LMFDB - Embedded newform 392.3.k.l.67.6

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			67.6
Root			$0.907369 + 0.0534805i$ of defining polynomial
Character	$\chi$	$=$	392.67
Dual form			392.3.k.l.275.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.98615 - 0.234945i) q^{2} +(2.66613 - 4.61787i) q^{3} +(3.88960 - 0.933271i) q^{4} +(1.86796 - 1.07847i) q^{5} +(4.21039 - 9.79818i) q^{6} +(7.50608 - 2.76746i) q^{8} +(-9.71647 - 16.8294i) q^{9} +O(q^{10})$	\(q+(1.98615 - 0.234945i) q^{2} +(2.66613 - 4.61787i) q^{3} +(3.88960 - 0.933271i) q^{4} +(1.86796 - 1.07847i) q^{5} +(4.21039 - 9.79818i) q^{6} +(7.50608 - 2.76746i) q^{8} +(-9.71647 - 16.8294i) q^{9} +(3.45667 - 2.58086i) q^{10} +(-2.62956 + 4.55453i) q^{11} +(6.06045 - 20.4499i) q^{12} +21.4116i q^{13} -11.5013i q^{15} +(14.2580 - 7.26011i) q^{16} +(0.463429 - 0.802683i) q^{17} +(-23.2524 - 31.1430i) q^{18} +(-2.96505 - 5.13561i) q^{19} +(6.25911 - 5.93812i) q^{20} +(-4.15264 + 9.66378i) q^{22} +(-7.52507 + 4.34460i) q^{23} +(7.23239 - 42.0405i) q^{24} +(-10.1738 + 17.6216i) q^{25} +(5.03053 + 42.5266i) q^{26} -55.6311 q^{27} +9.42223i q^{29} +(-2.70217 - 22.8434i) q^{30} +(29.8813 + 17.2520i) q^{31} +(26.6129 - 17.7695i) q^{32} +(14.0215 + 24.2859i) q^{33} +(0.731855 - 1.70313i) q^{34} +(-53.4996 - 56.3916i) q^{36} +(11.0853 - 6.40011i) q^{37} +(-7.09562 - 9.50349i) q^{38} +(98.8758 + 57.0860i) q^{39} +(11.0364 - 13.2645i) q^{40} -43.1339 q^{41} -41.7382 q^{43} +(-5.97732 + 20.1694i) q^{44} +(-36.2999 - 20.9578i) q^{45} +(-13.9252 + 10.3970i) q^{46} +(39.8357 - 22.9991i) q^{47} +(4.48745 - 85.1980i) q^{48} +(-16.0667 + 37.3894i) q^{50} +(-2.47112 - 4.28011i) q^{51} +(19.9828 + 83.2825i) q^{52} +(-64.5031 - 37.2409i) q^{53} +(-110.492 + 13.0702i) q^{54} +11.3436i q^{55} -31.6208 q^{57} +(2.21370 + 18.7140i) q^{58} +(26.8367 - 46.4825i) q^{59} +(-10.7338 - 44.7355i) q^{60} +(-24.0893 + 13.9080i) q^{61} +(63.4020 + 27.2446i) q^{62} +(48.6823 - 41.5455i) q^{64} +(23.0916 + 39.9959i) q^{65} +(33.5546 + 44.9412i) q^{66} +(39.2453 - 67.9749i) q^{67} +(1.05343 - 3.55462i) q^{68} +46.3330i q^{69} +74.5100i q^{71} +(-119.507 - 99.4329i) q^{72} +(16.8020 - 29.1020i) q^{73} +(20.5134 - 15.3160i) q^{74} +(54.2494 + 93.9627i) q^{75} +(-16.3258 - 17.2083i) q^{76} +(209.794 + 90.1511i) q^{78} +(26.1642 - 15.1059i) q^{79} +(18.8036 - 28.9384i) q^{80} +(-60.8713 + 105.432i) q^{81} +(-85.6705 + 10.1341i) q^{82} +72.9274 q^{83} -1.99917i q^{85} +(-82.8984 + 9.80616i) q^{86} +(43.5106 + 25.1209i) q^{87} +(-7.13318 + 41.4638i) q^{88} +(-27.4198 - 47.4925i) q^{89} +(-77.0211 - 33.0968i) q^{90} +(-25.2148 + 23.9217i) q^{92} +(159.335 - 91.9919i) q^{93} +(73.7162 - 55.0390i) q^{94} +(-11.0772 - 6.39541i) q^{95} +(-11.1040 - 170.270i) q^{96} +53.7125 q^{97} +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 $

$2$	1.98615	−	0.234945i	0.993076	−	0.117472i
$2$	1.98615	−	0.234945i	0.993076	−	0.117472i
$3$	2.66613	−	4.61787i	0.888709	−	1.53929i	0.0473064	−	0.998880i	$-0.484936\pi$
$3$	2.66613	−	4.61787i	0.888709	−	1.53929i	0.841403	−	0.540409i	$-0.181730\pi$
$4$	3.88960	−	0.933271i	0.972401	−	0.233318i
$5$	1.86796	−	1.07847i	0.373592	−	0.215693i	−0.301435	−	0.953487i	$-0.597466\pi$
$5$	1.86796	−	1.07847i	0.373592	−	0.215693i	0.675026	+	0.737794i	$0.264132\pi$
$6$	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
$10$	3.45667	−	2.58086i	0.345667	−	0.258086i
$11$	−2.62956	+	4.55453i	−0.239051	+	0.414048i	−0.960442	−	0.278480i	$-0.910170\pi$
$11$	−2.62956	+	4.55453i	−0.239051	+	0.414048i	0.721392	+	0.692527i	$0.243503\pi$
$12$	6.06045	−	20.4499i	0.505038	−	1.70416i
$13$			21.4116i			1.64704i	0.567285	+	0.823522i	$0.307994\pi$
$13$			21.4116i			1.64704i	−0.567285	+	0.823522i	$0.692006\pi$
$14$		0			0
$15$		−	11.5013i		−	0.766754i
$16$	14.2580	−	7.26011i	0.891126	−	0.453757i
$17$	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	$0.157988\pi$
$18$	−23.2524	−	31.1430i	−1.29180	−	1.73016i
$19$	−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	−0.654587	−	0.755987i	$-0.727157\pi$
$23$	−7.52507	+	4.34460i	−0.327177	+	0.188896i	0.327410	+	0.944882i	$0.393824\pi$
$24$	7.23239	−	42.0405i	0.301350	−	1.75169i
$25$	−10.1738	+	17.6216i	−0.406953	+	0.704863i
$26$	5.03053	+	42.5266i	0.193482	+	1.63564i
$27$	−55.6311			−2.06041
$28$		0			0
$29$			9.42223i			0.324904i	0.986716	+	0.162452i	$0.0519403\pi$
$29$			9.42223i			0.324904i	−0.986716	+	0.162452i	$0.948060\pi$
$30$	−2.70217	−	22.8434i	−0.0900723	−	0.761445i
$31$	29.8813	+	17.2520i	0.963912	+	0.556515i	0.897375	−	0.441269i	$-0.145471\pi$
$31$	29.8813	+	17.2520i	0.963912	+	0.556515i	0.0665375	+	0.997784i	$0.478805\pi$
$32$	26.6129	−	17.7695i	0.831652	−	0.555298i
$33$	14.0215	+	24.2859i	0.424893	+	0.735936i
$34$	0.731855	−	1.70313i	0.0215252	−	0.0500921i
$35$		0			0
$36$	−53.4996	−	56.3916i	−1.48610	−	1.56643i
$37$	11.0853	−	6.40011i	0.299603	−	0.172976i	−0.342662	−	0.939459i	$-0.611328\pi$
$37$	11.0853	−	6.40011i	0.299603	−	0.172976i	0.642265	+	0.766483i	$0.277995\pi$
$38$	−7.09562	−	9.50349i	−0.186727	−	0.250092i
$39$	98.8758	+	57.0860i	2.53528	+	1.46374i
$40$	11.0364	−	13.2645i	0.275911	−	0.331614i
$41$	−43.1339			−1.05205			−0.526023	−	0.850470i	$-0.676317\pi$
$41$	−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	$0.661300\pi$
$44$	−5.97732	+	20.1694i	−0.135848	+	0.458395i
$45$	−36.2999	−	20.9578i	−0.806665	−	0.465728i
$46$	−13.9252	+	10.3970i	−0.302721	+	0.226022i
$47$	39.8357	−	22.9991i	0.847567	−	0.489343i	−0.0122620	−	0.999925i	$-0.503903\pi$
$47$	39.8357	−	22.9991i	0.847567	−	0.489343i	0.859829	+	0.510582i	$0.170570\pi$
$48$	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
$52$	19.9828	+	83.2825i	0.384285	+	1.60159i
$53$	−64.5031	−	37.2409i	−1.21704	−	0.702658i	−0.252756	−	0.967530i	$-0.581337\pi$
$53$	−64.5031	−	37.2409i	−1.21704	−	0.702658i	−0.964284	+	0.264872i	$0.914670\pi$
$54$	−110.492	+	13.0702i	−2.04614	+	0.242041i
$55$			11.3436i			0.206246i
$56$		0			0
$57$	−31.6208			−0.554751
$58$	2.21370	+	18.7140i	0.0381672	+	0.322655i
$59$	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	$0.0163561\pi$
$60$	−10.7338	−	44.7355i	−0.178897	−	0.745592i
$61$	−24.0893	+	13.9080i	−0.394907	+	0.228000i	−0.684284	−	0.729215i	$-0.739885\pi$
$61$	−24.0893	+	13.9080i	−0.394907	+	0.228000i	0.289377	+	0.957215i	$0.406552\pi$
$62$	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
$66$	33.5546	+	44.9412i	0.508403	+	0.680927i
$67$	39.2453	−	67.9749i	0.585751	−	1.01455i	−0.409030	−	0.912521i	$-0.634133\pi$
$67$	39.2453	−	67.9749i	0.585751	−	1.01455i	0.994781	−	0.102030i	$-0.0325338\pi$
$68$	1.05343	−	3.55462i	0.0154917	−	0.0522739i
$69$			46.3330i			0.671493i
$70$		0			0
$71$			74.5100i			1.04944i	0.851276	+	0.524719i	$0.175829\pi$
$71$			74.5100i			1.04944i	−0.851276	+	0.524719i	$0.824171\pi$
$72$	−119.507	−	99.4329i	−1.65982	−	1.38101i
$73$	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	$0.0927401\pi$
$74$	20.5134	−	15.3160i	0.277209	−	0.206973i
$75$	54.2494	+	93.9627i	0.723325	+	1.25284i
$76$	−16.3258	−	17.2083i	−0.214813	−	0.226425i
$77$		0			0
$78$	209.794	+	90.1511i	2.68967	+	1.15578i
$79$	26.1642	−	15.1059i	0.331192	−	0.191214i	−0.325178	−	0.945653i	$-0.605424\pi$
$79$	26.1642	−	15.1059i	0.331192	−	0.191214i	0.656370	+	0.754439i	$0.272091\pi$
$80$	18.8036	−	28.9384i	0.235045	−	0.361730i
$81$	−60.8713	+	105.432i	−0.751497	+	1.30163i
$82$	−85.6705	+	10.1341i	−1.04476	+	0.123586i
$83$	72.9274			0.878644			0.439322	−	0.898330i	$-0.355219\pi$
$83$	72.9274			0.878644			0.439322	+	0.898330i	$0.355219\pi$
$84$		0			0
$85$		−	1.99917i		−	0.0235197i
$86$	−82.8984	+	9.80616i	−0.963935	+	0.114025i
$87$	43.5106	+	25.1209i	0.500122	+	0.288745i
$88$	−7.13318	+	41.4638i	−0.0810589	+	0.471180i
$89$	−27.4198	−	47.4925i	−0.308088	−	0.533624i	0.669856	−	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
$94$	73.7162	−	55.0390i	0.784215	−	0.585521i
$95$	−11.0772	−	6.39541i	−0.116602	−	0.0673201i
$96$	−11.1040	−	170.270i	−0.115667	−	1.77365i
$97$	53.7125			0.553738			0.276869	−	0.960908i	$-0.410703\pi$
$97$	53.7125			0.553738			0.276869	+	0.960908i	$0.410703\pi$
$98$		0			0
$99$	102.200			1.03232
$100$	−23.1264	+	78.0359i	−0.231264	+	0.780359i
$101$	−78.2037	−	45.1509i	−0.774294	−	0.447039i	0.0601103	−	0.998192i	$-0.480855\pi$
$101$	−78.2037	−	45.1509i	−0.774294	−	0.447039i	−0.834404	+	0.551153i	$0.814188\pi$
$102$	−5.91362	−	7.92038i	−0.0579766	−	0.0776508i
$103$	−97.6980	+	56.4060i	−0.948525	+	0.547631i	−0.892622	−	0.450805i	$-0.851137\pi$
$103$	−97.6980	+	56.4060i	−0.948525	+	0.547631i	−0.0559023	+	0.998436i	$0.517804\pi$
$104$	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	$0.598403\pi$
$108$	−216.383	+	51.9189i	−2.00354	+	0.480730i
$109$	57.7477	+	33.3406i	0.529795	+	0.305877i	0.740933	−	0.671579i	$-0.234384\pi$
$109$	57.7477	+	33.3406i	0.529795	+	0.305877i	−0.211138	+	0.977456i	$0.567717\pi$
$110$	2.66511	+	22.5300i	0.0242282	+	0.204818i
$111$		−	68.2540i		−	0.614901i
$112$		0			0
$113$	7.16467			0.0634042			0.0317021	−	0.999497i	$-0.489907\pi$
$113$	7.16467			0.0634042			0.0317021	+	0.999497i	$0.489907\pi$
$114$	−62.8037	+	7.42913i	−0.550910	+	0.0651678i
$115$	−9.37101	+	16.2311i	−0.0814870	+	0.141140i
$116$	8.79349	+	36.6487i	0.0758060	+	0.315937i
$117$	360.344	−	208.045i	3.07986	−	1.77816i
$118$	42.3810	−	98.6266i	0.359161	−	0.835818i
$119$		0			0
$120$	−31.8294	−	86.3297i	−0.265245	−	0.719414i
$121$	46.6709	+	80.8363i	0.385710	+	0.668069i
$122$	−44.5775	+	33.2830i	−0.365389	+	0.272812i
$123$	−115.000	+	199.187i	−0.934963	+	1.61940i
$124$	132.327	+	39.2159i	1.06715	+	0.316258i
$125$			97.8118i			0.782494i
$126$		0			0
$127$			131.492i			1.03537i	0.855572	+	0.517684i	$0.173206\pi$
$127$			131.492i			1.03537i	−0.855572	+	0.517684i	$0.826794\pi$
$128$	86.9296	−	93.9534i	0.679138	−	0.734011i
$129$	−111.279	+	192.742i	−0.862631	+	1.49412i
$130$	55.2604	+	74.0127i	0.425080	+	0.569329i
$131$	−4.38060	−	7.58742i	−0.0334397	−	0.0579193i	0.848821	−	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
$136$	1.25714	−	7.30752i	0.00924370	−	0.0537318i
$137$	118.420	−	205.110i	0.864381	−	1.49715i	−0.00327850	−	0.999995i	$-0.501044\pi$
$137$	118.420	−	205.110i	0.864381	−	1.49715i	0.867660	−	0.497158i	$-0.165623\pi$
$138$	10.8857	+	92.0244i	0.0788818	+	0.666844i
$139$	−172.122			−1.23828			−0.619142	−	0.785279i	$-0.712520\pi$
$139$	−172.122			−1.23828			−0.619142	+	0.785279i	$0.712520\pi$
$140$		0			0
$141$		−	245.274i		−	1.73954i
$142$	17.5057	+	147.988i	0.123280	+	1.04217i
$143$	−97.5195	−	56.3029i	−0.681955	−	0.393727i
$144$	−260.721	−	169.411i	−1.81056	−	1.17647i
$145$	10.1616	+	17.6003i	0.0700797	+	0.121382i
$146$	26.5341	−	61.7485i	0.181740	−	0.422935i
$147$		0			0
$148$	37.1444	−	35.2395i	0.250976	−	0.238105i
$149$	−199.798	+	115.354i	−1.34093	+	0.774186i	−0.986944	−	0.161066i	$-0.948507\pi$
$149$	−199.798	+	115.354i	−1.34093	+	0.774186i	−0.353985	+	0.935251i	$0.615174\pi$
$150$	129.824	+	173.879i	0.865491	+	1.15919i
$151$	−128.077	−	73.9452i	−0.848190	−	0.489703i	0.0118494	−	0.999930i	$-0.496228\pi$
$151$	−128.077	−	73.9452i	−0.848190	−	0.489703i	−0.860040	+	0.510227i	$0.829561\pi$
$152$	−36.4685	−	30.3427i	−0.239924	−	0.199623i
$153$	−18.0116			−0.117723
$154$		0			0
$155$	74.4227			0.480146
$156$	437.864	+	129.764i	2.80682	+	0.831819i
$157$	−99.4450	−	57.4146i	−0.633407	−	0.365698i	0.148663	−	0.988888i	$-0.452503\pi$
$157$	−99.4450	−	57.4146i	−0.633407	−	0.365698i	−0.782070	+	0.623190i	$0.785836\pi$
$158$	48.4170	−	36.1498i	0.306437	−	0.228796i
$159$	−343.947	+	198.578i	−2.16319	+	1.24892i
$160$	30.5479	−	61.8938i	0.190924	−	0.386836i
$161$		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	$0.881665\pi$
$164$	−167.774	+	40.2556i	−1.02301	+	0.245461i
$165$	52.3830	+	30.2433i	0.317473	+	0.183293i
$166$	144.845	−	17.1339i	0.872560	−	0.103216i
$167$			241.457i			1.44585i	0.690926	+	0.722926i	$0.257203\pi$
$167$			241.457i			1.44585i	−0.690926	+	0.722926i	$0.742797\pi$
$168$		0			0
$169$	−289.455			−1.71275
$170$	−0.469695	−	3.97066i	−0.00276291	−	0.0233568i
$171$	−57.6196	+	99.8001i	−0.336957	+	0.583626i
$172$	−162.345	+	38.9531i	−0.943867	+	0.226471i
$173$	47.1300	−	27.2105i	0.272428	−	0.157286i	−0.357563	−	0.933889i	$-0.616392\pi$
$173$	47.1300	−	27.2105i	0.272428	−	0.157286i	0.629990	+	0.776603i	$0.283059\pi$
$174$	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
$178$	−65.6180	−	87.8852i	−0.368641	−	0.493737i
$179$	63.5100	−	110.003i	0.354805	−	0.614540i	−0.632280	−	0.774740i	$-0.717881\pi$
$179$	63.5100	−	110.003i	0.354805	−	0.614540i	0.987084	+	0.160200i	$0.0512141\pi$
$180$	−160.751	−	47.6397i	−0.893064	−	0.264665i
$181$		−	212.704i		−	1.17516i	−0.809165	−	0.587581i	$-0.800080\pi$
$181$		−	212.704i		−	1.17516i	0.809165	−	0.587581i	$-0.199920\pi$
$182$		0			0
$183$			148.322i			0.810502i
$184$	−44.4602	+	53.4362i	−0.241632	+	0.290414i
$185$	13.8046	−	23.9103i	0.0746194	−	0.129245i
$186$	294.850	−	220.145i	1.58521	−	1.18357i
$187$	2.43723	+	4.22140i	0.0130333	+	0.0225743i
$188$	133.480	−	126.635i	0.710002	−	0.673590i
$189$		0			0
$190$	−23.5035	−	10.0997i	−0.123703	−	0.0531565i
$191$	−35.1041	+	20.2674i	−0.183791	+	0.106112i	−0.589073	−	0.808080i	$-0.700507\pi$
$191$	−35.1041	+	20.2674i	−0.183791	+	0.106112i	0.405282	+	0.914192i	$0.367174\pi$
$192$	−62.0584	−	335.574i	−0.323221	−	1.74778i
$193$	−141.153	+	244.485i	−0.731364	+	1.26676i	0.224936	+	0.974374i	$0.427783\pi$
$193$	−141.153	+	244.485i	−0.731364	+	1.26676i	−0.956300	+	0.292387i	$0.905551\pi$
$194$	106.681	−	12.6195i	0.549904	−	0.0650488i
$195$	246.261			1.26288
$196$		0			0
$197$		−	261.806i		−	1.32896i	−0.747304	−	0.664482i	$-0.768652\pi$
$197$		−	261.806i		−	1.32896i	0.747304	−	0.664482i	$-0.231348\pi$
$198$	202.985	−	24.0113i	1.02518	−	0.121269i
$199$	278.968	+	161.062i	1.40185	+	0.809357i	0.994582	−	0.103953i	$-0.0331492\pi$
$199$	278.968	+	161.062i	1.40185	+	0.809357i	0.407265	+	0.913310i	$0.366482\pi$
$200$	−27.5985	+	160.425i	−0.137992	+	0.802123i
$201$	−209.266	−	362.460i	−1.04113	−	1.80328i
$202$	−165.932	−	71.3031i	−0.821448	−	0.352986i
$203$		0			0
$204$	−13.6062	−	14.3417i	−0.0666970	−	0.0703025i
$205$	−80.5723	+	46.5184i	−0.393036	+	0.226919i
$206$	−180.791	+	134.984i	−0.877626	+	0.655265i
$207$	146.234	+	84.4283i	0.706445	+	0.407866i
$208$	155.450	+	305.286i	0.747357	+	1.46772i
$209$	31.1870			0.149220
$210$		0			0
$211$	169.792			0.804702			0.402351	−	0.915485i	$-0.368193\pi$
$211$	169.792			0.804702			0.402351	+	0.915485i	$0.368193\pi$
$212$	−285.647	−	84.6533i	−1.34739	−	0.399308i
$213$	344.077	+	198.653i	1.61539	+	0.932644i
$214$	172.290	+	230.756i	0.805096	+	1.07830i
$215$	−77.9652	+	45.0133i	−0.362629	+	0.209364i
$216$	−417.571	+	153.957i	−1.93320	+	0.712763i
$217$		0			0
$218$	122.529	+	52.6521i	0.562059	+	0.241523i
$219$	−89.5927	−	155.179i	−0.409099	−	0.708581i
$220$	10.5866	+	44.1219i	0.0481210	+	0.200554i
$221$	17.1867	+	9.92275i	0.0777679	+	0.0448993i
$222$	−16.0359	−	135.563i	−0.0722338	−	0.610643i
$223$		−	45.4626i		−	0.203868i	−0.994791	−	0.101934i	$-0.967497\pi$
$223$		−	45.4626i		−	0.203868i	0.994791	−	0.101934i	$-0.0325031\pi$
$224$		0			0
$225$	395.414			1.75740
$226$	14.2301	−	1.68330i	0.0629652	−	0.00744823i
$227$	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	$0.0329708\pi$
$228$	−122.992	+	29.5108i	−0.539440	+	0.129433i
$229$	−160.173	+	92.4759i	−0.699445	+	0.403825i	−0.807141	−	0.590359i	$-0.798986\pi$
$229$	−160.173	+	92.4759i	−0.699445	+	0.403825i	0.107695	+	0.994184i	$0.465653\pi$
$230$	−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	$0.899870\pi$
$234$	666.819	−	497.869i	2.84966	−	2.12765i
$235$	49.6076	−	85.9228i	0.211096	−	0.365629i
$236$	61.0033	−	205.845i	0.258489	−	0.872223i
$237$		−	161.097i		−	0.679734i
$238$		0			0
$239$			163.185i			0.682782i	0.939921	+	0.341391i	$0.110898\pi$
$239$			163.185i			0.682782i	−0.939921	+	0.341391i	$0.889102\pi$
$240$	−83.5008	−	163.986i	−0.347920	−	0.683274i
$241$	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	$0.0264731\pi$
$242$	111.687	+	149.588i	0.461519	+	0.618133i
$243$	74.2413	+	128.590i	0.305520	+	0.529176i
$244$	−80.7180	+	76.5784i	−0.330812	+	0.313846i
$245$		0			0
$246$	−181.611	+	422.634i	−0.738254	+	1.71802i
$247$	109.962	−	63.4863i	0.445188	−	0.257030i
$248$	272.035	+	46.7993i	1.09692	+	0.188707i
$249$	194.434	−	336.769i	0.780859	−	1.35249i
$250$	22.9803	+	194.269i	0.0919214	+	0.777077i
$251$	159.299			0.634658			0.317329	−	0.948316i	$-0.397214\pi$
$251$	159.299			0.634658			0.317329	+	0.948316i	$0.397214\pi$
$252$		0			0
$253$		−	45.6975i		−	0.180622i
$254$	30.8932	+	261.162i	0.121627	+	1.02820i
$255$	−9.23191	−	5.33005i	−0.0362036	−	0.0209021i
$256$	150.582	−	207.029i	0.588210	−	0.808708i
$257$	107.889	+	186.868i	0.419800	+	0.727114i	0.995919	−	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
$262$	−10.4832	−	14.0406i	−0.0400121	−	0.0535900i
$263$	−285.059	−	164.579i	−1.08387	−	0.625775i	−0.151935	−	0.988391i	$-0.548550\pi$
$263$	−285.059	−	164.579i	−1.08387	−	0.625775i	−0.931939	+	0.362616i	$0.881884\pi$
$264$	172.456	+	143.488i	0.653244	+	0.543515i
$265$	−160.652			−0.606234
$266$		0			0
$267$	−292.419			−1.09520
$268$	89.2097	−	301.022i	0.332872	−	1.12322i
$269$	−253.803	−	146.533i	−0.943507	−	0.544734i	−0.0524492	−	0.998624i	$-0.516703\pi$
$269$	−253.803	−	146.533i	−0.943507	−	0.544734i	−0.891058	+	0.453889i	$0.850036\pi$
$270$	−192.298	+	143.576i	−0.712216	+	0.531764i
$271$	−23.2529	+	13.4251i	−0.0858042	+	0.0495391i	−0.542288	−	0.840193i	$-0.682442\pi$
$271$	−23.2529	+	13.4251i	−0.0858042	+	0.0495391i	0.456484	+	0.889732i	$0.349109\pi$
$272$	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
$276$	43.2413	+	180.217i	0.156671	+	0.652960i
$277$	−289.925	−	167.389i	−1.04666	−	0.604291i	−0.124949	−	0.992163i	$-0.539877\pi$
$277$	−289.925	−	167.389i	−1.04666	−	0.604291i	−0.921713	+	0.387872i	$0.873210\pi$
$278$	−341.860	+	40.4390i	−1.22971	+	0.145464i
$279$		−	670.513i		−	2.40327i
$280$		0			0
$281$	−123.357			−0.438994			−0.219497	−	0.975613i	$-0.570442\pi$
$281$	−123.357			−0.438994			−0.219497	+	0.975613i	$0.570442\pi$
$282$	−57.6259	−	487.152i	−0.204347	−	1.72749i
$283$	−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	$0.167015\pi$
$284$	69.5381	+	289.814i	0.244852	+	1.02047i
$285$	−59.0663	+	34.1019i	−0.207250	+	0.119656i
$286$	−206.917	−	88.9145i	−0.723485	−	0.310890i
$287$		0			0
$288$	−557.634	−	275.222i	−1.93623	−	0.955631i
$289$	144.070	+	249.537i	0.498514	+	0.863451i
$290$	24.3175	+	32.5695i	0.0838534	+	0.112309i
$291$	143.204	−	248.037i	0.492112	−	0.852362i
$292$	38.1932	−	128.876i	0.130799	−	0.441356i
$293$		−	28.2794i		−	0.0965169i	−0.998835	−	0.0482584i	$-0.984633\pi$
$293$		−	28.2794i		−	0.0965169i	0.998835	−	0.0482584i	$-0.0153671\pi$
$294$		0			0
$295$		−	115.770i		−	0.392440i
$296$	65.4951	−	78.7178i	0.221267	−	0.265939i
$297$	146.285	−	253.373i	0.492542	−	0.853108i
$298$	−369.728	+	276.051i	−1.24070	+	0.926347i
$299$	−93.0247	−	161.123i	−0.311119	−	0.538874i
$300$	298.701	+	314.848i	0.995671	+	1.04949i
$301$		0			0
$302$	−271.753	−	116.775i	−0.899844	−	0.386674i
$303$	−417.002	+	240.756i	−1.37624	+	0.794575i
$304$	−79.5608	−	51.6971i	−0.261713	−	0.170056i
$305$	−29.9986	+	51.9591i	−0.0983560	+	0.170358i
$306$	−35.7738	+	4.23172i	−0.116908	+	0.0138292i
$307$	−400.893			−1.30584			−0.652921	−	0.757426i	$-0.726457\pi$
$307$	−400.893			−1.30584			−0.652921	+	0.757426i	$0.726457\pi$
$308$		0			0
$309$			601.542i			1.94674i
$310$	147.815	−	17.4852i	0.476822	−	0.0564039i
$311$	−140.492	−	81.1132i	−0.451743	−	0.260814i	0.256823	−	0.966459i	$-0.417324\pi$
$311$	−140.492	−	81.1132i	−0.451743	−	0.260814i	−0.708566	+	0.705644i	$0.750658\pi$
$312$	900.152	+	154.857i	2.88510	+	0.496336i
$313$	−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	0.225936	−	0.974142i	$-0.427456\pi$
$317$	374.864	−	216.428i	1.18254	−	0.682737i	0.956600	+	0.291405i	$0.0941228\pi$
$318$	−636.476	+	475.214i	−2.00150	+	1.49438i
$319$	−42.9138	−	24.7763i	−0.134526	−	0.0776686i
$320$	46.1311	−	130.108i	0.144160	−	0.406586i
$321$	767.792			2.39187
$322$		0			0
$323$	−5.49636			−0.0170166
$324$	−138.368	+	466.898i	−0.427062	+	1.44104i
$325$	−377.305	−	217.837i	−1.16094	−	0.670269i
$326$	−59.0005	−	79.0220i	−0.180983	−	0.242399i
$327$	307.925	−	177.781i	0.941668	−	0.543672i
$328$	−323.766	+	119.371i	−0.987092	+	0.363937i
$329$		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	$0.872501\pi$
$332$	283.659	−	68.0611i	0.854394	−	0.205003i
$333$	−215.420	−	124.373i	−0.646907	−	0.373492i
$334$	56.7290	+	479.571i	0.169847	+	1.43584i
$335$		−	169.299i		−	0.505370i
$336$		0			0
$337$	−69.4941			−0.206214			−0.103107	−	0.994670i	$-0.532878\pi$
$337$	−69.4941			−0.206214			−0.103107	+	0.994670i	$0.532878\pi$
$338$	−574.902	+	68.0059i	−1.70089	+	0.201201i
$339$	19.1019	−	33.0855i	0.0563479	−	0.0975974i
$340$	−1.86577	−	7.77598i	−0.00548756	−	0.0228705i
$341$	−157.149	+	90.7300i	−0.460848	+	0.266071i
$342$	−90.9938	+	211.756i	−0.266064	+	0.619168i
$343$		0			0
$344$	−313.290	+	115.509i	−0.910727	+	0.335781i
$345$	49.9686	+	86.5481i	0.144836	+	0.250864i
$346$	87.2145	−	65.1172i	0.252065	−	0.188200i
$347$	174.677	−	302.549i	0.503391	−	0.871899i	−0.496601	−	0.867979i	$-0.665419\pi$
$347$	174.677	−	302.549i	0.503391	−	0.871899i	0.999992	−	0.00392020i	$-0.00124784\pi$
$348$	192.683	+	57.1029i	0.553688	+	0.164089i
$349$			165.836i			0.475174i	0.971366	+	0.237587i	$0.0763566\pi$
$349$			165.836i			0.475174i	−0.971366	+	0.237587i	$0.923643\pi$
$350$		0			0
$351$		−	1191.15i		−	3.39358i
$352$	10.9517	+	167.935i	0.0311129	+	0.477088i
$353$	−235.858	+	408.519i	−0.668154	+	1.15728i	0.310266	+	0.950650i	$0.399582\pi$
$353$	−235.858	+	408.519i	−0.668154	+	1.15728i	−0.978420	+	0.206627i	$0.933751\pi$
$354$	−342.451	−	458.661i	−0.967377	−	1.29565i
$355$	80.3566	+	139.182i	0.226356	+	0.392061i
$356$	−150.976	−	159.137i	−0.424089	−	0.447014i
$357$		0			0
$358$	100.296	−	233.403i	0.280157	−	0.651964i
$359$	568.967	−	328.493i	1.58487	−	0.915022i	0.590731	−	0.806869i	$-0.298839\pi$
$359$	568.967	−	328.493i	1.58487	−	0.915022i	0.994134	−	0.108154i	$-0.0344939\pi$
$360$	−330.470	−	56.8520i	−0.917971	−	0.157922i
$361$	162.917	−	282.180i	0.451294	−	0.781663i
$362$	−49.9737	−	422.463i	−0.138049	−	1.16703i
$363$	497.722			1.37113
$364$		0			0
$365$		−	72.4817i		−	0.198580i
$366$	34.8474	+	294.590i	0.0952115	+	0.804890i
$367$	307.850	+	177.737i	0.838829	+	0.484298i	0.856866	−	0.515539i	$-0.172408\pi$
$367$	307.850	+	177.737i	0.838829	+	0.484298i	−0.0180371	+	0.999837i	$0.505742\pi$
$368$	−75.7502	+	116.578i	−0.205843	+	0.316788i
$369$	419.109	+	725.918i	1.13580	+	1.96726i
$370$	21.8004	−	50.7327i	0.0589201	−	0.137116i
$371$		0			0
$372$	533.895	−	506.514i	1.43520	−	1.36160i
$373$	−273.662	+	157.999i	−0.733680	+	0.423590i	−0.819767	−	0.572698i	$-0.805897\pi$
$373$	−273.662	+	157.999i	−0.733680	+	0.423590i	0.0860872	+	0.996288i	$0.472564\pi$
$374$	5.83250	+	7.81173i	0.0155949	+	0.0208870i
$375$	451.682	+	260.779i	1.20449	+	0.695410i
$376$	235.360	−	282.877i	0.625958	−	0.752332i
$377$	−201.745			−0.535132
$378$		0			0
$379$	−178.404			−0.470723			−0.235361	−	0.971908i	$-0.575627\pi$
$379$	−178.404			−0.470723			−0.235361	+	0.971908i	$0.575627\pi$
$380$	−49.0544	−	14.5376i	−0.129091	−	0.0382568i
$381$	607.211	+	350.574i	1.59373	+	0.920140i
$382$	−64.9604	+	48.5016i	−0.170053	+	0.126968i
$383$	604.832	−	349.200i	1.57920	−	0.911750i	0.584225	−	0.811591i	$-0.301398\pi$
$383$	604.832	−	349.200i	1.57920	−	0.911750i	0.994972	−	0.100158i	$-0.0319349\pi$
$384$	−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
$388$	208.920	−	50.1284i	0.538455	−	0.129197i
$389$	−151.865	−	87.6790i	−0.390397	−	0.225396i	0.291935	−	0.956438i	$-0.405701\pi$
$389$	−151.865	−	87.6790i	−0.390397	−	0.225396i	−0.682332	+	0.731042i	$0.739034\pi$
$390$	489.112	−	57.8577i	1.25413	−	0.148353i
$391$			8.05366i			0.0205976i
$392$		0			0
$393$	−46.7170			−0.118873
$394$	−61.5099	−	519.987i	−0.156117	−	1.31976i
$395$	32.5824	−	56.4344i	0.0824871	−	0.142872i
$396$	397.517	−	95.3803i	1.00383	−	0.240859i
$397$	−334.033	+	192.854i	−0.841393	+	0.485778i	−0.857737	−	0.514088i	$-0.828130\pi$
$397$	−334.033	+	192.854i	−0.841393	+	0.485778i	0.0163447	+	0.999866i	$0.494797\pi$
$398$	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	$-0.394938\pi$
$402$	−500.792	−	670.734i	−1.24575	−	1.66849i
$403$	−369.392	+	639.805i	−0.916605	+	1.58761i
$404$	−346.319	−	102.634i	−0.857226	−	0.254044i
$405$			262.590i			0.648371i
$406$		0			0
$407$			67.3178i			0.165400i
$408$	−30.3935	−	25.2881i	−0.0744938	−	0.0619807i
$409$	−211.872	+	366.973i	−0.518025	+	0.897245i	0.481756	+	0.876305i	$0.339999\pi$
$409$	−211.872	+	366.973i	−0.518025	+	0.897245i	−0.999781	+	0.0209399i	$0.993334\pi$
$410$	−149.100	+	111.323i	−0.363658	+	0.271519i
$411$	−631.447	−	1093.70i	−1.53637	−	2.66107i
$412$	−327.364	+	310.576i	−0.794574	+	0.753824i
$413$		0			0
$414$	310.279	+	133.331i	0.749467	+	0.322055i
$415$	136.225	−	78.6498i	0.328254	−	0.189517i
$416$	380.473	+	569.823i	0.914599	+	1.36977i
$417$	−458.898	+	794.834i	−1.10047	+	1.90608i
$418$	61.9422	−	7.32723i	0.148187	−	0.0175292i
$419$	−295.598			−0.705485			−0.352742	−	0.935721i	$-0.614751\pi$
$419$	−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	$0.952088\pi$
$422$	337.233	−	39.8917i	0.799131	−	0.0945302i
$423$	−774.124	−	446.941i	−1.83008	−	1.05660i
$424$	−587.228	−	101.023i	−1.38497	−	0.238262i
$425$	9.42970	+	16.3327i	0.0221875	+	0.0384299i
$426$	730.063	+	313.716i	1.71376	+	0.736424i
$427$		0			0
$428$	396.410	+	417.839i	0.926192	+	0.976259i
$429$	−519.999	+	300.221i	−1.21212	+	0.699817i
$430$	−144.275	+	107.721i	−0.335524	+	0.250513i
$431$	220.198	+	127.131i	0.510900	+	0.294968i	0.733204	−	0.680009i	$-0.238024\pi$
$431$	220.198	+	127.131i	0.510900	+	0.294968i	−0.222303	+	0.974978i	$0.571358\pi$
$432$	−793.188	+	403.887i	−1.83608	+	0.934925i
$433$	−546.301			−1.26167			−0.630833	−	0.775919i	$-0.717287\pi$
$433$	−546.301			−1.26167			−0.630833	+	0.775919i	$0.717287\pi$
$434$		0			0
$435$	108.368			0.249122
$436$	255.731	+	75.7876i	0.586540	+	0.173825i
$437$	44.6244	+	25.7639i	0.102115	+	0.0589563i
$438$	−214.403	−	287.160i	−0.489505	−	0.655617i
$439$	236.715	−	136.667i	0.539214	−	0.311315i	−0.205546	−	0.978647i	$-0.565897\pi$
$439$	236.715	−	136.667i	0.539214	−	0.311315i	0.744760	+	0.667332i	$0.232564\pi$
$440$	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	$-0.346678\pi$
$444$	−63.6995	−	265.481i	−0.143467	−	0.597930i
$445$	−102.438	−	59.1427i	−0.230198	−	0.132905i
$446$	−10.6812	−	90.2957i	−0.0239489	−	0.202457i
$447$			1230.19i			2.75210i
$448$		0			0
$449$	782.101			1.74187			0.870936	−	0.491396i	$-0.163513\pi$
$449$	782.101			1.74187			0.870936	+	0.491396i	$0.163513\pi$
$450$	785.353	−	92.9004i	1.74523	−	0.206445i
$451$	113.423	−	196.454i	0.251492	−	0.435597i
$452$	27.8677	−	6.68658i	0.0616542	−	0.0147933i
$453$	−682.938	+	394.294i	−1.50759	+	0.870407i
$454$	146.181	−	340.183i	0.321984	−	0.749302i
$455$		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	$0.766835\pi$
$458$	−296.401	+	221.303i	−0.647164	+	0.483194i
$459$	−25.7811	+	44.6541i	−0.0561679	+	0.0972857i
$460$	−21.3015	+	71.8781i	−0.0463076	+	0.156257i
$461$		−	202.533i		−	0.439335i	−0.975575	−	0.219667i	$-0.929503\pi$
$461$		−	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	$0.750900\pi$
$464$	68.4064	+	134.342i	0.147428	+	0.289531i
$465$	198.420	−	343.674i	0.426710	−	0.739084i
$466$	−115.707	−	154.971i	−0.248298	−	0.332556i
$467$	272.725	+	472.373i	0.583993	+	1.01150i	0.995000	+	0.0998730i	$0.0318437\pi$
$467$	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
$472$	72.7998	−	423.171i	0.154237	−	0.896549i
$473$	109.753	−	190.098i	0.232036	−	0.401898i
$474$	−37.8489	−	319.963i	−0.0798499	−	0.675028i
$475$	120.663			0.254028
$476$		0			0
$477$			1447.40i			3.03438i
$478$	38.3394	+	324.110i	0.0802079	+	0.678054i
$479$	94.3079	+	54.4487i	0.196885	+	0.113672i	0.595202	−	0.803576i	$-0.297072\pi$
$479$	94.3079	+	54.4487i	0.196885	+	0.113672i	−0.398317	+	0.917248i	$0.630405\pi$
$480$	−204.373	−	306.083i	−0.425777	−	0.637672i
$481$	137.036	+	237.354i	0.284899	+	0.493459i
$482$	162.257	−	377.596i	0.336633	−	0.783394i
$483$		0			0
$484$	256.973	+	270.865i	0.530937	+	0.559637i
$485$	100.333	−	57.9272i	0.206872	−	0.119437i
$486$	177.666	+	237.956i	0.365568	+	0.489622i
$487$	371.831	+	214.677i	0.763513	+	0.440814i	0.830556	−	0.556936i	$-0.188023\pi$
$487$	371.831	+	214.677i	0.763513	+	0.440814i	−0.0670428	+	0.997750i	$0.521356\pi$
$488$	−142.327	+	171.061i	−0.291653	+	0.350534i
$489$	−262.929			−0.537686
$490$		0			0
$491$	453.887			0.924413			0.462206	−	0.886772i	$-0.347058\pi$
$491$	453.887			0.924413			0.462206	+	0.886772i	$0.347058\pi$
$492$	−261.411	+	882.083i	−0.531323	+	1.79285i
$493$	7.56306	+	4.36654i	0.0153409	+	0.00885707i
$494$	203.485	−	151.928i	0.411912	−	0.307547i
$495$	190.905	−	110.219i	0.385667	−	0.222665i
$496$	551.299	+	29.0374i	1.11149	+	0.0585431i
$497$		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	$0.941754\pi$
$500$	91.2849	+	380.449i	0.182570	+	0.760898i
$501$	1115.02	+	643.755i	2.22558	+	1.28494i
$502$	316.392	−	37.4265i	0.630264	−	0.0745547i
$503$			580.170i			1.15342i	0.816949	+	0.576710i	$0.195664\pi$
$503$			580.170i			1.15342i	−0.816949	+	0.576710i	$0.804336\pi$
$504$		0			0
$505$	−194.775			−0.385693
$506$	−10.7364	−	90.7621i	−0.0212181	−	0.179372i
$507$	−771.724	+	1336.67i	−1.52214	+	2.63642i
$508$	122.717	+	511.450i	0.241570	+	1.00679i
$509$	266.271	−	153.732i	0.523126	−	0.302027i	−0.215087	−	0.976595i	$-0.569003\pi$
$509$	266.271	−	153.732i	0.523126	−	0.302027i	0.738213	+	0.674568i	$0.235670\pi$
$510$	−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
$514$	258.187	+	345.801i	0.502309	+	0.672765i
$515$	−121.664	+	210.728i	−0.236241	+	0.409181i
$516$	−252.952	+	853.542i	−0.490218	+	1.65415i
$517$			241.910i			0.467911i
$518$		0			0
$519$		−	290.187i		−	0.559127i
$520$	284.015	+	236.307i	0.546182	+	0.454437i
$521$	360.480	−	624.369i	0.691899	−	1.19840i	−0.279316	−	0.960199i	$-0.590108\pi$
$521$	360.480	−	624.369i	0.691899	−	1.19840i	0.971215	−	0.238205i	$-0.0765591\pi$
$522$	293.436	−	219.089i	0.562138	−	0.419711i
$523$	−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
$528$	376.236	+	244.471i	0.712569	+	0.463013i
$529$	−226.749	+	392.741i	−0.428637	+	0.742421i
$530$	−319.080	+	37.7443i	−0.602037	+	0.0712157i
$531$	−1043.03			−1.96428
$532$		0			0
$533$		−	923.564i		−	1.73277i
$534$	−580.788	+	68.7022i	−1.08762	+	0.128656i
$535$	268.967	+	155.288i	0.502743	+	0.290259i
$536$	106.461	−	618.835i	0.198621	−	1.15454i
$537$	−338.652	−	586.562i	−0.630636	−	1.09229i
$538$	−538.520	−	231.408i	−1.00097	−	0.430127i
$539$		0			0
$540$	−348.201	+	330.344i	−0.644817	+	0.611748i
$541$	−785.695	+	453.621i	−1.45230	+	0.838486i	−0.998612	−	0.0526734i	$-0.983226\pi$
$541$	−785.695	+	453.621i	−1.45230	+	0.838486i	−0.453689	+	0.891160i	$0.649892\pi$
$542$	−43.0297	+	32.1274i	−0.0793907	+	0.0592757i
$543$	−982.241	−	567.097i	−1.80891	−	1.04438i
$544$	−1.93012	−	29.5966i	−0.00354801	−	0.0544055i
$545$	143.827			0.263903
$546$		0			0
$547$	−557.327			−1.01888			−0.509439	−	0.860506i	$-0.670147\pi$
$547$	−557.327			−1.01888			−0.509439	+	0.860506i	$0.670147\pi$
$548$	269.185	−	908.314i	0.491213	−	1.65751i
$549$	468.127	+	270.273i	0.852690	+	0.492301i
$550$	−128.043	−	171.494i	−0.232805	−	0.311807i
$551$	48.3889	−	27.9374i	0.0878202	−	0.0507030i
$552$	128.225	+	347.779i	0.232291	+	0.630035i
$553$		0			0
$554$	−615.163	−	264.343i	−1.11040	−	0.477153i
$555$	−73.6096	−	127.496i	−0.132630	−	0.229722i
$556$	−669.484	+	160.636i	−1.20411	+	0.288914i
$557$	741.896	+	428.334i	1.33195	+	0.769002i	0.985598	−	0.169103i	$-0.0540869\pi$
$557$	741.896	+	428.334i	1.33195	+	0.769002i	0.346352	+	0.938105i	$0.387420\pi$
$558$	−157.533	−	1331.74i	−0.282318	−	2.38663i
$559$		−	893.680i		−	1.59871i
$560$		0			0
$561$	25.9918			0.0463313
$562$	−245.006	+	28.9821i	−0.435954	+	0.0515696i
$563$	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	$0.162797\pi$
$564$	−228.908	−	954.020i	−0.405865	−	1.69152i
$565$	13.3833	−	7.72686i	0.0236873	−	0.0136759i
$566$	−0.488693	+	1.13726i	−0.000863416	+	0.00200929i
$567$		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	$0.424164\pi$
$570$	−109.303	+	81.6090i	−0.191759	+	0.143174i
$571$	−359.549	+	622.757i	−0.629683	+	1.09064i	0.357932	+	0.933747i	$0.383482\pi$
$571$	−359.549	+	622.757i	−0.629683	+	1.09064i	−0.987615	+	0.156895i	$0.949852\pi$
$572$	−431.858	−	127.984i	−0.754997	−	0.223748i
$573$			216.142i			0.377210i
$574$		0			0
$575$		−	176.805i		−	0.307486i
$576$	−1172.21	−	415.620i	−2.03508	−	0.721562i
$577$	−515.560	+	892.976i	−0.893518	+	1.54762i	−0.0578905	+	0.998323i	$0.518437\pi$
$577$	−515.560	+	892.976i	−0.893518	+	1.54762i	−0.835628	+	0.549296i	$0.814896\pi$
$578$	344.773	+	461.771i	0.596494	+	0.798911i
$579$	752.665	+	1303.65i	1.29994	+	2.25156i
$580$	55.9503	+	58.9748i	0.0964660	+	0.101681i
$581$		0			0
$582$	226.151	−	526.285i	0.388575	−	0.904270i
$583$	339.229	−	195.854i	0.581868	−	0.335942i
$584$	45.5788	−	264.941i	0.0780459	−	0.453666i
$585$	448.738	−	777.238i	0.767074	−	1.32861i
$586$	−6.64410	−	56.1673i	−0.0113381	−	0.0958486i
$587$	671.907			1.14464			0.572322	−	0.820029i	$-0.306043\pi$
$587$	671.907			1.14464			0.572322	+	0.820029i	$0.306043\pi$
$588$		0			0
$589$		−	204.612i		−	0.347388i
$590$	−27.1995	−	229.937i	−0.0461009	−	0.389723i
$591$	−1208.99	−	698.008i	−2.04566	−	1.18106i
$592$	111.589	−	171.733i	0.188495	−	0.290090i
$593$	176.999	+	306.572i	0.298481	+	0.516984i	0.975789	−	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
$598$	−222.616	−	298.160i	−0.372268	−	0.498595i
$599$	−983.923	−	568.068i	−1.64261	−	0.948361i	−0.979901	−	0.199484i	$-0.936074\pi$
$599$	−983.923	−	568.068i	−1.64261	−	0.948361i	−0.662708	−	0.748878i	$-0.730593\pi$
$600$	667.238	+	555.158i	1.11206	+	0.925264i
$601$	6.80783			0.0113275			0.00566375	−	0.999984i	$-0.498197\pi$
$601$	6.80783			0.0113275			0.00566375	+	0.999984i	$0.498197\pi$
$602$		0			0
$603$	−1525.30			−2.52953
$604$	−567.179	−	168.087i	−0.939037	−	0.278290i
$605$	174.358	+	100.666i	0.288196	+	0.166390i
$606$	−771.665	+	576.151i	−1.27337	+	0.950744i
$607$	−386.628	+	223.220i	−0.636948	+	0.367742i	−0.783438	−	0.621470i	$-0.786536\pi$
$607$	−386.628	+	223.220i	−0.636948	+	0.367742i	0.146490	+	0.989212i	$0.453202\pi$
$608$	−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
$612$	−70.0579	+	16.8097i	−0.114474	+	0.0274668i
$613$	555.650	+	320.805i	0.906443	+	0.523335i	0.879285	−	0.476296i	$-0.158021\pi$
$613$	555.650	+	320.805i	0.906443	+	0.523335i	0.0271583	+	0.999631i	$0.491354\pi$
$614$	−796.235	+	94.1877i	−1.29680	+	0.153400i
$615$			496.096i			0.806661i
$616$		0			0
$617$	−502.890			−0.815057			−0.407528	−	0.913193i	$-0.633609\pi$
$617$	−502.890			−0.815057			−0.407528	+	0.913193i	$0.633609\pi$
$618$	141.329	+	1194.75i	0.228688	+	1.93326i
$619$	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	$0.0529336\pi$
$620$	289.475	−	69.4565i	0.466894	−	0.112027i
$621$	418.627	−	241.695i	0.674118	−	0.389202i
$622$	−298.096	−	128.095i	−0.479254	−	0.205941i
$623$		0			0
$624$	1824.22	+	96.0833i	2.92343	+	0.153980i
$625$	−148.859	−	257.831i	−0.238174	−	0.412530i
$626$	−318.575	−	426.682i	−0.508906	−	0.681601i
$627$	83.1486	−	144.018i	0.132613	−	0.229693i
$628$	−440.385	−	130.511i	−0.701250	−	0.207820i
$629$		−	11.8640i		−	0.0188617i
$630$		0			0
$631$		−	238.957i		−	0.378695i	−0.981910	−	0.189348i	$-0.939363\pi$
$631$		−	238.957i		−	0.378695i	0.981910	−	0.189348i	$-0.0606373\pi$
$632$	154.585	−	185.794i	0.244597	−	0.293978i
$633$	452.687	−	784.078i	0.715146	−	1.23867i
$634$	693.688	−	517.930i	1.09414	−	0.816925i
$635$	141.809	+	245.621i	0.223322	+	0.386805i
$636$	−1152.49	+	1093.38i	−1.81209	+	1.71916i
$637$		0			0
$638$	−91.0543	−	39.1271i	−0.142718	−	0.0613277i
$639$	1253.96	−	723.974i	1.96238	−	1.13298i
$640$	61.0554	−	269.252i	0.0953991	−	0.420706i
$641$	3.98065	−	6.89469i	0.00621006	−	0.0107561i	−0.862904	−	0.505368i	$-0.831357\pi$
$641$	3.98065	−	6.89469i	0.00621006	−	0.0107561i	0.869114	+	0.494612i	$0.164690\pi$
$642$	1524.95	−	180.388i	2.37531	−	0.280979i
$643$	584.919			0.909672			0.454836	−	0.890575i	$-0.349698\pi$
$643$	584.919			0.909672			0.454836	+	0.890575i	$0.349698\pi$
$644$		0			0
$645$			480.044i			0.744255i
$646$	−10.9166	+	1.29134i	−0.0168988	+	0.00199898i
$647$	290.707	+	167.840i	0.449316	+	0.259413i	0.707541	−	0.706672i	$-0.249804\pi$
$647$	290.707	+	167.840i	0.449316	+	0.259413i	−0.258225	+	0.966085i	$0.583138\pi$
$648$	−165.125	+	959.840i	−0.254823	+	1.48123i
$649$	141.137	+	244.457i	0.217469	+	0.376667i
$650$	−800.566	−	344.012i	−1.23164	−	0.529250i
$651$		0			0
$652$	−135.750	−	143.088i	−0.208205	−	0.219460i
$653$	42.0252	−	24.2632i	0.0643571	−	0.0371566i	−0.467476	−	0.884006i	$-0.654837\pi$
$653$	42.0252	−	24.2632i	0.0643571	−	0.0371566i	0.531833	+	0.846849i	$0.321503\pi$
$654$	569.818	−	425.445i	0.871281	−	0.650528i
$655$	−16.3656	−	9.44866i	−0.0249856	−	0.0144254i
$656$	−615.003	+	313.157i	−0.937505	+	0.477373i
$657$	−653.026			−0.993951
$658$		0			0
$659$	1224.65			1.85835			0.929176	−	0.369638i	$-0.120518\pi$
$659$	1224.65			1.85835			0.929176	+	0.369638i	$0.120518\pi$
$660$	231.974	+	68.7470i	0.351476	+	0.104162i
$661$	−725.765	−	419.021i	−1.09798	−	0.633919i	−0.162291	−	0.986743i	$-0.551888\pi$
$661$	−725.765	−	419.021i	−1.09798	−	0.633919i	−0.935690	+	0.352823i	$0.885222\pi$
$662$	−97.2226	−	130.215i	−0.146862	−	0.196699i
$663$	91.6439	−	52.9106i	0.138226	−	0.0798049i
$664$	547.399	−	201.824i	0.824396	−	0.303951i
$665$		0			0
$666$	−457.078	−	196.412i	−0.686303	−	0.294912i
$667$	−40.9358	−	70.9029i	−0.0613730	−	0.106301i
$668$	225.345	+	939.172i	0.337343	+	1.40595i
$669$	−209.940	−	121.209i	−0.313812	−	0.181180i
$670$	−39.7759	−	336.254i	−0.0593670	−	0.501871i
$671$		−	146.287i		−	0.218014i
$672$		0			0
$673$	147.714			0.219486			0.109743	−	0.993960i	$-0.464997\pi$
$673$	147.714			0.219486			0.109743	+	0.993960i	$0.464997\pi$
$674$	−138.026	+	16.3273i	−0.204786	+	0.0242244i
$675$	565.980	−	980.307i	0.838490	−	1.45231i
$676$	−1125.87	+	270.140i	−1.66548	+	0.399616i
$677$	725.024	−	418.593i	1.07094	−	0.618305i	0.142499	−	0.989795i	$-0.454486\pi$
$677$	725.024	−	418.593i	1.07094	−	0.618305i	0.928437	+	0.371490i	$0.121153\pi$
$678$	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
$682$	−290.805	+	217.125i	−0.426401	+	0.318365i
$683$	32.2189	−	55.8047i	0.0471725	−	0.0817053i	−0.841475	−	0.540296i	$-0.818312\pi$
$683$	32.2189	−	55.8047i	0.0471725	−	0.0817053i	0.888648	+	0.458591i	$0.151646\pi$
$684$	−130.977	+	441.957i	−0.191486	+	0.646136i
$685$		−	510.849i		−	0.745765i
$686$		0			0
$687$			986.210i			1.43553i
$688$	−595.104	+	303.024i	−0.864976	+	0.440442i
$689$	797.385	−	1381.11i	1.15731	−	2.00452i
$690$	119.579	+	160.158i	0.173303	+	0.232113i
$691$	−263.374	−	456.177i	−0.381149	−	0.660169i	0.610078	−	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
$696$	396.115	+	68.1452i	0.569130	+	0.0979098i
$697$	−19.9895	+	34.6229i	−0.0286794	+	0.0496741i
$698$	38.9622	+	329.375i	0.0558198	+	0.471884i
$699$	−515.633			−0.737672
$700$		0			0
$701$		−	695.486i		−	0.992134i	−0.868284	−	0.496067i	$-0.834777\pi$
$701$		−	695.486i		−	0.992134i	0.868284	−	0.496067i	$-0.165223\pi$
$702$	−279.854	−	2365.80i	−0.398652	−	3.37009i
$703$	−65.7370	−	37.9532i	−0.0935092	−	0.0539875i
$704$	61.2072	+	330.971i	0.0869420	+	0.470130i
$705$	−264.520	−	458.162i	−0.375206	−	0.649876i
$706$	−372.471	+	866.794i	−0.527580	+	1.22775i
$707$		0			0
$708$	−787.920	−	830.513i	−1.11288	−	1.17304i
$709$	−803.161	+	463.705i	−1.13281	+	0.654027i	−0.944640	−	0.328110i	$-0.893588\pi$
$709$	−803.161	+	463.705i	−1.13281	+	0.654027i	−0.188168	+	0.982137i	$0.560255\pi$
$710$	192.300	+	257.557i	0.270846	+	0.362756i
$711$	−508.447	−	293.552i	−0.715115	−	0.412872i
$712$	−337.249	−	280.599i	−0.473664	−	0.394100i
$713$	−299.812			−0.420493
$714$		0			0
$715$	−242.883			−0.339697
$716$	144.366	−	487.138i	0.201629	−	0.680361i
$717$	753.566	+	435.071i	1.05100	+	0.606794i
$718$	1052.88	−	786.113i	1.46640	−	1.09486i
$719$	1150.37	−	664.169i	1.59996	−	0.923739i	0.608471	−	0.793576i	$-0.291783\pi$
$719$	1150.37	−	664.169i	1.59996	−	0.923739i	0.991493	−	0.130163i	$-0.0415501\pi$
$720$	−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
$724$	−198.511	−	827.335i	−0.274186	−	1.14273i
$725$	−166.034	−	95.8600i	−0.229013	−	0.132221i
$726$	988.551	−	116.937i	1.36164	−	0.161070i
$727$			539.401i			0.741954i	0.928642	+	0.370977i	$0.120977\pi$
$727$			539.401i			0.741954i	−0.928642	+	0.370977i	$0.879023\pi$
$728$		0			0
$729$	−303.936			−0.416922
$730$	−17.0292	−	143.960i	−0.0233277	−	0.197205i
$731$	−19.3427	+	33.5026i	−0.0264606	+	0.0458311i
$732$	138.425	+	576.913i	0.189105	+	0.788133i
$733$	382.859	−	221.044i	0.522318	−	0.301561i	−0.215564	−	0.976490i	$-0.569159\pi$
$733$	382.859	−	221.044i	0.522318	−	0.301561i	0.737883	+	0.674929i	$0.235826\pi$
$734$	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
$738$	1002.96	+	1343.32i	1.35903	+	1.82021i
$739$	574.116	−	994.398i	0.776882	−	1.34560i	−0.156848	−	0.987623i	$-0.550133\pi$
$739$	574.116	−	994.398i	0.776882	−	1.34560i	0.933730	−	0.357977i	$-0.116533\pi$
$740$	31.3796	−	105.885i	0.0424049	−	0.143088i
$741$		−	677.050i		−	0.913698i
$742$		0			0
$743$		−	588.688i		−	0.792313i	−0.918183	−	0.396156i	$-0.870344\pi$
$743$		−	588.688i		−	0.792313i	0.918183	−	0.396156i	$-0.129656\pi$
$744$	941.394	−	1131.45i	1.26531	−	1.52077i
$745$	−248.810	+	430.952i	−0.333973	+	0.578459i
$746$	−506.414	+	378.106i	−0.678840	+	0.506844i
$747$	−708.597	−	1227.33i	−0.948590	−	1.64301i
$748$	13.4196	+	14.1450i	0.0179406	+	0.0189104i
$749$		0			0
$750$	958.378	+	411.826i	1.27784	+	0.549101i
$751$	708.754	−	409.199i	0.943747	−	0.544873i	0.0526140	−	0.998615i	$-0.483245\pi$
$751$	708.754	−	409.199i	0.943747	−	0.544873i	0.891133	+	0.453742i	$0.149911\pi$
$752$	401.001	−	617.133i	0.533246	−	0.820656i
$753$	424.712	−	735.622i	0.564026	−	0.976922i
$754$	−400.695	+	47.3988i	−0.531426	+	0.0628631i
$755$	−318.989			−0.422503
$756$		0			0
$757$			105.101i			0.138838i	0.997588	+	0.0694192i	$0.0221146\pi$
$757$			105.101i			0.138838i	−0.997588	+	0.0694192i	$0.977885\pi$
$758$	−354.337	+	41.9150i	−0.467464	+	0.0552969i
$759$	−211.025	−	121.835i	−0.278030	−	0.160521i
$760$	−100.845	−	17.3488i	−0.132691	−	0.0228274i
$761$	507.117	+	878.352i	0.666382	+	1.15421i	0.978909	+	0.204299i	$0.0654913\pi$
$761$	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
$766$	1119.25	−	835.667i	1.46116	−	1.09095i
$767$	995.264	+	574.616i	1.29761	+	0.749173i
$768$	−554.564	−	1247.33i	−0.722089	−	1.62413i
$769$	1183.99			1.53964			0.769822	−	0.638258i	$-0.220345\pi$
$769$	1183.99			1.53964			0.769822	+	0.638258i	$0.220345\pi$
$770$		0			0
$771$	1150.58			1.49232
$772$	−320.860	+	1082.68i	−0.415621	+	1.40244i
$773$	280.862	+	162.156i	0.363340	+	0.209774i	0.670545	−	0.741869i	$-0.266060\pi$
$773$	280.862	+	162.156i	0.363340	+	0.209774i	−0.307205	+	0.951643i	$0.599394\pi$
$774$	970.512	+	1299.85i	1.25389	+	1.67939i
$775$	−608.014	+	351.037i	−0.784534	+	0.452951i
$776$	403.170	−	148.647i	0.519550	−	0.191556i
$777$		0			0
$778$	−322.226	−	138.464i	−0.414172	−	0.177975i
$779$	127.894	+	221.519i	0.164177	+	0.284363i
$780$	957.858	−	229.828i	1.22802	−	0.294652i
$781$	−339.358	−	195.928i	−0.434517	−	0.250869i
$782$	1.89216	+	15.9958i	0.00241965	+	0.0204550i
$783$		−	524.168i		−	0.669436i
$784$		0			0
$785$	−247.679			−0.315514
$786$	−92.7870	+	10.9759i	−0.118050	+	0.0139642i
$787$	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	$0.112094\pi$
$788$	−244.336	−	1018.32i	−0.310071	−	1.29229i
$789$	−1520.01	+	877.576i	−1.92650	+	1.11226i
$790$	51.4547	−	119.742i	0.0651325	−	0.151573i
$791$		0			0
$792$	767.121	−	282.834i	0.968587	−	0.357114i
$793$	−297.792	−	515.791i	−0.375526	−	0.650429i
$794$	−618.130	+	461.517i	−0.778502	+	0.581255i
$795$	−428.319	+	741.870i	−0.538766	+	0.933170i
$796$	1235.39	+	366.115i	1.55199	+	0.459943i
$797$		−	1502.06i		−	1.88465i	−0.334705	−	0.942323i	$-0.608637\pi$
$797$		−	1502.06i		−	1.88465i	0.334705	−	0.942323i	$-0.391363\pi$
$798$		0			0
$799$		−	42.6339i		−	0.0533591i
$800$	42.3725	+	649.744i	0.0529656	+	0.812180i
$801$	−532.848	+	922.919i	−0.665228	+	1.15221i
$802$	−630.694	−	844.718i	−0.786402	−	1.05326i
$803$	88.3638	+	153.051i	0.110042	+	0.190599i
$804$	−1152.24	−	1214.52i	−1.43313	−	1.51060i
$805$		0			0
$806$	−583.349	+	1357.54i	−0.723758	+	1.68429i
$807$	−1353.34	+	781.354i	−1.67701	+	0.968220i
$808$	−711.956	−	122.481i	−0.881134	−	0.151585i
$809$	−35.3793	+	61.2788i	−0.0437322	+	0.0757464i	−0.887063	−	0.461648i	$-0.847258\pi$
$809$	−35.3793	+	61.2788i	−0.0437322	+	0.0757464i	0.843331	+	0.537395i	$0.180591\pi$
$810$	61.6942	+	521.545i	0.0761657	+	0.643882i
$811$	−5.94522			−0.00733072			−0.00366536	−	0.999993i	$-0.501167\pi$
$811$	−5.94522			−0.00733072			−0.00366536	+	0.999993i	$0.501167\pi$
$812$		0			0
$813$			143.172i			0.176103i
$814$	15.8159	+	133.703i	0.0194299	+	0.164255i
$815$	−92.1073	−	53.1782i	−0.113015	−	0.0652493i
$816$	−66.3074	−	43.0852i	−0.0812590	−	0.0528005i
$817$	123.756	+	214.351i	0.151476	+	0.262364i
$818$	−334.592	+	778.643i	−0.409037	+	0.951886i
$819$		0			0
$820$	−269.980	+	256.134i	−0.329244	+	0.312359i
$821$	13.1159	−	7.57244i	0.0159755	−	0.00922344i	−0.491991	−	0.870600i	$-0.663731\pi$
$821$	13.1159	−	7.57244i	0.0159755	−	0.00922344i	0.507966	+	0.861377i	$0.330397\pi$
$822$	−1511.11	−	2023.90i	−1.83833	−	2.46216i
$823$	1284.10	+	741.378i	1.56027	+	0.900824i	0.997229	+	0.0743964i	$0.0237030\pi$
$823$	1284.10	+	741.378i	1.56027	+	0.900824i	0.563044	+	0.826427i	$0.309630\pi$
$824$	−577.227	+	693.763i	−0.700519	+	0.841945i
$825$	−570.607			−0.691645
$826$		0			0
$827$	−74.3070			−0.0898513			−0.0449257	−	0.998990i	$-0.514305\pi$
$827$	−74.3070			−0.0898513			−0.0449257	+	0.998990i	$0.514305\pi$
$828$	647.587	+	191.916i	0.782110	+	0.231783i
$829$	123.722	+	71.4311i	0.149243	+	0.0861654i	0.572762	−	0.819722i	$-0.305872\pi$
$829$	123.722	+	71.4311i	0.149243	+	0.0861654i	−0.423519	+	0.905887i	$0.639205\pi$
$830$	252.086	−	188.216i	0.303718	−	0.226766i
$831$	−1545.96	+	892.558i	−1.86036	+	1.07408i
$832$	889.555	+	1042.36i	1.06918	+	1.25284i
$833$		0			0
$834$	−724.699	+	1686.48i	−0.868944	+	2.02216i
$835$	260.403	+	451.032i	0.311860	+	0.540158i
$836$	121.305	−	29.1060i	0.145102	−	0.0348158i
$837$	−1662.33	−	959.745i	−1.98605	−	1.14665i
$838$	−587.103	+	69.4491i	−0.700600	+	0.0828749i
$839$		−	16.7454i		−	0.0199588i	−0.999950	−	0.00997940i	$-0.996823\pi$
$839$		−	16.7454i		−	0.0199588i	0.999950	−	0.00997940i	$-0.00317659\pi$
$840$		0			0
$841$	752.222			0.894437
$842$	29.6640	+	250.771i	0.0352304	+	0.297827i
$843$	−328.886	+	569.648i	−0.390138	+	0.675739i
$844$	660.424	−	158.462i	0.782493	−	0.187751i
$845$	−540.690	+	312.168i	−0.639870	+	0.369429i
$846$	−1642.53	−	705.816i	−1.94153	−	0.834298i
$847$		0			0
$848$	−1190.06	−	62.6814i	−1.40337	−	0.0739167i
$849$	1.65008	+	2.85803i	0.00194356	+	0.00336634i
$850$	22.5661	+	30.2238i	0.0265483	+	0.0355574i
$851$	−55.6118	+	96.3224i	−0.0653488	+	0.113187i
$852$	1523.72	+	451.564i	1.78841	+	0.530005i
$853$			1299.38i			1.52331i	0.647984	+	0.761654i	$0.275612\pi$
$853$			1299.38i			1.52331i	−0.647984	+	0.761654i	$0.724388\pi$
$854$		0			0
$855$			248.563i			0.290717i
$856$	885.500	+	736.757i	1.03446	+	0.860698i
$857$	−597.668	+	1035.19i	−0.697396	+	1.20792i	0.271971	+	0.962305i	$0.412325\pi$
$857$	−597.668	+	1035.19i	−0.697396	+	1.20792i	−0.969366	+	0.245619i	$0.921009\pi$
$858$	−962.262	+	718.456i	−1.12152	+	0.837362i
$859$	−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	−0.901788	−	0.432179i	$-0.857745\pi$
$863$	−844.362	+	487.493i	−0.978404	+	0.564882i	−0.0766158	+	0.997061i	$0.524411\pi$
$864$	−1480.50	+	988.537i	−1.71354	+	1.14414i
$865$	58.6913	−	101.656i	0.0678512	−	0.117522i
$866$	−1085.04	+	128.350i	−1.25293	+	0.148211i
$867$	1536.44			1.77213
$868$		0			0
$869$			158.887i			0.182839i
$870$	215.235	−	25.4605i	0.247397	−	0.0292649i
$871$	1455.45	+	840.304i	1.67101	+	0.964758i
$872$	525.727	+	90.4430i	0.602898	+	0.103719i
$873$	−521.896	−	903.951i	−0.597819	−	1.03545i
$874$	94.6839	+	40.6868i	0.108334	+	0.0465524i
$875$		0			0
$876$	−493.304	−	519.971i	−0.563133	−	0.593574i
$877$	274.158	−	158.285i	0.312609	−	0.180485i	−0.335484	−	0.942046i	$-0.608900\pi$
$877$	274.158	−	158.285i	0.312609	−	0.180485i	0.648093	+	0.761561i	$0.275567\pi$
$878$	438.043	−	327.057i	0.498910	−	0.372503i
$879$	−130.591	−	75.3966i	−0.148567	−	0.0857754i
$880$	82.3554	+	161.736i	0.0935857	+	0.183791i
$881$	464.977			0.527783			0.263891	−	0.964552i	$-0.414994\pi$
$881$	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	$0.487477\pi$
$884$	76.1101	+	22.5557i	0.0860974	+	0.0255155i
$885$	−534.610	−	308.657i	−0.604079	−	0.348765i
$886$	−568.083	−	760.860i	−0.641178	−	0.858758i
$887$	−9.46740	+	5.46601i	−0.0106735	+	0.00616235i	−0.505327	−	0.862928i	$-0.668628\pi$
$887$	−9.46740	+	5.46601i	−0.0106735	+	0.00616235i	0.494654	+	0.869090i	$0.335295\pi$
$888$	−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
$892$	−42.4290	−	176.832i	−0.0475661	−	0.198242i
$893$	−236.229	−	136.387i	−0.264535	−	0.152729i
$894$	289.026	+	2443.34i	0.323296	+	2.73305i
$895$		−	273.974i		−	0.306116i
$896$		0			0
$897$	−992.062			−1.10598
$898$	1553.37	−	183.750i	1.72981	−	0.204622i
$899$	−162.552	+	281.548i	−0.180814	+	0.313179i
$900$	1538.00	−	369.029i	1.70889	−	0.410032i
$901$	−59.7853	+	34.5170i	−0.0663543	+	0.0383097i
$902$	179.119	−	416.837i	0.198580	−	0.462125i
$903$		0			0
$904$	53.7786	−	19.8279i	0.0594896	−	0.0219336i
$905$	−229.395	−	397.323i	−0.253475	−	0.439031i
$906$	−1263.78	+	943.581i	−1.39490	+	1.04148i
$907$	11.3588	−	19.6740i	0.0125235	−	0.0216913i	−0.859696	−	0.510806i	$-0.829347\pi$
$907$	11.3588	−	19.6740i	0.0125235	−	0.0216913i	0.872219	+	0.489115i	$0.162680\pi$
$908$	210.413	−	710.000i	0.231732	−	0.781938i
$909$			1754.83i			1.93051i
$910$		0			0
$911$		−	721.866i		−	0.792389i	−0.918167	−	0.396194i	$-0.870331\pi$
$911$		−	721.866i		−	0.792389i	0.918167	−	0.396194i	$-0.129669\pi$
$912$	−450.849	+	229.570i	−0.494352	+	0.251722i
$913$	−191.767	+	332.150i	−0.210040	+	0.363800i
$914$	226.815	+	303.784i	0.248157	+	0.332368i
$915$	159.960	+	277.059i	0.174820	+	0.302797i
$916$	−536.704	+	509.179i	−0.585922	+	0.555873i
$917$		0			0
$918$	−40.7139	+	94.7470i	−0.0443506	+	0.103210i
$919$	113.209	−	65.3612i	0.123187	−	0.0711221i	−0.437140	−	0.899393i	$-0.644009\pi$
$919$	113.209	−	65.3612i	0.123187	−	0.0711221i	0.560327	+	0.828271i	$0.310675\pi$
$920$	−25.4207	+	147.765i	−0.0276312	+	0.160615i
$921$	−1068.83	+	1851.27i	−1.16051	+	2.01007i
$922$	−47.5841	−	402.262i	−0.0516097	−	0.436293i
$923$	−1595.38			−1.72847
$924$		0			0
$925$			260.454i			0.281572i
$926$	153.402	+	1296.81i	0.165661	+	1.40045i
$927$	1898.56	+	1096.13i	2.04807	+	1.18245i
$928$	167.428	+	250.752i	0.180419	+	0.270207i
$929$	−227.643	−	394.289i	−0.245041	−	0.424423i	0.717102	−	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
$934$	652.654	+	874.129i	0.698773	+	0.935899i
$935$	9.10528	+	5.25694i	0.00973827	+	0.00562239i
$936$	2129.01	−	2558.84i	2.27459	−	2.73380i
$937$	1242.79			1.32635			0.663176	−	0.748464i	$-0.269208\pi$
$937$	1242.79			1.32635			0.663176	+	0.748464i	$0.269208\pi$
$938$		0			0
$939$	−1419.69			−1.51192
$940$	112.764	−	380.503i	0.119962	−	0.404790i
$941$	−984.767	−	568.556i	−1.04651	−	0.604204i	−0.124841	−	0.992177i	$-0.539842\pi$
$941$	−984.767	−	568.556i	−1.04651	−	0.604204i	−0.921671	+	0.387973i	$0.873175\pi$
$942$	−981.261	+	732.642i	−1.04168	+	0.777751i
$943$	324.585	−	187.399i	0.344205	−	0.198727i
$944$	45.1698	−	857.586i	0.0478493	−	0.908460i
$945$		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	$0.954711\pi$
$948$	−150.347	−	626.603i	−0.158594	−	0.660974i
$949$	623.119	+	359.758i	0.656606	+	0.379092i
$950$	239.656	−	28.3492i	0.252270	−	0.0298413i
$951$		−	2308.09i		−	2.42702i
$952$		0			0
$953$	765.039			0.802769			0.401384	−	0.915910i	$-0.368529\pi$
$953$	765.039			0.802769			0.401384	+	0.915910i	$0.368529\pi$
$954$	340.059	+	2874.76i	0.356455	+	3.01337i
$955$	−43.7153	+	75.7172i	−0.0457752	+	0.0792850i
$956$	152.296	+	634.724i	0.159305	+	0.663937i
$957$	−228.827	+	132.113i	−0.239109	+	0.138050i
$958$	200.102	+	85.9863i	0.208875	+	0.0897561i
$959$		0			0
$960$	−477.828	−	559.911i	−0.497737	−	0.583240i
$961$	114.761	+	198.772i	0.119418	+	0.206838i
$962$	327.940	+	439.225i	0.340894	+	0.456575i
$963$	1399.07	−	2423.27i	1.45283	−	2.51637i
$964$	233.554	−	788.084i	0.242275	−	0.817515i
$965$			608.916i			0.631001i
$966$		0			0
$967$		−	771.494i		−	0.797822i	−0.916990	−	0.398911i	$-0.869388\pi$
$967$		−	771.494i		−	0.797822i	0.916990	−	0.398911i	$-0.130612\pi$
$968$	574.026	+	477.604i	0.593002	+	0.493392i
$969$	−14.6540	+	25.3815i	−0.0151228	+	0.0261935i
$970$	185.667	−	138.625i	0.191409	−	0.142912i
$971$	458.754	+	794.586i	0.472456	+	0.818317i	0.999503	−	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
$976$	−242.493	+	373.191i	−0.248456	+	0.382368i
$977$	−133.301	+	230.883i	−0.136439	+	0.236319i	−0.926146	−	0.377165i	$-0.876899\pi$
$977$	−133.301	+	230.883i	−0.136439	+	0.236319i	0.789707	+	0.613484i	$0.210232\pi$
$978$	−522.216	+	61.7736i	−0.533963	+	0.0631632i
$979$	288.408			0.294594
$980$		0			0
$981$		−	1295.81i		−	1.32091i
$982$	901.488	−	106.638i	0.918012	−	0.108593i
$983$	−1601.95	−	924.884i	−1.62965	−	0.940879i	−0.984197	−	0.177080i	$-0.943335\pi$
$983$	−1601.95	−	924.884i	−1.62965	−	0.940879i	−0.645454	−	0.763799i	$-0.723332\pi$
$984$	−311.961	+	1813.37i	−0.317034	+	1.84285i
$985$	−282.349	−	489.043i	−0.286649	−	0.496490i
$986$	16.0473	+	6.89571i	0.0162751	+	0.00699362i
$987$		0			0
$988$	368.457	−	349.560i	0.372932	−	0.353806i
$989$	314.083	−	181.336i	0.317576	−	0.183353i
$990$	353.272	−	263.764i	0.356840	−	0.266429i
$991$	−303.420	−	175.180i	−0.306175	−	0.176770i	0.339038	−	0.940773i	$-0.389898\pi$
$991$	−303.420	−	175.180i	−0.306175	−	0.176770i	−0.645214	+	0.764002i	$0.723232\pi$
$992$	1101.79	−	71.8520i	1.11067	−	0.0724314i
$993$	−433.261			−0.436315
$994$		0			0
$995$	694.800			0.698291
$996$	441.973	−	1491.36i	0.443748	−	1.49735i
$997$	−455.495	−	262.980i	−0.456866	−	0.263772i	0.253860	−	0.967241i	$-0.418300\pi$
$997$	−455.495	−	262.980i	−0.456866	−	0.263772i	−0.710726	+	0.703469i	$0.751633\pi$
$998$	−398.923	−	534.296i	−0.399723	−	0.535367i
$999$	−616.687	+	356.045i	−0.617305	+	0.356401i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(1.98615 - 0.234945i) q^{2} +(2.66613 - 4.61787i) q^{3} +(3.88960 - 0.933271i) q^{4} +(1.86796 - 1.07847i) q^{5} +(4.21039 - 9.79818i) q^{6} +(7.50608 - 2.76746i) q^{8} +(-9.71647 - 16.8294i) q^{9} +O(q^{10})\)	\(q+(1.98615 - 0.234945i) q^{2} +(2.66613 - 4.61787i) q^{3} +(3.88960 - 0.933271i) q^{4} +(1.86796 - 1.07847i) q^{5} +(4.21039 - 9.79818i) q^{6} +(7.50608 - 2.76746i) q^{8} +(-9.71647 - 16.8294i) q^{9} +(3.45667 - 2.58086i) q^{10} +(-2.62956 + 4.55453i) q^{11} +(6.06045 - 20.4499i) q^{12} +21.4116i q^{13} -11.5013i q^{15} +(14.2580 - 7.26011i) q^{16} +(0.463429 - 0.802683i) q^{17} +(-23.2524 - 31.1430i) q^{18} +(-2.96505 - 5.13561i) q^{19} +(6.25911 - 5.93812i) q^{20} +(-4.15264 + 9.66378i) q^{22} +(-7.52507 + 4.34460i) q^{23} +(7.23239 - 42.0405i) q^{24} +(-10.1738 + 17.6216i) q^{25} +(5.03053 + 42.5266i) q^{26} -55.6311 q^{27} +9.42223i q^{29} +(-2.70217 - 22.8434i) q^{30} +(29.8813 + 17.2520i) q^{31} +(26.6129 - 17.7695i) q^{32} +(14.0215 + 24.2859i) q^{33} +(0.731855 - 1.70313i) q^{34} +(-53.4996 - 56.3916i) q^{36} +(11.0853 - 6.40011i) q^{37} +(-7.09562 - 9.50349i) q^{38} +(98.8758 + 57.0860i) q^{39} +(11.0364 - 13.2645i) q^{40} -43.1339 q^{41} -41.7382 q^{43} +(-5.97732 + 20.1694i) q^{44} +(-36.2999 - 20.9578i) q^{45} +(-13.9252 + 10.3970i) q^{46} +(39.8357 - 22.9991i) q^{47} +(4.48745 - 85.1980i) q^{48} +(-16.0667 + 37.3894i) q^{50} +(-2.47112 - 4.28011i) q^{51} +(19.9828 + 83.2825i) q^{52} +(-64.5031 - 37.2409i) q^{53} +(-110.492 + 13.0702i) q^{54} +11.3436i q^{55} -31.6208 q^{57} +(2.21370 + 18.7140i) q^{58} +(26.8367 - 46.4825i) q^{59} +(-10.7338 - 44.7355i) q^{60} +(-24.0893 + 13.9080i) q^{61} +(63.4020 + 27.2446i) q^{62} +(48.6823 - 41.5455i) q^{64} +(23.0916 + 39.9959i) q^{65} +(33.5546 + 44.9412i) q^{66} +(39.2453 - 67.9749i) q^{67} +(1.05343 - 3.55462i) q^{68} +46.3330i q^{69} +74.5100i q^{71} +(-119.507 - 99.4329i) q^{72} +(16.8020 - 29.1020i) q^{73} +(20.5134 - 15.3160i) q^{74} +(54.2494 + 93.9627i) q^{75} +(-16.3258 - 17.2083i) q^{76} +(209.794 + 90.1511i) q^{78} +(26.1642 - 15.1059i) q^{79} +(18.8036 - 28.9384i) q^{80} +(-60.8713 + 105.432i) q^{81} +(-85.6705 + 10.1341i) q^{82} +72.9274 q^{83} -1.99917i q^{85} +(-82.8984 + 9.80616i) q^{86} +(43.5106 + 25.1209i) q^{87} +(-7.13318 + 41.4638i) q^{88} +(-27.4198 - 47.4925i) q^{89} +(-77.0211 - 33.0968i) q^{90} +(-25.2148 + 23.9217i) q^{92} +(159.335 - 91.9919i) q^{93} +(73.7162 - 55.0390i) q^{94} +(-11.0772 - 6.39541i) q^{95} +(-11.1040 - 170.270i) q^{96} +53.7125 q^{97} +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

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