LMFDB - Embedded newform 8.12.b.a.5.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8,12,Mod(5,8)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("8.5");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	8.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:	$6.14674544448$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} - 48 x^{8} + 8836 x^{7} - 92554 x^{6} - 2200342 x^{5} - 88894588 x^{4} + \cdots + 34431558027300 $ x^10 - x^9 - 48x^8 + 8836x^7 - 92554x^6 - 2200342x^5 - 88894588x^4 + 2040335460x^3 + 7439251985x^2 - 747501940689x + 34431558027300
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{45}\cdot 3^{2}\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.1
Root			$-23.4302 - 2.98090i$ of defining polynomial
Character	$\chi$	$=$	8.5
Dual form			8.12.b.a.5.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-44.8604 - 5.96180i) q^{2} -614.710i q^{3} +(1976.91 + 534.897i) q^{4} -4397.69i q^{5} +(-3664.78 + 27576.1i) q^{6} -41556.6 q^{7} +(-85496.2 - 35781.7i) q^{8} -200721. q^{9} +O(q^{10})$	\(q+(-44.8604 - 5.96180i) q^{2} -614.710i q^{3} +(1976.91 + 534.897i) q^{4} -4397.69i q^{5} +(-3664.78 + 27576.1i) q^{6} -41556.6 q^{7} +(-85496.2 - 35781.7i) q^{8} -200721. q^{9} +(-26218.2 + 197282. i) q^{10} +965832. i q^{11} +(328807. - 1.21523e6i) q^{12} -1.37046e6i q^{13} +(1.86425e6 + 247752. i) q^{14} -2.70331e6 q^{15} +(3.62207e6 + 2.11489e6i) q^{16} -3.12371e6 q^{17} +(9.00444e6 + 1.19666e6i) q^{18} -4.95136e6i q^{19} +(2.35231e6 - 8.69386e6i) q^{20} +2.55453e7i q^{21} +(5.75810e6 - 4.33276e7i) q^{22} -5.16680e7 q^{23} +(-2.19954e7 + 5.25554e7i) q^{24} +2.94884e7 q^{25} +(-8.17042e6 + 6.14795e7i) q^{26} +1.44914e7i q^{27} +(-8.21539e7 - 2.22285e7i) q^{28} -1.45390e8i q^{29} +(1.21271e8 + 1.61166e7i) q^{30} +3.49245e7 q^{31} +(-1.49879e8 - 1.16469e8i) q^{32} +5.93707e8 q^{33} +(1.40131e8 + 1.86229e7i) q^{34} +1.82753e8i q^{35} +(-3.96809e8 - 1.07365e8i) q^{36} -2.21788e7i q^{37} +(-2.95190e7 + 2.22120e8i) q^{38} -8.42437e8 q^{39} +(-1.57357e8 + 3.75986e8i) q^{40} +9.44266e6 q^{41} +(1.52296e8 - 1.14597e9i) q^{42} -7.85539e8i q^{43} +(-5.16621e8 + 1.90937e9i) q^{44} +8.82711e8i q^{45} +(2.31785e9 + 3.08034e8i) q^{46} -1.72329e9 q^{47} +(1.30005e9 - 2.22652e9i) q^{48} -2.50373e8 q^{49} +(-1.32286e9 - 1.75804e8i) q^{50} +1.92017e9i q^{51} +(7.33057e8 - 2.70929e9i) q^{52} -7.35431e8i q^{53} +(8.63947e7 - 6.50089e8i) q^{54} +4.24743e9 q^{55} +(3.55294e9 + 1.48697e9i) q^{56} -3.04365e9 q^{57} +(-8.66783e8 + 6.52224e9i) q^{58} -5.74556e7i q^{59} +(-5.34420e9 - 1.44599e9i) q^{60} -7.93436e9i q^{61} +(-1.56673e9 - 2.08213e8i) q^{62} +8.34130e9 q^{63} +(6.02928e9 + 6.11840e9i) q^{64} -6.02687e9 q^{65} +(-2.66339e10 - 3.53956e9i) q^{66} -5.62177e9i q^{67} +(-6.17530e9 - 1.67086e9i) q^{68} +3.17608e10i q^{69} +(1.08954e9 - 8.19839e9i) q^{70} +1.32318e10 q^{71} +(1.71609e10 + 7.18215e9i) q^{72} +5.44421e9 q^{73} +(-1.32225e8 + 9.94948e8i) q^{74} -1.81268e10i q^{75} +(2.64847e9 - 9.78842e9i) q^{76} -4.01367e10i q^{77} +(3.77921e10 + 5.02244e9i) q^{78} -1.46058e9 q^{79} +(9.30065e9 - 1.59288e10i) q^{80} -2.66492e10 q^{81} +(-4.23602e8 - 5.62952e7i) q^{82} +4.76924e10i q^{83} +(-1.36641e10 + 5.05008e10i) q^{84} +1.37371e10i q^{85} +(-4.68322e9 + 3.52396e10i) q^{86} -8.93724e10 q^{87} +(3.45591e10 - 8.25750e10i) q^{88} +1.31610e10 q^{89} +(5.26254e9 - 3.95988e10i) q^{90} +5.69518e10i q^{91} +(-1.02143e11 - 2.76371e10i) q^{92} -2.14684e10i q^{93} +(7.73076e10 + 1.02739e10i) q^{94} -2.17746e10 q^{95} +(-7.15947e10 + 9.21322e10i) q^{96} +1.22593e11 q^{97} +(1.12318e10 + 1.49267e9i) q^{98} -1.93863e11i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 22 q^{2} + 436 q^{4} - 24308 q^{6} - 33616 q^{7} - 208472 q^{8} - 472394 q^{9}+O(q^{10}) $ 10 * q + 22 * q^2 + 436 * q^4 - 24308 * q^6 - 33616 * q^7 - 208472 * q^8 - 472394 * q^9	\( 10 q + 22 q^{2} + 436 q^{4} - 24308 q^{6} - 33616 q^{7} - 208472 q^{8} - 472394 q^{9} + 29864 q^{10} - 476216 q^{12} + 2264272 q^{14} + 3391792 q^{15} + 3757072 q^{16} + 2639732 q^{17} + 2329130 q^{18} + 8296432 q^{20} - 24201892 q^{22} - 45357808 q^{23} + 10668944 q^{24} - 41502654 q^{25} - 101931080 q^{26} - 95722144 q^{28} + 261362768 q^{30} + 442035392 q^{31} + 343908512 q^{32} - 54732216 q^{33} - 187103796 q^{34} - 431195700 q^{36} + 375100844 q^{38} - 431459312 q^{39} + 1519138784 q^{40} - 654907964 q^{41} - 3697737056 q^{42} - 4127012952 q^{44} + 6028867440 q^{46} - 560226528 q^{47} + 9357606048 q^{48} + 1143661722 q^{49} - 9626584226 q^{50} - 11595427248 q^{52} + 20050494008 q^{54} + 5632783984 q^{55} + 18698733760 q^{56} - 783862360 q^{57} - 22828679464 q^{58} - 43681325472 q^{60} + 40774631744 q^{62} - 14483624624 q^{63} + 55266728512 q^{64} - 80291360 q^{65} - 83128448712 q^{66} - 83303223768 q^{68} + 100120831168 q^{70} - 11769460176 q^{71} + 112862051672 q^{72} + 32304890372 q^{73} - 102103996184 q^{74} - 97501928568 q^{76} + 144445560944 q^{78} + 57291670496 q^{79} + 128322038976 q^{80} - 23172996094 q^{81} - 123309929604 q^{82} - 199990865984 q^{84} + 130201908124 q^{86} - 73844404272 q^{87} + 169216119632 q^{88} - 108276011804 q^{89} - 228506434984 q^{90} - 141139403232 q^{92} + 145336130016 q^{94} + 70146835376 q^{95} + 109508068928 q^{96} + 60995282900 q^{97} - 6194726778 q^{98}+O(q^{100}) \) 10 * q + 22 * q^2 + 436 * q^4 - 24308 * q^6 - 33616 * q^7 - 208472 * q^8 - 472394 * q^9 + 29864 * q^10 - 476216 * q^12 + 2264272 * q^14 + 3391792 * q^15 + 3757072 * q^16 + 2639732 * q^17 + 2329130 * q^18 + 8296432 * q^20 - 24201892 * q^22 - 45357808 * q^23 + 10668944 * q^24 - 41502654 * q^25 - 101931080 * q^26 - 95722144 * q^28 + 261362768 * q^30 + 442035392 * q^31 + 343908512 * q^32 - 54732216 * q^33 - 187103796 * q^34 - 431195700 * q^36 + 375100844 * q^38 - 431459312 * q^39 + 1519138784 * q^40 - 654907964 * q^41 - 3697737056 * q^42 - 4127012952 * q^44 + 6028867440 * q^46 - 560226528 * q^47 + 9357606048 * q^48 + 1143661722 * q^49 - 9626584226 * q^50 - 11595427248 * q^52 + 20050494008 * q^54 + 5632783984 * q^55 + 18698733760 * q^56 - 783862360 * q^57 - 22828679464 * q^58 - 43681325472 * q^60 + 40774631744 * q^62 - 14483624624 * q^63 + 55266728512 * q^64 - 80291360 * q^65 - 83128448712 * q^66 - 83303223768 * q^68 + 100120831168 * q^70 - 11769460176 * q^71 + 112862051672 * q^72 + 32304890372 * q^73 - 102103996184 * q^74 - 97501928568 * q^76 + 144445560944 * q^78 + 57291670496 * q^79 + 128322038976 * q^80 - 23172996094 * q^81 - 123309929604 * q^82 - 199990865984 * q^84 + 130201908124 * q^86 - 73844404272 * q^87 + 169216119632 * q^88 - 108276011804 * q^89 - 228506434984 * q^90 - 141139403232 * q^92 + 145336130016 * q^94 + 70146835376 * q^95 + 109508068928 * q^96 + 60995282900 * q^97 - 6194726778 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/8\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$-1$	$1$

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 $

$2$	−44.8604	−	5.96180i	−0.991285	−	0.131738i
$2$	−44.8604	−	5.96180i	−0.991285	−	0.131738i
$3$		−	614.710i		−	1.46051i	−0.683177	−	0.730253i	$-0.739402\pi$
$3$		−	614.710i		−	1.46051i	0.683177	−	0.730253i	$-0.260598\pi$
$4$	1976.91	+	534.897i	0.965290	+	0.261180i
$5$		−	4397.69i		−	0.629347i	−0.949200	−	0.314673i	$-0.898105\pi$
$5$		−	4397.69i		−	0.629347i	0.949200	−	0.314673i	$-0.101895\pi$
$6$	−3664.78	+	27576.1i	−0.192405	+	1.44778i
$7$	−41556.6			−0.934547			−0.467274	−	0.884113i	$-0.654764\pi$
$7$	−41556.6			−0.934547			−0.467274	+	0.884113i	$0.654764\pi$
$8$	−85496.2	−	35781.7i	−0.922470	−	0.386070i
$9$	−200721.			−1.13308
$10$	−26218.2	+	197282.i	−0.0829091	+	0.623861i
$11$			965832.i			1.80818i	0.427341	+	0.904090i	$0.359450\pi$
$11$			965832.i			1.80818i	−0.427341	+	0.904090i	$0.640550\pi$
$12$	328807.	−	1.21523e6i	0.381456	−	1.40981i
$13$		−	1.37046e6i		−	1.02371i	−0.859071	−	0.511857i	$-0.828958\pi$
$13$		−	1.37046e6i		−	1.02371i	0.859071	−	0.511857i	$-0.171042\pi$
$14$	1.86425e6	+	247752.i	0.926402	+	0.123116i
$15$	−2.70331e6			−0.919164
$16$	3.62207e6	+	2.11489e6i	0.863570	+	0.504230i
$17$	−3.12371e6			−0.533582			−0.266791	−	0.963754i	$-0.585963\pi$
$17$	−3.12371e6			−0.533582			−0.266791	+	0.963754i	$0.585963\pi$
$18$	9.00444e6	+	1.19666e6i	1.12320	+	0.149270i
$19$		−	4.95136e6i		−	0.458754i	−0.973338	−	0.229377i	$-0.926331\pi$
$19$		−	4.95136e6i		−	0.458754i	0.973338	−	0.229377i	$-0.0736689\pi$
$20$	2.35231e6	−	8.69386e6i	0.164373	−	0.607502i
$21$			2.55453e7i			1.36491i
$22$	5.75810e6	−	4.33276e7i	0.238207	−	1.79242i
$23$	−5.16680e7			−1.67386			−0.836929	−	0.547312i	$-0.815651\pi$
$23$	−5.16680e7			−1.67386			−0.836929	+	0.547312i	$0.815651\pi$
$24$	−2.19954e7	+	5.25554e7i	−0.563857	+	1.34727i
$25$	2.94884e7			0.603923
$26$	−8.17042e6	+	6.14795e7i	−0.134862	+	1.01479i
$27$			1.44914e7i			0.194361i
$28$	−8.21539e7	−	2.22285e7i	−0.902109	−	0.244085i
$29$		−	1.45390e8i		−	1.31627i	−0.752901	−	0.658134i	$-0.771346\pi$
$29$		−	1.45390e8i		−	1.31627i	0.752901	−	0.658134i	$-0.228654\pi$
$30$	1.21271e8	+	1.61166e7i	0.911153	+	0.121089i
$31$	3.49245e7			0.219099			0.109550	−	0.993981i	$-0.465059\pi$
$31$	3.49245e7			0.219099			0.109550	+	0.993981i	$0.465059\pi$
$32$	−1.49879e8	−	1.16469e8i	−0.789617	−	0.613600i
$33$	5.93707e8			2.64086
$34$	1.40131e8	+	1.86229e7i	0.528932	+	0.0702932i
$35$			1.82753e8i			0.588154i
$36$	−3.96809e8	−	1.07365e8i	−1.09375	−	0.295938i
$37$		−	2.21788e7i		−	0.0525808i	−0.999654	−	0.0262904i	$-0.991631\pi$
$37$		−	2.21788e7i		−	0.0525808i	0.999654	−	0.0262904i	$-0.00836947\pi$
$38$	−2.95190e7	+	2.22120e8i	−0.0604355	+	0.454756i
$39$	−8.42437e8			−1.49514
$40$	−1.57357e8	+	3.75986e8i	−0.242972	+	0.580553i
$41$	9.44266e6			0.0127287			0.00636434	−	0.999980i	$-0.497974\pi$
$41$	9.44266e6			0.0127287			0.00636434	+	0.999980i	$0.497974\pi$
$42$	1.52296e8	−	1.14597e9i	0.179811	−	1.35302i
$43$		−	7.85539e8i		−	0.814875i	−0.913233	−	0.407438i	$-0.866422\pi$
$43$		−	7.85539e8i		−	0.814875i	0.913233	−	0.407438i	$-0.133578\pi$
$44$	−5.16621e8	+	1.90937e9i	−0.472261	+	1.74542i
$45$			8.82711e8i			0.713099i
$46$	2.31785e9	+	3.08034e8i	1.65927	+	0.220511i
$47$	−1.72329e9			−1.09603			−0.548013	−	0.836470i	$-0.684615\pi$
$47$	−1.72329e9			−1.09603			−0.548013	+	0.836470i	$0.684615\pi$
$48$	1.30005e9	−	2.22652e9i	0.736430	−	1.26125i
$49$	−2.50373e8			−0.126622
$50$	−1.32286e9	−	1.75804e8i	−0.598659	−	0.0795598i
$51$			1.92017e9i			0.779300i
$52$	7.33057e8	−	2.70929e9i	0.267374	−	0.988181i
$53$		−	7.35431e8i		−	0.241560i	−0.992679	−	0.120780i	$-0.961460\pi$
$53$		−	7.35431e8i		−	0.241560i	0.992679	−	0.120780i	$-0.0385395\pi$
$54$	8.63947e7	−	6.50089e8i	0.0256048	−	0.192667i
$55$	4.24743e9			1.13797
$56$	3.55294e9	+	1.48697e9i	0.862091	+	0.360800i
$57$	−3.04365e9			−0.670013
$58$	−8.66783e8	+	6.52224e9i	−0.173403	+	1.30480i
$59$		−	5.74556e7i		−	0.0104628i	−0.999986	−	0.00523138i	$-0.998335\pi$
$59$		−	5.74556e7i		−	0.0104628i	0.999986	−	0.00523138i	$-0.00166521\pi$
$60$	−5.34420e9	−	1.44599e9i	−0.887260	−	0.240068i
$61$		−	7.93436e9i		−	1.20281i	−0.798944	−	0.601406i	$-0.794608\pi$
$61$		−	7.93436e9i		−	1.20281i	0.798944	−	0.601406i	$-0.205392\pi$
$62$	−1.56673e9	−	2.08213e8i	−0.217190	−	0.0288638i
$63$	8.34130e9			1.05891
$64$	6.02928e9	+	6.11840e9i	0.701900	+	0.712275i
$65$	−6.02687e9			−0.644271
$66$	−2.66339e10	−	3.53956e9i	−2.61784	−	0.347902i
$67$		−	5.62177e9i		−	0.508700i	−0.967112	−	0.254350i	$-0.918138\pi$
$67$		−	5.62177e9i		−	0.508700i	0.967112	−	0.254350i	$-0.0818615\pi$
$68$	−6.17530e9	−	1.67086e9i	−0.515062	−	0.139361i
$69$			3.17608e10i			2.44468i
$70$	1.08954e9	−	8.19839e9i	0.0774824	−	0.583028i
$71$	1.32318e10			0.870358			0.435179	−	0.900344i	$-0.356685\pi$
$71$	1.32318e10			0.870358			0.435179	+	0.900344i	$0.356685\pi$
$72$	1.71609e10	+	7.18215e9i	1.04523	+	0.437447i
$73$	5.44421e9			0.307368			0.153684	−	0.988120i	$-0.450886\pi$
$73$	5.44421e9			0.307368			0.153684	+	0.988120i	$0.450886\pi$
$74$	−1.32225e8	+	9.94948e8i	−0.00692692	+	0.0521226i
$75$		−	1.81268e10i		−	0.882033i
$76$	2.64847e9	−	9.78842e9i	0.119818	−	0.442831i
$77$		−	4.01367e10i		−	1.68983i
$78$	3.77921e10	+	5.02244e9i	1.48211	+	0.196967i
$79$	−1.46058e9			−0.0534043			−0.0267022	−	0.999643i	$-0.508501\pi$
$79$	−1.46058e9			−0.0534043			−0.0267022	+	0.999643i	$0.508501\pi$
$80$	9.30065e9	−	1.59288e10i	0.317335	−	0.543485i
$81$	−2.66492e10			−0.849212
$82$	−4.23602e8	−	5.62952e7i	−0.0126177	−	0.00167685i
$83$			4.76924e10i			1.32898i	0.747295	+	0.664492i	$0.231352\pi$
$83$			4.76924e10i			1.32898i	−0.747295	+	0.664492i	$0.768648\pi$
$84$	−1.36641e10	+	5.05008e10i	−0.356488	+	1.31754i
$85$			1.37371e10i			0.335808i
$86$	−4.68322e9	+	3.52396e10i	−0.107350	+	0.807773i
$87$	−8.93724e10			−1.92242
$88$	3.45591e10	−	8.25750e10i	0.698084	−	1.66799i
$89$	1.31610e10			0.249829			0.124914	−	0.992168i	$-0.460134\pi$
$89$	1.31610e10			0.249829			0.124914	+	0.992168i	$0.460134\pi$
$90$	5.26254e9	−	3.95988e10i	0.0939424	−	0.706884i
$91$			5.69518e10i			0.956709i
$92$	−1.02143e11	−	2.76371e10i	−1.61576	−	0.437179i
$93$		−	2.14684e10i		−	0.319996i
$94$	7.73076e10	+	1.02739e10i	1.08647	+	0.144389i
$95$	−2.17746e10			−0.288715
$96$	−7.15947e10	+	9.21322e10i	−0.896167	+	1.15324i
$97$	1.22593e11			1.44951			0.724756	−	0.689006i	$-0.241953\pi$
$97$	1.22593e11			1.44951			0.724756	+	0.689006i	$0.241953\pi$
$98$	1.12318e10	+	1.49267e9i	0.125518	+	0.0166810i
$99$		−	1.93863e11i		−	2.04881i
$100$	5.82961e10	+	1.57733e10i	0.582961	+	0.157733i
$101$			1.10165e11i			1.04298i	0.853258	+	0.521490i	$0.174623\pi$
$101$			1.10165e11i			1.04298i	−0.853258	+	0.521490i	$0.825377\pi$
$102$	1.14477e10	−	8.61398e10i	0.102664	−	0.772508i
$103$	5.21564e10			0.443305			0.221653	−	0.975126i	$-0.428855\pi$
$103$	5.21564e10			0.443305			0.221653	+	0.975126i	$0.428855\pi$
$104$	−4.90374e10	+	1.17169e11i	−0.395225	+	0.944345i
$105$	1.12340e11			0.859002
$106$	−4.38449e9	+	3.29917e10i	−0.0318227	+	0.239454i
$107$			3.55806e10i			0.245246i	0.992453	+	0.122623i	$0.0391306\pi$
$107$			3.55806e10i			0.245246i	−0.992453	+	0.122623i	$0.960869\pi$
$108$	−7.75140e9	+	2.86482e10i	−0.0507633	+	0.187615i
$109$		−	2.39258e11i		−	1.48944i	−0.667380	−	0.744718i	$-0.732584\pi$
$109$		−	2.39258e11i		−	1.48944i	0.667380	−	0.744718i	$-0.267416\pi$
$110$	−1.90542e11	−	2.53223e10i	−1.12805	−	0.149915i
$111$	−1.36335e10			−0.0767946
$112$	−1.50521e11	−	8.78878e10i	−0.807046	−	0.471226i
$113$	8.51647e10			0.434838			0.217419	−	0.976078i	$-0.430236\pi$
$113$	8.51647e10			0.434838			0.217419	+	0.976078i	$0.430236\pi$
$114$	1.36539e11	+	1.81456e10i	0.664173	+	0.0882664i
$115$			2.27220e11i			1.05344i
$116$	7.77685e10	−	2.87423e11i	0.343783	−	1.27058i
$117$			2.75081e11i			1.15995i
$118$	−3.42539e8	+	2.57748e9i	−0.00137835	+	0.0103716i
$119$	1.29811e11			0.498658
$120$	2.31122e11	+	9.67288e10i	0.847901	+	0.354862i
$121$	−6.47520e11			−2.26952
$122$	−4.73030e10	+	3.55938e11i	−0.158456	+	1.19233i
$123$		−	5.80450e9i		−	0.0185903i
$124$	6.90427e10	+	1.86810e10i	0.211494	+	0.0572244i
$125$		−	3.44412e11i		−	1.00942i
$126$	−3.74194e11	−	4.97292e10i	−1.04969	−	0.139500i
$127$	−3.73294e10			−0.100261			−0.0501304	−	0.998743i	$-0.515964\pi$
$127$	−3.73294e10			−0.100261			−0.0501304	+	0.998743i	$0.515964\pi$
$128$	−2.33999e11	−	3.10419e11i	−0.601949	−	0.798535i
$129$	−4.82878e11			−1.19013
$130$	2.70368e11	+	3.59310e10i	0.638656	+	0.0848752i
$131$		−	1.88151e11i		−	0.426103i	−0.977041	−	0.213051i	$-0.931660\pi$
$131$		−	1.88151e11i		−	0.426103i	0.977041	−	0.213051i	$-0.0683402\pi$
$132$	1.17371e12	+	3.17572e11i	2.54919	+	0.689741i
$133$			2.05762e11i			0.428727i
$134$	−3.35159e10	+	2.52195e11i	−0.0670153	+	0.504267i
$135$	6.37286e10			0.122320
$136$	2.67065e11	+	1.11772e11i	0.492213	+	0.206000i
$137$	6.19233e11			1.09620			0.548101	−	0.836412i	$-0.315351\pi$
$137$	6.19233e11			1.09620			0.548101	+	0.836412i	$0.315351\pi$
$138$	1.89352e11	−	1.42480e12i	0.322058	−	2.42337i
$139$		−	3.33213e11i		−	0.544679i	−0.962201	−	0.272339i	$-0.912203\pi$
$139$		−	3.33213e11i		−	0.544679i	0.962201	−	0.272339i	$-0.0877973\pi$
$140$	−9.77543e10	+	3.61288e11i	−0.153614	+	0.567739i
$141$			1.05932e12i			1.60075i
$142$	−5.93584e11	−	7.88853e10i	−0.862773	−	0.114660i
$143$	1.32364e12			1.85106
$144$	−7.27027e11	−	4.24504e11i	−0.978492	−	0.571331i
$145$	−6.39379e11			−0.828388
$146$	−2.44229e11	−	3.24573e10i	−0.304689	−	0.0404922i
$147$			1.53907e11i			0.184932i
$148$	1.18634e10	−	4.38455e10i	0.0137331	−	0.0507558i
$149$		−	1.35605e12i		−	1.51270i	−0.654167	−	0.756350i	$-0.726981\pi$
$149$		−	1.35605e12i		−	1.51270i	0.654167	−	0.756350i	$-0.273019\pi$
$150$	−1.08068e11	+	8.13177e11i	−0.116198	+	0.874346i
$151$	−1.25866e12			−1.30477			−0.652385	−	0.757887i	$-0.726232\pi$
$151$	−1.25866e12			−1.30477			−0.652385	+	0.757887i	$0.726232\pi$
$152$	−1.77168e11	+	4.23323e11i	−0.177111	+	0.423187i
$153$	6.26995e11			0.604590
$154$	−2.39287e11	+	1.80055e12i	−0.222615	+	1.67510i
$155$		−	1.53587e11i		−	0.137889i
$156$	−1.66542e12	−	4.50617e11i	−1.44324	−	0.390501i
$157$			3.99241e11i			0.334031i	0.985954	+	0.167015i	$0.0534130\pi$
$157$			3.99241e11i			0.334031i	−0.985954	+	0.167015i	$0.946587\pi$
$158$	6.55222e10	+	8.70768e9i	0.0529389	+	0.00703540i
$159$	−4.52077e11			−0.352799
$160$	−5.12195e11	+	6.59122e11i	−0.386167	+	0.496943i
$161$	2.14715e12			1.56430
$162$	1.19549e12	+	1.58877e11i	0.841811	+	0.111874i
$163$			1.25328e12i			0.853134i	0.904456	+	0.426567i	$0.140277\pi$
$163$			1.25328e12i			0.853134i	−0.904456	+	0.426567i	$0.859723\pi$
$164$	1.86673e10	+	5.05086e9i	0.0122869	+	0.00332448i
$165$		−	2.61094e12i		−	1.66202i
$166$	2.84333e11	−	2.13950e12i	0.175078	−	1.31740i
$167$	−2.76577e10			−0.0164769			−0.00823845	−	0.999966i	$-0.502622\pi$
$167$	−2.76577e10			−0.0164769			−0.00823845	+	0.999966i	$0.502622\pi$
$168$	9.14053e11	−	2.18403e12i	0.526951	−	1.25909i
$169$	−8.60059e10			−0.0479900
$170$	8.18978e10	−	6.16252e11i	0.0442388	−	0.332881i
$171$			9.93844e11i			0.519804i
$172$	4.20183e11	−	1.55294e12i	0.212829	−	0.786591i
$173$			2.81906e12i			1.38309i	0.722333	+	0.691545i	$0.243070\pi$
$173$			2.81906e12i			1.38309i	−0.722333	+	0.691545i	$0.756930\pi$
$174$	4.00928e12	+	5.32820e11i	1.90566	+	0.253256i
$175$	−1.22544e12			−0.564394
$176$	−2.04263e12	+	3.49831e12i	−0.911738	+	1.56149i
$177$	−3.53185e10			−0.0152809
$178$	−5.90406e11	−	7.84629e10i	−0.247651	−	0.0329120i
$179$		−	2.44450e12i		−	0.994257i	−0.867677	−	0.497128i	$-0.834388\pi$
$179$		−	2.44450e12i		−	0.994257i	0.867677	−	0.497128i	$-0.165612\pi$
$180$	−4.72160e11	+	1.74504e12i	−0.186247	+	0.688347i
$181$			1.68134e12i			0.643313i	0.946856	+	0.321656i	$0.104240\pi$
$181$			1.68134e12i			0.643313i	−0.946856	+	0.321656i	$0.895760\pi$
$182$	3.39535e11	−	2.55488e12i	0.126035	−	0.948371i
$183$	−4.87733e12			−1.75671
$184$	4.41742e12	+	1.84877e12i	1.54408	+	0.646226i
$185$	−9.75353e10			−0.0330916
$186$	−1.27990e11	+	9.63082e11i	−0.0421557	+	0.317207i
$187$		−	3.01698e12i		−	0.964813i
$188$	−3.40680e12	−	9.21785e11i	−1.05798	−	0.286260i
$189$		−	6.02213e11i		−	0.181639i
$190$	9.76816e11	+	1.29816e11i	0.286199	+	0.0380349i
$191$	1.52171e12			0.433159			0.216579	−	0.976265i	$-0.430510\pi$
$191$	1.52171e12			0.433159			0.216579	+	0.976265i	$0.430510\pi$
$192$	3.76104e12	−	3.70626e12i	1.04028	−	1.02513i
$193$	−2.57110e12			−0.691122			−0.345561	−	0.938396i	$-0.612311\pi$
$193$	−2.57110e12			−0.691122			−0.345561	+	0.938396i	$0.612311\pi$
$194$	−5.49958e12	−	7.30876e11i	−1.43688	−	0.190956i
$195$			3.70478e12i			0.940961i
$196$	−4.94965e11	−	1.33924e11i	−0.122227	−	0.0330711i
$197$		−	1.29212e12i		−	0.310270i	−0.987893	−	0.155135i	$-0.950419\pi$
$197$		−	1.29212e12i		−	0.310270i	0.987893	−	0.155135i	$-0.0495813\pi$
$198$	−1.15577e12	+	8.69678e12i	−0.269907	+	2.03095i
$199$	5.73116e12			1.30182			0.650909	−	0.759156i	$-0.274388\pi$
$199$	5.73116e12			1.30182			0.650909	+	0.759156i	$0.274388\pi$
$200$	−2.52115e12	−	1.05515e12i	−0.557101	−	0.233156i
$201$	−3.45576e12			−0.742960
$202$	6.56781e11	−	4.94204e12i	0.137400	−	1.03389i
$203$			6.04190e12i			1.23011i
$204$	−1.02710e12	+	3.79602e12i	−0.203538	+	0.752250i
$205$		−	4.15259e10i		−	0.00801075i
$206$	−2.33976e12	−	3.10946e11i	−0.439442	−	0.0584003i
$207$	1.03709e13			1.89661
$208$	2.89838e12	−	4.96391e12i	0.516187	−	0.884048i
$209$	4.78218e12			0.829510
$210$	−5.03963e12	−	6.69750e11i	−0.851516	−	0.113164i
$211$		−	5.26177e12i		−	0.866120i	−0.901365	−	0.433060i	$-0.857434\pi$
$211$		−	5.26177e12i		−	0.866120i	0.901365	−	0.433060i	$-0.142566\pi$
$212$	3.93380e11	−	1.45388e12i	0.0630906	−	0.233175i
$213$		−	8.13372e12i		−	1.27116i
$214$	2.12124e11	−	1.59616e12i	0.0323083	−	0.243109i
$215$	−3.45456e12			−0.512839
$216$	5.18526e11	−	1.23896e12i	0.0750369	−	0.179292i
$217$	−1.45134e12			−0.204758
$218$	−1.42641e12	+	1.07332e13i	−0.196216	+	1.47645i
$219$		−	3.34661e12i		−	0.448913i
$220$	8.39681e12	+	2.27194e12i	1.09847	+	0.297216i
$221$			4.28092e12i			0.546235i
$222$	6.11604e11	+	8.12802e10i	0.0761253	+	0.0101168i
$223$	1.43803e13			1.74618			0.873091	−	0.487557i	$-0.162112\pi$
$223$	1.43803e13			1.74618			0.873091	+	0.487557i	$0.162112\pi$
$224$	6.22847e12	+	4.84006e12i	0.737934	+	0.573438i
$225$	−5.91896e12			−0.684292
$226$	−3.82052e12	−	5.07734e11i	−0.431049	−	0.0572849i
$227$		−	1.01260e13i		−	1.11505i	−0.830160	−	0.557526i	$-0.811751\pi$
$227$		−	1.01260e13i		−	1.11505i	0.830160	−	0.557526i	$-0.188249\pi$
$228$	−6.01704e12	−	1.62804e12i	−0.646757	−	0.174994i
$229$			1.58171e13i			1.65971i	0.557980	+	0.829855i	$0.311577\pi$
$229$			1.58171e13i			1.65971i	−0.557980	+	0.829855i	$0.688423\pi$
$230$	1.35464e12	−	1.01932e13i	0.138778	−	1.04426i
$231$	−2.46724e13			−2.46801
$232$	−5.20228e12	+	1.24303e13i	−0.508171	+	1.21422i
$233$	−2.84136e12			−0.271062			−0.135531	−	0.990773i	$-0.543274\pi$
$233$	−2.84136e12			−0.271062			−0.135531	+	0.990773i	$0.543274\pi$
$234$	1.63998e12	−	1.23402e13i	0.152810	−	1.14984i
$235$			7.57851e12i			0.689780i
$236$	3.07329e10	−	1.13585e11i	0.00273267	−	0.0100996i
$237$			8.97833e11i			0.0779973i
$238$	−5.82337e12	−	7.73906e11i	−0.494312	−	0.0656923i
$239$	−5.88968e12			−0.488543			−0.244272	−	0.969707i	$-0.578549\pi$
$239$	−5.88968e12			−0.488543			−0.244272	+	0.969707i	$0.578549\pi$
$240$	−9.79157e12	−	5.71720e12i	−0.793762	−	0.463470i
$241$	−1.09753e13			−0.869606			−0.434803	−	0.900526i	$-0.643182\pi$
$241$	−1.09753e13			−0.869606			−0.434803	+	0.900526i	$0.643182\pi$
$242$	2.90480e13	+	3.86038e12i	2.24974	+	0.298983i
$243$			1.89486e13i			1.43464i
$244$	4.24407e12	−	1.56855e13i	0.314151	−	1.16106i
$245$			1.10106e12i			0.0796890i
$246$	−3.46052e10	+	2.60392e11i	−0.00244906	+	0.0184283i
$247$	−6.78565e12			−0.469633
$248$	−2.98591e12	−	1.24966e12i	−0.202112	−	0.0845875i
$249$	2.93170e13			1.94099
$250$	−2.05332e12	+	1.54505e13i	−0.132980	+	1.00063i
$251$		−	9.75335e12i		−	0.617943i	−0.951071	−	0.308971i	$-0.900015\pi$
$251$		−	9.75335e12i		−	0.617943i	0.951071	−	0.308971i	$-0.0999848\pi$
$252$	1.64900e13	+	4.46174e12i	1.02216	+	0.276568i
$253$		−	4.99026e13i		−	3.02664i
$254$	1.67461e12	+	2.22550e11i	0.0993869	+	0.0132082i
$255$	8.44434e12			0.490450
$256$	8.64665e12	+	1.53206e13i	0.491505	+	0.870875i
$257$	1.22592e13			0.682072			0.341036	−	0.940050i	$-0.389222\pi$
$257$	1.22592e13			0.682072			0.341036	+	0.940050i	$0.389222\pi$
$258$	2.16621e13	+	2.87882e12i	1.17976	+	0.156786i
$259$			9.21674e11i			0.0491393i
$260$	−1.19146e13	−	3.22376e12i	−0.621908	−	0.168271i
$261$			2.91828e13i			1.49143i
$262$	−1.12172e12	+	8.44053e12i	−0.0561341	+	0.422389i
$263$	−2.88536e13			−1.41398			−0.706990	−	0.707223i	$-0.749948\pi$
$263$	−2.88536e13			−1.41398			−0.706990	+	0.707223i	$0.749948\pi$
$264$	−5.07597e13	−	2.12438e13i	−2.43611	−	1.01956i
$265$	−3.23420e12			−0.152025
$266$	1.22671e12	−	9.23057e12i	0.0564798	−	0.424991i
$267$		−	8.09017e12i		−	0.364876i
$268$	3.00707e12	−	1.11138e13i	0.132863	−	0.491043i
$269$		−	8.40804e12i		−	0.363963i	−0.983302	−	0.181982i	$-0.941749\pi$
$269$		−	8.40804e12i		−	0.363963i	0.983302	−	0.181982i	$-0.0582511\pi$
$270$	−2.85889e12	−	3.79937e11i	−0.121254	−	0.0161143i
$271$	3.44748e13			1.43275			0.716375	−	0.697715i	$-0.245800\pi$
$271$	3.44748e13			1.43275			0.716375	+	0.697715i	$0.245800\pi$
$272$	−1.13143e13	−	6.60631e12i	−0.460785	−	0.269048i
$273$	3.50088e13			1.39728
$274$	−2.77790e13	−	3.69174e12i	−1.08665	−	0.144412i
$275$			2.84809e13i			1.09200i
$276$	−1.69888e13	+	6.27884e13i	−0.638502	+	2.35982i
$277$			2.90437e13i			1.07007i	0.844829	+	0.535036i	$0.179702\pi$
$277$			2.90437e13i			1.07007i	−0.844829	+	0.535036i	$0.820298\pi$
$278$	−1.98655e12	+	1.49481e13i	−0.0717551	+	0.539932i
$279$	−7.01009e12			−0.248256
$280$	6.53922e12	−	1.56247e13i	0.227068	−	0.542554i
$281$	−2.02311e13			−0.688864			−0.344432	−	0.938811i	$-0.611929\pi$
$281$	−2.02311e13			−0.688864			−0.344432	+	0.938811i	$0.611929\pi$
$282$	6.31548e12	−	4.75218e13i	0.210880	−	1.58680i
$283$		−	2.54364e13i		−	0.832973i	−0.909142	−	0.416486i	$-0.863261\pi$
$283$		−	2.54364e13i		−	0.832973i	0.909142	−	0.416486i	$-0.136739\pi$
$284$	2.61581e13	+	7.07766e12i	0.840148	+	0.227320i
$285$			1.33850e13i			0.421670i
$286$	−5.93789e13	−	7.89125e12i	−1.83493	−	0.243856i
$287$	−3.92405e11			−0.0118955
$288$	3.00839e13	+	2.33778e13i	0.894697	+	0.695257i
$289$	−2.45143e13			−0.715290
$290$	2.86828e13	+	3.81185e12i	0.821169	+	0.109131i
$291$		−	7.53592e13i		−	2.11702i
$292$	1.07627e13	+	2.91209e12i	0.296699	+	0.0802785i
$293$		−	4.36528e13i		−	1.18097i	−0.807047	−	0.590487i	$-0.798936\pi$
$293$		−	4.36528e13i		−	1.18097i	0.807047	−	0.590487i	$-0.201064\pi$
$294$	9.17560e11	−	6.90432e12i	0.0243626	−	0.183320i
$295$	−2.52672e11			−0.00658470
$296$	−7.93593e11	+	1.89620e12i	−0.0202999	+	0.0485042i
$297$	−1.39962e13			−0.351440
$298$	−8.08452e12	+	6.08332e13i	−0.199281	+	1.49952i
$299$			7.08090e13i			1.71355i
$300$	9.69599e12	−	3.58352e13i	0.230370	−	0.851418i
$301$			3.26443e13i			0.761539i
$302$	5.64639e13	+	7.50386e12i	1.29340	+	0.171888i
$303$	6.77195e13			1.52328
$304$	1.04716e13	−	1.79342e13i	0.231317	−	0.396166i
$305$	−3.48929e13			−0.756985
$306$	−2.81272e13	−	3.73802e12i	−0.599321	−	0.0796477i
$307$			5.07739e13i			1.06262i	0.847177	+	0.531311i	$0.178301\pi$
$307$			5.07739e13i			1.06262i	−0.847177	+	0.531311i	$0.821699\pi$
$308$	2.14690e13	−	7.93469e13i	0.441350	−	1.63118i
$309$		−	3.20611e13i		−	0.647450i
$310$	−9.15655e11	+	6.88998e12i	−0.0181653	+	0.136687i
$311$	−6.19713e13			−1.20784			−0.603919	−	0.797046i	$-0.706395\pi$
$311$	−6.19713e13			−1.20784			−0.603919	+	0.797046i	$0.706395\pi$
$312$	7.20252e13	+	3.01438e13i	1.37922	+	0.577229i
$313$	−8.75349e13			−1.64698			−0.823488	−	0.567334i	$-0.807975\pi$
$313$	−8.75349e13			−1.64698			−0.823488	+	0.567334i	$0.807975\pi$
$314$	2.38019e12	−	1.79101e13i	0.0440047	−	0.331120i
$315$		−	3.66825e13i		−	0.666424i
$316$	−2.88744e12	−	7.81260e11i	−0.0515506	−	0.0139482i
$317$			3.51185e13i			0.616184i	0.951357	+	0.308092i	$0.0996904\pi$
$317$			3.51185e13i			0.616184i	−0.951357	+	0.308092i	$0.900310\pi$
$318$	2.02803e13	+	2.69519e12i	0.349725	+	0.0464772i
$319$	1.40422e14			2.38005
$320$	2.69068e13	−	2.65149e13i	0.448268	−	0.441738i
$321$	2.18717e13			0.358184
$322$	−9.63220e13	−	1.28009e13i	−1.55067	−	0.206078i
$323$			1.54666e13i			0.244783i
$324$	−5.26831e13	−	1.42546e13i	−0.819736	−	0.221798i
$325$		−	4.04128e13i		−	0.618244i
$326$	7.47182e12	−	5.62228e13i	0.112391	−	0.845699i
$327$	−1.47075e14			−2.17533
$328$	−8.07312e11	−	3.37874e11i	−0.0117418	−	0.00491416i
$329$	7.16142e13			1.02429
$330$	−1.55659e13	+	1.17128e14i	−0.218951	+	1.64753i
$331$			2.34774e13i			0.324785i	0.986726	+	0.162393i	$0.0519211\pi$
$331$			2.34774e13i			0.324785i	−0.986726	+	0.162393i	$0.948079\pi$
$332$	−2.55106e13	+	9.42838e13i	−0.347105	+	1.28286i
$333$			4.45175e12i			0.0595782i
$334$	1.24074e12	+	1.64890e11i	0.0163333	+	0.00217064i
$335$	−2.47228e13			−0.320149
$336$	−5.40255e13	+	9.25269e13i	−0.688229	+	1.17870i
$337$	−7.49908e13			−0.939817			−0.469909	−	0.882715i	$-0.655713\pi$
$337$	−7.49908e13			−0.939817			−0.469909	+	0.882715i	$0.655713\pi$
$338$	3.85826e12	+	5.12750e11i	0.0475718	+	0.00632213i
$339$		−	5.23516e13i		−	0.635084i
$340$	−7.34794e12	+	2.71571e13i	−0.0877065	+	0.324152i
$341$			3.37312e13i			0.396171i
$342$	5.92510e12	−	4.45843e13i	0.0684781	−	0.515274i
$343$	9.25757e13			1.05288
$344$	−2.81079e13	+	6.71606e13i	−0.314599	+	0.751698i
$345$	1.39674e14			1.53855
$346$	1.68067e13	−	1.26464e14i	0.182206	−	1.37104i
$347$		−	1.55759e14i		−	1.66204i	−0.556243	−	0.831020i	$-0.687758\pi$
$347$		−	1.55759e14i		−	1.66204i	0.556243	−	0.831020i	$-0.312242\pi$
$348$	−1.76682e14	−	4.78051e13i	−1.85569	−	0.502098i
$349$			8.33918e13i			0.862151i	0.902316	+	0.431075i	$0.141866\pi$
$349$			8.33918e13i			0.862151i	−0.902316	+	0.431075i	$0.858134\pi$
$350$	5.49737e13	+	7.30582e12i	0.559475	+	0.0743524i
$351$	1.98599e13			0.198970
$352$	1.12490e14	−	1.44758e14i	1.10950	−	1.42777i
$353$	1.49458e14			1.45130			0.725650	−	0.688064i	$-0.241539\pi$
$353$	1.49458e14			1.45130			0.725650	+	0.688064i	$0.241539\pi$
$354$	1.58440e12	+	2.10562e11i	0.0151477	+	0.00201308i
$355$		−	5.81894e13i		−	0.547757i
$356$	2.60181e13	+	7.03976e12i	0.241157	+	0.0652503i
$357$		−	7.97960e13i		−	0.728292i
$358$	−1.45736e13	+	1.09661e14i	−0.130982	+	0.985592i
$359$	−6.32768e13			−0.560048			−0.280024	−	0.959993i	$-0.590342\pi$
$359$	−6.32768e13			−0.560048			−0.280024	+	0.959993i	$0.590342\pi$
$360$	3.15849e13	−	7.54684e13i	0.275306	−	0.657812i
$361$	9.19743e13			0.789545
$362$	1.00238e13	−	7.54254e13i	0.0847490	−	0.637706i
$363$			3.98037e14i			3.31464i
$364$	−3.04634e13	+	1.12589e14i	−0.249874	+	0.923501i
$365$		−	2.39419e13i		−	0.193441i
$366$	2.18799e14	+	2.90776e13i	1.74140	+	0.231427i
$367$	−8.87827e13			−0.696089			−0.348045	−	0.937478i	$-0.613154\pi$
$367$	−8.87827e13			−0.696089			−0.348045	+	0.937478i	$0.613154\pi$
$368$	−1.87145e14	−	1.09272e14i	−1.44549	−	0.844009i
$369$	−1.89534e12			−0.0144226
$370$	4.37548e12	+	5.81486e11i	0.0328032	+	0.00435943i
$371$			3.05620e13i			0.225749i
$372$	1.14834e13	−	4.24412e13i	0.0835766	−	0.308888i
$373$		−	1.82710e14i		−	1.31028i	−0.755509	−	0.655138i	$-0.772610\pi$
$373$		−	1.82710e14i		−	1.31028i	0.755509	−	0.655138i	$-0.227390\pi$
$374$	−1.79866e13	+	1.35343e14i	−0.127103	+	0.956404i
$375$	−2.11714e14			−1.47427
$376$	1.47335e14	+	6.16623e13i	1.01105	+	0.423142i
$377$	−1.99251e14			−1.34748
$378$	−3.59027e12	+	2.70155e13i	−0.0239289	+	0.180056i
$379$		−	2.46172e14i		−	1.61705i	−0.588462	−	0.808525i	$-0.700266\pi$
$379$		−	2.46172e14i		−	1.61705i	0.588462	−	0.808525i	$-0.299734\pi$
$380$	−4.30464e13	−	1.16472e13i	−0.278694	−	0.0754068i
$381$			2.29468e13i			0.146431i
$382$	−6.82644e13	−	9.07211e12i	−0.429384	−	0.0570637i
$383$	−7.50083e13			−0.465067			−0.232534	−	0.972588i	$-0.574702\pi$
$383$	−7.50083e13			−0.465067			−0.232534	+	0.972588i	$0.574702\pi$
$384$	−1.90818e14	+	1.43842e14i	−1.16626	+	0.879150i
$385$	−1.76509e14			−1.06349
$386$	1.15341e14	+	1.53284e13i	0.685098	+	0.0910472i
$387$			1.57674e14i			0.923317i
$388$	2.42356e14	+	6.55748e13i	1.39920	+	0.378584i
$389$			5.05564e13i			0.287775i	0.989594	+	0.143888i	$0.0459604\pi$
$389$			5.05564e13i			0.287775i	−0.989594	+	0.143888i	$0.954040\pi$
$390$	2.20871e13	−	1.66198e14i	0.123961	−	0.932760i
$391$	1.61396e14			0.893141
$392$	2.14059e13	+	8.95876e12i	0.116805	+	0.0488849i
$393$	−1.15658e14			−0.622325
$394$	−7.70338e12	+	5.79652e13i	−0.0408745	+	0.307566i
$395$			6.42318e12i			0.0336098i
$396$	1.03697e14	−	3.83251e14i	0.535109	−	1.97770i
$397$			2.54153e14i			1.29345i	0.762725	+	0.646723i	$0.223861\pi$
$397$			2.54153e14i			1.29345i	−0.762725	+	0.646723i	$0.776139\pi$
$398$	−2.57102e14	−	3.41680e13i	−1.29047	−	0.171499i
$399$	1.26484e14			0.626159
$400$	1.06809e14	+	6.23649e13i	0.521530	+	0.304516i
$401$	2.66905e14			1.28547			0.642736	−	0.766087i	$-0.277799\pi$
$401$	2.66905e14			1.28547			0.642736	+	0.766087i	$0.277799\pi$
$402$	1.55027e14	+	2.06025e13i	0.736484	+	0.0978763i
$403$		−	4.78627e13i		−	0.224295i
$404$	−5.89269e13	+	2.17786e14i	−0.272406	+	1.00678i
$405$			1.17195e14i			0.534449i
$406$	3.60206e13	−	2.71042e14i	0.162053	−	1.21939i
$407$	2.14209e13			0.0950757
$408$	6.87071e13	−	1.64168e14i	0.300864	−	0.718880i
$409$	6.02544e13			0.260322			0.130161	−	0.991493i	$-0.458451\pi$
$409$	6.02544e13			0.260322			0.130161	+	0.991493i	$0.458451\pi$
$410$	−2.47569e11	+	1.86287e12i	−0.00105532	+	0.00794093i
$411$		−	3.80648e14i		−	1.60101i
$412$	1.03109e14	+	2.78983e13i	0.427918	+	0.115783i
$413$			2.38766e12i			0.00977794i
$414$	−4.65242e14	−	6.18290e13i	−1.88008	−	0.249856i
$415$	2.09737e14			0.836392
$416$	−1.59616e14	+	2.05404e14i	−0.628151	+	0.808342i
$417$	−2.04829e14			−0.795506
$418$	−2.14531e14	−	2.85104e13i	−0.822281	−	0.109278i
$419$		−	1.79929e14i		−	0.680652i	−0.940308	−	0.340326i	$-0.889463\pi$
$419$		−	1.79929e14i		−	0.680652i	0.940308	−	0.340326i	$-0.110537\pi$
$420$	2.22087e14	+	6.00905e13i	0.829186	+	0.224355i
$421$			3.46928e13i			0.127846i	0.997955	+	0.0639230i	$0.0203612\pi$
$421$			3.46928e13i			0.127846i	−0.997955	+	0.0639230i	$0.979639\pi$
$422$	−3.13696e13	+	2.36045e14i	−0.114101	+	0.858572i
$423$	3.45902e14			1.24188
$424$	−2.63149e13	+	6.28765e13i	−0.0932589	+	0.222831i
$425$	−9.21132e13			−0.322243
$426$	−4.84916e13	+	3.64882e14i	−0.167461	+	1.26008i
$427$			3.29725e14i			1.12408i
$428$	−1.90320e13	+	7.03398e13i	−0.0640535	+	0.236734i
$429$		−	8.13652e14i		−	2.70348i
$430$	1.54973e14	+	2.05954e13i	0.508369	+	0.0675606i
$431$	4.31764e14			1.39837			0.699183	−	0.714942i	$-0.253547\pi$
$431$	4.31764e14			1.39837			0.699183	+	0.714942i	$0.253547\pi$
$432$	−3.06477e13	+	5.24888e13i	−0.0980026	+	0.167844i
$433$	−2.28552e14			−0.721607			−0.360804	−	0.932642i	$-0.617498\pi$
$433$	−2.28552e14			−0.721607			−0.360804	+	0.932642i	$0.617498\pi$
$434$	6.51079e13	+	8.65262e12i	0.202974	+	0.0269745i
$435$			3.93032e14i			1.20987i
$436$	1.27979e14	−	4.72993e14i	0.389011	−	1.43774i
$437$			2.55827e14i			0.767889i
$438$	−1.99518e13	+	1.50130e14i	−0.0591391	+	0.445000i
$439$	−1.54004e14			−0.450793			−0.225396	−	0.974267i	$-0.572368\pi$
$439$	−1.54004e14			−0.450793			−0.225396	+	0.974267i	$0.572368\pi$
$440$	−3.63139e14	−	1.51980e14i	−1.04974	−	0.439337i
$441$	5.02552e13			0.143472
$442$	2.55220e13	−	1.92044e14i	0.0719602	−	0.541475i
$443$		−	3.23030e13i		−	0.0899544i	−0.998988	−	0.0449772i	$-0.985678\pi$
$443$		−	3.23030e13i		−	0.0899544i	0.998988	−	0.0449772i	$-0.0143215\pi$
$444$	−2.69523e13	−	7.29252e12i	−0.0741291	−	0.0200573i
$445$		−	5.78778e13i		−	0.157229i
$446$	−6.45104e14	−	8.57321e13i	−1.73096	−	0.230039i
$447$	−8.33580e14			−2.20931
$448$	−2.50556e14	−	2.54260e14i	−0.655959	−	0.665655i
$449$	4.84104e14			1.25194			0.625971	−	0.779847i	$-0.284703\pi$
$449$	4.84104e14			1.25194			0.625971	+	0.779847i	$0.284703\pi$
$450$	2.65527e14	+	3.52876e13i	0.678328	+	0.0901475i
$451$			9.12002e12i			0.0230157i
$452$	1.68363e14	+	4.55544e13i	0.419745	+	0.113571i
$453$			7.73709e14i			1.90563i
$454$	−6.03691e13	+	4.54256e14i	−0.146895	+	1.10533i
$455$	2.50456e14			0.602101
$456$	2.60221e14	+	1.08907e14i	0.618067	+	0.258672i
$457$	−4.79410e14			−1.12504			−0.562520	−	0.826784i	$-0.690168\pi$
$457$	−4.79410e14			−1.12504			−0.562520	+	0.826784i	$0.690168\pi$
$458$	9.42984e13	−	7.09562e14i	0.218647	−	1.64524i
$459$		−	4.52668e13i		−	0.103708i
$460$	−1.21539e14	+	4.49194e14i	−0.275137	+	1.01687i
$461$		−	5.25368e14i		−	1.17519i	−0.809155	−	0.587596i	$-0.800075\pi$
$461$		−	5.25368e14i		−	1.17519i	0.809155	−	0.587596i	$-0.199925\pi$
$462$	1.10682e15	+	1.47092e14i	2.44650	+	0.325131i
$463$	−6.31023e14			−1.37832			−0.689160	−	0.724609i	$-0.742020\pi$
$463$	−6.31023e14			−1.37832			−0.689160	+	0.724609i	$0.742020\pi$
$464$	3.07483e14	−	5.26612e14i	0.663701	−	1.13669i
$465$	−9.44115e13			−0.201388
$466$	1.27465e14	+	1.69396e13i	0.268700	+	0.0357093i
$467$		−	7.08089e13i		−	0.147518i	−0.997276	−	0.0737589i	$-0.976500\pi$
$467$		−	7.08089e13i		−	0.147518i	0.997276	−	0.0737589i	$-0.0234995\pi$
$468$	−1.47140e14	+	5.43811e14i	−0.302956	+	1.11969i
$469$			2.33622e14i			0.475404i
$470$	4.51815e13	−	3.39975e14i	0.0908705	−	0.683768i
$471$	2.45417e14			0.487854
$472$	−2.05586e12	+	4.91224e12i	−0.00403936	+	0.00965158i
$473$	7.58698e14			1.47344
$474$	5.35270e12	−	4.02772e13i	0.0102752	−	0.0773175i
$475$		−	1.46008e14i		−	0.277052i
$476$	2.56625e14	+	6.94355e13i	0.481349	+	0.130240i
$477$			1.47617e14i			0.273706i
$478$	2.64213e14	+	3.51131e13i	0.484285	+	0.0643599i
$479$	−4.34793e14			−0.787839			−0.393920	−	0.919145i	$-0.628881\pi$
$479$	−4.34793e14			−0.787839			−0.393920	+	0.919145i	$0.628881\pi$
$480$	4.05169e14	+	3.14851e14i	0.725788	+	0.564000i
$481$	−3.03951e13			−0.0538277
$482$	4.92356e14	+	6.54325e13i	0.862027	+	0.114560i
$483$		−	1.31987e15i		−	2.28467i
$484$	−1.28009e15	−	3.46357e14i	−2.19074	−	0.592753i
$485$		−	5.39127e14i		−	0.912245i
$486$	1.12968e14	−	8.50043e14i	0.188997	−	1.42214i
$487$	−2.70827e14			−0.448005			−0.224003	−	0.974589i	$-0.571912\pi$
$487$	−2.70827e14			−0.448005			−0.224003	+	0.974589i	$0.571912\pi$
$488$	−2.83905e14	+	6.78357e14i	−0.464369	+	1.10956i
$489$	7.70406e14			1.24601
$490$	6.56431e12	−	4.93941e13i	0.0104981	−	0.0789945i
$491$			1.12389e15i			1.77736i	0.458526	+	0.888681i	$0.348378\pi$
$491$			1.12389e15i			1.77736i	−0.458526	+	0.888681i	$0.651622\pi$
$492$	3.10481e12	−	1.14750e13i	0.00485542	−	0.0179450i
$493$			4.54154e14i			0.702337i
$494$	3.04407e14	+	4.04547e13i	0.465540	+	0.0618687i
$495$	−8.52550e14			−1.28941
$496$	1.26499e14	+	7.38615e13i	0.189207	+	0.110476i
$497$	−5.49869e14			−0.813391
$498$	−1.31517e15	−	1.74782e14i	−1.92407	−	0.255703i
$499$			1.21291e15i			1.75499i	0.479584	+	0.877496i	$0.340788\pi$
$499$			1.21291e15i			1.75499i	−0.479584	+	0.877496i	$0.659212\pi$
$500$	1.84225e14	−	6.80873e14i	0.263642	−	0.974386i
$501$			1.70015e13i			0.0240646i
$502$	−5.81475e13	+	4.37539e14i	−0.0814068	+	0.612557i
$503$	1.06469e15			1.47434			0.737171	−	0.675706i	$-0.236161\pi$
$503$	1.06469e15			1.47434			0.737171	+	0.675706i	$0.236161\pi$
$504$	−7.13150e14	−	2.98466e14i	−0.976816	−	0.408815i
$505$	4.84471e14			0.656395
$506$	−2.97509e14	+	2.23865e15i	−0.398724	+	3.00026i
$507$			5.28687e13i			0.0700898i
$508$	−7.37971e13	−	1.99674e13i	−0.0967807	−	0.0261861i
$509$			4.01457e13i			0.0520824i	0.999661	+	0.0260412i	$0.00829010\pi$
$509$			4.01457e13i			0.0520824i	−0.999661	+	0.0260412i	$0.991710\pi$
$510$	−3.78816e14	−	5.03434e13i	−0.486175	−	0.0646110i
$511$	−2.26243e14			−0.287250
$512$	−2.96554e14	−	7.38838e14i	−0.372494	−	0.928035i
$513$	7.17521e13			0.0891639
$514$	−5.49953e14	−	7.30869e13i	−0.676128	−	0.0898551i
$515$		−	2.29368e14i		−	0.278993i
$516$	−9.54609e14	−	2.58290e14i	−1.14882	−	0.310839i
$517$		−	1.66441e15i		−	1.98181i
$518$	5.49484e12	−	4.13467e13i	0.00647353	−	0.0487110i
$519$	1.73290e15			2.02001
$520$	5.15275e14	+	2.15652e14i	0.594320	+	0.248733i
$521$	−1.21993e15			−1.39228			−0.696139	−	0.717907i	$-0.745100\pi$
$521$	−1.21993e15			−1.39228			−0.696139	+	0.717907i	$0.745100\pi$
$522$	1.73982e14	−	1.30915e15i	0.196479	−	1.47844i
$523$		−	1.26264e15i		−	1.41098i	−0.708719	−	0.705491i	$-0.750726\pi$
$523$		−	1.26264e15i		−	1.41098i	0.708719	−	0.705491i	$-0.249274\pi$
$524$	1.00641e14	−	3.71958e14i	0.111290	−	0.411313i
$525$			7.53290e14i			0.824301i
$526$	1.29438e15	+	1.72019e14i	1.40166	+	0.186275i
$527$	−1.09094e14			−0.116907
$528$	2.15045e15	+	1.25563e15i	2.28057	+	1.33160i
$529$	1.71677e15			1.80180
$530$	1.45087e14	+	1.92816e13i	0.150700	+	0.0200275i
$531$			1.15326e13i			0.0118551i
$532$	−1.10062e14	+	4.06774e14i	−0.111975	+	0.413846i
$533$		−	1.29408e13i		−	0.0130305i
$534$	−4.82319e13	+	3.62928e14i	−0.0480682	+	0.361696i
$535$	1.56472e14			0.154345
$536$	−2.01156e14	+	4.80640e14i	−0.196394	+	0.469260i
$537$	−1.50266e15			−1.45212
$538$	−5.01270e13	+	3.77188e14i	−0.0479479	+	0.360791i
$539$		−	2.41818e14i		−	0.228955i
$540$	1.25986e14	+	3.40883e13i	0.118075	+	0.0319477i
$541$		−	3.54348e14i		−	0.328735i	−0.986399	−	0.164367i	$-0.947442\pi$
$541$		−	3.54348e14i		−	0.328735i	0.986399	−	0.164367i	$-0.0525582\pi$
$542$	−1.54655e15	−	2.05532e14i	−1.42026	−	0.188748i
$543$	1.03353e15			0.939562
$544$	4.68179e14	+	3.63815e14i	0.421325	+	0.327406i
$545$	−1.05219e15			−0.937371
$546$	−1.57051e15	−	2.08716e14i	−1.38510	−	0.184075i
$547$			7.75943e14i			0.677485i	0.940879	+	0.338742i	$0.110002\pi$
$547$			7.75943e14i			0.677485i	−0.940879	+	0.338742i	$0.889998\pi$
$548$	1.22417e15	+	3.31226e14i	1.05815	+	0.286307i
$549$			1.59259e15i			1.36288i
$550$	1.69797e14	−	1.27766e15i	0.143859	−	1.08248i
$551$	−7.19876e14			−0.603843
$552$	1.13646e15	−	2.71543e15i	0.943817	−	2.25514i
$553$	6.06968e13			0.0499088
$554$	1.73152e14	−	1.30291e15i	0.140969	−	1.06075i
$555$			5.99559e13i			0.0483304i
$556$	1.78235e14	−	6.58733e14i	0.142259	−	0.525773i
$557$			2.10320e15i			1.66217i	0.556142	+	0.831087i	$0.312281\pi$
$557$			2.10320e15i			1.66217i	−0.556142	+	0.831087i	$0.687719\pi$
$558$	3.14475e14	+	4.17927e13i	0.246093	+	0.0327049i
$559$	−1.07655e15			−0.834199
$560$	−3.86504e14	+	6.61946e14i	−0.296565	+	0.507912i
$561$	−1.85457e15			−1.40912
$562$	9.07573e14	+	1.20613e14i	0.682861	+	0.0907499i
$563$		−	1.63585e15i		−	1.21884i	−0.792847	−	0.609421i	$-0.791402\pi$
$563$		−	1.63585e15i		−	1.21884i	0.792847	−	0.609421i	$-0.208598\pi$
$564$	−5.66630e14	+	2.09419e15i	−0.418085	+	1.54519i
$565$		−	3.74528e14i		−	0.273664i
$566$	−1.51647e14	+	1.14109e15i	−0.109734	+	0.825713i
$567$	1.10745e15			0.793629
$568$	−1.13127e15	−	4.73456e14i	−0.802879	−	0.336019i
$569$	−1.39084e15			−0.977600			−0.488800	−	0.872396i	$-0.662565\pi$
$569$	−1.39084e15			−0.977600			−0.488800	+	0.872396i	$0.662565\pi$
$570$	7.97989e13	−	6.00459e14i	0.0555502	−	0.417995i
$571$			4.75616e14i			0.327912i	0.986468	+	0.163956i	$0.0524256\pi$
$571$			4.75616e14i			0.327912i	−0.986468	+	0.163956i	$0.947574\pi$
$572$	2.61671e15	+	7.08010e14i	1.78681	+	0.483460i
$573$		−	9.35408e14i		−	0.632631i
$574$	1.76035e13	+	2.33944e12i	0.0117919	+	0.00156710i
$575$	−1.52361e15			−1.01088
$576$	−1.21020e15	−	1.22809e15i	−0.795308	−	0.807063i
$577$	1.75308e15			1.14113			0.570565	−	0.821253i	$-0.306724\pi$
$577$	1.75308e15			1.14113			0.570565	+	0.821253i	$0.306724\pi$
$578$	1.09972e15	+	1.46150e14i	0.709056	+	0.0942311i
$579$			1.58048e15i			1.00939i
$580$	−1.26400e15	−	3.42002e14i	−0.799635	−	0.216359i
$581$		−	1.98194e15i		−	1.24200i
$582$	−4.49276e14	+	3.38065e15i	−0.278893	+	2.09857i
$583$	7.10302e14			0.436784
$584$	−4.65459e14	−	1.94803e14i	−0.283538	−	0.118666i
$585$	1.20972e15			0.730009
$586$	−2.60249e14	+	1.95828e15i	−0.155580	+	1.17068i
$587$			2.52743e14i			0.149682i	0.997195	+	0.0748411i	$0.0238450\pi$
$587$			2.52743e14i			0.149682i	−0.997195	+	0.0748411i	$0.976155\pi$
$588$	−8.23243e13	+	3.04260e14i	−0.0483006	+	0.178513i
$589$		−	1.72924e14i		−	0.100513i
$590$	1.13350e13	+	1.50638e12i	0.00652731	+	0.000867458i
$591$	−7.94281e14			−0.453151
$592$	4.69057e13	−	8.03331e13i	0.0265128	−	0.0454072i
$593$	−1.60285e15			−0.897620			−0.448810	−	0.893627i	$-0.648152\pi$
$593$	−1.60285e15			−0.897620			−0.448810	+	0.893627i	$0.648152\pi$
$594$	6.27877e14	+	8.34428e13i	0.348377	+	0.0462981i
$595$		−	5.70868e14i		−	0.313828i
$596$	7.25350e14	−	2.68080e15i	0.395088	−	1.46019i
$597$		−	3.52300e15i		−	1.90131i
$598$	4.22149e14	−	3.17652e15i	0.225740	−	1.69862i
$599$	1.39444e15			0.738845			0.369423	−	0.929262i	$-0.379556\pi$
$599$	1.39444e15			0.738845			0.369423	+	0.929262i	$0.379556\pi$
$600$	−6.48608e14	+	1.54978e15i	−0.340526	+	0.813649i
$601$	3.53611e15			1.83957			0.919785	−	0.392423i	$-0.128363\pi$
$601$	3.53611e15			1.83957			0.919785	+	0.392423i	$0.128363\pi$
$602$	1.94619e14	−	1.46444e15i	0.100324	−	0.754902i
$603$			1.12841e15i			0.576397i
$604$	−2.48826e15	−	6.73252e14i	−1.25948	−	0.340781i
$605$			2.84759e15i			1.42831i
$606$	−3.03792e15	−	4.03730e14i	−1.51000	−	0.200674i
$607$	−5.45509e14			−0.268698			−0.134349	−	0.990934i	$-0.542894\pi$
$607$	−5.45509e14			−0.268698			−0.134349	+	0.990934i	$0.542894\pi$
$608$	−5.76680e14	+	7.42106e14i	−0.281492	+	0.362240i
$609$	3.71402e15			1.79659
$610$	1.56531e15	+	2.08024e14i	0.750388	+	0.0997240i
$611$			2.36171e15i			1.12202i
$612$	1.23951e15	+	3.35378e14i	0.583605	+	0.157907i
$613$			2.17927e15i			1.01690i	0.861092	+	0.508449i	$0.169781\pi$
$613$			2.17927e15i			1.01690i	−0.861092	+	0.508449i	$0.830219\pi$
$614$	3.02703e14	−	2.27774e15i	0.139988	−	1.05336i
$615$	−2.55264e13			−0.0116997
$616$	−1.43616e15	+	3.43154e15i	−0.652392	+	1.55882i
$617$	2.32210e15			1.04547			0.522736	−	0.852495i	$-0.324911\pi$
$617$	2.32210e15			1.04547			0.522736	+	0.852495i	$0.324911\pi$
$618$	−1.91142e14	+	1.43827e15i	−0.0852940	+	0.641807i
$619$		−	4.01617e15i		−	1.77629i	−0.459565	−	0.888144i	$-0.651995\pi$
$619$		−	4.01617e15i		−	1.77629i	0.459565	−	0.888144i	$-0.348005\pi$
$620$	8.21533e13	−	3.03628e14i	0.0360140	−	0.133103i
$621$		−	7.48741e14i		−	0.325333i
$622$	2.78006e15	+	3.69460e14i	1.19731	+	0.159119i
$623$	−5.46925e14			−0.233477
$624$	−3.05137e15	−	1.78166e15i	−1.29116	−	0.753894i
$625$	−7.47540e13			−0.0313541
$626$	3.92685e15	+	5.21865e14i	1.63262	+	0.216970i
$627$		−	2.93966e15i		−	1.21150i
$628$	−2.13553e14	+	7.89264e14i	−0.0872423	+	0.322437i
$629$			6.92799e13i			0.0280562i
$630$	−2.18694e14	+	1.64559e15i	−0.0877936	+	0.660616i
$631$	−1.38773e15			−0.552259			−0.276129	−	0.961120i	$-0.589052\pi$
$631$	−1.38773e15			−0.552259			−0.276129	+	0.961120i	$0.589052\pi$
$632$	1.24874e14	+	5.22620e13i	0.0492638	+	0.0206178i
$633$	−3.23446e15			−1.26497
$634$	2.09370e14	−	1.57543e15i	0.0811750	−	0.610813i
$635$			1.64163e14i			0.0630987i
$636$	−8.93716e14	−	2.41815e14i	−0.340554	−	0.0921443i
$637$			3.43126e14i			0.129625i
$638$	−6.29938e15	−	8.37167e14i	−2.35931	−	0.313544i
$639$	−2.65590e15			−0.986183
$640$	−1.36513e15	+	1.02906e15i	−0.502555	+	0.378834i
$641$	−2.53590e15			−0.925578			−0.462789	−	0.886468i	$-0.653151\pi$
$641$	−2.53590e15			−0.925578			−0.462789	+	0.886468i	$0.653151\pi$
$642$	−9.81175e14	−	1.30395e14i	−0.355062	−	0.0471865i
$643$			1.12796e15i			0.404702i	0.979313	+	0.202351i	$0.0648581\pi$
$643$			1.12796e15i			0.404702i	−0.979313	+	0.202351i	$0.935142\pi$
$644$	4.24473e15	+	1.14850e15i	1.51000	+	0.408564i
$645$			2.12355e15i			0.749004i
$646$	9.22088e13	−	6.93838e14i	0.0322473	−	0.242650i
$647$	−2.17688e15			−0.754849			−0.377425	−	0.926040i	$-0.623190\pi$
$647$	−2.17688e15			−0.754849			−0.377425	+	0.926040i	$0.623190\pi$
$648$	2.27841e15	+	9.53553e14i	0.783373	+	0.327855i
$649$	5.54925e13			0.0189186
$650$	−2.40933e14	+	1.81293e15i	−0.0814465	+	0.612856i
$651$			8.92155e14i			0.299051i
$652$	−6.70378e14	+	2.47763e15i	−0.222822	+	0.823522i
$653$		−	1.39356e15i		−	0.459308i	−0.973272	−	0.229654i	$-0.926241\pi$
$653$		−	1.39356e15i		−	0.459308i	0.973272	−	0.229654i	$-0.0737595\pi$
$654$	6.59783e15	+	8.76829e14i	2.15637	+	0.286574i
$655$	−8.27430e14			−0.268166
$656$	3.42020e13	+	1.99702e13i	0.0109921	+	0.00641818i
$657$	−1.09277e15			−0.348272
$658$	−3.21264e15	−	4.26950e14i	−1.01536	−	0.134938i
$659$		−	3.27261e13i		−	0.0102571i	−0.999987	−	0.00512855i	$-0.998368\pi$
$659$		−	3.27261e13i		−	0.0102571i	0.999987	−	0.00512855i	$-0.00163248\pi$
$660$	1.39658e15	−	5.16160e15i	0.434086	−	1.60433i
$661$			2.81288e15i			0.867048i	0.901142	+	0.433524i	$0.142730\pi$
$661$			2.81288e15i			0.867048i	−0.901142	+	0.433524i	$0.857270\pi$
$662$	1.39968e14	−	1.05321e15i	0.0427866	−	0.321954i
$663$	2.63153e15			0.797780
$664$	1.70651e15	−	4.07752e15i	0.513081	−	1.22595i
$665$	9.04878e14			0.269818
$666$	2.65404e13	−	1.99707e14i	0.00784873	−	0.0590589i
$667$			7.51199e15i			2.20324i
$668$	−5.46769e13	−	1.47940e13i	−0.0159050	−	0.00430344i
$669$		−	8.83968e15i		−	2.55031i
$670$	1.10908e15	+	1.47392e14i	0.317358	+	0.0421759i
$671$	7.66325e15			2.17490
$672$	2.97523e15	−	3.82870e15i	0.837510	−	1.07776i
$673$	−5.96615e14			−0.166576			−0.0832878	−	0.996526i	$-0.526542\pi$
$673$	−5.96615e14			−0.166576			−0.0832878	+	0.996526i	$0.526542\pi$
$674$	3.36412e15	+	4.47080e14i	0.931626	+	0.123810i
$675$			4.27328e14i			0.117379i
$676$	−1.70026e14	−	4.60043e13i	−0.0463243	−	0.0125341i
$677$			1.72010e15i			0.464852i	0.972614	+	0.232426i	$0.0746664\pi$
$677$			1.72010e15i			0.464852i	−0.972614	+	0.232426i	$0.925334\pi$
$678$	−3.12109e14	+	2.34851e15i	−0.0836650	+	0.629549i
$679$	−5.09456e15			−1.35464
$680$	4.91537e14	−	1.17447e15i	0.129645	−	0.309773i
$681$	−6.22454e15			−1.62854
$682$	2.01098e14	−	1.51319e15i	0.0521909	−	0.392718i
$683$		−	3.47597e15i		−	0.894873i	−0.894316	−	0.447437i	$-0.852337\pi$
$683$		−	3.47597e15i		−	0.894873i	0.894316	−	0.447437i	$-0.147663\pi$
$684$	−5.31605e14	+	1.96474e15i	−0.135763	+	0.501762i
$685$		−	2.72319e15i		−	0.689891i
$686$	−4.15298e15	−	5.51918e14i	−1.04370	−	0.138705i
$687$	9.72293e15			2.42402
$688$	1.66133e15	−	2.84528e15i	0.410884	−	0.703701i
$689$	−1.00788e15			−0.247288
$690$	−6.26585e15	−	8.32710e14i	−1.52514	−	0.202686i
$691$		−	5.25598e15i		−	1.26918i	−0.772847	−	0.634592i	$-0.781168\pi$
$691$		−	5.25598e15i		−	1.26918i	0.772847	−	0.634592i	$-0.218832\pi$
$692$	−1.50791e15	+	5.57304e15i	−0.361236	+	1.33508i
$693$			8.05630e15i			1.91471i
$694$	−9.28604e14	+	6.98742e15i	−0.218954	+	1.64755i
$695$	−1.46537e15			−0.342792
$696$	7.64100e15	+	3.19790e15i	1.77337	+	0.742187i
$697$	−2.94961e13			−0.00679179
$698$	4.97165e14	−	3.74099e15i	0.113578	−	0.854637i
$699$			1.74661e15i			0.395888i
$700$	−2.42259e15	−	6.55485e14i	−0.544804	−	0.147409i
$701$			4.67964e14i			0.104415i	0.998636	+	0.0522075i	$0.0166257\pi$
$701$			4.67964e14i			0.104415i	−0.998636	+	0.0522075i	$0.983374\pi$
$702$	−8.90923e14	−	1.18401e14i	−0.197236	−	0.0262120i
$703$	−1.09815e14			−0.0241217
$704$	−5.90934e15	+	5.82327e15i	−1.28792	+	1.26916i
$705$	4.65858e15			1.00743
$706$	−6.70473e15	−	8.91036e14i	−1.43865	−	0.191192i
$707$		−	4.57808e15i		−	0.974713i
$708$	−6.98217e13	−	1.88918e13i	−0.0147505	−	0.00399108i
$709$		−	1.20690e15i		−	0.252999i	−0.991967	−	0.126499i	$-0.959626\pi$
$709$		−	1.20690e15i		−	0.252999i	0.991967	−	0.126499i	$-0.0403742\pi$
$710$	−3.46913e14	+	2.61040e15i	−0.0721606	+	0.542983i
$711$	2.93170e14			0.0605112
$712$	−1.12521e15	−	4.70921e14i	−0.230459	−	0.0964513i
$713$	−1.80448e15			−0.366741
$714$	−4.75727e14	+	3.57968e15i	−0.0959441	+	0.721945i
$715$		−	5.82094e15i		−	1.16496i
$716$	1.30756e15	−	4.83257e15i	0.259680	−	0.959746i
$717$			3.62044e15i			0.713520i
$718$	2.83862e15	+	3.77244e14i	0.555167	+	0.0737798i
$719$	−1.32049e15			−0.256287			−0.128144	−	0.991756i	$-0.540902\pi$
$719$	−1.32049e15			−0.256287			−0.128144	+	0.991756i	$0.540902\pi$
$720$	−1.86684e15	+	3.19724e15i	−0.359565	+	0.615810i
$721$	−2.16744e15			−0.414290
$722$	−4.12600e15	−	5.48332e14i	−0.782664	−	0.104013i
$723$			6.74662e15i			1.27006i
$724$	−8.99342e14	+	3.32385e15i	−0.168021	+	0.620983i
$725$		−	4.28731e15i		−	0.794924i
$726$	2.37302e15	−	1.78561e16i	0.436666	−	3.28576i
$727$	3.07963e14			0.0562419			0.0281209	−	0.999605i	$-0.491048\pi$
$727$	3.07963e14			0.0562419			0.0281209	+	0.999605i	$0.491048\pi$
$728$	2.03783e15	−	4.86916e15i	0.369356	−	0.882535i
$729$	6.92709e15			1.24609
$730$	−1.42737e14	+	1.07405e15i	−0.0254836	+	0.191755i
$731$			2.45379e15i			0.434803i
$732$	−9.64206e15	−	2.60887e15i	−1.69574	−	0.458819i
$733$			1.44204e15i			0.251713i	0.992048	+	0.125857i	$0.0401679\pi$
$733$			1.44204e15i			0.251713i	−0.992048	+	0.125857i	$0.959832\pi$
$734$	3.98283e15	+	5.29304e14i	0.690022	+	0.0917017i
$735$	6.76834e14			0.116386
$736$	7.74396e15	+	6.01772e15i	1.32171	+	1.02708i
$737$	5.42969e15			0.919822
$738$	8.50259e13	+	1.12997e13i	0.0142969	+	0.00190001i
$739$			5.97633e15i			0.997448i	0.866761	+	0.498724i	$0.166198\pi$
$739$			5.97633e15i			0.997448i	−0.866761	+	0.498724i	$0.833802\pi$
$740$	−1.92819e14	−	5.21714e13i	−0.0319430	−	0.00864287i
$741$			4.17121e15i			0.685902i
$742$	1.82205e14	−	1.37103e15i	0.0297398	−	0.223781i
$743$	6.49549e15			1.05238			0.526191	−	0.850366i	$-0.323620\pi$
$743$	6.49549e15			1.05238			0.526191	+	0.850366i	$0.323620\pi$
$744$	−7.68176e14	+	1.83547e15i	−0.123541	+	0.295186i
$745$	−5.96351e15			−0.952012
$746$	−1.08928e15	+	8.19643e15i	−0.172614	+	1.29886i
$747$		−	9.57289e15i		−	1.50584i
$748$	1.61377e15	−	5.96430e15i	0.251990	−	0.931324i
$749$		−	1.47861e15i		−	0.229194i
$750$	9.49756e15	+	1.26219e15i	1.46142	+	0.194218i
$751$	6.32748e14			0.0966520			0.0483260	−	0.998832i	$-0.484611\pi$
$751$	6.32748e14			0.0966520			0.0483260	+	0.998832i	$0.484611\pi$
$752$	−6.24189e15	−	3.64458e15i	−0.946494	−	0.552649i
$753$	−5.99548e15			−0.902509
$754$	8.93848e15	+	1.18789e15i	1.33574	+	0.177515i
$755$			5.53519e15i			0.821153i
$756$	3.22122e14	−	1.19052e15i	0.0474407	−	0.175335i
$757$		−	1.19933e16i		−	1.75353i	−0.480922	−	0.876763i	$-0.659698\pi$
$757$		−	1.19933e16i		−	1.75353i	0.480922	−	0.876763i	$-0.340302\pi$
$758$	−1.46763e15	+	1.10434e16i	−0.213027	+	1.60296i
$759$	−3.06756e16			−4.42042
$760$	1.86164e15	+	7.79131e14i	0.266331	+	0.111464i
$761$	1.09654e16			1.55743			0.778716	−	0.627377i	$-0.215872\pi$
$761$	1.09654e16			1.55743			0.778716	+	0.627377i	$0.215872\pi$
$762$	1.36804e14	−	1.02940e15i	0.0192906	−	0.145155i
$763$			9.94278e15i			1.39195i
$764$	3.00828e15	+	8.13957e14i	0.418124	+	0.113133i
$765$		−	2.75733e15i		−	0.380497i
$766$	3.36490e15	+	4.47184e14i	0.461014	+	0.0612672i
$767$	−7.87407e13			−0.0107109
$768$	9.41772e15	−	5.31518e15i	1.27192	−	0.717846i
$769$	3.33463e15			0.447150			0.223575	−	0.974687i	$-0.428227\pi$
$769$	3.33463e15			0.447150			0.223575	+	0.974687i	$0.428227\pi$
$770$	7.91827e15	+	1.05231e15i	1.05422	+	0.140102i
$771$		−	7.53586e15i		−	0.996171i
$772$	−5.08285e15	−	1.37528e15i	−0.667133	−	0.180507i
$773$		−	1.13411e16i		−	1.47798i	−0.673717	−	0.738989i	$-0.735303\pi$
$773$		−	1.13411e16i		−	1.47798i	0.673717	−	0.738989i	$-0.264697\pi$
$774$	9.40023e14	−	7.07334e15i	0.121636	−	0.915270i
$775$	1.02987e15			0.132319
$776$	−1.04813e16	−	4.38659e15i	−1.33713	−	0.559613i
$777$	5.66562e14			0.0717682
$778$	3.01407e14	−	2.26798e15i	0.0379110	−	0.285267i
$779$		−	4.67540e13i		−	0.00583933i
$780$	−1.98168e15	+	7.32403e15i	−0.245761	+	0.908301i
$781$			1.27797e16i			1.57376i
$782$	−7.24028e15	−	9.62209e14i	−0.885356	−	0.117661i
$783$	2.10690e15			0.255831
$784$	−9.06869e14	−	5.29512e14i	−0.109347	−	0.0638465i
$785$	1.75574e15			0.210221
$786$	5.18848e15	+	6.89531e14i	0.616902	+	0.0819841i
$787$			2.61393e14i			0.0308627i	0.999881	+	0.0154313i	$0.00491214\pi$
$787$			2.61393e14i			0.0308627i	−0.999881	+	0.0154313i	$0.995088\pi$
$788$	6.91154e14	−	2.55442e15i	0.0810365	−	0.299501i
$789$			1.77366e16i			2.06513i
$790$	3.82937e13	−	2.88147e14i	0.00442770	−	0.0333169i
$791$	−3.53916e15			−0.406377
$792$	−6.93675e15	+	1.65746e16i	−0.790983	+	1.88996i
$793$	−1.08737e16			−1.23133
$794$	1.51521e15	−	1.14014e16i	0.170396	−	1.28217i
$795$			1.98809e15i			0.222033i
$796$	1.13300e16	+	3.06558e15i	1.25663	+	0.340009i
$797$			1.42393e16i			1.56844i	0.620482	+	0.784220i	$0.286937\pi$
$797$			1.42393e16i			1.56844i	−0.620482	+	0.784220i	$0.713063\pi$
$798$	−5.67412e15	−	7.54071e14i	−0.620701	−	0.0824891i
$799$	5.38306e15			0.584820
$800$	−4.41970e15	−	3.43449e15i	−0.476868	−	0.370567i
$801$	−2.64168e15			−0.283075
$802$	−1.19735e16	−	1.59123e15i	−1.27427	−	0.169346i
$803$			5.25819e15i			0.555777i
$804$	−6.83174e15	−	1.84848e15i	−0.717171	−	0.194046i
$805$		−	9.44250e15i		−	0.984486i
$806$	−2.85348e14	+	2.14714e15i	−0.0295482	+	0.222340i
$807$	−5.16851e15			−0.531570
$808$	3.94188e15	−	9.41868e15i	0.402663	−	0.962117i
$809$	9.45677e15			0.959458			0.479729	−	0.877417i	$-0.340735\pi$
$809$	9.45677e15			0.959458			0.479729	+	0.877417i	$0.340735\pi$
$810$	6.98692e14	−	5.25741e15i	0.0704074	−	0.529791i
$811$		−	9.90431e15i		−	0.991310i	−0.868520	−	0.495655i	$-0.834928\pi$
$811$		−	9.90431e15i		−	0.991310i	0.868520	−	0.495655i	$-0.165072\pi$
$812$	−3.23180e15	+	1.19443e16i	−0.321282	+	1.18742i
$813$		−	2.11920e16i		−	2.09254i
$814$	−9.60953e14	−	1.27707e14i	−0.0942470	−	0.0125251i
$815$	5.51155e15			0.536917
$816$	−4.06096e15	+	6.95501e15i	−0.392946	+	0.672980i
$817$	−3.88949e15			−0.373827
$818$	−2.70304e15	−	3.59224e14i	−0.258053	−	0.0342944i
$819$		−	1.14314e16i		−	1.08403i
$820$	2.22121e13	−	8.20932e13i	0.00209225	−	0.00773269i
$821$		−	4.07136e15i		−	0.380936i	−0.981693	−	0.190468i	$-0.938999\pi$
$821$		−	4.07136e15i		−	0.380936i	0.981693	−	0.190468i	$-0.0610005\pi$
$822$	−2.26935e15	+	1.70760e16i	−0.210914	+	1.58706i
$823$	1.51561e16			1.39923			0.699613	−	0.714522i	$-0.253356\pi$
$823$	1.51561e16			1.39923			0.699613	+	0.714522i	$0.253356\pi$
$824$	−4.45917e15	−	1.86624e15i	−0.408936	−	0.171147i
$825$	1.75075e16			1.59488
$826$	1.42348e13	−	1.07111e14i	0.00128813	−	0.00969272i
$827$		−	6.99520e15i		−	0.628811i	−0.949289	−	0.314405i	$-0.898195\pi$
$827$		−	6.99520e15i		−	0.628811i	0.949289	−	0.314405i	$-0.101805\pi$
$828$	2.05023e16	+	5.54735e15i	1.83078	+	0.495358i
$829$			1.36664e16i			1.21228i	0.795357	+	0.606141i	$0.207283\pi$
$829$			1.36664e16i			1.21228i	−0.795357	+	0.606141i	$0.792717\pi$
$830$	−9.40887e15	−	1.25041e15i	−0.829102	−	0.110185i
$831$	1.78534e16			1.56285
$832$	8.38503e15	−	8.26290e15i	0.729166	−	0.718545i
$833$	7.82091e14			0.0675632
$834$	9.18873e15	+	1.22115e15i	0.788573	+	0.104799i
$835$			1.21630e14i			0.0103697i
$836$	9.45397e15	+	2.55798e15i	0.800718	+	0.216652i
$837$			5.06104e14i			0.0425843i
$838$	−1.07270e15	+	8.07171e15i	−0.0896679	+	0.674719i
$839$	−1.53291e16			−1.27299			−0.636496	−	0.771280i	$-0.719617\pi$
$839$	−1.53291e16			−1.27299			−0.636496	+	0.771280i	$0.719617\pi$
$840$	−9.60467e15	−	4.01972e15i	−0.792404	−	0.331635i
$841$	−8.93761e15			−0.732561
$842$	2.06831e14	−	1.55633e15i	0.0168422	−	0.126732i
$843$			1.24362e16i			1.00609i
$844$	2.81451e15	−	1.04021e16i	0.226214	−	0.836057i
$845$			3.78227e14i			0.0302024i
$846$	−1.55173e16	−	2.06219e15i	−1.23106	−	0.163604i
$847$	2.69087e16			2.12097
$848$	1.55536e15	−	2.66378e15i	0.121802	−	0.208604i
$849$	−1.56360e16			−1.21656
$850$	4.13224e15	+	5.49160e14i	0.319434	+	0.0424517i
$851$			1.14593e15i			0.0880129i
$852$	4.35071e15	−	1.60797e16i	0.332003	−	1.22704i
$853$		−	1.55682e16i		−	1.18038i	−0.807266	−	0.590188i	$-0.799054\pi$
$853$		−	1.55682e16i		−	1.18038i	0.807266	−	0.590188i	$-0.200946\pi$
$854$	1.96575e15	−	1.47916e16i	0.148085	−	1.11429i
$855$	4.37062e15			0.327137
$856$	1.27313e15	−	3.04201e15i	0.0946822	−	0.226232i
$857$	−2.38744e16			−1.76416			−0.882082	−	0.471097i	$-0.843858\pi$
$857$	−2.38744e16			−1.76416			−0.882082	+	0.471097i	$0.843858\pi$
$858$	−4.85083e15	+	3.65008e16i	−0.356153	+	2.67992i
$859$			1.16275e16i			0.848247i	0.905604	+	0.424123i	$0.139418\pi$
$859$			1.16275e16i			0.848247i	−0.905604	+	0.424123i	$0.860582\pi$
$860$	−6.82936e15	−	1.84783e15i	−0.495038	−	0.133943i
$861$			2.41215e14i			0.0173735i
$862$	−1.93691e16	−	2.57409e15i	−1.38618	−	0.184219i
$863$	−6.38682e15			−0.454177			−0.227089	−	0.973874i	$-0.572921\pi$
$863$	−6.38682e15			−0.454177			−0.227089	+	0.973874i	$0.572921\pi$
$864$	1.68780e15	−	2.17196e15i	0.119260	−	0.153471i
$865$	1.23974e16			0.870443
$866$	1.02529e16	+	1.36258e15i	0.715318	+	0.0950634i
$867$			1.50692e16i			1.04469i
$868$	−2.86918e15	−	7.76320e14i	−0.197651	−	0.0534789i
$869$		−	1.41067e15i		−	0.0965646i
$870$	2.34318e15	−	1.76316e16i	0.159386	−	1.19932i
$871$	−7.70443e15			−0.520763
$872$	−8.56107e15	+	2.04557e16i	−0.575026	+	1.37396i
$873$	−2.46071e16			−1.64241
$874$	1.52519e15	−	1.14765e16i	0.101160	−	0.761196i
$875$			1.43126e16i			0.943354i
$876$	1.79009e15	−	6.61595e15i	0.117247	−	0.433331i
$877$			2.06975e16i			1.34716i	0.739113	+	0.673582i	$0.235245\pi$
$877$			2.06975e16i			1.34716i	−0.739113	+	0.673582i	$0.764755\pi$
$878$	6.90868e15	+	9.18140e14i	0.446864	+	0.0593867i
$879$	−2.68338e16			−1.72482
$880$	1.53845e16	+	8.98286e15i	0.982718	+	0.573799i
$881$	−6.48714e15			−0.411799			−0.205900	−	0.978573i	$-0.566012\pi$
$881$	−6.48714e15			−0.411799			−0.205900	+	0.978573i	$0.566012\pi$
$882$	−2.25447e15	−	2.99611e14i	−0.142222	−	0.0189008i
$883$		−	2.68088e16i		−	1.68071i	−0.542035	−	0.840356i	$-0.682346\pi$
$883$		−	2.68088e16i		−	1.68071i	0.542035	−	0.840356i	$-0.317654\pi$
$884$	−2.28985e15	+	8.46302e15i	−0.142666	+	0.527276i
$885$			1.55320e14i			0.00961700i
$886$	−1.92584e14	+	1.44913e15i	−0.0118504	+	0.0891704i
$887$	−2.81538e15			−0.172170			−0.0860848	−	0.996288i	$-0.527436\pi$
$887$	−2.81538e15			−0.172170			−0.0860848	+	0.996288i	$0.527436\pi$
$888$	1.16561e15	+	4.87830e14i	0.0708407	+	0.0296481i
$889$	1.55129e15			0.0936984
$890$	−3.45056e14	+	2.59642e15i	−0.0207131	+	0.155858i
$891$		−	2.57386e16i		−	1.53553i
$892$	2.84285e16	+	7.69196e15i	1.68557	+	0.456069i
$893$			8.53264e15i			0.502806i
$894$	3.73948e16	+	4.96964e15i	2.19005	+	0.291051i
$895$	−1.07502e16			−0.625732
$896$	9.72422e15	+	1.29000e16i	0.562549	+	0.746268i
$897$	4.35270e16			2.50265
$898$	−2.17171e16	−	2.88613e15i	−1.24103	−	0.164929i
$899$		−	5.07765e15i		−	0.288393i
$900$	−1.17013e16	−	3.16603e15i	−0.660540	−	0.178724i
$901$			2.29727e15i			0.128892i
$902$	5.43717e13	−	4.09128e14i	0.00303206	−	0.0228152i
$903$	2.00668e16			1.11223
$904$	−7.28126e15	−	3.04733e15i	−0.401125	−	0.167878i
$905$	7.39400e15			0.404867
$906$	4.61270e15	−	3.47089e16i	0.251044	−	1.88902i
$907$		−	6.45266e15i		−	0.349059i	−0.984652	−	0.174529i	$-0.944160\pi$
$907$		−	6.45266e15i		−	0.349059i	0.984652	−	0.174529i	$-0.0558404\pi$
$908$	5.41636e15	−	2.00182e16i	0.291230	−	1.07635i
$909$		−	2.21124e16i		−	1.18178i
$910$	−1.12356e16	−	1.49317e15i	−0.596854	−	0.0793198i
$911$	−2.09200e15			−0.110462			−0.0552308	−	0.998474i	$-0.517589\pi$
$911$	−2.09200e15			−0.110462			−0.0552308	+	0.998474i	$0.517589\pi$
$912$	−1.10243e16	−	6.43700e15i	−0.578603	−	0.337840i
$913$	−4.60629e16			−2.40304
$914$	2.15065e16	+	2.85814e15i	1.11523	+	0.148211i
$915$			2.14490e16i			1.10558i
$916$	−8.46053e15	+	3.12691e16i	−0.433483	+	1.60210i
$917$			7.81892e15i			0.398213i
$918$	−2.69872e14	+	2.03069e15i	−0.0136623	+	0.102804i
$919$	1.89251e15			0.0952365			0.0476182	−	0.998866i	$-0.484837\pi$
$919$	1.89251e15			0.0952365			0.0476182	+	0.998866i	$0.484837\pi$
$920$	8.13031e15	−	1.94264e16i	0.406700	−	0.971763i
$921$	3.12112e16			1.55197
$922$	−3.13214e15	+	2.35682e16i	−0.154818	+	1.16495i
$923$		−	1.81337e16i		−	0.890998i
$924$	−4.87753e16	−	1.31972e16i	−2.38234	−	0.644595i
$925$		−	6.54016e14i		−	0.0317548i
$926$	2.83080e16	+	3.76203e15i	1.36631	+	0.181578i
$927$	−1.04689e16			−0.502299
$928$	−1.69334e16	+	2.17909e16i	−0.807662	+	1.03935i
$929$	4.05918e16			1.92465			0.962325	−	0.271903i	$-0.0876531\pi$
$929$	4.05918e16			1.92465			0.962325	+	0.271903i	$0.0876531\pi$
$930$	4.23534e15	+	5.62862e14i	0.199633	+	0.0265305i
$931$			1.23969e15i			0.0580883i
$932$	−5.61712e15	−	1.51984e15i	−0.261653	−	0.0707961i
$933$			3.80944e16i			1.76405i
$934$	−4.22148e14	+	3.17651e15i	−0.0194338	+	0.146232i
$935$	−1.32677e16			−0.607202
$936$	9.84286e15	−	2.35184e16i	0.447821	−	1.07002i
$937$	2.93519e16			1.32760			0.663801	−	0.747909i	$-0.268942\pi$
$937$	2.93519e16			1.32760			0.663801	+	0.747909i	$0.268942\pi$
$938$	1.39281e15	−	1.04804e16i	0.0626290	−	0.471261i
$939$			5.38086e16i			2.40542i
$940$	−4.05373e15	+	1.49821e16i	−0.180157	+	0.665838i
$941$		−	2.95392e16i		−	1.30514i	−0.757730	−	0.652568i	$-0.773692\pi$
$941$		−	2.95392e16i		−	1.30514i	0.757730	−	0.652568i	$-0.226308\pi$
$942$	−1.10095e16	−	1.46313e15i	−0.483602	−	0.0642691i
$943$	−4.87883e14			−0.0213060
$944$	1.21512e14	−	2.08108e14i	0.00527563	−	0.00903532i
$945$	−2.64835e15			−0.114314
$946$	−3.40355e16	−	4.52321e15i	−1.46060	−	0.194109i
$947$		−	2.40048e15i		−	0.102417i	−0.998688	−	0.0512087i	$-0.983693\pi$
$947$		−	2.40048e15i		−	0.102417i	0.998688	−	0.0512087i	$-0.0163074\pi$
$948$	−4.80249e14	+	1.77494e15i	−0.0203714	+	0.0752900i
$949$		−	7.46108e15i		−	0.314657i
$950$	−8.70469e14	+	6.54997e15i	−0.0364984	+	0.274637i
$951$	2.15877e16			0.899940
$952$	−1.10983e16	−	4.64485e15i	−0.459996	−	0.192517i
$953$	−1.05461e15			−0.0434593			−0.0217296	−	0.999764i	$-0.506917\pi$
$953$	−1.05461e15			−0.0434593			−0.0217296	+	0.999764i	$0.506917\pi$
$954$	8.80060e14	−	6.62214e15i	0.0360576	−	0.271320i
$955$		−	6.69200e15i		−	0.272607i
$956$	−1.16434e16	−	3.15037e15i	−0.471586	−	0.127598i
$957$		−	8.63187e16i		−	3.47608i
$958$	1.95050e16	+	2.59215e15i	0.780973	+	0.103789i
$959$	−2.57332e16			−1.02445
$960$	−1.62990e16	−	1.65399e16i	−0.645162	−	0.654698i
$961$	−2.41888e16			−0.951996
$962$	1.36354e15	+	1.81210e14i	0.0533586	+	0.00709118i
$963$		−	7.14178e15i		−	0.277883i
$964$	−2.16972e16	−	5.87066e15i	−0.839422	−	0.227124i
$965$			1.13069e16i			0.434955i
$966$	−7.86882e15	+	5.92101e16i	−0.300978	+	2.26476i
$967$	1.17425e16			0.446597			0.223298	−	0.974750i	$-0.428318\pi$
$967$	1.17425e16			0.446597			0.223298	+	0.974750i	$0.428318\pi$
$968$	5.53605e16	+	2.31693e16i	2.09356	+	0.876192i
$969$	9.50748e15			0.357507
$970$	−3.21417e15	+	2.41855e16i	−0.120178	+	0.904294i
$971$			5.32074e15i			0.197818i	0.995096	+	0.0989090i	$0.0315353\pi$
$971$			5.32074e15i			0.197818i	−0.995096	+	0.0989090i	$0.968465\pi$
$972$	−1.01356e16	+	3.74598e16i	−0.374700	+	1.38484i
$973$			1.38472e16i			0.509028i
$974$	1.21494e16	+	1.61462e15i	0.444101	+	0.0590195i
$975$	−2.48421e16			−0.902950
$976$	1.67803e16	−	2.87388e16i	0.606493	−	1.03871i
$977$	−2.03432e16			−0.731138			−0.365569	−	0.930784i	$-0.619126\pi$
$977$	−2.03432e16			−0.731138			−0.365569	+	0.930784i	$0.619126\pi$
$978$	−3.45607e16	−	4.59300e15i	−1.23515	−	0.164147i
$979$			1.27113e16i			0.451735i
$980$	−5.88956e14	+	2.17671e15i	−0.0208132	+	0.0769230i
$981$			4.80243e16i			1.68765i
$982$	6.70041e15	−	5.04182e16i	0.234147	−	1.76187i
$983$	2.70845e15			0.0941187			0.0470594	−	0.998892i	$-0.485015\pi$
$983$	2.70845e15			0.0941187			0.0470594	+	0.998892i	$0.485015\pi$
$984$	−2.07695e14	+	4.96263e14i	−0.00717716	+	0.0171490i
$985$	−5.68236e15			−0.195267
$986$	2.70758e15	−	2.03736e16i	0.0925247	−	0.696216i
$987$		−	4.40220e16i		−	1.49598i
$988$	−1.34147e16	−	3.62963e15i	−0.453332	−	0.122659i
$989$			4.05872e16i			1.36399i
$990$	3.82458e16	+	5.08273e15i	1.27817	+	0.169865i
$991$	2.65160e16			0.881257			0.440628	−	0.897690i	$-0.354756\pi$
$991$	2.65160e16			0.881257			0.440628	+	0.897690i	$0.354756\pi$
$992$	−5.23445e15	−	4.06762e15i	−0.173004	−	0.134439i
$993$	1.44318e16			0.474351
$994$	2.46674e16	+	3.27821e15i	0.806301	+	0.107155i
$995$		−	2.52039e16i		−	0.819295i
$996$	5.79572e16	+	1.56816e16i	1.87362	+	0.506948i
$997$			8.19176e15i			0.263362i	0.991292	+	0.131681i	$0.0420375\pi$
$997$			8.19176e15i			0.263362i	−0.991292	+	0.131681i	$0.957962\pi$
$998$	7.23112e15	−	5.44116e16i	0.231200	−	1.73970i
$999$	3.21401e14			0.0102197

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.12.b.a.5.1	✓	10
3.2	odd	2		72.12.d.b.37.10		10
4.3	odd	2		32.12.b.a.17.9		10
8.3	odd	2		32.12.b.a.17.2		10
8.5	even	2	inner	8.12.b.a.5.2	yes	10
16.3	odd	4		256.12.a.o.1.2		10
16.5	even	4		256.12.a.p.1.2		10
16.11	odd	4		256.12.a.o.1.9		10
16.13	even	4		256.12.a.p.1.9		10
24.5	odd	2		72.12.d.b.37.9		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.12.b.a.5.1	✓	10	1.1	even	1	trivial
8.12.b.a.5.2	yes	10	8.5	even	2	inner
32.12.b.a.17.2		10	8.3	odd	2
32.12.b.a.17.9		10	4.3	odd	2
72.12.d.b.37.9		10	24.5	odd	2
72.12.d.b.37.10		10	3.2	odd	2
256.12.a.o.1.2		10	16.3	odd	4
256.12.a.o.1.9		10	16.11	odd	4
256.12.a.p.1.2		10	16.5	even	4
256.12.a.p.1.9		10	16.13	even	4

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:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	8.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-44.8604 - 5.96180i) q^{2} -614.710i q^{3} +(1976.91 + 534.897i) q^{4} -4397.69i q^{5} +(-3664.78 + 27576.1i) q^{6} -41556.6 q^{7} +(-85496.2 - 35781.7i) q^{8} -200721. q^{9} +O(q^{10})\)	\(q+(-44.8604 - 5.96180i) q^{2} -614.710i q^{3} +(1976.91 + 534.897i) q^{4} -4397.69i q^{5} +(-3664.78 + 27576.1i) q^{6} -41556.6 q^{7} +(-85496.2 - 35781.7i) q^{8} -200721. q^{9} +(-26218.2 + 197282. i) q^{10} +965832. i q^{11} +(328807. - 1.21523e6i) q^{12} -1.37046e6i q^{13} +(1.86425e6 + 247752. i) q^{14} -2.70331e6 q^{15} +(3.62207e6 + 2.11489e6i) q^{16} -3.12371e6 q^{17} +(9.00444e6 + 1.19666e6i) q^{18} -4.95136e6i q^{19} +(2.35231e6 - 8.69386e6i) q^{20} +2.55453e7i q^{21} +(5.75810e6 - 4.33276e7i) q^{22} -5.16680e7 q^{23} +(-2.19954e7 + 5.25554e7i) q^{24} +2.94884e7 q^{25} +(-8.17042e6 + 6.14795e7i) q^{26} +1.44914e7i q^{27} +(-8.21539e7 - 2.22285e7i) q^{28} -1.45390e8i q^{29} +(1.21271e8 + 1.61166e7i) q^{30} +3.49245e7 q^{31} +(-1.49879e8 - 1.16469e8i) q^{32} +5.93707e8 q^{33} +(1.40131e8 + 1.86229e7i) q^{34} +1.82753e8i q^{35} +(-3.96809e8 - 1.07365e8i) q^{36} -2.21788e7i q^{37} +(-2.95190e7 + 2.22120e8i) q^{38} -8.42437e8 q^{39} +(-1.57357e8 + 3.75986e8i) q^{40} +9.44266e6 q^{41} +(1.52296e8 - 1.14597e9i) q^{42} -7.85539e8i q^{43} +(-5.16621e8 + 1.90937e9i) q^{44} +8.82711e8i q^{45} +(2.31785e9 + 3.08034e8i) q^{46} -1.72329e9 q^{47} +(1.30005e9 - 2.22652e9i) q^{48} -2.50373e8 q^{49} +(-1.32286e9 - 1.75804e8i) q^{50} +1.92017e9i q^{51} +(7.33057e8 - 2.70929e9i) q^{52} -7.35431e8i q^{53} +(8.63947e7 - 6.50089e8i) q^{54} +4.24743e9 q^{55} +(3.55294e9 + 1.48697e9i) q^{56} -3.04365e9 q^{57} +(-8.66783e8 + 6.52224e9i) q^{58} -5.74556e7i q^{59} +(-5.34420e9 - 1.44599e9i) q^{60} -7.93436e9i q^{61} +(-1.56673e9 - 2.08213e8i) q^{62} +8.34130e9 q^{63} +(6.02928e9 + 6.11840e9i) q^{64} -6.02687e9 q^{65} +(-2.66339e10 - 3.53956e9i) q^{66} -5.62177e9i q^{67} +(-6.17530e9 - 1.67086e9i) q^{68} +3.17608e10i q^{69} +(1.08954e9 - 8.19839e9i) q^{70} +1.32318e10 q^{71} +(1.71609e10 + 7.18215e9i) q^{72} +5.44421e9 q^{73} +(-1.32225e8 + 9.94948e8i) q^{74} -1.81268e10i q^{75} +(2.64847e9 - 9.78842e9i) q^{76} -4.01367e10i q^{77} +(3.77921e10 + 5.02244e9i) q^{78} -1.46058e9 q^{79} +(9.30065e9 - 1.59288e10i) q^{80} -2.66492e10 q^{81} +(-4.23602e8 - 5.62952e7i) q^{82} +4.76924e10i q^{83} +(-1.36641e10 + 5.05008e10i) q^{84} +1.37371e10i q^{85} +(-4.68322e9 + 3.52396e10i) q^{86} -8.93724e10 q^{87} +(3.45591e10 - 8.25750e10i) q^{88} +1.31610e10 q^{89} +(5.26254e9 - 3.95988e10i) q^{90} +5.69518e10i q^{91} +(-1.02143e11 - 2.76371e10i) q^{92} -2.14684e10i q^{93} +(7.73076e10 + 1.02739e10i) q^{94} -2.17746e10 q^{95} +(-7.15947e10 + 9.21322e10i) q^{96} +1.22593e11 q^{97} +(1.12318e10 + 1.49267e9i) q^{98} -1.93863e11i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 22 q^{2} + 436 q^{4} - 24308 q^{6} - 33616 q^{7} - 208472 q^{8} - 472394 q^{9}+O(q^{10}) \) 10 * q + 22 * q^2 + 436 * q^4 - 24308 * q^6 - 33616 * q^7 - 208472 * q^8 - 472394 * q^9	\( 10 q + 22 q^{2} + 436 q^{4} - 24308 q^{6} - 33616 q^{7} - 208472 q^{8} - 472394 q^{9} + 29864 q^{10} - 476216 q^{12} + 2264272 q^{14} + 3391792 q^{15} + 3757072 q^{16} + 2639732 q^{17} + 2329130 q^{18} + 8296432 q^{20} - 24201892 q^{22} - 45357808 q^{23} + 10668944 q^{24} - 41502654 q^{25} - 101931080 q^{26} - 95722144 q^{28} + 261362768 q^{30} + 442035392 q^{31} + 343908512 q^{32} - 54732216 q^{33} - 187103796 q^{34} - 431195700 q^{36} + 375100844 q^{38} - 431459312 q^{39} + 1519138784 q^{40} - 654907964 q^{41} - 3697737056 q^{42} - 4127012952 q^{44} + 6028867440 q^{46} - 560226528 q^{47} + 9357606048 q^{48} + 1143661722 q^{49} - 9626584226 q^{50} - 11595427248 q^{52} + 20050494008 q^{54} + 5632783984 q^{55} + 18698733760 q^{56} - 783862360 q^{57} - 22828679464 q^{58} - 43681325472 q^{60} + 40774631744 q^{62} - 14483624624 q^{63} + 55266728512 q^{64} - 80291360 q^{65} - 83128448712 q^{66} - 83303223768 q^{68} + 100120831168 q^{70} - 11769460176 q^{71} + 112862051672 q^{72} + 32304890372 q^{73} - 102103996184 q^{74} - 97501928568 q^{76} + 144445560944 q^{78} + 57291670496 q^{79} + 128322038976 q^{80} - 23172996094 q^{81} - 123309929604 q^{82} - 199990865984 q^{84} + 130201908124 q^{86} - 73844404272 q^{87} + 169216119632 q^{88} - 108276011804 q^{89} - 228506434984 q^{90} - 141139403232 q^{92} + 145336130016 q^{94} + 70146835376 q^{95} + 109508068928 q^{96} + 60995282900 q^{97} - 6194726778 q^{98}+O(q^{100}) \) 10 * q + 22 * q^2 + 436 * q^4 - 24308 * q^6 - 33616 * q^7 - 208472 * q^8 - 472394 * q^9 + 29864 * q^10 - 476216 * q^12 + 2264272 * q^14 + 3391792 * q^15 + 3757072 * q^16 + 2639732 * q^17 + 2329130 * q^18 + 8296432 * q^20 - 24201892 * q^22 - 45357808 * q^23 + 10668944 * q^24 - 41502654 * q^25 - 101931080 * q^26 - 95722144 * q^28 + 261362768 * q^30 + 442035392 * q^31 + 343908512 * q^32 - 54732216 * q^33 - 187103796 * q^34 - 431195700 * q^36 + 375100844 * q^38 - 431459312 * q^39 + 1519138784 * q^40 - 654907964 * q^41 - 3697737056 * q^42 - 4127012952 * q^44 + 6028867440 * q^46 - 560226528 * q^47 + 9357606048 * q^48 + 1143661722 * q^49 - 9626584226 * q^50 - 11595427248 * q^52 + 20050494008 * q^54 + 5632783984 * q^55 + 18698733760 * q^56 - 783862360 * q^57 - 22828679464 * q^58 - 43681325472 * q^60 + 40774631744 * q^62 - 14483624624 * q^63 + 55266728512 * q^64 - 80291360 * q^65 - 83128448712 * q^66 - 83303223768 * q^68 + 100120831168 * q^70 - 11769460176 * q^71 + 112862051672 * q^72 + 32304890372 * q^73 - 102103996184 * q^74 - 97501928568 * q^76 + 144445560944 * q^78 + 57291670496 * q^79 + 128322038976 * q^80 - 23172996094 * q^81 - 123309929604 * q^82 - 199990865984 * q^84 + 130201908124 * q^86 - 73844404272 * q^87 + 169216119632 * q^88 - 108276011804 * q^89 - 228506434984 * q^90 - 141139403232 * q^92 + 145336130016 * q^94 + 70146835376 * q^95 + 109508068928 * q^96 + 60995282900 * q^97 - 6194726778 * q^98

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