LMFDB - Embedded newform 1470.2.m.e.97.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(97,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("1470.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.m (of order $4$, degree $2$, 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:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
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} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			97.6
Root			$0.117630 + 0.893490i$ of defining polynomial
Character	$\chi$	$=$	1470.97
Dual form			1470.2.m.e.1273.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(-1.19306 - 1.89119i) q^{5} +1.00000i q^{6} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(-1.19306 - 1.89119i) q^{5} +1.00000i q^{6} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(0.493652 - 2.18090i) q^{10} -1.97875 q^{11} +(-0.707107 + 0.707107i) q^{12} +(-2.19222 - 2.19222i) q^{13} +(0.493652 - 2.18090i) q^{15} -1.00000 q^{16} +(-3.25469 + 3.25469i) q^{17} +(-0.707107 + 0.707107i) q^{18} -4.21878 q^{19} +(1.89119 - 1.19306i) q^{20} +(-1.39919 - 1.39919i) q^{22} +(-4.15953 + 4.15953i) q^{23} -1.00000 q^{24} +(-2.15321 + 4.51262i) q^{25} -3.10026i q^{26} +(-0.707107 + 0.707107i) q^{27} +8.94996i q^{29} +(1.89119 - 1.19306i) q^{30} -1.73386i q^{31} +(-0.707107 - 0.707107i) q^{32} +(-1.39919 - 1.39919i) q^{33} -4.60282 q^{34} -1.00000 q^{36} +(-1.96004 - 1.96004i) q^{37} +(-2.98313 - 2.98313i) q^{38} -3.10026i q^{39} +(2.18090 + 0.493652i) q^{40} +6.55691i q^{41} +(-6.33724 + 6.33724i) q^{43} -1.97875i q^{44} +(1.89119 - 1.19306i) q^{45} -5.88246 q^{46} +(4.29932 - 4.29932i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(-4.71345 + 1.66835i) q^{50} -4.60282 q^{51} +(2.19222 - 2.19222i) q^{52} +(8.08484 - 8.08484i) q^{53} -1.00000 q^{54} +(2.36077 + 3.74220i) q^{55} +(-2.98313 - 2.98313i) q^{57} +(-6.32858 + 6.32858i) q^{58} +4.20702 q^{59} +(2.18090 + 0.493652i) q^{60} -11.1200i q^{61} +(1.22602 - 1.22602i) q^{62} -1.00000i q^{64} +(-1.53045 + 6.76135i) q^{65} -1.97875i q^{66} +(3.89769 + 3.89769i) q^{67} +(-3.25469 - 3.25469i) q^{68} -5.88246 q^{69} -3.86002 q^{71} +(-0.707107 - 0.707107i) q^{72} +(-10.7621 - 10.7621i) q^{73} -2.77192i q^{74} +(-4.71345 + 1.66835i) q^{75} -4.21878i q^{76} +(2.19222 - 2.19222i) q^{78} -2.55514i q^{79} +(1.19306 + 1.89119i) q^{80} -1.00000 q^{81} +(-4.63643 + 4.63643i) q^{82} +(9.52969 + 9.52969i) q^{83} +(10.0383 + 2.27219i) q^{85} -8.96222 q^{86} +(-6.32858 + 6.32858i) q^{87} +(1.39919 - 1.39919i) q^{88} -6.19187 q^{89} +(2.18090 + 0.493652i) q^{90} +(-4.15953 - 4.15953i) q^{92} +(1.22602 - 1.22602i) q^{93} +6.08016 q^{94} +(5.03327 + 7.97853i) q^{95} -1.00000i q^{96} +(-1.48031 + 1.48031i) q^{97} -1.97875i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q + 4 q^{10} - 8 q^{11} + 16 q^{13} + 4 q^{15} - 16 q^{16} - 24 q^{17} - 16 q^{19} + 8 q^{20} + 4 q^{22} + 8 q^{23} - 16 q^{24} + 16 q^{25} + 8 q^{30} + 4 q^{33} - 16 q^{34} - 16 q^{36} + 16 q^{37} - 8 q^{38} - 24 q^{43} + 8 q^{45} + 8 q^{46} - 24 q^{47} - 16 q^{51} - 16 q^{52} - 16 q^{53} - 16 q^{54} + 56 q^{55} - 8 q^{57} - 36 q^{58} + 16 q^{59} - 8 q^{62} - 32 q^{65} + 48 q^{67} - 24 q^{68} + 8 q^{69} - 32 q^{71} - 56 q^{73} - 16 q^{78} - 16 q^{81} - 24 q^{82} + 16 q^{83} + 8 q^{85} + 16 q^{86} - 36 q^{87} - 4 q^{88} - 32 q^{89} + 8 q^{92} - 8 q^{93} + 16 q^{94} - 24 q^{95} - 44 q^{97}+O(q^{100}) $ 16 * q + 4 * q^10 - 8 * q^11 + 16 * q^13 + 4 * q^15 - 16 * q^16 - 24 * q^17 - 16 * q^19 + 8 * q^20 + 4 * q^22 + 8 * q^23 - 16 * q^24 + 16 * q^25 + 8 * q^30 + 4 * q^33 - 16 * q^34 - 16 * q^36 + 16 * q^37 - 8 * q^38 - 24 * q^43 + 8 * q^45 + 8 * q^46 - 24 * q^47 - 16 * q^51 - 16 * q^52 - 16 * q^53 - 16 * q^54 + 56 * q^55 - 8 * q^57 - 36 * q^58 + 16 * q^59 - 8 * q^62 - 32 * q^65 + 48 * q^67 - 24 * q^68 + 8 * q^69 - 32 * q^71 - 56 * q^73 - 16 * q^78 - 16 * q^81 - 24 * q^82 + 16 * q^83 + 8 * q^85 + 16 * q^86 - 36 * q^87 - 4 * q^88 - 32 * q^89 + 8 * q^92 - 8 * q^93 + 16 * q^94 - 24 * q^95 - 44 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$			1.00000i			0.500000i
$5$	−1.19306	−	1.89119i	−0.533554	−	0.845766i
$5$	−1.19306	−	1.89119i	−0.533554	−	0.845766i
$6$			1.00000i			0.408248i
$7$		0			0
$7$		0			0
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$			1.00000i			0.333333i
$10$	0.493652	−	2.18090i	0.156106	−	0.689660i
$11$	−1.97875			−0.596616			−0.298308	−	0.954470i	$-0.596422\pi$
$11$	−1.97875			−0.596616			−0.298308	+	0.954470i	$0.596422\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	−2.19222	−	2.19222i	−0.608011	−	0.608011i	0.334415	−	0.942426i	$-0.391461\pi$
$13$	−2.19222	−	2.19222i	−0.608011	−	0.608011i	−0.942426	+	0.334415i	$0.891461\pi$
$14$		0			0
$15$	0.493652	−	2.18090i	0.127460	−	0.563105i
$16$	−1.00000			−0.250000
$17$	−3.25469	+	3.25469i	−0.789378	+	0.789378i	−0.981392	−	0.192014i	$-0.938498\pi$
$17$	−3.25469	+	3.25469i	−0.789378	+	0.789378i	0.192014	+	0.981392i	$0.438498\pi$
$18$	−0.707107	+	0.707107i	−0.166667	+	0.166667i
$19$	−4.21878			−0.967856			−0.483928	−	0.875108i	$-0.660790\pi$
$19$	−4.21878			−0.967856			−0.483928	+	0.875108i	$0.660790\pi$
$20$	1.89119	−	1.19306i	0.422883	−	0.266777i
$21$		0			0
$22$	−1.39919	−	1.39919i	−0.298308	−	0.298308i
$23$	−4.15953	+	4.15953i	−0.867322	+	0.867322i	−0.992175	−	0.124854i	$-0.960154\pi$
$23$	−4.15953	+	4.15953i	−0.867322	+	0.867322i	0.124854	+	0.992175i	$0.460154\pi$
$24$	−1.00000			−0.204124
$25$	−2.15321	+	4.51262i	−0.430641	+	0.902523i
$26$		−	3.10026i		−	0.608011i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$		0			0
$29$			8.94996i			1.66197i	0.556298	+	0.830983i	$0.312221\pi$
$29$			8.94996i			1.66197i	−0.556298	+	0.830983i	$0.687779\pi$
$30$	1.89119	−	1.19306i	0.345283	−	0.217822i
$31$		−	1.73386i		−	0.311411i	−0.987804	−	0.155705i	$-0.950235\pi$
$31$		−	1.73386i		−	0.311411i	0.987804	−	0.155705i	$-0.0497650\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−1.39919	−	1.39919i	−0.243568	−	0.243568i
$34$	−4.60282			−0.789378
$35$		0			0
$36$	−1.00000			−0.166667
$37$	−1.96004	−	1.96004i	−0.322229	−	0.322229i	0.527393	−	0.849622i	$-0.323170\pi$
$37$	−1.96004	−	1.96004i	−0.322229	−	0.322229i	−0.849622	+	0.527393i	$0.823170\pi$
$38$	−2.98313	−	2.98313i	−0.483928	−	0.483928i
$39$		−	3.10026i		−	0.496439i
$40$	2.18090	+	0.493652i	0.344830	+	0.0780532i
$41$			6.55691i			1.02402i	0.858980	+	0.512008i	$0.171098\pi$
$41$			6.55691i			1.02402i	−0.858980	+	0.512008i	$0.828902\pi$
$42$		0			0
$43$	−6.33724	+	6.33724i	−0.966421	+	0.966421i	−0.999454	−	0.0330335i	$-0.989483\pi$
$43$	−6.33724	+	6.33724i	−0.966421	+	0.966421i	0.0330335	+	0.999454i	$0.489483\pi$
$44$		−	1.97875i		−	0.298308i
$45$	1.89119	−	1.19306i	0.281922	−	0.177851i
$46$	−5.88246			−0.867322
$47$	4.29932	−	4.29932i	0.627120	−	0.627120i	−0.320222	−	0.947343i	$-0.603758\pi$
$47$	4.29932	−	4.29932i	0.627120	−	0.627120i	0.947343	+	0.320222i	$0.103758\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$		0			0
$50$	−4.71345	+	1.66835i	−0.666582	+	0.235941i
$51$	−4.60282			−0.644524
$52$	2.19222	−	2.19222i	0.304006	−	0.304006i
$53$	8.08484	−	8.08484i	1.11054	−	1.11054i	0.117461	−	0.993077i	$-0.462524\pi$
$53$	8.08484	−	8.08484i	1.11054	−	1.11054i	0.993077	−	0.117461i	$-0.0374756\pi$
$54$	−1.00000			−0.136083
$55$	2.36077	+	3.74220i	0.318327	+	0.504598i
$56$		0			0
$57$	−2.98313	−	2.98313i	−0.395125	−	0.395125i
$58$	−6.32858	+	6.32858i	−0.830983	+	0.830983i
$59$	4.20702			0.547708			0.273854	−	0.961771i	$-0.411702\pi$
$59$	4.20702			0.547708			0.273854	+	0.961771i	$0.411702\pi$
$60$	2.18090	+	0.493652i	0.281552	+	0.0637302i
$61$		−	11.1200i		−	1.42377i	−0.702298	−	0.711883i	$-0.747843\pi$
$61$		−	11.1200i		−	1.42377i	0.702298	−	0.711883i	$-0.252157\pi$
$62$	1.22602	−	1.22602i	0.155705	−	0.155705i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−1.53045	+	6.76135i	−0.189829	+	0.838642i
$66$		−	1.97875i		−	0.243568i
$67$	3.89769	+	3.89769i	0.476179	+	0.476179i	0.903907	−	0.427729i	$-0.140686\pi$
$67$	3.89769	+	3.89769i	0.476179	+	0.476179i	−0.427729	+	0.903907i	$0.640686\pi$
$68$	−3.25469	−	3.25469i	−0.394689	−	0.394689i
$69$	−5.88246			−0.708165
$70$		0			0
$71$	−3.86002			−0.458100			−0.229050	−	0.973415i	$-0.573562\pi$
$71$	−3.86002			−0.458100			−0.229050	+	0.973415i	$0.573562\pi$
$72$	−0.707107	−	0.707107i	−0.0833333	−	0.0833333i
$73$	−10.7621	−	10.7621i	−1.25961	−	1.25961i	−0.951280	−	0.308328i	$-0.900231\pi$
$73$	−10.7621	−	10.7621i	−1.25961	−	1.25961i	−0.308328	−	0.951280i	$-0.599769\pi$
$74$		−	2.77192i		−	0.322229i
$75$	−4.71345	+	1.66835i	−0.544262	+	0.192645i
$76$		−	4.21878i		−	0.483928i
$77$		0			0
$78$	2.19222	−	2.19222i	0.248220	−	0.248220i
$79$		−	2.55514i		−	0.287476i	−0.989616	−	0.143738i	$-0.954088\pi$
$79$		−	2.55514i		−	0.287476i	0.989616	−	0.143738i	$-0.0459123\pi$
$80$	1.19306	+	1.89119i	0.133388	+	0.211442i
$81$	−1.00000			−0.111111
$82$	−4.63643	+	4.63643i	−0.512008	+	0.512008i
$83$	9.52969	+	9.52969i	1.04602	+	1.04602i	0.998889	+	0.0471311i	$0.0150078\pi$
$83$	9.52969	+	9.52969i	1.04602	+	1.04602i	0.0471311	+	0.998889i	$0.484992\pi$
$84$		0			0
$85$	10.0383	+	2.27219i	1.08880	+	0.246454i
$86$	−8.96222			−0.966421
$87$	−6.32858	+	6.32858i	−0.678495	+	0.678495i
$88$	1.39919	−	1.39919i	0.149154	−	0.149154i
$89$	−6.19187			−0.656337			−0.328168	−	0.944619i	$-0.606431\pi$
$89$	−6.19187			−0.656337			−0.328168	+	0.944619i	$0.606431\pi$
$90$	2.18090	+	0.493652i	0.229887	+	0.0520355i
$91$		0			0
$92$	−4.15953	−	4.15953i	−0.433661	−	0.433661i
$93$	1.22602	−	1.22602i	0.127133	−	0.127133i
$94$	6.08016			0.627120
$95$	5.03327	+	7.97853i	0.516403	+	0.818580i
$96$		−	1.00000i		−	0.102062i
$97$	−1.48031	+	1.48031i	−0.150303	+	0.150303i	−0.778253	−	0.627951i	$-0.783894\pi$
$97$	−1.48031	+	1.48031i	−0.150303	+	0.150303i	0.627951	+	0.778253i	$0.283894\pi$
$98$		0			0
$99$		−	1.97875i		−	0.198872i
$100$	−4.51262	−	2.15321i	−0.451262	−	0.215321i
$101$		−	10.0472i		−	0.999733i	−0.866102	−	0.499866i	$-0.833382\pi$
$101$		−	10.0472i		−	0.999733i	0.866102	−	0.499866i	$-0.166618\pi$
$102$	−3.25469	−	3.25469i	−0.322262	−	0.322262i
$103$	−3.52695	−	3.52695i	−0.347521	−	0.347521i	0.511665	−	0.859185i	$-0.329029\pi$
$103$	−3.52695	−	3.52695i	−0.347521	−	0.347521i	−0.859185	+	0.511665i	$0.829029\pi$
$104$	3.10026			0.304006
$105$		0			0
$106$	11.4337			1.11054
$107$	4.27775	+	4.27775i	0.413545	+	0.413545i	0.882972	−	0.469426i	$-0.155539\pi$
$107$	4.27775	+	4.27775i	0.413545	+	0.413545i	−0.469426	+	0.882972i	$0.655539\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$			9.74899i			0.933784i	0.884314	+	0.466892i	$0.154626\pi$
$109$			9.74899i			0.933784i	−0.884314	+	0.466892i	$0.845374\pi$
$110$	−0.976815	+	4.31545i	−0.0931356	+	0.411462i
$111$		−	2.77192i		−	0.263099i
$112$		0			0
$113$	6.02504	−	6.02504i	0.566788	−	0.566788i	−0.364439	−	0.931227i	$-0.618739\pi$
$113$	6.02504	−	6.02504i	0.566788	−	0.566788i	0.931227	+	0.364439i	$0.118739\pi$
$114$		−	4.21878i		−	0.395125i
$115$	12.8290	+	2.90389i	1.19631	+	0.270789i
$116$	−8.94996			−0.830983
$117$	2.19222	−	2.19222i	0.202670	−	0.202670i
$118$	2.97481	+	2.97481i	0.273854	+	0.273854i
$119$		0			0
$120$	1.19306	+	1.89119i	0.108911	+	0.172641i
$121$	−7.08454			−0.644049
$122$	7.86301	−	7.86301i	0.711883	−	0.711883i
$123$	−4.63643	+	4.63643i	−0.418053	+	0.418053i
$124$	1.73386			0.155705
$125$	11.1031	−	1.31171i	0.993094	−	0.117323i
$126$		0			0
$127$	−8.92770	−	8.92770i	−0.792205	−	0.792205i	0.189647	−	0.981852i	$-0.439266\pi$
$127$	−8.92770	−	8.92770i	−0.792205	−	0.792205i	−0.981852	+	0.189647i	$0.939266\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−8.96222			−0.789079
$130$	−5.86319	+	3.69881i	−0.514236	+	0.324407i
$131$			5.12160i			0.447476i	0.974649	+	0.223738i	$0.0718260\pi$
$131$			5.12160i			0.447476i	−0.974649	+	0.223738i	$0.928174\pi$
$132$	1.39919	−	1.39919i	0.121784	−	0.121784i
$133$		0			0
$134$			5.51217i			0.476179i
$135$	2.18090	+	0.493652i	0.187702	+	0.0424868i
$136$		−	4.60282i		−	0.394689i
$137$	−8.18996	−	8.18996i	−0.699715	−	0.699715i	0.264634	−	0.964349i	$-0.414749\pi$
$137$	−8.18996	−	8.18996i	−0.699715	−	0.699715i	−0.964349	+	0.264634i	$0.914749\pi$
$138$	−4.15953	−	4.15953i	−0.354083	−	0.354083i
$139$	2.87054			0.243476			0.121738	−	0.992562i	$-0.461153\pi$
$139$	2.87054			0.243476			0.121738	+	0.992562i	$0.461153\pi$
$140$		0			0
$141$	6.08016			0.512042
$142$	−2.72944	−	2.72944i	−0.229050	−	0.229050i
$143$	4.33785	+	4.33785i	0.362750	+	0.362750i
$144$		−	1.00000i		−	0.0833333i
$145$	16.9261	−	10.6779i	1.40563	−	0.886748i
$146$		−	15.2199i		−	1.25961i
$147$		0			0
$148$	1.96004	−	1.96004i	0.161114	−	0.161114i
$149$			15.5796i			1.27633i	0.769898	+	0.638167i	$0.220307\pi$
$149$			15.5796i			1.27633i	−0.769898	+	0.638167i	$0.779693\pi$
$150$	−4.51262	−	2.15321i	−0.368454	−	0.175809i
$151$	21.1906			1.72446			0.862232	−	0.506513i	$-0.169066\pi$
$151$	21.1906			1.72446			0.862232	+	0.506513i	$0.169066\pi$
$152$	2.98313	−	2.98313i	0.241964	−	0.241964i
$153$	−3.25469	−	3.25469i	−0.263126	−	0.263126i
$154$		0			0
$155$	−3.27906	+	2.06860i	−0.263381	+	0.166154i
$156$	3.10026			0.248220
$157$	−10.7362	+	10.7362i	−0.856846	+	0.856846i	−0.990965	−	0.134119i	$-0.957179\pi$
$157$	−10.7362	+	10.7362i	−0.856846	+	0.856846i	0.134119	+	0.990965i	$0.457179\pi$
$158$	1.80676	−	1.80676i	0.143738	−	0.143738i
$159$	11.4337			0.906751
$160$	−0.493652	+	2.18090i	−0.0390266	+	0.172415i
$161$		0			0
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	15.7848	−	15.7848i	1.23636	−	1.23636i	0.274879	−	0.961479i	$-0.411362\pi$
$163$	15.7848	−	15.7848i	1.23636	−	1.23636i	0.961479	−	0.274879i	$-0.0886378\pi$
$164$	−6.55691			−0.512008
$165$	−0.976815	+	4.31545i	−0.0760449	+	0.335958i
$166$			13.4770i			1.04602i
$167$	−6.91224	+	6.91224i	−0.534885	+	0.534885i	−0.922022	−	0.387137i	$-0.873464\pi$
$167$	−6.91224	+	6.91224i	−0.534885	+	0.534885i	0.387137	+	0.922022i	$0.373464\pi$
$168$		0			0
$169$		−	3.38837i		−	0.260644i
$170$	5.49145	+	8.70482i	0.421175	+	0.667629i
$171$		−	4.21878i		−	0.322619i
$172$	−6.33724	−	6.33724i	−0.483210	−	0.483210i
$173$	3.20151	+	3.20151i	0.243406	+	0.243406i	0.818258	−	0.574852i	$-0.194940\pi$
$173$	3.20151	+	3.20151i	0.243406	+	0.243406i	−0.574852	+	0.818258i	$0.694940\pi$
$174$	−8.94996			−0.678495
$175$		0			0
$176$	1.97875			0.149154
$177$	2.97481	+	2.97481i	0.223601	+	0.223601i
$178$	−4.37831	−	4.37831i	−0.328168	−	0.328168i
$179$			2.06788i			0.154561i	0.997009	+	0.0772803i	$0.0246236\pi$
$179$			2.06788i			0.154561i	−0.997009	+	0.0772803i	$0.975376\pi$
$180$	1.19306	+	1.89119i	0.0889256	+	0.140961i
$181$			6.13199i			0.455787i	0.973686	+	0.227894i	$0.0731839\pi$
$181$			6.13199i			0.455787i	−0.973686	+	0.227894i	$0.926816\pi$
$182$		0			0
$183$	7.86301	−	7.86301i	0.581250	−	0.581250i
$184$		−	5.88246i		−	0.433661i
$185$	−1.36836	+	6.04526i	−0.100604	+	0.444456i
$186$	1.73386			0.127133
$187$	6.44022	−	6.44022i	0.470956	−	0.470956i
$188$	4.29932	+	4.29932i	0.313560	+	0.313560i
$189$		0			0
$190$	−2.08261	+	9.20073i	−0.151088	+	0.667491i
$191$	−16.1661			−1.16974			−0.584869	−	0.811128i	$-0.698854\pi$
$191$	−16.1661			−1.16974			−0.584869	+	0.811128i	$0.698854\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$	15.4085	−	15.4085i	1.10913	−	1.10913i	0.115864	−	0.993265i	$-0.463036\pi$
$193$	15.4085	−	15.4085i	1.10913	−	1.10913i	0.993265	−	0.115864i	$-0.0369636\pi$
$194$	−2.09348			−0.150303
$195$	−5.86319	+	3.69881i	−0.419872	+	0.264877i
$196$		0			0
$197$	−0.628120	−	0.628120i	−0.0447517	−	0.0447517i	0.684377	−	0.729129i	$-0.260074\pi$
$197$	−0.628120	−	0.628120i	−0.0447517	−	0.0447517i	−0.729129	+	0.684377i	$0.760074\pi$
$198$	1.39919	−	1.39919i	0.0994361	−	0.0994361i
$199$	9.62495			0.682295			0.341147	−	0.940010i	$-0.389184\pi$
$199$	9.62495			0.682295			0.341147	+	0.940010i	$0.389184\pi$
$200$	−1.66835	−	4.71345i	−0.117970	−	0.333291i
$201$			5.51217i			0.388798i
$202$	7.10444	−	7.10444i	0.499866	−	0.499866i
$203$		0			0
$204$		−	4.60282i		−	0.322262i
$205$	12.4004	−	7.82280i	0.866079	−	0.546368i
$206$		−	4.98786i		−	0.347521i
$207$	−4.15953	−	4.15953i	−0.289107	−	0.289107i
$208$	2.19222	+	2.19222i	0.152003	+	0.152003i
$209$	8.34793			0.577439
$210$		0			0
$211$	11.2669			0.775648			0.387824	−	0.921733i	$-0.373227\pi$
$211$	11.2669			0.775648			0.387824	+	0.921733i	$0.373227\pi$
$212$	8.08484	+	8.08484i	0.555269	+	0.555269i
$213$	−2.72944	−	2.72944i	−0.187018	−	0.187018i
$214$			6.04965i			0.413545i
$215$	19.5457	+	4.42421i	1.33300	+	0.301729i
$216$		−	1.00000i		−	0.0680414i
$217$		0			0
$218$	−6.89357	+	6.89357i	−0.466892	+	0.466892i
$219$		−	15.2199i		−	1.02847i
$220$	−3.74220	+	2.36077i	−0.252299	+	0.159163i
$221$	14.2700			0.959901
$222$	1.96004	−	1.96004i	0.131549	−	0.131549i
$223$	−13.1718	−	13.1718i	−0.882048	−	0.882048i	0.111694	−	0.993743i	$-0.464372\pi$
$223$	−13.1718	−	13.1718i	−0.882048	−	0.882048i	−0.993743	+	0.111694i	$0.964372\pi$
$224$		0			0
$225$	−4.51262	−	2.15321i	−0.300841	−	0.143547i
$226$	8.52069			0.566788
$227$	−19.0312	+	19.0312i	−1.26314	+	1.26314i	−0.313583	+	0.949561i	$0.601529\pi$
$227$	−19.0312	+	19.0312i	−1.26314	+	1.26314i	−0.949561	+	0.313583i	$0.898471\pi$
$228$	2.98313	−	2.98313i	0.197563	−	0.197563i
$229$	−26.8905			−1.77697			−0.888486	−	0.458904i	$-0.848242\pi$
$229$	−26.8905			−1.77697			−0.888486	+	0.458904i	$0.848242\pi$
$230$	7.01814	+	11.1249i	0.462762	+	0.733551i
$231$		0			0
$232$	−6.32858	−	6.32858i	−0.415491	−	0.415491i
$233$	−0.651418	+	0.651418i	−0.0426758	+	0.0426758i	−0.728123	−	0.685447i	$-0.759607\pi$
$233$	−0.651418	+	0.651418i	−0.0426758	+	0.0426758i	0.685447	+	0.728123i	$0.259607\pi$
$234$	3.10026			0.202670
$235$	−13.2602	−	3.00148i	−0.865000	−	0.195795i
$236$			4.20702i			0.273854i
$237$	1.80676	−	1.80676i	0.117362	−	0.117362i
$238$		0			0
$239$			25.3432i			1.63931i	0.572856	+	0.819656i	$0.305836\pi$
$239$			25.3432i			1.63931i	−0.572856	+	0.819656i	$0.694164\pi$
$240$	−0.493652	+	2.18090i	−0.0318651	+	0.140776i
$241$			21.1200i			1.36046i	0.732999	+	0.680230i	$0.238120\pi$
$241$			21.1200i			1.36046i	−0.732999	+	0.680230i	$0.761880\pi$
$242$	−5.00952	−	5.00952i	−0.322024	−	0.322024i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	11.1200			0.711883
$245$		0			0
$246$	−6.55691			−0.418053
$247$	9.24849	+	9.24849i	0.588467	+	0.588467i
$248$	1.22602	+	1.22602i	0.0778527	+	0.0778527i
$249$			13.4770i			0.854072i
$250$	8.77861	+	6.92358i	0.555208	+	0.437886i
$251$			2.70623i			0.170816i	0.996346	+	0.0854078i	$0.0272193\pi$
$251$			2.70623i			0.170816i	−0.996346	+	0.0854078i	$0.972781\pi$
$252$		0			0
$253$	8.23068	−	8.23068i	0.517458	−	0.517458i
$254$		−	12.6257i		−	0.792205i
$255$	5.49145	+	8.70482i	0.343888	+	0.545117i
$256$	1.00000			0.0625000
$257$	−16.9862	+	16.9862i	−1.05957	+	1.05957i	−0.0614577	+	0.998110i	$0.519575\pi$
$257$	−16.9862	+	16.9862i	−1.05957	+	1.05957i	−0.998110	+	0.0614577i	$0.980425\pi$
$258$	−6.33724	−	6.33724i	−0.394540	−	0.394540i
$259$		0			0
$260$	−6.76135	−	1.53045i	−0.419321	−	0.0949145i
$261$	−8.94996			−0.553989
$262$	−3.62152	+	3.62152i	−0.223738	+	0.223738i
$263$	0.601271	−	0.601271i	0.0370759	−	0.0370759i	−0.688326	−	0.725402i	$-0.741654\pi$
$263$	0.601271	−	0.601271i	0.0370759	−	0.0370759i	0.725402	+	0.688326i	$0.241654\pi$
$264$	1.97875			0.121784
$265$	−24.9357	−	5.64426i	−1.53179	−	0.346724i
$266$		0			0
$267$	−4.37831	−	4.37831i	−0.267948	−	0.267948i
$268$	−3.89769	+	3.89769i	−0.238089	+	0.238089i
$269$	11.6434			0.709912			0.354956	−	0.934883i	$-0.384496\pi$
$269$	11.6434			0.709912			0.354956	+	0.934883i	$0.384496\pi$
$270$	1.19306	+	1.89119i	0.0726074	+	0.115094i
$271$			23.3447i			1.41809i	0.705162	+	0.709046i	$0.250874\pi$
$271$			23.3447i			1.41809i	−0.705162	+	0.709046i	$0.749126\pi$
$272$	3.25469	−	3.25469i	0.197344	−	0.197344i
$273$		0			0
$274$		−	11.5824i		−	0.699715i
$275$	4.26066	−	8.92935i	0.256928	−	0.538460i
$276$		−	5.88246i		−	0.354083i
$277$	6.68198	+	6.68198i	0.401481	+	0.401481i	0.878755	−	0.477274i	$-0.158375\pi$
$277$	6.68198	+	6.68198i	0.401481	+	0.401481i	−0.477274	+	0.878755i	$0.658375\pi$
$278$	2.02978	+	2.02978i	0.121738	+	0.121738i
$279$	1.73386			0.103804
$280$		0			0
$281$	−11.7320			−0.699871			−0.349935	−	0.936774i	$-0.613796\pi$
$281$	−11.7320			−0.699871			−0.349935	+	0.936774i	$0.613796\pi$
$282$	4.29932	+	4.29932i	0.256021	+	0.256021i
$283$	2.57938	+	2.57938i	0.153328	+	0.153328i	0.779603	−	0.626275i	$-0.215421\pi$
$283$	2.57938	+	2.57938i	0.153328	+	0.153328i	−0.626275	+	0.779603i	$0.715421\pi$
$284$		−	3.86002i		−	0.229050i
$285$	−2.08261	+	9.20073i	−0.123363	+	0.545004i
$286$			6.13465i			0.362750i
$287$		0			0
$288$	0.707107	−	0.707107i	0.0416667	−	0.0416667i
$289$		−	4.18598i		−	0.246234i
$290$	19.5189	+	4.41816i	1.14619	+	0.259443i
$291$	−2.09348			−0.122722
$292$	10.7621	−	10.7621i	0.629804	−	0.629804i
$293$	8.62354	+	8.62354i	0.503793	+	0.503793i	0.912614	−	0.408822i	$-0.134060\pi$
$293$	8.62354	+	8.62354i	0.503793	+	0.503793i	−0.408822	+	0.912614i	$0.634060\pi$
$294$		0			0
$295$	−5.01924	−	7.95628i	−0.292231	−	0.463233i
$296$	2.77192			0.161114
$297$	1.39919	−	1.39919i	0.0811892	−	0.0811892i
$298$	−11.0165	+	11.0165i	−0.638167	+	0.638167i
$299$	18.2372			1.05468
$300$	−1.66835	−	4.71345i	−0.0963225	−	0.272131i
$301$		0			0
$302$	14.9840	+	14.9840i	0.862232	+	0.862232i
$303$	7.10444	−	7.10444i	0.408139	−	0.408139i
$304$	4.21878			0.241964
$305$	−21.0300	+	13.2668i	−1.20417	+	0.759656i
$306$		−	4.60282i		−	0.263126i
$307$	−15.9933	+	15.9933i	−0.912785	+	0.912785i	−0.996490	−	0.0837060i	$-0.973324\pi$
$307$	−15.9933	+	15.9933i	−0.912785	+	0.912785i	0.0837060	+	0.996490i	$0.473324\pi$
$308$		0			0
$309$		−	4.98786i		−	0.283750i
$310$	−3.78137	−	0.855923i	−0.214767	−	0.0486132i
$311$			7.74252i			0.439038i	0.975608	+	0.219519i	$0.0704488\pi$
$311$			7.74252i			0.439038i	−0.975608	+	0.219519i	$0.929551\pi$
$312$	2.19222	+	2.19222i	0.124110	+	0.124110i
$313$	−14.1742	−	14.1742i	−0.801171	−	0.801171i	0.182108	−	0.983279i	$-0.441708\pi$
$313$	−14.1742	−	14.1742i	−0.801171	−	0.801171i	−0.983279	+	0.182108i	$0.941708\pi$
$314$	−15.1833			−0.856846
$315$		0			0
$316$	2.55514			0.143738
$317$	−2.10741	−	2.10741i	−0.118364	−	0.118364i	0.645444	−	0.763808i	$-0.276672\pi$
$317$	−2.10741	−	2.10741i	−0.118364	−	0.118364i	−0.763808	+	0.645444i	$0.776672\pi$
$318$	8.08484	+	8.08484i	0.453375	+	0.453375i
$319$		−	17.7098i		−	0.991556i
$320$	−1.89119	+	1.19306i	−0.105721	+	0.0666942i
$321$			6.04965i			0.337658i
$322$		0			0
$323$	13.7308	−	13.7308i	0.764004	−	0.764004i
$324$		−	1.00000i		−	0.0555556i
$325$	14.6129	−	5.17234i	0.810579	−	0.286910i
$326$	22.3230			1.23636
$327$	−6.89357	+	6.89357i	−0.381216	+	0.381216i
$328$	−4.63643	−	4.63643i	−0.256004	−	0.256004i
$329$		0			0
$330$	−3.74220	+	2.36077i	−0.206001	+	0.129956i
$331$	27.8372			1.53007			0.765035	−	0.643989i	$-0.222722\pi$
$331$	27.8372			1.53007			0.765035	+	0.643989i	$0.222722\pi$
$332$	−9.52969	+	9.52969i	−0.523010	+	0.523010i
$333$	1.96004	−	1.96004i	0.107410	−	0.107410i
$334$	−9.77538			−0.534885
$335$	2.72109	−	12.0215i	0.148669	−	0.656803i
$336$		0			0
$337$	−17.1567	−	17.1567i	−0.934583	−	0.934583i	0.0634051	−	0.997988i	$-0.479804\pi$
$337$	−17.1567	−	17.1567i	−0.934583	−	0.934583i	−0.997988	+	0.0634051i	$0.979804\pi$
$338$	2.39594	−	2.39594i	0.130322	−	0.130322i
$339$	8.52069			0.462780
$340$	−2.27219	+	10.0383i	−0.123227	+	0.544402i
$341$			3.43088i			0.185793i
$342$	2.98313	−	2.98313i	0.161309	−	0.161309i
$343$		0			0
$344$		−	8.96222i		−	0.483210i
$345$	7.01814	+	11.1249i	0.377844	+	0.598942i
$346$			4.52762i			0.243406i
$347$	−17.7080	−	17.7080i	−0.950613	−	0.950613i	0.0482236	−	0.998837i	$-0.484644\pi$
$347$	−17.7080	−	17.7080i	−0.950613	−	0.950613i	−0.998837	+	0.0482236i	$0.984644\pi$
$348$	−6.32858	−	6.32858i	−0.339247	−	0.339247i
$349$	18.0130			0.964212			0.482106	−	0.876113i	$-0.339872\pi$
$349$	18.0130			0.964212			0.482106	+	0.876113i	$0.339872\pi$
$350$		0			0
$351$	3.10026			0.165480
$352$	1.39919	+	1.39919i	0.0745770	+	0.0745770i
$353$	5.37260	+	5.37260i	0.285955	+	0.285955i	0.835478	−	0.549524i	$-0.185191\pi$
$353$	5.37260	+	5.37260i	0.285955	+	0.285955i	−0.549524	+	0.835478i	$0.685191\pi$
$354$			4.20702i			0.223601i
$355$	4.60524	+	7.30003i	0.244421	+	0.387445i
$356$		−	6.19187i		−	0.328168i
$357$		0			0
$358$	−1.46221	+	1.46221i	−0.0772803	+	0.0772803i
$359$		−	3.28672i		−	0.173466i	−0.996232	−	0.0867332i	$-0.972357\pi$
$359$		−	3.28672i		−	0.173466i	0.996232	−	0.0867332i	$-0.0276428\pi$
$360$	−0.493652	+	2.18090i	−0.0260177	+	0.114943i
$361$	−1.20185			−0.0632555
$362$	−4.33597	+	4.33597i	−0.227894	+	0.227894i
$363$	−5.00952	−	5.00952i	−0.262932	−	0.262932i
$364$		0			0
$365$	−7.51333	+	33.1930i	−0.393266	+	1.73740i
$366$	11.1200			0.581250
$367$	2.29639	−	2.29639i	0.119871	−	0.119871i	−0.644627	−	0.764497i	$-0.722987\pi$
$367$	2.29639	−	2.29639i	0.119871	−	0.119871i	0.764497	+	0.644627i	$0.222987\pi$
$368$	4.15953	−	4.15953i	0.216830	−	0.216830i
$369$	−6.55691			−0.341339
$370$	−5.24222	+	3.30707i	−0.272530	+	0.171926i
$371$		0			0
$372$	1.22602	+	1.22602i	0.0635664	+	0.0635664i
$373$	−11.1484	+	11.1484i	−0.577243	+	0.577243i	−0.934143	−	0.356900i	$-0.883834\pi$
$373$	−11.1484	+	11.1484i	−0.577243	+	0.577243i	0.356900	+	0.934143i	$0.383834\pi$
$374$	9.10785			0.470956
$375$	8.77861	+	6.92358i	0.453326	+	0.357532i
$376$			6.08016i			0.313560i
$377$	19.6203	−	19.6203i	1.01049	−	1.01049i
$378$		0			0
$379$			21.7428i			1.11685i	0.829555	+	0.558426i	$0.188594\pi$
$379$			21.7428i			1.11685i	−0.829555	+	0.558426i	$0.811406\pi$
$380$	−7.97853	+	5.03327i	−0.409290	+	0.258201i
$381$		−	12.6257i		−	0.646833i
$382$	−11.4312	−	11.4312i	−0.584869	−	0.584869i
$383$	12.6486	+	12.6486i	0.646316	+	0.646316i	0.952101	−	0.305785i	$-0.0989189\pi$
$383$	12.6486	+	12.6486i	0.646316	+	0.646316i	−0.305785	+	0.952101i	$0.598919\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	21.7909			1.10913
$387$	−6.33724	−	6.33724i	−0.322140	−	0.322140i
$388$	−1.48031	−	1.48031i	−0.0751514	−	0.0751514i
$389$		−	5.03599i		−	0.255335i	−0.991817	−	0.127667i	$-0.959251\pi$
$389$		−	5.03599i		−	0.255335i	0.991817	−	0.127667i	$-0.0407490\pi$
$390$	−6.76135	−	1.53045i	−0.342374	−	0.0774973i
$391$		−	27.0759i		−	1.36929i
$392$		0			0
$393$	−3.62152	+	3.62152i	−0.182681	+	0.182681i
$394$		−	0.888296i		−	0.0447517i
$395$	−4.83226	+	3.04844i	−0.243138	+	0.153384i
$396$	1.97875			0.0994361
$397$	−10.4332	+	10.4332i	−0.523625	+	0.523625i	−0.918664	−	0.395039i	$-0.870731\pi$
$397$	−10.4332	+	10.4332i	−0.523625	+	0.523625i	0.395039	+	0.918664i	$0.370731\pi$
$398$	6.80587	+	6.80587i	0.341147	+	0.341147i
$399$		0			0
$400$	2.15321	−	4.51262i	0.107660	−	0.225631i
$401$	−8.69371			−0.434143			−0.217072	−	0.976156i	$-0.569651\pi$
$401$	−8.69371			−0.434143			−0.217072	+	0.976156i	$0.569651\pi$
$402$	−3.89769	+	3.89769i	−0.194399	+	0.194399i
$403$	−3.80100	+	3.80100i	−0.189341	+	0.189341i
$404$	10.0472			0.499866
$405$	1.19306	+	1.89119i	0.0592837	+	0.0939740i
$406$		0			0
$407$	3.87844	+	3.87844i	0.192247	+	0.192247i
$408$	3.25469	−	3.25469i	0.161131	−	0.161131i
$409$	−18.9819			−0.938595			−0.469297	−	0.883040i	$-0.655493\pi$
$409$	−18.9819			−0.938595			−0.469297	+	0.883040i	$0.655493\pi$
$410$	14.2999	+	3.23683i	0.706223	+	0.159856i
$411$		−	11.5824i		−	0.571315i
$412$	3.52695	−	3.52695i	0.173760	−	0.173760i
$413$		0			0
$414$		−	5.88246i		−	0.289107i
$415$	6.65295	−	29.3920i	0.326581	−	1.44280i
$416$			3.10026i			0.152003i
$417$	2.02978	+	2.02978i	0.0993985	+	0.0993985i
$418$	5.90288	+	5.90288i	0.288719	+	0.288719i
$419$	−11.9171			−0.582188			−0.291094	−	0.956695i	$-0.594019\pi$
$419$	−11.9171			−0.582188			−0.291094	+	0.956695i	$0.594019\pi$
$420$		0			0
$421$	6.95263			0.338850			0.169425	−	0.985543i	$-0.445809\pi$
$421$	6.95263			0.338850			0.169425	+	0.985543i	$0.445809\pi$
$422$	7.96693	+	7.96693i	0.387824	+	0.387824i
$423$	4.29932	+	4.29932i	0.209040	+	0.209040i
$424$			11.4337i			0.555269i
$425$	−7.67914	−	21.6952i	−0.372493	−	1.05237i
$426$		−	3.86002i		−	0.187018i
$427$		0			0
$428$	−4.27775	+	4.27775i	−0.206773	+	0.206773i
$429$			6.13465i			0.296184i
$430$	10.6925	+	16.9493i	0.515637	+	0.817366i
$431$	6.24783			0.300947			0.150474	−	0.988614i	$-0.451920\pi$
$431$	6.24783			0.300947			0.150474	+	0.988614i	$0.451920\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	−15.1544	−	15.1544i	−0.728274	−	0.728274i	0.242002	−	0.970276i	$-0.422196\pi$
$433$	−15.1544	−	15.1544i	−0.728274	−	0.728274i	−0.970276	+	0.242002i	$0.922196\pi$
$434$		0			0
$435$	19.5189	+	4.41816i	0.935861	+	0.211835i
$436$	−9.74899			−0.466892
$437$	17.5482	−	17.5482i	0.839442	−	0.839442i
$438$	10.7621	−	10.7621i	0.514233	−	0.514233i
$439$	32.7459			1.56288			0.781438	−	0.623983i	$-0.214487\pi$
$439$	32.7459			1.56288			0.781438	+	0.623983i	$0.214487\pi$
$440$	−4.31545	−	0.976815i	−0.205731	−	0.0465678i
$441$		0			0
$442$	10.0904	+	10.0904i	0.479951	+	0.479951i
$443$	21.7443	−	21.7443i	1.03310	−	1.03310i	0.0336677	−	0.999433i	$-0.489281\pi$
$443$	21.7443	−	21.7443i	1.03310	−	1.03310i	0.999433	−	0.0336677i	$-0.0107188\pi$
$444$	2.77192			0.131549
$445$	7.38728	+	11.7100i	0.350191	+	0.555107i
$446$		−	18.6277i		−	0.882048i
$447$	−11.0165	+	11.0165i	−0.521061	+	0.521061i
$448$		0			0
$449$			16.8713i			0.796207i	0.917341	+	0.398103i	$0.130331\pi$
$449$			16.8713i			0.796207i	−0.917341	+	0.398103i	$0.869669\pi$
$450$	−1.66835	−	4.71345i	−0.0786470	−	0.222194i
$451$		−	12.9745i		−	0.610945i
$452$	6.02504	+	6.02504i	0.283394	+	0.283394i
$453$	14.9840	+	14.9840i	0.704010	+	0.704010i
$454$	−26.9142			−1.26314
$455$		0			0
$456$	4.21878			0.197563
$457$	14.0344	+	14.0344i	0.656503	+	0.656503i	0.954551	−	0.298048i	$-0.0963356\pi$
$457$	14.0344	+	14.0344i	0.656503	+	0.656503i	−0.298048	+	0.954551i	$0.596336\pi$
$458$	−19.0144	−	19.0144i	−0.888486	−	0.888486i
$459$		−	4.60282i		−	0.214841i
$460$	−2.90389	+	12.8290i	−0.135394	+	0.598157i
$461$			15.7775i			0.734830i	0.930057	+	0.367415i	$0.119757\pi$
$461$			15.7775i			0.734830i	−0.930057	+	0.367415i	$0.880243\pi$
$462$		0			0
$463$	4.48617	−	4.48617i	0.208490	−	0.208490i	−0.595135	−	0.803625i	$-0.702902\pi$
$463$	4.48617	−	4.48617i	0.208490	−	0.208490i	0.803625	+	0.595135i	$0.202902\pi$
$464$		−	8.94996i		−	0.415491i
$465$	−3.78137	−	0.855923i	−0.175357	−	0.0396925i
$466$	−0.921244			−0.0426758
$467$	−12.3390	+	12.3390i	−0.570982	+	0.570982i	−0.932403	−	0.361421i	$-0.882292\pi$
$467$	−12.3390	+	12.3390i	−0.570982	+	0.570982i	0.361421	+	0.932403i	$0.382292\pi$
$468$	2.19222	+	2.19222i	0.101335	+	0.101335i
$469$		0			0
$470$	−7.25401	−	11.4987i	−0.334602	−	0.530397i
$471$	−15.1833			−0.699612
$472$	−2.97481	+	2.97481i	−0.136927	+	0.136927i
$473$	12.5398	−	12.5398i	0.576582	−	0.576582i
$474$	2.55514			0.117362
$475$	9.08391	−	19.0378i	0.416799	−	0.873512i
$476$		0			0
$477$	8.08484	+	8.08484i	0.370180	+	0.370180i
$478$	−17.9203	+	17.9203i	−0.819656	+	0.819656i
$479$	31.7496			1.45068			0.725339	−	0.688392i	$-0.241683\pi$
$479$	31.7496			1.45068			0.725339	+	0.688392i	$0.241683\pi$
$480$	−1.89119	+	1.19306i	−0.0863207	+	0.0544556i
$481$			8.59367i			0.391837i
$482$	−14.9341	+	14.9341i	−0.680230	+	0.680230i
$483$		0			0
$484$		−	7.08454i		−	0.322024i
$485$	4.56565	+	1.03345i	0.207316	+	0.0469264i
$486$		−	1.00000i		−	0.0453609i
$487$	−21.1482	−	21.1482i	−0.958316	−	0.958316i	0.0408497	−	0.999165i	$-0.486994\pi$
$487$	−21.1482	−	21.1482i	−0.958316	−	0.958316i	−0.999165	+	0.0408497i	$0.986994\pi$
$488$	7.86301	+	7.86301i	0.355942	+	0.355942i
$489$	22.3230			1.00948
$490$		0			0
$491$	1.57179			0.0709340			0.0354670	−	0.999371i	$-0.488708\pi$
$491$	1.57179			0.0709340			0.0354670	+	0.999371i	$0.488708\pi$
$492$	−4.63643	−	4.63643i	−0.209027	−	0.209027i
$493$	−29.1293	−	29.1293i	−1.31192	−	1.31192i
$494$			13.0793i			0.588467i
$495$	−3.74220	+	2.36077i	−0.168199	+	0.106109i
$496$			1.73386i			0.0778527i
$497$		0			0
$498$	−9.52969	+	9.52969i	−0.427036	+	0.427036i
$499$			14.2595i			0.638345i	0.947697	+	0.319172i	$0.103405\pi$
$499$			14.2595i			0.638345i	−0.947697	+	0.319172i	$0.896595\pi$
$500$	1.31171	+	11.1031i	0.0586613	+	0.496547i
$501$	−9.77538			−0.436732
$502$	−1.91359	+	1.91359i	−0.0854078	+	0.0854078i
$503$	−28.7896	−	28.7896i	−1.28367	−	1.28367i	−0.938566	−	0.345100i	$-0.887845\pi$
$503$	−28.7896	−	28.7896i	−1.28367	−	1.28367i	−0.345100	−	0.938566i	$-0.612155\pi$
$504$		0			0
$505$	−19.0012	+	11.9869i	−0.845540	+	0.533411i
$506$	11.6399			0.517458
$507$	2.39594	−	2.39594i	0.106407	−	0.106407i
$508$	8.92770	−	8.92770i	0.396102	−	0.396102i
$509$	14.6188			0.647969			0.323984	−	0.946062i	$-0.394977\pi$
$509$	14.6188			0.647969			0.323984	+	0.946062i	$0.394977\pi$
$510$	−2.27219	+	10.0383i	−0.100614	+	0.444502i
$511$		0			0
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	2.98313	−	2.98313i	0.131708	−	0.131708i
$514$	−24.0221			−1.05957
$515$	−2.46227	+	10.8780i	−0.108500	+	0.479342i
$516$		−	8.96222i		−	0.394540i
$517$	−8.50729	+	8.50729i	−0.374150	+	0.374150i
$518$		0			0
$519$			4.52762i			0.198740i
$520$	−3.69881	−	5.86319i	−0.162203	−	0.257118i
$521$		−	15.3751i		−	0.673597i	−0.941577	−	0.336798i	$-0.890656\pi$
$521$		−	15.3751i		−	0.673597i	0.941577	−	0.336798i	$-0.109344\pi$
$522$	−6.32858	−	6.32858i	−0.276994	−	0.276994i
$523$	−16.5574	−	16.5574i	−0.724002	−	0.724002i	0.245416	−	0.969418i	$-0.421076\pi$
$523$	−16.5574	−	16.5574i	−0.724002	−	0.724002i	−0.969418	+	0.245416i	$0.921076\pi$
$524$	−5.12160			−0.223738
$525$		0			0
$526$	0.850325			0.0370759
$527$	5.64318	+	5.64318i	0.245821	+	0.245821i
$528$	1.39919	+	1.39919i	0.0608919	+	0.0608919i
$529$		−	11.6033i		−	0.504493i
$530$	−13.6411	−	21.6233i	−0.592532	−	0.939256i
$531$			4.20702i			0.182569i
$532$		0			0
$533$	14.3742	−	14.3742i	0.622614	−	0.622614i
$534$		−	6.19187i		−	0.267948i
$535$	2.98642	−	13.1937i	0.129114	−	0.570411i
$536$	−5.51217			−0.238089
$537$	−1.46221	+	1.46221i	−0.0630991	+	0.0630991i
$538$	8.23314	+	8.23314i	0.354956	+	0.354956i
$539$		0			0
$540$	−0.493652	+	2.18090i	−0.0212434	+	0.0938508i
$541$	7.96874			0.342603			0.171301	−	0.985219i	$-0.445203\pi$
$541$	7.96874			0.342603			0.171301	+	0.985219i	$0.445203\pi$
$542$	−16.5072	+	16.5072i	−0.709046	+	0.709046i
$543$	−4.33597	+	4.33597i	−0.186074	+	0.186074i
$544$	4.60282			0.197344
$545$	18.4372	−	11.6311i	0.789763	−	0.498224i
$546$		0			0
$547$	−5.88082	−	5.88082i	−0.251446	−	0.251446i	0.570117	−	0.821563i	$-0.306898\pi$
$547$	−5.88082	−	5.88082i	−0.251446	−	0.251446i	−0.821563	+	0.570117i	$0.806898\pi$
$548$	8.18996	−	8.18996i	0.349858	−	0.349858i
$549$	11.1200			0.474589
$550$	9.32675	−	3.30126i	0.397694	−	0.140766i
$551$		−	37.7580i		−	1.60854i
$552$	4.15953	−	4.15953i	0.177041	−	0.177041i
$553$		0			0
$554$			9.44974i			0.401481i
$555$	−5.24222	+	3.30707i	−0.222520	+	0.140377i
$556$			2.87054i			0.121738i
$557$	18.5354	+	18.5354i	0.785370	+	0.785370i	0.980731	−	0.195361i	$-0.0625878\pi$
$557$	18.5354	+	18.5354i	0.785370	+	0.785370i	−0.195361	+	0.980731i	$0.562588\pi$
$558$	1.22602	+	1.22602i	0.0519018	+	0.0519018i
$559$	27.7852			1.17519
$560$		0			0
$561$	9.10785			0.384534
$562$	−8.29575	−	8.29575i	−0.349935	−	0.349935i
$563$	0.618308	+	0.618308i	0.0260586	+	0.0260586i	0.720016	−	0.693957i	$-0.244134\pi$
$563$	0.618308	+	0.618308i	0.0260586	+	0.0260586i	−0.693957	+	0.720016i	$0.744134\pi$
$564$			6.08016i			0.256021i
$565$	−18.5827	−	4.20625i	−0.781782	−	0.176958i
$566$			3.64779i			0.153328i
$567$		0			0
$568$	2.72944	−	2.72944i	0.114525	−	0.114525i
$569$			33.0102i			1.38386i	0.721965	+	0.691929i	$0.243239\pi$
$569$			33.0102i			1.38386i	−0.721965	+	0.691929i	$0.756761\pi$
$570$	−7.97853	+	5.03327i	−0.334184	+	0.210821i
$571$	4.79189			0.200534			0.100267	−	0.994961i	$-0.468030\pi$
$571$	4.79189			0.200534			0.100267	+	0.994961i	$0.468030\pi$
$572$	−4.33785	+	4.33785i	−0.181375	+	0.181375i
$573$	−11.4312	−	11.4312i	−0.477544	−	0.477544i
$574$		0			0
$575$	−9.81403	−	27.7267i	−0.409273	−	1.15628i
$576$	1.00000			0.0416667
$577$	−23.0871	+	23.0871i	−0.961128	+	0.961128i	−0.999272	−	0.0381442i	$-0.987855\pi$
$577$	−23.0871	+	23.0871i	−0.961128	+	0.961128i	0.0381442	+	0.999272i	$0.487855\pi$
$578$	2.95994	−	2.95994i	0.123117	−	0.123117i
$579$	21.7909			0.905600
$580$	10.6779	+	16.9261i	0.443374	+	0.702817i
$581$		0			0
$582$	−1.48031	−	1.48031i	−0.0613609	−	0.0613609i
$583$	−15.9979	+	15.9979i	−0.662566	+	0.662566i
$584$	15.2199			0.629804
$585$	−6.76135	−	1.53045i	−0.279547	−	0.0632763i
$586$			12.1955i			0.503793i
$587$	−6.03856	+	6.03856i	−0.249238	+	0.249238i	−0.820658	−	0.571420i	$-0.806393\pi$
$587$	−6.03856	+	6.03856i	−0.249238	+	0.249238i	0.571420	+	0.820658i	$0.306393\pi$
$588$		0			0
$589$			7.31479i			0.301401i
$590$	2.07680	−	9.17508i	0.0855007	−	0.377732i
$591$		−	0.888296i		−	0.0365396i
$592$	1.96004	+	1.96004i	0.0805572	+	0.0805572i
$593$	−2.87821	−	2.87821i	−0.118194	−	0.118194i	0.645536	−	0.763730i	$-0.276634\pi$
$593$	−2.87821	−	2.87821i	−0.118194	−	0.118194i	−0.763730	+	0.645536i	$0.776634\pi$
$594$	1.97875			0.0811892
$595$		0			0
$596$	−15.5796			−0.638167
$597$	6.80587	+	6.80587i	0.278546	+	0.278546i
$598$	12.8956	+	12.8956i	0.527341	+	0.527341i
$599$			34.1269i			1.39439i	0.716884	+	0.697193i	$0.245568\pi$
$599$			34.1269i			1.39439i	−0.716884	+	0.697193i	$0.754432\pi$
$600$	2.15321	−	4.51262i	0.0879043	−	0.184227i
$601$			9.99405i			0.407666i	0.979006	+	0.203833i	$0.0653399\pi$
$601$			9.99405i			0.407666i	−0.979006	+	0.203833i	$0.934660\pi$
$602$		0			0
$603$	−3.89769	+	3.89769i	−0.158726	+	0.158726i
$604$			21.1906i			0.862232i
$605$	8.45229	+	13.3982i	0.343635	+	0.544715i
$606$	10.0472			0.408139
$607$	12.9256	−	12.9256i	0.524633	−	0.524633i	−0.394334	−	0.918967i	$-0.629025\pi$
$607$	12.9256	−	12.9256i	0.524633	−	0.524633i	0.918967	+	0.394334i	$0.129025\pi$
$608$	2.98313	+	2.98313i	0.120982	+	0.120982i
$609$		0			0
$610$	−24.2515	−	5.48939i	−0.981915	−	0.222259i
$611$	−18.8501			−0.762593
$612$	3.25469	−	3.25469i	0.131563	−	0.131563i
$613$	−21.0944	+	21.0944i	−0.851995	+	0.851995i	−0.990379	−	0.138383i	$-0.955809\pi$
$613$	−21.0944	+	21.0944i	−0.851995	+	0.851995i	0.138383	+	0.990379i	$0.455809\pi$
$614$	−22.6179			−0.912785
$615$	14.2999	+	3.23683i	0.576629	+	0.130521i
$616$		0			0
$617$	−35.0246	−	35.0246i	−1.41004	−	1.41004i	−0.759317	−	0.650721i	$-0.774467\pi$
$617$	−35.0246	−	35.0246i	−1.41004	−	1.41004i	−0.650721	−	0.759317i	$-0.725533\pi$
$618$	3.52695	−	3.52695i	0.141875	−	0.141875i
$619$	−11.5154			−0.462843			−0.231422	−	0.972854i	$-0.574338\pi$
$619$	−11.5154			−0.462843			−0.231422	+	0.972854i	$0.574338\pi$
$620$	−2.06860	−	3.27906i	−0.0830771	−	0.131690i
$621$		−	5.88246i		−	0.236055i
$622$	−5.47479	+	5.47479i	−0.219519	+	0.219519i
$623$		0			0
$624$			3.10026i			0.124110i
$625$	−15.7274	−	19.4332i	−0.629096	−	0.777327i
$626$		−	20.0453i		−	0.801171i
$627$	5.90288	+	5.90288i	0.235738	+	0.235738i
$628$	−10.7362	−	10.7362i	−0.428423	−	0.428423i
$629$	12.7586			0.508720
$630$		0			0
$631$	18.4477			0.734390			0.367195	−	0.930144i	$-0.380318\pi$
$631$	18.4477			0.734390			0.367195	+	0.930144i	$0.380318\pi$
$632$	1.80676	+	1.80676i	0.0718690	+	0.0718690i
$633$	7.96693	+	7.96693i	0.316657	+	0.316657i
$634$		−	2.98032i		−	0.118364i
$635$	−6.23268	+	27.5353i	−0.247336	+	1.09270i
$636$			11.4337i			0.453375i
$637$		0			0
$638$	12.5227	−	12.5227i	0.495778	−	0.495778i
$639$		−	3.86002i		−	0.152700i
$640$	−2.18090	−	0.493652i	−0.0862075	−	0.0195133i
$641$	−19.4846			−0.769594			−0.384797	−	0.923001i	$-0.625729\pi$
$641$	−19.4846			−0.769594			−0.384797	+	0.923001i	$0.625729\pi$
$642$	−4.27775	+	4.27775i	−0.168829	+	0.168829i
$643$	28.2707	+	28.2707i	1.11489	+	1.11489i	0.992480	+	0.122408i	$0.0390615\pi$
$643$	28.2707	+	28.2707i	1.11489	+	1.11489i	0.122408	+	0.992480i	$0.460938\pi$
$644$		0			0
$645$	10.6925	+	16.9493i	0.421016	+	0.667377i
$646$	19.4183			0.764004
$647$	17.6276	−	17.6276i	0.693012	−	0.693012i	−0.269882	−	0.962893i	$-0.586985\pi$
$647$	17.6276	−	17.6276i	0.693012	−	0.693012i	0.962893	+	0.269882i	$0.0869846\pi$
$648$	0.707107	−	0.707107i	0.0277778	−	0.0277778i
$649$	−8.32466			−0.326771
$650$	13.9903	+	6.67550i	0.548744	+	0.261835i
$651$		0			0
$652$	15.7848	+	15.7848i	0.618179	+	0.618179i
$653$	−35.1733	+	35.1733i	−1.37644	+	1.37644i	−0.525880	+	0.850559i	$0.676264\pi$
$653$	−35.1733	+	35.1733i	−1.37644	+	1.37644i	−0.850559	+	0.525880i	$0.823736\pi$
$654$	−9.74899			−0.381216
$655$	9.68592	−	6.11038i	0.378460	−	0.238752i
$656$		−	6.55691i		−	0.256004i
$657$	10.7621	−	10.7621i	0.419869	−	0.419869i
$658$		0			0
$659$		−	39.5644i		−	1.54121i	−0.637312	−	0.770606i	$-0.719954\pi$
$659$		−	39.5644i		−	1.54121i	0.637312	−	0.770606i	$-0.280046\pi$
$660$	−4.31545	−	0.976815i	−0.167979	−	0.0380225i
$661$		−	2.02066i		−	0.0785948i	−0.999228	−	0.0392974i	$-0.987488\pi$
$661$		−	2.02066i		−	0.0785948i	0.999228	−	0.0392974i	$-0.0125120\pi$
$662$	19.6839	+	19.6839i	0.765035	+	0.765035i
$663$	10.0904	+	10.0904i	0.391878	+	0.391878i
$664$	−13.4770			−0.523010
$665$		0			0
$666$	2.77192			0.107410
$667$	−37.2276	−	37.2276i	−1.44146	−	1.44146i
$668$	−6.91224	−	6.91224i	−0.267442	−	0.267442i
$669$		−	18.6277i		−	0.720190i
$670$	10.4246	−	6.57636i	0.402736	−	0.254067i
$671$			22.0037i			0.849442i
$672$		0			0
$673$	−19.7775	+	19.7775i	−0.762366	+	0.762366i	−0.976750	−	0.214383i	$-0.931226\pi$
$673$	−19.7775	+	19.7775i	−0.762366	+	0.762366i	0.214383	+	0.976750i	$0.431226\pi$
$674$		−	24.2632i		−	0.934583i
$675$	−1.66835	−	4.71345i	−0.0642150	−	0.181421i
$676$	3.38837			0.130322
$677$	−12.1336	+	12.1336i	−0.466332	+	0.466332i	−0.900724	−	0.434392i	$-0.856963\pi$
$677$	−12.1336	+	12.1336i	−0.466332	+	0.466332i	0.434392	+	0.900724i	$0.356963\pi$
$678$	6.02504	+	6.02504i	0.231390	+	0.231390i
$679$		0			0
$680$	−8.70482	+	5.49145i	−0.333815	+	0.210588i
$681$	−26.9142			−1.03135
$682$	−2.42600	+	2.42600i	−0.0928963	+	0.0928963i
$683$	0.356641	−	0.356641i	0.0136465	−	0.0136465i	−0.700251	−	0.713897i	$-0.746928\pi$
$683$	0.356641	−	0.356641i	0.0136465	−	0.0136465i	0.713897	+	0.700251i	$0.246928\pi$
$684$	4.21878			0.161309
$685$	−5.71765	+	25.2599i	−0.218460	+	0.965131i
$686$		0			0
$687$	−19.0144	−	19.0144i	−0.725445	−	0.725445i
$688$	6.33724	−	6.33724i	0.241605	−	0.241605i
$689$	−35.4475			−1.35044
$690$	−2.90389	+	12.8290i	−0.110549	+	0.488393i
$691$		−	15.6342i		−	0.594753i	−0.954760	−	0.297376i	$-0.903888\pi$
$691$		−	15.6342i		−	0.594753i	0.954760	−	0.297376i	$-0.0961116\pi$
$692$	−3.20151	+	3.20151i	−0.121703	+	0.121703i
$693$		0			0
$694$		−	25.0428i		−	0.950613i
$695$	−3.42473	−	5.42873i	−0.129907	−	0.205924i
$696$		−	8.94996i		−	0.339247i
$697$	−21.3407	−	21.3407i	−0.808336	−	0.808336i
$698$	12.7371	+	12.7371i	0.482106	+	0.482106i
$699$	−0.921244			−0.0348447
$700$		0			0
$701$	8.02724			0.303185			0.151592	−	0.988443i	$-0.451560\pi$
$701$	8.02724			0.303185			0.151592	+	0.988443i	$0.451560\pi$
$702$	2.19222	+	2.19222i	0.0827399	+	0.0827399i
$703$	8.26899	+	8.26899i	0.311871	+	0.311871i
$704$			1.97875i			0.0745770i
$705$	−7.25401	−	11.4987i	−0.273202	−	0.433068i
$706$			7.59800i			0.285955i
$707$		0			0
$708$	−2.97481	+	2.97481i	−0.111800	+	0.111800i
$709$			13.6783i			0.513698i	0.966452	+	0.256849i	$0.0826843\pi$
$709$			13.6783i			0.513698i	−0.966452	+	0.256849i	$0.917316\pi$
$710$	−1.90550	+	8.41829i	−0.0715123	+	0.315933i
$711$	2.55514			0.0958253
$712$	4.37831	−	4.37831i	0.164084	−	0.164084i
$713$	7.21204	+	7.21204i	0.270093	+	0.270093i
$714$		0			0
$715$	3.02838	−	13.3790i	0.113255	−	0.500348i
$716$	−2.06788			−0.0772803
$717$	−17.9203	+	17.9203i	−0.669246	+	0.669246i
$718$	2.32406	−	2.32406i	0.0867332	−	0.0867332i
$719$	−21.0471			−0.784924			−0.392462	−	0.919768i	$-0.628377\pi$
$719$	−21.0471			−0.784924			−0.392462	+	0.919768i	$0.628377\pi$
$720$	−1.89119	+	1.19306i	−0.0704805	+	0.0444628i
$721$		0			0
$722$	−0.849839	−	0.849839i	−0.0316277	−	0.0316277i
$723$	−14.9341	+	14.9341i	−0.555405	+	0.555405i
$724$	−6.13199			−0.227894
$725$	−40.3877	−	19.2711i	−1.49996	−	0.715711i
$726$		−	7.08454i		−	0.262932i
$727$	11.2251	−	11.2251i	0.416317	−	0.416317i	−0.467615	−	0.883932i	$-0.654887\pi$
$727$	11.2251	−	11.2251i	0.416317	−	0.416317i	0.883932	+	0.467615i	$0.154887\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$	−28.7837	+	18.1583i	−1.06533	+	0.672068i
$731$		−	41.2515i		−	1.52574i
$732$	7.86301	+	7.86301i	0.290625	+	0.290625i
$733$	−20.3304	−	20.3304i	−0.750922	−	0.750922i	0.223730	−	0.974651i	$-0.428177\pi$
$733$	−20.3304	−	20.3304i	−0.750922	−	0.750922i	−0.974651	+	0.223730i	$0.928177\pi$
$734$	3.24759			0.119871
$735$		0			0
$736$	5.88246			0.216830
$737$	−7.71257	−	7.71257i	−0.284096	−	0.284096i
$738$	−4.63643	−	4.63643i	−0.170669	−	0.170669i
$739$		−	41.9841i		−	1.54441i	−0.635373	−	0.772205i	$-0.719154\pi$
$739$		−	41.9841i		−	1.54441i	0.635373	−	0.772205i	$-0.280846\pi$
$740$	−6.04526	−	1.36836i	−0.222228	−	0.0503019i
$741$			13.0793i			0.480482i
$742$		0			0
$743$	8.63799	−	8.63799i	0.316897	−	0.316897i	−0.530677	−	0.847574i	$-0.678062\pi$
$743$	8.63799	−	8.63799i	0.316897	−	0.316897i	0.847574	+	0.530677i	$0.178062\pi$
$744$			1.73386i			0.0635664i
$745$	29.4641	−	18.5875i	1.07948	−	0.680993i
$746$	−15.7662			−0.577243
$747$	−9.52969	+	9.52969i	−0.348673	+	0.348673i
$748$	6.44022	+	6.44022i	0.235478	+	0.235478i
$749$		0			0
$750$	1.31171	+	11.1031i	0.0478968	+	0.405429i
$751$	31.7446			1.15838			0.579188	−	0.815194i	$-0.303370\pi$
$751$	31.7446			1.15838			0.579188	+	0.815194i	$0.303370\pi$
$752$	−4.29932	+	4.29932i	−0.156780	+	0.156780i
$753$	−1.91359	+	1.91359i	−0.0697351	+	0.0697351i
$754$	27.7472			1.01049
$755$	−25.2817	−	40.0754i	−0.920094	−	1.45849i
$756$		0			0
$757$	−9.81959	−	9.81959i	−0.356899	−	0.356899i	0.505770	−	0.862669i	$-0.331209\pi$
$757$	−9.81959	−	9.81959i	−0.356899	−	0.356899i	−0.862669	+	0.505770i	$0.831209\pi$
$758$	−15.3745	+	15.3745i	−0.558426	+	0.558426i
$759$	11.6399			0.422503
$760$	−9.20073	−	2.08261i	−0.333746	−	0.0755442i
$761$		−	31.9432i		−	1.15794i	−0.815349	−	0.578970i	$-0.803455\pi$
$761$		−	31.9432i		−	1.15794i	0.815349	−	0.578970i	$-0.196545\pi$
$762$	8.92770	−	8.92770i	0.323416	−	0.323416i
$763$		0			0
$764$		−	16.1661i		−	0.584869i
$765$	−2.27219	+	10.0383i	−0.0821513	+	0.362935i
$766$			17.8879i			0.646316i
$767$	−9.22271	−	9.22271i	−0.333013	−	0.333013i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$	26.3715			0.950981			0.475490	−	0.879721i	$-0.342271\pi$
$769$	26.3715			0.950981			0.475490	+	0.879721i	$0.342271\pi$
$770$		0			0
$771$	−24.0221			−0.865133
$772$	15.4085	+	15.4085i	0.554564	+	0.554564i
$773$	−32.5441	−	32.5441i	−1.17053	−	1.17053i	−0.982083	−	0.188448i	$-0.939654\pi$
$773$	−32.5441	−	32.5441i	−1.17053	−	1.17053i	−0.188448	−	0.982083i	$-0.560346\pi$
$774$		−	8.96222i		−	0.322140i
$775$	7.82425	+	3.73336i	0.281055	+	0.134106i
$776$		−	2.09348i		−	0.0751514i
$777$		0			0
$778$	3.56098	−	3.56098i	0.127667	−	0.127667i
$779$		−	27.6622i		−	0.991100i
$780$	−3.69881	−	5.86319i	−0.132438	−	0.209936i
$781$	7.63802			0.273310
$782$	19.1456	−	19.1456i	0.684644	−	0.684644i
$783$	−6.32858	−	6.32858i	−0.226165	−	0.226165i
$784$		0			0
$785$	33.1133	+	7.49528i	1.18186	+	0.267518i
$786$	−5.12160			−0.182681
$787$	8.01108	−	8.01108i	0.285564	−	0.285564i	−0.549759	−	0.835323i	$-0.685280\pi$
$787$	8.01108	−	8.01108i	0.285564	−	0.285564i	0.835323	+	0.549759i	$0.185280\pi$
$788$	0.628120	−	0.628120i	0.0223759	−	0.0223759i
$789$	0.850325			0.0302724
$790$	−5.57250	−	1.26135i	−0.198261	−	0.0448768i
$791$		0			0
$792$	1.39919	+	1.39919i	0.0497180	+	0.0497180i
$793$	−24.3774	+	24.3774i	−0.865666	+	0.865666i
$794$	−14.7547			−0.523625
$795$	−13.6411	−	21.6233i	−0.483800	−	0.766899i
$796$			9.62495i			0.341147i
$797$	−24.7239	+	24.7239i	−0.875767	+	0.875767i	−0.993093	−	0.117327i	$-0.962568\pi$
$797$	−24.7239	+	24.7239i	−0.875767	+	0.875767i	0.117327	+	0.993093i	$0.462568\pi$
$798$		0			0
$799$			27.9859i			0.990070i
$800$	4.71345	−	1.66835i	0.166646	−	0.0589852i
$801$		−	6.19187i		−	0.218779i
$802$	−6.14738	−	6.14738i	−0.217072	−	0.217072i
$803$	21.2955	+	21.2955i	0.751503	+	0.751503i
$804$	−5.51217			−0.194399
$805$		0			0
$806$	−5.37542			−0.189341
$807$	8.23314	+	8.23314i	0.289820	+	0.289820i
$808$	7.10444	+	7.10444i	0.249933	+	0.249933i
$809$		−	5.79908i		−	0.203885i	−0.994790	−	0.101942i	$-0.967494\pi$
$809$		−	5.79908i		−	0.203885i	0.994790	−	0.101942i	$-0.0325057\pi$
$810$	−0.493652	+	2.18090i	−0.0173452	+	0.0766289i
$811$		−	28.8064i		−	1.01153i	−0.862671	−	0.505765i	$-0.831210\pi$
$811$		−	28.8064i		−	1.01153i	0.862671	−	0.505765i	$-0.168790\pi$
$812$		0			0
$813$	−16.5072	+	16.5072i	−0.578934	+	0.578934i
$814$			5.48494i			0.192247i
$815$	−48.6842	−	11.0198i	−1.70533	−	0.386007i
$816$	4.60282			0.161131
$817$	26.7355	−	26.7355i	0.935356	−	0.935356i
$818$	−13.4222	−	13.4222i	−0.469297	−	0.469297i
$819$		0			0
$820$	7.82280	+	12.4004i	0.273184	+	0.433039i
$821$	4.51799			0.157679			0.0788395	−	0.996887i	$-0.474879\pi$
$821$	4.51799			0.157679			0.0788395	+	0.996887i	$0.474879\pi$
$822$	8.18996	−	8.18996i	0.285658	−	0.285658i
$823$	−15.8260	+	15.8260i	−0.551659	+	0.551659i	−0.926919	−	0.375261i	$-0.877553\pi$
$823$	−15.8260	+	15.8260i	−0.551659	+	0.551659i	0.375261	+	0.926919i	$0.377553\pi$
$824$	4.98786			0.173760
$825$	9.32675	−	3.30126i	0.324716	−	0.114935i
$826$		0			0
$827$	22.5410	+	22.5410i	0.783826	+	0.783826i	0.980474	−	0.196648i	$-0.0630057\pi$
$827$	22.5410	+	22.5410i	0.783826	+	0.783826i	−0.196648	+	0.980474i	$0.563006\pi$
$828$	4.15953	−	4.15953i	0.144554	−	0.144554i
$829$	7.22693			0.251002			0.125501	−	0.992094i	$-0.459946\pi$
$829$	7.22693			0.251002			0.125501	+	0.992094i	$0.459946\pi$
$830$	25.4876	−	16.0789i	0.884688	−	0.558108i
$831$			9.44974i			0.327808i
$832$	−2.19222	+	2.19222i	−0.0760014	+	0.0760014i
$833$		0			0
$834$			2.87054i			0.0993985i
$835$	21.3191	+	4.82563i	0.737777	+	0.166998i
$836$			8.34793i			0.288719i
$837$	1.22602	+	1.22602i	0.0423776	+	0.0423776i
$838$	−8.42665	−	8.42665i	−0.291094	−	0.291094i
$839$	−5.52622			−0.190786			−0.0953932	−	0.995440i	$-0.530411\pi$
$839$	−5.52622			−0.190786			−0.0953932	+	0.995440i	$0.530411\pi$
$840$		0			0
$841$	−51.1018			−1.76213
$842$	4.91625	+	4.91625i	0.169425	+	0.169425i
$843$	−8.29575	−	8.29575i	−0.285721	−	0.285721i
$844$			11.2669i			0.387824i
$845$	−6.40806	+	4.04254i	−0.220444	+	0.139068i
$846$			6.08016i			0.209040i
$847$		0			0
$848$	−8.08484	+	8.08484i	−0.277635	+	0.277635i
$849$			3.64779i			0.125192i
$850$	9.91083	−	20.7708i	0.339939	−	0.712432i
$851$	16.3057			0.558952
$852$	2.72944	−	2.72944i	0.0935092	−	0.0935092i
$853$	10.4649	+	10.4649i	0.358313	+	0.358313i	0.863191	−	0.504878i	$-0.168462\pi$
$853$	10.4649	+	10.4649i	0.358313	+	0.358313i	−0.504878	+	0.863191i	$0.668462\pi$
$854$		0			0
$855$	−7.97853	+	5.03327i	−0.272860	+	0.172134i
$856$	−6.04965			−0.206773
$857$	−1.52003	+	1.52003i	−0.0519233	+	0.0519233i	−0.732592	−	0.680668i	$-0.761689\pi$
$857$	−1.52003	+	1.52003i	−0.0519233	+	0.0519233i	0.680668	+	0.732592i	$0.261689\pi$
$858$	−4.33785	+	4.33785i	−0.148092	+	0.148092i
$859$	−7.18910			−0.245289			−0.122644	−	0.992451i	$-0.539137\pi$
$859$	−7.18910			−0.245289			−0.122644	+	0.992451i	$0.539137\pi$
$860$	−4.42421	+	19.5457i	−0.150864	+	0.666502i
$861$		0			0
$862$	4.41788	+	4.41788i	0.150474	+	0.150474i
$863$	28.6663	−	28.6663i	0.975812	−	0.975812i	−0.0239027	−	0.999714i	$-0.507609\pi$
$863$	28.6663	−	28.6663i	0.975812	−	0.975812i	0.999714	+	0.0239027i	$0.00760919\pi$
$864$	1.00000			0.0340207
$865$	2.23507	−	9.87426i	0.0759945	−	0.335735i
$866$		−	21.4316i		−	0.728274i
$867$	2.95994	−	2.95994i	0.100525	−	0.100525i
$868$		0			0
$869$			5.05600i			0.171513i
$870$	10.6779	+	16.9261i	0.362013	+	0.573848i
$871$		−	17.0892i		−	0.579044i
$872$	−6.89357	−	6.89357i	−0.233446	−	0.233446i
$873$	−1.48031	−	1.48031i	−0.0501009	−	0.0501009i
$874$	24.8168			0.839442
$875$		0			0
$876$	15.2199			0.514233
$877$	−36.1279	−	36.1279i	−1.21995	−	1.21995i	−0.967648	−	0.252303i	$-0.918812\pi$
$877$	−36.1279	−	36.1279i	−1.21995	−	1.21995i	−0.252303	−	0.967648i	$-0.581188\pi$
$878$	23.1548	+	23.1548i	0.781438	+	0.781438i
$879$			12.1955i			0.411345i
$880$	−2.36077	−	3.74220i	−0.0795817	−	0.126150i
$881$		−	27.9972i		−	0.943251i	−0.881799	−	0.471625i	$-0.843667\pi$
$881$		−	27.9972i		−	0.943251i	0.881799	−	0.471625i	$-0.156333\pi$
$882$		0			0
$883$	4.66131	−	4.66131i	0.156865	−	0.156865i	−0.624311	−	0.781176i	$-0.714620\pi$
$883$	4.66131	−	4.66131i	0.156865	−	0.156865i	0.781176	+	0.624311i	$0.214620\pi$
$884$			14.2700i			0.479951i
$885$	2.07680	−	9.17508i	0.0698110	−	0.308417i
$886$	30.7510			1.03310
$887$	−9.84950	+	9.84950i	−0.330714	+	0.330714i	−0.852857	−	0.522144i	$-0.825132\pi$
$887$	−9.84950	+	9.84950i	−0.330714	+	0.330714i	0.522144	+	0.852857i	$0.325132\pi$
$888$	1.96004	+	1.96004i	0.0657747	+	0.0657747i
$889$		0			0
$890$	−3.05663	+	13.5038i	−0.102458	+	0.452649i
$891$	1.97875			0.0662907
$892$	13.1718	−	13.1718i	0.441024	−	0.441024i
$893$	−18.1379	+	18.1379i	−0.606962	+	0.606962i
$894$	−15.5796			−0.521061
$895$	3.91075	−	2.46711i	0.130722	−	0.0824663i
$896$		0			0
$897$	12.8956	+	12.8956i	0.430573	+	0.430573i
$898$	−11.9298	+	11.9298i	−0.398103	+	0.398103i
$899$	15.5180			0.517554
$900$	2.15321	−	4.51262i	0.0717735	−	0.150421i
$901$			52.6273i			1.75327i
$902$	9.17435	−	9.17435i	0.305473	−	0.305473i
$903$		0			0
$904$			8.52069i			0.283394i
$905$	11.5968	−	7.31585i	0.385490	−	0.243187i
$906$			21.1906i			0.704010i
$907$	19.0839	+	19.0839i	0.633670	+	0.633670i	0.948987	−	0.315316i	$-0.102111\pi$
$907$	19.0839	+	19.0839i	0.633670	+	0.633670i	−0.315316	+	0.948987i	$0.602111\pi$
$908$	−19.0312	−	19.0312i	−0.631572	−	0.631572i
$909$	10.0472			0.333244
$910$		0			0
$911$	−15.5364			−0.514744			−0.257372	−	0.966312i	$-0.582857\pi$
$911$	−15.5364			−0.514744			−0.257372	+	0.966312i	$0.582857\pi$
$912$	2.98313	+	2.98313i	0.0987814	+	0.0987814i
$913$	−18.8569	−	18.8569i	−0.624073	−	0.624073i
$914$			19.8477i			0.656503i
$915$	−24.2515	−	5.48939i	−0.801730	−	0.181474i
$916$		−	26.8905i		−	0.888486i
$917$		0			0
$918$	3.25469	−	3.25469i	0.107421	−	0.107421i
$919$			37.8644i			1.24903i	0.781013	+	0.624515i	$0.214703\pi$
$919$			37.8644i			1.24903i	−0.781013	+	0.624515i	$0.785297\pi$
$920$	−11.1249	+	7.01814i	−0.366776	+	0.231381i
$921$	−22.6179			−0.745285
$922$	−11.1564	+	11.1564i	−0.367415	+	0.367415i
$923$	8.46199	+	8.46199i	0.278530	+	0.278530i
$924$		0			0
$925$	13.0653	−	4.62454i	0.429584	−	0.152054i
$926$	6.34440			0.208490
$927$	3.52695	−	3.52695i	0.115840	−	0.115840i
$928$	6.32858	−	6.32858i	0.207746	−	0.207746i
$929$	17.5137			0.574606			0.287303	−	0.957840i	$-0.407241\pi$
$929$	17.5137			0.574606			0.287303	+	0.957840i	$0.407241\pi$
$930$	−2.06860	−	3.27906i	−0.0678322	−	0.107525i
$931$		0			0
$932$	−0.651418	−	0.651418i	−0.0213379	−	0.0213379i
$933$	−5.47479	+	5.47479i	−0.179236	+	0.179236i
$934$	−17.4500			−0.570982
$935$	−19.8633	−	4.49610i	−0.649598	−	0.147038i
$936$			3.10026i			0.101335i
$937$	−2.68964	+	2.68964i	−0.0878666	+	0.0878666i	−0.749674	−	0.661807i	$-0.769790\pi$
$937$	−2.68964	+	2.68964i	−0.0878666	+	0.0878666i	0.661807	+	0.749674i	$0.269790\pi$
$938$		0			0
$939$		−	20.0453i		−	0.654153i
$940$	3.00148	−	13.2602i	0.0978975	−	0.432500i
$941$			32.4048i			1.05637i	0.849131	+	0.528183i	$0.177126\pi$
$941$			32.4048i			1.05637i	−0.849131	+	0.528183i	$0.822874\pi$
$942$	−10.7362	−	10.7362i	−0.349806	−	0.349806i
$943$	−27.2736	−	27.2736i	−0.888152	−	0.888152i
$944$	−4.20702			−0.136927
$945$		0			0
$946$	17.7340			0.576582
$947$	−27.1338	−	27.1338i	−0.881729	−	0.881729i	0.111982	−	0.993710i	$-0.464280\pi$
$947$	−27.1338	−	27.1338i	−0.881729	−	0.881729i	−0.993710	+	0.111982i	$0.964280\pi$
$948$	1.80676	+	1.80676i	0.0586808	+	0.0586808i
$949$			47.1857i			1.53171i
$950$	19.8850	−	7.03843i	0.645155	−	0.228357i
$951$		−	2.98032i		−	0.0966436i
$952$		0			0
$953$	12.2232	−	12.2232i	0.395949	−	0.395949i	−0.480853	−	0.876801i	$-0.659673\pi$
$953$	12.2232	−	12.2232i	0.395949	−	0.395949i	0.876801	+	0.480853i	$0.159673\pi$
$954$			11.4337i			0.370180i
$955$	19.2872	+	30.5732i	0.624118	+	0.989326i
$956$	−25.3432			−0.819656
$957$	12.5227	−	12.5227i	0.404801	−	0.404801i
$958$	22.4504	+	22.4504i	0.725339	+	0.725339i
$959$		0			0
$960$	−2.18090	−	0.493652i	−0.0703881	−	0.0159325i
$961$	27.9937			0.903023
$962$	−6.07664	+	6.07664i	−0.195919	+	0.195919i
$963$	−4.27775	+	4.27775i	−0.137848	+	0.137848i
$964$	−21.1200			−0.680230
$965$	−47.5237	−	10.7571i	−1.52984	−	0.346284i
$966$		0			0
$967$	24.7551	+	24.7551i	0.796071	+	0.796071i	0.982474	−	0.186402i	$-0.0596827\pi$
$967$	24.7551	+	24.7551i	0.796071	+	0.796071i	−0.186402	+	0.982474i	$0.559683\pi$
$968$	5.00952	−	5.00952i	0.161012	−	0.161012i
$969$	19.4183			0.623806
$970$	2.49765	+	3.95916i	0.0801946	+	0.127121i
$971$		−	10.2123i		−	0.327729i	−0.986483	−	0.163864i	$-0.947604\pi$
$971$		−	10.2123i		−	0.327729i	0.986483	−	0.163864i	$-0.0523959\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$		0			0
$974$		−	29.9080i		−	0.958316i
$975$	13.9903	+	6.67550i	0.448048	+	0.213787i
$976$			11.1200i			0.355942i
$977$	−11.3259	−	11.3259i	−0.362348	−	0.362348i	0.502328	−	0.864677i	$-0.332477\pi$
$977$	−11.3259	−	11.3259i	−0.362348	−	0.362348i	−0.864677	+	0.502328i	$0.832477\pi$
$978$	15.7848	+	15.7848i	0.504741	+	0.504741i
$979$	12.2522			0.391581
$980$		0			0
$981$	−9.74899			−0.311261
$982$	1.11143	+	1.11143i	0.0354670	+	0.0354670i
$983$	5.39290	+	5.39290i	0.172007	+	0.172007i	0.787860	−	0.615854i	$-0.211189\pi$
$983$	5.39290	+	5.39290i	0.172007	+	0.172007i	−0.615854	+	0.787860i	$0.711189\pi$
$984$		−	6.55691i		−	0.209027i
$985$	−0.438509	+	1.93728i	−0.0139721	+	0.0617269i
$986$		−	41.1951i		−	1.31192i
$987$		0			0
$988$	−9.24849	+	9.24849i	−0.294234	+	0.294234i
$989$		−	52.7199i		−	1.67640i
$990$	−4.31545	−	0.976815i	−0.137154	−	0.0310452i
$991$	50.8757			1.61612			0.808060	−	0.589100i	$-0.200517\pi$
$991$	50.8757			1.61612			0.808060	+	0.589100i	$0.200517\pi$
$992$	−1.22602	+	1.22602i	−0.0389263	+	0.0389263i
$993$	19.6839	+	19.6839i	0.624648	+	0.624648i
$994$		0			0
$995$	−11.4832	−	18.2026i	−0.364041	−	0.577062i
$996$	−13.4770			−0.427036
$997$	28.7960	−	28.7960i	0.911980	−	0.911980i	−0.0844482	−	0.996428i	$-0.526913\pi$
$997$	28.7960	−	28.7960i	0.911980	−	0.911980i	0.996428	+	0.0844482i	$0.0269128\pi$
$998$	−10.0830	+	10.0830i	−0.319172	+	0.319172i
$999$	2.77192			0.0876995

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.m.e.97.6		16
5.3	odd	4		1470.2.m.d.1273.7		16
7.4	even	3		210.2.u.b.187.2	yes	16
7.5	odd	6		210.2.u.a.157.3	yes	16
7.6	odd	2		1470.2.m.d.97.7		16
21.5	even	6		630.2.bv.a.577.2		16
21.11	odd	6		630.2.bv.b.397.3		16
35.4	even	6		1050.2.bc.g.607.4		16
35.12	even	12		1050.2.bc.g.493.4		16
35.13	even	4	inner	1470.2.m.e.1273.6		16
35.18	odd	12		210.2.u.a.103.3	✓	16
35.19	odd	6		1050.2.bc.h.157.2		16
35.32	odd	12		1050.2.bc.h.943.2		16
35.33	even	12		210.2.u.b.73.2	yes	16
105.53	even	12		630.2.bv.a.523.2		16
105.68	odd	12		630.2.bv.b.73.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.u.a.103.3	✓	16	35.18	odd	12
210.2.u.a.157.3	yes	16	7.5	odd	6
210.2.u.b.73.2	yes	16	35.33	even	12
210.2.u.b.187.2	yes	16	7.4	even	3
630.2.bv.a.523.2		16	105.53	even	12
630.2.bv.a.577.2		16	21.5	even	6
630.2.bv.b.73.3		16	105.68	odd	12
630.2.bv.b.397.3		16	21.11	odd	6
1050.2.bc.g.493.4		16	35.12	even	12
1050.2.bc.g.607.4		16	35.4	even	6
1050.2.bc.h.157.2		16	35.19	odd	6
1050.2.bc.h.943.2		16	35.32	odd	12
1470.2.m.d.97.7		16	7.6	odd	2
1470.2.m.d.1273.7		16	5.3	odd	4
1470.2.m.e.97.6		16	1.1	even	1	trivial
1470.2.m.e.1273.6		16	35.13	even	4	inner

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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(-1.19306 - 1.89119i) q^{5} +1.00000i q^{6} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(-1.19306 - 1.89119i) q^{5} +1.00000i q^{6} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(0.493652 - 2.18090i) q^{10} -1.97875 q^{11} +(-0.707107 + 0.707107i) q^{12} +(-2.19222 - 2.19222i) q^{13} +(0.493652 - 2.18090i) q^{15} -1.00000 q^{16} +(-3.25469 + 3.25469i) q^{17} +(-0.707107 + 0.707107i) q^{18} -4.21878 q^{19} +(1.89119 - 1.19306i) q^{20} +(-1.39919 - 1.39919i) q^{22} +(-4.15953 + 4.15953i) q^{23} -1.00000 q^{24} +(-2.15321 + 4.51262i) q^{25} -3.10026i q^{26} +(-0.707107 + 0.707107i) q^{27} +8.94996i q^{29} +(1.89119 - 1.19306i) q^{30} -1.73386i q^{31} +(-0.707107 - 0.707107i) q^{32} +(-1.39919 - 1.39919i) q^{33} -4.60282 q^{34} -1.00000 q^{36} +(-1.96004 - 1.96004i) q^{37} +(-2.98313 - 2.98313i) q^{38} -3.10026i q^{39} +(2.18090 + 0.493652i) q^{40} +6.55691i q^{41} +(-6.33724 + 6.33724i) q^{43} -1.97875i q^{44} +(1.89119 - 1.19306i) q^{45} -5.88246 q^{46} +(4.29932 - 4.29932i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(-4.71345 + 1.66835i) q^{50} -4.60282 q^{51} +(2.19222 - 2.19222i) q^{52} +(8.08484 - 8.08484i) q^{53} -1.00000 q^{54} +(2.36077 + 3.74220i) q^{55} +(-2.98313 - 2.98313i) q^{57} +(-6.32858 + 6.32858i) q^{58} +4.20702 q^{59} +(2.18090 + 0.493652i) q^{60} -11.1200i q^{61} +(1.22602 - 1.22602i) q^{62} -1.00000i q^{64} +(-1.53045 + 6.76135i) q^{65} -1.97875i q^{66} +(3.89769 + 3.89769i) q^{67} +(-3.25469 - 3.25469i) q^{68} -5.88246 q^{69} -3.86002 q^{71} +(-0.707107 - 0.707107i) q^{72} +(-10.7621 - 10.7621i) q^{73} -2.77192i q^{74} +(-4.71345 + 1.66835i) q^{75} -4.21878i q^{76} +(2.19222 - 2.19222i) q^{78} -2.55514i q^{79} +(1.19306 + 1.89119i) q^{80} -1.00000 q^{81} +(-4.63643 + 4.63643i) q^{82} +(9.52969 + 9.52969i) q^{83} +(10.0383 + 2.27219i) q^{85} -8.96222 q^{86} +(-6.32858 + 6.32858i) q^{87} +(1.39919 - 1.39919i) q^{88} -6.19187 q^{89} +(2.18090 + 0.493652i) q^{90} +(-4.15953 - 4.15953i) q^{92} +(1.22602 - 1.22602i) q^{93} +6.08016 q^{94} +(5.03327 + 7.97853i) q^{95} -1.00000i q^{96} +(-1.48031 + 1.48031i) q^{97} -1.97875i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q + 4 q^{10} - 8 q^{11} + 16 q^{13} + 4 q^{15} - 16 q^{16} - 24 q^{17} - 16 q^{19} + 8 q^{20} + 4 q^{22} + 8 q^{23} - 16 q^{24} + 16 q^{25} + 8 q^{30} + 4 q^{33} - 16 q^{34} - 16 q^{36} + 16 q^{37} - 8 q^{38} - 24 q^{43} + 8 q^{45} + 8 q^{46} - 24 q^{47} - 16 q^{51} - 16 q^{52} - 16 q^{53} - 16 q^{54} + 56 q^{55} - 8 q^{57} - 36 q^{58} + 16 q^{59} - 8 q^{62} - 32 q^{65} + 48 q^{67} - 24 q^{68} + 8 q^{69} - 32 q^{71} - 56 q^{73} - 16 q^{78} - 16 q^{81} - 24 q^{82} + 16 q^{83} + 8 q^{85} + 16 q^{86} - 36 q^{87} - 4 q^{88} - 32 q^{89} + 8 q^{92} - 8 q^{93} + 16 q^{94} - 24 q^{95} - 44 q^{97}+O(q^{100}) \) 16 * q + 4 * q^10 - 8 * q^11 + 16 * q^13 + 4 * q^15 - 16 * q^16 - 24 * q^17 - 16 * q^19 + 8 * q^20 + 4 * q^22 + 8 * q^23 - 16 * q^24 + 16 * q^25 + 8 * q^30 + 4 * q^33 - 16 * q^34 - 16 * q^36 + 16 * q^37 - 8 * q^38 - 24 * q^43 + 8 * q^45 + 8 * q^46 - 24 * q^47 - 16 * q^51 - 16 * q^52 - 16 * q^53 - 16 * q^54 + 56 * q^55 - 8 * q^57 - 36 * q^58 + 16 * q^59 - 8 * q^62 - 32 * q^65 + 48 * q^67 - 24 * q^68 + 8 * q^69 - 32 * q^71 - 56 * q^73 - 16 * q^78 - 16 * q^81 - 24 * q^82 + 16 * q^83 + 8 * q^85 + 16 * q^86 - 36 * q^87 - 4 * q^88 - 32 * q^89 + 8 * q^92 - 8 * q^93 + 16 * q^94 - 24 * q^95 - 44 * q^97

Introduction

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