LMFDB - Embedded newform 12.8.b.b.11.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,8,Mod(11,12)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(12, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("12.11");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	12.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.74862030581$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 41x^{6} + 1008x^{4} + 41984x^{2} + 1048576 $ x^8 + 41x^6 + 1008x^4 + 41984*x^2 + 1048576
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{20}\cdot 3^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.8
Root			$-4.51977 + 3.40172i$ of defining polynomial
Character	$\chi$	$=$	12.11
Dual form			12.8.b.b.11.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(9.03954 + 6.80344i) q^{2} +(-46.2722 + 6.77368i) q^{3} +(35.4264 + 123.000i) q^{4} +426.666i q^{5} +(-464.364 - 253.579i) q^{6} -780.788i q^{7} +(-516.584 + 1352.88i) q^{8} +(2095.23 - 626.867i) q^{9} +O(q^{10})$	\(q+(9.03954 + 6.80344i) q^{2} +(-46.2722 + 6.77368i) q^{3} +(35.4264 + 123.000i) q^{4} +426.666i q^{5} +(-464.364 - 253.579i) q^{6} -780.788i q^{7} +(-516.584 + 1352.88i) q^{8} +(2095.23 - 626.867i) q^{9} +(-2902.79 + 3856.86i) q^{10} +1923.23 q^{11} +(-2472.42 - 5451.51i) q^{12} +8028.82 q^{13} +(5312.05 - 7057.97i) q^{14} +(-2890.10 - 19742.8i) q^{15} +(-13873.9 + 8714.89i) q^{16} -8167.93i q^{17} +(23204.8 + 8588.22i) q^{18} +30292.2i q^{19} +(-52479.8 + 15115.2i) q^{20} +(5288.81 + 36128.8i) q^{21} +(17385.1 + 13084.6i) q^{22} +25899.2 q^{23} +(14739.5 - 66100.1i) q^{24} -103918. q^{25} +(72576.8 + 54623.6i) q^{26} +(-92704.9 + 43199.0i) q^{27} +(96036.9 - 27660.6i) q^{28} -109562. i q^{29} +(108194. - 198128. i) q^{30} +36004.5i q^{31} +(-184705. - 15611.9i) q^{32} +(-88992.3 + 13027.4i) q^{33} +(55570.0 - 73834.3i) q^{34} +333136. q^{35} +(151331. + 235506. i) q^{36} +318880. q^{37} +(-206091. + 273827. i) q^{38} +(-371511. + 54384.7i) q^{39} +(-577229. - 220408. i) q^{40} -64088.3i q^{41} +(-197992. + 362570. i) q^{42} -794243. i q^{43} +(68133.3 + 236558. i) q^{44} +(267462. + 893964. i) q^{45} +(234116. + 176203. i) q^{46} +60806.6 q^{47} +(582946. - 497235. i) q^{48} +213912. q^{49} +(-939375. - 707003. i) q^{50} +(55326.9 + 377948. i) q^{51} +(284433. + 987544. i) q^{52} -1.15180e6i q^{53} +(-1.13191e6 - 240214. i) q^{54} +820578. i q^{55} +(1.05632e6 + 403342. i) q^{56} +(-205190. - 1.40169e6i) q^{57} +(745397. - 990388. i) q^{58} +805492. q^{59} +(2.32597e6 - 1.05490e6i) q^{60} -2.13080e6 q^{61} +(-244954. + 325464. i) q^{62} +(-489450. - 1.63593e6i) q^{63} +(-1.56343e6 - 1.39775e6i) q^{64} +3.42562e6i q^{65} +(-893080. - 487692. i) q^{66} +4.05068e6i q^{67} +(1.00465e6 - 289361. i) q^{68} +(-1.19841e6 + 175433. i) q^{69} +(3.01139e6 + 2.26647e6i) q^{70} -4.95316e6 q^{71} +(-234286. + 3.15844e6i) q^{72} +1.26252e6 q^{73} +(2.88253e6 + 2.16948e6i) q^{74} +(4.80854e6 - 703911. i) q^{75} +(-3.72593e6 + 1.07314e6i) q^{76} -1.50164e6i q^{77} +(-3.72829e6 - 2.03594e6i) q^{78} -6.28094e6i q^{79} +(-3.71834e6 - 5.91953e6i) q^{80} +(3.99705e6 - 2.62686e6i) q^{81} +(436021. - 579329. i) q^{82} +3.29421e6 q^{83} +(-4.25647e6 + 1.93044e6i) q^{84} +3.48497e6 q^{85} +(5.40358e6 - 7.17959e6i) q^{86} +(742137. + 5.06967e6i) q^{87} +(-993511. + 2.60191e6i) q^{88} +1.58344e6i q^{89} +(-3.66430e6 + 9.90069e6i) q^{90} -6.26881e6i q^{91} +(917515. + 3.18559e6i) q^{92} +(-243883. - 1.66601e6i) q^{93} +(549664. + 413694. i) q^{94} -1.29246e7 q^{95} +(8.65247e6 - 528738. i) q^{96} +1.60064e6 q^{97} +(1.93367e6 + 1.45534e6i) q^{98} +(4.02963e6 - 1.20561e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 328 q^{4} - 1512 q^{6} + 2088 q^{9}+O(q^{10}) $ 8 * q - 328 * q^4 - 1512 * q^6 + 2088 * q^9	$ 8 q - 328 q^{4} - 1512 q^{6} + 2088 q^{9} - 4880 q^{10} - 12168 q^{12} + 54448 q^{13} - 10720 q^{16} - 50256 q^{18} - 133776 q^{21} + 140304 q^{22} + 37152 q^{24} - 195480 q^{25} + 202128 q^{28} - 43920 q^{30} + 183168 q^{33} + 361408 q^{34} + 1035864 q^{36} - 21776 q^{37} - 3028160 q^{40} - 1676592 q^{42} + 1992960 q^{45} + 496032 q^{46} + 1838880 q^{48} + 958040 q^{49} - 1484720 q^{52} - 4211352 q^{54} - 3798576 q^{57} + 12049168 q^{58} + 10255680 q^{60} - 3027920 q^{61} - 9073792 q^{64} - 15137136 q^{66} - 8149248 q^{69} + 13293600 q^{70} + 10585152 q^{72} + 3682768 q^{73} - 18402192 q^{76} - 12533616 q^{78} + 16656840 q^{81} + 16046560 q^{82} + 18942480 q^{84} + 12032000 q^{85} - 29650752 q^{88} - 34917840 q^{90} + 21380400 q^{93} + 8217408 q^{94} + 45277056 q^{96} - 15887216 q^{97}+O(q^{100}) $ 8 * q - 328 * q^4 - 1512 * q^6 + 2088 * q^9 - 4880 * q^10 - 12168 * q^12 + 54448 * q^13 - 10720 * q^16 - 50256 * q^18 - 133776 * q^21 + 140304 * q^22 + 37152 * q^24 - 195480 * q^25 + 202128 * q^28 - 43920 * q^30 + 183168 * q^33 + 361408 * q^34 + 1035864 * q^36 - 21776 * q^37 - 3028160 * q^40 - 1676592 * q^42 + 1992960 * q^45 + 496032 * q^46 + 1838880 * q^48 + 958040 * q^49 - 1484720 * q^52 - 4211352 * q^54 - 3798576 * q^57 + 12049168 * q^58 + 10255680 * q^60 - 3027920 * q^61 - 9073792 * q^64 - 15137136 * q^66 - 8149248 * q^69 + 13293600 * q^70 + 10585152 * q^72 + 3682768 * q^73 - 18402192 * q^76 - 12533616 * q^78 + 16656840 * q^81 + 16046560 * q^82 + 18942480 * q^84 + 12032000 * q^85 - 29650752 * q^88 - 34917840 * q^90 + 21380400 * q^93 + 8217408 * q^94 + 45277056 * q^96 - 15887216 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/12\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	9.03954	+	6.80344i	0.798990	+	0.601345i
$2$	9.03954	+	6.80344i	0.798990	+	0.601345i
$3$	−46.2722	+	6.77368i	−0.989455	+	0.144844i
$3$	−46.2722	+	6.77368i	−0.989455	+	0.144844i
$4$	35.4264	+	123.000i	0.276769	+	0.960936i
$5$			426.666i			1.52649i	0.646112	+	0.763243i	$0.276394\pi$
$5$			426.666i			1.52649i	−0.646112	+	0.763243i	$0.723606\pi$
$6$	−464.364	−	253.579i	−0.877665	−	0.479274i
$7$		−	780.788i		−	0.860380i	−0.902738	−	0.430190i	$-0.858447\pi$
$7$		−	780.788i		−	0.860380i	0.902738	−	0.430190i	$-0.141553\pi$
$8$	−516.584	+	1352.88i	−0.356718	+	0.934212i
$9$	2095.23	−	626.867i	0.958040	−	0.286633i
$10$	−2902.79	+	3856.86i	−0.917944	+	1.21965i
$11$	1923.23			0.435670			0.217835	−	0.975986i	$-0.430101\pi$
$11$	1923.23			0.435670			0.217835	+	0.975986i	$0.430101\pi$
$12$	−2472.42	−	5451.51i	−0.413036	−	0.910715i
$13$	8028.82			1.01356			0.506781	−	0.862075i	$-0.330835\pi$
$13$	8028.82			1.01356			0.506781	+	0.862075i	$0.330835\pi$
$14$	5312.05	−	7057.97i	0.517385	−	0.687435i
$15$	−2890.10	−	19742.8i	−0.221102	−	1.51039i
$16$	−13873.9	+	8714.89i	−0.846798	+	0.531915i
$17$		−	8167.93i		−	0.403219i	−0.979466	−	0.201609i	$-0.935383\pi$
$17$		−	8167.93i		−	0.403219i	0.979466	−	0.201609i	$-0.0646171\pi$
$18$	23204.8	+	8588.22i	0.937830	+	0.347096i
$19$			30292.2i			1.01319i	0.862183	+	0.506597i	$0.169097\pi$
$19$			30292.2i			1.01319i	−0.862183	+	0.506597i	$0.830903\pi$
$20$	−52479.8	+	15115.2i	−1.46686	+	0.422484i
$21$	5288.81	+	36128.8i	0.124621	+	0.851307i
$22$	17385.1	+	13084.6i	0.348096	+	0.261988i
$23$	25899.2			0.443852			0.221926	−	0.975064i	$-0.428766\pi$
$23$	25899.2			0.443852			0.221926	+	0.975064i	$0.428766\pi$
$24$	14739.5	−	66100.1i	0.217642	−	0.976029i
$25$	−103918.			−1.33016
$26$	72576.8	+	54623.6i	0.809825	+	0.609500i
$27$	−92704.9	+	43199.0i	−0.906420	+	0.422377i
$28$	96036.9	−	27660.6i	0.826770	−	0.238127i
$29$		−	109562.i		−	0.834193i	−0.908862	−	0.417096i	$-0.863048\pi$
$29$		−	109562.i		−	0.834193i	0.908862	−	0.417096i	$-0.136952\pi$
$30$	108194.	−	198128.i	0.731605	−	1.33974i
$31$			36004.5i			0.217065i	0.994093	+	0.108533i	$0.0346152\pi$
$31$			36004.5i			0.217065i	−0.994093	+	0.108533i	$0.965385\pi$
$32$	−184705.	−	15611.9i	−0.996447	−	0.0842229i
$33$	−88992.3	+	13027.4i	−0.431076	+	0.0631042i
$34$	55570.0	−	73834.3i	0.242473	−	0.322168i
$35$	333136.			1.31336
$36$	151331.	+	235506.i	0.540592	+	0.841285i
$37$	318880.			1.03496			0.517478	−	0.855697i	$-0.326871\pi$
$37$	318880.			1.03496			0.517478	+	0.855697i	$0.326871\pi$
$38$	−206091.	+	273827.i	−0.609279	+	0.809532i
$39$	−371511.	+	54384.7i	−1.00287	+	0.146808i
$40$	−577229.	−	220408.i	−1.42606	−	0.544525i
$41$		−	64088.3i		−	0.145223i	−0.997360	−	0.0726115i	$-0.976867\pi$
$41$		−	64088.3i		−	0.145223i	0.997360	−	0.0726115i	$-0.0231333\pi$
$42$	−197992.	+	362570.i	−0.412358	+	0.755125i
$43$		−	794243.i		−	1.52340i	−0.647930	−	0.761700i	$-0.724365\pi$
$43$		−	794243.i		−	1.52340i	0.647930	−	0.761700i	$-0.275635\pi$
$44$	68133.3	+	236558.i	0.120580	+	0.418651i
$45$	267462.	+	893964.i	0.437541	+	1.46243i
$46$	234116.	+	176203.i	0.354633	+	0.266908i
$47$	60806.6			0.0854296			0.0427148	−	0.999087i	$-0.486399\pi$
$47$	60806.6			0.0854296			0.0427148	+	0.999087i	$0.486399\pi$
$48$	582946.	−	497235.i	0.760823	−	0.648959i
$49$	213912.			0.259746
$50$	−939375.	−	707003.i	−1.06278	−	0.799883i
$51$	55326.9	+	377948.i	0.0584038	+	0.398967i
$52$	284433.	+	987544.i	0.280522	+	0.973968i
$53$		−	1.15180e6i		−	1.06270i	−0.847152	−	0.531351i	$-0.821685\pi$
$53$		−	1.15180e6i		−	1.06270i	0.847152	−	0.531351i	$-0.178315\pi$
$54$	−1.13191e6	−	240214.i	−0.978215	−	0.207596i
$55$			820578.i			0.665044i
$56$	1.05632e6	+	403342.i	0.803777	+	0.306913i
$57$	−205190.	−	1.40169e6i	−0.146755	−	1.00251i
$58$	745397.	−	990388.i	0.501637	−	0.666511i
$59$	805492.			0.510598			0.255299	−	0.966862i	$-0.417826\pi$
$59$	805492.			0.510598			0.255299	+	0.966862i	$0.417826\pi$
$60$	2.32597e6	−	1.05490e6i	1.39019	−	0.630494i
$61$	−2.13080e6			−1.20195			−0.600976	−	0.799267i	$-0.705221\pi$
$61$	−2.13080e6			−1.20195			−0.600976	+	0.799267i	$0.705221\pi$
$62$	−244954.	+	325464.i	−0.130531	+	0.173433i
$63$	−489450.	−	1.63593e6i	−0.246613	−	0.824279i
$64$	−1.56343e6	−	1.39775e6i	−0.745504	−	0.666501i
$65$			3.42562e6i			1.54719i
$66$	−893080.	−	487692.i	−0.382372	−	0.208806i
$67$			4.05068e6i			1.64538i	0.568489	+	0.822691i	$0.307528\pi$
$67$			4.05068e6i			1.64538i	−0.568489	+	0.822691i	$0.692472\pi$
$68$	1.00465e6	−	289361.i	0.387468	−	0.111598i
$69$	−1.19841e6	+	175433.i	−0.439171	+	0.0642893i
$70$	3.01139e6	+	2.26647e6i	1.04936	+	0.789780i
$71$	−4.95316e6			−1.64240			−0.821198	−	0.570644i	$-0.806694\pi$
$71$	−4.95316e6			−1.64240			−0.821198	+	0.570644i	$0.806694\pi$
$72$	−234286.	+	3.15844e6i	−0.0739747	+	0.997260i
$73$	1.26252e6			0.379846			0.189923	−	0.981799i	$-0.439176\pi$
$73$	1.26252e6			0.379846			0.189923	+	0.981799i	$0.439176\pi$
$74$	2.88253e6	+	2.16948e6i	0.826919	+	0.622365i
$75$	4.80854e6	−	703911.i	1.31613	−	0.192665i
$76$	−3.72593e6	+	1.07314e6i	−0.973615	+	0.280421i
$77$		−	1.50164e6i		−	0.374842i
$78$	−3.72829e6	−	2.03594e6i	−0.889568	−	0.485774i
$79$		−	6.28094e6i		−	1.43328i	−0.697445	−	0.716638i	$-0.745680\pi$
$79$		−	6.28094e6i		−	1.43328i	0.697445	−	0.716638i	$-0.254320\pi$
$80$	−3.71834e6	−	5.91953e6i	−0.811960	−	1.29262i
$81$	3.99705e6	−	2.62686e6i	0.835683	−	0.549212i
$82$	436021.	−	579329.i	0.0873291	−	0.116032i
$83$	3.29421e6			0.632379			0.316190	−	0.948696i	$-0.397596\pi$
$83$	3.29421e6			0.632379			0.316190	+	0.948696i	$0.397596\pi$
$84$	−4.25647e6	+	1.93044e6i	−0.783561	+	0.355368i
$85$	3.48497e6			0.615507
$86$	5.40358e6	−	7.17959e6i	0.916088	−	1.21718i
$87$	742137.	+	5.06967e6i	0.120828	+	0.825396i
$88$	−993511.	+	2.60191e6i	−0.155412	+	0.407008i
$89$			1.58344e6i			0.238088i	0.992889	+	0.119044i	$0.0379829\pi$
$89$			1.58344e6i			0.238088i	−0.992889	+	0.119044i	$0.962017\pi$
$90$	−3.66430e6	+	9.90069e6i	−0.529836	+	1.43158i
$91$		−	6.26881e6i		−	0.872048i
$92$	917515.	+	3.18559e6i	0.122844	+	0.426514i
$93$	−243883.	−	1.66601e6i	−0.0314406	−	0.214776i
$94$	549664.	+	413694.i	0.0682574	+	0.0513726i
$95$	−1.29246e7			−1.54663
$96$	8.65247e6	−	528738.i	0.998138	−	0.0609946i
$97$	1.60064e6			0.178071			0.0890353	−	0.996028i	$-0.471622\pi$
$97$	1.60064e6			0.178071			0.0890353	+	0.996028i	$0.471622\pi$
$98$	1.93367e6	+	1.45534e6i	0.207535	+	0.156197i
$99$	4.02963e6	−	1.20561e6i	0.417390	−	0.124877i
$100$	−3.68146e6	−	1.27820e7i	−0.368146	−	1.27820i
$101$			1.07533e7i			1.03852i	0.854615	+	0.519262i	$0.173793\pi$
$101$			1.07533e7i			1.03852i	−0.854615	+	0.519262i	$0.826207\pi$
$102$	−2.07122e6	+	3.79289e6i	−0.193252	+	0.353891i
$103$			8.97049e6i			0.808883i	0.914564	+	0.404442i	$0.132534\pi$
$103$			8.97049e6i			0.808883i	−0.914564	+	0.404442i	$0.867466\pi$
$104$	−4.14756e6	+	1.08621e7i	−0.361556	+	0.946881i
$105$	−1.54149e7	+	2.25655e6i	−1.29951	+	0.190232i
$106$	7.83619e6	−	1.04117e7i	0.639050	−	0.849087i
$107$	1.89815e7			1.49791			0.748957	−	0.662618i	$-0.230555\pi$
$107$	1.89815e7			1.49791			0.748957	+	0.662618i	$0.230555\pi$
$108$	−8.59767e6	−	9.87231e6i	−0.656746	−	0.754112i
$109$	−8.73038e6			−0.645714			−0.322857	−	0.946448i	$-0.604643\pi$
$109$	−8.73038e6			−0.645714			−0.322857	+	0.946448i	$0.604643\pi$
$110$	−5.58275e6	+	7.41764e6i	−0.399921	+	0.531363i
$111$	−1.47553e7	+	2.15999e6i	−1.02404	+	0.149907i
$112$	6.80449e6	+	1.08326e7i	0.457649	+	0.728568i
$113$		−	1.86584e7i		−	1.21647i	−0.793758	−	0.608234i	$-0.791878\pi$
$113$		−	1.86584e7i		−	1.21647i	0.793758	−	0.608234i	$-0.208122\pi$
$114$	7.68146e6	−	1.40666e7i	0.485598	−	0.889245i
$115$			1.10503e7i			0.677533i
$116$	1.34761e7	−	3.88139e6i	0.801606	−	0.230879i
$117$	1.68223e7	−	5.03300e6i	0.971033	−	0.290520i
$118$	7.28128e6	+	5.48012e6i	0.407963	+	0.307046i
$119$	−6.37742e6			−0.346921
$120$	2.82026e7	+	6.28882e6i	1.48989	+	0.332227i
$121$	−1.57883e7			−0.810192
$122$	−1.92614e7	−	1.44967e7i	−0.960348	−	0.722788i
$123$	434114.	+	2.96551e6i	0.0210347	+	0.143692i
$124$	−4.42854e6	+	1.27551e6i	−0.208586	+	0.0600769i
$125$		−	1.10052e7i		−	0.503979i
$126$	6.70558e6	−	1.81180e7i	0.298634	−	0.806890i
$127$		−	1.45185e7i		−	0.628940i	−0.949267	−	0.314470i	$-0.898173\pi$
$127$		−	1.45185e7i		−	0.628940i	0.949267	−	0.314470i	$-0.101827\pi$
$128$	−4.62319e6	−	2.32718e7i	−0.194853	−	0.980832i
$129$	5.37995e6	+	3.67514e7i	0.220655	+	1.50733i
$130$	−2.33060e7	+	3.09660e7i	−0.930393	+	1.23619i
$131$	2.24922e7			0.874144			0.437072	−	0.899427i	$-0.356016\pi$
$131$	2.24922e7			0.874144			0.437072	+	0.899427i	$0.356016\pi$
$132$	−4.75505e6	−	1.04845e7i	−0.179948	−	0.396771i
$133$	2.36518e7			0.871732
$134$	−2.75586e7	+	3.66163e7i	−0.989442	+	1.31464i
$135$	−1.84315e7	−	3.95540e7i	−0.644752	−	1.38364i
$136$	1.10503e7	+	4.21942e6i	0.376692	+	0.143836i
$137$		−	1.25189e7i		−	0.415952i	−0.978134	−	0.207976i	$-0.933312\pi$
$137$		−	1.25189e7i		−	0.415952i	0.978134	−	0.207976i	$-0.0666876\pi$
$138$	−1.20266e7	−	6.56749e6i	−0.389553	−	0.212727i
$139$			1.61585e7i			0.510327i	0.966898	+	0.255163i	$0.0821293\pi$
$139$			1.61585e7i			0.510327i	−0.966898	+	0.255163i	$0.917871\pi$
$140$	1.18018e7	+	4.09756e7i	0.363497	+	1.26205i
$141$	−2.81366e6	+	411885.i	−0.0845287	+	0.0123740i
$142$	−4.47742e7	−	3.36985e7i	−1.31226	−	0.987646i
$143$	1.54413e7			0.441579
$144$	−2.36061e7	+	2.69569e7i	−0.658802	+	0.752316i
$145$	4.67463e7			1.27338
$146$	1.14126e7	+	8.58946e6i	0.303493	+	0.228418i
$147$	−9.89820e6	+	1.44897e6i	−0.257007	+	0.0376227i
$148$	1.12968e7	+	3.92223e7i	0.286444	+	0.994527i
$149$			3.97985e7i			0.985632i	0.870134	+	0.492816i	$0.164032\pi$
$149$			3.97985e7i			0.985632i	−0.870134	+	0.492816i	$0.835968\pi$
$150$	4.82560e7	+	2.63516e7i	1.16743	+	0.637510i
$151$		−	3.61664e6i		−	0.0854843i	−0.999086	−	0.0427422i	$-0.986391\pi$
$151$		−	3.61664e6i		−	0.0854843i	0.999086	−	0.0427422i	$-0.0136094\pi$
$152$	−4.09818e7	−	1.56484e7i	−0.946538	−	0.361425i
$153$	−5.12020e6	−	1.71137e7i	−0.115576	−	0.386300i
$154$	1.02163e7	−	1.35741e7i	0.225409	−	0.299495i
$155$	−1.53619e7			−0.331347
$156$	−1.98506e7	−	4.37692e7i	−0.418638	−	0.923065i
$157$	−7.08283e7			−1.46069			−0.730345	−	0.683079i	$-0.760641\pi$
$157$	−7.08283e7			−1.46069			−0.730345	+	0.683079i	$0.760641\pi$
$158$	4.27320e7	−	5.67768e7i	0.861893	−	1.14517i
$159$	7.80192e6	+	5.32963e7i	0.153926	+	1.05149i
$160$	6.66105e6	−	7.88073e7i	0.128565	−	1.52106i
$161$		−	2.02218e7i		−	0.381881i
$162$	5.40032e7	+	3.44802e6i	0.997968	+	0.0637187i
$163$		−	7.16909e7i		−	1.29660i	−0.761383	−	0.648302i	$-0.775480\pi$
$163$		−	7.16909e7i		−	1.29660i	0.761383	−	0.648302i	$-0.224520\pi$
$164$	7.88286e6	−	2.27042e6i	0.139550	−	0.0401932i
$165$	−5.55833e6	−	3.79699e7i	−0.0963276	−	0.658031i
$166$	2.97781e7	+	2.24119e7i	0.505265	+	0.380278i
$167$	1.53328e6			0.0254749			0.0127375	−	0.999919i	$-0.495945\pi$
$167$	1.53328e6			0.0254749			0.0127375	+	0.999919i	$0.495945\pi$
$168$	−5.16102e7	−	1.15084e7i	−0.839755	−	0.187255i
$169$	1.71348e6			0.0273071
$170$	3.15025e7	+	2.37098e7i	0.491784	+	0.370132i
$171$	1.89891e7	+	6.34692e7i	0.290415	+	0.970681i
$172$	9.76918e7	−	2.81372e7i	1.46389	−	0.421630i
$173$		−	4.52208e7i		−	0.664013i	−0.943277	−	0.332007i	$-0.892274\pi$
$173$		−	4.52208e7i		−	0.664013i	0.943277	−	0.332007i	$-0.107726\pi$
$174$	−2.77826e7	+	5.08765e7i	−0.399807	+	0.732142i
$175$			8.11384e7i			1.14444i
$176$	−2.66828e7	+	1.67608e7i	−0.368925	+	0.231739i
$177$	−3.72719e7	+	5.45615e6i	−0.505214	+	0.0739571i
$178$	−1.07728e7	+	1.43136e7i	−0.143173	+	0.190230i
$179$	−7.34433e7			−0.957120			−0.478560	−	0.878055i	$-0.658841\pi$
$179$	−7.34433e7			−0.957120			−0.478560	+	0.878055i	$0.658841\pi$
$180$	−1.00482e8	+	6.45678e7i	−1.28421	+	0.825206i
$181$	−4.87737e7			−0.611380			−0.305690	−	0.952131i	$-0.598887\pi$
$181$	−4.87737e7			−0.611380			−0.305690	+	0.952131i	$0.598887\pi$
$182$	4.26495e7	−	5.66672e7i	0.524401	−	0.696757i
$183$	9.85966e7	−	1.44333e7i	1.18928	−	0.174096i
$184$	−1.33791e7	+	3.50385e7i	−0.158330	+	0.414652i
$185$			1.36055e8i			1.57984i
$186$	9.12998e6	−	1.67192e7i	0.104034	−	0.190511i
$187$		−	1.57088e7i		−	0.175670i
$188$	2.15416e6	+	7.47921e6i	0.0236443	+	0.0820924i
$189$	3.37292e7	+	7.23829e7i	0.363404	+	0.779866i
$190$	−1.16833e8	−	8.79319e7i	−1.23574	−	0.930055i
$191$	−5.27792e7			−0.548083			−0.274042	−	0.961718i	$-0.588361\pi$
$191$	−5.27792e7			−0.548083			−0.274042	+	0.961718i	$0.588361\pi$
$192$	8.18115e7	+	5.40870e7i	0.834181	+	0.551491i
$193$	1.10811e8			1.10951			0.554754	−	0.832014i	$-0.312812\pi$
$193$	1.10811e8			1.10951			0.554754	+	0.832014i	$0.312812\pi$
$194$	1.44690e7	+	1.08898e7i	0.142276	+	0.107082i
$195$	−2.32041e7	−	1.58511e8i	−0.224101	−	1.53087i
$196$	7.57815e6	+	2.63112e7i	0.0718898	+	0.249600i
$197$		−	1.52627e7i		−	0.142232i	−0.997468	−	0.0711162i	$-0.977344\pi$
$197$		−	1.52627e7i		−	0.142232i	0.997468	−	0.0711162i	$-0.0226561\pi$
$198$	4.46283e7	+	1.65172e7i	0.408584	+	0.151219i
$199$		−	4.93186e7i		−	0.443634i	−0.975088	−	0.221817i	$-0.928801\pi$
$199$		−	4.93186e7i		−	0.443634i	0.975088	−	0.221817i	$-0.0711988\pi$
$200$	5.36826e7	−	1.40590e8i	0.474491	−	1.24265i
$201$	−2.74381e7	−	1.87434e8i	−0.238324	−	1.62803i
$202$	−7.31593e7	+	9.72047e7i	−0.624510	+	0.829769i
$203$	−8.55446e7			−0.717722
$204$	−4.45275e7	+	2.01946e7i	−0.367217	+	0.166544i
$205$	2.73443e7			0.221681
$206$	−6.10302e7	+	8.10891e7i	−0.486418	+	0.646289i
$207$	5.42648e7	−	1.62353e7i	0.425228	−	0.127223i
$208$	−1.11391e8	+	6.99703e7i	−0.858282	+	0.539129i
$209$			5.82589e7i			0.441419i
$210$	−1.54696e8	−	8.44762e7i	−1.15269	−	0.629458i
$211$			1.68736e8i			1.23657i	0.785954	+	0.618285i	$0.212172\pi$
$211$			1.68736e8i			1.23657i	−0.785954	+	0.618285i	$0.787828\pi$
$212$	1.41671e8	−	4.08041e7i	1.02119	−	0.294123i
$213$	2.29193e8	−	3.35511e7i	1.62508	−	0.237891i
$214$	1.71584e8	+	1.29139e8i	1.19682	+	0.900763i
$215$	3.38876e8			2.32545
$216$	−1.05533e7	−	1.47735e8i	−0.0712525	−	0.997458i
$217$	2.81119e7			0.186759
$218$	−7.89186e7	−	5.93966e7i	−0.515919	−	0.388297i
$219$	−5.84195e7	+	8.55190e6i	−0.375840	+	0.0550184i
$220$	−1.00931e8	+	2.90701e7i	−0.639065	+	0.184064i
$221$		−	6.55788e7i		−	0.408687i
$222$	−1.48076e8	−	8.08614e7i	−0.908345	−	0.496028i
$223$		−	1.69375e8i		−	1.02278i	−0.859349	−	0.511389i	$-0.829131\pi$
$223$		−	1.69375e8i		−	1.02278i	0.859349	−	0.511389i	$-0.170869\pi$
$224$	−1.21896e7	+	1.44216e8i	−0.0724637	+	0.857323i
$225$	−2.17734e8	+	6.51430e7i	−1.27434	+	0.381267i
$226$	1.26941e8	−	1.68664e8i	0.731516	−	0.971945i
$227$	−3.06403e8			−1.73861			−0.869307	−	0.494273i	$-0.835434\pi$
$227$	−3.06403e8			−1.73861			−0.869307	+	0.494273i	$0.835434\pi$
$228$	1.65138e8	−	7.48950e7i	0.922731	−	0.418486i
$229$	−1.75334e8			−0.964810			−0.482405	−	0.875948i	$-0.660237\pi$
$229$	−1.75334e8			−0.964810			−0.482405	+	0.875948i	$0.660237\pi$
$230$	−7.51799e7	+	9.98894e7i	−0.407431	+	0.541342i
$231$	1.01716e7	+	6.94842e7i	0.0542936	+	0.370889i
$232$	1.48224e8	+	5.65978e7i	0.779313	+	0.297572i
$233$		−	8.69518e7i		−	0.450332i	−0.974320	−	0.225166i	$-0.927708\pi$
$233$		−	8.69518e7i		−	0.450332i	0.974320	−	0.225166i	$-0.0722924\pi$
$234$	1.86307e8	+	6.89533e7i	0.950548	+	0.351803i
$235$			2.59441e7i			0.130407i
$236$	2.85357e7	+	9.90754e7i	0.141318	+	0.490652i
$237$	4.25451e7	+	2.90633e8i	0.207601	+	1.41816i
$238$	−5.76490e7	−	4.33884e7i	−0.277186	−	0.208619i
$239$	−8.76527e6			−0.0415310			−0.0207655	−	0.999784i	$-0.506610\pi$
$239$	−8.76527e6			−0.0415310			−0.0207655	+	0.999784i	$0.506610\pi$
$240$	2.12153e8	+	2.48723e8i	0.990626	+	1.16139i
$241$	−1.39100e8			−0.640131			−0.320065	−	0.947395i	$-0.603705\pi$
$241$	−1.39100e8			−0.640131			−0.320065	+	0.947395i	$0.603705\pi$
$242$	−1.42719e8	−	1.07415e8i	−0.647335	−	0.487204i
$243$	−1.67159e8	+	1.48626e8i	−0.747320	+	0.664464i
$244$	−7.54865e7	−	2.62088e8i	−0.332663	−	1.15500i
$245$			9.12690e7i			0.396499i
$246$	−1.62515e7	+	2.97603e7i	−0.0696017	+	0.127457i
$247$			2.43210e8i			1.02693i
$248$	−4.87098e7	−	1.85993e7i	−0.202785	−	0.0774312i
$249$	−1.52430e8	+	2.23139e7i	−0.625711	+	0.0915963i
$250$	7.48732e7	−	9.94819e7i	0.303065	−	0.402674i
$251$	4.14947e8			1.65628			0.828142	−	0.560518i	$-0.189398\pi$
$251$	4.14947e8			1.65628			0.828142	+	0.560518i	$0.189398\pi$
$252$	1.83880e8	−	1.18158e8i	0.723825	−	0.465115i
$253$	4.98101e7			0.193373
$254$	9.87758e7	−	1.31241e8i	0.378210	−	0.502517i
$255$	−1.61257e8	+	2.36061e7i	−0.609016	+	0.0891525i
$256$	1.16537e8	−	2.41820e8i	0.434133	−	0.900849i
$257$		−	3.45042e8i		−	1.26796i	−0.773349	−	0.633980i	$-0.781420\pi$
$257$		−	3.45042e8i		−	1.26796i	0.773349	−	0.633980i	$-0.218580\pi$
$258$	−2.01404e8	+	3.68818e8i	−0.730127	+	1.33703i
$259$		−	2.48978e8i		−	0.890455i
$260$	−4.21351e8	+	1.21358e8i	−1.48675	+	0.428213i
$261$	−6.86806e7	−	2.29558e8i	−0.239107	−	0.799190i
$262$	2.03319e8	+	1.53024e8i	0.698432	+	0.525662i
$263$	1.86208e8			0.631179			0.315589	−	0.948896i	$-0.397798\pi$
$263$	1.86208e8			0.631179			0.315589	+	0.948896i	$0.397798\pi$
$264$	2.83474e7	−	1.27126e8i	0.0948200	−	0.425227i
$265$	4.91433e8			1.62220
$266$	2.13801e8	+	1.60913e8i	0.696505	+	0.524211i
$267$	−1.07257e7	−	7.32693e7i	−0.0344856	−	0.235577i
$268$	−4.98234e8	+	1.43501e8i	−1.58111	+	0.455391i
$269$		−	3.60850e8i		−	1.13030i	−0.824988	−	0.565150i	$-0.808818\pi$
$269$		−	3.60850e8i		−	1.13030i	0.824988	−	0.565150i	$-0.191182\pi$
$270$	1.02491e8	−	4.82947e8i	0.316893	−	1.49323i
$271$		−	6.62312e7i		−	0.202148i	−0.994879	−	0.101074i	$-0.967772\pi$
$271$		−	6.62312e7i		−	0.202148i	0.994879	−	0.101074i	$-0.0322279\pi$
$272$	7.11826e7	+	1.13321e8i	0.214478	+	0.341445i
$273$	4.24629e7	+	2.90072e8i	0.126311	+	0.862852i
$274$	8.51713e7	−	1.13165e8i	0.250130	−	0.332341i
$275$	−1.99860e8			−0.579510
$276$	−6.40336e7	−	1.41189e8i	−0.183327	−	0.404222i
$277$	−3.13853e8			−0.887252			−0.443626	−	0.896212i	$-0.646308\pi$
$277$	−3.13853e8			−0.887252			−0.443626	+	0.896212i	$0.646308\pi$
$278$	−1.09933e8	+	1.46065e8i	−0.306882	+	0.407746i
$279$	2.25700e7	+	7.54378e7i	0.0622181	+	0.207957i
$280$	−1.72092e8	+	4.50694e8i	−0.468499	+	1.22695i
$281$			6.26719e8i			1.68500i	0.538694	+	0.842502i	$0.318918\pi$
$281$			6.26719e8i			1.68500i	−0.538694	+	0.842502i	$0.681082\pi$
$282$	−2.82364e7	−	1.54193e7i	−0.0749786	−	0.0409442i
$283$		−	5.71657e8i		−	1.49928i	−0.661846	−	0.749640i	$-0.730227\pi$
$283$		−	5.71657e8i		−	1.49928i	0.661846	−	0.749640i	$-0.269773\pi$
$284$	−1.75473e8	−	6.09238e8i	−0.454564	−	1.57824i
$285$	5.98051e8	−	8.75473e7i	1.53032	−	0.224019i
$286$	1.39582e8	+	1.05054e8i	0.352817	+	0.265541i
$287$	−5.00394e7			−0.124947
$288$	−3.96787e8	+	8.30750e7i	−0.978778	+	0.204926i
$289$	3.43624e8			0.837415
$290$	4.22565e8	+	3.18035e8i	1.01742	+	0.765742i
$291$	−7.40650e7	+	1.08422e7i	−0.176193	+	0.0257924i
$292$	4.47265e7	+	1.55290e8i	0.105130	+	0.365008i
$293$			5.86700e8i			1.36264i	0.731988	+	0.681318i	$0.238593\pi$
$293$			5.86700e8i			1.36264i	−0.731988	+	0.681318i	$0.761407\pi$
$294$	−9.93331e7	−	5.42437e7i	−0.227970	−	0.124490i
$295$			3.43676e8i			0.779421i
$296$	−1.64728e8	+	4.31408e8i	−0.369188	+	0.966868i
$297$	−1.78293e8	+	8.30817e7i	−0.394900	+	0.184017i
$298$	−2.70767e8	+	3.59760e8i	−0.592704	+	0.787510i
$299$	2.07940e8			0.449871
$300$	2.56930e8	+	5.66513e8i	0.549403	+	1.21139i
$301$	−6.20136e8			−1.31070
$302$	2.46056e7	−	3.26928e7i	0.0514055	−	0.0683011i
$303$	−7.28393e7	−	4.97578e8i	−0.150424	−	1.02757i
$304$	−2.63993e8	−	4.20272e8i	−0.538933	−	0.857971i
$305$		−	9.09137e8i		−	1.83476i
$306$	7.01479e7	−	1.89535e8i	0.139955	−	0.378150i
$307$			8.69930e8i			1.71593i	0.513707	+	0.857965i	$0.328272\pi$
$307$			8.69930e8i			1.71593i	−0.513707	+	0.857965i	$0.671728\pi$
$308$	1.84701e8	−	5.31977e7i	0.360199	−	0.103745i
$309$	−6.07633e7	−	4.15084e8i	−0.117162	−	0.800353i
$310$	−1.38864e8	−	1.04513e8i	−0.264743	−	0.199254i
$311$	−5.26163e8			−0.991880			−0.495940	−	0.868357i	$-0.665176\pi$
$311$	−5.26163e8			−0.991880			−0.495940	+	0.868357i	$0.665176\pi$
$312$	1.18341e8	−	5.30706e8i	0.220593	−	0.989265i
$313$	6.56750e8			1.21058			0.605292	−	0.796004i	$-0.293056\pi$
$313$	6.56750e8			1.21058			0.605292	+	0.796004i	$0.293056\pi$
$314$	−6.40255e8	−	4.81876e8i	−1.16708	−	0.878378i
$315$	6.97997e8	−	2.08832e8i	1.25825	−	0.376452i
$316$	7.72555e8	−	2.22511e8i	1.37729	−	0.396686i
$317$			2.61603e8i			0.461249i	0.973043	+	0.230625i	$0.0740770\pi$
$317$			2.61603e8i			0.461249i	−0.973043	+	0.230625i	$0.925923\pi$
$318$	−2.92072e8	+	5.34854e8i	−0.509325	+	0.932696i
$319$		−	2.10713e8i		−	0.363433i
$320$	5.96374e8	−	6.67064e8i	1.01740	−	1.13800i
$321$	−8.78315e8	+	1.28575e8i	−1.48212	+	0.216964i
$322$	1.37578e8	−	1.82795e8i	0.229642	−	0.305119i
$323$	2.47424e8			0.408539
$324$	4.64705e8	+	3.98576e8i	0.759049	+	0.651033i
$325$	−8.34343e8			−1.34820
$326$	4.87744e8	−	6.48052e8i	0.779706	−	1.03597i
$327$	4.03974e8	−	5.91368e7i	0.638905	−	0.0935278i
$328$	8.67040e7	+	3.31070e7i	0.135669	+	0.0518037i
$329$		−	4.74771e7i		−	0.0735019i
$330$	2.08081e8	−	3.81047e8i	0.318739	−	0.583686i
$331$			1.08898e9i			1.65052i	0.564754	+	0.825259i	$0.308971\pi$
$331$			1.08898e9i			1.65052i	−0.564754	+	0.825259i	$0.691029\pi$
$332$	1.16702e8	+	4.05187e8i	0.175023	+	0.607676i
$333$	6.68129e8	−	1.99895e8i	0.991530	−	0.296653i
$334$	1.38601e7	+	1.04316e7i	0.0203542	+	0.0153192i
$335$	−1.72829e9			−2.51165
$336$	−3.88235e8	−	4.55157e8i	−0.558351	−	0.654597i
$337$	−2.06564e8			−0.294002			−0.147001	−	0.989136i	$-0.546962\pi$
$337$	−2.06564e8			−0.294002			−0.147001	+	0.989136i	$0.546962\pi$
$338$	1.54891e7	+	1.16576e7i	0.0218181	+	0.0164210i
$339$	1.26386e8	+	8.63367e8i	0.176198	+	1.20364i
$340$	1.23460e8	+	4.28651e8i	0.170353	+	0.591463i
$341$			6.92450e7i			0.0945689i
$342$	−2.60156e8	+	7.02924e8i	−0.351675	+	0.950204i
$343$		−	8.10033e8i		−	1.08386i
$344$	1.07452e9	+	4.10293e8i	1.42318	+	0.543425i
$345$	−7.48511e7	−	5.11321e8i	−0.0981366	−	0.670388i
$346$	3.07657e8	−	4.08775e8i	0.399301	−	0.530540i
$347$	7.01210e8			0.900938			0.450469	−	0.892792i	$-0.351257\pi$
$347$	7.01210e8			0.900938			0.450469	+	0.892792i	$0.351257\pi$
$348$	−5.97277e8	+	2.70883e8i	−0.759711	+	0.344552i
$349$	2.35223e8			0.296204			0.148102	−	0.988972i	$-0.452684\pi$
$349$	2.35223e8			0.296204			0.148102	+	0.988972i	$0.452684\pi$
$350$	−5.52020e8	+	7.33453e8i	−0.688203	+	0.914396i
$351$	−7.44311e8	+	3.46837e8i	−0.918713	+	0.428105i
$352$	−3.55231e8	−	3.00253e7i	−0.434122	−	0.0366934i
$353$			1.31897e9i			1.59596i	0.602682	+	0.797982i	$0.294099\pi$
$353$			1.31897e9i			1.59596i	−0.602682	+	0.797982i	$0.705901\pi$
$354$	−3.74041e8	−	2.04256e8i	−0.448134	−	0.244717i
$355$		−	2.11334e9i		−	2.50709i
$356$	−1.94763e8	+	5.60957e7i	−0.228787	+	0.0658953i
$357$	2.95097e8	−	4.31986e7i	0.343263	−	0.0502495i
$358$	−6.63893e8	−	4.99667e8i	−0.764729	−	0.575559i
$359$	1.30700e9			1.49089			0.745444	−	0.666569i	$-0.232238\pi$
$359$	1.30700e9			1.49089			0.745444	+	0.666569i	$0.232238\pi$
$360$	−1.34760e9	−	9.99619e7i	−1.52230	−	0.112921i
$361$	−2.37437e7			−0.0265628
$362$	−4.40892e8	−	3.31829e8i	−0.488486	−	0.367650i
$363$	7.30561e8	−	1.06945e8i	0.801648	−	0.117351i
$364$	7.71063e8	−	2.22082e8i	0.837983	−	0.241356i
$365$			5.38673e8i			0.579829i
$366$	9.89464e8	+	5.40325e8i	1.05491	+	0.576065i
$367$			2.85088e8i			0.301056i	0.988606	+	0.150528i	$0.0480974\pi$
$367$			2.85088e8i			0.301056i	−0.988606	+	0.150528i	$0.951903\pi$
$368$	−3.59323e8	+	2.25708e8i	−0.375853	+	0.236091i
$369$	−4.01748e7	−	1.34280e8i	−0.0416257	−	0.139130i
$370$	−9.25644e8	+	1.22988e9i	−0.950031	+	1.26228i
$371$	−8.99311e8			−0.914327
$372$	1.96279e8	−	8.90182e7i	0.197685	−	0.0896558i
$373$	1.69967e9			1.69583			0.847917	−	0.530129i	$-0.177857\pi$
$373$	1.69967e9			1.69583			0.847917	+	0.530129i	$0.177857\pi$
$374$	1.06874e8	−	1.42001e8i	0.105638	−	0.140359i
$375$	7.45457e7	+	5.09235e8i	0.0729984	+	0.498665i
$376$	−3.14117e7	+	8.22643e7i	−0.0304743	+	0.0798093i
$377$		−	8.79653e8i		−	0.845506i
$378$	−1.87556e8	+	8.83783e8i	−0.178612	+	0.841636i
$379$			6.51928e8i			0.615124i	0.951528	+	0.307562i	$0.0995131\pi$
$379$			6.51928e8i			0.615124i	−0.951528	+	0.307562i	$0.900487\pi$
$380$	−4.57873e8	−	1.58973e9i	−0.428058	−	1.48621i
$381$	9.83438e7	+	6.71804e8i	0.0910982	+	0.622307i
$382$	−4.77100e8	−	3.59080e8i	−0.437913	−	0.329587i
$383$	−1.33995e9			−1.21869			−0.609346	−	0.792904i	$-0.708568\pi$
$383$	−1.33995e9			−1.21869			−0.609346	+	0.792904i	$0.708568\pi$
$384$	3.71561e8	+	1.04552e9i	0.334866	+	0.942266i
$385$	6.40698e8			0.572190
$386$	1.00168e9	+	7.53893e8i	0.886486	+	0.667197i
$387$	−4.97884e8	−	1.66413e9i	−0.436657	−	1.45948i
$388$	5.67049e7	+	1.96878e8i	0.0492844	+	0.171114i
$389$		−	2.07807e9i		−	1.78994i	−0.446130	−	0.894968i	$-0.647198\pi$
$389$		−	2.07807e9i		−	1.78994i	0.446130	−	0.894968i	$-0.352802\pi$
$390$	8.68667e8	−	1.59073e9i	0.741527	−	1.35791i
$391$		−	2.11542e8i		−	0.178969i
$392$	−1.10504e8	+	2.89398e8i	−0.0926564	+	0.242658i
$393$	−1.04076e9	+	1.52355e8i	−0.864925	+	0.126614i
$394$	1.03839e8	−	1.37967e8i	0.0855307	−	0.113642i
$395$	2.67986e9			2.18787
$396$	2.91045e8	+	4.52933e8i	0.235520	+	0.366523i
$397$	−1.19859e9			−0.961399			−0.480699	−	0.876886i	$-0.659617\pi$
$397$	−1.19859e9			−0.961399			−0.480699	+	0.876886i	$0.659617\pi$
$398$	3.35536e8	−	4.45817e8i	0.266777	−	0.354459i
$399$	−1.09442e9	+	1.60210e8i	−0.862539	+	0.126265i
$400$	1.44176e9	−	9.05639e8i	1.12637	−	0.707530i
$401$			1.67418e8i			0.129657i	0.997896	+	0.0648287i	$0.0206501\pi$
$401$			1.67418e8i			0.129657i	−0.997896	+	0.0648287i	$0.979350\pi$
$402$	1.02717e9	−	1.88099e9i	0.788589	−	1.44409i
$403$			2.89073e8i			0.220009i
$404$	−1.32265e9	+	3.80950e8i	−0.997955	+	0.287431i
$405$	1.12079e9	+	1.70540e9i	0.838364	+	1.27566i
$406$	−7.73284e8	−	5.81998e8i	−0.573453	−	0.431599i
$407$	6.13282e8			0.450899
$408$	−5.39901e8	−	1.20391e8i	−0.393553	−	0.0877572i
$409$	−7.82103e8			−0.565239			−0.282620	−	0.959232i	$-0.591203\pi$
$409$	−7.82103e8			−0.565239			−0.282620	+	0.959232i	$0.591203\pi$
$410$	2.47180e8	+	1.86035e8i	0.177121	+	0.133307i
$411$	8.47988e7	+	5.79275e8i	0.0602481	+	0.411565i
$412$	−1.10337e9	+	3.17792e8i	−0.777285	+	0.223874i
$413$		−	6.28919e8i		−	0.439308i
$414$	6.00985e8	+	2.22428e8i	0.416258	+	0.154059i
$415$			1.40552e9i			0.965318i
$416$	−1.48297e9	−	1.25345e8i	−1.00996	−	0.0853651i
$417$	−1.09452e8	−	7.47688e8i	−0.0739178	−	0.504945i
$418$	−3.96361e8	+	5.26634e8i	−0.265445	+	0.352689i
$419$	−8.18700e8			−0.543721			−0.271860	−	0.962337i	$-0.587639\pi$
$419$	−8.18700e8			−0.543721			−0.271860	+	0.962337i	$0.587639\pi$
$420$	−8.23651e8	−	1.81609e9i	−0.542464	−	1.19609i
$421$	−2.58924e9			−1.69116			−0.845579	−	0.533850i	$-0.820745\pi$
$421$	−2.58924e9			−1.69116			−0.845579	+	0.533850i	$0.820745\pi$
$422$	−1.14798e9	+	1.52529e9i	−0.743605	+	0.988007i
$423$	1.27404e8	−	3.81176e7i	0.0818450	−	0.0244869i
$424$	1.55825e9	+	5.95000e8i	0.992788	+	0.379085i
$425$			8.48799e8i			0.536344i
$426$	2.30007e9	+	1.25602e9i	1.44147	+	0.787158i
$427$			1.66370e9i			1.03414i
$428$	6.72446e8	+	2.33472e9i	0.414576	+	1.43940i
$429$	−7.14503e8	+	1.04595e8i	−0.436922	+	0.0639600i
$430$	3.06328e9	+	2.30552e9i	1.85801	+	1.39840i
$431$	5.54888e8			0.333837			0.166919	−	0.985971i	$-0.446618\pi$
$431$	5.54888e8			0.333837			0.166919	+	0.985971i	$0.446618\pi$
$432$	9.09708e8	−	1.40725e9i	0.542886	−	0.839806i
$433$	1.55158e9			0.918476			0.459238	−	0.888313i	$-0.348122\pi$
$433$	1.55158e9			0.918476			0.459238	+	0.888313i	$0.348122\pi$
$434$	2.54118e8	+	1.91257e8i	0.149218	+	0.112306i
$435$	−2.16305e9	+	3.16644e8i	−1.25995	+	0.184442i
$436$	−3.09286e8	−	1.07384e9i	−0.178714	−	0.620490i
$437$			7.84541e8i			0.449708i
$438$	−5.86267e8	−	3.20148e8i	−0.333378	−	0.182050i
$439$		−	1.38100e9i		−	0.779055i	−0.921015	−	0.389527i	$-0.872638\pi$
$439$		−	1.38100e9i		−	0.779055i	0.921015	−	0.389527i	$-0.127362\pi$
$440$	−1.11015e9	−	4.23897e8i	−0.621292	−	0.237233i
$441$	4.48197e8	−	1.34094e8i	0.248848	−	0.0744519i
$442$	4.46162e8	−	5.92802e8i	0.245762	−	0.326537i
$443$	−1.84809e8			−0.100998			−0.0504988	−	0.998724i	$-0.516081\pi$
$443$	−1.84809e8			−0.100998			−0.0504988	+	0.998724i	$0.516081\pi$
$444$	−7.88407e8	−	1.73838e9i	−0.427474	−	0.942549i
$445$	−6.75600e8			−0.363437
$446$	1.15233e9	−	1.53107e9i	0.615043	−	0.817190i
$447$	−2.69582e8	−	1.84156e9i	−0.142763	−	0.975238i
$448$	−1.09135e9	+	1.22071e9i	−0.573444	+	0.641417i
$449$			1.46449e8i			0.0763529i	0.999271	+	0.0381765i	$0.0121549\pi$
$449$			1.46449e8i			0.0763529i	−0.999271	+	0.0381765i	$0.987845\pi$
$450$	−2.41141e9	−	8.92475e8i	−1.24746	−	0.461692i
$451$		−	1.23257e8i		−	0.0632693i
$452$	2.29498e9	−	6.61001e8i	1.16895	−	0.336680i
$453$	2.44980e7	+	1.67350e8i	0.0123819	+	0.0845828i
$454$	−2.76974e9	−	2.08460e9i	−1.38913	−	1.04551i
$455$	2.67469e9			1.33117
$456$	2.00231e9	+	4.46490e8i	0.988907	+	0.220513i
$457$	5.51134e8			0.270116			0.135058	−	0.990838i	$-0.456878\pi$
$457$	5.51134e8			0.270116			0.135058	+	0.990838i	$0.456878\pi$
$458$	−1.58494e9	−	1.19287e9i	−0.770874	−	0.580184i
$459$	3.52846e8	+	7.57207e8i	0.170310	+	0.365486i
$460$	−1.35918e9	+	3.91472e8i	−0.651067	+	0.187520i
$461$		−	1.56985e9i		−	0.746286i	−0.927774	−	0.373143i	$-0.878280\pi$
$461$		−	1.56985e9i		−	0.746286i	0.927774	−	0.373143i	$-0.121720\pi$
$462$	−3.80784e8	+	6.97307e8i	−0.179652	+	0.328986i
$463$		−	9.76113e7i		−	0.0457053i	−0.999739	−	0.0228526i	$-0.992725\pi$
$463$		−	9.76113e7i		−	0.0457053i	0.999739	−	0.0228526i	$-0.00727486\pi$
$464$	9.54820e8	+	1.52005e9i	0.443719	+	0.706392i
$465$	7.10827e8	−	1.04056e8i	0.327853	−	0.0479936i
$466$	5.91571e8	−	7.86004e8i	0.270805	−	0.359811i
$467$	−2.35639e9			−1.07063			−0.535313	−	0.844654i	$-0.679806\pi$
$467$	−2.35639e9			−1.07063			−0.535313	+	0.844654i	$0.679806\pi$
$468$	1.21501e9	+	1.89084e9i	0.547923	+	0.852694i
$469$	3.16273e9			1.41565
$470$	−1.76509e8	+	2.34523e8i	−0.0784196	+	0.104194i
$471$	3.27738e9	−	4.79768e8i	1.44529	−	0.211572i
$472$	−4.16104e8	+	1.08974e9i	−0.182140	+	0.477007i
$473$		−	1.52752e9i		−	0.663700i
$474$	−1.59272e9	+	2.91664e9i	−0.686933	+	1.25794i
$475$		−	3.14792e9i		−	1.34771i
$476$	−2.25929e8	−	7.84422e8i	−0.0960171	−	0.333369i
$477$	−7.22024e8	−	2.41329e9i	−0.304605	−	1.01811i
$478$	−7.92339e7	−	5.96340e7i	−0.0331828	−	0.0249745i
$479$	−7.79058e8			−0.323888			−0.161944	−	0.986800i	$-0.551776\pi$
$479$	−7.79058e8			−0.323888			−0.161944	+	0.986800i	$0.551776\pi$
$480$	2.25594e8	+	3.69171e9i	0.0931074	+	1.52364i
$481$	2.56023e9			1.04899
$482$	−1.25740e9	−	9.46361e8i	−0.511458	−	0.384939i
$483$	1.36976e8	+	9.35705e8i	0.0553132	+	0.377854i
$484$	−5.59325e8	−	1.94196e9i	−0.224236	−	0.778543i
$485$			6.82937e8i			0.271822i
$486$	−2.52220e9	+	2.06253e8i	−0.996673	+	0.0815029i
$487$			9.51918e8i			0.373464i	0.982411	+	0.186732i	$0.0597895\pi$
$487$			9.51918e8i			0.373464i	−0.982411	+	0.186732i	$0.940210\pi$
$488$	1.10073e9	−	2.88272e9i	0.428759	−	1.12288i
$489$	4.85611e8	+	3.31729e9i	0.187805	+	1.28293i
$490$	−6.20943e8	+	8.25030e8i	−0.238433	+	0.316799i
$491$	−2.14528e9			−0.817898			−0.408949	−	0.912557i	$-0.634105\pi$
$491$	−2.14528e9			−0.817898			−0.408949	+	0.912557i	$0.634105\pi$
$492$	−3.49378e8	+	1.58453e8i	−0.132257	+	0.0599824i
$493$	−8.94893e8			−0.336362
$494$	−1.65467e9	+	2.19851e9i	−0.617542	+	0.820510i
$495$	5.14393e8	+	1.71930e9i	0.190624	+	0.637139i
$496$	−3.13775e8	−	4.99524e8i	−0.115460	−	0.183810i
$497$			3.86737e9i			1.41308i
$498$	−1.52971e9	−	8.35343e8i	−0.555017	−	0.303083i
$499$		−	1.51537e9i		−	0.545968i	−0.962019	−	0.272984i	$-0.911989\pi$
$499$		−	1.51537e9i		−	0.545968i	0.962019	−	0.272984i	$-0.0880107\pi$
$500$	1.35364e9	−	3.89875e8i	0.484292	−	0.139486i
$501$	−7.09481e7	+	1.03859e7i	−0.0252063	+	0.00368989i
$502$	3.75093e9	+	2.82307e9i	1.32335	+	0.995998i
$503$	1.01725e9			0.356403			0.178201	−	0.983994i	$-0.442972\pi$
$503$	1.01725e9			0.356403			0.178201	+	0.983994i	$0.442972\pi$
$504$	2.46607e9	+	1.82928e8i	0.858023	+	0.0636464i
$505$	−4.58805e9			−1.58529
$506$	4.50261e8	+	3.38880e8i	0.154503	+	0.116284i
$507$	−7.92866e7	+	1.16066e7i	−0.0270192	+	0.00395527i
$508$	1.78578e9	−	5.14339e8i	0.604371	−	0.174071i
$509$			4.86300e9i			1.63453i	0.576264	+	0.817264i	$0.304510\pi$
$509$			4.86300e9i			1.63453i	−0.576264	+	0.817264i	$0.695490\pi$
$510$	−1.61829e9	−	8.83717e8i	−0.540209	−	0.294997i
$511$		−	9.85759e8i		−	0.326812i
$512$	2.69864e9	−	1.39309e9i	0.888588	−	0.458705i
$513$	−1.30859e9	−	2.80823e9i	−0.427950	−	0.918380i
$514$	2.34747e9	−	3.11902e9i	0.762481	−	1.01309i
$515$	−3.82740e9			−1.23475
$516$	−4.32982e9	+	1.96370e9i	−1.38738	+	0.629219i
$517$	1.16945e8			0.0372191
$518$	1.69391e9	−	2.25065e9i	0.535471	−	0.711465i
$519$	3.06311e8	+	2.09247e9i	0.0961783	+	0.657011i
$520$	−4.63447e9	−	1.76962e9i	−1.44540	−	0.551910i
$521$		−	4.13166e9i		−	1.27995i	−0.768396	−	0.639975i	$-0.778945\pi$
$521$		−	4.13166e9i		−	1.27995i	0.768396	−	0.639975i	$-0.221055\pi$
$522$	9.40941e8	−	2.54236e9i	0.289545	−	0.782331i
$523$		−	1.48751e9i		−	0.454677i	−0.973816	−	0.227339i	$-0.926998\pi$
$523$		−	1.48751e9i		−	0.454677i	0.973816	−	0.227339i	$-0.0730024\pi$
$524$	7.96819e8	+	2.76654e9i	0.241936	+	0.839997i
$525$	−5.49606e8	−	3.75445e9i	−0.165765	−	1.13237i
$526$	1.68323e9	+	1.26685e9i	0.504305	+	0.379556i
$527$	2.94082e8			0.0875248
$528$	1.12114e9	−	9.56299e8i	0.331468	−	0.282732i
$529$	−2.73406e9			−0.802995
$530$	4.44233e9	+	3.34343e9i	1.29612	+	0.975500i
$531$	1.68769e9	−	5.04936e8i	0.489174	−	0.146354i
$532$	8.37898e8	+	2.90917e9i	0.241268	+	0.837679i
$533$		−	5.14554e8i		−	0.147192i
$534$	4.01528e8	−	7.35292e8i	0.114109	−	0.208961i
$535$			8.09875e9i			2.28654i
$536$	−5.48010e9	−	2.09252e9i	−1.53714	−	0.586938i
$537$	3.39838e9	−	4.97481e8i	0.947027	−	0.138633i
$538$	2.45502e9	−	3.26191e9i	0.679700	−	0.903097i
$539$	4.11404e8			0.113164
$540$	4.21217e9	−	3.66833e9i	1.15114	−	1.00251i
$541$	2.61642e9			0.710422			0.355211	−	0.934786i	$-0.384409\pi$
$541$	2.61642e9			0.710422			0.355211	+	0.934786i	$0.384409\pi$
$542$	4.50600e8	−	5.98700e8i	0.121561	−	0.161514i
$543$	2.25687e9	−	3.30378e8i	0.604932	−	0.0885547i
$544$	−1.27517e8	+	1.50866e9i	−0.0339602	+	0.401786i
$545$		−	3.72495e9i		−	0.985673i
$546$	−1.58964e9	+	2.91101e9i	−0.417950	+	0.765366i
$547$			6.35065e9i			1.65906i	0.558460	+	0.829531i	$0.311392\pi$
$547$			6.35065e9i			1.65906i	−0.558460	+	0.829531i	$0.688608\pi$
$548$	1.53982e9	−	4.43499e8i	0.399703	−	0.115123i
$549$	−4.46452e9	+	1.33572e9i	−1.15152	+	0.344519i
$550$	−1.80664e9	−	1.35973e9i	−0.463022	−	0.348485i
$551$	3.31887e9			0.845199
$552$	3.81739e8	−	1.71194e9i	0.0966007	−	0.433212i
$553$	−4.90409e9			−1.23316
$554$	−2.83708e9	−	2.13528e9i	−0.708905	−	0.533544i
$555$	−9.21595e8	−	6.29558e9i	−0.228831	−	1.56318i
$556$	−1.98749e9	+	5.72437e8i	−0.490392	+	0.141243i
$557$			4.51932e9i			1.10810i	0.832483	+	0.554051i	$0.186919\pi$
$557$			4.51932e9i			1.10810i	−0.832483	+	0.554051i	$0.813081\pi$
$558$	−3.09214e8	+	8.35476e8i	−0.0753424	+	0.203570i
$559$		−	6.37684e9i		−	1.54406i
$560$	−4.62190e9	+	2.90324e9i	−1.11215	+	0.698594i
$561$	1.06407e8	+	7.26883e8i	0.0254448	+	0.173818i
$562$	−4.26384e9	+	5.66525e9i	−1.01327	+	1.34630i
$563$	−2.44488e9			−0.577401			−0.288700	−	0.957419i	$-0.593223\pi$
$563$	−2.44488e9			−0.577401			−0.288700	+	0.957419i	$0.593223\pi$
$564$	−1.50340e8	−	3.31488e8i	−0.0352855	−	0.0778020i
$565$	7.96091e9			1.85692
$566$	3.88923e9	−	5.16751e9i	0.901584	−	1.19791i
$567$	−2.05103e9	−	3.12085e9i	−0.472531	−	0.719005i
$568$	2.55872e9	−	6.70104e9i	0.585873	−	1.53435i
$569$			1.98279e9i			0.451216i	0.974218	+	0.225608i	$0.0724369\pi$
$569$			1.98279e9i			0.451216i	−0.974218	+	0.225608i	$0.927563\pi$
$570$	6.00173e9	+	3.27742e9i	1.35742	+	0.741258i
$571$			9.76352e8i			0.219472i	0.993961	+	0.109736i	$0.0350006\pi$
$571$			9.76352e8i			0.219472i	−0.993961	+	0.109736i	$0.964999\pi$
$572$	5.47031e8	+	1.89928e9i	0.122215	+	0.424329i
$573$	2.44221e9	−	3.57510e8i	0.542303	−	0.0793865i
$574$	−4.52333e8	−	3.40440e8i	−0.0998313	−	0.0751362i
$575$	−2.69140e9			−0.590393
$576$	−4.15197e9	−	1.94856e9i	−0.905264	−	0.424849i
$577$	−2.26570e8			−0.0491006			−0.0245503	−	0.999699i	$-0.507815\pi$
$577$	−2.26570e8			−0.0491006			−0.0245503	+	0.999699i	$0.507815\pi$
$578$	3.10620e9	+	2.33782e9i	0.669086	+	0.503575i
$579$	−5.12745e9	+	7.50595e8i	−1.09781	+	0.160706i
$580$	1.65605e9	+	5.74978e9i	0.352433	+	1.22364i
$581$		−	2.57208e9i		−	0.544086i
$582$	−7.43278e8	−	4.05888e8i	−0.156286	−	0.0853446i
$583$		−	2.21518e9i		−	0.462987i
$584$	−6.52196e8	+	1.70804e9i	−0.135498	+	0.354857i
$585$	2.14741e9	+	7.17748e9i	0.443475	+	1.48227i
$586$	−3.99158e9	+	5.30350e9i	−0.819414	+	1.08873i
$587$	5.85791e9			1.19539			0.597695	−	0.801724i	$-0.296084\pi$
$587$	5.85791e9			1.19539			0.597695	+	0.801724i	$0.296084\pi$
$588$	−5.28882e8	−	1.16614e9i	−0.107285	−	0.236555i
$589$	−1.09065e9			−0.219929
$590$	−2.33818e9	+	3.10667e9i	−0.468700	+	0.622749i
$591$	1.03384e8	+	7.06237e8i	0.0206015	+	0.140732i
$592$	−4.42413e9	+	2.77901e9i	−0.876398	+	0.550508i
$593$			1.09041e9i			0.214732i	0.994220	+	0.107366i	$0.0342417\pi$
$593$			1.09041e9i			0.214732i	−0.994220	+	0.107366i	$0.965758\pi$
$594$	−2.17693e9	−	4.61988e8i	−0.426179	−	0.0904436i
$595$		−	2.72103e9i		−	0.529570i
$596$	−4.89521e9	+	1.40992e9i	−0.947129	+	0.272792i
$597$	3.34068e8	+	2.28208e9i	0.0642577	+	0.438956i
$598$	1.87968e9	+	1.41471e9i	0.359443	+	0.270528i
$599$	3.25186e9			0.618212			0.309106	−	0.951028i	$-0.399970\pi$
$599$	3.25186e9			0.618212			0.309106	+	0.951028i	$0.399970\pi$
$600$	−1.53170e9	+	6.86902e9i	−0.289498	+	1.29827i
$601$	4.74867e9			0.892300			0.446150	−	0.894958i	$-0.352795\pi$
$601$	4.74867e9			0.892300			0.446150	+	0.894958i	$0.352795\pi$
$602$	−5.60574e9	−	4.21906e9i	−1.04724	−	0.788184i
$603$	2.53924e9	+	8.48713e9i	0.471621	+	1.57634i
$604$	4.44847e8	−	1.28125e8i	0.0821450	−	0.0236594i
$605$		−	6.73634e9i		−	1.23675i
$606$	2.72681e9	−	4.99343e9i	0.497738	−	0.911476i
$607$		−	4.10657e9i		−	0.745279i	−0.927976	−	0.372639i	$-0.878453\pi$
$607$		−	4.10657e9i		−	0.745279i	0.927976	−	0.372639i	$-0.121547\pi$
$608$	4.72918e8	−	5.59512e9i	0.0853342	−	1.00959i
$609$	3.95834e9	−	5.79452e8i	0.710154	−	0.103958i
$610$	6.18526e9	−	8.21818e9i	1.10332	−	1.46596i
$611$	4.88206e8			0.0865882
$612$	1.92360e9	−	1.23606e9i	0.339222	−	0.217977i
$613$	−3.90598e9			−0.684886			−0.342443	−	0.939539i	$-0.611254\pi$
$613$	−3.90598e9			−0.684886			−0.342443	+	0.939539i	$0.611254\pi$
$614$	−5.91851e9	+	7.86376e9i	−1.03187	+	1.37101i
$615$	−1.26528e9	+	1.85221e8i	−0.219343	+	0.0321091i
$616$	2.03154e9	+	7.75722e8i	0.350182	+	0.133713i
$617$		−	5.77043e9i		−	0.989031i	−0.869169	−	0.494515i	$-0.835346\pi$
$617$		−	5.77043e9i		−	0.989031i	0.869169	−	0.494515i	$-0.164654\pi$
$618$	2.27473e9	−	4.16557e9i	0.387677	−	0.709929i
$619$		−	5.08587e8i		−	0.0861883i	−0.999071	−	0.0430941i	$-0.986278\pi$
$619$		−	5.08587e8i		−	0.0861883i	0.999071	−	0.0430941i	$-0.0137215\pi$
$620$	−5.44216e8	−	1.88951e9i	−0.0917066	−	0.318403i
$621$	−2.40098e9	+	1.11882e9i	−0.402316	+	0.187473i
$622$	−4.75627e9	−	3.57972e9i	−0.792502	−	0.596462i
$623$	1.23633e9			0.204846
$624$	4.68037e9	−	3.99221e9i	0.771141	−	0.657760i
$625$	−3.42309e9			−0.560840
$626$	5.93671e9	+	4.46816e9i	0.967244	+	0.727978i
$627$	−3.94628e8	−	2.69577e9i	−0.0639368	−	0.436764i
$628$	−2.50919e9	−	8.71187e9i	−0.404274	−	1.40363i
$629$		−	2.60459e9i		−	0.417314i
$630$	7.73034e9	+	2.86104e9i	1.23171	+	0.455861i
$631$		−	2.19564e9i		−	0.347904i	−0.984754	−	0.173952i	$-0.944346\pi$
$631$		−	2.19564e9i		−	0.347904i	0.984754	−	0.173952i	$-0.0556537\pi$
$632$	8.49738e9	+	3.24463e9i	1.33898	+	0.511276i
$633$	−1.14296e9	−	7.80778e9i	−0.179110	−	1.22353i
$634$	−1.77980e9	+	2.36477e9i	−0.277370	+	0.368534i
$635$	6.19455e9			0.960067
$636$	−6.27904e9	+	2.84773e9i	−0.967817	+	0.438934i
$637$	1.71746e9			0.263269
$638$	1.43357e9	−	1.90475e9i	0.218548	−	0.290379i
$639$	−1.03780e10	+	3.10497e9i	−1.57348	+	0.470765i
$640$	9.92927e9	−	1.97256e9i	1.49723	−	0.297440i
$641$			8.27252e9i			1.24061i	0.784361	+	0.620305i	$0.212991\pi$
$641$			8.27252e9i			1.24061i	−0.784361	+	0.620305i	$0.787009\pi$
$642$	−8.81431e9	−	4.81331e9i	−1.31467	−	0.717912i
$643$			6.55753e9i			0.972751i	0.873750	+	0.486376i	$0.161681\pi$
$643$			6.55753e9i			0.972751i	−0.873750	+	0.486376i	$0.838319\pi$
$644$	2.48727e9	−	7.16385e8i	0.366964	−	0.105693i
$645$	−1.56805e10	+	2.29544e9i	−2.30092	+	0.336827i
$646$	2.23660e9	+	1.68334e9i	0.326418	+	0.245673i
$647$	−1.12339e10			−1.63067			−0.815333	−	0.578992i	$-0.803446\pi$
$647$	−1.12339e10			−1.63067			−0.815333	+	0.578992i	$0.803446\pi$
$648$	1.48903e9	+	6.76453e9i	0.214977	+	0.976619i
$649$	1.54915e9			0.222452
$650$	−7.54208e9	−	5.67640e9i	−1.07719	−	0.810730i
$651$	−1.30080e9	+	1.90421e8i	−0.184789	+	0.0270509i
$652$	8.81797e9	−	2.53975e9i	1.24595	−	0.358860i
$653$			2.40494e9i			0.337993i	0.985617	+	0.168997i	$0.0540527\pi$
$653$			2.40494e9i			0.337993i	−0.985617	+	0.168997i	$0.945947\pi$
$654$	4.05407e9	+	2.21384e9i	0.566721	+	0.309474i
$655$			9.59666e9i			1.33437i
$656$	5.58523e8	+	8.89157e8i	0.0772463	+	0.122975i
$657$	2.64527e9	−	7.91430e8i	0.363908	−	0.108876i
$658$	3.23008e8	−	4.29171e8i	0.0442000	−	0.0587273i
$659$	1.38475e10			1.88484			0.942419	−	0.334435i	$-0.108546\pi$
$659$	1.38475e10			1.88484			0.942419	+	0.334435i	$0.108546\pi$
$660$	4.47339e9	−	2.02881e9i	0.605665	−	0.274687i
$661$	1.75990e9			0.237019			0.118510	−	0.992953i	$-0.462188\pi$
$661$	1.75990e9			0.237019			0.118510	+	0.992953i	$0.462188\pi$
$662$	−7.40878e9	+	9.84384e9i	−0.992531	+	1.31875i
$663$	4.44210e8	+	3.03448e9i	0.0591958	+	0.404377i
$664$	−1.70173e9	+	4.45668e9i	−0.225581	+	0.590776i
$665$			1.00914e10i			1.33069i
$666$	7.39956e9	+	2.73861e9i	0.970612	+	0.359229i
$667$		−	2.83756e9i		−	0.370258i
$668$	5.43185e7	+	1.88593e8i	0.00705067	+	0.0244798i
$669$	1.14729e9	+	7.83735e9i	0.148143	+	1.01199i
$670$	−1.56229e10	−	1.17583e10i	−2.00678	−	1.51037i
$671$	−4.09802e9			−0.523655
$672$	−4.12833e8	−	6.75575e9i	−0.0524786	−	0.858778i
$673$	−1.39027e10			−1.75812			−0.879059	−	0.476714i	$-0.841828\pi$
$673$	−1.39027e10			−1.75812			−0.879059	+	0.476714i	$0.841828\pi$
$674$	−1.86724e9	−	1.40535e9i	−0.234904	−	0.176797i
$675$	9.63376e9	−	4.48917e9i	1.20568	−	0.561827i
$676$	6.07025e7	+	2.10758e8i	0.00755776	+	0.0262404i
$677$		−	1.15054e10i		−	1.42508i	−0.701631	−	0.712541i	$-0.747544\pi$
$677$		−	1.15054e10i		−	1.42508i	0.701631	−	0.712541i	$-0.252456\pi$
$678$	−4.73139e9	+	8.66429e9i	−0.583022	+	1.06765i
$679$		−	1.24976e9i		−	0.153208i
$680$	−1.80028e9	+	4.71476e9i	−0.219563	+	0.575014i
$681$	1.41780e10	−	2.07548e9i	1.72028	−	0.251828i
$682$	−4.71104e8	+	6.25943e8i	−0.0568685	+	0.0755595i
$683$	−1.27311e10			−1.52895			−0.764475	−	0.644653i	$-0.777002\pi$
$683$	−1.27311e10			−1.52895			−0.764475	+	0.644653i	$0.777002\pi$
$684$	−7.13398e9	+	4.58415e9i	−0.852385	+	0.547725i
$685$	5.34137e9			0.634944
$686$	5.51101e9	−	7.32232e9i	0.651774	−	0.865993i
$687$	8.11309e9	−	1.18766e9i	0.954636	−	0.139747i
$688$	6.92174e9	+	1.10193e10i	0.810319	+	1.29001i
$689$		−	9.24759e9i		−	1.07711i
$690$	2.80212e9	−	5.13135e9i	0.324724	−	0.594647i
$691$		−	1.60938e10i		−	1.85560i	−0.373073	−	0.927802i	$-0.621696\pi$
$691$		−	1.60938e10i		−	1.85560i	0.373073	−	0.927802i	$-0.378304\pi$
$692$	5.56215e9	−	1.60201e9i	0.638075	−	0.183778i
$693$	−9.41327e8	−	3.14629e9i	−0.107442	−	0.359114i
$694$	6.33861e9	+	4.77064e9i	0.719840	+	0.541774i
$695$	−6.89426e9			−0.779006
$696$	−7.24205e9	−	1.61488e9i	−0.814196	−	0.181555i
$697$	−5.23469e8			−0.0585566
$698$	2.12631e9	+	1.60033e9i	0.236664	+	0.178121i
$699$	5.88984e8	+	4.02345e9i	0.0652279	+	0.445583i
$700$	−9.98001e9	+	2.87444e9i	−1.09973	+	0.316746i
$701$			7.64097e9i			0.837790i	0.908035	+	0.418895i	$0.137582\pi$
$701$			7.64097e9i			0.837790i	−0.908035	+	0.418895i	$0.862418\pi$
$702$	−9.08791e9	−	1.92863e9i	−0.991481	−	0.210412i
$703$			9.65958e9i			1.04861i
$704$	−3.00685e9	−	2.68821e9i	−0.324794	−	0.290375i
$705$	−1.75737e8	−	1.20049e9i	−0.0188887	−	0.129032i
$706$	−8.97352e9	+	1.19229e10i	−0.959724	+	1.27516i
$707$	8.39604e9			0.893525
$708$	−1.99152e9	−	4.39115e9i	−0.210896	−	0.465009i
$709$	7.90579e9			0.833073			0.416537	−	0.909119i	$-0.363244\pi$
$709$	7.90579e9			0.833073			0.416537	+	0.909119i	$0.363244\pi$
$710$	1.43780e10	−	1.91036e10i	1.50763	−	2.00314i
$711$	−3.93731e9	−	1.31600e10i	−0.410824	−	1.37314i
$712$	−2.14221e9	−	8.17979e8i	−0.222424	−	0.0849302i
$713$			9.32485e8i			0.0963448i
$714$	2.96144e9	+	1.61718e9i	0.304481	+	0.166270i
$715$			6.58827e9i			0.674063i
$716$	−2.60183e9	−	9.03351e9i	−0.264901	−	0.919731i
$717$	4.05588e8	−	5.93731e7i	0.0410930	−	0.00601552i
$718$	1.18147e10	+	8.89209e9i	1.19120	+	0.896537i
$719$	1.59409e9			0.159941			0.0799707	−	0.996797i	$-0.474517\pi$
$719$	1.59409e9			0.159941			0.0799707	+	0.996797i	$0.474517\pi$
$720$	−1.15016e10	−	1.00719e10i	−1.14840	−	1.00565i
$721$	7.00406e9			0.695947
$722$	−2.14632e8	−	1.61539e8i	−0.0212234	−	0.0159734i
$723$	6.43648e9	−	9.42222e8i	0.633380	−	0.0927191i
$724$	−1.72788e9	−	5.99916e9i	−0.169211	−	0.587497i
$725$			1.13855e10i			1.10961i
$726$	7.33153e9	+	4.00359e9i	0.711077	+	0.388304i
$727$		−	8.90620e9i		−	0.859651i	−0.902912	−	0.429825i	$-0.858575\pi$
$727$		−	8.90620e9i		−	0.859651i	0.902912	−	0.429825i	$-0.141425\pi$
$728$	8.48097e9	+	3.23837e9i	0.814678	+	0.311076i
$729$	6.72805e9	−	8.00951e9i	0.643196	−	0.765702i
$730$	−3.66483e9	+	4.86935e9i	−0.348677	+	0.463278i
$731$	−6.48732e9			−0.614263
$732$	5.26822e9	+	1.16160e10i	0.496450	+	1.09464i
$733$	8.39573e9			0.787399			0.393699	−	0.919239i	$-0.371195\pi$
$733$	8.39573e9			0.787399			0.393699	+	0.919239i	$0.371195\pi$
$734$	−1.93958e9	+	2.57706e9i	−0.181038	+	0.240541i
$735$	−6.18228e8	−	4.22322e9i	−0.0574305	−	0.392318i
$736$	−4.78371e9	−	4.04334e8i	−0.442275	−	0.0373825i
$737$			7.79042e9i			0.716844i
$738$	5.50404e8	−	1.48716e9i	0.0504063	−	0.136194i
$739$			1.25749e10i			1.14617i	0.819496	+	0.573086i	$0.194254\pi$
$739$			1.25749e10i			1.14617i	−0.819496	+	0.573086i	$0.805746\pi$
$740$	−1.67348e10	+	4.81995e9i	−1.51813	+	0.437252i
$741$	−1.64743e9	−	1.12539e10i	−0.148745	−	1.01611i
$742$	−8.12936e9	−	6.11841e9i	−0.730538	−	0.549825i
$743$	−1.00041e10			−0.894778			−0.447389	−	0.894340i	$-0.647646\pi$
$743$	−1.00041e10			−0.894778			−0.447389	+	0.894340i	$0.647646\pi$
$744$	2.37990e9	+	5.30686e8i	0.211862	+	0.0472425i
$745$	−1.69806e10			−1.50455
$746$	1.53642e10	+	1.15636e10i	1.35495	+	1.01978i
$747$	6.90214e9	−	2.06503e9i	0.605845	−	0.181261i
$748$	1.93219e9	−	5.56508e8i	0.168808	−	0.0486201i
$749$		−	1.48205e10i		−	1.28878i
$750$	−2.79069e9	+	5.11041e9i	−0.241544	+	0.442325i
$751$		−	4.11959e9i		−	0.354907i	−0.984129	−	0.177453i	$-0.943214\pi$
$751$		−	4.11959e9i		−	0.354907i	0.984129	−	0.177453i	$-0.0567859\pi$
$752$	−8.43627e8	+	5.29923e8i	−0.0723416	+	0.0454413i
$753$	−1.92005e10	+	2.81072e9i	−1.63882	+	0.239903i
$754$	5.98466e9	−	7.95165e9i	0.508440	−	0.675550i
$755$	1.54310e9			0.130491
$756$	−7.70819e9	+	6.71296e9i	−0.648822	+	0.565051i
$757$	2.13007e8			0.0178467			0.00892336	−	0.999960i	$-0.497160\pi$
$757$	2.13007e8			0.0178467			0.00892336	+	0.999960i	$0.497160\pi$
$758$	−4.43535e9	+	5.89313e9i	−0.369902	+	0.491478i
$759$	−2.30483e9	+	3.37398e8i	−0.191334	+	0.0280089i
$760$	6.67665e9	−	1.74855e10i	0.551710	−	1.44488i
$761$			1.50066e10i			1.23434i	0.786828	+	0.617172i	$0.211722\pi$
$761$			1.50066e10i			1.23434i	−0.786828	+	0.617172i	$0.788278\pi$
$762$	−3.68159e9	+	6.74187e9i	−0.301435	+	0.551999i
$763$			6.81658e9i			0.555560i
$764$	−1.86978e9	−	6.49184e9i	−0.151692	−	0.526673i
$765$	7.30184e9	−	2.18461e9i	0.589681	−	0.176425i
$766$	−1.21126e10	−	9.11630e9i	−0.973723	−	0.732855i
$767$	6.46715e9			0.517523
$768$	−3.75440e9	+	1.19789e10i	−0.299072	+	0.954230i
$769$	1.78700e9			0.141704			0.0708519	−	0.997487i	$-0.477428\pi$
$769$	1.78700e9			0.141704			0.0708519	+	0.997487i	$0.477428\pi$
$770$	5.79161e9	+	4.35895e9i	0.457174	+	0.344084i
$771$	2.33720e9	+	1.59658e10i	0.183656	+	1.25459i
$772$	3.92562e9	+	1.36297e10i	0.307077	+	1.06617i
$773$			2.41300e10i			1.87901i	0.342531	+	0.939506i	$0.388716\pi$
$773$			2.41300e10i			1.87901i	−0.342531	+	0.939506i	$0.611284\pi$
$774$	6.82113e9	−	1.84303e10i	0.528766	−	1.42869i
$775$		−	3.74153e9i		−	0.288731i
$776$	−8.26863e8	+	2.16548e9i	−0.0635210	+	0.166356i
$777$	1.68650e9	+	1.15208e10i	0.128977	+	0.881065i
$778$	1.41381e10	−	1.87848e10i	1.07637	−	1.43014i
$779$	1.94137e9			0.147139
$780$	1.86748e10	−	8.46958e9i	1.40905	−	0.639044i
$781$	−9.52608e9			−0.715543
$782$	1.43922e9	−	1.91225e9i	0.107622	−	0.142995i
$783$	4.73296e9	+	1.01569e10i	0.352344	+	0.756129i
$784$	−2.96781e9	+	1.86422e9i	−0.219953	+	0.138163i
$785$		−	3.02200e10i		−	2.22972i
$786$	−1.04446e10	−	5.70356e9i	−0.767205	−	0.418955i
$787$		−	8.02598e9i		−	0.586930i	−0.955970	−	0.293465i	$-0.905192\pi$
$787$		−	8.02598e9i		−	0.586930i	0.955970	−	0.293465i	$-0.0948085\pi$
$788$	1.87731e9	−	5.40702e8i	0.136676	−	0.0393655i
$789$	−8.61624e9	+	1.26131e9i	−0.624523	+	0.0914224i
$790$	2.42247e10	+	1.82323e10i	1.74809	+	1.31567i
$791$	−1.45683e10			−1.04662
$792$	−4.50588e8	+	6.07441e9i	−0.0322286	+	0.434476i
$793$	−1.71078e10			−1.21825
$794$	−1.08347e10	−	8.15453e9i	−0.768148	−	0.578132i
$795$	−2.27397e10	+	3.32881e9i	−1.60509	+	0.234966i
$796$	6.06618e9	−	1.74718e9i	0.426304	−	0.122784i
$797$		−	1.01493e10i		−	0.710118i	−0.934844	−	0.355059i	$-0.884461\pi$
$797$		−	1.01493e10i		−	0.710118i	0.934844	−	0.355059i	$-0.115539\pi$
$798$	−1.09830e10	−	5.99760e9i	−0.765089	−	0.417799i
$799$		−	4.96664e8i		−	0.0344468i
$800$	1.91943e10	+	1.62236e9i	1.32543	+	0.112030i
$801$	9.92606e8	+	3.31768e9i	0.0682438	+	0.228098i
$802$	−1.13902e9	+	1.51338e9i	−0.0779687	+	0.103595i
$803$	2.42812e9			0.165488
$804$	2.20823e10	−	1.00150e10i	1.49847	−	0.679602i
$805$	8.62793e9			0.582936
$806$	−1.96669e9	+	2.61309e9i	−0.132301	+	0.175785i
$807$	2.44428e9	+	1.66973e10i	0.163717	+	1.11838i
$808$	−1.45479e10	−	5.55497e9i	−0.970201	−	0.370460i
$809$		−	2.29647e10i		−	1.52490i	−0.647050	−	0.762448i	$-0.723997\pi$
$809$		−	2.29647e10i		−	1.52490i	0.647050	−	0.762448i	$-0.276003\pi$
$810$	−1.47115e9	+	2.30413e10i	−0.0972657	+	1.52338i
$811$		−	6.39485e9i		−	0.420976i	−0.977596	−	0.210488i	$-0.932495\pi$
$811$		−	6.39485e9i		−	0.420976i	0.977596	−	0.210488i	$-0.0675053\pi$
$812$	−3.03054e9	−	1.05220e10i	−0.198643	−	0.689686i
$813$	4.48629e8	+	3.06466e9i	0.0292800	+	0.200017i
$814$	5.54378e9	+	4.17243e9i	0.360264	+	0.271146i
$815$	3.05880e10			1.97925
$816$	−4.06138e9	−	4.76146e9i	−0.261672	−	0.306778i
$817$	2.40593e10			1.54350
$818$	−7.06985e9	−	5.32099e9i	−0.451620	−	0.339904i
$819$	−3.92971e9	−	1.31346e10i	−0.249958	−	0.835457i
$820$	9.68710e8	+	3.36334e9i	0.0613544	+	0.213021i
$821$			8.31295e9i			0.524269i	0.965031	+	0.262134i	$0.0844264\pi$
$821$			8.31295e9i			0.524269i	−0.965031	+	0.262134i	$0.915574\pi$
$822$	−3.17452e9	+	5.81331e9i	−0.199355	+	0.365066i
$823$		−	9.92759e9i		−	0.620790i	−0.950608	−	0.310395i	$-0.899539\pi$
$823$		−	9.92759e9i		−	0.620790i	0.950608	−	0.310395i	$-0.100461\pi$
$824$	−1.21360e10	−	4.63401e9i	−0.755668	−	0.288544i
$825$	9.24795e9	−	1.35379e9i	0.573398	−	0.0839385i
$826$	4.27881e9	−	5.68514e9i	0.264176	−	0.351003i
$827$	−1.84754e10			−1.13586			−0.567929	−	0.823078i	$-0.692255\pi$
$827$	−1.84754e10			−1.13586			−0.567929	+	0.823078i	$0.692255\pi$
$828$	3.91935e9	+	6.09940e9i	0.239943	+	0.373406i
$829$	−1.30420e10			−0.795065			−0.397532	−	0.917588i	$-0.630133\pi$
$829$	−1.30420e10			−0.795065			−0.397532	+	0.917588i	$0.630133\pi$
$830$	−9.56240e9	+	1.27053e10i	−0.580489	+	0.771279i
$831$	1.45227e10	−	2.12594e9i	0.877895	−	0.128513i
$832$	−1.25525e10	−	1.12223e10i	−0.755614	−	0.675540i
$833$		−	1.74722e9i		−	0.104735i
$834$	4.09745e9	−	7.50341e9i	0.244587	−	0.447896i
$835$			6.54197e8i			0.0388871i
$836$	−7.16584e9	+	2.06391e9i	−0.424175	+	0.122171i
$837$	−1.55535e9	−	3.33779e9i	−0.0916833	−	0.196752i
$838$	−7.40067e9	−	5.56998e9i	−0.434427	−	0.326963i
$839$	2.35823e10			1.37854			0.689269	−	0.724505i	$-0.257932\pi$
$839$	2.35823e10			1.37854			0.689269	+	0.724505i	$0.257932\pi$
$840$	4.91024e9	−	2.20203e10i	0.285841	−	1.28187i
$841$	5.24608e9			0.304123
$842$	−2.34055e10	−	1.76157e10i	−1.35122	−	1.01697i
$843$	−4.24520e9	−	2.89997e10i	−0.244063	−	1.66723i
$844$	−2.07545e10	+	5.97771e9i	−1.18827	+	0.342244i
$845$			7.31083e8i			0.0416839i
$846$	1.41101e9	+	5.22220e8i	0.0801184	+	0.0296522i
$847$			1.23274e10i			0.697072i
$848$	1.00378e10	+	1.59800e10i	0.565267	+	0.899893i
$849$	3.87222e9	+	2.64518e10i	0.217162	+	1.48347i
$850$	−5.77475e9	+	7.67275e9i	−0.322528	+	0.428533i
$851$	8.25873e9			0.459367
$852$	1.22463e10	+	2.70022e10i	0.678369	+	1.49575i
$853$	1.76368e10			0.972966			0.486483	−	0.873690i	$-0.338279\pi$
$853$	1.76368e10			0.972966			0.486483	+	0.873690i	$0.338279\pi$
$854$	−1.13189e10	+	1.50391e10i	−0.621872	+	0.826264i
$855$	−2.70801e10	+	8.10201e9i	−1.48173	+	0.443314i
$856$	−9.80552e9	+	2.56797e10i	−0.534334	+	1.39937i
$857$			2.32627e10i			1.26249i	0.775585	+	0.631243i	$0.217455\pi$
$857$			2.32627e10i			1.26249i	−0.775585	+	0.631243i	$0.782545\pi$
$858$	−7.17038e9	−	3.91559e9i	−0.387558	−	0.211637i
$859$		−	1.34614e10i		−	0.724628i	−0.932056	−	0.362314i	$-0.881987\pi$
$859$		−	1.34614e10i		−	0.724628i	0.932056	−	0.362314i	$-0.118013\pi$
$860$	1.20052e10	+	4.16817e10i	0.643612	+	2.23461i
$861$	2.31543e9	−	3.38951e8i	0.123629	−	0.0180978i
$862$	5.01593e9	+	3.77515e9i	0.266733	+	0.200751i
$863$	3.00733e9			0.159274			0.0796368	−	0.996824i	$-0.474624\pi$
$863$	3.00733e9			0.159274			0.0796368	+	0.996824i	$0.474624\pi$
$864$	1.77975e10	−	6.53177e9i	0.938774	−	0.344535i
$865$	1.92942e10			1.01361
$866$	1.40256e10	+	1.05561e10i	0.733853	+	0.552321i
$867$	−1.59002e10	+	2.32760e9i	−0.828584	+	0.121294i
$868$	9.95903e8	+	3.45776e9i	0.0516890	+	0.179463i
$869$		−	1.20797e10i		−	0.624436i
$870$	−2.17073e10	−	1.18539e10i	−1.11760	−	0.610300i
$871$			3.25222e10i			1.66770i
$872$	4.50997e9	−	1.18112e10i	0.230338	−	0.603234i
$873$	3.35371e9	−	1.00339e9i	0.170599	−	0.0510409i
$874$	−5.33758e9	+	7.09189e9i	−0.270430	+	0.359312i
$875$	−8.59273e9			−0.433614
$876$	−3.12148e9	−	6.88263e9i	−0.156890	−	0.345931i
$877$	−2.35577e10			−1.17933			−0.589663	−	0.807649i	$-0.700740\pi$
$877$	−2.35577e10			−1.17933			−0.589663	+	0.807649i	$0.700740\pi$
$878$	9.39555e9	−	1.24836e10i	0.468481	−	0.622457i
$879$	−3.97412e9	−	2.71479e10i	−0.197370	−	1.34827i
$880$	−7.15125e9	−	1.13846e10i	−0.353747	−	0.563158i
$881$			7.25594e9i			0.357501i	0.983894	+	0.178751i	$0.0572056\pi$
$881$			7.25594e9i			0.357501i	−0.983894	+	0.178751i	$0.942794\pi$
$882$	4.96379e9	+	1.83713e9i	0.243598	+	0.0901569i
$883$			8.70188e9i			0.425354i	0.977123	+	0.212677i	$0.0682182\pi$
$883$			8.70188e9i			0.425354i	−0.977123	+	0.212677i	$0.931782\pi$
$884$	8.06619e9	−	2.32322e9i	0.392722	−	0.113112i
$885$	−2.32795e9	−	1.59026e10i	−0.112894	−	0.771201i
$886$	−1.67059e9	−	1.25734e9i	−0.0806960	−	0.0607344i
$887$	−9.35154e9			−0.449936			−0.224968	−	0.974366i	$-0.572228\pi$
$887$	−9.35154e9			−0.449936			−0.224968	+	0.974366i	$0.572228\pi$
$888$	4.70013e9	−	2.10780e10i	0.225250	−	1.01015i
$889$	−1.13359e10			−0.541127
$890$	−6.10711e9	−	4.59640e9i	−0.290383	−	0.218551i
$891$	7.68726e9	−	5.05208e9i	0.364082	−	0.239275i
$892$	2.08331e10	−	6.00034e9i	0.982825	−	0.283073i
$893$			1.84196e9i			0.0865568i
$894$	1.00921e10	−	1.84810e10i	0.472388	−	0.865055i
$895$		−	3.13357e10i		−	1.46103i
$896$	−1.81703e10	+	3.60973e9i	−0.843889	+	0.167647i
$897$	−9.62183e9	+	1.40852e9i	−0.445127	+	0.0651611i
$898$	−9.96360e8	+	1.32384e9i	−0.0459144	+	0.0610052i
$899$	3.94471e9			0.181074
$900$	−1.57261e10	−	2.44734e10i	−0.719072	−	1.11904i
$901$	−9.40781e9			−0.428501
$902$	8.38571e8	−	1.11418e9i	0.0380467	−	0.0505515i
$903$	2.86951e10	−	4.20060e9i	1.29688	−	0.189847i
$904$	2.52427e10	+	9.63864e9i	1.13644	+	0.433936i
$905$		−	2.08101e10i		−	0.933262i
$906$	−9.17106e8	+	1.67944e9i	−0.0409704	+	0.0750266i
$907$			1.51849e10i			0.675753i	0.941190	+	0.337876i	$0.109709\pi$
$907$			1.51849e10i			0.675753i	−0.941190	+	0.337876i	$0.890291\pi$
$908$	−1.08548e10	−	3.76876e10i	−0.481194	−	1.67070i
$909$	6.74087e9	+	2.25306e10i	0.297675	+	0.994947i
$910$	2.41779e10	+	1.81971e10i	1.06359	+	0.800491i
$911$	3.24000e10			1.41981			0.709905	−	0.704298i	$-0.248738\pi$
$911$	3.24000e10			1.41981			0.709905	+	0.704298i	$0.248738\pi$
$912$	1.50623e10	+	1.76587e10i	0.657522	+	0.770862i
$913$	6.33553e9			0.275509
$914$	4.98200e9	+	3.74961e9i	0.215820	+	0.162433i
$915$	6.15821e9	+	4.20678e10i	0.265754	+	1.81541i
$916$	−6.21146e9	−	2.15661e10i	−0.267030	−	0.927121i
$917$		−	1.75617e10i		−	0.752096i
$918$	−1.96205e9	+	9.24537e9i	−0.0837068	+	0.394434i
$919$			1.81741e10i			0.772413i	0.922412	+	0.386206i	$0.126215\pi$
$919$			1.81741e10i			0.772413i	−0.922412	+	0.386206i	$0.873785\pi$
$920$	−1.49497e10	−	5.70839e9i	−0.632960	−	0.241689i
$921$	−5.89263e9	−	4.02536e10i	−0.248542	−	1.69784i
$922$	1.06804e10	−	1.41907e10i	0.448775	−	0.596275i
$923$	−3.97680e10			−1.66467
$924$	−8.18620e9	+	3.71269e9i	−0.341374	+	0.154823i
$925$	−3.31376e10			−1.37665
$926$	6.64092e8	−	8.82361e8i	0.0274846	−	0.0365181i
$927$	5.62330e9	+	1.87953e10i	0.231853	+	0.774943i
$928$	−1.71047e9	+	2.02366e10i	−0.0702581	+	0.831229i
$929$			3.43885e8i			0.0140721i	0.999975	+	0.00703604i	$0.00223966\pi$
$929$			3.43885e8i			0.0140721i	−0.999975	+	0.00703604i	$0.997760\pi$
$930$	7.13349e9	+	3.89545e9i	0.290812	+	0.158806i
$931$			6.47987e9i			0.263174i
$932$	1.06951e10	−	3.08039e9i	0.432740	−	0.124638i
$933$	2.43467e10	−	3.56406e9i	0.981420	−	0.143668i
$934$	−2.13007e10	−	1.60315e10i	−0.855419	−	0.643815i
$935$	6.70242e9			0.268158
$936$	−1.88104e9	+	2.53585e10i	−0.0749779	+	1.01078i
$937$	−1.17195e10			−0.465395			−0.232697	−	0.972549i	$-0.574755\pi$
$937$	−1.17195e10			−0.465395			−0.232697	+	0.972549i	$0.574755\pi$
$938$	2.85896e10	+	2.15174e10i	1.13109	+	0.851296i
$939$	−3.03893e10	+	4.44862e9i	−1.19782	+	0.175346i
$940$	−3.19112e9	+	9.19107e8i	−0.125313	+	0.0360926i
$941$		−	7.71608e9i		−	0.301879i	−0.988543	−	0.150940i	$-0.951770\pi$
$941$		−	7.71608e9i		−	0.301879i	0.988543	−	0.150940i	$-0.0482299\pi$
$942$	3.28901e10	+	1.79606e10i	1.28200	+	0.700071i
$943$		−	1.65983e9i		−	0.0644575i
$944$	−1.11753e10	+	7.01978e9i	−0.432373	+	0.271595i
$945$	−3.08833e10	+	1.43911e10i	−1.19045	+	0.554732i
$946$	1.03924e10	−	1.38080e10i	0.399112	−	0.530289i
$947$	−1.72432e10			−0.659769			−0.329884	−	0.944021i	$-0.607010\pi$
$947$	−1.72432e10			−0.659769			−0.329884	+	0.944021i	$0.607010\pi$
$948$	−3.42406e10	+	1.55291e10i	−1.30531	+	0.591995i
$949$	1.01365e10			0.384997
$950$	2.14167e10	−	2.84557e10i	0.810437	−	1.07680i
$951$	−1.77202e9	−	1.21050e10i	−0.0668092	−	0.456385i
$952$	3.29447e9	−	8.62791e9i	0.123753	−	0.324098i
$953$			3.21881e10i			1.20468i	0.798241	+	0.602338i	$0.205764\pi$
$953$			3.21881e10i			1.20468i	−0.798241	+	0.602338i	$0.794236\pi$
$954$	9.89190e9	−	2.67273e10i	0.368859	−	0.996633i
$955$		−	2.25191e10i		−	0.836641i
$956$	−3.10522e8	−	1.07813e9i	−0.0114945	−	0.0399087i
$957$	1.42730e9	+	9.75016e9i	0.0526411	+	0.359600i
$958$	−7.04232e9	−	5.30027e9i	−0.258784	−	0.194769i
$959$	−9.77458e9			−0.357877
$960$	−2.30771e10	+	3.49062e10i	−0.841843	+	1.27336i
$961$	2.62163e10			0.952883
$962$	2.31433e10	+	1.74184e10i	0.838133	+	0.630806i
$963$	3.97707e10	−	1.18989e10i	1.43506	−	0.429352i
$964$	−4.92783e9	−	1.71093e10i	−0.177168	−	0.615125i
$965$			4.72790e10i			1.69365i
$966$	−5.12782e9	+	9.39025e9i	−0.183026	+	0.335164i
$967$		−	3.22700e10i		−	1.14764i	−0.818981	−	0.573820i	$-0.805461\pi$
$967$		−	3.22700e10i		−	1.14764i	0.818981	−	0.573820i	$-0.194539\pi$
$968$	8.15600e9	−	2.13598e10i	0.289010	−	0.756891i
$969$	−1.14489e10	+	1.67597e9i	−0.404231	+	0.0591744i
$970$	−4.64632e9	+	6.17343e9i	−0.163459	+	0.217183i
$971$	−1.66164e10			−0.582465			−0.291232	−	0.956652i	$-0.594065\pi$
$971$	−1.66164e10			−0.582465			−0.291232	+	0.956652i	$0.594065\pi$
$972$	−2.42028e10	−	1.52952e10i	−0.845343	−	0.534224i
$973$	1.26163e10			0.439075
$974$	−6.47632e9	+	8.60490e9i	−0.224580	+	0.298394i
$975$	3.86069e10	−	5.65158e9i	1.33398	−	0.195278i
$976$	2.95625e10	−	1.85697e10i	1.01781	−	0.639336i
$977$			2.11766e10i			0.726483i	0.931695	+	0.363242i	$0.118330\pi$
$977$			2.11766e10i			0.726483i	−0.931695	+	0.363242i	$0.881670\pi$
$978$	−1.81793e10	+	3.32906e10i	−0.621429	+	1.13798i
$979$			3.04533e9i			0.103728i
$980$	−1.12261e10	+	3.23334e9i	−0.381010	+	0.109739i
$981$	−1.82922e10	+	5.47278e9i	−0.618620	+	0.185083i
$982$	−1.93924e10	−	1.45953e10i	−0.653492	−	0.491839i
$983$	−4.49060e10			−1.50788			−0.753941	−	0.656942i	$-0.771850\pi$
$983$	−4.49060e10			−1.50788			−0.753941	+	0.656942i	$0.771850\pi$
$984$	−4.23624e9	−	9.44627e8i	−0.141742	−	0.0316066i
$985$	6.51205e9			0.217116
$986$	−8.08942e9	−	6.08835e9i	−0.268750	−	0.202270i
$987$	3.21595e8	+	2.19687e9i	0.0106463	+	0.0727268i
$988$	−2.99149e10	+	8.61608e9i	−0.986819	+	0.284224i
$989$		−	2.05702e10i		−	0.676164i
$990$	−7.04730e9	+	1.90413e10i	−0.230834	+	0.623698i
$991$			2.06832e10i			0.675089i	0.941310	+	0.337544i	$0.109596\pi$
$991$			2.06832e10i			0.675089i	−0.941310	+	0.337544i	$0.890404\pi$
$992$	5.62097e8	−	6.65021e9i	0.0182819	−	0.216294i
$993$	−7.37638e9	−	5.03893e10i	−0.239068	−	1.63311i
$994$	−2.63114e10	+	3.49592e10i	−0.849751	+	1.12904i
$995$	2.10425e10			0.677201
$996$	−8.14467e9	−	1.79584e10i	−0.261196	−	0.575917i
$997$	3.58951e10			1.14710			0.573551	−	0.819170i	$-0.305565\pi$
$997$	3.58951e10			1.14710			0.573551	+	0.819170i	$0.305565\pi$
$998$	1.03097e10	−	1.36983e10i	0.328315	−	0.436223i
$999$	−2.95618e10	+	1.37753e10i	−0.938105	+	0.437141i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.8.b.b.11.8	yes	8
3.2	odd	2	inner	12.8.b.b.11.1	✓	8
4.3	odd	2	inner	12.8.b.b.11.2	yes	8
8.3	odd	2		192.8.c.e.191.2		8
8.5	even	2		192.8.c.e.191.7		8
12.11	even	2	inner	12.8.b.b.11.7	yes	8
24.5	odd	2		192.8.c.e.191.1		8
24.11	even	2		192.8.c.e.191.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.8.b.b.11.1	✓	8	3.2	odd	2	inner
12.8.b.b.11.2	yes	8	4.3	odd	2	inner
12.8.b.b.11.7	yes	8	12.11	even	2	inner
12.8.b.b.11.8	yes	8	1.1	even	1	trivial
192.8.c.e.191.1		8	24.5	odd	2
192.8.c.e.191.2		8	8.3	odd	2
192.8.c.e.191.7		8	8.5	even	2
192.8.c.e.191.8		8	24.11	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:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	12.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(9.03954 + 6.80344i) q^{2} +(-46.2722 + 6.77368i) q^{3} +(35.4264 + 123.000i) q^{4} +426.666i q^{5} +(-464.364 - 253.579i) q^{6} -780.788i q^{7} +(-516.584 + 1352.88i) q^{8} +(2095.23 - 626.867i) q^{9} +O(q^{10})\)	\(q+(9.03954 + 6.80344i) q^{2} +(-46.2722 + 6.77368i) q^{3} +(35.4264 + 123.000i) q^{4} +426.666i q^{5} +(-464.364 - 253.579i) q^{6} -780.788i q^{7} +(-516.584 + 1352.88i) q^{8} +(2095.23 - 626.867i) q^{9} +(-2902.79 + 3856.86i) q^{10} +1923.23 q^{11} +(-2472.42 - 5451.51i) q^{12} +8028.82 q^{13} +(5312.05 - 7057.97i) q^{14} +(-2890.10 - 19742.8i) q^{15} +(-13873.9 + 8714.89i) q^{16} -8167.93i q^{17} +(23204.8 + 8588.22i) q^{18} +30292.2i q^{19} +(-52479.8 + 15115.2i) q^{20} +(5288.81 + 36128.8i) q^{21} +(17385.1 + 13084.6i) q^{22} +25899.2 q^{23} +(14739.5 - 66100.1i) q^{24} -103918. q^{25} +(72576.8 + 54623.6i) q^{26} +(-92704.9 + 43199.0i) q^{27} +(96036.9 - 27660.6i) q^{28} -109562. i q^{29} +(108194. - 198128. i) q^{30} +36004.5i q^{31} +(-184705. - 15611.9i) q^{32} +(-88992.3 + 13027.4i) q^{33} +(55570.0 - 73834.3i) q^{34} +333136. q^{35} +(151331. + 235506. i) q^{36} +318880. q^{37} +(-206091. + 273827. i) q^{38} +(-371511. + 54384.7i) q^{39} +(-577229. - 220408. i) q^{40} -64088.3i q^{41} +(-197992. + 362570. i) q^{42} -794243. i q^{43} +(68133.3 + 236558. i) q^{44} +(267462. + 893964. i) q^{45} +(234116. + 176203. i) q^{46} +60806.6 q^{47} +(582946. - 497235. i) q^{48} +213912. q^{49} +(-939375. - 707003. i) q^{50} +(55326.9 + 377948. i) q^{51} +(284433. + 987544. i) q^{52} -1.15180e6i q^{53} +(-1.13191e6 - 240214. i) q^{54} +820578. i q^{55} +(1.05632e6 + 403342. i) q^{56} +(-205190. - 1.40169e6i) q^{57} +(745397. - 990388. i) q^{58} +805492. q^{59} +(2.32597e6 - 1.05490e6i) q^{60} -2.13080e6 q^{61} +(-244954. + 325464. i) q^{62} +(-489450. - 1.63593e6i) q^{63} +(-1.56343e6 - 1.39775e6i) q^{64} +3.42562e6i q^{65} +(-893080. - 487692. i) q^{66} +4.05068e6i q^{67} +(1.00465e6 - 289361. i) q^{68} +(-1.19841e6 + 175433. i) q^{69} +(3.01139e6 + 2.26647e6i) q^{70} -4.95316e6 q^{71} +(-234286. + 3.15844e6i) q^{72} +1.26252e6 q^{73} +(2.88253e6 + 2.16948e6i) q^{74} +(4.80854e6 - 703911. i) q^{75} +(-3.72593e6 + 1.07314e6i) q^{76} -1.50164e6i q^{77} +(-3.72829e6 - 2.03594e6i) q^{78} -6.28094e6i q^{79} +(-3.71834e6 - 5.91953e6i) q^{80} +(3.99705e6 - 2.62686e6i) q^{81} +(436021. - 579329. i) q^{82} +3.29421e6 q^{83} +(-4.25647e6 + 1.93044e6i) q^{84} +3.48497e6 q^{85} +(5.40358e6 - 7.17959e6i) q^{86} +(742137. + 5.06967e6i) q^{87} +(-993511. + 2.60191e6i) q^{88} +1.58344e6i q^{89} +(-3.66430e6 + 9.90069e6i) q^{90} -6.26881e6i q^{91} +(917515. + 3.18559e6i) q^{92} +(-243883. - 1.66601e6i) q^{93} +(549664. + 413694. i) q^{94} -1.29246e7 q^{95} +(8.65247e6 - 528738. i) q^{96} +1.60064e6 q^{97} +(1.93367e6 + 1.45534e6i) q^{98} +(4.02963e6 - 1.20561e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 328 q^{4} - 1512 q^{6} + 2088 q^{9}+O(q^{10}) \) 8 * q - 328 * q^4 - 1512 * q^6 + 2088 * q^9	\( 8 q - 328 q^{4} - 1512 q^{6} + 2088 q^{9} - 4880 q^{10} - 12168 q^{12} + 54448 q^{13} - 10720 q^{16} - 50256 q^{18} - 133776 q^{21} + 140304 q^{22} + 37152 q^{24} - 195480 q^{25} + 202128 q^{28} - 43920 q^{30} + 183168 q^{33} + 361408 q^{34} + 1035864 q^{36} - 21776 q^{37} - 3028160 q^{40} - 1676592 q^{42} + 1992960 q^{45} + 496032 q^{46} + 1838880 q^{48} + 958040 q^{49} - 1484720 q^{52} - 4211352 q^{54} - 3798576 q^{57} + 12049168 q^{58} + 10255680 q^{60} - 3027920 q^{61} - 9073792 q^{64} - 15137136 q^{66} - 8149248 q^{69} + 13293600 q^{70} + 10585152 q^{72} + 3682768 q^{73} - 18402192 q^{76} - 12533616 q^{78} + 16656840 q^{81} + 16046560 q^{82} + 18942480 q^{84} + 12032000 q^{85} - 29650752 q^{88} - 34917840 q^{90} + 21380400 q^{93} + 8217408 q^{94} + 45277056 q^{96} - 15887216 q^{97}+O(q^{100}) \) 8 * q - 328 * q^4 - 1512 * q^6 + 2088 * q^9 - 4880 * q^10 - 12168 * q^12 + 54448 * q^13 - 10720 * q^16 - 50256 * q^18 - 133776 * q^21 + 140304 * q^22 + 37152 * q^24 - 195480 * q^25 + 202128 * q^28 - 43920 * q^30 + 183168 * q^33 + 361408 * q^34 + 1035864 * q^36 - 21776 * q^37 - 3028160 * q^40 - 1676592 * q^42 + 1992960 * q^45 + 496032 * q^46 + 1838880 * q^48 + 958040 * q^49 - 1484720 * q^52 - 4211352 * q^54 - 3798576 * q^57 + 12049168 * q^58 + 10255680 * q^60 - 3027920 * q^61 - 9073792 * q^64 - 15137136 * q^66 - 8149248 * q^69 + 13293600 * q^70 + 10585152 * q^72 + 3682768 * q^73 - 18402192 * q^76 - 12533616 * q^78 + 16656840 * q^81 + 16046560 * q^82 + 18942480 * q^84 + 12032000 * q^85 - 29650752 * q^88 - 34917840 * q^90 + 21380400 * q^93 + 8217408 * q^94 + 45277056 * q^96 - 15887216 * q^97

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