LMFDB - Embedded newform 637.2.i.a.489.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(489,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("637.489");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.i (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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			489.11
Character	$\chi$	$=$	637.489
Dual form			637.2.i.a.538.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.15715 + 1.15715i) q^{2} -1.98136i q^{3} +0.678010i q^{4} +(-2.02979 + 2.02979i) q^{5} +(2.29273 - 2.29273i) q^{6} +(1.52975 - 1.52975i) q^{8} -0.925772 q^{9} +O(q^{10})$	\(q+(1.15715 + 1.15715i) q^{2} -1.98136i q^{3} +0.678010i q^{4} +(-2.02979 + 2.02979i) q^{5} +(2.29273 - 2.29273i) q^{6} +(1.52975 - 1.52975i) q^{8} -0.925772 q^{9} -4.69755 q^{10} +(2.44444 - 2.44444i) q^{11} +1.34338 q^{12} +(-2.29273 - 2.78269i) q^{13} +(4.02173 + 4.02173i) q^{15} +4.89632 q^{16} +6.44887 q^{17} +(-1.07126 - 1.07126i) q^{18} +(2.14924 - 2.14924i) q^{19} +(-1.37622 - 1.37622i) q^{20} +5.65717 q^{22} -3.43181i q^{23} +(-3.03097 - 3.03097i) q^{24} -3.24008i q^{25} +(0.566956 - 5.87305i) q^{26} -4.10978i q^{27} -4.40371 q^{29} +9.30753i q^{30} +(-2.37198 + 2.37198i) q^{31} +(2.60631 + 2.60631i) q^{32} +(-4.84330 - 4.84330i) q^{33} +(7.46233 + 7.46233i) q^{34} -0.627683i q^{36} +(-2.75238 + 2.75238i) q^{37} +4.97401 q^{38} +(-5.51350 + 4.54272i) q^{39} +6.21012i q^{40} +(3.03989 - 3.03989i) q^{41} +4.48958i q^{43} +(1.65735 + 1.65735i) q^{44} +(1.87912 - 1.87912i) q^{45} +(3.97113 - 3.97113i) q^{46} +(4.03771 + 4.03771i) q^{47} -9.70136i q^{48} +(3.74927 - 3.74927i) q^{50} -12.7775i q^{51} +(1.88669 - 1.55450i) q^{52} -11.4505 q^{53} +(4.75565 - 4.75565i) q^{54} +9.92337i q^{55} +(-4.25841 - 4.25841i) q^{57} +(-5.09577 - 5.09577i) q^{58} +(2.09403 + 2.09403i) q^{59} +(-2.72677 + 2.72677i) q^{60} +3.50457i q^{61} -5.48950 q^{62} -3.76085i q^{64} +(10.3020 + 0.994510i) q^{65} -11.2089i q^{66} +(5.15836 + 5.15836i) q^{67} +4.37240i q^{68} -6.79964 q^{69} +(8.31408 + 8.31408i) q^{71} +(-1.41620 + 1.41620i) q^{72} +(3.30282 + 3.30282i) q^{73} -6.36984 q^{74} -6.41975 q^{75} +(1.45721 + 1.45721i) q^{76} +(-11.6366 - 1.12334i) q^{78} +1.08784 q^{79} +(-9.93850 + 9.93850i) q^{80} -10.9203 q^{81} +7.03523 q^{82} +(-2.01261 + 2.01261i) q^{83} +(-13.0898 + 13.0898i) q^{85} +(-5.19513 + 5.19513i) q^{86} +8.72532i q^{87} -7.47873i q^{88} +(-3.50857 - 3.50857i) q^{89} +4.34887 q^{90} +2.32680 q^{92} +(4.69974 + 4.69974i) q^{93} +9.34450i q^{94} +8.72501i q^{95} +(5.16402 - 5.16402i) q^{96} +(3.20816 - 3.20816i) q^{97} +(-2.26299 + 2.26299i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{2} - 16 q^{8} - 16 q^{9}+O(q^{10}) $ 32 * q + 4 * q^2 - 16 * q^8 - 16 * q^9	$ 32 q + 4 q^{2} - 16 q^{8} - 16 q^{9} + 20 q^{11} - 44 q^{15} - 24 q^{16} + 8 q^{18} - 8 q^{22} + 16 q^{29} - 8 q^{32} + 16 q^{37} + 12 q^{39} + 84 q^{44} - 24 q^{46} + 88 q^{50} + 24 q^{53} + 40 q^{57} - 52 q^{58} - 32 q^{60} + 16 q^{65} - 32 q^{67} - 36 q^{71} - 44 q^{72} - 24 q^{74} - 176 q^{78} + 64 q^{79} - 32 q^{81} - 84 q^{85} - 84 q^{86} + 48 q^{92} - 12 q^{93} - 24 q^{99}+O(q^{100}) $ 32 * q + 4 * q^2 - 16 * q^8 - 16 * q^9 + 20 * q^11 - 44 * q^15 - 24 * q^16 + 8 * q^18 - 8 * q^22 + 16 * q^29 - 8 * q^32 + 16 * q^37 + 12 * q^39 + 84 * q^44 - 24 * q^46 + 88 * q^50 + 24 * q^53 + 40 * q^57 - 52 * q^58 - 32 * q^60 + 16 * q^65 - 32 * q^67 - 36 * q^71 - 44 * q^72 - 24 * q^74 - 176 * q^78 + 64 * q^79 - 32 * q^81 - 84 * q^85 - 84 * q^86 + 48 * q^92 - 12 * q^93 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	1.15715	+	1.15715i	0.818231	+	0.818231i	0.985852	−	0.167620i	$-0.0536083\pi$
$2$	1.15715	+	1.15715i	0.818231	+	0.818231i	−0.167620	+	0.985852i	$0.553608\pi$
$3$		−	1.98136i		−	1.14394i	−0.820276	−	0.571968i	$-0.806180\pi$
$3$		−	1.98136i		−	1.14394i	0.820276	−	0.571968i	$-0.193820\pi$
$4$			0.678010i			0.339005i
$5$	−2.02979	+	2.02979i	−0.907749	+	0.907749i	−0.996090	−	0.0883414i	$-0.971843\pi$
$5$	−2.02979	+	2.02979i	−0.907749	+	0.907749i	0.0883414	+	0.996090i	$0.471843\pi$
$6$	2.29273	−	2.29273i	0.936005	−	0.936005i
$7$		0			0
$7$		0			0
$8$	1.52975	−	1.52975i	0.540847	−	0.540847i
$9$	−0.925772			−0.308591
$10$	−4.69755			−1.48550
$11$	2.44444	−	2.44444i	0.737025	−	0.737025i	−0.234976	−	0.972001i	$-0.575501\pi$
$11$	2.44444	−	2.44444i	0.737025	−	0.737025i	0.972001	+	0.234976i	$0.0755012\pi$
$12$	1.34338			0.387800
$13$	−2.29273	−	2.78269i	−0.635890	−	0.771780i
$13$	−2.29273	−	2.78269i	−0.635890	−	0.771780i
$14$		0			0
$15$	4.02173	+	4.02173i	1.03841	+	1.03841i
$16$	4.89632			1.22408
$17$	6.44887			1.56408			0.782040	−	0.623228i	$-0.214179\pi$
$17$	6.44887			1.56408			0.782040	+	0.623228i	$0.214179\pi$
$18$	−1.07126	−	1.07126i	−0.252499	−	0.252499i
$19$	2.14924	−	2.14924i	0.493070	−	0.493070i	−0.416202	−	0.909272i	$-0.636639\pi$
$19$	2.14924	−	2.14924i	0.493070	−	0.493070i	0.909272	+	0.416202i	$0.136639\pi$
$20$	−1.37622	−	1.37622i	−0.307731	−	0.307731i
$21$		0			0
$22$	5.65717			1.20611
$23$		−	3.43181i		−	0.715582i	−0.933802	−	0.357791i	$-0.883530\pi$
$23$		−	3.43181i		−	0.715582i	0.933802	−	0.357791i	$-0.116470\pi$
$24$	−3.03097	−	3.03097i	−0.618695	−	0.618695i
$25$		−	3.24008i		−	0.648016i
$26$	0.566956	−	5.87305i	0.111189	−	1.15180i
$27$		−	4.10978i		−	0.790928i
$28$		0			0
$29$	−4.40371			−0.817748			−0.408874	−	0.912591i	$-0.634079\pi$
$29$	−4.40371			−0.817748			−0.408874	+	0.912591i	$0.634079\pi$
$30$			9.30753i			1.69931i
$31$	−2.37198	+	2.37198i	−0.426021	+	0.426021i	−0.887270	−	0.461250i	$-0.847401\pi$
$31$	−2.37198	+	2.37198i	−0.426021	+	0.426021i	0.461250	+	0.887270i	$0.347401\pi$
$32$	2.60631	+	2.60631i	0.460734	+	0.460734i
$33$	−4.84330	−	4.84330i	−0.843110	−	0.843110i
$34$	7.46233	+	7.46233i	1.27978	+	1.27978i
$35$		0			0
$36$		−	0.627683i		−	0.104614i
$37$	−2.75238	+	2.75238i	−0.452488	+	0.452488i	−0.896179	−	0.443692i	$-0.853669\pi$
$37$	−2.75238	+	2.75238i	−0.452488	+	0.452488i	0.443692	+	0.896179i	$0.353669\pi$
$38$	4.97401			0.806890
$39$	−5.51350	+	4.54272i	−0.882867	+	0.727418i
$40$			6.21012i			0.981906i
$41$	3.03989	−	3.03989i	0.474751	−	0.474751i	−0.428697	−	0.903448i	$-0.641027\pi$
$41$	3.03989	−	3.03989i	0.474751	−	0.474751i	0.903448	+	0.428697i	$0.141027\pi$
$42$		0			0
$43$			4.48958i			0.684654i	0.939581	+	0.342327i	$0.111215\pi$
$43$			4.48958i			0.684654i	−0.939581	+	0.342327i	$0.888785\pi$
$44$	1.65735	+	1.65735i	0.249855	+	0.249855i
$45$	1.87912	−	1.87912i	0.280123	−	0.280123i
$46$	3.97113	−	3.97113i	0.585511	−	0.585511i
$47$	4.03771	+	4.03771i	0.588960	+	0.588960i	0.937350	−	0.348390i	$-0.113271\pi$
$47$	4.03771	+	4.03771i	0.588960	+	0.588960i	−0.348390	+	0.937350i	$0.613271\pi$
$48$		−	9.70136i		−	1.40027i
$49$		0			0
$50$	3.74927	−	3.74927i	0.530227	−	0.530227i
$51$		−	12.7775i		−	1.78921i
$52$	1.88669	−	1.55450i	0.261637	−	0.215570i
$53$	−11.4505			−1.57285			−0.786425	−	0.617686i	$-0.788070\pi$
$53$	−11.4505			−1.57285			−0.786425	+	0.617686i	$0.788070\pi$
$54$	4.75565	−	4.75565i	0.647162	−	0.647162i
$55$			9.92337i			1.33807i
$56$		0			0
$57$	−4.25841	−	4.25841i	−0.564041	−	0.564041i
$58$	−5.09577	−	5.09577i	−0.669107	−	0.669107i
$59$	2.09403	+	2.09403i	0.272620	+	0.272620i	0.830154	−	0.557534i	$-0.188252\pi$
$59$	2.09403	+	2.09403i	0.272620	+	0.272620i	−0.557534	+	0.830154i	$0.688252\pi$
$60$	−2.72677	+	2.72677i	−0.352025	+	0.352025i
$61$			3.50457i			0.448714i	0.974507	+	0.224357i	$0.0720281\pi$
$61$			3.50457i			0.448714i	−0.974507	+	0.224357i	$0.927972\pi$
$62$	−5.48950			−0.697167
$63$		0			0
$64$		−	3.76085i		−	0.470107i
$65$	10.3020	+	0.994510i	1.27781	+	0.123354i
$66$		−	11.2089i		−	1.37972i
$67$	5.15836	+	5.15836i	0.630194	+	0.630194i	0.948117	−	0.317923i	$-0.102985\pi$
$67$	5.15836	+	5.15836i	0.630194	+	0.630194i	−0.317923	+	0.948117i	$0.602985\pi$
$68$			4.37240i			0.530231i
$69$	−6.79964			−0.818580
$70$		0			0
$71$	8.31408	+	8.31408i	0.986700	+	0.986700i	0.999913	−	0.0132127i	$-0.00420586\pi$
$71$	8.31408	+	8.31408i	0.986700	+	0.986700i	−0.0132127	+	0.999913i	$0.504206\pi$
$72$	−1.41620	+	1.41620i	−0.166900	+	0.166900i
$73$	3.30282	+	3.30282i	0.386566	+	0.386566i	0.873461	−	0.486895i	$-0.161870\pi$
$73$	3.30282	+	3.30282i	0.386566	+	0.386566i	−0.486895	+	0.873461i	$0.661870\pi$
$74$	−6.36984			−0.740479
$75$	−6.41975			−0.741289
$76$	1.45721	+	1.45721i	0.167153	+	0.167153i
$77$		0			0
$78$	−11.6366	−	1.12334i	−1.31759	−	0.127193i
$79$	1.08784			0.122391			0.0611957	−	0.998126i	$-0.480509\pi$
$79$	1.08784			0.122391			0.0611957	+	0.998126i	$0.480509\pi$
$80$	−9.93850	+	9.93850i	−1.11116	+	1.11116i
$81$	−10.9203			−1.21336
$82$	7.03523			0.776912
$83$	−2.01261	+	2.01261i	−0.220913	+	0.220913i	−0.808883	−	0.587970i	$-0.799927\pi$
$83$	−2.01261	+	2.01261i	−0.220913	+	0.220913i	0.587970	+	0.808883i	$0.299927\pi$
$84$		0			0
$85$	−13.0898	+	13.0898i	−1.41979	+	1.41979i
$86$	−5.19513	+	5.19513i	−0.560205	+	0.560205i
$87$			8.72532i			0.935452i
$88$		−	7.47873i		−	0.797235i
$89$	−3.50857	−	3.50857i	−0.371908	−	0.371908i	0.496264	−	0.868172i	$-0.334705\pi$
$89$	−3.50857	−	3.50857i	−0.371908	−	0.371908i	−0.868172	+	0.496264i	$0.834705\pi$
$90$	4.34887			0.458411
$91$		0			0
$92$	2.32680			0.242586
$93$	4.69974	+	4.69974i	0.487341	+	0.487341i
$94$			9.34450i			0.963811i
$95$			8.72501i			0.895167i
$96$	5.16402	−	5.16402i	0.527051	−	0.527051i
$97$	3.20816	−	3.20816i	0.325739	−	0.325739i	−0.525225	−	0.850964i	$-0.676019\pi$
$97$	3.20816	−	3.20816i	0.325739	−	0.325739i	0.850964	+	0.525225i	$0.176019\pi$
$98$		0			0
$99$	−2.26299	+	2.26299i	−0.227439	+	0.227439i
$100$	2.19681			0.219681
$101$	−9.14073			−0.909537			−0.454769	−	0.890610i	$-0.650278\pi$
$101$	−9.14073			−0.909537			−0.454769	+	0.890610i	$0.650278\pi$
$102$	14.7855	−	14.7855i	1.46399	−	1.46399i
$103$	−5.12360			−0.504843			−0.252421	−	0.967617i	$-0.581227\pi$
$103$	−5.12360			−0.504843			−0.252421	+	0.967617i	$0.581227\pi$
$104$	−7.76411	−	0.749511i	−0.761334	−	0.0734956i
$105$		0			0
$106$	−13.2500	−	13.2500i	−1.28696	−	1.28696i
$107$	−12.5537			−1.21361			−0.606804	−	0.794851i	$-0.707549\pi$
$107$	−12.5537			−1.21361			−0.606804	+	0.794851i	$0.707549\pi$
$108$	2.78647			0.268128
$109$	13.8075	+	13.8075i	1.32252	+	1.32252i	0.911732	+	0.410786i	$0.134746\pi$
$109$	13.8075	+	13.8075i	1.32252	+	1.32252i	0.410786	+	0.911732i	$0.365254\pi$
$110$	−11.4829	+	11.4829i	−1.09485	+	1.09485i
$111$	5.45344	+	5.45344i	0.517617	+	0.517617i
$112$		0			0
$113$	0.000230976	0		2.17284e−5	0		1.08642e−5	−	1.00000i	$-0.499997\pi$
$113$	0.000230976	0		2.17284e−5	0		1.08642e−5		1.00000i	$0.499997\pi$
$114$		−	9.85528i		−	0.923031i
$115$	6.96585	+	6.96585i	0.649569	+	0.649569i
$116$		−	2.98576i		−	0.277221i
$117$	2.12255	+	2.57614i	0.196230	+	0.238164i
$118$			4.84623i			0.446132i
$119$		0			0
$120$	12.3045			1.12324
$121$		−	0.950526i		−	0.0864115i
$122$	−4.05532	+	4.05532i	−0.367152	+	0.367152i
$123$	−6.02310	−	6.02310i	−0.543085	−	0.543085i
$124$	−1.60823	−	1.60823i	−0.144423	−	0.144423i
$125$	−3.57226	−	3.57226i	−0.319513	−	0.319513i
$126$		0			0
$127$		−	12.4887i		−	1.10820i	−0.832452	−	0.554098i	$-0.813063\pi$
$127$		−	12.4887i		−	1.10820i	0.832452	−	0.554098i	$-0.186937\pi$
$128$	9.56450	−	9.56450i	0.845390	−	0.845390i
$129$	8.89545			0.783201
$130$	10.7702	+	13.0718i	0.944613	+	1.14648i
$131$			13.5868i			1.18708i	0.804803	+	0.593542i	$0.202271\pi$
$131$			13.5868i			1.18708i	−0.804803	+	0.593542i	$0.797729\pi$
$132$	3.28380	−	3.28380i	0.285818	−	0.285818i
$133$		0			0
$134$			11.9380i			1.03129i
$135$	8.34199	+	8.34199i	0.717964	+	0.717964i
$136$	9.86513	−	9.86513i	0.845928	−	0.845928i
$137$	0.955848	−	0.955848i	0.0816636	−	0.0816636i	−0.665095	−	0.746759i	$-0.731609\pi$
$137$	0.955848	−	0.955848i	0.0816636	−	0.0816636i	0.746759	+	0.665095i	$0.231609\pi$
$138$	−7.86823	−	7.86823i	−0.669788	−	0.669788i
$139$			18.8190i			1.59621i	0.602521	+	0.798103i	$0.294163\pi$
$139$			18.8190i			1.59621i	−0.602521	+	0.798103i	$0.705837\pi$
$140$		0			0
$141$	8.00014	−	8.00014i	0.673733	−	0.673733i
$142$			19.2413i			1.61470i
$143$	−12.4065	−	1.19767i	−1.03749	−	0.100154i
$144$	−4.53288			−0.377740
$145$	8.93860	−	8.93860i	0.742310	−	0.742310i
$146$			7.64375i			0.632601i
$147$		0			0
$148$	−1.86614	−	1.86614i	−0.153396	−	0.153396i
$149$	−15.0822	−	15.0822i	−1.23558	−	1.23558i	−0.961790	−	0.273789i	$-0.911723\pi$
$149$	−15.0822	−	15.0822i	−1.23558	−	1.23558i	−0.273789	−	0.961790i	$-0.588277\pi$
$150$	−7.42864	−	7.42864i	−0.606546	−	0.606546i
$151$	11.9297	−	11.9297i	0.970828	−	0.970828i	−0.0287588	−	0.999586i	$-0.509155\pi$
$151$	11.9297	−	11.9297i	0.970828	−	0.970828i	0.999586	+	0.0287588i	$0.00915547\pi$
$152$		−	6.57559i		−	0.533351i
$153$	−5.97019			−0.482661
$154$		0			0
$155$		−	9.62925i		−	0.773440i
$156$	−3.08001	−	3.73821i	−0.246598	−	0.299296i
$157$		−	10.9269i		−	0.872061i	−0.899932	−	0.436031i	$-0.856384\pi$
$157$		−	10.9269i		−	0.872061i	0.899932	−	0.436031i	$-0.143616\pi$
$158$	1.25880	+	1.25880i	0.100145	+	0.100145i
$159$			22.6876i			1.79924i
$160$	−10.5805			−0.836462
$161$		0			0
$162$	−12.6364	−	12.6364i	−0.992811	−	0.992811i
$163$	−6.13353	+	6.13353i	−0.480415	+	0.480415i	−0.905264	−	0.424849i	$-0.860327\pi$
$163$	−6.13353	+	6.13353i	−0.480415	+	0.480415i	0.424849	+	0.905264i	$0.360327\pi$
$164$	2.06107	+	2.06107i	0.160943	+	0.160943i
$165$	19.6617			1.53066
$166$	−4.65780			−0.361515
$167$	8.00174	+	8.00174i	0.619193	+	0.619193i	0.945324	−	0.326131i	$-0.105745\pi$
$167$	8.00174	+	8.00174i	0.619193	+	0.619193i	−0.326131	+	0.945324i	$0.605745\pi$
$168$		0			0
$169$	−2.48674	+	12.7599i	−0.191288	+	0.981534i
$170$	−30.2939			−2.32344
$171$	−1.98971	+	1.98971i	−0.152157	+	0.152157i
$172$	−3.04398			−0.232101
$173$	3.27667			0.249121			0.124560	−	0.992212i	$-0.460248\pi$
$173$	3.27667			0.249121			0.124560	+	0.992212i	$0.460248\pi$
$174$	−10.0965	+	10.0965i	−0.765416	+	0.765416i
$175$		0			0
$176$	11.9687	−	11.9687i	0.902178	−	0.902178i
$177$	4.14902	−	4.14902i	0.311860	−	0.311860i
$178$		−	8.11991i		−	0.608613i
$179$			2.25009i			0.168179i	0.996458	+	0.0840897i	$0.0267982\pi$
$179$			2.25009i			0.168179i	−0.996458	+	0.0840897i	$0.973202\pi$
$180$	1.27406	+	1.27406i	0.0949630	+	0.0949630i
$181$	15.5420			1.15523			0.577615	−	0.816310i	$-0.303984\pi$
$181$	15.5420			1.15523			0.577615	+	0.816310i	$0.303984\pi$
$182$		0			0
$183$	6.94380			0.513300
$184$	−5.24980	−	5.24980i	−0.387020	−	0.387020i
$185$		−	11.1735i		−	0.821491i
$186$			10.8767i			0.797515i
$187$	15.7638	−	15.7638i	1.15277	−	1.15277i
$188$	−2.73761	+	2.73761i	−0.199660	+	0.199660i
$189$		0			0
$190$	−10.0962	+	10.0962i	−0.732454	+	0.732454i
$191$	−2.37794			−0.172062			−0.0860308	−	0.996292i	$-0.527418\pi$
$191$	−2.37794			−0.172062			−0.0860308	+	0.996292i	$0.527418\pi$
$192$	−7.45159			−0.537772
$193$	−5.51979	+	5.51979i	−0.397323	+	0.397323i	−0.877288	−	0.479965i	$-0.840649\pi$
$193$	−5.51979	+	5.51979i	−0.397323	+	0.397323i	0.479965	+	0.877288i	$0.340649\pi$
$194$	7.42466			0.533060
$195$	1.97048	−	20.4120i	0.141109	−	1.46173i
$196$		0			0
$197$	−10.9402	−	10.9402i	−0.779454	−	0.779454i	0.200284	−	0.979738i	$-0.435813\pi$
$197$	−10.9402	−	10.9402i	−0.779454	−	0.779454i	−0.979738	+	0.200284i	$0.935813\pi$
$198$	−5.23726			−0.372196
$199$	−20.1735			−1.43006			−0.715031	−	0.699092i	$-0.753588\pi$
$199$	−20.1735			−1.43006			−0.715031	+	0.699092i	$0.753588\pi$
$200$	−4.95650	−	4.95650i	−0.350477	−	0.350477i
$201$	10.2206	−	10.2206i	0.720902	−	0.720902i
$202$	−10.5772	−	10.5772i	−0.744212	−	0.744212i
$203$		0			0
$204$	8.66327			0.606551
$205$			12.3407i			0.861909i
$206$	−5.92879	−	5.92879i	−0.413078	−	0.413078i
$207$			3.17707i			0.220822i
$208$	−11.2260	−	13.6250i	−0.778381	−	0.944721i
$209$		−	10.5074i		−	0.726809i
$210$		0			0
$211$	2.36943			0.163118			0.0815591	−	0.996669i	$-0.474010\pi$
$211$	2.36943			0.163118			0.0815591	+	0.996669i	$0.474010\pi$
$212$		−	7.76356i		−	0.533204i
$213$	16.4732	−	16.4732i	1.12872	−	1.12872i
$214$	−14.5265	−	14.5265i	−0.993012	−	0.993012i
$215$	−9.11289	−	9.11289i	−0.621494	−	0.621494i
$216$	−6.28693	−	6.28693i	−0.427771	−	0.427771i
$217$		0			0
$218$			31.9548i			2.16425i
$219$	6.54407	−	6.54407i	0.442207	−	0.442207i
$220$	−6.72814			−0.453611
$221$	−14.7855	−	17.9452i	−0.994583	−	1.20713i
$222$			12.6209i			0.847061i
$223$	−9.67825	+	9.67825i	−0.648103	+	0.648103i	−0.952534	−	0.304431i	$-0.901534\pi$
$223$	−9.67825	+	9.67825i	−0.648103	+	0.648103i	0.304431	+	0.952534i	$0.401534\pi$
$224$		0			0
$225$			2.99958i			0.199972i
$226$	0.000267274	0	0.000267274i	1.77788e−5	0	1.77788e-5i
$227$	9.21946	−	9.21946i	0.611917	−	0.611917i	−0.331528	−	0.943445i	$-0.607564\pi$
$227$	9.21946	−	9.21946i	0.611917	−	0.611917i	0.943445	+	0.331528i	$0.107564\pi$
$228$	2.88724	−	2.88724i	0.191212	−	0.191212i
$229$	−10.7471	−	10.7471i	−0.710191	−	0.710191i	0.256384	−	0.966575i	$-0.417469\pi$
$229$	−10.7471	−	10.7471i	−0.710191	−	0.710191i	−0.966575	+	0.256384i	$0.917469\pi$
$230$			16.1211i			1.06299i
$231$		0			0
$232$	−6.73656	+	6.73656i	−0.442277	+	0.442277i
$233$		−	7.73487i		−	0.506728i	−0.967371	−	0.253364i	$-0.918463\pi$
$233$		−	7.73487i		−	0.506728i	0.967371	−	0.253364i	$-0.0815370\pi$
$234$	−0.524873	+	5.43711i	−0.0343120	+	0.355435i
$235$	−16.3914			−1.06926
$236$	−1.41977	+	1.41977i	−0.0924194	+	0.0924194i
$237$		−	2.15540i		−	0.140008i
$238$		0			0
$239$	2.10971	+	2.10971i	0.136466	+	0.136466i	0.772040	−	0.635574i	$-0.219237\pi$
$239$	2.10971	+	2.10971i	0.136466	+	0.136466i	−0.635574	+	0.772040i	$0.719237\pi$
$240$	19.6917	+	19.6917i	1.27109	+	1.27109i
$241$	18.6721	+	18.6721i	1.20278	+	1.20278i	0.973318	+	0.229460i	$0.0736959\pi$
$241$	18.6721	+	18.6721i	1.20278	+	1.20278i	0.229460	+	0.973318i	$0.426304\pi$
$242$	1.09991	−	1.09991i	0.0707046	−	0.0707046i
$243$			9.30758i			0.597082i
$244$	−2.37613			−0.152116
$245$		0			0
$246$		−	13.9393i		−	0.888738i
$247$	−10.9083	−	1.05304i	−0.694079	−	0.0670032i
$248$			7.25706i			0.460824i
$249$	3.98770	+	3.98770i	0.252710	+	0.252710i
$250$		−	8.26732i		−	0.522871i
$251$	−7.06132			−0.445707			−0.222853	−	0.974852i	$-0.571537\pi$
$251$	−7.06132			−0.445707			−0.222853	+	0.974852i	$0.571537\pi$
$252$		0			0
$253$	−8.38884	−	8.38884i	−0.527402	−	0.527402i
$254$	14.4514	−	14.4514i	0.906760	−	0.906760i
$255$	25.9356	+	25.9356i	1.62415	+	1.62415i
$256$	14.6135			0.913342
$257$	13.0534			0.814250			0.407125	−	0.913373i	$-0.366531\pi$
$257$	13.0534			0.814250			0.407125	+	0.913373i	$0.366531\pi$
$258$	10.2934	+	10.2934i	0.640839	+	0.640839i
$259$		0			0
$260$	−0.674288	+	6.98488i	−0.0418175	+	0.433184i
$261$	4.07683			0.252350
$262$	−15.7220	+	15.7220i	−0.971309	+	0.971309i
$263$	22.3346			1.37721			0.688606	−	0.725136i	$-0.258223\pi$
$263$	22.3346			1.37721			0.688606	+	0.725136i	$0.258223\pi$
$264$	−14.8180			−0.911987
$265$	23.2421	−	23.2421i	1.42775	−	1.42775i
$266$		0			0
$267$	−6.95173	+	6.95173i	−0.425439	+	0.425439i
$268$	−3.49742	+	3.49742i	−0.213639	+	0.213639i
$269$			3.13431i			0.191102i	0.995425	+	0.0955511i	$0.0304613\pi$
$269$			3.13431i			0.191102i	−0.995425	+	0.0955511i	$0.969539\pi$
$270$			19.3059i			1.17492i
$271$	11.1792	+	11.1792i	0.679088	+	0.679088i	0.959794	−	0.280706i	$-0.0905686\pi$
$271$	11.1792	+	11.1792i	0.679088	+	0.679088i	−0.280706	+	0.959794i	$0.590569\pi$
$272$	31.5757			1.91456
$273$		0			0
$274$	2.21213			0.133639
$275$	−7.92017	−	7.92017i	−0.477604	−	0.477604i
$276$		−	4.61022i		−	0.277503i
$277$			29.4841i			1.77153i	0.464134	+	0.885765i	$0.346366\pi$
$277$			29.4841i			1.77153i	−0.464134	+	0.885765i	$0.653634\pi$
$278$	−21.7765	+	21.7765i	−1.30607	+	1.30607i
$279$	2.19592	−	2.19592i	0.131466	−	0.131466i
$280$		0			0
$281$	16.8969	−	16.8969i	1.00798	−	1.00798i	0.00801615	−	0.999968i	$-0.497448\pi$
$281$	16.8969	−	16.8969i	1.00798	−	1.00798i	0.999968	−	0.00801615i	$-0.00255165\pi$
$282$	18.5148			1.10254
$283$	9.33438			0.554871			0.277436	−	0.960744i	$-0.410515\pi$
$283$	9.33438			0.554871			0.277436	+	0.960744i	$0.410515\pi$
$284$	−5.63703	+	5.63703i	−0.334496	+	0.334496i
$285$	17.2874			1.02401
$286$	−12.9704	−	15.7422i	−0.766956	−	0.930854i
$287$		0			0
$288$	−2.41285	−	2.41285i	−0.142178	−	0.142178i
$289$	24.5879			1.44635
$290$	20.6867			1.21476
$291$	−6.35650	−	6.35650i	−0.372625	−	0.372625i
$292$	−2.23935	+	2.23935i	−0.131048	+	0.131048i
$293$	−2.08232	−	2.08232i	−0.121650	−	0.121650i	0.643661	−	0.765311i	$-0.277415\pi$
$293$	−2.08232	−	2.08232i	−0.121650	−	0.121650i	−0.765311	+	0.643661i	$0.777415\pi$
$294$		0			0
$295$	−8.50088			−0.494940
$296$			8.42087i			0.489453i
$297$	−10.0461	−	10.0461i	−0.582934	−	0.582934i
$298$		−	34.9048i		−	2.02198i
$299$	−9.54967	+	7.86823i	−0.552272	+	0.455031i
$300$		−	4.35265i		−	0.251301i
$301$		0			0
$302$	27.6091			1.58872
$303$			18.1111i			1.04045i
$304$	10.5234	−	10.5234i	0.603557	−	0.603557i
$305$	−7.11353	−	7.11353i	−0.407319	−	0.407319i
$306$	−6.90842	−	6.90842i	−0.394928	−	0.394928i
$307$	3.85597	+	3.85597i	0.220072	+	0.220072i	0.808529	−	0.588457i	$-0.200264\pi$
$307$	3.85597	+	3.85597i	0.220072	+	0.220072i	−0.588457	+	0.808529i	$0.700264\pi$
$308$		0			0
$309$			10.1517i			0.577508i
$310$	11.1425	−	11.1425i	0.632852	−	0.632852i
$311$	−14.0750			−0.798120			−0.399060	−	0.916925i	$-0.630663\pi$
$311$	−14.0750			−0.798120			−0.399060	+	0.916925i	$0.630663\pi$
$312$	−1.48505	+	15.3835i	−0.0840743	+	0.870918i
$313$		−	4.70655i		−	0.266030i	−0.991114	−	0.133015i	$-0.957534\pi$
$313$		−	4.70655i		−	0.266030i	0.991114	−	0.133015i	$-0.0424658\pi$
$314$	12.6441	−	12.6441i	0.713548	−	0.713548i
$315$		0			0
$316$			0.737566i			0.0414913i
$317$	20.7068	+	20.7068i	1.16301	+	1.16301i	0.983814	+	0.179195i	$0.0573492\pi$
$317$	20.7068	+	20.7068i	1.16301	+	1.16301i	0.179195	+	0.983814i	$0.442651\pi$
$318$	−26.2530	+	26.2530i	−1.47220	+	1.47220i
$319$	−10.7646	+	10.7646i	−0.602701	+	0.602701i
$320$	7.63373	+	7.63373i	0.426739	+	0.426739i
$321$			24.8733i			1.38829i
$322$		0			0
$323$	13.8602	−	13.8602i	0.771201	−	0.771201i
$324$		−	7.40404i		−	0.411336i
$325$	−9.01614	+	7.42864i	−0.500126	+	0.412067i
$326$	−14.1949			−0.786181
$327$	27.3576	−	27.3576i	1.51288	−	1.51288i
$328$		−	9.30051i		−	0.513535i
$329$		0			0
$330$	22.7516	+	22.7516i	1.25244	+	1.25244i
$331$	10.4784	+	10.4784i	0.575946	+	0.575946i	0.933784	−	0.357838i	$-0.116486\pi$
$331$	10.4784	+	10.4784i	0.575946	+	0.575946i	−0.357838	+	0.933784i	$0.616486\pi$
$332$	−1.36457	−	1.36457i	−0.0748905	−	0.0748905i
$333$	2.54807	−	2.54807i	0.139634	−	0.139634i
$334$			18.5185i			1.01329i
$335$	−20.9408			−1.14412
$336$		0			0
$337$			9.51919i			0.518543i	0.965804	+	0.259272i	$0.0834825\pi$
$337$			9.51919i			0.518543i	−0.965804	+	0.259272i	$0.916518\pi$
$338$	−17.6428	+	11.8877i	−0.959640	+	0.646604i
$339$		0	0.000457645i		0	2.48559e-5i
$340$	−8.87504	−	8.87504i	−0.481317	−	0.481317i
$341$			11.5963i			0.627976i
$342$	−4.60480			−0.248999
$343$		0			0
$344$	6.86791	+	6.86791i	0.370293	+	0.370293i
$345$	13.8018	−	13.8018i	0.743065	−	0.743065i
$346$	3.79161	+	3.79161i	0.203838	+	0.203838i
$347$	−35.1298			−1.88587			−0.942933	−	0.332983i	$-0.891945\pi$
$347$	−35.1298			−1.88587			−0.942933	+	0.332983i	$0.891945\pi$
$348$	−5.91585			−0.317123
$349$	6.64759	+	6.64759i	0.355837	+	0.355837i	0.862276	−	0.506439i	$-0.169038\pi$
$349$	6.64759	+	6.64759i	0.355837	+	0.355837i	−0.506439	+	0.862276i	$0.669038\pi$
$350$		0			0
$351$	−11.4363	+	9.42264i	−0.610422	+	0.502943i
$352$	12.7419			0.679145
$353$	−8.74920	+	8.74920i	−0.465673	+	0.465673i	−0.900509	−	0.434837i	$-0.856806\pi$
$353$	−8.74920	+	8.74920i	−0.465673	+	0.465673i	0.434837	+	0.900509i	$0.356806\pi$
$354$	9.60211			0.510347
$355$	−33.7517			−1.79135
$356$	2.37885	−	2.37885i	0.126079	−	0.126079i
$357$		0			0
$358$	−2.60370	+	2.60370i	−0.137610	+	0.137610i
$359$	−3.03173	+	3.03173i	−0.160009	+	0.160009i	−0.782571	−	0.622562i	$-0.786092\pi$
$359$	−3.03173	+	3.03173i	−0.160009	+	0.160009i	0.622562	+	0.782571i	$0.286092\pi$
$360$		−	5.74916i		−	0.303007i
$361$			9.76152i			0.513764i
$362$	17.9845	+	17.9845i	0.945245	+	0.945245i
$363$	−1.88333			−0.0988493
$364$		0			0
$365$	−13.4081			−0.701810
$366$	8.03504	+	8.03504i	0.419998	+	0.419998i
$367$		−	24.7345i		−	1.29113i	−0.763705	−	0.645565i	$-0.776622\pi$
$367$		−	24.7345i		−	1.29113i	0.763705	−	0.645565i	$-0.223378\pi$
$368$		−	16.8032i		−	0.875930i
$369$	−2.81424	+	2.81424i	−0.146504	+	0.146504i
$370$	12.9294	−	12.9294i	0.672169	−	0.672169i
$371$		0			0
$372$	−3.18647	+	3.18647i	−0.165211	+	0.165211i
$373$	−7.91354			−0.409747			−0.204874	−	0.978788i	$-0.565678\pi$
$373$	−7.91354			−0.409747			−0.204874	+	0.978788i	$0.565678\pi$
$374$	36.4824			1.88646
$375$	−7.07793	+	7.07793i	−0.365503	+	0.365503i
$376$	12.3533			0.637075
$377$	10.0965	+	12.2542i	0.519998	+	0.631122i
$378$		0			0
$379$	3.32389	+	3.32389i	0.170737	+	0.170737i	0.787303	−	0.616566i	$-0.211477\pi$
$379$	3.32389	+	3.32389i	0.170737	+	0.170737i	−0.616566	+	0.787303i	$0.711477\pi$
$380$	−5.91564			−0.303466
$381$	−24.7446			−1.26771
$382$	−2.75164	−	2.75164i	−0.140786	−	0.140786i
$383$	−6.40422	+	6.40422i	−0.327241	+	0.327241i	−0.851536	−	0.524296i	$-0.824329\pi$
$383$	−6.40422	+	6.40422i	−0.327241	+	0.327241i	0.524296	+	0.851536i	$0.324329\pi$
$384$	−18.9507	−	18.9507i	−0.967072	−	0.967072i
$385$		0			0
$386$	−12.7745			−0.650204
$387$		−	4.15633i		−	0.211278i
$388$	2.17516	+	2.17516i	0.110427	+	0.110427i
$389$		−	21.4608i		−	1.08811i	−0.839051	−	0.544053i	$-0.816889\pi$
$389$		−	21.4608i		−	1.08811i	0.839051	−	0.544053i	$-0.183111\pi$
$390$	25.9000	−	21.3397i	1.31150	−	1.08058i
$391$		−	22.1313i		−	1.11923i
$392$		0			0
$393$	26.9203			1.35795
$394$		−	25.3189i		−	1.27555i
$395$	−2.20808	+	2.20808i	−0.111101	+	0.111101i
$396$	−1.53433	−	1.53433i	−0.0771030	−	0.0771030i
$397$	9.24490	+	9.24490i	0.463988	+	0.463988i	0.899960	−	0.435972i	$-0.143595\pi$
$397$	9.24490	+	9.24490i	0.463988	+	0.463988i	−0.435972	+	0.899960i	$0.643595\pi$
$398$	−23.3439	−	23.3439i	−1.17012	−	1.17012i
$399$		0			0
$400$		−	15.8645i		−	0.793224i
$401$	−15.0072	+	15.0072i	−0.749423	+	0.749423i	−0.974371	−	0.224948i	$-0.927779\pi$
$401$	−15.0072	+	15.0072i	−0.749423	+	0.749423i	0.224948	+	0.974371i	$0.427779\pi$
$402$	23.6535			1.17973
$403$	12.0388	+	1.16217i	0.599696	+	0.0578919i
$404$		−	6.19751i		−	0.308337i
$405$	22.1658	−	22.1658i	1.10143	−	1.10143i
$406$		0			0
$407$			13.4560i			0.666990i
$408$	−19.5463	−	19.5463i	−0.967688	−	0.967688i
$409$	6.02317	−	6.02317i	0.297827	−	0.297827i	−0.542335	−	0.840162i	$-0.682460\pi$
$409$	6.02317	−	6.02317i	0.297827	−	0.297827i	0.840162	+	0.542335i	$0.182460\pi$
$410$	−14.2800	+	14.2800i	−0.705241	+	0.705241i
$411$	−1.89388	−	1.89388i	−0.0934180	−	0.0934180i
$412$		−	3.47385i		−	0.171144i
$413$		0			0
$414$	−3.67636	+	3.67636i	−0.180683	+	0.180683i
$415$		−	8.17035i		−	0.401067i
$416$	1.27698	−	13.2281i	0.0626091	−	0.648561i
$417$	37.2871			1.82596
$418$	12.1586	−	12.1586i	0.594698	−	0.594698i
$419$		−	8.39090i		−	0.409922i	−0.978770	−	0.204961i	$-0.934293\pi$
$419$		−	8.39090i		−	0.409922i	0.978770	−	0.204961i	$-0.0657068\pi$
$420$		0			0
$421$	20.5414	+	20.5414i	1.00113	+	1.00113i	0.999999	+	0.00112764i	$0.000358939\pi$
$421$	20.5414	+	20.5414i	1.00113	+	1.00113i	0.00112764	+	0.999999i	$0.499641\pi$
$422$	2.74179	+	2.74179i	0.133468	+	0.133468i
$423$	−3.73800	−	3.73800i	−0.181748	−	0.181748i
$424$	−17.5164	+	17.5164i	−0.850671	+	0.850671i
$425$		−	20.8949i		−	1.01355i
$426$	38.1240			1.84711
$427$		0			0
$428$		−	8.51150i		−	0.411419i
$429$	−2.37301	+	24.5818i	−0.114570	+	1.18682i
$430$		−	21.0900i		−	1.01705i
$431$	7.07391	+	7.07391i	0.340738	+	0.340738i	0.856645	−	0.515907i	$-0.172545\pi$
$431$	7.07391	+	7.07391i	0.340738	+	0.340738i	−0.515907	+	0.856645i	$0.672545\pi$
$432$		−	20.1228i		−	0.968160i
$433$	−41.3846			−1.98882			−0.994409	−	0.105595i	$-0.966325\pi$
$433$	−41.3846			−1.98882			−0.994409	+	0.105595i	$0.966325\pi$
$434$		0			0
$435$	−17.7105	−	17.7105i	−0.849156	−	0.849156i
$436$	−9.36161	+	9.36161i	−0.448340	+	0.448340i
$437$	−7.37579	−	7.37579i	−0.352832	−	0.352832i
$438$	15.1450			0.723655
$439$	−0.142577			−0.00680482			−0.00340241	−	0.999994i	$-0.501083\pi$
$439$	−0.142577			−0.00680482			−0.00340241	+	0.999994i	$0.501083\pi$
$440$	15.1802	+	15.1802i	0.723689	+	0.723689i
$441$		0			0
$442$	3.65623	−	37.8745i	0.173909	−	1.80151i
$443$	25.8736			1.22929			0.614647	−	0.788803i	$-0.289299\pi$
$443$	25.8736			1.22929			0.614647	+	0.788803i	$0.289299\pi$
$444$	−3.69748	+	3.69748i	−0.175475	+	0.175475i
$445$	14.2433			0.675198
$446$	−22.3984			−1.06060
$447$	−29.8831	+	29.8831i	−1.41342	+	1.41342i
$448$		0			0
$449$	1.26645	−	1.26645i	0.0597675	−	0.0597675i	−0.676591	−	0.736359i	$-0.736544\pi$
$449$	1.26645	−	1.26645i	0.0597675	−	0.0597675i	0.736359	+	0.676591i	$0.236544\pi$
$450$	−3.47097	+	3.47097i	−0.163623	+	0.163623i
$451$		−	14.8616i		−	0.699806i
$452$		0	0.000156604i		0	7.36602e-6i
$453$	−23.6370	−	23.6370i	−1.11057	−	1.11057i
$454$	21.3367			1.00138
$455$		0			0
$456$	−13.0286			−0.610119
$457$	−3.29682	−	3.29682i	−0.154219	−	0.154219i	0.625781	−	0.779999i	$-0.284781\pi$
$457$	−3.29682	−	3.29682i	−0.154219	−	0.154219i	−0.779999	+	0.625781i	$0.784781\pi$
$458$		−	24.8722i		−	1.16220i
$459$		−	26.5035i		−	1.23708i
$460$	−4.72291	+	4.72291i	−0.220207	+	0.220207i
$461$	−3.60896	+	3.60896i	−0.168086	+	0.168086i	−0.786137	−	0.618052i	$-0.787922\pi$
$461$	−3.60896	+	3.60896i	−0.168086	+	0.168086i	0.618052	+	0.786137i	$0.287922\pi$
$462$		0			0
$463$	−4.00230	+	4.00230i	−0.186003	+	0.186003i	−0.793965	−	0.607963i	$-0.791987\pi$
$463$	−4.00230	+	4.00230i	−0.186003	+	0.186003i	0.607963	+	0.793965i	$0.291987\pi$
$464$	−21.5620			−1.00099
$465$	−19.0790			−0.884766
$466$	8.95043	−	8.95043i	0.414621	−	0.414621i
$467$	−40.0619			−1.85384			−0.926921	−	0.375257i	$-0.877555\pi$
$467$	−40.0619			−1.85384			−0.926921	+	0.375257i	$0.877555\pi$
$468$	−1.74665	+	1.43911i	−0.0807388	+	0.0665228i
$469$		0			0
$470$	−18.9674	−	18.9674i	−0.874899	−	0.874899i
$471$	−21.6501			−0.997583
$472$	6.40667			0.294891
$473$	10.9745	+	10.9745i	0.504607	+	0.504607i
$474$	2.49413	−	2.49413i	0.114559	−	0.114559i
$475$	−6.96371	−	6.96371i	−0.319517	−	0.319517i
$476$		0			0
$477$	10.6006			0.485367
$478$			4.88252i			0.223321i
$479$	8.33722	+	8.33722i	0.380937	+	0.380937i	0.871440	−	0.490503i	$-0.163187\pi$
$479$	8.33722	+	8.33722i	0.380937	+	0.380937i	−0.490503	+	0.871440i	$0.663187\pi$
$480$			20.9637i			0.956859i
$481$	13.9695	+	1.34855i	0.636953	+	0.0614885i
$482$			43.2131i			1.96830i
$483$		0			0
$484$	0.644466			0.0292939
$485$			13.0238i			0.591379i
$486$	−10.7703	+	10.7703i	−0.488551	+	0.488551i
$487$	0.389122	+	0.389122i	0.0176328	+	0.0176328i	0.715868	−	0.698235i	$-0.246031\pi$
$487$	0.389122	+	0.389122i	0.0176328	+	0.0176328i	−0.698235	+	0.715868i	$0.746031\pi$
$488$	5.36110	+	5.36110i	0.242686	+	0.242686i
$489$	12.1527	+	12.1527i	0.549564	+	0.549564i
$490$		0			0
$491$		−	3.02403i		−	0.136472i	−0.997669	−	0.0682362i	$-0.978263\pi$
$491$		−	3.02403i		−	0.136472i	0.997669	−	0.0682362i	$-0.0217372\pi$
$492$	4.08372	−	4.08372i	0.184108	−	0.184108i
$493$	−28.3990			−1.27902
$494$	−11.4041	−	13.8411i	−0.513093	−	0.622742i
$495$		−	9.18678i		−	0.412915i
$496$	−11.6140	+	11.6140i	−0.521484	+	0.521484i
$497$		0			0
$498$			9.22876i			0.413551i
$499$	−27.1172	−	27.1172i	−1.21393	−	1.21393i	−0.969723	−	0.244208i	$-0.921472\pi$
$499$	−27.1172	−	27.1172i	−1.21393	−	1.21393i	−0.244208	−	0.969723i	$-0.578528\pi$
$500$	2.42203	−	2.42203i	0.108316	−	0.108316i
$501$	15.8543	−	15.8543i	0.708317	−	0.708317i
$502$	−8.17104	−	8.17104i	−0.364691	−	0.364691i
$503$		−	27.2615i		−	1.21553i	−0.794117	−	0.607765i	$-0.792066\pi$
$503$		−	27.2615i		−	1.21553i	0.794117	−	0.607765i	$-0.207934\pi$
$504$		0			0
$505$	18.5538	−	18.5538i	0.825631	−	0.825631i
$506$		−	19.4143i		−	0.863073i
$507$	25.2820	+	4.92712i	1.12281	+	0.218821i
$508$	8.46748			0.375684
$509$	−12.7798	+	12.7798i	−0.566454	+	0.566454i	−0.931133	−	0.364679i	$-0.881179\pi$
$509$	−12.7798	+	12.7798i	−0.566454	+	0.566454i	0.364679	+	0.931133i	$0.381179\pi$
$510$			60.0230i			2.65786i
$511$		0			0
$512$	−2.21895	−	2.21895i	−0.0980646	−	0.0980646i
$513$	−8.83292	−	8.83292i	−0.389983	−	0.389983i
$514$	15.1048	+	15.1048i	0.666245	+	0.666245i
$515$	10.3998	−	10.3998i	0.458271	−	0.458271i
$516$			6.03120i			0.265509i
$517$	19.7398			0.868157
$518$		0			0
$519$		−	6.49225i		−	0.284978i
$520$	17.2809	−	14.2382i	0.757815	−	0.624384i
$521$			11.5778i			0.507231i	0.967305	+	0.253616i	$0.0816198\pi$
$521$			11.5778i			0.507231i	−0.967305	+	0.253616i	$0.918380\pi$
$522$	4.71752	+	4.71752i	0.206480	+	0.206480i
$523$			9.65911i			0.422363i	0.977447	+	0.211182i	$0.0677312\pi$
$523$			9.65911i			0.422363i	−0.977447	+	0.211182i	$0.932269\pi$
$524$	−9.21198			−0.402427
$525$		0			0
$526$	25.8446	+	25.8446i	1.12688	+	1.12688i
$527$	−15.2966	+	15.2966i	−0.666331	+	0.666331i
$528$	−23.7143	−	23.7143i	−1.03203	−	1.03203i
$529$	11.2227			0.487943
$530$	53.7894			2.33646
$531$	−1.93860	−	1.93860i	−0.0841279	−	0.0841279i
$532$		0			0
$533$	−15.4287	−	1.48942i	−0.668292	−	0.0645138i
$534$	−16.0884			−0.696215
$535$	25.4813	−	25.4813i	1.10165	−	1.10165i
$536$	15.7820			0.681677
$537$	4.45823			0.192387
$538$	−3.62688	+	3.62688i	−0.156366	+	0.156366i
$539$		0			0
$540$	−5.65595	+	5.65595i	−0.243393	+	0.243393i
$541$	21.5333	−	21.5333i	0.925791	−	0.925791i	−0.0716399	−	0.997431i	$-0.522823\pi$
$541$	21.5333	−	21.5333i	0.925791	−	0.925791i	0.997431	+	0.0716399i	$0.0228232\pi$
$542$			25.8721i			1.11130i
$543$		−	30.7943i		−	1.32151i
$544$	16.8077	+	16.8077i	0.720625	+	0.720625i
$545$	−56.0526			−2.40103
$546$		0			0
$547$	41.0288			1.75427			0.877133	−	0.480247i	$-0.159453\pi$
$547$	41.0288			1.75427			0.877133	+	0.480247i	$0.159453\pi$
$548$	0.648074	+	0.648074i	0.0276844	+	0.0276844i
$549$		−	3.24443i		−	0.138469i
$550$		−	18.3297i		−	0.781581i
$551$	−9.46464	+	9.46464i	−0.403207	+	0.403207i
$552$	−10.4017	+	10.4017i	−0.442727	+	0.442727i
$553$		0			0
$554$	−34.1177	+	34.1177i	−1.44952	+	1.44952i
$555$	−22.1386			−0.939733
$556$	−12.7595			−0.541122
$557$	2.79438	−	2.79438i	0.118402	−	0.118402i	−0.645423	−	0.763825i	$-0.723319\pi$
$557$	2.79438	−	2.79438i	0.118402	−	0.118402i	0.763825	+	0.645423i	$0.223319\pi$
$558$	5.08203			0.215139
$559$	12.4931	−	10.2934i	0.528402	−	0.435365i
$560$		0			0
$561$	−31.2338	−	31.2338i	−1.31869	−	1.31869i
$562$	39.1046			1.64953
$563$	−29.7553			−1.25404			−0.627018	−	0.779004i	$-0.715725\pi$
$563$	−29.7553			−1.25404			−0.627018	+	0.779004i	$0.715725\pi$
$564$	5.42417	+	5.42417i	0.228399	+	0.228399i
$565$	−0.000468832	0	0.000468832i	−1.97239e−5	0	1.97239e-5i
$566$	10.8013	+	10.8013i	0.454013	+	0.454013i
$567$		0			0
$568$	25.4369			1.06731
$569$		−	11.9282i		−	0.500057i	−0.968239	−	0.250028i	$-0.919560\pi$
$569$		−	11.9282i		−	0.500057i	0.968239	−	0.250028i	$-0.0804400\pi$
$570$	20.0041	+	20.0041i	0.837881	+	0.837881i
$571$			11.4760i			0.480256i	0.970741	+	0.240128i	$0.0771894\pi$
$571$			11.4760i			0.480256i	−0.970741	+	0.240128i	$0.922811\pi$
$572$	0.812032	−	8.41176i	0.0339527	−	0.351713i
$573$			4.71154i			0.196828i
$574$		0			0
$575$	−11.1193			−0.463708
$576$			3.48169i			0.145071i
$577$	−2.72055	+	2.72055i	−0.113258	+	0.113258i	−0.761465	−	0.648207i	$-0.775519\pi$
$577$	−2.72055	+	2.72055i	−0.113258	+	0.113258i	0.648207	+	0.761465i	$0.275519\pi$
$578$	28.4520	+	28.4520i	1.18345	+	1.18345i
$579$	10.9367	+	10.9367i	0.454512	+	0.454512i
$580$	6.06046	+	6.06046i	0.251647	+	0.251647i
$581$		0			0
$582$		−	14.7109i		−	0.609787i
$583$	−27.9901	+	27.9901i	−1.15923	+	1.15923i
$584$	10.1050			0.418146
$585$	−9.53734	−	0.920690i	−0.394321	−	0.0380659i
$586$		−	4.81912i		−	0.199076i
$587$	26.9080	−	26.9080i	1.11061	−	1.11061i	0.117543	−	0.993068i	$-0.462498\pi$
$587$	26.9080	−	26.9080i	1.11061	−	1.11061i	0.993068	−	0.117543i	$-0.0375018\pi$
$588$		0			0
$589$			10.1959i			0.420116i
$590$	−9.83683	−	9.83683i	−0.404976	−	0.404976i
$591$	−21.6763	+	21.6763i	−0.891645	+	0.891645i
$592$	−13.4765	+	13.4765i	−0.553881	+	0.553881i
$593$	−7.21930	−	7.21930i	−0.296461	−	0.296461i	0.543165	−	0.839626i	$-0.317226\pi$
$593$	−7.21930	−	7.21930i	−0.296461	−	0.296461i	−0.839626	+	0.543165i	$0.817226\pi$
$594$		−	23.2498i		−	0.953949i
$595$		0			0
$596$	10.2258	−	10.2258i	0.418867	−	0.418867i
$597$			39.9709i			1.63590i
$598$	−20.1552	−	1.94569i	−0.824207	−	0.0795650i
$599$	−22.6509			−0.925490			−0.462745	−	0.886492i	$-0.653135\pi$
$599$	−22.6509			−0.925490			−0.462745	+	0.886492i	$0.653135\pi$
$600$	−9.82059	+	9.82059i	−0.400924	+	0.400924i
$601$			8.02946i			0.327529i	0.986499	+	0.163764i	$0.0523637\pi$
$601$			8.02946i			0.327529i	−0.986499	+	0.163764i	$0.947636\pi$
$602$		0			0
$603$	−4.77547	−	4.77547i	−0.194472	−	0.194472i
$604$	8.08847	+	8.08847i	0.329115	+	0.329115i
$605$	1.92937	+	1.92937i	0.0784399	+	0.0784399i
$606$	−20.9573	+	20.9573i	−0.851331	+	0.851331i
$607$		−	3.36912i		−	0.136748i	−0.997660	−	0.0683741i	$-0.978219\pi$
$607$		−	3.36912i		−	0.136748i	0.997660	−	0.0683741i	$-0.0217812\pi$
$608$	11.2032			0.454348
$609$		0			0
$610$		−	16.4629i		−	0.666563i
$611$	1.97831	−	20.4931i	0.0800337	−	0.829062i
$612$		−	4.04784i		−	0.163624i
$613$	−23.0156	−	23.0156i	−0.929591	−	0.929591i	0.0680884	−	0.997679i	$-0.478310\pi$
$613$	−23.0156	−	23.0156i	−0.929591	−	0.929591i	−0.997679	+	0.0680884i	$0.978310\pi$
$614$			8.92389i			0.360139i
$615$	24.4512			0.985969
$616$		0			0
$617$	−24.9178	−	24.9178i	−1.00315	−	1.00315i	−0.999995	−	0.00315687i	$-0.998995\pi$
$617$	−24.9178	−	24.9178i	−1.00315	−	1.00315i	−0.00315687	−	0.999995i	$-0.501005\pi$
$618$	−11.7470	+	11.7470i	−0.472535	+	0.472535i
$619$	11.2549	+	11.2549i	0.452372	+	0.452372i	0.896141	−	0.443769i	$-0.146359\pi$
$619$	11.2549	+	11.2549i	0.452372	+	0.452372i	−0.443769	+	0.896141i	$0.646359\pi$
$620$	6.52872			0.262200
$621$	−14.1040			−0.565974
$622$	−16.2869	−	16.2869i	−0.653047	−	0.653047i
$623$		0			0
$624$	−26.9959	+	22.2426i	−1.08070	+	0.890418i
$625$	30.7023			1.22809
$626$	5.44620	−	5.44620i	0.217674	−	0.217674i
$627$	−20.8188			−0.831424
$628$	7.40854			0.295633
$629$	−17.7497	+	17.7497i	−0.707727	+	0.707727i
$630$		0			0
$631$	−31.7103	+	31.7103i	−1.26237	+	1.26237i	−0.312427	+	0.949942i	$0.601142\pi$
$631$	−31.7103	+	31.7103i	−1.26237	+	1.26237i	−0.949942	+	0.312427i	$0.898858\pi$
$632$	1.66412	−	1.66412i	0.0661951	−	0.0661951i
$633$		−	4.69468i		−	0.186597i
$634$			47.9218i			1.90322i
$635$	25.3495	+	25.3495i	1.00596	+	1.00596i
$636$	−15.3824			−0.609951
$637$		0			0
$638$	−24.9126			−0.986298
$639$	−7.69695	−	7.69695i	−0.304487	−	0.304487i
$640$			38.8278i			1.53480i
$641$			4.11882i			0.162684i	0.996686	+	0.0813418i	$0.0259205\pi$
$641$			4.11882i			0.162684i	−0.996686	+	0.0813418i	$0.974079\pi$
$642$	−28.7822	+	28.7822i	−1.13594	+	1.13594i
$643$	−6.89221	+	6.89221i	−0.271802	+	0.271802i	−0.829825	−	0.558023i	$-0.811560\pi$
$643$	−6.89221	+	6.89221i	−0.271802	+	0.271802i	0.558023	+	0.829825i	$0.311560\pi$
$644$		0			0
$645$	−18.0559	+	18.0559i	−0.710950	+	0.710950i
$646$	32.0767			1.26204
$647$	−12.7884			−0.502762			−0.251381	−	0.967888i	$-0.580885\pi$
$647$	−12.7884			−0.502762			−0.251381	+	0.967888i	$0.580885\pi$
$648$	−16.7052	+	16.7052i	−0.656243	+	0.656243i
$649$	10.2374			0.401855
$650$	−19.0291	−	1.83698i	−0.746384	−	0.0720524i
$651$		0			0
$652$	−4.15859	−	4.15859i	−0.162863	−	0.162863i
$653$	14.2581			0.557961			0.278981	−	0.960297i	$-0.410003\pi$
$653$	14.2581			0.557961			0.278981	+	0.960297i	$0.410003\pi$
$654$	63.3138			2.47577
$655$	−27.5783	−	27.5783i	−1.07757	−	1.07757i
$656$	14.8843	−	14.8843i	0.581133	−	0.581133i
$657$	−3.05766	−	3.05766i	−0.119291	−	0.119291i
$658$		0			0
$659$	18.4714			0.719542			0.359771	−	0.933041i	$-0.382855\pi$
$659$	18.4714			0.719542			0.359771	+	0.933041i	$0.382855\pi$
$660$			13.3308i			0.518902i
$661$	−23.1384	−	23.1384i	−0.899978	−	0.899978i	0.0954556	−	0.995434i	$-0.469569\pi$
$661$	−23.1384	−	23.1384i	−0.899978	−	0.899978i	−0.995434	+	0.0954556i	$0.969569\pi$
$662$			24.2503i			0.942515i
$663$	−35.5559	+	29.2954i	−1.38088	+	1.13774i
$664$			6.15757i			0.238960i
$665$		0			0
$666$	5.89703			0.228505
$667$			15.1127i			0.585166i
$668$	−5.42525	+	5.42525i	−0.209909	+	0.209909i
$669$	19.1761	+	19.1761i	0.741389	+	0.741389i
$670$	−24.2317	−	24.2317i	−0.936151	−	0.936151i
$671$	8.56669	+	8.56669i	0.330713	+	0.330713i
$672$		0			0
$673$		−	35.6367i		−	1.37370i	−0.726801	−	0.686848i	$-0.758994\pi$
$673$		−	35.6367i		−	1.37370i	0.726801	−	0.686848i	$-0.241006\pi$
$674$	−11.0152	+	11.0152i	−0.424288	+	0.424288i
$675$	−13.3160			−0.512534
$676$	−8.65136	−	1.68604i	−0.332745	−	0.0648475i
$677$		−	27.6606i		−	1.06308i	−0.847032	−	0.531542i	$-0.821613\pi$
$677$		−	27.6606i		−	1.06308i	0.847032	−	0.531542i	$-0.178387\pi$
$678$	0.000529566	0	0.000529566i	2.03379e−5	0	2.03379e-5i
$679$		0			0
$680$			40.0483i			1.53578i
$681$	−18.2670	−	18.2670i	−0.699994	−	0.699994i
$682$	−13.4187	+	13.4187i	−0.513829	+	0.513829i
$683$	−1.14228	+	1.14228i	−0.0437082	+	0.0437082i	−0.728623	−	0.684915i	$-0.759839\pi$
$683$	−1.14228	+	1.14228i	−0.0437082	+	0.0437082i	0.684915	+	0.728623i	$0.259839\pi$
$684$	−1.34904	−	1.34904i	−0.0515819	−	0.0515819i
$685$			3.88034i			0.148260i
$686$		0			0
$687$	−21.2939	+	21.2939i	−0.812414	+	0.812414i
$688$			21.9824i			0.838072i
$689$	26.2530	+	31.8633i	1.00016	+	1.21389i
$690$	31.9417			1.21600
$691$	−18.8431	+	18.8431i	−0.716827	+	0.716827i	−0.967954	−	0.251127i	$-0.919199\pi$
$691$	−18.8431	+	18.8431i	−0.716827	+	0.716827i	0.251127	+	0.967954i	$0.419199\pi$
$692$			2.22161i			0.0844531i
$693$		0			0
$694$	−40.6506	−	40.6506i	−1.54307	−	1.54307i
$695$	−38.1986	−	38.1986i	−1.44895	−	1.44895i
$696$	13.3475	+	13.3475i	0.505936	+	0.505936i
$697$	19.6038	−	19.6038i	0.742548	−	0.742548i
$698$			15.3846i			0.582314i
$699$	−15.3255			−0.579665
$700$		0			0
$701$		−	5.72322i		−	0.216163i	−0.994142	−	0.108081i	$-0.965529\pi$
$701$		−	5.72322i		−	0.216163i	0.994142	−	0.108081i	$-0.0344707\pi$
$702$	−24.1370	−	2.33007i	−0.910991	−	0.0879427i
$703$			11.8310i			0.446216i
$704$	−9.19316	−	9.19316i	−0.346480	−	0.346480i
$705$			32.4772i			1.22316i
$706$	−20.2483			−0.762056
$707$		0			0
$708$	2.81308	+	2.81308i	0.105722	+	0.105722i
$709$	−8.47775	+	8.47775i	−0.318388	+	0.318388i	−0.848148	−	0.529759i	$-0.822282\pi$
$709$	−8.47775	+	8.47775i	−0.318388	+	0.318388i	0.529759	+	0.848148i	$0.322282\pi$
$710$	−39.0558	−	39.0558i	−1.46574	−	1.46574i
$711$	−1.00709			−0.0377689
$712$	−10.7344			−0.402290
$713$	8.14019	+	8.14019i	0.304853	+	0.304853i
$714$		0			0
$715$	27.6137	−	22.7516i	1.03269	−	0.850863i
$716$	−1.52558			−0.0570136
$717$	4.18009	−	4.18009i	0.156108	−	0.156108i
$718$	−7.01636			−0.261848
$719$	−15.2388			−0.568311			−0.284155	−	0.958778i	$-0.591713\pi$
$719$	−15.2388			−0.568311			−0.284155	+	0.958778i	$0.591713\pi$
$720$	9.20079	−	9.20079i	0.342893	−	0.342893i
$721$		0			0
$722$	−11.2956	+	11.2956i	−0.420378	+	0.420378i
$723$	36.9962	−	36.9962i	1.37590	−	1.37590i
$724$			10.5376i			0.391628i
$725$			14.2684i			0.529914i
$726$	−2.17930	−	2.17930i	−0.0808816	−	0.0808816i
$727$	19.4937			0.722981			0.361491	−	0.932376i	$-0.382268\pi$
$727$	19.4937			0.722981			0.361491	+	0.932376i	$0.382268\pi$
$728$		0			0
$729$	−14.3192			−0.530339
$730$	−15.5152	−	15.5152i	−0.574243	−	0.574243i
$731$			28.9527i			1.07085i
$732$			4.70796i			0.174011i
$733$	20.9891	−	20.9891i	0.775250	−	0.775250i	−0.203769	−	0.979019i	$-0.565319\pi$
$733$	20.9891	−	20.9891i	0.775250	−	0.775250i	0.979019	+	0.203769i	$0.0653192\pi$
$734$	28.6216	−	28.6216i	1.05644	−	1.05644i
$735$		0			0
$736$	8.94434	−	8.94434i	0.329693	−	0.329693i
$737$	25.2186			0.928938
$738$	−6.51303			−0.239748
$739$	−0.594151	+	0.594151i	−0.0218562	+	0.0218562i	−0.717950	−	0.696094i	$-0.754920\pi$
$739$	−0.594151	+	0.594151i	−0.0218562	+	0.0218562i	0.696094	+	0.717950i	$0.254920\pi$
$740$	7.57573			0.278489
$741$	−2.08644	+	21.6133i	−0.0766474	+	0.793983i
$742$		0			0
$743$	22.5891	+	22.5891i	0.828715	+	0.828715i	0.987339	−	0.158624i	$-0.0507056\pi$
$743$	22.5891	+	22.5891i	0.828715	+	0.828715i	−0.158624	+	0.987339i	$0.550706\pi$
$744$	14.3788			0.527153
$745$	61.2272			2.24319
$746$	−9.15718	−	9.15718i	−0.335268	−	0.335268i
$747$	1.86322	−	1.86322i	0.0681717	−	0.0681717i
$748$	10.6880	+	10.6880i	0.390793	+	0.390793i
$749$		0			0
$750$	−16.3805			−0.598131
$751$		−	14.9867i		−	0.546872i	−0.961890	−	0.273436i	$-0.911840\pi$
$751$		−	14.9867i		−	0.546872i	0.961890	−	0.273436i	$-0.0881602\pi$
$752$	19.7699	+	19.7699i	0.720935	+	0.720935i
$753$			13.9910i			0.509860i
$754$	−2.49671	+	25.8632i	−0.0909249	+	0.941882i
$755$			48.4296i			1.76254i
$756$		0			0
$757$	−4.27355			−0.155325			−0.0776624	−	0.996980i	$-0.524746\pi$
$757$	−4.27355			−0.155325			−0.0776624	+	0.996980i	$0.524746\pi$
$758$			7.69251i			0.279405i
$759$	−16.6213	+	16.6213i	−0.603314	+	0.603314i
$760$	13.3470	+	13.3470i	0.484148	+	0.484148i
$761$	5.54810	+	5.54810i	0.201118	+	0.201118i	0.800479	−	0.599361i	$-0.204578\pi$
$761$	5.54810	+	5.54810i	0.201118	+	0.201118i	−0.599361	+	0.800479i	$0.704578\pi$
$762$	−28.6333	−	28.6333i	−1.03728	−	1.03728i
$763$		0			0
$764$		−	1.61227i		−	0.0583297i
$765$	12.1182	−	12.1182i	0.438135	−	0.438135i
$766$	−14.8213			−0.535517
$767$	1.02599	−	10.6281i	0.0370462	−	0.383758i
$768$		−	28.9545i		−	1.04481i
$769$	5.34450	−	5.34450i	0.192727	−	0.192727i	−0.604146	−	0.796874i	$-0.706486\pi$
$769$	5.34450	−	5.34450i	0.192727	−	0.192727i	0.796874	+	0.604146i	$0.206486\pi$
$770$		0			0
$771$		−	25.8635i		−	0.931450i
$772$	−3.74247	−	3.74247i	−0.134694	−	0.134694i
$773$	21.5544	−	21.5544i	0.775257	−	0.775257i	−0.203763	−	0.979020i	$-0.565317\pi$
$773$	21.5544	−	21.5544i	0.775257	−	0.775257i	0.979020	+	0.203763i	$0.0653173\pi$
$774$	4.80951	−	4.80951i	0.172874	−	0.172874i
$775$	7.68541	+	7.68541i	0.276068	+	0.276068i
$776$		−	9.81534i		−	0.352350i
$777$		0			0
$778$	24.8335	−	24.8335i	0.890323	−	0.890323i
$779$		−	13.0669i		−	0.468170i
$780$	13.8395	+	1.33600i	0.495535	+	0.0478366i
$781$	40.6465			1.45444
$782$	25.6093	−	25.6093i	0.915787	−	0.915787i
$783$			18.0983i			0.646780i
$784$		0			0
$785$	22.1793	+	22.1793i	0.791613	+	0.791613i
$786$	31.1509	+	31.1509i	1.11112	+	1.11112i
$787$	−38.3225	−	38.3225i	−1.36605	−	1.36605i	−0.865994	−	0.500054i	$-0.833313\pi$
$787$	−38.3225	−	38.3225i	−1.36605	−	1.36605i	−0.500054	−	0.865994i	$-0.666687\pi$
$788$	7.41753	−	7.41753i	0.264239	−	0.264239i
$789$		−	44.2528i		−	1.57544i
$790$	−5.11018			−0.181812
$791$		0			0
$792$			6.92360i			0.246020i
$793$	9.75213	−	8.03504i	0.346308	−	0.285333i
$794$			21.3955i			0.759299i
$795$	−46.0509	−	46.0509i	−1.63326	−	1.63326i
$796$		−	13.6778i		−	0.484798i
$797$	28.0843			0.994797			0.497399	−	0.867522i	$-0.334289\pi$
$797$	28.0843			0.994797			0.497399	+	0.867522i	$0.334289\pi$
$798$		0			0
$799$	26.0387	+	26.0387i	0.921181	+	0.921181i
$800$	8.44464	−	8.44464i	0.298563	−	0.298563i
$801$	3.24814	+	3.24814i	0.114767	+	0.114767i
$802$	−34.7312			−1.22640
$803$	16.1471			0.569818
$804$	6.92963	+	6.92963i	0.244389	+	0.244389i
$805$		0			0
$806$	12.5860	+	15.2756i	0.443321	+	0.538059i
$807$	6.21018			0.218609
$808$	−13.9830	+	13.9830i	−0.491920	+	0.491920i
$809$	−12.7749			−0.449143			−0.224572	−	0.974458i	$-0.572098\pi$
$809$	−12.7749			−0.449143			−0.224572	+	0.974458i	$0.572098\pi$
$810$	51.2985			1.80245
$811$	−20.6613	+	20.6613i	−0.725515	+	0.725515i	−0.969723	−	0.244208i	$-0.921472\pi$
$811$	−20.6613	+	20.6613i	−0.725515	+	0.725515i	0.244208	+	0.969723i	$0.421472\pi$
$812$		0			0
$813$	22.1500	−	22.1500i	0.776833	−	0.776833i
$814$	−15.5707	+	15.5707i	−0.545752	+	0.545752i
$815$		−	24.8995i		−	0.872192i
$816$		−	62.5628i		−	2.19014i
$817$	9.64918	+	9.64918i	0.337582	+	0.337582i
$818$	13.9395			0.487382
$819$		0			0
$820$	−8.36708			−0.292191
$821$	0.901780	+	0.901780i	0.0314723	+	0.0314723i	0.722668	−	0.691195i	$-0.242916\pi$
$821$	0.901780	+	0.901780i	0.0314723	+	0.0314723i	−0.691195	+	0.722668i	$0.742916\pi$
$822$		−	4.38301i		−	0.152875i
$823$		−	22.0804i		−	0.769676i	−0.922984	−	0.384838i	$-0.874257\pi$
$823$		−	22.0804i		−	0.769676i	0.922984	−	0.384838i	$-0.125743\pi$
$824$	−7.83780	+	7.83780i	−0.273043	+	0.273043i
$825$	−15.6927	+	15.6927i	−0.546349	+	0.546349i
$826$		0			0
$827$	9.30639	−	9.30639i	0.323615	−	0.323615i	−0.526537	−	0.850152i	$-0.676510\pi$
$827$	9.30639	−	9.30639i	0.323615	−	0.323615i	0.850152	+	0.526537i	$0.176510\pi$
$828$	−2.15409			−0.0748597
$829$	30.9681			1.07557			0.537784	−	0.843083i	$-0.319262\pi$
$829$	30.9681			1.07557			0.537784	+	0.843083i	$0.319262\pi$
$830$	9.45435	−	9.45435i	0.328165	−	0.328165i
$831$	58.4186			2.02652
$832$	−10.4653	+	8.62263i	−0.362819	+	0.298936i
$833$		0			0
$834$	43.1470	+	43.1470i	1.49406	+	1.49406i
$835$	−32.4837			−1.12414
$836$	7.12409			0.246392
$837$	9.74834	+	9.74834i	0.336952	+	0.336952i
$838$	9.70956	−	9.70956i	0.335411	−	0.335411i
$839$	22.1620	+	22.1620i	0.765116	+	0.765116i	0.977242	−	0.212126i	$-0.0680389\pi$
$839$	22.1620	+	22.1620i	0.765116	+	0.765116i	−0.212126	+	0.977242i	$0.568039\pi$
$840$		0			0
$841$	−9.60734			−0.331288
$842$			47.5391i			1.63831i
$843$	−33.4788	−	33.4788i	−1.15307	−	1.15307i
$844$			1.60650i			0.0552979i
$845$	−20.8524	−	30.9475i	−0.717345	−	1.06463i
$846$		−	8.65088i		−	0.297423i
$847$		0			0
$848$	−56.0654			−1.92530
$849$		−	18.4947i		−	0.634737i
$850$	24.1786	−	24.1786i	0.829318	−	0.829318i
$851$	9.44563	+	9.44563i	0.323792	+	0.323792i
$852$	11.1690	+	11.1690i	0.382642	+	0.382642i
$853$	−15.0740	−	15.0740i	−0.516125	−	0.516125i	0.400271	−	0.916397i	$-0.368916\pi$
$853$	−15.0740	−	15.0740i	−0.516125	−	0.516125i	−0.916397	+	0.400271i	$0.868916\pi$
$854$		0			0
$855$		−	8.07737i		−	0.276240i
$856$	−19.2039	+	19.2039i	−0.656376	+	0.656376i
$857$	−37.6852			−1.28730			−0.643650	−	0.765320i	$-0.722581\pi$
$857$	−37.6852			−1.28730			−0.643650	+	0.765320i	$0.722581\pi$
$858$	−31.1908	+	25.6990i	−1.06484	+	0.877348i
$859$		−	9.30207i		−	0.317383i	−0.987328	−	0.158691i	$-0.949273\pi$
$859$		−	9.30207i		−	0.317383i	0.987328	−	0.158691i	$-0.0507275\pi$
$860$	6.17863	−	6.17863i	0.210689	−	0.210689i
$861$		0			0
$862$			16.3712i			0.557605i
$863$	16.2595	+	16.2595i	0.553481	+	0.553481i	0.927444	−	0.373962i	$-0.122001\pi$
$863$	16.2595	+	16.2595i	0.553481	+	0.553481i	−0.373962	+	0.927444i	$0.622001\pi$
$864$	10.7114	−	10.7114i	0.364408	−	0.364408i
$865$	−6.65094	+	6.65094i	−0.226139	+	0.226139i
$866$	−47.8884	−	47.8884i	−1.62731	−	1.62731i
$867$		−	48.7174i		−	1.65453i
$868$		0			0
$869$	2.65915	−	2.65915i	0.0902056	−	0.0902056i
$870$		−	40.9877i		−	1.38961i
$871$	2.52738	−	26.1809i	0.0856370	−	0.887105i
$872$	42.2439			1.43056
$873$	−2.97002	+	2.97002i	−0.100520	+	0.100520i
$874$		−	17.0698i		−	0.577396i
$875$		0			0
$876$	4.43694	+	4.43694i	0.149910	+	0.149910i
$877$	−7.47672	−	7.47672i	−0.252471	−	0.252471i	0.569512	−	0.821983i	$-0.307132\pi$
$877$	−7.47672	−	7.47672i	−0.252471	−	0.252471i	−0.821983	+	0.569512i	$0.807132\pi$
$878$	−0.164983	−	0.164983i	−0.00556791	−	0.00556791i
$879$	−4.12581	+	4.12581i	−0.139160	+	0.139160i
$880$			48.5880i			1.63790i
$881$	−19.0687			−0.642440			−0.321220	−	0.947005i	$-0.604093\pi$
$881$	−19.0687			−0.642440			−0.321220	+	0.947005i	$0.604093\pi$
$882$		0			0
$883$		−	4.27586i		−	0.143894i	−0.997408	−	0.0719471i	$-0.977079\pi$
$883$		−	4.27586i		−	0.143894i	0.997408	−	0.0719471i	$-0.0229213\pi$
$884$	12.1670	−	10.0247i	0.409221	−	0.337169i
$885$			16.8433i			0.566180i
$886$	29.9398	+	29.9398i	1.00585	+	1.00585i
$887$		−	6.64767i		−	0.223207i	−0.993753	−	0.111603i	$-0.964401\pi$
$887$		−	6.64767i		−	0.223207i	0.993753	−	0.111603i	$-0.0355986\pi$
$888$	16.6847			0.559903
$889$		0			0
$890$	16.4817	+	16.4817i	0.552468	+	0.552468i
$891$	−26.6939	+	26.6939i	−0.894278	+	0.894278i
$892$	−6.56194	−	6.56194i	−0.219710	−	0.219710i
$893$	17.3560			0.580797
$894$	−69.1587			−2.31301
$895$	−4.56720	−	4.56720i	−0.152665	−	0.152665i
$896$		0			0
$897$	15.5898	+	18.9213i	0.520527	+	0.631764i
$898$	2.93096			0.0978073
$899$	10.4455	−	10.4455i	0.348378	−	0.348378i
$900$	−2.03374			−0.0677914
$901$	−73.8429			−2.46006
$902$	17.1972	−	17.1972i	0.572603	−	0.572603i
$903$		0			0
$904$	0.000353334	0	0.000353334i	1.17517e−5	0	1.17517e-5i
$905$	−31.5470	+	31.5470i	−1.04866	+	1.04866i
$906$		−	54.7034i		−	1.81740i
$907$			14.6887i			0.487729i	0.969809	+	0.243865i	$0.0784152\pi$
$907$			14.6887i			0.487729i	−0.969809	+	0.243865i	$0.921585\pi$
$908$	6.25088	+	6.25088i	0.207443	+	0.207443i
$909$	8.46224			0.280675
$910$		0			0
$911$	17.7868			0.589301			0.294651	−	0.955605i	$-0.404797\pi$
$911$	17.7868			0.589301			0.294651	+	0.955605i	$0.404797\pi$
$912$	−20.8506	−	20.8506i	−0.690431	−	0.690431i
$913$			9.83940i			0.325636i
$914$		−	7.62985i		−	0.252373i
$915$	−14.0944	+	14.0944i	−0.465948	+	0.465948i
$916$	7.28667	−	7.28667i	0.240758	−	0.240758i
$917$		0			0
$918$	30.6686	−	30.6686i	1.01221	−	1.01221i
$919$	22.2865			0.735163			0.367581	−	0.929991i	$-0.380186\pi$
$919$	22.2865			0.735163			0.367581	+	0.929991i	$0.380186\pi$
$920$	21.3120			0.702634
$921$	7.64004	−	7.64004i	0.251748	−	0.251748i
$922$	−8.35223			−0.275066
$923$	4.07355	−	42.1975i	0.134082	−	1.38895i
$924$		0			0
$925$	8.91792	+	8.91792i	0.293219	+	0.293219i
$926$	−9.26255			−0.304386
$927$	4.74328			0.155790
$928$	−11.4774	−	11.4774i	−0.376765	−	0.376765i
$929$	30.3717	−	30.3717i	0.996464	−	0.996464i	−0.00352958	−	0.999994i	$-0.501124\pi$
$929$	30.3717	−	30.3717i	0.996464	−	0.996464i	0.999994	+	0.00352958i	$0.00112350\pi$
$930$	−22.0773	−	22.0773i	−0.723943	−	0.723943i
$931$		0			0
$932$	5.24431			0.171783
$933$			27.8876i			0.912998i
$934$	−46.3577	−	46.3577i	−1.51687	−	1.51687i
$935$			63.9945i			2.09285i
$936$	7.18780	+	0.693877i	0.234941	+	0.0226801i
$937$		−	52.3733i		−	1.71096i	−0.517835	−	0.855481i	$-0.673262\pi$
$937$		−	52.3733i		−	1.71096i	0.517835	−	0.855481i	$-0.326738\pi$
$938$		0			0
$939$	−9.32534			−0.304321
$940$		−	11.1135i		−	0.362483i
$941$	−11.0169	+	11.0169i	−0.359141	+	0.359141i	−0.863496	−	0.504355i	$-0.831730\pi$
$941$	−11.0169	+	11.0169i	−0.359141	+	0.359141i	0.504355	+	0.863496i	$0.331730\pi$
$942$	−25.0525	−	25.0525i	−0.816254	−	0.816254i
$943$	−10.4323	−	10.4323i	−0.339723	−	0.339723i
$944$	10.2531	+	10.2531i	0.333708	+	0.333708i
$945$		0			0
$946$			25.3983i			0.825771i
$947$	30.1246	−	30.1246i	0.978918	−	0.978918i	−0.0208644	−	0.999782i	$-0.506642\pi$
$947$	30.1246	−	30.1246i	0.978918	−	0.978918i	0.999782	+	0.0208644i	$0.00664182\pi$
$948$	1.46138			0.0474634
$949$	1.61824	−	16.7632i	0.0525304	−	0.544157i
$950$		−	16.1162i		−	0.522878i
$951$	41.0275	−	41.0275i	1.33041	−	1.33041i
$952$		0			0
$953$		−	35.9437i		−	1.16433i	−0.813070	−	0.582165i	$-0.802206\pi$
$953$		−	35.9437i		−	1.16433i	0.813070	−	0.582165i	$-0.197794\pi$
$954$	12.2665	+	12.2665i	0.397143	+	0.397143i
$955$	4.82671	−	4.82671i	0.156189	−	0.156189i
$956$	−1.43040	+	1.43040i	−0.0462626	+	0.0462626i
$957$	21.3285	+	21.3285i	0.689452	+	0.689452i
$958$			19.2949i			0.623390i
$959$		0			0
$960$	15.1251	−	15.1251i	0.488162	−	0.488162i
$961$			19.7474i			0.637013i
$962$	14.6044	+	17.7253i	0.470863	+	0.571487i
$963$	11.6218			0.374508
$964$	−12.6599	+	12.6599i	−0.407748	+	0.407748i
$965$		−	22.4080i		−	0.721339i
$966$		0			0
$967$	−31.7209	−	31.7209i	−1.02008	−	1.02008i	−0.999794	−	0.0202813i	$-0.993544\pi$
$967$	−31.7209	−	31.7209i	−1.02008	−	1.02008i	−0.0202813	−	0.999794i	$-0.506456\pi$
$968$	−1.45406	−	1.45406i	−0.0467354	−	0.0467354i
$969$	−27.4620	−	27.4620i	−0.882205	−	0.882205i
$970$	−15.0705	+	15.0705i	−0.483884	+	0.483884i
$971$		−	23.9259i		−	0.767818i	−0.923371	−	0.383909i	$-0.874578\pi$
$971$		−	23.9259i		−	0.767818i	0.923371	−	0.383909i	$-0.125422\pi$
$972$	−6.31063			−0.202414
$973$		0			0
$974$			0.900548i			0.0288554i
$975$	14.7188	+	17.8642i	0.471378	+	0.572112i
$976$			17.1595i			0.549262i
$977$	−31.2419	−	31.2419i	−0.999517	−	0.999517i	0.000483091	−	1.00000i	$-0.499846\pi$
$977$	−31.2419	−	31.2419i	−0.999517	−	0.999517i	−1.00000		0.000483091i	$0.999846\pi$
$978$			28.1251i			0.899341i
$979$	−17.1530			−0.548211
$980$		0			0
$981$	−12.7826	−	12.7826i	−0.408117	−	0.408117i
$982$	3.49927	−	3.49927i	0.111666	−	0.111666i
$983$	−2.85615	−	2.85615i	−0.0910971	−	0.0910971i	0.660090	−	0.751187i	$-0.270518\pi$
$983$	−2.85615	−	2.85615i	−0.0910971	−	0.0910971i	−0.751187	+	0.660090i	$0.770518\pi$
$984$	−18.4276			−0.587451
$985$	44.4124			1.41510
$986$	−32.8620	−	32.8620i	−1.04654	−	1.04654i
$987$		0			0
$988$	0.713969	−	7.39594i	0.0227144	−	0.235296i
$989$	15.4074			0.489926
$990$	10.6305	−	10.6305i	0.337860	−	0.337860i
$991$	−30.8167			−0.978925			−0.489463	−	0.872024i	$-0.662807\pi$
$991$	−30.8167			−0.978925			−0.489463	+	0.872024i	$0.662807\pi$
$992$	−12.3642			−0.392564
$993$	20.7615	−	20.7615i	0.658846	−	0.658846i
$994$		0			0
$995$	40.9480	−	40.9480i	1.29814	−	1.29814i
$996$	−2.70370	+	2.70370i	−0.0856700	+	0.0856700i
$997$			40.3578i			1.27814i	0.769147	+	0.639072i	$0.220681\pi$
$997$			40.3578i			1.27814i	−0.769147	+	0.639072i	$0.779319\pi$
$998$		−	62.7575i		−	1.98655i
$999$	11.3117	+	11.3117i	0.357885	+	0.357885i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.i.a.489.11		32
7.2	even	3		637.2.bc.b.619.6		32
7.3	odd	6		637.2.bc.b.411.3		32
7.4	even	3		91.2.bb.a.47.3	yes	32
7.5	odd	6		91.2.bb.a.73.6	yes	32
7.6	odd	2	inner	637.2.i.a.489.12		32
13.5	odd	4	inner	637.2.i.a.538.11		32
21.5	even	6		819.2.fn.e.73.3		32
21.11	odd	6		819.2.fn.e.775.6		32
91.5	even	12		91.2.bb.a.31.3	yes	32
91.18	odd	12		91.2.bb.a.5.6	✓	32
91.31	even	12		637.2.bc.b.460.6		32
91.44	odd	12		637.2.bc.b.31.3		32
91.83	even	4	inner	637.2.i.a.538.12		32
273.5	odd	12		819.2.fn.e.577.6		32
273.200	even	12		819.2.fn.e.460.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bb.a.5.6	✓	32	91.18	odd	12
91.2.bb.a.31.3	yes	32	91.5	even	12
91.2.bb.a.47.3	yes	32	7.4	even	3
91.2.bb.a.73.6	yes	32	7.5	odd	6
637.2.i.a.489.11		32	1.1	even	1	trivial
637.2.i.a.489.12		32	7.6	odd	2	inner
637.2.i.a.538.11		32	13.5	odd	4	inner
637.2.i.a.538.12		32	91.83	even	4	inner
637.2.bc.b.31.3		32	91.44	odd	12
637.2.bc.b.411.3		32	7.3	odd	6
637.2.bc.b.460.6		32	91.31	even	12
637.2.bc.b.619.6		32	7.2	even	3
819.2.fn.e.73.3		32	21.5	even	6
819.2.fn.e.460.3		32	273.200	even	12
819.2.fn.e.577.6		32	273.5	odd	12
819.2.fn.e.775.6		32	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.15715 + 1.15715i) q^{2} -1.98136i q^{3} +0.678010i q^{4} +(-2.02979 + 2.02979i) q^{5} +(2.29273 - 2.29273i) q^{6} +(1.52975 - 1.52975i) q^{8} -0.925772 q^{9} +O(q^{10})\)	\(q+(1.15715 + 1.15715i) q^{2} -1.98136i q^{3} +0.678010i q^{4} +(-2.02979 + 2.02979i) q^{5} +(2.29273 - 2.29273i) q^{6} +(1.52975 - 1.52975i) q^{8} -0.925772 q^{9} -4.69755 q^{10} +(2.44444 - 2.44444i) q^{11} +1.34338 q^{12} +(-2.29273 - 2.78269i) q^{13} +(4.02173 + 4.02173i) q^{15} +4.89632 q^{16} +6.44887 q^{17} +(-1.07126 - 1.07126i) q^{18} +(2.14924 - 2.14924i) q^{19} +(-1.37622 - 1.37622i) q^{20} +5.65717 q^{22} -3.43181i q^{23} +(-3.03097 - 3.03097i) q^{24} -3.24008i q^{25} +(0.566956 - 5.87305i) q^{26} -4.10978i q^{27} -4.40371 q^{29} +9.30753i q^{30} +(-2.37198 + 2.37198i) q^{31} +(2.60631 + 2.60631i) q^{32} +(-4.84330 - 4.84330i) q^{33} +(7.46233 + 7.46233i) q^{34} -0.627683i q^{36} +(-2.75238 + 2.75238i) q^{37} +4.97401 q^{38} +(-5.51350 + 4.54272i) q^{39} +6.21012i q^{40} +(3.03989 - 3.03989i) q^{41} +4.48958i q^{43} +(1.65735 + 1.65735i) q^{44} +(1.87912 - 1.87912i) q^{45} +(3.97113 - 3.97113i) q^{46} +(4.03771 + 4.03771i) q^{47} -9.70136i q^{48} +(3.74927 - 3.74927i) q^{50} -12.7775i q^{51} +(1.88669 - 1.55450i) q^{52} -11.4505 q^{53} +(4.75565 - 4.75565i) q^{54} +9.92337i q^{55} +(-4.25841 - 4.25841i) q^{57} +(-5.09577 - 5.09577i) q^{58} +(2.09403 + 2.09403i) q^{59} +(-2.72677 + 2.72677i) q^{60} +3.50457i q^{61} -5.48950 q^{62} -3.76085i q^{64} +(10.3020 + 0.994510i) q^{65} -11.2089i q^{66} +(5.15836 + 5.15836i) q^{67} +4.37240i q^{68} -6.79964 q^{69} +(8.31408 + 8.31408i) q^{71} +(-1.41620 + 1.41620i) q^{72} +(3.30282 + 3.30282i) q^{73} -6.36984 q^{74} -6.41975 q^{75} +(1.45721 + 1.45721i) q^{76} +(-11.6366 - 1.12334i) q^{78} +1.08784 q^{79} +(-9.93850 + 9.93850i) q^{80} -10.9203 q^{81} +7.03523 q^{82} +(-2.01261 + 2.01261i) q^{83} +(-13.0898 + 13.0898i) q^{85} +(-5.19513 + 5.19513i) q^{86} +8.72532i q^{87} -7.47873i q^{88} +(-3.50857 - 3.50857i) q^{89} +4.34887 q^{90} +2.32680 q^{92} +(4.69974 + 4.69974i) q^{93} +9.34450i q^{94} +8.72501i q^{95} +(5.16402 - 5.16402i) q^{96} +(3.20816 - 3.20816i) q^{97} +(-2.26299 + 2.26299i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{2} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) 32 * q + 4 * q^2 - 16 * q^8 - 16 * q^9	\( 32 q + 4 q^{2} - 16 q^{8} - 16 q^{9} + 20 q^{11} - 44 q^{15} - 24 q^{16} + 8 q^{18} - 8 q^{22} + 16 q^{29} - 8 q^{32} + 16 q^{37} + 12 q^{39} + 84 q^{44} - 24 q^{46} + 88 q^{50} + 24 q^{53} + 40 q^{57} - 52 q^{58} - 32 q^{60} + 16 q^{65} - 32 q^{67} - 36 q^{71} - 44 q^{72} - 24 q^{74} - 176 q^{78} + 64 q^{79} - 32 q^{81} - 84 q^{85} - 84 q^{86} + 48 q^{92} - 12 q^{93} - 24 q^{99}+O(q^{100}) \) 32 * q + 4 * q^2 - 16 * q^8 - 16 * q^9 + 20 * q^11 - 44 * q^15 - 24 * q^16 + 8 * q^18 - 8 * q^22 + 16 * q^29 - 8 * q^32 + 16 * q^37 + 12 * q^39 + 84 * q^44 - 24 * q^46 + 88 * q^50 + 24 * q^53 + 40 * q^57 - 52 * q^58 - 32 * q^60 + 16 * q^65 - 32 * q^67 - 36 * q^71 - 44 * q^72 - 24 * q^74 - 176 * q^78 + 64 * q^79 - 32 * q^81 - 84 * q^85 - 84 * q^86 + 48 * q^92 - 12 * q^93 - 24 * q^99

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