LMFDB - Embedded newform 273.2.l.b.16.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(16,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 2]))

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

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

chi := DirichletCharacter("273.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.l (of order $3$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 11 x^{14} - 4 x^{13} + 87 x^{12} - 35 x^{11} + 326 x^{10} - 205 x^{9} + 895 x^{8} - 481 x^{7} + \cdots + 1 $ x^16 + 11x^14 - 4x^13 + 87x^12 - 35x^11 + 326x^10 - 205x^9 + 895x^8 - 481x^7 + 1005x^6 - 544x^5 + 811x^4 - 312x^3 + 195x^2 + 13x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.8
Root			$-1.27528 - 2.20885i$ of defining polynomial
Character	$\chi$	$=$	273.16
Dual form			273.2.l.b.256.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.55056 q^{2} +(0.500000 - 0.866025i) q^{3} +4.50537 q^{4} +(-1.39351 + 2.41363i) q^{5} +(1.27528 - 2.20885i) q^{6} +(-2.46231 - 0.968004i) q^{7} +6.39011 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+2.55056 q^{2} +(0.500000 - 0.866025i) q^{3} +4.50537 q^{4} +(-1.39351 + 2.41363i) q^{5} +(1.27528 - 2.20885i) q^{6} +(-2.46231 - 0.968004i) q^{7} +6.39011 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-3.55423 + 6.15611i) q^{10} +(1.38373 - 2.39670i) q^{11} +(2.25269 - 3.90177i) q^{12} +(2.99297 + 2.01050i) q^{13} +(-6.28028 - 2.46895i) q^{14} +(1.39351 + 2.41363i) q^{15} +7.28763 q^{16} -5.88680 q^{17} +(-1.27528 - 2.20885i) q^{18} +(-1.70037 - 2.94513i) q^{19} +(-6.27828 + 10.8743i) q^{20} +(-2.06947 + 1.64842i) q^{21} +(3.52930 - 6.11292i) q^{22} -7.34492 q^{23} +(3.19505 - 5.53400i) q^{24} +(-1.38373 - 2.39670i) q^{25} +(7.63376 + 5.12791i) q^{26} -1.00000 q^{27} +(-11.0936 - 4.36122i) q^{28} +(1.56328 + 2.70768i) q^{29} +(3.55423 + 6.15611i) q^{30} +(1.93352 + 3.34896i) q^{31} +5.80735 q^{32} +(-1.38373 - 2.39670i) q^{33} -15.0147 q^{34} +(5.76765 - 4.59418i) q^{35} +(-2.25269 - 3.90177i) q^{36} +5.84347 q^{37} +(-4.33691 - 7.51175i) q^{38} +(3.23763 - 1.58674i) q^{39} +(-8.90467 + 15.4233i) q^{40} +(3.24124 + 5.61400i) q^{41} +(-5.27832 + 4.20440i) q^{42} +(2.99197 - 5.18224i) q^{43} +(6.23423 - 10.7980i) q^{44} +2.78702 q^{45} -18.7337 q^{46} +(3.95673 - 6.85325i) q^{47} +(3.64382 - 6.31127i) q^{48} +(5.12594 + 4.76705i) q^{49} +(-3.52930 - 6.11292i) q^{50} +(-2.94340 + 5.09812i) q^{51} +(13.4845 + 9.05806i) q^{52} +(6.34471 + 10.9894i) q^{53} -2.55056 q^{54} +(3.85649 + 6.67963i) q^{55} +(-15.7344 - 6.18565i) q^{56} -3.40075 q^{57} +(3.98724 + 6.90611i) q^{58} +2.73648 q^{59} +(6.27828 + 10.8743i) q^{60} +(-4.77631 - 8.27282i) q^{61} +(4.93157 + 8.54173i) q^{62} +(0.392839 + 2.61642i) q^{63} +0.236742 q^{64} +(-9.02334 + 4.42227i) q^{65} +(-3.52930 - 6.11292i) q^{66} +(4.34033 - 7.51767i) q^{67} -26.5222 q^{68} +(-3.67246 + 6.36089i) q^{69} +(14.7108 - 11.7177i) q^{70} +(-1.57062 + 2.72039i) q^{71} +(-3.19505 - 5.53400i) q^{72} +(-4.80291 - 8.31889i) q^{73} +14.9041 q^{74} -2.76747 q^{75} +(-7.66082 - 13.2689i) q^{76} +(-5.72719 + 4.56195i) q^{77} +(8.25778 - 4.04708i) q^{78} +(-1.88112 + 3.25819i) q^{79} +(-10.1554 + 17.5896i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(8.26699 + 14.3189i) q^{82} +4.82088 q^{83} +(-9.32374 + 7.42675i) q^{84} +(8.20331 - 14.2086i) q^{85} +(7.63120 - 13.2176i) q^{86} +3.12656 q^{87} +(8.84221 - 15.3151i) q^{88} +1.75557 q^{89} +7.10846 q^{90} +(-5.42345 - 7.84769i) q^{91} -33.0916 q^{92} +3.86705 q^{93} +(10.0919 - 17.4797i) q^{94} +9.47794 q^{95} +(2.90367 - 5.02931i) q^{96} +(8.48637 - 14.6988i) q^{97} +(13.0740 + 12.1587i) q^{98} -2.76747 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{3} + 12 q^{4} + q^{7} + 12 q^{8} - 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^3 + 12 * q^4 + q^7 + 12 * q^8 - 8 * q^9	\( 16 q + 8 q^{3} + 12 q^{4} + q^{7} + 12 q^{8} - 8 q^{9} - 4 q^{10} - 2 q^{11} + 6 q^{12} + 5 q^{13} - 7 q^{14} + 12 q^{16} + 4 q^{17} - 11 q^{19} - 20 q^{20} - q^{21} + 7 q^{22} - 8 q^{23} + 6 q^{24} + 2 q^{25} + 33 q^{26} - 16 q^{27} - q^{28} + 15 q^{29} + 4 q^{30} + 3 q^{31} - 6 q^{32} + 2 q^{33} - 68 q^{34} - 6 q^{36} - 8 q^{37} + 2 q^{38} + 4 q^{39} - 25 q^{40} + 19 q^{41} - 17 q^{42} + 11 q^{43} - 16 q^{44} - 4 q^{46} + 5 q^{47} + 6 q^{48} + 7 q^{49} - 7 q^{50} + 2 q^{51} - 18 q^{52} + 36 q^{53} - 15 q^{55} - 51 q^{56} - 22 q^{57} + 20 q^{58} + 34 q^{59} + 20 q^{60} - 22 q^{61} - 6 q^{62} - 2 q^{63} - 20 q^{64} - 24 q^{65} - 7 q^{66} + 26 q^{67} - 10 q^{68} - 4 q^{69} + 46 q^{70} + 9 q^{71} - 6 q^{72} - 6 q^{73} - 30 q^{74} + 4 q^{75} - 16 q^{76} - 36 q^{77} + 6 q^{78} + 16 q^{79} - 28 q^{80} - 8 q^{81} - q^{82} + 36 q^{83} - 8 q^{84} - 4 q^{85} + 16 q^{86} + 30 q^{87} + 24 q^{88} - 40 q^{89} + 8 q^{90} - 10 q^{91} - 94 q^{92} + 6 q^{93} - 20 q^{94} - 3 q^{96} + 7 q^{97} + 18 q^{98} + 4 q^{99}+O(q^{100}) \) 16 * q + 8 * q^3 + 12 * q^4 + q^7 + 12 * q^8 - 8 * q^9 - 4 * q^10 - 2 * q^11 + 6 * q^12 + 5 * q^13 - 7 * q^14 + 12 * q^16 + 4 * q^17 - 11 * q^19 - 20 * q^20 - q^21 + 7 * q^22 - 8 * q^23 + 6 * q^24 + 2 * q^25 + 33 * q^26 - 16 * q^27 - q^28 + 15 * q^29 + 4 * q^30 + 3 * q^31 - 6 * q^32 + 2 * q^33 - 68 * q^34 - 6 * q^36 - 8 * q^37 + 2 * q^38 + 4 * q^39 - 25 * q^40 + 19 * q^41 - 17 * q^42 + 11 * q^43 - 16 * q^44 - 4 * q^46 + 5 * q^47 + 6 * q^48 + 7 * q^49 - 7 * q^50 + 2 * q^51 - 18 * q^52 + 36 * q^53 - 15 * q^55 - 51 * q^56 - 22 * q^57 + 20 * q^58 + 34 * q^59 + 20 * q^60 - 22 * q^61 - 6 * q^62 - 2 * q^63 - 20 * q^64 - 24 * q^65 - 7 * q^66 + 26 * q^67 - 10 * q^68 - 4 * q^69 + 46 * q^70 + 9 * q^71 - 6 * q^72 - 6 * q^73 - 30 * q^74 + 4 * q^75 - 16 * q^76 - 36 * q^77 + 6 * q^78 + 16 * q^79 - 28 * q^80 - 8 * q^81 - q^82 + 36 * q^83 - 8 * q^84 - 4 * q^85 + 16 * q^86 + 30 * q^87 + 24 * q^88 - 40 * q^89 + 8 * q^90 - 10 * q^91 - 94 * q^92 + 6 * q^93 - 20 * q^94 - 3 * q^96 + 7 * q^97 + 18 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	2.55056			1.80352			0.901760	−	0.432237i	$-0.142275\pi$
$2$	2.55056			1.80352			0.901760	+	0.432237i	$0.142275\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	4.50537			2.25269
$5$	−1.39351	+	2.41363i	−0.623196	+	1.07941i	0.365691	+	0.930736i	$0.380833\pi$
$5$	−1.39351	+	2.41363i	−0.623196	+	1.07941i	−0.988887	+	0.148671i	$0.952501\pi$
$6$	1.27528	−	2.20885i	0.520632	−	0.901760i
$7$	−2.46231	−	0.968004i	−0.930666	−	0.365871i
$7$	−2.46231	−	0.968004i	−0.930666	−	0.365871i
$8$	6.39011			2.25924
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−3.55423	+	6.15611i	−1.12395	+	1.94673i
$11$	1.38373	−	2.39670i	0.417211	−	0.722631i	−0.578447	−	0.815720i	$-0.696341\pi$
$11$	1.38373	−	2.39670i	0.417211	−	0.722631i	0.995658	+	0.0930893i	$0.0296742\pi$
$12$	2.25269	−	3.90177i	0.650294	−	1.12634i
$13$	2.99297	+	2.01050i	0.830101	+	0.557613i
$13$	2.99297	+	2.01050i	0.830101	+	0.557613i
$14$	−6.28028	−	2.46895i	−1.67847	−	0.659856i
$15$	1.39351	+	2.41363i	0.359802	+	0.623196i
$16$	7.28763			1.82191
$17$	−5.88680			−1.42776			−0.713880	−	0.700268i	$-0.753064\pi$
$17$	−5.88680			−1.42776			−0.713880	+	0.700268i	$0.753064\pi$
$18$	−1.27528	−	2.20885i	−0.300587	−	0.520632i
$19$	−1.70037	−	2.94513i	−0.390093	−	0.675660i	0.602369	−	0.798218i	$-0.294224\pi$
$19$	−1.70037	−	2.94513i	−0.390093	−	0.675660i	−0.992461	+	0.122558i	$0.960890\pi$
$20$	−6.27828	+	10.8743i	−1.40386	+	2.43157i
$21$	−2.06947	+	1.64842i	−0.451596	+	0.359715i
$22$	3.52930	−	6.11292i	0.752449	−	1.30328i
$23$	−7.34492			−1.53152			−0.765761	−	0.643126i	$-0.777637\pi$
$23$	−7.34492			−1.53152			−0.765761	+	0.643126i	$0.777637\pi$
$24$	3.19505	−	5.53400i	0.652188	−	1.12962i
$25$	−1.38373	−	2.39670i	−0.276747	−	0.479339i
$26$	7.63376	+	5.12791i	1.49710	+	1.00567i
$27$	−1.00000			−0.192450
$28$	−11.0936	−	4.36122i	−2.09650	−	0.824193i
$29$	1.56328	+	2.70768i	0.290294	+	0.502803i	0.973879	−	0.227067i	$-0.0729137\pi$
$29$	1.56328	+	2.70768i	0.290294	+	0.502803i	−0.683585	+	0.729871i	$0.739580\pi$
$30$	3.55423	+	6.15611i	0.648911	+	1.12395i
$31$	1.93352	+	3.34896i	0.347271	+	0.601491i	0.985764	−	0.168137i	$-0.0537751\pi$
$31$	1.93352	+	3.34896i	0.347271	+	0.601491i	−0.638493	+	0.769628i	$0.720442\pi$
$32$	5.80735			1.02660
$33$	−1.38373	−	2.39670i	−0.240877	−	0.417211i
$34$	−15.0147			−2.57499
$35$	5.76765	−	4.59418i	0.974911	−	0.776558i
$36$	−2.25269	−	3.90177i	−0.375448	−	0.650294i
$37$	5.84347			0.960660			0.480330	−	0.877088i	$-0.340517\pi$
$37$	5.84347			0.960660			0.480330	+	0.877088i	$0.340517\pi$
$38$	−4.33691	−	7.51175i	−0.703540	−	1.21857i
$39$	3.23763	−	1.58674i	0.518436	−	0.254082i
$40$	−8.90467	+	15.4233i	−1.40795	+	2.43865i
$41$	3.24124	+	5.61400i	0.506197	+	0.876759i	0.999974	+	0.00717054i	$0.00228247\pi$
$41$	3.24124	+	5.61400i	0.506197	+	0.876759i	−0.493777	+	0.869588i	$0.664384\pi$
$42$	−5.27832	+	4.20440i	−0.814462	+	0.648753i
$43$	2.99197	−	5.18224i	0.456271	−	0.790284i	−0.542489	−	0.840063i	$-0.682518\pi$
$43$	2.99197	−	5.18224i	0.456271	−	0.790284i	0.998760	+	0.0497783i	$0.0158515\pi$
$44$	6.23423	−	10.7980i	0.939846	−	1.62786i
$45$	2.78702			0.415464
$46$	−18.7337			−2.76213
$47$	3.95673	−	6.85325i	0.577148	−	0.999650i	−0.418656	−	0.908145i	$-0.637499\pi$
$47$	3.95673	−	6.85325i	0.577148	−	0.999650i	0.995805	−	0.0915053i	$-0.0291678\pi$
$48$	3.64382	−	6.31127i	0.525940	−	0.910954i
$49$	5.12594	+	4.76705i	0.732277	+	0.681007i
$50$	−3.52930	−	6.11292i	−0.499118	−	0.864498i
$51$	−2.94340	+	5.09812i	−0.412159	+	0.713880i
$52$	13.4845	+	9.05806i	1.86996	+	1.25613i
$53$	6.34471	+	10.9894i	0.871513	+	1.50951i	0.860431	+	0.509567i	$0.170194\pi$
$53$	6.34471	+	10.9894i	0.871513	+	1.50951i	0.0110819	+	0.999939i	$0.496472\pi$
$54$	−2.55056			−0.347088
$55$	3.85649	+	6.67963i	0.520009	+	0.900682i
$56$	−15.7344	−	6.18565i	−2.10260	−	0.826592i
$57$	−3.40075			−0.450440
$58$	3.98724	+	6.90611i	0.523551	+	0.906816i
$59$	2.73648			0.356260			0.178130	−	0.984007i	$-0.442995\pi$
$59$	2.73648			0.356260			0.178130	+	0.984007i	$0.442995\pi$
$60$	6.27828	+	10.8743i	0.810522	+	1.40386i
$61$	−4.77631	−	8.27282i	−0.611544	−	1.05923i	−0.990980	−	0.134008i	$-0.957215\pi$
$61$	−4.77631	−	8.27282i	−0.611544	−	1.05923i	0.379436	−	0.925218i	$-0.376118\pi$
$62$	4.93157	+	8.54173i	0.626310	+	1.08480i
$63$	0.392839	+	2.61642i	0.0494930	+	0.329639i
$64$	0.236742			0.0295928
$65$	−9.02334	+	4.42227i	−1.11921	+	0.548515i
$66$	−3.52930	−	6.11292i	−0.434427	−	0.752449i
$67$	4.34033	−	7.51767i	0.530255	−	0.918429i	−0.469121	−	0.883134i	$-0.655429\pi$
$67$	4.34033	−	7.51767i	0.530255	−	0.918429i	0.999377	−	0.0352957i	$-0.0112373\pi$
$68$	−26.5222			−3.21629
$69$	−3.67246	+	6.36089i	−0.442112	+	0.765761i
$70$	14.7108	−	11.7177i	1.75827	−	1.40054i
$71$	−1.57062	+	2.72039i	−0.186398	+	0.322851i	−0.944047	−	0.329812i	$-0.893015\pi$
$71$	−1.57062	+	2.72039i	−0.186398	+	0.322851i	0.757649	+	0.652663i	$0.226348\pi$
$72$	−3.19505	−	5.53400i	−0.376541	−	0.652188i
$73$	−4.80291	−	8.31889i	−0.562138	−	0.973652i	−0.997310	−	0.0733045i	$-0.976646\pi$
$73$	−4.80291	−	8.31889i	−0.562138	−	0.973652i	0.435171	−	0.900348i	$-0.356688\pi$
$74$	14.9041			1.73257
$75$	−2.76747			−0.319559
$76$	−7.66082	−	13.2689i	−0.878756	−	1.52205i
$77$	−5.72719	+	4.56195i	−0.652674	+	0.519882i
$78$	8.25778	−	4.04708i	0.935010	−	0.458241i
$79$	−1.88112	+	3.25819i	−0.211642	+	0.366575i	−0.952229	−	0.305386i	$-0.901215\pi$
$79$	−1.88112	+	3.25819i	−0.211642	+	0.366575i	0.740586	+	0.671961i	$0.234548\pi$
$80$	−10.1554	+	17.5896i	−1.13541	+	1.96658i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	8.26699	+	14.3189i	0.912937	+	1.58125i
$83$	4.82088			0.529161			0.264580	−	0.964364i	$-0.414767\pi$
$83$	4.82088			0.529161			0.264580	+	0.964364i	$0.414767\pi$
$84$	−9.32374	+	7.42675i	−1.01730	+	0.810325i
$85$	8.20331	−	14.2086i	0.889774	−	1.54113i
$86$	7.63120	−	13.2176i	0.822894	−	1.42529i
$87$	3.12656			0.335202
$88$	8.84221	−	15.3151i	0.942582	−	1.63260i
$89$	1.75557			0.186091			0.0930453	−	0.995662i	$-0.470340\pi$
$89$	1.75557			0.186091			0.0930453	+	0.995662i	$0.470340\pi$
$90$	7.10846			0.749298
$91$	−5.42345	−	7.84769i	−0.568532	−	0.822661i
$92$	−33.0916			−3.45004
$93$	3.86705			0.400994
$94$	10.0919	−	17.4797i	1.04090	−	1.80289i
$95$	9.47794			0.972416
$96$	2.90367	−	5.02931i	0.296355	−	0.513302i
$97$	8.48637	−	14.6988i	0.861660	−	1.49244i	−0.00866511	−	0.999962i	$-0.502758\pi$
$97$	8.48637	−	14.6988i	0.861660	−	1.49244i	0.870325	−	0.492477i	$-0.163908\pi$
$98$	13.0740	+	12.1587i	1.32068	+	1.22821i
$99$	−2.76747			−0.278141
$100$	−6.23423	−	10.7980i	−0.623423	−	1.07980i
$101$	0.921364	−	1.59585i	0.0916791	−	0.158793i	−0.816539	−	0.577291i	$-0.804110\pi$
$101$	0.921364	−	1.59585i	0.0916791	−	0.158793i	0.908218	+	0.418498i	$0.137443\pi$
$102$	−7.50733	+	13.0031i	−0.743337	+	1.28750i
$103$	−2.38506	+	4.13105i	−0.235007	+	0.407045i	−0.959275	−	0.282474i	$-0.908845\pi$
$103$	−2.38506	+	4.13105i	−0.235007	+	0.407045i	0.724267	+	0.689519i	$0.242178\pi$
$104$	19.1254	+	12.8473i	1.87540	+	1.25978i
$105$	−1.09485	−	7.29202i	−0.106846	−	0.711628i
$106$	16.1826	+	28.0291i	1.57179	+	2.72242i
$107$	−12.0754			−1.16738			−0.583688	−	0.811978i	$-0.698391\pi$
$107$	−12.0754			−1.16738			−0.583688	+	0.811978i	$0.698391\pi$
$108$	−4.50537			−0.433530
$109$	3.40885	+	5.90430i	0.326508	+	0.565529i	0.981816	−	0.189832i	$-0.0607945\pi$
$109$	3.40885	+	5.90430i	0.326508	+	0.565529i	−0.655308	+	0.755362i	$0.727461\pi$
$110$	9.83622	+	17.0368i	0.937846	+	1.62440i
$111$	2.92173	−	5.06059i	0.277319	−	0.480330i
$112$	−17.9444	−	7.05446i	−1.69559	−	0.666583i
$113$	−2.72463	+	4.71920i	−0.256312	+	0.443945i	−0.965251	−	0.261325i	$-0.915841\pi$
$113$	−2.72463	+	4.71920i	−0.256312	+	0.443945i	0.708939	+	0.705270i	$0.249174\pi$
$114$	−8.67382			−0.812378
$115$	10.2352	−	17.7279i	0.954438	−	1.65314i
$116$	7.04316	+	12.1991i	0.653941	+	1.13266i
$117$	0.244659	−	3.59724i	0.0226188	−	0.332565i
$118$	6.97958			0.642522
$119$	14.4951	+	5.69845i	1.32877	+	0.522376i
$120$	8.90467	+	15.4233i	0.812882	+	1.40795i
$121$	1.67057	+	2.89350i	0.151870	+	0.263046i
$122$	−12.1823	−	21.1003i	−1.10293	−	1.91034i
$123$	6.48248			0.584506
$124$	8.71124	+	15.0883i	0.782292	+	1.35497i
$125$	−6.22211			−0.556523
$126$	1.00196	+	6.67336i	0.0892617	+	0.594510i
$127$	−0.886520	−	1.53550i	−0.0786660	−	0.136253i	0.824009	−	0.566577i	$-0.191733\pi$
$127$	−0.886520	−	1.53550i	−0.0786660	−	0.136253i	−0.902675	+	0.430324i	$0.858399\pi$
$128$	−11.0109			−0.973233
$129$	−2.99197	−	5.18224i	−0.263428	−	0.456271i
$130$	−23.0146	+	11.2793i	−2.01851	+	0.989258i
$131$	−3.50734	+	6.07490i	−0.306438	+	0.530766i	−0.977580	−	0.210562i	$-0.932471\pi$
$131$	−3.50734	+	6.07490i	−0.306438	+	0.530766i	0.671143	+	0.741328i	$0.265804\pi$
$132$	−6.23423	−	10.7980i	−0.542620	−	0.939846i
$133$	1.33595	+	8.89780i	0.115841	+	0.771537i
$134$	11.0703	−	19.1743i	0.956326	−	1.65641i
$135$	1.39351	−	2.41363i	0.119934	−	0.207732i
$136$	−37.6173			−3.22566
$137$	−19.6574			−1.67945			−0.839725	−	0.543013i	$-0.817284\pi$
$137$	−19.6574			−1.67945			−0.839725	+	0.543013i	$0.817284\pi$
$138$	−9.36684	+	16.2238i	−0.797358	+	1.38106i
$139$	−9.17342	+	15.8888i	−0.778079	+	1.34767i	0.154968	+	0.987919i	$0.450472\pi$
$139$	−9.17342	+	15.8888i	−0.778079	+	1.34767i	−0.933048	+	0.359753i	$0.882861\pi$
$140$	25.9854	−	20.6985i	2.19617	−	1.74934i
$141$	−3.95673	−	6.85325i	−0.333217	−	0.577148i
$142$	−4.00596	+	6.93852i	−0.336173	+	0.582268i
$143$	8.96004	−	4.39125i	0.749276	−	0.367215i
$144$	−3.64382	−	6.31127i	−0.303651	−	0.525940i
$145$	−8.71377			−0.723640
$146$	−12.2501	−	21.2178i	−1.01383	−	1.75600i
$147$	6.69136	−	2.05567i	0.551894	−	0.169549i
$148$	26.3270			2.16407
$149$	4.40145	+	7.62354i	0.360581	+	0.624545i	0.988057	−	0.154092i	$-0.0492451\pi$
$149$	4.40145	+	7.62354i	0.360581	+	0.624545i	−0.627476	+	0.778636i	$0.715912\pi$
$150$	−7.05860			−0.576332
$151$	−4.83567	−	8.37562i	−0.393521	−	0.681598i	0.599390	−	0.800457i	$-0.295410\pi$
$151$	−4.83567	−	8.37562i	−0.393521	−	0.681598i	−0.992911	+	0.118859i	$0.962076\pi$
$152$	−10.8656	−	18.8197i	−0.881314	−	1.52648i
$153$	2.94340	+	5.09812i	0.237960	+	0.412159i
$154$	−14.6076	+	11.6355i	−1.17711	+	0.937618i
$155$	−10.7775			−0.865672
$156$	14.5867	−	7.14885i	1.16787	−	0.572366i
$157$	−5.76601	−	9.98702i	−0.460177	−	0.797051i	0.538792	−	0.842439i	$-0.318881\pi$
$157$	−5.76601	−	9.98702i	−0.460177	−	0.797051i	−0.998969	+	0.0453882i	$0.985548\pi$
$158$	−4.79791	+	8.31023i	−0.381701	+	0.661126i
$159$	12.6894			1.00634
$160$	−8.09259	+	14.0168i	−0.639775	+	1.10812i
$161$	18.0855	+	7.10991i	1.42533	+	0.560339i
$162$	−1.27528	+	2.20885i	−0.100196	+	0.173544i
$163$	6.08521	+	10.5399i	0.476631	+	0.825548i	0.999641	−	0.0267776i	$-0.00852461\pi$
$163$	6.08521	+	10.5399i	0.476631	+	0.825548i	−0.523011	+	0.852326i	$0.675191\pi$
$164$	14.6030	+	25.2931i	1.14030	+	1.97506i
$165$	7.71298			0.600454
$166$	12.2960			0.954352
$167$	4.54697	+	7.87559i	0.351855	+	0.609431i	0.986575	−	0.163311i	$-0.0522175\pi$
$167$	4.54697	+	7.87559i	0.351855	+	0.609431i	−0.634719	+	0.772743i	$0.718884\pi$
$168$	−13.2241	+	10.5336i	−1.02026	+	0.812684i
$169$	4.91577	+	12.0348i	0.378136	+	0.925750i
$170$	20.9231	−	36.2398i	1.60473	−	2.77947i
$171$	−1.70037	+	2.94513i	−0.130031	+	0.225220i
$172$	13.4799	−	23.3479i	1.02783	−	1.78026i
$173$	0.673648	+	1.16679i	0.0512165	+	0.0887096i	0.890497	−	0.454989i	$-0.150357\pi$
$173$	0.673648	+	1.16679i	0.0512165	+	0.0887096i	−0.839281	+	0.543699i	$0.817023\pi$
$174$	7.97449			0.604544
$175$	1.08717	+	7.24087i	0.0821822	+	0.547358i
$176$	10.0841	−	17.4662i	0.760121	−	1.31657i
$177$	1.36824	−	2.36987i	0.102843	−	0.178130i
$178$	4.47770			0.335618
$179$	2.97996	−	5.16145i	0.222733	−	0.385785i	−0.732904	−	0.680332i	$-0.761836\pi$
$179$	2.97996	−	5.16145i	0.222733	−	0.385785i	0.955637	+	0.294547i	$0.0951689\pi$
$180$	12.5566			0.935910
$181$	10.4495			0.776707			0.388354	−	0.921510i	$-0.373044\pi$
$181$	10.4495			0.776707			0.388354	+	0.921510i	$0.373044\pi$
$182$	−13.8329	−	20.0160i	−1.02536	−	1.48369i
$183$	−9.55263			−0.706151
$184$	−46.9348			−3.46008
$185$	−8.14292	+	14.1040i	−0.598680	+	1.03694i
$186$	9.86314			0.723201
$187$	−8.14577	+	14.1089i	−0.595677	+	1.03174i
$188$	17.8265	−	30.8765i	1.30013	−	2.25190i
$189$	2.46231	+	0.968004i	0.179107	+	0.0704119i
$190$	24.1741			1.75377
$191$	0.329057	+	0.569943i	0.0238097	+	0.0412396i	0.877685	−	0.479238i	$-0.159087\pi$
$191$	0.329057	+	0.569943i	0.0238097	+	0.0412396i	−0.853875	+	0.520478i	$0.825754\pi$
$192$	0.118371	−	0.205025i	0.00854271	−	0.0147964i
$193$	−4.39278	+	7.60853i	−0.316200	+	0.547674i	−0.979692	−	0.200510i	$-0.935740\pi$
$193$	−4.39278	+	7.60853i	−0.316200	+	0.547674i	0.663492	+	0.748183i	$0.269074\pi$
$194$	21.6450	−	37.4903i	1.55402	−	2.69165i
$195$	−0.681870	+	10.0256i	−0.0488297	+	0.717946i
$196$	23.0943	+	21.4773i	1.64959	+	1.53410i
$197$	−9.29781	−	16.1043i	−0.662442	−	1.14738i	−0.979972	−	0.199135i	$-0.936187\pi$
$197$	−9.29781	−	16.1043i	−0.662442	−	1.14738i	0.317530	−	0.948248i	$-0.397146\pi$
$198$	−7.05860			−0.501633
$199$	15.2257			1.07932			0.539659	−	0.841884i	$-0.318553\pi$
$199$	15.2257			1.07932			0.539659	+	0.841884i	$0.318553\pi$
$200$	−8.84221	−	15.3151i	−0.625238	−	1.08294i
$201$	−4.34033	−	7.51767i	−0.306143	−	0.530255i
$202$	2.35000	−	4.07031i	0.165345	−	0.286386i
$203$	−1.22823	−	8.18041i	−0.0862051	−	0.574152i
$204$	−13.2611	+	22.9689i	−0.928464	+	1.60815i
$205$	−18.0668			−1.26184
$206$	−6.08326	+	10.5365i	−0.423841	+	0.734113i
$207$	3.67246	+	6.36089i	0.255254	+	0.442112i
$208$	21.8117	+	14.6518i	1.51237	+	1.01592i
$209$	−9.41145			−0.651004
$210$	−2.79248	−	18.5988i	−0.192699	−	1.28344i
$211$	−10.5945	−	18.3503i	−0.729357	−	1.26328i	−0.957155	−	0.289575i	$-0.906486\pi$
$211$	−10.5945	−	18.3503i	−0.729357	−	1.26328i	0.227798	−	0.973708i	$-0.426847\pi$
$212$	28.5853	+	49.5112i	1.96325	+	3.40044i
$213$	1.57062	+	2.72039i	0.107617	+	0.186398i
$214$	−30.7991			−2.10539
$215$	8.33867	+	14.4430i	0.568692	+	0.985004i
$216$	−6.39011			−0.434792
$217$	−1.51913	−	10.1178i	−0.103125	−	0.686843i
$218$	8.69448	+	15.0593i	0.588865	+	1.01994i
$219$	−9.60582			−0.649101
$220$	17.3749	+	30.0942i	1.17142	+	2.02895i
$221$	−17.6190	−	11.8354i	−1.18518	−	0.796137i
$222$	7.45207	−	12.9074i	0.500150	−	0.866285i
$223$	−0.453274	−	0.785093i	−0.0303534	−	0.0525737i	0.850450	−	0.526056i	$-0.176330\pi$
$223$	−0.453274	−	0.785093i	−0.0303534	−	0.0525737i	−0.880803	+	0.473483i	$0.842997\pi$
$224$	−14.2995	−	5.62154i	−0.955425	−	0.375605i
$225$	−1.38373	+	2.39670i	−0.0922489	+	0.159780i
$226$	−6.94935	+	12.0366i	−0.462264	+	0.800664i
$227$	1.92809			0.127972			0.0639859	−	0.997951i	$-0.479619\pi$
$227$	1.92809			0.127972			0.0639859	+	0.997951i	$0.479619\pi$
$228$	−15.3216			−1.01470
$229$	5.05578	−	8.75686i	0.334095	−	0.578670i	−0.649216	−	0.760604i	$-0.724903\pi$
$229$	5.05578	−	8.75686i	0.334095	−	0.578670i	0.983311	+	0.181935i	$0.0582360\pi$
$230$	26.1055	−	45.2161i	1.72135	−	2.98146i
$231$	1.08717	+	7.24087i	0.0715304	+	0.476414i
$232$	9.98953	+	17.3024i	0.655845	+	1.13596i
$233$	13.1134	−	22.7130i	0.859085	−	1.48798i	−0.0137178	−	0.999906i	$-0.504367\pi$
$233$	13.1134	−	22.7130i	0.859085	−	1.48798i	0.872803	−	0.488073i	$-0.162300\pi$
$234$	0.624019	−	9.17499i	0.0407934	−	0.599788i
$235$	11.0275	+	19.1001i	0.719353	+	1.24596i
$236$	12.3289			0.802542
$237$	1.88112	+	3.25819i	0.122192	+	0.211642i
$238$	36.9708	+	14.5343i	2.39646	+	0.942116i
$239$	28.0556			1.81476			0.907382	−	0.420306i	$-0.138077\pi$
$239$	28.0556			1.81476			0.907382	+	0.420306i	$0.138077\pi$
$240$	10.1554	+	17.5896i	0.655527	+	1.13541i
$241$	−4.45249			−0.286810			−0.143405	−	0.989664i	$-0.545805\pi$
$241$	−4.45249			−0.286810			−0.143405	+	0.989664i	$0.545805\pi$
$242$	4.26088	+	7.38007i	0.273900	+	0.474409i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−21.5191	−	37.2721i	−1.37762	−	2.38610i
$245$	−18.6489	+	5.72918i	−1.19144	+	0.366024i
$246$	16.5340			1.05417
$247$	0.832025	−	12.2333i	0.0529405	−	0.778387i
$248$	12.3554	+	21.4002i	0.784570	+	1.35892i
$249$	2.41044	−	4.17501i	0.152756	−	0.264580i
$250$	−15.8699			−1.00370
$251$	1.55413	−	2.69183i	0.0980956	−	0.169907i	−0.812801	−	0.582542i	$-0.802058\pi$
$251$	1.55413	−	2.69183i	0.0980956	−	0.169907i	0.910896	+	0.412635i	$0.135392\pi$
$252$	1.76989	+	11.7880i	0.111492	+	0.742572i
$253$	−10.1634	+	17.6035i	−0.638968	+	1.10672i
$254$	−2.26113	−	3.91638i	−0.141876	−	0.245736i
$255$	−8.20331	−	14.2086i	−0.513711	−	0.889774i
$256$	−28.5574			−1.78484
$257$	−25.9854			−1.62092			−0.810461	−	0.585793i	$-0.800783\pi$
$257$	−25.9854			−1.62092			−0.810461	+	0.585793i	$0.800783\pi$
$258$	−7.63120	−	13.2176i	−0.475098	−	0.822894i
$259$	−14.3884	−	5.65650i	−0.894053	−	0.351478i
$260$	−40.6535	+	19.9240i	−2.52122	+	1.23563i
$261$	1.56328	−	2.70768i	0.0967646	−	0.167601i
$262$	−8.94570	+	15.4944i	−0.552667	+	0.957247i
$263$	−6.39028	+	11.0683i	−0.394042	+	0.682500i	−0.992978	−	0.118296i	$-0.962257\pi$
$263$	−6.39028	+	11.0683i	−0.394042	+	0.682500i	0.598937	+	0.800796i	$0.295590\pi$
$264$	−8.84221	−	15.3151i	−0.544200	−	0.942582i
$265$	−35.3656			−2.17249
$266$	3.40741	+	22.6944i	0.208922	+	1.39148i
$267$	0.877787	−	1.52037i	0.0537197	−	0.0930453i
$268$	19.5548	−	33.8699i	1.19450	−	2.06893i
$269$	1.95749			0.119350			0.0596751	−	0.998218i	$-0.480994\pi$
$269$	1.95749			0.119350			0.0596751	+	0.998218i	$0.480994\pi$
$270$	3.55423	−	6.15611i	0.216304	−	0.374649i
$271$	26.9218			1.63538			0.817692	−	0.575656i	$-0.195253\pi$
$271$	26.9218			1.63538			0.817692	+	0.575656i	$0.195253\pi$
$272$	−42.9009			−2.60125
$273$	−9.50802	+	0.773003i	−0.575452	+	0.0467843i
$274$	−50.1376			−3.02892
$275$	−7.65887			−0.461847
$276$	−16.5458	+	28.6582i	−0.995940	+	1.72502i
$277$	−23.1556			−1.39129			−0.695643	−	0.718388i	$-0.744880\pi$
$277$	−23.1556			−1.39129			−0.695643	+	0.718388i	$0.744880\pi$
$278$	−23.3974	+	40.5254i	−1.40328	+	2.43055i
$279$	1.93352	−	3.34896i	0.115757	−	0.200497i
$280$	36.8559	−	29.3573i	2.20256	−	1.75443i
$281$	−26.9347			−1.60679			−0.803396	−	0.595446i	$-0.796976\pi$
$281$	−26.9347			−1.60679			−0.803396	+	0.595446i	$0.796976\pi$
$282$	−10.0919	−	17.4797i	−0.600963	−	1.04090i
$283$	−7.62216	+	13.2020i	−0.453091	+	0.784776i	−0.998576	−	0.0533442i	$-0.983012\pi$
$283$	−7.62216	+	13.2020i	−0.453091	+	0.784776i	0.545486	+	0.838120i	$0.316345\pi$
$284$	−7.07621	+	12.2564i	−0.419896	+	0.727281i
$285$	4.73897	−	8.20814i	0.280712	−	0.486208i
$286$	22.8531	−	11.2002i	1.35133	−	0.662279i
$287$	−2.54657	−	16.9609i	−0.150319	−	1.00117i
$288$	−2.90367	−	5.02931i	−0.171101	−	0.296355i
$289$	17.6545			1.03850
$290$	−22.2250			−1.30510
$291$	−8.48637	−	14.6988i	−0.497480	−	0.861660i
$292$	−21.6389	−	37.4797i	−1.26632	−	2.19333i
$293$	−2.04388	+	3.54010i	−0.119405	+	0.206815i	−0.919532	−	0.393015i	$-0.871432\pi$
$293$	−2.04388	+	3.54010i	−0.119405	+	0.206815i	0.800127	+	0.599830i	$0.204765\pi$
$294$	17.0667	−	5.24311i	0.995352	−	0.305784i
$295$	−3.81332	+	6.60486i	−0.222020	+	0.384550i
$296$	37.3404			2.17037
$297$	−1.38373	+	2.39670i	−0.0802923	+	0.139070i
$298$	11.2262	+	19.4443i	0.650315	+	1.12638i
$299$	−21.9831	−	14.7670i	−1.27132	−	0.853996i
$300$	−12.4685			−0.719867
$301$	−12.3836	+	9.86404i	−0.713778	+	0.568554i
$302$	−12.3337	−	21.3625i	−0.709723	−	1.22928i
$303$	−0.921364	−	1.59585i	−0.0529310	−	0.0916791i
$304$	−12.3917	−	21.4631i	−0.710713	−	1.23099i
$305$	26.6233			1.52445
$306$	7.50733	+	13.0031i	0.429166	+	0.743337i
$307$	1.04296			0.0595250			0.0297625	−	0.999557i	$-0.490525\pi$
$307$	1.04296			0.0595250			0.0297625	+	0.999557i	$0.490525\pi$
$308$	−25.8031	+	20.5533i	−1.47027	+	1.17113i
$309$	2.38506	+	4.13105i	0.135682	+	0.235007i
$310$	−27.4888			−1.56126
$311$	−3.88724	−	6.73290i	−0.220425	−	0.381788i	0.734512	−	0.678596i	$-0.237411\pi$
$311$	−3.88724	−	6.73290i	−0.220425	−	0.381788i	−0.954937	+	0.296808i	$0.904078\pi$
$312$	20.6888	−	10.1394i	1.17127	−	0.574033i
$313$	−12.1950	+	21.1224i	−0.689304	+	1.19391i	0.282759	+	0.959191i	$0.408750\pi$
$313$	−12.1950	+	21.1224i	−0.689304	+	1.19391i	−0.972063	+	0.234719i	$0.924583\pi$
$314$	−14.7066	−	25.4725i	−0.829939	−	1.43750i
$315$	−6.86250	−	2.69784i	−0.386658	−	0.152006i
$316$	−8.47514	+	14.6794i	−0.476764	+	0.825779i
$317$	−5.38045	+	9.31922i	−0.302196	+	0.523419i	−0.976633	−	0.214913i	$-0.931053\pi$
$317$	−5.38045	+	9.31922i	−0.302196	+	0.523419i	0.674437	+	0.738333i	$0.264386\pi$
$318$	32.3652			1.81495
$319$	8.65265			0.484455
$320$	−0.329903	+	0.571408i	−0.0184421	+	0.0319427i
$321$	−6.03771	+	10.4576i	−0.336992	+	0.583688i
$322$	46.1281	+	18.1343i	2.57062	+	1.01058i
$323$	10.0098	+	17.3374i	0.556958	+	0.964680i
$324$	−2.25269	+	3.90177i	−0.125149	+	0.216765i
$325$	0.677087	−	9.95524i	0.0375580	−	0.552217i
$326$	15.5207	+	26.8827i	0.859613	+	1.48889i
$327$	6.81770			0.377020
$328$	20.7119	+	35.8741i	1.14362	+	1.98081i
$329$	−16.3767	+	13.0447i	−0.902875	+	0.719178i
$330$	19.6724			1.08293
$331$	11.4845	+	19.8918i	0.631248	+	1.09335i	0.987297	+	0.158886i	$0.0507902\pi$
$331$	11.4845	+	19.8918i	0.631248	+	1.09335i	−0.356049	+	0.934467i	$0.615876\pi$
$332$	21.7199			1.19203
$333$	−2.92173	−	5.06059i	−0.160110	−	0.277319i
$334$	11.5973	+	20.0872i	0.634578	+	1.09912i
$335$	12.0966	+	20.9519i	0.660906	+	1.14472i
$336$	−15.0815	+	12.0131i	−0.822766	+	0.655367i
$337$	6.99034			0.380788			0.190394	−	0.981708i	$-0.439023\pi$
$337$	6.99034			0.380788			0.190394	+	0.981708i	$0.439023\pi$
$338$	12.5380	+	30.6954i	0.681976	+	1.66961i
$339$	2.72463	+	4.71920i	0.147982	+	0.256312i
$340$	36.9590	−	64.0148i	2.00438	−	3.47169i
$341$	10.7019			0.579541
$342$	−4.33691	+	7.51175i	−0.234513	+	0.406189i
$343$	−8.00712	−	16.6999i	−0.432344	−	0.901709i
$344$	19.1190	−	33.1151i	1.03083	−	1.78545i
$345$	−10.2352	−	17.7279i	−0.551045	−	0.954438i
$346$	1.71818	+	2.97598i	0.0923701	+	0.159990i
$347$	−2.15384			−0.115624			−0.0578120	−	0.998327i	$-0.518412\pi$
$347$	−2.15384			−0.115624			−0.0578120	+	0.998327i	$0.518412\pi$
$348$	14.0863			0.755106
$349$	−0.756384	−	1.31010i	−0.0404883	−	0.0701278i	0.845071	−	0.534654i	$-0.179558\pi$
$349$	−0.756384	−	1.31010i	−0.0404883	−	0.0701278i	−0.885559	+	0.464526i	$0.846225\pi$
$350$	2.77289	+	18.4683i	0.148217	+	0.987171i
$351$	−2.99297	−	2.01050i	−0.159753	−	0.107313i
$352$	8.03582	−	13.9184i	0.428311	−	0.741856i
$353$	16.1969	−	28.0538i	0.862073	−	1.49315i	−0.00785109	−	0.999969i	$-0.502499\pi$
$353$	16.1969	−	28.0538i	0.862073	−	1.49315i	0.869924	−	0.493185i	$-0.164168\pi$
$354$	3.48979	−	6.04449i	0.185480	−	0.321261i
$355$	−4.37734	−	7.58177i	−0.232325	−	0.402399i
$356$	7.90952			0.419204
$357$	12.1826	−	9.70393i	0.644770	−	0.513586i
$358$	7.60058	−	13.1646i	0.401703	−	0.695771i
$359$	−7.93156	+	13.7379i	−0.418612	+	0.725057i	−0.995800	−	0.0915543i	$-0.970816\pi$
$359$	−7.93156	+	13.7379i	−0.418612	+	0.725057i	0.577188	+	0.816611i	$0.304150\pi$
$360$	17.8093			0.938635
$361$	3.71746	−	6.43883i	0.195656	−	0.338886i
$362$	26.6522			1.40081
$363$	3.34113			0.175364
$364$	−24.4347	−	35.3567i	−1.28072	−	1.85320i
$365$	26.7716			1.40129
$366$	−24.3646			−1.27356
$367$	−6.29687	+	10.9065i	−0.328694	+	0.569315i	−0.982253	−	0.187561i	$-0.939942\pi$
$367$	−6.29687	+	10.9065i	−0.328694	+	0.569315i	0.653559	+	0.756876i	$0.273275\pi$
$368$	−53.5271			−2.79029
$369$	3.24124	−	5.61400i	0.168732	−	0.292253i
$370$	−20.7690	+	35.9730i	−1.07973	+	1.87015i
$371$	−4.98490	−	33.2009i	−0.258803	−	1.72371i
$372$	17.4225			0.903313
$373$	5.85178	+	10.1356i	0.302994	+	0.524800i	0.976813	−	0.214096i	$-0.0686806\pi$
$373$	5.85178	+	10.1356i	0.302994	+	0.524800i	−0.673819	+	0.738896i	$0.735347\pi$
$374$	−20.7763	+	35.9856i	−1.07432	+	1.86077i
$375$	−3.11106	+	5.38851i	−0.160654	+	0.278261i
$376$	25.2839	−	43.7930i	1.30392	−	2.25845i
$377$	−0.764942	+	11.2470i	−0.0393965	+	0.579249i
$378$	6.28028	+	2.46895i	0.323023	+	0.126989i
$379$	−16.4778	−	28.5403i	−0.846406	−	1.46602i	−0.884395	−	0.466740i	$-0.845428\pi$
$379$	−16.4778	−	28.5403i	−0.846406	−	1.46602i	0.0379888	−	0.999278i	$-0.487905\pi$
$380$	42.7017			2.19055
$381$	−1.77304			−0.0908356
$382$	0.839280	+	1.45368i	0.0429413	+	0.0743765i
$383$	−6.31803	−	10.9431i	−0.322836	−	0.559169i	0.658236	−	0.752812i	$-0.271303\pi$
$383$	−6.31803	−	10.9431i	−0.322836	−	0.559169i	−0.981072	+	0.193643i	$0.937970\pi$
$384$	−5.50543	+	9.53569i	−0.280948	+	0.486616i
$385$	−3.02996	−	20.1804i	−0.154421	−	1.02849i
$386$	−11.2041	+	19.4060i	−0.570272	+	0.987741i
$387$	−5.98394			−0.304181
$388$	38.2343	−	66.2237i	1.94105	−	3.36200i
$389$	−0.0593906	−	0.102868i	−0.00301122	−	0.00521559i	0.864516	−	0.502606i	$-0.167625\pi$
$389$	−0.0593906	−	0.102868i	−0.00301122	−	0.00521559i	−0.867527	+	0.497390i	$0.834292\pi$
$390$	−1.73915	+	25.5709i	−0.0880654	+	1.29483i
$391$	43.2381			2.18664
$392$	32.7553	+	30.4620i	1.65439	+	1.53856i
$393$	3.50734	+	6.07490i	0.176922	+	0.306438i
$394$	−23.7147	−	41.0750i	−1.19473	−	2.06933i
$395$	−5.24271	−	9.08064i	−0.263789	−	0.456897i
$396$	−12.4685			−0.626564
$397$	−3.49151	−	6.04747i	−0.175234	−	0.303514i	0.765008	−	0.644020i	$-0.222735\pi$
$397$	−3.49151	−	6.04747i	−0.175234	−	0.303514i	−0.940242	+	0.340506i	$0.889401\pi$
$398$	38.8340			1.94657
$399$	8.37369	+	3.29194i	0.419209	+	0.164803i
$400$	−10.0841	−	17.4662i	−0.504207	−	0.873312i
$401$	−19.1517			−0.956389			−0.478194	−	0.878254i	$-0.658709\pi$
$401$	−19.1517			−0.956389			−0.478194	+	0.878254i	$0.658709\pi$
$402$	−11.0703	−	19.1743i	−0.552135	−	0.956326i
$403$	−0.946109	+	13.9107i	−0.0471291	+	0.692941i
$404$	4.15109	−	7.18989i	0.206524	−	0.357711i
$405$	−1.39351	−	2.41363i	−0.0692440	−	0.119934i
$406$	−3.13269	−	20.8646i	−0.155473	−	1.03549i
$407$	8.08580	−	14.0050i	0.400798	−	0.694203i
$408$	−18.8087	+	32.5776i	−0.931167	+	1.61283i
$409$	11.6901			0.578039			0.289019	−	0.957323i	$-0.406671\pi$
$409$	11.6901			0.578039			0.289019	+	0.957323i	$0.406671\pi$
$410$	−46.0805			−2.27575
$411$	−9.82872	+	17.0239i	−0.484815	+	0.839725i
$412$	−10.7456	+	18.6119i	−0.529398	+	0.916944i
$413$	−6.73807	−	2.64893i	−0.331559	−	0.130345i
$414$	9.36684	+	16.2238i	0.460355	+	0.797358i
$415$	−6.71794	+	11.6358i	−0.329771	+	0.571180i
$416$	17.3812	+	11.6757i	0.852185	+	0.572447i
$417$	9.17342	+	15.8888i	0.449224	+	0.778079i
$418$	−24.0045			−1.17410
$419$	7.89905	+	13.6816i	0.385894	+	0.668388i	0.991893	−	0.127078i	$-0.0405598\pi$
$419$	7.89905	+	13.6816i	0.385894	+	0.668388i	−0.605999	+	0.795465i	$0.707226\pi$
$420$	−4.93270	−	32.8533i	−0.240691	−	1.60308i
$421$	8.58170			0.418247			0.209123	−	0.977889i	$-0.432939\pi$
$421$	8.58170			0.418247			0.209123	+	0.977889i	$0.432939\pi$
$422$	−27.0220	−	46.8035i	−1.31541	−	2.27836i
$423$	−7.91346			−0.384765
$424$	40.5434	+	70.2232i	1.96896	+	3.41034i
$425$	8.14577	+	14.1089i	0.395128	+	0.684381i
$426$	4.00596	+	6.93852i	0.194089	+	0.336173i
$427$	3.75264	+	24.9937i	0.181603	+	1.20953i
$428$	−54.4043			−2.62973
$429$	0.677087	−	9.95524i	0.0326901	−	0.480644i
$430$	21.2683	+	36.8378i	1.02565	+	1.77648i
$431$	9.72232	−	16.8396i	0.468308	−	0.811133i	−0.531036	−	0.847349i	$-0.678197\pi$
$431$	9.72232	−	16.8396i	0.468308	−	0.811133i	0.999344	+	0.0362164i	$0.0115306\pi$
$432$	−7.28763			−0.350626
$433$	2.35409	−	4.07740i	0.113130	−	0.195948i	−0.803900	−	0.594764i	$-0.797246\pi$
$433$	2.35409	−	4.07740i	0.113130	−	0.195948i	0.917031	+	0.398816i	$0.130579\pi$
$434$	−3.87463	−	25.8062i	−0.185988	−	1.23874i
$435$	−4.35689	+	7.54635i	−0.208897	+	0.361820i
$436$	15.3581	+	26.6011i	0.735521	+	1.27396i
$437$	12.4891	+	21.6318i	0.597435	+	1.03479i
$438$	−24.5003			−1.17067
$439$	−20.6623			−0.986157			−0.493078	−	0.869985i	$-0.664128\pi$
$439$	−20.6623			−0.986157			−0.493078	+	0.869985i	$0.664128\pi$
$440$	24.6434	+	42.6836i	1.17483	+	2.03486i
$441$	1.56542	−	6.82272i	0.0745437	−	0.324891i
$442$	−44.9385	−	30.1870i	−2.13751	−	1.43585i
$443$	6.14100	−	10.6365i	0.291768	−	0.505357i	−0.682460	−	0.730923i	$-0.739090\pi$
$443$	6.14100	−	10.6365i	0.291768	−	0.505357i	0.974228	+	0.225566i	$0.0724232\pi$
$444$	13.1635	−	22.7998i	0.624712	−	1.08203i
$445$	−2.44641	+	4.23730i	−0.115971	+	0.200867i
$446$	−1.15610	−	2.00243i	−0.0547430	−	0.0948177i
$447$	8.80290			0.416363
$448$	−0.582933	−	0.229168i	−0.0275410	−	0.0108272i
$449$	13.7884	−	23.8822i	0.650714	−	1.12707i	−0.332235	−	0.943196i	$-0.607803\pi$
$449$	13.7884	−	23.8822i	0.650714	−	1.12707i	0.982950	−	0.183874i	$-0.0588638\pi$
$450$	−3.52930	+	6.11292i	−0.166373	+	0.288166i
$451$	17.9401			0.844764
$452$	−12.2755	+	21.2618i	−0.577390	+	1.00007i
$453$	−9.67133			−0.454399
$454$	4.91771			0.230800
$455$	26.4990	−	2.15437i	1.24229	−	0.100999i
$456$	−21.7311			−1.01765
$457$	13.8786			0.649214			0.324607	−	0.945849i	$-0.394768\pi$
$457$	13.8786			0.649214			0.324607	+	0.945849i	$0.394768\pi$
$458$	12.8951	−	22.3349i	0.602547	−	1.04364i
$459$	5.88680			0.274772
$460$	46.1134	−	79.8708i	2.15005	−	3.72399i
$461$	−12.2050	+	21.1396i	−0.568441	+	0.984569i	0.428279	+	0.903647i	$0.359120\pi$
$461$	−12.2050	+	21.1396i	−0.568441	+	0.984569i	−0.996720	+	0.0809228i	$0.974213\pi$
$462$	2.77289	+	18.4683i	0.129007	+	0.859222i
$463$	−11.6449			−0.541185			−0.270593	−	0.962694i	$-0.587220\pi$
$463$	−11.6449			−0.541185			−0.270593	+	0.962694i	$0.587220\pi$
$464$	11.3926	+	19.7326i	0.528888	+	0.916062i
$465$	−5.38876	+	9.33361i	−0.249898	+	0.432836i
$466$	33.4465	−	57.9310i	1.54938	−	2.68360i
$467$	2.09483	−	3.62835i	0.0969370	−	0.167900i	−0.813478	−	0.581595i	$-0.802429\pi$
$467$	2.09483	−	3.62835i	0.0969370	−	0.167900i	0.910415	+	0.413695i	$0.135762\pi$
$468$	1.10228	−	16.2069i	0.0509530	−	0.749165i
$469$	−17.9644	+	14.3094i	−0.829517	+	0.660745i
$470$	28.1263	+	48.7161i	1.29737	+	2.24711i
$471$	−11.5320			−0.531367
$472$	17.4864			0.804879
$473$	−8.28017	−	14.3417i	−0.380723	−	0.659431i
$474$	4.79791	+	8.31023i	0.220375	+	0.381701i
$475$	−4.70573	+	8.15056i	−0.215914	+	0.373973i
$476$	65.3060	+	25.6736i	2.99329	+	1.17675i
$477$	6.34471	−	10.9894i	0.290504	−	0.503168i
$478$	71.5575			3.27297
$479$	7.50423	−	12.9977i	0.342877	−	0.593880i	−0.642089	−	0.766630i	$-0.721932\pi$
$479$	7.50423	−	12.9977i	0.342877	−	0.593880i	0.984966	+	0.172750i	$0.0552652\pi$
$480$	8.09259	+	14.0168i	0.369375	+	0.639775i
$481$	17.4893	+	11.7483i	0.797445	+	0.535676i
$482$	−11.3564			−0.517268
$483$	15.2001	−	12.1075i	0.691628	−	0.550911i
$484$	7.52652	+	13.0363i	0.342115	+	0.592560i
$485$	23.6517	+	40.9659i	1.07397	+	1.86016i
$486$	1.27528	+	2.20885i	0.0578479	+	0.100196i
$487$	6.60817			0.299445			0.149722	−	0.988728i	$-0.452162\pi$
$487$	6.60817			0.299445			0.149722	+	0.988728i	$0.452162\pi$
$488$	−30.5212	−	52.8642i	−1.38163	−	2.39305i
$489$	12.1704			0.550366
$490$	−47.5653	+	14.6126i	−2.14878	+	0.660131i
$491$	−16.4555	−	28.5018i	−0.742628	−	1.28627i	−0.951295	−	0.308283i	$-0.900246\pi$
$491$	−16.4555	−	28.5018i	−0.742628	−	1.28627i	0.208666	−	0.977987i	$-0.433088\pi$
$492$	29.2060			1.31671
$493$	−9.20272	−	15.9396i	−0.414470	−	0.717883i
$494$	2.12213	−	31.2018i	0.0954792	−	1.40384i
$495$	3.85649	−	6.67963i	0.173336	−	0.300227i
$496$	14.0908	+	24.4060i	0.632696	+	1.09586i
$497$	6.50069	−	5.17808i	0.291596	−	0.232268i
$498$	6.14798	−	10.6486i	0.275498	−	0.477176i
$499$	−17.9199	+	31.0381i	−0.802204	+	1.38946i	0.115959	+	0.993254i	$0.463006\pi$
$499$	−17.9199	+	31.0381i	−0.802204	+	1.38946i	−0.918163	+	0.396203i	$0.870328\pi$
$500$	−28.0329			−1.25367
$501$	9.09395			0.406288
$502$	3.96390	−	6.86567i	0.176917	−	0.306430i
$503$	−9.67700	+	16.7610i	−0.431476	+	0.747338i	−0.997001	−	0.0773931i	$-0.975340\pi$
$503$	−9.67700	+	16.7610i	−0.431476	+	0.747338i	0.565525	+	0.824731i	$0.308674\pi$
$504$	2.51028	+	16.7192i	0.111817	+	0.744734i
$505$	2.56786	+	4.44766i	0.114268	+	0.197918i
$506$	−25.9224	+	44.8989i	−1.15239	+	1.99600i
$507$	12.8803	+	1.76020i	0.572033	+	0.0781731i
$508$	−3.99410	−	6.91799i	−0.177210	−	0.306936i
$509$	10.4975			0.465292			0.232646	−	0.972561i	$-0.425262\pi$
$509$	10.4975			0.465292			0.232646	+	0.972561i	$0.425262\pi$
$510$	−20.9231	−	36.2398i	−0.926489	−	1.60473i
$511$	3.77354	+	25.1329i	0.166932	+	1.11181i
$512$	−50.8157			−2.24576
$513$	1.70037	+	2.94513i	0.0750733	+	0.130031i
$514$	−66.2773			−2.92337
$515$	−6.64721	−	11.5133i	−0.292911	−	0.507337i
$516$	−13.4799	−	23.3479i	−0.593421	−	1.02783i
$517$	−10.9501	−	18.9662i	−0.481585	−	0.834130i
$518$	−36.6986	−	14.4273i	−1.61244	−	0.633897i
$519$	1.34730			0.0591398
$520$	−57.6601	+	28.2588i	−2.52856	+	1.23923i
$521$	10.7923	+	18.6928i	0.472818	+	0.818945i	0.999516	−	0.0311074i	$-0.00990340\pi$
$521$	10.7923	+	18.6928i	0.472818	+	0.818945i	−0.526698	+	0.850053i	$0.676570\pi$
$522$	3.98724	−	6.90611i	0.174517	−	0.302272i
$523$	3.46379			0.151461			0.0757304	−	0.997128i	$-0.475871\pi$
$523$	3.46379			0.151461			0.0757304	+	0.997128i	$0.475871\pi$
$524$	−15.8019	+	27.3697i	−0.690308	+	1.19565i
$525$	6.81436	+	2.67892i	0.297403	+	0.116918i
$526$	−16.2988	+	28.2304i	−0.710662	+	1.23090i
$527$	−11.3823	−	19.7147i	−0.495819	−	0.858784i
$528$	−10.0841	−	17.4662i	−0.438856	−	0.760121i
$529$	30.9478			1.34556
$530$	−90.2023			−3.91814
$531$	−1.36824	−	2.36987i	−0.0593767	−	0.102843i
$532$	6.01893	+	40.0879i	0.260954	+	1.73803i
$533$	−1.58600	+	23.3191i	−0.0686973	+	1.01006i
$534$	2.23885	−	3.87781i	0.0968846	−	0.167809i
$535$	16.8272	−	29.1456i	0.727504	−	1.26007i
$536$	27.7352	−	48.0387i	1.19798	−	2.07496i
$537$	−2.97996	−	5.16145i	−0.128595	−	0.222733i
$538$	4.99270			0.215250
$539$	18.5181	−	5.68899i	0.797631	−	0.245042i
$540$	6.27828	−	10.8743i	0.270174	−	0.467955i
$541$	4.46427	−	7.73234i	0.191934	−	0.332439i	−0.753957	−	0.656924i	$-0.771857\pi$
$541$	4.46427	−	7.73234i	0.191934	−	0.332439i	0.945891	+	0.324484i	$0.105191\pi$
$542$	68.6658			2.94945
$543$	5.22477	−	9.04956i	0.224216	−	0.388354i
$544$	−34.1867			−1.46574
$545$	−19.0010			−0.813915
$546$	−24.2508	+	1.97159i	−1.03784	+	0.0843764i
$547$	−3.62704			−0.155081			−0.0775405	−	0.996989i	$-0.524707\pi$
$547$	−3.62704			−0.155081			−0.0775405	+	0.996989i	$0.524707\pi$
$548$	−88.5641			−3.78327
$549$	−4.77631	+	8.27282i	−0.203848	+	0.353075i
$550$	−19.5344			−0.832951
$551$	5.31632	−	9.20813i	0.226483	−	0.392280i
$552$	−23.4674	+	40.6468i	−0.998839	+	1.73004i
$553$	7.78584	−	6.20175i	0.331088	−	0.263725i
$554$	−59.0598			−2.50921
$555$	8.14292	+	14.1040i	0.345648	+	0.598680i
$556$	−41.3297	+	71.5851i	−1.75277	+	3.03588i
$557$	10.0223	−	17.3592i	0.424660	−	0.735533i	−0.571729	−	0.820443i	$-0.693727\pi$
$557$	10.0223	−	17.3592i	0.424660	−	0.735533i	0.996389	+	0.0849101i	$0.0270603\pi$
$558$	4.93157	−	8.54173i	0.208770	−	0.361600i
$559$	19.3738	−	9.49495i	0.819424	−	0.401593i
$560$	42.0325	−	33.4807i	1.77620	−	1.41482i
$561$	8.14577	+	14.1089i	0.343914	+	0.595677i
$562$	−68.6987			−2.89788
$563$	−7.55430			−0.318376			−0.159188	−	0.987248i	$-0.550888\pi$
$563$	−7.55430			−0.318376			−0.159188	+	0.987248i	$0.550888\pi$
$564$	−17.8265	−	30.8765i	−0.750632	−	1.30013i
$565$	−7.59360	−	13.1525i	−0.319465	−	0.553330i
$566$	−19.4408	+	33.6725i	−0.817158	+	1.41536i
$567$	2.06947	−	1.64842i	0.0869096	−	0.0692272i
$568$	−10.0364	+	17.3836i	−0.421119	+	0.729399i
$569$	28.1656			1.18076			0.590381	−	0.807125i	$-0.298977\pi$
$569$	28.1656			1.18076			0.590381	+	0.807125i	$0.298977\pi$
$570$	12.0870	−	20.9354i	0.506271	−	0.876886i
$571$	9.03604	+	15.6509i	0.378146	+	0.654969i	0.990793	−	0.135389i	$-0.0432283\pi$
$571$	9.03604	+	15.6509i	0.378146	+	0.654969i	−0.612646	+	0.790357i	$0.709895\pi$
$572$	40.3683	−	19.7842i	1.68788	−	0.827219i
$573$	0.658114			0.0274931
$574$	−6.49519	−	43.2599i	−0.271104	−	1.80563i
$575$	10.1634	+	17.6035i	0.423843	+	0.734118i
$576$	−0.118371	−	0.205025i	−0.00493213	−	0.00854271i
$577$	21.5383	+	37.3054i	0.896651	+	1.55305i	0.831747	+	0.555154i	$0.187341\pi$
$577$	21.5383	+	37.3054i	0.896651	+	1.55305i	0.0649040	+	0.997892i	$0.479326\pi$
$578$	45.0288			1.87295
$579$	4.39278	+	7.60853i	0.182558	+	0.316200i
$580$	−39.2588			−1.63013
$581$	−11.8705	−	4.66663i	−0.492472	−	0.193605i
$582$	−21.6450	−	37.4903i	−0.897215	−	1.55402i
$583$	35.1175			1.45442
$584$	−30.6911	−	53.1586i	−1.27001	−	2.19972i
$585$	8.34147	+	5.60330i	0.344877	+	0.231668i
$586$	−5.21304	+	9.02925i	−0.215349	+	0.372995i
$587$	2.26101	+	3.91619i	0.0933220	+	0.161638i	0.908907	−	0.416999i	$-0.136918\pi$
$587$	2.26101	+	3.91619i	0.0933220	+	0.161638i	−0.815585	+	0.578637i	$0.803585\pi$
$588$	30.1470	−	9.26154i	1.24324	−	0.381940i
$589$	6.57542	−	11.3890i	0.270936	−	0.469274i
$590$	−9.72610	+	16.8461i	−0.400417	+	0.693543i
$591$	−18.5956			−0.764922
$592$	42.5850			1.75023
$593$	1.43449	−	2.48460i	0.0589073	−	0.102030i	−0.835068	−	0.550147i	$-0.814572\pi$
$593$	1.43449	−	2.48460i	0.0589073	−	0.102030i	0.893975	+	0.448117i	$0.147905\pi$
$594$	−3.52930	+	6.11292i	−0.144809	+	0.250816i
$595$	−33.9530	+	27.0450i	−1.39194	+	1.10874i
$596$	19.8302	+	34.3469i	0.812276	+	1.40690i
$597$	7.61283	−	13.1858i	0.311572	−	0.539659i
$598$	−56.0694	−	37.6641i	−2.29285	−	1.54020i
$599$	−2.94653	−	5.10354i	−0.120392	−	0.208525i	0.799530	−	0.600626i	$-0.205082\pi$
$599$	−2.94653	−	5.10354i	−0.120392	−	0.208525i	−0.919922	+	0.392101i	$0.871748\pi$
$600$	−17.6844			−0.721963
$601$	−9.46284	−	16.3901i	−0.385997	−	0.668567i	0.605910	−	0.795533i	$-0.292809\pi$
$601$	−9.46284	−	16.3901i	−0.385997	−	0.668567i	−0.991907	+	0.126967i	$0.959476\pi$
$602$	−31.5851	+	25.1589i	−1.28731	+	1.02540i
$603$	−8.68066			−0.353504
$604$	−21.7865	−	37.7353i	−0.886479	−	1.53543i
$605$	−9.31179			−0.378578
$606$	−2.35000	−	4.07031i	−0.0954621	−	0.165345i
$607$	−21.9391	−	37.9997i	−0.890482	−	1.54236i	−0.839299	−	0.543671i	$-0.817034\pi$
$607$	−21.9391	−	37.9997i	−0.890482	−	1.54236i	−0.0511833	−	0.998689i	$-0.516299\pi$
$608$	−9.87466	−	17.1034i	−0.400470	−	0.693635i
$609$	−7.69856	−	3.02652i	−0.311961	−	0.122641i
$610$	67.9045			2.74937
$611$	25.6209	−	12.5566i	1.03651	−	0.507985i
$612$	13.2611	+	22.9689i	0.536049	+	0.928464i
$613$	−15.2913	+	26.4853i	−0.617610	+	1.06973i	0.372310	+	0.928108i	$0.378566\pi$
$613$	−15.2913	+	26.4853i	−0.617610	+	1.06973i	−0.989921	+	0.141624i	$0.954768\pi$
$614$	2.66014			0.107355
$615$	−9.03340	+	15.6463i	−0.364262	+	0.630920i
$616$	−36.5974	+	29.1513i	−1.47455	+	1.17454i
$617$	22.1042	−	38.2856i	0.889881	−	1.54132i	0.0498659	−	0.998756i	$-0.484121\pi$
$617$	22.1042	−	38.2856i	0.889881	−	1.54132i	0.840015	−	0.542563i	$-0.182546\pi$
$618$	6.08326	+	10.5365i	0.244704	+	0.423841i
$619$	0.184678	+	0.319871i	0.00742283	+	0.0128567i	0.869713	−	0.493558i	$-0.164304\pi$
$619$	0.184678	+	0.319871i	0.00742283	+	0.0128567i	−0.862290	+	0.506415i	$0.830971\pi$
$620$	−48.5568			−1.95009
$621$	7.34492			0.294741
$622$	−9.91466	−	17.1727i	−0.397542	−	0.688562i
$623$	−4.32277	−	1.69940i	−0.173188	−	0.0680851i
$624$	23.5947	−	11.5636i	0.944543	−	0.462913i
$625$	15.5892	−	27.0013i	0.623569	−	1.08005i
$626$	−31.1042	+	53.8741i	−1.24317	+	2.15324i
$627$	−4.70573	+	8.15056i	−0.187929	+	0.325502i
$628$	−25.9780	−	44.9952i	−1.03664	−	1.79550i
$629$	−34.3993			−1.37159
$630$	−17.5032	−	6.88102i	−0.697346	−	0.274146i
$631$	6.70906	−	11.6204i	0.267083	−	0.462602i	−0.701024	−	0.713138i	$-0.747273\pi$
$631$	6.70906	−	11.6204i	0.267083	−	0.462602i	0.968107	+	0.250536i	$0.0806067\pi$
$632$	−12.0206	+	20.8202i	−0.478152	+	0.828184i
$633$	−21.1890			−0.842189
$634$	−13.7232	+	23.7693i	−0.545017	+	0.943998i
$635$	4.94149			0.196097
$636$	57.1706			2.26696
$637$	5.75762	+	24.5734i	0.228125	+	0.973632i
$638$	22.0691			0.873725
$639$	3.14123			0.124265
$640$	15.3437	−	26.5761i	0.606515	−	1.05051i
$641$	43.0337			1.69973			0.849865	−	0.527000i	$-0.176683\pi$
$641$	43.0337			1.69973			0.849865	+	0.527000i	$0.176683\pi$
$642$	−15.3996	+	26.6728i	−0.607773	+	1.05269i
$643$	14.6688	−	25.4071i	0.578482	−	1.00196i	−0.417172	−	0.908828i	$-0.636979\pi$
$643$	14.6688	−	25.4071i	0.578482	−	1.00196i	0.995654	−	0.0931324i	$-0.0296880\pi$
$644$	81.4817	+	32.0328i	3.21083	+	1.26227i
$645$	16.6773			0.656669
$646$	25.5305	+	44.2202i	1.00449	+	1.73982i
$647$	9.00352	−	15.5945i	0.353965	−	0.613085i	−0.632975	−	0.774172i	$-0.718167\pi$
$647$	9.00352	−	15.5945i	0.353965	−	0.613085i	0.986940	+	0.161087i	$0.0514999\pi$
$648$	−3.19505	+	5.53400i	−0.125514	+	0.217396i
$649$	3.78656	−	6.55852i	0.148636	−	0.257445i
$650$	1.72695	−	25.3915i	0.0677366	−	0.995936i
$651$	−9.52186	−	3.74332i	−0.373191	−	0.146712i
$652$	27.4161	+	47.4862i	1.07370	+	1.85970i
$653$	34.6541			1.35612			0.678059	−	0.735007i	$-0.262821\pi$
$653$	34.6541			1.35612			0.678059	+	0.735007i	$0.262821\pi$
$654$	17.3890			0.679962
$655$	−9.77502	−	16.9308i	−0.381942	−	0.661543i
$656$	23.6210	+	40.9127i	0.922244	+	1.59737i
$657$	−4.80291	+	8.31889i	−0.187379	+	0.324551i
$658$	−41.7697	+	33.2713i	−1.62835	+	1.29705i
$659$	−2.68796	+	4.65569i	−0.104708	+	0.181360i	−0.913619	−	0.406572i	$-0.866724\pi$
$659$	−2.68796	+	4.65569i	−0.104708	+	0.181360i	0.808911	+	0.587931i	$0.200058\pi$
$660$	34.7498			1.35264
$661$	−20.2356	+	35.0490i	−0.787072	+	1.36325i	0.140681	+	0.990055i	$0.455071\pi$
$661$	−20.2356	+	35.0490i	−0.787072	+	1.36325i	−0.927753	+	0.373194i	$0.878263\pi$
$662$	29.2921	+	50.7353i	1.13847	+	1.97188i
$663$	−19.0593	+	9.34082i	−0.740202	+	0.362767i
$664$	30.8060			1.19550
$665$	−23.3376	−	9.17469i	−0.904994	−	0.355779i
$666$	−7.45207	−	12.9074i	−0.288762	−	0.500150i
$667$	−11.4822	−	19.8877i	−0.444591	−	0.770054i
$668$	20.4858	+	35.4825i	0.792620	+	1.37286i
$669$	−0.906547			−0.0350491
$670$	30.8531	+	53.4391i	1.19196	+	2.06453i
$671$	−26.4366			−1.02057
$672$	−12.0181	+	9.57295i	−0.463610	+	0.369285i
$673$	13.1634	+	22.7996i	0.507411	+	0.878861i	0.999963	+	0.00857837i	$0.00273061\pi$
$673$	13.1634	+	22.7996i	0.507411	+	0.878861i	−0.492553	+	0.870283i	$0.663936\pi$
$674$	17.8293			0.686759
$675$	1.38373	+	2.39670i	0.0532599	+	0.0922489i
$676$	22.1474	+	54.2210i	0.851821	+	2.08542i
$677$	−1.90262	+	3.29544i	−0.0731236	+	0.126654i	−0.900269	−	0.435335i	$-0.856630\pi$
$677$	−1.90262	+	3.29544i	−0.0731236	+	0.126654i	0.827145	+	0.561988i	$0.189963\pi$
$678$	6.94935	+	12.0366i	0.266888	+	0.462264i
$679$	−35.1246	+	27.9782i	−1.34796	+	1.07371i
$680$	52.4201	−	90.7942i	2.01022	−	3.48180i
$681$	0.964045	−	1.66977i	0.0369423	−	0.0639859i
$682$	27.2959			1.04521
$683$	10.3953			0.397765			0.198882	−	0.980023i	$-0.436269\pi$
$683$	10.3953			0.397765			0.198882	+	0.980023i	$0.436269\pi$
$684$	−7.66082	+	13.2689i	−0.292919	+	0.507350i
$685$	27.3928	−	47.4458i	1.04663	−	1.81281i
$686$	−20.4227	−	42.5941i	−0.779741	−	1.62625i
$687$	−5.05578	−	8.75686i	−0.192890	−	0.334095i
$688$	21.8044	−	37.7663i	0.831284	−	1.43983i
$689$	−3.10459	+	45.6469i	−0.118275	+	1.73901i
$690$	−26.1055	−	45.2161i	−0.993821	−	1.72135i
$691$	−8.19915			−0.311910			−0.155955	−	0.987764i	$-0.549846\pi$
$691$	−8.19915			−0.311910			−0.155955	+	0.987764i	$0.549846\pi$
$692$	3.03504	+	5.25684i	0.115375	+	0.199835i
$693$	6.81436	+	2.67892i	0.258856	+	0.101764i
$694$	−5.49350			−0.208530
$695$	−25.5665	−	44.2824i	−0.969792	−	1.67973i
$696$	19.9791			0.757304
$697$	−19.0806	−	33.0485i	−0.722728	−	1.25180i
$698$	−1.92921	−	3.34148i	−0.0730215	−	0.126477i
$699$	−13.1134	−	22.7130i	−0.495993	−	0.859085i
$700$	4.89810	+	32.6228i	0.185131	+	1.23303i
$701$	4.64503			0.175440			0.0877201	−	0.996145i	$-0.472042\pi$
$701$	4.64503			0.175440			0.0877201	+	0.996145i	$0.472042\pi$
$702$	−7.63376	−	5.12791i	−0.288118	−	0.193541i
$703$	−9.93608	−	17.2098i	−0.374746	−	0.649080i
$704$	0.327588	−	0.567400i	0.0123464	−	0.0213847i
$705$	22.0549			0.830637
$706$	41.3112	−	71.5531i	1.55477	−	2.69293i
$707$	−3.81347	+	3.03759i	−0.143420	+	0.114240i
$708$	6.16444	−	10.6771i	0.231674	−	0.401271i
$709$	22.1987	+	38.4494i	0.833691	+	1.44400i	0.895091	+	0.445883i	$0.147110\pi$
$709$	22.1987	+	38.4494i	0.833691	+	1.44400i	−0.0614001	+	0.998113i	$0.519557\pi$
$710$	−11.1647	−	19.3378i	−0.419003	−	0.725734i
$711$	3.76224			0.141095
$712$	11.2183			0.420424
$713$	−14.2016	−	24.5978i	−0.531853	−	0.921196i
$714$	31.0724	−	24.7505i	1.16286	−	0.926264i
$715$	−1.88705	+	27.7454i	−0.0705718	+	1.03762i
$716$	13.4258	−	23.2542i	0.501747	−	0.869052i
$717$	14.0278	−	24.2968i	0.523877	−	0.907382i
$718$	−20.2299	+	35.0393i	−0.754975	+	1.30765i
$719$	22.4689	+	38.9173i	0.837949	+	1.45137i	0.891606	+	0.452812i	$0.149579\pi$
$719$	22.4689	+	38.9173i	0.837949	+	1.45137i	−0.0536569	+	0.998559i	$0.517088\pi$
$720$	20.3108			0.756937
$721$	9.87164	−	7.86318i	0.367639	−	0.292840i
$722$	9.48161	−	16.4226i	0.352869	−	0.611187i
$723$	−2.22625	+	3.85597i	−0.0827950	+	0.143405i
$724$	47.0790			1.74968
$725$	4.32632	−	7.49341i	0.160676	−	0.278298i
$726$	8.52177			0.316272
$727$	−49.7876			−1.84652			−0.923260	−	0.384177i	$-0.874485\pi$
$727$	−49.7876			−1.84652			−0.923260	+	0.384177i	$0.874485\pi$
$728$	−34.6564	−	50.1476i	−1.28445	−	1.85859i
$729$	1.00000			0.0370370
$730$	68.2827			2.52725
$731$	−17.6131	+	30.5068i	−0.651445	+	1.12834i
$732$	−43.0381			−1.59074
$733$	9.96819	−	17.2654i	0.368184	−	0.637713i	−0.621098	−	0.783733i	$-0.713313\pi$
$733$	9.96819	−	17.2654i	0.368184	−	0.637713i	0.989282	+	0.146020i	$0.0466465\pi$
$734$	−16.0606	+	27.8177i	−0.592807	+	1.02677i
$735$	−4.36285	+	19.0150i	−0.160926	+	0.701380i
$736$	−42.6545			−1.57227
$737$	−12.0117	−	20.8049i	−0.442457	−	0.766358i
$738$	8.26699	−	14.3189i	0.304312	−	0.527084i
$739$	−24.0236	+	41.6100i	−0.883721	+	1.53065i	−0.0365482	+	0.999332i	$0.511636\pi$
$739$	−24.0236	+	41.6100i	−0.883721	+	1.53065i	−0.847173	+	0.531318i	$0.821697\pi$
$740$	−36.6869	+	63.5436i	−1.34864	+	2.33591i
$741$	−10.1783	−	6.83721i	−0.373911	−	0.251171i
$742$	−12.7143	−	84.6810i	−0.466757	−	3.10874i
$743$	−0.250266	−	0.433473i	−0.00918137	−	0.0159026i	0.861398	−	0.507930i	$-0.169589\pi$
$743$	−0.250266	−	0.433473i	−0.00918137	−	0.0159026i	−0.870580	+	0.492028i	$0.836256\pi$
$744$	24.7108			0.905943
$745$	−24.5338			−0.898850
$746$	14.9253	+	25.8514i	0.546455	+	0.946488i
$747$	−2.41044	−	4.17501i	−0.0881935	−	0.152756i
$748$	−36.6997	+	63.5657i	−1.34187	+	2.32419i
$749$	29.7334	+	11.6891i	1.08644	+	0.427109i
$750$	−7.93494	+	13.7437i	−0.289743	+	0.501850i
$751$	43.8051			1.59847			0.799235	−	0.601019i	$-0.205238\pi$
$751$	43.8051			1.59847			0.799235	+	0.601019i	$0.205238\pi$
$752$	28.8352	−	49.9440i	1.05151	−	1.82127i
$753$	−1.55413	−	2.69183i	−0.0566355	−	0.0980956i
$754$	−1.95103	+	28.6861i	−0.0710524	+	1.04469i
$755$	26.9542			0.980963
$756$	11.0936	+	4.36122i	0.403471	+	0.158616i
$757$	1.91271	+	3.31291i	0.0695186	+	0.120410i	0.898689	−	0.438585i	$-0.144520\pi$
$757$	1.91271	+	3.31291i	0.0695186	+	0.120410i	−0.829171	+	0.558995i	$0.811187\pi$
$758$	−42.0276	−	72.7939i	−1.52651	−	2.64399i
$759$	10.1634	+	17.6035i	0.368908	+	0.638968i
$760$	60.5651			2.19693
$761$	2.86572	+	4.96357i	0.103882	+	0.179929i	0.913281	−	0.407330i	$-0.133540\pi$
$761$	2.86572	+	4.96357i	0.103882	+	0.179929i	−0.809399	+	0.587259i	$0.800207\pi$
$762$	−4.52225			−0.163824
$763$	−2.67826	−	17.8380i	−0.0969594	−	0.645779i
$764$	1.48252	+	2.56781i	0.0536358	+	0.0928999i
$765$	−16.4066			−0.593183
$766$	−16.1145	−	27.9112i	−0.582242	−	1.00847i
$767$	8.19022	+	5.50171i	0.295732	+	0.198655i
$768$	−14.2787	+	24.7314i	−0.515238	+	0.892419i
$769$	8.50053	+	14.7234i	0.306537	+	0.530938i	0.977602	−	0.210461i	$-0.0674964\pi$
$769$	8.50053	+	14.7234i	0.306537	+	0.530938i	−0.671065	+	0.741398i	$0.734163\pi$
$770$	−7.72810	−	51.4714i	−0.278501	−	1.85490i
$771$	−12.9927	+	22.5040i	−0.467920	+	0.810461i
$772$	−19.7911	+	34.2792i	−0.712298	+	1.23374i
$773$	−12.1864			−0.438314			−0.219157	−	0.975690i	$-0.570331\pi$
$773$	−12.1864			−0.438314			−0.219157	+	0.975690i	$0.570331\pi$
$774$	−15.2624			−0.548596
$775$	5.35096	−	9.26813i	0.192212	−	0.332921i
$776$	54.2288	−	93.9271i	1.94670	−	3.37179i
$777$	−12.0929	+	9.63249i	−0.433830	+	0.345564i
$778$	−0.151480	−	0.262370i	−0.00543080	−	0.00940643i
$779$	11.0226	−	19.0918i	0.394927	−	0.684034i
$780$	−3.07208	+	45.1689i	−0.109998	+	1.61731i
$781$	4.34663	+	7.52858i	0.155535	+	0.269394i
$782$	110.281			3.94366
$783$	−1.56328	−	2.70768i	−0.0558671	−	0.0967646i
$784$	37.3559	+	34.7405i	1.33414	+	1.24073i
$785$	32.1399			1.14712
$786$	8.94570	+	15.4944i	0.319082	+	0.552667i
$787$	−4.62042			−0.164700			−0.0823501	−	0.996603i	$-0.526243\pi$
$787$	−4.62042			−0.164700			−0.0823501	+	0.996603i	$0.526243\pi$
$788$	−41.8901	−	72.5558i	−1.49227	−	2.58469i
$789$	6.39028	+	11.0683i	0.227500	+	0.394042i
$790$	−13.3719	−	23.1608i	−0.475750	−	0.824023i
$791$	11.2771	−	8.98268i	0.400967	−	0.319387i
$792$	−17.6844			−0.628388
$793$	2.33714	−	34.3631i	0.0829943	−	1.22027i
$794$	−8.90531	−	15.4245i	−0.316038	−	0.547393i
$795$	−17.6828	+	30.6275i	−0.627145	+	1.08625i
$796$	68.5972			2.43136
$797$	−9.12087	+	15.7978i	−0.323078	+	0.559587i	−0.981121	−	0.193393i	$-0.938051\pi$
$797$	−9.12087	+	15.7978i	−0.323078	+	0.559587i	0.658044	+	0.752980i	$0.271384\pi$
$798$	21.3576	+	8.39629i	0.756052	+	0.297226i
$799$	−23.2925	+	40.3438i	−0.824029	+	1.42726i
$800$	−8.03582	−	13.9184i	−0.284109	−	0.492091i
$801$	−0.877787	−	1.52037i	−0.0310151	−	0.0537197i
$802$	−48.8475			−1.72487
$803$	−26.5838			−0.938122
$804$	−19.5548	−	33.8699i	−0.689644	−	1.19450i
$805$	−42.3629	+	33.7439i	−1.49310	+	1.18931i
$806$	−2.41311	+	35.4801i	−0.0849982	+	1.24973i
$807$	0.978744	−	1.69523i	0.0344534	−	0.0596751i
$808$	5.88762	−	10.1976i	0.207126	−	0.358752i
$809$	17.2960	−	29.9576i	0.608096	−	1.05325i	−0.383457	−	0.923559i	$-0.625267\pi$
$809$	17.2960	−	29.9576i	0.608096	−	1.05325i	0.991554	−	0.129695i	$-0.0414000\pi$
$810$	−3.55423	−	6.15611i	−0.124883	−	0.216304i
$811$	−11.9774			−0.420582			−0.210291	−	0.977639i	$-0.567441\pi$
$811$	−11.9774			−0.420582			−0.210291	+	0.977639i	$0.567441\pi$
$812$	−5.53365	−	36.8558i	−0.194193	−	1.29338i
$813$	13.4609	−	23.3150i	0.472095	−	0.817692i
$814$	20.6233	−	35.7207i	0.722848	−	1.25201i
$815$	−33.9192			−1.18814
$816$	−21.4504	+	37.1532i	−0.750915	+	1.30062i
$817$	−20.3499			−0.711951
$818$	29.8164			1.04250
$819$	−4.08457	+	8.62069i	−0.142726	+	0.301231i
$820$	−81.3976			−2.84253
$821$	21.1872			0.739438			0.369719	−	0.929144i	$-0.379454\pi$
$821$	21.1872			0.739438			0.369719	+	0.929144i	$0.379454\pi$
$822$	−25.0688	+	43.4204i	−0.874374	+	1.51446i
$823$	19.9361			0.694930			0.347465	−	0.937693i	$-0.387043\pi$
$823$	19.9361			0.694930			0.347465	+	0.937693i	$0.387043\pi$
$824$	−15.2408	+	26.3979i	−0.530939	+	0.919614i
$825$	−3.82943	+	6.63277i	−0.133324	+	0.230924i
$826$	−17.1859	−	6.75626i	−0.597973	−	0.235080i
$827$	−15.0299			−0.522639			−0.261320	−	0.965252i	$-0.584158\pi$
$827$	−15.0299			−0.522639			−0.261320	+	0.965252i	$0.584158\pi$
$828$	16.5458	+	28.6582i	0.575006	+	0.995940i
$829$	−8.03587	+	13.9185i	−0.279097	+	0.483411i	−0.971161	−	0.238426i	$-0.923369\pi$
$829$	−8.03587	+	13.9185i	−0.279097	+	0.483411i	0.692063	+	0.721837i	$0.256702\pi$
$830$	−17.1345	+	29.6779i	−0.594749	+	1.03013i
$831$	−11.5778	+	20.0533i	−0.401629	+	0.695643i
$832$	0.708563	+	0.475971i	0.0245650	+	0.0165013i
$833$	−30.1754	−	28.0627i	−1.04552	−	0.972315i
$834$	23.3974	+	40.5254i	0.810185	+	1.40328i
$835$	−25.3450			−0.877100
$836$	−42.4021			−1.46651
$837$	−1.93352	−	3.34896i	−0.0668323	−	0.115757i
$838$	20.1470	+	34.8957i	0.695967	+	1.20545i
$839$	2.50930	−	4.34624i	0.0866307	−	0.150049i	−0.819454	−	0.573145i	$-0.805723\pi$
$839$	2.50930	−	4.34624i	0.0866307	−	0.150049i	0.906085	+	0.423096i	$0.139057\pi$
$840$	−6.99620	−	46.5968i	−0.241392	−	1.60774i
$841$	9.61231	−	16.6490i	0.331459	−	0.574104i
$842$	21.8882			0.754316
$843$	−13.4674	+	23.3262i	−0.463841	+	0.803396i
$844$	−47.7323	−	82.6747i	−1.64301	−	2.84578i
$845$	−35.8976	−	4.90570i	−1.23491	−	0.168761i
$846$	−20.1838			−0.693932
$847$	−1.31253	−	8.74182i	−0.0450989	−	0.300372i
$848$	46.2379	+	80.0864i	1.58782	+	2.75018i
$849$	7.62216	+	13.2020i	0.261592	+	0.453091i
$850$	20.7763	+	35.9856i	0.712621	+	1.23430i
$851$	−42.9198			−1.47127
$852$	7.07621	+	12.2564i	0.242427	+	0.419896i
$853$	−4.22423			−0.144635			−0.0723175	−	0.997382i	$-0.523039\pi$
$853$	−4.22423			−0.144635			−0.0723175	+	0.997382i	$0.523039\pi$
$854$	9.57136	+	63.7481i	0.327525	+	2.18141i
$855$	−4.73897	−	8.20814i	−0.162069	−	0.280712i
$856$	−77.1633			−2.63739
$857$	4.48428	+	7.76700i	0.153180	+	0.265316i	0.932395	−	0.361441i	$-0.117715\pi$
$857$	4.48428	+	7.76700i	0.153180	+	0.265316i	−0.779215	+	0.626757i	$0.784382\pi$
$858$	1.72695	−	25.3915i	0.0589572	−	0.866851i
$859$	18.3400	−	31.7658i	0.625753	−	1.08384i	−0.362642	−	0.931928i	$-0.618125\pi$
$859$	18.3400	−	31.7658i	0.625753	−	1.08384i	0.988395	−	0.151907i	$-0.0485414\pi$
$860$	37.5688	+	65.0711i	1.28109	+	2.21890i
$861$	−15.9619	−	6.27507i	−0.543980	−	0.213854i
$862$	24.7974	−	42.9503i	0.844602	−	1.46289i
$863$	−10.4237	+	18.0544i	−0.354828	+	0.614580i	−0.987088	−	0.160176i	$-0.948794\pi$
$863$	−10.4237	+	18.0544i	−0.354828	+	0.614580i	0.632261	+	0.774756i	$0.282127\pi$
$864$	−5.80735			−0.197570
$865$	−3.75494			−0.127672
$866$	6.00426	−	10.3997i	0.204033	−	0.353395i
$867$	8.82723	−	15.2892i	0.299788	−	0.519249i
$868$	−6.84423	−	45.5846i	−0.232308	−	1.54724i
$869$	5.20593	+	9.01694i	0.176599	+	0.305879i
$870$	−11.1125	+	19.2474i	−0.376750	+	0.652549i
$871$	28.1048	−	13.7739i	0.952294	−	0.466712i
$872$	21.7829	+	37.7291i	0.737663	+	1.27767i
$873$	−16.9727			−0.574440
$874$	31.8543	+	55.1732i	1.07749	+	1.86626i
$875$	15.3208	+	6.02303i	0.517936	+	0.203615i
$876$	−43.2778			−1.46222
$877$	13.8100	+	23.9197i	0.466331	+	0.807709i	0.999261	−	0.0384504i	$-0.0122422\pi$
$877$	13.8100	+	23.9197i	0.466331	+	0.807709i	−0.532929	+	0.846160i	$0.678909\pi$
$878$	−52.7004			−1.77855
$879$	2.04388	+	3.54010i	0.0689383	+	0.119405i
$880$	28.1047	+	48.6787i	0.947408	+	1.64096i
$881$	−12.7092	−	22.0130i	−0.428183	−	0.741635i	0.568528	−	0.822664i	$-0.307513\pi$
$881$	−12.7092	−	22.0130i	−0.428183	−	0.741635i	−0.996712	+	0.0810283i	$0.974180\pi$
$882$	3.99270	−	17.4018i	0.134441	−	0.585948i
$883$	32.7921			1.10354			0.551771	−	0.833995i	$-0.313952\pi$
$883$	32.7921			1.10354			0.551771	+	0.833995i	$0.313952\pi$
$884$	−79.3803	−	53.3230i	−2.66985	−	1.79345i
$885$	3.81332	+	6.60486i	0.128183	+	0.222020i
$886$	15.6630	−	27.1291i	0.526209	−	0.911421i
$887$	−7.93320			−0.266371			−0.133185	−	0.991091i	$-0.542521\pi$
$887$	−7.93320			−0.266371			−0.133185	+	0.991091i	$0.542521\pi$
$888$	18.6702	−	32.3377i	0.626531	−	1.08518i
$889$	0.696519	+	4.63903i	0.0233605	+	0.155588i
$890$	−6.23972	+	10.8075i	−0.209156	+	0.362269i
$891$	1.38373	+	2.39670i	0.0463568	+	0.0802923i
$892$	−2.04217	−	3.53713i	−0.0683768	−	0.118432i
$893$	−26.9117			−0.900565
$894$	22.4524			0.750919
$895$	8.30521	+	14.3850i	0.277613	+	0.480839i
$896$	27.1122	+	10.6586i	0.905754	+	0.356078i
$897$	−23.7801	+	11.6545i	−0.793996	+	0.389131i
$898$	35.1682	−	60.9130i	1.17358	−	2.03269i
$899$	−6.04527	+	10.4707i	−0.201621	+	0.349218i
$900$	−6.23423	+	10.7980i	−0.207808	+	0.359934i
$901$	−37.3501	−	64.6922i	−1.24431	−	2.15521i
$902$	45.7572			1.52355
$903$	2.35072	+	15.6565i	0.0782271	+	0.521016i
$904$	−17.4107	+	30.1562i	−0.579071	+	1.00298i
$905$	−14.5615	+	25.2213i	−0.484041	+	0.838384i
$906$	−24.6673			−0.819518
$907$	23.1186	−	40.0426i	0.767640	−	1.32959i	−0.171200	−	0.985236i	$-0.554764\pi$
$907$	23.1186	−	40.0426i	0.767640	−	1.32959i	0.938840	−	0.344355i	$-0.111902\pi$
$908$	8.68676			0.288280
$909$	−1.84273			−0.0611194
$910$	67.5874	−	5.49486i	2.24050	−	0.182153i
$911$	−21.5838			−0.715102			−0.357551	−	0.933894i	$-0.616388\pi$
$911$	−21.5838			−0.715102			−0.357551	+	0.933894i	$0.616388\pi$
$912$	−24.7834			−0.820660
$913$	6.67082	−	11.5542i	0.220772	−	0.382388i
$914$	35.3983			1.17087
$915$	13.3117	−	23.0565i	0.440070	−	0.762224i
$916$	22.7781	−	39.4529i	0.752611	−	1.30356i
$917$	14.5167	−	11.5632i	0.479383	−	0.381849i
$918$	15.0147			0.495558
$919$	4.40489	+	7.62950i	0.145304	+	0.251674i	0.929486	−	0.368857i	$-0.120251\pi$
$919$	4.40489	+	7.62950i	0.145304	+	0.251674i	−0.784182	+	0.620530i	$0.786917\pi$
$920$	65.4041	−	113.283i	2.15631	−	3.73484i
$921$	0.521481	−	0.903232i	0.0171834	−	0.0297625i
$922$	−31.1295	+	53.9179i	−1.02520	+	1.77569i
$923$	−10.1702	+	4.98432i	−0.334755	+	0.164061i
$924$	4.89810	+	32.6228i	0.161136	+	1.07321i
$925$	−8.08580	−	14.0050i	−0.265859	−	0.460482i
$926$	−29.7011			−0.976039
$927$	4.77013			0.156672
$928$	9.07851	+	15.7244i	0.298017	+	0.516180i
$929$	26.2347	+	45.4398i	0.860733	+	1.49083i	0.871223	+	0.490888i	$0.163328\pi$
$929$	26.2347	+	45.4398i	0.860733	+	1.49083i	−0.0104899	+	0.999945i	$0.503339\pi$
$930$	−13.7444	+	23.8060i	−0.450696	+	0.780628i
$931$	5.32359	−	23.2023i	0.174474	−	0.760426i
$932$	59.0806	−	102.331i	1.93525	−	3.35195i
$933$	−7.77448			−0.254525
$934$	5.34299	−	9.25433i	0.174828	−	0.302811i
$935$	−22.7024	−	39.3217i	−0.742448	−	1.28596i
$936$	1.56340	−	22.9868i	0.0511013	−	0.751346i
$937$	−19.3131			−0.630932			−0.315466	−	0.948937i	$-0.602161\pi$
$937$	−19.3131			−0.630932			−0.315466	+	0.948937i	$0.602161\pi$
$938$	−45.8192	+	36.4970i	−1.49605	+	1.19167i
$939$	12.1950	+	21.1224i	0.397970	+	0.689304i
$940$	49.6829	+	86.0532i	1.62048	+	2.80675i
$941$	−8.45918	−	14.6517i	−0.275761	−	0.477633i	0.694566	−	0.719429i	$-0.255597\pi$
$941$	−8.45918	−	14.6517i	−0.275761	−	0.477633i	−0.970327	+	0.241797i	$0.922263\pi$
$942$	−29.4131			−0.958331
$943$	−23.8067	−	41.2343i	−0.775251	−	1.34277i
$944$	19.9425			0.649073
$945$	−5.76765	+	4.59418i	−0.187622	+	0.149449i
$946$	−21.1191	−	36.5793i	−0.686641	−	1.18930i
$947$	−44.7022			−1.45263			−0.726313	−	0.687365i	$-0.758768\pi$
$947$	−44.7022			−1.45263			−0.726313	+	0.687365i	$0.758768\pi$
$948$	8.47514	+	14.6794i	0.275260	+	0.476764i
$949$	2.35016	−	34.5545i	0.0762893	−	1.12169i
$950$	−12.0023	+	20.7885i	−0.389405	+	0.674468i
$951$	5.38045	+	9.31922i	0.174473	+	0.302196i
$952$	92.6255	+	36.4137i	3.00201	+	1.18018i
$953$	−24.8774	+	43.0888i	−0.805857	+	1.39578i	0.109855	+	0.993948i	$0.464962\pi$
$953$	−24.8774	+	43.0888i	−0.805857	+	1.39578i	−0.915711	+	0.401837i	$0.868372\pi$
$954$	16.1826	−	28.0291i	0.523931	−	0.907474i
$955$	−1.83417			−0.0593525
$956$	126.401			4.08809
$957$	4.32632	−	7.49341i	0.139850	−	0.242228i
$958$	19.1400	−	33.1515i	0.618386	−	1.07108i
$959$	48.4027	+	19.0285i	1.56301	+	0.614462i
$960$	0.329903	+	0.571408i	0.0106476	+	0.0184421i
$961$	8.02298	−	13.8962i	0.258806	−	0.448265i
$962$	44.6076	+	29.9648i	1.43821	+	0.966103i
$963$	6.03771	+	10.4576i	0.194563	+	0.336992i
$964$	−20.0601			−0.646094
$965$	−12.2428	−	21.2051i	−0.394109	−	0.682616i
$966$	38.7688	−	30.8810i	1.24737	−	0.993579i
$967$	1.92897			0.0620315			0.0310158	−	0.999519i	$-0.490126\pi$
$967$	1.92897			0.0620315			0.0310158	+	0.999519i	$0.490126\pi$
$968$	10.6751	+	18.4898i	0.343111	+	0.594285i
$969$	20.0195			0.643120
$970$	60.3251	+	104.486i	1.93692	+	3.35485i
$971$	18.0616	+	31.2836i	0.579624	+	1.00394i	0.995522	+	0.0945270i	$0.0301339\pi$
$971$	18.0616	+	31.2836i	0.579624	+	1.00394i	−0.415898	+	0.909411i	$0.636533\pi$
$972$	2.25269	+	3.90177i	0.0722549	+	0.125149i
$973$	37.9682	−	30.2433i	1.21721	−	0.969556i
$974$	16.8546			0.540055
$975$	−8.28295	−	5.56400i	−0.265267	−	0.178190i
$976$	−34.8080	−	60.2893i	−1.11418	−	1.92981i
$977$	−16.4841	+	28.5513i	−0.527373	+	0.913436i	0.472118	+	0.881535i	$0.343490\pi$
$977$	−16.4841	+	28.5513i	−0.527373	+	0.913436i	−0.999491	+	0.0319012i	$0.989844\pi$
$978$	31.0414			0.992596
$979$	2.42925	−	4.20758i	0.0776391	−	0.134475i
$980$	−84.0203	+	25.8121i	−2.68393	+	0.824537i
$981$	3.40885	−	5.90430i	0.108836	−	0.188510i
$982$	−41.9709	−	72.6957i	−1.33935	−	2.31981i
$983$	7.52903	+	13.0407i	0.240139	+	0.415933i	0.960754	−	0.277403i	$-0.0894737\pi$
$983$	7.52903	+	13.0407i	0.240139	+	0.415933i	−0.720615	+	0.693336i	$0.756140\pi$
$984$	41.4238			1.32054
$985$	51.8263			1.65132
$986$	−23.4721	−	40.6549i	−0.747504	−	1.29472i
$987$	3.10871	+	20.7050i	0.0989514	+	0.659046i
$988$	3.74858	−	55.1156i	0.119258	−	1.75346i
$989$	−21.9758	+	38.0631i	−0.698789	+	1.21034i
$990$	9.83622	−	17.0368i	0.312615	−	0.541466i
$991$	−18.0676	+	31.2939i	−0.573935	+	0.994085i	0.422221	+	0.906493i	$0.361251\pi$
$991$	−18.0676	+	31.2939i	−0.573935	+	0.994085i	−0.996156	+	0.0875921i	$0.972083\pi$
$992$	11.2286	+	19.4486i	0.356510	+	0.617493i
$993$	22.9691			0.728902
$994$	16.5804	−	13.2070i	0.525899	−	0.418901i
$995$	−21.2171	+	36.7491i	−0.672627	+	1.16502i
$996$	10.8599	−	18.8100i	0.344110	−	0.596017i
$997$	3.81524			0.120830			0.0604149	−	0.998173i	$-0.480758\pi$
$997$	3.81524			0.120830			0.0604149	+	0.998173i	$0.480758\pi$
$998$	−45.7058	+	79.1647i	−1.44679	+	2.50591i
$999$	−5.84347			−0.184879

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.l.b.16.8	yes	16
3.2	odd	2		819.2.s.e.289.1		16
7.4	even	3		273.2.j.b.172.1	yes	16
13.9	even	3		273.2.j.b.100.1	✓	16
21.11	odd	6		819.2.n.e.172.8		16
39.35	odd	6		819.2.n.e.100.8		16
91.74	even	3	inner	273.2.l.b.256.8	yes	16
273.74	odd	6		819.2.s.e.802.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.b.100.1	✓	16	13.9	even	3
273.2.j.b.172.1	yes	16	7.4	even	3
273.2.l.b.16.8	yes	16	1.1	even	1	trivial
273.2.l.b.256.8	yes	16	91.74	even	3	inner
819.2.n.e.100.8		16	39.35	odd	6
819.2.n.e.172.8		16	21.11	odd	6
819.2.s.e.289.1		16	3.2	odd	2
819.2.s.e.802.1		16	273.74	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.55056 q^{2} +(0.500000 - 0.866025i) q^{3} +4.50537 q^{4} +(-1.39351 + 2.41363i) q^{5} +(1.27528 - 2.20885i) q^{6} +(-2.46231 - 0.968004i) q^{7} +6.39011 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+2.55056 q^{2} +(0.500000 - 0.866025i) q^{3} +4.50537 q^{4} +(-1.39351 + 2.41363i) q^{5} +(1.27528 - 2.20885i) q^{6} +(-2.46231 - 0.968004i) q^{7} +6.39011 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-3.55423 + 6.15611i) q^{10} +(1.38373 - 2.39670i) q^{11} +(2.25269 - 3.90177i) q^{12} +(2.99297 + 2.01050i) q^{13} +(-6.28028 - 2.46895i) q^{14} +(1.39351 + 2.41363i) q^{15} +7.28763 q^{16} -5.88680 q^{17} +(-1.27528 - 2.20885i) q^{18} +(-1.70037 - 2.94513i) q^{19} +(-6.27828 + 10.8743i) q^{20} +(-2.06947 + 1.64842i) q^{21} +(3.52930 - 6.11292i) q^{22} -7.34492 q^{23} +(3.19505 - 5.53400i) q^{24} +(-1.38373 - 2.39670i) q^{25} +(7.63376 + 5.12791i) q^{26} -1.00000 q^{27} +(-11.0936 - 4.36122i) q^{28} +(1.56328 + 2.70768i) q^{29} +(3.55423 + 6.15611i) q^{30} +(1.93352 + 3.34896i) q^{31} +5.80735 q^{32} +(-1.38373 - 2.39670i) q^{33} -15.0147 q^{34} +(5.76765 - 4.59418i) q^{35} +(-2.25269 - 3.90177i) q^{36} +5.84347 q^{37} +(-4.33691 - 7.51175i) q^{38} +(3.23763 - 1.58674i) q^{39} +(-8.90467 + 15.4233i) q^{40} +(3.24124 + 5.61400i) q^{41} +(-5.27832 + 4.20440i) q^{42} +(2.99197 - 5.18224i) q^{43} +(6.23423 - 10.7980i) q^{44} +2.78702 q^{45} -18.7337 q^{46} +(3.95673 - 6.85325i) q^{47} +(3.64382 - 6.31127i) q^{48} +(5.12594 + 4.76705i) q^{49} +(-3.52930 - 6.11292i) q^{50} +(-2.94340 + 5.09812i) q^{51} +(13.4845 + 9.05806i) q^{52} +(6.34471 + 10.9894i) q^{53} -2.55056 q^{54} +(3.85649 + 6.67963i) q^{55} +(-15.7344 - 6.18565i) q^{56} -3.40075 q^{57} +(3.98724 + 6.90611i) q^{58} +2.73648 q^{59} +(6.27828 + 10.8743i) q^{60} +(-4.77631 - 8.27282i) q^{61} +(4.93157 + 8.54173i) q^{62} +(0.392839 + 2.61642i) q^{63} +0.236742 q^{64} +(-9.02334 + 4.42227i) q^{65} +(-3.52930 - 6.11292i) q^{66} +(4.34033 - 7.51767i) q^{67} -26.5222 q^{68} +(-3.67246 + 6.36089i) q^{69} +(14.7108 - 11.7177i) q^{70} +(-1.57062 + 2.72039i) q^{71} +(-3.19505 - 5.53400i) q^{72} +(-4.80291 - 8.31889i) q^{73} +14.9041 q^{74} -2.76747 q^{75} +(-7.66082 - 13.2689i) q^{76} +(-5.72719 + 4.56195i) q^{77} +(8.25778 - 4.04708i) q^{78} +(-1.88112 + 3.25819i) q^{79} +(-10.1554 + 17.5896i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(8.26699 + 14.3189i) q^{82} +4.82088 q^{83} +(-9.32374 + 7.42675i) q^{84} +(8.20331 - 14.2086i) q^{85} +(7.63120 - 13.2176i) q^{86} +3.12656 q^{87} +(8.84221 - 15.3151i) q^{88} +1.75557 q^{89} +7.10846 q^{90} +(-5.42345 - 7.84769i) q^{91} -33.0916 q^{92} +3.86705 q^{93} +(10.0919 - 17.4797i) q^{94} +9.47794 q^{95} +(2.90367 - 5.02931i) q^{96} +(8.48637 - 14.6988i) q^{97} +(13.0740 + 12.1587i) q^{98} -2.76747 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} + 12 q^{4} + q^{7} + 12 q^{8} - 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^3 + 12 * q^4 + q^7 + 12 * q^8 - 8 * q^9	\( 16 q + 8 q^{3} + 12 q^{4} + q^{7} + 12 q^{8} - 8 q^{9} - 4 q^{10} - 2 q^{11} + 6 q^{12} + 5 q^{13} - 7 q^{14} + 12 q^{16} + 4 q^{17} - 11 q^{19} - 20 q^{20} - q^{21} + 7 q^{22} - 8 q^{23} + 6 q^{24} + 2 q^{25} + 33 q^{26} - 16 q^{27} - q^{28} + 15 q^{29} + 4 q^{30} + 3 q^{31} - 6 q^{32} + 2 q^{33} - 68 q^{34} - 6 q^{36} - 8 q^{37} + 2 q^{38} + 4 q^{39} - 25 q^{40} + 19 q^{41} - 17 q^{42} + 11 q^{43} - 16 q^{44} - 4 q^{46} + 5 q^{47} + 6 q^{48} + 7 q^{49} - 7 q^{50} + 2 q^{51} - 18 q^{52} + 36 q^{53} - 15 q^{55} - 51 q^{56} - 22 q^{57} + 20 q^{58} + 34 q^{59} + 20 q^{60} - 22 q^{61} - 6 q^{62} - 2 q^{63} - 20 q^{64} - 24 q^{65} - 7 q^{66} + 26 q^{67} - 10 q^{68} - 4 q^{69} + 46 q^{70} + 9 q^{71} - 6 q^{72} - 6 q^{73} - 30 q^{74} + 4 q^{75} - 16 q^{76} - 36 q^{77} + 6 q^{78} + 16 q^{79} - 28 q^{80} - 8 q^{81} - q^{82} + 36 q^{83} - 8 q^{84} - 4 q^{85} + 16 q^{86} + 30 q^{87} + 24 q^{88} - 40 q^{89} + 8 q^{90} - 10 q^{91} - 94 q^{92} + 6 q^{93} - 20 q^{94} - 3 q^{96} + 7 q^{97} + 18 q^{98} + 4 q^{99}+O(q^{100}) \) 16 * q + 8 * q^3 + 12 * q^4 + q^7 + 12 * q^8 - 8 * q^9 - 4 * q^10 - 2 * q^11 + 6 * q^12 + 5 * q^13 - 7 * q^14 + 12 * q^16 + 4 * q^17 - 11 * q^19 - 20 * q^20 - q^21 + 7 * q^22 - 8 * q^23 + 6 * q^24 + 2 * q^25 + 33 * q^26 - 16 * q^27 - q^28 + 15 * q^29 + 4 * q^30 + 3 * q^31 - 6 * q^32 + 2 * q^33 - 68 * q^34 - 6 * q^36 - 8 * q^37 + 2 * q^38 + 4 * q^39 - 25 * q^40 + 19 * q^41 - 17 * q^42 + 11 * q^43 - 16 * q^44 - 4 * q^46 + 5 * q^47 + 6 * q^48 + 7 * q^49 - 7 * q^50 + 2 * q^51 - 18 * q^52 + 36 * q^53 - 15 * q^55 - 51 * q^56 - 22 * q^57 + 20 * q^58 + 34 * q^59 + 20 * q^60 - 22 * q^61 - 6 * q^62 - 2 * q^63 - 20 * q^64 - 24 * q^65 - 7 * q^66 + 26 * q^67 - 10 * q^68 - 4 * q^69 + 46 * q^70 + 9 * q^71 - 6 * q^72 - 6 * q^73 - 30 * q^74 + 4 * q^75 - 16 * q^76 - 36 * q^77 + 6 * q^78 + 16 * q^79 - 28 * q^80 - 8 * q^81 - q^82 + 36 * q^83 - 8 * q^84 - 4 * q^85 + 16 * q^86 + 30 * q^87 + 24 * q^88 - 40 * q^89 + 8 * q^90 - 10 * q^91 - 94 * q^92 + 6 * q^93 - 20 * q^94 - 3 * q^96 + 7 * q^97 + 18 * q^98 + 4 * q^99

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