LMFDB - Embedded newform 392.3.k.l.275.2

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			275.2
Root			$-0.407369 - 0.812545i$ of defining polynomial
Character	$\chi$	$=$	392.275
Dual form			392.3.k.l.67.2

$q$-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 $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−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	0.841403	+	0.540409i	$0.181730\pi$
$3$	2.66613	+	4.61787i	0.888709	+	1.53929i	0.0473064	+	0.998880i	$0.484936\pi$
$4$	−1.13656	+	3.83513i	−0.284141	+	0.958782i
$5$	−1.86796	−	1.07847i	−0.373592	−	0.215693i	0.301435	−	0.953487i	$-0.402534\pi$
$5$	−1.86796	−	1.07847i	−0.373592	−	0.215693i	−0.675026	+	0.737794i	$0.735868\pi$
$6$	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	0.721392	−	0.692527i	$-0.243503\pi$
$11$	−2.62956	−	4.55453i	−0.239051	−	0.414048i	−0.960442	+	0.278480i	$0.910170\pi$
$12$	−20.7403	+	4.97644i	−1.72836	+	0.414703i
$13$			21.4116i			1.64704i	0.567285	+	0.823522i	$0.307994\pi$
$13$			21.4116i			1.64704i	−0.567285	+	0.823522i	$0.692006\pi$
$14$		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	0.879334	−	0.476206i	$-0.157988\pi$
$17$	0.463429	+	0.802683i	0.0272606	+	0.0472167i	−0.852073	+	0.523423i	$0.824655\pi$
$18$	38.5968	−	4.56566i	2.14426	−	0.253648i
$19$	−2.96505	+	5.13561i	−0.156055	+	0.270295i	−0.933443	−	0.358726i	$-0.883211\pi$
$19$	−2.96505	+	5.13561i	−0.156055	+	0.270295i	0.777388	+	0.629022i	$0.216544\pi$
$20$	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	0.654587	−	0.755987i	$-0.272843\pi$
$23$	7.52507	+	4.34460i	0.327177	+	0.188896i	−0.327410	+	0.944882i	$0.606176\pi$
$24$	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	$0.0519403\pi$
$29$			9.42223i			0.324904i	−0.986716	+	0.162452i	$0.948060\pi$
$30$	−18.4318	+	13.7618i	−0.614395	+	0.458728i
$31$	−29.8813	+	17.2520i	−0.963912	+	0.556515i	−0.897375	−	0.441269i	$-0.854529\pi$
$31$	−29.8813	+	17.2520i	−0.963912	+	0.556515i	−0.0665375	+	0.997784i	$0.521195\pi$
$32$	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	0.342662	−	0.939459i	$-0.388672\pi$
$37$	−11.0853	−	6.40011i	−0.299603	−	0.172976i	−0.642265	+	0.766483i	$0.722005\pi$
$38$	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	0.0122620	−	0.999925i	$-0.496097\pi$
$47$	−39.8357	−	22.9991i	−0.847567	−	0.489343i	−0.859829	+	0.510582i	$0.829430\pi$
$48$	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	0.252756	−	0.967530i	$-0.418663\pi$
$53$	64.5031	−	37.2409i	1.21704	−	0.702658i	0.964284	+	0.264872i	$0.0853297\pi$
$54$	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	0.998680	−	0.0513617i	$-0.0163561\pi$
$59$	26.8367	+	46.4825i	0.454860	+	0.787840i	−0.543821	+	0.839201i	$0.683023\pi$
$60$	44.1090	+	13.0720i	0.735150	+	0.217866i
$61$	24.0893	+	13.9080i	0.394907	+	0.228000i	0.684284	−	0.729215i	$-0.260115\pi$
$61$	24.0893	+	13.9080i	0.394907	+	0.228000i	−0.289377	+	0.957215i	$0.593448\pi$
$62$	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	0.994781	+	0.102030i	$0.0325338\pi$
$67$	39.2453	+	67.9749i	0.585751	+	1.01455i	−0.409030	+	0.912521i	$0.634133\pi$
$68$	−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	$0.175829\pi$
$71$			74.5100i			1.04944i	−0.851276	+	0.524719i	$0.824171\pi$
$72$	−26.3578	+	153.213i	−0.366081	+	2.12796i
$73$	16.8020	+	29.1020i	0.230165	+	0.398657i	0.957857	−	0.287247i	$-0.0927401\pi$
$73$	16.8020	+	29.1020i	0.230165	+	0.398657i	−0.727692	+	0.685904i	$0.759407\pi$
$74$	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	0.325178	−	0.945653i	$-0.394576\pi$
$79$	−26.1642	−	15.1059i	−0.331192	−	0.191214i	−0.656370	+	0.754439i	$0.727909\pi$
$80$	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	−0.977944	−	0.208867i	$-0.933022\pi$
$89$	−27.4198	+	47.4925i	−0.308088	+	0.533624i	0.669856	+	0.742491i	$0.266356\pi$
$90$	−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	−0.0601103	−	0.998192i	$-0.519145\pi$
$101$	78.2037	−	45.1509i	0.774294	−	0.447039i	0.834404	+	0.551153i	$0.185812\pi$
$102$	9.81606	−	1.16115i	0.0962358	−	0.0113839i
$103$	97.6980	+	56.4060i	0.948525	+	0.547631i	0.892622	−	0.450805i	$-0.148863\pi$
$103$	97.6980	+	56.4060i	0.948525	+	0.547631i	0.0559023	+	0.998436i	$0.482196\pi$
$104$	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	−0.304241	−	0.952595i	$-0.598403\pi$
$107$	71.9950	−	124.699i	0.672851	−	1.16541i	0.977092	−	0.212817i	$-0.0682637\pi$
$108$	63.2283	−	213.352i	0.585447	−	1.97548i
$109$	−57.7477	+	33.3406i	−0.529795	+	0.305877i	−0.740933	−	0.671579i	$-0.765616\pi$
$109$	−57.7477	+	33.3406i	−0.529795	+	0.305877i	0.211138	+	0.977456i	$0.432283\pi$
$110$	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	$0.173206\pi$
$127$			131.492i			1.03537i	−0.855572	+	0.517684i	$0.826794\pi$
$128$	−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	−0.882261	−	0.470761i	$-0.843980\pi$
$131$	−4.38060	+	7.58742i	−0.0334397	+	0.0579193i	0.848821	+	0.528680i	$0.177313\pi$
$132$	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	0.867660	+	0.497158i	$0.165623\pi$
$137$	118.420	+	205.110i	0.864381	+	1.49715i	−0.00327850	+	0.999995i	$0.501044\pi$
$138$	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	0.986944	−	0.161066i	$-0.0514931\pi$
$149$	199.798	+	115.354i	1.34093	+	0.774186i	0.353985	+	0.935251i	$0.384826\pi$
$150$	−215.495	+	25.4912i	−1.43663	+	0.169941i
$151$	128.077	−	73.9452i	0.848190	−	0.489703i	−0.0118494	−	0.999930i	$-0.503772\pi$
$151$	128.077	−	73.9452i	0.848190	−	0.489703i	0.860040	+	0.510227i	$0.170439\pi$
$152$	−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	−0.148663	−	0.988888i	$-0.547497\pi$
$157$	99.4450	−	57.4146i	0.633407	−	0.365698i	0.782070	+	0.623190i	$0.214164\pi$
$158$	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	−0.931689	−	0.363257i	$-0.881665\pi$
$163$	−24.6545	+	42.7029i	−0.151255	+	0.261981i	0.780434	+	0.625238i	$0.214998\pi$
$164$	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	$0.257203\pi$
$167$			241.457i			1.44585i	−0.690926	+	0.722926i	$0.742797\pi$
$168$		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	0.357563	−	0.933889i	$-0.383608\pi$
$173$	−47.1300	−	27.2105i	−0.272428	−	0.157286i	−0.629990	+	0.776603i	$0.716941\pi$
$174$	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	0.987084	−	0.160200i	$-0.0512141\pi$
$179$	63.5100	+	110.003i	0.354805	+	0.614540i	−0.632280	+	0.774740i	$0.717881\pi$
$180$	39.1186	+	163.035i	0.217325	+	0.905748i
$181$		−	212.704i		−	1.17516i	−0.809165	−	0.587581i	$-0.800080\pi$
$181$		−	212.704i		−	1.17516i	0.809165	−	0.587581i	$-0.199920\pi$
$182$		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	0.589073	−	0.808080i	$-0.299493\pi$
$191$	35.1041	+	20.2674i	0.183791	+	0.106112i	−0.405282	+	0.914192i	$0.632826\pi$
$192$	321.645	+	114.043i	1.67523	+	0.593974i
$193$	−141.153	−	244.485i	−0.731364	−	1.26676i	−0.956300	−	0.292387i	$-0.905551\pi$
$193$	−141.153	−	244.485i	−0.731364	−	1.26676i	0.224936	−	0.974374i	$-0.427783\pi$
$194$	−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	$-0.768652\pi$
$197$		−	261.806i		−	1.32896i	0.747304	−	0.664482i	$-0.231348\pi$
$198$	−122.287	−	163.784i	−0.617610	−	0.827193i
$199$	−278.968	+	161.062i	−1.40185	+	0.809357i	−0.994582	−	0.103953i	$-0.966851\pi$
$199$	−278.968	+	161.062i	−1.40185	+	0.809357i	−0.407265	+	0.913310i	$0.633518\pi$
$200$	−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	$-0.967497\pi$
$223$		−	45.4626i		−	0.203868i	0.994791	−	0.101934i	$-0.0325031\pi$
$224$		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	0.994640	−	0.103396i	$-0.0329708\pi$
$227$	92.5653	+	160.328i	0.407777	+	0.706290i	−0.586864	+	0.809686i	$0.699637\pi$
$228$	35.9391	−	121.270i	0.157627	−	0.531885i
$229$	160.173	+	92.4759i	0.699445	+	0.403825i	0.807141	−	0.590359i	$-0.201014\pi$
$229$	160.173	+	92.4759i	0.699445	+	0.403825i	−0.107695	+	0.994184i	$0.534347\pi$
$230$	−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	−0.950930	−	0.309405i	$-0.899870\pi$
$233$	−48.3504	+	83.7453i	−0.207512	+	0.359422i	0.743418	+	0.668827i	$0.233203\pi$
$234$	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	$0.110898\pi$
$239$			163.185i			0.682782i	−0.939921	+	0.341391i	$0.889102\pi$
$240$	−100.266	+	154.307i	−0.417773	+	0.642945i
$241$	102.745	+	177.960i	0.426330	+	0.738424i	0.996544	−	0.0830718i	$-0.0264731\pi$
$241$	102.745	+	177.960i	0.426330	+	0.738424i	−0.570214	+	0.821496i	$0.693140\pi$
$242$	−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	−0.576119	−	0.817366i	$-0.695434\pi$
$257$	107.889	−	186.868i	0.419800	−	0.727114i	0.995919	+	0.0902512i	$0.0287670\pi$
$258$	−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	0.151935	−	0.988391i	$-0.451450\pi$
$263$	285.059	−	164.579i	1.08387	−	0.625775i	0.931939	+	0.362616i	$0.118116\pi$
$264$	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	0.0524492	−	0.998624i	$-0.483297\pi$
$269$	253.803	−	146.533i	0.943507	−	0.544734i	0.891058	+	0.453889i	$0.149964\pi$
$270$	−28.1916	−	238.323i	−0.104413	−	0.882679i
$271$	23.2529	+	13.4251i	0.0858042	+	0.0495391i	0.542288	−	0.840193i	$-0.317558\pi$
$271$	23.2529	+	13.4251i	0.0858042	+	0.0495391i	−0.456484	+	0.889732i	$0.650891\pi$
$272$	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	0.124949	−	0.992163i	$-0.460123\pi$
$277$	289.925	−	167.389i	1.04666	−	0.604291i	0.921713	+	0.387872i	$0.126790\pi$
$278$	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	0.865478	−	0.500947i	$-0.167015\pi$
$283$	−0.309453	−	0.535988i	−0.00109347	−	0.00189395i	−0.866572	+	0.499053i	$0.833681\pi$
$284$	−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	$-0.984633\pi$
$293$		−	28.2794i		−	0.0965169i	0.998835	−	0.0482584i	$-0.0153671\pi$
$294$		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	−0.256823	−	0.966459i	$-0.582676\pi$
$311$	140.492	−	81.1132i	0.451743	−	0.260814i	0.708566	+	0.705644i	$0.249342\pi$
$312$	−584.186	+	702.126i	−1.87239	+	2.25040i
$313$	−133.123	+	230.576i	−0.425313	+	0.736664i	−0.996450	−	0.0841913i	$-0.973169\pi$
$313$	−133.123	+	230.576i	−0.425313	+	0.736664i	0.571137	+	0.820855i	$0.306503\pi$
$314$	−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	−0.225936	−	0.974142i	$-0.572544\pi$
$317$	−374.864	−	216.428i	−1.18254	−	0.682737i	−0.956600	+	0.291405i	$0.905877\pi$
$318$	−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	−0.920847	−	0.389925i	$-0.872501\pi$
$331$	−40.6264	+	70.3671i	−0.122738	+	0.212589i	0.798108	+	0.602514i	$0.205834\pi$
$332$	−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	0.999992	+	0.00392020i	$0.00124784\pi$
$347$	174.677	+	302.549i	0.503391	+	0.871899i	−0.496601	+	0.867979i	$0.665419\pi$
$348$	−46.8891	−	195.420i	−0.134739	−	0.561552i
$349$			165.836i			0.475174i	0.971366	+	0.237587i	$0.0763566\pi$
$349$			165.836i			0.475174i	−0.971366	+	0.237587i	$0.923643\pi$
$350$		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	−0.978420	−	0.206627i	$-0.933751\pi$
$353$	−235.858	−	408.519i	−0.668154	−	1.15728i	0.310266	−	0.950650i	$-0.399582\pi$
$354$	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	−0.994134	−	0.108154i	$-0.965506\pi$
$359$	−568.967	−	328.493i	−1.58487	−	0.915022i	−0.590731	−	0.806869i	$-0.701161\pi$
$360$	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	−0.856866	−	0.515539i	$-0.827592\pi$
$367$	−307.850	+	177.737i	−0.838829	+	0.484298i	0.0180371	+	0.999837i	$0.494258\pi$
$368$	−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	0.819767	−	0.572698i	$-0.194103\pi$
$373$	273.662	+	157.999i	0.733680	+	0.423590i	−0.0860872	+	0.996288i	$0.527436\pi$
$374$	−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	−0.994972	−	0.100158i	$-0.968065\pi$
$383$	−604.832	−	349.200i	−1.57920	−	0.911750i	−0.584225	−	0.811591i	$-0.698602\pi$
$384$	−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	−0.291935	−	0.956438i	$-0.594299\pi$
$389$	151.865	−	87.6790i	0.390397	−	0.225396i	0.682332	+	0.731042i	$0.260966\pi$
$390$	−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	0.857737	−	0.514088i	$-0.171870\pi$
$397$	334.033	+	192.854i	0.841393	+	0.485778i	−0.0163447	+	0.999866i	$0.505203\pi$
$398$	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	0.324103	+	0.946022i	$0.394938\pi$
$401$	−263.548	+	456.479i	−0.657228	+	1.13835i	−0.981330	+	0.192330i	$0.938396\pi$
$402$	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	−0.999781	−	0.0209399i	$-0.993334\pi$
$409$	−211.872	−	366.973i	−0.518025	−	0.897245i	0.481756	−	0.876305i	$-0.339999\pi$
$410$	−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	$0.0479119\pi$
$421$			126.260i			0.299904i	−0.988693	+	0.149952i	$0.952088\pi$
$422$	−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	−0.733204	−	0.680009i	$-0.761976\pi$
$431$	−220.198	+	127.131i	−0.510900	+	0.294968i	0.222303	+	0.974978i	$0.428642\pi$
$432$	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	0.205546	−	0.978647i	$-0.434103\pi$
$439$	−236.715	−	136.667i	−0.539214	−	0.311315i	−0.744760	+	0.667332i	$0.767436\pi$
$440$	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	0.463263	+	0.886221i	$0.346678\pi$
$443$	−237.385	+	411.163i	−0.535858	+	0.928133i	−0.999121	+	0.0419124i	$0.986655\pi$
$444$	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	−0.743498	−	0.668738i	$-0.766835\pi$
$457$	94.7793	−	164.163i	0.207395	−	0.359218i	0.950893	+	0.309520i	$0.100168\pi$
$458$	−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	$-0.929503\pi$
$461$		−	202.533i		−	0.439335i	0.975575	−	0.219667i	$-0.0704972\pi$
$462$		0			0
$463$			652.927i			1.41021i	0.709103	+	0.705105i	$0.249100\pi$
$463$			652.927i			1.41021i	−0.709103	+	0.705105i	$0.750900\pi$
$464$	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	−0.411008	−	0.911632i	$-0.634823\pi$
$467$	272.725	−	472.373i	0.583993	−	1.01150i	0.995000	−	0.0998730i	$-0.0318437\pi$
$468$	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	−0.595202	−	0.803576i	$-0.702928\pi$
$479$	−94.3079	+	54.4487i	−0.196885	+	0.113672i	0.398317	+	0.917248i	$0.369595\pi$
$480$	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	−0.830556	−	0.556936i	$-0.811977\pi$
$487$	−371.831	+	214.677i	−0.763513	+	0.440814i	0.0670428	+	0.997750i	$0.478644\pi$
$488$	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	−0.983305	−	0.181967i	$-0.941754\pi$
$499$	−166.698	+	288.730i	−0.334064	+	0.578617i	0.649240	+	0.760583i	$0.275087\pi$
$500$	−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	$0.195664\pi$
$503$			580.170i			1.15342i	−0.816949	+	0.576710i	$0.804336\pi$
$504$		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	0.215087	−	0.976595i	$-0.430997\pi$
$509$	−266.271	−	153.732i	−0.523126	−	0.302027i	−0.738213	+	0.674568i	$0.764330\pi$
$510$	−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	0.971215	+	0.238205i	$0.0765591\pi$
$521$	360.480	+	624.369i	0.691899	+	1.19840i	−0.279316	+	0.960199i	$0.590108\pi$
$522$	43.0187	+	363.667i	0.0824113	+	0.696681i
$523$	−134.988	+	233.807i	−0.258104	+	0.447049i	−0.965734	−	0.259534i	$-0.916431\pi$
$523$	−134.988	+	233.807i	−0.258104	+	0.447049i	0.707630	+	0.706583i	$0.249764\pi$
$524$	−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	0.998612	−	0.0526734i	$-0.0167742\pi$
$541$	785.695	+	453.621i	1.45230	+	0.838486i	0.453689	+	0.891160i	$0.350108\pi$
$542$	−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	−0.985598	−	0.169103i	$-0.945913\pi$
$557$	−741.896	+	428.334i	−1.33195	+	0.769002i	−0.346352	+	0.938105i	$0.612580\pi$
$558$	−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	0.872040	−	0.489435i	$-0.162797\pi$
$563$	6.84436	+	11.8548i	0.0121569	+	0.0210564i	−0.859883	+	0.510491i	$0.829464\pi$
$564$	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	0.235999	−	0.971753i	$-0.424164\pi$
$569$	545.991	−	945.684i	0.959563	−	1.66201i	0.723563	−	0.690258i	$-0.242503\pi$
$570$	−16.0241	−	135.463i	−0.0281125	−	0.237655i
$571$	−359.549	−	622.757i	−0.629683	−	1.09064i	−0.987615	−	0.156895i	$-0.949852\pi$
$571$	−359.549	−	622.757i	−0.629683	−	1.09064i	0.357932	−	0.933747i	$-0.383482\pi$
$572$	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	−0.835628	−	0.549296i	$-0.814896\pi$
$577$	−515.560	−	892.976i	−0.893518	−	1.54762i	−0.0578905	−	0.998323i	$-0.518437\pi$
$578$	−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	−0.677308	−	0.735700i	$-0.736853\pi$
$593$	176.999	−	306.572i	0.298481	−	0.516984i	0.975789	+	0.218716i	$0.0701867\pi$
$594$	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	0.662708	−	0.748878i	$-0.269407\pi$
$599$	983.923	−	568.068i	1.64261	−	0.948361i	0.979901	−	0.199484i	$-0.0639265\pi$
$600$	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	0.783438	−	0.621470i	$-0.213464\pi$
$607$	386.628	+	223.220i	0.636948	+	0.367742i	−0.146490	+	0.989212i	$0.546798\pi$
$608$	−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	−0.879285	−	0.476296i	$-0.841979\pi$
$613$	−555.650	+	320.805i	−0.906443	+	0.523335i	−0.0271583	+	0.999631i	$0.508646\pi$
$614$	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	0.986205	−	0.165530i	$-0.0529336\pi$
$619$	216.495	+	374.980i	0.349749	+	0.605783i	−0.636456	+	0.771313i	$0.719600\pi$
$620$	−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	$-0.939363\pi$
$631$		−	238.957i		−	0.378695i	0.981910	−	0.189348i	$-0.0606373\pi$
$632$	−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	0.869114	−	0.494612i	$-0.164690\pi$
$641$	3.98065	+	6.89469i	0.00621006	+	0.0107561i	−0.862904	+	0.505368i	$0.831357\pi$
$642$	−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	−0.707541	−	0.706672i	$-0.750196\pi$
$647$	−290.707	+	167.840i	−0.449316	+	0.259413i	0.258225	+	0.966085i	$0.416862\pi$
$648$	−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	0.467476	−	0.884006i	$-0.345163\pi$
$653$	−42.0252	−	24.2632i	−0.0643571	−	0.0371566i	−0.531833	+	0.846849i	$0.678497\pi$
$654$	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	0.162291	−	0.986743i	$-0.448112\pi$
$661$	725.765	−	419.021i	1.09798	−	0.633919i	0.935690	+	0.352823i	$0.114778\pi$
$662$	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	−0.142499	−	0.989795i	$-0.545514\pi$
$677$	−725.024	−	418.593i	−1.07094	−	0.618305i	−0.928437	+	0.371490i	$0.878847\pi$
$678$	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	0.888648	−	0.458591i	$-0.151646\pi$
$683$	32.2189	+	55.8047i	0.0471725	+	0.0817053i	−0.841475	+	0.540296i	$0.818312\pi$
$684$	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	−0.991227	−	0.132172i	$-0.957805\pi$
$691$	−263.374	+	456.177i	−0.381149	+	0.660169i	0.610078	+	0.792341i	$0.291138\pi$
$692$	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	$-0.834777\pi$
$701$		−	695.486i		−	0.992134i	0.868284	−	0.496067i	$-0.165223\pi$
$702$	−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	0.944640	−	0.328110i	$-0.106412\pi$
$709$	803.161	+	463.705i	1.13281	+	0.654027i	0.188168	+	0.982137i	$0.439745\pi$
$710$	−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	−0.991493	−	0.130163i	$-0.958450\pi$
$719$	−1150.37	−	664.169i	−1.59996	−	0.923739i	−0.608471	−	0.793576i	$-0.708217\pi$
$720$	−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	$0.120977\pi$
$727$			539.401i			0.741954i	−0.928642	+	0.370977i	$0.879023\pi$
$728$		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	0.215564	−	0.976490i	$-0.430841\pi$
$733$	−382.859	−	221.044i	−0.522318	−	0.301561i	−0.737883	+	0.674929i	$0.764174\pi$
$734$	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	0.933730	+	0.357977i	$0.116533\pi$
$739$	574.116	+	994.398i	0.776882	+	1.34560i	−0.156848	+	0.987623i	$0.550133\pi$
$740$	−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	$-0.870344\pi$
$743$		−	588.688i		−	0.792313i	0.918183	−	0.396156i	$-0.129656\pi$
$744$	−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	−0.0526140	−	0.998615i	$-0.516755\pi$
$751$	−708.754	−	409.199i	−0.943747	−	0.544873i	−0.891133	+	0.453742i	$0.850089\pi$
$752$	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	$0.0221146\pi$
$757$			105.101i			0.138838i	−0.997588	+	0.0694192i	$0.977885\pi$
$758$	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	−0.312527	−	0.949909i	$-0.601175\pi$
$761$	507.117	−	878.352i	0.666382	−	1.15421i	0.978909	−	0.204299i	$-0.0654913\pi$
$762$	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	−0.670545	−	0.741869i	$-0.733940\pi$
$773$	−280.862	+	162.156i	−0.363340	+	0.209774i	0.307205	+	0.951643i	$0.400606\pi$
$774$	−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	0.938632	−	0.344919i	$-0.112094\pi$
$787$	134.268	+	232.559i	0.170607	+	0.295500i	−0.768025	+	0.640420i	$0.778760\pi$
$788$	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	$-0.608637\pi$
$797$		−	1502.06i		−	1.88465i	0.334705	−	0.942323i	$-0.391363\pi$
$798$		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	0.843331	−	0.537395i	$-0.180591\pi$
$809$	−35.3793	−	61.2788i	−0.0437322	−	0.0757464i	−0.887063	+	0.461648i	$0.847258\pi$
$810$	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	0.491991	−	0.870600i	$-0.336269\pi$
$821$	−13.1159	−	7.57244i	−0.0159755	−	0.00922344i	−0.507966	+	0.861377i	$0.669603\pi$
$822$	2508.30	−	296.710i	3.05146	−	0.360961i
$823$	−1284.10	+	741.378i	−1.56027	+	0.900824i	−0.563044	+	0.826427i	$0.690370\pi$
$823$	−1284.10	+	741.378i	−1.56027	+	0.900824i	−0.997229	+	0.0743964i	$0.976297\pi$
$824$	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	−0.572762	−	0.819722i	$-0.694128\pi$
$829$	−123.722	+	71.4311i	−0.149243	+	0.0861654i	0.423519	+	0.905887i	$0.360795\pi$
$830$	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	$-0.996823\pi$
$839$		−	16.7454i		−	0.0199588i	0.999950	−	0.00997940i	$-0.00317659\pi$
$840$		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	$0.275612\pi$
$853$			1299.38i			1.52331i	−0.647984	+	0.761654i	$0.724388\pi$
$854$		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	−0.969366	−	0.245619i	$-0.921009\pi$
$857$	−597.668	−	1035.19i	−0.697396	−	1.20792i	0.271971	−	0.962305i	$-0.412325\pi$
$858$	−141.071	−	1192.57i	−0.164418	−	1.38994i
$859$	−170.885	+	295.981i	−0.198934	+	0.344564i	−0.948183	−	0.317724i	$-0.897081\pi$
$859$	−170.885	+	295.981i	−0.198934	+	0.344564i	0.749249	+	0.662289i	$0.230415\pi$
$860$	−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	0.901788	−	0.432179i	$-0.142255\pi$
$863$	844.362	+	487.493i	0.978404	+	0.564882i	0.0766158	+	0.997061i	$0.475589\pi$
$864$	−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	0.335484	−	0.942046i	$-0.391100\pi$
$877$	−274.158	−	158.285i	−0.312609	−	0.180485i	−0.648093	+	0.761561i	$0.724433\pi$
$878$	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	0.505327	−	0.862928i	$-0.331372\pi$
$887$	9.46740	+	5.46601i	0.0106735	+	0.00616235i	−0.494654	+	0.869090i	$0.664705\pi$
$888$	−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	0.872219	−	0.489115i	$-0.162680\pi$
$907$	11.3588	+	19.6740i	0.0125235	+	0.0216913i	−0.859696	+	0.510806i	$0.829347\pi$
$908$	−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	$-0.870331\pi$
$911$		−	721.866i		−	0.792389i	0.918167	−	0.396194i	$-0.129669\pi$
$912$	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	0.437140	−	0.899393i	$-0.355991\pi$
$919$	−113.209	−	65.3612i	−0.123187	−	0.0711221i	−0.560327	+	0.828271i	$0.689325\pi$
$920$	−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	−0.962143	−	0.272545i	$-0.912135\pi$
$929$	−227.643	+	394.289i	−0.245041	+	0.424423i	0.717102	+	0.696968i	$0.245468\pi$
$930$	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	0.124841	−	0.992177i	$-0.460158\pi$
$941$	984.767	−	568.556i	1.04651	−	0.604204i	0.921671	+	0.387973i	$0.126825\pi$
$942$	−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	−0.989895	−	0.141801i	$-0.954711\pi$
$947$	−352.421	+	610.411i	−0.372145	+	0.644573i	0.617751	+	0.786374i	$0.288044\pi$
$948$	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	$-0.869388\pi$
$967$		−	771.494i		−	0.797822i	0.916990	−	0.398911i	$-0.130612\pi$
$968$	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	−0.527047	−	0.849836i	$-0.676701\pi$
$971$	458.754	−	794.586i	0.472456	−	0.818317i	0.999503	+	0.0315186i	$0.0100343\pi$
$972$	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	0.789707	−	0.613484i	$-0.210232\pi$
$977$	−133.301	−	230.883i	−0.136439	−	0.236319i	−0.926146	+	0.377165i	$0.876899\pi$
$978$	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	0.645454	−	0.763799i	$-0.276668\pi$
$983$	1601.95	−	924.884i	1.62965	−	0.940879i	0.984197	−	0.177080i	$-0.0566650\pi$
$984$	−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	−0.339038	−	0.940773i	$-0.610102\pi$
$991$	303.420	−	175.180i	0.306175	−	0.176770i	0.645214	+	0.764002i	$0.276768\pi$
$992$	−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	−0.253860	−	0.967241i	$-0.581700\pi$
$997$	455.495	−	262.980i	0.456866	−	0.263772i	0.710726	+	0.703469i	$0.248367\pi$
$998$	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.275.2		12
7.2	even	3		392.3.g.i.99.4		6
7.3	odd	6		56.3.k.d.11.6	yes	12
7.4	even	3	inner	392.3.k.l.67.6		12
7.5	odd	6		392.3.g.j.99.4		6
7.6	odd	2		56.3.k.d.51.2	yes	12
8.3	odd	2	inner	392.3.k.l.275.6		12
28.3	even	6		224.3.o.d.207.5		12
28.19	even	6		1568.3.g.j.687.1		6
28.23	odd	6		1568.3.g.l.687.6		6
28.27	even	2		224.3.o.d.79.6		12
56.3	even	6		56.3.k.d.11.2	✓	12
56.5	odd	6		1568.3.g.j.687.2		6
56.11	odd	6	inner	392.3.k.l.67.2		12
56.13	odd	2		224.3.o.d.79.5		12
56.19	even	6		392.3.g.j.99.3		6
56.27	even	2		56.3.k.d.51.6	yes	12
56.37	even	6		1568.3.g.l.687.5		6
56.45	odd	6		224.3.o.d.207.6		12
56.51	odd	6		392.3.g.i.99.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.k.d.11.2	✓	12	56.3	even	6
56.3.k.d.11.6	yes	12	7.3	odd	6
56.3.k.d.51.2	yes	12	7.6	odd	2
56.3.k.d.51.6	yes	12	56.27	even	2
224.3.o.d.79.5		12	56.13	odd	2
224.3.o.d.79.6		12	28.27	even	2
224.3.o.d.207.5		12	28.3	even	6
224.3.o.d.207.6		12	56.45	odd	6
392.3.g.i.99.3		6	56.51	odd	6
392.3.g.i.99.4		6	7.2	even	3
392.3.g.j.99.3		6	56.19	even	6
392.3.g.j.99.4		6	7.5	odd	6
392.3.k.l.67.2		12	56.11	odd	6	inner
392.3.k.l.67.6		12	7.4	even	3	inner
392.3.k.l.275.2		12	1.1	even	1	trivial
392.3.k.l.275.6		12	8.3	odd	2	inner
1568.3.g.j.687.1		6	28.19	even	6
1568.3.g.j.687.2		6	56.5	odd	6
1568.3.g.l.687.5		6	56.37	even	6
1568.3.g.l.687.6		6	28.23	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
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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