LMFDB - Embedded newform 392.3.k.l.67.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,3,Mod(67,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, 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("392.67");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	392.k (of order $6$, degree $2$, not 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:	$10.6812263629$
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:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			67.2
Root			$-0.407369 + 0.812545i$ of defining polynomial
Character	$\chi$	$=$	392.67
Dual form			392.3.k.l.275.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.19654 + 1.60259i) q^{2} +(2.66613 - 4.61787i) q^{3} +(-1.13656 - 3.83513i) q^{4} +(-1.86796 + 1.07847i) q^{5} +(4.21039 + 9.79818i) q^{6} +(7.50608 + 2.76746i) q^{8} +(-9.71647 - 16.8294i) q^{9} +O(q^{10})$	\(q+(-1.19654 + 1.60259i) q^{2} +(2.66613 - 4.61787i) q^{3} +(-1.13656 - 3.83513i) q^{4} +(-1.86796 + 1.07847i) q^{5} +(4.21039 + 9.79818i) q^{6} +(7.50608 + 2.76746i) q^{8} +(-9.71647 - 16.8294i) q^{9} +(0.506759 - 4.28400i) q^{10} +(-2.62956 + 4.55453i) q^{11} +(-20.7403 - 4.97644i) q^{12} -21.4116i q^{13} +11.5013i q^{15} +(-13.4164 + 8.71774i) q^{16} +(0.463429 - 0.802683i) q^{17} +(38.5968 + 4.56566i) q^{18} +(-2.96505 - 5.13561i) q^{19} +(6.25911 + 5.93812i) q^{20} +(-4.15264 - 9.66378i) q^{22} +(7.52507 - 4.34460i) q^{23} +(32.7919 - 27.2837i) q^{24} +(-10.1738 + 17.6216i) q^{25} +(34.3139 + 25.6199i) q^{26} -55.6311 q^{27} -9.42223i q^{29} +(-18.4318 - 13.7618i) q^{30} +(-29.8813 - 17.2520i) q^{31} +(2.08243 - 31.9322i) q^{32} +(14.0215 + 24.2859i) q^{33} +(0.731855 + 1.70313i) q^{34} +(-53.4996 + 56.3916i) q^{36} +(-11.0853 + 6.40011i) q^{37} +(11.7781 + 1.39324i) q^{38} +(-98.8758 - 57.0860i) q^{39} +(-17.0056 + 2.92555i) q^{40} -43.1339 q^{41} -41.7382 q^{43} +(20.4559 + 4.90818i) q^{44} +(36.2999 + 20.9578i) q^{45} +(-2.04148 + 17.2581i) q^{46} +(-39.8357 + 22.9991i) q^{47} +(4.48745 + 85.1980i) q^{48} +(-16.0667 - 37.3894i) q^{50} +(-2.47112 - 4.28011i) q^{51} +(-82.1161 + 24.3356i) q^{52} +(64.5031 + 37.2409i) q^{53} +(66.5650 - 89.1536i) q^{54} -11.3436i q^{55} -31.6208 q^{57} +(15.0999 + 11.2741i) q^{58} +(26.8367 - 46.4825i) q^{59} +(44.1090 - 13.0720i) q^{60} +(24.0893 - 13.9080i) q^{61} +(63.4020 - 27.2446i) q^{62} +(48.6823 + 41.5455i) q^{64} +(23.0916 + 39.9959i) q^{65} +(-55.6975 - 6.58853i) q^{66} +(39.2453 - 67.9749i) q^{67} +(-3.60511 - 0.865011i) q^{68} -46.3330i q^{69} -74.5100i q^{71} +(-26.3578 - 153.213i) q^{72} +(16.8020 - 29.1020i) q^{73} +(3.00734 - 25.4232i) q^{74} +(54.2494 + 93.9627i) q^{75} +(-16.3258 + 17.2083i) q^{76} +(209.794 - 90.1511i) q^{78} +(-26.1642 + 15.1059i) q^{79} +(15.6596 - 30.7536i) q^{80} +(-60.8713 + 105.432i) q^{81} +(51.6116 - 69.1258i) q^{82} +72.9274 q^{83} +1.99917i q^{85} +(49.9416 - 66.8891i) q^{86} +(-43.5106 - 25.1209i) q^{87} +(-32.3421 + 26.9094i) q^{88} +(-27.4198 - 47.4925i) q^{89} +(-77.0211 + 33.0968i) q^{90} +(-25.2148 - 23.9217i) q^{92} +(-159.335 + 91.9919i) q^{93} +(10.8070 - 91.3596i) q^{94} +(11.0772 + 6.39541i) q^{95} +(-141.907 - 94.7516i) q^{96} +53.7125 q^{97} +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} + 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} - 16 q^{30} + 112 q^{32} + 78 q^{33} - 76 q^{34} - 248 q^{36} - 80 q^{38} - 44 q^{40} + 232 q^{41} - 200 q^{43} + 132 q^{44} - 156 q^{46} - 176 q^{48} + 48 q^{50} + 10 q^{51} - 132 q^{52} + 36 q^{54} + 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} - 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} + 240 q^{86} - 204 q^{88} - 214 q^{89} - 440 q^{90} + 160 q^{92} + 16 q^{94} - 48 q^{96} + 152 q^{97} + 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 + 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 - 16 * q^30 + 112 * q^32 + 78 * q^33 - 76 * q^34 - 248 * q^36 - 80 * q^38 - 44 * q^40 + 232 * q^41 - 200 * q^43 + 132 * q^44 - 156 * q^46 - 176 * q^48 + 48 * q^50 + 10 * q^51 - 132 * q^52 + 36 * q^54 + 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 - 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 + 240 * q^86 - 204 * q^88 - 214 * q^89 - 440 * q^90 + 160 * q^92 + 16 * q^94 - 48 * q^96 + 152 * q^97 + 504 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.19654	+	1.60259i	−0.598272	+	0.801293i
$2$	−1.19654	+	1.60259i	−0.598272	+	0.801293i
$3$	2.66613	−	4.61787i	0.888709	−	1.53929i	0.0473064	−	0.998880i	$-0.484936\pi$
$3$	2.66613	−	4.61787i	0.888709	−	1.53929i	0.841403	−	0.540409i	$-0.181730\pi$
$4$	−1.13656	−	3.83513i	−0.284141	−	0.958782i
$5$	−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
$7$		0			0
$7$		0			0
$8$	7.50608	+	2.76746i	0.938259	+	0.345932i
$9$	−9.71647	−	16.8294i	−1.07961	−	1.86993i
$10$	0.506759	−	4.28400i	0.0506759	−	0.428400i
$11$	−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	$0.243503\pi$
$12$	−20.7403	−	4.97644i	−1.72836	−	0.414703i
$13$		−	21.4116i		−	1.64704i	−0.567285	−	0.823522i	$-0.692006\pi$
$13$		−	21.4116i		−	1.64704i	0.567285	−	0.823522i	$-0.307994\pi$
$14$		0			0
$15$			11.5013i			0.766754i
$16$	−13.4164	+	8.71774i	−0.838528	+	0.544859i
$17$	0.463429	−	0.802683i	0.0272606	−	0.0472167i	−0.852073	−	0.523423i	$-0.824655\pi$
$17$	0.463429	−	0.802683i	0.0272606	−	0.0472167i	0.879334	+	0.476206i	$0.157988\pi$
$18$	38.5968	+	4.56566i	2.14426	+	0.253648i
$19$	−2.96505	−	5.13561i	−0.156055	−	0.270295i	0.777388	−	0.629022i	$-0.216544\pi$
$19$	−2.96505	−	5.13561i	−0.156055	−	0.270295i	−0.933443	+	0.358726i	$0.883211\pi$
$20$	6.25911	+	5.93812i	0.312956	+	0.296906i
$21$		0			0
$22$	−4.15264	−	9.66378i	−0.188756	−	0.439263i
$23$	7.52507	−	4.34460i	0.327177	−	0.188896i	−0.327410	−	0.944882i	$-0.606176\pi$
$23$	7.52507	−	4.34460i	0.327177	−	0.188896i	0.654587	+	0.755987i	$0.272843\pi$
$24$	32.7919	−	27.2837i	1.36633	−	1.13682i
$25$	−10.1738	+	17.6216i	−0.406953	+	0.704863i
$26$	34.3139	+	25.6199i	1.31976	+	0.985380i
$27$	−55.6311			−2.06041
$28$		0			0
$29$		−	9.42223i		−	0.324904i	−0.986716	−	0.162452i	$-0.948060\pi$
$29$		−	9.42223i		−	0.324904i	0.986716	−	0.162452i	$-0.0519403\pi$
$30$	−18.4318	−	13.7618i	−0.614395	−	0.458728i
$31$	−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	$0.854529\pi$
$32$	2.08243	−	31.9322i	0.0650759	−	0.997880i
$33$	14.0215	+	24.2859i	0.424893	+	0.735936i
$34$	0.731855	+	1.70313i	0.0215252	+	0.0500921i
$35$		0			0
$36$	−53.4996	+	56.3916i	−1.48610	+	1.56643i
$37$	−11.0853	+	6.40011i	−0.299603	+	0.172976i	−0.642265	−	0.766483i	$-0.722005\pi$
$37$	−11.0853	+	6.40011i	−0.299603	+	0.172976i	0.342662	+	0.939459i	$0.388672\pi$
$38$	11.7781	+	1.39324i	0.309949	+	0.0366643i
$39$	−98.8758	−	57.0860i	−2.53528	−	1.46374i
$40$	−17.0056	+	2.92555i	−0.425141	+	0.0731387i
$41$	−43.1339			−1.05205			−0.526023	−	0.850470i	$-0.676317\pi$
$41$	−43.1339			−1.05205			−0.526023	+	0.850470i	$0.676317\pi$
$42$		0			0
$43$	−41.7382			−0.970656			−0.485328	−	0.874332i	$-0.661300\pi$
$43$	−41.7382			−0.970656			−0.485328	+	0.874332i	$0.661300\pi$
$44$	20.4559	+	4.90818i	0.464906	+	0.111550i
$45$	36.2999	+	20.9578i	0.806665	+	0.465728i
$46$	−2.04148	+	17.2581i	−0.0443800	+	0.375175i
$47$	−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
$49$		0			0
$50$	−16.0667	−	37.3894i	−0.321333	−	0.747788i
$51$	−2.47112	−	4.28011i	−0.0484534	−	0.0839238i
$52$	−82.1161	+	24.3356i	−1.57916	+	0.467993i
$53$	64.5031	+	37.2409i	1.21704	+	0.702658i	0.964284	−	0.264872i	$-0.0853297\pi$
$53$	64.5031	+	37.2409i	1.21704	+	0.702658i	0.252756	+	0.967530i	$0.418663\pi$
$54$	66.5650	−	89.1536i	1.23269	−	1.65099i
$55$		−	11.3436i		−	0.206246i
$56$		0			0
$57$	−31.6208			−0.554751
$58$	15.0999	+	11.2741i	0.260344	+	0.194381i
$59$	26.8367	−	46.4825i	0.454860	−	0.787840i	−0.543821	−	0.839201i	$-0.683023\pi$
$59$	26.8367	−	46.4825i	0.454860	−	0.787840i	0.998680	+	0.0513617i	$0.0163561\pi$
$60$	44.1090	−	13.0720i	0.735150	−	0.217866i
$61$	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
$63$		0			0
$64$	48.6823	+	41.5455i	0.760661	+	0.649149i
$65$	23.0916	+	39.9959i	0.355256	+	0.615322i
$66$	−55.6975	−	6.58853i	−0.843902	−	0.0998262i
$67$	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	$-0.0325338\pi$
$68$	−3.60511	−	0.865011i	−0.0530164	−	0.0127207i
$69$		−	46.3330i		−	0.671493i
$70$		0			0
$71$		−	74.5100i		−	1.04944i	−0.851276	−	0.524719i	$-0.824171\pi$
$71$		−	74.5100i		−	1.04944i	0.851276	−	0.524719i	$-0.175829\pi$
$72$	−26.3578	−	153.213i	−0.366081	−	2.12796i
$73$	16.8020	−	29.1020i	0.230165	−	0.398657i	−0.727692	−	0.685904i	$-0.759407\pi$
$73$	16.8020	−	29.1020i	0.230165	−	0.398657i	0.957857	+	0.287247i	$0.0927401\pi$
$74$	3.00734	−	25.4232i	0.0406397	−	0.343556i
$75$	54.2494	+	93.9627i	0.723325	+	1.25284i
$76$	−16.3258	+	17.2083i	−0.214813	+	0.226425i
$77$		0			0
$78$	209.794	−	90.1511i	2.68967	−	1.15578i
$79$	−26.1642	+	15.1059i	−0.331192	+	0.191214i	−0.656370	−	0.754439i	$-0.727909\pi$
$79$	−26.1642	+	15.1059i	−0.331192	+	0.191214i	0.325178	+	0.945653i	$0.394576\pi$
$80$	15.6596	−	30.7536i	0.195745	−	0.384420i
$81$	−60.8713	+	105.432i	−0.751497	+	1.30163i
$82$	51.6116	−	69.1258i	0.629410	−	0.842997i
$83$	72.9274			0.878644			0.439322	−	0.898330i	$-0.355219\pi$
$83$	72.9274			0.878644			0.439322	+	0.898330i	$0.355219\pi$
$84$		0			0
$85$			1.99917i			0.0235197i
$86$	49.9416	−	66.8891i	0.580716	−	0.777780i
$87$	−43.5106	−	25.1209i	−0.500122	−	0.288745i
$88$	−32.3421	+	26.9094i	−0.367524	+	0.305789i
$89$	−27.4198	−	47.4925i	−0.308088	−	0.533624i	0.669856	−	0.742491i	$-0.266356\pi$
$89$	−27.4198	−	47.4925i	−0.308088	−	0.533624i	−0.977944	+	0.208867i	$0.933022\pi$
$90$	−77.0211	+	33.0968i	−0.855790	+	0.367743i
$91$		0			0
$92$	−25.2148	−	23.9217i	−0.274074	−	0.260018i
$93$	−159.335	+	91.9919i	−1.71328	+	0.989160i
$94$	10.8070	−	91.3596i	0.114969	−	0.971910i
$95$	11.0772	+	6.39541i	0.116602	+	0.0673201i
$96$	−141.907	−	94.7516i	−1.47819	−	0.986996i
$97$	53.7125			0.553738			0.276869	−	0.960908i	$-0.410703\pi$
$97$	53.7125			0.553738			0.276869	+	0.960908i	$0.410703\pi$
$98$		0			0
$99$	102.200			1.03232
$100$	79.1442	+	18.9899i	0.791442	+	0.189899i
$101$	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	$0.519145\pi$
$102$	9.81606	+	1.16115i	0.0962358	+	0.0113839i
$103$	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
$105$		0			0
$106$	−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	$0.598403\pi$
$108$	63.2283	+	213.352i	0.585447	+	1.97548i
$109$	−57.7477	−	33.3406i	−0.529795	−	0.305877i	0.211138	−	0.977456i	$-0.432283\pi$
$109$	−57.7477	−	33.3406i	−0.529795	−	0.305877i	−0.740933	+	0.671579i	$0.765616\pi$
$110$	18.1790	+	13.5731i	0.165264	+	0.123391i
$111$			68.2540i			0.614901i
$112$		0			0
$113$	7.16467			0.0634042			0.0317021	−	0.999497i	$-0.489907\pi$
$113$	7.16467			0.0634042			0.0317021	+	0.999497i	$0.489907\pi$
$114$	37.8357	−	50.6750i	0.331892	−	0.444518i
$115$	−9.37101	+	16.2311i	−0.0814870	+	0.141140i
$116$	−36.1355	+	10.7090i	−0.311513	+	0.0923187i
$117$	−360.344	+	208.045i	−3.07986	+	1.77816i
$118$	42.3810	+	98.6266i	0.359161	+	0.835818i
$119$		0			0
$120$	−31.8294	+	86.3297i	−0.265245	+	0.719414i
$121$	46.6709	+	80.8363i	0.385710	+	0.668069i
$122$	−6.53521	+	55.2468i	−0.0535673	+	0.452842i
$123$	−115.000	+	199.187i	−0.934963	+	1.61940i
$124$	−32.2015	+	134.207i	−0.259690	+	1.08231i
$125$		−	97.8118i		−	0.782494i
$126$		0			0
$127$		−	131.492i		−	1.03537i	−0.855572	−	0.517684i	$-0.826794\pi$
$127$		−	131.492i		−	1.03537i	0.855572	−	0.517684i	$-0.173206\pi$
$128$	−124.831	+	28.3066i	−0.975241	+	0.221145i
$129$	−111.279	+	192.742i	−0.862631	+	1.49412i
$130$	−91.7271	−	10.8505i	−0.705593	−	0.0834655i
$131$	−4.38060	−	7.58742i	−0.0334397	−	0.0579193i	0.848821	−	0.528680i	$-0.177313\pi$
$131$	−4.38060	−	7.58742i	−0.0334397	−	0.0579193i	−0.882261	+	0.470761i	$0.843980\pi$
$132$	77.2032	−	81.3766i	0.584873	−	0.616489i
$133$		0			0
$134$	61.9769	+	144.229i	0.462514	+	1.07634i
$135$	103.916	−	59.9962i	0.769752	−	0.444416i
$136$	5.69993	−	4.74248i	0.0419113	−	0.0348712i
$137$	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	$-0.165623\pi$
$138$	74.2526	+	55.4395i	0.538063	+	0.401735i
$139$	−172.122			−1.23828			−0.619142	−	0.785279i	$-0.712520\pi$
$139$	−172.122			−1.23828			−0.619142	+	0.785279i	$0.712520\pi$
$140$		0			0
$141$			245.274i			1.73954i
$142$	119.409	+	89.1545i	0.840907	+	0.627849i
$143$	97.5195	+	56.3029i	0.681955	+	0.393727i
$144$	277.075	+	141.085i	1.92413	+	0.979758i
$145$	10.1616	+	17.6003i	0.0700797	+	0.121382i
$146$	26.5341	+	61.7485i	0.181740	+	0.422935i
$147$		0			0
$148$	37.1444	+	35.2395i	0.250976	+	0.238105i
$149$	199.798	−	115.354i	1.34093	−	0.774186i	0.353985	−	0.935251i	$-0.384826\pi$
$149$	199.798	−	115.354i	1.34093	−	0.774186i	0.986944	+	0.161066i	$0.0514931\pi$
$150$	−215.495	−	25.4912i	−1.43663	−	0.169941i
$151$	128.077	+	73.9452i	0.848190	+	0.489703i	0.860040	−	0.510227i	$-0.170439\pi$
$151$	128.077	+	73.9452i	0.848190	+	0.489703i	−0.0118494	+	0.999930i	$0.503772\pi$
$152$	−8.04327	−	46.7540i	−0.0529163	−	0.307592i
$153$	−18.0116			−0.117723
$154$		0			0
$155$	74.4227			0.480146
$156$	−106.553	+	444.083i	−0.683034	+	2.84669i
$157$	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	$0.547497\pi$
$158$	7.09810	−	60.0052i	0.0449247	−	0.379780i
$159$	343.947	−	198.578i	2.16319	−	1.24892i
$160$	30.5479	+	61.8938i	0.190924	+	0.386836i
$161$		0			0
$162$	−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	$0.881665\pi$
$164$	49.0245	+	165.424i	0.298930	+	1.00868i
$165$	−52.3830	−	30.2433i	−0.317473	−	0.183293i
$166$	−87.2609	+	116.872i	−0.525668	+	0.704051i
$167$		−	241.457i		−	1.44585i	−0.690926	−	0.722926i	$-0.742797\pi$
$167$		−	241.457i		−	1.44585i	0.690926	−	0.722926i	$-0.257203\pi$
$168$		0			0
$169$	−289.455			−1.71275
$170$	−3.20385	−	2.39210i	−0.0188461	−	0.0140712i
$171$	−57.6196	+	99.8001i	−0.336957	+	0.583626i
$172$	47.4382	+	160.071i	0.275803	+	0.930648i
$173$	−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
$175$		0			0
$176$	−4.42590	−	84.0293i	−0.0251471	−	0.477439i
$177$	−143.100	−	247.857i	−0.808475	−	1.40032i
$178$	108.920	+	12.8843i	0.611909	+	0.0723836i
$179$	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	$0.0512141\pi$
$180$	39.1186	−	163.035i	0.217325	−	0.905748i
$181$			212.704i			1.17516i	0.809165	+	0.587581i	$0.199920\pi$
$181$			212.704i			1.17516i	−0.809165	+	0.587581i	$0.800080\pi$
$182$		0			0
$183$		−	148.322i		−	0.810502i
$184$	68.5072	−	11.7856i	0.372322	−	0.0640520i
$185$	13.8046	−	23.9103i	0.0746194	−	0.129245i
$186$	43.2260	−	365.420i	0.232398	−	1.96462i
$187$	2.43723	+	4.22140i	0.0130333	+	0.0225743i
$188$	133.480	+	126.635i	0.710002	+	0.673590i
$189$		0			0
$190$	−23.5035	+	10.0997i	−0.123703	+	0.0531565i
$191$	35.1041	−	20.2674i	0.183791	−	0.106112i	−0.405282	−	0.914192i	$-0.632826\pi$
$191$	35.1041	−	20.2674i	0.183791	−	0.106112i	0.589073	+	0.808080i	$0.299493\pi$
$192$	321.645	−	114.043i	1.67523	−	0.593974i
$193$	−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	$0.905551\pi$
$194$	−64.2694	+	86.0790i	−0.331286	+	0.443706i
$195$	246.261			1.26288
$196$		0			0
$197$			261.806i			1.32896i	0.747304	+	0.664482i	$0.231348\pi$
$197$			261.806i			1.32896i	−0.747304	+	0.664482i	$0.768652\pi$
$198$	−122.287	+	163.784i	−0.617610	+	0.827193i
$199$	−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	$0.966851\pi$
$200$	−125.132	+	104.113i	−0.625662	+	0.520566i
$201$	−209.266	−	362.460i	−1.04113	−	1.80328i
$202$	−165.932	+	71.3031i	−0.821448	+	0.352986i
$203$		0			0
$204$	−13.6062	+	14.3417i	−0.0666970	+	0.0703025i
$205$	80.5723	−	46.5184i	0.393036	−	0.226919i
$206$	−26.5046	+	224.062i	−0.128663	+	1.08768i
$207$	−146.234	−	84.4283i	−0.706445	−	0.407866i
$208$	186.661	+	287.267i	0.897406	+	1.38109i
$209$	31.1870			0.149220
$210$		0			0
$211$	169.792			0.804702			0.402351	−	0.915485i	$-0.368193\pi$
$211$	169.792			0.804702			0.402351	+	0.915485i	$0.368193\pi$
$212$	69.5117	−	289.704i	0.327885	−	1.36653i
$213$	−344.077	−	198.653i	−1.61539	−	0.932644i
$214$	−285.986	−	33.8297i	−1.33638	−	0.158083i
$215$	77.9652	−	45.0133i	0.362629	−	0.209364i
$216$	−417.571	−	153.957i	−1.93320	−	0.712763i
$217$		0			0
$218$	122.529	−	52.6521i	0.562059	−	0.241523i
$219$	−89.5927	−	155.179i	−0.409099	−	0.708581i
$220$	−43.5040	+	12.8927i	−0.197745	+	0.0586031i
$221$	−17.1867	−	9.92275i	−0.0777679	−	0.0448993i
$222$	−109.383	−	81.6689i	−0.492716	−	0.367878i
$223$			45.4626i			0.203868i	0.994791	+	0.101934i	$0.0325031\pi$
$223$			45.4626i			0.203868i	−0.994791	+	0.101934i	$0.967497\pi$
$224$		0			0
$225$	395.414			1.75740
$226$	−8.57285	+	11.4820i	−0.0379329	+	0.0508053i
$227$	92.5653	−	160.328i	0.407777	−	0.706290i	−0.586864	−	0.809686i	$-0.699637\pi$
$227$	92.5653	−	160.328i	0.407777	−	0.706290i	0.994640	+	0.103396i	$0.0329708\pi$
$228$	35.9391	+	121.270i	0.157627	+	0.531885i
$229$	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
$231$		0			0
$232$	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	$0.899870\pi$
$234$	97.7580	−	826.417i	0.417769	−	3.53170i
$235$	49.6076	−	85.9228i	0.211096	−	0.365629i
$236$	−208.768	−	50.0919i	−0.884611	−	0.212254i
$237$			161.097i			0.679734i
$238$		0			0
$239$		−	163.185i		−	0.682782i	−0.939921	−	0.341391i	$-0.889102\pi$
$239$		−	163.185i		−	0.682782i	0.939921	−	0.341391i	$-0.110898\pi$
$240$	−100.266	−	154.307i	−0.417773	−	0.642945i
$241$	102.745	−	177.960i	0.426330	−	0.738424i	−0.570214	−	0.821496i	$-0.693140\pi$
$241$	102.745	−	177.960i	0.426330	−	0.738424i	0.996544	+	0.0830718i	$0.0264731\pi$
$242$	−185.391	−	21.9301i	−0.766078	−	0.0906204i
$243$	74.2413	+	128.590i	0.305520	+	0.529176i
$244$	−80.7180	−	76.5784i	−0.330812	−	0.313846i
$245$		0			0
$246$	−181.611	−	422.634i	−0.738254	−	1.71802i
$247$	−109.962	+	63.4863i	−0.445188	+	0.257030i
$248$	−176.547	−	212.190i	−0.711883	−	0.855604i
$249$	194.434	−	336.769i	0.780859	−	1.35249i
$250$	156.752	+	117.036i	0.627007	+	0.468145i
$251$	159.299			0.634658			0.317329	−	0.948316i	$-0.397214\pi$
$251$	159.299			0.634658			0.317329	+	0.948316i	$0.397214\pi$
$252$		0			0
$253$			45.6975i			0.180622i
$254$	210.727	+	157.336i	0.829633	+	0.619431i
$255$	9.23191	+	5.33005i	0.0362036	+	0.0209021i
$256$	104.002	−	233.922i	0.406257	−	0.913759i
$257$	107.889	+	186.868i	0.419800	+	0.727114i	0.995919	−	0.0902512i	$-0.0287670\pi$
$257$	107.889	+	186.868i	0.419800	+	0.727114i	−0.576119	+	0.817366i	$0.695434\pi$
$258$	−175.734	−	408.959i	−0.681140	−	1.58511i
$259$		0			0
$260$	127.144	−	134.017i	0.489017	−	0.515452i
$261$	−158.571	+	91.5507i	−0.607550	+	0.350769i
$262$	17.4011	+	2.05840i	0.0664163	+	0.00785647i
$263$	285.059	+	164.579i	1.08387	+	0.625775i	0.931939	−	0.362616i	$-0.118116\pi$
$263$	285.059	+	164.579i	1.08387	+	0.625775i	0.151935	+	0.988391i	$0.451450\pi$
$264$	38.0360	+	221.096i	0.144076	+	0.837483i
$265$	−160.652			−0.606234
$266$		0			0
$267$	−292.419			−1.09520
$268$	−305.298	−	73.2531i	−1.13917	−	0.273332i
$269$	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	$0.483297\pi$
$270$	−28.1916	+	238.323i	−0.104413	+	0.882679i
$271$	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
$273$		0			0
$274$	187.011	+	435.202i	0.682523	+	1.58833i
$275$	−53.5053	−	92.6739i	−0.194565	−	0.336996i
$276$	−177.693	+	52.6605i	−0.643816	+	0.190799i
$277$	289.925	+	167.389i	1.04666	+	0.604291i	0.921713	−	0.387872i	$-0.126790\pi$
$277$	289.925	+	167.389i	1.04666	+	0.604291i	0.124949	+	0.992163i	$0.460123\pi$
$278$	205.951	−	275.840i	0.740831	−	0.992229i
$279$			670.513i			2.40327i
$280$		0			0
$281$	−123.357			−0.438994			−0.219497	−	0.975613i	$-0.570442\pi$
$281$	−123.357			−0.438994			−0.219497	+	0.975613i	$0.570442\pi$
$282$	−393.073	−	293.482i	−1.39388	−	1.04072i
$283$	−0.309453	+	0.535988i	−0.00109347	+	0.00189395i	−0.866572	−	0.499053i	$-0.833681\pi$
$283$	−0.309453	+	0.535988i	−0.00109347	+	0.00189395i	0.865478	+	0.500947i	$0.167015\pi$
$284$	−285.756	+	84.6855i	−1.00618	+	0.298188i
$285$	59.0663	−	34.1019i	0.207250	−	0.119656i
$286$	−206.917	+	88.9145i	−0.723485	+	0.310890i
$287$		0			0
$288$	−557.634	+	275.222i	−1.93623	+	0.955631i
$289$	144.070	+	249.537i	0.498514	+	0.863451i
$290$	−40.3648	−	4.77480i	−0.139189	−	0.0164648i
$291$	143.204	−	248.037i	0.492112	−	0.852362i
$292$	−130.707	−	31.3617i	−0.447625	−	0.107403i
$293$			28.2794i			0.0965169i	0.998835	+	0.0482584i	$0.0153671\pi$
$293$			28.2794i			0.0965169i	−0.998835	+	0.0482584i	$0.984633\pi$
$294$		0			0
$295$			115.770i			0.392440i
$296$	−100.919	+	17.3615i	−0.340943	+	0.0586538i
$297$	146.285	−	253.373i	0.492542	−	0.853108i
$298$	−54.2034	+	458.220i	−0.181891	+	1.53765i
$299$	−93.0247	−	161.123i	−0.311119	−	0.538874i
$300$	298.701	−	314.848i	0.995671	−	1.04949i
$301$		0			0
$302$	−271.753	+	116.775i	−0.899844	+	0.386674i
$303$	417.002	−	240.756i	1.37624	−	0.794575i
$304$	84.5514	+	43.0531i	0.278130	+	0.141622i
$305$	−29.9986	+	51.9591i	−0.0983560	+	0.170358i
$306$	21.5517	−	28.8651i	0.0704303	−	0.0943305i
$307$	−400.893			−1.30584			−0.652921	−	0.757426i	$-0.726457\pi$
$307$	−400.893			−1.30584			−0.652921	+	0.757426i	$0.726457\pi$
$308$		0			0
$309$		−	601.542i		−	1.94674i
$310$	−89.0500	+	119.269i	−0.287258	+	0.384738i
$311$	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	$0.582676\pi$
$312$	−584.186	−	702.126i	−1.87239	−	2.25040i
$313$	−133.123	−	230.576i	−0.425313	−	0.736664i	0.571137	−	0.820855i	$-0.306503\pi$
$313$	−133.123	−	230.576i	−0.425313	−	0.736664i	−0.996450	+	0.0841913i	$0.973169\pi$
$314$	−211.002	+	90.6700i	−0.671981	+	0.288758i
$315$		0			0
$316$	87.6704	+	83.1742i	0.277438	+	0.263210i
$317$	−374.864	+	216.428i	−1.18254	+	0.682737i	−0.956600	−	0.291405i	$-0.905877\pi$
$317$	−374.864	+	216.428i	−1.18254	+	0.682737i	−0.225936	+	0.974142i	$0.572544\pi$
$318$	−93.3096	+	788.812i	−0.293426	+	2.48054i
$319$	42.9138	+	24.7763i	0.134526	+	0.0776686i
$320$	−135.742	−	25.1030i	−0.424194	−	0.0784470i
$321$	767.792			2.39187
$322$		0			0
$323$	−5.49636			−0.0170166
$324$	473.530	+	113.619i	1.46151	+	0.350675i
$325$	377.305	+	217.837i	1.16094	+	0.670269i
$326$	97.9353	+	11.5849i	0.300415	+	0.0355365i
$327$	−307.925	+	177.781i	−0.941668	+	0.543672i
$328$	−323.766	−	119.371i	−0.987092	−	0.363937i
$329$		0			0
$330$	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	$0.872501\pi$
$332$	−82.8867	−	279.686i	−0.249659	−	0.842428i
$333$	215.420	+	124.373i	0.646907	+	0.373492i
$334$	386.956	+	288.914i	1.15855	+	0.865012i
$335$			169.299i			0.505370i
$336$		0			0
$337$	−69.4941			−0.206214			−0.103107	−	0.994670i	$-0.532878\pi$
$337$	−69.4941			−0.206214			−0.103107	+	0.994670i	$0.532878\pi$
$338$	346.346	−	463.877i	1.02469	−	1.37242i
$339$	19.1019	−	33.0855i	0.0563479	−	0.0975974i
$340$	7.66708	−	2.27219i	0.0225502	−	0.00668291i
$341$	157.149	−	90.7300i	0.460848	−	0.266071i
$342$	−90.9938	−	211.756i	−0.266064	−	0.619168i
$343$		0			0
$344$	−313.290	−	115.509i	−0.910727	−	0.335781i
$345$	49.9686	+	86.5481i	0.144836	+	0.250864i
$346$	12.7859	−	108.089i	0.0369536	−	0.312395i
$347$	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	$-0.00124784\pi$
$348$	−46.8891	+	195.420i	−0.134739	+	0.561552i
$349$		−	165.836i		−	0.475174i	−0.971366	−	0.237587i	$-0.923643\pi$
$349$		−	165.836i		−	0.475174i	0.971366	−	0.237587i	$-0.0763566\pi$
$350$		0			0
$351$			1191.15i			3.39358i
$352$	139.960	+	93.4519i	0.397614	+	0.265488i
$353$	−235.858	+	408.519i	−0.668154	+	1.15728i	0.310266	+	0.950650i	$0.399582\pi$
$353$	−235.858	+	408.519i	−0.668154	+	1.15728i	−0.978420	+	0.206627i	$0.933751\pi$
$354$	568.437	+	67.2412i	1.60576	+	0.189947i
$355$	80.3566	+	139.182i	0.226356	+	0.392061i
$356$	−150.976	+	159.137i	−0.424089	+	0.447014i
$357$		0			0
$358$	100.296	+	233.403i	0.280157	+	0.651964i
$359$	−568.967	+	328.493i	−1.58487	+	0.915022i	−0.590731	+	0.806869i	$0.701161\pi$
$359$	−568.967	+	328.493i	−1.58487	+	0.915022i	−0.994134	+	0.108154i	$0.965506\pi$
$360$	214.470	+	257.769i	0.595750	+	0.716025i
$361$	162.917	−	282.180i	0.451294	−	0.781663i
$362$	−340.877	−	254.510i	−0.941649	−	0.703067i
$363$	497.722			1.37113
$364$		0			0
$365$			72.4817i			0.198580i
$366$	237.699	+	177.474i	0.649450	+	0.484901i
$367$	−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	$0.827592\pi$
$368$	−63.0845	+	123.891i	−0.171425	+	0.336659i
$369$	419.109	+	725.918i	1.13580	+	1.96726i
$370$	21.8004	+	50.7327i	0.0589201	+	0.137116i
$371$		0			0
$372$	533.895	+	506.514i	1.43520	+	1.36160i
$373$	273.662	−	157.999i	0.733680	−	0.423590i	−0.0860872	−	0.996288i	$-0.527436\pi$
$373$	273.662	−	157.999i	0.733680	−	0.423590i	0.819767	+	0.572698i	$0.194103\pi$
$374$	−9.68141	−	1.14523i	−0.0258861	−	0.00306210i
$375$	−451.682	−	260.779i	−1.20449	−	0.695410i
$376$	−362.659	+	62.3896i	−0.964518	+	0.165930i
$377$	−201.745			−0.535132
$378$		0			0
$379$	−178.404			−0.470723			−0.235361	−	0.971908i	$-0.575627\pi$
$379$	−178.404			−0.470723			−0.235361	+	0.971908i	$0.575627\pi$
$380$	11.9373	−	49.7512i	0.0314140	−	0.130924i
$381$	−607.211	−	350.574i	−1.59373	−	0.920140i
$382$	−9.52341	+	80.5082i	−0.0249304	+	0.210754i
$383$	−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
$385$		0			0
$386$	−222.912	−	518.747i	−0.577491	−	1.34390i
$387$	405.548	+	702.430i	1.04793	+	1.81506i
$388$	−61.0478	−	205.995i	−0.157340	−	0.530914i
$389$	151.865	+	87.6790i	0.390397	+	0.225396i	0.682332	−	0.731042i	$-0.260966\pi$
$389$	151.865	+	87.6790i	0.390397	+	0.225396i	−0.291935	+	0.956438i	$0.594299\pi$
$390$	−294.662	+	394.655i	−0.755544	+	1.01193i
$391$		−	8.05366i		−	0.0205976i
$392$		0			0
$393$	−46.7170			−0.118873
$394$	−419.567	−	313.263i	−1.06489	−	0.795083i
$395$	32.5824	−	56.4344i	0.0824871	−	0.142872i
$396$	−116.157	−	391.950i	−0.293325	−	0.989773i
$397$	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
$399$		0			0
$400$	−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	$-0.394938\pi$
$402$	831.269	+	98.3319i	2.06783	+	0.244607i
$403$	−369.392	+	639.805i	−0.916605	+	1.58761i
$404$	84.2761	−	351.238i	0.208604	−	0.869402i
$405$		−	262.590i		−	0.648371i
$406$		0			0
$407$		−	67.3178i		−	0.165400i
$408$	−6.70340	−	38.9656i	−0.0164299	−	0.0955039i
$409$	−211.872	+	366.973i	−0.518025	+	0.897245i	0.481756	+	0.876305i	$0.339999\pi$
$409$	−211.872	+	366.973i	−0.518025	+	0.897245i	−0.999781	+	0.0209399i	$0.993334\pi$
$410$	−21.8585	+	184.785i	−0.0533134	+	0.450696i
$411$	−631.447	−	1093.70i	−1.53637	−	2.66107i
$412$	−327.364	−	310.576i	−0.794574	−	0.753824i
$413$		0			0
$414$	310.279	−	133.331i	0.749467	−	0.322055i
$415$	−136.225	+	78.6498i	−0.328254	+	0.189517i
$416$	−683.718	−	44.5881i	−1.64355	−	0.107183i
$417$	−458.898	+	794.834i	−1.10047	+	1.90608i
$418$	−37.3167	+	49.9799i	−0.0892743	+	0.119569i
$419$	−295.598			−0.705485			−0.352742	−	0.935721i	$-0.614751\pi$
$419$	−295.598			−0.705485			−0.352742	+	0.935721i	$0.614751\pi$
$420$		0			0
$421$		−	126.260i		−	0.299904i	−0.988693	−	0.149952i	$-0.952088\pi$
$421$		−	126.260i		−	0.299904i	0.988693	−	0.149952i	$-0.0479119\pi$
$422$	−203.164	+	272.107i	−0.481431	+	0.644802i
$423$	774.124	+	446.941i	1.83008	+	1.05660i
$424$	381.102	+	458.043i	0.898827	+	1.08029i
$425$	9.42970	+	16.3327i	0.0221875	+	0.0384299i
$426$	730.063	−	313.716i	1.71376	−	0.736424i
$427$		0			0
$428$	396.410	−	417.839i	0.926192	−	0.976259i
$429$	519.999	−	300.221i	1.21212	−	0.699817i
$430$	−21.1512	+	178.806i	−0.0491889	+	0.415829i
$431$	−220.198	−	127.131i	−0.510900	−	0.294968i	0.222303	−	0.974978i	$-0.428642\pi$
$431$	−220.198	−	127.131i	−0.510900	−	0.294968i	−0.733204	+	0.680009i	$0.761976\pi$
$432$	746.371	−	484.977i	1.72771	−	1.12263i
$433$	−546.301			−1.26167			−0.630833	−	0.775919i	$-0.717287\pi$
$433$	−546.301			−1.26167			−0.630833	+	0.775919i	$0.717287\pi$
$434$		0			0
$435$	108.368			0.249122
$436$	−62.2317	+	259.364i	−0.142733	+	0.594871i
$437$	−44.6244	−	25.7639i	−0.102115	−	0.0589563i
$438$	355.890	+	42.0987i	0.812534	+	0.0961156i
$439$	−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
$441$		0			0
$442$	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	$-0.346678\pi$
$444$	261.763	−	77.5751i	0.589556	−	0.174719i
$445$	102.438	+	59.1427i	0.230198	+	0.132905i
$446$	−72.8578	−	54.3981i	−0.163358	−	0.121969i
$447$		−	1230.19i		−	2.75210i
$448$		0			0
$449$	782.101			1.74187			0.870936	−	0.491396i	$-0.163513\pi$
$449$	782.101			1.74187			0.870936	+	0.491396i	$0.163513\pi$
$450$	−473.131	+	633.686i	−1.05140	+	1.40819i
$451$	113.423	−	196.454i	0.251492	−	0.435597i
$452$	−8.14311	−	27.4774i	−0.0180157	−	0.0607908i
$453$	682.938	−	394.294i	1.50759	−	0.870407i
$454$	146.181	+	340.183i	0.321984	+	0.749302i
$455$		0			0
$456$	−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	$0.766835\pi$
$458$	−43.4534	+	367.343i	−0.0948765	+	0.802058i
$459$	−25.7811	+	44.6541i	−0.0561679	+	0.0972857i
$460$	72.8990	+	17.4914i	0.158476	+	0.0380247i
$461$			202.533i			0.439335i	0.975575	+	0.219667i	$0.0704972\pi$
$461$			202.533i			0.439335i	−0.975575	+	0.219667i	$0.929503\pi$
$462$		0			0
$463$		−	652.927i		−	1.41021i	−0.709103	−	0.705105i	$-0.750900\pi$
$463$		−	652.927i		−	1.41021i	0.709103	−	0.705105i	$-0.249100\pi$
$464$	82.1406	+	126.413i	0.177027	+	0.272441i
$465$	198.420	−	343.674i	0.426710	−	0.739084i
$466$	192.062	+	22.7193i	0.412151	+	0.0487539i
$467$	272.725	+	472.373i	0.583993	+	1.01150i	0.995000	+	0.0998730i	$0.0318437\pi$
$467$	272.725	+	472.373i	0.583993	+	1.01150i	−0.411008	+	0.911632i	$0.634823\pi$
$468$	1207.43	+	1145.51i	2.57998	+	2.44767i
$469$		0			0
$470$	78.3411	+	182.311i	0.166683	+	0.387895i
$471$	530.266	−	306.149i	1.12583	−	0.649998i
$472$	330.077	−	274.632i	0.699316	−	0.581847i
$473$	109.753	−	190.098i	0.232036	−	0.401898i
$474$	−258.172	−	192.760i	−0.544666	−	0.406666i
$475$	120.663			0.254028
$476$		0			0
$477$		−	1447.40i		−	3.03438i
$478$	261.518	+	195.258i	0.547108	+	0.408489i
$479$	−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	$0.702928\pi$
$480$	367.262	+	23.9507i	0.765129	+	0.0498972i
$481$	137.036	+	237.354i	0.284899	+	0.493459i
$482$	162.257	+	377.596i	0.336633	+	0.783394i
$483$		0			0
$484$	256.973	−	270.865i	0.530937	−	0.559637i
$485$	−100.333	+	57.9272i	−0.206872	+	0.119437i
$486$	−294.909	−	34.8852i	−0.606809	−	0.0717802i
$487$	−371.831	−	214.677i	−0.763513	−	0.440814i	0.0670428	−	0.997750i	$-0.478644\pi$
$487$	−371.831	−	214.677i	−0.763513	−	0.440814i	−0.830556	+	0.556936i	$0.811977\pi$
$488$	219.306	−	37.7281i	0.449398	−	0.0773117i
$489$	−262.929			−0.537686
$490$		0			0
$491$	453.887			0.924413			0.462206	−	0.886772i	$-0.347058\pi$
$491$	453.887			0.924413			0.462206	+	0.886772i	$0.347058\pi$
$492$	894.612	+	214.653i	1.81832	+	0.436287i
$493$	−7.56306	−	4.36654i	−0.0153409	−	0.00885707i
$494$	29.8315	−	252.187i	0.0603877	−	0.510500i
$495$	−190.905	+	110.219i	−0.385667	+	0.222665i
$496$	551.299	−	29.0374i	1.11149	−	0.0585431i
$497$		0			0
$498$	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	$0.941754\pi$
$500$	−375.121	+	111.169i	−0.750242	+	0.222339i
$501$	−1115.02	−	643.755i	−2.22558	−	1.28494i
$502$	−190.608	+	255.291i	−0.379698	+	0.508547i
$503$		−	580.170i		−	1.15342i	−0.816949	−	0.576710i	$-0.804336\pi$
$503$		−	580.170i		−	1.15342i	0.816949	−	0.576710i	$-0.195664\pi$
$504$		0			0
$505$	−194.775			−0.385693
$506$	−73.2341	−	54.6790i	−0.144731	−	0.108061i
$507$	−771.724	+	1336.67i	−1.52214	+	2.63642i
$508$	−504.288	+	149.449i	−0.992692	+	0.294190i
$509$	−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
$511$		0			0
$512$	250.438	+	446.570i	0.489136	+	0.872207i
$513$	164.949	+	285.700i	0.321538	+	0.556919i
$514$	−428.566	−	50.6956i	−0.833786	−	0.0986296i
$515$	−121.664	+	210.728i	−0.236241	+	0.409181i
$516$	865.665	+	207.708i	1.67765	+	0.402534i
$517$		−	241.910i		−	0.467911i
$518$		0			0
$519$			290.187i			0.559127i
$520$	62.6406	+	364.118i	0.120463	+	0.700226i
$521$	360.480	−	624.369i	0.691899	−	1.19840i	−0.279316	−	0.960199i	$-0.590108\pi$
$521$	360.480	−	624.369i	0.691899	−	1.19840i	0.971215	−	0.238205i	$-0.0765591\pi$
$522$	43.0187	−	363.667i	0.0824113	−	0.696681i
$523$	−134.988	−	233.807i	−0.258104	−	0.447049i	0.707630	−	0.706583i	$-0.249764\pi$
$523$	−134.988	−	233.807i	−0.258104	−	0.447049i	−0.965734	+	0.259534i	$0.916431\pi$
$524$	−24.1199	+	25.4238i	−0.0460304	+	0.0485186i
$525$		0			0
$526$	−604.837	+	259.905i	−1.14988	+	0.494117i
$527$	−27.6957	+	15.9901i	−0.0525536	+	0.0303418i
$528$	−399.836	−	203.595i	−0.757266	−	0.385596i
$529$	−226.749	+	392.741i	−0.428637	+	0.742421i
$530$	192.227	−	257.459i	0.362693	−	0.485771i
$531$	−1043.03			−1.96428
$532$		0			0
$533$			923.564i			1.73277i
$534$	349.892	−	468.626i	0.655229	−	0.877578i
$535$	−268.967	−	155.288i	−0.502743	−	0.290259i
$536$	482.696	−	401.615i	0.900553	−	0.749282i
$537$	−338.652	−	586.562i	−0.630636	−	1.09229i
$538$	−538.520	+	231.408i	−1.00097	+	0.430127i
$539$		0			0
$540$	−348.201	−	330.344i	−0.644817	−	0.611748i
$541$	785.695	−	453.621i	1.45230	−	0.838486i	0.453689	−	0.891160i	$-0.350108\pi$
$541$	785.695	−	453.621i	1.45230	−	0.838486i	0.998612	+	0.0526734i	$0.0167742\pi$
$542$	−6.30831	+	53.3286i	−0.0116389	+	0.0983922i
$543$	982.241	+	567.097i	1.80891	+	1.04438i
$544$	−24.6664	−	16.4698i	−0.0453426	−	0.0302754i
$545$	143.827			0.263903
$546$		0			0
$547$	−557.327			−1.01888			−0.509439	−	0.860506i	$-0.670147\pi$
$547$	−557.327			−1.01888			−0.509439	+	0.860506i	$0.670147\pi$
$548$	−921.215	−	221.036i	−1.68105	−	0.403351i
$549$	−468.127	−	270.273i	−0.852690	−	0.492301i
$550$	212.539	+	25.1415i	0.386435	+	0.0457119i
$551$	−48.3889	+	27.9374i	−0.0878202	+	0.0507030i
$552$	128.225	−	347.779i	0.232291	−	0.630035i
$553$		0			0
$554$	−615.163	+	264.343i	−1.11040	+	0.477153i
$555$	−73.6096	−	127.496i	−0.132630	−	0.229722i
$556$	195.627	+	660.108i	0.351847	+	1.18725i
$557$	−741.896	−	428.334i	−1.33195	−	0.769002i	−0.346352	−	0.938105i	$-0.612580\pi$
$557$	−741.896	−	428.334i	−1.33195	−	0.769002i	−0.985598	+	0.169103i	$0.945913\pi$
$558$	−1074.55	−	802.298i	−1.92572	−	1.43781i
$559$			893.680i			1.59871i
$560$		0			0
$561$	25.9918			0.0463313
$562$	147.602	−	197.691i	0.262638	−	0.351763i
$563$	6.84436	−	11.8548i	0.0121569	−	0.0210564i	−0.859883	−	0.510491i	$-0.829464\pi$
$563$	6.84436	−	11.8548i	0.0121569	−	0.0210564i	0.872040	+	0.489435i	$0.162797\pi$
$564$	940.659	−	278.770i	1.66784	−	0.494273i
$565$	−13.3833	+	7.72686i	−0.0236873	+	0.0136759i
$566$	−0.488693	−	1.13726i	−0.000863416	−	0.00200929i
$567$		0			0
$568$	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	$0.424164\pi$
$570$	−16.0241	+	135.463i	−0.0281125	+	0.237655i
$571$	−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	$0.949852\pi$
$572$	105.092	−	437.992i	0.183727	−	0.765720i
$573$		−	216.142i		−	0.377210i
$574$		0			0
$575$			176.805i			0.307486i
$576$	226.166	−	1222.97i	0.392650	−	2.12321i
$577$	−515.560	+	892.976i	−0.893518	+	1.54762i	−0.0578905	+	0.998323i	$0.518437\pi$
$577$	−515.560	+	892.976i	−0.893518	+	1.54762i	−0.835628	+	0.549296i	$0.814896\pi$
$578$	−572.292	−	67.6971i	−0.990124	−	0.117123i
$579$	752.665	+	1303.65i	1.29994	+	2.25156i
$580$	55.9503	−	58.9748i	0.0964660	−	0.101681i
$581$		0			0
$582$	226.151	+	526.285i	0.388575	+	0.904270i
$583$	−339.229	+	195.854i	−0.581868	+	0.335942i
$584$	206.656	−	171.943i	0.353863	−	0.294423i
$585$	448.738	−	777.238i	0.767074	−	1.32861i
$586$	−45.3202	−	33.8376i	−0.0773383	−	0.0577434i
$587$	671.907			1.14464			0.572322	−	0.820029i	$-0.306043\pi$
$587$	671.907			1.14464			0.572322	+	0.820029i	$0.306043\pi$
$588$		0			0
$589$			204.612i			0.347388i
$590$	−185.531	−	138.524i	−0.314460	−	0.234786i
$591$	1208.99	+	698.008i	2.04566	+	1.18106i
$592$	92.9309	−	182.506i	0.156978	−	0.308286i
$593$	176.999	+	306.572i	0.298481	+	0.516984i	0.975789	−	0.218716i	$-0.0701867\pi$
$593$	176.999	+	306.572i	0.298481	+	0.516984i	−0.677308	+	0.735700i	$0.736853\pi$
$594$	231.016	+	537.606i	0.388915	+	0.905061i
$595$		0			0
$596$	−669.480	−	635.146i	−1.12329	−	1.06568i
$597$	−1487.53	+	858.824i	−2.49167	+	1.43857i
$598$	369.522	+	43.7113i	0.617930	+	0.0730958i
$599$	983.923	+	568.068i	1.64261	+	0.948361i	0.979901	+	0.199484i	$0.0639265\pi$
$599$	983.923	+	568.068i	1.64261	+	0.948361i	0.662708	+	0.748878i	$0.269407\pi$
$600$	147.162	+	855.424i	0.245270	+	1.42571i
$601$	6.80783			0.0113275			0.00566375	−	0.999984i	$-0.498197\pi$
$601$	6.80783			0.0113275			0.00566375	+	0.999984i	$0.498197\pi$
$602$		0			0
$603$	−1525.30			−2.52953
$604$	138.022	−	575.234i	0.228513	−	0.952375i
$605$	−174.358	−	100.666i	−0.288196	−	0.166390i
$606$	−113.129	+	956.357i	−0.186681	+	1.57815i
$607$	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
$609$		0			0
$610$	−47.3743	−	110.247i	−0.0776627	−	0.180732i
$611$	492.447	+	852.944i	0.805970	+	1.39598i
$612$	20.4713	+	69.0768i	0.0334499	+	0.112871i
$613$	−555.650	−	320.805i	−0.906443	−	0.523335i	−0.0271583	−	0.999631i	$-0.508646\pi$
$613$	−555.650	−	320.805i	−0.906443	−	0.523335i	−0.879285	+	0.476296i	$0.841979\pi$
$614$	479.687	−	642.466i	0.781249	−	1.04636i
$615$		−	496.096i		−	0.806661i
$616$		0			0
$617$	−502.890			−0.815057			−0.407528	−	0.913193i	$-0.633609\pi$
$617$	−502.890			−0.815057			−0.407528	+	0.913193i	$0.633609\pi$
$618$	964.023	+	719.772i	1.55991	+	1.16468i
$619$	216.495	−	374.980i	0.349749	−	0.605783i	−0.636456	−	0.771313i	$-0.719600\pi$
$619$	216.495	−	374.980i	0.349749	−	0.605783i	0.986205	+	0.165530i	$0.0529336\pi$
$620$	−84.5861	−	285.421i	−0.136429	−	0.460356i
$621$	−418.627	+	241.695i	−0.674118	+	0.389202i
$622$	−298.096	+	128.095i	−0.479254	+	0.205941i
$623$		0			0
$624$	1824.22	−	96.0833i	2.92343	−	0.153980i
$625$	−148.859	−	257.831i	−0.238174	−	0.412530i
$626$	528.805	+	62.5530i	0.844736	+	0.0999250i
$627$	83.1486	−	144.018i	0.132613	−	0.229693i
$628$	107.167	−	446.640i	0.170648	−	0.711210i
$629$			11.8640i			0.0188617i
$630$		0			0
$631$			238.957i			0.378695i	0.981910	+	0.189348i	$0.0606373\pi$
$631$			238.957i			0.378695i	−0.981910	+	0.189348i	$0.939363\pi$
$632$	−238.195	+	40.9777i	−0.376891	+	0.0648381i
$633$	452.687	−	784.078i	0.715146	−	1.23867i
$634$	101.697	−	859.717i	0.160405	−	1.35602i
$635$	141.809	+	245.621i	0.223322	+	0.386805i
$636$	−1152.49	−	1093.38i	−1.81209	−	1.71916i
$637$		0			0
$638$	−91.0543	+	39.1271i	−0.142718	+	0.0613277i
$639$	−1253.96	+	723.974i	−1.96238	+	1.13298i
$640$	202.651	−	187.501i	0.316642	−	0.292971i
$641$	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	$0.164690\pi$
$642$	−918.696	+	1230.45i	−1.43099	+	1.91659i
$643$	584.919			0.909672			0.454836	−	0.890575i	$-0.349698\pi$
$643$	584.919			0.909672			0.454836	+	0.890575i	$0.349698\pi$
$644$		0			0
$645$		−	480.044i		−	0.744255i
$646$	6.57664	−	8.80839i	0.0101806	−	0.0136353i
$647$	−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	$0.750196\pi$
$648$	−748.683	+	622.923i	−1.15538	+	0.961300i
$649$	141.137	+	244.457i	0.217469	+	0.376667i
$650$	−800.566	+	344.012i	−1.23164	+	0.529250i
$651$		0			0
$652$	−135.750	+	143.088i	−0.208205	+	0.219460i
$653$	−42.0252	+	24.2632i	−0.0643571	+	0.0371566i	−0.531833	−	0.846849i	$-0.678497\pi$
$653$	−42.0252	+	24.2632i	−0.0643571	+	0.0371566i	0.467476	+	0.884006i	$0.345163\pi$
$654$	83.5372	−	706.199i	0.127733	−	1.07982i
$655$	16.3656	+	9.44866i	0.0249856	+	0.0144254i
$656$	578.703	−	376.030i	0.882170	−	0.573217i
$657$	−653.026			−0.993951
$658$		0			0
$659$	1224.65			1.85835			0.929176	−	0.369638i	$-0.120518\pi$
$659$	1224.65			1.85835			0.929176	+	0.369638i	$0.120518\pi$
$660$	−56.4505	+	235.269i	−0.0855311	+	0.356468i
$661$	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	$0.448112\pi$
$662$	161.381	+	19.0899i	0.243777	+	0.0288367i
$663$	−91.6439	+	52.9106i	−0.138226	+	0.0798049i
$664$	547.399	+	201.824i	0.824396	+	0.303951i
$665$		0			0
$666$	−457.078	+	196.412i	−0.686303	+	0.294912i
$667$	−40.9358	−	70.9029i	−0.0613730	−	0.106301i
$668$	−926.019	+	274.432i	−1.38626	+	0.410826i
$669$	209.940	+	121.209i	0.313812	+	0.181180i
$670$	−271.316	−	202.574i	−0.404950	−	0.302349i
$671$			146.287i			0.218014i
$672$		0			0
$673$	147.714			0.219486			0.109743	−	0.993960i	$-0.464997\pi$
$673$	147.714			0.219486			0.109743	+	0.993960i	$0.464997\pi$
$674$	83.1528	−	111.370i	0.123372	−	0.165238i
$675$	565.980	−	980.307i	0.838490	−	1.45231i
$676$	328.984	+	1110.10i	0.486663	+	1.64216i
$677$	−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
$679$		0			0
$680$	−5.53263	+	15.0059i	−0.00813622	+	0.0220676i
$681$	−493.582	−	854.909i	−0.724790	−	1.25537i
$682$	−42.6331	+	360.407i	−0.0625118	+	0.528457i
$683$	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	$0.151646\pi$
$684$	448.235	+	107.549i	0.655314	+	0.157236i
$685$			510.849i			0.745765i
$686$		0			0
$687$		−	986.210i		−	1.43553i
$688$	559.978	−	363.863i	0.813922	−	0.528871i
$689$	797.385	−	1381.11i	1.15731	−	2.00452i
$690$	−198.490	−	23.4797i	−0.287667	−	0.0340285i
$691$	−263.374	−	456.177i	−0.381149	−	0.660169i	0.610078	−	0.792341i	$-0.291138\pi$
$691$	−263.374	−	456.177i	−0.381149	−	0.660169i	−0.991227	+	0.132172i	$0.957805\pi$
$692$	157.922	+	149.823i	0.228211	+	0.216508i
$693$		0			0
$694$	275.852	+	641.948i	0.397482	+	0.924997i
$695$	321.516	−	185.627i	0.462613	−	0.267090i
$696$	−257.073	−	308.973i	−0.369358	−	0.443926i
$697$	−19.9895	+	34.6229i	−0.0286794	+	0.0496741i
$698$	265.766	+	198.430i	0.380754	+	0.284284i
$699$	−515.633			−0.737672
$700$		0			0
$701$			695.486i			0.992134i	0.868284	+	0.496067i	$0.165223\pi$
$701$			695.486i			0.992134i	−0.868284	+	0.496067i	$0.834777\pi$
$702$	−1908.92	−	1425.26i	−2.71926	−	2.03029i
$703$	65.7370	+	37.9532i	0.0935092	+	0.0539875i
$704$	−317.233	+	112.479i	−0.450615	+	0.159771i
$705$	−264.520	−	458.162i	−0.375206	−	0.649876i
$706$	−372.471	−	866.794i	−0.527580	−	1.22775i
$707$		0			0
$708$	−787.920	+	830.513i	−1.11288	+	1.17304i
$709$	803.161	−	463.705i	1.13281	−	0.654027i	0.188168	−	0.982137i	$-0.439745\pi$
$709$	803.161	−	463.705i	1.13281	−	0.654027i	0.944640	+	0.328110i	$0.106412\pi$
$710$	−319.201	−	37.7587i	−0.449578	−	0.0531812i
$711$	508.447	+	293.552i	0.715115	+	0.412872i
$712$	−74.3816	−	432.366i	−0.104469	−	0.607255i
$713$	−299.812			−0.420493
$714$		0			0
$715$	−242.883			−0.339697
$716$	−494.057	−	118.544i	−0.690024	−	0.165564i
$717$	−753.566	−	435.071i	−1.05100	−	0.606794i
$718$	154.355	−	1304.87i	0.214979	−	1.81737i
$719$	−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
$721$		0			0
$722$	257.281	+	598.730i	0.356345	+	0.829266i
$723$	−547.865	−	948.929i	−0.757766	−	1.31249i
$724$	815.749	−	241.752i	1.12673	−	0.333912i
$725$	166.034	+	95.8600i	0.229013	+	0.132221i
$726$	−595.546	+	797.642i	−0.820311	+	1.09868i
$727$		−	539.401i		−	0.741954i	−0.928642	−	0.370977i	$-0.879023\pi$
$727$		−	539.401i		−	0.741954i	0.928642	−	0.370977i	$-0.120977\pi$
$728$		0			0
$729$	−303.936			−0.416922
$730$	−116.158	−	86.7276i	−0.159121	−	0.118805i
$731$	−19.3427	+	33.5026i	−0.0264606	+	0.0458311i
$732$	−568.834	+	168.577i	−0.777095	+	0.230297i
$733$	−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
$735$		0			0
$736$	−123.062	−	249.339i	−0.167204	−	0.338776i
$737$	206.396	+	357.488i	0.280048	+	0.485058i
$738$	−1664.83	−	196.935i	−2.25587	−	0.266849i
$739$	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	$-0.116533\pi$
$740$	−107.389	−	25.7669i	−0.145120	−	0.0348201i
$741$			677.050i			0.913698i
$742$		0			0
$743$			588.688i			0.792313i	0.918183	+	0.396156i	$0.129656\pi$
$743$			588.688i			0.792313i	−0.918183	+	0.396156i	$0.870344\pi$
$744$	−1450.56	+	249.546i	−1.94968	+	0.335411i
$745$	−248.810	+	430.952i	−0.333973	+	0.578459i
$746$	−74.2420	+	627.621i	−0.0995202	+	0.841314i
$747$	−708.597	−	1227.33i	−0.948590	−	1.64301i
$748$	13.4196	−	14.1450i	0.0179406	−	0.0189104i
$749$		0			0
$750$	958.378	−	411.826i	1.27784	−	0.549101i
$751$	−708.754	+	409.199i	−0.943747	+	0.544873i	−0.891133	−	0.453742i	$-0.850089\pi$
$751$	−708.754	+	409.199i	−0.943747	+	0.544873i	−0.0526140	+	0.998615i	$0.516755\pi$
$752$	333.952	−	655.844i	0.444086	−	0.872133i
$753$	424.712	−	735.622i	0.564026	−	0.976922i
$754$	241.396	−	323.313i	0.320154	−	0.428797i
$755$	−318.989			−0.422503
$756$		0			0
$757$		−	105.101i		−	0.138838i	−0.997588	−	0.0694192i	$-0.977885\pi$
$757$		−	105.101i		−	0.138838i	0.997588	−	0.0694192i	$-0.0221146\pi$
$758$	213.468	−	285.908i	0.281620	−	0.377187i
$759$	211.025	+	121.835i	0.278030	+	0.160521i
$760$	65.4471	+	78.6600i	0.0861146	+	0.103500i
$761$	507.117	+	878.352i	0.666382	+	1.15421i	0.978909	+	0.204299i	$0.0654913\pi$
$761$	507.117	+	878.352i	0.666382	+	1.15421i	−0.312527	+	0.949909i	$0.601175\pi$
$762$	1288.38	−	553.631i	1.69079	−	0.726550i
$763$		0			0
$764$	−117.626	−	111.594i	−0.153961	−	0.146065i
$765$	33.6449	−	19.4249i	0.0439803	−	0.0253920i
$766$	164.085	−	1387.13i	0.214211	−	1.81087i
$767$	−995.264	−	574.616i	−1.29761	−	0.749173i
$768$	−802.940	−	1103.93i	−1.04549	−	1.43741i
$769$	1183.99			1.53964			0.769822	−	0.638258i	$-0.220345\pi$
$769$	1183.99			1.53964			0.769822	+	0.638258i	$0.220345\pi$
$770$		0			0
$771$	1150.58			1.49232
$772$	1098.06	+	263.469i	1.42236	+	0.341281i
$773$	−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	$0.733940\pi$
$774$	−1610.96	−	190.563i	−2.08134	−	0.246205i
$775$	608.014	−	351.037i	0.784534	−	0.452951i
$776$	403.170	+	148.647i	0.519550	+	0.191556i
$777$		0			0
$778$	−322.226	+	138.464i	−0.414172	+	0.177975i
$779$	127.894	+	221.519i	0.164177	+	0.284363i
$780$	−279.892	−	944.443i	−0.358835	−	1.21082i
$781$	339.358	+	195.928i	0.434517	+	0.250869i
$782$	12.9067	+	9.63656i	0.0165047	+	0.0123230i
$783$			524.168i			0.669436i
$784$		0			0
$785$	−247.679			−0.315514
$786$	55.8989	−	74.8679i	0.0711182	−	0.0952518i
$787$	134.268	−	232.559i	0.170607	−	0.295500i	−0.768025	−	0.640420i	$-0.778760\pi$
$787$	134.268	−	232.559i	0.170607	−	0.295500i	0.938632	+	0.344919i	$0.112094\pi$
$788$	1004.06	−	297.559i	1.27419	−	0.377614i
$789$	1520.01	−	877.576i	1.92650	−	1.11226i
$790$	51.4547	+	119.742i	0.0651325	+	0.151573i
$791$		0			0
$792$	767.121	+	282.834i	0.968587	+	0.357114i
$793$	−297.792	−	515.791i	−0.375526	−	0.650429i
$794$	−90.6200	+	766.075i	−0.114131	+	0.964830i
$795$	−428.319	+	741.870i	−0.538766	+	0.933170i
$796$	−300.629	+	1252.93i	−0.377675	+	1.57404i
$797$			1502.06i			1.88465i	0.334705	+	0.942323i	$0.391363\pi$
$797$			1502.06i			1.88465i	−0.334705	+	0.942323i	$0.608637\pi$
$798$		0			0
$799$			42.6339i			0.0533591i
$800$	541.509	+	361.568i	0.676886	+	0.451960i
$801$	−532.848	+	922.919i	−0.665228	+	1.15221i
$802$	1046.89	+	123.838i	1.30535	+	0.154412i
$803$	88.3638	+	153.051i	0.110042	+	0.190599i
$804$	−1152.24	+	1214.52i	−1.43313	+	1.51060i
$805$		0			0
$806$	−583.349	−	1357.54i	−0.723758	−	1.68429i
$807$	1353.34	−	781.354i	1.67701	−	0.968220i
$808$	462.049	+	555.332i	0.571843	+	0.687292i
$809$	−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	$0.180591\pi$
$810$	420.824	+	314.201i	0.519535	+	0.387902i
$811$	−5.94522			−0.00733072			−0.00366536	−	0.999993i	$-0.501167\pi$
$811$	−5.94522			−0.00733072			−0.00366536	+	0.999993i	$0.501167\pi$
$812$		0			0
$813$		−	143.172i		−	0.176103i
$814$	107.883	+	80.5487i	0.132534	+	0.0989541i
$815$	92.1073	+	53.1782i	0.113015	+	0.0652493i
$816$	70.4666	+	35.8812i	0.0863561	+	0.0439721i
$817$	123.756	+	214.351i	0.151476	+	0.262364i
$818$	−334.592	−	778.643i	−0.409037	−	0.951886i
$819$		0			0
$820$	−269.980	−	256.134i	−0.329244	−	0.312359i
$821$	−13.1159	+	7.57244i	−0.0159755	+	0.00922344i	−0.507966	−	0.861377i	$-0.669603\pi$
$821$	−13.1159	+	7.57244i	−0.0159755	+	0.00922344i	0.491991	+	0.870600i	$0.336269\pi$
$822$	2508.30	+	296.710i	3.05146	+	0.360961i
$823$	−1284.10	−	741.378i	−1.56027	−	0.900824i	−0.997229	−	0.0743964i	$-0.976297\pi$
$823$	−1284.10	−	741.378i	−1.56027	−	0.900824i	−0.563044	−	0.826427i	$-0.690370\pi$
$824$	889.430	−	153.012i	1.07941	−	0.185694i
$825$	−570.607			−0.691645
$826$		0			0
$827$	−74.3070			−0.0898513			−0.0449257	−	0.998990i	$-0.514305\pi$
$827$	−74.3070			−0.0898513			−0.0449257	+	0.998990i	$0.514305\pi$
$828$	−157.589	+	656.785i	−0.190325	+	0.793219i
$829$	−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	$0.694128\pi$
$830$	36.9567	−	312.421i	0.0445261	−	0.376411i
$831$	1545.96	−	892.558i	1.86036	−	1.07408i
$832$	889.555	−	1042.36i	1.06918	−	1.25284i
$833$		0			0
$834$	−724.699	−	1686.48i	−0.868944	−	2.02216i
$835$	260.403	+	451.032i	0.311860	+	0.540158i
$836$	−35.4461	−	119.606i	−0.0423996	−	0.143070i
$837$	1662.33	+	959.745i	1.98605	+	1.14665i
$838$	353.696	−	473.721i	0.422072	−	0.565300i
$839$			16.7454i			0.0199588i	0.999950	+	0.00997940i	$0.00317659\pi$
$839$			16.7454i			0.0199588i	−0.999950	+	0.00997940i	$0.996823\pi$
$840$		0			0
$841$	752.222			0.894437
$842$	202.342	+	151.075i	0.240311	+	0.179424i
$843$	−328.886	+	569.648i	−0.390138	+	0.675739i
$844$	−192.980	−	651.175i	−0.228649	−	0.771534i
$845$	540.690	−	312.168i	0.639870	−	0.369429i
$846$	−1642.53	+	705.816i	−1.94153	+	0.834298i
$847$		0			0
$848$	−1190.06	+	62.6814i	−1.40337	+	0.0739167i
$849$	1.65008	+	2.85803i	0.00194356	+	0.00336634i
$850$	−37.4576	−	4.43091i	−0.0440678	−	0.00521284i
$851$	−55.6118	+	96.3224i	−0.0653488	+	0.113187i
$852$	−370.795	+	1545.36i	−0.435205	+	1.81381i
$853$		−	1299.38i		−	1.52331i	−0.647984	−	0.761654i	$-0.724388\pi$
$853$		−	1299.38i		−	1.52331i	0.647984	−	0.761654i	$-0.275612\pi$
$854$		0			0
$855$		−	248.563i		−	0.290717i
$856$	195.301	+	1135.24i	0.228155	+	1.32622i
$857$	−597.668	+	1035.19i	−0.697396	+	1.20792i	0.271971	+	0.962305i	$0.412325\pi$
$857$	−597.668	+	1035.19i	−0.697396	+	1.20792i	−0.969366	+	0.245619i	$0.921009\pi$
$858$	−141.071	+	1192.57i	−0.164418	+	1.38994i
$859$	−170.885	−	295.981i	−0.198934	−	0.344564i	0.749249	−	0.662289i	$-0.230415\pi$
$859$	−170.885	−	295.981i	−0.198934	−	0.344564i	−0.948183	+	0.317724i	$0.897081\pi$
$860$	−261.244	−	247.846i	−0.303772	−	0.288193i
$861$		0			0
$862$	467.216	−	200.768i	0.542014	−	0.232909i
$863$	844.362	−	487.493i	0.978404	−	0.564882i	0.0766158	−	0.997061i	$-0.475589\pi$
$863$	844.362	−	487.493i	0.978404	−	0.564882i	0.901788	+	0.432179i	$0.142255\pi$
$864$	−115.848	+	1776.42i	−0.134083	+	2.05604i
$865$	58.6913	−	101.656i	0.0678512	−	0.117522i
$866$	653.674	−	875.495i	0.754819	−	1.01096i
$867$	1536.44			1.77213
$868$		0			0
$869$		−	158.887i		−	0.182839i
$870$	−129.667	+	173.669i	−0.149043	+	0.199620i
$871$	−1455.45	−	840.304i	−1.67101	−	0.964758i
$872$	−341.190	−	410.072i	−0.391272	−	0.470266i
$873$	−521.896	−	903.951i	−0.597819	−	1.03545i
$874$	94.6839	−	40.6868i	0.108334	−	0.0465524i
$875$		0			0
$876$	−493.304	+	519.971i	−0.563133	+	0.593574i
$877$	−274.158	+	158.285i	−0.312609	+	0.180485i	−0.648093	−	0.761561i	$-0.724433\pi$
$877$	−274.158	+	158.285i	−0.312609	+	0.180485i	0.335484	+	0.942046i	$0.391100\pi$
$878$	64.2186	−	542.885i	0.0731419	−	0.618320i
$879$	130.591	+	75.3966i	0.148567	+	0.0857754i
$880$	98.8902	+	152.190i	0.112375	+	0.172943i
$881$	464.977			0.527783			0.263891	−	0.964552i	$-0.414994\pi$
$881$	464.977			0.527783			0.263891	+	0.964552i	$0.414994\pi$
$882$		0			0
$883$	69.4594			0.0786630			0.0393315	−	0.999226i	$-0.487477\pi$
$883$	69.4594			0.0786630			0.0393315	+	0.999226i	$0.487477\pi$
$884$	−18.5212	+	77.1911i	−0.0209516	+	0.0873202i
$885$	534.610	+	308.657i	0.604079	+	0.348765i
$886$	942.966	+	111.545i	1.06430	+	0.125897i
$887$	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
$889$		0			0
$890$	−217.353	+	93.3991i	−0.244217	+	0.104943i
$891$	−320.129	−	554.479i	−0.359292	−	0.622311i
$892$	174.355	−	51.6712i	0.195465	−	0.0579274i
$893$	236.229	+	136.387i	0.264535	+	0.152729i
$894$	1971.49	+	1471.98i	2.20524	+	1.64651i
$895$			273.974i			0.306116i
$896$		0			0
$897$	−992.062			−1.10598
$898$	−935.818	+	1253.38i	−1.04211	+	1.39575i
$899$	−162.552	+	281.548i	−0.180814	+	0.313179i
$900$	−449.414	−	1516.47i	−0.499349	−	1.68496i
$901$	59.7853	−	34.5170i	0.0663543	−	0.0383097i
$902$	179.119	+	416.837i	0.198580	+	0.462125i
$903$		0			0
$904$	53.7786	+	19.8279i	0.0594896	+	0.0219336i
$905$	−229.395	−	397.323i	−0.253475	−	0.439031i
$906$	−185.275	+	1566.26i	−0.204497	+	1.72876i
$907$	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	$0.162680\pi$
$908$	−720.085	−	172.777i	−0.793045	−	0.190283i
$909$		−	1754.83i		−	1.93051i
$910$		0			0
$911$			721.866i			0.792389i	0.918167	+	0.396194i	$0.129669\pi$
$911$			721.866i			0.792389i	−0.918167	+	0.396194i	$0.870331\pi$
$912$	424.238	−	275.662i	0.465174	−	0.302261i
$913$	−191.767	+	332.150i	−0.210040	+	0.363800i
$914$	−376.492	−	44.5358i	−0.411917	−	0.0487262i
$915$	159.960	+	277.059i	0.174820	+	0.302797i
$916$	−536.704	−	509.179i	−0.585922	−	0.555873i
$917$		0			0
$918$	−40.7139	−	94.7470i	−0.0443506	−	0.103210i
$919$	−113.209	+	65.3612i	−0.123187	+	0.0711221i	−0.560327	−	0.828271i	$-0.689325\pi$
$919$	−113.209	+	65.3612i	−0.123187	+	0.0711221i	0.437140	+	0.899393i	$0.355991\pi$
$920$	−115.258	+	95.8977i	−0.125281	+	0.104237i
$921$	−1068.83	+	1851.27i	−1.16051	+	2.01007i
$922$	−324.577	−	242.340i	−0.352036	−	0.262842i
$923$	−1595.38			−1.72847
$924$		0			0
$925$		−	260.454i		−	0.281572i
$926$	1046.37	+	781.256i	1.12999	+	0.843689i
$927$	−1898.56	−	1096.13i	−2.04807	−	1.18245i
$928$	−300.872	−	19.6211i	−0.324216	−	0.0211434i
$929$	−227.643	−	394.289i	−0.245041	−	0.424423i	0.717102	−	0.696968i	$-0.245468\pi$
$929$	−227.643	−	394.289i	−0.245041	−	0.424423i	−0.962143	+	0.272545i	$0.912135\pi$
$930$	313.349	+	729.207i	0.336934	+	0.784093i
$931$		0			0
$932$	−266.221	+	280.612i	−0.285645	+	0.301086i
$933$	749.140	−	432.516i	0.802937	−	0.463576i
$934$	−1083.35	−	128.150i	−1.15990	−	0.137206i
$935$	−9.10528	−	5.25694i	−0.00973827	−	0.00562239i
$936$	−3280.53	+	564.362i	−3.50483	+	0.602951i
$937$	1242.79			1.32635			0.663176	−	0.748464i	$-0.269208\pi$
$937$	1242.79			1.32635			0.663176	+	0.748464i	$0.269208\pi$
$938$		0			0
$939$	−1419.69			−1.51192
$940$	−385.907	−	92.5946i	−0.410540	−	0.0985049i
$941$	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	$0.460158\pi$
$942$	−143.856	+	1216.12i	−0.152713	+	1.29100i
$943$	−324.585	+	187.399i	−0.344205	+	0.198727i
$944$	45.1698	+	857.586i	0.0478493	+	0.908460i
$945$		0			0
$946$	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	$0.954711\pi$
$948$	617.828	−	183.097i	0.651717	−	0.193140i
$949$	−623.119	−	359.758i	−0.656606	−	0.379092i
$950$	−144.379	+	193.374i	−0.151978	+	0.203551i
$951$			2308.09i			2.42702i
$952$		0			0
$953$	765.039			0.802769			0.401384	−	0.915910i	$-0.368529\pi$
$953$	765.039			0.802769			0.401384	+	0.915910i	$0.368529\pi$
$954$	2319.58	+	1731.88i	2.43143	+	1.81538i
$955$	−43.7153	+	75.7172i	−0.0457752	+	0.0792850i
$956$	−625.835	+	185.470i	−0.654639	+	0.194006i
$957$	228.827	−	132.113i	0.239109	−	0.138050i
$958$	200.102	−	85.9863i	0.208875	−	0.0897561i
$959$		0			0
$960$	−477.828	+	559.911i	−0.497737	+	0.583240i
$961$	114.761	+	198.772i	0.119418	+	0.206838i
$962$	−544.350	−	64.3919i	−0.565852	−	0.0669354i
$963$	1399.07	−	2423.27i	1.45283	−	2.51637i
$964$	−799.278	−	191.779i	−0.829126	−	0.198941i
$965$		−	608.916i		−	0.631001i
$966$		0			0
$967$			771.494i			0.797822i	0.916990	+	0.398911i	$0.130612\pi$
$967$			771.494i			0.797822i	−0.916990	+	0.398911i	$0.869388\pi$
$968$	126.604	+	735.923i	0.130789	+	0.760251i
$969$	−14.6540	+	25.3815i	−0.0151228	+	0.0261935i
$970$	27.2193	−	230.104i	0.0280612	−	0.237221i
$971$	458.754	+	794.586i	0.472456	+	0.818317i	0.999503	−	0.0315186i	$-0.0100343\pi$
$971$	458.754	+	794.586i	0.472456	+	0.818317i	−0.527047	+	0.849836i	$0.676701\pi$
$972$	408.778	−	430.875i	0.420554	−	0.443287i
$973$		0			0
$974$	788.949	−	339.021i	0.810010	−	0.348071i
$975$	2011.89	−	1161.56i	2.06348	−	1.19135i
$976$	−201.947	+	396.600i	−0.206913	+	0.406353i
$977$	−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	$0.210232\pi$
$978$	314.606	−	421.366i	0.321683	−	0.430844i
$979$	288.408			0.294594
$980$		0			0
$981$			1295.81i			1.32091i
$982$	−543.095	+	727.392i	−0.553050	+	0.740726i
$983$	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	$0.276668\pi$
$984$	−1414.44	+	1176.85i	−1.43744	+	1.19599i
$985$	−282.349	−	489.043i	−0.286649	−	0.496490i
$986$	16.0473	−	6.89571i	0.0162751	−	0.00699362i
$987$		0			0
$988$	368.457	+	349.560i	0.372932	+	0.353806i
$989$	−314.083	+	181.336i	−0.317576	+	0.183353i
$990$	51.7908	−	437.824i	0.0523140	−	0.442247i
$991$	303.420	+	175.180i	0.306175	+	0.176770i	0.645214	−	0.764002i	$-0.276768\pi$
$991$	303.420	+	175.180i	0.306175	+	0.176770i	−0.339038	+	0.940773i	$0.610102\pi$
$992$	−613.118	+	918.248i	−0.618063	+	0.925654i
$993$	−433.261			−0.436315
$994$		0			0
$995$	694.800			0.698291
$996$	−1512.54	−	362.919i	−1.51861	−	0.364376i
$997$	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	$0.581700\pi$
$998$	662.176	+	78.3296i	0.663503	+	0.0784866i
$999$	616.687	−	356.045i	0.617305	−	0.356401i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.k.d.11.2	✓	12	7.6	odd	2
56.3.k.d.11.6	yes	12	56.27	even	2
56.3.k.d.51.2	yes	12	56.19	even	6
56.3.k.d.51.6	yes	12	7.5	odd	6
224.3.o.d.79.5		12	28.19	even	6
224.3.o.d.79.6		12	56.5	odd	6
224.3.o.d.207.5		12	56.13	odd	2
224.3.o.d.207.6		12	28.27	even	2
392.3.g.i.99.3		6	7.4	even	3
392.3.g.i.99.4		6	56.11	odd	6
392.3.g.j.99.3		6	7.3	odd	6
392.3.g.j.99.4		6	56.3	even	6
392.3.k.l.67.2		12	1.1	even	1	trivial
392.3.k.l.67.6		12	8.3	odd	2	inner
392.3.k.l.275.2		12	56.51	odd	6	inner
392.3.k.l.275.6		12	7.2	even	3	inner
1568.3.g.j.687.1		6	56.45	odd	6
1568.3.g.j.687.2		6	28.3	even	6
1568.3.g.l.687.5		6	28.11	odd	6
1568.3.g.l.687.6		6	56.53	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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	392.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.19654 + 1.60259i) q^{2} +(2.66613 - 4.61787i) q^{3} +(-1.13656 - 3.83513i) q^{4} +(-1.86796 + 1.07847i) q^{5} +(4.21039 + 9.79818i) q^{6} +(7.50608 + 2.76746i) q^{8} +(-9.71647 - 16.8294i) q^{9} +O(q^{10})\)	\(q+(-1.19654 + 1.60259i) q^{2} +(2.66613 - 4.61787i) q^{3} +(-1.13656 - 3.83513i) q^{4} +(-1.86796 + 1.07847i) q^{5} +(4.21039 + 9.79818i) q^{6} +(7.50608 + 2.76746i) q^{8} +(-9.71647 - 16.8294i) q^{9} +(0.506759 - 4.28400i) q^{10} +(-2.62956 + 4.55453i) q^{11} +(-20.7403 - 4.97644i) q^{12} -21.4116i q^{13} +11.5013i q^{15} +(-13.4164 + 8.71774i) q^{16} +(0.463429 - 0.802683i) q^{17} +(38.5968 + 4.56566i) q^{18} +(-2.96505 - 5.13561i) q^{19} +(6.25911 + 5.93812i) q^{20} +(-4.15264 - 9.66378i) q^{22} +(7.52507 - 4.34460i) q^{23} +(32.7919 - 27.2837i) q^{24} +(-10.1738 + 17.6216i) q^{25} +(34.3139 + 25.6199i) q^{26} -55.6311 q^{27} -9.42223i q^{29} +(-18.4318 - 13.7618i) q^{30} +(-29.8813 - 17.2520i) q^{31} +(2.08243 - 31.9322i) q^{32} +(14.0215 + 24.2859i) q^{33} +(0.731855 + 1.70313i) q^{34} +(-53.4996 + 56.3916i) q^{36} +(-11.0853 + 6.40011i) q^{37} +(11.7781 + 1.39324i) q^{38} +(-98.8758 - 57.0860i) q^{39} +(-17.0056 + 2.92555i) q^{40} -43.1339 q^{41} -41.7382 q^{43} +(20.4559 + 4.90818i) q^{44} +(36.2999 + 20.9578i) q^{45} +(-2.04148 + 17.2581i) q^{46} +(-39.8357 + 22.9991i) q^{47} +(4.48745 + 85.1980i) q^{48} +(-16.0667 - 37.3894i) q^{50} +(-2.47112 - 4.28011i) q^{51} +(-82.1161 + 24.3356i) q^{52} +(64.5031 + 37.2409i) q^{53} +(66.5650 - 89.1536i) q^{54} -11.3436i q^{55} -31.6208 q^{57} +(15.0999 + 11.2741i) q^{58} +(26.8367 - 46.4825i) q^{59} +(44.1090 - 13.0720i) q^{60} +(24.0893 - 13.9080i) q^{61} +(63.4020 - 27.2446i) q^{62} +(48.6823 + 41.5455i) q^{64} +(23.0916 + 39.9959i) q^{65} +(-55.6975 - 6.58853i) q^{66} +(39.2453 - 67.9749i) q^{67} +(-3.60511 - 0.865011i) q^{68} -46.3330i q^{69} -74.5100i q^{71} +(-26.3578 - 153.213i) q^{72} +(16.8020 - 29.1020i) q^{73} +(3.00734 - 25.4232i) q^{74} +(54.2494 + 93.9627i) q^{75} +(-16.3258 + 17.2083i) q^{76} +(209.794 - 90.1511i) q^{78} +(-26.1642 + 15.1059i) q^{79} +(15.6596 - 30.7536i) q^{80} +(-60.8713 + 105.432i) q^{81} +(51.6116 - 69.1258i) q^{82} +72.9274 q^{83} +1.99917i q^{85} +(49.9416 - 66.8891i) q^{86} +(-43.5106 - 25.1209i) q^{87} +(-32.3421 + 26.9094i) q^{88} +(-27.4198 - 47.4925i) q^{89} +(-77.0211 + 33.0968i) q^{90} +(-25.2148 - 23.9217i) q^{92} +(-159.335 + 91.9919i) q^{93} +(10.8070 - 91.3596i) q^{94} +(11.0772 + 6.39541i) q^{95} +(-141.907 - 94.7516i) q^{96} +53.7125 q^{97} +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	\( 12 q + 2 q^{2} + 6 q^{3} - 4 q^{4} + 56 q^{6} + 8 q^{8} - 40 q^{9} + 6 q^{10} + 30 q^{11} - 32 q^{12} + 16 q^{16} - 30 q^{17} - 16 q^{18} - 78 q^{19} - 48 q^{20} + 24 q^{22} + 76 q^{24} - 92 q^{25} + 128 q^{26} - 156 q^{27} - 16 q^{30} + 112 q^{32} + 78 q^{33} - 76 q^{34} - 248 q^{36} - 80 q^{38} - 44 q^{40} + 232 q^{41} - 200 q^{43} + 132 q^{44} - 156 q^{46} - 176 q^{48} + 48 q^{50} + 10 q^{51} - 132 q^{52} + 36 q^{54} + 332 q^{57} + 4 q^{58} + 110 q^{59} + 84 q^{60} + 96 q^{62} - 160 q^{64} - 32 q^{65} + 138 q^{66} + 434 q^{67} - 96 q^{68} - 328 q^{72} - 102 q^{73} - 34 q^{74} + 60 q^{75} + 168 q^{76} + 720 q^{78} + 256 q^{80} - 82 q^{81} + 24 q^{82} + 536 q^{83} + 240 q^{86} - 204 q^{88} - 214 q^{89} - 440 q^{90} + 160 q^{92} + 16 q^{94} - 48 q^{96} + 152 q^{97} + 504 q^{99}+O(q^{100}) \) 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 + 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 - 16 * q^30 + 112 * q^32 + 78 * q^33 - 76 * q^34 - 248 * q^36 - 80 * q^38 - 44 * q^40 + 232 * q^41 - 200 * q^43 + 132 * q^44 - 156 * q^46 - 176 * q^48 + 48 * q^50 + 10 * q^51 - 132 * q^52 + 36 * q^54 + 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 - 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 + 240 * q^86 - 204 * q^88 - 214 * q^89 - 440 * q^90 + 160 * q^92 + 16 * q^94 - 48 * q^96 + 152 * q^97 + 504 * q^99

Introduction

L-functions

Modular forms

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