LMFDB - Embedded newform 24.8.f.b.11.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [24,8,Mod(11,24)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(24, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("24.11");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 24 = 2^{3} \cdot 3 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	24.f (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:	$7.49724061162$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{6}, \sqrt{-26})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 10x^{2} + 64 $ x^4 + 10*x^2 + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.3
Root			$1.22474 - 2.54951i$ of defining polynomial
Character	$\chi$	$=$	24.11
Dual form			24.8.f.b.11.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.89898 - 10.1980i) q^{2} +(-9.00000 + 45.8912i) q^{3} +(-80.0000 - 99.9200i) q^{4} -97.9796 q^{5} +(423.909 + 316.602i) q^{6} +1548.76i q^{7} +(-1410.91 + 326.337i) q^{8} +(-2025.00 - 826.041i) q^{9} +O(q^{10})$	\(q+(4.89898 - 10.1980i) q^{2} +(-9.00000 + 45.8912i) q^{3} +(-80.0000 - 99.9200i) q^{4} -97.9796 q^{5} +(423.909 + 316.602i) q^{6} +1548.76i q^{7} +(-1410.91 + 326.337i) q^{8} +(-2025.00 - 826.041i) q^{9} +(-480.000 + 999.200i) q^{10} +1784.66i q^{11} +(5305.44 - 2772.01i) q^{12} +10141.9i q^{13} +(15794.3 + 7587.34i) q^{14} +(881.816 - 4496.40i) q^{15} +(-3584.00 + 15987.2i) q^{16} -27555.1i q^{17} +(-18344.4 + 16604.3i) q^{18} +11570.0 q^{19} +(7838.37 + 9790.12i) q^{20} +(-71074.4 - 13938.8i) q^{21} +(18200.0 + 8743.00i) q^{22} -55534.8 q^{23} +(-2277.85 - 67685.2i) q^{24} -68525.0 q^{25} +(103427. + 49684.8i) q^{26} +(56133.0 - 85495.3i) q^{27} +(154752. - 123901. i) q^{28} +54770.6 q^{29} +(-41534.4 - 31020.6i) q^{30} -71692.6i q^{31} +(145480. + 114871. i) q^{32} +(-81900.0 - 16061.9i) q^{33} +(-281008. - 134992. i) q^{34} -151747. i q^{35} +(79462.0 + 268421. i) q^{36} +282823. i q^{37} +(56681.2 - 117991. i) q^{38} +(-465423. - 91276.9i) q^{39} +(138240. - 31974.4i) q^{40} +403638. i q^{41} +(-490341. + 656533. i) q^{42} +495062. q^{43} +(178323. - 142773. i) q^{44} +(198409. + 80935.2i) q^{45} +(-272064. + 566346. i) q^{46} +1.13594e6 q^{47} +(-701415. - 308359. i) q^{48} -1.57511e6 q^{49} +(-335703. + 698821. i) q^{50} +(1.26454e6 + 247996. i) q^{51} +(1.01338e6 - 811350. i) q^{52} +572416. q^{53} +(-596890. - 991286. i) q^{54} -174860. i q^{55} +(-505418. - 2.18515e6i) q^{56} +(-104130. + 530961. i) q^{57} +(268320. - 558553. i) q^{58} +1.44050e6i q^{59} +(-519825. + 271601. i) q^{60} +1.78632e6i q^{61} +(-731124. - 351220. i) q^{62} +(1.27934e6 - 3.13624e6i) q^{63} +(1.88416e6 - 920862. i) q^{64} -993697. i q^{65} +(-565026. + 756532. i) q^{66} +1.40013e6 q^{67} +(-2.75330e6 + 2.20441e6i) q^{68} +(499813. - 2.54856e6i) q^{69} +(-1.54752e6 - 743405. i) q^{70} -3.56947e6 q^{71} +(3.12665e6 + 504634. i) q^{72} -2.22360e6 q^{73} +(2.88424e6 + 1.38555e6i) q^{74} +(616725. - 3.14469e6i) q^{75} +(-925600. - 1.15607e6i) q^{76} -2.76400e6 q^{77} +(-3.21094e6 + 4.29923e6i) q^{78} +5.59057e6i q^{79} +(351159. - 1.56642e6i) q^{80} +(3.41828e6 + 3.34547e6i) q^{81} +(4.11632e6 + 1.97742e6i) q^{82} -3.01333e6i q^{83} +(4.29318e6 + 8.21686e6i) q^{84} +2.69984e6i q^{85} +(2.42530e6 - 5.04866e6i) q^{86} +(-492935. + 2.51349e6i) q^{87} +(-582400. - 2.51798e6i) q^{88} -5.84533e6i q^{89} +(1.79738e6 - 1.62688e6i) q^{90} -1.57073e7 q^{91} +(4.44279e6 + 5.54904e6i) q^{92} +(3.29006e6 + 645233. i) q^{93} +(5.56493e6 - 1.15843e7i) q^{94} -1.13362e6 q^{95} +(-6.58087e6 + 5.64242e6i) q^{96} +6.86793e6 q^{97} +(-7.71645e6 + 1.60631e7i) q^{98} +(1.47420e6 - 3.61393e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 36 q^{3} - 320 q^{4} + 1872 q^{6} - 8100 q^{9}+O(q^{10}) $ 4 * q - 36 * q^3 - 320 * q^4 + 1872 * q^6 - 8100 * q^9	$ 4 q - 36 q^{3} - 320 q^{4} + 1872 q^{6} - 8100 q^{9} - 1920 q^{10} + 2880 q^{12} - 14336 q^{16} - 33696 q^{18} + 46280 q^{19} + 72800 q^{22} - 59904 q^{24} - 274100 q^{25} + 224532 q^{27} + 619008 q^{28} + 17280 q^{30} - 327600 q^{33} - 1124032 q^{34} + 648000 q^{36} + 552960 q^{40} - 1392768 q^{42} + 1980248 q^{43} - 1088256 q^{46} + 129024 q^{48} - 6300452 q^{49} + 5058144 q^{51} + 4053504 q^{52} - 3487536 q^{54} - 416520 q^{57} + 1073280 q^{58} - 1797120 q^{60} + 7536640 q^{64} - 655200 q^{66} + 5600504 q^{67} - 6190080 q^{70} + 1078272 q^{72} - 8894392 q^{73} + 2466900 q^{75} - 3702400 q^{76} - 9120384 q^{78} + 13673124 q^{81} + 16465280 q^{82} - 5571072 q^{84} - 2329600 q^{88} + 3888000 q^{90} - 62829312 q^{91} + 22259712 q^{94} - 21086208 q^{96} + 27471704 q^{97} + 5896800 q^{99}+O(q^{100}) $ 4 * q - 36 * q^3 - 320 * q^4 + 1872 * q^6 - 8100 * q^9 - 1920 * q^10 + 2880 * q^12 - 14336 * q^16 - 33696 * q^18 + 46280 * q^19 + 72800 * q^22 - 59904 * q^24 - 274100 * q^25 + 224532 * q^27 + 619008 * q^28 + 17280 * q^30 - 327600 * q^33 - 1124032 * q^34 + 648000 * q^36 + 552960 * q^40 - 1392768 * q^42 + 1980248 * q^43 - 1088256 * q^46 + 129024 * q^48 - 6300452 * q^49 + 5058144 * q^51 + 4053504 * q^52 - 3487536 * q^54 - 416520 * q^57 + 1073280 * q^58 - 1797120 * q^60 + 7536640 * q^64 - 655200 * q^66 + 5600504 * q^67 - 6190080 * q^70 + 1078272 * q^72 - 8894392 * q^73 + 2466900 * q^75 - 3702400 * q^76 - 9120384 * q^78 + 13673124 * q^81 + 16465280 * q^82 - 5571072 * q^84 - 2329600 * q^88 + 3888000 * q^90 - 62829312 * q^91 + 22259712 * q^94 - 21086208 * q^96 + 27471704 * q^97 + 5896800 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/24\mathbb{Z}\right)^\times$.

$n$	$7$	$13$	$17$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	4.89898	−	10.1980i	0.433013	−	0.901388i
$2$	4.89898	−	10.1980i	0.433013	−	0.901388i
$3$	−9.00000	+	45.8912i	−0.192450	+	0.981307i
$3$	−9.00000	+	45.8912i	−0.192450	+	0.981307i
$4$	−80.0000	−	99.9200i	−0.625000	−	0.780625i
$5$	−97.9796			−0.350542			−0.175271	−	0.984520i	$-0.556080\pi$
$5$	−97.9796			−0.350542			−0.175271	+	0.984520i	$0.556080\pi$
$6$	423.909	+	316.602i	0.801205	+	0.598390i
$7$			1548.76i			1.70664i	0.521391	+	0.853318i	$0.325413\pi$
$7$			1548.76i			1.70664i	−0.521391	+	0.853318i	$0.674587\pi$
$8$	−1410.91	+	326.337i	−0.974279	+	0.225347i
$9$	−2025.00	−	826.041i	−0.925926	−	0.377705i
$10$	−480.000	+	999.200i	−0.151789	+	0.315975i
$11$			1784.66i			0.404278i	0.979357	+	0.202139i	$0.0647893\pi$
$11$			1784.66i			0.404278i	−0.979357	+	0.202139i	$0.935211\pi$
$12$	5305.44	−	2772.01i	0.886314	−	0.463085i
$13$			10141.9i			1.28031i	0.768244	+	0.640157i	$0.221131\pi$
$13$			10141.9i			1.28031i	−0.768244	+	0.640157i	$0.778869\pi$
$14$	15794.3	+	7587.34i	1.53834	+	0.738995i
$15$	881.816	−	4496.40i	0.0674619	−	0.343990i
$16$	−3584.00	+	15987.2i	−0.218750	+	0.975781i
$17$		−	27555.1i		−	1.36029i	−0.733079	−	0.680144i	$-0.761917\pi$
$17$		−	27555.1i		−	1.36029i	0.733079	−	0.680144i	$-0.238083\pi$
$18$	−18344.4	+	16604.3i	−0.741397	+	0.671067i
$19$	11570.0			0.386986			0.193493	−	0.981102i	$-0.438018\pi$
$19$	11570.0			0.386986			0.193493	+	0.981102i	$0.438018\pi$
$20$	7838.37	+	9790.12i	0.219089	+	0.273642i
$21$	−71074.4	−	13938.8i	−1.67473	−	0.328442i
$22$	18200.0	+	8743.00i	0.364411	+	0.175058i
$23$	−55534.8			−0.951739			−0.475870	−	0.879516i	$-0.657867\pi$
$23$	−55534.8			−0.951739			−0.475870	+	0.879516i	$0.657867\pi$
$24$	−2277.85	−	67685.2i	−0.0336345	−	0.999434i
$25$	−68525.0			−0.877120
$26$	103427.	+	49684.8i	1.15406	+	0.554392i
$27$	56133.0	−	85495.3i	0.548839	−	0.835928i
$28$	154752.	−	123901.i	1.33224	−	1.06665i
$29$	54770.6			0.417018			0.208509	−	0.978020i	$-0.433139\pi$
$29$	54770.6			0.417018			0.208509	+	0.978020i	$0.433139\pi$
$30$	−41534.4	−	31020.6i	−0.280856	−	0.209761i
$31$		−	71692.6i		−	0.432223i	−0.976369	−	0.216112i	$-0.930662\pi$
$31$		−	71692.6i		−	0.432223i	0.976369	−	0.216112i	$-0.0693375\pi$
$32$	145480.	+	114871.i	0.784836	+	0.619704i
$33$	−81900.0	−	16061.9i	−0.396721	−	0.0778034i
$34$	−281008.	−	134992.i	−1.22615	−	0.589022i
$35$		−	151747.i		−	0.598248i
$36$	79462.0	+	268421.i	0.283858	+	0.958866i
$37$			282823.i			0.917930i	0.888454	+	0.458965i	$0.151780\pi$
$37$			282823.i			0.917930i	−0.888454	+	0.458965i	$0.848220\pi$
$38$	56681.2	−	117991.i	0.167570	−	0.348825i
$39$	−465423.	−	91276.9i	−1.25638	−	0.246397i
$40$	138240.	−	31974.4i	0.341526	−	0.0789937i
$41$			403638.i			0.914637i	0.889303	+	0.457319i	$0.151190\pi$
$41$			403638.i			0.914637i	−0.889303	+	0.457319i	$0.848810\pi$
$42$	−490341.	+	656533.i	−1.02123	+	1.36736i
$43$	495062.			0.949555			0.474777	−	0.880106i	$-0.342529\pi$
$43$	495062.			0.949555			0.474777	+	0.880106i	$0.342529\pi$
$44$	178323.	−	142773.i	0.315590	−	0.252674i
$45$	198409.	+	80935.2i	0.324576	+	0.132402i
$46$	−272064.	+	566346.i	−0.412115	+	0.857886i
$47$	1.13594e6			1.59592			0.797961	−	0.602710i	$-0.205912\pi$
$47$	1.13594e6			1.59592			0.797961	+	0.602710i	$0.205912\pi$
$48$	−701415.	−	308359.i	−0.915442	−	0.402450i
$49$	−1.57511e6			−1.91261
$50$	−335703.	+	698821.i	−0.379804	+	0.790625i
$51$	1.26454e6	+	247996.i	1.33486	+	0.261788i
$52$	1.01338e6	−	811350.i	0.999445	−	0.800196i
$53$	572416.			0.528137			0.264068	−	0.964504i	$-0.414936\pi$
$53$	572416.			0.528137			0.264068	+	0.964504i	$0.414936\pi$
$54$	−596890.	−	991286.i	−0.515841	−	0.856684i
$55$		−	174860.i		−	0.141717i
$56$	−505418.	−	2.18515e6i	−0.384585	−	1.66274i
$57$	−104130.	+	530961.i	−0.0744756	+	0.379752i
$58$	268320.	−	558553.i	0.180574	−	0.375895i
$59$			1.44050e6i			0.913129i	0.889690	+	0.456565i	$0.150920\pi$
$59$			1.44050e6i			0.913129i	−0.889690	+	0.456565i	$0.849080\pi$
$60$	−519825.	+	271601.i	−0.310691	+	0.162331i
$61$			1.78632e6i			1.00764i	0.863809	+	0.503819i	$0.168072\pi$
$61$			1.78632e6i			1.00764i	−0.863809	+	0.503819i	$0.831928\pi$
$62$	−731124.	−	351220.i	−0.389601	−	0.187158i
$63$	1.27934e6	−	3.13624e6i	0.644605	−	1.58022i
$64$	1.88416e6	−	920862.i	0.898438	−	0.439101i
$65$		−	993697.i		−	0.448804i
$66$	−565026.	+	756532.i	−0.241916	+	0.323910i
$67$	1.40013e6			0.568729			0.284364	−	0.958716i	$-0.408217\pi$
$67$	1.40013e6			0.568729			0.284364	+	0.958716i	$0.408217\pi$
$68$	−2.75330e6	+	2.20441e6i	−1.06187	+	0.850180i
$69$	499813.	−	2.54856e6i	0.183162	−	0.933948i
$70$	−1.54752e6	−	743405.i	−0.539254	−	0.259049i
$71$	−3.56947e6			−1.18359			−0.591793	−	0.806090i	$-0.701580\pi$
$71$	−3.56947e6			−1.18359			−0.591793	+	0.806090i	$0.701580\pi$
$72$	3.12665e6	+	504634.i	0.987225	+	0.159335i
$73$	−2.22360e6			−0.669000			−0.334500	−	0.942396i	$-0.608567\pi$
$73$	−2.22360e6			−0.669000			−0.334500	+	0.942396i	$0.608567\pi$
$74$	2.88424e6	+	1.38555e6i	0.827411	+	0.397475i
$75$	616725.	−	3.14469e6i	0.168802	−	0.860724i
$76$	−925600.	−	1.15607e6i	−0.241867	−	0.302091i
$77$	−2.76400e6			−0.689956
$78$	−3.21094e6	+	4.29923e6i	−0.766128	+	1.02579i
$79$			5.59057e6i			1.27574i	0.770145	+	0.637869i	$0.220184\pi$
$79$			5.59057e6i			1.27574i	−0.770145	+	0.637869i	$0.779816\pi$
$80$	351159.	−	1.56642e6i	0.0766812	−	0.342053i
$81$	3.41828e6	+	3.34547e6i	0.714678	+	0.699454i
$82$	4.11632e6	+	1.97742e6i	0.824443	+	0.396050i
$83$		−	3.01333e6i		−	0.578459i	−0.957260	−	0.289230i	$-0.906601\pi$
$83$		−	3.01333e6i		−	0.578459i	0.957260	−	0.289230i	$-0.0933991\pi$
$84$	4.29318e6	+	8.21686e6i	0.790318	+	1.51261i
$85$			2.69984e6i			0.476839i
$86$	2.42530e6	−	5.04866e6i	0.411169	−	0.855917i
$87$	−492935.	+	2.51349e6i	−0.0802551	+	0.409222i
$88$	−582400.	−	2.51798e6i	−0.0911029	−	0.393880i
$89$		−	5.84533e6i		−	0.878910i	−0.898265	−	0.439455i	$-0.855172\pi$
$89$		−	5.84533e6i		−	0.878910i	0.898265	−	0.439455i	$-0.144828\pi$
$90$	1.79738e6	−	1.62688e6i	0.259891	−	0.235238i
$91$	−1.57073e7			−2.18503
$92$	4.44279e6	+	5.54904e6i	0.594837	+	0.742951i
$93$	3.29006e6	+	645233.i	0.424144	+	0.0831814i
$94$	5.56493e6	−	1.15843e7i	0.691054	−	1.43854i
$95$	−1.13362e6			−0.135655
$96$	−6.58087e6	+	5.64242e6i	−0.759162	+	0.650902i
$97$	6.86793e6			0.764055			0.382027	−	0.924151i	$-0.375226\pi$
$97$	6.86793e6			0.764055			0.382027	+	0.924151i	$0.375226\pi$
$98$	−7.71645e6	+	1.60631e7i	−0.828183	+	1.72400i
$99$	1.47420e6	−	3.61393e6i	0.152698	−	0.374332i
$100$	5.48200e6	+	6.84702e6i	0.548200	+	0.684702i
$101$	−1.14364e7			−1.10449			−0.552246	−	0.833681i	$-0.686229\pi$
$101$	−1.14364e7			−1.10449			−0.552246	+	0.833681i	$0.686229\pi$
$102$	8.72401e6	−	1.16809e7i	0.813983	−	1.08987i
$103$		−	1.03302e6i		−	0.0931493i	−0.998915	−	0.0465746i	$-0.985169\pi$
$103$		−	1.03302e6i		−	0.0931493i	0.998915	−	0.0465746i	$-0.0148305\pi$
$104$	−3.30967e6	−	1.43092e7i	−0.288515	−	1.24738i
$105$	6.96384e6	+	1.36572e6i	0.587065	+	0.115133i
$106$	2.80426e6	−	5.83752e6i	0.228690	−	0.476056i
$107$			1.85726e7i			1.46565i	0.680419	+	0.732824i	$0.261798\pi$
$107$			1.85726e7i			1.46565i	−0.680419	+	0.732824i	$0.738202\pi$
$108$	−1.30333e7	+	1.23081e6i	−0.995571	+	0.0940176i
$109$		−	1.22187e7i		−	0.903714i	−0.892090	−	0.451857i	$-0.850762\pi$
$109$		−	1.22187e7i		−	0.903714i	0.892090	−	0.451857i	$-0.149238\pi$
$110$	−1.78323e6	−	856635.i	−0.127742	−	0.0613651i
$111$	−1.29791e7	−	2.54541e6i	−0.900771	−	0.176656i
$112$	−2.47603e7	−	5.55075e6i	−1.66530	−	0.373327i
$113$		−	1.41210e7i		−	0.920641i	−0.887753	−	0.460320i	$-0.847735\pi$
$113$		−	1.41210e7i		−	0.920641i	0.887753	−	0.460320i	$-0.152265\pi$
$114$	4.90463e6	+	3.66309e6i	0.310055	+	0.231569i
$115$	5.44128e6			0.333625
$116$	−4.38165e6	−	5.47268e6i	−0.260636	−	0.325534i
$117$	8.37761e6	−	2.05373e7i	0.483581	−	1.18548i
$118$	1.46903e7	+	7.05700e6i	0.823084	+	0.395397i
$119$	4.26762e7			2.32152
$120$	223182.	+	6.63177e6i	0.0117903	+	0.350344i
$121$	1.63022e7			0.836559
$122$	1.82170e7	+	8.75114e6i	0.908273	+	0.436320i
$123$	−1.85234e7	−	3.63275e6i	−0.897540	−	0.176022i
$124$	−7.16352e6	+	5.73541e6i	−0.337404	+	0.270140i
$125$	1.43687e7			0.658010
$126$	−2.57160e7	−	2.84111e7i	−1.14527	−	1.26529i
$127$			1.07474e7i			0.465578i	0.972527	+	0.232789i	$0.0747851\pi$
$127$			1.07474e7i			0.465578i	−0.972527	+	0.232789i	$0.925215\pi$
$128$	−160530.	−	2.37260e7i	−0.00676582	−	0.999977i
$129$	−4.45556e6	+	2.27190e7i	−0.182742	+	0.931804i
$130$	−1.01338e7	−	4.86810e6i	−0.404547	−	0.194338i
$131$			3.13305e7i			1.21764i	0.793310	+	0.608818i	$0.208356\pi$
$131$			3.13305e7i			1.21764i	−0.793310	+	0.608818i	$0.791644\pi$
$132$	4.94709e6	+	9.46840e6i	0.187215	+	0.358317i
$133$			1.79191e7i			0.660445i
$134$	6.85919e6	−	1.42785e7i	0.246267	−	0.512645i
$135$	−5.49989e6	+	8.37679e6i	−0.192391	+	0.293028i
$136$	8.99226e6	+	3.88777e7i	0.306537	+	1.32530i
$137$			5.53966e6i			0.184061i	0.995756	+	0.0920303i	$0.0293357\pi$
$137$			5.53966e6i			0.184061i	−0.995756	+	0.0920303i	$0.970664\pi$
$138$	−2.35417e7	−	1.75825e7i	−0.762538	−	0.569512i
$139$	−1.34182e7			−0.423783			−0.211891	−	0.977293i	$-0.567962\pi$
$139$	−1.34182e7			−0.423783			−0.211891	+	0.977293i	$0.567962\pi$
$140$	−1.51625e7	+	1.21397e7i	−0.467007	+	0.373905i
$141$	−1.02234e7	+	5.21294e7i	−0.307135	+	1.56609i
$142$	−1.74868e7	+	3.64016e7i	−0.512508	+	1.06687i
$143$	−1.80998e7			−0.517603
$144$	2.04637e7	−	2.94135e7i	0.571104	−	0.820878i
$145$	−5.36640e6			−0.146182
$146$	−1.08934e7	+	2.26763e7i	−0.289686	+	0.603029i
$147$	1.41760e7	−	7.22838e7i	0.368081	−	1.87685i
$148$	2.82597e7	−	2.26259e7i	0.716559	−	0.573706i
$149$	2.09354e7			0.518477			0.259238	−	0.965813i	$-0.416528\pi$
$149$	2.09354e7			0.518477			0.259238	+	0.965813i	$0.416528\pi$
$150$	−2.90484e7	−	2.16952e7i	−0.702753	−	0.524860i
$151$		−	3.02970e7i		−	0.716111i	−0.933700	−	0.358055i	$-0.883440\pi$
$151$		−	3.02970e7i		−	0.716111i	0.933700	−	0.358055i	$-0.116560\pi$
$152$	−1.63242e7	+	3.77572e6i	−0.377033	+	0.0872062i
$153$	−2.27616e7	+	5.57991e7i	−0.513788	+	1.25953i
$154$	−1.35408e7	+	2.81874e7i	−0.298760	+	0.621918i
$155$			7.02441e6i			0.151513i
$156$	2.81134e7	+	5.38072e7i	0.592895	+	1.13476i
$157$		−	8.03861e7i		−	1.65780i	−0.559397	−	0.828900i	$-0.688967\pi$
$157$		−	8.03861e7i		−	1.65780i	0.559397	−	0.828900i	$-0.311033\pi$
$158$	5.70129e7	+	2.73881e7i	1.14993	+	0.552411i
$159$	−5.15175e6	+	2.62689e7i	−0.101640	+	0.518264i
$160$	−1.42541e7	−	1.12550e7i	−0.275118	−	0.217233i
$161$		−	8.60101e7i		−	1.62427i
$162$	5.08633e7	−	1.84704e7i	0.939944	−	0.341329i
$163$	1.08125e8			1.95554			0.977772	−	0.209669i	$-0.0672388\pi$
$163$	1.08125e8			1.95554			0.977772	+	0.209669i	$0.0672388\pi$
$164$	4.03315e7	−	3.22911e7i	0.713989	−	0.571648i
$165$	8.02453e6	+	1.57374e6i	0.139068	+	0.0272734i
$166$	−3.07300e7	−	1.47622e7i	−0.521416	−	0.250480i
$167$	−3.92926e7			−0.652834			−0.326417	−	0.945226i	$-0.605841\pi$
$167$	−3.92926e7			−0.652834			−0.326417	+	0.945226i	$0.605841\pi$
$168$	1.04828e8	−	3.52783e6i	1.70567	−	0.0574018i
$169$	−4.01091e7			−0.639205
$170$	2.75330e7	+	1.32264e7i	0.429816	+	0.206477i
$171$	−2.34292e7	−	9.55730e6i	−0.358321	−	0.146167i
$172$	−3.96050e7	−	4.94666e7i	−0.593472	−	0.741246i
$173$	−1.29099e8			−1.89566			−0.947831	−	0.318772i	$-0.896730\pi$
$173$	−1.29099e8			−1.89566			−0.947831	+	0.318772i	$0.896730\pi$
$174$	2.32178e7	+	1.73405e7i	0.334116	+	0.249539i
$175$		−	1.06129e8i		−	1.49692i
$176$	−2.85317e7	−	6.39621e6i	−0.394487	−	0.0884359i
$177$	−6.61064e7	−	1.29645e7i	−0.896060	−	0.175732i
$178$	−5.96109e7	−	2.86362e7i	−0.792238	−	0.380579i
$179$		−	2.75640e6i		−	0.0359216i	−0.999839	−	0.0179608i	$-0.994283\pi$
$179$		−	2.75640e6i		−	0.0359216i	0.999839	−	0.0179608i	$-0.00571741\pi$
$180$	−7.78565e6	−	2.62998e7i	−0.0995042	−	0.336123i
$181$			1.11231e8i			1.39428i	0.716933	+	0.697142i	$0.245545\pi$
$181$			1.11231e8i			1.39428i	−0.716933	+	0.697142i	$0.754455\pi$
$182$	−7.69499e7	+	1.60184e8i	−0.946146	+	1.96956i
$183$	−8.19763e7	−	1.60769e7i	−0.988802	−	0.193920i
$184$	7.83544e7	−	1.81231e7i	0.927259	−	0.214472i
$185$		−	2.77109e7i		−	0.321773i
$186$	2.26980e7	−	3.03911e7i	0.258638	−	0.346299i
$187$	4.91764e7			0.549935
$188$	−9.08749e7	−	1.13503e8i	−0.997451	−	1.24582i
$189$	1.32412e8	+	8.69365e7i	1.42662	+	0.936669i
$190$	−5.55360e6	+	1.15607e7i	−0.0587404	+	0.122278i
$191$	1.09860e8			1.14084			0.570418	−	0.821354i	$-0.306781\pi$
$191$	1.09860e8			1.14084			0.570418	+	0.821354i	$0.306781\pi$
$192$	2.53020e7	+	9.47541e7i	0.257989	+	0.966148i
$193$	−5.60296e7			−0.561005			−0.280502	−	0.959853i	$-0.590501\pi$
$193$	−5.60296e7			−0.561005			−0.280502	+	0.959853i	$0.590501\pi$
$194$	3.36458e7	−	7.00394e7i	0.330845	−	0.688710i
$195$	4.56019e7	+	8.94327e6i	0.440415	+	0.0863725i
$196$	1.26009e8	+	1.57385e8i	1.19538	+	1.49303i
$197$	−9.45130e7			−0.880765			−0.440382	−	0.897810i	$-0.645157\pi$
$197$	−9.45130e7			−0.880765			−0.440382	+	0.897810i	$0.645157\pi$
$198$	−2.96329e7	−	3.27385e7i	−0.271298	−	0.299730i
$199$			9.00414e7i			0.809947i	0.914328	+	0.404974i	$0.132719\pi$
$199$			9.00414e7i			0.809947i	−0.914328	+	0.404974i	$0.867281\pi$
$200$	9.66823e7	−	2.23623e7i	0.854559	−	0.197656i
$201$	−1.26011e7	+	6.42534e7i	−0.109452	+	0.558098i
$202$	−5.60265e7	+	1.16628e8i	−0.478259	+	0.995576i
$203$			8.48265e7i			0.711697i
$204$	−7.63831e7	−	1.46192e8i	−0.629929	−	1.20564i
$205$		−	3.95483e7i		−	0.320619i
$206$	−1.05348e7	−	5.06076e6i	−0.0839636	−	0.0403348i
$207$	1.12458e8	+	4.58741e7i	0.881240	+	0.359477i
$208$	−1.62140e8	−	3.63485e7i	−1.24931	−	0.280069i
$209$			2.06485e7i			0.156450i
$210$	4.80434e7	−	6.43269e7i	0.357986	−	0.479319i
$211$	−9.47083e7			−0.694064			−0.347032	−	0.937853i	$-0.612810\pi$
$211$	−9.47083e7			−0.694064			−0.347032	+	0.937853i	$0.612810\pi$
$212$	−4.57933e7	−	5.71958e7i	−0.330086	−	0.412277i
$213$	3.21253e7	−	1.63807e8i	0.227781	−	1.16146i
$214$	1.89404e8	+	9.09868e7i	1.32112	+	0.634644i
$215$	−4.85060e7			−0.332859
$216$	−5.12981e7	+	1.38944e8i	−0.346348	+	0.938106i
$217$	1.11035e8			0.737648
$218$	−1.24606e8	−	5.98590e7i	−0.814597	−	0.391320i
$219$	2.00124e7	−	1.02044e8i	0.128749	−	0.656494i
$220$	−1.74720e7	+	1.39888e7i	−0.110628	+	0.0885729i
$221$	2.79460e8			1.74160
$222$	−8.95426e7	+	1.19891e8i	−0.549280	+	0.735450i
$223$			1.44671e7i			0.0873601i	0.999046	+	0.0436801i	$0.0139082\pi$
$223$			1.44671e7i			0.0873601i	−0.999046	+	0.0436801i	$0.986092\pi$
$224$	−1.77907e8	+	2.25314e8i	−1.05761	+	1.33943i
$225$	1.38763e8	+	5.66045e7i	0.812148	+	0.331293i
$226$	−1.44006e8	−	6.91784e7i	−0.829855	−	0.398649i
$227$			3.50766e7i			0.199034i	0.995036	+	0.0995169i	$0.0317297\pi$
$227$			3.50766e7i			0.199034i	−0.995036	+	0.0995169i	$0.968270\pi$
$228$	6.13840e7	−	3.20722e7i	0.342991	−	0.179208i
$229$			1.01759e7i			0.0559949i	0.999608	+	0.0279975i	$0.00891303\pi$
$229$			1.01759e7i			0.0559949i	−0.999608	+	0.0279975i	$0.991087\pi$
$230$	2.66567e7	−	5.54904e7i	0.144464	−	0.300726i
$231$	2.48760e7	−	1.26843e8i	0.132782	−	0.677058i
$232$	−7.72762e7	+	1.78737e7i	−0.406291	+	0.0939737i
$233$			1.39333e8i			0.721621i	0.932639	+	0.360811i	$0.117500\pi$
$233$			1.39333e8i			0.721621i	−0.932639	+	0.360811i	$0.882500\pi$
$234$	−1.68398e8	−	1.86047e8i	−0.859177	−	0.949221i
$235$	−1.11299e8			−0.559438
$236$	1.43935e8	−	1.15240e8i	0.712811	−	0.570706i
$237$	−2.56558e8	−	5.03151e7i	−1.25189	−	0.245516i
$238$	2.09070e8	−	4.35214e8i	1.00525	−	2.09259i
$239$	−6.12372e7			−0.290150			−0.145075	−	0.989421i	$-0.546342\pi$
$239$	−6.12372e7			−0.290150			−0.145075	+	0.989421i	$0.546342\pi$
$240$	6.87244e7	+	3.02129e7i	0.320901	+	0.141076i
$241$	1.39554e8			0.642218			0.321109	−	0.947042i	$-0.395944\pi$
$241$	1.39554e8			0.642218			0.321109	+	0.947042i	$0.395944\pi$
$242$	7.98640e7	−	1.66250e8i	0.362241	−	0.754064i
$243$	−1.84292e8	+	1.26760e8i	−0.823919	+	0.566708i
$244$	1.78489e8	−	1.42906e8i	0.786587	−	0.629774i
$245$	1.54329e8			0.670449
$246$	−1.27793e8	+	1.71106e8i	−0.547310	+	0.732812i
$247$			1.17342e8i			0.495464i
$248$	2.33960e7	+	1.01151e8i	0.0974002	+	0.421106i
$249$	1.38285e8	+	2.71199e7i	0.567646	+	0.111325i
$250$	7.03920e7	−	1.46533e8i	0.284927	−	0.593122i
$251$		−	3.29413e7i		−	0.131487i	−0.997837	−	0.0657436i	$-0.979058\pi$
$251$		−	3.29413e7i		−	0.131487i	0.997837	−	0.0657436i	$-0.0209419\pi$
$252$	−4.15720e8	+	1.23068e8i	−1.63644	+	0.484442i
$253$		−	9.91106e7i		−	0.384767i
$254$	1.09603e8	+	5.26515e7i	0.419666	+	0.201601i
$255$	−1.23899e8	−	2.42985e7i	−0.467925	−	0.0917676i
$256$	−2.42745e8	−	1.14596e8i	−0.904297	−	0.426904i
$257$		−	3.21918e8i		−	1.18299i	−0.806310	−	0.591493i	$-0.798539\pi$
$257$		−	3.21918e8i		−	1.18299i	0.806310	−	0.591493i	$-0.201461\pi$
$258$	2.09861e8	+	1.56738e8i	0.760788	+	0.568204i
$259$	−4.38026e8			−1.56657
$260$	−9.92902e7	+	7.94958e7i	−0.350348	+	0.280503i
$261$	−1.10910e8	−	4.52428e7i	−0.386127	−	0.157510i
$262$	3.19509e8	+	1.53487e8i	1.09756	+	0.527252i
$263$	3.65537e8			1.23904			0.619521	−	0.784980i	$-0.287327\pi$
$263$	3.65537e8			1.23904			0.619521	+	0.784980i	$0.287327\pi$
$264$	1.20795e8	−	4.06517e6i	0.404049	−	0.0135977i
$265$	−5.60851e7			−0.185134
$266$	1.82740e8	+	8.77855e7i	0.595317	+	0.285981i
$267$	2.68249e8	+	5.26080e7i	0.862480	+	0.169146i
$268$	−1.12010e8	−	1.39901e8i	−0.355456	−	0.443964i
$269$	−3.85128e8			−1.20635			−0.603173	−	0.797611i	$-0.706097\pi$
$269$	−3.85128e8			−1.20635			−0.603173	+	0.797611i	$0.706097\pi$
$270$	5.84830e7	+	9.71258e7i	0.180824	+	0.300304i
$271$			3.67394e8i			1.12135i	0.828037	+	0.560673i	$0.189457\pi$
$271$			3.67394e8i			1.12135i	−0.828037	+	0.560673i	$0.810543\pi$
$272$	4.40529e8	+	9.87575e7i	1.32734	+	0.297563i
$273$	1.41366e8	−	7.20828e8i	0.420509	−	2.14418i
$274$	5.64936e7	+	2.71387e7i	0.165910	+	0.0797006i
$275$		−	1.22294e8i		−	0.354600i
$276$	−2.94637e8	+	1.53943e8i	−0.843540	+	0.440737i
$277$			8.69908e6i			0.0245920i	0.999924	+	0.0122960i	$0.00391404\pi$
$277$			8.69908e6i			0.0245920i	−0.999924	+	0.0122960i	$0.996086\pi$
$278$	−6.57356e7	+	1.36840e8i	−0.183503	+	0.381993i
$279$	−5.92210e7	+	1.45177e8i	−0.163253	+	0.400207i
$280$	4.95206e7	+	2.14101e8i	0.134813	+	0.582860i
$281$			4.68539e8i			1.25972i	0.776710	+	0.629859i	$0.216887\pi$
$281$			4.68539e8i			1.25972i	−0.776710	+	0.629859i	$0.783113\pi$
$282$	4.81534e8	+	3.59640e8i	1.27866	+	0.954984i
$283$	1.79280e8			0.470197			0.235099	−	0.971972i	$-0.424459\pi$
$283$	1.79280e8			0.470197			0.235099	+	0.971972i	$0.424459\pi$
$284$	2.85558e8	+	3.56662e8i	0.739742	+	0.923937i
$285$	1.02026e7	−	5.20233e7i	0.0261069	−	0.133119i
$286$	−8.86704e7	+	1.84582e8i	−0.224129	+	0.466561i
$287$	−6.25139e8			−1.56095
$288$	−1.99709e8	−	3.52786e8i	−0.492634	−	0.870237i
$289$	−3.48945e8			−0.850383
$290$	−2.62899e7	+	5.47268e7i	−0.0632988	+	0.131767i
$291$	−6.18113e7	+	3.15177e8i	−0.147042	+	0.749772i
$292$	1.77888e8	+	2.22182e8i	0.418125	+	0.522238i
$293$	−7.75663e7			−0.180151			−0.0900755	−	0.995935i	$-0.528711\pi$
$293$	−7.75663e7			−0.180151			−0.0900755	+	0.995935i	$0.528711\pi$
$294$	−6.67705e8	−	4.98684e8i	−1.53239	−	1.14448i
$295$		−	1.41140e8i		−	0.320091i
$296$	−9.22958e7	−	3.99037e8i	−0.206853	−	0.894319i
$297$	1.52580e8	+	1.00178e8i	0.337947	+	0.221884i
$298$	1.02562e8	−	2.13500e8i	0.224507	−	0.467349i
$299$		−	5.63227e8i		−	1.21853i
$300$	−3.63556e8	+	1.89952e8i	−0.777403	+	0.406181i
$301$			7.66732e8i			1.62054i
$302$	−3.08970e8	−	1.48424e8i	−0.645493	−	0.310085i
$303$	1.02927e8	−	5.24828e8i	0.212560	−	1.08385i
$304$	−4.14669e7	+	1.84972e8i	−0.0846533	+	0.377614i
$305$		−	1.75023e8i		−	0.353220i
$306$	4.57532e8	+	5.05483e8i	0.912845	+	1.00851i
$307$	−1.34816e8			−0.265924			−0.132962	−	0.991121i	$-0.542449\pi$
$307$	−1.34816e8			−0.265924			−0.132962	+	0.991121i	$0.542449\pi$
$308$	2.21120e8	+	2.76179e8i	0.431222	+	0.538596i
$309$	4.74066e7	+	9.29720e6i	0.0914080	+	0.0179266i
$310$	7.16352e7	+	3.44124e7i	0.136572	+	0.0656069i
$311$	5.73695e7			0.108148			0.0540742	−	0.998537i	$-0.482779\pi$
$311$	5.73695e7			0.108148			0.0540742	+	0.998537i	$0.482779\pi$
$312$	6.86455e8	−	2.31016e7i	1.27959	−	0.0430627i
$313$	3.22598e8			0.594643			0.297321	−	0.954777i	$-0.403907\pi$
$313$	3.22598e8			0.594643			0.297321	+	0.954777i	$0.403907\pi$
$314$	−8.19780e8	−	3.93810e8i	−1.49432	−	0.717848i
$315$	−1.25349e8	+	3.07287e8i	−0.225961	+	0.553934i
$316$	5.58610e8	−	4.47246e8i	0.995873	−	0.797336i
$317$	6.42560e8			1.13294			0.566469	−	0.824083i	$-0.308309\pi$
$317$	6.42560e8			1.13294			0.566469	+	0.824083i	$0.308309\pi$
$318$	2.42653e8	+	1.81228e8i	0.423146	+	0.316032i
$319$			9.77467e7i			0.168591i
$320$	−1.84609e8	+	9.02257e7i	−0.314940	+	0.153924i
$321$	−8.52318e8	−	1.67153e8i	−1.43825	−	0.282064i
$322$	−8.77134e8	−	4.21362e8i	−1.46410	−	0.703331i
$323$		−	3.18813e8i		−	0.526413i
$324$	6.08164e7	−	6.09192e8i	0.0993376	−	0.995054i
$325$		−	6.94972e8i		−	1.12299i
$326$	5.29700e8	−	1.10266e9i	0.846776	−	1.76270i
$327$	5.60729e8	+	1.09968e8i	0.886821	+	0.173920i
$328$	−1.31722e8	−	5.69496e8i	−0.206111	−	0.891112i
$329$			1.75929e9i			2.72366i
$330$	5.53611e7	−	7.41247e7i	0.0848019	−	0.113544i
$331$	1.11052e9			1.68317			0.841583	−	0.540127i	$-0.181624\pi$
$331$	1.11052e9			1.68317			0.841583	+	0.540127i	$0.181624\pi$
$332$	−3.01092e8	+	2.41066e8i	−0.451560	+	0.361537i
$333$	2.33624e8	−	5.72718e8i	0.346707	−	0.849935i
$334$	−1.92494e8	+	4.00707e8i	−0.282686	+	0.588457i
$335$	−1.37184e8			−0.199364
$336$	4.77574e8	−	1.08632e9i	0.686836	−	1.56233i
$337$	−3.54194e8			−0.504123			−0.252062	−	0.967711i	$-0.581109\pi$
$337$	−3.54194e8			−0.504123			−0.252062	+	0.967711i	$0.581109\pi$
$338$	−1.96494e8	+	4.09035e8i	−0.276784	+	0.576171i
$339$	6.48028e8	+	1.27089e8i	0.903431	+	0.177177i
$340$	2.69768e8	−	2.15987e8i	0.372232	−	0.298024i
$341$	1.27947e8			0.174738
$342$	−2.12245e8	+	1.92111e8i	−0.286910	+	0.259694i
$343$		−	1.16400e9i		−	1.55749i
$344$	−6.98486e8	+	1.61557e8i	−0.925131	+	0.213979i
$345$	−4.89715e7	+	2.49707e8i	−0.0642062	+	0.327389i
$346$	−6.32453e8	+	1.31656e9i	−0.820846	+	1.70873i
$347$		−	4.20183e8i		−	0.539865i	−0.962879	−	0.269932i	$-0.912999\pi$
$347$		−	4.20183e8i		−	0.539865i	0.962879	−	0.269932i	$-0.0870014\pi$
$348$	2.90582e8	−	1.51825e8i	0.369608	−	0.193115i
$349$			2.71958e7i			0.0342462i	0.999853	+	0.0171231i	$0.00545072\pi$
$349$			2.71958e7i			0.0342462i	−0.999853	+	0.0171231i	$0.994549\pi$
$350$	−1.08231e9	−	5.19923e8i	−1.34931	−	0.648187i
$351$	8.67082e8	+	5.69294e8i	1.07025	+	0.702687i
$352$	−2.05005e8	+	2.59632e8i	−0.250533	+	0.317292i
$353$		−	8.90412e8i		−	1.07741i	−0.842496	−	0.538703i	$-0.818914\pi$
$353$		−	8.90412e8i		−	1.07741i	0.842496	−	0.538703i	$-0.181086\pi$
$354$	−4.56067e8	+	6.10643e8i	−0.546408	+	0.731603i
$355$	3.49736e8			0.414897
$356$	−5.84065e8	+	4.67627e8i	−0.686099	+	0.549318i
$357$	−3.84086e8	+	1.95846e9i	−0.446776	+	2.27812i
$358$	−2.81098e7	−	1.35035e7i	−0.0323793	−	0.0155545i
$359$	−1.13487e9			−1.29454			−0.647269	−	0.762261i	$-0.724089\pi$
$359$	−1.13487e9			−1.29454			−0.647269	+	0.762261i	$0.724089\pi$
$360$	−3.06348e8	−	4.94438e7i	−0.346064	−	0.0558538i
$361$	−7.60007e8			−0.850241
$362$	1.13434e9	+	5.44919e8i	1.25679	+	0.603743i
$363$	−1.46720e8	+	7.48126e8i	−0.160996	+	0.820921i
$364$	1.25659e9	+	1.56948e9i	1.36564	+	1.70569i
$365$	2.17867e8			0.234513
$366$	−5.65553e8	+	7.57237e8i	−0.602961	+	0.807324i
$367$		−	1.04021e9i		−	1.09847i	−0.835668	−	0.549235i	$-0.814919\pi$
$367$		−	1.04021e9i		−	1.09847i	0.835668	−	0.549235i	$-0.185081\pi$
$368$	1.99037e8	−	8.87846e8i	0.208193	−	0.928689i
$369$	3.33422e8	−	8.17368e8i	0.345463	−	0.846886i
$370$	−2.82597e8	−	1.35755e8i	−0.290043	−	0.139332i
$371$			8.86535e8i			0.901337i
$372$	−1.98733e8	−	3.80361e8i	−0.200156	−	0.383085i
$373$			3.18791e7i			0.0318072i	0.999874	+	0.0159036i	$0.00506249\pi$
$373$			3.18791e7i			0.0318072i	−0.999874	+	0.0159036i	$0.994938\pi$
$374$	2.40914e8	−	5.01503e8i	0.238129	−	0.495704i
$375$	−1.29318e8	+	6.59397e8i	−0.126634	+	0.645710i
$376$	−1.60270e9	+	3.70698e8i	−1.55487	+	0.359636i
$377$			5.55477e8i			0.533914i
$378$	1.53526e9	−	9.24438e8i	1.46205	−	0.880353i
$379$	5.34127e7			0.0503973			0.0251987	−	0.999682i	$-0.491978\pi$
$379$	5.34127e7			0.0503973			0.0251987	+	0.999682i	$0.491978\pi$
$380$	9.06899e7	+	1.13272e8i	0.0847845	+	0.105896i
$381$	−4.93213e8	−	9.67270e7i	−0.456874	−	0.0896005i
$382$	5.38202e8	−	1.12036e9i	0.493997	−	1.02834i
$383$	1.30505e9			1.18695			0.593473	−	0.804854i	$-0.297756\pi$
$383$	1.30505e9			1.18695			0.593473	+	0.804854i	$0.297756\pi$
$384$	1.09026e9	+	2.06167e8i	0.982586	+	0.185806i
$385$	2.70816e8			0.241859
$386$	−2.74488e8	+	5.71392e8i	−0.242922	+	0.505683i
$387$	−1.00250e9	−	4.08942e8i	−0.879217	−	0.358652i
$388$	−5.49434e8	−	6.86243e8i	−0.477534	−	0.596440i
$389$	7.16057e8			0.616771			0.308385	−	0.951262i	$-0.400211\pi$
$389$	7.16057e8			0.616771			0.308385	+	0.951262i	$0.400211\pi$
$390$	3.14607e8	−	4.21237e8i	0.268560	−	0.359584i
$391$			1.53027e9i			1.29464i
$392$	2.22234e9	−	5.14018e8i	1.86341	−	0.431000i
$393$	−1.43779e9	−	2.81974e8i	−1.19487	−	0.234334i
$394$	−4.63017e8	+	9.63847e8i	−0.381382	+	0.793910i
$395$		−	5.47762e8i		−	0.447200i
$396$	−4.79040e8	+	1.41812e8i	−0.387649	+	0.114757i
$397$			4.15822e7i			0.0333535i	0.999861	+	0.0166767i	$0.00530862\pi$
$397$			4.15822e7i			0.0333535i	−0.999861	+	0.0166767i	$0.994691\pi$
$398$	9.18246e8	+	4.41111e8i	0.730076	+	0.350717i
$399$	−8.22331e8	−	1.61272e8i	−0.648099	−	0.127103i
$400$	2.45594e8	−	1.09552e9i	0.191870	−	0.855877i
$401$		−	1.22525e9i		−	0.948895i	−0.880284	−	0.474447i	$-0.842648\pi$
$401$		−	1.22525e9i		−	0.948895i	0.880284	−	0.474447i	$-0.157352\pi$
$402$	5.93526e8	+	4.43283e8i	0.455668	+	0.340322i
$403$	7.27097e8			0.553382
$404$	9.14908e8	+	1.14272e9i	0.690308	+	0.862194i
$405$	−3.34922e8	−	3.27787e8i	−0.250525	−	0.245188i
$406$	8.65064e8	+	4.15563e8i	0.641515	+	0.308174i
$407$	−5.04743e8			−0.371099
$408$	−1.86507e9	+	6.27663e7i	−1.35952	+	0.0457526i
$409$	1.98246e9			1.43276			0.716381	−	0.697710i	$-0.245797\pi$
$409$	1.98246e9			1.43276			0.716381	+	0.697710i	$0.245797\pi$
$410$	−4.03315e8	−	1.93746e8i	−0.289002	−	0.138832i
$411$	−2.54221e8	−	4.98569e7i	−0.180620	−	0.0354225i
$412$	−1.03220e8	+	8.26418e7i	−0.0727146	+	0.0582183i
$413$	−2.23099e9			−1.55838
$414$	1.01876e9	−	9.22115e8i	0.705616	−	0.638681i
$415$			2.95245e8i			0.202775i
$416$	−1.16500e9	+	1.47544e9i	−0.793416	+	1.00484i
$417$	1.20764e8	−	6.15778e8i	0.0815571	−	0.415861i
$418$	2.10574e8	+	1.01156e8i	0.141022	+	0.0677449i
$419$		−	2.00028e9i		−	1.32844i	−0.747538	−	0.664219i	$-0.768764\pi$
$419$		−	2.00028e9i		−	1.32844i	0.747538	−	0.664219i	$-0.231236\pi$
$420$	−4.20644e8	−	8.05084e8i	−0.277040	−	0.530236i
$421$		−	2.32447e9i		−	1.51823i	−0.650959	−	0.759113i	$-0.725633\pi$
$421$		−	2.32447e9i		−	1.51823i	0.650959	−	0.759113i	$-0.274367\pi$
$422$	−4.63974e8	+	9.65839e8i	−0.300538	+	0.625620i
$423$	−2.30027e9	−	9.38330e8i	−1.47770	−	0.602788i
$424$	−8.07626e8	+	1.86801e8i	−0.514552	+	0.119014i
$425$			1.88821e9i			1.19314i
$426$	−1.51313e9	−	1.13010e9i	−0.948295	−	0.708247i
$427$	−2.76658e9			−1.71967
$428$	1.85577e9	−	1.48581e9i	1.14412	−	0.916029i
$429$	1.62898e8	−	8.30620e8i	0.0996128	−	0.507927i
$430$	−2.37630e8	+	4.94666e8i	−0.144132	+	0.300035i
$431$	7.11491e8			0.428055			0.214027	−	0.976828i	$-0.431342\pi$
$431$	7.11491e8			0.428055			0.214027	+	0.976828i	$0.431342\pi$
$432$	1.16565e9	+	1.20382e9i	0.695624	+	0.718406i
$433$	9.95747e8			0.589442			0.294721	−	0.955583i	$-0.404773\pi$
$433$	9.95747e8			0.589442			0.294721	+	0.955583i	$0.404773\pi$
$434$	5.43956e8	−	1.13233e9i	0.319411	−	0.664907i
$435$	4.82976e7	−	2.46270e8i	0.0281328	−	0.143450i
$436$	−1.22089e9	+	9.77493e8i	−0.705461	+	0.564821i
$437$	−6.42538e8			−0.368310
$438$	−9.42604e8	−	7.03996e8i	−0.536006	−	0.400323i
$439$		−	5.41401e8i		−	0.305417i	−0.988271	−	0.152708i	$-0.951200\pi$
$439$		−	5.41401e8i		−	0.305417i	0.988271	−	0.152708i	$-0.0487995\pi$
$440$	5.70633e7	+	2.46711e8i	0.0319354	+	0.138072i
$441$	3.18960e9	+	1.30111e9i	1.77093	+	0.722401i
$442$	1.36907e9	−	2.84995e9i	0.754133	−	1.56985i
$443$			2.02764e9i			1.10810i	0.832484	+	0.554050i	$0.186918\pi$
$443$			2.02764e9i			1.10810i	−0.832484	+	0.554050i	$0.813082\pi$
$444$	7.83991e8	+	1.50050e9i	0.425080	+	0.813574i
$445$			5.72723e8i			0.308095i
$446$	1.47536e8	+	7.08738e7i	0.0787454	+	0.0378281i
$447$	−1.88419e8	+	9.60750e8i	−0.0997809	+	0.508785i
$448$	1.42619e9	+	2.91811e9i	0.749386	+	1.53331i
$449$		−	2.36412e9i		−	1.23256i	−0.787528	−	0.616279i	$-0.788639\pi$
$449$		−	2.36412e9i		−	1.23256i	0.787528	−	0.616279i	$-0.211361\pi$
$450$	1.25705e9	−	1.13781e9i	0.650294	−	0.588606i
$451$	−7.20356e8			−0.369768
$452$	−1.41097e9	+	1.12968e9i	−0.718675	+	0.575401i
$453$	1.39036e9	+	2.72673e8i	0.702724	+	0.137816i
$454$	3.57712e8	+	1.71840e8i	0.179407	+	0.0861842i
$455$	1.53900e9			0.765946
$456$	−2.63547e7	−	7.83117e8i	−0.0130161	−	0.386767i
$457$	5.36394e8			0.262892			0.131446	−	0.991323i	$-0.458038\pi$
$457$	5.36394e8			0.262892			0.131446	+	0.991323i	$0.458038\pi$
$458$	1.03774e8	+	4.98515e7i	0.0504731	+	0.0242465i
$459$	−2.35583e9	−	1.54675e9i	−1.13710	−	0.746579i
$460$	−4.35302e8	−	5.43693e8i	−0.208516	−	0.260436i
$461$	3.68025e9			1.74954			0.874770	−	0.484539i	$-0.161013\pi$
$461$	3.68025e9			1.74954			0.874770	+	0.484539i	$0.161013\pi$
$462$	−1.17169e9	−	8.75090e8i	−0.552796	−	0.412863i
$463$			1.19699e9i			0.560478i	0.959930	+	0.280239i	$0.0904138\pi$
$463$			1.19699e9i			0.560478i	−0.959930	+	0.280239i	$0.909586\pi$
$464$	−1.96298e8	+	8.75628e8i	−0.0912226	+	0.406918i
$465$	−3.22358e8	−	6.32197e7i	−0.148680	−	0.0291586i
$466$	1.42093e9	+	6.82591e8i	0.650460	+	0.312471i
$467$			1.60918e9i			0.731130i	0.930786	+	0.365565i	$0.119124\pi$
$467$			1.60918e9i			0.731130i	−0.930786	+	0.365565i	$0.880876\pi$
$468$	−2.72230e9	+	8.05894e8i	−1.22765	+	0.363427i
$469$			2.16846e9i			0.970613i
$470$	−5.45249e8	+	1.13503e9i	−0.242244	+	0.504271i
$471$	3.68901e9	+	7.23475e8i	1.62681	+	0.319044i
$472$	−4.70090e8	−	2.03242e9i	−0.205771	−	0.889642i
$473$			8.83516e8i			0.383884i
$474$	−1.76999e9	+	2.36989e9i	−0.763389	+	1.02213i
$475$	−7.92834e8			−0.339434
$476$	−3.41410e9	−	4.26421e9i	−1.45095	−	1.81223i
$477$	−1.15914e9	−	4.72839e8i	−0.489016	−	0.199480i
$478$	−3.00000e8	+	6.24500e8i	−0.125639	+	0.261538i
$479$	−1.54958e9			−0.644227			−0.322114	−	0.946701i	$-0.604393\pi$
$479$	−1.54958e9			−0.644227			−0.322114	+	0.946701i	$0.604393\pi$
$480$	6.44791e8	−	5.52842e8i	0.266118	−	0.228169i
$481$	−2.86836e9			−1.17524
$482$	6.83672e8	−	1.42318e9i	0.278088	−	0.578887i
$483$	3.94710e9	+	7.74091e8i	1.59391	+	0.312591i
$484$	−1.30417e9	−	1.62891e9i	−0.522849	−	0.653039i
$485$	−6.72917e8			−0.267834
$486$	3.89858e8	+	2.50041e9i	0.154056	+	0.988062i
$487$			2.60156e9i			1.02066i	0.859978	+	0.510331i	$0.170477\pi$
$487$			2.60156e9i			1.02066i	−0.859978	+	0.510331i	$0.829523\pi$
$488$	−5.82943e8	−	2.52033e9i	−0.227068	−	0.981720i
$489$	−9.73121e8	+	4.96196e9i	−0.376345	+	1.91899i
$490$	7.56054e8	−	1.57385e9i	0.290313	−	0.604335i
$491$			4.79977e9i			1.82993i	0.403531	+	0.914966i	$0.367783\pi$
$491$			4.79977e9i			1.82993i	−0.403531	+	0.914966i	$0.632217\pi$
$492$	1.11889e9	+	2.14148e9i	0.423555	+	0.810656i
$493$		−	1.50921e9i		−	0.567264i
$494$	1.19665e9	+	5.74854e8i	0.446605	+	0.214542i
$495$	−1.44442e8	+	3.54091e8i	−0.0535271	+	0.131219i
$496$	1.14616e9	+	2.56946e8i	0.421755	+	0.0945489i
$497$		−	5.52826e9i		−	2.01995i
$498$	9.54026e8	−	1.27738e9i	0.346145	−	0.463464i
$499$	2.27878e8			0.0821015			0.0410508	−	0.999157i	$-0.486929\pi$
$499$	2.27878e8			0.0821015			0.0410508	+	0.999157i	$0.486929\pi$
$500$	−1.14950e9	−	1.43572e9i	−0.411256	−	0.513659i
$501$	3.53633e8	−	1.80318e9i	0.125638	−	0.640631i
$502$	−3.35937e8	−	1.61379e8i	−0.118521	−	0.0569356i
$503$	1.71998e9			0.602609			0.301304	−	0.953528i	$-0.402578\pi$
$503$	1.71998e9			0.602609			0.301304	+	0.953528i	$0.402578\pi$
$504$	−7.81556e8	+	4.84243e9i	−0.271928	+	1.68483i
$505$	1.12053e9			0.387172
$506$	−1.01073e9	−	4.85541e8i	−0.346825	−	0.166609i
$507$	3.60982e8	−	1.84066e9i	0.123015	−	0.627256i
$508$	1.07388e9	−	8.59795e8i	0.363441	−	0.290986i
$509$	−2.37984e9			−0.799900			−0.399950	−	0.916537i	$-0.630973\pi$
$509$	−2.37984e9			−0.799900			−0.399950	+	0.916537i	$0.630973\pi$
$510$	−8.54775e8	+	1.14449e9i	−0.285336	+	0.382045i
$511$		−	3.44382e9i		−	1.14174i
$512$	−2.35786e9	+	1.91412e9i	−0.776378	+	0.630267i
$513$	6.49459e8	−	9.89180e8i	0.212393	−	0.323493i
$514$	−3.28294e9	−	1.57707e9i	−1.06633	−	0.512248i
$515$			1.01215e8i			0.0326528i
$516$	2.62652e9	−	1.37232e9i	0.841603	−	0.439725i
$517$			2.02726e9i			0.645196i
$518$	−2.14588e9	+	4.46700e9i	−0.678345	+	1.41209i
$519$	1.16189e9	−	5.92450e9i	0.364820	−	1.86023i
$520$	3.24280e8	+	1.40201e9i	0.101137	+	0.437261i
$521$			1.09986e9i			0.340725i	0.985381	+	0.170362i	$0.0544938\pi$
$521$			1.09986e9i			0.340725i	−0.985381	+	0.170362i	$0.945506\pi$
$522$	−1.00474e9	+	9.09426e8i	−0.309175	+	0.279847i
$523$	1.33421e9			0.407821			0.203910	−	0.978990i	$-0.434635\pi$
$523$	1.33421e9			0.407821			0.203910	+	0.978990i	$0.434635\pi$
$524$	3.13054e9	−	2.50644e9i	0.950516	−	0.761022i
$525$	4.87037e9	+	9.55159e8i	1.46894	+	0.288083i
$526$	1.79076e9	−	3.72776e9i	0.536521	−	1.11686i
$527$	−1.97550e9			−0.587948
$528$	5.50315e8	−	1.25179e9i	0.162702	−	0.370093i
$529$	−3.20708e8			−0.0941922
$530$	−2.74760e8	+	5.71958e8i	−0.0801655	+	0.166878i
$531$	1.18992e9	−	2.91702e9i	0.344894	−	0.845490i
$532$	1.79048e9	−	1.43353e9i	0.515560	−	0.412778i
$533$	−4.09365e9			−1.17102
$534$	1.85065e9	−	2.47789e9i	0.525931	−	0.704186i
$535$		−	1.81974e9i		−	0.513772i
$536$	−1.97545e9	+	4.56913e8i	−0.554100	+	0.128161i
$537$	1.26494e8	+	2.48076e7i	0.0352502	+	0.00691312i
$538$	−1.88673e9	+	3.92755e9i	−0.522363	+	1.08739i
$539$		−	2.81104e9i		−	0.773225i
$540$	1.27700e9	−	1.20595e8i	0.348990	−	0.0329571i
$541$			2.75610e9i			0.748351i	0.927358	+	0.374175i	$0.122074\pi$
$541$			2.75610e9i			0.748351i	−0.927358	+	0.374175i	$0.877926\pi$
$542$	3.74670e9	+	1.79986e9i	1.01077	+	0.485557i
$543$	−5.10453e9	−	1.00108e9i	−1.36822	−	0.268330i
$544$	3.16527e9	−	4.00872e9i	0.842976	−	1.06760i
$545$			1.19718e9i			0.316790i
$546$	−6.65848e9	−	4.97298e9i	−1.75066	−	1.30750i
$547$	1.81654e9			0.474559			0.237280	−	0.971441i	$-0.423744\pi$
$547$	1.81654e9			0.474559			0.237280	+	0.971441i	$0.423744\pi$
$548$	5.53522e8	−	4.43173e8i	0.143682	−	0.115038i
$549$	1.47557e9	−	3.61730e9i	0.380590	−	0.932998i
$550$	−1.24716e9	−	5.99114e8i	−0.319633	−	0.153547i
$551$	6.33696e8			0.161380
$552$	1.26500e8	+	3.75888e9i	0.0320113	+	0.951201i
$553$	−8.65845e9			−2.17722
$554$	8.87136e7	+	4.26166e7i	0.0221669	+	0.0106487i
$555$	1.27169e9	+	2.49398e8i	0.315758	+	0.0619253i
$556$	1.07346e9	+	1.34075e9i	0.264864	+	0.330815i
$557$	−2.69747e9			−0.661400			−0.330700	−	0.943736i	$-0.607285\pi$
$557$	−2.69747e9			−0.661400			−0.330700	+	0.943736i	$0.607285\pi$
$558$	1.19040e9	+	1.31516e9i	0.290051	+	0.320449i
$559$			5.02086e9i			1.21573i
$560$	2.42601e9	+	5.43861e8i	0.583759	+	0.130867i
$561$	−4.42588e8	+	2.25676e9i	−0.105835	+	0.539655i
$562$	4.77817e9	+	2.29536e9i	1.13549	+	0.545474i
$563$		−	2.68748e9i		−	0.634695i	−0.948309	−	0.317348i	$-0.897208\pi$
$563$		−	2.68748e9i		−	0.634695i	0.948309	−	0.317348i	$-0.102792\pi$
$564$	6.02665e9	−	3.14883e9i	1.41449	−	0.739048i
$565$			1.38357e9i			0.322724i
$566$	8.78291e8	−	1.82831e9i	0.203601	−	0.423830i
$567$	−5.18132e9	+	5.29410e9i	−1.19371	+	1.21969i
$568$	5.03619e9	−	1.16485e9i	1.15314	−	0.266718i
$569$		−	1.62319e9i		−	0.369383i	−0.982797	−	0.184692i	$-0.940871\pi$
$569$		−	1.62319e9i		−	0.369383i	0.982797	−	0.184692i	$-0.0591286\pi$
$570$	−4.80554e8	−	3.58908e8i	−0.108688	−	0.0811748i
$571$	2.25862e9			0.507712			0.253856	−	0.967242i	$-0.418301\pi$
$571$	2.25862e9			0.507712			0.253856	+	0.967242i	$0.418301\pi$
$572$	1.44798e9	+	1.80853e9i	0.323502	+	0.404054i
$573$	−9.88741e8	+	5.04161e9i	−0.219554	+	1.11951i
$574$	−3.06254e9	+	6.37519e9i	−0.675912	+	1.40702i
$575$	3.80552e9			0.834790
$576$	−4.57609e9	+	3.08353e8i	−0.997737	+	0.0672309i
$577$	−2.78955e9			−0.604530			−0.302265	−	0.953224i	$-0.597743\pi$
$577$	−2.78955e9			−0.604530			−0.302265	+	0.953224i	$0.597743\pi$
$578$	−1.70947e9	+	3.55855e9i	−0.368227	+	0.766525i
$579$	5.04266e8	−	2.57126e9i	0.107965	−	0.550518i
$580$	4.29312e8	+	5.36211e8i	0.0913640	+	0.114114i
$581$	4.66692e9			0.987220
$582$	2.91138e9	+	2.17440e9i	0.612164	+	0.457203i
$583$			1.02157e9i			0.213514i
$584$	3.13729e9	−	7.25643e8i	0.651793	−	0.150757i
$585$	−8.20835e8	+	2.01224e9i	−0.169516	+	0.415560i
$586$	−3.79996e8	+	7.91024e8i	−0.0780076	+	0.162386i
$587$		−	1.54318e9i		−	0.314907i	−0.987526	−	0.157453i	$-0.949672\pi$
$587$		−	1.54318e9i		−	0.314907i	0.987526	−	0.157453i	$-0.0503284\pi$
$588$	−8.35668e9	+	4.36624e9i	−1.69517	+	0.885700i
$589$		−	8.29483e8i		−	0.167265i
$590$	−1.43935e9	−	6.91442e8i	−0.288526	−	0.138603i
$591$	8.50617e8	−	4.33731e9i	0.169503	−	0.864300i
$592$	−4.52155e9	−	1.01364e9i	−0.895698	−	0.200797i
$593$		−	2.51226e9i		−	0.494735i	−0.968922	−	0.247368i	$-0.920434\pi$
$593$		−	2.51226e9i		−	0.494735i	0.968922	−	0.247368i	$-0.0795655\pi$
$594$	1.76911e9	−	1.06524e9i	0.346339	−	0.208543i
$595$	−4.18140e9			−0.813790
$596$	−1.67483e9	−	2.09186e9i	−0.324048	−	0.404736i
$597$	−4.13211e9	−	8.10373e8i	−0.794806	−	0.155874i
$598$	−5.74382e9	−	2.75924e9i	−1.09836	−	0.527637i
$599$	−6.19749e9			−1.17821			−0.589104	−	0.808058i	$-0.700519\pi$
$599$	−6.19749e9			−1.17821			−0.589104	+	0.808058i	$0.700519\pi$
$600$	1.56089e8	+	4.63813e9i	0.0295015	+	0.876624i
$601$	7.79137e9			1.46404			0.732020	−	0.681283i	$-0.238578\pi$
$601$	7.79137e9			1.46404			0.732020	+	0.681283i	$0.238578\pi$
$602$	7.81916e9	+	3.75620e9i	1.46074	+	0.701716i
$603$	−2.83526e9	−	1.15656e9i	−0.526601	−	0.214812i
$604$	−3.02727e9	+	2.42376e9i	−0.559014	+	0.447569i
$605$	−1.59728e9			−0.293249
$606$	−4.84798e9	−	3.62078e9i	−0.884925	−	0.660918i
$607$		−	1.08410e9i		−	0.196748i	−0.995150	−	0.0983740i	$-0.968636\pi$
$607$		−	1.08410e9i		−	0.196748i	0.995150	−	0.0983740i	$-0.0313641\pi$
$608$	1.68320e9	+	1.32905e9i	0.303721	+	0.239817i
$609$	−3.89279e9	−	7.63438e8i	−0.698393	−	0.136966i
$610$	−1.78489e9	−	8.57433e8i	−0.318388	−	0.152949i
$611$			1.15205e10i			2.04328i
$612$	7.39637e9	−	2.18958e9i	1.30433	−	0.386128i
$613$			3.88620e9i			0.681418i	0.940169	+	0.340709i	$0.110667\pi$
$613$			3.88620e9i			0.681418i	−0.940169	+	0.340709i	$0.889333\pi$
$614$	−6.60461e8	+	1.37486e9i	−0.115148	+	0.239700i
$615$	1.81492e9	+	3.55935e8i	0.314626	+	0.0617032i
$616$	3.89975e9	−	9.01998e8i	0.672209	−	0.155479i
$617$		−	2.18111e9i		−	0.373834i	−0.982376	−	0.186917i	$-0.940150\pi$
$617$		−	2.18111e9i		−	0.373834i	0.982376	−	0.186917i	$-0.0598496\pi$
$618$	3.27057e8	−	4.37908e8i	0.0557396	−	0.0746316i
$619$	1.16433e10			1.97315			0.986574	−	0.163316i	$-0.0522191\pi$
$619$	1.16433e10			1.97315			0.986574	+	0.163316i	$0.0522191\pi$
$620$	7.01879e8	−	5.61953e8i	0.118275	−	0.0946954i
$621$	−3.11734e9	+	4.74796e9i	−0.522352	+	0.795586i
$622$	2.81052e8	−	5.85057e8i	0.0468296	−	0.0974836i
$623$	9.05301e9			1.49998
$624$	3.12734e9	−	7.11367e9i	0.515262	−	1.17205i
$625$	3.94568e9			0.646459
$626$	1.58040e9	−	3.28987e9i	0.257488	−	0.536004i
$627$	−9.47583e8	−	1.85836e8i	−0.153526	−	0.0301089i
$628$	−8.03217e9	+	6.43089e9i	−1.29412	+	1.03612i
$629$	7.79323e9			1.24865
$630$	2.51965e9	+	2.78371e9i	0.401465	+	0.443539i
$631$		−	1.06242e10i		−	1.68342i	−0.539927	−	0.841712i	$-0.681548\pi$
$631$		−	1.06242e10i		−	1.68342i	0.539927	−	0.841712i	$-0.318452\pi$
$632$	−1.82441e9	−	7.88777e9i	−0.287484	−	1.24292i
$633$	8.52374e8	−	4.34627e9i	0.133573	−	0.681089i
$634$	3.14789e9	−	6.55285e9i	0.490577	−	1.02122i
$635$		−	1.05303e9i		−	0.163205i
$636$	3.03692e9	−	1.58675e9i	0.468095	−	0.244572i
$637$		−	1.59746e10i		−	2.44874i
$638$	9.96825e8	+	4.78859e8i	0.151966	+	0.0730021i
$639$	7.22819e9	+	2.94853e9i	1.09591	+	0.447047i
$640$	1.57286e7	+	2.32467e9i	0.00237171	+	0.350534i
$641$			6.89527e9i			1.03407i	0.855965	+	0.517033i	$0.172964\pi$
$641$			6.89527e9i			1.03407i	−0.855965	+	0.517033i	$0.827036\pi$
$642$	−5.88013e9	+	7.87309e9i	−0.877029	+	1.17428i
$643$	−9.21146e9			−1.36644			−0.683219	−	0.730213i	$-0.739421\pi$
$643$	−9.21146e9			−1.36644			−0.683219	+	0.730213i	$0.739421\pi$
$644$	−8.59413e9	+	6.88081e9i	−1.26795	+	1.01517i
$645$	4.36554e8	−	2.22600e9i	0.0640588	−	0.326637i
$646$	−3.25126e9	−	1.56186e9i	−0.474502	−	0.227943i
$647$	−1.53229e8			−0.0222421			−0.0111210	−	0.999938i	$-0.503540\pi$
$647$	−1.53229e8			−0.0222421			−0.0111210	+	0.999938i	$0.503540\pi$
$648$	−5.91462e9	−	3.60463e9i	−0.853915	−	0.520413i
$649$	−2.57080e9			−0.369158
$650$	−7.08735e9	−	3.40465e9i	−1.01225	−	0.486269i
$651$	−9.99311e8	+	5.09551e9i	−0.141960	+	0.723859i
$652$	−8.64996e9	−	1.08038e10i	−1.22222	−	1.52655i
$653$	5.61194e9			0.788710			0.394355	−	0.918958i	$-0.370968\pi$
$653$	5.61194e9			0.788710			0.394355	+	0.918958i	$0.370968\pi$
$654$	3.86846e9	−	5.17960e9i	0.540774	−	0.724060i
$655$		−	3.06975e9i		−	0.426833i
$656$	−6.45305e9	−	1.44664e9i	−0.892486	−	0.200077i
$657$	4.50279e9	+	1.83678e9i	0.619445	+	0.252685i
$658$	1.79413e10	+	8.61874e9i	2.45507	+	1.17938i
$659$			1.89758e9i			0.258287i	0.991626	+	0.129143i	$0.0412228\pi$
$659$			1.89758e9i			0.258287i	−0.991626	+	0.129143i	$0.958777\pi$
$660$	−4.84714e8	−	9.27710e8i	−0.0656269	−	0.125605i
$661$		−	2.56052e9i		−	0.344844i	−0.985023	−	0.172422i	$-0.944841\pi$
$661$		−	2.56052e9i		−	0.344844i	0.985023	−	0.172422i	$-0.0551592\pi$
$662$	5.44040e9	−	1.13251e10i	0.728832	−	1.51719i
$663$	−2.51514e9	+	1.28248e10i	−0.335170	+	1.70904i
$664$	9.83361e8	+	4.25152e9i	0.130354	+	0.563581i
$665$		−	1.75571e9i		−	0.231514i
$666$	−4.69608e9	−	5.18824e9i	−0.615993	−	0.680550i
$667$	−3.04168e9			−0.396892
$668$	3.14341e9	+	3.92612e9i	0.408022	+	0.509619i
$669$	−6.63911e8	−	1.30204e8i	−0.0857271	−	0.0168125i
$670$	−6.72060e8	+	1.39901e9i	−0.0863270	+	0.179704i
$671$	−3.18797e9			−0.407366
$672$	−8.73875e9	−	1.01922e10i	−1.11085	−	1.29561i
$673$	9.40490e9			1.18933			0.594664	−	0.803974i	$-0.297285\pi$
$673$	9.40490e9			1.18933			0.594664	+	0.803974i	$0.297285\pi$
$674$	−1.73519e9	+	3.61209e9i	−0.218292	+	0.454411i
$675$	−3.84651e9	+	5.85856e9i	−0.481398	+	0.733209i
$676$	3.20873e9	+	4.00770e9i	0.399503	+	0.498979i
$677$	−1.31467e10			−1.62838			−0.814188	−	0.580601i	$-0.802818\pi$
$677$	−1.31467e10			−1.62838			−0.814188	+	0.580601i	$0.802818\pi$
$678$	4.47073e9	−	5.98601e9i	0.550903	−	0.737622i
$679$			1.06368e10i			1.30396i
$680$	−8.81058e8	−	3.80922e9i	−0.107454	−	0.464574i
$681$	−1.60971e9	−	3.15689e8i	−0.195313	−	0.0383041i
$682$	6.26808e8	−	1.30480e9i	0.0756640	−	0.157507i
$683$		−	1.03400e9i		−	0.124179i	−0.998071	−	0.0620894i	$-0.980224\pi$
$683$		−	1.03400e9i		−	0.124179i	0.998071	−	0.0620894i	$-0.0197764\pi$
$684$	9.19375e8	+	3.10563e9i	0.109849	+	0.371068i
$685$		−	5.42773e8i		−	0.0645211i
$686$	−1.18705e10	−	5.70242e9i	−1.40390	−	0.674411i
$687$	−4.66984e8	−	9.15831e7i	−0.0549482	−	0.0107762i
$688$	−1.77430e9	+	7.91465e9i	−0.207715	+	0.926557i
$689$			5.80538e9i			0.676181i
$690$	2.30661e9	+	1.72272e9i	0.267302	+	0.199638i
$691$	−5.74897e9			−0.662853			−0.331426	−	0.943481i	$-0.607530\pi$
$691$	−5.74897e9			−0.662853			−0.331426	+	0.943481i	$0.607530\pi$
$692$	1.03279e10	+	1.28996e10i	1.18479	+	1.47980i
$693$	5.59711e9	+	2.28318e9i	0.638848	+	0.260600i
$694$	−4.28504e9	−	2.05847e9i	−0.486628	−	0.233768i
$695$	1.31471e9			0.148554
$696$	−1.24759e8	−	3.70716e9i	−0.0140262	−	0.416782i
$697$	1.11223e10			1.24417
$698$	2.77343e8	+	1.33232e8i	0.0308691	+	0.0148290i
$699$	−6.39417e9	−	1.25400e9i	−0.708132	−	0.138876i
$700$	−1.06044e10	+	8.49030e9i	−1.16854	+	0.935578i
$701$	1.30713e10			1.43319			0.716596	−	0.697488i	$-0.245699\pi$
$701$	1.30713e10			1.43319			0.716596	+	0.697488i	$0.245699\pi$
$702$	1.00535e10	−	6.05358e9i	1.09683	−	0.660439i
$703$			3.27227e9i			0.355226i
$704$	1.64342e9	+	3.36258e9i	0.177519	+	0.363219i
$705$	1.00169e9	−	5.10762e9i	0.107664	−	0.548980i
$706$	−9.08045e9	−	4.36211e9i	−0.971161	−	0.466531i
$707$		−	1.77122e10i		−	1.88497i
$708$	3.99310e9	+	7.64251e9i	0.422857	+	0.809319i
$709$			2.53582e9i			0.267213i	0.991034	+	0.133606i	$0.0426558\pi$
$709$			2.53582e9i			0.267213i	−0.991034	+	0.133606i	$0.957344\pi$
$710$	1.71335e9	−	3.56662e9i	0.179656	−	0.373983i
$711$	4.61804e9	−	1.13209e10i	0.481853	−	1.18124i
$712$	1.90755e9	+	8.24722e9i	0.198060	+	0.856303i
$713$			3.98144e9i			0.411364i
$714$	1.80908e10	+	1.35114e10i	1.86001	+	1.38917i
$715$	1.77341e9			0.181442
$716$	−2.75419e8	+	2.20512e8i	−0.0280413	+	0.0224510i
$717$	5.51135e8	−	2.81025e9i	0.0558394	−	0.284726i
$718$	−5.55970e9	+	1.15734e10i	−0.560552	+	1.16688i
$719$	−9.86480e9			−0.989777			−0.494889	−	0.868956i	$-0.664791\pi$
$719$	−9.86480e9			−0.989777			−0.494889	+	0.868956i	$0.664791\pi$
$720$	−2.00502e9	+	2.88193e9i	−0.200196	+	0.287753i
$721$	1.59990e9			0.158972
$722$	−3.72326e9	+	7.75058e9i	−0.368165	+	0.766397i
$723$	−1.25598e9	+	6.40429e9i	−0.123595	+	0.630213i
$724$	1.11142e10	−	8.89849e9i	1.08841	−	0.871428i
$725$	−3.75315e9			−0.365775
$726$	6.91064e9	+	5.16130e9i	0.670255	+	0.500589i
$727$		−	6.26064e9i		−	0.604294i	−0.953261	−	0.302147i	$-0.902297\pi$
$727$		−	6.26064e9i		−	0.604294i	0.953261	−	0.302147i	$-0.0977033\pi$
$728$	2.21616e10	−	5.12589e9i	2.12883	−	0.492390i
$729$	−4.15853e9	−	9.59821e9i	−0.397551	−	0.917580i
$730$	1.06733e9	−	2.22182e9i	0.101547	−	0.211387i
$731$		−	1.36415e10i		−	1.29167i
$732$	4.95170e9	+	9.47722e9i	0.466623	+	0.893084i
$733$			1.23202e10i			1.15546i	0.816228	+	0.577730i	$0.196061\pi$
$733$			1.23202e10i			1.15546i	−0.816228	+	0.577730i	$0.803939\pi$
$734$	−1.06081e10	−	5.09595e9i	−0.990147	−	0.475651i
$735$	−1.38896e9	+	7.08234e9i	−0.129028	+	0.657917i
$736$	−8.07921e9	−	6.37933e9i	−0.746959	−	0.589797i
$737$			2.49874e9i			0.229925i
$738$	−6.70212e9	−	7.40452e9i	−0.613783	−	0.678109i
$739$	−4.48620e9			−0.408906			−0.204453	−	0.978876i	$-0.565542\pi$
$739$	−4.48620e9			−0.408906			−0.204453	+	0.978876i	$0.565542\pi$
$740$	−2.76887e9	+	2.21687e9i	−0.251184	+	0.201108i
$741$	−5.38494e9	−	1.05607e9i	−0.486202	−	0.0953521i
$742$	9.04092e9	+	4.34312e9i	0.812454	+	0.390290i
$743$	−5.92519e9			−0.529958			−0.264979	−	0.964254i	$-0.585365\pi$
$743$	−5.92519e9			−0.529958			−0.264979	+	0.964254i	$0.585365\pi$
$744$	−4.85252e9	+	1.63305e8i	−0.431979	+	0.0145376i
$745$	−2.05124e9			−0.181748
$746$	3.25104e8	+	1.56175e8i	0.0286706	+	0.0137729i
$747$	−2.48913e9	+	6.10199e9i	−0.218487	+	0.535611i
$748$	−3.93411e9	−	4.91370e9i	−0.343709	−	0.429293i
$749$	−2.87645e10			−2.50133
$750$	6.09103e9	+	4.54917e9i	0.527201	+	0.393747i
$751$			8.98243e9i			0.773845i	0.922112	+	0.386923i	$0.126462\pi$
$751$			8.98243e9i			0.773845i	−0.922112	+	0.386923i	$0.873538\pi$
$752$	−4.07120e9	+	1.81604e10i	−0.349108	+	1.55727i
$753$	1.51172e9	+	2.96472e8i	0.129029	+	0.0253047i
$754$	5.66477e9	+	2.72127e9i	0.481263	+	0.231191i
$755$			2.96849e9i			0.251027i
$756$	−1.90623e9	−	2.01855e10i	−0.160454	−	1.69908i
$757$		−	9.92682e9i		−	0.831715i	−0.909430	−	0.415857i	$-0.863482\pi$
$757$		−	9.92682e9i		−	0.831715i	0.909430	−	0.415857i	$-0.136518\pi$
$758$	2.61668e8	−	5.44705e8i	0.0218227	−	0.0454275i
$759$	4.54830e9	+	8.91996e8i	0.377575	+	0.0740485i
$760$	1.59944e9	−	3.69944e8i	0.132166	−	0.0305695i
$761$		−	1.63216e9i		−	0.134250i	−0.997745	−	0.0671252i	$-0.978617\pi$
$761$		−	1.63216e9i		−	0.134250i	0.997745	−	0.0671252i	$-0.0213827\pi$
$762$	−3.40266e9	+	4.55594e9i	−0.278597	+	0.373023i
$763$	1.89238e10			1.54231
$764$	−8.78881e9	−	1.09772e10i	−0.713023	−	0.890565i
$765$	2.23018e9	−	5.46717e9i	0.180104	−	0.441517i
$766$	6.39341e9	−	1.33089e10i	0.513963	−	1.06990i
$767$	−1.46094e10			−1.16909
$768$	7.44366e9	−	1.01085e10i	0.592956	−	0.805235i
$769$	−2.07502e10			−1.64543			−0.822717	−	0.568451i	$-0.807543\pi$
$769$	−2.07502e10			−1.64543			−0.822717	+	0.568451i	$0.807543\pi$
$770$	1.32672e9	−	2.76179e9i	0.104728	−	0.218009i
$771$	1.47732e10	+	2.89727e9i	1.16087	+	0.227666i
$772$	4.48236e9	+	5.59847e9i	0.350628	+	0.437934i
$773$	8.12995e9			0.633082			0.316541	−	0.948579i	$-0.397479\pi$
$773$	8.12995e9			0.633082			0.316541	+	0.948579i	$0.397479\pi$
$774$	−9.08163e9	+	8.22014e9i	−0.703997	+	0.637215i
$775$			4.91273e9i			0.379112i
$776$	−9.69000e9	+	2.24126e9i	−0.744402	+	0.172177i
$777$	3.94223e9	−	2.01015e10i	0.301487	−	1.53729i
$778$	3.50795e9	−	7.30237e9i	0.267070	−	0.555950i
$779$			4.67010e9i			0.353952i
$780$	−2.75454e9	−	5.27200e9i	−0.207835	−	0.397782i
$781$		−	6.37029e9i		−	0.478498i
$782$	1.56057e10	+	7.49675e9i	1.16697	+	0.560595i
$783$	3.07444e9	−	4.68263e9i	0.228876	−	0.348597i
$784$	5.64520e9	−	2.51816e10i	0.418382	−	1.86628i
$785$			7.87619e9i			0.581129i
$786$	−9.91930e9	+	1.32813e10i	−0.728622	+	0.975575i
$787$	−1.11155e10			−0.812863			−0.406431	−	0.913681i	$-0.633227\pi$
$787$	−1.11155e10			−0.812863			−0.406431	+	0.913681i	$0.633227\pi$
$788$	7.56104e9	+	9.44374e9i	0.550478	+	0.687547i
$789$	−3.28983e9	+	1.67749e10i	−0.238454	+	1.21588i
$790$	−5.58610e9	−	2.68347e9i	−0.403101	−	0.193643i
$791$	2.18700e10			1.57120
$792$	−9.00598e8	+	5.58000e9i	−0.0644158	+	0.399113i
$793$	−1.81166e10			−1.29009
$794$	4.24057e8	+	2.03711e8i	0.0300644	+	0.0144425i
$795$	5.04766e8	−	2.57381e9i	0.0356291	−	0.181674i
$796$	8.99694e9	−	7.20331e9i	0.632265	−	0.506217i
$797$	1.99468e10			1.39563			0.697813	−	0.716280i	$-0.254157\pi$
$797$	1.99468e10			1.39563			0.697813	+	0.716280i	$0.254157\pi$
$798$	−5.67324e9	+	7.59609e9i	−0.395204	+	0.529152i
$799$		−	3.13008e10i		−	2.17091i
$800$	−9.96902e9	−	7.87152e9i	−0.688395	−	0.543555i
$801$	−4.82849e9	+	1.18368e10i	−0.331969	+	0.813805i
$802$	−1.24951e10	−	6.00245e9i	−0.855322	−	0.410883i
$803$		−	3.96836e9i		−	0.270462i
$804$	7.42829e9	−	3.88117e9i	0.504072	−	0.263370i
$805$			8.42723e9i			0.569376i
$806$	3.56203e9	−	7.41497e9i	0.239621	−	0.498812i
$807$	3.46615e9	−	1.76740e10i	0.232161	−	1.18380i
$808$	1.61356e10	−	3.73211e9i	1.07608	−	0.248894i
$809$		−	1.49276e10i		−	0.991218i	−0.868546	−	0.495609i	$-0.834945\pi$
$809$		−	1.49276e10i		−	0.991218i	0.868546	−	0.495609i	$-0.165055\pi$
$810$	−4.98356e9	+	1.80972e9i	−0.329490	+	0.119650i
$811$	8.80023e9			0.579323			0.289662	−	0.957129i	$-0.406457\pi$
$811$	8.80023e9			0.579323			0.289662	+	0.957129i	$0.406457\pi$
$812$	8.47586e9	−	6.78612e9i	0.555568	−	0.444811i
$813$	−1.68601e10	−	3.30655e9i	−1.10038	−	0.215803i
$814$	−2.47272e9	+	5.14739e9i	−0.160691	+	0.334504i
$815$	−1.05940e10			−0.685501
$816$	−8.49686e9	+	1.93276e10i	−0.547448	+	1.24526i
$817$	5.72787e9			0.367465
$818$	9.71205e9	−	2.02172e10i	0.620404	−	1.29147i
$819$	3.18073e10	+	1.29749e10i	2.02318	+	0.825297i
$820$	−3.95167e9	+	3.16387e9i	−0.250283	+	0.200387i
$821$	3.08759e10			1.94723			0.973617	−	0.228187i	$-0.0732797\pi$
$821$	3.08759e10			1.94723			0.973617	+	0.228187i	$0.0732797\pi$
$822$	−1.75387e9	+	2.34831e9i	−0.110140	+	0.147470i
$823$			4.60692e9i			0.288079i	0.989572	+	0.144040i	$0.0460092\pi$
$823$			4.60692e9i			0.288079i	−0.989572	+	0.144040i	$0.953991\pi$
$824$	3.37114e8	+	1.45750e9i	0.0209909	+	0.0907534i
$825$	5.61220e9	+	1.10064e9i	0.347972	+	0.0682429i
$826$	−1.09296e10	+	2.27518e10i	−0.674798	+	1.40470i
$827$			3.42092e9i			0.210317i	0.994455	+	0.105158i	$0.0335349\pi$
$827$			3.42092e9i			0.210317i	−0.994455	+	0.105158i	$0.966465\pi$
$828$	−4.41291e9	−	1.49067e10i	−0.270159	−	0.912591i
$829$			2.62952e10i			1.60301i	0.597988	+	0.801505i	$0.295967\pi$
$829$			2.62952e10i			1.60301i	−0.597988	+	0.801505i	$0.704033\pi$
$830$	3.01092e9	+	1.44640e9i	0.182779	+	0.0878040i
$831$	−3.99211e8	−	7.82917e7i	−0.0241323	−	0.00473274i
$832$	9.33927e9	+	1.91089e10i	0.562188	+	1.15028i
$833$			4.34024e10i			2.60169i
$834$	−5.68811e9	−	4.24824e9i	−0.339537	−	0.253588i
$835$	3.84987e9			0.228846
$836$	2.06320e9	−	1.65188e9i	0.122129	−	0.0977814i
$837$	−6.12938e9	−	4.02432e9i	−0.361308	−	0.237221i
$838$	−2.03989e10	−	9.79932e9i	−1.19744	−	0.575230i
$839$	−5.64587e9			−0.330038			−0.165019	−	0.986290i	$-0.552769\pi$
$839$	−5.64587e9			−0.330038			−0.165019	+	0.986290i	$0.552769\pi$
$840$	−1.02710e10	+	3.45656e8i	−0.597910	+	0.0201218i
$841$	−1.42501e10			−0.826096
$842$	−2.37050e10	−	1.13875e10i	−1.36851	−	0.657411i
$843$	−2.15018e10	−	4.21685e9i	−1.23617	−	0.242433i
$844$	7.57666e9	+	9.46325e9i	0.433790	+	0.541803i
$845$	3.92988e9			0.224068
$846$	−2.08381e10	+	1.88614e10i	−1.18321	+	1.07097i
$847$			2.52481e10i			1.42770i
$848$	−2.05154e9	+	9.15133e9i	−0.115530	+	0.515346i
$849$	−1.61352e9	+	8.22739e9i	−0.0904895	+	0.461408i
$850$	1.92561e10	+	9.25032e9i	1.07548	+	0.516643i
$851$		−	1.57066e10i		−	0.873630i
$852$	−1.89377e10	+	9.89464e9i	−1.04903	+	0.548102i
$853$		−	9.85601e9i		−	0.543725i	−0.962336	−	0.271863i	$-0.912360\pi$
$853$		−	9.85601e9i		−	0.543725i	0.962336	−	0.271863i	$-0.0876396\pi$
$854$	−1.35534e10	+	2.82137e10i	−0.744640	+	1.55009i
$855$	2.29559e9	+	9.36420e8i	0.125607	+	0.0512377i
$856$	−6.06093e9	−	2.62042e10i	−0.330279	−	1.42795i
$857$		−	1.96505e10i		−	1.06645i	−0.845973	−	0.533226i	$-0.820980\pi$
$857$		−	1.96505e10i		−	1.06645i	0.845973	−	0.533226i	$-0.179020\pi$
$858$	−7.67266e9	−	5.73043e9i	−0.414706	−	0.309729i
$859$	4.48838e9			0.241609			0.120804	−	0.992676i	$-0.461453\pi$
$859$	4.48838e9			0.241609			0.120804	+	0.992676i	$0.461453\pi$
$860$	3.88048e9	+	4.84672e9i	0.208037	+	0.259838i
$861$	5.62625e9	−	2.86884e10i	0.300406	−	1.53177i
$862$	3.48558e9	−	7.25582e9i	0.185353	−	0.385843i
$863$	2.80201e10			1.48399			0.741996	−	0.670404i	$-0.233879\pi$
$863$	2.80201e10			1.48399			0.741996	+	0.670404i	$0.233879\pi$
$864$	1.79871e10	−	5.98982e9i	0.948776	−	0.315948i
$865$	1.26491e10			0.664510
$866$	4.87814e9	−	1.01547e10i	0.255236	−	0.531316i
$867$	3.14050e9	−	1.60135e10i	0.163656	−	0.834486i
$868$	−8.88276e9	−	1.10946e10i	−0.461030	−	0.575826i
$869$	−9.97725e9			−0.515753
$870$	−2.27487e9	−	1.69901e9i	−0.117122	−	0.0874741i
$871$			1.41999e10i			0.728152i
$872$	3.98740e9	+	1.72394e10i	0.203649	+	0.880469i
$873$	−1.39076e10	−	5.67319e9i	−0.707458	−	0.288587i
$874$	−3.14778e9	+	6.55263e9i	−0.159483	+	0.331990i
$875$			2.22537e10i			1.12298i
$876$	−1.17972e10	+	6.16385e9i	−0.592944	+	0.309804i
$877$			3.28468e10i			1.64435i	0.569235	+	0.822175i	$0.307239\pi$
$877$			3.28468e10i			1.64435i	−0.569235	+	0.822175i	$0.692761\pi$
$878$	−5.52123e9	−	2.65231e9i	−0.275299	−	0.132249i
$879$	6.98097e8	−	3.55961e9i	0.0346701	−	0.176783i
$880$	2.79552e9	+	6.26698e8i	0.138284	+	0.0310005i
$881$			3.01757e10i			1.48676i	0.668869	+	0.743381i	$0.266779\pi$
$881$			3.01757e10i			1.48676i	−0.668869	+	0.743381i	$0.733221\pi$
$882$	2.88946e10	−	2.61536e10i	1.41800	−	1.28349i
$883$	5.44440e9			0.266126			0.133063	−	0.991108i	$-0.457519\pi$
$883$	5.44440e9			0.266126			0.133063	+	0.991108i	$0.457519\pi$
$884$	−2.23568e10	−	2.79237e10i	−1.08850	−	1.35953i
$885$	6.47708e9	+	1.27026e9i	0.314107	+	0.0616015i
$886$	2.06780e10	+	9.93339e9i	0.998827	+	0.479821i
$887$	−3.12022e9			−0.150125			−0.0750623	−	0.997179i	$-0.523916\pi$
$887$	−3.12022e9			−0.150125			−0.0750623	+	0.997179i	$0.523916\pi$
$888$	1.91430e10	−	6.44228e8i	0.917410	−	0.0308741i
$889$	−1.66452e10			−0.794571
$890$	5.84065e9	+	2.80576e9i	0.277713	+	0.133409i
$891$	−5.97051e9	+	6.10046e9i	−0.282774	+	0.288929i
$892$	1.44555e9	−	1.15736e9i	0.0681955	−	0.0546001i
$893$	1.31428e10			0.617600
$894$	8.87471e9	+	6.62819e9i	0.415406	+	0.310252i
$895$			2.70071e8i			0.0125921i
$896$	3.67459e10	−	2.48622e8i	1.70660	−	0.0115468i
$897$	2.58472e10	+	5.06905e9i	1.19575	+	0.234505i
$898$	−2.41094e10	−	1.15818e10i	−1.11101	−	0.533713i
$899$		−	3.92664e9i		−	0.180245i
$900$	−5.44513e9	−	1.83936e10i	−0.248977	−	0.841041i
$901$		−	1.57730e10i		−	0.718418i
$902$	−3.52901e9	+	7.34622e9i	−0.160114	+	0.333304i
$903$	−3.51862e10	−	6.90059e9i	−1.59025	−	0.311874i
$904$	4.60820e9	+	1.99234e10i	0.207464	+	0.896961i
$905$		−	1.08984e10i		−	0.488756i
$906$	9.59209e9	−	1.28432e10i	0.428514	−	0.573751i
$907$	−2.77504e10			−1.23493			−0.617466	−	0.786597i	$-0.711841\pi$
$907$	−2.77504e10			−1.23493			−0.617466	+	0.786597i	$0.711841\pi$
$908$	3.50485e9	−	2.80613e9i	0.155371	−	0.124396i
$909$	2.31586e10	+	9.44690e9i	1.02268	+	0.417173i
$910$	7.53952e9	−	1.56948e10i	0.331664	−	0.690414i
$911$	8.55220e9			0.374769			0.187384	−	0.982287i	$-0.439999\pi$
$911$	8.55220e9			0.374769			0.187384	+	0.982287i	$0.439999\pi$
$912$	−8.11537e9	−	3.56771e9i	−0.354264	−	0.155743i
$913$	5.37775e9			0.233859
$914$	2.62778e9	−	5.47016e9i	0.113835	−	0.236967i
$915$	8.03200e9	+	1.57521e9i	0.346617	+	0.0679772i
$916$	1.01678e9	−	8.14072e8i	0.0437110	−	0.0349968i
$917$	−4.85234e10			−2.07806
$918$	−2.73150e10	+	1.64474e10i	−1.16534	+	0.701692i
$919$		−	2.54557e10i		−	1.08188i	−0.841060	−	0.540942i	$-0.818068\pi$
$919$		−	2.54557e10i		−	1.08188i	0.841060	−	0.540942i	$-0.181932\pi$
$920$	−7.67714e9	+	1.77569e9i	−0.325044	+	0.0751814i
$921$	1.21334e9	−	6.18686e9i	0.0511770	−	0.260953i
$922$	1.80295e10	−	3.75313e10i	0.757573	−	1.57701i
$923$		−	3.62012e10i		−	1.51536i
$924$	−1.46643e10	+	7.66186e9i	−0.611517	+	0.319508i
$925$		−	1.93805e10i		−	0.805134i
$926$	1.22070e10	+	5.86405e9i	0.505208	+	0.242694i
$927$	−8.53319e8	+	2.09187e9i	−0.0351830	+	0.0862493i
$928$	7.96803e9	+	6.29154e9i	0.327290	+	0.258428i
$929$		−	4.05513e10i		−	1.65940i	−0.558213	−	0.829698i	$-0.688513\pi$
$929$		−	4.05513e10i		−	1.65940i	0.558213	−	0.829698i	$-0.311487\pi$
$930$	−2.22394e9	+	2.97771e9i	−0.0906637	+	0.121393i
$931$	−1.82241e10			−0.740152
$932$	1.39222e10	−	1.11467e10i	0.563315	−	0.451013i
$933$	−5.16326e8	+	2.63275e9i	−0.0208132	+	0.106127i
$934$	1.64104e10	+	7.88332e9i	0.659032	+	0.316589i
$935$	−4.81828e9			−0.192775
$936$	−5.11793e9	+	3.17101e10i	−0.203999	+	1.26396i
$937$	3.65689e10			1.45219			0.726095	−	0.687595i	$-0.241333\pi$
$937$	3.65689e10			1.45219			0.726095	+	0.687595i	$0.241333\pi$
$938$	2.21140e10	+	1.06232e10i	0.874899	+	0.420288i
$939$	−2.90338e9	+	1.48044e10i	−0.114439	+	0.583527i
$940$	8.90388e9	+	1.11209e10i	0.349649	+	0.436711i
$941$	−3.29243e10			−1.28811			−0.644054	−	0.764980i	$-0.722749\pi$
$941$	−3.29243e10			−1.28811			−0.644054	+	0.764980i	$0.722749\pi$
$942$	2.54504e10	−	3.40764e10i	0.992011	−	1.32824i
$943$		−	2.24160e10i		−	0.870496i
$944$	−2.30296e10	−	5.16276e9i	−0.891014	−	0.199747i
$945$	−1.29736e10	−	8.51800e9i	−0.500092	−	0.328342i
$946$	9.01013e9	+	4.32833e9i	0.346029	+	0.166227i
$947$			4.41627e10i			1.68978i	0.534939	+	0.844890i	$0.320334\pi$
$947$			4.41627e10i			1.68978i	−0.534939	+	0.844890i	$0.679666\pi$
$948$	1.54971e10	+	2.96605e10i	0.590776	+	1.13070i
$949$		−	2.25515e10i		−	0.856531i
$950$	−3.88408e9	+	8.08535e9i	−0.146979	+	0.305961i
$951$	−5.78304e9	+	2.94878e10i	−0.218034	+	1.11176i
$952$	−6.02121e10	+	1.39268e10i	−2.26180	+	0.523147i
$953$		−	5.08539e10i		−	1.90326i	−0.307240	−	0.951632i	$-0.599405\pi$
$953$		−	5.08539e10i		−	1.90326i	0.307240	−	0.951632i	$-0.400595\pi$
$954$	−1.05007e10	+	9.50456e9i	−0.391559	+	0.354415i
$955$	−1.07640e10			−0.399912
$956$	4.89898e9	+	6.11882e9i	0.181344	+	0.226498i
$957$	−4.48571e9	−	8.79720e8i	−0.165440	−	0.0324454i
$958$	−7.59135e9	+	1.58027e10i	−0.278959	+	0.580699i
$959$	−8.57960e9			−0.314124
$960$	−2.47908e9	−	9.28397e9i	−0.0904360	−	0.338676i
$961$	2.23728e10			0.813183
$962$	−1.40520e10	+	2.92517e10i	−0.508893	+	1.05935i
$963$	1.53417e10	−	3.76095e10i	0.553582	−	1.35708i
$964$	−1.11643e10	−	1.39442e10i	−0.401386	−	0.501331i
$965$	5.48975e9			0.196656
$966$	2.72310e10	−	3.64605e10i	0.971949	−	1.30137i
$967$			2.73207e10i			0.971626i	0.874063	+	0.485813i	$0.161476\pi$
$967$			2.73207e10i			0.971626i	−0.874063	+	0.485813i	$0.838524\pi$
$968$	−2.30008e10	+	5.32001e9i	−0.815042	+	0.188516i
$969$	1.46307e10	+	2.86931e9i	0.516573	+	0.101308i
$970$	−3.29660e9	+	6.86243e9i	−0.115975	+	0.241422i
$971$			3.90577e10i			1.36911i	0.728960	+	0.684556i	$0.240004\pi$
$971$			3.90577e10i			1.36911i	−0.728960	+	0.684556i	$0.759996\pi$
$972$	2.74092e10	+	8.27366e9i	0.957335	+	0.288979i
$973$		−	2.07816e10i		−	0.723243i
$974$	2.65308e10	+	1.27450e10i	0.920013	+	0.441960i
$975$	3.18931e10	+	6.25475e9i	1.10200	+	0.216119i
$976$	−2.85582e10	−	6.40217e9i	−0.983234	−	0.220421i
$977$			2.40824e10i			0.826169i	0.910693	+	0.413084i	$0.135549\pi$
$977$			2.40824e10i			0.826169i	−0.910693	+	0.413084i	$0.864451\pi$
$978$	4.58350e10	+	3.42325e10i	1.56679	+	1.17018i
$979$	1.04319e10			0.355324
$980$	−1.23463e10	−	1.54205e10i	−0.419031	−	0.523369i
$981$	−1.00931e10	+	2.47428e10i	−0.341337	+	0.836772i
$982$	4.89482e10	+	2.35140e10i	1.64948	+	0.792384i
$983$	−3.69454e10			−1.24058			−0.620288	−	0.784374i	$-0.712984\pi$
$983$	−3.69454e10			−1.24058			−0.620288	+	0.784374i	$0.712984\pi$
$984$	2.73203e10	−	9.19426e8i	0.914120	−	0.0307634i
$985$	9.26035e9			0.308745
$986$	−1.53910e10	−	7.39358e9i	−0.511325	−	0.245633i
$987$	−8.07360e10	−	1.58336e10i	−2.67274	−	0.524168i
$988$	1.17248e10	−	9.38732e9i	0.386772	−	0.309665i
$989$	−2.74932e10			−0.903729
$990$	2.90342e9	+	3.20771e9i	0.0951014	+	0.105068i
$991$			3.49760e10i			1.14160i	0.821091	+	0.570798i	$0.193366\pi$
$991$			3.49760e10i			1.14160i	−0.821091	+	0.570798i	$0.806634\pi$
$992$	8.23538e9	−	1.04298e10i	0.267851	−	0.339224i
$993$	−9.99465e9	+	5.09629e10i	−0.323926	+	1.65170i
$994$	−5.63774e10	−	2.70828e10i	−1.82076	−	0.874665i
$995$		−	8.82222e9i		−	0.283921i
$996$	−8.35299e9	−	1.59870e10i	−0.267876	−	0.512696i
$997$			1.40243e10i			0.448174i	0.974569	+	0.224087i	$0.0719400\pi$
$997$			1.40243e10i			0.448174i	−0.974569	+	0.224087i	$0.928060\pi$
$998$	1.11637e9	−	2.32391e9i	0.0355510	−	0.0740053i
$999$	2.41801e10	+	1.58757e10i	0.767323	+	0.503796i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	24.8.f.b.11.3	yes	4
3.2	odd	2	inner	24.8.f.b.11.2	yes	4
4.3	odd	2		96.8.f.b.47.1		4
8.3	odd	2	inner	24.8.f.b.11.1	✓	4
8.5	even	2		96.8.f.b.47.2		4
12.11	even	2		96.8.f.b.47.4		4
24.5	odd	2		96.8.f.b.47.3		4
24.11	even	2	inner	24.8.f.b.11.4	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.8.f.b.11.1	✓	4	8.3	odd	2	inner
24.8.f.b.11.2	yes	4	3.2	odd	2	inner
24.8.f.b.11.3	yes	4	1.1	even	1	trivial
24.8.f.b.11.4	yes	4	24.11	even	2	inner
96.8.f.b.47.1		4	4.3	odd	2
96.8.f.b.47.2		4	8.5	even	2
96.8.f.b.47.3		4	24.5	odd	2
96.8.f.b.47.4		4	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:	\( N \)	\(=\)	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	24.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(4.89898 - 10.1980i) q^{2} +(-9.00000 + 45.8912i) q^{3} +(-80.0000 - 99.9200i) q^{4} -97.9796 q^{5} +(423.909 + 316.602i) q^{6} +1548.76i q^{7} +(-1410.91 + 326.337i) q^{8} +(-2025.00 - 826.041i) q^{9} +O(q^{10})\)	\(q+(4.89898 - 10.1980i) q^{2} +(-9.00000 + 45.8912i) q^{3} +(-80.0000 - 99.9200i) q^{4} -97.9796 q^{5} +(423.909 + 316.602i) q^{6} +1548.76i q^{7} +(-1410.91 + 326.337i) q^{8} +(-2025.00 - 826.041i) q^{9} +(-480.000 + 999.200i) q^{10} +1784.66i q^{11} +(5305.44 - 2772.01i) q^{12} +10141.9i q^{13} +(15794.3 + 7587.34i) q^{14} +(881.816 - 4496.40i) q^{15} +(-3584.00 + 15987.2i) q^{16} -27555.1i q^{17} +(-18344.4 + 16604.3i) q^{18} +11570.0 q^{19} +(7838.37 + 9790.12i) q^{20} +(-71074.4 - 13938.8i) q^{21} +(18200.0 + 8743.00i) q^{22} -55534.8 q^{23} +(-2277.85 - 67685.2i) q^{24} -68525.0 q^{25} +(103427. + 49684.8i) q^{26} +(56133.0 - 85495.3i) q^{27} +(154752. - 123901. i) q^{28} +54770.6 q^{29} +(-41534.4 - 31020.6i) q^{30} -71692.6i q^{31} +(145480. + 114871. i) q^{32} +(-81900.0 - 16061.9i) q^{33} +(-281008. - 134992. i) q^{34} -151747. i q^{35} +(79462.0 + 268421. i) q^{36} +282823. i q^{37} +(56681.2 - 117991. i) q^{38} +(-465423. - 91276.9i) q^{39} +(138240. - 31974.4i) q^{40} +403638. i q^{41} +(-490341. + 656533. i) q^{42} +495062. q^{43} +(178323. - 142773. i) q^{44} +(198409. + 80935.2i) q^{45} +(-272064. + 566346. i) q^{46} +1.13594e6 q^{47} +(-701415. - 308359. i) q^{48} -1.57511e6 q^{49} +(-335703. + 698821. i) q^{50} +(1.26454e6 + 247996. i) q^{51} +(1.01338e6 - 811350. i) q^{52} +572416. q^{53} +(-596890. - 991286. i) q^{54} -174860. i q^{55} +(-505418. - 2.18515e6i) q^{56} +(-104130. + 530961. i) q^{57} +(268320. - 558553. i) q^{58} +1.44050e6i q^{59} +(-519825. + 271601. i) q^{60} +1.78632e6i q^{61} +(-731124. - 351220. i) q^{62} +(1.27934e6 - 3.13624e6i) q^{63} +(1.88416e6 - 920862. i) q^{64} -993697. i q^{65} +(-565026. + 756532. i) q^{66} +1.40013e6 q^{67} +(-2.75330e6 + 2.20441e6i) q^{68} +(499813. - 2.54856e6i) q^{69} +(-1.54752e6 - 743405. i) q^{70} -3.56947e6 q^{71} +(3.12665e6 + 504634. i) q^{72} -2.22360e6 q^{73} +(2.88424e6 + 1.38555e6i) q^{74} +(616725. - 3.14469e6i) q^{75} +(-925600. - 1.15607e6i) q^{76} -2.76400e6 q^{77} +(-3.21094e6 + 4.29923e6i) q^{78} +5.59057e6i q^{79} +(351159. - 1.56642e6i) q^{80} +(3.41828e6 + 3.34547e6i) q^{81} +(4.11632e6 + 1.97742e6i) q^{82} -3.01333e6i q^{83} +(4.29318e6 + 8.21686e6i) q^{84} +2.69984e6i q^{85} +(2.42530e6 - 5.04866e6i) q^{86} +(-492935. + 2.51349e6i) q^{87} +(-582400. - 2.51798e6i) q^{88} -5.84533e6i q^{89} +(1.79738e6 - 1.62688e6i) q^{90} -1.57073e7 q^{91} +(4.44279e6 + 5.54904e6i) q^{92} +(3.29006e6 + 645233. i) q^{93} +(5.56493e6 - 1.15843e7i) q^{94} -1.13362e6 q^{95} +(-6.58087e6 + 5.64242e6i) q^{96} +6.86793e6 q^{97} +(-7.71645e6 + 1.60631e7i) q^{98} +(1.47420e6 - 3.61393e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 36 q^{3} - 320 q^{4} + 1872 q^{6} - 8100 q^{9}+O(q^{10}) \) 4 * q - 36 * q^3 - 320 * q^4 + 1872 * q^6 - 8100 * q^9	\( 4 q - 36 q^{3} - 320 q^{4} + 1872 q^{6} - 8100 q^{9} - 1920 q^{10} + 2880 q^{12} - 14336 q^{16} - 33696 q^{18} + 46280 q^{19} + 72800 q^{22} - 59904 q^{24} - 274100 q^{25} + 224532 q^{27} + 619008 q^{28} + 17280 q^{30} - 327600 q^{33} - 1124032 q^{34} + 648000 q^{36} + 552960 q^{40} - 1392768 q^{42} + 1980248 q^{43} - 1088256 q^{46} + 129024 q^{48} - 6300452 q^{49} + 5058144 q^{51} + 4053504 q^{52} - 3487536 q^{54} - 416520 q^{57} + 1073280 q^{58} - 1797120 q^{60} + 7536640 q^{64} - 655200 q^{66} + 5600504 q^{67} - 6190080 q^{70} + 1078272 q^{72} - 8894392 q^{73} + 2466900 q^{75} - 3702400 q^{76} - 9120384 q^{78} + 13673124 q^{81} + 16465280 q^{82} - 5571072 q^{84} - 2329600 q^{88} + 3888000 q^{90} - 62829312 q^{91} + 22259712 q^{94} - 21086208 q^{96} + 27471704 q^{97} + 5896800 q^{99}+O(q^{100}) \) 4 * q - 36 * q^3 - 320 * q^4 + 1872 * q^6 - 8100 * q^9 - 1920 * q^10 + 2880 * q^12 - 14336 * q^16 - 33696 * q^18 + 46280 * q^19 + 72800 * q^22 - 59904 * q^24 - 274100 * q^25 + 224532 * q^27 + 619008 * q^28 + 17280 * q^30 - 327600 * q^33 - 1124032 * q^34 + 648000 * q^36 + 552960 * q^40 - 1392768 * q^42 + 1980248 * q^43 - 1088256 * q^46 + 129024 * q^48 - 6300452 * q^49 + 5058144 * q^51 + 4053504 * q^52 - 3487536 * q^54 - 416520 * q^57 + 1073280 * q^58 - 1797120 * q^60 + 7536640 * q^64 - 655200 * q^66 + 5600504 * q^67 - 6190080 * q^70 + 1078272 * q^72 - 8894392 * q^73 + 2466900 * q^75 - 3702400 * q^76 - 9120384 * q^78 + 13673124 * q^81 + 16465280 * q^82 - 5571072 * q^84 - 2329600 * q^88 + 3888000 * q^90 - 62829312 * q^91 + 22259712 * q^94 - 21086208 * q^96 + 27471704 * q^97 + 5896800 * q^99

Introduction

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