LMFDB - Embedded newform 1110.2.ba.a.619.7

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			619.7
Character	$\chi$	$=$	1110.619
Dual form			1110.2.ba.a.529.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.00696233 - 2.23606i) q^{5} -1.00000i q^{6} +(3.60632 - 2.08211i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.00696233 - 2.23606i) q^{5} -1.00000i q^{6} +(3.60632 - 2.08211i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(1.93996 + 1.11200i) q^{10} +5.62355 q^{11} +(0.866025 + 0.500000i) q^{12} +(-2.80292 - 4.85480i) q^{13} +4.16422i q^{14} +(1.12406 + 1.93300i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.43213 - 2.48053i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-5.16423 + 2.98157i) q^{19} +(-1.93300 + 1.12406i) q^{20} +(-2.08211 + 3.60632i) q^{21} +(-2.81177 + 4.87013i) q^{22} -6.24179 q^{23} +(-0.866025 + 0.500000i) q^{24} +(-4.99990 + 0.0311363i) q^{25} +5.60584 q^{26} +1.00000i q^{27} +(-3.60632 - 2.08211i) q^{28} -9.90800i q^{29} +(-2.23606 + 0.00696233i) q^{30} +4.33846i q^{31} +(-0.500000 - 0.866025i) q^{32} +(-4.87013 + 2.81177i) q^{33} +(1.43213 + 2.48053i) q^{34} +(-4.68082 - 8.04944i) q^{35} -1.00000 q^{36} +(-2.01692 + 5.73864i) q^{37} -5.96313i q^{38} +(4.85480 + 2.80292i) q^{39} +(-0.00696233 - 2.23606i) q^{40} +(-0.470733 - 0.815334i) q^{41} +(-2.08211 - 3.60632i) q^{42} +4.29505 q^{43} +(-2.81177 - 4.87013i) q^{44} +(-1.93996 - 1.11200i) q^{45} +(3.12090 - 5.40555i) q^{46} +0.365900i q^{47} -1.00000i q^{48} +(5.17035 - 8.95532i) q^{49} +(2.47299 - 4.34561i) q^{50} +2.86427i q^{51} +(-2.80292 + 4.85480i) q^{52} +(-3.87603 - 2.23783i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(-0.0391530 - 12.5746i) q^{55} +(3.60632 - 2.08211i) q^{56} +(2.98157 - 5.16423i) q^{57} +(8.58058 + 4.95400i) q^{58} +(9.52048 + 5.49665i) q^{59} +(1.11200 - 1.93996i) q^{60} +(2.20880 - 1.27525i) q^{61} +(-3.75722 - 2.16923i) q^{62} -4.16422i q^{63} +1.00000 q^{64} +(-10.8361 + 6.30129i) q^{65} -5.62355i q^{66} +(1.92075 - 1.10894i) q^{67} -2.86427 q^{68} +(5.40555 - 3.12090i) q^{69} +(9.31143 - 0.0289927i) q^{70} +(-6.08527 - 10.5400i) q^{71} +(0.500000 - 0.866025i) q^{72} +11.5997i q^{73} +(-3.96135 - 4.61603i) q^{74} +(4.31447 - 2.52692i) q^{75} +(5.16423 + 2.98157i) q^{76} +(20.2803 - 11.7088i) q^{77} +(-4.85480 + 2.80292i) q^{78} +(-8.57325 + 4.94977i) q^{79} +(1.93996 + 1.11200i) q^{80} +(-0.500000 - 0.866025i) q^{81} +0.941466 q^{82} +(0.157099 + 0.0907014i) q^{83} +4.16422 q^{84} +(-5.55658 - 3.18506i) q^{85} +(-2.14753 + 3.71962i) q^{86} +(4.95400 + 8.58058i) q^{87} +5.62355 q^{88} +(-7.38304 - 4.26260i) q^{89} +(1.93300 - 1.12406i) q^{90} +(-20.2165 - 11.6720i) q^{91} +(3.12090 + 5.40555i) q^{92} +(-2.16923 - 3.75722i) q^{93} +(-0.316878 - 0.182950i) q^{94} +(6.70291 + 11.5267i) q^{95} +(0.866025 + 0.500000i) q^{96} -8.96250 q^{97} +(5.17035 + 8.95532i) q^{98} +(2.81177 - 4.87013i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9}+O(q^{10}) $ 36 * q - 18 * q^2 - 18 * q^4 + 2 * q^5 + 36 * q^8 + 18 * q^9	$ 36 q - 18 q^{2} - 18 q^{4} + 2 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} - 4 q^{20} - 2 q^{22} - 20 q^{23} + 4 q^{25} + 28 q^{26} - 2 q^{30} - 18 q^{32} - 6 q^{33} - 40 q^{35} - 36 q^{36} + 20 q^{37} + 6 q^{39} + 2 q^{40} + 10 q^{41} - 2 q^{44} - 2 q^{45} + 10 q^{46} + 10 q^{49} - 2 q^{50} - 14 q^{52} - 12 q^{53} + 56 q^{55} + 8 q^{57} + 30 q^{58} + 18 q^{59} + 4 q^{60} - 6 q^{61} - 12 q^{62} + 36 q^{64} + 40 q^{65} + 36 q^{67} + 12 q^{69} + 20 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} + 4 q^{90} - 36 q^{91} + 10 q^{92} + 12 q^{93} + 12 q^{94} - 30 q^{95} + 52 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) $ 36 * q - 18 * q^2 - 18 * q^4 + 2 * 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 - 4 * q^20 - 2 * q^22 - 20 * q^23 + 4 * q^25 + 28 * q^26 - 2 * q^30 - 18 * q^32 - 6 * q^33 - 40 * q^35 - 36 * q^36 + 20 * q^37 + 6 * q^39 + 2 * q^40 + 10 * q^41 - 2 * q^44 - 2 * q^45 + 10 * q^46 + 10 * q^49 - 2 * q^50 - 14 * q^52 - 12 * q^53 + 56 * q^55 + 8 * q^57 + 30 * q^58 + 18 * q^59 + 4 * q^60 - 6 * q^61 - 12 * q^62 + 36 * q^64 + 40 * q^65 + 36 * q^67 + 12 * q^69 + 20 * 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 + 4 * q^90 - 36 * q^91 + 10 * q^92 + 12 * q^93 + 12 * q^94 - 30 * 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 $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

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

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
$3$	−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
$5$	−0.00696233	−	2.23606i	−0.00311365	−	0.999995i
$5$	−0.00696233	−	2.23606i	−0.00311365	−	0.999995i
$6$		−	1.00000i		−	0.408248i
$7$	3.60632	−	2.08211i	1.36306	−	0.786963i	0.373030	−	0.927819i	$-0.378319\pi$
$7$	3.60632	−	2.08211i	1.36306	−	0.786963i	0.990030	+	0.140856i	$0.0449855\pi$
$8$	1.00000			0.353553
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	1.93996	+	1.11200i	0.613470	+	0.351645i
$11$	5.62355			1.69556			0.847782	−	0.530346i	$-0.177938\pi$
$11$	5.62355			1.69556			0.847782	+	0.530346i	$0.177938\pi$
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$	−2.80292	−	4.85480i	−0.777391	−	1.34648i	−0.933441	−	0.358731i	$-0.883210\pi$
$13$	−2.80292	−	4.85480i	−0.777391	−	1.34648i	0.156050	−	0.987749i	$-0.450124\pi$
$14$			4.16422i			1.11293i
$15$	1.12406	+	1.93300i	0.290231	+	0.499099i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.43213	−	2.48053i	0.347344	−	0.601617i	−0.638433	−	0.769677i	$-0.720417\pi$
$17$	1.43213	−	2.48053i	0.347344	−	0.601617i	0.985777	+	0.168061i	$0.0537504\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	−5.16423	+	2.98157i	−1.18475	+	0.684018i	−0.957110	−	0.289726i	$-0.906436\pi$
$19$	−5.16423	+	2.98157i	−1.18475	+	0.684018i	−0.227645	+	0.973744i	$0.573103\pi$
$20$	−1.93300	+	1.12406i	−0.432232	+	0.251347i
$21$	−2.08211	+	3.60632i	−0.454353	+	0.786963i
$22$	−2.81177	+	4.87013i	−0.599472	+	1.03832i
$23$	−6.24179			−1.30150			−0.650752	−	0.759291i	$-0.725546\pi$
$23$	−6.24179			−1.30150			−0.650752	+	0.759291i	$0.725546\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	−4.99990	+	0.0311363i	−0.999981	+	0.00622727i
$26$	5.60584			1.09940
$27$			1.00000i			0.192450i
$28$	−3.60632	−	2.08211i	−0.681530	−	0.393482i
$29$		−	9.90800i		−	1.83987i	−0.392071	−	0.919935i	$-0.628241\pi$
$29$		−	9.90800i		−	1.83987i	0.392071	−	0.919935i	$-0.371759\pi$
$30$	−2.23606	+	0.00696233i	−0.408246	+	0.00127114i
$31$			4.33846i			0.779210i	0.920982	+	0.389605i	$0.127388\pi$
$31$			4.33846i			0.779210i	−0.920982	+	0.389605i	$0.872612\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−4.87013	+	2.81177i	−0.847782	+	0.489467i
$34$	1.43213	+	2.48053i	0.245609	+	0.425407i
$35$	−4.68082	−	8.04944i	−0.791203	−	1.36060i
$36$	−1.00000			−0.166667
$37$	−2.01692	+	5.73864i	−0.331580	+	0.943427i
$37$	−2.01692	+	5.73864i	−0.331580	+	0.943427i
$38$		−	5.96313i		−	0.967348i
$39$	4.85480	+	2.80292i	0.777391	+	0.448827i
$40$	−0.00696233	−	2.23606i	−0.00110084	−	0.353552i
$41$	−0.470733	−	0.815334i	−0.0735162	−	0.127334i	0.826924	−	0.562314i	$-0.190089\pi$
$41$	−0.470733	−	0.815334i	−0.0735162	−	0.127334i	−0.900440	+	0.434980i	$0.856755\pi$
$42$	−2.08211	−	3.60632i	−0.321276	−	0.556467i
$43$	4.29505			0.654989			0.327495	−	0.944853i	$-0.393796\pi$
$43$	4.29505			0.654989			0.327495	+	0.944853i	$0.393796\pi$
$44$	−2.81177	−	4.87013i	−0.423891	−	0.734200i
$45$	−1.93996	−	1.11200i	−0.289193	−	0.165767i
$46$	3.12090	−	5.40555i	0.460151	−	0.797005i
$47$			0.365900i			0.0533719i	0.999644	+	0.0266860i	$0.00849542\pi$
$47$			0.365900i			0.0533719i	−0.999644	+	0.0266860i	$0.991505\pi$
$48$		−	1.00000i		−	0.144338i
$49$	5.17035	−	8.95532i	0.738622	−	1.27933i
$50$	2.47299	−	4.34561i	0.349733	−	0.614562i
$51$			2.86427i			0.401078i
$52$	−2.80292	+	4.85480i	−0.388695	+	0.673240i
$53$	−3.87603	−	2.23783i	−0.532414	−	0.307390i	0.209585	−	0.977790i	$-0.432789\pi$
$53$	−3.87603	−	2.23783i	−0.532414	−	0.307390i	−0.741999	+	0.670401i	$0.766122\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$	−0.0391530	−	12.5746i	−0.00527939	−	1.69555i
$56$	3.60632	−	2.08211i	0.481915	−	0.278233i
$57$	2.98157	−	5.16423i	0.394918	−	0.684018i
$58$	8.58058	+	4.95400i	1.12669	+	0.650492i
$59$	9.52048	+	5.49665i	1.23946	+	0.715603i	0.968984	−	0.247123i	$-0.0794853\pi$
$59$	9.52048	+	5.49665i	1.23946	+	0.715603i	0.270477	+	0.962726i	$0.412819\pi$
$60$	1.11200	−	1.93996i	0.143558	−	0.250448i
$61$	2.20880	−	1.27525i	0.282807	−	0.163279i	−0.351886	−	0.936043i	$-0.614460\pi$
$61$	2.20880	−	1.27525i	0.282807	−	0.163279i	0.634694	+	0.772764i	$0.281126\pi$
$62$	−3.75722	−	2.16923i	−0.477167	−	0.275492i
$63$		−	4.16422i		−	0.524642i
$64$	1.00000			0.125000
$65$	−10.8361	+	6.30129i	−1.34405	+	0.781579i
$66$		−	5.62355i		−	0.692211i
$67$	1.92075	−	1.10894i	0.234657	−	0.135479i	−0.378062	−	0.925780i	$-0.623409\pi$
$67$	1.92075	−	1.10894i	0.234657	−	0.135479i	0.612718	+	0.790301i	$0.290076\pi$
$68$	−2.86427			−0.347344
$69$	5.40555	−	3.12090i	0.650752	−	0.375712i
$70$	9.31143	−	0.0289927i	1.11293	−	0.00346529i
$71$	−6.08527	−	10.5400i	−0.722189	−	1.25087i	−0.960121	−	0.279587i	$-0.909803\pi$
$71$	−6.08527	−	10.5400i	−0.722189	−	1.25087i	0.237931	−	0.971282i	$-0.423531\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$			11.5997i			1.35764i	0.734303	+	0.678822i	$0.237509\pi$
$73$			11.5997i			1.35764i	−0.734303	+	0.678822i	$0.762491\pi$
$74$	−3.96135	−	4.61603i	−0.460498	−	0.536602i
$75$	4.31447	−	2.52692i	0.498193	−	0.291783i
$76$	5.16423	+	2.98157i	0.592377	+	0.342009i
$77$	20.2803	−	11.7088i	2.31115	−	1.33435i
$78$	−4.85480	+	2.80292i	−0.549698	+	0.317368i
$79$	−8.57325	+	4.94977i	−0.964566	+	0.556893i	−0.897575	−	0.440861i	$-0.854673\pi$
$79$	−8.57325	+	4.94977i	−0.964566	+	0.556893i	−0.0669909	+	0.997754i	$0.521340\pi$
$80$	1.93996	+	1.11200i	0.216895	+	0.124325i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.941466			0.103968
$83$	0.157099	+	0.0907014i	0.0172439	+	0.00995577i	0.508597	−	0.861005i	$-0.330164\pi$
$83$	0.157099	+	0.0907014i	0.0172439	+	0.00995577i	−0.491353	+	0.870960i	$0.663498\pi$
$84$	4.16422			0.454353
$85$	−5.55658	−	3.18506i	−0.602695	−	0.345469i
$86$	−2.14753	+	3.71962i	−0.231574	+	0.401097i
$87$	4.95400	+	8.58058i	0.531125	+	0.919935i
$88$	5.62355			0.599472
$89$	−7.38304	−	4.26260i	−0.782601	−	0.451835i	0.0547504	−	0.998500i	$-0.482564\pi$
$89$	−7.38304	−	4.26260i	−0.782601	−	0.451835i	−0.837351	+	0.546665i	$0.815897\pi$
$90$	1.93300	−	1.12406i	0.203756	−	0.118486i
$91$	−20.2165	−	11.6720i	−2.11926	−	1.22356i
$92$	3.12090	+	5.40555i	0.325376	+	0.563568i
$93$	−2.16923	−	3.75722i	−0.224939	−	0.389605i
$94$	−0.316878	−	0.182950i	−0.0326835	−	0.0188698i
$95$	6.70291	+	11.5267i	0.687704	+	1.18262i
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$	−8.96250			−0.910004			−0.455002	−	0.890490i	$-0.650361\pi$
$97$	−8.96250			−0.910004			−0.455002	+	0.890490i	$0.650361\pi$
$98$	5.17035	+	8.95532i	0.522285	+	0.904623i
$99$	2.81177	−	4.87013i	0.282594	−	0.489467i
$100$	2.52692	+	4.31447i	0.252692	+	0.431447i
$101$	17.5745			1.74872			0.874362	−	0.485274i	$-0.161280\pi$
$101$	17.5745			1.74872			0.874362	+	0.485274i	$0.161280\pi$
$102$	−2.48053	−	1.43213i	−0.245609	−	0.141802i
$103$	4.83675			0.476579			0.238290	−	0.971194i	$-0.423413\pi$
$103$	4.83675			0.476579			0.238290	+	0.971194i	$0.423413\pi$
$104$	−2.80292	−	4.85480i	−0.274849	−	0.476053i
$105$	8.07843	+	4.63061i	0.788374	+	0.451901i
$106$	3.87603	−	2.23783i	0.376474	−	0.217357i
$107$	13.4925	−	7.78991i	1.30437	−	0.753079i	0.323220	−	0.946324i	$-0.395235\pi$
$107$	13.4925	−	7.78991i	1.30437	−	0.753079i	0.981150	+	0.193245i	$0.0619013\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$	−1.14051	−	0.658472i	−0.109241	−	0.0630702i	0.444384	−	0.895836i	$-0.353423\pi$
$109$	−1.14051	−	0.658472i	−0.109241	−	0.0630702i	−0.553625	+	0.832766i	$0.686756\pi$
$110$	10.9095	+	6.25338i	1.04018	+	0.596236i
$111$	−1.12262	−	5.97827i	−0.106554	−	0.567432i
$112$			4.16422i			0.393482i
$113$	4.34832	−	7.53150i	0.409055	−	0.708504i	−0.585729	−	0.810507i	$-0.699192\pi$
$113$	4.34832	−	7.53150i	0.409055	−	0.708504i	0.994784	+	0.102003i	$0.0325250\pi$
$114$	2.98157	+	5.16423i	0.279249	+	0.483674i
$115$	0.0434574	+	13.9570i	0.00405243	+	1.30150i
$116$	−8.58058	+	4.95400i	−0.796687	+	0.459968i
$117$	−5.60584			−0.518260
$118$	−9.52048	+	5.49665i	−0.876431	+	0.506008i
$119$		−	11.9274i		−	1.09339i
$120$	1.12406	+	1.93300i	0.102612	+	0.176458i
$121$	20.6243			1.87493
$122$			2.55050i			0.230911i
$123$	0.815334	+	0.470733i	0.0735162	+	0.0424446i
$124$	3.75722	−	2.16923i	0.337408	−	0.194803i
$125$	0.104434	+	11.1799i	0.00934083	+	0.999956i
$126$	3.60632	+	2.08211i	0.321276	+	0.185489i
$127$	6.46743	+	3.73397i	0.573892	+	0.331336i	0.758702	−	0.651438i	$-0.225834\pi$
$127$	6.46743	+	3.73397i	0.573892	+	0.331336i	−0.184811	+	0.982774i	$0.559167\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−3.71962	+	2.14753i	−0.327495	+	0.189079i
$130$	−0.0390297	−	12.5350i	−0.00342313	−	1.09939i
$131$	−4.67400	−	2.69853i	−0.408369	−	0.235772i	0.281720	−	0.959497i	$-0.409095\pi$
$131$	−4.67400	−	2.69853i	−0.408369	−	0.235772i	−0.690089	+	0.723725i	$0.742429\pi$
$132$	4.87013	+	2.81177i	0.423891	+	0.244733i
$133$	−12.4159	+	21.5050i	−1.07659	+	1.86472i
$134$			2.21789i			0.191596i
$135$	2.23606	−	0.00696233i	0.192449	−	0.000599222i
$136$	1.43213	−	2.48053i	0.122805	−	0.212704i
$137$			3.45444i			0.295133i	0.989052	+	0.147566i	$0.0471440\pi$
$137$			3.45444i			0.295133i	−0.989052	+	0.147566i	$0.952856\pi$
$138$			6.24179i			0.531337i
$139$	4.16178	−	7.20841i	0.352997	−	0.611409i	−0.633776	−	0.773517i	$-0.718496\pi$
$139$	4.16178	−	7.20841i	0.352997	−	0.611409i	0.986773	+	0.162107i	$0.0518291\pi$
$140$	−4.63061	+	8.07843i	−0.391358	+	0.682752i
$141$	−0.182950	−	0.316878i	−0.0154072	−	0.0266860i
$142$	12.1705			1.02133
$143$	−15.7624	−	27.3012i	−1.31811	−	2.28304i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	−22.1549	+	0.0689828i	−1.83986	+	0.00572871i
$146$	−10.0456	−	5.79986i	−0.831384	−	0.480000i
$147$			10.3407i			0.852887i
$148$	5.97827	−	1.12262i	0.491411	−	0.0922786i
$149$	9.40193			0.770236			0.385118	−	0.922867i	$-0.374161\pi$
$149$	9.40193			0.770236			0.385118	+	0.922867i	$0.374161\pi$
$150$	0.0311363	+	4.99990i	0.00254227	+	0.408240i
$151$	−5.42704	−	9.39991i	−0.441646	−	0.764954i	0.556165	−	0.831072i	$-0.312272\pi$
$151$	−5.42704	−	9.39991i	−0.441646	−	0.764954i	−0.997812	+	0.0661176i	$0.978939\pi$
$152$	−5.16423	+	2.98157i	−0.418874	+	0.241837i
$153$	−1.43213	−	2.48053i	−0.115781	−	0.200539i
$154$			23.4177i			1.88705i
$155$	9.70104	−	0.0302058i	0.779206	−	0.00242619i
$156$		−	5.60584i		−	0.448827i
$157$	−13.0906	−	7.55789i	−1.04475	−	0.603185i	−0.123573	−	0.992335i	$-0.539435\pi$
$157$	−13.0906	−	7.55789i	−1.04475	−	0.603185i	−0.921174	+	0.389150i	$0.872769\pi$
$158$		−	9.89954i		−	0.787565i
$159$	4.47566			0.354943
$160$	−1.93300	+	1.12406i	−0.152817	+	0.0888646i
$161$	−22.5099	+	12.9961i	−1.77403	+	1.02424i
$162$	1.00000			0.0785674
$163$	2.95761	−	5.12274i	0.231658	−	0.401244i	−0.726638	−	0.687020i	$-0.758918\pi$
$163$	2.95761	−	5.12274i	0.231658	−	0.401244i	0.958296	+	0.285777i	$0.0922516\pi$
$164$	−0.470733	+	0.815334i	−0.0367581	+	0.0636669i
$165$	6.32119	+	10.8703i	0.492104	+	0.846253i
$166$	−0.157099	+	0.0907014i	−0.0121933	+	0.00703979i
$167$	3.04743	+	5.27831i	0.235817	+	0.408448i	0.959510	−	0.281675i	$-0.0908899\pi$
$167$	3.04743	+	5.27831i	0.235817	+	0.408448i	−0.723692	+	0.690123i	$0.757557\pi$
$168$	−2.08211	+	3.60632i	−0.160638	+	0.278233i
$169$	−9.21274	+	15.9569i	−0.708672	+	1.22746i
$170$	5.53664	−	3.21961i	0.424641	−	0.246932i
$171$			5.96313i			0.456012i
$172$	−2.14753	−	3.71962i	−0.163747	−	0.283619i
$173$	−6.21546	−	3.58850i	−0.472552	−	0.272828i	0.244755	−	0.969585i	$-0.421292\pi$
$173$	−6.21546	−	3.58850i	−0.472552	−	0.272828i	−0.717308	+	0.696757i	$0.754626\pi$
$174$	−9.90800			−0.751124
$175$	−17.9664	+	10.5226i	−1.35813	+	0.795436i
$176$	−2.81177	+	4.87013i	−0.211945	+	0.367100i
$177$	−10.9933			−0.826307
$178$	7.38304	−	4.26260i	0.553382	−	0.319495i
$179$			22.6831i			1.69541i	0.530465	+	0.847707i	$0.322017\pi$
$179$			22.6831i			1.69541i	−0.530465	+	0.847707i	$0.677983\pi$
$180$	0.00696233	+	2.23606i	0.000518942	+	0.166666i
$181$	−5.95683	−	10.3175i	−0.442768	−	0.766896i	0.555126	−	0.831766i	$-0.312670\pi$
$181$	−5.95683	−	10.3175i	−0.442768	−	0.766896i	−0.997894	+	0.0648700i	$0.979337\pi$
$182$	20.2165	−	11.6720i	1.49854	−	0.865184i
$183$	−1.27525	+	2.20880i	−0.0942691	+	0.163279i
$184$	−6.24179			−0.460151
$185$	12.8460	+	4.46999i	0.944455	+	0.328641i
$186$	4.33846			0.318111
$187$	8.05368	−	13.9494i	0.588943	−	1.02008i
$188$	0.316878	−	0.182950i	0.0231107	−	0.0133430i
$189$	2.08211	+	3.60632i	0.151451	+	0.262321i
$190$	−13.3339	+	0.0415173i	−0.967343	+	0.00301198i
$191$		−	23.9424i		−	1.73241i	−0.499690	−	0.866204i	$-0.666553\pi$
$191$		−	23.9424i		−	1.73241i	0.499690	−	0.866204i	$-0.333447\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	16.1408			1.16184			0.580919	−	0.813961i	$-0.302693\pi$
$193$	16.1408			1.16184			0.580919	+	0.813961i	$0.302693\pi$
$194$	4.48125	−	7.76175i	0.321735	−	0.557261i
$195$	6.23369	−	10.8751i	0.446404	−	0.778784i
$196$	−10.3407			−0.738622
$197$	21.2832	+	12.2879i	1.51637	+	0.875475i	0.999815	+	0.0192182i	$0.00611772\pi$
$197$	21.2832	+	12.2879i	1.51637	+	0.875475i	0.516551	+	0.856256i	$0.327216\pi$
$198$	2.81177	+	4.87013i	0.199824	+	0.346105i
$199$		−	17.4958i		−	1.24025i	−0.784505	−	0.620123i	$-0.787083\pi$
$199$		−	17.4958i		−	1.24025i	0.784505	−	0.620123i	$-0.212917\pi$
$200$	−4.99990	+	0.0311363i	−0.353547	+	0.00220167i
$201$	−1.10894	+	1.92075i	−0.0782189	+	0.135479i
$202$	−8.78723	+	15.2199i	−0.618267	+	1.07087i
$203$	−20.6295	−	35.7314i	−1.44791	−	2.50785i
$204$	2.48053	−	1.43213i	0.173672	−	0.100269i
$205$	−1.81986	+	1.05826i	−0.127104	+	0.0739123i
$206$	−2.41837	+	4.18875i	−0.168496	+	0.291844i
$207$	−3.12090	+	5.40555i	−0.216917	+	0.375712i
$208$	5.60584			0.388695
$209$	−29.0413	+	16.7670i	−2.00883	+	1.15980i
$210$	−8.04944	+	4.68082i	−0.555464	+	0.323007i
$211$	28.4494			1.95854			0.979268	−	0.202571i	$-0.0649297\pi$
$211$	28.4494			1.95854			0.979268	+	0.202571i	$0.0649297\pi$
$212$			4.47566i			0.307390i
$213$	10.5400	+	6.08527i	0.722189	+	0.416956i
$214$			15.5798i			1.06501i
$215$	−0.0299036	−	9.60398i	−0.00203941	−	0.654986i
$216$			1.00000i			0.0680414i
$217$	9.03314	+	15.6459i	0.613210	+	1.06211i
$218$	1.14051	−	0.658472i	0.0772449	−	0.0445974i
$219$	−5.79986	−	10.0456i	−0.391918	−	0.678822i
$220$	−10.8703	+	6.32119i	−0.732877	+	0.426175i
$221$	−16.0566			−1.08009
$222$	5.73864	+	2.01692i	0.385153	+	0.135367i
$223$			2.89406i			0.193800i	0.995294	+	0.0969002i	$0.0308928\pi$
$223$			2.89406i			0.193800i	−0.995294	+	0.0969002i	$0.969107\pi$
$224$	−3.60632	−	2.08211i	−0.240957	−	0.139117i
$225$	−2.47299	+	4.34561i	−0.164866	+	0.289707i
$226$	4.34832	+	7.53150i	0.289246	+	0.500988i
$227$	−2.39517	−	4.14855i	−0.158973	−	0.275349i	0.775526	−	0.631316i	$-0.217485\pi$
$227$	−2.39517	−	4.14855i	−0.158973	−	0.275349i	−0.934499	+	0.355967i	$0.884152\pi$
$228$	−5.96313			−0.394918
$229$	−0.352183	−	0.609999i	−0.0232729	−	0.0403099i	0.854154	−	0.520020i	$-0.174075\pi$
$229$	−0.352183	−	0.609999i	−0.0232729	−	0.0403099i	−0.877427	+	0.479710i	$0.840742\pi$
$230$	−12.1088	−	6.94087i	−0.798434	−	0.457667i
$231$	−11.7088	+	20.2803i	−0.770385	+	1.33435i
$232$		−	9.90800i		−	0.650492i
$233$			15.4170i			1.01000i	0.863118	+	0.505002i	$0.168508\pi$
$233$			15.4170i			1.01000i	−0.863118	+	0.505002i	$0.831492\pi$
$234$	2.80292	−	4.85480i	0.183233	−	0.317368i
$235$	0.818172	−	0.00254751i	0.0533717	−	0.000166181i
$236$		−	10.9933i		−	0.715603i
$237$	4.94977	−	8.57325i	0.321522	−	0.556893i
$238$	10.3295	+	5.96372i	0.669560	+	0.386571i
$239$	−6.13569	−	3.54245i	−0.396885	−	0.229142i	0.288254	−	0.957554i	$-0.406925\pi$
$239$	−6.13569	−	3.54245i	−0.396885	−	0.229142i	−0.685139	+	0.728412i	$0.740259\pi$
$240$	−2.23606	+	0.00696233i	−0.144337	+	0.000449417i
$241$	−19.6742	+	11.3589i	−1.26733	+	0.731692i	−0.974481	−	0.224468i	$-0.927936\pi$
$241$	−19.6742	+	11.3589i	−1.26733	+	0.731692i	−0.292846	+	0.956160i	$0.594602\pi$
$242$	−10.3121	+	17.8611i	−0.662889	+	1.14816i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−2.20880	−	1.27525i	−0.141404	−	0.0816395i
$245$	−20.0606	−	11.4989i	−1.28162	−	0.734635i
$246$	−0.815334	+	0.470733i	−0.0519838	+	0.0300128i
$247$	28.9498	+	16.7142i	1.84203	+	1.06350i
$248$			4.33846i			0.275492i
$249$	−0.181403			−0.0114959
$250$	−9.73425	−	5.49948i	−0.615648	−	0.347818i
$251$		−	0.437029i		−	0.0275850i	−0.999905	−	0.0137925i	$-0.995610\pi$
$251$		−	0.437029i		−	0.0275850i	0.999905	−	0.0137925i	$-0.00439043\pi$
$252$	−3.60632	+	2.08211i	−0.227177	+	0.131161i
$253$	−35.1010			−2.20678
$254$	−6.46743	+	3.73397i	−0.405803	+	0.234290i
$255$	6.40467	−	0.0199420i	0.401076	−	0.00124882i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	2.17930	−	3.77465i	0.135941	−	0.235456i	−0.790016	−	0.613087i	$-0.789928\pi$
$257$	2.17930	−	3.77465i	0.135941	−	0.235456i	0.925956	+	0.377630i	$0.123261\pi$
$258$		−	4.29505i		−	0.267398i
$259$	4.67482	+	24.8948i	0.290479	+	1.54689i
$260$	10.8751	+	6.23369i	0.674447	+	0.386597i
$261$	−8.58058	−	4.95400i	−0.531125	−	0.306645i
$262$	4.67400	−	2.69853i	0.288761	−	0.166716i
$263$	24.8970	−	14.3743i	1.53522	−	0.886358i	0.536109	−	0.844149i	$-0.319894\pi$
$263$	24.8970	−	14.3743i	1.53522	−	0.886358i	0.999109	−	0.0422094i	$-0.0134396\pi$
$264$	−4.87013	+	2.81177i	−0.299736	+	0.173053i
$265$	−4.97693	+	8.68262i	−0.305730	+	0.533369i
$266$	−12.4159	−	21.5050i	−0.761267	−	1.31855i
$267$	8.52520			0.521734
$268$	−1.92075	−	1.10894i	−0.117328	−	0.0677395i
$269$	2.96047			0.180503			0.0902516	−	0.995919i	$-0.471233\pi$
$269$	2.96047			0.180503			0.0902516	+	0.995919i	$0.471233\pi$
$270$	−1.11200	+	1.93996i	−0.0676741	+	0.118062i
$271$	−5.51239	+	9.54773i	−0.334854	+	0.579983i	−0.983457	−	0.181143i	$-0.942020\pi$
$271$	−5.51239	+	9.54773i	−0.334854	+	0.579983i	0.648603	+	0.761127i	$0.275354\pi$
$272$	1.43213	+	2.48053i	0.0868359	+	0.150404i
$273$	23.3440			1.41284
$274$	−2.99163	−	1.72722i	−0.180731	−	0.104345i
$275$	−28.1172	+	0.175097i	−1.69553	+	0.0105587i
$276$	−5.40555	−	3.12090i	−0.325376	−	0.187856i
$277$	5.97624	+	10.3511i	0.359077	+	0.621940i	0.987807	−	0.155684i	$-0.0497581\pi$
$277$	5.97624	+	10.3511i	0.359077	+	0.621940i	−0.628730	+	0.777624i	$0.716425\pi$
$278$	4.16178	+	7.20841i	0.249607	+	0.432332i
$279$	3.75722	+	2.16923i	0.224939	+	0.129868i
$280$	−4.68082	−	8.04944i	−0.279733	−	0.481046i
$281$	4.75144	+	2.74325i	0.283447	+	0.163648i	0.634983	−	0.772526i	$-0.281007\pi$
$281$	4.75144	+	2.74325i	0.283447	+	0.163648i	−0.351536	+	0.936174i	$0.614340\pi$
$282$	0.365900			0.0217890
$283$	5.73565	+	9.93443i	0.340949	+	0.590541i	0.984609	−	0.174771i	$-0.0559184\pi$
$283$	5.73565	+	9.93443i	0.340949	+	0.590541i	−0.643660	+	0.765311i	$0.722585\pi$
$284$	−6.08527	+	10.5400i	−0.361095	+	0.625434i
$285$	−11.5683	−	6.63100i	−0.685245	−	0.392787i
$286$	31.5247			1.86410
$287$	−3.39523	−	1.96024i	−0.200414	−	0.115709i
$288$	−1.00000			−0.0589256
$289$	4.39798	+	7.61753i	0.258705	+	0.448090i
$290$	11.0177	−	19.2212i	0.646981	−	1.12871i
$291$	7.76175	−	4.48125i	0.455002	−	0.262695i
$292$	10.0456	−	5.79986i	0.587877	−	0.339411i
$293$	−8.60014	+	4.96530i	−0.502426	+	0.290076i	−0.729715	−	0.683752i	$-0.760347\pi$
$293$	−8.60014	+	4.96530i	−0.502426	+	0.290076i	0.227289	+	0.973827i	$0.427014\pi$
$294$	−8.95532	−	5.17035i	−0.522285	−	0.301541i
$295$	12.2245	−	21.3266i	0.711740	−	1.24168i
$296$	−2.01692	+	5.73864i	−0.117231	+	0.333552i
$297$			5.62355i			0.326311i
$298$	−4.70096	+	8.14231i	−0.272320	+	0.471671i
$299$	17.4953	+	30.3027i	1.01178	+	1.75245i
$300$	−4.34561	−	2.47299i	−0.250894	−	0.142778i
$301$	15.4893	−	8.94276i	0.892790	−	0.515452i
$302$	10.8541			0.624582
$303$	−15.2199	+	8.78723i	−0.874362	+	0.504813i
$304$		−	5.96313i		−	0.342009i
$305$	−2.86691	−	4.93012i	−0.164159	−	0.282298i
$306$	2.86427			0.163739
$307$			1.24701i			0.0711705i	0.999367	+	0.0355852i	$0.0113295\pi$
$307$			1.24701i			0.0711705i	−0.999367	+	0.0355852i	$0.988670\pi$
$308$	−20.2803	−	11.7088i	−1.15558	−	0.667173i
$309$	−4.18875	+	2.41837i	−0.238290	+	0.137577i
$310$	−4.82436	+	8.41645i	−0.274005	+	0.478022i
$311$	−7.15158	−	4.12897i	−0.405529	−	0.234132i	0.283338	−	0.959020i	$-0.408558\pi$
$311$	−7.15158	−	4.12897i	−0.405529	−	0.234132i	−0.688867	+	0.724888i	$0.741892\pi$
$312$	4.85480	+	2.80292i	0.274849	+	0.158684i
$313$	−0.958252	+	1.65974i	−0.0541636	+	0.0938141i	−0.891836	−	0.452359i	$-0.850583\pi$
$313$	−0.958252	+	1.65974i	−0.0541636	+	0.0938141i	0.837672	+	0.546173i	$0.183916\pi$
$314$	13.0906	−	7.55789i	0.738748	−	0.426516i
$315$	−9.31143	+	0.0289927i	−0.524640	+	0.00163355i
$316$	8.57325	+	4.94977i	0.482283	+	0.278446i
$317$	1.54711	+	0.893227i	0.0868946	+	0.0501686i	0.542818	−	0.839851i	$-0.317357\pi$
$317$	1.54711	+	0.893227i	0.0868946	+	0.0501686i	−0.455923	+	0.890019i	$0.650691\pi$
$318$	−2.23783	+	3.87603i	−0.125491	+	0.217357i
$319$		−	55.7181i		−	3.11962i
$320$	−0.00696233	−	2.23606i	−0.000389206	−	0.124999i
$321$	−7.78991	+	13.4925i	−0.434790	+	0.753079i
$322$		−	25.9922i		−	1.44849i
$323$			17.0800i			0.950358i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	14.1655	+	24.1863i	0.785760	+	1.34161i
$326$	2.95761	+	5.12274i	0.163807	+	0.283722i
$327$	1.31694			0.0728272
$328$	−0.470733	−	0.815334i	−0.0259919	−	0.0450193i
$329$	0.761843	+	1.31955i	0.0420017	+	0.0727492i
$330$	−12.5746	+	0.0391530i	−0.692207	+	0.00215530i
$331$	12.2666	+	7.08211i	0.674232	+	0.389268i	0.797678	−	0.603083i	$-0.206061\pi$
$331$	12.2666	+	7.08211i	0.674232	+	0.389268i	−0.123446	+	0.992351i	$0.539395\pi$
$332$		−	0.181403i		−	0.00995577i
$333$	3.96135	+	4.61603i	0.217081	+	0.252957i
$334$	−6.09487			−0.333496
$335$	−2.49304	−	4.28718i	−0.136209	−	0.234234i
$336$	−2.08211	−	3.60632i	−0.113588	−	0.196741i
$337$	8.49393	−	4.90397i	0.462694	−	0.267136i	−0.250482	−	0.968121i	$-0.580589\pi$
$337$	8.49393	−	4.90397i	0.462694	−	0.267136i	0.713176	+	0.700985i	$0.247256\pi$
$338$	−9.21274	−	15.9569i	−0.501107	−	0.867943i
$339$			8.69663i			0.472336i
$340$	0.0199420	+	6.40467i	0.00108151	+	0.347342i
$341$			24.3975i			1.32120i
$342$	−5.16423	−	2.98157i	−0.279249	−	0.161225i
$343$		−	13.9114i		−	0.751147i
$344$	4.29505			0.231574
$345$	−7.01614	−	12.0654i	−0.377736	−	0.649579i
$346$	6.21546	−	3.58850i	0.334145	−	0.192919i
$347$	22.5282			1.20938			0.604688	−	0.796463i	$-0.293298\pi$
$347$	22.5282			1.20938			0.604688	+	0.796463i	$0.293298\pi$
$348$	4.95400	−	8.58058i	0.265562	−	0.459968i
$349$	−0.142907	+	0.247523i	−0.00764965	+	0.0132496i	−0.869825	−	0.493361i	$-0.835768\pi$
$349$	−0.142907	+	0.247523i	−0.00764965	+	0.0132496i	0.862175	+	0.506610i	$0.169102\pi$
$350$	−0.129659	−	20.8207i	−0.00693054	−	1.11291i
$351$	4.85480	−	2.80292i	0.259130	−	0.149609i
$352$	−2.81177	−	4.87013i	−0.149868	−	0.259579i
$353$	−8.58970	+	14.8778i	−0.457184	+	0.791865i	−0.998811	−	0.0487534i	$-0.984475\pi$
$353$	−8.58970	+	14.8778i	−0.457184	+	0.791865i	0.541627	+	0.840619i	$0.317808\pi$
$354$	5.49665	−	9.52048i	0.292144	−	0.506008i
$355$	−23.5257	+	13.6804i	−1.24861	+	0.726081i
$356$			8.52520i			0.451835i
$357$	5.96372	+	10.3295i	0.315634	+	0.546693i
$358$	−19.6441	−	11.3415i	−1.03822	−	0.599419i
$359$	7.99692			0.422061			0.211031	−	0.977479i	$-0.432318\pi$
$359$	7.99692			0.422061			0.211031	+	0.977479i	$0.432318\pi$
$360$	−1.93996	−	1.11200i	−0.102245	−	0.0586075i
$361$	8.27949	−	14.3405i	0.435762	−	0.754763i
$362$	11.9137			0.626168
$363$	−17.8611	+	10.3121i	−0.937467	+	0.541247i
$364$			23.3440i			1.22356i
$365$	25.9376	−	0.0807611i	1.35764	−	0.00422723i
$366$	−1.27525	−	2.20880i	−0.0666583	−	0.115456i
$367$	−20.1521	+	11.6348i	−1.05193	+	0.607332i	−0.923189	−	0.384347i	$-0.874427\pi$
$367$	−20.1521	+	11.6348i	−1.05193	+	0.607332i	−0.128741	+	0.991678i	$0.541093\pi$
$368$	3.12090	−	5.40555i	0.162688	−	0.281784i
$369$	−0.941466			−0.0490108
$370$	−10.2941	+	8.88995i	−0.535166	+	0.462166i
$371$	−18.6376			−0.967617
$372$	−2.16923	+	3.75722i	−0.112469	+	0.194803i
$373$	−19.6815	+	11.3631i	−1.01907	+	0.588360i	−0.913834	−	0.406087i	$-0.866893\pi$
$373$	−19.6815	+	11.3631i	−1.01907	+	0.588360i	−0.105235	+	0.994447i	$0.533560\pi$
$374$	8.05368	+	13.9494i	0.416446	+	0.721305i
$375$	−5.68037	−	9.62982i	−0.293333	−	0.497282i
$376$			0.365900i			0.0188698i
$377$	−48.1014	+	27.7714i	−2.47735	+	1.43030i
$378$	−4.16422			−0.214184
$379$	−11.1432	+	19.3005i	−0.572386	+	0.991402i	0.423934	+	0.905693i	$0.360649\pi$
$379$	−11.1432	+	19.3005i	−0.572386	+	0.991402i	−0.996320	+	0.0857086i	$0.972685\pi$
$380$	6.63100	−	11.5683i	0.340163	−	0.593439i
$381$	−7.46795			−0.382594
$382$	20.7347	+	11.9712i	1.06088	+	0.612499i
$383$	4.33722	+	7.51229i	0.221622	+	0.383860i	0.955301	−	0.295636i	$-0.0955317\pi$
$383$	4.33722	+	7.51229i	0.221622	+	0.383860i	−0.733679	+	0.679496i	$0.762198\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	−26.3228	−	45.2664i	−1.34154	−	2.30699i
$386$	−8.07038	+	13.9783i	−0.410772	+	0.711477i
$387$	2.14753	−	3.71962i	0.109165	−	0.189079i
$388$	4.48125	+	7.76175i	0.227501	+	0.394043i
$389$	32.7509	−	18.9088i	1.66054	−	0.958712i	0.688080	−	0.725635i	$-0.258454\pi$
$389$	32.7509	−	18.9088i	1.66054	−	0.958712i	0.972458	−	0.233077i	$-0.0748794\pi$
$390$	6.30129	+	10.8361i	0.319078	+	0.548707i
$391$	−8.93909	+	15.4829i	−0.452069	+	0.783006i
$392$	5.17035	−	8.95532i	0.261142	−	0.452312i
$393$	5.39707			0.272246
$394$	−21.2832	+	12.2879i	−1.07223	+	0.619054i
$395$	11.1277	+	19.1358i	0.559893	+	0.962828i
$396$	−5.62355			−0.282594
$397$		−	26.0656i		−	1.30819i	−0.756411	−	0.654097i	$-0.773049\pi$
$397$		−	26.0656i		−	1.30819i	0.756411	−	0.654097i	$-0.226951\pi$
$398$	15.1518	+	8.74791i	0.759492	+	0.438493i
$399$		−	24.8318i		−	1.24314i
$400$	2.47299	−	4.34561i	0.123649	−	0.217281i
$401$			8.98577i			0.448728i	0.974505	+	0.224364i	$0.0720305\pi$
$401$			8.98577i			0.448728i	−0.974505	+	0.224364i	$0.927970\pi$
$402$	−1.10894	−	1.92075i	−0.0553091	−	0.0957982i
$403$	21.0624	−	12.1604i	1.04919	−	0.605751i
$404$	−8.78723	−	15.2199i	−0.437181	−	0.757220i
$405$	−1.93300	+	1.12406i	−0.0960516	+	0.0558549i
$406$	41.2591			2.04765
$407$	−11.3422	+	32.2715i	−0.562214	+	1.59964i
$408$			2.86427i			0.141802i
$409$	4.54148	+	2.62202i	0.224561	+	0.129651i	0.608061	−	0.793891i	$-0.291948\pi$
$409$	4.54148	+	2.62202i	0.224561	+	0.129651i	−0.383499	+	0.923541i	$0.625281\pi$
$410$	−0.00655480	−	2.10517i	−0.000323719	−	0.103967i
$411$	−1.72722	−	2.99163i	−0.0851974	−	0.147566i
$412$	−2.41837	−	4.18875i	−0.119145	−	0.206365i
$413$	45.7785			2.25261
$414$	−3.12090	−	5.40555i	−0.153384	−	0.265668i
$415$	0.201720	−	0.351915i	0.00990203	−	0.0172748i
$416$	−2.80292	+	4.85480i	−0.137425	+	0.238026i
$417$			8.32355i			0.407606i
$418$		−	33.5340i		−	1.64020i
$419$	4.82659	−	8.35990i	0.235794	−	0.408408i	−0.723709	−	0.690105i	$-0.757564\pi$
$419$	4.82659	−	8.35990i	0.235794	−	0.408408i	0.959503	+	0.281698i	$0.0908975\pi$
$420$	−0.0289927	−	9.31143i	−0.00141470	−	0.454351i
$421$			2.40440i			0.117183i	0.998282	+	0.0585916i	$0.0186610\pi$
$421$			2.40440i			0.117183i	−0.998282	+	0.0585916i	$0.981339\pi$
$422$	−14.2247	+	24.6379i	−0.692447	+	1.19935i
$423$	0.316878	+	0.182950i	0.0154072	+	0.00889532i
$424$	−3.87603	−	2.23783i	−0.188237	−	0.108679i
$425$	−7.08330	+	12.4470i	−0.343590	+	0.603768i
$426$	−10.5400	+	6.08527i	−0.510665	+	0.294833i
$427$	5.31041	−	9.19791i	0.256989	−	0.445118i
$428$	−13.4925	−	7.78991i	−0.652185	−	0.376539i
$429$	27.3012	+	15.7624i	1.31811	+	0.761014i
$430$	8.33224	+	4.77609i	0.401816	+	0.230324i
$431$	−21.2626	+	12.2760i	−1.02418	+	0.591313i	−0.915313	−	0.402742i	$-0.868057\pi$
$431$	−21.2626	+	12.2760i	−1.02418	+	0.591313i	−0.108871	+	0.994056i	$0.534724\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$		−	24.7803i		−	1.19087i	−0.803405	−	0.595433i	$-0.796980\pi$
$433$		−	24.7803i		−	1.19087i	0.803405	−	0.595433i	$-0.203020\pi$
$434$	−18.0663			−0.867209
$435$	19.1522	−	11.1372i	0.918277	−	0.533987i
$436$			1.31694i			0.0630702i
$437$	32.2340	−	18.6103i	1.54196	−	0.890252i
$438$	11.5997			0.554256
$439$	23.1393	−	13.3595i	1.10438	−	0.637614i	0.167012	−	0.985955i	$-0.446588\pi$
$439$	23.1393	−	13.3595i	1.10438	−	0.637614i	0.937368	+	0.348341i	$0.113255\pi$
$440$	−0.0391530	−	12.5746i	−0.00186655	−	0.599469i
$441$	−5.17035	−	8.95532i	−0.246207	−	0.426444i
$442$	8.02832	−	13.9055i	0.381868	−	0.661415i
$443$			18.4378i			0.876008i	0.898973	+	0.438004i	$0.144314\pi$
$443$			18.4378i			0.876008i	−0.898973	+	0.438004i	$0.855686\pi$
$444$	−4.61603	+	3.96135i	−0.219067	+	0.187997i
$445$	−9.48002	+	16.5386i	−0.449396	+	0.784004i
$446$	−2.50633	−	1.44703i	−0.118678	−	0.0685188i
$447$	−8.14231	+	4.70096i	−0.385118	+	0.222348i
$448$	3.60632	−	2.08211i	0.170383	−	0.0983704i
$449$	29.6975	−	17.1459i	1.40151	−	0.809164i	0.406965	−	0.913444i	$-0.366587\pi$
$449$	29.6975	−	17.1459i	1.40151	−	0.809164i	0.994548	+	0.104280i	$0.0332539\pi$
$450$	−2.52692	−	4.31447i	−0.119120	−	0.203386i
$451$	−2.64719	−	4.58507i	−0.124651	−	0.215902i
$452$	−8.69663			−0.409055
$453$	9.39991	+	5.42704i	0.441646	+	0.254985i
$454$	4.79034			0.224822
$455$	−25.9584	+	45.2864i	−1.21695	+	2.12306i
$456$	2.98157	−	5.16423i	0.139625	−	0.241837i
$457$	12.2911	+	21.2888i	0.574954	+	0.995849i	0.996047	+	0.0888317i	$0.0283133\pi$
$457$	12.2911	+	21.2888i	0.574954	+	0.995849i	−0.421093	+	0.907018i	$0.638353\pi$
$458$	0.704366			0.0329129
$459$	2.48053	+	1.43213i	0.115781	+	0.0668463i
$460$	12.0654	−	7.01614i	0.562552	−	0.327129i
$461$	−9.81068	−	5.66420i	−0.456929	−	0.263808i	0.253823	−	0.967251i	$-0.418312\pi$
$461$	−9.81068	−	5.66420i	−0.456929	−	0.263808i	−0.710752	+	0.703443i	$0.751645\pi$
$462$	−11.7088	−	20.2803i	−0.544744	−	0.943525i
$463$	−0.261365	−	0.452698i	−0.0121467	−	0.0210387i	0.859888	−	0.510482i	$-0.170533\pi$
$463$	−0.261365	−	0.452698i	−0.0121467	−	0.0210387i	−0.872035	+	0.489444i	$0.837200\pi$
$464$	8.58058	+	4.95400i	0.398344	+	0.229984i
$465$	−8.38624	+	4.87668i	−0.388903	+	0.226151i
$466$	−13.3515	−	7.70852i	−0.618498	−	0.357090i
$467$	1.75438			0.0811830			0.0405915	−	0.999176i	$-0.487076\pi$
$467$	1.75438			0.0811830			0.0405915	+	0.999176i	$0.487076\pi$
$468$	2.80292	+	4.85480i	0.129565	+	0.224413i
$469$	4.61788	−	7.99841i	0.213234	−	0.369332i
$470$	−0.406880	+	0.709832i	−0.0187680	+	0.0327421i
$471$	15.1158			0.696498
$472$	9.52048	+	5.49665i	0.438216	+	0.253004i
$473$	24.1534			1.11058
$474$	4.94977	+	8.57325i	0.227350	+	0.393783i
$475$	25.7278	−	15.0683i	1.18047	−	0.691383i
$476$	−10.3295	+	5.96372i	−0.473450	+	0.273347i
$477$	−3.87603	+	2.23783i	−0.177471	+	0.102463i
$478$	6.13569	−	3.54245i	0.280640	−	0.162028i
$479$	−14.0589	−	8.11691i	−0.642368	−	0.370871i	0.143158	−	0.989700i	$-0.454274\pi$
$479$	−14.0589	−	8.11691i	−0.642368	−	0.370871i	−0.785526	+	0.618829i	$0.787608\pi$
$480$	1.11200	−	1.93996i	0.0507556	−	0.0885468i
$481$	33.5133	−	6.29322i	1.52807	−	0.286946i
$482$		−	22.7178i		−	1.03477i
$483$	12.9961	−	22.5099i	0.591342	−	1.02424i
$484$	−10.3121	−	17.8611i	−0.468734	−	0.811870i
$485$	0.0623999	+	20.0407i	0.00283343	+	0.909999i
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$	−27.4494			−1.24385			−0.621927	−	0.783076i	$-0.713650\pi$
$487$	−27.4494			−1.24385			−0.621927	+	0.783076i	$0.713650\pi$
$488$	2.20880	−	1.27525i	0.0999875	−	0.0577278i
$489$			5.91523i			0.267496i
$490$	19.9886	−	11.6236i	0.902993	−	0.525099i
$491$	24.9786			1.12727			0.563634	−	0.826024i	$-0.309403\pi$
$491$	24.9786			1.12727			0.563634	+	0.826024i	$0.309403\pi$
$492$		−	0.941466i		−	0.0424446i
$493$	−24.5771	−	14.1896i	−1.10690	−	0.639067i
$494$	−28.9498	+	16.7142i	−1.30251	+	0.752007i
$495$	−10.9095	−	6.25338i	−0.490344	−	0.281068i
$496$	−3.75722	−	2.16923i	−0.168704	−	0.0974013i
$497$	−43.8909	−	25.3404i	−1.96877	−	1.13667i
$498$	0.0907014	−	0.157099i	0.00406443	−	0.00703979i
$499$	8.21385	−	4.74227i	0.367702	−	0.212293i	−0.304752	−	0.952432i	$-0.598574\pi$
$499$	8.21385	−	4.74227i	0.367702	−	0.212293i	0.672454	+	0.740139i	$0.265240\pi$
$500$	9.62982	−	5.68037i	0.430659	−	0.254034i
$501$	−5.27831	−	3.04743i	−0.235817	−	0.136149i
$502$	0.378478	+	0.218514i	0.0168923	+	0.00975278i
$503$	2.11396	−	3.66149i	0.0942569	−	0.163258i	−0.815041	−	0.579403i	$-0.803286\pi$
$503$	2.11396	−	3.66149i	0.0942569	−	0.163258i	0.909298	+	0.416145i	$0.136619\pi$
$504$		−	4.16422i		−	0.185489i
$505$	−0.122359	−	39.2975i	−0.00544491	−	1.74872i
$506$	17.5505	−	30.3984i	0.780215	−	1.35137i
$507$		−	18.4255i		−	0.818304i
$508$		−	7.46795i		−	0.331336i
$509$	11.0937	−	19.2149i	0.491721	−	0.851685i	−0.508234	−	0.861219i	$-0.669701\pi$
$509$	11.0937	−	19.2149i	0.491721	−	0.851685i	0.999955	+	0.00953382i	$0.00303475\pi$
$510$	−3.18506	+	5.55658i	−0.141037	+	0.246049i
$511$	24.1519	+	41.8323i	1.06842	+	1.85055i
$512$	1.00000			0.0441942
$513$	−2.98157	−	5.16423i	−0.131639	−	0.228006i
$514$	2.17930	+	3.77465i	0.0961246	+	0.166493i
$515$	−0.0336750	−	10.8152i	−0.00148390	−	0.476577i
$516$	3.71962	+	2.14753i	0.163747	+	0.0945395i
$517$			2.05765i			0.0904955i
$518$	−23.8970	−	8.39889i	−1.04997	−	0.369026i
$519$	7.17699			0.315035
$520$	−10.8361	+	6.30129i	−0.475194	+	0.276330i
$521$	1.06382	+	1.84258i	0.0466066	+	0.0807250i	0.888388	−	0.459094i	$-0.151826\pi$
$521$	1.06382	+	1.84258i	0.0466066	+	0.0807250i	−0.841781	+	0.539819i	$0.818493\pi$
$522$	8.58058	−	4.95400i	0.375562	−	0.216831i
$523$	−2.71184	−	4.69705i	−0.118581	−	0.205388i	0.800625	−	0.599166i	$-0.204501\pi$
$523$	−2.71184	−	4.69705i	−0.118581	−	0.205388i	−0.919205	+	0.393778i	$0.871168\pi$
$524$			5.39707i			0.235772i
$525$	10.2981	−	18.0961i	0.449444	−	0.789777i
$526$			28.7486i			1.25350i
$527$	10.7617	+	6.21326i	0.468786	+	0.270654i
$528$		−	5.62355i		−	0.244733i
$529$	15.9600			0.693911
$530$	−5.03090	−	8.65145i	−0.218528	−	0.375795i
$531$	9.52048	−	5.49665i	0.413154	−	0.238534i
$532$	24.8318			1.07659
$533$	−2.63886	+	4.57063i	−0.114302	+	0.197976i
$534$	−4.26260	+	7.38304i	−0.184461	+	0.319495i
$535$	−17.5126	−	30.1158i	−0.757136	−	1.30202i
$536$	1.92075	−	1.10894i	0.0829637	−	0.0478991i
$537$	−11.3415	−	19.6441i	−0.489424	−	0.847707i
$538$	−1.48024	+	2.56384i	−0.0638175	+	0.110535i
$539$	29.0757	−	50.3606i	1.25238	−	2.16919i
$540$	−1.12406	−	1.93300i	−0.0483718	−	0.0831831i
$541$			7.00976i			0.301373i	0.988582	+	0.150687i	$0.0481484\pi$
$541$			7.00976i			0.301373i	−0.988582	+	0.150687i	$0.951852\pi$
$542$	−5.51239	−	9.54773i	−0.236777	−	0.410110i
$543$	10.3175	+	5.95683i	0.442768	+	0.255632i
$544$	−2.86427			−0.122805
$545$	−1.46444	+	2.55482i	−0.0627298	+	0.109437i
$546$	−11.6720	+	20.2165i	−0.499514	+	0.865184i
$547$	9.68332			0.414029			0.207014	−	0.978338i	$-0.433625\pi$
$547$	9.68332			0.414029			0.207014	+	0.978338i	$0.433625\pi$
$548$	2.99163	−	1.72722i	0.127796	−	0.0737832i
$549$		−	2.55050i		−	0.108853i
$550$	13.9070	−	24.4377i	0.592995	−	1.04203i
$551$	29.5414	+	51.1672i	1.25851	+	2.17979i
$552$	5.40555	−	3.12090i	0.230075	−	0.132834i
$553$	−20.6119	+	35.7009i	−0.876508	+	1.51816i
$554$	−11.9525			−0.507812
$555$	−13.3599	+	2.55186i	−0.567098	+	0.108320i
$556$	−8.32355			−0.352997
$557$	−7.32173	+	12.6816i	−0.310232	+	0.537337i	−0.978412	−	0.206662i	$-0.933740\pi$
$557$	−7.32173	+	12.6816i	−0.310232	+	0.537337i	0.668181	+	0.743999i	$0.267073\pi$
$558$	−3.75722	+	2.16923i	−0.159056	+	0.0918308i
$559$	−12.0387	−	20.8516i	−0.509182	−	0.881930i
$560$	9.31143	−	0.0289927i	0.393480	−	0.00122516i
$561$			16.1074i			0.680053i
$562$	−4.75144	+	2.74325i	−0.200428	+	0.115717i
$563$	−38.3820			−1.61761			−0.808804	−	0.588079i	$-0.799885\pi$
$563$	−38.3820			−1.61761			−0.808804	+	0.588079i	$0.799885\pi$
$564$	−0.182950	+	0.316878i	−0.00770358	+	0.0133430i
$565$	−16.8711	−	9.67065i	−0.709775	−	0.406847i
$566$	−11.4713			−0.482174
$567$	−3.60632	−	2.08211i	−0.151451	−	0.0874403i
$568$	−6.08527	−	10.5400i	−0.255332	−	0.442249i
$569$			18.5086i			0.775922i	0.921676	+	0.387961i	$0.126820\pi$
$569$			18.5086i			0.775922i	−0.921676	+	0.387961i	$0.873180\pi$
$570$	11.5267	−	6.70291i	0.482802	−	0.280754i
$571$	13.3669	−	23.1522i	0.559389	−	0.968890i	−0.438159	−	0.898898i	$-0.644369\pi$
$571$	13.3669	−	23.1522i	0.559389	−	0.968890i	0.997548	−	0.0699920i	$-0.0222974\pi$
$572$	−15.7624	+	27.3012i	−0.659057	+	1.14152i
$573$	11.9712	+	20.7347i	0.500103	+	0.866204i
$574$	3.39523	−	1.96024i	0.141714	−	0.0818186i
$575$	31.2084	−	0.194347i	1.30148	−	0.00810481i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	3.16251	−	5.47763i	0.131657	−	0.228037i	−0.792658	−	0.609666i	$-0.791304\pi$
$577$	3.16251	−	5.47763i	0.131657	−	0.228037i	0.924315	+	0.381629i	$0.124637\pi$
$578$	−8.79596			−0.365864
$579$	−13.9783	+	8.07038i	−0.580919	+	0.335394i
$580$	11.1372	+	19.1522i	0.462446	+	0.795251i
$581$	0.755401			0.0313393
$582$			8.96250i			0.371507i
$583$	−21.7971	−	12.5845i	−0.902742	−	0.521198i
$584$			11.5997i			0.480000i
$585$	0.0390297	+	12.5350i	0.00161368	+	0.518258i
$586$		−	9.93059i		−	0.410229i
$587$	−7.49315	−	12.9785i	−0.309276	−	0.535681i	0.668929	−	0.743327i	$-0.266753\pi$
$587$	−7.49315	−	12.9785i	−0.309276	−	0.535681i	−0.978204	+	0.207646i	$0.933420\pi$
$588$	8.95532	−	5.17035i	0.369311	−	0.213222i
$589$	−12.9354	−	22.4048i	−0.532994	−	0.923173i
$590$	12.3571	+	21.2501i	0.508734	+	0.874851i
$591$	−24.5757			−1.01091
$592$	−3.96135	−	4.61603i	−0.162811	−	0.189718i
$593$			17.7229i			0.727791i	0.931440	+	0.363896i	$0.118554\pi$
$593$			17.7229i			0.727791i	−0.931440	+	0.363896i	$0.881446\pi$
$594$	−4.87013	−	2.81177i	−0.199824	−	0.115368i
$595$	−26.6704	+	0.0830428i	−1.09338	+	0.00340442i
$596$	−4.70096	−	8.14231i	−0.192559	−	0.333522i
$597$	8.74791	+	15.1518i	0.358028	+	0.620123i
$598$	−34.9905			−1.43087
$599$	−16.2008	−	28.0606i	−0.661946	−	1.14652i	−0.980104	−	0.198486i	$-0.936397\pi$
$599$	−16.2008	−	28.0606i	−0.661946	−	1.14652i	0.318158	−	0.948038i	$-0.396936\pi$
$600$	4.31447	−	2.52692i	0.176138	−	0.103161i
$601$	16.3395	−	28.3009i	0.666502	−	1.15442i	−0.312373	−	0.949959i	$-0.601124\pi$
$601$	16.3395	−	28.3009i	0.666502	−	1.15442i	0.978876	−	0.204456i	$-0.0655427\pi$
$602$			17.8855i			0.728960i
$603$		−	2.21789i		−	0.0903194i
$604$	−5.42704	+	9.39991i	−0.220823	+	0.382477i
$605$	−0.143593	−	46.1171i	−0.00583789	−	1.87493i
$606$		−	17.5745i		−	0.713914i
$607$	−10.4901	+	18.1695i	−0.425782	+	0.737476i	−0.996493	−	0.0836749i	$-0.973334\pi$
$607$	−10.4901	+	18.1695i	−0.425782	+	0.737476i	0.570711	+	0.821151i	$0.306668\pi$
$608$	5.16423	+	2.98157i	0.209437	+	0.120919i
$609$	35.7314	+	20.6295i	1.44791	+	0.835951i
$610$	5.70306	−	0.0177574i	0.230910	−	0.000718977i
$611$	1.77637	−	1.02559i	0.0718642	−	0.0414908i
$612$	−1.43213	+	2.48053i	−0.0578906	+	0.100269i
$613$	18.1752	+	10.4935i	0.734090	+	0.423827i	0.819916	−	0.572483i	$-0.194020\pi$
$613$	18.1752	+	10.4935i	0.734090	+	0.423827i	−0.0858268	+	0.996310i	$0.527353\pi$
$614$	−1.07994	−	0.623504i	−0.0435828	−	0.0251626i
$615$	1.04691	−	1.82641i	0.0422155	−	0.0736480i
$616$	20.2803	−	11.7088i	0.817116	−	0.471762i
$617$	27.7087	+	15.9976i	1.11551	+	0.644040i	0.940251	−	0.340482i	$-0.110590\pi$
$617$	27.7087	+	15.9976i	1.11551	+	0.644040i	0.175259	+	0.984522i	$0.443924\pi$
$618$		−	4.83675i		−	0.194563i
$619$	−25.6784			−1.03210			−0.516051	−	0.856558i	$-0.672598\pi$
$619$	−25.6784			−1.03210			−0.516051	+	0.856558i	$0.672598\pi$
$620$	−4.87668	−	8.38624i	−0.195852	−	0.336800i
$621$		−	6.24179i		−	0.250474i
$622$	7.15158	−	4.12897i	0.286752	−	0.165556i
$623$	−35.5008			−1.42231
$624$	−4.85480	+	2.80292i	−0.194348	+	0.112207i
$625$	24.9981	−	0.311357i	0.999922	−	0.0124543i
$626$	−0.958252	−	1.65974i	−0.0382995	−	0.0663366i
$627$	16.7670	−	29.0413i	0.669609	−	1.15980i
$628$			15.1158i			0.603185i
$629$	11.3464	+	13.2215i	0.452410	+	0.527177i
$630$	4.63061	−	8.07843i	0.184488	−	0.321852i
$631$	5.85446	+	3.38007i	0.233062	+	0.134559i	0.611984	−	0.790870i	$-0.290372\pi$
$631$	5.85446	+	3.38007i	0.233062	+	0.134559i	−0.378922	+	0.925429i	$0.623705\pi$
$632$	−8.57325	+	4.94977i	−0.341026	+	0.196891i
$633$	−24.6379	+	14.2247i	−0.979268	+	0.565380i
$634$	−1.54711	+	0.893227i	−0.0614437	+	0.0354746i
$635$	8.30435	−	14.4875i	0.329548	−	0.574921i
$636$	−2.23783	−	3.87603i	−0.0887357	−	0.153695i
$637$	−57.9684			−2.29679
$638$	48.2533	+	27.8591i	1.91037	+	1.10295i
$639$	−12.1705			−0.481460
$640$	1.93996	+	1.11200i	0.0766838	+	0.0439556i
$641$	0.980805	−	1.69880i	0.0387395	−	0.0670987i	−0.846006	−	0.533174i	$-0.820999\pi$
$641$	0.980805	−	1.69880i	0.0387395	−	0.0670987i	0.884745	+	0.466075i	$0.154332\pi$
$642$	−7.78991	−	13.4925i	−0.307443	−	0.532507i
$643$	44.4122			1.75145			0.875723	−	0.482814i	$-0.160385\pi$
$643$	44.4122			1.75145			0.875723	+	0.482814i	$0.160385\pi$
$644$	22.5099	+	12.9961i	0.887014	+	0.512118i
$645$	4.82789	+	8.30234i	0.190098	+	0.326904i
$646$	−14.7917	−	8.54001i	−0.581973	−	0.336002i
$647$	10.0345	+	17.3803i	0.394499	+	0.683292i	0.993037	−	0.117802i	$-0.0375850\pi$
$647$	10.0345	+	17.3803i	0.394499	+	0.683292i	−0.598538	+	0.801094i	$0.704252\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	53.5389	+	30.9107i	2.10158	+	1.21335i
$650$	−28.0287	+	0.174545i	−1.09937	+	0.00684624i
$651$	−15.6459	−	9.03314i	−0.613210	−	0.354037i
$652$	−5.91523			−0.231658
$653$	5.72293	+	9.91240i	0.223955	+	0.387902i	0.956006	−	0.293349i	$-0.0947696\pi$
$653$	5.72293	+	9.91240i	0.223955	+	0.387902i	−0.732050	+	0.681251i	$0.761436\pi$
$654$	−0.658472	+	1.14051i	−0.0257483	+	0.0445974i
$655$	−6.00153	+	10.4701i	−0.234499	+	0.409101i
$656$	0.941466			0.0367581
$657$	10.0456	+	5.79986i	0.391918	+	0.226274i
$658$	−1.52369			−0.0593994
$659$	−1.70920	−	2.96042i	−0.0665809	−	0.115321i	0.830813	−	0.556551i	$-0.187876\pi$
$659$	−1.70920	−	2.96042i	−0.0665809	−	0.115321i	−0.897394	+	0.441230i	$0.854542\pi$
$660$	6.25338	−	10.9095i	0.243412	−	0.424651i
$661$	−6.13183	+	3.54021i	−0.238501	+	0.137698i	−0.614487	−	0.788927i	$-0.710637\pi$
$661$	−6.13183	+	3.54021i	−0.238501	+	0.137698i	0.375987	+	0.926625i	$0.377304\pi$
$662$	−12.2666	+	7.08211i	−0.476754	+	0.275254i
$663$	13.9055	−	8.02832i	0.540043	−	0.311794i
$664$	0.157099	+	0.0907014i	0.00609664	+	0.00351990i
$665$	48.1728	+	27.6129i	1.86806	+	1.07078i
$666$	−5.97827	+	1.12262i	−0.231653	+	0.0435006i
$667$			61.8437i			2.39460i
$668$	3.04743	−	5.27831i	0.117909	−	0.204224i
$669$	−1.44703	−	2.50633i	−0.0559454	−	0.0969002i
$670$	4.95932	−	0.0154417i	0.191595	−	0.000596564i
$671$	12.4213	−	7.17142i	0.479518	−	0.276850i
$672$	4.16422			0.160638
$673$	−12.4022	+	7.16039i	−0.478068	+	0.276013i	−0.719611	−	0.694377i	$-0.755680\pi$
$673$	−12.4022	+	7.16039i	−0.478068	+	0.276013i	0.241543	+	0.970390i	$0.422347\pi$
$674$			9.80795i			0.377788i
$675$	−0.0311363	−	4.99990i	−0.00119844	−	0.192446i
$676$	18.4255			0.708672
$677$		−	30.6482i		−	1.17791i	−0.808167	−	0.588954i	$-0.799540\pi$
$677$		−	30.6482i		−	1.17791i	0.808167	−	0.588954i	$-0.200460\pi$
$678$	−7.53150	−	4.34832i	−0.289246	−	0.166996i
$679$	−32.3216	+	18.6609i	−1.24039	+	0.716139i
$680$	−5.55658	−	3.18506i	−0.213085	−	0.122142i
$681$	4.14855	+	2.39517i	0.158973	+	0.0917830i
$682$	−21.1289	−	12.1988i	−0.809066	−	0.467115i
$683$	15.3305	−	26.5531i	0.586604	−	1.01603i	−0.408069	−	0.912951i	$-0.633798\pi$
$683$	15.3305	−	26.5531i	0.586604	−	1.01603i	0.994673	−	0.103077i	$-0.0328688\pi$
$684$	5.16423	−	2.98157i	0.197459	−	0.114003i
$685$	7.72432	−	0.0240509i	0.295131	−	0.000918939i
$686$	12.0477	+	6.95572i	0.459982	+	0.265570i
$687$	0.609999	+	0.352183i	0.0232729	+	0.0134366i
$688$	−2.14753	+	3.71962i	−0.0818737	+	0.141809i
$689$			25.0898i			0.955847i
$690$	13.9570	−	0.0434574i	0.531334	−	0.00165440i
$691$	0.00956990	−	0.0165756i	0.000364056	−	0.000630564i	−0.865843	−	0.500315i	$-0.833217\pi$
$691$	0.00956990	−	0.0165756i	0.000364056	−	0.000630564i	0.866207	+	0.499685i	$0.166551\pi$
$692$			7.17699i			0.272828i
$693$		−	23.4177i		−	0.889564i
$694$	−11.2641	+	19.5100i	−0.427579	+	0.740588i
$695$	−16.1474	−	9.25578i	−0.612505	−	0.351092i
$696$	4.95400	+	8.58058i	0.187781	+	0.325246i
$697$	−2.69661			−0.102141
$698$	−0.142907	−	0.247523i	−0.00540912	−	0.00936887i
$699$	−7.70852	−	13.3515i	−0.291563	−	0.505002i
$700$	18.0961	+	10.2981i	0.683967	+	0.389230i
$701$	5.55582	+	3.20765i	0.209840	+	0.121151i	0.601237	−	0.799071i	$-0.294675\pi$
$701$	5.55582	+	3.20765i	0.209840	+	0.121151i	−0.391397	+	0.920222i	$0.628008\pi$
$702$			5.60584i			0.211579i
$703$	−6.69432	−	35.6492i	−0.252481	−	1.34454i
$704$	5.62355			0.211945
$705$	−0.707284	+	0.411292i	−0.0266379	+	0.0154902i
$706$	−8.58970	−	14.8778i	−0.323278	−	0.559933i
$707$	63.3791	−	36.5919i	2.38362	−	1.37618i
$708$	5.49665	+	9.52048i	0.206577	+	0.357802i
$709$			1.36253i			0.0511709i	0.999673	+	0.0255855i	$0.00814500\pi$
$709$			1.36253i			0.0511709i	−0.999673	+	0.0255855i	$0.991855\pi$
$710$	−0.0847354	−	27.2140i	−0.00318006	−	1.02132i
$711$			9.89954i			0.371262i
$712$	−7.38304	−	4.26260i	−0.276691	−	0.159748i
$713$		−	27.0798i		−	1.01414i
$714$	−11.9274			−0.446373
$715$	−60.9373	+	35.4356i	−2.27893	+	1.32522i
$716$	19.6441	−	11.3415i	0.734136	−	0.423853i
$717$	7.08489			0.264590
$718$	−3.99846	+	6.92553i	−0.149221	+	0.258459i
$719$	−3.32757	+	5.76353i	−0.124098	+	0.214943i	−0.921380	−	0.388663i	$-0.872937\pi$
$719$	−3.32757	+	5.76353i	−0.124098	+	0.214943i	0.797282	+	0.603607i	$0.206270\pi$
$720$	1.93300	−	1.12406i	0.0720387	−	0.0418912i
$721$	17.4429	−	10.0706i	0.649606	−	0.375050i
$722$	8.27949	+	14.3405i	0.308131	+	0.533698i
$723$	11.3589	−	19.6742i	0.422442	−	0.731692i
$724$	−5.95683	+	10.3175i	−0.221384	+	0.383448i
$725$	0.308499	+	49.5391i	0.0114574	+	1.83983i
$726$		−	20.6243i		−	0.765439i
$727$	10.7619	+	18.6402i	0.399137	+	0.691325i	0.993620	−	0.112783i	$-0.0359766\pi$
$727$	10.7619	+	18.6402i	0.399137	+	0.691325i	−0.594483	+	0.804108i	$0.702643\pi$
$728$	−20.2165	−	11.6720i	−0.749272	−	0.432592i
$729$	−1.00000			−0.0370370
$730$	−12.8989	+	22.5030i	−0.477409	+	0.832874i
$731$	6.15109	−	10.6540i	0.227506	−	0.394053i
$732$	2.55050			0.0942691
$733$	28.2518	−	16.3112i	1.04350	−	0.602467i	0.122680	−	0.992446i	$-0.460851\pi$
$733$	28.2518	−	16.3112i	1.04350	−	0.602467i	0.920824	+	0.389979i	$0.127518\pi$
$734$		−	23.2696i		−	0.858897i
$735$	23.1224	−	0.0719954i	0.852883	−	0.00265559i
$736$	3.12090	+	5.40555i	0.115038	+	0.199251i
$737$	10.8014	−	6.23620i	0.397875	−	0.229713i
$738$	0.470733	−	0.815334i	0.0173279	−	0.0300128i
$739$	−43.8641			−1.61357			−0.806783	−	0.590848i	$-0.798793\pi$
$739$	−43.8641			−1.61357			−0.806783	+	0.590848i	$0.798793\pi$
$740$	−2.55186	−	13.3599i	−0.0938082	−	0.491121i
$741$	−33.4284			−1.22802
$742$	9.31881	−	16.1407i	0.342104	−	0.592542i
$743$	−6.39472	+	3.69199i	−0.234599	+	0.135446i	−0.612692	−	0.790322i	$-0.709913\pi$
$743$	−6.39472	+	3.69199i	−0.234599	+	0.135446i	0.378093	+	0.925768i	$0.376580\pi$
$744$	−2.16923	−	3.75722i	−0.0795278	−	0.137746i
$745$	−0.0654593	−	21.0233i	−0.00239824	−	0.770232i
$746$		−	22.7262i		−	0.832067i
$747$	0.157099	−	0.0907014i	0.00574797	−	0.00331859i
$748$	−16.1074			−0.588943
$749$	32.4389	−	56.1858i	1.18529	−	2.05298i
$750$	11.1799	−	0.104434i	0.408230	−	0.00381338i
$751$	11.2599			0.410881			0.205440	−	0.978670i	$-0.434137\pi$
$751$	11.2599			0.410881			0.205440	+	0.978670i	$0.434137\pi$
$752$	−0.316878	−	0.182950i	−0.0115554	−	0.00667149i
$753$	0.218514	+	0.378478i	0.00796311	+	0.0137925i
$754$		−	55.5427i		−	2.02275i
$755$	−20.9810	+	12.2006i	−0.763575	+	0.444026i
$756$	2.08211	−	3.60632i	0.0757256	−	0.131161i
$757$	14.2380	−	24.6609i	0.517489	−	0.896317i	−0.482305	−	0.876004i	$-0.660200\pi$
$757$	14.2380	−	24.6609i	0.517489	−	0.896317i	0.999794	−	0.0203136i	$-0.00646647\pi$
$758$	−11.1432	−	19.3005i	−0.404738	−	0.701027i
$759$	30.3984	−	17.5505i	1.10339	−	0.637043i
$760$	6.70291	+	11.5267i	0.243140	+	0.418119i
$761$	−6.86663	+	11.8934i	−0.248915	+	0.431134i	−0.963225	−	0.268696i	$-0.913407\pi$
$761$	−6.86663	+	11.8934i	−0.248915	+	0.431134i	0.714310	+	0.699829i	$0.246741\pi$
$762$	3.73397	−	6.46743i	0.135268	−	0.234290i
$763$	−5.48404			−0.198536
$764$	−20.7347	+	11.9712i	−0.750155	+	0.433102i
$765$	−5.53664	+	3.21961i	−0.200177	+	0.116405i
$766$	−8.67444			−0.313420
$767$		−	61.6267i		−	2.22521i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$		−	45.5375i		−	1.64212i	−0.570840	−	0.821061i	$-0.693382\pi$
$769$		−	45.5375i		−	1.64212i	0.570840	−	0.821061i	$-0.306618\pi$
$770$	52.3633	−	0.163042i	1.88704	−	0.00587561i
$771$			4.35859i			0.156971i
$772$	−8.07038	−	13.9783i	−0.290459	−	0.503090i
$773$	−39.5623	+	22.8413i	−1.42296	+	0.821545i	−0.996551	−	0.0829869i	$-0.973554\pi$
$773$	−39.5623	+	22.8413i	−1.42296	+	0.821545i	−0.426407	+	0.904532i	$0.640221\pi$
$774$	2.14753	+	3.71962i	0.0771912	+	0.133699i
$775$	−0.135084	−	21.6919i	−0.00485235	−	0.779195i
$776$	−8.96250			−0.321735
$777$	−16.4959	−	19.2221i	−0.591788	−	0.689590i
$778$			37.8175i			1.35582i
$779$	4.86194	+	2.80704i	0.174197	+	0.100573i
$780$	−12.5350	+	0.0390297i	−0.448824	+	0.00139749i
$781$	−34.2208	−	59.2722i	−1.22452	−	2.12093i
$782$	−8.93909	−	15.4829i	−0.319661	−	0.553669i
$783$	9.90800			0.354083
$784$	5.17035	+	8.95532i	0.184655	+	0.319833i
$785$	−16.8087	+	29.3241i	−0.599929	+	1.04662i
$786$	−2.69853	+	4.67400i	−0.0962535	+	0.166716i
$787$			36.7255i			1.30912i	0.756009	+	0.654561i	$0.227147\pi$
$787$			36.7255i			1.30912i	−0.756009	+	0.654561i	$0.772853\pi$
$788$		−	24.5757i		−	0.875475i
$789$	−14.3743	+	24.8970i	−0.511739	+	0.886358i
$790$	−22.1359	+	0.0689239i	−0.787561	+	0.00245220i
$791$		−	36.2147i		−	1.28765i
$792$	2.81177	−	4.87013i	0.0999120	−	0.173053i
$793$	−12.3822	−	7.14885i	−0.439704	−	0.253863i
$794$	22.5734	+	13.0328i	0.801102	+	0.462516i
$795$	−0.0311610	−	10.0078i	−0.00110517	−	0.354941i
$796$	−15.1518	+	8.74791i	−0.537042	+	0.310061i
$797$	−11.2290	+	19.4492i	−0.397751	+	0.688925i	−0.993448	−	0.114285i	$-0.963542\pi$
$797$	−11.2290	+	19.4492i	−0.397751	+	0.688925i	0.595697	+	0.803209i	$0.296876\pi$
$798$	21.5050	+	12.4159i	0.761267	+	0.439518i
$799$	0.907625	+	0.524017i	0.0321095	+	0.0185384i
$800$	2.52692	+	4.31447i	0.0893400	+	0.152540i
$801$	−7.38304	+	4.26260i	−0.260867	+	0.150612i
$802$	−7.78191	−	4.49289i	−0.274789	−	0.158649i
$803$			65.2315i			2.30197i
$804$	2.21789			0.0782189
$805$	29.2167	+	50.2429i	1.02975	+	1.77083i
$806$			24.3207i			0.856661i
$807$	−2.56384	+	1.48024i	−0.0902516	+	0.0521068i
$808$	17.5745			0.618267
$809$	−15.6803	+	9.05301i	−0.551289	+	0.318287i	−0.749642	−	0.661844i	$-0.769774\pi$
$809$	−15.6803	+	9.05301i	−0.551289	+	0.318287i	0.198353	+	0.980131i	$0.436441\pi$
$810$	−0.00696233	−	2.23606i	−0.000244631	−	0.0785670i
$811$	7.95176	+	13.7729i	0.279224	+	0.483630i	0.971192	−	0.238298i	$-0.0765894\pi$
$811$	7.95176	+	13.7729i	0.279224	+	0.483630i	−0.691968	+	0.721928i	$0.743256\pi$
$812$	−20.6295	+	35.7314i	−0.723955	+	1.25393i
$813$		−	11.0248i		−	0.386656i
$814$	−22.2768	−	25.9584i	−0.780803	−	0.909843i
$815$	−11.4753	−	6.57772i	−0.401963	−	0.230408i
$816$	−2.48053	−	1.43213i	−0.0868359	−	0.0501347i
$817$	−22.1806	+	12.8060i	−0.776002	+	0.448025i
$818$	−4.54148	+	2.62202i	−0.158789	+	0.0916768i
$819$	−20.2165	+	11.6720i	−0.706420	+	0.407852i
$820$	1.82641	+	1.04691i	0.0637810	+	0.0365597i
$821$	3.15409	+	5.46304i	0.110078	+	0.190661i	0.915802	−	0.401631i	$-0.131556\pi$
$821$	3.15409	+	5.46304i	0.110078	+	0.190661i	−0.805723	+	0.592292i	$0.798223\pi$
$822$	3.45444			0.120487
$823$	26.2973	+	15.1827i	0.916666	+	0.529237i	0.882570	−	0.470181i	$-0.155811\pi$
$823$	26.2973	+	15.1827i	0.916666	+	0.529237i	0.0340960	+	0.999419i	$0.489145\pi$
$824$	4.83675			0.168496
$825$	24.2627	−	14.2102i	0.844717	−	0.494737i
$826$	−22.8893	+	39.6454i	−0.796419	+	1.37944i
$827$	−7.21465	−	12.4961i	−0.250878	−	0.434533i	0.712890	−	0.701276i	$-0.247386\pi$
$827$	−7.21465	−	12.4961i	−0.250878	−	0.434533i	−0.963768	+	0.266743i	$0.914053\pi$
$828$	6.24179			0.216917
$829$	12.9413	+	7.47164i	0.449468	+	0.259501i	0.707606	−	0.706608i	$-0.249775\pi$
$829$	12.9413	+	7.47164i	0.449468	+	0.259501i	−0.258137	+	0.966108i	$0.583109\pi$
$830$	0.203907	+	0.350652i	0.00707773	+	0.0121713i
$831$	−10.3511	−	5.97624i	−0.359077	−	0.207313i
$832$	−2.80292	−	4.85480i	−0.0971738	−	0.168310i
$833$	−14.8093	−	25.6504i	−0.513111	−	0.888735i
$834$	−7.20841	−	4.16178i	−0.249607	−	0.144111i
$835$	11.7814	−	6.85098i	0.407712	−	0.237088i
$836$	29.0413	+	16.7670i	1.00441	+	0.579898i
$837$	−4.33846			−0.149959
$838$	4.82659	+	8.35990i	0.166732	+	0.288788i
$839$	−6.26033	+	10.8432i	−0.216131	+	0.374349i	−0.953622	−	0.301008i	$-0.902677\pi$
$839$	−6.26033	+	10.8432i	−0.216131	+	0.374349i	0.737491	+	0.675357i	$0.236010\pi$
$840$	8.07843	+	4.63061i	0.278732	+	0.159771i
$841$	−69.1685			−2.38512
$842$	−2.08227	−	1.20220i	−0.0717597	−	0.0414305i
$843$	−5.48649			−0.188965
$844$	−14.2247	−	24.6379i	−0.489634	−	0.848071i
$845$	35.7448	+	20.4891i	1.22966	+	0.704847i
$846$	−0.316878	+	0.182950i	−0.0108945	+	0.00628994i
$847$	74.3777	−	42.9420i	2.55565	−	1.47550i
$848$	3.87603	−	2.23783i	0.133104	−	0.0768474i
$849$	−9.93443	−	5.73565i	−0.340949	−	0.196847i
$850$	−7.23777	−	12.3578i	−0.248253	−	0.423870i
$851$	12.5892	−	35.8194i	0.431552	−	1.22787i
$852$		−	12.1705i		−	0.416956i
$853$	12.1760	−	21.0894i	0.416898	−	0.722088i	−0.578728	−	0.815521i	$-0.696451\pi$
$853$	12.1760	−	21.0894i	0.416898	−	0.722088i	0.995626	+	0.0934326i	$0.0297840\pi$
$854$	5.31041	+	9.19791i	0.181719	+	0.314746i
$855$	13.3339	−	0.0415173i	0.456010	−	0.00141986i
$856$	13.4925	−	7.78991i	0.461165	−	0.266253i
$857$	−30.3696			−1.03741			−0.518703	−	0.854955i	$-0.673585\pi$
$857$	−30.3696			−1.03741			−0.518703	+	0.854955i	$0.673585\pi$
$858$	−27.3012	+	15.7624i	−0.932048	+	0.538118i
$859$			28.1645i			0.960961i	0.877005	+	0.480480i	$0.159538\pi$
$859$			28.1645i			0.960961i	−0.877005	+	0.480480i	$0.840462\pi$
$860$	−8.30234	+	4.82789i	−0.283107	+	0.164630i
$861$	3.92047			0.133609
$862$		−	24.5520i		−	0.836243i
$863$	−15.7408	−	9.08796i	−0.535823	−	0.309358i	0.207561	−	0.978222i	$-0.433447\pi$
$863$	−15.7408	−	9.08796i	−0.535823	−	0.309358i	−0.743385	+	0.668864i	$0.766781\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$	−7.98081	+	13.9231i	−0.271356	+	0.473400i
$866$	21.4604	+	12.3902i	0.729254	+	0.421035i
$867$	−7.61753	−	4.39798i	−0.258705	−	0.149363i
$868$	9.03314	−	15.6459i	0.306605	−	0.531055i
$869$	−48.2121	+	27.8353i	−1.63548	+	0.944247i
$870$	0.0689828	+	22.1549i	0.00233874	+	0.751120i
$871$	−10.7674	−	6.21657i	−0.364840	−	0.210640i
$872$	−1.14051	−	0.658472i	−0.0386225	−	0.0222987i
$873$	−4.48125	+	7.76175i	−0.151667	+	0.262695i
$874$			37.2206i			1.25901i
$875$	23.6543	+	40.1007i	0.799661	+	1.35565i
$876$	−5.79986	+	10.0456i	−0.195959	+	0.339411i
$877$			31.8322i			1.07490i	0.843297	+	0.537448i	$0.180612\pi$
$877$			31.8322i			1.07490i	−0.843297	+	0.537448i	$0.819388\pi$
$878$			26.7190i			0.901722i
$879$	4.96530	−	8.60014i	0.167475	−	0.290076i
$880$	10.9095	+	6.25338i	0.367758	+	0.210801i
$881$	17.5474	+	30.3930i	0.591187	+	1.02397i	0.994073	+	0.108716i	$0.0346739\pi$
$881$	17.5474	+	30.3930i	0.591187	+	1.02397i	−0.402886	+	0.915250i	$0.631993\pi$
$882$	10.3407			0.348190
$883$	23.4051	+	40.5387i	0.787643	+	1.36424i	0.927408	+	0.374052i	$0.122032\pi$
$883$	23.4051	+	40.5387i	0.787643	+	1.36424i	−0.139765	+	0.990185i	$0.544635\pi$
$884$	8.02832	+	13.9055i	0.270022	+	0.467691i
$885$	0.0765390	+	24.5817i	0.00257283	+	0.826303i
$886$	−15.9676	−	9.21892i	−0.536443	−	0.309716i
$887$			12.7729i			0.428872i	0.976738	+	0.214436i	$0.0687913\pi$
$887$			12.7729i			0.428872i	−0.976738	+	0.214436i	$0.931209\pi$
$888$	−1.12262	−	5.97827i	−0.0376726	−	0.200618i
$889$	31.0981			1.04300
$890$	−9.58282	−	16.4792i	−0.321217	−	0.552385i
$891$	−2.81177	−	4.87013i	−0.0941979	−	0.163156i
$892$	2.50633	−	1.44703i	0.0839181	−	0.0484501i
$893$	−1.09095	−	1.88959i	−0.0365074	−	0.0632326i
$894$		−	9.40193i		−	0.314448i
$895$	50.7207	−	0.157927i	1.69541	−	0.00527892i
$896$			4.16422i			0.139117i
$897$	−30.3027	−	17.4953i	−1.01178	−	0.584149i
$898$			34.2917i			1.14433i
$899$	42.9855			1.43365
$900$	4.99990	−	0.0311363i	0.166663	−	0.00103788i
$901$	−11.1020	+	6.40975i	−0.369861	+	0.213540i
$902$	5.29438			0.176284
$903$	−8.94276	+	15.4893i	−0.297597	+	0.515452i
$904$	4.34832	−	7.53150i	0.144623	−	0.250494i
$905$	−23.0291	+	13.3917i	−0.765514	+	0.445154i
$906$	−9.39991	+	5.42704i	−0.312291	+	0.180301i
$907$	−13.8568	−	24.0006i	−0.460106	−	0.796928i	0.538859	−	0.842396i	$-0.318855\pi$
$907$	−13.8568	−	24.0006i	−0.460106	−	0.796928i	−0.998966	+	0.0454681i	$0.985522\pi$
$908$	−2.39517	+	4.14855i	−0.0794864	+	0.137675i
$909$	8.78723	−	15.2199i	0.291454	−	0.504813i
$910$	−26.2400	−	45.1239i	−0.869846	−	1.49584i
$911$			19.4856i			0.645587i	0.946469	+	0.322794i	$0.104622\pi$
$911$			19.4856i			0.645587i	−0.946469	+	0.322794i	$0.895378\pi$
$912$	2.98157	+	5.16423i	0.0987296	+	0.171005i
$913$	0.883456	+	0.510064i	0.0292381	+	0.0168806i
$914$	−24.5822			−0.813108
$915$	4.94787	+	2.83615i	0.163572	+	0.0937603i
$916$	−0.352183	+	0.609999i	−0.0116365	+	0.0201549i
$917$	−22.4746			−0.742175
$918$	−2.48053	+	1.43213i	−0.0818697	+	0.0472675i
$919$			28.6717i			0.945792i	0.881118	+	0.472896i	$0.156791\pi$
$919$			28.6717i			0.945792i	−0.881118	+	0.472896i	$0.843209\pi$
$920$	0.0434574	+	13.9570i	0.00143275	+	0.460149i
$921$	−0.623504	−	1.07994i	−0.0205451	−	0.0355852i
$922$	9.81068	−	5.66420i	0.323097	−	0.186540i
$923$	−34.1131	+	59.0856i	−1.12285	+	1.94483i
$924$	23.4177			0.770385
$925$	9.90573	−	28.7555i	0.325698	−	0.945474i
$926$	0.522731			0.0171780
$927$	2.41837	−	4.18875i	0.0794298	−	0.137577i
$928$	−8.58058	+	4.95400i	−0.281671	+	0.162623i
$929$	−14.8497	−	25.7204i	−0.487201	−	0.843858i	0.512690	−	0.858574i	$-0.328649\pi$
$929$	−14.8497	−	25.7204i	−0.487201	−	0.843858i	−0.999892	+	0.0147160i	$0.995316\pi$
$930$	−0.0302058	−	9.70104i	−0.000990487	−	0.318110i
$931$			61.6630i			2.02092i
$932$	13.3515	−	7.70852i	0.437344	−	0.252501i
$933$	8.25793			0.270353
$934$	−0.877189	+	1.51934i	−0.0287025	+	0.0497142i
$935$	−31.2477	−	17.9114i	−1.02191	−	0.585764i
$936$	−5.60584			−0.183233
$937$	−38.7008	−	22.3439i	−1.26430	−	0.729945i	−0.290398	−	0.956906i	$-0.593788\pi$
$937$	−38.7008	−	22.3439i	−1.26430	−	0.729945i	−0.973904	+	0.226961i	$0.927121\pi$
$938$	4.61788	+	7.99841i	0.150779	+	0.261157i
$939$		−	1.91650i		−	0.0625428i
$940$	−0.411292	−	0.707284i	−0.0134149	−	0.0230691i
$941$	−24.6951	+	42.7733i	−0.805039	+	1.39437i	0.111226	+	0.993795i	$0.464522\pi$
$941$	−24.6951	+	42.7733i	−0.805039	+	1.39437i	−0.916265	+	0.400573i	$0.868811\pi$
$942$	−7.55789	+	13.0906i	−0.246249	+	0.426516i
$943$	2.93822	+	5.08914i	0.0956815	+	0.165725i
$944$	−9.52048	+	5.49665i	−0.309865	+	0.178901i
$945$	8.04944	−	4.68082i	0.261848	−	0.152267i
$946$	−12.0767	+	20.9175i	−0.392648	+	0.680086i
$947$	14.7814	−	25.6022i	0.480332	−	0.831959i	−0.519413	−	0.854523i	$-0.673850\pi$
$947$	14.7814	−	25.6022i	0.480332	−	0.831959i	0.999745	+	0.0225636i	$0.00718284\pi$
$948$	−9.89954			−0.321522
$949$	56.3143	−	32.5131i	1.82804	−	1.05542i
$950$	0.185670	+	29.8151i	0.00602394	+	0.967329i
$951$	−1.78645			−0.0579297
$952$		−	11.9274i		−	0.386571i
$953$	−35.0001	−	20.2073i	−1.13376	−	0.654578i	−0.188884	−	0.981999i	$-0.560487\pi$
$953$	−35.0001	−	20.2073i	−1.13376	−	0.654578i	−0.944879	+	0.327421i	$0.893820\pi$
$954$		−	4.47566i		−	0.144905i
$955$	−53.5365	+	0.166695i	−1.73240	+	0.00539411i
$956$			7.08489i			0.229142i
$957$	27.8591	+	48.2533i	0.900556	+	1.55981i
$958$	14.0589	−	8.11691i	0.454223	−	0.262246i
$959$	7.19252	+	12.4578i	0.232258	+	0.402283i
$960$	1.12406	+	1.93300i	0.0362788	+	0.0623873i
$961$	12.1778			0.392832
$962$	−11.3065	+	32.1699i	−0.364537	+	1.03720i
$963$		−	15.5798i		−	0.502052i
$964$	19.6742	+	11.3589i	0.633664	+	0.365846i
$965$	−0.112377	−	36.0917i	−0.00361756	−	1.16183i
$966$	12.9961	+	22.5099i	0.418142	+	0.724244i
$967$	−26.2245	−	45.4221i	−0.843322	−	1.46068i	−0.887071	−	0.461633i	$-0.847264\pi$
$967$	−26.2245	−	45.4221i	−0.843322	−	1.46068i	0.0437492	−	0.999043i	$-0.486070\pi$
$968$	20.6243			0.662889
$969$	−8.54001	−	14.7917i	−0.274345	−	0.475179i
$970$	−17.3869	−	9.96629i	−0.558260	−	0.319998i
$971$	−29.1830	+	50.5464i	−0.936525	+	1.62211i	−0.164635	+	0.986355i	$0.552645\pi$
$971$	−29.1830	+	50.5464i	−0.936525	+	1.62211i	−0.771891	+	0.635755i	$0.780689\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		−	34.6611i		−	1.11118i
$974$	13.7247	−	23.7719i	0.439768	−	0.761701i
$975$	−24.3608	−	13.8632i	−0.780170	−	0.443977i
$976$			2.55050i			0.0816395i
$977$	−13.3641	+	23.1472i	−0.427554	+	0.740546i	−0.996655	−	0.0817219i	$-0.973958\pi$
$977$	−13.3641	+	23.1472i	−0.427554	+	0.740546i	0.569101	+	0.822268i	$0.307291\pi$
$978$	−5.12274	−	2.95761i	−0.163807	−	0.0945740i
$979$	−41.5189	−	23.9709i	−1.32695	−	0.766114i
$980$	0.0719954	+	23.1224i	0.00229981	+	0.738618i
$981$	−1.14051	+	0.658472i	−0.0364136	+	0.0210234i
$982$	−12.4893	+	21.6321i	−0.398550	+	0.690308i
$983$	26.7412	+	15.4391i	0.852913	+	0.492429i	0.861633	−	0.507533i	$-0.169442\pi$
$983$	26.7412	+	15.4391i	0.852913	+	0.492429i	−0.00871992	+	0.999962i	$0.502776\pi$
$984$	0.815334	+	0.470733i	0.0259919	+	0.0150064i
$985$	27.3282	−	47.6760i	0.870749	−	1.51908i
$986$	24.5771	−	14.1896i	0.782694	−	0.451889i
$987$	−1.31955	−	0.761843i	−0.0420017	−	0.0242497i
$988$		−	33.4284i		−	1.06350i
$989$	−26.8088			−0.852471
$990$	10.8703	−	6.32119i	0.345482	−	0.200901i
$991$			36.8757i			1.17140i	0.810530	+	0.585698i	$0.199179\pi$
$991$			36.8757i			1.17140i	−0.810530	+	0.585698i	$0.800821\pi$
$992$	3.75722	−	2.16923i	0.119292	−	0.0688731i
$993$	−14.1642			−0.449488
$994$	43.8909	−	25.3404i	1.39213	−	0.803749i
$995$	−39.1216	+	0.121812i	−1.24024	+	0.00386169i
$996$	0.0907014	+	0.157099i	0.00287398	+	0.00497789i
$997$	12.6457	−	21.9029i	0.400492	−	0.693672i	−0.593293	−	0.804986i	$-0.702173\pi$
$997$	12.6457	−	21.9029i	0.400492	−	0.693672i	0.993785	+	0.111314i	$0.0355059\pi$
$998$			9.48453i			0.300228i
$999$	−5.73864	−	2.01692i	−0.181563	−	0.0638125i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.ba.a.619.7	yes	36
5.4	even	2		1110.2.ba.b.619.12	yes	36
37.11	even	6		1110.2.ba.b.529.12	yes	36
185.159	even	6	inner	1110.2.ba.a.529.7	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.ba.a.529.7	✓	36	185.159	even	6	inner
1110.2.ba.a.619.7	yes	36	1.1	even	1	trivial
1110.2.ba.b.529.12	yes	36	37.11	even	6
1110.2.ba.b.619.12	yes	36	5.4	even	2

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)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.00696233 - 2.23606i) q^{5} -1.00000i q^{6} +(3.60632 - 2.08211i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.00696233 - 2.23606i) q^{5} -1.00000i q^{6} +(3.60632 - 2.08211i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(1.93996 + 1.11200i) q^{10} +5.62355 q^{11} +(0.866025 + 0.500000i) q^{12} +(-2.80292 - 4.85480i) q^{13} +4.16422i q^{14} +(1.12406 + 1.93300i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.43213 - 2.48053i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-5.16423 + 2.98157i) q^{19} +(-1.93300 + 1.12406i) q^{20} +(-2.08211 + 3.60632i) q^{21} +(-2.81177 + 4.87013i) q^{22} -6.24179 q^{23} +(-0.866025 + 0.500000i) q^{24} +(-4.99990 + 0.0311363i) q^{25} +5.60584 q^{26} +1.00000i q^{27} +(-3.60632 - 2.08211i) q^{28} -9.90800i q^{29} +(-2.23606 + 0.00696233i) q^{30} +4.33846i q^{31} +(-0.500000 - 0.866025i) q^{32} +(-4.87013 + 2.81177i) q^{33} +(1.43213 + 2.48053i) q^{34} +(-4.68082 - 8.04944i) q^{35} -1.00000 q^{36} +(-2.01692 + 5.73864i) q^{37} -5.96313i q^{38} +(4.85480 + 2.80292i) q^{39} +(-0.00696233 - 2.23606i) q^{40} +(-0.470733 - 0.815334i) q^{41} +(-2.08211 - 3.60632i) q^{42} +4.29505 q^{43} +(-2.81177 - 4.87013i) q^{44} +(-1.93996 - 1.11200i) q^{45} +(3.12090 - 5.40555i) q^{46} +0.365900i q^{47} -1.00000i q^{48} +(5.17035 - 8.95532i) q^{49} +(2.47299 - 4.34561i) q^{50} +2.86427i q^{51} +(-2.80292 + 4.85480i) q^{52} +(-3.87603 - 2.23783i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(-0.0391530 - 12.5746i) q^{55} +(3.60632 - 2.08211i) q^{56} +(2.98157 - 5.16423i) q^{57} +(8.58058 + 4.95400i) q^{58} +(9.52048 + 5.49665i) q^{59} +(1.11200 - 1.93996i) q^{60} +(2.20880 - 1.27525i) q^{61} +(-3.75722 - 2.16923i) q^{62} -4.16422i q^{63} +1.00000 q^{64} +(-10.8361 + 6.30129i) q^{65} -5.62355i q^{66} +(1.92075 - 1.10894i) q^{67} -2.86427 q^{68} +(5.40555 - 3.12090i) q^{69} +(9.31143 - 0.0289927i) q^{70} +(-6.08527 - 10.5400i) q^{71} +(0.500000 - 0.866025i) q^{72} +11.5997i q^{73} +(-3.96135 - 4.61603i) q^{74} +(4.31447 - 2.52692i) q^{75} +(5.16423 + 2.98157i) q^{76} +(20.2803 - 11.7088i) q^{77} +(-4.85480 + 2.80292i) q^{78} +(-8.57325 + 4.94977i) q^{79} +(1.93996 + 1.11200i) q^{80} +(-0.500000 - 0.866025i) q^{81} +0.941466 q^{82} +(0.157099 + 0.0907014i) q^{83} +4.16422 q^{84} +(-5.55658 - 3.18506i) q^{85} +(-2.14753 + 3.71962i) q^{86} +(4.95400 + 8.58058i) q^{87} +5.62355 q^{88} +(-7.38304 - 4.26260i) q^{89} +(1.93300 - 1.12406i) q^{90} +(-20.2165 - 11.6720i) q^{91} +(3.12090 + 5.40555i) q^{92} +(-2.16923 - 3.75722i) q^{93} +(-0.316878 - 0.182950i) q^{94} +(6.70291 + 11.5267i) q^{95} +(0.866025 + 0.500000i) q^{96} -8.96250 q^{97} +(5.17035 + 8.95532i) q^{98} +(2.81177 - 4.87013i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9}+O(q^{10}) \) 36 * q - 18 * q^2 - 18 * q^4 + 2 * q^5 + 36 * q^8 + 18 * q^9	\( 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9} + 2 q^{10} + 4 q^{11} - 14 q^{13} - 2 q^{15} - 18 q^{16} + 18 q^{18} + 6 q^{19} - 4 q^{20} - 2 q^{22} - 20 q^{23} + 4 q^{25} + 28 q^{26} - 2 q^{30} - 18 q^{32} - 6 q^{33} - 40 q^{35} - 36 q^{36} + 20 q^{37} + 6 q^{39} + 2 q^{40} + 10 q^{41} - 2 q^{44} - 2 q^{45} + 10 q^{46} + 10 q^{49} - 2 q^{50} - 14 q^{52} - 12 q^{53} + 56 q^{55} + 8 q^{57} + 30 q^{58} + 18 q^{59} + 4 q^{60} - 6 q^{61} - 12 q^{62} + 36 q^{64} + 40 q^{65} + 36 q^{67} + 12 q^{69} + 20 q^{70} - 24 q^{71} + 18 q^{72} - 34 q^{74} + 8 q^{75} - 6 q^{76} - 24 q^{77} - 6 q^{78} + 2 q^{80} - 18 q^{81} - 20 q^{82} + 36 q^{83} + 26 q^{85} - 10 q^{87} + 4 q^{88} + 4 q^{90} - 36 q^{91} + 10 q^{92} + 12 q^{93} + 12 q^{94} - 30 q^{95} + 52 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) \) 36 * q - 18 * q^2 - 18 * q^4 + 2 * 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 - 4 * q^20 - 2 * q^22 - 20 * q^23 + 4 * q^25 + 28 * q^26 - 2 * q^30 - 18 * q^32 - 6 * q^33 - 40 * q^35 - 36 * q^36 + 20 * q^37 + 6 * q^39 + 2 * q^40 + 10 * q^41 - 2 * q^44 - 2 * q^45 + 10 * q^46 + 10 * q^49 - 2 * q^50 - 14 * q^52 - 12 * q^53 + 56 * q^55 + 8 * q^57 + 30 * q^58 + 18 * q^59 + 4 * q^60 - 6 * q^61 - 12 * q^62 + 36 * q^64 + 40 * q^65 + 36 * q^67 + 12 * q^69 + 20 * 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 + 4 * q^90 - 36 * q^91 + 10 * q^92 + 12 * q^93 + 12 * q^94 - 30 * q^95 + 52 * q^97 + 10 * q^98 + 2 * q^99

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