LMFDB - Embedded newform 20.11.b.a.11.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [20,11,Mod(11,20)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(20, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("20.11");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 20 = 2^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	20.b (of order $2$, degree $1$, 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:	$12.7071450535$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 84 x^{18} - 86 x^{17} - 51565 x^{16} + 188134 x^{15} - 12946328 x^{14} + \cdots + 11\!\cdots\!25 $ x^20 - x^19 + 84x^18 - 86x^17 - 51565x^16 + 188134x^15 - 12946328x^14 + 95990512x^13 + 5401091173x^12 - 59241975423x^11 + 1752287752812x^10 - 13855072435862x^9 + 53025624411849x^8 + 4768661862568058x^7 - 71663288570646432x^6 + 1087383280946073208x^5 - 9530913414031332129x^4 - 22591082233500222765x^3 + 1758197001700115583660x^2 - 51913151006968686718150x + 1126337396992659918451525
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{94}\cdot 3^{4}\cdot 5^{29} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.14
Root			$5.61235 + 15.2006i$ of defining polynomial
Character	$\chi$	$=$	20.11
Dual form			20.11.b.a.11.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(9.98863 + 30.4011i) q^{2} +330.781i q^{3} +(-824.454 + 607.331i) q^{4} +1397.54 q^{5} +(-10056.1 + 3304.05i) q^{6} +29449.0i q^{7} +(-26698.7 - 18997.9i) q^{8} -50366.8 q^{9} +O(q^{10})$	\(q+(9.98863 + 30.4011i) q^{2} +330.781i q^{3} +(-824.454 + 607.331i) q^{4} +1397.54 q^{5} +(-10056.1 + 3304.05i) q^{6} +29449.0i q^{7} +(-26698.7 - 18997.9i) q^{8} -50366.8 q^{9} +(13959.5 + 42486.8i) q^{10} -122442. i q^{11} +(-200893. - 272713. i) q^{12} +449354. q^{13} +(-895281. + 294155. i) q^{14} +462280. i q^{15} +(310874. - 1.00143e6i) q^{16} -132144. q^{17} +(-503095. - 1.53120e6i) q^{18} -3.03458e6i q^{19} +(-1.15221e6 + 848771. i) q^{20} -9.74114e6 q^{21} +(3.72238e6 - 1.22303e6i) q^{22} +4.11212e6i q^{23} +(6.28414e6 - 8.83141e6i) q^{24} +1.95312e6 q^{25} +(4.48843e6 + 1.36609e7i) q^{26} +2.87192e6i q^{27} +(-1.78853e7 - 2.42793e7i) q^{28} -2.05671e7 q^{29} +(-1.40538e7 + 4.61754e6i) q^{30} +4.65842e7i q^{31} +(3.35499e7 - 552041. i) q^{32} +4.05016e7 q^{33} +(-1.31994e6 - 4.01731e6i) q^{34} +4.11562e7i q^{35} +(4.15251e7 - 3.05893e7i) q^{36} +7.43988e7 q^{37} +(9.22546e7 - 3.03113e7i) q^{38} +1.48637e8i q^{39} +(-3.73126e7 - 2.65504e7i) q^{40} +1.29152e7 q^{41} +(-9.73007e7 - 2.96141e8i) q^{42} -4.13136e7i q^{43} +(7.43631e7 + 1.00948e8i) q^{44} -7.03897e7 q^{45} +(-1.25013e8 + 4.10744e7i) q^{46} +1.40161e8i q^{47} +(3.31255e8 + 1.02831e8i) q^{48} -5.84766e8 q^{49} +(1.95091e7 + 5.93772e7i) q^{50} -4.37106e7i q^{51} +(-3.70472e8 + 2.72906e8i) q^{52} -7.63529e8 q^{53} +(-8.73095e7 + 2.86865e7i) q^{54} -1.71118e8i q^{55} +(5.59469e8 - 7.86249e8i) q^{56} +1.00378e9 q^{57} +(-2.05437e8 - 6.25262e8i) q^{58} -3.73192e8i q^{59} +(-2.80757e8 - 3.81129e8i) q^{60} +1.40526e9 q^{61} +(-1.41621e9 + 4.65313e8i) q^{62} -1.48325e9i q^{63} +(3.51900e8 + 1.01444e9i) q^{64} +6.27991e8 q^{65} +(4.04555e8 + 1.23129e9i) q^{66} +1.39456e9i q^{67} +(1.08946e8 - 8.02550e7i) q^{68} -1.36021e9 q^{69} +(-1.25119e9 + 4.11094e8i) q^{70} -7.53953e8i q^{71} +(1.34473e9 + 9.56863e8i) q^{72} +1.69785e8 q^{73} +(7.43142e8 + 2.26181e9i) q^{74} +6.46056e8i q^{75} +(1.84300e9 + 2.50187e9i) q^{76} +3.60580e9 q^{77} +(-4.51874e9 + 1.48469e9i) q^{78} -3.47862e9i q^{79} +(4.34460e8 - 1.39955e9i) q^{80} -3.92408e9 q^{81} +(1.29005e8 + 3.92637e8i) q^{82} -8.27276e8i q^{83} +(8.03113e9 - 5.91610e9i) q^{84} -1.84676e8 q^{85} +(1.25598e9 - 4.12667e8i) q^{86} -6.80319e9i q^{87} +(-2.32615e9 + 3.26905e9i) q^{88} +6.94167e9 q^{89} +(-7.03097e8 - 2.13992e9i) q^{90} +1.32330e10i q^{91} +(-2.49742e9 - 3.39025e9i) q^{92} -1.54092e10 q^{93} +(-4.26106e9 + 1.40002e9i) q^{94} -4.24096e9i q^{95} +(1.82605e8 + 1.10977e10i) q^{96} +1.99530e8 q^{97} +(-5.84101e9 - 1.77775e10i) q^{98} +6.16703e9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 22 q^{2} - 644 q^{4} - 14784 q^{6} + 3448 q^{8} - 414868 q^{9}+O(q^{10}) $ 20 * q + 22 * q^2 - 644 * q^4 - 14784 * q^6 + 3448 * q^8 - 414868 * q^9	\( 20 q + 22 q^{2} - 644 q^{4} - 14784 q^{6} + 3448 q^{8} - 414868 q^{9} - 31250 q^{10} + 1329640 q^{12} - 278864 q^{13} - 2240504 q^{14} + 4261360 q^{16} - 1921656 q^{17} - 3556082 q^{18} - 1187500 q^{20} + 4157512 q^{21} - 5811280 q^{22} - 19112144 q^{24} + 39062500 q^{25} + 25066884 q^{26} - 87415400 q^{28} - 66014888 q^{29} + 39875000 q^{30} - 33171328 q^{32} + 85980560 q^{33} - 27236084 q^{34} + 355456476 q^{36} - 153620656 q^{37} + 250352720 q^{38} - 112375000 q^{40} + 477406160 q^{41} - 570662040 q^{42} + 339141040 q^{44} - 140125000 q^{45} - 897549304 q^{46} - 479727360 q^{48} + 333772012 q^{49} + 42968750 q^{50} - 110465096 q^{52} - 1669491824 q^{53} + 706139792 q^{54} - 1362290224 q^{56} + 3973032960 q^{57} + 2075027916 q^{58} - 677375000 q^{60} - 4283166080 q^{61} + 1664032240 q^{62} + 340459456 q^{64} + 290125000 q^{65} + 1884031760 q^{66} + 3042411896 q^{68} - 5321669928 q^{69} - 2070000000 q^{70} + 1632326712 q^{72} + 2474287656 q^{73} + 188682276 q^{74} + 2323171200 q^{76} + 410885040 q^{77} - 19914223760 q^{78} + 3604750000 q^{80} + 9939722652 q^{81} - 3197757116 q^{82} + 2383099552 q^{84} + 4799500000 q^{85} + 19648321456 q^{86} + 2774318240 q^{88} + 3011851592 q^{89} - 2849906250 q^{90} - 27349072440 q^{92} - 11861394640 q^{93} + 15684681576 q^{94} - 1990377984 q^{96} - 39984502056 q^{97} + 38416891998 q^{98}+O(q^{100}) \) 20 * q + 22 * q^2 - 644 * q^4 - 14784 * q^6 + 3448 * q^8 - 414868 * q^9 - 31250 * q^10 + 1329640 * q^12 - 278864 * q^13 - 2240504 * q^14 + 4261360 * q^16 - 1921656 * q^17 - 3556082 * q^18 - 1187500 * q^20 + 4157512 * q^21 - 5811280 * q^22 - 19112144 * q^24 + 39062500 * q^25 + 25066884 * q^26 - 87415400 * q^28 - 66014888 * q^29 + 39875000 * q^30 - 33171328 * q^32 + 85980560 * q^33 - 27236084 * q^34 + 355456476 * q^36 - 153620656 * q^37 + 250352720 * q^38 - 112375000 * q^40 + 477406160 * q^41 - 570662040 * q^42 + 339141040 * q^44 - 140125000 * q^45 - 897549304 * q^46 - 479727360 * q^48 + 333772012 * q^49 + 42968750 * q^50 - 110465096 * q^52 - 1669491824 * q^53 + 706139792 * q^54 - 1362290224 * q^56 + 3973032960 * q^57 + 2075027916 * q^58 - 677375000 * q^60 - 4283166080 * q^61 + 1664032240 * q^62 + 340459456 * q^64 + 290125000 * q^65 + 1884031760 * q^66 + 3042411896 * q^68 - 5321669928 * q^69 - 2070000000 * q^70 + 1632326712 * q^72 + 2474287656 * q^73 + 188682276 * q^74 + 2323171200 * q^76 + 410885040 * q^77 - 19914223760 * q^78 + 3604750000 * q^80 + 9939722652 * q^81 - 3197757116 * q^82 + 2383099552 * q^84 + 4799500000 * q^85 + 19648321456 * q^86 + 2774318240 * q^88 + 3011851592 * q^89 - 2849906250 * q^90 - 27349072440 * q^92 - 11861394640 * q^93 + 15684681576 * q^94 - 1990377984 * q^96 - 39984502056 * q^97 + 38416891998 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/20\mathbb{Z}\right)^\times$.

$n$	$11$	$17$
$\chi(n)$	$-1$	$1$

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 $

$2$	9.98863	+	30.4011i	0.312145	+	0.950035i
$2$	9.98863	+	30.4011i	0.312145	+	0.950035i
$3$			330.781i			1.36124i	0.732638	+	0.680618i	$0.238289\pi$
$3$			330.781i			1.36124i	−0.732638	+	0.680618i	$0.761711\pi$
$4$	−824.454	+	607.331i	−0.805131	+	0.593097i
$5$	1397.54			0.447214
$5$	1397.54			0.447214
$6$	−10056.1	+	3304.05i	−1.29322	+	0.424903i
$7$			29449.0i			1.75218i	0.482144	+	0.876092i	$0.339858\pi$
$7$			29449.0i			1.75218i	−0.482144	+	0.876092i	$0.660142\pi$
$8$	−26698.7	−	18997.9i	−0.814780	−	0.579770i
$9$	−50366.8			−0.852965
$10$	13959.5	+	42486.8i	0.139595	+	0.424868i
$11$		−	122442.i		−	0.760271i	−0.924931	−	0.380136i	$-0.875877\pi$
$11$		−	122442.i		−	0.760271i	0.924931	−	0.380136i	$-0.124123\pi$
$12$	−200893.	−	272713.i	−0.807345	−	1.09597i
$13$	449354.			1.21024			0.605120	−	0.796134i	$-0.293125\pi$
$13$	449354.			1.21024			0.605120	+	0.796134i	$0.293125\pi$
$14$	−895281.	+	294155.i	−1.66464	+	0.546935i
$15$			462280.i			0.608764i
$16$	310874.	−	1.00143e6i	0.296473	−	0.955041i
$17$	−132144.			−0.0930683			−0.0465342	−	0.998917i	$-0.514818\pi$
$17$	−132144.			−0.0930683			−0.0465342	+	0.998917i	$0.514818\pi$
$18$	−503095.	−	1.53120e6i	−0.266249	−	0.810347i
$19$		−	3.03458e6i		−	1.22555i	−0.790258	−	0.612775i	$-0.790053\pi$
$19$		−	3.03458e6i		−	1.22555i	0.790258	−	0.612775i	$-0.209947\pi$
$20$	−1.15221e6	+	848771.i	−0.360066	+	0.265241i
$21$	−9.74114e6			−2.38514
$22$	3.72238e6	−	1.22303e6i	0.722284	−	0.237315i
$23$			4.11212e6i			0.638890i	0.947605	+	0.319445i	$0.103497\pi$
$23$			4.11212e6i			0.638890i	−0.947605	+	0.319445i	$0.896503\pi$
$24$	6.28414e6	−	8.83141e6i	0.789205	−	1.10911i
$25$	1.95312e6			0.200000
$26$	4.48843e6	+	1.36609e7i	0.377770	+	1.14977i
$27$			2.87192e6i			0.200149i
$28$	−1.78853e7	−	2.42793e7i	−1.03921	−	1.41074i
$29$	−2.05671e7			−1.00273			−0.501363	−	0.865237i	$-0.667168\pi$
$29$	−2.05671e7			−1.00273			−0.501363	+	0.865237i	$0.667168\pi$
$30$	−1.40538e7	+	4.61754e6i	−0.578346	+	0.190022i
$31$			4.65842e7i			1.62716i	0.581452	+	0.813581i	$0.302485\pi$
$31$			4.65842e7i			1.62716i	−0.581452	+	0.813581i	$0.697515\pi$
$32$	3.35499e7	−	552041.i	0.999865	−	0.0164521i
$33$	4.05016e7			1.03491
$34$	−1.31994e6	−	4.01731e6i	−0.0290508	−	0.0884181i
$35$			4.11562e7i			0.783601i
$36$	4.15251e7	−	3.05893e7i	0.686749	−	0.505891i
$37$	7.43988e7			1.07290			0.536448	−	0.843934i	$-0.319766\pi$
$37$	7.43988e7			1.07290			0.536448	+	0.843934i	$0.319766\pi$
$38$	9.22546e7	−	3.03113e7i	1.16431	−	0.382549i
$39$			1.48637e8i			1.64742i
$40$	−3.73126e7	−	2.65504e7i	−0.364381	−	0.259281i
$41$	1.29152e7			0.111476			0.0557382	−	0.998445i	$-0.482249\pi$
$41$	1.29152e7			0.111476			0.0557382	+	0.998445i	$0.482249\pi$
$42$	−9.73007e7	−	2.96141e8i	−0.744508	−	2.26596i
$43$		−	4.13136e7i		−	0.281029i	−0.990079	−	0.140515i	$-0.955124\pi$
$43$		−	4.13136e7i		−	0.281029i	0.990079	−	0.140515i	$-0.0448757\pi$
$44$	7.43631e7	+	1.00948e8i	0.450914	+	0.612118i
$45$	−7.03897e7			−0.381458
$46$	−1.25013e8	+	4.10744e7i	−0.606968	+	0.199426i
$47$			1.40161e8i			0.611138i	0.952170	+	0.305569i	$0.0988467\pi$
$47$			1.40161e8i			0.611138i	−0.952170	+	0.305569i	$0.901153\pi$
$48$	3.31255e8	+	1.02831e8i	1.30004	+	0.403569i
$49$	−5.84766e8			−2.07015
$50$	1.95091e7	+	5.93772e7i	0.0624290	+	0.190007i
$51$		−	4.37106e7i		−	0.126688i
$52$	−3.70472e8	+	2.72906e8i	−0.974402	+	0.717790i
$53$	−7.63529e8			−1.82577			−0.912885	−	0.408216i	$-0.866151\pi$
$53$	−7.63529e8			−1.82577			−0.912885	+	0.408216i	$0.866151\pi$
$54$	−8.73095e7	+	2.86865e7i	−0.190148	+	0.0624755i
$55$		−	1.71118e8i		−	0.340004i
$56$	5.59469e8	−	7.86249e8i	1.01586	−	1.42764i
$57$	1.00378e9			1.66826
$58$	−2.05437e8	−	6.25262e8i	−0.312996	−	0.952625i
$59$		−	3.73192e8i		−	0.522002i	−0.965338	−	0.261001i	$-0.915947\pi$
$59$		−	3.73192e8i		−	0.522002i	0.965338	−	0.261001i	$-0.0840527\pi$
$60$	−2.80757e8	−	3.81129e8i	−0.361056	−	0.490135i
$61$	1.40526e9			1.66383			0.831913	−	0.554906i	$-0.187246\pi$
$61$	1.40526e9			1.66383			0.831913	+	0.554906i	$0.187246\pi$
$62$	−1.41621e9	+	4.65313e8i	−1.54586	+	0.507910i
$63$		−	1.48325e9i		−	1.49455i
$64$	3.51900e8	+	1.01444e9i	0.327733	+	0.944771i
$65$	6.27991e8			0.541236
$66$	4.04555e8	+	1.23129e9i	0.323041	+	0.983199i
$67$			1.39456e9i			1.03291i	0.856314	+	0.516456i	$0.172749\pi$
$67$			1.39456e9i			1.03291i	−0.856314	+	0.516456i	$0.827251\pi$
$68$	1.08946e8	−	8.02550e7i	0.0749322	−	0.0551985i
$69$	−1.36021e9			−0.869681
$70$	−1.25119e9	+	4.11094e8i	−0.744448	+	0.244597i
$71$		−	7.53953e8i		−	0.417881i	−0.977928	−	0.208941i	$-0.932998\pi$
$71$		−	7.53953e8i		−	0.417881i	0.977928	−	0.208941i	$-0.0670015\pi$
$72$	1.34473e9	+	9.56863e8i	0.694979	+	0.494524i
$73$	1.69785e8			0.0819002			0.0409501	−	0.999161i	$-0.486962\pi$
$73$	1.69785e8			0.0819002			0.0409501	+	0.999161i	$0.486962\pi$
$74$	7.43142e8	+	2.26181e9i	0.334899	+	1.01929i
$75$			6.46056e8i			0.272247i
$76$	1.84300e9	+	2.50187e9i	0.726869	+	0.986728i
$77$	3.60580e9			1.33213
$78$	−4.51874e9	+	1.48469e9i	−1.56511	+	0.514235i
$79$		−	3.47862e9i		−	1.13050i	−0.824919	−	0.565251i	$-0.808779\pi$
$79$		−	3.47862e9i		−	1.13050i	0.824919	−	0.565251i	$-0.191221\pi$
$80$	4.34460e8	−	1.39955e9i	0.132587	−	0.427107i
$81$	−3.92408e9			−1.12542
$82$	1.29005e8	+	3.92637e8i	0.0347968	+	0.105906i
$83$		−	8.27276e8i		−	0.210020i	−0.994471	−	0.105010i	$-0.966513\pi$
$83$		−	8.27276e8i		−	0.210020i	0.994471	−	0.105010i	$-0.0334874\pi$
$84$	8.03113e9	−	5.91610e9i	1.92035	−	1.41462i
$85$	−1.84676e8			−0.0416214
$86$	1.25598e9	−	4.12667e8i	0.266987	−	0.0877218i
$87$		−	6.80319e9i		−	1.36495i
$88$	−2.32615e9	+	3.26905e9i	−0.440783	+	0.619454i
$89$	6.94167e9			1.24312			0.621561	−	0.783365i	$-0.286499\pi$
$89$	6.94167e9			1.24312			0.621561	+	0.783365i	$0.286499\pi$
$90$	−7.03097e8	−	2.13992e9i	−0.119070	−	0.362398i
$91$			1.32330e10i			2.12056i
$92$	−2.49742e9	−	3.39025e9i	−0.378924	−	0.514391i
$93$	−1.54092e10			−2.21495
$94$	−4.26106e9	+	1.40002e9i	−0.580602	+	0.190764i
$95$		−	4.24096e9i		−	0.548082i
$96$	1.82605e8	+	1.10977e10i	0.0223952	+	1.36105i
$97$	1.99530e8			0.0232354			0.0116177	−	0.999933i	$-0.496302\pi$
$97$	1.99530e8			0.0232354			0.0116177	+	0.999933i	$0.496302\pi$
$98$	−5.84101e9	−	1.77775e10i	−0.646186	−	1.96671i
$99$			6.16703e9i			0.648485i
$100$	−1.61026e9	+	1.18619e9i	−0.161026	+	0.118619i
$101$	1.55739e10			1.48180			0.740900	−	0.671615i	$-0.234399\pi$
$101$	1.55739e10			1.48180			0.740900	+	0.671615i	$0.234399\pi$
$102$	1.32885e9	−	4.36609e8i	0.120358	−	0.0395450i
$103$		−	5.68607e9i		−	0.490486i	−0.969462	−	0.245243i	$-0.921132\pi$
$103$		−	5.68607e9i		−	0.490486i	0.969462	−	0.245243i	$-0.0788677\pi$
$104$	−1.19972e10	−	8.53678e9i	−0.986080	−	0.701661i
$105$	−1.36137e10			−1.06667
$106$	−7.62661e9	−	2.32121e10i	−0.569905	−	1.73454i
$107$			1.17015e10i			0.834300i	0.908838	+	0.417150i	$0.136971\pi$
$107$			1.17015e10i			0.834300i	−0.908838	+	0.417150i	$0.863029\pi$
$108$	−1.74421e9	−	2.36777e9i	−0.118708	−	0.161146i
$109$	8.01843e9			0.521143			0.260571	−	0.965455i	$-0.416089\pi$
$109$	8.01843e9			0.521143			0.260571	+	0.965455i	$0.416089\pi$
$110$	5.20219e9	−	1.70924e9i	0.323015	−	0.106130i
$111$			2.46097e10i			1.46046i
$112$	2.94912e10	+	9.15491e9i	1.67341	+	0.519474i
$113$	−1.16116e10			−0.630231			−0.315116	−	0.949053i	$-0.602043\pi$
$113$	−1.16116e10			−0.630231			−0.315116	+	0.949053i	$0.602043\pi$
$114$	1.00264e10	+	3.05160e10i	0.520739	+	1.58491i
$115$			5.74686e9i			0.285720i
$116$	1.69566e10	−	1.24910e10i	0.807327	−	0.594714i
$117$	−2.26325e10			−1.03229
$118$	1.13455e10	−	3.72768e9i	0.495920	−	0.162940i
$119$		−	3.89149e9i		−	0.163073i
$120$	8.78235e9	−	1.23423e10i	0.352943	−	0.496008i
$121$	1.09453e10			0.421988
$122$	1.40366e10	+	4.27215e10i	0.519355	+	1.58069i
$123$			4.27210e9i			0.151746i
$124$	−2.82921e10	−	3.84066e10i	−0.965064	−	1.31008i
$125$	2.72958e9			0.0894427
$126$	4.50924e10	−	1.48156e10i	1.41988	−	0.466517i
$127$		−	1.28991e10i		−	0.390428i	−0.980761	−	0.195214i	$-0.937460\pi$
$127$		−	1.28991e10i		−	0.390428i	0.980761	−	0.195214i	$-0.0625401\pi$
$128$	−2.73251e10	+	2.08310e10i	−0.795265	+	0.606263i
$129$	1.36657e10			0.382547
$130$	6.27277e9	+	1.90916e10i	0.168944	+	0.514193i
$131$		−	2.97636e10i		−	0.771488i	−0.922606	−	0.385744i	$-0.873945\pi$
$131$		−	2.97636e10i		−	0.771488i	0.922606	−	0.385744i	$-0.126055\pi$
$132$	−3.33917e10	+	2.45979e10i	−0.833237	+	0.613801i
$133$	8.93652e10			2.14739
$134$	−4.23962e10	+	1.39297e10i	−0.981302	+	0.322418i
$135$			4.01363e9i			0.0895093i
$136$	3.52807e9	+	2.51045e9i	0.0758302	+	0.0539582i
$137$	−1.43872e10			−0.298107			−0.149053	−	0.988829i	$-0.547623\pi$
$137$	−1.43872e10			−0.298107			−0.149053	+	0.988829i	$0.547623\pi$
$138$	−1.35866e10	−	4.13518e10i	−0.271466	−	0.826227i
$139$			4.79542e10i			0.924172i	0.886835	+	0.462086i	$0.152899\pi$
$139$			4.79542e10i			0.924172i	−0.886835	+	0.462086i	$0.847101\pi$
$140$	−2.49954e10	−	3.39314e10i	−0.464751	−	0.630901i
$141$	−4.63627e10			−0.831904
$142$	2.29210e10	−	7.53096e9i	0.397001	−	0.130439i
$143$		−	5.50200e10i		−	0.920111i
$144$	−1.56577e10	+	5.04390e10i	−0.252881	+	0.814617i
$145$	−2.87434e10			−0.448433
$146$	1.69592e9	+	5.16165e9i	0.0255647	+	0.0778080i
$147$		−	1.93429e11i		−	2.81796i
$148$	−6.13384e10	+	4.51847e10i	−0.863821	+	0.636331i
$149$	−4.81786e10			−0.656029			−0.328014	−	0.944673i	$-0.606379\pi$
$149$	−4.81786e10			−0.656029			−0.328014	+	0.944673i	$0.606379\pi$
$150$	−1.96408e10	+	6.45321e9i	−0.258644	+	0.0849806i
$151$			1.16695e11i			1.48651i	0.669009	+	0.743254i	$0.266719\pi$
$151$			1.16695e11i			1.48651i	−0.669009	+	0.743254i	$0.733281\pi$
$152$	−5.76507e10	+	8.10194e10i	−0.710537	+	0.998553i
$153$	6.65565e9			0.0793840
$154$	3.60170e10	+	1.09620e11i	0.415819	+	1.26557i
$155$			6.51035e10i			0.727689i
$156$	−9.02722e10	−	1.22545e11i	−0.977082	−	1.32639i
$157$	1.19475e11			1.25250			0.626251	−	0.779621i	$-0.284588\pi$
$157$	1.19475e11			1.25250			0.626251	+	0.779621i	$0.284588\pi$
$158$	1.05754e11	−	3.47466e10i	1.07402	−	0.352880i
$159$		−	2.52561e11i		−	2.48531i
$160$	4.68874e10	−	7.71501e8i	0.447153	−	0.00735761i
$161$	−1.21098e11			−1.11945
$162$	−3.91962e10	−	1.19296e11i	−0.351293	−	1.06918i
$163$		−	2.89533e9i		−	0.0251629i	−0.999921	−	0.0125814i	$-0.995995\pi$
$163$		−	2.89533e9i		−	0.0251629i	0.999921	−	0.0125814i	$-0.00400490\pi$
$164$	−1.06480e10	+	7.84382e9i	−0.0897531	+	0.0661163i
$165$	5.66027e10			0.462825
$166$	2.51501e10	−	8.26336e9i	0.199526	−	0.0655566i
$167$		−	3.31302e10i		−	0.255060i	−0.991835	−	0.127530i	$-0.959295\pi$
$167$		−	3.31302e10i		−	0.255060i	0.991835	−	0.127530i	$-0.0407048\pi$
$168$	2.60076e11	+	1.85061e11i	1.94336	+	1.38283i
$169$	6.40603e10			0.464682
$170$	−1.84467e9	−	5.61437e9i	−0.0129919	−	0.0395418i
$171$			1.52842e11i			1.04535i
$172$	2.50911e10	+	3.40612e10i	0.166677	+	0.226265i
$173$	−1.42255e11			−0.917988			−0.458994	−	0.888439i	$-0.651790\pi$
$173$	−1.42255e11			−0.917988			−0.458994	+	0.888439i	$0.651790\pi$
$174$	2.06824e11	−	6.79546e10i	1.29675	−	0.426062i
$175$			5.75175e10i			0.350437i
$176$	−1.22618e11	−	3.80642e10i	−0.726090	−	0.225399i
$177$	1.23445e11			0.710569
$178$	6.93378e10	+	2.11034e11i	0.388034	+	1.18101i
$179$		−	3.52295e10i		−	0.191708i	−0.995395	−	0.0958542i	$-0.969442\pi$
$179$		−	3.52295e10i		−	0.191708i	0.995395	−	0.0958542i	$-0.0305583\pi$
$180$	5.80331e10	−	4.27498e10i	0.307124	−	0.226241i
$181$	−8.52774e10			−0.438977			−0.219488	−	0.975615i	$-0.570439\pi$
$181$	−8.52774e10			−0.438977			−0.219488	+	0.975615i	$0.570439\pi$
$182$	−4.02298e11	+	1.32180e11i	−2.01461	+	0.661923i
$183$			4.64833e11i			2.26486i
$184$	7.81217e10	−	1.09788e11i	0.370410	−	0.520555i
$185$	1.03975e11			0.479813
$186$	−1.53916e11	−	4.68455e11i	−0.691386	−	2.10428i
$187$			1.61800e10i			0.0707571i
$188$	−8.51244e10	−	1.15557e11i	−0.362464	−	0.492046i
$189$	−8.45750e10			−0.350698
$190$	1.28930e11	−	4.23614e10i	0.520697	−	0.171081i
$191$			3.50495e11i			1.37884i	0.724360	+	0.689422i	$0.242135\pi$
$191$			3.50495e11i			1.37884i	−0.724360	+	0.689422i	$0.757865\pi$
$192$	−3.35557e11	+	1.16402e11i	−1.28606	+	0.446122i
$193$	1.57930e11			0.589765			0.294883	−	0.955533i	$-0.404719\pi$
$193$	1.57930e11			0.589765			0.294883	+	0.955533i	$0.404719\pi$
$194$	1.99303e9	+	6.06593e9i	0.00725280	+	0.0220744i
$195$			2.07727e11i			0.736750i
$196$	4.82113e11	−	3.55147e11i	1.66674	−	1.22780i
$197$	3.95179e11			1.33187			0.665936	−	0.746009i	$-0.268032\pi$
$197$	3.95179e11			1.33187			0.665936	+	0.746009i	$0.268032\pi$
$198$	−1.87484e11	+	6.16002e10i	−0.616083	+	0.202421i
$199$		−	2.13388e10i		−	0.0683763i	−0.999415	−	0.0341881i	$-0.989115\pi$
$199$		−	2.13388e10i		−	0.0683763i	0.999415	−	0.0341881i	$-0.0108845\pi$
$200$	−5.21459e10	−	3.71053e10i	−0.162956	−	0.115954i
$201$	−4.61293e11			−1.40604
$202$	1.55562e11	+	4.73463e11i	0.462536	+	1.40776i
$203$		−	6.05679e11i		−	1.75696i
$204$	2.65468e10	+	3.60374e10i	0.0751382	+	0.102000i
$205$	1.80496e10			0.0498537
$206$	1.72863e11	−	5.67961e10i	0.465978	−	0.153103i
$207$		−	2.07114e11i		−	0.544951i
$208$	1.39692e11	−	4.49998e11i	0.358803	−	1.15583i
$209$	−3.71561e11			−0.931749
$210$	−1.35982e11	−	4.13870e11i	−0.332954	−	1.01337i
$211$		−	2.89532e11i		−	0.692283i	−0.938182	−	0.346141i	$-0.887492\pi$
$211$		−	2.89532e11i		−	0.692283i	0.938182	−	0.346141i	$-0.112508\pi$
$212$	6.29495e11	−	4.63715e11i	1.46998	−	1.08286i
$213$	2.49393e11			0.568835
$214$	−3.55738e11	+	1.16882e11i	−0.792614	+	0.260422i
$215$		−	5.77376e10i		−	0.125680i
$216$	5.45605e10	−	7.66765e10i	0.116040	−	0.163077i
$217$	−1.37186e12			−2.85109
$218$	8.00932e10	+	2.43769e11i	0.162672	+	0.495104i
$219$			5.61616e10i			0.111486i
$220$	1.03926e11	+	1.41079e11i	0.201655	+	0.273747i
$221$	−5.93793e10			−0.112635
$222$	−7.48161e11	+	2.45817e11i	−1.38749	+	0.455876i
$223$			7.87602e11i			1.42818i	0.700055	+	0.714089i	$0.253159\pi$
$223$			7.87602e11i			1.42818i	−0.700055	+	0.714089i	$0.746841\pi$
$224$	1.62570e10	+	9.88009e11i	0.0288271	+	1.75195i
$225$	−9.83726e10			−0.170593
$226$	−1.15984e11	−	3.53005e11i	−0.196723	−	0.598741i
$227$		−	1.02226e12i		−	1.69602i	−0.529982	−	0.848009i	$-0.677801\pi$
$227$		−	1.02226e12i		−	1.69602i	0.529982	−	0.848009i	$-0.322199\pi$
$228$	−8.27571e11	+	6.09627e11i	−1.34317	+	0.989441i
$229$	1.03140e12			1.63775			0.818877	−	0.573970i	$-0.194597\pi$
$229$	1.03140e12			1.63775			0.818877	+	0.573970i	$0.194597\pi$
$230$	−1.74711e11	+	5.74033e10i	−0.271444	+	0.0891862i
$231$			1.19273e12i			1.81335i
$232$	5.49115e11	+	3.90732e11i	0.817002	+	0.581351i
$233$	2.15652e11			0.314032			0.157016	−	0.987596i	$-0.449813\pi$
$233$	2.15652e11			0.314032			0.157016	+	0.987596i	$0.449813\pi$
$234$	−2.26068e11	−	6.88053e11i	−0.322225	−	0.980714i
$235$			1.95882e11i			0.273309i
$236$	2.26651e11	+	3.07680e11i	0.309598	+	0.420280i
$237$	1.15066e12			1.53888
$238$	1.18306e11	−	3.88707e10i	0.154925	−	0.0509023i
$239$		−	1.01800e12i		−	1.30545i	−0.757597	−	0.652723i	$-0.773627\pi$
$239$		−	1.01800e12i		−	1.30545i	0.757597	−	0.652723i	$-0.226373\pi$
$240$	4.62942e11	+	1.43711e11i	0.581394	+	0.180482i
$241$	7.81848e11			0.961694			0.480847	−	0.876804i	$-0.340329\pi$
$241$	7.81848e11			0.961694			0.480847	+	0.876804i	$0.340329\pi$
$242$	1.09328e11	+	3.32749e11i	0.131721	+	0.400903i
$243$		−	1.12843e12i		−	1.33181i
$244$	−1.15857e12	+	8.53459e11i	−1.33960	+	0.986810i
$245$	−8.17235e11			−0.925799
$246$	−1.29877e11	+	4.26725e10i	−0.144164	+	0.0473666i
$247$		−	1.36360e12i		−	1.48321i
$248$	8.85003e11	−	1.24374e12i	0.943380	−	1.32578i
$249$	2.73647e11			0.285887
$250$	2.72647e10	+	8.29821e10i	0.0279191	+	0.0849737i
$251$			6.23828e11i			0.626176i	0.949724	+	0.313088i	$0.101363\pi$
$251$			6.23828e11i			0.626176i	−0.949724	+	0.313088i	$0.898637\pi$
$252$	9.00823e11	+	1.22287e12i	0.886414	+	1.20331i
$253$	5.03498e11			0.485730
$254$	3.92147e11	−	1.28844e11i	0.370920	−	0.121870i
$255$		−	6.10874e10i		−	0.0566566i
$256$	−9.06226e11	−	6.22639e11i	−0.824208	−	0.566287i
$257$	1.04389e12			0.931086			0.465543	−	0.885025i	$-0.345859\pi$
$257$	1.04389e12			0.931086			0.465543	+	0.885025i	$0.345859\pi$
$258$	1.36502e11	+	4.15454e11i	0.119410	+	0.363433i
$259$			2.19097e12i			1.87991i
$260$	−5.17750e11	+	3.81398e11i	−0.435766	+	0.321005i
$261$	1.03590e12			0.855291
$262$	9.04847e11	−	2.97298e11i	0.732940	−	0.240816i
$263$		−	2.25563e12i		−	1.79262i	−0.443423	−	0.896312i	$-0.646236\pi$
$263$		−	2.25563e12i		−	1.79262i	0.443423	−	0.896312i	$-0.353764\pi$
$264$	−1.08134e12	−	7.69445e11i	−0.843223	−	0.600009i
$265$	−1.06706e12			−0.816509
$266$	8.92637e11	+	2.71680e12i	0.670296	+	2.04009i
$267$			2.29617e12i			1.69218i
$268$	−8.46959e11	−	1.14975e12i	−0.612616	−	0.831629i
$269$	4.57791e11			0.325017			0.162509	−	0.986707i	$-0.448042\pi$
$269$	4.57791e11			0.325017			0.162509	+	0.986707i	$0.448042\pi$
$270$	−1.22019e11	+	4.00907e10i	−0.0850369	+	0.0279399i
$271$		−	7.07347e10i		−	0.0483934i	−0.999707	−	0.0241967i	$-0.992297\pi$
$271$		−	7.07347e10i		−	0.0483934i	0.999707	−	0.0241967i	$-0.00770280\pi$
$272$	−4.10800e10	+	1.32333e11i	−0.0275922	+	0.0888841i
$273$	−4.37722e12			−2.88659
$274$	−1.43708e11	−	4.37385e11i	−0.0930525	−	0.283212i
$275$		−	2.39145e11i		−	0.152054i
$276$	1.12143e12	−	8.26097e11i	0.700207	−	0.515805i
$277$	−2.83728e12			−1.73982			−0.869908	−	0.493214i	$-0.835822\pi$
$277$	−2.83728e12			−1.73982			−0.869908	+	0.493214i	$0.835822\pi$
$278$	−1.45786e12	+	4.78997e11i	−0.877995	+	0.288475i
$279$		−	2.34630e12i		−	1.38791i
$280$	7.81881e11	−	1.09882e12i	0.454308	−	0.638462i
$281$	−4.75819e11			−0.271588			−0.135794	−	0.990737i	$-0.543358\pi$
$281$	−4.75819e11			−0.271588			−0.135794	+	0.990737i	$0.543358\pi$
$282$	−4.63100e11	−	1.40948e12i	−0.259674	−	0.790337i
$283$			9.46174e11i			0.521241i	0.965441	+	0.260621i	$0.0839272\pi$
$283$			9.46174e11i			0.521241i	−0.965441	+	0.260621i	$0.916073\pi$
$284$	4.57899e11	+	6.21600e11i	0.247844	+	0.336449i
$285$	1.40283e12			0.746070
$286$	1.67267e12	−	5.49574e11i	0.874137	−	0.287208i
$287$			3.80340e11i			0.195327i
$288$	−1.68980e12	+	2.78045e10i	−0.852850	+	0.0140331i
$289$	−1.99853e12			−0.991338
$290$	−2.87107e11	−	8.73830e11i	−0.139976	−	0.426027i
$291$			6.60006e10i			0.0316288i
$292$	−1.39980e11	+	1.03116e11i	−0.0659404	+	0.0485748i
$293$	2.37212e12			1.09849			0.549247	−	0.835660i	$-0.314915\pi$
$293$	2.37212e12			1.09849			0.549247	+	0.835660i	$0.314915\pi$
$294$	5.88046e12	−	1.93209e12i	2.67716	−	0.879613i
$295$		−	5.21552e11i		−	0.233447i
$296$	−1.98635e12	−	1.41342e12i	−0.874173	−	0.622033i
$297$	3.51645e11			0.152167
$298$	−4.81238e11	−	1.46468e12i	−0.204776	−	0.623250i
$299$			1.84780e12i			0.773211i
$300$	−3.92370e11	−	5.32643e11i	−0.161469	−	0.219195i
$301$	1.21664e12			0.492415
$302$	−3.54766e12	+	1.16562e12i	−1.41223	+	0.464006i
$303$			5.15153e12i			2.01708i
$304$	−3.03893e12	−	9.43372e11i	−1.17045	−	0.363342i
$305$	1.96391e12			0.744086
$306$	6.64808e10	+	2.02339e11i	0.0247793	+	0.0754176i
$307$			3.27142e12i			1.19962i	0.800142	+	0.599811i	$0.204757\pi$
$307$			3.27142e12i			1.19962i	−0.800142	+	0.599811i	$0.795243\pi$
$308$	−2.97282e12	+	2.18992e12i	−1.07254	+	0.790085i
$309$	1.88084e12			0.667667
$310$	−1.97922e12	+	6.50295e11i	−0.691329	+	0.227144i
$311$		−	2.94681e12i		−	1.01286i	−0.862280	−	0.506431i	$-0.830964\pi$
$311$		−	2.94681e12i		−	1.01286i	0.862280	−	0.506431i	$-0.169036\pi$
$312$	2.82380e12	−	3.96843e12i	0.955127	−	1.34229i
$313$	−3.18034e11			−0.105865			−0.0529324	−	0.998598i	$-0.516857\pi$
$313$	−3.18034e11			−0.105865			−0.0529324	+	0.998598i	$0.516857\pi$
$314$	1.19339e12	+	3.63217e12i	0.390962	+	1.18992i
$315$		−	2.07290e12i		−	0.668384i
$316$	2.11267e12	+	2.86796e12i	0.670497	+	0.910202i
$317$	3.80109e12			1.18744			0.593720	−	0.804672i	$-0.297659\pi$
$317$	3.80109e12			1.18744			0.593720	+	0.804672i	$0.297659\pi$
$318$	7.67812e12	−	2.52273e12i	2.36113	−	0.775775i
$319$			2.51828e12i			0.762344i
$320$	4.91796e11	+	1.41772e12i	0.146567	+	0.422514i
$321$	−3.87063e12			−1.13568
$322$	−1.20960e12	−	3.68150e12i	−0.349432	−	1.06352i
$323$			4.01001e11i			0.114060i
$324$	3.23523e12	−	2.38322e12i	0.906107	−	0.667480i
$325$	8.77644e11			0.242048
$326$	8.80213e10	−	2.89204e10i	0.0239056	−	0.00785447i
$327$			2.65234e12i			0.709399i
$328$	−3.44820e11	−	2.45362e11i	−0.0908287	−	0.0646307i
$329$	−4.12761e12			−1.07083
$330$	5.65383e11	+	1.72078e12i	0.144469	+	0.439700i
$331$		−	4.34328e12i		−	1.09315i	−0.837411	−	0.546573i	$-0.815932\pi$
$331$		−	4.34328e12i		−	1.09315i	0.837411	−	0.546573i	$-0.184068\pi$
$332$	5.02431e11	+	6.82051e11i	0.124562	+	0.169093i
$333$	−3.74723e12			−0.915142
$334$	1.00719e12	−	3.30925e11i	0.242315	−	0.0796155i
$335$			1.94896e12i			0.461932i
$336$	−3.02827e12	+	9.75511e12i	−0.707128	+	2.27790i
$337$	7.56835e11			0.174121			0.0870606	−	0.996203i	$-0.472253\pi$
$337$	7.56835e11			0.174121			0.0870606	+	0.996203i	$0.472253\pi$
$338$	6.39875e11	+	1.94750e12i	0.145048	+	0.441464i
$339$		−	3.84089e12i		−	0.857894i
$340$	1.52257e11	−	1.12160e11i	0.0335107	−	0.0246855i
$341$	5.70389e12			1.23708
$342$	−4.64657e12	+	1.52668e12i	−0.993119	+	0.326301i
$343$		−	8.90215e12i		−	1.87510i
$344$	−7.84873e11	+	1.10302e12i	−0.162932	+	0.228977i
$345$	−1.90095e12			−0.388933
$346$	−1.42093e12	−	4.32471e12i	−0.286545	−	0.872120i
$347$			4.88633e11i			0.0971260i	0.998820	+	0.0485630i	$0.0154642\pi$
$347$			4.88633e11i			0.0971260i	−0.998820	+	0.0485630i	$0.984536\pi$
$348$	4.13179e12	+	5.60892e12i	0.809547	+	1.09896i
$349$	−2.32017e12			−0.448118			−0.224059	−	0.974576i	$-0.571931\pi$
$349$	−2.32017e12			−0.448118			−0.224059	+	0.974576i	$0.571931\pi$
$350$	−1.74860e12	+	5.74521e11i	−0.332927	+	0.109387i
$351$			1.29051e12i			0.242228i
$352$	−6.75933e10	−	4.10793e12i	−0.0125081	−	0.760168i
$353$	2.85311e12			0.520529			0.260265	−	0.965537i	$-0.416190\pi$
$353$	2.85311e12			0.520529			0.260265	+	0.965537i	$0.416190\pi$
$354$	1.23304e12	+	3.75286e12i	0.221800	+	0.675065i
$355$		−	1.05368e12i		−	0.186882i
$356$	−5.72309e12	+	4.21589e12i	−1.00088	+	0.737292i
$357$	1.28723e12			0.221981
$358$	1.07102e12	−	3.51894e11i	0.182130	−	0.0598408i
$359$		−	1.59682e12i		−	0.267783i	−0.990996	−	0.133892i	$-0.957253\pi$
$359$		−	1.59682e12i		−	0.267783i	0.990996	−	0.133892i	$-0.0427474\pi$
$360$	1.87931e12	+	1.33726e12i	0.310804	+	0.221158i
$361$	−3.07761e12			−0.501971
$362$	−8.51805e11	−	2.59253e12i	−0.137024	−	0.417043i
$363$			3.62049e12i			0.574425i
$364$	−8.03681e12	−	1.09100e13i	−1.25770	−	1.70733i
$365$	2.37282e11			0.0366269
$366$	−1.41314e13	+	4.64305e12i	−2.15170	+	0.706965i
$367$			2.96640e11i			0.0445553i	0.999752	+	0.0222777i	$0.00709178\pi$
$367$			2.96640e11i			0.0445553i	−0.999752	+	0.0222777i	$0.992908\pi$
$368$	4.11801e12	+	1.27835e12i	0.610167	+	0.189413i
$369$	−6.50498e11			−0.0950855
$370$	1.03857e12	+	3.16097e12i	0.149771	+	0.455839i
$371$		−	2.24851e13i		−	3.19909i
$372$	1.27041e13	−	9.35846e12i	1.78333	−	1.31368i
$373$	9.87929e12			1.36830			0.684151	−	0.729341i	$-0.260173\pi$
$373$	9.87929e12			1.36830			0.684151	+	0.729341i	$0.260173\pi$
$374$	−4.91890e11	+	1.61616e11i	−0.0672217	+	0.0220865i
$375$			9.02890e11i			0.121753i
$376$	2.66278e12	−	3.74213e12i	0.354320	−	0.497943i
$377$	−9.24190e12			−1.21354
$378$	−8.44789e11	−	2.57117e12i	−0.109468	−	0.333175i
$379$			2.68525e12i			0.343391i	0.985150	+	0.171696i	$0.0549246\pi$
$379$			2.68525e12i			0.343391i	−0.985150	+	0.171696i	$0.945075\pi$
$380$	2.57566e12	+	3.49647e12i	0.325066	+	0.441278i
$381$	4.26677e12			0.531464
$382$	−1.06554e13	+	3.50097e12i	−1.30995	+	0.430399i
$383$			2.79218e12i			0.338805i	0.985547	+	0.169403i	$0.0541838\pi$
$383$			2.79218e12i			0.338805i	−0.985547	+	0.169403i	$0.945816\pi$
$384$	−6.89050e12	−	9.03860e12i	−0.825267	−	1.08254i
$385$	5.03926e12			0.595749
$386$	1.57751e12	+	4.80126e12i	0.184092	+	0.560297i
$387$			2.08083e12i			0.239708i
$388$	−1.64503e11	+	1.21181e11i	−0.0187075	+	0.0137808i
$389$	4.54004e12			0.509697			0.254848	−	0.966981i	$-0.417974\pi$
$389$	4.54004e12			0.509697			0.254848	+	0.966981i	$0.417974\pi$
$390$	−6.31514e12	+	2.07491e12i	−0.699938	+	0.229973i
$391$		−	5.43390e11i		−	0.0594604i
$392$	1.56125e13	+	1.11093e13i	1.68672	+	1.20021i
$393$	9.84523e12			1.05018
$394$	3.94730e12	+	1.20139e13i	0.415737	+	1.26533i
$395$		−	4.86151e12i		−	0.505576i
$396$	−3.74543e12	−	5.08443e12i	−0.384614	−	0.522115i
$397$	−1.56339e13			−1.58532			−0.792659	−	0.609666i	$-0.791304\pi$
$397$	−1.56339e13			−1.58532			−0.792659	+	0.609666i	$0.791304\pi$
$398$	6.48724e11	−	2.13146e11i	0.0649598	−	0.0213433i
$399$			2.95603e13i			2.92310i
$400$	6.07176e11	−	1.95592e12i	0.0592945	−	0.191008i
$401$	−9.95481e12			−0.960088			−0.480044	−	0.877244i	$-0.659379\pi$
$401$	−9.95481e12			−0.960088			−0.480044	+	0.877244i	$0.659379\pi$
$402$	−4.60769e12	−	1.40238e13i	−0.438887	−	1.33578i
$403$			2.09328e13i			1.96926i
$404$	−1.28399e13	+	9.45850e12i	−1.19304	+	0.878851i
$405$	−5.48407e12			−0.503301
$406$	1.84133e13	−	6.04991e12i	1.66917	−	0.548427i
$407$		−	9.10957e12i		−	0.815691i
$408$	−8.30409e11	+	1.16702e12i	−0.0734499	+	0.103223i
$409$	−3.95071e12			−0.345191			−0.172595	−	0.984993i	$-0.555215\pi$
$409$	−3.95071e12			−0.345191			−0.172595	+	0.984993i	$0.555215\pi$
$410$	1.80291e11	+	5.48727e11i	0.0155616	+	0.0473628i
$411$		−	4.75899e12i		−	0.405794i
$412$	3.45333e12	+	4.68791e12i	0.290905	+	0.394905i
$413$	1.09901e13			0.914644
$414$	6.29649e12	−	2.06879e12i	0.517723	−	0.170104i
$415$		−	1.15615e12i		−	0.0939237i
$416$	1.50758e13	−	2.48062e11i	1.21008	−	0.0199110i
$417$	−1.58623e13			−1.25802
$418$	−3.71139e12	−	1.12959e13i	−0.290841	−	0.885194i
$419$		−	1.57517e13i		−	1.21971i	−0.792513	−	0.609856i	$-0.791227\pi$
$419$		−	1.57517e13i		−	1.21971i	0.792513	−	0.609856i	$-0.208773\pi$
$420$	1.12238e13	−	8.26800e12i	0.858806	−	0.632636i
$421$	1.89265e12			0.143107			0.0715534	−	0.997437i	$-0.477204\pi$
$421$	1.89265e12			0.143107			0.0715534	+	0.997437i	$0.477204\pi$
$422$	8.80208e12	−	2.89202e12i	0.657693	−	0.216093i
$423$		−	7.05948e12i		−	0.521280i
$424$	2.03852e13	+	1.45055e13i	1.48760	+	1.05853i
$425$	−2.58093e11			−0.0186137
$426$	2.49110e12	+	7.58182e12i	0.177559	+	0.540413i
$427$			4.13835e13i			2.91533i
$428$	−7.10668e12	−	9.64735e12i	−0.494821	−	0.671721i
$429$	1.81995e13			1.25249
$430$	1.75529e12	−	5.76719e11i	0.119400	−	0.0392304i
$431$			1.61299e13i			1.08454i	0.840204	+	0.542271i	$0.182435\pi$
$431$			1.61299e13i			1.08454i	−0.840204	+	0.542271i	$0.817565\pi$
$432$	2.87604e12	+	8.92805e11i	0.191151	+	0.0593387i
$433$	−2.27857e13			−1.49700			−0.748501	−	0.663134i	$-0.769226\pi$
$433$	−2.27857e13			−1.49700			−0.748501	+	0.663134i	$0.769226\pi$
$434$	−1.37030e13	−	4.17060e13i	−0.889952	−	2.70863i
$435$		−	9.50775e12i		−	0.610424i
$436$	−6.61083e12	+	4.86984e12i	−0.419588	+	0.309088i
$437$	1.24786e13			0.782991
$438$	−1.70737e12	+	5.60977e11i	−0.105915	+	0.0347997i
$439$		−	7.33847e12i		−	0.450073i	−0.974350	−	0.225036i	$-0.927750\pi$
$439$		−	7.33847e12i		−	0.450073i	0.974350	−	0.225036i	$-0.0722501\pi$
$440$	−3.25089e12	+	4.56864e12i	−0.197124	+	0.277028i
$441$	2.94528e13			1.76577
$442$	−5.93118e11	−	1.80520e12i	−0.0351584	−	0.107007i
$443$			3.68107e11i			0.0215753i	0.999942	+	0.0107876i	$0.00343388\pi$
$443$			3.68107e11i			0.0215753i	−0.999942	+	0.0107876i	$0.996566\pi$
$444$	−1.49462e13	−	2.02896e13i	−0.866197	−	1.17587i
$445$	9.70128e12			0.555941
$446$	−2.39440e13	+	7.86707e12i	−1.35682	+	0.445799i
$447$		−	1.59365e13i		−	0.893010i
$448$	−2.98742e13	+	1.03631e13i	−1.65541	+	0.574248i
$449$	1.73670e13			0.951687			0.475844	−	0.879530i	$-0.342143\pi$
$449$	1.73670e13			0.951687			0.475844	+	0.879530i	$0.342143\pi$
$450$	−9.82608e11	−	2.99063e12i	−0.0532497	−	0.162069i
$451$		−	1.58137e12i		−	0.0847522i
$452$	9.57323e12	−	7.05209e12i	0.507419	−	0.373788i
$453$	−3.86004e13			−2.02349
$454$	3.10777e13	−	1.02109e13i	1.61128	−	0.529403i
$455$			1.84937e13i			0.948345i
$456$	−2.67996e13	−	1.90697e13i	−1.35927	−	0.967209i
$457$	1.79800e13			0.902005			0.451003	−	0.892523i	$-0.351067\pi$
$457$	1.79800e13			0.902005			0.451003	+	0.892523i	$0.351067\pi$
$458$	1.03022e13	+	3.13556e13i	0.511216	+	1.55592i
$459$		−	3.79506e11i		−	0.0186275i
$460$	−3.49025e12	−	4.73802e12i	−0.169460	−	0.230042i
$461$	−4.09031e13			−1.96450			−0.982249	−	0.187580i	$-0.939936\pi$
$461$	−4.09031e13			−1.96450			−0.982249	+	0.187580i	$0.939936\pi$
$462$	−3.62603e13	+	1.19137e13i	−1.72275	+	0.566028i
$463$		−	1.70952e13i		−	0.803469i	−0.915756	−	0.401735i	$-0.868407\pi$
$463$		−	1.70952e13i		−	0.803469i	0.915756	−	0.401735i	$-0.131593\pi$
$464$	−6.39377e12	+	2.05966e13i	−0.297281	+	0.957646i
$465$	−2.15350e13			−0.990556
$466$	2.15407e12	+	6.55607e12i	0.0980236	+	0.298342i
$467$		−	2.45776e13i		−	1.10651i	−0.833012	−	0.553255i	$-0.813386\pi$
$467$		−	2.45776e13i		−	1.10651i	0.833012	−	0.553255i	$-0.186614\pi$
$468$	1.86595e13	−	1.37454e13i	0.831131	−	0.612250i
$469$	−4.10683e13			−1.80985
$470$	−5.95502e12	+	1.95659e12i	−0.259653	+	0.0853121i
$471$			3.95200e13i			1.70495i
$472$	−7.08987e12	+	9.96375e12i	−0.302642	+	0.425317i
$473$	−5.05854e12			−0.213658
$474$	1.14935e13	+	3.49813e13i	0.480353	+	1.46199i
$475$		−	5.92692e12i		−	0.245110i
$476$	2.36343e12	+	3.20836e12i	0.0967180	+	0.131295i
$477$	3.84565e13			1.55732
$478$	3.09484e13	−	1.01684e13i	1.24022	−	0.407488i
$479$		−	3.22393e13i		−	1.27852i	−0.768990	−	0.639261i	$-0.779240\pi$
$479$		−	3.22393e13i		−	1.27852i	0.768990	−	0.639261i	$-0.220760\pi$
$480$	2.55198e11	+	1.55094e13i	0.0100155	+	0.608681i
$481$	3.34314e13			1.29846
$482$	7.80959e12	+	2.37690e13i	0.300188	+	0.913643i
$483$		−	4.00567e13i		−	1.52384i
$484$	−9.02388e12	+	6.64741e12i	−0.339756	+	0.250280i
$485$	2.78852e11			0.0103912
$486$	3.43054e13	−	1.12714e13i	1.26526	−	0.415717i
$487$		−	3.24299e13i		−	1.18386i	−0.805990	−	0.591930i	$-0.798366\pi$
$487$		−	3.24299e13i		−	1.18386i	0.805990	−	0.591930i	$-0.201634\pi$
$488$	−3.75187e13	−	2.66970e13i	−1.35565	−	0.964637i
$489$	9.57720e11			0.0342527
$490$	−8.16306e12	−	2.48449e13i	−0.288983	−	0.879541i
$491$			1.26956e13i			0.444882i	0.974946	+	0.222441i	$0.0714025\pi$
$491$			1.26956e13i			0.444882i	−0.974946	+	0.222441i	$0.928597\pi$
$492$	−2.59458e12	−	3.52216e12i	−0.0899999	−	0.122175i
$493$	2.71781e12			0.0933221
$494$	4.14550e13	−	1.36205e13i	1.40910	−	0.462976i
$495$			8.61868e12i			0.290011i
$496$	4.66510e13	+	1.44818e13i	1.55401	+	0.482409i
$497$	2.22031e13			0.732205
$498$	2.73336e12	+	8.31917e12i	0.0892380	+	0.271602i
$499$			1.08543e13i			0.350832i	0.984494	+	0.175416i	$0.0561270\pi$
$499$			1.08543e13i			0.350832i	−0.984494	+	0.175416i	$0.943873\pi$
$500$	−2.25041e12	+	1.65776e12i	−0.0720131	+	0.0530482i
$501$	1.09588e13			0.347196
$502$	−1.89651e13	+	6.23119e12i	−0.594889	+	0.195458i
$503$		−	1.24893e13i		−	0.387881i	−0.981013	−	0.193940i	$-0.937873\pi$
$503$		−	1.24893e13i		−	0.387881i	0.981013	−	0.193940i	$-0.0621269\pi$
$504$	−2.81786e13	+	3.96008e13i	−0.866497	+	1.21773i
$505$	2.17652e13			0.662681
$506$	5.02925e12	+	1.53069e13i	0.151618	+	0.461460i
$507$			2.11899e13i			0.632542i
$508$	7.83402e12	+	1.06347e13i	0.231561	+	0.314345i
$509$	−4.73601e12			−0.138619			−0.0693097	−	0.997595i	$-0.522080\pi$
$509$	−4.73601e12			−0.138619			−0.0693097	+	0.997595i	$0.522080\pi$
$510$	1.85712e12	−	6.10179e11i	0.0538257	−	0.0176851i
$511$			4.99999e12i			0.143504i
$512$	9.87695e12	−	3.37696e13i	0.280720	−	0.959790i
$513$	8.71507e12			0.245292
$514$	1.04270e13	+	3.17354e13i	0.290634	+	0.884564i
$515$		−	7.94653e12i		−	0.219352i
$516$	−1.12668e13	+	8.29963e12i	−0.308001	+	0.226887i
$517$	1.71617e13			0.464631
$518$	−6.66078e13	+	2.18848e13i	−1.78598	+	0.586804i
$519$		−	4.70552e13i		−	1.24960i
$520$	−1.67665e13	−	1.19305e13i	−0.440988	−	0.313793i
$521$	−3.60036e13			−0.937902			−0.468951	−	0.883224i	$-0.655368\pi$
$521$	−3.60036e13			−0.937902			−0.468951	+	0.883224i	$0.655368\pi$
$522$	1.03472e13	+	3.14924e13i	0.266975	+	0.812556i
$523$			4.44220e13i			1.13525i	0.823289	+	0.567623i	$0.192137\pi$
$523$			4.44220e13i			1.13525i	−0.823289	+	0.567623i	$0.807863\pi$
$524$	1.80764e13	+	2.45387e13i	0.457567	+	0.621149i
$525$	−1.90257e13			−0.477027
$526$	6.85737e13	−	2.25307e13i	1.70306	−	0.559559i
$527$		−	6.15581e12i		−	0.151437i
$528$	1.25909e13	−	4.05596e13i	0.306822	−	0.988381i
$529$	2.45170e13			0.591819
$530$	−1.06585e13	−	3.24399e13i	−0.254869	−	0.775712i
$531$			1.87965e13i			0.445250i
$532$	−7.36776e13	+	5.42743e13i	−1.72893	+	1.27361i
$533$	5.80350e12			0.134913
$534$	−6.98061e13	+	2.29356e13i	−1.60763	+	0.528207i
$535$			1.63533e13i			0.373110i
$536$	2.64937e13	−	3.72329e13i	0.598851	−	0.841596i
$537$	1.16532e13			0.260960
$538$	4.57271e12	+	1.39174e13i	0.101452	+	0.308777i
$539$			7.16001e13i			1.57387i
$540$	−2.43760e12	−	3.30905e12i	−0.0530877	−	0.0720667i
$541$	−8.68078e12			−0.187315			−0.0936575	−	0.995604i	$-0.529856\pi$
$541$	−8.68078e12			−0.187315			−0.0936575	+	0.995604i	$0.529856\pi$
$542$	2.15041e12	−	7.06543e11i	0.0459754	−	0.0151058i
$543$		−	2.82081e13i		−	0.597551i
$544$	−4.43341e12	+	7.29488e10i	−0.0930557	+	0.00153117i
$545$	1.12061e13			0.233062
$546$	−4.37224e13	−	1.33072e14i	−0.901034	−	2.74236i
$547$		−	1.93160e13i		−	0.394439i	−0.980359	−	0.197220i	$-0.936809\pi$
$547$		−	1.93160e13i		−	0.394439i	0.980359	−	0.197220i	$-0.0631912\pi$
$548$	1.18616e13	−	8.73777e12i	0.240015	−	0.176806i
$549$	−7.07784e13			−1.41919
$550$	7.27028e12	−	2.38874e12i	0.144457	−	0.0474629i
$551$			6.24125e13i			1.22889i
$552$	3.63158e13	+	2.58411e13i	0.708599	+	0.504215i
$553$	1.02442e14			1.98085
$554$	−2.83406e13	−	8.62565e13i	−0.543075	−	1.65289i
$555$			3.43931e13i			0.653139i
$556$	−2.91241e13	−	3.95360e13i	−0.548123	−	0.744079i
$557$	−9.40071e13			−1.75341			−0.876707	−	0.481024i	$-0.840265\pi$
$557$	−9.40071e13			−1.75341			−0.876707	+	0.481024i	$0.840265\pi$
$558$	7.13300e13	−	2.34363e13i	1.31856	−	0.433230i
$559$		−	1.85644e13i		−	0.340113i
$560$	4.12152e13	+	1.27944e13i	0.748371	+	0.232316i
$561$	−5.35203e12			−0.0963172
$562$	−4.75278e12	−	1.44654e13i	−0.0847747	−	0.258018i
$563$		−	1.01341e13i		−	0.179162i	−0.995980	−	0.0895808i	$-0.971447\pi$
$563$		−	1.01341e13i		−	0.179162i	0.995980	−	0.0895808i	$-0.0285527\pi$
$564$	3.82239e13	−	2.81575e13i	0.669792	−	0.493399i
$565$	−1.62277e13			−0.281848
$566$	−2.87647e13	+	9.45099e12i	−0.495197	+	0.162703i
$567$		−	1.15560e14i		−	1.97194i
$568$	−1.43235e13	+	2.01296e13i	−0.242275	+	0.340481i
$569$	−4.06690e13			−0.681871			−0.340936	−	0.940087i	$-0.610744\pi$
$569$	−4.06690e13			−0.681871			−0.340936	+	0.940087i	$0.610744\pi$
$570$	1.40123e13	+	4.26474e13i	0.232882	+	0.708792i
$571$		−	8.31022e13i		−	1.36909i	−0.728970	−	0.684545i	$-0.760001\pi$
$571$		−	8.31022e13i		−	1.36909i	0.728970	−	0.684545i	$-0.239999\pi$
$572$	3.34153e13	+	4.53614e13i	0.545715	+	0.740810i
$573$	−1.15937e14			−1.87693
$574$	−1.15628e13	+	3.79908e12i	−0.185567	+	0.0609703i
$575$			8.03148e12i			0.127778i
$576$	−1.77241e13	−	5.10940e13i	−0.279545	−	0.805857i
$577$	−4.07454e13			−0.637089			−0.318544	−	0.947908i	$-0.603194\pi$
$577$	−4.07454e13			−0.637089			−0.318544	+	0.947908i	$0.603194\pi$
$578$	−1.99626e13	−	6.07576e13i	−0.309441	−	0.941806i
$579$			5.22403e13i			0.802810i
$580$	2.36976e13	−	1.74567e13i	0.361048	−	0.265964i
$581$	2.43624e13			0.367993
$582$	−2.00649e12	+	6.59256e11i	−0.0300485	+	0.00987278i
$583$			9.34883e13i			1.38808i
$584$	−4.53304e12	−	3.22556e12i	−0.0667307	−	0.0474833i
$585$	−3.16299e13			−0.461656
$586$	2.36942e13	+	7.21149e13i	0.342889	+	1.04361i
$587$			1.26918e14i			1.82109i	0.413408	+	0.910546i	$0.364338\pi$
$587$			1.26918e14i			1.82109i	−0.413408	+	0.910546i	$0.635662\pi$
$588$	1.17476e14	+	1.59474e14i	1.67132	+	2.26883i
$589$	1.41364e14			1.99417
$590$	1.58558e13	−	5.20959e12i	0.221782	−	0.0728691i
$591$			1.30718e14i			1.81299i
$592$	2.31286e13	−	7.45054e13i	0.318084	−	1.02466i
$593$	1.08224e13			0.147588			0.0737941	−	0.997273i	$-0.476489\pi$
$593$	1.08224e13			0.147588			0.0737941	+	0.997273i	$0.476489\pi$
$594$	3.51245e12	+	1.06904e13i	0.0474983	+	0.144564i
$595$		−	5.43853e12i		−	0.0729284i
$596$	3.97211e13	−	2.92604e13i	0.528189	−	0.389088i
$597$	7.05847e12			0.0930763
$598$	−5.61750e13	+	1.84570e13i	−0.734577	+	0.241354i
$599$		−	1.11833e14i		−	1.45023i	−0.688630	−	0.725113i	$-0.741788\pi$
$599$		−	1.11833e14i		−	1.45023i	0.688630	−	0.725113i	$-0.258212\pi$
$600$	1.22737e13	−	1.72489e13i	0.157841	−	0.221822i
$601$	−1.24369e14			−1.58613			−0.793067	−	0.609134i	$-0.791517\pi$
$601$	−1.24369e14			−1.58613			−0.793067	+	0.609134i	$0.791517\pi$
$602$	1.21526e13	+	3.69873e13i	0.153705	+	0.467811i
$603$		−	7.02394e13i		−	0.881038i
$604$	−7.08725e13	−	9.62097e13i	−0.881643	−	1.19683i
$605$	1.52965e13			0.188719
$606$	−1.56612e14	+	5.14568e13i	−1.91630	+	0.629622i
$607$		−	1.04683e14i		−	1.27038i	−0.772355	−	0.635192i	$-0.780921\pi$
$607$		−	1.04683e14i		−	1.27038i	0.772355	−	0.635192i	$-0.219079\pi$
$608$	−1.67521e12	−	1.01810e14i	−0.0201629	−	1.22538i
$609$	2.00347e14			2.39164
$610$	1.96168e13	+	5.97051e13i	0.232262	+	0.706907i
$611$			6.29821e13i			0.739624i
$612$	−5.48728e12	+	4.04218e12i	−0.0639146	+	0.0470824i
$613$	6.83052e13			0.789135			0.394567	−	0.918867i	$-0.370894\pi$
$613$	6.83052e13			0.789135			0.394567	+	0.918867i	$0.370894\pi$
$614$	−9.94547e13	+	3.26770e13i	−1.13968	+	0.374456i
$615$			5.97045e12i			0.0678627i
$616$	−9.62702e13	−	6.85027e13i	−1.08540	−	0.772332i
$617$	1.45376e14			1.62580			0.812899	−	0.582405i	$-0.197888\pi$
$617$	1.45376e14			1.62580			0.812899	+	0.582405i	$0.197888\pi$
$618$	1.87870e13	+	5.71797e13i	0.208409	+	0.634307i
$619$		−	8.38798e13i		−	0.923005i	−0.887139	−	0.461503i	$-0.847310\pi$
$619$		−	8.38798e13i		−	0.923005i	0.887139	−	0.461503i	$-0.152690\pi$
$620$	−3.95394e13	−	5.36748e13i	−0.431590	−	0.585885i
$621$	−1.18097e13			−0.127873
$622$	8.95863e13	−	2.94346e13i	0.962254	−	0.316160i
$623$			2.04425e14i			2.17818i
$624$	1.48851e14	+	4.62075e13i	1.57336	+	0.488416i
$625$	3.81470e12			0.0400000
$626$	−3.17672e12	−	9.66858e12i	−0.0330451	−	0.100575i
$627$		−	1.22905e14i		−	1.26833i
$628$	−9.85017e13	+	7.25609e13i	−1.00843	+	0.742855i
$629$	−9.83133e12			−0.0998525
$630$	6.30185e13	−	2.07055e13i	0.634988	−	0.208633i
$631$			8.77540e13i			0.877244i	0.898672	+	0.438622i	$0.144533\pi$
$631$			8.77540e13i			0.877244i	−0.898672	+	0.438622i	$0.855467\pi$
$632$	−6.60865e13	+	9.28746e13i	−0.655431	+	0.921110i
$633$	9.57714e13			0.942361
$634$	3.79677e13	+	1.15557e14i	0.370653	+	1.12811i
$635$		−	1.80270e13i		−	0.174605i
$636$	1.53388e14	+	2.08225e14i	1.47403	+	2.00100i
$637$	−2.62767e14			−2.50538
$638$	−7.65586e13	+	2.51542e13i	−0.724253	+	0.237962i
$639$			3.79742e13i			0.356438i
$640$	−3.81880e13	+	2.91122e13i	−0.355653	+	0.271129i
$641$	−7.91930e12			−0.0731807			−0.0365903	−	0.999330i	$-0.511650\pi$
$641$	−7.91930e12			−0.0731807			−0.0365903	+	0.999330i	$0.511650\pi$
$642$	−3.86623e13	−	1.17671e14i	−0.354497	−	1.07894i
$643$		−	6.97979e13i		−	0.635020i	−0.948255	−	0.317510i	$-0.897153\pi$
$643$		−	6.97979e13i		−	0.635020i	0.948255	−	0.317510i	$-0.102847\pi$
$644$	9.98394e13	−	7.35463e13i	0.901307	−	0.663944i
$645$	1.90985e13			0.171080
$646$	−1.21909e13	+	4.00545e12i	−0.108361	+	0.0356032i
$647$			3.64847e13i			0.321803i	0.986970	+	0.160901i	$0.0514401\pi$
$647$			3.64847e13i			0.321803i	−0.986970	+	0.160901i	$0.948560\pi$
$648$	1.04768e14	+	7.45494e13i	0.916966	+	0.652483i
$649$	−4.56946e13			−0.396863
$650$	8.76647e12	+	2.66813e13i	0.0755541	+	0.229954i
$651$		−	4.53784e14i		−	3.88100i
$652$	1.75843e12	+	2.38707e12i	0.0149240	+	0.0202594i
$653$	1.18590e14			0.998811			0.499406	−	0.866368i	$-0.333552\pi$
$653$	1.18590e14			0.998811			0.499406	+	0.866368i	$0.333552\pi$
$654$	−8.06341e13	+	2.64933e13i	−0.673953	+	0.221435i
$655$		−	4.15959e13i		−	0.345020i
$656$	4.01501e12	−	1.29337e13i	0.0330497	−	0.106465i
$657$	−8.55152e12			−0.0698581
$658$	−4.12292e13	−	1.25484e14i	−0.334253	−	1.01732i
$659$			8.68704e13i			0.698948i	0.936946	+	0.349474i	$0.113640\pi$
$659$			8.68704e13i			0.698948i	−0.936946	+	0.349474i	$0.886360\pi$
$660$	−4.66663e13	+	3.43766e13i	−0.372635	+	0.274500i
$661$	−1.41387e14			−1.12048			−0.560238	−	0.828332i	$-0.689290\pi$
$661$	−1.41387e14			−1.12048			−0.560238	+	0.828332i	$0.689290\pi$
$662$	1.32041e14	−	4.33835e13i	1.03853	−	0.341220i
$663$		−	1.96415e13i		−	0.153323i
$664$	−1.57165e13	+	2.20872e13i	−0.121763	+	0.171120i
$665$	1.24892e14			0.960341
$666$	−3.74297e13	−	1.13920e14i	−0.285657	−	0.869417i
$667$		−	8.45743e13i		−	0.640633i
$668$	2.01210e13	+	2.73143e13i	0.151275	+	0.205356i
$669$	−2.60523e14			−1.94409
$670$	−5.92504e13	+	1.94674e13i	−0.438851	+	0.144190i
$671$		−	1.72064e14i		−	1.26496i
$672$	−3.26814e14	+	5.37751e12i	−2.38481	+	0.0392406i
$673$	−8.61618e13			−0.624079			−0.312039	−	0.950069i	$-0.601012\pi$
$673$	−8.61618e13			−0.624079			−0.312039	+	0.950069i	$0.601012\pi$
$674$	7.55975e12	+	2.30086e13i	0.0543510	+	0.165421i
$675$			5.60922e12i			0.0400298i
$676$	−5.28148e13	+	3.89058e13i	−0.374130	+	0.275601i
$677$	1.26787e14			0.891520			0.445760	−	0.895152i	$-0.352933\pi$
$677$	1.26787e14			0.891520			0.445760	+	0.895152i	$0.352933\pi$
$678$	1.16767e14	−	3.83653e13i	0.815029	−	0.267787i
$679$			5.87595e12i			0.0407126i
$680$	4.93062e12	+	3.50847e12i	0.0339123	+	0.0241309i
$681$	3.38142e14			2.30868
$682$	5.69740e13	+	1.73404e14i	0.386149	+	1.17527i
$683$		−	1.04109e14i		−	0.700461i	−0.936664	−	0.350230i	$-0.886103\pi$
$683$		−	1.04109e14i		−	0.700461i	0.936664	−	0.350230i	$-0.113897\pi$
$684$	−9.28257e13	−	1.26011e14i	−0.619994	−	0.841645i
$685$	−2.01067e13			−0.133317
$686$	2.70635e14	−	8.89203e13i	1.78141	−	0.585302i
$687$			3.41166e14i			2.22937i
$688$	−4.13729e13	−	1.28433e13i	−0.268394	−	0.0833174i
$689$	−3.43095e14			−2.20962
$690$	−1.89879e13	−	5.77909e13i	−0.121403	−	0.369500i
$691$			3.73752e13i			0.237243i	0.992940	+	0.118621i	$0.0378475\pi$
$691$			3.73752e13i			0.237243i	−0.992940	+	0.118621i	$0.962153\pi$
$692$	1.17283e14	−	8.63959e13i	0.739101	−	0.544456i
$693$	−1.81613e14			−1.13626
$694$	−1.48550e13	+	4.88078e12i	−0.0922730	+	0.0303174i
$695$			6.70180e13i			0.413302i
$696$	−1.29246e14	+	1.81636e14i	−0.791357	+	1.11213i
$697$	−1.70667e12			−0.0103749
$698$	−2.31753e13	−	7.05357e13i	−0.139878	−	0.425727i
$699$			7.13336e13i			0.427472i
$700$	−3.49322e13	−	4.74206e13i	−0.207843	−	0.282148i
$701$	−1.57586e13			−0.0930950			−0.0465475	−	0.998916i	$-0.514822\pi$
$701$	−1.57586e13			−0.0930950			−0.0465475	+	0.998916i	$0.514822\pi$
$702$	−3.92328e13	+	1.28904e13i	−0.230125	+	0.0756103i
$703$		−	2.25769e14i		−	1.31489i
$704$	1.24210e14	−	4.30875e13i	0.718282	−	0.249166i
$705$	−6.47938e13			−0.372039
$706$	2.84987e13	+	8.67377e13i	0.162481	+	0.494521i
$707$			4.58634e14i			2.59639i
$708$	−1.01775e14	+	7.49718e13i	−0.572101	+	0.421436i
$709$	2.52712e14			1.41057			0.705285	−	0.708924i	$-0.250819\pi$
$709$	2.52712e14			1.41057			0.705285	+	0.708924i	$0.250819\pi$
$710$	3.20331e13	−	1.05248e13i	0.177544	−	0.0583343i
$711$			1.75207e14i			0.964278i
$712$	−1.85334e14	−	1.31877e14i	−1.01287	−	0.720726i
$713$	−1.91560e14			−1.03958
$714$	1.28577e13	+	3.91332e13i	0.0692901	+	0.210889i
$715$		−	7.68927e13i		−	0.411486i
$716$	2.13960e13	+	2.90451e13i	0.113702	+	0.154350i
$717$	3.36735e14			1.77702
$718$	4.85450e13	−	1.59500e13i	0.254403	−	0.0835871i
$719$			1.11740e13i			0.0581517i	0.999577	+	0.0290759i	$0.00925644\pi$
$719$			1.11740e13i			0.0581517i	−0.999577	+	0.0290759i	$0.990744\pi$
$720$	−2.18823e13	+	7.04906e13i	−0.113092	+	0.364308i
$721$	1.67449e14			0.859421
$722$	−3.07412e13	−	9.35629e13i	−0.156688	−	0.476889i
$723$			2.58620e14i			1.30909i
$724$	7.03074e13	−	5.17916e13i	0.353434	−	0.260356i
$725$	−4.01701e13			−0.200545
$726$	−1.10067e14	+	3.61637e13i	−0.545724	+	0.179304i
$727$			1.13819e14i			0.560455i	0.959934	+	0.280228i	$0.0904100\pi$
$727$			1.13819e14i			0.560455i	−0.959934	+	0.280228i	$0.909590\pi$
$728$	2.51399e14	−	3.53304e14i	1.22944	−	1.72779i
$729$	1.41548e14			0.687490
$730$	2.37012e12	+	7.21363e12i	0.0114329	+	0.0347968i
$731$			5.45934e12i			0.0261549i
$732$	−2.82308e14	−	3.83234e14i	−1.34328	−	1.82351i
$733$	3.18416e12			0.0150479			0.00752393	−	0.999972i	$-0.497605\pi$
$733$	3.18416e12			0.0150479			0.00752393	+	0.999972i	$0.497605\pi$
$734$	−9.01819e12	+	2.96303e12i	−0.0423291	+	0.0139077i
$735$		−	2.70325e14i		−	1.26023i
$736$	2.27006e12	+	1.37961e14i	0.0105111	+	0.638804i
$737$	1.70753e14			0.785293
$738$	−6.49759e12	−	1.97759e13i	−0.0296804	−	0.0903345i
$739$			1.84171e14i			0.835599i	0.908539	+	0.417800i	$0.137199\pi$
$739$			1.84171e14i			0.835599i	−0.908539	+	0.417800i	$0.862801\pi$
$740$	−8.57230e13	+	6.31475e13i	−0.386313	+	0.284576i
$741$	4.51052e14			2.01900
$742$	6.83573e14	−	2.24596e14i	3.03924	−	0.998578i
$743$		−	2.17569e14i		−	0.960844i	−0.877037	−	0.480422i	$-0.840483\pi$
$743$		−	2.17569e14i		−	0.960844i	0.877037	−	0.480422i	$-0.159517\pi$
$744$	4.11405e14	+	2.92742e14i	1.80470	+	1.28416i
$745$	−6.73316e13			−0.293385
$746$	9.86807e13	+	3.00341e14i	0.427108	+	1.29993i
$747$			4.16672e13i			0.179140i
$748$	−9.82661e12	−	1.33397e13i	−0.0419658	−	0.0569688i
$749$	−3.44597e14			−1.46185
$750$	−2.74489e13	+	9.01864e12i	−0.115669	+	0.0380045i
$751$		−	2.81405e14i		−	1.17797i	−0.808146	−	0.588983i	$-0.799529\pi$
$751$		−	2.81405e14i		−	1.17797i	0.808146	−	0.588983i	$-0.200471\pi$
$752$	1.40362e14	+	4.35725e13i	0.583662	+	0.181186i
$753$	−2.06350e14			−0.852374
$754$	−9.23139e13	−	2.80964e14i	−0.378800	−	1.15291i
$755$			1.63086e14i			0.664787i
$756$	6.97282e13	−	5.13650e13i	0.282358	−	0.207998i
$757$	−8.77891e13			−0.353152			−0.176576	−	0.984287i	$-0.556502\pi$
$757$	−8.77891e13			−0.353152			−0.176576	+	0.984287i	$0.556502\pi$
$758$	−8.16347e13	+	2.68220e13i	−0.326234	+	0.107188i
$759$			1.66547e14i			0.661193i
$760$	−8.05693e13	+	1.13228e14i	−0.317762	+	0.446566i
$761$	−3.64374e14			−1.42766			−0.713829	−	0.700320i	$-0.753041\pi$
$761$	−3.64374e14			−1.42766			−0.713829	+	0.700320i	$0.753041\pi$
$762$	4.26192e13	+	1.29714e14i	0.165894	+	0.504909i
$763$			2.36134e14i			0.913138i
$764$	−2.12867e14	−	2.88967e14i	−0.817788	−	1.11015i
$765$	9.30155e12			0.0355016
$766$	−8.48855e13	+	2.78901e13i	−0.321877	+	0.105756i
$767$		−	1.67695e14i		−	0.631748i
$768$	2.05957e14	−	2.99762e14i	0.770851	−	1.12194i
$769$	−2.27454e14			−0.845790			−0.422895	−	0.906179i	$-0.638986\pi$
$769$	−2.27454e14			−0.845790			−0.422895	+	0.906179i	$0.638986\pi$
$770$	5.03353e13	+	1.53199e14i	0.185960	+	0.565982i
$771$			3.45299e14i			1.26743i
$772$	−1.30206e14	+	9.59161e13i	−0.474839	+	0.349788i
$773$	−2.31980e14			−0.840531			−0.420265	−	0.907401i	$-0.638063\pi$
$773$	−2.31980e14			−0.840531			−0.420265	+	0.907401i	$0.638063\pi$
$774$	−6.32596e13	+	2.07847e13i	−0.227731	+	0.0748236i
$775$			9.09848e13i			0.325432i
$776$	−5.32719e12	−	3.79065e12i	−0.0189317	−	0.0134712i
$777$	−7.24729e14			−2.55900
$778$	4.53488e13	+	1.38022e14i	0.159099	+	0.484230i
$779$		−	3.91923e13i		−	0.136620i
$780$	−1.26159e14	−	1.71262e14i	−0.436964	−	0.593181i
$781$	−9.23159e13			−0.317703
$782$	1.65197e13	−	5.42773e12i	0.0564895	−	0.0185603i
$783$		−	5.90670e13i		−	0.200695i
$784$	−1.81788e14	+	5.85604e14i	−0.613742	+	1.97708i
$785$	1.66971e14			0.560136
$786$	9.83404e13	+	2.99306e14i	0.327808	+	0.997705i
$787$		−	4.63128e14i		−	1.53401i	−0.641644	−	0.767003i	$-0.721747\pi$
$787$		−	4.63128e14i		−	1.53401i	0.641644	−	0.767003i	$-0.278253\pi$
$788$	−3.25807e14	+	2.40004e14i	−1.07233	+	0.789929i
$789$	7.46119e14			2.44019
$790$	1.47795e14	−	4.85599e13i	0.480314	−	0.157813i
$791$		−	3.41950e14i		−	1.10428i
$792$	1.17161e14	−	1.64652e14i	0.375972	−	0.528372i
$793$	6.31459e14			2.01363
$794$	−1.56162e14	−	4.75289e14i	−0.494849	−	1.50611i
$795$		−	3.52964e14i		−	1.11146i
$796$	1.29597e13	+	1.75929e13i	0.0405537	+	0.0550519i
$797$	5.47068e13			0.170118			0.0850588	−	0.996376i	$-0.472892\pi$
$797$	5.47068e13			0.170118			0.0850588	+	0.996376i	$0.472892\pi$
$798$	−8.98665e14	+	2.95267e14i	−2.77705	+	0.912431i
$799$		−	1.85215e13i		−	0.0568776i
$800$	6.55271e13	−	1.07821e12i	0.199973	−	0.00329042i
$801$	−3.49629e14			−1.06034
$802$	−9.94350e13	−	3.02637e14i	−0.299687	−	0.912117i
$803$		−	2.07889e13i		−	0.0622664i
$804$	3.80315e14	−	2.80158e14i	1.13204	−	0.833916i
$805$	−1.69239e14			−0.500635
$806$	−6.36380e14	+	2.09090e14i	−1.87086	+	0.614693i
$807$			1.51428e14i			0.442425i
$808$	−4.15802e14	−	2.95871e14i	−1.20734	−	0.859104i
$809$	3.59793e14			1.03827			0.519135	−	0.854692i	$-0.326254\pi$
$809$	3.59793e14			1.03827			0.519135	+	0.854692i	$0.326254\pi$
$810$	−5.47784e13	−	1.66722e14i	−0.157103	−	0.478153i
$811$		−	4.03312e13i		−	0.114957i	−0.998347	−	0.0574787i	$-0.981694\pi$
$811$		−	4.03312e13i		−	0.114957i	0.998347	−	0.0574787i	$-0.0183061\pi$
$812$	3.67848e14	+	4.99355e14i	1.04205	+	1.41459i
$813$	2.33977e13			0.0658749
$814$	2.76941e14	−	9.09921e13i	0.774935	−	0.254614i
$815$		−	4.04635e12i		−	0.0112532i
$816$	−4.37732e13	−	1.35885e13i	−0.120992	−	0.0375595i
$817$	−1.25370e14			−0.344415
$818$	−3.94622e13	−	1.20106e14i	−0.107749	−	0.327943i
$819$		−	6.66503e14i		−	1.80877i
$820$	−1.48811e13	+	1.09621e13i	−0.0401388	+	0.0295681i
$821$	6.29121e14			1.68662			0.843312	−	0.537424i	$-0.180602\pi$
$821$	6.29121e14			1.68662			0.843312	+	0.537424i	$0.180602\pi$
$822$	1.44679e14	−	4.75358e13i	0.385518	−	0.126667i
$823$			3.91664e13i			0.103732i	0.998654	+	0.0518662i	$0.0165169\pi$
$823$			3.91664e13i			0.103732i	−0.998654	+	0.0518662i	$0.983483\pi$
$824$	−1.08024e14	+	1.51811e14i	−0.284369	+	0.399638i
$825$	7.91046e13			0.206982
$826$	1.09776e14	+	3.34112e14i	0.285502	+	0.868944i
$827$			5.12246e14i			1.32419i	0.749419	+	0.662096i	$0.230333\pi$
$827$			5.12246e14i			1.32419i	−0.749419	+	0.662096i	$0.769667\pi$
$828$	1.25787e14	+	1.70756e14i	0.323209	+	0.438757i
$829$	2.87121e14			0.733317			0.366658	−	0.930356i	$-0.380502\pi$
$829$	2.87121e14			0.733317			0.366658	+	0.930356i	$0.380502\pi$
$830$	3.51483e13	−	1.15484e13i	0.0892307	−	0.0293178i
$831$		−	9.38517e14i		−	2.36830i
$832$	1.58128e14	+	4.55842e14i	0.396635	+	1.14340i
$833$	7.72731e13			0.192665
$834$	−1.58443e14	−	4.82232e14i	−0.392683	−	1.19516i
$835$		−	4.63008e13i		−	0.114066i
$836$	3.06335e14	−	2.25661e14i	0.750181	−	0.552618i
$837$	−1.33786e14			−0.325675
$838$	4.78869e14	−	1.57338e14i	1.15877	−	0.380727i
$839$			2.95325e14i			0.710379i	0.934794	+	0.355190i	$0.115584\pi$
$839$			2.95325e14i			0.710379i	−0.934794	+	0.355190i	$0.884416\pi$
$840$	3.63467e14	+	2.58631e14i	0.869098	+	0.618421i
$841$	2.29764e12			0.00546136
$842$	1.89050e13	+	5.75387e13i	0.0446700	+	0.135956i
$843$		−	1.57392e14i		−	0.369695i
$844$	1.75841e14	+	2.38706e14i	0.410591	+	0.557379i
$845$	8.95270e13			0.207812
$846$	2.14616e14	−	7.05145e13i	0.495234	−	0.162715i
$847$			3.22327e14i			0.739401i
$848$	−2.37361e14	+	7.64623e14i	−0.541291	+	1.74369i
$849$	−3.12976e14			−0.709533
$850$	−2.57800e12	−	7.84632e12i	−0.00581016	−	0.0176836i
$851$			3.05937e14i			0.685462i
$852$	−2.05613e14	+	1.51464e14i	−0.457987	+	0.337374i
$853$	−1.08283e14			−0.239780			−0.119890	−	0.992787i	$-0.538254\pi$
$853$	−1.08283e14			−0.239780			−0.119890	+	0.992787i	$0.538254\pi$
$854$	−1.25810e15	+	4.13364e14i	−2.76966	+	0.910005i
$855$			2.13603e14i			0.467495i
$856$	2.22304e14	−	3.12415e14i	0.483702	−	0.679771i
$857$	−3.60461e14			−0.779748			−0.389874	−	0.920868i	$-0.627481\pi$
$857$	−3.60461e14			−0.779748			−0.389874	+	0.920868i	$0.627481\pi$
$858$	1.81788e14	+	5.53286e14i	0.390958	+	1.18991i
$859$			6.06012e13i			0.129573i	0.997899	+	0.0647866i	$0.0206367\pi$
$859$			6.06012e13i			0.129573i	−0.997899	+	0.0647866i	$0.979363\pi$
$860$	3.50658e13	+	4.76020e13i	0.0745404	+	0.101189i
$861$	−1.25809e14			−0.265886
$862$	−4.90368e14	+	1.61116e14i	−1.03035	+	0.338534i
$863$			1.17507e13i			0.0245476i	0.999925	+	0.0122738i	$0.00390698\pi$
$863$			1.17507e13i			0.0245476i	−0.999925	+	0.0122738i	$0.996093\pi$
$864$	1.58542e12	+	9.63525e13i	0.00329287	+	0.200122i
$865$	−1.98807e14			−0.410537
$866$	−2.27598e14	−	6.92709e14i	−0.467281	−	1.42220i
$867$		−	6.61075e14i		−	1.34945i
$868$	1.13103e15	−	8.33172e14i	2.29550	−	1.69097i
$869$	−4.25930e14			−0.859487
$870$	2.89046e14	−	9.49694e13i	0.579924	−	0.190541i
$871$			6.26651e14i			1.25007i
$872$	−2.14082e14	−	1.52333e14i	−0.424617	−	0.302143i
$873$	−1.00497e13			−0.0198190
$874$	1.24644e14	+	3.79362e14i	0.244407	+	0.743869i
$875$			8.03831e13i			0.156720i
$876$	−3.41087e13	−	4.63027e13i	−0.0661217	−	0.0897605i
$877$	6.85003e14			1.32037			0.660183	−	0.751104i	$-0.270479\pi$
$877$	6.85003e14			1.32037			0.660183	+	0.751104i	$0.270479\pi$
$878$	2.23098e14	−	7.33013e13i	0.427585	−	0.140488i
$879$			7.84650e14i			1.49531i
$880$	−1.71364e14	−	5.31963e13i	−0.324717	−	0.100802i
$881$	−2.09299e14			−0.394355			−0.197177	−	0.980368i	$-0.563177\pi$
$881$	−2.09299e14			−0.394355			−0.197177	+	0.980368i	$0.563177\pi$
$882$	2.94193e14	+	8.95396e14i	0.551175	+	1.67754i
$883$			6.25256e14i			1.16481i	0.812899	+	0.582404i	$0.197888\pi$
$883$			6.25256e14i			1.16481i	−0.812899	+	0.582404i	$0.802112\pi$
$884$	4.89555e13	−	3.60629e13i	0.0906860	−	0.0668035i
$885$	1.72519e14			0.317776
$886$	−1.11909e13	+	3.67689e12i	−0.0204972	+	0.00673460i
$887$		−	7.59597e14i		−	1.38346i	−0.722158	−	0.691728i	$-0.756850\pi$
$887$		−	7.59597e14i		−	1.38346i	0.722158	−	0.691728i	$-0.243150\pi$
$888$	4.67532e14	−	6.57046e14i	0.846734	−	1.18996i
$889$	3.79865e14			0.684101
$890$	9.69025e13	+	2.94930e14i	0.173534	+	0.528164i
$891$			4.80474e14i			0.855621i
$892$	−4.78335e14	−	6.49342e14i	−0.847048	−	1.14987i
$893$	4.25331e14			0.748980
$894$	4.84488e14	−	1.59184e14i	0.848391	−	0.278749i
$895$		−	4.92347e13i		−	0.0857346i
$896$	−6.13452e14	−	8.04695e14i	−1.06228	−	1.39345i
$897$	−6.11215e14			−1.05252
$898$	1.73473e14	+	5.27977e14i	0.297064	+	0.904136i
$899$		−	9.58102e14i		−	1.63160i
$900$	8.11037e13	−	5.97447e13i	0.137350	−	0.101178i
$901$	1.00896e14			0.169921
$902$	4.80754e13	−	1.57957e13i	0.0805175	−	0.0264550i
$903$			4.02442e14i			0.670293i
$904$	3.10015e14	+	2.20596e14i	0.513500	+	0.365389i
$905$	−1.19179e14			−0.196316
$906$	−3.85566e14	−	1.17350e15i	−0.631622	−	1.92239i
$907$		−	6.72197e13i		−	0.109512i	−0.998500	−	0.0547558i	$-0.982562\pi$
$907$		−	6.72197e13i		−	0.109512i	0.998500	−	0.0547558i	$-0.0174380\pi$
$908$	6.20848e14	+	8.42804e14i	1.00590	+	1.36552i
$909$	−7.84405e14			−1.26392
$910$	−5.62228e14	+	1.84727e14i	−0.900960	+	0.296021i
$911$		−	9.95355e14i		−	1.58630i	−0.609025	−	0.793151i	$-0.708439\pi$
$911$		−	9.95355e14i		−	1.58630i	0.609025	−	0.793151i	$-0.291561\pi$
$912$	3.12049e14	−	1.00522e15i	0.494594	−	1.59326i
$913$	−1.01294e14			−0.159672
$914$	1.79596e14	+	5.46612e14i	0.281556	+	0.856936i
$915$			6.49624e14i			1.01288i
$916$	−8.50340e14	+	6.26399e14i	−1.31861	+	0.971346i
$917$	8.76508e14			1.35179
$918$	1.15374e13	−	3.79075e12i	0.0176968	−	0.00581448i
$919$			3.20262e14i			0.488572i	0.969703	+	0.244286i	$0.0785535\pi$
$919$			3.20262e14i			0.488572i	−0.969703	+	0.244286i	$0.921447\pi$
$920$	1.09178e14	−	1.53434e14i	0.165652	−	0.232799i
$921$	−1.08212e15			−1.63297
$922$	−4.08566e14	−	1.24350e15i	−0.613208	−	1.86634i
$923$		−	3.38792e14i		−	0.505736i
$924$	−7.24381e14	−	9.83351e14i	−1.07549	−	1.45999i
$925$	1.45310e14			0.214579
$926$	5.19713e14	−	1.70758e14i	0.763324	−	0.250799i
$927$			2.86389e14i			0.418367i
$928$	−6.90023e14	+	1.13539e13i	−1.00259	+	0.0164970i
$929$	−6.44525e14			−0.931454			−0.465727	−	0.884929i	$-0.654207\pi$
$929$	−6.44525e14			−0.931454			−0.465727	+	0.884929i	$0.654207\pi$
$930$	−2.15105e14	−	6.54686e14i	−0.309197	−	0.941063i
$931$			1.77452e15i			2.53707i
$932$	−1.77795e14	+	1.30972e14i	−0.252837	+	0.186252i
$933$	9.74748e14			1.37875
$934$	7.47186e14	−	2.45497e14i	1.05122	−	0.345391i
$935$			2.26122e13i			0.0316436i
$936$	6.04258e14	+	4.29970e14i	0.841092	+	0.598493i
$937$	1.17565e15			1.62772			0.813860	−	0.581061i	$-0.197362\pi$
$937$	1.17565e15			1.62772			0.813860	+	0.581061i	$0.197362\pi$
$938$	−4.10217e14	−	1.24852e15i	−0.564936	−	1.71942i
$939$		−	1.05199e14i		−	0.144107i
$940$	−1.18965e14	−	1.61495e14i	−0.162099	−	0.220050i
$941$	−1.07542e14			−0.145757			−0.0728787	−	0.997341i	$-0.523219\pi$
$941$	−1.07542e14			−0.145757			−0.0728787	+	0.997341i	$0.523219\pi$
$942$	−1.20145e15	+	3.94751e14i	−1.61976	+	0.532192i
$943$			5.31089e13i			0.0712212i
$944$	−3.73727e14	−	1.16016e14i	−0.498534	−	0.154759i
$945$	−1.18197e14			−0.156837
$946$	−5.05279e13	−	1.53785e14i	−0.0666923	−	0.202983i
$947$		−	9.03973e14i		−	1.18688i	−0.804880	−	0.593438i	$-0.797770\pi$
$947$		−	9.03973e14i		−	1.18688i	0.804880	−	0.593438i	$-0.202230\pi$
$948$	−9.48665e14	+	6.98831e14i	−1.23900	+	0.912705i
$949$	7.62935e13			0.0991190
$950$	1.80185e14	−	5.92018e13i	0.232863	−	0.0765098i
$951$			1.25733e15i			1.61639i
$952$	−7.39303e13	+	1.03898e14i	−0.0945448	+	0.132868i
$953$	−6.08081e13			−0.0773565			−0.0386783	−	0.999252i	$-0.512315\pi$
$953$	−6.08081e13			−0.0773565			−0.0386783	+	0.999252i	$0.512315\pi$
$954$	3.84128e14	+	1.16912e15i	0.486109	+	1.47951i
$955$			4.89832e14i			0.616638i
$956$	6.18264e14	+	8.39296e14i	0.774256	+	1.05106i
$957$	−8.32999e14			−1.03773
$958$	9.80111e14	−	3.22027e14i	1.21464	−	0.399084i
$959$		−	4.23687e14i		−	0.522338i
$960$	−4.68955e14	+	1.62676e14i	−0.575142	+	0.199512i
$961$	−1.35046e15			−1.64765
$962$	3.33934e14	+	1.01635e15i	0.405308	+	1.23358i
$963$		−	5.89366e14i		−	0.711629i
$964$	−6.44598e14	+	4.74841e14i	−0.774290	+	0.570378i
$965$	2.20714e14			0.263751
$966$	1.21777e15	−	4.00112e14i	1.44770	−	0.475659i
$967$			2.41545e13i			0.0285671i	0.999898	+	0.0142836i	$0.00454675\pi$
$967$			2.41545e13i			0.0285671i	−0.999898	+	0.0142836i	$0.995453\pi$
$968$	−2.92225e14	−	2.07938e14i	−0.343827	−	0.244656i
$969$	−1.32643e14			−0.155262
$970$	2.78535e12	+	8.47740e12i	0.00324355	+	0.00987197i
$971$		−	4.34211e14i		−	0.503042i	−0.967852	−	0.251521i	$-0.919069\pi$
$971$		−	4.34211e14i		−	0.503042i	0.967852	−	0.251521i	$-0.0809308\pi$
$972$	6.85328e14	+	9.30335e14i	0.789891	+	1.07228i
$973$	−1.41220e15			−1.61932
$974$	9.85903e14	−	3.23930e14i	1.12471	−	0.369536i
$975$			2.90308e14i			0.329485i
$976$	4.36859e14	−	1.40728e15i	0.493279	−	1.58902i
$977$	8.83322e14			0.992308			0.496154	−	0.868235i	$-0.334745\pi$
$977$	8.83322e14			0.992308			0.496154	+	0.868235i	$0.334745\pi$
$978$	9.56631e12	+	2.91157e13i	0.0106918	+	0.0325412i
$979$		−	8.49955e14i		−	0.945110i
$980$	6.73773e14	−	4.96332e14i	0.745390	−	0.549088i
$981$	−4.03862e14			−0.444517
$982$	−3.85960e14	+	1.26812e14i	−0.422654	+	0.138868i
$983$		−	9.46697e14i		−	1.03144i	−0.856758	−	0.515719i	$-0.827525\pi$
$983$		−	9.46697e14i		−	1.03144i	0.856758	−	0.515719i	$-0.172475\pi$
$984$	8.11611e13	−	1.14060e14i	0.0879776	−	0.123639i
$985$	5.52279e14			0.595632
$986$	2.71472e13	+	8.26244e13i	0.0291300	+	0.0886592i
$987$		−	1.36533e15i		−	1.45765i
$988$	8.28157e14	+	1.12423e15i	0.879686	+	1.19418i
$989$	1.69887e14			0.179547
$990$	−2.62017e14	+	8.60889e13i	−0.275521	+	0.0905255i
$991$		−	6.43587e14i		−	0.673347i	−0.941621	−	0.336674i	$-0.890698\pi$
$991$		−	6.43587e14i		−	0.673347i	0.941621	−	0.336674i	$-0.109302\pi$
$992$	2.57164e13	+	1.56290e15i	0.0267702	+	1.62694i
$993$	1.43667e15			1.48803
$994$	2.21779e14	+	6.75000e14i	0.228554	+	0.695620i
$995$		−	2.98219e13i		−	0.0305788i
$996$	−2.25609e14	+	1.66194e14i	−0.230176	+	0.169558i
$997$	3.34658e14			0.339723			0.169862	−	0.985468i	$-0.445668\pi$
$997$	3.34658e14			0.339723			0.169862	+	0.985468i	$0.445668\pi$
$998$	−3.29983e14	+	1.08420e14i	−0.333303	+	0.109510i
$999$			2.13667e14i			0.214739i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.11.b.a.11.14	yes	20
3.2	odd	2		180.11.c.a.91.7		20
4.3	odd	2	inner	20.11.b.a.11.13	✓	20
5.2	odd	4		100.11.d.c.99.6		40
5.3	odd	4		100.11.d.c.99.35		40
5.4	even	2		100.11.b.e.51.7		20
8.3	odd	2		320.11.b.d.191.18		20
8.5	even	2		320.11.b.d.191.3		20
12.11	even	2		180.11.c.a.91.8		20
20.3	even	4		100.11.d.c.99.5		40
20.7	even	4		100.11.d.c.99.36		40
20.19	odd	2		100.11.b.e.51.8		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.11.b.a.11.13	✓	20	4.3	odd	2	inner
20.11.b.a.11.14	yes	20	1.1	even	1	trivial
100.11.b.e.51.7		20	5.4	even	2
100.11.b.e.51.8		20	20.19	odd	2
100.11.d.c.99.5		40	20.3	even	4
100.11.d.c.99.6		40	5.2	odd	4
100.11.d.c.99.35		40	5.3	odd	4
100.11.d.c.99.36		40	20.7	even	4
180.11.c.a.91.7		20	3.2	odd	2
180.11.c.a.91.8		20	12.11	even	2
320.11.b.d.191.3		20	8.5	even	2
320.11.b.d.191.18		20	8.3	odd	2

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:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	20.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(9.98863 + 30.4011i) q^{2} +330.781i q^{3} +(-824.454 + 607.331i) q^{4} +1397.54 q^{5} +(-10056.1 + 3304.05i) q^{6} +29449.0i q^{7} +(-26698.7 - 18997.9i) q^{8} -50366.8 q^{9} +O(q^{10})\)	\(q+(9.98863 + 30.4011i) q^{2} +330.781i q^{3} +(-824.454 + 607.331i) q^{4} +1397.54 q^{5} +(-10056.1 + 3304.05i) q^{6} +29449.0i q^{7} +(-26698.7 - 18997.9i) q^{8} -50366.8 q^{9} +(13959.5 + 42486.8i) q^{10} -122442. i q^{11} +(-200893. - 272713. i) q^{12} +449354. q^{13} +(-895281. + 294155. i) q^{14} +462280. i q^{15} +(310874. - 1.00143e6i) q^{16} -132144. q^{17} +(-503095. - 1.53120e6i) q^{18} -3.03458e6i q^{19} +(-1.15221e6 + 848771. i) q^{20} -9.74114e6 q^{21} +(3.72238e6 - 1.22303e6i) q^{22} +4.11212e6i q^{23} +(6.28414e6 - 8.83141e6i) q^{24} +1.95312e6 q^{25} +(4.48843e6 + 1.36609e7i) q^{26} +2.87192e6i q^{27} +(-1.78853e7 - 2.42793e7i) q^{28} -2.05671e7 q^{29} +(-1.40538e7 + 4.61754e6i) q^{30} +4.65842e7i q^{31} +(3.35499e7 - 552041. i) q^{32} +4.05016e7 q^{33} +(-1.31994e6 - 4.01731e6i) q^{34} +4.11562e7i q^{35} +(4.15251e7 - 3.05893e7i) q^{36} +7.43988e7 q^{37} +(9.22546e7 - 3.03113e7i) q^{38} +1.48637e8i q^{39} +(-3.73126e7 - 2.65504e7i) q^{40} +1.29152e7 q^{41} +(-9.73007e7 - 2.96141e8i) q^{42} -4.13136e7i q^{43} +(7.43631e7 + 1.00948e8i) q^{44} -7.03897e7 q^{45} +(-1.25013e8 + 4.10744e7i) q^{46} +1.40161e8i q^{47} +(3.31255e8 + 1.02831e8i) q^{48} -5.84766e8 q^{49} +(1.95091e7 + 5.93772e7i) q^{50} -4.37106e7i q^{51} +(-3.70472e8 + 2.72906e8i) q^{52} -7.63529e8 q^{53} +(-8.73095e7 + 2.86865e7i) q^{54} -1.71118e8i q^{55} +(5.59469e8 - 7.86249e8i) q^{56} +1.00378e9 q^{57} +(-2.05437e8 - 6.25262e8i) q^{58} -3.73192e8i q^{59} +(-2.80757e8 - 3.81129e8i) q^{60} +1.40526e9 q^{61} +(-1.41621e9 + 4.65313e8i) q^{62} -1.48325e9i q^{63} +(3.51900e8 + 1.01444e9i) q^{64} +6.27991e8 q^{65} +(4.04555e8 + 1.23129e9i) q^{66} +1.39456e9i q^{67} +(1.08946e8 - 8.02550e7i) q^{68} -1.36021e9 q^{69} +(-1.25119e9 + 4.11094e8i) q^{70} -7.53953e8i q^{71} +(1.34473e9 + 9.56863e8i) q^{72} +1.69785e8 q^{73} +(7.43142e8 + 2.26181e9i) q^{74} +6.46056e8i q^{75} +(1.84300e9 + 2.50187e9i) q^{76} +3.60580e9 q^{77} +(-4.51874e9 + 1.48469e9i) q^{78} -3.47862e9i q^{79} +(4.34460e8 - 1.39955e9i) q^{80} -3.92408e9 q^{81} +(1.29005e8 + 3.92637e8i) q^{82} -8.27276e8i q^{83} +(8.03113e9 - 5.91610e9i) q^{84} -1.84676e8 q^{85} +(1.25598e9 - 4.12667e8i) q^{86} -6.80319e9i q^{87} +(-2.32615e9 + 3.26905e9i) q^{88} +6.94167e9 q^{89} +(-7.03097e8 - 2.13992e9i) q^{90} +1.32330e10i q^{91} +(-2.49742e9 - 3.39025e9i) q^{92} -1.54092e10 q^{93} +(-4.26106e9 + 1.40002e9i) q^{94} -4.24096e9i q^{95} +(1.82605e8 + 1.10977e10i) q^{96} +1.99530e8 q^{97} +(-5.84101e9 - 1.77775e10i) q^{98} +6.16703e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 22 q^{2} - 644 q^{4} - 14784 q^{6} + 3448 q^{8} - 414868 q^{9}+O(q^{10}) \) 20 * q + 22 * q^2 - 644 * q^4 - 14784 * q^6 + 3448 * q^8 - 414868 * q^9	\( 20 q + 22 q^{2} - 644 q^{4} - 14784 q^{6} + 3448 q^{8} - 414868 q^{9} - 31250 q^{10} + 1329640 q^{12} - 278864 q^{13} - 2240504 q^{14} + 4261360 q^{16} - 1921656 q^{17} - 3556082 q^{18} - 1187500 q^{20} + 4157512 q^{21} - 5811280 q^{22} - 19112144 q^{24} + 39062500 q^{25} + 25066884 q^{26} - 87415400 q^{28} - 66014888 q^{29} + 39875000 q^{30} - 33171328 q^{32} + 85980560 q^{33} - 27236084 q^{34} + 355456476 q^{36} - 153620656 q^{37} + 250352720 q^{38} - 112375000 q^{40} + 477406160 q^{41} - 570662040 q^{42} + 339141040 q^{44} - 140125000 q^{45} - 897549304 q^{46} - 479727360 q^{48} + 333772012 q^{49} + 42968750 q^{50} - 110465096 q^{52} - 1669491824 q^{53} + 706139792 q^{54} - 1362290224 q^{56} + 3973032960 q^{57} + 2075027916 q^{58} - 677375000 q^{60} - 4283166080 q^{61} + 1664032240 q^{62} + 340459456 q^{64} + 290125000 q^{65} + 1884031760 q^{66} + 3042411896 q^{68} - 5321669928 q^{69} - 2070000000 q^{70} + 1632326712 q^{72} + 2474287656 q^{73} + 188682276 q^{74} + 2323171200 q^{76} + 410885040 q^{77} - 19914223760 q^{78} + 3604750000 q^{80} + 9939722652 q^{81} - 3197757116 q^{82} + 2383099552 q^{84} + 4799500000 q^{85} + 19648321456 q^{86} + 2774318240 q^{88} + 3011851592 q^{89} - 2849906250 q^{90} - 27349072440 q^{92} - 11861394640 q^{93} + 15684681576 q^{94} - 1990377984 q^{96} - 39984502056 q^{97} + 38416891998 q^{98}+O(q^{100}) \) 20 * q + 22 * q^2 - 644 * q^4 - 14784 * q^6 + 3448 * q^8 - 414868 * q^9 - 31250 * q^10 + 1329640 * q^12 - 278864 * q^13 - 2240504 * q^14 + 4261360 * q^16 - 1921656 * q^17 - 3556082 * q^18 - 1187500 * q^20 + 4157512 * q^21 - 5811280 * q^22 - 19112144 * q^24 + 39062500 * q^25 + 25066884 * q^26 - 87415400 * q^28 - 66014888 * q^29 + 39875000 * q^30 - 33171328 * q^32 + 85980560 * q^33 - 27236084 * q^34 + 355456476 * q^36 - 153620656 * q^37 + 250352720 * q^38 - 112375000 * q^40 + 477406160 * q^41 - 570662040 * q^42 + 339141040 * q^44 - 140125000 * q^45 - 897549304 * q^46 - 479727360 * q^48 + 333772012 * q^49 + 42968750 * q^50 - 110465096 * q^52 - 1669491824 * q^53 + 706139792 * q^54 - 1362290224 * q^56 + 3973032960 * q^57 + 2075027916 * q^58 - 677375000 * q^60 - 4283166080 * q^61 + 1664032240 * q^62 + 340459456 * q^64 + 290125000 * q^65 + 1884031760 * q^66 + 3042411896 * q^68 - 5321669928 * q^69 - 2070000000 * q^70 + 1632326712 * q^72 + 2474287656 * q^73 + 188682276 * q^74 + 2323171200 * q^76 + 410885040 * q^77 - 19914223760 * q^78 + 3604750000 * q^80 + 9939722652 * q^81 - 3197757116 * q^82 + 2383099552 * q^84 + 4799500000 * q^85 + 19648321456 * q^86 + 2774318240 * q^88 + 3011851592 * q^89 - 2849906250 * q^90 - 27349072440 * q^92 - 11861394640 * q^93 + 15684681576 * q^94 - 1990377984 * q^96 - 39984502056 * q^97 + 38416891998 * q^98

Introduction

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