LMFDB - Embedded newform 20.11.b.a.11.9

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			11.9
Root			$-2.00318 - 15.9954i$ of defining polynomial
Character	$\chi$	$=$	20.11
Dual form			20.11.b.a.11.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.770283 - 31.9907i) q^{2} +80.5620i q^{3} +(-1022.81 + 49.2838i) q^{4} -1397.54 q^{5} +(2577.24 - 62.0555i) q^{6} -345.112i q^{7} +(2364.48 + 32682.6i) q^{8} +52558.8 q^{9} +O(q^{10})$	\(q+(-0.770283 - 31.9907i) q^{2} +80.5620i q^{3} +(-1022.81 + 49.2838i) q^{4} -1397.54 q^{5} +(2577.24 - 62.0555i) q^{6} -345.112i q^{7} +(2364.48 + 32682.6i) q^{8} +52558.8 q^{9} +(1076.50 + 44708.4i) q^{10} +167110. i q^{11} +(-3970.40 - 82399.9i) q^{12} +95695.6 q^{13} +(-11040.4 + 265.834i) q^{14} -112589. i q^{15} +(1.04372e6 - 100816. i) q^{16} +2.26205e6 q^{17} +(-40485.1 - 1.68139e6i) q^{18} -1.35682e6i q^{19} +(1.42943e6 - 68876.2i) q^{20} +27802.9 q^{21} +(5.34596e6 - 128722. i) q^{22} +7.72397e6i q^{23} +(-2.63297e6 + 190487. i) q^{24} +1.95312e6 q^{25} +(-73712.7 - 3.06137e6i) q^{26} +8.99135e6i q^{27} +(17008.4 + 352985. i) q^{28} -6.87281e6 q^{29} +(-3.60180e6 + 86725.3i) q^{30} +4.09489e7i q^{31} +(-4.02915e6 - 3.33116e7i) q^{32} -1.34627e7 q^{33} +(-1.74242e6 - 7.23647e7i) q^{34} +482309. i q^{35} +(-5.37578e7 + 2.59030e6i) q^{36} -4.60291e7 q^{37} +(-4.34058e7 + 1.04514e6i) q^{38} +7.70943e6i q^{39} +(-3.30446e6 - 4.56753e7i) q^{40} +1.22306e7 q^{41} +(-21416.1 - 889435. i) q^{42} +2.14512e8i q^{43} +(-8.23580e6 - 1.70922e8i) q^{44} -7.34531e7 q^{45} +(2.47095e8 - 5.94964e6i) q^{46} +1.55391e8i q^{47} +(8.12196e6 + 8.40840e7i) q^{48} +2.82356e8 q^{49} +(-1.50446e6 - 6.24819e7i) q^{50} +1.82235e8i q^{51} +(-9.78788e7 + 4.71625e6i) q^{52} -5.32341e7 q^{53} +(2.87640e8 - 6.92588e6i) q^{54} -2.33543e8i q^{55} +(1.12791e7 - 816010. i) q^{56} +1.09309e8 q^{57} +(5.29401e6 + 2.19866e8i) q^{58} -9.05250e8i q^{59} +(5.54881e6 + 1.15157e8i) q^{60} +7.30533e8 q^{61} +(1.30998e9 - 3.15422e7i) q^{62} -1.81387e7i q^{63} +(-1.06256e9 + 1.54555e8i) q^{64} -1.33739e8 q^{65} +(1.03701e7 + 4.30681e8i) q^{66} -5.67307e8i q^{67} +(-2.31366e9 + 1.11483e8i) q^{68} -6.22259e8 q^{69} +(1.54294e7 - 371514. i) q^{70} -2.07599e9i q^{71} +(1.24274e8 + 1.71776e9i) q^{72} -3.04740e9 q^{73} +(3.54554e7 + 1.47250e9i) q^{74} +1.57348e8i q^{75} +(6.68695e7 + 1.38778e9i) q^{76} +5.76715e7 q^{77} +(2.46630e8 - 5.93845e6i) q^{78} +2.49153e9i q^{79} +(-1.45864e9 + 1.40895e8i) q^{80} +2.37918e9 q^{81} +(-9.42105e6 - 3.91267e8i) q^{82} -6.00897e9i q^{83} +(-2.84372e7 + 1.37023e6i) q^{84} -3.16131e9 q^{85} +(6.86238e9 - 1.65235e8i) q^{86} -5.53687e8i q^{87} +(-5.46157e9 + 3.95128e8i) q^{88} +5.14975e9 q^{89} +(5.65797e7 + 2.34982e9i) q^{90} -3.30257e7i q^{91} +(-3.80667e8 - 7.90018e9i) q^{92} -3.29892e9 q^{93} +(4.97108e9 - 1.19695e8i) q^{94} +1.89622e9i q^{95} +(2.68365e9 - 3.24596e8i) q^{96} +6.01008e9 q^{97} +(-2.17494e8 - 9.03278e9i) q^{98} +8.78308e9i 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 $

$2$	−0.770283	−	31.9907i	−0.0240713	−	0.999710i
$2$	−0.770283	−	31.9907i	−0.0240713	−	0.999710i
$3$			80.5620i			0.331531i	0.986165	+	0.165765i	$0.0530095\pi$
$3$			80.5620i			0.331531i	−0.986165	+	0.165765i	$0.946991\pi$
$4$	−1022.81	+	49.2838i	−0.998841	+	0.0481287i
$5$	−1397.54			−0.447214
$5$	−1397.54			−0.447214
$6$	2577.24	−	62.0555i	0.331435	−	0.00798039i
$7$		−	345.112i		−	0.0205338i	−0.999947	−	0.0102669i	$-0.996732\pi$
$7$		−	345.112i		−	0.0205338i	0.999947	−	0.0102669i	$-0.00326812\pi$
$8$	2364.48	+	32682.6i	0.0721582	+	0.997393i
$9$	52558.8			0.890087
$10$	1076.50	+	44708.4i	0.0107650	+	0.447084i
$11$			167110.i			1.03762i	0.854890	+	0.518810i	$0.173625\pi$
$11$			167110.i			1.03762i	−0.854890	+	0.518810i	$0.826375\pi$
$12$	−3970.40	−	82399.9i	−0.0159562	−	0.331147i
$13$	95695.6			0.257736			0.128868	−	0.991662i	$-0.458866\pi$
$13$	95695.6			0.257736			0.128868	+	0.991662i	$0.458866\pi$
$14$	−11040.4	+	265.834i	−0.0205279	+	0.000494277i
$15$		−	112589.i		−	0.148265i
$16$	1.04372e6	−	100816.i	0.995367	−	0.0961459i
$17$	2.26205e6			1.59315			0.796577	−	0.604537i	$-0.206642\pi$
$17$	2.26205e6			1.59315			0.796577	+	0.604537i	$0.206642\pi$
$18$	−40485.1	−	1.68139e6i	−0.0214256	−	0.889829i
$19$		−	1.35682e6i		−	0.547969i	−0.961734	−	0.273984i	$-0.911658\pi$
$19$		−	1.35682e6i		−	0.547969i	0.961734	−	0.273984i	$-0.0883417\pi$
$20$	1.42943e6	−	68876.2i	0.446695	−	0.0215238i
$21$	27802.9			0.00680760
$22$	5.34596e6	−	128722.i	1.03732	−	0.0249769i
$23$			7.72397e6i			1.20006i	0.799979	+	0.600028i	$0.204844\pi$
$23$			7.72397e6i			1.20006i	−0.799979	+	0.600028i	$0.795156\pi$
$24$	−2.63297e6	+	190487.i	−0.330667	+	0.0239227i
$25$	1.95312e6			0.200000
$26$	−73712.7	−	3.06137e6i	−0.00620406	−	0.257662i
$27$			8.99135e6i			0.626622i
$28$	17008.4	+	352985.i	0.000988267	+	0.0205100i
$29$	−6.87281e6			−0.335077			−0.167538	−	0.985866i	$-0.553582\pi$
$29$	−6.87281e6			−0.335077			−0.167538	+	0.985866i	$0.553582\pi$
$30$	−3.60180e6	+	86725.3i	−0.148222	+	0.00356894i
$31$			4.09489e7i			1.43032i	0.698961	+	0.715160i	$0.253646\pi$
$31$			4.09489e7i			1.43032i	−0.698961	+	0.715160i	$0.746354\pi$
$32$	−4.02915e6	−	3.33116e7i	−0.120078	−	0.992764i
$33$	−1.34627e7			−0.344003
$34$	−1.74242e6	−	7.23647e7i	−0.0383494	−	1.59269i
$35$			482309.i			0.00918300i
$36$	−5.37578e7	+	2.59030e6i	−0.889056	+	0.0428388i
$37$	−4.60291e7			−0.663779			−0.331889	−	0.943318i	$-0.607686\pi$
$37$	−4.60291e7			−0.663779			−0.331889	+	0.943318i	$0.607686\pi$
$38$	−4.34058e7	+	1.04514e6i	−0.547810	+	0.0131903i
$39$			7.70943e6i			0.0854475i
$40$	−3.30446e6	−	4.56753e7i	−0.0322701	−	0.446048i
$41$	1.22306e7			0.105567			0.0527837	−	0.998606i	$-0.483191\pi$
$41$	1.22306e7			0.105567			0.0527837	+	0.998606i	$0.483191\pi$
$42$	−21416.1	−	889435.i	−0.000163868	−	0.00680562i
$43$			2.14512e8i			1.45918i	0.683886	+	0.729589i	$0.260289\pi$
$43$			2.14512e8i			1.45918i	−0.683886	+	0.729589i	$0.739711\pi$
$44$	−8.23580e6	−	1.70922e8i	−0.0499393	−	1.03642i
$45$	−7.34531e7			−0.398059
$46$	2.47095e8	−	5.94964e6i	1.19971	−	0.0288870i
$47$			1.55391e8i			0.677544i	0.940869	+	0.338772i	$0.110012\pi$
$47$			1.55391e8i			0.677544i	−0.940869	+	0.338772i	$0.889988\pi$
$48$	8.12196e6	+	8.40840e7i	0.0318753	+	0.329995i
$49$	2.82356e8			0.999578
$50$	−1.50446e6	−	6.24819e7i	−0.00481427	−	0.199942i
$51$			1.82235e8i			0.528180i
$52$	−9.78788e7	+	4.71625e6i	−0.257438	+	0.0124045i
$53$	−5.32341e7			−0.127295			−0.0636474	−	0.997972i	$-0.520273\pi$
$53$	−5.32341e7			−0.127295			−0.0636474	+	0.997972i	$0.520273\pi$
$54$	2.87640e8	−	6.92588e6i	0.626441	−	0.0150836i
$55$		−	2.33543e8i		−	0.464038i
$56$	1.12791e7	−	816010.i	0.0204803	−	0.00148168i
$57$	1.09309e8			0.181669
$58$	5.29401e6	+	2.19866e8i	0.00806574	+	0.334980i
$59$		−	9.05250e8i		−	1.26622i	−0.774062	−	0.633109i	$-0.781778\pi$
$59$		−	9.05250e8i		−	1.26622i	0.774062	−	0.633109i	$-0.218222\pi$
$60$	5.54881e6	+	1.15157e8i	0.00713581	+	0.148093i
$61$	7.30533e8			0.864950			0.432475	−	0.901646i	$-0.357640\pi$
$61$	7.30533e8			0.864950			0.432475	+	0.901646i	$0.357640\pi$
$62$	1.30998e9	−	3.15422e7i	1.42991	−	0.0344297i
$63$		−	1.81387e7i		−	0.0182769i
$64$	−1.06256e9	+	1.54555e8i	−0.989586	+	0.143940i
$65$	−1.33739e8			−0.115263
$66$	1.03701e7	+	4.30681e8i	0.00828061	+	0.343903i
$67$		−	5.67307e8i		−	0.420188i	−0.977681	−	0.210094i	$-0.932623\pi$
$67$		−	5.67307e8i		−	0.420188i	0.977681	−	0.210094i	$-0.0673770\pi$
$68$	−2.31366e9	+	1.11483e8i	−1.59131	+	0.0766765i
$69$	−6.22259e8			−0.397856
$70$	1.54294e7	−	371514.i	0.00918034	−	0.000221047i
$71$		−	2.07599e9i		−	1.15063i	−0.817934	−	0.575313i	$-0.804880\pi$
$71$		−	2.07599e9i		−	1.15063i	0.817934	−	0.575313i	$-0.195120\pi$
$72$	1.24274e8	+	1.71776e9i	0.0642271	+	0.887767i
$73$	−3.04740e9			−1.46999			−0.734996	−	0.678071i	$-0.762816\pi$
$73$	−3.04740e9			−1.46999			−0.734996	+	0.678071i	$0.762816\pi$
$74$	3.54554e7	+	1.47250e9i	0.0159780	+	0.663587i
$75$			1.57348e8i			0.0663062i
$76$	6.68695e7	+	1.38778e9i	0.0263730	+	0.547334i
$77$	5.76715e7			0.0213063
$78$	2.46630e8	−	5.93845e6i	0.0854228	−	0.00205684i
$79$			2.49153e9i			0.809711i	0.914381	+	0.404855i	$0.132678\pi$
$79$			2.49153e9i			0.809711i	−0.914381	+	0.404855i	$0.867322\pi$
$80$	−1.45864e9	+	1.40895e8i	−0.445142	+	0.0429978i
$81$	2.37918e9			0.682343
$82$	−9.42105e6	−	3.91267e8i	−0.00254115	−	0.105537i
$83$		−	6.00897e9i		−	1.52549i	−0.646699	−	0.762745i	$-0.723851\pi$
$83$		−	6.00897e9i		−	1.52549i	0.646699	−	0.762745i	$-0.276149\pi$
$84$	−2.84372e7	+	1.37023e6i	−0.00679971	+	0.000327641i
$85$	−3.16131e9			−0.712480
$86$	6.86238e9	−	1.65235e8i	1.45876	−	0.0351244i
$87$		−	5.53687e8i		−	0.111088i
$88$	−5.46157e9	+	3.95128e8i	−1.03491	+	0.0748728i
$89$	5.14975e9			0.922223			0.461111	−	0.887342i	$-0.347451\pi$
$89$	5.14975e9			0.922223			0.461111	+	0.887342i	$0.347451\pi$
$90$	5.65797e7	+	2.34982e9i	0.00958182	+	0.397944i
$91$		−	3.30257e7i		−	0.00529231i
$92$	−3.80667e8	−	7.90018e9i	−0.0577572	−	1.19867i
$93$	−3.29892e9			−0.474195
$94$	4.97108e9	−	1.19695e8i	0.677348	−	0.0163094i
$95$			1.89622e9i			0.245059i
$96$	2.68365e9	−	3.24596e8i	0.329132	−	0.0398095i
$97$	6.01008e9			0.699877			0.349938	−	0.936773i	$-0.386203\pi$
$97$	6.01008e9			0.699877			0.349938	+	0.936773i	$0.386203\pi$
$98$	−2.17494e8	−	9.03278e9i	−0.0240612	−	0.999289i
$99$			8.78308e9i			0.923572i
$100$	−1.99768e9	+	9.62575e7i	−0.199768	+	0.00962575i
$101$	1.41252e10			1.34396			0.671980	−	0.740569i	$-0.265444\pi$
$101$	1.41252e10			1.34396			0.671980	+	0.740569i	$0.265444\pi$
$102$	5.82984e9	−	1.40373e8i	0.528027	−	0.0127140i
$103$			1.31381e10i			1.13330i	0.823957	+	0.566652i	$0.191762\pi$
$103$			1.31381e10i			1.13330i	−0.823957	+	0.566652i	$0.808238\pi$
$104$	2.26271e8	+	3.12758e9i	0.0185978	+	0.257064i
$105$	−3.88557e7			−0.00304445
$106$	4.10053e7	+	1.70300e9i	0.00306416	+	0.127258i
$107$			1.84954e10i			1.31870i	0.751836	+	0.659350i	$0.229168\pi$
$107$			1.84954e10i			1.31870i	−0.751836	+	0.659350i	$0.770832\pi$
$108$	−4.43128e8	−	9.19647e9i	−0.0301585	−	0.625896i
$109$	−9.29496e9			−0.604108			−0.302054	−	0.953291i	$-0.597672\pi$
$109$	−9.29496e9			−0.604108			−0.302054	+	0.953291i	$0.597672\pi$
$110$	−7.47121e9	+	1.79894e8i	−0.463903	+	0.0111700i
$111$		−	3.70819e9i		−	0.220063i
$112$	−3.47929e7	−	3.60200e8i	−0.00197424	−	0.0204387i
$113$	−2.83775e10			−1.54021			−0.770107	−	0.637914i	$-0.779797\pi$
$113$	−2.83775e10			−1.54021			−0.770107	+	0.637914i	$0.779797\pi$
$114$	−8.41985e7	−	3.49686e9i	−0.00437301	−	0.181616i
$115$		−	1.07946e10i		−	0.536681i
$116$	7.02960e9	−	3.38718e8i	0.334688	−	0.0161268i
$117$	5.02964e9			0.229408
$118$	−2.89596e10	+	6.97299e8i	−1.26585	+	0.0304796i
$119$		−	7.80661e8i		−	0.0327135i
$120$	3.67969e9	−	2.66214e8i	0.147879	−	0.0106986i
$121$	−1.98821e9			−0.0766543
$122$	−5.62717e8	−	2.33703e10i	−0.0208205	−	0.864699i
$123$			9.85325e8i			0.0349989i
$124$	−2.01812e9	−	4.18830e10i	−0.0688395	−	1.42866i
$125$	−2.72958e9			−0.0894427
$126$	−5.80269e8	+	1.39719e7i	−0.0182716	+	0.000439949i
$127$			2.03618e10i			0.616306i	0.951337	+	0.308153i	$0.0997109\pi$
$127$			2.03618e10i			0.616306i	−0.951337	+	0.308153i	$0.900289\pi$
$128$	5.76279e9	+	3.38730e10i	0.167719	+	0.985835i
$129$	−1.72815e10			−0.483763
$130$	1.03017e8	+	4.27840e9i	0.00277454	+	0.115230i
$131$		−	3.67281e10i		−	0.952010i	−0.879442	−	0.476005i	$-0.842084\pi$
$131$		−	3.67281e10i		−	0.952010i	0.879442	−	0.476005i	$-0.157916\pi$
$132$	1.37698e10	−	6.63493e8i	0.343604	−	0.0165564i
$133$	−4.68256e8			−0.0112519
$134$	−1.81485e10	+	4.36987e8i	−0.420066	+	0.0101145i
$135$		−	1.25658e10i		−	0.280234i
$136$	5.34858e9	+	7.39297e10i	0.114959	+	1.58900i
$137$	3.94095e10			0.816578			0.408289	−	0.912853i	$-0.366126\pi$
$137$	3.94095e10			0.816578			0.408289	+	0.912853i	$0.366126\pi$
$138$	4.79315e8	+	1.99065e10i	0.00957692	+	0.397740i
$139$		−	2.13638e10i		−	0.411723i	−0.978581	−	0.205861i	$-0.934000\pi$
$139$		−	2.13638e10i		−	0.411723i	0.978581	−	0.205861i	$-0.0659996\pi$
$140$	−2.37700e7	−	4.93312e8i	−0.000441966	−	0.00917236i
$141$	−1.25186e10			−0.224627
$142$	−6.64125e10	+	1.59910e9i	−1.15029	+	0.0276971i
$143$			1.59917e10i			0.267432i
$144$	5.48565e10	−	5.29878e9i	0.885964	−	0.0855783i
$145$	9.60504e9			0.149851
$146$	2.34736e9	+	9.74885e10i	0.0353847	+	1.46957i
$147$			2.27472e10i			0.331391i
$148$	4.70791e10	−	2.26849e9i	0.663010	−	0.0319468i
$149$	8.44522e10			1.14995			0.574976	−	0.818170i	$-0.305011\pi$
$149$	8.44522e10			1.14995			0.574976	+	0.818170i	$0.305011\pi$
$150$	5.03367e9	−	1.21202e8i	0.0662870	−	0.00159608i
$151$		−	1.37451e11i		−	1.75091i	−0.483298	−	0.875456i	$-0.660561\pi$
$151$		−	1.37451e11i		−	1.75091i	0.483298	−	0.875456i	$-0.339439\pi$
$152$	4.43445e10	−	3.20819e9i	0.546540	−	0.0395405i
$153$	1.18891e11			1.41805
$154$	−4.44234e7	−	1.84495e9i	−0.000512871	−	0.0213001i
$155$		−	5.72278e10i		−	0.639659i
$156$	−3.79950e8	−	7.88531e9i	−0.00411248	−	0.0853485i
$157$	−1.68284e11			−1.76418			−0.882091	−	0.471079i	$-0.843865\pi$
$157$	−1.68284e11			−1.76418			−0.882091	+	0.471079i	$0.843865\pi$
$158$	7.97057e10	−	1.91918e9i	0.809476	−	0.0194908i
$159$		−	4.28865e9i		−	0.0422022i
$160$	5.63090e9	+	4.65544e10i	0.0537005	+	0.443978i
$161$	2.66563e9			0.0246417
$162$	−1.83264e9	−	7.61117e10i	−0.0164249	−	0.682145i
$163$		−	3.14917e10i		−	0.273689i	−0.990593	−	0.136845i	$-0.956304\pi$
$163$		−	3.14917e10i		−	0.273689i	0.990593	−	0.136845i	$-0.0436961\pi$
$164$	−1.25097e10	+	6.02772e8i	−0.105445	+	0.00508082i
$165$	1.88147e10			0.153843
$166$	−1.92231e11	+	4.62861e9i	−1.52505	+	0.0367206i
$167$			9.91909e10i			0.763642i	0.924236	+	0.381821i	$0.124703\pi$
$167$			9.91909e10i			0.763642i	−0.924236	+	0.381821i	$0.875297\pi$
$168$	6.57395e7	+	9.08671e8i	0.000491224	+	0.00678985i
$169$	−1.28701e11			−0.933572
$170$	2.43511e9	+	1.01133e11i	0.0171504	+	0.712274i
$171$		−	7.13130e10i		−	0.487740i
$172$	−1.05720e10	−	2.19405e11i	−0.0702284	−	1.45749i
$173$	1.01217e10			0.0653166			0.0326583	−	0.999467i	$-0.489603\pi$
$173$	1.01217e10			0.0653166			0.0326583	+	0.999467i	$0.489603\pi$
$174$	−1.77129e10	+	4.26496e8i	−0.111056	+	0.00267404i
$175$		−	6.74047e8i		−	0.00410676i
$176$	1.68474e10	+	1.74415e11i	0.0997629	+	1.03281i
$177$	7.29288e10			0.419791
$178$	−3.96676e9	−	1.64744e11i	−0.0221991	−	0.921956i
$179$			2.93205e11i			1.59553i	0.602966	+	0.797767i	$0.293985\pi$
$179$			2.93205e11i			1.59553i	−0.602966	+	0.797767i	$0.706015\pi$
$180$	7.51288e10	−	3.62005e9i	0.397598	−	0.0191581i
$181$	−2.98370e11			−1.53590			−0.767949	−	0.640511i	$-0.778723\pi$
$181$	−2.98370e11			−1.53590			−0.767949	+	0.640511i	$0.778723\pi$
$182$	−1.05652e9	+	2.54391e7i	−0.00529077	+	0.000127393i
$183$			5.88532e10i			0.286758i
$184$	−2.52439e11	+	1.82632e10i	−1.19693	+	0.0865939i
$185$	6.43276e10			0.296851
$186$	2.54110e9	+	1.05535e11i	0.0114145	+	0.474058i
$187$			3.78011e11i			1.65309i
$188$	−7.65828e9	−	1.58936e11i	−0.0326093	−	0.676759i
$189$	3.10302e9			0.0128670
$190$	6.06615e10	−	1.46063e9i	0.244988	−	0.00589890i
$191$		−	4.51966e11i		−	1.77803i	−0.457880	−	0.889014i	$-0.651391\pi$
$191$		−	4.51966e11i		−	1.77803i	0.457880	−	0.889014i	$-0.348609\pi$
$192$	−1.24512e10	−	8.56020e10i	−0.0477207	−	0.328079i
$193$	2.81708e11			1.05199			0.525996	−	0.850487i	$-0.323693\pi$
$193$	2.81708e11			1.05199			0.525996	+	0.850487i	$0.323693\pi$
$194$	−4.62946e9	−	1.92267e11i	−0.0168470	−	0.699674i
$195$		−	1.07743e10i		−	0.0382133i
$196$	−2.88798e11	+	1.39156e10i	−0.998420	+	0.0481084i
$197$	−1.40740e11			−0.474336			−0.237168	−	0.971469i	$-0.576219\pi$
$197$	−1.40740e11			−0.474336			−0.237168	+	0.971469i	$0.576219\pi$
$198$	2.80977e11	−	6.76545e9i	0.923304	−	0.0222316i
$199$			4.94062e11i			1.58313i	0.611087	+	0.791564i	$0.290733\pi$
$199$			4.94062e11i			1.58313i	−0.611087	+	0.791564i	$0.709267\pi$
$200$	4.61813e9	+	6.38332e10i	0.0144316	+	0.199479i
$201$	4.57034e10			0.139305
$202$	−1.08804e10	−	4.51874e11i	−0.0323509	−	1.34357i
$203$			2.37189e9i			0.00688040i
$204$	−8.98126e9	−	1.86393e11i	−0.0254206	−	0.527568i
$205$	−1.70928e10			−0.0472112
$206$	4.20297e11	−	1.01201e10i	1.13298	−	0.0272801i
$207$			4.05962e11i			1.06815i
$208$	9.98793e10	−	9.64768e9i	0.256542	−	0.0247803i
$209$	2.26739e11			0.568583
$210$	2.99299e7	+	1.24302e9i	7.32840e−5	+	0.00304357i
$211$		−	3.76526e11i		−	0.900291i	−0.892955	−	0.450146i	$-0.851372\pi$
$211$		−	3.76526e11i		−	0.900291i	0.892955	−	0.450146i	$-0.148628\pi$
$212$	5.44486e10	−	2.62358e9i	0.127147	−	0.00612654i
$213$	1.67246e11			0.381468
$214$	5.91683e11	−	1.42467e10i	1.31832	−	0.0317429i
$215$		−	2.99789e11i		−	0.652564i
$216$	−2.93860e11	+	2.12599e10i	−0.624989	+	0.0452160i
$217$	1.41319e10			0.0293699
$218$	7.15975e9	+	2.97352e11i	0.0145417	+	0.603933i
$219$		−	2.45505e11i		−	0.487348i
$220$	1.15099e10	+	2.38871e11i	0.0223335	+	0.463500i
$221$	2.16468e11			0.410614
$222$	−1.18628e11	+	2.85636e9i	−0.219999	+	0.00529722i
$223$			1.01270e11i			0.183636i	0.995776	+	0.0918178i	$0.0292677\pi$
$223$			1.01270e11i			0.183636i	−0.995776	+	0.0918178i	$0.970732\pi$
$224$	−1.14962e10	+	1.39051e9i	−0.0203852	+	0.00246566i
$225$	1.02654e11			0.178017
$226$	2.18587e10	+	9.07816e11i	0.0370750	+	1.53977i
$227$			6.65566e10i			0.110424i	0.998475	+	0.0552118i	$0.0175834\pi$
$227$			6.65566e10i			0.110424i	−0.998475	+	0.0552118i	$0.982417\pi$
$228$	−1.11802e11	+	5.38714e9i	−0.181458	+	0.00874348i
$229$	−3.57386e11			−0.567492			−0.283746	−	0.958900i	$-0.591577\pi$
$229$	−3.57386e11			−0.567492			−0.283746	+	0.958900i	$0.591577\pi$
$230$	−3.45326e11	+	8.31488e9i	−0.536526	+	0.0129186i
$231$			4.64613e9i			0.00706369i
$232$	−1.62506e10	−	2.24621e11i	−0.0241785	−	0.334203i
$233$	−5.97154e11			−0.869574			−0.434787	−	0.900533i	$-0.643176\pi$
$233$	−5.97154e11			−0.869574			−0.434787	+	0.900533i	$0.643176\pi$
$234$	−3.87425e9	−	1.60902e11i	−0.00552215	−	0.229341i
$235$		−	2.17166e11i		−	0.303007i
$236$	4.46142e10	+	9.25902e11i	0.0609415	+	1.26475i
$237$	−2.00722e11			−0.268444
$238$	−2.49739e10	+	6.01330e8i	−0.0327041	+	0.000787459i
$239$		−	1.11084e12i		−	1.42450i	−0.701928	−	0.712248i	$-0.747677\pi$
$239$		−	1.11084e12i		−	1.42450i	0.701928	−	0.712248i	$-0.252323\pi$
$240$	−1.13508e10	−	1.17511e11i	−0.0142551	−	0.147578i
$241$	3.11125e11			0.382692			0.191346	−	0.981523i	$-0.438715\pi$
$241$	3.11125e11			0.382692			0.191346	+	0.981523i	$0.438715\pi$
$242$	1.53149e9	+	6.36044e10i	0.00184517	+	0.0766321i
$243$			7.22602e11i			0.852840i
$244$	−7.47199e11	+	3.60035e10i	−0.863947	+	0.0416289i
$245$	−3.94605e11			−0.447025
$246$	3.15213e10	−	7.58979e8i	0.0349887	−	0.000842469i
$247$		−	1.29842e11i		−	0.141231i
$248$	−1.33831e12	+	9.68228e10i	−1.42659	+	0.103209i
$249$	4.84095e11			0.505747
$250$	2.10255e9	+	8.73211e10i	0.00215301	+	0.0894168i
$251$		−	1.51632e12i		−	1.52203i	−0.648737	−	0.761013i	$-0.724702\pi$
$251$		−	1.51632e12i		−	1.52203i	0.648737	−	0.761013i	$-0.275298\pi$
$252$	8.93942e8	+	1.85525e10i	0.000879644	+	0.0182557i
$253$	−1.29075e12			−1.24520
$254$	6.51387e11	−	1.56843e10i	0.616128	−	0.0148353i
$255$		−	2.54682e11i		−	0.236209i
$256$	1.07918e12	−	2.10448e11i	0.981512	−	0.191401i
$257$	1.58328e12			1.41219			0.706094	−	0.708118i	$-0.250456\pi$
$257$	1.58328e12			1.41219			0.706094	+	0.708118i	$0.250456\pi$
$258$	1.33116e10	+	5.52847e11i	0.0116448	+	0.483623i
$259$			1.58852e10i			0.0136299i
$260$	1.36790e11	−	6.59116e9i	0.115130	−	0.00554747i
$261$	−3.61226e11			−0.298247
$262$	−1.17496e12	+	2.82910e10i	−0.951735	+	0.0229162i
$263$		−	1.48239e12i		−	1.17810i	−0.808095	−	0.589052i	$-0.799501\pi$
$263$		−	1.48239e12i		−	1.17810i	0.808095	−	0.589052i	$-0.200499\pi$
$264$	−3.18323e10	−	4.39996e11i	−0.0248226	−	0.343106i
$265$	7.43969e10			0.0569280
$266$	3.60690e8	+	1.49799e10i	0.000270848	+	0.0112486i
$267$			4.14874e11i			0.305745i
$268$	2.79590e10	+	5.80249e11i	0.0202231	+	0.419701i
$269$	−1.75617e12			−1.24682			−0.623411	−	0.781895i	$-0.714254\pi$
$269$	−1.75617e12			−1.24682			−0.623411	+	0.781895i	$0.714254\pi$
$270$	−4.01989e11	+	9.67921e9i	−0.280153	+	0.00674561i
$271$			1.83455e12i			1.25512i	0.778570	+	0.627558i	$0.215945\pi$
$271$			1.83455e12i			1.25512i	−0.778570	+	0.627558i	$0.784055\pi$
$272$	2.36094e12	−	2.28052e11i	1.58577	−	0.153175i
$273$	2.66062e9			0.00175456
$274$	−3.03564e10	−	1.26074e12i	−0.0196561	−	0.816341i
$275$			3.26386e11i			0.207524i
$276$	6.36455e11	−	3.06673e10i	0.397395	−	0.0191483i
$277$	5.98846e11			0.367212			0.183606	−	0.983000i	$-0.441223\pi$
$277$	5.98846e11			0.367212			0.183606	+	0.983000i	$0.441223\pi$
$278$	−6.83444e11	+	1.64562e10i	−0.411603	+	0.00991071i
$279$			2.15222e12i			1.27311i
$280$	−1.57631e10	+	1.14041e9i	−0.00915906	+	0.000662629i
$281$	2.81093e12			1.60442			0.802211	−	0.597040i	$-0.203657\pi$
$281$	2.81093e12			1.60442			0.802211	+	0.597040i	$0.203657\pi$
$282$	9.64289e9	+	4.00480e11i	0.00540707	+	0.224562i
$283$			5.79586e11i			0.319290i	0.987174	+	0.159645i	$0.0510350\pi$
$283$			5.79586e11i			0.319290i	−0.987174	+	0.159645i	$0.948965\pi$
$284$	1.02313e11	+	2.12335e12i	0.0553781	+	1.14929i
$285$	−1.52763e11			−0.0812447
$286$	5.11585e11	−	1.23181e10i	0.267355	−	0.00643745i
$287$		−	4.22094e9i		−	0.00216770i
$288$	−2.11767e11	−	1.75082e12i	−0.106880	−	0.883647i
$289$	3.10088e12			1.53814
$290$	−7.39860e9	−	3.07272e11i	−0.00360711	−	0.149807i
$291$			4.84184e11i			0.232031i
$292$	3.11692e12	−	1.50187e11i	1.46829	−	0.0707489i
$293$	−1.72641e12			−0.799479			−0.399739	−	0.916629i	$-0.630899\pi$
$293$	−1.72641e12			−0.799479			−0.399739	+	0.916629i	$0.630899\pi$
$294$	7.27699e11	−	1.75218e10i	0.331295	−	0.00797703i
$295$			1.26513e12i			0.566270i
$296$	−1.08835e11	−	1.50435e12i	−0.0478971	−	0.662048i
$297$	−1.50254e12			−0.650196
$298$	−6.50521e10	−	2.70169e12i	−0.0276809	−	1.14962i
$299$			7.39150e11i			0.309298i
$300$	−7.75470e9	−	1.60937e11i	−0.00319123	−	0.0662293i
$301$	7.40305e10			0.0299625
$302$	−4.39717e12	+	1.05876e11i	−1.75040	+	0.0421468i
$303$			1.13795e12i			0.445564i
$304$	−1.36790e11	−	1.41614e12i	−0.0526850	−	0.545430i
$305$	−1.02095e12			−0.386817
$306$	−9.15794e10	−	3.80340e12i	−0.0341343	−	1.41764i
$307$		−	1.35975e12i		−	0.498616i	−0.968424	−	0.249308i	$-0.919797\pi$
$307$		−	1.35975e12i		−	0.498616i	0.968424	−	0.249308i	$-0.0802032\pi$
$308$	−5.89872e10	+	2.84227e9i	−0.0212816	+	0.00102544i
$309$	−1.05843e12			−0.375725
$310$	−1.83076e12	+	4.40816e10i	−0.639473	+	0.0153974i
$311$			3.21142e11i			0.110381i	0.998476	+	0.0551906i	$0.0175767\pi$
$311$			3.21142e11i			0.110381i	−0.998476	+	0.0551906i	$0.982423\pi$
$312$	−2.51964e11	+	1.82288e10i	−0.0852248	+	0.00616574i
$313$	2.93115e12			0.975700			0.487850	−	0.872927i	$-0.337781\pi$
$313$	2.93115e12			0.975700			0.487850	+	0.872927i	$0.337781\pi$
$314$	1.29626e11	+	5.38351e12i	0.0424662	+	1.76367i
$315$			2.53495e10i			0.00817367i
$316$	−1.22792e11	−	2.54837e12i	−0.0389704	−	0.808773i
$317$	−2.71023e12			−0.846663			−0.423331	−	0.905975i	$-0.639139\pi$
$317$	−2.71023e12			−0.846663			−0.423331	+	0.905975i	$0.639139\pi$
$318$	−1.37197e11	+	3.30347e9i	−0.0421899	+	0.00101586i
$319$		−	1.14851e12i		−	0.347682i
$320$	1.48497e12	−	2.15997e11i	0.442556	−	0.0643720i
$321$	−1.49003e12			−0.437190
$322$	−2.05329e9	−	8.52756e10i	−0.000593159	−	0.0246346i
$323$		−	3.06921e12i		−	0.872999i
$324$	−2.43346e12	+	1.17255e11i	−0.681552	+	0.0328403i
$325$	1.86906e11			0.0515472
$326$	−1.00744e12	+	2.42575e10i	−0.273610	+	0.00658807i
$327$		−	7.48821e11i		−	0.200281i
$328$	2.89191e10	+	3.99729e11i	0.00761756	+	0.105292i
$329$	5.36274e10			0.0139126
$330$	−1.44926e10	−	6.01895e11i	−0.00370320	−	0.153798i
$331$			7.47010e12i			1.88012i	0.341003	+	0.940062i	$0.389233\pi$
$331$			7.47010e12i			1.88012i	−0.341003	+	0.940062i	$0.610767\pi$
$332$	2.96145e11	+	6.14605e12i	0.0734199	+	1.52372i
$333$	−2.41923e12			−0.590821
$334$	3.17319e12	−	7.64051e10i	0.763420	−	0.0183819i
$335$			7.92835e11i			0.187914i
$336$	2.90184e10	−	2.80299e9i	0.00677606	−	0.000654523i
$337$	2.36492e12			0.544085			0.272043	−	0.962285i	$-0.412301\pi$
$337$	2.36492e12			0.544085			0.272043	+	0.962285i	$0.412301\pi$
$338$	9.91361e10	+	4.11723e12i	0.0224723	+	0.933302i
$339$		−	2.28615e12i		−	0.510629i
$340$	3.23343e12	−	1.55802e11i	0.711655	−	0.0342908i
$341$	−6.84295e12			−1.48413
$342$	−2.28136e12	+	5.49312e10i	−0.487599	+	0.0117406i
$343$		−	1.94930e11i		−	0.0410590i
$344$	−7.01079e12	+	5.07209e11i	−1.45537	+	0.105292i
$345$	8.69633e11			0.177926
$346$	−7.79658e9	−	3.23801e11i	−0.00157226	−	0.0652976i
$347$		−	8.77595e12i		−	1.74440i	−0.489147	−	0.872201i	$-0.662692\pi$
$347$		−	8.77595e12i		−	1.74440i	0.489147	−	0.872201i	$-0.337308\pi$
$348$	2.72878e10	+	5.66319e11i	0.00534654	+	0.110960i
$349$	−9.81518e11			−0.189571			−0.0947853	−	0.995498i	$-0.530216\pi$
$349$	−9.81518e11			−0.189571			−0.0947853	+	0.995498i	$0.530216\pi$
$350$	−2.15632e10	+	5.19207e8i	−0.00410557	+	9.88553e-5i
$351$			8.60433e11i			0.161503i
$352$	5.56670e12	−	6.73309e11i	1.03011	−	0.124595i
$353$	8.89401e12			1.62265			0.811324	−	0.584597i	$-0.198747\pi$
$353$	8.89401e12			1.62265			0.811324	+	0.584597i	$0.198747\pi$
$354$	−5.61758e10	−	2.33305e12i	−0.0101049	−	0.419669i
$355$			2.90129e12i			0.514575i
$356$	−5.26723e12	+	2.53799e11i	−0.921154	+	0.0443854i
$357$	6.28916e10			0.0108456
$358$	9.37984e12	−	2.25851e11i	1.59507	−	0.0384066i
$359$		−	8.74192e12i		−	1.46600i	−0.680228	−	0.733001i	$-0.738119\pi$
$359$		−	8.74192e12i		−	1.46600i	0.680228	−	0.733001i	$-0.261881\pi$
$360$	−1.73678e11	−	2.40064e12i	−0.0287232	−	0.397021i
$361$	4.29009e12			0.699730
$362$	2.29829e11	+	9.54508e12i	0.0369711	+	1.53545i
$363$		−	1.60175e11i		−	0.0254133i
$364$	1.62763e9	+	3.37791e10i	0.000254712	+	0.00528618i
$365$	4.25887e12			0.657401
$366$	1.88276e12	−	4.53336e10i	0.286674	−	0.00690264i
$367$		−	1.06875e13i		−	1.60526i	−0.596478	−	0.802629i	$-0.703434\pi$
$367$		−	1.06875e13i		−	1.60526i	0.596478	−	0.802629i	$-0.296566\pi$
$368$	7.78702e11	+	8.06165e12i	0.115380	+	1.19450i
$369$	6.42827e11			0.0939642
$370$	−4.95504e10	−	2.05789e12i	−0.00714560	−	0.296765i
$371$			1.83717e10i			0.00261385i
$372$	3.37418e12	−	1.62584e11i	0.473646	−	0.0228224i
$373$	1.48573e12			0.205776			0.102888	−	0.994693i	$-0.467192\pi$
$373$	1.48573e12			0.205776			0.102888	+	0.994693i	$0.467192\pi$
$374$	1.20928e13	−	2.91175e11i	1.65261	−	0.0397920i
$375$		−	2.19900e11i		−	0.0296530i
$376$	−5.07859e12	+	3.67420e11i	−0.675778	+	0.0488904i
$377$	−6.57698e11			−0.0863614
$378$	−2.39020e9	−	9.92679e10i	−0.000309725	−	0.0128632i
$379$		−	4.09611e12i		−	0.523812i	−0.965093	−	0.261906i	$-0.915649\pi$
$379$		−	4.09611e12i		−	0.523812i	0.965093	−	0.261906i	$-0.0843511\pi$
$380$	−9.34530e10	−	1.93948e12i	−0.0117944	−	0.244775i
$381$	−1.64038e12			−0.204325
$382$	−1.44587e13	+	3.48141e11i	−1.77751	+	0.0427995i
$383$			1.17512e12i			0.142590i	0.997455	+	0.0712951i	$0.0227132\pi$
$383$			1.17512e12i			0.142590i	−0.997455	+	0.0712951i	$0.977287\pi$
$384$	−2.72888e12	+	4.64262e11i	−0.326835	+	0.0556041i
$385$	−8.05984e10			−0.00952846
$386$	−2.16995e11	−	9.01204e12i	−0.0253229	−	1.05169i
$387$			1.12745e13i			1.29880i
$388$	−6.14719e12	+	2.96200e11i	−0.699065	+	0.0336842i
$389$	−1.60662e12			−0.180370			−0.0901851	−	0.995925i	$-0.528746\pi$
$389$	−1.60662e12			−0.180370			−0.0901851	+	0.995925i	$0.528746\pi$
$390$	−3.44676e11	+	8.29923e9i	−0.0382022	+	0.000919845i
$391$			1.74720e13i			1.91187i
$392$	6.67626e11	+	9.22813e12i	0.0721278	+	0.996973i
$393$	2.95889e12			0.315621
$394$	1.08410e11	+	4.50237e12i	0.0114179	+	0.474199i
$395$		−	3.48201e12i		−	0.362114i
$396$	−4.32864e11	−	8.98345e12i	−0.0444503	−	0.922502i
$397$	−6.57304e12			−0.666521			−0.333261	−	0.942835i	$-0.608149\pi$
$397$	−6.57304e12			−0.666521			−0.333261	+	0.942835i	$0.608149\pi$
$398$	1.58054e13	−	3.80567e11i	1.58267	−	0.0381080i
$399$		−	3.77237e10i		−	0.00373035i
$400$	2.03851e12	−	1.96907e11i	0.199073	−	0.0192292i
$401$	−1.11148e13			−1.07196			−0.535980	−	0.844231i	$-0.680058\pi$
$401$	−1.11148e13			−1.07196			−0.535980	+	0.844231i	$0.680058\pi$
$402$	−3.52045e10	−	1.46208e12i	−0.00335327	−	0.139265i
$403$			3.91863e12i			0.368645i
$404$	−1.44474e13	+	6.96142e11i	−1.34240	+	0.0646831i
$405$	−3.32501e12			−0.305153
$406$	7.58784e10	−	1.82702e9i	0.00687841	−	0.000165621i
$407$		−	7.69190e12i		−	0.688750i
$408$	−5.95592e12	+	4.30892e11i	−0.526803	+	0.0381125i
$409$	−1.05269e12			−0.0919783			−0.0459892	−	0.998942i	$-0.514644\pi$
$409$	−1.05269e12			−0.0919783			−0.0459892	+	0.998942i	$0.514644\pi$
$410$	1.31663e10	+	5.46812e11i	0.00113644	+	0.0471975i
$411$			3.17491e12i			0.270721i
$412$	−6.47496e11	−	1.34378e13i	−0.0545445	−	1.13199i
$413$	−3.12413e11			−0.0260003
$414$	1.29870e13	−	3.12706e11i	1.06784	−	0.0257119i
$415$			8.39779e12i			0.682220i
$416$	−3.85572e11	−	3.18778e12i	−0.0309484	−	0.255871i
$417$	1.72111e12			0.136499
$418$	−1.74653e11	−	7.25353e12i	−0.0136866	−	0.568418i
$419$			4.96270e12i			0.384280i	0.981368	+	0.192140i	$0.0615428\pi$
$419$			4.96270e12i			0.384280i	−0.981368	+	0.192140i	$0.938457\pi$
$420$	3.97422e10	−	1.91496e9i	0.00304092	−	0.000146525i
$421$	−4.69126e12			−0.354715			−0.177357	−	0.984147i	$-0.556755\pi$
$421$	−4.69126e12			−0.354715			−0.177357	+	0.984147i	$0.556755\pi$
$422$	−1.20454e13	+	2.90032e11i	−0.900031	+	0.0216712i
$423$			8.16717e12i			0.603073i
$424$	−1.25871e11	−	1.73983e12i	−0.00918537	−	0.126963i
$425$	4.41807e12			0.318631
$426$	−1.28827e11	−	5.35032e12i	−0.00918244	−	0.381357i
$427$		−	2.52116e11i		−	0.0177607i
$428$	−9.11526e11	−	1.89174e13i	−0.0634673	−	1.31717i
$429$	−1.28832e12			−0.0886620
$430$	−9.59047e12	+	2.30922e11i	−0.652375	+	0.0157081i
$431$		−	9.67981e12i		−	0.650849i	−0.945568	−	0.325425i	$-0.894493\pi$
$431$		−	9.67981e12i		−	0.650849i	0.945568	−	0.325425i	$-0.105507\pi$
$432$	9.06474e11	+	9.38443e12i	0.0602472	+	0.623719i
$433$	−1.28911e13			−0.846936			−0.423468	−	0.905911i	$-0.639187\pi$
$433$	−1.28911e13			−0.846936			−0.423468	+	0.905911i	$0.639187\pi$
$434$	−1.08856e10	−	4.52091e11i	−0.000706974	−	0.0293614i
$435$			7.73801e11i			0.0496802i
$436$	9.50701e12	−	4.58091e11i	0.603408	−	0.0290750i
$437$	1.04801e13			0.657593
$438$	−7.85387e12	+	1.89108e11i	−0.487207	+	0.0117311i
$439$			1.54725e13i			0.948936i	0.880273	+	0.474468i	$0.157360\pi$
$439$			1.54725e13i			0.948936i	−0.880273	+	0.474468i	$0.842640\pi$
$440$	7.63278e12	−	5.52208e11i	0.462828	−	0.0334841i
$441$	1.48403e13			0.889712
$442$	−1.66742e11	−	6.92498e12i	−0.00988402	−	0.410495i
$443$		−	1.43716e13i		−	0.842340i	−0.906982	−	0.421170i	$-0.861620\pi$
$443$		−	1.43716e13i		−	0.842340i	0.906982	−	0.421170i	$-0.138380\pi$
$444$	1.82754e11	+	3.79279e12i	0.0105914	+	0.219808i
$445$	−7.19699e12			−0.412431
$446$	3.23970e12	−	7.80066e10i	0.183582	−	0.00442036i
$447$			6.80364e12i			0.381245i
$448$	5.33387e10	+	3.66702e11i	0.00295564	+	0.0203200i
$449$	1.18428e12			0.0648967			0.0324484	−	0.999473i	$-0.489670\pi$
$449$	1.18428e12			0.0648967			0.0324484	+	0.999473i	$0.489670\pi$
$450$	−7.90725e10	−	3.28397e12i	−0.00428512	−	0.177966i
$451$			2.04386e12i			0.109539i
$452$	2.90248e13	−	1.39855e12i	1.53843	−	0.0741286i
$453$	1.10734e13			0.580481
$454$	2.12919e12	−	5.12674e10i	0.110392	−	0.00265804i
$455$			4.61548e10i			0.00236679i
$456$	2.58458e11	+	3.57249e12i	0.0131089	+	0.181195i
$457$	9.05816e12			0.454422			0.227211	−	0.973846i	$-0.427039\pi$
$457$	9.05816e12			0.454422			0.227211	+	0.973846i	$0.427039\pi$
$458$	2.75288e11	+	1.14330e13i	0.0136603	+	0.567327i
$459$			2.03389e13i			0.998306i
$460$	5.31998e11	+	1.10408e13i	0.0258298	+	0.536059i
$461$	3.36386e13			1.61560			0.807800	−	0.589457i	$-0.200658\pi$
$461$	3.36386e13			1.61560			0.807800	+	0.589457i	$0.200658\pi$
$462$	1.48633e11	−	3.57884e9i	0.00706165	−	0.000170033i
$463$		−	2.11734e13i		−	0.995143i	−0.867423	−	0.497572i	$-0.834225\pi$
$463$		−	2.11734e13i		−	0.995143i	0.867423	−	0.497572i	$-0.165775\pi$
$464$	−7.17327e12	+	6.92891e11i	−0.333524	+	0.0322162i
$465$	4.61038e12			0.212067
$466$	4.59977e11	+	1.91034e13i	0.0209318	+	0.869322i
$467$			1.26794e13i			0.570838i	0.958403	+	0.285419i	$0.0921328\pi$
$467$			1.26794e13i			0.570838i	−0.958403	+	0.285419i	$0.907867\pi$
$468$	−5.14439e12	+	2.47880e11i	−0.229142	+	0.0110411i
$469$	−1.95784e11			−0.00862807
$470$	−6.94730e12	+	1.67279e11i	−0.302919	+	0.00729378i
$471$		−	1.35573e13i		−	0.584881i
$472$	2.95859e13	−	2.14045e12i	1.26292	−	0.0913681i
$473$	−3.58470e13			−1.51407
$474$	1.54613e11	+	6.42126e12i	0.00646181	+	0.268366i
$475$		−	2.65005e12i		−	0.109594i
$476$	3.84739e10	+	7.98470e11i	0.00157446	+	0.0326756i
$477$	−2.79792e12			−0.113303
$478$	−3.55365e13	+	8.55660e11i	−1.42408	+	0.0342895i
$479$		−	1.62583e13i		−	0.644760i	−0.946610	−	0.322380i	$-0.895517\pi$
$479$		−	1.62583e13i		−	0.644760i	0.946610	−	0.322380i	$-0.104483\pi$
$480$	−3.75052e12	+	4.53637e11i	−0.147192	+	0.0178034i
$481$	−4.40478e12			−0.171080
$482$	−2.39654e11	−	9.95311e12i	−0.00921191	−	0.382581i
$483$			2.14749e11i			0.00816950i
$484$	2.03357e12	−	9.79868e10i	0.0765655	−	0.00368927i
$485$	−8.39934e12			−0.312994
$486$	2.31166e13	−	5.56608e11i	0.852593	−	0.0205290i
$487$		−	1.15134e13i		−	0.420300i	−0.977669	−	0.210150i	$-0.932605\pi$
$487$		−	1.15134e13i		−	0.420300i	0.977669	−	0.210150i	$-0.0673952\pi$
$488$	1.72733e12	+	2.38757e13i	0.0624132	+	0.862695i
$489$	2.53703e12			0.0907364
$490$	3.03957e11	+	1.26237e13i	0.0107605	+	0.446896i
$491$		−	4.44463e13i		−	1.55750i	−0.627334	−	0.778750i	$-0.715854\pi$
$491$		−	4.44463e13i		−	1.55750i	0.627334	−	0.778750i	$-0.284146\pi$
$492$	−4.85606e10	−	1.00780e12i	−0.00168445	−	0.0349583i
$493$	−1.55466e13			−0.533829
$494$	−4.15375e12	+	1.00015e11i	−0.141190	+	0.00339963i
$495$		−	1.22747e13i		−	0.413034i
$496$	4.12831e12	+	4.27391e13i	0.137519	+	1.42369i
$497$	−7.16449e11			−0.0236267
$498$	−3.72890e11	−	1.54865e13i	−0.0121740	−	0.505601i
$499$		−	3.66572e13i		−	1.18483i	−0.805633	−	0.592415i	$-0.798175\pi$
$499$		−	3.66572e13i		−	1.18483i	0.805633	−	0.592415i	$-0.201825\pi$
$500$	2.79185e12	−	1.34524e11i	0.0893391	−	0.00430476i
$501$	−7.99102e12			−0.253171
$502$	−4.85081e13	+	1.16799e12i	−1.52158	+	0.0366372i
$503$			2.14439e13i			0.665983i	0.942930	+	0.332991i	$0.108058\pi$
$503$			2.14439e13i			0.665983i	−0.942930	+	0.332991i	$0.891942\pi$
$504$	5.92818e11	−	4.28885e10i	0.0182292	−	0.00131883i
$505$	−1.97405e13			−0.601037
$506$	9.94243e11	+	4.12920e13i	0.0299737	+	1.24484i
$507$		−	1.03684e13i		−	0.309508i
$508$	−1.00351e12	−	2.08263e13i	−0.0296620	−	0.615592i
$509$	2.89310e13			0.846788			0.423394	−	0.905946i	$-0.360839\pi$
$509$	2.89310e13			0.846788			0.423394	+	0.905946i	$0.360839\pi$
$510$	−8.14745e12	+	1.96177e11i	−0.236141	+	0.00568587i
$511$			1.05169e12i			0.0301846i
$512$	−7.56365e12	−	3.43618e13i	−0.214972	−	0.976620i
$513$	1.21997e13			0.343370
$514$	−1.21957e12	−	5.06503e13i	−0.0339933	−	1.41178i
$515$		−	1.83611e13i		−	0.506829i
$516$	1.76757e13	−	8.51698e11i	0.483202	−	0.0232829i
$517$	−2.59674e13			−0.703033
$518$	5.08178e11	−	1.22361e10i	0.0136260	−	0.000328090i
$519$			8.15425e11i			0.0216545i
$520$	−3.16223e11	−	4.37093e12i	−0.00831718	−	0.114963i
$521$	−4.43463e12			−0.115523			−0.0577616	−	0.998330i	$-0.518396\pi$
$521$	−4.43463e12			−0.115523			−0.0577616	+	0.998330i	$0.518396\pi$
$522$	2.78246e11	+	1.15559e13i	0.00717922	+	0.298161i
$523$			4.05278e13i			1.03573i	0.855464	+	0.517863i	$0.173272\pi$
$523$			4.05278e13i			1.03573i	−0.855464	+	0.517863i	$0.826728\pi$
$524$	1.81010e12	+	3.75660e13i	0.0458191	+	0.950907i
$525$	5.43026e10			0.00136152
$526$	−4.74227e13	+	1.14186e12i	−1.17776	+	0.0283586i
$527$			9.26284e13i			2.27872i
$528$	−1.40513e13	+	1.35726e12i	−0.342409	+	0.0330745i
$529$	−1.82332e13			−0.440134
$530$	−5.73067e10	−	2.38001e12i	−0.00137033	−	0.0569115i
$531$		−	4.75788e13i		−	1.12704i
$532$	4.78939e11	−	2.30775e10i	0.0112389	−	0.000541539i
$533$	1.17042e12			0.0272085
$534$	1.32721e13	−	3.19570e11i	0.305657	−	0.00735970i
$535$		−	2.58482e13i		−	0.589740i
$536$	1.85410e13	−	1.34139e12i	0.419093	−	0.0303200i
$537$	−2.36212e13			−0.528969
$538$	1.35275e12	+	5.61810e13i	0.0300127	+	1.24646i
$539$			4.71844e13i			1.03718i
$540$	6.19290e11	+	1.28525e13i	0.0134873	+	0.279909i
$541$	4.05839e13			0.875725			0.437863	−	0.899042i	$-0.355736\pi$
$541$	4.05839e13			0.875725			0.437863	+	0.899042i	$0.355736\pi$
$542$	5.86887e13	−	1.41312e12i	1.25475	−	0.0302123i
$543$		−	2.40373e13i		−	0.509198i
$544$	−9.11413e12	−	7.53527e13i	−0.191303	−	1.58163i
$545$	1.29901e13			0.270166
$546$	−2.04943e9	−	8.51151e10i	−4.22347e−5	−	0.00175406i
$547$			4.17118e13i			0.851769i	0.904777	+	0.425885i	$0.140037\pi$
$547$			4.17118e13i			0.851769i	−0.904777	+	0.425885i	$0.859963\pi$
$548$	−4.03085e13	+	1.94225e12i	−0.815632	+	0.0393009i
$549$	3.83959e13			0.769881
$550$	1.04413e13	−	2.51410e11i	0.207464	−	0.00499538i
$551$			9.32520e12i			0.183612i
$552$	−1.47132e12	−	2.03370e13i	−0.0287086	−	0.396819i
$553$	8.59855e11			0.0166265
$554$	−4.61281e11	−	1.91575e13i	−0.00883928	−	0.367105i
$555$			5.18236e12i			0.0984153i
$556$	1.05289e12	+	2.18512e13i	0.0198157	+	0.411245i
$557$	9.55402e13			1.78201			0.891005	−	0.453994i	$-0.150001\pi$
$557$	9.55402e13			1.78201			0.891005	+	0.453994i	$0.150001\pi$
$558$	6.88511e13	−	1.65782e12i	1.27274	−	0.0306455i
$559$			2.05278e13i			0.376083i
$560$	4.86246e10	+	5.03394e11i	0.000882908	+	0.00914046i
$561$	−3.04533e13			−0.548050
$562$	−2.16521e12	−	8.99237e13i	−0.0386206	−	1.60396i
$563$			4.37094e13i			0.772739i	0.922344	+	0.386369i	$0.126271\pi$
$563$			4.37094e13i			0.772739i	−0.922344	+	0.386369i	$0.873729\pi$
$564$	1.28042e13	−	6.16966e11i	0.224366	−	0.0108110i
$565$	3.96587e13			0.688805
$566$	1.85414e13	−	4.46445e11i	0.319198	−	0.00768574i
$567$		−	8.21084e11i		−	0.0140111i
$568$	6.78488e13	−	4.90864e12i	1.14763	−	0.0830271i
$569$	−1.14503e14			−1.91979			−0.959896	−	0.280356i	$-0.909548\pi$
$569$	−1.14503e14			−1.91979			−0.959896	+	0.280356i	$0.909548\pi$
$570$	1.17671e11	+	4.88701e12i	0.00195567	+	0.0812211i
$571$		−	5.05065e13i		−	0.832084i	−0.909345	−	0.416042i	$-0.863417\pi$
$571$		−	5.05065e13i		−	0.832084i	0.909345	−	0.416042i	$-0.136583\pi$
$572$	−7.88131e11	−	1.63565e13i	−0.0128712	−	0.267122i
$573$	3.64113e13			0.589471
$574$	−1.35031e11	+	3.25132e9i	−0.00216707	+	5.21795e-5i
$575$			1.50859e13i			0.240011i
$576$	−5.58469e13	+	8.12320e12i	−0.880818	+	0.128119i
$577$	−3.55790e13			−0.556308			−0.278154	−	0.960537i	$-0.589722\pi$
$577$	−3.55790e13			−0.556308			−0.278154	+	0.960537i	$0.589722\pi$
$578$	−2.38856e12	−	9.91995e13i	−0.0370251	−	1.53769i
$579$			2.26950e13i			0.348768i
$580$	−9.82416e12	+	4.73373e11i	−0.149677	+	0.00721213i
$581$	−2.07377e12			−0.0313241
$582$	1.54894e13	−	3.72959e11i	0.231963	−	0.00558529i
$583$		−	8.89594e12i		−	0.132084i
$584$	−7.20552e12	−	9.95969e13i	−0.106072	−	1.46616i
$585$	−7.02914e12			−0.102594
$586$	1.32983e12	+	5.52292e13i	0.0192445	+	0.799247i
$587$			5.30294e13i			0.760897i	0.924802	+	0.380449i	$0.124230\pi$
$587$			5.30294e13i			0.760897i	−0.924802	+	0.380449i	$0.875770\pi$
$588$	−1.12107e12	−	2.32661e13i	−0.0159494	−	0.331007i
$589$	5.55604e13			0.783771
$590$	4.04723e13	−	9.74505e11i	0.566106	−	0.0136309i
$591$		−	1.13383e13i		−	0.157257i
$592$	−4.80414e13	+	4.64048e12i	−0.660704	+	0.0638196i
$593$	2.00349e13			0.273221			0.136610	−	0.990625i	$-0.456379\pi$
$593$	2.00349e13			0.273221			0.136610	+	0.990625i	$0.456379\pi$
$594$	1.15738e12	+	4.80674e13i	0.0156511	+	0.650007i
$595$			1.09101e12i			0.0146299i
$596$	−8.63789e13	+	4.16213e12i	−1.14862	+	0.0553457i
$597$	−3.98026e13			−0.524856
$598$	2.36460e13	−	5.69355e11i	0.309208	−	0.00744521i
$599$			6.78769e13i			0.880214i	0.897945	+	0.440107i	$0.145059\pi$
$599$			6.78769e13i			0.880214i	−0.897945	+	0.440107i	$0.854941\pi$
$600$	−5.14253e12	+	3.72046e11i	−0.0661333	+	0.00478454i
$601$	−1.12390e14			−1.43336			−0.716679	−	0.697403i	$-0.754339\pi$
$601$	−1.12390e14			−1.43336			−0.716679	+	0.697403i	$0.754339\pi$
$602$	−5.70244e10	−	2.36829e12i	−0.000721238	−	0.0299538i
$603$		−	2.98169e13i		−	0.374004i
$604$	6.77413e12	+	1.40587e14i	0.0842692	+	1.74888i
$605$	2.77861e12			0.0342808
$606$	3.64039e13	−	8.76544e11i	0.445435	−	0.0107253i
$607$		−	5.32604e13i		−	0.646340i	−0.946341	−	0.323170i	$-0.895251\pi$
$607$		−	5.32604e13i		−	0.646340i	0.946341	−	0.323170i	$-0.104749\pi$
$608$	−4.51981e13	+	5.46684e12i	−0.544004	+	0.0657989i
$609$	−1.91084e11			−0.00228107
$610$	7.86421e11	+	3.26610e13i	0.00931121	+	0.386705i
$611$			1.48703e13i			0.174628i
$612$	−1.21603e14	+	5.85938e12i	−1.41640	+	0.0682488i
$613$	8.16071e13			0.942813			0.471407	−	0.881916i	$-0.343746\pi$
$613$	8.16071e13			0.942813			0.471407	+	0.881916i	$0.343746\pi$
$614$	−4.34993e13	+	1.04739e12i	−0.498472	+	0.0120024i
$615$		−	1.37703e12i		−	0.0156520i
$616$	1.36363e11	+	1.88485e12i	0.00153742	+	0.0212507i
$617$	−9.91689e12			−0.110905			−0.0554523	−	0.998461i	$-0.517660\pi$
$617$	−9.91689e12			−0.110905			−0.0554523	+	0.998461i	$0.517660\pi$
$618$	8.15292e11	+	3.38600e13i	0.00904421	+	0.375616i
$619$		−	4.79435e12i		−	0.0527565i	−0.999652	−	0.0263783i	$-0.991603\pi$
$619$		−	4.79435e12i		−	0.0527565i	0.999652	−	0.0263783i	$-0.00839743\pi$
$620$	2.82040e12	+	5.85333e13i	0.0307860	+	0.638917i
$621$	−6.94489e13			−0.751982
$622$	1.02736e13	−	2.47370e11i	0.110349	−	0.00265703i
$623$		−	1.77724e12i		−	0.0189368i
$624$	7.77237e11	+	8.04648e12i	0.00821543	+	0.0850517i
$625$	3.81470e12			0.0400000
$626$	−2.25782e12	−	9.37697e13i	−0.0234864	−	0.975418i
$627$			1.82665e13i			0.188503i
$628$	1.72123e14	−	8.29366e12i	1.76214	−	0.0849079i
$629$	−1.04120e14			−1.05750
$630$	8.10950e11	−	1.95263e10i	0.00817130	−	0.000196751i
$631$		−	7.60539e13i		−	0.760282i	−0.924928	−	0.380141i	$-0.875875\pi$
$631$		−	7.60539e13i		−	0.760282i	0.924928	−	0.380141i	$-0.124125\pi$
$632$	−8.14295e13	+	5.89117e12i	−0.807600	+	0.0584273i
$633$	3.03337e13			0.298474
$634$	2.08765e12	+	8.67023e13i	0.0203803	+	0.846417i
$635$		−	2.84564e13i		−	0.275621i
$636$	2.11361e11	+	4.38649e12i	0.00203114	+	0.0421533i
$637$	2.70203e13			0.257628
$638$	−3.67417e13	+	8.84679e11i	−0.347581	+	0.00836917i
$639$		−	1.09112e14i		−	1.02416i
$640$	−8.05374e12	−	4.73390e13i	−0.0750063	−	0.440879i
$641$	1.81432e13			0.167657			0.0838287	−	0.996480i	$-0.473285\pi$
$641$	1.81432e13			0.167657			0.0838287	+	0.996480i	$0.473285\pi$
$642$	1.14774e12	+	4.76672e13i	0.0105237	+	0.437063i
$643$		−	1.38974e14i		−	1.26438i	−0.774812	−	0.632192i	$-0.782155\pi$
$643$		−	1.38974e14i		−	1.26438i	0.774812	−	0.632192i	$-0.217845\pi$
$644$	−2.72645e12	+	1.31373e11i	−0.0246132	+	0.00118598i
$645$	2.41516e13			0.216345
$646$	−9.81862e13	+	2.36416e12i	−0.872746	+	0.0210143i
$647$		−	1.35425e14i		−	1.19447i	−0.802065	−	0.597236i	$-0.796265\pi$
$647$		−	1.35425e14i		−	1.19447i	0.802065	−	0.597236i	$-0.203735\pi$
$648$	5.62553e12	+	7.77578e13i	0.0492366	+	0.680564i
$649$	1.51276e14			1.31385
$650$	−1.43970e11	−	5.97924e12i	−0.00124081	−	0.0515323i
$651$			1.13850e12i			0.00973704i
$652$	1.55203e12	+	3.22101e13i	0.0131723	+	0.273372i
$653$	−6.82928e13			−0.575187			−0.287593	−	0.957753i	$-0.592855\pi$
$653$	−6.82928e13			−0.575187			−0.287593	+	0.957753i	$0.592855\pi$
$654$	−2.39553e13	+	5.76804e11i	−0.200223	+	0.00482102i
$655$			5.13290e13i			0.425752i
$656$	1.27653e13	−	1.23305e12i	0.105078	−	0.0101499i
$657$	−1.60168e14			−1.30842
$658$	−4.13083e10	−	1.71558e12i	−0.000334894	−	0.0139085i
$659$		−	2.60660e13i		−	0.209724i	−0.994487	−	0.104862i	$-0.966560\pi$
$659$		−	2.60660e13i		−	0.209724i	0.994487	−	0.104862i	$-0.0334401\pi$
$660$	−1.92439e13	+	9.27260e11i	−0.153665	+	0.00740426i
$661$	1.44276e14			1.14337			0.571686	−	0.820472i	$-0.306289\pi$
$661$	1.44276e14			1.14337			0.571686	+	0.820472i	$0.306289\pi$
$662$	2.38974e14	−	5.75409e12i	1.87958	−	0.0452571i
$663$			1.74391e13i			0.136131i
$664$	1.96389e14	−	1.42081e13i	1.52151	−	0.110077i
$665$	6.54408e11			0.00503200
$666$	1.86349e12	+	7.73929e13i	0.0142219	+	0.590650i
$667$		−	5.30854e13i		−	0.402111i
$668$	−4.88851e12	−	1.01454e14i	−0.0367531	−	0.762757i
$669$	−8.15852e12			−0.0608809
$670$	2.53634e13	−	6.10707e11i	0.187859	−	0.00452334i
$671$			1.22079e14i			0.897489i
$672$	−1.12022e11	−	9.26161e11i	−0.000817442	−	0.00675834i
$673$	9.53562e13			0.690675			0.345337	−	0.938479i	$-0.387764\pi$
$673$	9.53562e13			0.690675			0.345337	+	0.938479i	$0.387764\pi$
$674$	−1.82166e12	−	7.56555e13i	−0.0130969	−	0.543928i
$675$			1.75612e13i			0.125324i
$676$	1.31637e14	−	6.34287e12i	0.932490	−	0.0449316i
$677$	1.36824e14			0.962099			0.481050	−	0.876693i	$-0.340256\pi$
$677$	1.36824e14			0.962099			0.481050	+	0.876693i	$0.340256\pi$
$678$	−7.31355e13	+	1.76098e12i	−0.510481	+	0.0122915i
$679$		−	2.07415e12i		−	0.0143711i
$680$	−7.47486e12	−	1.03320e14i	−0.0514113	−	0.710623i
$681$	−5.36193e12			−0.0366088
$682$	5.27101e12	+	2.18911e14i	0.0357250	+	1.48370i
$683$			9.14281e13i			0.615143i	0.951525	+	0.307572i	$0.0995164\pi$
$683$			9.14281e13i			0.615143i	−0.951525	+	0.307572i	$0.900484\pi$
$684$	3.51458e12	+	7.29399e13i	0.0234743	+	0.487175i
$685$	−5.50764e13			−0.365185
$686$	−6.23595e12	+	1.50151e11i	−0.0410471	+	0.000988345i
$687$		−	2.87917e13i		−	0.188141i
$688$	2.16263e13	+	2.23890e14i	0.140294	+	1.45242i
$689$	−5.09427e12			−0.0328085
$690$	−6.69863e11	−	2.78202e13i	−0.00428293	−	0.177875i
$691$			8.12382e13i			0.515668i	0.966189	+	0.257834i	$0.0830088\pi$
$691$			8.12382e13i			0.515668i	−0.966189	+	0.257834i	$0.916991\pi$
$692$	−1.03526e13	+	4.98836e11i	−0.0652409	+	0.00314360i
$693$	3.03114e12			0.0189645
$694$	−2.80749e14	+	6.75996e12i	−1.74390	+	0.0419901i
$695$			2.98568e13i			0.184128i
$696$	1.80959e13	−	1.30918e12i	0.110799	−	0.00801593i
$697$	2.76663e13			0.168185
$698$	7.56046e11	+	3.13995e13i	0.00456322	+	0.189516i
$699$		−	4.81079e13i		−	0.288291i
$700$	3.32196e10	+	6.89424e11i	0.000197653	+	0.00410200i
$701$	1.02931e13			0.0608073			0.0304036	−	0.999538i	$-0.490321\pi$
$701$	1.02931e13			0.0608073			0.0304036	+	0.999538i	$0.490321\pi$
$702$	2.75259e13	−	6.62777e11i	0.161456	−	0.00388760i
$703$			6.24534e13i			0.363730i
$704$	−2.58276e13	−	1.77564e14i	−0.149355	−	1.02681i
$705$	1.74953e13			0.100456
$706$	−6.85091e12	−	2.84526e14i	−0.0390593	−	1.62218i
$707$		−	4.87476e12i		−	0.0275966i
$708$	−7.45926e13	+	3.59421e12i	−0.419304	+	0.0202040i
$709$	−6.64211e13			−0.370745			−0.185372	−	0.982668i	$-0.559349\pi$
$709$	−6.64211e13			−0.370745			−0.185372	+	0.982668i	$0.559349\pi$
$710$	9.28143e13	−	2.23481e12i	0.514426	−	0.0123865i
$711$			1.30952e14i			0.720713i
$712$	1.21765e13	+	1.68307e14i	0.0665460	+	0.919819i
$713$	−3.16288e14			−1.71646
$714$	−4.84443e10	−	2.01195e12i	−0.000261067	−	0.0108424i
$715$		−	2.23490e13i		−	0.119599i
$716$	−1.44503e13	−	2.99894e14i	−0.0767910	−	1.59368i
$717$	8.94914e13			0.472265
$718$	−2.79660e14	+	6.73375e12i	−1.46558	+	0.0352886i
$719$		−	1.14349e14i		−	0.595097i	−0.954707	−	0.297549i	$-0.903831\pi$
$719$		−	1.14349e14i		−	0.595097i	0.954707	−	0.297549i	$-0.0961690\pi$
$720$	−7.66643e13	+	7.40527e12i	−0.396215	+	0.0382718i
$721$	4.53411e12			0.0232711
$722$	−3.30458e12	−	1.37243e14i	−0.0168434	−	0.699527i
$723$			2.50648e13i			0.126874i
$724$	3.05177e14	−	1.47048e13i	1.53412	−	0.0739208i
$725$	−1.34234e13			−0.0670153
$726$	−5.12410e12	+	1.23380e11i	−0.0254059	+	0.000611731i
$727$			6.85116e13i			0.337359i	0.985671	+	0.168680i	$0.0539503\pi$
$727$			6.85116e13i			0.337359i	−0.985671	+	0.168680i	$0.946050\pi$
$728$	1.07937e12	−	7.80887e10i	0.00527851	−	0.000381884i
$729$	8.22740e13			0.399600
$730$	−3.28053e12	−	1.36244e14i	−0.0158245	−	0.657210i
$731$			4.85236e14i			2.32470i
$732$	−2.90051e12	−	6.01959e13i	−0.0138013	−	0.286425i
$733$	−1.62363e14			−0.767304			−0.383652	−	0.923478i	$-0.625334\pi$
$733$	−1.62363e14			−0.767304			−0.383652	+	0.923478i	$0.625334\pi$
$734$	−3.41900e14	+	8.23238e12i	−1.60479	+	0.0386407i
$735$		−	3.17902e13i		−	0.148203i
$736$	2.57298e14	−	3.11210e13i	1.19137	−	0.144100i
$737$	9.48024e13			0.435995
$738$	−4.95159e11	−	2.05645e13i	−0.00226184	−	0.0939369i
$739$		−	4.58877e13i		−	0.208197i	−0.994567	−	0.104099i	$-0.966804\pi$
$739$		−	4.58877e13i		−	0.208197i	0.994567	−	0.104099i	$-0.0331957\pi$
$740$	−6.57951e13	+	3.17031e12i	−0.296507	+	0.0142871i
$741$	1.04604e13			0.0468226
$742$	5.87725e11	−	1.41514e10i	0.00261309	−	6.29188e-5i
$743$			1.13654e14i			0.501927i	0.967997	+	0.250963i	$0.0807473\pi$
$743$			1.13654e14i			0.501927i	−0.967997	+	0.250963i	$0.919253\pi$
$744$	−7.80024e12	−	1.07817e14i	−0.0342171	−	0.472959i
$745$	−1.18026e14			−0.514274
$746$	−1.14443e12	−	4.75295e13i	−0.00495331	−	0.205717i
$747$		−	3.15824e14i		−	1.35782i
$748$	−1.86298e13	−	3.86634e14i	−0.0795610	−	1.65117i
$749$	6.38300e12			0.0270779
$750$	−7.03476e12	+	1.69385e11i	−0.0296444	+	0.000713788i
$751$			6.48512e13i			0.271468i	0.990745	+	0.135734i	$0.0433392\pi$
$751$			6.48512e13i			0.271468i	−0.990745	+	0.135734i	$0.956661\pi$
$752$	1.56660e13	+	1.62185e14i	0.0651431	+	0.674405i
$753$	1.22158e14			0.504599
$754$	5.06613e11	+	2.10402e13i	0.00207883	+	0.0863363i
$755$			1.92094e14i			0.783032i
$756$	−3.17381e12	+	1.52929e11i	−0.0128520	+	0.000619270i
$757$	−3.59034e14			−1.44430			−0.722148	−	0.691739i	$-0.756845\pi$
$757$	−3.59034e14			−1.44430			−0.722148	+	0.691739i	$0.756845\pi$
$758$	−1.31038e14	+	3.15517e12i	−0.523661	+	0.0126089i
$759$		−	1.03985e14i		−	0.412823i
$760$	−6.19734e13	+	4.48358e12i	−0.244420	+	0.0176830i
$761$	1.08335e14			0.424467			0.212233	−	0.977219i	$-0.431926\pi$
$761$	1.08335e14			0.424467			0.212233	+	0.977219i	$0.431926\pi$
$762$	1.26356e12	+	5.24771e13i	0.00491837	+	0.204265i
$763$			3.20780e12i			0.0124047i
$764$	2.22746e13	+	4.62277e14i	0.0855742	+	1.77597i
$765$	−1.66155e14			−0.634170
$766$	3.75931e13	−	9.05178e11i	0.142549	−	0.00343234i
$767$		−	8.66285e13i		−	0.326350i
$768$	1.69541e13	+	8.69412e13i	0.0634554	+	0.325402i
$769$	9.76902e13			0.363261			0.181631	−	0.983367i	$-0.441862\pi$
$769$	9.76902e13			0.363261			0.181631	+	0.983367i	$0.441862\pi$
$770$	6.20836e10	+	2.57840e12i	0.000229363	+	0.00952570i
$771$			1.27552e14i			0.468184i
$772$	−2.88135e14	+	1.38836e13i	−1.05077	+	0.0506311i
$773$	−1.76068e14			−0.637943			−0.318972	−	0.947764i	$-0.603337\pi$
$773$	−1.76068e14			−0.637943			−0.318972	+	0.947764i	$0.603337\pi$
$774$	3.60678e14	−	8.68453e12i	1.29842	−	0.0312638i
$775$			7.99782e13i			0.286064i
$776$	1.42107e13	+	1.96425e14i	0.0505019	+	0.698052i
$777$	−1.27974e12			−0.00451874
$778$	1.23755e12	+	5.13969e13i	0.00434175	+	0.180318i
$779$		−	1.65948e13i		−	0.0578476i
$780$	5.30997e11	+	1.10201e13i	0.00183916	+	0.0381690i
$781$	3.46918e14			1.19391
$782$	5.58943e14	−	1.34584e13i	1.91132	−	0.0460214i
$783$		−	6.17958e13i		−	0.209967i
$784$	2.94700e14	−	2.84661e13i	0.994948	−	0.0961054i
$785$	2.35183e14			0.788966
$786$	−2.27918e12	−	9.46570e13i	−0.00759742	−	0.315529i
$787$		−	1.51760e14i		−	0.502671i	−0.967900	−	0.251335i	$-0.919130\pi$
$787$		−	1.51760e14i		−	0.502671i	0.967900	−	0.251335i	$-0.0808697\pi$
$788$	1.43951e14	−	6.93620e12i	0.473786	−	0.0228292i
$789$	1.19424e14			0.390578
$790$	−1.11392e14	+	2.68214e12i	−0.362009	+	0.00871656i
$791$			9.79340e12i			0.0316265i
$792$	−2.87054e14	+	2.07674e13i	−0.921164	+	0.0666433i
$793$	6.99089e13			0.222929
$794$	5.06310e12	+	2.10276e14i	0.0160441	+	0.666328i
$795$			5.99357e12i			0.0188734i
$796$	−2.43493e13	−	5.05333e14i	−0.0761939	−	1.58129i
$797$	4.10760e14			1.27731			0.638656	−	0.769493i	$-0.279491\pi$
$797$	4.10760e14			1.27731			0.638656	+	0.769493i	$0.279491\pi$
$798$	−1.20681e12	+	2.90579e10i	−0.00372927	+	8.97945e-5i
$799$			3.51503e14i			1.07943i
$800$	−7.86942e12	−	6.50618e13i	−0.0240156	−	0.198553i
$801$	2.70664e14			0.820859
$802$	8.56152e12	+	3.55570e14i	0.0258035	+	1.07165i
$803$		−	5.09250e14i		−	1.52529i
$804$	−4.67460e13	+	2.25244e12i	−0.139144	+	0.00670459i
$805$	−3.72534e12			−0.0110201
$806$	1.25360e14	−	3.01845e12i	0.368539	−	0.00887379i
$807$		−	1.41480e14i		−	0.413360i
$808$	3.33987e13	+	4.61647e14i	0.0969778	+	1.34046i
$809$	−3.49456e14			−1.00844			−0.504220	−	0.863575i	$-0.668220\pi$
$809$	−3.49456e14			−1.00844			−0.504220	+	0.863575i	$0.668220\pi$
$810$	2.56120e12	+	1.06369e14i	0.00734544	+	0.305064i
$811$		−	4.15248e14i		−	1.18360i	−0.806086	−	0.591798i	$-0.798418\pi$
$811$		−	4.15248e14i		−	1.18360i	0.806086	−	0.591798i	$-0.201582\pi$
$812$	−1.16896e11	−	2.42600e12i	−0.000331145	−	0.00687243i
$813$	−1.47795e14			−0.416110
$814$	−2.46069e14	+	5.92494e12i	−0.688550	+	0.0165791i
$815$			4.40110e13i			0.122398i
$816$	1.83723e13	+	1.90202e14i	0.0507823	+	0.525733i
$817$	2.91055e14			0.799584
$818$	8.10872e11	+	3.36764e13i	0.00221404	+	0.0919517i
$819$		−	1.73579e12i		−	0.00471062i
$820$	1.74828e13	−	8.42400e11i	0.0471565	−	0.00227221i
$821$	−6.64516e14			−1.78152			−0.890758	−	0.454478i	$-0.849826\pi$
$821$	−6.64516e14			−1.78152			−0.890758	+	0.454478i	$0.849826\pi$
$822$	1.01568e14	−	2.44558e12i	0.270642	−	0.00651662i
$823$		−	5.45678e14i		−	1.44523i	−0.691250	−	0.722615i	$-0.742940\pi$
$823$		−	5.45678e14i		−	1.44523i	0.691250	−	0.722615i	$-0.257060\pi$
$824$	−4.29387e14	+	3.10648e13i	−1.13035	+	0.0817772i
$825$	−2.62943e13			−0.0688006
$826$	2.40646e11	+	9.99431e12i	0.000625862	+	0.0259928i
$827$		−	4.51590e13i		−	0.116739i	−0.998295	−	0.0583696i	$-0.981410\pi$
$827$		−	4.51590e13i		−	0.116739i	0.998295	−	0.0583696i	$-0.0185902\pi$
$828$	−2.00074e13	−	4.15224e14i	−0.0514089	−	1.06692i
$829$	3.08333e13			0.0787494			0.0393747	−	0.999225i	$-0.487463\pi$
$829$	3.08333e13			0.0787494			0.0393747	+	0.999225i	$0.487463\pi$
$830$	2.68651e14	−	6.46868e12i	0.682023	−	0.0164220i
$831$			4.82443e13i			0.121742i
$832$	−1.01682e14	+	1.47902e13i	−0.255052	+	0.0370986i
$833$	6.38704e14			1.59248
$834$	−1.32574e12	−	5.50596e13i	−0.00328571	−	0.136459i
$835$		−	1.38624e14i		−	0.341511i
$836$	−2.31911e14	+	1.11745e13i	−0.567924	+	0.0273652i
$837$	−3.68185e14			−0.896271
$838$	1.58760e14	−	3.82268e12i	0.384169	−	0.00925014i
$839$		−	1.61246e14i		−	0.387863i	−0.981015	−	0.193932i	$-0.937876\pi$
$839$		−	1.61246e14i		−	0.387863i	0.981015	−	0.193932i	$-0.0621240\pi$
$840$	−9.18737e10	−	1.26991e12i	−0.000219682	−	0.00303651i
$841$	−3.73472e14			−0.887724
$842$	3.61360e12	+	1.50077e14i	0.00853846	+	0.354612i
$843$			2.26454e14i			0.531916i
$844$	1.85567e13	+	3.85116e14i	0.0433299	+	0.899248i
$845$	1.79865e14			0.417506
$846$	2.61274e14	−	6.29103e12i	0.602898	−	0.0145168i
$847$			6.86157e11i			0.00157401i
$848$	−5.55614e13	+	5.36687e12i	−0.126705	+	0.0122389i
$849$	−4.66926e13			−0.105855
$850$	−3.40316e12	−	1.41337e14i	−0.00766987	−	0.318539i
$851$		−	3.55527e14i		−	0.796572i
$852$	−1.71062e14	+	8.24253e12i	−0.381026	+	0.0183596i
$853$	−4.83432e14			−1.07051			−0.535254	−	0.844691i	$-0.679784\pi$
$853$	−4.83432e14			−1.07051			−0.535254	+	0.844691i	$0.679784\pi$
$854$	−8.06536e12	+	1.94200e11i	−0.0177556	+	0.000427524i
$855$			9.96630e13i			0.218124i
$856$	−6.04479e14	+	4.37321e13i	−1.31526	+	0.0951550i
$857$	3.50953e14			0.759181			0.379591	−	0.925155i	$-0.376065\pi$
$857$	3.50953e14			0.759181			0.379591	+	0.925155i	$0.376065\pi$
$858$	9.92372e11	+	4.12143e13i	0.00213421	+	0.0886363i
$859$			2.20560e13i			0.0471586i	0.999722	+	0.0235793i	$0.00750622\pi$
$859$			2.20560e13i			0.0471586i	−0.999722	+	0.0235793i	$0.992494\pi$
$860$	1.47747e13	+	3.06628e14i	0.0314071	+	0.651808i
$861$	3.40047e11			0.000718660
$862$	−3.09664e14	+	7.45619e12i	−0.650661	+	0.0156668i
$863$			4.34426e14i			0.907532i	0.891121	+	0.453766i	$0.149920\pi$
$863$			4.34426e14i			0.907532i	−0.891121	+	0.453766i	$0.850080\pi$
$864$	2.99517e14	−	3.62274e13i	0.622088	−	0.0752435i
$865$	−1.41455e13			−0.0292105
$866$	9.92979e12	+	4.12396e14i	0.0203869	+	0.846690i
$867$			2.49813e14i			0.509941i
$868$	−1.44543e13	+	6.96476e11i	−0.0293359	+	0.00141354i
$869$	−4.16358e14			−0.840172
$870$	2.47545e13	−	5.96046e11i	0.0496658	−	0.00119587i
$871$		−	5.42888e13i		−	0.108298i
$872$	−2.19778e13	−	3.03783e14i	−0.0435914	−	0.602534i
$873$	3.15882e14			0.622951
$874$	−8.07262e12	−	3.35265e14i	−0.0158291	−	0.657403i
$875$			9.42009e11i			0.00183660i
$876$	1.20994e13	+	2.51105e14i	0.0234554	+	0.486783i
$877$	−7.88973e14			−1.52077			−0.760386	−	0.649471i	$-0.774990\pi$
$877$	−7.88973e14			−1.52077			−0.760386	+	0.649471i	$0.774990\pi$
$878$	4.94976e14	−	1.19182e13i	0.948661	−	0.0228422i
$879$		−	1.39083e14i		−	0.265052i
$880$	−2.35449e13	−	2.43753e14i	−0.0446153	−	0.461888i
$881$	−1.58307e14			−0.298277			−0.149139	−	0.988816i	$-0.547650\pi$
$881$	−1.58307e14			−0.298277			−0.149139	+	0.988816i	$0.547650\pi$
$882$	−1.14312e13	−	4.74752e14i	−0.0214166	−	0.889454i
$883$			8.37422e14i			1.56006i	0.625743	+	0.780029i	$0.284796\pi$
$883$			8.37422e14i			1.56006i	−0.625743	+	0.780029i	$0.715204\pi$
$884$	−2.21407e14	+	1.06684e13i	−0.410138	+	0.0197623i
$885$	−1.01921e14			−0.187736
$886$	−4.59759e14	+	1.10702e13i	−0.842096	+	0.0202763i
$887$			1.81020e14i			0.329692i	0.986319	+	0.164846i	$0.0527127\pi$
$887$			1.81020e14i			0.329692i	−0.986319	+	0.164846i	$0.947287\pi$
$888$	1.21193e14	−	8.76795e12i	0.219490	−	0.0158794i
$889$	7.02708e12			0.0126551
$890$	5.54372e12	+	2.30237e14i	0.00992776	+	0.412311i
$891$			3.97584e14i			0.708012i
$892$	−4.99098e12	−	1.03580e14i	−0.00883815	−	0.183423i
$893$	2.10839e14			0.371273
$894$	2.17653e14	−	5.24073e12i	0.381134	−	0.00917707i
$895$		−	4.09766e14i		−	0.713544i
$896$	1.16900e13	−	1.98881e12i	0.0202430	−	0.00344392i
$897$	−5.95475e13			−0.102542
$898$	−9.12231e11	−	3.78860e13i	−0.00156215	−	0.0648779i
$899$		−	2.81434e14i		−	0.479267i
$900$	−1.04996e14	+	5.05917e12i	−0.177811	+	0.00856775i
$901$	−1.20418e14			−0.202800
$902$	6.53845e13	−	1.57435e12i	0.109507	−	0.00263675i
$903$			5.96405e12i			0.00993350i
$904$	−6.70980e13	−	9.27449e14i	−0.111139	−	1.53620i
$905$	4.16985e14			0.686875
$906$	−8.52962e12	−	3.54245e14i	−0.0139730	−	0.580313i
$907$			9.90432e14i			1.61357i	0.590844	+	0.806786i	$0.298795\pi$
$907$			9.90432e14i			1.61357i	−0.590844	+	0.806786i	$0.701205\pi$
$908$	−3.28016e12	−	6.80750e13i	−0.00531455	−	0.110296i
$909$	7.42401e14			1.19624
$910$	1.47653e12	−	3.55523e10i	0.00236611	−	5.69719e-5i
$911$		−	2.52110e14i		−	0.401788i	−0.979613	−	0.200894i	$-0.935615\pi$
$911$		−	2.52110e14i		−	0.401788i	0.979613	−	0.200894i	$-0.0643847\pi$
$912$	1.14087e14	−	1.10201e13i	0.180827	−	0.0174667i
$913$	1.00416e15			1.58288
$914$	−6.97735e12	−	2.89777e14i	−0.0109385	−	0.454290i
$915$		−	8.22499e13i		−	0.128242i
$916$	3.65539e14	−	1.76133e13i	0.566834	−	0.0273127i
$917$	−1.26753e13			−0.0195484
$918$	6.50656e14	−	1.56667e13i	0.998017	−	0.0240306i
$919$			6.58794e14i			1.00501i	0.864573	+	0.502507i	$0.167589\pi$
$919$			6.58794e14i			1.00501i	−0.864573	+	0.502507i	$0.832411\pi$
$920$	3.52795e14	−	2.55236e13i	0.535282	−	0.0387260i
$921$	1.09544e14			0.165307
$922$	−2.59113e13	−	1.07612e15i	−0.0388897	−	1.61513i
$923$		−	1.98663e14i		−	0.296558i
$924$	−2.28979e11	−	4.75213e12i	−0.000339967	−	0.00705551i
$925$	−8.99005e13			−0.132756
$926$	−6.77352e14	+	1.63095e13i	−0.994855	+	0.0239544i
$927$			6.90522e14i			1.00874i
$928$	2.76915e13	+	2.28945e14i	0.0402353	+	0.332652i
$929$	3.95978e14			0.572259			0.286129	−	0.958191i	$-0.407631\pi$
$929$	3.95978e14			0.572259			0.286129	+	0.958191i	$0.407631\pi$
$930$	−3.55130e12	−	1.47490e14i	−0.00510473	−	0.212005i
$931$		−	3.83108e14i		−	0.547738i
$932$	6.10777e14	−	2.94300e13i	0.868566	−	0.0418515i
$933$	−2.58719e13			−0.0365948
$934$	4.05622e14	−	9.76669e12i	0.570673	−	0.0137408i
$935$		−	5.28286e14i		−	0.739283i
$936$	1.18925e13	+	1.64382e14i	0.0165537	+	0.228810i
$937$	−6.67632e14			−0.924356			−0.462178	−	0.886787i	$-0.652932\pi$
$937$	−6.67632e14			−0.924356			−0.462178	+	0.886787i	$0.652932\pi$
$938$	1.50809e11	+	6.26328e12i	0.000207689	+	0.00862557i
$939$			2.36139e14i			0.323475i
$940$	1.07028e13	+	2.22120e14i	0.0145833	+	0.302656i
$941$	5.42638e14			0.735465			0.367733	−	0.929932i	$-0.380134\pi$
$941$	5.42638e14			0.735465			0.367733	+	0.929932i	$0.380134\pi$
$942$	−4.33707e14	+	1.04429e13i	−0.584711	+	0.0140789i
$943$			9.44691e13i			0.126687i
$944$	−9.12640e13	−	9.44826e14i	−0.121742	−	1.26035i
$945$	−4.33660e12			−0.00575428
$946$	2.76123e13	+	1.14677e15i	0.0364457	+	1.51363i
$947$		−	8.96999e14i		−	1.17772i	−0.808235	−	0.588860i	$-0.799577\pi$
$947$		−	8.96999e14i		−	1.17772i	0.808235	−	0.588860i	$-0.200423\pi$
$948$	2.05302e14	−	9.89237e12i	0.268133	−	0.0129199i
$949$	−2.91623e14			−0.378870
$950$	−8.47770e13	+	2.04129e12i	−0.109562	+	0.00263807i
$951$		−	2.18342e14i		−	0.280695i
$952$	2.55140e13	−	1.84586e12i	0.0326283	−	0.00236055i
$953$	−6.68742e13			−0.0850735			−0.0425368	−	0.999095i	$-0.513544\pi$
$953$	−6.68742e13			−0.0850735			−0.0425368	+	0.999095i	$0.513544\pi$
$954$	2.15519e12	+	8.95075e13i	0.00272737	+	0.113271i
$955$			6.31641e14i			0.795158i
$956$	5.47464e13	+	1.13618e15i	0.0685592	+	1.42285i
$957$	9.25265e13			0.115267
$958$	−5.20116e14	+	1.25235e13i	−0.644573	+	0.0155202i
$959$		−	1.36007e13i		−	0.0167675i
$960$	1.74011e13	+	1.19632e14i	0.0213413	+	0.146721i
$961$	−8.57181e14			−1.04582
$962$	3.39293e12	+	1.40912e14i	0.00411812	+	0.171030i
$963$			9.72098e14i			1.17376i
$964$	−3.18223e14	+	1.53334e13i	−0.382249	+	0.0184185i
$965$	−3.93699e14			−0.470465
$966$	6.86997e12	−	1.65417e11i	0.00816713	−	0.000196651i
$967$			1.09537e15i			1.29547i	0.761865	+	0.647735i	$0.224284\pi$
$967$			1.09537e15i			1.29547i	−0.761865	+	0.647735i	$0.775716\pi$
$968$	−4.70110e12	−	6.49800e13i	−0.00553124	−	0.0764545i
$969$	2.47262e14			0.289426
$970$	6.46987e12	+	2.68701e14i	0.00753419	+	0.312904i
$971$		−	8.64271e14i		−	1.00128i	−0.865657	−	0.500638i	$-0.833099\pi$
$971$		−	8.64271e14i		−	1.00128i	0.865657	−	0.500638i	$-0.166901\pi$
$972$	−3.56126e13	−	7.39087e14i	−0.0410461	−	0.851852i
$973$	−7.37290e12			−0.00845424
$974$	−3.68322e14	+	8.86858e12i	−0.420178	+	0.0101172i
$975$			1.50575e13i			0.0170895i
$976$	7.62471e14	−	7.36497e13i	0.860943	−	0.0831614i
$977$	9.80844e14			1.10186			0.550931	−	0.834551i	$-0.314273\pi$
$977$	9.80844e14			1.10186			0.550931	+	0.834551i	$0.314273\pi$
$978$	−1.95423e12	−	8.11615e13i	−0.00218415	−	0.0907102i
$979$			8.60572e14i			0.956916i
$980$	4.03607e14	−	1.94476e13i	0.446507	−	0.0215147i
$981$	−4.88531e14			−0.537709
$982$	−1.42187e15	+	3.42362e13i	−1.55705	+	0.0374911i
$983$		−	3.16524e14i		−	0.344858i	−0.985022	−	0.172429i	$-0.944839\pi$
$983$		−	3.16524e14i		−	0.344858i	0.985022	−	0.172429i	$-0.0551615\pi$
$984$	−3.22030e13	+	2.32978e12i	−0.0349076	+	0.00252546i
$985$	1.96690e14			0.212130
$986$	1.19753e13	+	4.97348e14i	0.0128500	+	0.533674i
$987$			4.32033e12i			0.00461244i
$988$	6.39912e12	+	1.32804e14i	0.00679729	+	0.141068i
$989$	−1.65688e15			−1.75110
$990$	−3.92677e14	+	9.45501e12i	−0.412914	+	0.00994228i
$991$		−	1.51439e15i		−	1.58442i	−0.610251	−	0.792208i	$-0.708932\pi$
$991$		−	1.51439e15i		−	1.58442i	0.610251	−	0.792208i	$-0.291068\pi$
$992$	1.36407e15	−	1.64989e14i	1.41997	−	0.171750i
$993$	−6.01807e14			−0.623319
$994$	5.51869e11	+	2.29197e13i	0.000568727	+	0.0236199i
$995$		−	6.90472e14i		−	0.707996i
$996$	−4.95139e14	+	2.38580e13i	−0.505161	+	0.0243410i
$997$	4.03612e14			0.409721			0.204861	−	0.978791i	$-0.434326\pi$
$997$	4.03612e14			0.409721			0.204861	+	0.978791i	$0.434326\pi$
$998$	−1.17269e15	+	2.82364e13i	−1.18449	+	0.0285205i
$999$		−	4.13863e14i		−	0.415939i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.11.b.a.11.9	✓	20
3.2	odd	2		180.11.c.a.91.12		20
4.3	odd	2	inner	20.11.b.a.11.10	yes	20
5.2	odd	4		100.11.d.c.99.39		40
5.3	odd	4		100.11.d.c.99.2		40
5.4	even	2		100.11.b.e.51.12		20
8.3	odd	2		320.11.b.d.191.12		20
8.5	even	2		320.11.b.d.191.9		20
12.11	even	2		180.11.c.a.91.11		20
20.3	even	4		100.11.d.c.99.40		40
20.7	even	4		100.11.d.c.99.1		40
20.19	odd	2		100.11.b.e.51.11		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.11.b.a.11.9	✓	20	1.1	even	1	trivial
20.11.b.a.11.10	yes	20	4.3	odd	2	inner
100.11.b.e.51.11		20	20.19	odd	2
100.11.b.e.51.12		20	5.4	even	2
100.11.d.c.99.1		40	20.7	even	4
100.11.d.c.99.2		40	5.3	odd	4
100.11.d.c.99.39		40	5.2	odd	4
100.11.d.c.99.40		40	20.3	even	4
180.11.c.a.91.11		20	12.11	even	2
180.11.c.a.91.12		20	3.2	odd	2
320.11.b.d.191.9		20	8.5	even	2
320.11.b.d.191.12		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)

\(f(q)\)	\(=\)	\(q+(-0.770283 - 31.9907i) q^{2} +80.5620i q^{3} +(-1022.81 + 49.2838i) q^{4} -1397.54 q^{5} +(2577.24 - 62.0555i) q^{6} -345.112i q^{7} +(2364.48 + 32682.6i) q^{8} +52558.8 q^{9} +O(q^{10})\)	\(q+(-0.770283 - 31.9907i) q^{2} +80.5620i q^{3} +(-1022.81 + 49.2838i) q^{4} -1397.54 q^{5} +(2577.24 - 62.0555i) q^{6} -345.112i q^{7} +(2364.48 + 32682.6i) q^{8} +52558.8 q^{9} +(1076.50 + 44708.4i) q^{10} +167110. i q^{11} +(-3970.40 - 82399.9i) q^{12} +95695.6 q^{13} +(-11040.4 + 265.834i) q^{14} -112589. i q^{15} +(1.04372e6 - 100816. i) q^{16} +2.26205e6 q^{17} +(-40485.1 - 1.68139e6i) q^{18} -1.35682e6i q^{19} +(1.42943e6 - 68876.2i) q^{20} +27802.9 q^{21} +(5.34596e6 - 128722. i) q^{22} +7.72397e6i q^{23} +(-2.63297e6 + 190487. i) q^{24} +1.95312e6 q^{25} +(-73712.7 - 3.06137e6i) q^{26} +8.99135e6i q^{27} +(17008.4 + 352985. i) q^{28} -6.87281e6 q^{29} +(-3.60180e6 + 86725.3i) q^{30} +4.09489e7i q^{31} +(-4.02915e6 - 3.33116e7i) q^{32} -1.34627e7 q^{33} +(-1.74242e6 - 7.23647e7i) q^{34} +482309. i q^{35} +(-5.37578e7 + 2.59030e6i) q^{36} -4.60291e7 q^{37} +(-4.34058e7 + 1.04514e6i) q^{38} +7.70943e6i q^{39} +(-3.30446e6 - 4.56753e7i) q^{40} +1.22306e7 q^{41} +(-21416.1 - 889435. i) q^{42} +2.14512e8i q^{43} +(-8.23580e6 - 1.70922e8i) q^{44} -7.34531e7 q^{45} +(2.47095e8 - 5.94964e6i) q^{46} +1.55391e8i q^{47} +(8.12196e6 + 8.40840e7i) q^{48} +2.82356e8 q^{49} +(-1.50446e6 - 6.24819e7i) q^{50} +1.82235e8i q^{51} +(-9.78788e7 + 4.71625e6i) q^{52} -5.32341e7 q^{53} +(2.87640e8 - 6.92588e6i) q^{54} -2.33543e8i q^{55} +(1.12791e7 - 816010. i) q^{56} +1.09309e8 q^{57} +(5.29401e6 + 2.19866e8i) q^{58} -9.05250e8i q^{59} +(5.54881e6 + 1.15157e8i) q^{60} +7.30533e8 q^{61} +(1.30998e9 - 3.15422e7i) q^{62} -1.81387e7i q^{63} +(-1.06256e9 + 1.54555e8i) q^{64} -1.33739e8 q^{65} +(1.03701e7 + 4.30681e8i) q^{66} -5.67307e8i q^{67} +(-2.31366e9 + 1.11483e8i) q^{68} -6.22259e8 q^{69} +(1.54294e7 - 371514. i) q^{70} -2.07599e9i q^{71} +(1.24274e8 + 1.71776e9i) q^{72} -3.04740e9 q^{73} +(3.54554e7 + 1.47250e9i) q^{74} +1.57348e8i q^{75} +(6.68695e7 + 1.38778e9i) q^{76} +5.76715e7 q^{77} +(2.46630e8 - 5.93845e6i) q^{78} +2.49153e9i q^{79} +(-1.45864e9 + 1.40895e8i) q^{80} +2.37918e9 q^{81} +(-9.42105e6 - 3.91267e8i) q^{82} -6.00897e9i q^{83} +(-2.84372e7 + 1.37023e6i) q^{84} -3.16131e9 q^{85} +(6.86238e9 - 1.65235e8i) q^{86} -5.53687e8i q^{87} +(-5.46157e9 + 3.95128e8i) q^{88} +5.14975e9 q^{89} +(5.65797e7 + 2.34982e9i) q^{90} -3.30257e7i q^{91} +(-3.80667e8 - 7.90018e9i) q^{92} -3.29892e9 q^{93} +(4.97108e9 - 1.19695e8i) q^{94} +1.89622e9i q^{95} +(2.68365e9 - 3.24596e8i) q^{96} +6.01008e9 q^{97} +(-2.17494e8 - 9.03278e9i) q^{98} +8.78308e9i 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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