LMFDB - Embedded newform 69.7.f.a.34.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,7,Mod(7,69)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 19]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("69.7");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	69.f (of order $22$, degree $10$, 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:	$15.8737317698$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			34.8
Character	$\chi$	$=$	69.34
Dual form			69.7.f.a.67.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.97036 + 3.83691i) q^{2} +(-2.21847 + 15.4298i) q^{3} +(-5.66333 + 12.4010i) q^{4} +(7.37292 + 25.1099i) q^{5} +(-45.9577 - 100.633i) q^{6} +(-258.102 + 223.647i) q^{7} +(-78.4096 - 545.351i) q^{8} +(-233.157 - 68.4610i) q^{9} +O(q^{10})$	\(q+(-5.97036 + 3.83691i) q^{2} +(-2.21847 + 15.4298i) q^{3} +(-5.66333 + 12.4010i) q^{4} +(7.37292 + 25.1099i) q^{5} +(-45.9577 - 100.633i) q^{6} +(-258.102 + 223.647i) q^{7} +(-78.4096 - 545.351i) q^{8} +(-233.157 - 68.4610i) q^{9} +(-140.363 - 121.626i) q^{10} +(-783.776 + 1219.58i) q^{11} +(-178.780 - 114.895i) q^{12} +(-412.023 + 475.499i) q^{13} +(682.849 - 2325.57i) q^{14} +(-403.797 + 58.0572i) q^{15} +(1989.23 + 2295.69i) q^{16} +(-1055.51 + 482.033i) q^{17} +(1654.71 - 485.866i) q^{18} +(-3982.43 - 1818.71i) q^{19} +(-353.142 - 50.7741i) q^{20} +(-2878.23 - 4478.62i) q^{21} -10288.6i q^{22} +(11985.2 - 2095.64i) q^{23} +8588.60 q^{24} +(12568.4 - 8077.25i) q^{25} +(635.471 - 4419.80i) q^{26} +(1573.59 - 3445.68i) q^{27} +(-1311.72 - 4467.30i) q^{28} +(5919.82 + 12962.6i) q^{29} +(2188.05 - 1895.96i) q^{30} +(-8359.18 - 58139.4i) q^{31} +(13148.3 + 3860.68i) q^{32} +(-17079.1 - 14799.1i) q^{33} +(4452.22 - 6927.79i) q^{34} +(-7518.72 - 4831.99i) q^{35} +(2169.42 - 2503.65i) q^{36} +(-69.9427 + 238.203i) q^{37} +(30754.8 - 4421.87i) q^{38} +(-6422.80 - 7412.30i) q^{39} +(13115.6 - 5989.69i) q^{40} +(100098. - 29391.3i) q^{41} +(34368.2 + 15695.4i) q^{42} +(-80542.4 - 11580.2i) q^{43} +(-10685.2 - 16626.4i) q^{44} -6359.29i q^{45} +(-63514.9 + 58497.8i) q^{46} +9106.37 q^{47} +(-39835.1 + 25600.4i) q^{48} +(-144.325 + 1003.80i) q^{49} +(-44046.4 + 96448.1i) q^{50} +(-5096.07 - 17355.6i) q^{51} +(-3563.23 - 7802.38i) q^{52} +(-155280. + 134551. i) q^{53} +(3825.89 + 26609.7i) q^{54} +(-36402.2 - 10688.6i) q^{55} +(142204. + 123220. i) q^{56} +(36897.3 - 57413.3i) q^{57} +(-85079.8 - 54677.5i) q^{58} +(-175846. + 202937. i) q^{59} +(1566.87 - 5336.26i) q^{60} +(-7498.35 + 1078.10i) q^{61} +(272983. + 315039. i) q^{62} +(75489.4 - 34474.9i) q^{63} +(-279847. + 82170.4i) q^{64} +(-14977.5 - 6840.01i) q^{65} +(158751. + 22824.9i) q^{66} +(-190576. - 296542. i) q^{67} -15819.2i q^{68} +(5746.57 + 189578. i) q^{69} +63429.3 q^{70} +(-1689.46 + 1085.75i) q^{71} +(-19053.5 + 132520. i) q^{72} +(-52762.9 + 115535. i) q^{73} +(-496.382 - 1690.52i) q^{74} +(96747.5 + 211848. i) q^{75} +(45107.6 - 39085.9i) q^{76} +(-70460.8 - 490066. i) q^{77} +(66786.7 + 19610.4i) q^{78} +(-403196. - 349371. i) q^{79} +(-42978.1 + 66875.2i) q^{80} +(49675.2 + 31924.3i) q^{81} +(-484846. + 559542. i) q^{82} +(187599. - 638904. i) q^{83} +(71839.5 - 10329.0i) q^{84} +(-19886.0 - 22949.6i) q^{85} +(525299. - 239896. i) q^{86} +(-213143. + 62584.5i) q^{87} +(726554. + 331806. i) q^{88} +(524397. + 75396.9i) q^{89} +(24400.1 + 37967.3i) q^{90} -214875. i q^{91} +(-41888.0 + 160496. i) q^{92} +915623. q^{93} +(-54368.3 + 34940.4i) q^{94} +(16305.5 - 113408. i) q^{95} +(-88738.5 + 194310. i) q^{96} +(-366290. - 1.24747e6i) q^{97} +(-2989.82 - 6546.80i) q^{98} +(266236. - 230695. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9}+O(q^{10}) $ 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9	\( 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9} - 384 q^{13} + 33816 q^{16} + 22880 q^{17} + 4860 q^{18} - 31680 q^{19} - 157696 q^{20} + 36488 q^{23} + 39204 q^{24} + 200664 q^{25} + 99032 q^{26} - 202752 q^{28} - 181712 q^{29} - 128496 q^{31} + 439300 q^{32} - 400026 q^{34} + 368744 q^{35} + 42282 q^{36} + 446688 q^{37} + 550550 q^{38} - 52488 q^{39} - 156750 q^{40} - 606080 q^{41} - 1274130 q^{42} - 429000 q^{43} - 867482 q^{44} + 309288 q^{46} + 1111152 q^{47} + 837864 q^{48} + 722136 q^{49} + 1786926 q^{50} + 463320 q^{51} - 812550 q^{52} - 367840 q^{53} - 354294 q^{54} - 398088 q^{55} - 3696550 q^{56} - 1240272 q^{57} + 1903134 q^{58} + 545800 q^{59} + 2450250 q^{60} - 495264 q^{61} + 488776 q^{62} - 2699808 q^{64} - 290400 q^{67} + 23328 q^{69} - 392616 q^{70} + 255392 q^{71} + 228420 q^{72} + 1346880 q^{73} - 5387470 q^{74} + 365472 q^{75} + 2123022 q^{76} + 6134240 q^{77} + 171072 q^{78} + 4025472 q^{79} + 10626462 q^{80} - 1417176 q^{81} + 2025492 q^{82} - 2474560 q^{83} - 8866152 q^{85} - 15634300 q^{86} - 611712 q^{87} - 10636560 q^{88} - 5901720 q^{89} + 6566394 q^{92} - 2484432 q^{93} + 13931490 q^{94} + 8183072 q^{95} - 4682124 q^{96} + 12319560 q^{97} + 14139580 q^{98} + 2993760 q^{99}+O(q^{100}) \) 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9 - 384 * q^13 + 33816 * q^16 + 22880 * q^17 + 4860 * q^18 - 31680 * q^19 - 157696 * q^20 + 36488 * q^23 + 39204 * q^24 + 200664 * q^25 + 99032 * q^26 - 202752 * q^28 - 181712 * q^29 - 128496 * q^31 + 439300 * q^32 - 400026 * q^34 + 368744 * q^35 + 42282 * q^36 + 446688 * q^37 + 550550 * q^38 - 52488 * q^39 - 156750 * q^40 - 606080 * q^41 - 1274130 * q^42 - 429000 * q^43 - 867482 * q^44 + 309288 * q^46 + 1111152 * q^47 + 837864 * q^48 + 722136 * q^49 + 1786926 * q^50 + 463320 * q^51 - 812550 * q^52 - 367840 * q^53 - 354294 * q^54 - 398088 * q^55 - 3696550 * q^56 - 1240272 * q^57 + 1903134 * q^58 + 545800 * q^59 + 2450250 * q^60 - 495264 * q^61 + 488776 * q^62 - 2699808 * q^64 - 290400 * q^67 + 23328 * q^69 - 392616 * q^70 + 255392 * q^71 + 228420 * q^72 + 1346880 * q^73 - 5387470 * q^74 + 365472 * q^75 + 2123022 * q^76 + 6134240 * q^77 + 171072 * q^78 + 4025472 * q^79 + 10626462 * q^80 - 1417176 * q^81 + 2025492 * q^82 - 2474560 * q^83 - 8866152 * q^85 - 15634300 * q^86 - 611712 * q^87 - 10636560 * q^88 - 5901720 * q^89 + 6566394 * q^92 - 2484432 * q^93 + 13931490 * q^94 + 8183072 * q^95 - 4682124 * q^96 + 12319560 * q^97 + 14139580 * q^98 + 2993760 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{9}{22}\right)$	$1$

Coefficient data

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

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

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

$2$	−5.97036	+	3.83691i	−0.746294	+	0.479614i	−0.857693	−	0.514161i	$-0.828103\pi$
$2$	−5.97036	+	3.83691i	−0.746294	+	0.479614i	0.111399	+	0.993776i	$0.464467\pi$
$3$	−2.21847	+	15.4298i	−0.0821655	+	0.571474i
$3$	−2.21847	+	15.4298i	−0.0821655	+	0.571474i
$4$	−5.66333	+	12.4010i	−0.0884895	+	0.193765i
$5$	7.37292	+	25.1099i	0.0589834	+	0.200879i	0.983713	−	0.179745i	$-0.0575273\pi$
$5$	7.37292	+	25.1099i	0.0589834	+	0.200879i	−0.924730	+	0.380624i	$0.875709\pi$
$6$	−45.9577	−	100.633i	−0.212767	−	0.465895i
$7$	−258.102	+	223.647i	−0.752485	+	0.652032i	−0.944183	−	0.329422i	$-0.893146\pi$
$7$	−258.102	+	223.647i	−0.752485	+	0.652032i	0.191698	+	0.981454i	$0.438601\pi$
$8$	−78.4096	−	545.351i	−0.153144	−	1.06514i
$9$	−233.157	−	68.4610i	−0.319831	−	0.0939109i
$10$	−140.363	−	121.626i	−0.140363	−	0.121626i
$11$	−783.776	+	1219.58i	−0.588862	+	0.916288i	0.411126	+	0.911578i	$0.365135\pi$
$11$	−783.776	+	1219.58i	−0.588862	+	0.916288i	−0.999989	+	0.00470955i	$0.998501\pi$
$12$	−178.780	−	114.895i	−0.103461	−	0.0664902i
$13$	−412.023	+	475.499i	−0.187539	+	0.216431i	−0.841731	−	0.539897i	$-0.818463\pi$
$13$	−412.023	+	475.499i	−0.187539	+	0.216431i	0.654192	+	0.756328i	$0.273009\pi$
$14$	682.849	−	2325.57i	0.248852	−	0.847511i
$15$	−403.797	+	58.0572i	−0.119643	+	0.0172021i
$16$	1989.23	+	2295.69i	0.485651	+	0.560472i
$17$	−1055.51	+	482.033i	−0.214839	+	0.0981138i	−0.519928	−	0.854210i	$-0.674041\pi$
$17$	−1055.51	+	482.033i	−0.214839	+	0.0981138i	0.305089	+	0.952324i	$0.401314\pi$
$18$	1654.71	−	485.866i	0.283729	−	0.0833104i
$19$	−3982.43	−	1818.71i	−0.580614	−	0.265157i	0.103384	−	0.994642i	$-0.467033\pi$
$19$	−3982.43	−	1818.71i	−0.580614	−	0.265157i	−0.683998	+	0.729484i	$0.739760\pi$
$20$	−353.142	−	50.7741i	−0.0441427	−	0.00634676i
$21$	−2878.23	−	4478.62i	−0.310791	−	0.483600i
$22$		−	10288.6i		−	0.966247i
$23$	11985.2	−	2095.64i	0.985055	−	0.172240i
$23$	11985.2	−	2095.64i	0.985055	−	0.172240i
$24$	8588.60			0.621282
$25$	12568.4	−	8077.25i	0.804380	−	0.516944i
$26$	635.471	−	4419.80i	0.0361556	−	0.251468i
$27$	1573.59	−	3445.68i	0.0799467	−	0.175059i
$28$	−1311.72	−	4467.30i	−0.0597539	−	0.203503i
$29$	5919.82	+	12962.6i	0.242725	+	0.531494i	0.991310	−	0.131545i	$-0.0419938\pi$
$29$	5919.82	+	12962.6i	0.242725	+	0.531494i	−0.748585	+	0.663039i	$0.769267\pi$
$30$	2188.05	−	1895.96i	0.0810388	−	0.0702206i
$31$	−8359.18	−	58139.4i	−0.280594	−	1.95157i	−0.306386	−	0.951907i	$-0.599120\pi$
$31$	−8359.18	−	58139.4i	−0.280594	−	1.95157i	0.0257915	−	0.999667i	$-0.491789\pi$
$32$	13148.3	+	3860.68i	0.401253	+	0.117819i
$33$	−17079.1	−	14799.1i	−0.475250	−	0.411807i
$34$	4452.22	−	6927.79i	0.113277	−	0.176262i
$35$	−7518.72	−	4831.99i	−0.175364	−	0.112699i
$36$	2169.42	−	2503.65i	0.0464983	−	0.0536619i
$37$	−69.9427	+	238.203i	−0.00138082	+	0.00470264i	−0.960181	−	0.279380i	$-0.909871\pi$
$37$	−69.9427	+	238.203i	−0.00138082	+	0.00470264i	0.958800	+	0.284083i	$0.0916891\pi$
$38$	30754.8	−	4421.87i	0.560482	−	0.0805851i
$39$	−6422.80	−	7412.30i	−0.108276	−	0.124957i
$40$	13115.6	−	5989.69i	0.204931	−	0.0935889i
$41$	100098.	−	29391.3i	1.45235	−	0.426449i	0.542033	−	0.840357i	$-0.317655\pi$
$41$	100098.	−	29391.3i	1.45235	−	0.426449i	0.910319	+	0.413908i	$0.135837\pi$
$42$	34368.2	+	15695.4i	0.463883	+	0.211848i
$43$	−80542.4	−	11580.2i	−1.01302	−	0.145651i	−0.384241	−	0.923233i	$-0.625537\pi$
$43$	−80542.4	−	11580.2i	−1.01302	−	0.145651i	−0.628781	+	0.777582i	$0.716446\pi$
$44$	−10685.2	−	16626.4i	−0.125436	−	0.195183i
$45$		−	6359.29i		−	0.0697865i
$46$	−63514.9	+	58497.8i	−0.652533	+	0.600988i
$47$	9106.37			0.0877105			0.0438553	−	0.999038i	$-0.486036\pi$
$47$	9106.37			0.0877105			0.0438553	+	0.999038i	$0.486036\pi$
$48$	−39835.1	+	25600.4i	−0.360199	+	0.231486i
$49$	−144.325	+	1003.80i	−0.00122674	+	0.00853215i
$50$	−44046.4	+	96448.1i	−0.352371	+	0.771585i
$51$	−5096.07	−	17355.6i	−0.0384171	−	0.130837i
$52$	−3563.23	−	7802.38i	−0.0253416	−	0.0554903i
$53$	−155280.	+	134551.i	−1.04301	+	0.903771i	−0.995468	−	0.0950984i	$-0.969683\pi$
$53$	−155280.	+	134551.i	−1.04301	+	0.903771i	−0.0475394	+	0.998869i	$0.515138\pi$
$54$	3825.89	+	26609.7i	0.0242969	+	0.168989i
$55$	−36402.2	−	10688.6i	−0.218796	−	0.0642443i
$56$	142204.	+	123220.i	0.809743	+	0.701647i
$57$	36897.3	−	57413.3i	0.199237	−	0.310019i
$58$	−85079.8	−	54677.5i	−0.436056	−	0.280236i
$59$	−175846.	+	202937.i	−0.856201	+	0.988108i	−0.999999	−	0.00149872i	$-0.999523\pi$
$59$	−175846.	+	202937.i	−0.856201	+	0.988108i	0.143798	+	0.989607i	$0.454068\pi$
$60$	1566.87	−	5336.26i	0.00725401	−	0.0247049i
$61$	−7498.35	+	1078.10i	−0.0330352	+	0.00474974i	−0.158813	−	0.987309i	$-0.550767\pi$
$61$	−7498.35	+	1078.10i	−0.0330352	+	0.00474974i	0.125777	+	0.992058i	$0.459857\pi$
$62$	272983.	+	315039.i	1.14541	+	1.32187i
$63$	75489.4	−	34474.9i	0.301901	−	0.137874i
$64$	−279847.	+	82170.4i	−1.06753	+	0.313455i
$65$	−14977.5	−	6840.01i	−0.0545381	−	0.0249067i
$66$	158751.	+	22824.9i	0.552185	+	0.0793922i
$67$	−190576.	−	296542.i	−0.633641	−	0.985964i	−0.998492	−	0.0548985i	$-0.982516\pi$
$67$	−190576.	−	296542.i	−0.633641	−	0.985964i	0.364851	−	0.931066i	$-0.381120\pi$
$68$		−	15819.2i		−	0.0503104i
$69$	5746.57	+	189578.i	0.0174929	+	0.577085i
$70$	63429.3			0.184925
$71$	−1689.46	+	1085.75i	−0.00472034	+	0.00303358i	−0.542999	−	0.839733i	$-0.682711\pi$
$71$	−1689.46	+	1085.75i	−0.00472034	+	0.00303358i	0.538279	+	0.842767i	$0.319075\pi$
$72$	−19053.5	+	132520.i	−0.0510479	+	0.355046i
$73$	−52762.9	+	115535.i	−0.135631	+	0.296991i	−0.965245	−	0.261347i	$-0.915833\pi$
$73$	−52762.9	+	115535.i	−0.135631	+	0.296991i	0.829614	+	0.558338i	$0.188561\pi$
$74$	−496.382	−	1690.52i	−0.00122496	−	0.00417182i
$75$	96747.5	+	211848.i	0.229327	+	0.502157i
$76$	45107.6	−	39085.9i	0.102756	−	0.0890389i
$77$	−70460.8	−	490066.i	−0.154339	−	1.07345i
$78$	66786.7	+	19610.4i	0.140736	+	0.0413239i
$79$	−403196.	−	349371.i	−0.817777	−	0.708608i	0.141849	−	0.989888i	$-0.454695\pi$
$79$	−403196.	−	349371.i	−0.817777	−	0.708608i	−0.959626	+	0.281281i	$0.909241\pi$
$80$	−42978.1	+	66875.2i	−0.0839416	+	0.130616i
$81$	49675.2	+	31924.3i	0.0934726	+	0.0600712i
$82$	−484846.	+	559542.i	−0.879351	+	1.01483i
$83$	187599.	−	638904.i	0.328093	−	1.11738i	−0.616013	−	0.787736i	$-0.711253\pi$
$83$	187599.	−	638904.i	0.328093	−	1.11738i	0.944105	−	0.329644i	$-0.106929\pi$
$84$	71839.5	−	10329.0i	0.121206	−	0.0174269i
$85$	−19886.0	−	22949.6i	−0.0323810	−	0.0373696i
$86$	525299.	−	239896.i	0.825869	−	0.377162i
$87$	−213143.	+	62584.5i	−0.323678	+	0.0950405i
$88$	726554.	+	331806.i	1.06615	+	0.486896i
$89$	524397.	+	75396.9i	0.743858	+	0.106951i	0.503815	−	0.863812i	$-0.331929\pi$
$89$	524397.	+	75396.9i	0.743858	+	0.106951i	0.240043	+	0.970762i	$0.422838\pi$
$90$	24400.1	+	37967.3i	0.0334706	+	0.0520813i
$91$		−	214875.i		−	0.285143i
$92$	−41888.0	+	160496.i	−0.0537930	+	0.206110i
$93$	915623.			1.13833
$94$	−54368.3	+	34940.4i	−0.0654579	+	0.0420672i
$95$	16305.5	−	113408.i	0.0190180	−	0.132273i
$96$	−88738.5	+	194310.i	−0.100299	+	0.219625i
$97$	−366290.	−	1.24747e6i	−0.401337	−	1.36683i	−0.874145	−	0.485664i	$-0.838578\pi$
$97$	−366290.	−	1.24747e6i	−0.401337	−	1.36683i	0.472808	−	0.881165i	$-0.343240\pi$
$98$	−2989.82	−	6546.80i	−0.00317663	−	0.00695586i
$99$	266236.	−	230695.i	0.274386	−	0.237757i
$100$	28986.4	+	201605.i	0.0289864	+	0.201605i
$101$	−748599.	−	219808.i	−0.726582	−	0.213344i	−0.102534	−	0.994730i	$-0.532695\pi$
$101$	−748599.	−	219808.i	−0.726582	−	0.213344i	−0.624048	+	0.781386i	$0.714513\pi$
$102$	97017.3	+	84066.0i	0.0914216	+	0.0792172i
$103$	−146535.	+	228014.i	−0.134101	+	0.208665i	−0.901809	−	0.432135i	$-0.857761\pi$
$103$	−146535.	+	228014.i	−0.134101	+	0.208665i	0.767708	+	0.640799i	$0.221397\pi$
$104$	291621.	+	187413.i	0.259250	+	0.166610i
$105$	91236.6	−	105293.i	0.0788136	−	0.0909557i
$106$	410816.	−	1.39911e6i	0.344929	−	1.17472i
$107$	−372152.	+	53507.4i	−0.303787	+	0.0436779i	−0.292523	−	0.956259i	$-0.594495\pi$
$107$	−372152.	+	53507.4i	−0.303787	+	0.0436779i	−0.0112642	+	0.999937i	$0.503586\pi$
$108$	33818.0	+	39028.0i	0.0268458	+	0.0309817i
$109$	−1.44570e6	+	660230.i	−1.11635	+	0.509818i	−0.886184	−	0.463334i	$-0.846653\pi$
$109$	−1.44570e6	+	660230.i	−1.11635	+	0.509818i	−0.230163	+	0.973152i	$0.573926\pi$
$110$	258345.	−	75857.1i	0.194099	−	0.0569925i
$111$	−3520.26	−	1607.65i	−0.00257398	−	0.00117550i
$112$	−1.02685e6	−	147639.i	−0.730891	−	0.105086i
$113$	−659580.	−	1.02633e6i	−0.457122	−	0.711296i	0.533818	−	0.845599i	$-0.320757\pi$
$113$	−659580.	−	1.02633e6i	−0.457122	−	0.711296i	−0.990940	+	0.134304i	$0.957120\pi$
$114$			484349.i			0.326922i
$115$	140987.	+	285495.i	0.0927012	+	0.187718i
$116$	−194274.			−0.124463
$117$	128619.	−	82658.4i	0.0803059	−	0.0516095i
$118$	271210.	−	1.88631e6i	0.165067	−	1.14807i
$119$	164623.	−	360475.i	0.0976900	−	0.213911i
$120$	63323.1	+	215659.i	0.0366453	+	0.124802i
$121$	−137136.	−	300285.i	−0.0774095	−	0.169503i
$122$	40631.2	−	35207.2i	0.0223759	−	0.0193888i
$123$	231438.	+	1.60969e6i	0.124371	+	0.865020i
$124$	768324.	+	225600.i	0.402976	+	0.118325i
$125$	604515.	+	523815.i	0.309512	+	0.268193i
$126$	−318422.	+	495474.i	−0.159181	+	0.247690i
$127$	134650.	+	86534.3i	0.0657348	+	0.0422452i	0.573095	−	0.819489i	$-0.305742\pi$
$127$	134650.	+	86534.3i	0.0657348	+	0.0422452i	−0.507361	+	0.861734i	$0.669379\pi$
$128$	781181.	−	901531.i	0.372496	−	0.429884i
$129$	357361.	−	1.21706e6i	0.166471	−	0.566948i
$130$	115666.	−	16630.2i	0.0526471	−	0.00756952i
$131$	−894265.	−	1.03204e6i	−0.397788	−	0.459072i	0.521155	−	0.853462i	$-0.325501\pi$
$131$	−894265.	−	1.03204e6i	−0.397788	−	0.459072i	−0.918943	+	0.394390i	$0.870956\pi$
$132$	280247.	−	127985.i	0.121848	−	0.0556463i
$133$	1.43462e6	−	421244.i	0.609794	−	0.179052i
$134$	2.27561e6	+	1.03924e6i	0.945765	+	0.431917i
$135$	98122.6	+	14107.9i	0.0398811	+	0.00573404i
$136$	345639.	+	537825.i	0.137406	+	0.213808i
$137$			3.34127e6i			1.29942i	0.760182	+	0.649710i	$0.225110\pi$
$137$			3.34127e6i			1.29942i	−0.760182	+	0.649710i	$0.774890\pi$
$138$	−761702.	−	1.10980e6i	−0.289833	−	0.422286i
$139$	−3.46180e6			−1.28902			−0.644508	−	0.764598i	$-0.722938\pi$
$139$	−3.46180e6			−1.28902			−0.644508	+	0.764598i	$0.722938\pi$
$140$	102502.	−	65874.2i	0.0373550	−	0.0240066i
$141$	−20202.2	+	140509.i	−0.00720678	+	0.0501243i
$142$	5920.76	−	12964.6i	0.00206782	−	0.00452789i
$143$	−256976.	−	875179.i	−0.0878788	−	0.299288i
$144$	−306637.	−	671441.i	−0.102692	−	0.224864i
$145$	−281843.	+	244218.i	−0.0924491	+	0.0801076i
$146$	−128283.	−	892230.i	−0.0412203	−	0.286694i
$147$	−15168.2	−	4453.79i	−0.00477510	−	0.00140210i
$148$	−2557.84	−	2216.38i	−0.000789019	−	0.000683689i
$149$	−1.29286e6	+	2.01174e6i	−0.390836	+	0.608152i	−0.979794	−	0.200012i	$-0.935902\pi$
$149$	−1.29286e6	+	2.01174e6i	−0.390836	+	0.608152i	0.588958	+	0.808164i	$0.299538\pi$
$150$	−1.39046e6	−	893593.i	−0.411988	−	0.264768i
$151$	−606039.	+	699406.i	−0.176023	+	0.203141i	−0.836905	−	0.547349i	$-0.815637\pi$
$151$	−606039.	+	699406.i	−0.176023	+	0.203141i	0.660882	+	0.750490i	$0.270183\pi$
$152$	−679577.	+	2.31443e6i	−0.193512	+	0.659041i
$153$	279099.	−	40128.3i	0.0779262	−	0.0112041i
$154$	2.30102e6	+	2.65551e6i	0.630024	+	0.727087i
$155$	1.39824e6	−	638555.i	0.375480	−	0.171476i
$156$	128294.	−	37670.5i	0.0337934	−	0.00992265i
$157$	2.99177e6	+	1.36630e6i	0.773090	+	0.353058i	0.762586	−	0.646887i	$-0.223929\pi$
$157$	2.99177e6	+	1.36630e6i	0.773090	+	0.353058i	0.0105035	+	0.999945i	$0.496657\pi$
$158$	3.74773e6	+	538842.i	0.950161	+	0.136612i
$159$	−1.73161e6	−	2.69443e6i	−0.430782	−	0.670310i
$160$			358616.i			0.0875527i
$161$	−2.62472e6	+	3.22134e6i	−0.628934	+	0.771895i
$162$	−419069.			−0.0985691
$163$	4.57347e6	−	2.93919e6i	1.05605	−	0.678680i	0.107143	−	0.994244i	$-0.465830\pi$
$163$	4.57347e6	−	2.93919e6i	1.05605	−	0.678680i	0.948904	+	0.315563i	$0.102194\pi$
$164$	−202405.	+	1.40776e6i	−0.0458870	+	0.319151i
$165$	245681.	−	537966.i	0.0546914	−	0.119758i
$166$	1.33139e6	+	4.53429e6i	0.291058	+	0.991253i
$167$	−254201.	−	556622.i	−0.0545792	−	0.119512i	0.880378	−	0.474274i	$-0.157289\pi$
$167$	−254201.	−	556622.i	−0.0545792	−	0.119512i	−0.934957	+	0.354762i	$0.884562\pi$
$168$	−2.21674e6	+	1.92082e6i	−0.467506	+	0.405096i
$169$	630589.	+	4.38585e6i	0.130643	+	0.908643i
$170$	206782.	+	60716.6i	0.0420887	+	0.0123584i
$171$	804019.	+	696687.i	0.160797	+	0.139331i
$172$	599744.	−	933220.i	0.117864	−	0.183400i
$173$	−2.90936e6	−	1.86973e6i	−0.561901	−	0.361112i	0.228650	−	0.973509i	$-0.426569\pi$
$173$	−2.90936e6	−	1.86973e6i	−0.561901	−	0.361112i	−0.790550	+	0.612397i	$0.790205\pi$
$174$	1.03241e6	−	1.19146e6i	0.195976	−	0.226169i
$175$	−1.43749e6	+	4.89565e6i	−0.268220	+	0.913474i
$176$	−4.35889e6	+	626713.i	−0.799535	+	0.114956i
$177$	−2.74116e6	−	3.16347e6i	−0.494328	−	0.570485i
$178$	−3.42013e6	+	1.56192e6i	−0.606432	+	0.276948i
$179$	−6.74376e6	+	1.98015e6i	−1.17583	+	0.345254i	−0.810563	−	0.585651i	$-0.800839\pi$
$179$	−6.74376e6	+	1.98015e6i	−1.17583	+	0.345254i	−0.365263	+	0.930905i	$0.619021\pi$
$180$	78861.3	+	36014.8i	0.0135222	+	0.00617537i
$181$	−6.98897e6	−	1.00486e6i	−1.17863	−	0.169461i	−0.474972	−	0.880001i	$-0.657542\pi$
$181$	−6.98897e6	−	1.00486e6i	−1.17863	−	0.169461i	−0.703657	+	0.710539i	$0.748451\pi$
$182$	824458.	+	1.28288e6i	0.136758	+	0.212800i
$183$		−	118090.i		−	0.0192690i
$184$	−2.08261e6	−	6.37180e6i	−0.334314	−	1.02284i
$185$	−6496.93			−0.00102611
$186$	−5.46659e6	+	3.51317e6i	−0.849529	+	0.545959i
$187$	239402.	−	1.66508e6i	0.0366103	−	0.254630i
$188$	−51572.3	+	112928.i	−0.00776146	+	0.0169952i
$189$	364469.	+	1.24127e6i	0.0539853	+	0.183857i
$190$	337785.	+	739646.i	0.0492470	+	0.107836i
$191$	−3.36468e6	+	2.91552e6i	−0.482886	+	0.418423i	−0.861985	−	0.506933i	$-0.830779\pi$
$191$	−3.36468e6	+	2.91552e6i	−0.482886	+	0.418423i	0.379100	+	0.925356i	$0.376234\pi$
$192$	−647041.	−	4.50027e6i	−0.0914172	−	0.635821i
$193$	5.18146e6	+	1.52141e6i	0.720743	+	0.211629i	0.621478	−	0.783432i	$-0.286533\pi$
$193$	5.18146e6	+	1.52141e6i	0.720743	+	0.211629i	0.0992650	+	0.995061i	$0.468351\pi$
$194$	6.97331e6	+	6.04241e6i	0.955067	+	0.827570i
$195$	138767.	−	215926.i	0.0187147	−	0.0291206i
$196$	−11630.7	−	7474.60i	−0.00154468	−	0.000992704i
$197$	8.30663e6	−	9.58636e6i	1.08649	−	1.25388i	0.121220	−	0.992626i	$-0.461319\pi$
$197$	8.30663e6	−	9.58636e6i	1.08649	−	1.25388i	0.965271	−	0.261251i	$-0.0841351\pi$
$198$	−704368.	+	2.39886e6i	−0.0907411	+	0.309036i
$199$	7.53679e6	−	1.08363e6i	0.956372	−	0.137506i	0.353580	−	0.935404i	$-0.384964\pi$
$199$	7.53679e6	−	1.08363e6i	0.956372	−	0.137506i	0.602792	+	0.797899i	$0.294055\pi$
$200$	−5.39042e6	−	6.22088e6i	−0.673803	−	0.777610i
$201$	4.99836e6	−	2.28267e6i	0.615516	−	0.281097i
$202$	5.31279e6	−	1.55997e6i	0.644567	−	0.189262i
$203$	−4.42697e6	−	2.02173e6i	−0.529198	−	0.241677i
$204$	244087.	+	35094.4i	0.0287510	+	0.00413378i
$205$	1.47602e6	+	2.29674e6i	0.171329	+	0.266593i
$206$		−	1.92357e6i		−	0.220042i
$207$	−2.93789e6	−	331904.i	−0.331226	−	0.0374198i
$208$	−1.91121e6			−0.212382
$209$	5.33940e6	−	3.43142e6i	0.584862	−	0.375868i
$210$	−140716.	+	978701.i	−0.0151945	+	0.105680i
$211$	4.56806e6	−	1.00027e7i	0.486278	−	1.06480i	−0.494411	−	0.869228i	$-0.664616\pi$
$211$	4.56806e6	−	1.00027e7i	0.486278	−	1.06480i	0.980689	−	0.195572i	$-0.0626564\pi$
$212$	−789157.	−	2.68762e6i	−0.0828239	−	0.282072i
$213$	−13004.9	−	28476.8i	−0.00134576	−	0.00294681i
$214$	2.01658e6	−	1.74737e6i	0.205766	−	0.178297i
$215$	−303054.	−	2.10779e6i	−0.0304933	−	0.212086i
$216$	−2.00249e6	−	587984.i	−0.198705	−	0.0583451i
$217$	1.51602e7	+	1.31364e7i	1.48363	+	1.28557i
$218$	6.09811e6	−	9.48884e6i	0.588607	−	0.915890i
$219$	−1.66562e6	−	1.07043e6i	−0.158578	−	0.101912i
$220$	338707.	−	390889.i	0.0318094	−	0.0367101i
$221$	205686.	−	700501.i	0.0190558	−	0.0648981i
$222$	27185.6	−	3908.70i	0.00248473	−	0.000357251i
$223$	−237251.	−	273802.i	−0.0213941	−	0.0246901i	0.744952	−	0.667118i	$-0.232472\pi$
$223$	−237251.	−	273802.i	−0.0213941	−	0.0246901i	−0.766346	+	0.642428i	$0.777927\pi$
$224$	−4.25703e6	+	1.94412e6i	−0.378759	+	0.172973i
$225$	−3.48339e6	+	1.02282e6i	−0.305812	+	0.0897946i
$226$	7.87585e6	+	3.59678e6i	0.682295	+	0.311594i
$227$	−7.87830e6	−	1.13273e6i	−0.673527	−	0.0968385i	−0.202939	−	0.979191i	$-0.565049\pi$
$227$	−7.87830e6	−	1.13273e6i	−0.673527	−	0.0968385i	−0.470588	+	0.882353i	$0.655958\pi$
$228$	503018.	+	782711.i	0.0424404	+	0.0660385i
$229$		−	1.35925e7i		−	1.13186i	−0.824454	−	0.565929i	$-0.808518\pi$
$229$		−	1.35925e7i		−	1.13186i	0.824454	−	0.565929i	$-0.191482\pi$
$230$	−1.93716e6	−	1.16355e6i	−0.159214	−	0.0956317i
$231$	7.71792e6			0.626130
$232$	6.60500e6	−	4.24477e6i	0.528943	−	0.339931i
$233$	3.12507e6	−	2.17353e7i	0.247054	−	1.71830i	−0.368010	−	0.929822i	$-0.619961\pi$
$233$	3.12507e6	−	2.17353e7i	0.247054	−	1.71830i	0.615064	−	0.788477i	$-0.289130\pi$
$234$	−450748.	+	987000.i	−0.0351792	+	0.0770318i
$235$	67140.6	+	228660.i	0.00517346	+	0.0176192i
$236$	−1.52074e6	−	3.32995e6i	−0.115696	−	0.253339i
$237$	6.28520e6	−	5.44616e6i	0.472144	−	0.409115i
$238$	400251.	+	2.78381e6i	0.0296894	+	0.206494i
$239$	1.47351e7	+	4.32662e6i	1.07934	+	0.316924i	0.772617	−	0.634873i	$-0.218948\pi$
$239$	1.47351e7	+	4.32662e6i	1.07934	+	0.316924i	0.306728	+	0.951797i	$0.400766\pi$
$240$	−936525.	−	811503.i	−0.0677463	−	0.0587025i
$241$	−1.04935e7	+	1.63282e7i	−0.749667	+	1.16650i	0.231404	+	0.972858i	$0.425668\pi$
$241$	−1.04935e7	+	1.63282e7i	−0.749667	+	1.16650i	−0.981071	+	0.193647i	$0.937968\pi$
$242$	1.97092e6	+	1.26663e6i	0.139066	+	0.0893725i
$243$	−602788.	+	695654.i	−0.0420093	+	0.0484814i
$244$	29096.1	−	99092.3i	0.00200293	−	0.00682135i
$245$	−26269.4	+	3776.96i	−0.00178629	+	0.000256829i
$246$	−7.55800e6	−	8.72240e6i	−0.507693	−	0.585910i
$247$	2.50565e6	−	1.14429e6i	0.166276	−	0.0759356i
$248$	−3.10509e7	+	9.11737e6i	−2.03573	+	0.597743i
$249$	9.44197e6	+	4.31200e6i	0.611596	+	0.279306i
$250$	−5.61900e6	−	807890.i	−0.359616	−	0.0517050i
$251$	−5.81679e6	−	9.05110e6i	−0.367843	−	0.572374i	0.607157	−	0.794582i	$-0.292310\pi$
$251$	−5.81679e6	−	9.05110e6i	−0.367843	−	0.572374i	−0.974999	+	0.222208i	$0.928674\pi$
$252$			1.13138e6i			0.0706982i
$253$	−6.83789e6	+	1.62594e7i	−0.422241	+	1.00402i
$254$	−1.13593e6			−0.0693189
$255$	398224.	−	255923.i	0.0240163	−	0.0154344i
$256$	1.45166e6	−	1.00965e7i	0.0865257	−	0.601800i
$257$	139224.	−	304858.i	0.00820191	−	0.0179597i	−0.905487	−	0.424375i	$-0.860494\pi$
$257$	139224.	−	304858.i	0.00820191	−	0.0179597i	0.913689	+	0.406415i	$0.133221\pi$
$258$	2.53619e6	+	8.63746e6i	0.147680	+	0.502952i
$259$	−35221.0	−	77123.3i	−0.00202723	−	0.00443901i
$260$	169645.	−	146999.i	0.00965210	−	0.00836359i
$261$	−492814.	−	3.42759e6i	−0.0277180	−	0.192783i
$262$	9.29891e6	+	2.73041e6i	0.517045	+	0.151818i
$263$	−5.54962e6	−	4.80877e6i	−0.305067	−	0.264342i	0.488850	−	0.872368i	$-0.337416\pi$
$263$	−5.54962e6	−	4.80877e6i	−0.305067	−	0.264342i	−0.793918	+	0.608025i	$0.791962\pi$
$264$	−6.73154e6	+	1.04745e7i	−0.365850	+	0.569273i
$265$	−4.52342e6	−	2.90702e6i	−0.243069	−	0.156211i
$266$	−6.94894e6	+	8.01951e6i	−0.369210	+	0.426091i
$267$	−2.32672e6	+	7.92407e6i	−0.122239	+	0.416308i
$268$	4.75669e6	−	683909.i	0.247116	−	0.0355299i
$269$	1.43776e7	+	1.65926e7i	0.738634	+	0.852429i	0.993415	−	0.114570i	$-0.0365489\pi$
$269$	1.43776e7	+	1.65926e7i	0.738634	+	0.852429i	−0.254781	+	0.966999i	$0.582003\pi$
$270$	−639957.	+	292259.i	−0.0325132	+	0.0148483i
$271$	−2.06731e7	+	6.07017e6i	−1.03872	+	0.304995i	−0.756251	−	0.654282i	$-0.772971\pi$
$271$	−2.06731e7	+	6.07017e6i	−1.03872	+	0.304995i	−0.282467	+	0.959277i	$0.591153\pi$
$272$	−3.20624e6	−	1.46424e6i	−0.159327	−	0.0727622i
$273$	3.31548e6	+	476694.i	0.162951	+	0.0234289i
$274$	−1.28202e7	−	1.99486e7i	−0.623220	−	0.969750i
$275$			2.16590e7i			1.04145i
$276$	−2.38349e6	−	1.00238e6i	−0.113367	−	0.0476765i
$277$	−1.28928e7			−0.606606			−0.303303	−	0.952894i	$-0.598089\pi$
$277$	−1.28928e7			−0.606606			−0.303303	+	0.952894i	$0.598089\pi$
$278$	2.06682e7	−	1.32826e7i	0.961985	−	0.618230i
$279$	−2.03128e6	+	1.41279e7i	−0.0935314	+	0.650525i
$280$	−2.04559e6	+	4.47922e6i	−0.0931846	+	0.204046i
$281$	6.55861e6	+	2.23366e7i	0.295592	+	1.00669i	0.964661	+	0.263494i	$0.0848749\pi$
$281$	6.55861e6	+	2.23366e7i	0.295592	+	1.00669i	−0.669069	+	0.743200i	$0.733307\pi$
$282$	−418508.	−	916405.i	−0.0186619	−	0.0408639i
$283$	−2.66482e7	+	2.30908e7i	−1.17573	+	1.01878i	−0.176325	+	0.984332i	$0.556421\pi$
$283$	−2.66482e7	+	2.30908e7i	−1.17573	+	1.01878i	−0.999407	+	0.0344457i	$0.989033\pi$
$284$	−3896.38	−	27099.9i	−0.000170101	−	0.00118308i
$285$	1.71368e6	+	503182.i	0.0740279	+	0.0217365i
$286$	4.89222e6	+	4.23914e6i	0.209126	+	0.181209i
$287$	−1.92621e7	+	2.99725e7i	−0.814815	+	1.26788i
$288$	−2.80130e6	−	1.80029e6i	−0.117269	−	0.0753641i
$289$	−1.49250e7	+	1.72244e7i	−0.618331	+	0.713592i
$290$	745657.	−	2.53948e6i	0.0305735	−	0.104124i
$291$	2.00608e7	−	2.88430e6i	0.814083	−	0.117047i
$292$	−1.13393e6	−	1.30862e6i	−0.0455445	−	0.0525612i
$293$	3.59871e7	−	1.64347e7i	1.43068	−	0.653372i	0.458737	−	0.888572i	$-0.348302\pi$
$293$	3.59871e7	−	1.64347e7i	1.43068	−	0.653372i	0.971947	+	0.235200i	$0.0755747\pi$
$294$	107649.	−	31608.5i	0.00423610	−	0.00124383i
$295$	−6.39221e6	−	2.91922e6i	−0.248992	−	0.113711i
$296$	135388.	+	19465.9i	0.00522043	+	0.000750585i
$297$	2.96894e6	+	4.61976e6i	0.113327	+	0.176340i
$298$		−	1.69714e7i		−	0.641311i
$299$	−3.94168e6	+	6.56239e6i	−0.147458	+	0.245498i
$300$	−3.17502e6			−0.117593
$301$	2.33781e7	−	1.50242e7i	0.857253	−	0.550923i
$302$	934706.	−	6.50102e6i	0.0339355	−	0.236027i
$303$	5.05234e6	−	1.10631e7i	0.181620	−	0.397693i
$304$	−3.74675e6	−	1.27603e7i	−0.133363	−	0.454191i
$305$	−82355.7	−	180334.i	−0.00290265	−	0.00635591i
$306$	−1.51235e6	+	1.31046e6i	−0.0527823	+	0.0457361i
$307$	5.93757e6	+	4.12967e7i	0.205208	+	1.42725i	0.788523	+	0.615005i	$0.210846\pi$
$307$	5.93757e6	+	4.12967e7i	0.205208	+	1.42725i	−0.583316	+	0.812245i	$0.698245\pi$
$308$	6.47632e6	+	1.90162e6i	0.221654	+	0.0650836i
$309$	−3.19312e6	−	2.76685e6i	−0.108228	−	0.0937801i
$310$	−5.89791e6	+	9.17733e6i	−0.197976	+	0.308057i
$311$	2.75683e7	+	1.77170e7i	0.916491	+	0.588993i	0.911638	−	0.410995i	$-0.134819\pi$
$311$	2.75683e7	+	1.77170e7i	0.916491	+	0.588993i	0.00485363	+	0.999988i	$0.498455\pi$
$312$	−3.53870e6	+	4.08387e6i	−0.116514	+	0.134465i
$313$	9.60847e6	−	3.27235e7i	0.313344	−	1.06715i	−0.640776	−	0.767728i	$-0.721387\pi$
$313$	9.60847e6	−	3.27235e7i	0.313344	−	1.06715i	0.954120	−	0.299424i	$-0.0967945\pi$
$314$	−2.31043e7	+	3.32190e6i	−0.746284	+	0.107299i
$315$	1.42224e6	+	1.64135e6i	0.0455030	+	0.0525133i
$316$	6.61596e6	−	3.02141e6i	0.209668	−	0.0957521i
$317$	8.02718e6	−	2.35699e6i	0.251991	−	0.0739913i	−0.153297	−	0.988180i	$-0.548989\pi$
$317$	8.02718e6	−	2.35699e6i	0.251991	−	0.0739913i	0.405289	+	0.914189i	$0.367171\pi$
$318$	2.06766e7	+	9.44269e6i	0.642981	+	0.293639i
$319$	−2.04487e7	−	2.94008e6i	−0.629933	−	0.0905707i
$320$	−4.12658e6	−	6.42108e6i	−0.125933	−	0.195956i
$321$		−	5.86093e6i		−	0.177195i
$322$	3.31050e6	−	2.93033e7i	0.0991576	−	0.877707i
$323$	5.08016e6			0.150754
$324$	−677218.	+	435222.i	−0.0199110	+	0.0127960i
$325$	−1.33776e6	+	9.30429e6i	−0.0389697	+	0.271040i
$326$	−1.60278e7	+	3.50960e7i	−0.462617	+	1.01299i
$327$	−6.97996e6	−	2.37716e7i	−0.199623	−	0.679852i
$328$	−2.38772e7	−	5.22837e7i	−0.676646	−	1.48165i
$329$	−2.35038e6	+	2.03661e6i	−0.0660009	+	0.0571901i
$330$	597327.	+	4.15450e6i	0.0166215	+	0.115605i
$331$	−3.03262e7	−	8.90458e6i	−0.836246	−	0.245544i	−0.164548	−	0.986369i	$-0.552617\pi$
$331$	−3.03262e7	−	8.90458e6i	−0.836246	−	0.245544i	−0.671698	+	0.740825i	$0.734435\pi$
$332$	6.86058e6	+	5.94473e6i	0.187476	+	0.162449i
$333$	32615.2	−	50750.3i	0.000883259	−	0.00137438i
$334$	3.65338e6	+	2.34788e6i	0.0980517	+	0.0630140i
$335$	6.04102e6	−	6.97171e6i	0.160685	−	0.185441i
$336$	4.55607e6	−	1.55165e7i	0.120108	−	0.409051i
$337$	−1.26781e6	+	182283.i	−0.0331256	+	0.00476274i	−0.158858	−	0.987301i	$-0.550781\pi$
$337$	−1.26781e6	+	182283.i	−0.0331256	+	0.00476274i	0.125732	+	0.992064i	$0.459872\pi$
$338$	−2.05930e7	−	2.37655e7i	−0.533296	−	0.615457i
$339$	1.72993e7	−	7.90031e6i	0.444046	−	0.202789i
$340$	397218.	−	116634.i	0.0101063	−	0.00296748i
$341$	7.74573e7	+	3.53736e7i	1.95344	+	0.892104i
$342$	−7.47341e6	−	1.07451e6i	−0.186827	−	0.0268617i
$343$	−2.19098e7	−	3.40923e7i	−0.542946	−	0.844840i
$344$			4.48319e7i			1.10132i
$345$	−4.71790e6	+	1.54204e6i	−0.114892	+	0.0375524i
$346$	2.45439e7			0.592538
$347$	1.09245e7	−	7.02073e6i	0.261464	−	0.168033i	−0.403341	−	0.915050i	$-0.632151\pi$
$347$	1.09245e7	−	7.02073e6i	0.261464	−	0.168033i	0.664805	+	0.747017i	$0.268515\pi$
$348$	430992.	−	2.99761e6i	0.0102266	−	0.0711276i
$349$	−4.21462e6	+	9.22872e6i	−0.0991475	+	0.217103i	−0.952706	−	0.303895i	$-0.901713\pi$
$349$	−4.21462e6	+	9.22872e6i	−0.0991475	+	0.217103i	0.853558	+	0.520998i	$0.174440\pi$
$350$	−1.02019e7	−	3.47443e7i	−0.237944	−	0.810363i
$351$	990065.	+	2.16794e6i	0.0228951	+	0.0501332i
$352$	−1.50137e7	+	1.30095e7i	−0.344239	+	0.298285i
$353$	−9.48217e6	−	6.59499e7i	−0.215568	−	1.49931i	−0.754133	−	0.656722i	$-0.771942\pi$
$353$	−9.48217e6	−	6.59499e7i	−0.215568	−	1.49931i	0.538565	−	0.842584i	$-0.318967\pi$
$354$	2.85037e7	+	8.36944e6i	0.642527	+	0.188663i
$355$	−39719.4	−	34417.0i	−0.000887804	−	0.000769287i
$356$	−3.90482e6	+	6.07602e6i	−0.0865469	+	0.134670i
$357$	5.19684e6	+	3.33980e6i	0.114218	+	0.0734034i
$358$	3.26650e7	−	3.76974e7i	0.711924	−	0.821604i
$359$	−1.82722e7	+	6.22293e7i	−0.394918	+	1.34497i	0.486934	+	0.873439i	$0.338115\pi$
$359$	−1.82722e7	+	6.22293e7i	−0.394918	+	1.34497i	−0.881851	+	0.471527i	$0.843703\pi$
$360$	−3.46805e6	+	498630.i	−0.0743323	+	0.0106874i
$361$	−1.82565e7	−	2.10691e7i	−0.388057	−	0.447842i
$362$	4.55822e7	−	2.08167e7i	0.960881	−	0.438820i
$363$	4.93757e6	−	1.44980e6i	0.103227	−	0.0303102i
$364$	2.66466e6	+	1.21691e6i	0.0552506	+	0.0252321i
$365$	−3.29008e6	−	473042.i	−0.0676593	−	0.00972794i
$366$	453100.	+	705038.i	0.00924168	+	0.0143803i
$367$		−	1.99495e7i		−	0.403584i	−0.979428	−	0.201792i	$-0.935323\pi$
$367$		−	1.99495e7i		−	0.403584i	0.979428	−	0.201792i	$-0.0646765\pi$
$368$	2.86522e7	+	2.33455e7i	0.574929	+	0.468447i
$369$	−2.53506e7			−0.504555
$370$	38789.0	−	24928.2i	0.000765779	−	0.000492136i
$371$	9.98623e6	−	6.94557e7i	0.195560	−	1.36015i
$372$	−5.18547e6	+	1.13546e7i	−0.100730	+	0.220568i
$373$	−1.77277e7	−	6.03749e7i	−0.341606	−	1.16340i	−0.933856	−	0.357648i	$-0.883579\pi$
$373$	−1.77277e7	−	6.03749e7i	−0.341606	−	1.16340i	0.592251	−	0.805754i	$-0.298240\pi$
$374$	4.95945e6	+	1.08597e7i	0.0948022	+	0.207588i
$375$	−9.42345e6	+	8.16547e6i	−0.178697	+	0.154841i
$376$	−714027.	−	4.96617e6i	−0.0134323	−	0.0934239i
$377$	−8.60281e6	−	2.52601e6i	−0.160552	−	0.0471424i
$378$	−6.93865e6	−	6.01237e6i	−0.128469	−	0.111319i
$379$	−5.28547e7	+	8.22435e7i	−0.970881	+	1.51072i	−0.115118	+	0.993352i	$0.536725\pi$
$379$	−5.28547e7	+	8.22435e7i	−0.970881	+	1.51072i	−0.855763	+	0.517369i	$0.826912\pi$
$380$	1.31402e6	+	844468.i	0.0239470	+	0.0153898i
$381$	−1.63392e6	+	1.88565e6i	−0.0295432	+	0.0340946i
$382$	8.90178e6	−	3.03167e7i	0.159693	−	0.543866i
$383$	2.21469e7	−	3.18425e6i	0.394200	−	0.0566775i	0.0576354	−	0.998338i	$-0.481644\pi$
$383$	2.21469e7	−	3.18425e6i	0.394200	−	0.0566775i	0.336565	+	0.941660i	$0.390735\pi$
$384$	1.21774e7	+	1.40535e7i	0.215061	+	0.248193i
$385$	1.17860e7	−	5.38248e6i	0.206530	−	0.0943192i
$386$	−3.67727e7	+	1.07974e7i	−0.639387	+	0.187741i
$387$	1.79862e7	+	8.21403e6i	0.310318	+	0.141717i
$388$	1.75442e7	+	2.52248e6i	0.300358	+	0.0431849i
$389$	−3.91309e7	−	6.08888e7i	−0.664769	−	1.03440i	−0.995869	−	0.0908052i	$-0.971056\pi$
$389$	−3.91309e7	−	6.08888e7i	−0.664769	−	1.03440i	0.331100	−	0.943596i	$-0.392580\pi$
$390$			1.82159e6i			0.0307084i
$391$	−1.16402e7	+	7.98921e6i	−0.194729	+	0.133651i
$392$	558739.			0.00927579
$393$	1.79080e7	−	1.15088e7i	0.295032	−	0.189606i
$394$	−1.28115e7	+	8.91058e7i	−0.209465	+	1.45686i
$395$	5.79993e6	−	1.27001e7i	0.0941091	−	0.206070i
$396$	1.35306e6	+	4.60809e6i	0.0217886	+	0.0742053i
$397$	−1.34385e7	−	2.94262e7i	−0.214772	−	0.470286i	0.771328	−	0.636438i	$-0.219593\pi$
$397$	−1.34385e7	−	2.94262e7i	−0.214772	−	0.470286i	−0.986100	+	0.166152i	$0.946866\pi$
$398$	−4.08395e7	+	3.53876e7i	−0.647786	+	0.561309i
$399$	3.31703e6	+	2.30705e7i	0.0522193	+	0.363193i
$400$	4.35444e7	+	1.27858e7i	0.680381	+	0.199778i
$401$	3.51110e7	+	3.04238e7i	0.544515	+	0.471825i	0.883148	−	0.469094i	$-0.155419\pi$
$401$	3.51110e7	+	3.04238e7i	0.544515	+	0.471825i	−0.338634	+	0.940918i	$0.609965\pi$
$402$	−2.10836e7	+	3.28067e7i	−0.324538	+	0.504991i
$403$	3.10894e7	+	1.99799e7i	0.475004	+	0.305266i
$404$	6.96539e6	−	8.03849e6i	0.105633	−	0.121907i
$405$	−435364.	+	1.48271e6i	−0.00655371	+	0.0223199i
$406$	3.41878e7	−	4.91546e6i	0.510849	−	0.0734490i
$407$	−235688.	−	271998.i	−0.00349586	−	0.00403444i
$408$	−9.06532e6	+	4.13999e6i	−0.133476	+	0.0609563i
$409$	−4.48824e7	+	1.31787e7i	−0.656004	+	0.192620i	−0.592761	−	0.805378i	$-0.701962\pi$
$409$	−4.48824e7	+	1.31787e7i	−0.656004	+	0.192620i	−0.0632424	+	0.997998i	$0.520144\pi$
$410$	−1.76248e7	−	8.04896e6i	−0.255724	−	0.116785i
$411$	−5.15550e7	−	7.41250e6i	−0.742584	−	0.106767i
$412$	−1.99771e6	−	3.10850e6i	−0.0285654	−	0.0444487i
$413$		−	9.17058e7i		−	1.30181i
$414$	1.88137e7	−	9.29086e6i	0.265139	−	0.130935i
$415$	1.74259e7			0.243810
$416$	−7.25314e6	+	4.66131e6i	−0.100750	+	0.0647482i
$417$	7.67990e6	−	5.34149e7i	0.105913	−	0.736638i
$418$	−1.87120e7	+	4.09736e7i	−0.256208	+	0.561016i
$419$	−2.91550e7	−	9.92929e7i	−0.396343	−	1.34982i	−0.880171	−	0.474657i	$-0.842572\pi$
$419$	−2.91550e7	−	9.92929e7i	−0.396343	−	1.34982i	0.483828	−	0.875163i	$-0.339246\pi$
$420$	789026.	+	1.72773e6i	0.0106499	+	0.0233199i
$421$	1.56888e7	−	1.35944e7i	0.210254	−	0.182186i	−0.543367	−	0.839495i	$-0.682851\pi$
$421$	1.56888e7	−	1.35944e7i	0.210254	−	0.182186i	0.753621	+	0.657309i	$0.228305\pi$
$422$	1.11064e7	+	7.72467e7i	0.147787	+	1.02788i
$423$	−2.12321e6	−	623431.i	−0.0280525	−	0.00823697i
$424$	8.55528e7	+	7.41319e7i	1.12237	+	0.972541i
$425$	−9.37256e6	+	1.45840e7i	−0.122093	+	0.189981i
$426$	186907.	+	120118.i	0.00241767	+	0.00155374i
$427$	1.69423e6	−	1.95524e6i	0.0217615	−	0.0251141i
$428$	1.44407e6	−	4.91807e6i	0.0184187	−	0.0627282i
$429$	1.40739e7	−	2.02352e6i	0.178256	−	0.0256293i
$430$	9.89675e6	+	1.14215e7i	0.124476	+	0.143653i
$431$	−1.67058e7	+	7.62927e6i	−0.208658	+	0.0952909i	−0.517003	−	0.855984i	$-0.672952\pi$
$431$	−1.67058e7	+	7.62927e6i	−0.208658	+	0.0952909i	0.308345	+	0.951275i	$0.400225\pi$
$432$	1.10405e7	−	3.24177e6i	0.136942	−	0.0402097i
$433$	8.50711e7	+	3.88507e7i	1.04790	+	0.478558i	0.863529	−	0.504299i	$-0.168249\pi$
$433$	8.50711e7	+	3.88507e7i	1.04790	+	0.478558i	0.184368	+	0.982857i	$0.440976\pi$
$434$	−1.40915e8	−	2.02605e7i	−1.72381	−	0.247846i
$435$	−3.14297e6	−	4.89056e6i	−0.0381833	−	0.0594143i
$436$		−	2.16672e7i		−	0.261422i
$437$	−5.15414e7	−	1.34519e7i	−0.617607	−	0.161190i
$438$	1.40515e7			0.167225
$439$	−7.53219e7	+	4.84064e7i	−0.890282	+	0.572149i	−0.903893	−	0.427758i	$-0.859304\pi$
$439$	−7.53219e7	+	4.84064e7i	−0.890282	+	0.572149i	0.0136115	+	0.999907i	$0.495667\pi$
$440$	−2.97478e6	+	2.06901e7i	−0.0349218	+	0.242887i
$441$	102371.	−	224162.i	0.00119361	−	0.00261364i
$442$	1.45975e6	+	4.97144e6i	0.0169048	+	0.0575725i
$443$	−1.91325e7	−	4.18943e7i	−0.220069	−	0.481885i	0.767107	−	0.641520i	$-0.221696\pi$
$443$	−1.91325e7	−	4.18943e7i	−0.220069	−	0.481885i	−0.987176	+	0.159635i	$0.948968\pi$
$444$	39872.7	−	34549.9i	0.000455541	−	0.000394728i
$445$	1.97313e6	+	1.37234e7i	0.0223911	+	0.155734i
$446$	2.46703e6	+	724385.i	0.0278080	+	0.00816516i
$447$	−2.81725e7	−	2.44116e7i	−0.315430	−	0.273321i
$448$	5.38520e7	−	8.37953e7i	0.598918	−	0.931935i
$449$	1.12977e8	+	7.26056e7i	1.24810	+	0.802105i	0.986609	−	0.163101i	$-0.0521498\pi$
$449$	1.12977e8	+	7.26056e7i	1.24810	+	0.802105i	0.261490	+	0.965206i	$0.415786\pi$
$450$	1.68726e7	−	1.94721e7i	0.185159	−	0.213685i
$451$	−4.26090e7	+	1.45113e8i	−0.464485	+	1.58189i
$452$	1.64628e7	−	2.36700e6i	0.178275	−	0.0256320i
$453$	−9.44721e6	−	1.09027e7i	−0.101627	−	0.117284i
$454$	5.13824e7	−	2.34656e7i	0.549094	−	0.250763i
$455$	5.39549e6	−	1.58426e6i	0.0572791	−	0.0168187i
$456$	−3.42035e7	−	1.56202e7i	−0.360725	−	0.164737i
$457$	−4.65269e6	−	668955.i	−0.0487478	−	0.00700888i	0.117898	−	0.993026i	$-0.462384\pi$
$457$	−4.65269e6	−	668955.i	−0.0487478	−	0.00700888i	−0.166646	+	0.986017i	$0.553294\pi$
$458$	5.21531e7	+	8.11518e7i	0.542855	+	0.844699i
$459$			4.39546e6i			0.0454534i
$460$	−4.33886e6	+	131522.i	−0.0445762	+	0.00135121i
$461$	−1.15097e8			−1.17479			−0.587394	−	0.809301i	$-0.699846\pi$
$461$	−1.15097e8			−1.17479			−0.587394	+	0.809301i	$0.699846\pi$
$462$	−4.60787e7	+	2.96130e7i	−0.467277	+	0.300301i
$463$	1.76585e7	−	1.22818e8i	0.177915	−	1.23742i	−0.683663	−	0.729798i	$-0.739614\pi$
$463$	1.76585e7	−	1.22818e8i	0.177915	−	1.23742i	0.861577	−	0.507626i	$-0.169477\pi$
$464$	−1.79823e7	+	3.93756e7i	−0.180007	+	0.394161i
$465$	6.75082e6	+	2.29912e7i	0.0671425	+	0.228666i
$466$	6.47389e7	+	1.41758e8i	0.639746	+	1.40085i
$467$	−6.38199e7	+	5.53003e7i	−0.626622	+	0.542971i	−0.909246	−	0.416260i	$-0.863341\pi$
$467$	−6.38199e7	+	5.53003e7i	−0.626622	+	0.542971i	0.282624	+	0.959231i	$0.408795\pi$
$468$	296632.	+	2.06312e6i	0.00289388	+	0.0201274i
$469$	1.15509e8	+	3.39164e7i	1.11969	+	0.328769i
$470$	−1.27820e6	−	1.10757e6i	−0.0123113	−	0.0106678i
$471$	−2.77188e7	+	4.31314e7i	−0.265285	+	0.412791i
$472$	1.24460e8	+	7.99854e7i	1.18359	+	0.760650i
$473$	7.72502e7	−	8.91515e7i	0.729989	−	0.842452i
$474$	−1.66284e7	+	5.66313e7i	−0.156141	+	0.531767i
$475$	−6.47431e7	+	9.30866e6i	−0.604106	+	0.0868573i
$476$	3.53791e6	+	4.08297e6i	0.0328040	+	0.0378578i
$477$	4.54160e7	−	2.07408e7i	0.418460	−	0.191104i
$478$	−1.04575e8	+	3.07059e7i	−0.957510	+	0.281150i
$479$	−6.41907e7	−	2.93149e7i	−0.584071	−	0.266736i	0.101389	−	0.994847i	$-0.467671\pi$
$479$	−6.41907e7	−	2.93149e7i	−0.584071	−	0.266736i	−0.685460	+	0.728111i	$0.740399\pi$
$480$	−5.53337e6	−	795578.i	−0.0500341	−	0.00719381i
$481$	−84447.4	−	131403.i	−0.000758842	−	0.00118078i
$482$		−	1.37748e8i		−	1.23011i
$483$	−4.38817e7	−	4.76453e7i	−0.389441	−	0.422842i
$484$	4.50046e6			0.0396937
$485$	2.86231e7	−	1.83950e7i	0.250895	−	0.161240i
$486$	929692.	−	6.46615e6i	0.00809898	−	0.0563297i
$487$	−6.28078e7	+	1.37530e8i	−0.543784	+	1.19072i	0.415840	+	0.909438i	$0.363488\pi$
$487$	−6.28078e7	+	1.37530e8i	−0.543784	+	1.19072i	−0.959625	+	0.281284i	$0.909240\pi$
$488$	1.17589e6	+	4.00470e6i	0.0101183	+	0.0344596i
$489$	3.52050e7	+	7.70882e7i	0.301077	+	0.659267i
$490$	142346.	−	123343.i	0.00120992	−	0.00104840i
$491$	3.62187e6	+	2.51906e7i	0.0305977	+	0.212811i	0.999384	−	0.0350844i	$-0.0111700\pi$
$491$	3.62187e6	+	2.51906e7i	0.0305977	+	0.212811i	−0.968787	+	0.247896i	$0.920261\pi$
$492$	−2.12724e7	−	6.24613e6i	−0.178616	−	0.0524464i
$493$	−1.24968e7	−	1.08285e7i	−0.104294	−	0.0903710i
$494$	−1.05691e7	+	1.64458e7i	−0.0876709	+	0.136419i
$495$	7.75566e6	+	4.98426e6i	0.0639445	+	0.0410946i
$496$	1.16842e8	−	1.34843e8i	0.957531	−	1.10505i
$497$	193229.	−	658079.i	0.00157400	−	0.00536054i
$498$	−7.29167e7	+	1.04838e7i	−0.590390	+	0.0848853i
$499$	−1.43862e8	−	1.66025e8i	−1.15783	−	1.33620i	−0.932181	−	0.361993i	$-0.882096\pi$
$499$	−1.43862e8	−	1.66025e8i	−1.15783	−	1.33620i	−0.225646	−	0.974209i	$-0.572449\pi$
$500$	−9.91937e6	+	4.53002e6i	−0.0793550	+	0.0362402i
$501$	9.15249e6	−	2.68741e6i	0.0727824	−	0.0213708i
$502$	6.94566e7	+	3.17198e7i	0.549038	+	0.250737i
$503$	−9.90028e7	−	1.42345e7i	−0.777935	−	0.111850i	−0.258102	−	0.966118i	$-0.583097\pi$
$503$	−9.90028e7	−	1.42345e7i	−0.777935	−	0.111850i	−0.519834	+	0.854268i	$0.674006\pi$
$504$	−2.47200e7	−	3.84651e7i	−0.193089	−	0.300452i
$505$		−	2.04178e7i		−	0.158539i
$506$	−2.15612e7	−	1.23311e8i	−0.166426	−	0.951807i
$507$	−6.90716e7			−0.530000
$508$	−1.83568e6	+	1.17972e6i	−0.0140025	+	0.00899884i
$509$	−1.19681e7	+	8.32400e7i	−0.0907554	+	0.631217i	0.892779	+	0.450495i	$0.148753\pi$
$509$	−1.19681e7	+	8.32400e7i	−0.0907554	+	0.631217i	−0.983534	+	0.180722i	$0.942157\pi$
$510$	−1.39558e6	+	3.05590e6i	−0.0105207	+	0.0230372i
$511$	−1.22207e7	−	4.16201e7i	−0.0915873	−	0.311918i
$512$	6.17876e7	+	1.35296e8i	0.460353	+	1.00803i
$513$	−1.25334e7	+	1.08603e7i	−0.0928362	+	0.0804431i
$514$	338498.	+	2.35430e6i	0.00249268	+	0.0173370i
$515$	−6.80579e6	−	1.99836e6i	−0.0498261	−	0.0146303i
$516$	1.30689e7	+	1.13242e7i	0.0951237	+	0.0824252i
$517$	−7.13735e6	+	1.11059e7i	−0.0516494	+	0.0803681i
$518$	506197.	+	325313.i	0.00364192	+	0.00234052i
$519$	3.53039e7	−	4.07429e7i	0.252535	−	0.291441i
$520$	−2.55582e6	+	8.70434e6i	−0.0181769	+	0.0619050i
$521$	1.20736e8	−	1.73592e7i	0.853737	−	0.122749i	0.298468	−	0.954420i	$-0.403524\pi$
$521$	1.20736e8	−	1.73592e7i	0.853737	−	0.122749i	0.555269	+	0.831671i	$0.312615\pi$
$522$	1.60937e7	+	1.85731e7i	0.113147	+	0.130579i
$523$	2.25437e7	−	1.02954e7i	0.157587	−	0.0719676i	−0.335060	−	0.942197i	$-0.608757\pi$
$523$	2.25437e7	−	1.02954e7i	0.157587	−	0.0719676i	0.492647	+	0.870229i	$0.336029\pi$
$524$	1.78627e7	−	5.24498e6i	0.124152	−	0.0364544i
$525$	−7.23498e7	−	3.30411e7i	−0.499988	−	0.228337i
$526$	5.15840e7	+	7.41666e6i	0.354452	+	0.0509626i
$527$	3.68483e7	+	5.73370e7i	0.251759	+	0.391745i
$528$		−	6.86470e7i		−	0.466359i
$529$	1.39252e8	−	5.02332e7i	0.940667	−	0.339331i
$530$	3.81604e7			0.256322
$531$	5.48929e7	−	3.52775e7i	0.366634	−	0.235621i
$532$	−2.90092e6	+	2.01764e7i	−0.0192664	+	0.134001i
$533$	−2.72669e7	+	5.97062e7i	−0.180075	+	0.394310i
$534$	−1.65126e7	−	5.62369e7i	−0.108441	−	0.369316i
$535$	−4.08741e6	−	8.95018e6i	−0.0266923	−	0.0584481i
$536$	−1.46776e8	+	1.27182e8i	−0.953151	+	0.825910i
$537$	−1.55924e7	−	1.08448e8i	−0.100691	−	0.700322i
$538$	−1.49504e8	−	4.38983e7i	−0.960076	−	0.281904i
$539$	−1.11109e6	−	962769.i	−0.00709553	−	0.00614831i
$540$	−730651.	+	1.13692e6i	−0.00464012	+	0.00722016i
$541$	1.37916e8	+	8.86331e7i	0.871008	+	0.559763i	0.898061	−	0.439871i	$-0.144976\pi$
$541$	1.37916e8	+	8.86331e7i	0.871008	+	0.559763i	−0.0270530	+	0.999634i	$0.508612\pi$
$542$	1.00135e8	−	1.15562e8i	0.628910	−	0.725800i
$543$	3.10096e7	−	1.05609e8i	0.193685	−	0.659632i
$544$	−1.57391e7	+	2.26293e6i	−0.0977647	+	0.0140564i
$545$	−2.72373e7	−	3.14335e7i	−0.168258	−	0.194180i
$546$	−2.16236e7	+	9.87518e6i	−0.132847	+	0.0606690i
$547$	−1.71316e8	+	5.03030e7i	−1.04674	+	0.307349i	−0.759497	−	0.650510i	$-0.774555\pi$
$547$	−1.71316e8	+	5.03030e7i	−1.04674	+	0.307349i	−0.287238	+	0.957859i	$0.592737\pi$
$548$	−4.14349e7	−	1.89227e7i	−0.251782	−	0.114985i
$549$	1.82210e6	+	261978.i	0.0110117	+	0.00158325i
$550$	−8.31036e7	−	1.29312e8i	−0.499496	−	0.777230i
$551$		−	6.23891e7i		−	0.372953i
$552$	1.02936e8	−	1.79986e7i	0.611997	−	0.107009i
$553$	1.82202e8			1.07740
$554$	7.69744e7	−	4.94684e7i	0.452707	−	0.290937i
$555$	14413.2	−	100246.i	8.43107e−5	−	0.000586394i
$556$	1.96053e7	−	4.29297e7i	0.114064	−	0.249766i
$557$	1.62020e7	+	5.51788e7i	0.0937567	+	0.319306i	0.992996	−	0.118152i	$-0.0376971\pi$
$557$	1.62020e7	+	5.51788e7i	0.0937567	+	0.319306i	−0.899239	+	0.437458i	$0.855879\pi$
$558$	−4.20800e7	−	9.21422e7i	−0.242199	−	0.530342i
$559$	3.86917e7	−	3.35265e7i	0.221504	−	0.191935i
$560$	−3.86369e6	−	2.68726e7i	−0.0220008	−	0.153019i
$561$	2.51607e7	+	7.38785e6i	0.142506	+	0.0418436i
$562$	−1.24861e8	−	1.08192e8i	−0.703424	−	0.609520i
$563$	−1.03752e8	+	1.61441e8i	−0.581395	+	0.904668i	−0.999994	−	0.00350281i	$-0.998885\pi$
$563$	−1.03752e8	+	1.61441e8i	−0.581395	+	0.904668i	0.418599	+	0.908171i	$0.362521\pi$
$564$	−1.62804e6	−	1.04628e6i	−0.00907460	−	0.00583189i
$565$	2.09079e7	−	2.41290e7i	0.115922	−	0.133781i
$566$	7.05018e7	−	2.40107e8i	0.388822	−	1.32421i
$567$	−1.99611e7	+	2.86997e6i	−0.109505	+	0.0157445i
$568$	724586.	+	836217.i	0.00395408	+	0.00456325i
$569$	4.62550e7	−	2.11240e7i	0.251086	−	0.114667i	−0.285897	−	0.958260i	$-0.592291\pi$
$569$	4.62550e7	−	2.11240e7i	0.251086	−	0.114667i	0.536982	+	0.843593i	$0.319564\pi$
$570$	−1.21619e7	+	3.57107e6i	−0.0656718	+	0.0192830i
$571$	2.13047e8	+	9.72954e7i	1.14437	+	0.522617i	0.895122	−	0.445822i	$-0.147088\pi$
$571$	2.13047e8	+	9.72954e7i	1.14437	+	0.522617i	0.249251	+	0.968439i	$0.419816\pi$
$572$	1.23084e7	+	1.76968e6i	0.0657678	+	0.00945598i
$573$	−3.75214e7	−	5.83844e7i	−0.199441	−	0.310336i
$574$		−	2.52854e8i		−	1.33701i
$575$	1.33708e8	−	1.23146e8i	0.703321	−	0.647764i
$576$	7.08736e7			0.370866
$577$	2.53041e8	−	1.62619e8i	1.31723	−	0.846535i	0.322259	−	0.946652i	$-0.395558\pi$
$577$	2.53041e8	−	1.62619e8i	1.31723	−	0.846535i	0.994976	+	0.100116i	$0.0319215\pi$
$578$	2.30191e7	−	1.60102e8i	0.119208	−	0.829110i
$579$	−3.49700e7	+	7.65736e7i	−0.180161	+	0.394497i
$580$	−1.43237e6	−	4.87821e6i	−0.00734127	−	0.0250021i
$581$	9.44692e7	+	2.06859e8i	0.481683	+	1.05474i
$582$	−1.08703e8	+	9.41918e7i	−0.551408	+	0.477798i
$583$	−4.23907e7	−	2.94834e8i	−0.213927	−	1.48789i
$584$	6.71441e7	+	1.97153e7i	0.337108	+	0.0989839i
$585$	3.02384e6	+	2.62017e6i	0.0151040	+	0.0130877i
$586$	−1.51797e8	+	2.36201e8i	−0.754345	+	1.17378i
$587$	6.14769e7	+	3.95088e7i	0.303947	+	0.195335i	0.683719	−	0.729745i	$-0.260361\pi$
$587$	6.14769e7	+	3.95088e7i	0.303947	+	0.195335i	−0.379772	+	0.925080i	$0.623998\pi$
$588$	141134.	−	162877.i	0.000694224	−	0.000801177i
$589$	−7.24491e7	+	2.46739e8i	−0.354558	+	1.20751i
$590$	4.93646e7	−	7.09756e6i	0.240358	−	0.0345583i
$591$	1.29487e8	+	1.49437e8i	0.627286	+	0.723926i
$592$	−685973.	+	313273.i	−0.00330630	+	0.00150993i
$593$	1.20724e7	−	3.54478e6i	0.0578935	−	0.0169991i	−0.252658	−	0.967556i	$-0.581305\pi$
$593$	1.20724e7	−	3.54478e6i	0.0578935	−	0.0169991i	0.310551	+	0.950557i	$0.399486\pi$
$594$	−3.54512e7	−	1.61900e7i	−0.169150	−	0.0772483i
$595$	1.02652e7	+	1.47592e6i	0.0487324	+	0.00700666i
$596$	−1.76255e7	−	2.74259e7i	−0.0832537	−	0.129545i
$597$			1.18695e8i			0.557840i
$598$	−1.64608e6	−	5.43037e7i	−0.00769746	−	0.253937i
$599$	1.32921e8			0.618464			0.309232	−	0.950987i	$-0.399928\pi$
$599$	1.32921e8			0.618464			0.309232	+	0.950987i	$0.399928\pi$
$600$	1.07945e8	−	6.93723e7i	0.499747	−	0.321168i
$601$	−3.86729e7	+	2.68976e8i	−0.178149	+	1.23905i	0.682892	+	0.730519i	$0.260722\pi$
$601$	−3.86729e7	+	2.68976e8i	−0.178149	+	1.23905i	−0.861041	+	0.508535i	$0.830187\pi$
$602$	−8.19289e7	+	1.79399e8i	−0.375533	+	0.822302i
$603$	2.41325e7	+	8.21877e7i	0.110065	+	0.374848i
$604$	−5.24111e6	−	1.14764e7i	−0.0237855	−	0.0520830i
$605$	6.52903e6	−	5.65743e6i	0.0294837	−	0.0255478i
$606$	1.22838e7	+	8.54359e7i	0.0551971	+	0.383904i
$607$	−3.62811e8	−	1.06531e8i	−1.62224	−	0.476332i	−0.660619	−	0.750722i	$-0.729706\pi$
$607$	−3.62811e8	−	1.06531e8i	−1.62224	−	0.476332i	−0.961618	+	0.274390i	$0.911524\pi$
$608$	−4.53406e7	−	3.92878e7i	−0.201733	−	0.174802i
$609$	4.10159e7	−	6.38220e7i	0.181594	−	0.282565i
$610$	1.18362e6	+	760666.i	0.00521462	+	0.00335123i
$611$	−3.75203e6	+	4.33007e6i	−0.0164491	+	0.0189833i
$612$	−1.08300e6	+	3.68835e6i	−0.00472469	+	0.0160908i
$613$	−1.45798e8	+	2.09626e7i	−0.632953	+	0.0910049i	−0.451321	−	0.892362i	$-0.649047\pi$
$613$	−1.45798e8	+	2.09626e7i	−0.632953	+	0.0910049i	−0.181632	+	0.983367i	$0.558138\pi$
$614$	−1.93901e8	−	2.23774e8i	−0.837675	−	0.966728i
$615$	−3.87127e7	+	1.76795e7i	−0.166428	+	0.0760053i
$616$	−2.61733e8	+	7.68517e7i	−1.11974	+	0.328785i
$617$	2.53568e8	+	1.15801e8i	1.07954	+	0.493010i	0.874143	−	0.485668i	$-0.161424\pi$
$617$	2.53568e8	+	1.15801e8i	1.07954	+	0.493010i	0.205399	+	0.978678i	$0.434151\pi$
$618$	2.96802e7	+	4.26737e6i	0.125748	+	0.0180799i
$619$	2.05558e8	+	3.19855e8i	0.866689	+	1.34859i	0.936366	+	0.351024i	$0.114167\pi$
$619$	2.05558e8	+	3.19855e8i	0.866689	+	1.34859i	−0.0696778	+	0.997570i	$0.522197\pi$
$620$			2.09559e7i			0.0879286i
$621$	1.16388e7	−	4.45947e7i	0.0485998	−	0.186213i
$622$	−2.32571e8			−0.966462
$623$	−1.52210e8	+	9.78197e7i	−0.629477	+	0.404541i
$624$	4.23995e6	−	2.94895e7i	0.0174505	−	0.121371i
$625$	8.82784e7	−	1.93303e8i	0.361588	−	0.791768i
$626$	6.81911e7	+	2.32238e8i	0.277974	+	0.946694i
$627$	4.11008e7	+	8.99983e7i	0.166743	+	0.365117i
$628$	−3.38868e7	+	2.93631e7i	−0.136821	+	0.118556i
$629$	−40996.8	−	285139.i	−0.000164740	−	0.00114579i
$630$	−1.47890e7	−	4.34244e6i	−0.0591448	−	0.0173665i
$631$	−5.51191e7	−	4.77610e7i	−0.219389	−	0.190101i	0.538232	−	0.842797i	$-0.319093\pi$
$631$	−5.51191e7	−	4.77610e7i	−0.219389	−	0.190101i	−0.757620	+	0.652696i	$0.773638\pi$
$632$	−1.58915e8	+	2.47277e8i	−0.629528	+	0.979565i
$633$	1.44205e8	+	9.26748e7i	0.568550	+	0.365385i
$634$	−3.88816e7	+	4.48717e7i	−0.152572	+	0.176078i
$635$	−1.18010e6	+	4.01906e6i	−0.00460891	+	0.0156965i
$636$	4.32202e7	−	6.21412e6i	0.168002	−	0.0241551i
$637$	−417841.	−	482214.i	−0.00161656	−	0.00186561i
$638$	1.33367e8	−	6.09067e7i	0.513554	−	0.234532i
$639$	468241.	−	137488.i	0.00179460	−	0.000526942i
$640$	2.83969e7	+	1.29684e7i	0.108326	+	0.0494707i
$641$	−2.04154e8	−	2.93529e7i	−0.775146	−	0.111449i	−0.256622	−	0.966512i	$-0.582609\pi$
$641$	−2.04154e8	−	2.93529e7i	−0.775146	−	0.111449i	−0.518524	+	0.855063i	$0.673518\pi$
$642$	2.24879e7	+	3.49918e7i	0.0849852	+	0.132240i
$643$		−	3.82417e8i		−	1.43848i	−0.694761	−	0.719240i	$-0.744490\pi$
$643$		−	3.82417e8i		−	1.43848i	0.694761	−	0.719240i	$-0.255510\pi$
$644$	−2.50830e7	−	5.07925e7i	−0.0939122	−	0.190170i
$645$	3.31951e7			0.123707
$646$	−3.03303e7	+	1.94921e7i	−0.112507	+	0.0723039i
$647$	−7.15252e7	+	4.97468e8i	−0.264086	+	1.83676i	0.237177	+	0.971466i	$0.423778\pi$
$647$	−7.15252e7	+	4.97468e8i	−0.264086	+	1.83676i	−0.501264	+	0.865295i	$0.667131\pi$
$648$	1.35149e7	−	2.95936e7i	0.0496694	−	0.108761i
$649$	−1.09674e8	−	3.73515e8i	−0.401207	−	1.36639i
$650$	−2.77129e7	−	6.06828e7i	−0.100912	−	0.220966i
$651$	−2.36324e8	+	2.04776e8i	−0.856576	+	0.742227i
$652$	1.05477e7	+	7.33610e7i	0.0380554	+	0.264681i
$653$	−2.75779e8	−	8.09760e7i	−0.990425	−	0.290815i	−0.253904	−	0.967229i	$-0.581715\pi$
$653$	−2.75779e8	−	8.09760e7i	−0.990425	−	0.290815i	−0.736521	+	0.676414i	$0.763533\pi$
$654$	1.32882e8	+	1.15143e8i	0.475044	+	0.411628i
$655$	1.93210e7	−	3.00640e7i	0.0687551	−	0.106985i
$656$	2.66590e8	+	1.71327e8i	0.944349	+	0.606896i
$657$	2.02117e7	−	2.33255e7i	0.0712698	−	0.0822498i
$658$	6.21827e6	−	2.11775e7i	0.0218269	−	0.0743356i
$659$	−4.50674e8	+	6.47971e7i	−1.57473	+	0.226412i	−0.873608	−	0.486630i	$-0.838226\pi$
$659$	−4.50674e8	+	6.47971e7i	−1.57473	+	0.226412i	−0.701121	+	0.713042i	$0.747317\pi$
$660$	5.27992e6	+	6.09335e6i	0.0183652	+	0.0211946i
$661$	−3.79510e8	+	1.73317e8i	−1.31407	+	0.600117i	−0.944325	−	0.329015i	$-0.893283\pi$
$661$	−3.79510e8	+	1.73317e8i	−1.31407	+	0.600117i	−0.369748	+	0.929132i	$0.620556\pi$
$662$	2.15224e8	−	6.31956e7i	0.741852	−	0.217828i
$663$	1.03523e7	+	4.72772e6i	0.0355218	+	0.0162223i
$664$	−3.63136e8	−	5.22111e7i	−1.24041	−	0.178344i
$665$	2.11548e7	+	3.29174e7i	0.0719355	+	0.111934i
$666$			428139.i			0.00144931i
$667$	9.81150e7	+	1.42953e8i	0.330642	+	0.481744i
$668$	8.34226e6			0.0279869
$669$	4.75105e6	−	3.05331e6i	0.0158676	−	0.0101975i
$670$	−9.31719e6	+	6.48025e7i	−0.0309785	+	0.215460i
$671$	4.56220e6	−	9.98982e6i	0.0151010	−	0.0330667i
$672$	−2.05533e7	−	6.99981e7i	−0.0677288	−	0.230663i
$673$	2.40306e8	+	5.26198e8i	0.788352	+	1.72625i	0.681310	+	0.731995i	$0.261411\pi$
$673$	2.40306e8	+	5.26198e8i	0.788352	+	1.72625i	0.107042	+	0.994254i	$0.465862\pi$
$674$	6.86986e6	−	5.95276e6i	0.0224372	−	0.0194419i
$675$	−8.05405e6	−	5.60171e7i	−0.0261880	−	0.182142i
$676$	−5.79599e7	−	1.70186e7i	−0.187624	−	0.0550913i
$677$	−2.47058e8	−	2.14077e8i	−0.796218	−	0.689927i	0.158526	−	0.987355i	$-0.449326\pi$
$677$	−2.47058e8	−	2.14077e8i	−0.796218	−	0.689927i	−0.954744	+	0.297428i	$0.903871\pi$
$678$	−7.29699e7	+	1.13543e8i	−0.234129	+	0.364312i
$679$	3.73533e8	+	2.40055e8i	1.19322	+	0.766834i
$680$	−1.09563e7	+	1.26443e7i	−0.0348449	+	0.0402131i
$681$	3.49555e7	−	1.19048e8i	0.110681	−	0.376946i
$682$	−5.98173e8	+	8.60043e7i	−1.88570	+	0.271123i
$683$	−4.37993e7	−	5.05470e7i	−0.137469	−	0.158648i	0.682841	−	0.730567i	$-0.260744\pi$
$683$	−4.37993e7	−	5.05470e7i	−0.137469	−	0.158648i	−0.820310	+	0.571920i	$0.806199\pi$
$684$	−1.31930e7	+	6.02504e6i	−0.0412264	+	0.0188275i
$685$	−8.38988e7	+	2.46349e7i	−0.261026	+	0.0766442i
$686$	2.61619e8	+	1.19477e8i	0.810395	+	0.370095i
$687$	2.09729e8	+	3.01545e7i	0.646827	+	0.0929996i
$688$	−1.33632e8	−	2.07936e8i	−0.410343	−	0.638506i
$689$		−	1.29273e8i		−	0.395231i
$690$	2.22509e7	−	2.73087e7i	0.0677330	−	0.0831292i
$691$	6.11566e8			1.85357			0.926785	−	0.375592i	$-0.122561\pi$
$691$	6.11566e8			1.85357			0.926785	+	0.375592i	$0.122561\pi$
$692$	3.96632e7	−	2.54900e7i	0.119693	−	0.0769221i
$693$	−1.71220e7	+	1.19086e8i	−0.0514463	+	0.357817i
$694$	−3.82850e7	+	8.38326e7i	−0.114538	+	0.250804i
$695$	−2.55236e7	−	8.69255e7i	−0.0760305	−	0.258936i
$696$	5.08430e7	+	1.11331e8i	0.150801	+	0.330207i
$697$	−9.14859e7	+	7.92730e7i	−0.270182	+	0.234114i
$698$	−1.02471e7	−	7.12699e7i	−0.0301324	−	0.209575i
$699$	3.28439e8	+	9.64384e7i	0.961663	+	0.282370i
$700$	−5.25698e7	−	4.55520e7i	−0.153265	−	0.132805i
$701$	1.28262e8	−	1.99579e8i	0.372343	−	0.579377i	−0.603631	−	0.797264i	$-0.706280\pi$
$701$	1.28262e8	−	1.99579e8i	0.372343	−	0.579377i	0.975974	+	0.217887i	$0.0699164\pi$
$702$	−1.42292e7	−	9.14458e6i	−0.0411311	−	0.0264334i
$703$	711765.	−	821421.i	0.00204866	−	0.00236428i
$704$	1.19124e8	−	4.05698e8i	0.341413	−	1.16275i
$705$	−3.67712e6	+	528690.i	−0.0104940	+	0.00150881i
$706$	3.09656e8	+	3.57362e8i	0.879966	+	1.01553i
$707$	2.42375e8	−	1.10689e8i	0.685850	−	0.313217i
$708$	5.47541e7	−	1.60773e7i	0.154283	−	0.0453015i
$709$	−7.81262e7	−	3.56790e7i	−0.219209	−	0.100109i	0.302784	−	0.953059i	$-0.402084\pi$
$709$	−7.81262e7	−	3.56790e7i	−0.219209	−	0.100109i	−0.521993	+	0.852950i	$0.674811\pi$
$710$	369194.	+	53082.1i	0.00103152	+	0.000148311i
$711$	7.00895e7	+	1.09061e8i	0.195004	+	0.303433i
$712$		−	2.91892e8i		−	0.808691i
$713$	−2.22025e8	−	6.79292e8i	−0.612539	−	1.87408i
$714$	−4.38415e7			−0.120446
$715$	2.00810e7	−	1.29053e7i	0.0549372	−	0.0353060i
$716$	1.36364e7	−	9.48433e7i	0.0371502	−	0.258385i
$717$	−9.94483e7	+	2.17761e8i	−0.269799	+	0.590777i
$718$	−1.29677e8	−	4.41640e8i	−0.350340	−	1.19315i
$719$	1.31072e8	+	2.87008e8i	0.352634	+	0.772161i	0.999951	+	0.00993959i	$0.00316392\pi$
$719$	1.31072e8	+	2.87008e8i	0.352634	+	0.772161i	−0.647317	+	0.762221i	$0.724109\pi$
$720$	1.45990e7	−	1.26501e7i	0.0391133	−	0.0338919i
$721$	−1.31734e7	−	9.16231e7i	−0.0351473	−	0.244455i
$722$	1.89838e8	+	5.57415e7i	0.504396	+	0.148104i
$723$	−2.28661e8	−	1.98136e8i	−0.605030	−	0.524261i
$724$	5.20420e7	−	8.09790e7i	0.137132	−	0.213381i
$725$	1.79105e8	+	1.15104e8i	0.469995	+	0.302048i
$726$	−2.39163e7	+	2.76008e7i	−0.0625005	+	0.0721294i
$727$	1.69282e8	−	5.76522e8i	0.440563	−	1.50042i	−0.377893	−	0.925849i	$-0.623351\pi$
$727$	1.69282e8	−	5.76522e8i	0.440563	−	1.50042i	0.818455	−	0.574570i	$-0.194831\pi$
$728$	−1.17182e8	+	1.68483e7i	−0.303716	+	0.0436678i
$729$	−9.39654e6	−	1.08442e7i	−0.0242541	−	0.0279907i
$730$	2.14580e7	−	9.79952e6i	0.0551594	−	0.0251905i
$731$	9.05950e7	−	2.66011e7i	0.231927	−	0.0681000i
$732$	1.46443e6	+	668781.i	0.00373365	+	0.00170510i
$733$	1.30952e8	+	1.88281e7i	0.332507	+	0.0478073i	0.306546	−	0.951856i	$-0.400827\pi$
$733$	1.30952e8	+	1.88281e7i	0.332507	+	0.0478073i	0.0259604	+	0.999663i	$0.491736\pi$
$734$	7.65446e7	+	1.19106e8i	0.193565	+	0.301193i
$735$		−	413710.i		−	0.00104192i
$736$	1.65675e8	+	1.87169e7i	0.415550	+	0.0469461i
$737$	5.11025e8			1.27655
$738$	1.51352e8	−	9.72680e7i	0.376547	−	0.241992i
$739$	4.74211e7	−	3.29821e8i	0.117500	−	0.817230i	−0.842793	−	0.538238i	$-0.819090\pi$
$739$	4.74211e7	−	3.29821e8i	0.117500	−	0.817230i	0.960293	−	0.278993i	$-0.0900006\pi$
$740$	36794.2	−	80568.1i	9.07997e−5	−	0.000198824i
$741$	1.20975e7	+	4.12002e7i	0.0297331	+	0.101262i
$742$	2.06874e8	+	4.52992e8i	0.506402	+	1.10886i
$743$	−3.63119e8	+	3.14644e8i	−0.885283	+	0.767102i	−0.973425	−	0.229006i	$-0.926453\pi$
$743$	−3.63119e8	+	3.14644e8i	−0.885283	+	0.767102i	0.0881418	+	0.996108i	$0.471907\pi$
$744$	−7.17937e7	−	4.99336e8i	−0.174328	−	1.21248i
$745$	−6.00466e7	−	1.76313e7i	−0.145218	−	0.0426398i
$746$	3.37494e8	+	2.92440e8i	0.812923	+	0.704402i
$747$	−8.74800e7	+	1.36122e8i	−0.209868	+	0.326562i
$748$	1.92928e7	+	1.23987e7i	0.0460988	+	0.0296259i
$749$	8.40865e7	−	9.70410e7i	0.200116	−	0.230946i
$750$	2.49312e7	−	8.49077e7i	0.0590961	−	0.201263i
$751$	−2.63106e8	+	3.78289e7i	−0.621170	+	0.0893107i	−0.445712	−	0.895176i	$-0.647050\pi$
$751$	−2.63106e8	+	3.78289e7i	−0.621170	+	0.0893107i	−0.175458	+	0.984487i	$0.556140\pi$
$752$	1.81146e7	+	2.09054e7i	0.0425967	+	0.0491593i
$753$	1.52561e8	−	6.96722e7i	0.357321	−	0.163183i
$754$	6.10539e7	−	1.79270e7i	0.142429	−	0.0418210i
$755$	−2.20303e7	−	1.00609e7i	−0.0511893	−	0.0233774i
$756$	−1.74570e7	−	2.50994e6i	−0.0404021	−	0.00580895i
$757$	−8.44687e7	−	1.31436e8i	−0.194719	−	0.302988i	0.730141	−	0.683296i	$-0.239454\pi$
$757$	−8.44687e7	−	1.31436e8i	−0.194719	−	0.302988i	−0.924860	+	0.380308i	$0.875818\pi$
$758$		−	6.93822e8i		−	1.59309i
$759$	−2.35709e8	−	1.41578e8i	−0.539077	−	0.323795i
$760$	−6.31254e7			−0.143802
$761$	−8.14996e7	+	5.23766e7i	−0.184927	+	0.118846i	−0.629829	−	0.776734i	$-0.716875\pi$
$761$	−8.14996e7	+	5.23766e7i	−0.184927	+	0.118846i	0.444902	+	0.895579i	$0.353239\pi$
$762$	2.52003e6	−	1.75272e7i	0.00569563	−	0.0396139i
$763$	2.25481e8	−	4.93734e8i	0.507616	−	1.11152i
$764$	−1.70999e7	−	5.82368e7i	−0.0383454	−	0.130592i
$765$	3.06539e6	+	6.71227e6i	0.00684702	+	0.0149929i
$766$	−1.20007e8	+	1.03987e8i	−0.267006	+	0.231362i
$767$	−2.40439e7	−	1.67229e8i	−0.0532867	−	0.370617i
$768$	1.52567e8	+	4.47976e7i	0.336803	+	0.0988944i
$769$	1.81902e8	+	1.57619e8i	0.399998	+	0.346600i	0.831513	−	0.555506i	$-0.187475\pi$
$769$	1.81902e8	+	1.57619e8i	0.399998	+	0.346600i	−0.431515	+	0.902106i	$0.642021\pi$
$770$	−4.97144e7	+	7.73571e7i	−0.108896	+	0.169445i
$771$	4.39504e6	+	2.82452e6i	0.00958957	+	0.00616284i
$772$	−4.82113e7	+	5.56388e7i	−0.104784	+	0.120928i
$773$	−2.84724e7	+	9.69681e7i	−0.0616433	+	0.209938i	−0.984556	−	0.175073i	$-0.943984\pi$
$773$	−2.84724e7	+	9.69681e7i	−0.0616433	+	0.209938i	0.922912	+	0.385010i	$0.125802\pi$
$774$	−1.38901e8	+	1.99709e7i	−0.299558	+	0.0430700i
$775$	−5.74668e8	−	6.63202e8i	−1.23456	−	1.42476i
$776$	−6.51588e8	+	2.97570e8i	−1.39440	+	0.636802i
$777$	1.26813e6	−	372357.i	0.00270335	−	0.000793774i
$778$	4.67251e8	+	2.13386e8i	0.992227	+	0.453135i
$779$	−4.52086e8	−	6.50001e7i	−0.956331	−	0.137500i
$780$	1.89180e6	+	2.94370e6i	0.00398650	+	0.00620312i
$781$		−	2.91142e6i		−	0.00611156i
$782$	3.88425e7	−	9.23610e7i	0.0812244	−	0.193138i
$783$	5.39804e7			0.112448
$784$	−2.59151e6	+	1.66546e6i	−0.00537780	+	0.00345610i
$785$	−1.22494e7	+	8.51967e7i	−0.0253225	+	0.176122i
$786$	−6.27590e7	+	1.37423e8i	−0.129243	+	0.283003i
$787$	−4.15940e7	−	1.41656e8i	−0.0853309	−	0.290610i	0.905761	−	0.423788i	$-0.139300\pi$
$787$	−4.15940e7	−	1.41656e8i	−0.0853309	−	0.290610i	−0.991092	+	0.133178i	$0.957482\pi$
$788$	7.18368e7	+	1.57301e8i	0.146814	+	0.321479i
$789$	8.65099e7	−	7.49613e7i	0.176131	−	0.152618i
$790$	1.41015e7	+	9.80778e7i	0.0286011	+	0.198925i
$791$	3.99774e8	+	1.17384e8i	0.807765	+	0.237181i
$792$	−1.46685e8	−	1.27104e8i	−0.295264	−	0.255848i
$793$	2.57685e6	−	4.00966e6i	0.00516738	−	0.00804060i
$794$	1.93138e8	+	1.24122e8i	0.385840	+	0.247964i
$795$	5.48898e7	−	6.33462e7i	0.109242	−	0.126072i
$796$	−2.92453e7	+	9.96003e7i	−0.0579851	+	0.197479i
$797$	−3.16886e8	+	4.55614e7i	−0.625934	+	0.0899957i	−0.447981	−	0.894043i	$-0.647857\pi$
$797$	−3.16886e8	+	4.55614e7i	−0.625934	+	0.0899957i	−0.177953	+	0.984039i	$0.556948\pi$
$798$	−1.08323e8	−	1.25012e8i	−0.213164	−	0.246004i
$799$	−9.61182e6	+	4.38957e6i	−0.0188437	+	0.00860561i
$800$	1.96437e8	−	5.76791e7i	0.383666	−	0.112654i
$801$	−1.17105e8	−	5.34800e7i	−0.227865	−	0.104062i
$802$	−3.26359e8	−	4.69233e7i	−0.632662	−	0.0909631i
$803$	−9.95494e7	−	1.54902e8i	−0.192261	−	0.299164i
$804$			7.49120e7i			0.144140i
$805$	−1.00239e8	−	4.21556e7i	−0.192154	−	0.0808105i
$806$	−2.62276e8			−0.500903
$807$	−2.87917e8	+	1.85033e8i	−0.547831	+	0.352070i
$808$	−6.11754e7	+	4.25484e8i	−0.115969	+	0.806583i
$809$	−2.35331e8	+	5.15302e8i	−0.444460	+	0.973232i	0.546298	+	0.837591i	$0.316037\pi$
$809$	−2.35331e8	+	5.15302e8i	−0.444460	+	0.973232i	−0.990758	+	0.135641i	$0.956691\pi$
$810$	−3.08977e6	−	1.05228e7i	−0.00581394	−	0.0198005i
$811$	3.55061e7	+	7.77476e7i	0.0665642	+	0.145755i	0.939990	−	0.341202i	$-0.110834\pi$
$811$	3.55061e7	+	7.77476e7i	0.0665642	+	0.145755i	−0.873426	+	0.486957i	$0.838107\pi$
$812$	5.01427e7	−	4.34489e7i	0.0936569	−	0.0811542i
$813$	−4.77988e7	−	3.32448e8i	−0.0889499	−	0.618660i
$814$	2.45078e6	+	719613.i	0.00454392	+	0.00133421i
$815$	1.07523e8	+	9.31689e7i	0.198622	+	0.172107i
$816$	2.97059e7	−	4.62232e7i	0.0546729	−	0.0850727i
$817$	2.99693e8	+	1.92601e8i	0.549554	+	0.353177i
$818$	2.17399e8	−	2.50891e8i	0.397189	−	0.458380i
$819$	−1.47106e7	+	5.00996e7i	−0.0267780	+	0.0911974i
$820$	−3.68409e7	+	5.29692e6i	−0.0668173	+	0.00960688i
$821$	−4.25208e8	−	4.90717e8i	−0.768374	−	0.886750i	0.227839	−	0.973699i	$-0.426834\pi$
$821$	−4.25208e8	−	4.90717e8i	−0.768374	−	0.886750i	−0.996213	+	0.0869484i	$0.972288\pi$
$822$	3.36243e8	−	1.53557e8i	0.605394	−	0.276474i
$823$	−3.18068e8	+	9.33932e7i	−0.570585	+	0.167539i	−0.554283	−	0.832328i	$-0.687008\pi$
$823$	−3.18068e8	+	9.33932e7i	−0.570585	+	0.167539i	−0.0163021	+	0.999867i	$0.505189\pi$
$824$	1.35837e8	+	6.20348e7i	0.242794	+	0.110880i
$825$	−3.34193e8	−	4.80497e7i	−0.595163	−	0.0855715i
$826$	3.51867e8	+	5.47516e8i	0.624366	+	0.971532i
$827$			1.09241e9i			1.93138i	0.259696	+	0.965690i	$0.416378\pi$
$827$			1.09241e9i			1.93138i	−0.259696	+	0.965690i	$0.583622\pi$
$828$	2.07542e7	−	3.45530e7i	0.0365607	−	0.0608688i
$829$	7.95445e8			1.39620			0.698099	−	0.716002i	$-0.254030\pi$
$829$	7.95445e8			1.39620			0.698099	+	0.716002i	$0.254030\pi$
$830$	−1.04039e8	+	6.68619e7i	−0.181954	+	0.116935i
$831$	2.86022e7	−	1.98933e8i	0.0498421	−	0.346659i
$832$	7.62312e7	−	1.66923e8i	0.132362	−	0.289832i
$833$	−331529.	−	1.12908e6i	−0.000573570	−	0.00195340i
$834$	1.59097e8	+	3.48373e8i	0.274260	+	0.600546i
$835$	1.21025e7	−	1.04869e7i	0.0207881	−	0.0180130i
$836$	1.23142e7	+	8.56469e7i	0.0210759	+	0.146586i
$837$	−2.13484e8	−	6.26845e7i	−0.364073	−	0.106901i
$838$	5.55044e8	+	4.80948e8i	0.943182	+	0.817272i
$839$	3.17167e8	−	4.93521e8i	0.537034	−	0.835642i	−0.461642	−	0.887066i	$-0.652740\pi$
$839$	3.17167e8	−	4.93521e8i	0.537034	−	0.835642i	0.998677	+	0.0514242i	$0.0163761\pi$
$840$	−6.45753e7	−	4.15000e7i	−0.108950	−	0.0700181i
$841$	2.56542e8	−	2.96065e8i	0.431291	−	0.497736i
$842$	−4.15071e7	+	1.41360e8i	−0.0695323	+	0.236805i
$843$	−3.59199e8	+	5.16450e7i	−0.599587	+	0.0862075i
$844$	9.81721e7	+	1.13297e8i	0.163290	+	0.188447i
$845$	−1.05479e8	+	4.81705e7i	−0.174821	+	0.0798383i
$846$	1.50684e7	−	4.42448e6i	0.0248860	−	0.00730720i
$847$	1.02553e8	+	4.68343e7i	0.168771	+	0.0770751i
$848$	−6.17774e8	−	8.88225e7i	−1.01308	−	0.145658i
$849$	−2.97168e8	−	4.62402e8i	−0.485600	−	0.755608i
$850$		−	1.23033e8i		−	0.200339i
$851$	−339087.	+	3.00148e6i	−0.000550203	+	0.00487020i
$852$	426790.			0.000690074
$853$	−2.43562e8	+	1.56528e8i	−0.392430	+	0.252199i	−0.721944	−	0.691951i	$-0.756751\pi$
$853$	−2.43562e8	+	1.56528e8i	−0.392430	+	0.252199i	0.329515	+	0.944151i	$0.393115\pi$
$854$	−2.61304e6	+	1.81741e7i	−0.00419540	+	0.0291796i
$855$	−1.15657e7	+	2.53254e7i	−0.0185044	+	0.0405190i
$856$	5.83606e7	+	1.98758e8i	0.0930461	+	0.316886i
$857$	1.58106e8	+	3.46204e8i	0.251192	+	0.550034i	0.992658	−	0.120957i	$-0.0385962\pi$
$857$	1.58106e8	+	3.46204e8i	0.251192	+	0.550034i	−0.741466	+	0.670991i	$0.765869\pi$
$858$	−7.62622e7	+	6.60816e7i	−0.120739	+	0.104621i
$859$	1.00246e8	+	6.97229e8i	0.158157	+	1.10001i	0.902026	+	0.431683i	$0.142080\pi$
$859$	1.00246e8	+	6.97229e8i	0.158157	+	1.10001i	−0.743868	+	0.668326i	$0.767011\pi$
$860$	2.78549e7	+	8.17893e6i	0.0437931	+	0.0128588i
$861$	−4.19737e8	−	3.63704e8i	−0.657608	−	0.569821i
$862$	7.04666e7	−	1.09648e8i	0.110017	−	0.171190i
$863$	−5.56249e7	−	3.57479e7i	−0.0865439	−	0.0556184i	0.496653	−	0.867949i	$-0.334562\pi$
$863$	−5.56249e7	−	3.57479e7i	−0.0865439	−	0.0556184i	−0.583197	+	0.812331i	$0.698198\pi$
$864$	3.39927e7	−	3.92296e7i	0.0527041	−	0.0608237i
$865$	2.54983e7	−	8.68391e7i	0.0393969	−	0.134174i
$866$	−6.56972e8	+	9.44583e7i	−1.01156	+	0.145441i
$867$	−2.32658e8	−	2.68502e8i	−0.356994	−	0.411993i
$868$	−2.48761e8	+	1.13605e8i	−0.380385	+	0.173716i
$869$	7.42101e8	−	2.17901e8i	1.13085	−	0.332046i
$870$	3.75294e7	+	1.71391e7i	0.0569919	+	0.0260273i
$871$	2.19527e8	+	3.15632e7i	0.332226	+	0.0477668i
$872$	4.73414e8	+	7.36646e8i	0.713989	+	1.11099i
$873$			3.15932e8i			0.474844i
$874$	3.59334e8	−	1.17448e8i	0.538226	−	0.175918i
$875$	−2.73176e8			−0.407774
$876$	2.27073e7	−	1.45931e7i	0.0337795	−	0.0217088i
$877$	−5.52297e7	+	3.84131e8i	−0.0818792	+	0.569483i	0.907042	+	0.421040i	$0.138335\pi$
$877$	−5.52297e7	+	3.84131e8i	−0.0818792	+	0.569483i	−0.988921	+	0.148442i	$0.952574\pi$
$878$	2.63967e8	−	5.78007e8i	0.390001	−	0.853984i
$879$	1.73748e8	+	5.91733e8i	0.255832	+	0.871283i
$880$	−4.78744e7	−	1.04830e8i	−0.0702515	−	0.153829i
$881$	−8.62271e8	+	7.47162e8i	−1.26100	+	1.09266i	−0.269442	+	0.963017i	$0.586839\pi$
$881$	−8.62271e8	+	7.47162e8i	−1.26100	+	1.09266i	−0.991560	+	0.129648i	$0.958615\pi$
$882$	248897.	+	1.73112e6i	0.000362755	+	0.00252302i
$883$	−2.85201e8	−	8.37425e7i	−0.414256	−	0.121637i	0.0679618	−	0.997688i	$-0.478350\pi$
$883$	−2.85201e8	−	8.37425e7i	−0.414256	−	0.121637i	−0.482218	+	0.876051i	$0.660169\pi$
$884$	7.52201e6	+	6.51786e6i	0.0108887	+	0.00943514i
$885$	5.92239e7	−	9.21542e7i	0.0854412	−	0.132949i
$886$	2.74972e8	+	1.76714e8i	0.395355	+	0.254080i
$887$	5.91586e8	−	6.82727e8i	0.847710	−	0.978309i	−0.152240	−	0.988344i	$-0.548649\pi$
$887$	5.91586e8	−	6.82727e8i	0.847710	−	0.978309i	0.999950	+	0.0100344i	$0.00319409\pi$
$888$	−600710.	+	2.04583e6i	−0.000857879	+	0.00292167i
$889$	−5.41067e7	+	7.77936e6i	−0.0770097	+	0.0110723i
$890$	−6.44359e7	−	7.43630e7i	−0.0914025	−	0.105484i
$891$	−7.78684e7	+	3.55613e7i	−0.110085	+	0.0502741i
$892$	4.73904e6	−	1.39151e6i	0.00667722	−	0.00196061i
$893$	−3.62655e7	−	1.65619e7i	−0.0509259	−	0.0232571i
$894$	2.61865e8	+	3.76505e7i	0.366492	+	0.0526936i
$895$	−9.94425e7	−	1.54735e8i	−0.138708	−	0.215834i
$896$			4.07396e8i			0.566361i
$897$	−9.25118e7	−	7.53778e7i	−0.128180	−	0.104440i
$898$	−9.53092e8			−1.31615
$899$	7.04152e8	−	4.52531e8i	0.969142	−	0.622830i
$900$	7.04369e6	−	4.89900e7i	0.00966213	−	0.0672016i
$901$	9.90408e7	−	2.16869e8i	0.135407	−	0.296499i
$902$	−3.02395e8	−	1.02986e9i	−0.412055	−	1.40333i
$903$	1.79956e8	+	3.94049e8i	0.244401	+	0.535165i
$904$	−5.07991e8	+	4.40177e8i	−0.687623	+	0.595829i
$905$	−2.62972e7	−	1.82901e8i	−0.0354783	−	0.246757i
$906$	9.82358e7	+	2.88446e7i	0.132095	+	0.0387865i
$907$	9.32134e8	+	8.07699e8i	1.24927	+	1.08250i	0.993270	+	0.115823i	$0.0369506\pi$
$907$	9.32134e8	+	8.07699e8i	1.24927	+	1.08250i	0.256001	+	0.966676i	$0.417595\pi$
$908$	5.86643e7	−	9.12834e7i	0.0783639	−	0.121937i
$909$	1.59493e8	+	1.02500e8i	0.212348	+	0.136468i
$910$	−2.61343e7	+	3.01606e7i	−0.0346806	+	0.0400236i
$911$	−2.30842e8	+	7.86176e8i	−0.305323	+	1.03984i	0.653758	+	0.756704i	$0.273192\pi$
$911$	−2.30842e8	+	7.86176e8i	−0.305323	+	1.03984i	−0.959081	+	0.283132i	$0.908627\pi$
$912$	2.05200e8	−	2.95033e7i	0.270516	−	0.0388944i
$913$	6.32158e8	+	7.29549e8i	0.830641	+	0.958611i
$914$	3.03449e7	−	1.38581e7i	0.0397418	−	0.0181495i
$915$	2.96522e6	−	870666.i	0.00387073	−	0.00113655i
$916$	1.68559e8	+	7.69785e7i	0.219314	+	0.100157i
$917$	4.61624e8	+	6.63715e7i	0.598660	+	0.0860743i
$918$	−1.68650e7	−	2.62425e7i	−0.0218001	−	0.0339216i
$919$		−	1.42679e9i		−	1.83829i	−0.393919	−	0.919145i	$-0.628881\pi$
$919$		−	1.42679e9i		−	1.83829i	0.393919	−	0.919145i	$-0.371119\pi$
$920$	1.44640e8	−	9.92729e7i	0.185749	−	0.127487i
$921$	−6.50372e8			−0.832497
$922$	6.87168e8	−	4.41616e8i	0.876739	−	0.563446i
$923$	179822.	−	1.25069e6i	0.000228686	−	0.00159054i
$924$	−4.37091e7	+	9.57096e7i	−0.0554059	+	0.121322i
$925$	1.04495e6	+	3.55879e6i	0.00132030	+	0.00449652i
$926$	3.65814e8	+	8.01021e8i	0.460710	+	1.00881i
$927$	4.97758e7	−	4.31310e7i	0.0624855	−	0.0541440i
$928$	2.77910e7	+	1.93290e8i	0.0347744	+	0.241861i
$929$	−1.12827e9	−	3.31291e8i	−1.40724	−	0.413202i	−0.512073	−	0.858942i	$-0.671122\pi$
$929$	−1.12827e9	−	3.31291e8i	−1.40724	−	0.413202i	−0.895162	+	0.445740i	$0.852941\pi$
$930$	−1.28520e8	−	1.11363e8i	−0.159780	−	0.138450i
$931$	2.40039e6	−	3.73507e6i	0.00297462	−	0.00462860i
$932$	2.51841e8	+	1.61848e8i	0.311084	+	0.199922i
$933$	−3.34530e8	+	3.86068e8i	−0.411898	+	0.475356i
$934$	1.68845e8	−	5.75034e8i	0.207228	−	0.705753i
$935$	4.35750e7	−	6.26514e6i	0.0533092	−	0.00766471i
$936$	−5.51628e7	−	6.36613e7i	−0.0672696	−	0.0776333i
$937$	−1.15197e9	+	5.26087e8i	−1.40030	+	0.639497i	−0.965351	−	0.260956i	$-0.915962\pi$
$937$	−1.15197e9	+	5.26087e8i	−1.40030	+	0.639497i	−0.434952	+	0.900453i	$0.643235\pi$
$938$	−8.19763e8	+	2.40704e8i	−0.993298	+	0.291659i
$939$	4.83600e8	+	2.20853e8i	0.584103	+	0.266751i
$940$	−3.21584e6	−	462368.i	−0.00387178	−	0.000556678i
$941$	−3.43833e8	−	5.35014e8i	−0.412647	−	0.642091i	0.571261	−	0.820768i	$-0.306454\pi$
$941$	−3.43833e8	−	5.35014e8i	−0.412647	−	0.642091i	−0.983908	+	0.178678i	$0.942818\pi$
$942$		−	3.63864e8i		−	0.435298i
$943$	1.13809e9	−	5.62028e8i	1.35719	−	0.670228i
$944$	−8.15677e8			−0.969622
$945$	−2.84809e7	+	1.83035e7i	−0.0337488	+	0.0216890i
$946$	−1.19145e8	+	8.28669e8i	−0.140735	+	0.978830i
$947$	1.42502e8	−	3.12035e8i	0.167791	−	0.367412i	−0.806993	−	0.590561i	$-0.798906\pi$
$947$	1.42502e8	−	3.12035e8i	0.167791	−	0.367412i	0.974784	+	0.223149i	$0.0716337\pi$
$948$	3.19424e7	+	1.08786e8i	0.0374923	+	0.127687i
$949$	−3.31971e7	−	7.26916e7i	−0.0388421	−	0.0850522i
$950$	3.50823e8	−	3.03990e8i	0.409183	−	0.354559i
$951$	1.85599e7	+	1.29087e8i	0.0215791	+	0.150086i
$952$	−2.09493e8	−	6.15128e7i	−0.242806	−	0.0712943i
$953$	−1.01440e9	−	8.78982e8i	−1.17201	−	1.01555i	−0.999534	−	0.0305352i	$-0.990279\pi$
$953$	−1.01440e9	−	8.78982e8i	−1.17201	−	1.01555i	−0.172473	−	0.985014i	$-0.555176\pi$
$954$	−1.91569e8	+	2.98087e8i	−0.220638	+	0.343319i
$955$	−9.80158e7	−	6.29909e7i	−0.112535	−	0.0723216i
$956$	−1.37104e8	+	1.58227e8i	−0.156919	+	0.181095i
$957$	9.07297e7	−	3.08997e8i	0.103517	−	0.352548i
$958$	4.95720e8	−	7.12738e7i	0.563820	−	0.0810650i
$959$	−7.47265e8	−	8.62389e8i	−0.847264	−	0.977794i
$960$	1.08231e8	−	4.94272e7i	0.122331	−	0.0558667i
$961$	−2.45876e9	+	7.21956e8i	−2.77042	+	0.813468i
$962$	1.00836e6	+	460504.i	0.00113264	+	0.000517259i
$963$	9.04329e7	+	1.30023e7i	0.101262	+	0.0145593i
$964$	−1.43057e8	−	2.22601e8i	−0.159690	−	0.248483i
$965$			1.41323e8i			0.157265i
$966$	4.44800e8	+	1.16089e8i	0.493439	+	0.128783i
$967$	9.17267e8			1.01442			0.507208	−	0.861824i	$-0.330678\pi$
$967$	9.17267e8			1.01442			0.507208	+	0.861824i	$0.330678\pi$
$968$	−1.53008e8	+	9.83323e7i	−0.168690	+	0.108410i
$969$	−1.12702e7	+	7.83857e7i	−0.0123868	+	0.0861521i
$970$	−1.00310e8	+	2.19649e8i	−0.109908	+	0.240666i
$971$	3.03446e8	+	1.03344e9i	0.331455	+	1.12883i	0.941654	+	0.336583i	$0.109271\pi$
$971$	3.03446e8	+	1.03344e9i	0.331455	+	1.12883i	−0.610199	+	0.792248i	$0.708911\pi$
$972$	−5.21299e6	−	1.14149e7i	−0.00567660	−	0.0124300i
$973$	8.93500e8	−	7.74222e8i	0.969965	−	0.840480i
$974$	−1.52706e8	−	1.06209e9i	−0.165264	−	1.14944i
$975$	−1.40596e8	−	4.12826e7i	−0.151690	−	0.0445403i
$976$	−1.73909e7	−	1.50693e7i	−0.0187057	−	0.0162085i
$977$	−4.89235e8	+	7.61265e8i	−0.524607	+	0.816304i	−0.997912	−	0.0645946i	$-0.979425\pi$
$977$	−4.89235e8	+	7.61265e8i	−0.524607	+	0.816304i	0.473305	+	0.880899i	$0.343061\pi$
$978$	−5.05967e8	−	3.25165e8i	−0.540886	−	0.347606i
$979$	−5.02962e8	+	5.80449e8i	−0.536028	+	0.618609i
$980$	101934.	−	347155.i	0.000108303	−	0.000368846i
$981$	3.82275e8	−	5.49628e7i	0.404920	−	0.0582187i
$982$	−1.18278e8	−	1.36500e8i	−0.124902	−	0.144145i
$983$	1.08809e9	−	4.96916e8i	1.14553	−	0.523145i	0.250043	−	0.968235i	$-0.419555\pi$
$983$	1.08809e9	−	4.96916e8i	1.14553	−	0.523145i	0.895486	+	0.445089i	$0.146828\pi$
$984$	8.59698e8	−	2.52430e8i	0.902320	−	0.264945i
$985$	3.01956e8	+	1.37899e8i	0.315962	+	0.144295i
$986$	1.16159e8	+	1.67011e7i	0.121177	+	0.0174226i
$987$	−2.62103e7	−	4.07840e7i	−0.0272596	−	0.0424168i
$988$			3.75529e7i			0.0389379i
$989$	−9.89582e8	+	2.99967e7i	−1.02297	+	0.0310087i
$990$	−6.54283e7			−0.0674310
$991$	4.64820e8	−	2.98722e8i	0.477599	−	0.306934i	−0.279602	−	0.960116i	$-0.590203\pi$
$991$	4.64820e8	−	2.98722e8i	0.477599	−	0.306934i	0.757201	+	0.653182i	$0.226566\pi$
$992$	1.14549e8	−	7.96704e8i	0.117343	−	0.816135i
$993$	2.04674e8	−	4.48173e8i	0.209033	−	0.457717i
$994$	1.37134e6	+	4.67037e6i	0.00139633	+	0.00475545i
$995$	8.27778e7	+	1.81258e8i	0.0840320	+	0.184004i
$996$	−1.06946e8	+	9.26691e7i	−0.108240	+	0.0937901i
$997$	1.30402e8	+	9.06962e8i	0.131582	+	0.915174i	0.943493	+	0.331393i	$0.107518\pi$
$997$	1.30402e8	+	9.06962e8i	0.131582	+	0.915174i	−0.811911	+	0.583782i	$0.801572\pi$
$998$	1.49593e9	+	4.39245e8i	1.50494	+	0.441891i
$999$	710711.	+	615834.i	0.000712847	+	0.000617685i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.7.f.a.34.8	✓	240
23.21	odd	22	inner	69.7.f.a.67.8	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.7.f.a.34.8	✓	240	1.1	even	1	trivial
69.7.f.a.67.8	yes	240	23.21	odd	22	inner

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:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	69.f (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.97036 + 3.83691i) q^{2} +(-2.21847 + 15.4298i) q^{3} +(-5.66333 + 12.4010i) q^{4} +(7.37292 + 25.1099i) q^{5} +(-45.9577 - 100.633i) q^{6} +(-258.102 + 223.647i) q^{7} +(-78.4096 - 545.351i) q^{8} +(-233.157 - 68.4610i) q^{9} +O(q^{10})\)	\(q+(-5.97036 + 3.83691i) q^{2} +(-2.21847 + 15.4298i) q^{3} +(-5.66333 + 12.4010i) q^{4} +(7.37292 + 25.1099i) q^{5} +(-45.9577 - 100.633i) q^{6} +(-258.102 + 223.647i) q^{7} +(-78.4096 - 545.351i) q^{8} +(-233.157 - 68.4610i) q^{9} +(-140.363 - 121.626i) q^{10} +(-783.776 + 1219.58i) q^{11} +(-178.780 - 114.895i) q^{12} +(-412.023 + 475.499i) q^{13} +(682.849 - 2325.57i) q^{14} +(-403.797 + 58.0572i) q^{15} +(1989.23 + 2295.69i) q^{16} +(-1055.51 + 482.033i) q^{17} +(1654.71 - 485.866i) q^{18} +(-3982.43 - 1818.71i) q^{19} +(-353.142 - 50.7741i) q^{20} +(-2878.23 - 4478.62i) q^{21} -10288.6i q^{22} +(11985.2 - 2095.64i) q^{23} +8588.60 q^{24} +(12568.4 - 8077.25i) q^{25} +(635.471 - 4419.80i) q^{26} +(1573.59 - 3445.68i) q^{27} +(-1311.72 - 4467.30i) q^{28} +(5919.82 + 12962.6i) q^{29} +(2188.05 - 1895.96i) q^{30} +(-8359.18 - 58139.4i) q^{31} +(13148.3 + 3860.68i) q^{32} +(-17079.1 - 14799.1i) q^{33} +(4452.22 - 6927.79i) q^{34} +(-7518.72 - 4831.99i) q^{35} +(2169.42 - 2503.65i) q^{36} +(-69.9427 + 238.203i) q^{37} +(30754.8 - 4421.87i) q^{38} +(-6422.80 - 7412.30i) q^{39} +(13115.6 - 5989.69i) q^{40} +(100098. - 29391.3i) q^{41} +(34368.2 + 15695.4i) q^{42} +(-80542.4 - 11580.2i) q^{43} +(-10685.2 - 16626.4i) q^{44} -6359.29i q^{45} +(-63514.9 + 58497.8i) q^{46} +9106.37 q^{47} +(-39835.1 + 25600.4i) q^{48} +(-144.325 + 1003.80i) q^{49} +(-44046.4 + 96448.1i) q^{50} +(-5096.07 - 17355.6i) q^{51} +(-3563.23 - 7802.38i) q^{52} +(-155280. + 134551. i) q^{53} +(3825.89 + 26609.7i) q^{54} +(-36402.2 - 10688.6i) q^{55} +(142204. + 123220. i) q^{56} +(36897.3 - 57413.3i) q^{57} +(-85079.8 - 54677.5i) q^{58} +(-175846. + 202937. i) q^{59} +(1566.87 - 5336.26i) q^{60} +(-7498.35 + 1078.10i) q^{61} +(272983. + 315039. i) q^{62} +(75489.4 - 34474.9i) q^{63} +(-279847. + 82170.4i) q^{64} +(-14977.5 - 6840.01i) q^{65} +(158751. + 22824.9i) q^{66} +(-190576. - 296542. i) q^{67} -15819.2i q^{68} +(5746.57 + 189578. i) q^{69} +63429.3 q^{70} +(-1689.46 + 1085.75i) q^{71} +(-19053.5 + 132520. i) q^{72} +(-52762.9 + 115535. i) q^{73} +(-496.382 - 1690.52i) q^{74} +(96747.5 + 211848. i) q^{75} +(45107.6 - 39085.9i) q^{76} +(-70460.8 - 490066. i) q^{77} +(66786.7 + 19610.4i) q^{78} +(-403196. - 349371. i) q^{79} +(-42978.1 + 66875.2i) q^{80} +(49675.2 + 31924.3i) q^{81} +(-484846. + 559542. i) q^{82} +(187599. - 638904. i) q^{83} +(71839.5 - 10329.0i) q^{84} +(-19886.0 - 22949.6i) q^{85} +(525299. - 239896. i) q^{86} +(-213143. + 62584.5i) q^{87} +(726554. + 331806. i) q^{88} +(524397. + 75396.9i) q^{89} +(24400.1 + 37967.3i) q^{90} -214875. i q^{91} +(-41888.0 + 160496. i) q^{92} +915623. q^{93} +(-54368.3 + 34940.4i) q^{94} +(16305.5 - 113408. i) q^{95} +(-88738.5 + 194310. i) q^{96} +(-366290. - 1.24747e6i) q^{97} +(-2989.82 - 6546.80i) q^{98} +(266236. - 230695. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9}+O(q^{10}) \) 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9	\( 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9} - 384 q^{13} + 33816 q^{16} + 22880 q^{17} + 4860 q^{18} - 31680 q^{19} - 157696 q^{20} + 36488 q^{23} + 39204 q^{24} + 200664 q^{25} + 99032 q^{26} - 202752 q^{28} - 181712 q^{29} - 128496 q^{31} + 439300 q^{32} - 400026 q^{34} + 368744 q^{35} + 42282 q^{36} + 446688 q^{37} + 550550 q^{38} - 52488 q^{39} - 156750 q^{40} - 606080 q^{41} - 1274130 q^{42} - 429000 q^{43} - 867482 q^{44} + 309288 q^{46} + 1111152 q^{47} + 837864 q^{48} + 722136 q^{49} + 1786926 q^{50} + 463320 q^{51} - 812550 q^{52} - 367840 q^{53} - 354294 q^{54} - 398088 q^{55} - 3696550 q^{56} - 1240272 q^{57} + 1903134 q^{58} + 545800 q^{59} + 2450250 q^{60} - 495264 q^{61} + 488776 q^{62} - 2699808 q^{64} - 290400 q^{67} + 23328 q^{69} - 392616 q^{70} + 255392 q^{71} + 228420 q^{72} + 1346880 q^{73} - 5387470 q^{74} + 365472 q^{75} + 2123022 q^{76} + 6134240 q^{77} + 171072 q^{78} + 4025472 q^{79} + 10626462 q^{80} - 1417176 q^{81} + 2025492 q^{82} - 2474560 q^{83} - 8866152 q^{85} - 15634300 q^{86} - 611712 q^{87} - 10636560 q^{88} - 5901720 q^{89} + 6566394 q^{92} - 2484432 q^{93} + 13931490 q^{94} + 8183072 q^{95} - 4682124 q^{96} + 12319560 q^{97} + 14139580 q^{98} + 2993760 q^{99}+O(q^{100}) \) 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9 - 384 * q^13 + 33816 * q^16 + 22880 * q^17 + 4860 * q^18 - 31680 * q^19 - 157696 * q^20 + 36488 * q^23 + 39204 * q^24 + 200664 * q^25 + 99032 * q^26 - 202752 * q^28 - 181712 * q^29 - 128496 * q^31 + 439300 * q^32 - 400026 * q^34 + 368744 * q^35 + 42282 * q^36 + 446688 * q^37 + 550550 * q^38 - 52488 * q^39 - 156750 * q^40 - 606080 * q^41 - 1274130 * q^42 - 429000 * q^43 - 867482 * q^44 + 309288 * q^46 + 1111152 * q^47 + 837864 * q^48 + 722136 * q^49 + 1786926 * q^50 + 463320 * q^51 - 812550 * q^52 - 367840 * q^53 - 354294 * q^54 - 398088 * q^55 - 3696550 * q^56 - 1240272 * q^57 + 1903134 * q^58 + 545800 * q^59 + 2450250 * q^60 - 495264 * q^61 + 488776 * q^62 - 2699808 * q^64 - 290400 * q^67 + 23328 * q^69 - 392616 * q^70 + 255392 * q^71 + 228420 * q^72 + 1346880 * q^73 - 5387470 * q^74 + 365472 * q^75 + 2123022 * q^76 + 6134240 * q^77 + 171072 * q^78 + 4025472 * q^79 + 10626462 * q^80 - 1417176 * q^81 + 2025492 * q^82 - 2474560 * q^83 - 8866152 * q^85 - 15634300 * q^86 - 611712 * q^87 - 10636560 * q^88 - 5901720 * q^89 + 6566394 * q^92 - 2484432 * q^93 + 13931490 * q^94 + 8183072 * q^95 - 4682124 * q^96 + 12319560 * q^97 + 14139580 * q^98 + 2993760 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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