LMFDB - Embedded newform 630.2.bf.e.209.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [630,2,Mod(209,630)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(630, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 3, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("630.209"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.bf (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,-16,0,-16,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			209.15
Character	$\chi$	$=$	630.209
Dual form			630.2.bf.e.419.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(1.65659 + 0.505669i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.150780 - 2.23098i) q^{5} +(-1.26622 + 1.18182i) q^{6} +(0.00309790 - 2.64575i) q^{7} +1.00000 q^{8} +(2.48860 + 1.67538i) q^{9} +(1.85669 + 1.24607i) q^{10} +(-2.86892 - 1.65637i) q^{11} +(-0.390374 - 1.68749i) q^{12} +(-2.91974 - 5.05714i) q^{13} +(2.28974 + 1.32556i) q^{14} +(1.37792 - 3.61958i) q^{15} +(-0.500000 + 0.866025i) q^{16} +2.78294i q^{17} +(-2.69522 + 1.31750i) q^{18} +0.0210849i q^{19} +(-2.00747 + 0.984910i) q^{20} +(1.34301 - 4.38136i) q^{21} +(2.86892 - 1.65637i) q^{22} +(-2.80015 - 4.85001i) q^{23} +(1.65659 + 0.505669i) q^{24} +(-4.95453 - 0.672775i) q^{25} +5.83948 q^{26} +(3.27540 + 4.03382i) q^{27} +(-2.29284 + 1.32019i) q^{28} +(1.43484 + 0.828404i) q^{29} +(2.44569 + 3.00310i) q^{30} +(5.24289 - 3.02698i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-3.91506 - 4.19466i) q^{33} +(-2.41010 - 1.39147i) q^{34} +(-5.90214 - 0.405838i) q^{35} +(0.206620 - 2.99288i) q^{36} -4.54272i q^{37} +(-0.0182600 - 0.0105424i) q^{38} +(-2.27958 - 9.85404i) q^{39} +(0.150780 - 2.23098i) q^{40} +(5.58921 + 9.68080i) q^{41} +(3.12287 + 3.35376i) q^{42} +(2.13226 + 1.23106i) q^{43} +3.31275i q^{44} +(4.11296 - 5.29939i) q^{45} +5.60031 q^{46} +(3.89705 + 2.24996i) q^{47} +(-1.26622 + 1.18182i) q^{48} +(-6.99998 - 0.0163925i) q^{49} +(3.05991 - 3.95436i) q^{50} +(-1.40725 + 4.61020i) q^{51} +(-2.91974 + 5.05714i) q^{52} +0.154097 q^{53} +(-5.13110 + 0.819671i) q^{54} +(-4.12791 + 6.15076i) q^{55} +(0.00309790 - 2.64575i) q^{56} +(-0.0106620 + 0.0349290i) q^{57} +(-1.43484 + 0.828404i) q^{58} +(3.32508 + 5.75921i) q^{59} +(-3.82361 + 0.616476i) q^{60} +(7.58810 + 4.38099i) q^{61} +6.05396i q^{62} +(4.44034 - 6.57901i) q^{63} +1.00000 q^{64} +(-11.7226 + 5.75136i) q^{65} +(5.59022 - 1.29321i) q^{66} +(11.9504 - 6.89958i) q^{67} +(2.41010 - 1.39147i) q^{68} +(-2.18621 - 9.45044i) q^{69} +(3.30254 - 4.90849i) q^{70} +14.4531i q^{71} +(2.48860 + 1.67538i) q^{72} +0.567999 q^{73} +(3.93411 + 2.27136i) q^{74} +(-7.86744 - 3.61987i) q^{75} +(0.0182600 - 0.0105424i) q^{76} +(-4.39124 + 7.58532i) q^{77} +(9.67364 + 2.95285i) q^{78} +(2.02885 - 3.51406i) q^{79} +(1.85669 + 1.24607i) q^{80} +(3.38623 + 8.33867i) q^{81} -11.1784 q^{82} +(11.5525 + 6.66983i) q^{83} +(-4.46587 + 1.02760i) q^{84} +(6.20868 + 0.419612i) q^{85} +(-2.13226 + 1.23106i) q^{86} +(1.95804 + 2.09788i) q^{87} +(-2.86892 - 1.65637i) q^{88} -6.33024 q^{89} +(2.53293 + 6.21162i) q^{90} +(-13.3890 + 7.70923i) q^{91} +(-2.80015 + 4.85001i) q^{92} +(10.2160 - 2.36331i) q^{93} +(-3.89705 + 2.24996i) q^{94} +(0.0470399 + 0.00317918i) q^{95} +(-0.390374 - 1.68749i) q^{96} +(4.93235 - 8.54307i) q^{97} +(3.51419 - 6.05396i) q^{98} +(-4.36455 - 8.92857i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} - 6 q^{9} - 24 q^{11} - 16 q^{15} - 16 q^{16} + 6 q^{18} + 2 q^{21} + 24 q^{22} - 24 q^{23} - 58 q^{25} - 36 q^{29} - 10 q^{30} - 16 q^{32} - 48 q^{35} - 66 q^{39}+ \cdots + 58 q^{99}+O(q^{100}) $ 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 - 6 * q^9 - 24 * q^11 - 16 * q^15 - 16 * q^16 + 6 * q^18 + 2 * q^21 + 24 * q^22 - 24 * q^23 - 58 * q^25 - 36 * q^29 - 10 * q^30 - 16 * q^32 - 48 * q^35 - 66 * q^39 + 2 * q^42 - 54 * q^43 + 48 * q^46 + 32 * q^49 + 50 * q^50 - 26 * q^51 - 24 * q^53 + 110 * q^57 + 36 * q^58 + 26 * q^60 + 20 * q^63 + 32 * q^64 - 90 * q^65 - 66 * q^67 + 36 * q^70 - 6 * q^72 + 12 * q^74 + 18 * q^77 + 60 * q^78 + 34 * q^79 + 2 * q^81 - 4 * q^84 + 4 * q^85 + 54 * q^86 - 24 * q^88 + 16 * q^91 - 24 * q^92 + 28 * q^93 + 12 * q^95 - 64 * q^98 + 58 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	1.65659	+	0.505669i	0.956434	+	0.291948i
$3$	1.65659	+	0.505669i	0.956434	+	0.291948i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.150780	−	2.23098i	0.0674310	−	0.997724i
$5$	0.150780	−	2.23098i	0.0674310	−	0.997724i
$6$	−1.26622	+	1.18182i	−0.516932	+	0.482475i
$7$	0.00309790	−	2.64575i	0.00117090	−	0.999999i
$7$	0.00309790	−	2.64575i	0.00117090	−	0.999999i
$8$	1.00000			0.353553
$9$	2.48860	+	1.67538i	0.829532	+	0.558459i
$10$	1.85669	+	1.24607i	0.587138	+	0.394042i
$11$	−2.86892	−	1.65637i	−0.865013	−	0.499416i	0.000674708	−	1.00000i	$-0.499785\pi$
$11$	−2.86892	−	1.65637i	−0.865013	−	0.499416i	−0.865688	+	0.500584i	$0.833119\pi$
$12$	−0.390374	−	1.68749i	−0.112691	−	0.487135i
$13$	−2.91974	−	5.05714i	−0.809790	−	1.40260i	−0.913009	−	0.407939i	$-0.866248\pi$
$13$	−2.91974	−	5.05714i	−0.809790	−	1.40260i	0.103219	−	0.994659i	$-0.467086\pi$
$14$	2.28974	+	1.32556i	0.611958	+	0.354270i
$15$	1.37792	−	3.61958i	0.355777	−	0.934571i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$			2.78294i			0.674962i	0.941332	+	0.337481i	$0.109575\pi$
$17$			2.78294i			0.674962i	−0.941332	+	0.337481i	$0.890425\pi$
$18$	−2.69522	+	1.31750i	−0.635269	+	0.310538i
$19$			0.0210849i			0.00483720i	0.999997	+	0.00241860i	$0.000769865\pi$
$19$			0.0210849i			0.00483720i	−0.999997	+	0.00241860i	$0.999230\pi$
$20$	−2.00747	+	0.984910i	−0.448885	+	0.220233i
$21$	1.34301	−	4.38136i	0.293068	−	0.956092i
$22$	2.86892	−	1.65637i	0.611657	−	0.353140i
$23$	−2.80015	−	4.85001i	−0.583873	−	1.01130i	−0.995015	−	0.0997259i	$-0.968203\pi$
$23$	−2.80015	−	4.85001i	−0.583873	−	1.01130i	0.411142	−	0.911571i	$-0.365130\pi$
$24$	1.65659	+	0.505669i	0.338151	+	0.103219i
$25$	−4.95453	−	0.672775i	−0.990906	−	0.134555i
$26$	5.83948			1.14522
$27$	3.27540	+	4.03382i	0.630352	+	0.776310i
$28$	−2.29284	+	1.32019i	−0.433305	+	0.249493i
$29$	1.43484	+	0.828404i	0.266443	+	0.153831i	0.627270	−	0.778802i	$-0.284172\pi$
$29$	1.43484	+	0.828404i	0.266443	+	0.153831i	−0.360827	+	0.932633i	$0.617506\pi$
$30$	2.44569	+	3.00310i	0.446519	+	0.548289i
$31$	5.24289	−	3.02698i	0.941650	−	0.543662i	0.0511731	−	0.998690i	$-0.483704\pi$
$31$	5.24289	−	3.02698i	0.941650	−	0.543662i	0.890477	+	0.455028i	$0.150371\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−3.91506	−	4.19466i	−0.681524	−	0.730197i
$34$	−2.41010	−	1.39147i	−0.413328	−	0.238635i
$35$	−5.90214	−	0.405838i	−0.997644	−	0.0685992i
$36$	0.206620	−	2.99288i	0.0344367	−	0.498813i
$37$		−	4.54272i		−	0.746819i	−0.927667	−	0.373410i	$-0.878189\pi$
$37$		−	4.54272i		−	0.746819i	0.927667	−	0.373410i	$-0.121811\pi$
$38$	−0.0182600	−	0.0105424i	−0.00296217	−	0.00171021i
$39$	−2.27958	−	9.85404i	−0.365025	−	1.57791i
$40$	0.150780	−	2.23098i	0.0238404	−	0.352749i
$41$	5.58921	+	9.68080i	0.872888	+	1.51189i	0.858995	+	0.511984i	$0.171089\pi$
$41$	5.58921	+	9.68080i	0.872888	+	1.51189i	0.0138932	+	0.999903i	$0.495578\pi$
$42$	3.12287	+	3.35376i	0.481869	+	0.517496i
$43$	2.13226	+	1.23106i	0.325166	+	0.187735i	0.653693	−	0.756760i	$-0.273219\pi$
$43$	2.13226	+	1.23106i	0.325166	+	0.187735i	−0.328527	+	0.944495i	$0.606552\pi$
$44$			3.31275i			0.499416i
$45$	4.11296	−	5.29939i	0.613124	−	0.789987i
$46$	5.60031			0.825721
$47$	3.89705	+	2.24996i	0.568443	+	0.328191i	0.756527	−	0.653962i	$-0.226894\pi$
$47$	3.89705	+	2.24996i	0.568443	+	0.328191i	−0.188084	+	0.982153i	$0.560228\pi$
$48$	−1.26622	+	1.18182i	−0.182763	+	0.170580i
$49$	−6.99998	−	0.0163925i	−0.999997	−	0.00234179i
$50$	3.05991	−	3.95436i	0.432736	−	0.559231i
$51$	−1.40725	+	4.61020i	−0.197054	+	0.645557i
$52$	−2.91974	+	5.05714i	−0.404895	+	0.701299i
$53$	0.154097			0.0211669			0.0105835	−	0.999944i	$-0.496631\pi$
$53$	0.154097			0.0211669			0.0105835	+	0.999944i	$0.496631\pi$
$54$	−5.13110	+	0.819671i	−0.698254	+	0.111543i
$55$	−4.12791	+	6.15076i	−0.556608	+	0.829368i
$56$	0.00309790	−	2.64575i	0.000413974	−	0.353553i
$57$	−0.0106620	+	0.0349290i	−0.00141221	+	0.00462646i
$58$	−1.43484	+	0.828404i	−0.188404	+	0.108775i
$59$	3.32508	+	5.75921i	0.432889	+	0.749786i	0.997121	−	0.0758307i	$-0.0241608\pi$
$59$	3.32508	+	5.75921i	0.432889	+	0.749786i	−0.564232	+	0.825617i	$0.690828\pi$
$60$	−3.82361	+	0.616476i	−0.493625	+	0.0795867i
$61$	7.58810	+	4.38099i	0.971556	+	0.560928i	0.899710	−	0.436487i	$-0.143778\pi$
$61$	7.58810	+	4.38099i	0.971556	+	0.560928i	0.0718459	+	0.997416i	$0.477111\pi$
$62$			6.05396i			0.768854i
$63$	4.44034	−	6.57901i	0.559430	−	0.828878i
$64$	1.00000			0.125000
$65$	−11.7226	+	5.75136i	−1.45401	+	0.713368i
$66$	5.59022	−	1.29321i	0.688108	−	0.159183i
$67$	11.9504	−	6.89958i	1.45998	−	0.842918i	0.460968	−	0.887417i	$-0.347502\pi$
$67$	11.9504	−	6.89958i	1.45998	−	0.842918i	0.999009	+	0.0444983i	$0.0141689\pi$
$68$	2.41010	−	1.39147i	0.292267	−	0.168741i
$69$	−2.18621	−	9.45044i	−0.263189	−	1.13770i
$70$	3.30254	−	4.90849i	0.394729	−	0.586676i
$71$			14.4531i			1.71527i	0.514257	+	0.857636i	$0.328068\pi$
$71$			14.4531i			1.71527i	−0.514257	+	0.857636i	$0.671932\pi$
$72$	2.48860	+	1.67538i	0.293284	+	0.197445i
$73$	0.567999			0.0664793			0.0332396	−	0.999447i	$-0.489418\pi$
$73$	0.567999			0.0664793			0.0332396	+	0.999447i	$0.489418\pi$
$74$	3.93411	+	2.27136i	0.457332	+	0.264040i
$75$	−7.86744	−	3.61987i	−0.908453	−	0.417986i
$76$	0.0182600	−	0.0105424i	0.00209457	−	0.00120930i
$77$	−4.39124	+	7.58532i	−0.500428	+	0.864428i
$78$	9.67364	+	2.95285i	1.09532	+	0.334344i
$79$	2.02885	−	3.51406i	0.228263	−	0.395363i	−0.729030	−	0.684481i	$-0.760029\pi$
$79$	2.02885	−	3.51406i	0.228263	−	0.395363i	0.957293	+	0.289118i	$0.0933621\pi$
$80$	1.85669	+	1.24607i	0.207585	+	0.139315i
$81$	3.38623	+	8.33867i	0.376248	+	0.926519i
$82$	−11.1784			−1.23445
$83$	11.5525	+	6.66983i	1.26805	+	0.732109i	0.974619	−	0.223872i	$-0.0718696\pi$
$83$	11.5525	+	6.66983i	1.26805	+	0.732109i	0.293431	+	0.955980i	$0.405203\pi$
$84$	−4.46587	+	1.02760i	−0.487267	+	0.112121i
$85$	6.20868	+	0.419612i	0.673426	+	0.0455134i
$86$	−2.13226	+	1.23106i	−0.229927	+	0.132749i
$87$	1.95804	+	2.09788i	0.209924	+	0.224917i
$88$	−2.86892	−	1.65637i	−0.305828	−	0.176570i
$89$	−6.33024			−0.671004			−0.335502	−	0.942040i	$-0.608906\pi$
$89$	−6.33024			−0.671004			−0.335502	+	0.942040i	$0.608906\pi$
$90$	2.53293	+	6.21162i	0.266994	+	0.654763i
$91$	−13.3890	+	7.70923i	−1.40354	+	0.808147i
$92$	−2.80015	+	4.85001i	−0.291936	+	0.505649i
$93$	10.2160	−	2.36331i	1.05935	−	0.245064i
$94$	−3.89705	+	2.24996i	−0.401950	+	0.232066i
$95$	0.0470399	+	0.00317918i	0.00482619	+	0.000326177i
$96$	−0.390374	−	1.68749i	−0.0398423	−	0.172228i
$97$	4.93235	−	8.54307i	0.500804	−	0.867418i	−0.499196	−	0.866489i	$-0.666371\pi$
$97$	4.93235	−	8.54307i	0.500804	−	0.867418i	1.00000		0.000928464i	$-0.000295539\pi$
$98$	3.51419	−	6.05396i	0.354986	−	0.611543i
$99$	−4.36455	−	8.92857i	−0.438653	−	0.897356i
$100$	1.89463	+	4.62714i	0.189463	+	0.462714i
$101$	4.81017	−	8.33145i	0.478630	−	0.829011i	−0.521070	−	0.853514i	$-0.674467\pi$
$101$	4.81017	−	8.33145i	0.478630	−	0.829011i	0.999700	+	0.0245031i	$0.00780036\pi$
$102$	−3.28892	−	3.52381i	−0.325652	−	0.348909i
$103$	−9.20075	−	15.9362i	−0.906577	−	1.57024i	−0.818787	−	0.574098i	$-0.805353\pi$
$103$	−9.20075	−	15.9362i	−0.906577	−	1.57024i	−0.0877898	−	0.996139i	$-0.527980\pi$
$104$	−2.91974	−	5.05714i	−0.286304	−	0.495893i
$105$	−9.57223	−	3.65684i	−0.934154	−	0.356871i
$106$	−0.0770487	+	0.133452i	−0.00748363	+	0.0129620i
$107$	8.66665			0.837837			0.418918	−	0.908024i	$-0.362409\pi$
$107$	8.66665			0.837837			0.418918	+	0.908024i	$0.362409\pi$
$108$	1.85569	−	4.85349i	0.178564	−	0.467028i
$109$	−4.72231			−0.452316			−0.226158	−	0.974091i	$-0.572616\pi$
$109$	−4.72231			−0.452316			−0.226158	+	0.974091i	$0.572616\pi$
$110$	−3.26276	−	6.65026i	−0.311092	−	0.634077i
$111$	2.29712	−	7.52544i	0.218033	−	0.714283i
$112$	2.28974	+	1.32556i	0.216360	+	0.125253i
$113$	−8.68986	−	15.0513i	−0.817473	−	1.41590i	−0.907538	−	0.419969i	$-0.862041\pi$
$113$	−8.68986	−	15.0513i	−0.817473	−	1.41590i	0.0900654	−	0.995936i	$-0.471292\pi$
$114$	−0.0249184	−	0.0266980i	−0.00233382	−	0.00250050i
$115$	−11.2425	+	5.51580i	−1.04837	+	0.514351i
$116$		−	1.65681i		−	0.153831i
$117$	1.20655	−	17.4768i	0.111546	−	1.61573i
$118$	−6.65017			−0.612198
$119$	7.36296	+	0.00862127i	0.674962	+	0.000790310i
$120$	1.37792	−	3.61958i	0.125786	−	0.330421i
$121$	−0.0128499	−	0.0222567i	−0.00116817	−	0.00202334i
$122$	−7.58810	+	4.38099i	−0.686994	+	0.396636i
$123$	4.36376	+	18.8634i	0.393467	+	1.70086i
$124$	−5.24289	−	3.02698i	−0.470825	−	0.271831i
$125$	−2.24799	+	10.9520i	−0.201067	+	0.979578i
$126$	3.47742	+	7.13495i	0.309794	+	0.635632i
$127$			17.1354i			1.52052i	0.649618	+	0.760260i	$0.274929\pi$
$127$			17.1354i			1.52052i	−0.649618	+	0.760260i	$0.725071\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	2.90977	+	3.11758i	0.256191	+	0.274488i
$130$	0.880478	−	13.0278i	0.0772230	−	1.14261i
$131$	−1.23726	−	2.14299i	−0.108100	−	0.187234i	0.806901	−	0.590687i	$-0.201143\pi$
$131$	−1.23726	−	2.14299i	−0.108100	−	0.187234i	−0.915000	+	0.403453i	$0.867810\pi$
$132$	−1.67516	+	5.48787i	−0.145804	+	0.477658i
$133$	0.0557852		6.53187e-5i	0.00483719		5.66385e-6i
$134$			13.7992i			1.19207i
$135$	9.49324	−	6.69913i	0.817048	−	0.576570i
$136$			2.78294i			0.238635i
$137$	−6.68489	+	11.5786i	−0.571129	+	0.989224i	0.425322	+	0.905042i	$0.360161\pi$
$137$	−6.68489	+	11.5786i	−0.571129	+	0.989224i	−0.996450	+	0.0841815i	$0.973172\pi$
$138$	9.27743	+	2.83191i	0.789747	+	0.241068i
$139$	8.17233	−	4.71830i	0.693168	−	0.400201i	−0.111630	−	0.993750i	$-0.535607\pi$
$139$	8.17233	−	4.71830i	0.693168	−	0.400201i	0.804798	+	0.593549i	$0.202274\pi$
$140$	2.59961	+	5.31433i	0.219707	+	0.449142i
$141$	5.31809	+	5.69789i	0.447864	+	0.479849i
$142$	−12.5168	−	7.22657i	−1.05039	−	0.606440i
$143$			19.3447i			1.61769i
$144$	−2.69522	+	1.31750i	−0.224601	+	0.109792i
$145$	2.06450	−	3.07619i	0.171447	−	0.255463i
$146$	−0.284000	+	0.491902i	−0.0235040	+	0.0407101i
$147$	−11.5878	−	3.56683i	−0.955748	−	0.294187i
$148$	−3.93411	+	2.27136i	−0.323382	+	0.186705i
$149$	1.96371	−	1.13375i	0.160873	−	0.0928803i	−0.417402	−	0.908722i	$-0.637059\pi$
$149$	1.96371	−	1.13375i	0.160873	−	0.0928803i	0.578275	+	0.815842i	$0.303726\pi$
$150$	7.06862	−	5.00347i	0.577150	−	0.408531i
$151$	−5.68081	+	9.83946i	−0.462298	+	0.800724i	−0.999075	−	0.0430005i	$-0.986308\pi$
$151$	−5.68081	+	9.83946i	−0.462298	+	0.800724i	0.536777	+	0.843724i	$0.319642\pi$
$152$			0.0210849i			0.00171021i
$153$	−4.66247	+	6.92562i	−0.376939	+	0.559903i
$154$	−4.37346	−	7.59559i	−0.352424	−	0.612070i
$155$	−5.96261	−	12.1532i	−0.478928	−	0.976167i
$156$	−7.39406	+	6.90119i	−0.591998	+	0.552537i
$157$	6.02781	+	10.4405i	0.481071	+	0.833240i	0.999764	−	0.0217208i	$-0.00691450\pi$
$157$	6.02781	+	10.4405i	0.481071	+	0.833240i	−0.518693	+	0.854961i	$0.673581\pi$
$158$	2.02885	+	3.51406i	0.161406	+	0.279564i
$159$	0.255277	+	0.0779223i	0.0202447	+	0.00617964i
$160$	−2.00747	+	0.984910i	−0.158705	+	0.0778640i
$161$	−12.8406	+	7.39348i	−1.01198	+	0.582688i
$162$	−8.91462	−	1.23678i	−0.700398	−	0.0971704i
$163$		−	11.3370i		−	0.887986i	−0.896030	−	0.443993i	$-0.853561\pi$
$163$		−	11.3370i		−	0.887986i	0.896030	−	0.443993i	$-0.146439\pi$
$164$	5.58921	−	9.68080i	0.436444	−	0.755944i
$165$	−9.94852	+	8.10194i	−0.774491	+	0.630735i
$166$	−11.5525	+	6.66983i	−0.896646	+	0.517679i
$167$	7.97315	−	4.60330i	0.616981	−	0.356214i	−0.158712	−	0.987325i	$-0.550734\pi$
$167$	7.97315	−	4.60330i	0.616981	−	0.356214i	0.775693	+	0.631111i	$0.217401\pi$
$168$	1.34301	−	4.38136i	0.103615	−	0.338029i
$169$	−10.5498	+	18.2727i	−0.811520	+	1.40559i
$170$	−3.46774	+	5.16707i	−0.265963	+	0.396296i
$171$	−0.0353251	+	0.0524717i	−0.00270138	+	0.00401261i
$172$		−	2.46212i		−	0.187735i
$173$	−16.9261	−	9.77231i	−1.28687	−	0.742975i	−0.308776	−	0.951135i	$-0.599919\pi$
$173$	−16.9261	−	9.77231i	−1.28687	−	0.742975i	−0.978095	+	0.208160i	$0.933253\pi$
$174$	−2.79584	+	0.646774i	−0.211952	+	0.0490318i
$175$	−1.79534	+	13.1064i	−0.135715	+	0.990748i
$176$	2.86892	−	1.65637i	0.216253	−	0.124854i
$177$	2.59605	+	11.2221i	0.195131	+	0.843502i
$178$	3.16512	−	5.48214i	0.237236	−	0.410904i
$179$		−	3.69210i		−	0.275960i	−0.990435	−	0.137980i	$-0.955939\pi$
$179$		−	3.69210i		−	0.275960i	0.990435	−	0.137980i	$-0.0440610\pi$
$180$	−6.64589	−	0.912232i	−0.495355	−	0.0679937i
$181$			9.83581i			0.731090i	0.930794	+	0.365545i	$0.119117\pi$
$181$			9.83581i			0.731090i	−0.930794	+	0.365545i	$0.880883\pi$
$182$	0.0180901	−	15.4498i	0.00134093	−	1.14522i
$183$	10.3551	+	11.0946i	0.765467	+	0.820135i
$184$	−2.80015	−	4.85001i	−0.206430	−	0.357547i
$185$	−10.1347	−	0.684953i	−0.745119	−	0.0503588i
$186$	−3.06131	+	10.0290i	−0.224466	+	0.735358i
$187$	4.60959	−	7.98405i	0.337087	−	0.583851i
$188$		−	4.49993i		−	0.328191i
$189$	10.6826	−	8.65340i	0.777047	−	0.629442i
$190$	−0.0262732	+	0.0391481i	−0.00190606	+	0.00284010i
$191$	−21.2231	−	12.2531i	−1.53565	−	0.886606i	−0.999086	−	0.0427436i	$-0.986390\pi$
$191$	−21.2231	−	12.2531i	−1.53565	−	0.886606i	−0.536560	−	0.843862i	$-0.680277\pi$
$192$	1.65659	+	0.505669i	0.119554	+	0.0364936i
$193$	−17.4708	+	10.0868i	−1.25757	+	0.726061i	−0.972602	−	0.232475i	$-0.925318\pi$
$193$	−17.4708	+	10.0868i	−1.25757	+	0.726061i	−0.284972	+	0.958536i	$0.591984\pi$
$194$	4.93235	+	8.54307i	0.354122	+	0.613357i
$195$	−22.3279	+	3.59990i	−1.59893	+	0.257794i
$196$	3.48579	+	6.07036i	0.248985	+	0.433597i
$197$	−12.2435			−0.872314			−0.436157	−	0.899871i	$-0.643661\pi$
$197$	−12.2435			−0.872314			−0.436157	+	0.899871i	$0.643661\pi$
$198$	9.91465	+	0.684481i	0.704603	+	0.0486439i
$199$		−	4.63305i		−	0.328428i	−0.986425	−	0.164214i	$-0.947491\pi$
$199$		−	4.63305i		−	0.328428i	0.986425	−	0.164214i	$-0.0525087\pi$
$200$	−4.95453	−	0.672775i	−0.350338	−	0.0475724i
$201$	23.2859	−	5.38683i	1.64246	−	0.379958i
$202$	4.81017	+	8.33145i	0.338442	+	0.586199i
$203$	2.19620	−	3.79366i	0.154143	−	0.266262i
$204$	4.69617	−	1.08639i	0.328798	−	0.0760623i
$205$	22.4404	−	11.0097i	1.56731	−	0.768954i
$206$	18.4015			1.28209
$207$	1.15714	−	16.7610i	0.0804266	−	1.16497i
$208$	5.83948			0.404895
$209$	0.0349244	−	0.0604908i	0.00241577	−	0.00418424i
$210$	7.95303	−	6.46137i	0.548811	−	0.445877i
$211$	0.00959279	+	0.0166152i	0.000660395	+	0.00114384i	0.866355	−	0.499428i	$-0.166456\pi$
$211$	0.00959279	+	0.0166152i	0.000660395	+	0.00114384i	−0.865695	+	0.500572i	$0.833123\pi$
$212$	−0.0770487	−	0.133452i	−0.00529173	−	0.00916554i
$213$	−7.30851	+	23.9430i	−0.500771	+	1.64054i
$214$	−4.33332	+	7.50554i	−0.296220	+	0.513068i
$215$	3.06797	−	4.57140i	0.209234	−	0.311767i
$216$	3.27540	+	4.03382i	0.222863	+	0.274467i
$217$	−7.99240	−	13.8807i	−0.542559	−	0.942286i
$218$	2.36116	−	4.08964i	0.159918	−	0.276986i
$219$	0.940943	+	0.287220i	0.0635831	+	0.0194085i
$220$	7.39067	+	0.499497i	0.498279	+	0.0336761i
$221$	14.0737	−	8.12546i	0.946700	−	0.546578i
$222$	5.36867	+	5.75208i	0.360321	+	0.386055i
$223$	−3.22276	+	5.58199i	−0.215812	+	0.373797i	−0.953523	−	0.301319i	$-0.902573\pi$
$223$	−3.22276	+	5.58199i	−0.215812	+	0.373797i	0.737711	+	0.675116i	$0.235907\pi$
$224$	−2.29284	+	1.32019i	−0.153196	+	0.0882090i
$225$	−11.2027	−	9.97497i	−0.746845	−	0.664998i
$226$	17.3797			1.15608
$227$	0.186994	+	0.107961i	0.0124113	+	0.00716564i	0.506193	−	0.862420i	$-0.331052\pi$
$227$	0.186994	+	0.107961i	0.0124113	+	0.00716564i	−0.493782	+	0.869586i	$0.664386\pi$
$228$	0.0355804	−	0.00823097i	0.00235637	−	0.000545109i
$229$	−13.7857	+	7.95917i	−0.910984	+	0.525957i	−0.880748	−	0.473586i	$-0.842959\pi$
$229$	−13.7857	+	7.95917i	−0.910984	+	0.525957i	−0.0302361	+	0.999543i	$0.509626\pi$
$230$	0.844416	−	12.4942i	0.0556791	−	0.823841i
$231$	−11.1102	+	10.3453i	−0.730995	+	0.680669i
$232$	1.43484	+	0.828404i	0.0942018	+	0.0543874i
$233$	−6.15993			−0.403550			−0.201775	−	0.979432i	$-0.564671\pi$
$233$	−6.15993			−0.403550			−0.201775	+	0.979432i	$0.564671\pi$
$234$	14.5321	+	9.78332i	0.949994	+	0.639556i
$235$	5.60722	−	8.35499i	0.365775	−	0.545019i
$236$	3.32508	−	5.75921i	0.216445	−	0.374893i
$237$	5.13792	−	4.79544i	0.333744	−	0.311498i
$238$	−3.68895	+	6.37220i	−0.239119	+	0.413049i
$239$	11.9037	−	6.87261i	0.769987	−	0.444552i	−0.0628829	−	0.998021i	$-0.520029\pi$
$239$	11.9037	−	6.87261i	0.769987	−	0.444552i	0.832870	+	0.553469i	$0.186696\pi$
$240$	2.44569	+	3.00310i	0.157868	+	0.193849i
$241$	13.5191	+	7.80524i	0.870840	+	0.502780i	0.867627	−	0.497215i	$-0.165644\pi$
$241$	13.5191	+	7.80524i	0.870840	+	0.502780i	0.00321270	+	0.999995i	$0.498977\pi$
$242$	0.0256998			0.00165205
$243$	1.39299	+	15.5261i	0.0893601	+	0.995999i
$244$		−	8.76198i		−	0.560928i
$245$	−1.09203	+	15.6143i	−0.0697672	+	0.997563i
$246$	−18.5181	−	5.65259i	−1.18067	−	0.360396i
$247$	0.106629	−	0.0615623i	0.00678464	−	0.00391711i
$248$	5.24289	−	3.02698i	0.332924	−	0.192214i
$249$	15.7650	+	16.8909i	0.999068	+	1.07042i
$250$	−8.36072	−	7.42282i	−0.528779	−	0.469461i
$251$	15.1753			0.957856			0.478928	−	0.877854i	$-0.341026\pi$
$251$	15.1753			0.957856			0.478928	+	0.877854i	$0.341026\pi$
$252$	−7.91776	−	0.555937i	−0.498772	−	0.0350207i
$253$			18.5524i			1.16638i
$254$	−14.8397	−	8.56770i	−0.931125	−	0.537585i
$255$	10.0731	+	3.83467i	0.630800	+	0.240136i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.303030	+	0.174954i	−0.0189025	+	0.0109134i	−0.509421	−	0.860517i	$-0.670141\pi$
$257$	−0.303030	+	0.174954i	−0.0189025	+	0.0109134i	0.490519	+	0.871431i	$0.336807\pi$
$258$	−4.15479	+	0.961147i	−0.258666	+	0.0598384i
$259$	−12.0189	−	0.0140729i	−0.746819	−	0.000874447i
$260$	10.8421	+	7.27639i	0.672400	+	0.451263i
$261$	2.18285	+	4.46546i	0.135115	+	0.276405i
$262$	2.47452			0.152876
$263$	13.4046	−	23.2174i	0.826561	−	1.43165i	−0.0741586	−	0.997246i	$-0.523627\pi$
$263$	13.4046	−	23.2174i	0.826561	−	1.43165i	0.900720	−	0.434400i	$-0.143040\pi$
$264$	−3.91506	−	4.19466i	−0.240955	−	0.258164i
$265$	0.0232348	−	0.343788i	0.00142730	−	0.0211187i
$266$	−0.0279492	+	0.0482788i	−0.00171367	+	0.00296016i
$267$	−10.4866	−	3.20101i	−0.641771	−	0.195898i
$268$	−11.9504	−	6.89958i	−0.729989	−	0.421459i
$269$	−14.1709			−0.864014			−0.432007	−	0.901870i	$-0.642194\pi$
$269$	−14.1709			−0.864014			−0.432007	+	0.901870i	$0.642194\pi$
$270$	1.05500	+	11.5710i	0.0642053	+	0.704186i
$271$		−	19.1244i		−	1.16172i	−0.814002	−	0.580862i	$-0.802715\pi$
$271$		−	19.1244i		−	1.16172i	0.814002	−	0.580862i	$-0.197285\pi$
$272$	−2.41010	−	1.39147i	−0.146134	−	0.0843703i
$273$	−26.0784	+	6.00067i	−1.57834	+	0.363177i
$274$	−6.68489	−	11.5786i	−0.403849	−	0.699487i
$275$	13.0998	+	10.1367i	0.789948	+	0.611266i
$276$	−7.09122	+	6.61854i	−0.426841	+	0.398389i
$277$	16.0289	+	9.25427i	0.963082	+	0.556035i	0.897120	−	0.441787i	$-0.145655\pi$
$277$	16.0289	+	9.25427i	0.963082	+	0.556035i	0.0659615	+	0.997822i	$0.478989\pi$
$278$			9.43660i			0.565969i
$279$	18.1188	+	1.25087i	1.08474	+	0.0748877i
$280$	−5.90214	−	0.405838i	−0.352721	−	0.0242535i
$281$	12.3152	+	7.11019i	0.734664	+	0.424159i	0.820126	−	0.572183i	$-0.193903\pi$
$281$	12.3152	+	7.11019i	0.734664	+	0.424159i	−0.0854618	+	0.996341i	$0.527237\pi$
$282$	−7.59356	+	1.75665i	−0.452190	+	0.104607i
$283$	3.87175	+	6.70606i	0.230152	+	0.398634i	0.957853	−	0.287260i	$-0.0927445\pi$
$283$	3.87175	+	6.70606i	0.230152	+	0.398634i	−0.727701	+	0.685894i	$0.759411\pi$
$284$	12.5168	−	7.22657i	0.742735	−	0.428818i
$285$	0.0763183	+	0.0290532i	0.00452070	+	0.00172096i
$286$	−16.7530	−	9.67236i	−0.990627	−	0.571939i
$287$	25.6303	−	14.7577i	1.51291	−	0.871118i
$288$	0.206620	−	2.99288i	0.0121752	−	0.176357i
$289$	9.25524			0.544426
$290$	1.63181	+	3.32600i	0.0958230	+	0.195309i
$291$	12.4909	−	11.6583i	0.732227	−	0.683419i
$292$	−0.284000	−	0.491902i	−0.0166198	−	0.0287864i
$293$	8.56477	−	4.94487i	0.500359	−	0.288882i	−0.228503	−	0.973543i	$-0.573383\pi$
$293$	8.56477	−	4.94487i	0.500359	−	0.288882i	0.728862	+	0.684661i	$0.240050\pi$
$294$	8.88288	−	8.25194i	0.518060	−	0.481263i
$295$	13.3500	−	6.54982i	0.777269	−	0.381345i
$296$		−	4.54272i		−	0.264040i
$297$	−2.71536	−	16.9980i	−0.157561	−	0.986326i
$298$			2.26750i			0.131353i
$299$	−16.3514	+	28.3215i	−0.945628	+	1.63788i
$300$	0.798820	+	8.62333i	0.0461199	+	0.497868i
$301$	3.26368	−	5.63761i	0.188116	−	0.324946i
$302$	−5.68081	−	9.83946i	−0.326894	−	0.566197i
$303$	12.1814	−	11.3695i	0.699806	−	0.653159i
$304$	−0.0182600	−	0.0105424i	−0.00104728	−	0.000604650i
$305$	10.9180	−	16.2683i	0.625165	−	0.931521i
$306$	−3.66652	−	7.50063i	−0.209601	−	0.428782i
$307$	10.4384			0.595752			0.297876	−	0.954605i	$-0.403722\pi$
$307$	10.4384			0.595752			0.297876	+	0.954605i	$0.403722\pi$
$308$	8.76470	+	0.0102626i	0.499415	+	0.000584763i
$309$	−7.18346	−	31.0523i	−0.408653	−	1.76650i
$310$	13.5063	+	0.912818i	0.767104	+	0.0518446i
$311$	2.84870	+	4.93410i	0.161535	+	0.279787i	0.935419	−	0.353540i	$-0.115022\pi$
$311$	2.84870	+	4.93410i	0.161535	+	0.279787i	−0.773884	+	0.633327i	$0.781689\pi$
$312$	−2.27958	−	9.85404i	−0.129056	−	0.557875i
$313$	5.43340	−	9.41092i	0.307114	−	0.531937i	−0.670616	−	0.741805i	$-0.733970\pi$
$313$	5.43340	−	9.41092i	0.307114	−	0.531937i	0.977730	+	0.209868i	$0.0673034\pi$
$314$	−12.0556			−0.680337
$315$	−14.0081	−	10.8983i	−0.789268	−	0.614048i
$316$	−4.05769			−0.228263
$317$	−15.6097	+	27.0368i	−0.876729	+	1.51854i	−0.0218195	+	0.999762i	$0.506946\pi$
$317$	−15.6097	+	27.0368i	−0.876729	+	1.51854i	−0.854909	+	0.518777i	$0.826387\pi$
$318$	−0.195121	+	0.182115i	−0.0109418	+	0.0102125i
$319$	−2.74429	−	4.75326i	−0.153651	−	0.266131i
$320$	0.150780	−	2.23098i	0.00842887	−	0.124715i
$321$	14.3571	+	4.38246i	0.801335	+	0.244605i
$322$	0.0173492	−	14.8170i	0.000966832	−	0.825720i
$323$	−0.0586779			−0.00326493
$324$	5.52839	−	7.10190i	0.307133	−	0.394550i
$325$	11.0636	+	27.0201i	0.613699	+	1.49880i
$326$	9.81817	+	5.66852i	0.543778	+	0.313951i
$327$	−7.82295	−	2.38793i	−0.432610	−	0.132053i
$328$	5.58921	+	9.68080i	0.308613	+	0.534533i
$329$	5.96491	−	10.3037i	0.328856	−	0.568059i
$330$	−2.04223	−	12.6666i	−0.112421	−	0.697276i
$331$	14.8390	−	25.7018i	0.815623	−	1.41270i	−0.0932572	−	0.995642i	$-0.529728\pi$
$331$	14.8390	−	25.7018i	0.815623	−	1.41270i	0.908880	−	0.417058i	$-0.136939\pi$
$332$		−	13.3397i		−	0.732109i
$333$	7.61077	−	11.3050i	0.417068	−	0.619511i
$334$			9.20661i			0.503763i
$335$	−13.5909	−	27.7015i	−0.742552	−	1.51349i
$336$	3.12287	+	3.35376i	0.170366	+	0.182963i
$337$	−22.3741	+	12.9177i	−1.21879	+	0.703670i	−0.964660	−	0.263499i	$-0.915123\pi$
$337$	−22.3741	+	12.9177i	−1.21879	+	0.703670i	−0.254133	+	0.967169i	$0.581790\pi$
$338$	−10.5498	−	18.2727i	−0.573831	−	0.993904i
$339$	−6.78458	−	29.3280i	−0.368488	−	1.59288i
$340$	−2.74095	−	5.58668i	−0.148649	−	0.302980i
$341$	−20.0553			−1.08605
$342$	−0.0277793	−	0.0568283i	−0.00150213	−	0.00307292i
$343$	−0.0650557	+	18.5201i	−0.00351268	+	0.999994i
$344$	2.13226	+	1.23106i	0.114964	+	0.0663743i
$345$	−21.4134	+	3.45245i	−1.15286	+	0.185874i
$346$	16.9261	−	9.77231i	0.909955	−	0.525363i
$347$	−5.52659	−	9.57234i	−0.296683	−	0.513870i	0.678692	−	0.734423i	$-0.262547\pi$
$347$	−5.52659	−	9.57234i	−0.296683	−	0.513870i	−0.975375	+	0.220553i	$0.929214\pi$
$348$	0.837798	−	2.74466i	0.0449107	−	0.147129i
$349$	27.9803	+	16.1544i	1.49775	+	0.864727i	0.999997	−	0.00259132i	$-0.000824843\pi$
$349$	27.9803	+	16.1544i	1.49775	+	0.864727i	0.497754	+	0.867318i	$0.334158\pi$
$350$	−10.4528	−	8.10799i	−0.558724	−	0.433390i
$351$	10.8363	−	28.3419i	0.578397	−	1.51278i
$352$			3.31275i			0.176570i
$353$	13.4192	+	7.74759i	0.714233	+	0.412362i	0.812626	−	0.582785i	$-0.198037\pi$
$353$	13.4192	+	7.74759i	0.714233	+	0.412362i	−0.0983936	+	0.995148i	$0.531370\pi$
$354$	−11.0166	−	3.36279i	−0.585527	−	0.178730i
$355$	32.2446	+	2.17925i	1.71137	+	0.115662i
$356$	3.16512	+	5.48214i	0.167751	+	0.290553i
$357$	12.1931	+	3.73751i	0.645326	+	0.197810i
$358$	3.19745	+	1.84605i	0.168990	+	0.0975667i
$359$			2.94433i			0.155396i	0.996977	+	0.0776980i	$0.0247570\pi$
$359$			2.94433i			0.155396i	−0.996977	+	0.0776980i	$0.975243\pi$
$360$	4.11296	−	5.29939i	0.216772	−	0.279303i
$361$	18.9996			0.999977
$362$	−8.51806	−	4.91791i	−0.447699	−	0.258479i
$363$	−0.0100325	−	0.0433681i	−0.000526571	−	0.00227623i
$364$	13.3709	+	7.74056i	0.700824	+	0.405716i
$365$	0.0856431	−	1.26719i	0.00448276	−	0.0663280i
$366$	−14.7857	+	3.42045i	−0.772862	+	0.178790i
$367$	−5.59040	+	9.68286i	−0.291817	+	0.505441i	−0.974239	−	0.225516i	$-0.927593\pi$
$367$	−5.59040	+	9.68286i	−0.291817	+	0.505441i	0.682423	+	0.730958i	$0.260926\pi$
$368$	5.60031			0.291936
$369$	−2.30969	+	33.4556i	−0.120238	+	1.74163i
$370$	5.66055	−	8.43445i	0.294278	−	0.438486i
$371$	0.000477378	−	0.407703i	2.47842e−5	−	0.0211669i
$372$	−7.15467	−	7.66564i	−0.370953	−	0.397445i
$373$	−20.8509	+	12.0383i	−1.07962	+	0.623319i	−0.930794	−	0.365544i	$-0.880883\pi$
$373$	−20.8509	+	12.0383i	−1.07962	+	0.623319i	−0.148827	+	0.988863i	$0.547550\pi$
$374$	4.60959	+	7.98405i	0.238356	+	0.412845i
$375$	−9.26210	+	17.0063i	−0.478293	+	0.878200i
$376$	3.89705	+	2.24996i	0.200975	+	0.116033i
$377$		−	9.67490i		−	0.498283i
$378$	2.15275	+	13.5781i	0.110725	+	0.698384i
$379$	−1.29955			−0.0667532			−0.0333766	−	0.999443i	$-0.510626\pi$
$379$	−1.29955			−0.0667532			−0.0333766	+	0.999443i	$0.510626\pi$
$380$	−0.0207667	−	0.0423273i	−0.00106531	−	0.00217134i
$381$	−8.66485	+	28.3864i	−0.443914	+	1.45428i
$382$	21.2231	−	12.2531i	1.08587	−	0.626925i
$383$	22.3017	−	12.8759i	1.13956	−	0.657927i	0.193240	−	0.981152i	$-0.438100\pi$
$383$	22.3017	−	12.8759i	1.13956	−	0.657927i	0.946322	+	0.323225i	$0.104767\pi$
$384$	−1.26622	+	1.18182i	−0.0646165	+	0.0603093i
$385$	16.2606	+	10.9405i	0.828716	+	0.557578i
$386$		−	20.1735i		−	1.02681i
$387$	3.24384	+	6.63595i	0.164894	+	0.337324i
$388$	−9.86469			−0.500804
$389$	−19.9368	−	11.5105i	−1.01083	−	0.583606i	−0.0993987	−	0.995048i	$-0.531692\pi$
$389$	−19.9368	−	11.5105i	−1.01083	−	0.583606i	−0.911436	+	0.411442i	$0.865025\pi$
$390$	8.04633	−	21.1364i	0.407442	−	1.07029i
$391$	13.4973	−	7.79266i	0.682587	−	0.394092i
$392$	−6.99998	−	0.0163925i	−0.353552	−	0.000827948i
$393$	−0.965986	−	4.17571i	−0.0487275	−	0.210637i
$394$	6.12176	−	10.6032i	0.308410	−	0.534181i
$395$	−7.53389	−	5.05616i	−0.379071	−	0.254403i
$396$	−5.55010	+	8.24409i	−0.278903	+	0.414281i
$397$	13.8085			0.693031			0.346515	−	0.938044i	$-0.387365\pi$
$397$	13.8085			0.693031			0.346515	+	0.938044i	$0.387365\pi$
$398$	4.01234	+	2.31652i	0.201120	+	0.116117i
$399$	0.0923804	+	0.0283171i	0.00462480	+	0.00141763i
$400$	3.05991	−	3.95436i	0.152995	−	0.197718i
$401$	−19.7632	+	11.4103i	−0.986929	+	0.569804i	−0.904355	−	0.426781i	$-0.859648\pi$
$401$	−19.7632	+	11.4103i	−0.986929	+	0.569804i	−0.0825743	+	0.996585i	$0.526314\pi$
$402$	−6.97782	+	22.8596i	−0.348022	+	1.14013i
$403$	−30.6157	−	17.6760i	−1.52508	−	0.880504i
$404$	−9.62034			−0.478630
$405$	19.1140	−	6.29729i	0.949781	−	0.312915i
$406$	2.18731	+	3.79879i	0.108554	+	0.188531i
$407$	−7.52445	+	13.0327i	−0.372973	+	0.646008i
$408$	−1.40725	+	4.61020i	−0.0696692	+	0.228239i
$409$	−5.52654	+	3.19075i	−0.273270	+	0.157772i	−0.630373	−	0.776293i	$-0.717098\pi$
$409$	−5.52654	+	3.19075i	−0.273270	+	0.157772i	0.357103	+	0.934065i	$0.383765\pi$
$410$	−1.68549	+	24.9388i	−0.0832402	+	1.23164i
$411$	−16.9291	+	15.8006i	−0.835049	+	0.779387i
$412$	−9.20075	+	15.9362i	−0.453288	+	0.785118i
$413$	15.2477	−	8.77950i	0.750292	−	0.432011i
$414$	13.9369	+	9.38263i	0.684962	+	0.461131i
$415$	16.6221	−	24.7677i	0.815948	−	1.21580i
$416$	−2.91974	+	5.05714i	−0.143152	+	0.247947i
$417$	15.9241	−	3.68380i	0.779808	−	0.180396i
$418$	0.0349244	+	0.0604908i	0.00170821	+	0.00295870i
$419$	−0.937538	−	1.62386i	−0.0458017	−	0.0793309i	0.842216	−	0.539141i	$-0.181251\pi$
$419$	−0.937538	−	1.62386i	−0.0458017	−	0.0793309i	−0.888017	+	0.459810i	$0.847918\pi$
$420$	1.61919	+	10.1182i	0.0790086	+	0.493718i
$421$	−5.71561	+	9.89973i	−0.278562	+	0.482483i	−0.971028	−	0.238967i	$-0.923191\pi$
$421$	−5.71561	+	9.89973i	−0.278562	+	0.482483i	0.692466	+	0.721451i	$0.256524\pi$
$422$	−0.0191856			−0.000933940
$423$	5.92865	+	12.1283i	0.288261	+	0.589697i
$424$	0.154097			0.00748363
$425$	1.87229	−	13.7882i	0.0908195	−	0.668824i
$426$	−17.0810	−	18.3008i	−0.827575	−	0.886679i
$427$	11.6145	−	20.0626i	0.562065	−	0.970899i
$428$	−4.33332	−	7.50554i	−0.209459	−	0.362794i
$429$	−9.78204	+	32.0463i	−0.472281	+	1.54721i
$430$	2.42497	+	4.94264i	0.116942	+	0.238355i
$431$			24.1730i			1.16437i	0.813055	+	0.582186i	$0.197803\pi$
$431$			24.1730i			1.16437i	−0.813055	+	0.582186i	$0.802197\pi$
$432$	−5.13110	+	0.819671i	−0.246870	+	0.0394365i
$433$	11.2842			0.542285			0.271143	−	0.962539i	$-0.412598\pi$
$433$	11.2842			0.542285			0.271143	+	0.962539i	$0.412598\pi$
$434$	16.0173	+	0.0187546i	0.768854	+	0.000900248i
$435$	4.97556	−	4.05203i	0.238560	−	0.194280i
$436$	2.36116	+	4.08964i	0.113079	+	0.195858i
$437$	0.102262	−	0.0590409i	0.00489184	−	0.00282431i
$438$	−0.719212	+	0.671271i	−0.0343653	+	0.0320746i
$439$	17.1147	+	9.88117i	0.816839	+	0.471602i	0.849325	−	0.527870i	$-0.177009\pi$
$439$	17.1147	+	9.88117i	0.816839	+	0.471602i	−0.0324860	+	0.999472i	$0.510342\pi$
$440$	−4.12791	+	6.15076i	−0.196790	+	0.293226i
$441$	−17.3927	−	11.7684i	−0.828222	−	0.560400i
$442$			16.2509i			0.772978i
$443$	−5.98704	+	10.3699i	−0.284453	+	0.492687i	−0.972476	−	0.233001i	$-0.925145\pi$
$443$	−5.98704	+	10.3699i	−0.284453	+	0.492687i	0.688023	+	0.725689i	$0.258479\pi$
$444$	−7.66578	+	1.77336i	−0.363802	+	0.0841599i
$445$	−0.954474	+	14.1226i	−0.0452464	+	0.669476i
$446$	−3.22276	−	5.58199i	−0.152602	−	0.264315i
$447$	3.82637	−	0.885171i	0.180981	−	0.0418671i
$448$	0.00309790	−	2.64575i	0.000146362	−	0.125000i
$449$		−	3.84633i		−	0.181520i	−0.995873	−	0.0907598i	$-0.971070\pi$
$449$		−	3.84633i		−	0.181520i	0.995873	−	0.0907598i	$-0.0289296\pi$
$450$	14.2399	−	4.71432i	0.671276	−	0.222235i
$451$		−	37.0313i		−	1.74374i
$452$	−8.68986	+	15.0513i	−0.408737	+	0.707952i
$453$	−14.3863	+	13.4274i	−0.675928	+	0.630872i
$454$	−0.186994	+	0.107961i	−0.00877608	+	0.00506687i
$455$	15.1803	+	31.0329i	0.711665	+	1.45484i
$456$	−0.0106620	+	0.0349290i	−0.000499292	+	0.00163570i
$457$	−5.42777	−	3.13372i	−0.253900	−	0.146589i	0.367649	−	0.929965i	$-0.380163\pi$
$457$	−5.42777	−	3.13372i	−0.253900	−	0.146589i	−0.621549	+	0.783375i	$0.713496\pi$
$458$		−	15.9183i		−	0.743815i
$459$	−11.2259	+	9.11525i	−0.523980	+	0.425464i
$460$	10.3981	+	6.97837i	0.484812	+	0.325368i
$461$	−6.72032	+	11.6399i	−0.312997	+	0.542126i	−0.979010	−	0.203814i	$-0.934666\pi$
$461$	−6.72032	+	11.6399i	−0.312997	+	0.542126i	0.666013	+	0.745940i	$0.268000\pi$
$462$	−3.40419	−	14.7943i	−0.158377	−	0.688294i
$463$	−18.1912	+	10.5027i	−0.845419	+	0.488103i	−0.859102	−	0.511804i	$-0.828978\pi$
$463$	−18.1912	+	10.5027i	−0.845419	+	0.488103i	0.0136838	+	0.999906i	$0.495644\pi$
$464$	−1.43484	+	0.828404i	−0.0666107	+	0.0384577i
$465$	−3.73212	−	23.1480i	−0.173073	−	1.07346i
$466$	3.07997	−	5.33466i	0.142677	−	0.247123i
$467$		−	10.7461i		−	0.497269i	−0.968597	−	0.248634i	$-0.920018\pi$
$467$		−	10.7461i		−	0.497269i	0.968597	−	0.248634i	$-0.0799818\pi$
$468$	−15.7387	+	7.69351i	−0.727520	+	0.355633i
$469$	−18.2176	−	31.6392i	−0.841208	−	1.46096i
$470$	4.43202	+	9.03349i	0.204434	+	0.416684i
$471$	4.70619	+	20.3437i	0.216850	+	0.937387i
$472$	3.32508	+	5.75921i	0.153049	+	0.265089i
$473$	−4.07819	−	7.06364i	−0.187515	−	0.324786i
$474$	1.58402	+	6.84730i	0.0727562	+	0.314507i
$475$	0.0141854	−	0.104466i	0.000650869	−	0.00479321i
$476$	−3.67402	−	6.38082i	−0.168398	−	0.292465i
$477$	0.383486	+	0.258171i	0.0175586	+	0.0118208i
$478$			13.7452i			0.628692i
$479$	3.20350	−	5.54862i	0.146372	−	0.253523i	−0.783512	−	0.621376i	$-0.786574\pi$
$479$	3.20350	−	5.54862i	0.146372	−	0.253523i	0.929884	+	0.367853i	$0.119907\pi$
$480$	−3.82361	+	0.616476i	−0.174523	+	0.0281381i
$481$	−22.9732	+	13.2636i	−1.04749	+	0.604767i
$482$	−13.5191	+	7.80524i	−0.615777	+	0.355519i
$483$	−25.0103	+	5.75489i	−1.13801	+	0.261857i
$484$	−0.0128499	+	0.0222567i	−0.000584087	+	0.00101167i
$485$	−18.3157	−	12.2921i	−0.831674	−	0.558155i
$486$	−14.1425	−	6.55668i	−0.641516	−	0.297417i
$487$		−	14.8054i		−	0.670895i	−0.942059	−	0.335447i	$-0.891113\pi$
$487$		−	14.8054i		−	0.670895i	0.942059	−	0.335447i	$-0.108887\pi$
$488$	7.58810	+	4.38099i	0.343497	+	0.198318i
$489$	5.73280	−	18.7809i	0.259246	−	0.849300i
$490$	−12.9764	−	8.75289i	−0.586214	−	0.395415i
$491$	−11.3475	+	6.55150i	−0.512107	+	0.295665i	−0.733699	−	0.679474i	$-0.762208\pi$
$491$	−11.3475	+	6.55150i	−0.512107	+	0.295665i	0.221592	+	0.975139i	$0.428875\pi$
$492$	14.1543	−	13.2108i	0.638127	−	0.595591i
$493$	−2.30540	+	3.99307i	−0.103830	+	0.179839i
$494$			0.123125i			0.00553964i
$495$	−20.5775	+	8.39095i	−0.924892	+	0.377145i
$496$			6.05396i			0.271831i
$497$	38.2394	+	0.0447744i	1.71527	+	0.00200840i
$498$	−22.5105	+	5.20745i	−1.00872	+	0.233351i
$499$	21.9780	+	38.0670i	0.983870	+	1.70411i	0.646856	+	0.762612i	$0.276083\pi$
$499$	21.9780	+	38.0670i	0.983870	+	1.70411i	0.337014	+	0.941500i	$0.390583\pi$
$500$	10.6087	−	3.52919i	0.474436	−	0.157830i
$501$	15.5360	−	3.59402i	0.694098	−	0.160569i
$502$	−7.58764	+	13.1422i	−0.338653	+	0.586564i
$503$			1.65037i			0.0735862i	0.999323	+	0.0367931i	$0.0117143\pi$
$503$			1.65037i			0.0735862i	−0.999323	+	0.0367931i	$0.988286\pi$
$504$	4.44034	−	6.57901i	0.197788	−	0.293053i
$505$	−17.8620	−	11.9876i	−0.794849	−	0.533441i
$506$	−16.0669	−	9.27621i	−0.714259	−	0.412378i
$507$	−26.7166	+	24.9357i	−1.18653	+	1.10744i
$508$	14.8397	−	8.56770i	0.658405	−	0.380130i
$509$	−6.52579	−	11.3030i	−0.289250	−	0.500996i	0.684381	−	0.729125i	$-0.260073\pi$
$509$	−6.52579	−	11.3030i	−0.289250	−	0.500996i	−0.973631	+	0.228128i	$0.926739\pi$
$510$	−8.35745	+	6.80620i	−0.370074	+	0.301384i
$511$	0.00175960	−	1.50278i	7.78403e−5	−	0.0664793i
$512$	1.00000			0.0441942
$513$	−0.0850526	+	0.0690614i	−0.00375516	+	0.00304914i
$514$		−	0.349909i		−	0.0154338i
$515$	−36.9405	+	18.1238i	−1.62779	+	0.798631i
$516$	1.24502	−	4.07873i	0.0548089	−	0.179556i
$517$	−7.45356	−	12.9100i	−0.327807	−	0.567779i
$518$	6.02164	−	10.4016i	0.264576	−	0.457022i
$519$	−23.0982	−	24.7478i	−1.01390	−	1.08631i
$520$	−11.7226	+	5.75136i	−0.514070	+	0.252214i
$521$	−25.9230			−1.13571			−0.567854	−	0.823129i	$-0.692226\pi$
$521$	−25.9230			−1.13571			−0.567854	+	0.823129i	$0.692226\pi$
$522$	−4.95862	−	0.342330i	−0.217033	−	0.0149834i
$523$	−11.8695			−0.519016			−0.259508	−	0.965741i	$-0.583560\pi$
$523$	−11.8695			−0.519016			−0.259508	+	0.965741i	$0.583560\pi$
$524$	−1.23726	+	2.14299i	−0.0540499	+	0.0936171i
$525$	−9.60164	+	20.8041i	−0.419050	+	0.907963i
$526$	13.4046	+	23.2174i	0.584467	+	1.01233i
$527$	8.42391	+	14.5906i	0.366951	+	0.635578i
$528$	5.59022	−	1.29321i	0.243283	−	0.0562797i
$529$	−4.18173	+	7.24297i	−0.181814	+	0.314912i
$530$	0.286112	+	0.192016i	0.0124279	+	0.00834064i
$531$	−1.37406	+	19.9031i	−0.0596291	+	0.863722i
$532$	−0.0278361	−	0.0483441i	−0.00120685	−	0.00209598i
$533$	32.6381	−	56.5308i	1.41371	−	2.44862i
$534$	8.01546	−	7.48118i	0.346863	−	0.323742i
$535$	1.30676	−	19.3351i	0.0564961	−	0.835930i
$536$	11.9504	−	6.89958i	0.516180	−	0.298017i
$537$	1.86698	−	6.11630i	0.0805662	−	0.263938i
$538$	7.08544	−	12.2723i	0.305475	−	0.529098i
$539$	20.0553	+	11.6416i	0.863841	+	0.501440i
$540$	−10.5482	−	4.87182i	−0.453924	−	0.209650i
$541$	−26.8705			−1.15525			−0.577626	−	0.816301i	$-0.696021\pi$
$541$	−26.8705			−1.15525			−0.577626	+	0.816301i	$0.696021\pi$
$542$	16.5622	+	9.56220i	0.711408	+	0.410732i
$543$	−4.97367	+	16.2939i	−0.213441	+	0.699240i
$544$	2.41010	−	1.39147i	0.103332	−	0.0596588i
$545$	−0.712032	+	10.5354i	−0.0305001	+	0.451286i
$546$	7.84246	−	25.5849i	0.335626	−	1.09493i
$547$	29.8651	+	17.2426i	1.27694	+	0.737240i	0.976284	−	0.216493i	$-0.0694620\pi$
$547$	29.8651	+	17.2426i	1.27694	+	0.737240i	0.300653	+	0.953733i	$0.402795\pi$
$548$	13.3698			0.571129
$549$	11.5439	+	23.6154i	0.492682	+	1.00788i
$550$	−15.3285	+	6.27642i	−0.653611	+	0.267627i
$551$	−0.0174668	+	0.0302534i	−0.000744110	+	0.00128884i
$552$	−2.18621	−	9.45044i	−0.0930514	−	0.402238i
$553$	−9.29105	−	5.37870i	−0.395095	−	0.228726i
$554$	−16.0289	+	9.25427i	−0.681002	+	0.393176i
$555$	−16.4427	−	6.25951i	−0.697955	−	0.265701i
$556$	−8.17233	−	4.71830i	−0.346584	−	0.200100i
$557$	40.6266			1.72140			0.860702	−	0.509109i	$-0.170025\pi$
$557$	40.6266			1.72140			0.860702	+	0.509109i	$0.170025\pi$
$558$	−10.1427	+	15.0659i	−0.429373	+	0.637789i
$559$		−	14.3775i		−	0.608103i
$560$	3.30254	−	4.90849i	0.139558	−	0.207421i
$561$	11.6735	−	10.8954i	0.492856	−	0.460003i
$562$	−12.3152	+	7.11019i	−0.519486	+	0.299925i
$563$	9.96779	−	5.75491i	0.420092	−	0.242540i	−0.275025	−	0.961437i	$-0.588686\pi$
$563$	9.96779	−	5.75491i	0.420092	−	0.242540i	0.695117	+	0.718897i	$0.255353\pi$
$564$	2.27548	−	7.45455i	0.0958148	−	0.313893i
$565$	−34.8893	+	17.1175i	−1.46781	+	0.720137i
$566$	−7.74350			−0.325483
$567$	22.0725	−	8.93328i	0.926959	−	0.375162i
$568$			14.4531i			0.606440i
$569$	−8.74906	−	5.05127i	−0.366780	−	0.211760i	0.305271	−	0.952266i	$-0.401253\pi$
$569$	−8.74906	−	5.05127i	−0.366780	−	0.211760i	−0.672051	+	0.740505i	$0.734586\pi$
$570$	−0.0633200	+	0.0515669i	−0.00265218	+	0.00215990i
$571$	−0.146826	−	0.254309i	−0.00614446	−	0.0106425i	0.862937	−	0.505312i	$-0.168623\pi$
$571$	−0.146826	−	0.254309i	−0.00614446	−	0.0106425i	−0.869081	+	0.494669i	$0.835289\pi$
$572$	16.7530	−	9.67236i	0.700479	−	0.404422i
$573$	−28.9619	−	31.0303i	−1.20990	−	1.29631i
$574$	−0.0346296	+	29.5753i	−0.00144541	+	1.23445i
$575$	10.6105	+	25.9134i	0.442488	+	1.08066i
$576$	2.48860	+	1.67538i	0.103692	+	0.0698074i
$577$	26.4319			1.10038			0.550188	−	0.835041i	$-0.314556\pi$
$577$	26.4319			1.10038			0.550188	+	0.835041i	$0.314556\pi$
$578$	−4.62762	+	8.01527i	−0.192484	+	0.333391i
$579$	−34.0425	+	7.87521i	−1.41476	+	0.327283i
$580$	−3.69630	−	0.249814i	−0.153481	−	0.0103730i
$581$	17.6825	−	30.5443i	0.733593	−	1.26719i
$582$	3.85092	+	16.6465i	0.159626	+	0.690021i
$583$	−0.442094	−	0.255243i	−0.0183096	−	0.0105711i
$584$	0.567999			0.0235040
$585$	−38.8085	−	5.32696i	−1.60453	−	0.220243i
$586$			9.88974i			0.408542i
$587$	−29.9856	−	17.3122i	−1.23764	−	0.714552i	−0.269028	−	0.963132i	$-0.586703\pi$
$587$	−29.9856	−	17.3122i	−1.23764	−	0.714552i	−0.968611	+	0.248581i	$0.920036\pi$
$588$	2.70495	+	11.8188i	0.111550	+	0.487398i
$589$	0.0638235	+	0.110546i	0.00262980	+	0.00455495i
$590$	−1.00271	+	14.8364i	−0.0412811	+	0.610804i
$591$	−20.2825	−	6.19117i	−0.834311	−	0.254671i
$592$	3.93411	+	2.27136i	0.161691	+	0.0933524i
$593$			25.3186i			1.03971i	0.854255	+	0.519855i	$0.174014\pi$
$593$			25.3186i			1.03971i	−0.854255	+	0.519855i	$0.825986\pi$
$594$	16.0784	+	6.14744i	0.659705	+	0.252232i
$595$	1.12942	−	16.4253i	0.0463018	−	0.673372i
$596$	−1.96371	−	1.13375i	−0.0804367	−	0.0464401i
$597$	2.34279	−	7.67507i	0.0958840	−	0.314120i
$598$	−16.3514	−	28.3215i	−0.668660	−	1.15815i
$599$	−19.5167	+	11.2680i	−0.797433	+	0.460398i	−0.842573	−	0.538583i	$-0.818960\pi$
$599$	−19.5167	+	11.2680i	−0.797433	+	0.460398i	0.0451400	+	0.998981i	$0.485627\pi$
$600$	−7.86744	−	3.61987i	−0.321187	−	0.147781i
$601$	−39.4649	−	22.7851i	−1.60981	−	0.929422i	−0.989413	−	0.145131i	$-0.953640\pi$
$601$	−39.4649	−	22.7851i	−1.60981	−	0.929422i	−0.620393	−	0.784291i	$-0.713027\pi$
$602$	3.25047	+	5.64524i	0.132479	+	0.230083i
$603$	41.2992	+	2.85119i	1.68183	+	0.116109i
$604$	11.3616			0.462298
$605$	−0.0515917	+	0.0253120i	−0.00209750	+	0.00102908i
$606$	3.75552	+	16.2342i	0.152558	+	0.659468i
$607$	19.2637	+	33.3657i	0.781890	+	1.35427i	0.930839	+	0.365428i	$0.119078\pi$
$607$	19.2637	+	33.3657i	0.781890	+	1.35427i	−0.148949	+	0.988845i	$0.547589\pi$
$608$	0.0182600	−	0.0105424i	0.000740542	−	0.000427552i
$609$	5.55654	−	5.17399i	0.225162	−	0.209661i
$610$	8.62976	+	17.5894i	0.349409	+	0.712176i
$611$		−	26.2772i		−	1.06306i
$612$	8.32900	+	0.575012i	0.336680	+	0.0232435i
$613$			3.39696i			0.137202i	0.997644	+	0.0686011i	$0.0218536\pi$
$613$			3.39696i			0.137202i	−0.997644	+	0.0686011i	$0.978146\pi$
$614$	−5.21921	+	9.03994i	−0.210630	+	0.364822i
$615$	42.7419	−	6.89123i	1.72352	−	0.277881i
$616$	−4.39124	+	7.58532i	−0.176928	+	0.305621i
$617$	1.91706	+	3.32044i	0.0771778	+	0.133676i	0.902031	−	0.431671i	$-0.142076\pi$
$617$	1.91706	+	3.32044i	0.0771778	+	0.133676i	−0.824853	+	0.565347i	$0.808742\pi$
$618$	30.4838	+	9.30507i	1.22624	+	0.374305i
$619$	−19.9022	−	11.4905i	−0.799936	−	0.461843i	0.0435128	−	0.999053i	$-0.486145\pi$
$619$	−19.9022	−	11.4905i	−0.799936	−	0.461843i	−0.843449	+	0.537210i	$0.819478\pi$
$620$	−7.54366	+	11.2404i	−0.302961	+	0.451424i
$621$	10.3924	−	27.1811i	0.417035	−	1.09074i
$622$	−5.69741			−0.228445
$623$	−0.0196104	+	16.7482i	−0.000785675	+	0.671003i
$624$	9.67364	+	2.95285i	0.387255	+	0.118208i
$625$	24.0947	+	6.66657i	0.963790	+	0.266663i
$626$	5.43340	+	9.41092i	0.217162	+	0.376136i
$627$	0.0884439	−	0.0825485i	0.00353211	−	0.00329667i
$628$	6.02781	−	10.4405i	0.240536	−	0.416620i
$629$	12.6421			0.504075
$630$	16.4422	−	6.68225i	0.655075	−	0.266227i
$631$	−9.64515			−0.383967			−0.191984	−	0.981398i	$-0.561492\pi$
$631$	−9.64515			−0.383967			−0.191984	+	0.981398i	$0.561492\pi$
$632$	2.02885	−	3.51406i	0.0807031	−	0.139782i
$633$	0.00748955	+	0.0323754i	0.000297683	+	0.00128681i
$634$	−15.6097	−	27.0368i	−0.619941	−	1.07377i
$635$	38.2287	+	2.58368i	1.51706	+	0.102530i
$636$	−0.0601555	−	0.260037i	−0.00238532	−	0.0103111i
$637$	20.3552	+	35.4477i	0.806503	+	1.40449i
$638$	5.48859			0.217295
$639$	−24.2145	+	35.9680i	−0.957909	+	1.42287i
$640$	1.85669	+	1.24607i	0.0733923	+	0.0492552i
$641$	−13.0157	−	7.51461i	−0.514089	−	0.296809i	0.220424	−	0.975404i	$-0.429256\pi$
$641$	−13.0157	−	7.51461i	−0.514089	−	0.296809i	−0.734513	+	0.678595i	$0.762589\pi$
$642$	−10.9739	+	10.2424i	−0.433104	+	0.404235i
$643$	1.01830	+	1.76375i	0.0401578	+	0.0695554i	0.885406	−	0.464819i	$-0.153881\pi$
$643$	1.01830	+	1.76375i	0.0401578	+	0.0695554i	−0.845248	+	0.534374i	$0.820547\pi$
$644$	12.8232	+	7.42353i	0.505306	+	0.292528i
$645$	7.39400	−	6.02157i	0.291138	−	0.237099i
$646$	0.0293390	−	0.0508166i	0.00115433	−	0.00199935i
$647$		−	27.8332i		−	1.09424i	−0.837055	−	0.547118i	$-0.815725\pi$
$647$		−	27.8332i		−	1.09424i	0.837055	−	0.547118i	$-0.184275\pi$
$648$	3.38623	+	8.33867i	0.133024	+	0.327574i
$649$		−	22.0303i		−	0.864766i
$650$	−28.9319	−	3.92865i	−1.13480	−	0.154095i
$651$	−6.22107	−	27.0362i	−0.243823	−	1.05963i
$652$	−9.81817	+	5.66852i	−0.384509	+	0.221997i
$653$	0.152462	+	0.264071i	0.00596629	+	0.0103339i	0.868993	−	0.494824i	$-0.164768\pi$
$653$	0.152462	+	0.264071i	0.00596629	+	0.0103339i	−0.863027	+	0.505158i	$0.831434\pi$
$654$	5.97948	−	5.58091i	0.233816	−	0.218231i
$655$	−4.96753	+	2.43718i	−0.194097	+	0.0952283i
$656$	−11.1784			−0.436444
$657$	1.41352	+	0.951613i	0.0551467	+	0.0371260i
$658$	5.94077	+	10.3176i	0.231595	+	0.402222i
$659$	33.8347	+	19.5345i	1.31801	+	0.760955i	0.983409	−	0.181404i	$-0.0580640\pi$
$659$	33.8347	+	19.5345i	1.31801	+	0.760955i	0.334604	+	0.942359i	$0.391397\pi$
$660$	11.9907	+	4.56470i	0.466739	+	0.177681i
$661$	3.76232	−	2.17218i	0.146337	−	0.0844879i	−0.425044	−	0.905173i	$-0.639741\pi$
$661$	3.76232	−	2.17218i	0.146337	−	0.0844879i	0.571381	+	0.820685i	$0.306408\pi$
$662$	14.8390	+	25.7018i	0.576732	+	0.998930i
$663$	27.4232	−	6.34393i	1.06503	−	0.246378i
$664$	11.5525	+	6.66983i	0.448323	+	0.258840i
$665$	0.00855704	−	0.124446i	0.000331828	−	0.00482580i
$666$	5.98504	+	12.2436i	0.231916	+	0.474431i
$667$		−	9.27864i		−	0.359270i
$668$	−7.97315	−	4.60330i	−0.308491	−	0.178107i
$669$	−8.16144	+	7.61742i	−0.315540	+	0.294507i
$670$	30.7857	+	2.08064i	1.18935	+	0.0803822i
$671$	−14.5131	−	25.1375i	−0.560273	−	0.970421i
$672$	−4.46587	+	1.02760i	−0.172275	+	0.0396406i
$673$	−8.16480	−	4.71395i	−0.314730	−	0.181709i	0.334311	−	0.942463i	$-0.391496\pi$
$673$	−8.16480	−	4.71395i	−0.314730	−	0.181709i	−0.649041	+	0.760753i	$0.724830\pi$
$674$		−	25.8353i		−	0.995140i
$675$	−13.5142	−	22.1893i	−0.520163	−	0.854067i
$676$	21.0995			0.811520
$677$	−2.59469	−	1.49804i	−0.0997219	−	0.0575745i	0.449310	−	0.893376i	$-0.351670\pi$
$677$	−2.59469	−	1.49804i	−0.0997219	−	0.0575745i	−0.549032	+	0.835802i	$0.685003\pi$
$678$	28.7911	+	8.78839i	1.10572	+	0.337516i
$679$	−22.5876	−	13.0762i	−0.866831	−	0.501819i
$680$	6.20868	+	0.419612i	0.238092	+	0.0160914i
$681$	0.255181	+	0.273405i	0.00977855	+	0.0104769i
$682$	10.0276	−	17.3684i	0.383978	−	0.665069i
$683$	−22.0783			−0.844802			−0.422401	−	0.906409i	$-0.638813\pi$
$683$	−22.0783			−0.844802			−0.422401	+	0.906409i	$0.638813\pi$
$684$	0.0631044	+	0.00435656i	0.00241286	+	0.000166577i
$685$	24.8236	+	16.6597i	0.948460	+	0.636533i
$686$	−16.0064	−	9.31641i	−0.611127	−	0.355702i
$687$	−26.8620	+	6.21410i	−1.02485	+	0.237083i
$688$	−2.13226	+	1.23106i	−0.0812916	+	0.0469337i
$689$	−0.449924	−	0.779291i	−0.0171407	−	0.0296886i
$690$	7.71677	−	20.2708i	0.293773	−	0.771694i
$691$	26.9763	+	15.5748i	1.02623	+	0.592492i	0.915901	−	0.401404i	$-0.131478\pi$
$691$	26.9763	+	15.5748i	1.02623	+	0.592492i	0.110325	+	0.993896i	$0.464811\pi$
$692$			19.5446i			0.742975i
$693$	−23.6363	+	11.5198i	−0.897869	+	0.437602i
$694$	11.0532			0.419573
$695$	−9.29420	−	18.9437i	−0.352549	−	0.718576i
$696$	1.95804	+	2.09788i	0.0742194	+	0.0795200i
$697$	−26.9411	+	15.5544i	−1.02047	+	0.589167i
$698$	−27.9803	+	16.1544i	−1.05907	+	0.611454i
$699$	−10.2045	−	3.11489i	−0.385969	−	0.117816i
$700$	12.2481	−	4.99837i	0.462935	−	0.188921i
$701$			11.1523i			0.421217i	0.977570	+	0.210609i	$0.0675446\pi$
$701$			11.1523i			0.421217i	−0.977570	+	0.210609i	$0.932455\pi$
$702$	19.1266	+	23.5554i	0.721889	+	0.889042i
$703$	0.0957827			0.00361251
$704$	−2.86892	−	1.65637i	−0.108127	−	0.0624269i
$705$	13.5137	−	11.0054i	0.508957	−	0.414488i
$706$	−13.4192	+	7.74759i	−0.505039	+	0.291584i
$707$	−22.0280	−	12.7523i	−0.828450	−	0.479600i
$708$	8.42057	−	7.85928i	0.316464	−	0.295370i
$709$	21.9499	−	38.0183i	0.824345	−	1.42781i	−0.0780746	−	0.996948i	$-0.524877\pi$
$709$	21.9499	−	38.0183i	0.824345	−	1.42781i	0.902419	−	0.430859i	$-0.141789\pi$
$710$	−18.0096	+	26.8351i	−0.675889	+	1.00710i
$711$	10.9364	−	5.34601i	0.410145	−	0.200491i
$712$	−6.33024			−0.237236
$713$	−29.3618	−	16.9520i	−1.09961	−	0.634859i
$714$	−9.33331	+	8.69076i	−0.349290	+	0.325243i
$715$	43.1577	+	2.91680i	1.61400	+	0.109082i
$716$	−3.19745	+	1.84605i	−0.119494	+	0.0689901i
$717$	23.1949	−	5.36577i	0.866228	−	0.200388i
$718$	−2.54987	−	1.47217i	−0.0951602	−	0.0549408i
$719$	52.2052			1.94692			0.973462	−	0.228848i	$-0.0734958\pi$
$719$	52.2052			1.94692			0.973462	+	0.228848i	$0.0734958\pi$
$720$	2.53293	+	6.21162i	0.0943967	+	0.231494i
$721$	−42.1916	+	24.2935i	−1.57130	+	0.904737i
$722$	−9.49978	+	16.4541i	−0.353545	+	0.612358i
$723$	18.4487	+	19.7663i	0.686115	+	0.735116i
$724$	8.51806	−	4.91791i	0.316571	−	0.182773i
$725$	−6.55162	−	5.06968i	−0.243321	−	0.188283i
$726$	0.0425741	+	0.0129956i	0.00158007	+	0.000482312i
$727$	−10.8410	+	18.7771i	−0.402069	+	0.696404i	−0.993976	−	0.109602i	$-0.965042\pi$
$727$	−10.8410	+	18.7771i	−0.402069	+	0.696404i	0.591906	+	0.806007i	$0.298376\pi$
$728$	−13.3890	+	7.70923i	−0.496228	+	0.285723i
$729$	−5.54346	+	26.4248i	−0.205313	+	0.978696i
$730$	1.05460	+	0.707766i	0.0390325	+	0.0261956i
$731$	−3.42597	+	5.93395i	−0.126714	+	0.219475i
$732$	4.43067	−	14.5150i	0.163762	−	0.536491i
$733$	−4.27097	−	7.39754i	−0.157752	−	0.273234i	0.776306	−	0.630357i	$-0.217091\pi$
$733$	−4.27097	−	7.39754i	−0.157752	−	0.273234i	−0.934058	+	0.357122i	$0.883758\pi$
$734$	−5.59040	−	9.68286i	−0.206346	−	0.357401i
$735$	−9.70474	+	25.3144i	−0.357965	+	0.933735i
$736$	−2.80015	+	4.85001i	−0.103215	+	0.178774i
$737$	−45.7132			−1.68387
$738$	−27.8186	−	18.7281i	−1.02402	−	0.689390i
$739$	46.5168			1.71115			0.855575	−	0.517679i	$-0.173204\pi$
$739$	46.5168			1.71115			0.855575	+	0.517679i	$0.173204\pi$
$740$	4.47417	+	9.11940i	0.164474	+	0.335236i
$741$	0.207771	−	0.0480646i	0.00763266	−	0.00176570i
$742$	0.352842	+	0.204265i	0.0129533	+	0.00749880i
$743$	7.44987	+	12.9036i	0.273309	+	0.473386i	0.969707	−	0.244270i	$-0.0785484\pi$
$743$	7.44987	+	12.9036i	0.273309	+	0.473386i	−0.696398	+	0.717656i	$0.745215\pi$
$744$	10.2160	−	2.36331i	0.374536	−	0.0866431i
$745$	−2.23328	−	4.55194i	−0.0818210	−	0.166770i
$746$		−	24.0766i		−	0.881507i
$747$	17.5750	+	35.9533i	0.643035	+	1.31546i
$748$	−9.21918			−0.337087
$749$	0.0268484	−	22.9298i	0.000981019	−	0.837836i
$750$	−10.0968	−	16.5244i	−0.368684	−	0.603384i
$751$	−18.2600	−	31.6273i	−0.666317	−	1.15410i	−0.978926	−	0.204213i	$-0.934536\pi$
$751$	−18.2600	−	31.6273i	−0.666317	−	1.15410i	0.312609	−	0.949882i	$-0.398797\pi$
$752$	−3.89705	+	2.24996i	−0.142111	+	0.0820477i
$753$	25.1393	+	7.67368i	0.916126	+	0.279644i
$754$	8.37871	+	4.83745i	0.305135	+	0.176170i
$755$	21.0951	+	14.1574i	0.767728	+	0.515239i
$756$	−12.8354	−	4.92473i	−0.466818	−	0.179111i
$757$		−	2.35490i		−	0.0855903i	−0.999084	−	0.0427951i	$-0.986374\pi$
$757$		−	2.35490i		−	0.0855903i	0.999084	−	0.0427951i	$-0.0136263\pi$
$758$	0.649773	−	1.12544i	0.0236008	−	0.0408778i
$759$	−9.38139	+	30.7338i	−0.340523	+	1.11557i
$760$	0.0470399	+	0.00317918i	0.00170632	+	0.000115321i
$761$	−17.6608	−	30.5893i	−0.640202	−	1.10886i	−0.985387	−	0.170328i	$-0.945517\pi$
$761$	−17.6608	−	30.5893i	−0.640202	−	1.10886i	0.345185	−	0.938535i	$-0.387816\pi$
$762$	−20.2509	−	21.6972i	−0.733613	−	0.786005i
$763$	−0.0146292	+	12.4941i	−0.000529614	+	0.452315i
$764$			24.5063i			0.886606i
$765$	14.7479	+	11.4461i	0.533211	+	0.413835i
$766$			25.7518i			0.930449i
$767$	19.4168	−	33.6308i	0.701098	−	1.21434i
$768$	−0.390374	−	1.68749i	−0.0140864	−	0.0608919i
$769$	−26.9721	+	15.5724i	−0.972640	+	0.561554i	−0.900040	−	0.435807i	$-0.856463\pi$
$769$	−26.9721	+	15.5724i	−0.972640	+	0.561554i	−0.0726000	+	0.997361i	$0.523130\pi$
$770$	−17.6050	+	8.61184i	−0.634441	+	0.310349i
$771$	−0.590466	+	0.136595i	−0.0212651	+	0.00491936i
$772$	17.4708	+	10.0868i	0.628787	+	0.363030i
$773$		−	12.0111i		−	0.432011i	−0.976392	−	0.216005i	$-0.930697\pi$
$773$		−	12.0111i		−	0.432011i	0.976392	−	0.216005i	$-0.0693028\pi$
$774$	−7.36882	−	0.508724i	−0.264867	−	0.0182857i
$775$	−28.0125	+	11.4700i	−1.00624	+	0.412014i
$776$	4.93235	−	8.54307i	0.177061	−	0.306678i
$777$	−19.9033	−	6.10091i	−0.714028	−	0.218869i
$778$	19.9368	−	11.5105i	0.714768	−	0.412672i
$779$	−0.204118	+	0.117848i	−0.00731330	+	0.00422233i
$780$	14.2815	+	17.5365i	0.511361	+	0.627909i
$781$	23.9398	−	41.4650i	0.856634	−	1.48373i
$782$			15.5853i			0.557330i
$783$	1.35804	+	8.50124i	0.0485323	+	0.303810i
$784$	3.51419	−	6.05396i	0.125507	−	0.216213i
$785$	24.2013	−	11.8737i	0.863782	−	0.423790i
$786$	4.09926	+	1.25129i	0.146216	+	0.0446319i
$787$	−27.0080	−	46.7792i	−0.962731	−	1.66750i	−0.715590	−	0.698520i	$-0.753842\pi$
$787$	−27.0080	−	46.7792i	−0.962731	−	1.66750i	−0.247141	−	0.968980i	$-0.579491\pi$
$788$	6.12176	+	10.6032i	0.218079	+	0.377723i
$789$	33.9462	−	31.6835i	1.20852	−	1.12796i
$790$	8.14571	−	3.99646i	0.289811	−	0.142188i
$791$	−39.8488	+	22.9446i	−1.41686	+	0.815815i
$792$	−4.36455	−	8.92857i	−0.155087	−	0.317263i
$793$		−	51.1654i		−	1.81694i
$794$	−6.90427	+	11.9585i	−0.245023	+	0.424393i
$795$	0.212334	−	0.557767i	0.00753070	−	0.0197820i
$796$	−4.01234	+	2.31652i	−0.142213	+	0.0821070i
$797$	−11.0584	+	6.38454i	−0.391707	+	0.226152i	−0.682899	−	0.730512i	$-0.739281\pi$
$797$	−11.0584	+	6.38454i	−0.391707	+	0.226152i	0.291193	+	0.956664i	$0.405948\pi$
$798$	−0.0707135	+	0.0658452i	−0.00250323	+	0.00233090i
$799$	−6.26152	+	10.8453i	−0.221517	+	0.383678i
$800$	1.89463	+	4.62714i	0.0669851	+	0.163594i
$801$	−15.7534	−	10.6055i	−0.556619	−	0.374728i
$802$		−	22.8206i		−	0.805824i
$803$	−1.62955	−	0.940819i	−0.0575055	−	0.0332008i
$804$	−16.3081	−	17.4728i	−0.575142	−	0.616217i
$805$	14.5586	+	29.7619i	0.513123	+	1.04897i
$806$	30.6157	−	17.6760i	1.07839	−	0.622610i
$807$	−23.4754	−	7.16578i	−0.826372	−	0.252247i
$808$	4.81017	−	8.33145i	0.169221	−	0.293100i
$809$			24.6158i			0.865445i	0.901527	+	0.432723i	$0.142447\pi$
$809$			24.6158i			0.865445i	−0.901527	+	0.432723i	$0.857553\pi$
$810$	−4.10337	+	19.7018i	−0.144178	+	0.692252i
$811$		−	7.06824i		−	0.248199i	−0.992270	−	0.124100i	$-0.960396\pi$
$811$		−	7.06824i		−	0.248199i	0.992270	−	0.124100i	$-0.0396043\pi$
$812$	−4.38350	−	0.00513262i	−0.153831	−	0.000180120i
$813$	9.67062	−	31.6813i	0.339164	−	1.11111i
$814$	−7.52445	−	13.0327i	−0.263732	−	0.456797i
$815$	−25.2927	−	1.70940i	−0.885965	−	0.0598778i
$816$	−3.28892	−	3.52381i	−0.115135	−	0.123358i
$817$	−0.0259567	+	0.0449584i	−0.000908111	+	0.00157289i
$818$		−	6.38150i		−	0.223124i
$819$	−46.2356	−	3.24638i	−1.61560	−	0.113438i
$820$	−20.7549	−	13.9291i	−0.724793	−	0.486425i
$821$	26.9629	+	15.5670i	0.941012	+	0.543293i	0.890277	−	0.455419i	$-0.150510\pi$
$821$	26.9629	+	15.5670i	0.941012	+	0.543293i	0.0507345	+	0.998712i	$0.483844\pi$
$822$	−5.21921	−	22.5613i	−0.182041	−	0.786916i
$823$	−19.9909	+	11.5418i	−0.696840	+	0.402321i	−0.806170	−	0.591685i	$-0.798463\pi$
$823$	−19.9909	+	11.5418i	−0.696840	+	0.402321i	0.109329	+	0.994006i	$0.465130\pi$
$824$	−9.20075	−	15.9362i	−0.320523	−	0.555163i
$825$	16.5752	+	23.4165i	0.577075	+	0.815259i
$826$	−0.0206015	+	17.5947i	−0.000716819	+	0.612197i
$827$	−17.5943			−0.611814			−0.305907	−	0.952061i	$-0.598960\pi$
$827$	−17.5943			−0.611814			−0.305907	+	0.952061i	$0.598960\pi$
$828$	−15.0940	+	7.37841i	−0.524554	+	0.256417i
$829$			34.9888i			1.21521i	0.794239	+	0.607605i	$0.207870\pi$
$829$			34.9888i			1.21521i	−0.794239	+	0.607605i	$0.792130\pi$
$830$	13.1384	+	26.7790i	0.456039	+	0.929513i
$831$	21.8737	+	23.4359i	0.758790	+	0.812981i
$832$	−2.91974	−	5.05714i	−0.101224	−	0.175325i
$833$	0.0456194	−	19.4805i	0.00158062	−	0.674960i
$834$	−4.77180	+	15.6326i	−0.165234	+	0.541313i
$835$	−9.06768	−	18.4820i	−0.313800	−	0.639597i
$836$	−0.0698488			−0.00241577
$837$	29.3829	+	11.2343i	1.01562	+	0.388314i
$838$	1.87508			0.0647734
$839$	1.56260	−	2.70651i	0.0539470	−	0.0934390i	−0.837791	−	0.545991i	$-0.816153\pi$
$839$	1.56260	−	2.70651i	0.0539470	−	0.0934390i	0.891738	+	0.452552i	$0.149486\pi$
$840$	−9.57223	−	3.65684i	−0.330273	−	0.126173i
$841$	−13.1275	−	22.7375i	−0.452672	−	0.784051i
$842$	−5.71561	−	9.89973i	−0.196973	−	0.341167i
$843$	16.8059	+	18.0061i	0.578826	+	0.620164i
$844$	0.00959279	−	0.0166152i	0.000330198	−	0.000571919i
$845$	39.1753	+	26.2914i	1.34767	+	0.904453i
$846$	−13.4677	−	0.929776i	−0.463030	−	0.0319664i
$847$	−0.0589254	+	0.0339287i	−0.00202470	+	0.00116580i
$848$	−0.0770487	+	0.133452i	−0.00264586	+	0.00458277i
$849$	3.02286	+	13.0670i	0.103744	+	0.448460i
$850$	11.0048	+	8.51554i	0.377460	+	0.292080i
$851$	−22.0323	+	12.7203i	−0.755256	+	0.436047i
$852$	24.3895	−	5.64212i	0.835570	−	0.193296i
$853$	−18.8954	+	32.7278i	−0.646967	+	1.12058i	0.336877	+	0.941549i	$0.390629\pi$
$853$	−18.8954	+	32.7278i	−0.646967	+	1.12058i	−0.983844	+	0.179030i	$0.942704\pi$
$854$	11.5675	+	20.0898i	0.395832	+	0.687458i
$855$	0.111737	+	0.0867212i	0.00382132	+	0.00296580i
$856$	8.66665			0.296220
$857$	22.7409	+	13.1295i	0.776815	+	0.448495i	0.835300	−	0.549794i	$-0.185294\pi$
$857$	22.7409	+	13.1295i	0.776815	+	0.448495i	−0.0584850	+	0.998288i	$0.518627\pi$
$858$	−22.8619	−	24.4946i	−0.780493	−	0.836234i
$859$	−24.1275	+	13.9300i	−0.823221	+	0.475287i	−0.851526	−	0.524313i	$-0.824322\pi$
$859$	−24.1275	+	13.9300i	−0.823221	+	0.475287i	0.0283052	+	0.999599i	$0.490989\pi$
$860$	−5.49294	−	0.371239i	−0.187308	−	0.0126591i
$861$	49.9214	−	11.4870i	1.70132	−	0.391475i
$862$	−20.9344	−	12.0865i	−0.713030	−	0.411668i
$863$	−1.59730			−0.0543727			−0.0271864	−	0.999630i	$-0.508655\pi$
$863$	−1.59730			−0.0543727			−0.0271864	+	0.999630i	$0.508655\pi$
$864$	1.85569	−	4.85349i	0.0631319	−	0.165119i
$865$	−24.3539	+	36.2884i	−0.828059	+	1.23384i
$866$	−5.64211	+	9.77243i	−0.191727	+	0.332081i
$867$	15.3322	+	4.68009i	0.520708	+	0.158944i
$868$	−8.02488	+	13.8620i	−0.272382	+	0.470507i
$869$	−11.6412	+	6.72105i	−0.394901	+	0.227996i
$870$	1.02138	+	6.33498i	0.0346281	+	0.214776i
$871$	−69.7843	−	40.2900i	−2.36455	−	1.36517i
$872$	−4.72231			−0.159918
$873$	26.5875	−	12.9967i	0.899850	−	0.439873i
$874$			0.118082i			0.00399417i
$875$	28.9693	+	5.98155i	0.979341	+	0.202213i
$876$	−0.221732	−	0.958491i	−0.00749163	−	0.0323844i
$877$	33.5915	−	19.3941i	1.13431	−	0.654892i	0.189292	−	0.981921i	$-0.439381\pi$
$877$	33.5915	−	19.3941i	1.13431	−	0.654892i	0.945014	+	0.327029i	$0.106048\pi$
$878$	−17.1147	+	9.88117i	−0.577593	+	0.333473i
$879$	16.6888	−	3.86069i	0.562899	−	0.130218i
$880$	−3.26276	−	6.65026i	−0.109988	−	0.224180i
$881$	22.6988			0.764741			0.382370	−	0.924009i	$-0.375108\pi$
$881$	22.6988			0.764741			0.382370	+	0.924009i	$0.375108\pi$
$882$	18.8881	−	9.17829i	0.635994	−	0.309049i
$883$		−	2.88769i		−	0.0971784i	−0.998819	−	0.0485892i	$-0.984527\pi$
$883$		−	2.88769i		−	0.0971784i	0.998819	−	0.0485892i	$-0.0154725\pi$
$884$	−14.0737	−	8.12546i	−0.473350	−	0.273289i
$885$	25.4276	−	4.09967i	0.854740	−	0.137809i
$886$	−5.98704	−	10.3699i	−0.201139	−	0.348382i
$887$	−41.2357	+	23.8075i	−1.38456	+	0.799376i	−0.992696	−	0.120647i	$-0.961503\pi$
$887$	−41.2357	+	23.8075i	−1.38456	+	0.799376i	−0.391865	+	0.920023i	$0.628170\pi$
$888$	2.29712	−	7.52544i	0.0770862	−	0.252537i
$889$	45.3360	+	0.0530837i	1.52052	+	0.00178037i
$890$	−11.7533	−	7.88791i	−0.393972	−	0.264403i
$891$	4.09713	−	29.5319i	0.137259	−	0.989355i
$892$	6.44552			0.215812
$893$	−0.0474402	+	0.0821688i	−0.00158752	+	0.00274967i
$894$	−1.14660	+	3.75632i	−0.0383482	+	0.125630i
$895$	−8.23699	−	0.556695i	−0.275332	−	0.0186083i
$896$	2.28974	+	1.32556i	0.0764948	+	0.0442838i
$897$	−41.4090	+	38.6488i	−1.38261	+	1.29045i
$898$	3.33102	+	1.92317i	0.111158	+	0.0641769i
$899$	10.0303			0.334528
$900$	−3.03724	+	14.6893i	−0.101241	+	0.489643i
$901$			0.428844i			0.0142869i
$902$	32.0701	+	18.5157i	1.06782	+	0.616504i
$903$	8.25736	−	7.68888i	0.274788	−	0.255870i
$904$	−8.68986	−	15.0513i	−0.289020	−	0.500598i
$905$	21.9435	+	1.48305i	0.729426	+	0.0492981i
$906$	−4.43528	−	19.1726i	−0.147352	−	0.636966i
$907$	−32.4514	−	18.7358i	−1.07753	−	0.622113i	−0.147302	−	0.989092i	$-0.547059\pi$
$907$	−32.4514	−	18.7358i	−1.07753	−	0.622113i	−0.930229	+	0.366979i	$0.880392\pi$
$908$		−	0.215922i		−	0.00716564i
$909$	25.9289	−	12.6748i	0.860007	−	0.420396i
$910$	−34.4654	−	2.36988i	−1.14252	−	0.0785608i
$911$	38.1165	+	22.0066i	1.26286	+	0.729111i	0.973626	−	0.228148i	$-0.0732671\pi$
$911$	38.1165	+	22.0066i	1.26286	+	0.729111i	0.289231	+	0.957259i	$0.406600\pi$
$912$	−0.0249184	−	0.0266980i	−0.000825132	−	0.000884060i
$913$	−22.0955	−	38.2705i	−0.731253	−	1.26657i
$914$	5.42777	−	3.13372i	0.179535	−	0.103654i
$915$	26.3131	−	21.4291i	0.869885	−	0.708423i
$916$	13.7857	+	7.95917i	0.455492	+	0.262978i
$917$	−5.67366	+	3.26684i	−0.187361	+	0.107880i
$918$	−2.28110	−	14.2795i	−0.0752874	−	0.471295i
$919$	32.6919			1.07841			0.539203	−	0.842176i	$-0.318725\pi$
$919$	32.6919			1.07841			0.539203	+	0.842176i	$0.318725\pi$
$920$	−11.2425	+	5.51580i	−0.370653	+	0.181851i
$921$	17.2922	+	5.27839i	0.569798	+	0.173929i
$922$	−6.72032	−	11.6399i	−0.221322	−	0.383341i
$923$	73.0915	−	42.1994i	2.40584	−	1.38901i
$924$	14.5143	+	4.44904i	0.477487	+	0.146363i
$925$	−3.05623	+	22.5071i	−0.100488	+	0.740028i
$926$		−	21.0054i		−	0.690281i
$927$	3.80212	−	55.0734i	0.124878	−	1.80885i
$928$		−	1.65681i		−	0.0543874i
$929$	16.0115	−	27.7328i	0.525321	−	0.909882i	−0.474244	−	0.880393i	$-0.657279\pi$
$929$	16.0115	−	27.7328i	0.525321	−	0.909882i	0.999565	−	0.0294890i	$-0.00938799\pi$
$930$	21.9128	+	8.34187i	0.718549	+	0.273541i
$931$	0.000345634	−	0.147594i	1.13277e−5	−	0.00483718i
$932$	3.07997	+	5.33466i	0.100888	+	0.174742i
$933$	2.22412	+	9.61429i	0.0728143	+	0.314758i
$934$	9.30637	+	5.37304i	0.304514	+	0.175811i
$935$	−17.1172	−	11.4877i	−0.559792	−	0.375689i
$936$	1.20655	−	17.4768i	0.0394375	−	0.571248i
$937$	1.71222			0.0559359			0.0279680	−	0.999609i	$-0.491096\pi$
$937$	1.71222			0.0559359			0.0279680	+	0.999609i	$0.491096\pi$
$938$	36.5091	+	0.0427484i	1.19207	+	0.00139579i
$939$	13.7597	−	12.8426i	0.449032	−	0.419101i
$940$	−10.0392	−	0.678500i	−0.327444	−	0.0221302i
$941$	27.4368	+	47.5220i	0.894415	+	1.54917i	0.834527	+	0.550968i	$0.185741\pi$
$941$	27.4368	+	47.5220i	0.894415	+	1.54917i	0.0598886	+	0.998205i	$0.480925\pi$
$942$	−19.9712	−	6.09615i	−0.650698	−	0.198623i
$943$	31.3013	−	54.2155i	1.01931	−	1.76550i
$944$	−6.65017			−0.216445
$945$	−17.6948	−	25.1375i	−0.575613	−	0.817723i
$946$	8.15639			0.265187
$947$	−12.9347	+	22.4036i	−0.420322	+	0.728019i	−0.995971	−	0.0896780i	$-0.971416\pi$
$947$	−12.9347	+	22.4036i	−0.420322	+	0.728019i	0.575649	+	0.817697i	$0.304750\pi$
$948$	−6.72194	−	2.05185i	−0.218318	−	0.0666410i
$949$	−1.65841	−	2.87245i	−0.0538343	−	0.0932437i
$950$	0.0833771	+	0.0645177i	0.00270511	+	0.00209323i
$951$	−39.5306	+	36.8956i	−1.28187	+	1.19642i
$952$	7.36296	+	0.00862127i	0.238635	+	0.000279417i
$953$	7.01251			0.227158			0.113579	−	0.993529i	$-0.463769\pi$
$953$	7.01251			0.227158			0.113579	+	0.993529i	$0.463769\pi$
$954$	−0.415326	+	0.203023i	−0.0134467	+	0.00657312i
$955$	−30.5365	+	45.5006i	−0.988138	+	1.47237i
$956$	−11.9037	−	6.87261i	−0.384994	−	0.222276i
$957$	−2.14260	−	9.26192i	−0.0692604	−	0.299395i
$958$	3.20350	+	5.54862i	0.103500	+	0.179268i
$959$	30.6133	+	17.7224i	0.988554	+	0.572286i
$960$	1.37792	−	3.61958i	0.0444721	−	0.116821i
$961$	2.82525	−	4.89347i	0.0911370	−	0.157854i
$962$		−	26.5271i		−	0.855269i
$963$	21.5678	+	14.5199i	0.695012	+	0.467897i
$964$		−	15.6105i		−	0.502780i
$965$	19.8691	+	40.4978i	0.639609	+	1.30367i
$966$	7.52125	−	24.5370i	0.241992	−	0.789464i
$967$	−33.0101	+	19.0584i	−1.06153	+	0.612877i	−0.925856	−	0.377876i	$-0.876654\pi$
$967$	−33.0101	+	19.0584i	−1.06153	+	0.612877i	−0.135677	+	0.990753i	$0.543321\pi$
$968$	−0.0128499	−	0.0222567i	−0.000413012	−	0.000715357i
$969$	−0.0972054	−	0.0296716i	−0.00312269	−	0.000953190i
$970$	19.8031	−	9.71583i	0.635840	−	0.311957i
$971$	16.6238			0.533484			0.266742	−	0.963768i	$-0.414053\pi$
$971$	16.6238			0.533484			0.266742	+	0.963768i	$0.414053\pi$
$972$	12.7495	−	8.96941i	0.408940	−	0.287694i
$973$	−12.4581	−	21.6366i	−0.399389	−	0.693636i
$974$	12.8218	+	7.40268i	0.410837	+	0.237197i
$975$	4.66469	+	50.3558i	0.149390	+	1.61268i
$976$	−7.58810	+	4.38099i	−0.242889	+	0.140232i
$977$	−22.9139	−	39.6880i	−0.733080	−	1.26973i	−0.955561	−	0.294795i	$-0.904749\pi$
$977$	−22.9139	−	39.6880i	−0.733080	−	1.26973i	0.222481	−	0.974937i	$-0.428585\pi$
$978$	13.3983	+	14.3552i	0.428431	+	0.459028i
$979$	18.1610	+	10.4852i	0.580427	+	0.335110i
$980$	14.0684	−	6.86144i	0.449399	−	0.219181i
$981$	−11.7519	−	7.91165i	−0.375210	−	0.252600i
$982$		−	13.1030i		−	0.418134i
$983$	−18.7423	−	10.8209i	−0.597787	−	0.345132i	0.170384	−	0.985378i	$-0.445499\pi$
$983$	−18.7423	−	10.8209i	−0.597787	−	0.345132i	−0.768170	+	0.640246i	$0.778833\pi$
$984$	4.36376	+	18.8634i	0.139112	+	0.601344i
$985$	−1.84608	+	27.3150i	−0.0588210	+	0.870329i
$986$	−2.30540	−	3.99307i	−0.0734189	−	0.127165i
$987$	15.0917	−	14.0527i	0.480373	−	0.447302i
$988$	−0.106629	−	0.0615623i	−0.00339232	−	0.00195856i
$989$		−	13.7886i		−	0.438453i
$990$	3.02199	−	22.0162i	0.0960453	−	0.699719i
$991$	−37.0001			−1.17535			−0.587674	−	0.809098i	$-0.699956\pi$
$991$	−37.0001			−1.17535			−0.587674	+	0.809098i	$0.699956\pi$
$992$	−5.24289	−	3.02698i	−0.166462	−	0.0961068i
$993$	37.5787	−	35.0738i	1.19252	−	1.11303i
$994$	−19.1585	+	33.0939i	−0.607670	+	1.04967i
$995$	−10.3362	−	0.698572i	−0.327680	−	0.0221462i
$996$	6.74546	−	22.0984i	0.213738	−	0.700214i
$997$	−11.4148	+	19.7710i	−0.361510	+	0.626153i	−0.988210	−	0.153108i	$-0.951072\pi$
$997$	−11.4148	+	19.7710i	−0.361510	+	0.626153i	0.626700	+	0.779261i	$0.284405\pi$
$998$	−43.9560			−1.39140
$999$	18.3245	−	14.8793i	0.579763	−	0.470759i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bf.e.209.15	yes	32
3.2	odd	2		1890.2.bf.f.629.8		32
5.4	even	2		630.2.bf.f.209.2	yes	32
7.6	odd	2	inner	630.2.bf.e.209.2	✓	32
9.4	even	3		1890.2.bf.e.1259.5		32
9.5	odd	6		630.2.bf.f.419.15	yes	32
15.14	odd	2		1890.2.bf.e.629.12		32
21.20	even	2		1890.2.bf.f.629.9		32
35.34	odd	2		630.2.bf.f.209.15	yes	32
45.4	even	6		1890.2.bf.f.1259.9		32
45.14	odd	6	inner	630.2.bf.e.419.2	yes	32
63.13	odd	6		1890.2.bf.e.1259.12		32
63.41	even	6		630.2.bf.f.419.2	yes	32
105.104	even	2		1890.2.bf.e.629.5		32
315.104	even	6	inner	630.2.bf.e.419.15	yes	32
315.139	odd	6		1890.2.bf.f.1259.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bf.e.209.2	✓	32	7.6	odd	2	inner
630.2.bf.e.209.15	yes	32	1.1	even	1	trivial
630.2.bf.e.419.2	yes	32	45.14	odd	6	inner
630.2.bf.e.419.15	yes	32	315.104	even	6	inner
630.2.bf.f.209.2	yes	32	5.4	even	2
630.2.bf.f.209.15	yes	32	35.34	odd	2
630.2.bf.f.419.2	yes	32	63.41	even	6
630.2.bf.f.419.15	yes	32	9.5	odd	6
1890.2.bf.e.629.5		32	105.104	even	2
1890.2.bf.e.629.12		32	15.14	odd	2
1890.2.bf.e.1259.5		32	9.4	even	3
1890.2.bf.e.1259.12		32	63.13	odd	6
1890.2.bf.f.629.8		32	3.2	odd	2
1890.2.bf.f.629.9		32	21.20	even	2
1890.2.bf.f.1259.8		32	315.139	odd	6
1890.2.bf.f.1259.9		32	45.4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.65659 + 0.505669i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.150780 - 2.23098i) q^{5} +(-1.26622 + 1.18182i) q^{6} +(0.00309790 - 2.64575i) q^{7} +1.00000 q^{8} +(2.48860 + 1.67538i) q^{9} +(1.85669 + 1.24607i) q^{10} +(-2.86892 - 1.65637i) q^{11} +(-0.390374 - 1.68749i) q^{12} +(-2.91974 - 5.05714i) q^{13} +(2.28974 + 1.32556i) q^{14} +(1.37792 - 3.61958i) q^{15} +(-0.500000 + 0.866025i) q^{16} +2.78294i q^{17} +(-2.69522 + 1.31750i) q^{18} +0.0210849i q^{19} +(-2.00747 + 0.984910i) q^{20} +(1.34301 - 4.38136i) q^{21} +(2.86892 - 1.65637i) q^{22} +(-2.80015 - 4.85001i) q^{23} +(1.65659 + 0.505669i) q^{24} +(-4.95453 - 0.672775i) q^{25} +5.83948 q^{26} +(3.27540 + 4.03382i) q^{27} +(-2.29284 + 1.32019i) q^{28} +(1.43484 + 0.828404i) q^{29} +(2.44569 + 3.00310i) q^{30} +(5.24289 - 3.02698i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-3.91506 - 4.19466i) q^{33} +(-2.41010 - 1.39147i) q^{34} +(-5.90214 - 0.405838i) q^{35} +(0.206620 - 2.99288i) q^{36} -4.54272i q^{37} +(-0.0182600 - 0.0105424i) q^{38} +(-2.27958 - 9.85404i) q^{39} +(0.150780 - 2.23098i) q^{40} +(5.58921 + 9.68080i) q^{41} +(3.12287 + 3.35376i) q^{42} +(2.13226 + 1.23106i) q^{43} +3.31275i q^{44} +(4.11296 - 5.29939i) q^{45} +5.60031 q^{46} +(3.89705 + 2.24996i) q^{47} +(-1.26622 + 1.18182i) q^{48} +(-6.99998 - 0.0163925i) q^{49} +(3.05991 - 3.95436i) q^{50} +(-1.40725 + 4.61020i) q^{51} +(-2.91974 + 5.05714i) q^{52} +0.154097 q^{53} +(-5.13110 + 0.819671i) q^{54} +(-4.12791 + 6.15076i) q^{55} +(0.00309790 - 2.64575i) q^{56} +(-0.0106620 + 0.0349290i) q^{57} +(-1.43484 + 0.828404i) q^{58} +(3.32508 + 5.75921i) q^{59} +(-3.82361 + 0.616476i) q^{60} +(7.58810 + 4.38099i) q^{61} +6.05396i q^{62} +(4.44034 - 6.57901i) q^{63} +1.00000 q^{64} +(-11.7226 + 5.75136i) q^{65} +(5.59022 - 1.29321i) q^{66} +(11.9504 - 6.89958i) q^{67} +(2.41010 - 1.39147i) q^{68} +(-2.18621 - 9.45044i) q^{69} +(3.30254 - 4.90849i) q^{70} +14.4531i q^{71} +(2.48860 + 1.67538i) q^{72} +0.567999 q^{73} +(3.93411 + 2.27136i) q^{74} +(-7.86744 - 3.61987i) q^{75} +(0.0182600 - 0.0105424i) q^{76} +(-4.39124 + 7.58532i) q^{77} +(9.67364 + 2.95285i) q^{78} +(2.02885 - 3.51406i) q^{79} +(1.85669 + 1.24607i) q^{80} +(3.38623 + 8.33867i) q^{81} -11.1784 q^{82} +(11.5525 + 6.66983i) q^{83} +(-4.46587 + 1.02760i) q^{84} +(6.20868 + 0.419612i) q^{85} +(-2.13226 + 1.23106i) q^{86} +(1.95804 + 2.09788i) q^{87} +(-2.86892 - 1.65637i) q^{88} -6.33024 q^{89} +(2.53293 + 6.21162i) q^{90} +(-13.3890 + 7.70923i) q^{91} +(-2.80015 + 4.85001i) q^{92} +(10.2160 - 2.36331i) q^{93} +(-3.89705 + 2.24996i) q^{94} +(0.0470399 + 0.00317918i) q^{95} +(-0.390374 - 1.68749i) q^{96} +(4.93235 - 8.54307i) q^{97} +(3.51419 - 6.05396i) q^{98} +(-4.36455 - 8.92857i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} - 6 q^{9} - 24 q^{11} - 16 q^{15} - 16 q^{16} + 6 q^{18} + 2 q^{21} + 24 q^{22} - 24 q^{23} - 58 q^{25} - 36 q^{29} - 10 q^{30} - 16 q^{32} - 48 q^{35} - 66 q^{39}+ \cdots + 58 q^{99}+O(q^{100}) \) 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 - 6 * q^9 - 24 * q^11 - 16 * q^15 - 16 * q^16 + 6 * q^18 + 2 * q^21 + 24 * q^22 - 24 * q^23 - 58 * q^25 - 36 * q^29 - 10 * q^30 - 16 * q^32 - 48 * q^35 - 66 * q^39 + 2 * q^42 - 54 * q^43 + 48 * q^46 + 32 * q^49 + 50 * q^50 - 26 * q^51 - 24 * q^53 + 110 * q^57 + 36 * q^58 + 26 * q^60 + 20 * q^63 + 32 * q^64 - 90 * q^65 - 66 * q^67 + 36 * q^70 - 6 * q^72 + 12 * q^74 + 18 * q^77 + 60 * q^78 + 34 * q^79 + 2 * q^81 - 4 * q^84 + 4 * q^85 + 54 * q^86 - 24 * q^88 + 16 * q^91 - 24 * q^92 + 28 * q^93 + 12 * q^95 - 64 * q^98 + 58 * q^99

Introduction

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