LMFDB - Embedded newform 637.2.h.l.471.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(165,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 4]))

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

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

chi := DirichletCharacter("637.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.h (of order $3$, degree $2$, not 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:	$12$
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			471.4
Root			$-0.437442 - 0.757672i$ of defining polynomial
Character	$\chi$	$=$	637.471
Dual form			637.2.h.l.165.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.268125 q^{2} +(-0.571504 + 0.989875i) q^{3} -1.92811 q^{4} +(-1.28088 + 2.21854i) q^{5} +(0.153235 - 0.265410i) q^{6} +1.05323 q^{8} +(0.846765 + 1.46664i) q^{9} +O(q^{10})$	\(q-0.268125 q^{2} +(-0.571504 + 0.989875i) q^{3} -1.92811 q^{4} +(-1.28088 + 2.21854i) 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} +(1.10192 - 1.90859i) q^{12} +(3.15374 + 1.74755i) q^{13} +(-1.46405 - 2.53582i) q^{15} +3.57382 q^{16} -0.785100 q^{17} +(-0.227039 - 0.393243i) q^{18} +(-3.74764 - 6.49110i) q^{19} +(2.46967 - 4.27760i) q^{20} +(0.529011 - 0.916274i) q^{22} -7.95518 q^{23} +(-0.601923 + 1.04256i) q^{24} +(-0.781294 - 1.35324i) q^{25} +(-0.845598 - 0.468561i) q^{26} -5.36475 q^{27} +(-1.17586 - 2.03666i) q^{29} +(0.392550 + 0.679916i) q^{30} +(-1.27718 - 2.21215i) q^{31} -3.06468 q^{32} +(-2.25516 - 3.90605i) q^{33} +0.210505 q^{34} +(-1.63266 - 2.82784i) q^{36} +6.75716 q^{37} +(1.00484 + 1.74043i) q^{38} +(-3.53223 + 2.12308i) q^{39} +(-1.34905 + 2.33663i) q^{40} +(-1.21874 - 2.11091i) q^{41} +(1.12473 - 1.94809i) q^{43} +(3.80416 - 6.58900i) q^{44} -4.33841 q^{45} +2.13298 q^{46} +(0.658276 - 1.14017i) q^{47} +(-2.04246 + 3.53764i) q^{48} +(0.209485 + 0.362838i) q^{50} +(0.448688 - 0.777151i) q^{51} +(-6.08076 - 3.36946i) q^{52} +(-4.63977 - 8.03632i) q^{53} +1.43842 q^{54} +(-5.05434 - 8.75438i) q^{55} +8.56716 q^{57} +(0.315279 + 0.546079i) q^{58} +8.96671 q^{59} +(2.82286 + 4.88933i) q^{60} +(4.72273 + 8.18002i) q^{61} +(0.342445 + 0.593132i) q^{62} -6.32592 q^{64} +(-7.91657 + 4.75832i) q^{65} +(0.604665 + 1.04731i) q^{66} +(0.676281 - 1.17135i) q^{67} +1.51376 q^{68} +(4.54642 - 7.87463i) q^{69} +(-6.15808 + 10.6661i) q^{71} +(0.891834 + 1.54470i) q^{72} +(0.384295 + 0.665619i) q^{73} -1.81176 q^{74} +1.78605 q^{75} +(7.22585 + 12.5155i) q^{76} +(0.947080 - 0.569251i) q^{78} +(-3.09642 + 5.36316i) 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} +(-0.301568 + 0.522332i) q^{86} +2.68805 q^{87} +(-2.07801 + 3.59923i) q^{88} -7.66299 q^{89} +1.16324 q^{90} +15.3384 q^{92} +2.91966 q^{93} +(-0.176501 + 0.305708i) q^{94} +19.2010 q^{95} +(1.75148 - 3.03365i) q^{96} +(-1.18601 + 2.05423i) q^{97} -6.68267 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} - q^{3} + 8 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 12 * q - 4 * q^2 - q^3 + 8 * q^4 - q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9	$ 12 q - 4 q^{2} - q^{3} + 8 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9} - 4 q^{10} + 4 q^{11} - 5 q^{12} + 2 q^{13} - 2 q^{15} - 16 q^{16} + 10 q^{17} + 3 q^{18} + q^{19} + q^{20} - 5 q^{22} + 2 q^{23} + 11 q^{24} + 7 q^{25} + 16 q^{26} + 8 q^{27} + 3 q^{29} - 5 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 32 q^{34} - 21 q^{36} + 26 q^{37} + 17 q^{38} - 20 q^{39} + 5 q^{40} + 8 q^{41} - 11 q^{43} + 21 q^{44} - 14 q^{45} - 32 q^{46} + q^{47} - 21 q^{48} + 6 q^{50} - 20 q^{51} - 41 q^{52} - 2 q^{53} - 36 q^{54} - 9 q^{55} + 42 q^{57} - 8 q^{58} + 26 q^{59} + 20 q^{60} + 5 q^{61} - 5 q^{62} - 30 q^{64} - 5 q^{65} - 18 q^{66} - 11 q^{67} + 58 q^{68} - 23 q^{69} + 6 q^{71} + 25 q^{72} + 30 q^{73} + 6 q^{74} - 6 q^{75} + 9 q^{76} + 16 q^{78} + 7 q^{79} + 7 q^{80} - 6 q^{81} - q^{82} + 54 q^{83} - q^{85} - 7 q^{86} + 32 q^{87} + 8 q^{89} + 16 q^{90} + 54 q^{92} + 14 q^{93} - 45 q^{94} + 12 q^{95} - 19 q^{96} + 35 q^{97} - 20 q^{99}+O(q^{100}) $ 12 * q - 4 * q^2 - q^3 + 8 * q^4 - q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9 - 4 * q^10 + 4 * q^11 - 5 * q^12 + 2 * q^13 - 2 * q^15 - 16 * q^16 + 10 * q^17 + 3 * q^18 + q^19 + q^20 - 5 * q^22 + 2 * q^23 + 11 * q^24 + 7 * q^25 + 16 * q^26 + 8 * q^27 + 3 * q^29 - 5 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 32 * q^34 - 21 * q^36 + 26 * q^37 + 17 * q^38 - 20 * q^39 + 5 * q^40 + 8 * q^41 - 11 * q^43 + 21 * q^44 - 14 * q^45 - 32 * q^46 + q^47 - 21 * q^48 + 6 * q^50 - 20 * q^51 - 41 * q^52 - 2 * q^53 - 36 * q^54 - 9 * q^55 + 42 * q^57 - 8 * q^58 + 26 * q^59 + 20 * q^60 + 5 * q^61 - 5 * q^62 - 30 * q^64 - 5 * q^65 - 18 * q^66 - 11 * q^67 + 58 * q^68 - 23 * q^69 + 6 * q^71 + 25 * q^72 + 30 * q^73 + 6 * q^74 - 6 * q^75 + 9 * q^76 + 16 * q^78 + 7 * q^79 + 7 * q^80 - 6 * q^81 - q^82 + 54 * q^83 - q^85 - 7 * q^86 + 32 * q^87 + 8 * q^89 + 16 * q^90 + 54 * q^92 + 14 * q^93 - 45 * q^94 + 12 * q^95 - 19 * q^96 + 35 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.268125			−0.189593			−0.0947966	−	0.995497i	$-0.530220\pi$
$2$	−0.268125			−0.189593			−0.0947966	+	0.995497i	$0.530220\pi$
$3$	−0.571504	+	0.989875i	−0.329958	+	0.571504i	−0.982503	−	0.186246i	$-0.940368\pi$
$3$	−0.571504	+	0.989875i	−0.329958	+	0.571504i	0.652545	+	0.757750i	$0.273701\pi$
$4$	−1.92811			−0.964054
$5$	−1.28088	+	2.21854i	−0.572826	+	0.992163i	0.423448	+	0.905920i	$0.360820\pi$
$5$	−1.28088	+	2.21854i	−0.572826	+	0.992163i	−0.996274	+	0.0862431i	$0.972514\pi$
$6$	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	0.398681	+	0.917090i	$0.369468\pi$
$11$	−1.97300	+	3.41734i	−0.594882	+	1.03037i	−0.993563	+	0.113277i	$0.963865\pi$
$12$	1.10192	−	1.90859i	0.318098	−	0.550961i
$13$	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
$16$	3.57382			0.893455
$17$	−0.785100			−0.190415			−0.0952073	−	0.995457i	$-0.530351\pi$
$17$	−0.785100			−0.190415			−0.0952073	+	0.995457i	$0.530351\pi$
$18$	−0.227039	−	0.393243i	−0.0535136	−	0.0926883i
$19$	−3.74764	−	6.49110i	−0.859767	−	1.48916i	−0.872151	−	0.489236i	$-0.837276\pi$
$19$	−3.74764	−	6.49110i	−0.859767	−	1.48916i	0.0123849	−	0.999923i	$-0.496058\pi$
$20$	2.46967	−	4.27760i	0.552235	−	0.956500i
$21$		0			0
$22$	0.529011	−	0.916274i	0.112786	−	0.195350i
$23$	−7.95518			−1.65877			−0.829384	−	0.558678i	$-0.811309\pi$
$23$	−7.95518			−1.65877			−0.829384	+	0.558678i	$0.811309\pi$
$24$	−0.601923	+	1.04256i	−0.122867	+	0.212812i
$25$	−0.781294	−	1.35324i	−0.156259	−	0.270648i
$26$	−0.845598	−	0.468561i	−0.165835	−	0.0918924i
$27$	−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
$31$	−1.27718	−	2.21215i	−0.229389	−	0.397313i	0.728238	−	0.685324i	$-0.240339\pi$
$31$	−1.27718	−	2.21215i	−0.229389	−	0.397313i	−0.957627	+	0.288011i	$0.907006\pi$
$32$	−3.06468			−0.541764
$33$	−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
$37$	6.75716			1.11087			0.555435	−	0.831560i	$-0.312552\pi$
$37$	6.75716			1.11087			0.555435	+	0.831560i	$0.312552\pi$
$38$	1.00484	+	1.74043i	0.163006	+	0.282334i
$39$	−3.53223	+	2.12308i	−0.565609	+	0.339965i
$40$	−1.34905	+	2.33663i	−0.213304	+	0.369453i
$41$	−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	$0.111799\pi$
$44$	3.80416	−	6.58900i	0.573499	−	0.993329i
$45$	−4.33841			−0.646732
$46$	2.13298			0.314491
$47$	0.658276	−	1.14017i	0.0960195	−	0.166311i	−0.814014	−	0.580845i	$-0.802722\pi$
$47$	0.658276	−	1.14017i	0.0960195	−	0.166311i	0.910034	+	0.414534i	$0.136056\pi$
$48$	−2.04246	+	3.53764i	−0.294803	+	0.510614i
$49$		0			0
$50$	0.209485	+	0.362838i	0.0296256	+	0.0513130i
$51$	0.448688	−	0.777151i	0.0628289	−	0.108823i
$52$	−6.08076	−	3.36946i	−0.843249	−	0.467260i
$53$	−4.63977	−	8.03632i	−0.637321	−	1.10387i	−0.986018	−	0.166637i	$-0.946709\pi$
$53$	−4.63977	−	8.03632i	−0.637321	−	1.10387i	0.348697	−	0.937236i	$-0.386624\pi$
$54$	1.43842			0.195745
$55$	−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
$59$	8.96671			1.16737			0.583683	−	0.811982i	$-0.301611\pi$
$59$	8.96671			1.16737			0.583683	+	0.811982i	$0.301611\pi$
$60$	2.82286	+	4.88933i	0.364429	+	0.631210i
$61$	4.72273	+	8.18002i	0.604684	+	1.04734i	0.992101	+	0.125439i	$0.0400340\pi$
$61$	4.72273	+	8.18002i	0.604684	+	1.04734i	−0.387417	+	0.921905i	$0.626633\pi$
$62$	0.342445	+	0.593132i	0.0434906	+	0.0753279i
$63$		0			0
$64$	−6.32592			−0.790741
$65$	−7.91657	+	4.75832i	−0.981929	+	0.590197i
$66$	0.604665	+	1.04731i	0.0744291	+	0.128915i
$67$	0.676281	−	1.17135i	0.0826209	−	0.143104i	−0.821754	−	0.569842i	$-0.807004\pi$
$67$	0.676281	−	1.17135i	0.0826209	−	0.143104i	0.904375	+	0.426739i	$0.140338\pi$
$68$	1.51376			0.183570
$69$	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
$73$	0.384295	+	0.665619i	0.0449783	+	0.0779048i	0.887638	−	0.460542i	$-0.152345\pi$
$73$	0.384295	+	0.665619i	0.0449783	+	0.0779048i	−0.842660	+	0.538446i	$0.819011\pi$
$74$	−1.81176			−0.210613
$75$	1.78605			0.206236
$76$	7.22585	+	12.5155i	0.828862	+	1.43563i
$77$		0			0
$78$	0.947080	−	0.569251i	0.107236	−	0.0644550i
$79$	−3.09642	+	5.36316i	−0.348375	+	0.603402i	−0.985961	−	0.166976i	$-0.946600\pi$
$79$	−3.09642	+	5.36316i	−0.348375	+	0.603402i	0.637586	+	0.770379i	$0.279933\pi$
$80$	−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
$86$	−0.301568	+	0.522332i	−0.0325190	+	0.0563245i
$87$	2.68805			0.288189
$88$	−2.07801	+	3.59923i	−0.221517	+	0.383679i
$89$	−7.66299			−0.812275			−0.406138	−	0.913812i	$-0.633125\pi$
$89$	−7.66299			−0.812275			−0.406138	+	0.913812i	$0.633125\pi$
$90$	1.16324			0.122616
$91$		0			0
$92$	15.3384			1.59914
$93$	2.91966			0.302755
$94$	−0.176501	+	0.305708i	−0.0182046	+	0.0315314i
$95$	19.2010			1.96999
$96$	1.75148	−	3.03365i	0.178760	−	0.309621i
$97$	−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	−0.885178	−	0.465252i	$-0.845964\pi$
$101$	−0.398665	+	0.690508i	−0.0396686	+	0.0687081i	0.845509	+	0.533961i	$0.179297\pi$
$102$	−0.120305	+	0.208374i	−0.0119119	+	0.0206321i
$103$	1.08309	−	1.87597i	0.106720	−	0.184844i	−0.807720	−	0.589567i	$-0.799299\pi$
$103$	1.08309	−	1.87597i	0.106720	−	0.184844i	0.914440	+	0.404722i	$0.132632\pi$
$104$	3.32160	+	1.84056i	0.325710	+	0.180482i
$105$		0			0
$106$	1.24404	+	2.15474i	0.120832	+	0.209287i
$107$	−11.5262			−1.11428			−0.557141	−	0.830418i	$-0.688102\pi$
$107$	−11.5262			−1.11428			−0.557141	+	0.830418i	$0.688102\pi$
$108$	10.3438			0.995334
$109$	−4.03912	−	6.99595i	−0.386877	−	0.670091i	0.605151	−	0.796111i	$-0.293113\pi$
$109$	−4.03912	−	6.99595i	−0.386877	−	0.670091i	−0.992028	+	0.126020i	$0.959780\pi$
$110$	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	$0.290135\pi$
$114$	−2.29707			−0.215141
$115$	10.1896	−	17.6489i	0.950186	−	1.64577i
$116$	2.26719	+	3.92690i	0.210504	+	0.364603i
$117$	0.107456	+	6.10517i	0.00993431	+	0.564423i
$118$	−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
$122$	−1.26628	−	2.19327i	−0.114644	−	0.198569i
$123$	2.78605			0.251210
$124$	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	$0.858612\pi$
$128$	7.82550			0.691683
$129$	1.28558	+	2.22668i	0.113189	+	0.196049i
$130$	2.12263	−	1.27583i	0.186167	−	0.111897i
$131$	−3.19545	+	5.53469i	−0.279188	+	0.483568i	−0.971183	−	0.238334i	$-0.923399\pi$
$131$	−3.19545	+	5.53469i	−0.279188	+	0.483568i	0.691995	+	0.721902i	$0.256732\pi$
$132$	4.34819	+	7.53129i	0.378461	+	0.655514i
$133$		0			0
$134$	−0.181328	+	0.314069i	−0.0156644	+	0.0271315i
$135$	6.87158	−	11.9019i	0.591412	−	1.02436i
$136$	−0.826887			−0.0709050
$137$	10.0365			0.857480			0.428740	−	0.903428i	$-0.358958\pi$
$137$	10.0365			0.857480			0.428740	+	0.903428i	$0.358958\pi$
$138$	−1.21901	+	2.11139i	−0.103769	+	0.179733i
$139$	−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
$142$	1.65114	−	2.85985i	0.138560	−	0.239993i
$143$	−12.1943	+	7.32949i	−1.01974	+	0.612922i
$144$	3.02619	+	5.24151i	0.252182	+	0.436793i
$145$	6.02455			0.500312
$146$	−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	−0.944696	−	0.327947i	$-0.893643\pi$
$149$	−9.23254	−	15.9912i	−0.756359	−	1.31005i	0.188337	−	0.982104i	$-0.439690\pi$
$150$	−0.478886			−0.0391009
$151$	−0.803678	−	1.39201i	−0.0654024	−	0.113280i	0.831470	−	0.555570i	$-0.187500\pi$
$151$	−0.803678	−	1.39201i	−0.0654024	−	0.113280i	−0.896872	+	0.442289i	$0.854166\pi$
$152$	−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
$156$	6.81052	−	4.09353i	0.545278	−	0.327744i
$157$	−0.822967	−	1.42542i	−0.0656799	−	0.113761i	0.831315	−	0.555801i	$-0.187588\pi$
$157$	−0.822967	−	1.42542i	−0.0656799	−	0.113761i	−0.896995	+	0.442040i	$0.854255\pi$
$158$	0.830229	−	1.43800i	0.0660494	−	0.114401i
$159$	10.6066			0.841158
$160$	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	0.965287	−	0.261190i	$-0.0841148\pi$
$163$	3.27409	+	5.67090i	0.256447	+	0.444179i	−0.708841	+	0.705369i	$0.750782\pi$
$164$	2.34986	+	4.07007i	0.183493	+	0.317819i
$165$	11.5543			0.899503
$166$	−0.287677			−0.0223281
$167$	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
$170$	−0.269631	+	0.467015i	−0.0206798	+	0.0358184i
$171$	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	0.996247	−	0.0865588i	$-0.0275870\pi$
$173$	5.56582	+	9.64028i	0.423161	+	0.732937i	−0.573085	+	0.819496i	$0.694254\pi$
$174$	−0.720733			−0.0546386
$175$		0			0
$176$	−7.05115	+	12.2130i	−0.531501	+	0.920586i
$177$	−5.12451	+	8.87592i	−0.385182	+	0.667155i
$178$	2.05464			0.154002
$179$	6.32173	−	10.9496i	0.472508	−	0.818409i	−0.526997	−	0.849867i	$-0.676682\pi$
$179$	6.32173	−	10.9496i	0.472508	−	0.818409i	0.999505	+	0.0314588i	$0.0100153\pi$
$180$	8.36493			0.623485
$181$	−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
$184$	−8.37859			−0.617678
$185$	−8.65509	+	14.9911i	−0.636335	+	1.10216i
$186$	−0.782836			−0.0574003
$187$	1.54900	−	2.68295i	0.113274	−	0.196197i
$188$	−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	0.999915	+	0.0130110i	$0.00414165\pi$
$191$	7.06528	+	12.2374i	0.511226	+	0.885469i	−0.488690	+	0.872458i	$0.662525\pi$
$192$	3.61529	−	6.26187i	0.260911	−	0.451912i
$193$	−1.94727	+	3.37277i	−0.140167	+	0.242777i	−0.927560	−	0.373675i	$-0.878097\pi$
$193$	−1.94727	+	3.37277i	−0.140167	+	0.242777i	0.787392	+	0.616452i	$0.211431\pi$
$194$	0.317999	−	0.550790i	0.0228310	−	0.0395444i
$195$	−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	$0.696376\pi$
$198$	1.79179			0.127337
$199$	−3.49684			−0.247884			−0.123942	−	0.992289i	$-0.539554\pi$
$199$	−3.49684			−0.247884			−0.123942	+	0.992289i	$0.539554\pi$
$200$	−0.822878	−	1.42527i	−0.0581863	−	0.100782i
$201$	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
$205$	6.24421			0.436114
$206$	−0.290403	+	0.502994i	−0.0202334	+	0.0350452i
$207$	−6.73617	−	11.6674i	−0.468196	−	0.810939i
$208$	11.2709	+	6.24542i	0.781497	+	0.433042i
$209$	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
$213$	−7.03874	−	12.1915i	−0.482286	−	0.835345i
$214$	3.09047			0.211260
$215$	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
$219$	−0.878506			−0.0593639
$220$	9.74533	+	16.8794i	0.657030	+	1.13801i
$221$	−2.47600	−	1.37200i	−0.166554	−	0.0922906i
$222$	1.03543	−	1.79342i	0.0694936	−	0.120366i
$223$	−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
$226$	1.07804	−	1.86723i	0.0717104	−	0.124206i
$227$	−15.3842			−1.02108			−0.510542	−	0.859853i	$-0.670555\pi$
$227$	−15.3842			−1.02108			−0.510542	+	0.859853i	$0.670555\pi$
$228$	−16.5184			−1.09396
$229$	4.33084	−	7.50123i	0.286190	−	0.495695i	−0.686707	−	0.726934i	$-0.740945\pi$
$229$	4.33084	−	7.50123i	0.286190	−	0.495695i	0.972897	+	0.231239i	$0.0742779\pi$
$230$	−2.73209	+	4.73212i	−0.180149	+	0.312027i
$231$		0			0
$232$	−1.23845	−	2.14506i	−0.0813082	−	0.140830i
$233$	−10.1253	+	17.5376i	−0.663333	+	1.14893i	0.316402	+	0.948625i	$0.397525\pi$
$233$	−10.1253	+	17.5376i	−0.663333	+	1.14893i	−0.979734	+	0.200301i	$0.935808\pi$
$234$	−0.0288117	−	1.63695i	−0.00188348	−	0.107011i
$235$	1.68634	+	2.92083i	0.110005	+	0.190534i
$236$	−17.2888			−1.12540
$237$	−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
$241$	16.4008			1.05647			0.528233	−	0.849100i	$-0.322855\pi$
$241$	16.4008			1.05647			0.528233	+	0.849100i	$0.322855\pi$
$242$	0.612791	+	1.06138i	0.0393917	+	0.0682284i
$243$	−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
$247$	−0.475582	−	27.0204i	−0.0302605	−	1.71927i
$248$	−1.34516	−	2.32989i	−0.0854178	−	0.147948i
$249$	−0.613178	+	1.06206i	−0.0388586	+	0.0673051i
$250$	2.36106			0.149326
$251$	−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
$255$	1.14943	+	1.99087i	0.0719800	+	0.124673i
$256$	10.5536			0.659602
$257$	−13.7779			−0.859442			−0.429721	−	0.902962i	$-0.641388\pi$
$257$	−13.7779			−0.859442			−0.429721	+	0.902962i	$0.641388\pi$
$258$	−0.344695	−	0.597030i	−0.0214598	−	0.0371695i
$259$		0			0
$260$	15.2640	−	9.17456i	0.946633	−	0.568982i
$261$	1.99136	−	3.44914i	0.123262	−	0.213496i
$262$	0.856782	−	1.48399i	0.0529321	−	0.0916812i
$263$	−12.9587	+	22.4451i	−0.799065	+	1.38402i	0.121160	+	0.992633i	$0.461338\pi$
$263$	−12.9587	+	22.4451i	−0.799065	+	1.38402i	−0.920225	+	0.391389i	$0.871995\pi$
$264$	−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
$268$	−1.30394	+	2.25850i	−0.0796510	+	0.137960i
$269$	30.0666			1.83319			0.916596	−	0.399814i	$-0.130925\pi$
$269$	30.0666			1.83319			0.916596	+	0.399814i	$0.130925\pi$
$270$	−1.84245	+	3.19121i	−0.112128	+	0.194211i
$271$	−14.4505			−0.877808			−0.438904	−	0.898534i	$-0.644633\pi$
$271$	−14.4505			−0.877808			−0.438904	+	0.898534i	$0.644633\pi$
$272$	−2.80581			−0.170127
$273$		0			0
$274$	−2.69105			−0.162572
$275$	6.16598			0.371822
$276$	−8.76599	+	15.1831i	−0.527651	+	0.913918i
$277$	−15.3255			−0.920819			−0.460409	−	0.887707i	$-0.652297\pi$
$277$	−15.3255			−0.920819			−0.460409	+	0.887707i	$0.652297\pi$
$278$	0.743453	−	1.28770i	0.0445894	−	0.0772310i
$279$	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	−0.108036	+	0.994147i	$0.534456\pi$
$283$	−15.3923	+	26.6602i	−0.914975	+	1.58478i	−0.806938	+	0.590636i	$0.798877\pi$
$284$	11.8734	−	20.5654i	0.704559	−	1.22033i
$285$	−10.9735	+	19.0066i	−0.650013	+	1.12586i
$286$	3.26960	−	1.96522i	0.193335	−	0.116206i
$287$		0			0
$288$	−2.59507	−	4.49479i	−0.152916	−	0.264858i
$289$	−16.3836			−0.963742
$290$	−1.61533			−0.0948557
$291$	−1.35562	−	2.34800i	−0.0794677	−	0.137642i
$292$	−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
$296$	7.11681			0.413656
$297$	10.5847	−	18.3332i	0.614184	−	1.06380i
$298$	2.47548	+	4.28765i	0.143400	+	0.248377i
$299$	−25.0886	−	13.9020i	−1.45091	−	0.803976i
$300$	−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
$304$	−13.3934	−	23.1980i	−0.768163	−	1.33050i
$305$	−24.1970			−1.38551
$306$	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
$310$	−1.75452			−0.0996501
$311$	−8.21130	−	14.2224i	−0.465620	−	0.806478i	0.533609	−	0.845731i	$-0.320835\pi$
$311$	−8.21130	−	14.2224i	−0.465620	−	0.806478i	−0.999229	+	0.0392535i	$0.987502\pi$
$312$	−3.72023	+	2.23608i	−0.210617	+	0.126593i
$313$	5.02308	−	8.70024i	0.283921	−	0.491766i	−0.688426	−	0.725307i	$-0.741698\pi$
$313$	5.02308	−	8.70024i	0.283921	−	0.491766i	0.972347	+	0.233541i	$0.0750312\pi$
$314$	0.220658	+	0.382191i	0.0124525	+	0.0215683i
$315$		0			0
$316$	5.97024	−	10.3408i	0.335852	−	0.581713i
$317$	−5.07249	+	8.78581i	−0.284899	+	0.493460i	−0.972585	−	0.232549i	$-0.925294\pi$
$317$	−5.07249	+	8.78581i	−0.284899	+	0.493460i	0.687685	+	0.726009i	$0.258627\pi$
$318$	−2.84390			−0.159478
$319$	9.27992			0.519576
$320$	8.10273	−	14.0343i	0.452957	−	0.784544i
$321$	6.58729	−	11.4095i	0.367667	−	0.636817i
$322$		0			0
$323$	2.94227	+	5.09616i	0.163712	+	0.283558i
$324$	−1.01357	+	1.75556i	−0.0563095	+	0.0975310i
$325$	−0.0991476	−	5.63312i	−0.00549972	−	0.312469i
$326$	−0.877867	−	1.52051i	−0.0486206	−	0.0842133i
$327$	9.23349			0.510613
$328$	−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	0.832396	−	0.554181i	$-0.186968\pi$
$331$	−1.15958	−	2.00845i	−0.0637363	−	0.110395i	−0.896133	+	0.443786i	$0.853635\pi$
$332$	−2.06871			−0.113535
$333$	5.72172	+	9.91032i	0.313549	+	0.543082i
$334$	−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	$0.643528\pi$
$338$	−1.84796	−	2.95544i	−0.100516	−	0.160755i
$339$	−4.59567	−	7.95993i	−0.249602	−	0.432324i
$340$	−1.93894	+	3.35834i	−0.105154	+	0.182132i
$341$	10.0795			0.545837
$342$	−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
$346$	−1.49234	−	2.58480i	−0.0802285	−	0.138960i
$347$	−22.8208			−1.22509			−0.612543	−	0.790437i	$-0.709853\pi$
$347$	−22.8208			−1.22509			−0.612543	+	0.790437i	$0.709853\pi$
$348$	−5.18285			−0.277830
$349$	−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
$352$	6.04662	−	10.4731i	0.322286	−	0.558216i
$353$	−13.6322	+	23.6116i	−0.725568	+	1.25672i	0.233171	+	0.972436i	$0.425090\pi$
$353$	−13.6322	+	23.6116i	−0.725568	+	1.25672i	−0.958740	+	0.284286i	$0.908244\pi$
$354$	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
$359$	7.21309	−	12.4934i	0.380692	−	0.659378i	−0.610469	−	0.792040i	$-0.709019\pi$
$359$	7.21309	−	12.4934i	0.380692	−	0.659378i	0.991161	+	0.132662i	$0.0423524\pi$
$360$	−4.56932			−0.240824
$361$	−18.5895	+	32.1980i	−0.978397	+	1.69463i
$362$	3.99930			0.210199
$363$	5.22461			0.274221
$364$		0			0
$365$	−1.96894			−0.103059
$366$	2.89475			0.151311
$367$	−5.69586	+	9.86553i	−0.297322	+	0.514976i	−0.975522	−	0.219901i	$-0.929427\pi$
$367$	−5.69586	+	9.86553i	−0.297322	+	0.514976i	0.678201	+	0.734877i	$0.262760\pi$
$368$	−28.4304			−1.48204
$369$	2.06397	−	3.57489i	0.107446	−	0.186102i
$370$	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	0.918563	+	0.395274i	$0.129351\pi$
$373$	15.4815	+	26.8147i	0.801599	+	1.38841i	−0.116964	+	0.993136i	$0.537316\pi$
$374$	−0.415327	+	0.719367i	−0.0214760	+	0.0371976i
$375$	5.03256	−	8.71665i	0.259880	−	0.450126i
$376$	0.693313	−	1.20085i	0.0357549	−	0.0619293i
$377$	−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	$0.920985\pi$
$380$	−37.0217			−1.89917
$381$	2.04375			0.104705
$382$	−1.89438	−	3.28116i	−0.0969249	−	0.167879i
$383$	15.3758	+	26.6317i	0.785668	+	1.36082i	0.928599	+	0.371084i	$0.121014\pi$
$383$	15.3758	+	26.6317i	0.785668	+	1.36082i	−0.142931	+	0.989733i	$0.545653\pi$
$384$	−4.47231	+	7.74627i	−0.228227	+	0.395300i
$385$		0			0
$386$	0.522112	−	0.904324i	0.0265748	−	0.0460289i
$387$	3.80953			0.193649
$388$	2.28675	−	3.96077i	0.116092	−	0.201078i
$389$	8.18978	+	14.1851i	0.415239	+	0.719214i	0.995453	−	0.0952492i	$-0.0303648\pi$
$389$	8.18978	+	14.1851i	0.415239	+	0.719214i	−0.580215	+	0.814463i	$0.697031\pi$
$390$	0.0498153	+	2.83028i	0.00252249	+	0.143317i
$391$	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
$395$	−7.93227	−	13.7391i	−0.399116	−	0.691289i
$396$	12.8849			0.647492
$397$	−7.94133	−	13.7548i	−0.398564	−	0.690333i	0.594985	−	0.803737i	$-0.297158\pi$
$397$	−7.94133	−	13.7548i	−0.398564	−	0.690333i	−0.993549	+	0.113404i	$0.963825\pi$
$398$	0.937591			0.0469972
$399$		0			0
$400$	−2.79221	−	4.83624i	−0.139610	−	0.241812i
$401$	6.63573			0.331373			0.165686	−	0.986178i	$-0.447016\pi$
$401$	6.63573			0.331373			0.165686	+	0.986178i	$0.447016\pi$
$402$	−0.207259	−	0.358984i	−0.0103372	−	0.0179045i
$403$	−0.162077	−	9.20847i	−0.00807362	−	0.458707i
$404$	0.768670	−	1.33137i	0.0382427	−	0.0662384i
$405$	1.34667	+	2.33250i	0.0669164	+	0.115903i
$406$		0			0
$407$	−13.3319	+	23.0915i	−0.660836	+	1.14460i
$408$	0.472570	−	0.818515i	0.0233957	−	0.0405225i
$409$	−5.87235			−0.290369			−0.145184	−	0.989405i	$-0.546378\pi$
$409$	−5.87235			−0.290369			−0.145184	+	0.989405i	$0.546378\pi$
$410$	−1.67423			−0.0826843
$411$	−5.73593	+	9.93492i	−0.282933	+	0.490053i
$412$	−2.08831	+	3.61707i	−0.102884	+	0.178200i
$413$		0			0
$414$	1.80614	+	3.12832i	0.0887667	+	0.153749i
$415$	−1.37428	+	2.38032i	−0.0674607	+	0.116845i
$416$	−9.66521	−	5.35567i	−0.473876	−	0.262584i
$417$	−3.16932	−	5.48942i	−0.155202	−	0.268818i
$418$	−7.93017			−0.387877
$419$	−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
$423$	2.22962			0.108408
$424$	−4.88672	−	8.46405i	−0.237320	−	0.411051i
$425$	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
$429$	−0.286184	−	16.2597i	−0.0138171	−	0.785024i
$430$	−0.772544	−	1.33809i	−0.0372554	−	0.0645282i
$431$	1.95793	−	3.39124i	0.0943104	−	0.163350i	−0.815010	−	0.579447i	$-0.803269\pi$
$431$	1.95793	−	3.39124i	0.0943104	−	0.163350i	0.909321	+	0.416096i	$0.136602\pi$
$432$	−19.1726			−0.922445
$433$	−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
$437$	29.8131	+	51.6378i	1.42615	+	2.47017i
$438$	0.235549			0.0112550
$439$	25.5623			1.22002			0.610010	−	0.792394i	$-0.291165\pi$
$439$	25.5623			1.22002			0.610010	+	0.792394i	$0.291165\pi$
$440$	−5.32336	−	9.22033i	−0.253781	−	0.439562i
$441$		0			0
$442$	0.663878	+	0.367867i	0.0315775	+	0.0174977i
$443$	13.7282	−	23.7779i	0.652247	−	1.12972i	−0.330330	−	0.943866i	$-0.607160\pi$
$443$	13.7282	−	23.7779i	0.652247	−	1.12972i	0.982576	−	0.185859i	$-0.0595067\pi$
$444$	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	$0.0530816\pi$
$450$	−0.354769	+	0.614477i	−0.0167240	+	0.0289667i
$451$	9.61827			0.452907
$452$	7.75230	−	13.4274i	0.364637	−	0.631571i
$453$	1.83722			0.0863203
$454$	4.12489			0.193590
$455$		0			0
$456$	9.02315			0.422548
$457$	−0.651951			−0.0304970			−0.0152485	−	0.999884i	$-0.504854\pi$
$457$	−0.651951			−0.0304970			−0.0152485	+	0.999884i	$0.504854\pi$
$458$	−1.16121	+	2.01127i	−0.0542596	+	0.0939805i
$459$	4.21186			0.196593
$460$	−19.6467	+	34.0290i	−0.916031	+	1.58661i
$461$	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
$467$	12.2387	−	21.1980i	0.566338	−	0.980926i	−0.430586	−	0.902549i	$-0.641693\pi$
$467$	12.2387	−	21.1980i	0.566338	−	0.980926i	0.996924	−	0.0783762i	$-0.0249735\pi$
$468$	−0.207187	−	11.7714i	−0.00957722	−	0.544134i
$469$		0			0
$470$	−0.452151	−	0.783149i	−0.0208562	−	0.0361240i
$471$	1.88132			0.0866865
$472$	9.44396			0.434694
$473$	4.43818	+	7.68716i	0.204068	+	0.353456i
$474$	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
$478$	−4.43817			−0.202997
$479$	4.06925	−	7.04815i	0.185929	−	0.322038i	−0.757960	−	0.652301i	$-0.773804\pi$
$479$	4.06925	−	7.04815i	0.185929	−	0.322038i	0.943889	+	0.330262i	$0.107137\pi$
$480$	4.48686	+	7.77147i	0.204796	+	0.354718i
$481$	21.3103	+	11.8084i	0.971667	+	0.538419i
$482$	−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
$486$	1.99653	+	3.45809i	0.0905645	+	0.156862i
$487$	4.60960			0.208881			0.104440	−	0.994531i	$-0.466695\pi$
$487$	4.60960			0.208881			0.104440	+	0.994531i	$0.466695\pi$
$488$	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	$0.928243\pi$
$492$	−5.37181			−0.242180
$493$	0.923171	+	1.59898i	0.0415775	+	0.0720144i
$494$	0.127515	+	7.24485i	0.00573719	+	0.325961i
$495$	8.55969	−	14.8258i	0.384729	−	0.666371i
$496$	−4.56443	−	7.90582i	−0.204949	−	0.354982i
$497$		0			0
$498$	0.164409	−	0.284764i	0.00736733	−	0.0127606i
$499$	16.1603	−	27.9905i	0.723436	−	1.25303i	−0.236178	−	0.971710i	$-0.575895\pi$
$499$	16.1603	−	27.9905i	0.723436	−	1.25303i	0.959614	−	0.281319i	$-0.0907717\pi$
$500$	16.9786			0.759304
$501$	−10.9144			−0.487618
$502$	2.73900	−	4.74408i	0.122247	−	0.211739i
$503$	−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
$506$	−4.20838	+	7.28912i	−0.187085	+	0.324041i
$507$	−14.8499	+	0.522904i	−0.659508	+	0.0232230i
$508$	1.72377	+	2.98566i	0.0764801	+	0.132467i
$509$	−2.25575			−0.0999845			−0.0499922	−	0.998750i	$-0.515920\pi$
$509$	−2.25575			−0.0999845			−0.0499922	+	0.998750i	$0.515920\pi$
$510$	−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
$514$	3.69420			0.162944
$515$	2.77461	+	4.80576i	0.122264	+	0.211767i
$516$	−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
$520$	−8.33793	+	5.01158i	−0.365642	+	0.219773i
$521$	5.38562	+	9.32817i	0.235948	+	0.408675i	0.959548	−	0.281546i	$-0.0908471\pi$
$521$	5.38562	+	9.32817i	0.235948	+	0.408675i	−0.723600	+	0.690220i	$0.757514\pi$
$522$	−0.533934	+	0.924801i	−0.0233697	+	0.0404775i
$523$	−7.40793			−0.323926			−0.161963	−	0.986797i	$-0.551783\pi$
$523$	−7.40793			−0.323926			−0.161963	+	0.986797i	$0.551783\pi$
$524$	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
$528$	−8.05953	−	13.9595i	−0.350746	−	0.607510i
$529$	40.2848			1.75151
$530$	−6.37385			−0.276862
$531$	7.59270	+	13.1509i	0.329495	+	0.570702i
$532$		0			0
$533$	−0.154660	−	8.78707i	−0.00669906	−	0.380610i
$534$	−1.17424	+	2.03384i	−0.0508142	+	0.0880127i
$535$	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
$541$	−16.2741	+	28.1875i	−0.699676	+	1.21188i	0.268902	+	0.963168i	$0.413339\pi$
$541$	−16.2741	+	28.1875i	−0.699676	+	1.21188i	−0.968579	+	0.248708i	$0.919994\pi$
$542$	3.87455			0.166426
$543$	8.52445	−	14.7648i	0.365819	−	0.633617i
$544$	2.40608			0.103160
$545$	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	$0.593191\pi$
$548$	−19.3515			−0.826657
$549$	−7.99810	+	13.8531i	−0.341350	+	0.591236i
$550$	−1.65325			−0.0704950
$551$	−8.81342	+	15.2653i	−0.375464	+	0.650323i
$552$	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	−0.356705	−	0.934217i	$-0.616100\pi$
$557$	14.8851	−	25.7818i	0.630703	−	1.09241i	0.987408	−	0.158193i	$-0.0505668\pi$
$558$	−0.579941	+	1.00449i	−0.0245509	+	0.0425233i
$559$	6.95148	−	4.17825i	0.294016	−	0.176721i
$560$		0			0
$561$	1.77052	+	3.06664i	0.0747516	+	0.129474i
$562$	−1.41913			−0.0598624
$563$	−14.1326			−0.595617			−0.297809	−	0.954626i	$-0.596256\pi$
$563$	−14.1326			−0.595617			−0.297809	+	0.954626i	$0.596256\pi$
$564$	−1.45074	−	2.51275i	−0.0610872	−	0.105806i
$565$	−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
$569$	−24.2540			−1.01678			−0.508391	−	0.861127i	$-0.669759\pi$
$569$	−24.2540			−1.01678			−0.508391	+	0.861127i	$0.669759\pi$
$570$	2.94227	−	5.09616i	0.123238	−	0.213455i
$571$	−0.604159	−	1.04643i	−0.0252832	−	0.0437919i	0.853107	−	0.521736i	$-0.174715\pi$
$571$	−0.604159	−	1.04643i	−0.0252832	−	0.0437919i	−0.878390	+	0.477944i	$0.841382\pi$
$572$	23.5119	−	14.1320i	0.983083	−	0.590891i
$573$	−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
$577$	−7.30518	−	12.6529i	−0.304119	−	0.526749i	0.672946	−	0.739692i	$-0.265029\pi$
$577$	−7.30518	−	12.6529i	−0.304119	−	0.526749i	−0.977065	+	0.212943i	$0.931695\pi$
$578$	4.39286			0.182719
$579$	−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
$583$	36.6171			1.51652
$584$	0.404749	+	0.701046i	0.0167486	+	0.0290095i
$585$	−13.6822	−	7.58157i	−0.565690	−	0.313459i
$586$	2.34841	−	4.06757i	0.0970120	−	0.168030i
$587$	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
$590$	3.07949	−	5.33383i	0.126780	−	0.219590i
$591$	−13.3834			−0.550518
$592$	24.1489			0.992512
$593$	−1.32429	+	2.29373i	−0.0543820	+	0.0941923i	−0.891935	−	0.452164i	$-0.850652\pi$
$593$	−1.32429	+	2.29373i	−0.0543820	+	0.0941923i	0.837553	+	0.546356i	$0.183986\pi$
$594$	−2.83801	+	4.91558i	−0.116445	+	0.201689i
$595$		0			0
$596$	17.8013	+	30.8328i	0.729171	+	1.26296i
$597$	1.99846	−	3.46143i	0.0817915	−	0.141667i
$598$	6.72688	+	3.72749i	0.275082	+	0.152428i
$599$	20.1250	+	34.8576i	0.822287	+	1.42424i	0.903975	+	0.427584i	$0.140635\pi$
$599$	20.1250	+	34.8576i	0.822287	+	1.42424i	−0.0816889	+	0.996658i	$0.526031\pi$
$600$	1.88112			0.0767962
$601$	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
$605$	11.7096			0.476063
$606$	0.122179	+	0.211620i	0.00496317	+	0.00859646i
$607$	21.2773	+	36.8534i	0.863620	+	1.49583i	0.868411	+	0.495845i	$0.165142\pi$
$607$	21.2773	+	36.8534i	0.863620	+	1.49583i	−0.00479063	+	0.999989i	$0.501525\pi$
$608$	11.4853	+	19.8931i	0.465791	+	0.806773i
$609$		0			0
$610$	6.48782			0.262684
$611$	4.06853	−	2.44543i	0.164595	−	0.0989314i
$612$	1.28180	+	2.22014i	0.0518136	+	0.0897438i
$613$	−7.63261	+	13.2201i	−0.308278	+	0.533953i	−0.977986	−	0.208672i	$-0.933086\pi$
$613$	−7.63261	+	13.2201i	−0.308278	+	0.533953i	0.669708	+	0.742625i	$0.266419\pi$
$614$	−2.31546			−0.0934442
$615$	−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
$619$	−4.25792	−	7.37494i	−0.171140	−	0.296424i	0.767678	−	0.640835i	$-0.221412\pi$
$619$	−4.25792	−	7.37494i	−0.171140	−	0.296424i	−0.938819	+	0.344411i	$0.888079\pi$
$620$	−12.6169			−0.506707
$621$	42.6775			1.71259
$622$	2.20166	+	3.81338i	0.0882784	+	0.152903i
$623$		0			0
$624$	−12.6236	+	7.58750i	−0.505347	+	0.303743i
$625$	15.1856	−	26.3023i	0.607425	−	1.05209i
$626$	−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	$0.904752\pi$
$632$	−3.26123	+	5.64861i	−0.129725	+	0.224690i
$633$	21.7231			0.863414
$634$	1.36006	−	2.35570i	0.0540150	−	0.0935567i
$635$	4.58053			0.181773
$636$	−20.4507			−0.810922
$637$		0			0
$638$	−2.48818			−0.0985081
$639$	−20.8578			−0.825121
$640$	−10.0235	+	17.3612i	−0.396214	+	0.686263i
$641$	25.8747			1.02199			0.510996	−	0.859583i	$-0.329277\pi$
$641$	25.8747			1.02199			0.510996	+	0.859583i	$0.329277\pi$
$642$	−1.76622	+	3.05918i	−0.0697071	+	0.120736i
$643$	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	−0.847959	−	0.530062i	$-0.822168\pi$
$647$	0.892002	−	1.54499i	0.0350682	−	0.0607399i	0.883027	+	0.469322i	$0.155502\pi$
$648$	0.553661	−	0.958969i	0.0217499	−	0.0376719i
$649$	−17.6913	+	30.6423i	−0.694445	+	1.20281i
$650$	0.0265840	+	1.51038i	0.00104271	+	0.0592420i
$651$		0			0
$652$	−6.31281	−	10.9341i	−0.247229	−	0.428213i
$653$	12.4042			0.485414			0.242707	−	0.970100i	$-0.421965\pi$
$653$	12.4042			0.485414			0.242707	+	0.970100i	$0.421965\pi$
$654$	−2.47573			−0.0968088
$655$	−8.18597	−	14.1785i	−0.319852	−	0.554000i
$656$	−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	$0.159669\pi$
$660$	−22.2780			−0.867170
$661$	−14.4627	+	25.0502i	−0.562534	+	0.974338i	0.434740	+	0.900556i	$0.356840\pi$
$661$	−14.4627	+	25.0502i	−0.562534	+	0.974338i	−0.997274	+	0.0737821i	$0.976493\pi$
$662$	0.310913	+	0.538517i	0.0120840	+	0.0209301i
$663$	2.77315	−	1.66683i	0.107700	−	0.0647342i
$664$	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
$668$	−9.20556	−	15.9445i	−0.356174	−	0.616911i
$669$	13.6775			0.528802
$670$	−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	$0.789640\pi$
$674$	4.28995			0.165243
$675$	4.19145	+	7.25980i	0.161329	+	0.279430i
$676$	−13.2888	−	21.2528i	−0.511109	−	0.817416i
$677$	−25.2010	+	43.6494i	−0.968552	+	1.67758i	−0.268800	+	0.963196i	$0.586627\pi$
$677$	−25.2010	+	43.6494i	−0.968552	+	1.67758i	−0.699752	+	0.714386i	$0.746706\pi$
$678$	1.23221	+	2.13426i	0.0473229	+	0.0819657i
$679$		0			0
$680$	1.05914	−	1.83449i	0.0406162	−	0.0703493i
$681$	8.79213	−	15.2284i	0.336915	−	0.583554i
$682$	−2.70258			−0.103487
$683$	27.5282			1.05334			0.526669	−	0.850070i	$-0.323441\pi$
$683$	27.5282			1.05334			0.526669	+	0.850070i	$0.323441\pi$
$684$	−12.2372	+	21.1954i	−0.467901	+	0.810428i
$685$	−12.8556	+	22.2665i	−0.491186	+	0.850760i
$686$		0			0
$687$	4.95019	+	8.57398i	0.188861	+	0.327118i
$688$	4.01958	−	6.96212i	0.153245	−	0.265428i
$689$	−0.588795	−	33.4527i	−0.0224313	−	1.27445i
$690$	−3.12280	−	5.40885i	−0.118883	−	0.205912i
$691$	24.3338			0.925702			0.462851	−	0.886436i	$-0.346826\pi$
$691$	24.3338			0.925702			0.462851	+	0.886436i	$0.346826\pi$
$692$	−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
$696$	2.83112			0.107313
$697$	0.956829	+	1.65728i	0.0362425	+	0.0627738i
$698$	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	$0.626919\pi$
$702$	4.53642	+	2.51371i	0.171216	+	0.0948740i
$703$	−25.3234	−	43.8613i	−0.955088	−	1.65426i
$704$	12.4811	−	21.6178i	0.470397	−	0.814752i
$705$	−3.85501			−0.145188
$706$	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	−0.938547	−	0.345151i	$-0.887828\pi$
$709$	−20.4544	−	35.4281i	−0.768183	−	1.33053i	0.170364	−	0.985381i	$-0.445506\pi$
$710$	4.22981	+	7.32624i	0.158742	+	0.274949i
$711$	−10.4878			−0.393322
$712$	−8.07085			−0.302468
$713$	10.1602	+	17.5980i	0.380503	+	0.659051i
$714$		0			0
$715$	−0.641405	−	36.4418i	−0.0239872	−	1.36284i
$716$	−12.1890	+	21.1119i	−0.455524	+	0.788990i
$717$	−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	0.854626	−	0.519245i	$-0.173787\pi$
$719$	−0.599734	−	1.03877i	−0.0223663	−	0.0387396i	−0.876992	+	0.480505i	$0.840453\pi$
$720$	−15.5047			−0.577826
$721$		0			0
$722$	4.98433	−	8.63311i	0.185497	−	0.321291i
$723$	−9.37311	+	16.2347i	−0.348590	+	0.603775i
$724$	28.7593			1.06883
$725$	−1.83739	+	3.18246i	−0.0682390	+	0.118193i
$726$	−1.40085			−0.0519904
$727$	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
$730$	0.527922			0.0195393
$731$	−0.883025	+	1.52944i	−0.0326599	+	0.0565685i
$732$	20.8164			0.769395
$733$	15.0310	−	26.0345i	0.555184	−	0.961606i	−0.442706	−	0.896667i	$-0.645981\pi$
$733$	15.0310	−	26.0345i	0.555184	−	0.961606i	0.997889	−	0.0649392i	$-0.0206853\pi$
$734$	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	0.0960970	+	0.995372i	$0.469364\pi$
$739$	−22.1274	+	38.3257i	−0.813969	+	1.40984i	−0.910066	+	0.414464i	$0.863969\pi$
$740$	16.6880	−	28.9044i	0.613461	−	1.06255i
$741$	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	$0.782752\pi$
$744$	3.07506			0.112737
$745$	47.3030			1.73305
$746$	−4.15097	−	7.18969i	−0.151978	−	0.263233i
$747$	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
$751$	5.72211			0.208803			0.104401	−	0.994535i	$-0.466707\pi$
$751$	5.72211			0.208803			0.104401	+	0.994535i	$0.466707\pi$
$752$	2.35256	−	4.07476i	0.0857891	−	0.148591i
$753$	−11.6763	−	20.2239i	−0.425506	−	0.736998i
$754$	0.0400094	+	2.27316i	0.00145706	+	0.0827835i
$755$	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
$759$	17.9402	+	31.0733i	0.651187	+	1.12789i
$760$	20.2230			0.733566
$761$	−26.5867	−	46.0496i	−0.963768	−	1.66930i	−0.712888	−	0.701278i	$-0.752613\pi$
$761$	−26.5867	−	46.0496i	−0.963768	−	1.66930i	−0.250880	−	0.968018i	$-0.580720\pi$
$762$	−0.547981			−0.0198513
$763$		0			0
$764$	−13.6226	−	23.5951i	−0.492849	−	0.853640i
$765$	3.40609			0.123147
$766$	−4.12265	−	7.14063i	−0.148957	−	0.258002i
$767$	28.2787	+	15.6697i	1.02108	+	0.565801i
$768$	−6.03145	+	10.4468i	−0.217641	+	0.376966i
$769$	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
$772$	3.75455	−	6.50306i	0.135129	−	0.234050i
$773$	22.9807			0.826557			0.413279	−	0.910605i	$-0.364384\pi$
$773$	22.9807			0.826557			0.413279	+	0.910605i	$0.364384\pi$
$774$	−1.02143			−0.0367146
$775$

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.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-0.268125 q^{2} +(-0.571504 + 0.989875i) q^{3} -1.92811 q^{4} +(-1.28088 + 2.21854i) q^{5} +(0.153235 - 0.265410i) q^{6} +1.05323 q^{8} +(0.846765 + 1.46664i) q^{9} +O(q^{10})\)	\(q-0.268125 q^{2} +(-0.571504 + 0.989875i) q^{3} -1.92811 q^{4} +(-1.28088 + 2.21854i) 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} +(1.10192 - 1.90859i) q^{12} +(3.15374 + 1.74755i) q^{13} +(-1.46405 - 2.53582i) q^{15} +3.57382 q^{16} -0.785100 q^{17} +(-0.227039 - 0.393243i) q^{18} +(-3.74764 - 6.49110i) q^{19} +(2.46967 - 4.27760i) q^{20} +(0.529011 - 0.916274i) q^{22} -7.95518 q^{23} +(-0.601923 + 1.04256i) q^{24} +(-0.781294 - 1.35324i) q^{25} +(-0.845598 - 0.468561i) q^{26} -5.36475 q^{27} +(-1.17586 - 2.03666i) q^{29} +(0.392550 + 0.679916i) q^{30} +(-1.27718 - 2.21215i) q^{31} -3.06468 q^{32} +(-2.25516 - 3.90605i) q^{33} +0.210505 q^{34} +(-1.63266 - 2.82784i) q^{36} +6.75716 q^{37} +(1.00484 + 1.74043i) q^{38} +(-3.53223 + 2.12308i) q^{39} +(-1.34905 + 2.33663i) q^{40} +(-1.21874 - 2.11091i) q^{41} +(1.12473 - 1.94809i) q^{43} +(3.80416 - 6.58900i) q^{44} -4.33841 q^{45} +2.13298 q^{46} +(0.658276 - 1.14017i) q^{47} +(-2.04246 + 3.53764i) q^{48} +(0.209485 + 0.362838i) q^{50} +(0.448688 - 0.777151i) q^{51} +(-6.08076 - 3.36946i) q^{52} +(-4.63977 - 8.03632i) q^{53} +1.43842 q^{54} +(-5.05434 - 8.75438i) q^{55} +8.56716 q^{57} +(0.315279 + 0.546079i) q^{58} +8.96671 q^{59} +(2.82286 + 4.88933i) q^{60} +(4.72273 + 8.18002i) q^{61} +(0.342445 + 0.593132i) q^{62} -6.32592 q^{64} +(-7.91657 + 4.75832i) q^{65} +(0.604665 + 1.04731i) q^{66} +(0.676281 - 1.17135i) q^{67} +1.51376 q^{68} +(4.54642 - 7.87463i) q^{69} +(-6.15808 + 10.6661i) q^{71} +(0.891834 + 1.54470i) q^{72} +(0.384295 + 0.665619i) q^{73} -1.81176 q^{74} +1.78605 q^{75} +(7.22585 + 12.5155i) q^{76} +(0.947080 - 0.569251i) q^{78} +(-3.09642 + 5.36316i) 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} +(-0.301568 + 0.522332i) q^{86} +2.68805 q^{87} +(-2.07801 + 3.59923i) q^{88} -7.66299 q^{89} +1.16324 q^{90} +15.3384 q^{92} +2.91966 q^{93} +(-0.176501 + 0.305708i) q^{94} +19.2010 q^{95} +(1.75148 - 3.03365i) q^{96} +(-1.18601 + 2.05423i) q^{97} -6.68267 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} - q^{3} + 8 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 12 * q - 4 * q^2 - q^3 + 8 * q^4 - q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9	\( 12 q - 4 q^{2} - q^{3} + 8 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9} - 4 q^{10} + 4 q^{11} - 5 q^{12} + 2 q^{13} - 2 q^{15} - 16 q^{16} + 10 q^{17} + 3 q^{18} + q^{19} + q^{20} - 5 q^{22} + 2 q^{23} + 11 q^{24} + 7 q^{25} + 16 q^{26} + 8 q^{27} + 3 q^{29} - 5 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 32 q^{34} - 21 q^{36} + 26 q^{37} + 17 q^{38} - 20 q^{39} + 5 q^{40} + 8 q^{41} - 11 q^{43} + 21 q^{44} - 14 q^{45} - 32 q^{46} + q^{47} - 21 q^{48} + 6 q^{50} - 20 q^{51} - 41 q^{52} - 2 q^{53} - 36 q^{54} - 9 q^{55} + 42 q^{57} - 8 q^{58} + 26 q^{59} + 20 q^{60} + 5 q^{61} - 5 q^{62} - 30 q^{64} - 5 q^{65} - 18 q^{66} - 11 q^{67} + 58 q^{68} - 23 q^{69} + 6 q^{71} + 25 q^{72} + 30 q^{73} + 6 q^{74} - 6 q^{75} + 9 q^{76} + 16 q^{78} + 7 q^{79} + 7 q^{80} - 6 q^{81} - q^{82} + 54 q^{83} - q^{85} - 7 q^{86} + 32 q^{87} + 8 q^{89} + 16 q^{90} + 54 q^{92} + 14 q^{93} - 45 q^{94} + 12 q^{95} - 19 q^{96} + 35 q^{97} - 20 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 - q^3 + 8 * q^4 - q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9 - 4 * q^10 + 4 * q^11 - 5 * q^12 + 2 * q^13 - 2 * q^15 - 16 * q^16 + 10 * q^17 + 3 * q^18 + q^19 + q^20 - 5 * q^22 + 2 * q^23 + 11 * q^24 + 7 * q^25 + 16 * q^26 + 8 * q^27 + 3 * q^29 - 5 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 32 * q^34 - 21 * q^36 + 26 * q^37 + 17 * q^38 - 20 * q^39 + 5 * q^40 + 8 * q^41 - 11 * q^43 + 21 * q^44 - 14 * q^45 - 32 * q^46 + q^47 - 21 * q^48 + 6 * q^50 - 20 * q^51 - 41 * q^52 - 2 * q^53 - 36 * q^54 - 9 * q^55 + 42 * q^57 - 8 * q^58 + 26 * q^59 + 20 * q^60 + 5 * q^61 - 5 * q^62 - 30 * q^64 - 5 * q^65 - 18 * q^66 - 11 * q^67 + 58 * q^68 - 23 * q^69 + 6 * q^71 + 25 * q^72 + 30 * q^73 + 6 * q^74 - 6 * q^75 + 9 * q^76 + 16 * q^78 + 7 * q^79 + 7 * q^80 - 6 * q^81 - q^82 + 54 * q^83 - q^85 - 7 * q^86 + 32 * q^87 + 8 * q^89 + 16 * q^90 + 54 * q^92 + 14 * q^93 - 45 * q^94 + 12 * q^95 - 19 * q^96 + 35 * q^97 - 20 * q^99

Introduction

L-functions

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