LMFDB - Embedded newform 24.8.f.c.11.11

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:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 274 x^{18} + 45864 x^{16} - 5031360 x^{14} + 776389632 x^{12} - 102828146688 x^{10} + \cdots + 11\!\cdots\!24 $ x^20 - 274x^18 + 45864x^16 - 5031360x^14 + 776389632x^12 - 102828146688x^10 + 12720367730688x^8 - 1350595415900160x^6 + 201712005185273856x^4 - 19743780766392254464*x^2 + 1180591620717411303424
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{52}\cdot 3^{20} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.11
Root			$-3.79334 - 10.6588i$ of defining polynomial
Character	$\chi$	$=$	24.11
Dual form			24.8.f.c.11.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.79334 - 10.6588i) q^{2} +(46.6816 + 2.79715i) q^{3} +(-99.2212 - 80.8651i) q^{4} -395.205 q^{5} +(206.894 - 486.961i) q^{6} -1395.40i q^{7} +(-1238.31 + 750.833i) q^{8} +(2171.35 + 261.151i) q^{9} +O(q^{10})$	\(q+(3.79334 - 10.6588i) q^{2} +(46.6816 + 2.79715i) q^{3} +(-99.2212 - 80.8651i) q^{4} -395.205 q^{5} +(206.894 - 486.961i) q^{6} -1395.40i q^{7} +(-1238.31 + 750.833i) q^{8} +(2171.35 + 261.151i) q^{9} +(-1499.14 + 4212.42i) q^{10} -5391.17i q^{11} +(-4405.62 - 4052.45i) q^{12} +3927.39i q^{13} +(-14873.3 - 5293.22i) q^{14} +(-18448.8 - 1105.45i) q^{15} +(3305.68 + 16047.1i) q^{16} +5903.54i q^{17} +(11020.2 - 22153.4i) q^{18} +14851.3 q^{19} +(39212.7 + 31958.2i) q^{20} +(3903.14 - 65139.5i) q^{21} +(-57463.6 - 20450.6i) q^{22} +73616.8 q^{23} +(-59906.4 + 31586.4i) q^{24} +78061.6 q^{25} +(41861.4 + 14897.9i) q^{26} +(100632. + 18264.5i) q^{27} +(-112839. + 138453. i) q^{28} -26579.4 q^{29} +(-81765.3 + 192449. i) q^{30} -205272. i q^{31} +(183582. + 25637.3i) q^{32} +(15079.9 - 251669. i) q^{33} +(62924.8 + 22394.1i) q^{34} +551468. i q^{35} +(-194326. - 201498. i) q^{36} +172154. i q^{37} +(56335.9 - 158297. i) q^{38} +(-10985.5 + 183337. i) q^{39} +(489384. - 296732. i) q^{40} -741464. i q^{41} +(-679505. - 288699. i) q^{42} -279102. q^{43} +(-435958. + 534919. i) q^{44} +(-858128. - 103208. i) q^{45} +(279254. - 784669. i) q^{46} +418307. q^{47} +(109429. + 758349. i) q^{48} -1.12359e6 q^{49} +(296114. - 832045. i) q^{50} +(-16513.1 + 275587. i) q^{51} +(317589. - 389680. i) q^{52} +427120. q^{53} +(576409. - 1.00333e6i) q^{54} +2.13062e6i q^{55} +(1.04771e6 + 1.72793e6i) q^{56} +(693282. + 41541.2i) q^{57} +(-100825. + 283305. i) q^{58} +1.65127e6i q^{59} +(1.74112e6 + 1.60155e6i) q^{60} +1.02459e6i q^{61} +(-2.18796e6 - 778666. i) q^{62} +(364410. - 3.02990e6i) q^{63} +(969653. - 1.85952e6i) q^{64} -1.55212e6i q^{65} +(-2.62529e6 - 1.11540e6i) q^{66} -2.38005e6 q^{67} +(477391. - 585756. i) q^{68} +(3.43656e6 + 205917. i) q^{69} +(5.87800e6 + 2.09190e6i) q^{70} +822295. q^{71} +(-2.88488e6 + 1.30694e6i) q^{72} -1.84283e6 q^{73} +(1.83496e6 + 653040. i) q^{74} +(3.64404e6 + 218350. i) q^{75} +(-1.47356e6 - 1.20095e6i) q^{76} -7.52284e6 q^{77} +(1.91249e6 + 812552. i) q^{78} +846282. i q^{79} +(-1.30642e6 - 6.34187e6i) q^{80} +(4.64657e6 + 1.13410e6i) q^{81} +(-7.90313e6 - 2.81262e6i) q^{82} -130811. i q^{83} +(-5.65479e6 + 6.14759e6i) q^{84} -2.33311e6i q^{85} +(-1.05873e6 + 2.97489e6i) q^{86} +(-1.24077e6 - 74346.4i) q^{87} +(4.04787e6 + 6.67593e6i) q^{88} -4.39906e6i q^{89} +(-4.35525e6 + 8.75514e6i) q^{90} +5.48027e6 q^{91} +(-7.30435e6 - 5.95303e6i) q^{92} +(574176. - 9.58243e6i) q^{93} +(1.58678e6 - 4.45866e6i) q^{94} -5.86929e6 q^{95} +(8.49821e6 + 1.71030e6i) q^{96} +3.64708e6 q^{97} +(-4.26218e6 + 1.19762e7i) q^{98} +(1.40791e6 - 1.17061e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 120 q^{3} + 548 q^{4} - 1416 q^{6} + 5076 q^{9}+O(q^{10}) $ 20 * q + 120 * q^3 + 548 * q^4 - 1416 * q^6 + 5076 * q^9	$ 20 q + 120 q^{3} + 548 q^{4} - 1416 q^{6} + 5076 q^{9} - 3384 q^{10} - 26700 q^{12} - 33304 q^{16} - 11880 q^{18} + 133744 q^{19} - 166880 q^{22} - 74424 q^{24} + 711596 q^{25} + 85320 q^{27} - 669360 q^{28} - 41904 q^{30} + 263640 q^{33} + 24112 q^{34} - 409428 q^{36} - 437088 q^{40} + 1724040 q^{42} - 2292080 q^{43} + 1466400 q^{46} + 1846200 q^{48} + 2495228 q^{49} - 7417536 q^{51} - 2511360 q^{52} + 5680584 q^{54} - 5067120 q^{57} + 1427880 q^{58} + 2211120 q^{60} - 4070608 q^{64} + 1062024 q^{66} + 3654640 q^{67} + 11712816 q^{70} + 7004880 q^{72} + 19892680 q^{73} - 8612088 q^{75} - 11799464 q^{76} - 1226160 q^{78} - 6817932 q^{81} - 52710080 q^{82} - 6585408 q^{84} - 13470800 q^{88} + 10393704 q^{90} + 67826976 q^{91} - 24601920 q^{94} + 35857680 q^{96} + 5561800 q^{97} + 10152864 q^{99}+O(q^{100}) $ 20 * q + 120 * q^3 + 548 * q^4 - 1416 * q^6 + 5076 * q^9 - 3384 * q^10 - 26700 * q^12 - 33304 * q^16 - 11880 * q^18 + 133744 * q^19 - 166880 * q^22 - 74424 * q^24 + 711596 * q^25 + 85320 * q^27 - 669360 * q^28 - 41904 * q^30 + 263640 * q^33 + 24112 * q^34 - 409428 * q^36 - 437088 * q^40 + 1724040 * q^42 - 2292080 * q^43 + 1466400 * q^46 + 1846200 * q^48 + 2495228 * q^49 - 7417536 * q^51 - 2511360 * q^52 + 5680584 * q^54 - 5067120 * q^57 + 1427880 * q^58 + 2211120 * q^60 - 4070608 * q^64 + 1062024 * q^66 + 3654640 * q^67 + 11712816 * q^70 + 7004880 * q^72 + 19892680 * q^73 - 8612088 * q^75 - 11799464 * q^76 - 1226160 * q^78 - 6817932 * q^81 - 52710080 * q^82 - 6585408 * q^84 - 13470800 * q^88 + 10393704 * q^90 + 67826976 * q^91 - 24601920 * q^94 + 35857680 * q^96 + 5561800 * q^97 + 10152864 * 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 $

$2$	3.79334	−	10.6588i	0.335287	−	0.942116i
$2$	3.79334	−	10.6588i	0.335287	−	0.942116i
$3$	46.6816	+	2.79715i	0.998210	+	0.0598124i
$3$	46.6816	+	2.79715i	0.998210	+	0.0598124i
$4$	−99.2212	−	80.8651i	−0.775165	−	0.631758i
$5$	−395.205			−1.41393			−0.706963	−	0.707250i	$-0.749935\pi$
$5$	−395.205			−1.41393			−0.706963	+	0.707250i	$0.749935\pi$
$6$	206.894	−	486.961i	0.391037	−	0.920375i
$7$		−	1395.40i		−	1.53764i	−0.639464	−	0.768821i	$-0.720844\pi$
$7$		−	1395.40i		−	1.53764i	0.639464	−	0.768821i	$-0.279156\pi$
$8$	−1238.31	+	750.833i	−0.855093	+	0.518475i
$9$	2171.35	+	261.151i	0.992845	+	0.119411i
$10$	−1499.14	+	4212.42i	−0.474071	+	1.33208i
$11$		−	5391.17i		−	1.22126i	−0.791915	−	0.610631i	$-0.790916\pi$
$11$		−	5391.17i		−	1.22126i	0.791915	−	0.610631i	$-0.209084\pi$
$12$	−4405.62	−	4052.45i	−0.735991	−	0.676992i
$13$			3927.39i			0.495795i	0.968786	+	0.247898i	$0.0797396\pi$
$13$			3927.39i			0.495795i	−0.968786	+	0.247898i	$0.920260\pi$
$14$	−14873.3	−	5293.22i	−1.44864	−	0.515551i
$15$	−18448.8	−	1105.45i	−1.41140	−	0.0845703i
$16$	3305.68	+	16047.1i	0.201763	+	0.979434i
$17$			5903.54i			0.291435i	0.989326	+	0.145717i	$0.0465490\pi$
$17$			5903.54i			0.291435i	−0.989326	+	0.145717i	$0.953451\pi$
$18$	11020.2	−	22153.4i	0.445387	−	0.895338i
$19$	14851.3			0.496737			0.248368	−	0.968666i	$-0.420106\pi$
$19$	14851.3			0.496737			0.248368	+	0.968666i	$0.420106\pi$
$20$	39212.7	+	31958.2i	1.09603	+	0.893260i
$21$	3903.14	−	65139.5i	0.0919700	−	1.53489i
$22$	−57463.6	−	20450.6i	−1.15057	−	0.409473i
$23$	73616.8			1.26162			0.630812	−	0.775936i	$-0.282722\pi$
$23$	73616.8			1.26162			0.630812	+	0.775936i	$0.282722\pi$
$24$	−59906.4	+	31586.4i	−0.884573	+	0.466402i
$25$	78061.6			0.999189
$26$	41861.4	+	14897.9i	0.467097	+	0.166234i
$27$	100632.	+	18264.5i	0.983925	+	0.178581i
$28$	−112839.	+	138453.i	−0.971418	+	1.19193i
$29$	−26579.4			−0.202373			−0.101186	−	0.994867i	$-0.532264\pi$
$29$	−26579.4			−0.202373			−0.101186	+	0.994867i	$0.532264\pi$
$30$	−81765.3	+	192449.i	−0.552897	+	1.30134i
$31$		−	205272.i		−	1.23755i	−0.785567	−	0.618776i	$-0.787629\pi$
$31$		−	205272.i		−	1.23755i	0.785567	−	0.618776i	$-0.212371\pi$
$32$	183582.	+	25637.3i	0.990389	+	0.138308i
$33$	15079.9	−	251669.i	0.0730466	−	1.21908i
$34$	62924.8	+	22394.1i	0.274565	+	0.0977143i
$35$			551468.i			2.17411i
$36$	−194326.	−	201498.i	−0.694180	−	0.719801i
$37$			172154.i			0.558743i	0.960183	+	0.279371i	$0.0901261\pi$
$37$			172154.i			0.558743i	−0.960183	+	0.279371i	$0.909874\pi$
$38$	56335.9	−	158297.i	0.166549	−	0.467984i
$39$	−10985.5	+	183337.i	−0.0296547	+	0.494907i
$40$	489384.	−	296732.i	1.20904	−	0.733086i
$41$		−	741464.i		−	1.68014i	−0.542476	−	0.840072i	$-0.682513\pi$
$41$		−	741464.i		−	1.68014i	0.542476	−	0.840072i	$-0.317487\pi$
$42$	−679505.	−	288699.i	−1.41521	−	0.601275i
$43$	−279102.			−0.535331			−0.267666	−	0.963512i	$-0.586252\pi$
$43$	−279102.			−0.535331			−0.267666	+	0.963512i	$0.586252\pi$
$44$	−435958.	+	534919.i	−0.771543	+	0.946680i
$45$	−858128.	−	103208.i	−1.40381	−	0.168838i
$46$	279254.	−	784669.i	0.423006	−	1.18860i
$47$	418307.			0.587696			0.293848	−	0.955852i	$-0.405064\pi$
$47$	418307.			0.587696			0.293848	+	0.955852i	$0.405064\pi$
$48$	109429.	+	758349.i	0.142819	+	0.989749i
$49$	−1.12359e6			−1.36434
$50$	296114.	−	832045.i	0.335015	−	0.941352i
$51$	−16513.1	+	275587.i	−0.0174314	+	0.290913i
$52$	317589.	−	389680.i	0.313223	−	0.384323i
$53$	427120.			0.394080			0.197040	−	0.980395i	$-0.436867\pi$
$53$	427120.			0.394080			0.197040	+	0.980395i	$0.436867\pi$
$54$	576409.	−	1.00333e6i	0.498141	−	0.867096i
$55$			2.13062e6i			1.72678i
$56$	1.04771e6	+	1.72793e6i	0.797229	+	1.31483i
$57$	693282.	+	41541.2i	0.495847	+	0.0297110i
$58$	−100825.	+	283305.i	−0.0678529	+	0.190658i
$59$			1.65127e6i			1.04674i	0.852107	+	0.523368i	$0.175325\pi$
$59$			1.65127e6i			1.04674i	−0.852107	+	0.523368i	$0.824675\pi$
$60$	1.74112e6	+	1.60155e6i	1.04064	+	0.957217i
$61$			1.02459e6i			0.577957i	0.957336	+	0.288979i	$0.0933156\pi$
$61$			1.02459e6i			0.577957i	−0.957336	+	0.288979i	$0.906684\pi$
$62$	−2.18796e6	−	778666.i	−1.16592	−	0.414935i
$63$	364410.	−	3.02990e6i	0.183611	−	1.52664i
$64$	969653.	−	1.85952e6i	0.462367	−	0.886689i
$65$		−	1.55212e6i		−	0.701018i
$66$	−2.62529e6	−	1.11540e6i	−1.12402	−	0.477559i
$67$	−2.38005e6			−0.966772			−0.483386	−	0.875407i	$-0.660593\pi$
$67$	−2.38005e6			−0.966772			−0.483386	+	0.875407i	$0.660593\pi$
$68$	477391.	−	585756.i	0.184116	−	0.225910i
$69$	3.43656e6	+	205917.i	1.25936	+	0.0754607i
$70$	5.87800e6	+	2.09190e6i	2.04827	+	0.728952i
$71$	822295.			0.272661			0.136331	−	0.990663i	$-0.456469\pi$
$71$	822295.			0.272661			0.136331	+	0.990663i	$0.456469\pi$
$72$	−2.88488e6	+	1.30694e6i	−0.910886	+	0.412659i
$73$	−1.84283e6			−0.554441			−0.277220	−	0.960806i	$-0.589413\pi$
$73$	−1.84283e6			−0.554441			−0.277220	+	0.960806i	$0.589413\pi$
$74$	1.83496e6	+	653040.i	0.526401	+	0.187339i
$75$	3.64404e6	+	218350.i	0.997400	+	0.0597638i
$76$	−1.47356e6	−	1.20095e6i	−0.385053	−	0.313818i
$77$	−7.52284e6			−1.87786
$78$	1.91249e6	+	812552.i	0.456317	+	0.193874i
$79$			846282.i			0.193117i	0.995327	+	0.0965584i	$0.0307835\pi$
$79$			846282.i			0.193117i	−0.995327	+	0.0965584i	$0.969217\pi$
$80$	−1.30642e6	−	6.34187e6i	−0.285277	−	1.38485i
$81$	4.64657e6	+	1.13410e6i	0.971482	+	0.237112i
$82$	−7.90313e6	−	2.81262e6i	−1.58289	−	0.563330i
$83$		−	130811.i		−	0.0251115i	−0.999921	−	0.0125557i	$-0.996003\pi$
$83$		−	130811.i		−	0.0251115i	0.999921	−	0.0125557i	$-0.00399672\pi$
$84$	−5.65479e6	+	6.14759e6i	−1.04097	+	1.13169i
$85$		−	2.33311e6i		−	0.412068i
$86$	−1.05873e6	+	2.97489e6i	−0.179490	+	0.504344i
$87$	−1.24077e6	−	74346.4i	−0.202010	−	0.0121044i
$88$	4.04787e6	+	6.67593e6i	0.633194	+	1.04429i
$89$		−	4.39906e6i		−	0.661447i	−0.943728	−	0.330724i	$-0.892707\pi$
$89$		−	4.39906e6i		−	0.661447i	0.943728	−	0.330724i	$-0.107293\pi$
$90$	−4.35525e6	+	8.75514e6i	−0.629744	+	1.26594i
$91$	5.48027e6			0.762355
$92$	−7.30435e6	−	5.95303e6i	−0.977967	−	0.797041i
$93$	574176.	−	9.58243e6i	0.0740209	−	1.23534i
$94$	1.58678e6	−	4.45866e6i	0.197047	−	0.553677i
$95$	−5.86929e6			−0.702349
$96$	8.49821e6	+	1.71030e6i	0.980344	+	0.197298i
$97$	3.64708e6			0.405736			0.202868	−	0.979206i	$-0.434974\pi$
$97$	3.64708e6			0.405736			0.202868	+	0.979206i	$0.434974\pi$
$98$	−4.26218e6	+	1.19762e7i	−0.457446	+	1.28537i
$99$	1.40791e6	−	1.17061e7i	0.145832	−	1.21252i
$100$	−7.74536e6	−	6.31246e6i	−0.774536	−	0.631246i
$101$	1.50610e7			1.45456			0.727278	−	0.686343i	$-0.240785\pi$
$101$	1.50610e7			1.45456			0.727278	+	0.686343i	$0.240785\pi$
$102$	2.87480e6	+	1.22141e6i	0.268229	+	0.113962i
$103$		−	1.04154e7i		−	0.939176i	−0.882886	−	0.469588i	$-0.844402\pi$
$103$		−	1.04154e7i		−	0.939176i	0.882886	−	0.469588i	$-0.155598\pi$
$104$	−2.94881e6	−	4.86331e6i	−0.257058	−	0.423951i
$105$	−1.54254e6	+	2.57434e7i	−0.130039	+	2.17022i
$106$	1.62021e6	−	4.55260e6i	0.132130	−	0.371269i
$107$		−	7.91002e6i		−	0.624215i	−0.950047	−	0.312108i	$-0.898965\pi$
$107$		−	7.91002e6i		−	0.624215i	0.950047	−	0.312108i	$-0.101035\pi$
$108$	−8.50784e6	−	9.94983e6i	−0.649885	−	0.760033i
$109$			1.78544e7i			1.32054i	0.751026	+	0.660272i	$0.229559\pi$
$109$			1.78544e7i			1.32054i	−0.751026	+	0.660272i	$0.770441\pi$
$110$	2.27099e7	+	8.08215e6i	1.62682	+	0.578965i
$111$	−481541.	+	8.03645e6i	−0.0334197	+	0.557743i
$112$	2.23920e7	−	4.61274e6i	1.50602	−	0.310239i
$113$			1.86836e7i			1.21811i	0.793130	+	0.609053i	$0.208450\pi$
$113$			1.86836e7i			1.21811i	−0.793130	+	0.609053i	$0.791550\pi$
$114$	3.07263e6	−	7.23199e6i	0.194242	−	0.457184i
$115$	−2.90937e7			−1.78384
$116$	2.63724e6	+	2.14934e6i	0.156872	+	0.127851i
$117$	−1.02564e6	+	8.52775e6i	−0.0592032	+	0.492248i
$118$	1.76006e7	+	6.26384e6i	0.986147	+	0.350957i
$119$	8.23780e6			0.448123
$120$	2.36753e7	−	1.24831e7i	1.25072	−	0.659458i
$121$	−9.57759e6			−0.491482
$122$	1.09209e7	+	3.88662e6i	0.544503	+	0.193781i
$123$	2.07398e6	−	3.46127e7i	0.100493	−	1.67714i
$124$	−1.65993e7	+	2.03673e7i	−0.781834	+	0.959308i
$125$	25049.8			0.00114715
$126$	−3.09129e7	−	1.53776e7i	−1.37671	−	0.684845i
$127$			2.78676e7i			1.20722i	0.797280	+	0.603609i	$0.206271\pi$
$127$			2.78676e7i			1.20722i	−0.797280	+	0.603609i	$0.793729\pi$
$128$	−1.61421e7	−	1.73892e7i	−0.680338	−	0.732898i
$129$	−1.30289e7	−	780688.i	−0.534373	−	0.0320194i
$130$	−1.65438e7	−	5.88773e6i	−0.660440	−	0.235042i
$131$			2.92965e7i			1.13859i	0.822134	+	0.569293i	$0.192783\pi$
$131$			2.92965e7i			1.13859i	−0.822134	+	0.569293i	$0.807217\pi$
$132$	−2.18475e7	+	2.37514e7i	−0.826785	+	0.898838i
$133$		−	2.07235e7i		−	0.763803i
$134$	−9.02833e6	+	2.53685e7i	−0.324146	+	0.910811i
$135$	−3.97701e7	−	7.21823e6i	−1.39120	−	0.252501i
$136$	−4.43257e6	−	7.31040e6i	−0.151102	−	0.249204i
$137$		−	3.76195e7i		−	1.24995i	−0.780646	−	0.624973i	$-0.785110\pi$
$137$		−	3.76195e7i		−	1.24995i	0.780646	−	0.624973i	$-0.214890\pi$
$138$	1.52309e7	−	3.58485e7i	0.493341	−	1.16117i
$139$	4.68128e7			1.47847			0.739235	−	0.673447i	$-0.235187\pi$
$139$	4.68128e7			1.47847			0.739235	+	0.673447i	$0.235187\pi$
$140$	4.45945e7	−	5.47173e7i	1.37351	−	1.68530i
$141$	1.95272e7	+	1.17007e6i	0.586643	+	0.0351515i
$142$	3.11924e6	−	8.76470e6i	0.0914198	−	0.256879i
$143$	2.11732e7			0.605496
$144$	2.98709e6	+	3.57071e7i	0.0833642	+	0.996519i
$145$	1.05043e7			0.286140
$146$	−6.99048e6	+	1.96424e7i	−0.185897	+	0.522348i
$147$	−5.24513e7	−	3.14286e6i	−1.36190	−	0.0816045i
$148$	1.39213e7	−	1.70814e7i	0.352991	−	0.433118i
$149$	−6.47201e7			−1.60283			−0.801415	−	0.598108i	$-0.795919\pi$
$149$	−6.47201e7			−1.60283			−0.801415	+	0.598108i	$0.795919\pi$
$150$	1.61504e7	−	3.80130e7i	0.390720	−	0.919628i
$151$		−	1.82260e7i		−	0.430796i	−0.976526	−	0.215398i	$-0.930895\pi$
$151$		−	1.82260e7i		−	0.430796i	0.976526	−	0.215398i	$-0.0691049\pi$
$152$	−1.83904e7	+	1.11508e7i	−0.424756	+	0.257546i
$153$	−1.54172e6	+	1.28187e7i	−0.0348004	+	0.289350i
$154$	−2.85367e7	+	8.01846e7i	−0.629623	+	1.76917i
$155$			8.11244e7i			1.74981i
$156$	1.59156e7	−	1.73026e7i	0.335649	−	0.364901i
$157$		−	2.67214e7i		−	0.551075i	−0.961290	−	0.275537i	$-0.911144\pi$
$157$		−	2.67214e7i		−	0.551075i	0.961290	−	0.275537i	$-0.0888558\pi$
$158$	9.02037e6	+	3.21023e6i	0.181938	+	0.0647495i
$159$	1.99387e7	+	1.19472e6i	0.393374	+	0.0235708i
$160$	−7.25526e7	−	1.01320e7i	−1.40034	−	0.195557i
$161$		−	1.02725e8i		−	1.93993i
$162$	2.97142e7	−	4.52249e7i	0.549113	−	0.835748i
$163$	3.30452e7			0.597656			0.298828	−	0.954307i	$-0.403404\pi$
$163$	3.30452e7			0.597656			0.298828	+	0.954307i	$0.403404\pi$
$164$	−5.99585e7	+	7.35689e7i	−1.06144	+	1.30239i
$165$	−5.95965e6	+	9.94607e7i	−0.103283	+	1.72368i
$166$	−1.39430e6	−	496212.i	−0.0236579	−	0.00841956i
$167$	8.08422e7			1.34317			0.671584	−	0.740928i	$-0.265614\pi$
$167$	8.08422e7			1.34317			0.671584	+	0.740928i	$0.265614\pi$
$168$	4.40756e7	+	8.35933e7i	0.717159	+	1.36016i
$169$	4.73241e7			0.754187
$170$	−2.48682e7	−	8.85027e6i	−0.388215	−	0.138161i
$171$	3.22474e7	+	3.87842e6i	0.493183	+	0.0593156i
$172$	2.76928e7	+	2.25696e7i	0.414970	+	0.338200i
$173$	5.95705e7			0.874722			0.437361	−	0.899286i	$-0.355913\pi$
$173$	5.95705e7			0.874722			0.437361	+	0.899286i	$0.355913\pi$
$174$	−5.49910e6	+	1.29431e7i	−0.0791351	+	0.186259i
$175$		−	1.08927e8i		−	1.53639i
$176$	8.65125e7	−	1.78215e7i	1.19615	−	0.246405i
$177$	−4.61886e6	+	7.70842e7i	−0.0626077	+	1.04486i
$178$	−4.68889e7	−	1.66871e7i	−0.623160	−	0.221775i
$179$			5.29640e7i			0.690232i	0.938560	+	0.345116i	$0.112160\pi$
$179$			5.29640e7i			0.690232i	−0.938560	+	0.345116i	$0.887840\pi$
$180$	7.67985e7	+	7.96330e7i	0.981520	+	1.01775i
$181$		−	1.19135e8i		−	1.49336i	−0.665182	−	0.746681i	$-0.731646\pi$
$181$		−	1.19135e8i		−	1.49336i	0.665182	−	0.746681i	$-0.268354\pi$
$182$	2.07885e7	−	5.84133e7i	0.255608	−	0.718227i
$183$	−2.86593e6	+	4.78295e7i	−0.0345690	+	0.576922i
$184$	−9.11602e7	+	5.52739e7i	−1.07880	+	0.654121i
$185$		−	6.80362e7i		−	0.790021i
$186$	−9.99594e7	−	4.24694e7i	−1.13901	−	0.483928i
$187$	3.18270e7			0.355919
$188$	−4.15049e7	−	3.38264e7i	−0.455561	−	0.371282i
$189$	2.54863e7	−	1.40421e8i	0.274594	−	1.51292i
$190$	−2.22642e7	+	6.25598e7i	−0.235489	+	0.661694i
$191$	−1.80634e8			−1.87578			−0.937890	−	0.346934i	$-0.887223\pi$
$191$	−1.80634e8			−1.87578			−0.937890	+	0.346934i	$0.887223\pi$
$192$	5.04664e7	−	8.40932e7i	0.514574	−	0.857446i
$193$	8.94746e7			0.895879			0.447939	−	0.894064i	$-0.352158\pi$
$193$	8.94746e7			0.895879			0.447939	+	0.894064i	$0.352158\pi$
$194$	1.38346e7	−	3.88736e7i	0.136038	−	0.382251i
$195$	4.34151e6	−	7.24556e7i	0.0419295	−	0.699763i
$196$	1.11484e8	+	9.08596e7i	1.05759	+	0.861935i
$197$	−1.48244e8			−1.38148			−0.690741	−	0.723102i	$-0.742716\pi$
$197$	−1.48244e8			−1.38148			−0.690741	+	0.723102i	$0.742716\pi$
$198$	−1.19433e8	−	5.94120e7i	−1.09344	−	0.543934i
$199$			1.18822e8i			1.06884i	0.845219	+	0.534419i	$0.179470\pi$
$199$			1.18822e8i			1.06884i	−0.845219	+	0.534419i	$0.820530\pi$
$200$	−9.66642e7	+	5.86112e7i	−0.854399	+	0.518055i
$201$	−1.11105e8	−	6.65735e6i	−0.965041	−	0.0578249i
$202$	5.71316e7	−	1.60533e8i	0.487693	−	1.37036i
$203$			3.70888e7i			0.311176i
$204$	2.39238e7	−	2.60087e7i	0.197299	−	0.214493i
$205$			2.93030e8i			2.37560i
$206$	−1.11016e8	−	3.95093e7i	−0.884813	−	0.314894i
$207$	1.59848e8	+	1.92251e7i	1.25260	+	0.150651i
$208$	−6.30230e7	+	1.29827e7i	−0.485599	+	0.100033i
$209$		−	8.00658e7i		−	0.606646i
$210$	2.68543e8	+	1.14095e8i	2.00100	+	0.850158i
$211$	−1.14249e8			−0.837270			−0.418635	−	0.908155i	$-0.637491\pi$
$211$	−1.14249e8			−0.837270			−0.418635	+	0.908155i	$0.637491\pi$
$212$	−4.23793e7	−	3.45391e7i	−0.305477	−	0.248963i
$213$	3.83861e7	+	2.30008e6i	0.272173	+	0.0163085i
$214$	−8.43115e7	−	3.00054e7i	−0.588083	−	0.209291i
$215$	1.10302e8			0.756919
$216$	−1.38327e8	+	5.29405e7i	−0.933937	+	0.357438i
$217$	−2.86436e8			−1.90291
$218$	1.90307e8	+	6.77279e7i	1.24411	+	0.442761i
$219$	−8.60263e7	−	5.15467e6i	−0.553448	−	0.0331624i
$220$	1.72292e8	−	2.11402e8i	1.09091	−	1.33854i
$221$	−2.31855e7			−0.144492
$222$	8.38325e7	+	3.56176e7i	0.514253	+	0.218489i
$223$		−	5.04402e7i		−	0.304586i	−0.988335	−	0.152293i	$-0.951334\pi$
$223$		−	5.04402e7i		−	0.304586i	0.988335	−	0.152293i	$-0.0486657\pi$
$224$	3.57742e7	−	2.56171e8i	0.212668	−	1.52286i
$225$	1.69499e8	+	2.03859e7i	0.992039	+	0.119314i
$226$	1.99145e8	+	7.08731e7i	1.14760	+	0.408415i
$227$			1.22989e6i			0.00697871i	0.999994	+	0.00348935i	$0.00111070\pi$
$227$			1.22989e6i			0.00697871i	−0.999994	+	0.00348935i	$0.998889\pi$
$228$	−6.54290e7	−	6.01841e7i	−0.365593	−	0.336287i
$229$			6.31617e7i			0.347560i	0.984784	+	0.173780i	$0.0555982\pi$
$229$			6.31617e7i			0.347560i	−0.984784	+	0.173780i	$0.944402\pi$
$230$	−1.10362e8	+	3.10105e8i	−0.598099	+	1.68059i
$231$	−3.51178e8	−	2.10425e7i	−1.87450	−	0.112319i
$232$	3.29134e7	−	1.99566e7i	0.173047	−	0.104925i
$233$			2.38993e8i			1.23777i	0.785482	+	0.618885i	$0.212415\pi$
$233$			2.38993e8i			1.23777i	−0.785482	+	0.618885i	$0.787585\pi$
$234$	8.70052e7	+	4.32808e7i	0.443904	+	0.220820i
$235$	−1.65317e8			−0.830958
$236$	1.33530e8	−	1.63841e8i	0.661284	−	0.811393i
$237$	−2.36717e6	+	3.95058e7i	−0.0115508	+	0.192771i
$238$	3.12488e7	−	8.78053e7i	0.150250	−	0.422183i
$239$	1.24523e8			0.590007			0.295003	−	0.955496i	$-0.404679\pi$
$239$	1.24523e8			0.590007			0.295003	+	0.955496i	$0.404679\pi$
$240$	−4.32466e7	−	2.99703e8i	−0.201936	−	1.39943i
$241$	1.12969e8			0.519874			0.259937	−	0.965626i	$-0.416298\pi$
$241$	1.12969e8			0.519874			0.259937	+	0.965626i	$0.416298\pi$
$242$	−3.63311e7	+	1.02086e8i	−0.164787	+	0.463033i
$243$	2.13737e8	+	6.59388e7i	0.955561	+	0.294794i
$244$	8.28535e7	−	1.01661e8i	0.365129	−	0.448012i
$245$	4.44050e8			1.92908
$246$	−3.61064e8	−	1.53404e8i	−1.54636	−	0.656998i
$247$			5.83268e7i			0.246280i
$248$	1.54125e8	+	2.54189e8i	0.641640	+	1.05822i
$249$	365899.	−	6.10649e6i	0.00150198	−	0.0250665i
$250$	95022.3	−	267001.i	0.000384623	−	0.00108075i
$251$		−	3.91541e8i		−	1.56286i	−0.623995	−	0.781429i	$-0.714491\pi$
$251$		−	3.91541e8i		−	1.56286i	0.623995	−	0.781429i	$-0.285509\pi$
$252$	−2.81170e8	+	2.71162e8i	−1.10680	+	1.06740i
$253$		−	3.96881e8i		−	1.54077i
$254$	2.97036e8	+	1.05711e8i	1.13734	+	0.404765i
$255$	6.52604e6	−	1.08913e8i	0.0246467	−	0.411330i
$256$	−2.46580e8	+	1.06093e8i	−0.918584	+	0.395226i
$257$			3.55429e8i			1.30613i	0.757301	+	0.653066i	$0.226517\pi$
$257$			3.55429e8i			1.30613i	−0.757301	+	0.653066i	$0.773483\pi$
$258$	−5.77443e7	+	1.35912e8i	−0.209334	+	0.492706i
$259$	2.40224e8			0.859146
$260$	−1.25512e8	+	1.54003e8i	−0.442874	+	0.543405i
$261$	−5.77132e7	−	6.94122e6i	−0.200925	−	0.0241654i
$262$	3.12266e8	+	1.11132e8i	1.07268	+	0.381753i
$263$	9.21831e7			0.312468			0.156234	−	0.987720i	$-0.450065\pi$
$263$	9.21831e7			0.312468			0.156234	+	0.987720i	$0.450065\pi$
$264$	1.70288e8	+	3.22966e8i	0.569599	+	1.08030i
$265$	−1.68800e8			−0.557200
$266$	−2.20888e8	−	7.86111e7i	−0.719591	−	0.256093i
$267$	1.23048e7	−	2.05356e8i	0.0395627	−	0.660263i
$268$	2.36151e8	+	1.92463e8i	0.749408	+	0.610766i
$269$	−2.82781e8			−0.885762			−0.442881	−	0.896580i	$-0.646044\pi$
$269$	−2.82781e8			−0.885762			−0.442881	+	0.896580i	$0.646044\pi$
$270$	−2.27799e8	+	3.96522e8i	−0.704335	+	1.22601i
$271$			5.09934e8i			1.55640i	0.628015	+	0.778201i	$0.283867\pi$
$271$			5.09934e8i			1.55640i	−0.628015	+	0.778201i	$0.716133\pi$
$272$	−9.47345e7	+	1.95152e7i	−0.285441	+	0.0588007i
$273$	2.55828e8	+	1.53291e7i	0.760990	+	0.0455983i
$274$	−4.00980e8	−	1.42704e8i	−1.17759	−	0.419091i
$275$		−	4.20844e8i		−	1.22027i
$276$	−3.24327e8	−	2.98329e8i	−0.928543	−	0.854109i
$277$			4.69811e7i			0.132814i	0.997793	+	0.0664071i	$0.0211536\pi$
$277$			4.69811e7i			0.132814i	−0.997793	+	0.0664071i	$0.978846\pi$
$278$	1.77577e8	−	4.98969e8i	0.495712	−	1.39289i
$279$	5.36069e7	−	4.45717e8i	0.147777	−	1.22870i
$280$	−4.14060e8	−	6.82886e8i	−1.12722	−	1.85907i
$281$			4.69927e8i			1.26345i	0.775192	+	0.631726i	$0.217653\pi$
$281$			4.69927e8i			1.26345i	−0.775192	+	0.631726i	$0.782347\pi$
$282$	8.65450e7	−	2.03699e8i	0.229811	−	0.540900i
$283$	−3.07291e8			−0.805929			−0.402965	−	0.915216i	$-0.632020\pi$
$283$	−3.07291e8			−0.805929			−0.402965	+	0.915216i	$0.632020\pi$
$284$	−8.15891e7	−	6.64950e7i	−0.211358	−	0.172256i
$285$	−2.73988e8	−	1.64173e7i	−0.701092	−	0.0420092i
$286$	8.03173e7	−	2.25682e8i	0.203015	−	0.570448i
$287$	−1.03464e9			−2.58346
$288$	3.91927e8	+	1.03610e8i	0.966788	+	0.255581i
$289$	3.75487e8			0.915066
$290$	3.98463e7	−	1.11963e8i	0.0959390	−	0.269577i
$291$	1.70252e8	+	1.02014e7i	0.405010	+	0.0242680i
$292$	1.82848e8	+	1.49021e8i	0.429783	+	0.350273i
$293$	4.83537e8			1.12303			0.561517	−	0.827465i	$-0.310218\pi$
$293$	4.83537e8			1.12303			0.561517	+	0.827465i	$0.310218\pi$
$294$	−2.32465e8	+	5.47147e8i	−0.533508	+	1.25571i
$295$		−	6.52591e8i		−	1.48001i
$296$	−1.29259e8	−	2.13180e8i	−0.289694	−	0.477777i
$297$	9.84673e7	−	5.42524e8i	0.218094	−	1.20163i
$298$	−2.45505e8	+	6.89841e8i	−0.537408	+	1.51005i
$299$			2.89122e8i			0.625507i
$300$	−3.43909e8	−	3.16341e8i	−0.735393	−	0.676443i
$301$			3.89458e8i			0.823148i
$302$	−1.94268e8	−	6.91374e7i	−0.405860	−	0.144440i
$303$	7.03074e8	+	4.21280e7i	1.45195	+	0.0870004i
$304$	4.90935e7	+	2.38319e8i	0.100223	+	0.486521i
$305$		−	4.04922e8i		−	0.817189i
$306$	1.30784e8	+	6.50584e7i	0.260933	+	0.129801i
$307$	4.04574e8			0.798020			0.399010	−	0.916947i	$-0.369354\pi$
$307$	4.04574e8			0.798020			0.399010	+	0.916947i	$0.369354\pi$
$308$	7.46425e8	+	6.08335e8i	1.45566	+	1.18636i
$309$	2.91335e7	−	4.86210e8i	0.0561744	−	0.937495i
$310$	8.64691e8	+	3.07732e8i	1.64852	+	0.586688i
$311$	4.29205e8			0.809103			0.404551	−	0.914515i	$-0.367428\pi$
$311$	4.29205e8			0.809103			0.404551	+	0.914515i	$0.367428\pi$
$312$	−1.24052e8	−	2.35276e8i	−0.231240	−	0.438567i
$313$	−7.31946e8			−1.34919			−0.674597	−	0.738187i	$-0.735682\pi$
$313$	−7.31946e8			−1.34919			−0.674597	+	0.738187i	$0.735682\pi$
$314$	−2.84819e8	−	1.01363e8i	−0.519176	−	0.184768i
$315$	−1.44016e8	+	1.19743e9i	−0.259612	+	2.15856i
$316$	6.84346e7	−	8.39690e7i	0.122003	−	0.149697i
$317$	−1.09363e8			−0.192824			−0.0964120	−	0.995342i	$-0.530737\pi$
$317$	−1.09363e8			−0.192824			−0.0964120	+	0.995342i	$0.530737\pi$
$318$	8.83684e7	−	2.07991e8i	0.154100	−	0.362701i
$319$			1.43294e8i			0.247150i
$320$	−3.83211e8	+	7.34891e8i	−0.653753	+	1.25371i
$321$	2.21255e7	−	3.69253e8i	0.0373358	−	0.623098i
$322$	−1.09493e9	−	3.89670e8i	−1.82763	−	0.650432i
$323$			8.76752e7i			0.144766i
$324$	−3.69329e8	−	4.88272e8i	−0.603262	−	0.797543i
$325$			3.06578e8i			0.495393i
$326$	1.25352e8	−	3.52223e8i	0.200386	−	0.563061i
$327$	−4.99415e7	+	8.33474e8i	−0.0789849	+	1.31818i
$328$	5.56715e8	+	9.18159e8i	0.871113	+	1.43668i
$329$		−	5.83705e8i		−	0.903665i
$330$	1.03753e9	+	4.40811e8i	1.58928	+	0.675233i
$331$	−4.72046e8			−0.715461			−0.357731	−	0.933825i	$-0.616449\pi$
$331$	−4.72046e8			−0.715461			−0.357731	+	0.933825i	$0.616449\pi$
$332$	−1.05781e7	+	1.29793e7i	−0.0158644	+	0.0194656i
$333$	−4.49583e7	+	3.73808e8i	−0.0667198	+	0.554745i
$334$	3.06662e8	−	8.61683e8i	0.450347	−	1.26542i
$335$	9.40606e8			1.36694
$336$	1.05820e9	−	1.52696e8i	1.52188	−	0.219605i
$337$	6.25292e8			0.889975			0.444988	−	0.895537i	$-0.353208\pi$
$337$	6.25292e8			0.889975			0.444988	+	0.895537i	$0.353208\pi$
$338$	1.79516e8	−	5.04420e8i	0.252869	−	0.710532i
$339$	−5.22607e7	+	8.72179e8i	−0.0728578	+	1.21592i
$340$	−1.88667e8	+	2.31494e8i	−0.260327	+	0.319421i
$341$	−1.10666e9			−1.51138
$342$	1.63665e8	−	3.29007e8i	0.221240	−	0.444747i
$343$			4.18692e8i			0.560229i
$344$	3.45613e8	−	2.09559e8i	0.457758	−	0.277556i
$345$	−1.35814e9	−	8.13794e7i	−1.78065	−	0.106696i
$346$	2.25971e8	−	6.34952e8i	0.293283	−	0.824089i
$347$		−	1.63000e8i		−	0.209428i	−0.994502	−	0.104714i	$-0.966607\pi$
$347$		−	1.63000e8i		−	0.209428i	0.994502	−	0.104714i	$-0.0333927\pi$
$348$	1.17098e8	+	1.07712e8i	0.148944	+	0.137005i
$349$		−	5.70900e8i		−	0.718904i	−0.933164	−	0.359452i	$-0.882964\pi$
$349$		−	5.70900e8i		−	0.718904i	0.933164	−	0.359452i	$-0.117036\pi$
$350$	−1.16103e9	−	4.13197e8i	−1.44746	−	0.515133i
$351$	−7.17320e7	+	3.95220e8i	−0.0885397	+	0.487825i
$352$	1.38215e8	−	9.89724e8i	0.168910	−	1.20953i
$353$			6.12270e8i			0.740852i	0.928862	+	0.370426i	$0.120788\pi$
$353$			6.12270e8i			0.740852i	−0.928862	+	0.370426i	$0.879212\pi$
$354$	8.04106e8	+	3.41638e8i	0.963389	+	0.409312i
$355$	−3.24975e8			−0.385523
$356$	−3.55731e8	+	4.36480e8i	−0.417875	+	0.512731i
$357$	3.84554e8	+	2.30423e7i	0.447320	+	0.0268033i
$358$	5.64534e8	+	2.00910e8i	0.650278	+	0.231426i
$359$	−8.45852e8			−0.964859			−0.482429	−	0.875935i	$-0.660246\pi$
$359$	−8.45852e8			−0.964859			−0.482429	+	0.875935i	$0.660246\pi$
$360$	1.14012e9	−	5.16507e8i	1.28793	−	0.583469i
$361$	−6.73311e8			−0.753253
$362$	−1.26984e9	−	4.51920e8i	−1.40692	−	0.500705i
$363$	−4.47098e8	−	2.67899e7i	−0.490602	−	0.0293967i
$364$	−5.43759e8	−	4.43163e8i	−0.590951	−	0.481624i
$365$	7.28295e8			0.783939
$366$	4.98935e8	+	2.11981e8i	0.531937	+	0.226002i
$367$		−	1.51065e9i		−	1.59526i	−0.603144	−	0.797632i	$-0.706086\pi$
$367$		−	1.51065e9i		−	1.59526i	0.603144	−	0.797632i	$-0.293914\pi$
$368$	2.43354e8	+	1.18133e9i	0.254548	+	1.23568i
$369$	1.93634e8	−	1.60998e9i	0.200627	−	1.66812i
$370$	−7.25186e8	−	2.58084e8i	−0.744292	−	0.264884i
$371$		−	5.96003e8i		−	0.605954i
$372$	−8.31854e8	+	9.04349e8i	−0.837813	+	0.910827i
$373$			7.49026e8i			0.747336i	0.927563	+	0.373668i	$0.121900\pi$
$373$			7.49026e8i			0.747336i	−0.927563	+	0.373668i	$0.878100\pi$
$374$	1.20731e8	−	3.39239e8i	0.119335	−	0.335317i
$375$	1.16937e6	+	70068.0i	0.00114509	+	6.86136e-5i
$376$	−5.17992e8	+	3.14078e8i	−0.502534	+	0.304706i
$377$		−	1.04388e8i		−	0.100335i
$378$	−1.40005e9	−	8.04321e8i	−1.33328	−	0.765963i
$379$	1.35776e9			1.28110			0.640552	−	0.767915i	$-0.278706\pi$
$379$	1.35776e9			1.28110			0.640552	+	0.767915i	$0.278706\pi$
$380$	5.82358e8	+	4.74621e8i	0.544437	+	0.443715i
$381$	−7.79497e7	+	1.30090e9i	−0.0722066	+	1.20506i
$382$	−6.85204e8	+	1.92534e9i	−0.628924	+	1.76720i
$383$	−8.99150e8			−0.817780			−0.408890	−	0.912584i	$-0.634084\pi$
$383$	−8.99150e8			−0.817780			−0.408890	+	0.912584i	$0.634084\pi$
$384$	−7.04899e8	−	8.56906e8i	−0.635284	−	0.772279i
$385$	2.97306e9			2.65516
$386$	3.39408e8	−	9.53694e8i	0.300376	−	0.844022i
$387$	−6.06028e8	−	7.28876e7i	−0.531501	−	0.0639242i
$388$	−3.61867e8	−	2.94921e8i	−0.314513	−	0.256327i
$389$	−4.99376e8			−0.430134			−0.215067	−	0.976599i	$-0.568997\pi$
$389$	−4.99376e8			−0.430134			−0.215067	+	0.976599i	$0.568997\pi$
$390$	−7.55823e8	−	3.21124e8i	−0.645199	−	0.274124i
$391$			4.34600e8i			0.367681i
$392$	1.39135e9	−	8.43632e8i	1.16664	−	0.707378i
$393$	−8.19466e7	+	1.36761e9i	−0.0681016	+	1.13655i
$394$	−5.62340e8	+	1.58011e9i	−0.463193	+	1.30152i
$395$		−	3.34454e8i		−	0.273053i
$396$	−1.08631e9	+	1.04765e9i	−0.879066	+	0.847776i
$397$		−	2.45172e9i		−	1.96655i	−0.182128	−	0.983275i	$-0.558298\pi$
$397$		−	2.45172e9i		−	1.96655i	0.182128	−	0.983275i	$-0.441702\pi$
$398$	1.26651e9	+	4.50733e8i	1.00697	+	0.358368i
$399$	5.79666e7	−	9.67405e8i	0.0456849	−	0.762436i
$400$	2.58047e8	+	1.25266e9i	0.201599	+	0.978640i
$401$			1.46965e9i			1.13818i	0.822276	+	0.569088i	$0.192704\pi$
$401$			1.46965e9i			1.13818i	−0.822276	+	0.569088i	$0.807296\pi$
$402$	−4.92417e8	+	1.15899e9i	−0.378043	+	0.889793i
$403$	8.06183e8			0.613572
$404$	−1.49437e9	−	1.21791e9i	−1.12752	−	0.918928i
$405$	−1.83635e9	−	4.48202e8i	−1.37360	−	0.335259i
$406$	3.95323e8	+	1.40690e8i	0.293164	+	0.104333i
$407$	9.28114e8			0.682372
$408$	−1.86472e8	−	3.53660e8i	−0.135926	−	0.257795i
$409$	−2.67821e9			−1.93559			−0.967794	−	0.251742i	$-0.918997\pi$
$409$	−2.67821e9			−1.93559			−0.967794	+	0.251742i	$0.918997\pi$
$410$	3.12335e9	+	1.11156e9i	2.23809	+	0.796507i
$411$	1.05227e8	−	1.75614e9i	0.0747622	−	1.24771i
$412$	−8.42245e8	+	1.03343e9i	−0.593333	+	0.728017i
$413$	2.30419e9			1.60950
$414$	8.11275e8	−	1.63087e9i	0.561910	−	1.12958i
$415$			5.16973e7i			0.0355058i
$416$	−1.00688e8	+	7.20999e8i	−0.0685724	+	0.491030i
$417$	2.18530e9	+	1.30942e8i	1.47582	+	0.0884308i
$418$	−8.53408e8	−	3.03717e8i	−0.571531	−	0.203400i
$419$			1.25323e9i			0.832301i	0.909296	+	0.416151i	$0.136621\pi$
$419$			1.25323e9i			0.832301i	−0.909296	+	0.416151i	$0.863379\pi$
$420$	2.23480e9	−	2.42956e9i	1.47186	−	1.60013i
$421$		−	1.03003e9i		−	0.672761i	−0.941726	−	0.336380i	$-0.890797\pi$
$421$		−	1.03003e9i		−	0.672761i	0.941726	−	0.336380i	$-0.109203\pi$
$422$	−4.33387e8	+	1.21776e9i	−0.280726	+	0.788805i
$423$	9.08291e8	+	1.09241e8i	0.583491	+	0.0701770i
$424$	−5.28905e8	+	3.20695e8i	−0.336975	+	0.204321i
$425$			4.60840e8i			0.291198i
$426$	1.70128e8	−	4.00426e8i	0.106621	−	0.250951i
$427$	1.42971e9			0.888691
$428$	−6.39644e8	+	7.84841e8i	−0.394353	+	0.483870i
$429$	9.88402e8	+	5.92247e7i	0.604412	+	0.0362161i
$430$	4.18414e8	−	1.17569e9i	0.253785	−	0.713106i
$431$	9.25332e8			0.556708			0.278354	−	0.960479i	$-0.410211\pi$
$431$	9.25332e8			0.556708			0.278354	+	0.960479i	$0.410211\pi$
$432$	3.95642e7	+	1.67522e9i	0.0236107	+	0.999721i
$433$	9.64856e8			0.571156			0.285578	−	0.958355i	$-0.407814\pi$
$433$	9.64856e8			0.571156			0.285578	+	0.958355i	$0.407814\pi$
$434$	−1.08655e9	+	3.05307e9i	−0.638022	+	1.79276i
$435$	4.90357e8	+	2.93820e7i	0.285628	+	0.0171147i
$436$	1.44380e9	−	1.77154e9i	0.834265	−	1.02364i
$437$	1.09330e9			0.626695
$438$	−3.81270e8	+	8.97387e8i	−0.216807	+	0.510294i
$439$			1.03378e9i			0.583181i	0.956543	+	0.291590i	$0.0941844\pi$
$439$			1.03378e9i			0.583181i	−0.956543	+	0.291590i	$0.905816\pi$
$440$	−1.59974e9	−	2.63836e9i	−0.895291	−	1.47655i
$441$	−2.43972e9	−	2.93428e8i	−1.35458	−	0.162917i
$442$	−8.79505e7	+	2.47130e8i	−0.0484463	+	0.136128i
$443$		−	8.76781e8i		−	0.479157i	−0.970877	−	0.239579i	$-0.922991\pi$
$443$		−	8.76781e8i		−	0.479157i	0.970877	−	0.239579i	$-0.0770093\pi$
$444$	6.97647e8	−	7.58446e8i	0.378264	−	0.411229i
$445$			1.73853e9i			0.935238i
$446$	−5.37633e8	−	1.91337e8i	−0.286955	−	0.102124i
$447$	−3.02124e9	−	1.81032e8i	−1.59996	−	0.0958691i
$448$	−2.59477e9	−	1.35305e9i	−1.36341	−	0.710954i
$449$		−	1.54847e9i		−	0.807310i	−0.914911	−	0.403655i	$-0.867740\pi$
$449$		−	1.54847e9i		−	0.807310i	0.914911	−	0.403655i	$-0.132260\pi$
$450$	8.60257e8	−	1.72933e9i	0.445025	−	0.894612i
$451$	−3.99736e9			−2.05190
$452$	1.51085e9	−	1.85380e9i	0.769549	−	0.944233i
$453$	5.09808e7	−	8.50819e8i	0.0257669	−	0.430025i
$454$	1.31092e7	+	4.66538e6i	0.00657475	+	0.00233987i
$455$	−2.16583e9			−1.07791
$456$	−8.89686e8	+	4.69098e8i	−0.439400	+	0.231679i
$457$	9.48722e8			0.464978			0.232489	−	0.972599i	$-0.425313\pi$
$457$	9.48722e8			0.464978			0.232489	+	0.972599i	$0.425313\pi$
$458$	6.73230e8	+	2.39594e8i	0.327442	+	0.116532i
$459$	−1.07826e8	+	5.94084e8i	−0.0520448	+	0.286750i
$460$	2.88671e9	+	2.35267e9i	1.38277	+	1.12696i
$461$	−2.35261e9			−1.11840			−0.559199	−	0.829033i	$-0.688891\pi$
$461$	−2.35261e9			−1.11840			−0.559199	+	0.829033i	$0.688891\pi$
$462$	−1.55643e9	+	3.66333e9i	−0.734314	+	1.72834i
$463$			8.53974e8i			0.399863i	0.979810	+	0.199931i	$0.0640719\pi$
$463$			8.53974e8i			0.399863i	−0.979810	+	0.199931i	$0.935928\pi$
$464$	−8.78628e7	−	4.26520e8i	−0.0408312	−	0.198211i
$465$	−2.26917e8	+	3.78702e9i	−0.104660	+	1.74668i
$466$	2.54739e9	+	9.06582e8i	1.16612	+	0.415008i
$467$		−	1.92473e9i		−	0.874504i	−0.899339	−	0.437252i	$-0.855952\pi$
$467$		−	1.92473e9i		−	0.874504i	0.899339	−	0.437252i	$-0.144048\pi$
$468$	7.91362e8	−	7.63194e8i	0.356874	−	0.344171i
$469$			3.32112e9i			1.48655i
$470$	−6.27102e8	+	1.76208e9i	−0.278610	+	0.782859i
$471$	7.47437e7	−	1.24740e9i	0.0329611	−	0.550088i
$472$	−1.23983e9	−	2.04478e9i	−0.542707	−	0.895056i
$473$			1.50469e9i			0.653780i
$474$	4.12106e8	+	1.75090e8i	0.177740	+	0.0755158i
$475$	1.15931e9			0.496334
$476$	−8.17364e8	−	6.66150e8i	−0.347369	−	0.283105i
$477$	9.27428e8	+	1.11543e8i	0.391260	+	0.0470573i
$478$	4.72358e8	−	1.32727e9i	0.197822	−	0.555855i
$479$	2.65564e9			1.10406			0.552032	−	0.833823i	$-0.313853\pi$
$479$	2.65564e9			1.10406			0.552032	+	0.833823i	$0.313853\pi$
$480$	−3.35853e9	−	6.75917e8i	−1.38613	−	0.278965i
$481$	−6.76117e8			−0.277022
$482$	4.28528e8	−	1.20411e9i	0.174307	−	0.489781i
$483$	2.87337e8	−	4.79537e9i	0.116031	−	1.93645i
$484$	9.50300e8	+	7.74493e8i	0.380980	+	0.310498i
$485$	−1.44134e9			−0.573681
$486$	1.51361e9	−	2.02806e9i	0.598118	−	0.801408i
$487$		−	3.63297e9i		−	1.42531i	−0.701514	−	0.712656i	$-0.747492\pi$
$487$		−	3.63297e9i		−	1.42531i	0.701514	−	0.712656i	$-0.252508\pi$
$488$	−7.69295e8	−	1.26876e9i	−0.299656	−	0.494207i
$489$	1.54260e9	+	9.24322e7i	0.596586	+	0.0357472i
$490$	1.68443e9	−	4.73305e9i	0.646795	−	1.81742i
$491$			5.81674e8i			0.221766i	0.993833	+	0.110883i	$0.0353678\pi$
$491$			5.81674e8i			0.221766i	−0.993833	+	0.110883i	$0.964632\pi$
$492$	−3.00474e9	+	3.26660e9i	−1.13744	+	1.23657i
$493$		−	1.56912e8i		−	0.0589784i
$494$	6.21695e8	+	2.21253e8i	0.232024	+	0.0825743i
$495$	−5.56412e8	+	4.62632e9i	−0.206195	+	1.71442i
$496$	3.29401e9	−	6.78563e8i	1.21210	−	0.249692i
$497$		−	1.14743e9i		−	0.419256i
$498$	−6.37001e7	−	2.70641e7i	−0.0231120	−	0.00981952i
$499$	−4.26487e9			−1.53658			−0.768288	−	0.640104i	$-0.778891\pi$
$499$	−4.26487e9			−1.53658			−0.768288	+	0.640104i	$0.778891\pi$
$500$	−2.48547e6	−	2.02565e6i	−0.000889229	−	0.000724720i
$501$	3.77385e9	+	2.26128e8i	1.34076	+	0.0803381i
$502$	−4.17337e9	−	1.48525e9i	−1.47239	−	0.524006i
$503$	−1.91118e9			−0.669596			−0.334798	−	0.942290i	$-0.608668\pi$
$503$	−1.91118e9			−0.669596			−0.334798	+	0.942290i	$0.608668\pi$
$504$	1.82370e9	+	4.02556e9i	0.634521	+	1.40062i
$505$	−5.95219e9			−2.05663
$506$	−4.23029e9	−	1.50551e9i	−1.45159	−	0.516601i
$507$	2.20917e9	+	1.32373e8i	0.752837	+	0.0451097i
$508$	2.25351e9	−	2.76505e9i	0.762671	−	0.935794i
$509$	−2.87618e9			−0.966726			−0.483363	−	0.875420i	$-0.660585\pi$
$509$	−2.87618e9			−0.966726			−0.483363	+	0.875420i	$0.660585\pi$
$510$	−1.13613e9	−	4.82705e8i	−0.379257	−	0.161134i
$511$			2.57148e9i			0.852532i
$512$	1.95461e8	+	3.03070e9i	0.0643600	+	0.997927i
$513$	1.49451e9	+	2.71252e8i	0.488752	+	0.0887078i
$514$	3.78845e9	+	1.34826e9i	1.23053	+	0.437929i
$515$			4.11623e9i			1.32793i
$516$	1.22961e9	+	1.13105e9i	0.393999	+	0.362415i
$517$		−	2.25516e9i		−	0.717731i
$518$	9.11251e8	−	2.56051e9i	0.288061	−	0.809416i
$519$	2.78085e9	+	1.66627e8i	0.873156	+	0.0523192i
$520$	1.16538e9	+	1.92200e9i	0.363461	+	0.599435i
$521$		−	3.00108e9i		−	0.929706i	−0.885388	−	0.464853i	$-0.846107\pi$
$521$		−	3.00108e9i		−	0.929706i	0.885388	−	0.464853i	$-0.153893\pi$
$522$	−2.92911e8	+	5.88824e8i	−0.0901340	+	0.181192i
$523$	−4.84455e8			−0.148080			−0.0740402	−	0.997255i	$-0.523589\pi$
$523$	−4.84455e8			−0.148080			−0.0740402	+	0.997255i	$0.523589\pi$
$524$	2.36906e9	−	2.90683e9i	0.719312	−	0.882593i
$525$	3.04685e8	−	5.08490e9i	0.0918954	−	1.53364i
$526$	3.49682e8	−	9.82564e8i	0.104767	−	0.294382i
$527$	1.21183e9			0.360666
$528$	4.08839e9	−	5.89948e8i	1.20874	−	0.174420i
$529$	2.01461e9			0.591694
$530$	−6.40314e8	+	1.79921e9i	−0.186822	+	0.524947i
$531$	−4.31232e8	+	3.58550e9i	−0.124991	+	1.03925i
$532$	−1.67580e9	+	2.05621e9i	−0.482539	+	0.592074i
$533$	2.91202e9			0.833007
$534$	−2.14217e9	−	9.10138e8i	−0.608780	−	0.258650i
$535$			3.12607e9i			0.882594i
$536$	2.94723e9	−	1.78702e9i	0.826680	−	0.501247i
$537$	−1.48148e8	+	2.47244e9i	−0.0412844	+	0.688996i
$538$	−1.07268e9	+	3.01411e9i	−0.296984	+	0.834490i
$539$			6.05750e9i			1.66622i
$540$	3.36234e9	+	3.93222e9i	0.918889	+	1.07463i
$541$			7.15006e9i			1.94142i	0.240259	+	0.970709i	$0.422768\pi$
$541$			7.15006e9i			1.94142i	−0.240259	+	0.970709i	$0.577232\pi$
$542$	5.43530e9	+	1.93435e9i	1.46631	+	0.521841i
$543$	3.33239e8	−	5.56143e9i	0.0893215	−	1.49069i
$544$	−1.51351e8	+	1.08379e9i	−0.0403077	+	0.288634i
$545$		−	7.05615e9i		−	1.86715i
$546$	1.13383e9	−	2.66868e9i	0.298109	−	0.701653i
$547$	6.19208e9			1.61764			0.808818	−	0.588060i	$-0.200108\pi$
$547$	6.19208e9			1.61764			0.808818	+	0.588060i	$0.200108\pi$
$548$	−3.04211e9	+	3.73265e9i	−0.789664	+	0.968915i
$549$	−2.67572e8	+	2.22474e9i	−0.0690142	+	0.573822i
$550$	−4.48570e9	−	1.59640e9i	−1.14964	−	0.409141i
$551$	−3.94738e8			−0.100526
$552$	−4.41012e9	+	2.32529e9i	−1.11600	+	0.588424i
$553$	1.18090e9			0.296945
$554$	5.00764e8	+	1.78215e8i	0.125126	+	0.0445308i
$555$	1.90307e8	−	3.17604e9i	0.0472530	−	0.788607i
$556$	−4.64482e9	−	3.78552e9i	−1.14606	−	0.934036i
$557$	−3.28030e9			−0.804304			−0.402152	−	0.915573i	$-0.631738\pi$
$557$	−3.28030e9			−0.804304			−0.402152	+	0.915573i	$0.631738\pi$
$558$	−4.54748e9	−	2.26214e9i	−1.10803	−	0.551189i
$559$		−	1.09614e9i		−	0.265415i
$560$	−8.84944e9	+	1.82298e9i	−2.12940	+	0.438655i
$561$	1.48574e9	+	8.90249e7i	0.355281	+	0.0212883i
$562$	5.00887e9	+	1.78259e9i	1.19032	+	0.423619i
$563$			2.76254e9i			0.652422i	0.945297	+	0.326211i	$0.105772\pi$
$563$			2.76254e9i			0.652422i	−0.945297	+	0.326211i	$0.894228\pi$
$564$	−1.84290e9	−	1.69517e9i	−0.432538	−	0.397865i
$565$		−	7.38383e9i		−	1.72231i
$566$	−1.16566e9	+	3.27536e9i	−0.270217	+	0.759279i
$567$	1.58252e9	−	6.48382e9i	0.364594	−	1.49379i
$568$	−1.01825e9	+	6.17406e8i	−0.233151	+	0.141368i
$569$		−	7.17944e9i		−	1.63379i	−0.576783	−	0.816897i	$-0.695692\pi$
$569$		−	7.17944e9i		−	1.63379i	0.576783	−	0.816897i	$-0.304308\pi$
$570$	−1.21432e9	+	2.85812e9i	−0.274644	+	0.646425i
$571$	−4.49621e8			−0.101069			−0.0505347	−	0.998722i	$-0.516093\pi$
$571$	−4.49621e8			−0.101069			−0.0505347	+	0.998722i	$0.516093\pi$
$572$	−2.10083e9	−	1.71218e9i	−0.469360	−	0.382527i
$573$	−8.43227e9	−	5.05259e8i	−1.87242	−	0.112195i
$574$	−3.92473e9	+	1.10280e10i	−0.866200	+	2.43392i
$575$	5.74665e9			1.26060
$576$	2.59107e9	−	3.78445e9i	0.564938	−	0.825133i
$577$	5.82230e9			1.26177			0.630883	−	0.775878i	$-0.282693\pi$
$577$	5.82230e9			1.26177			0.630883	+	0.775878i	$0.282693\pi$
$578$	1.42435e9	−	4.00225e9i	0.306810	−	0.862098i
$579$	4.17682e9	+	2.50274e8i	0.894275	+	0.0535846i
$580$	−1.04225e9	−	8.49430e8i	−0.221806	−	0.180771i
$581$	−1.82534e8			−0.0386125
$582$	7.54557e8	−	1.77598e9i	0.158658	−	0.373430i
$583$		−	2.30268e9i		−	0.481275i
$584$	2.28199e9	−	1.38366e9i	0.474098	−	0.287464i
$585$	4.05338e8	−	3.37020e9i	0.0837089	−	0.696002i
$586$	1.83422e9	−	5.15393e9i	0.376538	−	1.05803i
$587$			2.29761e9i			0.468859i	0.972133	+	0.234430i	$0.0753222\pi$
$587$			2.29761e9i			0.468859i	−0.972133	+	0.234430i	$0.924678\pi$
$588$	4.95013e9	+	4.55331e9i	1.00414	+	0.923649i
$589$		−	3.04855e9i		−	0.614738i
$590$	−6.95585e9	−	2.47550e9i	−1.39434	−	0.496227i
$591$	−6.92028e9	−	4.14660e8i	−1.37901	−	0.0826297i
$592$	−2.76257e9	+	5.69087e8i	−0.547252	+	0.112733i
$593$		−	8.62589e8i		−	0.169868i	−0.996387	−	0.0849341i	$-0.972932\pi$
$593$		−	8.62589e8i		−	0.169868i	0.996387	−	0.0849341i	$-0.0270680\pi$
$594$	−5.40915e9	−	3.10752e9i	−1.05895	−	0.608361i
$595$	−3.25561e9			−0.633612
$596$	6.42161e9	+	5.23360e9i	1.24246	+	1.01260i
$597$	−3.32363e8	+	5.54682e9i	−0.0639298	+	1.06693i
$598$	3.08170e9	+	1.09674e9i	0.589300	+	0.209724i
$599$	−4.12221e8			−0.0783675			−0.0391838	−	0.999232i	$-0.512476\pi$
$599$	−4.12221e8			−0.0783675			−0.0391838	+	0.999232i	$0.512476\pi$
$600$	−4.67639e9	+	2.46568e9i	−0.883855	+	0.466024i
$601$	−5.17314e9			−0.972060			−0.486030	−	0.873942i	$-0.661555\pi$
$601$	−5.17314e9			−0.972060			−0.486030	+	0.873942i	$0.661555\pi$
$602$	4.15116e9	+	1.47735e9i	0.775501	+	0.275991i
$603$	−5.16792e9	−	6.21552e8i	−0.959855	−	0.115443i
$604$	−1.47385e9	+	1.80840e9i	−0.272159	+	0.333938i
$605$	3.78511e9			0.694920
$606$	3.11603e9	−	7.33414e9i	0.568785	−	1.33874i
$607$			1.01542e9i			0.184283i	0.995746	+	0.0921415i	$0.0293712\pi$
$607$			1.01542e9i			0.184283i	−0.995746	+	0.0921415i	$0.970629\pi$
$608$	2.72643e9	+	3.80746e8i	0.491963	+	0.0687026i
$609$	−1.03743e8	+	1.73137e9i	−0.0186122	+	0.310619i
$610$	−4.31600e9	−	1.53601e9i	−0.769887	−	0.273993i
$611$			1.64285e9i			0.291377i
$612$	1.18955e9	−	1.14721e9i	0.209775	−	0.202308i
$613$			1.48233e9i			0.259917i	0.991519	+	0.129958i	$0.0414843\pi$
$613$			1.48233e9i			0.259917i	−0.991519	+	0.129958i	$0.958516\pi$
$614$	1.53469e9	−	4.31228e9i	0.267566	−	0.751827i
$615$	−8.19647e8	+	1.36791e10i	−0.142090	+	2.37135i
$616$	9.31558e9	−	5.64839e9i	1.60575	−	0.973626i
$617$			1.09684e10i			1.87995i	0.341247	+	0.939974i	$0.389151\pi$
$617$			1.09684e10i			1.87995i	−0.341247	+	0.939974i	$0.610849\pi$
$618$	−5.07191e9	−	2.15489e9i	−0.864395	−	0.367253i
$619$	4.52266e9			0.766438			0.383219	−	0.923658i	$-0.374816\pi$
$619$	4.52266e9			0.766438			0.383219	+	0.923658i	$0.374816\pi$
$620$	6.56013e9	−	8.04925e9i	1.10546	−	1.35639i
$621$	7.40820e9	+	1.34458e9i	1.24134	+	0.225302i
$622$	1.62812e9	−	4.57483e9i	0.271282	−	0.762269i
$623$	−6.13845e9			−1.01707
$624$	−2.97833e9	+	4.29768e8i	−0.490713	+	0.0708090i
$625$	−6.10846e9			−1.00081
$626$	−2.77652e9	+	7.80169e9i	−0.452367	+	1.27110i
$627$	2.23956e8	−	3.73760e9i	0.0362849	−	0.605560i
$628$	−2.16083e9	+	2.65133e9i	−0.348146	+	0.427174i
$629$	−1.01632e9			−0.162837
$630$	1.22169e10	+	6.07731e9i	1.94657	+	0.968321i
$631$			5.92517e9i			0.938854i	0.882971	+	0.469427i	$0.155539\pi$
$631$			5.92517e9i			0.938854i	−0.882971	+	0.469427i	$0.844461\pi$
$632$	−6.35416e8	−	1.04796e9i	−0.100126	−	0.165133i
$633$	−5.33335e9	−	3.19572e8i	−0.835771	−	0.0500791i
$634$	−4.14849e8	+	1.16568e9i	−0.0646514	+	0.181663i
$635$		−	1.10134e10i		−	1.70692i
$636$	−1.88173e9	−	1.73088e9i	−0.290039	−	0.266789i
$637$		−	4.41279e9i		−	0.676434i
$638$	1.52735e9	+	5.43563e8i	0.232844	+	0.0828662i
$639$	1.78549e9	+	2.14743e8i	0.270710	+	0.0325586i
$640$	6.37943e9	+	6.87227e9i	0.961948	+	1.03626i
$641$			8.25130e9i			1.23743i	0.785617	+	0.618713i	$0.212346\pi$
$641$			8.25130e9i			1.23743i	−0.785617	+	0.618713i	$0.787654\pi$
$642$	−3.85187e9	−	1.63653e9i	−0.574512	−	0.244091i
$643$	−3.43913e8			−0.0510164			−0.0255082	−	0.999675i	$-0.508120\pi$
$643$	−3.43913e8			−0.0510164			−0.0255082	+	0.999675i	$0.508120\pi$
$644$	−8.30685e9	+	1.01925e10i	−1.22556	+	1.50376i
$645$	5.14909e9	+	3.08531e8i	0.755564	+	0.0452731i
$646$	9.34514e8	+	3.32582e8i	0.136387	+	0.0485383i
$647$	7.67816e9			1.11453			0.557265	−	0.830334i	$-0.311851\pi$
$647$	7.67816e9			1.11453			0.557265	+	0.830334i	$0.311851\pi$
$648$	−6.60540e9	+	2.08443e9i	−0.953644	+	0.300937i
$649$	8.90231e9			1.27834
$650$	3.26777e9	+	1.16296e9i	0.466718	+	0.166099i
$651$	−1.33713e10	−	8.01204e8i	−1.89951	−	0.113818i
$652$	−3.27878e9	−	2.67220e9i	−0.463282	−	0.377574i
$653$	4.81816e8			0.0677150			0.0338575	−	0.999427i	$-0.489221\pi$
$653$	4.81816e8			0.0677150			0.0338575	+	0.999427i	$0.489221\pi$
$654$	8.69441e9	+	3.69397e9i	1.21540	+	0.516382i
$655$		−	1.15781e10i		−	1.60988i
$656$	1.18983e10	−	2.45104e9i	1.64559	−	0.338990i
$657$	−4.00143e9	−	4.81257e8i	−0.550474	−	0.0662061i
$658$	−6.22161e9	−	2.21419e9i	−0.851358	−	0.302987i
$659$		−	5.69152e9i		−	0.774693i	−0.921934	−	0.387346i	$-0.873392\pi$
$659$		−	5.69152e9i		−	0.774693i	0.921934	−	0.387346i	$-0.126608\pi$
$660$	8.63422e9	−	9.38668e9i	1.16901	−	1.27089i
$661$			4.21717e9i			0.567957i	0.958831	+	0.283979i	$0.0916545\pi$
$661$			4.21717e9i			0.567957i	−0.958831	+	0.283979i	$0.908346\pi$
$662$	−1.79063e9	+	5.03145e9i	−0.239885	+	0.674047i
$663$	−1.08234e9	−	6.48533e7i	−0.144233	−	0.00864241i
$664$	9.82175e7	+	1.61985e8i	0.0130197	+	0.0214726i
$665$			8.19000e9i			1.07996i
$666$	3.81381e9	+	1.89718e9i	0.500264	+	0.248857i
$667$	−1.95669e9			−0.255318
$668$	−8.02126e9	−	6.53731e9i	−1.04118	−	0.848558i
$669$	1.41089e8	−	2.35463e9i	0.0182180	−	0.304041i
$670$	3.56804e9	−	1.00258e10i	0.458319	−	1.28782i
$671$	5.52374e9			0.705837
$672$	2.38655e9	−	1.18584e10i	0.303373	−	1.50742i
$673$	4.64381e9			0.587248			0.293624	−	0.955921i	$-0.405139\pi$
$673$	4.64381e9			0.587248			0.293624	+	0.955921i	$0.405139\pi$
$674$	2.37194e9	−	6.66487e9i	0.298397	−	0.838460i
$675$	7.85548e9	+	1.42576e9i	0.983127	+	0.178436i
$676$	−4.69555e9	−	3.82687e9i	−0.584620	−	0.476464i
$677$	−2.53205e9			−0.313626			−0.156813	−	0.987628i	$-0.550122\pi$
$677$	−2.53205e9			−0.313626			−0.156813	+	0.987628i	$0.550122\pi$
$678$	9.09816e9	+	3.86551e9i	1.12111	+	0.476324i
$679$		−	5.08913e9i		−	0.623877i
$680$	1.75177e9	+	2.88910e9i	0.213647	+	0.352356i
$681$	−3.44018e6	+	5.74132e7i	−0.000417413	+	0.00696621i
$682$	−4.19792e9	+	1.17957e10i	−0.506745	+	1.42389i
$683$			2.88044e9i			0.345928i	0.984928	+	0.172964i	$0.0553345\pi$
$683$			2.88044e9i			0.345928i	−0.984928	+	0.172964i	$0.944666\pi$
$684$	−2.88599e9	−	2.99251e9i	−0.344825	−	0.357552i
$685$			1.48674e10i			1.76733i
$686$	4.46276e9	+	1.58824e9i	0.527800	+	0.187837i
$687$	−1.76673e8	+	2.94849e9i	−0.0207884	+	0.346938i
$688$	−9.22620e8	−	4.47876e9i	−0.108010	−	0.524322i
$689$			1.67747e9i			0.195383i
$690$	−6.01930e9	+	1.41675e10i	−0.697548	+	1.64180i
$691$	3.73498e9			0.430641			0.215320	−	0.976543i	$-0.430920\pi$
$691$	3.73498e9			0.430641			0.215320	+	0.976543i	$0.430920\pi$
$692$	−5.91065e9	−	4.81717e9i	−0.678054	−	0.552613i
$693$	−1.63347e10	−	1.96460e9i	−1.86443	−	0.224237i
$694$	−1.73739e9	−	6.18314e8i	−0.197305	−	0.0702184i
$695$	−1.85006e10			−2.09045
$696$	1.59227e9	−	8.39546e8i	0.179013	−	0.0943870i
$697$	4.37726e9			0.489652
$698$	−6.08512e9	−	2.16562e9i	−0.677291	−	0.241039i
$699$	−6.68499e8	+	1.11566e10i	−0.0740339	+	1.23555i
$700$	−8.80840e9	+	1.08079e10i	−0.970630	+	1.19096i
$701$	1.55641e10			1.70652			0.853258	−	0.521489i	$-0.174623\pi$
$701$	1.55641e10			1.70652			0.853258	+	0.521489i	$0.174623\pi$
$702$	3.94048e9	+	2.26378e9i	0.429902	+	0.246976i
$703$			2.55671e9i			0.277548i
$704$	−1.00250e10	−	5.22757e9i	−1.08288	−	0.564671i
$705$	−7.71726e9	−	4.62415e8i	−0.829471	−	0.0497016i
$706$	6.52607e9	+	2.32255e9i	0.697968	+	0.248398i
$707$		−	2.10162e10i		−	2.23659i
$708$	6.69171e9	−	7.27488e9i	0.708632	−	0.770388i
$709$		−	9.20870e9i		−	0.970369i	−0.874412	−	0.485184i	$-0.838753\pi$
$709$		−	9.20870e9i		−	0.970369i	0.874412	−	0.485184i	$-0.161247\pi$
$710$	−1.23274e9	+	3.46385e9i	−0.129261	+	0.363208i
$711$	−2.21007e8	+	1.83758e9i	−0.0230602	+	0.191735i
$712$	3.30296e9	+	5.44739e9i	0.342944	+	0.565599i
$713$		−	1.51115e10i		−	1.56132i
$714$	1.70435e9	−	4.01149e9i	0.175232	−	0.412441i
$715$	−8.36776e9			−0.856127
$716$	4.28293e9	−	5.25515e9i	0.436060	−	0.535044i
$717$	5.81294e9	+	3.48309e8i	0.588951	+	0.0352897i
$718$	−3.20860e9	+	9.01579e9i	−0.323505	+	0.909009i
$719$	−1.27732e10			−1.28159			−0.640795	−	0.767712i	$-0.721395\pi$
$719$	−1.27732e10			−1.28159			−0.640795	+	0.767712i	$0.721395\pi$
$720$	−1.18051e9	−	1.41116e10i	−0.117871	−	1.40901i
$721$	−1.45337e10			−1.44412
$722$	−2.55410e9	+	7.17671e9i	−0.252556	+	0.709651i
$723$	5.27356e9	+	3.15990e8i	0.518943	+	0.0310949i
$724$	−9.63388e9	+	1.18207e10i	−0.943444	+	1.15760i
$725$	−2.07483e9			−0.202208
$726$	−1.98154e9	+	4.66391e9i	−0.192188	+	0.452348i
$727$			1.86923e8i			0.0180423i	0.999959	+	0.00902115i	$0.00287156\pi$
$727$			1.86923e8i			0.0180423i	−0.999959	+	0.00902115i	$0.997128\pi$
$728$	−6.78626e9	+	4.11477e9i	−0.651884	+	0.395262i
$729$	9.79317e9	+	3.67599e9i	0.936218	+	0.351421i
$730$	2.76267e9	−	7.76277e9i	0.262844	−	0.738561i
$731$		−	1.64769e9i		−	0.156014i
$732$	4.15210e9	−	4.51395e9i	0.391272	−	0.425371i
$733$		−	1.02749e10i		−	0.963635i	−0.876271	−	0.481818i	$-0.839977\pi$
$733$		−	1.02749e10i		−	0.963635i	0.876271	−	0.481818i	$-0.160023\pi$
$734$	−1.61018e10	−	5.73041e9i	−1.50292	−	0.534871i
$735$	2.07290e10	+	1.24207e9i	1.92563	+	0.115383i
$736$	1.35148e10	+	1.88733e9i	1.24950	+	0.174492i
$737$			1.28313e10i			1.18068i
$738$	−1.64260e10	−	8.17110e9i	−1.50430	−	0.748313i
$739$	5.65503e9			0.515441			0.257721	−	0.966219i	$-0.417029\pi$
$739$	5.65503e9			0.515441			0.257721	+	0.966219i	$0.417029\pi$
$740$	−5.50175e9	+	6.75063e9i	−0.499103	+	0.612397i
$741$	−1.63149e8	+	2.72279e9i	−0.0147306	+	0.245839i
$742$	−6.35269e9	−	2.26084e9i	−0.570879	−	0.203168i
$743$	4.48489e9			0.401136			0.200568	−	0.979680i	$-0.435721\pi$
$743$	4.48489e9			0.401136			0.200568	+	0.979680i	$0.435721\pi$
$744$	6.48379e9	+	1.22971e10i	0.577197	+	1.09471i
$745$	2.55777e10			2.26628
$746$	7.98374e9	+	2.84131e9i	0.704077	+	0.250572i
$747$	3.41615e7	−	2.84038e8i	0.00299858	−	0.0249318i
$748$	−3.15792e9	−	2.57370e9i	−0.275896	−	0.224855i
$749$	−1.10376e10			−0.959819
$750$	5.18264e6	−	1.21983e7i	0.000448577	−	0.00105581i
$751$			1.25488e10i			1.08109i	0.841314	+	0.540547i	$0.181783\pi$
$751$			1.25488e10i			1.08109i	−0.841314	+	0.540547i	$0.818217\pi$
$752$	1.38279e9	+	6.71259e9i	0.118575	+	0.575609i
$753$	1.09520e9	−	1.82778e10i	0.0934782	−	1.56006i
$754$	−1.11265e9	−	3.95977e8i	−0.0945275	−	0.0336411i
$755$			7.20299e9i			0.609114i
$756$	−1.38840e10	+	1.18718e10i	−1.16866	+	0.999290i
$757$		−	1.12493e10i		−	0.942518i	−0.881995	−	0.471259i	$-0.843800\pi$
$757$		−	1.12493e10i		−	0.942518i	0.881995	−	0.471259i	$-0.156200\pi$
$758$	5.15043e9	−	1.44721e10i	0.429538	−	1.20695i
$759$	1.11014e9	−	1.85271e10i	0.0921573	−	1.53801i
$760$	7.26798e9	−	4.40686e9i	0.600574	−	0.364151i
$761$			1.04257e10i			0.857546i	0.903412	+	0.428773i	$0.141054\pi$
$761$			1.04257e10i			0.857546i	−0.903412	+	0.428773i	$0.858946\pi$
$762$	1.35704e10	+	5.76562e9i	1.11109	+	0.472067i
$763$	2.49140e10			2.03053
$764$	1.79227e10	+	1.46069e10i	1.45404	+	1.18504i
$765$	6.09293e8	−	5.06600e9i	0.0492052	−	0.409119i
$766$	−3.41078e9	+	9.58388e9i	−0.274191	+	0.770444i
$767$	−6.48520e9			−0.518967
$768$	−1.18075e10	+	4.26286e9i	−0.940579	+	0.339576i
$769$	−1.79503e10			−1.42341			−0.711706	−	0.702478i	$-0.752077\pi$
$769$	−1.79503e10			−1.42341			−0.711706	+	0.702478i	$0.752077\pi$
$770$	1.12778e10	−	3.16893e10i	0.890241	−	2.50147i
$771$	−9.94187e8	+	1.65920e10i	−0.0781228	+	1.30379i
$772$	−8.87778e9	−	7.23537e9i	−0.694454	−	0.565979i
$773$	−1.30886e9			−0.101922			−0.0509608	−	0.998701i	$-0.516228\pi$
$773$	−1.30886e9			−0.101922			−0.0509608	+	0.998701i	$0.516228\pi$
$774$	−3.07576e9	+	6.18306e9i	−0.238429	+	0.479303i
$775$		−	1.60239e10i		−	1.23655i
$776$	−4.51620e9	+	2.73834e9i	−0.346942	+	0.210364i
$777$	1.12141e10	+	6.71942e8i	0.857608	+	0.0513876i
$778$	−1.89430e9	+	5.32276e9i	−0.144218	+	0.405236i
$779$		−	1.10117e10i		−	0.834589i
$780$	−6.28990e9	+	6.83805e9i	−0.474583	+	0.515943i
$781$		−	4.43314e9i		−	0.332991i
$782$	4.63233e9	+	1.64859e9i	0.346398	+	0.123279i
$783$	−2.67473e9	−	4.85460e8i	−0.199119	−	0.0361399i
$784$	−3.71424e9	−	1.80304e10i	−0.275273	−	1.33628i
$785$			1.05604e10i			0.779179i
$786$	1.42663e10	+	6.06126e9i	1.04793	+	0.445229i
$787$	−1.43246e10			−1.04754			−0.523770	−	0.851860i	$-0.675475\pi$
$787$	−1.43246e10			−1.04754			−0.523770	+	0.851860i	$0.675475\pi$
$788$	1.47089e10	+	1.19878e10i	1.07088	+	0.872763i
$789$	4.30326e9	+	2.57850e8i	0.311909	+	0.0186895i
$790$	−3.56489e9	−	1.26870e9i	−0.257248	−	0.0915511i
$791$	2.60710e10			1.87301
$792$	7.04592e9	+	1.55529e10i	0.503964	+	1.11243i
$793$	−4.02396e9			−0.286548
$794$	−2.61325e10	−	9.30022e9i	−1.85272	−	0.659358i
$795$	−7.87985e9	−	4.72158e8i	−0.556202	−	0.0333274i
$796$	9.60858e9	−	1.17897e10i	0.675248	−	0.828527i
$797$	9.85671e9			0.689649			0.344824	−	0.938667i	$-0.387938\pi$
$797$	9.85671e9			0.689649			0.344824	+	0.938667i	$0.387938\pi$
$798$	−1.00915e10	−	4.28755e9i	−0.702985	−	0.298675i
$799$			2.46949e9i			0.171275i
$800$	1.43307e10	+	2.00129e9i	0.989586	+	0.138196i
$801$	1.14882e9	−	9.55192e9i	0.0789838	−	0.656715i
$802$	1.56648e10	+	5.57490e9i	1.07229	+	0.381616i
$803$			9.93502e9i			0.677118i
$804$	1.04856e10	+	9.64503e9i	0.711535	+	0.654497i
$805$			4.05973e10i			2.74291i
$806$	3.05812e9	−	8.59296e9i	0.205723	−	0.578056i
$807$	−1.32007e10	−	7.90980e8i	−0.884176	−	0.0529795i
$808$	−1.86502e10	+	1.13083e10i	−1.24378	+	0.754151i
$809$		−	1.39740e10i		−	0.927903i	−0.885861	−	0.463951i	$-0.846431\pi$
$809$		−	1.39740e10i		−	0.927903i	0.885861	−	0.463951i	$-0.153569\pi$
$810$	−1.17432e10	+	1.78731e10i	−0.776405	+	1.18169i
$811$	−1.11611e10			−0.734740			−0.367370	−	0.930075i	$-0.619742\pi$
$811$	−1.11611e10			−0.734740			−0.367370	+	0.930075i	$0.619742\pi$
$812$	2.99919e9	−	3.67999e9i	0.196588	−	0.241213i
$813$	−1.42636e9	+	2.38046e10i	−0.0930921	+	1.55362i
$814$	3.52065e9	−	9.89261e9i	0.228790	−	0.642873i
$815$	−1.30596e10			−0.845042
$816$	−4.47695e9	+	6.46016e8i	−0.288447	+	0.0416225i
$817$	−4.14501e9			−0.265919
$818$	−1.01594e10	+	2.85466e10i	−0.648978	+	1.82355i
$819$	1.18996e10	+	1.43118e9i	0.756901	+	0.0910333i
$820$	2.36959e10	−	2.90748e10i	1.50080	−	1.84148i
$821$	2.98833e9			0.188464			0.0942320	−	0.995550i	$-0.469960\pi$
$821$	2.98833e9			0.188464			0.0942320	+	0.995550i	$0.469960\pi$
$822$	−1.83192e10	−	7.78324e9i	−1.15042	−	0.488775i
$823$			2.49854e10i			1.56238i	0.624293	+	0.781191i	$0.285387\pi$
$823$			2.49854e10i			1.56238i	−0.624293	+	0.781191i	$0.714613\pi$
$824$	7.82025e9	+	1.28975e10i	0.486940	+	0.803083i
$825$	1.17716e9	−	1.96457e10i	0.0729873	−	1.21809i
$826$	8.74056e9	−	2.45599e10i	0.539646	−	1.51634i
$827$			6.85599e9i			0.421503i	0.977540	+	0.210752i	$0.0675911\pi$
$827$			6.85599e9i			0.421503i	−0.977540	+	0.210752i	$0.932409\pi$
$828$	−1.43057e10	−	1.48337e10i	−0.875794	−	0.908118i
$829$		−	2.08320e10i		−	1.26996i	−0.772529	−	0.634979i	$-0.781009\pi$
$829$		−	2.08320e10i		−	1.26996i	0.772529	−	0.634979i	$-0.218991\pi$
$830$	5.51032e8	+	1.96105e8i	0.0334506	+	0.0119046i
$831$	−1.31413e8	+	2.19316e9i	−0.00794393	+	0.132576i
$832$	7.30306e9	+	3.80821e9i	0.439616	+	0.229239i
$833$		−	6.63319e9i		−	0.397617i
$834$	9.68527e9	−	2.27960e10i	0.578137	−	1.36075i
$835$	−3.19492e10			−1.89914
$836$	−6.47453e9	+	7.94423e9i	−0.383254	+	0.470251i
$837$	3.74920e9	−	2.06569e10i	0.221003	−	1.21766i
$838$	1.33579e10	+	4.75391e9i	0.784124	+	0.279060i
$839$	1.94903e10			1.13933			0.569667	−	0.821876i	$-0.307072\pi$
$839$	1.94903e10			1.13933			0.569667	+	0.821876i	$0.307072\pi$
$840$	−1.74189e10	−	3.30364e10i	−1.01401	−	1.92316i
$841$	−1.65434e10			−0.959045
$842$	−1.09789e10	−	3.90723e9i	−0.633818	−	0.225568i
$843$	−1.31446e9	+	2.19370e10i	−0.0755700	+	1.26119i
$844$	1.13360e10	+	9.23879e9i	0.649022	+	0.528952i
$845$	−1.87027e10			−1.06637
$846$	4.60984e9	−	9.26693e9i	0.261752	−	0.526186i
$847$			1.33646e10i			0.755723i
$848$	1.41192e9	+	6.85402e9i	0.0795106	+	0.385975i
$849$	−1.43448e10	−	8.59537e8i	−0.804486	−	0.0482045i
$850$	4.91202e9	+	1.74812e9i	0.274343	+	0.0976350i
$851$			1.26735e10i			0.704923i
$852$	−3.62272e9	−	3.33231e9i	−0.200676	−	0.184590i
$853$			7.36557e9i			0.406336i	0.979144	+	0.203168i	$0.0651237\pi$
$853$			7.36557e9i			0.406336i	−0.979144	+	0.203168i	$0.934876\pi$
$854$	5.42338e9	−	1.52390e10i	0.297966	−	0.837250i
$855$	−1.27443e10	−	1.53277e9i	−0.697324	−	0.0838679i
$856$	5.93910e9	+	9.79503e9i	0.323640	+	0.533762i
$857$		−	1.02885e10i		−	0.558368i	−0.960238	−	0.279184i	$-0.909936\pi$
$857$		−	1.02885e10i		−	0.558368i	0.960238	−	0.279184i	$-0.0900639\pi$
$858$	4.38061e9	−	1.03105e10i	0.236771	−	0.557283i
$859$	2.10847e10			1.13499			0.567494	−	0.823378i	$-0.307913\pi$
$859$	2.10847e10			1.13499			0.567494	+	0.823378i	$0.307913\pi$
$860$	−1.09443e10	−	8.91960e9i	−0.586738	−	0.478190i
$861$	−4.82986e10	−	2.89403e9i	−2.57883	−	0.154523i
$862$	3.51010e9	−	9.86296e9i	0.186657	−	0.524483i
$863$	1.03713e10			0.549282			0.274641	−	0.961547i	$-0.411441\pi$
$863$	1.03713e10			0.549282			0.274641	+	0.961547i	$0.411441\pi$
$864$	1.80060e10	+	5.93297e9i	0.949770	+	0.312949i
$865$	−2.35425e10			−1.23679
$866$	3.66003e9	−	1.02842e10i	0.191501	−	0.538096i
$867$	1.75283e10	+	1.05029e9i	0.913427	+	0.0547322i
$868$	2.84205e10	+	2.31627e10i	1.47507	+	1.20218i
$869$	4.56245e9			0.235846
$870$	2.17327e9	−	5.11518e9i	0.111891	−	0.263356i
$871$		−	9.34738e9i		−	0.479321i
$872$	−1.34057e10	−	2.21093e10i	−0.684670	−	1.12919i
$873$	7.91909e9	+	9.52437e8i	0.402833	+	0.0484492i
$874$	4.14727e9	−	1.16533e10i	0.210123	−	0.590419i
$875$		−	3.49545e7i		−	0.00176390i
$876$	8.11880e9	+	7.46798e9i	0.408063	+	0.375352i
$877$			1.96006e10i			0.981230i	0.871376	+	0.490615i	$0.163228\pi$
$877$			1.96006e10i			0.981230i	−0.871376	+	0.490615i	$0.836772\pi$
$878$	1.10189e10	+	3.92149e9i	0.549424	+	0.195533i
$879$	2.25723e10	+	1.35252e9i	1.12102	+	0.0671713i
$880$	−3.41901e10	+	7.04313e9i	−1.69126	+	0.348399i
$881$		−	2.80833e10i		−	1.38367i	−0.722055	−	0.691836i	$-0.756802\pi$
$881$		−	2.80833e10i		−	1.38367i	0.722055	−	0.691836i	$-0.243198\pi$
$882$	−1.23823e10	+	2.48915e10i	−0.607660	+	1.22155i
$883$	−2.34002e10			−1.14382			−0.571910	−	0.820316i	$-0.693797\pi$
$883$	−2.34002e10			−1.14382			−0.571910	+	0.820316i	$0.693797\pi$
$884$	2.30049e9	+	1.87490e9i	0.112005	+	0.0912840i
$885$	1.82539e9	−	3.04640e10i	0.0885227	−	1.47736i
$886$	−9.34546e9	−	3.32593e9i	−0.451422	−	0.160655i
$887$	−2.34643e10			−1.12895			−0.564475	−	0.825450i	$-0.690921\pi$
$887$	−2.34643e10			−1.12895			−0.564475	+	0.825450i	$0.690921\pi$
$888$	−5.43773e9	−	1.03131e10i	−0.260599	−	0.494249i
$889$	3.88864e10			1.85627
$890$	1.85307e10	+	6.59483e9i	0.881103	+	0.313573i
$891$	6.11414e9	−	2.50505e10i	0.289576	−	1.18643i
$892$	−4.07885e9	+	5.00474e9i	−0.192425	+	0.236104i
$893$	6.21239e9			0.291930
$894$	−1.33902e10	+	3.15162e10i	−0.626766	+	1.47521i
$895$		−	2.09316e10i		−	0.975937i
$896$	−2.42648e10	+	2.25247e10i	−1.12694	+	1.04612i
$897$	−8.08717e8	+	1.34967e10i	−0.0374130	+	0.624387i
$898$	−1.65049e10	−	5.87386e9i	−0.760579	−	0.270680i
$899$			5.45600e9i			0.250447i
$900$	−1.51694e10	−	1.57293e10i	−0.693617	−	0.719217i
$901$			2.52152e9i			0.114849i
$902$	−1.51633e10	+	4.26072e10i	−0.687974	+	1.93312i
$903$	−1.08937e9	+	1.81805e10i	−0.0492344	+	0.821674i
$904$	−1.40282e10	−	2.31360e10i	−0.631558	−	1.04159i
$905$			4.70828e10i			2.11150i
$906$	−8.87535e9	−	3.77084e9i	−0.396494	−	0.168457i
$907$	2.07542e10			0.923592			0.461796	−	0.886986i	$-0.347205\pi$
$907$	2.07542e10			0.923592			0.461796	+	0.886986i	$0.347205\pi$
$908$	9.94550e7	−	1.22031e8i	0.00440886	−	0.00540965i
$909$	3.27028e10	+	3.93320e9i	1.44415	+	0.173689i
$910$	−8.21572e9	+	2.30852e10i	−0.361411	+	1.01552i
$911$	8.39905e9			0.368058			0.184029	−	0.982921i	$-0.441086\pi$
$911$	8.39905e9			0.368058			0.184029	+	0.982921i	$0.441086\pi$
$912$	1.62515e9	+	1.12625e10i	0.0709435	+	0.491645i
$913$	−7.05227e8			−0.0306677
$914$	3.59882e9	−	1.01123e10i	0.155901	−	0.438063i
$915$	1.13263e9	−	1.89024e10i	0.0488780	−	0.815726i
$916$	5.10758e9	−	6.26698e9i	0.219574	−	0.269417i
$917$	4.08803e10			1.75074
$918$	5.92322e9	+	3.40286e9i	0.252702	+	0.145176i
$919$			1.77784e10i			0.755594i	0.925889	+	0.377797i	$0.123318\pi$
$919$			1.77784e10i			0.755594i	−0.925889	+	0.377797i	$0.876682\pi$
$920$	3.60269e10	−	2.18445e10i	1.52535	−	0.924879i
$921$	1.88862e10	+	1.13165e9i	0.796591	+	0.0477314i
$922$	−8.92425e9	+	2.50761e10i	−0.374984	+	1.05366i
$923$			3.22947e9i			0.135184i
$924$	3.31427e10	+	3.04859e10i	1.38209	+	1.27130i
$925$			1.34386e10i			0.558290i
$926$	9.10236e9	+	3.23941e9i	0.376717	+	0.134069i
$927$	2.72000e9	−	2.26156e10i	0.112148	−	0.932457i
$928$	−4.87950e9	−	6.81422e8i	−0.200428	−	0.0279897i
$929$		−	8.89605e8i		−	0.0364034i	−0.999834	−	0.0182017i	$-0.994206\pi$
$929$		−	8.89605e8i		−	0.0364034i	0.999834	−	0.0182017i	$-0.00579411\pi$
$930$	3.95044e10	+	1.67841e10i	1.61048	+	0.684239i
$931$	−1.66868e10			−0.677719
$932$	1.93262e10	−	2.37132e10i	0.781972	−	0.959476i
$933$	2.00360e10	+	1.20055e9i	0.807654	+	0.0483944i
$934$	−2.05154e10	−	7.30117e9i	−0.823884	−	0.293210i
$935$	−1.25782e10			−0.503243
$936$	−5.13285e9	−	1.13300e10i	−0.204594	−	0.451613i
$937$	1.09174e10			0.433543			0.216772	−	0.976222i	$-0.430447\pi$
$937$	1.09174e10			0.433543			0.216772	+	0.976222i	$0.430447\pi$
$938$	3.53992e10	+	1.25981e10i	1.40050	+	0.498420i
$939$	−3.41685e10	−	2.04736e9i	−1.34678	−	0.0806984i
$940$	1.64029e10	+	1.33684e10i	0.644130	+	0.524965i
$941$	−1.58749e10			−0.621080			−0.310540	−	0.950560i	$-0.600510\pi$
$941$	−1.58749e10			−0.621080			−0.310540	+	0.950560i	$0.600510\pi$
$942$	−1.30123e10	−	5.52849e9i	−0.507195	−	0.215491i
$943$		−	5.45842e10i		−	2.11971i
$944$	−2.64981e10	+	5.45858e9i	−1.02521	+	0.211192i
$945$	−1.00723e10	+	5.54952e10i	−0.388256	+	2.13916i
$946$	1.60382e10	+	5.70778e9i	0.615937	+	0.219204i
$947$		−	3.05808e10i		−	1.17010i	−0.810996	−	0.585051i	$-0.801074\pi$
$947$		−	3.05808e10i		−	1.17010i	0.810996	−	0.585051i	$-0.198926\pi$
$948$	3.42951e9	−	3.72839e9i	0.130739	−	0.142132i
$949$		−	7.23751e9i		−	0.274889i
$950$	4.39767e9	−	1.23569e10i	0.166414	−	0.467604i
$951$	−5.10522e9	−	3.05903e8i	−0.192479	−	0.0115333i
$952$	−1.02009e10	+	6.18521e9i	−0.383186	+	0.232340i
$953$		−	5.23582e9i		−	0.195956i	−0.995189	−	0.0979782i	$-0.968762\pi$
$953$		−	5.23582e9i		−	0.195956i	0.995189	−	0.0979782i	$-0.0312375\pi$
$954$	4.70696e9	−	9.46217e9i	0.175518	−	0.352835i
$955$	7.13872e10			2.65221
$956$	−1.23553e10	−	1.00696e10i	−0.457353	−	0.372742i
$957$	−4.00814e8	+	6.68920e9i	−0.0147826	+	0.246707i
$958$	1.00737e10	−	2.83060e10i	0.370178	−	1.04016i
$959$	−5.24943e10			−1.92197
$960$	−1.99445e10	+	3.32340e10i	−0.727570	+	1.21237i
$961$	−1.46239e10			−0.531535
$962$	−2.56474e9	+	7.20662e9i	−0.0928819	+	0.260987i
$963$	2.06571e9	−	1.71754e10i	0.0745379	−	0.619749i
$964$	−1.12089e10	−	9.13521e9i	−0.402988	−	0.328435i
$965$	−3.53608e10			−1.26671
$966$	−5.00230e10	−	2.12531e10i	−1.78546	−	0.758582i
$967$			2.00071e9i			0.0711526i	0.999367	+	0.0355763i	$0.0113267\pi$
$967$			2.00071e9i			0.0711526i	−0.999367	+	0.0355763i	$0.988673\pi$
$968$	1.18600e10	−	7.19117e9i	0.420263	−	0.254821i
$969$	−2.45240e8	+	4.09282e9i	−0.00865882	+	0.144507i
$970$	−5.46750e9	+	1.53630e10i	−0.192348	+	0.540474i
$971$		−	5.74860e9i		−	0.201509i	−0.994911	−	0.100755i	$-0.967874\pi$
$971$		−	5.74860e9i		−	0.201509i	0.994911	−	0.100755i	$-0.0321257\pi$
$972$	−1.58751e10	−	2.38264e10i	−0.554479	−	0.832198i
$973$		−	6.53225e10i		−	2.27336i
$974$	−3.87232e10	−	1.37811e10i	−1.34281	−	0.477889i
$975$	−8.57545e8	+	1.43116e10i	−0.0296306	+	0.494506i
$976$	−1.64416e10	+	3.38696e9i	−0.566071	+	0.116610i
$977$			3.65906e10i			1.25527i	0.778506	+	0.627637i	$0.215978\pi$
$977$			3.65906e10i			1.25527i	−0.778506	+	0.627637i	$0.784022\pi$
$978$	6.83683e9	−	1.60917e10i	0.233706	−	0.550068i
$979$	−2.37161e10			−0.807801
$980$	−4.40591e10	−	3.59081e10i	−1.49536	−	1.21871i
$981$	−4.66270e9	+	3.87682e10i	−0.157687	+	1.31110i
$982$	6.19996e9	+	2.20649e9i	0.208929	+	0.0743551i
$983$	5.43661e10			1.82554			0.912769	−	0.408476i	$-0.133939\pi$
$983$	5.43661e10			1.82554			0.912769	+	0.408476i	$0.133939\pi$
$984$	2.34201e10	+	4.44184e10i	0.783622	+	1.48621i
$985$	5.85867e10			1.95332
$986$	−1.67250e9	−	5.95222e8i	−0.0555645	−	0.0197747i
$987$	1.63271e9	−	2.72483e10i	0.0540504	−	0.902047i
$988$	4.71660e9	−	5.78725e9i	0.155589	−	0.190907i
$989$	−2.05466e10			−0.675386
$990$	4.72005e10	+	2.34799e10i	1.54605	+	0.769083i
$991$			4.42393e10i			1.44394i	0.691922	+	0.721972i	$0.256764\pi$
$991$			4.42393e10i			1.44394i	−0.691922	+	0.721972i	$0.743236\pi$
$992$	5.26261e9	−	3.76843e10i	0.171163	−	1.22566i
$993$	−2.20359e10	−	1.32038e9i	−0.714180	−	0.0427934i
$994$	−1.22303e10	−	4.35259e9i	−0.394987	−	0.140571i
$995$		−	4.69591e10i		−	1.51126i
$996$	−5.30107e8	+	5.76305e8i	−0.0170003	+	0.0184818i
$997$		−	3.33656e10i		−	1.06627i	−0.846031	−	0.533133i	$-0.821014\pi$
$997$		−	3.33656e10i		−	1.06627i	0.846031	−	0.533133i	$-0.178986\pi$
$998$	−1.61781e10	+	4.54585e10i	−0.515194	+	1.44763i
$999$	−3.14432e9	+	1.73242e10i	−0.0997809	+	0.549761i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	24.8.f.c.11.11	yes	20
3.2	odd	2	inner	24.8.f.c.11.10	yes	20
4.3	odd	2		96.8.f.c.47.1		20
8.3	odd	2	inner	24.8.f.c.11.9	✓	20
8.5	even	2		96.8.f.c.47.2		20
12.11	even	2		96.8.f.c.47.4		20
24.5	odd	2		96.8.f.c.47.3		20
24.11	even	2	inner	24.8.f.c.11.12	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.8.f.c.11.9	✓	20	8.3	odd	2	inner
24.8.f.c.11.10	yes	20	3.2	odd	2	inner
24.8.f.c.11.11	yes	20	1.1	even	1	trivial
24.8.f.c.11.12	yes	20	24.11	even	2	inner
96.8.f.c.47.1		20	4.3	odd	2
96.8.f.c.47.2		20	8.5	even	2
96.8.f.c.47.3		20	24.5	odd	2
96.8.f.c.47.4		20	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)

\(f(q)\)	\(=\)	\(q+(3.79334 - 10.6588i) q^{2} +(46.6816 + 2.79715i) q^{3} +(-99.2212 - 80.8651i) q^{4} -395.205 q^{5} +(206.894 - 486.961i) q^{6} -1395.40i q^{7} +(-1238.31 + 750.833i) q^{8} +(2171.35 + 261.151i) q^{9} +O(q^{10})\)	\(q+(3.79334 - 10.6588i) q^{2} +(46.6816 + 2.79715i) q^{3} +(-99.2212 - 80.8651i) q^{4} -395.205 q^{5} +(206.894 - 486.961i) q^{6} -1395.40i q^{7} +(-1238.31 + 750.833i) q^{8} +(2171.35 + 261.151i) q^{9} +(-1499.14 + 4212.42i) q^{10} -5391.17i q^{11} +(-4405.62 - 4052.45i) q^{12} +3927.39i q^{13} +(-14873.3 - 5293.22i) q^{14} +(-18448.8 - 1105.45i) q^{15} +(3305.68 + 16047.1i) q^{16} +5903.54i q^{17} +(11020.2 - 22153.4i) q^{18} +14851.3 q^{19} +(39212.7 + 31958.2i) q^{20} +(3903.14 - 65139.5i) q^{21} +(-57463.6 - 20450.6i) q^{22} +73616.8 q^{23} +(-59906.4 + 31586.4i) q^{24} +78061.6 q^{25} +(41861.4 + 14897.9i) q^{26} +(100632. + 18264.5i) q^{27} +(-112839. + 138453. i) q^{28} -26579.4 q^{29} +(-81765.3 + 192449. i) q^{30} -205272. i q^{31} +(183582. + 25637.3i) q^{32} +(15079.9 - 251669. i) q^{33} +(62924.8 + 22394.1i) q^{34} +551468. i q^{35} +(-194326. - 201498. i) q^{36} +172154. i q^{37} +(56335.9 - 158297. i) q^{38} +(-10985.5 + 183337. i) q^{39} +(489384. - 296732. i) q^{40} -741464. i q^{41} +(-679505. - 288699. i) q^{42} -279102. q^{43} +(-435958. + 534919. i) q^{44} +(-858128. - 103208. i) q^{45} +(279254. - 784669. i) q^{46} +418307. q^{47} +(109429. + 758349. i) q^{48} -1.12359e6 q^{49} +(296114. - 832045. i) q^{50} +(-16513.1 + 275587. i) q^{51} +(317589. - 389680. i) q^{52} +427120. q^{53} +(576409. - 1.00333e6i) q^{54} +2.13062e6i q^{55} +(1.04771e6 + 1.72793e6i) q^{56} +(693282. + 41541.2i) q^{57} +(-100825. + 283305. i) q^{58} +1.65127e6i q^{59} +(1.74112e6 + 1.60155e6i) q^{60} +1.02459e6i q^{61} +(-2.18796e6 - 778666. i) q^{62} +(364410. - 3.02990e6i) q^{63} +(969653. - 1.85952e6i) q^{64} -1.55212e6i q^{65} +(-2.62529e6 - 1.11540e6i) q^{66} -2.38005e6 q^{67} +(477391. - 585756. i) q^{68} +(3.43656e6 + 205917. i) q^{69} +(5.87800e6 + 2.09190e6i) q^{70} +822295. q^{71} +(-2.88488e6 + 1.30694e6i) q^{72} -1.84283e6 q^{73} +(1.83496e6 + 653040. i) q^{74} +(3.64404e6 + 218350. i) q^{75} +(-1.47356e6 - 1.20095e6i) q^{76} -7.52284e6 q^{77} +(1.91249e6 + 812552. i) q^{78} +846282. i q^{79} +(-1.30642e6 - 6.34187e6i) q^{80} +(4.64657e6 + 1.13410e6i) q^{81} +(-7.90313e6 - 2.81262e6i) q^{82} -130811. i q^{83} +(-5.65479e6 + 6.14759e6i) q^{84} -2.33311e6i q^{85} +(-1.05873e6 + 2.97489e6i) q^{86} +(-1.24077e6 - 74346.4i) q^{87} +(4.04787e6 + 6.67593e6i) q^{88} -4.39906e6i q^{89} +(-4.35525e6 + 8.75514e6i) q^{90} +5.48027e6 q^{91} +(-7.30435e6 - 5.95303e6i) q^{92} +(574176. - 9.58243e6i) q^{93} +(1.58678e6 - 4.45866e6i) q^{94} -5.86929e6 q^{95} +(8.49821e6 + 1.71030e6i) q^{96} +3.64708e6 q^{97} +(-4.26218e6 + 1.19762e7i) q^{98} +(1.40791e6 - 1.17061e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 120 q^{3} + 548 q^{4} - 1416 q^{6} + 5076 q^{9}+O(q^{10}) \) 20 * q + 120 * q^3 + 548 * q^4 - 1416 * q^6 + 5076 * q^9	\( 20 q + 120 q^{3} + 548 q^{4} - 1416 q^{6} + 5076 q^{9} - 3384 q^{10} - 26700 q^{12} - 33304 q^{16} - 11880 q^{18} + 133744 q^{19} - 166880 q^{22} - 74424 q^{24} + 711596 q^{25} + 85320 q^{27} - 669360 q^{28} - 41904 q^{30} + 263640 q^{33} + 24112 q^{34} - 409428 q^{36} - 437088 q^{40} + 1724040 q^{42} - 2292080 q^{43} + 1466400 q^{46} + 1846200 q^{48} + 2495228 q^{49} - 7417536 q^{51} - 2511360 q^{52} + 5680584 q^{54} - 5067120 q^{57} + 1427880 q^{58} + 2211120 q^{60} - 4070608 q^{64} + 1062024 q^{66} + 3654640 q^{67} + 11712816 q^{70} + 7004880 q^{72} + 19892680 q^{73} - 8612088 q^{75} - 11799464 q^{76} - 1226160 q^{78} - 6817932 q^{81} - 52710080 q^{82} - 6585408 q^{84} - 13470800 q^{88} + 10393704 q^{90} + 67826976 q^{91} - 24601920 q^{94} + 35857680 q^{96} + 5561800 q^{97} + 10152864 q^{99}+O(q^{100}) \) 20 * q + 120 * q^3 + 548 * q^4 - 1416 * q^6 + 5076 * q^9 - 3384 * q^10 - 26700 * q^12 - 33304 * q^16 - 11880 * q^18 + 133744 * q^19 - 166880 * q^22 - 74424 * q^24 + 711596 * q^25 + 85320 * q^27 - 669360 * q^28 - 41904 * q^30 + 263640 * q^33 + 24112 * q^34 - 409428 * q^36 - 437088 * q^40 + 1724040 * q^42 - 2292080 * q^43 + 1466400 * q^46 + 1846200 * q^48 + 2495228 * q^49 - 7417536 * q^51 - 2511360 * q^52 + 5680584 * q^54 - 5067120 * q^57 + 1427880 * q^58 + 2211120 * q^60 - 4070608 * q^64 + 1062024 * q^66 + 3654640 * q^67 + 11712816 * q^70 + 7004880 * q^72 + 19892680 * q^73 - 8612088 * q^75 - 11799464 * q^76 - 1226160 * q^78 - 6817932 * q^81 - 52710080 * q^82 - 6585408 * q^84 - 13470800 * q^88 + 10393704 * q^90 + 67826976 * q^91 - 24601920 * q^94 + 35857680 * q^96 + 5561800 * q^97 + 10152864 * q^99

Introduction

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