LMFDB - Embedded newform 637.2.h.l.165.4

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			165.4
Root			$-0.437442 + 0.757672i$ of defining polynomial
Character	$\chi$	$=$	637.165
Dual form			637.2.h.l.471.4

$q$-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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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	0.652545	−	0.757750i	$-0.273701\pi$
$3$	−0.571504	−	0.989875i	−0.329958	−	0.571504i	−0.982503	+	0.186246i	$0.940368\pi$
$4$	−1.92811			−0.964054
$5$	−1.28088	−	2.21854i	−0.572826	−	0.992163i	−0.996274	−	0.0862431i	$-0.972514\pi$
$5$	−1.28088	−	2.21854i	−0.572826	−	0.992163i	0.423448	−	0.905920i	$-0.360820\pi$
$6$	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	$-0.369468\pi$
$12$	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	0.0123849	+	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
$23$	−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	−0.954304	−	0.298836i	$-0.903402\pi$
$29$	−1.17586	+	2.03666i	−0.218353	+	0.378198i	0.735952	+	0.677034i	$0.236735\pi$
$30$	0.392550	−	0.679916i	0.0716695	−	0.124135i
$31$	−1.27718	+	2.21215i	−0.229389	+	0.397313i	−0.957627	−	0.288011i	$-0.907006\pi$
$31$	−1.27718	+	2.21215i	−0.229389	+	0.397313i	0.728238	+	0.685324i	$0.240339\pi$
$32$	−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	−0.945361	−	0.326025i	$-0.894291\pi$
$41$	−1.21874	+	2.11091i	−0.190335	+	0.329669i	0.755027	+	0.655694i	$0.227624\pi$
$42$		0			0
$43$	1.12473	+	1.94809i	0.171520	+	0.297081i	0.938951	−	0.344050i	$-0.111799\pi$
$43$	1.12473	+	1.94809i	0.171520	+	0.297081i	−0.767432	+	0.641131i	$0.778466\pi$
$44$	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	0.910034	−	0.414534i	$-0.136056\pi$
$47$	0.658276	+	1.14017i	0.0960195	+	0.166311i	−0.814014	+	0.580845i	$0.802722\pi$
$48$	−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	0.348697	+	0.937236i	$0.386624\pi$
$53$	−4.63977	+	8.03632i	−0.637321	+	1.10387i	−0.986018	+	0.166637i	$0.946709\pi$
$54$	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	−0.387417	−	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
$65$	−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	0.904375	−	0.426739i	$-0.140338\pi$
$67$	0.676281	+	1.17135i	0.0826209	+	0.143104i	−0.821754	+	0.569842i	$0.807004\pi$
$68$	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	−0.956529	−	0.291637i	$-0.905800\pi$
$71$	−6.15808	−	10.6661i	−0.730829	−	1.26583i	0.225700	−	0.974197i	$-0.427533\pi$
$72$	0.891834	−	1.54470i	0.105104	−	0.182045i
$73$	0.384295	−	0.665619i	0.0449783	−	0.0779048i	−0.842660	−	0.538446i	$-0.819011\pi$
$73$	0.384295	−	0.665619i	0.0449783	−	0.0779048i	0.887638	+	0.460542i	$0.152345\pi$
$74$	−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	0.637586	−	0.770379i	$-0.279933\pi$
$79$	−3.09642	−	5.36316i	−0.348375	−	0.603402i	−0.985961	+	0.166976i	$0.946600\pi$
$80$	−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	0.799513	−	0.600649i	$-0.205091\pi$
$97$	−1.18601	−	2.05423i	−0.120421	−	0.208575i	−0.919934	+	0.392074i	$0.871758\pi$
$98$		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
$103$	1.08309	+	1.87597i	0.106720	+	0.184844i	0.914440	−	0.404722i	$-0.132632\pi$
$103$	1.08309	+	1.87597i	0.106720	+	0.184844i	−0.807720	+	0.589567i	$0.799299\pi$
$104$	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	−0.992028	−	0.126020i	$-0.959780\pi$
$109$	−4.03912	+	6.99595i	−0.386877	+	0.670091i	0.605151	+	0.796111i	$0.293113\pi$
$110$	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	0.612572	−	0.790415i	$-0.290135\pi$
$113$	−4.02067	−	6.96401i	−0.378233	−	0.655119i	−0.990805	+	0.135296i	$0.956802\pi$
$114$	−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	−0.902962	−	0.429721i	$-0.858612\pi$
$127$	−0.894023	+	1.54849i	−0.0793317	+	0.137406i	0.823630	+	0.567127i	$0.191945\pi$
$128$	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	0.691995	−	0.721902i	$-0.256732\pi$
$131$	−3.19545	−	5.53469i	−0.279188	−	0.483568i	−0.971183	+	0.238334i	$0.923399\pi$
$132$	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	0.724142	−	0.689651i	$-0.242236\pi$
$139$	−2.77278	−	4.80260i	−0.235184	−	0.407351i	−0.959326	+	0.282300i	$0.908903\pi$
$140$		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	0.188337	+	0.982104i	$0.439690\pi$
$149$	−9.23254	+	15.9912i	−0.756359	+	1.31005i	−0.944696	+	0.327947i	$0.893643\pi$
$150$	−0.478886			−0.0391009
$151$	−0.803678	+	1.39201i	−0.0654024	+	0.113280i	−0.896872	−	0.442289i	$-0.854166\pi$
$151$	−0.803678	+	1.39201i	−0.0654024	+	0.113280i	0.831470	+	0.555570i	$0.187500\pi$
$152$	−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	−0.896995	−	0.442040i	$-0.854255\pi$
$157$	−0.822967	+	1.42542i	−0.0656799	+	0.113761i	0.831315	+	0.555801i	$0.187588\pi$
$158$	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	−0.708841	−	0.705369i	$-0.750782\pi$
$163$	3.27409	−	5.67090i	0.256447	−	0.444179i	0.965287	+	0.261190i	$0.0841148\pi$
$164$	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	−0.620026	−	0.784581i	$-0.712878\pi$
$167$	4.77440	−	8.26950i	0.369454	−	0.639913i	0.989480	+	0.144668i	$0.0462114\pi$
$168$		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	−0.573085	−	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
$177$	−5.12451	−	8.87592i	−0.385182	−	0.667155i
$178$	2.05464			0.154002
$179$	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	$0.676682\pi$
$180$	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	−0.488690	−	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	$0.878097\pi$
$194$	0.317999	+	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	−0.578536	−	0.815657i	$-0.696376\pi$
$197$	5.85445	−	10.1402i	0.417112	−	0.722459i	0.995648	+	0.0931979i	$0.0297089\pi$
$198$	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	0.327913	+	0.944708i	$0.393655\pi$
$211$	−9.50258	+	16.4589i	−0.654184	+	1.13308i	−0.982098	+	0.188373i	$0.939679\pi$
$212$	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	−0.993805	−	0.111133i	$-0.964552\pi$
$223$	−5.98311	+	10.3630i	−0.400658	+	0.693961i	0.593147	+	0.805094i	$0.297885\pi$
$224$		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	0.972897	−	0.231239i	$-0.0742779\pi$
$229$	4.33084	+	7.50123i	0.286190	+	0.495695i	−0.686707	+	0.726934i	$0.740945\pi$
$230$	−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	−0.979734	−	0.200301i	$-0.935808\pi$
$233$	−10.1253	−	17.5376i	−0.663333	−	1.14893i	0.316402	−	0.948625i	$-0.397525\pi$
$234$	−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	−0.984350	−	0.176222i	$-0.943612\pi$
$251$	−10.2154	−	17.6935i	−0.644788	−	1.11681i	0.339563	−	0.940583i	$-0.389721\pi$
$252$		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	−0.920225	−	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
$268$	−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	−0.806938	−	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
$285$	−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	−0.999908	−	0.0135461i	$-0.995688\pi$
$293$	−8.75864	−	15.1704i	−0.511685	−	0.886265i	0.488223	−	0.872719i	$-0.337645\pi$
$294$		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	−0.999229	−	0.0392535i	$-0.987502\pi$
$311$	−8.21130	+	14.2224i	−0.465620	+	0.806478i	0.533609	+	0.845731i	$0.320835\pi$
$312$	−3.72023	−	2.23608i	−0.210617	−	0.126593i
$313$	5.02308	+	8.70024i	0.283921	+	0.491766i	0.972347	−	0.233541i	$-0.0750312\pi$
$313$	5.02308	+	8.70024i	0.283921	+	0.491766i	−0.688426	+	0.725307i	$0.741698\pi$
$314$	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	0.687685	−	0.726009i	$-0.258627\pi$
$317$	−5.07249	−	8.78581i	−0.284899	−	0.493460i	−0.972585	+	0.232549i	$0.925294\pi$
$318$	−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	−0.896133	−	0.443786i	$-0.853635\pi$
$331$	−1.15958	+	2.00845i	−0.0637363	+	0.110395i	0.832396	+	0.554181i	$0.186968\pi$
$332$	−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	0.384021	+	0.923324i	$0.374539\pi$
$349$	−11.3511	+	19.6607i	−0.607612	+	1.05241i	−0.991633	+	0.129090i	$0.958794\pi$
$350$		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	−0.958740	−	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
$359$	7.21309	+	12.4934i	0.380692	+	0.659378i	0.991161	−	0.132662i	$-0.0423524\pi$
$359$	7.21309	+	12.4934i	0.380692	+	0.659378i	−0.610469	+	0.792040i	$0.709019\pi$
$360$	−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	0.678201	−	0.734877i	$-0.262760\pi$
$367$	−5.69586	−	9.86553i	−0.297322	−	0.514976i	−0.975522	+	0.219901i	$0.929427\pi$
$368$	−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	−0.116964	−	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
$376$	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	−0.969348	−	0.245692i	$-0.920985\pi$
$379$	−5.29330	+	9.16826i	−0.271898	+	0.470942i	0.697450	+	0.716634i	$0.254318\pi$
$380$	−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	−0.142931	−	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
$387$	3.80953			0.193649
$388$	2.28675	+	3.96077i	0.116092	+	0.201078i
$389$	8.18978	−	14.1851i	0.415239	−	0.719214i	−0.580215	−	0.814463i	$-0.697031\pi$
$389$	8.18978	−	14.1851i	0.415239	−	0.719214i	0.995453	+	0.0952492i	$0.0303648\pi$
$390$	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	−0.993549	−	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
$401$	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	0.217888	+	0.975974i	$0.430083\pi$
$419$	−15.0712	+	26.1040i	−0.736274	+	1.27526i	−0.954162	+	0.299290i	$0.903250\pi$
$420$		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	0.909321	−	0.416096i	$-0.136602\pi$
$431$	1.95793	+	3.39124i	0.0943104	+	0.163350i	−0.815010	+	0.579447i	$0.803269\pi$
$432$	−19.1726			−0.922445
$433$	−20.3963	−	35.3274i	−0.980182	−	1.69772i	−0.661650	−	0.749813i	$-0.730144\pi$
$433$	−20.3963	−	35.3274i	−0.980182	−	1.69772i	−0.318532	−	0.947912i	$-0.603190\pi$
$434$		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	0.982576	+	0.185859i	$0.0595067\pi$
$443$	13.7282	+	23.7779i	0.652247	+	1.12972i	−0.330330	+	0.943866i	$0.607160\pi$
$444$	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	0.986128	−	0.165989i	$-0.0530816\pi$
$449$	7.40181	+	12.8203i	0.349313	+	0.605028i	−0.636815	+	0.771017i	$0.719748\pi$
$450$	−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	0.974043	−	0.226362i	$-0.0726833\pi$
$461$	6.24774	+	10.8214i	0.290986	+	0.504003i	−0.683057	+	0.730365i	$0.739350\pi$
$462$		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	0.996924	+	0.0783762i	$0.0249735\pi$
$467$	12.2387	+	21.1980i	0.566338	+	0.980926i	−0.430586	+	0.902549i	$0.641693\pi$
$468$	−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	0.943889	−	0.330262i	$-0.107137\pi$
$479$	4.06925	+	7.04815i	0.185929	+	0.322038i	−0.757960	+	0.652301i	$0.773804\pi$
$480$	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	−0.974698	−	0.223527i	$-0.928243\pi$
$491$	−6.50947	+	11.2747i	−0.293768	+	0.508822i	0.680929	+	0.732349i	$0.261576\pi$
$492$	−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	0.959614	+	0.281319i	$0.0907717\pi$
$499$	16.1603	+	27.9905i	0.723436	+	1.25303i	−0.236178	+	0.971710i	$0.575895\pi$
$500$	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	−0.965039	−	0.262105i	$-0.915583\pi$
$503$	−15.9126	−	27.5615i	−0.709509	−	1.22891i	0.255531	−	0.966801i	$-0.417750\pi$
$504$		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	−0.723600	−	0.690220i	$-0.757514\pi$
$521$	5.38562	−	9.32817i	0.235948	−	0.408675i	0.959548	+	0.281546i	$0.0908471\pi$
$522$	−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	−0.968579	−	0.248708i	$-0.919994\pi$
$541$	−16.2741	−	28.1875i	−0.699676	−	1.21188i	0.268902	−	0.963168i	$-0.413339\pi$
$542$	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	0.987408	+	0.158193i	$0.0505668\pi$
$557$	14.8851	+	25.7818i	0.630703	+	1.09241i	−0.356705	+	0.934217i	$0.616100\pi$
$558$	−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	−0.878390	−	0.477944i	$-0.841382\pi$
$571$	−0.604159	+	1.04643i	−0.0252832	+	0.0437919i	0.853107	+	0.521736i	$0.174715\pi$
$572$	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	−0.977065	−	0.212943i	$-0.931695\pi$
$577$	−7.30518	+	12.6529i	−0.304119	+	0.526749i	0.672946	+	0.739692i	$0.265029\pi$
$578$	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	−0.554078	−	0.832465i	$-0.686929\pi$
$587$	10.7548	−	18.6278i	0.443897	−	0.768852i	0.997975	+	0.0636132i	$0.0202624\pi$
$588$		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	0.837553	−	0.546356i	$-0.183986\pi$
$593$	−1.32429	−	2.29373i	−0.0543820	−	0.0941923i	−0.891935	+	0.452164i	$0.850652\pi$
$594$	−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	−0.0816889	−	0.996658i	$-0.526031\pi$
$599$	20.1250	−	34.8576i	0.822287	−	1.42424i	0.903975	−	0.427584i	$-0.140635\pi$
$600$	1.88112			0.0767962
$601$	19.1725	−	33.2077i	0.782061	−	1.35457i	−0.148679	−	0.988886i	$-0.547502\pi$
$601$	19.1725	−	33.2077i	0.782061	−	1.35457i	0.930739	−	0.365683i	$-0.119165\pi$
$602$		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	−0.00479063	−	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
$611$	4.06853	+	2.44543i	0.164595	+	0.0989314i
$612$	1.28180	−	2.22014i	0.0518136	−	0.0897438i
$613$	−7.63261	−	13.2201i	−0.308278	−	0.533953i	0.669708	−	0.742625i	$-0.266419\pi$
$613$	−7.63261	−	13.2201i	−0.308278	−	0.533953i	−0.977986	+	0.208672i	$0.933086\pi$
$614$	−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	0.690306	−	0.723517i	$-0.257476\pi$
$617$	−6.99061	−	12.1081i	−0.281431	−	0.487453i	−0.971737	+	0.236064i	$0.924142\pi$
$618$	−0.331934	+	0.574926i	−0.0133523	+	0.0231269i
$619$	−4.25792	+	7.37494i	−0.171140	+	0.296424i	−0.938819	−	0.344411i	$-0.888079\pi$
$619$	−4.25792	+	7.37494i	−0.171140	+	0.296424i	0.767678	+	0.640835i	$0.221412\pi$
$620$	−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	−0.955563	−	0.294786i	$-0.904752\pi$
$631$	−18.4146	−	31.8950i	−0.733074	−	1.26972i	0.222490	−	0.974935i	$-0.428582\pi$
$632$	−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	0.920217	+	0.391408i	$0.128012\pi$
$643$	20.2626	+	35.0958i	0.799078	+	1.38404i	−0.121139	+	0.992636i	$0.538655\pi$
$644$		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
$649$	−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	0.876808	−	0.480841i	$-0.159669\pi$
$659$	0.564336	+	0.977458i	0.0219834	+	0.0380764i	−0.854824	+	0.518917i	$0.826335\pi$
$660$	−22.2780			−0.867170
$661$	−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	$-0.356840\pi$
$662$	0.310913	−	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	−0.789462	−	0.613799i	$-0.789640\pi$
$673$	3.54980	−	6.14843i	0.136835	−	0.237005i	0.926297	+	0.376795i	$0.122974\pi$
$674$	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	−0.699752	−	0.714386i	$-0.746706\pi$
$677$	−25.2010	−	43.6494i	−0.968552	−	1.67758i	−0.268800	−	0.963196i	$-0.586627\pi$
$678$	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	0.170364	+	0.985381i	$0.445506\pi$
$709$	−20.4544	+	35.4281i	−0.768183	+	1.33053i	−0.938547	+	0.345151i	$0.887828\pi$
$710$	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	−0.876992	−	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
$723$	−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	0.997889	+	0.0649392i	$0.0206853\pi$
$733$	15.0310	+	26.0345i	0.555184	+	0.961606i	−0.442706	+	0.896667i	$0.645981\pi$
$734$	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	$-0.469364\pi$
$740$	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	−0.775995	−	0.630739i	$-0.782752\pi$
$743$	4.31326	−	7.47078i	0.158238	−	0.274076i	0.934233	+	0.356662i	$0.116085\pi$
$744$	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	−0.356347	−	0.934354i	$-0.615978\pi$
$757$	17.3611	−	30.0703i	0.631000	−	1.09292i	0.987348	−	0.158571i	$-0.0506887\pi$
$758$	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	−0.250880	+	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
$765$	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	−0.818344	−	0.574729i	$-0.805108\pi$
$769$	2.45578	−	4.25354i	0.0885578	−	0.153387i	0.906902	+	0.421342i	$0.138441\pi$
$770$		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
$775$	−1.99571	−	3.45667i	−0.0716881	−	0.124167i
$776$	−1.24913	−	2.16356i	−0.0448413	−	0.0776674i
$777$		0			0
$778$	−2.19589	+	3.80339i	−0.0787264	+	0.136358i
$779$	−9.13476	−	15.8219i	−0.327287	−	0.566877i
$780$	0.358225	−	20.3528i	0.0128265	−	0.728745i
$781$	−24.2998	+	42.0885i	−0.869515	+	1.50604i
$782$	−1.67460			−0.0598837
$783$	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
$787$	3.18774			0.113631			0.0568154	−	0.998385i	$-0.481905\pi$
$787$	3.18774			0.113631			0.0568154	+	0.998385i	$0.481905\pi$
$788$	−11.2880	+	19.5514i	−0.402119	+	0.696490i
$789$	−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
$793$	0.599323	−	34.0509i	0.0212826	−	1.20918i
$794$	2.12927	−	3.68800i	0.0755650	−	0.130882i
$795$	−13.5857	−	23.5312i	−0.481837	−	0.834566i
$796$	6.74229			0.238974
$797$	27.3255	+	47.3291i	0.967918	+	1.67648i	0.701562	+	0.712608i	$0.252486\pi$
$797$	27.3255	+	47.3291i	0.967918	+	1.67648i	0.266355	+	0.963875i	$0.414180\pi$
$798$		0			0
$799$	−0.516813	−	0.895146i	−0.0182835	−	0.0316680i
$800$	2.39442	−	4.14725i	0.0846554	−	0.146628i
$801$	−6.48875	+	11.2388i	−0.229269	+	0.397105i
$802$	−1.77921			−0.0628260
$803$	−3.03286			−0.107027
$804$	−1.49042	+	2.58148i	−0.0525630	+	0.0910418i
$805$		0			0
$806$	0.0434569	−	2.46902i	0.00153070	−	0.0869677i
$807$	−17.1832	−	29.7622i	−0.604877	−	1.04768i
$808$	−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
$814$	3.57461	+	6.19141i	0.125290	+	0.217009i
$815$	−16.7748			−0.587597
$816$	1.60353	+	2.77740i	0.0561348	+	0.0972284i
$817$	−16.8603			−0.589867
$818$	1.57452			0.0550519
$819$		0			0
$820$	−12.0395			−0.420438
$821$	45.3524			1.58281			0.791405	−	0.611292i	$-0.209350\pi$
$821$	45.3524			1.58281			0.791405	+	0.611292i	$0.209350\pi$
$822$	1.53795	+	2.66380i	0.0536421	+	0.0929108i
$823$	−2.75742			−0.0961177			−0.0480588	−	0.998845i	$-0.515303\pi$
$823$	−2.75742			−0.0961177			−0.0480588	+	0.998845i	$0.515303\pi$
$824$	1.14074	+	1.97581i	0.0397394	+	0.0688307i
$825$	−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
$831$	8.75858	+	15.1703i	0.303832	+	0.526252i
$832$	−19.9503	+	11.0548i	−0.691653	+	0.383258i
$833$		0			0
$834$	0.849774	−	1.47185i	0.0294253	−	0.0509660i
$835$	−24.4617			−0.846531
$836$	−57.0264			−1.97230
$837$	6.85177	−	11.8676i	0.236832	−	0.410204i
$838$	4.04096	−	6.99914i	0.139593	−	0.241781i
$839$	12.6236	+	21.8648i	0.435817	+	0.754857i	0.997362	−	0.0725895i	$-0.0231263\pi$
$839$	12.6236	+	21.8648i	0.435817	+	0.754857i	−0.561545	+	0.827446i	$0.689793\pi$
$840$		0			0
$841$	11.7347	+	20.3251i	0.404644	+	0.700865i
$842$	−10.7406			−0.370144
$843$	−3.02485	−	5.23920i	−0.104182	−	0.180448i
$844$	18.3220	−	31.7346i	0.630669	−	1.09235i
$845$	−33.2822	−	1.17195i	−1.14494	−	0.0403164i
$846$	−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
$850$	−0.164466	+	0.284864i	−0.00564115	+	0.00977076i
$851$	−53.7544			−1.84268
$852$	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
$856$	−12.1397			−0.414927
$857$	−0.671345	+	1.16280i	−0.0229327	+	0.0397206i	−0.877264	−	0.480008i	$-0.840634\pi$
$857$	−0.671345	+	1.16280i	−0.0229327	+	0.0397206i	0.854331	+	0.519729i	$0.173967\pi$
$858$	0.0767330	−	4.35962i	0.00261962	−	0.148835i
$859$	2.38386	+	4.12897i	0.0813363	+	0.140879i	0.903824	−	0.427904i	$-0.140748\pi$
$859$	2.38386	+	4.12897i	0.0813363	+	0.140879i	−0.822488	+	0.568783i	$0.807415\pi$
$860$	−5.55542	+	9.62228i	−0.189438	+	0.328117i
$861$		0			0
$862$	−0.524972	−	0.909278i	−0.0178806	−	0.0309701i
$863$	13.3052	+	23.0453i	0.452915	+	0.784472i	0.998566	−	0.0535407i	$-0.0170507\pi$
$863$	13.3052	+	23.0453i	0.452915	+	0.784472i	−0.545650	+	0.838013i	$0.683717\pi$
$864$	16.4412			0.559343
$865$	−28.5165			−0.969591
$866$	5.46875	+	9.47216i	0.185836	+	0.321877i
$867$	9.36331	+	16.2177i	0.317995	+	0.550783i
$868$		0			0
$869$	−12.2185	+	21.1630i	−0.414484	+	0.717907i
$870$	0.923171	+	1.59898i	0.0312984	+	0.0542105i
$871$	4.17981	+	2.51231i	0.141627	+	0.0851264i
$872$	−4.25410	+	7.36831i	−0.144062	+	0.249523i
$873$	−4.01708			−0.135958
$874$	−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	$0.209993\pi$
$878$	−6.85389			−0.231307
$879$	−10.0112	+	17.3399i	−0.337670	+	0.584861i
$880$	−18.0633	+	31.2866i	−0.608915	+	1.05467i
$881$	−27.3349	+	47.3454i	−0.920935	+	1.59511i	−0.122964	+	0.992411i	$0.539240\pi$
$881$	−27.3349	+	47.3454i	−0.920935	+	1.59511i	−0.797971	+	0.602695i	$0.794093\pi$
$882$		0			0
$883$	−8.45085			−0.284394			−0.142197	−	0.989838i	$-0.545417\pi$
$883$	−8.45085			−0.284394			−0.142197	+	0.989838i	$0.545417\pi$
$884$	4.77400	−	2.64536i	0.160567	−	0.0889732i
$885$	−13.1277	+	22.7379i	−0.441284	+	0.764327i
$886$	−3.68088	−	6.37547i	−0.123662	−	0.214188i
$887$	10.3557			0.347710			0.173855	−	0.984771i	$-0.444378\pi$
$887$	10.3557			0.347710			0.173855	+	0.984771i	$0.444378\pi$
$888$	−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
$892$	11.5361	−	19.9811i	0.386256	−	0.669016i
$893$	−9.86792			−0.330217
$894$	−5.65898			−0.189265
$895$	16.1947	−	28.0501i	0.541330	−	0.937611i
$896$		0			0
$897$	28.0995	+	16.8895i	0.938215	+	0.563923i
$898$	−1.98461	−	3.43745i	−0.0662274	−	0.114709i
$899$	−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
$905$	19.1053	+	33.0914i	0.635082	+	1.09999i
$906$	−0.492606			−0.0163657
$907$	−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	$0.932597\pi$
$908$	29.6624			0.984380
$909$	−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	$0.645417\pi$
$912$	30.6175			1.01385
$913$	−2.11687	−	3.66653i	−0.0700582	−	0.121344i
$914$	0.174804			0.00578202
$915$	13.8287	+	23.9520i	0.457162	+	0.791828i
$916$	−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
$922$	−1.67518	−	2.90149i	−0.0551690	−	0.0955555i
$923$	−38.0605	−	22.8766i	−1.25278	−	0.752993i
$924$		0			0
$925$	−5.27933	+	9.14406i	−0.173583	+	0.300655i
$926$	0.0829855			0.00272707
$927$	3.66849			0.120489
$928$	3.60365	−	6.24170i	0.118296	−	0.204894i
$929$	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
$933$	18.7712			0.614541
$934$	−3.28149	−	5.68371i	−0.107374	−	0.185977i
$935$	3.96817	−	6.87306i	0.129773	−	0.224773i
$936$	0.113175	−	6.43011i	0.00369925	−	0.210175i
$937$	−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
$941$	−9.89466	+	17.1381i	−0.322557	+	0.558685i	−0.981015	−	0.193933i	$-0.937876\pi$
$941$	−9.89466	+	17.1381i	−0.322557	+	0.558685i	0.658458	+	0.752617i	$0.271209\pi$
$942$	−0.504429			−0.0164352
$943$	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
$947$	9.94796			0.323265			0.161633	−	0.986851i	$-0.448324\pi$
$947$	9.94796			0.323265			0.161633	+	0.986851i	$0.448324\pi$
$948$	6.82403	−	11.8196i	0.221634	−	0.383882i
$949$	0.0487677	−	2.77076i	0.00158307	−	0.0899427i
$950$	1.57014	+	2.71957i	0.0509422	+	0.0882345i
$951$	−5.79790	+	10.0423i	−0.188010	+	0.325643i
$952$		0			0
$953$	−0.0105567	−	0.0182847i	−0.000341965	−	0.000592300i	0.865854	−	0.500296i	$-0.166776\pi$
$953$	−0.0105567	−	0.0182847i	−0.000341965	−	0.000592300i	−0.866196	+	0.499704i	$0.833442\pi$
$954$	−2.10682	−	3.64912i	−0.0682108	−	0.118144i
$955$	−36.1990			−1.17137
$956$	−31.9152			−1.03221
$957$	−5.30352	−	9.18596i	−0.171438	−	0.296940i
$958$	−1.09107	−	1.88979i	−0.0352508	−	0.0610562i
$959$		0			0
$960$	9.26150	−	16.0414i	0.298914	−	0.517733i
$961$	12.2376	+	21.1962i	0.394761	+	0.683747i
$962$	−5.71383	+	3.16614i	−0.184221	+	0.102081i
$963$	−9.76001	+	16.9048i	−0.314512	+	0.544751i
$964$	−31.6224			−1.01849
$965$	−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
$969$	−6.72608			−0.216073
$970$	0.814635	−	1.41099i	0.0261563	−	0.0453041i
$971$	−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
$975$	5.63275	−	3.12121i	0.180392	−	0.0999587i
$976$	16.8782	−	29.2339i	0.540258	−	0.935755i
$977$	−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	$0.844342\pi$
$978$	2.00682			0.0641710
$979$	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
$983$	−15.0545	+	26.0752i	−0.480165	+	0.831671i	−0.999741	−	0.0227535i	$-0.992757\pi$
$983$	−15.0545	+	26.0752i	−0.480165	+	0.831671i	0.519576	+	0.854424i	$0.326090\pi$
$984$	2.93434			0.0935433
$985$	−29.9953			−0.955730
$986$	−0.247525	+	0.428727i	−0.00788281	+	0.0136534i
$987$		0			0
$988$	0.916973	−	52.0983i	0.0291728	−	1.65747i
$989$	−8.94742	−	15.4974i	−0.284511	−	0.492788i
$990$	−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
$996$	1.18227	+	2.04776i	0.0374618	+	0.0648858i
$997$	−50.8009			−1.60888			−0.804441	−	0.594033i	$-0.797535\pi$
$997$	−50.8009			−1.60888			−0.804441	+	0.594033i	$0.797535\pi$
$998$	−4.33300	−	7.50497i	−0.137159	−	0.237566i
$999$	−36.2504			−1.14691

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.3	✓	12	7.5	odd	6
91.2.g.b.81.3	yes	12	91.55	odd	6
91.2.h.b.16.4	yes	12	91.68	odd	6
91.2.h.b.74.4	yes	12	7.6	odd	2
637.2.f.j.295.3		12	7.4	even	3
637.2.f.j.393.3		12	91.81	even	3
637.2.f.k.295.3		12	7.3	odd	6
637.2.f.k.393.3		12	91.3	odd	6
637.2.g.l.263.3		12	13.3	even	3
637.2.g.l.373.3		12	7.2	even	3
637.2.h.l.165.4		12	1.1	even	1	trivial
637.2.h.l.471.4		12	91.16	even	3	inner
819.2.n.d.100.4		12	21.5	even	6
819.2.n.d.172.4		12	273.146	even	6
819.2.s.d.289.3		12	273.68	even	6
819.2.s.d.802.3		12	21.20	even	2
1183.2.e.g.170.4		12	91.82	odd	6
1183.2.e.g.508.4		12	91.69	odd	6
1183.2.e.h.170.3		12	91.61	odd	6
1183.2.e.h.508.3		12	91.48	odd	6
8281.2.a.bz.1.4		6	91.87	odd	6
8281.2.a.ca.1.4		6	91.74	even	3
8281.2.a.ce.1.3		6	91.17	odd	6
8281.2.a.cf.1.3		6	91.4	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 $\F_{q}$

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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