LMFDB - Embedded newform 420.2.c.a.391.11

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			391.11
Root			$1.07312 - 0.921096i$ of defining polynomial
Character	$\chi$	$=$	420.391
Dual form			420.2.c.a.391.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.07312 - 0.921096i) q^{2} -1.00000 q^{3} +(0.303166 - 1.97689i) q^{4} -1.00000i q^{5} +(-1.07312 + 0.921096i) q^{6} +(-1.82575 + 1.91485i) q^{7} +(-1.49557 - 2.40068i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(1.07312 - 0.921096i) q^{2} -1.00000 q^{3} +(0.303166 - 1.97689i) q^{4} -1.00000i q^{5} +(-1.07312 + 0.921096i) q^{6} +(-1.82575 + 1.91485i) q^{7} +(-1.49557 - 2.40068i) q^{8} +1.00000 q^{9} +(-0.921096 - 1.07312i) q^{10} -6.24043i q^{11} +(-0.303166 + 1.97689i) q^{12} -2.40312i q^{13} +(-0.195481 + 3.73655i) q^{14} +1.00000i q^{15} +(-3.81618 - 1.19865i) q^{16} -1.30768i q^{17} +(1.07312 - 0.921096i) q^{18} -3.94796 q^{19} +(-1.97689 - 0.303166i) q^{20} +(1.82575 - 1.91485i) q^{21} +(-5.74803 - 6.69672i) q^{22} +3.55648i q^{23} +(1.49557 + 2.40068i) q^{24} -1.00000 q^{25} +(-2.21350 - 2.57883i) q^{26} -1.00000 q^{27} +(3.23194 + 4.18981i) q^{28} +1.44221 q^{29} +(0.921096 + 1.07312i) q^{30} +10.9517 q^{31} +(-5.19929 + 2.22877i) q^{32} +6.24043i q^{33} +(-1.20450 - 1.40329i) q^{34} +(1.91485 + 1.82575i) q^{35} +(0.303166 - 1.97689i) q^{36} -5.06265 q^{37} +(-4.23663 + 3.63645i) q^{38} +2.40312i q^{39} +(-2.40068 + 1.49557i) q^{40} +1.26175i q^{41} +(0.195481 - 3.73655i) q^{42} +2.19850i q^{43} +(-12.3366 - 1.89189i) q^{44} -1.00000i q^{45} +(3.27586 + 3.81652i) q^{46} +11.6743 q^{47} +(3.81618 + 1.19865i) q^{48} +(-0.333303 - 6.99206i) q^{49} +(-1.07312 + 0.921096i) q^{50} +1.30768i q^{51} +(-4.75070 - 0.728544i) q^{52} +11.7545 q^{53} +(-1.07312 + 0.921096i) q^{54} -6.24043 q^{55} +(7.32748 + 1.51924i) q^{56} +3.94796 q^{57} +(1.54766 - 1.32842i) q^{58} +0.415368 q^{59} +(1.97689 + 0.303166i) q^{60} -12.6848i q^{61} +(11.7524 - 10.0875i) q^{62} +(-1.82575 + 1.91485i) q^{63} +(-3.52653 + 7.18078i) q^{64} -2.40312 q^{65} +(5.74803 + 6.69672i) q^{66} +3.10097i q^{67} +(-2.58513 - 0.396443i) q^{68} -3.55648i q^{69} +(3.73655 + 0.195481i) q^{70} -10.4762i q^{71} +(-1.49557 - 2.40068i) q^{72} -1.64141i q^{73} +(-5.43282 + 4.66319i) q^{74} +1.00000 q^{75} +(-1.19689 + 7.80468i) q^{76} +(11.9495 + 11.3934i) q^{77} +(2.21350 + 2.57883i) q^{78} +9.18952i q^{79} +(-1.19865 + 3.81618i) q^{80} +1.00000 q^{81} +(1.16219 + 1.35401i) q^{82} +7.39922 q^{83} +(-3.23194 - 4.18981i) q^{84} -1.30768 q^{85} +(2.02502 + 2.35925i) q^{86} -1.44221 q^{87} +(-14.9813 + 9.33301i) q^{88} +11.4448i q^{89} +(-0.921096 - 1.07312i) q^{90} +(4.60162 + 4.38749i) q^{91} +(7.03076 + 1.07820i) q^{92} -10.9517 q^{93} +(12.5279 - 10.7531i) q^{94} +3.94796i q^{95} +(5.19929 - 2.22877i) q^{96} +12.4433i q^{97} +(-6.79803 - 7.19630i) q^{98} -6.24043i 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 $

$2$	1.07312	−	0.921096i	0.758809	−	0.651313i
$2$	1.07312	−	0.921096i	0.758809	−	0.651313i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	0.303166	−	1.97689i	0.151583	−	0.988445i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−1.07312	+	0.921096i	−0.438099	+	0.376036i
$7$	−1.82575	+	1.91485i	−0.690067	+	0.723745i
$7$	−1.82575	+	1.91485i	−0.690067	+	0.723745i
$8$	−1.49557	−	2.40068i	−0.528764	−	0.848769i
$9$	1.00000			0.333333
$10$	−0.921096	−	1.07312i	−0.291276	−	0.339350i
$11$		−	6.24043i		−	1.88156i	−0.339016	−	0.940780i	$-0.610094\pi$
$11$		−	6.24043i		−	1.88156i	0.339016	−	0.940780i	$-0.389906\pi$
$12$	−0.303166	+	1.97689i	−0.0875164	+	0.570679i
$13$		−	2.40312i		−	0.666506i	−0.942837	−	0.333253i	$-0.891854\pi$
$13$		−	2.40312i		−	0.666506i	0.942837	−	0.333253i	$-0.108146\pi$
$14$	−0.195481	+	3.73655i	−0.0522446	+	0.998634i
$15$			1.00000i			0.258199i
$16$	−3.81618	−	1.19865i	−0.954045	−	0.299663i
$17$		−	1.30768i		−	0.317159i	−0.987346	−	0.158579i	$-0.949309\pi$
$17$		−	1.30768i		−	0.317159i	0.987346	−	0.158579i	$-0.0506913\pi$
$18$	1.07312	−	0.921096i	0.252936	−	0.217104i
$19$	−3.94796			−0.905724			−0.452862	−	0.891581i	$-0.649597\pi$
$19$	−3.94796			−0.905724			−0.452862	+	0.891581i	$0.649597\pi$
$20$	−1.97689	−	0.303166i	−0.442046	−	0.0677899i
$21$	1.82575	−	1.91485i	0.398410	−	0.417855i
$22$	−5.74803	−	6.69672i	−1.22548	−	1.42775i
$23$			3.55648i			0.741577i	0.928717	+	0.370788i	$0.120912\pi$
$23$			3.55648i			0.741577i	−0.928717	+	0.370788i	$0.879088\pi$
$24$	1.49557	+	2.40068i	0.305282	+	0.490037i
$25$	−1.00000			−0.200000
$26$	−2.21350	−	2.57883i	−0.434104	−	0.505751i
$27$	−1.00000			−0.192450
$28$	3.23194	+	4.18981i	0.610780	+	0.791801i
$29$	1.44221			0.267812			0.133906	−	0.990994i	$-0.457248\pi$
$29$	1.44221			0.267812			0.133906	+	0.990994i	$0.457248\pi$
$30$	0.921096	+	1.07312i	0.168168	+	0.195924i
$31$	10.9517			1.96698			0.983488	−	0.180974i	$-0.0579249\pi$
$31$	10.9517			1.96698			0.983488	+	0.180974i	$0.0579249\pi$
$32$	−5.19929	+	2.22877i	−0.919112	+	0.393995i
$33$			6.24043i			1.08632i
$34$	−1.20450	−	1.40329i	−0.206569	−	0.240663i
$35$	1.91485	+	1.82575i	0.323669	+	0.308607i
$36$	0.303166	−	1.97689i	0.0505276	−	0.329482i
$37$	−5.06265			−0.832295			−0.416147	−	0.909297i	$-0.636620\pi$
$37$	−5.06265			−0.832295			−0.416147	+	0.909297i	$0.636620\pi$
$38$	−4.23663	+	3.63645i	−0.687272	+	0.589910i
$39$			2.40312i			0.384807i
$40$	−2.40068	+	1.49557i	−0.379581	+	0.236471i
$41$			1.26175i			0.197052i	0.995134	+	0.0985260i	$0.0314128\pi$
$41$			1.26175i			0.197052i	−0.995134	+	0.0985260i	$0.968587\pi$
$42$	0.195481	−	3.73655i	0.0301634	−	0.576562i
$43$			2.19850i			0.335267i	0.985849	+	0.167634i	$0.0536126\pi$
$43$			2.19850i			0.335267i	−0.985849	+	0.167634i	$0.946387\pi$
$44$	−12.3366	−	1.89189i	−1.85982	−	0.285212i
$45$		−	1.00000i		−	0.149071i
$46$	3.27586	+	3.81652i	0.482999	+	0.562715i
$47$	11.6743			1.70287			0.851434	−	0.524462i	$-0.175733\pi$
$47$	11.6743			1.70287			0.851434	+	0.524462i	$0.175733\pi$
$48$	3.81618	+	1.19865i	0.550818	+	0.173010i
$49$	−0.333303	−	6.99206i	−0.0476147	−	0.998866i
$50$	−1.07312	+	0.921096i	−0.151762	+	0.130263i
$51$			1.30768i			0.183112i
$52$	−4.75070	−	0.728544i	−0.658804	−	0.101031i
$53$	11.7545			1.61461			0.807303	−	0.590137i	$-0.200926\pi$
$53$	11.7545			1.61461			0.807303	+	0.590137i	$0.200926\pi$
$54$	−1.07312	+	0.921096i	−0.146033	+	0.125345i
$55$	−6.24043			−0.841460
$56$	7.32748	+	1.51924i	0.979175	+	0.203017i
$57$	3.94796			0.522920
$58$	1.54766	−	1.32842i	0.203218	−	0.174430i
$59$	0.415368			0.0540763			0.0270382	−	0.999634i	$-0.491392\pi$
$59$	0.415368			0.0540763			0.0270382	+	0.999634i	$0.491392\pi$
$60$	1.97689	+	0.303166i	0.255215	+	0.0391385i
$61$		−	12.6848i		−	1.62412i	−0.583574	−	0.812060i	$-0.698346\pi$
$61$		−	12.6848i		−	1.62412i	0.583574	−	0.812060i	$-0.301654\pi$
$62$	11.7524	−	10.0875i	1.49256	−	1.28112i
$63$	−1.82575	+	1.91485i	−0.230022	+	0.241248i
$64$	−3.52653	+	7.18078i	−0.440817	+	0.897597i
$65$	−2.40312			−0.298070
$66$	5.74803	+	6.69672i	0.707534	+	0.824309i
$67$			3.10097i			0.378844i	0.981896	+	0.189422i	$0.0606614\pi$
$67$			3.10097i			0.378844i	−0.981896	+	0.189422i	$0.939339\pi$
$68$	−2.58513	−	0.396443i	−0.313494	−	0.0480758i
$69$		−	3.55648i		−	0.428150i
$70$	3.73655	+	0.195481i	0.446603	+	0.0233645i
$71$		−	10.4762i		−	1.24330i	−0.783296	−	0.621649i	$-0.786463\pi$
$71$		−	10.4762i		−	1.24330i	0.783296	−	0.621649i	$-0.213537\pi$
$72$	−1.49557	−	2.40068i	−0.176255	−	0.282923i
$73$		−	1.64141i		−	0.192112i	−0.995376	−	0.0960562i	$-0.969377\pi$
$73$		−	1.64141i		−	0.192112i	0.995376	−	0.0960562i	$-0.0306229\pi$
$74$	−5.43282	+	4.66319i	−0.631553	+	0.542084i
$75$	1.00000			0.115470
$76$	−1.19689	+	7.80468i	−0.137292	+	0.895258i
$77$	11.9495	+	11.3934i	1.36177	+	1.29840i
$78$	2.21350	+	2.57883i	0.250630	+	0.291995i
$79$			9.18952i			1.03390i	0.856015	+	0.516951i	$0.172933\pi$
$79$			9.18952i			1.03390i	−0.856015	+	0.516951i	$0.827067\pi$
$80$	−1.19865	+	3.81618i	−0.134013	+	0.426662i
$81$	1.00000			0.111111
$82$	1.16219	+	1.35401i	0.128343	+	0.149525i
$83$	7.39922			0.812170			0.406085	−	0.913835i	$-0.366894\pi$
$83$	7.39922			0.812170			0.406085	+	0.913835i	$0.366894\pi$
$84$	−3.23194	−	4.18981i	−0.352634	−	0.457146i
$85$	−1.30768			−0.141838
$86$	2.02502	+	2.35925i	0.218364	+	0.254404i
$87$	−1.44221			−0.154621
$88$	−14.9813	+	9.33301i	−1.59701	+	0.994902i
$89$			11.4448i			1.21314i	0.795028	+	0.606572i	$0.207456\pi$
$89$			11.4448i			1.21314i	−0.795028	+	0.606572i	$0.792544\pi$
$90$	−0.921096	−	1.07312i	−0.0970920	−	0.113117i
$91$	4.60162	+	4.38749i	0.482380	+	0.459934i
$92$	7.03076	+	1.07820i	0.733008	+	0.112410i
$93$	−10.9517			−1.13563
$94$	12.5279	−	10.7531i	1.29215	−	1.10910i
$95$			3.94796i			0.405052i
$96$	5.19929	−	2.22877i	0.530650	−	0.227473i
$97$			12.4433i			1.26343i	0.775202	+	0.631714i	$0.217648\pi$
$97$			12.4433i			1.26343i	−0.775202	+	0.631714i	$0.782352\pi$
$98$	−6.79803	−	7.19630i	−0.686705	−	0.726936i
$99$		−	6.24043i		−	0.627187i
$100$	−0.303166	+	1.97689i	−0.0303166	+	0.197689i
$101$		−	4.25585i		−	0.423473i	−0.977327	−	0.211737i	$-0.932088\pi$
$101$		−	4.25585i		−	0.423473i	0.977327	−	0.211737i	$-0.0679119\pi$
$102$	1.20450	+	1.40329i	0.119263	+	0.138947i
$103$	−15.3254			−1.51006			−0.755029	−	0.655691i	$-0.772377\pi$
$103$	−15.3254			−1.51006			−0.755029	+	0.655691i	$0.772377\pi$
$104$	−5.76913	+	3.59404i	−0.565709	+	0.352424i
$105$	−1.91485	−	1.82575i	−0.186870	−	0.178175i
$106$	12.6140	−	10.8270i	1.22518	−	1.05161i
$107$			4.83844i			0.467750i	0.972267	+	0.233875i	$0.0751406\pi$
$107$			4.83844i			0.467750i	−0.972267	+	0.233875i	$0.924859\pi$
$108$	−0.303166	+	1.97689i	−0.0291721	+	0.190226i
$109$	8.77146			0.840153			0.420077	−	0.907489i	$-0.362003\pi$
$109$	8.77146			0.840153			0.420077	+	0.907489i	$0.362003\pi$
$110$	−6.69672	+	5.74803i	−0.638507	+	0.548054i
$111$	5.06265			0.480526
$112$	9.26261	−	5.11898i	0.875235	−	0.483699i
$113$	4.09511			0.385236			0.192618	−	0.981274i	$-0.438302\pi$
$113$	4.09511			0.385236			0.192618	+	0.981274i	$0.438302\pi$
$114$	4.23663	−	3.63645i	0.396796	−	0.340584i
$115$	3.55648			0.331643
$116$	0.437230	−	2.85109i	0.0405957	−	0.264717i
$117$		−	2.40312i		−	0.222169i
$118$	0.445739	−	0.382594i	0.0410336	−	0.0352206i
$119$	2.50401	+	2.38749i	0.229542	+	0.218861i
$120$	2.40068	−	1.49557i	0.219151	−	0.136526i
$121$	−27.9430			−2.54027
$122$	−11.6839	−	13.6123i	−1.05781	−	1.23240i
$123$		−	1.26175i		−	0.113768i
$124$	3.32017	−	21.6502i	0.298160	−	1.94425i
$125$			1.00000i			0.0894427i
$126$	−0.195481	+	3.73655i	−0.0174149	+	0.332878i
$127$		−	6.68595i		−	0.593282i	−0.954989	−	0.296641i	$-0.904134\pi$
$127$		−	6.68595i		−	0.593282i	0.954989	−	0.296641i	$-0.0958664\pi$
$128$	2.82979	+	10.9541i	0.250121	+	0.968215i
$129$		−	2.19850i		−	0.193567i
$130$	−2.57883	+	2.21350i	−0.226179	+	0.194137i
$131$	13.3308			1.16472			0.582360	−	0.812931i	$-0.302129\pi$
$131$	13.3308			1.16472			0.582360	+	0.812931i	$0.302129\pi$
$132$	12.3366	+	1.89189i	1.07377	+	0.164668i
$133$	7.20797	−	7.55975i	0.625010	−	0.655513i
$134$	2.85629	+	3.32771i	0.246746	+	0.287470i
$135$			1.00000i			0.0860663i
$136$	−3.13932	+	1.95573i	−0.269194	+	0.167702i
$137$	5.59837			0.478301			0.239151	−	0.970982i	$-0.423131\pi$
$137$	5.59837			0.478301			0.239151	+	0.970982i	$0.423131\pi$
$138$	−3.27586	−	3.81652i	−0.278859	−	0.324884i
$139$	−6.13537			−0.520395			−0.260198	−	0.965555i	$-0.583788\pi$
$139$	−6.13537			−0.520395			−0.260198	+	0.965555i	$0.583788\pi$
$140$	4.18981	−	3.23194i	0.354104	−	0.273149i
$141$	−11.6743			−0.983151
$142$	−9.64959	−	11.2422i	−0.809776	−	0.943425i
$143$	−14.9965			−1.25407
$144$	−3.81618	−	1.19865i	−0.318015	−	0.0998875i
$145$		−	1.44221i		−	0.119769i
$146$	−1.51189	−	1.76143i	−0.125125	−	0.145777i
$147$	0.333303	+	6.99206i	0.0274904	+	0.576695i
$148$	−1.53482	+	10.0083i	−0.126162	+	0.822677i
$149$	−12.3505			−1.01179			−0.505895	−	0.862595i	$-0.668838\pi$
$149$	−12.3505			−1.01179			−0.505895	+	0.862595i	$0.668838\pi$
$150$	1.07312	−	0.921096i	0.0876197	−	0.0752071i
$151$		−	15.9654i		−	1.29924i	−0.760258	−	0.649621i	$-0.774928\pi$
$151$		−	15.9654i		−	1.29924i	0.760258	−	0.649621i	$-0.225072\pi$
$152$	5.90445	+	9.47779i	0.478914	+	0.768750i
$153$		−	1.30768i		−	0.105720i
$154$	23.3177	+	1.21989i	1.87899	+	0.0983014i
$155$		−	10.9517i		−	0.879658i
$156$	4.75070	+	0.728544i	0.380361	+	0.0583302i
$157$		−	5.15966i		−	0.411786i	−0.978575	−	0.205893i	$-0.933990\pi$
$157$		−	5.15966i		−	0.411786i	0.978575	−	0.205893i	$-0.0660098\pi$
$158$	8.46443	+	9.86144i	0.673394	+	0.784534i
$159$	−11.7545			−0.932194
$160$	2.22877	+	5.19929i	0.176200	+	0.411040i
$161$	−6.81012	−	6.49322i	−0.536713	−	0.511738i
$162$	1.07312	−	0.921096i	0.0843121	−	0.0723681i
$163$		−	1.27295i		−	0.0997052i	−0.998757	−	0.0498526i	$-0.984125\pi$
$163$		−	1.27295i		−	0.0997052i	0.998757	−	0.0498526i	$-0.0158751\pi$
$164$	2.49434	+	0.382519i	0.194775	+	0.0298697i
$165$	6.24043			0.485817
$166$	7.94023	−	6.81539i	0.616282	−	0.528977i
$167$	−21.6628			−1.67632			−0.838158	−	0.545428i	$-0.816367\pi$
$167$	−21.6628			−1.67632			−0.838158	+	0.545428i	$0.816367\pi$
$168$	−7.32748	−	1.51924i	−0.565327	−	0.117212i
$169$	7.22501			0.555770
$170$	−1.40329	+	1.20450i	−0.107628	+	0.0923807i
$171$	−3.94796			−0.301908
$172$	4.34618	+	0.666509i	0.331393	+	0.0508208i
$173$			12.9769i			0.986617i	0.869855	+	0.493308i	$0.164213\pi$
$173$			12.9769i			0.986617i	−0.869855	+	0.493308i	$0.835787\pi$
$174$	−1.54766	+	1.32842i	−0.117328	+	0.100707i
$175$	1.82575	−	1.91485i	0.138013	−	0.144749i
$176$	−7.48010	+	23.8146i	−0.563833	+	1.79509i
$177$	−0.415368			−0.0312210
$178$	10.5417	+	12.2816i	0.790137	+	0.920545i
$179$		−	15.1508i		−	1.13242i	−0.824261	−	0.566210i	$-0.808409\pi$
$179$		−	15.1508i		−	1.13242i	0.824261	−	0.566210i	$-0.191591\pi$
$180$	−1.97689	−	0.303166i	−0.147349	−	0.0225966i
$181$			2.92356i			0.217307i	0.994080	+	0.108653i	$0.0346538\pi$
$181$			2.92356i			0.217307i	−0.994080	+	0.108653i	$0.965346\pi$
$182$	8.97937	+	0.469765i	0.665596	+	0.0348213i
$183$			12.6848i			0.937686i
$184$	8.53797	−	5.31896i	0.629427	−	0.392119i
$185$			5.06265i			0.372214i
$186$	−11.7524	+	10.0875i	−0.861730	+	0.739653i
$187$	−8.16048			−0.596753
$188$	3.53924	−	23.0788i	0.258126	−	1.68319i
$189$	1.82575	−	1.91485i	0.132803	−	0.139285i
$190$	3.63645	+	4.23663i	0.263816	+	0.307357i
$191$		−	13.9477i		−	1.00922i	−0.863348	−	0.504608i	$-0.831637\pi$
$191$		−	13.9477i		−	1.00922i	0.863348	−	0.504608i	$-0.168363\pi$
$192$	3.52653	−	7.18078i	0.254506	−	0.518228i
$193$	−13.3869			−0.963607			−0.481803	−	0.876279i	$-0.660018\pi$
$193$	−13.3869			−0.963607			−0.481803	+	0.876279i	$0.660018\pi$
$194$	11.4615	+	13.3532i	0.822887	+	0.958701i
$195$	2.40312			0.172091
$196$	−13.9236	−	1.46085i	−0.994541	−	0.104346i
$197$	4.07989			0.290680			0.145340	−	0.989382i	$-0.453572\pi$
$197$	4.07989			0.290680			0.145340	+	0.989382i	$0.453572\pi$
$198$	−5.74803	−	6.69672i	−0.408495	−	0.475915i
$199$	3.66884			0.260077			0.130039	−	0.991509i	$-0.458490\pi$
$199$	3.66884			0.260077			0.130039	+	0.991509i	$0.458490\pi$
$200$	1.49557	+	2.40068i	0.105753	+	0.169754i
$201$		−	3.10097i		−	0.218726i
$202$	−3.92005	−	4.56703i	−0.275814	−	0.321335i
$203$	−2.63311	+	2.76162i	−0.184808	+	0.193828i
$204$	2.58513	+	0.396443i	0.180996	+	0.0277566i
$205$	1.26175			0.0881244
$206$	−16.4460	+	14.1162i	−1.14585	+	0.983521i
$207$			3.55648i			0.247192i
$208$	−2.88050	+	9.17074i	−0.199727	+	0.635877i
$209$			24.6370i			1.70417i
$210$	−3.73655	−	0.195481i	−0.257846	−	0.0134895i
$211$			5.67817i			0.390901i	0.980714	+	0.195451i	$0.0626170\pi$
$211$			5.67817i			0.390901i	−0.980714	+	0.195451i	$0.937383\pi$
$212$	3.56357	−	23.2374i	0.244747	−	1.59595i
$213$			10.4762i			0.717818i
$214$	4.45667	+	5.19222i	0.304651	+	0.354933i
$215$	2.19850			0.149936
$216$	1.49557	+	2.40068i	0.101761	+	0.163346i
$217$	−19.9949	+	20.9708i	−1.35735	+	1.42359i
$218$	9.41281	−	8.07935i	0.637516	−	0.547203i
$219$			1.64141i			0.110916i
$220$	−1.89189	+	12.3366i	−0.127551	+	0.831736i
$221$	−3.14251			−0.211388
$222$	5.43282	−	4.66319i	0.364627	−	0.312973i
$223$	3.97664			0.266296			0.133148	−	0.991096i	$-0.457491\pi$
$223$	3.97664			0.266296			0.133148	+	0.991096i	$0.457491\pi$
$224$	5.22481	−	14.0250i	0.349097	−	0.937087i
$225$	−1.00000			−0.0666667
$226$	4.39454	−	3.77199i	0.292321	−	0.250909i
$227$	−2.54691			−0.169045			−0.0845223	−	0.996422i	$-0.526936\pi$
$227$	−2.54691			−0.169045			−0.0845223	+	0.996422i	$0.526936\pi$
$228$	1.19689	−	7.80468i	0.0792657	−	0.516877i
$229$			10.6638i			0.704681i	0.935872	+	0.352341i	$0.114614\pi$
$229$			10.6638i			0.704681i	−0.935872	+	0.352341i	$0.885386\pi$
$230$	3.81652	−	3.27586i	0.251654	−	0.216004i
$231$	−11.9495	−	11.3934i	−0.786219	−	0.749634i
$232$	−2.15693	−	3.46229i	−0.141609	−	0.227311i
$233$	−20.4421			−1.33921			−0.669605	−	0.742718i	$-0.733536\pi$
$233$	−20.4421			−1.33921			−0.669605	+	0.742718i	$0.733536\pi$
$234$	−2.21350	−	2.57883i	−0.144701	−	0.168584i
$235$		−	11.6743i		−	0.761546i
$236$	0.125925	−	0.821137i	0.00819705	−	0.0534515i
$237$		−	9.18952i		−	0.596923i
$238$	4.88620	+	0.255627i	0.316725	+	0.0165698i
$239$			4.38800i			0.283836i	0.989878	+	0.141918i	$0.0453270\pi$
$239$			4.38800i			0.283836i	−0.989878	+	0.141918i	$0.954673\pi$
$240$	1.19865	−	3.81618i	0.0773726	−	0.246333i
$241$			22.5909i			1.45521i	0.685996	+	0.727605i	$0.259367\pi$
$241$			22.5909i			1.45521i	−0.685996	+	0.727605i	$0.740633\pi$
$242$	−29.9861	+	25.7382i	−1.92758	+	1.65451i
$243$	−1.00000			−0.0641500
$244$	−25.0764	−	3.84559i	−1.60535	−	0.246189i
$245$	−6.99206	+	0.333303i	−0.446706	+	0.0212940i
$246$	−1.16219	−	1.35401i	−0.0740986	−	0.0863283i
$247$			9.48742i			0.603670i
$248$	−16.3790	−	26.2914i	−1.04007	−	1.66951i
$249$	−7.39922			−0.468906
$250$	0.921096	+	1.07312i	0.0582552	+	0.0678700i
$251$	12.0822			0.762624			0.381312	−	0.924446i	$-0.375472\pi$
$251$	12.0822			0.762624			0.381312	+	0.924446i	$0.375472\pi$
$252$	3.23194	+	4.18981i	0.203593	+	0.263934i
$253$	22.1940			1.39532
$254$	−6.15840	−	7.17481i	−0.386412	−	0.450188i
$255$	1.30768			0.0818900
$256$	13.1265	+	9.14853i	0.820405	+	0.571783i
$257$		−	14.1869i		−	0.884957i	−0.896779	−	0.442478i	$-0.854099\pi$
$257$		−	14.1869i		−	0.884957i	0.896779	−	0.442478i	$-0.145901\pi$
$258$	−2.02502	−	2.35925i	−0.126073	−	0.146880i
$259$	9.24311	−	9.69422i	0.574339	−	0.602369i
$260$	−0.728544	+	4.75070i	−0.0451824	+	0.294626i
$261$	1.44221			0.0892707
$262$	14.3056	−	12.2790i	0.883801	−	0.758598i
$263$		−	13.5093i		−	0.833021i	−0.909131	−	0.416511i	$-0.863253\pi$
$263$		−	13.5093i		−	0.833021i	0.909131	−	0.416511i	$-0.136747\pi$
$264$	14.9813	−	9.33301i	0.922034	−	0.574407i
$265$		−	11.7545i		−	0.722074i
$266$	0.771752	−	14.7517i	0.0473192	−	0.904487i
$267$		−	11.4448i		−	0.700409i
$268$	6.13027	+	0.940108i	0.374466	+	0.0574262i
$269$		−	9.57770i		−	0.583963i	−0.956424	−	0.291981i	$-0.905685\pi$
$269$		−	9.57770i		−	0.583963i	0.956424	−	0.291981i	$-0.0943145\pi$
$270$	0.921096	+	1.07312i	0.0560561	+	0.0653079i
$271$	7.20379			0.437599			0.218800	−	0.975770i	$-0.429786\pi$
$271$	7.20379			0.437599			0.218800	+	0.975770i	$0.429786\pi$
$272$	−1.56745	+	4.99034i	−0.0950406	+	0.302584i
$273$	−4.60162	−	4.38749i	−0.278502	−	0.265543i
$274$	6.00771	−	5.15663i	0.362939	−	0.311524i
$275$			6.24043i			0.376312i
$276$	−7.03076	−	1.07820i	−0.423202	−	0.0649002i
$277$	22.2563			1.33725			0.668627	−	0.743598i	$-0.266882\pi$
$277$	22.2563			1.33725			0.668627	+	0.743598i	$0.266882\pi$
$278$	−6.58398	+	5.65126i	−0.394881	+	0.338940i
$279$	10.9517			0.655659
$280$	1.51924	−	7.32748i	0.0907919	−	0.437900i
$281$	27.2215			1.62390			0.811950	−	0.583727i	$-0.198406\pi$
$281$	27.2215			1.62390			0.811950	+	0.583727i	$0.198406\pi$
$282$	−12.5279	+	10.7531i	−0.746024	+	0.640339i
$283$	−18.6312			−1.10751			−0.553754	−	0.832680i	$-0.686805\pi$
$283$	−18.6312			−1.10751			−0.553754	+	0.832680i	$0.686805\pi$
$284$	−20.7103	−	3.17603i	−1.22893	−	0.188463i
$285$		−	3.94796i		−	0.233857i
$286$	−16.0930	+	13.8132i	−0.951601	+	0.816793i
$287$	−2.41606	−	2.30363i	−0.142616	−	0.135979i
$288$	−5.19929	+	2.22877i	−0.306371	+	0.131332i
$289$	15.2900			0.899410
$290$	−1.32842	−	1.54766i	−0.0780073	−	0.0908820i
$291$		−	12.4433i		−	0.729440i
$292$	−3.24488	−	0.497619i	−0.189892	−	0.0291210i
$293$		−	15.4578i		−	0.903057i	−0.892257	−	0.451528i	$-0.850879\pi$
$293$		−	15.4578i		−	0.903057i	0.892257	−	0.451528i	$-0.149121\pi$
$294$	6.79803	+	7.19630i	0.396469	+	0.419697i
$295$		−	0.415368i		−	0.0241837i
$296$	7.57155	+	12.1538i	0.440088	+	0.706426i
$297$			6.24043i			0.362107i
$298$	−13.2535	+	11.3760i	−0.767756	+	0.658992i
$299$	8.54664			0.494265
$300$	0.303166	−	1.97689i	0.0175033	−	0.114136i
$301$	−4.20979	−	4.01389i	−0.242648	−	0.231357i
$302$	−14.7056	−	17.1327i	−0.846213	−	0.985877i
$303$			4.25585i			0.244492i
$304$	15.0661	+	4.73222i	0.864101	+	0.271412i
$305$	−12.6848			−0.726329
$306$	−1.20450	−	1.40329i	−0.0688565	−	0.0802209i
$307$	−30.4225			−1.73630			−0.868151	−	0.496299i	$-0.834692\pi$
$307$	−30.4225			−1.73630			−0.868151	+	0.496299i	$0.834692\pi$
$308$	26.1463	−	20.1687i	1.48982	−	1.14922i
$309$	15.3254			0.871833
$310$	−10.0875	−	11.7524i	−0.572933	−	0.667493i
$311$	−6.24557			−0.354154			−0.177077	−	0.984197i	$-0.556664\pi$
$311$	−6.24557			−0.354154			−0.177077	+	0.984197i	$0.556664\pi$
$312$	5.76913	−	3.59404i	0.326612	−	0.203472i
$313$			14.5063i			0.819945i	0.912098	+	0.409973i	$0.134462\pi$
$313$			14.5063i			0.819945i	−0.912098	+	0.409973i	$0.865538\pi$
$314$	−4.75254	−	5.53692i	−0.268201	−	0.312467i
$315$	1.91485	+	1.82575i	0.107890	+	0.102869i
$316$	18.1667	+	2.78595i	1.02195	+	0.156722i
$317$	2.29755			0.129043			0.0645215	−	0.997916i	$-0.479448\pi$
$317$	2.29755			0.129043			0.0645215	+	0.997916i	$0.479448\pi$
$318$	−12.6140	+	10.8270i	−0.707357	+	0.607150i
$319$		−	9.00003i		−	0.503905i
$320$	7.18078	+	3.52653i	0.401418	+	0.197139i
$321$		−	4.83844i		−	0.270055i
$322$	−13.2889	−	0.695225i	−0.740564	−	0.0387434i
$323$			5.16266i			0.287258i
$324$	0.303166	−	1.97689i	0.0168425	−	0.109827i
$325$			2.40312i			0.133301i
$326$	−1.17251	−	1.36603i	−0.0649393	−	0.0756572i
$327$	−8.77146			−0.485063
$328$	3.02906	−	1.88704i	0.167252	−	0.104194i
$329$	−21.3143	+	22.3545i	−1.17509	+	1.23244i
$330$	6.69672	−	5.74803i	0.368642	−	0.316419i
$331$			23.4483i			1.28884i	0.764673	+	0.644419i	$0.222901\pi$
$331$			23.4483i			1.28884i	−0.764673	+	0.644419i	$0.777099\pi$
$332$	2.24319	−	14.6274i	0.123111	−	0.802785i
$333$	−5.06265			−0.277432
$334$	−23.2467	+	19.9535i	−1.27200	+	1.09181i
$335$	3.10097			0.169424
$336$	−9.26261	+	5.11898i	−0.505317	+	0.279263i
$337$	14.6709			0.799174			0.399587	−	0.916695i	$-0.369153\pi$
$337$	14.6709			0.799174			0.399587	+	0.916695i	$0.369153\pi$
$338$	7.75329	−	6.65493i	0.421723	−	0.361980i
$339$	−4.09511			−0.222416
$340$	−0.396443	+	2.58513i	−0.0215002	+	0.140199i
$341$		−	68.3431i		−	3.70099i
$342$	−4.23663	+	3.63645i	−0.229091	+	0.196637i
$343$	13.9973	+	12.1275i	0.755782	+	0.654823i
$344$	5.27789	−	3.28801i	0.284565	−	0.177277i
$345$	−3.55648			−0.191474
$346$	11.9530	+	13.9258i	0.642596	+	0.748654i
$347$		−	21.6099i		−	1.16008i	−0.814587	−	0.580041i	$-0.803036\pi$
$347$		−	21.6099i		−	1.16008i	0.814587	−	0.580041i	$-0.196964\pi$
$348$	−0.437230	+	2.85109i	−0.0234380	+	0.152835i
$349$			0.885917i			0.0474220i	0.999719	+	0.0237110i	$0.00754816\pi$
$349$			0.885917i			0.0474220i	−0.999719	+	0.0237110i	$0.992452\pi$
$350$	0.195481	−	3.73655i	0.0104489	−	0.199727i
$351$			2.40312i			0.128269i
$352$	13.9085	+	32.4458i	0.741326	+	1.72937i
$353$		−	14.2476i		−	0.758325i	−0.925330	−	0.379163i	$-0.876212\pi$
$353$		−	14.2476i		−	0.758325i	0.925330	−	0.379163i	$-0.123788\pi$
$354$	−0.445739	+	0.382594i	−0.0236908	+	0.0203346i
$355$	−10.4762			−0.556019
$356$	22.6251	+	3.46967i	1.19913	+	0.183892i
$357$	−2.50401	−	2.38749i	−0.132526	−	0.126359i
$358$	−13.9553	−	16.2586i	−0.737560	−	0.859291i
$359$			23.9005i			1.26142i	0.776018	+	0.630710i	$0.217236\pi$
$359$			23.9005i			1.26142i	−0.776018	+	0.630710i	$0.782764\pi$
$360$	−2.40068	+	1.49557i	−0.126527	+	0.0788235i
$361$	−3.41362			−0.179664
$362$	2.69288	+	3.13733i	0.141535	+	0.164894i
$363$	27.9430			1.46663
$364$	10.0686	−	7.76675i	0.527740	−	0.407088i
$365$	−1.64141			−0.0859153
$366$	11.6839	+	13.6123i	0.610727	+	0.711525i
$367$	32.8358			1.71401			0.857007	−	0.515304i	$-0.172321\pi$
$367$	32.8358			1.71401			0.857007	+	0.515304i	$0.172321\pi$
$368$	4.26297	−	13.5722i	0.222223	−	0.707498i
$369$			1.26175i			0.0656840i
$370$	4.66319	+	5.43282i	0.242427	+	0.282439i
$371$	−21.4608	+	22.5081i	−1.11419	+	1.16856i
$372$	−3.32017	+	21.6502i	−0.172143	+	1.12251i
$373$	11.9520			0.618852			0.309426	−	0.950923i	$-0.399863\pi$
$373$	11.9520			0.618852			0.309426	+	0.950923i	$0.399863\pi$
$374$	−8.75716	+	7.51658i	−0.452822	+	0.388673i
$375$		−	1.00000i		−	0.0516398i
$376$	−17.4597	−	28.0262i	−0.900416	−	1.44534i
$377$		−	3.46581i		−	0.178498i
$378$	0.195481	−	3.73655i	0.0100545	−	0.192187i
$379$			21.9351i			1.12673i	0.826208	+	0.563366i	$0.190494\pi$
$379$			21.9351i			1.12673i	−0.826208	+	0.563366i	$0.809506\pi$
$380$	7.80468	+	1.19689i	0.400371	+	0.0613990i
$381$			6.68595i			0.342531i
$382$	−12.8471	−	14.9675i	−0.657316	−	0.765803i
$383$	28.3845			1.45038			0.725190	−	0.688549i	$-0.241752\pi$
$383$	28.3845			1.45038			0.725190	+	0.688549i	$0.241752\pi$
$384$	−2.82979	−	10.9541i	−0.144407	−	0.558999i
$385$	11.3934	−	11.9495i	0.580664	−	0.609003i
$386$	−14.3657	+	12.3306i	−0.731194	+	0.627610i
$387$			2.19850i			0.111756i
$388$	24.5991	+	3.77239i	1.24883	+	0.191514i
$389$	22.0568			1.11832			0.559162	−	0.829058i	$-0.311123\pi$
$389$	22.0568			1.11832			0.559162	+	0.829058i	$0.311123\pi$
$390$	2.57883	−	2.21350i	0.130584	−	0.112085i
$391$	4.65073			0.235197
$392$	−16.2872	+	11.2573i	−0.822629	+	0.568578i
$393$	−13.3308			−0.672452
$394$	4.37821	−	3.75797i	0.220571	−	0.189324i
$395$	9.18952			0.462375
$396$	−12.3366	−	1.89189i	−0.619940	−	0.0950708i
$397$			37.0058i			1.85727i	0.370997	+	0.928634i	$0.379016\pi$
$397$			37.0058i			1.85727i	−0.370997	+	0.928634i	$0.620984\pi$
$398$	3.93710	−	3.37935i	0.197349	−	0.169392i
$399$	−7.20797	+	7.55975i	−0.360850	+	0.378461i
$400$	3.81618	+	1.19865i	0.190809	+	0.0599325i
$401$	−1.70729			−0.0852580			−0.0426290	−	0.999091i	$-0.513573\pi$
$401$	−1.70729			−0.0852580			−0.0426290	+	0.999091i	$0.513573\pi$
$402$	−2.85629	−	3.32771i	−0.142459	−	0.165971i
$403$		−	26.3182i		−	1.31100i
$404$	−8.41335	−	1.29023i	−0.418580	−	0.0641913i
$405$		−	1.00000i		−	0.0496904i
$406$	−0.281926	+	5.38890i	−0.0139917	+	0.267446i
$407$			31.5931i			1.56601i
$408$	3.13932	−	1.95573i	0.155419	−	0.0968228i
$409$		−	26.3062i		−	1.30076i	−0.759609	−	0.650379i	$-0.774610\pi$
$409$		−	26.3062i		−	1.30076i	0.759609	−	0.650379i	$-0.225390\pi$
$410$	1.35401	−	1.16219i	0.0668696	−	0.0573965i
$411$	−5.59837			−0.276147
$412$	−4.64614	+	30.2967i	−0.228899	+	1.49261i
$413$	−0.758357	+	0.795368i	−0.0373163	+	0.0391375i
$414$	3.27586	+	3.81652i	0.161000	+	0.187572i
$415$		−	7.39922i		−	0.363213i
$416$	5.35601	+	12.4945i	0.262600	+	0.612594i
$417$	6.13537			0.300450
$418$	22.6930	+	26.4384i	1.10995	+	1.29314i
$419$	5.33293			0.260531			0.130265	−	0.991479i	$-0.458417\pi$
$419$	5.33293			0.260531			0.130265	+	0.991479i	$0.458417\pi$
$420$	−4.18981	+	3.23194i	−0.204442	+	0.157703i
$421$	−14.7096			−0.716903			−0.358451	−	0.933548i	$-0.616695\pi$
$421$	−14.7096			−0.716903			−0.358451	+	0.933548i	$0.616695\pi$
$422$	5.23014	+	6.09335i	0.254599	+	0.296620i
$423$	11.6743			0.567623
$424$	−17.5797	−	28.2188i	−0.853746	−	1.37043i
$425$			1.30768i			0.0634317i
$426$	9.64959	+	11.2422i	0.467524	+	0.544687i
$427$	24.2895	+	23.1592i	1.17545	+	1.12075i
$428$	9.56506	+	1.46685i	0.462345	+	0.0709029i
$429$	14.9965			0.724038
$430$	2.35925	−	2.02502i	0.113773	−	0.0976554i
$431$			20.0200i			0.964331i	0.876080	+	0.482166i	$0.160150\pi$
$431$			20.0200i			0.964331i	−0.876080	+	0.482166i	$0.839850\pi$
$432$	3.81618	+	1.19865i	0.183606	+	0.0576701i
$433$		−	8.87770i		−	0.426635i	−0.976983	−	0.213317i	$-0.931573\pi$
$433$		−	8.87770i		−	0.426635i	0.976983	−	0.213317i	$-0.0684268\pi$
$434$	−2.14084	+	40.9214i	−0.102764	+	1.96429i
$435$			1.44221i			0.0691488i
$436$	2.65921	−	17.3402i	0.127353	−	0.830445i
$437$		−	14.0408i		−	0.671664i
$438$	1.51189	+	1.76143i	0.0722411	+	0.0841642i
$439$	25.3037			1.20768			0.603841	−	0.797105i	$-0.293636\pi$
$439$	25.3037			1.20768			0.603841	+	0.797105i	$0.293636\pi$
$440$	9.33301	+	14.9813i	0.444934	+	0.714205i
$441$	−0.333303	−	6.99206i	−0.0158716	−	0.332955i
$442$	−3.37228	+	2.89455i	−0.160403	+	0.137680i
$443$			27.9709i			1.32894i	0.747317	+	0.664468i	$0.231342\pi$
$443$			27.9709i			1.32894i	−0.747317	+	0.664468i	$0.768658\pi$
$444$	1.53482	−	10.0083i	0.0728395	−	0.474973i
$445$	11.4448			0.542535
$446$	4.26741	−	3.66287i	0.202068	−	0.173442i
$447$	12.3505			0.584158
$448$	−7.31156	−	19.8631i	−0.345439	−	0.938441i
$449$	−36.0790			−1.70267			−0.851337	−	0.524619i	$-0.824208\pi$
$449$	−36.0790			−1.70267			−0.851337	+	0.524619i	$0.824208\pi$
$450$	−1.07312	+	0.921096i	−0.0505873	+	0.0434209i
$451$	7.87386			0.370765
$452$	1.24150	−	8.09559i	0.0583952	−	0.380784i
$453$			15.9654i			0.750118i
$454$	−2.73314	+	2.34595i	−0.128273	+	0.110101i
$455$	4.38749	−	4.60162i	0.205689	−	0.215727i
$456$	−5.90445	−	9.47779i	−0.276501	−	0.443838i
$457$	−4.26370			−0.199448			−0.0997238	−	0.995015i	$-0.531796\pi$
$457$	−4.26370			−0.199448			−0.0997238	+	0.995015i	$0.531796\pi$
$458$	9.82235	+	11.4435i	0.458968	+	0.534719i
$459$			1.30768i			0.0610372i
$460$	1.07820	−	7.03076i	0.0502714	−	0.327811i
$461$			18.7953i			0.875386i	0.899124	+	0.437693i	$0.144204\pi$
$461$			18.7953i			0.875386i	−0.899124	+	0.437693i	$0.855796\pi$
$462$	−23.3177	−	1.21989i	−1.08484	−	0.0567543i
$463$		−	38.2151i		−	1.77601i	−0.459836	−	0.888004i	$-0.652092\pi$
$463$		−	38.2151i		−	1.77601i	0.459836	−	0.888004i	$-0.347908\pi$
$464$	−5.50374	−	1.72871i	−0.255505	−	0.0802533i
$465$			10.9517i			0.507871i
$466$	−21.9368	+	18.8292i	−1.01620	+	0.872244i
$467$	−15.7945			−0.730882			−0.365441	−	0.930834i	$-0.619082\pi$
$467$	−15.7945			−0.730882			−0.365441	+	0.930834i	$0.619082\pi$
$468$	−4.75070	−	0.728544i	−0.219601	−	0.0336770i
$469$	−5.93789	−	5.66158i	−0.274186	−	0.261428i
$470$	−10.7531	−	12.5279i	−0.496005	−	0.577868i
$471$			5.15966i			0.237744i
$472$	−0.621213	−	0.997166i	−0.0285936	−	0.0458983i
$473$	13.7196			0.630826
$474$	−8.46443	−	9.86144i	−0.388784	−	0.452951i
$475$	3.94796			0.181145
$476$	5.47893	−	4.22634i	0.251126	−	0.193714i
$477$	11.7545			0.538202
$478$	4.04177	+	4.70885i	0.184866	+	0.215378i
$479$	−33.1809			−1.51608			−0.758038	−	0.652210i	$-0.773842\pi$
$479$	−33.1809			−1.51608			−0.758038	+	0.652210i	$0.773842\pi$
$480$	−2.22877	−	5.19929i	−0.101729	−	0.237314i
$481$			12.1662i			0.554729i
$482$	20.8084	+	24.2428i	0.947798	+	1.10423i
$483$	6.81012	+	6.49322i	0.309871	+	0.295452i
$484$	−8.47136	+	55.2402i	−0.385062	+	2.51092i
$485$	12.4433			0.565022
$486$	−1.07312	+	0.921096i	−0.0486776	+	0.0417817i
$487$			18.8854i			0.855781i	0.903831	+	0.427891i	$0.140743\pi$
$487$			18.8854i			0.855781i	−0.903831	+	0.427891i	$0.859257\pi$
$488$	−30.4521	+	18.9710i	−1.37850	+	0.858777i
$489$			1.27295i			0.0575648i
$490$	−7.19630	+	6.79803i	−0.325096	+	0.307104i
$491$		−	1.14336i		−	0.0515989i	−0.999667	−	0.0257995i	$-0.991787\pi$
$491$		−	1.14336i		−	0.0515989i	0.999667	−	0.0257995i	$-0.00821314\pi$
$492$	−2.49434	−	0.382519i	−0.112453	−	0.0172453i
$493$		−	1.88595i		−	0.0849389i
$494$	8.73882	+	10.1811i	0.393178	+	0.458070i
$495$	−6.24043			−0.280487
$496$	−41.7935	−	13.1272i	−1.87658	−	0.589429i
$497$	20.0604	+	19.1269i	0.899831	+	0.857959i
$498$	−7.94023	+	6.81539i	−0.355810	+	0.305405i
$499$			18.8734i			0.844890i	0.906389	+	0.422445i	$0.138828\pi$
$499$			18.8734i			0.844890i	−0.906389	+	0.422445i	$0.861172\pi$
$500$	1.97689	+	0.303166i	0.0884092	+	0.0135580i
$501$	21.6628			0.967821
$502$	12.9657	−	11.1289i	0.578686	−	0.496707i
$503$	18.8624			0.841035			0.420517	−	0.907284i	$-0.361849\pi$
$503$	18.8624			0.841035			0.420517	+	0.907284i	$0.361849\pi$
$504$	7.32748	+	1.51924i	0.326392	+	0.0676723i
$505$	−4.25585			−0.189383
$506$	23.8167	−	20.4428i	1.05878	−	0.908791i
$507$	−7.22501			−0.320874
$508$	−13.2174	−	2.02695i	−0.586426	−	0.0899314i
$509$		−	24.1765i		−	1.07160i	−0.844344	−	0.535801i	$-0.820010\pi$
$509$		−	24.1765i		−	1.07160i	0.844344	−	0.535801i	$-0.179990\pi$
$510$	1.40329	−	1.20450i	0.0621389	−	0.0533360i
$511$	3.14305	+	2.99680i	0.139040	+	0.132570i
$512$	22.5129	−	2.27328i	0.994941	−	0.100466i
$513$	3.94796			0.174307
$514$	−13.0675	−	15.2243i	−0.576384	−	0.671513i
$515$			15.3254i			0.675319i
$516$	−4.34618	−	0.666509i	−0.191330	−	0.0293414i
$517$		−	72.8525i		−	3.20405i
$518$	0.989654	−	18.9168i	0.0434829	−	0.831158i
$519$		−	12.9769i		−	0.569623i
$520$	3.59404	+	5.76913i	0.157609	+	0.252993i
$521$			17.2367i			0.755152i	0.925979	+	0.377576i	$0.123242\pi$
$521$			17.2367i			0.755152i	−0.925979	+	0.377576i	$0.876758\pi$
$522$	1.54766	−	1.32842i	0.0677394	−	0.0581432i
$523$	−14.1555			−0.618975			−0.309487	−	0.950904i	$-0.600157\pi$
$523$	−14.1555			−0.618975			−0.309487	+	0.950904i	$0.600157\pi$
$524$	4.04145	−	26.3536i	0.176552	−	1.15126i
$525$	−1.82575	+	1.91485i	−0.0796821	+	0.0835709i
$526$	−12.4434	−	14.4971i	−0.542557	−	0.632104i
$527$		−	14.3212i		−	0.623843i
$528$	7.48010	−	23.8146i	0.325529	−	1.03640i
$529$	10.3515			0.450064
$530$	−10.8270	−	12.6140i	−0.470296	−	0.547916i
$531$	0.415368			0.0180254
$532$	−12.7596	−	16.5412i	−0.553198	−	0.717153i
$533$	3.03213			0.131336
$534$	−10.5417	−	12.2816i	−0.456186	−	0.531477i
$535$	4.83844			0.209184
$536$	7.44444	−	4.63772i	0.321551	−	0.200319i
$537$			15.1508i			0.653803i
$538$	−8.82198	−	10.2780i	−0.380342	−	0.443116i
$539$	−43.6335	+	2.07996i	−1.87943	+	0.0895900i
$540$	1.97689	+	0.303166i	0.0850718	+	0.0130462i
$541$	20.6842			0.889283			0.444642	−	0.895709i	$-0.353331\pi$
$541$	20.6842			0.889283			0.444642	+	0.895709i	$0.353331\pi$
$542$	7.73052	−	6.63538i	0.332054	−	0.285014i
$543$		−	2.92356i		−	0.125462i
$544$	2.91452	+	6.79899i	0.124959	+	0.291504i
$545$		−	8.77146i		−	0.375728i
$546$	−8.97937	−	0.469765i	−0.384282	−	0.0201041i
$547$		−	14.1854i		−	0.606526i	−0.952907	−	0.303263i	$-0.901924\pi$
$547$		−	14.1854i		−	0.606526i	0.952907	−	0.303263i	$-0.0980760\pi$
$548$	1.69723	−	11.0674i	0.0725023	−	0.472774i
$549$		−	12.6848i		−	0.541374i
$550$	5.74803	+	6.69672i	0.245097	+	0.285549i
$551$	−5.69380			−0.242564
$552$	−8.53797	+	5.31896i	−0.363400	+	0.226390i
$553$	−17.5966	−	16.7777i	−0.748282	−	0.713462i
$554$	23.8837	−	20.5002i	1.01472	−	0.870971i
$555$		−	5.06265i		−	0.214898i
$556$	−1.86003	+	12.1289i	−0.0788830	+	0.514382i
$557$	−23.5297			−0.996987			−0.498494	−	0.866893i	$-0.666113\pi$
$557$	−23.5297			−0.996987			−0.498494	+	0.866893i	$0.666113\pi$
$558$	11.7524	−	10.0875i	0.497520	−	0.427039i
$559$	5.28325			0.223458
$560$	−5.11898	−	9.26261i	−0.216317	−	0.391417i
$561$	8.16048			0.344536
$562$	29.2119	−	25.0736i	1.23223	−	1.05767i
$563$	30.5742			1.28855			0.644275	−	0.764794i	$-0.277159\pi$
$563$	30.5742			1.28855			0.644275	+	0.764794i	$0.277159\pi$
$564$	−3.53924	+	23.0788i	−0.149029	+	0.971791i
$565$		−	4.09511i		−	0.172283i
$566$	−19.9935	+	17.1611i	−0.840388	+	0.721335i
$567$	−1.82575	+	1.91485i	−0.0766741	+	0.0804162i
$568$	−25.1500	+	15.6679i	−1.05527	+	0.657411i
$569$	12.0943			0.507018			0.253509	−	0.967333i	$-0.418415\pi$
$569$	12.0943			0.507018			0.253509	+	0.967333i	$0.418415\pi$
$570$	−3.63645	−	4.23663i	−0.152314	−	0.177453i
$571$			20.1686i			0.844029i	0.906589	+	0.422015i	$0.138677\pi$
$571$			20.1686i			0.844029i	−0.906589	+	0.422015i	$0.861323\pi$
$572$	−4.54643	+	29.6464i	−0.190096	+	1.23958i
$573$			13.9477i			0.582672i
$574$	−4.71458	−	0.246648i	−0.196783	−	0.0102949i
$575$		−	3.55648i		−	0.148315i
$576$	−3.52653	+	7.18078i	−0.146939	+	0.299199i
$577$			2.82405i			0.117567i	0.998271	+	0.0587834i	$0.0187221\pi$
$577$			2.82405i			0.117567i	−0.998271	+	0.0587834i	$0.981278\pi$
$578$	16.4080	−	14.0835i	0.682481	−	0.585798i
$579$	13.3869			0.556339
$580$	−2.85109	−	0.437230i	−0.118385	−	0.0181550i
$581$	−13.5091	+	14.1684i	−0.560451	+	0.587804i
$582$	−11.4615	−	13.3532i	−0.475094	−	0.553506i
$583$		−	73.3532i		−	3.03798i
$584$	−3.94050	+	2.45484i	−0.163059	+	0.101582i
$585$	−2.40312			−0.0993568
$586$	−14.2381	−	16.5881i	−0.588172	−	0.685248i
$587$	−0.0213868			−0.000882727			−0.000441363	−	1.00000i	$-0.500140\pi$
$587$	−0.0213868			−0.000882727			−0.000441363		1.00000i	$0.500140\pi$
$588$	13.9236	+	1.46085i	0.574199	+	0.0602445i
$589$	−43.2367			−1.78154
$590$	−0.382594	−	0.445739i	−0.0157511	−	0.0183508i
$591$	−4.07989			−0.167824
$592$	19.3200	+	6.06835i	0.794047	+	0.249408i
$593$		−	31.7082i		−	1.30210i	−0.759036	−	0.651049i	$-0.774329\pi$
$593$		−	31.7082i		−	1.30210i	0.759036	−	0.651049i	$-0.225671\pi$
$594$	5.74803	+	6.69672i	0.235845	+	0.274770i
$595$	2.38749	−	2.50401i	0.0978775	−	0.102654i
$596$	−3.74424	+	24.4155i	−0.153370	+	1.00010i
$597$	−3.66884			−0.150156
$598$	9.17156	−	7.87228i	0.375053	−	0.321921i
$599$			17.4804i			0.714229i	0.934061	+	0.357114i	$0.116239\pi$
$599$			17.4804i			0.714229i	−0.934061	+	0.357114i	$0.883761\pi$
$600$	−1.49557	−	2.40068i	−0.0610564	−	0.0980074i
$601$			45.4399i			1.85353i	0.375637	+	0.926767i	$0.377424\pi$
$601$			45.4399i			1.85353i	−0.375637	+	0.926767i	$0.622576\pi$
$602$	−8.21478	−	0.429765i	−0.334810	−	0.0175159i
$603$			3.10097i			0.126281i
$604$	−31.5617	−	4.84015i	−1.28423	−	0.196943i
$605$			27.9430i			1.13604i
$606$	3.92005	+	4.56703i	0.159241	+	0.185523i
$607$	−12.3160			−0.499893			−0.249946	−	0.968260i	$-0.580413\pi$
$607$	−12.3160			−0.499893			−0.249946	+	0.968260i	$0.580413\pi$
$608$	20.5266	−	8.79911i	0.832462	−	0.356851i
$609$	2.63311	−	2.76162i	0.106699	−	0.111907i
$610$	−13.6123	+	11.6839i	−0.551145	+	0.473067i
$611$		−	28.0547i		−	1.13497i
$612$	−2.58513	−	0.396443i	−0.104498	−	0.0160253i
$613$	27.3548			1.10485			0.552424	−	0.833563i	$-0.313703\pi$
$613$	27.3548			1.10485			0.552424	+	0.833563i	$0.313703\pi$
$614$	−32.6469	+	28.0220i	−1.31752	+	1.13088i
$615$	−1.26175			−0.0508786
$616$	9.48070	−	45.7266i	0.381988	−	1.84238i
$617$	−44.5457			−1.79334			−0.896671	−	0.442698i	$-0.854021\pi$
$617$	−44.5457			−1.79334			−0.896671	+	0.442698i	$0.854021\pi$
$618$	16.4460	−	14.1162i	0.661555	−	0.567836i
$619$	−23.1713			−0.931334			−0.465667	−	0.884960i	$-0.654185\pi$
$619$	−23.1713			−0.931334			−0.465667	+	0.884960i	$0.654185\pi$
$620$	−21.6502	−	3.32017i	−0.869494	−	0.133341i
$621$		−	3.55648i		−	0.142717i
$622$	−6.70223	+	5.75276i	−0.268735	+	0.230665i
$623$	−21.9150	−	20.8953i	−0.878008	−	0.837151i
$624$	2.88050	−	9.17074i	0.115312	−	0.367124i
$625$	1.00000			0.0400000
$626$	13.3617	+	15.5670i	0.534041	+	0.622182i
$627$		−	24.6370i		−	0.983906i
$628$	−10.2001	−	1.56423i	−0.407027	−	0.0624197i
$629$			6.62032i			0.263969i
$630$	3.73655	+	0.195481i	0.148868	+	0.00778816i
$631$			10.4615i			0.416464i	0.978079	+	0.208232i	$0.0667709\pi$
$631$			10.4615i			0.416464i	−0.978079	+	0.208232i	$0.933229\pi$
$632$	22.0611	−	13.7436i	0.877543	−	0.546690i
$633$		−	5.67817i		−	0.225687i
$634$	2.46554	−	2.11626i	0.0979190	−	0.0840474i
$635$	−6.68595			−0.265324
$636$	−3.56357	+	23.2374i	−0.141305	+	0.921422i
$637$	−16.8028	+	0.800968i	−0.665750	+	0.0317355i
$638$	−8.28989	−	9.65810i	−0.328200	−	0.382368i
$639$		−	10.4762i		−	0.414432i
$640$	10.9541	−	2.82979i	0.432999	−	0.111857i
$641$	21.4122			0.845731			0.422866	−	0.906192i	$-0.361024\pi$
$641$	21.4122			0.845731			0.422866	+	0.906192i	$0.361024\pi$
$642$	−4.45667	−	5.19222i	−0.175891	−	0.204921i
$643$	−26.2531			−1.03532			−0.517661	−	0.855586i	$-0.673197\pi$
$643$	−26.2531			−1.03532			−0.517661	+	0.855586i	$0.673197\pi$
$644$	−14.9010	+	11.4943i	−0.587181	+	0.452940i
$645$	−2.19850			−0.0865657
$646$	4.75530	+	5.54014i	0.187095	+	0.217974i
$647$	−6.99553			−0.275023			−0.137511	−	0.990500i	$-0.543910\pi$
$647$	−6.99553			−0.275023			−0.137511	+	0.990500i	$0.543910\pi$
$648$	−1.49557	−	2.40068i	−0.0587516	−	0.0943076i
$649$		−	2.59208i		−	0.101748i
$650$	2.21350	+	2.57883i	0.0868208	+	0.101150i
$651$	19.9949	−	20.9708i	0.783664	−	0.821910i
$652$	−2.51648	−	0.385915i	−0.0985530	−	0.0151136i
$653$	21.1729			0.828559			0.414280	−	0.910150i	$-0.364034\pi$
$653$	21.1729			0.828559			0.414280	+	0.910150i	$0.364034\pi$
$654$	−9.41281	+	8.07935i	−0.368070	+	0.315928i
$655$		−	13.3308i		−	0.520879i
$656$	1.51240	−	4.81506i	0.0590491	−	0.187997i
$657$		−	1.64141i		−	0.0640375i
$658$	−2.28210	+	43.6215i	−0.0889656	+	1.70054i
$659$		−	21.4552i		−	0.835774i	−0.908499	−	0.417887i	$-0.862771\pi$
$659$		−	21.4552i		−	0.835774i	0.908499	−	0.417887i	$-0.137229\pi$
$660$	1.89189	−	12.3366i	0.0736416	−	0.480203i
$661$			19.5116i			0.758914i	0.925209	+	0.379457i	$0.123889\pi$
$661$			19.5116i			0.758914i	−0.925209	+	0.379457i	$0.876111\pi$
$662$	21.5982	+	25.1628i	0.839437	+	0.977982i
$663$	3.14251			0.122045
$664$	−11.0661	−	17.7632i	−0.429446	−	0.689344i
$665$	−7.55975	−	7.20797i	−0.293155	−	0.279513i
$666$	−5.43282	+	4.66319i	−0.210518	+	0.180695i
$667$			5.12920i			0.198603i
$668$	−6.56741	+	42.8249i	−0.254101	+	1.65695i
$669$	−3.97664			−0.153746
$670$	3.32771	−	2.85629i	0.128561	−	0.110348i
$671$	−79.1585			−3.05588
$672$	−5.22481	+	14.0250i	−0.201551	+	0.541027i
$673$	2.26978			0.0874936			0.0437468	−	0.999043i	$-0.486071\pi$
$673$	2.26978			0.0874936			0.0437468	+	0.999043i	$0.486071\pi$
$674$	15.7436	−	13.5133i	0.606421	−	0.520513i
$675$	1.00000			0.0384900
$676$	2.19038	−	14.2830i	0.0842452	−	0.549348i
$677$			17.8761i			0.687035i	0.939146	+	0.343518i	$0.111619\pi$
$677$			17.8761i			0.687035i	−0.939146	+	0.343518i	$0.888381\pi$
$678$	−4.39454	+	3.77199i	−0.168771	+	0.144862i
$679$	−23.8271	−	22.7183i	−0.914400	−	0.871850i
$680$	1.95573	+	3.13932i	0.0749986	+	0.120387i
$681$	2.54691			0.0975979
$682$	−62.9505	−	73.3402i	−2.41050	−	2.80834i
$683$			4.47109i			0.171081i	0.996335	+	0.0855407i	$0.0272618\pi$
$683$			4.47109i			0.171081i	−0.996335	+	0.0855407i	$0.972738\pi$
$684$	−1.19689	+	7.80468i	−0.0457641	+	0.298419i
$685$		−	5.59837i		−	0.213903i
$686$	26.1913	+	0.121414i	0.999989	+	0.00463560i
$687$		−	10.6638i		−	0.406848i
$688$	2.63523	−	8.38986i	0.100467	−	0.319860i
$689$		−	28.2475i		−	1.07614i
$690$	−3.81652	+	3.27586i	−0.145292	+	0.124710i
$691$	2.13713			0.0813003			0.0406502	−	0.999173i	$-0.487057\pi$
$691$	2.13713			0.0813003			0.0406502	+	0.999173i	$0.487057\pi$
$692$	25.6539	+	3.93416i	0.975216	+	0.149554i
$693$	11.9495	+	11.3934i	0.453924	+	0.432801i
$694$	−19.9048	−	23.1900i	−0.755577	−	0.880281i
$695$			6.13537i			0.232728i
$696$	2.15693	+	3.46229i	0.0817583	+	0.131238i
$697$	1.64996			0.0624967
$698$	0.816014	+	0.950694i	0.0308866	+	0.0359843i
$699$	20.4421			0.773193
$700$	−3.23194	−	4.18981i	−0.122156	−	0.158360i
$701$	2.37715			0.0897836			0.0448918	−	0.998992i	$-0.485706\pi$
$701$	2.37715			0.0897836			0.0448918	+	0.998992i	$0.485706\pi$
$702$	2.21350	+	2.57883i	0.0835433	+	0.0973318i
$703$	19.9871			0.753829
$704$	44.8111	+	22.0071i	1.68888	+	0.829424i
$705$			11.6743i			0.439679i
$706$	−13.1234	−	15.2894i	−0.493907	−	0.575424i
$707$	8.14932	+	7.77011i	0.306487	+	0.292225i
$708$	−0.125925	+	0.821137i	−0.00473257	+	0.0308602i
$709$	−11.2074			−0.420904			−0.210452	−	0.977604i	$-0.567494\pi$
$709$	−11.2074			−0.420904			−0.210452	+	0.977604i	$0.567494\pi$
$710$	−11.2422	+	9.64959i	−0.421913	+	0.362143i
$711$			9.18952i			0.344634i
$712$	27.4753	−	17.1165i	1.02968	−	0.641467i
$713$			38.9493i			1.45866i
$714$	−4.88620	−	0.255627i	−0.182861	−	0.00956659i
$715$			14.9965i			0.560838i
$716$	−29.9514	−	4.59319i	−1.11934	−	0.171656i
$717$		−	4.38800i		−	0.163873i
$718$	22.0147	+	25.6481i	0.821580	+	0.957178i
$719$	43.4702			1.62116			0.810582	−	0.585624i	$-0.199151\pi$
$719$	43.4702			1.62116			0.810582	+	0.585624i	$0.199151\pi$
$720$	−1.19865	+	3.81618i	−0.0446711	+	0.142221i
$721$	27.9803	−	29.3459i	1.04204	−	1.09290i
$722$	−3.66322	+	3.14427i	−0.136331	+	0.117018i
$723$		−	22.5909i		−	0.840166i
$724$	5.77956	+	0.886324i	0.214795	+	0.0329400i
$725$	−1.44221			−0.0535624
$726$	29.9861	−	25.7382i	1.11289	−	0.955233i
$727$	8.53645			0.316599			0.158300	−	0.987391i	$-0.449399\pi$
$727$	8.53645			0.316599			0.158300	+	0.987391i	$0.449399\pi$
$728$	3.65091	−	17.6088i	0.135312	−	0.652626i
$729$	1.00000			0.0370370
$730$	−1.76143	+	1.51189i	−0.0651933	+	0.0559577i
$731$	2.87492			0.106333
$732$	25.0764	+	3.84559i	0.926851	+	0.142137i
$733$			12.7274i			0.470098i	0.971984	+	0.235049i	$0.0755250\pi$
$733$			12.7274i			0.470098i	−0.971984	+	0.235049i	$0.924475\pi$
$734$	35.2367	−	30.2449i	1.30061	−	1.11636i
$735$	6.99206	−	0.333303i	0.257906	−	0.0122941i
$736$	−7.92658	−	18.4911i	−0.292178	−	0.681592i
$737$	19.3514			0.712818
$738$	1.16219	+	1.35401i	0.0427809	+	0.0498416i
$739$		−	17.6922i		−	0.650817i	−0.945573	−	0.325409i	$-0.894498\pi$
$739$		−	17.6922i		−	0.650817i	0.945573	−	0.325409i	$-0.105502\pi$
$740$	10.0083	+	1.53482i	0.367912	+	0.0564212i
$741$		−	9.48742i		−	0.348529i
$742$	−2.29779	+	43.9213i	−0.0843544	+	1.61240i
$743$			11.0428i			0.405122i	0.979270	+	0.202561i	$0.0649265\pi$
$743$			11.0428i			0.405122i	−0.979270	+	0.202561i	$0.935074\pi$
$744$	16.3790	+	26.2914i	0.600483	+	0.963891i
$745$			12.3505i			0.452486i
$746$	12.8259	−	11.0090i	0.469591	−	0.403066i
$747$	7.39922			0.270723
$748$	−2.47398	+	16.1324i	−0.0904576	+	0.589857i
$749$	−9.26489	−	8.83376i	−0.338532	−	0.322779i
$750$	−0.921096	−	1.07312i	−0.0336337	−	0.0391847i
$751$			18.4917i			0.674771i	0.941367	+	0.337385i	$0.109543\pi$
$751$			18.4917i			0.674771i	−0.941367	+	0.337385i	$0.890457\pi$
$752$	−44.5512	−	13.9934i	−1.62461	−	0.510286i
$753$	−12.0822			−0.440301
$754$	−3.19234	−	3.71923i	−0.116258	−	0.135446i
$755$	−15.9654			−0.581039
$756$	−3.23194	−	4.18981i	−0.117545	−	0.152382i
$757$	−20.2498			−0.735992			−0.367996	−	0.929827i	$-0.619956\pi$
$757$	−20.2498			−0.735992			−0.367996	+	0.929827i	$0.619956\pi$
$758$	20.2043	+	23.5390i	0.733855	+	0.854974i
$759$	−22.1940			−0.805589
$760$	9.47779	−	5.90445i	0.343795	−	0.214177i
$761$			25.4306i			0.921857i	0.887437	+	0.460928i	$0.152484\pi$
$761$			25.4306i			0.921857i	−0.887437	+	0.460928i	$0.847516\pi$
$762$	6.15840	+	7.17481i	0.223095	+	0.259916i
$763$	−16.0145	+	16.7960i	−0.579762	+	0.608057i
$764$	−27.5730	−	4.22845i	−0.997555	−	0.152980i
$765$	−1.30768			−0.0472792
$766$	30.4599	−	26.1448i	1.10056	−	0.944651i
$767$		−	0.998180i		−	0.0360422i
$768$	−13.1265	−	9.14853i	−0.473661	−	0.330119i
$769$			31.4563i			1.13434i	0.823600	+	0.567172i	$0.191962\pi$
$769$			31.4563i			1.13434i	−0.823600	+	0.567172i	$0.808038\pi$
$770$	1.21989	−	23.3177i	0.0439617	−	0.840310i
$771$			14.1869i			0.510930i
$772$	−4.05844	+	26.4643i	−0.146066	+	0.952472i
$773$			9.51127i			0.342097i	0.985263	+	0.171048i	$0.0547154\pi$
$773$			9.51127i			0.342097i	−0.985263	+	0.171048i	$0.945285\pi$
$774$	2.02502	+	2.35925i	0.0727880	+	0.0848013i
$775$	−10.9517			−0.393395
$776$	29.8724	−	18.6099i	1.07236	−	0.668055i
$777$	−9.24311	+	9.69422i	−0.331595	+	0.347778i
$778$	23.6696	−	20.3164i	0.848595	−	0.728379i
$779$		−	4.98133i		−	0.178475i
$780$	0.728544	−	4.75070i	0.0260861	−	0.170102i
$781$	−65.3761			−2.33934
$782$	4.99078	−	4.28376i	0.178470	−	0.153187i
$783$	−1.44221			−0.0515405
$784$	−7.10909	+	27.0825i	−0.253896	+	0.967231i
$785$	−5.15966			−0.184156
$786$	−14.3056	+	12.2790i	−0.510263	+	0.437976i
$787$	23.8141			0.848880			0.424440	−	0.905456i	$-0.360471\pi$
$787$	23.8141			0.848880			0.424440	+	0.905456i	$0.360471\pi$
$788$	1.23688	−	8.06550i	0.0440622	−	0.287321i
$789$			13.5093i			0.480945i
$790$	9.86144	−	8.46443i	0.350854	−	0.301151i
$791$	−7.47664	+	7.84153i	−0.265839	+	0.278813i
$792$	−14.9813	+	9.33301i	−0.532337	+	0.331634i
$793$	−30.4831			−1.08249
$794$	34.0859	+	39.7116i	1.20966	+	1.40931i
$795$			11.7545i			0.416890i
$796$	1.11227	−	7.25289i	0.0394233	−	0.257072i
$797$		−	38.0855i		−	1.34906i	−0.738248	−	0.674529i	$-0.764347\pi$
$797$		−	38.0855i		−	1.34906i	0.738248	−	0.674529i	$-0.235653\pi$
$798$	−0.771752	+	14.7517i	−0.0273197	+	0.522206i
$799$		−	15.2662i		−	0.540079i
$800$	5.19929	−	2.22877i	0.183822	−	0.0787990i
$801$			11.4448i			0.404382i
$802$	−1.83212	+	1.57258i	−0.0646945	+	0.0555296i
$803$	−10.2431			−0.361471
$804$	−6.13027	−	0.940108i	−0.216198	−	0.0331551i
$805$	−6.49322	+	6.81012i	−0.228856	+	0.240025i
$806$	−24.2415	−	28.2425i	−0.853872	−	0.994800i
$807$			9.57770i			0.337151i
$808$	−10.2169	+	6.36493i	−0.359431	+	0.223917i
$809$	0.368855			0.0129682			0.00648412	−	0.999979i	$-0.497936\pi$
$809$	0.368855			0.0129682			0.00648412	+	0.999979i	$0.497936\pi$
$810$	−0.921096	−	1.07312i	−0.0323640	−	0.0377055i
$811$	−4.21418			−0.147980			−0.0739900	−	0.997259i	$-0.523573\pi$
$811$	−4.21418			−0.147980			−0.0739900	+	0.997259i	$0.523573\pi$
$812$	4.66115	+	6.04260i	0.163574	+	0.212054i
$813$	−7.20379			−0.252648
$814$	29.1003	+	33.9032i	1.01996	+	1.18831i
$815$	−1.27295			−0.0445895
$816$	1.56745	−	4.99034i	0.0548717	−	0.174697i
$817$		−	8.67957i		−	0.303660i
$818$	−24.2305	−	28.2297i	−0.847201	−	0.987028i
$819$	4.60162	+	4.38749i	0.160793	+	0.153311i
$820$	0.382519	−	2.49434i	0.0133581	−	0.0871060i
$821$	−5.15654			−0.179964			−0.0899822	−	0.995943i	$-0.528681\pi$
$821$	−5.15654			−0.179964			−0.0899822	+	0.995943i	$0.528681\pi$
$822$	−6.00771	+	5.15663i	−0.209543	+	0.179858i
$823$			53.4133i			1.86187i	0.365185	+	0.930935i	$0.381006\pi$
$823$			53.4133i			1.86187i	−0.365185	+	0.930935i	$0.618994\pi$
$824$	22.9203	+	36.7914i	0.798465	+	1.28169i
$825$		−	6.24043i		−	0.217264i
$826$	−0.0811967	+	1.55204i	−0.00282520	+	0.0540025i
$827$		−	13.7009i		−	0.476426i	−0.971213	−	0.238213i	$-0.923438\pi$
$827$		−	13.7009i		−	0.476426i	0.971213	−	0.238213i	$-0.0765617\pi$
$828$	7.03076	+	1.07820i	0.244336	+	0.0374701i
$829$			19.5764i			0.679915i	0.940441	+	0.339958i	$0.110413\pi$
$829$			19.5764i			0.679915i	−0.940441	+	0.339958i	$0.889587\pi$
$830$	−6.81539	−	7.94023i	−0.236565	−	0.275610i
$831$	−22.2563			−0.772064
$832$	17.2563	+	8.47469i	0.598254	+	0.293807i
$833$	−9.14336	+	0.435853i	−0.316799	+	0.0151014i
$834$	6.58398	−	5.65126i	0.227984	−	0.195687i
$835$			21.6628i			0.749671i
$836$	48.7045	+	7.46909i	1.68448	+	0.258324i
$837$	−10.9517			−0.378545
$838$	5.72286	−	4.91214i	0.197693	−	0.169687i
$839$	48.5281			1.67537			0.837687	−	0.546150i	$-0.183907\pi$
$839$	48.5281			1.67537			0.837687	+	0.546150i	$0.183907\pi$
$840$	−1.51924	+	7.32748i	−0.0524187	+	0.252822i
$841$	−26.9200			−0.928277
$842$	−15.7852	+	13.5490i	−0.543993	+	0.466928i
$843$	−27.2215			−0.937559
$844$	11.2251	+	1.72143i	0.386384	+	0.0592540i
$845$		−	7.22501i		−	0.248548i
$846$	12.5279	−	10.7531i	0.430717	−	0.369700i
$847$	51.0168	−	53.5066i	1.75296	−	1.83851i
$848$	−44.8574	−	14.0896i	−1.54041	−	0.483837i
$849$	18.6312			0.639420
$850$	1.20450	+	1.40329i	0.0413139	+	0.0481326i
$851$		−	18.0052i		−	0.617210i
$852$	20.7103	+	3.17603i	0.709523	+	0.108809i
$853$		−	2.55438i		−	0.0874603i	−0.999043	−	0.0437302i	$-0.986076\pi$
$853$		−	2.55438i		−	0.0874603i	0.999043	−	0.0437302i	$-0.0139242\pi$
$854$	47.3973	+	2.47964i	1.62190	+	0.0848515i
$855$			3.94796i			0.135017i
$856$	11.6155	−	7.23623i	0.397011	−	0.247329i
$857$		−	17.1530i		−	0.585937i	−0.956122	−	0.292968i	$-0.905357\pi$
$857$		−	17.1530i		−	0.585937i	0.956122	−	0.292968i	$-0.0946430\pi$
$858$	16.0930	−	13.8132i	0.549407	−	0.471576i
$859$	−43.1437			−1.47204			−0.736022	−	0.676958i	$-0.763298\pi$
$859$	−43.1437			−1.47204			−0.736022	+	0.676958i	$0.763298\pi$
$860$	0.666509	−	4.34618i	0.0227278	−	0.148204i
$861$	2.41606	+	2.30363i	0.0823391	+	0.0785076i
$862$	18.4404	+	21.4839i	0.628082	+	0.731744i
$863$			36.5532i			1.24429i	0.782904	+	0.622143i	$0.213738\pi$
$863$			36.5532i			1.24429i	−0.782904	+	0.622143i	$0.786262\pi$
$864$	5.19929	−	2.22877i	0.176883	−	0.0758244i
$865$	12.9769			0.441228
$866$	−8.17721	−	9.52682i	−0.277873	−	0.323734i
$867$	−15.2900			−0.519275
$868$	35.3951	+	45.8854i	1.20139	+	1.55745i
$869$	57.3466			1.94535
$870$	1.32842	+	1.54766i	0.0450375	+	0.0524707i
$871$	7.45200			0.252502
$872$	−13.1183	−	21.0575i	−0.444243	−	0.713096i
$873$			12.4433i			0.421143i
$874$	−12.9329	−	15.0675i	−0.437463	−	0.509665i
$875$	−1.91485	−	1.82575i	−0.0647338	−	0.0617215i
$876$	3.24488	+	0.497619i	0.109634	+	0.0168130i
$877$	−14.8376			−0.501031			−0.250515	−	0.968113i	$-0.580600\pi$
$877$	−14.8376			−0.501031			−0.250515	+	0.968113i	$0.580600\pi$
$878$	27.1539	−	23.3072i	0.916400	−	0.786579i
$879$			15.4578i			0.521380i
$880$	23.8146	+	7.48010i	0.802791	+	0.252154i
$881$			9.84229i			0.331595i	0.986160	+	0.165798i	$0.0530198\pi$
$881$			9.84229i			0.331595i	−0.986160	+	0.165798i	$0.946980\pi$
$882$	−6.79803	−	7.19630i	−0.228902	−	0.242312i
$883$			0.749575i			0.0252252i	0.999920	+	0.0126126i	$0.00401482\pi$
$883$			0.749575i			0.0252252i	−0.999920	+	0.0126126i	$0.995985\pi$
$884$	−0.952701	+	6.21239i	−0.0320428	+	0.208945i
$885$			0.415368i			0.0139625i
$886$	25.7638	+	30.0161i	0.865553	+	1.00841i
$887$	26.2358			0.880913			0.440456	−	0.897774i	$-0.354817\pi$
$887$	26.2358			0.880913			0.440456	+	0.897774i	$0.354817\pi$
$888$	−7.57155	−	12.1538i	−0.254085	−	0.407855i
$889$	12.8026	+	12.2068i	0.429385	+	0.409404i
$890$	12.2816	−	10.5417i	0.411680	−	0.353360i
$891$		−	6.24043i		−	0.209062i
$892$	1.20558	−	7.86138i	0.0403659	−	0.263219i
$893$	−46.0896			−1.54233
$894$	13.2535	−	11.3760i	0.443264	−	0.380469i
$895$	−15.1508			−0.506434
$896$	−26.1419	−	14.5808i	−0.873341	−	0.487109i
$897$	−8.54664			−0.285364
$898$	−38.7170	+	33.2322i	−1.29200	+	1.10897i
$899$	15.7946			0.526780
$900$	−0.303166	+	1.97689i	−0.0101055	+	0.0658963i
$901$		−	15.3711i		−	0.512086i
$902$	8.44958	−	7.25258i	0.281340	−	0.241484i
$903$	4.20979	+	4.01389i	0.140093	+	0.133574i
$904$	−6.12453	−	9.83106i	−0.203699	−	0.326976i
$905$	2.92356			0.0971825
$906$	14.7056	+	17.1327i	0.488561	+	0.569196i
$907$			12.6248i			0.419201i	0.977787	+	0.209601i	$0.0672164\pi$
$907$			12.6248i			0.419201i	−0.977787	+	0.209601i	$0.932784\pi$
$908$	−0.772137	+	5.03496i	−0.0256243	+	0.167091i
$909$		−	4.25585i		−	0.141158i
$910$	0.469765	−	8.97937i	0.0155726	−	0.297663i
$911$			25.1171i			0.832167i	0.909326	+	0.416084i	$0.136598\pi$
$911$			25.1171i			0.832167i	−0.909326	+	0.416084i	$0.863402\pi$
$912$	−15.0661	−	4.73222i	−0.498889	−	0.156700i
$913$		−	46.1743i		−	1.52815i
$914$	−4.57546	+	3.92728i	−0.151343	+	0.129903i
$915$	12.6848			0.419346
$916$	21.0811	+	3.23289i	0.696539	+	0.106818i
$917$	−24.3387	+	25.5266i	−0.803735	+	0.842961i
$918$	1.20450	+	1.40329i	0.0397543	+	0.0463156i
$919$		−	53.9495i		−	1.77963i	−0.456323	−	0.889814i	$-0.650834\pi$
$919$		−	53.9495i		−	1.77963i	0.456323	−	0.889814i	$-0.349166\pi$
$920$	−5.31896	−	8.53797i	−0.175361	−	0.281488i
$921$	30.4225			1.00245
$922$	17.3123	+	20.1696i	0.570150	+	0.664251i
$923$	−25.1756			−0.828665
$924$	−26.1463	+	20.1687i	−0.860149	+	0.663502i
$925$	5.06265			0.166459
$926$	−35.1998	−	41.0094i	−1.15674	−	1.34765i
$927$	−15.3254			−0.503353
$928$	−7.49847	+	3.21437i	−0.246149	+	0.105517i
$929$		−	21.0953i		−	0.692116i	−0.938213	−	0.346058i	$-0.887520\pi$
$929$		−	21.0953i		−	0.692116i	0.938213	−	0.346058i	$-0.112480\pi$
$930$	10.0875	+	11.7524i	0.330783	+	0.385377i
$931$	1.31587	+	27.6044i	0.0431258	+	0.904696i
$932$	−6.19736	+	40.4118i	−0.203001	+	1.32373i
$933$	6.24557			0.204471
$934$	−16.9494	+	14.5482i	−0.554600	+	0.476033i
$935$			8.16048i			0.266876i
$936$	−5.76913	+	3.59404i	−0.188570	+	0.117475i
$937$		−	4.64561i		−	0.151765i	−0.997117	−	0.0758827i	$-0.975823\pi$
$937$		−	4.64561i		−	0.151765i	0.997117	−	0.0758827i	$-0.0241774\pi$
$938$	−11.5869	−	0.606182i	−0.378326	−	0.0197925i
$939$		−	14.5063i		−	0.473396i
$940$	−23.0788	−	3.53924i	−0.752746	−	0.115437i
$941$			28.8306i			0.939849i	0.882707	+	0.469925i	$0.155719\pi$
$941$			28.8306i			0.939849i	−0.882707	+	0.469925i	$0.844281\pi$
$942$	4.75254	+	5.53692i	0.154846	+	0.180403i
$943$	−4.48738			−0.146129
$944$	−1.58512	−	0.497881i	−0.0515913	−	0.0162047i
$945$	−1.91485	−	1.82575i	−0.0622901	−	0.0593915i
$946$	14.7227	−	12.6370i	0.478677	−	0.410865i
$947$		−	18.9318i		−	0.615200i	−0.951516	−	0.307600i	$-0.900474\pi$
$947$		−	18.9318i		−	0.615200i	0.951516	−	0.307600i	$-0.0995259\pi$
$948$	−18.1667	−	2.78595i	−0.590026	−	0.0904834i
$949$	−3.94450			−0.128044
$950$	4.23663	−	3.63645i	0.137454	−	0.117982i
$951$	−2.29755			−0.0745030
$952$	1.98667	−	9.58198i	0.0643885	−	0.310554i
$953$	−57.1800			−1.85224			−0.926122	−	0.377225i	$-0.876878\pi$
$953$	−57.1800			−1.85224			−0.926122	+	0.377225i	$0.876878\pi$
$954$	12.6140	−	10.8270i	0.408393	−	0.350538i
$955$	−13.9477			−0.451336
$956$	8.67460	+	1.33029i	0.280557	+	0.0430248i
$957$			9.00003i			0.290930i
$958$	−35.6071	+	30.5628i	−1.15041	+	0.987440i
$959$	−10.2212	+	10.7200i	−0.330060	+	0.346168i
$960$	−7.18078	−	3.52653i	−0.231759	−	0.113818i
$961$	88.9388			2.86899
$962$	11.2062	+	13.0557i	0.361302	+	0.420934i
$963$			4.83844i			0.155917i
$964$	44.6598	+	6.84880i	1.43840	+	0.220585i
$965$			13.3869i			0.430938i
$966$	13.2889	+	0.695225i	0.427565	+	0.0223685i
$967$			31.9569i			1.02767i	0.857890	+	0.513833i	$0.171775\pi$
$967$			31.9569i			1.02767i	−0.857890	+	0.513833i	$0.828225\pi$
$968$	41.7907	+	67.0822i	1.34320	+	2.15610i
$969$		−	5.16266i		−	0.165848i
$970$	13.3532	−	11.4615i	0.428744	−	0.368006i
$971$	7.21917			0.231674			0.115837	−	0.993268i	$-0.463045\pi$
$971$	7.21917			0.231674			0.115837	+	0.993268i	$0.463045\pi$
$972$	−0.303166	+	1.97689i	−0.00972405	+	0.0634087i
$973$	11.2016	−	11.7483i	0.359108	−	0.376634i
$974$	17.3953	+	20.2663i	0.557381	+	0.649375i
$975$		−	2.40312i		−	0.0769615i
$976$	−15.2046	+	48.4074i	−0.486688	+	1.54948i
$977$	−14.2131			−0.454716			−0.227358	−	0.973811i	$-0.573009\pi$
$977$	−14.2131			−0.454716			−0.227358	+	0.973811i	$0.573009\pi$
$978$	1.17251	+	1.36603i	0.0374927	+	0.0436807i
$979$	71.4204			2.28261
$980$	−1.46085	+	13.9236i	−0.0466652	+	0.444772i
$981$	8.77146			0.280051
$982$	−1.05314	−	1.22696i	−0.0336071	−	0.0391538i
$983$	−23.1081			−0.737034			−0.368517	−	0.929621i	$-0.620134\pi$
$983$	−23.1081			−0.737034			−0.368517	+	0.929621i	$0.620134\pi$
$984$	−3.02906	+	1.88704i	−0.0965628	+	0.0601565i
$985$		−	4.07989i		−	0.129996i
$986$	−1.73714	−	2.02385i	−0.0553218	−	0.0644524i
$987$	21.3143	−	22.3545i	0.678440	−	0.711551i
$988$	18.7556	+	2.87626i	0.596694	+	0.0915061i
$989$	−7.81890			−0.248627
$990$	−6.69672	+	5.74803i	−0.212836	+	0.182685i
$991$			11.3485i			0.360497i	0.983621	+	0.180248i	$0.0576902\pi$
$991$			11.3485i			0.360497i	−0.983621	+	0.180248i	$0.942310\pi$
$992$	−56.9408	+	24.4088i	−1.80787	+	0.774979i
$993$		−	23.4483i		−	0.744111i
$994$	39.1449	+	2.04790i	1.24160	+	0.0649555i
$995$		−	3.66884i		−	0.116310i
$996$	−2.24319	+	14.6274i	−0.0710782	+	0.463488i
$997$		−	10.4798i		−	0.331900i	−0.986134	−	0.165950i	$-0.946931\pi$
$997$		−	10.4798i		−	0.331900i	0.986134	−	0.165950i	$-0.0530690\pi$
$998$	17.3842	+	20.2534i	0.550288	+	0.641110i
$999$	5.06265			0.160175

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.c.a.391.11	✓	16
3.2	odd	2		1260.2.c.d.811.6		16
4.3	odd	2		420.2.c.b.391.12	yes	16
7.6	odd	2		420.2.c.b.391.11	yes	16
12.11	even	2		1260.2.c.e.811.5		16
21.20	even	2		1260.2.c.e.811.6		16
28.27	even	2	inner	420.2.c.a.391.12	yes	16
84.83	odd	2		1260.2.c.d.811.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.c.a.391.11	✓	16	1.1	even	1	trivial
420.2.c.a.391.12	yes	16	28.27	even	2	inner
420.2.c.b.391.11	yes	16	7.6	odd	2
420.2.c.b.391.12	yes	16	4.3	odd	2
1260.2.c.d.811.5		16	84.83	odd	2
1260.2.c.d.811.6		16	3.2	odd	2
1260.2.c.e.811.5		16	12.11	even	2
1260.2.c.e.811.6		16	21.20	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)

\(f(q)\)	\(=\)	\(q+(1.07312 - 0.921096i) q^{2} -1.00000 q^{3} +(0.303166 - 1.97689i) q^{4} -1.00000i q^{5} +(-1.07312 + 0.921096i) q^{6} +(-1.82575 + 1.91485i) q^{7} +(-1.49557 - 2.40068i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(1.07312 - 0.921096i) q^{2} -1.00000 q^{3} +(0.303166 - 1.97689i) q^{4} -1.00000i q^{5} +(-1.07312 + 0.921096i) q^{6} +(-1.82575 + 1.91485i) q^{7} +(-1.49557 - 2.40068i) q^{8} +1.00000 q^{9} +(-0.921096 - 1.07312i) q^{10} -6.24043i q^{11} +(-0.303166 + 1.97689i) q^{12} -2.40312i q^{13} +(-0.195481 + 3.73655i) q^{14} +1.00000i q^{15} +(-3.81618 - 1.19865i) q^{16} -1.30768i q^{17} +(1.07312 - 0.921096i) q^{18} -3.94796 q^{19} +(-1.97689 - 0.303166i) q^{20} +(1.82575 - 1.91485i) q^{21} +(-5.74803 - 6.69672i) q^{22} +3.55648i q^{23} +(1.49557 + 2.40068i) q^{24} -1.00000 q^{25} +(-2.21350 - 2.57883i) q^{26} -1.00000 q^{27} +(3.23194 + 4.18981i) q^{28} +1.44221 q^{29} +(0.921096 + 1.07312i) q^{30} +10.9517 q^{31} +(-5.19929 + 2.22877i) q^{32} +6.24043i q^{33} +(-1.20450 - 1.40329i) q^{34} +(1.91485 + 1.82575i) q^{35} +(0.303166 - 1.97689i) q^{36} -5.06265 q^{37} +(-4.23663 + 3.63645i) q^{38} +2.40312i q^{39} +(-2.40068 + 1.49557i) q^{40} +1.26175i q^{41} +(0.195481 - 3.73655i) q^{42} +2.19850i q^{43} +(-12.3366 - 1.89189i) q^{44} -1.00000i q^{45} +(3.27586 + 3.81652i) q^{46} +11.6743 q^{47} +(3.81618 + 1.19865i) q^{48} +(-0.333303 - 6.99206i) q^{49} +(-1.07312 + 0.921096i) q^{50} +1.30768i q^{51} +(-4.75070 - 0.728544i) q^{52} +11.7545 q^{53} +(-1.07312 + 0.921096i) q^{54} -6.24043 q^{55} +(7.32748 + 1.51924i) q^{56} +3.94796 q^{57} +(1.54766 - 1.32842i) q^{58} +0.415368 q^{59} +(1.97689 + 0.303166i) q^{60} -12.6848i q^{61} +(11.7524 - 10.0875i) q^{62} +(-1.82575 + 1.91485i) q^{63} +(-3.52653 + 7.18078i) q^{64} -2.40312 q^{65} +(5.74803 + 6.69672i) q^{66} +3.10097i q^{67} +(-2.58513 - 0.396443i) q^{68} -3.55648i q^{69} +(3.73655 + 0.195481i) q^{70} -10.4762i q^{71} +(-1.49557 - 2.40068i) q^{72} -1.64141i q^{73} +(-5.43282 + 4.66319i) q^{74} +1.00000 q^{75} +(-1.19689 + 7.80468i) q^{76} +(11.9495 + 11.3934i) q^{77} +(2.21350 + 2.57883i) q^{78} +9.18952i q^{79} +(-1.19865 + 3.81618i) q^{80} +1.00000 q^{81} +(1.16219 + 1.35401i) q^{82} +7.39922 q^{83} +(-3.23194 - 4.18981i) q^{84} -1.30768 q^{85} +(2.02502 + 2.35925i) q^{86} -1.44221 q^{87} +(-14.9813 + 9.33301i) q^{88} +11.4448i q^{89} +(-0.921096 - 1.07312i) q^{90} +(4.60162 + 4.38749i) q^{91} +(7.03076 + 1.07820i) q^{92} -10.9517 q^{93} +(12.5279 - 10.7531i) q^{94} +3.94796i q^{95} +(5.19929 - 2.22877i) q^{96} +12.4433i q^{97} +(-6.79803 - 7.19630i) q^{98} -6.24043i 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

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