LMFDB - Embedded newform 56.3.k.d.11.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [56,3,Mod(11,56)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(56, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("56.11");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 56 = 2^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	56.k (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:	$1.52588948042$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 4 x^{10} + 3 x^{9} + 86 x^{8} - 163 x^{7} + 155 x^{6} - 166 x^{5} + 164 x^{4} + \cdots + 4 $ x^12 - 3x^11 - 4x^10 + 3x^9 + 86x^8 - 163x^7 + 155x^6 - 166x^5 + 164x^4 - 116x^3 + 60x^2 - 20*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.6
Root			$0.907369 - 0.0534805i$ of defining polynomial
Character	$\chi$	$=$	56.11
Dual form			56.3.k.d.51.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.98615 - 0.234945i) q^{2} +(-2.66613 + 4.61787i) q^{3} +(3.88960 - 0.933271i) q^{4} +(-1.86796 + 1.07847i) q^{5} +(-4.21039 + 9.79818i) q^{6} +(6.91861 - 1.06433i) q^{7} +(7.50608 - 2.76746i) q^{8} +(-9.71647 - 16.8294i) q^{9} +O(q^{10})$	\(q+(1.98615 - 0.234945i) q^{2} +(-2.66613 + 4.61787i) q^{3} +(3.88960 - 0.933271i) q^{4} +(-1.86796 + 1.07847i) q^{5} +(-4.21039 + 9.79818i) q^{6} +(6.91861 - 1.06433i) q^{7} +(7.50608 - 2.76746i) q^{8} +(-9.71647 - 16.8294i) q^{9} +(-3.45667 + 2.58086i) q^{10} +(-2.62956 + 4.55453i) q^{11} +(-6.06045 + 20.4499i) q^{12} -21.4116i q^{13} +(13.4914 - 3.73941i) q^{14} -11.5013i q^{15} +(14.2580 - 7.26011i) q^{16} +(-0.463429 + 0.802683i) q^{17} +(-23.2524 - 31.1430i) q^{18} +(2.96505 + 5.13561i) q^{19} +(-6.25911 + 5.93812i) q^{20} +(-13.5310 + 34.7869i) q^{21} +(-4.15264 + 9.66378i) q^{22} +(-7.52507 + 4.34460i) q^{23} +(-7.23239 + 42.0405i) q^{24} +(-10.1738 + 17.6216i) q^{25} +(-5.03053 - 42.5266i) q^{26} +55.6311 q^{27} +(25.9173 - 10.5968i) q^{28} +9.42223i q^{29} +(-2.70217 - 22.8434i) q^{30} +(-29.8813 - 17.2520i) q^{31} +(26.6129 - 17.7695i) q^{32} +(-14.0215 - 24.2859i) q^{33} +(-0.731855 + 1.70313i) q^{34} +(-11.7758 + 9.44961i) q^{35} +(-53.4996 - 56.3916i) q^{36} +(11.0853 - 6.40011i) q^{37} +(7.09562 + 9.50349i) q^{38} +(98.8758 + 57.0860i) q^{39} +(-11.0364 + 13.2645i) q^{40} +43.1339 q^{41} +(-18.7016 + 72.2711i) q^{42} -41.7382 q^{43} +(-5.97732 + 20.1694i) q^{44} +(36.2999 + 20.9578i) q^{45} +(-13.9252 + 10.3970i) q^{46} +(-39.8357 + 22.9991i) q^{47} +(-4.48745 + 85.1980i) q^{48} +(46.7344 - 14.7273i) q^{49} +(-16.0667 + 37.3894i) q^{50} +(-2.47112 - 4.28011i) q^{51} +(-19.9828 - 83.2825i) q^{52} +(-64.5031 - 37.2409i) q^{53} +(110.492 - 13.0702i) q^{54} -11.3436i q^{55} +(48.9861 - 27.1359i) q^{56} -31.6208 q^{57} +(2.21370 + 18.7140i) q^{58} +(-26.8367 + 46.4825i) q^{59} +(-10.7338 - 44.7355i) q^{60} +(24.0893 - 13.9080i) q^{61} +(-63.4020 - 27.2446i) q^{62} +(-85.1365 - 106.095i) q^{63} +(48.6823 - 41.5455i) q^{64} +(23.0916 + 39.9959i) q^{65} +(-33.5546 - 44.9412i) q^{66} +(39.2453 - 67.9749i) q^{67} +(-1.05343 + 3.55462i) q^{68} -46.3330i q^{69} +(-21.1685 + 21.5350i) q^{70} +74.5100i q^{71} +(-119.507 - 99.4329i) q^{72} +(-16.8020 + 29.1020i) q^{73} +(20.5134 - 15.3160i) q^{74} +(-54.2494 - 93.9627i) q^{75} +(16.3258 + 17.2083i) q^{76} +(-13.3454 + 34.3097i) q^{77} +(209.794 + 90.1511i) q^{78} +(26.1642 - 15.1059i) q^{79} +(-18.8036 + 28.9384i) q^{80} +(-60.8713 + 105.432i) q^{81} +(85.6705 - 10.1341i) q^{82} -72.9274 q^{83} +(-20.1645 + 147.935i) q^{84} -1.99917i q^{85} +(-82.8984 + 9.80616i) q^{86} +(-43.5106 - 25.1209i) q^{87} +(-7.13318 + 41.4638i) q^{88} +(27.4198 + 47.4925i) q^{89} +(77.0211 + 33.0968i) q^{90} +(-22.7889 - 148.138i) q^{91} +(-25.2148 + 23.9217i) q^{92} +(159.335 - 91.9919i) q^{93} +(-73.7162 + 55.0390i) q^{94} +(-11.0772 - 6.39541i) q^{95} +(11.1040 + 170.270i) q^{96} -53.7125 q^{97} +(89.3616 - 40.2307i) q^{98} +102.200 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} - 6 q^{3} - 4 q^{4} - 56 q^{6} + 8 q^{8} - 40 q^{9}+O(q^{10}) $ 12 * q + 2 * q^2 - 6 * q^3 - 4 * q^4 - 56 * q^6 + 8 * q^8 - 40 * q^9	$ 12 q + 2 q^{2} - 6 q^{3} - 4 q^{4} - 56 q^{6} + 8 q^{8} - 40 q^{9} - 6 q^{10} + 30 q^{11} + 32 q^{12} + 52 q^{14} + 16 q^{16} + 30 q^{17} - 16 q^{18} + 78 q^{19} + 48 q^{20} + 24 q^{22} - 76 q^{24} - 92 q^{25} - 128 q^{26} + 156 q^{27} - 4 q^{28} - 16 q^{30} + 112 q^{32} - 78 q^{33} + 76 q^{34} - 222 q^{35} - 248 q^{36} + 80 q^{38} + 44 q^{40} - 232 q^{41} + 132 q^{42} - 200 q^{43} + 132 q^{44} - 156 q^{46} + 176 q^{48} + 372 q^{49} + 48 q^{50} + 10 q^{51} + 132 q^{52} - 36 q^{54} - 112 q^{56} + 332 q^{57} + 4 q^{58} - 110 q^{59} + 84 q^{60} - 96 q^{62} - 160 q^{64} - 32 q^{65} - 138 q^{66} + 434 q^{67} + 96 q^{68} - 188 q^{70} - 328 q^{72} + 102 q^{73} - 34 q^{74} - 60 q^{75} - 168 q^{76} + 720 q^{78} - 256 q^{80} - 82 q^{81} - 24 q^{82} - 536 q^{83} - 624 q^{84} + 240 q^{86} - 204 q^{88} + 214 q^{89} + 440 q^{90} - 8 q^{91} + 160 q^{92} - 16 q^{94} + 48 q^{96} - 152 q^{97} + 382 q^{98} + 504 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 - 6 * q^3 - 4 * q^4 - 56 * q^6 + 8 * q^8 - 40 * q^9 - 6 * q^10 + 30 * q^11 + 32 * q^12 + 52 * q^14 + 16 * q^16 + 30 * q^17 - 16 * q^18 + 78 * q^19 + 48 * q^20 + 24 * q^22 - 76 * q^24 - 92 * q^25 - 128 * q^26 + 156 * q^27 - 4 * q^28 - 16 * q^30 + 112 * q^32 - 78 * q^33 + 76 * q^34 - 222 * q^35 - 248 * q^36 + 80 * q^38 + 44 * q^40 - 232 * q^41 + 132 * q^42 - 200 * q^43 + 132 * q^44 - 156 * q^46 + 176 * q^48 + 372 * q^49 + 48 * q^50 + 10 * q^51 + 132 * q^52 - 36 * q^54 - 112 * q^56 + 332 * q^57 + 4 * q^58 - 110 * q^59 + 84 * q^60 - 96 * q^62 - 160 * q^64 - 32 * q^65 - 138 * q^66 + 434 * q^67 + 96 * q^68 - 188 * q^70 - 328 * q^72 + 102 * q^73 - 34 * q^74 - 60 * q^75 - 168 * q^76 + 720 * q^78 - 256 * q^80 - 82 * q^81 - 24 * q^82 - 536 * q^83 - 624 * q^84 + 240 * q^86 - 204 * q^88 + 214 * q^89 + 440 * q^90 - 8 * q^91 + 160 * q^92 - 16 * q^94 + 48 * q^96 - 152 * q^97 + 382 * q^98 + 504 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/56\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$29$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.98615	−	0.234945i	0.993076	−	0.117472i
$2$	1.98615	−	0.234945i	0.993076	−	0.117472i
$3$	−2.66613	+	4.61787i	−0.888709	+	1.53929i	−0.0473064	+	0.998880i	$0.515064\pi$
$3$	−2.66613	+	4.61787i	−0.888709	+	1.53929i	−0.841403	+	0.540409i	$0.818270\pi$
$4$	3.88960	−	0.933271i	0.972401	−	0.233318i
$5$	−1.86796	+	1.07847i	−0.373592	+	0.215693i	−0.675026	−	0.737794i	$-0.735868\pi$
$5$	−1.86796	+	1.07847i	−0.373592	+	0.215693i	0.301435	+	0.953487i	$0.402534\pi$
$6$	−4.21039	+	9.79818i	−0.701732	+	1.63303i
$7$	6.91861	−	1.06433i	0.988373	−	0.152047i
$7$	6.91861	−	1.06433i	0.988373	−	0.152047i
$8$	7.50608	−	2.76746i	0.938259	−	0.345932i
$9$	−9.71647	−	16.8294i	−1.07961	−	1.86993i
$10$	−3.45667	+	2.58086i	−0.345667	+	0.258086i
$11$	−2.62956	+	4.55453i	−0.239051	+	0.414048i	−0.960442	−	0.278480i	$-0.910170\pi$
$11$	−2.62956	+	4.55453i	−0.239051	+	0.414048i	0.721392	+	0.692527i	$0.243503\pi$
$12$	−6.06045	+	20.4499i	−0.505038	+	1.70416i
$13$		−	21.4116i		−	1.64704i	−0.567285	−	0.823522i	$-0.692006\pi$
$13$		−	21.4116i		−	1.64704i	0.567285	−	0.823522i	$-0.307994\pi$
$14$	13.4914	−	3.73941i	0.963669	−	0.267101i
$15$		−	11.5013i		−	0.766754i
$16$	14.2580	−	7.26011i	0.891126	−	0.453757i
$17$	−0.463429	+	0.802683i	−0.0272606	+	0.0472167i	−0.879334	−	0.476206i	$-0.842012\pi$
$17$	−0.463429	+	0.802683i	−0.0272606	+	0.0472167i	0.852073	+	0.523423i	$0.175345\pi$
$18$	−23.2524	−	31.1430i	−1.29180	−	1.73016i
$19$	2.96505	+	5.13561i	0.156055	+	0.270295i	0.933443	−	0.358726i	$-0.116789\pi$
$19$	2.96505	+	5.13561i	0.156055	+	0.270295i	−0.777388	+	0.629022i	$0.783456\pi$
$20$	−6.25911	+	5.93812i	−0.312956	+	0.296906i
$21$	−13.5310	+	34.7869i	−0.644332	+	1.65652i
$22$	−4.15264	+	9.66378i	−0.188756	+	0.439263i
$23$	−7.52507	+	4.34460i	−0.327177	+	0.188896i	−0.654587	−	0.755987i	$-0.727157\pi$
$23$	−7.52507	+	4.34460i	−0.327177	+	0.188896i	0.327410	+	0.944882i	$0.393824\pi$
$24$	−7.23239	+	42.0405i	−0.301350	+	1.75169i
$25$	−10.1738	+	17.6216i	−0.406953	+	0.704863i
$26$	−5.03053	−	42.5266i	−0.193482	−	1.63564i
$27$	55.6311			2.06041
$28$	25.9173	−	10.5968i	0.925619	−	0.378456i
$29$			9.42223i			0.324904i	0.986716	+	0.162452i	$0.0519403\pi$
$29$			9.42223i			0.324904i	−0.986716	+	0.162452i	$0.948060\pi$
$30$	−2.70217	−	22.8434i	−0.0900723	−	0.761445i
$31$	−29.8813	−	17.2520i	−0.963912	−	0.556515i	−0.0665375	−	0.997784i	$-0.521195\pi$
$31$	−29.8813	−	17.2520i	−0.963912	−	0.556515i	−0.897375	+	0.441269i	$0.854529\pi$
$32$	26.6129	−	17.7695i	0.831652	−	0.555298i
$33$	−14.0215	−	24.2859i	−0.424893	−	0.735936i
$34$	−0.731855	+	1.70313i	−0.0215252	+	0.0500921i
$35$	−11.7758	+	9.44961i	−0.336453	+	0.269989i
$36$	−53.4996	−	56.3916i	−1.48610	−	1.56643i
$37$	11.0853	−	6.40011i	0.299603	−	0.172976i	−0.342662	−	0.939459i	$-0.611328\pi$
$37$	11.0853	−	6.40011i	0.299603	−	0.172976i	0.642265	+	0.766483i	$0.277995\pi$
$38$	7.09562	+	9.50349i	0.186727	+	0.250092i
$39$	98.8758	+	57.0860i	2.53528	+	1.46374i
$40$	−11.0364	+	13.2645i	−0.275911	+	0.331614i
$41$	43.1339			1.05205			0.526023	−	0.850470i	$-0.323683\pi$
$41$	43.1339			1.05205			0.526023	+	0.850470i	$0.323683\pi$
$42$	−18.7016	+	72.2711i	−0.445276	+	1.72074i
$43$	−41.7382			−0.970656			−0.485328	−	0.874332i	$-0.661300\pi$
$43$	−41.7382			−0.970656			−0.485328	+	0.874332i	$0.661300\pi$
$44$	−5.97732	+	20.1694i	−0.135848	+	0.458395i
$45$	36.2999	+	20.9578i	0.806665	+	0.465728i
$46$	−13.9252	+	10.3970i	−0.302721	+	0.226022i
$47$	−39.8357	+	22.9991i	−0.847567	+	0.489343i	−0.859829	−	0.510582i	$-0.829430\pi$
$47$	−39.8357	+	22.9991i	−0.847567	+	0.489343i	0.0122620	+	0.999925i	$0.496097\pi$
$48$	−4.48745	+	85.1980i	−0.0934885	+	1.77496i
$49$	46.7344	−	14.7273i	0.953764	−	0.300558i
$50$	−16.0667	+	37.3894i	−0.321333	+	0.747788i
$51$	−2.47112	−	4.28011i	−0.0484534	−	0.0839238i
$52$	−19.9828	−	83.2825i	−0.384285	−	1.60159i
$53$	−64.5031	−	37.2409i	−1.21704	−	0.702658i	−0.252756	−	0.967530i	$-0.581337\pi$
$53$	−64.5031	−	37.2409i	−1.21704	−	0.702658i	−0.964284	+	0.264872i	$0.914670\pi$
$54$	110.492	−	13.0702i	2.04614	−	0.242041i
$55$		−	11.3436i		−	0.206246i
$56$	48.9861	−	27.1359i	0.874753	−	0.484570i
$57$	−31.6208			−0.554751
$58$	2.21370	+	18.7140i	0.0381672	+	0.322655i
$59$	−26.8367	+	46.4825i	−0.454860	+	0.787840i	−0.998680	−	0.0513617i	$-0.983644\pi$
$59$	−26.8367	+	46.4825i	−0.454860	+	0.787840i	0.543821	+	0.839201i	$0.316977\pi$
$60$	−10.7338	−	44.7355i	−0.178897	−	0.745592i
$61$	24.0893	−	13.9080i	0.394907	−	0.228000i	−0.289377	−	0.957215i	$-0.593448\pi$
$61$	24.0893	−	13.9080i	0.394907	−	0.228000i	0.684284	+	0.729215i	$0.260115\pi$
$62$	−63.4020	−	27.2446i	−1.02261	−	0.439429i
$63$	−85.1365	−	106.095i	−1.35137	−	1.68404i
$64$	48.6823	−	41.5455i	0.760661	−	0.649149i
$65$	23.0916	+	39.9959i	0.355256	+	0.615322i
$66$	−33.5546	−	44.9412i	−0.508403	−	0.680927i
$67$	39.2453	−	67.9749i	0.585751	−	1.01455i	−0.409030	−	0.912521i	$-0.634133\pi$
$67$	39.2453	−	67.9749i	0.585751	−	1.01455i	0.994781	−	0.102030i	$-0.0325338\pi$
$68$	−1.05343	+	3.55462i	−0.0154917	+	0.0522739i
$69$		−	46.3330i		−	0.671493i
$70$	−21.1685	+	21.5350i	−0.302407	+	0.307643i
$71$			74.5100i			1.04944i	0.851276	+	0.524719i	$0.175829\pi$
$71$			74.5100i			1.04944i	−0.851276	+	0.524719i	$0.824171\pi$
$72$	−119.507	−	99.4329i	−1.65982	−	1.38101i
$73$	−16.8020	+	29.1020i	−0.230165	+	0.398657i	−0.957857	−	0.287247i	$-0.907260\pi$
$73$	−16.8020	+	29.1020i	−0.230165	+	0.398657i	0.727692	+	0.685904i	$0.240593\pi$
$74$	20.5134	−	15.3160i	0.277209	−	0.206973i
$75$	−54.2494	−	93.9627i	−0.723325	−	1.25284i
$76$	16.3258	+	17.2083i	0.214813	+	0.226425i
$77$	−13.3454	+	34.3097i	−0.173317	+	0.445581i
$78$	209.794	+	90.1511i	2.68967	+	1.15578i
$79$	26.1642	−	15.1059i	0.331192	−	0.191214i	−0.325178	−	0.945653i	$-0.605424\pi$
$79$	26.1642	−	15.1059i	0.331192	−	0.191214i	0.656370	+	0.754439i	$0.272091\pi$
$80$	−18.8036	+	28.9384i	−0.235045	+	0.361730i
$81$	−60.8713	+	105.432i	−0.751497	+	1.30163i
$82$	85.6705	−	10.1341i	1.04476	−	0.123586i
$83$	−72.9274			−0.878644			−0.439322	−	0.898330i	$-0.644781\pi$
$83$	−72.9274			−0.878644			−0.439322	+	0.898330i	$0.644781\pi$
$84$	−20.1645	+	147.935i	−0.240054	+	1.76113i
$85$		−	1.99917i		−	0.0235197i
$86$	−82.8984	+	9.80616i	−0.963935	+	0.114025i
$87$	−43.5106	−	25.1209i	−0.500122	−	0.288745i
$88$	−7.13318	+	41.4638i	−0.0810589	+	0.471180i
$89$	27.4198	+	47.4925i	0.308088	+	0.533624i	0.977944	−	0.208867i	$-0.0669776\pi$
$89$	27.4198	+	47.4925i	0.308088	+	0.533624i	−0.669856	+	0.742491i	$0.733644\pi$
$90$	77.0211	+	33.0968i	0.855790	+	0.367743i
$91$	−22.7889	−	148.138i	−0.250428	−	1.62789i
$92$	−25.2148	+	23.9217i	−0.274074	+	0.260018i
$93$	159.335	−	91.9919i	1.71328	−	0.989160i
$94$	−73.7162	+	55.0390i	−0.784215	+	0.585521i
$95$	−11.0772	−	6.39541i	−0.116602	−	0.0673201i
$96$	11.1040	+	170.270i	0.115667	+	1.77365i
$97$	−53.7125			−0.553738			−0.276869	−	0.960908i	$-0.589297\pi$
$97$	−53.7125			−0.553738			−0.276869	+	0.960908i	$0.589297\pi$
$98$	89.3616	−	40.2307i	0.911853	−	0.410518i
$99$	102.200			1.03232
$100$	−23.1264	+	78.0359i	−0.231264	+	0.780359i
$101$	78.2037	+	45.1509i	0.774294	+	0.447039i	0.834404	−	0.551153i	$-0.185812\pi$
$101$	78.2037	+	45.1509i	0.774294	+	0.447039i	−0.0601103	+	0.998192i	$0.519145\pi$
$102$	−5.91362	−	7.92038i	−0.0579766	−	0.0776508i
$103$	97.6980	−	56.4060i	0.948525	−	0.547631i	0.0559023	−	0.998436i	$-0.482196\pi$
$103$	97.6980	−	56.4060i	0.948525	−	0.547631i	0.892622	+	0.450805i	$0.148863\pi$
$104$	−59.2556	−	160.717i	−0.569766	−	1.54535i
$105$	−12.2412	−	79.5731i	−0.116583	−	0.757839i
$106$	−136.863	−	58.8114i	−1.29116	−	0.554825i
$107$	71.9950	+	124.699i	0.672851	+	1.16541i	0.977092	+	0.212817i	$0.0682637\pi$
$107$	71.9950	+	124.699i	0.672851	+	1.16541i	−0.304241	+	0.952595i	$0.598403\pi$
$108$	216.383	−	51.9189i	2.00354	−	0.480730i
$109$	57.7477	+	33.3406i	0.529795	+	0.305877i	0.740933	−	0.671579i	$-0.234384\pi$
$109$	57.7477	+	33.3406i	0.529795	+	0.305877i	−0.211138	+	0.977456i	$0.567717\pi$
$110$	−2.66511	−	22.5300i	−0.0242282	−	0.204818i
$111$			68.2540i			0.614901i
$112$	90.9185	−	65.4051i	0.811772	−	0.583974i
$113$	7.16467			0.0634042			0.0317021	−	0.999497i	$-0.489907\pi$
$113$	7.16467			0.0634042			0.0317021	+	0.999497i	$0.489907\pi$
$114$	−62.8037	+	7.42913i	−0.550910	+	0.0651678i
$115$	9.37101	−	16.2311i	0.0814870	−	0.141140i
$116$	8.79349	+	36.6487i	0.0758060	+	0.315937i
$117$	−360.344	+	208.045i	−3.07986	+	1.77816i
$118$	−42.3810	+	98.6266i	−0.359161	+	0.835818i
$119$	−2.35197	+	6.04670i	−0.0197645	+	0.0508126i
$120$	−31.8294	−	86.3297i	−0.265245	−	0.719414i
$121$	46.6709	+	80.8363i	0.385710	+	0.668069i
$122$	44.5775	−	33.2830i	0.365389	−	0.272812i
$123$	−115.000	+	199.187i	−0.934963	+	1.61940i
$124$	−132.327	−	39.2159i	−1.06715	−	0.316258i
$125$		−	97.8118i		−	0.782494i
$126$	−194.020	−	190.718i	−1.53984	−	1.51363i
$127$			131.492i			1.03537i	0.855572	+	0.517684i	$0.173206\pi$
$127$			131.492i			1.03537i	−0.855572	+	0.517684i	$0.826794\pi$
$128$	86.9296	−	93.9534i	0.679138	−	0.734011i
$129$	111.279	−	192.742i	0.862631	−	1.49412i
$130$	55.2604	+	74.0127i	0.425080	+	0.569329i
$131$	4.38060	+	7.58742i	0.0334397	+	0.0579193i	0.882261	−	0.470761i	$-0.156020\pi$
$131$	4.38060	+	7.58742i	0.0334397	+	0.0579193i	−0.848821	+	0.528680i	$0.822687\pi$
$132$	−77.2032	−	81.3766i	−0.584873	−	0.616489i
$133$	25.9800	+	32.3755i	0.195338	+	0.243425i
$134$	61.9769	−	144.229i	0.462514	−	1.07634i
$135$	−103.916	+	59.9962i	−0.769752	+	0.444416i
$136$	−1.25714	+	7.30752i	−0.00924370	+	0.0537318i
$137$	118.420	−	205.110i	0.864381	−	1.49715i	−0.00327850	−	0.999995i	$-0.501044\pi$
$137$	118.420	−	205.110i	0.864381	−	1.49715i	0.867660	−	0.497158i	$-0.165623\pi$
$138$	−10.8857	−	92.0244i	−0.0788818	−	0.666844i
$139$	172.122			1.23828			0.619142	−	0.785279i	$-0.287480\pi$
$139$	172.122			1.23828			0.619142	+	0.785279i	$0.287480\pi$
$140$	−36.9843	+	47.7453i	−0.264173	+	0.341038i
$141$		−	245.274i		−	1.73954i
$142$	17.5057	+	147.988i	0.123280	+	1.04217i
$143$	97.5195	+	56.3029i	0.681955	+	0.393727i
$144$	−260.721	−	169.411i	−1.81056	−	1.17647i
$145$	−10.1616	−	17.6003i	−0.0700797	−	0.121382i
$146$	−26.5341	+	61.7485i	−0.181740	+	0.422935i
$147$	−56.5909	+	255.078i	−0.384972	+	1.73523i
$148$	37.1444	−	35.2395i	0.250976	−	0.238105i
$149$	−199.798	+	115.354i	−1.34093	+	0.774186i	−0.986944	−	0.161066i	$-0.948507\pi$
$149$	−199.798	+	115.354i	−1.34093	+	0.774186i	−0.353985	+	0.935251i	$0.615174\pi$
$150$	−129.824	−	173.879i	−0.865491	−	1.15919i
$151$	−128.077	−	73.9452i	−0.848190	−	0.489703i	0.0118494	−	0.999930i	$-0.496228\pi$
$151$	−128.077	−	73.9452i	−0.848190	−	0.489703i	−0.860040	+	0.510227i	$0.829561\pi$
$152$	36.4685	+	30.3427i	0.239924	+	0.199623i
$153$	18.0116			0.117723
$154$	−18.4451	+	71.2797i	−0.119773	+	0.462855i
$155$	74.4227			0.480146
$156$	437.864	+	129.764i	2.80682	+	0.831819i
$157$	99.4450	+	57.4146i	0.633407	+	0.365698i	0.782070	−	0.623190i	$-0.214164\pi$
$157$	99.4450	+	57.4146i	0.633407	+	0.365698i	−0.148663	+	0.988888i	$0.547497\pi$
$158$	48.4170	−	36.1498i	0.306437	−	0.228796i
$159$	343.947	−	198.578i	2.16319	−	1.24892i
$160$	−30.5479	+	61.8938i	−0.190924	+	0.386836i
$161$	−47.4389	+	38.0677i	−0.294652	+	0.236446i
$162$	−96.1289	+	223.706i	−0.593388	+	1.38090i
$163$	−24.6545	−	42.7029i	−0.151255	−	0.261981i	0.780434	−	0.625238i	$-0.214998\pi$
$163$	−24.6545	−	42.7029i	−0.151255	−	0.261981i	−0.931689	+	0.363257i	$0.881665\pi$
$164$	167.774	−	40.2556i	1.02301	−	0.245461i
$165$	52.3830	+	30.2433i	0.317473	+	0.183293i
$166$	−144.845	+	17.1339i	−0.872560	+	0.103216i
$167$		−	241.457i		−	1.44585i	−0.690926	−	0.722926i	$-0.742797\pi$
$167$		−	241.457i		−	1.44585i	0.690926	−	0.722926i	$-0.257203\pi$
$168$	−5.29326	+	298.559i	−0.0315075	+	1.77714i
$169$	−289.455			−1.71275
$170$	−0.469695	−	3.97066i	−0.00276291	−	0.0233568i
$171$	57.6196	−	99.8001i	0.336957	−	0.583626i
$172$	−162.345	+	38.9531i	−0.943867	+	0.226471i
$173$	−47.1300	+	27.2105i	−0.272428	+	0.157286i	−0.629990	−	0.776603i	$-0.716941\pi$
$173$	−47.1300	+	27.2105i	−0.272428	+	0.157286i	0.357563	+	0.933889i	$0.383608\pi$
$174$	−92.3207	−	39.6713i	−0.530579	−	0.227996i
$175$	−51.6336	+	132.745i	−0.295049	+	0.758544i
$176$	−4.42590	+	84.0293i	−0.0251471	+	0.477439i
$177$	−143.100	−	247.857i	−0.808475	−	1.40032i
$178$	65.6180	+	87.8852i	0.368641	+	0.493737i
$179$	63.5100	−	110.003i	0.354805	−	0.614540i	−0.632280	−	0.774740i	$-0.717881\pi$
$179$	63.5100	−	110.003i	0.354805	−	0.614540i	0.987084	+	0.160200i	$0.0512141\pi$
$180$	160.751	+	47.6397i	0.893064	+	0.264665i
$181$			212.704i			1.17516i	0.809165	+	0.587581i	$0.199920\pi$
$181$			212.704i			1.17516i	−0.809165	+	0.587581i	$0.800080\pi$
$182$	−80.0666	−	288.871i	−0.439926	−	1.58720i
$183$			148.322i			0.810502i
$184$	−44.4602	+	53.4362i	−0.241632	+	0.290414i
$185$	−13.8046	+	23.9103i	−0.0746194	+	0.129245i
$186$	294.850	−	220.145i	1.58521	−	1.18357i
$187$	−2.43723	−	4.22140i	−0.0130333	−	0.0225743i
$188$	−133.480	+	126.635i	−0.710002	+	0.673590i
$189$	384.890	−	59.2097i	2.03645	−	0.313279i
$190$	−23.5035	−	10.0997i	−0.123703	−	0.0531565i
$191$	−35.1041	+	20.2674i	−0.183791	+	0.106112i	−0.589073	−	0.808080i	$-0.700507\pi$
$191$	−35.1041	+	20.2674i	−0.183791	+	0.106112i	0.405282	+	0.914192i	$0.367174\pi$
$192$	62.0584	+	335.574i	0.323221	+	1.74778i
$193$	−141.153	+	244.485i	−0.731364	+	1.26676i	0.224936	+	0.974374i	$0.427783\pi$
$193$	−141.153	+	244.485i	−0.731364	+	1.26676i	−0.956300	+	0.292387i	$0.905551\pi$
$194$	−106.681	+	12.6195i	−0.549904	+	0.0650488i
$195$	−246.261			−1.26288
$196$	168.034	−	100.899i	0.857315	−	0.514793i
$197$		−	261.806i		−	1.32896i	−0.747304	−	0.664482i	$-0.768652\pi$
$197$		−	261.806i		−	1.32896i	0.747304	−	0.664482i	$-0.231348\pi$
$198$	202.985	−	24.0113i	1.02518	−	0.121269i
$199$	−278.968	−	161.062i	−1.40185	−	0.809357i	−0.407265	−	0.913310i	$-0.633518\pi$
$199$	−278.968	−	161.062i	−1.40185	−	0.809357i	−0.994582	+	0.103953i	$0.966851\pi$
$200$	−27.5985	+	160.425i	−0.137992	+	0.802123i
$201$	209.266	+	362.460i	1.04113	+	1.80328i
$202$	165.932	+	71.3031i	0.821448	+	0.352986i
$203$	10.0283	+	65.1887i	0.0494007	+	0.321127i
$204$	−13.6062	−	14.3417i	−0.0666970	−	0.0703025i
$205$	−80.5723	+	46.5184i	−0.393036	+	0.226919i
$206$	180.791	−	134.984i	0.877626	−	0.655265i
$207$	146.234	+	84.4283i	0.706445	+	0.407866i
$208$	−155.450	−	305.286i	−0.747357	−	1.46772i
$209$	−31.1870			−0.149220
$210$	−43.0081	−	155.168i	−0.204800	−	0.738897i
$211$	169.792			0.804702			0.402351	−	0.915485i	$-0.368193\pi$
$211$	169.792			0.804702			0.402351	+	0.915485i	$0.368193\pi$
$212$	−285.647	−	84.6533i	−1.34739	−	0.399308i
$213$	−344.077	−	198.653i	−1.61539	−	0.932644i
$214$	172.290	+	230.756i	0.805096	+	1.07830i
$215$	77.9652	−	45.0133i	0.362629	−	0.209364i
$216$	417.571	−	153.957i	1.93320	−	0.712763i
$217$	−225.099	−	87.5562i	−1.03732	−	0.403485i
$218$	122.529	+	52.6521i	0.562059	+	0.241523i
$219$	−89.5927	−	155.179i	−0.409099	−	0.708581i
$220$	−10.5866	−	44.1219i	−0.0481210	−	0.200554i
$221$	17.1867	+	9.92275i	0.0777679	+	0.0448993i
$222$	16.0359	+	135.563i	0.0722338	+	0.610643i
$223$			45.4626i			0.203868i	0.994791	+	0.101934i	$0.0325031\pi$
$223$			45.4626i			0.203868i	−0.994791	+	0.101934i	$0.967497\pi$
$224$	165.211	−	151.265i	0.737551	−	0.675291i
$225$	395.414			1.75740
$226$	14.2301	−	1.68330i	0.0629652	−	0.00744823i
$227$	−92.5653	+	160.328i	−0.407777	+	0.706290i	−0.994640	−	0.103396i	$-0.967029\pi$
$227$	−92.5653	+	160.328i	−0.407777	+	0.706290i	0.586864	+	0.809686i	$0.300363\pi$
$228$	−122.992	+	29.5108i	−0.539440	+	0.129433i
$229$	160.173	−	92.4759i	0.699445	−	0.403825i	−0.107695	−	0.994184i	$-0.534347\pi$
$229$	160.173	−	92.4759i	0.699445	−	0.403825i	0.807141	+	0.590359i	$0.201014\pi$
$230$	14.7988	−	34.4390i	0.0643428	−	0.149735i
$231$	−122.857	−	153.101i	−0.531849	−	0.662776i
$232$	26.0756	+	70.7239i	0.112395	+	0.304845i
$233$	−48.3504	−	83.7453i	−0.207512	−	0.359422i	0.743418	−	0.668827i	$-0.233203\pi$
$233$	−48.3504	−	83.7453i	−0.207512	−	0.359422i	−0.950930	+	0.309405i	$0.899870\pi$
$234$	−666.819	+	497.869i	−2.84966	+	2.12765i
$235$	49.6076	−	85.9228i	0.211096	−	0.365629i
$236$	−61.0033	+	205.845i	−0.258489	+	0.872223i
$237$			161.097i			0.679734i
$238$	−3.25073	+	12.5622i	−0.0136585	+	0.0527825i
$239$			163.185i			0.682782i	0.939921	+	0.341391i	$0.110898\pi$
$239$			163.185i			0.682782i	−0.939921	+	0.341391i	$0.889102\pi$
$240$	−83.5008	−	163.986i	−0.347920	−	0.683274i
$241$	−102.745	+	177.960i	−0.426330	+	0.738424i	−0.996544	−	0.0830718i	$-0.973527\pi$
$241$	−102.745	+	177.960i	−0.426330	+	0.738424i	0.570214	+	0.821496i	$0.306860\pi$
$242$	111.687	+	149.588i	0.461519	+	0.618133i
$243$	−74.2413	−	128.590i	−0.305520	−	0.529176i
$244$	80.7180	−	76.5784i	0.330812	−	0.313846i
$245$	−71.4150	+	77.9116i	−0.291490	+	0.318006i
$246$	−181.611	+	422.634i	−0.738254	+	1.71802i
$247$	109.962	−	63.4863i	0.445188	−	0.257030i
$248$	−272.035	−	46.7993i	−1.09692	−	0.188707i
$249$	194.434	−	336.769i	0.780859	−	1.35249i
$250$	−22.9803	−	194.269i	−0.0919214	−	0.777077i
$251$	−159.299			−0.634658			−0.317329	−	0.948316i	$-0.602786\pi$
$251$	−159.299			−0.634658			−0.317329	+	0.948316i	$0.602786\pi$
$252$	−430.162	−	333.211i	−1.70699	−	1.32226i
$253$		−	45.6975i		−	0.180622i
$254$	30.8932	+	261.162i	0.121627	+	1.02820i
$255$	9.23191	+	5.33005i	0.0362036	+	0.0209021i
$256$	150.582	−	207.029i	0.588210	−	0.808708i
$257$	−107.889	−	186.868i	−0.419800	−	0.727114i	0.576119	−	0.817366i	$-0.304566\pi$
$257$	−107.889	−	186.868i	−0.419800	−	0.727114i	−0.995919	+	0.0902512i	$0.971233\pi$
$258$	175.734	−	408.959i	0.681140	−	1.58511i
$259$	69.8832	−	56.0783i	0.269819	−	0.216518i
$260$	127.144	+	134.017i	0.489017	+	0.515452i
$261$	158.571	−	91.5507i	0.607550	−	0.350769i
$262$	10.4832	+	14.0406i	0.0400121	+	0.0535900i
$263$	−285.059	−	164.579i	−1.08387	−	0.625775i	−0.151935	−	0.988391i	$-0.548550\pi$
$263$	−285.059	−	164.579i	−1.08387	−	0.625775i	−0.931939	+	0.362616i	$0.881884\pi$
$264$	−172.456	−	143.488i	−0.653244	−	0.543515i
$265$	160.652			0.606234
$266$	59.2067	+	58.1989i	0.222582	+	0.218793i
$267$	−292.419			−1.09520
$268$	89.2097	−	301.022i	0.332872	−	1.12322i
$269$	253.803	+	146.533i	0.943507	+	0.544734i	0.891058	−	0.453889i	$-0.149964\pi$
$269$	253.803	+	146.533i	0.943507	+	0.544734i	0.0524492	+	0.998624i	$0.483297\pi$
$270$	−192.298	+	143.576i	−0.712216	+	0.531764i
$271$	23.2529	−	13.4251i	0.0858042	−	0.0495391i	−0.456484	−	0.889732i	$-0.650891\pi$
$271$	23.2529	−	13.4251i	0.0858042	−	0.0495391i	0.542288	+	0.840193i	$0.317558\pi$
$272$	−0.780014	+	14.8092i	−0.00286770	+	0.0544456i
$273$	744.841	+	289.719i	2.72836	+	1.06124i
$274$	187.011	−	435.202i	0.682523	−	1.58833i
$275$	−53.5053	−	92.6739i	−0.194565	−	0.336996i
$276$	−43.2413	−	180.217i	−0.156671	−	0.652960i
$277$	−289.925	−	167.389i	−1.04666	−	0.604291i	−0.124949	−	0.992163i	$-0.539877\pi$
$277$	−289.925	−	167.389i	−1.04666	−	0.604291i	−0.921713	+	0.387872i	$0.873210\pi$
$278$	341.860	−	40.4390i	1.22971	−	0.145464i
$279$			670.513i			2.40327i
$280$	−62.2389	+	103.519i	−0.222282	+	0.369709i
$281$	−123.357			−0.438994			−0.219497	−	0.975613i	$-0.570442\pi$
$281$	−123.357			−0.438994			−0.219497	+	0.975613i	$0.570442\pi$
$282$	−57.6259	−	487.152i	−0.204347	−	1.72749i
$283$	0.309453	−	0.535988i	0.00109347	−	0.00189395i	−0.865478	−	0.500947i	$-0.832985\pi$
$283$	0.309453	−	0.535988i	0.00109347	−	0.00189395i	0.866572	+	0.499053i	$0.166319\pi$
$284$	69.5381	+	289.814i	0.244852	+	1.02047i
$285$	59.0663	−	34.1019i	0.207250	−	0.119656i
$286$	206.917	+	88.9145i	0.723485	+	0.310890i
$287$	298.427	−	45.9086i	1.03981	−	0.159960i
$288$	−557.634	−	275.222i	−1.93623	−	0.955631i
$289$	144.070	+	249.537i	0.498514	+	0.863451i
$290$	−24.3175	−	32.5695i	−0.0838534	−	0.112309i
$291$	143.204	−	248.037i	0.492112	−	0.852362i
$292$	−38.1932	+	128.876i	−0.130799	+	0.441356i
$293$			28.2794i			0.0965169i	0.998835	+	0.0482584i	$0.0153671\pi$
$293$			28.2794i			0.0965169i	−0.998835	+	0.0482584i	$0.984633\pi$
$294$	−52.4690	+	519.920i	−0.178466	+	1.76844i
$295$		−	115.770i		−	0.392440i
$296$	65.4951	−	78.7178i	0.221267	−	0.265939i
$297$	−146.285	+	253.373i	−0.492542	+	0.853108i
$298$	−369.728	+	276.051i	−1.24070	+	0.926347i
$299$	93.0247	+	161.123i	0.311119	+	0.538874i
$300$	−298.701	−	314.848i	−0.995671	−	1.04949i
$301$	−288.771	+	44.4231i	−0.959371	+	0.147585i
$302$	−271.753	−	116.775i	−0.899844	−	0.386674i
$303$	−417.002	+	240.756i	−1.37624	+	0.794575i
$304$	79.5608	+	51.6971i	0.261713	+	0.170056i
$305$	−29.9986	+	51.9591i	−0.0983560	+	0.170358i
$306$	35.7738	−	4.23172i	0.116908	−	0.0138292i
$307$	400.893			1.30584			0.652921	−	0.757426i	$-0.273543\pi$
$307$	400.893			1.30584			0.652921	+	0.757426i	$0.273543\pi$
$308$	−19.8879	+	145.906i	−0.0645712	+	0.473721i
$309$			601.542i			1.94674i
$310$	147.815	−	17.4852i	0.476822	−	0.0564039i
$311$	140.492	+	81.1132i	0.451743	+	0.260814i	0.708566	−	0.705644i	$-0.249342\pi$
$311$	140.492	+	81.1132i	0.451743	+	0.260814i	−0.256823	+	0.966459i	$0.582676\pi$
$312$	900.152	+	154.857i	2.88510	+	0.496336i
$313$	133.123	+	230.576i	0.425313	+	0.736664i	0.996450	−	0.0841913i	$-0.0268307\pi$
$313$	133.123	+	230.576i	0.425313	+	0.736664i	−0.571137	+	0.820855i	$0.693497\pi$
$314$	211.002	+	90.6700i	0.671981	+	0.288758i
$315$	273.451	+	106.364i	0.868098	+	0.337662i
$316$	87.6704	−	83.1742i	0.277438	−	0.263210i
$317$	374.864	−	216.428i	1.18254	−	0.682737i	0.225936	−	0.974142i	$-0.427456\pi$
$317$	374.864	−	216.428i	1.18254	−	0.682737i	0.956600	+	0.291405i	$0.0941228\pi$
$318$	636.476	−	475.214i	2.00150	−	1.49438i
$319$	−42.9138	−	24.7763i	−0.134526	−	0.0776686i
$320$	−46.1311	+	130.108i	−0.144160	+	0.406586i
$321$	−767.792			−2.39187
$322$	−85.2772	+	86.7538i	−0.264836	+	0.269422i
$323$	−5.49636			−0.0170166
$324$	−138.368	+	466.898i	−0.427062	+	1.44104i
$325$	377.305	+	217.837i	1.16094	+	0.670269i
$326$	−59.0005	−	79.0220i	−0.180983	−	0.242399i
$327$	−307.925	+	177.781i	−0.941668	+	0.543672i
$328$	323.766	−	119.371i	0.987092	−	0.363937i
$329$	−251.129	+	201.520i	−0.763310	+	0.612524i
$330$	111.146	+	47.7608i	0.336807	+	0.144730i
$331$	−40.6264	−	70.3671i	−0.122738	−	0.212589i	0.798108	−	0.602514i	$-0.205834\pi$
$331$	−40.6264	−	70.3671i	−0.122738	−	0.212589i	−0.920847	+	0.389925i	$0.872501\pi$
$332$	−283.659	+	68.0611i	−0.854394	+	0.205003i
$333$	−215.420	−	124.373i	−0.646907	−	0.373492i
$334$	−56.7290	−	479.571i	−0.169847	−	1.43584i
$335$			169.299i			0.505370i
$336$	59.6317	+	594.228i	0.177475	+	1.76854i
$337$	−69.4941			−0.206214			−0.103107	−	0.994670i	$-0.532878\pi$
$337$	−69.4941			−0.206214			−0.103107	+	0.994670i	$0.532878\pi$
$338$	−574.902	+	68.0059i	−1.70089	+	0.201201i
$339$	−19.1019	+	33.0855i	−0.0563479	+	0.0975974i
$340$	−1.86577	−	7.77598i	−0.00548756	−	0.0228705i
$341$	157.149	−	90.7300i	0.460848	−	0.266071i
$342$	90.9938	−	211.756i	0.266064	−	0.619168i
$343$	307.663	−	151.634i	0.896975	−	0.442080i
$344$	−313.290	+	115.509i	−0.910727	+	0.335781i
$345$	49.9686	+	86.5481i	0.144836	+	0.250864i
$346$	−87.2145	+	65.1172i	−0.252065	+	0.188200i
$347$	174.677	−	302.549i	0.503391	−	0.871899i	−0.496601	−	0.867979i	$-0.665419\pi$
$347$	174.677	−	302.549i	0.503391	−	0.871899i	0.999992	−	0.00392020i	$-0.00124784\pi$
$348$	−192.683	−	57.1029i	−0.553688	−	0.164089i
$349$		−	165.836i		−	0.475174i	−0.971366	−	0.237587i	$-0.923643\pi$
$349$		−	165.836i		−	0.475174i	0.971366	−	0.237587i	$-0.0763566\pi$
$350$	−71.3644	+	275.783i	−0.203898	+	0.787952i
$351$		−	1191.15i		−	3.39358i
$352$	10.9517	+	167.935i	0.0311129	+	0.477088i
$353$	235.858	−	408.519i	0.668154	−	1.15728i	−0.310266	−	0.950650i	$-0.600418\pi$
$353$	235.858	−	408.519i	0.668154	−	1.15728i	0.978420	−	0.206627i	$-0.0662486\pi$
$354$	−342.451	−	458.661i	−0.967377	−	1.29565i
$355$	−80.3566	−	139.182i	−0.226356	−	0.392061i
$356$	150.976	+	159.137i	0.424089	+	0.447014i
$357$	−21.6522	−	26.9823i	−0.0606504	−	0.0755808i
$358$	100.296	−	233.403i	0.280157	−	0.651964i
$359$	568.967	−	328.493i	1.58487	−	0.915022i	0.590731	−	0.806869i	$-0.298839\pi$
$359$	568.967	−	328.493i	1.58487	−	0.915022i	0.994134	−	0.108154i	$-0.0344939\pi$
$360$	330.470	+	56.8520i	0.917971	+	0.157922i
$361$	162.917	−	282.180i	0.451294	−	0.781663i
$362$	49.9737	+	422.463i	0.138049	+	1.16703i
$363$	−497.722			−1.37113
$364$	−226.893	−	554.931i	−0.623333	−	1.52454i
$365$		−	72.4817i		−	0.198580i
$366$	34.8474	+	294.590i	0.0952115	+	0.804890i
$367$	−307.850	−	177.737i	−0.838829	−	0.484298i	0.0180371	−	0.999837i	$-0.494258\pi$
$367$	−307.850	−	177.737i	−0.838829	−	0.484298i	−0.856866	+	0.515539i	$0.827592\pi$
$368$	−75.7502	+	116.578i	−0.205843	+	0.316788i
$369$	−419.109	−	725.918i	−1.13580	−	1.96726i
$370$	−21.8004	+	50.7327i	−0.0589201	+	0.137116i
$371$	−485.908	−	189.003i	−1.30973	−	0.509441i
$372$	533.895	−	506.514i	1.43520	−	1.36160i
$373$	−273.662	+	157.999i	−0.733680	+	0.423590i	−0.819767	−	0.572698i	$-0.805897\pi$
$373$	−273.662	+	157.999i	−0.733680	+	0.423590i	0.0860872	+	0.996288i	$0.472564\pi$
$374$	−5.83250	−	7.81173i	−0.0155949	−	0.0208870i
$375$	451.682	+	260.779i	1.20449	+	0.695410i
$376$	−235.360	+	282.877i	−0.625958	+	0.752332i
$377$	201.745			0.535132
$378$	750.539	−	208.027i	1.98555	−	0.550337i
$379$	−178.404			−0.470723			−0.235361	−	0.971908i	$-0.575627\pi$
$379$	−178.404			−0.470723			−0.235361	+	0.971908i	$0.575627\pi$
$380$	−49.0544	−	14.5376i	−0.129091	−	0.0382568i
$381$	−607.211	−	350.574i	−1.59373	−	0.920140i
$382$	−64.9604	+	48.5016i	−0.170053	+	0.126968i
$383$	−604.832	+	349.200i	−1.57920	+	0.911750i	−0.584225	+	0.811591i	$0.698602\pi$
$383$	−604.832	+	349.200i	−1.57920	+	0.911750i	−0.994972	+	0.100158i	$0.968065\pi$
$384$	202.099	+	651.921i	0.526299	+	1.69771i
$385$	−12.0733	−	78.4816i	−0.0313591	−	0.203848i
$386$	−222.912	+	518.747i	−0.577491	+	1.34390i
$387$	405.548	+	702.430i	1.04793	+	1.81506i
$388$	−208.920	+	50.1284i	−0.538455	+	0.129197i
$389$	−151.865	−	87.6790i	−0.390397	−	0.225396i	0.291935	−	0.956438i	$-0.405701\pi$
$389$	−151.865	−	87.6790i	−0.390397	−	0.225396i	−0.682332	+	0.731042i	$0.739034\pi$
$390$	−489.112	+	57.8577i	−1.25413	+	0.148353i
$391$		−	8.05366i		−	0.0205976i
$392$	310.035	−	239.880i	0.790905	−	0.611939i
$393$	−46.7170			−0.118873
$394$	−61.5099	−	519.987i	−0.156117	−	1.31976i
$395$	−32.5824	+	56.4344i	−0.0824871	+	0.142872i
$396$	397.517	−	95.3803i	1.00383	−	0.240859i
$397$	334.033	−	192.854i	0.841393	−	0.485778i	−0.0163447	−	0.999866i	$-0.505203\pi$
$397$	334.033	−	192.854i	0.841393	−	0.485778i	0.857737	+	0.514088i	$0.171870\pi$
$398$	−591.913	−	254.352i	−1.48722	−	0.639075i
$399$	−218.772	+	33.6549i	−0.548301	+	0.0843481i
$400$	−17.1239	+	325.112i	−0.0428098	+	0.812779i
$401$	−263.548	−	456.479i	−0.657228	−	1.13835i	−0.981330	−	0.192330i	$-0.938396\pi$
$401$	−263.548	−	456.479i	−0.657228	−	1.13835i	0.324103	−	0.946022i	$-0.394938\pi$
$402$	500.792	+	670.734i	1.24575	+	1.66849i
$403$	−369.392	+	639.805i	−0.916605	+	1.58761i
$404$	346.319	+	102.634i	0.857226	+	0.254044i
$405$		−	262.590i		−	0.648371i
$406$	35.2335	+	127.119i	0.0867821	+	0.313100i
$407$			67.3178i			0.165400i
$408$	−30.3935	−	25.2881i	−0.0744938	−	0.0619807i
$409$	211.872	−	366.973i	0.518025	−	0.897245i	−0.481756	−	0.876305i	$-0.660001\pi$
$409$	211.872	−	366.973i	0.518025	−	0.897245i	0.999781	−	0.0209399i	$-0.00666585\pi$
$410$	−149.100	+	111.323i	−0.363658	+	0.271519i
$411$	631.447	+	1093.70i	1.53637	+	2.66107i
$412$	327.364	−	310.576i	0.794574	−	0.753824i
$413$	−136.200	+	350.158i	−0.329782	+	0.847840i
$414$	310.279	+	133.331i	0.749467	+	0.322055i
$415$	136.225	−	78.6498i	0.328254	−	0.189517i
$416$	−380.473	−	569.823i	−0.914599	−	1.36977i
$417$	−458.898	+	794.834i	−1.10047	+	1.90608i
$418$	−61.9422	+	7.32723i	−0.148187	+	0.0175292i
$419$	295.598			0.705485			0.352742	−	0.935721i	$-0.385249\pi$
$419$	295.598			0.705485			0.352742	+	0.935721i	$0.385249\pi$
$420$	−121.877	−	298.083i	−0.290182	−	0.709723i
$421$			126.260i			0.299904i	0.988693	+	0.149952i	$0.0479119\pi$
$421$			126.260i			0.299904i	−0.988693	+	0.149952i	$0.952088\pi$
$422$	337.233	−	39.8917i	0.799131	−	0.0945302i
$423$	774.124	+	446.941i	1.83008	+	1.05660i
$424$	−587.228	−	101.023i	−1.38497	−	0.238262i
$425$	−9.42970	−	16.3327i	−0.0221875	−	0.0384299i
$426$	−730.063	−	313.716i	−1.71376	−	0.736424i
$427$	151.862	−	121.863i	0.355649	−	0.285393i
$428$	396.410	+	417.839i	0.926192	+	0.976259i
$429$	−519.999	+	300.221i	−1.21212	+	0.699817i
$430$	144.275	−	107.721i	0.335524	−	0.250513i
$431$	220.198	+	127.131i	0.510900	+	0.294968i	0.733204	−	0.680009i	$-0.238024\pi$
$431$	220.198	+	127.131i	0.510900	+	0.294968i	−0.222303	+	0.974978i	$0.571358\pi$
$432$	793.188	−	403.887i	1.83608	−	0.934925i
$433$	546.301			1.26167			0.630833	−	0.775919i	$-0.282713\pi$
$433$	546.301			1.26167			0.630833	+	0.775919i	$0.282713\pi$
$434$	−467.651	−	121.014i	−1.07754	−	0.278835i
$435$	108.368			0.249122
$436$	255.731	+	75.7876i	0.586540	+	0.173825i
$437$	−44.6244	−	25.7639i	−0.102115	−	0.0589563i
$438$	−214.403	−	287.160i	−0.489505	−	0.655617i
$439$	−236.715	+	136.667i	−0.539214	+	0.311315i	−0.744760	−	0.667332i	$-0.767436\pi$
$439$	−236.715	+	136.667i	−0.539214	+	0.311315i	0.205546	+	0.978647i	$0.434103\pi$
$440$	−31.3928	−	85.1456i	−0.0713473	−	0.193513i
$441$	−701.946	−	643.415i	−1.59171	−	1.45899i
$442$	36.4667	+	15.6702i	0.0825039	+	0.0354529i
$443$	−237.385	−	411.163i	−0.535858	−	0.928133i	−0.999121	−	0.0419124i	$-0.986655\pi$
$443$	−237.385	−	411.163i	−0.535858	−	0.928133i	0.463263	−	0.886221i	$-0.346678\pi$
$444$	63.6995	+	265.481i	0.143467	+	0.597930i
$445$	−102.438	−	59.1427i	−0.230198	−	0.132905i
$446$	10.6812	+	90.2957i	0.0239489	+	0.202457i
$447$		−	1230.19i		−	2.75210i
$448$	292.596	−	339.251i	0.653116	−	0.757257i
$449$	782.101			1.74187			0.870936	−	0.491396i	$-0.163513\pi$
$449$	782.101			1.74187			0.870936	+	0.491396i	$0.163513\pi$
$450$	785.353	−	92.9004i	1.74523	−	0.206445i
$451$	−113.423	+	196.454i	−0.251492	+	0.435597i
$452$	27.8677	−	6.68658i	0.0616542	−	0.0147933i
$453$	682.938	−	394.294i	1.50759	−	0.870407i
$454$	−146.181	+	340.183i	−0.321984	+	0.749302i
$455$	202.331	+	252.139i	0.444683	+	0.554152i
$456$	−237.348	+	87.5092i	−0.520500	+	0.191906i
$457$	94.7793	+	164.163i	0.207395	+	0.359218i	0.950893	−	0.309520i	$-0.100168\pi$
$457$	94.7793	+	164.163i	0.207395	+	0.359218i	−0.743498	+	0.668738i	$0.766835\pi$
$458$	296.401	−	221.303i	0.647164	−	0.483194i
$459$	−25.7811	+	44.6541i	−0.0561679	+	0.0972857i
$460$	21.3015	−	71.8781i	0.0463076	−	0.156257i
$461$			202.533i			0.439335i	0.975575	+	0.219667i	$0.0704972\pi$
$461$			202.533i			0.439335i	−0.975575	+	0.219667i	$0.929503\pi$
$462$	−279.983	−	275.218i	−0.606025	−	0.595709i
$463$			652.927i			1.41021i	0.709103	+	0.705105i	$0.249100\pi$
$463$			652.927i			1.41021i	−0.709103	+	0.705105i	$0.750900\pi$
$464$	68.4064	+	134.342i	0.147428	+	0.289531i
$465$	−198.420	+	343.674i	−0.426710	+	0.739084i
$466$	−115.707	−	154.971i	−0.248298	−	0.332556i
$467$	−272.725	−	472.373i	−0.583993	−	1.01150i	−0.995000	−	0.0998730i	$-0.968156\pi$
$467$	−272.725	−	472.373i	−0.583993	−	1.01150i	0.411008	−	0.911632i	$-0.365177\pi$
$468$	−1207.43	+	1145.51i	−2.57998	+	2.44767i
$469$	199.176	−	512.062i	0.424682	−	1.09182i
$470$	78.3411	−	182.311i	0.166683	−	0.387895i
$471$	−530.266	+	306.149i	−1.12583	+	0.649998i
$472$	−72.7998	+	423.171i	−0.154237	+	0.896549i
$473$	109.753	−	190.098i	0.232036	−	0.401898i
$474$	37.8489	+	319.963i	0.0798499	+	0.675028i
$475$	−120.663			−0.254028
$476$	−3.50502	+	25.7143i	−0.00736349	+	0.0540216i
$477$			1447.40i			3.03438i
$478$	38.3394	+	324.110i	0.0802079	+	0.678054i
$479$	−94.3079	−	54.4487i	−0.196885	−	0.113672i	0.398317	−	0.917248i	$-0.369595\pi$
$479$	−94.3079	−	54.4487i	−0.196885	−	0.113672i	−0.595202	+	0.803576i	$0.702928\pi$
$480$	−204.373	−	306.083i	−0.425777	−	0.637672i
$481$	−137.036	−	237.354i	−0.284899	−	0.493459i
$482$	−162.257	+	377.596i	−0.336633	+	0.783394i
$483$	−49.3135	−	320.560i	−0.102098	−	0.663686i
$484$	256.973	+	270.865i	0.530937	+	0.559637i
$485$	100.333	−	57.9272i	0.206872	−	0.119437i
$486$	−177.666	−	237.956i	−0.365568	−	0.489622i
$487$	371.831	+	214.677i	0.763513	+	0.440814i	0.830556	−	0.556936i	$-0.188023\pi$
$487$	371.831	+	214.677i	0.763513	+	0.440814i	−0.0670428	+	0.997750i	$0.521356\pi$
$488$	142.327	−	171.061i	0.291653	−	0.350534i
$489$	262.929			0.537686
$490$	−123.536	+	171.523i	−0.252115	+	0.350046i
$491$	453.887			0.924413			0.462206	−	0.886772i	$-0.347058\pi$
$491$	453.887			0.924413			0.462206	+	0.886772i	$0.347058\pi$
$492$	−261.411	+	882.083i	−0.531323	+	1.79285i
$493$	−7.56306	−	4.36654i	−0.0153409	−	0.00885707i
$494$	203.485	−	151.928i	0.411912	−	0.307547i
$495$	−190.905	+	110.219i	−0.385667	+	0.222665i
$496$	−551.299	−	29.0374i	−1.11149	−	0.0585431i
$497$	79.3031	+	515.506i	0.159564	+	1.03724i
$498$	307.053	−	714.556i	0.616572	−	1.43485i
$499$	−166.698	−	288.730i	−0.334064	−	0.578617i	0.649240	−	0.760583i	$-0.275087\pi$
$499$	−166.698	−	288.730i	−0.334064	−	0.578617i	−0.983305	+	0.181967i	$0.941754\pi$
$500$	−91.2849	−	380.449i	−0.182570	−	0.760898i
$501$	1115.02	+	643.755i	2.22558	+	1.28494i
$502$	−316.392	+	37.4265i	−0.630264	+	0.0745547i
$503$		−	580.170i		−	1.15342i	−0.816949	−	0.576710i	$-0.804336\pi$
$503$		−	580.170i		−	1.15342i	0.816949	−	0.576710i	$-0.195664\pi$
$504$	−932.654	−	560.743i	−1.85050	−	1.11259i
$505$	−194.775			−0.385693
$506$	−10.7364	−	90.7621i	−0.0212181	−	0.179372i
$507$	771.724	−	1336.67i	1.52214	−	2.63642i
$508$	122.717	+	511.450i	0.241570	+	1.00679i
$509$	−266.271	+	153.732i	−0.523126	+	0.302027i	−0.738213	−	0.674568i	$-0.764330\pi$
$509$	−266.271	+	153.732i	−0.523126	+	0.302027i	0.215087	+	0.976595i	$0.430997\pi$
$510$	19.5882	+	8.41730i	0.0384083	+	0.0165045i
$511$	−85.2728	+	219.228i	−0.166874	+	0.429018i
$512$	250.438	−	446.570i	0.489136	−	0.872207i
$513$	164.949	+	285.700i	0.321538	+	0.556919i
$514$	−258.187	−	345.801i	−0.502309	−	0.672765i
$515$	−121.664	+	210.728i	−0.236241	+	0.409181i
$516$	252.952	−	853.542i	0.490218	−	1.65415i
$517$		−	241.910i		−	0.467911i
$518$	125.623	−	127.799i	0.242516	−	0.246716i
$519$		−	290.187i		−	0.559127i
$520$	284.015	+	236.307i	0.546182	+	0.454437i
$521$	−360.480	+	624.369i	−0.691899	+	1.19840i	0.279316	+	0.960199i	$0.409892\pi$
$521$	−360.480	+	624.369i	−0.691899	+	1.19840i	−0.971215	+	0.238205i	$0.923441\pi$
$522$	293.436	−	219.089i	0.562138	−	0.419711i
$523$	134.988	+	233.807i	0.258104	+	0.447049i	0.965734	−	0.259534i	$-0.0835689\pi$
$523$	134.988	+	233.807i	0.258104	+	0.447049i	−0.707630	+	0.706583i	$0.750236\pi$
$524$	24.1199	+	25.4238i	0.0460304	+	0.0485186i
$525$	−475.338	−	592.353i	−0.905405	−	1.12829i
$526$	−604.837	−	259.905i	−1.14988	−	0.494117i
$527$	27.6957	−	15.9901i	0.0525536	−	0.0303418i
$528$	−376.236	−	244.471i	−0.712569	−	0.463013i
$529$	−226.749	+	392.741i	−0.428637	+	0.742421i
$530$	319.080	−	37.7443i	0.602037	−	0.0712157i
$531$	1043.03			1.96428
$532$	131.267	+	101.682i	0.246743	+	0.191131i
$533$		−	923.564i		−	1.73277i
$534$	−580.788	+	68.7022i	−1.08762	+	0.128656i
$535$	−268.967	−	155.288i	−0.502743	−	0.290259i
$536$	106.461	−	618.835i	0.198621	−	1.15454i
$537$	338.652	+	586.562i	0.630636	+	1.09229i
$538$	538.520	+	231.408i	1.00097	+	0.430127i
$539$	−55.8147	+	251.579i	−0.103552	+	0.466752i
$540$	−348.201	+	330.344i	−0.644817	+	0.611748i
$541$	−785.695	+	453.621i	−1.45230	+	0.838486i	−0.998612	−	0.0526734i	$-0.983226\pi$
$541$	−785.695	+	453.621i	−1.45230	+	0.838486i	−0.453689	+	0.891160i	$0.649892\pi$
$542$	43.0297	−	32.1274i	0.0793907	−	0.0592757i
$543$	−982.241	−	567.097i	−1.80891	−	1.04438i
$544$	1.93012	+	29.5966i	0.00354801	+	0.0544055i
$545$	−143.827			−0.263903
$546$	1547.44	+	400.430i	2.83413	+	0.733389i
$547$	−557.327			−1.01888			−0.509439	−	0.860506i	$-0.670147\pi$
$547$	−557.327			−1.01888			−0.509439	+	0.860506i	$0.670147\pi$
$548$	269.185	−	908.314i	0.491213	−	1.65751i
$549$	−468.127	−	270.273i	−0.852690	−	0.492301i
$550$	−128.043	−	171.494i	−0.232805	−	0.311807i
$551$	−48.3889	+	27.9374i	−0.0878202	+	0.0507030i
$552$	−128.225	−	347.779i	−0.232291	−	0.630035i
$553$	164.942	−	132.359i	0.298268	−	0.239347i
$554$	−615.163	−	264.343i	−1.11040	−	0.477153i
$555$	−73.6096	−	127.496i	−0.132630	−	0.229722i
$556$	669.484	−	160.636i	1.20411	−	0.288914i
$557$	741.896	+	428.334i	1.33195	+	0.769002i	0.985598	−	0.169103i	$-0.0540869\pi$
$557$	741.896	+	428.334i	1.33195	+	0.769002i	0.346352	+	0.938105i	$0.387420\pi$
$558$	157.533	+	1331.74i	0.282318	+	2.38663i
$559$			893.680i			1.59871i
$560$	−99.2948	+	220.226i	−0.177312	+	0.393262i
$561$	25.9918			0.0463313
$562$	−245.006	+	28.9821i	−0.435954	+	0.0515696i
$563$	−6.84436	+	11.8548i	−0.0121569	+	0.0210564i	−0.872040	−	0.489435i	$-0.837203\pi$
$563$	−6.84436	+	11.8548i	−0.0121569	+	0.0210564i	0.859883	+	0.510491i	$0.170536\pi$
$564$	−228.908	−	954.020i	−0.405865	−	1.69152i
$565$	−13.3833	+	7.72686i	−0.0236873	+	0.0136759i
$566$	0.488693	−	1.13726i	0.000863416	−	0.00200929i
$567$	−308.930	+	794.231i	−0.544851	+	1.40076i
$568$	206.204	+	559.278i	0.363034	+	0.984644i
$569$	545.991	+	945.684i	0.959563	+	1.66201i	0.723563	+	0.690258i	$0.242503\pi$
$569$	545.991	+	945.684i	0.959563	+	1.66201i	0.235999	+	0.971753i	$0.424164\pi$
$570$	109.303	−	81.6090i	0.191759	−	0.143174i
$571$	−359.549	+	622.757i	−0.629683	+	1.09064i	0.357932	+	0.933747i	$0.383482\pi$
$571$	−359.549	+	622.757i	−0.629683	+	1.09064i	−0.987615	+	0.156895i	$0.949852\pi$
$572$	431.858	+	127.984i	0.754997	+	0.223748i
$573$		−	216.142i		−	0.377210i
$574$	581.935	−	161.295i	1.01382	−	0.281002i
$575$		−	176.805i		−	0.307486i
$576$	−1172.21	−	415.620i	−2.03508	−	0.721562i
$577$	515.560	−	892.976i	0.893518	−	1.54762i	0.0578905	−	0.998323i	$-0.481563\pi$
$577$	515.560	−	892.976i	0.893518	−	1.54762i	0.835628	−	0.549296i	$-0.185104\pi$
$578$	344.773	+	461.771i	0.596494	+	0.798911i
$579$	−752.665	−	1303.65i	−1.29994	−	2.25156i
$580$	−55.9503	−	58.9748i	−0.0964660	−	0.101681i
$581$	−504.557	+	77.6187i	−0.868428	+	0.133595i
$582$	226.151	−	526.285i	0.388575	−	0.904270i
$583$	339.229	−	195.854i	0.581868	−	0.335942i
$584$	−45.5788	+	264.941i	−0.0780459	+	0.453666i
$585$	448.738	−	777.238i	0.767074	−	1.32861i
$586$	6.64410	+	56.1673i	0.0113381	+	0.0958486i
$587$	−671.907			−1.14464			−0.572322	−	0.820029i	$-0.693957\pi$
$587$	−671.907			−1.14464			−0.572322	+	0.820029i	$0.693957\pi$
$588$	17.9410	+	1044.97i	0.0305119	+	1.77716i
$589$		−	204.612i		−	0.347388i
$590$	−27.1995	−	229.937i	−0.0461009	−	0.389723i
$591$	1208.99	+	698.008i	2.04566	+	1.18106i
$592$	111.589	−	171.733i	0.188495	−	0.290090i
$593$	−176.999	−	306.572i	−0.298481	−	0.516984i	0.677308	−	0.735700i	$-0.263147\pi$
$593$	−176.999	−	306.572i	−0.298481	−	0.516984i	−0.975789	+	0.218716i	$0.929813\pi$
$594$	−231.016	+	537.606i	−0.388915	+	0.905061i
$595$	−2.12777	−	13.8315i	−0.00357609	−	0.0232462i
$596$	−669.480	+	635.146i	−1.12329	+	1.06568i
$597$	1487.53	−	858.824i	2.49167	−	1.43857i
$598$	222.616	+	298.160i	0.372268	+	0.498595i
$599$	−983.923	−	568.068i	−1.64261	−	0.948361i	−0.979901	−	0.199484i	$-0.936074\pi$
$599$	−983.923	−	568.068i	−1.64261	−	0.948361i	−0.662708	−	0.748878i	$-0.730593\pi$
$600$	−667.238	−	555.158i	−1.11206	−	0.925264i
$601$	−6.80783			−0.0113275			−0.00566375	−	0.999984i	$-0.501803\pi$
$601$	−6.80783			−0.0113275			−0.00566375	+	0.999984i	$0.501803\pi$
$602$	−563.105	+	156.076i	−0.935391	+	0.259263i
$603$	−1525.30			−2.52953
$604$	−567.179	−	168.087i	−0.939037	−	0.278290i
$605$	−174.358	−	100.666i	−0.288196	−	0.166390i
$606$	−771.665	+	576.151i	−1.27337	+	0.950744i
$607$	386.628	−	223.220i	0.636948	−	0.367742i	−0.146490	−	0.989212i	$-0.546798\pi$
$607$	386.628	−	223.220i	0.636948	−	0.367742i	0.783438	+	0.621470i	$0.213464\pi$
$608$	170.166	+	83.9859i	0.279878	+	0.138135i
$609$	−327.770	−	127.492i	−0.538210	−	0.209346i
$610$	−47.3743	+	110.247i	−0.0776627	+	0.180732i
$611$	492.447	+	852.944i	0.805970	+	1.39598i
$612$	70.0579	−	16.8097i	0.114474	−	0.0274668i
$613$	555.650	+	320.805i	0.906443	+	0.523335i	0.879285	−	0.476296i	$-0.158021\pi$
$613$	555.650	+	320.805i	0.906443	+	0.523335i	0.0271583	+	0.999631i	$0.491354\pi$
$614$	796.235	−	94.1877i	1.29680	−	0.153400i
$615$		−	496.096i		−	0.806661i
$616$	−5.22065	+	294.464i	−0.00847509	+	0.478026i
$617$	−502.890			−0.815057			−0.407528	−	0.913193i	$-0.633609\pi$
$617$	−502.890			−0.815057			−0.407528	+	0.913193i	$0.633609\pi$
$618$	141.329	+	1194.75i	0.228688	+	1.93326i
$619$	−216.495	+	374.980i	−0.349749	+	0.605783i	−0.986205	−	0.165530i	$-0.947066\pi$
$619$	−216.495	+	374.980i	−0.349749	+	0.605783i	0.636456	+	0.771313i	$0.280400\pi$
$620$	289.475	−	69.4565i	0.466894	−	0.112027i
$621$	−418.627	+	241.695i	−0.674118	+	0.389202i
$622$	298.096	+	128.095i	0.479254	+	0.205941i
$623$	240.255	+	299.399i	0.385642	+	0.480576i
$624$	1824.22	+	96.0833i	2.92343	+	0.153980i
$625$	−148.859	−	257.831i	−0.238174	−	0.412530i
$626$	318.575	+	426.682i	0.508906	+	0.681601i
$627$	83.1486	−	144.018i	0.132613	−	0.229693i
$628$	440.385	+	130.511i	0.701250	+	0.207820i
$629$			11.8640i			0.0188617i
$630$	568.105	+	147.009i	0.901754	+	0.233347i
$631$		−	238.957i		−	0.378695i	−0.981910	−	0.189348i	$-0.939363\pi$
$631$		−	238.957i		−	0.378695i	0.981910	−	0.189348i	$-0.0606373\pi$
$632$	154.585	−	185.794i	0.244597	−	0.293978i
$633$	−452.687	+	784.078i	−0.715146	+	1.23867i
$634$	693.688	−	517.930i	1.09414	−	0.816925i
$635$	−141.809	−	245.621i	−0.223322	−	0.386805i
$636$	1152.49	−	1093.38i	1.81209	−	1.71916i
$637$	−315.336	−	1000.66i	−0.495032	−	1.57089i
$638$	−91.0543	−	39.1271i	−0.142718	−	0.0613277i
$639$	1253.96	−	723.974i	1.96238	−	1.13298i
$640$	−61.0554	+	269.252i	−0.0953991	+	0.420706i
$641$	3.98065	−	6.89469i	0.00621006	−	0.0107561i	−0.862904	−	0.505368i	$-0.831357\pi$
$641$	3.98065	−	6.89469i	0.00621006	−	0.0107561i	0.869114	+	0.494612i	$0.164690\pi$
$642$	−1524.95	+	180.388i	−2.37531	+	0.280979i
$643$	−584.919			−0.909672			−0.454836	−	0.890575i	$-0.650302\pi$
$643$	−584.919			−0.909672			−0.454836	+	0.890575i	$0.650302\pi$
$644$	−148.991	+	192.342i	−0.231353	+	0.298667i
$645$			480.044i			0.744255i
$646$	−10.9166	+	1.29134i	−0.0168988	+	0.00199898i
$647$	−290.707	−	167.840i	−0.449316	−	0.259413i	0.258225	−	0.966085i	$-0.416862\pi$
$647$	−290.707	−	167.840i	−0.449316	−	0.259413i	−0.707541	+	0.706672i	$0.750196\pi$
$648$	−165.125	+	959.840i	−0.254823	+	1.48123i
$649$	−141.137	−	244.457i	−0.217469	−	0.376667i
$650$	800.566	+	344.012i	1.23164	+	0.529250i
$651$	1004.46	−	806.040i	1.54296	−	1.23816i
$652$	−135.750	−	143.088i	−0.208205	−	0.219460i
$653$	42.0252	−	24.2632i	0.0643571	−	0.0371566i	−0.467476	−	0.884006i	$-0.654837\pi$
$653$	42.0252	−	24.2632i	0.0643571	−	0.0371566i	0.531833	+	0.846849i	$0.321503\pi$
$654$	−569.818	+	425.445i	−0.871281	+	0.650528i
$655$	−16.3656	−	9.44866i	−0.0249856	−	0.0144254i
$656$	615.003	−	313.157i	0.937505	−	0.477373i
$657$	653.026			0.993951
$658$	−451.434	+	459.251i	−0.686070	+	0.697950i
$659$	1224.65			1.85835			0.929176	−	0.369638i	$-0.120518\pi$
$659$	1224.65			1.85835			0.929176	+	0.369638i	$0.120518\pi$
$660$	231.974	+	68.7470i	0.351476	+	0.104162i
$661$	725.765	+	419.021i	1.09798	+	0.633919i	0.935690	−	0.352823i	$-0.114778\pi$
$661$	725.765	+	419.021i	1.09798	+	0.633919i	0.162291	+	0.986743i	$0.448112\pi$
$662$	−97.2226	−	130.215i	−0.146862	−	0.196699i
$663$	−91.6439	+	52.9106i	−0.138226	+	0.0798049i
$664$	−547.399	+	201.824i	−0.824396	+	0.303951i
$665$	−83.4455	−	32.4576i	−0.125482	−	0.0488084i
$666$	−457.078	−	196.412i	−0.686303	−	0.294912i
$667$	−40.9358	−	70.9029i	−0.0613730	−	0.106301i
$668$	−225.345	−	939.172i	−0.337343	−	1.40595i
$669$	−209.940	−	121.209i	−0.313812	−	0.181180i
$670$	39.7759	+	336.254i	0.0593670	+	0.501871i
$671$			146.287i			0.218014i
$672$	258.048	+	1166.22i	0.384000	+	1.73544i
$673$	147.714			0.219486			0.109743	−	0.993960i	$-0.464997\pi$
$673$	147.714			0.219486			0.109743	+	0.993960i	$0.464997\pi$
$674$	−138.026	+	16.3273i	−0.204786	+	0.0242244i
$675$	−565.980	+	980.307i	−0.838490	+	1.45231i
$676$	−1125.87	+	270.140i	−1.66548	+	0.399616i
$677$	−725.024	+	418.593i	−1.07094	+	0.618305i	−0.928437	−	0.371490i	$-0.878847\pi$
$677$	−725.024	+	418.593i	−1.07094	+	0.618305i	−0.142499	+	0.989795i	$0.545514\pi$
$678$	−30.1661	+	70.2007i	−0.0444927	+	0.103541i
$679$	−371.616	+	57.1678i	−0.547299	+	0.0841941i
$680$	−5.53263	−	15.0059i	−0.00813622	−	0.0220676i
$681$	−493.582	−	854.909i	−0.724790	−	1.25537i
$682$	290.805	−	217.125i	0.426401	−	0.318365i
$683$	32.2189	−	55.8047i	0.0471725	−	0.0817053i	−0.841475	−	0.540296i	$-0.818312\pi$
$683$	32.2189	−	55.8047i	0.0471725	−	0.0817053i	0.888648	+	0.458591i	$0.151646\pi$
$684$	130.977	−	441.957i	0.191486	−	0.646136i
$685$			510.849i			0.745765i
$686$	575.439	−	373.451i	0.838833	−	0.544389i
$687$			986.210i			1.43553i
$688$	−595.104	+	303.024i	−0.864976	+	0.440442i
$689$	−797.385	+	1381.11i	−1.15731	+	2.00452i
$690$	119.579	+	160.158i	0.173303	+	0.232113i
$691$	263.374	+	456.177i	0.381149	+	0.660169i	0.991227	−	0.132172i	$-0.0421953\pi$
$691$	263.374	+	456.177i	0.381149	+	0.660169i	−0.610078	+	0.792341i	$0.708862\pi$
$692$	−157.922	+	149.823i	−0.228211	+	0.216508i
$693$	707.082	−	108.774i	1.02032	−	0.156961i
$694$	275.852	−	641.948i	0.397482	−	0.924997i
$695$	−321.516	+	185.627i	−0.462613	+	0.267090i
$696$	−396.115	−	68.1452i	−0.569130	−	0.0979098i
$697$	−19.9895	+	34.6229i	−0.0286794	+	0.0496741i
$698$	−38.9622	−	329.375i	−0.0558198	−	0.471884i
$699$	515.633			0.737672
$700$	−76.9469	+	564.514i	−0.109924	+	0.806448i
$701$		−	695.486i		−	0.992134i	−0.868284	−	0.496067i	$-0.834777\pi$
$701$		−	695.486i		−	0.992134i	0.868284	−	0.496067i	$-0.165223\pi$
$702$	−279.854	−	2365.80i	−0.398652	−	3.37009i
$703$	65.7370	+	37.9532i	0.0935092	+	0.0539875i
$704$	61.2072	+	330.971i	0.0869420	+	0.470130i
$705$	264.520	+	458.162i	0.375206	+	0.649876i
$706$	372.471	−	866.794i	0.527580	−	1.22775i
$707$	589.117	+	229.147i	0.833262	+	0.324112i
$708$	−787.920	−	830.513i	−1.11288	−	1.17304i
$709$	−803.161	+	463.705i	−1.13281	+	0.654027i	−0.944640	−	0.328110i	$-0.893588\pi$
$709$	−803.161	+	463.705i	−1.13281	+	0.654027i	−0.188168	+	0.982137i	$0.560255\pi$
$710$	−192.300	−	257.557i	−0.270846	−	0.362756i
$711$	−508.447	−	293.552i	−0.715115	−	0.412872i
$712$	337.249	+	280.599i	0.473664	+	0.394100i
$713$	299.812			0.420493
$714$	−49.3439	−	48.5040i	−0.0691091	−	0.0679328i
$715$	−242.883			−0.339697
$716$	144.366	−	487.138i	0.201629	−	0.680361i
$717$	−753.566	−	435.071i	−1.05100	−	0.606794i
$718$	1052.88	−	786.113i	1.46640	−	1.09486i
$719$	−1150.37	+	664.169i	−1.59996	+	0.923739i	−0.608471	+	0.793576i	$0.708217\pi$
$719$	−1150.37	+	664.169i	−1.59996	+	0.923739i	−0.991493	+	0.130163i	$0.958450\pi$
$720$	669.720	+	35.2747i	0.930167	+	0.0489927i
$721$	615.900	−	494.234i	0.854231	−	0.685484i
$722$	257.281	−	598.730i	0.356345	−	0.829266i
$723$	−547.865	−	948.929i	−0.757766	−	1.31249i
$724$	198.511	+	827.335i	0.274186	+	1.14273i
$725$	−166.034	−	95.8600i	−0.229013	−	0.132221i
$726$	−988.551	+	116.937i	−1.36164	+	0.161070i
$727$		−	539.401i		−	0.741954i	−0.928642	−	0.370977i	$-0.879023\pi$
$727$		−	539.401i		−	0.741954i	0.928642	−	0.370977i	$-0.120977\pi$
$728$	−581.022	−	1048.87i	−0.798107	−	1.44076i
$729$	−303.936			−0.416922
$730$	−17.0292	−	143.960i	−0.0233277	−	0.197205i
$731$	19.3427	−	33.5026i	0.0264606	−	0.0458311i
$732$	138.425	+	576.913i	0.189105	+	0.788133i
$733$	−382.859	+	221.044i	−0.522318	+	0.301561i	−0.737883	−	0.674929i	$-0.764174\pi$
$733$	−382.859	+	221.044i	−0.522318	+	0.301561i	0.215564	+	0.976490i	$0.430841\pi$
$734$	−653.196	−	280.686i	−0.889913	−	0.382406i
$735$	−169.384	−	537.507i	−0.230454	−	0.731302i
$736$	−123.062	+	249.339i	−0.167204	+	0.338776i
$737$	206.396	+	357.488i	0.280048	+	0.485058i
$738$	−1002.96	−	1343.32i	−1.35903	−	1.82021i
$739$	574.116	−	994.398i	0.776882	−	1.34560i	−0.156848	−	0.987623i	$-0.550133\pi$
$739$	574.116	−	994.398i	0.776882	−	1.34560i	0.933730	−	0.357977i	$-0.116533\pi$
$740$	−31.3796	+	105.885i	−0.0424049	+	0.143088i
$741$			677.050i			0.913698i
$742$	−1009.49	−	261.227i	−1.36050	−	0.352058i
$743$		−	588.688i		−	0.792313i	−0.918183	−	0.396156i	$-0.870344\pi$
$743$		−	588.688i		−	0.792313i	0.918183	−	0.396156i	$-0.129656\pi$
$744$	941.394	−	1131.45i	1.26531	−	1.52077i
$745$	248.810	−	430.952i	0.333973	−	0.578459i
$746$	−506.414	+	378.106i	−0.678840	+	0.506844i
$747$	708.597	+	1227.33i	0.948590	+	1.64301i
$748$	−13.4196	−	14.1450i	−0.0179406	−	0.0189104i
$749$	630.826	+	786.118i	0.842225	+	1.04956i
$750$	958.378	+	411.826i	1.27784	+	0.549101i
$751$	708.754	−	409.199i	0.943747	−	0.544873i	0.0526140	−	0.998615i	$-0.483245\pi$
$751$	708.754	−	409.199i	0.943747	−	0.544873i	0.891133	+	0.453742i	$0.149911\pi$
$752$	−401.001	+	617.133i	−0.533246	+	0.820656i
$753$	424.712	−	735.622i	0.564026	−	0.976922i
$754$	400.695	−	47.3988i	0.531426	−	0.0628631i
$755$	318.989			0.422503
$756$	1441.81	−	589.509i	1.90716	−	0.779773i
$757$			105.101i			0.138838i	0.997588	+	0.0694192i	$0.0221146\pi$
$757$			105.101i			0.138838i	−0.997588	+	0.0694192i	$0.977885\pi$
$758$	−354.337	+	41.9150i	−0.467464	+	0.0552969i
$759$	211.025	+	121.835i	0.278030	+	0.160521i
$760$	−100.845	−	17.3488i	−0.132691	−	0.0228274i
$761$	−507.117	−	878.352i	−0.666382	−	1.15421i	−0.978909	−	0.204299i	$-0.934509\pi$
$761$	−507.117	−	878.352i	−0.666382	−	1.15421i	0.312527	−	0.949909i	$-0.398825\pi$
$762$	−1288.38	−	553.631i	−1.69079	−	0.726550i
$763$	435.019	+	169.209i	0.570143	+	0.221767i
$764$	−117.626	+	111.594i	−0.153961	+	0.146065i
$765$	−33.6449	+	19.4249i	−0.0439803	+	0.0253920i
$766$	−1119.25	+	835.667i	−1.46116	+	1.09095i
$767$	995.264	+	574.616i	1.29761	+	0.749173i
$768$	554.564	+	1247.33i	0.722089	+	1.62413i
$769$	−1183.99			−1.53964			−0.769822	−	0.638258i	$-0.779655\pi$
$769$	−1183.99			−1.53964			−0.769822	+	0.638258i	$0.779655\pi$
$770$	−42.4182	−	153.040i	−0.0550885	−	0.198753i
$771$	1150.58			1.49232
$772$	−320.860	+	1082.68i	−0.415621	+	1.40244i
$773$	−280.862	−	162.156i	−0.363340	−	0.209774i	0.307205	−	0.951643i	$-0.400606\pi$
$773$	−280.862	−	162.156i	−0.363340	−	0.209774i	−0.670545	+	0.741869i	$0.733940\pi$
$774$	970.512	+	1299.85i	1.25389	+	1.67939i
$775$	608.014	−	351.037i	0.784534	−	0.452951i
$776$	−403.170	+	148.647i	−0.519550	+	0.191556i
$777$	72.6446	+	472.223i	0.0934937	+	0.607751i
$778$	−322.226	−	138.464i	−0.414172	−	0.177975i
$779$	127.894	+	221.519i	0.164177	+	0.284363i
$780$	−957.858	+	229.828i	−1.22802	+	0.294652i
$781$	−339.358	−	195.928i	−0.434517	−	0.250869i
$782$	−1.89216	−	15.9958i	−0.00241965	−	0.0204550i
$783$			524.168i			0.669436i
$784$	559.418	−	549.280i	0.713543	−	0.700612i
$785$	−247.679			−0.315514
$786$	−92.7870	+	10.9759i	−0.118050	+	0.0139642i
$787$	−134.268	+	232.559i	−0.170607	+	0.295500i	−0.938632	−	0.344919i	$-0.887906\pi$
$787$	−134.268	+	232.559i	−0.170607	+	0.295500i	0.768025	+	0.640420i	$0.221240\pi$
$788$	−244.336	−	1018.32i	−0.310071	−	1.29229i
$789$	1520.01	−	877.576i	1.92650	−	1.11226i
$790$	−51.4547	+	119.742i	−0.0651325	+	0.151573i
$791$	49.5696	−	7.62556i	0.0626670	−	0.00964040i
$792$	767.121	−	282.834i	0.968587	−	0.357114i
$793$	−297.792	−	515.791i	−0.375526	−	0.650429i
$794$	618.130	−	461.517i	0.778502	−	0.581255i
$795$	−428.319	+	741.870i	−0.538766	+	0.933170i
$796$	−1235.39	−	366.115i	−1.55199	−	0.459943i
$797$			1502.06i			1.88465i	0.334705	+	0.942323i	$0.391363\pi$
$797$			1502.06i			1.88465i	−0.334705	+	0.942323i	$0.608637\pi$
$798$	−426.607	+	118.243i	−0.534596	+	0.148174i
$799$		−	42.6339i		−	0.0533591i
$800$	42.3725	+	649.744i	0.0529656	+	0.812180i
$801$	532.848	−	922.919i	0.665228	−	1.15221i
$802$	−630.694	−	844.718i	−0.786402	−	1.05326i
$803$	−88.3638	−	153.051i	−0.110042	−	0.190599i
$804$	1152.24	+	1214.52i	1.43313	+	1.51060i
$805$	47.5592	−	122.270i	0.0590797	−	0.151888i
$806$	−583.349	+	1357.54i	−0.723758	+	1.68429i
$807$	−1353.34	+	781.354i	−1.67701	+	0.968220i
$808$	711.956	+	122.481i	0.881134	+	0.151585i
$809$	−35.3793	+	61.2788i	−0.0437322	+	0.0757464i	−0.887063	−	0.461648i	$-0.847258\pi$
$809$	−35.3793	+	61.2788i	−0.0437322	+	0.0757464i	0.843331	+	0.537395i	$0.180591\pi$
$810$	−61.6942	−	521.545i	−0.0761657	−	0.643882i
$811$	5.94522			0.00733072			0.00366536	−	0.999993i	$-0.498833\pi$
$811$	5.94522			0.00733072			0.00366536	+	0.999993i	$0.498833\pi$
$812$	99.8450	+	244.199i	0.122962	+	0.300738i
$813$			143.172i			0.176103i
$814$	15.8159	+	133.703i	0.0194299	+	0.164255i
$815$	92.1073	+	53.1782i	0.113015	+	0.0652493i
$816$	−66.3074	−	43.0852i	−0.0812590	−	0.0528005i
$817$	−123.756	−	214.351i	−0.151476	−	0.262364i
$818$	334.592	−	778.643i	0.409037	−	0.951886i
$819$	−2271.65	+	1822.91i	−2.77369	+	2.22577i
$820$	−269.980	+	256.134i	−0.329244	+	0.312359i
$821$	13.1159	−	7.57244i	0.0159755	−	0.00922344i	−0.491991	−	0.870600i	$-0.663731\pi$
$821$	13.1159	−	7.57244i	0.0159755	−	0.00922344i	0.507966	+	0.861377i	$0.330397\pi$
$822$	1511.11	+	2023.90i	1.83833	+	2.46216i
$823$	1284.10	+	741.378i	1.56027	+	0.900824i	0.997229	+	0.0743964i	$0.0237030\pi$
$823$	1284.10	+	741.378i	1.56027	+	0.900824i	0.563044	+	0.826427i	$0.309630\pi$
$824$	577.227	−	693.763i	0.700519	−	0.841945i
$825$	570.607			0.691645
$826$	−188.247	+	727.466i	−0.227901	+	0.880710i
$827$	−74.3070			−0.0898513			−0.0449257	−	0.998990i	$-0.514305\pi$
$827$	−74.3070			−0.0898513			−0.0449257	+	0.998990i	$0.514305\pi$
$828$	647.587	+	191.916i	0.782110	+	0.231783i
$829$	−123.722	−	71.4311i	−0.149243	−	0.0861654i	0.423519	−	0.905887i	$-0.360795\pi$
$829$	−123.722	−	71.4311i	−0.149243	−	0.0861654i	−0.572762	+	0.819722i	$0.694128\pi$
$830$	252.086	−	188.216i	0.303718	−	0.226766i
$831$	1545.96	−	892.558i	1.86036	−	1.07408i
$832$	−889.555	−	1042.36i	−1.06918	−	1.25284i
$833$	−9.83671	+	44.3380i	−0.0118088	+	0.0532269i
$834$	−724.699	+	1686.48i	−0.868944	+	2.02216i
$835$	260.403	+	451.032i	0.311860	+	0.540158i
$836$	−121.305	+	29.1060i	−0.145102	+	0.0348158i
$837$	−1662.33	−	959.745i	−1.98605	−	1.14665i
$838$	587.103	−	69.4491i	0.700600	−	0.0828749i
$839$			16.7454i			0.0199588i	0.999950	+	0.00997940i	$0.00317659\pi$
$839$			16.7454i			0.0199588i	−0.999950	+	0.00997940i	$0.996823\pi$
$840$	−312.099	−	563.405i	−0.371546	−	0.670720i
$841$	752.222			0.894437
$842$	29.6640	+	250.771i	0.0352304	+	0.297827i
$843$	328.886	−	569.648i	0.390138	−	0.675739i
$844$	660.424	−	158.462i	0.782493	−	0.187751i
$845$	540.690	−	312.168i	0.639870	−	0.369429i
$846$	1642.53	+	705.816i	1.94153	+	0.834298i
$847$	408.934	+	509.602i	0.482803	+	0.601655i
$848$	−1190.06	−	62.6814i	−1.40337	−	0.0739167i
$849$	1.65008	+	2.85803i	0.00194356	+	0.00336634i
$850$	−22.5661	−	30.2238i	−0.0265483	−	0.0355574i
$851$	−55.6118	+	96.3224i	−0.0653488	+	0.113187i
$852$	−1523.72	−	451.564i	−1.78841	−	0.530005i
$853$		−	1299.38i		−	1.52331i	−0.647984	−	0.761654i	$-0.724388\pi$
$853$		−	1299.38i		−	1.52331i	0.647984	−	0.761654i	$-0.275612\pi$
$854$	272.990	−	277.718i	0.319661	−	0.325196i
$855$			248.563i			0.290717i
$856$	885.500	+	736.757i	1.03446	+	0.860698i
$857$	597.668	−	1035.19i	0.697396	−	1.20792i	−0.271971	−	0.962305i	$-0.587675\pi$
$857$	597.668	−	1035.19i	0.697396	−	1.20792i	0.969366	−	0.245619i	$-0.0789912\pi$
$858$	−962.262	+	718.456i	−1.12152	+	0.837362i
$859$	170.885	+	295.981i	0.198934	+	0.344564i	0.948183	−	0.317724i	$-0.102919\pi$
$859$	170.885	+	295.981i	0.198934	+	0.344564i	−0.749249	+	0.662289i	$0.769585\pi$
$860$	261.244	−	247.846i	0.303772	−	0.288193i
$861$	−583.644	+	1500.49i	−0.677867	+	1.74273i
$862$	467.216	+	200.768i	0.542014	+	0.232909i
$863$	−844.362	+	487.493i	−0.978404	+	0.564882i	−0.901788	−	0.432179i	$-0.857745\pi$
$863$	−844.362	+	487.493i	−0.978404	+	0.564882i	−0.0766158	+	0.997061i	$0.524411\pi$
$864$	1480.50	−	988.537i	1.71354	−	1.14414i
$865$	58.6913	−	101.656i	0.0678512	−	0.117522i
$866$	1085.04	−	128.350i	1.25293	−	0.148211i
$867$	−1536.44			−1.77213
$868$	−957.258	−	130.481i	−1.10283	−	0.150323i
$869$			158.887i			0.182839i
$870$	215.235	−	25.4605i	0.247397	−	0.0292649i
$871$	−1455.45	−	840.304i	−1.67101	−	0.964758i
$872$	525.727	+	90.4430i	0.602898	+	0.103719i
$873$	521.896	+	903.951i	0.597819	+	1.03545i
$874$	−94.6839	−	40.6868i	−0.108334	−	0.0465524i
$875$	−104.104	−	676.722i	−0.118976	−	0.773397i
$876$	−493.304	−	519.971i	−0.563133	−	0.593574i
$877$	274.158	−	158.285i	0.312609	−	0.180485i	−0.335484	−	0.942046i	$-0.608900\pi$
$877$	274.158	−	158.285i	0.312609	−	0.180485i	0.648093	+	0.761561i	$0.275567\pi$
$878$	−438.043	+	327.057i	−0.498910	+	0.372503i
$879$	−130.591	−	75.3966i	−0.148567	−	0.0857754i
$880$	−82.3554	−	161.736i	−0.0935857	−	0.183791i
$881$	−464.977			−0.527783			−0.263891	−	0.964552i	$-0.585006\pi$
$881$	−464.977			−0.527783			−0.263891	+	0.964552i	$0.585006\pi$
$882$	−1545.34	−	1113.00i	−1.75208	−	1.26191i
$883$	69.4594			0.0786630			0.0393315	−	0.999226i	$-0.487477\pi$
$883$	69.4594			0.0786630			0.0393315	+	0.999226i	$0.487477\pi$
$884$	76.1101	+	22.5557i	0.0860974	+	0.0255155i
$885$	534.610	+	308.657i	0.604079	+	0.348765i
$886$	−568.083	−	760.860i	−0.641178	−	0.858758i
$887$	9.46740	−	5.46601i	0.0106735	−	0.00616235i	−0.494654	−	0.869090i	$-0.664705\pi$
$887$	9.46740	−	5.46601i	0.0106735	−	0.00616235i	0.505327	+	0.862928i	$0.331372\pi$
$888$	188.890	+	512.320i	0.212714	+	0.576936i
$889$	139.950	+	909.740i	0.157424	+	1.02333i
$890$	−217.353	−	93.3991i	−0.244217	−	0.104943i
$891$	−320.129	−	554.479i	−0.359292	−	0.622311i
$892$	42.4290	+	176.832i	0.0475661	+	0.198242i
$893$	−236.229	−	136.387i	−0.264535	−	0.152729i
$894$	−289.026	−	2443.34i	−0.323296	−	2.73305i
$895$			273.974i			0.306116i
$896$	501.435	−	742.549i	0.559638	−	0.828737i
$897$	−992.062			−1.10598
$898$	1553.37	−	183.750i	1.72981	−	0.204622i
$899$	162.552	−	281.548i	0.180814	−	0.313179i
$900$	1538.00	−	369.029i	1.70889	−	0.410032i
$901$	59.7853	−	34.5170i	0.0663543	−	0.0383097i
$902$	−179.119	+	416.837i	−0.198580	+	0.462125i
$903$	564.759	−	1451.94i	0.625425	−	1.60791i
$904$	53.7786	−	19.8279i	0.0594896	−	0.0219336i
$905$	−229.395	−	397.323i	−0.253475	−	0.439031i
$906$	1263.78	−	943.581i	1.39490	−	1.04148i
$907$	11.3588	−	19.6740i	0.0125235	−	0.0216913i	−0.859696	−	0.510806i	$-0.829347\pi$
$907$	11.3588	−	19.6740i	0.0125235	−	0.0216913i	0.872219	+	0.489115i	$0.162680\pi$
$908$	−210.413	+	710.000i	−0.231732	+	0.781938i
$909$		−	1754.83i		−	1.93051i
$910$	461.099	+	453.250i	0.506702	+	0.498077i
$911$		−	721.866i		−	0.792389i	−0.918167	−	0.396194i	$-0.870331\pi$
$911$		−	721.866i		−	0.792389i	0.918167	−	0.396194i	$-0.129669\pi$
$912$	−450.849	+	229.570i	−0.494352	+	0.251722i
$913$	191.767	−	332.150i	0.210040	−	0.363800i
$914$	226.815	+	303.784i	0.248157	+	0.332368i
$915$	−159.960	−	277.059i	−0.174820	−	0.302797i
$916$	536.704	−	509.179i	0.585922	−	0.555873i
$917$	38.3832	+	47.8320i	0.0418573	+	0.0521614i
$918$	−40.7139	+	94.7470i	−0.0443506	+	0.103210i
$919$	113.209	−	65.3612i	0.123187	−	0.0711221i	−0.437140	−	0.899393i	$-0.644009\pi$
$919$	113.209	−	65.3612i	0.123187	−	0.0711221i	0.560327	+	0.828271i	$0.310675\pi$
$920$	25.4207	−	147.765i	0.0276312	−	0.160615i
$921$	−1068.83	+	1851.27i	−1.16051	+	2.01007i
$922$	47.5841	+	402.262i	0.0516097	+	0.436293i
$923$	1595.38			1.72847
$924$	−620.751	−	480.844i	−0.671808	−	0.520394i
$925$			260.454i			0.281572i
$926$	153.402	+	1296.81i	0.165661	+	1.40045i
$927$	−1898.56	−	1096.13i	−2.04807	−	1.18245i
$928$	167.428	+	250.752i	0.180419	+	0.270207i
$929$	227.643	+	394.289i	0.245041	+	0.424423i	0.962143	−	0.272545i	$-0.0878654\pi$
$929$	227.643	+	394.289i	0.245041	+	0.424423i	−0.717102	+	0.696968i	$0.754532\pi$
$930$	−313.349	+	729.207i	−0.336934	+	0.784093i
$931$	214.204	+	196.343i	0.230079	+	0.210894i
$932$	−266.221	−	280.612i	−0.285645	−	0.301086i
$933$	−749.140	+	432.516i	−0.802937	+	0.463576i
$934$	−652.654	−	874.129i	−0.698773	−	0.935899i
$935$	9.10528	+	5.25694i	0.00973827	+	0.00562239i
$936$	−2129.01	+	2558.84i	−2.27459	+	2.73380i
$937$	−1242.79			−1.32635			−0.663176	−	0.748464i	$-0.730792\pi$
$937$	−1242.79			−1.32635			−0.663176	+	0.748464i	$0.730792\pi$
$938$	275.287	−	1063.83i	0.293483	−	1.13415i
$939$	−1419.69			−1.51192
$940$	112.764	−	380.503i	0.119962	−	0.404790i
$941$	984.767	+	568.556i	1.04651	+	0.604204i	0.921671	−	0.387973i	$-0.126825\pi$
$941$	984.767	+	568.556i	1.04651	+	0.604204i	0.124841	+	0.992177i	$0.460158\pi$
$942$	−981.261	+	732.642i	−1.04168	+	0.777751i
$943$	−324.585	+	187.399i	−0.344205	+	0.198727i
$944$	−45.1698	+	857.586i	−0.0478493	+	0.908460i
$945$	−655.102	+	525.692i	−0.693230	+	0.556288i
$946$	173.324	−	403.349i	0.183217	−	0.426373i
$947$	−352.421	−	610.411i	−0.372145	−	0.644573i	0.617751	−	0.786374i	$-0.288044\pi$
$947$	−352.421	−	610.411i	−0.372145	−	0.644573i	−0.989895	+	0.141801i	$0.954711\pi$
$948$	150.347	+	626.603i	0.158594	+	0.660974i
$949$	623.119	+	359.758i	0.656606	+	0.379092i
$950$	−239.656	+	28.3492i	−0.252270	+	0.0298413i
$951$			2308.09i			2.42702i
$952$	−0.920081	+	51.8959i	−0.000966471	+	0.0545125i
$953$	765.039			0.802769			0.401384	−	0.915910i	$-0.368529\pi$
$953$	765.039			0.802769			0.401384	+	0.915910i	$0.368529\pi$
$954$	340.059	+	2874.76i	0.356455	+	3.01337i
$955$	43.7153	−	75.7172i	0.0457752	−	0.0792850i
$956$	152.296	+	634.724i	0.159305	+	0.663937i
$957$	228.827	−	132.113i	0.239109	−	0.138050i
$958$	−200.102	−	85.9863i	−0.208875	−	0.0897561i
$959$	601.000	−	1545.11i	0.626694	−	1.61117i
$960$	−477.828	−	559.911i	−0.497737	−	0.583240i
$961$	114.761	+	198.772i	0.119418	+	0.206838i
$962$	−327.940	−	439.225i	−0.340894	−	0.456575i
$963$	1399.07	−	2423.27i	1.45283	−	2.51637i
$964$	−233.554	+	788.084i	−0.242275	+	0.817515i
$965$		−	608.916i		−	0.631001i
$966$	−173.258	−	625.095i	−0.179356	−	0.647097i
$967$		−	771.494i		−	0.797822i	−0.916990	−	0.398911i	$-0.869388\pi$
$967$		−	771.494i		−	0.797822i	0.916990	−	0.398911i	$-0.130612\pi$
$968$	574.026	+	477.604i	0.593002	+	0.493392i
$969$	14.6540	−	25.3815i	0.0151228	−	0.0261935i
$970$	185.667	−	138.625i	0.191409	−	0.142912i
$971$	−458.754	−	794.586i	−0.472456	−	0.818317i	0.527047	−	0.849836i	$-0.323299\pi$
$971$	−458.754	−	794.586i	−0.472456	−	0.818317i	−0.999503	+	0.0315186i	$0.989966\pi$
$972$	−408.778	−	430.875i	−0.420554	−	0.443287i
$973$	1190.84	−	183.194i	1.22389	−	0.188277i
$974$	788.949	+	339.021i	0.810010	+	0.348071i
$975$	−2011.89	+	1161.56i	−2.06348	+	1.19135i
$976$	242.493	−	373.191i	0.248456	−	0.382368i
$977$	−133.301	+	230.883i	−0.136439	+	0.236319i	−0.926146	−	0.377165i	$-0.876899\pi$
$977$	−133.301	+	230.883i	−0.136439	+	0.236319i	0.789707	+	0.613484i	$0.210232\pi$
$978$	522.216	−	61.7736i	0.533963	−	0.0631632i
$979$	−288.408			−0.294594
$980$	−205.063	+	369.695i	−0.209248	+	0.377239i
$981$		−	1295.81i		−	1.32091i
$982$	901.488	−	106.638i	0.918012	−	0.108593i
$983$	1601.95	+	924.884i	1.62965	+	0.940879i	0.984197	+	0.177080i	$0.0566650\pi$
$983$	1601.95	+	924.884i	1.62965	+	0.940879i	0.645454	+	0.763799i	$0.276668\pi$
$984$	−311.961	+	1813.37i	−0.317034	+	1.84285i
$985$	282.349	+	489.043i	0.286649	+	0.496490i
$986$	−16.0473	−	6.89571i	−0.0162751	−	0.00699362i
$987$	−261.052	−	1696.96i	−0.264491	−	1.71931i
$988$	368.457	−	349.560i	0.372932	−	0.353806i
$989$	314.083	−	181.336i	0.317576	−	0.183353i
$990$	−353.272	+	263.764i	−0.356840	+	0.266429i
$991$	−303.420	−	175.180i	−0.306175	−	0.176770i	0.339038	−	0.940773i	$-0.389898\pi$
$991$	−303.420	−	175.180i	−0.306175	−	0.176770i	−0.645214	+	0.764002i	$0.723232\pi$
$992$	−1101.79	+	71.8520i	−1.11067	+	0.0724314i
$993$	433.261			0.436315
$994$	278.623	+	1005.24i	0.280305	+	1.01131i
$995$	694.800			0.698291
$996$	441.973	−	1491.36i	0.443748	−	1.49735i
$997$	455.495	+	262.980i	0.456866	+	0.263772i	0.710726	−	0.703469i	$-0.248367\pi$
$997$	455.495	+	262.980i	0.456866	+	0.263772i	−0.253860	+	0.967241i	$0.581700\pi$
$998$	−398.923	−	534.296i	−0.399723	−	0.535367i
$999$	616.687	−	356.045i	0.617305	−	0.356401i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	56.3.k.d.11.6	yes	12
4.3	odd	2		224.3.o.d.207.5		12
7.2	even	3	inner	56.3.k.d.51.2	yes	12
7.3	odd	6		392.3.g.i.99.4		6
7.4	even	3		392.3.g.j.99.4		6
7.5	odd	6		392.3.k.l.275.2		12
7.6	odd	2		392.3.k.l.67.6		12
8.3	odd	2	inner	56.3.k.d.11.2	✓	12
8.5	even	2		224.3.o.d.207.6		12
28.3	even	6		1568.3.g.l.687.6		6
28.11	odd	6		1568.3.g.j.687.1		6
28.23	odd	6		224.3.o.d.79.6		12
56.3	even	6		392.3.g.i.99.3		6
56.11	odd	6		392.3.g.j.99.3		6
56.19	even	6		392.3.k.l.275.6		12
56.27	even	2		392.3.k.l.67.2		12
56.37	even	6		224.3.o.d.79.5		12
56.45	odd	6		1568.3.g.l.687.5		6
56.51	odd	6	inner	56.3.k.d.51.6	yes	12
56.53	even	6		1568.3.g.j.687.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.k.d.11.2	✓	12	8.3	odd	2	inner
56.3.k.d.11.6	yes	12	1.1	even	1	trivial
56.3.k.d.51.2	yes	12	7.2	even	3	inner
56.3.k.d.51.6	yes	12	56.51	odd	6	inner
224.3.o.d.79.5		12	56.37	even	6
224.3.o.d.79.6		12	28.23	odd	6
224.3.o.d.207.5		12	4.3	odd	2
224.3.o.d.207.6		12	8.5	even	2
392.3.g.i.99.3		6	56.3	even	6
392.3.g.i.99.4		6	7.3	odd	6
392.3.g.j.99.3		6	56.11	odd	6
392.3.g.j.99.4		6	7.4	even	3
392.3.k.l.67.2		12	56.27	even	2
392.3.k.l.67.6		12	7.6	odd	2
392.3.k.l.275.2		12	7.5	odd	6
392.3.k.l.275.6		12	56.19	even	6
1568.3.g.j.687.1		6	28.11	odd	6
1568.3.g.j.687.2		6	56.53	even	6
1568.3.g.l.687.5		6	56.45	odd	6
1568.3.g.l.687.6		6	28.3	even	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:	\( N \)	\(=\)	\( 56 = 2^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	56.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.98615 - 0.234945i) q^{2} +(-2.66613 + 4.61787i) q^{3} +(3.88960 - 0.933271i) q^{4} +(-1.86796 + 1.07847i) q^{5} +(-4.21039 + 9.79818i) q^{6} +(6.91861 - 1.06433i) q^{7} +(7.50608 - 2.76746i) q^{8} +(-9.71647 - 16.8294i) q^{9} +O(q^{10})\)	\(q+(1.98615 - 0.234945i) q^{2} +(-2.66613 + 4.61787i) q^{3} +(3.88960 - 0.933271i) q^{4} +(-1.86796 + 1.07847i) q^{5} +(-4.21039 + 9.79818i) q^{6} +(6.91861 - 1.06433i) q^{7} +(7.50608 - 2.76746i) q^{8} +(-9.71647 - 16.8294i) q^{9} +(-3.45667 + 2.58086i) q^{10} +(-2.62956 + 4.55453i) q^{11} +(-6.06045 + 20.4499i) q^{12} -21.4116i q^{13} +(13.4914 - 3.73941i) q^{14} -11.5013i q^{15} +(14.2580 - 7.26011i) q^{16} +(-0.463429 + 0.802683i) q^{17} +(-23.2524 - 31.1430i) q^{18} +(2.96505 + 5.13561i) q^{19} +(-6.25911 + 5.93812i) q^{20} +(-13.5310 + 34.7869i) q^{21} +(-4.15264 + 9.66378i) q^{22} +(-7.52507 + 4.34460i) q^{23} +(-7.23239 + 42.0405i) q^{24} +(-10.1738 + 17.6216i) q^{25} +(-5.03053 - 42.5266i) q^{26} +55.6311 q^{27} +(25.9173 - 10.5968i) q^{28} +9.42223i q^{29} +(-2.70217 - 22.8434i) q^{30} +(-29.8813 - 17.2520i) q^{31} +(26.6129 - 17.7695i) q^{32} +(-14.0215 - 24.2859i) q^{33} +(-0.731855 + 1.70313i) q^{34} +(-11.7758 + 9.44961i) q^{35} +(-53.4996 - 56.3916i) q^{36} +(11.0853 - 6.40011i) q^{37} +(7.09562 + 9.50349i) q^{38} +(98.8758 + 57.0860i) q^{39} +(-11.0364 + 13.2645i) q^{40} +43.1339 q^{41} +(-18.7016 + 72.2711i) q^{42} -41.7382 q^{43} +(-5.97732 + 20.1694i) q^{44} +(36.2999 + 20.9578i) q^{45} +(-13.9252 + 10.3970i) q^{46} +(-39.8357 + 22.9991i) q^{47} +(-4.48745 + 85.1980i) q^{48} +(46.7344 - 14.7273i) q^{49} +(-16.0667 + 37.3894i) q^{50} +(-2.47112 - 4.28011i) q^{51} +(-19.9828 - 83.2825i) q^{52} +(-64.5031 - 37.2409i) q^{53} +(110.492 - 13.0702i) q^{54} -11.3436i q^{55} +(48.9861 - 27.1359i) q^{56} -31.6208 q^{57} +(2.21370 + 18.7140i) q^{58} +(-26.8367 + 46.4825i) q^{59} +(-10.7338 - 44.7355i) q^{60} +(24.0893 - 13.9080i) q^{61} +(-63.4020 - 27.2446i) q^{62} +(-85.1365 - 106.095i) q^{63} +(48.6823 - 41.5455i) q^{64} +(23.0916 + 39.9959i) q^{65} +(-33.5546 - 44.9412i) q^{66} +(39.2453 - 67.9749i) q^{67} +(-1.05343 + 3.55462i) q^{68} -46.3330i q^{69} +(-21.1685 + 21.5350i) q^{70} +74.5100i q^{71} +(-119.507 - 99.4329i) q^{72} +(-16.8020 + 29.1020i) q^{73} +(20.5134 - 15.3160i) q^{74} +(-54.2494 - 93.9627i) q^{75} +(16.3258 + 17.2083i) q^{76} +(-13.3454 + 34.3097i) q^{77} +(209.794 + 90.1511i) q^{78} +(26.1642 - 15.1059i) q^{79} +(-18.8036 + 28.9384i) q^{80} +(-60.8713 + 105.432i) q^{81} +(85.6705 - 10.1341i) q^{82} -72.9274 q^{83} +(-20.1645 + 147.935i) q^{84} -1.99917i q^{85} +(-82.8984 + 9.80616i) q^{86} +(-43.5106 - 25.1209i) q^{87} +(-7.13318 + 41.4638i) q^{88} +(27.4198 + 47.4925i) q^{89} +(77.0211 + 33.0968i) q^{90} +(-22.7889 - 148.138i) q^{91} +(-25.2148 + 23.9217i) q^{92} +(159.335 - 91.9919i) q^{93} +(-73.7162 + 55.0390i) q^{94} +(-11.0772 - 6.39541i) q^{95} +(11.1040 + 170.270i) q^{96} -53.7125 q^{97} +(89.3616 - 40.2307i) q^{98} +102.200 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - 6 q^{3} - 4 q^{4} - 56 q^{6} + 8 q^{8} - 40 q^{9}+O(q^{10}) \) 12 * q + 2 * q^2 - 6 * q^3 - 4 * q^4 - 56 * q^6 + 8 * q^8 - 40 * q^9	\( 12 q + 2 q^{2} - 6 q^{3} - 4 q^{4} - 56 q^{6} + 8 q^{8} - 40 q^{9} - 6 q^{10} + 30 q^{11} + 32 q^{12} + 52 q^{14} + 16 q^{16} + 30 q^{17} - 16 q^{18} + 78 q^{19} + 48 q^{20} + 24 q^{22} - 76 q^{24} - 92 q^{25} - 128 q^{26} + 156 q^{27} - 4 q^{28} - 16 q^{30} + 112 q^{32} - 78 q^{33} + 76 q^{34} - 222 q^{35} - 248 q^{36} + 80 q^{38} + 44 q^{40} - 232 q^{41} + 132 q^{42} - 200 q^{43} + 132 q^{44} - 156 q^{46} + 176 q^{48} + 372 q^{49} + 48 q^{50} + 10 q^{51} + 132 q^{52} - 36 q^{54} - 112 q^{56} + 332 q^{57} + 4 q^{58} - 110 q^{59} + 84 q^{60} - 96 q^{62} - 160 q^{64} - 32 q^{65} - 138 q^{66} + 434 q^{67} + 96 q^{68} - 188 q^{70} - 328 q^{72} + 102 q^{73} - 34 q^{74} - 60 q^{75} - 168 q^{76} + 720 q^{78} - 256 q^{80} - 82 q^{81} - 24 q^{82} - 536 q^{83} - 624 q^{84} + 240 q^{86} - 204 q^{88} + 214 q^{89} + 440 q^{90} - 8 q^{91} + 160 q^{92} - 16 q^{94} + 48 q^{96} - 152 q^{97} + 382 q^{98} + 504 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 - 6 * q^3 - 4 * q^4 - 56 * q^6 + 8 * q^8 - 40 * q^9 - 6 * q^10 + 30 * q^11 + 32 * q^12 + 52 * q^14 + 16 * q^16 + 30 * q^17 - 16 * q^18 + 78 * q^19 + 48 * q^20 + 24 * q^22 - 76 * q^24 - 92 * q^25 - 128 * q^26 + 156 * q^27 - 4 * q^28 - 16 * q^30 + 112 * q^32 - 78 * q^33 + 76 * q^34 - 222 * q^35 - 248 * q^36 + 80 * q^38 + 44 * q^40 - 232 * q^41 + 132 * q^42 - 200 * q^43 + 132 * q^44 - 156 * q^46 + 176 * q^48 + 372 * q^49 + 48 * q^50 + 10 * q^51 + 132 * q^52 - 36 * q^54 - 112 * q^56 + 332 * q^57 + 4 * q^58 - 110 * q^59 + 84 * q^60 - 96 * q^62 - 160 * q^64 - 32 * q^65 - 138 * q^66 + 434 * q^67 + 96 * q^68 - 188 * q^70 - 328 * q^72 + 102 * q^73 - 34 * q^74 - 60 * q^75 - 168 * q^76 + 720 * q^78 - 256 * q^80 - 82 * q^81 - 24 * q^82 - 536 * q^83 - 624 * q^84 + 240 * q^86 - 204 * q^88 + 214 * q^89 + 440 * q^90 - 8 * q^91 + 160 * q^92 - 16 * q^94 + 48 * q^96 - 152 * q^97 + 382 * q^98 + 504 * q^99

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