LMFDB - Embedded newform 441.2.h.b.373.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(214,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("441.214");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			373.1
Root			$0.500000 + 2.05195i$ of defining polynomial
Character	$\chi$	$=$	441.373
Dual form			441.2.h.b.214.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.46050 q^{2} +(-0.796790 - 1.53790i) q^{3} +4.05408 q^{4} +(-1.29679 - 2.24611i) q^{5} +(1.96050 + 3.78400i) q^{6} -5.05408 q^{8} +(-1.73025 + 2.45076i) q^{9} +O(q^{10})$	\(q-2.46050 q^{2} +(-0.796790 - 1.53790i) q^{3} +4.05408 q^{4} +(-1.29679 - 2.24611i) q^{5} +(1.96050 + 3.78400i) q^{6} -5.05408 q^{8} +(-1.73025 + 2.45076i) q^{9} +(3.19076 + 5.52655i) q^{10} +(-2.25729 + 3.90975i) q^{11} +(-3.23025 - 6.23476i) q^{12} +(0.500000 - 0.866025i) q^{13} +(-2.42101 + 3.78400i) q^{15} +4.32743 q^{16} +(-0.472958 - 0.819187i) q^{17} +(4.25729 - 6.03011i) q^{18} +(-2.02704 + 3.51094i) q^{19} +(-5.25729 - 9.10590i) q^{20} +(5.55408 - 9.61996i) q^{22} +(0.136673 + 0.236725i) q^{23} +(4.02704 + 7.77266i) q^{24} +(-0.863327 + 1.49533i) q^{25} +(-1.23025 + 2.13086i) q^{26} +(5.14766 + 0.708209i) q^{27} +(-1.23025 - 2.13086i) q^{29} +(5.95691 - 9.31056i) q^{30} -2.32743 q^{31} -0.539495 q^{32} +(7.81138 + 0.356238i) q^{33} +(1.16372 + 2.01561i) q^{34} +(-7.01459 + 9.93559i) q^{36} +(-0.890369 + 1.54216i) q^{37} +(4.98755 - 8.63868i) q^{38} +(-1.73025 - 0.0789082i) q^{39} +(6.55408 + 11.3520i) q^{40} +(-3.20321 + 5.54812i) q^{41} +(5.21780 + 9.03749i) q^{43} +(-9.15126 + 15.8505i) q^{44} +(7.74844 + 0.708209i) q^{45} +(-0.336285 - 0.582462i) q^{46} +12.1623 q^{47} +(-3.44805 - 6.65514i) q^{48} +(2.12422 - 3.67926i) q^{50} +(-0.882977 + 1.38008i) q^{51} +(2.02704 - 3.51094i) q^{52} +(3.13667 + 5.43288i) q^{53} +(-12.6659 - 1.74255i) q^{54} +11.7089 q^{55} +(7.01459 + 0.319901i) q^{57} +(3.02704 + 5.24299i) q^{58} +2.72665 q^{59} +(-9.81498 + 15.3407i) q^{60} +2.27335 q^{61} +5.72665 q^{62} -7.32743 q^{64} -2.59358 q^{65} +(-19.2199 - 0.876526i) q^{66} -15.8171 q^{67} +(-1.91741 - 3.32105i) q^{68} +(0.255158 - 0.398809i) q^{69} +3.27335 q^{71} +(8.74484 - 12.3863i) q^{72} +(-0.753696 - 1.30544i) q^{73} +(2.19076 - 3.79450i) q^{74} +(2.98755 + 0.136247i) q^{75} +(-8.21780 + 14.2336i) q^{76} +(4.25729 + 0.194154i) q^{78} +14.7089 q^{79} +(-5.61177 - 9.71987i) q^{80} +(-3.01245 - 8.48087i) q^{81} +(7.88151 - 13.6512i) q^{82} +(-0.472958 - 0.819187i) q^{83} +(-1.22665 + 2.12463i) q^{85} +(-12.8384 - 22.2368i) q^{86} +(-2.29679 + 3.58985i) q^{87} +(11.4086 - 19.7602i) q^{88} +(-7.17830 + 12.4332i) q^{89} +(-19.0651 - 1.74255i) q^{90} +(0.554084 + 0.959702i) q^{92} +(1.85447 + 3.57935i) q^{93} -29.9253 q^{94} +10.5146 q^{95} +(0.429864 + 0.829688i) q^{96} +(-5.74484 - 9.95036i) q^{97} +(-5.67617 - 12.2969i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 2 q^{3} + 6 q^{4} - 5 q^{5} - q^{6} - 12 q^{8} - 4 q^{9}+O(q^{10}) $ 6 * q - 2 * q^2 - 2 * q^3 + 6 * q^4 - 5 * q^5 - q^6 - 12 * q^8 - 4 * q^9	$ 6 q - 2 q^{2} - 2 q^{3} + 6 q^{4} - 5 q^{5} - q^{6} - 12 q^{8} - 4 q^{9} + 2 q^{11} - 13 q^{12} + 3 q^{13} + 11 q^{15} + 6 q^{16} - 12 q^{17} + 10 q^{18} - 3 q^{19} - 16 q^{20} + 15 q^{22} + 15 q^{24} - 6 q^{25} - q^{26} + 7 q^{27} - q^{29} + 31 q^{30} + 6 q^{31} - 16 q^{32} + 13 q^{33} - 3 q^{34} - 11 q^{36} + 3 q^{37} + 8 q^{38} - 4 q^{39} + 21 q^{40} - 22 q^{41} + 3 q^{43} - 23 q^{44} + q^{45} - 12 q^{46} + 18 q^{47} + 14 q^{48} - 10 q^{50} - 12 q^{51} + 3 q^{52} + 18 q^{53} - 13 q^{54} + 12 q^{55} + 11 q^{57} + 9 q^{58} + 18 q^{59} - 17 q^{60} + 12 q^{61} + 36 q^{62} - 24 q^{64} - 10 q^{65} - 34 q^{66} + 6 q^{68} + 39 q^{69} + 18 q^{71} + 15 q^{72} + 3 q^{73} - 6 q^{74} - 4 q^{75} - 21 q^{76} + 10 q^{78} + 30 q^{79} + 11 q^{80} - 40 q^{81} + 9 q^{82} - 12 q^{83} - 9 q^{85} - 34 q^{86} - 11 q^{87} + 21 q^{88} - 2 q^{89} - 73 q^{90} - 15 q^{92} - 18 q^{93} - 48 q^{94} + 32 q^{95} + 7 q^{96} + 3 q^{97} - 46 q^{99}+O(q^{100}) $ 6 * q - 2 * q^2 - 2 * q^3 + 6 * q^4 - 5 * q^5 - q^6 - 12 * q^8 - 4 * q^9 + 2 * q^11 - 13 * q^12 + 3 * q^13 + 11 * q^15 + 6 * q^16 - 12 * q^17 + 10 * q^18 - 3 * q^19 - 16 * q^20 + 15 * q^22 + 15 * q^24 - 6 * q^25 - q^26 + 7 * q^27 - q^29 + 31 * q^30 + 6 * q^31 - 16 * q^32 + 13 * q^33 - 3 * q^34 - 11 * q^36 + 3 * q^37 + 8 * q^38 - 4 * q^39 + 21 * q^40 - 22 * q^41 + 3 * q^43 - 23 * q^44 + q^45 - 12 * q^46 + 18 * q^47 + 14 * q^48 - 10 * q^50 - 12 * q^51 + 3 * q^52 + 18 * q^53 - 13 * q^54 + 12 * q^55 + 11 * q^57 + 9 * q^58 + 18 * q^59 - 17 * q^60 + 12 * q^61 + 36 * q^62 - 24 * q^64 - 10 * q^65 - 34 * q^66 + 6 * q^68 + 39 * q^69 + 18 * q^71 + 15 * q^72 + 3 * q^73 - 6 * q^74 - 4 * q^75 - 21 * q^76 + 10 * q^78 + 30 * q^79 + 11 * q^80 - 40 * q^81 + 9 * q^82 - 12 * q^83 - 9 * q^85 - 34 * q^86 - 11 * q^87 + 21 * q^88 - 2 * q^89 - 73 * q^90 - 15 * q^92 - 18 * q^93 - 48 * q^94 + 32 * q^95 + 7 * q^96 + 3 * q^97 - 46 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−2.46050			−1.73984			−0.869920	−	0.493193i	$-0.835830\pi$
$2$	−2.46050			−1.73984			−0.869920	+	0.493193i	$0.835830\pi$
$3$	−0.796790	−	1.53790i	−0.460027	−	0.887905i
$3$	−0.796790	−	1.53790i	−0.460027	−	0.887905i
$4$	4.05408			2.02704
$5$	−1.29679	−	2.24611i	−0.579942	−	1.00449i	−0.995485	−	0.0949156i	$-0.969742\pi$
$5$	−1.29679	−	2.24611i	−0.579942	−	1.00449i	0.415543	−	0.909573i	$-0.363591\pi$
$6$	1.96050	+	3.78400i	0.800373	+	1.54481i
$7$		0			0
$7$		0			0
$8$	−5.05408			−1.78689
$9$	−1.73025	+	2.45076i	−0.576751	+	0.816920i
$10$	3.19076	+	5.52655i	1.00901	+	1.74765i
$11$	−2.25729	+	3.90975i	−0.680600	+	1.17883i	0.294198	+	0.955744i	$0.404947\pi$
$11$	−2.25729	+	3.90975i	−0.680600	+	1.17883i	−0.974798	+	0.223089i	$0.928386\pi$
$12$	−3.23025	−	6.23476i	−0.932494	−	1.79982i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i	−0.788320	−	0.615265i	$-0.789049\pi$
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i	0.926995	+	0.375073i	$0.122382\pi$
$14$		0			0
$15$	−2.42101	+	3.78400i	−0.625102	+	0.977025i
$16$	4.32743			1.08186
$17$	−0.472958	−	0.819187i	−0.114709	−	0.198682i	0.802954	−	0.596041i	$-0.203260\pi$
$17$	−0.472958	−	0.819187i	−0.114709	−	0.198682i	−0.917663	+	0.397359i	$0.869927\pi$
$18$	4.25729	−	6.03011i	1.00345	−	1.42131i
$19$	−2.02704	+	3.51094i	−0.465035	+	0.805465i	−0.999203	−	0.0399136i	$-0.987292\pi$
$19$	−2.02704	+	3.51094i	−0.465035	+	0.805465i	0.534168	+	0.845378i	$0.320625\pi$
$20$	−5.25729	−	9.10590i	−1.17557	−	2.03614i
$21$		0			0
$22$	5.55408	−	9.61996i	1.18413	−	2.05098i
$23$	0.136673	+	0.236725i	0.0284983	+	0.0493605i	0.879923	−	0.475117i	$-0.157594\pi$
$23$	0.136673	+	0.236725i	0.0284983	+	0.0493605i	−0.851425	+	0.524477i	$0.824261\pi$
$24$	4.02704	+	7.77266i	0.822017	+	1.58659i
$25$	−0.863327	+	1.49533i	−0.172665	+	0.299065i
$26$	−1.23025	+	2.13086i	−0.241272	+	0.417896i
$27$	5.14766	+	0.708209i	0.990668	+	0.136295i
$28$		0			0
$29$	−1.23025	−	2.13086i	−0.228452	−	0.395691i	0.728897	−	0.684623i	$-0.240033\pi$
$29$	−1.23025	−	2.13086i	−0.228452	−	0.395691i	−0.957350	+	0.288932i	$0.906700\pi$
$30$	5.95691	−	9.31056i	1.08758	−	1.69987i
$31$	−2.32743			−0.418019			−0.209009	−	0.977914i	$-0.567024\pi$
$31$	−2.32743			−0.418019			−0.209009	+	0.977914i	$0.567024\pi$
$32$	−0.539495			−0.0953702
$33$	7.81138	+	0.356238i	1.35979	+	0.0620131i
$34$	1.16372	+	2.01561i	0.199576	+	0.345675i
$35$		0			0
$36$	−7.01459	+	9.93559i	−1.16910	+	1.65593i
$37$	−0.890369	+	1.54216i	−0.146376	+	0.253530i	−0.929885	−	0.367849i	$-0.880094\pi$
$37$	−0.890369	+	1.54216i	−0.146376	+	0.253530i	0.783510	+	0.621380i	$0.213428\pi$
$38$	4.98755	−	8.63868i	0.809087	−	1.40138i
$39$	−1.73025	−	0.0789082i	−0.277062	−	0.0126354i
$40$	6.55408	+	11.3520i	1.03629	+	1.79491i
$41$	−3.20321	+	5.54812i	−0.500257	+	0.866471i	0.499743	+	0.866174i	$0.333428\pi$
$41$	−3.20321	+	5.54812i	−0.500257	+	0.866471i	−1.00000		0.000297253i	$0.999905\pi$
$42$		0			0
$43$	5.21780	+	9.03749i	0.795707	+	1.37820i	0.922389	+	0.386262i	$0.126234\pi$
$43$	5.21780	+	9.03749i	0.795707	+	1.37820i	−0.126682	+	0.991943i	$0.540433\pi$
$44$	−9.15126	+	15.8505i	−1.37960	+	2.38955i
$45$	7.74844	+	0.708209i	1.15507	+	0.105574i
$46$	−0.336285	−	0.582462i	−0.0495825	−	0.0858794i
$47$	12.1623			1.77405			0.887023	−	0.461724i	$-0.152769\pi$
$47$	12.1623			1.77405			0.887023	+	0.461724i	$0.152769\pi$
$48$	−3.44805	−	6.65514i	−0.497683	−	0.960587i
$49$		0			0
$50$	2.12422	−	3.67926i	0.300410	−	0.520326i
$51$	−0.882977	+	1.38008i	−0.123642	+	0.193250i
$52$	2.02704	−	3.51094i	0.281100	−	0.486880i
$53$	3.13667	+	5.43288i	0.430855	+	0.746263i	0.996947	−	0.0780790i	$-0.0248786\pi$
$53$	3.13667	+	5.43288i	0.430855	+	0.746263i	−0.566092	+	0.824342i	$0.691545\pi$
$54$	−12.6659	−	1.74255i	−1.72360	−	0.237131i
$55$	11.7089			1.57883
$56$		0			0
$57$	7.01459	+	0.319901i	0.929105	+	0.0423719i
$58$	3.02704	+	5.24299i	0.397470	+	0.688438i
$59$	2.72665			0.354980			0.177490	−	0.984123i	$-0.443202\pi$
$59$	2.72665			0.354980			0.177490	+	0.984123i	$0.443202\pi$
$60$	−9.81498	+	15.3407i	−1.26711	+	1.98047i
$61$	2.27335			0.291072			0.145536	−	0.989353i	$-0.453509\pi$
$61$	2.27335			0.291072			0.145536	+	0.989353i	$0.453509\pi$
$62$	5.72665			0.727286
$63$		0			0
$64$	−7.32743			−0.915929
$65$	−2.59358			−0.321694
$66$	−19.2199	−	0.876526i	−2.36581	−	0.107893i
$67$	−15.8171			−1.93237			−0.966184	−	0.257854i	$-0.916985\pi$
$67$	−15.8171			−1.93237			−0.966184	+	0.257854i	$0.916985\pi$
$68$	−1.91741	−	3.32105i	−0.232520	−	0.402737i
$69$	0.255158	−	0.398809i	0.0307175	−	0.0480110i
$70$		0			0
$71$	3.27335			0.388475			0.194237	−	0.980955i	$-0.437777\pi$
$71$	3.27335			0.388475			0.194237	+	0.980955i	$0.437777\pi$
$72$	8.74484	−	12.3863i	1.03059	−	1.45975i
$73$	−0.753696	−	1.30544i	−0.0882134	−	0.152790i	0.818543	−	0.574446i	$-0.194782\pi$
$73$	−0.753696	−	1.30544i	−0.0882134	−	0.152790i	−0.906756	+	0.421656i	$0.861449\pi$
$74$	2.19076	−	3.79450i	0.254670	−	0.441102i
$75$	2.98755	+	0.136247i	0.344972	+	0.0157325i
$76$	−8.21780	+	14.2336i	−0.942646	+	1.63271i
$77$		0			0
$78$	4.25729	+	0.194154i	0.482044	+	0.0219836i
$79$	14.7089			1.65489			0.827443	−	0.561550i	$-0.189795\pi$
$79$	14.7089			1.65489			0.827443	+	0.561550i	$0.189795\pi$
$80$	−5.61177	−	9.71987i	−0.627415	−	1.08671i
$81$	−3.01245	−	8.48087i	−0.334717	−	0.942319i
$82$	7.88151	−	13.6512i	0.870368	−	1.50752i
$83$	−0.472958	−	0.819187i	−0.0519139	−	0.0899175i	0.838901	−	0.544285i	$-0.183199\pi$
$83$	−0.472958	−	0.819187i	−0.0519139	−	0.0899175i	−0.890815	+	0.454367i	$0.849865\pi$
$84$		0			0
$85$	−1.22665	+	2.12463i	−0.133049	+	0.230448i
$86$	−12.8384	−	22.2368i	−1.38440	−	2.39786i
$87$	−2.29679	+	3.58985i	−0.246242	+	0.384872i
$88$	11.4086	−	19.7602i	1.21616	−	2.10644i
$89$	−7.17830	+	12.4332i	−0.760899	+	1.31792i	0.181489	+	0.983393i	$0.441908\pi$
$89$	−7.17830	+	12.4332i	−0.760899	+	1.31792i	−0.942388	+	0.334522i	$0.891425\pi$
$90$	−19.0651	−	1.74255i	−2.00964	−	0.183681i
$91$		0			0
$92$	0.554084	+	0.959702i	0.0577673	+	0.100056i
$93$	1.85447	+	3.57935i	0.192300	+	0.371161i
$94$	−29.9253			−3.08656
$95$	10.5146			1.07877
$96$	0.429864	+	0.829688i	0.0438728	+	0.0846797i
$97$	−5.74484	−	9.95036i	−0.583300	−	1.01031i	−0.995085	−	0.0990246i	$-0.968428\pi$
$97$	−5.74484	−	9.95036i	−0.583300	−	1.01031i	0.411785	−	0.911281i	$-0.364906\pi$
$98$		0			0
$99$	−5.67617	−	12.2969i	−0.570476	−	1.23589i
$100$	−3.50000	+	6.06218i	−0.350000	+	0.606218i
$101$	−1.83988	+	3.18677i	−0.183075	+	0.317096i	−0.942926	−	0.333002i	$-0.891939\pi$
$101$	−1.83988	+	3.18677i	−0.183075	+	0.317096i	0.759851	+	0.650097i	$0.225272\pi$
$102$	2.17257	−	3.39569i	0.215116	−	0.336224i
$103$	−4.86333	−	8.42353i	−0.479198	−	0.829995i	0.520518	−	0.853851i	$-0.325739\pi$
$103$	−4.86333	−	8.42353i	−0.479198	−	0.829995i	−0.999715	+	0.0238560i	$0.992406\pi$
$104$	−2.52704	+	4.37697i	−0.247797	+	0.429197i
$105$		0			0
$106$	−7.71780	−	13.3676i	−0.749619	−	1.29838i
$107$	0.687159	−	1.19019i	0.0664301	−	0.115060i	−0.830897	−	0.556426i	$-0.812172\pi$
$107$	0.687159	−	1.19019i	0.0664301	−	0.115060i	0.897327	+	0.441365i	$0.145506\pi$
$108$	20.8691	+	2.87114i	2.00813	+	0.276275i
$109$	1.69961	+	2.94381i	0.162793	+	0.281966i	0.935869	−	0.352347i	$-0.114616\pi$
$109$	1.69961	+	2.94381i	0.162793	+	0.281966i	−0.773076	+	0.634313i	$0.781283\pi$
$110$	−28.8099			−2.74692
$111$	3.08113	+	0.140515i	0.292448	+	0.0133371i
$112$		0			0
$113$	−5.19436	+	8.99689i	−0.488644	+	0.846356i	−0.999915	−	0.0130636i	$-0.995842\pi$
$113$	−5.19436	+	8.99689i	−0.488644	+	0.846356i	0.511271	+	0.859420i	$0.329175\pi$
$114$	−17.2594	−	0.787117i	−1.61649	−	0.0737203i
$115$	0.354473	−	0.613964i	0.0330547	−	0.0572525i
$116$	−4.98755	−	8.63868i	−0.463082	−	0.802082i
$117$	1.25729	+	2.72382i	0.116237	+	0.251818i
$118$	−6.70895			−0.617608
$119$		0			0
$120$	12.2360	−	19.1247i	1.11699	−	1.74584i
$121$	−4.69076	−	8.12463i	−0.426432	−	0.738603i
$122$	−5.59358			−0.506419
$123$	11.0847	+	0.505519i	0.999476	+	0.0455812i
$124$	−9.43560			−0.847342
$125$	−8.48968			−0.759340
$126$		0			0
$127$	0.672570			0.0596809			0.0298405	−	0.999555i	$-0.490500\pi$
$127$	0.672570			0.0596809			0.0298405	+	0.999555i	$0.490500\pi$
$128$	19.1082			1.68894
$129$	9.74124	−	15.2254i	0.857669	−	1.34052i
$130$	6.38151			0.559696
$131$	3.95691	+	6.85356i	0.345717	+	0.598799i	0.985484	−	0.169770i	$-0.0543026\pi$
$131$	3.95691	+	6.85356i	0.345717	+	0.598799i	−0.639767	+	0.768569i	$0.720969\pi$
$132$	31.6680	+	1.44422i	2.75634	+	0.125703i
$133$		0			0
$134$	38.9181			3.36201
$135$	−5.08472	−	12.4806i	−0.437623	−	1.07416i
$136$	2.39037	+	4.14024i	0.204972	+	0.355023i
$137$	1.83628	−	3.18054i	0.156884	−	0.271732i	−0.776859	−	0.629674i	$-0.783188\pi$
$137$	1.83628	−	3.18054i	0.156884	−	0.271732i	0.933744	+	0.357943i	$0.116522\pi$
$138$	−0.627819	+	0.981271i	−0.0534435	+	0.0835314i
$139$	−1.02704	+	1.77889i	−0.0871126	+	0.150883i	−0.906289	−	0.422658i	$-0.861097\pi$
$139$	−1.02704	+	1.77889i	−0.0871126	+	0.150883i	0.819177	+	0.573541i	$0.194431\pi$
$140$		0			0
$141$	−9.69076	−	18.7043i	−0.816109	−	1.57519i
$142$	−8.05408			−0.675884
$143$	2.25729	+	3.90975i	0.188764	+	0.326950i
$144$	−7.48755	+	10.6055i	−0.623962	+	0.883791i
$145$	−3.19076	+	5.52655i	−0.264978	+	0.458955i
$146$	1.85447	+	3.21204i	0.153477	+	0.265830i
$147$		0			0
$148$	−3.60963	+	6.25206i	−0.296710	+	0.513917i
$149$	6.77188	+	11.7292i	0.554774	+	0.960897i	0.997921	+	0.0644482i	$0.0205287\pi$
$149$	6.77188	+	11.7292i	0.554774	+	0.960897i	−0.443147	+	0.896449i	$0.646138\pi$
$150$	−7.35087	−	0.335237i	−0.600196	−	0.0273720i
$151$	−4.96410	+	8.59808i	−0.403973	+	0.699702i	−0.994201	−	0.107535i	$-0.965704\pi$
$151$	−4.96410	+	8.59808i	−0.403973	+	0.699702i	0.590228	+	0.807236i	$0.299038\pi$
$152$	10.2448	−	17.7446i	0.830966	−	1.43928i
$153$	2.82597	+	0.258294i	0.228466	+	0.0208818i
$154$		0			0
$155$	3.01819	+	5.22765i	0.242427	+	0.419895i
$156$	−7.01459	−	0.319901i	−0.561617	−	0.0256126i
$157$	−6.05408			−0.483169			−0.241584	−	0.970380i	$-0.577667\pi$
$157$	−6.05408			−0.483169			−0.241584	+	0.970380i	$0.577667\pi$
$158$	−36.1914			−2.87924
$159$	5.85594	−	9.15274i	0.464406	−	0.725859i
$160$	0.699612	+	1.21176i	0.0553092	+	0.0957983i
$161$		0			0
$162$	7.41216	+	20.8672i	0.582354	+	1.63948i
$163$	−8.90856	+	15.4301i	−0.697772	+	1.20858i	0.271465	+	0.962448i	$0.412492\pi$
$163$	−8.90856	+	15.4301i	−0.697772	+	1.20858i	−0.969237	+	0.246128i	$0.920842\pi$
$164$	−12.9861	+	22.4926i	−1.01404	+	1.75637i
$165$	−9.32957	−	18.0071i	−0.726306	−	1.40185i
$166$	1.16372	+	2.01561i	0.0903218	+	0.156442i
$167$	−4.23385	+	7.33325i	−0.327625	+	0.567464i	−0.982040	−	0.188672i	$-0.939582\pi$
$167$	−4.23385	+	7.33325i	−0.327625	+	0.567464i	0.654415	+	0.756136i	$0.272915\pi$
$168$		0			0
$169$	6.00000	+	10.3923i	0.461538	+	0.799408i
$170$	3.01819	−	5.22765i	0.231484	−	0.400943i
$171$	−5.09718	−	11.0426i	−0.389791	−	0.844449i
$172$	21.1534	+	36.6388i	1.61293	+	2.79368i
$173$	−17.3566			−1.31960			−0.659799	−	0.751442i	$-0.729359\pi$
$173$	−17.3566			−1.31960			−0.659799	+	0.751442i	$0.729359\pi$
$174$	5.65126	−	8.83284i	0.428421	−	0.669616i
$175$		0			0
$176$	−9.76829	+	16.9192i	−0.736312	+	1.27533i
$177$	−2.17257	−	4.19331i	−0.163300	−	0.315189i
$178$	17.6623	−	30.5919i	1.32384	−	2.29296i
$179$	5.67471	+	9.82888i	0.424147	+	0.734645i	0.996340	−	0.0854741i	$-0.0272405\pi$
$179$	5.67471	+	9.82888i	0.424147	+	0.734645i	−0.572193	+	0.820119i	$0.693907\pi$
$180$	31.4128	+	2.87114i	2.34137	+	0.214002i
$181$	−21.8889			−1.62699			−0.813495	−	0.581572i	$-0.802438\pi$
$181$	−21.8889			−1.62699			−0.813495	+	0.581572i	$0.802438\pi$
$182$		0			0
$183$	−1.81138	−	3.49617i	−0.133901	−	0.258444i
$184$	−0.690757	−	1.19643i	−0.0509233	−	0.0882018i
$185$	4.61849			0.339558
$186$	−4.56294	−	8.80700i	−0.334571	−	0.645761i
$187$	4.27042			0.312284
$188$	49.3068			3.59607
$189$		0			0
$190$	−25.8712			−1.87689
$191$	−0.701748			−0.0507767			−0.0253883	−	0.999678i	$-0.508082\pi$
$191$	−0.701748			−0.0507767			−0.0253883	+	0.999678i	$0.508082\pi$
$192$	5.83842	+	11.2688i	0.421352	+	0.813258i
$193$	12.1445			0.874183			0.437092	−	0.899417i	$-0.356009\pi$
$193$	12.1445			0.874183			0.437092	+	0.899417i	$0.356009\pi$
$194$	14.1352	+	24.4829i	1.01485	+	1.75777i
$195$	2.06654	+	3.98866i	0.147988	+	0.285634i
$196$		0			0
$197$	−16.4107			−1.16921			−0.584607	−	0.811317i	$-0.698751\pi$
$197$	−16.4107			−1.16921			−0.584607	+	0.811317i	$0.698751\pi$
$198$	13.9662	+	30.2567i	0.992537	+	2.15025i
$199$	11.3530	+	19.6640i	0.804794	+	1.39394i	0.916430	+	0.400194i	$0.131057\pi$
$199$	11.3530	+	19.6640i	0.804794	+	1.39394i	−0.111637	+	0.993749i	$0.535609\pi$
$200$	4.36333	−	7.55750i	0.308534	−	0.534396i
$201$	12.6029	+	24.3251i	0.888941	+	1.71576i
$202$	4.52704	−	7.84107i	0.318522	−	0.551696i
$203$		0			0
$204$	−3.57966	+	5.59496i	−0.250627	+	0.391726i
$205$	16.6156			1.16048
$206$	11.9662	+	20.7261i	0.833727	+	1.44406i
$207$	−0.816635	−	0.0746406i	−0.0567600	−	0.00518788i
$208$	2.16372	−	3.74766i	0.150027	−	0.259854i
$209$	−9.15126	−	15.8505i	−0.633006	−	1.09640i
$210$		0			0
$211$	−2.28074	+	3.95035i	−0.157012	+	0.271954i	−0.933790	−	0.357822i	$-0.883520\pi$
$211$	−2.28074	+	3.95035i	−0.157012	+	0.271954i	0.776778	+	0.629775i	$0.216853\pi$
$212$	12.7163	+	22.0253i	0.873362	+	1.51271i
$213$	−2.60817	−	5.03407i	−0.178709	−	0.344929i
$214$	−1.69076	+	2.92848i	−0.115578	+	0.200187i
$215$	13.5328	−	23.4395i	0.922928	−	1.59856i
$216$	−26.0167	−	3.57935i	−1.77021	−	0.243544i
$217$		0			0
$218$	−4.18190	−	7.24327i	−0.283234	−	0.490576i
$219$	−1.40709	+	2.19927i	−0.0950826	+	0.148613i
$220$	47.4690			3.20036
$221$	−0.945916			−0.0636292
$222$	−7.58113	−	0.345738i	−0.508812	−	0.0232044i
$223$	6.66225	+	11.5394i	0.446137	+	0.772733i	0.998131	−	0.0611159i	$-0.0194659\pi$
$223$	6.66225	+	11.5394i	0.446137	+	0.772733i	−0.551993	+	0.833849i	$0.686133\pi$
$224$		0			0
$225$	−2.17091	−	4.70310i	−0.144727	−	0.313540i
$226$	12.7807	−	22.1369i	0.850162	−	1.47252i
$227$	0.690757	−	1.19643i	0.0458472	−	0.0794096i	−0.842191	−	0.539179i	$-0.818735\pi$
$227$	0.690757	−	1.19643i	0.0458472	−	0.0794096i	0.888038	+	0.459769i	$0.152068\pi$
$228$	28.4377	+	1.29690i	1.88334	+	0.0858896i
$229$	−8.98968	−	15.5706i	−0.594055	−	1.02893i	−0.993679	−	0.112254i	$-0.964193\pi$
$229$	−8.98968	−	15.5706i	−0.594055	−	1.02893i	0.399625	−	0.916679i	$-0.369141\pi$
$230$	−0.872181	+	1.51066i	−0.0575099	+	0.0996101i
$231$		0			0
$232$	6.21780	+	10.7695i	0.408219	+	0.707055i
$233$	9.49115	−	16.4391i	0.621786	−	1.07696i	−0.367367	−	0.930076i	$-0.619741\pi$
$233$	9.49115	−	16.4391i	0.621786	−	1.07696i	0.989153	−	0.146888i	$-0.0469258\pi$
$234$	−3.09358	−	6.70198i	−0.202234	−	0.438122i
$235$	−15.7719	−	27.3177i	−1.02884	−	1.78201i
$236$	11.0541			0.719560
$237$	−11.7199	−	22.6208i	−0.761292	−	1.46938i
$238$		0			0
$239$	−2.44592	+	4.23645i	−0.158213	+	0.274033i	−0.934224	−	0.356686i	$-0.883907\pi$
$239$	−2.44592	+	4.23645i	−0.158213	+	0.274033i	0.776011	+	0.630719i	$0.217240\pi$
$240$	−10.4768	+	16.3750i	−0.676271	+	1.05700i
$241$	−13.0797	+	22.6546i	−0.842535	+	1.45931i	0.0452094	+	0.998978i	$0.485604\pi$
$241$	−13.0797	+	22.6546i	−0.842535	+	1.45931i	−0.887745	+	0.460336i	$0.847729\pi$
$242$	11.5416	+	19.9907i	0.741924	+	1.28505i
$243$	−10.6424	+	11.3903i	−0.682711	+	0.730689i
$244$	9.21634			0.590016
$245$		0			0
$246$	−27.2740	−	1.24383i	−1.73893	−	0.0793039i
$247$	2.02704	+	3.51094i	0.128978	+	0.223396i
$248$	11.7630			0.746953
$249$	−0.882977	+	1.38008i	−0.0559564	+	0.0874590i
$250$	20.8889			1.32113
$251$	−18.4576			−1.16503			−0.582516	−	0.812819i	$-0.697932\pi$
$251$	−18.4576			−1.16503			−0.582516	+	0.812819i	$0.697932\pi$
$252$		0			0
$253$	−1.23405			−0.0775838
$254$	−1.65486			−0.103835
$255$	4.24484	+	0.193586i	0.265822	+	0.0121228i
$256$	−32.3609			−2.02256
$257$	−5.86693	−	10.1618i	−0.365969	−	0.633876i	0.622962	−	0.782252i	$-0.285929\pi$
$257$	−5.86693	−	10.1618i	−0.365969	−	0.633876i	−0.988931	+	0.148375i	$0.952596\pi$
$258$	−23.9684	+	37.4622i	−1.49221	+	2.33230i
$259$		0			0
$260$	−10.5146			−0.652087
$261$	7.35087	+	0.671871i	0.455008	+	0.0415878i
$262$	−9.73599	−	16.8632i	−0.601491	−	1.04181i
$263$	3.76089	−	6.51406i	0.231907	−	0.401674i	−0.726463	−	0.687206i	$-0.758837\pi$
$263$	3.76089	−	6.51406i	0.231907	−	0.401674i	0.958369	+	0.285532i	$0.0921703\pi$
$264$	−39.4794	−	1.80046i	−2.42979	−	0.110811i
$265$	8.13521	−	14.0906i	0.499742	−	0.865579i
$266$		0			0
$267$	24.8406	+	1.13285i	1.52022	+	0.0693296i
$268$	−64.1239			−3.91699
$269$	−9.41741	−	16.3114i	−0.574190	−	0.994526i	−0.996129	−	0.0879017i	$-0.971984\pi$
$269$	−9.41741	−	16.3114i	−0.574190	−	0.994526i	0.421939	−	0.906624i	$-0.361349\pi$
$270$	12.5110	+	30.7086i	0.761395	+	1.86886i
$271$	−11.9911	+	20.7693i	−0.728410	+	1.26164i	0.229145	+	0.973392i	$0.426407\pi$
$271$	−11.9911	+	20.7693i	−0.728410	+	1.26164i	−0.957555	+	0.288251i	$0.906926\pi$
$272$	−2.04669	−	3.54498i	−0.124099	−	0.214946i
$273$		0			0
$274$	−4.51819	+	7.82573i	−0.272954	+	0.472770i
$275$	−3.89757	−	6.75078i	−0.235032	−	0.407088i
$276$	1.03443	−	1.61680i	0.0622656	−	0.0973202i
$277$	−3.58113	+	6.20269i	−0.215169	+	0.372684i	−0.953325	−	0.301947i	$-0.902364\pi$
$277$	−3.58113	+	6.20269i	−0.215169	+	0.372684i	0.738156	+	0.674630i	$0.235697\pi$
$278$	2.52704	−	4.37697i	0.151562	−	0.262513i
$279$	4.02704	−	5.70397i	0.241093	−	0.341488i
$280$		0			0
$281$	−7.44085	−	12.8879i	−0.443884	−	0.768830i	0.554090	−	0.832457i	$-0.313067\pi$
$281$	−7.44085	−	12.8879i	−0.443884	−	0.768830i	−0.997974	+	0.0636271i	$0.979733\pi$
$282$	23.8442	+	46.0220i	1.41990	+	2.74057i
$283$	−19.9971			−1.18870			−0.594351	−	0.804205i	$-0.702591\pi$
$283$	−19.9971			−1.18870			−0.594351	+	0.804205i	$0.702591\pi$
$284$	13.2704			0.787455
$285$	−8.37792	−	16.1704i	−0.496265	−	0.957849i
$286$	−5.55408	−	9.61996i	−0.328420	−	0.568840i
$287$		0			0
$288$	0.933463	−	1.32217i	0.0550048	−	0.0779098i
$289$	8.05262	−	13.9475i	0.473684	−	0.820444i
$290$	7.85087	−	13.5981i	0.461019	−	0.798509i
$291$	−10.7252	+	16.7633i	−0.628722	+	0.982683i
$292$	−3.05555	−	5.29236i	−0.178812	−	0.309712i
$293$	7.53278	−	13.0472i	0.440070	−	0.762223i	−0.557625	−	0.830093i	$-0.688287\pi$
$293$	7.53278	−	13.0472i	0.440070	−	0.762223i	0.997694	+	0.0678705i	$0.0216205\pi$
$294$		0			0
$295$	−3.53590	−	6.12435i	−0.205868	−	0.356574i
$296$	4.50000	−	7.79423i	0.261557	−	0.453030i
$297$	−14.3887	+	18.5274i	−0.834918	+	1.07507i
$298$	−16.6623	−	28.8599i	−0.965218	−	1.67181i
$299$	0.273346			0.0158080
$300$	12.1118	+	0.552358i	0.699273	+	0.0318904i
$301$		0			0
$302$	12.2142	−	21.1556i	0.702848	−	1.21737i
$303$	6.36693	+	0.290364i	0.365770	+	0.0166810i
$304$	−8.77188	+	15.1933i	−0.503102	+	0.871398i
$305$	−2.94805	−	5.10618i	−0.168805	−	0.292379i
$306$	−6.95331	−	0.635534i	−0.397494	−	0.0363310i
$307$	27.2704			1.55641			0.778203	−	0.628013i	$-0.216132\pi$
$307$	27.2704			1.55641			0.778203	+	0.628013i	$0.216132\pi$
$308$		0			0
$309$	−9.07947	+	14.1911i	−0.516513	+	0.807302i
$310$	−7.42627	−	12.8627i	−0.421784	−	0.730551i
$311$	15.9823			0.906273			0.453136	−	0.891441i	$-0.350305\pi$
$311$	15.9823			0.906273			0.453136	+	0.891441i	$0.350305\pi$
$312$	8.74484	+	0.398809i	0.495079	+	0.0225781i
$313$	−11.5979			−0.655549			−0.327775	−	0.944756i	$-0.606299\pi$
$313$	−11.5979			−0.655549			−0.327775	+	0.944756i	$0.606299\pi$
$314$	14.8961			0.840636
$315$		0			0
$316$	59.6313			3.35452
$317$	−2.01771			−0.113326			−0.0566629	−	0.998393i	$-0.518046\pi$
$317$	−2.01771			−0.113326			−0.0566629	+	0.998393i	$0.518046\pi$
$318$	−14.4086	+	22.5204i	−0.807992	+	1.26288i
$319$	11.1082			0.621938
$320$	9.50214	+	16.4582i	0.531186	+	0.920040i
$321$	−2.37792	−	0.108445i	−0.132722	−	0.00605281i
$322$		0			0
$323$	3.83482			0.213375
$324$	−12.2127	−	34.3822i	−0.678485	−	1.91012i
$325$	0.863327	+	1.49533i	0.0478888	+	0.0829458i
$326$	21.9195	−	37.9658i	1.21401	−	2.10273i
$327$	3.17305	−	4.95943i	0.175470	−	0.274257i
$328$	16.1893	−	28.0407i	0.893904	−	1.54829i
$329$		0			0
$330$	22.9554	+	44.3067i	1.26366	+	2.43900i
$331$	−19.7089			−1.08330			−0.541651	−	0.840604i	$-0.682200\pi$
$331$	−19.7089			−1.08330			−0.541651	+	0.840604i	$0.682200\pi$
$332$	−1.91741	−	3.32105i	−0.105232	−	0.182266i
$333$	−2.23891	−	4.85041i	−0.122692	−	0.265801i
$334$	10.4174	−	18.0435i	0.570015	−	0.987296i
$335$	20.5115	+	35.5269i	1.12066	+	1.94104i
$336$		0			0
$337$	14.5256	−	25.1590i	0.791259	−	1.37050i	−0.133929	−	0.990991i	$-0.542759\pi$
$337$	14.5256	−	25.1590i	0.791259	−	1.37050i	0.925188	−	0.379509i	$-0.123907\pi$
$338$	−14.7630	−	25.5703i	−0.803003	−	1.39084i
$339$	17.9751	+	0.819755i	0.976273	+	0.0445230i
$340$	−4.97296	+	8.61342i	−0.269697	+	0.467128i
$341$	5.25370	−	9.09967i	0.284504	−	0.492775i
$342$	12.5416	+	27.1704i	0.678174	+	1.46921i
$343$		0			0
$344$	−26.3712	−	45.6763i	−1.42184	−	2.46270i
$345$	−1.22665	−	0.0559416i	−0.0660408	−	0.00301179i
$346$	42.7060			2.29589
$347$	29.0833			1.56127			0.780636	−	0.624986i	$-0.214895\pi$
$347$	29.0833			1.56127			0.780636	+	0.624986i	$0.214895\pi$
$348$	−9.31138	+	14.5535i	−0.499142	+	0.780152i
$349$	12.3815	+	21.4454i	0.662767	+	1.14795i	0.979885	+	0.199561i	$0.0639515\pi$
$349$	12.3815	+	21.4454i	0.662767	+	1.14795i	−0.317118	+	0.948386i	$0.602715\pi$
$350$		0			0
$351$	3.18716	−	4.10390i	0.170118	−	0.219050i
$352$	1.21780	−	2.10929i	0.0649089	−	0.112426i
$353$	−16.6513	+	28.8408i	−0.886257	+	1.53504i	−0.0419914	+	0.999118i	$0.513370\pi$
$353$	−16.6513	+	28.8408i	−0.886257	+	1.53504i	−0.844266	+	0.535925i	$0.819963\pi$
$354$	5.34562	+	10.3177i	0.284116	+	0.548378i
$355$	−4.24484	−	7.35228i	−0.225293	−	0.390219i
$356$	−29.1015	+	50.4052i	−1.54237	+	2.67147i
$357$		0			0
$358$	−13.9626	−	24.1840i	−0.737949	−	1.27816i
$359$	−12.7683	+	22.1153i	−0.673884	+	1.16720i	0.302909	+	0.953019i	$0.402042\pi$
$359$	−12.7683	+	22.1153i	−0.673884	+	1.16720i	−0.976794	+	0.214182i	$0.931291\pi$
$360$	−39.1613	−	3.57935i	−2.06398	−	0.188648i
$361$	1.28220	+	2.22084i	0.0674842	+	0.116886i
$362$	53.8578			2.83070
$363$	−8.75729	+	13.6875i	−0.459639	+	0.718409i
$364$		0			0
$365$	−1.95477	+	3.38576i	−0.102317	+	0.177219i
$366$	4.45691	+	8.60235i	0.232966	+	0.449652i
$367$	13.7252	−	23.7727i	0.716449	−	1.24093i	−0.245949	−	0.969283i	$-0.579100\pi$
$367$	13.7252	−	23.7727i	0.716449	−	1.24093i	0.962398	−	0.271644i	$-0.0875672\pi$
$368$	0.591443	+	1.02441i	0.0308311	+	0.0534011i
$369$	−8.05476	−	17.4500i	−0.419314	−	0.908408i
$370$	−11.3638			−0.590776
$371$		0			0
$372$	7.51819	+	14.5110i	0.389800	+	0.752359i
$373$	−8.16372	−	14.1400i	−0.422701	−	0.732140i	0.573502	−	0.819204i	$-0.305585\pi$
$373$	−8.16372	−	14.1400i	−0.422701	−	0.732140i	−0.996203	+	0.0870646i	$0.972251\pi$
$374$	−10.5074			−0.543324
$375$	6.76449	+	13.0563i	0.349317	+	0.674222i
$376$	−61.4690			−3.17002
$377$	−2.46050			−0.126722
$378$		0			0
$379$	12.0364			0.618267			0.309134	−	0.951019i	$-0.399961\pi$
$379$	12.0364			0.618267			0.309134	+	0.951019i	$0.399961\pi$
$380$	42.6270			2.18672
$381$	−0.535897	−	1.03434i	−0.0274548	−	0.0529910i
$382$	1.72665			0.0883433
$383$	−6.21780	−	10.7695i	−0.317715	−	0.550298i	0.662296	−	0.749242i	$-0.269582\pi$
$383$	−6.21780	−	10.7695i	−0.317715	−	0.550298i	−0.980011	+	0.198944i	$0.936249\pi$
$384$	−15.2252	−	29.3864i	−0.776957	−	1.49962i
$385$		0			0
$386$	−29.8817			−1.52094
$387$	−31.1768	−	2.84957i	−1.58481	−	0.144852i
$388$	−23.2901	−	40.3396i	−1.18237	−	2.04793i
$389$	−10.3004	+	17.8408i	−0.522250	+	0.904564i	0.477414	+	0.878678i	$0.341574\pi$
$389$	−10.3004	+	17.8408i	−0.522250	+	0.904564i	−0.999665	+	0.0258860i	$0.991759\pi$
$390$	−5.08472	−	9.81411i	−0.257475	−	0.496957i
$391$	0.129281	−	0.223922i	0.00653803	−	0.0113242i
$392$		0			0
$393$	7.38725	−	11.5462i	0.372637	−	0.582427i
$394$	40.3786			2.03424
$395$	−19.0744	−	33.0378i	−0.959738	−	1.66231i
$396$	−23.0117	−	49.8528i	−1.15638	−	2.50520i
$397$	−11.8186	+	20.4704i	−0.593157	+	1.02738i	0.400647	+	0.916233i	$0.368785\pi$
$397$	−11.8186	+	20.4704i	−0.593157	+	1.02738i	−0.993804	+	0.111146i	$0.964548\pi$
$398$	−27.9341	−	48.3833i	−1.40021	−	2.42524i
$399$		0			0
$400$	−3.73599	+	6.47092i	−0.186799	+	0.323546i
$401$	1.28220	+	2.22084i	0.0640300	+	0.110903i	0.896263	−	0.443522i	$-0.146271\pi$
$401$	1.28220	+	2.22084i	0.0640300	+	0.110903i	−0.832233	+	0.554426i	$0.812938\pi$
$402$	−31.0095	−	59.8520i	−1.54661	−	2.98515i
$403$	−1.16372	+	2.01561i	−0.0579688	+	0.100405i
$404$	−7.45904	+	12.9194i	−0.371101	+	0.642766i
$405$	−15.1424	+	17.7642i	−0.752432	+	0.882710i
$406$		0			0
$407$	−4.01965	−	6.96224i	−0.199247	−	0.345105i
$408$	4.46264	−	6.97504i	0.220934	−	0.345316i
$409$	34.3245			1.69724			0.848619	−	0.529005i	$-0.177435\pi$
$409$	34.3245			1.69724			0.848619	+	0.529005i	$0.177435\pi$
$410$	−40.8827			−2.01905
$411$	−6.35447	−	0.289796i	−0.313443	−	0.0142946i
$412$	−19.7163	−	34.1497i	−0.971354	−	1.68243i
$413$		0			0
$414$	2.00933	+	0.183653i	0.0987533	+	0.00902607i
$415$	−1.22665	+	2.12463i	−0.0602141	+	0.104294i
$416$	−0.269748	+	0.467216i	−0.0132255	+	0.0229072i
$417$	3.55408	+	0.162084i	0.174044	+	0.00793730i
$418$	22.5167	+	39.0001i	1.10133	+	1.90756i
$419$	2.02850	−	3.51347i	0.0990989	−	0.171644i	−0.812213	−	0.583361i	$-0.801737\pi$
$419$	2.02850	−	3.51347i	0.0990989	−	0.171644i	0.911312	+	0.411717i	$0.135071\pi$
$420$		0			0
$421$	10.5344	+	18.2462i	0.513417	+	0.889264i	0.999879	+	0.0155624i	$0.00495387\pi$
$421$	10.5344	+	18.2462i	0.513417	+	0.889264i	−0.486462	+	0.873702i	$0.661713\pi$
$422$	5.61177	−	9.71987i	0.273177	−	0.473156i
$423$	−21.0438	+	29.8068i	−1.02318	+	1.44925i
$424$	−15.8530	−	27.4582i	−0.769890	−	1.33349i
$425$	1.63327			0.0792252
$426$	6.41741	+	12.3863i	0.310925	+	0.600121i
$427$		0			0
$428$	2.78580	−	4.82515i	0.134657	−	0.233232i
$429$	4.21420	−	6.58673i	0.203464	−	0.318010i
$430$	−33.2975	+	57.6729i	−1.60575	+	2.78123i
$431$	−11.3092	−	19.5882i	−0.544747	−	0.943530i	−0.998623	−	0.0524646i	$-0.983292\pi$
$431$	−11.3092	−	19.5882i	−0.544747	−	0.943530i	0.453876	−	0.891065i	$-0.350041\pi$
$432$	22.2762	+	3.06472i	1.07176	+	0.147452i
$433$	−2.41789			−0.116196			−0.0580982	−	0.998311i	$-0.518504\pi$
$433$	−2.41789			−0.116196			−0.0580982	+	0.998311i	$0.518504\pi$
$434$		0			0
$435$	11.0416	+	0.503554i	0.529406	+	0.0241436i
$436$	6.89037	+	11.9345i	0.329989	+	0.571557i
$437$	−1.10817			−0.0530109
$438$	3.46216	−	5.41131i	0.165429	−	0.258562i
$439$	23.4897			1.12110			0.560551	−	0.828120i	$-0.310589\pi$
$439$	23.4897			1.12110			0.560551	+	0.828120i	$0.310589\pi$
$440$	−59.1780			−2.82120
$441$		0			0
$442$	2.32743			0.110705
$443$	−13.4179			−0.637503			−0.318752	−	0.947838i	$-0.603264\pi$
$443$	−13.4179			−0.637503			−0.318752	+	0.947838i	$0.603264\pi$
$444$	12.4911	+	0.569659i	0.592804	+	0.0270348i
$445$	37.2350			1.76511
$446$	−16.3925	−	28.3927i	−0.776208	−	1.34443i
$447$	12.6426	−	19.7602i	0.597975	−	0.934625i
$448$		0			0
$449$	−9.16225			−0.432393			−0.216197	−	0.976350i	$-0.569365\pi$
$449$	−9.16225			−0.432393			−0.216197	+	0.976350i	$0.569365\pi$
$450$	5.34154	+	11.5720i	0.251803	+	0.545509i
$451$	−14.4612	−	25.0475i	−0.680950	−	1.17944i
$452$	−21.0584	+	36.4741i	−0.990502	+	1.71560i
$453$	17.1783	+	0.783417i	0.807107	+	0.0368082i
$454$	−1.69961	+	2.94381i	−0.0797667	+	0.138160i
$455$		0			0
$456$	−35.4523	−	1.61680i	−1.66021	−	0.0757138i
$457$	8.81711			0.412447			0.206224	−	0.978505i	$-0.433883\pi$
$457$	8.81711			0.412447			0.206224	+	0.978505i	$0.433883\pi$
$458$	22.1192	+	38.3115i	1.03356	+	1.79018i
$459$	−1.85447	−	4.55185i	−0.0865594	−	0.212462i
$460$	1.43706	−	2.48906i	0.0670033	−	0.116053i
$461$	−2.82957	−	4.90095i	−0.131786	−	0.228260i	0.792579	−	0.609769i	$-0.208738\pi$
$461$	−2.82957	−	4.90095i	−0.131786	−	0.228260i	−0.924365	+	0.381509i	$0.875405\pi$
$462$		0			0
$463$	−7.86333	+	13.6197i	−0.365440	+	0.632960i	−0.988847	−	0.148937i	$-0.952415\pi$
$463$	−7.86333	+	13.6197i	−0.365440	+	0.632960i	0.623407	+	0.781898i	$0.285748\pi$
$464$	−5.32383	−	9.22115i	−0.247153	−	0.428081i
$465$	5.63473	−	8.80700i	0.261304	−	0.408415i
$466$	−23.3530	+	40.4486i	−1.08181	+	1.87375i
$467$	−10.9985	+	19.0500i	−0.508952	+	0.881530i	0.490995	+	0.871163i	$0.336633\pi$
$467$	−10.9985	+	19.0500i	−0.508952	+	0.881530i	−0.999946	+	0.0103675i	$0.996700\pi$
$468$	5.09718	+	11.0426i	0.235617	+	0.510445i
$469$		0			0
$470$	38.8068	+	67.2153i	1.79002	+	3.10041i
$471$	4.82383	+	9.31056i	0.222270	+	0.429008i
$472$	−13.7807			−0.634310
$473$	−47.1124			−2.16623
$474$	28.8370	+	55.6587i	1.32453	+	2.55649i
$475$	−3.50000	−	6.06218i	−0.160591	−	0.278152i
$476$		0			0
$477$	−18.7419	−	1.71301i	−0.858133	−	0.0784336i
$478$	6.01819	−	10.4238i	0.275265	−	0.476774i
$479$	12.4875	−	21.6291i	0.570571	−	0.988257i	−0.425937	−	0.904753i	$-0.640055\pi$
$479$	12.4875	−	21.6291i	0.570571	−	0.988257i	0.996507	−	0.0835043i	$-0.0266112\pi$
$480$	1.30612	−	2.04145i	0.0596161	−	0.0931791i
$481$	0.890369	+	1.54216i	0.0405973	+	0.0703166i
$482$	32.1826	−	55.7419i	1.46588	−	2.53897i
$483$		0			0
$484$	−19.0167	−	32.9379i	−0.864397	−	1.49718i
$485$	−14.8997	+	25.8070i	−0.676561	+	1.17184i
$486$	26.1857	−	28.0259i	1.18781	−	1.27128i
$487$	8.79893	+	15.2402i	0.398717	+	0.690599i	0.993568	−	0.113238i	$-0.0361221\pi$
$487$	8.79893	+	15.2402i	0.398717	+	0.690599i	−0.594851	+	0.803836i	$0.702789\pi$
$488$	−11.4897			−0.520114
$489$	30.8281	+	1.40592i	1.39410	+	0.0635778i
$490$		0			0
$491$	−6.89757	+	11.9469i	−0.311283	+	0.539158i	−0.978640	−	0.205580i	$-0.934092\pi$
$491$	−6.89757	+	11.9469i	−0.311283	+	0.539158i	0.667358	+	0.744737i	$0.267425\pi$
$492$	44.9384	+	2.04942i	2.02598	+	0.0923949i
$493$	−1.16372	+	2.01561i	−0.0524111	+	0.0907787i
$494$	−4.98755	−	8.63868i	−0.224400	−	0.388673i
$495$	−20.2594	+	28.6958i	−0.910594	+	1.28978i
$496$	−10.0718			−0.452237
$497$		0			0
$498$	2.17257	−	3.39569i	0.0973552	−	0.152165i
$499$	−6.54377	−	11.3341i	−0.292939	−	0.507386i	0.681564	−	0.731758i	$-0.261300\pi$
$499$	−6.54377	−	11.3341i	−0.292939	−	0.507386i	−0.974503	+	0.224373i	$0.927967\pi$
$500$	−34.4179			−1.53921
$501$	14.6513	+	0.668172i	0.654570	+	0.0298517i
$502$	45.4150			2.02697
$503$	22.3068			0.994611			0.497305	−	0.867576i	$-0.334323\pi$
$503$	22.3068			0.994611			0.497305	+	0.867576i	$0.334323\pi$
$504$		0			0
$505$	9.54377			0.424692
$506$	3.03638			0.134983
$507$	11.2016	−	17.5079i	0.497478	−	0.777551i
$508$	2.72665			0.120976
$509$	−7.94659	−	13.7639i	−0.352226	−	0.610074i	0.634413	−	0.772994i	$-0.281242\pi$
$509$	−7.94659	−	13.7639i	−0.352226	−	0.610074i	−0.986639	+	0.162920i	$0.947909\pi$
$510$	−10.4445	−	0.476320i	−0.462488	−	0.0210918i
$511$		0			0
$512$	41.4078			1.82998
$513$	−12.9210	+	16.6376i	−0.570477	+	0.734567i
$514$	14.4356	+	25.0032i	0.636727	+	1.10284i
$515$	−12.6134	+	21.8471i	−0.555814	+	0.962698i
$516$	39.4918	−	61.7251i	1.73853	−	2.71730i
$517$	−27.4538	+	47.5514i	−1.20742	+	2.09131i
$518$		0			0
$519$	13.8296	+	26.6927i	0.607051	+	1.17168i
$520$	13.1082			0.574831
$521$	2.20895	+	3.82600i	0.0967756	+	0.167620i	0.910348	−	0.413843i	$-0.135814\pi$
$521$	2.20895	+	3.82600i	0.0967756	+	0.167620i	−0.813573	+	0.581463i	$0.802480\pi$
$522$	−18.0869	−	1.65314i	−0.791640	−	0.0723561i
$523$	12.6367	−	21.8874i	0.552563	−	0.957067i	−0.445526	−	0.895269i	$-0.646983\pi$
$523$	12.6367	−	21.8874i	0.552563	−	0.957067i	0.998089	−	0.0617982i	$-0.0196835\pi$
$524$	16.0416	+	27.7849i	0.700782	+	1.21379i
$525$		0			0
$526$	−9.25370	+	16.0279i	−0.403480	+	0.698848i
$527$	1.10078	+	1.90660i	0.0479506	+	0.0830528i
$528$	33.8032	+	1.54160i	1.47110	+	0.0670894i
$529$	11.4626	−	19.8539i	0.498376	−	0.863212i
$530$	−20.0167	+	34.6700i	−0.869471	+	1.50597i
$531$	−4.71780	+	6.68238i	−0.204735	+	0.289990i
$532$		0			0
$533$	3.20321	+	5.54812i	0.138746	+	0.240316i
$534$	−61.1203	−	2.78739i	−2.64493	−	0.120622i
$535$	−3.56440			−0.154103
$536$	79.9410			3.45293
$537$	10.5943	−	16.5587i	0.457176	−	0.714559i
$538$	23.1716	+	40.1344i	0.998998	+	1.73032i
$539$		0			0
$540$	−20.6139	−	50.5974i	−0.887081	−	2.17736i
$541$	1.71926	−	2.97785i	0.0739168	−	0.128028i	−0.826698	−	0.562646i	$-0.809783\pi$
$541$	1.71926	−	2.97785i	0.0739168	−	0.128028i	0.900615	+	0.434618i	$0.143117\pi$
$542$	29.5043	−	51.1029i	1.26732	−	2.19506i
$543$	17.4409	+	33.6629i	0.748459	+	1.44461i
$544$	0.255158	+	0.441947i	0.0109398	+	0.0189483i
$545$	4.40808	−	7.63501i	0.188821	−	0.327048i
$546$		0			0
$547$	3.46410	+	6.00000i	0.148114	+	0.256542i	0.930531	−	0.366214i	$-0.119346\pi$
$547$	3.46410	+	6.00000i	0.148114	+	0.256542i	−0.782416	+	0.622756i	$0.786013\pi$
$548$	7.44445	−	12.8942i	0.318011	−	0.550812i
$549$	−3.93346	+	5.57143i	−0.167876	+	0.237783i
$550$	9.58998	+	16.6103i	0.408918	+	0.708267i
$551$	9.97509			0.424953
$552$	−1.28959	+	2.01561i	−0.0548887	+	0.0857902i
$553$		0			0
$554$	8.81138	−	15.2618i	0.374360	−	0.648410i
$555$	−3.67996	−	7.10275i	−0.156206	−	0.301495i
$556$	−4.16372	+	7.21177i	−0.176581	+	0.305847i
$557$	−16.7917	−	29.0841i	−0.711488	−	1.23233i	−0.964298	−	0.264818i	$-0.914688\pi$
$557$	−16.7917	−	29.0841i	−0.711488	−	1.23233i	0.252810	−	0.967516i	$-0.418645\pi$
$558$	−9.90856	+	14.0347i	−0.419463	+	0.594134i
$559$	10.4356			0.441379
$560$		0			0
$561$	−3.40263	−	6.56747i	−0.143659	−	0.277279i
$562$	18.3083	+	31.7108i	0.772287	+	1.33764i
$563$	−42.4792			−1.79028			−0.895142	−	0.445781i	$-0.852926\pi$
$563$	−42.4792			−1.79028			−0.895142	+	0.445781i	$0.852926\pi$
$564$	−39.2871	−	75.8288i	−1.65429	−	3.19297i
$565$	26.9439			1.13354
$566$	49.2029			2.06815
$567$		0			0
$568$	−16.5438			−0.694161
$569$	10.4035			0.436137			0.218069	−	0.975933i	$-0.430024\pi$
$569$	10.4035			0.436137			0.218069	+	0.975933i	$0.430024\pi$
$570$	20.6139	+	39.7872i	0.863421	+	1.66650i
$571$	17.8496			0.746983			0.373491	−	0.927634i	$-0.378161\pi$
$571$	17.8496			0.746983			0.373491	+	0.927634i	$0.378161\pi$
$572$	9.15126	+	15.8505i	0.382633	+	0.662741i
$573$	0.559145	+	1.07922i	0.0233586	+	0.0450849i
$574$		0			0
$575$	−0.471974			−0.0196827
$576$	12.6783	−	17.9578i	0.528263	−	0.748241i
$577$	5.97150	+	10.3429i	0.248597	+	0.430582i	0.963137	−	0.269013i	$-0.0866973\pi$
$577$	5.97150	+	10.3429i	0.248597	+	0.430582i	−0.714540	+	0.699595i	$0.753364\pi$
$578$	−19.8135	+	34.3180i	−0.824134	+	1.42744i
$579$	−9.67665	−	18.6771i	−0.402148	−	0.776192i
$580$	−12.9356	+	22.4051i	−0.537122	+	0.930322i
$581$		0			0
$582$	26.3894	−	41.2462i	1.09388	−	1.70971i
$583$	−28.3216			−1.17296
$584$	3.80924	+	6.59780i	0.157628	+	0.273019i
$585$	4.48755	−	6.35624i	0.185537	−	0.262798i
$586$	−18.5344	+	32.1026i	−0.765650	+	1.32615i
$587$	11.9299	+	20.6631i	0.492398	+	0.852859i	0.999962	−	0.00875568i	$-0.00278706\pi$
$587$	11.9299	+	20.6631i	0.492398	+	0.852859i	−0.507563	+	0.861614i	$0.669454\pi$
$588$		0			0
$589$	4.71780	−	8.17147i	0.194394	−	0.336699i
$590$	8.70009	+	15.0690i	0.358177	+	0.620381i
$591$	13.0759	+	25.2380i	0.537869	+	1.03815i
$592$	−3.85301	+	6.67361i	−0.158358	+	0.274284i
$593$	9.79007	−	16.9569i	0.402030	−	0.696336i	−0.591941	−	0.805981i	$-0.701638\pi$
$593$	9.79007	−	16.9569i	0.402030	−	0.696336i	0.993971	+	0.109645i	$0.0349714\pi$
$594$	35.4035	−	45.5868i	1.45262	−	1.87045i
$595$		0			0
$596$	27.4538	+	47.5514i	1.12455	+	1.94778i
$597$	21.1952	−	33.1278i	0.867463	−	1.35583i
$598$	−0.672570			−0.0275034
$599$	18.5467			0.757797			0.378899	−	0.925438i	$-0.376303\pi$
$599$	18.5467			0.757797			0.378899	+	0.925438i	$0.376303\pi$
$600$	−15.0993	−	0.688605i	−0.616427	−	0.0281122i
$601$	−9.09931	−	15.7605i	−0.371169	−	0.642883i	0.618577	−	0.785724i	$-0.287710\pi$
$601$	−9.09931	−	15.7605i	−0.371169	−	0.642883i	−0.989746	+	0.142841i	$0.954376\pi$
$602$		0			0
$603$	27.3676	−	38.7640i	1.11449	−	1.57859i
$604$	−20.1249	+	34.8573i	−0.818870	+	1.41832i
$605$	−12.1659	+	21.0719i	−0.494612	+	0.856693i
$606$	−15.6659	−	0.714442i	−0.636382	−	0.0290222i
$607$	−11.1549	−	19.3208i	−0.452762	−	0.784206i	0.545795	−	0.837919i	$-0.316228\pi$
$607$	−11.1549	−	19.3208i	−0.452762	−	0.784206i	−0.998556	+	0.0537125i	$0.982895\pi$
$608$	1.09358	−	1.89413i	0.0443505	−	0.0768173i
$609$		0			0
$610$	7.25370	+	12.5638i	0.293694	+	0.508692i
$611$	6.08113	−	10.5328i	0.246016	−	0.426112i
$612$	11.4567	+	1.04715i	0.463110	+	0.0423284i
$613$	−5.11849	−	8.86548i	−0.206734	−	0.358073i	0.743950	−	0.668235i	$-0.232950\pi$
$613$	−5.11849	−	8.86548i	−0.206734	−	0.358073i	−0.950684	+	0.310162i	$0.899617\pi$
$614$	−67.0990			−2.70790
$615$	−13.2391	−	25.5530i	−0.533852	−	1.03040i
$616$		0			0
$617$	5.66372	−	9.80984i	0.228013	−	0.394929i	−0.729206	−	0.684294i	$-0.760111\pi$
$617$	5.66372	−	9.80984i	0.228013	−	0.394929i	0.957219	+	0.289364i	$0.0934439\pi$
$618$	22.3401	−	34.9172i	0.898650	−	1.40458i
$619$	4.31663	−	7.47663i	0.173500	−	0.300511i	−0.766141	−	0.642672i	$-0.777826\pi$
$619$	4.31663	−	7.47663i	0.173500	−	0.300511i	0.939641	+	0.342161i	$0.111159\pi$
$620$	12.2360	+	21.1934i	0.491409	+	0.851145i
$621$	0.535897	+	1.31537i	0.0215048	+	0.0527841i
$622$	−39.3245			−1.57677
$623$		0			0
$624$	−7.48755	−	0.341470i	−0.299742	−	0.0136697i
$625$	15.3260	+	26.5454i	0.613039	+	1.06181i
$626$	28.5366			1.14055
$627$	−17.0847	+	26.7032i	−0.682298	+	1.06642i
$628$	−24.5438			−0.979403
$629$	1.68443			0.0671626
$630$		0			0
$631$	−14.8535			−0.591308			−0.295654	−	0.955295i	$-0.595538\pi$
$631$	−14.8535			−0.591308			−0.295654	+	0.955295i	$0.595538\pi$
$632$	−74.3402			−2.95710
$633$	7.89251	+	0.359938i	0.313699	+	0.0143063i
$634$	4.96458			0.197169
$635$	−0.872181	−	1.51066i	−0.0346115	−	0.0599488i
$636$	23.7405	−	37.1060i	0.941370	−	1.47135i
$637$		0			0
$638$	−27.3317			−1.08207
$639$	−5.66372	+	8.02219i	−0.224053	+	0.317353i
$640$	−24.7793	−	42.9190i	−0.979487	−	1.69652i
$641$	17.0797	−	29.5828i	0.674606	−	1.16845i	−0.301978	−	0.953315i	$-0.597647\pi$
$641$	17.0797	−	29.5828i	0.674606	−	1.16845i	0.976584	−	0.215137i	$-0.0690199\pi$
$642$	5.85087	+	0.266829i	0.230916	+	0.0105309i
$643$	−5.41741	+	9.38323i	−0.213642	+	0.370039i	−0.952852	−	0.303437i	$-0.901866\pi$
$643$	−5.41741	+	9.38323i	−0.213642	+	0.370039i	0.739210	+	0.673475i	$0.235199\pi$
$644$		0			0
$645$	−46.8302	−	2.13570i	−1.84394	−	0.0840929i
$646$	−9.43560			−0.371239
$647$	16.4846	+	28.5522i	0.648077	+	1.12250i	0.983582	+	0.180464i	$0.0577600\pi$
$647$	16.4846	+	28.5522i	0.648077	+	1.12250i	−0.335504	+	0.942039i	$0.608907\pi$
$648$	15.2252	+	42.8630i	0.598102	+	1.68382i
$649$	−6.15486	+	10.6605i	−0.241599	+	0.418462i
$650$	−2.12422	−	3.67926i	−0.0833188	−	0.144312i
$651$		0			0
$652$	−36.1160	+	62.5548i	−1.41441	+	2.44984i
$653$	1.96557	+	3.40446i	0.0769185	+	0.133227i	0.901919	−	0.431905i	$-0.142159\pi$
$653$	1.96557	+	3.40446i	0.0769185	+	0.133227i	−0.825000	+	0.565132i	$0.808825\pi$
$654$	−7.80730	+	12.2027i	−0.305290	+	0.477163i
$655$	10.2626	−	17.7753i	0.400991	−	0.694537i
$656$	−13.8617	+	24.0091i	−0.541207	+	0.937399i
$657$	4.50340	+	0.411612i	0.175695	+	0.0160585i
$658$		0			0
$659$	−8.40856	−	14.5640i	−0.327551	−	0.567335i	0.654474	−	0.756084i	$-0.272890\pi$
$659$	−8.40856	−	14.5640i	−0.327551	−	0.567335i	−0.982025	+	0.188749i	$0.939557\pi$
$660$	−37.8228	−	73.0025i	−1.47225	−	2.84162i
$661$	17.0216			0.662063			0.331032	−	0.943620i	$-0.392603\pi$
$661$	17.0216			0.662063			0.331032	+	0.943620i	$0.392603\pi$
$662$	48.4940			1.88477
$663$	0.753696	+	1.45472i	0.0292711	+	0.0564967i
$664$	2.39037	+	4.14024i	0.0927643	+	0.160672i
$665$		0			0
$666$	5.50885	+	11.9345i	0.213464	+	0.462451i
$667$	0.336285	−	0.582462i	0.0130210	−	0.0225530i
$668$	−17.1644	+	29.7296i	−0.664110	+	1.15027i
$669$	12.4379	−	19.4403i	0.480878	−	0.751605i
$670$	−50.4686	−	87.4141i	−1.94977	−	3.37710i
$671$	−5.13161	+	8.88821i	−0.198104	+	0.343126i
$672$		0			0
$673$	−14.3727	−	24.8942i	−0.554025	−	0.959600i	−0.997979	−	0.0635501i	$-0.979758\pi$
$673$	−14.3727	−	24.8942i	−0.554025	−	0.959600i	0.443953	−	0.896050i	$-0.353576\pi$
$674$	−35.7403	+	61.9039i	−1.37666	+	2.38445i
$675$	−5.50312	+	7.08602i	−0.211815	+	0.272741i
$676$	24.3245	+	42.1313i	0.935558	+	1.62043i
$677$	6.03638			0.231997			0.115998	−	0.993249i	$-0.462993\pi$
$677$	6.03638			0.231997			0.115998	+	0.993249i	$0.462993\pi$
$678$	−44.2278	−	2.01701i	−1.69856	−	0.0774628i
$679$		0			0
$680$	6.19961	−	10.7380i	0.237744	−	0.411785i
$681$	−2.39037	−	0.109013i	−0.0915991	−	0.00417738i
$682$	−12.9267	+	22.3898i	−0.494991	+	0.857349i
$683$	−10.2556	−	17.7633i	−0.392421	−	0.679693i	0.600347	−	0.799739i	$-0.295029\pi$
$683$	−10.2556	−	17.7633i	−0.392421	−	0.679693i	−0.992768	+	0.120046i	$0.961696\pi$
$684$	−20.6644	−	44.7677i	−0.790123	−	1.71173i
$685$	−9.52510			−0.363935
$686$		0			0
$687$	−16.7831	+	26.2317i	−0.640314	+	1.00080i
$688$	22.5797	+	39.1091i	0.860842	+	1.49102i
$689$	6.27335			0.238995
$690$	3.01819	+	0.137645i	0.114900	+	0.00524004i
$691$	15.0029			0.570738			0.285369	−	0.958418i	$-0.407884\pi$
$691$	15.0029			0.570738			0.285369	+	0.958418i	$0.407884\pi$
$692$	−70.3652			−2.67488
$693$		0			0
$694$	−71.5595			−2.71636
$695$	5.32743			0.202081
$696$	11.6082	−	18.1434i	0.440006	−	0.687724i
$697$	6.05993			0.229536
$698$	−30.4648	−	52.7665i	−1.15311	−	1.99724i
$699$	−32.8442	−	1.49786i	−1.24228	−	0.0566542i
$700$		0			0
$701$	38.5113			1.45455			0.727275	−	0.686346i	$-0.240786\pi$
$701$	38.5113			1.45455			0.727275	+	0.686346i	$0.240786\pi$
$702$	−7.84202	+	10.0977i	−0.295978	+	0.381112i
$703$	−3.60963	−	6.25206i	−0.136140	−	0.235801i
$704$	16.5402	−	28.6484i	0.623381	−	1.07973i
$705$	−29.4449	+	46.0220i	−1.10896	+	1.73329i
$706$	40.9705	−	70.9630i	1.54195	−	2.67073i
$707$		0			0
$708$	−8.80778	−	17.0000i	−0.331017	−	0.638901i
$709$	7.64008			0.286929			0.143465	−	0.989655i	$-0.454176\pi$
$709$	7.64008			0.286929			0.143465	+	0.989655i	$0.454176\pi$
$710$	10.4445	+	18.0903i	0.391973	+	0.678918i
$711$	−25.4502	+	36.0481i	−0.954457	+	1.35191i
$712$	36.2798	−	62.8384i	1.35964	−	2.35497i
$713$	−0.318097	−	0.550960i	−0.0119128	−	0.0206336i
$714$		0			0
$715$	5.85447	−	10.1402i	0.218945	−	0.379224i
$716$	23.0057	+	39.8471i	0.859765	+	1.48916i
$717$	8.46410	+	0.386006i	0.316098	+	0.0144157i
$718$	31.4164	−	54.4148i	1.17245	−	2.03074i
$719$	−15.0182	+	26.0123i	−0.560084	+	0.970094i	0.437405	+	0.899265i	$0.355898\pi$
$719$	−15.0182	+	26.0123i	−0.560084	+	0.970094i	−0.997488	+	0.0708289i	$0.977436\pi$
$720$	33.5308	+	3.06472i	1.24962	+	0.114216i
$721$		0			0
$722$	−3.15486	−	5.46438i	−0.117412	−	0.203363i
$723$	45.2622	+	2.06419i	1.68332	+	0.0767679i
$724$	−88.7395			−3.29798
$725$	4.24844			0.157783
$726$	21.5474	−	33.6782i	0.799698	−	1.24992i
$727$	1.72812	+	2.99319i	0.0640923	+	0.111011i	0.896291	−	0.443466i	$-0.146251\pi$
$727$	1.72812	+	2.99319i	0.0640923	+	0.111011i	−0.832199	+	0.554478i	$0.812918\pi$
$728$		0			0
$729$	25.9969	+	7.29124i	0.962847	+	0.270046i
$730$	4.80972	−	8.33068i	0.178016	−	0.308332i
$731$	4.93560	−	8.54871i	0.182550	−	0.316185i
$732$	−7.34348	−	14.1738i	−0.271423	−	0.523878i
$733$	19.2630	+	33.3645i	0.711496	+	1.23235i	0.964295	+	0.264829i	$0.0853155\pi$
$733$	19.2630	+	33.3645i	0.711496	+	1.23235i	−0.252799	+	0.967519i	$0.581351\pi$
$734$	−33.7709	+	58.4929i	−1.24651	+	2.15901i
$735$		0			0
$736$	−0.0737345	−	0.127712i	−0.00271789	−	0.00470752i
$737$	35.7039	−	61.8409i	1.31517	−	2.27794i
$738$	19.8188	+	42.9357i	0.729539	+	1.58048i
$739$	−22.5620	−	39.0785i	−0.829955	−	1.43752i	−0.898073	−	0.439847i	$-0.855033\pi$
$739$	−22.5620	−	39.0785i	−0.829955	−	1.43752i	0.0681179	−	0.997677i	$-0.478301\pi$
$740$	18.7237			0.688298
$741$	3.78434	−	5.91486i	0.139021	−	0.217288i
$742$		0			0
$743$	−4.74338	+	8.21577i	−0.174018	+	0.301407i	−0.939821	−	0.341668i	$-0.889008\pi$
$743$	−4.74338	+	8.21577i	−0.174018	+	0.301407i	0.765803	+	0.643075i	$0.222342\pi$
$744$	−9.37266	−	18.0903i	−0.343618	−	0.663223i
$745$	17.5634	−	30.4207i	0.643474	−	1.11453i
$746$	20.0869	+	34.7915i	0.735432	+	1.27381i
$747$	2.82597	+	0.258294i	0.103397	+	0.00945048i
$748$	17.3126			0.633013
$749$		0			0
$750$	−16.6441	−	32.1250i	−0.607755	−	1.17304i
$751$	4.91595	+	8.51467i	0.179386	+	0.310705i	0.941670	−	0.336537i	$-0.109256\pi$
$751$	4.91595	+	8.51467i	0.179386	+	0.310705i	−0.762285	+	0.647242i	$0.775922\pi$
$752$	52.6313			1.91927
$753$	14.7068	+	28.3859i	0.535946	+	1.03444i
$754$	6.05408			0.220477
$755$	25.7496			0.937124
$756$		0			0
$757$	−41.8171			−1.51987			−0.759934	−	0.650000i	$-0.774769\pi$
$757$	−41.8171			−1.51987			−0.759934	+	0.650000i	$0.774769\pi$
$758$	−29.6156			−1.07569
$759$	0.983275	+	1.89783i	0.0356906	+	0.0688870i
$760$	−53.1416			−1.92765
$761$	11.4897	+	19.9007i	0.416501	+	0.721400i	0.995585	−	0.0938675i	$-0.0299230\pi$
$761$	11.4897	+	19.9007i	0.416501	+	0.721400i	−0.579084	+	0.815268i	$0.696590\pi$
$762$	1.31858	+	2.54500i	0.0477670	+	0.0921958i
$763$		0			0
$764$	−2.84494			−0.102926
$765$	−3.08453	−	6.68238i	−0.111521	−	0.241602i
$766$	15.2989	+	26.4985i	0.552773	+	0.957430i
$767$	1.36333	−	2.36135i	0.0492269	−	0.0852635i
$768$	25.7848	+	49.7677i	0.930429	+	1.79584i
$769$	3.04329	−	5.27113i	0.109744	−	0.190082i	−0.805923	−	0.592021i	$-0.798330\pi$
$769$	3.04329	−	5.27113i	0.109744	−	0.190082i	0.915666	+	0.401939i	$0.131664\pi$
$770$		0			0
$771$	−10.9531	+	17.1196i	−0.394467	+	0.616546i
$772$	49.2350			1.77201
$773$	−20.9107	−	36.2184i	−0.752105	−	1.30268i	−0.946801	−	0.321821i	$-0.895705\pi$
$773$	−20.9107	−	36.2184i	−0.752105	−	1.30268i	0.194695	−	0.980864i	$-0.437628\pi$
$774$	76.7108	+	7.01138i	2.75731	+	0.252019i
$775$	2.00933	−	3.48027i	0.0721774	−	0.125015i
$776$	29.0349	+	50.2899i	1.04229	+	1.80530i
$777$		0			0
$778$	25.3442	−	43.8974i	0.908632	−	1.57380i
$779$	−12.9861	−	22.4926i	−0.465275	−	0.805880i
$780$	8.37792	+	16.1704i	0.299978	+	0.578991i
$781$	−7.38891	+	12.7980i	−0.264396	+	0.457947i
$782$	−0.318097	+	0.550960i	−0.0113751	+	0.0197023i
$783$	−4.82383	−	11.8402i	−0.172390	−	0.423135i
$784$		0			0
$785$	7.85087	+	13.5981i	0.280210	+	0.485337i
$786$	−18.1764	+	28.4094i	−0.648329	+	1.01333i
$787$	−32.2920			−1.15109			−0.575543	−	0.817772i	$-0.695209\pi$
$787$	−32.2920			−1.15109			−0.575543	+	0.817772i	$0.695209\pi$
$788$	−66.5303			−2.37004
$789$	−13.0146	−	0.593531i	−0.463332	−	0.0211303i
$790$	46.9327	+	81.2898i	1.66979	+	2.89216i
$791$		0			0
$792$	28.6878	+	62.1498i	1.01938	+	2.20840i
$793$	1.13667	−	1.96878i	0.0403644	−	0.0699133i
$794$	29.0797	−	50.3675i	1.03200	−	1.78747i
$795$	−28.1519	−	1.28387i	−0.998446	−	0.0455342i
$796$	46.0261	+	79.7195i	1.63135	+	2.82558i
$797$	23.2829	−	40.3271i	0.824722	−	1.42846i	−0.0774101	−	0.996999i	$-0.524665\pi$
$797$	23.2829	−	40.3271i	0.824722	−	1.42846i	0.902132	−	0.431461i	$-0.142002\pi$
$798$		0			0
$799$	−5.75223	−	9.96316i	−0.203499	−	0.352471i
$800$	0.465761	−	0.806721i	0.0164671	−	0.0285219i
$801$	−18.0505	−	39.1049i	−0.637783	−	1.38170i
$802$	−3.15486	−	5.46438i	−0.111402	−	0.192954i
$803$	6.80525			0.240152
$804$	51.0933	+	98.6159i	1.80192	+	3.47792i
$805$		0			0
$806$	2.86333	−	4.95943i	0.100856	−	0.174688i
$807$	−17.5816	+	27.4798i	−0.618902	+	0.967334i
$808$	9.29893	−	16.1062i	0.327135	−	0.566615i
$809$	5.40116	+	9.35509i	0.189895	+	0.328908i	0.945215	−	0.326448i	$-0.105852\pi$
$809$	5.40116	+	9.35509i	0.189895	+	0.328908i	−0.755320	+	0.655356i	$0.772519\pi$
$810$	37.2580	−	43.7089i	1.30911	−	1.53577i
$811$	−5.58307			−0.196048			−0.0980240	−	0.995184i	$-0.531252\pi$
$811$	−5.58307			−0.196048			−0.0980240	+	0.995184i	$0.531252\pi$
$812$		0			0
$813$	41.4954	+	1.89240i	1.45531	+	0.0663694i
$814$	9.89037	+	17.1306i	0.346657	+	0.600428i
$815$	46.2101			1.61867
$816$	−3.82102	+	5.97220i	−0.133763	+	0.209069i
$817$	−42.3068			−1.48013
$818$	−84.4556			−2.95292
$819$		0			0
$820$	67.3609			2.35234
$821$	−31.7879			−1.10941			−0.554703	−	0.832048i	$-0.687168\pi$
$821$	−31.7879			−1.10941			−0.554703	+	0.832048i	$0.687168\pi$
$822$	15.6352	+	0.713045i	0.545341	+	0.0248703i
$823$	−36.0000			−1.25488			−0.627441	−	0.778664i	$-0.715897\pi$
$823$	−36.0000			−1.25488			−0.627441	+	0.778664i	$0.715897\pi$
$824$	24.5797	+	42.5732i	0.856273	+	1.48311i
$825$	−7.27647	+	11.3730i	−0.253334	+	0.395957i
$826$		0			0
$827$	15.9224			0.553675			0.276837	−	0.960917i	$-0.410714\pi$
$827$	15.9224			0.553675			0.276837	+	0.960917i	$0.410714\pi$
$828$	−3.31071	−	0.302599i	−0.115055	−	0.0105160i
$829$	17.7360	+	30.7196i	0.615996	+	1.06694i	0.990209	+	0.139594i	$0.0445797\pi$
$829$	17.7360	+	30.7196i	0.615996	+	1.06694i	−0.374213	+	0.927343i	$0.622087\pi$
$830$	3.01819	−	5.22765i	0.104763	−	0.181455i
$831$	12.3925	+	0.565161i	0.429891	+	0.0196052i
$832$	−3.66372	+	6.34574i	−0.127016	+	0.219999i
$833$		0			0
$834$	−8.74484	−	0.398809i	−0.302809	−	0.0138096i
$835$	21.9617			0.760014
$836$	−37.1000	−	64.2591i	−1.28313	−	2.22245i
$837$	−11.9808	−	1.64831i	−0.414118	−	0.0569738i
$838$	−4.99115	+	8.64492i	−0.172416	+	0.298634i
$839$	−27.3391	−	47.3527i	−0.943850	−	1.63480i	−0.758037	−	0.652212i	$-0.773841\pi$
$839$	−27.3391	−	47.3527i	−0.943850	−	1.63480i	−0.185814	−	0.982585i	$-0.559492\pi$
$840$		0			0
$841$	11.4730	−	19.8717i	0.395619	−	0.685233i
$842$	−25.9200	−	44.8948i	−0.893263	−	1.54718i
$843$	−13.8915	+	21.7122i	−0.478449	+	0.747809i
$844$	−9.24630	+	16.0151i	−0.318271	+	0.551261i
$845$	15.5615	−	26.9533i	0.535331	−	0.927221i
$846$	51.7783	−	73.3397i	1.78017	−	2.52147i
$847$		0			0
$848$	13.5737	+	23.5104i	0.466124	+	0.807350i
$849$	15.9335	+	30.7534i	0.546835	+	1.05546i
$850$	−4.01867			−0.137839
$851$	−0.486758			−0.0166858
$852$	−10.5737	−	20.4085i	−0.362250	−	0.699185i
$853$	−1.09884	−	1.90324i	−0.0376234	−	0.0651656i	0.846601	−	0.532229i	$-0.178645\pi$
$853$	−1.09884	−	1.90324i	−0.0376234	−	0.0651656i	−0.884224	+	0.467063i	$0.845312\pi$
$854$		0			0
$855$	−18.1929	+	25.7687i	−0.622184	+	0.881272i
$856$	−3.47296	+	6.01534i	−0.118703	+	0.205600i
$857$	−7.88823	+	13.6628i	−0.269457	+	0.466713i	−0.968722	−	0.248150i	$-0.920178\pi$
$857$	−7.88823	+	13.6628i	−0.269457	+	0.466713i	0.699265	+	0.714863i	$0.253511\pi$
$858$	−10.3691	+	16.2067i	−0.353994	+	0.553287i
$859$	2.78813	+	4.82918i	0.0951298	+	0.164770i	0.909663	−	0.415348i	$-0.136340\pi$
$859$	2.78813	+	4.82918i	0.0951298	+	0.164770i	−0.814533	+	0.580117i	$0.803007\pi$
$860$	54.8630	−	95.0255i	1.87081	−	3.24034i
$861$		0			0
$862$	27.8264	+	48.1968i	0.947773	+	1.64159i
$863$	−11.5634	+	20.0284i	−0.393623	+	0.681776i	−0.992924	−	0.118748i	$-0.962112\pi$
$863$	−11.5634	+	20.0284i	−0.393623	+	0.681776i	0.599301	+	0.800524i	$0.295445\pi$
$864$	−2.77714	−	0.382075i	−0.0944802	−	0.0129985i
$865$	22.5079	+	38.9848i	0.765291	+	1.32552i
$866$	5.94923			0.202163
$867$	−27.8661	−	1.27084i	−0.946384	−	0.0431599i
$868$		0			0
$869$	−33.2024	+	57.5083i	−1.12631	+	1.95083i
$870$	−27.1680	−	1.23900i	−0.921081	−	0.0420059i
$871$	−7.90856	+	13.6980i	−0.267971	+	0.464140i
$872$	−8.58998	−	14.8783i	−0.290893	−	0.503842i
$873$	34.3260	+	3.13740i	1.16176	+	0.106185i
$874$	2.72665			0.0922304
$875$		0			0
$876$	−5.70448	+	8.91601i	−0.192736	+	0.301244i
$877$	−1.96264	−	3.39939i	−0.0662737	−	0.114789i	0.830985	−	0.556295i	$-0.187778\pi$
$877$	−1.96264	−	3.39939i	−0.0662737	−	0.114789i	−0.897258	+	0.441506i	$0.854444\pi$
$878$	−57.7965			−1.95054
$879$	−26.0672	−	1.18880i	−0.879225	−	0.0400971i
$880$	50.6696			1.70807
$881$	−27.1986			−0.916345			−0.458173	−	0.888863i	$-0.651496\pi$
$881$	−27.1986			−0.916345			−0.458173	+	0.888863i	$0.651496\pi$
$882$		0			0
$883$	8.21341			0.276403			0.138202	−	0.990404i	$-0.455868\pi$
$883$	8.21341			0.276403			0.138202	+	0.990404i	$0.455868\pi$
$884$	−3.83482			−0.128979
$885$	−6.60126	+	10.3177i	−0.221899	+	0.346824i
$886$	33.0148			1.10915
$887$	−3.24057	−	5.61283i	−0.108808	−	0.188460i	0.806480	−	0.591262i	$-0.201370\pi$
$887$	−3.24057	−	5.61283i	−0.108808	−	0.188460i	−0.915287	+	0.402801i	$0.868037\pi$
$888$	−15.5723	−	0.710174i	−0.522571	−	0.0238319i
$889$		0			0
$890$	−91.6169			−3.07101
$891$	39.9581	+	7.36588i	1.33865	+	0.246766i
$892$	27.0093	+	46.7815i	0.904339	+	1.56636i
$893$	−24.6534	+	42.7009i	−0.824995	+	1.42893i
$894$	−31.1072	+	48.6201i	−1.04038	+	1.62610i
$895$	14.7178	−	25.4920i	0.491962	−	0.852103i
$896$		0			0
$897$	−0.217799	−	0.420378i	−0.00727211	−	0.0140360i
$898$	22.5438			0.752295
$899$	2.86333	+	4.95943i	0.0954973	+	0.165406i
$900$	−8.80106	−	19.0668i	−0.293369	−	0.635559i
$901$	2.96703	−	5.13904i	0.0988461	−	0.171206i
$902$	35.5818	+	61.6295i	1.18474	+	2.05204i
$903$		0			0
$904$	26.2527	−	45.4710i	0.873152	−	1.51234i
$905$	28.3853	+	49.1648i	0.943560	+	1.63429i
$906$	−42.2673	−	1.92760i	−1.40424	−	0.0640403i
$907$	−5.06440	+	8.77180i	−0.168161	+	0.291263i	−0.937773	−	0.347248i	$-0.887116\pi$
$907$	−5.06440	+	8.77180i	−0.168161	+	0.291263i	0.769613	+	0.638511i	$0.220449\pi$
$908$	2.80039	−	4.85041i	0.0929341	−	0.160967i
$909$	−4.62655	−	10.0230i	−0.153453	−	0.332443i
$910$		0			0
$911$	−22.9612	−	39.7699i	−0.760738	−	1.31764i	−0.942471	−	0.334289i	$-0.891504\pi$
$911$	−22.9612	−	39.7699i	−0.760738	−	1.31764i	0.181733	−	0.983348i	$-0.441829\pi$
$912$	30.3551	+	1.38435i	1.00516	+	0.0458403i
$913$	4.27042			0.141330
$914$	−21.6946			−0.717592
$915$	−5.50379	+	8.60235i	−0.181950	+	0.284385i
$916$	−36.4449	−	63.1245i	−1.20417	−	2.08569i
$917$		0			0
$918$	4.56294	+	11.1999i	0.150599	+	0.369650i
$919$	2.46216	−	4.26459i	0.0812192	−	0.140676i	−0.822555	−	0.568686i	$-0.807452\pi$
$919$	2.46216	−	4.26459i	0.0812192	−	0.140676i	0.903774	+	0.428010i	$0.140785\pi$
$920$	−1.79153	+	3.10303i	−0.0590651	+	0.102304i
$921$	−21.7288	−	41.9391i	−0.715988	−	1.38194i
$922$	6.96216	+	12.0588i	0.229287	+	0.397136i
$923$	1.63667	−	2.83480i	0.0538718	−	0.0933086i
$924$		0			0
$925$	−1.53736	−	2.66278i	−0.0505481	−	0.0875518i
$926$	19.3478	−	33.5113i	0.635807	−	1.10125i
$927$	29.0588	+	2.65598i	0.954417	+	0.0872339i
$928$	0.663715	+	1.14959i	0.0217875	+	0.0377371i
$929$	−0.00758649			−0.000248905			−0.000124452	−	1.00000i	$-0.500040\pi$
$929$	−0.00758649			−0.000248905			−0.000124452		1.00000i	$0.500040\pi$
$930$	−13.8643	+	21.6697i	−0.454628	+	0.710577i
$931$		0			0
$932$	38.4779	−	66.6457i	1.26039	−	2.18305i
$933$	−12.7345	−	24.5791i	−0.416910	−	0.804684i
$934$	27.0620	−	46.8727i	0.885494	−	1.53372i
$935$	−5.53784	−	9.59182i	−0.181107	−	0.313686i
$936$	−6.35447	−	13.7664i	−0.207702	−	0.449970i
$937$	−21.1623			−0.691341			−0.345670	−	0.938356i	$-0.612348\pi$
$937$	−21.1623			−0.691341			−0.345670	+	0.938356i	$0.612348\pi$
$938$		0			0
$939$	9.24105	+	17.8363i	0.301570	+	0.582066i
$940$	−63.9405	−	110.748i	−2.08551	−	3.61221i
$941$	−4.55816			−0.148592			−0.0742959	−	0.997236i	$-0.523671\pi$
$941$	−4.55816			−0.148592			−0.0742959	+	0.997236i	$0.523671\pi$
$942$	−11.8691	−	22.9087i	−0.386715	−	0.746405i
$943$	−1.75117			−0.0570260
$944$	11.7994			0.384038
$945$		0			0
$946$	115.920			3.76890
$947$	13.7352			0.446334			0.223167	−	0.974780i	$-0.428360\pi$
$947$	13.7352			0.446334			0.223167	+	0.974780i	$0.428360\pi$
$948$	−47.5136	−	91.7068i	−1.54317	−	2.97850i
$949$	−1.50739			−0.0489320
$950$	8.61177	+	14.9160i	0.279403	+	0.483940i
$951$	1.60769	+	3.10303i	0.0521329	+	0.100623i
$952$		0			0
$953$	8.80699			0.285286			0.142643	−	0.989774i	$-0.454440\pi$
$953$	8.80699			0.285286			0.142643	+	0.989774i	$0.454440\pi$
$954$	46.1146	+	4.21488i	1.49301	+	0.136462i
$955$	0.910019	+	1.57620i	0.0294475	+	0.0510046i
$956$	−9.91595	+	17.1749i	−0.320705	+	0.555477i
$957$	−8.85087	−	17.0832i	−0.286108	−	0.552222i
$958$	−30.7257	+	53.2184i	−0.992701	+	1.71941i
$959$		0			0
$960$	17.7398	−	27.7270i	0.572549	−	0.894886i
$961$	−25.5831			−0.825260
$962$	−2.19076	−	3.79450i	−0.0706329	−	0.122340i
$963$	1.72792	+	3.74340i	0.0556815	+	0.120629i
$964$	−53.0261	+	91.8438i	−1.70785	+	2.95809i
$965$	−15.7489	−	27.2779i	−0.506976	−	0.878108i
$966$		0			0
$967$	−19.1642	+	33.1934i	−0.616279	+	1.06743i	0.373880	+	0.927477i	$0.378027\pi$
$967$	−19.1642	+	33.1934i	−0.616279	+	1.06743i	−0.990159	+	0.139949i	$0.955306\pi$
$968$	23.7075	+	41.0626i	0.761987	+	1.31980i
$969$	−3.05555	−	5.89756i	−0.0981583	−	0.189457i
$970$	36.6608	−	63.4984i	1.17711	−	2.03881i
$971$	−15.5093	+	26.8630i	−0.497718	+	0.862073i	−0.999997	−	0.00263281i	$-0.999162\pi$
$971$	−15.5093	+	26.8630i	−0.497718	+	0.862073i	0.502278	+	0.864706i	$0.332495\pi$
$972$	−43.1452	+	46.1773i	−1.38388	+	1.48114i
$973$		0			0
$974$	−21.6498	−	37.4986i	−0.693704	−	1.20153i
$975$	1.61177	−	2.51917i	0.0516179	−	0.0806779i
$976$	9.83775			0.314899
$977$	−52.7424			−1.68738			−0.843689	−	0.536832i	$-0.819621\pi$
$977$	−52.7424			−1.68738			−0.843689	+	0.536832i	$0.819621\pi$
$978$	−75.8527	−	3.45927i	−2.42550	−	0.110615i
$979$	−32.4071	−	56.1307i	−1.03574	−	1.79395i
$980$		0			0
$981$	−10.1553	−	0.928200i	−0.324235	−	0.0296351i
$982$	16.9715	−	29.3955i	0.541582	−	0.938048i
$983$	−9.15146	+	15.8508i	−0.291886	+	0.505562i	−0.974256	−	0.225446i	$-0.927616\pi$
$983$	−9.15146	+	15.8508i	−0.291886	+	0.505562i	0.682370	+	0.731007i	$0.260950\pi$
$984$	−56.0231	−	2.55494i	−1.78595	−	0.0814484i
$985$	21.2812	+	36.8601i	0.678076	+	1.17446i
$986$	2.86333	−	4.95943i	0.0911869	−	0.157940i
$987$		0			0
$988$	8.21780	+	14.2336i	0.261443	+	0.452833i
$989$	−1.42627	+	2.47036i	−0.0453526	+	0.0785530i
$990$	49.8484	−	70.6062i	1.58429	−	2.24401i
$991$	6.30039	+	10.9126i	0.200138	+	0.346650i	0.948573	−	0.316559i	$-0.102527\pi$
$991$	6.30039	+	10.9126i	0.200138	+	0.346650i	−0.748434	+	0.663209i	$0.769194\pi$
$992$	1.25564			0.0398665
$993$	15.7039	+	30.3103i	0.498348	+	0.961869i
$994$		0			0
$995$	29.4449	−	51.0001i	0.933467	−	1.61681i
$996$	−3.57966	+	5.59496i	−0.113426	+	0.177283i
$997$	5.87120	−	10.1692i	0.185943	−	0.322062i	−0.757951	−	0.652311i	$-0.773799\pi$
$997$	5.87120	−	10.1692i	0.185943	−	0.322062i	0.943894	+	0.330249i	$0.107133\pi$
$998$	16.1010	+	27.8877i	0.509667	+	0.882770i
$999$	−5.67549	+	7.30798i	−0.179565	+	0.231214i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.h.b.373.1		6
3.2	odd	2		1323.2.h.e.226.3		6
7.2	even	3		441.2.f.d.148.3		6
7.3	odd	6		441.2.g.e.67.3		6
7.4	even	3		441.2.g.d.67.3		6
7.5	odd	6		63.2.f.b.22.3	✓	6
7.6	odd	2		441.2.h.c.373.1		6
9.2	odd	6		1323.2.g.b.667.1		6
9.7	even	3		441.2.g.d.79.3		6
21.2	odd	6		1323.2.f.c.442.1		6
21.5	even	6		189.2.f.a.64.1		6
21.11	odd	6		1323.2.g.b.361.1		6
21.17	even	6		1323.2.g.c.361.1		6
21.20	even	2		1323.2.h.d.226.3		6
28.19	even	6		1008.2.r.k.337.3		6
63.2	odd	6		1323.2.f.c.883.1		6
63.5	even	6		567.2.a.g.1.3		3
63.11	odd	6		1323.2.h.e.802.3		6
63.16	even	3		441.2.f.d.295.3		6
63.20	even	6		1323.2.g.c.667.1		6
63.23	odd	6		3969.2.a.p.1.3		3
63.25	even	3	inner	441.2.h.b.214.1		6
63.34	odd	6		441.2.g.e.79.3		6
63.38	even	6		1323.2.h.d.802.3		6
63.40	odd	6		567.2.a.d.1.1		3
63.47	even	6		189.2.f.a.127.1		6
63.52	odd	6		441.2.h.c.214.1		6
63.58	even	3		3969.2.a.m.1.1		3
63.61	odd	6		63.2.f.b.43.3	yes	6
84.47	odd	6		3024.2.r.g.1009.2		6
252.47	odd	6		3024.2.r.g.2017.2		6
252.103	even	6		9072.2.a.bq.1.2		3
252.131	odd	6		9072.2.a.cd.1.2		3
252.187	even	6		1008.2.r.k.673.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.b.22.3	✓	6	7.5	odd	6
63.2.f.b.43.3	yes	6	63.61	odd	6
189.2.f.a.64.1		6	21.5	even	6
189.2.f.a.127.1		6	63.47	even	6
441.2.f.d.148.3		6	7.2	even	3
441.2.f.d.295.3		6	63.16	even	3
441.2.g.d.67.3		6	7.4	even	3
441.2.g.d.79.3		6	9.7	even	3
441.2.g.e.67.3		6	7.3	odd	6
441.2.g.e.79.3		6	63.34	odd	6
441.2.h.b.214.1		6	63.25	even	3	inner
441.2.h.b.373.1		6	1.1	even	1	trivial
441.2.h.c.214.1		6	63.52	odd	6
441.2.h.c.373.1		6	7.6	odd	2
567.2.a.d.1.1		3	63.40	odd	6
567.2.a.g.1.3		3	63.5	even	6
1008.2.r.k.337.3		6	28.19	even	6
1008.2.r.k.673.3		6	252.187	even	6
1323.2.f.c.442.1		6	21.2	odd	6
1323.2.f.c.883.1		6	63.2	odd	6
1323.2.g.b.361.1		6	21.11	odd	6
1323.2.g.b.667.1		6	9.2	odd	6
1323.2.g.c.361.1		6	21.17	even	6
1323.2.g.c.667.1		6	63.20	even	6
1323.2.h.d.226.3		6	21.20	even	2
1323.2.h.d.802.3		6	63.38	even	6
1323.2.h.e.226.3		6	3.2	odd	2
1323.2.h.e.802.3		6	63.11	odd	6
3024.2.r.g.1009.2		6	84.47	odd	6
3024.2.r.g.2017.2		6	252.47	odd	6
3969.2.a.m.1.1		3	63.58	even	3
3969.2.a.p.1.3		3	63.23	odd	6
9072.2.a.bq.1.2		3	252.103	even	6
9072.2.a.cd.1.2		3	252.131	odd	6

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.46050 q^{2} +(-0.796790 - 1.53790i) q^{3} +4.05408 q^{4} +(-1.29679 - 2.24611i) q^{5} +(1.96050 + 3.78400i) q^{6} -5.05408 q^{8} +(-1.73025 + 2.45076i) q^{9} +O(q^{10})\)	\(q-2.46050 q^{2} +(-0.796790 - 1.53790i) q^{3} +4.05408 q^{4} +(-1.29679 - 2.24611i) q^{5} +(1.96050 + 3.78400i) q^{6} -5.05408 q^{8} +(-1.73025 + 2.45076i) q^{9} +(3.19076 + 5.52655i) q^{10} +(-2.25729 + 3.90975i) q^{11} +(-3.23025 - 6.23476i) q^{12} +(0.500000 - 0.866025i) q^{13} +(-2.42101 + 3.78400i) q^{15} +4.32743 q^{16} +(-0.472958 - 0.819187i) q^{17} +(4.25729 - 6.03011i) q^{18} +(-2.02704 + 3.51094i) q^{19} +(-5.25729 - 9.10590i) q^{20} +(5.55408 - 9.61996i) q^{22} +(0.136673 + 0.236725i) q^{23} +(4.02704 + 7.77266i) q^{24} +(-0.863327 + 1.49533i) q^{25} +(-1.23025 + 2.13086i) q^{26} +(5.14766 + 0.708209i) q^{27} +(-1.23025 - 2.13086i) q^{29} +(5.95691 - 9.31056i) q^{30} -2.32743 q^{31} -0.539495 q^{32} +(7.81138 + 0.356238i) q^{33} +(1.16372 + 2.01561i) q^{34} +(-7.01459 + 9.93559i) q^{36} +(-0.890369 + 1.54216i) q^{37} +(4.98755 - 8.63868i) q^{38} +(-1.73025 - 0.0789082i) q^{39} +(6.55408 + 11.3520i) q^{40} +(-3.20321 + 5.54812i) q^{41} +(5.21780 + 9.03749i) q^{43} +(-9.15126 + 15.8505i) q^{44} +(7.74844 + 0.708209i) q^{45} +(-0.336285 - 0.582462i) q^{46} +12.1623 q^{47} +(-3.44805 - 6.65514i) q^{48} +(2.12422 - 3.67926i) q^{50} +(-0.882977 + 1.38008i) q^{51} +(2.02704 - 3.51094i) q^{52} +(3.13667 + 5.43288i) q^{53} +(-12.6659 - 1.74255i) q^{54} +11.7089 q^{55} +(7.01459 + 0.319901i) q^{57} +(3.02704 + 5.24299i) q^{58} +2.72665 q^{59} +(-9.81498 + 15.3407i) q^{60} +2.27335 q^{61} +5.72665 q^{62} -7.32743 q^{64} -2.59358 q^{65} +(-19.2199 - 0.876526i) q^{66} -15.8171 q^{67} +(-1.91741 - 3.32105i) q^{68} +(0.255158 - 0.398809i) q^{69} +3.27335 q^{71} +(8.74484 - 12.3863i) q^{72} +(-0.753696 - 1.30544i) q^{73} +(2.19076 - 3.79450i) q^{74} +(2.98755 + 0.136247i) q^{75} +(-8.21780 + 14.2336i) q^{76} +(4.25729 + 0.194154i) q^{78} +14.7089 q^{79} +(-5.61177 - 9.71987i) q^{80} +(-3.01245 - 8.48087i) q^{81} +(7.88151 - 13.6512i) q^{82} +(-0.472958 - 0.819187i) q^{83} +(-1.22665 + 2.12463i) q^{85} +(-12.8384 - 22.2368i) q^{86} +(-2.29679 + 3.58985i) q^{87} +(11.4086 - 19.7602i) q^{88} +(-7.17830 + 12.4332i) q^{89} +(-19.0651 - 1.74255i) q^{90} +(0.554084 + 0.959702i) q^{92} +(1.85447 + 3.57935i) q^{93} -29.9253 q^{94} +10.5146 q^{95} +(0.429864 + 0.829688i) q^{96} +(-5.74484 - 9.95036i) q^{97} +(-5.67617 - 12.2969i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 2 q^{3} + 6 q^{4} - 5 q^{5} - q^{6} - 12 q^{8} - 4 q^{9}+O(q^{10}) \) 6 * q - 2 * q^2 - 2 * q^3 + 6 * q^4 - 5 * q^5 - q^6 - 12 * q^8 - 4 * q^9	\( 6 q - 2 q^{2} - 2 q^{3} + 6 q^{4} - 5 q^{5} - q^{6} - 12 q^{8} - 4 q^{9} + 2 q^{11} - 13 q^{12} + 3 q^{13} + 11 q^{15} + 6 q^{16} - 12 q^{17} + 10 q^{18} - 3 q^{19} - 16 q^{20} + 15 q^{22} + 15 q^{24} - 6 q^{25} - q^{26} + 7 q^{27} - q^{29} + 31 q^{30} + 6 q^{31} - 16 q^{32} + 13 q^{33} - 3 q^{34} - 11 q^{36} + 3 q^{37} + 8 q^{38} - 4 q^{39} + 21 q^{40} - 22 q^{41} + 3 q^{43} - 23 q^{44} + q^{45} - 12 q^{46} + 18 q^{47} + 14 q^{48} - 10 q^{50} - 12 q^{51} + 3 q^{52} + 18 q^{53} - 13 q^{54} + 12 q^{55} + 11 q^{57} + 9 q^{58} + 18 q^{59} - 17 q^{60} + 12 q^{61} + 36 q^{62} - 24 q^{64} - 10 q^{65} - 34 q^{66} + 6 q^{68} + 39 q^{69} + 18 q^{71} + 15 q^{72} + 3 q^{73} - 6 q^{74} - 4 q^{75} - 21 q^{76} + 10 q^{78} + 30 q^{79} + 11 q^{80} - 40 q^{81} + 9 q^{82} - 12 q^{83} - 9 q^{85} - 34 q^{86} - 11 q^{87} + 21 q^{88} - 2 q^{89} - 73 q^{90} - 15 q^{92} - 18 q^{93} - 48 q^{94} + 32 q^{95} + 7 q^{96} + 3 q^{97} - 46 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 2 * q^3 + 6 * q^4 - 5 * q^5 - q^6 - 12 * q^8 - 4 * q^9 + 2 * q^11 - 13 * q^12 + 3 * q^13 + 11 * q^15 + 6 * q^16 - 12 * q^17 + 10 * q^18 - 3 * q^19 - 16 * q^20 + 15 * q^22 + 15 * q^24 - 6 * q^25 - q^26 + 7 * q^27 - q^29 + 31 * q^30 + 6 * q^31 - 16 * q^32 + 13 * q^33 - 3 * q^34 - 11 * q^36 + 3 * q^37 + 8 * q^38 - 4 * q^39 + 21 * q^40 - 22 * q^41 + 3 * q^43 - 23 * q^44 + q^45 - 12 * q^46 + 18 * q^47 + 14 * q^48 - 10 * q^50 - 12 * q^51 + 3 * q^52 + 18 * q^53 - 13 * q^54 + 12 * q^55 + 11 * q^57 + 9 * q^58 + 18 * q^59 - 17 * q^60 + 12 * q^61 + 36 * q^62 - 24 * q^64 - 10 * q^65 - 34 * q^66 + 6 * q^68 + 39 * q^69 + 18 * q^71 + 15 * q^72 + 3 * q^73 - 6 * q^74 - 4 * q^75 - 21 * q^76 + 10 * q^78 + 30 * q^79 + 11 * q^80 - 40 * q^81 + 9 * q^82 - 12 * q^83 - 9 * q^85 - 34 * q^86 - 11 * q^87 + 21 * q^88 - 2 * q^89 - 73 * q^90 - 15 * q^92 - 18 * q^93 - 48 * q^94 + 32 * q^95 + 7 * q^96 + 3 * q^97 - 46 * q^99

Introduction

L-functions

Modular forms

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