LMFDB - Embedded newform 273.2.t.c.4.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(4,273)]

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, 4, 1]))

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

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

chi := DirichletCharacter("273.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.t (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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.2346760387617129.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + \cdots + 64 $ x^12 - 3x^11 + x^10 + 10x^9 - 15x^8 - 10x^7 + 45x^6 - 20x^5 - 60x^4 + 80x^3 + 16x^2 - 96x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			4.2
Root			$-1.18541 - 0.771231i$ of defining polynomial
Character	$\chi$	$=$	273.4
Dual form			273.2.t.c.205.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.54246i q^{2} +(-0.500000 - 0.866025i) q^{3} -0.379188 q^{4} +(1.27069 - 0.733632i) q^{5} +(-1.33581 + 0.771231i) q^{6} +(2.63491 - 0.239300i) q^{7} -2.50004i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q-1.54246i q^{2} +(-0.500000 - 0.866025i) q^{3} -0.379188 q^{4} +(1.27069 - 0.733632i) q^{5} +(-1.33581 + 0.771231i) q^{6} +(2.63491 - 0.239300i) q^{7} -2.50004i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.13160 - 1.95999i) q^{10} +(-1.93300 + 1.11602i) q^{11} +(0.189594 + 0.328387i) q^{12} +(3.57691 + 0.453537i) q^{13} +(-0.369112 - 4.06424i) q^{14} +(-1.27069 - 0.733632i) q^{15} -4.61459 q^{16} -2.52122 q^{17} +(1.33581 + 0.771231i) q^{18} +(-0.829287 - 0.478789i) q^{19} +(-0.481830 + 0.278185i) q^{20} +(-1.52469 - 2.16225i) q^{21} +(1.72142 + 2.98158i) q^{22} -2.64900 q^{23} +(-2.16510 + 1.25002i) q^{24} +(-1.42357 + 2.46569i) q^{25} +(0.699564 - 5.51725i) q^{26} +1.00000 q^{27} +(-0.999126 + 0.0907399i) q^{28} +(-0.728078 + 1.26107i) q^{29} +(-1.13160 + 1.95999i) q^{30} +(-2.89114 - 1.66920i) q^{31} +2.11775i q^{32} +(1.93300 + 1.11602i) q^{33} +3.88889i q^{34} +(3.17259 - 2.23713i) q^{35} +(0.189594 - 0.328387i) q^{36} +7.41040i q^{37} +(-0.738514 + 1.27914i) q^{38} +(-1.39568 - 3.32447i) q^{39} +(-1.83411 - 3.17677i) q^{40} +(3.52497 + 2.03514i) q^{41} +(-3.33518 + 2.35178i) q^{42} +(3.00991 + 5.21332i) q^{43} +(0.732971 - 0.423181i) q^{44} +1.46726i q^{45} +4.08598i q^{46} +(9.05536 - 5.22812i) q^{47} +(2.30730 + 3.99635i) q^{48} +(6.88547 - 1.26107i) q^{49} +(3.80323 + 2.19580i) q^{50} +(1.26061 + 2.18344i) q^{51} +(-1.35632 - 0.171976i) q^{52} +(1.74412 - 3.02090i) q^{53} -1.54246i q^{54} +(-1.63749 + 2.83622i) q^{55} +(-0.598261 - 6.58737i) q^{56} +0.957578i q^{57} +(1.94515 + 1.12303i) q^{58} +0.767344i q^{59} +(0.481830 + 0.278185i) q^{60} +(6.05695 - 10.4909i) q^{61} +(-2.57468 + 4.45947i) q^{62} +(-1.11021 + 2.40155i) q^{63} -5.96263 q^{64} +(4.87787 - 2.04783i) q^{65} +(1.72142 - 2.98158i) q^{66} +(-8.35667 + 4.82473i) q^{67} +0.956018 q^{68} +(1.32450 + 2.29410i) q^{69} +(-3.45069 - 4.89359i) q^{70} +(-2.50519 + 1.44637i) q^{71} +(2.16510 + 1.25002i) q^{72} +(11.3623 + 6.56004i) q^{73} +11.4303 q^{74} +2.84713 q^{75} +(0.314456 + 0.181551i) q^{76} +(-4.82621 + 3.40317i) q^{77} +(-5.12786 + 2.15279i) q^{78} +(-1.88401 - 3.26320i) q^{79} +(-5.86371 + 3.38541i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.13913 - 5.43712i) q^{82} +3.89258i q^{83} +(0.578146 + 0.819898i) q^{84} +(-3.20369 + 1.84965i) q^{85} +(8.04135 - 4.64268i) q^{86} +1.45616 q^{87} +(2.79009 + 4.83258i) q^{88} +10.1478i q^{89} +2.26320 q^{90} +(9.53336 + 0.339072i) q^{91} +1.00447 q^{92} +3.33840i q^{93} +(-8.06417 - 13.9676i) q^{94} -1.40502 q^{95} +(1.83403 - 1.05888i) q^{96} +(-5.44296 + 3.14250i) q^{97} +(-1.94515 - 10.6206i) q^{98} -2.23204i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} - 10 q^{4} - 6 q^{5} - 3 q^{6} - 3 q^{7} - 6 q^{9}+O(q^{10}) $ 12 * q - 6 * q^3 - 10 * q^4 - 6 * q^5 - 3 * q^6 - 3 * q^7 - 6 * q^9	$ 12 q - 6 q^{3} - 10 q^{4} - 6 q^{5} - 3 q^{6} - 3 q^{7} - 6 q^{9} - 7 q^{10} - 18 q^{11} + 5 q^{12} - q^{13} - 16 q^{14} + 6 q^{15} - 6 q^{16} + 3 q^{18} + 9 q^{19} - 27 q^{20} - 3 q^{21} + 7 q^{22} + 32 q^{23} + 6 q^{24} + 10 q^{25} - 7 q^{26} + 12 q^{27} + 36 q^{28} - 5 q^{29} - 7 q^{30} - 15 q^{31} + 18 q^{33} - 2 q^{35} + 5 q^{36} + 24 q^{38} - 10 q^{39} + 21 q^{40} - 15 q^{41} + 5 q^{42} - 13 q^{43} + 30 q^{44} + 9 q^{47} + 3 q^{48} - 3 q^{49} - 63 q^{50} + 32 q^{52} + 18 q^{53} + 13 q^{55} + 3 q^{56} - 57 q^{58} + 27 q^{60} + 26 q^{61} - 13 q^{62} + 6 q^{63} - 4 q^{64} + 10 q^{65} + 7 q^{66} - 24 q^{67} - 16 q^{69} + 42 q^{70} - 15 q^{71} - 6 q^{72} + 18 q^{73} - 76 q^{74} - 20 q^{75} - 30 q^{76} + 20 q^{77} - q^{78} - 4 q^{79} + 39 q^{80} - 6 q^{81} - 14 q^{82} - 12 q^{84} - 12 q^{85} + 15 q^{86} + 10 q^{87} + 16 q^{88} + 14 q^{90} + 4 q^{91} - 40 q^{92} - 3 q^{94} + 56 q^{95} + 6 q^{96} + 45 q^{97} + 57 q^{98}+O(q^{100}) $ 12 * q - 6 * q^3 - 10 * q^4 - 6 * q^5 - 3 * q^6 - 3 * q^7 - 6 * q^9 - 7 * q^10 - 18 * q^11 + 5 * q^12 - q^13 - 16 * q^14 + 6 * q^15 - 6 * q^16 + 3 * q^18 + 9 * q^19 - 27 * q^20 - 3 * q^21 + 7 * q^22 + 32 * q^23 + 6 * q^24 + 10 * q^25 - 7 * q^26 + 12 * q^27 + 36 * q^28 - 5 * q^29 - 7 * q^30 - 15 * q^31 + 18 * q^33 - 2 * q^35 + 5 * q^36 + 24 * q^38 - 10 * q^39 + 21 * q^40 - 15 * q^41 + 5 * q^42 - 13 * q^43 + 30 * q^44 + 9 * q^47 + 3 * q^48 - 3 * q^49 - 63 * q^50 + 32 * q^52 + 18 * q^53 + 13 * q^55 + 3 * q^56 - 57 * q^58 + 27 * q^60 + 26 * q^61 - 13 * q^62 + 6 * q^63 - 4 * q^64 + 10 * q^65 + 7 * q^66 - 24 * q^67 - 16 * q^69 + 42 * q^70 - 15 * q^71 - 6 * q^72 + 18 * q^73 - 76 * q^74 - 20 * q^75 - 30 * q^76 + 20 * q^77 - q^78 - 4 * q^79 + 39 * q^80 - 6 * q^81 - 14 * q^82 - 12 * q^84 - 12 * q^85 + 15 * q^86 + 10 * q^87 + 16 * q^88 + 14 * q^90 + 4 * q^91 - 40 * q^92 - 3 * q^94 + 56 * q^95 + 6 * q^96 + 45 * q^97 + 57 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$		−	1.54246i		−	1.09069i	−0.838213	−	0.545343i	$-0.816400\pi$
$2$		−	1.54246i		−	1.09069i	0.838213	−	0.545343i	$-0.183600\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.379188			−0.189594
$5$	1.27069	−	0.733632i	0.568269	−	0.328090i	−0.188189	−	0.982133i	$-0.560262\pi$
$5$	1.27069	−	0.733632i	0.568269	−	0.328090i	0.756458	+	0.654043i	$0.226928\pi$
$6$	−1.33581	+	0.771231i	−0.545343	+	0.314854i
$7$	2.63491	−	0.239300i	0.995901	−	0.0904471i
$7$	2.63491	−	0.239300i	0.995901	−	0.0904471i
$8$		−	2.50004i		−	0.883898i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.13160	−	1.95999i	−0.357843	−	0.619803i
$11$	−1.93300	+	1.11602i	−0.582822	+	0.336492i	−0.762254	−	0.647278i	$-0.775907\pi$
$11$	−1.93300	+	1.11602i	−0.582822	+	0.336492i	0.179432	+	0.983770i	$0.442574\pi$
$12$	0.189594	+	0.328387i	0.0547311	+	0.0947971i
$13$	3.57691	+	0.453537i	0.992057	+	0.125789i
$13$	3.57691	+	0.453537i	0.992057	+	0.125789i
$14$	−0.369112	−	4.06424i	−0.0986493	−	1.08621i
$15$	−1.27069	−	0.733632i	−0.328090	−	0.189423i
$16$	−4.61459			−1.15365
$17$	−2.52122			−0.611487			−0.305743	−	0.952114i	$-0.598905\pi$
$17$	−2.52122			−0.611487			−0.305743	+	0.952114i	$0.598905\pi$
$18$	1.33581	+	0.771231i	0.314854	+	0.181781i
$19$	−0.829287	−	0.478789i	−0.190252	−	0.109842i	0.401849	−	0.915706i	$-0.368368\pi$
$19$	−0.829287	−	0.478789i	−0.190252	−	0.109842i	−0.592100	+	0.805864i	$0.701701\pi$
$20$	−0.481830	+	0.278185i	−0.107740	+	0.0622040i
$21$	−1.52469	−	2.16225i	−0.332715	−	0.471841i
$22$	1.72142	+	2.98158i	0.367007	+	0.635675i
$23$	−2.64900			−0.552355			−0.276178	−	0.961107i	$-0.589068\pi$
$23$	−2.64900			−0.552355			−0.276178	+	0.961107i	$0.589068\pi$
$24$	−2.16510	+	1.25002i	−0.441949	+	0.255159i
$25$	−1.42357	+	2.46569i	−0.284713	+	0.493138i
$26$	0.699564	−	5.51725i	0.137196	−	1.08202i
$27$	1.00000			0.192450
$28$	−0.999126	+	0.0907399i	−0.188817	+	0.0171482i
$29$	−0.728078	+	1.26107i	−0.135201	+	0.234175i	−0.925674	−	0.378322i	$-0.876501\pi$
$29$	−0.728078	+	1.26107i	−0.135201	+	0.234175i	0.790473	+	0.612496i	$0.209835\pi$
$30$	−1.13160	+	1.95999i	−0.206601	+	0.357843i
$31$	−2.89114	−	1.66920i	−0.519264	−	0.299797i	0.217369	−	0.976089i	$-0.430252\pi$
$31$	−2.89114	−	1.66920i	−0.519264	−	0.299797i	−0.736633	+	0.676292i	$0.763586\pi$
$32$			2.11775i			0.374369i
$33$	1.93300	+	1.11602i	0.336492	+	0.194274i
$34$			3.88889i			0.666939i
$35$	3.17259	−	2.23713i	0.536265	−	0.378144i
$36$	0.189594	−	0.328387i	0.0315990	−	0.0547311i
$37$			7.41040i			1.21826i	0.793070	+	0.609131i	$0.208482\pi$
$37$			7.41040i			1.21826i	−0.793070	+	0.609131i	$0.791518\pi$
$38$	−0.738514	+	1.27914i	−0.119803	+	0.207505i
$39$	−1.39568	−	3.32447i	−0.223488	−	0.532341i
$40$	−1.83411	−	3.17677i	−0.289998	−	0.502292i
$41$	3.52497	+	2.03514i	0.550507	+	0.317835i	0.749327	−	0.662201i	$-0.230377\pi$
$41$	3.52497	+	2.03514i	0.550507	+	0.317835i	−0.198819	+	0.980036i	$0.563711\pi$
$42$	−3.33518	+	2.35178i	−0.514630	+	0.362888i
$43$	3.00991	+	5.21332i	0.459008	+	0.795024i	0.998909	−	0.0467040i	$-0.0148718\pi$
$43$	3.00991	+	5.21332i	0.459008	+	0.795024i	−0.539901	+	0.841728i	$0.681538\pi$
$44$	0.732971	−	0.423181i	0.110500	−	0.0637970i
$45$			1.46726i			0.218727i
$46$			4.08598i			0.602446i
$47$	9.05536	−	5.22812i	1.32086	−	0.762599i	0.336995	−	0.941507i	$-0.390590\pi$
$47$	9.05536	−	5.22812i	1.32086	−	0.762599i	0.983866	+	0.178907i	$0.0572563\pi$
$48$	2.30730	+	3.99635i	0.333030	+	0.576824i
$49$	6.88547	−	1.26107i	0.983639	−	0.180153i
$50$	3.80323	+	2.19580i	0.537859	+	0.310533i
$51$	1.26061	+	2.18344i	0.176521	+	0.305743i
$52$	−1.35632	−	0.171976i	−0.188088	−	0.0238488i
$53$	1.74412	−	3.02090i	0.239573	−	0.414953i	−0.721019	−	0.692916i	$-0.756326\pi$
$53$	1.74412	−	3.02090i	0.239573	−	0.414953i	0.960592	+	0.277963i	$0.0896592\pi$
$54$		−	1.54246i		−	0.209902i
$55$	−1.63749	+	2.83622i	−0.220800	+	0.382436i
$56$	−0.598261	−	6.58737i	−0.0799459	−	0.880275i
$57$			0.957578i			0.126834i
$58$	1.94515	+	1.12303i	0.255411	+	0.147461i
$59$			0.767344i			0.0998997i	0.998752	+	0.0499499i	$0.0159062\pi$
$59$			0.767344i			0.0998997i	−0.998752	+	0.0499499i	$0.984094\pi$
$60$	0.481830	+	0.278185i	0.0622040	+	0.0359135i
$61$	6.05695	−	10.4909i	0.775513	−	1.34323i	−0.158993	−	0.987280i	$-0.550825\pi$
$61$	6.05695	−	10.4909i	0.775513	−	1.34323i	0.934506	−	0.355948i	$-0.115842\pi$
$62$	−2.57468	+	4.45947i	−0.326984	+	0.566354i
$63$	−1.11021	+	2.40155i	−0.139874	+	0.302566i
$64$	−5.96263			−0.745329
$65$	4.87787	−	2.04783i	0.605025	−	0.254003i
$66$	1.72142	−	2.98158i	0.211892	−	0.367007i
$67$	−8.35667	+	4.82473i	−1.02093	+	0.589434i	−0.914373	−	0.404872i	$-0.867316\pi$
$67$	−8.35667	+	4.82473i	−1.02093	+	0.589434i	−0.106557	+	0.994307i	$0.533983\pi$
$68$	0.956018			0.115934
$69$	1.32450	+	2.29410i	0.159451	+	0.276178i
$70$	−3.45069	−	4.89359i	−0.412436	−	0.584896i
$71$	−2.50519	+	1.44637i	−0.297311	+	0.171652i	−0.641234	−	0.767345i	$-0.721577\pi$
$71$	−2.50519	+	1.44637i	−0.297311	+	0.171652i	0.343923	+	0.938998i	$0.388244\pi$
$72$	2.16510	+	1.25002i	0.255159	+	0.147316i
$73$	11.3623	+	6.56004i	1.32986	+	0.767795i	0.985278	−	0.170962i	$-0.0546874\pi$
$73$	11.3623	+	6.56004i	1.32986	+	0.767795i	0.344582	+	0.938756i	$0.388021\pi$
$74$	11.4303			1.32874
$75$	2.84713			0.328759
$76$	0.314456	+	0.181551i	0.0360706	+	0.0208254i
$77$	−4.82621	+	3.40317i	−0.549998	+	0.387828i
$78$	−5.12786	+	2.15279i	−0.580616	+	0.243755i
$79$	−1.88401	−	3.26320i	−0.211968	−	0.367139i	0.740362	−	0.672208i	$-0.234654\pi$
$79$	−1.88401	−	3.26320i	−0.211968	−	0.367139i	−0.952330	+	0.305069i	$0.901321\pi$
$80$	−5.86371	+	3.38541i	−0.655583	+	0.378501i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	3.13913	−	5.43712i	0.346658	−	0.600430i
$83$			3.89258i			0.427266i	0.976914	+	0.213633i	$0.0685296\pi$
$83$			3.89258i			0.427266i	−0.976914	+	0.213633i	$0.931470\pi$
$84$	0.578146	+	0.819898i	0.0630809	+	0.0894582i
$85$	−3.20369	+	1.84965i	−0.347489	+	0.200623i
$86$	8.04135	−	4.64268i	0.867121	−	0.500633i
$87$	1.45616			0.156116
$88$	2.79009	+	4.83258i	0.297425	+	0.515155i
$89$			10.1478i			1.07567i	0.843051	+	0.537834i	$0.180757\pi$
$89$			10.1478i			1.07567i	−0.843051	+	0.537834i	$0.819243\pi$
$90$	2.26320			0.238562
$91$	9.53336	+	0.339072i	0.999368	+	0.0355444i
$92$	1.00447			0.104723
$93$			3.33840i			0.346176i
$94$	−8.06417	−	13.9676i	−0.831756	−	1.44064i
$95$	−1.40502			−0.144152
$96$	1.83403	−	1.05888i	0.187185	−	0.108071i
$97$	−5.44296	+	3.14250i	−0.552649	+	0.319072i	−0.750190	−	0.661223i	$-0.770038\pi$
$97$	−5.44296	+	3.14250i	−0.552649	+	0.319072i	0.197541	+	0.980295i	$0.436705\pi$
$98$	−1.94515	−	10.6206i	−0.196490	−	1.07284i
$99$		−	2.23204i		−	0.224328i
$100$	0.539800	−	0.934961i	0.0539800	−	0.0934961i
$101$	−1.30339	−	2.25754i	−0.129692	−	0.224634i	0.793865	−	0.608094i	$-0.208066\pi$
$101$	−1.30339	−	2.25754i	−0.129692	−	0.224634i	−0.923557	+	0.383460i	$0.874732\pi$
$102$	3.36788	−	1.94445i	0.333470	−	0.192529i
$103$	−6.25199	−	10.8288i	−0.616027	−	1.06699i	−0.990203	−	0.139633i	$-0.955408\pi$
$103$	−6.25199	−	10.8288i	−0.616027	−	1.06699i	0.374176	−	0.927358i	$-0.377926\pi$
$104$	1.13386	−	8.94243i	0.111184	−	0.876877i
$105$	−3.52370	−	1.62898i	−0.343878	−	0.158972i
$106$	−4.65963	−	2.69024i	−0.452583	−	0.261299i
$107$	−18.2516			−1.76445			−0.882227	−	0.470825i	$-0.843956\pi$
$107$	−18.2516			−1.76445			−0.882227	+	0.470825i	$0.843956\pi$
$108$	−0.379188			−0.0364874
$109$	−1.37903	−	0.796181i	−0.132087	−	0.0762603i	0.432501	−	0.901634i	$-0.357631\pi$
$109$	−1.37903	−	0.796181i	−0.132087	−	0.0762603i	−0.564587	+	0.825373i	$0.690965\pi$
$110$	4.37477	+	2.52577i	0.417118	+	0.240823i
$111$	6.41759	−	3.70520i	0.609131	−	0.351682i
$112$	−12.1590	+	1.10427i	−1.14892	+	0.104344i
$113$	10.1371	+	17.5580i	0.953617	+	1.65171i	0.737502	+	0.675345i	$0.236005\pi$
$113$	10.1371	+	17.5580i	0.953617	+	1.65171i	0.216115	+	0.976368i	$0.430661\pi$
$114$	1.47703			0.138336
$115$	−3.36606	+	1.94339i	−0.313886	+	0.181222i
$116$	0.276079	−	0.478182i	0.0256333	−	0.0443981i
$117$	−2.18123	+	2.87093i	−0.201655	+	0.265417i
$118$	1.18360			0.108959
$119$	−6.64319	+	0.603330i	−0.608980	+	0.0553072i
$120$	−1.83411	+	3.17677i	−0.167431	+	0.289998i
$121$	−3.00900	+	5.21175i	−0.273546	+	0.473795i
$122$	−16.1819	−	9.34261i	−1.46504	−	0.845840i
$123$		−	4.07028i		−	0.367005i
$124$	1.09629	+	0.632941i	0.0984494	+	0.0568398i
$125$			11.5138i			1.02983i
$126$	3.70429	+	1.71246i	0.330005	+	0.152558i
$127$	2.15084	−	3.72537i	0.190856	−	0.330573i	−0.754678	−	0.656095i	$-0.772207\pi$
$127$	2.15084	−	3.72537i	0.190856	−	0.330573i	0.945534	+	0.325523i	$0.105540\pi$
$128$			13.4326i			1.18729i
$129$	3.00991	−	5.21332i	0.265008	−	0.459008i
$130$	−3.15871	−	7.52393i	−0.277037	−	0.659892i
$131$	7.41308	+	12.8398i	0.647684	+	1.12182i	0.983675	+	0.179957i	$0.0575957\pi$
$131$	7.41308	+	12.8398i	0.647684	+	1.12182i	−0.335990	+	0.941865i	$0.609071\pi$
$132$	−0.732971	−	0.423181i	−0.0637970	−	0.0368332i
$133$	−2.29967	−	1.06312i	−0.199407	−	0.0921839i
$134$	7.44196	+	12.8898i	0.642887	+	1.11351i
$135$	1.27069	−	0.733632i	0.109363	−	0.0631410i
$136$			6.30316i			0.540492i
$137$		−	5.17843i		−	0.442423i	−0.975226	−	0.221211i	$-0.928999\pi$
$137$		−	5.17843i		−	0.442423i	0.975226	−	0.221211i	$-0.0710011\pi$
$138$	3.53857	−	2.04299i	0.301223	−	0.173911i
$139$	−10.3510	−	17.9284i	−0.877959	−	1.52067i	−0.853577	−	0.520966i	$-0.825572\pi$
$139$	−10.3510	−	17.9284i	−0.877959	−	1.52067i	−0.0243815	−	0.999703i	$-0.507762\pi$
$140$	−1.20301	+	0.848293i	−0.101673	+	0.0716938i
$141$	−9.05536	−	5.22812i	−0.762599	−	0.440287i
$142$	2.23097	+	3.86415i	0.187219	+	0.324272i
$143$	−7.42033	+	3.11521i	−0.620519	+	0.260507i
$144$	2.30730	−	3.99635i	0.192275	−	0.333030i
$145$			2.13657i			0.177432i
$146$	10.1186	−	17.5259i	0.837422	−	1.45046i
$147$	−4.53485	−	5.33246i	−0.374028	−	0.439814i
$148$		−	2.80994i		−	0.230975i
$149$	−15.2801	−	8.82198i	−1.25180	−	0.722725i	−0.280331	−	0.959904i	$-0.590444\pi$
$149$	−15.2801	−	8.82198i	−1.25180	−	0.722725i	−0.971466	+	0.237178i	$0.923777\pi$
$150$		−	4.39160i		−	0.358572i
$151$	13.1219	+	7.57592i	1.06784	+	0.616520i	0.927591	−	0.373596i	$-0.121875\pi$
$151$	13.1219	+	7.57592i	1.06784	+	0.616520i	0.140252	+	0.990116i	$0.455209\pi$
$152$	−1.19699	+	2.07325i	−0.0970889	+	0.168163i
$153$	1.26061	−	2.18344i	0.101914	−	0.176521i
$154$	5.24927	+	7.44425i	0.422998	+	0.599875i
$155$	−4.89832			−0.393442
$156$	0.529226	+	1.26060i	0.0423720	+	0.100929i
$157$	8.38350	−	14.5206i	0.669076	−	1.15887i	−0.309087	−	0.951034i	$-0.600023\pi$
$157$	8.38350	−	14.5206i	0.669076	−	1.15887i	0.978163	−	0.207840i	$-0.0666433\pi$
$158$	−5.03337	+	2.90602i	−0.400433	+	0.231190i
$159$	−3.48824			−0.276635
$160$	1.55365	+	2.69100i	0.122827	+	0.212743i
$161$	−6.97988	+	0.633907i	−0.550091	+	0.0499589i
$162$	−1.33581	+	0.771231i	−0.104951	+	0.0605936i
$163$	−13.9910	−	8.07769i	−1.09586	−	0.632693i	−0.160727	−	0.986999i	$-0.551384\pi$
$163$	−13.9910	−	8.07769i	−1.09586	−	0.632693i	−0.935130	+	0.354306i	$0.884717\pi$
$164$	−1.33663	−	0.771701i	−0.104373	−	0.0602597i
$165$	3.27499			0.254958
$166$	6.00415			0.466012
$167$	−17.1116	−	9.87941i	−1.32414	−	0.764492i	−0.339752	−	0.940515i	$-0.610343\pi$
$167$	−17.1116	−	9.87941i	−1.32414	−	0.764492i	−0.984386	+	0.176023i	$0.943677\pi$
$168$	−5.40570	+	3.81180i	−0.417059	+	0.294086i
$169$	12.5886	+	3.24453i	0.968354	+	0.249579i
$170$	2.85302	+	4.94157i	0.218816	+	0.379001i
$171$	0.829287	−	0.478789i	0.0634172	−	0.0366139i
$172$	−1.14132	−	1.97683i	−0.0870251	−	0.150732i
$173$	−0.817014	+	1.41511i	−0.0621164	+	0.107589i	−0.895411	−	0.445240i	$-0.853118\pi$
$173$	−0.817014	+	1.41511i	−0.0621164	+	0.107589i	0.833295	+	0.552829i	$0.186452\pi$
$174$		−	2.24607i		−	0.170274i
$175$	−3.16093	+	6.83753i	−0.238944	+	0.516868i
$176$	8.92001	−	5.14997i	0.672371	−	0.388194i
$177$	0.664540	−	0.383672i	0.0499499	−	0.0288386i
$178$	15.6526			1.17322
$179$	−8.73157	−	15.1235i	−0.652628	−	1.13038i	−0.982483	−	0.186353i	$-0.940333\pi$
$179$	−8.73157	−	15.1235i	−0.652628	−	1.13038i	0.329855	−	0.944032i	$-0.393000\pi$
$180$		−	0.556369i		−	0.0414693i
$181$	−0.848669			−0.0630811			−0.0315405	−	0.999502i	$-0.510041\pi$
$181$	−0.848669			−0.0630811			−0.0315405	+	0.999502i	$0.510041\pi$
$182$	0.523005	−	14.7048i	0.0387677	−	1.09000i
$183$	−12.1139			−0.895485
$184$			6.62261i			0.488225i
$185$	5.43651	+	9.41631i	0.399700	+	0.692301i
$186$	5.14935			0.377569
$187$	4.87353	−	2.81373i	0.356388	−	0.205761i
$188$	−3.43369	+	1.98244i	−0.250427	+	0.144584i
$189$	2.63491	−	0.239300i	0.191661	−	0.0174065i
$190$			2.16719i			0.157225i
$191$	13.6803	−	23.6950i	0.989875	−	1.71451i	0.372010	−	0.928229i	$-0.378669\pi$
$191$	13.6803	−	23.6950i	0.989875	−	1.71451i	0.617865	−	0.786284i	$-0.287998\pi$
$192$	2.98132	+	5.16379i	0.215158	+	0.372665i
$193$	10.2145	−	5.89736i	0.735258	−	0.424501i	−0.0850849	−	0.996374i	$-0.527116\pi$
$193$	10.2145	−	5.89736i	0.735258	−	0.424501i	0.820342	+	0.571873i	$0.193783\pi$
$194$	4.84718	+	8.39556i	0.348007	+	0.602766i
$195$	−4.21241	−	3.20044i	−0.301657	−	0.229188i
$196$	−2.61089	+	0.478182i	−0.186492	+	0.0341559i
$197$	7.28644	+	4.20683i	0.519137	+	0.299724i	0.736582	−	0.676349i	$-0.236439\pi$
$197$	7.28644	+	4.20683i	0.519137	+	0.299724i	−0.217444	+	0.976073i	$0.569772\pi$
$198$	−3.44283			−0.244671
$199$	−5.06886			−0.359322			−0.179661	−	0.983729i	$-0.557500\pi$
$199$	−5.06886			−0.359322			−0.179661	+	0.983729i	$0.557500\pi$
$200$	6.16433	+	3.55898i	0.435884	+	0.251658i
$201$	8.35667	+	4.82473i	0.589434	+	0.340310i
$202$	−3.48217	+	2.01043i	−0.245005	+	0.141454i
$203$	−1.61664	+	3.49703i	−0.113466	+	0.245443i
$204$	−0.478009	−	0.827936i	−0.0334673	−	0.0579671i
$205$	5.97218			0.417115
$206$	−16.7030	+	9.64346i	−1.16375	+	0.671892i
$207$	1.32450	−	2.29410i	0.0920592	−	0.159451i
$208$	−16.5060	−	2.09289i	−1.14448	−	0.145116i
$209$	2.13735			0.147844
$210$	−2.51263	+	5.43518i	−0.173388	+	0.375063i
$211$	10.2926	−	17.8273i	0.708570	−	1.22728i	−0.256817	−	0.966460i	$-0.582674\pi$
$211$	10.2926	−	17.8273i	0.708570	−	1.22728i	0.965388	−	0.260820i	$-0.0839928\pi$
$212$	−0.661349	+	1.14549i	−0.0454217	+	0.0786726i
$213$	2.50519	+	1.44637i	0.171652	+	0.0991036i
$214$			28.1525i			1.92446i
$215$	7.64932	+	4.41634i	0.521680	+	0.301192i
$216$		−	2.50004i		−	0.170106i
$217$	−8.01732	−	3.70634i	−0.544251	−	0.251603i
$218$	−1.22808	+	2.12709i	−0.0831760	+	0.144065i
$219$		−	13.1201i		−	0.886573i
$220$	0.620919	−	1.07546i	0.0418623	−	0.0725077i
$221$	−9.01820	−	1.14347i	−0.606630	−	0.0769180i
$222$	−5.71513	−	9.89889i	−0.383574	−	0.664370i
$223$	7.09390	+	4.09566i	0.475042	+	0.274266i	0.718348	−	0.695684i	$-0.244898\pi$
$223$	7.09390	+	4.09566i	0.475042	+	0.274266i	−0.243306	+	0.969950i	$0.578232\pi$
$224$	0.506779	+	5.58008i	0.0338606	+	0.372835i
$225$	−1.42357	−	2.46569i	−0.0949045	−	0.164379i
$226$	27.0825	−	15.6361i	1.80150	−	1.04010i
$227$			22.8768i			1.51839i	0.650865	+	0.759193i	$0.274406\pi$
$227$			22.8768i			1.51839i	−0.650865	+	0.759193i	$0.725594\pi$
$228$		−	0.363102i		−	0.0240470i
$229$	−12.3924	+	7.15476i	−0.818913	+	0.472800i	−0.850041	−	0.526716i	$-0.823423\pi$
$229$	−12.3924	+	7.15476i	−0.818913	+	0.472800i	0.0311285	+	0.999515i	$0.490090\pi$
$230$	2.99761	+	5.19201i	0.197657	+	0.342351i
$231$	5.36034	+	2.47804i	0.352685	+	0.163043i
$232$	3.15272	+	1.82023i	0.206986	+	0.119504i
$233$	5.03403	+	8.71920i	0.329790	+	0.571213i	0.982470	−	0.186420i	$-0.0596886\pi$
$233$	5.03403	+	8.71920i	0.329790	+	0.571213i	−0.652680	+	0.757634i	$0.726355\pi$
$234$	4.42830	+	3.36447i	0.289487	+	0.219942i
$235$	7.67103	−	13.2866i	0.500403	−	0.866723i
$236$		−	0.290968i		−	0.0189404i
$237$	−1.88401	+	3.26320i	−0.122380	+	0.211968i
$238$	0.930613	+	10.2469i	0.0603227	+	0.664206i
$239$			27.8817i			1.80351i	0.432242	+	0.901757i	$0.357722\pi$
$239$			27.8817i			1.80351i	−0.432242	+	0.901757i	$0.642278\pi$
$240$	5.86371	+	3.38541i	0.378501	+	0.218528i
$241$			12.1304i			0.781390i	0.920520	+	0.390695i	$0.127765\pi$
$241$			12.1304i			0.781390i	−0.920520	+	0.390695i	$0.872235\pi$
$242$	8.03892	+	4.64127i	0.516762	+	0.298352i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−2.29672	+	3.97804i	−0.147033	+	0.254668i
$245$	7.82413	−	6.65383i	0.499865	−	0.425098i
$246$	−6.27825			−0.400287
$247$	−2.74914	−	2.08870i	−0.174924	−	0.132901i
$248$	−4.17307	+	7.22796i	−0.264990	+	0.458976i
$249$	3.37107	−	1.94629i	0.213633	−	0.123341i
$250$	17.7596			1.12322
$251$	−5.86315	−	10.1553i	−0.370079	−	0.640995i	0.619499	−	0.784998i	$-0.287336\pi$
$251$	−5.86315	−	10.1553i	−0.370079	−	0.640995i	−0.989577	+	0.144003i	$0.954003\pi$
$252$	0.420980	−	0.910638i	0.0265192	−	0.0573648i
$253$	5.12052	−	2.95634i	0.321925	−	0.185863i
$254$	−5.74624	−	3.31759i	−0.360551	−	0.208164i
$255$	3.20369	+	1.84965i	0.200623	+	0.115830i
$256$	8.79407			0.549629
$257$	−22.4611			−1.40108			−0.700541	−	0.713612i	$-0.747058\pi$
$257$	−22.4611			−1.40108			−0.700541	+	0.713612i	$0.747058\pi$
$258$	−8.04135	−	4.64268i	−0.500633	−	0.289040i
$259$	1.77331	+	19.5257i	0.110188	+	1.21327i
$260$	−1.84963	+	0.776515i	−0.114709	+	0.0481574i
$261$	−0.728078	−	1.26107i	−0.0450669	−	0.0780582i
$262$	19.8050	−	11.4344i	1.22355	−	0.706420i
$263$	7.07387	+	12.2523i	0.436194	+	0.755510i	0.997392	−	0.0721716i	$-0.0229929\pi$
$263$	7.07387	+	12.2523i	0.436194	+	0.755510i	−0.561199	+	0.827681i	$0.689660\pi$
$264$	2.79009	−	4.83258i	0.171718	−	0.297425i
$265$		−	5.11817i		−	0.314406i
$266$	−1.63982	+	3.54715i	−0.100544	+	0.217490i
$267$	8.78828	−	5.07392i	0.537834	−	0.310519i
$268$	3.16875	−	1.82948i	0.193562	−	0.111753i
$269$	12.7409			0.776829			0.388415	−	0.921485i	$-0.373023\pi$
$269$	12.7409			0.776829			0.388415	+	0.921485i	$0.373023\pi$
$270$	−1.13160	−	1.95999i	−0.0688670	−	0.119281i
$271$		−	3.75688i		−	0.228214i	−0.993468	−	0.114107i	$-0.963599\pi$
$271$		−	3.75688i		−	0.228214i	0.993468	−	0.114107i	$-0.0364007\pi$
$272$	11.6344			0.705440
$273$	−4.47304	−	8.42567i	−0.270721	−	0.509945i
$274$	−7.98752			−0.482544
$275$		−	6.35491i		−	0.383216i
$276$	−0.502235	−	0.869897i	−0.0302310	−	0.0523616i
$277$	4.92202			0.295736			0.147868	−	0.989007i	$-0.452759\pi$
$277$	4.92202			0.295736			0.147868	+	0.989007i	$0.452759\pi$
$278$	−27.6539	+	15.9660i	−1.65857	+	0.957577i
$279$	2.89114	−	1.66920i	0.173088	−	0.0999324i
$280$	−5.59291	−	7.93160i	−0.334240	−	0.474003i
$281$		−	21.9099i		−	1.30703i	−0.756912	−	0.653516i	$-0.773293\pi$
$281$		−	21.9099i		−	1.30703i	0.756912	−	0.653516i	$-0.226707\pi$
$282$	−8.06417	+	13.9676i	−0.480214	+	0.831756i
$283$	−15.2086	−	26.3420i	−0.904055	−	1.56587i	−0.822181	−	0.569227i	$-0.807243\pi$
$283$	−15.2086	−	26.3420i	−0.904055	−	1.56587i	−0.0818746	−	0.996643i	$-0.526091\pi$
$284$	0.949937	−	0.548446i	0.0563684	−	0.0325443i
$285$	0.702510	+	1.21678i	0.0416131	+	0.0720760i
$286$	4.80510	+	11.4456i	0.284131	+	0.676791i
$287$	9.77497	+	4.51888i	0.576998	+	0.266741i
$288$	−1.83403	−	1.05888i	−0.108071	−	0.0623949i
$289$	−10.6434			−0.626084
$290$	3.29557			0.193523
$291$	5.44296	+	3.14250i	0.319072	+	0.184216i
$292$	−4.30846	−	2.48749i	−0.252134	−	0.145569i
$293$	−9.06140	+	5.23160i	−0.529372	+	0.305633i	−0.740761	−	0.671769i	$-0.765535\pi$
$293$	−9.06140	+	5.23160i	−0.529372	+	0.305633i	0.211388	+	0.977402i	$0.432202\pi$
$294$	−8.22511	+	6.99484i	−0.479698	+	0.407947i
$295$	0.562949	+	0.975056i	0.0327761	+	0.0567699i
$296$	18.5263			1.07682
$297$	−1.93300	+	1.11602i	−0.112164	+	0.0647580i
$298$	−13.6076	+	23.5690i	−0.788266	+	1.36532i
$299$	−9.47525	−	1.20142i	−0.547968	−	0.0694800i
$300$	−1.07960			−0.0623307
$301$	9.17839	+	13.0163i	0.529034	+	0.750250i
$302$	11.6856	−	20.2400i	0.672429	−	1.16468i
$303$	−1.30339	+	2.25754i	−0.0748780	+	0.129692i
$304$	3.82682	+	2.20942i	0.219483	+	0.126719i
$305$		−	17.7743i		−	1.01775i
$306$	−3.36788	−	1.94445i	−0.192529	−	0.111157i
$307$			11.2995i			0.644896i	0.946587	+	0.322448i	$0.104506\pi$
$307$			11.2995i			0.644896i	−0.946587	+	0.322448i	$0.895494\pi$
$308$	1.83004	−	1.29044i	0.104276	−	0.0735298i
$309$	−6.25199	+	10.8288i	−0.355664	+	0.616027i
$310$			7.55547i			0.429122i
$311$	−3.38424	+	5.86168i	−0.191903	+	0.332385i	−0.945881	−	0.324514i	$-0.894799\pi$
$311$	−3.38424	+	5.86168i	−0.191903	+	0.332385i	0.753978	+	0.656900i	$0.228132\pi$
$312$	−8.31130	+	3.48926i	−0.470535	+	0.197540i
$313$	1.36847	+	2.37027i	0.0773507	+	0.133975i	0.902106	−	0.431514i	$-0.142021\pi$
$313$	1.36847	+	2.37027i	0.0773507	+	0.133975i	−0.824755	+	0.565490i	$0.808687\pi$
$314$	−22.3975	−	12.9312i	−1.26397	−	0.729751i
$315$	0.351117	+	3.86611i	0.0197832	+	0.217830i
$316$	0.714395	+	1.23737i	0.0401879	+	0.0696074i
$317$	−13.0303	+	7.52306i	−0.731856	+	0.422537i	−0.819101	−	0.573650i	$-0.805527\pi$
$317$	−13.0303	+	7.52306i	−0.731856	+	0.422537i	0.0872447	+	0.996187i	$0.472194\pi$
$318$			5.38047i			0.301722i
$319$		−	3.25020i		−	0.181976i
$320$	−7.57665	+	4.37438i	−0.423548	+	0.244535i
$321$	9.12582	+	15.8064i	0.509354	+	0.882227i
$322$	0.977778	+	10.7662i	0.0544894	+	0.599976i
$323$	2.09082	+	1.20713i	0.116336	+	0.0671668i
$324$	0.189594	+	0.328387i	0.0105330	+	0.0182437i
$325$	−6.21026	+	8.17392i	−0.344483	+	0.453408i
$326$	−12.4595	+	21.5805i	−0.690069	+	1.19523i
$327$			1.59236i			0.0880578i
$328$	5.08793	−	8.81256i	0.280934	−	0.486592i
$329$	22.6090	−	15.9426i	1.24647	−	0.878941i
$330$		−	5.05155i		−	0.278078i
$331$	4.99837	+	2.88581i	0.274735	+	0.158619i	0.631038	−	0.775752i	$-0.282629\pi$
$331$	4.99837	+	2.88581i	0.274735	+	0.158619i	−0.356302	+	0.934371i	$0.615963\pi$
$332$		−	1.47602i		−	0.0810071i
$333$	−6.41759	−	3.70520i	−0.351682	−	0.203044i
$334$	−15.2386	+	26.3941i	−0.833820	+	1.44422i
$335$	−7.07915	+	12.2615i	−0.386775	+	0.669915i
$336$	7.03584	+	9.97789i	0.383837	+	0.544338i
$337$	−26.5503			−1.44628			−0.723142	−	0.690699i	$-0.757303\pi$
$337$	−26.5503			−1.44628			−0.723142	+	0.690699i	$0.757303\pi$
$338$	5.00456	−	19.4174i	0.272212	−	1.05617i
$339$	10.1371	−	17.5580i	0.550571	−	0.953617i
$340$	1.21480	−	0.701366i	0.0658819	−	0.0380369i
$341$	7.45143			0.403518
$342$	−0.738514	−	1.27914i	−0.0399343	−	0.0691682i
$343$	17.8408	−	4.97049i	0.963313	−	0.268381i
$344$	13.0335	−	7.52491i	0.702720	−	0.405716i
$345$	3.36606	+	1.94339i	0.181222	+	0.104629i
$346$	2.18275	+	1.26021i	0.117345	+	0.0677494i
$347$	−11.9494			−0.641478			−0.320739	−	0.947168i	$-0.603931\pi$
$347$	−11.9494			−0.641478			−0.320739	+	0.947168i	$0.603931\pi$
$348$	−0.552158			−0.0295987
$349$	−30.8266	−	17.7977i	−1.65011	−	0.952692i	−0.977024	−	0.213127i	$-0.931635\pi$
$349$	−30.8266	−	17.7977i	−1.65011	−	0.952692i	−0.673086	−	0.739564i	$-0.735032\pi$
$350$	10.5466	+	4.87561i	0.563741	+	0.260612i
$351$	3.57691	+	0.453537i	0.190921	+	0.0242080i
$352$	−2.36345	−	4.09362i	−0.125972	−	0.218191i
$353$	28.4860	−	16.4464i	1.51615	−	0.875352i	0.516335	−	0.856387i	$-0.327296\pi$
$353$	28.4860	−	16.4464i	1.51615	−	0.875352i	0.999820	−	0.0189653i	$-0.00603721\pi$
$354$	−0.591800	−	1.02503i	−0.0314538	−	0.0544796i
$355$	−2.12221	+	3.67577i	−0.112635	+	0.195090i
$356$		−	3.84794i		−	0.203940i
$357$	3.84409	+	5.45151i	0.203451	+	0.288524i
$358$	−23.3274	+	13.4681i	−1.23289	+	0.711812i
$359$	9.62271	−	5.55567i	0.507867	−	0.293217i	−0.224089	−	0.974569i	$-0.571941\pi$
$359$	9.62271	−	5.55567i	0.507867	−	0.293217i	0.731956	+	0.681351i	$0.238607\pi$
$360$	3.66822			0.193332
$361$	−9.04152	−	15.6604i	−0.475870	−	0.824230i
$362$			1.30904i			0.0688016i
$363$	6.01801			0.315864
$364$	−3.61494	−	0.128572i	−0.189474	−	0.00673900i
$365$	19.2506			1.00762
$366$			18.6852i			0.976692i
$367$	4.16652	+	7.21663i	0.217491	+	0.376705i	0.954040	−	0.299679i	$-0.0968795\pi$
$367$	4.16652	+	7.21663i	0.217491	+	0.376705i	−0.736550	+	0.676384i	$0.763546\pi$
$368$	12.2241			0.637224
$369$	−3.52497	+	2.03514i	−0.183502	+	0.105945i
$370$	14.5243	−	8.38560i	0.755082	−	0.435947i
$371$	3.87269	−	8.37716i	0.201060	−	0.434921i
$372$		−	1.26588i		−	0.0656329i
$373$	−6.37494	+	11.0417i	−0.330082	+	0.571718i	−0.982528	−	0.186117i	$-0.940410\pi$
$373$	−6.37494	+	11.0417i	−0.330082	+	0.571718i	0.652446	+	0.757835i	$0.273743\pi$
$374$	−4.34008	−	7.51723i	−0.224420	−	0.388707i
$375$	9.97126	−	5.75691i	0.514914	−	0.297286i
$376$	−13.0705	−	22.6388i	−0.674060	−	1.16751i
$377$	−3.17621	+	4.18052i	−0.163583	+	0.215308i
$378$	−0.369112	−	4.06424i	−0.0189851	−	0.209042i
$379$	−27.6640	−	15.9718i	−1.42100	−	0.820416i	−0.424617	−	0.905373i	$-0.639591\pi$
$379$	−27.6640	−	15.9718i	−1.42100	−	0.820416i	−0.996385	+	0.0849569i	$0.972925\pi$
$380$	0.532767			0.0273304
$381$	−4.30168			−0.220382
$382$	−36.5487	−	21.1014i	−1.86999	−	1.07964i
$383$	14.7030	+	8.48876i	0.751286	+	0.433755i	0.826158	−	0.563438i	$-0.190522\pi$
$383$	14.7030	+	8.48876i	0.751286	+	0.433755i	−0.0748724	+	0.997193i	$0.523855\pi$
$384$	11.6330	−	6.71632i	0.593644	−	0.342741i
$385$	−3.63594	+	7.86504i	−0.185304	+	0.400840i
$386$	−9.09645	−	15.7555i	−0.462997	−	0.801934i
$387$	−6.01983			−0.306005
$388$	2.06391	−	1.19160i	0.104779	−	0.0604942i
$389$	0.862649	−	1.49415i	0.0437381	−	0.0757565i	−0.843328	−	0.537400i	$-0.819407\pi$
$389$	0.862649	−	1.49415i	0.0437381	−	0.0757565i	0.887066	+	0.461643i	$0.152740\pi$
$390$	−4.93656	+	6.49748i	−0.249972	+	0.329013i
$391$	6.67873			0.337758
$392$	−3.15272	−	17.2140i	−0.159237	−	0.869436i
$393$	7.41308	−	12.8398i	0.373941	−	0.647684i
$394$	6.48887	−	11.2391i	0.326905	−	0.566215i
$395$	−4.78798	−	2.76434i	−0.240910	−	0.139089i
$396$			0.846362i			0.0425313i
$397$	2.69264	+	1.55459i	0.135140	+	0.0780229i	0.566046	−	0.824374i	$-0.308473\pi$
$397$	2.69264	+	1.55459i	0.135140	+	0.0780229i	−0.430906	+	0.902397i	$0.641806\pi$
$398$			7.81853i			0.391907i
$399$	0.229149	+	2.52313i	0.0114718	+	0.126314i
$400$	6.56918	−	11.3782i	0.328459	−	0.568908i
$401$		−	30.5453i		−	1.52536i	−0.646777	−	0.762679i	$-0.723883\pi$
$401$		−	30.5453i		−	1.52536i	0.646777	−	0.762679i	$-0.276117\pi$
$402$	7.44196	−	12.8898i	0.371171	−	0.642887i
$403$	−9.58431	−	7.28182i	−0.477428	−	0.362733i
$404$	0.494231	+	0.856034i	0.0245889	+	0.0425893i
$405$	−1.27069	−	0.733632i	−0.0631410	−	0.0364545i
$406$	5.39403	+	2.49361i	0.267701	+	0.123756i
$407$	−8.27014	−	14.3243i	−0.409936	−	0.710029i
$408$	5.45870	−	3.15158i	0.270246	−	0.156026i
$409$		−	7.34845i		−	0.363357i	−0.983358	−	0.181679i	$-0.941847\pi$
$409$		−	7.34845i		−	0.363357i	0.983358	−	0.181679i	$-0.0581531\pi$
$410$		−	9.21185i		−	0.454941i
$411$	−4.48465	+	2.58921i	−0.221211	+	0.127716i
$412$	2.37068	+	4.10614i	0.116795	+	0.202295i
$413$	0.183626	+	2.02188i	0.00903564	+	0.0994903i
$414$	−3.53857	−	2.04299i	−0.173911	−	0.100408i
$415$	2.85572	+	4.94625i	0.140182	+	0.242802i
$416$	−0.960479	+	7.57502i	−0.0470914	+	0.371396i
$417$	−10.3510	+	17.9284i	−0.506890	+	0.877959i
$418$		−	3.29678i		−	0.161251i
$419$	5.78350	−	10.0173i	0.282542	−	0.489378i	−0.689468	−	0.724316i	$-0.742156\pi$
$419$	5.78350	−	10.0173i	0.282542	−	0.489378i	0.972010	+	0.234938i	$0.0754889\pi$
$420$	1.33615	+	0.617689i	0.0651973	+	0.0301401i
$421$		−	7.57918i		−	0.369386i	−0.982796	−	0.184693i	$-0.940871\pi$
$421$		−	7.57918i		−	0.369386i	0.982796	−	0.184693i	$-0.0591291\pi$
$422$	−27.4979	−	15.8759i	−1.33858	−	0.772827i
$423$			10.4562i			0.508399i
$424$	−7.55238	−	4.36037i	−0.366776	−	0.211758i
$425$	3.58913	−	6.21656i	0.174098	−	0.301547i
$426$	2.23097	−	3.86415i	0.108091	−	0.187219i
$427$	13.4490	−	29.0921i	0.650843	−	1.40787i
$428$	6.92081			0.334530
$429$	6.40802	+	4.86859i	0.309382	+	0.235058i
$430$	6.81203	−	11.7988i	0.328505	−	0.568988i
$431$	−2.14410	+	1.23790i	−0.103278	+	0.0596274i	−0.550749	−	0.834671i	$-0.685658\pi$
$431$	−2.14410	+	1.23790i	−0.103278	+	0.0596274i	0.447471	+	0.894298i	$0.352325\pi$
$432$	−4.61459			−0.222020
$433$	0.513211	+	0.888908i	0.0246634	+	0.0427182i	0.878094	−	0.478489i	$-0.158815\pi$
$433$	0.513211	+	0.888908i	0.0246634	+	0.0427182i	−0.853430	+	0.521207i	$0.825482\pi$
$434$	−5.71688	+	12.3664i	−0.274419	+	0.593607i
$435$	1.85032	−	1.06828i	0.0887161	−	0.0512203i
$436$	0.522910	+	0.301902i	0.0250429	+	0.0144585i
$437$	2.19678	+	1.26831i	0.105086	+	0.0606717i
$438$	−20.2372			−0.966972
$439$	−9.07569			−0.433159			−0.216580	−	0.976265i	$-0.569490\pi$
$439$	−9.07569			−0.433159			−0.216580	+	0.976265i	$0.569490\pi$
$440$	7.09067	+	4.09380i	0.338035	+	0.195164i
$441$	−2.35062	+	6.59353i	−0.111934	+	0.313977i
$442$	−1.76376	+	13.9102i	−0.0838933	+	0.661642i
$443$	12.9878	+	22.4955i	0.617069	+	1.06879i	0.990018	+	0.140943i	$0.0450134\pi$
$443$	12.9878	+	22.4955i	0.617069	+	1.06879i	−0.372949	+	0.927852i	$0.621653\pi$
$444$	−2.43348	+	1.40497i	−0.115488	+	0.0666768i
$445$	7.44478	+	12.8947i	0.352916	+	0.611269i
$446$	6.31740	−	10.9421i	0.299138	−	0.518122i
$447$			17.6440i			0.834531i
$448$	−15.7110	+	1.42686i	−0.742274	+	0.0674128i
$449$	27.6762	−	15.9789i	1.30612	−	0.754089i	0.324674	−	0.945826i	$-0.394745\pi$
$449$	27.6762	−	15.9789i	1.30612	−	0.754089i	0.981446	+	0.191737i	$0.0614120\pi$
$450$	−3.80323	+	2.19580i	−0.179286	+	0.103511i
$451$	−9.08502			−0.427797
$452$	−3.84386	−	6.65777i	−0.180800	−	0.313155i
$453$		−	15.1518i		−	0.711896i
$454$	35.2866			1.65608
$455$	12.3627	−	6.56313i	0.579572	−	0.307684i
$456$	2.39398			0.112109
$457$			41.1453i			1.92470i	0.271817	+	0.962349i	$0.412376\pi$
$457$			41.1453i			1.92470i	−0.271817	+	0.962349i	$0.587624\pi$
$458$	11.0359	+	19.1148i	0.515675	+	0.893176i
$459$	−2.52122			−0.117681
$460$	1.27637	−	0.736912i	0.0595110	−	0.0343587i
$461$	5.19415	−	2.99884i	0.241916	−	0.139670i	−0.374141	−	0.927372i	$-0.622062\pi$
$461$	5.19415	−	2.99884i	0.241916	−	0.139670i	0.616057	+	0.787702i	$0.288729\pi$
$462$	3.82228	−	8.26812i	0.177828	−	0.384668i
$463$		−	27.1770i		−	1.26302i	−0.775367	−	0.631511i	$-0.782435\pi$
$463$		−	27.1770i		−	1.26302i	0.775367	−	0.631511i	$-0.217565\pi$
$464$	3.35979	−	5.81932i	0.155974	−	0.270155i
$465$	2.44916	+	4.24207i	0.113577	+	0.196721i
$466$	13.4490	−	7.76480i	0.623014	−	0.359697i
$467$	2.29607	+	3.97690i	0.106249	+	0.184029i	0.914248	−	0.405155i	$-0.132783\pi$
$467$	2.29607	+	3.97690i	0.106249	+	0.184029i	−0.807999	+	0.589184i	$0.799449\pi$
$468$	0.827097	−	1.08862i	0.0382326	−	0.0503216i
$469$	−20.8645	+	14.7125i	−0.963433	+	0.679359i
$470$	−20.4941	−	11.8323i	−0.945322	−	0.545782i
$471$	−16.7670			−0.772582
$472$	1.91839			0.0883011
$473$	−11.6363	−	6.71824i	−0.535039	−	0.308905i
$474$	5.03337	+	2.90602i	0.231190	+	0.133478i
$475$	2.36109	−	1.36318i	0.108334	−	0.0625469i
$476$	2.51902	−	0.228776i	0.115459	−	0.0104859i
$477$	1.74412	+	3.02090i	0.0798577	+	0.138318i
$478$	43.0064			1.96707
$479$	−7.37621	+	4.25866i	−0.337028	+	0.194583i	−0.658957	−	0.752181i	$-0.729002\pi$
$479$	−7.37621	+	4.25866i	−0.337028	+	0.194583i	0.321929	+	0.946764i	$0.395669\pi$
$480$	1.55365	−	2.69100i	0.0709142	−	0.122827i
$481$	−3.36089	+	26.5063i	−0.153243	+	1.20859i
$482$	18.7107			0.852250
$483$	4.03892	+	5.72780i	0.183777	+	0.260624i
$484$	1.14098	−	1.97623i	0.0518627	−	0.0898288i
$485$	−4.61087	+	7.98626i	−0.209369	+	0.362638i
$486$	1.33581	+	0.771231i	0.0605936	+	0.0349837i
$487$		−	6.53675i		−	0.296208i	−0.988972	−	0.148104i	$-0.952683\pi$
$487$		−	6.53675i		−	0.296208i	0.988972	−	0.148104i	$-0.0473171\pi$
$488$	−26.2278	−	15.1426i	−1.18728	−	0.685474i
$489$			16.1554i			0.730571i
$490$	−10.2633	−	12.0684i	−0.463648	−	0.545195i
$491$	−18.2580	+	31.6237i	−0.823970	+	1.42716i	0.0787336	+	0.996896i	$0.474912\pi$
$491$	−18.2580	+	31.6237i	−0.823970	+	1.42716i	−0.902704	+	0.430263i	$0.858421\pi$
$492$			1.54340i			0.0695820i
$493$	1.83565	−	3.17944i	0.0826734	−	0.143195i
$494$	−3.22174	+	4.24044i	−0.144953	+	0.190787i
$495$	−1.63749	−	2.83622i	−0.0735999	−	0.127479i
$496$	13.3414	+	7.70268i	0.599048	+	0.345860i
$497$	−6.25481	+	4.41054i	−0.280567	+	0.197840i
$498$	−3.00207	−	5.19974i	−0.134526	−	0.233006i
$499$	−19.5923	+	11.3116i	−0.877070	+	0.506377i	−0.869691	−	0.493596i	$-0.835682\pi$
$499$	−19.5923	+	11.3116i	−0.877070	+	0.506377i	−0.00737889	+	0.999973i	$0.502349\pi$
$500$		−	4.36591i		−	0.195249i
$501$			19.7588i			0.882759i
$502$	−15.6641	+	9.04368i	−0.699124	+	0.403639i
$503$	−6.05831	−	10.4933i	−0.270127	−	0.467873i	0.698767	−	0.715349i	$-0.253732\pi$
$503$	−6.05831	−	10.4933i	−0.270127	−	0.467873i	−0.968894	+	0.247476i	$0.920399\pi$
$504$	6.00396	+	2.77558i	0.267438	+	0.123634i
$505$	−3.31241	−	1.91242i	−0.147400	−	0.0851017i
$506$	−4.56004	−	7.89821i	−0.202718	−	0.351118i
$507$	−3.48446	−	12.5243i	−0.154750	−	0.556224i
$508$	−0.815574	+	1.41262i	−0.0361852	+	0.0626747i
$509$		−	18.6029i		−	0.824561i	−0.911057	−	0.412280i	$-0.864732\pi$
$509$		−	18.6029i		−	0.824561i	0.911057	−	0.412280i	$-0.135268\pi$
$510$	2.85302	−	4.94157i	0.126334	−	0.218816i
$511$	31.5085	+	14.5661i	1.39385	+	0.644366i
$512$			13.3008i			0.587816i
$513$	−0.829287	−	0.478789i	−0.0366139	−	0.0211391i
$514$			34.6453i			1.52814i
$515$	−15.8887	−	9.17333i	−0.700139	−	0.404225i
$516$	−1.14132	+	1.97683i	−0.0502440	+	0.0870251i
$517$	−11.6694	+	20.2119i	−0.513218	+	0.888919i
$518$	30.1177	−	2.73526i	1.32329	−	0.120181i
$519$	1.63403			0.0717258
$520$	−5.11967	−	12.1949i	−0.224512	−	0.534781i
$521$	2.14960	−	3.72321i	0.0941756	−	0.163117i	−0.815089	−	0.579336i	$-0.803312\pi$
$521$	2.14960	−	3.72321i	0.0941756	−	0.163117i	0.909264	+	0.416219i	$0.136645\pi$
$522$	−1.94515	+	1.12303i	−0.0851369	+	0.0491538i
$523$	6.23463			0.272622			0.136311	−	0.990666i	$-0.456475\pi$
$523$	6.23463			0.272622			0.136311	+	0.990666i	$0.456475\pi$
$524$	−2.81095	−	4.86872i	−0.122797	−	0.212691i
$525$	7.50194	−	0.681321i	0.327411	−	0.0297353i
$526$	18.8987	−	10.9112i	0.824023	−	0.475750i
$527$	7.28921	+	4.20843i	0.317523	+	0.183322i
$528$	−8.92001	−	5.14997i	−0.388194	−	0.224124i
$529$	−15.9828			−0.694904
$530$	−7.89458			−0.342918
$531$	−0.664540	−	0.383672i	−0.0288386	−	0.0166500i
$532$	0.872008	+	0.403121i	0.0378063	+	0.0174775i
$533$	11.6855	+	8.87822i	0.506154	+	0.384558i
$534$	−7.82632	−	13.5556i	−0.338678	−	0.586608i
$535$	−23.1922	+	13.3900i	−1.00268	+	0.578900i
$536$	12.0620	+	20.8920i	0.521000	+	0.902398i
$537$	−8.73157	+	15.1235i	−0.376795	+	0.652628i
$538$		−	19.6524i		−	0.847276i
$539$	−11.9022	+	10.1220i	−0.512666	+	0.435984i
$540$	−0.481830	+	0.278185i	−0.0207347	+	0.0119712i
$541$	−4.56161	+	2.63365i	−0.196119	+	0.113229i	−0.594844	−	0.803841i	$-0.702786\pi$
$541$	−4.56161	+	2.63365i	−0.196119	+	0.113229i	0.398725	+	0.917071i	$0.369453\pi$
$542$	−5.79485			−0.248910
$543$	0.424335	+	0.734969i	0.0182099	+	0.0315405i
$544$		−	5.33933i		−	0.228922i
$545$	−2.33642			−0.100081
$546$	−12.9963	+	6.89949i	−0.556189	+	0.295271i
$547$	3.35409			0.143411			0.0717053	−	0.997426i	$-0.477156\pi$
$547$	3.35409			0.143411			0.0717053	+	0.997426i	$0.477156\pi$
$548$			1.96360i			0.0838808i
$549$	6.05695	+	10.4909i	0.258504	+	0.447743i
$550$	−9.80221			−0.417968
$551$	1.20757	−	0.697192i	0.0514443	−	0.0297014i
$552$	5.73535	−	3.31131i	0.244113	−	0.140939i
$553$	−5.74508	−	8.14739i	−0.244306	−	0.346462i
$554$		−	7.59203i		−	0.322555i
$555$	5.43651	−	9.41631i	0.230767	−	0.399700i
$556$	3.92497	+	6.79825i	0.166456	+	0.288310i
$557$	−6.93267	+	4.00258i	−0.293747	+	0.169595i	−0.639630	−	0.768683i	$-0.720913\pi$
$557$	−6.93267	+	4.00258i	−0.293747	+	0.169595i	0.345884	+	0.938277i	$0.387579\pi$
$558$	−2.57468	−	4.45947i	−0.108995	−	0.188785i
$559$	8.40176	+	20.0127i	0.355357	+	0.846447i
$560$	−14.6402	+	10.3234i	−0.618661	+	0.436245i
$561$	−4.87353	−	2.81373i	−0.205761	−	0.118796i
$562$	−33.7951			−1.42556
$563$	−34.6065			−1.45849			−0.729246	−	0.684252i	$-0.760129\pi$
$563$	−34.6065			−1.45849			−0.729246	+	0.684252i	$0.760129\pi$
$564$	3.43369	+	1.98244i	0.144584	+	0.0834758i
$565$	25.7622	+	14.8738i	1.08382	+	0.625745i
$566$	−40.6315	+	23.4586i	−1.70787	+	0.986040i
$567$	−1.52469	−	2.16225i	−0.0640311	−	0.0908058i
$568$	3.61598	+	6.26306i	0.151723	+	0.262792i
$569$	−4.76640			−0.199818			−0.0999089	−	0.994997i	$-0.531855\pi$
$569$	−4.76640			−0.199818			−0.0999089	+	0.994997i	$0.531855\pi$
$570$	1.87684	−	1.08360i	0.0786123	−	0.0453868i
$571$	17.3388	−	30.0317i	0.725607	−	1.25679i	−0.233117	−	0.972449i	$-0.574893\pi$
$571$	17.3388	−	30.0317i	0.725607	−	1.25679i	0.958724	−	0.284339i	$-0.0917741\pi$
$572$	2.81370	−	1.18125i	0.117647	−	0.0493906i
$573$	−27.3607			−1.14301
$574$	6.97020	−	15.0775i	0.290930	−	0.629323i
$575$	3.77103	−	6.53162i	0.157263	−	0.272387i
$576$	2.98132	−	5.16379i	0.124222	−	0.215158i
$577$	33.2462	+	19.1947i	1.38406	+	0.799085i	0.992637	−	0.121128i	$-0.0386510\pi$
$577$	33.2462	+	19.1947i	1.38406	+	0.799085i	0.391419	+	0.920213i	$0.371984\pi$
$578$			16.4171i			0.682861i
$579$	−10.2145	−	5.89736i	−0.424501	−	0.245086i
$580$		−	0.810161i		−	0.0336401i
$581$	0.931495	+	10.2566i	0.0386449	+	0.425514i
$582$	4.84718	−	8.39556i	0.200922	−	0.348007i
$583$			7.78588i			0.322458i
$584$	16.4004	−	28.4063i	0.678652	−	1.17546i
$585$	−0.665459	+	5.24828i	−0.0275133	+	0.216990i
$586$	8.06954	+	13.9769i	0.333350	+	0.577379i
$587$	13.2140	+	7.62912i	0.545401	+	0.314887i	0.747265	−	0.664526i	$-0.231367\pi$
$587$	13.2140	+	7.62912i	0.545401	+	0.314887i	−0.201864	+	0.979414i	$0.564700\pi$
$588$	1.71956	+	2.02201i	0.0709136	+	0.0833861i
$589$	1.59839	+	2.76849i	0.0658605	+	0.114074i
$590$	1.50399	−	0.868327i	0.0619181	−	0.0357484i
$591$		−	8.41365i		−	0.346091i
$592$		−	34.1960i		−	1.40545i
$593$	36.2229	−	20.9133i	1.48750	−	0.858807i	0.487599	−	0.873068i	$-0.337873\pi$
$593$	36.2229	−	20.9133i	1.48750	−	0.858807i	0.999898	+	0.0142607i	$0.00453947\pi$
$594$	1.72142	+	2.98158i	0.0706306	+	0.122336i
$595$	−7.99880	+	5.64030i	−0.327919	+	0.231230i
$596$	5.79404	+	3.34519i	0.237333	+	0.137024i
$597$	2.53443	+	4.38977i	0.103727	+	0.179661i
$598$	−1.85315	+	14.6152i	−0.0757808	+	0.597660i
$599$	−21.7048	+	37.5937i	−0.886832	+	1.53604i	−0.0432328	+	0.999065i	$0.513766\pi$
$599$	−21.7048	+	37.5937i	−0.886832	+	1.53604i	−0.843599	+	0.536973i	$0.819568\pi$
$600$		−	7.11795i		−	0.290589i
$601$	−12.1988	+	21.1289i	−0.497599	+	0.861866i	−0.999996	−	0.00277068i	$-0.999118\pi$
$601$	−12.1988	+	21.1289i	−0.497599	+	0.861866i	0.502398	+	0.864637i	$0.332451\pi$
$602$	20.0772	−	14.1573i	0.818286	−	0.577009i
$603$		−	9.64946i		−	0.392956i
$604$	−4.97566	−	2.87270i	−0.202457	−	0.116889i
$605$			8.83001i			0.358991i
$606$	3.48217	+	2.01043i	0.141454	+	0.0816683i
$607$	−0.234017	+	0.405330i	−0.00949847	+	0.0164518i	−0.870736	−	0.491752i	$-0.836357\pi$
$607$	−0.234017	+	0.405330i	−0.00949847	+	0.0164518i	0.861237	+	0.508203i	$0.169690\pi$
$608$	1.01396	−	1.75623i	0.0411214	−	0.0712243i
$609$	3.83684	−	0.348459i	0.155477	−	0.0141203i
$610$	−27.4162			−1.11005
$611$	34.7614	−	14.5936i	1.40630	−	0.590393i
$612$	−0.478009	+	0.827936i	−0.0193224	+	0.0334673i
$613$	29.7884	−	17.1983i	1.20314	−	0.694635i	0.241890	−	0.970304i	$-0.422233\pi$
$613$	29.7884	−	17.1983i	1.20314	−	0.694635i	0.961253	+	0.275669i	$0.0888994\pi$
$614$	17.4290			0.703378
$615$	−2.98609	−	5.17206i	−0.120411	−	0.208557i
$616$	8.50807	+	12.0657i	0.342800	+	0.486142i
$617$	8.47087	−	4.89066i	0.341024	−	0.196890i	−0.319701	−	0.947519i	$-0.603582\pi$
$617$	8.47087	−	4.89066i	0.341024	−	0.196890i	0.660725	+	0.750628i	$0.270249\pi$
$618$	16.7030	+	9.64346i	0.671892	+	0.387917i
$619$	18.7382	+	10.8185i	0.753152	+	0.434833i	0.826832	−	0.562449i	$-0.190141\pi$
$619$	18.7382	+	10.8185i	0.753152	+	0.434833i	−0.0736794	+	0.997282i	$0.523474\pi$
$620$	1.85738			0.0745943
$621$	−2.64900			−0.106301
$622$	9.04142	+	5.22006i	0.362528	+	0.209305i
$623$	2.42838	+	26.7386i	0.0972910	+	1.07126i
$624$	6.44050	+	15.3411i	0.257826	+	0.614134i
$625$	1.32907	+	2.30202i	0.0531630	+	0.0920810i
$626$	3.65605	−	2.11082i	0.146125	−	0.0843653i
$627$	−1.06868	−	1.85100i	−0.0426788	−	0.0739218i
$628$	−3.17892	+	5.50606i	−0.126853	+	0.219716i
$629$		−	18.6833i		−	0.744951i
$630$	5.96332	−	0.541585i	0.237584	−	0.0215772i
$631$	−12.0447	+	6.95404i	−0.479494	+	0.276836i	−0.720206	−	0.693761i	$-0.755953\pi$
$631$	−12.0447	+	6.95404i	−0.479494	+	0.276836i	0.240712	+	0.970597i	$0.422619\pi$
$632$	−8.15814	+	4.71010i	−0.324513	+	0.187358i
$633$	−20.5852			−0.818186
$634$	11.6040	+	20.0988i	0.460855	+	0.798225i
$635$		−	6.31171i		−	0.250472i
$636$	1.32270			0.0524484
$637$	25.2007	−	1.38792i	0.998487	−	0.0549912i
$638$	−5.01330			−0.198479
$639$		−	2.89274i		−	0.114435i
$640$	9.85462	+	17.0687i	0.389538	+	0.674700i
$641$	−23.6700			−0.934908			−0.467454	−	0.884017i	$-0.654829\pi$
$641$	−23.6700			−0.934908			−0.467454	+	0.884017i	$0.654829\pi$
$642$	24.3807	−	14.0762i	0.962231	−	0.555545i
$643$	19.6315	−	11.3342i	0.774190	−	0.446979i	−0.0601776	−	0.998188i	$-0.519167\pi$
$643$	19.6315	−	11.3342i	0.774190	−	0.446979i	0.834367	+	0.551209i	$0.185833\pi$
$644$	2.64669	−	0.240370i	0.104294	−	0.00947191i
$645$		−	8.83268i		−	0.347786i
$646$	1.86196	−	3.22501i	0.0732578	−	0.126886i
$647$	11.7855	+	20.4131i	0.463336	+	0.802521i	0.999125	−	0.0418310i	$-0.0133191\pi$
$647$	11.7855	+	20.4131i	0.463336	+	0.802521i	−0.535789	+	0.844352i	$0.679986\pi$
$648$	−2.16510	+	1.25002i	−0.0850531	+	0.0491054i
$649$	−0.856371	−	1.48328i	−0.0336155	−	0.0582237i
$650$	12.6080	+	9.57909i	0.494525	+	0.375723i
$651$	0.798881	+	8.79637i	0.0313106	+	0.344757i
$652$	5.30521	+	3.06296i	0.207768	+	0.119955i
$653$	8.91076			0.348705			0.174353	−	0.984683i	$-0.444217\pi$
$653$	8.91076			0.348705			0.174353	+	0.984683i	$0.444217\pi$
$654$	2.45616			0.0960433
$655$	18.8394	+	10.8770i	0.736118	+	0.424998i
$656$	−16.2663	−	9.39134i	−0.635092	−	0.366670i
$657$	−11.3623	+	6.56004i	−0.443286	+	0.255932i
$658$	−24.5908	−	34.8734i	−0.958648	−	1.35951i
$659$	−4.92457	−	8.52960i	−0.191834	−	0.332266i	0.754024	−	0.656847i	$-0.228110\pi$
$659$	−4.92457	−	8.52960i	−0.191834	−	0.332266i	−0.945858	+	0.324581i	$0.894777\pi$
$660$	−1.24184			−0.0483385
$661$	−0.385266	+	0.222433i	−0.0149851	+	0.00865166i	−0.507474	−	0.861667i	$-0.669421\pi$
$661$	−0.385266	+	0.222433i	−0.0149851	+	0.00865166i	0.492489	+	0.870319i	$0.336087\pi$
$662$	4.45125	−	7.70980i	0.173003	−	0.299650i
$663$	3.51883	+	8.38172i	0.136660	+	0.325519i
$664$	9.73159			0.377659
$665$	−3.70210	+	0.336222i	−0.143561	+	0.0130381i
$666$	−5.71513	+	9.89889i	−0.221457	+	0.383574i
$667$	1.92868	−	3.34057i	0.0746788	−	0.129348i
$668$	6.48853	+	3.74616i	0.251049	+	0.144943i
$669$		−	8.19133i		−	0.316695i
$670$	18.9128	+	10.9193i	0.730666	+	0.421850i
$671$			27.0387i			1.04382i
$672$	4.57910	−	3.22892i	0.176643	−	0.124558i
$673$	2.77793	−	4.81152i	0.107081	−	0.185470i	−0.807505	−	0.589860i	$-0.799183\pi$
$673$	2.77793	−	4.81152i	0.107081	−	0.185470i	0.914587	+	0.404390i	$0.132516\pi$
$674$			40.9528i			1.57744i
$675$	−1.42357	+	2.46569i	−0.0547931	+	0.0949045i
$676$	−4.77345	−	1.23029i	−0.183594	−	0.0473187i
$677$	4.65253	+	8.05842i	0.178811	+	0.309710i	0.941474	−	0.337087i	$-0.109442\pi$
$677$	4.65253	+	8.05842i	0.178811	+	0.309710i	−0.762662	+	0.646797i	$0.776108\pi$
$678$	−27.0825	−	15.6361i	−1.04010	−	0.600500i
$679$	−13.5897	+	9.58269i	−0.521525	+	0.367750i
$680$	4.62420	+	8.00935i	0.177330	+	0.307145i
$681$	19.8119	−	11.4384i	0.759193	−	0.438321i
$682$		−	11.4936i		−	0.440111i
$683$		−	21.8103i		−	0.834549i	−0.908780	−	0.417275i	$-0.862985\pi$
$683$		−	21.8103i		−	0.834549i	0.908780	−	0.417275i	$-0.137015\pi$
$684$	−0.314456	+	0.181551i	−0.0120235	+	0.00694178i
$685$	−3.79906	−	6.58017i	−0.145155	−	0.251415i
$686$	−7.66680	−	27.5188i	−0.292720	−	1.05067i
$687$	12.3924	+	7.15476i	0.472800	+	0.272971i
$688$	−13.8895	−	24.0574i	−0.529533	−	0.917178i
$689$	7.60865	−	10.0145i	0.289866	−	0.381521i
$690$	2.99761	−	5.19201i	0.114117	−	0.197657i
$691$			8.12516i			0.309096i	0.987985	+	0.154548i	$0.0493921\pi$
$691$			8.12516i			0.309096i	−0.987985	+	0.154548i	$0.950608\pi$
$692$	0.309802	−	0.536593i	0.0117769	−	0.0203982i
$693$	−0.534127	−	5.88121i	−0.0202898	−	0.223409i
$694$			18.4315i			0.699650i
$695$	−26.3057	−	15.1876i	−0.997834	−	0.576100i
$696$		−	3.64045i		−	0.137991i
$697$	−8.88723	−	5.13104i	−0.336628	−	0.194352i
$698$	−27.4523	+	47.5489i	−1.03909	+	1.79975i
$699$	5.03403	−	8.71920i	0.190404	−	0.329790i
$700$	1.19859	−	2.59271i	0.0453023	−	0.0979952i
$701$	−28.5599			−1.07869			−0.539347	−	0.842084i	$-0.681329\pi$
$701$	−28.5599			−1.07869			−0.539347	+	0.842084i	$0.681329\pi$
$702$	0.699564	−	5.51725i	0.0264033	−	0.208235i
$703$	3.54802	−	6.14535i	0.133816	−	0.231776i
$704$	11.5258	−	6.65441i	0.434394	−	0.250798i
$705$	−15.3421			−0.577815
$706$	−25.3679	−	43.9385i	−0.954734	−	1.65365i
$707$	−3.97455	−	5.63651i	−0.149478	−	0.211983i
$708$	−0.251986	+	0.145484i	−0.00947020	+	0.00546762i
$709$	30.8663	+	17.8207i	1.15921	+	0.669269i	0.951114	−	0.308840i	$-0.0999408\pi$
$709$	30.8663	+	17.8207i	1.15921	+	0.669269i	0.208094	+	0.978109i	$0.433274\pi$
$710$	5.66973	+	3.27342i	0.212781	+	0.122849i
$711$	3.76802			0.141312
$712$	25.3700			0.950780
$713$	7.65864	+	4.42172i	0.286818	+	0.165595i
$714$	8.40874	−	5.92937i	0.314689	−	0.221901i
$715$	−7.14351	+	9.40226i	−0.267152	+	0.351625i
$716$	3.31091	+	5.73466i	0.123734	+	0.214314i
$717$	24.1462	−	13.9408i	0.901757	−	0.520630i
$718$	−8.56941	−	14.8427i	−0.319808	−	0.553923i
$719$	−7.54188	+	13.0629i	−0.281265	+	0.487165i	−0.971696	−	0.236233i	$-0.924087\pi$
$719$	−7.54188	+	13.0629i	−0.281265	+	0.487165i	0.690432	+	0.723397i	$0.257421\pi$
$720$		−	6.77083i		−	0.252334i
$721$	−19.0648	−	27.0367i	−0.710009	−	1.00690i
$722$	−24.1555	+	13.9462i	−0.898976	+	0.519024i
$723$	10.5053	−	6.06521i	0.390695	−	0.225568i
$724$	0.321805			0.0119598
$725$	−2.07294	−	3.59043i	−0.0769870	−	0.133345i
$726$		−	9.28255i		−	0.344508i
$727$	40.1445			1.48888			0.744439	−	0.667690i	$-0.232717\pi$
$727$	40.1445			1.48888			0.744439	+	0.667690i	$0.232717\pi$
$728$	0.847692	−	23.8338i	0.0314176	−	0.883339i
$729$	1.00000			0.0370370
$730$		−	29.6934i		−	1.09900i
$731$	−7.58867	−	13.1440i	−0.280677	−	0.486147i
$732$	4.59345			0.169779
$733$	24.3833	−	14.0777i	0.900619	−	0.519973i	0.0232181	−	0.999730i	$-0.492609\pi$
$733$	24.3833	−	14.0777i	0.900619	−	0.519973i	0.877401	+	0.479758i	$0.159275\pi$
$734$	11.1314	−	6.42670i	0.410866	−	0.237214i
$735$	−9.67445	−	3.44898i	−0.356847	−	0.127217i
$736$		−	5.60993i		−	0.206785i
$737$	10.7690	−	18.6524i	0.396680	−	0.687070i
$738$	3.13913	+	5.43712i	0.115553	+	0.200143i
$739$	20.2757	−	11.7062i	0.745855	−	0.430619i	−0.0783395	−	0.996927i	$-0.524962\pi$
$739$	20.2757	−	11.7062i	0.745855	−	0.430619i	0.824194	+	0.566307i	$0.191628\pi$
$740$	−2.06146	−	3.57055i	−0.0757808	−	0.131256i
$741$	−0.434297	+	3.42517i	−0.0159543	+	0.125827i
$742$	−12.9215	−	5.97347i	−0.474362	−	0.219293i
$743$	27.8733	+	16.0926i	1.02257	+	0.590382i	0.914848	−	0.403799i	$-0.132311\pi$
$743$	27.8733	+	16.0926i	1.02257	+	0.590382i	0.107723	+	0.994181i	$0.465644\pi$
$744$	8.34613			0.305984
$745$	−25.8884			−0.948476
$746$	17.0314	+	9.83310i	0.623565	+	0.360015i
$747$	−3.37107	−	1.94629i	−0.123341	−	0.0712109i
$748$	−1.84798	+	1.06693i	−0.0675690	+	0.0390110i
$749$	−48.0914	+	4.36763i	−1.75722	+	0.159590i
$750$	−8.87982	−	15.3803i	−0.324245	−	0.561609i
$751$	17.2533			0.629583			0.314791	−	0.949161i	$-0.398065\pi$
$751$	17.2533			0.629583			0.314791	+	0.949161i	$0.398065\pi$
$752$	−41.7868	+	24.1256i	−1.52381	+	0.879771i
$753$	−5.86315	+	10.1553i	−0.213665	+	0.370079i
$754$	6.44830	+	4.89919i	0.234833	+	0.178418i
$755$	22.2318			0.809097
$756$	−0.999126	+	0.0907399i	−0.0363379	+	0.00330018i
$757$	0.137120	−	0.237499i	0.00498371	−	0.00863204i	−0.863523	−	0.504310i	$-0.831747\pi$
$757$	0.137120	−	0.237499i	0.00498371	−	0.00863204i	0.868507	+	0.495678i	$0.165080\pi$
$758$	−24.6359	+	42.6706i	−0.894816	+	1.54987i
$759$	−5.12052	−	2.95634i	−0.185863	−	0.107308i
$760$			3.51261i			0.127416i
$761$	−0.726332	−	0.419348i	−0.0263295	−	0.0152013i	0.486777	−	0.873526i	$-0.338172\pi$
$761$	−0.726332	−	0.419348i	−0.0263295	−	0.0152013i	−0.513107	+	0.858325i	$0.671506\pi$
$762$			6.63518i			0.240367i
$763$	−3.82413	−	1.76786i	−0.138443	−	0.0640009i
$764$	−5.18742	+	8.98488i	−0.187674	+	0.325062i
$765$		−	3.69930i		−	0.133749i
$766$	13.0936	−	22.6787i	0.473090	−	0.819416i
$767$	−0.348019	+	2.74472i	−0.0125662	+	0.0991062i
$768$	−4.39703	−	7.61588i	−0.158664	−	0.274815i
$769$	−19.0211	−	10.9818i	−0.685918	−	0.396015i	0.116163	−	0.993230i	$-0.462941\pi$
$769$	−19.0211	−	10.9818i	−0.685918	−	0.396015i	−0.802081	+	0.597215i	$0.796274\pi$
$770$	12.1315	+	5.60829i	0.437190	+	0.202109i
$771$	11.2305	+	19.4518i	0.404458	+	0.700541i
$772$	−3.87323	+	2.23621i	−0.139401	+	0.0804829i
$773$		−	53.2366i		−	1.91479i	−0.288787	−	0.957394i	$-0.593252\pi$
$773$		−	53.2366i		−	1.91479i	0.288787	−	0.957394i	$-0.406748\pi$
$774$			9.28535i			0.333755i
$775$	8.23146	−	4.75244i	0.295683	−	0.170713i
$776$	7.85636	+	13.6076i	0.282027	+	0.488485i
$777$	16.0231	−	11.2986i	0.574826	−	0.405335i
$778$	−2.30467	−	1.33060i	−0.0826265	−	0.0477044i
$779$	−1.94881	−	3.37543i	−0.0698232	−	0.120937i
$780$	1.59730	+	1.21357i	0.0571924	+	0.0434528i
$781$	3.22835	−	5.59167i	0.115519	−	0.200086i
$782$		−	10.3017i		−	0.368387i
$783$	−0.728078	+	1.26107i	−0.0260194	+	0.0450669i
$784$	−31.7736	+	5.81932i	−1.13477	+	0.207833i
$785$		−	24.6016i		−	0.878069i
$786$	−19.8050	−	11.4344i	−0.706420	−	0.407852i
$787$			18.3408i			0.653780i	0.945062	+	0.326890i	$0.106001\pi$
$787$			18.3408i			0.653780i	−0.945062	+	0.326890i	$0.893999\pi$
$788$	−2.76293	−	1.59518i	−0.0984254	−	0.0568259i
$789$	7.07387	−	12.2523i	0.251837	−	0.436194i
$790$	−4.26389	+	7.38528i	−0.151702	+	0.262756i
$791$	30.9119	+	43.8378i	1.09910	+	1.55869i
$792$	−5.58018			−0.198283
$793$	26.4232	−	34.7781i	0.938316	−	1.23501i
$794$	2.39790	−	4.15329i	0.0850984	−	0.147395i
$795$	−4.43246	+	2.55908i	−0.157203	+	0.0907613i
$796$	1.92205			0.0681254
$797$	−14.8967	−	25.8018i	−0.527667	−	0.913945i	−0.999480	−	0.0322469i	$-0.989734\pi$
$797$	−14.8967	−	25.8018i	−0.527667	−	0.913945i	0.471813	−	0.881698i	$-0.343600\pi$
$798$	3.89183	−	0.353453i	0.137769	−	0.0125121i
$799$	−22.8306	+	13.1813i	−0.807688	+	0.466319i
$800$	−5.22172	−	3.01476i	−0.184616	−	0.106588i
$801$	−8.78828	−	5.07392i	−0.310519	−	0.179278i
$802$	−47.1149			−1.66369
$803$	−29.2845			−1.03343
$804$	−3.16875	−	1.82948i	−0.111753	−	0.0645208i
$805$	−8.40419	+	5.92616i	−0.296209	+	0.208870i
$806$	−11.2319	+	14.7834i	−0.395628	+	0.520724i
$807$	−6.37047	−	11.0340i	−0.224251	−	0.388415i
$808$	−5.64395	+	3.25853i	−0.198553	+	0.114635i
$809$	13.0496	+	22.6026i	0.458799	+	0.794663i	0.998898	−	0.0469383i	$-0.0149464\pi$
$809$	13.0496	+	22.6026i	0.458799	+	0.794663i	−0.540099	+	0.841602i	$0.681613\pi$
$810$	−1.13160	+	1.95999i	−0.0397604	+	0.0688670i
$811$			29.8679i			1.04880i	0.851471	+	0.524402i	$0.175711\pi$
$811$			29.8679i			1.04880i	−0.851471	+	0.524402i	$0.824289\pi$
$812$	0.613013	−	1.32603i	0.0215125	−	0.0465346i
$813$	−3.25356	+	1.87844i	−0.114107	+	0.0658798i
$814$	−22.0947	+	12.7564i	−0.774419	+	0.447111i
$815$	−23.7042			−0.830322
$816$	−5.81721	−	10.0757i	−0.203643	−	0.352720i
$817$		−	5.76446i		−	0.201673i
$818$	−11.3347			−0.396308
$819$	−5.06033	+	8.08660i	−0.176822	+	0.282569i
$820$	−2.26458			−0.0790825
$821$			46.8412i			1.63477i	0.576093	+	0.817384i	$0.304577\pi$
$821$			46.8412i			1.63477i	−0.576093	+	0.817384i	$0.695423\pi$
$822$	3.99376	+	6.91740i	0.139298	+	0.241272i
$823$	17.8744			0.623062			0.311531	−	0.950236i	$-0.399158\pi$
$823$	17.8744			0.623062			0.311531	+	0.950236i	$0.399158\pi$
$824$	−27.0724	+	15.6302i	−0.943111	+	0.544505i
$825$	−5.50351	+	3.17746i	−0.191608	+	0.110625i
$826$	3.11867	−	0.283236i	0.108513	−	0.00985503i
$827$		−	23.3454i		−	0.811799i	−0.913918	−	0.405899i	$-0.866958\pi$
$827$		−	23.3454i		−	0.811799i	0.913918	−	0.405899i	$-0.133042\pi$
$828$	−0.502235	+	0.869897i	−0.0174539	+	0.0302310i
$829$	−27.8730	−	48.2775i	−0.968071	−	1.67675i	−0.701128	−	0.713036i	$-0.747320\pi$
$829$	−27.8730	−	48.2775i	−0.968071	−	1.67675i	−0.266943	−	0.963712i	$-0.586014\pi$
$830$	7.62940	−	4.40484i	0.264820	−	0.152894i
$831$	−2.46101	−	4.26260i	−0.0853715	−	0.147868i
$832$	−21.3278	−	2.70428i	−0.739409	−	0.0937539i
$833$	−17.3598	+	3.17944i	−0.601482	+	0.110161i
$834$	27.6539	+	15.9660i	0.957577	+	0.552857i
$835$	−28.9914			−1.00329
$836$	−0.810458			−0.0280303
$837$	−2.89114	−	1.66920i	−0.0999324	−	0.0576960i
$838$	−15.4513	−	8.92083i	−0.533757	−	0.308165i
$839$	−16.1000	+	9.29535i	−0.555834	+	0.320911i	−0.751472	−	0.659765i	$-0.770656\pi$
$839$	−16.1000	+	9.29535i	−0.555834	+	0.320911i	0.195638	+	0.980676i	$0.437322\pi$
$840$	−4.07251	+	8.80940i	−0.140515	+	0.303953i
$841$	13.4398	+	23.2784i	0.463442	+	0.802704i
$842$	−11.6906			−0.402884
$843$	−18.9745	+	10.9549i	−0.653516	+	0.377308i
$844$	−3.90282	+	6.75989i	−0.134341	+	0.232685i
$845$	18.3765	−	5.11263i	0.632170	−	0.175880i
$846$	16.1283			0.554504
$847$	−6.68127	+	14.4525i	−0.229571	+	0.496595i
$848$	−8.04840	+	13.9402i	−0.276383	+	0.478710i
$849$	−15.2086	+	26.3420i	−0.521956	+	0.904055i
$850$	−9.58880	−	5.53610i	−0.328893	−	0.189887i
$851$		−	19.6302i		−	0.672913i
$852$	−0.949937	−	0.548446i	−0.0325443	−	0.0187895i
$853$		−	31.4429i		−	1.07659i	−0.842758	−	0.538293i	$-0.819069\pi$
$853$		−	31.4429i		−	1.07659i	0.842758	−	0.538293i	$-0.180931\pi$
$854$	−44.8734	−	20.7446i	−1.53554	−	0.709865i
$855$	0.702510	−	1.21678i	0.0240253	−	0.0416131i
$856$			45.6298i			1.55960i
$857$	28.3523	−	49.1076i	0.968495	−	1.67748i	0.268579	−	0.963258i	$-0.413446\pi$
$857$	28.3523	−	49.1076i	0.968495	−	1.67748i	0.699916	−	0.714225i	$-0.253221\pi$
$858$	7.50961	−	9.88413i	0.256374	−	0.337439i
$859$	−0.915541	−	1.58576i	−0.0312379	−	0.0541056i	0.849984	−	0.526809i	$-0.176612\pi$
$859$	−0.915541	−	1.58576i	−0.0312379	−	0.0541056i	−0.881222	+	0.472703i	$0.843278\pi$
$860$	−2.90053	−	1.67462i	−0.0989074	−	0.0571042i
$861$	−0.974020	−	10.7248i	−0.0331945	−	0.365501i
$862$	1.90941	+	3.30719i	0.0650347	+	0.112643i
$863$	19.2517	−	11.1150i	0.655336	−	0.378358i	−0.135162	−	0.990824i	$-0.543155\pi$
$863$	19.2517	−	11.1150i	0.655336	−	0.378358i	0.790497	+	0.612465i	$0.209822\pi$
$864$			2.11775i			0.0720474i
$865$			2.39755i			0.0815192i
$866$	1.37111	−	0.791609i	0.0465921	−	0.0269000i
$867$	5.32172	+	9.21748i	0.180735	+	0.313042i
$868$	3.04008	+	1.40540i	0.103187	+	0.0477024i
$869$	7.28359	+	4.20518i	0.247079	+	0.142651i
$870$	−1.64779	−	2.85405i	−0.0558652	−	0.0967614i
$871$	−32.0793	+	13.4676i	−1.08697	+	0.456331i
$872$	−1.99048	+	3.44762i	−0.0674063	+	0.116751i
$873$		−	6.28499i		−	0.212715i
$874$	1.95633	−	3.38845i	0.0661737	−	0.114616i
$875$	2.75526	+	30.3379i	0.0931449	+	1.02561i
$876$			4.97498i			0.168089i
$877$	−19.4370	−	11.2220i	−0.656341	−	0.378939i	0.134540	−	0.990908i	$-0.457044\pi$
$877$	−19.4370	−	11.2220i	−0.656341	−	0.378939i	−0.790881	+	0.611969i	$0.790378\pi$
$878$			13.9989i			0.472440i
$879$	9.06140	+	5.23160i	0.305633	+	0.176457i
$880$	7.55637	−	13.0880i	0.254725	−	0.441197i
$881$	16.2431	−	28.1338i	0.547242	−	0.947852i	−0.451220	−	0.892413i	$-0.649011\pi$
$881$	16.2431	−	28.1338i	0.547242	−	0.947852i	0.998462	−	0.0554388i	$-0.0176558\pi$
$882$	10.1703	+	3.62574i	0.342451	+	0.122085i
$883$	16.1468			0.543383			0.271691	−	0.962384i	$-0.412417\pi$
$883$	16.1468			0.543383			0.271691	+	0.962384i	$0.412417\pi$
$884$	3.41959	+	0.433590i	0.115013	+	0.0145832i
$885$	0.562949	−	0.975056i	0.0189233	−	0.0327761i
$886$	34.6985	−	20.0332i	1.16572	−	0.673028i
$887$	11.9870			0.402484			0.201242	−	0.979542i	$-0.435502\pi$
$887$	11.9870			0.402484			0.201242	+	0.979542i	$0.435502\pi$
$888$	−9.26315	−	16.0442i	−0.310851	−	0.538409i
$889$	4.77579	−	10.3307i	0.160175	−	0.346480i
$890$	19.8896	−	11.4833i	0.666702	−	0.384921i
$891$	1.93300	+	1.11602i	0.0647580	+	0.0373880i
$892$	−2.68992	−	1.55303i	−0.0900653	−	0.0519992i
$893$	−10.0127			−0.335061
$894$	27.2151			0.910211
$895$	−22.1902	−	12.8115i	−0.741737	−	0.428242i
$896$	3.21444	+	35.3938i	0.107387	+	1.18242i
$897$	3.69716	+	8.80652i	0.123445	+	0.294041i
$898$	−24.6468	−	42.6895i	−0.822474	−	1.42457i
$899$	4.20995	−	2.43062i	0.140410	−	0.0810656i
$900$	0.539800	+	0.934961i	0.0179933	+	0.0311654i
$901$	−4.39731	+	7.61637i	−0.146496	+	0.253738i
$902$			14.0133i			0.466592i
$903$	6.68329	−	14.4569i	0.222406	−	0.481095i
$904$	43.8956	−	25.3431i	1.45995	−	0.842900i
$905$	−1.07839	+	0.622611i	−0.0358470	+	0.0206963i
$906$	−23.3711			−0.776454
$907$	8.39927	+	14.5480i	0.278893	+	0.483057i	0.971110	−	0.238632i	$-0.0766991\pi$
$907$	8.39927	+	14.5480i	0.278893	+	0.483057i	−0.692217	+	0.721690i	$0.743366\pi$
$908$		−	8.67462i		−	0.287877i
$909$	2.60679			0.0864616
$910$	−10.1234	−	19.0690i	−0.335587	−	0.632130i
$911$	18.7103			0.619899			0.309949	−	0.950753i	$-0.399688\pi$
$911$	18.7103			0.619899			0.309949	+	0.950753i	$0.399688\pi$
$912$		−	4.41883i		−	0.146322i
$913$	−4.34419	−	7.52435i	−0.143772	−	0.249020i
$914$	63.4651			2.09924
$915$	−15.3930	+	8.88715i	−0.508877	+	0.293800i
$916$	4.69905	−	2.71300i	0.155261	−	0.0896400i
$917$	22.6054	+	32.0578i	0.746495	+	1.05864i
$918$			3.88889i			0.128353i
$919$	6.74748	−	11.6870i	0.222579	−	0.385518i	−0.733011	−	0.680216i	$-0.761886\pi$
$919$	6.74748	−	11.6870i	0.222579	−	0.385518i	0.955590	+	0.294698i	$0.0952192\pi$
$920$	4.85856	+	8.41528i	0.160182	+	0.277443i
$921$	9.78564	−	5.64974i	0.322448	−	0.186165i
$922$	−4.62560	−	8.01177i	−0.152336	−	0.263854i
$923$	−9.61681	+	4.03734i	−0.316541	+	0.132891i
$924$	−2.03258	−	0.939643i	−0.0668669	−	0.0309120i
$925$	−18.2718	−	10.5492i	−0.600771	−	0.346856i
$926$	−41.9195			−1.37756
$927$	12.5040			0.410685
$928$	−2.67063	−	1.54189i	−0.0876678	−	0.0506150i
$929$	−20.1751	−	11.6481i	−0.661924	−	0.382162i	0.131086	−	0.991371i	$-0.458154\pi$
$929$	−20.1751	−	11.6481i	−0.661924	−	0.382162i	−0.793010	+	0.609209i	$0.791487\pi$
$930$	6.54322	−	3.77773i	0.214561	−	0.123877i
$931$	−6.31382	−	2.25090i	−0.206927	−	0.0737703i
$932$	−1.90884	−	3.30622i	−0.0625263	−	0.108299i
$933$	6.76848			0.221590
$934$	6.13422	−	3.54160i	0.200718	−	0.115885i
$935$	4.12849	−	7.15075i	0.135016	−	0.233855i
$936$	7.17744	+	5.45316i	0.234602	+	0.178242i
$937$	−46.4351			−1.51697			−0.758484	−	0.651692i	$-0.774060\pi$
$937$	−46.4351			−1.51697			−0.758484	+	0.651692i	$0.774060\pi$
$938$	22.6934	+	32.1827i	0.740966	+	1.05080i
$939$	1.36847	−	2.37027i	0.0446585	−	0.0773507i
$940$	−2.90876	+	5.03813i	−0.0948734	+	0.164326i
$941$	−25.5347	−	14.7424i	−0.832406	−	0.480590i	0.0222695	−	0.999752i	$-0.492911\pi$
$941$	−25.5347	−	14.7424i	−0.832406	−	0.480590i	−0.854676	+	0.519162i	$0.826244\pi$
$942$			25.8624i			0.842644i
$943$	−9.33764	−	5.39109i	−0.304075	−	0.175558i
$944$		−	3.54098i		−	0.115249i
$945$	3.17259	−	2.23713i	0.103204	−	0.0727738i
$946$	−10.3626	+	17.9486i	−0.336918	+	0.583559i
$947$			39.9526i			1.29828i	0.760667	+	0.649142i	$0.224872\pi$
$947$			39.9526i			1.29828i	−0.760667	+	0.649142i	$0.775128\pi$
$948$	0.714395	−	1.23737i	0.0232025	−	0.0401879i
$949$	37.6668	+	28.6179i	1.22272	+	0.928977i
$950$	−2.10265	−	3.64189i	−0.0682189	−	0.118159i
$951$	13.0303	+	7.52306i	0.422537	+	0.243952i
$952$	1.50835	+	16.6082i	0.0488859	+	0.538276i
$953$	1.93532	+	3.35208i	0.0626913	+	0.108584i	0.895668	−	0.444724i	$-0.146698\pi$
$953$	1.93532	+	3.35208i	0.0626913	+	0.108584i	−0.832976	+	0.553309i	$0.813365\pi$
$954$	4.65963	−	2.69024i	0.150861	−	0.0870996i
$955$		−	40.1454i		−	1.29907i
$956$		−	10.5724i		−	0.341936i
$957$	−2.81475	+	1.62510i	−0.0909880	+	0.0525320i
$958$	6.56882	+	11.3775i	0.212229	+	0.367591i
$959$	−1.23920	−	13.6447i	−0.0400158	−	0.440609i
$960$	7.57665	+	4.37438i	0.244535	+	0.141183i
$961$	−9.92754	−	17.1950i	−0.320243	−	0.554678i
$962$	40.8850	+	5.18404i	1.31819	+	0.167140i
$963$	9.12582	−	15.8064i	0.294076	−	0.509354i
$964$		−	4.59972i		−	0.148147i
$965$	8.65298	−	14.9874i	0.278549	−	0.482462i
$966$	8.83491	−	6.22988i	0.284258	−	0.200443i
$967$			29.8554i			0.960086i	0.877245	+	0.480043i	$0.159379\pi$
$967$			29.8554i			0.960086i	−0.877245	+	0.480043i	$0.840621\pi$
$968$	13.0296	+	7.52263i	0.418787	+	0.241787i
$969$		−	2.41427i		−	0.0775575i
$970$	12.3185	+	7.11209i	0.395523	+	0.228356i
$971$	23.2584	−	40.2847i	0.746397	−	1.29280i	−0.203142	−	0.979149i	$-0.565115\pi$
$971$	23.2584	−	40.2847i	0.746397	−	1.29280i	0.949539	−	0.313649i	$-0.101551\pi$
$972$	0.189594	−	0.328387i	0.00608123	−	0.0105330i
$973$	−31.5642	−	44.7627i	−1.01190	−	1.43503i
$974$	−10.0827			−0.323070
$975$	10.1840	+	1.29128i	0.326148	+	0.0413541i
$976$	−27.9504	+	48.4114i	−0.894669	+	1.54961i
$977$	2.04067	−	1.17818i	0.0652867	−	0.0376933i	−0.467001	−	0.884257i	$-0.654666\pi$
$977$	2.04067	−	1.17818i	0.0652867	−	0.0376933i	0.532288	+	0.846563i	$0.321332\pi$
$978$	24.9190			0.796823
$979$	−11.3252	−	19.6158i	−0.361954	−	0.626923i
$980$	−2.96682	+	2.52305i	−0.0947715	+	0.0805960i
$981$	1.37903	−	0.796181i	0.0440289	−	0.0254201i
$982$	48.7784	+	28.1622i	1.55658	+	0.898692i
$983$	24.9474	+	14.4034i	0.795697	+	0.459396i	0.841964	−	0.539533i	$-0.181399\pi$
$983$	24.9474	+	14.4034i	0.795697	+	0.459396i	−0.0462672	+	0.998929i	$0.514733\pi$
$984$	−10.1759			−0.324395
$985$	12.3451			0.393346
$986$	−4.90416	−	2.83142i	−0.156180	−	0.0901707i
$987$	−25.1111	−	11.6086i	−0.799296	−	0.369507i
$988$	1.04244	+	0.792010i	0.0331645	+	0.0251972i
$989$	−7.97327	−	13.8101i	−0.253535	−	0.439136i
$990$	−4.37477	+	2.52577i	−0.139039	+	0.0802743i
$991$	22.4345	+	38.8576i	0.712654	+	1.23435i	0.963857	+	0.266419i	$0.0858404\pi$
$991$	22.4345	+	38.8576i	0.712654	+	1.23435i	−0.251203	+	0.967934i	$0.580826\pi$
$992$	3.53495	−	6.12272i	0.112235	−	0.194396i
$993$		−	5.77162i		−	0.183157i
$994$	6.80309	+	9.64781i	0.215781	+	0.306010i
$995$	−6.44095	+	3.71868i	−0.204192	+	0.117890i
$996$	−1.27827	+	0.738009i	−0.0405035	+	0.0233847i
$997$	29.0851			0.921136			0.460568	−	0.887624i	$-0.347646\pi$
$997$	29.0851			0.921136			0.460568	+	0.887624i	$0.347646\pi$
$998$	17.4477	+	30.2203i	0.552298	+	0.956607i
$999$			7.41040i			0.234455i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.t.c.4.2	✓	12
3.2	odd	2		819.2.bm.e.550.5		12
7.2	even	3		273.2.bl.c.121.2	yes	12
13.10	even	6		273.2.bl.c.88.2	yes	12
21.2	odd	6		819.2.do.f.667.5		12
39.23	odd	6		819.2.do.f.361.5		12
91.23	even	6	inner	273.2.t.c.205.5	yes	12
273.23	odd	6		819.2.bm.e.478.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.t.c.4.2	✓	12	1.1	even	1	trivial
273.2.t.c.205.5	yes	12	91.23	even	6	inner
273.2.bl.c.88.2	yes	12	13.10	even	6
273.2.bl.c.121.2	yes	12	7.2	even	3
819.2.bm.e.478.2		12	273.23	odd	6
819.2.bm.e.550.5		12	3.2	odd	2
819.2.do.f.361.5		12	39.23	odd	6
819.2.do.f.667.5		12	21.2	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.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.54246i q^{2} +(-0.500000 - 0.866025i) q^{3} -0.379188 q^{4} +(1.27069 - 0.733632i) q^{5} +(-1.33581 + 0.771231i) q^{6} +(2.63491 - 0.239300i) q^{7} -2.50004i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q-1.54246i q^{2} +(-0.500000 - 0.866025i) q^{3} -0.379188 q^{4} +(1.27069 - 0.733632i) q^{5} +(-1.33581 + 0.771231i) q^{6} +(2.63491 - 0.239300i) q^{7} -2.50004i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.13160 - 1.95999i) q^{10} +(-1.93300 + 1.11602i) q^{11} +(0.189594 + 0.328387i) q^{12} +(3.57691 + 0.453537i) q^{13} +(-0.369112 - 4.06424i) q^{14} +(-1.27069 - 0.733632i) q^{15} -4.61459 q^{16} -2.52122 q^{17} +(1.33581 + 0.771231i) q^{18} +(-0.829287 - 0.478789i) q^{19} +(-0.481830 + 0.278185i) q^{20} +(-1.52469 - 2.16225i) q^{21} +(1.72142 + 2.98158i) q^{22} -2.64900 q^{23} +(-2.16510 + 1.25002i) q^{24} +(-1.42357 + 2.46569i) q^{25} +(0.699564 - 5.51725i) q^{26} +1.00000 q^{27} +(-0.999126 + 0.0907399i) q^{28} +(-0.728078 + 1.26107i) q^{29} +(-1.13160 + 1.95999i) q^{30} +(-2.89114 - 1.66920i) q^{31} +2.11775i q^{32} +(1.93300 + 1.11602i) q^{33} +3.88889i q^{34} +(3.17259 - 2.23713i) q^{35} +(0.189594 - 0.328387i) q^{36} +7.41040i q^{37} +(-0.738514 + 1.27914i) q^{38} +(-1.39568 - 3.32447i) q^{39} +(-1.83411 - 3.17677i) q^{40} +(3.52497 + 2.03514i) q^{41} +(-3.33518 + 2.35178i) q^{42} +(3.00991 + 5.21332i) q^{43} +(0.732971 - 0.423181i) q^{44} +1.46726i q^{45} +4.08598i q^{46} +(9.05536 - 5.22812i) q^{47} +(2.30730 + 3.99635i) q^{48} +(6.88547 - 1.26107i) q^{49} +(3.80323 + 2.19580i) q^{50} +(1.26061 + 2.18344i) q^{51} +(-1.35632 - 0.171976i) q^{52} +(1.74412 - 3.02090i) q^{53} -1.54246i q^{54} +(-1.63749 + 2.83622i) q^{55} +(-0.598261 - 6.58737i) q^{56} +0.957578i q^{57} +(1.94515 + 1.12303i) q^{58} +0.767344i q^{59} +(0.481830 + 0.278185i) q^{60} +(6.05695 - 10.4909i) q^{61} +(-2.57468 + 4.45947i) q^{62} +(-1.11021 + 2.40155i) q^{63} -5.96263 q^{64} +(4.87787 - 2.04783i) q^{65} +(1.72142 - 2.98158i) q^{66} +(-8.35667 + 4.82473i) q^{67} +0.956018 q^{68} +(1.32450 + 2.29410i) q^{69} +(-3.45069 - 4.89359i) q^{70} +(-2.50519 + 1.44637i) q^{71} +(2.16510 + 1.25002i) q^{72} +(11.3623 + 6.56004i) q^{73} +11.4303 q^{74} +2.84713 q^{75} +(0.314456 + 0.181551i) q^{76} +(-4.82621 + 3.40317i) q^{77} +(-5.12786 + 2.15279i) q^{78} +(-1.88401 - 3.26320i) q^{79} +(-5.86371 + 3.38541i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.13913 - 5.43712i) q^{82} +3.89258i q^{83} +(0.578146 + 0.819898i) q^{84} +(-3.20369 + 1.84965i) q^{85} +(8.04135 - 4.64268i) q^{86} +1.45616 q^{87} +(2.79009 + 4.83258i) q^{88} +10.1478i q^{89} +2.26320 q^{90} +(9.53336 + 0.339072i) q^{91} +1.00447 q^{92} +3.33840i q^{93} +(-8.06417 - 13.9676i) q^{94} -1.40502 q^{95} +(1.83403 - 1.05888i) q^{96} +(-5.44296 + 3.14250i) q^{97} +(-1.94515 - 10.6206i) q^{98} -2.23204i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} - 10 q^{4} - 6 q^{5} - 3 q^{6} - 3 q^{7} - 6 q^{9}+O(q^{10}) \) 12 * q - 6 * q^3 - 10 * q^4 - 6 * q^5 - 3 * q^6 - 3 * q^7 - 6 * q^9	\( 12 q - 6 q^{3} - 10 q^{4} - 6 q^{5} - 3 q^{6} - 3 q^{7} - 6 q^{9} - 7 q^{10} - 18 q^{11} + 5 q^{12} - q^{13} - 16 q^{14} + 6 q^{15} - 6 q^{16} + 3 q^{18} + 9 q^{19} - 27 q^{20} - 3 q^{21} + 7 q^{22} + 32 q^{23} + 6 q^{24} + 10 q^{25} - 7 q^{26} + 12 q^{27} + 36 q^{28} - 5 q^{29} - 7 q^{30} - 15 q^{31} + 18 q^{33} - 2 q^{35} + 5 q^{36} + 24 q^{38} - 10 q^{39} + 21 q^{40} - 15 q^{41} + 5 q^{42} - 13 q^{43} + 30 q^{44} + 9 q^{47} + 3 q^{48} - 3 q^{49} - 63 q^{50} + 32 q^{52} + 18 q^{53} + 13 q^{55} + 3 q^{56} - 57 q^{58} + 27 q^{60} + 26 q^{61} - 13 q^{62} + 6 q^{63} - 4 q^{64} + 10 q^{65} + 7 q^{66} - 24 q^{67} - 16 q^{69} + 42 q^{70} - 15 q^{71} - 6 q^{72} + 18 q^{73} - 76 q^{74} - 20 q^{75} - 30 q^{76} + 20 q^{77} - q^{78} - 4 q^{79} + 39 q^{80} - 6 q^{81} - 14 q^{82} - 12 q^{84} - 12 q^{85} + 15 q^{86} + 10 q^{87} + 16 q^{88} + 14 q^{90} + 4 q^{91} - 40 q^{92} - 3 q^{94} + 56 q^{95} + 6 q^{96} + 45 q^{97} + 57 q^{98}+O(q^{100}) \) 12 * q - 6 * q^3 - 10 * q^4 - 6 * q^5 - 3 * q^6 - 3 * q^7 - 6 * q^9 - 7 * q^10 - 18 * q^11 + 5 * q^12 - q^13 - 16 * q^14 + 6 * q^15 - 6 * q^16 + 3 * q^18 + 9 * q^19 - 27 * q^20 - 3 * q^21 + 7 * q^22 + 32 * q^23 + 6 * q^24 + 10 * q^25 - 7 * q^26 + 12 * q^27 + 36 * q^28 - 5 * q^29 - 7 * q^30 - 15 * q^31 + 18 * q^33 - 2 * q^35 + 5 * q^36 + 24 * q^38 - 10 * q^39 + 21 * q^40 - 15 * q^41 + 5 * q^42 - 13 * q^43 + 30 * q^44 + 9 * q^47 + 3 * q^48 - 3 * q^49 - 63 * q^50 + 32 * q^52 + 18 * q^53 + 13 * q^55 + 3 * q^56 - 57 * q^58 + 27 * q^60 + 26 * q^61 - 13 * q^62 + 6 * q^63 - 4 * q^64 + 10 * q^65 + 7 * q^66 - 24 * q^67 - 16 * q^69 + 42 * q^70 - 15 * q^71 - 6 * q^72 + 18 * q^73 - 76 * q^74 - 20 * q^75 - 30 * q^76 + 20 * q^77 - q^78 - 4 * q^79 + 39 * q^80 - 6 * q^81 - 14 * q^82 - 12 * q^84 - 12 * q^85 + 15 * q^86 + 10 * q^87 + 16 * q^88 + 14 * q^90 + 4 * q^91 - 40 * q^92 - 3 * q^94 + 56 * q^95 + 6 * q^96 + 45 * q^97 + 57 * q^98

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