LMFDB - Embedded newform 637.2.r.g.324.5

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			324.5
Character	$\chi$	$=$	637.324
Dual form			637.2.r.g.116.5

$q$-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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−1.31930	−	0.761698i	−0.932885	−	0.538602i	−0.0451623	−	0.998980i	$-0.514381\pi$
$2$	−1.31930	−	0.761698i	−0.932885	−	0.538602i	−0.887723	+	0.460378i	$0.847714\pi$
$3$	−1.49755	−	2.59383i	−0.864611	−	1.49755i	−0.867433	−	0.497554i	$-0.834232\pi$
$3$	−1.49755	−	2.59383i	−0.864611	−	1.49755i	0.00282181	−	0.999996i	$-0.499102\pi$
$4$	0.160367	+	0.277763i	0.0801833	+	0.138882i
$5$	2.55136	+	1.47303i	1.14100	+	0.658759i	0.946679	−	0.322178i	$-0.104415\pi$
$5$	2.55136	+	1.47303i	1.14100	+	0.658759i	0.194325	+	0.980937i	$0.437748\pi$
$6$			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	−0.157401	−	0.987535i	$-0.550312\pi$
$11$	2.05342	−	1.18554i	0.619128	−	0.357454i	0.776530	+	0.630081i	$0.216978\pi$
$12$	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	0.982832	+	0.184504i	$0.0590679\pi$
$17$	2.68497	+	4.65051i	0.651201	+	1.12791i	−0.331631	+	0.943409i	$0.607599\pi$
$18$	7.87704	−	4.54781i	1.85664	−	1.07193i
$19$	4.63703	+	2.67719i	1.06381	+	0.614189i	0.926483	−	0.376337i	$-0.122817\pi$
$19$	4.63703	+	2.67719i	1.06381	+	0.614189i	0.137324	+	0.990526i	$0.456150\pi$
$20$			0.944899i			0.211286i
$21$		0			0
$22$	−3.61209			−0.770101
$23$	1.39528	−	2.41670i	0.290936	−	0.503917i	−0.683095	−	0.730330i	$-0.739367\pi$
$23$	1.39528	−	2.41670i	0.290936	−	0.503917i	0.974031	+	0.226413i	$0.0726999\pi$
$24$	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	0.316505	−	0.948591i	$-0.397491\pi$
$31$	7.21727	−	4.16690i	1.29626	−	0.748397i	0.979756	+	0.200194i	$0.0641574\pi$
$32$	−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	0.547330	−	0.836917i	$-0.315644\pi$
$37$	0.585182	+	0.337855i	0.0962033	+	0.0555430i	−0.451127	+	0.892460i	$0.648978\pi$
$38$	−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	$0.343000\pi$
$41$			11.2799i			1.76162i	−0.473473	+	0.880808i	$0.657000\pi$
$42$		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	0.533580	−	0.845750i	$-0.320846\pi$
$47$	0.465700	+	0.268872i	0.0679293	+	0.0392190i	−0.465651	+	0.884969i	$0.654180\pi$
$48$	−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	−0.998741	−	0.0501612i	$-0.984026\pi$
$53$	−3.95173	−	6.84459i	−0.542811	−	0.940177i	0.455930	−	0.890016i	$-0.349307\pi$
$54$	−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	−0.111769	−	0.993734i	$-0.535652\pi$
$59$	5.32262	−	3.07301i	0.692946	−	0.400072i	0.804715	+	0.593662i	$0.202318\pi$
$60$	2.45091	−	1.41503i	0.316411	−	0.182680i
$61$	1.39344	−	2.41352i	0.178412	−	0.309019i	−0.762925	−	0.646487i	$-0.776237\pi$
$61$	1.39344	−	2.41352i	0.178412	−	0.309019i	0.941337	+	0.337468i	$0.109571\pi$
$62$	−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	−0.260255	−	0.965540i	$-0.583807\pi$
$67$	3.64902	−	2.10676i	0.445799	−	0.257382i	0.706054	+	0.708158i	$0.250473\pi$
$68$	−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	$0.0236607\pi$
$71$			1.25151i			0.148527i	−0.997239	+	0.0742637i	$0.976339\pi$
$72$	−13.2277	−	7.63699i	−1.55889	−	0.900028i
$73$	−9.40676	+	5.43100i	−1.10098	+	0.635650i	−0.936478	−	0.350727i	$-0.885935\pi$
$73$	−9.40676	+	5.43100i	−1.10098	+	0.635650i	−0.164501	+	0.986377i	$0.552601\pi$
$74$	−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	−0.986932	−	0.161138i	$-0.948484\pi$
$79$	−3.14568	+	5.44848i	−0.353917	+	0.613002i	0.633015	+	0.774139i	$0.281817\pi$
$80$	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	$-0.969429\pi$
$83$		−	1.74725i		−	0.191786i	0.995392	−	0.0958928i	$-0.0305706\pi$
$84$		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	0.889801	−	0.456348i	$-0.150843\pi$
$89$	8.86315	+	5.11714i	0.939492	+	0.542416i	0.0496912	+	0.998765i	$0.484176\pi$
$90$	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	$-0.832259\pi$
$97$		−	9.90640i		−	1.00584i	0.864332	−	0.502921i	$-0.167741\pi$
$98$		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	0.810491	−	0.585751i	$-0.199200\pi$
$101$	−1.02539	−	1.77602i	−0.102030	−	0.176721i	−0.912521	+	0.409030i	$0.865867\pi$
$102$	−21.2190	+	12.2508i	−2.10099	+	1.21301i
$103$	−1.51481	+	2.62373i	−0.149259	+	0.258523i	−0.930954	−	0.365137i	$-0.881022\pi$
$103$	−1.51481	+	2.62373i	−0.149259	+	0.258523i	0.781695	+	0.623661i	$0.214355\pi$
$104$	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	−0.391840	−	0.920033i	$-0.628161\pi$
$107$	6.21526	−	10.7652i	0.600852	−	1.04071i	0.992692	−	0.120673i	$-0.0385053\pi$
$108$	1.42683	+	2.47135i	0.137297	+	0.237806i
$109$	−3.06384	+	1.76891i	−0.293463	+	0.169431i	−0.639502	−	0.768789i	$-0.720860\pi$
$109$	−3.06384	+	1.76891i	−0.293463	+	0.169431i	0.346040	+	0.938220i	$0.387526\pi$
$110$	−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	0.342271	−	0.939601i	$-0.388804\pi$
$131$	11.2722	−	19.5240i	0.984854	−	1.70582i	0.642583	−	0.766216i	$-0.277863\pi$
$132$		−	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	−0.537793	−	0.843077i	$-0.680742\pi$
$137$	−0.896156	+	0.517396i	−0.0765638	+	0.0442041i	0.461229	+	0.887281i	$0.347409\pi$
$138$	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	0.339120	−	0.940743i	$-0.389871\pi$
$149$	−3.73554	−	2.15672i	−0.306028	−	0.176685i	−0.645148	+	0.764058i	$0.723204\pi$
$150$	−14.5384	+	8.39374i	−1.18705	+	0.685346i
$151$	−10.6043	+	6.12237i	−0.862963	+	0.498232i	−0.865003	−	0.501766i	$-0.832684\pi$
$151$	−10.6043	+	6.12237i	−0.862963	+	0.498232i	0.00204066	+	0.999998i	$0.499350\pi$
$152$	−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	−0.844523	−	0.535519i	$-0.820116\pi$
$157$	−11.1020	−	19.2292i	−0.886035	−	1.53466i	−0.0415118	−	0.999138i	$-0.513217\pi$
$158$	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	0.833186	−	0.552993i	$-0.186515\pi$
$163$	9.84184	+	5.68219i	0.770872	+	0.445063i	−0.0623134	+	0.998057i	$0.519848\pi$
$164$	−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	$-0.976810\pi$
$167$		−	1.88127i		−	0.145577i	0.997347	−	0.0727885i	$-0.0231898\pi$
$168$		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	−0.740490	−	0.672068i	$-0.765406\pi$
$173$	2.78557	−	4.82474i	0.211783	−	0.366818i	0.952273	+	0.305249i	$0.0987398\pi$
$174$			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	0.765681	−	0.643221i	$-0.222402\pi$
$179$	−2.33071	−	4.03691i	−0.174205	−	0.301733i	−0.939886	+	0.341488i	$0.889069\pi$
$180$	−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	−0.841206	−	0.540715i	$-0.818154\pi$
$191$	0.658818	−	1.14111i	0.0476704	−	0.0825676i	0.888876	+	0.458148i	$0.151487\pi$
$192$	9.49234	+	16.4412i	0.685051	+	1.18654i
$193$	13.1155	−	7.57223i	0.944073	−	0.545061i	0.0528385	−	0.998603i	$-0.483173\pi$
$193$	13.1155	−	7.57223i	0.944073	−	0.545061i	0.891235	+	0.453542i	$0.149840\pi$
$194$	−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	$0.114796\pi$
$197$			9.90571i			0.705753i	−0.935670	+	0.352876i	$0.885204\pi$
$198$	10.7832	−	18.6771i	0.766331	−	1.32732i
$199$	4.28663	+	7.42466i	0.303871	+	0.526320i	0.977009	−	0.213197i	$-0.0683875\pi$
$199$	4.28663	+	7.42466i	0.303871	+	0.526320i	−0.673138	+	0.739517i	$0.735054\pi$
$200$	−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	$-0.832573\pi$
$223$		−	14.9949i		−	1.00413i	0.864829	−	0.502067i	$-0.167427\pi$
$224$		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	−0.532468	−	0.846450i	$-0.678735\pi$
$227$	−0.989174	+	0.571100i	−0.0656538	+	0.0379052i	0.466814	+	0.884356i	$0.345402\pi$
$228$	4.45446	−	2.57178i	0.295004	−	0.170320i
$229$	−5.42942	−	3.13467i	−0.358786	−	0.207145i	0.309762	−	0.950814i	$-0.399751\pi$
$229$	−5.42942	−	3.13467i	−0.358786	−	0.207145i	−0.668548	+	0.743669i	$0.733084\pi$
$230$	−12.5241			−0.825814
$231$		0			0
$232$			1.49863i			0.0983900i
$233$	−3.08347	+	5.34073i	−0.202005	+	0.349883i	−0.949174	−	0.314751i	$-0.898079\pi$
$233$	−3.08347	+	5.34073i	−0.202005	+	0.349883i	0.747169	+	0.664634i	$0.231412\pi$
$234$	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	$0.347963\pi$
$239$			27.4589i			1.77617i	−0.459684	+	0.888083i	$0.652037\pi$
$240$	−34.6821	−	20.0237i	−2.23872	−	1.29252i
$241$	−8.48166	+	4.89689i	−0.546352	+	0.315436i	−0.747649	−	0.664094i	$-0.768818\pi$
$241$	−8.48166	+	4.89689i	−0.546352	+	0.315436i	0.201298	+	0.979530i	$0.435484\pi$
$242$	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	0.394416	+	0.918932i	$0.370947\pi$
$257$	−9.59645	+	16.6215i	−0.598610	+	1.03682i	−0.993026	+	0.117891i	$0.962387\pi$
$258$		−	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	−0.841749	−	0.539869i	$-0.818474\pi$
$263$	−14.4077	−	24.9548i	−0.888415	−	1.53878i	−0.0466659	−	0.998911i	$-0.514860\pi$
$264$	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	0.963133	−	0.269024i	$-0.0867012\pi$
$269$	4.07709	+	7.06173i	0.248585	+	0.430561i	−0.714549	+	0.699586i	$0.753368\pi$
$270$	−19.9657	−	34.5815i	−1.21507	−	2.10457i
$271$	16.0897	+	9.28939i	0.977379	+	0.564290i	0.901478	−	0.432825i	$-0.142483\pi$
$271$	16.0897	+	9.28939i	0.977379	+	0.564290i	0.0759014	+	0.997115i	$0.475817\pi$
$272$	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	−0.999787	−	0.0206205i	$-0.993436\pi$
$277$	−8.61710	−	14.9253i	−0.517752	−	0.896772i	0.482036	−	0.876152i	$-0.339898\pi$
$278$	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	$-0.888863\pi$
$281$		−	11.4691i		−	0.684191i	0.939665	−	0.342096i	$-0.111137\pi$
$282$	−1.22679	+	2.12486i	−0.0730541	+	0.126533i
$283$	−0.727876	−	1.26072i	−0.0432678	−	0.0749420i	0.843580	−	0.537003i	$-0.180444\pi$
$283$	−0.727876	−	1.26072i	−0.0432678	−	0.0749420i	−0.886848	+	0.462061i	$0.847110\pi$
$284$	−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	$0.354003\pi$
$293$			30.6962i			1.79329i	−0.442750	+	0.896645i	$0.645997\pi$
$294$		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	$0.207504\pi$
$307$			21.2602i			1.21339i	−0.794936	+	0.606693i	$0.792496\pi$
$308$		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	0.796082	−	0.605189i	$-0.206902\pi$
$311$	−2.22324	−	3.85076i	−0.126068	−	0.218357i	−0.922150	+	0.386833i	$0.873569\pi$
$312$	4.89322	−	27.1890i	0.277024	−	1.53928i
$313$	−1.14343	+	1.98049i	−0.0646307	+	0.111944i	−0.896530	−	0.442983i	$-0.853920\pi$
$313$	−1.14343	+	1.98049i	−0.0646307	+	0.111944i	0.831899	+	0.554926i	$0.187254\pi$
$314$			33.8254i			1.90888i
$315$		0			0
$316$	−2.01785			−0.113513
$317$	−7.01555	−	4.05043i	−0.394033	−	0.227495i	0.289873	−	0.957065i	$-0.406387\pi$
$317$	−7.01555	−	4.05043i	−0.394033	−	0.227495i	−0.683906	+	0.729570i	$0.739720\pi$
$318$	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	0.192538	−	0.981290i	$-0.438328\pi$
$331$	−10.2068	−	5.89288i	−0.561015	−	0.323902i	−0.753553	+	0.657388i	$0.771661\pi$
$332$	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	0.793983	−	0.607940i	$-0.208004\pi$
$347$	−2.41231	−	4.17825i	−0.129500	−	0.224300i	−0.923483	+	0.383640i	$0.874670\pi$
$348$	0.281377	−	0.487358i	0.0150834	−	0.0261252i
$349$			17.5231i			0.937991i	0.883201	+	0.468995i	$0.155384\pi$
$349$			17.5231i			0.937991i	−0.883201	+	0.468995i	$0.844616\pi$
$350$		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	−0.644280	−	0.764790i	$-0.722843\pi$
$353$	−5.71338	+	3.29862i	−0.304092	+	0.175568i	0.340188	+	0.940358i	$0.389509\pi$
$354$	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	−0.129856	−	0.991533i	$-0.541452\pi$
$359$	−19.9605	−	11.5242i	−1.05348	−	0.608225i	−0.923621	+	0.383308i	$0.874785\pi$
$360$	−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	0.579698	−	0.814831i	$-0.303170\pi$
$367$	−7.96588	−	13.7973i	−0.415815	−	0.720213i	−0.995514	+	0.0946179i	$0.969837\pi$
$368$	−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	0.385252	+	0.922811i	$0.374115\pi$
$373$	−11.7145	+	20.2901i	−0.606552	+	1.05058i	−0.991804	+	0.127768i	$0.959219\pi$
$374$	−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	$0.281331\pi$
$379$			30.1041i			1.54634i	−0.634196	+	0.773172i	$0.718669\pi$
$380$	−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	0.187710	−	0.982224i	$-0.439893\pi$
$383$	−11.1368	−	6.42986i	−0.569066	−	0.328551i	−0.756776	+	0.653674i	$0.773227\pi$
$384$		−	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	0.775941	+	0.630806i	$0.217275\pi$
$389$	18.4266	+	31.9158i	0.934264	+	1.61819i	0.158323	+	0.987387i	$0.449391\pi$
$390$	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	0.871550	−	0.490307i	$-0.163115\pi$
$397$	17.5878	+	10.1543i	0.882707	+	0.509631i	0.0111570	+	0.999938i	$0.496449\pi$
$398$		−	13.0605i		−	0.654662i
$399$		0			0
$400$	16.6987			0.834935
$401$	17.0346	+	9.83495i	0.850669	+	0.491134i	0.860877	−	0.508814i	$-0.169916\pi$
$401$	17.0346	+	9.83495i	0.850669	+	0.491134i	−0.0102075	+	0.999948i	$0.503249\pi$
$402$	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	−0.905998	−	0.423282i	$-0.860878\pi$
$409$	−20.0705	+	11.5877i	−0.992424	+	0.572976i	−0.0864259	+	0.996258i	$0.527545\pi$
$410$	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	$-0.654032\pi$
$421$		−	36.3249i		−	1.77037i	0.465241	−	0.885184i	$-0.345968\pi$
$422$	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	−0.325366	−	0.945588i	$-0.605487\pi$
$431$	6.86872	−	3.96566i	0.330855	−	0.191019i	0.656220	+	0.754569i	$0.272154\pi$
$432$	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	−0.904423	−	0.426637i	$-0.859698\pi$
$439$	−1.73345	+	3.00243i	−0.0827332	+	0.143298i	0.821690	+	0.569935i	$0.193032\pi$
$440$			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	−0.893729	−	0.448607i	$-0.851920\pi$
$443$	−1.22834	+	2.12754i	−0.0583600	+	0.101082i	0.835369	+	0.549689i	$0.185254\pi$
$444$	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	$0.180363\pi$
$449$			22.7487i			1.07358i	−0.843716	+	0.536790i	$0.819637\pi$
$450$	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	0.230746	−	0.973014i	$-0.425883\pi$
$457$	−10.6147	−	6.12840i	−0.496535	−	0.286675i	−0.727282	+	0.686339i	$0.759217\pi$
$458$	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	$-0.810644\pi$
$461$		−	24.0650i		−	1.12082i	0.828216	−	0.560409i	$-0.189356\pi$
$462$		0			0
$463$		−	19.3956i		−	0.901390i	−0.892678	−	0.450695i	$-0.851176\pi$
$463$		−	19.3956i		−	0.901390i	0.892678	−	0.450695i	$-0.148824\pi$
$464$	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	−0.995286	−	0.0969829i	$-0.969081\pi$
$467$	−8.93912	+	15.4830i	−0.413653	+	0.716469i	0.581633	+	0.813452i	$0.302414\pi$
$468$	−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	−0.851019	−	0.525134i	$-0.824015\pi$
$479$	−17.9849	+	10.3836i	−0.821750	+	0.474437i	0.0292699	+	0.999572i	$0.490682\pi$
$480$	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	−0.826929	−	0.562306i	$-0.809914\pi$
$487$	−16.6266	+	9.59936i	−0.753422	+	0.434988i	0.0735069	+	0.997295i	$0.476581\pi$
$488$	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	−0.999756	−	0.0220840i	$-0.992970\pi$
$499$	−33.9265	−	19.5875i	−1.51876	−	0.876856i	−0.519003	−	0.854772i	$-0.673697\pi$
$500$	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	0.887903	−	0.460032i	$-0.152162\pi$
$509$	21.0597	+	12.1588i	0.933455	+	0.538930i	0.0455523	+	0.998962i	$0.485495\pi$
$510$	−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	0.945498	+	0.325627i	$0.105575\pi$
$521$	17.2275	+	29.8389i	0.754750	+	1.30727i	−0.190748	+	0.981639i	$0.561091\pi$
$522$	4.61451	−	2.66419i	0.201972	−	0.116608i
$523$	−17.3433	+	30.0394i	−0.758368	+	1.31353i	0.185315	+	0.982679i	$0.440670\pi$
$523$	−17.3433	+	30.0394i	−0.758368	+	1.31353i	−0.943683	+	0.330852i	$0.892664\pi$
$524$	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	0.254151	−	0.967164i	$-0.418204\pi$
$541$	−10.6147	−	6.12840i	−0.456362	−	0.263481i	−0.710513	+	0.703684i	$0.751537\pi$
$542$	−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	−0.981815	−	0.189842i	$-0.939202\pi$
$557$	−30.8773	+	17.8270i	−1.30831	+	0.755356i	−0.326499	+	0.945197i	$0.605869\pi$
$558$	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	0.956933	−	0.290309i	$-0.0937580\pi$
$563$	5.38740	+	9.33124i	0.227052	+	0.393265i	−0.729881	+	0.683574i	$0.760425\pi$
$564$	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	−0.558820	−	0.829289i	$-0.688746\pi$
$569$	10.4664	−	18.1284i	0.438775	−	0.759980i	0.997595	+	0.0693083i	$0.0220792\pi$
$570$	−62.3311	+	35.9869i	−2.61076	+	1.50733i
$571$	16.1334	+	27.9438i	0.675161	+	1.16941i	0.976422	+	0.215871i	$0.0692592\pi$
$571$	16.1334	+	27.9438i	0.675161	+	1.16941i	−0.301261	+	0.953542i	$0.597407\pi$
$572$	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	−0.496428	−	0.868078i	$-0.665355\pi$
$577$	0.171383	−	0.0989479i	0.00713476	−	0.00411925i	0.503563	+	0.863958i	$0.332022\pi$
$578$	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	$0.0670058\pi$
$587$			10.1251i			0.417907i	−0.977926	+	0.208954i	$0.932994\pi$
$588$		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	0.926693	−	0.375819i	$-0.122638\pi$
$593$	25.9240	+	14.9672i	1.06457	+	0.614631i	0.137878	+	0.990449i	$0.455972\pi$
$594$	−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	−0.998323	−	0.0578839i	$-0.981565\pi$
$599$	−13.4436	−	23.2850i	−0.549291	−	0.951399i	0.449033	−	0.893515i	$-0.351769\pi$
$600$	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	−0.832940	−	0.553364i	$-0.813344\pi$
$607$	1.54617	−	2.67805i	0.0627573	−	0.108699i	0.895697	+	0.444665i	$0.146677\pi$
$608$	−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	0.161525	−	0.986869i	$-0.448359\pi$
$613$	27.1590	−	15.6802i	1.09694	−	0.633319i	0.935416	+	0.353550i	$0.115026\pi$
$614$	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	$0.0811678\pi$
$617$			12.5311i			0.504484i	−0.967664	+	0.252242i	$0.918832\pi$
$618$	−11.9713	−	6.91165i	−0.481558	−	0.278027i
$619$	−10.0556	+	5.80559i	−0.404167	+	0.233346i	−0.688281	−	0.725445i	$-0.741634\pi$
$619$	−10.0556	+	5.80559i	−0.404167	+	0.233346i	0.284113	+	0.958791i	$0.408301\pi$
$620$	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	$0.0813725\pi$
$631$			12.7037i			0.505728i	−0.967502	+	0.252864i	$0.918628\pi$
$632$	−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	−0.922262	−	0.386565i	$-0.873662\pi$
$641$	−20.1507	−	34.9021i	−0.795906	−	1.37855i	0.126356	−	0.991985i	$-0.459672\pi$
$642$	49.1184	+	28.3585i	1.93855	+	1.11922i
$643$		−	11.6643i		−	0.459997i	−0.973191	−	0.229998i	$-0.926128\pi$
$643$		−	11.6643i		−	0.459997i	0.973191	−	0.229998i	$-0.0738721\pi$
$644$		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	0.953886	−	0.300170i	$-0.0970433\pi$
$647$	5.51936	+	9.55981i	0.216988	+	0.375835i	−0.736897	+	0.676005i	$0.763710\pi$
$648$	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	−0.990211	−	0.139576i	$-0.955426\pi$
$653$	−9.56300	+	16.5636i	−0.374229	+	0.648184i	0.615982	+	0.787760i	$0.288759\pi$
$654$	−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	0.639304	−	0.768954i	$-0.279222\pi$
$661$	41.7758	−	24.1193i	1.62489	−	0.938131i	0.985586	−	0.169177i	$-0.0541109\pi$
$662$	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	−0.674544	−	0.738235i	$-0.735660\pi$
$677$	7.85932	−	13.6127i	0.302058	−	0.523180i	0.976602	+	0.215055i	$0.0689929\pi$
$678$			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	−0.937677	−	0.347508i	$-0.887028\pi$
$683$	−28.8931	+	16.6815i	−1.10556	+	0.638298i	−0.167888	+	0.985806i	$0.553695\pi$
$684$	−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	−0.494108	−	0.869401i	$-0.664505\pi$
$691$	−39.2748	−	22.6753i	−1.49408	−	0.862610i	−0.999977	+	0.00679070i	$0.997838\pi$
$692$	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	0.634312	−	0.773077i	$-0.281283\pi$
$709$	7.50786	+	4.33466i	0.281963	+	0.162792i	−0.352349	+	0.935869i	$0.614617\pi$
$710$	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	−0.950192	−	0.311665i	$-0.899113\pi$
$719$	−5.50190	+	9.52958i	−0.205186	+	0.355393i	0.745006	+	0.667058i	$0.232447\pi$
$720$			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	0.325183	−	0.945651i	$-0.394574\pi$
$733$	−8.96647	−	5.17679i	−0.331184	−	0.191209i	−0.656367	+	0.754442i	$0.727908\pi$
$734$			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	0.547664	−	0.836698i	$-0.315517\pi$
$739$	42.0300	−	24.2660i	1.54610	−	0.892640i	0.998434	−	0.0559423i	$-0.0178163\pi$
$740$	−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	$-0.851494\pi$
$743$		−	24.5215i		−	0.899608i	0.893127	−	0.449804i	$-0.148506\pi$
$744$	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	0.487825	+	0.872942i	$0.337790\pi$
$751$	−14.0332	+	24.3061i	−0.512077	+	0.886944i	−0.999902	+	0.0140020i	$0.995543\pi$
$752$	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	0.374310	−	0.927304i	$-0.377879\pi$
$761$	−6.66491	−	3.84799i	−0.241603	−	0.139490i	−0.615913	+	0.787814i	$0.711213\pi$
$762$		−	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	$0.0876245\pi$
$769$			15.0754i			0.543634i	−0.962349	+	0.271817i	$0.912375\pi$
$770$		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	−0.130854	−	0.991402i	$-0.541772\pi$
$773$	18.4138	−	10.6312i	0.662298	−	0.382378i	0.793152	+	0.609024i	$0.208439\pi$
$774$	−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	−0.636483	−	0.771290i	$-0.719612\pi$
$787$	−8.04485	+	4.64469i	−0.286768	+	0.165565i	0.349715	+	0.936856i	$0.386278\pi$
$788$	−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	0.937949	−	0.346774i	$-0.112723\pi$
$809$	4.79717	+	8.30894i	0.168659	+	0.292127i	−0.769289	+	0.638901i	$0.779390\pi$
$810$	−19.6048	+	33.9565i	−0.688842	+	1.19311i
$811$		−	35.6060i		−	1.25030i	−0.780506	−	0.625148i	$-0.785038\pi$
$811$		−	35.6060i		−	1.25030i	0.780506	−	0.625148i	$-0.214962\pi$
$812$		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	0.495508	−	0.868603i	$-0.334982\pi$
$821$	−0.257019	−	0.148390i	−0.00897002	−	0.00517884i	−0.504478	+	0.863424i	$0.668315\pi$
$822$	−2.36073	−	4.08891i	−0.0823400	−	0.142617i
$823$	11.4559	+	19.8423i	0.399329	+	0.691658i	0.993643	−	0.112575i	$-0.0359098\pi$
$823$	11.4559	+	19.8423i	0.399329	+	0.691658i	−0.594314	+	0.804233i	$0.702576\pi$
$824$	−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	$0.0472230\pi$
$827$			8.50142i			0.295623i	−0.989016	+	0.147812i	$0.952777\pi$
$828$	−2.67194	+	4.62793i	−0.0928562	+	0.160832i
$829$	−27.1802	−	47.0776i	−0.944009	−	1.63507i	−0.757723	−	0.652576i	$-0.773688\pi$
$829$	−27.1802	−	47.0776i	−0.944009	−	1.63507i	−0.186286	−	0.982496i	$-0.559645\pi$
$830$	−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	$-0.904916\pi$
$839$		−	17.0486i		−	0.588585i	0.955715	−	0.294292i	$-0.0950839\pi$
$840$		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	$0.280279\pi$
$853$			45.0401i			1.54214i	−0.636747	+	0.771072i	$0.719721\pi$
$854$		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	0.975088	+	0.221820i	$0.0711998\pi$
$857$	19.8963	+	34.4615i	0.679646	+	1.17718i	−0.295442	+	0.955361i	$0.595467\pi$
$858$	38.3902	+	6.90911i	1.31062	+	0.235873i
$859$	11.1689	−	19.3452i	0.381079	−	0.660048i	−0.610138	−	0.792295i	$-0.708886\pi$
$859$	11.1689	−	19.3452i	0.381079	−	0.660048i	0.991217	+	0.132247i	$0.0422193\pi$
$860$		−	9.94702i		−	0.339191i
$861$		0			0
$862$	−12.0825			−0.411532
$863$	12.2650	+	7.08120i	0.417505	+	0.241047i	0.694009	−	0.719966i	$-0.255843\pi$
$863$	12.2650	+	7.08120i	0.417505	+	0.241047i	−0.276504	+	0.961013i	$0.589176\pi$
$864$	−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	0.977828	−	0.209407i	$-0.0671535\pi$
$877$	38.0658	+	21.9773i	1.28539	+	0.742121i	0.307562	+	0.951528i	$0.400487\pi$
$878$	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	−0.698555	−	0.715557i	$-0.746173\pi$
$887$	8.05359	−	13.9492i	0.270413	−	0.468369i	0.968968	+	0.247188i	$0.0795064\pi$
$888$	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	0.978114	−	0.208071i	$-0.0667184\pi$
$907$	9.30183	+	16.1112i	0.308862	+	0.534965i	−0.669251	+	0.743036i	$0.733385\pi$
$908$	−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	−0.694029	−	0.719947i	$-0.744166\pi$
$919$	8.38144	−	14.5171i	0.276478	−	0.478874i	0.970507	+	0.241073i	$0.0774993\pi$
$920$	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	0.403467	−	0.914994i	$-0.367805\pi$
$929$	−5.70599	−	3.29436i	−0.187207	−	0.108084i	−0.590675	+	0.806910i	$0.701138\pi$
$930$			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	−0.675051	−	0.737771i	$-0.735878\pi$
$941$	−11.4619	+	6.61755i	−0.373648	+	0.215726i	0.301403	+	0.953497i	$0.402545\pi$
$942$	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	−0.415623	−	0.909537i	$-0.636437\pi$
$947$	−43.4248	−	25.0713i	−1.41112	−	0.814709i	−0.995494	+	0.0948281i	$0.969770\pi$
$948$	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	$-0.791829\pi$
$967$		−	37.8356i		−	1.21671i	0.793665	−	0.608356i	$-0.208171\pi$
$968$	−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	−0.962467	−	0.271400i	$-0.912513\pi$
$971$	−7.67162	+	13.2876i	−0.246194	+	0.426421i	0.716273	+	0.697821i	$0.245847\pi$
$972$	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	−0.820458	−	0.571707i	$-0.806281\pi$
$977$	−22.9918	+	13.2743i	−0.735573	+	0.424684i	0.0848842	+	0.996391i	$0.472948\pi$
$978$	−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	−0.606658	−	0.794963i	$-0.707490\pi$
$983$	−6.94555	+	4.01002i	−0.221529	+	0.127900i	0.385129	+	0.922863i	$0.374157\pi$
$984$	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	−0.932063	−	0.362296i	$-0.881993\pi$
$991$	−24.5479	−	42.5182i	−0.779789	−	1.35063i	0.152274	−	0.988338i	$-0.451340\pi$
$992$	−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	0.663750	−	0.747955i	$-0.268964\pi$
$997$	−9.97378	−	17.2751i	−0.315873	−	0.547108i	−0.979623	+	0.200847i	$0.935631\pi$
$998$	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.324.5		32
7.2	even	3		637.2.c.g.246.12	yes	16
7.3	odd	6	inner	637.2.r.g.116.12		32
7.4	even	3	inner	637.2.r.g.116.11		32
7.5	odd	6		637.2.c.g.246.11	yes	16
7.6	odd	2	inner	637.2.r.g.324.6		32
13.12	even	2	inner	637.2.r.g.324.11		32
91.5	even	12		8281.2.a.cs.1.11		16
91.12	odd	6		637.2.c.g.246.5	✓	16
91.25	even	6	inner	637.2.r.g.116.5		32
91.38	odd	6	inner	637.2.r.g.116.6		32
91.44	odd	12		8281.2.a.cs.1.12		16
91.47	even	12		8281.2.a.cs.1.5		16
91.51	even	6		637.2.c.g.246.6	yes	16
91.86	odd	12		8281.2.a.cs.1.6		16
91.90	odd	2	inner	637.2.r.g.324.12		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.c.g.246.5	✓	16	91.12	odd	6
637.2.c.g.246.6	yes	16	91.51	even	6
637.2.c.g.246.11	yes	16	7.5	odd	6
637.2.c.g.246.12	yes	16	7.2	even	3
637.2.r.g.116.5		32	91.25	even	6	inner
637.2.r.g.116.6		32	91.38	odd	6	inner
637.2.r.g.116.11		32	7.4	even	3	inner
637.2.r.g.116.12		32	7.3	odd	6	inner
637.2.r.g.324.5		32	1.1	even	1	trivial
637.2.r.g.324.6		32	7.6	odd	2	inner
637.2.r.g.324.11		32	13.12	even	2	inner
637.2.r.g.324.12		32	91.90	odd	2	inner
8281.2.a.cs.1.5		16	91.47	even	12
8281.2.a.cs.1.6		16	91.86	odd	12
8281.2.a.cs.1.11		16	91.5	even	12
8281.2.a.cs.1.12		16	91.44	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

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