LMFDB - Embedded newform 49.6.c.c.18.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,6,Mod(18,49)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("49.18");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	49.c (of order $3$, 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:	$7.85880717084$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 7)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			18.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	49.18
Dual form			49.6.c.c.30.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.00000 + 8.66025i) q^{2} +(7.00000 - 12.1244i) q^{3} +(-34.0000 + 58.8897i) q^{4} +(28.0000 + 48.4974i) q^{5} +140.000 q^{6} -360.000 q^{8} +(23.5000 + 40.7032i) q^{9} +O(q^{10})$	\(q+(5.00000 + 8.66025i) q^{2} +(7.00000 - 12.1244i) q^{3} +(-34.0000 + 58.8897i) q^{4} +(28.0000 + 48.4974i) q^{5} +140.000 q^{6} -360.000 q^{8} +(23.5000 + 40.7032i) q^{9} +(-280.000 + 484.974i) q^{10} +(-116.000 + 200.918i) q^{11} +(476.000 + 824.456i) q^{12} -140.000 q^{13} +784.000 q^{15} +(-712.000 - 1233.22i) q^{16} +(861.000 - 1491.30i) q^{17} +(-235.000 + 407.032i) q^{18} +(49.0000 + 84.8705i) q^{19} -3808.00 q^{20} -2320.00 q^{22} +(-912.000 - 1579.63i) q^{23} +(-2520.00 + 4364.77i) q^{24} +(-5.50000 + 9.52628i) q^{25} +(-700.000 - 1212.44i) q^{26} +4060.00 q^{27} +3418.00 q^{29} +(3920.00 + 6789.64i) q^{30} +(3822.00 - 6619.90i) q^{31} +(1360.00 - 2355.59i) q^{32} +(1624.00 + 2812.85i) q^{33} +17220.0 q^{34} -3196.00 q^{36} +(5199.00 + 9004.93i) q^{37} +(-490.000 + 848.705i) q^{38} +(-980.000 + 1697.41i) q^{39} +(-10080.0 - 17459.1i) q^{40} -17962.0 q^{41} +10880.0 q^{43} +(-7888.00 - 13662.4i) q^{44} +(-1316.00 + 2279.38i) q^{45} +(9120.00 - 15796.3i) q^{46} +(-4662.00 - 8074.82i) q^{47} -19936.0 q^{48} -110.000 q^{50} +(-12054.0 - 20878.1i) q^{51} +(4760.00 - 8244.56i) q^{52} +(-1131.00 + 1958.95i) q^{53} +(20300.0 + 35160.6i) q^{54} -12992.0 q^{55} +1372.00 q^{57} +(17090.0 + 29600.7i) q^{58} +(1365.00 - 2364.25i) q^{59} +(-26656.0 + 46169.5i) q^{60} +(-12824.0 - 22211.8i) q^{61} +76440.0 q^{62} -18368.0 q^{64} +(-3920.00 - 6789.64i) q^{65} +(-16240.0 + 28128.5i) q^{66} +(24202.0 - 41919.1i) q^{67} +(58548.0 + 101408. i) q^{68} -25536.0 q^{69} -58560.0 q^{71} +(-8460.00 - 14653.1i) q^{72} +(-34041.0 + 58960.7i) q^{73} +(-51990.0 + 90049.3i) q^{74} +(77.0000 + 133.368i) q^{75} -6664.00 q^{76} -19600.0 q^{78} +(-15892.0 - 27525.8i) q^{79} +(39872.0 - 69060.3i) q^{80} +(22709.5 - 39334.0i) q^{81} +(-89810.0 - 155555. i) q^{82} -20538.0 q^{83} +96432.0 q^{85} +(54400.0 + 94223.6i) q^{86} +(23926.0 - 41441.0i) q^{87} +(41760.0 - 72330.4i) q^{88} +(25291.0 + 43805.3i) q^{89} -26320.0 q^{90} +124032. q^{92} +(-53508.0 - 92678.6i) q^{93} +(46620.0 - 80748.2i) q^{94} +(-2744.00 + 4752.75i) q^{95} +(-19040.0 - 32978.2i) q^{96} -58506.0 q^{97} -10904.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 10 q^{2} + 14 q^{3} - 68 q^{4} + 56 q^{5} + 280 q^{6} - 720 q^{8} + 47 q^{9}+O(q^{10}) $ 2 * q + 10 * q^2 + 14 * q^3 - 68 * q^4 + 56 * q^5 + 280 * q^6 - 720 * q^8 + 47 * q^9	\( 2 q + 10 q^{2} + 14 q^{3} - 68 q^{4} + 56 q^{5} + 280 q^{6} - 720 q^{8} + 47 q^{9} - 560 q^{10} - 232 q^{11} + 952 q^{12} - 280 q^{13} + 1568 q^{15} - 1424 q^{16} + 1722 q^{17} - 470 q^{18} + 98 q^{19} - 7616 q^{20} - 4640 q^{22} - 1824 q^{23} - 5040 q^{24} - 11 q^{25} - 1400 q^{26} + 8120 q^{27} + 6836 q^{29} + 7840 q^{30} + 7644 q^{31} + 2720 q^{32} + 3248 q^{33} + 34440 q^{34} - 6392 q^{36} + 10398 q^{37} - 980 q^{38} - 1960 q^{39} - 20160 q^{40} - 35924 q^{41} + 21760 q^{43} - 15776 q^{44} - 2632 q^{45} + 18240 q^{46} - 9324 q^{47} - 39872 q^{48} - 220 q^{50} - 24108 q^{51} + 9520 q^{52} - 2262 q^{53} + 40600 q^{54} - 25984 q^{55} + 2744 q^{57} + 34180 q^{58} + 2730 q^{59} - 53312 q^{60} - 25648 q^{61} + 152880 q^{62} - 36736 q^{64} - 7840 q^{65} - 32480 q^{66} + 48404 q^{67} + 117096 q^{68} - 51072 q^{69} - 117120 q^{71} - 16920 q^{72} - 68082 q^{73} - 103980 q^{74} + 154 q^{75} - 13328 q^{76} - 39200 q^{78} - 31784 q^{79} + 79744 q^{80} + 45419 q^{81} - 179620 q^{82} - 41076 q^{83} + 192864 q^{85} + 108800 q^{86} + 47852 q^{87} + 83520 q^{88} + 50582 q^{89} - 52640 q^{90} + 248064 q^{92} - 107016 q^{93} + 93240 q^{94} - 5488 q^{95} - 38080 q^{96} - 117012 q^{97} - 21808 q^{99}+O(q^{100}) \) 2 * q + 10 * q^2 + 14 * q^3 - 68 * q^4 + 56 * q^5 + 280 * q^6 - 720 * q^8 + 47 * q^9 - 560 * q^10 - 232 * q^11 + 952 * q^12 - 280 * q^13 + 1568 * q^15 - 1424 * q^16 + 1722 * q^17 - 470 * q^18 + 98 * q^19 - 7616 * q^20 - 4640 * q^22 - 1824 * q^23 - 5040 * q^24 - 11 * q^25 - 1400 * q^26 + 8120 * q^27 + 6836 * q^29 + 7840 * q^30 + 7644 * q^31 + 2720 * q^32 + 3248 * q^33 + 34440 * q^34 - 6392 * q^36 + 10398 * q^37 - 980 * q^38 - 1960 * q^39 - 20160 * q^40 - 35924 * q^41 + 21760 * q^43 - 15776 * q^44 - 2632 * q^45 + 18240 * q^46 - 9324 * q^47 - 39872 * q^48 - 220 * q^50 - 24108 * q^51 + 9520 * q^52 - 2262 * q^53 + 40600 * q^54 - 25984 * q^55 + 2744 * q^57 + 34180 * q^58 + 2730 * q^59 - 53312 * q^60 - 25648 * q^61 + 152880 * q^62 - 36736 * q^64 - 7840 * q^65 - 32480 * q^66 + 48404 * q^67 + 117096 * q^68 - 51072 * q^69 - 117120 * q^71 - 16920 * q^72 - 68082 * q^73 - 103980 * q^74 + 154 * q^75 - 13328 * q^76 - 39200 * q^78 - 31784 * q^79 + 79744 * q^80 + 45419 * q^81 - 179620 * q^82 - 41076 * q^83 + 192864 * q^85 + 108800 * q^86 + 47852 * q^87 + 83520 * q^88 + 50582 * q^89 - 52640 * q^90 + 248064 * q^92 - 107016 * q^93 + 93240 * q^94 - 5488 * q^95 - 38080 * q^96 - 117012 * q^97 - 21808 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	5.00000	+	8.66025i	0.883883	+	1.53093i	0.846988	+	0.531612i	$0.178414\pi$
$2$	5.00000	+	8.66025i	0.883883	+	1.53093i	0.0368954	+	0.999319i	$0.488253\pi$
$3$	7.00000	−	12.1244i	0.449050	−	0.777778i	−0.549274	−	0.835642i	$-0.685096\pi$
$3$	7.00000	−	12.1244i	0.449050	−	0.777778i	0.998324	+	0.0578644i	$0.0184291\pi$
$4$	−34.0000	+	58.8897i	−1.06250	+	1.84030i
$5$	28.0000	+	48.4974i	0.500879	+	0.867548i	0.999999	+	0.00101554i	$0.000323257\pi$
$5$	28.0000	+	48.4974i	0.500879	+	0.867548i	−0.499120	+	0.866533i	$0.666343\pi$
$6$	140.000			1.58763
$7$		0			0
$7$		0			0
$8$	−360.000			−1.98874
$9$	23.5000	+	40.7032i	0.0967078	+	0.167503i
$10$	−280.000	+	484.974i	−0.885438	+	1.53362i
$11$	−116.000	+	200.918i	−0.289052	+	0.500653i	−0.973584	−	0.228330i	$-0.926673\pi$
$11$	−116.000	+	200.918i	−0.289052	+	0.500653i	0.684532	+	0.728983i	$0.260007\pi$
$12$	476.000	+	824.456i	0.954232	+	1.65278i
$13$	−140.000			−0.229757			−0.114879	−	0.993380i	$-0.536648\pi$
$13$	−140.000			−0.229757			−0.114879	+	0.993380i	$0.536648\pi$
$14$		0			0
$15$	784.000			0.899680
$16$	−712.000	−	1233.22i	−0.695312	−	1.20432i
$17$	861.000	−	1491.30i	0.722572	−	1.25153i	−0.237394	−	0.971413i	$-0.576293\pi$
$17$	861.000	−	1491.30i	0.722572	−	1.25153i	0.959966	−	0.280117i	$-0.0903733\pi$
$18$	−235.000	+	407.032i	−0.170957	+	0.296106i
$19$	49.0000	+	84.8705i	0.0311395	+	0.0539353i	0.881175	−	0.472790i	$-0.156753\pi$
$19$	49.0000	+	84.8705i	0.0311395	+	0.0539353i	−0.850036	+	0.526725i	$0.823420\pi$
$20$	−3808.00			−2.12874
$21$		0			0
$22$	−2320.00			−1.02195
$23$	−912.000	−	1579.63i	−0.359480	−	0.622638i	0.628394	−	0.777895i	$-0.283713\pi$
$23$	−912.000	−	1579.63i	−0.359480	−	0.622638i	−0.987874	+	0.155257i	$0.950379\pi$
$24$	−2520.00	+	4364.77i	−0.893043	+	1.54680i
$25$	−5.50000	+	9.52628i	−0.00176000	+	0.00304841i
$26$	−700.000	−	1212.44i	−0.203079	−	0.351743i
$27$	4060.00			1.07181
$28$		0			0
$29$	3418.00			0.754705			0.377352	−	0.926070i	$-0.376835\pi$
$29$	3418.00			0.754705			0.377352	+	0.926070i	$0.376835\pi$
$30$	3920.00	+	6789.64i	0.795212	+	1.37735i
$31$	3822.00	−	6619.90i	0.714310	−	1.23722i	−0.248916	−	0.968525i	$-0.580074\pi$
$31$	3822.00	−	6619.90i	0.714310	−	1.23722i	0.963225	−	0.268695i	$-0.0865925\pi$
$32$	1360.00	−	2355.59i	0.234782	−	0.406654i
$33$	1624.00	+	2812.85i	0.259598	+	0.449637i
$34$	17220.0			2.55468
$35$		0			0
$36$	−3196.00			−0.411008
$37$	5199.00	+	9004.93i	0.624332	+	1.08137i	0.988670	+	0.150108i	$0.0479620\pi$
$37$	5199.00	+	9004.93i	0.624332	+	1.08137i	−0.364338	+	0.931267i	$0.618705\pi$
$38$	−490.000	+	848.705i	−0.0550474	+	0.0953450i
$39$	−980.000	+	1697.41i	−0.103173	+	0.178700i
$40$	−10080.0	−	17459.1i	−0.996117	−	1.72533i
$41$	−17962.0			−1.66876			−0.834382	−	0.551186i	$-0.814175\pi$
$41$	−17962.0			−1.66876			−0.834382	+	0.551186i	$0.814175\pi$
$42$		0			0
$43$	10880.0			0.897342			0.448671	−	0.893697i	$-0.351898\pi$
$43$	10880.0			0.897342			0.448671	+	0.893697i	$0.351898\pi$
$44$	−7888.00	−	13662.4i	−0.614236	−	1.06389i
$45$	−1316.00	+	2279.38i	−0.0968779	+	0.167797i
$46$	9120.00	−	15796.3i	0.635478	−	1.10068i
$47$	−4662.00	−	8074.82i	−0.307842	−	0.533198i	0.670048	−	0.742318i	$-0.266273\pi$
$47$	−4662.00	−	8074.82i	−0.307842	−	0.533198i	−0.977890	+	0.209120i	$0.932940\pi$
$48$	−19936.0			−1.24892
$49$		0			0
$50$	−110.000			−0.00622254
$51$	−12054.0	−	20878.1i	−0.648942	−	1.12400i
$52$	4760.00	−	8244.56i	0.244117	−	0.422824i
$53$	−1131.00	+	1958.95i	−0.0553061	+	0.0957930i	−0.892353	−	0.451338i	$-0.850947\pi$
$53$	−1131.00	+	1958.95i	−0.0553061	+	0.0957930i	0.837047	+	0.547131i	$0.184280\pi$
$54$	20300.0	+	35160.6i	0.947353	+	1.64086i
$55$	−12992.0			−0.579121
$56$		0			0
$57$	1372.00			0.0559329
$58$	17090.0	+	29600.7i	0.667071	+	1.15540i
$59$	1365.00	−	2364.25i	0.0510508	−	0.0884226i	−0.839371	−	0.543559i	$-0.817076\pi$
$59$	1365.00	−	2364.25i	0.0510508	−	0.0884226i	0.890422	+	0.455137i	$0.150410\pi$
$60$	−26656.0	+	46169.5i	−0.955910	+	1.65568i
$61$	−12824.0	−	22211.8i	−0.441264	−	0.764292i	0.556519	−	0.830835i	$-0.312137\pi$
$61$	−12824.0	−	22211.8i	−0.441264	−	0.764292i	−0.997784	+	0.0665424i	$0.978803\pi$
$62$	76440.0			2.52547
$63$		0			0
$64$	−18368.0			−0.560547
$65$	−3920.00	−	6789.64i	−0.115081	−	0.199326i
$66$	−16240.0	+	28128.5i	−0.458909	+	0.794853i
$67$	24202.0	−	41919.1i	0.658664	−	1.14084i	−0.322297	−	0.946639i	$-0.604455\pi$
$67$	24202.0	−	41919.1i	0.658664	−	1.14084i	0.980962	−	0.194202i	$-0.0622117\pi$
$68$	58548.0	+	101408.i	1.53546	+	2.65950i
$69$	−25536.0			−0.645699
$70$		0			0
$71$	−58560.0			−1.37865			−0.689327	−	0.724450i	$-0.742094\pi$
$71$	−58560.0			−1.37865			−0.689327	+	0.724450i	$0.742094\pi$
$72$	−8460.00	−	14653.1i	−0.192326	−	0.333119i
$73$	−34041.0	+	58960.7i	−0.747645	+	1.29496i	0.201304	+	0.979529i	$0.435482\pi$
$73$	−34041.0	+	58960.7i	−0.747645	+	1.29496i	−0.948949	+	0.315430i	$0.897851\pi$
$74$	−51990.0	+	90049.3i	−1.10367	+	1.91162i
$75$	77.0000	+	133.368i	0.00158066	+	0.00273778i
$76$	−6664.00			−0.132343
$77$		0			0
$78$	−19600.0			−0.364770
$79$	−15892.0	−	27525.8i	−0.286491	−	0.496217i	0.686479	−	0.727150i	$-0.259155\pi$
$79$	−15892.0	−	27525.8i	−0.286491	−	0.496217i	−0.972970	+	0.230933i	$0.925822\pi$
$80$	39872.0	−	69060.3i	0.696535	−	1.20643i
$81$	22709.5	−	39334.0i	0.384587	−	0.666125i
$82$	−89810.0	−	155555.i	−1.47499	−	2.55476i
$83$	−20538.0			−0.327237			−0.163619	−	0.986524i	$-0.552317\pi$
$83$	−20538.0			−0.327237			−0.163619	+	0.986524i	$0.552317\pi$
$84$		0			0
$85$	96432.0			1.44768
$86$	54400.0	+	94223.6i	0.793145	+	1.37377i
$87$	23926.0	−	41441.0i	0.338900	−	0.586993i
$88$	41760.0	−	72330.4i	0.574849	−	0.995668i
$89$	25291.0	+	43805.3i	0.338447	+	0.586208i	0.984141	−	0.177389i	$-0.0567650\pi$
$89$	25291.0	+	43805.3i	0.338447	+	0.586208i	−0.645694	+	0.763597i	$0.723432\pi$
$90$	−26320.0			−0.342515
$91$		0			0
$92$	124032.			1.52779
$93$	−53508.0	−	92678.6i	−0.641522	−	1.11115i
$94$	46620.0	−	80748.2i	0.544193	−	0.942569i
$95$	−2744.00	+	4752.75i	−0.0311943	+	0.0540301i
$96$	−19040.0	−	32978.2i	−0.210857	−	0.365216i
$97$	−58506.0			−0.631351			−0.315676	−	0.948867i	$-0.602231\pi$
$97$	−58506.0			−0.631351			−0.315676	+	0.948867i	$0.602231\pi$
$98$		0			0
$99$	−10904.0			−0.111814
$100$	−374.000	−	647.787i	−0.00374000	−	0.00647787i
$101$	−19348.0	+	33511.7i	−0.188726	+	0.326884i	−0.944826	−	0.327573i	$-0.893769\pi$
$101$	−19348.0	+	33511.7i	−0.188726	+	0.326884i	0.756099	+	0.654457i	$0.227103\pi$
$102$	120540.	−	208781.i	1.14718	−	1.98697i
$103$	−26530.0	−	45951.3i	−0.246402	−	0.426781i	0.716123	−	0.697974i	$-0.245915\pi$
$103$	−26530.0	−	45951.3i	−0.246402	−	0.426781i	−0.962525	+	0.271193i	$0.912582\pi$
$104$	50400.0			0.456927
$105$		0			0
$106$	−22620.0			−0.195537
$107$	73162.0	+	126720.i	0.617769	+	1.07001i	0.989892	+	0.141824i	$0.0452967\pi$
$107$	73162.0	+	126720.i	0.617769	+	1.07001i	−0.372123	+	0.928183i	$0.621370\pi$
$108$	−138040.	+	239092.i	−1.13880	+	1.97245i
$109$	−46449.0	+	80452.0i	−0.374464	+	0.648591i	−0.990247	−	0.139325i	$-0.955507\pi$
$109$	−46449.0	+	80452.0i	−0.374464	+	0.648591i	0.615783	+	0.787916i	$0.288840\pi$
$110$	−64960.0	−	112514.i	−0.511875	−	0.886594i
$111$	145572.			1.12143
$112$		0			0
$113$	−83354.0			−0.614088			−0.307044	−	0.951695i	$-0.599340\pi$
$113$	−83354.0			−0.614088			−0.307044	+	0.951695i	$0.599340\pi$
$114$	6860.00	+	11881.9i	0.0494381	+	0.0856293i
$115$	51072.0	−	88459.3i	0.360113	−	0.623733i
$116$	−116212.	+	201285.i	−0.801874	+	1.38889i
$117$	−3290.00	−	5698.45i	−0.0222193	−	0.0384850i
$118$	27300.0			0.180492
$119$		0			0
$120$	−282240.			−1.78923
$121$	53613.5	+	92861.3i	0.332898	+	0.576596i
$122$	128240.	−	222118.i	0.780053	−	1.35109i
$123$	−125734.	+	217778.i	−0.749359	+	1.29793i
$124$	259896.	+	450153.i	1.51791	+	2.62909i
$125$	174384.			0.998232
$126$		0			0
$127$	60384.0			0.332210			0.166105	−	0.986108i	$-0.446881\pi$
$127$	60384.0			0.332210			0.166105	+	0.986108i	$0.446881\pi$
$128$	−135360.	−	234450.i	−0.730240	−	1.26481i
$129$	76160.0	−	131913.i	0.402951	−	0.697932i
$130$	39200.0	−	67896.4i	0.203436	−	0.352361i
$131$	30793.0	+	53335.0i	0.156774	+	0.271540i	0.933704	−	0.358047i	$-0.116557\pi$
$131$	30793.0	+	53335.0i	0.156774	+	0.271540i	−0.776930	+	0.629587i	$0.783224\pi$
$132$	−220864.			−1.10329
$133$		0			0
$134$	484040.			2.32873
$135$	113680.	+	196900.i	0.536846	+	0.929844i
$136$	−309960.	+	536866.i	−1.43701	+	2.48897i
$137$	102231.	−	177069.i	0.465352	−	0.806013i	−0.533866	−	0.845569i	$-0.679261\pi$
$137$	102231.	−	177069.i	0.465352	−	0.806013i	0.999217	+	0.0395567i	$0.0125946\pi$
$138$	−127680.	−	221148.i	−0.570723	−	0.988521i
$139$	−35406.0			−0.155432			−0.0777159	−	0.996976i	$-0.524763\pi$
$139$	−35406.0			−0.155432			−0.0777159	+	0.996976i	$0.524763\pi$
$140$		0			0
$141$	−130536.			−0.552946
$142$	−292800.	−	507144.i	−1.21857	−	2.11062i
$143$	16240.0	−	28128.5i	0.0664119	−	0.115029i
$144$	33464.0	−	57961.3i	0.134484	−	0.232934i
$145$	95704.0	+	165764.i	0.378016	+	0.654743i
$146$	−680820.			−2.64332
$147$		0			0
$148$	−707064.			−2.65341
$149$	10113.0	+	17516.2i	0.0373177	+	0.0646361i	0.884081	−	0.467334i	$-0.154785\pi$
$149$	10113.0	+	17516.2i	0.0373177	+	0.0646361i	−0.846763	+	0.531970i	$0.821452\pi$
$150$	−770.000	+	1333.68i	−0.00279423	+	0.00483975i
$151$	−35452.0	+	61404.7i	−0.126531	+	0.219159i	−0.922331	−	0.386402i	$-0.873718\pi$
$151$	−35452.0	+	61404.7i	−0.126531	+	0.219159i	0.795799	+	0.605561i	$0.207051\pi$
$152$	−17640.0	−	30553.4i	−0.0619284	−	0.107263i
$153$	80934.0			0.279513
$154$		0			0
$155$	428064.			1.43113
$156$	−66640.0	−	115424.i	−0.219242	−	0.379738i
$157$	−146762.	+	254199.i	−0.475187	+	0.823048i	−0.999596	−	0.0284185i	$-0.990953\pi$
$157$	−146762.	+	254199.i	−0.475187	+	0.823048i	0.524409	+	0.851466i	$0.324286\pi$
$158$	158920.	−	275258.i	0.506449	−	0.877196i
$159$	15834.0	+	27425.3i	0.0496704	+	0.0860317i
$160$	152320.			0.470389
$161$		0			0
$162$	454190.			1.35972
$163$	−6596.00	−	11424.6i	−0.0194452	−	0.0336800i	0.856139	−	0.516745i	$-0.172857\pi$
$163$	−6596.00	−	11424.6i	−0.0194452	−	0.0336800i	−0.875584	+	0.483065i	$0.839523\pi$
$164$	610708.	−	1.05778e6i	1.77306	−	3.07103i
$165$	−90944.0	+	157520.i	−0.260054	+	0.450427i
$166$	−102690.	−	177864.i	−0.289240	−	0.500978i
$167$	493612.			1.36960			0.684801	−	0.728730i	$-0.259889\pi$
$167$	493612.			1.36960			0.684801	+	0.728730i	$0.259889\pi$
$168$		0			0
$169$	−351693.			−0.947212
$170$	482160.	+	835126.i	1.27958	+	2.21630i
$171$	−2303.00	+	3988.91i	−0.00602287	+	0.0104319i
$172$	−369920.	+	640720.i	−0.953425	+	1.65138i
$173$	−120358.	−	208466.i	−0.305745	−	0.529566i	0.671682	−	0.740840i	$-0.265572\pi$
$173$	−120358.	−	208466.i	−0.305745	−	0.529566i	−0.977427	+	0.211274i	$0.932239\pi$
$174$	478520.			1.19819
$175$		0			0
$176$	330368.			0.803926
$177$	−19110.0	−	33099.5i	−0.0458488	−	0.0794124i
$178$	−252910.	+	438053.i	−0.598296	+	1.03628i
$179$	−147466.	+	255419.i	−0.344001	+	0.595827i	−0.985172	−	0.171571i	$-0.945116\pi$
$179$	−147466.	+	255419.i	−0.344001	+	0.595827i	0.641171	+	0.767398i	$0.278449\pi$
$180$	−89488.0	−	154998.i	−0.205865	−	0.356569i
$181$	−336980.			−0.764553			−0.382277	−	0.924048i	$-0.624860\pi$
$181$	−336980.			−0.764553			−0.382277	+	0.924048i	$0.624860\pi$
$182$		0			0
$183$	−359072.			−0.792600
$184$	328320.	+	568667.i	0.714912	+	1.23826i
$185$	−291144.	+	504276.i	−0.625430	+	1.08328i
$186$	535080.	−	926786.i	1.13406	−	1.96425i
$187$	199752.	+	345981.i	0.417722	+	0.723515i
$188$	634032.			1.30833
$189$		0			0
$190$	−54880.0			−0.110288
$191$	−179132.	−	310266.i	−0.355296	−	0.615390i	0.631873	−	0.775072i	$-0.282286\pi$
$191$	−179132.	−	310266.i	−0.355296	−	0.615390i	−0.987168	+	0.159682i	$0.948953\pi$
$192$	−128576.	+	222700.i	−0.251714	+	0.435981i
$193$	494777.	−	856979.i	0.956128	−	1.65606i	0.224364	−	0.974505i	$-0.427970\pi$
$193$	494777.	−	856979.i	0.956128	−	1.65606i	0.731764	−	0.681558i	$-0.238697\pi$
$194$	−292530.	−	506677.i	−0.558041	−	0.966555i
$195$	−109760.			−0.206708
$196$		0			0
$197$	−990050.			−1.81757			−0.908786	−	0.417263i	$-0.862989\pi$
$197$	−990050.			−1.81757			−0.908786	+	0.417263i	$0.862989\pi$
$198$	−54520.0	−	94431.4i	−0.0988309	−	0.171180i
$199$	420378.	−	728116.i	0.752501	−	1.30337i	−0.194106	−	0.980981i	$-0.562180\pi$
$199$	420378.	−	728116.i	0.752501	−	1.30337i	0.946607	−	0.322390i	$-0.104486\pi$
$200$	1980.00	−	3429.46i	0.00350018	−	0.00606249i
$201$	−338828.	−	586867.i	−0.591547	−	1.02459i
$202$	−386960.			−0.667249
$203$		0			0
$204$	1.63934e6			2.75800
$205$	−502936.	−	871111.i	−0.835849	−	1.44773i
$206$	265300.	−	459513.i	0.435581	−	0.754449i
$207$	42864.0	−	74242.6i	0.0695291	−	0.120428i
$208$	99680.0	+	172651.i	0.159753	+	0.276701i
$209$	−22736.0			−0.0360038
$210$		0			0
$211$	1.15073e6			1.77938			0.889689	−	0.456568i	$-0.150921\pi$
$211$	1.15073e6			1.77938			0.889689	+	0.456568i	$0.150921\pi$
$212$	−76908.0	−	133209.i	−0.117525	−	0.203560i
$213$	−409920.	+	710002.i	−0.619085	+	1.07229i
$214$	−731620.	+	1.26720e6i	−1.09207	+	1.89152i
$215$	304640.	+	527652.i	0.449460	+	0.778487i
$216$	−1.46160e6			−2.13154
$217$		0			0
$218$	−928980.			−1.32393
$219$	476574.	+	825450.i	0.671460	+	1.16300i
$220$	441728.	−	765095.i	0.615316	−	1.06576i
$221$	−120540.	+	208781.i	−0.166016	+	0.287549i
$222$	727860.	+	1.26069e6i	0.991209	+	1.71683i
$223$	−824264.			−1.10995			−0.554976	−	0.831866i	$-0.687273\pi$
$223$	−824264.			−1.10995			−0.554976	+	0.831866i	$0.687273\pi$
$224$		0			0
$225$	−517.000			−0.000680823
$226$	−416770.	−	721867.i	−0.542782	−	0.940126i
$227$	−37191.0	+	64416.7i	−0.0479042	+	0.0829724i	−0.888983	−	0.457940i	$-0.848588\pi$
$227$	−37191.0	+	64416.7i	−0.0479042	+	0.0829724i	0.841079	+	0.540912i	$0.181921\pi$
$228$	−46648.0	+	80796.7i	−0.0594287	+	0.102933i
$229$	−565978.	−	980303.i	−0.713199	−	1.23530i	−0.963650	−	0.267168i	$-0.913912\pi$
$229$	−565978.	−	980303.i	−0.713199	−	1.23530i	0.250451	−	0.968129i	$-0.419421\pi$
$230$	1.02144e6			1.27319
$231$		0			0
$232$	−1.23048e6			−1.50091
$233$	99363.0	+	172102.i	0.119904	+	0.207680i	0.919730	−	0.392553i	$-0.128408\pi$
$233$	99363.0	+	172102.i	0.119904	+	0.207680i	−0.799825	+	0.600233i	$0.795075\pi$
$234$	32900.0	−	56984.5i	0.0392786	−	0.0680326i
$235$	261072.	−	452190.i	0.308383	−	0.534135i
$236$	92820.0	+	160769.i	0.108483	+	0.187898i
$237$	−444976.			−0.514595
$238$		0			0
$239$	482904.			0.546847			0.273424	−	0.961894i	$-0.411844\pi$
$239$	482904.			0.546847			0.273424	+	0.961894i	$0.411844\pi$
$240$	−558208.	−	966845.i	−0.625559	−	1.08350i
$241$	−402955.	+	697939.i	−0.446904	+	0.774060i	−0.998183	−	0.0602611i	$-0.980807\pi$
$241$	−402955.	+	697939.i	−0.446904	+	0.774060i	0.551279	+	0.834321i	$0.314140\pi$
$242$	−536135.	+	928613.i	−0.588485	+	1.01929i
$243$	175357.	+	303727.i	0.190505	+	0.329965i
$244$	1.74406e6			1.87537
$245$		0			0
$246$	−2.51468e6			−2.64938
$247$	−6860.00	−	11881.9i	−0.00715454	−	0.0123920i
$248$	−1.37592e6	+	2.38316e6i	−1.42057	+	2.46051i
$249$	−143766.	+	249010.i	−0.146946	+	0.254518i
$250$	871920.	+	1.51021e6i	0.882321	+	1.52822i
$251$	430738.			0.431548			0.215774	−	0.976443i	$-0.430773\pi$
$251$	430738.			0.431548			0.215774	+	0.976443i	$0.430773\pi$
$252$		0			0
$253$	423168.			0.415634
$254$	301920.	+	522941.i	0.293635	+	0.508590i
$255$	675024.	−	1.16918e6i	0.650083	−	1.12598i
$256$	1.05971e6	−	1.83548e6i	1.01062	−	1.75045i
$257$	588455.	+	1.01923e6i	0.555751	+	0.962589i	0.997845	+	0.0656204i	$0.0209026\pi$
$257$	588455.	+	1.01923e6i	0.555751	+	0.962589i	−0.442093	+	0.896969i	$0.645764\pi$
$258$	1.52320e6			1.42465
$259$		0			0
$260$	533120.			0.489093
$261$	80323.0	+	139124.i	0.0729858	+	0.126415i
$262$	−307930.	+	533350.i	−0.277140	+	0.480020i
$263$	−645488.	+	1.11802e6i	−0.575438	+	0.996688i	0.420556	+	0.907267i	$0.361835\pi$
$263$	−645488.	+	1.11802e6i	−0.575438	+	0.996688i	−0.995994	+	0.0894216i	$0.971498\pi$
$264$	−584640.	−	1.01263e6i	−0.516272	−	0.894210i
$265$	−126672.			−0.110807
$266$		0			0
$267$	708148.			0.607919
$268$	1.64574e6	+	2.85050e6i	1.39966	+	2.42429i
$269$	638778.	−	1.10640e6i	0.538232	−	0.932245i	−0.460768	−	0.887521i	$-0.652426\pi$
$269$	638778.	−	1.10640e6i	0.538232	−	0.932245i	0.998999	−	0.0447238i	$-0.0142408\pi$
$270$	−1.13680e6	+	1.96900e6i	−0.949018	+	1.64375i
$271$	−825272.	−	1.42941e6i	−0.682612	−	1.18232i	−0.974181	−	0.225769i	$-0.927511\pi$
$271$	−825272.	−	1.42941e6i	−0.682612	−	1.18232i	0.291569	−	0.956550i	$-0.405823\pi$
$272$	−2.45213e6			−2.00965
$273$		0			0
$274$	2.04462e6			1.64527
$275$	−1276.00	−	2210.10i	−0.00101746	−	0.00176230i
$276$	868224.	−	1.50381e6i	0.686055	−	1.18828i
$277$	532045.	−	921529.i	0.416628	−	0.721622i	−0.578969	−	0.815349i	$-0.696545\pi$
$277$	532045.	−	921529.i	0.416628	−	0.721622i	0.995598	+	0.0937276i	$0.0298783\pi$
$278$	−177030.	−	306625.i	−0.137384	−	0.237955i
$279$	359268.			0.276317
$280$		0			0
$281$	−22342.0			−0.0168794			−0.00843969	−	0.999964i	$-0.502686\pi$
$281$	−22342.0			−0.0168794			−0.00843969	+	0.999964i	$0.502686\pi$
$282$	−652680.	−	1.13047e6i	−0.488740	−	0.846522i
$283$	1.24787e6	−	2.16137e6i	0.926196	−	1.60422i	0.136570	−	0.990630i	$-0.456392\pi$
$283$	1.24787e6	−	2.16137e6i	0.926196	−	1.60422i	0.789626	−	0.613588i	$-0.210274\pi$
$284$	1.99104e6	−	3.44858e6i	1.46482	−	2.53714i
$285$	38416.0	+	66538.5i	0.0280156	+	0.0485244i
$286$	324800.			0.234802
$287$		0			0
$288$	127840.			0.0908208
$289$	−772714.	−	1.33838e6i	−0.544219	−	0.942615i
$290$	−957040.	+	1.65764e6i	−0.668244	+	1.15743i
$291$	−409542.	+	709348.i	−0.283508	+	0.491051i
$292$	−2.31479e6	−	4.00933e6i	−1.58874	−	2.75179i
$293$	−1.93178e6			−1.31458			−0.657291	−	0.753637i	$-0.728298\pi$
$293$	−1.93178e6			−1.31458			−0.657291	+	0.753637i	$0.728298\pi$
$294$		0			0
$295$	152880.			0.102281
$296$	−1.87164e6	−	3.24178e6i	−1.24163	−	2.15057i
$297$	−470960.	+	815727.i	−0.309808	+	0.536604i
$298$	−101130.	+	175162.i	−0.0659689	+	0.114262i
$299$	127680.	+	221148.i	0.0825933	+	0.143056i
$300$	−10472.0			−0.00671779
$301$		0			0
$302$	−709040.			−0.447356
$303$	270872.	+	469164.i	0.169495	+	0.293574i
$304$	69776.0	−	120856.i	0.0433034	−	0.0750037i
$305$	718144.	−	1.24386e6i	0.442040	−	0.765636i
$306$	404670.	+	700909.i	0.247057	+	0.427916i
$307$	−459074.			−0.277995			−0.138997	−	0.990293i	$-0.544388\pi$
$307$	−459074.			−0.277995			−0.138997	+	0.990293i	$0.544388\pi$
$308$		0			0
$309$	−742840.			−0.442587
$310$	2.14032e6	+	3.70714e6i	1.26495	+	2.19096i
$311$	−333564.	+	577750.i	−0.195559	+	0.338718i	−0.947084	−	0.320987i	$-0.895986\pi$
$311$	−333564.	+	577750.i	−0.195559	+	0.338718i	0.751525	+	0.659705i	$0.229319\pi$
$312$	352800.	−	611068.i	0.205183	−	0.355388i
$313$	55517.0	+	96158.3i	0.0320306	+	0.0554786i	0.881596	−	0.472004i	$-0.156469\pi$
$313$	55517.0	+	96158.3i	0.0320306	+	0.0554786i	−0.849566	+	0.527483i	$0.823136\pi$
$314$	−2.93524e6			−1.68004
$315$		0			0
$316$	2.16131e6			1.21759
$317$	34389.0	+	59563.5i	0.0192208	+	0.0332914i	0.875476	−	0.483262i	$-0.160548\pi$
$317$	34389.0	+	59563.5i	0.0192208	+	0.0332914i	−0.856255	+	0.516553i	$0.827215\pi$
$318$	−158340.	+	274253.i	−0.0878057	+	0.152084i
$319$	−396488.	+	686737.i	−0.218149	+	0.377845i
$320$	−514304.	−	890801.i	−0.280766	−	0.486301i
$321$	2.04854e6			1.10964
$322$		0			0
$323$	168756.			0.0900022
$324$	1.54425e6	+	2.67471e6i	0.817248	+	1.41552i
$325$	770.000	−	1333.68i	0.000404373	−	0.000700395i
$326$	65960.0	−	114246.i	0.0343745	−	0.0595384i
$327$	650286.	+	1.12633e6i	0.336306	+	0.582500i
$328$	6.46632e6			3.31874
$329$		0			0
$330$	−1.81888e6			−0.919431
$331$	282224.	+	488826.i	0.141587	+	0.245236i	0.928094	−	0.372345i	$-0.121446\pi$
$331$	282224.	+	488826.i	0.141587	+	0.245236i	−0.786507	+	0.617581i	$0.788113\pi$
$332$	698292.	−	1.20948e6i	0.347690	−	0.602216i
$333$	−244353.	+	423232.i	−0.120756	+	0.209155i
$334$	2.46806e6	+	4.27481e6i	1.21057	+	2.09677i
$335$	2.71062e6			1.31965
$336$		0			0
$337$	2.07729e6			0.996376			0.498188	−	0.867069i	$-0.333999\pi$
$337$	2.07729e6			0.996376			0.498188	+	0.867069i	$0.333999\pi$
$338$	−1.75847e6	−	3.04575e6i	−0.837225	−	1.45012i
$339$	−583478.	+	1.01061e6i	−0.275756	+	0.477624i
$340$	−3.27869e6	+	5.67885e6i	−1.53816	+	2.66418i
$341$	886704.	+	1.53582e6i	0.412945	+	0.715243i
$342$	−46060.0			−0.0212941
$343$		0			0
$344$	−3.91680e6			−1.78458
$345$	−715008.	−	1.23843e6i	−0.323417	−	0.560175i
$346$	1.20358e6	−	2.08466e6i	0.540486	−	0.936150i
$347$	26624.0	−	46114.1i	0.0118700	−	0.0205594i	−0.860029	−	0.510244i	$-0.829555\pi$
$347$	26624.0	−	46114.1i	0.0118700	−	0.0205594i	0.871899	+	0.489685i	$0.162888\pi$
$348$	1.62697e6	+	2.81799e6i	0.720163	+	1.24736i
$349$	−2.27200e6			−0.998494			−0.499247	−	0.866460i	$-0.666390\pi$
$349$	−2.27200e6			−0.998494			−0.499247	+	0.866460i	$0.666390\pi$
$350$		0			0
$351$	−568400.			−0.246256
$352$	315520.	+	546497.i	0.135728	+	0.235088i
$353$	−2.00322e6	+	3.46969e6i	−0.855644	+	1.48202i	0.0204028	+	0.999792i	$0.493505\pi$
$353$	−2.00322e6	+	3.46969e6i	−0.855644	+	1.48202i	−0.876047	+	0.482227i	$0.839828\pi$
$354$	191100.	−	330995.i	0.0810499	−	0.140383i
$355$	−1.63968e6	−	2.84001e6i	−0.690539	−	1.19605i
$356$	−3.43958e6			−1.43840
$357$		0			0
$358$	−2.94932e6			−1.21623
$359$	−36892.0	−	63898.8i	−0.0151076	−	0.0261672i	0.858373	−	0.513027i	$-0.171476\pi$
$359$	−36892.0	−	63898.8i	−0.0151076	−	0.0261672i	−0.873480	+	0.486859i	$0.838142\pi$
$360$	473760.	−	820576.i	0.192665	−	0.333705i
$361$	1.23325e6	−	2.13605e6i	0.498061	−	0.862666i
$362$	−1.68490e6	−	2.91833e6i	−0.675776	−	1.17048i
$363$	1.50118e6			0.597951
$364$		0			0
$365$	−3.81259e6			−1.49792
$366$	−1.79536e6	−	3.10965e6i	−0.700566	−	1.21342i
$367$	−702156.	+	1.21617e6i	−0.272125	+	0.471334i	−0.969406	−	0.245464i	$-0.921060\pi$
$367$	−702156.	+	1.21617e6i	−0.272125	+	0.471334i	0.697281	+	0.716798i	$0.254393\pi$
$368$	−1.29869e6	+	2.24939e6i	−0.499902	+	0.865856i
$369$	−422107.	−	731111.i	−0.161383	−	0.279523i
$370$	−5.82288e6			−2.21123
$371$		0			0
$372$	7.27709e6			2.72647
$373$	801617.	+	1.38844e6i	0.298329	+	0.516720i	0.975754	−	0.218872i	$-0.0702376\pi$
$373$	801617.	+	1.38844e6i	0.298329	+	0.516720i	−0.677425	+	0.735592i	$0.736904\pi$
$374$	−1.99752e6	+	3.45981e6i	−0.738435	+	1.27901i
$375$	1.22069e6	−	2.11429e6i	0.448256	−	0.776403i
$376$	1.67832e6	+	2.90694e6i	0.612217	+	1.06039i
$377$	−478520.			−0.173399
$378$		0			0
$379$	−4.77012e6			−1.70581			−0.852906	−	0.522064i	$-0.825162\pi$
$379$	−4.77012e6			−1.70581			−0.852906	+	0.522064i	$0.825162\pi$
$380$	−186592.	−	323187.i	−0.0662879	−	0.114814i
$381$	422688.	−	732117.i	0.149179	−	0.258385i
$382$	1.79132e6	−	3.10266e6i	0.628080	−	1.08787i
$383$	1.11539e6	+	1.93192e6i	0.388536	+	0.672964i	0.992253	−	0.124235i	$-0.0396475\pi$
$383$	1.11539e6	+	1.93192e6i	0.388536	+	0.672964i	−0.603717	+	0.797199i	$0.706314\pi$
$384$	−3.79008e6			−1.31166
$385$		0			0
$386$	9.89554e6			3.38042
$387$	255680.	+	442851.i	0.0867799	+	0.150307i
$388$	1.98920e6	−	3.44540e6i	0.670811	−	1.16188i
$389$	−2.42012e6	+	4.19177e6i	−0.810892	+	1.40451i	0.101348	+	0.994851i	$0.467684\pi$
$389$	−2.42012e6	+	4.19177e6i	−0.810892	+	1.40451i	−0.912240	+	0.409655i	$0.865649\pi$
$390$	−548800.	−	950549.i	−0.182706	−	0.316456i
$391$	−3.14093e6			−1.03900
$392$		0			0
$393$	862204.			0.281597
$394$	−4.95025e6	−	8.57408e6i	−1.60652	−	2.78258i
$395$	889952.	−	1.54144e6i	0.286995	−	0.497089i
$396$	370736.	−	642134.i	0.118803	−	0.205773i
$397$	−497910.	−	862405.i	−0.158553	−	0.274622i	0.775794	−	0.630986i	$-0.217350\pi$
$397$	−497910.	−	862405.i	−0.158553	−	0.274622i	−0.934347	+	0.356364i	$0.884016\pi$
$398$	8.40756e6			2.66049
$399$		0			0
$400$	15664.0			0.00489500
$401$	1.65802e6	+	2.87178e6i	0.514909	+	0.891848i	0.999850	+	0.0173014i	$0.00550748\pi$
$401$	1.65802e6	+	2.87178e6i	0.514909	+	0.891848i	−0.484942	+	0.874546i	$0.661159\pi$
$402$	3.38828e6	−	5.86867e6i	1.04572	−	1.81123i
$403$	−535080.	+	926786.i	−0.164118	+	0.284261i
$404$	−1.31566e6	−	2.27880e6i	−0.401044	−	0.694628i
$405$	2.54346e6			0.770527
$406$		0			0
$407$	−2.41234e6			−0.721858
$408$	4.33944e6	+	7.51613e6i	1.29058	+	2.23534i
$409$	−1.53637e6	+	2.66107e6i	−0.454137	+	0.786588i	−0.998638	−	0.0521720i	$-0.983386\pi$
$409$	−1.53637e6	+	2.66107e6i	−0.454137	+	0.786588i	0.544501	+	0.838760i	$0.316719\pi$
$410$	5.02936e6	−	8.71111e6i	1.47759	−	2.55926i
$411$	−1.43123e6	−	2.47897e6i	−0.417932	−	0.723880i
$412$	3.60808e6			1.04721
$413$		0			0
$414$	857280.			0.245823
$415$	−575064.	−	996040.i	−0.163906	−	0.283894i
$416$	−190400.	+	329782.i	−0.0539428	+	0.0934317i
$417$	−247842.	+	429275.i	−0.0697967	+	0.120891i
$418$	−113680.	−	196900.i	−0.0318232	−	0.0551193i
$419$	2.81438e6			0.783154			0.391577	−	0.920145i	$-0.371930\pi$
$419$	2.81438e6			0.783154			0.391577	+	0.920145i	$0.371930\pi$
$420$		0			0
$421$	3.05802e6			0.840883			0.420441	−	0.907320i	$-0.361875\pi$
$421$	3.05802e6			0.840883			0.420441	+	0.907320i	$0.361875\pi$
$422$	5.75366e6	+	9.96563e6i	1.57276	+	2.72410i
$423$	219114.	−	379517.i	0.0595414	−	0.103129i
$424$	407160.	−	705222.i	0.109989	−	0.190507i
$425$	9471.00	+	16404.3i	0.00254345	+	0.00440539i
$426$	−8.19840e6			−2.18880
$427$		0			0
$428$	−9.95003e6			−2.62552
$429$	−227360.	−	393799.i	−0.0596446	−	0.103307i
$430$	−3.04640e6	+	5.27652e6i	−0.794540	+	1.37618i
$431$	−968748.	+	1.67792e6i	−0.251199	+	0.435089i	−0.963856	−	0.266423i	$-0.914158\pi$
$431$	−968748.	+	1.67792e6i	−0.251199	+	0.435089i	0.712657	+	0.701512i	$0.247491\pi$
$432$	−2.89072e6	−	5.00687e6i	−0.745241	−	1.29080i
$433$	3.94790e6			1.01192			0.505961	−	0.862557i	$-0.331138\pi$
$433$	3.94790e6			1.01192			0.505961	+	0.862557i	$0.331138\pi$
$434$		0			0
$435$	2.67971e6			0.678993
$436$	−3.15853e6	−	5.47074e6i	−0.795736	−	1.37826i
$437$	89376.0	−	154804.i	0.0223881	−	0.0387773i
$438$	−4.76574e6	+	8.25450e6i	−1.18698	+	2.05592i
$439$	3.70885e6	+	6.42392e6i	0.918498	+	1.59089i	0.801698	+	0.597730i	$0.203930\pi$
$439$	3.70885e6	+	6.42392e6i	0.918498	+	1.59089i	0.116800	+	0.993155i	$0.462736\pi$
$440$	4.67712e6			1.15172
$441$		0			0
$442$	−2.41080e6			−0.586956
$443$	−701346.	−	1.21477e6i	−0.169794	−	0.294092i	0.768553	−	0.639786i	$-0.220977\pi$
$443$	−701346.	−	1.21477e6i	−0.169794	−	0.294092i	−0.938347	+	0.345694i	$0.887644\pi$
$444$	−4.94945e6	+	8.57270e6i	−1.19151	+	2.06376i
$445$	−1.41630e6	+	2.45310e6i	−0.339042	+	0.587239i
$446$	−4.12132e6	−	7.13834e6i	−0.981068	−	1.69926i
$447$	283164.			0.0670300
$448$		0			0
$449$	−590574.			−0.138248			−0.0691239	−	0.997608i	$-0.522020\pi$
$449$	−590574.			−0.138248			−0.0691239	+	0.997608i	$0.522020\pi$
$450$	−2585.00	−	4477.35i	−0.000601768	−	0.00104229i
$451$	2.08359e6	−	3.60889e6i	0.482360	−	0.835472i
$452$	2.83404e6	−	4.90869e6i	0.652468	−	1.13011i
$453$	496328.	+	859665.i	0.113638	+	0.196827i
$454$	−743820.			−0.169367
$455$		0			0
$456$	−493920.			−0.111236
$457$	1.45242e6	+	2.51567e6i	0.325313	+	0.563459i	0.981576	−	0.191073i	$-0.0611969\pi$
$457$	1.45242e6	+	2.51567e6i	0.325313	+	0.563459i	−0.656262	+	0.754533i	$0.727864\pi$
$458$	5.65978e6	−	9.80303e6i	1.26077	−	2.18372i
$459$	3.49566e6	−	6.05466e6i	0.774457	−	1.34140i
$460$	3.47290e6	+	6.01523e6i	0.765239	+	1.32543i
$461$	−922684.			−0.202209			−0.101105	−	0.994876i	$-0.532238\pi$
$461$	−922684.			−0.202209			−0.101105	+	0.994876i	$0.532238\pi$
$462$		0			0
$463$	7.18235e6			1.55709			0.778546	−	0.627588i	$-0.215958\pi$
$463$	7.18235e6			1.55709			0.778546	+	0.627588i	$0.215958\pi$
$464$	−2.43362e6	−	4.21515e6i	−0.524756	−	0.908903i
$465$	2.99645e6	−	5.19000e6i	0.642650	−	1.11310i
$466$	−993630.	+	1.72102e6i	−0.211963	+	0.367131i
$467$	306285.	+	530501.i	0.0649881	+	0.112563i	0.896689	−	0.442662i	$-0.145966\pi$
$467$	306285.	+	530501.i	0.0649881	+	0.112563i	−0.831701	+	0.555224i	$0.812632\pi$
$468$	447440.			0.0944322
$469$		0			0
$470$	5.22144e6			1.09030
$471$	2.05467e6	+	3.55879e6i	0.426766	+	0.739180i
$472$	−491400.	+	851130.i	−0.101527	+	0.175849i
$473$	−1.26208e6	+	2.18599e6i	−0.259379	+	0.449257i
$474$	−2.22488e6	−	3.85361e6i	−0.454842	−	0.787810i
$475$	−1078.00			−0.000219222
$476$		0			0
$477$	−106314.			−0.0213941
$478$	2.41452e6	+	4.18207e6i	0.483349	+	0.837185i
$479$	−1.30165e6	+	2.25452e6i	−0.259212	+	0.448969i	−0.966031	−	0.258426i	$-0.916796\pi$
$479$	−1.30165e6	+	2.25452e6i	−0.259212	+	0.448969i	0.706819	+	0.707395i	$0.250130\pi$
$480$	1.06624e6	−	1.84678e6i	0.211228	−	0.365858i
$481$	−727860.	−	1.26069e6i	−0.143445	−	0.248454i
$482$	−8.05910e6			−1.58004
$483$		0			0
$484$	−7.29144e6			−1.41482
$485$	−1.63817e6	−	2.83739e6i	−0.316231	−	0.547728i
$486$	−1.75357e6	+	3.03727e6i	−0.336769	+	0.583301i
$487$	−2.73154e6	+	4.73117e6i	−0.521898	+	0.903954i	0.477777	+	0.878481i	$0.341443\pi$
$487$	−2.73154e6	+	4.73117e6i	−0.521898	+	0.903954i	−0.999676	+	0.0254732i	$0.991891\pi$
$488$	4.61664e6	+	7.99626e6i	0.877559	+	1.51998i
$489$	−184688.			−0.0349274
$490$		0			0
$491$	1.64090e6			0.307170			0.153585	−	0.988135i	$-0.450918\pi$
$491$	1.64090e6			0.307170			0.153585	+	0.988135i	$0.450918\pi$
$492$	−8.54991e6	−	1.48089e7i	−1.59239	−	2.75810i
$493$	2.94290e6	−	5.09725e6i	0.545328	−	0.944536i
$494$	68600.0	−	118819.i	0.0126476	−	0.0219062i
$495$	−305312.	−	528816.i	−0.0560055	−	0.0970044i
$496$	−1.08851e7			−1.98667
$497$		0			0
$498$	−2.87532e6			−0.519533
$499$	−1.49898e6	−	2.59631e6i	−0.269491	−	0.466773i	0.699239	−	0.714888i	$-0.253522\pi$
$499$	−1.49898e6	−	2.59631e6i	−0.269491	−	0.466773i	−0.968731	+	0.248115i	$0.920189\pi$
$500$	−5.92906e6	+	1.02694e7i	−1.06062	+	1.83705i
$501$	3.45528e6	−	5.98473e6i	0.615020	−	1.06525i
$502$	2.15369e6	+	3.73030e6i	0.381438	+	0.660670i
$503$	−6.89405e6			−1.21494			−0.607469	−	0.794343i	$-0.707815\pi$
$503$	−6.89405e6			−1.21494			−0.607469	+	0.794343i	$0.707815\pi$
$504$		0			0
$505$	−2.16698e6			−0.378117
$506$	2.11584e6	+	3.66474e6i	0.367372	+	0.636308i
$507$	−2.46185e6	+	4.26405e6i	−0.425346	+	0.736720i
$508$	−2.05306e6	+	3.55600e6i	−0.352973	+	0.611367i
$509$	−1.15238e6	−	1.99598e6i	−0.197152	−	0.341478i	0.750452	−	0.660925i	$-0.229836\pi$
$509$	−1.15238e6	−	1.99598e6i	−0.197152	−	0.341478i	−0.947604	+	0.319447i	$0.896503\pi$
$510$	1.35005e7			2.29839
$511$		0			0
$512$	1.25312e7			2.11260
$513$	198940.	+	344574.i	0.0333756	+	0.0578082i
$514$	−5.88455e6	+	1.01923e7i	−0.982439	+	1.70163i
$515$	1.48568e6	−	2.57327e6i	0.246835	−	0.427531i
$516$	5.17888e6	+	8.97008e6i	0.856272	+	1.48311i
$517$	2.16317e6			0.355929
$518$		0			0
$519$	−3.37002e6			−0.549180
$520$	1.41120e6	+	2.44427e6i	0.228865	+	0.396407i
$521$	6.04802e6	−	1.04755e7i	0.976155	−	1.69075i	0.300087	−	0.953912i	$-0.402984\pi$
$521$	6.04802e6	−	1.04755e7i	0.976155	−	1.69075i	0.676068	−	0.736839i	$-0.263682\pi$
$522$	−803230.	+	1.39124e6i	−0.129022	+	0.223473i
$523$	−2.74221e6	−	4.74966e6i	−0.438377	−	0.759290i	0.559188	−	0.829041i	$-0.311113\pi$
$523$	−2.74221e6	−	4.74966e6i	−0.438377	−	0.759290i	−0.997564	+	0.0697505i	$0.977780\pi$
$524$	−4.18785e6			−0.666289
$525$		0			0
$526$	−1.29098e7			−2.03448
$527$	−6.58148e6	−	1.13995e7i	−1.03228	−	1.78796i
$528$	2.31258e6	−	4.00550e6i	0.361003	−	0.625276i
$529$	1.55468e6	−	2.69279e6i	0.241548	−	0.418373i
$530$	−633360.	−	1.09701e6i	−0.0979402	−	0.169637i
$531$	128310.			0.0197480
$532$		0			0
$533$	2.51468e6			0.383411
$534$	3.54074e6	+	6.13274e6i	0.537330	+	0.930682i
$535$	−4.09707e6	+	7.09634e6i	−0.618855	+	1.07189i
$536$	−8.71272e6	+	1.50909e7i	−1.30991	+	2.26883i
$537$	2.06452e6	+	3.57586e6i	0.308947	+	0.535112i
$538$	1.27756e7			1.90294
$539$		0			0
$540$	−1.54605e7			−2.28160
$541$	3.35900e6	+	5.81795e6i	0.493420	+	0.854628i	0.999971	−	0.00758172i	$-0.00241336\pi$
$541$	3.35900e6	+	5.81795e6i	0.493420	+	0.854628i	−0.506552	+	0.862210i	$0.669080\pi$
$542$	8.25272e6	−	1.42941e7i	1.20670	−	2.09006i
$543$	−2.35886e6	+	4.08567e6i	−0.343323	+	0.594652i
$544$	−2.34192e6	−	4.05632e6i	−0.339293	−	0.587673i
$545$	−5.20229e6			−0.750245
$546$		0			0
$547$	−5.00235e6			−0.714835			−0.357418	−	0.933945i	$-0.616343\pi$
$547$	−5.00235e6			−0.714835			−0.357418	+	0.933945i	$0.616343\pi$
$548$	6.95171e6	+	1.20407e7i	0.988872	+	1.71278i
$549$	602728.	−	1.04396e6i	0.0853474	−	0.147826i
$550$	12760.0	−	22101.0i	0.00179864	−	0.00311533i
$551$	167482.	+	290087.i	0.0235012	+	0.0407052i
$552$	9.19296e6			1.28413
$553$		0			0
$554$	1.06409e7			1.47300
$555$	4.07602e6	+	7.05987e6i	0.561699	+	0.972891i
$556$	1.20380e6	−	2.08505e6i	0.165146	−	0.286042i
$557$	−4.50980e6	+	7.81121e6i	−0.615913	+	1.06679i	0.374310	+	0.927304i	$0.377880\pi$
$557$	−4.50980e6	+	7.81121e6i	−0.615913	+	1.06679i	−0.990224	+	0.139490i	$0.955454\pi$
$558$	1.79634e6	+	3.11135e6i	0.244232	+	0.423023i
$559$	−1.52320e6			−0.206171
$560$		0			0
$561$	5.59306e6			0.750312
$562$	−111710.	−	193487.i	−0.0149194	−	0.0258412i
$563$	−6.20255e6	+	1.07431e7i	−0.824707	+	1.42843i	0.0774366	+	0.996997i	$0.475326\pi$
$563$	−6.20255e6	+	1.07431e7i	−0.824707	+	1.42843i	−0.902143	+	0.431437i	$0.858007\pi$
$564$	4.43822e6	−	7.68723e6i	0.587505	−	1.01759i
$565$	−2.33391e6	−	4.04245e6i	−0.307584	−	0.532751i
$566$	2.49574e7			3.27460
$567$		0			0
$568$	2.10816e7			2.74178
$569$	−3.24402e6	−	5.61881e6i	−0.420052	−	0.727551i	0.575892	−	0.817526i	$-0.304655\pi$
$569$	−3.24402e6	−	5.61881e6i	−0.420052	−	0.727551i	−0.995944	+	0.0899747i	$0.971321\pi$
$570$	−384160.	+	665385.i	−0.0495251	+	0.0857799i
$571$	5.11425e6	−	8.85814e6i	0.656435	−	1.13698i	−0.325097	−	0.945681i	$-0.605397\pi$
$571$	5.11425e6	−	8.85814e6i	0.656435	−	1.13698i	0.981532	−	0.191298i	$-0.0612698\pi$
$572$	1.10432e6	+	1.91274e6i	0.141125	+	0.244436i
$573$	−5.01570e6			−0.638182
$574$		0			0
$575$	20064.0			0.00253074
$576$	−431648.	−	747636.i	−0.0542093	−	0.0938932i
$577$	−1.32669e6	+	2.29789e6i	−0.165894	+	0.287336i	−0.936972	−	0.349404i	$-0.886384\pi$
$577$	−1.32669e6	+	2.29789e6i	−0.165894	+	0.287336i	0.771079	+	0.636740i	$0.219717\pi$
$578$	7.72714e6	−	1.33838e7i	0.962053	−	1.66632i
$579$	−6.92688e6	−	1.19977e7i	−0.858699	−	1.48731i
$580$	−1.30157e7			−1.60657
$581$		0			0
$582$	−8.19084e6			−1.00235
$583$	−262392.	−	454476.i	−0.0319727	−	0.0553783i
$584$	1.22548e7	−	2.12259e7i	1.48687	−	2.57533i
$585$	184240.	−	319113.i	0.0222584	−	0.0385527i
$586$	−9.65888e6	−	1.67297e7i	−1.16194	−	2.01253i
$587$	−1.43044e7			−1.71346			−0.856729	−	0.515766i	$-0.827507\pi$
$587$	−1.43044e7			−1.71346			−0.856729	+	0.515766i	$0.827507\pi$
$588$		0			0
$589$	749112.			0.0889731
$590$	764400.	+	1.32398e6i	0.0904046	+	0.156585i
$591$	−6.93035e6	+	1.20037e7i	−0.816181	+	1.41367i
$592$	7.40338e6	−	1.28230e7i	0.868212	−	1.50379i
$593$	5.01327e6	+	8.68323e6i	0.585442	+	1.01402i	0.994820	+	0.101651i	$0.0324125\pi$
$593$	5.01327e6	+	8.68323e6i	0.585442	+	1.01402i	−0.409378	+	0.912365i	$0.634254\pi$
$594$	−9.41920e6			−1.09534
$595$		0			0
$596$	−1.37537e6			−0.158600
$597$	−5.88529e6	−	1.01936e7i	−0.675822	−	1.17056i
$598$	−1.27680e6	+	2.21148e6i	−0.146006	+	0.252889i
$599$	3.76146e6	−	6.51504e6i	0.428341	−	0.741908i	−0.568385	−	0.822763i	$-0.692432\pi$
$599$	3.76146e6	−	6.51504e6i	0.428341	−	0.741908i	0.996726	+	0.0808547i	$0.0257650\pi$
$600$	−27720.0	−	48012.4i	−0.00314351	−	0.00544472i
$601$	3.38625e6			0.382413			0.191207	−	0.981550i	$-0.438760\pi$
$601$	3.38625e6			0.382413			0.191207	+	0.981550i	$0.438760\pi$
$602$		0			0
$603$	2.27499e6			0.254792
$604$	−2.41074e6	−	4.17552e6i	−0.268879	−	0.465713i
$605$	−3.00236e6	+	5.20023e6i	−0.333483	+	0.577610i
$606$	−2.70872e6	+	4.69164e6i	−0.299628	+	0.518971i
$607$	3.45430e6	+	5.98303e6i	0.380530	+	0.659097i	0.991138	−	0.132836i	$-0.0424083\pi$
$607$	3.45430e6	+	5.98303e6i	0.380530	+	0.659097i	−0.610608	+	0.791933i	$0.709075\pi$
$608$	266560.			0.0292439
$609$		0			0
$610$	1.43629e7			1.56285
$611$	652680.	+	1.13047e6i	0.0707290	+	0.122506i
$612$	−2.75176e6	+	4.76618e6i	−0.296983	+	0.514389i
$613$	4.84448e6	−	8.39088e6i	0.520710	−	0.901896i	−0.479000	−	0.877815i	$-0.659001\pi$
$613$	4.84448e6	−	8.39088e6i	0.520710	−	0.901896i	0.999710	−	0.0240812i	$-0.00766604\pi$
$614$	−2.29537e6	−	3.97570e6i	−0.245715	−	0.425591i
$615$	−1.40822e7			−1.50135
$616$		0			0
$617$	−7.84742e6			−0.829877			−0.414939	−	0.909849i	$-0.636197\pi$
$617$	−7.84742e6			−0.829877			−0.414939	+	0.909849i	$0.636197\pi$
$618$	−3.71420e6	−	6.43318e6i	−0.391196	−	0.677571i
$619$	5.09860e6	−	8.83103e6i	0.534840	−	0.926370i	−0.464331	−	0.885662i	$-0.653705\pi$
$619$	5.09860e6	−	8.83103e6i	0.534840	−	0.926370i	0.999171	−	0.0407086i	$-0.0129615\pi$
$620$	−1.45542e7	+	2.52086e7i	−1.52058	+	2.63372i
$621$	−3.70272e6	−	6.41330e6i	−0.385294	−	0.667348i
$622$	−6.67128e6			−0.691406
$623$		0			0
$624$	2.79104e6			0.286949
$625$	4.89994e6	+	8.48694e6i	0.501754	+	0.869063i
$626$	−555170.	+	961583.i	−0.0566226	+	0.0980733i
$627$	−159152.	+	275659.i	−0.0161675	+	0.0280030i
$628$	−9.97982e6	−	1.72855e7i	−1.00977	−	1.74898i
$629$	1.79054e7			1.80450
$630$		0			0
$631$	−8.36258e6			−0.836116			−0.418058	−	0.908420i	$-0.637289\pi$
$631$	−8.36258e6			−0.836116			−0.418058	+	0.908420i	$0.637289\pi$
$632$	5.72112e6	+	9.90927e6i	0.569755	+	0.986845i
$633$	8.05512e6	−	1.39519e7i	0.799030	−	1.38396i
$634$	−343890.	+	595635.i	−0.0339779	+	0.0588514i
$635$	1.69075e6	+	2.92847e6i	0.166397	+	0.288208i
$636$	−2.15342e6			−0.211099
$637$		0			0
$638$	−7.92976e6			−0.771273
$639$	−1.37616e6	−	2.38358e6i	−0.133327	−	0.230928i
$640$	7.58016e6	−	1.31292e7i	0.731524	−	1.26704i
$641$	−551415.	+	955079.i	−0.0530070	+	0.0918109i	−0.891311	−	0.453392i	$-0.850214\pi$
$641$	−551415.	+	955079.i	−0.0530070	+	0.0918109i	0.838304	+	0.545203i	$0.183547\pi$
$642$	1.02427e7	+	1.77408e7i	0.980790	+	1.69878i
$643$	1.71354e7			1.63443			0.817217	−	0.576330i	$-0.195516\pi$
$643$	1.71354e7			1.63443			0.817217	+	0.576330i	$0.195516\pi$
$644$		0			0
$645$	8.52992e6			0.807320
$646$	843780.	+	1.46147e6i	0.0795514	+	0.137787i
$647$	27482.0	−	47600.2i	0.00258100	−	0.00447042i	−0.864732	−	0.502234i	$-0.832512\pi$
$647$	27482.0	−	47600.2i	0.00258100	−	0.00447042i	0.867313	+	0.497763i	$0.165845\pi$
$648$	−8.17542e6	+	1.41602e7i	−0.764843	+	1.32475i
$649$	316680.	+	548506.i	0.0295127	+	0.0511175i
$650$	15400.0			0.00142968
$651$		0			0
$652$	897056.			0.0826420
$653$	242583.	+	420166.i	0.0222627	+	0.0385601i	0.876942	−	0.480596i	$-0.159580\pi$
$653$	242583.	+	420166.i	0.0222627	+	0.0385601i	−0.854679	+	0.519156i	$0.826246\pi$
$654$	−6.50286e6	+	1.12633e7i	−0.594511	+	1.02972i
$655$	−1.72441e6	+	2.98676e6i	−0.157050	+	0.272018i
$656$	1.27889e7	+	2.21511e7i	1.16031	+	2.00972i
$657$	−3.19985e6			−0.289212
$658$		0			0
$659$	−2.72136e6			−0.244103			−0.122051	−	0.992524i	$-0.538947\pi$
$659$	−2.72136e6			−0.244103			−0.122051	+	0.992524i	$0.538947\pi$
$660$	−6.18419e6	−	1.07113e7i	−0.552616	−	0.957158i
$661$	1.07262e6	−	1.85784e6i	0.0954869	−	0.165388i	−0.814325	−	0.580409i	$-0.802893\pi$
$661$	1.07262e6	−	1.85784e6i	0.0954869	−	0.165388i	0.909812	+	0.415021i	$0.136226\pi$
$662$	−2.82224e6	+	4.88826e6i	−0.250293	+	0.433520i
$663$	1.68756e6	+	2.92294e6i	0.149099	+	0.258247i
$664$	7.39368e6			0.650789
$665$		0			0
$666$	−4.88706e6			−0.426935
$667$	−3.11722e6	−	5.39918e6i	−0.271302	−	0.469908i
$668$	−1.67828e7	+	2.90687e7i	−1.45520	+	2.52048i
$669$	−5.76985e6	+	9.99367e6i	−0.498424	+	0.863296i
$670$	1.35531e7	+	2.34747e7i	1.16641	+	2.02029i
$671$	5.95034e6			0.510194
$672$		0			0
$673$	2.92796e6			0.249188			0.124594	−	0.992208i	$-0.460237\pi$
$673$	2.92796e6			0.249188			0.124594	+	0.992208i	$0.460237\pi$
$674$	1.03865e7	+	1.79899e7i	0.880680	+	1.52538i
$675$	−22330.0	+	38676.7i	−0.00188638	+	0.00326731i
$676$	1.19576e7	−	2.07111e7i	1.00641	−	1.74316i
$677$	6.74961e6	+	1.16907e7i	0.565988	+	0.980319i	0.996957	+	0.0779529i	$0.0248384\pi$
$677$	6.74961e6	+	1.16907e7i	0.565988	+	0.980319i	−0.430969	+	0.902367i	$0.641828\pi$
$678$	−1.16696e7			−0.974945
$679$		0			0
$680$	−3.47155e7			−2.87906
$681$	520674.	+	901834.i	0.0430227	+	0.0745176i
$682$	−8.86704e6	+	1.53582e7i	−0.729991	+	1.26438i
$683$	2.71486e6	−	4.70228e6i	0.222688	−	0.385706i	−0.732936	−	0.680298i	$-0.761850\pi$
$683$	2.71486e6	−	4.70228e6i	0.222688	−	0.385706i	0.955623	+	0.294592i	$0.0951837\pi$
$684$	−156604.	−	271246.i	−0.0127986	−	0.0221678i
$685$	1.14499e7			0.932340
$686$		0			0
$687$	−1.58474e7			−1.28105
$688$	−7.74656e6	−	1.34174e7i	−0.623933	−	1.08068i
$689$	158340.	−	274253.i	0.0127070	−	0.0220091i
$690$	7.15008e6	−	1.23843e7i	0.571726	−	0.990259i
$691$	−1.04140e7	−	1.80376e7i	−0.829702	−	1.43709i	−0.898272	−	0.439440i	$-0.855177\pi$
$691$	−1.04140e7	−	1.80376e7i	−0.829702	−	1.43709i	0.0685703	−	0.997646i	$-0.478156\pi$
$692$	1.63687e7			1.29942
$693$		0			0
$694$	532480.			0.0419667
$695$	−991368.	−	1.71710e6i	−0.0778526	−	0.134845i
$696$	−8.61336e6	+	1.49188e7i	−0.673984	+	1.16737i
$697$	−1.54653e7	+	2.67867e7i	−1.20580	+	2.08851i
$698$	−1.13600e7	−	1.96761e7i	−0.882552	−	1.52863i
$699$	2.78216e6			0.215372
$700$		0			0
$701$	2.35141e7			1.80731			0.903655	−	0.428261i	$-0.140874\pi$
$701$	2.35141e7			1.80731			0.903655	+	0.428261i	$0.140874\pi$
$702$	−2.84200e6	−	4.92249e6i	−0.217661	−	0.377000i
$703$	−509502.	+	882483.i	−0.0388828	+	0.0673470i
$704$	2.13069e6	−	3.69046e6i	0.162027	−	0.280640i
$705$	−3.65501e6	−	6.33066e6i	−0.276959	−	0.479707i
$706$	−4.00645e7			−3.02516
$707$		0			0
$708$	2.59896e6			0.194857
$709$	9.78734e6	+	1.69522e7i	0.731221	+	1.26651i	0.956361	+	0.292186i	$0.0943827\pi$
$709$	9.78734e6	+	1.69522e7i	0.731221	+	1.26651i	−0.225140	+	0.974326i	$0.572284\pi$
$710$	1.63968e7	−	2.84001e7i	1.22071	−	2.11434i
$711$	746924.	−	1.29371e6i	0.0554118	−	0.0959761i
$712$	−9.10476e6	−	1.57699e7i	−0.673083	−	1.16581i
$713$	−1.39427e7			−1.02712
$714$		0			0
$715$	1.81888e6			0.133057
$716$	−1.00277e7	−	1.73685e7i	−0.731001	−	1.26613i
$717$	3.38033e6	−	5.85490e6i	0.245562	−	0.425326i
$718$	368920.	−	638988.i	0.0267068	−	0.0462575i
$719$	1.30576e7	+	2.26164e7i	0.941978	+	1.63155i	0.761692	+	0.647940i	$0.224369\pi$
$719$	1.30576e7	+	2.26164e7i	0.941978	+	1.63155i	0.180287	+	0.983614i	$0.442298\pi$
$720$	3.74797e6			0.269442
$721$		0			0
$722$	2.46650e7			1.76091
$723$	5.64137e6	+	9.77114e6i	0.401364	+	0.695184i
$724$	1.14573e7	−	1.98447e7i	0.812338	−	1.40701i
$725$	−18799.0	+	32560.8i	−0.00132828	+	0.00230065i
$726$	7.50589e6	+	1.30006e7i	0.528519	+	0.915422i
$727$	1.54126e7			1.08154			0.540768	−	0.841172i	$-0.318134\pi$
$727$	1.54126e7			1.08154			0.540768	+	0.841172i	$0.318134\pi$
$728$		0			0
$729$	1.59468e7			1.11136
$730$	−1.90630e7	−	3.30180e7i	−1.32399	−	2.29321i
$731$	9.36768e6	−	1.62253e7i	0.648393	−	1.12305i
$732$	1.22084e7	−	2.11457e7i	0.842137	−	1.45862i
$733$	8.49341e6	+	1.47110e7i	0.583878	+	1.01131i	0.995014	+	0.0997324i	$0.0317987\pi$
$733$	8.49341e6	+	1.47110e7i	0.583878	+	1.01131i	−0.411136	+	0.911574i	$0.634868\pi$
$734$	−1.40431e7			−0.962107
$735$		0			0
$736$	−4.96128e6			−0.337597
$737$	5.61486e6	+	9.72523e6i	0.380777	+	0.659525i
$738$	4.22107e6	−	7.31111e6i	0.285287	−	0.494131i
$739$	−1.00756e6	+	1.74514e6i	−0.0678669	+	0.117549i	−0.897962	−	0.440073i	$-0.854953\pi$
$739$	−1.00756e6	+	1.74514e6i	−0.0678669	+	0.117549i	0.830095	+	0.557622i	$0.188286\pi$
$740$	−1.97978e7	−	3.42908e7i	−1.32904	−	2.30196i
$741$	−192080.			−0.0128510
$742$		0			0
$743$	−1.51381e7			−1.00600			−0.503001	−	0.864286i	$-0.667771\pi$
$743$	−1.51381e7			−1.00600			−0.503001	+	0.864286i	$0.667771\pi$
$744$	1.92629e7	+	3.33643e7i	1.27582	+	2.20978i
$745$	−566328.	+	980909.i	−0.0373833	+	0.0647497i
$746$	−8.01617e6	+	1.38844e7i	−0.527375	+	0.913441i
$747$	−482643.	−	835962.i	−0.0316464	−	0.0548132i
$748$	−2.71663e7			−1.77532
$749$		0			0
$750$	2.44138e7			1.58483
$751$	−3.60700e6	−	6.24751e6i	−0.233371	−	0.404210i	0.725427	−	0.688299i	$-0.241642\pi$
$751$	−3.60700e6	−	6.24751e6i	−0.233371	−	0.404210i	−0.958798	+	0.284089i	$0.908309\pi$
$752$	−6.63869e6	+	1.14985e7i	−0.428093	+	0.741478i
$753$	3.01517e6	−	5.22242e6i	0.193787	−	0.335648i
$754$	−2.39260e6	−	4.14410e6i	−0.153265	−	0.265462i
$755$	−3.97062e6			−0.253508
$756$		0			0
$757$	−1.09697e7			−0.695755			−0.347877	−	0.937540i	$-0.613097\pi$
$757$	−1.09697e7			−0.695755			−0.347877	+	0.937540i	$0.613097\pi$
$758$	−2.38506e7	−	4.13105e7i	−1.50774	−	2.61148i
$759$	2.96218e6	−	5.13064e6i	0.186641	−	0.323271i
$760$	987840.	−	1.71099e6i	0.0620373	−	0.107452i
$761$	−9.62210e6	−	1.66660e7i	−0.602293	−	1.04320i	−0.992473	−	0.122464i	$-0.960920\pi$
$761$	−9.62210e6	−	1.66660e7i	−0.602293	−	1.04320i	0.390180	−	0.920739i	$-0.372413\pi$
$762$	8.45376e6			0.527427
$763$		0			0
$764$	2.43620e7			1.51001
$765$	2.26615e6	+	3.92509e6i	0.140002	+	0.242491i
$766$	−1.11539e7	+	1.93192e7i	−0.686841	+	1.18964i
$767$	−191100.	+	330995.i	−0.0117293	+	0.0203158i
$768$	−1.48360e7	−	2.56967e7i	−0.907638	−	1.57208i
$769$	8.21185e6			0.500755			0.250378	−	0.968148i	$-0.419445\pi$
$769$	8.21185e6			0.500755			0.250378	+	0.968148i	$0.419445\pi$
$770$		0			0
$771$	1.64767e7			0.998241
$772$	3.36448e7	+	5.82746e7i	2.03177	+	3.51913i
$773$	−9.30933e6	+	1.61242e7i	−0.560363	+	0.970578i	0.437101	+	0.899412i	$0.356005\pi$
$773$	−9.30933e6	+	1.61242e7i	−0.560363	+	0.970578i	−0.997465	+	0.0711653i	$0.977328\pi$
$774$	−2.55680e6	+	4.42851e6i	−0.153407	+	0.265708i
$775$	42042.0	+	72818.9i	0.00251437	+	0.00435502i
$776$	2.10622e7			1.25559
$777$		0			0
$778$	−4.84024e7			−2.86694
$779$	−880138.	−	1.52444e6i	−0.0519645	−	0.0900052i
$780$	3.73184e6	−	6.46374e6i	0.219627	−	0.380406i
$781$	6.79296e6	−	1.17658e7i	0.398503	−	0.690227i
$782$	−1.57046e7	−	2.72012e7i	−0.918356	−	1.59064i
$783$	1.38771e7			0.808898
$784$		0			0
$785$	−1.64373e7			−0.952045
$786$	4.31102e6	+	7.46691e6i	0.248899	+	0.431106i
$787$	−1.31250e7	+	2.27332e7i	−0.755377	+	1.30835i	0.189810	+	0.981821i	$0.439213\pi$
$787$	−1.31250e7	+	2.27332e7i	−0.755377	+	1.30835i	−0.945187	+	0.326530i	$0.894121\pi$
$788$	3.36617e7	−	5.83038e7i	1.93117	−	3.34488i
$789$	9.03683e6	+	1.56523e7i	0.516801	+	0.895126i
$790$	1.77990e7			1.01468
$791$		0			0
$792$	3.92544e6			0.222370
$793$	1.79536e6	+	3.10965e6i	0.101384	+	0.175602i
$794$	4.97910e6	−	8.62405e6i	0.280285	−	0.485468i
$795$	−886704.	+	1.53582e6i	−0.0497578	+	0.0861830i
$796$	2.85857e7	+	4.95119e7i	1.59907	+	2.76966i
$797$	−1.00373e7			−0.559720			−0.279860	−	0.960041i	$-0.590288\pi$
$797$	−1.00373e7			−0.559720			−0.279860	+	0.960041i	$0.590288\pi$
$798$		0			0
$799$	−1.60559e7			−0.889751
$800$	14960.0	+	25911.5i	0.000826431	+	0.00143142i
$801$	−1.18868e6	+	2.05885e6i	−0.0654610	+	0.113382i
$802$	−1.65802e7	+	2.87178e7i	−0.910238	+	1.57658i
$803$	−7.89751e6	−	1.36789e7i	−0.432217	−	0.748621i
$804$	4.60806e7			2.51407
$805$		0			0
$806$	−1.07016e7			−0.580245
$807$	−8.94289e6	−	1.54895e7i	−0.483386	−	0.837249i
$808$	6.96528e6	−	1.20642e7i	0.375327	−	0.650086i
$809$	−7.04420e6	+	1.22009e7i	−0.378408	+	0.655422i	−0.990831	−	0.135109i	$-0.956862\pi$
$809$	−7.04420e6	+	1.22009e7i	−0.378408	+	0.655422i	0.612423	+	0.790530i	$0.290195\pi$
$810$	1.27173e7	+	2.20270e7i	0.681056	+	1.17962i
$811$	1.81433e7			0.968646			0.484323	−	0.874889i	$-0.339066\pi$
$811$	1.81433e7			0.968646			0.484323	+	0.874889i	$0.339066\pi$
$812$		0			0
$813$	−2.31076e7			−1.22611
$814$	−1.20617e7	−	2.08914e7i	−0.638038	−	1.10511i
$815$	369376.	−	639778.i	0.0194794	−	0.0337392i
$816$	−1.71649e7	+	2.97305e7i	−0.902435	+	1.56306i
$817$	533120.	+	923391.i	0.0279428	+	0.0483983i
$818$	−3.07273e7			−1.60562
$819$		0			0
$820$	6.83993e7			3.55236
$821$	1.06835e7	+	1.85043e7i	0.553164	+	0.958109i	0.998044	+	0.0625181i	$0.0199131\pi$
$821$	1.06835e7	+	1.85043e7i	0.553164	+	0.958109i	−0.444880	+	0.895590i	$0.646754\pi$
$822$	1.43123e7	−	2.47897e7i	0.738807	−	1.27965i
$823$	−8.90087e6	+	1.54168e7i	−0.458071	+	0.793402i	−0.998859	−	0.0477567i	$-0.984793\pi$
$823$	−8.90087e6	+	1.54168e7i	−0.458071	+	0.793402i	0.540788	+	0.841159i	$0.318126\pi$
$824$	9.55080e6	+	1.65425e7i	0.490029	+	0.848755i
$825$	−35728.0			−0.00182757
$826$		0			0
$827$	1.62921e7			0.828350			0.414175	−	0.910197i	$-0.364070\pi$
$827$	1.62921e7			0.828350			0.414175	+	0.910197i	$0.364070\pi$
$828$	2.91475e6	+	5.04850e6i	0.147749	+	0.255909i
$829$	1.04250e6	−	1.80566e6i	0.0526851	−	0.0912533i	−0.838480	−	0.544932i	$-0.816555\pi$
$829$	1.04250e6	−	1.80566e6i	0.0526851	−	0.0912533i	0.891165	+	0.453679i	$0.149889\pi$
$830$	5.75064e6	−	9.96040e6i	0.289748	−	0.501859i
$831$	−7.44863e6	−	1.29014e7i	−0.374174	−	0.648089i
$832$	2.57152e6			0.128790
$833$		0			0
$834$	−4.95684e6			−0.246769
$835$	1.38211e7	+	2.39389e7i	0.686005	+	1.18820i
$836$	773024.	−	1.33892e6i	0.0382540	−	0.0662579i
$837$	1.55173e7	−	2.68768e7i	0.765602	−	1.32606i
$838$	1.40719e7	+	2.43732e7i	0.692217	+	1.19896i
$839$	−2.27850e7			−1.11749			−0.558745	−	0.829340i	$-0.688717\pi$
$839$	−2.27850e7			−1.11749			−0.558745	+	0.829340i	$0.688717\pi$
$840$		0			0
$841$	−8.82842e6			−0.430421
$842$	1.52901e7	+	2.64832e7i	0.743242	+	1.28733i
$843$	−156394.	+	270882.i	−0.00757968	+	0.0131284i
$844$	−3.91249e7	+	6.77663e7i	−1.89059	+	3.27460i
$845$	−9.84740e6	−	1.70562e7i	−0.474439	−	0.821752i
$846$	4.38228e6			0.210511
$847$		0			0
$848$	3.22109e6			0.153820
$849$	−1.74702e7	−	3.02592e7i	−0.831817	−	1.44075i
$850$	−94710.0	+	164043.i	−0.00449623	+	0.00778770i
$851$	9.48298e6	−	1.64250e7i	0.448870	−	0.777466i
$852$	−2.78746e7	−	4.82802e7i	−1.31556	−	2.27861i
$853$	−2.26975e7			−1.06808			−0.534042	−	0.845458i	$-0.679328\pi$
$853$	−2.26975e7			−1.06808			−0.534042	+	0.845458i	$0.679328\pi$
$854$		0			0
$855$	−257936.			−0.0120669
$856$	−2.63383e7	−	4.56193e7i	−1.22858	−	2.12796i
$857$	−1.26450e7	+	2.19017e7i	−0.588120	+	1.01865i	0.406359	+	0.913714i	$0.366798\pi$
$857$	−1.26450e7	+	2.19017e7i	−0.588120	+	1.01865i	−0.994479	+	0.104940i	$0.966535\pi$
$858$	2.27360e6	−	3.93799e6i	0.105438	−	0.182623i
$859$	5.19737e6	+	9.00210e6i	0.240326	+	0.416257i	0.960807	−	0.277218i	$-0.0894124\pi$
$859$	5.19737e6	+	9.00210e6i	0.240326	+	0.416257i	−0.720481	+	0.693474i	$0.756079\pi$
$860$	−4.14310e7			−1.91020
$861$		0			0
$862$	−1.93750e7			−0.888122
$863$	−2.16700e7	−	3.75335e7i	−0.990447	−	1.71551i	−0.614642	−	0.788807i	$-0.710699\pi$
$863$	−2.16700e7	−	3.75335e7i	−0.990447	−	1.71551i	−0.375806	−	0.926698i	$-0.622634\pi$
$864$	5.52160e6	−	9.56369e6i	0.251641	−	0.435854i
$865$	6.74005e6	−	1.16741e7i	0.306283	−	0.530498i
$866$	1.97395e7	+	3.41898e7i	0.894420	+	1.54918i
$867$	−2.16360e7			−0.977527
$868$		0			0
$869$	7.37389e6			0.331243
$870$	1.33986e7	+	2.32070e7i	0.600150	+	1.03949i
$871$	−3.38828e6	+	5.86867e6i	−0.151333	+	0.262117i
$872$	1.67216e7	−	2.89627e7i	0.744711	−	1.28988i
$873$	−1.37489e6	−	2.38138e6i	−0.0610566	−	0.105753i
$874$	1.78752e6			0.0791539
$875$		0			0
$876$	−6.48141e7			−2.85370
$877$	−1.85830e7	−	3.21866e7i	−0.815861	−	1.41311i	−0.908708	−	0.417432i	$-0.862930\pi$
$877$	−1.85830e7	−	3.21866e7i	−0.815861	−	1.41311i	0.0928475	−	0.995680i	$-0.470403\pi$
$878$	−3.70885e7	+	6.42392e7i	−1.62369	+	2.81231i
$879$	−1.35224e7	+	2.34215e7i	−0.590313	+	1.02245i
$880$	9.25030e6	+	1.60220e7i	0.402670	+	0.697445i
$881$	9.04785e6			0.392740			0.196370	−	0.980530i	$-0.437085\pi$
$881$	9.04785e6			0.392740			0.196370	+	0.980530i	$0.437085\pi$
$882$		0			0
$883$	3.29679e7			1.42295			0.711474	−	0.702712i	$-0.248028\pi$
$883$	3.29679e7			1.42295			0.711474	+	0.702712i	$0.248028\pi$
$884$	−8.19672e6	−	1.41971e7i	−0.352784	−	0.611041i
$885$	1.07016e6	−	1.85357e6i	0.0459294	−	0.0795520i
$886$	7.01346e6	−	1.21477e7i	0.300157	−	0.519887i
$887$	8.05494e6	+	1.39516e7i	0.343758	+	0.595407i	0.985127	−	0.171826i	$-0.0549665\pi$
$887$	8.05494e6	+	1.39516e7i	0.343758	+	0.595407i	−0.641369	+	0.767233i	$0.721633\pi$
$888$	−5.24059e7			−2.23022
$889$		0			0
$890$	−2.83259e7			−1.19870
$891$	5.26860e6	+	9.12549e6i	0.222332	+	0.385090i
$892$	2.80250e7	−	4.85407e7i	1.17932	−	2.04265i
$893$	456876.	−	791332.i	0.0191721	−	0.0332071i
$894$	1.41582e6	+	2.45227e6i	0.0592467	+	0.102618i
$895$	−1.65162e7			−0.689211
$896$		0			0
$897$	3.57504e6			0.148354
$898$	−2.95287e6	−	5.11452e6i	−0.122195	−	0.211648i
$899$	1.30636e7	−	2.26268e7i	0.539093	−	0.933736i
$900$	17578.0	−	30446.0i	0.000723374	−	0.00125292i
$901$	1.94758e6	+	3.37331e6i	0.0799252	+	0.138435i
$902$	4.16718e7			1.70540
$903$		0			0
$904$	3.00074e7			1.22126
$905$	−9.43544e6	−	1.63427e7i	−0.382949	−	0.663287i
$906$	−4.96328e6	+	8.59665e6i	−0.200885	+	0.347944i
$907$	2.23643e7	−	3.87361e7i	0.902686	−	1.56350i	0.0786925	−	0.996899i	$-0.474925\pi$
$907$	2.23643e7	−	3.87361e7i	0.902686	−	1.56350i	0.823994	−	0.566599i	$-0.191741\pi$
$908$	−2.52899e6	−	4.38034e6i	−0.101796	−	0.176316i
$909$	−1.81871e6			−0.0730053
$910$		0			0
$911$	−6.60518e6			−0.263687			−0.131844	−	0.991271i	$-0.542090\pi$
$911$	−6.60518e6			−0.263687			−0.131844	+	0.991271i	$0.542090\pi$
$912$	−976864.	−	1.69198e6i	−0.0388908	−	0.0673609i
$913$	2.38241e6	−	4.12645e6i	0.0945887	−	0.163832i
$914$	−1.45242e7	+	2.51567e7i	−0.575078	+	0.996065i
$915$	−1.00540e7	−	1.74141e7i	−0.396997	−	0.687618i
$916$	7.69730e7			3.03110
$917$		0			0
$918$	6.99132e7			2.73812
$919$	1.54465e7	+	2.67541e7i	0.603311	+	1.04496i	0.992316	+	0.123729i	$0.0394855\pi$
$919$	1.54465e7	+	2.67541e7i	0.603311	+	1.04496i	−0.389005	+	0.921236i	$0.627181\pi$
$920$	−1.83859e7	+	3.18453e7i	−0.716169	+	1.24044i
$921$	−3.21352e6	+	5.56598e6i	−0.124834	+	0.216218i
$922$	−4.61342e6	−	7.99068e6i	−0.178729	−	0.309568i
$923$	8.19840e6			0.316756
$924$		0			0
$925$	−114378.			−0.00439530
$926$	3.59118e7	+	6.22010e7i	1.37629	+	2.38380i
$927$	1.24691e6	−	2.15971e6i	0.0476580	−	0.0825461i
$928$	4.64848e6	−	8.05140e6i	0.177191	−	0.306903i
$929$	2.43608e6	+	4.21941e6i	0.0926087	+	0.160403i	0.908608	−	0.417650i	$-0.137146\pi$
$929$	2.43608e6	+	4.21941e6i	0.0926087	+	0.160403i	−0.815999	+	0.578053i	$0.803813\pi$
$930$	5.99290e7			2.27211
$931$		0			0
$932$	−1.35134e7			−0.509593
$933$	4.66990e6	+	8.08850e6i	0.175632	+	0.304203i
$934$	−3.06285e6	+	5.30501e6i	−0.114884	+	0.198984i
$935$	−1.11861e7	+	1.93749e7i	−0.418456	+	0.724788i
$936$	1.18440e6	+	2.05144e6i	0.0441885	+	0.0765366i
$937$	−3.25004e7			−1.20932			−0.604658	−	0.796485i	$-0.706690\pi$
$937$	−3.25004e7			−1.20932			−0.604658	+	0.796485i	$0.706690\pi$
$938$		0			0
$939$	1.55448e6			0.0575334
$940$	1.77529e7	+	3.07489e7i	0.655314	+	1.13504i
$941$	1.32020e6	−	2.28665e6i	0.0486033	−	0.0841834i	−0.840700	−	0.541501i	$-0.817856\pi$
$941$	1.32020e6	−	2.28665e6i	0.0486033	−	0.0841834i	0.889304	+	0.457317i	$0.151190\pi$
$942$	−2.05467e7	+	3.55879e7i	−0.754422	+	1.30670i
$943$	1.63813e7	+	2.83733e7i	0.599888	+	1.03904i
$944$	−3.88752e6			−0.141985
$945$		0			0
$946$	−2.52416e7			−0.917042
$947$	2.04090e7	+	3.53494e7i	0.739513	+	1.28087i	0.952715	+	0.303866i	$0.0982776\pi$
$947$	2.04090e7	+	3.53494e7i	0.739513	+	1.28087i	−0.213202	+	0.977008i	$0.568389\pi$
$948$	1.51292e7	−	2.62045e7i	0.546757	−	0.947012i
$949$	4.76574e6	−	8.25450e6i	0.171777	−	0.297526i
$950$	−5390.00	−	9335.75i	−0.000193767	−	0.000335614i
$951$	962892.			0.0345244
$952$		0			0
$953$	−6.71983e6			−0.239677			−0.119838	−	0.992793i	$-0.538238\pi$
$953$	−6.71983e6			−0.239677			−0.119838	+	0.992793i	$0.538238\pi$
$954$	−531570.	−	920706.i	−0.0189099	−	0.0327529i
$955$	1.00314e7	−	1.73749e7i	0.355920	−	0.616472i
$956$	−1.64187e7	+	2.84381e7i	−0.581025	+	1.00637i
$957$	5.55083e6	+	9.61432e6i	0.195920	+	0.339343i
$958$	−2.60330e7			−0.916454
$959$		0			0
$960$	−1.44005e7			−0.504313
$961$	−1.49008e7	−	2.58089e7i	−0.520476	−	0.901491i
$962$	7.27860e6	−	1.26069e7i	0.253577	−	0.439209i
$963$	−3.43861e6	+	5.95585e6i	−0.119486	+	0.206956i
$964$	−2.74009e7	−	4.74598e7i	−0.949670	−	1.64488i
$965$	5.54150e7			1.91562
$966$		0			0
$967$	−2.78979e6			−0.0959413			−0.0479707	−	0.998849i	$-0.515275\pi$
$967$	−2.78979e6			−0.0959413			−0.0479707	+	0.998849i	$0.515275\pi$
$968$	−1.93009e7	−	3.34301e7i	−0.662046	−	1.14670i
$969$	1.18129e6	−	2.04606e6i	0.0404155	−	0.0700017i
$970$	1.63817e7	−	2.83739e7i	0.559022	−	0.968255i
$971$	−1.66797e7	−	2.88901e7i	−0.567727	−	0.983333i	−0.996790	−	0.0800582i	$-0.974489\pi$
$971$	−1.66797e7	−	2.88901e7i	−0.567727	−	0.983333i	0.429063	−	0.903275i	$-0.358844\pi$
$972$	−2.38486e7			−0.809648
$973$		0			0
$974$	−5.46309e7			−1.84519
$975$	−10780.0	−	18671.5i	−0.000363168	−	0.000629025i
$976$	−1.82614e7	+	3.16296e7i	−0.613633	+	1.06284i
$977$	3.80016e6	−	6.58208e6i	0.127370	−	0.220611i	−0.795287	−	0.606233i	$-0.792680\pi$
$977$	3.80016e6	−	6.58208e6i	0.127370	−	0.220611i	0.922657	+	0.385622i	$0.126013\pi$
$978$	−923440.	−	1.59944e6i	−0.0308718	−	0.0534715i
$979$	−1.17350e7			−0.391316
$980$		0			0
$981$	−4.36621e6			−0.144854
$982$	8.20450e6	+	1.42106e7i	0.271502	+	0.470256i
$983$	2.89880e6	−	5.02087e6i	0.0956829	−	0.165728i	−0.814211	−	0.580570i	$-0.802830\pi$
$983$	2.89880e6	−	5.02087e6i	0.0956829	−	0.165728i	0.909893	+	0.414842i	$0.136163\pi$
$984$	4.52642e7	−	7.84000e7i	1.49028	−	2.58124i
$985$	−2.77214e7	−	4.80149e7i	−0.910384	−	1.57683i
$986$	5.88580e7			1.92803
$987$		0			0
$988$	932960.			0.0304068
$989$	−9.92256e6	−	1.71864e7i	−0.322577	−	0.558719i
$990$	3.05312e6	−	5.28816e6i	0.0990047	−	0.171481i
$991$	−6.34125e6	+	1.09834e7i	−0.205112	+	0.355264i	−0.950168	−	0.311737i	$-0.899089\pi$
$991$	−6.34125e6	+	1.09834e7i	−0.205112	+	0.355264i	0.745057	+	0.667001i	$0.232422\pi$
$992$	−1.03958e7	−	1.80061e7i	−0.335413	−	0.580953i
$993$	7.90227e6			0.254319
$994$		0			0
$995$	4.70823e7			1.50765
$996$	−9.77609e6	−	1.69327e7i	−0.312260	−	0.540851i
$997$	−7.22002e6	+	1.25054e7i	−0.230039	+	0.398439i	−0.957819	−	0.287371i	$-0.907219\pi$
$997$	−7.22002e6	+	1.25054e7i	−0.230039	+	0.398439i	0.727781	+	0.685810i	$0.240552\pi$
$998$	1.49898e7	−	2.59631e7i	0.476398	−	0.825146i
$999$	2.11079e7	+	3.65600e7i	0.669163	+	1.15902i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.6.c.c.18.1		2
7.2	even	3	inner	49.6.c.c.30.1		2
7.3	odd	6		49.6.a.a.1.1		1
7.4	even	3		7.6.a.a.1.1	✓	1
7.5	odd	6		49.6.c.b.30.1		2
7.6	odd	2		49.6.c.b.18.1		2
21.11	odd	6		63.6.a.e.1.1		1
21.17	even	6		441.6.a.k.1.1		1
28.3	even	6		784.6.a.c.1.1		1
28.11	odd	6		112.6.a.g.1.1		1
35.4	even	6		175.6.a.b.1.1		1
35.18	odd	12		175.6.b.a.99.2		2
35.32	odd	12		175.6.b.a.99.1		2
56.11	odd	6		448.6.a.c.1.1		1
56.53	even	6		448.6.a.m.1.1		1
77.32	odd	6		847.6.a.b.1.1		1
84.11	even	6		1008.6.a.y.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.6.a.a.1.1	✓	1	7.4	even	3
49.6.a.a.1.1		1	7.3	odd	6
49.6.c.b.18.1		2	7.6	odd	2
49.6.c.b.30.1		2	7.5	odd	6
49.6.c.c.18.1		2	1.1	even	1	trivial
49.6.c.c.30.1		2	7.2	even	3	inner
63.6.a.e.1.1		1	21.11	odd	6
112.6.a.g.1.1		1	28.11	odd	6
175.6.a.b.1.1		1	35.4	even	6
175.6.b.a.99.1		2	35.32	odd	12
175.6.b.a.99.2		2	35.18	odd	12
441.6.a.k.1.1		1	21.17	even	6
448.6.a.c.1.1		1	56.11	odd	6
448.6.a.m.1.1		1	56.53	even	6
784.6.a.c.1.1		1	28.3	even	6
847.6.a.b.1.1		1	77.32	odd	6
1008.6.a.y.1.1		1	84.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	49.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(5.00000 + 8.66025i) q^{2} +(7.00000 - 12.1244i) q^{3} +(-34.0000 + 58.8897i) q^{4} +(28.0000 + 48.4974i) q^{5} +140.000 q^{6} -360.000 q^{8} +(23.5000 + 40.7032i) q^{9} +O(q^{10})\)	\(q+(5.00000 + 8.66025i) q^{2} +(7.00000 - 12.1244i) q^{3} +(-34.0000 + 58.8897i) q^{4} +(28.0000 + 48.4974i) q^{5} +140.000 q^{6} -360.000 q^{8} +(23.5000 + 40.7032i) q^{9} +(-280.000 + 484.974i) q^{10} +(-116.000 + 200.918i) q^{11} +(476.000 + 824.456i) q^{12} -140.000 q^{13} +784.000 q^{15} +(-712.000 - 1233.22i) q^{16} +(861.000 - 1491.30i) q^{17} +(-235.000 + 407.032i) q^{18} +(49.0000 + 84.8705i) q^{19} -3808.00 q^{20} -2320.00 q^{22} +(-912.000 - 1579.63i) q^{23} +(-2520.00 + 4364.77i) q^{24} +(-5.50000 + 9.52628i) q^{25} +(-700.000 - 1212.44i) q^{26} +4060.00 q^{27} +3418.00 q^{29} +(3920.00 + 6789.64i) q^{30} +(3822.00 - 6619.90i) q^{31} +(1360.00 - 2355.59i) q^{32} +(1624.00 + 2812.85i) q^{33} +17220.0 q^{34} -3196.00 q^{36} +(5199.00 + 9004.93i) q^{37} +(-490.000 + 848.705i) q^{38} +(-980.000 + 1697.41i) q^{39} +(-10080.0 - 17459.1i) q^{40} -17962.0 q^{41} +10880.0 q^{43} +(-7888.00 - 13662.4i) q^{44} +(-1316.00 + 2279.38i) q^{45} +(9120.00 - 15796.3i) q^{46} +(-4662.00 - 8074.82i) q^{47} -19936.0 q^{48} -110.000 q^{50} +(-12054.0 - 20878.1i) q^{51} +(4760.00 - 8244.56i) q^{52} +(-1131.00 + 1958.95i) q^{53} +(20300.0 + 35160.6i) q^{54} -12992.0 q^{55} +1372.00 q^{57} +(17090.0 + 29600.7i) q^{58} +(1365.00 - 2364.25i) q^{59} +(-26656.0 + 46169.5i) q^{60} +(-12824.0 - 22211.8i) q^{61} +76440.0 q^{62} -18368.0 q^{64} +(-3920.00 - 6789.64i) q^{65} +(-16240.0 + 28128.5i) q^{66} +(24202.0 - 41919.1i) q^{67} +(58548.0 + 101408. i) q^{68} -25536.0 q^{69} -58560.0 q^{71} +(-8460.00 - 14653.1i) q^{72} +(-34041.0 + 58960.7i) q^{73} +(-51990.0 + 90049.3i) q^{74} +(77.0000 + 133.368i) q^{75} -6664.00 q^{76} -19600.0 q^{78} +(-15892.0 - 27525.8i) q^{79} +(39872.0 - 69060.3i) q^{80} +(22709.5 - 39334.0i) q^{81} +(-89810.0 - 155555. i) q^{82} -20538.0 q^{83} +96432.0 q^{85} +(54400.0 + 94223.6i) q^{86} +(23926.0 - 41441.0i) q^{87} +(41760.0 - 72330.4i) q^{88} +(25291.0 + 43805.3i) q^{89} -26320.0 q^{90} +124032. q^{92} +(-53508.0 - 92678.6i) q^{93} +(46620.0 - 80748.2i) q^{94} +(-2744.00 + 4752.75i) q^{95} +(-19040.0 - 32978.2i) q^{96} -58506.0 q^{97} -10904.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 10 q^{2} + 14 q^{3} - 68 q^{4} + 56 q^{5} + 280 q^{6} - 720 q^{8} + 47 q^{9}+O(q^{10}) \) 2 * q + 10 * q^2 + 14 * q^3 - 68 * q^4 + 56 * q^5 + 280 * q^6 - 720 * q^8 + 47 * q^9	\( 2 q + 10 q^{2} + 14 q^{3} - 68 q^{4} + 56 q^{5} + 280 q^{6} - 720 q^{8} + 47 q^{9} - 560 q^{10} - 232 q^{11} + 952 q^{12} - 280 q^{13} + 1568 q^{15} - 1424 q^{16} + 1722 q^{17} - 470 q^{18} + 98 q^{19} - 7616 q^{20} - 4640 q^{22} - 1824 q^{23} - 5040 q^{24} - 11 q^{25} - 1400 q^{26} + 8120 q^{27} + 6836 q^{29} + 7840 q^{30} + 7644 q^{31} + 2720 q^{32} + 3248 q^{33} + 34440 q^{34} - 6392 q^{36} + 10398 q^{37} - 980 q^{38} - 1960 q^{39} - 20160 q^{40} - 35924 q^{41} + 21760 q^{43} - 15776 q^{44} - 2632 q^{45} + 18240 q^{46} - 9324 q^{47} - 39872 q^{48} - 220 q^{50} - 24108 q^{51} + 9520 q^{52} - 2262 q^{53} + 40600 q^{54} - 25984 q^{55} + 2744 q^{57} + 34180 q^{58} + 2730 q^{59} - 53312 q^{60} - 25648 q^{61} + 152880 q^{62} - 36736 q^{64} - 7840 q^{65} - 32480 q^{66} + 48404 q^{67} + 117096 q^{68} - 51072 q^{69} - 117120 q^{71} - 16920 q^{72} - 68082 q^{73} - 103980 q^{74} + 154 q^{75} - 13328 q^{76} - 39200 q^{78} - 31784 q^{79} + 79744 q^{80} + 45419 q^{81} - 179620 q^{82} - 41076 q^{83} + 192864 q^{85} + 108800 q^{86} + 47852 q^{87} + 83520 q^{88} + 50582 q^{89} - 52640 q^{90} + 248064 q^{92} - 107016 q^{93} + 93240 q^{94} - 5488 q^{95} - 38080 q^{96} - 117012 q^{97} - 21808 q^{99}+O(q^{100}) \) 2 * q + 10 * q^2 + 14 * q^3 - 68 * q^4 + 56 * q^5 + 280 * q^6 - 720 * q^8 + 47 * q^9 - 560 * q^10 - 232 * q^11 + 952 * q^12 - 280 * q^13 + 1568 * q^15 - 1424 * q^16 + 1722 * q^17 - 470 * q^18 + 98 * q^19 - 7616 * q^20 - 4640 * q^22 - 1824 * q^23 - 5040 * q^24 - 11 * q^25 - 1400 * q^26 + 8120 * q^27 + 6836 * q^29 + 7840 * q^30 + 7644 * q^31 + 2720 * q^32 + 3248 * q^33 + 34440 * q^34 - 6392 * q^36 + 10398 * q^37 - 980 * q^38 - 1960 * q^39 - 20160 * q^40 - 35924 * q^41 + 21760 * q^43 - 15776 * q^44 - 2632 * q^45 + 18240 * q^46 - 9324 * q^47 - 39872 * q^48 - 220 * q^50 - 24108 * q^51 + 9520 * q^52 - 2262 * q^53 + 40600 * q^54 - 25984 * q^55 + 2744 * q^57 + 34180 * q^58 + 2730 * q^59 - 53312 * q^60 - 25648 * q^61 + 152880 * q^62 - 36736 * q^64 - 7840 * q^65 - 32480 * q^66 + 48404 * q^67 + 117096 * q^68 - 51072 * q^69 - 117120 * q^71 - 16920 * q^72 - 68082 * q^73 - 103980 * q^74 + 154 * q^75 - 13328 * q^76 - 39200 * q^78 - 31784 * q^79 + 79744 * q^80 + 45419 * q^81 - 179620 * q^82 - 41076 * q^83 + 192864 * q^85 + 108800 * q^86 + 47852 * q^87 + 83520 * q^88 + 50582 * q^89 - 52640 * q^90 + 248064 * q^92 - 107016 * q^93 + 93240 * q^94 - 5488 * q^95 - 38080 * q^96 - 117012 * q^97 - 21808 * q^99

Introduction

L-functions

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