LMFDB - Embedded newform 1110.2.ba.b.529.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(529,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("1110.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.ba (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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			529.3
Character	$\chi$	$=$	1110.529
Dual form			1110.2.ba.b.619.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.56260 + 1.59947i) q^{5} -1.00000i q^{6} +(-0.998396 - 0.576424i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.56260 + 1.59947i) q^{5} -1.00000i q^{6} +(-0.998396 - 0.576424i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.16648 - 0.553515i) q^{10} +1.60140 q^{11} +(0.866025 - 0.500000i) q^{12} +(-1.89712 + 3.28591i) q^{13} -1.15285i q^{14} +(2.15298 - 0.603880i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.28940 - 5.69741i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-0.174421 - 0.100702i) q^{19} +(-0.603880 - 2.15298i) q^{20} +(0.576424 + 0.998396i) q^{21} +(0.800700 + 1.38685i) q^{22} +0.633422 q^{23} +(0.866025 + 0.500000i) q^{24} +(-0.116584 - 4.99864i) q^{25} -3.79425 q^{26} -1.00000i q^{27} +(0.998396 - 0.576424i) q^{28} +5.73899i q^{29} +(1.59947 + 1.56260i) q^{30} -8.34912i q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.38685 - 0.800700i) q^{33} +(3.28940 - 5.69741i) q^{34} +(2.48206 - 0.696182i) q^{35} -1.00000 q^{36} +(-6.07690 + 0.267030i) q^{37} -0.201405i q^{38} +(3.28591 - 1.89712i) q^{39} +(1.56260 - 1.59947i) q^{40} +(4.00330 - 6.93392i) q^{41} +(-0.576424 + 0.998396i) q^{42} -1.95146 q^{43} +(-0.800700 + 1.38685i) q^{44} +(-2.16648 - 0.553515i) q^{45} +(0.316711 + 0.548560i) q^{46} -4.65434i q^{47} +1.00000i q^{48} +(-2.83547 - 4.91118i) q^{49} +(4.27066 - 2.60029i) q^{50} +6.57881i q^{51} +(-1.89712 - 3.28591i) q^{52} +(7.47374 - 4.31497i) q^{53} +(0.866025 - 0.500000i) q^{54} +(-2.50234 + 2.56138i) q^{55} +(0.998396 + 0.576424i) q^{56} +(0.100702 + 0.174421i) q^{57} +(-4.97011 + 2.86950i) q^{58} +(10.3918 - 5.99970i) q^{59} +(-0.553515 + 2.16648i) q^{60} +(-11.3423 - 6.54846i) q^{61} +(7.23055 - 4.17456i) q^{62} -1.15285i q^{63} +1.00000 q^{64} +(-2.29127 - 8.16894i) q^{65} -1.60140i q^{66} +(-9.33087 - 5.38718i) q^{67} +6.57881 q^{68} +(-0.548560 - 0.316711i) q^{69} +(1.84394 + 1.80144i) q^{70} +(-5.52164 + 9.56376i) q^{71} +(-0.500000 - 0.866025i) q^{72} +4.32373i q^{73} +(-3.26970 - 5.12923i) q^{74} +(-2.39836 + 4.38724i) q^{75} +(0.174421 - 0.100702i) q^{76} +(-1.59883 - 0.923086i) q^{77} +(3.28591 + 1.89712i) q^{78} +(6.91117 + 3.99017i) q^{79} +(2.16648 + 0.553515i) q^{80} +(-0.500000 + 0.866025i) q^{81} +8.00660 q^{82} +(-12.4882 + 7.21006i) q^{83} -1.15285 q^{84} +(14.2528 + 3.64147i) q^{85} +(-0.975731 - 1.69002i) q^{86} +(2.86950 - 4.97011i) q^{87} -1.60140 q^{88} +(15.6356 - 9.02723i) q^{89} +(-0.603880 - 2.15298i) q^{90} +(3.78816 - 2.18710i) q^{91} +(-0.316711 + 0.548560i) q^{92} +(-4.17456 + 7.23055i) q^{93} +(4.03078 - 2.32717i) q^{94} +(0.433620 - 0.121624i) q^{95} +(-0.866025 + 0.500000i) q^{96} -2.93176 q^{97} +(2.83547 - 4.91118i) q^{98} +(0.800700 + 1.38685i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 18 q^{2} - 18 q^{4} + 4 q^{5} - 36 q^{8} + 18 q^{9}+O(q^{10}) $ 36 * q + 18 * q^2 - 18 * q^4 + 4 * q^5 - 36 * q^8 + 18 * q^9	$ 36 q + 18 q^{2} - 18 q^{4} + 4 q^{5} - 36 q^{8} + 18 q^{9} + 2 q^{10} + 4 q^{11} + 14 q^{13} + 2 q^{15} - 18 q^{16} - 18 q^{18} + 6 q^{19} - 2 q^{20} + 2 q^{22} + 20 q^{23} - 2 q^{25} + 28 q^{26} - 2 q^{30} + 18 q^{32} + 6 q^{33} - 20 q^{35} - 36 q^{36} - 20 q^{37} + 6 q^{39} - 4 q^{40} + 10 q^{41} - 2 q^{44} + 2 q^{45} + 10 q^{46} + 10 q^{49} - 4 q^{50} + 14 q^{52} + 12 q^{53} + 40 q^{55} - 8 q^{57} - 30 q^{58} + 18 q^{59} - 4 q^{60} - 6 q^{61} + 12 q^{62} + 36 q^{64} - 32 q^{65} - 36 q^{67} + 12 q^{69} - 40 q^{70} - 24 q^{71} - 18 q^{72} - 34 q^{74} + 8 q^{75} - 6 q^{76} + 24 q^{77} + 6 q^{78} - 2 q^{80} - 18 q^{81} + 20 q^{82} - 36 q^{83} + 26 q^{85} + 10 q^{87} - 4 q^{88} - 2 q^{90} - 36 q^{91} - 10 q^{92} - 12 q^{93} + 12 q^{94} + 18 q^{95} - 52 q^{97} - 10 q^{98} + 2 q^{99}+O(q^{100}) $ 36 * q + 18 * q^2 - 18 * q^4 + 4 * q^5 - 36 * q^8 + 18 * q^9 + 2 * q^10 + 4 * q^11 + 14 * q^13 + 2 * q^15 - 18 * q^16 - 18 * q^18 + 6 * q^19 - 2 * q^20 + 2 * q^22 + 20 * q^23 - 2 * q^25 + 28 * q^26 - 2 * q^30 + 18 * q^32 + 6 * q^33 - 20 * q^35 - 36 * q^36 - 20 * q^37 + 6 * q^39 - 4 * q^40 + 10 * q^41 - 2 * q^44 + 2 * q^45 + 10 * q^46 + 10 * q^49 - 4 * q^50 + 14 * q^52 + 12 * q^53 + 40 * q^55 - 8 * q^57 - 30 * q^58 + 18 * q^59 - 4 * q^60 - 6 * q^61 + 12 * q^62 + 36 * q^64 - 32 * q^65 - 36 * q^67 + 12 * q^69 - 40 * q^70 - 24 * q^71 - 18 * q^72 - 34 * q^74 + 8 * q^75 - 6 * q^76 + 24 * q^77 + 6 * q^78 - 2 * q^80 - 18 * q^81 + 20 * q^82 - 36 * q^83 + 26 * q^85 + 10 * q^87 - 4 * q^88 - 2 * q^90 - 36 * q^91 - 10 * q^92 - 12 * q^93 + 12 * q^94 + 18 * q^95 - 52 * q^97 - 10 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.56260	+	1.59947i	−0.698814	+	0.715303i
$5$	−1.56260	+	1.59947i	−0.698814	+	0.715303i
$6$		−	1.00000i		−	0.408248i
$7$	−0.998396	−	0.576424i	−0.377358	−	0.217868i	0.299310	−	0.954156i	$-0.403244\pi$
$7$	−0.998396	−	0.576424i	−0.377358	−	0.217868i	−0.676668	+	0.736288i	$0.736577\pi$
$8$	−1.00000			−0.353553
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−2.16648	−	0.553515i	−0.685100	−	0.175037i
$11$	1.60140			0.482840			0.241420	−	0.970421i	$-0.422387\pi$
$11$	1.60140			0.482840			0.241420	+	0.970421i	$0.422387\pi$
$12$	0.866025	−	0.500000i	0.250000	−	0.144338i
$13$	−1.89712	+	3.28591i	−0.526167	+	0.911349i	0.473368	+	0.880865i	$0.343038\pi$
$13$	−1.89712	+	3.28591i	−0.526167	+	0.911349i	−0.999535	+	0.0304838i	$0.990295\pi$
$14$		−	1.15285i		−	0.308112i
$15$	2.15298	−	0.603880i	0.555897	−	0.155921i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.28940	−	5.69741i	−0.797798	−	1.38183i	−0.921048	−	0.389450i	$-0.872665\pi$
$17$	−3.28940	−	5.69741i	−0.797798	−	1.38183i	0.123250	−	0.992376i	$-0.460668\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	−0.174421	−	0.100702i	−0.0400150	−	0.0231027i	0.479859	−	0.877346i	$-0.340688\pi$
$19$	−0.174421	−	0.100702i	−0.0400150	−	0.0231027i	−0.519874	+	0.854243i	$0.674021\pi$
$20$	−0.603880	−	2.15298i	−0.135032	−	0.481421i
$21$	0.576424	+	0.998396i	0.125786	+	0.217868i
$22$	0.800700	+	1.38685i	0.170710	+	0.295678i
$23$	0.633422			0.132078			0.0660388	−	0.997817i	$-0.478964\pi$
$23$	0.633422			0.132078			0.0660388	+	0.997817i	$0.478964\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	−0.116584	−	4.99864i	−0.0233168	−	0.999728i
$26$	−3.79425			−0.744113
$27$		−	1.00000i		−	0.192450i
$28$	0.998396	−	0.576424i	0.188679	−	0.108934i
$29$			5.73899i			1.06570i	0.846208	+	0.532852i	$0.178880\pi$
$29$			5.73899i			1.06570i	−0.846208	+	0.532852i	$0.821120\pi$
$30$	1.59947	+	1.56260i	0.292021	+	0.285290i
$31$		−	8.34912i		−	1.49955i	−0.661695	−	0.749773i	$-0.730163\pi$
$31$		−	8.34912i		−	1.49955i	0.661695	−	0.749773i	$-0.269837\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−1.38685	−	0.800700i	−0.241420	−	0.139384i
$34$	3.28940	−	5.69741i	0.564128	−	0.977098i
$35$	2.48206	−	0.696182i	0.419545	−	0.117676i
$36$	−1.00000			−0.166667
$37$	−6.07690	+	0.267030i	−0.999036	+	0.0438995i
$37$	−6.07690	+	0.267030i	−0.999036	+	0.0438995i
$38$		−	0.201405i		−	0.0326721i
$39$	3.28591	−	1.89712i	0.526167	−	0.303783i
$40$	1.56260	−	1.59947i	0.247068	−	0.252898i
$41$	4.00330	−	6.93392i	0.625211	−	1.08290i	−0.363289	−	0.931676i	$-0.618346\pi$
$41$	4.00330	−	6.93392i	0.625211	−	1.08290i	0.988500	−	0.151220i	$-0.0483203\pi$
$42$	−0.576424	+	0.998396i	−0.0889442	+	0.154056i
$43$	−1.95146			−0.297595			−0.148798	−	0.988868i	$-0.547540\pi$
$43$	−1.95146			−0.297595			−0.148798	+	0.988868i	$0.547540\pi$
$44$	−0.800700	+	1.38685i	−0.120710	+	0.209076i
$45$	−2.16648	−	0.553515i	−0.322959	−	0.0825132i
$46$	0.316711	+	0.548560i	0.0466965	+	0.0808807i
$47$		−	4.65434i		−	0.678905i	−0.940623	−	0.339453i	$-0.889758\pi$
$47$		−	4.65434i		−	0.678905i	0.940623	−	0.339453i	$-0.110242\pi$
$48$			1.00000i			0.144338i
$49$	−2.83547	−	4.91118i	−0.405067	−	0.701597i
$50$	4.27066	−	2.60029i	0.603962	−	0.367736i
$51$			6.57881i			0.921217i
$52$	−1.89712	−	3.28591i	−0.263084	−	0.455674i
$53$	7.47374	−	4.31497i	1.02660	−	0.592706i	0.110589	−	0.993866i	$-0.464726\pi$
$53$	7.47374	−	4.31497i	1.02660	−	0.592706i	0.916008	+	0.401160i	$0.131393\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$	−2.50234	+	2.56138i	−0.337416	+	0.345377i
$56$	0.998396	+	0.576424i	0.133416	+	0.0770279i
$57$	0.100702	+	0.174421i	0.0133383	+	0.0231027i
$58$	−4.97011	+	2.86950i	−0.652608	+	0.376783i
$59$	10.3918	−	5.99970i	1.35289	−	0.781094i	0.364241	−	0.931305i	$-0.381329\pi$
$59$	10.3918	−	5.99970i	1.35289	−	0.781094i	0.988654	+	0.150211i	$0.0479953\pi$
$60$	−0.553515	+	2.16648i	−0.0714585	+	0.279691i
$61$	−11.3423	−	6.54846i	−1.45223	−	0.838445i	−0.453621	−	0.891195i	$-0.649868\pi$
$61$	−11.3423	−	6.54846i	−1.45223	−	0.838445i	−0.998608	+	0.0527502i	$0.983201\pi$
$62$	7.23055	−	4.17456i	0.918280	−	0.530169i
$63$		−	1.15285i		−	0.145245i
$64$	1.00000			0.125000
$65$	−2.29127	−	8.16894i	−0.284197	−	1.01323i
$66$		−	1.60140i		−	0.197119i
$67$	−9.33087	−	5.38718i	−1.13995	−	0.658149i	−0.193529	−	0.981094i	$-0.561993\pi$
$67$	−9.33087	−	5.38718i	−1.13995	−	0.658149i	−0.946417	+	0.322946i	$0.895327\pi$
$68$	6.57881			0.797798
$69$	−0.548560	−	0.316711i	−0.0660388	−	0.0381275i
$70$	1.84394	+	1.80144i	0.220393	+	0.215313i
$71$	−5.52164	+	9.56376i	−0.655298	+	1.13501i	0.326521	+	0.945190i	$0.394124\pi$
$71$	−5.52164	+	9.56376i	−0.655298	+	1.13501i	−0.981819	+	0.189819i	$0.939210\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$			4.32373i			0.506054i	0.967459	+	0.253027i	$0.0814262\pi$
$73$			4.32373i			0.506054i	−0.967459	+	0.253027i	$0.918574\pi$
$74$	−3.26970	−	5.12923i	−0.380095	−	0.596261i
$75$	−2.39836	+	4.38724i	−0.276938	+	0.506595i
$76$	0.174421	−	0.100702i	0.0200075	−	0.0115513i
$77$	−1.59883	−	0.923086i	−0.182204	−	0.105195i
$78$	3.28591	+	1.89712i	0.372057	+	0.214807i
$79$	6.91117	+	3.99017i	0.777568	+	0.448929i	0.835568	−	0.549388i	$-0.185139\pi$
$79$	6.91117	+	3.99017i	0.777568	+	0.448929i	−0.0580000	+	0.998317i	$0.518472\pi$
$80$	2.16648	+	0.553515i	0.242219	+	0.0618849i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	8.00660			0.884181
$83$	−12.4882	+	7.21006i	−1.37076	+	0.791407i	−0.991023	−	0.133689i	$-0.957318\pi$
$83$	−12.4882	+	7.21006i	−1.37076	+	0.791407i	−0.379734	+	0.925096i	$0.623984\pi$
$84$	−1.15285			−0.125786
$85$	14.2528	+	3.64147i	1.54594	+	0.394973i
$86$	−0.975731	−	1.69002i	−0.105216	−	0.182239i
$87$	2.86950	−	4.97011i	0.307642	−	0.532852i
$88$	−1.60140			−0.170710
$89$	15.6356	−	9.02723i	1.65737	−	0.956885i	0.683452	−	0.729995i	$-0.260478\pi$
$89$	15.6356	−	9.02723i	1.65737	−	0.956885i	0.973920	−	0.226890i	$-0.0728557\pi$
$90$	−0.603880	−	2.15298i	−0.0636545	−	0.226944i
$91$	3.78816	−	2.18710i	0.397107	−	0.229270i
$92$	−0.316711	+	0.548560i	−0.0330194	+	0.0571913i
$93$	−4.17456	+	7.23055i	−0.432882	+	0.749773i
$94$	4.03078	−	2.32717i	0.415743	−	0.240029i
$95$	0.433620	−	0.121624i	0.0444885	−	0.0124784i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$	−2.93176			−0.297675			−0.148838	−	0.988862i	$-0.547553\pi$
$97$	−2.93176			−0.297675			−0.148838	+	0.988862i	$0.547553\pi$
$98$	2.83547	−	4.91118i	0.286426	−	0.496104i
$99$	0.800700	+	1.38685i	0.0804734	+	0.139384i
$100$	4.38724	+	2.39836i	0.438724	+	0.239836i
$101$	−14.8756			−1.48018			−0.740088	−	0.672510i	$-0.765216\pi$
$101$	−14.8756			−1.48018			−0.740088	+	0.672510i	$0.765216\pi$
$102$	−5.69741	+	3.28940i	−0.564128	+	0.325699i
$103$	2.82877			0.278727			0.139363	−	0.990241i	$-0.455494\pi$
$103$	2.82877			0.278727			0.139363	+	0.990241i	$0.455494\pi$
$104$	1.89712	−	3.28591i	0.186028	−	0.322210i
$105$	−2.49762	−	0.638119i	−0.243743	−	0.0622741i
$106$	7.47374	+	4.31497i	0.725914	+	0.419107i
$107$	8.16662	+	4.71500i	0.789497	+	0.455816i	0.839786	−	0.542918i	$-0.182681\pi$
$107$	8.16662	+	4.71500i	0.789497	+	0.455816i	−0.0502882	+	0.998735i	$0.516014\pi$
$108$	0.866025	+	0.500000i	0.0833333	+	0.0481125i
$109$	−11.8873	+	6.86312i	−1.13859	+	0.657367i	−0.946082	−	0.323927i	$-0.894997\pi$
$109$	−11.8873	+	6.86312i	−1.13859	+	0.657367i	−0.192512	+	0.981295i	$0.561663\pi$
$110$	−3.46940	−	0.886399i	−0.330794	−	0.0845148i
$111$	5.39626	+	2.80719i	0.512191	+	0.266447i
$112$			1.15285i			0.108934i
$113$	−4.45519	−	7.71661i	−0.419109	−	0.725917i	0.576741	−	0.816927i	$-0.304324\pi$
$113$	−4.45519	−	7.71661i	−0.419109	−	0.725917i	−0.995850	+	0.0910093i	$0.970991\pi$
$114$	−0.100702	+	0.174421i	−0.00943163	+	0.0163361i
$115$	−0.989784	+	1.01314i	−0.0922978	+	0.0944756i
$116$	−4.97011	−	2.86950i	−0.461463	−	0.266426i
$117$	−3.79425			−0.350778
$118$	10.3918	+	5.99970i	0.956641	+	0.552317i
$119$			7.58437i			0.695258i
$120$	−2.15298	+	0.603880i	−0.196539	+	0.0551265i
$121$	−8.43552			−0.766865
$122$		−	13.0969i		−	1.18574i
$123$	−6.93392	+	4.00330i	−0.625211	+	0.360966i
$124$	7.23055	+	4.17456i	0.649322	+	0.374886i
$125$	8.17733	+	7.62439i	0.731403	+	0.681946i
$126$	0.998396	−	0.576424i	0.0889442	−	0.0513520i
$127$	−10.7457	+	6.20405i	−0.953529	+	0.550520i	−0.894175	−	0.447717i	$-0.852237\pi$
$127$	−10.7457	+	6.20405i	−0.953529	+	0.550520i	−0.0593538	+	0.998237i	$0.518904\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	1.69002	+	0.975731i	0.148798	+	0.0859083i
$130$	5.92888	−	6.06877i	0.519997	−	0.532266i
$131$	−0.150501	+	0.0868917i	−0.0131493	+	0.00759176i	−0.506560	−	0.862205i	$-0.669083\pi$
$131$	−0.150501	+	0.0868917i	−0.0131493	+	0.00759176i	0.493411	+	0.869796i	$0.335750\pi$
$132$	1.38685	−	0.800700i	0.120710	−	0.0696920i
$133$	0.116094	+	0.201082i	0.0100667	+	0.0174360i
$134$		−	10.7744i		−	0.930763i
$135$	1.59947	+	1.56260i	0.137660	+	0.134487i
$136$	3.28940	+	5.69741i	0.282064	+	0.488549i
$137$			0.163889i			0.0140020i	0.999975	+	0.00700100i	$0.00222850\pi$
$137$			0.163889i			0.0140020i	−0.999975	+	0.00700100i	$0.997771\pi$
$138$		−	0.633422i		−	0.0539205i
$139$	−0.808880	−	1.40102i	−0.0686083	−	0.118833i	0.829681	−	0.558238i	$-0.188523\pi$
$139$	−0.808880	−	1.40102i	−0.0686083	−	0.118833i	−0.898289	+	0.439405i	$0.855189\pi$
$140$	−0.638119	+	2.49762i	−0.0539309	+	0.211087i
$141$	−2.32717	+	4.03078i	−0.195983	+	0.339453i
$142$	−11.0433			−0.926731
$143$	−3.03805	+	5.26206i	−0.254055	+	0.440036i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	−9.17932	−	8.96773i	−0.762301	−	0.744729i
$146$	−3.74446	+	2.16187i	−0.309894	+	0.178917i
$147$			5.67094i			0.467731i
$148$	2.80719	−	5.39626i	0.230750	−	0.443570i
$149$	−16.0986			−1.31885			−0.659423	−	0.751772i	$-0.729200\pi$
$149$	−16.0986			−1.31885			−0.659423	+	0.751772i	$0.729200\pi$
$150$	−4.99864	+	0.116584i	−0.408137	+	0.00951905i
$151$	3.14518	−	5.44761i	0.255951	−	0.443320i	−0.709202	−	0.705005i	$-0.750945\pi$
$151$	3.14518	−	5.44761i	0.255951	−	0.443320i	0.965153	+	0.261685i	$0.0842780\pi$
$152$	0.174421	+	0.100702i	0.0141474	+	0.00816803i
$153$	3.28940	−	5.69741i	0.265933	−	0.460609i
$154$		−	1.84617i		−	0.148769i
$155$	13.3541	+	13.0463i	1.07263	+	1.04790i
$156$			3.79425i			0.303783i
$157$	3.38321	−	1.95330i	0.270009	−	0.155890i	−0.358883	−	0.933383i	$-0.616842\pi$
$157$	3.38321	−	1.95330i	0.270009	−	0.155890i	0.628892	+	0.777493i	$0.283509\pi$
$158$			7.98033i			0.634881i
$159$	−8.62993			−0.684398
$160$	0.603880	+	2.15298i	0.0477409	+	0.170208i
$161$	−0.632406	−	0.365120i	−0.0498406	−	0.0287755i
$162$	−1.00000			−0.0785674
$163$	3.44377	+	5.96478i	0.269737	+	0.467198i	0.968794	−	0.247868i	$-0.0797300\pi$
$163$	3.44377	+	5.96478i	0.269737	+	0.467198i	−0.699057	+	0.715066i	$0.746397\pi$
$164$	4.00330	+	6.93392i	0.312605	+	0.541448i
$165$	3.44778	−	0.967053i	0.268410	−	0.0752850i
$166$	−12.4882	−	7.21006i	−0.969272	−	0.559609i
$167$	−2.06388	+	3.57474i	−0.159708	+	0.276622i	−0.934763	−	0.355271i	$-0.884389\pi$
$167$	−2.06388	+	3.57474i	−0.159708	+	0.276622i	0.775055	+	0.631893i	$0.217722\pi$
$168$	−0.576424	−	0.998396i	−0.0444721	−	0.0770279i
$169$	−0.698155	−	1.20924i	−0.0537042	−	0.0930185i
$170$	3.97281	+	14.1640i	0.304701	+	1.08633i
$171$		−	0.201405i		−	0.0154018i
$172$	0.975731	−	1.69002i	0.0743988	−	0.128862i
$173$	20.7126	−	11.9584i	1.57475	−	0.909181i	0.579173	−	0.815204i	$-0.303375\pi$
$173$	20.7126	−	11.9584i	1.57475	−	0.909181i	0.995574	−	0.0939768i	$-0.0299579\pi$
$174$	5.73899			0.435072
$175$	−2.76494	+	5.05783i	−0.209010	+	0.382336i
$176$	−0.800700	−	1.38685i	−0.0603550	−	0.104538i
$177$	−11.9994			−0.901930
$178$	15.6356	+	9.02723i	1.17194	+	0.676620i
$179$			16.2259i			1.21278i	0.795167	+	0.606390i	$0.207383\pi$
$179$			16.2259i			1.21278i	−0.795167	+	0.606390i	$0.792617\pi$
$180$	1.56260	−	1.59947i	0.116469	−	0.119217i
$181$	−2.06172	+	3.57100i	−0.153246	+	0.265431i	−0.932419	−	0.361379i	$-0.882306\pi$
$181$	−2.06172	+	3.57100i	−0.153246	+	0.265431i	0.779173	+	0.626809i	$0.215639\pi$
$182$	3.78816	+	2.18710i	0.280797	+	0.162118i
$183$	6.54846	+	11.3423i	0.484076	+	0.838445i
$184$	−0.633422			−0.0466965
$185$	9.06863	−	10.1371i	0.666739	−	0.745291i
$186$	−8.34912			−0.612187
$187$	−5.26765	−	9.12384i	−0.385209	−	0.667201i
$188$	4.03078	+	2.32717i	0.293975	+	0.169726i
$189$	−0.576424	+	0.998396i	−0.0419287	+	0.0726226i
$190$	0.322140	+	0.314714i	0.0233705	+	0.0228318i
$191$		−	4.40002i		−	0.318374i	−0.987248	−	0.159187i	$-0.949113\pi$
$191$		−	4.40002i		−	0.318374i	0.987248	−	0.159187i	$-0.0508873\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	−1.15300			−0.0829950			−0.0414975	−	0.999139i	$-0.513213\pi$
$193$	−1.15300			−0.0829950			−0.0414975	+	0.999139i	$0.513213\pi$
$194$	−1.46588	−	2.53898i	−0.105244	−	0.182288i
$195$	−2.10017	+	8.22015i	−0.150397	+	0.588657i
$196$	5.67094			0.405067
$197$	−1.50044	+	0.866279i	−0.106902	+	0.0617199i	−0.552498	−	0.833514i	$-0.686325\pi$
$197$	−1.50044	+	0.866279i	−0.106902	+	0.0617199i	0.445596	+	0.895234i	$0.352992\pi$
$198$	−0.800700	+	1.38685i	−0.0569033	+	0.0985593i
$199$			19.8702i			1.40856i	0.709922	+	0.704281i	$0.248730\pi$
$199$			19.8702i			1.40856i	−0.709922	+	0.704281i	$0.751270\pi$
$200$	0.116584	+	4.99864i	0.00824374	+	0.353457i
$201$	5.38718	+	9.33087i	0.379982	+	0.658149i
$202$	−7.43779	−	12.8826i	−0.523321	−	0.906419i
$203$	3.30809	−	5.72979i	0.232183	−	0.402152i
$204$	−5.69741	−	3.28940i	−0.398899	−	0.230304i
$205$	4.83503	+	17.2381i	0.337693	+	1.20396i
$206$	1.41438	+	2.44978i	0.0985447	+	0.170684i
$207$	0.316711	+	0.548560i	0.0220129	+	0.0381275i
$208$	3.79425			0.263084
$209$	−0.279319	−	0.161265i	−0.0193209	−	0.0111549i
$210$	−0.696182	−	2.48206i	−0.0480411	−	0.171279i
$211$	−15.6536			−1.07764			−0.538820	−	0.842421i	$-0.681130\pi$
$211$	−15.6536			−1.07764			−0.538820	+	0.842421i	$0.681130\pi$
$212$			8.62993i			0.592706i
$213$	9.56376	−	5.52164i	0.655298	−	0.378336i
$214$			9.43000i			0.644622i
$215$	3.04935	−	3.12130i	0.207964	−	0.212871i
$216$			1.00000i			0.0680414i
$217$	−4.81263	+	8.33573i	−0.326703	+	0.565866i
$218$	−11.8873	−	6.86312i	−0.805107	−	0.464829i
$219$	2.16187	−	3.74446i	0.146085	−	0.253027i
$220$	−0.967053	−	3.44778i	−0.0651987	−	0.232450i
$221$	24.9616			1.67910
$222$	0.267030	+	6.07690i	0.0179219	+	0.407855i
$223$			16.3946i			1.09786i	0.835867	+	0.548932i	$0.184965\pi$
$223$			16.3946i			1.09786i	−0.835867	+	0.548932i	$0.815035\pi$
$224$	−0.998396	+	0.576424i	−0.0667081	+	0.0385140i
$225$	4.27066	−	2.60029i	0.284711	−	0.173352i
$226$	4.45519	−	7.71661i	0.296355	−	0.513301i
$227$	13.6135	−	23.5793i	0.903562	−	1.56502i	0.0807258	−	0.996736i	$-0.474276\pi$
$227$	13.6135	−	23.5793i	0.903562	−	1.56502i	0.822836	−	0.568279i	$-0.192390\pi$
$228$	−0.201405			−0.0133383
$229$	−6.12750	+	10.6131i	−0.404917	+	0.701336i	−0.994312	−	0.106509i	$-0.966033\pi$
$229$	−6.12750	+	10.6131i	−0.404917	+	0.701336i	0.589395	+	0.807845i	$0.299366\pi$
$230$	−1.37229	−	0.350609i	−0.0904864	−	0.0231185i
$231$	0.923086	+	1.59883i	0.0607346	+	0.105195i
$232$		−	5.73899i		−	0.376783i
$233$		−	12.4646i		−	0.816581i	−0.912852	−	0.408290i	$-0.866125\pi$
$233$		−	12.4646i		−	0.816581i	0.912852	−	0.408290i	$-0.133875\pi$
$234$	−1.89712	−	3.28591i	−0.124019	−	0.214807i
$235$	7.44446	+	7.27285i	0.485623	+	0.474429i
$236$			11.9994i			0.781094i
$237$	−3.99017	−	6.91117i	−0.259189	−	0.448929i
$238$	−6.56826	+	3.79218i	−0.425757	+	0.245811i
$239$	−13.9717	+	8.06659i	−0.903757	+	0.521784i	−0.878417	−	0.477894i	$-0.841400\pi$
$239$	−13.9717	+	8.06659i	−0.903757	+	0.521784i	−0.0253399	+	0.999679i	$0.508067\pi$
$240$	−1.59947	−	1.56260i	−0.103245	−	0.100865i
$241$	−0.462479	−	0.267013i	−0.0297909	−	0.0171998i	0.485031	−	0.874497i	$-0.338808\pi$
$241$	−0.462479	−	0.267013i	−0.0297909	−	0.0171998i	−0.514821	+	0.857297i	$0.672142\pi$
$242$	−4.21776	−	7.30537i	−0.271128	−	0.469607i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	11.3423	−	6.54846i	0.726114	−	0.419222i
$245$	12.2860	+	3.13895i	0.784921	+	0.200540i
$246$	−6.93392	−	4.00330i	−0.442091	−	0.255241i
$247$	0.661798	−	0.382089i	0.0421092	−	0.0243118i
$248$			8.34912i			0.530169i
$249$	14.4201			0.913838
$250$	−2.51425	+	10.8940i	−0.159015	+	0.688995i
$251$			17.0952i			1.07904i	0.841973	+	0.539520i	$0.181394\pi$
$251$			17.0952i			1.07904i	−0.841973	+	0.539520i	$0.818606\pi$
$252$	0.998396	+	0.576424i	0.0628930	+	0.0363113i
$253$	1.01436			0.0637724
$254$	−10.7457	−	6.20405i	−0.674247	−	0.389277i
$255$	−10.5226	−	10.2800i	−0.658949	−	0.643760i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−2.85889	−	4.95174i	−0.178333	−	0.308881i	0.762977	−	0.646426i	$-0.223737\pi$
$257$	−2.85889	−	4.95174i	−0.178333	−	0.308881i	−0.941310	+	0.337544i	$0.890404\pi$
$258$			1.95146i			0.121493i
$259$	6.22107	+	3.23627i	0.386559	+	0.201092i
$260$	8.22015	+	2.10017i	0.509792	+	0.130247i
$261$	−4.97011	+	2.86950i	−0.307642	+	0.177617i
$262$	−0.150501	−	0.0868917i	−0.00929797	−	0.00536819i
$263$	−26.5295	−	15.3168i	−1.63588	−	0.944474i	−0.982232	−	0.187672i	$-0.939906\pi$
$263$	−26.5295	−	15.3168i	−1.63588	−	0.944474i	−0.653645	−	0.756802i	$-0.726761\pi$
$264$	1.38685	+	0.800700i	0.0853549	+	0.0492797i
$265$	−4.77680	+	18.6965i	−0.293436	+	1.14852i
$266$	−0.116094	+	0.201082i	−0.00711821	+	0.0123291i
$267$	−18.0545			−1.10492
$268$	9.33087	−	5.38718i	0.569973	−	0.329074i
$269$	11.7982			0.719351			0.359675	−	0.933077i	$-0.382887\pi$
$269$	11.7982			0.719351			0.359675	+	0.933077i	$0.382887\pi$
$270$	−0.553515	+	2.16648i	−0.0336859	+	0.131848i
$271$	−5.06391	−	8.77094i	−0.307610	−	0.532797i	0.670229	−	0.742155i	$-0.266196\pi$
$271$	−5.06391	−	8.77094i	−0.307610	−	0.532797i	−0.977839	+	0.209358i	$0.932863\pi$
$272$	−3.28940	+	5.69741i	−0.199449	+	0.345456i
$273$	−4.37419			−0.264738
$274$	−0.141932	+	0.0819446i	−0.00857443	+	0.00495045i
$275$	−0.186698	−	8.00482i	−0.0112583	−	0.482709i
$276$	0.548560	−	0.316711i	0.0330194	−	0.0190638i
$277$	14.9276	−	25.8554i	0.896913	−	1.55350i	0.0654936	−	0.997853i	$-0.479138\pi$
$277$	14.9276	−	25.8554i	0.896913	−	1.55350i	0.831419	−	0.555646i	$-0.187529\pi$
$278$	0.808880	−	1.40102i	0.0485134	−	0.0840277i
$279$	7.23055	−	4.17456i	0.432882	−	0.249924i
$280$	−2.48206	+	0.696182i	−0.148332	+	0.0416048i
$281$	−14.1619	+	8.17640i	−0.844831	+	0.487763i	−0.858903	−	0.512138i	$-0.828854\pi$
$281$	−14.1619	+	8.17640i	−0.844831	+	0.487763i	0.0140724	+	0.999901i	$0.495520\pi$
$282$	−4.65434			−0.277162
$283$	2.38752	−	4.13531i	0.141924	−	0.245819i	−0.786297	−	0.617848i	$-0.788005\pi$
$283$	2.38752	−	4.13531i	0.141924	−	0.245819i	0.928221	+	0.372029i	$0.121338\pi$
$284$	−5.52164	−	9.56376i	−0.327649	−	0.567505i
$285$	−0.436338	−	0.111480i	−0.0258464	−	0.00660353i
$286$	−6.07611			−0.359288
$287$	−7.99376	+	4.61520i	−0.471857	+	0.272427i
$288$	1.00000			0.0589256
$289$	−13.1403	+	22.7598i	−0.772962	+	1.33881i
$290$	3.17662	−	12.4334i	0.186538	−	0.730114i
$291$	2.53898	+	1.46588i	0.148838	+	0.0859314i
$292$	−3.74446	−	2.16187i	−0.219128	−	0.126514i
$293$	3.03946	+	1.75483i	0.177567	+	0.102518i	0.586149	−	0.810203i	$-0.300643\pi$
$293$	3.03946	+	1.75483i	0.177567	+	0.102518i	−0.408582	+	0.912722i	$0.633977\pi$
$294$	−4.91118	+	2.83547i	−0.286426	+	0.165368i
$295$	−6.64185	+	25.9964i	−0.386703	+	1.51357i
$296$	6.07690	−	0.267030i	0.353213	−	0.0155208i
$297$		−	1.60140i		−	0.0929226i
$298$	−8.04929	−	13.9418i	−0.466283	−	0.807625i
$299$	−1.20168	+	2.08137i	−0.0694950	+	0.120369i
$300$	−2.60029	−	4.27066i	−0.150128	−	0.246567i
$301$	1.94833	+	1.12487i	0.112300	+	0.0648364i
$302$	6.29036			0.361970
$303$	12.8826	+	7.43779i	0.740088	+	0.427290i
$304$			0.201405i			0.0115513i
$305$	28.1974	−	7.90897i	1.61458	−	0.452866i
$306$	6.57881			0.376085
$307$			13.8678i			0.791479i	0.918363	+	0.395739i	$0.129512\pi$
$307$			13.8678i			0.791479i	−0.918363	+	0.395739i	$0.870488\pi$
$308$	1.59883	−	0.923086i	0.0911019	−	0.0525977i
$309$	−2.44978	−	1.41438i	−0.139363	−	0.0804614i
$310$	−4.62136	+	18.0882i	−0.262476	+	1.02734i
$311$	−13.6673	+	7.89080i	−0.775000	+	0.447446i	−0.834655	−	0.550773i	$-0.814333\pi$
$311$	−13.6673	+	7.89080i	−0.775000	+	0.447446i	0.0596555	+	0.998219i	$0.481000\pi$
$312$	−3.28591	+	1.89712i	−0.186028	+	0.107403i
$313$	−6.99253	−	12.1114i	−0.395241	−	0.684578i	0.597891	−	0.801578i	$-0.296006\pi$
$313$	−6.99253	−	12.1114i	−0.395241	−	0.684578i	−0.993132	+	0.117000i	$0.962672\pi$
$314$	3.38321	+	1.95330i	0.190925	+	0.110231i
$315$	1.84394	+	1.80144i	0.103894	+	0.101499i
$316$	−6.91117	+	3.99017i	−0.388784	+	0.224464i
$317$	4.22693	−	2.44042i	0.237408	−	0.137068i	−0.376577	−	0.926385i	$-0.622899\pi$
$317$	4.22693	−	2.44042i	0.237408	−	0.137068i	0.613985	+	0.789318i	$0.289566\pi$
$318$	−4.31497	−	7.47374i	−0.241971	−	0.419107i
$319$			9.19042i			0.514565i
$320$	−1.56260	+	1.59947i	−0.0873518	+	0.0894129i
$321$	−4.71500	−	8.16662i	−0.263166	−	0.455816i
$322$		−	0.730240i		−	0.0406947i
$323$			1.32500i			0.0737251i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	16.6463	+	9.09995i	0.923369	+	0.504775i
$326$	−3.44377	+	5.96478i	−0.190733	+	0.330359i
$327$	13.7262			0.759063
$328$	−4.00330	+	6.93392i	−0.221045	+	0.382862i
$329$	−2.68287	+	4.64687i	−0.147912	+	0.256190i
$330$	2.56138	+	2.50234i	0.141000	+	0.137749i
$331$	8.03353	−	4.63816i	0.441563	−	0.254936i	−0.262698	−	0.964878i	$-0.584612\pi$
$331$	8.03353	−	4.63816i	0.441563	−	0.254936i	0.704260	+	0.709942i	$0.251279\pi$
$332$		−	14.4201i		−	0.791407i
$333$	−3.26970	−	5.12923i	−0.179179	−	0.281080i
$334$	−4.12776			−0.225861
$335$	23.1970	−	6.50642i	1.26739	−	0.355484i
$336$	0.576424	−	0.998396i	0.0314465	−	0.0544670i
$337$	−26.0610	−	15.0463i	−1.41963	−	0.819625i	−0.423367	−	0.905958i	$-0.639152\pi$
$337$	−26.0610	−	15.0463i	−1.41963	−	0.819625i	−0.996266	+	0.0863330i	$0.972485\pi$
$338$	0.698155	−	1.20924i	0.0379746	−	0.0657740i
$339$			8.91037i			0.483945i
$340$	−10.2800	+	10.5226i	−0.557512	+	0.570667i
$341$		−	13.3703i		−	0.724041i
$342$	0.174421	−	0.100702i	0.00943163	−	0.00544536i
$343$			14.6077i			0.788740i
$344$	1.95146			0.105216
$345$	1.36375	−	0.382511i	0.0734216	−	0.0205937i
$346$	20.7126	+	11.9584i	1.11351	+	0.642888i
$347$	−24.1815			−1.29813			−0.649066	−	0.760733i	$-0.724840\pi$
$347$	−24.1815			−1.29813			−0.649066	+	0.760733i	$0.724840\pi$
$348$	2.86950	+	4.97011i	0.153821	+	0.266426i
$349$	−3.22778	−	5.59068i	−0.172779	−	0.299262i	0.766611	−	0.642111i	$-0.221941\pi$
$349$	−3.22778	−	5.59068i	−0.172779	−	0.299262i	−0.939390	+	0.342849i	$0.888608\pi$
$350$	−5.76268	+	0.134404i	−0.308028	+	0.00718419i
$351$	3.28591	+	1.89712i	0.175389	+	0.101261i
$352$	0.800700	−	1.38685i	0.0426774	−	0.0739195i
$353$	5.33390	+	9.23859i	0.283895	+	0.491721i	0.972341	−	0.233567i	$-0.0750399\pi$
$353$	5.33390	+	9.23859i	0.283895	+	0.491721i	−0.688446	+	0.725288i	$0.741707\pi$
$354$	−5.99970	−	10.3918i	−0.318880	−	0.552317i
$355$	−6.66882	−	23.7760i	−0.353944	−	1.26190i
$356$			18.0545i			0.956885i
$357$	3.79218	−	6.56826i	0.200704	−	0.347629i
$358$	−14.0520	+	8.11294i	−0.742673	+	0.428782i
$359$	−7.32628			−0.386666			−0.193333	−	0.981133i	$-0.561930\pi$
$359$	−7.32628			−0.386666			−0.193333	+	0.981133i	$0.561930\pi$
$360$	2.16648	+	0.553515i	0.114183	+	0.0291728i
$361$	−9.47972	−	16.4194i	−0.498933	−	0.864176i
$362$	−4.12344			−0.216723
$363$	7.30537	+	4.21776i	0.383433	+	0.221375i
$364$			4.37419i			0.229270i
$365$	−6.91566	−	6.75625i	−0.361982	−	0.353638i
$366$	−6.54846	+	11.3423i	−0.342294	+	0.592870i
$367$	−3.73951	−	2.15901i	−0.195201	−	0.112699i	0.399214	−	0.916858i	$-0.369283\pi$
$367$	−3.73951	−	2.15901i	−0.195201	−	0.112699i	−0.594415	+	0.804159i	$0.702616\pi$
$368$	−0.316711	−	0.548560i	−0.0165097	−	0.0285957i
$369$	8.00660			0.416807
$370$	13.3133	+	2.78514i	0.692124	+	0.144793i
$371$	−9.94900			−0.516527
$372$	−4.17456	−	7.23055i	−0.216441	−	0.374886i
$373$	−0.164880	−	0.0951938i	−0.00853719	−	0.00492895i	0.495725	−	0.868479i	$-0.334902\pi$
$373$	−0.164880	−	0.0951938i	−0.00853719	−	0.00492895i	−0.504263	+	0.863550i	$0.668236\pi$
$374$	5.26765	−	9.12384i	0.272384	−	0.471782i
$375$	−3.26958	−	10.6916i	−0.168841	−	0.552111i
$376$			4.65434i			0.240029i
$377$	−18.8578	−	10.8876i	−0.971228	−	0.560739i
$378$	−1.15285			−0.0592961
$379$	−15.9392	−	27.6075i	−0.818742	−	1.41810i	−0.906610	−	0.421970i	$-0.861339\pi$
$379$	−15.9392	−	27.6075i	−0.818742	−	1.41810i	0.0878680	−	0.996132i	$-0.471995\pi$
$380$	−0.111480	+	0.436338i	−0.00571883	+	0.0223837i
$381$	12.4081			0.635686
$382$	3.81053	−	2.20001i	0.194963	−	0.112562i
$383$	11.9491	−	20.6964i	0.610569	−	1.05754i	−0.380575	−	0.924750i	$-0.624274\pi$
$383$	11.9491	−	20.6964i	0.610569	−	1.05754i	0.991145	−	0.132787i	$-0.0423926\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	3.97477	−	1.11487i	0.202573	−	0.0568188i
$386$	−0.576502	−	0.998530i	−0.0293432	−	0.0508238i
$387$	−0.975731	−	1.69002i	−0.0495992	−	0.0859083i
$388$	1.46588	−	2.53898i	0.0744188	−	0.128897i
$389$	6.13244	+	3.54056i	0.310927	+	0.179514i	0.647341	−	0.762200i	$-0.275881\pi$
$389$	6.13244	+	3.54056i	0.310927	+	0.179514i	−0.336414	+	0.941714i	$0.609214\pi$
$390$	−8.16894	+	2.29127i	−0.413651	+	0.116023i
$391$	−2.08358	−	3.60887i	−0.105371	−	0.182508i
$392$	2.83547	+	4.91118i	0.143213	+	0.248052i
$393$	0.173783			0.00876621
$394$	−1.50044	−	0.866279i	−0.0755911	−	0.0436425i
$395$	−17.1815	+	4.81916i	−0.864496	+	0.242478i
$396$	−1.60140			−0.0804734
$397$			1.61077i			0.0808422i	0.999183	+	0.0404211i	$0.0128699\pi$
$397$			1.61077i			0.0808422i	−0.999183	+	0.0404211i	$0.987130\pi$
$398$	−17.2081	+	9.93510i	−0.862564	+	0.498002i
$399$		−	0.232189i		−	0.0116240i
$400$	−4.27066	+	2.60029i	−0.213533	+	0.130014i
$401$			8.93803i			0.446344i	0.974779	+	0.223172i	$0.0716411\pi$
$401$			8.93803i			0.446344i	−0.974779	+	0.223172i	$0.928359\pi$
$402$	−5.38718	+	9.33087i	−0.268688	+	0.465381i
$403$	27.4345	+	15.8393i	1.36661	+	0.789012i
$404$	7.43779	−	12.8826i	0.370044	−	0.640935i
$405$	−0.603880	−	2.15298i	−0.0300070	−	0.106983i
$406$	6.61619			0.328356
$407$	−9.73154	+	0.427622i	−0.482375	+	0.0211964i
$408$		−	6.57881i		−	0.325699i
$409$	−24.5929	+	14.1987i	−1.21604	+	0.702080i	−0.964068	−	0.265654i	$-0.914412\pi$
$409$	−24.5929	+	14.1987i	−1.21604	+	0.702080i	−0.251971	+	0.967735i	$0.581079\pi$
$410$	−12.5111	+	12.8063i	−0.617879	+	0.632458i
$411$	0.0819446	−	0.141932i	0.00404203	−	0.00700100i
$412$	−1.41438	+	2.44978i	−0.0696816	+	0.120692i
$413$	−13.8335			−0.680701
$414$	−0.316711	+	0.548560i	−0.0155655	+	0.0269602i
$415$	7.98176	−	31.2409i	0.391809	−	1.53355i
$416$	1.89712	+	3.28591i	0.0930141	+	0.161105i
$417$			1.61776i			0.0792221i
$418$		−	0.322529i		−	0.0157754i
$419$	−17.6867	−	30.6343i	−0.864053	−	1.49658i	−0.867984	−	0.496592i	$-0.834584\pi$
$419$	−17.6867	−	30.6343i	−0.864053	−	1.49658i	0.00393056	−	0.999992i	$-0.498749\pi$
$420$	1.80144	−	1.84394i	0.0879011	−	0.0899752i
$421$		−	6.87298i		−	0.334968i	−0.985875	−	0.167484i	$-0.946436\pi$
$421$		−	6.87298i		−	0.334968i	0.985875	−	0.167484i	$-0.0535643\pi$
$422$	−7.82681	−	13.5564i	−0.381003	−	0.659917i
$423$	4.03078	−	2.32717i	0.195983	−	0.113151i
$424$	−7.47374	+	4.31497i	−0.362957	+	0.209553i
$425$	−28.0958	+	17.1068i	−1.36285	+	0.829800i
$426$	9.56376	+	5.52164i	0.463366	+	0.267524i
$427$	7.54938	+	13.0759i	0.365340	+	0.632788i
$428$	−8.16662	+	4.71500i	−0.394749	+	0.227908i
$429$	5.26206	−	3.03805i	0.254055	−	0.146679i
$430$	4.22780	+	1.08016i	0.203882	+	0.0520901i
$431$	29.8230	+	17.2183i	1.43652	+	0.829376i	0.997606	−	0.0691529i	$-0.0220296\pi$
$431$	29.8230	+	17.2183i	1.43652	+	0.829376i	0.438915	+	0.898529i	$0.355363\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$		−	17.7398i		−	0.852520i	−0.904601	−	0.426260i	$-0.859831\pi$
$433$		−	17.7398i		−	0.852520i	0.904601	−	0.426260i	$-0.140169\pi$
$434$	−9.62527			−0.462028
$435$	3.46566	+	12.3559i	0.166166	+	0.592422i
$436$		−	13.7262i		−	0.657367i
$437$	−0.110482	−	0.0637871i	−0.00528509	−	0.00305135i
$438$	4.32373			0.206596
$439$	−4.36970	−	2.52285i	−0.208554	−	0.120409i	0.392085	−	0.919929i	$-0.371754\pi$
$439$	−4.36970	−	2.52285i	−0.208554	−	0.120409i	−0.600639	+	0.799520i	$0.705087\pi$
$440$	2.50234	−	2.56138i	0.119294	−	0.122109i
$441$	2.83547	−	4.91118i	0.135022	−	0.233866i
$442$	12.4808	+	21.6174i	0.593652	+	1.02823i
$443$			5.67021i			0.269400i	0.990886	+	0.134700i	$0.0430070\pi$
$443$			5.67021i			0.269400i	−0.990886	+	0.134700i	$0.956993\pi$
$444$	−5.12923	+	3.26970i	−0.243423	+	0.155173i
$445$	−9.99342	+	39.1146i	−0.473734	+	1.85421i
$446$	−14.1981	+	8.19730i	−0.672301	+	0.388153i
$447$	13.9418	+	8.04929i	0.659423	+	0.380718i
$448$	−0.998396	−	0.576424i	−0.0471698	−	0.0272335i
$449$	−5.83240	−	3.36734i	−0.275248	−	0.158914i	0.356022	−	0.934477i	$-0.384133\pi$
$449$	−5.83240	−	3.36734i	−0.275248	−	0.158914i	−0.631270	+	0.775563i	$0.717466\pi$
$450$	4.38724	+	2.39836i	0.206817	+	0.113060i
$451$	6.41089	−	11.1040i	0.301877	−	0.522866i
$452$	8.91037			0.419109
$453$	−5.44761	+	3.14518i	−0.255951	+	0.147773i
$454$	27.2271			1.27783
$455$	−2.42118	+	9.47659i	−0.113507	+	0.444269i
$456$	−0.100702	−	0.174421i	−0.00471582	−	0.00816803i
$457$	12.5902	−	21.8068i	0.588944	−	1.02008i	−0.405427	−	0.914127i	$-0.632877\pi$
$457$	12.5902	−	21.8068i	0.588944	−	1.02008i	0.994371	−	0.105953i	$-0.0337894\pi$
$458$	−12.2550			−0.572639
$459$	−5.69741	+	3.28940i	−0.265933	+	0.153536i
$460$	−0.382511	−	1.36375i	−0.0178347	−	0.0635850i
$461$	30.6749	−	17.7102i	1.42867	−	0.824846i	0.431658	−	0.902037i	$-0.357929\pi$
$461$	30.6749	−	17.7102i	1.42867	−	0.824846i	0.997016	+	0.0771914i	$0.0245952\pi$
$462$	−0.923086	+	1.59883i	−0.0429458	+	0.0743844i
$463$	10.5328	−	18.2434i	0.489502	−	0.847842i	−0.510425	−	0.859922i	$-0.670512\pi$
$463$	10.5328	−	18.2434i	0.489502	−	0.847842i	0.999927	+	0.0120800i	$0.00384527\pi$
$464$	4.97011	−	2.86950i	0.230732	−	0.133213i
$465$	−5.04187	−	17.9755i	−0.233811	−	0.833594i
$466$	10.7946	−	6.23228i	0.500052	−	0.288705i
$467$	36.8742			1.70634			0.853168	−	0.521636i	$-0.174678\pi$
$467$	36.8742			1.70634			0.853168	+	0.521636i	$0.174678\pi$
$468$	1.89712	−	3.28591i	0.0876946	−	0.151891i
$469$	6.21060	+	10.7571i	0.286779	+	0.496716i
$470$	−2.57625	+	10.0835i	−0.118833	+	0.465118i
$471$	−3.90659			−0.180006
$472$	−10.3918	+	5.99970i	−0.478320	+	0.276158i
$473$	−3.12507			−0.143691
$474$	3.99017	−	6.91117i	0.183274	−	0.317441i
$475$	−0.483040	+	0.883611i	−0.0221634	+	0.0405428i
$476$	−6.56826	−	3.79218i	−0.301055	−	0.173814i
$477$	7.47374	+	4.31497i	0.342199	+	0.197569i
$478$	−13.9717	−	8.06659i	−0.639053	−	0.368957i
$479$	3.93591	−	2.27240i	0.179836	−	0.103829i	−0.407379	−	0.913259i	$-0.633557\pi$
$479$	3.93591	−	2.27240i	0.179836	−	0.103829i	0.587216	+	0.809430i	$0.300224\pi$
$480$	0.553515	−	2.16648i	0.0252644	−	0.0988857i
$481$	10.6512	−	20.4748i	0.485652	−	0.933569i
$482$		−	0.534025i		−	0.0243242i
$483$	0.365120	+	0.632406i	0.0166135	+	0.0287755i
$484$	4.21776	−	7.30537i	0.191716	−	0.332062i
$485$	4.58116	−	4.68925i	0.208020	−	0.212928i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	26.0473			1.18032			0.590158	−	0.807288i	$-0.299065\pi$
$487$	26.0473			1.18032			0.590158	+	0.807288i	$0.299065\pi$
$488$	11.3423	+	6.54846i	0.513440	+	0.296435i
$489$		−	6.88754i		−	0.311465i
$490$	3.42457	+	12.2094i	0.154706	+	0.551566i
$491$	28.0039			1.26380			0.631900	−	0.775050i	$-0.282276\pi$
$491$	28.0039			1.26380			0.631900	+	0.775050i	$0.282276\pi$
$492$		−	8.00660i		−	0.360966i
$493$	32.6974	−	18.8779i	1.47262	−	0.850216i
$494$	0.661798	+	0.382089i	0.0297757	+	0.0171910i
$495$	−3.46940	−	0.886399i	−0.155938	−	0.0398407i
$496$	−7.23055	+	4.17456i	−0.324661	+	0.187443i
$497$	11.0256	−	6.36561i	0.494564	−	0.285537i
$498$	7.21006	+	12.4882i	0.323091	+	0.559609i
$499$	22.5995	+	13.0478i	1.01169	+	0.584100i	0.911686	−	0.410887i	$-0.134781\pi$
$499$	22.5995	+	13.0478i	1.01169	+	0.584100i	0.100005	+	0.994987i	$0.468114\pi$
$500$	−10.6916	+	3.26958i	−0.478142	+	0.146220i
$501$	3.57474	−	2.06388i	0.159708	−	0.0922073i
$502$	−14.8049	+	8.54760i	−0.660774	+	0.381498i
$503$	14.5457	+	25.1938i	0.648559	+	1.12334i	0.983467	+	0.181087i	$0.0579615\pi$
$503$	14.5457	+	25.1938i	0.648559	+	1.12334i	−0.334908	+	0.942251i	$0.608705\pi$
$504$			1.15285i			0.0513520i
$505$	23.2445	−	23.7930i	1.03437	−	1.05877i
$506$	0.507181	+	0.878464i	0.0225470	+	0.0390525i
$507$			1.39631i			0.0620123i
$508$		−	12.4081i		−	0.550520i
$509$	−5.98303	−	10.3629i	−0.265193	−	0.459328i	0.702421	−	0.711762i	$-0.252102\pi$
$509$	−5.98303	−	10.3629i	−0.265193	−	0.459328i	−0.967614	+	0.252434i	$0.918769\pi$
$510$	3.64147	−	14.2528i	0.161247	−	0.631126i
$511$	2.49230	−	4.31680i	0.110253	−	0.190964i
$512$	−1.00000			−0.0441942
$513$	−0.100702	+	0.174421i	−0.00444611	+	0.00770090i
$514$	2.85889	−	4.95174i	0.126100	−	0.218412i
$515$	−4.42022	+	4.52451i	−0.194778	+	0.199374i
$516$	−1.69002	+	0.975731i	−0.0743988	+	0.0429542i
$517$		−	7.45346i		−	0.327803i
$518$	0.307845	+	7.00574i	0.0135259	+	0.307815i
$519$	−23.9168			−1.04983
$520$	2.29127	+	8.16894i	0.100479	+	0.358232i
$521$	18.7348	−	32.4496i	0.820787	−	1.42164i	−0.0843099	−	0.996440i	$-0.526869\pi$
$521$	18.7348	−	32.4496i	0.820787	−	1.42164i	0.905097	−	0.425205i	$-0.139798\pi$
$522$	−4.97011	−	2.86950i	−0.217536	−	0.125594i
$523$	−17.4308	+	30.1910i	−0.762195	+	1.32016i	0.179522	+	0.983754i	$0.442545\pi$
$523$	−17.4308	+	30.1910i	−0.762195	+	1.32016i	−0.941717	+	0.336407i	$0.890788\pi$
$524$		−	0.173783i		−	0.00759176i
$525$	4.92342	−	2.99773i	0.214876	−	0.130832i
$526$		−	30.6336i		−	1.33569i
$527$	−47.5684	+	27.4636i	−2.07211	+	1.19633i
$528$			1.60140i			0.0696920i
$529$	−22.5988			−0.982555
$530$	−18.5801	+	5.21144i	−0.807067	+	0.226371i
$531$	10.3918	+	5.99970i	0.450965	+	0.260365i
$532$	−0.232189			−0.0100667
$533$	15.1895	+	26.3090i	0.657931	+	1.13957i
$534$	−9.02723	−	15.6356i	−0.390647	−	0.676620i
$535$	−20.3026	+	5.69459i	−0.877759	+	0.246199i
$536$	9.33087	+	5.38718i	0.403032	+	0.232691i
$537$	8.11294	−	14.0520i	0.350099	−	0.606390i
$538$	5.89911	+	10.2176i	0.254329	+	0.440511i
$539$	−4.54072	−	7.86476i	−0.195583	−	0.338759i
$540$	−2.15298	+	0.603880i	−0.0926496	+	0.0259869i
$541$		−	6.10400i		−	0.262432i	−0.991354	−	0.131216i	$-0.958112\pi$
$541$		−	6.10400i		−	0.262432i	0.991354	−	0.131216i	$-0.0418881\pi$
$542$	5.06391	−	8.77094i	0.217513	−	0.376744i
$543$	3.57100	−	2.06172i	0.153246	−	0.0884769i
$544$	−6.57881			−0.282064
$545$	7.59768	−	29.7376i	0.325449	−	1.27382i
$546$	−2.18710	−	3.78816i	−0.0935991	−	0.162118i
$547$	28.0504			1.19935			0.599675	−	0.800243i	$-0.295296\pi$
$547$	28.0504			1.19935			0.599675	+	0.800243i	$0.295296\pi$
$548$	−0.141932	−	0.0819446i	−0.00606304	−	0.00350050i
$549$		−	13.0969i		−	0.558963i
$550$	6.83903	−	4.16410i	0.291617	−	0.177558i
$551$	0.577930	−	1.00100i	0.0246206	−	0.0426442i
$552$	0.548560	+	0.316711i	0.0233483	+	0.0134801i
$553$	−4.60006	−	7.96753i	−0.195614	−	0.338814i
$554$	29.8552			1.26843
$555$	−12.9222	+	4.24463i	−0.548517	+	0.180174i
$556$	1.61776			0.0686083
$557$	−1.04224	−	1.80521i	−0.0441610	−	0.0764890i	0.843100	−	0.537757i	$-0.180728\pi$
$557$	−1.04224	−	1.80521i	−0.0441610	−	0.0764890i	−0.887261	+	0.461268i	$0.847395\pi$
$558$	7.23055	+	4.17456i	0.306093	+	0.176723i
$559$	3.70216	−	6.41234i	0.156585	−	0.271213i
$560$	−1.84394	−	1.80144i	−0.0779208	−	0.0761246i
$561$			10.5353i			0.444801i
$562$	−14.1619	−	8.17640i	−0.597386	−	0.344901i
$563$	6.83925			0.288240			0.144120	−	0.989560i	$-0.453965\pi$
$563$	6.83925			0.288240			0.144120	+	0.989560i	$0.453965\pi$
$564$	−2.32717	−	4.03078i	−0.0979915	−	0.169726i
$565$	19.3041	+	4.93203i	0.812130	+	0.207492i
$566$	4.77505			0.200710
$567$	0.998396	−	0.576424i	0.0419287	−	0.0242075i
$568$	5.52164	−	9.56376i	0.231683	−	0.401286i
$569$			1.30706i			0.0547947i	0.999625	+	0.0273973i	$0.00872194\pi$
$569$			1.30706i			0.0547947i	−0.999625	+	0.0273973i	$0.991278\pi$
$570$	−0.121624	−	0.433620i	−0.00509428	−	0.0181624i
$571$	12.5935	+	21.8126i	0.527022	+	0.912829i	0.999504	+	0.0314890i	$0.0100249\pi$
$571$	12.5935	+	21.8126i	0.527022	+	0.912829i	−0.472482	+	0.881340i	$0.656642\pi$
$572$	−3.03805	−	5.26206i	−0.127027	−	0.220018i
$573$	−2.20001	+	3.81053i	−0.0919066	+	0.159187i
$574$	−7.99376	−	4.61520i	−0.333653	−	0.192635i
$575$	−0.0738470	−	3.16625i	−0.00307963	−	0.132042i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	14.3582	+	24.8692i	0.597741	+	1.03532i	0.993154	+	0.116814i	$0.0372681\pi$
$577$	14.3582	+	24.8692i	0.597741	+	1.03532i	−0.395413	+	0.918503i	$0.629399\pi$
$578$	−26.2807			−1.09313
$579$	0.998530	+	0.576502i	0.0414975	+	0.0239586i
$580$	12.3559	−	3.46566i	0.513053	−	0.143904i
$581$	16.6242			0.689689
$582$			2.93176i			0.121525i
$583$	11.9684	−	6.90999i	0.495682	−	0.286182i
$584$		−	4.32373i		−	0.178917i
$585$	5.92888	−	6.06877i	0.245129	−	0.250913i
$586$			3.50966i			0.144983i
$587$	−19.0536	+	33.0018i	−0.786427	+	1.36213i	0.141716	+	0.989907i	$0.454738\pi$
$587$	−19.0536	+	33.0018i	−0.786427	+	1.36213i	−0.928143	+	0.372224i	$0.878595\pi$
$588$	−4.91118	−	2.83547i	−0.202534	−	0.116933i
$589$	−0.840775	+	1.45627i	−0.0346435	+	0.0600044i
$590$	−25.8345	+	7.24620i	−1.06359	+	0.298321i
$591$	1.73256			0.0712679
$592$	3.26970	+	5.12923i	0.134384	+	0.210810i
$593$			10.9777i			0.450800i	0.974266	+	0.225400i	$0.0723688\pi$
$593$			10.9777i			0.450800i	−0.974266	+	0.225400i	$0.927631\pi$
$594$	1.38685	−	0.800700i	0.0569033	−	0.0328531i
$595$	−12.1309	−	11.8513i	−0.497320	−	0.485856i
$596$	8.04929	−	13.9418i	0.329712	−	0.571077i
$597$	9.93510	−	17.2081i	0.406617	−	0.704281i
$598$	−2.40336			−0.0982807
$599$	6.68729	−	11.5827i	0.273235	−	0.473258i	−0.696453	−	0.717602i	$-0.745240\pi$
$599$	6.68729	−	11.5827i	0.273235	−	0.473258i	0.969688	+	0.244345i	$0.0785729\pi$
$600$	2.39836	−	4.38724i	0.0979125	−	0.179108i
$601$	−8.44195	−	14.6219i	−0.344354	−	0.596439i	0.640882	−	0.767639i	$-0.278569\pi$
$601$	−8.44195	−	14.6219i	−0.344354	−	0.596439i	−0.985236	+	0.171200i	$0.945235\pi$
$602$			2.24974i			0.0916926i
$603$		−	10.7744i		−	0.438766i
$604$	3.14518	+	5.44761i	0.127976	+	0.221660i
$605$	13.1813	−	13.4923i	0.535897	−	0.548541i
$606$			14.8756i			0.604279i
$607$	−12.0273	−	20.8319i	−0.488172	−	0.845539i	0.511735	−	0.859143i	$-0.329003\pi$
$607$	−12.0273	−	20.8319i	−0.488172	−	0.845539i	−0.999907	+	0.0136043i	$0.995669\pi$
$608$	−0.174421	+	0.100702i	−0.00707372	+	0.00408402i
$609$	−5.72979	+	3.30809i	−0.232183	+	0.134051i
$610$	20.9481	+	20.4652i	0.848163	+	0.828612i
$611$	15.2938	+	8.82986i	0.618719	+	0.357218i
$612$	3.28940	+	5.69741i	0.132966	+	0.230304i
$613$	−17.7700	+	10.2595i	−0.717724	+	0.414378i	−0.813914	−	0.580985i	$-0.802668\pi$
$613$	−17.7700	+	10.2595i	−0.717724	+	0.414378i	0.0961906	+	0.995363i	$0.469334\pi$
$614$	−12.0099	+	6.93391i	−0.484680	+	0.279830i
$615$	4.43178	−	17.3461i	0.178706	−	0.699463i
$616$	1.59883	+	0.923086i	0.0644188	+	0.0371922i
$617$	17.4897	−	10.0977i	0.704108	−	0.406517i	−0.104767	−	0.994497i	$-0.533410\pi$
$617$	17.4897	−	10.0977i	0.704108	−	0.406517i	0.808876	+	0.587980i	$0.200076\pi$
$618$		−	2.82877i		−	0.113790i
$619$	1.21856			0.0489782			0.0244891	−	0.999700i	$-0.492204\pi$
$619$	1.21856			0.0489782			0.0244891	+	0.999700i	$0.492204\pi$
$620$	−17.9755	+	5.04187i	−0.721913	+	0.202486i
$621$		−	0.633422i		−	0.0254184i
$622$	−13.6673	−	7.89080i	−0.548008	−	0.316392i
$623$	−20.8141			−0.833898
$624$	−3.28591	−	1.89712i	−0.131542	−	0.0759457i
$625$	−24.9728	+	1.16552i	−0.998913	+	0.0466210i
$626$	6.99253	−	12.1114i	0.279478	−	0.484070i
$627$	0.161265	+	0.279319i	0.00644029	+	0.0111549i
$628$			3.90659i			0.155890i
$629$	21.5108	+	33.7442i	0.857690	+	1.34547i
$630$	−0.638119	+	2.49762i	−0.0254233	+	0.0995075i
$631$	35.4811	−	20.4850i	1.41248	−	0.815497i	0.416860	−	0.908971i	$-0.363131\pi$
$631$	35.4811	−	20.4850i	1.41248	−	0.815497i	0.995622	+	0.0934743i	$0.0297973\pi$
$632$	−6.91117	−	3.99017i	−0.274912	−	0.158720i
$633$	13.5564	+	7.82681i	0.538820	+	0.311088i
$634$	4.22693	+	2.44042i	0.167873	+	0.0969215i
$635$	6.86807	−	26.8819i	0.272551	−	1.06677i
$636$	4.31497	−	7.47374i	0.171100	−	0.296353i
$637$	21.5169			0.852533
$638$	−7.95914	+	4.59521i	−0.315105	+	0.181926i
$639$	−11.0433			−0.436865
$640$	−2.16648	−	0.553515i	−0.0856375	−	0.0218796i
$641$	−7.32583	−	12.6887i	−0.289353	−	0.501174i	0.684302	−	0.729198i	$-0.260107\pi$
$641$	−7.32583	−	12.6887i	−0.289353	−	0.501174i	−0.973655	+	0.228024i	$0.926773\pi$
$642$	4.71500	−	8.16662i	0.186086	−	0.322311i
$643$	−26.8103			−1.05730			−0.528648	−	0.848841i	$-0.677301\pi$
$643$	−26.8103			−1.05730			−0.528648	+	0.848841i	$0.677301\pi$
$644$	0.632406	−	0.365120i	0.0249203	−	0.0143877i
$645$	−4.20146	+	1.17845i	−0.165432	+	0.0464014i
$646$	−1.14749	+	0.662501i	−0.0451472	+	0.0260657i
$647$	−10.9636	+	18.9895i	−0.431024	+	0.746555i	−0.996962	−	0.0778928i	$-0.975181\pi$
$647$	−10.9636	+	18.9895i	−0.431024	+	0.746555i	0.565938	+	0.824448i	$0.308514\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	16.6414	−	9.60791i	0.653232	−	0.377144i
$650$	0.442349	+	18.9661i	0.0173504	+	0.743911i
$651$	8.33573	−	4.81263i	0.326703	−	0.188622i
$652$	−6.88754			−0.269737
$653$	−13.8367	+	23.9659i	−0.541473	+	0.937859i	0.457346	+	0.889289i	$0.348800\pi$
$653$	−13.8367	+	23.9659i	−0.541473	+	0.937859i	−0.998820	+	0.0485707i	$0.984533\pi$
$654$	6.86312	+	11.8873i	0.268369	+	0.464829i
$655$	0.0961918	−	0.376498i	0.00375852	−	0.0147110i
$656$	−8.00660			−0.312605
$657$	−3.74446	+	2.16187i	−0.146085	+	0.0843424i
$658$	−5.36575			−0.209179
$659$	−24.2847	+	42.0624i	−0.945998	+	1.63852i	−0.192258	+	0.981344i	$0.561581\pi$
$659$	−24.2847	+	42.0624i	−0.945998	+	1.63852i	−0.753740	+	0.657172i	$0.771752\pi$
$660$	−0.886399	+	3.46940i	−0.0345030	+	0.135046i
$661$	−24.9498	−	14.4048i	−0.970434	−	0.560280i	−0.0710652	−	0.997472i	$-0.522640\pi$
$661$	−24.9498	−	14.4048i	−0.970434	−	0.560280i	−0.899368	+	0.437192i	$0.855973\pi$
$662$	8.03353	+	4.63816i	0.312232	+	0.180267i
$663$	−21.6174	−	12.4808i	−0.839550	−	0.484714i
$664$	12.4882	−	7.21006i	0.484636	−	0.279805i
$665$	−0.503032	−	0.128520i	−0.0195067	−	0.00498380i
$666$	2.80719	−	5.39626i	0.108777	−	0.209101i
$667$			3.63521i			0.140756i
$668$	−2.06388	−	3.57474i	−0.0798539	−	0.138311i
$669$	8.19730	−	14.1981i	0.316926	−	0.548932i
$670$	17.2332	+	16.8360i	0.665777	+	0.650430i
$671$	−18.1635	−	10.4867i	−0.701194	−	0.404835i
$672$	1.15285			0.0444721
$673$	25.5316	+	14.7407i	0.984171	+	0.568211i	0.903527	−	0.428532i	$-0.140969\pi$
$673$	25.5316	+	14.7407i	0.984171	+	0.568211i	0.0806443	+	0.996743i	$0.474302\pi$
$674$		−	30.0926i		−	1.15913i
$675$	−4.99864	+	0.116584i	−0.192398	+	0.00448733i
$676$	1.39631			0.0537042
$677$		−	15.7058i		−	0.603625i	−0.953367	−	0.301812i	$-0.902408\pi$
$677$		−	15.7058i		−	0.603625i	0.953367	−	0.301812i	$-0.0975916\pi$
$678$	−7.71661	+	4.45519i	−0.296355	+	0.171100i
$679$	2.92706	+	1.68994i	0.112330	+	0.0648539i
$680$	−14.2528	−	3.64147i	−0.546571	−	0.139644i
$681$	−23.5793	+	13.6135i	−0.903562	+	0.521672i
$682$	11.5790	−	6.68514i	0.443383	−	0.255987i
$683$	−10.5991	−	18.3581i	−0.405562	−	0.702454i	0.588825	−	0.808261i	$-0.299591\pi$
$683$	−10.5991	−	18.3581i	−0.405562	−	0.702454i	−0.994387	+	0.105807i	$0.966257\pi$
$684$	0.174421	+	0.100702i	0.00666917	+	0.00385045i
$685$	−0.262135	−	0.256093i	−0.0100157	−	0.00978479i
$686$	−12.6506	+	7.30384i	−0.483003	+	0.278862i
$687$	10.6131	−	6.12750i	0.404917	−	0.233779i
$688$	0.975731	+	1.69002i	0.0371994	+	0.0644312i
$689$			32.7441i			1.24745i
$690$	1.01314	+	0.989784i	0.0385695	+	0.0376804i
$691$	−24.3436	−	42.1643i	−0.926073	−	1.60401i	−0.789826	−	0.613331i	$-0.789829\pi$
$691$	−24.3436	−	42.1643i	−0.926073	−	1.60401i	−0.136247	−	0.990675i	$-0.543504\pi$
$692$			23.9168i			0.909181i
$693$		−	1.84617i		−	0.0701303i
$694$	−12.0908	−	20.9418i	−0.458959	−	0.794940i
$695$	3.50484	+	0.895455i	0.132946	+	0.0339665i
$696$	−2.86950	+	4.97011i	−0.108768	+	0.188392i
$697$	−52.6739			−1.99517
$698$	3.22778	−	5.59068i	0.122173	−	0.211610i
$699$	−6.23228	+	10.7946i	−0.235727	+	0.408290i
$700$	−2.99773	−	4.92342i	−0.113304	−	0.186088i
$701$	−26.2855	+	15.1759i	−0.992788	+	0.573186i	−0.906106	−	0.423050i	$-0.860960\pi$
$701$	−26.2855	+	15.1759i	−0.992788	+	0.573186i	−0.0866814	+	0.996236i	$0.527626\pi$
$702$			3.79425i			0.143205i
$703$	1.08683	+	0.565382i	0.0409906	+	0.0213238i
$704$	1.60140			0.0603550
$705$	−2.81066	−	10.0207i	−0.105856	−	0.377402i
$706$	−5.33390	+	9.23859i	−0.200744	+	0.347699i
$707$	14.8517	+	8.57465i	0.558557	+	0.322483i
$708$	5.99970	−	10.3918i	0.225482	−	0.390547i
$709$		−	12.2106i		−	0.458577i	−0.973358	−	0.229289i	$-0.926360\pi$
$709$		−	12.2106i		−	0.458577i	0.973358	−	0.229289i	$-0.0736400\pi$
$710$	17.2562	−	17.6633i	0.647613	−	0.662894i
$711$			7.98033i			0.299286i
$712$	−15.6356	+	9.02723i	−0.585970	+	0.338310i
$713$		−	5.28852i		−	0.198057i
$714$	7.58437			0.283838
$715$	−3.66924	−	13.0817i	−0.137222	−	0.489230i
$716$	−14.0520	−	8.11294i	−0.525149	−	0.303195i
$717$	16.1332			0.602505
$718$	−3.66314	−	6.34474i	−0.136707	−	0.236784i
$719$	−6.58657	−	11.4083i	−0.245637	−	0.425457i	0.716673	−	0.697409i	$-0.245664\pi$
$719$	−6.58657	−	11.4083i	−0.245637	−	0.425457i	−0.962311	+	0.271953i	$0.912331\pi$
$720$	0.603880	+	2.15298i	0.0225053	+	0.0802369i
$721$	−2.82423	−	1.63057i	−0.105180	−	0.0607256i
$722$	9.47972	−	16.4194i	0.352799	−	0.611065i
$723$	0.267013	+	0.462479i	0.00993031	+	0.0171998i
$724$	−2.06172	−	3.57100i	−0.0766232	−	0.132715i
$725$	28.6872	−	0.669075i	1.06541	−	0.0248488i
$726$			8.43552i			0.313071i
$727$	−4.14865	+	7.18568i	−0.153865	+	0.266502i	−0.932645	−	0.360795i	$-0.882505\pi$
$727$	−4.14865	+	7.18568i	−0.153865	+	0.266502i	0.778780	+	0.627297i	$0.215839\pi$
$728$	−3.78816	+	2.18710i	−0.140399	+	0.0810592i
$729$	−1.00000			−0.0370370
$730$	2.39325	−	9.36726i	0.0885782	−	0.346698i
$731$	6.41915	+	11.1183i	0.237421	+	0.411225i
$732$	−13.0969			−0.484076
$733$	−25.5218	−	14.7350i	−0.942669	−	0.544250i	−0.0518729	−	0.998654i	$-0.516519\pi$
$733$	−25.5218	−	14.7350i	−0.942669	−	0.544250i	−0.890796	+	0.454404i	$0.849852\pi$
$734$		−	4.31801i		−	0.159381i
$735$	−9.07048	−	8.86139i	−0.334570	−	0.326857i
$736$	0.316711	−	0.548560i	0.0116741	−	0.0202202i
$737$	−14.9424	−	8.62703i	−0.550412	−	0.317781i
$738$	4.00330	+	6.93392i	0.147364	+	0.255241i
$739$	45.4776			1.67292			0.836461	−	0.548027i	$-0.184621\pi$
$739$	45.4776			1.67292			0.836461	+	0.548027i	$0.184621\pi$
$740$	4.24463	+	12.9222i	0.156036	+	0.475029i
$741$	−0.764179			−0.0280728
$742$	−4.97450	−	8.61609i	−0.182620	−	0.316307i
$743$	19.0245	+	10.9838i	0.697941	+	0.402957i	0.806580	−	0.591125i	$-0.201316\pi$
$743$	19.0245	+	10.9838i	0.697941	+	0.402957i	−0.108639	+	0.994081i	$0.534649\pi$
$744$	4.17456	−	7.23055i	0.153047	−	0.265085i
$745$	25.1556	−	25.7491i	0.921629	−	0.943375i
$746$		−	0.190388i		−	0.00697058i
$747$	−12.4882	−	7.21006i	−0.456919	−	0.263802i
$748$	10.5353			0.385209
$749$	−5.43568	−	9.41488i	−0.198616	−	0.344012i
$750$	7.62439	−	8.17733i	0.278403	−	0.298594i
$751$	20.1290			0.734517			0.367258	−	0.930119i	$-0.380296\pi$
$751$	20.1290			0.734517			0.367258	+	0.930119i	$0.380296\pi$
$752$	−4.03078	+	2.32717i	−0.146987	+	0.0848631i
$753$	8.54760	−	14.8049i	0.311492	−	0.539520i
$754$		−	21.7752i		−	0.793004i
$755$	3.79862	+	13.5430i	0.138246	+	0.492881i
$756$	−0.576424	−	0.998396i	−0.0209643	−	0.0363113i
$757$	9.99404	+	17.3102i	0.363239	+	0.629149i	0.988492	−	0.151273i	$-0.0483374\pi$
$757$	9.99404	+	17.3102i	0.363239	+	0.629149i	−0.625253	+	0.780422i	$0.715004\pi$
$758$	15.9392	−	27.6075i	0.578938	−	1.00275i
$759$	−0.878464	−	0.507181i	−0.0318862	−	0.0184095i
$760$	−0.433620	+	0.121624i	−0.0157291	+	0.00441177i
$761$	−3.62729	−	6.28264i	−0.131489	−	0.227746i	0.792762	−	0.609532i	$-0.208642\pi$
$761$	−3.62729	−	6.28264i	−0.131489	−	0.227746i	−0.924251	+	0.381786i	$0.875309\pi$
$762$	6.20405	+	10.7457i	0.224749	+	0.389277i
$763$	15.8243			0.572877
$764$	3.81053	+	2.20001i	0.137860	+	0.0795935i
$765$	3.97281	+	14.1640i	0.143637	+	0.512102i
$766$	23.8982			0.863475
$767$			45.5287i			1.64394i
$768$	0.866025	−	0.500000i	0.0312500	−	0.0180422i
$769$			17.8233i			0.642724i	0.946956	+	0.321362i	$0.104141\pi$
$769$			17.8233i			0.642724i	−0.946956	+	0.321362i	$0.895859\pi$
$770$	2.95289	+	2.88482i	0.106415	+	0.103962i
$771$			5.71778i			0.205921i
$772$	0.576502	−	0.998530i	0.0207487	−	0.0359379i
$773$	−40.0301	−	23.1114i	−1.43978	−	0.831260i	−0.441950	−	0.897040i	$-0.645713\pi$
$773$	−40.0301	−	23.1114i	−1.43978	−	0.831260i	−0.997834	+	0.0657804i	$0.979046\pi$
$774$	0.975731	−	1.69002i	0.0350719	−	0.0607464i
$775$	−41.7342	+	0.973374i	−1.49914	+	0.0349646i
$776$	2.93176			0.105244
$777$	−3.76947	−	5.91323i	−0.135229	−	0.212136i
$778$			7.08113i			0.253871i
$779$	−1.39652	+	0.806283i	−0.0500356	+	0.0288881i
$780$	−6.06877	−	5.92888i	−0.217297	−	0.212288i
$781$	−8.84235	+	15.3154i	−0.316404	+	0.548028i
$782$	2.08358	−	3.60887i	0.0745087	−	0.129053i
$783$	5.73899			0.205095
$784$	−2.83547	+	4.91118i	−0.101267	+	0.175399i
$785$	−2.16236	+	8.46354i	−0.0771778	+	0.302077i
$786$	0.0868917	+	0.150501i	0.00309932	+	0.00536819i
$787$		−	37.3668i		−	1.33198i	−0.745960	−	0.665991i	$-0.768009\pi$
$787$		−	37.3668i		−	1.33198i	0.745960	−	0.665991i	$-0.231991\pi$
$788$		−	1.73256i		−	0.0617199i
$789$	15.3168	+	26.5295i	0.545292	+	0.944474i
$790$	−12.7643	−	12.4700i	−0.454132	−	0.443664i
$791$			10.2723i			0.365241i
$792$	−0.800700	−	1.38685i	−0.0284516	−	0.0492797i
$793$	43.0354	−	24.8465i	1.52823	−	0.882324i
$794$	−1.39497	+	0.805384i	−0.0495055	+	0.0285820i
$795$	13.4851	−	13.8033i	0.478267	−	0.489552i
$796$	−17.2081	−	9.93510i	−0.609925	−	0.352140i
$797$	0.885326	+	1.53343i	0.0313598	+	0.0543168i	0.881279	−	0.472596i	$-0.156683\pi$
$797$	0.885326	+	1.53343i	0.0313598	+	0.0543168i	−0.849920	+	0.526913i	$0.823350\pi$
$798$	0.201082	−	0.116094i	0.00711821	−	0.00410970i
$799$	−26.5177	+	15.3100i	−0.938129	+	0.541629i
$800$	−4.38724	−	2.39836i	−0.155112	−	0.0847947i
$801$	15.6356	+	9.02723i	0.552458	+	0.318962i
$802$	−7.74056	+	4.46901i	−0.273329	+	0.157806i
$803$			6.92402i			0.244343i
$804$	−10.7744			−0.379982
$805$	1.57219	−	0.440977i	0.0554125	−	0.0155424i
$806$			31.6786i			1.11583i
$807$	−10.2176	−	5.89911i	−0.359675	−	0.207659i
$808$	14.8756			0.523321
$809$	−1.26629	−	0.731091i	−0.0445202	−	0.0257038i	0.477575	−	0.878591i	$-0.341516\pi$
$809$	−1.26629	−	0.731091i	−0.0445202	−	0.0257038i	−0.522095	+	0.852887i	$0.674849\pi$
$810$	1.56260	−	1.59947i	0.0549040	−	0.0561995i
$811$	13.5792	−	23.5198i	0.476830	−	0.825893i	−0.522818	−	0.852444i	$-0.675119\pi$
$811$	13.5792	−	23.5198i	0.476830	−	0.825893i	0.999647	+	0.0265514i	$0.00845256\pi$
$812$	3.30809	+	5.72979i	0.116091	+	0.201076i
$813$			10.1278i			0.355198i
$814$	−5.23610	−	8.21395i	−0.183525	−	0.287899i
$815$	−14.9217	−	3.81236i	−0.522684	−	0.133541i
$816$	5.69741	−	3.28940i	0.199449	−	0.115152i
$817$	0.340377	+	0.196517i	0.0119083	+	0.00687525i
$818$	−24.5929	−	14.1987i	−0.859869	−	0.496446i
$819$	3.78816	+	2.18710i	0.132369	+	0.0764233i
$820$	−17.3461	−	4.43178i	−0.605753	−	0.154764i
$821$	−22.8564	+	39.5884i	−0.797693	+	1.38164i	0.123422	+	0.992354i	$0.460613\pi$
$821$	−22.8564	+	39.5884i	−0.797693	+	1.38164i	−0.921115	+	0.389291i	$0.872720\pi$
$822$	0.163889			0.00571629
$823$	−13.9921	+	8.07837i	−0.487735	+	0.281594i	−0.723634	−	0.690183i	$-0.757530\pi$
$823$	−13.9921	+	8.07837i	−0.487735	+	0.281594i	0.235899	+	0.971778i	$0.424196\pi$
$824$	−2.82877			−0.0985447
$825$	−3.84073	+	7.02573i	−0.133717	+	0.244604i
$826$	−6.91674	−	11.9801i	−0.240664	−	0.416843i
$827$	8.32393	−	14.4175i	0.289452	−	0.501345i	−0.684227	−	0.729269i	$-0.739860\pi$
$827$	8.32393	−	14.4175i	0.289452	−	0.501345i	0.973679	+	0.227924i	$0.0731938\pi$
$828$	−0.633422			−0.0220129
$829$	−21.9579	+	12.6774i	−0.762630	+	0.440305i	−0.830239	−	0.557407i	$-0.811796\pi$
$829$	−21.9579	+	12.6774i	−0.762630	+	0.440305i	0.0676091	+	0.997712i	$0.478463\pi$
$830$	31.0463	−	8.70802i	1.07763	−	0.302260i
$831$	−25.8554	+	14.9276i	−0.896913	+	0.517833i
$832$	−1.89712	+	3.28591i	−0.0657709	+	0.113919i
$833$	−18.6540	+	32.3097i	−0.646323	+	1.11946i
$834$	−1.40102	+	0.808880i	−0.0485134	+	0.0280092i
$835$	−2.49267	−	8.88699i	−0.0862625	−	0.307547i
$836$	0.279319	−	0.161265i	0.00966043	−	0.00557745i
$837$	−8.34912			−0.288588
$838$	17.6867	−	30.6343i	0.610978	−	1.05825i
$839$	−20.0824	−	34.7837i	−0.693322	−	1.20087i	−0.970743	−	0.240120i	$-0.922813\pi$
$839$	−20.0824	−	34.7837i	−0.693322	−	1.20087i	0.277422	−	0.960748i	$-0.410520\pi$
$840$	2.49762	+	0.638119i	0.0861761	+	0.0220172i
$841$	−3.93603			−0.135725
$842$	5.95217	−	3.43649i	0.205125	−	0.118429i
$843$	16.3528			0.563221
$844$	7.82681	−	13.5564i	0.269410	−	0.466632i
$845$	3.02507	+	0.772879i	0.104066	+	0.0265878i
$846$	4.03078	+	2.32717i	0.138581	+	0.0800097i
$847$	8.42199	+	4.86244i	0.289383	+	0.167075i
$848$	−7.47374	−	4.31497i	−0.256649	−	0.148177i
$849$	−4.13531	+	2.38752i	−0.141924	+	0.0819396i
$850$	−28.8628	−	15.7783i	−0.989986	−	0.541192i
$851$	−3.84924	+	0.169143i	−0.131950	+	0.00579814i
$852$			11.0433i			0.378336i
$853$	1.89354	+	3.27971i	0.0648336	+	0.112295i	0.896620	−	0.442801i	$-0.146015\pi$
$853$	1.89354	+	3.27971i	0.0648336	+	0.112295i	−0.831787	+	0.555096i	$0.812682\pi$
$854$	−7.54938	+	13.0759i	−0.258335	+	0.447449i
$855$	0.322140	+	0.314714i	0.0110169	+	0.0107630i
$856$	−8.16662	−	4.71500i	−0.279129	−	0.161155i
$857$	−28.2901			−0.966370			−0.483185	−	0.875518i	$-0.660520\pi$
$857$	−28.2901			−0.966370			−0.483185	+	0.875518i	$0.660520\pi$
$858$	5.26206	+	3.03805i	0.179644	+	0.103717i
$859$		−	19.6040i		−	0.668881i	−0.942417	−	0.334441i	$-0.891453\pi$
$859$		−	19.6040i		−	0.668881i	0.942417	−	0.334441i	$-0.108547\pi$
$860$	1.17845	+	4.20146i	0.0401848	+	0.143269i
$861$	9.23040			0.314571
$862$			34.4366i			1.17291i
$863$	4.36914	−	2.52252i	0.148727	−	0.0858676i	−0.423790	−	0.905761i	$-0.639300\pi$
$863$	4.36914	−	2.52252i	0.148727	−	0.0858676i	0.572517	+	0.819893i	$0.305967\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$	−13.2383	+	51.8152i	−0.450117	+	1.76177i
$866$	15.3631	−	8.86990i	0.522060	−	0.301411i
$867$	22.7598	−	13.1403i	0.772962	−	0.446270i
$868$	−4.81263	−	8.33573i	−0.163351	−	0.282933i
$869$	11.0675	+	6.38985i	0.375441	+	0.216761i
$870$	−8.96773	+	9.17932i	−0.304034	+	0.311208i
$871$	35.4036	−	20.4403i	1.19961	−	0.692593i
$872$	11.8873	−	6.86312i	0.402554	−	0.232415i
$873$	−1.46588	−	2.53898i	−0.0496125	−	0.0859314i
$874$		−	0.127574i		−	0.00431526i
$875$	−3.76933	−	12.3258i	−0.127427	−	0.416687i
$876$	2.16187	+	3.74446i	0.0730427	+	0.126514i
$877$		−	18.6496i		−	0.629752i	−0.949133	−	0.314876i	$-0.898037\pi$
$877$		−	18.6496i		−	0.629752i	0.949133	−	0.314876i	$-0.101963\pi$
$878$		−	5.04569i		−	0.170284i
$879$	−1.75483	−	3.03946i	−0.0591890	−	0.102518i
$880$	3.46940	+	0.886399i	0.116953	+	0.0298805i
$881$	−4.23407	+	7.33362i	−0.142649	+	0.247076i	−0.928493	−	0.371349i	$-0.878895\pi$
$881$	−4.23407	+	7.33362i	−0.142649	+	0.247076i	0.785844	+	0.618425i	$0.212229\pi$
$882$	5.67094			0.190950
$883$	−22.3120	+	38.6455i	−0.750858	+	1.30052i	0.196549	+	0.980494i	$0.437026\pi$
$883$	−22.3120	+	38.6455i	−0.750858	+	1.30052i	−0.947407	+	0.320030i	$0.896307\pi$
$884$	−12.4808	+	21.6174i	−0.419775	+	0.727072i
$885$	18.7502	−	19.1926i	0.630281	−	0.645153i
$886$	−4.91055	+	2.83510i	−0.164973	+	0.0952472i
$887$			10.6967i			0.359159i	0.983743	+	0.179579i	$0.0574737\pi$
$887$			10.6967i			0.359159i	−0.983743	+	0.179579i	$0.942526\pi$
$888$	−5.39626	−	2.80719i	−0.181087	−	0.0942033i
$889$	14.3047			0.479763
$890$	−38.8709	+	10.9027i	−1.30296	+	0.365460i
$891$	−0.800700	+	1.38685i	−0.0268245	+	0.0464613i
$892$	−14.1981	−	8.19730i	−0.475389	−	0.274466i
$893$	−0.468703	+	0.811817i	−0.0156845	+	0.0271664i
$894$			16.0986i			0.538417i
$895$	−25.9528	−	25.3545i	−0.867505	−	0.847508i
$896$		−	1.15285i		−	0.0385140i
$897$	2.08137	−	1.20168i	0.0694950	−	0.0401229i
$898$		−	6.73467i		−	0.224739i
$899$	47.9155			1.59807
$900$	0.116584	+	4.99864i	0.00388614	+	0.166621i
$901$	−49.1683	−	28.3873i	−1.63803	−	0.945719i
$902$	12.8218			0.426918
$903$	−1.12487	−	1.94833i	−0.0374333	−	0.0648364i
$904$	4.45519	+	7.71661i	0.148177	+	0.256651i
$905$	−2.49006	−	8.87769i	−0.0827725	−	0.295104i
$906$	−5.44761	−	3.14518i	−0.180985	−	0.104492i
$907$	9.54454	−	16.5316i	0.316921	−	0.548924i	−0.662923	−	0.748688i	$-0.730684\pi$
$907$	9.54454	−	16.5316i	0.316921	−	0.548924i	0.979844	+	0.199764i	$0.0640175\pi$
$908$	13.6135	+	23.5793i	0.451781	+	0.782508i
$909$	−7.43779	−	12.8826i	−0.246696	−	0.427290i
$910$	−9.41755	+	2.64149i	−0.312189	+	0.0875645i
$911$			40.2529i			1.33364i	0.745219	+	0.666819i	$0.232345\pi$
$911$			40.2529i			1.33364i	−0.745219	+	0.666819i	$0.767655\pi$
$912$	0.100702	−	0.174421i	0.00333459	−	0.00577567i
$913$	−19.9986	+	11.5462i	−0.661857	+	0.382123i
$914$	25.1804			0.832892
$915$	−28.3742	−	7.24935i	−0.938021	−	0.239656i
$916$	−6.12750	−	10.6131i	−0.202458	−	0.350668i
$917$	0.200346			0.00661601
$918$	−5.69741	−	3.28940i	−0.188043	−	0.108566i
$919$			36.0859i			1.19036i	0.803591	+	0.595181i	$0.202920\pi$
$919$			36.0859i			1.19036i	−0.803591	+	0.595181i	$0.797080\pi$
$920$	0.989784	−	1.01314i	0.0326322	−	0.0334022i
$921$	6.93391	−	12.0099i	0.228480	−	0.395739i
$922$	30.6749	+	17.7102i	1.01023	+	0.583254i
$923$	−20.9505	−	36.2873i	−0.689593	−	1.19441i
$924$	−1.84617			−0.0607346
$925$	2.04326	+	30.3451i	0.0671819	+	0.997741i
$926$	21.0657			0.692260
$927$	1.41438	+	2.44978i	0.0464544	+	0.0804614i
$928$	4.97011	+	2.86950i	0.163152	+	0.0941958i
$929$	−11.7507	+	20.3528i	−0.385528	+	0.667753i	−0.991842	−	0.127471i	$-0.959314\pi$
$929$	−11.7507	+	20.3528i	−0.385528	+	0.667753i	0.606315	+	0.795225i	$0.292647\pi$
$930$	13.0463	−	13.3541i	0.427805	−	0.437899i
$931$			1.14215i			0.0374326i
$932$	10.7946	+	6.23228i	0.353590	+	0.204145i
$933$	15.7816			0.516666
$934$	18.4371	+	31.9340i	0.603281	+	1.04491i
$935$	22.8245	+	5.83145i	0.746440	+	0.190709i
$936$	3.79425			0.124019
$937$	40.1652	−	23.1894i	1.31214	−	0.757564i	0.329690	−	0.944089i	$-0.393056\pi$
$937$	40.1652	−	23.1894i	1.31214	−	0.757564i	0.982450	+	0.186525i	$0.0597226\pi$
$938$	−6.21060	+	10.7571i	−0.202783	+	0.351231i
$939$			13.9851i			0.456385i
$940$	−10.0207	+	2.81066i	−0.326839	+	0.0916737i
$941$	−15.7891	−	27.3476i	−0.514711	−	0.891506i	−0.999854	−	0.0170715i	$-0.994566\pi$
$941$	−15.7891	−	27.3476i	−0.514711	−	0.891506i	0.485143	−	0.874435i	$-0.338768\pi$
$942$	−1.95330	−	3.38321i	−0.0636418	−	0.110231i
$943$	2.53578	−	4.39210i	0.0825764	−	0.143026i
$944$	−10.3918	−	5.99970i	−0.338224	−	0.195274i
$945$	−0.696182	−	2.48206i	−0.0226468	−	0.0807415i
$946$	−1.56254	−	2.70639i	−0.0508024	−	0.0879924i
$947$	17.5747	+	30.4402i	0.571100	+	0.989174i	0.996453	+	0.0841466i	$0.0268164\pi$
$947$	17.5747	+	30.4402i	0.571100	+	0.989174i	−0.425354	+	0.905027i	$0.639850\pi$
$948$	7.98033			0.259189
$949$	−14.2074	−	8.20265i	−0.461192	−	0.266269i
$950$	−1.00675	+	0.0234806i	−0.0326633	+	0.000761810i
$951$	−4.88084			−0.158272
$952$		−	7.58437i		−	0.245811i
$953$	−26.4316	+	15.2603i	−0.856203	+	0.494329i	−0.862739	−	0.505650i	$-0.831253\pi$
$953$	−26.4316	+	15.2603i	−0.856203	+	0.494329i	0.00653627	+	0.999979i	$0.497919\pi$
$954$			8.62993i			0.279404i
$955$	7.03768	+	6.87545i	0.227734	+	0.222484i
$956$		−	16.1332i		−	0.521784i
$957$	4.59521	−	7.95914i	0.148542	−	0.257282i
$958$	3.93591	+	2.27240i	0.127163	+	0.0734179i
$959$	0.0944697	−	0.163626i	0.00305058	−	0.00528377i
$960$	2.15298	−	0.603880i	0.0694872	−	0.0194901i
$961$	−38.7077			−1.24864
$962$	23.0573	−	1.01318i	0.743396	−	0.0326662i
$963$			9.43000i			0.303878i
$964$	0.462479	−	0.267013i	0.0148955	−	0.00859990i
$965$	1.80168	−	1.84419i	0.0579981	−	0.0593666i
$966$	−0.365120	+	0.632406i	−0.0117475	+	0.0203473i
$967$	11.3064	−	19.5833i	0.363590	−	0.629757i	−0.624959	−	0.780658i	$-0.714884\pi$
$967$	11.3064	−	19.5833i	0.363590	−	0.629757i	0.988549	+	0.150901i	$0.0482175\pi$
$968$	8.43552			0.271128
$969$	0.662501	−	1.14749i	0.0212826	−	0.0368625i
$970$	6.35159	+	1.62277i	0.203937	+	0.0521041i
$971$	16.9557	+	29.3682i	0.544135	+	0.942470i	0.998661	+	0.0517360i	$0.0164754\pi$
$971$	16.9557	+	29.3682i	0.544135	+	0.942470i	−0.454526	+	0.890734i	$0.650191\pi$
$972$			1.00000i			0.0320750i
$973$			1.86503i			0.0597902i
$974$	13.0237	+	22.5576i	0.417305	+	0.722793i
$975$	−9.86612	−	16.2039i	−0.315969	−	0.518941i
$976$			13.0969i			0.419222i
$977$	−9.31401	−	16.1323i	−0.297982	−	0.516119i	0.677693	−	0.735345i	$-0.262980\pi$
$977$	−9.31401	−	16.1323i	−0.297982	−	0.516119i	−0.975674	+	0.219226i	$0.929647\pi$
$978$	5.96478	−	3.44377i	0.190733	−	0.110120i
$979$	25.0389	−	14.4562i	0.800246	−	0.462022i
$980$	−8.86139	+	9.07048i	−0.283067	+	0.289746i
$981$	−11.8873	−	6.86312i	−0.379531	−	0.219122i
$982$	14.0020	+	24.2521i	0.446820	+	0.773916i
$983$	−6.82940	+	3.94296i	−0.217824	+	0.125761i	−0.604942	−	0.796269i	$-0.706804\pi$
$983$	−6.82940	+	3.94296i	−0.217824	+	0.125761i	0.387118	+	0.922030i	$0.373471\pi$
$984$	6.93392	−	4.00330i	0.221045	−	0.127621i
$985$	0.958998	−	3.75355i	0.0305562	−	0.119598i
$986$	32.6974	+	18.8779i	1.04130	+	0.601193i
$987$	4.64687	−	2.68287i	0.147912	−	0.0853968i
$988$			0.764179i			0.0243118i
$989$	−1.23610			−0.0393057
$990$	−0.967053	−	3.44778i	−0.0307350	−	0.109578i
$991$		−	8.71571i		−	0.276864i	−0.990372	−	0.138432i	$-0.955794\pi$
$991$		−	8.71571i		−	0.276864i	0.990372	−	0.138432i	$-0.0442062\pi$
$992$	−7.23055	−	4.17456i	−0.229570	−	0.132542i
$993$	−9.27632			−0.294375
$994$	11.0256	+	6.36561i	0.349710	+	0.201905i
$995$	−31.7817	−	31.0491i	−1.00755	−	0.984323i
$996$	−7.21006	+	12.4882i	−0.228460	+	0.395704i
$997$	28.8512	+	49.9718i	0.913728	+	1.58262i	0.808753	+	0.588149i	$0.200143\pi$
$997$	28.8512	+	49.9718i	0.913728	+	1.58262i	0.104975	+	0.994475i	$0.466524\pi$
$998$			26.0956i			0.826042i
$999$	0.267030	+	6.07690i	0.00844846	+	0.192265i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.ba.b.529.3	yes	36
5.4	even	2		1110.2.ba.a.529.16	✓	36
37.27	even	6		1110.2.ba.a.619.16	yes	36
185.64	even	6	inner	1110.2.ba.b.619.3	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.ba.a.529.16	✓	36	5.4	even	2
1110.2.ba.a.619.16	yes	36	37.27	even	6
1110.2.ba.b.529.3	yes	36	1.1	even	1	trivial
1110.2.ba.b.619.3	yes	36	185.64	even	6	inner

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.56260 + 1.59947i) q^{5} -1.00000i q^{6} +(-0.998396 - 0.576424i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.56260 + 1.59947i) q^{5} -1.00000i q^{6} +(-0.998396 - 0.576424i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.16648 - 0.553515i) q^{10} +1.60140 q^{11} +(0.866025 - 0.500000i) q^{12} +(-1.89712 + 3.28591i) q^{13} -1.15285i q^{14} +(2.15298 - 0.603880i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.28940 - 5.69741i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-0.174421 - 0.100702i) q^{19} +(-0.603880 - 2.15298i) q^{20} +(0.576424 + 0.998396i) q^{21} +(0.800700 + 1.38685i) q^{22} +0.633422 q^{23} +(0.866025 + 0.500000i) q^{24} +(-0.116584 - 4.99864i) q^{25} -3.79425 q^{26} -1.00000i q^{27} +(0.998396 - 0.576424i) q^{28} +5.73899i q^{29} +(1.59947 + 1.56260i) q^{30} -8.34912i q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.38685 - 0.800700i) q^{33} +(3.28940 - 5.69741i) q^{34} +(2.48206 - 0.696182i) q^{35} -1.00000 q^{36} +(-6.07690 + 0.267030i) q^{37} -0.201405i q^{38} +(3.28591 - 1.89712i) q^{39} +(1.56260 - 1.59947i) q^{40} +(4.00330 - 6.93392i) q^{41} +(-0.576424 + 0.998396i) q^{42} -1.95146 q^{43} +(-0.800700 + 1.38685i) q^{44} +(-2.16648 - 0.553515i) q^{45} +(0.316711 + 0.548560i) q^{46} -4.65434i q^{47} +1.00000i q^{48} +(-2.83547 - 4.91118i) q^{49} +(4.27066 - 2.60029i) q^{50} +6.57881i q^{51} +(-1.89712 - 3.28591i) q^{52} +(7.47374 - 4.31497i) q^{53} +(0.866025 - 0.500000i) q^{54} +(-2.50234 + 2.56138i) q^{55} +(0.998396 + 0.576424i) q^{56} +(0.100702 + 0.174421i) q^{57} +(-4.97011 + 2.86950i) q^{58} +(10.3918 - 5.99970i) q^{59} +(-0.553515 + 2.16648i) q^{60} +(-11.3423 - 6.54846i) q^{61} +(7.23055 - 4.17456i) q^{62} -1.15285i q^{63} +1.00000 q^{64} +(-2.29127 - 8.16894i) q^{65} -1.60140i q^{66} +(-9.33087 - 5.38718i) q^{67} +6.57881 q^{68} +(-0.548560 - 0.316711i) q^{69} +(1.84394 + 1.80144i) q^{70} +(-5.52164 + 9.56376i) q^{71} +(-0.500000 - 0.866025i) q^{72} +4.32373i q^{73} +(-3.26970 - 5.12923i) q^{74} +(-2.39836 + 4.38724i) q^{75} +(0.174421 - 0.100702i) q^{76} +(-1.59883 - 0.923086i) q^{77} +(3.28591 + 1.89712i) q^{78} +(6.91117 + 3.99017i) q^{79} +(2.16648 + 0.553515i) q^{80} +(-0.500000 + 0.866025i) q^{81} +8.00660 q^{82} +(-12.4882 + 7.21006i) q^{83} -1.15285 q^{84} +(14.2528 + 3.64147i) q^{85} +(-0.975731 - 1.69002i) q^{86} +(2.86950 - 4.97011i) q^{87} -1.60140 q^{88} +(15.6356 - 9.02723i) q^{89} +(-0.603880 - 2.15298i) q^{90} +(3.78816 - 2.18710i) q^{91} +(-0.316711 + 0.548560i) q^{92} +(-4.17456 + 7.23055i) q^{93} +(4.03078 - 2.32717i) q^{94} +(0.433620 - 0.121624i) q^{95} +(-0.866025 + 0.500000i) q^{96} -2.93176 q^{97} +(2.83547 - 4.91118i) q^{98} +(0.800700 + 1.38685i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 18 q^{2} - 18 q^{4} + 4 q^{5} - 36 q^{8} + 18 q^{9}+O(q^{10}) \) 36 * q + 18 * q^2 - 18 * q^4 + 4 * q^5 - 36 * q^8 + 18 * q^9	\( 36 q + 18 q^{2} - 18 q^{4} + 4 q^{5} - 36 q^{8} + 18 q^{9} + 2 q^{10} + 4 q^{11} + 14 q^{13} + 2 q^{15} - 18 q^{16} - 18 q^{18} + 6 q^{19} - 2 q^{20} + 2 q^{22} + 20 q^{23} - 2 q^{25} + 28 q^{26} - 2 q^{30} + 18 q^{32} + 6 q^{33} - 20 q^{35} - 36 q^{36} - 20 q^{37} + 6 q^{39} - 4 q^{40} + 10 q^{41} - 2 q^{44} + 2 q^{45} + 10 q^{46} + 10 q^{49} - 4 q^{50} + 14 q^{52} + 12 q^{53} + 40 q^{55} - 8 q^{57} - 30 q^{58} + 18 q^{59} - 4 q^{60} - 6 q^{61} + 12 q^{62} + 36 q^{64} - 32 q^{65} - 36 q^{67} + 12 q^{69} - 40 q^{70} - 24 q^{71} - 18 q^{72} - 34 q^{74} + 8 q^{75} - 6 q^{76} + 24 q^{77} + 6 q^{78} - 2 q^{80} - 18 q^{81} + 20 q^{82} - 36 q^{83} + 26 q^{85} + 10 q^{87} - 4 q^{88} - 2 q^{90} - 36 q^{91} - 10 q^{92} - 12 q^{93} + 12 q^{94} + 18 q^{95} - 52 q^{97} - 10 q^{98} + 2 q^{99}+O(q^{100}) \) 36 * q + 18 * q^2 - 18 * q^4 + 4 * q^5 - 36 * q^8 + 18 * q^9 + 2 * q^10 + 4 * q^11 + 14 * q^13 + 2 * q^15 - 18 * q^16 - 18 * q^18 + 6 * q^19 - 2 * q^20 + 2 * q^22 + 20 * q^23 - 2 * q^25 + 28 * q^26 - 2 * q^30 + 18 * q^32 + 6 * q^33 - 20 * q^35 - 36 * q^36 - 20 * q^37 + 6 * q^39 - 4 * q^40 + 10 * q^41 - 2 * q^44 + 2 * q^45 + 10 * q^46 + 10 * q^49 - 4 * q^50 + 14 * q^52 + 12 * q^53 + 40 * q^55 - 8 * q^57 - 30 * q^58 + 18 * q^59 - 4 * q^60 - 6 * q^61 + 12 * q^62 + 36 * q^64 - 32 * q^65 - 36 * q^67 + 12 * q^69 - 40 * q^70 - 24 * q^71 - 18 * q^72 - 34 * q^74 + 8 * q^75 - 6 * q^76 + 24 * q^77 + 6 * q^78 - 2 * q^80 - 18 * q^81 + 20 * q^82 - 36 * q^83 + 26 * q^85 + 10 * q^87 - 4 * q^88 - 2 * q^90 - 36 * q^91 - 10 * q^92 - 12 * q^93 + 12 * q^94 + 18 * q^95 - 52 * q^97 - 10 * q^98 + 2 * q^99

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