LMFDB - Embedded newform 552.2.f.c.277.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [552,2,Mod(277,552)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("552.277"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(552, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.f (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [18] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 4 x^{16} - 2 x^{15} + 5 x^{14} + 2 x^{13} + 6 x^{12} + 24 x^{11} - 12 x^{10} - 88 x^{9} + \cdots + 512 $ x^18 - 4x^16 - 2x^15 + 5x^14 + 2x^13 + 6x^12 + 24x^11 - 12x^10 - 88x^9 - 24x^8 + 96x^7 + 48x^6 + 32x^5 + 160x^4 - 128x^3 - 512*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			277.10
Root			$1.39509 - 0.231756i$ of defining polynomial
Character	$\chi$	$=$	552.277
Dual form			552.2.f.c.277.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.231756 + 1.39509i) q^{2} +1.00000i q^{3} +(-1.89258 + 0.646644i) q^{4} +2.83774i q^{5} +(-1.39509 + 0.231756i) q^{6} +0.890209 q^{7} +(-1.34075 - 2.49046i) q^{8} -1.00000 q^{9} +(-3.95892 + 0.657665i) q^{10} -0.936187i q^{11} +(-0.646644 - 1.89258i) q^{12} +5.48475i q^{13} +(0.206311 + 1.24193i) q^{14} -2.83774 q^{15} +(3.16370 - 2.44765i) q^{16} -5.50356 q^{17} +(-0.231756 - 1.39509i) q^{18} +1.52878i q^{19} +(-1.83501 - 5.37065i) q^{20} +0.890209i q^{21} +(1.30607 - 0.216967i) q^{22} -1.00000 q^{23} +(2.49046 - 1.34075i) q^{24} -3.05279 q^{25} +(-7.65175 + 1.27113i) q^{26} -1.00000i q^{27} +(-1.68479 + 0.575648i) q^{28} -9.39159i q^{29} +(-0.657665 - 3.95892i) q^{30} +9.44830 q^{31} +(4.14791 + 3.84641i) q^{32} +0.936187 q^{33} +(-1.27549 - 7.67799i) q^{34} +2.52618i q^{35} +(1.89258 - 0.646644i) q^{36} -4.28514i q^{37} +(-2.13280 + 0.354305i) q^{38} -5.48475 q^{39} +(7.06729 - 3.80469i) q^{40} +0.0216292 q^{41} +(-1.24193 + 0.206311i) q^{42} +5.79646i q^{43} +(0.605380 + 1.77181i) q^{44} -2.83774i q^{45} +(-0.231756 - 1.39509i) q^{46} -3.89677 q^{47} +(2.44765 + 3.16370i) q^{48} -6.20753 q^{49} +(-0.707503 - 4.25893i) q^{50} -5.50356i q^{51} +(-3.54668 - 10.3803i) q^{52} +2.58232i q^{53} +(1.39509 - 0.231756i) q^{54} +2.65666 q^{55} +(-1.19354 - 2.21703i) q^{56} -1.52878 q^{57} +(13.1022 - 2.17656i) q^{58} +12.0370i q^{59} +(5.37065 - 1.83501i) q^{60} +12.2985i q^{61} +(2.18970 + 13.1813i) q^{62} -0.890209 q^{63} +(-4.40480 + 6.67815i) q^{64} -15.5643 q^{65} +(0.216967 + 1.30607i) q^{66} +2.40852i q^{67} +(10.4159 - 3.55885i) q^{68} -1.00000i q^{69} +(-3.52427 + 0.585459i) q^{70} +1.87434 q^{71} +(1.34075 + 2.49046i) q^{72} -4.05585 q^{73} +(5.97818 - 0.993109i) q^{74} -3.05279i q^{75} +(-0.988579 - 2.89334i) q^{76} -0.833402i q^{77} +(-1.27113 - 7.65175i) q^{78} +15.1043 q^{79} +(6.94580 + 8.97778i) q^{80} +1.00000 q^{81} +(0.00501271 + 0.0301748i) q^{82} +3.92999i q^{83} +(-0.575648 - 1.68479i) q^{84} -15.6177i q^{85} +(-8.08662 + 1.34337i) q^{86} +9.39159 q^{87} +(-2.33154 + 1.25519i) q^{88} +13.6414 q^{89} +(3.95892 - 0.657665i) q^{90} +4.88258i q^{91} +(1.89258 - 0.646644i) q^{92} +9.44830i q^{93} +(-0.903101 - 5.43636i) q^{94} -4.33830 q^{95} +(-3.84641 + 4.14791i) q^{96} -5.80642 q^{97} +(-1.43863 - 8.66009i) q^{98} +0.936187i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 8 q^{4} + 8 q^{7} - 6 q^{8} - 18 q^{9} + 12 q^{10} - 4 q^{12} - 14 q^{14} + 8 q^{15} + 12 q^{16} - 8 q^{17} - 16 q^{20} - 30 q^{22} - 18 q^{23} + 6 q^{24} - 22 q^{25} + 8 q^{26} - 2 q^{28} + 4 q^{30}+ \cdots - 48 q^{98}+O(q^{100}) $ 18 * q - 8 * q^4 + 8 * q^7 - 6 * q^8 - 18 * q^9 + 12 * q^10 - 4 * q^12 - 14 * q^14 + 8 * q^15 + 12 * q^16 - 8 * q^17 - 16 * q^20 - 30 * q^22 - 18 * q^23 + 6 * q^24 - 22 * q^25 + 8 * q^26 - 2 * q^28 + 4 * q^30 - 44 * q^31 + 10 * q^32 - 24 * q^33 + 18 * q^34 + 8 * q^36 - 20 * q^38 - 8 * q^39 + 40 * q^40 + 28 * q^41 + 6 * q^42 - 26 * q^44 + 42 * q^49 + 60 * q^50 - 36 * q^52 + 40 * q^55 - 2 * q^56 + 12 * q^57 + 52 * q^58 + 16 * q^60 + 24 * q^62 - 8 * q^63 + 16 * q^64 - 104 * q^65 + 2 * q^66 + 54 * q^68 - 48 * q^70 - 24 * q^71 + 6 * q^72 + 12 * q^73 - 22 * q^74 - 4 * q^78 + 8 * q^79 - 32 * q^80 + 18 * q^81 - 20 * q^82 + 34 * q^84 + 12 * q^87 + 10 * q^88 + 24 * q^89 - 12 * q^90 + 8 * q^92 - 56 * q^94 - 16 * q^95 - 30 * q^96 + 12 * q^97 - 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$1$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.231756	+	1.39509i	0.163876	+	0.986481i
$2$	0.231756	+	1.39509i	0.163876	+	0.986481i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−1.89258	+	0.646644i	−0.946289	+	0.323322i
$5$			2.83774i			1.26908i	0.772891	+	0.634539i	$0.218810\pi$
$5$			2.83774i			1.26908i	−0.772891	+	0.634539i	$0.781190\pi$
$6$	−1.39509	+	0.231756i	−0.569545	+	0.0946141i
$7$	0.890209			0.336467			0.168234	−	0.985747i	$-0.446194\pi$
$7$	0.890209			0.336467			0.168234	+	0.985747i	$0.446194\pi$
$8$	−1.34075	−	2.49046i	−0.474025	−	0.880511i
$9$	−1.00000			−0.333333
$10$	−3.95892	+	0.657665i	−1.25192	+	0.207972i
$11$		−	0.936187i		−	0.282271i	−0.989990	−	0.141136i	$-0.954925\pi$
$11$		−	0.936187i		−	0.282271i	0.989990	−	0.141136i	$-0.0450753\pi$
$12$	−0.646644	−	1.89258i	−0.186670	−	0.546340i
$13$			5.48475i			1.52120i	0.649223	+	0.760598i	$0.275094\pi$
$13$			5.48475i			1.52120i	−0.649223	+	0.760598i	$0.724906\pi$
$14$	0.206311	+	1.24193i	0.0551391	+	0.331919i
$15$	−2.83774			−0.732702
$16$	3.16370	−	2.44765i	0.790926	−	0.611912i
$17$	−5.50356			−1.33481			−0.667405	−	0.744695i	$-0.732595\pi$
$17$	−5.50356			−1.33481			−0.667405	+	0.744695i	$0.732595\pi$
$18$	−0.231756	−	1.39509i	−0.0546255	−	0.328827i
$19$			1.52878i			0.350727i	0.984504	+	0.175364i	$0.0561101\pi$
$19$			1.52878i			0.350727i	−0.984504	+	0.175364i	$0.943890\pi$
$20$	−1.83501	−	5.37065i	−0.410321	−	1.20091i
$21$			0.890209i			0.194260i
$22$	1.30607	−	0.216967i	0.278455	−	0.0462576i
$23$	−1.00000			−0.208514
$23$	−1.00000			−0.208514
$24$	2.49046	−	1.34075i	0.508363	−	0.273679i
$25$	−3.05279			−0.610558
$26$	−7.65175	+	1.27113i	−1.50063	+	0.249288i
$27$		−	1.00000i		−	0.192450i
$28$	−1.68479	+	0.575648i	−0.318395	+	0.108787i
$29$		−	9.39159i		−	1.74397i	−0.489529	−	0.871987i	$-0.662831\pi$
$29$		−	9.39159i		−	1.74397i	0.489529	−	0.871987i	$-0.337169\pi$
$30$	−0.657665	−	3.95892i	−0.120073	−	0.722797i
$31$	9.44830			1.69697			0.848483	−	0.529223i	$-0.177517\pi$
$31$	9.44830			1.69697			0.848483	+	0.529223i	$0.177517\pi$
$32$	4.14791	+	3.84641i	0.733253	+	0.679955i
$33$	0.936187			0.162969
$34$	−1.27549	−	7.67799i	−0.218744	−	1.31676i
$35$			2.52618i			0.427003i
$36$	1.89258	−	0.646644i	0.315430	−	0.107774i
$37$		−	4.28514i		−	0.704473i	−0.935911	−	0.352237i	$-0.885421\pi$
$37$		−	4.28514i		−	0.704473i	0.935911	−	0.352237i	$-0.114579\pi$
$38$	−2.13280	+	0.354305i	−0.345986	+	0.0574759i
$39$	−5.48475			−0.878263
$40$	7.06729	−	3.80469i	1.11744	−	0.601575i
$41$	0.0216292			0.00337792			0.00168896	−	0.999999i	$-0.499462\pi$
$41$	0.0216292			0.00337792			0.00168896	+	0.999999i	$0.499462\pi$
$42$	−1.24193	+	0.206311i	−0.191633	+	0.0318346i
$43$			5.79646i			0.883952i	0.897027	+	0.441976i	$0.145722\pi$
$43$			5.79646i			0.883952i	−0.897027	+	0.441976i	$0.854278\pi$
$44$	0.605380	+	1.77181i	0.0912644	+	0.267110i
$45$		−	2.83774i		−	0.423026i
$46$	−0.231756	−	1.39509i	−0.0341706	−	0.205695i
$47$	−3.89677			−0.568403			−0.284201	−	0.958765i	$-0.591728\pi$
$47$	−3.89677			−0.568403			−0.284201	+	0.958765i	$0.591728\pi$
$48$	2.44765	+	3.16370i	0.353288	+	0.456641i
$49$	−6.20753			−0.886790
$50$	−0.707503	−	4.25893i	−0.100056	−	0.602303i
$51$		−	5.50356i		−	0.770653i
$52$	−3.54668	−	10.3803i	−0.491836	−	1.43949i
$53$			2.58232i			0.354709i	0.984147	+	0.177354i	$0.0567539\pi$
$53$			2.58232i			0.354709i	−0.984147	+	0.177354i	$0.943246\pi$
$54$	1.39509	−	0.231756i	0.189848	−	0.0315380i
$55$	2.65666			0.358224
$56$	−1.19354	−	2.21703i	−0.159494	−	0.296263i
$57$	−1.52878			−0.202492
$58$	13.1022	−	2.17656i	1.72040	−	0.285796i
$59$			12.0370i			1.56709i	0.621336	+	0.783544i	$0.286590\pi$
$59$			12.0370i			1.56709i	−0.621336	+	0.783544i	$0.713410\pi$
$60$	5.37065	−	1.83501i	0.693348	−	0.236899i
$61$			12.2985i			1.57466i	0.616533	+	0.787329i	$0.288537\pi$
$61$			12.2985i			1.57466i	−0.616533	+	0.787329i	$0.711463\pi$
$62$	2.18970	+	13.1813i	0.278093	+	1.67402i
$63$	−0.890209			−0.112156
$64$	−4.40480	+	6.67815i	−0.550600	+	0.834769i
$65$	−15.5643			−1.93052
$66$	0.216967	+	1.30607i	0.0267068	+	0.160766i
$67$			2.40852i			0.294248i	0.989118	+	0.147124i	$0.0470016\pi$
$67$			2.40852i			0.294248i	−0.989118	+	0.147124i	$0.952998\pi$
$68$	10.4159	−	3.55885i	1.26312	−	0.431573i
$69$		−	1.00000i		−	0.120386i
$70$	−3.52427	+	0.585459i	−0.421230	+	0.0699757i
$71$	1.87434			0.222443			0.111222	−	0.993796i	$-0.464524\pi$
$71$	1.87434			0.222443			0.111222	+	0.993796i	$0.464524\pi$
$72$	1.34075	+	2.49046i	0.158008	+	0.293504i
$73$	−4.05585			−0.474701			−0.237351	−	0.971424i	$-0.576279\pi$
$73$	−4.05585			−0.474701			−0.237351	+	0.971424i	$0.576279\pi$
$74$	5.97818	−	0.993109i	0.694950	−	0.115447i
$75$		−	3.05279i		−	0.352506i
$76$	−0.988579	−	2.89334i	−0.113398	−	0.331889i
$77$		−	0.833402i		−	0.0949750i
$78$	−1.27113	−	7.65175i	−0.143927	−	0.866390i
$79$	15.1043			1.69937			0.849685	−	0.527291i	$-0.176792\pi$
$79$	15.1043			1.69937			0.849685	+	0.527291i	$0.176792\pi$
$80$	6.94580	+	8.97778i	0.776564	+	1.00375i
$81$	1.00000			0.111111
$82$	0.00501271	+	0.0301748i	0.000553561	+	0.00333225i
$83$			3.92999i			0.431373i	0.976463	+	0.215686i	$0.0691988\pi$
$83$			3.92999i			0.431373i	−0.976463	+	0.215686i	$0.930801\pi$
$84$	−0.575648	−	1.68479i	−0.0628084	−	0.183826i
$85$		−	15.6177i		−	1.69398i
$86$	−8.08662	+	1.34337i	−0.872002	+	0.144859i
$87$	9.39159			1.00688
$88$	−2.33154	+	1.25519i	−0.248543	+	0.133804i
$89$	13.6414			1.44599			0.722994	−	0.690854i	$-0.242765\pi$
$89$	13.6414			1.44599			0.722994	+	0.690854i	$0.242765\pi$
$90$	3.95892	−	0.657665i	0.417307	−	0.0693239i
$91$			4.88258i			0.511833i
$92$	1.89258	−	0.646644i	0.197315	−	0.0674173i
$93$			9.44830i			0.979743i
$94$	−0.903101	−	5.43636i	−0.0931478	−	0.560718i
$95$	−4.33830			−0.445100
$96$	−3.84641	+	4.14791i	−0.392572	+	0.423344i
$97$	−5.80642			−0.589553			−0.294776	−	0.955566i	$-0.595245\pi$
$97$	−5.80642			−0.589553			−0.294776	+	0.955566i	$0.595245\pi$
$98$	−1.43863	−	8.66009i	−0.145324	−	0.874801i
$99$			0.936187i			0.0940903i
$100$	5.77764	−	1.97407i	0.577764	−	0.197407i
$101$			10.7961i			1.07425i	0.843502	+	0.537126i	$0.180490\pi$
$101$			10.7961i			1.07425i	−0.843502	+	0.537126i	$0.819510\pi$
$102$	7.67799	−	1.27549i	0.760235	−	0.126292i
$103$	6.35902			0.626573			0.313286	−	0.949659i	$-0.398570\pi$
$103$	6.35902			0.626573			0.313286	+	0.949659i	$0.398570\pi$
$104$	13.6596	−	7.35366i	1.33943	−	0.721086i
$105$	−2.52618			−0.246530
$106$	−3.60258	+	0.598468i	−0.349913	+	0.0581284i
$107$		−	1.81592i		−	0.175552i	−0.996140	−	0.0877760i	$-0.972024\pi$
$107$		−	1.81592i		−	0.175552i	0.996140	−	0.0877760i	$-0.0279760\pi$
$108$	0.646644	+	1.89258i	0.0622233	+	0.182113i
$109$		−	5.46967i		−	0.523899i	−0.965082	−	0.261950i	$-0.915635\pi$
$109$		−	5.46967i		−	0.523899i	0.965082	−	0.261950i	$-0.0843654\pi$
$110$	0.615697	+	3.70629i	0.0587044	+	0.353381i
$111$	4.28514			0.406728
$112$	2.81636	−	2.17892i	0.266121	−	0.205888i
$113$	−0.0347532			−0.00326930			−0.00163465	−	0.999999i	$-0.500520\pi$
$113$	−0.0347532			−0.00326930			−0.00163465	+	0.999999i	$0.500520\pi$
$114$	−0.354305	−	2.13280i	−0.0331837	−	0.199755i
$115$		−	2.83774i		−	0.264621i
$116$	6.07301	+	17.7743i	0.563865	+	1.65030i
$117$		−	5.48475i		−	0.507066i
$118$	−16.7928	+	2.78966i	−1.54590	+	0.256809i
$119$	−4.89932			−0.449120
$120$	3.80469	+	7.06729i	0.347319	+	0.645153i
$121$	10.1236			0.920323
$122$	−17.1575	+	2.85025i	−1.55337	+	0.258049i
$123$			0.0216292i			0.00195024i
$124$	−17.8817	+	6.10969i	−1.60582	+	0.548666i
$125$			5.52569i			0.494233i
$126$	−0.206311	−	1.24193i	−0.0183797	−	0.110640i
$127$	1.84483			0.163703			0.0818513	−	0.996645i	$-0.473917\pi$
$127$	1.84483			0.163703			0.0818513	+	0.996645i	$0.473917\pi$
$128$	−10.3375	−	4.59741i	−0.913714	−	0.406357i
$129$	−5.79646			−0.510350
$130$	−3.60713	−	21.7137i	−0.316366	−	1.90442i
$131$			16.4740i			1.43934i	0.694314	+	0.719672i	$0.255708\pi$
$131$			16.4740i			1.43934i	−0.694314	+	0.719672i	$0.744292\pi$
$132$	−1.77181	+	0.605380i	−0.154216	+	0.0526915i
$133$			1.36094i			0.118008i
$134$	−3.36011	+	0.558190i	−0.290270	+	0.0482203i
$135$	2.83774			0.244234
$136$	7.37888	+	13.7064i	0.632734	+	1.17532i
$137$	−20.8369			−1.78022			−0.890109	−	0.455748i	$-0.849372\pi$
$137$	−20.8369			−1.78022			−0.890109	+	0.455748i	$0.849372\pi$
$138$	1.39509	−	0.231756i	0.118758	−	0.0197284i
$139$		−	10.9007i		−	0.924586i	−0.886727	−	0.462293i	$-0.847027\pi$
$139$		−	10.9007i		−	0.924586i	0.886727	−	0.462293i	$-0.152973\pi$
$140$	−1.63354	−	4.78100i	−0.138059	−	0.404068i
$141$		−	3.89677i		−	0.328167i
$142$	0.434390	+	2.61488i	0.0364532	+	0.219436i
$143$	5.13475			0.429390
$144$	−3.16370	+	2.44765i	−0.263642	+	0.203971i
$145$	26.6509			2.21324
$146$	−0.939969	−	5.65830i	−0.0777924	−	0.468284i
$147$		−	6.20753i		−	0.511988i
$148$	2.77096	+	8.10997i	0.227772	+	0.666635i
$149$		−	6.06252i		−	0.496661i	−0.968675	−	0.248331i	$-0.920118\pi$
$149$		−	6.06252i		−	0.496661i	0.968675	−	0.248331i	$-0.0798819\pi$
$150$	4.25893	−	0.707503i	0.347740	−	0.0577673i
$151$	18.1644			1.47819			0.739097	−	0.673599i	$-0.235253\pi$
$151$	18.1644			1.47819			0.739097	+	0.673599i	$0.235253\pi$
$152$	3.80738	−	2.04971i	0.308819	−	0.166254i
$153$	5.50356			0.444937
$154$	1.16267	−	0.193146i	0.0936910	−	0.0155642i
$155$			26.8119i			2.15358i
$156$	10.3803	−	3.54668i	0.831091	−	0.283962i
$157$			23.0266i			1.83772i	0.394583	+	0.918860i	$0.370889\pi$
$157$			23.0266i			1.83772i	−0.394583	+	0.918860i	$0.629111\pi$
$158$	3.50052	+	21.0720i	0.278487	+	1.67640i
$159$	−2.58232			−0.204791
$160$	−10.9151	+	11.7707i	−0.862916	+	0.930555i
$161$	−0.890209			−0.0701583
$162$	0.231756	+	1.39509i	0.0182085	+	0.109609i
$163$		−	15.0535i		−	1.17908i	−0.807740	−	0.589539i	$-0.799309\pi$
$163$		−	15.0535i		−	1.17908i	0.807740	−	0.589539i	$-0.200691\pi$
$164$	−0.0409350	+	0.0139864i	−0.00319649	+	0.00109215i
$165$			2.65666i			0.206821i
$166$	−5.48271	+	0.910800i	−0.425541	+	0.0706918i
$167$	−5.76320			−0.445970			−0.222985	−	0.974822i	$-0.571580\pi$
$167$	−5.76320			−0.445970			−0.222985	+	0.974822i	$0.571580\pi$
$168$	2.21703	−	1.19354i	0.171048	−	0.0920839i
$169$	−17.0825			−1.31404
$170$	21.7882	−	3.61950i	1.67108	−	0.277603i
$171$		−	1.52878i		−	0.116909i
$172$	−3.74825	−	10.9703i	−0.285801	−	0.836475i
$173$		−	12.1852i		−	0.926420i	−0.886249	−	0.463210i	$-0.846698\pi$
$173$		−	12.1852i		−	0.926420i	0.886249	−	0.463210i	$-0.153302\pi$
$174$	2.17656	+	13.1022i	0.165005	+	0.993272i
$175$	−2.71762			−0.205433
$176$	−2.29146	−	2.96182i	−0.172725	−	0.223255i
$177$	−12.0370			−0.904759
$178$	3.16149	+	19.0311i	0.236963	+	1.42644i
$179$		−	5.96321i		−	0.445711i	−0.974851	−	0.222855i	$-0.928462\pi$
$179$		−	5.96321i		−	0.445711i	0.974851	−	0.222855i	$-0.0715378\pi$
$180$	1.83501	+	5.37065i	0.136774	+	0.400305i
$181$		−	8.69859i		−	0.646561i	−0.946303	−	0.323281i	$-0.895214\pi$
$181$		−	8.69859i		−	0.646561i	0.946303	−	0.323281i	$-0.104786\pi$
$182$	−6.81166	+	1.13157i	−0.504914	+	0.0838774i
$183$	−12.2985			−0.909129
$184$	1.34075	+	2.49046i	0.0988411	+	0.183599i
$185$	12.1601			0.894031
$186$	−13.1813	+	2.18970i	−0.966498	+	0.160557i
$187$			5.15237i			0.376778i
$188$	7.37494	−	2.51982i	0.537873	−	0.183777i
$189$		−	0.890209i		−	0.0647532i
$190$	−1.00543	−	6.05234i	−0.0729414	−	0.439083i
$191$	20.3419			1.47189			0.735945	−	0.677041i	$-0.236738\pi$
$191$	20.3419			1.47189			0.735945	+	0.677041i	$0.236738\pi$
$192$	−6.67815	−	4.40480i	−0.481954	−	0.317889i
$193$	0.765442			0.0550977			0.0275489	−	0.999620i	$-0.491230\pi$
$193$	0.765442			0.0550977			0.0275489	+	0.999620i	$0.491230\pi$
$194$	−1.34567	−	8.10051i	−0.0966138	−	0.581582i
$195$		−	15.5643i		−	1.11458i
$196$	11.7482	−	4.01406i	0.839159	−	0.286719i
$197$		−	2.37943i		−	0.169528i	−0.996401	−	0.0847638i	$-0.972986\pi$
$197$		−	2.37943i		−	0.169528i	0.996401	−	0.0847638i	$-0.0270136\pi$
$198$	−1.30607	+	0.216967i	−0.0928183	+	0.0154192i
$199$	−6.67709			−0.473326			−0.236663	−	0.971592i	$-0.576054\pi$
$199$	−6.67709			−0.473326			−0.236663	+	0.971592i	$0.576054\pi$
$200$	4.09301	+	7.60285i	0.289420	+	0.537603i
$201$	−2.40852			−0.169884
$202$	−15.0616	+	2.50206i	−1.05973	+	0.176044i
$203$		−	8.36048i		−	0.586791i
$204$	3.55885	+	10.4159i	0.249169	+	0.729261i
$205$			0.0613782i			0.00428684i
$206$	1.47374	+	8.87143i	0.102681	+	0.618102i
$207$	1.00000			0.0695048
$208$	13.4247	+	17.3521i	0.930838	+	1.20315i
$209$	1.43123			0.0990001
$210$	−0.585459	−	3.52427i	−0.0404005	−	0.243198i
$211$		−	18.1905i		−	1.25229i	−0.779708	−	0.626143i	$-0.784633\pi$
$211$		−	18.1905i		−	1.25229i	0.779708	−	0.626143i	$-0.215367\pi$
$212$	−1.66984	−	4.88724i	−0.114685	−	0.335657i
$213$			1.87434i			0.128428i
$214$	2.53339	−	0.420852i	0.173179	−	0.0287688i
$215$	−16.4489			−1.12180
$216$	−2.49046	+	1.34075i	−0.169454	+	0.0912262i
$217$	8.41096			0.570973
$218$	7.63071	−	1.26763i	0.516817	−	0.0858547i
$219$		−	4.05585i		−	0.274069i
$220$	−5.02793	+	1.71791i	−0.338983	+	0.115822i
$221$		−	30.1857i		−	2.03051i
$222$	0.993109	+	5.97818i	0.0666531	+	0.401229i
$223$	2.94480			0.197198			0.0985992	−	0.995127i	$-0.468564\pi$
$223$	2.94480			0.197198			0.0985992	+	0.995127i	$0.468564\pi$
$224$	3.69251	+	3.42411i	0.246716	+	0.228783i
$225$	3.05279			0.203519
$226$	−0.00805427	−	0.0484840i	−0.000535762	−	0.00322511i
$227$		−	24.4030i		−	1.61969i	−0.586647	−	0.809843i	$-0.699552\pi$
$227$		−	24.4030i		−	1.61969i	0.586647	−	0.809843i	$-0.300448\pi$
$228$	2.89334	−	0.988579i	0.191616	−	0.0654702i
$229$			23.5632i			1.55710i	0.627581	+	0.778551i	$0.284045\pi$
$229$			23.5632i			1.55710i	−0.627581	+	0.778551i	$0.715955\pi$
$230$	3.95892	−	0.657665i	0.261043	−	0.0433651i
$231$	0.833402			0.0548338
$232$	−23.3894	+	12.5917i	−1.53559	+	0.826688i
$233$	10.4421			0.684084			0.342042	−	0.939685i	$-0.388882\pi$
$233$	10.4421			0.684084			0.342042	+	0.939685i	$0.388882\pi$
$234$	7.65175	−	1.27113i	0.500210	−	0.0830961i
$235$		−	11.0580i		−	0.721347i
$236$	−7.78367	−	22.7810i	−0.506674	−	1.48292i
$237$			15.1043i			0.981132i
$238$	−1.13545	−	6.83502i	−0.0736002	−	0.443048i
$239$	18.1944			1.17690			0.588449	−	0.808535i	$-0.299739\pi$
$239$	18.1944			1.17690			0.588449	+	0.808535i	$0.299739\pi$
$240$	−8.97778	+	6.94580i	−0.579513	+	0.448349i
$241$	−14.8535			−0.956798			−0.478399	−	0.878143i	$-0.658783\pi$
$241$	−14.8535			−0.956798			−0.478399	+	0.878143i	$0.658783\pi$
$242$	2.34620	+	14.1233i	0.150819	+	0.907881i
$243$			1.00000i			0.0641500i
$244$	−7.95273	−	23.2758i	−0.509121	−	1.49008i
$245$		−	17.6154i		−	1.12540i
$246$	−0.0301748	+	0.00501271i	−0.00192388	+	0.000319598i
$247$	−8.38500			−0.533525
$248$	−12.6678	−	23.5306i	−0.804404	−	1.49420i
$249$	−3.92999			−0.249053
$250$	−7.70886	+	1.28061i	−0.487551	+	0.0809931i
$251$		−	7.01248i		−	0.442624i	−0.975203	−	0.221312i	$-0.928966\pi$
$251$		−	7.01248i		−	0.442624i	0.975203	−	0.221312i	$-0.0710339\pi$
$252$	1.68479	−	0.575648i	0.106132	−	0.0362624i
$253$			0.936187i			0.0588576i
$254$	0.427552	+	2.57372i	0.0268270	+	0.161489i
$255$	15.6177			0.978018
$256$	4.01804	−	15.4873i	0.251128	−	0.967954i
$257$	−0.159321			−0.00993819			−0.00496909	−	0.999988i	$-0.501582\pi$
$257$	−0.159321			−0.00993819			−0.00496909	+	0.999988i	$0.501582\pi$
$258$	−1.34337	−	8.08662i	−0.0836344	−	0.503451i
$259$		−	3.81467i		−	0.237032i
$260$	29.4567	−	10.0646i	1.82683	−	0.624178i
$261$			9.39159i			0.581325i
$262$	−22.9829	+	3.81796i	−1.41989	+	0.235875i
$263$	6.29544			0.388194			0.194097	−	0.980982i	$-0.437822\pi$
$263$	6.29544			0.388194			0.194097	+	0.980982i	$0.437822\pi$
$264$	−1.25519	−	2.33154i	−0.0772515	−	0.143496i
$265$	−7.32796			−0.450153
$266$	−1.89864	+	0.315406i	−0.116413	+	0.0193388i
$267$			13.6414i			0.834842i
$268$	−1.55746	−	4.55831i	−0.0951367	−	0.278443i
$269$		−	16.8235i		−	1.02575i	−0.858464	−	0.512874i	$-0.828581\pi$
$269$		−	16.8235i		−	1.02575i	0.858464	−	0.512874i	$-0.171419\pi$
$270$	0.657665	+	3.95892i	0.0400242	+	0.240932i
$271$	14.9393			0.907498			0.453749	−	0.891129i	$-0.350086\pi$
$271$	14.9393			0.907498			0.453749	+	0.891129i	$0.350086\pi$
$272$	−17.4116	+	13.4708i	−1.05574	+	0.816786i
$273$	−4.88258			−0.295507
$274$	−4.82908	−	29.0695i	−0.291736	−	1.75615i
$275$			2.85798i			0.172343i
$276$	0.646644	+	1.89258i	0.0389234	+	0.113920i
$277$			17.9789i			1.08025i	0.841586	+	0.540123i	$0.181622\pi$
$277$			17.9789i			1.08025i	−0.841586	+	0.540123i	$0.818378\pi$
$278$	15.2075	−	2.52631i	0.912087	−	0.151518i
$279$	−9.44830			−0.565655
$280$	6.29137	−	3.38697i	0.375981	−	0.202410i
$281$	−9.24768			−0.551670			−0.275835	−	0.961205i	$-0.588954\pi$
$281$	−9.24768			−0.551670			−0.275835	+	0.961205i	$0.588954\pi$
$282$	5.43636	−	0.903101i	0.323731	−	0.0537789i
$283$			3.18546i			0.189356i	0.995508	+	0.0946778i	$0.0301821\pi$
$283$			3.18546i			0.189356i	−0.995508	+	0.0946778i	$0.969818\pi$
$284$	−3.54734	+	1.21203i	−0.210496	+	0.0719208i
$285$		−	4.33830i		−	0.256979i
$286$	1.19001	+	7.16347i	0.0703668	+	0.423585i
$287$	0.0192545			0.00113656
$288$	−4.14791	−	3.84641i	−0.244418	−	0.226652i
$289$	13.2892			0.781719
$290$	6.17652	+	37.1806i	0.362698	+	2.18332i
$291$		−	5.80642i		−	0.340378i
$292$	7.67602	−	2.62269i	0.449205	−	0.153481i
$293$			5.85220i			0.341889i	0.985281	+	0.170945i	$0.0546819\pi$
$293$			5.85220i			0.341889i	−0.985281	+	0.170945i	$0.945318\pi$
$294$	8.66009	−	1.43863i	0.505067	−	0.0839028i
$295$	−34.1580			−1.98876
$296$	−10.6720	+	5.74529i	−0.620297	+	0.333938i
$297$	−0.936187			−0.0543231
$298$	8.45779	−	1.40503i	0.489947	−	0.0813910i
$299$		−	5.48475i		−	0.317191i
$300$	1.97407	+	5.77764i	0.113973	+	0.333572i
$301$			5.16006i			0.297421i
$302$	4.20970	+	25.3410i	0.242241	+	1.45821i
$303$	−10.7961			−0.620219
$304$	3.74193	+	4.83662i	0.214614	+	0.277399i
$305$	−34.8999			−1.99836
$306$	1.27549	+	7.67799i	0.0729146	+	0.438922i
$307$		−	32.1986i		−	1.83767i	−0.394639	−	0.918836i	$-0.629130\pi$
$307$		−	32.1986i		−	1.83767i	0.394639	−	0.918836i	$-0.370870\pi$
$308$	0.538914	+	1.57728i	0.0307075	+	0.0898738i
$309$			6.35902i			0.361752i
$310$	−37.4051	+	6.21382i	−2.12447	+	0.352921i
$311$	12.4786			0.707594			0.353797	−	0.935322i	$-0.384890\pi$
$311$	12.4786			0.707594			0.353797	+	0.935322i	$0.384890\pi$
$312$	7.35366	+	13.6596i	0.416319	+	0.773321i
$313$	26.4482			1.49494			0.747469	−	0.664296i	$-0.231269\pi$
$313$	26.4482			1.49494			0.747469	+	0.664296i	$0.231269\pi$
$314$	−32.1243	+	5.33655i	−1.81288	+	0.301159i
$315$		−	2.52618i		−	0.142334i
$316$	−28.5861	+	9.76712i	−1.60810	+	0.549443i
$317$		−	29.2653i		−	1.64370i	−0.569703	−	0.821851i	$-0.692942\pi$
$317$		−	29.2653i		−	1.64370i	0.569703	−	0.821851i	$-0.307058\pi$
$318$	−0.598468	−	3.60258i	−0.0335604	−	0.202023i
$319$	−8.79228			−0.492273
$320$	−18.9509	−	12.4997i	−1.05939	−	0.698754i
$321$	1.81592			0.101355
$322$	−0.206311	−	1.24193i	−0.0114973	−	0.0692098i
$323$		−	8.41376i		−	0.468154i
$324$	−1.89258	+	0.646644i	−0.105143	+	0.0359247i
$325$		−	16.7438i		−	0.928778i
$326$	21.0010	−	3.48873i	1.16314	−	0.193223i
$327$	5.46967			0.302473
$328$	−0.0289993	−	0.0538667i	−0.00160122	−	0.00297429i
$329$	−3.46894			−0.191249
$330$	−3.70629	+	0.615697i	−0.204025	+	0.0338930i
$331$			20.2766i			1.11450i	0.830344	+	0.557251i	$0.188144\pi$
$331$			20.2766i			1.11450i	−0.830344	+	0.557251i	$0.811856\pi$
$332$	−2.54130	−	7.43781i	−0.139472	−	0.408203i
$333$			4.28514i			0.234824i
$334$	−1.33566	−	8.04021i	−0.0730839	−	0.439941i
$335$	−6.83476			−0.373423
$336$	2.17892	+	2.81636i	0.118870	+	0.153645i
$337$	17.7997			0.969613			0.484807	−	0.874621i	$-0.338890\pi$
$337$	17.7997			0.969613			0.484807	+	0.874621i	$0.338890\pi$
$338$	−3.95898	−	23.8317i	−0.215340	−	1.29627i
$339$		−	0.0347532i		−	0.00188753i
$340$	10.0991	+	29.5577i	0.547700	+	1.60299i
$341$		−	8.84538i		−	0.479004i
$342$	2.13280	−	0.354305i	0.115329	−	0.0191586i
$343$	−11.7575			−0.634843
$344$	14.4359	−	7.77159i	0.778330	−	0.419016i
$345$	2.83774			0.152779
$346$	16.9994	−	2.82399i	0.913896	−	0.151818i
$347$			18.6578i			1.00160i	0.865562	+	0.500802i	$0.166962\pi$
$347$			18.6578i			1.00160i	−0.865562	+	0.500802i	$0.833038\pi$
$348$	−17.7743	+	6.07301i	−0.952803	+	0.325548i
$349$		−	17.2080i		−	0.921122i	−0.887628	−	0.460561i	$-0.847648\pi$
$349$		−	17.2080i		−	0.921122i	0.887628	−	0.460561i	$-0.152352\pi$
$350$	−0.629825	−	3.79134i	−0.0336656	−	0.202655i
$351$	5.48475			0.292754
$352$	3.60096	−	3.88322i	0.191932	−	0.206976i
$353$	8.56738			0.455996			0.227998	−	0.973662i	$-0.426782\pi$
$353$	8.56738			0.455996			0.227998	+	0.973662i	$0.426782\pi$
$354$	−2.78966	−	16.7928i	−0.148269	−	0.892527i
$355$			5.31890i			0.282298i
$356$	−25.8175	+	8.82115i	−1.36832	+	0.467520i
$357$		−	4.89932i		−	0.259300i
$358$	8.31924	−	1.38201i	0.439685	−	0.0730415i
$359$	−35.4018			−1.86844			−0.934218	−	0.356702i	$-0.883901\pi$
$359$	−35.4018			−1.86844			−0.934218	+	0.356702i	$0.883901\pi$
$360$	−7.06729	+	3.80469i	−0.372479	+	0.200525i
$361$	16.6628			0.876990
$362$	12.1354	−	2.01595i	0.637820	−	0.105956i
$363$			10.1236i			0.531349i
$364$	−3.15729	−	9.24066i	−0.165487	−	0.484342i
$365$		−	11.5095i		−	0.602433i
$366$	−2.85025	−	17.1575i	−0.148985	−	0.896838i
$367$	−34.7871			−1.81587			−0.907937	−	0.419108i	$-0.862343\pi$
$367$	−34.7871			−1.81587			−0.907937	+	0.419108i	$0.862343\pi$
$368$	−3.16370	+	2.44765i	−0.164919	+	0.127592i
$369$	−0.0216292			−0.00112597
$370$	2.81819	+	16.9645i	0.146511	+	0.881945i
$371$			2.29880i			0.119348i
$372$	−6.10969	−	17.8817i	−0.316772	−	0.927120i
$373$		−	20.5625i		−	1.06468i	−0.846529	−	0.532342i	$-0.821312\pi$
$373$		−	20.5625i		−	1.06468i	0.846529	−	0.532342i	$-0.178688\pi$
$374$	−7.18804	+	1.19409i	−0.371685	+	0.0617451i
$375$	−5.52569			−0.285345
$376$	5.22458	+	9.70476i	0.269437	+	0.500485i
$377$	51.5105			2.65293
$378$	1.24193	−	0.206311i	0.0638778	−	0.0106115i
$379$			7.28469i			0.374189i	0.982342	+	0.187095i	$0.0599071\pi$
$379$			7.28469i			0.374189i	−0.982342	+	0.187095i	$0.940093\pi$
$380$	8.21057	−	2.80533i	0.421193	−	0.143911i
$381$			1.84483i			0.0945137i
$382$	4.71437	+	28.3789i	0.241208	+	1.45199i
$383$	6.44746			0.329450			0.164725	−	0.986340i	$-0.447326\pi$
$383$	6.44746			0.329450			0.164725	+	0.986340i	$0.447326\pi$
$384$	4.59741	−	10.3375i	0.234611	−	0.527533i
$385$	2.36498			0.120531
$386$	0.177396	+	1.06786i	0.00902921	+	0.0543528i
$387$		−	5.79646i		−	0.294651i
$388$	10.9891	−	3.75469i	0.557887	−	0.190615i
$389$			12.0384i			0.610373i	0.952293	+	0.305187i	$0.0987188\pi$
$389$			12.0384i			0.610373i	−0.952293	+	0.305187i	$0.901281\pi$
$390$	21.7137	−	3.60713i	1.09952	−	0.182654i
$391$	5.50356			0.278327
$392$	8.32272	+	15.4596i	0.420361	+	0.780828i
$393$	−16.4740			−0.831006
$394$	3.31954	−	0.551449i	0.167236	−	0.0277816i
$395$			42.8622i			2.15663i
$396$	−0.605380	−	1.77181i	−0.0304215	−	0.0890367i
$397$		−	17.0627i		−	0.856352i	−0.903695	−	0.428176i	$-0.859156\pi$
$397$		−	17.0627i		−	0.856352i	0.903695	−	0.428176i	$-0.140844\pi$
$398$	−1.54746	−	9.31517i	−0.0775670	−	0.466927i
$399$	−1.36094			−0.0681321
$400$	−9.65812	+	7.47215i	−0.482906	+	0.373607i
$401$	−10.8167			−0.540162			−0.270081	−	0.962838i	$-0.587051\pi$
$401$	−10.8167			−0.540162			−0.270081	+	0.962838i	$0.587051\pi$
$402$	−0.558190	−	3.36011i	−0.0278400	−	0.167587i
$403$			51.8216i			2.58142i
$404$	−6.98123	−	20.4325i	−0.347329	−	1.01655i
$405$			2.83774i			0.141009i
$406$	11.6637	−	1.93759i	0.578858	−	0.0961611i
$407$	−4.01170			−0.198852
$408$	−13.7064	+	7.37888i	−0.678569	+	0.365309i
$409$	−10.8859			−0.538275			−0.269137	−	0.963102i	$-0.586739\pi$
$409$	−10.8859			−0.538275			−0.269137	+	0.963102i	$0.586739\pi$
$410$	−0.0856284	+	0.0142248i	−0.00422888	+	0.000702511i
$411$		−	20.8369i		−	1.02781i
$412$	−12.0349	+	4.11202i	−0.592919	+	0.202585i
$413$			10.7155i			0.527274i
$414$	0.231756	+	1.39509i	0.0113902	+	0.0685652i
$415$	−11.1523			−0.547445
$416$	−21.0966	+	22.7502i	−1.03435	+	1.11542i
$417$	10.9007			0.533810
$418$	0.331696	+	1.99670i	0.0162238	+	0.0976617i
$419$		−	33.3526i		−	1.62938i	−0.579897	−	0.814690i	$-0.696907\pi$
$419$		−	33.3526i		−	1.62938i	0.579897	−	0.814690i	$-0.303093\pi$
$420$	4.78100	−	1.63354i	0.233289	−	0.0797087i
$421$			5.61450i			0.273634i	0.990596	+	0.136817i	$0.0436872\pi$
$421$			5.61450i			0.273634i	−0.990596	+	0.136817i	$0.956313\pi$
$422$	25.3775	−	4.21576i	1.23536	−	0.205220i
$423$	3.89677			0.189468
$424$	6.43116	−	3.46223i	0.312325	−	0.168141i
$425$	16.8012			0.814979
$426$	−2.61488	+	0.434390i	−0.126692	+	0.0210463i
$427$			10.9482i			0.529821i
$428$	1.17426	+	3.43678i	0.0567598	+	0.166123i
$429$			5.13475i			0.247908i
$430$	−3.81213	−	22.9477i	−0.183837	−	1.10664i
$431$	13.0940			0.630714			0.315357	−	0.948973i	$-0.397876\pi$
$431$	13.0940			0.630714			0.315357	+	0.948973i	$0.397876\pi$
$432$	−2.44765	−	3.16370i	−0.117763	−	0.152214i
$433$	−9.95140			−0.478234			−0.239117	−	0.970991i	$-0.576858\pi$
$433$	−9.95140			−0.478234			−0.239117	+	0.970991i	$0.576858\pi$
$434$	1.94929	+	11.7341i	0.0935691	+	0.563254i
$435$			26.6509i			1.27781i
$436$	3.53693	+	10.3518i	0.169388	+	0.495760i
$437$		−	1.52878i		−	0.0731317i
$438$	5.65830	−	0.939969i	0.270364	−	0.0449134i
$439$	4.94947			0.236225			0.118113	−	0.993000i	$-0.462316\pi$
$439$	4.94947			0.236225			0.118113	+	0.993000i	$0.462316\pi$
$440$	−3.56190	−	6.61631i	−0.169807	−	0.315420i
$441$	6.20753			0.295597
$442$	42.1119	−	6.99572i	2.00306	−	0.332753i
$443$			6.53082i			0.310289i	0.987892	+	0.155144i	$0.0495843\pi$
$443$			6.53082i			0.310289i	−0.987892	+	0.155144i	$0.950416\pi$
$444$	−8.10997	+	2.77096i	−0.384882	+	0.131504i
$445$			38.7109i			1.83507i
$446$	0.682476	+	4.10827i	0.0323162	+	0.194532i
$447$	6.06252			0.286747
$448$	−3.92119	+	5.94495i	−0.185259	+	0.280873i
$449$	40.5217			1.91234			0.956168	−	0.292820i	$-0.0945937\pi$
$449$	40.5217			1.91234			0.956168	+	0.292820i	$0.0945937\pi$
$450$	0.707503	+	4.25893i	0.0333520	+	0.200768i
$451$		−	0.0202490i		−	0.000953488i
$452$	0.0657731	−	0.0224729i	0.00309371	−	0.00105704i
$453$			18.1644i			0.853436i
$454$	34.0445	−	5.65555i	1.59779	−	0.265428i
$455$	−13.8555			−0.649556
$456$	2.04971	+	3.80738i	0.0959866	+	0.178297i
$457$	−15.4741			−0.723847			−0.361923	−	0.932208i	$-0.617880\pi$
$457$	−15.4741			−0.723847			−0.361923	+	0.932208i	$0.617880\pi$
$458$	−32.8729	+	5.46092i	−1.53605	+	0.255172i
$459$			5.50356i			0.256884i
$460$	1.83501	+	5.37065i	0.0855577	+	0.250408i
$461$		−	15.7779i		−	0.734850i	−0.930053	−	0.367425i	$-0.880240\pi$
$461$		−	15.7779i		−	0.734850i	0.930053	−	0.367425i	$-0.119760\pi$
$462$	0.193146	+	1.16267i	0.00898597	+	0.0540925i
$463$	16.6018			0.771549			0.385775	−	0.922593i	$-0.373934\pi$
$463$	16.6018			0.771549			0.385775	+	0.922593i	$0.373934\pi$
$464$	−22.9873	−	29.7122i	−1.06716	−	1.37935i
$465$	−26.8119			−1.24337
$466$	2.42002	+	14.5677i	0.112105	+	0.674836i
$467$			24.9885i			1.15633i	0.815920	+	0.578165i	$0.196231\pi$
$467$			24.9885i			1.15633i	−0.815920	+	0.578165i	$0.803769\pi$
$468$	3.54668	+	10.3803i	0.163945	+	0.479831i
$469$			2.14409i			0.0990047i
$470$	15.4270	−	2.56277i	0.711595	−	0.118212i
$471$	−23.0266			−1.06101
$472$	29.9778	−	16.1386i	1.37984	−	0.742839i
$473$	5.42657			0.249514
$474$	−21.0720	+	3.50052i	−0.967868	+	0.160784i
$475$		−	4.66705i		−	0.214139i
$476$	9.27235	−	3.16812i	0.424997	−	0.145210i
$477$		−	2.58232i		−	0.118236i
$478$	4.21666	+	25.3829i	0.192866	+	1.16099i
$479$	−36.0645			−1.64783			−0.823915	−	0.566713i	$-0.808215\pi$
$479$	−36.0645			−1.64783			−0.823915	+	0.566713i	$0.808215\pi$
$480$	−11.7707	−	10.9151i	−0.537256	−	0.498205i
$481$	23.5030			1.07164
$482$	−3.44239	−	20.7220i	−0.156797	−	0.943863i
$483$		−	0.890209i		−	0.0405059i
$484$	−19.1596	+	6.54633i	−0.870892	+	0.297561i
$485$		−	16.4771i		−	0.748188i
$486$	−1.39509	+	0.231756i	−0.0632828	+	0.0105127i
$487$	28.5063			1.29174			0.645871	−	0.763447i	$-0.276494\pi$
$487$	28.5063			1.29174			0.645871	+	0.763447i	$0.276494\pi$
$488$	30.6289	−	16.4891i	1.38650	−	0.746428i
$489$	15.0535			0.680741
$490$	24.5751	−	4.08247i	1.11019	−	0.184427i
$491$		−	25.0171i		−	1.12900i	−0.825432	−	0.564502i	$-0.809068\pi$
$491$		−	25.0171i		−	1.12900i	0.825432	−	0.564502i	$-0.190932\pi$
$492$	−0.0139864	−	0.0409350i	−0.000630556	−	0.00184549i
$493$			51.6872i			2.32788i
$494$	−1.94328	−	11.6979i	−0.0874322	−	0.526312i
$495$	−2.65666			−0.119408
$496$	29.8916	−	23.1261i	1.34217	−	1.03839i
$497$	1.66856			0.0748450
$498$	−0.910800	−	5.48271i	−0.0408139	−	0.245686i
$499$		−	35.0287i		−	1.56810i	−0.620698	−	0.784050i	$-0.713151\pi$
$499$		−	35.0287i		−	1.56810i	0.620698	−	0.784050i	$-0.286849\pi$
$500$	−3.57315	−	10.4578i	−0.159796	−	0.467687i
$501$		−	5.76320i		−	0.257481i
$502$	9.78308	−	1.62519i	0.436640	−	0.0725356i
$503$	−4.49687			−0.200505			−0.100253	−	0.994962i	$-0.531965\pi$
$503$	−4.49687			−0.200505			−0.100253	+	0.994962i	$0.531965\pi$
$504$	1.19354	+	2.21703i	0.0531647	+	0.0987544i
$505$	−30.6365			−1.36331
$506$	−1.30607	+	0.216967i	−0.0580619	+	0.00964537i
$507$		−	17.0825i		−	0.758661i
$508$	−3.49149	+	1.19295i	−0.154910	+	0.0529286i
$509$		−	6.97668i		−	0.309236i	−0.987974	−	0.154618i	$-0.950585\pi$
$509$		−	6.97668i		−	0.309236i	0.987974	−	0.154618i	$-0.0494146\pi$
$510$	3.61950	+	21.7882i	0.160274	+	0.964797i
$511$	−3.61056			−0.159722
$512$	22.5374	+	2.01628i	0.996022	+	0.0891078i
$513$	1.52878			0.0674975
$514$	−0.0369237	−	0.222268i	−0.00162863	−	0.00980383i
$515$			18.0453i			0.795169i
$516$	10.9703	−	3.74825i	0.482939	−	0.165007i
$517$			3.64811i			0.160444i
$518$	5.32183	−	0.884075i	0.233828	−	0.0388440i
$519$	12.1852			0.534869
$520$	20.8678	+	38.7623i	0.915114	+	1.69984i
$521$	−21.0831			−0.923666			−0.461833	−	0.886967i	$-0.652808\pi$
$521$	−21.0831			−0.923666			−0.461833	+	0.886967i	$0.652808\pi$
$522$	−13.1022	+	2.17656i	−0.573466	+	0.0952654i
$523$			11.3654i			0.496975i	0.968635	+	0.248488i	$0.0799335\pi$
$523$			11.3654i			0.496975i	−0.968635	+	0.248488i	$0.920066\pi$
$524$	−10.6528	−	31.1784i	−0.465371	−	1.36204i
$525$		−	2.71762i		−	0.118607i
$526$	1.45901	+	8.78274i	0.0636158	+	0.382946i
$527$	−51.9993			−2.26513
$528$	2.96182	−	2.29146i	0.128897	−	0.0997228i
$529$	1.00000			0.0434783
$530$	−1.69830	−	10.2232i	−0.0737694	−	0.444067i
$531$		−	12.0370i		−	0.522363i
$532$	−0.880042	−	2.57568i	−0.0381547	−	0.111670i
$533$			0.118631i			0.00513847i
$534$	−19.0311	+	3.16149i	−0.823556	+	0.136811i
$535$	5.15312			0.222789
$536$	5.99833	−	3.22921i	0.259088	−	0.139481i
$537$	5.96321			0.257331
$538$	23.4704	−	3.89895i	1.01188	−	0.168096i
$539$			5.81141i			0.250315i
$540$	−5.37065	+	1.83501i	−0.231116	+	0.0789662i
$541$			2.66640i			0.114637i	0.998356	+	0.0573187i	$0.0182551\pi$
$541$			2.66640i			0.114637i	−0.998356	+	0.0573187i	$0.981745\pi$
$542$	3.46228	+	20.8417i	0.148718	+	0.895230i
$543$	8.69859			0.373292
$544$	−22.8283	−	21.1690i	−0.978754	−	0.907611i
$545$	15.5215			0.664869
$546$	−1.13157	−	6.81166i	−0.0484266	−	0.291512i
$547$			11.8725i			0.507632i	0.967253	+	0.253816i	$0.0816858\pi$
$547$			11.8725i			0.507632i	−0.967253	+	0.253816i	$0.918314\pi$
$548$	39.4355	−	13.4741i	1.68460	−	0.575583i
$549$		−	12.2985i		−	0.524886i
$550$	−3.98715	+	0.662355i	−0.170013	+	0.0282429i
$551$	14.3577			0.611659
$552$	−2.49046	+	1.34075i	−0.106001	+	0.0570659i
$553$	13.4460			0.571783
$554$	−25.0822	+	4.16672i	−1.06564	+	0.177027i
$555$			12.1601i			0.516169i
$556$	7.04888	+	20.6304i	0.298939	+	0.874926i
$557$			45.1820i			1.91442i	0.289387	+	0.957212i	$0.406548\pi$
$557$			45.1820i			1.91442i	−0.289387	+	0.957212i	$0.593452\pi$
$558$	−2.18970	−	13.1813i	−0.0926975	−	0.558008i
$559$	−31.7922			−1.34467
$560$	6.18321	+	7.99210i	0.261288	+	0.337728i
$561$	−5.15237			−0.217533
$562$	−2.14321	−	12.9014i	−0.0904057	−	0.544212i
$563$			11.5047i			0.484865i	0.970168	+	0.242432i	$0.0779453\pi$
$563$			11.5047i			0.484865i	−0.970168	+	0.242432i	$0.922055\pi$
$564$	2.51982	+	7.37494i	0.106104	+	0.310541i
$565$		−	0.0986206i		−	0.00414900i
$566$	−4.44401	+	0.738249i	−0.186796	+	0.0310309i
$567$	0.890209			0.0373853
$568$	−2.51302	−	4.66798i	−0.105444	−	0.195864i
$569$	−24.3175			−1.01944			−0.509721	−	0.860340i	$-0.670251\pi$
$569$	−24.3175			−1.01944			−0.509721	+	0.860340i	$0.670251\pi$
$570$	6.05234	−	1.00543i	0.253504	−	0.0421127i
$571$			13.9107i			0.582145i	0.956701	+	0.291073i	$0.0940121\pi$
$571$			13.9107i			0.582145i	−0.956701	+	0.291073i	$0.905988\pi$
$572$	−9.71792	+	3.32036i	−0.406327	+	0.138831i
$573$			20.3419i			0.849796i
$574$	0.00446236	+	0.0268619i	0.000186255	+	0.00112119i
$575$	3.05279			0.127310
$576$	4.40480	−	6.67815i	0.183533	−	0.278256i
$577$	11.9747			0.498514			0.249257	−	0.968437i	$-0.419814\pi$
$577$	11.9747			0.498514			0.249257	+	0.968437i	$0.419814\pi$
$578$	3.07986	+	18.5397i	0.128105	+	0.771151i
$579$			0.765442i			0.0318107i
$580$	−50.4390	+	17.2337i	−2.09436	+	0.715588i
$581$			3.49851i			0.145143i
$582$	8.10051	−	1.34567i	0.335777	−	0.0557800i
$583$	2.41753			0.100124
$584$	5.43787	+	10.1009i	0.225021	+	0.417980i
$585$	15.5643			0.643505
$586$	−8.16437	+	1.35628i	−0.337267	+	0.0560275i
$587$			30.5566i			1.26121i	0.776106	+	0.630603i	$0.217192\pi$
$587$			30.5566i			1.26121i	−0.776106	+	0.630603i	$0.782808\pi$
$588$	4.01406	+	11.7482i	0.165537	+	0.484489i
$589$			14.4444i			0.595172i
$590$	−7.91633	−	47.6536i	−0.325910	−	1.96187i
$591$	2.37943			0.0978768
$592$	−10.4885	−	13.5569i	−0.431076	−	0.557186i
$593$	42.6936			1.75322			0.876608	−	0.481205i	$-0.159801\pi$
$593$	42.6936			1.75322			0.876608	+	0.481205i	$0.159801\pi$
$594$	−0.216967	−	1.30607i	−0.00890227	−	0.0535887i
$595$		−	13.9030i		−	0.569968i
$596$	3.92029	+	11.4738i	0.160581	+	0.469985i
$597$		−	6.67709i		−	0.273275i
$598$	7.65175	−	1.27113i	0.312903	−	0.0519802i
$599$	37.0727			1.51475			0.757374	−	0.652982i	$-0.226482\pi$
$599$	37.0727			1.51475			0.757374	+	0.652982i	$0.226482\pi$
$600$	−7.60285	+	4.09301i	−0.310385	+	0.167097i
$601$	4.29031			0.175005			0.0875027	−	0.996164i	$-0.472111\pi$
$601$	4.29031			0.175005			0.0875027	+	0.996164i	$0.472111\pi$
$602$	−7.19878	+	1.19588i	−0.293400	+	0.0487403i
$603$		−	2.40852i		−	0.0980826i
$604$	−34.3775	+	11.7459i	−1.39880	+	0.477932i
$605$			28.7280i			1.16796i
$606$	−2.50206	−	15.0616i	−0.101639	−	0.611835i
$607$	−9.00676			−0.365573			−0.182787	−	0.983153i	$-0.558512\pi$
$607$	−9.00676			−0.365573			−0.182787	+	0.983153i	$0.558512\pi$
$608$	−5.88033	+	6.34126i	−0.238479	+	0.257172i
$609$	8.36048			0.338784
$610$	−8.08827	−	48.6887i	−0.327484	−	1.97135i
$611$		−	21.3728i		−	0.864652i
$612$	−10.4159	+	3.55885i	−0.421039	+	0.143858i
$613$			15.3897i			0.621585i	0.950478	+	0.310792i	$0.100594\pi$
$613$			15.3897i			0.621585i	−0.950478	+	0.310792i	$0.899406\pi$
$614$	44.9201	−	7.46223i	1.81283	−	0.301151i
$615$	−0.0613782			−0.00247501
$616$	−2.07556	+	1.11738i	−0.0836265	+	0.0450205i
$617$	40.2820			1.62169			0.810846	−	0.585260i	$-0.199007\pi$
$617$	40.2820			1.62169			0.810846	+	0.585260i	$0.199007\pi$
$618$	−8.87143	+	1.47374i	−0.356861	+	0.0592826i
$619$		−	45.7347i		−	1.83823i	−0.393986	−	0.919116i	$-0.628904\pi$
$619$		−	45.7347i		−	1.83823i	0.393986	−	0.919116i	$-0.371096\pi$
$620$	−17.3377	−	50.7435i	−0.696300	−	2.03791i
$621$			1.00000i			0.0401286i
$622$	2.89198	+	17.4088i	0.115958	+	0.698028i
$623$	12.1437			0.486528
$624$	−17.3521	+	13.4247i	−0.694641	+	0.537420i
$625$	−30.9444			−1.23778
$626$	6.12953	+	36.8977i	0.244985	+	1.47473i
$627$			1.43123i			0.0571578i
$628$	−14.8900	−	43.5796i	−0.594175	−	1.73902i
$629$			23.5836i			0.940338i
$630$	3.52427	−	0.585459i	0.140410	−	0.0233252i
$631$	20.8218			0.828902			0.414451	−	0.910072i	$-0.363974\pi$
$631$	20.8218			0.828902			0.414451	+	0.910072i	$0.363974\pi$
$632$	−20.2511	−	37.6168i	−0.805544	−	1.49631i
$633$	18.1905			0.723008
$634$	40.8278	−	6.78241i	1.62148	−	0.269364i
$635$			5.23516i			0.207751i
$636$	4.88724	−	1.66984i	0.193792	−	0.0662135i
$637$		−	34.0468i		−	1.34898i
$638$	−2.03767	−	12.2661i	−0.0806720	−	0.485618i
$639$	−1.87434			−0.0741478
$640$	13.0463	−	29.3352i	0.515699	−	1.15957i
$641$	19.0595			0.752807			0.376403	−	0.926456i	$-0.377161\pi$
$641$	19.0595			0.752807			0.376403	+	0.926456i	$0.377161\pi$
$642$	0.420852	+	2.53339i	0.0166097	+	0.0999847i
$643$		−	2.79547i		−	0.110243i	−0.998480	−	0.0551213i	$-0.982445\pi$
$643$		−	2.79547i		−	0.110243i	0.998480	−	0.0551213i	$-0.0175546\pi$
$644$	1.68479	−	0.575648i	0.0663900	−	0.0226837i
$645$		−	16.4489i		−	0.647674i
$646$	11.7380	−	1.94994i	0.461825	−	0.0767195i
$647$	8.31986			0.327088			0.163544	−	0.986536i	$-0.447707\pi$
$647$	8.31986			0.327088			0.163544	+	0.986536i	$0.447707\pi$
$648$	−1.34075	−	2.49046i	−0.0526695	−	0.0978346i
$649$	11.2689			0.442343
$650$	23.3592	−	3.88048i	0.916222	−	0.152205i
$651$			8.41096i			0.329652i
$652$	9.73423	+	28.4899i	0.381222	+	1.11575i
$653$			15.5492i			0.608489i	0.952594	+	0.304244i	$0.0984039\pi$
$653$			15.5492i			0.608489i	−0.952594	+	0.304244i	$0.901596\pi$
$654$	1.26763	+	7.63071i	0.0495683	+	0.298384i
$655$	−46.7491			−1.82664
$656$	0.0684284	−	0.0529407i	0.00267168	−	0.00206699i
$657$	4.05585			0.158234
$658$	−0.803949	−	4.83950i	−0.0313412	−	0.188663i
$659$		−	30.9157i		−	1.20430i	−0.798382	−	0.602151i	$-0.794310\pi$
$659$		−	30.9157i		−	1.20430i	0.798382	−	0.602151i	$-0.205690\pi$
$660$	−1.71791	−	5.02793i	−0.0668696	−	0.195712i
$661$			16.5944i			0.645448i	0.946493	+	0.322724i	$0.104599\pi$
$661$			16.5944i			0.645448i	−0.946493	+	0.322724i	$0.895401\pi$
$662$	−28.2878	+	4.69923i	−1.09944	+	0.182641i
$663$	30.1857			1.17231
$664$	9.78749	−	5.26912i	0.379828	−	0.204481i
$665$	−3.86199			−0.149762
$666$	−5.97818	+	0.993109i	−0.231650	+	0.0384822i
$667$			9.39159i			0.363644i
$668$	10.9073	−	3.72674i	0.422016	−	0.144192i
$669$			2.94480i			0.113853i
$670$	−1.58400	−	9.53514i	−0.0611952	−	0.368375i
$671$	11.5137			0.444480
$672$	−3.42411	+	3.69251i	−0.132088	+	0.142441i
$673$	−48.6343			−1.87471			−0.937357	−	0.348371i	$-0.886735\pi$
$673$	−48.6343			−1.87471			−0.937357	+	0.348371i	$0.886735\pi$
$674$	4.12520	+	24.8323i	0.158897	+	0.956505i
$675$			3.05279i			0.117502i
$676$	32.3300	−	11.0463i	1.24346	−	0.424858i
$677$			23.3867i			0.898822i	0.893325	+	0.449411i	$0.148366\pi$
$677$			23.3867i			0.898822i	−0.893325	+	0.449411i	$0.851634\pi$
$678$	0.0484840	−	0.00805427i	0.00186202	−	0.000309322i
$679$	−5.16893			−0.198365
$680$	−38.8953	+	20.9394i	−1.49157	+	0.802988i
$681$	24.4030			0.935126
$682$	12.3401	−	2.04997i	0.472528	−	0.0784975i
$683$			15.5204i			0.593872i	0.954897	+	0.296936i	$0.0959648\pi$
$683$			15.5204i			0.593872i	−0.954897	+	0.296936i	$0.904035\pi$
$684$	0.988579	+	2.89334i	0.0377993	+	0.110630i
$685$		−	59.1298i		−	2.25923i
$686$	−2.72486	−	16.4028i	−0.104036	−	0.626261i
$687$	−23.5632			−0.898993
$688$	14.1877	+	18.3383i	0.540901	+	0.699141i
$689$	−14.1634			−0.539582
$690$	0.657665	+	3.95892i	0.0250369	+	0.150714i
$691$		−	30.4436i		−	1.15813i	−0.815282	−	0.579064i	$-0.803418\pi$
$691$		−	30.4436i		−	1.15813i	0.815282	−	0.579064i	$-0.196582\pi$
$692$	7.87945	+	23.0614i	0.299532	+	0.876661i
$693$			0.833402i			0.0316583i
$694$	−26.0294	+	4.32407i	−0.988064	+	0.164139i
$695$	30.9334			1.17337
$696$	−12.5917	−	23.3894i	−0.477289	−	0.886573i
$697$	−0.119038			−0.00450888
$698$	24.0067	−	3.98805i	0.908669	−	0.150950i
$699$			10.4421i			0.394956i
$700$	5.14331	−	1.75733i	0.194399	−	0.0664209i
$701$		−	25.1251i		−	0.948963i	−0.880266	−	0.474481i	$-0.842636\pi$
$701$		−	25.1251i		−	0.948963i	0.880266	−	0.474481i	$-0.157364\pi$
$702$	1.27113	+	7.65175i	0.0479755	+	0.288797i
$703$	6.55106			0.247078
$704$	6.25200	+	4.12372i	0.235631	+	0.155418i
$705$	11.0580			0.416470
$706$	1.98554	+	11.9523i	0.0747269	+	0.449831i
$707$			9.61078i			0.361451i
$708$	22.7810	−	7.78367i	0.856163	−	0.292528i
$709$			37.0858i			1.39279i	0.717660	+	0.696393i	$0.245213\pi$
$709$			37.0858i			1.39279i	−0.717660	+	0.696393i	$0.754787\pi$
$710$	−7.42037	+	1.23269i	−0.278481	+	0.0462620i
$711$	−15.1043			−0.566457
$712$	−18.2897	−	33.9735i	−0.685435	−	1.27321i
$713$	−9.44830			−0.353842
$714$	6.83502	−	1.13545i	0.255794	−	0.0424931i
$715$			14.5711i			0.544929i
$716$	3.85607	+	11.2858i	0.144108	+	0.421771i
$717$			18.1944i			0.679482i
$718$	−8.20459	−	49.3889i	−0.306193	−	1.84318i
$719$	−8.12420			−0.302982			−0.151491	−	0.988459i	$-0.548407\pi$
$719$	−8.12420			−0.302982			−0.151491	+	0.988459i	$0.548407\pi$
$720$	−6.94580	−	8.97778i	−0.258855	−	0.334582i
$721$	5.66086			0.210821
$722$	3.86171	+	23.2462i	0.143718	+	0.865134i
$723$		−	14.8535i		−	0.552407i
$724$	5.62489	+	16.4628i	0.209047	+	0.611834i
$725$			28.6705i			1.06480i
$726$	−14.1233	+	2.34620i	−0.524165	+	0.0870755i
$727$	34.3376			1.27351			0.636756	−	0.771065i	$-0.280276\pi$
$727$	34.3376			1.27351			0.636756	+	0.771065i	$0.280276\pi$
$728$	12.1599	−	6.54629i	0.450675	−	0.242622i
$729$	−1.00000			−0.0370370
$730$	16.0568	−	2.66739i	0.594289	−	0.0987245i
$731$		−	31.9012i		−	1.17991i
$732$	23.2758	−	7.95273i	0.860299	−	0.293941i
$733$		−	2.20609i		−	0.0814837i	−0.999170	−	0.0407419i	$-0.987028\pi$
$733$		−	2.20609i		−	0.0814837i	0.999170	−	0.0407419i	$-0.0129721\pi$
$734$	−8.06213	−	48.5313i	−0.297579	−	1.79132i
$735$	17.6154			0.649753
$736$	−4.14791	−	3.84641i	−0.152894	−	0.141780i
$737$	2.25483			0.0830576
$738$	−0.00501271	−	0.0301748i	−0.000184520	−	0.00111075i
$739$		−	26.2583i		−	0.965926i	−0.875641	−	0.482963i	$-0.839561\pi$
$739$		−	26.2583i		−	0.965926i	0.875641	−	0.482963i	$-0.160439\pi$
$740$	−23.0140	+	7.86328i	−0.846012	+	0.289060i
$741$		−	8.38500i		−	0.308031i
$742$	−3.20705	+	0.532762i	−0.117734	+	0.0195583i
$743$	3.05264			0.111991			0.0559953	−	0.998431i	$-0.482167\pi$
$743$	3.05264			0.111991			0.0559953	+	0.998431i	$0.482167\pi$
$744$	23.5306	−	12.6678i	0.862675	−	0.464423i
$745$	17.2039			0.630301
$746$	28.6866	−	4.76548i	1.05029	−	0.174477i
$747$		−	3.92999i		−	0.143791i
$748$	−3.33174	−	9.75125i	−0.121821	−	0.356541i
$749$		−	1.61655i		−	0.0590675i
$750$	−1.28061	−	7.70886i	−0.0467614	−	0.281488i
$751$	−41.5945			−1.51781			−0.758903	−	0.651203i	$-0.774264\pi$
$751$	−41.5945			−1.51781			−0.758903	+	0.651203i	$0.774264\pi$
$752$	−12.3282	+	9.53792i	−0.449564	+	0.347812i
$753$	7.01248			0.255549
$754$	11.9379	+	71.8621i	0.434752	+	2.61706i
$755$			51.5458i			1.87594i
$756$	0.575648	+	1.68479i	0.0209361	+	0.0612752i
$757$		−	40.6694i		−	1.47815i	−0.673621	−	0.739077i	$-0.735262\pi$
$757$		−	40.6694i		−	1.47815i	0.673621	−	0.739077i	$-0.264738\pi$
$758$	−10.1628	+	1.68827i	−0.369130	+	0.0613208i
$759$	−0.936187			−0.0339814
$760$	5.81656	+	10.8044i	0.210989	+	0.391916i
$761$	−33.8323			−1.22642			−0.613211	−	0.789919i	$-0.710122\pi$
$761$	−33.8323			−1.22642			−0.613211	+	0.789919i	$0.710122\pi$
$762$	−2.57372	+	0.427552i	−0.0932359	+	0.0154886i
$763$		−	4.86915i		−	0.176275i
$764$	−38.4987	+	13.1540i	−1.39283	+	0.475894i
$765$			15.6177i			0.564659i
$766$	1.49424	+	8.99482i	0.0539891	+	0.324996i
$767$	−66.0201			−2.38385
$768$	15.4873	+	4.01804i	0.558848	+	0.144989i
$769$	−31.6921			−1.14285			−0.571423	−	0.820656i	$-0.693608\pi$
$769$	−31.6921			−1.14285			−0.571423	+	0.820656i	$0.693608\pi$
$770$	0.548099	+	3.29937i	0.0197521	+	0.118901i
$771$		−	0.159321i		−	0.00573782i
$772$	−1.44866	+	0.494968i	−0.0521384	+	0.0178143i
$773$			20.7404i			0.745980i	0.927835	+	0.372990i	$0.121667\pi$
$773$			20.7404i			0.745980i	−0.927835	+	0.372990i	$0.878333\pi$
$774$	8.08662	−	1.34337i	0.290667	−	0.0482863i
$775$	−28.8437			−1.03609
$776$	7.78494	+	14.4607i	0.279463	+	0.519108i
$777$	3.81467			0.136851
$778$	−16.7948	+	2.78998i	−0.602121	+	0.100026i
$779$			0.0330664i			0.00118473i
$780$	10.0646	+	29.4567i	0.360369	+	1.05472i
$781$		−	1.75473i		−	0.0627893i
$782$	1.27549	+	7.67799i	0.0456113	+	0.274564i
$783$	−9.39159			−0.335628
$784$	−19.6388	+	15.1938i	−0.701385	+	0.542637i
$785$	−65.3435			−2.33221
$786$	−3.81796	−	22.9829i	−0.136182	−	0.819771i
$787$		−	52.7313i		−	1.87967i	−0.341631	−	0.939834i	$-0.610979\pi$
$787$		−	52.7313i		−	1.87967i	0.341631	−	0.939834i	$-0.389021\pi$
$788$	1.53865	+	4.50326i	0.0548120	+	0.160422i
$789$			6.29544i			0.224124i
$790$	−59.7968	+	9.93358i	−2.12748	+	0.353421i
$791$	−0.0309376			−0.00110001
$792$	2.33154	−	1.25519i	0.0828476	−	0.0446012i
$793$	−67.4541			−2.39536
$794$	23.8041	−	3.95438i	0.844775	−	0.140336i
$795$		−	7.32796i		−	0.259896i
$796$	12.6369	−	4.31770i	0.447903	−	0.153037i
$797$			12.0581i			0.427120i	0.976930	+	0.213560i	$0.0685059\pi$
$797$			12.0581i			0.427120i	−0.976930	+	0.213560i	$0.931494\pi$
$798$	−0.315406	−	1.89864i	−0.0111652	−	0.0672110i
$799$	21.4461			0.758710
$800$	−12.6627	−	11.7423i	−0.447693	−	0.415152i
$801$	−13.6414			−0.481996
$802$	−2.50685	−	15.0904i	−0.0885198	−	0.532860i
$803$			3.79704i			0.133994i
$804$	4.55831	−	1.55746i	0.160759	−	0.0549272i
$805$		−	2.52618i		−	0.0890363i
$806$	−72.2960	+	12.0100i	−2.54652	+	0.423033i
$807$	16.8235			0.592216
$808$	26.8873	−	14.4748i	0.945891	−	0.509222i
$809$	−19.6669			−0.691450			−0.345725	−	0.938336i	$-0.612367\pi$
$809$	−19.6669			−0.691450			−0.345725	+	0.938336i	$0.612367\pi$
$810$	−3.95892	+	0.657665i	−0.139102	+	0.0231080i
$811$			36.4649i			1.28046i	0.768185	+	0.640228i	$0.221160\pi$
$811$			36.4649i			1.28046i	−0.768185	+	0.640228i	$0.778840\pi$
$812$	5.40625	+	15.8229i	0.189722	+	0.555273i
$813$			14.9393i			0.523944i
$814$	−0.929736	−	5.59670i	−0.0325872	−	0.196164i
$815$	42.7179			1.49634
$816$	−13.4708	−	17.4116i	−0.471572	−	0.609530i
$817$	−8.86154			−0.310026
$818$	−2.52288	−	15.1869i	−0.0882105	−	0.530998i
$819$		−	4.88258i		−	0.170611i
$820$	−0.0396898	−	0.116163i	−0.00138603	−	0.00405659i
$821$			21.9423i			0.765791i	0.923792	+	0.382895i	$0.125073\pi$
$821$			21.9423i			0.765791i	−0.923792	+	0.382895i	$0.874927\pi$
$822$	29.0695	−	4.82908i	1.01391	−	0.168434i
$823$	−30.6399			−1.06804			−0.534020	−	0.845472i	$-0.679319\pi$
$823$	−30.6399			−1.06804			−0.534020	+	0.845472i	$0.679319\pi$
$824$	−8.52583	−	15.8369i	−0.297011	−	0.551704i
$825$	−2.85798			−0.0995021
$826$	−14.9491	+	2.48338i	−0.520146	+	0.0864078i
$827$			22.7457i			0.790945i	0.918478	+	0.395473i	$0.129419\pi$
$827$			22.7457i			0.790945i	−0.918478	+	0.395473i	$0.870581\pi$
$828$	−1.89258	+	0.646644i	−0.0657716	+	0.0224724i
$829$		−	3.40930i		−	0.118410i	−0.998246	−	0.0592050i	$-0.981143\pi$
$829$		−	3.40930i		−	0.118410i	0.998246	−	0.0592050i	$-0.0188566\pi$
$830$	−2.58462	−	15.5585i	−0.0897133	−	0.540044i
$831$	−17.9789			−0.623680
$832$	−36.6280	−	24.1592i	−1.26985	−	0.837571i
$833$	34.1635			1.18370
$834$	2.52631	+	15.2075i	0.0874789	+	0.526593i
$835$		−	16.3545i		−	0.565970i
$836$	−2.70871	+	0.925495i	−0.0936827	+	0.0320089i
$837$		−	9.44830i		−	0.326581i
$838$	46.5300	−	7.72966i	1.60735	−	0.267017i
$839$	0.414531			0.0143112			0.00715561	−	0.999974i	$-0.497722\pi$
$839$	0.414531			0.0143112			0.00715561	+	0.999974i	$0.497722\pi$
$840$	3.38697	+	6.29137i	0.116862	+	0.217073i
$841$	−59.2020			−2.04145
$842$	−7.83275	+	1.30119i	−0.269934	+	0.0448421i
$843$		−	9.24768i		−	0.318507i
$844$	11.7628	+	34.4270i	0.404892	+	1.18503i
$845$		−	48.4758i		−	1.66762i
$846$	0.903101	+	5.43636i	0.0310493	+	0.186906i
$847$	9.01208			0.309659
$848$	6.32060	+	8.16969i	0.217050	+	0.280548i
$849$	−3.18546			−0.109325
$850$	3.89379	+	23.4393i	0.133556	+	0.803961i
$851$			4.28514i			0.146893i
$852$	−1.21203	−	3.54734i	−0.0415235	−	0.121530i
$853$		−	30.6663i		−	1.04999i	−0.851104	−	0.524997i	$-0.824066\pi$
$853$		−	30.6663i		−	1.04999i	0.851104	−	0.524997i	$-0.175934\pi$
$854$	−15.2738	+	2.53732i	−0.522658	+	0.0868252i
$855$	4.33830			0.148367
$856$	−4.52249	+	2.43469i	−0.154575	+	0.0832161i
$857$	−23.1729			−0.791571			−0.395785	−	0.918343i	$-0.629528\pi$
$857$	−23.1729			−0.791571			−0.395785	+	0.918343i	$0.629528\pi$
$858$	−7.16347	+	1.19001i	−0.244557	+	0.0406263i
$859$			38.4693i			1.31256i	0.754519	+	0.656278i	$0.227870\pi$
$859$			38.4693i			1.31256i	−0.754519	+	0.656278i	$0.772130\pi$
$860$	31.1308	−	10.6366i	1.06155	−	0.362704i
$861$			0.0192545i			0.000656192i
$862$	3.03461	+	18.2673i	0.103359	+	0.622188i
$863$	−50.5935			−1.72222			−0.861111	−	0.508417i	$-0.830231\pi$
$863$	−50.5935			−1.72222			−0.861111	+	0.508417i	$0.830231\pi$
$864$	3.84641	−	4.14791i	0.130857	−	0.141115i
$865$	34.5783			1.17570
$866$	−2.30630	−	13.8831i	−0.0783713	−	0.471769i
$867$			13.2892i			0.451326i
$868$	−15.9184	+	5.43890i	−0.540306	+	0.184608i
$869$		−	14.1405i		−	0.479683i
$870$	−37.1806	+	6.17652i	−1.26054	+	0.209404i
$871$	−13.2101			−0.447609
$872$	−13.6220	+	7.33344i	−0.461299	+	0.248342i
$873$	5.80642			0.196518
$874$	2.13280	−	0.354305i	0.0721430	−	0.0119846i
$875$			4.91902i			0.166293i
$876$	2.62269	+	7.67602i	0.0886125	+	0.259349i
$877$		−	21.3371i		−	0.720504i	−0.932855	−	0.360252i	$-0.882691\pi$
$877$		−	21.3371i		−	0.720504i	0.932855	−	0.360252i	$-0.117309\pi$
$878$	1.14707	+	6.90498i	0.0387118	+	0.233032i
$879$	−5.85220			−0.197390
$880$	8.40488	−	6.50256i	0.283328	−	0.219201i
$881$	−13.4223			−0.452209			−0.226105	−	0.974103i	$-0.572599\pi$
$881$	−13.4223			−0.452209			−0.226105	+	0.974103i	$0.572599\pi$
$882$	1.43863	+	8.66009i	0.0484413	+	0.291600i
$883$			2.12861i			0.0716333i	0.999358	+	0.0358167i	$0.0114032\pi$
$883$			2.12861i			0.0716333i	−0.999358	+	0.0358167i	$0.988597\pi$
$884$	19.5194	+	57.1288i	0.656508	+	1.92145i
$885$		−	34.1580i		−	1.14821i
$886$	−9.11112	+	1.51356i	−0.306094	+	0.0508490i
$887$	12.8400			0.431124			0.215562	−	0.976490i	$-0.430842\pi$
$887$	12.8400			0.431124			0.215562	+	0.976490i	$0.430842\pi$
$888$	−5.74529	−	10.6720i	−0.192799	−	0.358128i
$889$	1.64229			0.0550806
$890$	−54.0053	+	8.97149i	−1.81026	+	0.300725i
$891$		−	0.936187i		−	0.0313634i
$892$	−5.57326	+	1.90424i	−0.186607	+	0.0637586i
$893$		−	5.95732i		−	0.199354i
$894$	1.40503	+	8.45779i	0.0469911	+	0.282871i
$895$	16.9220			0.565642
$896$	−9.20253	−	4.09266i	−0.307435	−	0.136726i
$897$	5.48475			0.183131
$898$	9.39115	+	56.5315i	0.313387	+	1.88648i
$899$		−	88.7346i		−	2.95946i
$900$	−5.77764	+	1.97407i	−0.192588	+	0.0658022i
$901$		−	14.2120i		−	0.473469i
$902$	0.0282493	−	0.00469283i	0.000940598	−	0.000156254i
$903$	−5.16006			−0.171716
$904$	0.0465952	+	0.0865515i	0.00154973	+	0.00287866i
$905$	24.6844			0.820536
$906$	−25.3410	+	4.20970i	−0.841898	+	0.139858i
$907$		−	7.04110i		−	0.233796i	−0.993144	−	0.116898i	$-0.962705\pi$
$907$		−	7.04110i		−	0.233796i	0.993144	−	0.116898i	$-0.0372951\pi$
$908$	15.7801	+	46.1846i	0.523680	+	1.53269i
$909$		−	10.7961i		−	0.358084i
$910$	−3.21110	−	19.3297i	−0.106447	−	0.640774i
$911$	14.3418			0.475164			0.237582	−	0.971368i	$-0.423645\pi$
$911$	14.3418			0.475164			0.237582	+	0.971368i	$0.423645\pi$
$912$	−4.83662	+	3.74193i	−0.160157	+	0.123908i
$913$	3.67921			0.121764
$914$	−3.58621	−	21.5878i	−0.118621	−	0.714061i
$915$		−	34.8999i		−	1.15376i
$916$	−15.2370	−	44.5952i	−0.503445	−	1.47347i
$917$			14.6653i			0.484292i
$918$	−7.67799	+	1.27549i	−0.253412	+	0.0420973i
$919$	0.825271			0.0272232			0.0136116	−	0.999907i	$-0.495667\pi$
$919$	0.825271			0.0272232			0.0136116	+	0.999907i	$0.495667\pi$
$920$	−7.06729	+	3.80469i	−0.233002	+	0.125437i
$921$	32.1986			1.06098
$922$	22.0116	−	3.65662i	0.724915	−	0.120425i
$923$			10.2803i			0.338380i
$924$	−1.57728	+	0.538914i	−0.0518887	+	0.0177290i
$925$			13.0816i			0.430122i
$926$	3.84756	+	23.1610i	0.126439	+	0.761119i
$927$	−6.35902			−0.208858
$928$	36.1239	−	38.9555i	1.18582	−	1.27878i
$929$	−43.5415			−1.42855			−0.714274	−	0.699866i	$-0.753243\pi$
$929$	−43.5415			−1.42855			−0.714274	+	0.699866i	$0.753243\pi$
$930$	−6.21382	−	37.4051i	−0.203759	−	1.22656i
$931$		−	9.48997i		−	0.311021i
$932$	−19.7625	+	6.75231i	−0.647341	+	0.221179i
$933$			12.4786i			0.408529i
$934$	−34.8613	+	5.79124i	−1.14070	+	0.189495i
$935$	−14.6211			−0.478161
$936$	−13.6596	+	7.35366i	−0.446477	+	0.240362i
$937$	−49.8125			−1.62730			−0.813652	−	0.581352i	$-0.802524\pi$
$937$	−49.8125			−1.62730			−0.813652	+	0.581352i	$0.802524\pi$
$938$	−2.99120	+	0.496906i	−0.0976663	+	0.0162245i
$939$			26.4482i			0.863103i
$940$	7.15061	+	20.9282i	0.233227	+	0.682603i
$941$			27.1784i			0.885991i	0.896524	+	0.442995i	$0.146084\pi$
$941$			27.1784i			0.885991i	−0.896524	+	0.442995i	$0.853916\pi$
$942$	−5.33655	−	32.1243i	−0.173874	−	1.04666i
$943$	−0.0216292			−0.000704344
$944$	29.4624	+	38.0816i	0.958920	+	1.23945i
$945$	2.52618			0.0821768
$946$	1.25764	+	7.57058i	0.0408895	+	0.246141i
$947$		−	10.3189i		−	0.335319i	−0.985845	−	0.167660i	$-0.946379\pi$
$947$		−	10.3189i		−	0.335319i	0.985845	−	0.167660i	$-0.0536209\pi$
$948$	−9.76712	−	28.5861i	−0.317221	−	0.928434i
$949$		−	22.2453i		−	0.722114i
$950$	6.51098	−	1.08162i	0.211244	−	0.0350924i
$951$	29.2653			0.948991
$952$	6.56875	+	12.2016i	0.212894	+	0.395455i
$953$	39.9454			1.29396			0.646980	−	0.762507i	$-0.276032\pi$
$953$	39.9454			1.29396			0.646980	+	0.762507i	$0.276032\pi$
$954$	3.60258	−	0.598468i	0.116638	−	0.0193761i
$955$			57.7252i			1.86794i
$956$	−34.4343	+	11.7653i	−1.11368	+	0.380517i
$957$		−	8.79228i		−	0.284214i
$958$	−8.35818	−	50.3134i	−0.270040	−	1.62555i
$959$	−18.5492			−0.598985
$960$	12.4997	−	18.9509i	0.403426	−	0.611637i
$961$	58.2704			1.87969
$962$	5.44696	+	32.7888i	0.175617	+	1.05715i
$963$			1.81592i			0.0585173i
$964$	28.1114	−	9.60492i	0.905407	−	0.309354i
$965$			2.17213i			0.0699233i
$966$	1.24193	−	0.206311i	0.0399583	−	0.00663796i
$967$	−13.3341			−0.428795			−0.214397	−	0.976746i	$-0.568779\pi$
$967$	−13.3341			−0.428795			−0.214397	+	0.976746i	$0.568779\pi$
$968$	−13.5731	−	25.2123i	−0.436256	−	0.810355i
$969$	8.41376			0.270289
$970$	22.9872	−	3.81868i	0.738073	−	0.122610i
$971$			11.5973i			0.372176i	0.982533	+	0.186088i	$0.0595809\pi$
$971$			11.5973i			0.372176i	−0.982533	+	0.186088i	$0.940419\pi$
$972$	−0.646644	−	1.89258i	−0.0207411	−	0.0607045i
$973$		−	9.70391i		−	0.311093i
$974$	6.60650	+	39.7689i	0.211686	+	1.27428i
$975$	16.7438			0.536230
$976$	30.1023	+	38.9087i	0.963552	+	1.24544i
$977$	40.0070			1.27994			0.639968	−	0.768402i	$-0.278948\pi$
$977$	40.0070			1.27994			0.639968	+	0.768402i	$0.278948\pi$
$978$	3.48873	+	21.0010i	0.111557	+	0.671538i
$979$		−	12.7709i		−	0.408161i
$980$	11.3909	+	33.3385i	0.363868	+	1.06496i
$981$			5.46967i			0.174633i
$982$	34.9012	−	5.79786i	1.11374	−	0.185017i
$983$	54.9873			1.75382			0.876911	−	0.480653i	$-0.159600\pi$
$983$	54.9873			1.75382			0.876911	+	0.480653i	$0.159600\pi$
$984$	0.0538667	−	0.0289993i	0.00171721	−	0.000924463i
$985$	6.75222			0.215144
$986$	−72.1086	+	11.9788i	−2.29640	+	0.381484i
$987$		−	3.46894i		−	0.110418i
$988$	15.8693	−	5.42211i	0.504869	−	0.172500i
$989$		−	5.79646i		−	0.184317i
$990$	−0.615697	−	3.70629i	−0.0195681	−	0.117794i
$991$	24.7623			0.786599			0.393300	−	0.919410i	$-0.371334\pi$
$991$	24.7623			0.786599			0.393300	+	0.919410i	$0.371334\pi$
$992$	39.1907	+	36.3420i	1.24431	+	1.15386i
$993$	−20.2766			−0.643458
$994$	0.386698	+	2.32779i	0.0122653	+	0.0738331i
$995$		−	18.9479i		−	0.600688i
$996$	7.43781	−	2.54130i	0.235676	−	0.0805243i
$997$		−	26.0855i		−	0.826135i	−0.910700	−	0.413068i	$-0.864457\pi$
$997$		−	26.0855i		−	0.826135i	0.910700	−	0.413068i	$-0.135543\pi$
$998$	48.8683	−	8.11812i	1.54690	−	0.256975i
$999$	−4.28514			−0.135576

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.f.c.277.10	yes	18
4.3	odd	2		2208.2.f.c.1105.8		18
8.3	odd	2		2208.2.f.c.1105.11		18
8.5	even	2	inner	552.2.f.c.277.9	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.f.c.277.9	✓	18	8.5	even	2	inner
552.2.f.c.277.10	yes	18	1.1	even	1	trivial
2208.2.f.c.1105.8		18	4.3	odd	2
2208.2.f.c.1105.11		18	8.3	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.231756 + 1.39509i) q^{2} +1.00000i q^{3} +(-1.89258 + 0.646644i) q^{4} +2.83774i q^{5} +(-1.39509 + 0.231756i) q^{6} +0.890209 q^{7} +(-1.34075 - 2.49046i) q^{8} -1.00000 q^{9} +(-3.95892 + 0.657665i) q^{10} -0.936187i q^{11} +(-0.646644 - 1.89258i) q^{12} +5.48475i q^{13} +(0.206311 + 1.24193i) q^{14} -2.83774 q^{15} +(3.16370 - 2.44765i) q^{16} -5.50356 q^{17} +(-0.231756 - 1.39509i) q^{18} +1.52878i q^{19} +(-1.83501 - 5.37065i) q^{20} +0.890209i q^{21} +(1.30607 - 0.216967i) q^{22} -1.00000 q^{23} +(2.49046 - 1.34075i) q^{24} -3.05279 q^{25} +(-7.65175 + 1.27113i) q^{26} -1.00000i q^{27} +(-1.68479 + 0.575648i) q^{28} -9.39159i q^{29} +(-0.657665 - 3.95892i) q^{30} +9.44830 q^{31} +(4.14791 + 3.84641i) q^{32} +0.936187 q^{33} +(-1.27549 - 7.67799i) q^{34} +2.52618i q^{35} +(1.89258 - 0.646644i) q^{36} -4.28514i q^{37} +(-2.13280 + 0.354305i) q^{38} -5.48475 q^{39} +(7.06729 - 3.80469i) q^{40} +0.0216292 q^{41} +(-1.24193 + 0.206311i) q^{42} +5.79646i q^{43} +(0.605380 + 1.77181i) q^{44} -2.83774i q^{45} +(-0.231756 - 1.39509i) q^{46} -3.89677 q^{47} +(2.44765 + 3.16370i) q^{48} -6.20753 q^{49} +(-0.707503 - 4.25893i) q^{50} -5.50356i q^{51} +(-3.54668 - 10.3803i) q^{52} +2.58232i q^{53} +(1.39509 - 0.231756i) q^{54} +2.65666 q^{55} +(-1.19354 - 2.21703i) q^{56} -1.52878 q^{57} +(13.1022 - 2.17656i) q^{58} +12.0370i q^{59} +(5.37065 - 1.83501i) q^{60} +12.2985i q^{61} +(2.18970 + 13.1813i) q^{62} -0.890209 q^{63} +(-4.40480 + 6.67815i) q^{64} -15.5643 q^{65} +(0.216967 + 1.30607i) q^{66} +2.40852i q^{67} +(10.4159 - 3.55885i) q^{68} -1.00000i q^{69} +(-3.52427 + 0.585459i) q^{70} +1.87434 q^{71} +(1.34075 + 2.49046i) q^{72} -4.05585 q^{73} +(5.97818 - 0.993109i) q^{74} -3.05279i q^{75} +(-0.988579 - 2.89334i) q^{76} -0.833402i q^{77} +(-1.27113 - 7.65175i) q^{78} +15.1043 q^{79} +(6.94580 + 8.97778i) q^{80} +1.00000 q^{81} +(0.00501271 + 0.0301748i) q^{82} +3.92999i q^{83} +(-0.575648 - 1.68479i) q^{84} -15.6177i q^{85} +(-8.08662 + 1.34337i) q^{86} +9.39159 q^{87} +(-2.33154 + 1.25519i) q^{88} +13.6414 q^{89} +(3.95892 - 0.657665i) q^{90} +4.88258i q^{91} +(1.89258 - 0.646644i) q^{92} +9.44830i q^{93} +(-0.903101 - 5.43636i) q^{94} -4.33830 q^{95} +(-3.84641 + 4.14791i) q^{96} -5.80642 q^{97} +(-1.43863 - 8.66009i) q^{98} +0.936187i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 8 q^{4} + 8 q^{7} - 6 q^{8} - 18 q^{9} + 12 q^{10} - 4 q^{12} - 14 q^{14} + 8 q^{15} + 12 q^{16} - 8 q^{17} - 16 q^{20} - 30 q^{22} - 18 q^{23} + 6 q^{24} - 22 q^{25} + 8 q^{26} - 2 q^{28} + 4 q^{30}+ \cdots - 48 q^{98}+O(q^{100}) \) 18 * q - 8 * q^4 + 8 * q^7 - 6 * q^8 - 18 * q^9 + 12 * q^10 - 4 * q^12 - 14 * q^14 + 8 * q^15 + 12 * q^16 - 8 * q^17 - 16 * q^20 - 30 * q^22 - 18 * q^23 + 6 * q^24 - 22 * q^25 + 8 * q^26 - 2 * q^28 + 4 * q^30 - 44 * q^31 + 10 * q^32 - 24 * q^33 + 18 * q^34 + 8 * q^36 - 20 * q^38 - 8 * q^39 + 40 * q^40 + 28 * q^41 + 6 * q^42 - 26 * q^44 + 42 * q^49 + 60 * q^50 - 36 * q^52 + 40 * q^55 - 2 * q^56 + 12 * q^57 + 52 * q^58 + 16 * q^60 + 24 * q^62 - 8 * q^63 + 16 * q^64 - 104 * q^65 + 2 * q^66 + 54 * q^68 - 48 * q^70 - 24 * q^71 + 6 * q^72 + 12 * q^73 - 22 * q^74 - 4 * q^78 + 8 * q^79 - 32 * q^80 + 18 * q^81 - 20 * q^82 + 34 * q^84 + 12 * q^87 + 10 * q^88 + 24 * q^89 - 12 * q^90 + 8 * q^92 - 56 * q^94 - 16 * q^95 - 30 * q^96 + 12 * q^97 - 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more