LMFDB - Embedded newform 630.2.bf.e.209.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(209,630)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.03057532734$
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			209.2
Character	$\chi$	$=$	630.209
Dual form			630.2.bf.e.419.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-1.65659 - 0.505669i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.150780 + 2.23098i) q^{5} +(1.26622 - 1.18182i) q^{6} +(-2.28974 + 1.32556i) q^{7} +1.00000 q^{8} +(2.48860 + 1.67538i) q^{9} +O(q^{10})$	\(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} +(-2.28974 + 1.32556i) 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} +(-0.00309790 - 2.64575i) 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} +(4.46346 - 1.03806i) 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} +(-2.61204 - 5.30822i) 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} +(-1.33274 + 4.38450i) 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} +(3.48579 - 6.07036i) 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} +(-2.28974 + 1.32556i) 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} +(-7.91904 - 0.537394i) 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} +(5.90308 + 0.392015i) 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} +(8.76470 - 0.0102626i) 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} +(-3.13071 - 3.34644i) 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}+O(q^{10}) $ 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 - 6 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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
$7$	−2.28974	+	1.32556i	−0.865439	+	0.501014i
$7$	−2.28974	+	1.32556i	−0.865439	+	0.501014i
$8$	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	$0.133752\pi$
$13$	2.91974	+	5.05714i	0.809790	+	1.40260i	−0.103219	+	0.994659i	$0.532914\pi$
$14$	−0.00309790	−	2.64575i	−0.000827948	−	0.707106i
$15$	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	$-0.890425\pi$
$17$		−	2.78294i		−	0.674962i	0.941332	−	0.337481i	$-0.109575\pi$
$18$	−2.69522	+	1.31750i	−0.635269	+	0.310538i
$19$		−	0.0210849i		−	0.00483720i	−0.999997	−	0.00241860i	$-0.999230\pi$
$19$		−	0.0210849i		−	0.00483720i	0.999997	−	0.00241860i	$-0.000769865\pi$
$20$	2.00747	−	0.984910i	0.448885	−	0.220233i
$21$	4.46346	−	1.03806i	0.974006	−	0.226523i
$22$	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	−0.890477	−	0.455028i	$-0.849629\pi$
$31$	−5.24289	+	3.02698i	−0.941650	+	0.543662i	−0.0511731	+	0.998690i	$0.516296\pi$
$32$	−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
$35$	−2.61204	−	5.30822i	−0.441516	−	0.897253i
$36$	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	$-0.828911\pi$
$41$	−5.58921	−	9.68080i	−0.872888	−	1.51189i	−0.0138932	−	0.999903i	$-0.504422\pi$
$42$	−1.33274	+	4.38450i	−0.205647	+	0.676542i
$43$	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	0.188084	−	0.982153i	$-0.439772\pi$
$47$	−3.89705	−	2.24996i	−0.568443	−	0.328191i	−0.756527	+	0.653962i	$0.773106\pi$
$48$	1.26622	−	1.18182i	0.182763	−	0.170580i
$49$	3.48579	−	6.07036i	0.497971	−	0.867194i
$50$	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
$56$	−2.28974	+	1.32556i	−0.305979	+	0.177135i
$57$	−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	0.564232	−	0.825617i	$-0.309172\pi$
$59$	−3.32508	−	5.75921i	−0.432889	−	0.749786i	−0.997121	+	0.0758307i	$0.975839\pi$
$60$	−3.82361	+	0.616476i	−0.493625	+	0.0795867i
$61$	−7.58810	−	4.38099i	−0.971556	−	0.560928i	−0.0718459	−	0.997416i	$-0.522889\pi$
$61$	−7.58810	−	4.38099i	−0.971556	−	0.560928i	−0.899710	+	0.436487i	$0.856222\pi$
$62$		−	6.05396i		−	0.768854i
$63$	−7.91904	−	0.537394i	−0.997705	−	0.0677052i
$64$	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
$70$	5.90308	+	0.392015i	0.705553	+	0.0468548i
$71$			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	$-0.510582\pi$
$73$	−0.567999			−0.0664793			−0.0332396	+	0.999447i	$0.510582\pi$
$74$	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
$77$	8.76470	−	0.0102626i	0.998830	−	0.00116953i
$78$	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	−0.293431	−	0.955980i	$-0.594797\pi$
$83$	−11.5525	−	6.66983i	−1.26805	−	0.732109i	−0.974619	+	0.223872i	$0.928130\pi$
$84$	−3.13071	−	3.34644i	−0.341589	−	0.365126i
$85$	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	$-0.391094\pi$
$89$	6.33024			0.671004			0.335502	+	0.942040i	$0.391094\pi$
$90$	−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	$0.333629\pi$
$97$	−4.93235	+	8.54307i	−0.500804	+	0.867418i	−1.00000		0.000928464i	$0.999704\pi$
$98$	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	−0.999700	−	0.0245031i	$-0.992200\pi$
$101$	−4.81017	+	8.33145i	−0.478630	+	0.829011i	0.521070	+	0.853514i	$0.325533\pi$
$102$	−3.28892	−	3.52381i	−0.325652	−	0.348909i
$103$	9.20075	+	15.9362i	0.906577	+	1.57024i	0.818787	+	0.574098i	$0.194647\pi$
$103$	9.20075	+	15.9362i	0.906577	+	1.57024i	0.0877898	+	0.996139i	$0.472020\pi$
$104$	2.91974	+	5.05714i	0.286304	+	0.495893i
$105$	1.64289	+	10.1144i	0.160329	+	0.987064i
$106$	−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
$112$	−0.00309790	−	2.64575i	−0.000292724	−	0.250000i
$113$	−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
$119$	3.68895	+	6.37220i	0.338165	+	0.584139i
$120$	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
$126$	4.42492	−	6.58939i	0.394203	−	0.587030i
$127$			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	0.915000	−	0.403453i	$-0.132190\pi$
$131$	1.23726	+	2.14299i	0.108100	+	0.187234i	−0.806901	+	0.590687i	$0.798857\pi$
$132$	1.67516	−	5.48787i	0.145804	−	0.477658i
$133$	0.0279492	+	0.0482788i	0.00242350	+	0.00418630i
$134$			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	−0.804798	−	0.593549i	$-0.797726\pi$
$139$	−8.17233	+	4.71830i	−0.693168	+	0.400201i	0.111630	+	0.993750i	$0.464393\pi$
$140$	−3.29103	+	4.91621i	−0.278143	+	0.415495i
$141$	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
$147$	−8.84413	+	8.29345i	−0.729452	+	0.684032i
$148$	−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	0.518693	−	0.854961i	$-0.326419\pi$
$157$	−6.02781	−	10.4405i	−0.481071	−	0.833240i	−0.999764	+	0.0217208i	$0.993085\pi$
$158$	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	−0.775693	−	0.631111i	$-0.782599\pi$
$167$	−7.97315	+	4.60330i	−0.616981	+	0.356214i	0.158712	+	0.987325i	$0.449266\pi$
$168$	4.46346	−	1.03806i	0.344363	−	0.0800879i
$169$	−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	0.978095	−	0.208160i	$-0.0667474\pi$
$173$	16.9261	+	9.77231i	1.28687	+	0.742975i	0.308776	+	0.951135i	$0.400081\pi$
$174$	2.79584	−	0.646774i	0.211952	−	0.0490318i
$175$	12.2364	−	5.02704i	0.924983	−	0.380008i
$176$	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	$-0.880883\pi$
$181$		−	9.83581i		−	0.731090i	0.930794	−	0.365545i	$-0.119117\pi$
$182$	13.3709	−	7.74056i	0.991115	−	0.573769i
$183$	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
$189$	12.8469	+	4.89466i	0.934473	+	0.356034i
$190$	−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
$196$	−6.99998	+	0.0163925i	−0.499999	+	0.00117089i
$197$	−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	$0.0525087\pi$
$199$			4.63305i			0.328428i	−0.986425	+	0.164214i	$0.947491\pi$
$200$	−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
$203$	−4.38350	+	0.00513262i	−0.307661	+	0.000360240i
$204$	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
$210$	−9.58076	−	3.63442i	−0.661135	−	0.250799i
$211$	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	−0.737711	−	0.675116i	$-0.764093\pi$
$223$	3.22276	−	5.58199i	0.215812	−	0.373797i	0.953523	+	0.301319i	$0.0974268\pi$
$224$	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	0.493782	−	0.869586i	$-0.335614\pi$
$227$	−0.186994	−	0.107961i	−0.0124113	−	0.00716564i	−0.506193	+	0.862420i	$0.668948\pi$
$228$	0.0355804	−	0.00823097i	0.00235637	−	0.000545109i
$229$	13.7857	−	7.95917i	0.910984	−	0.525957i	0.0302361	−	0.999543i	$-0.490374\pi$
$229$	13.7857	−	7.95917i	0.910984	−	0.525957i	0.880748	+	0.473586i	$0.157041\pi$
$230$	−0.844416	+	12.4942i	−0.0556791	+	0.823841i
$231$	−14.5247	−	4.41504i	−0.955657	−	0.290488i
$232$	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
$238$	−7.36296	+	0.00862127i	−0.477270	+	0.000558834i
$239$	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	−0.00321270	−	0.999995i	$-0.501023\pi$
$241$	−13.5191	−	7.80524i	−0.870840	−	0.502780i	−0.867627	+	0.497215i	$0.834356\pi$
$242$	0.0256998			0.00165205
$243$	−1.39299	−	15.5261i	−0.0893601	−	0.995999i
$244$			8.76198i			0.560928i
$245$	13.0172	+	8.69202i	0.831641	+	0.555313i
$246$	−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	$-0.658974\pi$
$251$	−15.1753			−0.957856			−0.478928	+	0.877854i	$0.658974\pi$
$252$	3.49412	+	7.12679i	0.220109	+	0.448945i
$253$			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	−0.490519	−	0.871431i	$-0.663193\pi$
$257$	0.303030	−	0.174954i	0.0189025	−	0.0109134i	0.509421	+	0.860517i	$0.329859\pi$
$258$	4.15479	−	0.961147i	0.258666	−	0.0598384i
$259$	6.02164	+	10.4016i	0.374167	+	0.646327i
$260$	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
$266$	−0.0557852		6.53187e-5i	−0.00342041		4.00495e-6i
$267$	−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	$-0.357806\pi$
$269$	14.1709			0.864014			0.432007	+	0.901870i	$0.357806\pi$
$270$	1.05500	+	11.5710i	0.0642053	+	0.704186i
$271$			19.1244i			1.16172i	0.814002	+	0.580862i	$0.197285\pi$
$271$			19.1244i			1.16172i	−0.814002	+	0.580862i	$0.802715\pi$
$272$	2.41010	+	1.39147i	0.146134	+	0.0843703i
$273$	18.2817	+	19.5414i	1.10646	+	1.18270i
$274$	−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
$280$	−2.61204	−	5.30822i	−0.156099	−	0.317227i
$281$	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	0.727701	−	0.685894i	$-0.240589\pi$
$283$	−3.87175	−	6.70606i	−0.230152	−	0.398634i	−0.957853	+	0.287260i	$0.907256\pi$
$284$	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	−0.728862	−	0.684661i	$-0.759950\pi$
$293$	−8.56477	+	4.94487i	−0.500359	+	0.288882i	0.228503	+	0.973543i	$0.426617\pi$
$294$	−2.76027	−	11.8060i	−0.160982	−	0.688538i
$295$	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
$301$	−6.51415	+	0.00762740i	−0.375470	+	0.000439636i
$302$	−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	$-0.596278\pi$
$307$	−10.4384			−0.595752			−0.297876	+	0.954605i	$0.596278\pi$
$308$	−4.39124	−	7.58532i	−0.250214	−	0.432214i
$309$	−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	0.773884	−	0.633327i	$-0.218311\pi$
$311$	−2.84870	−	4.93410i	−0.161535	−	0.279787i	−0.935419	+	0.353540i	$0.884978\pi$
$312$	−2.27958	−	9.85404i	−0.129056	−	0.557875i
$313$	−5.43340	+	9.41092i	−0.307114	+	0.531937i	−0.977730	−	0.209868i	$-0.932697\pi$
$313$	−5.43340	+	9.41092i	−0.307114	+	0.531937i	0.670616	+	0.741805i	$0.266030\pi$
$314$	12.0556			0.680337
$315$	2.39295	−	17.5862i	0.134827	−	0.990869i
$316$	−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
$322$	−12.8232	+	7.42353i	−0.714611	+	0.413697i
$323$	−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
$329$	11.9057	−	0.0139403i	0.656381	−	0.000768555i
$330$	−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
$336$	−1.33274	+	4.38450i	−0.0727071	+	0.239194i
$337$	−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	−0.497754	−	0.867318i	$-0.665842\pi$
$349$	−27.9803	−	16.1544i	−1.49775	−	0.864727i	−0.999997	+	0.00259132i	$0.999175\pi$
$350$	−1.76465	+	13.1105i	−0.0943243	+	0.700787i
$351$	10.8363	−	28.3419i	0.578397	−	1.51278i
$352$			3.31275i			0.176570i
$353$	−13.4192	−	7.74759i	−0.714233	−	0.412362i	0.0983936	−	0.995148i	$-0.468630\pi$
$353$	−13.4192	−	7.74759i	−0.714233	−	0.412362i	−0.812626	+	0.582785i	$0.801963\pi$
$354$	−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
$357$	−2.88885	−	12.4215i	−0.152894	−	0.657417i
$358$	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
$364$	0.0180901	+	15.4498i	0.000948179	+	0.809789i
$365$	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	−0.682423	−	0.730958i	$-0.739074\pi$
$367$	5.59040	−	9.68286i	0.291817	−	0.505441i	0.974239	+	0.225516i	$0.0724070\pi$
$368$	5.60031			0.291936
$369$	2.30969	−	33.4556i	0.120238	−	1.74163i
$370$	−5.66055	+	8.43445i	−0.294278	+	0.438486i
$371$	−0.352842	+	0.204265i	−0.0183187	+	0.0106049i
$372$	−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
$378$	−10.6623	+	8.67839i	−0.548412	+	0.446368i
$379$	−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	−0.946322	−	0.323225i	$-0.895233\pi$
$383$	−22.3017	+	12.8759i	−1.13956	+	0.657927i	−0.193240	+	0.981152i	$0.561900\pi$
$384$	1.26622	−	1.18182i	0.0646165	−	0.0603093i
$385$	−1.29865	+	19.5554i	−0.0661852	+	0.996636i
$386$		−	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
$392$	3.48579	−	6.07036i	0.176059	−	0.306599i
$393$	−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	$-0.612635\pi$
$397$	−13.8085			−0.693031			−0.346515	+	0.938044i	$0.612635\pi$
$398$	−4.01234	−	2.31652i	−0.201120	−	0.116117i
$399$	−0.0218873	−	0.0941113i	−0.00109574	−	0.00471146i
$400$	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	−0.357103	−	0.934065i	$-0.616235\pi$
$409$	5.52654	−	3.19075i	0.273270	−	0.157772i	0.630373	+	0.776293i	$0.282902\pi$
$410$	−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	0.888017	−	0.459810i	$-0.152082\pi$
$419$	0.937538	+	1.62386i	0.0458017	+	0.0793309i	−0.842216	+	0.539141i	$0.818749\pi$
$420$	7.93788	−	6.47998i	0.387329	−	0.316190i
$421$	−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
$427$	23.1820	−	0.0271437i	1.12186	−	0.00131358i
$428$	−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	$-0.587402\pi$
$433$	−11.2842			−0.542285			−0.271143	+	0.962539i	$0.587402\pi$
$434$	8.02488	+	13.8620i	0.385207	+	0.665397i
$435$	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	0.0324860	−	0.999472i	$-0.489658\pi$
$439$	−17.1147	−	9.88117i	−0.816839	−	0.471602i	−0.849325	+	0.527870i	$0.822991\pi$
$440$	4.12791	−	6.15076i	0.196790	−	0.293226i
$441$	18.8449	−	9.26665i	0.897375	−	0.441269i
$442$			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
$448$	−2.28974	+	1.32556i	−0.108180	+	0.0626267i
$449$		−	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
$455$	19.2179	−	28.7081i	0.900950	−	1.34586i
$456$	−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	−0.666013	−	0.745940i	$-0.732000\pi$
$461$	6.72032	−	11.6399i	0.312997	−	0.542126i	0.979010	+	0.203814i	$0.0653338\pi$
$462$	11.0859	−	10.3713i	0.515763	−	0.482515i
$463$	−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	$0.0799818\pi$
$467$			10.7461i			0.497269i	−0.968597	+	0.248634i	$0.920018\pi$
$468$	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	−0.929884	−	0.367853i	$-0.880093\pi$
$479$	−3.20350	+	5.54862i	−0.146372	+	0.253523i	0.783512	+	0.621376i	$0.213426\pi$
$480$	−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
$483$	−17.5330	−	18.7411i	−0.797777	−	0.852749i
$484$	−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
$490$	−14.0361	+	6.92726i	−0.634088	+	0.312942i
$491$	−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
$497$	−19.1585	−	33.0939i	−0.859375	−	1.48446i
$498$	−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	$-0.988286\pi$
$503$		−	1.65037i		−	0.0735862i	0.999323	−	0.0367931i	$-0.0117143\pi$
$504$	−7.91904	−	0.537394i	−0.352742	−	0.0239374i
$505$	−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	0.973631	−	0.228128i	$-0.0732606\pi$
$509$	6.52579	+	11.3030i	0.289250	+	0.500996i	−0.684381	+	0.729125i	$0.739927\pi$
$510$	8.35745	−	6.80620i	0.370074	−	0.301384i
$511$	1.30057	−	0.752916i	0.0575338	−	0.0333070i
$512$	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
$518$	−12.0189	+	0.0140729i	−0.528081	+	0.000618328i
$519$	−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	$-0.307774\pi$
$521$	25.9230			1.13571			0.567854	+	0.823129i	$0.307774\pi$
$522$	−4.95862	−	0.342330i	−0.217033	−	0.0149834i
$523$	11.8695			0.519016			0.259508	−	0.965741i	$-0.416440\pi$
$523$	11.8695			0.519016			0.259508	+	0.965741i	$0.416440\pi$
$524$	1.23726	−	2.14299i	0.0540499	−	0.0936171i
$525$	−22.8127	+	2.14019i	−0.995628	+	0.0934056i
$526$	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
$546$	−26.0643	+	6.06172i	−1.11545	+	0.259418i
$547$	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
$553$	0.0125703	+	10.7356i	0.000534544	+	0.456526i
$554$	−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
$560$	5.90308	+	0.392015i	0.249451	+	0.0165657i
$561$	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	−0.695117	−	0.718897i	$-0.744647\pi$
$563$	−9.96779	+	5.75491i	−0.420092	+	0.242540i	0.275025	+	0.961437i	$0.411314\pi$
$564$	2.27548	−	7.45455i	0.0958148	−	0.313893i
$565$	34.8893	−	17.1175i	1.46781	−	0.720137i
$566$	7.74350			0.325483
$567$	−18.8070	−	14.6047i	−0.789818	−	0.613341i
$568$			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
$574$	−25.5957	+	14.8176i	−1.06834	+	0.618477i
$575$	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	$-0.685444\pi$
$577$	−26.4319			−1.10038			−0.550188	+	0.835041i	$0.685444\pi$
$578$	−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
$581$	35.2934	−	0.0413249i	1.46422	−	0.00171445i
$582$	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	0.968611	−	0.248581i	$-0.0799641\pi$
$587$	29.9856	+	17.3122i	1.23764	+	0.714552i	0.269028	+	0.963132i	$0.413297\pi$
$588$	11.6044	+	3.51252i	0.478558	+	0.144854i
$589$	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	$-0.825986\pi$
$593$		−	25.3186i		−	1.03971i	0.854255	−	0.519855i	$-0.174014\pi$
$594$	−16.0784	−	6.14744i	−0.659705	−	0.252232i
$595$	−14.7725	+	7.26916i	−0.605612	+	0.298007i
$596$	−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	$0.0463602\pi$
$601$	39.4649	+	22.7851i	1.60981	+	0.929422i	0.620393	+	0.784291i	$0.286973\pi$
$602$	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	$-0.880922\pi$
$607$	−19.2637	−	33.3657i	−0.781890	−	1.35427i	0.148949	−	0.988845i	$-0.452411\pi$
$608$	−0.0182600	+	0.0105424i	−0.000740542	+	0.000427552i
$609$	7.26427	+	2.20810i	0.294363	+	0.0894767i
$610$	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
$616$	8.76470	−	0.0102626i	0.353140	−	0.000413490i
$617$	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	0.843449	−	0.537210i	$-0.180522\pi$
$619$	19.9022	+	11.4905i	0.799936	+	0.461843i	−0.0435128	+	0.999053i	$0.513855\pi$
$620$	−7.54366	+	11.2404i	−0.302961	+	0.451424i
$621$	−10.3924	+	27.1811i	−0.417035	+	1.09074i
$622$	5.69741			0.228445
$623$	−14.4946	+	8.39109i	−0.580713	+	0.336182i
$624$	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
$630$	14.0336	+	10.8654i	0.559112	+	0.432890i
$631$	−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
$637$	40.8762	−	0.0957238i	1.61958	−	0.00379271i
$638$	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	0.845248	−	0.534374i	$-0.179453\pi$
$643$	−1.01830	−	1.76375i	−0.0401578	−	0.0695554i	−0.885406	+	0.464819i	$0.846119\pi$
$644$	−0.0173492	−	14.8170i	−0.000683654	−	0.583872i
$645$	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	$0.184275\pi$
$647$			27.8332i			1.09424i	−0.837055	+	0.547118i	$0.815725\pi$
$648$	3.38623	+	8.33867i	0.133024	+	0.327574i
$649$			22.0303i			0.864766i
$650$	28.9319	+	3.92865i	1.13480	+	0.154095i
$651$	−20.2592	+	18.9532i	−0.794021	+	0.742835i
$652$	−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	−0.571381	−	0.820685i	$-0.693592\pi$
$661$	−3.76232	+	2.17218i	−0.146337	+	0.0844879i	0.425044	+	0.905173i	$0.360259\pi$
$662$	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
$665$	−0.111923	+	0.0550746i	−0.00434019	+	0.00213570i
$666$	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
$672$	−3.13071	−	3.34644i	−0.120770	−	0.129092i
$673$	−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	0.549032	−	0.835802i	$-0.314997\pi$
$677$	2.59469	+	1.49804i	0.0997219	+	0.0575745i	−0.449310	+	0.893376i	$0.648330\pi$
$678$	−28.7911	−	8.78839i	−1.10572	−	0.337516i
$679$	−0.0305598	−	26.0995i	−0.00117278	−	1.00161i
$680$	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
$686$	−16.0714	−	9.20373i	−0.613611	−	0.351400i
$687$	−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	−0.110325	−	0.993896i	$-0.535189\pi$
$691$	−26.9763	−	15.5748i	−1.02623	−	0.592492i	−0.915901	+	0.401404i	$0.868522\pi$
$692$		−	19.5446i		−	0.742975i
$693$	21.8290	+	14.6586i	0.829215	+	0.556836i
$694$	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
$700$	−10.4717	−	8.08349i	−0.395794	−	0.305527i
$701$			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
$707$	−0.0298028	−	25.4530i	−0.00112085	−	0.957258i
$708$	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
$714$	12.2018	+	3.70894i	0.456641	+	0.138804i
$715$	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	$-0.926504\pi$
$719$	−52.2052			−1.94692			−0.973462	+	0.228848i	$0.926504\pi$
$720$	−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	−0.591906	−	0.806007i	$-0.701624\pi$
$727$	10.8410	−	18.7771i	0.402069	−	0.696404i	0.993976	+	0.109602i	$0.0349578\pi$
$728$	−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	0.934058	−	0.357122i	$-0.116242\pi$
$733$	4.27097	+	7.39754i	0.157752	+	0.273234i	−0.776306	+	0.630357i	$0.782909\pi$
$734$	5.59040	+	9.68286i	0.206346	+	0.357401i
$735$	−17.1690	−	20.9816i	−0.633288	−	0.773917i
$736$	−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
$742$	−0.000477378	−	0.407703i	−1.75251e−5	−	0.0149672i
$743$	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
$749$	−19.8443	+	11.4881i	−0.725097	+	0.419768i
$750$	−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
$756$	−2.18454	−	13.5731i	−0.0794510	−	0.493647i
$757$		−	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	$0.0544828\pi$
$761$	17.6608	+	30.5893i	0.640202	+	1.10886i	−0.345185	+	0.938535i	$0.612184\pi$
$762$	20.2509	+	21.6972i	0.733613	+	0.786005i
$763$	10.8129	−	6.25970i	0.391452	−	0.226616i
$764$			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	0.0726000	−	0.997361i	$-0.476870\pi$
$769$	26.9721	−	15.5724i	0.972640	−	0.561554i	0.900040	+	0.435807i	$0.143537\pi$
$770$	−16.2862	−	10.9024i	−0.586912	−	0.392894i
$771$	−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	$0.0693028\pi$
$773$			12.0111i			0.432011i	−0.976392	+	0.216005i	$0.930697\pi$
$774$	−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
$777$	−4.71561	−	20.2762i	−0.169172	−	0.727406i
$778$	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	$0.246158\pi$
$787$	27.0080	+	46.7792i	0.962731	+	1.66750i	0.247141	+	0.968980i	$0.420509\pi$
$788$	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	−0.291193	−	0.956664i	$-0.594052\pi$
$797$	11.0584	−	6.38454i	0.391707	−	0.226152i	0.682899	+	0.730512i	$0.260719\pi$
$798$	0.0924464	+	0.0281007i	0.00327257	+	0.000994754i
$799$	−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
$805$	−18.4308	+	27.5323i	−0.649601	+	0.970385i
$806$	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	$0.0396043\pi$
$811$			7.06824i			0.248199i	−0.992270	+	0.124100i	$0.960396\pi$
$812$	2.19620	+	3.79366i	0.0770713	+	0.133131i
$813$	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
$819$	−20.4039	−	41.6167i	−0.712969	−	1.45421i
$820$	−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
$826$	−15.2271	+	8.81518i	−0.529820	+	0.306719i
$827$	−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	$-0.792130\pi$
$829$		−	34.9888i		−	1.21521i	0.794239	−	0.607605i	$-0.207870\pi$
$830$	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
$833$	−16.8934	−	9.70076i	−0.585323	−	0.336111i
$834$	−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	−0.891738	−	0.452552i	$-0.850514\pi$
$839$	−1.56260	+	2.70651i	−0.0539470	+	0.0934390i	0.837791	+	0.545991i	$0.183847\pi$
$840$	1.64289	+	10.1144i	0.0566849	+	0.348980i
$841$	−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	$-0.609371\pi$
$853$	18.8954	−	32.7278i	0.646967	−	1.12058i	0.983844	−	0.179030i	$-0.0572960\pi$
$854$	−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	0.0584850	−	0.998288i	$-0.481373\pi$
$857$	−22.7409	−	13.1295i	−0.776815	−	0.448495i	−0.835300	+	0.549794i	$0.814706\pi$
$858$	−22.8619	−	24.4946i	−0.780493	−	0.836234i
$859$	24.1275	−	13.9300i	0.823221	−	0.475287i	−0.0283052	−	0.999599i	$-0.509011\pi$
$859$	24.1275	−	13.9300i	0.823221	−	0.475287i	0.851526	+	0.524313i	$0.175678\pi$
$860$	5.49294	+	0.371239i	0.187308	+	0.0126591i
$861$	−34.9964	−	37.4079i	−1.19268	−	1.27486i
$862$	−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
$868$	−16.0173	+	0.0187546i	−0.543662	+	0.000636571i
$869$	−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
$875$	9.37021	+	28.0571i	0.316771	+	0.948502i
$876$	−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	$-0.624892\pi$
$881$	−22.6988			−0.764741			−0.382370	+	0.924009i	$0.624892\pi$
$882$	−1.39728	+	20.9535i	−0.0470487	+	0.705540i
$883$		−	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	0.391865	−	0.920023i	$-0.371830\pi$
$887$	41.2357	−	23.8075i	1.38456	−	0.799376i	0.992696	+	0.120647i	$0.0384968\pi$
$888$	−2.29712	+	7.52544i	−0.0770862	+	0.252537i
$889$	−22.7140	−	39.2356i	−0.761802	−	1.31592i
$890$	−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
$896$	−0.00309790	−	2.64575i	−0.000103494	−	0.0883883i
$897$	−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
$903$	10.7952	+	3.28137i	0.359240	+	0.109197i
$904$	−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
$910$	15.2530	+	30.9973i	0.505631	+	1.02755i
$911$	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
$924$	3.43883	+	14.7863i	0.113129	+	0.486434i
$925$	−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	$0.342721\pi$
$929$	−16.0115	+	27.7328i	−0.525321	+	0.909882i	−0.999565	+	0.0294890i	$0.990612\pi$
$930$	−21.9128	−	8.34187i	−0.718549	−	0.273541i
$931$	−0.127993	−	0.0734975i	−0.00419479	−	0.00240878i
$932$	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	$-0.508904\pi$
$937$	−1.71222			−0.0559359			−0.0279680	+	0.999609i	$0.508904\pi$
$938$	−18.2916	−	31.5965i	−0.597242	−	1.03166i
$939$	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	$-0.814259\pi$
$941$	−27.4368	−	47.5220i	−0.894415	−	1.54917i	−0.0598886	−	0.998205i	$-0.519075\pi$
$942$	−19.9712	−	6.09615i	−0.650698	−	0.198623i
$943$	−31.3013	+	54.2155i	−1.01931	+	1.76550i
$944$	6.65017			0.216445
$945$	−12.8569	+	27.9231i	−0.418236	+	0.908338i
$946$	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
$952$	3.68895	+	6.37220i	0.119560	+	0.206524i
$953$	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
$959$	−0.0414182	−	35.3731i	−0.00133746	−	1.14226i
$960$	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
$966$	24.9967	−	5.81345i	0.804257	−	0.187045i
$967$	−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	$-0.585947\pi$
$971$	−16.6238			−0.533484			−0.266742	+	0.963768i	$0.585947\pi$
$972$	−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
$980$	1.01889	−	15.6193i	0.0325472	−	0.498940i
$981$	−11.7519	−	7.91165i	−0.375210	−	0.252600i
$982$		−	13.1030i		−	0.418134i
$983$	18.7423	+	10.8209i	0.597787	+	0.345132i	0.768170	−	0.640246i	$-0.221167\pi$
$983$	18.7423	+	10.8209i	0.597787	+	0.345132i	−0.170384	+	0.985378i	$0.554501\pi$
$984$	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
$987$	−19.7299	−	5.99725i	−0.628010	−	0.190894i
$988$	−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
$994$	38.2394	−	0.0447744i	1.21288	−	0.00142016i
$995$	−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	−0.626700	−	0.779261i	$-0.715595\pi$
$997$	11.4148	−	19.7710i	0.361510	−	0.626153i	0.988210	+	0.153108i	$0.0489281\pi$
$998$	−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.209.2	✓	32
3.2	odd	2		1890.2.bf.f.629.9		32
5.4	even	2		630.2.bf.f.209.15	yes	32
7.6	odd	2	inner	630.2.bf.e.209.15	yes	32
9.4	even	3		1890.2.bf.e.1259.12		32
9.5	odd	6		630.2.bf.f.419.2	yes	32
15.14	odd	2		1890.2.bf.e.629.5		32
21.20	even	2		1890.2.bf.f.629.8		32
35.34	odd	2		630.2.bf.f.209.2	yes	32
45.4	even	6		1890.2.bf.f.1259.8		32
45.14	odd	6	inner	630.2.bf.e.419.15	yes	32
63.13	odd	6		1890.2.bf.e.1259.5		32
63.41	even	6		630.2.bf.f.419.15	yes	32
105.104	even	2		1890.2.bf.e.629.12		32
315.104	even	6	inner	630.2.bf.e.419.2	yes	32
315.139	odd	6		1890.2.bf.f.1259.9		32

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.65659 - 0.505669i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.150780 + 2.23098i) q^{5} +(1.26622 - 1.18182i) q^{6} +(-2.28974 + 1.32556i) q^{7} +1.00000 q^{8} +(2.48860 + 1.67538i) q^{9} +O(q^{10})\)	\(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} +(-2.28974 + 1.32556i) 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} +(-0.00309790 - 2.64575i) 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} +(4.46346 - 1.03806i) 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} +(-2.61204 - 5.30822i) 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} +(-1.33274 + 4.38450i) 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} +(3.48579 - 6.07036i) 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} +(-2.28974 + 1.32556i) 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} +(-7.91904 - 0.537394i) 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} +(5.90308 + 0.392015i) 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} +(8.76470 - 0.0102626i) 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} +(-3.13071 - 3.34644i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} - 6 q^{9}+O(q^{10}) \) 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 - 6 * q^9	\( 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} - 6 q^{9} - 24 q^{11} - 16 q^{15} - 16 q^{16} + 6 q^{18} + 2 q^{21} + 24 q^{22} - 24 q^{23} - 58 q^{25} - 36 q^{29} - 10 q^{30} - 16 q^{32} - 48 q^{35} - 66 q^{39} + 2 q^{42} - 54 q^{43} + 48 q^{46} + 32 q^{49} + 50 q^{50} - 26 q^{51} - 24 q^{53} + 110 q^{57} + 36 q^{58} + 26 q^{60} + 20 q^{63} + 32 q^{64} - 90 q^{65} - 66 q^{67} + 36 q^{70} - 6 q^{72} + 12 q^{74} + 18 q^{77} + 60 q^{78} + 34 q^{79} + 2 q^{81} - 4 q^{84} + 4 q^{85} + 54 q^{86} - 24 q^{88} + 16 q^{91} - 24 q^{92} + 28 q^{93} + 12 q^{95} - 64 q^{98} + 58 q^{99}+O(q^{100}) \) 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

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