LMFDB - Embedded newform 552.2.f.c.277.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(277,552)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.231756 - 1.39509i) q^{2} -1.00000i q^{3} +(-1.89258 - 0.646644i) q^{4} -2.83774i q^{5} +(-1.39509 - 0.231756i) q^{6} +0.890209 q^{7} +(-1.34075 + 2.49046i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 18 * q - 8 * q^4 + 8 * q^7 - 6 * q^8 - 18 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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	$-0.781190\pi$
$5$		−	2.83774i		−	1.26908i	0.772891	−	0.634539i	$-0.218810\pi$
$6$	−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	$0.0450753\pi$
$11$			0.936187i			0.282271i	−0.989990	+	0.141136i	$0.954925\pi$
$12$	−0.646644	+	1.89258i	−0.186670	+	0.546340i
$13$		−	5.48475i		−	1.52120i	−0.649223	−	0.760598i	$-0.724906\pi$
$13$		−	5.48475i		−	1.52120i	0.649223	−	0.760598i	$-0.275094\pi$
$14$	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	$-0.943890\pi$
$19$		−	1.52878i		−	0.350727i	0.984504	−	0.175364i	$-0.0561101\pi$
$20$	−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	$0.337169\pi$
$29$			9.39159i			1.74397i	−0.489529	+	0.871987i	$0.662831\pi$
$30$	−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	$0.114579\pi$
$37$			4.28514i			0.704473i	−0.935911	+	0.352237i	$0.885421\pi$
$38$	−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	$-0.854278\pi$
$43$		−	5.79646i		−	0.883952i	0.897027	−	0.441976i	$-0.145722\pi$
$44$	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	$-0.943246\pi$
$53$		−	2.58232i		−	0.354709i	0.984147	−	0.177354i	$-0.0567539\pi$
$54$	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	$-0.713410\pi$
$59$		−	12.0370i		−	1.56709i	0.621336	−	0.783544i	$-0.286590\pi$
$60$	5.37065	+	1.83501i	0.693348	+	0.236899i
$61$		−	12.2985i		−	1.57466i	−0.616533	−	0.787329i	$-0.711463\pi$
$61$		−	12.2985i		−	1.57466i	0.616533	−	0.787329i	$-0.288537\pi$
$62$	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	$-0.952998\pi$
$67$		−	2.40852i		−	0.294248i	0.989118	−	0.147124i	$-0.0470016\pi$
$68$	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	$-0.930801\pi$
$83$		−	3.92999i		−	0.431373i	0.976463	−	0.215686i	$-0.0691988\pi$
$84$	−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	$-0.819510\pi$
$101$		−	10.7961i		−	1.07425i	0.843502	−	0.537126i	$-0.180490\pi$
$102$	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	$0.0279760\pi$
$107$			1.81592i			0.175552i	−0.996140	+	0.0877760i	$0.972024\pi$
$108$	0.646644	−	1.89258i	0.0622233	−	0.182113i
$109$			5.46967i			0.523899i	0.965082	+	0.261950i	$0.0843654\pi$
$109$			5.46967i			0.523899i	−0.965082	+	0.261950i	$0.915635\pi$
$110$	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	$-0.744292\pi$
$131$		−	16.4740i		−	1.43934i	0.694314	−	0.719672i	$-0.255708\pi$
$132$	−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	$0.152973\pi$
$139$			10.9007i			0.924586i	−0.886727	+	0.462293i	$0.847027\pi$
$140$	−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	$0.0798819\pi$
$149$			6.06252i			0.496661i	−0.968675	+	0.248331i	$0.920118\pi$
$150$	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	$-0.629111\pi$
$157$		−	23.0266i		−	1.83772i	0.394583	−	0.918860i	$-0.370889\pi$
$158$	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	$0.200691\pi$
$163$			15.0535i			1.17908i	−0.807740	+	0.589539i	$0.799309\pi$
$164$	−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	$0.153302\pi$
$173$			12.1852i			0.926420i	−0.886249	+	0.463210i	$0.846698\pi$
$174$	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	$0.0715378\pi$
$179$			5.96321i			0.445711i	−0.974851	+	0.222855i	$0.928462\pi$
$180$	1.83501	−	5.37065i	0.136774	−	0.400305i
$181$			8.69859i			0.646561i	0.946303	+	0.323281i	$0.104786\pi$
$181$			8.69859i			0.646561i	−0.946303	+	0.323281i	$0.895214\pi$
$182$	−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	$0.0270136\pi$
$197$			2.37943i			0.169528i	−0.996401	+	0.0847638i	$0.972986\pi$
$198$	−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	$0.215367\pi$
$211$			18.1905i			1.25229i	−0.779708	+	0.626143i	$0.784633\pi$
$212$	−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	$0.300448\pi$
$227$			24.4030i			1.61969i	−0.586647	+	0.809843i	$0.699552\pi$
$228$	2.89334	+	0.988579i	0.191616	+	0.0654702i
$229$		−	23.5632i		−	1.55710i	−0.627581	−	0.778551i	$-0.715955\pi$
$229$		−	23.5632i		−	1.55710i	0.627581	−	0.778551i	$-0.284045\pi$
$230$	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	$0.0710339\pi$
$251$			7.01248i			0.442624i	−0.975203	+	0.221312i	$0.928966\pi$
$252$	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	$0.171419\pi$
$269$			16.8235i			1.02575i	−0.858464	+	0.512874i	$0.828581\pi$
$270$	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	$-0.818378\pi$
$277$		−	17.9789i		−	1.08025i	0.841586	−	0.540123i	$-0.181622\pi$
$278$	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	$-0.969818\pi$
$283$		−	3.18546i		−	0.189356i	0.995508	−	0.0946778i	$-0.0301821\pi$
$284$	−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	$-0.945318\pi$
$293$		−	5.85220i		−	0.341889i	0.985281	−	0.170945i	$-0.0546819\pi$
$294$	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	$0.370870\pi$
$307$			32.1986i			1.83767i	−0.394639	+	0.918836i	$0.629130\pi$
$308$	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	$0.307058\pi$
$317$			29.2653i			1.64370i	−0.569703	+	0.821851i	$0.692942\pi$
$318$	−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	$-0.811856\pi$
$331$		−	20.2766i		−	1.11450i	0.830344	−	0.557251i	$-0.188144\pi$
$332$	−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	$-0.833038\pi$
$347$		−	18.6578i		−	1.00160i	0.865562	−	0.500802i	$-0.166962\pi$
$348$	−17.7743	−	6.07301i	−0.952803	−	0.325548i
$349$			17.2080i			0.921122i	0.887628	+	0.460561i	$0.152352\pi$
$349$			17.2080i			0.921122i	−0.887628	+	0.460561i	$0.847648\pi$
$350$	−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	$0.178688\pi$
$373$			20.5625i			1.06468i	−0.846529	+	0.532342i	$0.821312\pi$
$374$	−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	$-0.940093\pi$
$379$		−	7.28469i		−	0.374189i	0.982342	−	0.187095i	$-0.0599071\pi$
$380$	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	$-0.901281\pi$
$389$		−	12.0384i		−	0.610373i	0.952293	−	0.305187i	$-0.0987188\pi$
$390$	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	$0.140844\pi$
$397$			17.0627i			0.856352i	−0.903695	+	0.428176i	$0.859156\pi$
$398$	−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	$0.303093\pi$
$419$			33.3526i			1.62938i	−0.579897	+	0.814690i	$0.696907\pi$
$420$	4.78100	+	1.63354i	0.233289	+	0.0797087i
$421$		−	5.61450i		−	0.273634i	−0.990596	−	0.136817i	$-0.956313\pi$
$421$		−	5.61450i		−	0.273634i	0.990596	−	0.136817i	$-0.0436872\pi$
$422$	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	$-0.950416\pi$
$443$		−	6.53082i		−	0.310289i	0.987892	−	0.155144i	$-0.0495843\pi$
$444$	−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	$0.119760\pi$
$461$			15.7779i			0.734850i	−0.930053	+	0.367425i	$0.880240\pi$
$462$	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	$-0.803769\pi$
$467$		−	24.9885i		−	1.15633i	0.815920	−	0.578165i	$-0.196231\pi$
$468$	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	$0.190932\pi$
$491$			25.0171i			1.12900i	−0.825432	+	0.564502i	$0.809068\pi$
$492$	−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	$0.286849\pi$
$499$			35.0287i			1.56810i	−0.620698	+	0.784050i	$0.713151\pi$
$500$	−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	$0.0494146\pi$
$509$			6.97668i			0.309236i	−0.987974	+	0.154618i	$0.950585\pi$
$510$	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	$-0.920066\pi$
$523$		−	11.3654i		−	0.496975i	0.968635	−	0.248488i	$-0.0799335\pi$
$524$	−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	$-0.981745\pi$
$541$		−	2.66640i		−	0.114637i	0.998356	−	0.0573187i	$-0.0182551\pi$
$542$	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	$-0.918314\pi$
$547$		−	11.8725i		−	0.507632i	0.967253	−	0.253816i	$-0.0816858\pi$
$548$	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	$-0.593452\pi$
$557$		−	45.1820i		−	1.91442i	0.289387	−	0.957212i	$-0.406548\pi$
$558$	−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	$-0.922055\pi$
$563$		−	11.5047i		−	0.484865i	0.970168	−	0.242432i	$-0.0779453\pi$
$564$	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	$-0.905988\pi$
$571$		−	13.9107i		−	0.582145i	0.956701	−	0.291073i	$-0.0940121\pi$
$572$	−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	$-0.782808\pi$
$587$		−	30.5566i		−	1.26121i	0.776106	−	0.630603i	$-0.217192\pi$
$588$	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	$-0.899406\pi$
$613$		−	15.3897i		−	0.621585i	0.950478	−	0.310792i	$-0.100594\pi$
$614$	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	$0.371096\pi$
$619$			45.7347i			1.83823i	−0.393986	+	0.919116i	$0.628904\pi$
$620$	−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	$0.0175546\pi$
$643$			2.79547i			0.110243i	−0.998480	+	0.0551213i	$0.982445\pi$
$644$	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	$-0.901596\pi$
$653$		−	15.5492i		−	0.608489i	0.952594	−	0.304244i	$-0.0984039\pi$
$654$	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	$0.205690\pi$
$659$			30.9157i			1.20430i	−0.798382	+	0.602151i	$0.794310\pi$
$660$	−1.71791	+	5.02793i	−0.0668696	+	0.195712i
$661$		−	16.5944i		−	0.645448i	−0.946493	−	0.322724i	$-0.895401\pi$
$661$		−	16.5944i		−	0.645448i	0.946493	−	0.322724i	$-0.104599\pi$
$662$	−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	$-0.851634\pi$
$677$		−	23.3867i		−	0.898822i	0.893325	−	0.449411i	$-0.148366\pi$
$678$	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	$-0.904035\pi$
$683$		−	15.5204i		−	0.593872i	0.954897	−	0.296936i	$-0.0959648\pi$
$684$	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	$0.196582\pi$
$691$			30.4436i			1.15813i	−0.815282	+	0.579064i	$0.803418\pi$
$692$	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	$0.157364\pi$
$701$			25.1251i			0.948963i	−0.880266	+	0.474481i	$0.842636\pi$
$702$	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	$-0.754787\pi$
$709$		−	37.0858i		−	1.39279i	0.717660	−	0.696393i	$-0.245213\pi$
$710$	−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	$0.0129721\pi$
$733$			2.20609i			0.0814837i	−0.999170	+	0.0407419i	$0.987028\pi$
$734$	−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	$0.160439\pi$
$739$			26.2583i			0.965926i	−0.875641	+	0.482963i	$0.839561\pi$
$740$	−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	$0.264738\pi$
$757$			40.6694i			1.47815i	−0.673621	+	0.739077i	$0.735262\pi$
$758$	−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	$-0.878333\pi$
$773$		−	20.7404i		−	0.745980i	0.927835	−	0.372990i	$-0.121667\pi$
$774$	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	$0.389021\pi$
$787$			52.7313i			1.87967i	−0.341631	+	0.939834i	$0.610979\pi$
$788$	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	$-0.931494\pi$
$797$		−	12.0581i		−	0.427120i	0.976930	−	0.213560i	$-0.0685059\pi$
$798$	−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	$-0.778840\pi$
$811$		−	36.4649i		−	1.28046i	0.768185	−	0.640228i	$-0.221160\pi$
$812$	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	$-0.874927\pi$
$821$		−	21.9423i		−	0.765791i	0.923792	−	0.382895i	$-0.125073\pi$
$822$	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	$-0.870581\pi$
$827$		−	22.7457i		−	0.790945i	0.918478	−	0.395473i	$-0.129419\pi$
$828$	−1.89258	−	0.646644i	−0.0657716	−	0.0224724i
$829$			3.40930i			0.118410i	0.998246	+	0.0592050i	$0.0188566\pi$
$829$			3.40930i			0.118410i	−0.998246	+	0.0592050i	$0.981143\pi$
$830$	−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	$0.175934\pi$
$853$			30.6663i			1.04999i	−0.851104	+	0.524997i	$0.824066\pi$
$854$	−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	$-0.772130\pi$
$859$		−	38.4693i		−	1.31256i	0.754519	−	0.656278i	$-0.227870\pi$
$860$	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	$0.117309\pi$
$877$			21.3371i			0.720504i	−0.932855	+	0.360252i	$0.882691\pi$
$878$	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	$-0.988597\pi$
$883$		−	2.12861i		−	0.0716333i	0.999358	−	0.0358167i	$-0.0114032\pi$
$884$	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	$0.0372951\pi$
$907$			7.04110i			0.233796i	−0.993144	+	0.116898i	$0.962705\pi$
$908$	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	$-0.853916\pi$
$941$		−	27.1784i		−	0.885991i	0.896524	−	0.442995i	$-0.146084\pi$
$942$	−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	$0.0536209\pi$
$947$			10.3189i			0.335319i	−0.985845	+	0.167660i	$0.946379\pi$
$948$	−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	$-0.940419\pi$
$971$		−	11.5973i		−	0.372176i	0.982533	−	0.186088i	$-0.0595809\pi$
$972$	−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	$0.135543\pi$
$997$			26.0855i			0.826135i	−0.910700	+	0.413068i	$0.864457\pi$
$998$	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.277.9	✓	18
4.3	odd	2		2208.2.f.c.1105.11		18
8.3	odd	2		2208.2.f.c.1105.8		18
8.5	even	2	inner	552.2.f.c.277.10	yes	18

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

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

\(f(q)\)	\(=\)	\(q+(0.231756 - 1.39509i) q^{2} -1.00000i q^{3} +(-1.89258 - 0.646644i) q^{4} -2.83774i q^{5} +(-1.39509 - 0.231756i) q^{6} +0.890209 q^{7} +(-1.34075 + 2.49046i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 8 q^{4} + 8 q^{7} - 6 q^{8} - 18 q^{9}+O(q^{10}) \) 18 * q - 8 * q^4 + 8 * q^7 - 6 * q^8 - 18 * q^9	\( 18 q - 8 q^{4} + 8 q^{7} - 6 q^{8} - 18 q^{9} + 12 q^{10} - 4 q^{12} - 14 q^{14} + 8 q^{15} + 12 q^{16} - 8 q^{17} - 16 q^{20} - 30 q^{22} - 18 q^{23} + 6 q^{24} - 22 q^{25} + 8 q^{26} - 2 q^{28} + 4 q^{30} - 44 q^{31} + 10 q^{32} - 24 q^{33} + 18 q^{34} + 8 q^{36} - 20 q^{38} - 8 q^{39} + 40 q^{40} + 28 q^{41} + 6 q^{42} - 26 q^{44} + 42 q^{49} + 60 q^{50} - 36 q^{52} + 40 q^{55} - 2 q^{56} + 12 q^{57} + 52 q^{58} + 16 q^{60} + 24 q^{62} - 8 q^{63} + 16 q^{64} - 104 q^{65} + 2 q^{66} + 54 q^{68} - 48 q^{70} - 24 q^{71} + 6 q^{72} + 12 q^{73} - 22 q^{74} - 4 q^{78} + 8 q^{79} - 32 q^{80} + 18 q^{81} - 20 q^{82} + 34 q^{84} + 12 q^{87} + 10 q^{88} + 24 q^{89} - 12 q^{90} + 8 q^{92} - 56 q^{94} - 16 q^{95} - 30 q^{96} + 12 q^{97} - 48 q^{98}+O(q^{100}) \) 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