LMFDB - Embedded newform 420.2.c.a.391.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [420,2,Mod(391,420)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(420, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))

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

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

chi := DirichletCharacter("420.391");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	420.c (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:	$3.35371688489$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 3 x^{12} + 2 x^{11} - 7 x^{10} + 12 x^{9} - 28 x^{8} + \cdots + 256 $ x^16 - 2x^15 + 3x^14 - 4x^13 + 3x^12 + 2x^11 - 7x^10 + 12x^9 - 28x^8 + 24x^7 - 28x^6 + 16x^5 + 48x^4 - 128x^3 + 192x^2 - 256*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			391.14
Root			$1.10145 + 0.887017i$ of defining polynomial
Character	$\chi$	$=$	420.391
Dual form			420.2.c.a.391.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.10145 + 0.887017i) q^{2} -1.00000 q^{3} +(0.426402 + 1.95402i) q^{4} -1.00000i q^{5} +(-1.10145 - 0.887017i) q^{6} +(0.391948 + 2.61656i) q^{7} +(-1.26358 + 2.53049i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(1.10145 + 0.887017i) q^{2} -1.00000 q^{3} +(0.426402 + 1.95402i) q^{4} -1.00000i q^{5} +(-1.10145 - 0.887017i) q^{6} +(0.391948 + 2.61656i) q^{7} +(-1.26358 + 2.53049i) q^{8} +1.00000 q^{9} +(0.887017 - 1.10145i) q^{10} -0.770756i q^{11} +(-0.426402 - 1.95402i) q^{12} +5.60576i q^{13} +(-1.88922 + 3.22968i) q^{14} +1.00000i q^{15} +(-3.63636 + 1.66639i) q^{16} +0.503042i q^{17} +(1.10145 + 0.887017i) q^{18} +1.63506 q^{19} +(1.95402 - 0.426402i) q^{20} +(-0.391948 - 2.61656i) q^{21} +(0.683673 - 0.848952i) q^{22} +1.42475i q^{23} +(1.26358 - 2.53049i) q^{24} -1.00000 q^{25} +(-4.97240 + 6.17449i) q^{26} -1.00000 q^{27} +(-4.94567 + 1.88158i) q^{28} +5.03595 q^{29} +(-0.887017 + 1.10145i) q^{30} -8.23212 q^{31} +(-5.48341 - 1.39006i) q^{32} +0.770756i q^{33} +(-0.446206 + 0.554077i) q^{34} +(2.61656 - 0.391948i) q^{35} +(0.426402 + 1.95402i) q^{36} +10.1403 q^{37} +(1.80094 + 1.45033i) q^{38} -5.60576i q^{39} +(2.53049 + 1.26358i) q^{40} -5.07885i q^{41} +(1.88922 - 3.22968i) q^{42} -9.06204i q^{43} +(1.50607 - 0.328652i) q^{44} -1.00000i q^{45} +(-1.26378 + 1.56930i) q^{46} +4.64967 q^{47} +(3.63636 - 1.66639i) q^{48} +(-6.69275 + 2.05111i) q^{49} +(-1.10145 - 0.887017i) q^{50} -0.503042i q^{51} +(-10.9537 + 2.39031i) q^{52} +0.455805 q^{53} +(-1.10145 - 0.887017i) q^{54} -0.770756 q^{55} +(-7.11642 - 2.31442i) q^{56} -1.63506 q^{57} +(5.54687 + 4.46697i) q^{58} +10.4908 q^{59} +(-1.95402 + 0.426402i) q^{60} +3.32394i q^{61} +(-9.06730 - 7.30202i) q^{62} +(0.391948 + 2.61656i) q^{63} +(-4.80671 - 6.39496i) q^{64} +5.60576 q^{65} +(-0.683673 + 0.848952i) q^{66} -8.70791i q^{67} +(-0.982952 + 0.214498i) q^{68} -1.42475i q^{69} +(3.22968 + 1.88922i) q^{70} -10.8176i q^{71} +(-1.26358 + 2.53049i) q^{72} -2.29564i q^{73} +(11.1691 + 8.99464i) q^{74} +1.00000 q^{75} +(0.697193 + 3.19494i) q^{76} +(2.01673 - 0.302096i) q^{77} +(4.97240 - 6.17449i) q^{78} +2.56336i q^{79} +(1.66639 + 3.63636i) q^{80} +1.00000 q^{81} +(4.50503 - 5.59412i) q^{82} +13.9979 q^{83} +(4.94567 - 1.88158i) q^{84} +0.503042 q^{85} +(8.03818 - 9.98142i) q^{86} -5.03595 q^{87} +(1.95039 + 0.973914i) q^{88} -2.98877i q^{89} +(0.887017 - 1.10145i) q^{90} +(-14.6678 + 2.19717i) q^{91} +(-2.78399 + 0.607518i) q^{92} +8.23212 q^{93} +(5.12139 + 4.12433i) q^{94} -1.63506i q^{95} +(5.48341 + 1.39006i) q^{96} +15.5818i q^{97} +(-9.19113 - 3.67738i) q^{98} -0.770756i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{2} - 16 q^{3} - 2 q^{4} - 2 q^{6} - 4 q^{7} + 2 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q + 2 * q^2 - 16 * q^3 - 2 * q^4 - 2 * q^6 - 4 * q^7 + 2 * q^8 + 16 * q^9	$ 16 q + 2 q^{2} - 16 q^{3} - 2 q^{4} - 2 q^{6} - 4 q^{7} + 2 q^{8} + 16 q^{9} + 2 q^{12} - 2 q^{14} + 6 q^{16} + 2 q^{18} - 24 q^{19} + 4 q^{21} - 12 q^{22} - 2 q^{24} - 16 q^{25} - 12 q^{26} - 16 q^{27} + 14 q^{28} + 16 q^{29} + 8 q^{31} - 18 q^{32} + 24 q^{34} - 2 q^{36} + 24 q^{37} + 28 q^{38} + 12 q^{40} + 2 q^{42} - 8 q^{44} - 20 q^{46} + 16 q^{47} - 6 q^{48} - 16 q^{49} - 2 q^{50} - 20 q^{52} - 32 q^{53} - 2 q^{54} + 2 q^{56} + 24 q^{57} - 32 q^{58} + 8 q^{59} + 16 q^{62} - 4 q^{63} - 2 q^{64} - 8 q^{65} + 12 q^{66} + 4 q^{68} + 2 q^{72} - 4 q^{74} + 16 q^{75} + 16 q^{76} - 8 q^{77} + 12 q^{78} - 16 q^{80} + 16 q^{81} - 4 q^{82} + 8 q^{83} - 14 q^{84} + 64 q^{86} - 16 q^{87} - 52 q^{88} + 16 q^{91} + 64 q^{92} - 8 q^{93} + 16 q^{94} + 18 q^{96} - 86 q^{98}+O(q^{100}) $ 16 * q + 2 * q^2 - 16 * q^3 - 2 * q^4 - 2 * q^6 - 4 * q^7 + 2 * q^8 + 16 * q^9 + 2 * q^12 - 2 * q^14 + 6 * q^16 + 2 * q^18 - 24 * q^19 + 4 * q^21 - 12 * q^22 - 2 * q^24 - 16 * q^25 - 12 * q^26 - 16 * q^27 + 14 * q^28 + 16 * q^29 + 8 * q^31 - 18 * q^32 + 24 * q^34 - 2 * q^36 + 24 * q^37 + 28 * q^38 + 12 * q^40 + 2 * q^42 - 8 * q^44 - 20 * q^46 + 16 * q^47 - 6 * q^48 - 16 * q^49 - 2 * q^50 - 20 * q^52 - 32 * q^53 - 2 * q^54 + 2 * q^56 + 24 * q^57 - 32 * q^58 + 8 * q^59 + 16 * q^62 - 4 * q^63 - 2 * q^64 - 8 * q^65 + 12 * q^66 + 4 * q^68 + 2 * q^72 - 4 * q^74 + 16 * q^75 + 16 * q^76 - 8 * q^77 + 12 * q^78 - 16 * q^80 + 16 * q^81 - 4 * q^82 + 8 * q^83 - 14 * q^84 + 64 * q^86 - 16 * q^87 - 52 * q^88 + 16 * q^91 + 64 * q^92 - 8 * q^93 + 16 * q^94 + 18 * q^96 - 86 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$.

$n$	$211$	$241$	$281$	$337$
$\chi(n)$	$-1$	$-1$	$1$	$1$

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 $

$2$	1.10145	+	0.887017i	0.778846	+	0.627216i
$2$	1.10145	+	0.887017i	0.778846	+	0.627216i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	0.426402	+	1.95402i	0.213201	+	0.977008i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−1.10145	−	0.887017i	−0.449667	−	0.362123i
$7$	0.391948	+	2.61656i	0.148142	+	0.988966i
$7$	0.391948	+	2.61656i	0.148142	+	0.988966i
$8$	−1.26358	+	2.53049i	−0.446744	+	0.894662i
$9$	1.00000			0.333333
$10$	0.887017	−	1.10145i	0.280499	−	0.348310i
$11$		−	0.770756i		−	0.232392i	−0.993226	−	0.116196i	$-0.962930\pi$
$11$		−	0.770756i		−	0.232392i	0.993226	−	0.116196i	$-0.0370700\pi$
$12$	−0.426402	−	1.95402i	−0.123092	−	0.564076i
$13$			5.60576i			1.55476i	0.629032	+	0.777379i	$0.283451\pi$
$13$			5.60576i			1.55476i	−0.629032	+	0.777379i	$0.716549\pi$
$14$	−1.88922	+	3.22968i	−0.504915	+	0.863169i
$15$			1.00000i			0.258199i
$16$	−3.63636	+	1.66639i	−0.909091	+	0.416598i
$17$			0.503042i			0.122005i	0.998138	+	0.0610027i	$0.0194298\pi$
$17$			0.503042i			0.122005i	−0.998138	+	0.0610027i	$0.980570\pi$
$18$	1.10145	+	0.887017i	0.259615	+	0.209072i
$19$	1.63506			0.375109			0.187554	−	0.982254i	$-0.439944\pi$
$19$	1.63506			0.375109			0.187554	+	0.982254i	$0.439944\pi$
$20$	1.95402	−	0.426402i	0.436931	−	0.0953464i
$21$	−0.391948	−	2.61656i	−0.0855300	−	0.570980i
$22$	0.683673	−	0.848952i	0.145760	−	0.180997i
$23$			1.42475i			0.297082i	0.988906	+	0.148541i	$0.0474577\pi$
$23$			1.42475i			0.297082i	−0.988906	+	0.148541i	$0.952542\pi$
$24$	1.26358	−	2.53049i	0.257928	−	0.516533i
$25$	−1.00000			−0.200000
$26$	−4.97240	+	6.17449i	−0.975169	+	1.21092i
$27$	−1.00000			−0.192450
$28$	−4.94567	+	1.88158i	−0.934644	+	0.355585i
$29$	5.03595			0.935152			0.467576	−	0.883953i	$-0.345127\pi$
$29$	5.03595			0.935152			0.467576	+	0.883953i	$0.345127\pi$
$30$	−0.887017	+	1.10145i	−0.161946	+	0.201097i
$31$	−8.23212			−1.47853			−0.739266	−	0.673414i	$-0.764827\pi$
$31$	−8.23212			−1.47853			−0.739266	+	0.673414i	$0.764827\pi$
$32$	−5.48341	−	1.39006i	−0.969338	−	0.245730i
$33$			0.770756i			0.134171i
$34$	−0.446206	+	0.554077i	−0.0765238	+	0.0950235i
$35$	2.61656	−	0.391948i	0.442279	−	0.0662513i
$36$	0.426402	+	1.95402i	0.0710670	+	0.325669i
$37$	10.1403			1.66706			0.833530	−	0.552475i	$-0.186316\pi$
$37$	10.1403			1.66706			0.833530	+	0.552475i	$0.186316\pi$
$38$	1.80094	+	1.45033i	0.292152	+	0.235274i
$39$		−	5.60576i		−	0.897640i
$40$	2.53049	+	1.26358i	0.400105	+	0.199790i
$41$		−	5.07885i		−	0.793184i	−0.917995	−	0.396592i	$-0.870193\pi$
$41$		−	5.07885i		−	0.793184i	0.917995	−	0.396592i	$-0.129807\pi$
$42$	1.88922	−	3.22968i	0.291513	−	0.498351i
$43$		−	9.06204i		−	1.38195i	−0.722880	−	0.690974i	$-0.757182\pi$
$43$		−	9.06204i		−	1.38195i	0.722880	−	0.690974i	$-0.242818\pi$
$44$	1.50607	−	0.328652i	0.227049	−	0.0495461i
$45$		−	1.00000i		−	0.149071i
$46$	−1.26378	+	1.56930i	−0.186334	+	0.231381i
$47$	4.64967			0.678223			0.339112	−	0.940746i	$-0.389874\pi$
$47$	4.64967			0.678223			0.339112	+	0.940746i	$0.389874\pi$
$48$	3.63636	−	1.66639i	0.524864	−	0.240523i
$49$	−6.69275	+	2.05111i	−0.956108	+	0.293016i
$50$	−1.10145	−	0.887017i	−0.155769	−	0.125443i
$51$		−	0.503042i		−	0.0704399i
$52$	−10.9537	+	2.39031i	−1.51901	+	0.331476i
$53$	0.455805			0.0626096			0.0313048	−	0.999510i	$-0.490034\pi$
$53$	0.455805			0.0626096			0.0313048	+	0.999510i	$0.490034\pi$
$54$	−1.10145	−	0.887017i	−0.149889	−	0.120708i
$55$	−0.770756			−0.103929
$56$	−7.11642	−	2.31442i	−0.950972	−	0.309277i
$57$	−1.63506			−0.216569
$58$	5.54687	+	4.46697i	0.728339	+	0.586542i
$59$	10.4908			1.36578			0.682890	−	0.730521i	$-0.260723\pi$
$59$	10.4908			1.36578			0.682890	+	0.730521i	$0.260723\pi$
$60$	−1.95402	+	0.426402i	−0.252262	+	0.0550483i
$61$			3.32394i			0.425587i	0.977097	+	0.212794i	$0.0682562\pi$
$61$			3.32394i			0.425587i	−0.977097	+	0.212794i	$0.931744\pi$
$62$	−9.06730	−	7.30202i	−1.15155	−	0.927358i
$63$	0.391948	+	2.61656i	0.0493808	+	0.329655i
$64$	−4.80671	−	6.39496i	−0.600839	−	0.799370i
$65$	5.60576			0.695309
$66$	−0.683673	+	0.848952i	−0.0841544	+	0.104499i
$67$		−	8.70791i		−	1.06384i	−0.846794	−	0.531920i	$-0.821471\pi$
$67$		−	8.70791i		−	1.06384i	0.846794	−	0.531920i	$-0.178529\pi$
$68$	−0.982952	+	0.214498i	−0.119200	+	0.0260117i
$69$		−	1.42475i		−	0.171520i
$70$	3.22968	+	1.88922i	0.386021	+	0.225805i
$71$		−	10.8176i		−	1.28382i	−0.766781	−	0.641909i	$-0.778143\pi$
$71$		−	10.8176i		−	1.28382i	0.766781	−	0.641909i	$-0.221857\pi$
$72$	−1.26358	+	2.53049i	−0.148915	+	0.298221i
$73$		−	2.29564i		−	0.268685i	−0.990935	−	0.134342i	$-0.957108\pi$
$73$		−	2.29564i		−	0.268685i	0.990935	−	0.134342i	$-0.0428922\pi$
$74$	11.1691	+	8.99464i	1.29838	+	1.04561i
$75$	1.00000			0.115470
$76$	0.697193	+	3.19494i	0.0799736	+	0.366484i
$77$	2.01673	−	0.302096i	0.229827	−	0.0344270i
$78$	4.97240	−	6.17449i	0.563014	−	0.699123i
$79$			2.56336i			0.288400i	0.989549	+	0.144200i	$0.0460609\pi$
$79$			2.56336i			0.288400i	−0.989549	+	0.144200i	$0.953939\pi$
$80$	1.66639	+	3.63636i	0.186309	+	0.406558i
$81$	1.00000			0.111111
$82$	4.50503	−	5.59412i	0.497497	−	0.617768i
$83$	13.9979			1.53646			0.768232	−	0.640171i	$-0.221137\pi$
$83$	13.9979			1.53646			0.768232	+	0.640171i	$0.221137\pi$
$84$	4.94567	−	1.88158i	0.539617	−	0.205297i
$85$	0.503042			0.0545625
$86$	8.03818	−	9.98142i	0.866779	−	1.07632i
$87$	−5.03595			−0.539911
$88$	1.95039	+	0.973914i	0.207912	+	0.103820i
$89$		−	2.98877i		−	0.316809i	−0.987374	−	0.158404i	$-0.949365\pi$
$89$		−	2.98877i		−	0.316809i	0.987374	−	0.158404i	$-0.0506349\pi$
$90$	0.887017	−	1.10145i	0.0934998	−	0.116103i
$91$	−14.6678	+	2.19717i	−1.53760	+	0.230326i
$92$	−2.78399	+	0.607518i	−0.290251	+	0.0633382i
$93$	8.23212			0.853631
$94$	5.12139	+	4.12433i	0.528231	+	0.425392i
$95$		−	1.63506i		−	0.167754i
$96$	5.48341	+	1.39006i	0.559648	+	0.141872i
$97$			15.5818i			1.58209i	0.611756	+	0.791046i	$0.290463\pi$
$97$			15.5818i			1.58209i	−0.611756	+	0.791046i	$0.709537\pi$
$98$	−9.19113	−	3.67738i	−0.928444	−	0.371472i
$99$		−	0.770756i		−	0.0774639i
$100$	−0.426402	−	1.95402i	−0.0426402	−	0.195402i
$101$		−	18.9661i		−	1.88719i	−0.331097	−	0.943597i	$-0.607419\pi$
$101$		−	18.9661i		−	1.88719i	0.331097	−	0.943597i	$-0.392581\pi$
$102$	0.446206	−	0.554077i	0.0441810	−	0.0548618i
$103$	8.23760			0.811675			0.405837	−	0.913945i	$-0.366980\pi$
$103$	8.23760			0.811675			0.405837	+	0.913945i	$0.366980\pi$
$104$	−14.1853	−	7.08335i	−1.39098	−	0.694579i
$105$	−2.61656	+	0.391948i	−0.255350	+	0.0382502i
$106$	0.502048	+	0.404306i	0.0487632	+	0.0392697i
$107$			11.8042i			1.14115i	0.821244	+	0.570577i	$0.193280\pi$
$107$			11.8042i			1.14115i	−0.821244	+	0.570577i	$0.806720\pi$
$108$	−0.426402	−	1.95402i	−0.0410306	−	0.188025i
$109$	−9.80783			−0.939419			−0.469710	−	0.882821i	$-0.655641\pi$
$109$	−9.80783			−0.939419			−0.469710	+	0.882821i	$0.655641\pi$
$110$	−0.848952	−	0.683673i	−0.0809444	−	0.0651857i
$111$	−10.1403			−0.962477
$112$	−5.78548	−	8.86161i	−0.546677	−	0.837344i
$113$	−10.0104			−0.941702			−0.470851	−	0.882213i	$-0.656053\pi$
$113$	−10.0104			−0.941702			−0.470851	+	0.882213i	$0.656053\pi$
$114$	−1.80094	−	1.45033i	−0.168674	−	0.135836i
$115$	1.42475			0.132859
$116$	2.14734	+	9.84033i	0.199376	+	0.913652i
$117$			5.60576i			0.518253i
$118$	11.5551	+	9.30548i	1.06373	+	0.856638i
$119$	−1.31624	+	0.197166i	−0.120659	+	0.0180742i
$120$	−2.53049	−	1.26358i	−0.231001	−	0.115349i
$121$	10.4059			0.945994
$122$	−2.94839	+	3.66117i	−0.266935	+	0.331467i
$123$			5.07885i			0.457945i
$124$	−3.51019	−	16.0857i	−0.315225	−	1.44454i
$125$			1.00000i			0.0894427i
$126$	−1.88922	+	3.22968i	−0.168305	+	0.287723i
$127$			3.09530i			0.274663i	0.990525	+	0.137332i	$0.0438526\pi$
$127$			3.09530i			0.274663i	−0.990525	+	0.137332i	$0.956147\pi$
$128$	0.378061	−	11.3074i	0.0334162	−	0.999442i
$129$			9.06204i			0.797868i
$130$	6.17449	+	4.97240i	0.541538	+	0.436109i
$131$	−17.5001			−1.52899			−0.764495	−	0.644630i	$-0.777011\pi$
$131$	−17.5001			−1.52899			−0.764495	+	0.644630i	$0.777011\pi$
$132$	−1.50607	+	0.328652i	−0.131087	+	0.0286055i
$133$	0.640859	+	4.27823i	0.0555695	+	0.370970i
$134$	7.72407	−	9.59137i	0.667258	−	0.828568i
$135$			1.00000i			0.0860663i
$136$	−1.27294	−	0.635635i	−0.109154	−	0.0545052i
$137$	−15.6542			−1.33742			−0.668712	−	0.743521i	$-0.733154\pi$
$137$	−15.6542			−1.33742			−0.668712	+	0.743521i	$0.733154\pi$
$138$	1.26378	−	1.56930i	0.107580	−	0.133588i
$139$	1.13095			0.0959261			0.0479630	−	0.998849i	$-0.484727\pi$
$139$	1.13095			0.0959261			0.0479630	+	0.998849i	$0.484727\pi$
$140$	1.88158	+	4.94567i	0.159022	+	0.417985i
$141$	−4.64967			−0.391572
$142$	9.59542	−	11.9151i	0.805230	−	0.999895i
$143$	4.32067			0.361313
$144$	−3.63636	+	1.66639i	−0.303030	+	0.138866i
$145$		−	5.03595i		−	0.418213i
$146$	2.03627	−	2.52855i	0.168523	−	0.209264i
$147$	6.69275	−	2.05111i	0.552009	−	0.169173i
$148$	4.32386	+	19.8144i	0.355419	+	1.62873i
$149$	21.3643			1.75023			0.875117	−	0.483911i	$-0.160784\pi$
$149$	21.3643			1.75023			0.875117	+	0.483911i	$0.160784\pi$
$150$	1.10145	+	0.887017i	0.0899333	+	0.0724246i
$151$			2.83045i			0.230339i	0.993346	+	0.115169i	$0.0367411\pi$
$151$			2.83045i			0.230339i	−0.993346	+	0.115169i	$0.963259\pi$
$152$	−2.06604	+	4.13750i	−0.167578	+	0.335595i
$153$			0.503042i			0.0406685i
$154$	2.48930	+	1.45613i	0.200593	+	0.117338i
$155$			8.23212i			0.661219i
$156$	10.9537	−	2.39031i	0.877002	−	0.191378i
$157$			18.7903i			1.49963i	0.661649	+	0.749814i	$0.269857\pi$
$157$			18.7903i			1.49963i	−0.661649	+	0.749814i	$0.730143\pi$
$158$	−2.27374	+	2.82342i	−0.180889	+	0.224619i
$159$	−0.455805			−0.0361477
$160$	−1.39006	+	5.48341i	−0.109894	+	0.433501i
$161$	−3.72795	+	0.558430i	−0.293804	+	0.0440104i
$162$	1.10145	+	0.887017i	0.0865384	+	0.0696906i
$163$			7.40744i			0.580195i	0.956997	+	0.290098i	$0.0936878\pi$
$163$			7.40744i			0.580195i	−0.956997	+	0.290098i	$0.906312\pi$
$164$	9.92417	−	2.16563i	0.774947	−	0.169108i
$165$	0.770756			0.0600032
$166$	15.4180	+	12.4163i	1.19667	+	0.963694i
$167$	−2.96147			−0.229165			−0.114583	−	0.993414i	$-0.536553\pi$
$167$	−2.96147			−0.229165			−0.114583	+	0.993414i	$0.536553\pi$
$168$	7.11642	+	2.31442i	0.549044	+	0.178561i
$169$	−18.4246			−1.41727
$170$	0.554077	+	0.446206i	0.0424958	+	0.0342225i
$171$	1.63506			0.125036
$172$	17.7074	−	3.86407i	1.35017	−	0.294633i
$173$		−	15.0215i		−	1.14206i	−0.820928	−	0.571031i	$-0.806543\pi$
$173$		−	15.0215i		−	1.14206i	0.820928	−	0.571031i	$-0.193457\pi$
$174$	−5.54687	−	4.46697i	−0.420507	−	0.338640i
$175$	−0.391948	−	2.61656i	−0.0296285	−	0.197793i
$176$	1.28438	+	2.80275i	0.0968140	+	0.211265i
$177$	−10.4908			−0.788533
$178$	2.65109	−	3.29199i	0.198707	−	0.246745i
$179$		−	4.82936i		−	0.360963i	−0.983578	−	0.180482i	$-0.942234\pi$
$179$		−	4.82936i		−	0.360963i	0.983578	−	0.180482i	$-0.0577656\pi$
$180$	1.95402	−	0.426402i	0.145644	−	0.0317821i
$181$		−	18.2050i		−	1.35316i	−0.736367	−	0.676582i	$-0.763460\pi$
$181$		−	18.2050i		−	1.35316i	0.736367	−	0.676582i	$-0.236540\pi$
$182$	−18.1048	−	10.5905i	−1.34202	−	0.785021i
$183$		−	3.32394i		−	0.245713i
$184$	−3.60532	−	1.80030i	−0.265788	−	0.132720i
$185$		−	10.1403i		−	0.745532i
$186$	9.06730	+	7.30202i	0.664846	+	0.535410i
$187$	0.387722			0.0283531
$188$	1.98263	+	9.08552i	0.144598	+	0.662630i
$189$	−0.391948	−	2.61656i	−0.0285100	−	0.190327i
$190$	1.45033	−	1.80094i	0.105218	−	0.130654i
$191$			5.65184i			0.408953i	0.978871	+	0.204476i	$0.0655492\pi$
$191$			5.65184i			0.408953i	−0.978871	+	0.204476i	$0.934451\pi$
$192$	4.80671	+	6.39496i	0.346895	+	0.461516i
$193$	−16.0978			−1.15874			−0.579372	−	0.815063i	$-0.696702\pi$
$193$	−16.0978			−1.15874			−0.579372	+	0.815063i	$0.696702\pi$
$194$	−13.8213	+	17.1626i	−0.992313	+	1.23221i
$195$	−5.60576			−0.401437
$196$	−6.86171	−	12.2032i	−0.490122	−	0.871654i
$197$	−12.2972			−0.876141			−0.438071	−	0.898941i	$-0.644338\pi$
$197$	−12.2972			−0.876141			−0.438071	+	0.898941i	$0.644338\pi$
$198$	0.683673	−	0.848952i	0.0485865	−	0.0603324i
$199$	−16.8234			−1.19258			−0.596290	−	0.802769i	$-0.703359\pi$
$199$	−16.8234			−1.19258			−0.596290	+	0.802769i	$0.703359\pi$
$200$	1.26358	−	2.53049i	0.0893488	−	0.178932i
$201$			8.70791i			0.614209i
$202$	16.8232	−	20.8902i	1.18368	−	1.46983i
$203$	1.97383	+	13.1769i	0.138536	+	0.924834i
$204$	0.982952	−	0.214498i	0.0688204	−	0.0150179i
$205$	−5.07885			−0.354723
$206$	9.07333	+	7.30689i	0.632169	+	0.509095i
$207$			1.42475i			0.0990273i
$208$	−9.34141	−	20.3846i	−0.647710	−	1.41342i
$209$		−	1.26023i		−	0.0871721i
$210$	−3.22968	−	1.88922i	−0.222869	−	0.130368i
$211$			9.19446i			0.632973i	0.948597	+	0.316486i	$0.102503\pi$
$211$			9.19446i			0.632973i	−0.948597	+	0.316486i	$0.897497\pi$
$212$	0.194356	+	0.890650i	0.0133484	+	0.0611701i
$213$			10.8176i			0.741212i
$214$	−10.4705	+	13.0018i	−0.715749	+	0.888782i
$215$	−9.06204			−0.618026
$216$	1.26358	−	2.53049i	0.0859760	−	0.172178i
$217$	−3.22656	−	21.5398i	−0.219033	−	1.46222i
$218$	−10.8029	−	8.69971i	−0.731663	−	0.589219i
$219$			2.29564i			0.155125i
$220$	−0.328652	−	1.50607i	−0.0221577	−	0.101539i
$221$	−2.81993			−0.189689
$222$	−11.1691	−	8.99464i	−0.749621	−	0.603681i
$223$	22.8560			1.53055			0.765275	−	0.643704i	$-0.222603\pi$
$223$	22.8560			1.53055			0.765275	+	0.643704i	$0.222603\pi$
$224$	1.48796	−	14.8925i	0.0994185	−	0.995046i
$225$	−1.00000			−0.0666667
$226$	−11.0260	−	8.87942i	−0.733440	−	0.590650i
$227$	17.4680			1.15939			0.579697	−	0.814832i	$-0.303171\pi$
$227$	17.4680			1.15939			0.579697	+	0.814832i	$0.303171\pi$
$228$	−0.697193	−	3.19494i	−0.0461728	−	0.211590i
$229$			12.6233i			0.834169i	0.908868	+	0.417085i	$0.136948\pi$
$229$			12.6233i			0.834169i	−0.908868	+	0.417085i	$0.863052\pi$
$230$	1.56930	+	1.26378i	0.103477	+	0.0833313i
$231$	−2.01673	+	0.302096i	−0.132691	+	0.0198765i
$232$	−6.36334	+	12.7434i	−0.417774	+	0.836645i
$233$	−3.89410			−0.255111			−0.127555	−	0.991831i	$-0.540713\pi$
$233$	−3.89410			−0.255111			−0.127555	+	0.991831i	$0.540713\pi$
$234$	−4.97240	+	6.17449i	−0.325056	+	0.403639i
$235$		−	4.64967i		−	0.303311i
$236$	4.47328	+	20.4991i	0.291186	+	1.33438i
$237$		−	2.56336i		−	0.166508i
$238$	−1.62466	−	0.950355i	−0.105311	−	0.0616024i
$239$			11.6497i			0.753559i	0.926303	+	0.376779i	$0.122968\pi$
$239$			11.6497i			0.753559i	−0.926303	+	0.376779i	$0.877032\pi$
$240$	−1.66639	−	3.63636i	−0.107565	−	0.234726i
$241$		−	21.0259i		−	1.35440i	−0.735799	−	0.677200i	$-0.763193\pi$
$241$		−	21.0259i		−	1.35440i	0.735799	−	0.677200i	$-0.236807\pi$
$242$	11.4617	+	9.23024i	0.736783	+	0.593342i
$243$	−1.00000			−0.0641500
$244$	−6.49504	+	1.41734i	−0.415802	+	0.0907357i
$245$	2.05111	+	6.69275i	0.131041	+	0.427584i
$246$	−4.50503	+	5.59412i	−0.287230	+	0.356668i
$247$			9.16576i			0.583203i
$248$	10.4020	−	20.8312i	0.660525	−	1.32279i
$249$	−13.9979			−0.887078
$250$	−0.887017	+	1.10145i	−0.0560999	+	0.0696621i
$251$	1.36484			0.0861478			0.0430739	−	0.999072i	$-0.486285\pi$
$251$	1.36484			0.0861478			0.0430739	+	0.999072i	$0.486285\pi$
$252$	−4.94567	+	1.88158i	−0.311548	+	0.118528i
$253$	1.09814			0.0690393
$254$	−2.74558	+	3.40933i	−0.172273	+	0.213920i
$255$	−0.503042			−0.0315017
$256$	10.4463	−	12.1192i	0.652891	−	0.757452i
$257$			4.44214i			0.277093i	0.990356	+	0.138547i	$0.0442431\pi$
$257$			4.44214i			0.277093i	−0.990356	+	0.138547i	$0.955757\pi$
$258$	−8.03818	+	9.98142i	−0.500435	+	0.621416i
$259$	3.97448	+	26.5328i	0.246962	+	1.64866i
$260$	2.39031	+	10.9537i	0.148241	+	0.679323i
$261$	5.03595			0.311717
$262$	−19.2755	−	15.5229i	−1.19085	−	0.959006i
$263$		−	4.92839i		−	0.303898i	−0.988388	−	0.151949i	$-0.951445\pi$
$263$		−	4.92839i		−	0.303898i	0.988388	−	0.151949i	$-0.0485549\pi$
$264$	−1.95039	−	0.973914i	−0.120038	−	0.0599403i
$265$		−	0.455805i		−	0.0279999i
$266$	−3.08899	+	5.28073i	−0.189398	+	0.323782i
$267$			2.98877i			0.182910i
$268$	17.0154	−	3.71307i	1.03938	−	0.226812i
$269$			25.0193i			1.52546i	0.646719	+	0.762728i	$0.276141\pi$
$269$			25.0193i			1.52546i	−0.646719	+	0.762728i	$0.723859\pi$
$270$	−0.887017	+	1.10145i	−0.0539821	+	0.0670324i
$271$	12.1353			0.737170			0.368585	−	0.929594i	$-0.379842\pi$
$271$	12.1353			0.737170			0.368585	+	0.929594i	$0.379842\pi$
$272$	−0.838265	−	1.82924i	−0.0508273	−	0.110914i
$273$	14.6678	−	2.19717i	0.887736	−	0.132979i
$274$	−17.2423	−	13.8855i	−1.04165	−	0.838854i
$275$			0.770756i			0.0464783i
$276$	2.78399	−	0.607518i	0.167577	−	0.0365683i
$277$	19.4692			1.16979			0.584896	−	0.811108i	$-0.301135\pi$
$277$	19.4692			1.16979			0.584896	+	0.811108i	$0.301135\pi$
$278$	1.24569	+	1.00317i	0.0747116	+	0.0601663i
$279$	−8.23212			−0.492844
$280$	−2.31442	+	7.11642i	−0.138313	+	0.425288i
$281$	−17.7452			−1.05859			−0.529296	−	0.848437i	$-0.677544\pi$
$281$	−17.7452			−1.05859			−0.529296	+	0.848437i	$0.677544\pi$
$282$	−5.12139	−	4.12433i	−0.304975	−	0.245600i
$283$	−29.4942			−1.75325			−0.876623	−	0.481177i	$-0.840209\pi$
$283$	−29.4942			−1.75325			−0.876623	+	0.481177i	$0.840209\pi$
$284$	21.1378	−	4.61266i	1.25430	−	0.273711i
$285$			1.63506i			0.0968526i
$286$	4.75902	+	3.83251i	0.281407	+	0.226621i
$287$	13.2891	−	1.99065i	0.784432	−	0.117504i
$288$	−5.48341	−	1.39006i	−0.323113	−	0.0819100i
$289$	16.7469			0.985115
$290$	4.46697	−	5.54687i	0.262310	−	0.325723i
$291$		−	15.5818i		−	0.913422i
$292$	4.48573	−	0.978867i	0.262507	−	0.0572839i
$293$			19.8780i			1.16129i	0.814158	+	0.580643i	$0.197199\pi$
$293$			19.8780i			1.16129i	−0.814158	+	0.580643i	$0.802801\pi$
$294$	9.19113	+	3.67738i	0.536038	+	0.214469i
$295$		−	10.4908i		−	0.610795i
$296$	−12.8131	+	25.6599i	−0.744749	+	1.49145i
$297$			0.770756i			0.0447238i
$298$	23.5318	+	18.9505i	1.36316	+	1.09777i
$299$	−7.98683			−0.461890
$300$	0.426402	+	1.95402i	0.0246183	+	0.112815i
$301$	23.7114	−	3.55185i	1.36670	−	0.204725i
$302$	−2.51065	+	3.11761i	−0.144472	+	0.179398i
$303$			18.9661i			1.08957i
$304$	−5.94567	+	2.72466i	−0.341008	+	0.156270i
$305$	3.32394			0.190328
$306$	−0.446206	+	0.554077i	−0.0255079	+	0.0316745i
$307$	2.12425			0.121238			0.0606188	−	0.998161i	$-0.480693\pi$
$307$	2.12425			0.121238			0.0606188	+	0.998161i	$0.480693\pi$
$308$	1.45024	+	3.81190i	0.0826350	+	0.217203i
$309$	−8.23760			−0.468621
$310$	−7.30202	+	9.06730i	−0.414727	+	0.514988i
$311$	10.2870			0.583323			0.291661	−	0.956522i	$-0.405792\pi$
$311$	10.2870			0.583323			0.291661	+	0.956522i	$0.405792\pi$
$312$	14.1853	+	7.08335i	0.803084	+	0.401015i
$313$		−	17.8800i		−	1.01064i	−0.862932	−	0.505320i	$-0.831374\pi$
$313$		−	17.8800i		−	1.01064i	0.862932	−	0.505320i	$-0.168626\pi$
$314$	−16.6673	+	20.6966i	−0.940590	+	1.16798i
$315$	2.61656	−	0.391948i	0.147426	−	0.0220838i
$316$	−5.00884	+	1.09302i	−0.281769	+	0.0614872i
$317$	12.3840			0.695557			0.347778	−	0.937577i	$-0.386936\pi$
$317$	12.3840			0.695557			0.347778	+	0.937577i	$0.386936\pi$
$318$	−0.502048	−	0.404306i	−0.0281534	−	0.0226724i
$319$		−	3.88149i		−	0.217322i
$320$	−6.39496	+	4.80671i	−0.357489	+	0.268703i
$321$		−	11.8042i		−	0.658845i
$322$	−4.60151	−	2.69167i	−0.256432	−	0.150001i
$323$			0.822503i			0.0457653i
$324$	0.426402	+	1.95402i	0.0236890	+	0.108556i
$325$		−	5.60576i		−	0.310952i
$326$	−6.57052	+	8.15895i	−0.363908	+	0.451883i
$327$	9.80783			0.542374
$328$	12.8520	+	6.41756i	0.709631	+	0.354350i
$329$	1.82243	+	12.1661i	0.100474	+	0.670740i
$330$	0.848952	+	0.683673i	0.0467333	+	0.0376350i
$331$			21.3000i			1.17075i	0.810762	+	0.585376i	$0.199053\pi$
$331$			21.3000i			1.17075i	−0.810762	+	0.585376i	$0.800947\pi$
$332$	5.96872	+	27.3520i	0.327576	+	1.50114i
$333$	10.1403			0.555686
$334$	−3.26192	−	2.62687i	−0.178484	−	0.143736i
$335$	−8.70791			−0.475764
$336$	5.78548	+	8.86161i	0.315624	+	0.483441i
$337$	−0.875789			−0.0477073			−0.0238536	−	0.999715i	$-0.507594\pi$
$337$	−0.875789			−0.0477073			−0.0238536	+	0.999715i	$0.507594\pi$
$338$	−20.2938	−	16.3429i	−1.10384	−	0.888936i
$339$	10.0104			0.543692
$340$	0.214498	+	0.982952i	0.0116328	+	0.0533080i
$341$			6.34495i			0.343598i
$342$	1.80094	+	1.45033i	0.0973839	+	0.0784247i
$343$	−7.99006	−	16.7081i	−0.431423	−	0.902150i
$344$	22.9314	+	11.4506i	1.23638	+	0.617377i
$345$	−1.42475			−0.0767062
$346$	13.3243	−	16.5455i	0.716320	−	0.889491i
$347$		−	34.9081i		−	1.87396i	−0.349379	−	0.936981i	$-0.613608\pi$
$347$		−	34.9081i		−	1.87396i	0.349379	−	0.936981i	$-0.386392\pi$
$348$	−2.14734	−	9.84033i	−0.115110	−	0.527497i
$349$		−	21.1880i		−	1.13417i	−0.823660	−	0.567084i	$-0.808071\pi$
$349$		−	21.1880i		−	1.13417i	0.823660	−	0.567084i	$-0.191929\pi$
$350$	1.88922	−	3.22968i	0.100983	−	0.172634i
$351$		−	5.60576i		−	0.299213i
$352$	−1.07140	+	4.22637i	−0.0571056	+	0.225266i
$353$		−	7.69915i		−	0.409785i	−0.978785	−	0.204892i	$-0.934316\pi$
$353$		−	7.69915i		−	0.409785i	0.978785	−	0.204892i	$-0.0656844\pi$
$354$	−11.5551	−	9.30548i	−0.614146	−	0.494580i
$355$	−10.8176			−0.574140
$356$	5.84010	−	1.27442i	0.309525	−	0.0675439i
$357$	1.31624	−	0.197166i	0.0696627	−	0.0104351i
$358$	4.28372	−	5.31931i	0.226402	−	0.281134i
$359$		−	2.14821i		−	0.113378i	−0.998392	−	0.0566890i	$-0.981946\pi$
$359$		−	2.14821i		−	0.113378i	0.998392	−	0.0566890i	$-0.0180543\pi$
$360$	2.53049	+	1.26358i	0.133368	+	0.0665967i
$361$	−16.3266			−0.859294
$362$	16.1481	−	20.0519i	0.848726	−	1.05391i
$363$	−10.4059			−0.546170
$364$	−10.5477	−	27.7242i	−0.552849	−	1.45315i
$365$	−2.29564			−0.120159
$366$	2.94839	−	3.66117i	0.154115	−	0.191372i
$367$	26.6962			1.39353			0.696764	−	0.717300i	$-0.254622\pi$
$367$	26.6962			1.39353			0.696764	+	0.717300i	$0.254622\pi$
$368$	−2.37420	−	5.18092i	−0.123764	−	0.270074i
$369$		−	5.07885i		−	0.264395i
$370$	8.99464	−	11.1691i	0.467609	−	0.580654i
$371$	0.178652	+	1.19264i	0.00927513	+	0.0619187i
$372$	3.51019	+	16.0857i	0.181995	+	0.834004i
$373$	−8.51430			−0.440854			−0.220427	−	0.975403i	$-0.570745\pi$
$373$	−8.51430			−0.440854			−0.220427	+	0.975403i	$0.570745\pi$
$374$	0.427058	+	0.343916i	0.0220826	+	0.0177835i
$375$		−	1.00000i		−	0.0516398i
$376$	−5.87524	+	11.7659i	−0.302992	+	0.606781i
$377$			28.2303i			1.45394i
$378$	1.88922	−	3.22968i	0.0971709	−	0.166117i
$379$		−	31.1693i		−	1.60106i	−0.599295	−	0.800529i	$-0.704552\pi$
$379$		−	31.1693i		−	1.60106i	0.599295	−	0.800529i	$-0.295448\pi$
$380$	3.19494	−	0.697193i	0.163897	−	0.0357653i
$381$		−	3.09530i		−	0.158577i
$382$	−5.01328	+	6.22524i	−0.256502	+	0.318511i
$383$	−33.7311			−1.72358			−0.861788	−	0.507268i	$-0.830655\pi$
$383$	−33.7311			−1.72358			−0.861788	+	0.507268i	$0.830655\pi$
$384$	−0.378061	+	11.3074i	−0.0192929	+	0.577028i
$385$	−0.302096	−	2.01673i	−0.0153962	−	0.102782i
$386$	−17.7310	−	14.2790i	−0.902483	−	0.726783i
$387$		−	9.06204i		−	0.460649i
$388$	−30.4471	+	6.64412i	−1.54572	+	0.337304i
$389$	25.9912			1.31780			0.658902	−	0.752228i	$-0.271021\pi$
$389$	25.9912			1.31780			0.658902	+	0.752228i	$0.271021\pi$
$390$	−6.17449	−	4.97240i	−0.312657	−	0.251787i
$391$	−0.716711			−0.0362456
$392$	3.26655	−	19.5277i	0.164986	−	0.986296i
$393$	17.5001			0.882762
$394$	−13.5448	−	10.9078i	−0.682379	−	0.549529i
$395$	2.56336			0.128977
$396$	1.50607	−	0.328652i	0.0756828	−	0.0165154i
$397$		−	1.63535i		−	0.0820760i	−0.999158	−	0.0410380i	$-0.986934\pi$
$397$		−	1.63535i		−	0.0820760i	0.999158	−	0.0410380i	$-0.0130665\pi$
$398$	−18.5302	−	14.9226i	−0.928835	−	0.748004i
$399$	−0.640859	−	4.27823i	−0.0320831	−	0.214179i
$400$	3.63636	−	1.66639i	0.181818	−	0.0833197i
$401$	−11.7906			−0.588797			−0.294398	−	0.955683i	$-0.595119\pi$
$401$	−11.7906			−0.588797			−0.294398	+	0.955683i	$0.595119\pi$
$402$	−7.72407	+	9.59137i	−0.385241	+	0.478374i
$403$		−	46.1473i		−	2.29876i
$404$	37.0600	−	8.08717i	1.84380	−	0.402352i
$405$		−	1.00000i		−	0.0496904i
$406$	−9.51401	+	16.2645i	−0.472172	+	0.807195i
$407$		−	7.81571i		−	0.387411i
$408$	1.27294	+	0.635635i	0.0630199	+	0.0314686i
$409$			9.74926i			0.482070i	0.970516	+	0.241035i	$0.0774868\pi$
$409$			9.74926i			0.482070i	−0.970516	+	0.241035i	$0.922513\pi$
$410$	−5.59412	−	4.50503i	−0.276274	−	0.222488i
$411$	15.6542			0.772163
$412$	3.51253	+	16.0964i	0.173050	+	0.793013i
$413$	4.11183	+	27.4497i	0.202330	+	1.35071i
$414$	−1.26378	+	1.56930i	−0.0621115	+	0.0771270i
$415$		−	13.9979i		−	0.687128i
$416$	7.79233	−	30.7387i	0.382051	−	1.50709i
$417$	−1.13095			−0.0553829
$418$	1.11785	−	1.38809i	0.0546757	−	0.0678936i
$419$	15.3501			0.749902			0.374951	−	0.927045i	$-0.377659\pi$
$419$	15.3501			0.749902			0.374951	+	0.927045i	$0.377659\pi$
$420$	−1.88158	−	4.94567i	−0.0918116	−	0.241324i
$421$	36.0738			1.75813			0.879064	−	0.476703i	$-0.158168\pi$
$421$	36.0738			1.75813			0.879064	+	0.476703i	$0.158168\pi$
$422$	−8.15564	+	10.1273i	−0.397011	+	0.492988i
$423$	4.64967			0.226074
$424$	−0.575947	+	1.15341i	−0.0279705	+	0.0560144i
$425$		−	0.503042i		−	0.0244011i
$426$	−9.59542	+	11.9151i	−0.464900	+	0.577290i
$427$	−8.69729	+	1.30281i	−0.420891	+	0.0630475i
$428$	−23.0656	+	5.03333i	−1.11492	+	0.243295i
$429$	−4.32067			−0.208604
$430$	−9.98142	−	8.03818i	−0.481347	−	0.387635i
$431$		−	20.9842i		−	1.01077i	−0.862893	−	0.505387i	$-0.831350\pi$
$431$		−	20.9842i		−	1.01077i	0.862893	−	0.505387i	$-0.168650\pi$
$432$	3.63636	−	1.66639i	0.174955	−	0.0801744i
$433$		−	10.4424i		−	0.501828i	−0.968009	−	0.250914i	$-0.919269\pi$
$433$		−	10.4424i		−	0.501828i	0.968009	−	0.250914i	$-0.0807312\pi$
$434$	15.5523	−	26.5871i	0.746533	−	1.27622i
$435$			5.03595i			0.241455i
$436$	−4.18208	−	19.1647i	−0.200285	−	0.917821i
$437$			2.32956i			0.111438i
$438$	−2.03627	+	2.52855i	−0.0972970	+	0.120819i
$439$	36.2996			1.73249			0.866243	−	0.499624i	$-0.166528\pi$
$439$	36.2996			1.73249			0.866243	+	0.499624i	$0.166528\pi$
$440$	0.973914	−	1.95039i	0.0464295	−	0.0929810i
$441$	−6.69275	+	2.05111i	−0.318703	+	0.0976719i
$442$	−3.10602	−	2.50133i	−0.147738	−	0.118976i
$443$		−	3.71212i		−	0.176368i	−0.996104	−	0.0881842i	$-0.971894\pi$
$443$		−	3.71212i		−	0.176368i	0.996104	−	0.0881842i	$-0.0281064\pi$
$444$	−4.32386	−	19.8144i	−0.205201	−	0.940348i
$445$	−2.98877			−0.141681
$446$	25.1748	+	20.2736i	1.19206	+	0.959985i
$447$	−21.3643			−1.01050
$448$	14.8488	−	15.0835i	0.701540	−	0.712630i
$449$	8.56515			0.404215			0.202107	−	0.979363i	$-0.435221\pi$
$449$	8.56515			0.404215			0.202107	+	0.979363i	$0.435221\pi$
$450$	−1.10145	−	0.887017i	−0.0519230	−	0.0418144i
$451$	−3.91456			−0.184329
$452$	−4.26847	−	19.5605i	−0.200772	−	0.920051i
$453$		−	2.83045i		−	0.132986i
$454$	19.2402	+	15.4944i	0.902989	+	0.727190i
$455$	2.19717	+	14.6678i	0.103005	+	0.687637i
$456$	2.06604	−	4.13750i	0.0967510	−	0.193756i
$457$	−14.6705			−0.686259			−0.343129	−	0.939288i	$-0.611487\pi$
$457$	−14.6705			−0.686259			−0.343129	+	0.939288i	$0.611487\pi$
$458$	−11.1971	+	13.9040i	−0.523204	+	0.649689i
$459$		−	0.503042i		−	0.0234800i
$460$	0.607518	+	2.78399i	0.0283257	+	0.129804i
$461$		−	19.3683i		−	0.902072i	−0.892506	−	0.451036i	$-0.851055\pi$
$461$		−	19.3683i		−	0.902072i	0.892506	−	0.451036i	$-0.148945\pi$
$462$	−2.48930	−	1.45613i	−0.115813	−	0.0677451i
$463$			4.34277i			0.201826i	0.994895	+	0.100913i	$0.0321763\pi$
$463$			4.34277i			0.201826i	−0.994895	+	0.100913i	$0.967824\pi$
$464$	−18.3125	+	8.39188i	−0.850138	+	0.389583i
$465$		−	8.23212i		−	0.381755i
$466$	−4.28917	−	3.45413i	−0.198692	−	0.160009i
$467$	−15.4501			−0.714943			−0.357472	−	0.933924i	$-0.616361\pi$
$467$	−15.4501			−0.714943			−0.357472	+	0.933924i	$0.616361\pi$
$468$	−10.9537	+	2.39031i	−0.506337	+	0.110492i
$469$	22.7848	−	3.41305i	1.05210	−	0.157600i
$470$	4.12433	−	5.12139i	0.190241	−	0.236232i
$471$		−	18.7903i		−	0.865810i
$472$	−13.2559	+	26.5467i	−0.610154	+	1.22191i
$473$	−6.98462			−0.321153
$474$	2.27374	−	2.82342i	0.104436	−	0.129684i
$475$	−1.63506			−0.0750217
$476$	−0.946512	−	2.48788i	−0.0433833	−	0.114032i
$477$	0.455805			0.0208699
$478$	−10.3335	+	12.8316i	−0.472644	+	0.586906i
$479$	−22.4129			−1.02407			−0.512035	−	0.858964i	$-0.671108\pi$
$479$	−22.4129			−1.02407			−0.512035	+	0.858964i	$0.671108\pi$
$480$	1.39006	−	5.48341i	0.0634472	−	0.250282i
$481$			56.8442i			2.59187i
$482$	18.6504	−	23.1591i	0.849501	−	1.05487i
$483$	3.72795	−	0.558430i	0.169628	−	0.0254094i
$484$	4.43711	+	20.3334i	0.201687	+	0.924244i
$485$	15.5818			0.707533
$486$	−1.10145	−	0.887017i	−0.0499630	−	0.0402359i
$487$			14.7901i			0.670202i	0.942182	+	0.335101i	$0.108770\pi$
$487$			14.7901i			0.670202i	−0.942182	+	0.335101i	$0.891230\pi$
$488$	−8.41119	−	4.20008i	−0.380757	−	0.190129i
$489$		−	7.40744i		−	0.334976i
$490$	−3.67738	+	9.19113i	−0.166127	+	0.415213i
$491$		−	18.0235i		−	0.813388i	−0.913565	−	0.406694i	$-0.866682\pi$
$491$		−	18.0235i		−	0.813388i	0.913565	−	0.406694i	$-0.133318\pi$
$492$	−9.92417	+	2.16563i	−0.447416	+	0.0976343i
$493$			2.53329i			0.114094i
$494$	−8.13018	+	10.0957i	−0.365794	+	0.454225i
$495$	−0.770756			−0.0346429
$496$	29.9350	−	13.7179i	1.34412	−	0.615954i
$497$	28.3050	−	4.23995i	1.26965	−	0.190188i
$498$	−15.4180	−	12.4163i	−0.690897	−	0.556389i
$499$		−	13.6272i		−	0.610036i	−0.952347	−	0.305018i	$-0.901338\pi$
$499$		−	13.6272i		−	0.610036i	0.952347	−	0.305018i	$-0.0986625\pi$
$500$	−1.95402	+	0.426402i	−0.0873863	+	0.0190693i
$501$	2.96147			0.132309
$502$	1.50331	+	1.21063i	0.0670959	+	0.0540333i
$503$	−23.8378			−1.06287			−0.531436	−	0.847098i	$-0.678348\pi$
$503$	−23.8378			−1.06287			−0.531436	+	0.847098i	$0.678348\pi$
$504$	−7.11642	−	2.31442i	−0.316991	−	0.103092i
$505$	−18.9661			−0.843979
$506$	1.20955	+	0.974067i	0.0537710	+	0.0433025i
$507$	18.4246			0.818263
$508$	−6.04827	+	1.31984i	−0.268348	+	0.0585585i
$509$		−	35.2475i		−	1.56232i	−0.624332	−	0.781159i	$-0.714629\pi$
$509$		−	35.2475i		−	1.56232i	0.624332	−	0.781159i	$-0.285371\pi$
$510$	−0.554077	−	0.446206i	−0.0245349	−	0.0197583i
$511$	6.00668	−	0.899773i	0.265720	−	0.0398036i
$512$	22.2560	−	4.08276i	0.983587	−	0.180434i
$513$	−1.63506			−0.0721897
$514$	−3.94026	+	4.89282i	−0.173797	+	0.215813i
$515$		−	8.23760i		−	0.362992i
$516$	−17.7074	+	3.86407i	−0.779524	+	0.170106i
$517$		−	3.58376i		−	0.157613i
$518$	−19.1573	+	32.7500i	−0.841723	+	1.43895i
$519$			15.0215i			0.659370i
$520$	−7.08335	+	14.1853i	−0.310625	+	0.622066i
$521$			5.38270i			0.235820i	0.993024	+	0.117910i	$0.0376195\pi$
$521$			5.38270i			0.235820i	−0.993024	+	0.117910i	$0.962381\pi$
$522$	5.54687	+	4.46697i	0.242780	+	0.195514i
$523$	0.0967711			0.00423150			0.00211575	−	0.999998i	$-0.499327\pi$
$523$	0.0967711			0.00423150			0.00211575	+	0.999998i	$0.499327\pi$
$524$	−7.46207	−	34.1954i	−0.325982	−	1.49384i
$525$	0.391948	+	2.61656i	0.0171060	+	0.114196i
$526$	4.37156	−	5.42839i	0.190609	−	0.236689i
$527$		−	4.14110i		−	0.180389i
$528$	−1.28438	−	2.80275i	−0.0558956	−	0.121974i
$529$	20.9701			0.911742
$530$	0.404306	−	0.502048i	0.0175619	−	0.0218076i
$531$	10.4908			0.455260
$532$	−8.08647	+	3.07650i	−0.350593	+	0.133383i
$533$	28.4708			1.23321
$534$	−2.65109	+	3.29199i	−0.114724	+	0.142458i
$535$	11.8042			0.510339
$536$	22.0352	+	11.0032i	0.951778	+	0.475265i
$537$			4.82936i			0.208402i
$538$	−22.1926	+	27.5577i	−0.956790	+	1.18810i
$539$	1.58090	+	5.15848i	0.0680944	+	0.222191i
$540$	−1.95402	+	0.426402i	−0.0840875	+	0.0183494i
$541$	2.76915			0.119055			0.0595275	−	0.998227i	$-0.481041\pi$
$541$	2.76915			0.119055			0.0595275	+	0.998227i	$0.481041\pi$
$542$	13.3665	+	10.7643i	0.574141	+	0.462364i
$543$			18.2050i			0.781250i
$544$	0.699257	−	2.75838i	0.0299804	−	0.118265i
$545$			9.80783i			0.420121i
$546$	18.1048	+	10.5905i	0.774815	+	0.453232i
$547$			25.1688i			1.07614i	0.842900	+	0.538071i	$0.180847\pi$
$547$			25.1688i			1.07614i	−0.842900	+	0.538071i	$0.819153\pi$
$548$	−6.67497	−	30.5885i	−0.285140	−	1.30668i
$549$			3.32394i			0.141862i
$550$	−0.683673	+	0.848952i	−0.0291519	+	0.0361994i
$551$	8.23408			0.350784
$552$	3.60532	+	1.80030i	0.153453	+	0.0766257i
$553$	−6.70717	+	1.00470i	−0.285218	+	0.0427243i
$554$	21.4445	+	17.2695i	0.911088	+	0.733712i
$555$			10.1403i			0.430433i
$556$	0.482240	+	2.20990i	0.0204515	+	0.0937206i
$557$	−39.1885			−1.66047			−0.830235	−	0.557413i	$-0.811794\pi$
$557$	−39.1885			−1.66047			−0.830235	+	0.557413i	$0.811794\pi$
$558$	−9.06730	−	7.30202i	−0.383849	−	0.309119i
$559$	50.7996			2.14859
$560$	−8.86161	+	5.78548i	−0.374472	+	0.244481i
$561$	−0.387722			−0.0163696
$562$	−19.5455	−	15.7403i	−0.824479	−	0.663965i
$563$	−23.3400			−0.983665			−0.491832	−	0.870690i	$-0.663673\pi$
$563$	−23.3400			−0.983665			−0.491832	+	0.870690i	$0.663673\pi$
$564$	−1.98263	−	9.08552i	−0.0834837	−	0.382570i
$565$			10.0104i			0.421142i
$566$	−32.4865	−	26.1618i	−1.36551	−	1.09966i
$567$	0.391948	+	2.61656i	0.0164603	+	0.109885i
$568$	27.3739	+	13.6690i	1.14858	+	0.573538i
$569$	−35.0677			−1.47011			−0.735057	−	0.678005i	$-0.762845\pi$
$569$	−35.0677			−1.47011			−0.735057	+	0.678005i	$0.762845\pi$
$570$	−1.45033	+	1.80094i	−0.0607475	+	0.0754333i
$571$			8.01227i			0.335303i	0.985846	+	0.167651i	$0.0536183\pi$
$571$			8.01227i			0.335303i	−0.985846	+	0.167651i	$0.946382\pi$
$572$	1.84234	+	8.44266i	0.0770323	+	0.353006i
$573$		−	5.65184i		−	0.236109i
$574$	16.4031	+	9.59507i	0.684652	+	0.400490i
$575$		−	1.42475i		−	0.0594164i
$576$	−4.80671	−	6.39496i	−0.200280	−	0.266457i
$577$			27.1156i			1.12884i	0.825489	+	0.564418i	$0.190900\pi$
$577$			27.1156i			1.12884i	−0.825489	+	0.564418i	$0.809100\pi$
$578$	18.4460	+	14.8548i	0.767252	+	0.617879i
$579$	16.0978			0.669002
$580$	9.84033	−	2.14734i	0.408598	−	0.0891634i
$581$	5.48643	+	36.6262i	0.227615	+	1.51951i
$582$	13.8213	−	17.1626i	0.572912	−	0.711415i
$583$		−	0.351314i		−	0.0145499i
$584$	5.80909	+	2.90074i	0.240382	+	0.120033i
$585$	5.60576			0.231770
$586$	−17.6321	+	21.8947i	−0.728377	+	0.904463i
$587$	−44.6409			−1.84253			−0.921264	−	0.388939i	$-0.872842\pi$
$587$	−44.6409			−1.84253			−0.921264	+	0.388939i	$0.872842\pi$
$588$	6.86171	+	12.2032i	0.282972	+	0.503250i
$589$	−13.4600			−0.554610
$590$	9.30548	−	11.5551i	0.383100	−	0.475715i
$591$	12.2972			0.505840
$592$	−36.8739	+	16.8978i	−1.51551	+	0.694494i
$593$		−	42.8848i		−	1.76107i	−0.473984	−	0.880534i	$-0.657184\pi$
$593$		−	42.8848i		−	1.76107i	0.473984	−	0.880534i	$-0.342816\pi$
$594$	−0.683673	+	0.848952i	−0.0280515	+	0.0348329i
$595$	0.197166	+	1.31624i	0.00808302	+	0.0539605i
$596$	9.10980	+	41.7463i	0.373152	+	1.70999i
$597$	16.8234			0.688536
$598$	−8.79713	−	7.08445i	−0.359741	−	0.289705i
$599$			17.8050i			0.727492i	0.931498	+	0.363746i	$0.118502\pi$
$599$			17.8050i			0.727492i	−0.931498	+	0.363746i	$0.881498\pi$
$600$	−1.26358	+	2.53049i	−0.0515856	+	0.103307i
$601$			7.15463i			0.291843i	0.989296	+	0.145922i	$0.0466148\pi$
$601$			7.15463i			0.291843i	−0.989296	+	0.145922i	$0.953385\pi$
$602$	29.2675	+	17.1202i	1.19285	+	0.697766i
$603$		−	8.70791i		−	0.354614i
$604$	−5.53074	+	1.20691i	−0.225043	+	0.0491084i
$605$		−	10.4059i		−	0.423061i
$606$	−16.8232	+	20.8902i	−0.683396	+	0.848608i
$607$	11.8573			0.481272			0.240636	−	0.970615i	$-0.422644\pi$
$607$	11.8573			0.481272			0.240636	+	0.970615i	$0.422644\pi$
$608$	−8.96570	−	2.27283i	−0.363607	−	0.0921754i
$609$	−1.97383	−	13.1769i	−0.0799836	−	0.533953i
$610$	3.66117	+	2.94839i	0.148236	+	0.119377i
$611$			26.0649i			1.05447i
$612$	−0.982952	+	0.214498i	−0.0397335	+	0.00867057i
$613$	−22.6111			−0.913254			−0.456627	−	0.889658i	$-0.650943\pi$
$613$	−22.6111			−0.913254			−0.456627	+	0.889658i	$0.650943\pi$
$614$	2.33977	+	1.88425i	0.0944254	+	0.0760421i
$615$	5.07885			0.204799
$616$	−1.78385	+	5.48502i	−0.0718735	+	0.220998i
$617$	18.4097			0.741146			0.370573	−	0.928803i	$-0.379161\pi$
$617$	18.4097			0.741146			0.370573	+	0.928803i	$0.379161\pi$
$618$	−9.07333	−	7.30689i	−0.364983	−	0.293926i
$619$	−33.4715			−1.34533			−0.672667	−	0.739946i	$-0.734851\pi$
$619$	−33.4715			−1.34533			−0.672667	+	0.739946i	$0.734851\pi$
$620$	−16.0857	+	3.51019i	−0.646017	+	0.140973i
$621$		−	1.42475i		−	0.0571734i
$622$	11.3307	+	9.12475i	0.454318	+	0.365869i
$623$	7.82028	−	1.17144i	0.313313	−	0.0469328i
$624$	9.34141	+	20.3846i	0.373955	+	0.816036i
$625$	1.00000			0.0400000
$626$	15.8599	−	19.6941i	0.633889	−	0.787133i
$627$			1.26023i			0.0503288i
$628$	−36.7165	+	8.01221i	−1.46515	+	0.319722i
$629$			5.10101i			0.203390i
$630$	3.22968	+	1.88922i	0.128674	+	0.0752683i
$631$			43.0583i			1.71412i	0.515213	+	0.857062i	$0.327713\pi$
$631$			43.0583i			1.71412i	−0.515213	+	0.857062i	$0.672287\pi$
$632$	−6.48654	−	3.23902i	−0.258021	−	0.128841i
$633$		−	9.19446i		−	0.365447i
$634$	13.6404	+	10.9848i	0.541731	+	0.436264i
$635$	3.09530			0.122833
$636$	−0.194356	−	0.890650i	−0.00770672	−	0.0353166i
$637$	−11.4980	−	37.5180i	−0.455568	−	1.48652i
$638$	3.44294	−	4.27528i	0.136307	−	0.169260i
$639$		−	10.8176i		−	0.427939i
$640$	−11.3074	−	0.378061i	−0.446964	−	0.0149442i
$641$	−12.3471			−0.487681			−0.243841	−	0.969815i	$-0.578407\pi$
$641$	−12.3471			−0.487681			−0.243841	+	0.969815i	$0.578407\pi$
$642$	10.4705	−	13.0018i	0.413238	−	0.513139i
$643$	−9.21215			−0.363292			−0.181646	−	0.983364i	$-0.558142\pi$
$643$	−9.21215			−0.363292			−0.181646	+	0.983364i	$0.558142\pi$
$644$	−2.68079	−	7.04637i	−0.105638	−	0.277666i
$645$	9.06204			0.356817
$646$	−0.729574	+	0.905950i	−0.0287047	+	0.0356441i
$647$	−19.8210			−0.779243			−0.389622	−	0.920975i	$-0.627394\pi$
$647$	−19.8210			−0.779243			−0.389622	+	0.920975i	$0.627394\pi$
$648$	−1.26358	+	2.53049i	−0.0496382	+	0.0994069i
$649$		−	8.08581i		−	0.317396i
$650$	4.97240	−	6.17449i	0.195034	−	0.242183i
$651$	3.22656	+	21.5398i	0.126459	+	0.844212i
$652$	−14.4743	+	3.15855i	−0.566856	+	0.123698i
$653$	−19.0538			−0.745635			−0.372817	−	0.927905i	$-0.621608\pi$
$653$	−19.0538			−0.745635			−0.372817	+	0.927905i	$0.621608\pi$
$654$	10.8029	+	8.69971i	0.422426	+	0.340185i
$655$			17.5001i			0.683785i
$656$	8.46337	+	18.4686i	0.330439	+	0.721076i
$657$		−	2.29564i		−	0.0895616i
$658$	−8.78424	+	15.0169i	−0.342445	+	0.585422i
$659$		−	10.4331i		−	0.406416i	−0.979136	−	0.203208i	$-0.934863\pi$
$659$		−	10.4331i		−	0.406416i	0.979136	−	0.203208i	$-0.0651367\pi$
$660$	0.328652	+	1.50607i	0.0127928	+	0.0586237i
$661$		−	9.84122i		−	0.382779i	−0.981514	−	0.191389i	$-0.938701\pi$
$661$		−	9.84122i		−	0.382779i	0.981514	−	0.191389i	$-0.0612994\pi$
$662$	−18.8934	+	23.4609i	−0.734314	+	0.911836i
$663$	2.81993			0.109517
$664$	−17.6875	+	35.4214i	−0.686406	+	1.37462i
$665$	4.27823	−	0.640859i	0.165903	−	0.0248514i
$666$	11.1691	+	8.99464i	0.432794	+	0.348535i
$667$			7.17499i			0.277817i
$668$	−1.26278	−	5.78676i	−0.0488583	−	0.223896i
$669$	−22.8560			−0.883663
$670$	−9.59137	−	7.72407i	−0.370547	−	0.298407i
$671$	2.56195			0.0989029
$672$	−1.48796	+	14.8925i	−0.0573993	+	0.574490i
$673$	5.51471			0.212577			0.106288	−	0.994335i	$-0.466103\pi$
$673$	5.51471			0.212577			0.106288	+	0.994335i	$0.466103\pi$
$674$	−0.964641	−	0.776840i	−0.0371566	−	0.0299227i
$675$	1.00000			0.0384900
$676$	−7.85627	−	36.0019i	−0.302164	−	1.38469i
$677$		−	44.8711i		−	1.72454i	−0.506451	−	0.862269i	$-0.669043\pi$
$677$		−	44.8711i		−	1.72454i	0.506451	−	0.862269i	$-0.330957\pi$
$678$	11.0260	+	8.87942i	0.423452	+	0.341012i
$679$	−40.7707	+	6.10726i	−1.56464	+	0.234375i
$680$	−0.635635	+	1.27294i	−0.0243755	+	0.0488150i
$681$	−17.4680			−0.669377
$682$	−5.62808	+	6.98867i	−0.215510	+	0.267610i
$683$			34.0718i			1.30372i	0.758338	+	0.651862i	$0.226012\pi$
$683$			34.0718i			1.30372i	−0.758338	+	0.651862i	$0.773988\pi$
$684$	0.697193	+	3.19494i	0.0266579	+	0.122161i
$685$			15.6542i			0.598115i
$686$	6.01964	−	25.4905i	0.229831	−	0.973231i
$687$		−	12.6233i		−	0.481608i
$688$	15.1009	+	32.9529i	0.575717	+	1.25632i
$689$			2.55513i			0.0973428i
$690$	−1.56930	−	1.26378i	−0.0597423	−	0.0481113i
$691$	−0.264224			−0.0100515			−0.00502577	−	0.999987i	$-0.501600\pi$
$691$	−0.264224			−0.0100515			−0.00502577	+	0.999987i	$0.501600\pi$
$692$	29.3522	−	6.40520i	1.11581	−	0.243489i
$693$	2.01673	−	0.302096i	0.0766091	−	0.0114757i
$694$	30.9640	−	38.4496i	1.17538	−	1.45953i
$695$		−	1.13095i		−	0.0428994i
$696$	6.36334	−	12.7434i	0.241202	−	0.483037i
$697$	2.55487			0.0967728
$698$	18.7941	−	23.3376i	0.711368	−	0.883342i
$699$	3.89410			0.147288
$700$	4.94567	−	1.88158i	0.186929	−	0.0711170i
$701$	17.5109			0.661376			0.330688	−	0.943740i	$-0.392719\pi$
$701$	17.5109			0.661376			0.330688	+	0.943740i	$0.392719\pi$
$702$	4.97240	−	6.17449i	0.187671	−	0.233041i
$703$	16.5800			0.625328
$704$	−4.92895	+	3.70480i	−0.185767	+	0.139630i
$705$			4.64967i			0.175117i
$706$	6.82928	−	8.48026i	0.257023	−	0.319159i
$707$	49.6258	−	7.43371i	1.86637	−	0.279573i
$708$	−4.47328	−	20.4991i	−0.168116	−	0.770404i
$709$	−13.0797			−0.491219			−0.245610	−	0.969369i	$-0.578988\pi$
$709$	−13.0797			−0.491219			−0.245610	+	0.969369i	$0.578988\pi$
$710$	−11.9151	−	9.59542i	−0.447167	−	0.360110i
$711$			2.56336i			0.0961334i
$712$	7.56303	+	3.77656i	0.283437	+	0.141532i
$713$		−	11.7287i		−	0.439245i
$714$	1.62466	+	0.950355i	0.0608016	+	0.0355662i
$715$		−	4.32067i		−	0.161584i
$716$	9.43664	−	2.05925i	0.352664	−	0.0769577i
$717$		−	11.6497i		−	0.435067i
$718$	1.90549	−	2.36615i	0.0711124	−	0.0883039i
$719$	−16.9650			−0.632689			−0.316345	−	0.948644i	$-0.602456\pi$
$719$	−16.9650			−0.632689			−0.316345	+	0.948644i	$0.602456\pi$
$720$	1.66639	+	3.63636i	0.0621028	+	0.135519i
$721$	3.22871	+	21.5542i	0.120243	+	0.802719i
$722$	−17.9830	−	14.4819i	−0.669257	−	0.538962i
$723$			21.0259i			0.781963i
$724$	35.5728	−	7.76264i	1.32205	−	0.288496i
$725$	−5.03595			−0.187030
$726$	−11.4617	−	9.23024i	−0.425382	−	0.342566i
$727$	−32.4836			−1.20475			−0.602375	−	0.798213i	$-0.705779\pi$
$727$	−32.4836			−1.20475			−0.602375	+	0.798213i	$0.705779\pi$
$728$	12.9741	−	39.8930i	0.480852	−	1.47853i
$729$	1.00000			0.0370370
$730$	−2.52855	−	2.03627i	−0.0935857	−	0.0753659i
$731$	4.55858			0.168605
$732$	6.49504	−	1.41734i	0.240064	−	0.0523863i
$733$			35.8223i			1.32313i	0.749890	+	0.661563i	$0.230106\pi$
$733$			35.8223i			1.32313i	−0.749890	+	0.661563i	$0.769894\pi$
$734$	29.4046	+	23.6799i	1.08534	+	0.874043i
$735$	−2.05111	−	6.69275i	−0.0756563	−	0.246866i
$736$	1.98049	−	7.81251i	0.0730019	−	0.287973i
$737$	−6.71167			−0.247228
$738$	4.50503	−	5.59412i	0.165832	−	0.205923i
$739$			21.8037i			0.802060i	0.916065	+	0.401030i	$0.131348\pi$
$739$			21.8037i			0.802060i	−0.916065	+	0.401030i	$0.868652\pi$
$740$	19.8144	−	4.32386i	0.728391	−	0.158948i
$741$		−	9.16576i		−	0.336713i
$742$	−0.861115	+	1.47210i	−0.0316125	+	0.0540427i
$743$			23.4618i			0.860731i	0.902655	+	0.430365i	$0.141615\pi$
$743$			23.4618i			0.860731i	−0.902655	+	0.430365i	$0.858385\pi$
$744$	−10.4020	+	20.8312i	−0.381354	+	0.763711i
$745$		−	21.3643i		−	0.782729i
$746$	−9.37811	−	7.55233i	−0.343357	−	0.276510i
$747$	13.9979			0.512155
$748$	0.165326	+	0.757616i	0.00604490	+	0.0277012i
$749$	−30.8863	+	4.62662i	−1.12856	+	0.169053i
$750$	0.887017	−	1.10145i	0.0323893	−	0.0402194i
$751$		−	15.9484i		−	0.581965i	−0.956728	−	0.290983i	$-0.906018\pi$
$751$		−	15.9484i		−	0.581965i	0.956728	−	0.290983i	$-0.0939822\pi$
$752$	−16.9079	+	7.74817i	−0.616567	+	0.282547i
$753$	−1.36484			−0.0497375
$754$	−25.0408	+	31.0944i	−0.911931	+	1.13239i
$755$	2.83045			0.103011
$756$	4.94567	−	1.88158i	0.179872	−	0.0684324i
$757$	27.9746			1.01675			0.508377	−	0.861135i	$-0.330246\pi$
$757$	27.9746			1.01675			0.508377	+	0.861135i	$0.330246\pi$
$758$	27.6477	−	34.3315i	1.00421	−	1.24698i
$759$	−1.09814			−0.0398599
$760$	4.13750	+	2.06604i	0.150083	+	0.0749430i
$761$			17.5525i			0.636277i	0.948044	+	0.318138i	$0.103058\pi$
$761$			17.5525i			0.636277i	−0.948044	+	0.318138i	$0.896942\pi$
$762$	2.74558	−	3.40933i	0.0994620	−	0.123507i
$763$	−3.84416	−	25.6627i	−0.139168	−	0.929054i
$764$	−11.0438	+	2.40996i	−0.399550	+	0.0871892i
$765$	0.503042			0.0181875
$766$	−37.1532	−	29.9200i	−1.34240	−	1.08105i
$767$			58.8087i			2.12346i
$768$	−10.4463	+	12.1192i	−0.376947	+	0.437315i
$769$		−	5.74365i		−	0.207121i	−0.994623	−	0.103561i	$-0.966976\pi$
$769$		−	5.74365i		−	0.207121i	0.994623	−	0.103561i	$-0.0330236\pi$
$770$	1.45613	−	2.48930i	0.0524751	−	0.0897080i
$771$		−	4.44214i		−	0.159980i
$772$	−6.86414	−	31.4554i	−0.247046	−	1.13210i
$773$			46.0638i			1.65680i	0.560138	+	0.828399i	$0.310748\pi$
$773$			46.0638i			1.65680i	−0.560138	+	0.828399i	$0.689252\pi$
$774$	8.03818	−	9.98142i	0.288926	−	0.358775i
$775$	8.23212			0.295706
$776$	−39.4295	−	19.6889i	−1.41544	−	0.706791i
$777$	−3.97448	−	26.5328i	−0.142584	−	0.951857i
$778$	28.6281	+	23.0546i	1.02637	+	0.826548i
$779$		−	8.30423i		−	0.297530i
$780$	−2.39031	−	10.9537i	−0.0855868	−	0.392207i
$781$	−8.33775			−0.298348
$782$	−0.789424	−	0.635734i	−0.0282297	−	0.0227338i
$783$	−5.03595			−0.179970
$784$	20.9193	−	18.6113i	0.747119	−	0.664691i
$785$	18.7903			0.670654
$786$	19.2755	+	15.5229i	0.687536	+	0.553682i
$787$	−26.5373			−0.945951			−0.472976	−	0.881075i	$-0.656820\pi$
$787$	−26.5373			−0.945951			−0.472976	+	0.881075i	$0.656820\pi$
$788$	−5.24356	−	24.0290i	−0.186794	−	0.855997i
$789$			4.92839i			0.175455i
$790$	2.82342	+	2.27374i	0.100453	+	0.0808961i
$791$	−3.92357	−	26.1929i	−0.139506	−	0.931311i
$792$	1.95039	+	0.973914i	0.0693040	+	0.0346065i
$793$	−18.6332			−0.661685
$794$	1.45059	−	1.80127i	0.0514794	−	0.0639245i
$795$			0.455805i			0.0161657i
$796$	−7.17353	−	32.8732i	−0.254259	−	1.16516i
$797$			29.3245i			1.03873i	0.854553	+	0.519364i	$0.173831\pi$
$797$			29.3245i			1.03873i	−0.854553	+	0.519364i	$0.826169\pi$
$798$	3.08899	−	5.28073i	0.109349	−	0.186936i
$799$			2.33898i			0.0827470i
$800$	5.48341	+	1.39006i	0.193868	+	0.0491460i
$801$		−	2.98877i		−	0.105603i
$802$	−12.9869	−	10.4585i	−0.458582	−	0.369302i
$803$	−1.76938			−0.0624401
$804$	−17.0154	+	3.71307i	−0.600087	+	0.130950i
$805$	0.558430	+	3.72795i	0.0196821	+	0.131393i
$806$	40.9334	−	50.8291i	1.44182	−	1.79038i
$807$		−	25.0193i		−	0.880723i
$808$	47.9933	+	23.9652i	1.68840	+	0.843093i
$809$	−15.6127			−0.548913			−0.274456	−	0.961600i	$-0.588498\pi$
$809$	−15.6127			−0.548913			−0.274456	+	0.961600i	$0.588498\pi$
$810$	0.887017	−	1.10145i	0.0311666	−	0.0387012i
$811$	24.0925			0.846004			0.423002	−	0.906129i	$-0.360976\pi$
$811$	24.0925			0.846004			0.423002	+	0.906129i	$0.360976\pi$
$812$	−24.9062	+	9.47554i	−0.874035	+	0.332526i
$813$	−12.1353			−0.425605
$814$	6.93267	−	8.60865i	0.242990	−	0.301733i
$815$	7.40744			0.259471
$816$	0.838265	+	1.82924i	0.0293452	+	0.0640363i
$817$		−	14.8170i		−	0.518381i
$818$	−8.64776	+	10.7384i	−0.302362	+	0.375458i
$819$	−14.6678	+	2.19717i	−0.512534	+	0.0767752i
$820$	−2.16563	−	9.92417i	−0.0756272	−	0.346567i
$821$	−47.2309			−1.64837			−0.824185	−	0.566321i	$-0.808366\pi$
$821$	−47.2309			−1.64837			−0.824185	+	0.566321i	$0.808366\pi$
$822$	17.2423	+	13.8855i	0.601396	+	0.484312i
$823$		−	15.0076i		−	0.523133i	−0.965185	−	0.261566i	$-0.915761\pi$
$823$		−	15.0076i		−	0.523133i	0.965185	−	0.261566i	$-0.0842390\pi$
$824$	−10.4089	+	20.8451i	−0.362611	+	0.726174i
$825$		−	0.770756i		−	0.0268343i
$826$	−19.8193	+	33.8818i	−0.689603	+	1.17890i
$827$		−	8.53837i		−	0.296908i	−0.988919	−	0.148454i	$-0.952570\pi$
$827$		−	8.53837i		−	0.296908i	0.988919	−	0.148454i	$-0.0474297\pi$
$828$	−2.78399	+	0.607518i	−0.0967505	+	0.0211127i
$829$			19.3755i			0.672941i	0.941694	+	0.336470i	$0.109233\pi$
$829$			19.3755i			0.672941i	−0.941694	+	0.336470i	$0.890767\pi$
$830$	12.4163	−	15.4180i	0.430977	−	0.535166i
$831$	−19.4692			−0.675380
$832$	35.8486	−	26.9453i	1.24283	−	0.934160i
$833$	−1.03179	−	3.36673i	−0.0357495	−	0.116650i
$834$	−1.24569	−	1.00317i	−0.0431348	−	0.0347370i
$835$			2.96147i			0.102486i
$836$	2.46251	−	0.537366i	0.0851679	−	0.0185852i
$837$	8.23212			0.284544
$838$	16.9074	+	13.6158i	0.584058	+	0.470350i
$839$	33.8009			1.16693			0.583467	−	0.812137i	$-0.301696\pi$
$839$	33.8009			1.16693			0.583467	+	0.812137i	$0.301696\pi$
$840$	2.31442	−	7.11642i	0.0798551	−	0.245540i
$841$	−3.63920			−0.125490
$842$	39.7336	+	31.9981i	1.36931	+	1.10273i
$843$	17.7452			0.611178
$844$	−17.9661	+	3.92054i	−0.618420	+	0.134951i
$845$			18.4246i			0.633824i
$846$	5.12139	+	4.12433i	0.176077	+	0.141797i
$847$	4.07858	+	27.2277i	0.140142	+	0.935556i
$848$	−1.65747	+	0.759550i	−0.0569178	+	0.0260831i
$849$	29.4942			1.01224
$850$	0.446206	−	0.554077i	0.0153048	−	0.0190047i
$851$			14.4475i			0.495253i
$852$	−21.1378	+	4.61266i	−0.724170	+	0.158027i
$853$		−	20.5520i		−	0.703688i	−0.936059	−	0.351844i	$-0.885555\pi$
$853$		−	20.5520i		−	0.703688i	0.936059	−	0.351844i	$-0.114445\pi$
$854$	−10.7353	−	6.27965i	−0.367354	−	0.214885i
$855$		−	1.63506i		−	0.0559179i
$856$	−29.8703	−	14.9156i	−1.02095	−	0.509803i
$857$		−	12.0420i		−	0.411346i	−0.978621	−	0.205673i	$-0.934062\pi$
$857$		−	12.0420i		−	0.411346i	0.978621	−	0.205673i	$-0.0659384\pi$
$858$	−4.75902	−	3.83251i	−0.162470	−	0.130840i
$859$	−19.0195			−0.648938			−0.324469	−	0.945896i	$-0.605186\pi$
$859$	−19.0195			−0.648938			−0.324469	+	0.945896i	$0.605186\pi$
$860$	−3.86407	−	17.7074i	−0.131764	−	0.603816i
$861$	−13.2891	+	1.99065i	−0.452892	+	0.0678410i
$862$	18.6133	−	23.1131i	0.633973	−	0.787236i
$863$		−	51.7910i		−	1.76299i	−0.472198	−	0.881493i	$-0.656539\pi$
$863$		−	51.7910i		−	1.76299i	0.472198	−	0.881493i	$-0.343461\pi$
$864$	5.48341	+	1.39006i	0.186549	+	0.0472907i
$865$	−15.0215			−0.510746
$866$	9.26256	−	11.5018i	0.314755	−	0.390847i
$867$	−16.7469			−0.568756
$868$	40.7133	−	15.4894i	1.38190	−	0.525744i
$869$	1.97572			0.0670218
$870$	−4.46697	+	5.54687i	−0.151445	+	0.188056i
$871$	48.8145			1.65402
$872$	12.3930	−	24.8186i	0.419680	−	0.840463i
$873$			15.5818i			0.527364i
$874$	−2.06636	+	2.56590i	−0.0698956	+	0.0867930i
$875$	−2.61656	+	0.391948i	−0.0884558	+	0.0132503i
$876$	−4.48573	+	0.978867i	−0.151559	+	0.0330729i
$877$	−46.5940			−1.57337			−0.786683	−	0.617357i	$-0.788204\pi$
$877$	−46.5940			−1.57337			−0.786683	+	0.617357i	$0.788204\pi$
$878$	39.9823	+	32.1984i	1.34934	+	1.08664i
$879$		−	19.8780i		−	0.670469i
$880$	2.80275	−	1.28438i	0.0944806	−	0.0432965i
$881$			53.7772i			1.81180i	0.423491	+	0.905901i	$0.360805\pi$
$881$			53.7772i			1.81180i	−0.423491	+	0.905901i	$0.639195\pi$
$882$	−9.19113	−	3.67738i	−0.309481	−	0.123824i
$883$		−	17.0329i		−	0.573202i	−0.958050	−	0.286601i	$-0.907475\pi$
$883$		−	17.0329i		−	0.573202i	0.958050	−	0.286601i	$-0.0925255\pi$
$884$	−1.20242	−	5.51019i	−0.0404419	−	0.185328i
$885$			10.4908i			0.352643i
$886$	3.29272	−	4.08873i	0.110621	−	0.137364i
$887$	−47.8749			−1.60748			−0.803741	−	0.594980i	$-0.797160\pi$
$887$	−47.8749			−1.60748			−0.803741	+	0.594980i	$0.797160\pi$
$888$	12.8131	−	25.6599i	0.429981	−	0.861091i
$889$	−8.09903	+	1.21320i	−0.271633	+	0.0406893i
$890$	−3.29199	−	2.65109i	−0.110348	−	0.0888646i
$891$		−	0.770756i		−	0.0258213i
$892$	9.74584	+	44.6610i	0.326315	+	1.49536i
$893$	7.60249			0.254407
$894$	−23.5318	−	18.9505i	−0.787022	−	0.633800i
$895$	−4.82936			−0.161428
$896$	29.7346	−	3.44269i	0.993364	−	0.115012i
$897$	7.98683			0.266673
$898$	9.43412	+	7.59744i	0.314821	+	0.253530i
$899$	−41.4565			−1.38265
$900$	−0.426402	−	1.95402i	−0.0142134	−	0.0651339i
$901$			0.229289i			0.00763871i
$902$	−4.31170	−	3.47228i	−0.143564	−	0.115614i
$903$	−23.7114	+	3.55185i	−0.789064	+	0.118198i
$904$	12.6490	−	25.3312i	0.420700	−	0.842505i
$905$	−18.2050			−0.605154
$906$	2.51065	−	3.11761i	0.0834109	−	0.103576i
$907$		−	22.5992i		−	0.750395i	−0.926945	−	0.375197i	$-0.877575\pi$
$907$		−	22.5992i		−	0.750395i	0.926945	−	0.375197i	$-0.122425\pi$
$908$	7.44841	+	34.1328i	0.247184	+	1.13274i
$909$		−	18.9661i		−	0.629065i
$910$	−10.5905	+	18.1048i	−0.351072	+	0.600169i
$911$		−	38.2369i		−	1.26685i	−0.773806	−	0.633423i	$-0.781650\pi$
$911$		−	38.2369i		−	1.26685i	0.773806	−	0.633423i	$-0.218350\pi$
$912$	5.94567	−	2.72466i	0.196881	−	0.0902223i
$913$		−	10.7889i		−	0.357061i
$914$	−16.1589	−	13.0130i	−0.534490	−	0.430432i
$915$	−3.32394			−0.109886
$916$	−24.6661	+	5.38259i	−0.814990	+	0.177846i
$917$	−6.85912	−	45.7900i	−0.226508	−	1.51212i
$918$	0.446206	−	0.554077i	0.0147270	−	0.0182873i
$919$		−	17.0673i		−	0.562999i	−0.959561	−	0.281500i	$-0.909168\pi$
$919$		−	17.0673i		−	0.562999i	0.959561	−	0.281500i	$-0.0908318\pi$
$920$	−1.80030	+	3.60532i	−0.0593540	+	0.118864i
$921$	−2.12425			−0.0699966
$922$	17.1800	−	21.3333i	0.565794	−	0.702575i
$923$	60.6411			1.99603
$924$	−1.45024	−	3.81190i	−0.0477093	−	0.125402i
$925$	−10.1403			−0.333412
$926$	−3.85211	+	4.78336i	−0.126588	+	0.157191i
$927$	8.23760			0.270558
$928$	−27.6142	−	7.00027i	−0.906479	−	0.229795i
$929$		−	19.7796i		−	0.648947i	−0.945895	−	0.324473i	$-0.894813\pi$
$929$		−	19.7796i		−	0.648947i	0.945895	−	0.324473i	$-0.105187\pi$
$930$	7.30202	−	9.06730i	0.239443	−	0.297328i
$931$	−10.9431	+	3.35369i	−0.358644	+	0.109913i
$932$	−1.66045	−	7.60913i	−0.0543899	−	0.249245i
$933$	−10.2870			−0.336781
$934$	−17.0175	−	13.7045i	−0.556830	−	0.448424i
$935$		−	0.387722i		−	0.0126799i
$936$	−14.1853	−	7.08335i	−0.463661	−	0.231526i
$937$			21.4491i			0.700712i	0.936617	+	0.350356i	$0.113939\pi$
$937$			21.4491i			0.700712i	−0.936617	+	0.350356i	$0.886061\pi$
$938$	28.1238	+	16.4512i	0.918275	+	0.537149i
$939$			17.8800i			0.583493i
$940$	9.08552	−	1.98263i	0.296337	−	0.0646662i
$941$		−	42.2481i		−	1.37725i	−0.725119	−	0.688624i	$-0.758215\pi$
$941$		−	42.2481i		−	1.37725i	0.725119	−	0.688624i	$-0.241785\pi$
$942$	16.6673	−	20.6966i	0.543050	−	0.674333i
$943$	7.23612			0.235640
$944$	−38.1482	+	17.4817i	−1.24162	+	0.568982i
$945$	−2.61656	+	0.391948i	−0.0851166	+	0.0127501i
$946$	−7.69324	−	6.19547i	−0.250129	−	0.201432i
$947$			17.0774i			0.554939i	0.960734	+	0.277470i	$0.0894958\pi$
$947$			17.0774i			0.554939i	−0.960734	+	0.277470i	$0.910504\pi$
$948$	5.00884	−	1.09302i	0.162680	−	0.0354997i
$949$	12.8688			0.417740
$950$	−1.80094	−	1.45033i	−0.0584303	−	0.0470548i
$951$	−12.3840			−0.401580
$952$	1.16425	−	3.57986i	0.0377336	−	0.116024i
$953$	−9.75364			−0.315951			−0.157976	−	0.987443i	$-0.550497\pi$
$953$	−9.75364			−0.315951			−0.157976	+	0.987443i	$0.550497\pi$
$954$	0.502048	+	0.404306i	0.0162544	+	0.0130899i
$955$	5.65184			0.182889
$956$	−22.7638	+	4.96747i	−0.736233	+	0.160659i
$957$			3.88149i			0.125471i
$958$	−24.6868	−	19.8806i	−0.797593	−	0.642313i
$959$	−6.13561	−	40.9600i	−0.198129	−	1.32267i
$960$	6.39496	−	4.80671i	0.206396	−	0.155136i
$961$	36.7677			1.18606
$962$	−50.4218	+	62.6113i	−1.62566	+	2.01867i
$963$			11.8042i			0.380384i
$964$	41.0850	−	8.96551i	1.32326	−	0.288759i
$965$			16.0978i			0.518206i
$966$	4.60151	+	2.69167i	0.148051	+	0.0866031i
$967$		−	24.1757i		−	0.777437i	−0.921356	−	0.388719i	$-0.872918\pi$
$967$		−	24.1757i		−	0.777437i	0.921356	−	0.388719i	$-0.127082\pi$
$968$	−13.1488	+	26.3321i	−0.422617	+	0.846345i
$969$		−	0.822503i		−	0.0264226i
$970$	17.1626	+	13.8213i	0.551059	+	0.443776i
$971$	30.5804			0.981373			0.490686	−	0.871336i	$-0.336746\pi$
$971$	30.5804			0.981373			0.490686	+	0.871336i	$0.336746\pi$
$972$	−0.426402	−	1.95402i	−0.0136769	−	0.0626751i
$973$	0.443274	+	2.95920i	0.0142107	+	0.0948676i
$974$	−13.1190	+	16.2906i	−0.420361	+	0.521984i
$975$			5.60576i			0.179528i
$976$	−5.53900	−	12.0871i	−0.177299	−	0.386897i
$977$	26.4757			0.847031			0.423516	−	0.905889i	$-0.360796\pi$
$977$	26.4757			0.847031			0.423516	+	0.905889i	$0.360796\pi$
$978$	6.57052	−	8.15895i	0.210102	−	0.260895i
$979$	−2.30361			−0.0736237
$980$	−12.2032	+	6.86171i	−0.389815	+	0.219189i
$981$	−9.80783			−0.313140
$982$	15.9871	−	19.8520i	0.510169	−	0.633503i
$983$	1.44944			0.0462300			0.0231150	−	0.999733i	$-0.492642\pi$
$983$	1.44944			0.0462300			0.0231150	+	0.999733i	$0.492642\pi$
$984$	−12.8520	−	6.41756i	−0.409706	−	0.204584i
$985$			12.2972i			0.391822i
$986$	−2.24707	+	2.79031i	−0.0715614	+	0.0888614i
$987$	−1.82243	−	12.1661i	−0.0580085	−	0.387252i
$988$	−17.9100	+	3.90830i	−0.569794	+	0.124340i
$989$	12.9112			0.410552
$990$	−0.848952	−	0.683673i	−0.0269815	−	0.0217286i
$991$			43.1709i			1.37137i	0.727899	+	0.685684i	$0.240497\pi$
$991$			43.1709i			1.37137i	−0.727899	+	0.685684i	$0.759503\pi$
$992$	45.1400	+	11.4431i	1.43320	+	0.363319i
$993$		−	21.3000i		−	0.675934i
$994$	34.9375	+	20.4369i	1.10815	+	0.648218i
$995$			16.8234i			0.533338i
$996$	−5.96872	−	27.3520i	−0.189126	−	0.866683i
$997$		−	59.0825i		−	1.87116i	−0.353114	−	0.935580i	$-0.614877\pi$
$997$		−	59.0825i		−	1.87116i	0.353114	−	0.935580i	$-0.385123\pi$
$998$	12.0875	−	15.0097i	0.382624	−	0.475124i
$999$	−10.1403			−0.320826

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.c.a.391.14	yes	16
3.2	odd	2		1260.2.c.d.811.3		16
4.3	odd	2		420.2.c.b.391.13	yes	16
7.6	odd	2		420.2.c.b.391.14	yes	16
12.11	even	2		1260.2.c.e.811.4		16
21.20	even	2		1260.2.c.e.811.3		16
28.27	even	2	inner	420.2.c.a.391.13	✓	16
84.83	odd	2		1260.2.c.d.811.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.c.a.391.13	✓	16	28.27	even	2	inner
420.2.c.a.391.14	yes	16	1.1	even	1	trivial
420.2.c.b.391.13	yes	16	4.3	odd	2
420.2.c.b.391.14	yes	16	7.6	odd	2
1260.2.c.d.811.3		16	3.2	odd	2
1260.2.c.d.811.4		16	84.83	odd	2
1260.2.c.e.811.3		16	21.20	even	2
1260.2.c.e.811.4		16	12.11	even	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:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	420.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.10145 + 0.887017i) q^{2} -1.00000 q^{3} +(0.426402 + 1.95402i) q^{4} -1.00000i q^{5} +(-1.10145 - 0.887017i) q^{6} +(0.391948 + 2.61656i) q^{7} +(-1.26358 + 2.53049i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(1.10145 + 0.887017i) q^{2} -1.00000 q^{3} +(0.426402 + 1.95402i) q^{4} -1.00000i q^{5} +(-1.10145 - 0.887017i) q^{6} +(0.391948 + 2.61656i) q^{7} +(-1.26358 + 2.53049i) q^{8} +1.00000 q^{9} +(0.887017 - 1.10145i) q^{10} -0.770756i q^{11} +(-0.426402 - 1.95402i) q^{12} +5.60576i q^{13} +(-1.88922 + 3.22968i) q^{14} +1.00000i q^{15} +(-3.63636 + 1.66639i) q^{16} +0.503042i q^{17} +(1.10145 + 0.887017i) q^{18} +1.63506 q^{19} +(1.95402 - 0.426402i) q^{20} +(-0.391948 - 2.61656i) q^{21} +(0.683673 - 0.848952i) q^{22} +1.42475i q^{23} +(1.26358 - 2.53049i) q^{24} -1.00000 q^{25} +(-4.97240 + 6.17449i) q^{26} -1.00000 q^{27} +(-4.94567 + 1.88158i) q^{28} +5.03595 q^{29} +(-0.887017 + 1.10145i) q^{30} -8.23212 q^{31} +(-5.48341 - 1.39006i) q^{32} +0.770756i q^{33} +(-0.446206 + 0.554077i) q^{34} +(2.61656 - 0.391948i) q^{35} +(0.426402 + 1.95402i) q^{36} +10.1403 q^{37} +(1.80094 + 1.45033i) q^{38} -5.60576i q^{39} +(2.53049 + 1.26358i) q^{40} -5.07885i q^{41} +(1.88922 - 3.22968i) q^{42} -9.06204i q^{43} +(1.50607 - 0.328652i) q^{44} -1.00000i q^{45} +(-1.26378 + 1.56930i) q^{46} +4.64967 q^{47} +(3.63636 - 1.66639i) q^{48} +(-6.69275 + 2.05111i) q^{49} +(-1.10145 - 0.887017i) q^{50} -0.503042i q^{51} +(-10.9537 + 2.39031i) q^{52} +0.455805 q^{53} +(-1.10145 - 0.887017i) q^{54} -0.770756 q^{55} +(-7.11642 - 2.31442i) q^{56} -1.63506 q^{57} +(5.54687 + 4.46697i) q^{58} +10.4908 q^{59} +(-1.95402 + 0.426402i) q^{60} +3.32394i q^{61} +(-9.06730 - 7.30202i) q^{62} +(0.391948 + 2.61656i) q^{63} +(-4.80671 - 6.39496i) q^{64} +5.60576 q^{65} +(-0.683673 + 0.848952i) q^{66} -8.70791i q^{67} +(-0.982952 + 0.214498i) q^{68} -1.42475i q^{69} +(3.22968 + 1.88922i) q^{70} -10.8176i q^{71} +(-1.26358 + 2.53049i) q^{72} -2.29564i q^{73} +(11.1691 + 8.99464i) q^{74} +1.00000 q^{75} +(0.697193 + 3.19494i) q^{76} +(2.01673 - 0.302096i) q^{77} +(4.97240 - 6.17449i) q^{78} +2.56336i q^{79} +(1.66639 + 3.63636i) q^{80} +1.00000 q^{81} +(4.50503 - 5.59412i) q^{82} +13.9979 q^{83} +(4.94567 - 1.88158i) q^{84} +0.503042 q^{85} +(8.03818 - 9.98142i) q^{86} -5.03595 q^{87} +(1.95039 + 0.973914i) q^{88} -2.98877i q^{89} +(0.887017 - 1.10145i) q^{90} +(-14.6678 + 2.19717i) q^{91} +(-2.78399 + 0.607518i) q^{92} +8.23212 q^{93} +(5.12139 + 4.12433i) q^{94} -1.63506i q^{95} +(5.48341 + 1.39006i) q^{96} +15.5818i q^{97} +(-9.19113 - 3.67738i) q^{98} -0.770756i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} - 16 q^{3} - 2 q^{4} - 2 q^{6} - 4 q^{7} + 2 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q + 2 * q^2 - 16 * q^3 - 2 * q^4 - 2 * q^6 - 4 * q^7 + 2 * q^8 + 16 * q^9	\( 16 q + 2 q^{2} - 16 q^{3} - 2 q^{4} - 2 q^{6} - 4 q^{7} + 2 q^{8} + 16 q^{9} + 2 q^{12} - 2 q^{14} + 6 q^{16} + 2 q^{18} - 24 q^{19} + 4 q^{21} - 12 q^{22} - 2 q^{24} - 16 q^{25} - 12 q^{26} - 16 q^{27} + 14 q^{28} + 16 q^{29} + 8 q^{31} - 18 q^{32} + 24 q^{34} - 2 q^{36} + 24 q^{37} + 28 q^{38} + 12 q^{40} + 2 q^{42} - 8 q^{44} - 20 q^{46} + 16 q^{47} - 6 q^{48} - 16 q^{49} - 2 q^{50} - 20 q^{52} - 32 q^{53} - 2 q^{54} + 2 q^{56} + 24 q^{57} - 32 q^{58} + 8 q^{59} + 16 q^{62} - 4 q^{63} - 2 q^{64} - 8 q^{65} + 12 q^{66} + 4 q^{68} + 2 q^{72} - 4 q^{74} + 16 q^{75} + 16 q^{76} - 8 q^{77} + 12 q^{78} - 16 q^{80} + 16 q^{81} - 4 q^{82} + 8 q^{83} - 14 q^{84} + 64 q^{86} - 16 q^{87} - 52 q^{88} + 16 q^{91} + 64 q^{92} - 8 q^{93} + 16 q^{94} + 18 q^{96} - 86 q^{98}+O(q^{100}) \) 16 * q + 2 * q^2 - 16 * q^3 - 2 * q^4 - 2 * q^6 - 4 * q^7 + 2 * q^8 + 16 * q^9 + 2 * q^12 - 2 * q^14 + 6 * q^16 + 2 * q^18 - 24 * q^19 + 4 * q^21 - 12 * q^22 - 2 * q^24 - 16 * q^25 - 12 * q^26 - 16 * q^27 + 14 * q^28 + 16 * q^29 + 8 * q^31 - 18 * q^32 + 24 * q^34 - 2 * q^36 + 24 * q^37 + 28 * q^38 + 12 * q^40 + 2 * q^42 - 8 * q^44 - 20 * q^46 + 16 * q^47 - 6 * q^48 - 16 * q^49 - 2 * q^50 - 20 * q^52 - 32 * q^53 - 2 * q^54 + 2 * q^56 + 24 * q^57 - 32 * q^58 + 8 * q^59 + 16 * q^62 - 4 * q^63 - 2 * q^64 - 8 * q^65 + 12 * q^66 + 4 * q^68 + 2 * q^72 - 4 * q^74 + 16 * q^75 + 16 * q^76 - 8 * q^77 + 12 * q^78 - 16 * q^80 + 16 * q^81 - 4 * q^82 + 8 * q^83 - 14 * q^84 + 64 * q^86 - 16 * q^87 - 52 * q^88 + 16 * q^91 + 64 * q^92 - 8 * q^93 + 16 * q^94 + 18 * q^96 - 86 * q^98

Introduction

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