728i	0.967502	−	0.252864i	$-0.0813725\pi$
$632$	−13.9382	+	8.04724i	−0.554433	+	0.320102i
$633$	2.16418	−	3.74847i	0.0860185	−	0.148988i
$634$	6.17041	−	10.6875i	0.245058	−	0.424453i
$635$	−12.9993	+	7.50515i	−0.515861	+	0.297833i
$636$	−7.59228			−0.301054
$637$		0			0
$638$	−2.11603			−0.0837744
$639$	−6.47122	+	3.73616i	−0.255998	+	0.147800i
$640$	19.5200	−	33.8096i	0.771594	−	1.33644i
$641$	−20.1507	+	34.9021i	−0.795906	+	1.37855i	0.126356	+	0.991985i	$0.459672\pi$
$641$	−20.1507	+	34.9021i	−0.795906	+	1.37855i	−0.922262	+	0.386565i	$0.873662\pi$
$642$	49.1184	−	28.3585i	1.93855	−	1.11922i
$643$			11.6643i			0.459997i	0.973191	+	0.229998i	$0.0738721\pi$
$643$			11.6643i			0.459997i	−0.973191	+	0.229998i	$0.926128\pi$
$644$		0			0
$645$		−	92.8882i		−	3.65747i
$646$	21.9009	+	37.9334i	0.861678	+	1.49247i
$647$	5.51936	−	9.55981i	0.216988	−	0.375835i	−0.736897	−	0.676005i	$-0.763710\pi$
$647$	5.51936	−	9.55981i	0.216988	−	0.375835i	0.953886	+	0.300170i	$0.0970433\pi$
$648$	19.3553	+	11.1748i	0.760350	+	0.438988i
$649$	7.28637	+	12.6204i	0.286015	+	0.495392i
$650$	−15.4350	+	13.0447i	−0.605412	+	0.511656i
$651$		0			0
$652$		−	3.64493i		−	0.142747i
$653$	−9.56300	−	16.5636i	−0.374229	−	0.648184i	0.615982	−	0.787760i	$-0.288759\pi$
$653$	−9.56300	−	16.5636i	−0.374229	−	0.648184i	−0.990211	+	0.139576i	$0.955426\pi$
$654$	−8.07105	+	13.9795i	−0.315603	+	0.546640i
$655$	57.5188	+	33.2085i	2.24744	+	1.29756i
$656$	44.3359	−	25.5973i	1.73103	−	0.999408i
$657$			64.8529i			2.53015i
$658$		0			0
$659$	28.8233			1.12279			0.561397	−	0.827546i	$-0.310264\pi$
$659$	28.8233			1.12279			0.561397	+	0.827546i	$0.310264\pi$
$660$	3.35516	+	5.81131i	0.130599	+	0.226205i
$661$	41.7758	+	24.1193i	1.62489	+	0.938131i	0.985586	+	0.169177i	$0.0541109\pi$
$661$	41.7758	+	24.1193i	1.62489	+	0.938131i	0.639304	+	0.768954i	$0.279222\pi$
$662$	8.97719	−	15.5489i	0.348908	−	0.604327i
$663$	−19.6412	+	54.5624i	−0.762800	+	2.11903i
$664$	4.46979			0.173462
$665$		0			0
$666$	6.14600			0.238153
$667$	0.817381	+	1.41575i	0.0316491	+	0.0548179i
$668$	0.522548	+	0.301693i	0.0202180	+	0.0116729i
$669$	−38.8943	−	22.4556i	−1.50374	−	0.868185i
$670$	−16.3769	+	9.45519i	−0.632694	+	0.365286i
$671$			6.60794i			0.255097i
$672$		0			0
$673$	33.0426			1.27370			0.636849	−	0.770989i	$-0.280238\pi$
$673$	33.0426			1.27370			0.636849	+	0.770989i	$0.280238\pi$
$674$	3.47035	−	2.00361i	0.133673	−	0.0771762i
$675$	16.3678	−	28.3499i	0.629998	−	1.09119i
$676$	3.21290	+	2.65750i	0.123573	+	0.102211i
$677$	7.85932	+	13.6127i	0.302058	+	0.523180i	0.976602	−	0.215055i	$-0.0689929\pi$
$677$	7.85932	+	13.6127i	0.302058	+	0.523180i	−0.674544	+	0.738235i	$0.735660\pi$
$678$		−	47.3830i		−	1.81973i
$679$		0			0
$680$	−40.4710			−1.55199
$681$	2.96268	−	1.71050i	0.113530	−	0.0655466i
$682$	−26.0695	−	15.0512i	−0.998252	−	0.576341i
$683$	−28.8931	−	16.6815i	−1.10556	−	0.638298i	−0.167888	−	0.985806i	$-0.553695\pi$
$683$	−28.8931	−	16.6815i	−1.10556	−	0.638298i	−0.937677	+	0.347508i	$0.887028\pi$
$684$	−8.87980	+	5.12676i	−0.339528	+	0.196026i
$685$	−3.04856			−0.116479
$686$		0			0
$687$		−	18.7773i		−	0.716400i
$688$	−23.8891	−	41.3771i	−0.910762	−	1.57749i
$689$	−28.0457	+	5.04741i	−1.06846	+	0.192291i
$690$	18.7555	−	32.4854i	0.714008	−	1.23670i
$691$	−39.2748	+	22.6753i	−1.49408	+	0.862610i	−0.999977	−	0.00679070i	$-0.997838\pi$
$691$	−39.2748	+	22.6753i	−1.49408	+	0.862610i	−0.494108	+	0.869401i	$0.664505\pi$
$692$	1.78685			0.0679257
$693$		0			0
$694$		−	7.34981i		−	0.278995i
$695$	−21.6727	+	12.5127i	−0.822092	+	0.474635i
$696$	3.88720	+	2.24428i	0.147344	+	0.0850691i
$697$	−52.4570	−	30.2861i	−1.98695	−	1.14717i
$698$	13.3473	+	23.1182i	0.505203	+	0.875038i
$699$	18.4706			0.698623
$700$		0			0
$701$	−23.5681			−0.890155			−0.445077	−	0.895492i	$-0.646824\pi$
$701$	−23.5681			−0.890155			−0.445077	+	0.895492i	$0.646824\pi$
$702$	−45.9817	−	16.5523i	−1.73547	−	0.624726i
$703$	1.80900	−	3.13328i	0.0682278	−	0.118174i
$704$	−13.0157	−	7.51465i	−0.490549	−	0.283219i
$705$	2.37246	+	4.10922i	0.0893519	+	0.154762i
$706$	10.0502			0.378244
$707$		0			0
$708$			5.90405i			0.221888i
$709$	7.50786	−	4.33466i	0.281963	−	0.162792i	−0.352349	−	0.935869i	$-0.614617\pi$
$709$	7.50786	−	4.33466i	0.281963	−	0.162792i	0.634312	+	0.773077i	$0.281283\pi$
$710$	4.86430	+	2.80841i	0.182554	+	0.105398i
$711$	−18.7817	+	32.5308i	−0.704368	+	1.22000i
$712$	−13.0906	−	22.6736i	−0.490591	−	0.849729i
$713$			23.2560i			0.870943i
$714$		0			0
$715$	16.2573	+	19.2363i	0.607988	+	0.719398i
$716$	0.747536	+	1.29477i	0.0279367	+	0.0483878i
$717$	71.2237	+	41.1210i	2.65990	+	1.53569i
$718$	17.5559	−	30.4078i	0.655182	−	1.13481i
$719$	−5.50190	−	9.52958i	−0.205186	−	0.355393i	0.745006	−	0.667058i	$-0.232447\pi$
$719$	−5.50190	−	9.52958i	−0.205186	−	0.355393i	−0.950192	+	0.311665i	$0.899113\pi$
$720$		−	79.8331i		−	2.97520i
$721$		0			0
$722$			14.7302i			0.548202i
$723$	25.4034	−	14.6667i	0.944763	−	0.545459i
$724$	2.01036	−	3.48204i	0.0747143	−	0.129409i
$725$	1.07769	−	1.86661i	0.0400244	−	0.0693243i
$726$	−21.2507	+	12.2691i	−0.788688	+	0.455349i
$727$	−40.7049			−1.50966			−0.754831	−	0.655919i	$-0.772281\pi$
$727$	−40.7049			−1.50966			−0.754831	+	0.655919i	$0.772281\pi$
$728$		0			0
$729$	−27.7827			−1.02899
$730$	42.2177	−	24.3744i	1.56255	−	0.902137i
$731$	−28.2649	+	48.9562i	−1.04541	+	1.81071i
$732$	−1.33858	+	2.31849i	−0.0494754	+	0.0856939i
$733$	−8.96647	+	5.17679i	−0.331184	+	0.191209i	−0.656367	−	0.754442i	$-0.727908\pi$
$733$	−8.96647	+	5.17679i	−0.331184	+	0.191209i	0.325183	+	0.945651i	$0.394574\pi$
$734$		−	24.2704i		−	0.895835i
$735$		0			0
$736$		−	5.01660i		−	0.184914i
$737$	4.99531	+	8.65213i	0.184005	+	0.318705i
$738$	51.2986	−	88.8519i	1.88833	−	3.27068i
$739$	42.0300	+	24.2660i	1.54610	+	0.892640i	0.998434	+	0.0559423i	$0.0178163\pi$
$739$	42.0300	+	24.2660i	1.54610	+	0.892640i	0.547664	+	0.836698i	$0.315517\pi$
$740$	−0.319239	−	0.552938i	−0.0117354	−	0.0203264i
$741$	−44.1626	+	37.3234i	−1.62235	+	1.37111i
$742$		0			0
$743$			24.5215i			0.899608i	0.893127	+	0.449804i	$0.148506\pi$
$743$			24.5215i			0.899608i	−0.893127	+	0.449804i	$0.851494\pi$
$744$	31.9269	+	55.2990i	1.17050	+	2.02736i
$745$	−6.35382	+	11.0051i	−0.232786	+	0.403197i
$746$	30.9098	+	17.8458i	1.13169	+	0.653380i
$747$	9.03454	−	5.21609i	0.330556	−	0.190847i
$748$		−	4.08376i		−	0.149317i
$749$		0			0
$750$	17.7534			0.648261
$751$	−14.0332	−	24.3061i	−0.512077	−	0.886944i	−0.999902	−	0.0140020i	$-0.995543\pi$
$751$	−14.0332	−	24.3061i	−0.512077	−	0.886944i	0.487825	−	0.872942i	$-0.337790\pi$
$752$	2.11362	+	1.22030i	0.0770759	+	0.0444998i
$753$	−18.7111	+	32.4086i	−0.681870	+	1.18103i
$754$	−3.02753	−	1.08984i	−0.110256	−	0.0396895i
$755$	−36.0738			−1.31286
$756$		0			0
$757$	5.70864			0.207484			0.103742	−	0.994604i	$-0.466918\pi$
$757$	5.70864			0.207484			0.103742	+	0.994604i	$0.466918\pi$
$758$	22.9302	+	39.7163i	0.832863	+	1.44256i
$759$	−17.1625	−	9.90877i	−0.622959	−	0.359666i
$760$	−34.9473	−	20.1768i	−1.26767	−	0.731890i
$761$	−6.66491	+	3.84799i	−0.241603	+	0.139490i	−0.615913	−	0.787814i	$-0.711213\pi$
$761$	−6.66491	+	3.84799i	−0.241603	+	0.139490i	0.374310	+	0.927304i	$0.377879\pi$
$762$			23.2473i			0.842159i
$763$		0			0
$764$	0.422610			0.0152895
$765$	−81.8016	+	47.2282i	−2.95754	+	1.70754i
$766$	9.79522	−	16.9658i	0.353916	−	0.613000i
$767$	3.92506	+	21.8094i	0.141726	+	0.787493i
$768$	−11.2469	−	19.4803i	−0.405839	−	0.702933i
$769$		−	15.0754i		−	0.543634i	−0.962349	−	0.271817i	$-0.912375\pi$
$769$		−	15.0754i		−	0.543634i	0.962349	−	0.271817i	$-0.0876245\pi$
$770$		0			0
$771$	57.4847			2.07026
$772$	4.20657	−	2.42867i	0.151398	−	0.0874096i
$773$	18.4138	+	10.6312i	0.662298	+	0.382378i	0.793152	−	0.609024i	$-0.208439\pi$
$773$	18.4138	+	10.6312i	0.662298	+	0.382378i	−0.130854	+	0.991402i	$0.541772\pi$
$774$	−82.9222	−	47.8752i	−2.98058	−	1.72084i
$775$	26.5543	−	15.3311i	0.953858	−	0.550710i
$776$	25.3424			0.909740
$777$		0			0
$778$			56.1419i			2.01278i
$779$	−30.1983	−	52.3049i	−1.08197	−	1.87402i
$780$	1.80738	+	10.0426i	0.0647144	+	0.359583i
$781$	1.48372	−	2.56988i	0.0530917	−	0.0919575i
$782$	−19.7699	+	11.4142i	−0.706971	+	0.408170i
$783$	5.21221			0.186269
$784$		0			0
$785$			65.4142i			2.33473i
$786$	89.0824	−	51.4318i	3.17747	−	1.83451i
$787$	−8.04485	−	4.64469i	−0.286768	−	0.165565i	0.349715	−	0.936856i	$-0.386278\pi$
$787$	−8.04485	−	4.64469i	−0.286768	−	0.165565i	−0.636483	+	0.771290i	$0.719612\pi$
$788$	−2.75144	−	1.58855i	−0.0980160	−	0.0565896i
$789$	−43.1524	−	74.7422i	−1.53627	−	2.66089i
$790$	28.2357			1.00458
$791$		0			0
$792$	−36.2158			−1.28687
$793$	−3.40334	+	9.45436i	−0.120856	+	0.335734i
$794$	−15.4691	+	26.7932i	−0.548976	+	0.950855i
$795$	−60.3949	−	34.8690i	−2.14199	−	1.23668i
$796$	−1.37486	−	2.38133i	−0.0487308	−	0.0844042i
$797$	−49.7686			−1.76289			−0.881447	−	0.472283i	$-0.843430\pi$
$797$	−49.7686			−1.76289			−0.881447	+	0.472283i	$0.843430\pi$
$798$		0			0
$799$		−	2.88765i		−	0.102158i
$800$	−5.72809	+	3.30711i	−0.202519	+	0.116924i
$801$	−52.9186	−	30.5526i	−1.86979	−	1.07952i
$802$	−14.9825	+	25.9505i	−0.529051	+	0.916343i
$803$	−12.8773	−	22.3042i	−0.454431	−	0.787098i
$804$			4.04764i			0.142749i
$805$		0			0
$806$	−29.5472	−	34.9614i	−1.04075	−	1.23146i
$807$	12.2113	+	21.1506i	0.429858	+	0.744536i
$808$	4.54339	+	2.62313i	0.159836	+	0.0922813i
$809$	4.79717	−	8.30894i	0.168659	−	0.292127i	−0.769289	−	0.638901i	$-0.779390\pi$
$809$	4.79717	−	8.30894i	0.168659	−	0.292127i	0.937949	+	0.346774i	$0.112723\pi$
$810$	−19.6048	−	33.9565i	−0.688842	−	1.19311i
$811$			35.6060i			1.25030i	0.780506	+	0.625148i	$0.214962\pi$
$811$			35.6060i			1.25030i	−0.780506	+	0.625148i	$0.785038\pi$
$812$		0			0
$813$			55.6453i			1.95157i
$814$	−2.11373	+	1.22036i	−0.0740862	+	0.0427737i
$815$	16.7401	−	28.9946i	0.586379	−	1.01564i
$816$	−36.4983	+	63.2169i	−1.27770	+	2.21303i
$817$	−48.8143	+	28.1829i	−1.70780	+	0.985997i
$818$	35.3054			1.23442
$819$		0			0
$820$	−10.6583			−0.372205
$821$	−0.257019	+	0.148390i	−0.00897002	+	0.00517884i	−0.504478	−	0.863424i	$-0.668315\pi$
$821$	−0.257019	+	0.148390i	−0.00897002	+	0.00517884i	0.495508	+	0.868603i	$0.334982\pi$
$822$	−2.36073	+	4.08891i	−0.0823400	+	0.142617i
$823$	11.4559	−	19.8423i	0.399329	−	0.691658i	−0.594314	−	0.804233i	$-0.702576\pi$
$823$	11.4559	−	19.8423i	0.399329	−	0.691658i	0.993643	+	0.112575i	$0.0359098\pi$
$824$	−6.71198	+	3.87516i	−0.233823	+	0.134998i
$825$			26.1288i			0.909687i
$826$		0			0
$827$		−	8.50142i		−	0.295623i	−0.989016	−	0.147812i	$-0.952777\pi$
$827$		−	8.50142i		−	0.295623i	0.989016	−	0.147812i	$-0.0472230\pi$
$828$	−2.67194	−	4.62793i	−0.0928562	−	0.160832i
$829$	−27.1802	+	47.0776i	−0.944009	+	1.63507i	−0.186286	+	0.982496i	$0.559645\pi$
$829$	−27.1802	+	47.0776i	−0.944009	+	1.63507i	−0.757723	+	0.652576i	$0.773688\pi$
$830$	−6.79110	−	3.92084i	−0.235722	−	0.136094i
$831$	−25.8091	−	44.7027i	−0.895307	−	1.55072i
$832$	−14.7521	−	17.4553i	−0.511436	−	0.605152i
$833$		0			0
$834$			38.7583i			1.34209i
$835$	2.77117	+	4.79980i	0.0959002	+	0.166104i
$836$	2.03596	−	3.52639i	0.0704151	−	0.121963i
$837$	64.2145	+	37.0742i	2.21958	+	1.28147i
$838$	37.7950	−	21.8209i	1.30561	−	0.753791i
$839$			17.0486i			0.588585i	0.955715	+	0.294292i	$0.0950839\pi$
$839$			17.0486i			0.588585i	−0.955715	+	0.294292i	$0.904916\pi$
$840$		0			0
$841$	−28.6568			−0.988166
$842$	−27.6686	−	47.9234i	−0.953523	−	1.65155i
$843$	−29.7490	−	17.1756i	−1.02461	−	0.591559i
$844$	−0.231753	+	0.401409i	−0.00797728	+	0.0138171i
$845$	13.3528	+	35.8957i	0.459351	+	1.23485i
$846$	4.89112			0.168160
$847$		0			0
$848$	−35.8706			−1.23180
$849$	−2.18006	−	3.77598i	−0.0748196	−	0.129591i
$850$	26.0660	+	15.0492i	0.894056	+	0.516183i
$851$	1.63299	+	0.942805i	0.0559781	+	0.0323190i
$852$	1.04117	−	0.601120i	0.0356699	−	0.0205940i
$853$		−	45.0401i		−	1.54214i	−0.636747	−	0.771072i	$-0.719721\pi$
$853$		−	45.0401i		−	1.54214i	0.636747	−	0.771072i	$-0.280279\pi$
$854$		0			0
$855$	−94.1825			−3.22097
$856$	27.5393	−	15.8998i	0.941273	−	0.543444i
$857$	19.8963	−	34.4615i	0.679646	−	1.17718i	−0.295442	−	0.955361i	$-0.595467\pi$
$857$	19.8963	−	34.4615i	0.679646	−	1.17718i	0.975088	−	0.221820i	$-0.0711998\pi$
$858$	38.3902	−	6.90911i	1.31062	−	0.235873i
$859$	11.1689	+	19.3452i	0.381079	+	0.660048i	0.991217	−	0.132247i	$-0.0422193\pi$
$859$	11.1689	+	19.3452i	0.381079	+	0.660048i	−0.610138	+	0.792295i	$0.708886\pi$
$860$			9.94702i			0.339191i
$861$		0			0
$862$	−12.0825			−0.411532
$863$	12.2650	−	7.08120i	0.417505	−	0.241047i	−0.276504	−	0.961013i	$-0.589176\pi$
$863$	12.2650	−	7.08120i	0.417505	−	0.241047i	0.694009	+	0.719966i	$0.255843\pi$
$864$	−13.8519	−	7.99737i	−0.471250	−	0.272076i
$865$	14.2140	+	8.20644i	0.483290	+	0.279027i
$866$	−12.6784	+	7.31987i	−0.430829	+	0.248739i
$867$	35.4509			1.20397
$868$		0			0
$869$		−	14.9173i		−	0.506036i
$870$	−3.93730	−	6.81960i	−0.133487	−	0.231206i
$871$	2.69090	+	14.9519i	0.0911777	+	0.506625i
$872$	−4.52520	+	7.83788i	−0.153243	+	0.265424i
$873$	51.2232	−	29.5737i	1.73364	−	1.00092i
$874$	−22.7622			−0.769941
$875$		0			0
$876$		−	10.4343i		−	0.352544i
$877$	38.0658	−	21.9773i	1.28539	−	0.742121i	0.307562	−	0.951528i	$-0.400487\pi$
$877$	38.0658	−	21.9773i	1.28539	−	0.742121i	0.977828	+	0.209407i	$0.0671535\pi$
$878$	4.57388	+	2.64073i	0.154361	+	0.0891204i
$879$	79.6208	+	45.9691i	2.68554	+	1.55050i
$880$	15.8518	+	27.4562i	0.534365	+	0.925548i
$881$	15.3849			0.518331			0.259165	−	0.965833i	$-0.416553\pi$
$881$	15.3849			0.518331			0.259165	+	0.965833i	$0.416553\pi$
$882$		0			0
$883$	44.5262			1.49842			0.749212	−	0.662330i	$-0.230432\pi$
$883$	44.5262			1.49842			0.749212	+	0.662330i	$0.230432\pi$
$884$	2.10329	−	5.84287i	0.0707414	−	0.196517i
$885$	−27.1155	+	46.9654i	−0.911477	+	1.57873i
$886$	3.24108	+	1.87124i	0.108886	+	0.0628656i
$887$	8.05359	+	13.9492i	0.270413	+	0.468369i	0.968968	−	0.247188i	$-0.0795064\pi$
$887$	8.05359	+	13.9492i	0.270413	+	0.468369i	−0.698555	+	0.715557i	$0.746173\pi$
$888$	5.17731			0.173739
$889$		0			0
$890$			45.9316i			1.53963i
$891$	−17.9397	+	10.3575i	−0.601002	+	0.346989i
$892$	4.16503	+	2.40468i	0.139456	+	0.0805147i
$893$	1.43964	−	2.49353i	0.0481757	−	0.0834428i
$894$	9.84050	+	17.0442i	0.329116	+	0.570045i
$895$			13.7328i			0.459037i
$896$		0			0
$897$	−19.4520	−	23.0164i	−0.649483	−	0.768495i
$898$	17.3277	+	30.0124i	0.578231	+	1.00153i
$899$	4.22801	+	2.44104i	0.141012	+	0.0814133i
$900$	−3.52286	+	6.10177i	−0.117429	+	0.203392i
$901$	21.2205	+	36.7551i	0.706959	+	1.22449i
$902$			40.7439i			1.35662i
$903$		0			0
$904$		−	26.5663i		−	0.883582i
$905$	31.9839	−	18.4659i	1.06318	−	0.613828i
$906$	−27.9347	+	48.3843i	−0.928068	+	1.60746i
$907$	9.30183	−	16.1112i	0.308862	−	0.534965i	−0.669251	−	0.743036i	$-0.733385\pi$
$907$	9.30183	−	16.1112i	0.308862	−	0.534965i	0.978114	+	0.208071i	$0.0667184\pi$
$908$	−0.317261	+	0.183171i	−0.0105287	+	0.00607873i
$909$	12.2444			0.406121
$910$		0			0
$911$	38.1801			1.26496			0.632481	−	0.774576i	$-0.282037\pi$
$911$	38.1801			1.26496			0.632481	+	0.774576i	$0.282037\pi$
$912$	−63.0336	+	36.3925i	−2.08725	+	1.20508i
$913$	−2.07144	+	3.58783i	−0.0685545	+	0.118740i
$914$	9.33598	−	16.1704i	0.308807	−	0.534869i
$915$	−21.2962	+	12.2954i	−0.704032	+	0.406473i
$916$			2.01079i			0.0664383i
$917$		0			0
$918$			72.7850i			2.40226i
$919$	8.38144	+	14.5171i	0.276478	+	0.478874i	0.970507	−	0.241073i	$-0.0774993\pi$
$919$	8.38144	+	14.5171i	0.276478	+	0.478874i	−0.694029	+	0.719947i	$0.744166\pi$
$920$	10.5156	−	18.2136i	0.346690	−	0.600486i
$921$	55.1455	+	31.8383i	1.81711	+	1.04911i
$922$	−18.3303	−	31.7489i	−0.603675	−	1.04560i
$923$	3.44643	−	2.91270i	0.113441	−	0.0958728i
$924$		0			0
$925$		−	2.48612i		−	0.0817430i
$926$	−14.7736	−	25.5886i	−0.485490	−	0.840893i
$927$	−9.04436	+	15.6653i	−0.297056	+	0.514516i
$928$	−0.912034	−	0.526563i	−0.0299390	−	0.0172853i
$929$	−5.70599	+	3.29436i	−0.187207	+	0.108084i	−0.590675	−	0.806910i	$-0.701138\pi$
$929$	−5.70599	+	3.29436i	−0.187207	+	0.108084i	0.403467	+	0.914994i	$0.367805\pi$
$930$		−	112.023i		−	3.67339i
$931$		0			0
$932$	−1.97794			−0.0647897
$933$	−6.65882	−	11.5334i	−0.218000	−	0.377587i
$934$	23.5868	+	13.6178i	0.771782	+	0.445589i
$935$	18.7555	−	32.4854i	0.613369	−	1.06239i
$936$	−51.8161	−	18.6526i	−1.69366	−	0.609678i
$937$	−39.0958			−1.27721			−0.638603	−	0.769537i	$-0.720487\pi$
$937$	−39.0958			−1.27721			−0.638603	+	0.769537i	$0.720487\pi$
$938$		0			0
$939$	6.84940			0.223522
$940$	−0.254057	−	0.440039i	−0.00828642	−	0.0143525i
$941$	−11.4619	−	6.61755i	−0.373648	−	0.215726i	0.301403	−	0.953497i	$-0.402545\pi$
$941$	−11.4619	−	6.61755i	−0.373648	−	0.215726i	−0.675051	+	0.737771i	$0.735878\pi$
$942$	87.7375	+	50.6553i	2.85864	+	1.65044i
$943$	27.2600	−	15.7386i	0.887708	−	0.512518i
$944$			27.8943i			0.907884i
$945$		0			0
$946$	38.0248			1.23629
$947$	−43.4248	+	25.0713i	−1.41112	+	0.814709i	−0.995494	−	0.0948281i	$-0.969770\pi$
$947$	−43.4248	+	25.0713i	−1.41112	+	0.814709i	−0.415623	+	0.909537i	$0.636437\pi$
$948$	3.02183	−	5.23396i	0.0981445	−	0.169991i
$949$	−6.93683	−	38.5442i	−0.225179	−	1.25120i
$950$	15.0056	+	25.9904i	0.486845	+	0.843241i
$951$		−	24.2629i		−	0.786778i
$952$		0			0
$953$	−29.9832			−0.971252			−0.485626	−	0.874167i	$-0.661408\pi$
$953$	−29.9832			−0.971252			−0.485626	+	0.874167i	$0.661408\pi$
$954$	−62.2558	+	35.9434i	−2.01561	+	1.16371i
$955$	3.36177	+	1.94092i	0.108784	+	0.0628066i
$956$	−7.62706	−	4.40348i	−0.246677	−	0.142419i
$957$	−3.60289	+	2.08013i	−0.116465	+	0.0672410i
$958$	31.6366			1.02213
$959$		0			0
$960$		−	55.9300i		−	1.80513i
$961$	19.2260	+	33.3005i	0.620195	+	1.07421i
$962$	−3.65277	+	0.657392i	−0.117770	+	0.0211952i
$963$	37.1090	−	64.2747i	1.19582	−	2.07122i
$964$	−2.72035	+	1.57059i	−0.0876166	+	0.0505855i
$965$	44.6165			1.43626
$966$		0			0
$967$			37.8356i			1.21671i	0.793665	+	0.608356i	$0.208171\pi$
$967$			37.8356i			1.21671i	−0.793665	+	0.608356i	$0.791829\pi$
$968$	−11.9147	+	6.87893i	−0.382952	+	0.221097i
$969$	74.5797	+	43.0586i	2.39584	+	1.38324i
$970$	−38.5035	−	22.2300i	−1.23627	−	0.713763i
$971$	−7.67162	−	13.2876i	−0.246194	−	0.426421i	0.716273	−	0.697821i	$-0.245847\pi$
$971$	−7.67162	−	13.2876i	−0.246194	−	0.426421i	−0.962467	+	0.271400i	$0.912513\pi$
$972$	0.168469			0.00540364
$973$		0			0
$974$	29.2472			0.937142
$975$	−13.4573	+	37.3840i	−0.430979	+	1.19725i
$976$	−6.32428	+	10.9540i	−0.202435	+	0.350628i
$977$	−22.9918	−	13.2743i	−0.735573	−	0.424684i	0.0848842	−	0.996391i	$-0.472948\pi$
$977$	−22.9918	−	13.2743i	−0.735573	−	0.424684i	−0.820458	+	0.571707i	$0.806281\pi$
$978$	−25.9262	−	44.9056i	−0.829030	−	1.43592i
$979$	24.2663			0.775555
$980$		0			0
$981$			21.1230i			0.674406i
$982$	10.4442	−	6.02997i	0.333288	−	0.192424i
$983$	−6.94555	−	4.01002i	−0.221529	−	0.127900i	0.385129	−	0.922863i	$-0.374157\pi$
$983$	−6.94555	−	4.01002i	−0.221529	−	0.127900i	−0.606658	+	0.794963i	$0.707490\pi$
$984$	43.2133	−	74.8476i	1.37759	−	2.38605i
$985$	−14.5914	−	25.2731i	−0.464921	−	0.805266i
$986$			4.79231i			0.152618i
$987$		0			0
$988$	4.72919	−	3.99681i	0.150456	−	0.127155i
$989$	−14.6882	−	25.4408i	−0.467059	−	0.808969i
$990$	55.0239	+	31.7680i	1.74877	+	1.00965i
$991$	−24.5479	+	42.5182i	−0.779789	+	1.35063i	0.152274	+	0.988338i	$0.451340\pi$
$991$	−24.5479	+	42.5182i	−0.779789	+	1.35063i	−0.932063	+	0.362296i	$0.881993\pi$
$992$	−7.49084	−	12.9745i	−0.237834	−	0.411941i
$993$		−	35.2995i		−	1.12020i
$994$		0			0
$995$		−	25.2573i		−	0.800711i
$996$	−1.45359	+	0.839229i	−0.0460587	+	0.0265920i
$997$	−9.97378	+	17.2751i	−0.315873	+	0.547108i	−0.979623	−	0.200847i	$-0.935631\pi$
$997$	−9.97378	+	17.2751i	−0.315873	+	0.547108i	0.663750	+	0.747955i	$0.268964\pi$
$998$	29.8395	−	51.6835i	0.944552	−	1.63601i
$999$	5.20655	−	3.00600i	0.164728	−	0.0951058i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.r.g.116.5		32
7.2	even	3	inner	637.2.r.g.324.11		32
7.3	odd	6		637.2.c.g.246.5	✓	16
7.4	even	3		637.2.c.g.246.6	yes	16
7.5	odd	6	inner	637.2.r.g.324.12		32
7.6	odd	2	inner	637.2.r.g.116.6		32
13.12	even	2	inner	637.2.r.g.116.11		32
91.12	odd	6	inner	637.2.r.g.324.6		32
91.18	odd	12		8281.2.a.cs.1.6		16
91.25	even	6		637.2.c.g.246.12	yes	16
91.31	even	12		8281.2.a.cs.1.5		16
91.38	odd	6		637.2.c.g.246.11	yes	16
91.51	even	6	inner	637.2.r.g.324.5		32
91.60	odd	12		8281.2.a.cs.1.12		16
91.73	even	12		8281.2.a.cs.1.11		16
91.90	odd	2	inner	637.2.r.g.116.12		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.c.g.246.5	✓	16	7.3	odd	6
637.2.c.g.246.6	yes	16	7.4	even	3
637.2.c.g.246.11	yes	16	91.38	odd	6
637.2.c.g.246.12	yes	16	91.25	even	6
637.2.r.g.116.5		32	1.1	even	1	trivial
637.2.r.g.116.6		32	7.6	odd	2	inner
637.2.r.g.116.11		32	13.12	even	2	inner
637.2.r.g.116.12		32	91.90	odd	2	inner
637.2.r.g.324.5		32	91.51	even	6	inner
637.2.r.g.324.6		32	91.12	odd	6	inner
637.2.r.g.324.11		32	7.2	even	3	inner
637.2.r.g.324.12		32	7.5	odd	6	inner
8281.2.a.cs.1.5		16	91.31	even	12
8281.2.a.cs.1.6		16	91.18	odd	12
8281.2.a.cs.1.11		16	91.73	even	12
8281.2.a.cs.1.12		16	91.60	odd	12

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.31930 + 0.761698i) q^{2} +(-1.49755 + 2.59383i) q^{3} +(0.160367 - 0.277763i) q^{4} +(2.55136 - 1.47303i) q^{5} -4.56272i q^{6} -2.55819i q^{8} +(-2.98531 - 5.17071i) q^{9} +O(q^{10})\)	\(q+(-1.31930 + 0.761698i) q^{2} +(-1.49755 + 2.59383i) q^{3} +(0.160367 - 0.277763i) q^{4} +(2.55136 - 1.47303i) q^{5} -4.56272i q^{6} -2.55819i q^{8} +(-2.98531 - 5.17071i) q^{9} +(-2.24401 + 3.88673i) q^{10} +(2.05342 + 1.18554i) q^{11} +(0.480314 + 0.831928i) q^{12} +(2.32734 + 2.75381i) q^{13} +8.82374i q^{15} +(2.26930 + 3.93054i) q^{16} +(2.68497 - 4.65051i) q^{17} +(7.87704 + 4.54781i) q^{18} +(4.63703 - 2.67719i) q^{19} -0.944899i q^{20} -3.61209 q^{22} +(1.39528 + 2.41670i) q^{23} +(6.63551 + 3.83101i) q^{24} +(1.83963 - 3.18634i) q^{25} +(-5.16803 - 1.86037i) q^{26} +8.89733 q^{27} +0.585818 q^{29} +(-6.72103 - 11.6412i) q^{30} +(7.21727 + 4.16690i) q^{31} +(-1.55686 - 0.898851i) q^{32} +(-6.15019 + 3.55081i) q^{33} +8.18054i q^{34} -1.91498 q^{36} +(0.585182 - 0.337855i) q^{37} +(-4.07842 + 7.06402i) q^{38} +(-10.6282 + 1.91277i) q^{39} +(-3.76829 - 6.52686i) q^{40} -11.2799i q^{41} -10.5271 q^{43} +(0.658599 - 0.380242i) q^{44} +(-15.2332 - 8.79491i) q^{45} +(-3.68159 - 2.12557i) q^{46} +(0.465700 - 0.268872i) q^{47} -13.5936 q^{48} +5.60498i q^{50} +(8.04176 + 13.9287i) q^{51} +(1.13814 - 0.204831i) q^{52} +(-3.95173 + 6.84459i) q^{53} +(-11.7382 + 6.77707i) q^{54} +6.98535 q^{55} +16.0369i q^{57} +(-0.772869 + 0.446216i) q^{58} +(5.32262 + 3.07301i) q^{59} +(2.45091 + 1.41503i) q^{60} +(1.39344 + 2.41352i) q^{61} -12.6957 q^{62} -6.33858 q^{64} +(9.99434 + 3.59772i) q^{65} +(5.40929 - 9.36917i) q^{66} +(3.64902 + 2.10676i) q^{67} +(-0.861159 - 1.49157i) q^{68} -8.35802 q^{69} -1.25151i q^{71} +(-13.2277 + 7.63699i) q^{72} +(-9.40676 - 5.43100i) q^{73} +(-0.514686 + 0.891463i) q^{74} +(5.50989 + 9.54340i) q^{75} -1.71733i q^{76} +(12.5649 - 10.6190i) q^{78} +(-3.14568 - 5.44848i) q^{79} +(11.5796 + 6.68549i) q^{80} +(-4.36825 + 7.56604i) q^{81} +(8.59184 + 14.8815i) q^{82} +1.74725i q^{83} -15.8202i q^{85} +(13.8884 - 8.01845i) q^{86} +(-0.877292 + 1.51951i) q^{87} +(3.03283 - 5.25302i) q^{88} +(8.86315 - 5.11714i) q^{89} +26.7963 q^{90} +0.895027 q^{92} +(-21.6165 + 12.4803i) q^{93} +(-0.409598 + 0.709445i) q^{94} +(7.88715 - 13.6610i) q^{95} +(4.66294 - 2.69215i) q^{96} +9.90640i q^{97} -14.1568i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 20 q^{4} - 16 q^{9}+O(q^{10}) \) 32 * q + 20 * q^4 - 16 * q^9	\( 32 q + 20 q^{4} - 16 q^{9} - 28 q^{16} - 16 q^{22} + 36 q^{23} + 44 q^{25} + 72 q^{29} + 104 q^{36} - 32 q^{39} - 72 q^{43} + 72 q^{51} - 12 q^{53} - 328 q^{64} + 24 q^{65} - 96 q^{74} + 48 q^{78} - 36 q^{79} - 16 q^{81} - 136 q^{88} + 48 q^{92} + 84 q^{95}+O(q^{100}) \) 32 * q + 20 * q^4 - 16 * q^9 - 28 * q^16 - 16 * q^22 + 36 * q^23 + 44 * q^25 + 72 * q^29 + 104 * q^36 - 32 * q^39 - 72 * q^43 + 72 * q^51 - 12 * q^53 - 328 * q^64 + 24 * q^65 - 96 * q^74 + 48 * q^78 - 36 * q^79 - 16 * q^81 - 136 * q^88 + 48 * q^92 + 84 * q^95

Introduction

L-functions

Modular forms

Varieties

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Database

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