LMFDB - Embedded newform 24.8.f.b.11.1

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			11.1
Root			$-1.22474 - 2.54951i$ of defining polynomial
Character	$\chi$	$=$	24.11
Dual form			24.8.f.b.11.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.89898 - 10.1980i) q^{2} +(-9.00000 + 45.8912i) q^{3} +(-80.0000 + 99.9200i) q^{4} +97.9796 q^{5} +(512.091 - 133.038i) q^{6} -1548.76i q^{7} +(1410.91 + 326.337i) q^{8} +(-2025.00 - 826.041i) q^{9} +O(q^{10})$	\(q+(-4.89898 - 10.1980i) q^{2} +(-9.00000 + 45.8912i) q^{3} +(-80.0000 + 99.9200i) q^{4} +97.9796 q^{5} +(512.091 - 133.038i) 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} +(-3865.44 - 4570.57i) 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} +(1496.43 + 24697.8i) 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} +(-27674.2 + 61811.1i) 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} +(50174.4 - 13035.0i) 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} +(244538. - 136255. 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} +(-206043. - 793106. 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} +(765927. - 20589.2i) 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} +(-1.14688e6 - 153607. 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} +(-378735. - 447823. 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} +(237426. + 913906. 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} +(-2.58752e6 - 1.82630e6i) 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} +(-1.34925e6 - 5.19356e6i) 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} +(-7.07872e6 + 5.98664e6i) 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} +(146620. + 2.41988e6i) 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} +(-3.96223e6 - 7.71009e6i) 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	$-0.443920\pi$
$5$	97.9796			0.350542			0.175271	+	0.984520i	$0.443920\pi$
$6$	512.091	−	133.038i	0.967871	−	0.251446i
$7$		−	1548.76i		−	1.70664i	−0.521391	−	0.853318i	$-0.674587\pi$
$7$		−	1548.76i		−	1.70664i	0.521391	−	0.853318i	$-0.325413\pi$
$8$	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	$0.935211\pi$
$12$	−3865.44	−	4570.57i	−0.645751	−	0.763548i
$13$		−	10141.9i		−	1.28031i	−0.768244	−	0.640157i	$-0.778869\pi$
$13$		−	10141.9i		−	1.28031i	0.768244	−	0.640157i	$-0.221131\pi$
$14$	−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	$-0.238083\pi$
$18$	1496.43	+	24697.8i	0.0604789	+	0.998169i
$19$	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	$-0.342133\pi$
$23$	55534.8			0.951739			0.475870	+	0.879516i	$0.342133\pi$
$24$	−27674.2	+	61811.1i	−0.408634	+	0.912698i
$25$	−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	$-0.566861\pi$
$29$	−54770.6			−0.417018			−0.208509	+	0.978020i	$0.566861\pi$
$30$	50174.4	−	13035.0i	0.339280	−	0.0881425i
$31$			71692.6i			0.432223i	0.976369	+	0.216112i	$0.0693375\pi$
$31$			71692.6i			0.432223i	−0.976369	+	0.216112i	$0.930662\pi$
$32$	−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
$36$	244538.	−	136255.i	0.873550	−	0.486735i
$37$		−	282823.i		−	0.917930i	−0.888454	−	0.458965i	$-0.848220\pi$
$37$		−	282823.i		−	0.917930i	0.888454	−	0.458965i	$-0.151780\pi$
$38$	−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	$0.848810\pi$
$42$	−206043.	−	793106.i	−0.429127	−	1.65180i
$43$	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	$-0.794088\pi$
$47$	−1.13594e6			−1.59592			−0.797961	+	0.602710i	$0.794088\pi$
$48$	765927.	−	20589.2i	0.999639	−	0.0268717i
$49$	−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	$-0.585064\pi$
$53$	−572416.			−0.528137			−0.264068	+	0.964504i	$0.585064\pi$
$54$	−1.14688e6	−	153607.i	−0.991150	−	0.132749i
$55$			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	$0.849080\pi$
$60$	−378735.	−	447823.i	−0.226363	−	0.267656i
$61$		−	1.78632e6i		−	1.00764i	−0.863809	−	0.503819i	$-0.831928\pi$
$61$		−	1.78632e6i		−	1.00764i	0.863809	−	0.503819i	$-0.168072\pi$
$62$	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
$66$	237426.	+	913906.i	0.101654	+	0.391289i
$67$	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	$-0.298420\pi$
$71$	3.56947e6			1.18359			0.591793	+	0.806090i	$0.298420\pi$
$72$	−2.58752e6	−	1.82630e6i	−0.816995	−	0.576645i
$73$	−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
$78$	−1.34925e6	−	5.19356e6i	−0.321930	−	1.23918i
$79$		−	5.59057e6i		−	1.27574i	−0.770145	−	0.637869i	$-0.779816\pi$
$79$		−	5.59057e6i		−	1.27574i	0.770145	−	0.637869i	$-0.220184\pi$
$80$	−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	$-0.0933991\pi$
$84$	−7.07872e6	+	5.98664e6i	−1.30310	+	1.10206i
$85$		−	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	$-0.144828\pi$
$90$	146620.	+	2.41988e6i	0.0212004	+	0.349901i
$91$	−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
$96$	−3.96223e6	−	7.71009e6i	−0.457078	−	0.889427i
$97$	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	$-0.313771\pi$
$101$	1.14364e7			1.10449			0.552246	+	0.833681i	$0.313771\pi$
$102$	−3.66586e6	−	1.41107e7i	−0.342039	−	1.31658i
$103$			1.03302e6i			0.0931493i	0.998915	+	0.0465746i	$0.0148305\pi$
$103$			1.03302e6i			0.0931493i	−0.998915	+	0.0465746i	$0.985169\pi$
$104$	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	$0.738202\pi$
$108$	4.05204e6	+	1.24484e7i	0.309522	+	0.950892i
$109$			1.22187e7i			0.903714i	0.892090	+	0.451857i	$0.149238\pi$
$109$			1.22187e7i			0.903714i	−0.892090	+	0.451857i	$0.850762\pi$
$110$	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	$-0.152265\pi$
$114$	5.92489e6	−	1.53924e6i	0.374553	−	0.0973062i
$115$	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
$120$	−2.71150e6	+	6.05623e6i	−0.143244	+	0.319939i
$121$	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
$126$	3.82509e7	−	2.31762e6i	1.70351	−	0.103215i
$127$		−	1.07474e7i		−	0.465578i	−0.972527	−	0.232789i	$-0.925215\pi$
$127$		−	1.07474e7i		−	0.465578i	0.972527	−	0.232789i	$-0.0747851\pi$
$128$	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	$0.791644\pi$
$132$	8.15691e6	−	6.89849e6i	0.308686	−	0.261063i
$133$		−	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	$0.970664\pi$
$138$	2.84389e7	−	7.38822e6i	0.921161	−	0.239311i
$139$	−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
$144$	−5.94848e6	+	3.53346e7i	−0.166011	+	0.986124i
$145$	−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	$-0.583472\pi$
$149$	−2.09354e7			−0.518477			−0.259238	+	0.965813i	$0.583472\pi$
$150$	−3.50910e7	+	9.11640e6i	−0.848939	+	0.220548i
$151$			3.02970e7i			0.716111i	0.933700	+	0.358055i	$0.116560\pi$
$151$			3.02970e7i			0.716111i	−0.933700	+	0.358055i	$0.883440\pi$
$152$	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
$156$	−4.63542e7	+	3.92029e7i	−0.977581	+	0.826764i
$157$			8.03861e7i			1.65780i	0.559397	+	0.828900i	$0.311033\pi$
$157$			8.03861e7i			1.65780i	−0.559397	+	0.828900i	$0.688967\pi$
$158$	−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
$162$	1.73711e7	−	5.12491e7i	0.321015	−	0.947074i
$163$	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	$-0.394159\pi$
$167$	3.92926e7			0.652834			0.326417	+	0.945226i	$0.394159\pi$
$168$	9.57305e7	+	4.28606e7i	1.55764	+	0.697390i
$169$	−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	$-0.103270\pi$
$173$	1.29099e8			1.89566			0.947831	+	0.318772i	$0.103270\pi$
$174$	−2.80475e7	+	7.28655e6i	−0.403619	+	0.104857i
$175$			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	$-0.00571741\pi$
$180$	2.39597e7	−	1.33502e7i	0.306216	−	0.170621i
$181$		−	1.11231e8i		−	1.39428i	−0.716933	−	0.697142i	$-0.754455\pi$
$181$		−	1.11231e8i		−	1.39428i	0.716933	−	0.697142i	$-0.245545\pi$
$182$	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
$186$	9.53781e6	+	3.67131e7i	0.108681	+	0.418337i
$187$	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	$-0.693219\pi$
$191$	−1.09860e8			−1.14084			−0.570418	+	0.821354i	$0.693219\pi$
$192$	−5.92169e7	+	7.81786e7i	−0.603798	+	0.797138i
$193$	−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	$-0.354843\pi$
$197$	9.45130e7			0.880765			0.440382	+	0.897810i	$0.354843\pi$
$198$	−4.40771e7	+	2.67062e6i	−0.403538	+	0.0244503i
$199$		−	9.00414e7i		−	0.809947i	−0.914328	−	0.404974i	$-0.867281\pi$
$199$		−	9.00414e7i		−	0.809947i	0.914328	−	0.404974i	$-0.132719\pi$
$200$	−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
$204$	−1.25943e8	+	1.06513e8i	−1.03865	+	0.878407i
$205$			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
$210$	−2.01880e7	−	7.77082e7i	−0.150427	−	0.579027i
$211$	−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
$216$	1.07099e8	−	1.02307e8i	0.723096	−	0.690747i
$217$	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
$222$	−3.76261e7	−	1.44831e8i	−0.230810	−	0.888438i
$223$		−	1.44671e7i		−	0.0873601i	−0.999046	−	0.0436801i	$-0.986092\pi$
$223$		−	1.44671e7i		−	0.0873601i	0.999046	−	0.0436801i	$-0.0139082\pi$
$224$	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	$0.968270\pi$
$228$	−4.47232e7	−	5.28815e7i	−0.249897	−	0.295483i
$229$		−	1.01759e7i		−	0.0559949i	−0.999608	−	0.0279975i	$-0.991087\pi$
$229$		−	1.01759e7i		−	0.0559949i	0.999608	−	0.0279975i	$-0.00891303\pi$
$230$	−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	$0.882500\pi$
$234$	2.50482e8	−	1.51766e7i	1.27797	−	0.0774320i
$235$	−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	$-0.453658\pi$
$239$	6.12372e7			0.290150			0.145075	+	0.989421i	$0.453658\pi$
$240$	7.50452e7	−	2.01732e6i	0.350416	−	0.00941968i
$241$	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
$246$	5.36991e7	+	2.06700e8i	0.229982	+	0.885251i
$247$		−	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	$-0.0209419\pi$
$252$	−2.11026e8	−	3.78731e8i	−0.830679	−	1.49083i
$253$			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	$-0.201461\pi$
$258$	2.53517e8	−	6.58618e7i	0.919047	−	0.238762i
$259$	−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	$-0.712673\pi$
$263$	−3.65537e8			−1.23904			−0.619521	+	0.784980i	$0.712673\pi$
$264$	−1.10312e8	−	4.93889e7i	−0.368984	−	0.165202i
$265$	−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	$-0.293903\pi$
$269$	3.85128e8			1.20635			0.603173	+	0.797611i	$0.293903\pi$
$270$	−1.12371e8	−	1.50504e7i	−0.347440	−	0.0465343i
$271$		−	3.67394e8i		−	1.12135i	−0.828037	−	0.560673i	$-0.810543\pi$
$271$		−	3.67394e8i		−	1.12135i	0.828037	−	0.560673i	$-0.189457\pi$
$272$	−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
$276$	−2.14667e8	−	2.53826e8i	−0.614587	−	0.726699i
$277$		−	8.69908e6i		−	0.0245920i	−0.999924	−	0.0122960i	$-0.996086\pi$
$277$		−	8.69908e6i		−	0.0245920i	0.999924	−	0.0122960i	$-0.00391404\pi$
$278$	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	$0.783113\pi$
$282$	−5.81702e8	+	1.51122e8i	−1.54465	+	0.401288i
$283$	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
$288$	3.89485e8	−	1.12441e8i	0.960765	−	0.277364i
$289$	−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	$-0.471289\pi$
$293$	7.75663e7			0.180151			0.0900755	+	0.995935i	$0.471289\pi$
$294$	−8.06601e8	+	2.09549e8i	−1.85116	+	0.480917i
$295$			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
$300$	2.64880e8	+	3.13199e8i	0.566401	+	0.669723i
$301$		−	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
$306$	6.80550e8	−	4.12344e7i	1.35780	−	0.0822687i
$307$	−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	$-0.517221\pi$
$311$	−5.73695e7			−0.108148			−0.0540742	+	0.998537i	$0.517221\pi$
$312$	6.26881e8	+	2.80668e8i	1.16854	+	0.523181i
$313$	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	$-0.691691\pi$
$317$	−6.42560e8			−1.13294			−0.566469	+	0.824083i	$0.691691\pi$
$318$	−2.93129e8	+	7.61529e7i	−0.511169	+	0.132798i
$319$		−	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
$324$	−6.07741e8	+	7.39172e7i	−0.992685	+	0.120736i
$325$			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
$330$	2.32629e7	+	8.95442e7i	0.0356341	+	0.137163i
$331$	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
$336$	−3.18877e7	−	1.18624e9i	−0.0458602	−	1.70602i
$337$	−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
$342$	1.73137e7	+	2.85753e8i	0.0234045	+	0.386278i
$343$			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	$-0.0870014\pi$
$348$	2.11713e8	+	2.50333e8i	0.269290	+	0.318413i
$349$		−	2.71958e7i		−	0.0342462i	−0.999853	−	0.0171231i	$-0.994549\pi$
$349$		−	2.71958e7i		−	0.0342462i	0.999853	−	0.0171231i	$-0.00545072\pi$
$350$	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	$-0.181086\pi$
$354$	1.91641e8	+	7.37669e8i	0.229603	+	0.883792i
$355$	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	$-0.275911\pi$
$359$	1.13487e9			1.29454			0.647269	+	0.762261i	$0.275911\pi$
$360$	−2.53524e8	−	1.78940e8i	−0.286391	−	0.202138i
$361$	−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
$366$	−2.37648e8	−	9.14758e8i	−0.253367	−	0.975264i
$367$			1.04021e9i			1.09847i	0.835668	+	0.549235i	$0.185081\pi$
$367$			1.04021e9i			1.09847i	−0.835668	+	0.549235i	$0.814919\pi$
$368$	−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
$372$	3.27676e8	−	2.77124e8i	0.330023	−	0.279109i
$373$		−	3.18791e7i		−	0.0318072i	−0.999874	−	0.0159036i	$-0.994938\pi$
$373$		−	3.18791e7i		−	0.0318072i	0.999874	−	0.0159036i	$-0.00506249\pi$
$374$	−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
$378$	−2.37900e8	+	1.77624e9i	−0.226555	+	1.69153i
$379$	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	$-0.702244\pi$
$383$	−1.30505e9			−1.18695			−0.593473	+	0.804854i	$0.702244\pi$
$384$	1.08737e9	+	2.20901e8i	0.979982	+	0.199085i
$385$	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	$-0.599789\pi$
$389$	−7.16057e8			−0.616771			−0.308385	+	0.951262i	$0.599789\pi$
$390$	−1.32199e8	−	5.08863e8i	−0.112850	−	0.434385i
$391$		−	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
$396$	2.43168e8	+	4.36416e8i	0.196776	+	0.353157i
$397$		−	4.15822e7i		−	0.0333535i	−0.999861	−	0.0166767i	$-0.994691\pi$
$397$		−	4.15822e7i		−	0.0333535i	0.999861	−	0.0166767i	$-0.00530862\pi$
$398$	−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	$-0.157352\pi$
$402$	7.16992e8	−	1.86269e8i	0.550456	−	0.143005i
$403$	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
$408$	1.70321e9	+	7.62564e8i	1.24153	+	0.555860i
$409$	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
$414$	8.31042e7	+	1.37159e9i	0.0575601	+	0.949997i
$415$		−	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	$-0.231236\pi$
$420$	−6.93570e8	+	5.86569e8i	−0.456791	+	0.386319i
$421$			2.32447e9i			1.51823i	0.650959	+	0.759113i	$0.274367\pi$
$421$			2.32447e9i			1.51823i	−0.650959	+	0.759113i	$0.725633\pi$
$422$	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
$426$	1.82790e9	−	4.74874e8i	1.14556	−	0.297608i
$427$	−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	$-0.568658\pi$
$431$	−7.11491e8			−0.428055			−0.214027	+	0.976828i	$0.568658\pi$
$432$	−1.56801e9	−	5.90994e8i	−0.935741	−	0.352688i
$433$	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
$438$	−1.13868e9	+	2.95822e8i	−0.647506	+	0.168218i
$439$			5.41401e8i			0.305417i	0.988271	+	0.152708i	$0.0487995\pi$
$439$			5.41401e8i			0.305417i	−0.988271	+	0.152708i	$0.951200\pi$
$440$	−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	$0.813082\pi$
$444$	−1.29267e9	+	1.09324e9i	−0.700883	+	0.592754i
$445$		−	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	$-0.211361\pi$
$450$	−1.02543e8	−	1.69242e9i	−0.0530472	−	0.875514i
$451$	−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
$456$	−3.20190e8	+	7.15154e8i	−0.158136	+	0.353202i
$457$	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	$-0.838987\pi$
$461$	−3.68025e9			−1.74954			−0.874770	+	0.484539i	$0.838987\pi$
$462$	1.41542e9	−	3.67716e8i	0.667788	−	0.173487i
$463$		−	1.19699e9i		−	0.560478i	−0.959930	−	0.280239i	$-0.909586\pi$
$463$		−	1.19699e9i		−	0.560478i	0.959930	−	0.280239i	$-0.0904138\pi$
$464$	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	$0.880876\pi$
$468$	−1.38188e9	−	2.48007e9i	−0.623174	−	1.11842i
$469$		−	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
$474$	−7.43756e8	−	2.86288e9i	−0.320779	−	1.23475i
$475$	−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	$-0.395607\pi$
$479$	1.54958e9			0.644227			0.322114	+	0.946701i	$0.395607\pi$
$480$	−3.88218e8	−	7.55431e8i	−0.160225	−	0.311782i
$481$	−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
$486$	2.19554e9	+	1.25842e9i	0.867591	+	0.497279i
$487$		−	2.60156e9i		−	1.02066i	−0.859978	−	0.510331i	$-0.829523\pi$
$487$		−	2.60156e9i		−	1.02066i	0.859978	−	0.510331i	$-0.170477\pi$
$488$	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	$0.632217\pi$
$492$	1.84486e9	−	1.56024e9i	0.698370	−	0.590628i
$493$			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
$498$	−4.00886e8	−	1.54310e9i	−0.145451	−	0.559874i
$499$	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	$-0.597422\pi$
$503$	−1.71998e9			−0.602609			−0.301304	+	0.953528i	$0.597422\pi$
$504$	−2.82850e9	+	4.00744e9i	−0.984122	+	1.39431i
$505$	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	$-0.369027\pi$
$509$	2.37984e9			0.799900			0.399950	+	0.916537i	$0.369027\pi$
$510$	−3.59180e8	−	1.38256e9i	−0.119899	−	0.461518i
$511$			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
$516$	−1.91363e9	−	2.26272e9i	−0.613176	−	0.725031i
$517$		−	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	$0.945506\pi$
$522$	−8.19605e7	−	1.35271e9i	−0.0252208	−	0.416254i
$523$	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
$528$	3.67447e7	+	1.36692e9i	0.0108637	+	0.404132i
$529$	−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
$534$	−7.77649e8	−	2.99334e9i	−0.220998	−	0.850671i
$535$			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
$540$	3.97018e8	+	1.21969e9i	0.108500	+	0.333328i
$541$		−	2.75610e9i		−	0.748351i	−0.927358	−	0.374175i	$-0.877926\pi$
$541$		−	2.75610e9i		−	0.748351i	0.927358	−	0.374175i	$-0.122074\pi$
$542$	−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
$546$	−8.04358e9	+	2.08966e9i	−2.11483	+	0.549417i
$547$	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
$552$	−1.53688e9	+	3.43267e9i	−0.388914	+	0.868651i
$553$	−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	$-0.392715\pi$
$557$	2.69747e9			0.661400			0.330700	+	0.943736i	$0.392715\pi$
$558$	−1.77065e9	+	1.07283e8i	−0.431432	+	0.0261404i
$559$		−	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	$-0.102792\pi$
$564$	4.39090e9	+	5.19188e9i	1.03057	+	1.21856i
$565$		−	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	$-0.0591286\pi$
$570$	5.80518e8	−	1.50815e8i	0.131297	−	0.0341100i
$571$	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
$576$	−3.05475e9	−	3.42114e9i	−0.666036	−	0.745920i
$577$	−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
$582$	3.51700e9	−	9.13692e8i	0.739507	−	0.192119i
$583$		−	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	$-0.0503284\pi$
$588$	6.08851e9	+	7.19917e9i	1.23507	+	1.46037i
$589$			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	$-0.0795655\pi$
$594$	2.74136e8	−	2.04678e9i	0.0536677	−	0.400700i
$595$	−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	$-0.299481\pi$
$599$	6.19749e9			1.17821			0.589104	+	0.808058i	$0.299481\pi$
$600$	1.89637e9	−	4.23561e9i	0.358421	−	0.800546i
$601$	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
$606$	5.85645e9	−	1.52146e9i	1.06901	−	0.277720i
$607$			1.08410e9i			0.196748i	0.995150	+	0.0983740i	$0.0313641\pi$
$607$			1.08410e9i			0.196748i	−0.995150	+	0.0983740i	$0.968636\pi$
$608$	−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
$612$	−3.75451e9	−	6.73827e9i	−0.662100	−	1.18828i
$613$		−	3.88620e9i		−	0.681418i	−0.940169	−	0.340709i	$-0.889333\pi$
$613$		−	3.88620e9i		−	0.681418i	0.940169	−	0.340709i	$-0.110667\pi$
$614$	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	$-0.0598496\pi$
$618$	1.37431e8	+	5.29001e8i	0.0234220	+	0.0901565i
$619$	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
$624$	−2.08813e8	−	7.76794e9i	−0.0344043	−	1.27985i
$625$	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
$630$	3.74781e9	−	2.27079e8i	0.597153	−	0.0361814i
$631$			1.06242e10i			1.68342i	0.539927	+	0.841712i	$0.318452\pi$
$631$			1.06242e10i			1.68342i	−0.539927	+	0.841712i	$0.681548\pi$
$632$	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
$636$	2.21264e9	+	2.61627e9i	0.341045	+	0.403258i
$637$			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	$0.827036\pi$
$642$	2.47085e9	+	9.51086e9i	0.368531	+	1.41856i
$643$	−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	$-0.496460\pi$
$647$	1.53229e8			0.0222421			0.0111210	+	0.999938i	$0.496460\pi$
$648$	3.73112e9	+	5.83565e9i	0.538675	+	0.842513i
$649$	−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	$-0.629032\pi$
$653$	−5.61194e9			−0.788710			−0.394355	+	0.918958i	$0.629032\pi$
$654$	1.62554e9	+	6.25707e9i	0.227235	+	0.874679i
$655$			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	$0.958777\pi$
$660$	7.99210e8	−	6.75911e8i	0.108207	−	0.0915137i
$661$			2.56052e9i			0.344844i	0.985023	+	0.172422i	$0.0551592\pi$
$661$			2.56052e9i			0.344844i	−0.985023	+	0.172422i	$0.944841\pi$
$662$	−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
$666$	6.98511e9	−	4.23227e8i	0.916249	−	0.0555153i
$667$	−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
$672$	−1.19411e10	+	6.13654e9i	−1.51793	+	0.780066i
$673$	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	$-0.197182\pi$
$677$	1.31467e10			1.62838			0.814188	+	0.580601i	$0.197182\pi$
$678$	−1.87862e9	−	7.23122e9i	−0.231492	−	0.891062i
$679$		−	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	$-0.0197764\pi$
$684$	2.82930e9	−	1.57647e9i	0.338052	−	0.188360i
$685$			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
$690$	2.78643e9	−	7.23895e8i	0.322906	−	0.0838887i
$691$	−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
$696$	1.51573e9	−	3.38543e9i	0.170408	−	0.380611i
$697$	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	$-0.754301\pi$
$701$	−1.30713e10			−1.43319			−0.716596	+	0.697488i	$0.754301\pi$
$702$	−1.55786e9	+	1.16315e10i	−0.169961	+	1.26898i
$703$		−	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
$708$	6.58393e9	−	5.56819e9i	0.697218	−	0.589654i
$709$		−	2.53582e9i		−	0.267213i	−0.991034	−	0.133606i	$-0.957344\pi$
$709$		−	2.53582e9i		−	0.267213i	0.991034	−	0.133606i	$-0.0426558\pi$
$710$	−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
$714$	−2.18541e10	+	5.67754e9i	−2.24693	+	0.583736i
$715$	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	$-0.335209\pi$
$719$	9.86480e9			0.989777			0.494889	+	0.868956i	$0.335209\pi$
$720$	−5.82830e8	+	3.46207e9i	−0.0581940	+	0.345678i
$721$	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
$726$	8.34819e9	−	2.16880e9i	0.809682	−	0.210350i
$727$			6.26064e9i			0.604294i	0.953261	+	0.302147i	$0.0977033\pi$
$727$			6.26064e9i			0.604294i	−0.953261	+	0.302147i	$0.902297\pi$
$728$	−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
$732$	−8.16450e9	+	6.90492e9i	−0.769380	+	0.650683i
$733$		−	1.23202e10i		−	1.15546i	−0.816228	−	0.577730i	$-0.803939\pi$
$733$		−	1.23202e10i		−	1.15546i	0.816228	−	0.577730i	$-0.196061\pi$
$734$	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
$738$	−9.96898e9	+	6.04018e8i	−0.912963	+	0.0553162i
$739$	−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	$-0.414635\pi$
$743$	5.92519e9			0.529958			0.264979	+	0.964254i	$0.414635\pi$
$744$	−4.43140e9	−	1.98403e9i	−0.394489	−	0.176621i
$745$	−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
$750$	−7.35808e9	+	1.91158e9i	−0.636869	+	0.165454i
$751$		−	8.98243e9i		−	0.773845i	−0.922112	−	0.386923i	$-0.873538\pi$
$751$		−	8.98243e9i		−	0.773845i	0.922112	−	0.386923i	$-0.126462\pi$
$752$	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
$756$	1.92796e10	−	6.27564e9i	1.62283	−	0.528241i
$757$			9.92682e9i			0.831715i	0.909430	+	0.415857i	$0.136518\pi$
$757$			9.92682e9i			0.831715i	−0.909430	+	0.415857i	$0.863482\pi$
$758$	−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	$-0.0213827\pi$
$762$	−1.42981e9	−	5.50367e9i	−0.117068	−	0.450619i
$763$	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
$768$	−3.07425e9	−	1.21712e10i	−0.244892	−	0.969550i
$769$	−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	$-0.602521\pi$
$773$	−8.12995e9			−0.633082			−0.316541	+	0.948579i	$0.602521\pi$
$774$	7.40827e8	+	1.22269e10i	0.0574280	+	0.947817i
$775$		−	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
$780$	−4.54177e9	+	3.84108e9i	−0.342684	+	0.289816i
$781$			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
$786$	4.16813e9	+	1.60440e10i	0.306170	+	1.17851i
$787$	−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
$792$	3.25932e9	−	4.61783e9i	0.233125	−	0.330293i
$793$	−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	$-0.745843\pi$
$797$	−1.99468e10			−1.39563			−0.697813	+	0.716280i	$0.745843\pi$
$798$	−2.38392e9	−	9.17623e9i	−0.166066	−	0.639226i
$799$			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
$804$	−5.41211e9	−	6.39938e9i	−0.367257	−	0.434252i
$805$		−	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	$-0.165055\pi$
$810$	1.70201e9	−	5.02137e9i	0.112529	−	0.331990i
$811$	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
$816$	−5.67338e8	−	2.11052e10i	−0.0365533	−	1.35980i
$817$	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	$-0.926720\pi$
$821$	−3.08759e10			−1.94723			−0.973617	+	0.228187i	$0.926720\pi$
$822$	7.36982e8	+	2.83681e9i	0.0462813	+	0.178147i
$823$		−	4.60692e9i		−	0.288079i	−0.989572	−	0.144040i	$-0.953991\pi$
$823$		−	4.60692e9i		−	0.288079i	0.989572	−	0.144040i	$-0.0460092\pi$
$824$	−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	$0.966465\pi$
$828$	1.35804e10	−	7.56688e9i	0.831392	−	0.463245i
$829$		−	2.62952e10i		−	1.60301i	−0.597988	−	0.801505i	$-0.704033\pi$
$829$		−	2.62952e10i		−	1.60301i	0.597988	−	0.801505i	$-0.295967\pi$
$830$	−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
$834$	−6.87135e9	+	1.78513e9i	−0.410167	+	0.106559i
$835$	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	$-0.447231\pi$
$839$	5.64587e9			0.330038			0.165019	+	0.986290i	$0.447231\pi$
$840$	9.37964e9	+	4.19947e9i	0.546020	+	0.244465i
$841$	−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
$846$	−1.69985e9	−	2.80551e10i	−0.0965195	−	1.59300i
$847$		−	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
$852$	−1.37976e10	−	1.63145e10i	−0.764302	−	0.903725i
$853$			9.85601e9i			0.543725i	0.962336	+	0.271863i	$0.0876396\pi$
$853$			9.85601e9i			0.543725i	−0.962336	+	0.271863i	$0.912360\pi$
$854$	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	$-0.179020\pi$
$858$	9.26873e9	−	2.40795e9i	0.500973	−	0.130149i
$859$	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	$-0.766121\pi$
$863$	−2.80201e10			−1.48399			−0.741996	+	0.670404i	$0.766121\pi$
$864$	1.65467e9	+	1.88859e10i	0.0872796	+	0.996184i
$865$	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
$870$	−2.74808e9	+	7.13933e8i	−0.141486	+	0.0367570i
$871$		−	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
$876$	8.59520e9	+	1.01631e10i	0.432008	+	0.510814i
$877$		−	3.28468e10i		−	1.64435i	−0.569235	−	0.822175i	$-0.692761\pi$
$877$		−	3.28468e10i		−	1.64435i	0.569235	−	0.822175i	$-0.307239\pi$
$878$	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	$0.733221\pi$
$882$	−2.35705e9	−	3.89018e10i	−0.115672	−	1.90910i
$883$	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	$-0.476084\pi$
$887$	3.12022e9			0.150125			0.0750623	+	0.997179i	$0.476084\pi$
$888$	1.74816e10	+	7.82690e9i	0.837793	+	0.375098i
$889$	−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
$894$	−1.07208e10	+	2.78519e9i	−0.501819	+	0.130369i
$895$		−	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
$900$	−1.67570e10	+	9.33685e9i	−0.766208	+	0.426925i
$901$			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
$906$	4.03064e9	+	1.55148e10i	0.180063	+	0.693103i
$907$	−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	$-0.560001\pi$
$911$	−8.55220e9			−0.374769			−0.187384	+	0.982287i	$0.560001\pi$
$912$	8.86178e9	−	2.38217e8i	0.386847	−	0.0103990i
$913$	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
$918$	−4.23266e9	+	3.16024e10i	−0.180577	+	1.34825i
$919$			2.54557e10i			1.08188i	0.841060	+	0.540942i	$0.181932\pi$
$919$			2.54557e10i			1.08188i	−0.841060	+	0.540942i	$0.818068\pi$
$920$	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
$924$	−1.06841e10	−	1.26331e10i	−0.445540	−	0.526814i
$925$			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	$-0.311487\pi$
$930$	9.34510e8	+	3.59714e9i	0.0380973	+	0.146645i
$931$	−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
$936$	−1.85221e10	+	2.62423e10i	−0.738286	+	1.04601i
$937$	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	$-0.277251\pi$
$941$	3.29243e10			1.28811			0.644054	+	0.764980i	$0.277251\pi$
$942$	1.06944e10	+	4.11650e10i	0.416847	+	1.60454i
$943$			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	$0.679666\pi$
$948$	−2.55521e10	+	2.16100e10i	−0.974087	+	0.823809i
$949$			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	$-0.400595\pi$
$954$	−8.56583e8	−	1.41374e10i	−0.0319411	−	0.527170i
$955$	−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
$960$	−5.80205e9	+	7.65990e9i	−0.211657	+	0.279431i
$961$	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
$966$	−1.14426e10	−	4.40450e10i	−0.408417	−	1.57209i
$967$		−	2.73207e10i		−	0.971626i	−0.874063	−	0.485813i	$-0.838524\pi$
$967$		−	2.73207e10i		−	0.971626i	0.874063	−	0.485813i	$-0.161476\pi$
$968$	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	$0.759996\pi$
$972$	2.07753e9	−	2.85552e10i	0.0725629	−	0.997364i
$973$			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	$0.864451\pi$
$978$	5.53696e10	−	1.43846e10i	1.89272	−	0.491714i
$979$	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	$-0.287016\pi$
$983$	3.69454e10			1.24058			0.620288	+	0.784374i	$0.287016\pi$
$984$	−2.49493e10	−	1.11704e10i	−0.834788	−	0.373752i
$985$	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
$990$	−4.31865e9	+	2.61666e8i	−0.141457	+	0.00857086i
$991$		−	3.49760e10i		−	1.14160i	−0.821091	−	0.570798i	$-0.806634\pi$
$991$		−	3.49760e10i		−	1.14160i	0.821091	−	0.570798i	$-0.193366\pi$
$992$	−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
$996$	−1.37726e10	+	1.16478e10i	−0.441682	+	0.373541i
$997$		−	1.40243e10i		−	0.448174i	−0.974569	−	0.224087i	$-0.928060\pi$
$997$		−	1.40243e10i		−	0.448174i	0.974569	−	0.224087i	$-0.0719400\pi$
$998$	−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.11.1	✓	4
3.2	odd	2	inner	24.8.f.b.11.4	yes	4
4.3	odd	2		96.8.f.b.47.2		4
8.3	odd	2	inner	24.8.f.b.11.3	yes	4
8.5	even	2		96.8.f.b.47.1		4
12.11	even	2		96.8.f.b.47.3		4
24.5	odd	2		96.8.f.b.47.4		4
24.11	even	2	inner	24.8.f.b.11.2	yes	4

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	24.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.89898 - 10.1980i) q^{2} +(-9.00000 + 45.8912i) q^{3} +(-80.0000 + 99.9200i) q^{4} +97.9796 q^{5} +(512.091 - 133.038i) q^{6} -1548.76i q^{7} +(1410.91 + 326.337i) q^{8} +(-2025.00 - 826.041i) q^{9} +O(q^{10})\)	\(q+(-4.89898 - 10.1980i) q^{2} +(-9.00000 + 45.8912i) q^{3} +(-80.0000 + 99.9200i) q^{4} +97.9796 q^{5} +(512.091 - 133.038i) 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} +(-3865.44 - 4570.57i) 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} +(1496.43 + 24697.8i) 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} +(-27674.2 + 61811.1i) 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} +(50174.4 - 13035.0i) 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} +(244538. - 136255. 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} +(-206043. - 793106. 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} +(765927. - 20589.2i) 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} +(-1.14688e6 - 153607. 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} +(-378735. - 447823. 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} +(237426. + 913906. 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} +(-2.58752e6 - 1.82630e6i) 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} +(-1.34925e6 - 5.19356e6i) 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} +(-7.07872e6 + 5.98664e6i) 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} +(146620. + 2.41988e6i) 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} +(-3.96223e6 - 7.71009e6i) 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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