LMFDB - Embedded newform 8.8.b.a.5.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8,8,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, 8, names="a")

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

chi := DirichletCharacter("8.5");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 8 $
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:	$2.49908020387$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 10x^{4} - 24x^{3} - 320x^{2} - 3072x + 32768 $ x^6 - 3x^5 - 10x^4 - 24x^3 - 320x^2 - 3072*x + 32768
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{15} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.2
Root			$-4.85268 - 2.90715i$ of defining polynomial
Character	$\chi$	$=$	8.5
Dual form			8.8.b.a.5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-9.70536 + 5.81430i) q^{2} -40.2163i q^{3} +(60.3879 - 112.860i) q^{4} -324.492i q^{5} +(233.829 + 390.313i) q^{6} -956.960 q^{7} +(70.1132 + 1446.46i) q^{8} +569.651 q^{9} +O(q^{10})$	\(q+(-9.70536 + 5.81430i) q^{2} -40.2163i q^{3} +(60.3879 - 112.860i) q^{4} -324.492i q^{5} +(233.829 + 390.313i) q^{6} -956.960 q^{7} +(70.1132 + 1446.46i) q^{8} +569.651 q^{9} +(1886.69 + 3149.31i) q^{10} -5452.20i q^{11} +(-4538.80 - 2428.58i) q^{12} +6289.38i q^{13} +(9287.64 - 5564.05i) q^{14} -13049.8 q^{15} +(-9090.60 - 13630.7i) q^{16} +34587.3 q^{17} +(-5528.66 + 3312.12i) q^{18} +14595.6i q^{19} +(-36622.0 - 19595.4i) q^{20} +38485.4i q^{21} +(31700.7 + 52915.6i) q^{22} -24667.5 q^{23} +(58171.1 - 2819.69i) q^{24} -27169.8 q^{25} +(-36568.3 - 61040.6i) q^{26} -110862. i q^{27} +(-57788.8 + 108002. i) q^{28} -171116. i q^{29} +(126653. - 75875.7i) q^{30} +111688. q^{31} +(167481. + 79435.5i) q^{32} -219267. q^{33} +(-335682. + 201101. i) q^{34} +310526. i q^{35} +(34400.0 - 64290.6i) q^{36} +103636. i q^{37} +(-84863.4 - 141656. i) q^{38} +252935. q^{39} +(469363. - 22751.1i) q^{40} +71691.3 q^{41} +(-223765. - 373514. i) q^{42} +328419. i q^{43} +(-615334. - 329247. i) q^{44} -184847. i q^{45} +(239406. - 143424. i) q^{46} +119043. q^{47} +(-548177. + 365590. i) q^{48} +92230.3 q^{49} +(263693. - 157973. i) q^{50} -1.39097e6i q^{51} +(709817. + 379802. i) q^{52} +1.04011e6i q^{53} +(644586. + 1.07596e6i) q^{54} -1.76919e6 q^{55} +(-67095.6 - 1.38420e6i) q^{56} +586982. q^{57} +(994918. + 1.66074e6i) q^{58} +225984. i q^{59} +(-788053. + 1.47280e6i) q^{60} -1.55268e6i q^{61} +(-1.08398e6 + 649390. i) q^{62} -545133. q^{63} +(-2.08732e6 + 202831. i) q^{64} +2.04085e6 q^{65} +(2.12807e6 - 1.27489e6i) q^{66} -316375. i q^{67} +(2.08865e6 - 3.90351e6i) q^{68} +992033. i q^{69} +(-1.80549e6 - 3.01376e6i) q^{70} +538965. q^{71} +(39940.0 + 823975. i) q^{72} -2.68512e6 q^{73} +(-602570. - 1.00582e6i) q^{74} +1.09267e6i q^{75} +(1.64726e6 + 881400. i) q^{76} +5.21754e6i q^{77} +(-2.45483e6 + 1.47064e6i) q^{78} +8.22632e6 q^{79} +(-4.42305e6 + 2.94982e6i) q^{80} -3.21264e6 q^{81} +(-695790. + 416834. i) q^{82} +5.89510e6i q^{83} +(4.34345e6 + 2.32405e6i) q^{84} -1.12233e7i q^{85} +(-1.90952e6 - 3.18742e6i) q^{86} -6.88164e6 q^{87} +(7.88638e6 - 382271. i) q^{88} +437005. q^{89} +(1.07475e6 + 1.79400e6i) q^{90} -6.01868e6i q^{91} +(-1.48962e6 + 2.78396e6i) q^{92} -4.49169e6i q^{93} +(-1.15536e6 + 692152. i) q^{94} +4.73616e6 q^{95} +(3.19460e6 - 6.73545e6i) q^{96} -7.84322e6 q^{97} +(-895128. + 536254. i) q^{98} -3.10585e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 116 q^{4} + 268 q^{6} - 688 q^{7} + 1512 q^{8} - 2918 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 116 * q^4 + 268 * q^6 - 688 * q^7 + 1512 * q^8 - 2918 * q^9	\( 6 q + 6 q^{2} + 116 q^{4} + 268 q^{6} - 688 q^{7} + 1512 q^{8} - 2918 q^{9} - 1656 q^{10} - 4088 q^{12} + 12048 q^{14} + 17872 q^{15} + 35344 q^{16} + 1452 q^{17} - 89062 q^{18} - 114768 q^{20} + 152860 q^{22} - 1296 q^{23} + 282512 q^{24} - 39314 q^{25} - 316968 q^{26} - 480800 q^{28} + 821648 q^{30} - 89280 q^{31} + 817056 q^{32} + 53880 q^{33} - 1009108 q^{34} - 1253556 q^{36} + 974124 q^{38} - 328208 q^{39} + 954464 q^{40} + 521244 q^{41} - 1093088 q^{42} - 1096344 q^{44} + 929840 q^{46} + 1566432 q^{47} + 853920 q^{48} - 511050 q^{49} - 148626 q^{50} + 823952 q^{52} - 1077064 q^{54} - 3270256 q^{55} - 2468928 q^{56} - 1889896 q^{57} + 3130744 q^{58} + 5715168 q^{60} - 7055808 q^{62} + 5776816 q^{63} - 4792768 q^{64} + 1416480 q^{65} + 7926264 q^{66} + 6608040 q^{68} - 7406912 q^{70} - 7597104 q^{71} - 11363944 q^{72} + 2089564 q^{73} + 7744200 q^{74} + 9241288 q^{76} - 9471184 q^{78} + 16015904 q^{79} - 12600384 q^{80} - 723058 q^{81} + 10715932 q^{82} + 4220608 q^{84} - 5639076 q^{86} - 37453776 q^{87} + 1541200 q^{88} + 2169084 q^{89} - 121864 q^{90} + 669600 q^{92} + 15503712 q^{94} + 48537936 q^{95} + 21402176 q^{96} - 1088308 q^{97} - 14983242 q^{98}+O(q^{100}) \) 6 * q + 6 * q^2 + 116 * q^4 + 268 * q^6 - 688 * q^7 + 1512 * q^8 - 2918 * q^9 - 1656 * q^10 - 4088 * q^12 + 12048 * q^14 + 17872 * q^15 + 35344 * q^16 + 1452 * q^17 - 89062 * q^18 - 114768 * q^20 + 152860 * q^22 - 1296 * q^23 + 282512 * q^24 - 39314 * q^25 - 316968 * q^26 - 480800 * q^28 + 821648 * q^30 - 89280 * q^31 + 817056 * q^32 + 53880 * q^33 - 1009108 * q^34 - 1253556 * q^36 + 974124 * q^38 - 328208 * q^39 + 954464 * q^40 + 521244 * q^41 - 1093088 * q^42 - 1096344 * q^44 + 929840 * q^46 + 1566432 * q^47 + 853920 * q^48 - 511050 * q^49 - 148626 * q^50 + 823952 * q^52 - 1077064 * q^54 - 3270256 * q^55 - 2468928 * q^56 - 1889896 * q^57 + 3130744 * q^58 + 5715168 * q^60 - 7055808 * q^62 + 5776816 * q^63 - 4792768 * q^64 + 1416480 * q^65 + 7926264 * q^66 + 6608040 * q^68 - 7406912 * q^70 - 7597104 * q^71 - 11363944 * q^72 + 2089564 * q^73 + 7744200 * q^74 + 9241288 * q^76 - 9471184 * q^78 + 16015904 * q^79 - 12600384 * q^80 - 723058 * q^81 + 10715932 * q^82 + 4220608 * q^84 - 5639076 * q^86 - 37453776 * q^87 + 1541200 * q^88 + 2169084 * q^89 - 121864 * q^90 + 669600 * q^92 + 15503712 * q^94 + 48537936 * q^95 + 21402176 * q^96 - 1088308 * q^97 - 14983242 * 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 $

$2$	−9.70536	+	5.81430i	−0.857840	+	0.513916i
$2$	−9.70536	+	5.81430i	−0.857840	+	0.513916i
$3$		−	40.2163i		−	0.859959i	−0.902839	−	0.429979i	$-0.858521\pi$
$3$		−	40.2163i		−	0.859959i	0.902839	−	0.429979i	$-0.141479\pi$
$4$	60.3879	−	112.860i	0.471781	−	0.881716i
$5$		−	324.492i		−	1.16094i	−0.814283	−	0.580468i	$-0.802870\pi$
$5$		−	324.492i		−	1.16094i	0.814283	−	0.580468i	$-0.197130\pi$
$6$	233.829	+	390.313i	0.441947	+	0.737707i
$7$	−956.960			−1.05451			−0.527255	−	0.849707i	$-0.676779\pi$
$7$	−956.960			−1.05451			−0.527255	+	0.849707i	$0.676779\pi$
$8$	70.1132	+	1446.46i	0.0484155	+	0.998827i
$9$	569.651			0.260471
$10$	1886.69	+	3149.31i	0.596624	+	0.995898i
$11$		−	5452.20i		−	1.23509i	−0.786537	−	0.617544i	$-0.788128\pi$
$11$		−	5452.20i		−	1.23509i	0.786537	−	0.617544i	$-0.211872\pi$
$12$	−4538.80	−	2428.58i	−0.758239	−	0.405712i
$13$			6289.38i			0.793973i	0.917824	+	0.396987i	$0.129944\pi$
$13$			6289.38i			0.793973i	−0.917824	+	0.396987i	$0.870056\pi$
$14$	9287.64	−	5564.05i	0.904602	−	0.541930i
$15$	−13049.8			−0.998357
$16$	−9090.60	−	13630.7i	−0.554846	−	0.831953i
$17$	34587.3			1.70744			0.853720	−	0.520733i	$-0.174341\pi$
$17$	34587.3			1.70744			0.853720	+	0.520733i	$0.174341\pi$
$18$	−5528.66	+	3312.12i	−0.223443	+	0.133860i
$19$			14595.6i			0.488186i	0.969752	+	0.244093i	$0.0784903\pi$
$19$			14595.6i			0.488186i	−0.969752	+	0.244093i	$0.921510\pi$
$20$	−36622.0	−	19595.4i	−1.02362	−	0.547707i
$21$			38485.4i			0.906835i
$22$	31700.7	+	52915.6i	0.634731	+	1.05951i
$23$	−24667.5			−0.422743			−0.211372	−	0.977406i	$-0.567793\pi$
$23$	−24667.5			−0.422743			−0.211372	+	0.977406i	$0.567793\pi$
$24$	58171.1	−	2819.69i	0.858950	−	0.0416354i
$25$	−27169.8			−0.347774
$26$	−36568.3	−	61040.6i	−0.408036	−	0.681102i
$27$		−	110862.i		−	1.08395i
$28$	−57788.8	+	108002.i	−0.497497	+	0.929779i
$29$		−	171116.i		−	1.30286i	−0.758710	−	0.651429i	$-0.774170\pi$
$29$		−	171116.i		−	1.30286i	0.758710	−	0.651429i	$-0.225830\pi$
$30$	126653.	−	75875.7i	0.856431	−	0.513072i
$31$	111688.			0.673352			0.336676	−	0.941620i	$-0.390697\pi$
$31$	111688.			0.673352			0.336676	+	0.941620i	$0.390697\pi$
$32$	167481.	+	79435.5i	0.903524	+	0.428539i
$33$	−219267.			−1.06212
$34$	−335682.	+	201101.i	−1.46471	+	0.877480i
$35$			310526.i			1.22422i
$36$	34400.0	−	64290.6i	0.122885	−	0.229662i
$37$			103636.i			0.336360i	0.985756	+	0.168180i	$0.0537890\pi$
$37$			103636.i			0.336360i	−0.985756	+	0.168180i	$0.946211\pi$
$38$	−84863.4	−	141656.i	−0.250887	−	0.418786i
$39$	252935.			0.682784
$40$	469363.	−	22751.1i	1.15958	−	0.0562074i
$41$	71691.3			0.162451			0.0812256	−	0.996696i	$-0.474117\pi$
$41$	71691.3			0.162451			0.0812256	+	0.996696i	$0.474117\pi$
$42$	−223765.	−	373514.i	−0.466037	−	0.777920i
$43$			328419.i			0.629925i	0.949104	+	0.314962i	$0.101992\pi$
$43$			328419.i			0.629925i	−0.949104	+	0.314962i	$0.898008\pi$
$44$	−615334.	−	329247.i	−1.08900	−	0.582690i
$45$		−	184847.i		−	0.302391i
$46$	239406.	−	143424.i	0.362646	−	0.217255i
$47$	119043.			0.167248			0.0836241	−	0.996497i	$-0.473350\pi$
$47$	119043.			0.167248			0.0836241	+	0.996497i	$0.473350\pi$
$48$	−548177.	+	365590.i	−0.715445	+	0.477145i
$49$	92230.3			0.111992
$50$	263693.	−	157973.i	0.298334	−	0.178727i
$51$		−	1.39097e6i		−	1.46833i
$52$	709817.	+	379802.i	0.700059	+	0.374581i
$53$			1.04011e6i			0.959648i	0.877365	+	0.479824i	$0.159300\pi$
$53$			1.04011e6i			0.959648i	−0.877365	+	0.479824i	$0.840700\pi$
$54$	644586.	+	1.07596e6i	0.557061	+	0.929859i
$55$	−1.76919e6			−1.43386
$56$	−67095.6	−	1.38420e6i	−0.0510547	−	1.05327i
$57$	586982.			0.419820
$58$	994918.	+	1.66074e6i	0.669559	+	1.11764i
$59$			225984.i			0.143250i	0.997432	+	0.0716250i	$0.0228185\pi$
$59$			225984.i			0.143250i	−0.997432	+	0.0716250i	$0.977182\pi$
$60$	−788053.	+	1.47280e6i	−0.471006	+	0.880268i
$61$		−	1.55268e6i		−	0.875843i	−0.899013	−	0.437922i	$-0.855715\pi$
$61$		−	1.55268e6i		−	0.875843i	0.899013	−	0.437922i	$-0.144285\pi$
$62$	−1.08398e6	+	649390.i	−0.577629	+	0.346047i
$63$	−545133.			−0.274670
$64$	−2.08732e6	+	202831.i	−0.995312	+	0.0967175i
$65$	2.04085e6			0.921753
$66$	2.12807e6	−	1.27489e6i	0.911133	−	0.545843i
$67$		−	316375.i		−	0.128511i	−0.997933	−	0.0642555i	$-0.979533\pi$
$67$		−	316375.i		−	0.128511i	0.997933	−	0.0642555i	$-0.0204673\pi$
$68$	2.08865e6	−	3.90351e6i	0.805537	−	1.50548i
$69$			992033.i			0.363542i
$70$	−1.80549e6	−	3.01376e6i	−0.629146	−	1.05019i
$71$	538965.			0.178713			0.0893566	−	0.996000i	$-0.471519\pi$
$71$	538965.			0.178713			0.0893566	+	0.996000i	$0.471519\pi$
$72$	39940.0	+	823975.i	0.0126109	+	0.260166i
$73$	−2.68512e6			−0.807856			−0.403928	−	0.914791i	$-0.632355\pi$
$73$	−2.68512e6			−0.807856			−0.403928	+	0.914791i	$0.632355\pi$
$74$	−602570.	−	1.00582e6i	−0.172861	−	0.288543i
$75$			1.09267e6i			0.299071i
$76$	1.64726e6	+	881400.i	0.430442	+	0.230317i
$77$			5.21754e6i			1.30241i
$78$	−2.45483e6	+	1.47064e6i	−0.585720	+	0.350894i
$79$	8.22632e6			1.87720			0.938600	−	0.345007i	$-0.112123\pi$
$79$	8.22632e6			1.87720			0.938600	+	0.345007i	$0.112123\pi$
$80$	−4.42305e6	+	2.94982e6i	−0.965845	+	0.644141i
$81$	−3.21264e6			−0.671684
$82$	−695790.	+	416834.i	−0.139357	+	0.0834863i
$83$			5.89510e6i			1.13167i	0.824520	+	0.565833i	$0.191445\pi$
$83$			5.89510e6i			1.13167i	−0.824520	+	0.565833i	$0.808555\pi$
$84$	4.34345e6	+	2.32405e6i	0.799571	+	0.427827i
$85$		−	1.12233e7i		−	1.98223i
$86$	−1.90952e6	−	3.18742e6i	−0.323728	−	0.540375i
$87$	−6.88164e6			−1.12040
$88$	7.88638e6	−	382271.i	1.23364	−	0.0597974i
$89$	437005.			0.0657085			0.0328542	−	0.999460i	$-0.489540\pi$
$89$	437005.			0.0657085			0.0328542	+	0.999460i	$0.489540\pi$
$90$	1.07475e6	+	1.79400e6i	0.155403	+	0.259403i
$91$		−	6.01868e6i		−	0.837253i
$92$	−1.48962e6	+	2.78396e6i	−0.199442	+	0.372740i
$93$		−	4.49169e6i		−	0.579055i
$94$	−1.15536e6	+	692152.i	−0.143472	+	0.0859516i
$95$	4.73616e6			0.566753
$96$	3.19460e6	−	6.73545e6i	0.368525	−	0.776993i
$97$	−7.84322e6			−0.872556			−0.436278	−	0.899812i	$-0.643704\pi$
$97$	−7.84322e6			−0.872556			−0.436278	+	0.899812i	$0.643704\pi$
$98$	−895128.	+	536254.i	−0.0960713	+	0.0575545i
$99$		−	3.10585e6i		−	0.321705i
$100$	−1.64073e6	+	3.06638e6i	−0.164073	+	0.306638i
$101$			6.19757e6i			0.598545i	0.954168	+	0.299272i	$0.0967439\pi$
$101$			6.19757e6i			0.598545i	−0.954168	+	0.299272i	$0.903256\pi$
$102$	8.08752e6	+	1.34999e7i	0.754597	+	1.25959i
$103$	−6.59816e6			−0.594966			−0.297483	−	0.954727i	$-0.596147\pi$
$103$	−6.59816e6			−0.594966			−0.297483	+	0.954727i	$0.596147\pi$
$104$	−9.09731e6	+	440968.i	−0.793042	+	0.0384406i
$105$	1.24882e7			1.05278
$106$	−6.04748e6	−	1.00946e7i	−0.493179	−	0.823225i
$107$		−	512845.i		−	0.0404709i	−0.999795	−	0.0202354i	$-0.993558\pi$
$107$		−	512845.i		−	0.0404709i	0.999795	−	0.0202354i	$-0.00644158\pi$
$108$	−1.25119e7	−	6.69474e6i	−0.955739	−	0.511388i
$109$			1.95882e7i			1.44878i	0.689393	+	0.724388i	$0.257877\pi$
$109$			1.95882e7i			1.44878i	−0.689393	+	0.724388i	$0.742123\pi$
$110$	1.71707e7	−	1.02866e7i	1.23002	−	0.736883i
$111$	4.16785e6			0.289256
$112$	8.69934e6	+	1.30441e7i	0.585091	+	0.877303i
$113$	1.88876e7			1.23141			0.615705	−	0.787977i	$-0.288871\pi$
$113$	1.88876e7			1.23141			0.615705	+	0.787977i	$0.288871\pi$
$114$	−5.69687e6	+	3.41289e6i	−0.360139	+	0.215752i
$115$			8.00438e6i			0.490778i
$116$	−1.93121e7	−	1.03333e7i	−1.14875	−	0.614663i
$117$			3.58275e6i			0.206807i
$118$	−1.31394e6	−	2.19325e6i	−0.0736185	−	0.122886i
$119$	−3.30987e7			−1.80051
$120$	−914967.	−	1.88760e7i	−0.0483360	−	0.997187i
$121$	−1.02394e7			−0.525441
$122$	9.02772e6	+	1.50693e7i	0.450110	+	0.751334i
$123$		−	2.88316e6i		−	0.139701i
$124$	6.74463e6	−	1.26051e7i	0.317675	−	0.593706i
$125$		−	1.65345e7i		−	0.757193i
$126$	5.29071e6	−	3.16957e6i	0.235623	−	0.141157i
$127$	3.96314e7			1.71683			0.858413	−	0.512959i	$-0.171451\pi$
$127$	3.96314e7			1.71683			0.858413	+	0.512959i	$0.171451\pi$
$128$	1.90789e7	−	1.41048e7i	0.804114	−	0.594475i
$129$	1.32078e7			0.541709
$130$	−1.98072e7	+	1.18661e7i	−0.790717	+	0.473703i
$131$		−	3.65337e7i		−	1.41986i	−0.704274	−	0.709928i	$-0.748727\pi$
$131$		−	3.65337e7i		−	1.41986i	0.704274	−	0.709928i	$-0.251273\pi$
$132$	−1.32411e7	+	2.47464e7i	−0.501090	+	0.936492i
$133$		−	1.39675e7i		−	0.514797i
$134$	1.83950e6	+	3.07053e6i	0.0660439	+	0.110242i
$135$	−3.59739e7			−1.25840
$136$	2.42503e6	+	5.00290e7i	0.0826666	+	1.70544i
$137$	−2.56967e7			−0.853799			−0.426899	−	0.904299i	$-0.640394\pi$
$137$	−2.56967e7			−0.853799			−0.426899	+	0.904299i	$0.640394\pi$
$138$	−5.76798e6	−	9.62804e6i	−0.186830	−	0.311861i
$139$			5.23001e7i			1.65177i	0.563836	+	0.825886i	$0.309325\pi$
$139$			5.23001e7i			1.65177i	−0.563836	+	0.825886i	$0.690675\pi$
$140$	3.50458e7	+	1.87520e7i	1.07941	+	0.577563i
$141$		−	4.78747e6i		−	0.143827i
$142$	−5.23085e6	+	3.13370e6i	−0.153307	+	0.0918436i
$143$	3.42910e7			0.980626
$144$	−5.17847e6	−	7.76475e6i	−0.144521	−	0.216700i
$145$	−5.55256e7			−1.51254
$146$	2.60601e7	−	1.56121e7i	0.693011	−	0.415170i
$147$		−	3.70916e6i		−	0.0963085i
$148$	1.16963e7	+	6.25836e6i	0.296574	+	0.158688i
$149$			1.80406e7i			0.446785i	0.974729	+	0.223392i	$0.0717131\pi$
$149$			1.80406e7i			0.446785i	−0.974729	+	0.223392i	$0.928287\pi$
$150$	−6.35311e6	−	1.06047e7i	−0.153697	−	0.256555i
$151$	3.87385e7			0.915637			0.457818	−	0.889046i	$-0.348631\pi$
$151$	3.87385e7			0.915637			0.457818	+	0.889046i	$0.348631\pi$
$152$	−2.11120e7	+	1.02335e6i	−0.487614	+	0.0236358i
$153$	1.97027e7			0.444739
$154$	−3.03363e7	−	5.06381e7i	−0.669331	−	1.11726i
$155$		−	3.62420e7i		−	0.781719i
$156$	1.52742e7	−	2.85462e7i	0.322124	−	0.602022i
$157$		−	5.12341e7i		−	1.05660i	−0.849058	−	0.528300i	$-0.822830\pi$
$157$		−	5.12341e7i		−	1.05660i	0.849058	−	0.528300i	$-0.177170\pi$
$158$	−7.98393e7	+	4.78302e7i	−1.61034	+	0.964723i
$159$	4.18292e7			0.825258
$160$	2.57762e7	−	5.43460e7i	0.497506	−	1.04893i
$161$	2.36058e7			0.445787
$162$	3.11798e7	−	1.86793e7i	0.576197	−	0.345189i
$163$			8.57572e7i			1.55101i	0.631343	+	0.775504i	$0.282504\pi$
$163$			8.57572e7i			1.55101i	−0.631343	+	0.775504i	$0.717496\pi$
$164$	4.32929e6	−	8.09105e6i	0.0766413	−	0.143236i
$165$			7.11504e7i			1.23306i
$166$	−3.42759e7	−	5.72141e7i	−0.581581	−	0.970789i
$167$	−1.05871e8			−1.75901			−0.879503	−	0.475893i	$-0.842125\pi$
$167$	−1.05871e8			−1.75901			−0.879503	+	0.475893i	$0.842125\pi$
$168$	−5.56674e7	+	2.69833e6i	−0.905772	+	0.0439049i
$169$	2.31923e7			0.369606
$170$	6.52555e7	+	1.08926e8i	1.01870	+	1.70044i
$171$			8.31441e6i			0.127158i
$172$	3.70652e7	+	1.98325e7i	0.555415	+	0.297186i
$173$		−	1.98148e7i		−	0.290956i	−0.989361	−	0.145478i	$-0.953528\pi$
$173$		−	1.98148e7i		−	0.290956i	0.989361	−	0.145478i	$-0.0464720\pi$
$174$	6.67888e7	−	4.00119e7i	0.961128	−	0.575793i
$175$	2.60005e7			0.366731
$176$	−7.43175e7	+	4.95638e7i	−1.02753	+	0.685284i
$177$	9.08822e6			0.123189
$178$	−4.24129e6	+	2.54088e6i	−0.0563674	+	0.0337686i
$179$		−	2.97800e7i		−	0.388096i	−0.980992	−	0.194048i	$-0.937838\pi$
$179$		−	2.97800e7i		−	0.388096i	0.980992	−	0.194048i	$-0.0621618\pi$
$180$	−2.08617e7	−	1.11625e7i	−0.266623	−	0.142662i
$181$		−	3.96227e6i		−	0.0496671i	−0.999692	−	0.0248335i	$-0.992094\pi$
$181$		−	3.96227e6i		−	0.0496671i	0.999692	−	0.0248335i	$-0.00790558\pi$
$182$	3.49944e7	+	5.84135e7i	0.430278	+	0.718230i
$183$	−6.24429e7			−0.753189
$184$	−1.72951e6	−	3.56804e7i	−0.0204674	−	0.422248i
$185$	3.36290e7			0.390493
$186$	2.61160e7	+	4.35935e7i	0.297586	+	0.496737i
$187$		−	1.88577e8i		−	2.10884i
$188$	7.18876e6	−	1.34352e7i	0.0789045	−	0.147465i
$189$			1.06091e8i			1.14304i
$190$	−4.59662e7	+	2.75375e7i	−0.486184	+	0.291264i
$191$	−4.80105e7			−0.498562			−0.249281	−	0.968431i	$-0.580194\pi$
$191$	−4.80105e7			−0.498562			−0.249281	+	0.968431i	$0.580194\pi$
$192$	8.15712e6	+	8.39443e7i	0.0831731	+	0.855927i
$193$	−4.72502e6			−0.0473100			−0.0236550	−	0.999720i	$-0.507530\pi$
$193$	−4.72502e6			−0.0473100			−0.0236550	+	0.999720i	$0.507530\pi$
$194$	7.61212e7	−	4.56028e7i	0.748514	−	0.448420i
$195$		−	8.20754e7i		−	0.792669i
$196$	5.56959e6	−	1.04091e7i	0.0528357	−	0.0987452i
$197$		−	1.14882e8i		−	1.07058i	−0.844668	−	0.535290i	$-0.820202\pi$
$197$		−	1.14882e8i		−	1.07058i	0.844668	−	0.535290i	$-0.179798\pi$
$198$	1.80583e7	+	3.01434e7i	0.165329	+	0.275971i
$199$	1.20933e7			0.108782			0.0543911	−	0.998520i	$-0.482678\pi$
$199$	1.20933e7			0.108782			0.0543911	+	0.998520i	$0.482678\pi$
$200$	−1.90496e6	−	3.93000e7i	−0.0168377	−	0.347366i
$201$	−1.27234e7			−0.110514
$202$	−3.60345e7	−	6.01496e7i	−0.307602	−	0.513456i
$203$			1.63751e8i			1.37388i
$204$	−1.56985e8	−	8.39979e7i	−1.29465	−	0.692728i
$205$		−	2.32632e7i		−	0.188596i
$206$	6.40375e7	−	3.83636e7i	0.510386	−	0.305763i
$207$	−1.40518e7			−0.110112
$208$	8.57287e7	−	5.71742e7i	0.660548	−	0.440533i
$209$	7.95784e7			0.602953
$210$	−1.21202e8	+	7.26100e7i	−0.903116	+	0.541040i
$211$			1.95850e8i			1.43527i	0.696418	+	0.717636i	$0.254776\pi$
$211$			1.95850e8i			1.43527i	−0.696418	+	0.717636i	$0.745224\pi$
$212$	1.17386e8	+	6.28098e7i	0.846137	+	0.452743i
$213$		−	2.16752e7i		−	0.153686i
$214$	2.98183e6	+	4.97734e6i	0.0207986	+	0.0347176i
$215$	1.06569e8			0.731302
$216$	1.60357e8	−	7.77291e6i	1.08268	−	0.0524802i
$217$	−1.06881e8			−0.710057
$218$	−1.13891e8	−	1.90110e8i	−0.744549	−	1.24282i
$219$			1.07986e8i			0.694723i
$220$	−1.06838e8	+	1.99671e8i	−0.676466	+	1.26426i
$221$			2.17532e8i			1.35566i
$222$	−4.04505e7	+	2.42331e7i	−0.248135	+	0.148653i
$223$	1.08024e8			0.652311			0.326156	−	0.945316i	$-0.394247\pi$
$223$	1.08024e8			0.652311			0.326156	+	0.945316i	$0.394247\pi$
$224$	−1.60272e8	−	7.60167e7i	−0.952775	−	0.451898i
$225$	−1.54773e7			−0.0905851
$226$	−1.83311e8	+	1.09818e8i	−1.05635	+	0.632841i
$227$		−	1.61144e8i		−	0.914374i	−0.889371	−	0.457187i	$-0.848857\pi$
$227$		−	1.61144e8i		−	0.914374i	0.889371	−	0.457187i	$-0.151143\pi$
$228$	3.54466e7	−	6.62466e7i	0.198063	−	0.370162i
$229$		−	5.27173e7i		−	0.290088i	−0.989425	−	0.145044i	$-0.953668\pi$
$229$		−	5.27173e7i		−	0.290088i	0.989425	−	0.145044i	$-0.0463323\pi$
$230$	−4.65399e7	−	7.76854e7i	−0.252219	−	0.421010i
$231$	2.09830e8			1.12002
$232$	2.47511e8	−	1.19975e7i	1.30133	−	0.0630786i
$233$	−1.79423e8			−0.929249			−0.464625	−	0.885508i	$-0.653811\pi$
$233$	−1.79423e8			−0.929249			−0.464625	+	0.885508i	$0.653811\pi$
$234$	−2.08312e7	−	3.47718e7i	−0.106282	−	0.177408i
$235$		−	3.86285e7i		−	0.194165i
$236$	2.55044e7	+	1.36467e7i	0.126306	+	0.0675826i
$237$		−	3.30832e8i		−	1.61431i
$238$	3.21234e8	−	1.92445e8i	1.54455	−	0.925312i
$239$	−8.42441e7			−0.399160			−0.199580	−	0.979882i	$-0.563958\pi$
$239$	−8.42441e7			−0.399160			−0.199580	+	0.979882i	$0.563958\pi$
$240$	1.18631e8	+	1.77879e8i	0.553935	+	0.830586i
$241$	−2.12302e8			−0.977000			−0.488500	−	0.872564i	$-0.662456\pi$
$241$	−2.12302e8			−0.977000			−0.488500	+	0.872564i	$0.662456\pi$
$242$	9.93766e7	−	5.95347e7i	0.450745	−	0.270033i
$243$		−	1.13255e8i		−	0.506333i
$244$	−1.75234e8	−	9.37629e7i	−0.772245	−	0.413206i
$245$		−	2.99280e7i		−	0.130016i
$246$	1.67635e7	+	2.79821e7i	0.0717947	+	0.119841i
$247$	−9.17975e7			−0.387607
$248$	7.83083e6	+	1.61552e8i	0.0326007	+	0.672563i
$249$	2.37079e8			0.973186
$250$	9.61366e7	+	1.60473e8i	0.389134	+	0.649551i
$251$			1.18102e8i			0.471411i	0.971825	+	0.235706i	$0.0757401\pi$
$251$			1.18102e8i			0.471411i	−0.971825	+	0.235706i	$0.924260\pi$
$252$	−3.29194e7	+	6.15235e7i	−0.129584	+	0.242181i
$253$			1.34492e8i			0.522125i
$254$	−3.84637e8	+	2.30429e8i	−1.47276	+	0.882304i
$255$	−4.51359e8			−1.70463
$256$	−1.03157e8	+	2.47823e8i	−0.384291	+	0.923212i
$257$	1.27463e8			0.468402			0.234201	−	0.972188i	$-0.424753\pi$
$257$	1.27463e8			0.468402			0.234201	+	0.972188i	$0.424753\pi$
$258$	−1.28186e8	+	7.67940e7i	−0.464700	+	0.278393i
$259$		−	9.91755e7i		−	0.354695i
$260$	1.23243e8	−	2.30330e8i	0.434865	−	0.812724i
$261$		−	9.74762e7i		−	0.339357i
$262$	2.12418e8	+	3.54573e8i	0.729687	+	1.21801i
$263$	4.33125e8			1.46814			0.734071	−	0.679073i	$-0.237618\pi$
$263$	4.33125e8			1.46814			0.734071	+	0.679073i	$0.237618\pi$
$264$	−1.53735e7	−	3.17161e8i	−0.0514233	−	1.06088i
$265$	3.37506e8			1.11409
$266$	8.12109e7	+	1.35559e8i	0.264563	+	0.441614i
$267$		−	1.75747e7i		−	0.0565066i
$268$	−3.57060e7	−	1.91052e7i	−0.113310	−	0.0606290i
$269$			3.44748e8i			1.07986i	0.841709	+	0.539931i	$0.181550\pi$
$269$			3.44748e8i			1.07986i	−0.841709	+	0.539931i	$0.818450\pi$
$270$	3.49139e8	−	2.09163e8i	1.07951	−	0.646712i
$271$	−4.42513e8			−1.35062			−0.675311	−	0.737533i	$-0.735990\pi$
$271$	−4.42513e8			−1.35062			−0.675311	+	0.737533i	$0.735990\pi$
$272$	−3.14419e8	−	4.71450e8i	−0.947366	−	1.42051i
$273$	−2.42049e8			−0.720003
$274$	2.49396e8	−	1.49408e8i	0.732423	−	0.438781i
$275$			1.48135e8i			0.429531i
$276$	1.11961e8	+	5.99068e7i	0.320541	+	0.171512i
$277$			3.18148e8i			0.899395i	0.893181	+	0.449697i	$0.148468\pi$
$277$			3.18148e8i			0.899395i	−0.893181	+	0.449697i	$0.851532\pi$
$278$	−3.04088e8	−	5.07591e8i	−0.848873	−	1.41696i
$279$	6.36234e7			0.175389
$280$	−4.49162e8	+	2.17719e7i	−1.22278	+	0.0592713i
$281$	1.28497e8			0.345478			0.172739	−	0.984968i	$-0.444738\pi$
$281$	1.28497e8			0.345478			0.172739	+	0.984968i	$0.444738\pi$
$282$	2.78358e7	+	4.64641e7i	0.0739148	+	0.123380i
$283$		−	3.98970e8i		−	1.04637i	−0.852218	−	0.523187i	$-0.824743\pi$
$283$		−	3.98970e8i		−	1.04637i	0.852218	−	0.523187i	$-0.175257\pi$
$284$	3.25470e7	−	6.08274e7i	0.0843134	−	0.157574i
$285$		−	1.90471e8i		−	0.487384i
$286$	−3.32806e8	+	1.99378e8i	−0.841221	+	0.503960i
$287$	−6.86057e7			−0.171306
$288$	9.54054e7	+	4.52505e7i	0.235342	+	0.111622i
$289$	7.85942e8			1.91535
$290$	5.38896e8	−	3.22842e8i	1.29751	−	0.777316i
$291$			3.15425e8i			0.750362i
$292$	−1.62149e8	+	3.03042e8i	−0.381131	+	0.712299i
$293$			2.00958e8i			0.466732i	0.972389	+	0.233366i	$0.0749741\pi$
$293$			2.00958e8i			0.466732i	−0.972389	+	0.233366i	$0.925026\pi$
$294$	2.15662e7	+	3.59987e7i	0.0494945	+	0.0826174i
$295$	7.33298e7			0.166304
$296$	−1.49905e8	+	7.26625e6i	−0.335965	+	0.0162850i
$297$	−6.04444e8			−1.33878
$298$	−1.04893e8	−	1.75090e8i	−0.229610	−	0.383270i
$299$		−	1.55143e8i		−	0.335647i
$300$	1.23318e8	+	6.59840e7i	0.263696	+	0.141096i
$301$		−	3.14284e8i		−	0.664262i
$302$	−3.75971e8	+	2.25237e8i	−0.785470	+	0.470560i
$303$	2.49243e8			0.514724
$304$	1.98949e8	−	1.32683e8i	0.406148	−	0.270868i
$305$	−5.03830e8			−1.01680
$306$	−1.91221e8	+	1.14557e8i	−0.381515	+	0.228558i
$307$			1.58918e7i			0.0313465i	0.999877	+	0.0156733i	$0.00498916\pi$
$307$			1.58918e7i			0.0313465i	−0.999877	+	0.0156733i	$0.995011\pi$
$308$	5.88850e8	+	3.15077e8i	1.14836	+	0.614453i
$309$			2.65353e8i			0.511646i
$310$	2.10722e8	+	3.51741e8i	0.401738	+	0.670591i
$311$	4.87710e8			0.919391			0.459695	−	0.888077i	$-0.347959\pi$
$311$	4.87710e8			0.919391			0.459695	+	0.888077i	$0.347959\pi$
$312$	1.77341e7	+	3.65860e8i	0.0330574	+	0.681983i
$313$	−3.24731e8			−0.598576			−0.299288	−	0.954163i	$-0.596749\pi$
$313$	−3.24731e8			−0.598576			−0.299288	+	0.954163i	$0.596749\pi$
$314$	2.97890e8	+	4.97245e8i	0.543003	+	0.906394i
$315$			1.76891e8i			0.318874i
$316$	4.96770e8	−	9.28419e8i	0.885627	−	1.65516i
$317$		−	1.06084e9i		−	1.87043i	−0.354086	−	0.935213i	$-0.615208\pi$
$317$		−	1.06084e9i		−	1.87043i	0.354086	−	0.935213i	$-0.384792\pi$
$318$	−4.05967e8	+	2.43207e8i	−0.707939	+	0.424113i
$319$	−9.32958e8			−1.60914
$320$	6.58171e7	+	6.77318e8i	0.112283	+	1.15549i
$321$	−2.06247e7			−0.0348033
$322$	−2.29102e8	+	1.37251e8i	−0.382414	+	0.229097i
$323$			5.04824e8i			0.833548i
$324$	−1.94005e8	+	3.62578e8i	−0.316887	+	0.592234i
$325$		−	1.70881e8i		−	0.276123i
$326$	−4.98618e8	−	8.32304e8i	−0.797088	−	1.33052i
$327$	7.87763e8			1.24589
$328$	5.02651e6	+	1.03698e8i	0.00786516	+	0.162261i
$329$	−1.13919e8			−0.176365
$330$	−4.13690e8	−	6.90540e8i	−0.633689	−	1.05777i
$331$		−	2.88487e8i		−	0.437249i	−0.975809	−	0.218624i	$-0.929843\pi$
$331$		−	2.88487e8i		−	0.437249i	0.975809	−	0.218624i	$-0.0701569\pi$
$332$	6.65319e8	+	3.55993e8i	0.997808	+	0.533898i
$333$			5.90363e7i			0.0876121i
$334$	1.02751e9	−	6.15563e8i	1.50895	−	0.903982i
$335$	−1.02661e8			−0.149193
$336$	5.24583e8	−	3.49855e8i	0.754444	−	0.503154i
$337$	−1.10595e8			−0.157410			−0.0787051	−	0.996898i	$-0.525079\pi$
$337$	−1.10595e8			−0.157410			−0.0787051	+	0.996898i	$0.525079\pi$
$338$	−2.25089e8	+	1.34847e8i	−0.317063	+	0.189947i
$339$		−	7.59590e8i		−	1.05896i
$340$	−1.26666e9	−	6.77751e8i	−1.74776	−	0.935177i
$341$		−	6.08948e8i		−	0.831649i
$342$	−4.83425e7	−	8.06944e7i	−0.0653488	−	0.109082i
$343$	6.99837e8			0.936414
$344$	−4.75044e8	+	2.30265e7i	−0.629186	+	0.0304981i
$345$	3.21907e8			0.422049
$346$	1.15209e8	+	1.92309e8i	0.149527	+	0.249594i
$347$			1.10651e9i			1.42168i	0.703352	+	0.710841i	$0.251686\pi$
$347$			1.10651e9i			1.42168i	−0.703352	+	0.710841i	$0.748314\pi$
$348$	−4.15568e8	+	7.76659e8i	−0.528585	+	0.987878i
$349$			1.38337e9i			1.74201i	0.491278	+	0.871003i	$0.336530\pi$
$349$			1.38337e9i			1.74201i	−0.491278	+	0.871003i	$0.663470\pi$
$350$	−2.52344e8	+	1.51174e8i	−0.314597	+	0.188469i
$351$	6.97254e8			0.860630
$352$	4.33099e8	−	9.13138e8i	0.529283	−	1.11593i
$353$	−2.47617e8			−0.299618			−0.149809	−	0.988715i	$-0.547866\pi$
$353$	−2.47617e8			−0.299618			−0.149809	+	0.988715i	$0.547866\pi$
$354$	−8.82044e7	+	5.28416e7i	−0.105677	+	0.0633089i
$355$		−	1.74890e8i		−	0.207475i
$356$	2.63898e7	−	4.93202e7i	0.0310000	−	0.0579362i
$357$			1.33111e9i			1.54837i
$358$	1.73150e8	+	2.89026e8i	0.199449	+	0.332925i
$359$	−1.38641e9			−1.58148			−0.790738	−	0.612155i	$-0.790303\pi$
$359$	−1.38641e9			−1.58148			−0.790738	+	0.612155i	$0.790303\pi$
$360$	2.67373e8	−	1.29602e7i	0.302036	−	0.0146404i
$361$	6.80839e8			0.761674
$362$	2.30378e7	+	3.84552e7i	0.0255247	+	0.0426064i
$363$			4.11789e8i			0.451858i
$364$	−6.79267e8	−	3.63456e8i	−0.738219	−	0.395000i
$365$			8.71299e8i			0.937869i
$366$	6.06030e8	−	3.63061e8i	0.646116	−	0.387076i
$367$	−7.49367e8			−0.791341			−0.395670	−	0.918393i	$-0.629488\pi$
$367$	−7.49367e8			−0.791341			−0.395670	+	0.918393i	$0.629488\pi$
$368$	2.24242e8	+	3.36235e8i	0.234558	+	0.351703i
$369$	4.08390e7			0.0423139
$370$	−3.26381e8	+	1.95529e8i	−0.334980	+	0.200680i
$371$		−	9.95340e8i		−	1.01196i
$372$	−5.06931e8	−	2.71244e8i	−0.510562	−	0.273187i
$373$		−	1.49519e9i		−	1.49181i	−0.666051	−	0.745906i	$-0.732017\pi$
$373$		−	1.49519e9i		−	1.49181i	0.666051	−	0.745906i	$-0.267983\pi$
$374$	1.09644e9	+	1.83021e9i	1.08377	+	1.80905i
$375$	−6.64957e8			−0.651155
$376$	8.34649e6	+	1.72191e8i	0.00809741	+	0.167052i
$377$	1.07621e9			1.03443
$378$	−6.16843e8	−	1.02965e9i	−0.587426	−	0.980546i
$379$			7.92096e7i			0.0747379i	0.999302	+	0.0373689i	$0.0118977\pi$
$379$			7.92096e7i			0.0747379i	−0.999302	+	0.0373689i	$0.988102\pi$
$380$	2.86007e8	−	5.34522e8i	0.267383	−	0.499715i
$381$		−	1.59383e9i		−	1.47640i
$382$	4.65959e8	−	2.79147e8i	0.427687	−	0.256219i
$383$	4.80285e8			0.436820			0.218410	−	0.975857i	$-0.429913\pi$
$383$	4.80285e8			0.436820			0.218410	+	0.975857i	$0.429913\pi$
$384$	−5.67245e8	−	7.67281e8i	−0.511224	−	0.691505i
$385$	1.69305e9			1.51202
$386$	4.58580e7	−	2.74726e7i	0.0405844	−	0.0243134i
$387$			1.87084e8i			0.164077i
$388$	−4.73636e8	+	8.85183e8i	−0.411655	+	0.769346i
$389$		−	1.07150e9i		−	0.922928i	−0.887159	−	0.461464i	$-0.847324\pi$
$389$		−	1.07150e9i		−	0.922928i	0.887159	−	0.461464i	$-0.152676\pi$
$390$	4.77211e8	+	7.96571e8i	0.407365	+	0.679984i
$391$	−8.53180e8			−0.721809
$392$	6.46656e6	+	1.33407e8i	0.00542216	+	0.111861i
$393$	−1.46925e9			−1.22102
$394$	6.67957e8	+	1.11497e9i	0.550189	+	0.918387i
$395$		−	2.66937e9i		−	2.17931i
$396$	−3.50525e8	−	1.87556e8i	−0.283652	−	0.151774i
$397$			2.03185e9i			1.62976i	0.579627	+	0.814882i	$0.303198\pi$
$397$			2.03185e9i			1.62976i	−0.579627	+	0.814882i	$0.696802\pi$
$398$	−1.17369e8	+	7.03138e7i	−0.0933178	+	0.0559049i
$399$	−5.61719e8			−0.442705
$400$	2.46990e8	+	3.70344e8i	0.192961	+	0.289331i
$401$	−2.57759e9			−1.99622			−0.998111	−	0.0614301i	$-0.980434\pi$
$401$	−2.57759e9			−1.99622			−0.998111	+	0.0614301i	$0.980434\pi$
$402$	1.23485e8	−	7.39778e7i	0.0948035	−	0.0567950i
$403$			7.02451e8i			0.534624i
$404$	6.99455e8	+	3.74258e8i	0.527746	+	0.282382i
$405$			1.04248e9i			0.779782i
$406$	−9.52097e8	−	1.58926e9i	−0.706057	−	1.17857i
$407$	5.65044e8			0.415434
$408$	2.01198e9	−	9.75255e7i	1.46661	−	0.0710899i
$409$	3.30242e8			0.238672			0.119336	−	0.992854i	$-0.461923\pi$
$409$	3.30242e8			0.238672			0.119336	+	0.992854i	$0.461923\pi$
$410$	1.35259e8	+	2.25778e8i	0.0969223	+	0.161785i
$411$			1.03343e9i			0.734232i
$412$	−3.98449e8	+	7.44666e8i	−0.280693	+	0.524591i
$413$		−	2.16257e8i		−	0.151059i
$414$	1.36378e8	−	8.17015e7i	0.0944590	−	0.0565886i
$415$	1.91291e9			1.31379
$416$	−4.99600e8	+	1.05335e9i	−0.340248	+	0.717374i
$417$	2.10331e9			1.42046
$418$	−7.72337e8	+	4.62692e8i	−0.517237	+	0.309867i
$419$			5.80021e7i			0.0385207i	0.999815	+	0.0192604i	$0.00613114\pi$
$419$			5.80021e7i			0.0385207i	−0.999815	+	0.0192604i	$0.993869\pi$
$420$	7.54136e8	−	1.40941e9i	0.496680	−	0.928251i
$421$			1.90609e8i			0.124496i	0.998061	+	0.0622480i	$0.0198270\pi$
$421$			1.90609e8i			0.124496i	−0.998061	+	0.0622480i	$0.980173\pi$
$422$	−1.13873e9	−	1.90079e9i	−0.737610	−	1.23123i
$423$	6.78129e7			0.0435633
$424$	−1.50447e9	+	7.29251e7i	−0.958523	+	0.0464619i
$425$	−9.39731e8			−0.593803
$426$	1.26026e8	+	2.10365e8i	0.0789817	+	0.131838i
$427$			1.48585e9i			0.923586i
$428$	−5.78795e7	−	3.09696e7i	−0.0356838	−	0.0190934i
$429$		−	1.37906e9i		−	0.843298i
$430$	−1.03429e9	+	6.19625e8i	−0.627341	+	0.375828i
$431$	2.42923e9			1.46150			0.730749	−	0.682646i	$-0.239171\pi$
$431$	2.42923e9			1.46150			0.730749	+	0.682646i	$0.239171\pi$
$432$	−1.51113e9	+	1.00780e9i	−0.901798	+	0.601427i
$433$	−2.37902e9			−1.40828			−0.704141	−	0.710060i	$-0.748668\pi$
$433$	−2.37902e9			−1.40828			−0.704141	+	0.710060i	$0.748668\pi$
$434$	1.03732e9	−	6.21440e8i	0.609116	−	0.364910i
$435$			2.23303e9i			1.30072i
$436$	2.21071e9	+	1.18289e9i	1.27741	+	0.683504i
$437$		−	3.60037e8i		−	0.206378i
$438$	−6.27860e8	−	1.04804e9i	−0.357029	−	0.595961i
$439$	−1.33161e9			−0.751194			−0.375597	−	0.926783i	$-0.622562\pi$
$439$	−1.33161e9			−0.751194			−0.375597	+	0.926783i	$0.622562\pi$
$440$	−1.24044e8	−	2.55906e9i	−0.0694210	−	1.43218i
$441$	5.25390e7			0.0291707
$442$	−1.26480e9	−	2.11123e9i	−0.696696	−	1.16294i
$443$			5.02643e8i			0.274692i	0.990523	+	0.137346i	$0.0438573\pi$
$443$			5.02643e8i			0.274692i	−0.990523	+	0.137346i	$0.956143\pi$
$444$	2.51688e8	−	4.70382e8i	0.136465	−	0.255041i
$445$		−	1.41805e8i		−	0.0762834i
$446$	−1.04842e9	+	6.28086e8i	−0.559579	+	0.335233i
$447$	7.25525e8			0.384217
$448$	1.99748e9	−	1.94102e8i	1.04957	−	0.101990i
$449$	3.14785e9			1.64116			0.820580	−	0.571531i	$-0.193650\pi$
$449$	3.14785e9			1.64116			0.820580	+	0.571531i	$0.193650\pi$
$450$	1.50213e8	−	8.99897e7i	0.0777075	−	0.0465531i
$451$		−	3.90876e8i		−	0.200641i
$452$	1.14058e9	−	2.13165e9i	0.580955	−	1.08575i
$453$		−	1.55792e9i		−	0.787410i
$454$	9.36939e8	+	1.56396e9i	0.469911	+	0.784387i
$455$	−1.95301e9			−0.971998
$456$	4.11552e7	+	8.49044e8i	0.0203258	+	0.419328i
$457$	−2.68422e9			−1.31556			−0.657782	−	0.753209i	$-0.728505\pi$
$457$	−2.68422e9			−1.31556			−0.657782	+	0.753209i	$0.728505\pi$
$458$	3.06514e8	+	5.11641e8i	0.149081	+	0.248849i
$459$		−	3.83442e9i		−	1.85078i
$460$	9.03372e8	+	4.83368e8i	0.432727	+	0.231540i
$461$			1.30434e9i			0.620065i	0.950726	+	0.310033i	$0.100340\pi$
$461$			1.30434e9i			0.620065i	−0.950726	+	0.310033i	$0.899660\pi$
$462$	−2.03648e9	+	1.22002e9i	−0.960799	+	0.575597i
$463$	2.86853e9			1.34315			0.671577	−	0.740934i	$-0.265617\pi$
$463$	2.86853e9			1.34315			0.671577	+	0.740934i	$0.265617\pi$
$464$	−2.33243e9	+	1.55554e9i	−1.08392	+	0.722886i
$465$	−1.45752e9			−0.672246
$466$	1.74136e9	−	1.04322e9i	0.797148	−	0.477556i
$467$			5.96519e8i			0.271029i	0.990775	+	0.135514i	$0.0432687\pi$
$467$			5.96519e8i			0.271029i	−0.990775	+	0.135514i	$0.956731\pi$
$468$	4.04348e8	+	2.16355e8i	0.182345	+	0.0975676i
$469$			3.02758e8i			0.135516i
$470$	2.24597e8	+	3.74903e8i	0.0997843	+	0.166562i
$471$	−2.06045e9			−0.908632
$472$	−3.26875e8	+	1.58444e7i	−0.143082	+	0.00693553i
$473$	1.79061e9			0.778012
$474$	1.92355e9	+	3.21084e9i	0.829622	+	1.38482i
$475$		−	3.96561e8i		−	0.169778i
$476$	−1.99876e9	+	3.73550e9i	−0.849447	+	1.58754i
$477$			5.92497e8i			0.249961i
$478$	8.17619e8	−	4.89820e8i	0.342416	−	0.205135i
$479$	−2.16068e9			−0.898289			−0.449144	−	0.893459i	$-0.648271\pi$
$479$	−2.16068e9			−0.898289			−0.449144	+	0.893459i	$0.648271\pi$
$480$	−2.18560e9	−	1.03662e9i	−0.902039	−	0.427835i
$481$	−6.51805e8			−0.267061
$482$	2.06047e9	−	1.23439e9i	0.838110	−	0.502096i
$483$		−	9.49337e8i		−	0.383359i
$484$	−6.18334e8	+	1.15561e9i	−0.247893	+	0.463290i
$485$			2.54506e9i			1.01298i
$486$	6.58499e8	+	1.09918e9i	0.260213	+	0.434353i
$487$	1.41934e8			0.0556847			0.0278424	−	0.999612i	$-0.491136\pi$
$487$	1.41934e8			0.0556847			0.0278424	+	0.999612i	$0.491136\pi$
$488$	2.24588e9	−	1.08863e8i	0.874816	−	0.0424044i
$489$	3.44884e9			1.33380
$490$	1.74010e8	+	2.90462e8i	0.0668172	+	0.111533i
$491$			2.38677e9i			0.909966i	0.890500	+	0.454983i	$0.150355\pi$
$491$			2.38677e9i			0.909966i	−0.890500	+	0.454983i	$0.849645\pi$
$492$	−3.25392e8	−	1.74108e8i	−0.123177	−	0.0659084i
$493$		−	5.91843e9i		−	2.22455i
$494$	8.90927e8	−	5.33738e8i	0.332505	−	0.199197i
$495$	−1.00782e9			−0.373479
$496$	−1.01532e9	−	1.52239e9i	−0.373607	−	0.560197i
$497$	−5.15769e8			−0.188455
$498$	−2.30094e9	+	1.37845e9i	−0.834838	+	0.500136i
$499$		−	5.23900e9i		−	1.88754i	−0.330601	−	0.943771i	$-0.607251\pi$
$499$		−	5.23900e9i		−	1.88754i	0.330601	−	0.943771i	$-0.392749\pi$
$500$	−1.86608e9	−	9.98486e8i	−0.667629	−	0.357229i
$501$			4.25772e9i			1.51267i
$502$	−6.86681e8	−	1.14622e9i	−0.242266	−	0.404396i
$503$	−3.63292e9			−1.27282			−0.636411	−	0.771350i	$-0.719582\pi$
$503$	−3.63292e9			−1.27282			−0.636411	+	0.771350i	$0.719582\pi$
$504$	−3.82210e7	−	7.88511e8i	−0.0132983	−	0.274347i
$505$	2.01106e9			0.694872
$506$	−7.81976e8	−	1.30529e9i	−0.268328	−	0.447900i
$507$		−	9.32706e8i		−	0.317846i
$508$	2.39326e9	−	4.47278e9i	0.809965	−	1.51375i
$509$			2.58693e9i			0.869505i	0.900550	+	0.434753i	$0.143164\pi$
$509$			2.58693e9i			0.869505i	−0.900550	+	0.434753i	$0.856836\pi$
$510$	4.38060e9	−	2.62433e9i	1.46230	−	0.876039i
$511$	2.56955e9			0.851892
$512$	−4.39735e8	−	3.00500e9i	−0.144793	−	0.989462i
$513$	1.61811e9			0.529171
$514$	−1.23708e9	+	7.41108e8i	−0.401814	+	0.240719i
$515$			2.14105e9i			0.690718i
$516$	7.97591e8	−	1.49063e9i	0.255568	−	0.477633i
$517$		−	6.49047e8i		−	0.206566i
$518$	5.76636e8	+	9.62533e8i	0.182283	+	0.304272i
$519$	−7.96876e8			−0.250210
$520$	1.43091e8	+	2.95200e9i	0.0446272	+	0.920672i
$521$	1.08542e8			0.0336253			0.0168127	−	0.999859i	$-0.494648\pi$
$521$	1.08542e8			0.0336253			0.0168127	+	0.999859i	$0.494648\pi$
$522$	5.66755e8	+	9.46041e8i	0.174401	+	0.291114i
$523$			6.10725e9i			1.86676i	0.358884	+	0.933382i	$0.383157\pi$
$523$			6.10725e9i			1.86676i	−0.358884	+	0.933382i	$0.616843\pi$
$524$	−4.12318e9	−	2.20620e9i	−1.25191	−	0.669861i
$525$		−	1.04564e9i		−	0.315374i
$526$	−4.20363e9	+	2.51832e9i	−1.25943	+	0.754502i
$527$	3.86300e9			1.14971
$528$	1.99327e9	+	2.98877e9i	0.589315	+	0.883637i
$529$	−2.79634e9			−0.821288
$530$	−3.27561e9	+	1.96236e9i	−0.955712	+	0.572549i
$531$			1.28732e8i			0.0373125i
$532$	−1.57636e9	−	8.43465e8i	−0.453905	−	0.242871i
$533$			4.50894e8i			0.128982i
$534$	1.02185e8	+	1.70569e8i	0.0290396	+	0.0484736i
$535$	−1.66414e8			−0.0469841
$536$	4.57623e8	−	2.21821e7i	0.128360	−	0.00622193i
$537$	−1.19764e9			−0.333747
$538$	−2.00446e9	−	3.34590e9i	−0.554958	−	0.926349i
$539$		−	5.02858e8i		−	0.138320i
$540$	−2.17239e9	+	4.06000e9i	−0.593689	+	1.10955i
$541$			5.39345e8i			0.146445i	0.997316	+	0.0732227i	$0.0233284\pi$
$541$			5.39345e8i			0.146445i	−0.997316	+	0.0732227i	$0.976672\pi$
$542$	4.29475e9	−	2.57290e9i	1.15862	−	0.694106i
$543$	−1.59348e8			−0.0427116
$544$	5.79270e9	+	2.74746e9i	1.54271	+	0.731704i
$545$	6.35620e9			1.68194
$546$	2.34917e9	−	1.40735e9i	0.617648	−	0.370021i
$547$			8.82287e7i			0.0230491i	0.999934	+	0.0115246i	$0.00366846\pi$
$547$			8.82287e7i			0.0230491i	−0.999934	+	0.0115246i	$0.996332\pi$
$548$	−1.55177e9	+	2.90012e9i	−0.402806	+	0.752808i
$549$		−	8.84483e8i		−	0.228132i
$550$	−8.61304e8	−	1.43771e9i	−0.220743	−	0.368469i
$551$	2.49754e9			0.636037
$552$	−1.43493e9	+	6.95546e7i	−0.363116	+	0.0176011i
$553$	−7.87226e9			−1.97953
$554$	−1.84981e9	−	3.08774e9i	−0.462213	−	0.771537i
$555$		−	1.35243e9i		−	0.335807i
$556$	5.90257e9	+	3.15829e9i	1.45639	+	0.779274i
$557$		−	5.57233e8i		−	0.136629i	−0.997664	−	0.0683147i	$-0.978238\pi$
$557$		−	5.57233e8i		−	0.136629i	0.997664	−	0.0683147i	$-0.0217622\pi$
$558$	−6.17488e8	+	3.69925e8i	−0.150456	+	0.0901352i
$559$	−2.06555e9			−0.500143
$560$	4.23269e9	−	2.82286e9i	1.01849	−	0.679254i
$561$	−7.58386e9			−1.81351
$562$	−1.24711e9	+	7.47119e8i	−0.296365	+	0.177547i
$563$		−	1.17012e9i		−	0.276344i	−0.990408	−	0.138172i	$-0.955877\pi$
$563$		−	1.17012e9i		−	0.276344i	0.990408	−	0.138172i	$-0.0441227\pi$
$564$	−5.40312e8	−	2.89105e8i	−0.126814	−	0.0678546i
$565$		−	6.12887e9i		−	1.42959i
$566$	2.31973e9	+	3.87214e9i	0.537749	+	0.897623i
$567$	3.07437e9			0.708297
$568$	3.77886e7	+	7.79590e8i	0.00865250	+	0.178504i
$569$	−2.39181e9			−0.544295			−0.272147	−	0.962256i	$-0.587734\pi$
$569$	−2.39181e9			−0.544295			−0.272147	+	0.962256i	$0.587734\pi$
$570$	1.10745e9	+	1.84859e9i	0.250475	+	0.418098i
$571$		−	3.15823e9i		−	0.709933i	−0.934879	−	0.354966i	$-0.884492\pi$
$571$		−	3.15823e9i		−	0.709933i	0.934879	−	0.354966i	$-0.115508\pi$
$572$	2.07076e9	−	3.87007e9i	0.462640	−	0.864634i
$573$			1.93080e9i			0.428743i
$574$	6.65843e8	−	3.98894e8i	0.146954	−	0.0880371i
$575$	6.70211e8			0.147019
$576$	−1.18904e9	+	1.15543e8i	−0.259250	+	0.0251921i
$577$	4.03435e9			0.874296			0.437148	−	0.899390i	$-0.355989\pi$
$577$	4.03435e9			0.874296			0.437148	+	0.899390i	$0.355989\pi$
$578$	−7.62785e9	+	4.56970e9i	−1.64306	+	0.984329i
$579$			1.90023e8i			0.0406846i
$580$	−3.35308e9	+	6.26660e9i	−0.713585	+	1.33363i
$581$		−	5.64138e9i		−	1.19335i
$582$	−1.83398e9	−	3.06131e9i	−0.385623	−	0.643691i
$583$	5.67087e9			1.18525
$584$	−1.88262e8	−	3.88391e9i	−0.0391128	−	0.806908i
$585$	1.16257e9			0.240090
$586$	−1.16843e9	−	1.95037e9i	−0.239861	−	0.400382i
$587$		−	2.72240e9i		−	0.555544i	−0.960647	−	0.277772i	$-0.910404\pi$
$587$		−	2.72240e9i		−	0.555544i	0.960647	−	0.277772i	$-0.0895960\pi$
$588$	−4.18614e8	−	2.23988e8i	−0.0849168	−	0.0454365i
$589$			1.63016e9i			0.328721i
$590$	−7.11692e8	+	4.26361e8i	−0.142662	+	0.0854664i
$591$	−4.62012e9			−0.920655
$592$	1.41263e9	−	9.42113e8i	0.279836	−	0.186628i
$593$	−2.29251e9			−0.451460			−0.225730	−	0.974190i	$-0.572477\pi$
$593$	−2.29251e9			−0.451460			−0.225730	+	0.974190i	$0.572477\pi$
$594$	5.86634e9	−	3.51441e9i	1.14846	−	0.688019i
$595$			1.07402e10i			2.09028i
$596$	2.03605e9	+	1.08943e9i	0.393937	+	0.210784i
$597$		−	4.86346e8i		−	0.0935482i
$598$	9.02047e8	+	1.50572e9i	0.172494	+	0.287932i
$599$	−3.58734e9			−0.681991			−0.340995	−	0.940065i	$-0.610764\pi$
$599$	−3.58734e9			−0.681991			−0.340995	+	0.940065i	$0.610764\pi$
$600$	−1.58050e9	+	7.66106e7i	−0.298720	+	0.0144797i
$601$	8.20369e9			1.54152			0.770759	−	0.637127i	$-0.219877\pi$
$601$	8.20369e9			1.54152			0.770759	+	0.637127i	$0.219877\pi$
$602$	1.82734e9	+	3.05024e9i	0.341375	+	0.569831i
$603$		−	1.80223e8i		−	0.0334734i
$604$	2.33934e9	−	4.37201e9i	0.431980	−	0.807332i
$605$			3.32259e9i			0.610004i
$606$	−2.41899e9	+	1.44917e9i	−0.441551	+	0.264525i
$607$	−4.60087e9			−0.834986			−0.417493	−	0.908680i	$-0.637091\pi$
$607$	−4.60087e9			−0.834986			−0.417493	+	0.908680i	$0.637091\pi$
$608$	−1.15941e9	+	2.44449e9i	−0.209207	+	0.441088i
$609$	6.58546e9			1.18148
$610$	4.88985e9	−	2.92942e9i	0.872251	−	0.522549i
$611$			7.48707e8i			0.132791i
$612$	1.18980e9	−	2.22364e9i	0.209819	−	0.392133i
$613$			8.55728e9i			1.50046i	0.661178	+	0.750229i	$0.270057\pi$
$613$			8.55728e9i			1.50046i	−0.661178	+	0.750229i	$0.729943\pi$
$614$	−9.23998e7	−	1.54236e8i	−0.0161095	−	0.0268903i
$615$	−9.35561e8			−0.162184
$616$	−7.54695e9	+	3.65819e8i	−1.30089	+	0.0630570i
$617$	−2.58089e9			−0.442355			−0.221178	−	0.975234i	$-0.570990\pi$
$617$	−2.58089e9			−0.442355			−0.221178	+	0.975234i	$0.570990\pi$
$618$	−1.54284e9	−	2.57535e9i	−0.262943	−	0.438911i
$619$			5.26641e9i			0.892478i	0.894914	+	0.446239i	$0.147237\pi$
$619$			5.26641e9i			0.892478i	−0.894914	+	0.446239i	$0.852763\pi$
$620$	−4.09026e9	−	2.18858e9i	−0.689255	−	0.368800i
$621$			2.73469e9i			0.458234i
$622$	−4.73340e9	+	2.83569e9i	−0.788690	+	0.472490i
$623$	−4.18197e8			−0.0692903
$624$	−2.29933e9	−	3.44769e9i	−0.378840	−	0.568044i
$625$	−7.48796e9			−1.22683
$626$	3.15164e9	−	1.88809e9i	0.513483	−	0.307618i
$627$		−	3.20035e9i		−	0.518514i
$628$	−5.78226e9	−	3.09392e9i	−0.931621	−	0.498483i
$629$			3.58449e9i			0.574314i
$630$	−1.02850e9	−	1.71679e9i	−0.163874	−	0.273543i
$631$	8.32515e9			1.31914			0.659568	−	0.751645i	$-0.270739\pi$
$631$	8.32515e9			1.31914			0.659568	+	0.751645i	$0.270739\pi$
$632$	5.76773e8	+	1.18990e10i	0.0908857	+	1.87500i
$633$	7.87635e9			1.23428
$634$	6.16801e9	+	1.02958e10i	0.961242	+	1.60453i
$635$		−	1.28601e10i		−	1.99313i
$636$	2.52598e9	−	4.72083e9i	0.389341	−	0.727643i
$637$			5.80071e8i			0.0889187i
$638$	9.05469e9	−	5.42449e9i	1.38039	−	0.826965i
$639$	3.07022e8			0.0465496
$640$	−4.57691e9	−	6.19093e9i	−0.690148	−	0.933526i
$641$	4.26190e9			0.639146			0.319573	−	0.947562i	$-0.396460\pi$
$641$	4.26190e9			0.639146			0.319573	+	0.947562i	$0.396460\pi$
$642$	2.00170e8	−	1.19918e8i	0.0298557	−	0.0178860i
$643$		−	1.26588e10i		−	1.87782i	−0.344167	−	0.938908i	$-0.611839\pi$
$643$		−	1.26588e10i		−	1.87782i	0.344167	−	0.938908i	$-0.388161\pi$
$644$	1.42550e9	−	2.66414e9i	0.210314	−	0.393058i
$645$		−	4.28582e9i		−	0.628890i
$646$	−2.93519e9	−	4.89949e9i	−0.428374	−	0.715052i
$647$	−7.38061e9			−1.07134			−0.535670	−	0.844427i	$-0.679941\pi$
$647$	−7.38061e9			−1.07134			−0.535670	+	0.844427i	$0.679941\pi$
$648$	−2.25249e8	−	4.64695e9i	−0.0325199	−	0.670896i
$649$	1.23211e9			0.176926
$650$	9.93555e8	+	1.65846e9i	0.141904	+	0.236870i
$651$			4.29837e9i			0.610620i
$652$	9.67853e9	+	5.17870e9i	1.36755	+	0.731735i
$653$		−	3.21579e9i		−	0.451951i	−0.974133	−	0.225975i	$-0.927443\pi$
$653$		−	3.21579e9i		−	0.451951i	0.974133	−	0.225975i	$-0.0725569\pi$
$654$	−7.64552e9	+	4.58029e9i	−1.06877	+	0.640281i
$655$	−1.18549e10			−1.64836
$656$	−6.51717e8	−	9.77204e8i	−0.0901354	−	0.135152i
$657$	−1.52958e9			−0.210423
$658$	1.10563e9	−	6.62362e8i	0.151293	−	0.0906368i
$659$			5.17004e9i			0.703711i	0.936054	+	0.351856i	$0.114449\pi$
$659$			5.17004e9i			0.703711i	−0.936054	+	0.351856i	$0.885551\pi$
$660$	8.03001e9	+	4.29663e9i	1.08721	+	0.581733i
$661$		−	1.95604e9i		−	0.263435i	−0.991287	−	0.131717i	$-0.957951\pi$
$661$		−	1.95604e9i		−	0.263435i	0.991287	−	0.131717i	$-0.0420491\pi$
$662$	1.67735e9	+	2.79987e9i	0.224709	+	0.375090i
$663$	8.74835e9			1.16581
$664$	−8.52701e9	+	4.13325e8i	−1.13034	+	0.0547902i
$665$	−4.53232e9			−0.597647
$666$	−3.43254e8	−	5.72968e8i	−0.0450253	−	0.0751572i
$667$			4.22099e9i			0.550775i
$668$	−6.39330e9	+	1.19485e10i	−0.829865	+	1.55094i
$669$		−	4.34434e9i		−	0.560961i
$670$	9.96362e8	−	5.96902e8i	0.127984	−	0.0766727i
$671$	−8.46551e9			−1.08174
$672$	−3.05711e9	+	6.44555e9i	−0.388614	+	0.819347i
$673$	1.54679e9			0.195605			0.0978024	−	0.995206i	$-0.468819\pi$
$673$	1.54679e9			0.195605			0.0978024	+	0.995206i	$0.468819\pi$
$674$	1.07337e9	−	6.43035e8i	0.135033	−	0.0808956i
$675$			3.01211e9i			0.376971i
$676$	1.40053e9	−	2.61747e9i	0.174373	−	0.325888i
$677$		−	8.55209e9i		−	1.05928i	−0.848222	−	0.529642i	$-0.822326\pi$
$677$		−	8.55209e9i		−	1.05928i	0.848222	−	0.529642i	$-0.177674\pi$
$678$	4.41648e9	+	7.37209e9i	0.544217	+	0.908420i
$679$	7.50565e9			0.920119
$680$	1.62340e10	−	7.86900e8i	1.97990	−	0.0959707i
$681$	−6.48061e9			−0.786323
$682$	3.54061e9	+	5.91006e9i	0.427398	+	0.713422i
$683$			7.26976e9i			0.873067i	0.899688	+	0.436534i	$0.143794\pi$
$683$			7.26976e9i			0.873067i	−0.899688	+	0.436534i	$0.856206\pi$
$684$	9.38362e8	+	5.02090e8i	0.112118	+	0.0599909i
$685$			8.33837e9i			0.991206i
$686$	−6.79217e9	+	4.06906e9i	−0.803293	+	0.481238i
$687$	−2.12010e9			−0.249463
$688$	4.47658e9	−	2.98552e9i	0.524068	−	0.349511i
$689$	−6.54162e9			−0.761935
$690$	−3.12422e9	+	1.87166e9i	−0.362051	+	0.216898i
$691$		−	5.19893e9i		−	0.599434i	−0.954028	−	0.299717i	$-0.903108\pi$
$691$		−	5.19893e9i		−	0.599434i	0.954028	−	0.299717i	$-0.0968922\pi$
$692$	−2.23629e9	−	1.19657e9i	−0.256541	−	0.137268i
$693$			2.97218e9i			0.339241i
$694$	−6.43358e9	−	1.07391e10i	−0.730626	−	1.21958i
$695$	1.69709e10			1.91760
$696$	−4.82494e8	−	9.95399e9i	−0.0542449	−	1.11909i
$697$	2.47961e9			0.277376
$698$	−8.04333e9	−	1.34261e10i	−0.895245	−	1.49436i
$699$			7.21572e9i			0.799116i
$700$	1.57011e9	−	2.93440e9i	0.173017	−	0.323353i
$701$		−	1.35221e10i		−	1.48262i	−0.671163	−	0.741310i	$-0.734205\pi$
$701$		−	1.35221e10i		−	1.48262i	0.671163	−	0.741310i	$-0.265795\pi$
$702$	−6.76710e9	+	4.05404e9i	−0.738283	+	0.442291i
$703$	−1.51263e9			−0.164206
$704$	1.10588e9	+	1.13805e10i	0.119455	+	1.22930i
$705$	−1.55349e9			−0.166974
$706$	2.40321e9	−	1.43972e9i	0.257025	−	0.153979i
$707$		−	5.93083e9i		−	0.631172i
$708$	5.48819e8	−	1.02569e9i	0.0581182	−	0.108618i
$709$			1.05901e10i			1.11594i	0.829862	+	0.557969i	$0.188419\pi$
$709$			1.05901e10i			1.11594i	−0.829862	+	0.557969i	$0.811581\pi$
$710$	1.01686e9	+	1.69737e9i	0.106625	+	0.177980i
$711$	4.68613e9			0.488957
$712$	3.06398e7	+	6.32109e8i	0.00318131	+	0.0656314i
$713$	−2.75507e9			−0.284655
$714$	−7.73944e9	−	1.29189e10i	−0.795730	−	1.32825i
$715$		−	1.11271e10i		−	1.13845i
$716$	−3.36096e9	−	1.79835e9i	−0.342191	−	0.183096i
$717$			3.38799e9i			0.343261i
$718$	1.34556e10	−	8.06102e9i	1.35665	−	0.812746i
$719$	1.49161e10			1.49659			0.748297	−	0.663363i	$-0.230872\pi$
$719$	1.49161e10			1.49659			0.748297	+	0.663363i	$0.230872\pi$
$720$	−2.51959e9	+	1.68037e9i	−0.251575	+	0.167780i
$721$	6.31417e9			0.627398
$722$	−6.60779e9	+	3.95860e9i	−0.653395	+	0.391437i
$723$			8.53800e9i			0.840180i
$724$	−4.47180e8	−	2.39273e8i	−0.0437923	−	0.0234320i
$725$			4.64919e9i			0.453100i
$726$	−2.39426e9	−	3.99656e9i	−0.232217	−	0.387622i
$727$	−8.90159e9			−0.859206			−0.429603	−	0.903018i	$-0.641346\pi$
$727$	−8.90159e9			−0.859206			−0.429603	+	0.903018i	$0.641346\pi$
$728$	8.70577e9	−	4.21989e8i	0.836271	−	0.0405361i
$729$	−1.15808e10			−1.10711
$730$	−5.06599e9	−	8.45627e9i	−0.481986	−	0.804542i
$731$			1.13591e10i			1.07556i
$732$	−3.77079e9	+	7.04728e9i	−0.355340	+	0.664099i
$733$		−	7.99792e9i		−	0.750090i	−0.927007	−	0.375045i	$-0.877627\pi$
$733$		−	7.99792e9i		−	0.750090i	0.927007	−	0.375045i	$-0.122373\pi$
$734$	7.27288e9	−	4.35704e9i	0.678844	−	0.406683i
$735$	−1.20359e9			−0.111808
$736$	−4.13132e9	−	1.95947e9i	−0.381959	−	0.181162i
$737$	−1.72494e9			−0.158722
$738$	−3.96357e8	+	2.37450e8i	−0.0362985	+	0.0217458i
$739$			1.03852e10i			0.946588i	0.880905	+	0.473294i	$0.156935\pi$
$739$			1.03852e10i			0.946588i	−0.880905	+	0.473294i	$0.843065\pi$
$740$	2.03078e9	−	3.79536e9i	0.184227	−	0.344304i
$741$			3.69175e9i			0.333326i
$742$	5.78720e9	+	9.66013e9i	0.520062	+	0.868099i
$743$	−3.73477e9			−0.334044			−0.167022	−	0.985953i	$-0.553415\pi$
$743$	−3.73477e9			−0.334044			−0.167022	+	0.985953i	$0.553415\pi$
$744$	6.49704e9	−	3.14927e8i	0.578376	−	0.0280353i
$745$	5.85402e9			0.518689
$746$	8.69345e9	+	1.45113e10i	0.766666	+	1.27974i
$747$			3.35815e9i			0.294766i
$748$	−2.12827e10	−	1.13878e10i	−1.85940	−	0.994908i
$749$			4.90772e8i			0.0426770i
$750$	6.45365e9	−	3.86626e9i	0.558587	−	0.334639i
$751$	−1.34330e10			−1.15726			−0.578631	−	0.815589i	$-0.696413\pi$
$751$	−1.34330e10			−1.15726			−0.578631	+	0.815589i	$0.696413\pi$
$752$	−1.08217e9	−	1.62264e9i	−0.0927970	−	0.139143i
$753$	4.74963e9			0.405394
$754$	−1.04450e10	+	6.25741e9i	−0.887379	+	0.531612i
$755$		−	1.25703e10i		−	1.06300i
$756$	1.19734e10	+	6.40660e9i	1.00784	+	0.539264i
$757$		−	6.78007e9i		−	0.568065i	−0.958815	−	0.284033i	$-0.908328\pi$
$757$		−	6.78007e9i		−	0.568065i	0.958815	−	0.284033i	$-0.0916724\pi$
$758$	−4.60548e8	−	7.68758e8i	−0.0384090	−	0.0641132i
$759$	5.40877e9			0.449006
$760$	3.32068e8	+	6.85065e9i	0.0274397	+	0.566089i
$761$	8.01137e9			0.658962			0.329481	−	0.944162i	$-0.393126\pi$
$761$	8.01137e9			0.658962			0.329481	+	0.944162i	$0.393126\pi$
$762$	9.26698e9	+	1.54687e10i	0.758745	+	1.26652i
$763$		−	1.87451e10i		−	1.52775i
$764$	−2.89925e9	+	5.41845e9i	−0.235212	+	0.439590i
$765$		−	6.39335e9i		−	0.516314i
$766$	−4.66133e9	+	2.79252e9i	−0.374722	+	0.224489i
$767$	−1.42130e9			−0.113737
$768$	9.96651e9	+	4.14861e9i	0.793924	+	0.330475i
$769$	1.46553e10			1.16213			0.581063	−	0.813858i	$-0.302637\pi$
$769$	1.46553e10			1.16213			0.581063	+	0.813858i	$0.302637\pi$
$770$	−1.64316e10	+	9.84389e9i	−1.29707	+	0.777051i
$771$		−	5.12609e9i		−	0.402806i
$772$	−2.85334e8	+	5.33264e8i	−0.0223199	+	0.0417140i
$773$			2.33296e10i			1.81668i	0.418233	+	0.908340i	$0.362650\pi$
$773$			2.33296e10i			1.81668i	−0.418233	+	0.908340i	$0.637350\pi$
$774$	−1.08776e9	−	1.81572e9i	−0.0843219	−	0.140752i
$775$	−3.03456e9			−0.234174
$776$	−5.49913e8	−	1.13449e10i	−0.0422453	−	0.871533i
$777$	−3.98847e9			−0.305023
$778$	6.23001e9	+	1.03993e10i	0.474307	+	0.791725i
$779$			1.04638e9i			0.0793064i
$780$	−9.26300e9	−	4.95636e9i	−0.698909	−	0.373966i
$781$		−	2.93855e9i		−	0.220726i
$782$	8.28042e9	−	4.96064e9i	0.619197	−	0.370949i
$783$	−1.89703e10			−1.41224
$784$	−8.38429e8	−	1.25716e9i	−0.0621384	−	0.0931721i
$785$	−1.66250e10			−1.22664
$786$	1.42596e10	−	8.54266e9i	1.04744	−	0.627501i
$787$		−	5.27740e8i		−	0.0385930i	−0.999814	−	0.0192965i	$-0.993857\pi$
$787$		−	5.27740e8i		−	0.0385930i	0.999814	−	0.0192965i	$-0.00614264\pi$
$788$	−1.29655e10	−	6.93747e9i	−0.943948	−	0.505079i
$789$		−	1.74187e10i		−	1.26254i
$790$	1.55205e10	+	2.59072e10i	1.11998	+	1.86950i
$791$	−1.80747e10			−1.29853
$792$	4.49248e9	−	2.17761e8i	0.321327	−	0.0155755i
$793$	9.76536e9			0.695396
$794$	−1.18138e10	−	1.97198e10i	−0.837562	−	1.39808i
$795$		−	1.35732e10i		−	0.958072i
$796$	7.30287e8	−	1.36484e9i	0.0513213	−	0.0959150i
$797$			2.41514e9i			0.168981i	0.996424	+	0.0844907i	$0.0269263\pi$
$797$			2.41514e9i			0.168981i	−0.996424	+	0.0844907i	$0.973074\pi$
$798$	5.45168e9	−	3.26600e9i	0.379770	−	0.227513i
$799$	4.11738e9			0.285566
$800$	−4.55042e9	−	2.15825e9i	−0.314222	−	0.149034i
$801$	2.48940e8			0.0171152
$802$	2.50165e10	−	1.49869e10i	1.71244	−	1.02589i
$803$			1.46398e10i			0.997773i
$804$	−7.68341e8	+	1.43596e9i	−0.0521384	+	0.0974421i
$805$		−	7.65988e9i		−	0.517531i
$806$	−4.08426e9	−	6.81754e9i	−0.274752	−	0.458622i
$807$	1.38645e10			0.928636
$808$	−8.96451e9	+	4.34531e8i	−0.597843	+	0.0289789i
$809$	1.16364e10			0.772679			0.386340	−	0.922357i	$-0.373739\pi$
$809$	1.16364e10			0.772679			0.386340	+	0.922357i	$0.373739\pi$
$810$	−6.06126e9	−	1.01176e10i	−0.400743	−	0.668929i
$811$		−	1.44359e10i		−	0.950320i	−0.879899	−	0.475160i	$-0.842390\pi$
$811$		−	1.44359e10i		−	0.950320i	0.879899	−	0.475160i	$-0.157610\pi$
$812$	1.84809e10	+	9.88858e9i	1.21137	+	0.648168i
$813$			1.77962e10i			1.16148i
$814$	−5.48396e9	+	3.28533e9i	−0.356376	+	0.213498i
$815$	2.78275e10			1.80062
$816$	−1.89599e10	+	1.26448e10i	−1.22158	+	0.814696i
$817$	−4.79348e9			−0.307521
$818$	−3.20512e9	+	1.92013e9i	−0.204742	+	0.122657i
$819$		−	3.42855e9i		−	0.218080i
$820$	−2.62548e9	−	1.40482e9i	−0.166288	−	0.0889757i
$821$			7.63805e9i			0.481706i	0.970562	+	0.240853i	$0.0774271\pi$
$821$			7.63805e9i			0.481706i	−0.970562	+	0.240853i	$0.922573\pi$
$822$	−6.00865e9	−	1.00298e10i	−0.377333	−	0.629854i
$823$	−2.16446e10			−1.35348			−0.676738	−	0.736224i	$-0.736607\pi$
$823$	−2.16446e10			−1.35348			−0.676738	+	0.736224i	$0.736607\pi$
$824$	−4.62618e8	−	9.54395e9i	−0.0288056	−	0.594268i
$825$	5.95746e9			0.369379
$826$	1.25738e9	+	2.09885e9i	0.0776315	+	0.129584i
$827$			1.57823e10i			0.970288i	0.874434	+	0.485144i	$0.161233\pi$
$827$			1.57823e10i			0.970288i	−0.874434	+	0.485144i	$0.838767\pi$
$828$	−8.48561e8	+	1.58588e9i	−0.0519489	+	0.0970879i
$829$			2.63296e10i			1.60510i	0.596582	+	0.802552i	$0.296525\pi$
$829$			2.63296e10i			1.60510i	−0.596582	+	0.802552i	$0.703475\pi$
$830$	−1.85655e10	+	1.11222e10i	−1.12702	+	0.675179i
$831$	1.27947e10			0.773442
$832$	−1.27568e9	−	1.31279e10i	−0.0767911	−	0.790251i
$833$	3.19000e9			0.191220
$834$	−2.04134e10	+	1.22293e10i	−1.21852	+	0.729995i
$835$			3.43541e10i			2.04210i
$836$	4.80557e9	−	8.98119e9i	0.284461	−	0.531633i
$837$		−	1.23820e10i		−	0.729882i
$838$	−3.37241e8	−	5.62931e8i	−0.0197964	−	0.0330446i
$839$	−1.84995e9			−0.108142			−0.0540710	−	0.998537i	$-0.517220\pi$
$839$	−1.84995e9			−0.108142			−0.0540710	+	0.998537i	$0.517220\pi$
$840$	8.75587e8	+	1.80636e10i	0.0509708	+	1.05154i
$841$	−1.20307e10			−0.697438
$842$	−1.10826e9	−	1.84993e9i	−0.0639805	−	0.106798i
$843$		−	5.16767e9i		−	0.297097i
$844$	2.21035e10	+	1.18270e10i	1.26550	+	0.677134i
$845$		−	7.52569e9i		−	0.429090i
$846$	−6.58149e8	+	3.94285e8i	−0.0373704	+	0.0223879i
$847$	9.79866e9			0.554083
$848$	1.41774e10	−	9.45519e9i	0.798382	−	0.532457i
$849$	−1.60451e10			−0.899839
$850$	9.12042e9	−	5.46387e9i	0.509388	−	0.305165i
$851$		−	2.55643e9i		−	0.142194i
$852$	−2.44625e9	−	1.30892e9i	−0.135507	−	0.0725060i
$853$			6.28088e7i			0.00346496i	0.999998	+	0.00173248i	$0.000551466\pi$
$853$			6.28088e7i			0.00346496i	−0.999998	+	0.00173248i	$0.999449\pi$
$854$	−8.63917e9	−	1.44207e10i	−0.474646	−	0.792289i
$855$	2.69796e9			0.147623
$856$	7.41808e8	−	3.59572e7i	0.0404234	−	0.00195942i
$857$	−6.25595e9			−0.339516			−0.169758	−	0.985486i	$-0.554299\pi$
$857$	−6.25595e9			−0.339516			−0.169758	+	0.985486i	$0.554299\pi$
$858$	8.01824e9	+	1.33842e10i	0.433384	+	0.723415i
$859$			2.48119e10i			1.33562i	0.744331	+	0.667811i	$0.232769\pi$
$859$			2.48119e10i			1.33562i	−0.744331	+	0.667811i	$0.767231\pi$
$860$	6.43549e9	−	1.20274e10i	0.345014	−	0.644801i
$861$			2.75907e9i			0.147316i
$862$	−2.35765e10	+	1.41243e10i	−1.25373	+	0.751087i
$863$	1.28944e10			0.682909			0.341455	−	0.939898i	$-0.389080\pi$
$863$	1.28944e10			0.682909			0.341455	+	0.939898i	$0.389080\pi$
$864$	8.80640e9	−	1.85673e10i	0.464516	−	0.979377i
$865$	−6.42973e9			−0.337782
$866$	2.30892e10	−	1.38323e10i	1.20808	−	0.723739i
$867$		−	3.16077e10i		−	1.64712i
$868$	−6.45435e9	+	1.20626e10i	−0.334991	+	0.626069i
$869$		−	4.48516e10i		−	2.31851i
$870$	−1.29835e10	−	2.16724e10i	−0.668460	−	1.11581i
$871$	1.98980e9			0.102034
$872$	−2.83334e10	+	1.37339e9i	−1.44708	+	0.0701432i
$873$	−4.46789e9			−0.227276
$874$	2.09336e9	+	3.49429e9i	0.106061	+	0.177039i
$875$			1.58229e10i			0.798468i
$876$	1.21872e10	+	6.52102e9i	0.612548	+	0.327757i
$877$		−	2.75670e10i		−	1.38004i	−0.723792	−	0.690018i	$-0.757603\pi$
$877$		−	2.75670e10i		−	1.38004i	0.723792	−	0.690018i	$-0.242397\pi$
$878$	1.29238e10	−	7.74239e9i	0.644404	−	0.386051i
$879$	8.08177e9			0.401371
$880$	1.60830e10	+	2.41154e10i	0.795571	+	1.19290i
$881$	2.74343e10			1.35169			0.675847	−	0.737042i	$-0.263778\pi$
$881$	2.74343e10			1.35169			0.675847	+	0.737042i	$0.263778\pi$
$882$	−5.09910e8	+	3.05478e8i	−0.0250238	+	0.0149913i
$883$		−	2.09906e10i		−	1.02604i	−0.858378	−	0.513018i	$-0.828527\pi$
$883$		−	2.09906e10i		−	1.02604i	0.858378	−	0.513018i	$-0.171473\pi$
$884$	2.45506e10	+	1.31363e10i	1.19531	+	0.639575i
$885$		−	2.94905e9i		−	0.143015i
$886$	−2.92251e9	−	4.87833e9i	−0.141169	−	0.235642i
$887$	−2.39134e10			−1.15056			−0.575280	−	0.817957i	$-0.695107\pi$
$887$	−2.39134e10			−1.15056			−0.575280	+	0.817957i	$0.695107\pi$
$888$	2.92221e8	+	6.02862e9i	0.0140045	+	0.288916i
$889$	−3.79257e10			−1.81041
$890$	8.24493e8	+	1.37626e9i	0.0392033	+	0.0654390i
$891$			1.75160e10i			0.829588i
$892$	6.52337e9	−	1.21916e10i	0.307748	−	0.575153i
$893$			1.73751e9i			0.0816483i
$894$	−7.04148e9	+	4.21842e9i	−0.329596	+	0.197455i
$895$	−9.66337e9			−0.450555
$896$	−1.82577e10	+	1.34978e10i	−0.847947	+	0.626880i
$897$	−6.23927e9			−0.288643
$898$	−3.05510e10	+	1.83025e10i	−1.40785	+	0.843419i
$899$		−	1.91117e10i		−	0.877282i
$900$	−9.34642e8	+	1.74676e9i	−0.0427363	+	0.0798703i
$901$			3.59744e10i			1.63854i
$902$	2.27267e9	+	3.79359e9i	0.103113	+	0.172118i
$903$	−1.26393e10			−0.571238
$904$	1.32427e9	+	2.73201e10i	0.0596194	+	1.22997i
$905$	−1.28572e9			−0.0576603
$906$	9.05819e9	+	1.51201e10i	0.404662	+	0.675472i
$907$		−	3.84425e10i		−	1.71075i	−0.518012	−	0.855373i	$-0.673328\pi$
$907$		−	3.84425e10i		−	1.71075i	0.518012	−	0.855373i	$-0.326672\pi$
$908$	−1.81867e10	−	9.73115e9i	−0.806218	−	0.431384i
$909$			3.53045e9i			0.155904i
$910$	1.89547e10	−	1.13554e10i	0.833819	−	0.499525i
$911$	3.64507e10			1.59732			0.798660	−	0.601783i	$-0.205543\pi$
$911$	3.64507e10			1.59732			0.798660	+	0.601783i	$0.205543\pi$
$912$	−5.33602e9	−	8.00099e9i	−0.232936	−	0.349270i
$913$	3.21413e10			1.39771
$914$	2.60513e10	−	1.56069e10i	1.12854	−	0.676089i
$915$			2.02622e10i			0.874405i
$916$	−5.94966e9	−	3.18349e9i	−0.255775	−	0.136858i
$917$			3.49613e10i			1.49725i
$918$	2.22945e10	+	3.72145e10i	0.951148	+	1.58768i
$919$	2.37343e10			1.00872			0.504361	−	0.863493i	$-0.331728\pi$
$919$	2.37343e10			1.00872			0.504361	+	0.863493i	$0.331728\pi$
$920$	−1.15780e10	+	5.61213e8i	−0.490203	+	0.0237613i
$921$	6.39111e8			0.0269567
$922$	−7.58382e9	−	1.26591e10i	−0.318662	−	0.531917i
$923$			3.38976e9i			0.141894i
$924$	1.26712e10	−	2.36814e10i	0.528404	−	0.987540i
$925$		−	2.81577e9i		−	0.116977i
$926$	−2.78401e10	+	1.66785e10i	−1.15221	+	0.690269i
$927$	−3.75864e9			−0.154972
$928$	1.35927e10	−	2.86586e10i	0.558325	−	1.17716i
$929$	−4.23952e10			−1.73485			−0.867424	−	0.497570i	$-0.834226\pi$
$929$	−4.23952e10			−1.73485			−0.867424	+	0.497570i	$0.834226\pi$
$930$	1.41457e10	−	8.47444e9i	0.576680	−	0.345478i
$931$			1.34616e9i			0.0546730i
$932$	−1.08350e10	+	2.02496e10i	−0.438402	+	0.819334i
$933$		−	1.96139e10i		−	0.790638i
$934$	−3.46834e9	−	5.78943e9i	−0.139286	−	0.232499i
$935$	−6.11916e10			−2.44823
$936$	−5.18229e9	+	2.51198e8i	−0.206565	+	0.0100127i
$937$	3.70014e10			1.46937			0.734683	−	0.678411i	$-0.237331\pi$
$937$	3.70014e10			1.46937			0.734683	+	0.678411i	$0.237331\pi$
$938$	−1.76033e9	−	2.93838e9i	−0.0696439	−	0.116251i
$939$			1.30595e10i			0.514750i
$940$	−4.35960e9	−	2.33269e9i	−0.171198	−	0.0916031i
$941$			2.10617e10i			0.824005i	0.911183	+	0.412003i	$0.135171\pi$
$941$			2.10617e10i			0.824005i	−0.911183	+	0.412003i	$0.864829\pi$
$942$	1.99974e10	−	1.19800e10i	0.779461	−	0.466960i
$943$	−1.76844e9			−0.0686752
$944$	3.08032e9	−	2.05433e9i	0.119177	−	0.0794817i
$945$	3.44256e10			1.32700
$946$	−1.73785e10	+	1.04111e10i	−0.667410	+	0.399833i
$947$			1.35146e10i			0.517104i	0.965997	+	0.258552i	$0.0832454\pi$
$947$			1.35146e10i			0.517104i	−0.965997	+	0.258552i	$0.916755\pi$
$948$	−3.73376e10	−	1.99782e10i	−1.42337	−	0.761602i
$949$		−	1.68877e10i		−	0.641416i
$950$	2.30572e9	+	3.84877e9i	0.0872519	+	0.145643i
$951$	−4.26628e10			−1.60849
$952$	−2.32065e9	−	4.78758e10i	−0.0871728	−	1.79840i
$953$	4.26831e10			1.59746			0.798731	−	0.601688i	$-0.205505\pi$
$953$	4.26831e10			1.59746			0.798731	+	0.601688i	$0.205505\pi$
$954$	−3.44495e9	−	5.75039e9i	−0.128459	−	0.214426i
$955$			1.55790e10i			0.578799i
$956$	−5.08733e9	+	9.50776e9i	−0.188316	+	0.351946i
$957$			3.75201e10i			1.38380i
$958$	2.09702e10	−	1.25628e10i	0.770588	−	0.461645i
$959$	2.45907e10			0.900340
$960$	2.72392e10	−	2.64692e9i	0.993677	−	0.0965587i
$961$	−1.50383e10			−0.546597
$962$	6.32600e9	−	3.78979e9i	0.229096	−	0.137247i
$963$		−	2.92142e8i		−	0.0105415i
$964$	−1.28205e10	+	2.39603e10i	−0.460930	+	0.861437i
$965$			1.53323e9i			0.0549239i
$966$	5.51972e9	+	9.21365e9i	0.197014	+	0.328861i
$967$	2.32274e10			0.826053			0.413026	−	0.910719i	$-0.364472\pi$
$967$	2.32274e10			0.826053			0.413026	+	0.910719i	$0.364472\pi$
$968$	−7.17914e8	−	1.48108e10i	−0.0254395	−	0.524825i
$969$	2.03021e10			0.716817
$970$	−1.47977e10	−	2.47007e10i	−0.520588	−	0.868977i
$971$		−	4.85678e10i		−	1.70248i	−0.524780	−	0.851238i	$-0.675852\pi$
$971$		−	4.85678e10i		−	1.70248i	0.524780	−	0.851238i	$-0.324148\pi$
$972$	−1.27819e10	−	6.83925e9i	−0.446442	−	0.238878i
$973$		−	5.00491e10i		−	1.74181i
$974$	−1.37752e9	+	8.25248e8i	−0.0477686	+	0.0286173i
$975$	−6.87221e9			−0.237454
$976$	−2.11641e10	+	1.41148e10i	−0.728660	+	0.485958i
$977$	1.54549e10			0.530193			0.265096	−	0.964222i	$-0.414596\pi$
$977$	1.54549e10			0.530193			0.265096	+	0.964222i	$0.414596\pi$
$978$	−3.34722e10	+	2.00526e10i	−1.14419	+	0.685463i
$979$		−	2.38264e9i		−	0.0811557i
$980$	−3.37766e9	−	1.80729e9i	−0.114637	−	0.0613389i
$981$			1.11584e10i			0.377364i
$982$	−1.38774e10	−	2.31644e10i	−0.467646	−	0.780606i
$983$	−1.59192e10			−0.534546			−0.267273	−	0.963621i	$-0.586123\pi$
$983$	−1.59192e10			−0.534546			−0.267273	+	0.963621i	$0.586123\pi$
$984$	4.17036e9	−	2.02147e8i	0.139537	−	0.00676371i
$985$	−3.72782e10			−1.24288
$986$	3.44115e10	+	5.74405e10i	1.14323	+	1.90831i
$987$			4.58142e9i			0.151667i
$988$	−5.54346e9	+	1.03602e10i	−0.182865	+	0.341759i
$989$		−	8.10126e9i		−	0.266296i
$990$	9.78128e9	−	5.85978e9i	0.320385	−	0.191937i
$991$	1.49883e10			0.489208			0.244604	−	0.969623i	$-0.421342\pi$
$991$	1.49883e10			0.489208			0.244604	+	0.969623i	$0.421342\pi$
$992$	1.87056e10	+	8.87203e9i	0.608390	+	0.288557i
$993$	−1.16019e10			−0.376016
$994$	5.00572e9	−	2.99883e9i	0.161664	−	0.0968500i
$995$		−	3.92416e9i		−	0.126289i
$996$	1.43167e10	−	2.67567e10i	0.459130	−	0.858073i
$997$			3.44101e10i			1.09965i	0.835281	+	0.549824i	$0.185305\pi$
$997$			3.44101e10i			1.09965i	−0.835281	+	0.549824i	$0.814695\pi$
$998$	3.04611e10	+	5.08464e10i	0.970038	+	1.61921i
$999$	1.14893e10			0.364598

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.8.b.a.5.2	yes	6
3.2	odd	2		72.8.d.b.37.5		6
4.3	odd	2		32.8.b.a.17.5		6
8.3	odd	2		32.8.b.a.17.2		6
8.5	even	2	inner	8.8.b.a.5.1	✓	6
12.11	even	2		288.8.d.b.145.5		6
16.3	odd	4		256.8.a.q.1.2		6
16.5	even	4		256.8.a.r.1.2		6
16.11	odd	4		256.8.a.q.1.5		6
16.13	even	4		256.8.a.r.1.5		6
24.5	odd	2		72.8.d.b.37.6		6
24.11	even	2		288.8.d.b.145.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.8.b.a.5.1	✓	6	8.5	even	2	inner
8.8.b.a.5.2	yes	6	1.1	even	1	trivial
32.8.b.a.17.2		6	8.3	odd	2
32.8.b.a.17.5		6	4.3	odd	2
72.8.d.b.37.5		6	3.2	odd	2
72.8.d.b.37.6		6	24.5	odd	2
256.8.a.q.1.2		6	16.3	odd	4
256.8.a.q.1.5		6	16.11	odd	4
256.8.a.r.1.2		6	16.5	even	4
256.8.a.r.1.5		6	16.13	even	4
288.8.d.b.145.2		6	24.11	even	2
288.8.d.b.145.5		6	12.11	even	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:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	8.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-9.70536 + 5.81430i) q^{2} -40.2163i q^{3} +(60.3879 - 112.860i) q^{4} -324.492i q^{5} +(233.829 + 390.313i) q^{6} -956.960 q^{7} +(70.1132 + 1446.46i) q^{8} +569.651 q^{9} +O(q^{10})\)	\(q+(-9.70536 + 5.81430i) q^{2} -40.2163i q^{3} +(60.3879 - 112.860i) q^{4} -324.492i q^{5} +(233.829 + 390.313i) q^{6} -956.960 q^{7} +(70.1132 + 1446.46i) q^{8} +569.651 q^{9} +(1886.69 + 3149.31i) q^{10} -5452.20i q^{11} +(-4538.80 - 2428.58i) q^{12} +6289.38i q^{13} +(9287.64 - 5564.05i) q^{14} -13049.8 q^{15} +(-9090.60 - 13630.7i) q^{16} +34587.3 q^{17} +(-5528.66 + 3312.12i) q^{18} +14595.6i q^{19} +(-36622.0 - 19595.4i) q^{20} +38485.4i q^{21} +(31700.7 + 52915.6i) q^{22} -24667.5 q^{23} +(58171.1 - 2819.69i) q^{24} -27169.8 q^{25} +(-36568.3 - 61040.6i) q^{26} -110862. i q^{27} +(-57788.8 + 108002. i) q^{28} -171116. i q^{29} +(126653. - 75875.7i) q^{30} +111688. q^{31} +(167481. + 79435.5i) q^{32} -219267. q^{33} +(-335682. + 201101. i) q^{34} +310526. i q^{35} +(34400.0 - 64290.6i) q^{36} +103636. i q^{37} +(-84863.4 - 141656. i) q^{38} +252935. q^{39} +(469363. - 22751.1i) q^{40} +71691.3 q^{41} +(-223765. - 373514. i) q^{42} +328419. i q^{43} +(-615334. - 329247. i) q^{44} -184847. i q^{45} +(239406. - 143424. i) q^{46} +119043. q^{47} +(-548177. + 365590. i) q^{48} +92230.3 q^{49} +(263693. - 157973. i) q^{50} -1.39097e6i q^{51} +(709817. + 379802. i) q^{52} +1.04011e6i q^{53} +(644586. + 1.07596e6i) q^{54} -1.76919e6 q^{55} +(-67095.6 - 1.38420e6i) q^{56} +586982. q^{57} +(994918. + 1.66074e6i) q^{58} +225984. i q^{59} +(-788053. + 1.47280e6i) q^{60} -1.55268e6i q^{61} +(-1.08398e6 + 649390. i) q^{62} -545133. q^{63} +(-2.08732e6 + 202831. i) q^{64} +2.04085e6 q^{65} +(2.12807e6 - 1.27489e6i) q^{66} -316375. i q^{67} +(2.08865e6 - 3.90351e6i) q^{68} +992033. i q^{69} +(-1.80549e6 - 3.01376e6i) q^{70} +538965. q^{71} +(39940.0 + 823975. i) q^{72} -2.68512e6 q^{73} +(-602570. - 1.00582e6i) q^{74} +1.09267e6i q^{75} +(1.64726e6 + 881400. i) q^{76} +5.21754e6i q^{77} +(-2.45483e6 + 1.47064e6i) q^{78} +8.22632e6 q^{79} +(-4.42305e6 + 2.94982e6i) q^{80} -3.21264e6 q^{81} +(-695790. + 416834. i) q^{82} +5.89510e6i q^{83} +(4.34345e6 + 2.32405e6i) q^{84} -1.12233e7i q^{85} +(-1.90952e6 - 3.18742e6i) q^{86} -6.88164e6 q^{87} +(7.88638e6 - 382271. i) q^{88} +437005. q^{89} +(1.07475e6 + 1.79400e6i) q^{90} -6.01868e6i q^{91} +(-1.48962e6 + 2.78396e6i) q^{92} -4.49169e6i q^{93} +(-1.15536e6 + 692152. i) q^{94} +4.73616e6 q^{95} +(3.19460e6 - 6.73545e6i) q^{96} -7.84322e6 q^{97} +(-895128. + 536254. i) q^{98} -3.10585e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 116 q^{4} + 268 q^{6} - 688 q^{7} + 1512 q^{8} - 2918 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 116 * q^4 + 268 * q^6 - 688 * q^7 + 1512 * q^8 - 2918 * q^9	\( 6 q + 6 q^{2} + 116 q^{4} + 268 q^{6} - 688 q^{7} + 1512 q^{8} - 2918 q^{9} - 1656 q^{10} - 4088 q^{12} + 12048 q^{14} + 17872 q^{15} + 35344 q^{16} + 1452 q^{17} - 89062 q^{18} - 114768 q^{20} + 152860 q^{22} - 1296 q^{23} + 282512 q^{24} - 39314 q^{25} - 316968 q^{26} - 480800 q^{28} + 821648 q^{30} - 89280 q^{31} + 817056 q^{32} + 53880 q^{33} - 1009108 q^{34} - 1253556 q^{36} + 974124 q^{38} - 328208 q^{39} + 954464 q^{40} + 521244 q^{41} - 1093088 q^{42} - 1096344 q^{44} + 929840 q^{46} + 1566432 q^{47} + 853920 q^{48} - 511050 q^{49} - 148626 q^{50} + 823952 q^{52} - 1077064 q^{54} - 3270256 q^{55} - 2468928 q^{56} - 1889896 q^{57} + 3130744 q^{58} + 5715168 q^{60} - 7055808 q^{62} + 5776816 q^{63} - 4792768 q^{64} + 1416480 q^{65} + 7926264 q^{66} + 6608040 q^{68} - 7406912 q^{70} - 7597104 q^{71} - 11363944 q^{72} + 2089564 q^{73} + 7744200 q^{74} + 9241288 q^{76} - 9471184 q^{78} + 16015904 q^{79} - 12600384 q^{80} - 723058 q^{81} + 10715932 q^{82} + 4220608 q^{84} - 5639076 q^{86} - 37453776 q^{87} + 1541200 q^{88} + 2169084 q^{89} - 121864 q^{90} + 669600 q^{92} + 15503712 q^{94} + 48537936 q^{95} + 21402176 q^{96} - 1088308 q^{97} - 14983242 q^{98}+O(q^{100}) \) 6 * q + 6 * q^2 + 116 * q^4 + 268 * q^6 - 688 * q^7 + 1512 * q^8 - 2918 * q^9 - 1656 * q^10 - 4088 * q^12 + 12048 * q^14 + 17872 * q^15 + 35344 * q^16 + 1452 * q^17 - 89062 * q^18 - 114768 * q^20 + 152860 * q^22 - 1296 * q^23 + 282512 * q^24 - 39314 * q^25 - 316968 * q^26 - 480800 * q^28 + 821648 * q^30 - 89280 * q^31 + 817056 * q^32 + 53880 * q^33 - 1009108 * q^34 - 1253556 * q^36 + 974124 * q^38 - 328208 * q^39 + 954464 * q^40 + 521244 * q^41 - 1093088 * q^42 - 1096344 * q^44 + 929840 * q^46 + 1566432 * q^47 + 853920 * q^48 - 511050 * q^49 - 148626 * q^50 + 823952 * q^52 - 1077064 * q^54 - 3270256 * q^55 - 2468928 * q^56 - 1889896 * q^57 + 3130744 * q^58 + 5715168 * q^60 - 7055808 * q^62 + 5776816 * q^63 - 4792768 * q^64 + 1416480 * q^65 + 7926264 * q^66 + 6608040 * q^68 - 7406912 * q^70 - 7597104 * q^71 - 11363944 * q^72 + 2089564 * q^73 + 7744200 * q^74 + 9241288 * q^76 - 9471184 * q^78 + 16015904 * q^79 - 12600384 * q^80 - 723058 * q^81 + 10715932 * q^82 + 4220608 * q^84 - 5639076 * q^86 - 37453776 * q^87 + 1541200 * q^88 + 2169084 * q^89 - 121864 * q^90 + 669600 * q^92 + 15503712 * q^94 + 48537936 * q^95 + 21402176 * q^96 - 1088308 * q^97 - 14983242 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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