LMFDB - Embedded newform 637.2.f.j.393.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [637,2,Mod(295,637)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(637, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("637.295"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.f (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,2,-1,-4,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 $ x^12 - x^11 + 7x^10 - 2x^9 + 33x^8 - 11x^7 + 55x^6 + 17x^5 + 47x^4 + x^3 + 8x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			393.3
Root			$-0.437442 + 0.757672i$ of defining polynomial
Character	$\chi$	$=$	637.393
Dual form			637.2.f.j.295.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.134063 + 0.232203i) q^{2} +(-0.571504 - 0.989875i) q^{3} +(0.964054 - 1.66979i) q^{4} +2.56175 q^{5} +(0.153235 - 0.265410i) q^{6} +1.05323 q^{8} +(0.846765 - 1.46664i) q^{9} +(0.343436 + 0.594848i) q^{10} +(-1.97300 - 3.41734i) q^{11} -2.20385 q^{12} +(3.15374 + 1.74755i) q^{13} +(-1.46405 - 2.53582i) q^{15} +(-1.78691 - 3.09502i) q^{16} +(0.392550 - 0.679916i) q^{17} +0.454078 q^{18} +(-3.74764 + 6.49110i) q^{19} +(2.46967 - 4.27760i) q^{20} +(0.529011 - 0.916274i) q^{22} +(3.97759 + 6.88938i) q^{23} +(-0.601923 - 1.04256i) q^{24} +1.56259 q^{25} +(0.0170128 + 0.966590i) q^{26} -5.36475 q^{27} +(-1.17586 - 2.03666i) q^{29} +(0.392550 - 0.679916i) q^{30} +2.55437 q^{31} +(1.53234 - 2.65409i) q^{32} +(-2.25516 + 3.90605i) q^{33} +0.210505 q^{34} +(-1.63266 - 2.82784i) q^{36} +(-3.37858 - 5.85187i) q^{37} -2.00967 q^{38} +(-0.0725249 - 4.12054i) q^{39} +2.69810 q^{40} +(-1.21874 - 2.11091i) q^{41} +(1.12473 - 1.94809i) q^{43} -7.60832 q^{44} +(2.16920 - 3.75717i) q^{45} +(-1.06649 + 1.84722i) q^{46} -1.31655 q^{47} +(-2.04246 + 3.53764i) q^{48} +(0.209485 + 0.362838i) q^{50} -0.897376 q^{51} +(5.95842 - 3.58136i) q^{52} +9.27954 q^{53} +(-0.719212 - 1.24571i) q^{54} +(-5.05434 - 8.75438i) q^{55} +8.56716 q^{57} +(0.315279 - 0.546079i) q^{58} +(-4.48335 + 7.76540i) q^{59} -5.64571 q^{60} +(4.72273 - 8.18002i) q^{61} +(0.342445 + 0.593132i) q^{62} -6.32592 q^{64} +(8.07911 + 4.47679i) q^{65} -1.20933 q^{66} +(0.676281 + 1.17135i) q^{67} +(-0.756879 - 1.31095i) q^{68} +(4.54642 - 7.87463i) q^{69} +(-6.15808 + 10.6661i) q^{71} +(0.891834 - 1.54470i) q^{72} -0.768590 q^{73} +(0.905882 - 1.56903i) q^{74} +(-0.893026 - 1.54677i) q^{75} +(7.22585 + 12.5155i) q^{76} +(0.947080 - 0.569251i) q^{78} +6.19284 q^{79} +(-4.57763 - 7.92868i) q^{80} +(0.525682 + 0.910507i) q^{81} +(0.326774 - 0.565989i) q^{82} +1.07292 q^{83} +(1.00562 - 1.74178i) q^{85} +0.603137 q^{86} +(-1.34402 + 2.32792i) q^{87} +(-2.07801 - 3.59923i) q^{88} +(3.83149 + 6.63634i) q^{89} +1.16324 q^{90} +15.3384 q^{92} +(-1.45983 - 2.52850i) q^{93} +(-0.176501 - 0.305708i) q^{94} +(-9.60052 + 16.6286i) q^{95} -3.50296 q^{96} +(-1.18601 + 2.05423i) q^{97} -6.68267 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} - q^{3} - 4 q^{4} + 2 q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9} - 4 q^{10} + 4 q^{11} + 10 q^{12} + 2 q^{13} - 2 q^{15} + 8 q^{16} - 5 q^{17} - 6 q^{18} + q^{19} + q^{20} - 5 q^{22} - q^{23}+ \cdots - 20 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 - q^3 - 4 * q^4 + 2 * q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9 - 4 * q^10 + 4 * q^11 + 10 * q^12 + 2 * q^13 - 2 * q^15 + 8 * q^16 - 5 * q^17 - 6 * q^18 + q^19 + q^20 - 5 * q^22 - q^23 + 11 * q^24 - 14 * q^25 - 11 * q^26 + 8 * q^27 + 3 * q^29 - 5 * q^30 + 32 * q^31 + 8 * q^32 - 16 * q^33 - 32 * q^34 - 21 * q^36 - 13 * q^37 - 34 * q^38 + 43 * q^39 - 10 * q^40 + 8 * q^41 - 11 * q^43 - 42 * q^44 + 7 * q^45 + 16 * q^46 - 2 * q^47 - 21 * q^48 + 6 * q^50 + 40 * q^51 + 16 * q^52 + 4 * q^53 + 18 * q^54 - 9 * q^55 + 42 * q^57 - 8 * q^58 - 13 * q^59 - 40 * q^60 + 5 * q^61 - 5 * q^62 - 30 * q^64 - 14 * q^65 + 36 * q^66 - 11 * q^67 - 29 * q^68 - 23 * q^69 + 6 * q^71 + 25 * q^72 - 60 * q^73 - 3 * q^74 + 3 * q^75 + 9 * q^76 + 16 * q^78 - 14 * q^79 + 7 * q^80 - 6 * q^81 - q^82 + 54 * q^83 - q^85 + 14 * q^86 - 16 * q^87 - 4 * q^89 + 16 * q^90 + 54 * q^92 - 7 * q^93 - 45 * q^94 - 6 * q^95 + 38 * q^96 + 35 * q^97 - 20 * q^99

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.134063	+	0.232203i	0.0947966	+	0.164193i	0.909524	−	0.415652i	$-0.136447\pi$
$2$	0.134063	+	0.232203i	0.0947966	+	0.164193i	−0.814727	+	0.579845i	$0.803113\pi$
$3$	−0.571504	−	0.989875i	−0.329958	−	0.571504i	0.652545	−	0.757750i	$-0.273701\pi$
$3$	−0.571504	−	0.989875i	−0.329958	−	0.571504i	−0.982503	+	0.186246i	$0.940368\pi$
$4$	0.964054	−	1.66979i	0.482027	−	0.834896i
$5$	2.56175			1.14565			0.572826	−	0.819677i	$-0.305847\pi$
$5$	2.56175			1.14565			0.572826	+	0.819677i	$0.305847\pi$
$6$	0.153235	−	0.265410i	0.0625578	−	0.108353i
$7$		0			0
$7$		0			0
$8$	1.05323			0.372371
$9$	0.846765	−	1.46664i	0.282255	−	0.488880i
$10$	0.343436	+	0.594848i	0.108604	+	0.188107i
$11$	−1.97300	−	3.41734i	−0.594882	−	1.03037i	−0.993563	−	0.113277i	$-0.963865\pi$
$11$	−1.97300	−	3.41734i	−0.594882	−	1.03037i	0.398681	−	0.917090i	$-0.369468\pi$
$12$	−2.20385			−0.636195
$13$	3.15374	+	1.74755i	0.874690	+	0.484682i
$13$	3.15374	+	1.74755i	0.874690	+	0.484682i
$14$		0			0
$15$	−1.46405	−	2.53582i	−0.378017	−	0.654745i
$16$	−1.78691	−	3.09502i	−0.446728	−	0.773755i
$17$	0.392550	−	0.679916i	0.0952073	−	0.164904i	−0.814488	−	0.580181i	$-0.802982\pi$
$17$	0.392550	−	0.679916i	0.0952073	−	0.164904i	0.909695	+	0.415277i	$0.136315\pi$
$18$	0.454078			0.107027
$19$	−3.74764	+	6.49110i	−0.859767	+	1.48916i	0.0123849	+	0.999923i	$0.496058\pi$
$19$	−3.74764	+	6.49110i	−0.859767	+	1.48916i	−0.872151	+	0.489236i	$0.837276\pi$
$20$	2.46967	−	4.27760i	0.552235	−	0.956500i
$21$		0			0
$22$	0.529011	−	0.916274i	0.112786	−	0.195350i
$23$	3.97759	+	6.88938i	0.829384	+	1.43654i	0.898522	+	0.438929i	$0.144642\pi$
$23$	3.97759	+	6.88938i	0.829384	+	1.43654i	−0.0691375	+	0.997607i	$0.522025\pi$
$24$	−0.601923	−	1.04256i	−0.122867	−	0.212812i
$25$	1.56259			0.312518
$26$	0.0170128	+	0.966590i	0.00333648	+	0.189564i
$27$	−5.36475			−1.03245
$28$		0			0
$29$	−1.17586	−	2.03666i	−0.218353	−	0.378198i	0.735952	−	0.677034i	$-0.236735\pi$
$29$	−1.17586	−	2.03666i	−0.218353	−	0.378198i	−0.954304	+	0.298836i	$0.903402\pi$
$30$	0.392550	−	0.679916i	0.0716695	−	0.124135i
$31$	2.55437			0.458778			0.229389	−	0.973335i	$-0.426327\pi$
$31$	2.55437			0.458778			0.229389	+	0.973335i	$0.426327\pi$
$32$	1.53234	−	2.65409i	0.270882	−	0.469182i
$33$	−2.25516	+	3.90605i	−0.392573	+	0.679956i
$34$	0.210505			0.0361013
$35$		0			0
$36$	−1.63266	−	2.82784i	−0.272109	−	0.471307i
$37$	−3.37858	−	5.85187i	−0.555435	−	0.962041i	−0.997870	−	0.0652406i	$-0.979219\pi$
$37$	−3.37858	−	5.85187i	−0.555435	−	0.962041i	0.442435	−	0.896801i	$-0.354115\pi$
$38$	−2.00967			−0.326012
$39$	−0.0725249	−	4.12054i	−0.0116133	−	0.659814i
$40$	2.69810			0.426608
$41$	−1.21874	−	2.11091i	−0.190335	−	0.329669i	0.755027	−	0.655694i	$-0.227624\pi$
$41$	−1.21874	−	2.11091i	−0.190335	−	0.329669i	−0.945361	+	0.326025i	$0.894291\pi$
$42$		0			0
$43$	1.12473	−	1.94809i	0.171520	−	0.297081i	−0.767432	−	0.641131i	$-0.778466\pi$
$43$	1.12473	−	1.94809i	0.171520	−	0.297081i	0.938951	+	0.344050i	$0.111799\pi$
$44$	−7.60832			−1.14700
$45$	2.16920	−	3.75717i	0.323366	−	0.560086i
$46$	−1.06649	+	1.84722i	−0.157246	+	0.272357i
$47$	−1.31655			−0.192039			−0.0960195	−	0.995379i	$-0.530611\pi$
$47$	−1.31655			−0.192039			−0.0960195	+	0.995379i	$0.530611\pi$
$48$	−2.04246	+	3.53764i	−0.294803	+	0.510614i
$49$		0			0
$50$	0.209485	+	0.362838i	0.0296256	+	0.0513130i
$51$	−0.897376			−0.125658
$52$	5.95842	−	3.58136i	0.826284	−	0.496645i
$53$	9.27954			1.27464			0.637321	−	0.770598i	$-0.280042\pi$
$53$	9.27954			1.27464			0.637321	+	0.770598i	$0.280042\pi$
$54$	−0.719212	−	1.24571i	−0.0978724	−	0.169520i
$55$	−5.05434	−	8.75438i	−0.681528	−	1.18044i
$56$		0			0
$57$	8.56716			1.13475
$58$	0.315279	−	0.546079i	0.0413981	−	0.0717037i
$59$	−4.48335	+	7.76540i	−0.583683	+	1.01097i	0.411355	+	0.911475i	$0.365056\pi$
$59$	−4.48335	+	7.76540i	−0.583683	+	1.01097i	−0.995038	+	0.0994935i	$0.968278\pi$
$60$	−5.64571			−0.728858
$61$	4.72273	−	8.18002i	0.604684	−	1.04734i	−0.387417	−	0.921905i	$-0.626633\pi$
$61$	4.72273	−	8.18002i	0.604684	−	1.04734i	0.992101	−	0.125439i	$-0.0400340\pi$
$62$	0.342445	+	0.593132i	0.0434906	+	0.0753279i
$63$		0			0
$64$	−6.32592			−0.790741
$65$	8.07911	+	4.47679i	1.00209	+	0.555277i
$66$	−1.20933			−0.148858
$67$	0.676281	+	1.17135i	0.0826209	+	0.143104i	0.904375	−	0.426739i	$-0.140338\pi$
$67$	0.676281	+	1.17135i	0.0826209	+	0.143104i	−0.821754	+	0.569842i	$0.807004\pi$
$68$	−0.756879	−	1.31095i	−0.0917851	−	0.158976i
$69$	4.54642	−	7.87463i	0.547324	−	0.947994i
$70$		0			0
$71$	−6.15808	+	10.6661i	−0.730829	+	1.26583i	0.225700	+	0.974197i	$0.427533\pi$
$71$	−6.15808	+	10.6661i	−0.730829	+	1.26583i	−0.956529	+	0.291637i	$0.905800\pi$
$72$	0.891834	−	1.54470i	0.105104	−	0.182045i
$73$	−0.768590			−0.0899567			−0.0449783	−	0.998988i	$-0.514322\pi$
$73$	−0.768590			−0.0899567			−0.0449783	+	0.998988i	$0.514322\pi$
$74$	0.905882	−	1.56903i	0.105307	−	0.182396i
$75$	−0.893026	−	1.54677i	−0.103118	−	0.178605i
$76$	7.22585	+	12.5155i	0.828862	+	1.43563i
$77$		0			0
$78$	0.947080	−	0.569251i	0.107236	−	0.0644550i
$79$	6.19284			0.696749			0.348375	−	0.937355i	$-0.386734\pi$
$79$	6.19284			0.696749			0.348375	+	0.937355i	$0.386734\pi$
$80$	−4.57763	−	7.92868i	−0.511794	−	0.886454i
$81$	0.525682	+	0.910507i	0.0584091	+	0.101167i
$82$	0.326774	−	0.565989i	0.0360861	−	0.0625030i
$83$	1.07292			0.117768			0.0588841	−	0.998265i	$-0.481246\pi$
$83$	1.07292			0.117768			0.0588841	+	0.998265i	$0.481246\pi$
$84$		0			0
$85$	1.00562	−	1.74178i	0.109074	−	0.188922i
$86$	0.603137			0.0650379
$87$	−1.34402	+	2.32792i	−0.144094	+	0.249579i
$88$	−2.07801	−	3.59923i	−0.221517	−	0.383679i
$89$	3.83149	+	6.63634i	0.406138	+	0.703451i	0.994453	−	0.105180i	$-0.0335420\pi$
$89$	3.83149	+	6.63634i	0.406138	+	0.703451i	−0.588316	+	0.808631i	$0.700209\pi$
$90$	1.16324			0.122616
$91$		0			0
$92$	15.3384			1.59914
$93$	−1.45983	−	2.52850i	−0.151378	−	0.262194i
$94$	−0.176501	−	0.305708i	−0.0182046	−	0.0315314i
$95$	−9.60052	+	16.6286i	−0.984993	+	1.70606i
$96$	−3.50296			−0.357519
$97$	−1.18601	+	2.05423i	−0.120421	+	0.208575i	−0.919934	−	0.392074i	$-0.871758\pi$
$97$	−1.18601	+	2.05423i	−0.120421	+	0.208575i	0.799513	+	0.600649i	$0.205091\pi$
$98$		0			0
$99$	−6.68267			−0.671634
$100$	1.50642	−	2.60920i	0.150642	−	0.260920i
$101$	−0.398665	−	0.690508i	−0.0396686	−	0.0687081i	0.845509	−	0.533961i	$-0.179297\pi$
$101$	−0.398665	−	0.690508i	−0.0396686	−	0.0687081i	−0.885178	+	0.465252i	$0.845964\pi$
$102$	−0.120305	−	0.208374i	−0.0119119	−	0.0206321i
$103$	−2.16618			−0.213440			−0.106720	−	0.994289i	$-0.534035\pi$
$103$	−2.16618			−0.213440			−0.106720	+	0.994289i	$0.534035\pi$
$104$	3.32160	+	1.84056i	0.325710	+	0.180482i
$105$		0			0
$106$	1.24404	+	2.15474i	0.120832	+	0.209287i
$107$	5.76311	+	9.98201i	0.557141	+	0.964997i	0.997733	+	0.0672896i	$0.0214351\pi$
$107$	5.76311	+	9.98201i	0.557141	+	0.964997i	−0.440592	+	0.897707i	$0.645232\pi$
$108$	−5.17191	+	8.95801i	−0.497667	+	0.861985i
$109$	8.07823			0.773754			0.386877	−	0.922131i	$-0.373554\pi$
$109$	8.07823			0.773754			0.386877	+	0.922131i	$0.373554\pi$
$110$	1.35520	−	2.34727i	0.129213	−	0.223803i
$111$	−3.86174	+	6.68874i	−0.366541	+	0.634867i
$112$		0			0
$113$	−4.02067	+	6.96401i	−0.378233	+	0.655119i	−0.990805	−	0.135296i	$-0.956802\pi$
$113$	−4.02067	+	6.96401i	−0.378233	+	0.655119i	0.612572	+	0.790415i	$0.290135\pi$
$114$	1.14854	+	1.98932i	0.107570	+	0.186317i
$115$	10.1896	+	17.6489i	0.950186	+	1.64577i
$116$	−4.53439			−0.421007
$117$	5.23350	−	3.14564i	0.483837	−	0.290815i
$118$	−2.40420			−0.221325
$119$		0			0
$120$	−1.54198	−	2.67079i	−0.140763	−	0.243808i
$121$	−2.28546	+	3.95854i	−0.207769	+	0.359867i
$122$	2.53257			0.229288
$123$	−1.39303	+	2.41279i	−0.125605	+	0.217554i
$124$	2.46255	−	4.26526i	0.221143	−	0.383032i
$125$	−8.80581			−0.787615
$126$		0			0
$127$	−0.894023	−	1.54849i	−0.0793317	−	0.137406i	0.823630	−	0.567127i	$-0.191945\pi$
$127$	−0.894023	−	1.54849i	−0.0793317	−	0.137406i	−0.902962	+	0.429721i	$0.858612\pi$
$128$	−3.91275	−	6.77709i	−0.345842	−	0.599015i
$129$	−2.57115			−0.226377
$130$	0.0435826	+	2.47617i	0.00382245	+	0.217174i
$131$	6.39091			0.558376			0.279188	−	0.960236i	$-0.409935\pi$
$131$	6.39091			0.558376			0.279188	+	0.960236i	$0.409935\pi$
$132$	4.34819	+	7.53129i	0.378461	+	0.655514i
$133$		0			0
$134$	−0.181328	+	0.314069i	−0.0156644	+	0.0271315i
$135$	−13.7432			−1.18282
$136$	0.413443	−	0.716105i	0.0354525	−	0.0614055i
$137$	−5.01827	+	8.69190i	−0.428740	+	0.742599i	−0.996762	−	0.0804144i	$-0.974376\pi$
$137$	−5.01827	+	8.69190i	−0.428740	+	0.742599i	0.568022	+	0.823014i	$0.307709\pi$
$138$	2.43802			0.207538
$139$	−2.77278	+	4.80260i	−0.235184	+	0.407351i	−0.959326	−	0.282300i	$-0.908903\pi$
$139$	−2.77278	+	4.80260i	−0.235184	+	0.407351i	0.724142	+	0.689651i	$0.242236\pi$
$140$		0			0
$141$	0.752416	+	1.30322i	0.0633648	+	0.109751i
$142$	−3.30227			−0.277121
$143$	−0.250377	−	14.2253i	−0.0209376	−	1.18958i
$144$	−6.05238			−0.504365
$145$	−3.01228	−	5.21742i	−0.250156	−	0.433283i
$146$	−0.103039	−	0.178469i	−0.00852759	−	0.0147702i
$147$		0			0
$148$	−13.0285			−1.07094
$149$	−9.23254	+	15.9912i	−0.756359	+	1.31005i	0.188337	+	0.982104i	$0.439690\pi$
$149$	−9.23254	+	15.9912i	−0.756359	+	1.31005i	−0.944696	+	0.327947i	$0.893643\pi$
$150$	0.239443	−	0.414727i	0.0195504	−	0.0338623i
$151$	1.60736			0.130805			0.0654024	−	0.997859i	$-0.479167\pi$
$151$	1.60736			0.130805			0.0654024	+	0.997859i	$0.479167\pi$
$152$	−3.94710	+	6.83658i	−0.320152	+	0.554520i
$153$	−0.664795	−	1.15146i	−0.0537455	−	0.0930900i
$154$		0			0
$155$	6.54366			0.525600
$156$	−6.95036	−	3.85132i	−0.556474	−	0.308353i
$157$	1.64593			0.131360			0.0656799	−	0.997841i	$-0.479078\pi$
$157$	1.64593			0.131360			0.0656799	+	0.997841i	$0.479078\pi$
$158$	0.830229	+	1.43800i	0.0660494	+	0.114401i
$159$	−5.30330	−	9.18558i	−0.420579	−	0.728464i
$160$	3.92548	−	6.79913i	0.310337	−	0.537519i
$161$		0			0
$162$	−0.140949	+	0.244130i	−0.0110740	+	0.0191807i
$163$	3.27409	−	5.67090i	0.256447	−	0.444179i	−0.708841	−	0.705369i	$-0.750782\pi$
$163$	3.27409	−	5.67090i	0.256447	−	0.444179i	0.965287	+	0.261190i	$0.0841148\pi$
$164$	−4.69971			−0.366986
$165$	−5.77716	+	10.0063i	−0.449751	+	0.778992i
$166$	0.143838	+	0.249135i	0.0111640	+	0.0193367i
$167$	4.77440	+	8.26950i	0.369454	+	0.639913i	0.989480	−	0.144668i	$-0.0462114\pi$
$167$	4.77440	+	8.26950i	0.369454	+	0.639913i	−0.620026	+	0.784581i	$0.712878\pi$
$168$		0			0
$169$	6.89216	+	11.0226i	0.530166	+	0.847894i
$170$	0.539262			0.0413595
$171$	6.34673	+	10.9929i	0.485347	+	0.840646i
$172$	−2.16860	−	3.75613i	−0.165354	−	0.286402i
$173$	5.56582	−	9.64028i	0.423161	−	0.732937i	−0.573085	−	0.819496i	$-0.694254\pi$
$173$	5.56582	−	9.64028i	0.423161	−	0.732937i	0.996247	+	0.0865588i	$0.0275870\pi$
$174$	−0.720733			−0.0546386
$175$		0			0
$176$	−7.05115	+	12.2130i	−0.531501	+	0.920586i
$177$	10.2490			0.770364
$178$	−1.02732	+	1.77937i	−0.0770009	+	0.133369i
$179$	6.32173	+	10.9496i	0.472508	+	0.818409i	0.999505	−	0.0314588i	$-0.0100153\pi$
$179$	6.32173	+	10.9496i	0.472508	+	0.818409i	−0.526997	+	0.849867i	$0.676682\pi$
$180$	−4.18246	−	7.24424i	−0.311742	−	0.539954i
$181$	−14.9158			−1.10868			−0.554341	−	0.832289i	$-0.687030\pi$
$181$	−14.9158			−1.10868			−0.554341	+	0.832289i	$0.687030\pi$
$182$		0			0
$183$	−10.7963			−0.798082
$184$	4.18930	+	7.25607i	0.308839	+	0.534925i
$185$	−8.65509	−	14.9911i	−0.636335	−	1.10216i
$186$	0.391418	−	0.677956i	0.0287001	−	0.0497101i
$187$	−3.09801			−0.226549
$188$	−1.26923	+	2.19837i	−0.0925680	+	0.160332i
$189$		0			0
$190$	−5.14829			−0.373496
$191$	7.06528	−	12.2374i	0.511226	−	0.885469i	−0.488690	−	0.872458i	$-0.662525\pi$
$191$	7.06528	−	12.2374i	0.511226	−	0.885469i	0.999915	−	0.0130110i	$-0.00414165\pi$
$192$	3.61529	+	6.26187i	0.260911	+	0.451912i
$193$	−1.94727	−	3.37277i	−0.140167	−	0.242777i	0.787392	−	0.616452i	$-0.211431\pi$
$193$	−1.94727	−	3.37277i	−0.140167	−	0.242777i	−0.927560	+	0.373675i	$0.878097\pi$
$194$	−0.635998			−0.0456620
$195$	−0.185791	−	10.5558i	−0.0133048	−	0.755917i
$196$		0			0
$197$	5.85445	+	10.1402i	0.417112	+	0.722459i	0.995648	−	0.0931979i	$-0.0297089\pi$
$197$	5.85445	+	10.1402i	0.417112	+	0.722459i	−0.578536	+	0.815657i	$0.696376\pi$
$198$	−0.895897	−	1.55174i	−0.0636686	−	0.110277i
$199$	1.74842	−	3.02835i	0.123942	−	0.214674i	−0.797377	−	0.603482i	$-0.793780\pi$
$199$	1.74842	−	3.02835i	0.123942	−	0.214674i	0.921319	+	0.388808i	$0.127113\pi$
$200$	1.64576			0.116373
$201$	0.772995	−	1.33887i	0.0545229	−	0.0944364i
$202$	0.106892	−	0.185143i	0.00752090	−	0.0130266i
$203$		0			0
$204$	−0.865120	+	1.49843i	−0.0605705	+	0.104911i
$205$	−3.12210	−	5.40764i	−0.218057	−	0.377686i
$206$	−0.290403	−	0.502994i	−0.0202334	−	0.0350452i
$207$	13.4723			0.936392
$208$	−0.226762	−	12.8836i	−0.0157231	−	0.893317i
$209$	29.5764			2.04584
$210$		0			0
$211$	−9.50258	−	16.4589i	−0.654184	−	1.13308i	−0.982098	−	0.188373i	$-0.939679\pi$
$211$	−9.50258	−	16.4589i	−0.654184	−	1.13308i	0.327913	−	0.944708i	$-0.393655\pi$
$212$	8.94598	−	15.4949i	0.614412	−	1.06419i
$213$	14.0775			0.964573
$214$	−1.54524	+	2.67643i	−0.105630	+	0.182957i
$215$	2.88128	−	4.99053i	0.196502	−	0.340351i
$216$	−5.65029			−0.384453
$217$		0			0
$218$	1.08299	+	1.87579i	0.0733492	+	0.127045i
$219$	0.439253	+	0.760808i	0.0296820	+	0.0514106i
$220$	−19.4907			−1.31406
$221$	2.42619	−	1.45828i	0.163203	−	0.0980946i
$222$	−2.07086			−0.138987
$223$	−5.98311	−	10.3630i	−0.400658	−	0.693961i	0.593147	−	0.805094i	$-0.297885\pi$
$223$	−5.98311	−	10.3630i	−0.400658	−	0.693961i	−0.993805	+	0.111133i	$0.964552\pi$
$224$		0			0
$225$	1.32315	−	2.29175i	0.0882097	−	0.152784i
$226$	−2.15609			−0.143421
$227$	7.69209	−	13.3231i	0.510542	−	0.884284i	−0.489384	−	0.872069i	$-0.662778\pi$
$227$	7.69209	−	13.3231i	0.510542	−	0.884284i	0.999925	−	0.0122157i	$-0.00388847\pi$
$228$	8.25921	−	14.3054i	0.546980	−	0.947396i
$229$	−8.66168			−0.572380			−0.286190	−	0.958173i	$-0.592389\pi$
$229$	−8.66168			−0.572380			−0.286190	+	0.958173i	$0.592389\pi$
$230$	−2.73209	+	4.73212i	−0.180149	+	0.312027i
$231$		0			0
$232$	−1.23845	−	2.14506i	−0.0813082	−	0.140830i
$233$	20.2507			1.32667			0.663333	−	0.748325i	$-0.269141\pi$
$233$	20.2507			1.32667			0.663333	+	0.748325i	$0.269141\pi$
$234$	1.43205	+	0.793523i	0.0936157	+	0.0518742i
$235$	−3.37269			−0.220010
$236$	8.64440	+	14.9725i	0.562702	+	0.974629i
$237$	−3.53924	−	6.13014i	−0.229898	−	0.398195i
$238$		0			0
$239$	16.5526			1.07070			0.535350	−	0.844630i	$-0.320180\pi$
$239$	16.5526			1.07070			0.535350	+	0.844630i	$0.320180\pi$
$240$	−5.23227	+	9.06256i	−0.337742	+	0.584985i
$241$	−8.20038	+	14.2035i	−0.528233	+	0.914926i	0.471225	+	0.882013i	$0.343812\pi$
$241$	−8.20038	+	14.2035i	−0.528233	+	0.914926i	−0.999458	+	0.0329132i	$0.989522\pi$
$242$	−1.22558			−0.0787834
$243$	−7.44626	+	12.8973i	−0.477678	+	0.827362i
$244$	−9.10595	−	15.7720i	−0.582949	−	1.00970i
$245$		0			0
$246$	−0.747011			−0.0476277
$247$	−23.1626	+	13.9221i	−1.47380	+	0.885840i
$248$	2.69032			0.170836
$249$	−0.613178	−	1.06206i	−0.0388586	−	0.0673051i
$250$	−1.18053	−	2.04474i	−0.0746632	−	0.129321i
$251$	−10.2154	+	17.6935i	−0.644788	+	1.11681i	0.339563	+	0.940583i	$0.389721\pi$
$251$	−10.2154	+	17.6935i	−0.644788	+	1.11681i	−0.984350	+	0.176222i	$0.943612\pi$
$252$		0			0
$253$	15.6956	−	27.1855i	0.986772	−	1.70914i
$254$	0.239710	−	0.415190i	0.0150407	−	0.0260513i
$255$	−2.29886			−0.143960
$256$	−5.27682	+	9.13972i	−0.329801	+	0.571232i
$257$	6.88895	+	11.9320i	0.429721	+	0.744299i	0.996848	−	0.0793315i	$-0.0252786\pi$
$257$	6.88895	+	11.9320i	0.429721	+	0.744299i	−0.567127	+	0.823630i	$0.691945\pi$
$258$	−0.344695	−	0.597030i	−0.0214598	−	0.0371695i
$259$		0			0
$260$	15.2640	−	9.17456i	0.946633	−	0.568982i
$261$	−3.98272			−0.246524
$262$	0.856782	+	1.48399i	0.0529321	+	0.0916812i
$263$	−12.9587	−	22.4451i	−0.799065	−	1.38402i	−0.920225	−	0.391389i	$-0.871995\pi$
$263$	−12.9587	−	22.4451i	−0.799065	−	1.38402i	0.121160	−	0.992633i	$-0.461338\pi$
$264$	−2.37519	+	4.11395i	−0.146183	+	0.253196i
$265$	23.7719			1.46030
$266$		0			0
$267$	4.37943	−	7.58540i	0.268017	−	0.464219i
$268$	2.60789			0.159302
$269$	−15.0333	+	26.0384i	−0.916596	+	1.58759i	−0.112050	+	0.993703i	$0.535742\pi$
$269$	−15.0333	+	26.0384i	−0.916596	+	1.58759i	−0.804547	+	0.593889i	$0.797592\pi$
$270$	−1.84245	−	3.19121i	−0.112128	−	0.194211i
$271$	7.22527	+	12.5145i	0.438904	+	0.760204i	0.997605	−	0.0691651i	$-0.0220335\pi$
$271$	7.22527	+	12.5145i	0.438904	+	0.760204i	−0.558701	+	0.829369i	$0.688700\pi$
$272$	−2.80581			−0.170127
$273$		0			0
$274$	−2.69105			−0.162572
$275$	−3.08299	−	5.33989i	−0.185911	−	0.322008i
$276$	−8.76599	−	15.1831i	−0.527651	−	0.913918i
$277$	7.66274	−	13.2723i	0.460409	−	0.797452i	−0.538572	−	0.842580i	$-0.681036\pi$
$277$	7.66274	−	13.2723i	0.460409	−	0.797452i	0.998981	+	0.0451272i	$0.0143693\pi$
$278$	−1.48691			−0.0891787
$279$	2.16295	−	3.74634i	0.129492	−	0.224287i
$280$		0			0
$281$	5.29279			0.315741			0.157871	−	0.987460i	$-0.449537\pi$
$281$	5.29279			0.315741			0.157871	+	0.987460i	$0.449537\pi$
$282$	−0.201742	+	0.349427i	−0.0120135	+	0.0208081i
$283$	−15.3923	−	26.6602i	−0.914975	−	1.58478i	−0.806938	−	0.590636i	$-0.798877\pi$
$283$	−15.3923	−	26.6602i	−0.914975	−	1.58478i	−0.108036	−	0.994147i	$-0.534456\pi$
$284$	11.8734	+	20.5654i	0.704559	+	1.22033i
$285$	21.9470			1.30003
$286$	3.26960	−	1.96522i	0.193335	−	0.116206i
$287$		0			0
$288$	−2.59507	−	4.49479i	−0.152916	−	0.264858i
$289$	8.19181	+	14.1886i	0.481871	+	0.834625i
$290$	0.807667	−	1.39892i	0.0474279	−	0.0821474i
$291$	2.71124			0.158935
$292$	−0.740963	+	1.28339i	−0.0433616	+	0.0751044i
$293$	−8.75864	+	15.1704i	−0.511685	+	0.886265i	0.488223	+	0.872719i	$0.337645\pi$
$293$	−8.75864	+	15.1704i	−0.511685	+	0.886265i	−0.999908	+	0.0135461i	$0.995688\pi$
$294$		0			0
$295$	−11.4853	+	19.8930i	−0.668697	+	1.15822i
$296$	−3.55840	−	6.16333i	−0.206828	−	0.358237i
$297$	10.5847	+	18.3332i	0.614184	+	1.06380i
$298$	−4.95095			−0.286801
$299$	0.504763	+	28.6784i	0.0291912	+	1.65851i
$300$	−3.44370			−0.198822
$301$		0			0
$302$	0.215486	+	0.373233i	0.0123998	+	0.0214772i
$303$	−0.455678	+	0.789257i	−0.0261780	+	0.0453416i
$304$	26.7868			1.53633
$305$	12.0985	−	20.9552i	0.692757	−	1.19989i
$306$	0.178248	−	0.308735i	0.0101898	−	0.0176492i
$307$	8.63573			0.492867			0.246434	−	0.969160i	$-0.420741\pi$
$307$	8.63573			0.492867			0.246434	+	0.969160i	$0.420741\pi$
$308$		0			0
$309$	1.23798	+	2.14425i	0.0704262	+	0.121982i
$310$	0.877260	+	1.51946i	0.0498250	+	0.0862995i
$311$	16.4226			0.931240			0.465620	−	0.884985i	$-0.345831\pi$
$311$	16.4226			0.931240			0.465620	+	0.884985i	$0.345831\pi$
$312$	−0.0763851	−	4.33986i	−0.00432445	−	0.245696i
$313$	−10.0462			−0.567843			−0.283921	−	0.958848i	$-0.591636\pi$
$313$	−10.0462			−0.567843			−0.283921	+	0.958848i	$0.591636\pi$
$314$	0.220658	+	0.382191i	0.0124525	+	0.0215683i
$315$		0			0
$316$	5.97024	−	10.3408i	0.335852	−	0.581713i
$317$	10.1450			0.569799			0.284899	−	0.958557i	$-0.408040\pi$
$317$	10.1450			0.569799			0.284899	+	0.958557i	$0.408040\pi$
$318$	1.42195	−	2.46289i	0.0797389	−	0.138112i
$319$	−4.63996	+	8.03665i	−0.259788	+	0.449966i
$320$	−16.2055			−0.905913
$321$	6.58729	−	11.4095i	0.367667	−	0.636817i
$322$		0			0
$323$	2.94227	+	5.09616i	0.163712	+	0.283558i
$324$	2.02714			0.112619
$325$	4.92800	+	2.73070i	0.273356	+	0.151472i
$326$	1.75573			0.0972411
$327$	−4.61674	−	7.99644i	−0.255307	−	0.442204i
$328$	−1.28360	−	2.22327i	−0.0708751	−	0.122759i
$329$		0			0
$330$	−3.09801			−0.170540
$331$	−1.15958	+	2.00845i	−0.0637363	+	0.110395i	−0.896133	−	0.443786i	$-0.853635\pi$
$331$	−1.15958	+	2.00845i	−0.0637363	+	0.110395i	0.832396	+	0.554181i	$0.186968\pi$
$332$	1.03435	−	1.79155i	0.0567675	−	0.0983242i
$333$	−11.4434			−0.627097
$334$	−1.28014	+	2.21726i	−0.0700460	+	0.121323i
$335$	1.73247	+	3.00072i	0.0946547	+	0.163947i
$336$		0			0
$337$	−15.9998			−0.871565			−0.435783	−	0.900052i	$-0.643528\pi$
$337$	−15.9998			−0.871565			−0.435783	+	0.900052i	$0.643528\pi$
$338$	−1.63551	+	3.07810i	−0.0889598	+	0.167427i
$339$	9.19133			0.499205
$340$	−1.93894	−	3.35834i	−0.105154	−	0.182132i
$341$	−5.03977	−	8.72913i	−0.272919	−	0.472709i
$342$	−1.70172	+	2.94747i	−0.0920185	+	0.159381i
$343$		0			0
$344$	1.18459	−	2.05178i	0.0638690	−	0.110624i
$345$	11.6468	−	20.1729i	0.627043	−	1.08607i
$346$	2.98467			0.160457
$347$	11.4104	−	19.7634i	0.612543	−	1.06096i	−0.378267	−	0.925696i	$-0.623480\pi$
$347$	11.4104	−	19.7634i	0.612543	−	1.06096i	0.990810	−	0.135259i	$-0.0431867\pi$
$348$	2.59142	+	4.48848i	0.138915	+	0.240608i
$349$	−11.3511	−	19.6607i	−0.607612	−	1.05241i	−0.991633	−	0.129090i	$-0.958794\pi$
$349$	−11.3511	−	19.6607i	−0.607612	−	1.05241i	0.384021	−	0.923324i	$-0.374539\pi$
$350$		0			0
$351$	−16.9190	−	9.37515i	−0.903071	−	0.500408i
$352$	−12.0932			−0.644572
$353$	−13.6322	−	23.6116i	−0.725568	−	1.25672i	−0.958740	−	0.284286i	$-0.908244\pi$
$353$	−13.6322	−	23.6116i	−0.725568	−	1.25672i	0.233171	−	0.972436i	$-0.425090\pi$
$354$	1.37401	+	2.37986i	0.0730279	+	0.126488i
$355$	−15.7755	+	27.3239i	−0.837276	+	1.45020i
$356$	14.7751			0.783077
$357$		0			0
$358$	−1.69502	+	2.93585i	−0.0895844	+	0.155165i
$359$	−14.4262			−0.761385			−0.380692	−	0.924702i	$-0.624314\pi$
$359$	−14.4262			−0.761385			−0.380692	+	0.924702i	$0.624314\pi$
$360$	2.28466	−	3.95715i	0.120412	−	0.208560i
$361$	−18.5895	−	32.1980i	−0.978397	−	1.69463i
$362$	−1.99965	−	3.46350i	−0.105099	−	0.182037i
$363$	5.22461			0.274221
$364$		0			0
$365$	−1.96894			−0.103059
$366$	−1.44737	−	2.50693i	−0.0756555	−	0.131039i
$367$	−5.69586	−	9.86553i	−0.297322	−	0.514976i	0.678201	−	0.734877i	$-0.262760\pi$
$367$	−5.69586	−	9.86553i	−0.297322	−	0.514976i	−0.975522	+	0.219901i	$0.929427\pi$
$368$	14.2152	−	24.6214i	0.741018	−	1.28348i
$369$	−4.12793			−0.214892
$370$	2.32065	−	4.01948i	0.120645	−	0.208963i
$371$		0			0
$372$	−5.62943			−0.291872
$373$	15.4815	−	26.8147i	0.801599	−	1.38841i	−0.116964	−	0.993136i	$-0.537316\pi$
$373$	15.4815	−	26.8147i	0.801599	−	1.38841i	0.918563	−	0.395274i	$-0.129351\pi$
$374$	−0.415327	−	0.719367i	−0.0214760	−	0.0371976i
$375$	5.03256	+	8.71665i	0.259880	+	0.450126i
$376$	−1.38663			−0.0715098
$377$	−0.149219	−	8.47796i	−0.00768518	−	0.436637i
$378$		0			0
$379$	−5.29330	−	9.16826i	−0.271898	−	0.470942i	0.697450	−	0.716634i	$-0.254318\pi$
$379$	−5.29330	−	9.16826i	−0.271898	−	0.470942i	−0.969348	+	0.245692i	$0.920985\pi$
$380$	18.5109	+	32.0617i	0.949587	+	1.64473i
$381$	−1.02188	+	1.76994i	−0.0523523	+	0.0906768i
$382$	3.78876			0.193850
$383$	15.3758	−	26.6317i	0.785668	−	1.36082i	−0.142931	−	0.989733i	$-0.545653\pi$
$383$	15.3758	−	26.6317i	0.785668	−	1.36082i	0.928599	−	0.371084i	$-0.121014\pi$
$384$	−4.47231	+	7.74627i	−0.228227	+	0.395300i
$385$		0			0
$386$	0.522112	−	0.904324i	0.0265748	−	0.0460289i
$387$	−1.90476	−	3.29915i	−0.0968246	−	0.167705i
$388$	2.28675	+	3.96077i	0.116092	+	0.201078i
$389$	−16.3796			−0.830477			−0.415239	−	0.909713i	$-0.636302\pi$
$389$	−16.3796			−0.830477			−0.415239	+	0.909713i	$0.636302\pi$
$390$	2.42619	−	1.45828i	0.122855	−	0.0738429i
$391$	6.24561			0.315854
$392$		0			0
$393$	−3.65243	−	6.32620i	−0.184241	−	0.319114i
$394$	−1.56972	+	2.71884i	−0.0790816	+	0.136973i
$395$	15.8645			0.798232
$396$	−6.44246	+	11.1587i	−0.323746	+	0.560744i
$397$	−7.94133	+	13.7548i	−0.398564	+	0.690333i	−0.993549	−	0.113404i	$-0.963825\pi$
$397$	−7.94133	+	13.7548i	−0.398564	+	0.690333i	0.594985	+	0.803737i	$0.297158\pi$
$398$	0.937591			0.0469972
$399$		0			0
$400$	−2.79221	−	4.83624i	−0.139610	−	0.241812i
$401$	−3.31787	−	5.74671i	−0.165686	−	0.286977i	0.771212	−	0.636578i	$-0.219651\pi$
$401$	−3.31787	−	5.74671i	−0.165686	−	0.286977i	−0.936899	+	0.349601i	$0.886317\pi$
$402$	0.414519			0.0206743
$403$	8.05581	+	4.46387i	0.401289	+	0.222361i
$404$	−1.53734			−0.0764855
$405$	1.34667	+	2.33250i	0.0669164	+	0.115903i
$406$		0			0
$407$	−13.3319	+	23.0915i	−0.660836	+	1.14460i
$408$	−0.945139			−0.0467914
$409$	2.93617	−	5.08560i	0.145184	−	0.251467i	−0.784257	−	0.620436i	$-0.786956\pi$
$409$	2.93617	−	5.08560i	0.145184	−	0.251467i	0.929442	+	0.368969i	$0.120289\pi$
$410$	0.837115	−	1.44992i	0.0413421	−	0.0716067i
$411$	11.4719			0.565865
$412$	−2.08831	+	3.61707i	−0.102884	+	0.178200i
$413$		0			0
$414$	1.80614	+	3.12832i	0.0887667	+	0.153749i
$415$	2.74856			0.134921
$416$	9.47076	−	5.69248i	0.464342	−	0.279097i
$417$	6.33863			0.310404
$418$	3.96508	+	6.86773i	0.193939	+	0.335911i
$419$	−15.0712	−	26.1040i	−0.736274	−	1.27526i	−0.954162	−	0.299290i	$-0.903250\pi$
$419$	−15.0712	−	26.1040i	−0.736274	−	1.27526i	0.217888	−	0.975974i	$-0.430083\pi$
$420$		0			0
$421$	40.0580			1.95231			0.976153	−	0.217083i	$-0.0696543\pi$
$421$	40.0580			1.95231			0.976153	+	0.217083i	$0.0696543\pi$
$422$	2.54788	−	4.41306i	0.124029	−	0.214824i
$423$	−1.11481	+	1.93091i	−0.0542040	+	0.0938840i
$424$	9.77344			0.474640
$425$	0.613394	−	1.06243i	0.0297540	−	0.0515354i
$426$	1.88726	+	3.26884i	0.0914382	+	0.158376i
$427$		0			0
$428$	22.2238			1.07423
$429$	−13.9382	+	8.37767i	−0.672942	+	0.404478i
$430$	1.54509			0.0745108
$431$	1.95793	+	3.39124i	0.0943104	+	0.163350i	0.909321	−	0.416096i	$-0.136602\pi$
$431$	1.95793	+	3.39124i	0.0943104	+	0.163350i	−0.815010	+	0.579447i	$0.803269\pi$
$432$	9.58632	+	16.6040i	0.461222	+	0.798860i
$433$	−20.3963	+	35.3274i	−0.980182	+	1.69772i	−0.318532	+	0.947912i	$0.603190\pi$
$433$	−20.3963	+	35.3274i	−0.980182	+	1.69772i	−0.661650	+	0.749813i	$0.730144\pi$
$434$		0			0
$435$	−3.44306	+	5.96355i	−0.165082	+	0.285930i
$436$	7.78785	−	13.4890i	0.372971	−	0.646004i
$437$	−59.6262			−2.85231
$438$	−0.117775	+	0.203992i	−0.00562750	+	0.00974711i
$439$	−12.7811	−	22.1376i	−0.610010	−	1.05657i	−0.991238	−	0.132087i	$-0.957832\pi$
$439$	−12.7811	−	22.1376i	−0.610010	−	1.05657i	0.381228	−	0.924481i	$-0.375501\pi$
$440$	−5.32336	−	9.22033i	−0.253781	−	0.439562i
$441$		0			0
$442$	0.663878	+	0.367867i	0.0315775	+	0.0174977i
$443$	−27.4564			−1.30449			−0.652247	−	0.758007i	$-0.726173\pi$
$443$	−27.4564			−1.30449			−0.652247	+	0.758007i	$0.726173\pi$
$444$	7.44586	+	12.8966i	0.353365	+	0.612046i
$445$	9.81535	+	17.0007i	0.465292	+	0.805910i
$446$	1.60422	−	2.77859i	0.0759621	−	0.131570i
$447$	21.1057			0.998267
$448$		0			0
$449$	7.40181	−	12.8203i	0.349313	−	0.605028i	−0.636815	−	0.771017i	$-0.719748\pi$
$449$	7.40181	−	12.8203i	0.349313	−	0.605028i	0.986128	+	0.165989i	$0.0530816\pi$
$450$	0.709537			0.0334479
$451$	−4.80913	+	8.32966i	−0.226453	+	0.392229i
$452$	7.75230	+	13.4274i	0.364637	+	0.631571i
$453$	−0.918611	−	1.59108i	−0.0431601	−	0.0747555i
$454$	4.12489			0.193590
$455$		0			0
$456$	9.02315			0.422548
$457$	0.325975	+	0.564606i	0.0152485	+	0.0264112i	0.873549	−	0.486736i	$-0.161813\pi$
$457$	0.325975	+	0.564606i	0.0152485	+	0.0264112i	−0.858300	+	0.513147i	$0.828479\pi$
$458$	−1.16121	−	2.01127i	−0.0542596	−	0.0939805i
$459$	−2.10593	+	3.64758i	−0.0982965	+	0.170254i
$460$	39.2933			1.83206
$461$	6.24774	−	10.8214i	0.290986	−	0.504003i	−0.683057	−	0.730365i	$-0.739350\pi$
$461$	6.24774	−	10.8214i	0.290986	−	0.504003i	0.974043	+	0.226362i	$0.0726833\pi$
$462$		0			0
$463$	−0.309503			−0.0143838			−0.00719190	−	0.999974i	$-0.502289\pi$
$463$	−0.309503			−0.0143838			−0.00719190	+	0.999974i	$0.502289\pi$
$464$	−4.20233	+	7.27865i	−0.195088	+	0.337903i
$465$	−3.73973	−	6.47741i	−0.173426	−	0.300382i
$466$	2.71486	+	4.70227i	0.125763	+	0.217829i
$467$	−24.4773			−1.13268			−0.566338	−	0.824173i	$-0.691640\pi$
$467$	−24.4773			−1.13268			−0.566338	+	0.824173i	$0.691640\pi$
$468$	−0.207187	−	11.7714i	−0.00957722	−	0.544134i
$469$		0			0
$470$	−0.452151	−	0.783149i	−0.0208562	−	0.0361240i
$471$	−0.940659	−	1.62927i	−0.0433433	−	0.0750727i
$472$	−4.72198	+	8.17871i	−0.217347	+	0.376456i
$473$	−8.87637			−0.408136
$474$	0.948959	−	1.64364i	0.0435871	−	0.0754951i
$475$	−5.85601	+	10.1429i	−0.268692	+	0.465389i
$476$		0			0
$477$	7.85759	−	13.6097i	0.359774	−	0.623147i
$478$	2.21909	+	3.84357i	0.101499	+	0.175801i
$479$	4.06925	+	7.04815i	0.185929	+	0.322038i	0.943889	−	0.330262i	$-0.107137\pi$
$479$	4.06925	+	7.04815i	0.185929	+	0.322038i	−0.757960	+	0.652301i	$0.773804\pi$
$480$	−8.97372			−0.409593
$481$	−0.428748	−	24.3595i	−0.0195492	−	1.11070i
$482$	−4.39746			−0.200299
$483$		0			0
$484$	4.40662	+	7.63250i	0.200301	+	0.346932i
$485$	−3.03826	+	5.26243i	−0.137960	+	0.238954i
$486$	−3.99306			−0.181129
$487$	−2.30480	+	3.99203i	−0.104440	+	0.180896i	−0.913509	−	0.406817i	$-0.866638\pi$
$487$	−2.30480	+	3.99203i	−0.104440	+	0.180896i	0.809069	+	0.587714i	$0.199972\pi$
$488$	4.97410	−	8.61540i	0.225167	−	0.390001i
$489$	−7.48464			−0.338467
$490$		0			0
$491$	−6.50947	−	11.2747i	−0.293768	−	0.508822i	0.680929	−	0.732349i	$-0.261576\pi$
$491$	−6.50947	−	11.2747i	−0.293768	−	0.508822i	−0.974698	+	0.223527i	$0.928243\pi$
$492$	2.68591	+	4.65213i	0.121090	+	0.209734i
$493$	−1.84634			−0.0831551
$494$	−6.33798	−	3.51199i	−0.285159	−	0.158012i
$495$	−17.1194			−0.769459
$496$	−4.56443	−	7.90582i	−0.204949	−	0.354982i
$497$		0			0
$498$	0.164409	−	0.284764i	0.00736733	−	0.0127606i
$499$	−32.3207			−1.44687			−0.723436	−	0.690391i	$-0.757438\pi$
$499$	−32.3207			−1.44687			−0.723436	+	0.690391i	$0.757438\pi$
$500$	−8.48928	+	14.7039i	−0.379652	+	0.657577i
$501$	5.45718	−	9.45211i	0.243809	−	0.422289i
$502$	−5.47799			−0.244495
$503$	−15.9126	+	27.5615i	−0.709509	+	1.22891i	0.255531	+	0.966801i	$0.417750\pi$
$503$	−15.9126	+	27.5615i	−0.709509	+	1.22891i	−0.965039	+	0.262105i	$0.915583\pi$
$504$		0			0
$505$	−1.02128	−	1.76891i	−0.0454465	−	0.0787156i
$506$	8.41676			0.374170
$507$	6.97211	−	13.1219i	0.309642	−	0.582762i
$508$	−3.44755			−0.152960
$509$	1.12788	+	1.95354i	0.0499922	+	0.0865891i	0.889939	−	0.456080i	$-0.150747\pi$
$509$	1.12788	+	1.95354i	0.0499922	+	0.0865891i	−0.839946	+	0.542669i	$0.817414\pi$
$510$	−0.308191	−	0.533802i	−0.0136469	−	0.0236372i
$511$		0			0
$512$	−18.4807			−0.816739
$513$	20.1051	−	34.8231i	0.887663	−	1.53748i
$514$	−1.84710	+	3.19927i	−0.0814722	+	0.141114i
$515$	−5.54922			−0.244528
$516$	−2.47873	+	4.29329i	−0.109120	+	0.189001i
$517$	2.59756	+	4.49911i	0.114241	+	0.197870i
$518$		0			0
$519$	−12.7236			−0.558502
$520$	8.50912	+	4.71506i	0.373150	+	0.206769i
$521$	−10.7712			−0.471897			−0.235948	−	0.971766i	$-0.575820\pi$
$521$	−10.7712			−0.471897			−0.235948	+	0.971766i	$0.575820\pi$
$522$	−0.533934	−	0.924801i	−0.0233697	−	0.0404775i
$523$	3.70397	+	6.41546i	0.161963	+	0.280528i	0.935573	−	0.353134i	$-0.114884\pi$
$523$	3.70397	+	6.41546i	0.161963	+	0.280528i	−0.773610	+	0.633663i	$0.781551\pi$
$524$	6.16118	−	10.6715i	0.269152	−	0.466186i
$525$		0			0
$526$	3.47454	−	6.01809i	0.151497	−	0.262401i
$527$	1.00272	−	1.73676i	0.0436790	−	0.0756543i
$528$	16.1191			0.701492
$529$	−20.1424	+	34.8877i	−0.875757	+	1.51686i
$530$	3.18692	+	5.51991i	0.138431	+	0.239770i
$531$	7.59270	+	13.1509i	0.329495	+	0.570702i
$532$		0			0
$533$	−0.154660	−	8.78707i	−0.00669906	−	0.380610i
$534$	2.34847			0.101628
$535$	14.7637	+	25.5715i	0.638290	+	1.10555i
$536$	0.712276	+	1.23370i	0.0307656	+	0.0532876i
$537$	7.22580	−	12.5154i	0.311816	−	0.540081i
$538$	−8.06161			−0.347561
$539$		0			0
$540$	−13.2492	+	22.9482i	−0.570153	+	0.987534i
$541$	32.5481			1.39935			0.699676	−	0.714460i	$-0.253327\pi$
$541$	32.5481			1.39935			0.699676	+	0.714460i	$0.253327\pi$
$542$	−1.93728	+	3.35546i	−0.0832132	+	0.144129i
$543$	8.52445	+	14.7648i	0.365819	+	0.633617i
$544$	−1.20304	−	2.08373i	−0.0515799	−	0.0893391i
$545$	20.6944			0.886453
$546$		0			0
$547$	−13.4997			−0.577206			−0.288603	−	0.957449i	$-0.593191\pi$
$547$	−13.4997			−0.577206			−0.288603	+	0.957449i	$0.593191\pi$
$548$	9.67577	+	16.7589i	0.413329	+	0.715906i
$549$	−7.99810	−	13.8531i	−0.341350	−	0.591236i
$550$	0.826627	−	1.43176i	0.0352475	−	0.0610504i
$551$	17.6268			0.750929
$552$	4.78840	−	8.29376i	0.203808	−	0.353006i
$553$		0			0
$554$	4.10915			0.174581
$555$	−9.89284	+	17.1349i	−0.419928	+	0.727336i
$556$	5.34623	+	9.25994i	0.226731	+	0.392709i
$557$	14.8851	+	25.7818i	0.630703	+	1.09241i	0.987408	+	0.158193i	$0.0505668\pi$
$557$	14.8851	+	25.7818i	0.630703	+	1.09241i	−0.356705	+	0.934217i	$0.616100\pi$
$558$	1.15988			0.0491017
$559$	6.95148	−	4.17825i	0.294016	−	0.176721i
$560$		0			0
$561$	1.77052	+	3.06664i	0.0747516	+	0.129474i
$562$	0.709566	+	1.22900i	0.0299312	+	0.0518424i
$563$	7.06629	−	12.2392i	0.297809	−	0.515819i	−0.677826	−	0.735223i	$-0.737078\pi$
$563$	7.06629	−	12.2392i	0.297809	−	0.515819i	0.975634	+	0.219403i	$0.0704110\pi$
$564$	2.90148			0.122174
$565$	−10.3000	+	17.8401i	−0.433324	+	0.750538i
$566$	4.12705	−	7.14826i	0.173473	−	0.300464i
$567$		0			0
$568$	−6.48584	+	11.2338i	−0.272140	+	0.471360i
$569$	12.1270	+	21.0046i	0.508391	+	0.880558i	0.999953	+	0.00971585i	$0.00309270\pi$
$569$	12.1270	+	21.0046i	0.508391	+	0.880558i	−0.491562	+	0.870842i	$0.663574\pi$
$570$	2.94227	+	5.09616i	0.123238	+	0.213455i
$571$	1.20832			0.0505665			0.0252832	−	0.999680i	$-0.491951\pi$
$571$	1.20832			0.0505665			0.0252832	+	0.999680i	$0.491951\pi$
$572$	−23.9947	−	13.2959i	−1.00327	−	0.555929i
$573$	−16.1514			−0.674732
$574$		0			0
$575$	6.21533	+	10.7653i	0.259197	+	0.448943i
$576$	−5.35657	+	9.27786i	−0.223191	+	0.386577i
$577$	14.6104			0.608237			0.304119	−	0.952634i	$-0.401638\pi$
$577$	14.6104			0.608237			0.304119	+	0.952634i	$0.401638\pi$
$578$	−2.19643	+	3.80433i	−0.0913595	+	0.158239i
$579$	−2.22575	+	3.85510i	−0.0924988	+	0.160213i
$580$	−11.6160			−0.482328
$581$		0			0
$582$	0.363475	+	0.629558i	0.0150665	+	0.0260960i
$583$	−18.3085	−	31.7113i	−0.758262	−	1.31335i
$584$	−0.809498			−0.0334973
$585$	13.4069	−	8.05836i	0.554309	−	0.333172i
$586$	−4.69683			−0.194024
$587$	10.7548	+	18.6278i	0.443897	+	0.768852i	0.997975	−	0.0636132i	$-0.0202624\pi$
$587$	10.7548	+	18.6278i	0.443897	+	0.768852i	−0.554078	+	0.832465i	$0.686929\pi$
$588$		0			0
$589$	−9.57284	+	16.5806i	−0.394442	+	0.683193i
$590$	−6.15897			−0.253561
$591$	6.69168	−	11.5903i	0.275259	−	0.476763i
$592$	−12.0744	+	20.9135i	−0.496256	+	0.859541i
$593$	2.64857			0.108764			0.0543820	−	0.998520i	$-0.482681\pi$
$593$	2.64857			0.108764			0.0543820	+	0.998520i	$0.482681\pi$
$594$	−2.83801	+	4.91558i	−0.116445	+	0.201689i
$595$		0			0
$596$	17.8013	+	30.8328i	0.729171	+	1.26296i
$597$	−3.99692			−0.163583
$598$	−6.59154	+	3.96190i	−0.269548	+	0.162014i
$599$	−40.2501			−1.64457			−0.822287	−	0.569074i	$-0.807302\pi$
$599$	−40.2501			−1.64457			−0.822287	+	0.569074i	$0.807302\pi$
$600$	−0.940558	−	1.62909i	−0.0383981	−	0.0665075i
$601$	19.1725	+	33.2077i	0.782061	+	1.35457i	0.930739	+	0.365683i	$0.119165\pi$
$601$	19.1725	+	33.2077i	0.782061	+	1.35457i	−0.148679	+	0.988886i	$0.547502\pi$
$602$		0			0
$603$	2.29060			0.0932806
$604$	1.54958	−	2.68395i	0.0630515	−	0.109208i
$605$	−5.85480	+	10.1408i	−0.238031	+	0.412283i
$606$	−0.244357			−0.00992634
$607$	21.2773	−	36.8534i	0.863620	−	1.49583i	−0.00479063	−	0.999989i	$-0.501525\pi$
$607$	21.2773	−	36.8534i	0.863620	−	1.49583i	0.868411	−	0.495845i	$-0.165142\pi$
$608$	11.4853	+	19.8931i	0.465791	+	0.806773i
$609$		0			0
$610$	6.48782			0.262684
$611$	−4.15207	−	2.30074i	−0.167975	−	0.0930779i
$612$	−2.56360			−0.103627
$613$	−7.63261	−	13.2201i	−0.308278	−	0.533953i	0.669708	−	0.742625i	$-0.266419\pi$
$613$	−7.63261	−	13.2201i	−0.308278	−	0.533953i	−0.977986	+	0.208672i	$0.933086\pi$
$614$	1.15773	+	2.00524i	0.0467221	+	0.0809251i
$615$	−3.56859	+	6.18098i	−0.143899	+	0.249241i
$616$		0			0
$617$	−6.99061	+	12.1081i	−0.281431	+	0.487453i	−0.971737	−	0.236064i	$-0.924142\pi$
$617$	−6.99061	+	12.1081i	−0.281431	+	0.487453i	0.690306	+	0.723517i	$0.257476\pi$
$618$	−0.331934	+	0.574926i	−0.0133523	+	0.0231269i
$619$	8.51585			0.342281			0.171140	−	0.985247i	$-0.445255\pi$
$619$	8.51585			0.342281			0.171140	+	0.985247i	$0.445255\pi$
$620$	6.30845	−	10.9265i	0.253353	−	0.438821i
$621$	−21.3388	−	36.9598i	−0.856295	−	1.48315i
$622$	2.20166	+	3.81338i	0.0882784	+	0.152903i
$623$		0			0
$624$	−12.6236	+	7.58750i	−0.505347	+	0.303743i
$625$	−30.3713			−1.21485
$626$	−1.34682	−	2.33275i	−0.0538296	−	0.0932356i
$627$	−16.9030	−	29.2769i	−0.675042	−	1.16921i
$628$	1.58677	−	2.74837i	0.0633190	−	0.109672i
$629$	−5.30504			−0.211526
$630$		0			0
$631$	−18.4146	+	31.8950i	−0.733074	+	1.26972i	0.222490	+	0.974935i	$0.428582\pi$
$631$	−18.4146	+	31.8950i	−0.733074	+	1.26972i	−0.955563	+	0.294786i	$0.904752\pi$
$632$	6.52246			0.259449
$633$	−10.8615	+	18.8127i	−0.431707	+	0.747739i
$634$	1.36006	+	2.35570i	0.0540150	+	0.0935567i
$635$	−2.29027	−	3.96686i	−0.0908865	−	0.157420i
$636$	−20.4507			−0.810922
$637$		0			0
$638$	−2.48818			−0.0985081
$639$	10.4289	+	18.0634i	0.412561	+	0.714576i
$640$	−10.0235	−	17.3612i	−0.396214	−	0.686263i
$641$	−12.9374	+	22.4082i	−0.510996	+	0.885070i	0.488923	+	0.872327i	$0.337390\pi$
$641$	−12.9374	+	22.4082i	−0.510996	+	0.885070i	−0.999919	+	0.0127435i	$0.995944\pi$
$642$	3.53244			0.139414
$643$	20.2626	−	35.0958i	0.799078	−	1.38404i	−0.121139	−	0.992636i	$-0.538655\pi$
$643$	20.2626	−	35.0958i	0.799078	−	1.38404i	0.920217	−	0.391408i	$-0.128012\pi$
$644$		0			0
$645$	−6.58666			−0.259350
$646$	−0.788896	+	1.36641i	−0.0310387	+	0.0537606i
$647$	0.892002	+	1.54499i	0.0350682	+	0.0607399i	0.883027	−	0.469322i	$-0.155502\pi$
$647$	0.892002	+	1.54499i	0.0350682	+	0.0607399i	−0.847959	+	0.530062i	$0.822168\pi$
$648$	0.553661	+	0.958969i	0.0217499	+	0.0376719i
$649$	35.3826			1.38889
$650$	0.0265840	+	1.51038i	0.00104271	+	0.0592420i
$651$		0			0
$652$	−6.31281	−	10.9341i	−0.247229	−	0.428213i
$653$	−6.20210	−	10.7424i	−0.242707	−	0.420381i	0.718778	−	0.695240i	$-0.244702\pi$
$653$	−6.20210	−	10.7424i	−0.242707	−	0.420381i	−0.961484	+	0.274860i	$0.911369\pi$
$654$	1.23787	−	2.14405i	0.0484044	−	0.0838389i
$655$	16.3719			0.639704
$656$	−4.35554	+	7.54402i	−0.170055	+	0.294545i
$657$	−0.650815	+	1.12725i	−0.0253907	+	0.0439780i
$658$		0			0
$659$	0.564336	−	0.977458i	0.0219834	−	0.0380764i	−0.854824	−	0.518917i	$-0.826335\pi$
$659$	0.564336	−	0.977458i	0.0219834	−	0.0380764i	0.876808	+	0.480841i	$0.159669\pi$
$660$	11.1390	+	19.2933i	0.433585	+	0.750991i
$661$	−14.4627	−	25.0502i	−0.562534	−	0.974338i	−0.997274	−	0.0737821i	$-0.976493\pi$
$661$	−14.4627	−	25.0502i	−0.562534	−	0.974338i	0.434740	−	0.900556i	$-0.356840\pi$
$662$	−0.621826			−0.0241680
$663$	−2.83009	−	1.56821i	−0.109912	−	0.0609041i
$664$	1.13003			0.0438535
$665$		0			0
$666$	−1.53414	−	2.65721i	−0.0594467	−	0.102965i
$667$	9.35421	−	16.2020i	0.362196	−	0.627342i
$668$	18.4111			0.712348
$669$	−6.83874	+	11.8451i	−0.264401	+	0.457956i
$670$	−0.464518	+	0.804568i	−0.0179459	+	0.0310832i
$671$	−37.2718			−1.43886
$672$		0			0
$673$	3.54980	+	6.14843i	0.136835	+	0.237005i	0.926297	−	0.376795i	$-0.122974\pi$
$673$	3.54980	+	6.14843i	0.136835	+	0.237005i	−0.789462	+	0.613799i	$0.789640\pi$
$674$	−2.14498	−	3.71521i	−0.0826214	−	0.143104i
$675$	−8.38289			−0.322658
$676$	25.0499	−	0.882071i	0.963457	−	0.0339258i
$677$	50.4020			1.93710			0.968552	−	0.248811i	$-0.0800397\pi$
$677$	50.4020			1.93710			0.968552	+	0.248811i	$0.0800397\pi$
$678$	1.23221	+	2.13426i	0.0473229	+	0.0819657i
$679$		0			0
$680$	1.05914	−	1.83449i	0.0406162	−	0.0703493i
$681$	−17.5843			−0.673830
$682$	1.35129	−	2.34050i	0.0517435	−	0.0896224i
$683$	−13.7641	+	23.8401i	−0.526669	+	0.912217i	0.472848	+	0.881144i	$0.343226\pi$
$683$	−13.7641	+	23.8401i	−0.526669	+	0.912217i	−0.999517	+	0.0310735i	$0.990107\pi$
$684$	24.4744			0.935802
$685$	−12.8556	+	22.2665i	−0.491186	+	0.850760i
$686$		0			0
$687$	4.95019	+	8.57398i	0.188861	+	0.327118i
$688$	−8.03917			−0.306490
$689$	29.2653	+	16.2164i	1.11492	+	0.617796i
$690$	6.24561			0.237766
$691$	−12.1669	−	21.0737i	−0.462851	−	0.801682i	0.536251	−	0.844059i	$-0.319840\pi$
$691$	−12.1669	−	21.0737i	−0.462851	−	0.801682i	−0.999102	+	0.0423772i	$0.986507\pi$
$692$	−10.7315	−	18.5875i	−0.407950	−	0.706591i
$693$		0			0
$694$	6.11884			0.232268
$695$	−7.10319	+	12.3031i	−0.269439	+	0.466683i
$696$	−1.41556	+	2.45182i	−0.0536566	+	0.0929360i
$697$	−1.91366			−0.0724850
$698$	3.04352	−	5.27153i	0.115199	−	0.199531i
$699$	−11.5733	−	20.0456i	−0.437744	−	0.758195i
$700$		0			0
$701$	−20.5588			−0.776495			−0.388248	−	0.921555i	$-0.626919\pi$
$701$	−20.5588			−0.776495			−0.388248	+	0.921555i	$0.626919\pi$
$702$	−0.0912693	−	5.18551i	−0.00344474	−	0.195714i
$703$	50.6467			1.91018
$704$	12.4811	+	21.6178i	0.470397	+	0.814752i
$705$	1.92751	+	3.33854i	0.0725940	+	0.125737i
$706$	3.65513	−	6.33088i	0.137563	−	0.238266i
$707$		0			0
$708$	9.88062	−	17.1137i	0.371336	−	0.643174i
$709$	−20.4544	+	35.4281i	−0.768183	+	1.33053i	0.170364	+	0.985381i	$0.445506\pi$
$709$	−20.4544	+	35.4281i	−0.768183	+	1.33053i	−0.938547	+	0.345151i	$0.887828\pi$
$710$	−8.45961			−0.317484
$711$	5.24388	−	9.08267i	0.196661	−	0.340627i
$712$	4.03543	+	6.98956i	0.151234	+	0.261945i
$713$	10.1602	+	17.5980i	0.380503	+	0.659051i
$714$		0			0
$715$	−0.641405	−	36.4418i	−0.0239872	−	1.36284i
$716$	24.3780			0.911048
$717$	−9.45989	−	16.3850i	−0.353286	−	0.611910i
$718$	−1.93401	−	3.34981i	−0.0721767	−	0.125014i
$719$	−0.599734	+	1.03877i	−0.0223663	+	0.0387396i	−0.876992	−	0.480505i	$-0.840453\pi$
$719$	−0.599734	+	1.03877i	−0.0223663	+	0.0387396i	0.854626	+	0.519245i	$0.173787\pi$
$720$	−15.5047			−0.577826
$721$		0			0
$722$	4.98433	−	8.63311i	0.185497	−	0.321291i
$723$	18.7462			0.697179
$724$	−14.3796	+	24.9063i	−0.534415	+	0.925634i
$725$	−1.83739	−	3.18246i	−0.0682390	−	0.118193i
$726$	0.700425	+	1.21317i	0.0259952	+	0.0450250i
$727$	2.06230			0.0764865			0.0382433	−	0.999268i	$-0.487824\pi$
$727$	2.06230			0.0764865			0.0382433	+	0.999268i	$0.487824\pi$
$728$		0			0
$729$	20.1764			0.747273
$730$	−0.263961	−	0.457194i	−0.00976964	−	0.0169215i
$731$	−0.883025	−	1.52944i	−0.0326599	−	0.0565685i
$732$	−10.4082	+	18.0275i	−0.384697	+	0.666315i
$733$	−30.0621			−1.11037			−0.555184	−	0.831728i	$-0.687352\pi$
$733$	−30.0621			−1.11037			−0.555184	+	0.831728i	$0.687352\pi$
$734$	1.52720	−	2.64520i	0.0563702	−	0.0976360i
$735$		0			0
$736$	24.3801			0.898662
$737$	2.66861	−	4.62216i	0.0982993	−	0.170259i
$738$	−0.553401	−	0.958519i	−0.0203710	−	0.0352836i
$739$	−22.1274	−	38.3257i	−0.813969	−	1.40984i	−0.910066	−	0.414464i	$-0.863969\pi$
$739$	−22.1274	−	38.3257i	−0.813969	−	1.40984i	0.0960970	−	0.995372i	$-0.469364\pi$
$740$	−33.3759			−1.22692
$741$	27.0186	+	14.9715i	0.992553	+	0.549992i
$742$		0			0
$743$	4.31326	+	7.47078i	0.158238	+	0.274076i	0.934233	−	0.356662i	$-0.116085\pi$
$743$	4.31326	+	7.47078i	0.158238	+	0.274076i	−0.775995	+	0.630739i	$0.782752\pi$
$744$	−1.53753	−	2.66308i	−0.0563686	−	0.0976334i
$745$	−23.6515	+	40.9656i	−0.866524	+	1.50086i
$746$	8.30194			0.303955
$747$	0.908511	−	1.57359i	0.0332407	−	0.0575746i
$748$	−2.98665	+	5.17302i	−0.109203	+	0.189144i
$749$		0			0
$750$	−1.34936	+	2.33715i	−0.0492715	+	0.0853408i
$751$	−2.86105	−	4.95549i	−0.104401	−	0.180828i	0.809092	−	0.587682i	$-0.199959\pi$
$751$	−2.86105	−	4.95549i	−0.104401	−	0.180828i	−0.913493	+	0.406853i	$0.866626\pi$
$752$	2.35256	+	4.07476i	0.0857891	+	0.148591i
$753$	23.3525			0.851012
$754$	1.94861	−	1.17123i	0.0709641	−	0.0426536i
$755$	4.11765			0.149857
$756$		0			0
$757$	17.3611	+	30.0703i	0.631000	+	1.09292i	0.987348	+	0.158571i	$0.0506887\pi$
$757$	17.3611	+	30.0703i	0.631000	+	1.09292i	−0.356347	+	0.934354i	$0.615978\pi$
$758$	1.41927	−	2.45824i	0.0515501	−	0.0892873i
$759$	−35.8803			−1.30237
$760$	−10.1115	+	17.5137i	−0.366783	+	0.635287i
$761$	−26.5867	+	46.0496i	−0.963768	+	1.66930i	−0.250880	+	0.968018i	$0.580720\pi$
$761$	−26.5867	+	46.0496i	−0.963768	+	1.66930i	−0.712888	+	0.701278i	$0.752613\pi$
$762$	−0.547981			−0.0198513
$763$		0			0
$764$	−13.6226	−	23.5951i	−0.492849	−	0.853640i
$765$	−1.70304	−	2.94976i	−0.0615736	−	0.106649i
$766$	8.24529			0.297915
$767$	−27.7097	+	16.6552i	−1.00054	+	0.601384i
$768$	12.0629			0.435282
$769$	2.45578	+	4.25354i	0.0885578	+	0.153387i	0.906902	−	0.421342i	$-0.138441\pi$
$769$	2.45578	+	4.25354i	0.0885578	+	0.153387i	−0.818344	+	0.574729i	$0.805108\pi$
$770$		0			0
$771$	7.87414	−	13.6384i	0.283580	−	0.491175i
$772$	−7.50909			−0.270258
$773$	−11.4903	+	19.9018i	−0.413279	+	0.715819i	−0.995246	−	0.0973926i	$-0.968950\pi$
$773$	−11.4903	+	19.9018i	−0.413279	+	0.715819i	0.581967	+	0.813212i	$0.302283\pi$
$774$	0.510715	−	0.884585i	0.0183573	−	0.0317957i
$775$	3.99142			0.143376
$776$	−1.24913	+	2.16356i	−0.0448413	+	0.0776674i
$777$		0			0
$778$	−2.19589	−	3.80339i	−0.0787264	−	0.136358i
$779$	18.2695			0.654573
$780$	−17.8051	−	9.86614i	−0.637525	−	0.353265i
$781$	48.5996			1.73903
$782$	0.837302	+	1.45025i	0.0299419	+	0.0518608i
$783$	6.30821	+	10.9261i	0.225437	+	0.390469i
$784$		0			0
$785$	4.21648			0.150493
$786$	0.979309	−	1.69621i	0.0349308	−	0.0605019i
$787$	−1.59387	+	2.76067i	−0.0568154	+	0.0984071i	−0.893034	−	0.449989i	$-0.851428\pi$
$787$	−1.59387	+	2.76067i	−0.0568154	+	0.0984071i	0.836219	+	0.548396i	$0.184761\pi$
$788$	22.5760			0.804237
$789$	−14.8119	+	25.6549i	−0.527316	+	0.913339i
$790$	2.12684	+	3.68380i	0.0756696	+	0.131064i
$791$		0			0
$792$	−7.03836			−0.250097
$793$	29.1892	−	17.5445i	1.03654	−	0.623022i
$794$	−4.25854			−0.151130
$795$	−13.5857	−	23.5312i	−0.481837	−	0.834566i
$796$	−3.37114	−	5.83899i	−0.119487	−	0.206958i
$797$	27.3255	−	47.3291i	0.967918	−	1.67648i	0.266355	−	0.963875i	$-0.414180\pi$
$797$	27.3255	−	47.3291i	0.967918	−	1.67648i	0.701562	−	0.712608i	$-0.252486\pi$
$798$		0			0
$799$	−0.516813	+	0.895146i	−0.0182835	+	0.0316680i
$800$	2.39442	−	4.14725i	0.0846554	−	0.146628i
$801$	12.9775			0.458538
$802$	0.889604	−	1.54084i	0.0314130	−	0.0544089i
$803$	1.51643	+	2.62653i	0.0535136	+	0.0926883i
$804$	−1.49042	−	2.58148i	−0.0525630	−	0.0910418i
$805$		0			0
$806$	0.0434569	+	2.46902i	0.00153070	+	0.0869677i
$807$	34.3664			1.20975
$808$	−0.419884	−	0.727260i	−0.0147715	−	0.0255849i
$809$	10.1498	+	17.5799i	0.356847	+	0.618077i	0.987432	−	0.158043i	$-0.0505185\pi$
$809$	10.1498	+	17.5799i	0.356847	+	0.618077i	−0.630585	+	0.776120i	$0.717185\pi$
$810$	−0.361076	+	0.625401i	−0.0126869	+	0.0219744i
$811$	−2.43587			−0.0855350			−0.0427675	−	0.999085i	$-0.513617\pi$
$811$	−2.43587			−0.0855350			−0.0427675	+	0.999085i	$0.513617\pi$
$812$		0			0
$813$	8.25855	−	14.3042i	0.289640	−	0.501671i
$814$	−7.14922			−0.250580
$815$	8.38742	−	14.5274i	0.293799	−	0.508874i
$816$	1.60353	+	2.77740i	0.0561348	+	0.0972284i
$817$	8.43015	+	14.6015i	0.294934	+	0.510840i
$818$	1.57452			0.0550519
$819$		0			0
$820$	−12.0395			−0.420438
$821$	−22.6762	−	39.2763i	−0.791405	−	1.37075i	−0.925097	−	0.379731i	$-0.876017\pi$
$821$	−22.6762	−	39.2763i	−0.791405	−	1.37075i	0.133692	−	0.991023i	$-0.457317\pi$
$822$	1.53795	+	2.66380i	0.0536421	+	0.0929108i
$823$	1.37871	−	2.38800i	0.0480588	−	0.0832403i	−0.840995	−	0.541042i	$-0.818030\pi$
$823$	1.37871	−	2.38800i	0.0480588	−	0.0832403i	0.889054	+	0.457802i	$0.151363\pi$
$824$	−2.28147			−0.0794789
$825$	−3.52388	+	6.10354i	−0.122686	+	0.212498i
$826$		0			0
$827$	−8.64504			−0.300618			−0.150309	−	0.988639i	$-0.548027\pi$
$827$	−8.64504			−0.300618			−0.150309	+	0.988639i	$0.548027\pi$
$828$	12.9881	−	22.4960i	0.451366	−	0.781789i
$829$	−14.7871	−	25.6119i	−0.513576	−	0.889540i	−0.999876	−	0.0157478i	$-0.994987\pi$
$829$	−14.7871	−	25.6119i	−0.513576	−	0.889540i	0.486300	−	0.873792i	$-0.338346\pi$
$830$	0.368479	+	0.638224i	0.0127901	+	0.0221531i
$831$	−17.5172			−0.607663
$832$	−19.9503	−	11.0548i	−0.691653	−	0.383258i
$833$		0			0
$834$	0.849774	+	1.47185i	0.0294253	+	0.0509660i
$835$	12.2308	+	21.1844i	0.423266	+	0.733117i
$836$	28.5132	−	49.3863i	0.986150	−	1.70806i
$837$	−13.7035			−0.473663
$838$	4.04096	−	6.99914i	0.139593	−	0.241781i
$839$	12.6236	−	21.8648i	0.435817	−	0.754857i	−0.561545	−	0.827446i	$-0.689793\pi$
$839$	12.6236	−	21.8648i	0.435817	−	0.754857i	0.997362	+	0.0725895i	$0.0231263\pi$
$840$		0			0
$841$	11.7347	−	20.3251i	0.404644	−	0.700865i
$842$	5.37028	+	9.30159i	0.185072	+	0.320554i
$843$	−3.02485	−	5.23920i	−0.104182	−	0.180448i
$844$	−36.6440			−1.26134
$845$	17.6560	+	28.2372i	0.607386	+	0.971391i
$846$	−0.597818			−0.0205534
$847$		0			0
$848$	−16.5817	−	28.7204i	−0.569418	−	0.986261i
$849$	−17.5935	+	30.4728i	−0.603807	+	1.04582i
$850$	0.328933			0.0112823
$851$	26.8772	−	46.5526i	0.921338	−	1.59580i
$852$	13.5715	−	23.5064i	0.464950	−	0.805318i
$853$	35.1368			1.20306			0.601531	−	0.798850i	$-0.294558\pi$
$853$	35.1368			1.20306			0.601531	+	0.798850i	$0.294558\pi$
$854$		0			0
$855$	16.2588	+	28.1610i	0.556039	+	0.963087i
$856$	6.06986	+	10.5133i	0.207463	+	0.359337i
$857$	1.34269			0.0458654			0.0229327	−	0.999737i	$-0.492700\pi$
$857$	1.34269			0.0458654			0.0229327	+	0.999737i	$0.492700\pi$
$858$	−3.81391	−	2.11336i	−0.130205	−	0.0721489i
$859$	−4.76772			−0.162673			−0.0813363	−	0.996687i	$-0.525919\pi$
$859$	−4.76772			−0.162673			−0.0813363	+	0.996687i	$0.525919\pi$
$860$	−5.55542	−	9.62228i	−0.189438	−	0.328117i
$861$		0			0
$862$	−0.524972	+	0.909278i	−0.0178806	+	0.0309701i
$863$	−26.6105			−0.905830			−0.452915	−	0.891554i	$-0.649616\pi$
$863$	−26.6105			−0.905830			−0.452915	+	0.891554i	$0.649616\pi$
$864$	−8.22062	+	14.2385i	−0.279671	+	0.484405i
$865$	14.2583	−	24.6960i	0.484795	−	0.839690i
$866$	−10.9375			−0.371672
$867$	9.36331	−	16.2177i	0.317995	−	0.550783i
$868$		0			0
$869$	−12.2185	−	21.1630i	−0.414484	−	0.717907i
$870$	−1.84634			−0.0625968
$871$	0.0858212	+	4.87598i	0.00290794	+	0.165216i
$872$	8.50819			0.288124
$873$	2.00854	+	3.47890i	0.0679788	+	0.117743i
$874$	−7.99364	−	13.8454i	−0.270389	−	0.468328i
$875$		0			0
$876$	1.69385			0.0572300
$877$	−4.01848	+	6.96022i	−0.135695	+	0.235030i	−0.925863	−	0.377860i	$-0.876660\pi$
$877$	−4.01848	+	6.96022i	−0.135695	+	0.235030i	0.790168	+	0.612890i	$0.209993\pi$
$878$	3.42694	−	5.93564i	0.115654	−	0.200318i
$879$	20.0224			0.675339
$880$	−18.0633	+	31.2866i	−0.608915	+	1.05467i
$881$	−27.3349	−	47.3454i	−0.920935	−	1.59511i	−0.797971	−	0.602695i	$-0.794093\pi$
$881$	−27.3349	−	47.3454i	−0.920935	−	1.59511i	−0.122964	−	0.992411i	$-0.539240\pi$
$882$		0			0
$883$	−8.45085			−0.284394			−0.142197	−	0.989838i	$-0.545417\pi$
$883$	−8.45085			−0.284394			−0.142197	+	0.989838i	$0.545417\pi$
$884$	−0.0960493	−	5.45709i	−0.00323049	−	0.183542i
$885$	26.2555			0.882569
$886$	−3.68088	−	6.37547i	−0.123662	−	0.214188i
$887$	−5.17784	−	8.96829i	−0.173855	−	0.301126i	0.765909	−	0.642948i	$-0.222289\pi$
$887$	−5.17784	−	8.96829i	−0.173855	−	0.301126i	−0.939764	+	0.341823i	$0.888956\pi$
$888$	−4.06729	+	7.04475i	−0.136489	+	0.236406i
$889$		0			0
$890$	−2.63174	+	4.55831i	−0.0882162	+	0.152795i
$891$	2.07434	−	3.59286i	0.0694930	−	0.120365i
$892$	−23.0722			−0.772513
$893$	4.93396	−	8.54587i	0.165109	−	0.285977i
$894$	2.82949	+	4.90082i	0.0946323	+	0.163908i
$895$	16.1947	+	28.0501i	0.541330	+	0.937611i
$896$		0			0
$897$	28.0995	−	16.8895i	0.938215	−	0.563923i
$898$	3.96922			0.132455
$899$	−3.00359	−	5.20237i	−0.100175	−	0.173509i
$900$	−2.55117	−	4.41875i	−0.0850389	−	0.147292i
$901$	3.64268	−	6.30931i	0.121355	−	0.210194i
$902$	−2.57890			−0.0858680
$903$		0			0
$904$	−4.23468	+	7.33467i	−0.140843	+	0.243948i
$905$	−38.2106			−1.27016
$906$	0.246303	−	0.426609i	0.00818287	−	0.0141731i
$907$	−9.24019	−	16.0045i	−0.306815	−	0.531420i	0.670849	−	0.741594i	$-0.265930\pi$
$907$	−9.24019	−	16.0045i	−0.306815	−	0.531420i	−0.977664	+	0.210175i	$0.932597\pi$
$908$	−14.8312	−	25.6884i	−0.492190	−	0.852498i
$909$	−1.35030			−0.0447867
$910$		0			0
$911$	−26.6282			−0.882230			−0.441115	−	0.897451i	$-0.645417\pi$
$911$	−26.6282			−0.882230			−0.441115	+	0.897451i	$0.645417\pi$
$912$	−15.3088	−	26.5155i	−0.506924	−	0.878017i
$913$	−2.11687	−	3.66653i	−0.0700582	−	0.121344i
$914$	−0.0874022	+	0.151385i	−0.00289101	+	0.00500737i
$915$	−27.6574			−0.914324
$916$	−8.35033	+	14.4632i	−0.275903	+	0.477877i
$917$		0			0
$918$	−1.12931			−0.0372727
$919$	5.57467	−	9.65561i	0.183891	−	0.318509i	−0.759311	−	0.650728i	$-0.774464\pi$
$919$	5.57467	−	9.65561i	0.183891	−	0.318509i	0.943202	+	0.332219i	$0.107797\pi$
$920$	10.7319	+	18.5883i	0.353822	+	0.612837i
$921$	−4.93536	−	8.54829i	−0.162626	−	0.281676i
$922$	3.35035			0.110338
$923$	−38.0605	+	22.8766i	−1.25278	+	0.752993i
$924$		0			0
$925$	−5.27933	−	9.14406i	−0.173583	−	0.300655i
$926$	−0.0414927	−	0.0718675i	−0.00136354	−	0.00236171i
$927$	−1.83424	+	3.17700i	−0.0602445	+	0.104347i
$928$	−7.20730			−0.236591
$929$	3.87255	−	6.70745i	0.127054	−	0.220064i	−0.795480	−	0.605980i	$-0.792781\pi$
$929$	3.87255	−	6.70745i	0.127054	−	0.220064i	0.922534	+	0.385916i	$0.126114\pi$
$930$	1.00272	−	1.73676i	0.0328804	−	0.0569505i
$931$		0			0
$932$	19.5227	−	33.8144i	0.639489	−	1.10763i
$933$	−9.38559	−	16.2563i	−0.307270	−	0.532208i
$934$	−3.28149	−	5.68371i	−0.107374	−	0.185977i
$935$	−7.93633			−0.259546
$936$	5.51205	−	3.31307i	0.180167	−	0.108291i
$937$	−36.4239			−1.18992			−0.594959	−	0.803756i	$-0.702832\pi$
$937$	−36.4239			−1.18992			−0.594959	+	0.803756i	$0.702832\pi$
$938$		0			0
$939$	5.74143	+	9.94445i	0.187364	+	0.324525i
$940$	−3.25145	+	5.63168i	−0.106051	+	0.183685i
$941$	19.7893			0.645114			0.322557	−	0.946550i	$-0.395458\pi$
$941$	19.7893			0.645114			0.322557	+	0.946550i	$0.395458\pi$
$942$	0.252214	−	0.436848i	0.00821759	−	0.0142333i
$943$	9.69526	−	16.7927i	0.315721	−	0.546845i
$944$	32.0454			1.04299
$945$		0			0
$946$	−1.18999	−	2.06112i	−0.0386899	−	0.0670129i
$947$	−4.97398	−	8.61519i	−0.161633	−	0.279956i	0.773822	−	0.633403i	$-0.218343\pi$
$947$	−4.97398	−	8.61519i	−0.161633	−	0.279956i	−0.935454	+	0.353448i	$0.885009\pi$
$948$	−13.6481			−0.443269
$949$	−2.42393	−	1.34315i	−0.0786842	−	0.0436004i
$950$	−3.14029			−0.101884
$951$	−5.79790	−	10.0423i	−0.188010	−	0.325643i
$952$		0			0
$953$	−0.0105567	+	0.0182847i	−0.000341965	+	0.000592300i	−0.866196	−	0.499704i	$-0.833442\pi$
$953$	−0.0105567	+	0.0182847i	−0.000341965	+	0.000592300i	0.865854	+	0.500296i	$0.166776\pi$
$954$	4.21364			0.136422
$955$	18.0995	−	31.3493i	0.585686	−	1.01444i
$956$	15.9576	−	27.6394i	0.516106	−	0.893922i
$957$	10.6070			0.342877
$958$	−1.09107	+	1.88979i	−0.0352508	+	0.0610562i
$959$		0			0
$960$	9.26150	+	16.0414i	0.298914	+	0.517733i
$961$	−24.4752			−0.789523
$962$	5.59888	−	3.36525i	0.180515	−	0.108500i
$963$	19.5200			0.629024
$964$	15.8112	+	27.3858i	0.509245	+	0.882039i
$965$	−4.98842	−	8.64020i	−0.160583	−	0.278138i
$966$		0			0
$967$	−19.8102			−0.637053			−0.318526	−	0.947914i	$-0.603188\pi$
$967$	−19.8102			−0.637053			−0.318526	+	0.947914i	$0.603188\pi$
$968$	−2.40711	+	4.16923i	−0.0773674	+	0.134004i
$969$	3.36304	−	5.82495i	0.108036	−	0.187124i
$970$	−1.62927			−0.0523127
$971$	−1.80887	+	3.13305i	−0.0580493	+	0.100544i	−0.893590	−	0.448885i	$-0.851821\pi$
$971$	−1.80887	+	3.13305i	−0.0580493	+	0.100544i	0.835540	+	0.549429i	$0.185155\pi$
$972$	14.3572	+	24.8674i	0.460508	+	0.797622i
$973$		0			0
$974$	−1.23595			−0.0396024
$975$	−0.113327	−	6.43871i	−0.00362936	−	0.206204i
$976$	−33.7564			−1.08052
$977$	−1.08085	−	1.87208i	−0.0345793	−	0.0598931i	0.848218	−	0.529648i	$-0.177676\pi$
$977$	−1.08085	−	1.87208i	−0.0345793	−	0.0598931i	−0.882797	+	0.469754i	$0.844342\pi$
$978$	−1.00341	−	1.73796i	−0.0320855	−	0.0555737i
$979$	15.1191	−	26.1870i	0.483208	−	0.836941i
$980$		0			0
$981$	6.84036	−	11.8479i	0.218396	−	0.378273i
$982$	1.74535	−	3.02304i	0.0556965	−	0.0964692i
$983$	30.1091			0.960331			0.480165	−	0.877178i	$-0.340577\pi$
$983$	30.1091			0.960331			0.480165	+	0.877178i	$0.340577\pi$
$984$	−1.46717	+	2.54121i	−0.0467717	+	0.0810109i
$985$	14.9977	+	25.9767i	0.477865	+	0.827687i
$986$	−0.247525	−	0.428727i	−0.00788281	−	0.0136534i
$987$		0			0
$988$	0.916973	+	52.0983i	0.0291728	+	1.65747i
$989$	17.8948			0.569023
$990$	−2.29507	−	3.97517i	−0.0729420	−	0.126339i
$991$	13.5730	+	23.5092i	0.431161	+	0.746793i	0.996974	−	0.0777408i	$-0.0247706\pi$
$991$	13.5730	+	23.5092i	0.431161	+	0.746793i	−0.565812	+	0.824534i	$0.691437\pi$
$992$	3.91416	−	6.77953i	0.124275	−	0.215250i
$993$	2.65082			0.0841213
$994$		0			0
$995$	4.47902	−	7.75790i	0.141995	−	0.245942i
$996$	−2.36455			−0.0749236
$997$	25.4005	−	43.9949i	0.804441	−	1.39333i	−0.112227	−	0.993683i	$-0.535798\pi$
$997$	25.4005	−	43.9949i	0.804441	−	1.39333i	0.916668	−	0.399650i	$-0.130868\pi$
$998$	−4.33300	−	7.50497i	−0.137159	−	0.237566i
$999$	18.1252	+	31.3938i	0.573456	+	0.993256i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.f.j.393.3		12
7.2	even	3		637.2.g.l.263.3		12
7.3	odd	6		91.2.h.b.16.4	yes	12
7.4	even	3		637.2.h.l.471.4		12
7.5	odd	6		91.2.g.b.81.3	yes	12
7.6	odd	2		637.2.f.k.393.3		12
13.3	even	3		8281.2.a.ca.1.4		6
13.9	even	3	inner	637.2.f.j.295.3		12
13.10	even	6		8281.2.a.cf.1.3		6
21.5	even	6		819.2.n.d.172.4		12
21.17	even	6		819.2.s.d.289.3		12
91.3	odd	6		1183.2.e.h.170.3		12
91.9	even	3		637.2.h.l.165.4		12
91.10	odd	6		1183.2.e.g.170.4		12
91.48	odd	6		637.2.f.k.295.3		12
91.55	odd	6		8281.2.a.bz.1.4		6
91.61	odd	6		91.2.h.b.74.4	yes	12
91.62	odd	6		8281.2.a.ce.1.3		6
91.68	odd	6		1183.2.e.h.508.3		12
91.74	even	3		637.2.g.l.373.3		12
91.75	odd	6		1183.2.e.g.508.4		12
91.87	odd	6		91.2.g.b.9.3	✓	12
273.152	even	6		819.2.s.d.802.3		12
273.269	even	6		819.2.n.d.100.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.3	✓	12	91.87	odd	6
91.2.g.b.81.3	yes	12	7.5	odd	6
91.2.h.b.16.4	yes	12	7.3	odd	6
91.2.h.b.74.4	yes	12	91.61	odd	6
637.2.f.j.295.3		12	13.9	even	3	inner
637.2.f.j.393.3		12	1.1	even	1	trivial
637.2.f.k.295.3		12	91.48	odd	6
637.2.f.k.393.3		12	7.6	odd	2
637.2.g.l.263.3		12	7.2	even	3
637.2.g.l.373.3		12	91.74	even	3
637.2.h.l.165.4		12	91.9	even	3
637.2.h.l.471.4		12	7.4	even	3
819.2.n.d.100.4		12	273.269	even	6
819.2.n.d.172.4		12	21.5	even	6
819.2.s.d.289.3		12	21.17	even	6
819.2.s.d.802.3		12	273.152	even	6
1183.2.e.g.170.4		12	91.10	odd	6
1183.2.e.g.508.4		12	91.75	odd	6
1183.2.e.h.170.3		12	91.3	odd	6
1183.2.e.h.508.3		12	91.68	odd	6
8281.2.a.bz.1.4		6	91.55	odd	6
8281.2.a.ca.1.4		6	13.3	even	3
8281.2.a.ce.1.3		6	91.62	odd	6
8281.2.a.cf.1.3		6	13.10	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.134063 + 0.232203i) q^{2} +(-0.571504 - 0.989875i) q^{3} +(0.964054 - 1.66979i) q^{4} +2.56175 q^{5} +(0.153235 - 0.265410i) q^{6} +1.05323 q^{8} +(0.846765 - 1.46664i) q^{9} +(0.343436 + 0.594848i) q^{10} +(-1.97300 - 3.41734i) q^{11} -2.20385 q^{12} +(3.15374 + 1.74755i) q^{13} +(-1.46405 - 2.53582i) q^{15} +(-1.78691 - 3.09502i) q^{16} +(0.392550 - 0.679916i) q^{17} +0.454078 q^{18} +(-3.74764 + 6.49110i) q^{19} +(2.46967 - 4.27760i) q^{20} +(0.529011 - 0.916274i) q^{22} +(3.97759 + 6.88938i) q^{23} +(-0.601923 - 1.04256i) q^{24} +1.56259 q^{25} +(0.0170128 + 0.966590i) q^{26} -5.36475 q^{27} +(-1.17586 - 2.03666i) q^{29} +(0.392550 - 0.679916i) q^{30} +2.55437 q^{31} +(1.53234 - 2.65409i) q^{32} +(-2.25516 + 3.90605i) q^{33} +0.210505 q^{34} +(-1.63266 - 2.82784i) q^{36} +(-3.37858 - 5.85187i) q^{37} -2.00967 q^{38} +(-0.0725249 - 4.12054i) q^{39} +2.69810 q^{40} +(-1.21874 - 2.11091i) q^{41} +(1.12473 - 1.94809i) q^{43} -7.60832 q^{44} +(2.16920 - 3.75717i) q^{45} +(-1.06649 + 1.84722i) q^{46} -1.31655 q^{47} +(-2.04246 + 3.53764i) q^{48} +(0.209485 + 0.362838i) q^{50} -0.897376 q^{51} +(5.95842 - 3.58136i) q^{52} +9.27954 q^{53} +(-0.719212 - 1.24571i) q^{54} +(-5.05434 - 8.75438i) q^{55} +8.56716 q^{57} +(0.315279 - 0.546079i) q^{58} +(-4.48335 + 7.76540i) q^{59} -5.64571 q^{60} +(4.72273 - 8.18002i) q^{61} +(0.342445 + 0.593132i) q^{62} -6.32592 q^{64} +(8.07911 + 4.47679i) q^{65} -1.20933 q^{66} +(0.676281 + 1.17135i) q^{67} +(-0.756879 - 1.31095i) q^{68} +(4.54642 - 7.87463i) q^{69} +(-6.15808 + 10.6661i) q^{71} +(0.891834 - 1.54470i) q^{72} -0.768590 q^{73} +(0.905882 - 1.56903i) q^{74} +(-0.893026 - 1.54677i) q^{75} +(7.22585 + 12.5155i) q^{76} +(0.947080 - 0.569251i) q^{78} +6.19284 q^{79} +(-4.57763 - 7.92868i) q^{80} +(0.525682 + 0.910507i) q^{81} +(0.326774 - 0.565989i) q^{82} +1.07292 q^{83} +(1.00562 - 1.74178i) q^{85} +0.603137 q^{86} +(-1.34402 + 2.32792i) q^{87} +(-2.07801 - 3.59923i) q^{88} +(3.83149 + 6.63634i) q^{89} +1.16324 q^{90} +15.3384 q^{92} +(-1.45983 - 2.52850i) q^{93} +(-0.176501 - 0.305708i) q^{94} +(-9.60052 + 16.6286i) q^{95} -3.50296 q^{96} +(-1.18601 + 2.05423i) q^{97} -6.68267 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - q^{3} - 4 q^{4} + 2 q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9} - 4 q^{10} + 4 q^{11} + 10 q^{12} + 2 q^{13} - 2 q^{15} + 8 q^{16} - 5 q^{17} - 6 q^{18} + q^{19} + q^{20} - 5 q^{22} - q^{23}+ \cdots - 20 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 - q^3 - 4 * q^4 + 2 * q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9 - 4 * q^10 + 4 * q^11 + 10 * q^12 + 2 * q^13 - 2 * q^15 + 8 * q^16 - 5 * q^17 - 6 * q^18 + q^19 + q^20 - 5 * q^22 - q^23 + 11 * q^24 - 14 * q^25 - 11 * q^26 + 8 * q^27 + 3 * q^29 - 5 * q^30 + 32 * q^31 + 8 * q^32 - 16 * q^33 - 32 * q^34 - 21 * q^36 - 13 * q^37 - 34 * q^38 + 43 * q^39 - 10 * q^40 + 8 * q^41 - 11 * q^43 - 42 * q^44 + 7 * q^45 + 16 * q^46 - 2 * q^47 - 21 * q^48 + 6 * q^50 + 40 * q^51 + 16 * q^52 + 4 * q^53 + 18 * q^54 - 9 * q^55 + 42 * q^57 - 8 * q^58 - 13 * q^59 - 40 * q^60 + 5 * q^61 - 5 * q^62 - 30 * q^64 - 14 * q^65 + 36 * q^66 - 11 * q^67 - 29 * q^68 - 23 * q^69 + 6 * q^71 + 25 * q^72 - 60 * q^73 - 3 * q^74 + 3 * q^75 + 9 * q^76 + 16 * q^78 - 14 * q^79 + 7 * q^80 - 6 * q^81 - q^82 + 54 * q^83 - q^85 + 14 * q^86 - 16 * q^87 - 4 * q^89 + 16 * q^90 + 54 * q^92 - 7 * q^93 - 45 * q^94 - 6 * q^95 + 38 * q^96 + 35 * q^97 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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