LMFDB - Embedded newform 8.8.b.a.5.3

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			5.3
Root			$0.776001 + 5.60338i$ of defining polynomial
Character	$\chi$	$=$	8.5
Dual form			8.8.b.a.5.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.55200 - 11.2068i) q^{2} -21.9408i q^{3} +(-123.183 - 34.7858i) q^{4} -184.916i q^{5} +(-245.885 - 34.0522i) q^{6} +1051.96 q^{7} +(-581.015 + 1326.49i) q^{8} +1705.60 q^{9} +O(q^{10})$	\(q+(1.55200 - 11.2068i) q^{2} -21.9408i q^{3} +(-123.183 - 34.7858i) q^{4} -184.916i q^{5} +(-245.885 - 34.0522i) q^{6} +1051.96 q^{7} +(-581.015 + 1326.49i) q^{8} +1705.60 q^{9} +(-2072.30 - 286.989i) q^{10} +4324.35i q^{11} +(-763.228 + 2702.73i) q^{12} -11253.2i q^{13} +(1632.64 - 11789.0i) q^{14} -4057.20 q^{15} +(13963.9 + 8570.01i) q^{16} -21746.4 q^{17} +(2647.10 - 19114.2i) q^{18} +45466.5i q^{19} +(-6432.44 + 22778.4i) q^{20} -23080.8i q^{21} +(48462.0 + 6711.41i) q^{22} +4414.37 q^{23} +(29104.2 + 12747.9i) q^{24} +43931.2 q^{25} +(-126112. - 17465.1i) q^{26} -85406.8i q^{27} +(-129583. - 36593.2i) q^{28} +23687.1i q^{29} +(-6296.78 + 45468.0i) q^{30} +72941.9 q^{31} +(117714. - 143189. i) q^{32} +94879.8 q^{33} +(-33750.5 + 243707. i) q^{34} -194523. i q^{35} +(-210100. - 59330.7i) q^{36} +483338. i q^{37} +(509532. + 70564.1i) q^{38} -246905. q^{39} +(245289. + 107439. i) q^{40} -411040. q^{41} +(-258661. - 35821.4i) q^{42} -96165.3i q^{43} +(150426. - 532685. i) q^{44} -315392. i q^{45} +(6851.11 - 49470.7i) q^{46} -156171. q^{47} +(188033. - 306379. i) q^{48} +283070. q^{49} +(68181.3 - 492326. i) q^{50} +477134. i q^{51} +(-391453. + 1.38620e6i) q^{52} -686962. i q^{53} +(-957133. - 132552. i) q^{54} +799641. q^{55} +(-611203. + 1.39541e6i) q^{56} +997572. q^{57} +(265456. + 36762.4i) q^{58} +1.79961e6i q^{59} +(499776. + 141133. i) q^{60} -1.36394e6i q^{61} +(113206. - 817441. i) q^{62} +1.79422e6 q^{63} +(-1.42199e6 - 1.54142e6i) q^{64} -2.08090e6 q^{65} +(147254. - 1.06329e6i) q^{66} -1.08853e6i q^{67} +(2.67878e6 + 756466. i) q^{68} -96854.8i q^{69} +(-2.17997e6 - 301900. i) q^{70} -5.60830e6 q^{71} +(-990980. + 2.26246e6i) q^{72} +21698.7 q^{73} +(5.41665e6 + 750142. i) q^{74} -963886. i q^{75} +(1.58159e6 - 5.60068e6i) q^{76} +4.54903e6i q^{77} +(-383197. + 2.76701e6i) q^{78} +2.34010e6 q^{79} +(1.58473e6 - 2.58214e6i) q^{80} +1.85626e6 q^{81} +(-637935. + 4.60643e6i) q^{82} -882169. i q^{83} +(-802883. + 2.84315e6i) q^{84} +4.02125e6i q^{85} +(-1.07770e6 - 149249. i) q^{86} +519714. q^{87} +(-5.73621e6 - 2.51252e6i) q^{88} -1.34738e6 q^{89} +(-3.53452e6 - 489489. i) q^{90} -1.18379e7i q^{91} +(-543773. - 153557. i) q^{92} -1.60040e6i q^{93} +(-242378. + 1.75017e6i) q^{94} +8.40746e6 q^{95} +(-3.14169e6 - 2.58274e6i) q^{96} +7.32798e6 q^{97} +(439325. - 3.17229e6i) q^{98} +7.37562e6i 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 $

$2$	1.55200	−	11.2068i	0.137179	−	0.990546i
$2$	1.55200	−	11.2068i	0.137179	−	0.990546i
$3$		−	21.9408i		−	0.469168i	−0.972096	−	0.234584i	$-0.924627\pi$
$3$		−	21.9408i		−	0.469168i	0.972096	−	0.234584i	$-0.0753728\pi$
$4$	−123.183	−	34.7858i	−0.962364	−	0.271764i
$5$		−	184.916i		−	0.661574i	−0.943705	−	0.330787i	$-0.892686\pi$
$5$		−	184.916i		−	0.661574i	0.943705	−	0.330787i	$-0.107314\pi$
$6$	−245.885	−	34.0522i	−0.464732	−	0.0643599i
$7$	1051.96			1.15919			0.579595	−	0.814905i	$-0.303211\pi$
$7$	1051.96			1.15919			0.579595	+	0.814905i	$0.303211\pi$
$8$	−581.015	+	1326.49i	−0.401211	+	0.915986i
$9$	1705.60			0.779882
$10$	−2072.30	−	286.989i	−0.655320	−	0.0907540i
$11$			4324.35i			0.979596i	0.871836	+	0.489798i	$0.162929\pi$
$11$			4324.35i			0.979596i	−0.871836	+	0.489798i	$0.837071\pi$
$12$	−763.228	+	2702.73i	−0.127503	+	0.451510i
$13$		−	11253.2i		−	1.42061i	−0.703892	−	0.710307i	$-0.748556\pi$
$13$		−	11253.2i		−	1.42061i	0.703892	−	0.710307i	$-0.251444\pi$
$14$	1632.64	−	11789.0i	0.159016	−	1.14823i
$15$	−4057.20			−0.310389
$16$	13963.9	+	8570.01i	0.852289	+	0.523072i
$17$	−21746.4			−1.07354			−0.536768	−	0.843730i	$-0.680355\pi$
$17$	−21746.4			−1.07354			−0.536768	+	0.843730i	$0.680355\pi$
$18$	2647.10	−	19114.2i	0.106983	−	0.772509i
$19$			45466.5i			1.52074i	0.649492	+	0.760368i	$0.274981\pi$
$19$			45466.5i			1.52074i	−0.649492	+	0.760368i	$0.725019\pi$
$20$	−6432.44	+	22778.4i	−0.179792	+	0.636675i
$21$		−	23080.8i		−	0.543855i
$22$	48462.0	+	6711.41i	0.970335	+	0.134380i
$23$	4414.37			0.0756522			0.0378261	−	0.999284i	$-0.487957\pi$
$23$	4414.37			0.0756522			0.0378261	+	0.999284i	$0.487957\pi$
$24$	29104.2	+	12747.9i	0.429751	+	0.188235i
$25$	43931.2			0.562320
$26$	−126112.	−	17465.1i	−1.40718	−	0.194878i
$27$		−	85406.8i		−	0.835063i
$28$	−129583.	−	36593.2i	−1.11556	−	0.315026i
$29$			23687.1i			0.180351i	0.995926	+	0.0901756i	$0.0287428\pi$
$29$			23687.1i			0.180351i	−0.995926	+	0.0901756i	$0.971257\pi$
$30$	−6296.78	+	45468.0i	−0.0425789	+	0.307455i
$31$	72941.9			0.439755			0.219878	−	0.975527i	$-0.429434\pi$
$31$	72941.9			0.439755			0.219878	+	0.975527i	$0.429434\pi$
$32$	117714.	−	143189.i	0.635043	−	0.772477i
$33$	94879.8			0.459595
$34$	−33750.5	+	243707.i	−0.147266	+	1.06339i
$35$		−	194523.i		−	0.766890i
$36$	−210100.	−	59330.7i	−0.750530	−	0.211944i
$37$			483338.i			1.56872i	0.620307	+	0.784359i	$0.287008\pi$
$37$			483338.i			1.56872i	−0.620307	+	0.784359i	$0.712992\pi$
$38$	509532.	+	70564.1i	1.50636	+	0.208613i
$39$	−246905.			−0.666506
$40$	245289.	+	107439.i	0.605992	+	0.265431i
$41$	−411040.			−0.931410			−0.465705	−	0.884940i	$-0.654199\pi$
$41$	−411040.			−0.931410			−0.465705	+	0.884940i	$0.654199\pi$
$42$	−258661.	−	35821.4i	−0.538713	−	0.0746054i
$43$		−	96165.3i		−	0.184450i	−0.995738	−	0.0922250i	$-0.970602\pi$
$43$		−	96165.3i		−	0.184450i	0.995738	−	0.0922250i	$-0.0293979\pi$
$44$	150426.	−	532685.i	0.266219	−	0.942728i
$45$		−	315392.i		−	0.515949i
$46$	6851.11	−	49470.7i	0.0103779	−	0.0749370i
$47$	−156171.			−0.219411			−0.109705	−	0.993964i	$-0.534991\pi$
$47$	−156171.			−0.219411			−0.109705	+	0.993964i	$0.534991\pi$
$48$	188033.	−	306379.i	0.245408	−	0.399866i
$49$	283070.			0.343722
$50$	68181.3	−	492326.i	0.0771384	−	0.557004i
$51$			477134.i			0.503668i
$52$	−391453.	+	1.38620e6i	−0.386072	+	1.36715i
$53$		−	686962.i		−	0.633822i	−0.948455	−	0.316911i	$-0.897354\pi$
$53$		−	686962.i		−	0.633822i	0.948455	−	0.316911i	$-0.102646\pi$
$54$	−957133.	−	132552.i	−0.827169	−	0.114553i
$55$	799641.			0.648075
$56$	−611203.	+	1.39541e6i	−0.465080	+	1.06180i
$57$	997572.			0.713480
$58$	265456.	+	36762.4i	0.178646	+	0.0247404i
$59$			1.79961e6i			1.14077i	0.821378	+	0.570384i	$0.193206\pi$
$59$			1.79961e6i			1.14077i	−0.821378	+	0.570384i	$0.806794\pi$
$60$	499776.	+	141133.i	0.298707	+	0.0843527i
$61$		−	1.36394e6i		−	0.769379i	−0.923046	−	0.384690i	$-0.874308\pi$
$61$		−	1.36394e6i		−	0.769379i	0.923046	−	0.384690i	$-0.125692\pi$
$62$	113206.	−	817441.i	0.0603251	−	0.435598i
$63$	1.79422e6			0.904031
$64$	−1.42199e6	−	1.54142e6i	−0.678060	−	0.735007i
$65$	−2.08090e6			−0.939841
$66$	147254.	−	1.06329e6i	0.0630467	−	0.455250i
$67$		−	1.08853e6i		−	0.442160i	−0.975256	−	0.221080i	$-0.929042\pi$
$67$		−	1.08853e6i		−	0.442160i	0.975256	−	0.221080i	$-0.0709582\pi$
$68$	2.67878e6	+	756466.i	1.03313	+	0.291748i
$69$		−	96854.8i		−	0.0354936i
$70$	−2.17997e6	−	301900.i	−0.759640	−	0.105201i
$71$	−5.60830e6			−1.85963			−0.929816	−	0.368025i	$-0.880034\pi$
$71$	−5.60830e6			−1.85963			−0.929816	+	0.368025i	$0.880034\pi$
$72$	−990980.	+	2.26246e6i	−0.312897	+	0.714360i
$73$	21698.7			0.00652837			0.00326418	−	0.999995i	$-0.498961\pi$
$73$	21698.7			0.00652837			0.00326418	+	0.999995i	$0.498961\pi$
$74$	5.41665e6	+	750142.i	1.55389	+	0.215195i
$75$		−	963886.i		−	0.263822i
$76$	1.58159e6	−	5.60068e6i	0.413281	−	1.46350i
$77$			4.54903e6i			1.13554i
$78$	−383197.	+	2.76701e6i	−0.0914306	+	0.660205i
$79$	2.34010e6			0.533998			0.266999	−	0.963697i	$-0.413968\pi$
$79$	2.34010e6			0.533998			0.266999	+	0.963697i	$0.413968\pi$
$80$	1.58473e6	−	2.58214e6i	0.346051	−	0.563852i
$81$	1.85626e6			0.388097
$82$	−637935.	+	4.60643e6i	−0.127770	+	0.922605i
$83$		−	882169.i		−	0.169347i	−0.996409	−	0.0846736i	$-0.973015\pi$
$83$		−	882169.i		−	0.169347i	0.996409	−	0.0846736i	$-0.0269848\pi$
$84$	−802883.	+	2.84315e6i	−0.147800	+	0.523386i
$85$			4.02125e6i			0.710223i
$86$	−1.07770e6	−	149249.i	−0.182706	−	0.0253026i
$87$	519714.			0.0846150
$88$	−5.73621e6	−	2.51252e6i	−0.897296	−	0.393024i
$89$	−1.34738e6			−0.202594			−0.101297	−	0.994856i	$-0.532299\pi$
$89$	−1.34738e6			−0.202594			−0.101297	+	0.994856i	$0.532299\pi$
$90$	−3.53452e6	−	489489.i	−0.511072	−	0.0707774i
$91$		−	1.18379e7i		−	1.64676i
$92$	−543773.	−	153557.i	−0.0728049	−	0.0205595i
$93$		−	1.60040e6i		−	0.206319i
$94$	−242378.	+	1.75017e6i	−0.0300985	+	0.217337i
$95$	8.40746e6			1.00608
$96$	−3.14169e6	−	2.58274e6i	−0.362421	−	0.297942i
$97$	7.32798e6			0.815236			0.407618	−	0.913153i	$-0.366360\pi$
$97$	7.32798e6			0.815236			0.407618	+	0.913153i	$0.366360\pi$
$98$	439325.	−	3.17229e6i	0.0471514	−	0.340473i
$99$			7.37562e6i			0.763969i
$100$	−5.41156e6	−	1.52818e6i	−0.541156	−	0.152818i
$101$		−	9.66027e6i		−	0.932963i	−0.884531	−	0.466482i	$-0.845521\pi$
$101$		−	9.66027e6i		−	0.932963i	0.884531	−	0.466482i	$-0.154479\pi$
$102$	5.34712e6	+	740512.i	0.498907	+	0.0690926i
$103$	−1.38659e7			−1.25031			−0.625154	−	0.780501i	$-0.714964\pi$
$103$	−1.38659e7			−1.25031			−0.625154	+	0.780501i	$0.714964\pi$
$104$	1.49273e7	+	6.53831e6i	1.30126	+	0.569966i
$105$	−4.26800e6			−0.359800
$106$	−7.69862e6	−	1.06617e6i	−0.627830	−	0.0869470i
$107$			1.88354e7i			1.48638i	0.669078	+	0.743192i	$0.266689\pi$
$107$			1.88354e7i			1.48638i	−0.669078	+	0.743192i	$0.733311\pi$
$108$	−2.97094e6	+	1.05206e7i	−0.226940	+	0.803635i
$109$			8.60619e6i			0.636529i	0.948002	+	0.318265i	$0.103100\pi$
$109$			8.60619e6i			0.636529i	−0.948002	+	0.318265i	$0.896900\pi$
$110$	1.24104e6	−	8.96137e6i	0.0889022	−	0.641949i
$111$	1.06048e7			0.735992
$112$	1.46894e7	+	9.01528e6i	0.987965	+	0.606340i
$113$	−1.31340e7			−0.856292			−0.428146	−	0.903709i	$-0.640833\pi$
$113$	−1.31340e7			−0.856292			−0.428146	+	0.903709i	$0.640833\pi$
$114$	1.54823e6	−	1.11795e7i	0.0978744	−	0.706735i
$115$		−	816286.i		−	0.0500495i
$116$	823975.	−	2.91784e6i	0.0490130	−	0.173564i
$117$		−	1.91935e7i		−	1.10791i
$118$	2.01678e7	+	2.79301e6i	1.12998	+	0.156489i
$119$	−2.28763e7			−1.24443
$120$	2.35729e6	−	5.38183e6i	0.124532	−	0.284312i
$121$	787128.			0.0403921
$122$	−1.52853e7	−	2.11684e6i	−0.762106	−	0.105543i
$123$			9.01856e6i			0.436988i
$124$	−8.98517e6	−	2.53734e6i	−0.423205	−	0.119510i
$125$		−	2.25701e7i		−	1.03359i
$126$	2.78463e6	−	2.01074e7i	0.124014	−	0.895485i
$127$	3.18768e7			1.38090			0.690449	−	0.723381i	$-0.257413\pi$
$127$	3.18768e7			1.38090			0.690449	+	0.723381i	$0.257413\pi$
$128$	−1.94813e7	+	1.35436e7i	−0.821074	+	0.570822i
$129$	−2.10994e6			−0.0865380
$130$	−3.22956e6	+	2.33201e7i	−0.128926	+	0.930956i
$131$		−	1.17050e7i		−	0.454905i	−0.973789	−	0.227453i	$-0.926960\pi$
$131$		−	1.17050e7i		−	0.454905i	0.973789	−	0.227453i	$-0.0730397\pi$
$132$	−1.16875e7	−	3.30047e6i	−0.442297	−	0.124901i
$133$			4.78288e7i			1.76282i
$134$	−1.21989e7	−	1.68940e6i	−0.437980	−	0.0606551i
$135$	−1.57931e7			−0.552456
$136$	1.26350e7	−	2.88464e7i	0.430714	−	0.983343i
$137$	3.79174e7			1.25984			0.629921	−	0.776659i	$-0.283087\pi$
$137$	3.79174e7			1.25984			0.629921	+	0.776659i	$0.283087\pi$
$138$	−1.08543e6	−	150319.i	−0.0351580	−	0.00486897i
$139$		−	2.80300e7i		−	0.885260i	−0.896704	−	0.442630i	$-0.854045\pi$
$139$		−	2.80300e7i		−	0.885260i	0.896704	−	0.442630i	$-0.145955\pi$
$140$	−6.76665e6	+	2.39619e7i	−0.208413	+	0.738028i
$141$			3.42652e6i			0.102941i
$142$	−8.70409e6	+	6.28508e7i	−0.255102	+	1.84205i
$143$	4.86630e7			1.39163
$144$	2.38168e7	+	1.46170e7i	0.664684	+	0.407934i
$145$	4.38012e6			0.119316
$146$	33676.5	−	243173.i	0.000895554	−	0.00646665i
$147$		−	6.21078e6i		−	0.161263i
$148$	1.68133e7	−	5.95388e7i	0.426321	−	1.50968i
$149$			6.82083e6i			0.168922i	0.996427	+	0.0844608i	$0.0269168\pi$
$149$			6.82083e6i			0.168922i	−0.996427	+	0.0844608i	$0.973083\pi$
$150$	−1.08020e7	−	1.49595e6i	−0.261328	−	0.0361908i
$151$	−7.62068e7			−1.80125			−0.900626	−	0.434595i	$-0.856891\pi$
$151$	−7.62068e7			−1.80125			−0.900626	+	0.434595i	$0.856891\pi$
$152$	−6.03108e7	−	2.64167e7i	−1.39297	−	0.610136i
$153$	−3.70907e7			−0.837230
$154$	5.09799e7	+	7.06011e6i	1.12480	+	0.155772i
$155$		−	1.34881e7i		−	0.290931i
$156$	3.04144e7	+	8.58879e6i	0.641421	+	0.181132i
$157$			4.28737e7i			0.884183i	0.896970	+	0.442092i	$0.145763\pi$
$157$			4.28737e7i			0.884183i	−0.896970	+	0.442092i	$0.854237\pi$
$158$	3.63184e6	−	2.62249e7i	0.0732532	−	0.528950i
$159$	−1.50725e7			−0.297369
$160$	−2.64779e7	−	2.17671e7i	−0.511051	−	0.420128i
$161$	4.64373e6			0.0876952
$162$	2.88091e6	−	2.08026e7i	0.0532387	−	0.384428i
$163$		−	4.12127e7i		−	0.745374i	−0.927957	−	0.372687i	$-0.878437\pi$
$163$		−	4.12127e7i		−	0.745374i	0.927957	−	0.372687i	$-0.121563\pi$
$164$	5.06330e7	+	1.42984e7i	0.896356	+	0.253124i
$165$		−	1.75448e7i		−	0.304056i
$166$	−9.88624e6	−	1.36913e6i	−0.167746	−	0.0232309i
$167$	2.41703e7			0.401582			0.200791	−	0.979634i	$-0.435649\pi$
$167$	2.41703e7			0.401582			0.200791	+	0.979634i	$0.435649\pi$
$168$	3.06164e7	+	1.34103e7i	0.498163	+	0.218200i
$169$	−6.38869e7			−1.01814
$170$	4.50652e7	+	6.24099e6i	0.703509	+	0.0974276i
$171$			7.75477e7i			1.18599i
$172$	−3.34519e6	+	1.18459e7i	−0.0501269	+	0.177508i
$173$		−	5.90454e7i		−	0.867011i	−0.901151	−	0.433505i	$-0.857277\pi$
$173$		−	5.90454e7i		−	0.867011i	0.901151	−	0.433505i	$-0.142723\pi$
$174$	806598.	−	5.82431e6i	0.0116074	−	0.0838151i
$175$	4.62137e7			0.651835
$176$	−3.70598e7	+	6.03848e7i	−0.512399	+	0.834898i
$177$	3.94850e7			0.535212
$178$	−2.09114e6	+	1.50998e7i	−0.0277916	+	0.200679i
$179$			1.20311e8i			1.56791i	0.620819	+	0.783954i	$0.286800\pi$
$179$			1.20311e8i			1.56791i	−0.620819	+	0.783954i	$0.713200\pi$
$180$	−1.09712e7	+	3.88508e7i	−0.140217	+	0.496531i
$181$			3.21539e6i			0.0403049i	0.999797	+	0.0201525i	$0.00641517\pi$
$181$			3.21539e6i			0.0403049i	−0.999797	+	0.0201525i	$0.993585\pi$
$182$	−1.32665e8	−	1.83725e7i	−1.63119	−	0.225901i
$183$	−2.99259e7			−0.360968
$184$	−2.56482e6	+	5.85561e6i	−0.0303525	+	0.0692963i
$185$	8.93768e7			1.03782
$186$	−1.79353e7	−	2.48383e6i	−0.204368	−	0.0283026i
$187$		−	9.40392e7i		−	1.05163i
$188$	1.92376e7	+	5.43254e6i	0.211153	+	0.0596280i
$189$		−	8.98443e7i		−	0.967997i
$190$	1.30484e7	−	9.42204e7i	0.138013	−	0.996569i
$191$	7.04122e7			0.731191			0.365596	−	0.930774i	$-0.380865\pi$
$191$	7.04122e7			0.731191			0.365596	+	0.930774i	$0.380865\pi$
$192$	−3.38200e7	+	3.11997e7i	−0.344842	+	0.318124i
$193$	1.17861e7			0.118010			0.0590050	−	0.998258i	$-0.481207\pi$
$193$	1.17861e7			0.118010			0.0590050	+	0.998258i	$0.481207\pi$
$194$	1.13730e7	−	8.21229e7i	0.111833	−	0.807529i
$195$			4.56566e7i			0.440943i
$196$	−3.48693e7	−	9.84682e6i	−0.330786	−	0.0934113i
$197$		−	8.97008e7i		−	0.835920i	−0.908465	−	0.417960i	$-0.862745\pi$
$197$		−	8.97008e7i		−	0.835920i	0.908465	−	0.417960i	$-0.137255\pi$
$198$	8.26568e7	+	1.14470e7i	0.756746	+	0.104800i
$199$	−3.98955e7			−0.358871			−0.179436	−	0.983770i	$-0.557427\pi$
$199$	−3.98955e7			−0.358871			−0.179436	+	0.983770i	$0.557427\pi$
$200$	−2.55247e7	+	5.82743e7i	−0.225609	+	0.515077i
$201$	−2.38833e7			−0.207447
$202$	−1.08260e8	−	1.49928e7i	−0.924143	−	0.127983i
$203$			2.49178e7i			0.209061i
$204$	1.65975e7	−	5.87746e7i	0.136879	−	0.484712i
$205$			7.60078e7i			0.616197i
$206$	−2.15199e7	+	1.55392e8i	−0.171516	+	1.23849i
$207$	7.52915e6			0.0589997
$208$	9.64404e7	−	1.57139e8i	0.743083	−	1.21077i
$209$	−1.96613e8			−1.48971
$210$	−6.62394e6	+	4.78304e7i	−0.0493570	+	0.356399i
$211$		−	6.63604e7i		−	0.486318i	−0.969986	−	0.243159i	$-0.921816\pi$
$211$		−	6.63604e7i		−	0.486318i	0.969986	−	0.243159i	$-0.0781837\pi$
$212$	−2.38965e7	+	8.46218e7i	−0.172250	+	0.609967i
$213$			1.23051e8i			0.872479i
$214$	2.11083e8	+	2.92325e7i	1.47233	+	0.203901i
$215$	−1.77825e7			−0.122027
$216$	1.13291e8	+	4.96227e7i	0.764906	+	0.335036i
$217$	7.67317e7			0.509760
$218$	9.64475e7	+	1.33568e7i	0.630512	+	0.0873184i
$219$		−	476088.i		−	0.00306290i
$220$	−9.85018e7	−	2.78161e7i	−0.623684	−	0.176124i
$221$			2.44718e8i			1.52508i
$222$	1.64587e7	−	1.18846e8i	0.100963	−	0.729034i
$223$	−1.57269e8			−0.949675			−0.474837	−	0.880074i	$-0.657493\pi$
$223$	−1.57269e8			−0.949675			−0.474837	+	0.880074i	$0.657493\pi$
$224$	1.23830e8	−	1.50629e8i	0.736136	−	0.895448i
$225$	7.49291e7			0.438543
$226$	−2.03840e7	+	1.47189e8i	−0.117465	+	0.848197i
$227$		−	1.95129e8i		−	1.10721i	−0.832778	−	0.553607i	$-0.813251\pi$
$227$		−	1.95129e8i		−	1.10721i	0.832778	−	0.553607i	$-0.186749\pi$
$228$	−1.22883e8	−	3.47013e7i	−0.686628	−	0.193898i
$229$		−	6.95136e7i		−	0.382512i	−0.981540	−	0.191256i	$-0.938744\pi$
$229$		−	6.95136e7i		−	0.382512i	0.981540	−	0.191256i	$-0.0612561\pi$
$230$	−9.14791e6	−	1.26688e6i	−0.0495764	−	0.00686574i
$231$	9.98095e7			0.532758
$232$	−3.14207e7	−	1.37626e7i	−0.165199	−	0.0723589i
$233$	−3.81872e7			−0.197776			−0.0988878	−	0.995099i	$-0.531528\pi$
$233$	−3.81872e7			−0.197776			−0.0988878	+	0.995099i	$0.531528\pi$
$234$	−2.15097e8	−	2.97884e7i	−1.09744	−	0.151982i
$235$			2.88785e7i			0.145157i
$236$	6.26010e7	−	2.21681e8i	0.310020	−	1.09783i
$237$		−	5.13437e7i		−	0.250535i
$238$	−3.55040e7	+	2.56369e8i	−0.170710	+	1.23267i
$239$	−2.63549e8			−1.24873			−0.624366	−	0.781132i	$-0.714643\pi$
$239$	−2.63549e8			−1.24873			−0.624366	+	0.781132i	$0.714643\pi$
$240$	−5.66543e7	−	3.47702e7i	−0.264541	−	0.162356i
$241$	1.21337e8			0.558386			0.279193	−	0.960235i	$-0.409933\pi$
$241$	1.21337e8			0.558386			0.279193	+	0.960235i	$0.409933\pi$
$242$	1.22162e6	−	8.82115e6i	0.00554094	−	0.0400102i
$243$		−	2.27512e8i		−	1.01715i
$244$	−4.74457e7	+	1.68014e8i	−0.209090	+	0.740423i
$245$		−	5.23441e7i		−	0.227398i
$246$	1.01069e8	+	1.39968e7i	0.432857	+	0.0599455i
$247$	5.11645e8			2.16038
$248$	−4.23803e7	+	9.67566e7i	−0.176435	+	0.402809i
$249$	−1.93555e7			−0.0794523
$250$	−2.52938e8	−	3.50288e7i	−1.02382	−	0.141787i
$251$			3.62042e7i			0.144511i	0.997386	+	0.0722555i	$0.0230197\pi$
$251$			3.62042e7i			0.144511i	−0.997386	+	0.0722555i	$0.976980\pi$
$252$	−2.21016e8	−	6.24133e7i	−0.870007	−	0.245683i
$253$			1.90893e7i			0.0741085i
$254$	4.94728e7	−	3.57235e8i	0.189430	−	1.36784i
$255$	8.82295e7			0.333214
$256$	1.21545e8	+	2.39341e8i	0.452792	+	0.891616i
$257$	1.75550e8			0.645111			0.322555	−	0.946551i	$-0.395458\pi$
$257$	1.75550e8			0.645111			0.322555	+	0.946551i	$0.395458\pi$
$258$	−3.27464e6	+	2.36456e7i	−0.0118712	+	0.0857199i
$259$			5.08451e8i			1.81844i
$260$	2.56331e8	+	7.23858e7i	0.904469	+	0.255415i
$261$			4.04008e7i			0.140653i
$262$	−1.31175e8	−	1.81661e7i	−0.450605	−	0.0624034i
$263$	−1.10733e8			−0.375348			−0.187674	−	0.982231i	$-0.560095\pi$
$263$	−1.10733e8			−0.375348			−0.187674	+	0.982231i	$0.560095\pi$
$264$	−5.51266e7	+	1.25857e8i	−0.184394	+	0.420982i
$265$	−1.27030e8			−0.419320
$266$	5.36005e8	+	7.42304e7i	1.74616	+	0.241822i
$267$			2.95627e7i			0.0950505i
$268$	−3.78655e7	+	1.34088e8i	−0.120163	+	0.425519i
$269$		−	3.07561e8i		−	0.963382i	−0.876341	−	0.481691i	$-0.840023\pi$
$269$		−	3.07561e8i		−	0.963382i	0.876341	−	0.481691i	$-0.159977\pi$
$270$	−2.45108e7	+	1.76989e8i	−0.0757853	+	0.547233i
$271$	−2.86036e8			−0.873027			−0.436513	−	0.899698i	$-0.643787\pi$
$271$	−2.86036e8			−0.873027			−0.436513	+	0.899698i	$0.643787\pi$
$272$	−3.03665e8	−	1.86367e8i	−0.914962	−	0.561536i
$273$	−2.59734e8			−0.772607
$274$	5.88478e7	−	4.24930e8i	0.172824	−	1.24793i
$275$			1.89974e8i			0.550846i
$276$	−3.36917e6	+	1.19308e7i	−0.00964587	+	0.0341577i
$277$		−	3.15642e8i		−	0.892309i	−0.894956	−	0.446155i	$-0.852793\pi$
$277$		−	3.15642e8i		−	0.892309i	0.894956	−	0.446155i	$-0.147207\pi$
$278$	−3.14125e8	−	4.35026e7i	−0.876891	−	0.121439i
$279$	1.24410e8			0.342957
$280$	2.58033e8	+	1.13021e8i	0.702461	+	0.307685i
$281$	−2.50451e8			−0.673366			−0.336683	−	0.941618i	$-0.609305\pi$
$281$	−2.50451e8			−0.673366			−0.336683	+	0.941618i	$0.609305\pi$
$282$	3.84002e7	+	5.31797e6i	0.101967	+	0.0141213i
$283$			3.47387e7i			0.0911088i	0.998962	+	0.0455544i	$0.0145054\pi$
$283$			3.47387e7i			0.0911088i	−0.998962	+	0.0455544i	$0.985495\pi$
$284$	6.90845e8	+	1.95089e8i	1.78964	+	0.505381i
$285$		−	1.84467e8i		−	0.472020i
$286$	7.55251e7	−	5.45354e8i	0.190902	−	1.37847i
$287$	−4.32397e8			−1.07968
$288$	2.00773e8	−	2.44224e8i	0.495258	−	0.602441i
$289$	6.25676e7			0.152478
$290$	6.79795e6	−	4.90869e7i	0.0163676	−	0.118188i
$291$		−	1.60782e8i		−	0.382482i
$292$	−2.67291e6	−	754808.i	−0.00628267	−	0.00177418i
$293$			5.34336e8i			1.24102i	0.784200	+	0.620508i	$0.213074\pi$
$293$			5.34336e8i			1.24102i	−0.784200	+	0.620508i	$0.786926\pi$
$294$	−6.96027e7	−	9.63915e6i	−0.159739	−	0.0221219i
$295$	3.32777e8			0.754703
$296$	−6.41143e8	−	2.80827e8i	−1.43692	−	0.629387i
$297$	3.69329e8			0.818024
$298$	7.64393e7	+	1.05859e7i	0.167325	+	0.0231725i
$299$		−	4.96760e7i		−	0.107472i
$300$	−3.35296e7	+	1.18734e8i	−0.0716974	+	0.253893i
$301$		−	1.01162e8i		−	0.213813i
$302$	−1.18273e8	+	8.54031e8i	−0.247094	+	1.78422i
$303$	−2.11954e8			−0.437716
$304$	−3.89648e8	+	6.34889e8i	−0.795454	+	1.29611i
$305$	−2.52214e8			−0.509002
$306$	−5.75648e7	+	4.15666e8i	−0.114850	+	0.829315i
$307$			1.68851e8i			0.333057i	0.986037	+	0.166529i	$0.0532558\pi$
$307$			1.68851e8i			0.333057i	−0.986037	+	0.166529i	$0.946744\pi$
$308$	1.58242e8	−	5.60362e8i	0.308598	−	1.09280i
$309$			3.04229e8i			0.586605i
$310$	−1.51158e8	−	2.09335e7i	−0.288180	−	0.0399095i
$311$	6.99677e8			1.31897			0.659487	−	0.751716i	$-0.270774\pi$
$311$	6.99677e8			1.31897			0.659487	+	0.751716i	$0.270774\pi$
$312$	1.43456e8	−	3.27517e8i	0.267409	−	0.610510i
$313$	5.06345e8			0.933343			0.466671	−	0.884431i	$-0.345453\pi$
$313$	5.06345e8			0.933343			0.466671	+	0.884431i	$0.345453\pi$
$314$	4.80475e8	+	6.65401e7i	0.875825	+	0.121291i
$315$		−	3.31779e8i		−	0.598084i
$316$	−2.88260e8	−	8.14022e7i	−0.513900	−	0.145121i
$317$			4.78996e8i			0.844548i	0.906468	+	0.422274i	$0.138768\pi$
$317$			4.78996e8i			0.844548i	−0.906468	+	0.422274i	$0.861232\pi$
$318$	−2.33926e7	+	1.68914e8i	−0.0407927	+	0.294558i
$319$	−1.02431e8			−0.176671
$320$	−2.85033e8	+	2.62949e8i	−0.486262	+	0.448587i
$321$	4.13263e8			0.697364
$322$	7.20707e6	−	5.20411e7i	0.0120299	−	0.0868662i
$323$		−	9.88733e8i		−	1.63256i
$324$	−2.28658e8	−	6.45713e7i	−0.373490	−	0.105471i
$325$		−	4.94369e8i		−	0.798839i
$326$	−4.61860e8	−	6.39621e7i	−0.738327	−	0.102250i
$327$	1.88827e8			0.298639
$328$	2.38821e8	−	5.45241e8i	0.373692	−	0.853159i
$329$	−1.64285e8			−0.254339
$330$	−1.96620e8	−	2.72295e7i	−0.301182	−	0.0417101i
$331$		−	4.20825e8i		−	0.637828i	−0.947784	−	0.318914i	$-0.896682\pi$
$331$		−	4.20825e8i		−	0.637828i	0.947784	−	0.318914i	$-0.103318\pi$
$332$	−3.06869e7	+	1.08668e8i	−0.0460225	+	0.162974i
$333$			8.24382e8i			1.22341i
$334$	3.75123e7	−	2.70871e8i	0.0550886	−	0.397786i
$335$	−2.01287e8			−0.292522
$336$	1.97802e8	−	3.22298e8i	0.284475	−	0.463521i
$337$	−1.02987e9			−1.46580			−0.732902	−	0.680334i	$-0.761835\pi$
$337$	−1.02987e9			−1.46580			−0.732902	+	0.680334i	$0.761835\pi$
$338$	−9.91526e7	+	7.15965e8i	−0.139668	+	1.00852i
$339$			2.88170e8i			0.401745i
$340$	1.39882e8	−	4.95348e8i	0.193013	−	0.683493i
$341$			3.15427e8i			0.430782i
$342$	8.69058e8	+	1.20354e8i	1.17478	+	0.162693i
$343$	−5.68554e8			−0.760751
$344$	1.27562e8	+	5.58735e7i	0.168954	+	0.0740033i
$345$	−1.79100e7			−0.0234816
$346$	−6.61707e8	−	9.16385e7i	−0.858814	−	0.118936i
$347$			5.31496e8i			0.682883i	0.939903	+	0.341442i	$0.110915\pi$
$347$			5.31496e8i			0.682883i	−0.939903	+	0.341442i	$0.889085\pi$
$348$	−6.40198e7	−	1.80787e7i	−0.0814304	−	0.0229953i
$349$		−	1.31436e9i		−	1.65511i	−0.561385	−	0.827555i	$-0.689731\pi$
$349$		−	1.31436e9i		−	1.65511i	0.561385	−	0.827555i	$-0.310269\pi$
$350$	7.17238e7	−	5.17906e8i	0.0894181	−	0.645673i
$351$	−9.61103e8			−1.18630
$352$	6.19201e8	+	5.09037e8i	0.756715	+	0.622085i
$353$	1.42031e9			1.71858			0.859291	−	0.511486i	$-0.170905\pi$
$353$	1.42031e9			1.71858			0.859291	+	0.511486i	$0.170905\pi$
$354$	6.12808e7	−	4.42499e8i	0.0734198	−	0.530152i
$355$			1.03706e9i			1.23028i
$356$	1.65974e8	+	4.68698e7i	0.194969	+	0.0550577i
$357$			5.01924e8i			0.583847i
$358$	1.34830e9	+	1.86723e8i	1.55309	+	0.215084i
$359$	7.59524e8			0.866385			0.433193	−	0.901301i	$-0.357387\pi$
$359$	7.59524e8			0.866385			0.433193	+	0.901301i	$0.357387\pi$
$360$	4.18364e8	+	1.83248e8i	0.472602	+	0.207005i
$361$	−1.17333e9			−1.31264
$362$	3.60340e7	+	4.99029e6i	0.0399239	+	0.00552899i
$363$		−	1.72702e7i		−	0.0189507i
$364$	−4.11792e8	+	1.45823e9i	−0.447531	+	1.58478i
$365$		−	4.01244e6i		−	0.00431900i
$366$	−4.64451e7	+	3.35372e8i	−0.0495172	+	0.357556i
$367$	3.76159e8			0.397228			0.198614	−	0.980078i	$-0.436356\pi$
$367$	3.76159e8			0.397228			0.198614	+	0.980078i	$0.436356\pi$
$368$	6.16418e7	+	3.78312e7i	0.0644775	+	0.0395715i
$369$	−7.01071e8			−0.726390
$370$	1.38713e8	−	1.00162e9i	0.142368	−	1.02801i
$371$		−	7.22655e8i		−	0.734720i
$372$	−5.56713e7	+	1.97142e8i	−0.0560701	+	0.198554i
$373$		−	4.57130e8i		−	0.456099i	−0.973650	−	0.228049i	$-0.926765\pi$
$373$		−	4.57130e8i		−	0.456099i	0.973650	−	0.228049i	$-0.0732347\pi$
$374$	−1.05387e9	−	1.45949e8i	−1.04169	−	0.144262i
$375$	−4.95206e8			−0.484927
$376$	9.07378e7	−	2.07159e8i	0.0880301	−	0.200977i
$377$	2.66557e8			0.256209
$378$	−1.00686e9	−	1.39438e8i	−0.958846	−	0.132789i
$379$			1.91565e9i			1.80750i	0.428056	+	0.903752i	$0.359199\pi$
$379$			1.91565e9i			1.80750i	−0.428056	+	0.903752i	$0.640801\pi$
$380$	−1.03565e9	−	2.92460e8i	−0.968215	−	0.273416i
$381$		−	6.99402e8i		−	0.647873i
$382$	1.09280e8	−	7.89092e8i	0.100304	−	0.724279i
$383$	1.57853e9			1.43568			0.717839	−	0.696209i	$-0.245131\pi$
$383$	1.57853e9			1.43568			0.717839	+	0.696209i	$0.245131\pi$
$384$	2.97159e8	+	4.27435e8i	0.267811	+	0.385221i
$385$	8.41187e8			0.751243
$386$	1.82920e7	−	1.32084e8i	0.0161885	−	0.116894i
$387$		−	1.64020e8i		−	0.143849i
$388$	−9.02680e8	−	2.54910e8i	−0.784554	−	0.221552i
$389$		−	2.21214e9i		−	1.90541i	−0.303890	−	0.952707i	$-0.598285\pi$
$389$		−	2.21214e9i		−	1.90541i	0.303890	−	0.952707i	$-0.401715\pi$
$390$	5.11662e8	+	7.08592e7i	0.436775	+	0.0604881i
$391$	−9.59967e7			−0.0812153
$392$	−1.64468e8	+	3.75489e8i	−0.137905	+	0.314845i
$393$	−2.56817e8			−0.213427
$394$	−1.00526e9	−	1.39216e8i	−0.828017	−	0.114671i
$395$		−	4.32721e8i		−	0.353279i
$396$	2.56567e8	−	9.08548e8i	0.207619	−	0.735216i
$397$			1.30879e9i			1.04979i	0.851167	+	0.524896i	$0.175896\pi$
$397$			1.30879e9i			1.04979i	−0.851167	+	0.524896i	$0.824104\pi$
$398$	−6.19180e7	+	4.47100e8i	−0.0492296	+	0.355479i
$399$	1.04940e9			0.827060
$400$	6.13451e8	+	3.76491e8i	0.479259	+	0.294134i
$401$	1.04514e8			0.0809413			0.0404706	−	0.999181i	$-0.487114\pi$
$401$	1.04514e8			0.0809413			0.0404706	+	0.999181i	$0.487114\pi$
$402$	−3.70669e7	+	2.67654e8i	−0.0284574	+	0.205486i
$403$		−	8.20832e8i		−	0.624722i
$404$	−3.36040e8	+	1.18998e9i	−0.253546	+	0.897850i
$405$		−	3.43251e8i		−	0.256755i
$406$	2.79248e8	+	3.86725e7i	0.207085	+	0.0286788i
$407$	−2.09013e9			−1.53671
$408$	−6.32913e8	−	2.77222e8i	−0.461353	−	0.202077i
$409$	1.94107e9			1.40284			0.701421	−	0.712747i	$-0.252549\pi$
$409$	1.94107e9			1.40284			0.701421	+	0.712747i	$0.252549\pi$
$410$	8.51800e8	+	1.17964e8i	0.610372	+	0.0845292i
$411$		−	8.31937e8i		−	0.591077i
$412$	1.70804e9	+	4.82336e8i	1.20325	+	0.339789i
$413$			1.89312e9i			1.32237i
$414$	1.16853e7	−	8.43774e7i	0.00809352	−	0.0584420i
$415$	−1.63127e8			−0.112036
$416$	−1.61134e9	−	1.32466e9i	−1.09739	−	0.902150i
$417$	−6.15000e8			−0.415336
$418$	−3.05144e8	+	2.20340e9i	−0.204356	+	1.47562i
$419$			1.96429e9i			1.30454i	0.757989	+	0.652268i	$0.226182\pi$
$419$			1.96429e9i			1.30454i	−0.757989	+	0.652268i	$0.773818\pi$
$420$	5.25743e8	+	1.48466e8i	0.346259	+	0.0977808i
$421$			2.33176e9i			1.52299i	0.648174	+	0.761493i	$0.275533\pi$
$421$			2.33176e9i			1.52299i	−0.648174	+	0.761493i	$0.724467\pi$
$422$	−7.43685e8	−	1.02992e8i	−0.481721	−	0.0667126i
$423$	−2.66366e8			−0.171115
$424$	9.11248e8	+	3.99136e8i	0.580572	+	0.254296i
$425$	−9.55346e8			−0.603670
$426$	1.37900e9	+	1.90975e8i	0.864231	+	0.119686i
$427$		−	1.43480e9i		−	0.891857i
$428$	6.55204e8	−	2.32019e9i	0.403946	−	1.43044i
$429$		−	1.06771e9i		−	0.652907i
$430$	−2.75984e7	+	1.99284e8i	−0.0167396	+	0.120874i
$431$	1.72745e8			0.103929			0.0519643	−	0.998649i	$-0.483452\pi$
$431$	1.72745e8			0.103929			0.0519643	+	0.998649i	$0.483452\pi$
$432$	7.31937e8	−	1.19261e9i	0.436798	−	0.711715i
$433$	−2.71381e9			−1.60647			−0.803233	−	0.595665i	$-0.796889\pi$
$433$	−2.71381e9			−1.60647			−0.803233	+	0.595665i	$0.796889\pi$
$434$	1.19088e8	−	8.59913e8i	0.0699283	−	0.504941i
$435$		−	9.61033e7i		−	0.0559791i
$436$	2.99373e8	−	1.06013e9i	0.172986	−	0.612573i
$437$			2.00706e8i			0.115047i
$438$	−5.33540e6	−	738890.i	−0.00303394	−	0.000420165i
$439$	−2.73808e8			−0.154461			−0.0772307	−	0.997013i	$-0.524608\pi$
$439$	−2.73808e8			−0.154461			−0.0772307	+	0.997013i	$0.524608\pi$
$440$	−4.64604e8	+	1.06071e9i	−0.260015	+	0.593628i
$441$	4.82804e8			0.268063
$442$	2.74249e9	+	3.79802e8i	1.51066	+	0.209209i
$443$		−	2.72048e9i		−	1.48673i	−0.668886	−	0.743365i	$-0.733229\pi$
$443$		−	2.72048e9i		−	1.48673i	0.668886	−	0.743365i	$-0.266771\pi$
$444$	−1.30633e9	−	3.68897e8i	−0.708292	−	0.200016i
$445$			2.49152e8i			0.134031i
$446$	−2.44081e8	+	1.76247e9i	−0.130275	+	0.940697i
$447$	1.49654e8			0.0792526
$448$	−1.49588e9	−	1.62151e9i	−0.786000	−	0.852013i
$449$	1.69111e9			0.881675			0.440837	−	0.897587i	$-0.354682\pi$
$449$	1.69111e9			0.881675			0.440837	+	0.897587i	$0.354682\pi$
$450$	1.16290e8	−	8.39712e8i	0.0601588	−	0.434397i
$451$		−	1.77748e9i		−	0.912406i
$452$	1.61788e9	+	4.56876e8i	0.824065	+	0.232709i
$453$			1.67204e9i			0.845089i
$454$	−2.18676e9	−	3.02841e8i	−1.09675	−	0.151886i
$455$	−2.18902e9			−1.08945
$456$	−5.79604e8	+	1.32327e9i	−0.286256	+	0.653538i
$457$	−1.15773e8			−0.0567413			−0.0283706	−	0.999597i	$-0.509032\pi$
$457$	−1.15773e8			−0.0567413			−0.0283706	+	0.999597i	$0.509032\pi$
$458$	−7.79021e8	−	1.07885e8i	−0.378896	−	0.0524726i
$459$			1.85729e9i			0.896470i
$460$	−2.83952e7	+	1.00552e8i	−0.0136017	+	0.0481658i
$461$		−	9.34713e8i		−	0.444350i	−0.975007	−	0.222175i	$-0.928684\pi$
$461$		−	9.34713e8i		−	0.444350i	0.975007	−	0.222175i	$-0.0713156\pi$
$462$	1.54904e8	−	1.11854e9i	0.0730831	−	0.527721i
$463$	1.91738e9			0.897790			0.448895	−	0.893584i	$-0.351818\pi$
$463$	1.91738e9			0.897790			0.448895	+	0.893584i	$0.351818\pi$
$464$	−2.02999e8	+	3.30764e8i	−0.0943367	+	0.153711i
$465$	−2.95940e8			−0.136495
$466$	−5.92667e7	+	4.27955e8i	−0.0271306	+	0.195906i
$467$			1.65838e9i			0.753485i	0.926318	+	0.376742i	$0.122956\pi$
$467$			1.65838e9i			0.753485i	−0.926318	+	0.376742i	$0.877044\pi$
$468$	−6.67663e8	+	2.36431e9i	−0.301090	+	1.06621i
$469$		−	1.14509e9i		−	0.512548i
$470$	3.23634e8	+	4.48195e7i	0.143784	+	0.0199124i
$471$	9.40684e8			0.414830
$472$	−2.38717e9	−	1.04560e9i	−1.04493	−	0.457689i
$473$	4.15853e8			0.180686
$474$	−5.75396e8	−	7.96855e7i	−0.248166	−	0.0343681i
$475$			1.99740e9i			0.855140i
$476$	2.81796e9	+	7.95770e8i	1.19760	+	0.338192i
$477$		−	1.17168e9i		−	0.494306i
$478$	−4.09029e8	+	2.95353e9i	−0.171300	+	1.23693i
$479$	4.09755e9			1.70353			0.851766	−	0.523923i	$-0.175532\pi$
$479$	4.09755e9			1.70353			0.851766	+	0.523923i	$0.175532\pi$
$480$	−4.77589e8	+	5.80947e8i	−0.197111	+	0.239769i
$481$	5.43912e9			2.22854
$482$	1.88316e8	−	1.35980e9i	0.0765988	−	0.553107i
$483$		−	1.01887e8i		−	0.0411438i
$484$	−9.69604e7	−	2.73809e7i	−0.0388719	−	0.0109771i
$485$		−	1.35506e9i		−	0.539339i
$486$	−2.54968e9	−	3.53100e8i	−1.00753	−	0.139531i
$487$	−3.24167e9			−1.27180			−0.635898	−	0.771773i	$-0.719370\pi$
$487$	−3.24167e9			−1.27180			−0.635898	+	0.771773i	$0.719370\pi$
$488$	1.80925e9	+	7.92470e8i	0.704741	+	0.308683i
$489$	−9.04239e8			−0.349705
$490$	−5.86607e8	−	8.12381e7i	−0.225248	−	0.0311942i
$491$			2.16351e9i			0.824847i	0.910992	+	0.412423i	$0.135318\pi$
$491$			2.16351e9i			0.824847i	−0.910992	+	0.412423i	$0.864682\pi$
$492$	3.13718e8	−	1.11093e9i	0.118758	−	0.420541i
$493$		−	5.15110e8i		−	0.193613i
$494$	7.94075e8	−	5.73388e9i	0.296358	−	2.13995i
$495$	1.36387e9			0.505422
$496$	1.01855e9	+	6.25112e8i	0.374798	+	0.230024i
$497$	−5.89969e9			−2.15567
$498$	−3.00398e7	+	2.16912e8i	−0.0108992	+	0.0787012i
$499$		−	2.16713e9i		−	0.780787i	−0.920648	−	0.390394i	$-0.872339\pi$
$499$		−	2.16713e9i		−	0.780787i	0.920648	−	0.390394i	$-0.127661\pi$
$500$	−7.85119e8	+	2.78024e9i	−0.280893	+	0.994690i
$501$		−	5.30316e8i		−	0.188409i
$502$	4.05731e8	+	5.61890e7i	0.143145	+	0.0198238i
$503$	−2.58480e9			−0.905606			−0.452803	−	0.891611i	$-0.649576\pi$
$503$	−2.58480e9			−0.905606			−0.452803	+	0.891611i	$0.649576\pi$
$504$	−1.04247e9	+	2.38001e9i	−0.362707	+	0.828080i
$505$	−1.78633e9			−0.617224
$506$	2.13929e8	+	2.96266e7i	0.0734079	+	0.0101661i
$507$			1.40173e9i			0.477680i
$508$	−3.92666e9	−	1.10886e9i	−1.32893	−	0.375278i
$509$		−	2.11747e9i		−	0.711712i	−0.934541	−	0.355856i	$-0.884189\pi$
$509$		−	2.11747e9i		−	0.711712i	0.934541	−	0.355856i	$-0.115811\pi$
$510$	1.36932e8	−	9.88766e8i	0.0457099	−	0.330064i
$511$	2.28261e7			0.00756762
$512$	2.87088e9	−	9.90670e8i	0.945301	−	0.326200i
$513$	3.88315e9			1.26991
$514$	2.72454e8	−	1.96734e9i	0.0884956	−	0.639012i
$515$			2.56402e9i			0.827172i
$516$	2.59908e8	+	7.33961e7i	0.0832810	+	0.0235179i
$517$		−	6.75339e8i		−	0.214934i
$518$	5.69808e9	+	7.89117e8i	1.80125	+	0.249452i
$519$	−1.29550e9			−0.406773
$520$	1.20903e9	−	2.76029e9i	0.377074	−	0.860881i
$521$	−2.34354e9			−0.726006			−0.363003	−	0.931788i	$-0.618249\pi$
$521$	−2.34354e9			−0.726006			−0.363003	+	0.931788i	$0.618249\pi$
$522$	4.52761e8	+	6.27021e7i	0.139323	+	0.0192946i
$523$		−	3.26155e9i		−	0.996939i	−0.866907	−	0.498470i	$-0.833896\pi$
$523$		−	3.26155e9i		−	0.996939i	0.866907	−	0.498470i	$-0.166104\pi$
$524$	−4.07167e8	+	1.44185e9i	−0.123627	+	0.437785i
$525$		−	1.01397e9i		−	0.305820i
$526$	−1.71859e8	+	1.24096e9i	−0.0514898	+	0.371799i
$527$	−1.58622e9			−0.472093
$528$	1.32489e9	+	8.13121e8i	0.391707	+	0.240401i
$529$	−3.38534e9			−0.994277
$530$	−1.97151e8	+	1.42359e9i	−0.0575219	+	0.415356i
$531$			3.06942e9i			0.889664i
$532$	1.66376e9	−	5.89167e9i	0.479072	−	1.69648i
$533$			4.62554e9i			1.32317i
$534$	3.31302e8	+	4.58814e7i	0.0941520	+	0.0130389i
$535$	3.48296e9			0.983354
$536$	1.44393e9	+	6.32454e8i	0.405013	+	0.177400i
$537$	2.63973e9			0.735612
$538$	−3.44676e9	−	4.77336e8i	−0.954275	−	0.132156i
$539$			1.22409e9i			0.336709i
$540$	1.94543e9	+	5.49374e8i	0.531664	+	0.150138i
$541$			7.24638e9i			1.96757i	0.179344	+	0.983787i	$0.442603\pi$
$541$			7.24638e9i			1.96757i	−0.179344	+	0.983787i	$0.557397\pi$
$542$	−4.43928e8	+	3.20553e9i	−0.119761	+	0.864773i
$543$	7.05482e7			0.0189098
$544$	−2.55986e9	+	3.11385e9i	−0.681741	+	0.829281i
$545$	1.59142e9			0.421111
$546$	−4.03107e8	+	2.91077e9i	−0.105985	+	0.765303i
$547$		−	6.41460e9i		−	1.67577i	−0.545848	−	0.837884i	$-0.683793\pi$
$547$		−	6.41460e9i		−	1.67577i	0.545848	−	0.837884i	$-0.316207\pi$
$548$	−4.67076e9	−	1.31899e9i	−1.21243	−	0.342380i
$549$		−	2.32634e9i		−	0.600025i
$550$	2.12899e9	+	2.94840e8i	0.545638	+	0.0755644i
$551$	−1.07697e9			−0.274267
$552$	1.28477e8	+	5.62742e7i	0.0325116	+	0.0142404i
$553$	2.46168e9			0.619005
$554$	−3.53732e9	−	4.89877e8i	−0.883873	−	0.122406i
$555$		−	1.96100e9i		−	0.486914i
$556$	−9.75045e8	+	3.45281e9i	−0.240582	+	0.851943i
$557$		−	1.76223e9i		−	0.432085i	−0.976384	−	0.216042i	$-0.930685\pi$
$557$		−	1.76223e9i		−	0.432085i	0.976384	−	0.216042i	$-0.0693149\pi$
$558$	1.93084e8	−	1.39423e9i	0.0470464	−	0.339715i
$559$	−1.08217e9			−0.262032
$560$	1.66707e9	−	2.71630e9i	0.401139	−	0.653612i
$561$	−2.06330e9			−0.493391
$562$	−3.88701e8	+	2.80674e9i	−0.0923715	+	0.667000i
$563$		−	2.33270e9i		−	0.550909i	−0.961314	−	0.275454i	$-0.911172\pi$
$563$		−	2.33270e9i		−	0.550909i	0.961314	−	0.275454i	$-0.0888283\pi$
$564$	1.19194e8	−	4.22088e8i	0.0279755	−	0.0990663i
$565$			2.42868e9i			0.566501i
$566$	3.89307e8	+	5.39144e7i	0.0902475	+	0.0124982i
$567$	1.95270e9			0.449878
$568$	3.25851e9	−	7.43935e9i	0.746104	−	1.70340i
$569$	5.53591e9			1.25978			0.629892	−	0.776683i	$-0.283099\pi$
$569$	5.53591e9			1.25978			0.629892	+	0.776683i	$0.283099\pi$
$570$	−2.06727e9	−	2.86292e8i	−0.467558	−	0.0647512i
$571$		−	3.70890e9i		−	0.833717i	−0.908971	−	0.416858i	$-0.863131\pi$
$571$		−	3.70890e9i		−	0.833717i	0.908971	−	0.416858i	$-0.136869\pi$
$572$	−5.99444e9	−	1.69278e9i	−1.33925	−	0.378194i
$573$		−	1.54490e9i		−	0.343051i
$574$	−6.71081e8	+	4.84576e9i	−0.148110	+	1.06947i
$575$	1.93929e8			0.0425407
$576$	−2.42535e9	−	2.62905e9i	−0.528806	−	0.573218i
$577$	3.63713e9			0.788212			0.394106	−	0.919065i	$-0.371054\pi$
$577$	3.63713e9			0.788212			0.394106	+	0.919065i	$0.371054\pi$
$578$	9.71050e7	−	7.01180e8i	0.0209168	−	0.151036i
$579$		−	2.58596e8i		−	0.0553665i
$580$	−5.39554e8	−	1.52366e8i	−0.114825	−	0.0324257i
$581$		−	9.28003e8i		−	0.196306i
$582$	−1.80184e9	−	2.49534e8i	−0.378867	−	0.0524685i
$583$	2.97067e9			0.620889
$584$	−1.26073e7	+	2.87832e7i	−0.00261925	+	0.00597989i
$585$	−3.54919e9			−0.732965
$586$	5.98817e9	+	8.29290e8i	1.22928	+	0.170241i
$587$			2.04311e9i			0.416926i	0.978030	+	0.208463i	$0.0668461\pi$
$587$			2.04311e9i			0.416926i	−0.978030	+	0.208463i	$0.933154\pi$
$588$	−2.16047e8	+	7.65060e8i	−0.0438256	+	0.155194i
$589$			3.31641e9i			0.668752i
$590$	5.16470e8	−	3.72935e9i	0.103529	−	0.747568i
$591$	−1.96811e9			−0.392187
$592$	−4.14221e9	+	6.74928e9i	−0.820553	+	1.33700i
$593$	−5.74764e9			−1.13187			−0.565937	−	0.824448i	$-0.691486\pi$
$593$	−5.74764e9			−1.13187			−0.565937	+	0.824448i	$0.691486\pi$
$594$	5.73200e8	−	4.13898e9i	0.112216	−	0.810291i
$595$			4.23018e9i			0.823284i
$596$	2.37268e8	−	8.40207e8i	0.0459068	−	0.162564i
$597$			8.75341e8i			0.168371i
$598$	−5.56706e8	−	7.70972e7i	−0.106456	−	0.0147430i
$599$	3.14564e8			0.0598020			0.0299010	−	0.999553i	$-0.490481\pi$
$599$	3.14564e8			0.0598020			0.0299010	+	0.999553i	$0.490481\pi$
$600$	1.27858e9	+	5.60033e8i	0.241657	+	0.105848i
$601$	−2.49586e9			−0.468985			−0.234493	−	0.972118i	$-0.575343\pi$
$601$	−2.49586e9			−0.468985			−0.234493	+	0.972118i	$0.575343\pi$
$602$	−1.13369e9	−	1.57003e8i	−0.211791	−	0.0293306i
$603$		−	1.85660e9i		−	0.344833i
$604$	9.38735e9	+	2.65091e9i	1.73346	+	0.489516i
$605$		−	1.45552e8i		−	0.0267224i
$606$	−3.28953e8	+	2.37532e9i	−0.0600454	+	0.433578i
$607$	−2.81126e9			−0.510200			−0.255100	−	0.966915i	$-0.582108\pi$
$607$	−2.81126e9			−0.510200			−0.255100	+	0.966915i	$0.582108\pi$
$608$	6.51031e9	+	5.35204e9i	1.17473	+	0.965733i
$609$	5.46717e8			0.0980849
$610$	−3.91436e8	+	2.82650e9i	−0.0698243	+	0.504190i
$611$			1.75743e9i			0.311698i
$612$	4.56893e9	+	1.29023e9i	0.805720	+	0.227529i
$613$		−	2.34343e9i		−	0.410904i	−0.978667	−	0.205452i	$-0.934134\pi$
$613$		−	2.34343e9i		−	0.410904i	0.978667	−	0.205452i	$-0.0658664\pi$
$614$	1.89227e9	+	2.62057e8i	0.329908	+	0.0456884i
$615$	1.66767e9			0.289100
$616$	−6.03424e9	−	2.64306e9i	−1.04014	−	0.455590i
$617$	−6.26737e8			−0.107420			−0.0537102	−	0.998557i	$-0.517105\pi$
$617$	−6.26737e8			−0.107420			−0.0537102	+	0.998557i	$0.517105\pi$
$618$	3.40942e9	+	4.72164e8i	0.581059	+	0.0804698i
$619$			8.90879e9i			1.50974i	0.655876	+	0.754869i	$0.272300\pi$
$619$			8.90879e9i			1.50974i	−0.655876	+	0.754869i	$0.727700\pi$
$620$	−4.69194e8	+	1.66150e9i	−0.0790645	+	0.279981i
$621$		−	3.77017e8i		−	0.0631743i
$622$	1.08590e9	−	7.84110e9i	0.180935	−	1.30650i
$623$	−1.41739e9			−0.234845
$624$	−3.44776e9	−	2.11598e9i	−0.568056	−	0.348631i
$625$	−7.41437e8			−0.121477
$626$	7.85848e8	−	5.67448e9i	0.128035	−	0.924519i
$627$			4.31385e9i			0.698922i
$628$	1.49140e9	−	5.28130e9i	0.240289	−	0.850906i
$629$		−	1.05109e10i		−	1.68407i
$630$	−3.71816e9	−	5.14922e8i	−0.592430	−	0.0820444i
$631$	−2.21942e9			−0.351671			−0.175835	−	0.984420i	$-0.556263\pi$
$631$	−2.21942e9			−0.351671			−0.175835	+	0.984420i	$0.556263\pi$
$632$	−1.35963e9	+	3.10412e9i	−0.214246	+	0.489134i
$633$	−1.45600e9			−0.228165
$634$	5.36799e9	+	7.43403e8i	0.836564	+	0.115854i
$635$		−	5.89451e9i		−	0.913566i
$636$	1.85667e9	+	5.24309e8i	0.286177	+	0.0808142i
$637$		−	3.18545e9i		−	0.488296i
$638$	−1.58974e8	+	1.14792e9i	−0.0242356	+	0.175001i
$639$	−9.56552e9			−1.45029
$640$	2.50443e9	+	3.60239e9i	0.377641	+	0.543201i
$641$	8.58104e9			1.28688			0.643438	−	0.765498i	$-0.277507\pi$
$641$	8.58104e9			1.28688			0.643438	+	0.765498i	$0.277507\pi$
$642$	6.41386e8	−	4.63134e9i	0.0956636	−	0.690771i
$643$			7.71279e9i			1.14412i	0.820210	+	0.572062i	$0.193856\pi$
$643$			7.71279e9i			1.14412i	−0.820210	+	0.572062i	$0.806144\pi$
$644$	−5.72026e8	−	1.61536e8i	−0.0843947	−	0.0238324i
$645$			3.90161e8i			0.0572513i
$646$	−1.10805e10	−	1.53452e9i	−1.61713	−	0.223953i
$647$	1.18898e10			1.72587			0.862935	−	0.505316i	$-0.168624\pi$
$647$	1.18898e10			1.72587			0.862935	+	0.505316i	$0.168624\pi$
$648$	−1.07851e9	+	2.46230e9i	−0.155709	+	0.355491i
$649$	−7.78217e9			−1.11749
$650$	−5.54027e9	−	7.67261e8i	−0.791287	−	0.109584i
$651$		−	1.68356e9i		−	0.239163i
$652$	−1.43362e9	+	5.07668e9i	−0.202566	+	0.717321i
$653$			2.00345e9i			0.281567i	0.990040	+	0.140784i	$0.0449622\pi$
$653$			2.00345e9i			0.281567i	−0.990040	+	0.140784i	$0.955038\pi$
$654$	2.93060e8	−	2.11614e9i	0.0409670	−	0.295816i
$655$	−2.16443e9			−0.300954
$656$	−5.73973e9	−	3.52262e9i	−0.793830	−	0.487194i
$657$	3.70094e7			0.00509135
$658$	−2.54971e8	+	1.84110e9i	−0.0348899	+	0.251935i
$659$		−	7.66944e9i		−	1.04391i	−0.852972	−	0.521957i	$-0.825202\pi$
$659$		−	7.66944e9i		−	1.04391i	0.852972	−	0.521957i	$-0.174798\pi$
$660$	−6.10309e8	+	2.16121e9i	−0.0826315	+	0.292613i
$661$		−	4.04041e9i		−	0.544152i	−0.962276	−	0.272076i	$-0.912290\pi$
$661$		−	4.04041e9i		−	0.544152i	0.962276	−	0.272076i	$-0.0877103\pi$
$662$	−4.71608e9	−	6.53121e8i	−0.631798	−	0.0874965i
$663$	5.36930e9			0.715518
$664$	1.17019e9	+	5.12554e8i	0.155120	+	0.0679440i
$665$	8.84429e9			1.16624
$666$	9.23865e9	+	1.27944e9i	1.21185	+	0.167827i
$667$			1.04564e8i			0.0136440i
$668$	−2.97736e9	−	8.40783e8i	−0.386468	−	0.109136i
$669$			3.45060e9i			0.445557i
$670$	−3.12397e8	+	2.25577e9i	−0.0401278	+	0.289756i
$671$	5.89816e9			0.753681
$672$	−3.30492e9	−	2.71693e9i	−0.420115	−	0.345371i
$673$	4.11138e9			0.519918			0.259959	−	0.965620i	$-0.416291\pi$
$673$	4.11138e9			0.519918			0.259959	+	0.965620i	$0.416291\pi$
$674$	−1.59835e9	+	1.15414e10i	−0.201077	+	1.45195i
$675$		−	3.75203e9i		−	0.469572i
$676$	7.86976e9	+	2.22236e9i	0.979824	+	0.276695i
$677$			1.12671e10i			1.39557i	0.716305	+	0.697787i	$0.245832\pi$
$677$			1.12671e10i			1.39557i	−0.716305	+	0.697787i	$0.754168\pi$
$678$	3.22945e9	+	4.47241e8i	0.397947	+	0.0551109i
$679$	7.70872e9			0.945014
$680$	−5.33414e9	−	2.33641e9i	−0.650554	−	0.284949i
$681$	−4.28129e9			−0.519469
$682$	3.53491e9	+	4.89543e8i	0.426710	+	0.0590942i
$683$			8.00228e9i			0.961039i	0.876984	+	0.480520i	$0.159552\pi$
$683$			8.00228e9i			0.961039i	−0.876984	+	0.480520i	$0.840448\pi$
$684$	2.69756e9	−	9.55253e9i	0.322311	−	1.14136i
$685$		−	7.01151e9i		−	0.833479i
$686$	−8.82397e8	+	6.37165e9i	−0.104359	+	0.753559i
$687$	−1.52518e9			−0.179462
$688$	8.24137e8	−	1.34284e9i	0.0964806	−	0.157205i
$689$	−7.73055e9			−0.900416
$690$	−2.77963e7	+	2.00713e8i	−0.00322118	+	0.0232596i
$691$		−	7.24716e9i		−	0.835593i	−0.908541	−	0.417797i	$-0.862803\pi$
$691$		−	7.24716e9i		−	0.835593i	0.908541	−	0.417797i	$-0.137197\pi$
$692$	−2.05394e9	+	7.27336e9i	−0.235622	+	0.834380i
$693$			7.75884e9i			0.885585i
$694$	5.95634e9	+	8.24882e8i	0.676428	+	0.0936772i
$695$	−5.18318e9			−0.585665
$696$	−3.01962e8	+	6.89395e8i	−0.0339485	+	0.0775061i
$697$	8.93865e9			0.999902
$698$	−1.47298e10	−	2.03990e9i	−1.63946	−	0.227046i
$699$			8.37859e8i			0.0927899i
$700$	−5.69273e9	−	1.60758e9i	−0.627303	−	0.177145i
$701$			4.68293e8i			0.0513458i	0.999670	+	0.0256729i	$0.00817283\pi$
$701$			4.68293e8i			0.0513458i	−0.999670	+	0.0256729i	$0.991827\pi$
$702$	−1.49163e9	+	1.07708e10i	−0.162736	+	1.17509i
$703$	−2.19757e10			−2.38561
$704$	6.66565e9	−	6.14921e9i	0.720010	−	0.664224i
$705$	6.33617e8			0.0681028
$706$	2.20432e9	−	1.59170e10i	0.235753	−	1.70234i
$707$		−	1.01622e10i		−	1.08148i
$708$	−4.86386e9	−	1.37352e9i	−0.515069	−	0.145451i
$709$			1.08926e10i			1.14781i	0.818923	+	0.573903i	$0.194571\pi$
$709$			1.08926e10i			1.14781i	−0.818923	+	0.573903i	$0.805429\pi$
$710$	1.16221e10	+	1.60952e9i	1.21865	+	0.168769i
$711$	3.99128e9			0.416455
$712$	7.82851e8	−	1.78729e9i	0.0812829	−	0.185573i
$713$	3.21992e8			0.0332684
$714$	5.62494e9	+	7.78987e8i	0.578328	+	0.0800915i
$715$		−	8.99855e9i		−	0.920664i
$716$	4.18512e9	−	1.48203e10i	0.426101	−	1.50890i
$717$			5.78249e9i			0.585865i
$718$	1.17878e9	−	8.51180e9i	0.118850	−	0.858195i
$719$	−7.40284e9			−0.742758			−0.371379	−	0.928481i	$-0.621115\pi$
$719$	−7.40284e9			−0.742758			−0.371379	+	0.928481i	$0.621115\pi$
$720$	2.70291e9	−	4.40410e9i	0.269879	−	0.439738i
$721$	−1.45863e10			−1.44935
$722$	−1.82101e9	+	1.31492e10i	−0.180066	+	1.30023i
$723$		−	2.66224e9i		−	0.261977i
$724$	1.11850e8	−	3.96080e8i	0.0109534	−	0.0387880i
$725$			1.04060e9i			0.101415i
$726$	−1.93543e8	−	2.68034e7i	−0.0187715	−	0.00259963i
$727$	1.04295e10			1.00668			0.503342	−	0.864087i	$-0.332103\pi$
$727$	1.04295e10			1.00668			0.503342	+	0.864087i	$0.332103\pi$
$728$	1.57029e10	+	6.87802e9i	1.50841	+	0.660699i
$729$	−9.32176e8			−0.0891152
$730$	−4.49664e7	−	6.22731e6i	−0.00427817	−	0.000592476i
$731$			2.09125e9i			0.198014i
$732$	3.68635e9	+	1.04100e9i	0.347383	+	0.0980981i
$733$		−	1.55538e10i		−	1.45873i	−0.684127	−	0.729363i	$-0.739816\pi$
$733$		−	1.55538e10i		−	1.45873i	0.684127	−	0.729363i	$-0.260184\pi$
$734$	5.83799e8	−	4.21552e9i	0.0544913	−	0.393473i
$735$	−1.14847e9			−0.106688
$736$	5.19633e8	−	6.32090e8i	0.0480424	−	0.0584395i
$737$	4.70720e9			0.433138
$738$	−1.08806e9	+	7.85673e9i	−0.0996453	+	0.719523i
$739$			1.07140e10i			0.976554i	0.872689	+	0.488277i	$0.162374\pi$
$739$			1.07140e10i			0.976554i	−0.872689	+	0.488277i	$0.837626\pi$
$740$	−1.10097e10	−	3.10904e9i	−0.998764	−	0.282043i
$741$		−	1.12259e10i		−	1.01358i
$742$	−8.09861e9	−	1.12156e9i	−0.727775	−	0.100788i
$743$	−5.46982e9			−0.489229			−0.244615	−	0.969620i	$-0.578661\pi$
$743$	−5.46982e9			−0.489229			−0.244615	+	0.969620i	$0.578661\pi$
$744$	2.12292e9	+	9.29859e8i	0.188985	+	0.0827774i
$745$	1.26128e9			0.111754
$746$	−5.12294e9	−	7.09467e8i	−0.451787	−	0.0625671i
$747$		−	1.50463e9i		−	0.132071i
$748$	−3.27123e9	+	1.15840e10i	−0.285795	+	1.01205i
$749$			1.98140e10i			1.72300i
$750$	−7.68561e8	+	5.54965e9i	−0.0665218	+	0.480343i
$751$	5.68185e9			0.489497			0.244749	−	0.969587i	$-0.421295\pi$
$751$	5.68185e9			0.489497			0.244749	+	0.969587i	$0.421295\pi$
$752$	−2.18076e9	−	1.33839e9i	−0.187001	−	0.114768i
$753$	7.94349e8			0.0677999
$754$	4.13697e8	−	2.98724e9i	0.0351465	−	0.253787i
$755$			1.40918e10i			1.19166i
$756$	−3.12530e9	+	1.10672e10i	−0.263067	+	0.931565i
$757$		−	5.38304e9i		−	0.451016i	−0.974241	−	0.225508i	$-0.927596\pi$
$757$		−	5.38304e9i		−	0.451016i	0.974241	−	0.225508i	$-0.0724043\pi$
$758$	2.14682e10	+	2.97310e9i	1.79042	+	0.247951i
$759$	4.18835e8			0.0347693
$760$	−4.88487e9	+	1.11524e10i	−0.403650	+	0.921555i
$761$	−3.28593e9			−0.270279			−0.135139	−	0.990827i	$-0.543148\pi$
$761$	−3.28593e9			−0.270279			−0.135139	+	0.990827i	$0.543148\pi$
$762$	−7.83803e9	−	1.08547e9i	−0.641748	−	0.0888745i
$763$			9.05334e9i			0.737858i
$764$	−8.67355e9	−	2.44934e9i	−0.703672	−	0.198711i
$765$			6.85865e9i			0.553890i
$766$	2.44988e9	−	1.76902e10i	0.196945	−	1.42211i
$767$	2.02515e10			1.62059
$768$	5.25134e9	−	2.66680e9i	0.418318	−	0.212435i
$769$	7.10914e9			0.563735			0.281868	−	0.959453i	$-0.409046\pi$
$769$	7.10914e9			0.563735			0.281868	+	0.959453i	$0.409046\pi$
$770$	1.30552e9	−	9.42698e9i	0.103055	−	0.744141i
$771$		−	3.85170e9i		−	0.302665i
$772$	−1.45184e9	−	4.09988e8i	−0.113569	−	0.0320709i
$773$		−	1.08690e10i		−	0.846370i	−0.906043	−	0.423185i	$-0.860912\pi$
$773$		−	1.08690e10i		−	0.846370i	0.906043	−	0.423185i	$-0.139088\pi$
$774$	−1.83813e9	−	2.54559e8i	−0.142489	−	0.0197331i
$775$	3.20443e9			0.247283
$776$	−4.25767e9	+	9.72049e9i	−0.327082	+	0.746745i
$777$	1.11558e10			0.853155
$778$	−2.47909e10	−	3.43325e9i	−1.88740	−	0.261383i
$779$		−	1.86886e10i		−	1.41643i
$780$	1.58820e9	−	5.62410e9i	0.119833	−	0.424348i
$781$		−	2.42523e10i		−	1.82169i
$782$	−1.48987e8	+	1.07581e9i	−0.0111410	+	0.0804475i
$783$	2.02304e9			0.150605
$784$	3.95276e9	+	2.42591e9i	0.292950	+	0.179791i
$785$	7.92802e9			0.584953
$786$	−3.98580e8	+	2.87808e9i	−0.0292777	+	0.211409i
$787$			1.94246e10i			1.42050i	0.703951	+	0.710248i	$0.251417\pi$
$787$			1.94246e10i			1.42050i	−0.703951	+	0.710248i	$0.748583\pi$
$788$	−3.12032e9	+	1.10496e10i	−0.227173	+	0.804459i
$789$			2.42958e9i			0.176101i
$790$	−4.84940e9	−	6.71584e8i	−0.349939	−	0.0484624i
$791$	−1.38164e10			−0.992606
$792$	−9.78368e9	−	4.28535e9i	−0.699784	−	0.306513i
$793$	−1.53487e10			−1.09299
$794$	1.46673e10	+	2.03124e9i	1.03987	+	0.144009i
$795$			2.78714e9i			0.196732i
$796$	4.91444e9	+	1.38780e9i	0.345365	+	0.0975283i
$797$		−	2.30309e10i		−	1.61141i	−0.592314	−	0.805707i	$-0.701786\pi$
$797$		−	2.30309e10i		−	1.61141i	0.592314	−	0.805707i	$-0.298214\pi$
$798$	1.62867e9	−	1.17604e10i	0.113455	−	0.819241i
$799$	3.39616e9			0.235545
$800$	5.17132e9	−	6.29048e9i	0.357097	−	0.434379i
$801$	−2.29810e9			−0.157999
$802$	1.62206e8	−	1.17126e9i	0.0111034	−	0.0801761i
$803$			9.38331e7i			0.00639516i
$804$	2.94201e9	+	8.30799e8i	0.199640	+	0.0563767i
$805$		−	8.58697e8i		−	0.0580169i
$806$	−9.19887e9	−	1.27393e9i	−0.618816	−	0.0856987i
$807$	−6.74814e9			−0.451988
$808$	1.28142e10	+	5.61277e9i	0.854581	+	0.374315i
$809$	−1.50546e10			−0.999656			−0.499828	−	0.866125i	$-0.666603\pi$
$809$	−1.50546e10			−0.999656			−0.499828	+	0.866125i	$0.666603\pi$
$810$	−3.84672e9	−	5.32725e8i	−0.254328	−	0.0352213i
$811$			1.98821e10i			1.30885i	0.756128	+	0.654424i	$0.227089\pi$
$811$			1.98821e10i			1.30885i	−0.756128	+	0.654424i	$0.772911\pi$
$812$	8.66786e8	−	3.06944e9i	0.0568154	−	0.201193i
$813$			6.27585e9i			0.409596i
$814$	−3.24388e9	+	2.34235e10i	−0.210804	+	1.52218i
$815$	−7.62086e9			−0.493120
$816$	−4.08904e9	+	6.66265e9i	−0.263455	+	0.429271i
$817$	4.37230e9			0.280500
$818$	3.01254e9	−	2.17530e10i	0.192440	−	1.38958i
$819$		−	2.01908e10i		−	1.28428i
$820$	2.64399e9	−	9.36284e9i	0.167460	−	0.593006i
$821$			2.29870e10i			1.44971i	0.688901	+	0.724855i	$0.258093\pi$
$821$			2.29870e10i			1.44971i	−0.688901	+	0.724855i	$0.741907\pi$
$822$	−9.32331e9	−	1.29117e9i	−0.585489	−	0.0810833i
$823$	1.46696e10			0.917316			0.458658	−	0.888613i	$-0.348330\pi$
$823$	1.46696e10			0.917316			0.458658	+	0.888613i	$0.348330\pi$
$824$	8.05629e9	−	1.83929e10i	0.501638	−	1.14527i
$825$	4.16819e9			0.258439
$826$	2.12157e10	+	2.93812e9i	1.30987	+	0.181401i
$827$		−	1.26591e9i		−	0.0778277i	−0.999243	−	0.0389138i	$-0.987610\pi$
$827$		−	1.26591e9i		−	0.0778277i	0.999243	−	0.0389138i	$-0.0123898\pi$
$828$	−9.27461e8	−	2.61908e8i	−0.0567792	−	0.0160340i
$829$			2.49778e10i			1.52270i	0.648342	+	0.761349i	$0.275463\pi$
$829$			2.49778e10i			1.52270i	−0.648342	+	0.761349i	$0.724537\pi$
$830$	−2.53173e8	+	1.82812e9i	−0.0153689	+	0.110977i
$831$	−6.92544e9			−0.418643
$832$	−1.73460e10	+	1.60020e10i	−1.04416	+	0.963261i
$833$	−6.15576e9			−0.368998
$834$	−9.54482e8	+	6.89216e9i	−0.0569753	+	0.411409i
$835$		−	4.46947e9i		−	0.265676i
$836$	2.42193e10	+	6.83935e9i	1.43364	+	0.404849i
$837$		−	6.22973e9i		−	0.367223i
$838$	2.20133e10	+	3.04858e9i	1.29220	+	0.178955i
$839$	−3.09477e10			−1.80909			−0.904547	−	0.426373i	$-0.859791\pi$
$839$	−3.09477e10			−1.80909			−0.904547	+	0.426373i	$0.859791\pi$
$840$	2.47977e9	−	5.66145e9i	0.144356	−	0.329572i
$841$	1.66888e10			0.967473
$842$	2.61314e10	+	3.61889e9i	1.50859	+	0.208921i
$843$			5.49510e9i			0.315921i
$844$	−2.30840e9	+	8.17445e9i	−0.132164	+	0.468015i
$845$			1.18137e10i			0.673577i
$846$	−4.13400e8	+	2.98509e9i	−0.0234733	+	0.169497i
$847$	8.28024e8			0.0468221
$848$	5.88727e9	−	9.59267e9i	0.331534	−	0.540199i
$849$	7.62194e8			0.0427453
$850$	−1.48270e9	+	1.07063e10i	−0.0828108	+	0.597963i
$851$			2.13363e9i			0.118677i
$852$	4.28041e9	−	1.51577e10i	0.237109	−	0.839643i
$853$		−	1.86385e10i		−	1.02823i	−0.857723	−	0.514113i	$-0.828121\pi$
$853$		−	1.86385e10i		−	1.02823i	0.857723	−	0.514113i	$-0.171879\pi$
$854$	−1.60795e10	−	2.22682e9i	−0.883426	−	0.122344i
$855$	1.43398e10			0.784623
$856$	−2.49849e10	−	1.09436e10i	−1.36151	−	0.596354i
$857$	−2.37366e10			−1.28821			−0.644103	−	0.764939i	$-0.722769\pi$
$857$	−2.37366e10			−1.28821			−0.644103	+	0.764939i	$0.722769\pi$
$858$	−1.19655e10	−	1.65708e9i	−0.646734	−	0.0895650i
$859$		−	2.46268e10i		−	1.32566i	−0.748770	−	0.662830i	$-0.769355\pi$
$859$		−	2.46268e10i		−	1.32566i	0.748770	−	0.662830i	$-0.230645\pi$
$860$	2.19049e9	+	6.18577e8i	0.117435	+	0.0331626i
$861$			9.48713e9i			0.506552i
$862$	2.68100e8	−	1.93591e9i	0.0142568	−	0.102946i
$863$	2.50051e10			1.32431			0.662157	−	0.749365i	$-0.269641\pi$
$863$	2.50051e10			1.32431			0.662157	+	0.749365i	$0.269641\pi$
$864$	−1.22293e10	−	1.00536e10i	−0.645067	−	0.530301i
$865$	−1.09184e10			−0.573592
$866$	−4.21184e9	+	3.04130e10i	−0.220373	+	1.59128i
$867$		−	1.37278e9i		−	0.0715378i
$868$	−9.45201e9	−	2.66917e9i	−0.490575	−	0.138534i
$869$			1.01194e10i			0.523102i
$870$	−1.07701e9	−	1.49152e8i	−0.0554499	−	0.00767915i
$871$	−1.22495e10			−0.628139
$872$	−1.14160e10	−	5.00033e9i	−0.583052	−	0.255382i
$873$	1.24986e10			0.635788
$874$	2.24926e9	+	3.11496e8i	0.113959	+	0.0157820i
$875$		−	2.37428e10i		−	1.19813i
$876$	−1.65611e7	+	5.86458e7i	−0.000832386	+	0.00294762i
$877$			1.07280e10i			0.537057i	0.963272	+	0.268528i	$0.0865373\pi$
$877$			1.07280e10i			0.537057i	−0.963272	+	0.268528i	$0.913463\pi$
$878$	−4.24950e8	+	3.06850e9i	−0.0211888	+	0.153001i
$879$	1.17238e10			0.582245
$880$	1.11661e10	+	6.85293e9i	0.552347	+	0.338990i
$881$	5.94499e9			0.292911			0.146455	−	0.989217i	$-0.453214\pi$
$881$	5.94499e9			0.292911			0.146455	+	0.989217i	$0.453214\pi$
$882$	7.49313e8	−	5.41067e9i	0.0367725	−	0.265528i
$883$		−	1.60870e10i		−	0.786342i	−0.919465	−	0.393171i	$-0.871378\pi$
$883$		−	1.60870e10i		−	0.786342i	0.919465	−	0.393171i	$-0.128622\pi$
$884$	8.51270e9	−	3.01449e10i	0.414462	−	1.46768i
$885$		−	7.30139e9i		−	0.354082i
$886$	−3.04877e10	−	4.22219e9i	−1.47267	−	0.203948i
$887$	−2.61884e10			−1.26001			−0.630007	−	0.776589i	$-0.716948\pi$
$887$	−2.61884e10			−1.26001			−0.630007	+	0.776589i	$0.716948\pi$
$888$	−6.16157e9	+	1.40672e10i	−0.295288	+	0.674158i
$889$	3.35330e10			1.60072
$890$	2.79219e9	+	3.86685e8i	0.132764	+	0.0183862i
$891$			8.02711e9i			0.380178i
$892$	1.93727e10	+	5.47071e9i	0.913933	+	0.258087i
$893$		−	7.10056e9i		−	0.333666i
$894$	2.32264e8	−	1.67714e9i	0.0108718	−	0.0785033i
$895$	2.22474e10			1.03729
$896$	−2.04934e10	+	1.42473e10i	−0.951781	+	0.661691i
$897$	−1.08993e9			−0.0504226
$898$	2.62460e9	−	1.89518e10i	0.120947	−	0.873340i
$899$			1.72778e9i			0.0793104i
$900$	−9.22996e9	−	2.60647e9i	−0.422038	−	0.119180i
$901$			1.49390e10i			0.680430i
$902$	−1.99198e10	−	2.75866e9i	−0.903780	−	0.125163i
$903$	−2.21957e9			−0.100314
$904$	7.63105e9	−	1.74221e10i	0.343554	−	0.784352i
$905$	5.94575e8			0.0266647
$906$	1.87381e10	+	2.59501e9i	0.837100	+	0.115928i
$907$			1.79753e9i			0.0799929i	0.999200	+	0.0399964i	$0.0127347\pi$
$907$			1.79753e9i			0.0799929i	−0.999200	+	0.0399964i	$0.987265\pi$
$908$	−6.78772e9	+	2.40365e10i	−0.300901	+	1.06554i
$909$		−	1.64766e10i		−	0.727601i
$910$	−3.39736e9	+	2.45318e10i	−0.149450	+	1.07916i
$911$	3.70021e10			1.62148			0.810740	−	0.585406i	$-0.199065\pi$
$911$	3.70021e10			1.62148			0.810740	+	0.585406i	$0.199065\pi$
$912$	1.39300e10	+	8.54920e9i	0.608091	+	0.373202i
$913$	3.81481e9			0.165892
$914$	−1.79679e8	+	1.29743e9i	−0.00778370	+	0.0562048i
$915$			5.53377e9i			0.238807i
$916$	−2.41809e9	+	8.56286e9i	−0.103953	+	0.368116i
$917$		−	1.23131e10i		−	0.527322i
$918$	2.08142e10	+	2.88252e9i	0.887995	+	0.122977i
$919$	−2.44812e10			−1.04047			−0.520234	−	0.854024i	$-0.674155\pi$
$919$	−2.44812e10			−1.04047			−0.520234	+	0.854024i	$0.674155\pi$
$920$	1.08279e9	+	4.74275e8i	0.0458446	+	0.0200804i
$921$	3.70472e9			0.156260
$922$	−1.04751e10	−	1.45068e9i	−0.440149	−	0.0609554i
$923$			6.31115e10i			2.64182i
$924$	−1.22948e10	−	3.47195e9i	−0.512707	−	0.144784i
$925$			2.12336e10i			0.882121i
$926$	2.97578e9	−	2.14876e10i	0.123158	−	0.889303i
$927$	−2.36497e10			−0.975093
$928$	3.39174e9	+	2.78830e9i	0.139317	+	0.114531i
$929$	−6.19981e9			−0.253702			−0.126851	−	0.991922i	$-0.540487\pi$
$929$	−6.19981e9			−0.253702			−0.126851	+	0.991922i	$0.540487\pi$
$930$	−4.59299e8	+	3.31652e9i	−0.0187243	+	0.135205i
$931$			1.28702e10i			0.522711i
$932$	4.70400e9	+	1.32837e9i	0.190332	+	0.0537483i
$933$		−	1.53515e10i		−	0.618820i
$934$	1.85850e10	+	2.57381e9i	0.746361	+	0.103362i
$935$	−1.73893e10			−0.695732
$936$	2.54600e10	+	1.11517e10i	1.01483	+	0.444506i
$937$	−2.78747e10			−1.10693			−0.553466	−	0.832871i	$-0.686695\pi$
$937$	−2.78747e10			−1.10693			−0.553466	+	0.832871i	$0.686695\pi$
$938$	−1.28327e10	−	1.77718e9i	−0.507702	−	0.0703107i
$939$		−	1.11096e10i		−	0.437894i
$940$	1.00456e9	−	3.55733e9i	0.0394484	−	0.139693i
$941$		−	3.45921e10i		−	1.35336i	−0.736277	−	0.676680i	$-0.763418\pi$
$941$		−	3.45921e10i		−	1.35336i	0.736277	−	0.676680i	$-0.236582\pi$
$942$	1.45994e9	−	1.05420e10i	0.0569060	−	0.410909i
$943$	−1.81448e9			−0.0704632
$944$	−1.54227e10	+	2.51296e10i	−0.596704	+	0.972264i
$945$	−1.66136e10			−0.640402
$946$	6.45404e8	−	4.66036e9i	0.0247864	−	0.178978i
$947$		−	2.20475e10i		−	0.843598i	−0.906689	−	0.421799i	$-0.861399\pi$
$947$		−	2.20475e10i		−	0.843598i	0.906689	−	0.421799i	$-0.138601\pi$
$948$	−1.78603e9	+	6.32465e9i	−0.0680863	+	0.241105i
$949$		−	2.44181e8i		−	0.00927429i
$950$	2.23844e10	+	3.09997e9i	0.847056	+	0.117307i
$951$	1.05096e10			0.396235
$952$	1.32915e10	−	3.03451e10i	0.499280	−	1.13988i
$953$	−3.95876e9			−0.148161			−0.0740805	−	0.997252i	$-0.523602\pi$
$953$	−3.95876e9			−0.148161			−0.0740805	+	0.997252i	$0.523602\pi$
$954$	−1.31308e10	−	1.81845e9i	−0.489633	−	0.0678084i
$955$		−	1.30203e10i		−	0.483737i
$956$	3.24647e10	+	9.16778e9i	1.20174	+	0.339361i
$957$			2.24743e9i			0.0828885i
$958$	6.35941e9	−	4.59203e10i	0.233689	−	1.68743i
$959$	3.98874e10			1.46040
$960$	5.76931e9	+	6.25385e9i	0.210462	+	0.228138i
$961$	−2.21921e10			−0.806615
$962$	8.44153e9	−	6.09549e10i	0.305709	−	2.20747i
$963$			3.21256e10i			1.15920i
$964$	−1.49466e10	−	4.22082e9i	−0.537371	−	0.151749i
$965$		−	2.17943e9i		−	0.0780724i
$966$	−1.14182e9	−	1.58129e8i	−0.0407548	−	0.00564406i
$967$	−9.76598e9			−0.347315			−0.173657	−	0.984806i	$-0.555559\pi$
$967$	−9.76598e9			−0.347315			−0.173657	+	0.984806i	$0.555559\pi$
$968$	−4.57333e8	+	1.04412e9i	−0.0162058	+	0.0369986i
$969$	−2.16936e10			−0.765946
$970$	−1.51858e10	−	2.10305e9i	−0.534240	−	0.0739859i
$971$			2.15553e10i			0.755589i	0.925889	+	0.377795i	$0.123317\pi$
$971$			2.15553e10i			0.755589i	−0.925889	+	0.377795i	$0.876683\pi$
$972$	−7.91420e9	+	2.80256e10i	−0.276424	+	0.978864i
$973$		−	2.94863e10i		−	1.02619i
$974$	−5.03108e9	+	3.63286e10i	−0.174464	+	1.25977i
$975$	−1.08468e10			−0.374789
$976$	1.16890e10	−	1.90459e10i	0.402441	−	0.655733i
$977$	5.24340e10			1.79880			0.899398	−	0.437131i	$-0.144005\pi$
$977$	5.24340e10			1.79880			0.899398	+	0.437131i	$0.144005\pi$
$978$	−1.40338e9	+	1.01336e10i	−0.0479722	+	0.346399i
$979$		−	5.82657e9i		−	0.198460i
$980$	−1.82083e9	+	6.44788e9i	−0.0617985	+	0.218839i
$981$			1.46787e10i			0.496417i
$982$	2.42459e10	+	3.35777e9i	0.817049	+	0.113152i
$983$	−2.85116e10			−0.957380			−0.478690	−	0.877984i	$-0.658888\pi$
$983$	−2.85116e10			−0.957380			−0.478690	+	0.877984i	$0.658888\pi$
$984$	−1.19630e10	−	5.23992e9i	−0.400275	−	0.175324i
$985$	−1.65871e10			−0.553023
$986$	−5.77271e9	−	7.99451e8i	−0.191783	−	0.0265597i
$987$			3.60455e9i			0.119328i
$988$	−6.30258e10	−	1.77980e10i	−2.07907	−	0.587113i
$989$		−	4.24509e8i		−	0.0139540i
$990$	2.11673e9	−	1.52845e10i	0.0693332	−	0.500644i
$991$	−2.72290e10			−0.888738			−0.444369	−	0.895844i	$-0.646572\pi$
$991$	−2.72290e10			−0.888738			−0.444369	+	0.895844i	$0.646572\pi$
$992$	8.58628e9	−	1.04445e10i	0.279263	−	0.339701i
$993$	−9.23324e9			−0.299248
$994$	−9.15633e9	+	6.61163e10i	−0.295712	+	2.13529i
$995$			7.37731e9i			0.237420i
$996$	2.38426e9	+	6.73296e8i	0.0764620	+	0.0215923i
$997$			1.30057e10i			0.415624i	0.978169	+	0.207812i	$0.0666343\pi$
$997$			1.30057e10i			0.415624i	−0.978169	+	0.207812i	$0.933366\pi$
$998$	−2.42865e10	−	3.36339e9i	−0.773406	−	0.107107i
$999$	4.12804e10			1.30998

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.8.b.a.5.3	✓	6
3.2	odd	2		72.8.d.b.37.4		6
4.3	odd	2		32.8.b.a.17.4		6
8.3	odd	2		32.8.b.a.17.3		6
8.5	even	2	inner	8.8.b.a.5.4	yes	6
12.11	even	2		288.8.d.b.145.4		6
16.3	odd	4		256.8.a.q.1.3		6
16.5	even	4		256.8.a.r.1.3		6
16.11	odd	4		256.8.a.q.1.4		6
16.13	even	4		256.8.a.r.1.4		6
24.5	odd	2		72.8.d.b.37.3		6
24.11	even	2		288.8.d.b.145.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.8.b.a.5.3	✓	6	1.1	even	1	trivial
8.8.b.a.5.4	yes	6	8.5	even	2	inner
32.8.b.a.17.3		6	8.3	odd	2
32.8.b.a.17.4		6	4.3	odd	2
72.8.d.b.37.3		6	24.5	odd	2
72.8.d.b.37.4		6	3.2	odd	2
256.8.a.q.1.3		6	16.3	odd	4
256.8.a.q.1.4		6	16.11	odd	4
256.8.a.r.1.3		6	16.5	even	4
256.8.a.r.1.4		6	16.13	even	4
288.8.d.b.145.3		6	24.11	even	2
288.8.d.b.145.4		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)

\(f(q)\)	\(=\)	\(q+(1.55200 - 11.2068i) q^{2} -21.9408i q^{3} +(-123.183 - 34.7858i) q^{4} -184.916i q^{5} +(-245.885 - 34.0522i) q^{6} +1051.96 q^{7} +(-581.015 + 1326.49i) q^{8} +1705.60 q^{9} +O(q^{10})\)	\(q+(1.55200 - 11.2068i) q^{2} -21.9408i q^{3} +(-123.183 - 34.7858i) q^{4} -184.916i q^{5} +(-245.885 - 34.0522i) q^{6} +1051.96 q^{7} +(-581.015 + 1326.49i) q^{8} +1705.60 q^{9} +(-2072.30 - 286.989i) q^{10} +4324.35i q^{11} +(-763.228 + 2702.73i) q^{12} -11253.2i q^{13} +(1632.64 - 11789.0i) q^{14} -4057.20 q^{15} +(13963.9 + 8570.01i) q^{16} -21746.4 q^{17} +(2647.10 - 19114.2i) q^{18} +45466.5i q^{19} +(-6432.44 + 22778.4i) q^{20} -23080.8i q^{21} +(48462.0 + 6711.41i) q^{22} +4414.37 q^{23} +(29104.2 + 12747.9i) q^{24} +43931.2 q^{25} +(-126112. - 17465.1i) q^{26} -85406.8i q^{27} +(-129583. - 36593.2i) q^{28} +23687.1i q^{29} +(-6296.78 + 45468.0i) q^{30} +72941.9 q^{31} +(117714. - 143189. i) q^{32} +94879.8 q^{33} +(-33750.5 + 243707. i) q^{34} -194523. i q^{35} +(-210100. - 59330.7i) q^{36} +483338. i q^{37} +(509532. + 70564.1i) q^{38} -246905. q^{39} +(245289. + 107439. i) q^{40} -411040. q^{41} +(-258661. - 35821.4i) q^{42} -96165.3i q^{43} +(150426. - 532685. i) q^{44} -315392. i q^{45} +(6851.11 - 49470.7i) q^{46} -156171. q^{47} +(188033. - 306379. i) q^{48} +283070. q^{49} +(68181.3 - 492326. i) q^{50} +477134. i q^{51} +(-391453. + 1.38620e6i) q^{52} -686962. i q^{53} +(-957133. - 132552. i) q^{54} +799641. q^{55} +(-611203. + 1.39541e6i) q^{56} +997572. q^{57} +(265456. + 36762.4i) q^{58} +1.79961e6i q^{59} +(499776. + 141133. i) q^{60} -1.36394e6i q^{61} +(113206. - 817441. i) q^{62} +1.79422e6 q^{63} +(-1.42199e6 - 1.54142e6i) q^{64} -2.08090e6 q^{65} +(147254. - 1.06329e6i) q^{66} -1.08853e6i q^{67} +(2.67878e6 + 756466. i) q^{68} -96854.8i q^{69} +(-2.17997e6 - 301900. i) q^{70} -5.60830e6 q^{71} +(-990980. + 2.26246e6i) q^{72} +21698.7 q^{73} +(5.41665e6 + 750142. i) q^{74} -963886. i q^{75} +(1.58159e6 - 5.60068e6i) q^{76} +4.54903e6i q^{77} +(-383197. + 2.76701e6i) q^{78} +2.34010e6 q^{79} +(1.58473e6 - 2.58214e6i) q^{80} +1.85626e6 q^{81} +(-637935. + 4.60643e6i) q^{82} -882169. i q^{83} +(-802883. + 2.84315e6i) q^{84} +4.02125e6i q^{85} +(-1.07770e6 - 149249. i) q^{86} +519714. q^{87} +(-5.73621e6 - 2.51252e6i) q^{88} -1.34738e6 q^{89} +(-3.53452e6 - 489489. i) q^{90} -1.18379e7i q^{91} +(-543773. - 153557. i) q^{92} -1.60040e6i q^{93} +(-242378. + 1.75017e6i) q^{94} +8.40746e6 q^{95} +(-3.14169e6 - 2.58274e6i) q^{96} +7.32798e6 q^{97} +(439325. - 3.17229e6i) q^{98} +7.37562e6i 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

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