LMFDB - Embedded newform 12.8.b.b.11.5

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			11.5
Root			$-1.14965 - 5.53880i$ of defining polynomial
Character	$\chi$	$=$	12.11
Dual form			12.8.b.b.11.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.29930 - 11.0776i) q^{2} +(17.5181 - 43.3603i) q^{3} +(-117.426 - 50.9415i) q^{4} +151.910i q^{5} +(-440.049 - 293.757i) q^{6} -893.278i q^{7} +(-834.308 + 1183.67i) q^{8} +(-1573.23 - 1519.18i) q^{9} +O(q^{10})$	\(q+(2.29930 - 11.0776i) q^{2} +(17.5181 - 43.3603i) q^{3} +(-117.426 - 50.9415i) q^{4} +151.910i q^{5} +(-440.049 - 293.757i) q^{6} -893.278i q^{7} +(-834.308 + 1183.67i) q^{8} +(-1573.23 - 1519.18i) q^{9} +(1682.79 + 349.286i) q^{10} +7694.02 q^{11} +(-4265.92 + 4199.25i) q^{12} +5583.18 q^{13} +(-9895.37 - 2053.91i) q^{14} +(6586.85 + 2661.16i) q^{15} +(11193.9 + 11963.7i) q^{16} +3139.85i q^{17} +(-20446.2 + 13934.6i) q^{18} -17169.0i q^{19} +(7738.49 - 17838.2i) q^{20} +(-38732.8 - 15648.5i) q^{21} +(17690.9 - 85231.2i) q^{22} -47887.8 q^{23} +(36709.0 + 56911.5i) q^{24} +55048.5 q^{25} +(12837.4 - 61848.2i) q^{26} +(-93432.1 + 41602.9i) q^{27} +(-45504.9 + 104894. i) q^{28} +204638. i q^{29} +(44624.4 - 66847.6i) q^{30} +128896. i q^{31} +(158268. - 96493.7i) q^{32} +(134784. - 333615. i) q^{33} +(34782.0 + 7219.46i) q^{34} +135697. q^{35} +(107350. + 258535. i) q^{36} -324324. q^{37} +(-190192. - 39476.8i) q^{38} +(97806.5 - 242088. i) q^{39} +(-179811. - 126739. i) q^{40} +322779. i q^{41} +(-262406. + 393086. i) q^{42} -418323. i q^{43} +(-903481. - 391944. i) q^{44} +(230778. - 238989. i) q^{45} +(-110108. + 530481. i) q^{46} +654411. q^{47} +(714848. - 275791. i) q^{48} +25597.6 q^{49} +(126573. - 609805. i) q^{50} +(136145. + 55004.1i) q^{51} +(-655613. - 284415. i) q^{52} -50664.2i q^{53} +(246032. + 1.13066e6i) q^{54} +1.16879e6i q^{55} +(1.05735e6 + 745269. i) q^{56} +(-744454. - 300768. i) q^{57} +(2.26689e6 + 470524. i) q^{58} -1.93811e6 q^{59} +(-637906. - 648034. i) q^{60} +1.37382e6 q^{61} +(1.42786e6 + 296371. i) q^{62} +(-1.35705e6 + 1.40534e6i) q^{63} +(-705013. - 1.97510e6i) q^{64} +848138. i q^{65} +(-3.38574e6 - 2.26017e6i) q^{66} -2.50568e6i q^{67} +(159949. - 368701. i) q^{68} +(-838901. + 2.07643e6i) q^{69} +(312009. - 1.50320e6i) q^{70} +168073. q^{71} +(3.11077e6 - 594734. i) q^{72} -341826. q^{73} +(-745719. + 3.59274e6i) q^{74} +(964343. - 2.38692e6i) q^{75} +(-874615. + 2.01610e6i) q^{76} -6.87289e6i q^{77} +(-2.45687e6 - 1.64009e6i) q^{78} +3.19089e6i q^{79} +(-1.81741e6 + 1.70047e6i) q^{80} +(167164. + 4.78005e6i) q^{81} +(3.57562e6 + 742166. i) q^{82} +2.25902e6 q^{83} +(3.75110e6 + 3.81065e6i) q^{84} -476973. q^{85} +(-4.63401e6 - 961849. i) q^{86} +(8.87316e6 + 3.58486e6i) q^{87} +(-6.41918e6 + 9.10720e6i) q^{88} -4.66598e6i q^{89} +(-2.11680e6 - 3.10597e6i) q^{90} -4.98733e6i q^{91} +(5.62329e6 + 2.43947e6i) q^{92} +(5.58898e6 + 2.25801e6i) q^{93} +(1.50469e6 - 7.24931e6i) q^{94} +2.60814e6 q^{95} +(-1.41145e6 - 8.55293e6i) q^{96} -5.57244e6 q^{97} +(58856.6 - 283560. i) q^{98} +(-1.21045e7 - 1.16886e7i) 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 $

$2$	2.29930	−	11.0776i	0.203231	−	0.979131i
$2$	2.29930	−	11.0776i	0.203231	−	0.979131i
$3$	17.5181	−	43.3603i	0.374595	−	0.927189i
$3$	17.5181	−	43.3603i	0.374595	−	0.927189i
$4$	−117.426	−	50.9415i	−0.917394	−	0.397980i
$5$			151.910i			0.543488i	0.962370	+	0.271744i	$0.0876004\pi$
$5$			151.910i			0.543488i	−0.962370	+	0.271744i	$0.912400\pi$
$6$	−440.049	−	293.757i	−0.831709	−	0.555211i
$7$		−	893.278i		−	0.984336i	−0.870500	−	0.492168i	$-0.836205\pi$
$7$		−	893.278i		−	0.984336i	0.870500	−	0.492168i	$-0.163795\pi$
$8$	−834.308	+	1183.67i	−0.576118	+	0.817367i
$9$	−1573.23	−	1519.18i	−0.719357	−	0.694640i
$10$	1682.79	+	349.286i	0.532146	+	0.110454i
$11$	7694.02			1.74292			0.871462	−	0.490462i	$-0.163172\pi$
$11$	7694.02			1.74292			0.871462	+	0.490462i	$0.163172\pi$
$12$	−4265.92	+	4199.25i	−0.712654	+	0.701516i
$13$	5583.18			0.704822			0.352411	−	0.935845i	$-0.385362\pi$
$13$	5583.18			0.704822			0.352411	+	0.935845i	$0.385362\pi$
$14$	−9895.37	−	2053.91i	−0.963794	−	0.200048i
$15$	6586.85	+	2661.16i	0.503916	+	0.203588i
$16$	11193.9	+	11963.7i	0.683224	+	0.730209i
$17$			3139.85i			0.155002i	0.996992	+	0.0775011i	$0.0246941\pi$
$17$			3139.85i			0.155002i	−0.996992	+	0.0775011i	$0.975306\pi$
$18$	−20446.2	+	13934.6i	−0.826340	+	0.563172i
$19$		−	17169.0i		−	0.574259i	−0.957892	−	0.287130i	$-0.907299\pi$
$19$		−	17169.0i		−	0.574259i	0.957892	−	0.287130i	$-0.0927011\pi$
$20$	7738.49	−	17838.2i	0.216297	−	0.498593i
$21$	−38732.8	−	15648.5i	−0.912665	−	0.368727i
$22$	17690.9	−	85231.2i	0.354217	−	1.70655i
$23$	−47887.8			−0.820686			−0.410343	−	0.911931i	$-0.634591\pi$
$23$	−47887.8			−0.820686			−0.410343	+	0.911931i	$0.634591\pi$
$24$	36709.0	+	56911.5i	0.542042	+	0.840351i
$25$	55048.5			0.704621
$26$	12837.4	−	61848.2i	0.143242	−	0.690113i
$27$	−93432.1	+	41602.9i	−0.913530	+	0.406771i
$28$	−45504.9	+	104894.i	−0.391746	+	0.903024i
$29$			204638.i			1.55809i	0.626968	+	0.779045i	$0.284296\pi$
$29$			204638.i			1.55809i	−0.626968	+	0.779045i	$0.715704\pi$
$30$	44624.4	−	66847.6i	0.301751	−	0.452024i
$31$			128896.i			0.777095i	0.921429	+	0.388548i	$0.127023\pi$
$31$			128896.i			0.777095i	−0.921429	+	0.388548i	$0.872977\pi$
$32$	158268.	−	96493.7i	0.853823	−	0.520564i
$33$	134784.	−	333615.i	0.652891	−	1.61602i
$34$	34782.0	+	7219.46i	0.151767	+	0.0315013i
$35$	135697.			0.534975
$36$	107350.	+	258535.i	0.383481	+	0.923549i
$37$	−324324.			−1.05262			−0.526312	−	0.850291i	$-0.676426\pi$
$37$	−324324.			−1.05262			−0.526312	+	0.850291i	$0.676426\pi$
$38$	−190192.	−	39476.8i	−0.562275	−	0.116708i
$39$	97806.5	−	242088.i	0.264023	−	0.653503i
$40$	−179811.	−	126739.i	−0.444229	−	0.313113i
$41$			322779.i			0.731412i	0.930730	+	0.365706i	$0.119172\pi$
$41$			322779.i			0.731412i	−0.930730	+	0.365706i	$0.880828\pi$
$42$	−262406.	+	393086.i	−0.546514	+	0.818682i
$43$		−	418323.i		−	0.802365i	−0.915998	−	0.401182i	$-0.868599\pi$
$43$		−	418323.i		−	0.802365i	0.915998	−	0.401182i	$-0.131401\pi$
$44$	−903481.	−	391944.i	−1.59895	−	0.693649i
$45$	230778.	−	238989.i	0.377529	−	0.390962i
$46$	−110108.	+	530481.i	−0.166789	+	0.803559i
$47$	654411.			0.919408			0.459704	−	0.888072i	$-0.347955\pi$
$47$	654411.			0.919408			0.459704	+	0.888072i	$0.347955\pi$
$48$	714848.	−	275791.i	0.932974	−	0.359944i
$49$	25597.6			0.0310823
$50$	126573.	−	609805.i	0.143201	−	0.689916i
$51$	136145.	+	55004.1i	0.143716	+	0.0580630i
$52$	−655613.	−	284415.i	−0.646600	−	0.280505i
$53$		−	50664.2i		−	0.0467450i	−0.999727	−	0.0233725i	$-0.992560\pi$
$53$		−	50664.2i		−	0.0467450i	0.999727	−	0.0233725i	$-0.00744038\pi$
$54$	246032.	+	1.13066e6i	0.212624	+	0.977134i
$55$			1.16879e6i			0.947259i
$56$	1.05735e6	+	745269.i	0.804564	+	0.567094i
$57$	−744454.	−	300768.i	−0.532447	−	0.215115i
$58$	2.26689e6	+	470524.i	1.52557	+	0.316653i
$59$	−1.93811e6			−1.22856			−0.614280	−	0.789088i	$-0.710553\pi$
$59$	−1.93811e6			−1.22856			−0.614280	+	0.789088i	$0.710553\pi$
$60$	−637906.	−	648034.i	−0.381266	−	0.387319i
$61$	1.37382e6			0.774950			0.387475	−	0.921880i	$-0.373347\pi$
$61$	1.37382e6			0.774950			0.387475	+	0.921880i	$0.373347\pi$
$62$	1.42786e6	+	296371.i	0.760878	+	0.157930i
$63$	−1.35705e6	+	1.40534e6i	−0.683760	+	0.708089i
$64$	−705013.	−	1.97510e6i	−0.336176	−	0.941799i
$65$			848138.i			0.383063i
$66$	−3.38574e6	−	2.26017e6i	−1.44961	−	0.967691i
$67$		−	2.50568e6i		−	1.01780i	−0.860825	−	0.508901i	$-0.830052\pi$
$67$		−	2.50568e6i		−	1.01780i	0.860825	−	0.508901i	$-0.169948\pi$
$68$	159949.	−	368701.i	0.0616878	−	0.142198i
$69$	−838901.	+	2.07643e6i	−0.307425	+	0.760931i
$70$	312009.	−	1.50320e6i	0.108724	−	0.523810i
$71$	168073.			0.0557307			0.0278654	−	0.999612i	$-0.491129\pi$
$71$	168073.			0.0557307			0.0278654	+	0.999612i	$0.491129\pi$
$72$	3.11077e6	−	594734.i	0.982210	−	0.187784i
$73$	−341826.			−0.102843			−0.0514215	−	0.998677i	$-0.516375\pi$
$73$	−341826.			−0.102843			−0.0514215	+	0.998677i	$0.516375\pi$
$74$	−745719.	+	3.59274e6i	−0.213926	+	1.03066i
$75$	964343.	−	2.38692e6i	0.263947	−	0.653316i
$76$	−874615.	+	2.01610e6i	−0.228544	+	0.526822i
$77$		−	6.87289e6i		−	1.71562i
$78$	−2.45687e6	−	1.64009e6i	−0.586207	−	0.391325i
$79$			3.19089e6i			0.728144i	0.931371	+	0.364072i	$0.118614\pi$
$79$			3.19089e6i			0.728144i	−0.931371	+	0.364072i	$0.881386\pi$
$80$	−1.81741e6	+	1.70047e6i	−0.396860	+	0.371324i
$81$	167164.	+	4.78005e6i	0.0349499	+	0.999389i
$82$	3.57562e6	+	742166.i	0.716148	+	0.148646i
$83$	2.25902e6			0.433658			0.216829	−	0.976210i	$-0.430429\pi$
$83$	2.25902e6			0.433658			0.216829	+	0.976210i	$0.430429\pi$
$84$	3.75110e6	+	3.81065e6i	0.690527	+	0.701491i
$85$	−476973.			−0.0842418
$86$	−4.63401e6	−	961849.i	−0.785620	−	0.163066i
$87$	8.87316e6	+	3.58486e6i	1.44464	+	0.583653i
$88$	−6.41918e6	+	9.10720e6i	−1.00413	+	1.42461i
$89$		−	4.66598e6i		−	0.701581i	−0.936454	−	0.350791i	$-0.885913\pi$
$89$		−	4.66598e6i		−	0.701581i	0.936454	−	0.350791i	$-0.114087\pi$
$90$	−2.11680e6	−	3.10597e6i	−0.306077	−	0.449106i
$91$		−	4.98733e6i		−	0.693782i
$92$	5.62329e6	+	2.43947e6i	0.752892	+	0.326617i
$93$	5.58898e6	+	2.25801e6i	0.720514	+	0.291096i
$94$	1.50469e6	−	7.24931e6i	0.186853	−	0.900221i
$95$	2.60814e6			0.312103
$96$	−1.41145e6	−	8.55293e6i	−0.162823	−	0.986655i
$97$	−5.57244e6			−0.619933			−0.309966	−	0.950748i	$-0.600318\pi$
$97$	−5.57244e6			−0.619933			−0.309966	+	0.950748i	$0.600318\pi$
$98$	58856.6	−	283560.i	0.00631690	−	0.0304337i
$99$	−1.21045e7	−	1.16886e7i	−1.25379	−	1.21071i
$100$	−6.46415e6	−	2.80425e6i	−0.646415	−	0.280425i
$101$			8.71015e6i			0.841203i	0.907246	+	0.420601i	$0.138181\pi$
$101$			8.71015e6i			0.841203i	−0.907246	+	0.420601i	$0.861819\pi$
$102$	922352.	−	1.38169e6i	0.0860589	−	0.128917i
$103$			9.99180e6i			0.900976i	0.892782	+	0.450488i	$0.148750\pi$
$103$			9.99180e6i			0.900976i	−0.892782	+	0.450488i	$0.851250\pi$
$104$	−4.65809e6	+	6.60866e6i	−0.406061	+	0.576098i
$105$	2.37716e6	−	5.88388e6i	0.200399	−	0.496023i
$106$	−561237.	−	116492.i	−0.0457695	−	0.00950006i
$107$	−1.40125e7			−1.10579			−0.552893	−	0.833252i	$-0.686476\pi$
$107$	−1.40125e7			−1.10579			−0.552893	+	0.833252i	$0.686476\pi$
$108$	1.30907e7	−	125711.i	0.999954	−	0.00960262i
$109$	−8.05294e6			−0.595609			−0.297805	−	0.954627i	$-0.596254\pi$
$109$	−8.05294e6			−0.595609			−0.297805	+	0.954627i	$0.596254\pi$
$110$	1.29474e7	+	2.68741e6i	0.927490	+	0.192513i
$111$	−5.68154e6	+	1.40628e7i	−0.394308	+	0.975982i
$112$	1.06870e7	−	9.99929e6i	0.718771	−	0.672522i
$113$			2.48582e6i			0.162067i	0.996711	+	0.0810337i	$0.0258221\pi$
$113$			2.48582e6i			0.162067i	−0.996711	+	0.0810337i	$0.974178\pi$
$114$	−5.04351e6	+	7.55521e6i	−0.318835	+	0.477617i
$115$		−	7.27461e6i		−	0.446033i
$116$	1.04245e7	−	2.40299e7i	0.620089	−	1.42938i
$117$	−8.78365e6	−	8.48184e6i	−0.507019	−	0.489598i
$118$	−4.45630e6	+	2.14696e7i	−0.249682	+	1.20292i
$119$	2.80476e6			0.152574
$120$	−8.64540e6	+	5.57645e6i	−0.456721	+	0.294593i
$121$	3.97107e7			2.03779
$122$	3.15881e6	−	1.52186e7i	0.157494	−	0.758778i
$123$	1.39958e7	+	5.65447e6i	0.678157	+	0.273983i
$124$	6.56616e6	−	1.51358e7i	0.309269	−	0.712903i
$125$			2.02303e7i			0.926441i
$126$	1.24475e7	+	1.82641e7i	0.554351	+	0.813396i
$127$			1.33866e7i			0.579905i	0.957041	+	0.289952i	$0.0936395\pi$
$127$			1.33866e7i			0.579905i	−0.957041	+	0.289952i	$0.906360\pi$
$128$	−2.35004e7	+	3.26852e6i	−0.990466	+	0.137758i
$129$	−1.81386e7	−	7.32821e6i	−0.743943	−	0.300562i
$130$	9.39533e6	+	1.95012e6i	0.375068	+	0.0778503i
$131$	1.08402e7			0.421298			0.210649	−	0.977562i	$-0.432442\pi$
$131$	1.08402e7			0.421298			0.210649	+	0.977562i	$0.432442\pi$
$132$	−3.28221e7	+	3.23091e7i	−1.24210	+	1.22269i
$133$	−1.53367e7			−0.565264
$134$	−2.77569e7	−	5.76130e6i	−0.996561	−	0.206849i
$135$	−6.31987e6	−	1.41932e7i	−0.221075	−	0.496493i
$136$	−3.71656e6	−	2.61960e6i	−0.126694	−	0.0892995i
$137$		−	5.25035e6i		−	0.174448i	−0.996189	−	0.0872240i	$-0.972200\pi$
$137$		−	5.25035e6i		−	0.174448i	0.996189	−	0.0872240i	$-0.0277996\pi$
$138$	2.10730e7	+	1.40673e7i	0.682572	+	0.455654i
$139$		−	5.35708e7i		−	1.69191i	−0.533256	−	0.845954i	$-0.679032\pi$
$139$		−	5.35708e7i		−	1.69191i	0.533256	−	0.845954i	$-0.320968\pi$
$140$	−1.59345e7	−	6.91263e6i	−0.490783	−	0.212909i
$141$	1.14640e7	−	2.83755e7i	0.344406	−	0.852465i
$142$	386451.	−	1.86185e6i	0.0113262	−	0.0545677i
$143$	4.29571e7			1.22845
$144$	564380.	−	3.58274e7i	0.0157508	−	0.999876i
$145$	−3.10864e7			−0.846804
$146$	−785960.	+	3.78661e6i	−0.0209009	+	0.100697i
$147$	448421.	−	1.10992e6i	0.0116433	−	0.0288192i
$148$	3.80843e7	+	1.65216e7i	0.965672	+	0.418924i
$149$			1.81718e7i			0.450035i	0.974355	+	0.225018i	$0.0722440\pi$
$149$			1.81718e7i			0.450035i	−0.974355	+	0.225018i	$0.927756\pi$
$150$	−2.42240e7	−	1.61709e7i	−0.586040	−	0.391213i
$151$			2.62559e7i			0.620595i	0.950640	+	0.310297i	$0.100429\pi$
$151$			2.62559e7i			0.620595i	−0.950640	+	0.310297i	$0.899571\pi$
$152$	2.03225e7	+	1.43243e7i	0.469380	+	0.330841i
$153$	4.76999e6	−	4.93972e6i	0.107671	−	0.111502i
$154$	−7.61352e7	−	1.58028e7i	−1.67982	−	0.348669i
$155$	−1.95806e7			−0.422342
$156$	−2.38174e7	+	2.34452e7i	−0.502294	+	0.494444i
$157$	3.87538e7			0.799218			0.399609	−	0.916686i	$-0.369146\pi$
$157$	3.87538e7			0.799218			0.399609	+	0.916686i	$0.369146\pi$
$158$	3.53474e7	+	7.33682e6i	0.712949	+	0.147982i
$159$	−2.19681e6	−	887539.i	−0.0433415	−	0.0175105i
$160$	1.46583e7	+	2.40424e7i	0.282920	+	0.464042i
$161$			4.27771e7i			0.807831i
$162$	5.33358e7	+	9.13899e6i	0.985635	+	0.168887i
$163$			7.71205e7i			1.39480i	0.716680	+	0.697402i	$0.245661\pi$
$163$			7.71205e7i			1.39480i	−0.716680	+	0.697402i	$0.754339\pi$
$164$	1.64428e7	−	3.79028e7i	0.291087	−	0.670993i
$165$	5.06793e7	+	2.04750e7i	0.878288	+	0.354838i
$166$	5.19417e6	−	2.50246e7i	0.0881329	−	0.424608i
$167$	−7.67209e7			−1.27469			−0.637347	−	0.770577i	$-0.719968\pi$
$167$	−7.67209e7			−1.27469			−0.637347	+	0.770577i	$0.719968\pi$
$168$	5.08378e7	−	3.27913e7i	0.827188	−	0.533552i
$169$	−3.15767e7			−0.503225
$170$	−1.09670e6	+	5.28372e6i	−0.0171206	+	0.0824838i
$171$	−2.60828e7	+	2.70109e7i	−0.398904	+	0.413098i
$172$	−2.13100e7	+	4.91221e7i	−0.319325	+	0.736085i
$173$		−	1.31412e8i		−	1.92963i	−0.262924	−	0.964816i	$-0.584687\pi$
$173$		−	1.31412e8i		−	1.92963i	0.262924	−	0.964816i	$-0.415313\pi$
$174$	6.01137e7	−	9.00506e7i	0.865069	−	1.29588i
$175$		−	4.91736e7i		−	0.693584i
$176$	8.61263e7	+	9.20493e7i	1.19081	+	1.27270i
$177$	−3.39519e7	+	8.40370e7i	−0.460212	+	1.13911i
$178$	−5.16879e7	−	1.07285e7i	−0.686940	−	0.142583i
$179$	1.24203e6			0.0161862			0.00809311	−	0.999967i	$-0.497424\pi$
$179$	1.24203e6			0.0161862			0.00809311	+	0.999967i	$0.497424\pi$
$180$	−3.92739e7	+	1.63075e7i	−0.501938	+	0.208417i
$181$	−8.99706e7			−1.12778			−0.563892	−	0.825849i	$-0.690696\pi$
$181$	−8.99706e7			−1.12778			−0.563892	+	0.825849i	$0.690696\pi$
$182$	−5.52476e7	−	1.14674e7i	−0.679303	−	0.140998i
$183$	2.40666e7	−	5.95691e7i	0.290292	−	0.718525i
$184$	3.99531e7	−	5.66835e7i	0.472812	−	0.670801i
$185$		−	4.92680e7i		−	0.572089i
$186$	3.78641e7	−	5.67207e7i	0.431452	−	0.646318i
$187$			2.41581e7i			0.270157i
$188$	−7.68452e7	−	3.33367e7i	−0.843460	−	0.365906i
$189$	3.71629e7	+	8.34608e7i	0.400400	+	0.899221i
$190$	5.99689e6	−	2.88919e7i	0.0634291	−	0.305590i
$191$	−4.55873e7			−0.473398			−0.236699	−	0.971583i	$-0.576066\pi$
$191$	−4.55873e7			−0.473398			−0.236699	+	0.971583i	$0.576066\pi$
$192$	−9.79912e7	−	4.03027e6i	−0.999155	−	0.0410941i
$193$	1.60369e8			1.60572			0.802861	−	0.596167i	$-0.203310\pi$
$193$	1.60369e8			1.60572			0.802861	+	0.596167i	$0.203310\pi$
$194$	−1.28127e7	+	6.17293e7i	−0.125990	+	0.606995i
$195$	3.67755e7	+	1.48577e7i	0.355171	+	0.143493i
$196$	−3.00584e6	−	1.30398e6i	−0.0285147	−	0.0123701i
$197$			4.80833e7i			0.448088i	0.974579	+	0.224044i	$0.0719259\pi$
$197$			4.80833e7i			0.448088i	−0.974579	+	0.224044i	$0.928074\pi$
$198$	−1.57313e8	+	1.07213e8i	−1.44025	+	0.981567i
$199$		−	1.49813e8i		−	1.34761i	−0.738911	−	0.673803i	$-0.764659\pi$
$199$		−	1.49813e8i		−	1.34761i	0.738911	−	0.673803i	$-0.235341\pi$
$200$	−4.59274e7	+	6.51594e7i	−0.405945	+	0.575933i
$201$	−1.08647e8	−	4.38946e7i	−0.943694	−	0.381263i
$202$	9.64875e7	+	2.00272e7i	0.823647	+	0.170959i
$203$	1.82798e8			1.53368
$204$	−1.31850e7	−	1.33944e7i	−0.108736	−	0.110463i
$205$	−4.90332e7			−0.397514
$206$	1.10685e8	+	2.29741e7i	0.882173	+	0.183107i
$207$	7.53387e7	+	7.27500e7i	0.590366	+	0.570082i
$208$	6.24977e7	+	6.67957e7i	0.481551	+	0.514668i
$209$		−	1.32099e8i		−	1.00089i
$210$	−5.97135e7	−	3.98620e7i	−0.444944	−	0.297024i
$211$			1.44351e8i			1.05787i	0.848663	+	0.528934i	$0.177408\pi$
$211$			1.44351e8i			1.05787i	−0.848663	+	0.528934i	$0.822592\pi$
$212$	−2.58091e6	+	5.94931e6i	−0.0186036	+	0.0428836i
$213$	2.94432e6	−	7.28771e6i	0.0208764	−	0.0516729i
$214$	−3.22189e7	+	1.55225e8i	−0.224731	+	1.08271i
$215$	6.35472e7			0.436076
$216$	2.87069e7	−	1.45303e8i	0.193820	−	0.981037i
$217$	1.15140e8			0.764923
$218$	−1.85161e7	+	8.92072e7i	−0.121047	+	0.583179i
$219$	−5.98813e6	+	1.48217e7i	−0.0385245	+	0.0953549i
$220$	5.95401e7	−	1.37247e8i	0.376990	−	0.869010i
$221$			1.75303e7i			0.109249i
$222$	1.42719e8	+	9.52724e7i	0.875478	+	0.584429i
$223$		−	1.12778e8i		−	0.681014i	−0.940242	−	0.340507i	$-0.889401\pi$
$223$		−	1.12778e8i		−	0.681014i	0.940242	−	0.340507i	$-0.110599\pi$
$224$	−8.61957e7	−	1.41377e8i	−0.512410	−	0.840449i
$225$	−8.66042e7	−	8.36285e7i	−0.506874	−	0.489458i
$226$	2.75370e7	+	5.71565e6i	0.158685	+	0.0329372i
$227$	−1.17206e8			−0.665060			−0.332530	−	0.943093i	$-0.607902\pi$
$227$	−1.17206e8			−0.665060			−0.332530	+	0.943093i	$0.607902\pi$
$228$	7.20971e7	+	7.32417e7i	0.402852	+	0.409248i
$229$	−9.20182e7			−0.506348			−0.253174	−	0.967421i	$-0.581475\pi$
$229$	−9.20182e7			−0.506348			−0.253174	+	0.967421i	$0.581475\pi$
$230$	−8.05852e7	−	1.67265e7i	−0.436725	−	0.0906479i
$231$	−2.98011e8	−	1.20400e8i	−1.59071	−	0.642664i
$232$	−2.42224e8	−	1.70731e8i	−1.27353	−	0.897644i
$233$			3.10484e8i			1.60803i	0.594611	+	0.804014i	$0.297306\pi$
$233$			3.10484e8i			1.60803i	−0.594611	+	0.804014i	$0.702694\pi$
$234$	−1.14155e8	+	7.77994e7i	−0.582423	+	0.396936i
$235$			9.94113e7i			0.499687i
$236$	2.27585e8	+	9.87301e7i	1.12707	+	0.488942i
$237$	1.38358e8	+	5.58983e7i	0.675127	+	0.272759i
$238$	6.44898e6	−	3.10700e7i	0.0310079	−	0.149390i
$239$	−2.17330e8			−1.02974			−0.514870	−	0.857268i	$-0.672160\pi$
$239$	−2.17330e8			−1.02974			−0.514870	+	0.857268i	$0.672160\pi$
$240$	4.18953e7	+	1.08592e8i	0.195626	+	0.507060i
$241$	8.72196e7			0.401379			0.200689	−	0.979655i	$-0.435682\pi$
$241$	8.72196e7			0.401379			0.200689	+	0.979655i	$0.435682\pi$
$242$	9.13068e7	−	4.39899e8i	0.414142	−	1.99526i
$243$	2.10193e8	+	7.64889e7i	0.939714	+	0.341961i
$244$	−1.61322e8	−	6.99842e7i	−0.710935	−	0.308415i
$245$			3.88852e6i			0.0168929i
$246$	9.48185e7	−	1.42039e8i	0.406088	−	0.608322i
$247$		−	9.58577e7i		−	0.404751i
$248$	−1.52571e8	−	1.07539e8i	−0.635172	−	0.447699i
$249$	3.95737e7	−	9.79520e7i	0.162446	−	0.402083i
$250$	2.24103e8	+	4.65156e7i	0.907107	+	0.188282i
$251$	−1.45283e8			−0.579906			−0.289953	−	0.957041i	$-0.593640\pi$
$251$	−1.45283e8			−0.579906			−0.289953	+	0.957041i	$0.593640\pi$
$252$	2.30943e8	−	9.58935e7i	0.909082	−	0.377474i
$253$	−3.68449e8			−1.43039
$254$	1.48291e8	+	3.07798e7i	0.567803	+	0.117855i
$255$	−8.35565e6	+	2.06817e7i	−0.0315566	+	0.0781081i
$256$	−1.78271e7	+	2.67843e8i	−0.0664110	+	0.997792i
$257$		−	1.34994e8i		−	0.496077i	−0.968750	−	0.248039i	$-0.920214\pi$
$257$		−	1.34994e8i		−	0.496077i	0.968750	−	0.248039i	$-0.0797860\pi$
$258$	−1.22885e8	+	1.84082e8i	−0.445482	+	0.667334i
$259$			2.89712e8i			1.03614i
$260$	4.32054e7	−	9.95938e7i	0.152451	−	0.351419i
$261$	3.10881e8	−	3.21943e8i	1.08231	−	1.12082i
$262$	2.49250e7	−	1.20084e8i	0.0856210	−	0.412506i
$263$	2.87053e8			0.973008			0.486504	−	0.873678i	$-0.338272\pi$
$263$	2.87053e8			0.973008			0.486504	+	0.873678i	$0.338272\pi$
$264$	2.82440e8	+	4.37878e8i	0.944739	+	1.46467i
$265$	7.69637e6			0.0254054
$266$	−3.52637e7	+	1.69894e8i	−0.114879	+	0.553468i
$267$	−2.02318e8	−	8.17390e7i	−0.650498	−	0.262809i
$268$	−1.27643e8	+	2.94233e8i	−0.405065	+	0.933725i
$269$			5.19096e8i			1.62598i	0.582278	+	0.812990i	$0.302162\pi$
$269$			5.19096e8i			1.62598i	−0.582278	+	0.812990i	$0.697838\pi$
$270$	−1.71758e8	+	3.73745e7i	−0.531061	+	0.115559i
$271$			2.39573e8i			0.731214i	0.930769	+	0.365607i	$0.119139\pi$
$271$			2.39573e8i			0.731214i	−0.930769	+	0.365607i	$0.880861\pi$
$272$	−3.75644e7	+	3.51473e7i	−0.113184	+	0.105901i
$273$	−2.16252e8	−	8.73684e7i	−0.643267	−	0.259887i
$274$	−5.81613e7	−	1.20721e7i	−0.170807	−	0.0354533i
$275$	4.23544e8			1.22810
$276$	2.04285e8	−	2.01093e8i	0.584865	−	0.575724i
$277$	1.04590e8			0.295672			0.147836	−	0.989012i	$-0.452769\pi$
$277$	1.04590e8			0.295672			0.147836	+	0.989012i	$0.452769\pi$
$278$	−5.93436e8	−	1.23175e8i	−1.65660	−	0.343849i
$279$	1.95816e8	−	2.02784e8i	0.539802	−	0.559009i
$280$	−1.13213e8	+	1.60621e8i	−0.308209	+	0.437271i
$281$			6.58421e7i			0.177024i	0.996075	+	0.0885119i	$0.0282111\pi$
$281$			6.58421e7i			0.177024i	−0.996075	+	0.0885119i	$0.971789\pi$
$282$	−2.87973e8	−	1.92238e8i	−0.764680	−	0.510466i
$283$		−	6.76985e8i		−	1.77552i	−0.460303	−	0.887762i	$-0.652259\pi$
$283$		−	6.76985e8i		−	1.77552i	0.460303	−	0.887762i	$-0.347741\pi$
$284$	−1.97363e7	−	8.56190e6i	−0.0511270	−	0.0221797i
$285$	4.56896e7	−	1.13090e8i	0.116912	−	0.289378i
$286$	9.87712e7	−	4.75861e8i	0.249660	−	1.20282i
$287$	2.88332e8			0.719955
$288$	−3.95584e8	−	8.86299e7i	−0.975808	−	0.218628i
$289$	4.00480e8			0.975974
$290$	−7.14770e7	+	3.44363e8i	−0.172097	+	0.829131i
$291$	−9.76184e7	+	2.41623e8i	−0.232224	+	0.574794i
$292$	4.01394e7	+	1.74131e7i	0.0943476	+	0.0409295i
$293$		−	5.13491e8i		−	1.19260i	−0.802760	−	0.596302i	$-0.796636\pi$
$293$		−	5.13491e8i		−	1.19260i	0.802760	−	0.596302i	$-0.203364\pi$
$294$	−1.12642e7	−	7.51947e6i	−0.0258515	−	0.0172573i
$295$		−	2.94417e8i		−	0.667708i
$296$	2.70586e8	−	3.83894e8i	0.606436	−	0.860380i
$297$	−7.18868e8	+	3.20093e8i	−1.59221	+	0.708972i
$298$	2.01300e8	+	4.17825e7i	0.440643	+	0.0914613i
$299$	−2.67366e8			−0.578438
$300$	−2.34833e8	+	2.31162e8i	−0.502151	+	0.494303i
$301$	−3.73678e8			−0.789797
$302$	2.90853e8	+	6.03703e7i	0.607643	+	0.126124i
$303$	3.77675e8	+	1.52585e8i	0.779954	+	0.315110i
$304$	2.05406e8	−	1.92189e8i	0.419329	−	0.392348i
$305$			2.08696e8i			0.421176i
$306$	−4.37526e7	−	6.41980e7i	−0.0872929	−	0.128084i
$307$		−	1.35757e8i		−	0.267779i	−0.990996	−	0.133890i	$-0.957253\pi$
$307$		−	1.35757e8i		−	0.267779i	0.990996	−	0.133890i	$-0.0427468\pi$
$308$	−3.50115e8	+	8.07059e8i	−0.682784	+	1.57390i
$309$	4.33247e8	+	1.75037e8i	0.835375	+	0.337501i
$310$	−4.50216e7	+	2.16906e8i	−0.0858332	+	0.413528i
$311$	−1.00476e9			−1.89408			−0.947042	−	0.321109i	$-0.895944\pi$
$311$	−1.00476e9			−1.89408			−0.947042	+	0.321109i	$0.895944\pi$
$312$	2.04953e8	+	3.17747e8i	0.382043	+	0.592298i
$313$	2.92615e8			0.539376			0.269688	−	0.962948i	$-0.413079\pi$
$313$	2.92615e8			0.539376			0.269688	+	0.962948i	$0.413079\pi$
$314$	8.91066e7	−	4.29299e8i	0.162426	−	0.782539i
$315$	−2.13484e8	−	2.06149e8i	−0.384838	−	0.371615i
$316$	1.62549e8	−	3.74695e8i	0.289787	−	0.667995i
$317$		−	7.38044e8i		−	1.30129i	−0.759381	−	0.650646i	$-0.774498\pi$
$317$		−	7.38044e8i		−	1.30129i	0.759381	−	0.650646i	$-0.225502\pi$
$318$	−1.48829e7	+	2.22947e7i	−0.0259534	+	0.0388783i
$319$			1.57449e9i			2.71563i
$320$	3.00036e8	−	1.07098e8i	0.511857	−	0.182708i
$321$	−2.45471e8	+	6.07585e8i	−0.414222	+	1.02527i
$322$	4.73867e8	+	9.83573e7i	0.790972	+	0.164177i
$323$	5.39082e7			0.0890114
$324$	2.23873e8	−	5.69819e8i	0.365674	−	0.930743i
$325$	3.07345e8			0.496632
$326$	8.54310e8	+	1.77323e8i	1.36570	+	0.283468i
$327$	−1.41072e8	+	3.49178e8i	−0.223112	+	0.552242i
$328$	−3.82065e8	−	2.69297e8i	−0.597832	−	0.421379i
$329$		−	5.84571e8i		−	0.905007i
$330$	3.43341e8	−	5.14327e8i	0.525929	−	0.787844i
$331$		−	5.26161e8i		−	0.797481i	−0.917064	−	0.398740i	$-0.869447\pi$
$331$		−	5.26161e8i		−	0.797481i	0.917064	−	0.398740i	$-0.130553\pi$
$332$	−2.65269e8	−	1.15078e8i	−0.397835	−	0.172587i
$333$	5.10238e8	+	4.92707e8i	0.757213	+	0.731196i
$334$	−1.76404e8	+	8.49883e8i	−0.259058	+	1.24809i
$335$	3.80636e8			0.553163
$336$	−2.46358e8	−	6.38558e8i	−0.354306	−	0.918360i
$337$	1.39316e8			0.198288			0.0991442	−	0.995073i	$-0.468389\pi$
$337$	1.39316e8			0.198288			0.0991442	+	0.995073i	$0.468389\pi$
$338$	−7.26042e7	+	3.49794e8i	−0.102271	+	0.492724i
$339$	1.07786e8	+	4.35468e7i	0.150267	+	0.0607096i
$340$	5.60093e7	+	2.42977e7i	0.0772829	+	0.0335266i
$341$			9.91730e8i			1.35442i
$342$	2.39244e8	+	3.51041e8i	0.323407	+	0.474533i
$343$		−	7.58519e8i		−	1.01493i
$344$	4.95157e8	+	3.49010e8i	0.655826	+	0.462257i
$345$	−3.15429e8	−	1.27437e8i	−0.413557	−	0.167082i
$346$	−1.45573e9	−	3.02156e8i	−1.88936	−	0.392162i
$347$	−7.36166e8			−0.945851			−0.472925	−	0.881102i	$-0.656802\pi$
$347$	−7.36166e8			−0.945851			−0.472925	+	0.881102i	$0.656802\pi$
$348$	−8.59325e8	−	8.72969e8i	−1.09303	−	1.11038i
$349$	−1.08415e9			−1.36521			−0.682604	−	0.730788i	$-0.739153\pi$
$349$	−1.08415e9			−1.36521			−0.682604	+	0.730788i	$0.739153\pi$
$350$	−5.44725e8	−	1.13065e8i	−0.679109	−	0.140958i
$351$	−5.21648e8	+	2.32276e8i	−0.643876	+	0.286701i
$352$	1.21772e9	−	7.42424e8i	1.48815	−	0.907304i
$353$		−	1.04425e9i		−	1.26356i	−0.775150	−	0.631778i	$-0.782326\pi$
$353$		−	1.04425e9i		−	1.26356i	0.775150	−	0.631778i	$-0.217674\pi$
$354$	8.52863e8	+	5.69332e8i	1.02180	+	0.682110i
$355$			2.55319e7i			0.0302890i
$356$	−2.37692e8	+	5.47910e8i	−0.279215	+	0.643627i
$357$	4.91340e7	−	1.21615e8i	0.0571535	−	0.141465i
$358$	2.85579e6	−	1.37587e7i	0.00328955	−	0.0158484i
$359$	8.69582e8			0.991928			0.495964	−	0.868343i	$-0.334815\pi$
$359$	8.69582e8			0.991928			0.495964	+	0.868343i	$0.334815\pi$
$360$	9.03457e7	+	4.72556e8i	0.102058	+	0.533820i
$361$	5.99096e8			0.670226
$362$	−2.06870e8	+	9.96659e8i	−0.229201	+	1.10425i
$363$	6.95655e8	−	1.72187e9i	0.763345	−	1.88941i
$364$	−2.54062e8	+	5.85644e8i	−0.276112	+	0.636472i
$365$		−	5.19266e7i		−	0.0558940i
$366$	−6.04546e8	−	4.03567e8i	−0.644534	−	0.430261i
$367$			7.56352e8i			0.798716i	0.916795	+	0.399358i	$0.130767\pi$
$367$			7.56352e8i			0.798716i	−0.916795	+	0.399358i	$0.869233\pi$
$368$	−5.36052e8	−	5.72917e8i	−0.560712	−	0.599273i
$369$	4.90359e8	−	5.07807e8i	0.508068	−	0.526147i
$370$	−5.45771e8	−	1.13282e8i	−0.560150	−	0.116266i
$371$	−4.52572e7			−0.0460128
$372$	−5.41268e8	−	5.49861e8i	−0.545145	−	0.553800i
$373$	−1.86017e9			−1.85597			−0.927985	−	0.372617i	$-0.878461\pi$
$373$	−1.86017e9			−1.85597			−0.927985	+	0.372617i	$0.878461\pi$
$374$	2.67613e8	+	5.55466e7i	0.264519	+	0.0549044i
$375$	8.77193e8	+	3.54396e8i	0.858986	+	0.347040i
$376$	−5.45980e8	+	7.74609e8i	−0.529687	+	0.751494i
$377$			1.14253e9i			1.09818i
$378$	1.00999e9	−	2.19775e8i	0.961828	−	0.209294i
$379$		−	5.20287e8i		−	0.490914i	−0.969407	−	0.245457i	$-0.921062\pi$
$379$		−	5.20287e8i		−	0.490914i	0.969407	−	0.245457i	$-0.0789380\pi$
$380$	−3.06264e8	−	1.32862e8i	−0.286322	−	0.124211i
$381$	5.80447e8	+	2.34507e8i	0.537681	+	0.217229i
$382$	−1.04819e8	+	5.04998e8i	−0.0962094	+	0.463519i
$383$	1.94374e9			1.76784			0.883920	−	0.467638i	$-0.154895\pi$
$383$	1.94374e9			1.76784			0.883920	+	0.467638i	$0.154895\pi$
$384$	−2.69957e8	+	1.07624e9i	−0.243296	+	0.969952i
$385$	1.04406e9			0.932421
$386$	3.68737e8	−	1.77650e9i	0.326333	−	1.57221i
$387$	−6.35507e8	+	6.58120e8i	−0.557355	+	0.577187i
$388$	6.54352e8	+	2.83868e8i	0.568722	+	0.246721i
$389$		−	8.69533e8i		−	0.748967i	−0.927234	−	0.374483i	$-0.877820\pi$
$389$		−	8.69533e8i		−	0.748967i	0.927234	−	0.374483i	$-0.122180\pi$
$390$	2.49146e8	−	3.73222e8i	0.212681	−	0.318597i
$391$		−	1.50360e8i		−	0.127208i
$392$	−2.13563e7	+	3.02992e7i	−0.0179071	+	0.0254057i
$393$	1.89900e8	−	4.70036e8i	0.157816	−	0.390623i
$394$	5.32648e8	+	1.10558e8i	0.438736	+	0.0910654i
$395$	−4.84727e8			−0.395738
$396$	8.25954e8	+	1.98917e9i	0.668379	+	1.60968i
$397$	1.13274e9			0.908581			0.454290	−	0.890854i	$-0.349893\pi$
$397$	1.13274e9			0.908581			0.454290	+	0.890854i	$0.349893\pi$
$398$	−1.65957e9	−	3.44465e8i	−1.31948	−	0.273876i
$399$	−2.68670e8	+	6.65005e8i	−0.211745	+	0.524107i
$400$	6.16209e8	+	6.58586e8i	0.481413	+	0.514521i
$401$			5.49064e8i			0.425224i	0.977137	+	0.212612i	$0.0681970\pi$
$401$			5.49064e8i			0.425224i	−0.977137	+	0.212612i	$0.931803\pi$
$402$	−7.36059e8	+	1.10262e9i	−0.565095	+	0.846515i
$403$			7.19651e8i			0.547714i
$404$	4.43708e8	−	1.02280e9i	0.334782	−	0.771714i
$405$	−7.26135e8	+	2.53938e7i	−0.543156	+	0.0189948i
$406$	4.20308e8	−	2.02497e9i	0.311693	−	1.50168i
$407$	−2.49536e9			−1.83465
$408$	−1.78694e8	+	1.15261e8i	−0.130256	+	0.0840177i
$409$	−5.47741e8			−0.395862			−0.197931	−	0.980216i	$-0.563422\pi$
$409$	−5.47741e8			−0.395862			−0.197931	+	0.980216i	$0.563422\pi$
$410$	−1.12742e8	+	5.43171e8i	−0.0807872	+	0.389218i
$411$	−2.27657e8	−	9.19760e7i	−0.161746	−	0.0653473i
$412$	5.08997e8	−	1.17330e9i	0.358571	−	0.826550i
$413$			1.73127e9i			1.20932i
$414$	9.79122e8	−	6.67297e8i	0.678165	−	0.462188i
$415$			3.43167e8i			0.235688i
$416$	8.83637e8	−	5.38741e8i	0.601793	−	0.366905i
$417$	−2.32285e9	−	9.38458e8i	−1.56872	−	0.633780i
$418$	−1.46334e9	−	3.03735e8i	−0.980003	−	0.203412i
$419$	3.16638e8			0.210288			0.105144	−	0.994457i	$-0.466470\pi$
$419$	3.16638e8			0.210288			0.105144	+	0.994457i	$0.466470\pi$
$420$	−5.78875e8	+	5.69828e8i	−0.381252	+	0.375293i
$421$	8.55366e8			0.558682			0.279341	−	0.960192i	$-0.409884\pi$
$421$	8.55366e8			0.558682			0.279341	+	0.960192i	$0.409884\pi$
$422$	1.59906e9	+	3.31906e8i	1.03579	+	0.214992i
$423$	−1.02954e9	−	9.94168e8i	−0.661383	−	0.638658i
$424$	5.99698e7	+	4.22695e7i	0.0382078	+	0.0269306i
$425$			1.72844e8i			0.109218i
$426$	−7.39605e7	−	4.93727e7i	−0.0463518	−	0.0309423i
$427$		−	1.22720e9i		−	0.762812i
$428$	1.64543e9	+	7.13816e8i	1.01444	+	0.440081i
$429$	7.52525e8	−	1.86263e9i	0.460172	−	1.13901i
$430$	1.46114e8	−	7.03950e8i	0.0886242	−	0.426975i
$431$	−8.62621e8			−0.518979			−0.259489	−	0.965746i	$-0.583554\pi$
$431$	−8.62621e8			−0.518979			−0.259489	+	0.965746i	$0.583554\pi$
$432$	−1.54360e9	−	6.52098e8i	−0.921173	−	0.389152i
$433$	−5.88264e7			−0.0348229			−0.0174114	−	0.999848i	$-0.505543\pi$
$433$	−5.88264e7			−0.0348229			−0.0174114	+	0.999848i	$0.505543\pi$
$434$	2.64742e8	−	1.27548e9i	0.155456	−	0.748960i
$435$	−5.44574e8	+	1.34792e9i	−0.317208	+	0.785147i
$436$	9.45628e8	+	4.10228e8i	0.546408	+	0.237041i
$437$			8.22186e8i			0.471287i
$438$	1.50420e8	+	1.00414e8i	0.0855355	+	0.0570996i
$439$		−	1.74683e9i		−	0.985425i	−0.870192	−	0.492713i	$-0.836005\pi$
$439$		−	1.74683e9i		−	0.985425i	0.870192	−	0.492713i	$-0.163995\pi$
$440$	−1.38347e9	−	9.75134e8i	−0.774258	−	0.545733i
$441$	−4.02711e7	−	3.88874e7i	−0.0223593	−	0.0215910i
$442$	1.94194e8	+	4.03075e7i	0.106969	+	0.0222028i
$443$	9.63038e8			0.526297			0.263148	−	0.964755i	$-0.415239\pi$
$443$	9.63038e8			0.526297			0.263148	+	0.964755i	$0.415239\pi$
$444$	1.38354e9	−	1.36192e9i	0.750157	−	0.738433i
$445$	7.08807e8			0.381301
$446$	−1.24931e9	−	2.59310e8i	−0.666802	−	0.138403i
$447$	7.87936e8	+	3.18335e8i	0.417268	+	0.168581i
$448$	−1.76431e9	+	6.29773e8i	−0.927047	+	0.330911i
$449$			3.18511e9i			1.66059i	0.557326	+	0.830294i	$0.311827\pi$
$449$			3.18511e9i			1.66059i	−0.557326	+	0.830294i	$0.688173\pi$
$450$	−1.12553e9	+	7.67080e8i	−0.582256	+	0.396823i
$451$			2.48347e9i			1.27480i
$452$	1.26631e8	−	2.91901e8i	0.0644996	−	0.148680i
$453$	1.13847e9	+	4.59953e8i	0.575408	+	0.232472i
$454$	−2.69493e8	+	1.29837e9i	−0.135161	+	0.651181i
$455$	7.57623e8			0.377062
$456$	9.77115e8	−	6.30258e8i	0.482580	−	0.311273i
$457$	7.00152e8			0.343151			0.171576	−	0.985171i	$-0.445114\pi$
$457$	7.00152e8			0.343151			0.171576	+	0.985171i	$0.445114\pi$
$458$	−2.11577e8	+	1.01934e9i	−0.102906	+	0.495781i
$459$	−1.30627e8	−	2.93363e8i	−0.0630504	−	0.141599i
$460$	−3.70579e8	+	8.54231e8i	−0.177512	+	0.409188i
$461$		−	3.65644e9i		−	1.73822i	−0.494618	−	0.869110i	$-0.664692\pi$
$461$		−	3.65644e9i		−	1.73822i	0.494618	−	0.869110i	$-0.335308\pi$
$462$	−2.01896e9	+	3.02441e9i	−0.952534	+	1.42690i
$463$			1.45892e9i			0.683119i	0.939860	+	0.341560i	$0.110955\pi$
$463$			1.45892e9i			0.683119i	−0.939860	+	0.341560i	$0.889045\pi$
$464$	−2.44823e9	+	2.29070e9i	−1.13773	+	1.06452i
$465$	−3.43014e8	+	8.49020e8i	−0.158207	+	0.391591i
$466$	3.43942e9	+	7.13896e8i	1.57447	+	0.326802i
$467$	3.37921e9			1.53534			0.767672	−	0.640843i	$-0.221415\pi$
$467$	3.37921e9			1.53534			0.767672	+	0.640843i	$0.221415\pi$
$468$	5.99355e8	+	1.44344e9i	0.270286	+	0.650938i
$469$	−2.23827e9			−1.00186
$470$	1.10124e9	+	2.28577e8i	0.489259	+	0.101552i
$471$	6.78892e8	−	1.68038e9i	0.299383	−	0.741026i
$472$	1.61698e9	−	2.29409e9i	0.707795	−	1.00418i
$473$		−	3.21858e9i		−	1.39846i
$474$	9.37346e8	−	1.40415e9i	0.404274	−	0.605605i
$475$		−	9.45129e8i		−	0.404635i
$476$	−3.29353e8	−	1.42879e8i	−0.139971	−	0.0607215i
$477$	−7.69679e7	+	7.97066e7i	−0.0324710	+	0.0336264i
$478$	−4.99708e8	+	2.40750e9i	−0.209276	+	1.00825i
$479$	−9.51642e7			−0.0395639			−0.0197820	−	0.999804i	$-0.506297\pi$
$479$	−9.51642e7			−0.0395639			−0.0197820	+	0.999804i	$0.506297\pi$
$480$	1.29927e9	−	2.14413e8i	0.536235	−	0.0884924i
$481$	−1.81076e9			−0.741914
$482$	2.00544e8	−	9.66184e8i	0.0815728	−	0.393003i
$483$	1.85483e9	+	7.49372e8i	0.749012	+	0.302609i
$484$	−4.66309e9	−	2.02292e9i	−1.86945	−	0.810999i
$485$		−	8.46507e8i		−	0.336926i
$486$	1.33061e9	−	2.15256e9i	0.525804	−	0.850606i
$487$		−	3.29873e9i		−	1.29418i	−0.762412	−	0.647092i	$-0.775985\pi$
$487$		−	3.29873e9i		−	1.29418i	0.762412	−	0.647092i	$-0.224015\pi$
$488$	−1.14618e9	+	1.62615e9i	−0.446463	+	0.633419i
$489$	3.34397e9	+	1.35100e9i	1.29325	+	0.522486i
$490$	4.30755e7	+	8.94089e6i	0.0165403	+	0.00343316i
$491$	−2.42468e9			−0.924419			−0.462210	−	0.886771i	$-0.652943\pi$
$491$	−2.42468e9			−0.924419			−0.462210	+	0.886771i	$0.652943\pi$
$492$	−1.35543e9	−	1.37695e9i	−0.513097	−	0.521244i
$493$	−6.42532e8			−0.241507
$494$	−1.06187e9	−	2.20406e8i	−0.396304	−	0.0822581i
$495$	1.77561e9	−	1.83879e9i	0.658004	−	0.681418i
$496$	−1.54208e9	+	1.44286e9i	−0.567442	+	0.530930i
$497$		−	1.50136e8i		−	0.0548578i
$498$	−9.94081e8	−	6.63603e8i	−0.360677	−	0.240772i
$499$			1.79712e9i			0.647478i	0.946146	+	0.323739i	$0.104940\pi$
$499$			1.79712e9i			0.647478i	−0.946146	+	0.323739i	$0.895060\pi$
$500$	1.03056e9	−	2.37557e9i	0.368705	−	0.849911i
$501$	−1.34400e9	+	3.32664e9i	−0.477494	+	1.18188i
$502$	−3.34050e8	+	1.60939e9i	−0.117855	+	0.567804i
$503$	−2.04951e9			−0.718063			−0.359032	−	0.933325i	$-0.616893\pi$
$503$	−2.04951e9			−0.718063			−0.359032	+	0.933325i	$0.616893\pi$
$504$	−5.31262e8	−	2.77878e9i	−0.184843	−	0.966825i
$505$	−1.32315e9			−0.457184
$506$	−8.47175e8	+	4.08153e9i	−0.290701	+	1.40054i
$507$	−5.53162e8	+	1.36917e9i	−0.188506	+	0.466585i
$508$	6.81932e8	−	1.57194e9i	0.230791	−	0.532001i
$509$			2.00694e9i			0.674562i	0.941404	+	0.337281i	$0.109507\pi$
$509$			2.00694e9i			0.674562i	−0.941404	+	0.337281i	$0.890493\pi$
$510$	2.09892e8	+	1.40114e8i	0.0700647	+	0.0467720i
$511$			3.05345e8i			0.101232i
$512$	2.92607e9	+	8.13332e8i	0.963472	+	0.267808i
$513$	7.14281e8	+	1.60414e9i	0.233592	+	0.524603i
$514$	−1.49541e9	−	3.10392e8i	−0.485725	−	0.100818i
$515$	−1.51785e9			−0.489670
$516$	1.75664e9	+	1.78453e9i	0.562872	+	0.571808i
$517$	5.03505e9			1.60246
$518$	3.20931e9	+	6.66135e8i	1.01451	+	0.210575i
$519$	−5.69808e9	−	2.30209e9i	−1.78913	−	0.722831i
$520$	−1.00392e9	−	7.07608e8i	−0.313103	−	0.220689i
$521$		−	4.71335e9i		−	1.46015i	−0.683367	−	0.730075i	$-0.739485\pi$
$521$		−	4.71335e9i		−	1.46015i	0.683367	−	0.730075i	$-0.260515\pi$
$522$	−2.85155e9	−	4.18406e9i	−0.877473	−	1.28751i
$523$			2.80991e9i			0.858889i	0.903093	+	0.429444i	$0.141291\pi$
$523$			2.80991e9i			0.858889i	−0.903093	+	0.429444i	$0.858709\pi$
$524$	−1.27293e9	−	5.52218e8i	−0.386496	−	0.167668i
$525$	−2.13218e9	−	8.61427e8i	−0.643083	−	0.259813i
$526$	6.60021e8	−	3.17986e9i	0.197746	−	0.952703i
$527$	−4.04715e8			−0.120451
$528$	5.50005e9	−	2.12194e9i	1.62610	−	0.627356i
$529$	−1.11159e9			−0.326474
$530$	1.76963e7	−	8.52573e7i	0.00516317	−	0.0248752i
$531$	3.04910e9	+	2.94433e9i	0.883773	+	0.853407i
$532$	1.80094e9	+	7.81274e8i	0.518570	+	0.224964i
$533$			1.80213e9i			0.515516i
$534$	−1.37066e9	+	2.05326e9i	−0.389526	+	0.583512i
$535$		−	2.12863e9i		−	0.600982i
$536$	2.96590e9	+	2.09051e9i	0.831917	+	0.586374i
$537$	2.17579e7	−	5.38547e7i	0.00606328	−	0.0150077i
$538$	5.75034e9	+	1.19356e9i	1.59205	+	0.330450i
$539$	1.96949e8			0.0541742
$540$	1.90967e7	+	1.98860e9i	0.00521891	+	0.543463i
$541$	−3.86708e8			−0.105001			−0.0525004	−	0.998621i	$-0.516719\pi$
$541$	−3.86708e8			−0.105001			−0.0525004	+	0.998621i	$0.516719\pi$
$542$	2.65389e9	+	5.50849e8i	0.715954	+	0.148606i
$543$	−1.57611e9	+	3.90116e9i	−0.422462	+	1.04567i
$544$	3.02976e8	+	4.96937e8i	0.0806885	+	0.132344i
$545$		−	1.22332e9i		−	0.323707i
$546$	−1.46506e9	+	2.19467e9i	−0.385196	+	0.577025i
$547$			3.91056e9i			1.02161i	0.859698	+	0.510803i	$0.170652\pi$
$547$			3.91056e9i			1.02161i	−0.859698	+	0.510803i	$0.829348\pi$
$548$	−2.67460e8	+	6.16530e8i	−0.0694269	+	0.160038i
$549$	−2.16133e9	−	2.08707e9i	−0.557466	−	0.538312i
$550$	9.73855e8	−	4.69185e9i	0.249589	−	1.20247i
$551$	3.51343e9			0.894748
$552$	−1.75791e9	−	2.72536e9i	−0.444846	−	0.689665i
$553$	2.85035e9			0.716739
$554$	2.40484e8	−	1.15861e9i	0.0600899	−	0.289502i
$555$	−2.13628e9	−	8.63080e8i	−0.530434	−	0.214302i
$556$	−2.72898e9	+	6.29063e9i	−0.673346	+	1.55215i
$557$		−	1.24857e8i		−	0.0306141i	−0.999883	−	0.0153070i	$-0.995127\pi$
$557$		−	1.24857e8i		−	0.0306141i	0.999883	−	0.0153070i	$-0.00487257\pi$
$558$	−1.79612e9	−	2.63544e9i	−0.437639	−	0.642145i
$559$		−	2.33557e9i		−	0.565525i
$560$	1.51899e9	+	1.62345e9i	0.365508	+	0.390644i
$561$	1.04750e9	+	4.23203e8i	0.250487	+	0.101199i
$562$	7.29373e8	+	1.51391e8i	0.173329	+	0.0359768i
$563$	−2.98122e9			−0.704068			−0.352034	−	0.935987i	$-0.614510\pi$
$563$	−2.98122e9			−0.704068			−0.352034	+	0.935987i	$0.614510\pi$
$564$	−2.79167e9	+	2.74804e9i	−0.655220	+	0.644979i
$565$	−3.77620e8			−0.0880817
$566$	−7.49937e9	−	1.55659e9i	−1.73847	−	0.360842i
$567$	4.26991e9	−	1.49324e8i	0.983735	−	0.0344024i
$568$	−1.40225e8	+	1.98944e8i	−0.0321075	+	0.0455524i
$569$			6.15858e9i			1.40148i	0.713416	+	0.700741i	$0.247147\pi$
$569$			6.15858e9i			1.40148i	−0.713416	+	0.700741i	$0.752853\pi$
$570$	−1.14771e9	−	7.66158e8i	−0.259579	−	0.173283i
$571$		−	5.67032e9i		−	1.27462i	−0.770607	−	0.637311i	$-0.780047\pi$
$571$		−	5.67032e9i		−	1.27462i	0.770607	−	0.637311i	$-0.219953\pi$
$572$	−5.04429e9	−	2.18829e9i	−1.12697	−	0.488900i
$573$	−7.98601e8	+	1.97668e9i	−0.177333	+	0.438930i
$574$	6.62961e8	−	3.19402e9i	0.146317	−	0.704930i
$575$	−2.63615e9			−0.578272
$576$	−1.89137e9	+	4.17833e9i	−0.412380	+	0.911012i
$577$	5.17119e8			0.112066			0.0560332	−	0.998429i	$-0.482155\pi$
$577$	5.17119e8			0.112066			0.0560332	+	0.998429i	$0.482155\pi$
$578$	9.20824e8	−	4.43636e9i	0.198349	−	0.955606i
$579$	2.80936e9	−	6.95366e9i	0.601495	−	1.48881i
$580$	3.65037e9	+	1.58359e9i	0.776853	+	0.337011i
$581$		−	2.01794e9i		−	0.426865i
$582$	2.45215e9	+	1.63694e9i	0.515604	+	0.344194i
$583$		−	3.89811e8i		−	0.0814731i
$584$	2.85188e8	−	4.04610e8i	0.0592497	−	0.0840605i
$585$	1.28847e9	−	1.33432e9i	0.266091	−	0.275559i
$586$	−5.68825e9	−	1.18067e9i	−1.16772	−	0.242375i
$587$	7.64033e9			1.55912			0.779559	−	0.626329i	$-0.215443\pi$
$587$	7.64033e9			1.55912			0.779559	+	0.626329i	$0.215443\pi$
$588$	−1.09198e8	+	1.07491e8i	−0.0221509	+	0.0218047i
$589$	2.21302e9			0.446254
$590$	−3.26144e9	−	6.76954e8i	−0.653773	−	0.135699i
$591$	2.08491e9	+	8.42327e8i	0.415462	+	0.167851i
$592$	−3.63047e9	−	3.88014e9i	−0.719178	−	0.768636i
$593$		−	5.10235e9i		−	1.00480i	−0.864636	−	0.502399i	$-0.832451\pi$
$593$		−	5.10235e9i		−	1.00480i	0.864636	−	0.502399i	$-0.167549\pi$
$594$	1.89297e9	+	8.69932e9i	0.370588	+	1.70307i
$595$			4.26070e8i			0.0829223i
$596$	9.25699e8	−	2.13385e9i	0.179105	−	0.412860i
$597$	−6.49593e9	−	2.62443e9i	−1.24949	−	0.504807i
$598$	−6.14754e8	+	2.96177e9i	−0.117557	+	0.566366i
$599$	2.42673e9			0.461347			0.230673	−	0.973031i	$-0.425907\pi$
$599$	2.42673e9			0.461347			0.230673	+	0.973031i	$0.425907\pi$
$600$	2.02077e9	+	3.13289e9i	0.381934	+	0.592129i
$601$	−8.12424e9			−1.52659			−0.763294	−	0.646051i	$-0.776419\pi$
$601$	−8.12424e9			−1.52659			−0.763294	+	0.646051i	$0.776419\pi$
$602$	−8.59199e8	+	4.13946e9i	−0.160511	+	0.773314i
$603$	−3.80657e9	+	3.94202e9i	−0.707006	+	0.732163i
$604$	1.33752e9	−	3.08314e9i	0.246984	−	0.569330i
$605$			6.03243e9i			1.10751i
$606$	2.55866e9	−	3.83289e9i	0.467045	−	0.699636i
$607$		−	1.10027e9i		−	0.199682i	−0.995003	−	0.0998412i	$-0.968167\pi$
$607$		−	1.10027e9i		−	0.199682i	0.995003	−	0.0998412i	$-0.0318335\pi$
$608$	−1.65670e9	−	2.71730e9i	−0.298939	−	0.490316i
$609$	3.20227e9	−	7.92619e9i	0.574511	−	1.42202i
$610$	2.31185e9	+	4.79854e8i	0.412387	+	0.0855962i
$611$	3.65369e9			0.648019
$612$	−8.11760e8	+	3.37063e8i	−0.143152	+	0.0594404i
$613$	3.31609e9			0.581452			0.290726	−	0.956806i	$-0.406103\pi$
$613$	3.31609e9			0.581452			0.290726	+	0.956806i	$0.406103\pi$
$614$	−1.50386e9	−	3.12145e8i	−0.262191	−	0.0544211i
$615$	−8.58968e8	+	2.12610e9i	−0.148907	+	0.368570i
$616$	8.13526e9	+	5.73411e9i	1.40229	+	0.988402i
$617$			6.06980e9i			1.04034i	0.854062	+	0.520171i	$0.174132\pi$
$617$			6.06980e9i			1.04034i	−0.854062	+	0.520171i	$0.825868\pi$
$618$	2.93516e9	−	4.39688e9i	0.500232	−	0.749350i
$619$			1.99572e9i			0.338206i	0.985598	+	0.169103i	$0.0540871\pi$
$619$			1.99572e9i			0.338206i	−0.985598	+	0.169103i	$0.945913\pi$
$620$	2.29928e9	+	9.97463e8i	0.387454	+	0.168084i
$621$	4.47425e9	−	1.99227e9i	0.749721	−	0.333831i
$622$	−2.31024e9	+	1.11303e10i	−0.384937	+	1.85456i
$623$	−4.16802e9			−0.690592
$624$	3.99112e9	−	1.53979e9i	0.657581	−	0.253697i
$625$	1.22748e9			0.201111
$626$	6.72810e8	−	3.24147e9i	0.109618	−	0.528120i
$627$	−5.72784e9	−	2.31412e9i	−0.928015	−	0.374929i
$628$	−4.55072e9	−	1.97417e9i	−0.733198	−	0.318073i
$629$		−	1.01833e9i		−	0.163159i
$630$	−2.77449e9	+	1.89089e9i	−0.442071	+	0.301283i
$631$			1.06585e10i			1.68885i	0.535672	+	0.844426i	$0.320059\pi$
$631$			1.06585e10i			1.68885i	−0.535672	+	0.844426i	$0.679941\pi$
$632$	−3.77698e9	−	2.66219e9i	−0.595161	−	0.419497i
$633$	6.25911e9	+	2.52875e9i	0.980843	+	0.396272i
$634$	−8.17576e9	−	1.69699e9i	−1.27414	−	0.264464i
$635$	−2.03355e9			−0.315171
$636$	2.12752e8	+	2.16129e8i	0.0327924	+	0.0333130i
$637$	1.42916e8			0.0219075
$638$	1.74415e10	+	3.62022e9i	2.65896	+	0.551902i
$639$	−2.64419e8	−	2.55333e8i	−0.0400903	−	0.0387128i
$640$	−4.96519e8	−	3.56993e9i	−0.0748696	−	0.538306i
$641$			9.04119e9i			1.35588i	0.735115	+	0.677942i	$0.237128\pi$
$641$			9.04119e9i			1.35588i	−0.735115	+	0.677942i	$0.762872\pi$
$642$	6.16617e9	+	4.11625e9i	0.919693	+	0.613945i
$643$		−	7.29293e8i		−	0.108184i	−0.998536	−	0.0540921i	$-0.982774\pi$
$643$		−	7.29293e8i		−	0.108184i	0.998536	−	0.0540921i	$-0.0172264\pi$
$644$	2.17913e9	−	5.02316e9i	0.321501	−	0.741099i
$645$	1.11322e9	−	2.75543e9i	0.163352	−	0.404324i
$646$	1.23951e8	−	5.97173e8i	0.0180899	−	0.0871538i
$647$	−4.24459e9			−0.616127			−0.308064	−	0.951366i	$-0.599681\pi$
$647$	−4.24459e9			−0.616127			−0.308064	+	0.951366i	$0.599681\pi$
$648$	−5.79748e9	−	3.79016e9i	−0.837003	−	0.547199i
$649$	−1.49118e10			−2.14129
$650$	7.06680e8	−	3.40465e9i	0.100931	−	0.486268i
$651$	2.01703e9	−	4.99251e9i	0.286536	−	0.709228i
$652$	3.92863e9	−	9.05598e9i	0.555104	−	1.27958i
$653$			3.74961e8i			0.0526975i	0.999653	+	0.0263488i	$0.00838804\pi$
$653$			3.74961e8i			0.0526975i	−0.999653	+	0.0263488i	$0.991612\pi$
$654$	3.54369e9	+	2.36560e9i	0.495374	+	0.330689i
$655$			1.64674e9i			0.228971i
$656$	−3.86165e9	+	3.61317e9i	−0.534084	+	0.499718i
$657$	5.37772e8	+	5.19294e8i	0.0739809	+	0.0714389i
$658$	−6.47565e9	−	1.34410e9i	−0.886120	−	0.183926i
$659$	−8.66557e9			−1.17950			−0.589750	−	0.807586i	$-0.700774\pi$
$659$	−8.66557e9			−1.17950			−0.589750	+	0.807586i	$0.700774\pi$
$660$	−4.90806e9	−	4.98599e9i	−0.664517	−	0.675068i
$661$	1.02849e10			1.38514			0.692569	−	0.721352i	$-0.256479\pi$
$661$	1.02849e10			1.38514			0.692569	+	0.721352i	$0.256479\pi$
$662$	−5.82860e9	−	1.20980e9i	−0.780838	−	0.162073i
$663$	7.60121e8	+	3.07098e8i	0.101294	+	0.0409241i
$664$	−1.88472e9	+	2.67395e9i	−0.249838	+	0.354458i
$665$		−	2.32979e9i		−	0.307214i
$666$	6.63120e9	−	4.51934e9i	0.869826	−	0.592809i
$667$		−	9.79964e9i		−	1.27870i
$668$	9.00906e9	+	3.90827e9i	1.16940	+	0.507303i
$669$	−4.89008e9	−	1.97565e9i	−0.631429	−	0.255104i
$670$	8.75197e8	−	4.21654e9i	0.112420	−	0.541619i
$671$	1.05702e10			1.35068
$672$	−7.64014e9	+	1.26082e9i	−0.971200	+	0.160273i
$673$	−5.11808e8			−0.0647223			−0.0323612	−	0.999476i	$-0.510303\pi$
$673$	−5.11808e8			−0.0647223			−0.0323612	+	0.999476i	$0.510303\pi$
$674$	3.20330e8	−	1.54329e9i	0.0402984	−	0.194150i
$675$	−5.14330e9	+	2.29018e9i	−0.643692	+	0.286619i
$676$	3.70793e9	+	1.60856e9i	0.461656	+	0.200274i
$677$		−	8.58087e9i		−	1.06285i	−0.847106	−	0.531424i	$-0.821657\pi$
$677$		−	8.58087e9i		−	1.06285i	0.847106	−	0.531424i	$-0.178343\pi$
$678$	7.30227e8	−	1.09388e9i	0.0899816	−	0.134793i
$679$			4.97774e9i			0.610222i
$680$	3.97942e8	−	5.64580e8i	0.0485332	−	0.0688565i
$681$	−2.05323e9	+	5.08211e9i	−0.249128	+	0.616636i
$682$	1.09860e10	+	2.28028e9i	1.32615	+	0.275260i
$683$	−1.18169e10			−1.41915			−0.709577	−	0.704628i	$-0.751114\pi$
$683$	−1.18169e10			−1.41915			−0.709577	+	0.704628i	$0.751114\pi$
$684$	4.43879e9	−	1.84310e9i	0.530356	−	0.220218i
$685$	7.97578e8			0.0948104
$686$	−8.40256e9	−	1.74406e9i	−0.993751	−	0.206266i
$687$	−1.61198e9	+	3.98994e9i	−0.189676	+	0.469481i
$688$	5.00471e9	−	4.68268e9i	0.585894	−	0.548194i
$689$		−	2.82867e8i		−	0.0329469i
$690$	−2.13696e9	+	3.20118e9i	−0.247643	+	0.370970i
$691$		−	1.49118e10i		−	1.71932i	−0.510870	−	0.859658i	$-0.670677\pi$
$691$		−	1.49118e10i		−	1.71932i	0.510870	−	0.859658i	$-0.329323\pi$
$692$	−6.69433e9	+	1.54313e10i	−0.767956	+	1.77023i
$693$	−1.04412e10	+	1.08127e10i	−1.19174	+	1.23415i
$694$	−1.69267e9	+	8.15495e9i	−0.192227	+	0.926112i
$695$	8.13792e9			0.919532
$696$	−1.16462e10	+	7.51204e9i	−1.30934	+	0.844551i
$697$	−1.01348e9			−0.113370
$698$	−2.49278e9	+	1.20097e10i	−0.277453	+	1.33672i
$699$	1.34627e10	+	5.43908e9i	1.49094	+	0.602359i
$700$	−2.50497e9	+	5.77428e9i	−0.276033	+	0.636289i
$701$		−	1.32771e10i		−	1.45576i	−0.685704	−	0.727881i	$-0.740506\pi$
$701$		−	1.32771e10i		−	1.45576i	0.685704	−	0.727881i	$-0.259494\pi$
$702$	1.37364e9	+	6.31268e9i	0.149862	+	0.688706i
$703$			5.56833e9i			0.604480i
$704$	−5.42438e9	−	1.51964e10i	−0.585930	−	1.64148i
$705$	4.31051e9	+	1.74149e9i	0.463304	+	0.187180i
$706$	−1.15678e10	−	2.40105e9i	−1.23719	−	0.256794i
$707$	7.78058e9			0.828026
$708$	8.26782e9	−	8.13861e9i	0.875538	−	0.861854i
$709$	1.62054e10			1.70764			0.853822	−	0.520565i	$-0.174279\pi$
$709$	1.62054e10			1.70764			0.853822	+	0.520565i	$0.174279\pi$
$710$	2.82833e8	+	5.87056e7i	0.0296569	+	0.00615567i
$711$	4.84754e9	−	5.02002e9i	0.505798	−	0.523796i
$712$	5.52300e9	+	3.89287e9i	0.573449	+	0.404194i
$713$		−	6.17255e9i		−	0.637751i
$714$	−1.23423e9	−	8.23916e8i	−0.126897	−	0.0847109i
$715$			6.52559e9i			0.667649i
$716$	−1.45847e8	−	6.32707e7i	−0.0148491	−	0.00644179i
$717$	−3.80721e9	+	9.42351e9i	−0.385735	+	0.954763i
$718$	1.99943e9	−	9.63289e9i	0.201591	−	0.971227i
$719$	1.10786e10			1.11157			0.555783	−	0.831327i	$-0.312418\pi$
$719$	1.10786e10			1.11157			0.555783	+	0.831327i	$0.312418\pi$
$720$	5.44252e9	+	8.57348e7i	0.543421	+	0.00856038i
$721$	8.92545e9			0.886863
$722$	1.37750e9	−	6.63655e9i	0.136211	−	0.656239i
$723$	1.52792e9	−	3.78187e9i	0.150355	−	0.372154i
$724$	1.05649e10	+	4.58324e9i	1.03462	+	0.448835i
$725$			1.12650e10i			1.09786i
$726$	−1.74747e10	−	1.16653e10i	−1.69485	−	1.13140i
$727$			6.77623e9i			0.654060i	0.945014	+	0.327030i	$0.106048\pi$
$727$			6.77623e9i			0.654060i	−0.945014	+	0.327030i	$0.893952\pi$
$728$	5.90337e9	+	4.16097e9i	0.567074	+	0.399700i
$729$	6.99875e9	−	7.77409e9i	0.669074	−	0.743195i
$730$	−5.75222e8	−	1.19395e8i	−0.0547275	−	0.0113594i
$731$	1.31347e9			0.124368
$732$	−5.86059e9	+	5.76900e9i	−0.552271	+	0.543640i
$733$	−1.70741e10			−1.60131			−0.800653	−	0.599129i	$-0.795514\pi$
$733$	−1.70741e10			−1.60131			−0.800653	+	0.599129i	$0.795514\pi$
$734$	8.37856e9	+	1.73908e9i	0.782048	+	0.162324i
$735$	1.68608e8	+	6.81194e7i	0.0156629	+	0.00632798i
$736$	−7.57909e9	+	4.62087e9i	−0.700720	+	0.427219i
$737$		−	1.92787e10i		−	1.77395i
$738$	−4.49780e9	−	6.59960e9i	−0.411911	−	0.604395i
$739$		−	1.17577e10i		−	1.07168i	−0.844319	−	0.535841i	$-0.819994\pi$
$739$		−	1.17577e10i		−	1.07168i	0.844319	−	0.535841i	$-0.180006\pi$
$740$	−2.50978e9	+	5.78536e9i	−0.227680	+	0.524831i
$741$	−4.15642e9	−	1.67924e9i	−0.375280	−	0.151618i
$742$	−1.04060e8	+	5.01341e8i	−0.00935125	+	0.0450526i
$743$	−1.63694e10			−1.46410			−0.732052	−	0.681249i	$-0.761437\pi$
$743$	−1.63694e10			−1.46410			−0.732052	+	0.681249i	$0.761437\pi$
$744$	−7.33568e9	+	4.73165e9i	−0.653033	+	0.421219i
$745$	−2.76047e9			−0.244589
$746$	−4.27708e9	+	2.06062e10i	−0.377191	+	1.81724i
$747$	−3.55397e9	−	3.43186e9i	−0.311955	−	0.301236i
$748$	1.23065e9	−	2.83679e9i	0.107517	−	0.247841i
$749$			1.25170e10i			1.08847i
$750$	5.94279e9	−	8.90233e9i	0.514370	−	0.770530i
$751$		−	1.26000e10i		−	1.08551i	−0.839893	−	0.542753i	$-0.817382\pi$
$751$		−	1.26000e10i		−	1.08551i	0.839893	−	0.542753i	$-0.182618\pi$
$752$	7.32544e9	+	7.82921e9i	0.628161	+	0.671360i
$753$	−2.54508e9	+	6.29953e9i	−0.217230	+	0.537683i
$754$	1.26565e10	+	2.62702e9i	1.07526	+	0.223184i
$755$	−3.98853e9			−0.337286
$756$	−1.12295e8	−	1.16936e10i	−0.00945221	−	0.984291i
$757$	−3.55621e9			−0.297955			−0.148978	−	0.988841i	$-0.547598\pi$
$757$	−3.55621e9			−0.297955			−0.148978	+	0.988841i	$0.547598\pi$
$758$	−5.76353e9	−	1.19629e9i	−0.480669	−	0.0997691i
$759$	−6.45452e9	+	1.59761e10i	−0.535818	+	1.32625i
$760$	−2.17599e9	+	3.08718e9i	−0.179808	+	0.255103i
$761$			4.41993e9i			0.363554i	0.983340	+	0.181777i	$0.0581850\pi$
$761$			4.41993e9i			0.363554i	−0.983340	+	0.181777i	$0.941815\pi$
$762$	3.93240e9	−	5.89075e9i	0.321970	−	0.482312i
$763$			7.19351e9i			0.586280i
$764$	5.35315e9	+	2.32228e9i	0.434293	+	0.188403i
$765$	7.50391e8	+	7.24607e8i	0.0606000	+	0.0585178i
$766$	4.46925e9	−	2.15320e10i	0.359281	−	1.73095i
$767$	−1.08208e10			−0.865916
$768$	1.13015e10	+	5.46508e9i	0.900264	+	0.435343i
$769$	−4.20265e9			−0.333259			−0.166629	−	0.986020i	$-0.553288\pi$
$769$	−4.20265e9			−0.333259			−0.166629	+	0.986020i	$0.553288\pi$
$770$	2.40060e9	−	1.15657e10i	0.189497	−	0.912962i
$771$	−5.85339e9	−	2.36484e9i	−0.459957	−	0.185828i
$772$	−1.88316e10	−	8.16944e9i	−1.47308	−	0.639045i
$773$		−	9.46793e9i		−	0.737270i	−0.929574	−	0.368635i	$-0.879825\pi$
$773$		−	9.46793e9i		−	0.737270i	0.929574	−	0.368635i	$-0.120175\pi$
$774$	5.82916e9	+	8.55310e9i	0.451869	+	0.663026i
$775$			7.09554e9i			0.547558i
$776$	4.64913e9	−	6.59595e9i	0.357154	−	0.506712i
$777$	1.25620e10	+	5.07519e9i	0.960694	+	0.388132i
$778$	−9.63234e9	−	1.99932e9i	−0.733336	−	0.152214i
$779$	5.54180e9			0.420020
$780$	−3.56154e9	−	3.61809e9i	−0.268724	−	0.272991i
$781$	1.29316e9			0.0971345
$782$	−1.66563e9	−	3.45724e8i	−0.124553	−	0.0258527i
$783$	−8.51352e9	−	1.91197e10i	−0.633786	−	1.42336i
$784$	2.86538e8	+	3.06244e8i	0.0212362	+	0.0226966i
$785$			5.88707e9i			0.434366i
$786$	−4.77024e9	−	3.18439e9i	−0.350398	−	0.233909i
$787$			1.03585e10i			0.757508i	0.925497	+	0.378754i	$0.123647\pi$
$787$			1.03585e10i			0.757508i	−0.925497	+	0.378754i	$0.876353\pi$
$788$	2.44944e9	−	5.64626e9i	0.178330	−	0.411073i
$789$	5.02861e9	−	1.24467e10i	0.364484	−	0.902162i
$790$	−1.11453e9	+	5.36961e9i	−0.0804263	+	0.387479i
$791$	2.22053e9			0.159529
$792$	2.39343e10	−	4.57589e9i	1.71192	−	0.327293i
$793$	7.67025e9			0.546202
$794$	2.60451e9	−	1.25480e10i	0.184652	−	0.889619i
$795$	1.34826e8	−	3.33717e8i	0.00951672	−	0.0235556i
$796$	−7.63168e9	+	1.75920e10i	−0.536321	+	1.23629i
$797$			3.25001e9i			0.227395i	0.993515	+	0.113697i	$0.0362695\pi$
$797$			3.25001e9i			0.227395i	−0.993515	+	0.113697i	$0.963731\pi$
$798$	6.74890e9	+	4.50526e9i	0.470136	+	0.313841i
$799$			2.05475e9i			0.142510i
$800$	8.71241e9	−	5.31183e9i	0.601621	−	0.366800i
$801$	−7.08846e9	+	7.34068e9i	−0.487347	+	0.504688i
$802$	6.08231e9	+	1.26246e9i	0.416350	+	0.0864188i
$803$	−2.63001e9			−0.179248
$804$	1.05220e10	+	1.06890e10i	0.714004	+	0.725340i
$805$	−6.49825e9			−0.439046
$806$	7.97200e9	+	1.65469e9i	0.536284	+	0.111313i
$807$	2.25082e10	+	9.09357e9i	1.50759	+	0.609084i
$808$	−1.03100e10	−	7.26694e9i	−0.687571	−	0.484632i
$809$			4.08255e9i			0.271089i	0.990771	+	0.135544i	$0.0432783\pi$
$809$			4.08255e9i			0.271089i	−0.990771	+	0.135544i	$0.956722\pi$
$810$	−1.38830e9	+	8.10222e9i	−0.0917879	+	0.535681i
$811$			1.68910e10i			1.11194i	0.831202	+	0.555971i	$0.187653\pi$
$811$			1.68910e10i			1.11194i	−0.831202	+	0.555971i	$0.812347\pi$
$812$	−2.14654e10	−	9.31201e9i	−1.40699	−	0.610376i
$813$	1.03879e10	+	4.19685e9i	0.677973	+	0.273909i
$814$	−5.73758e9	+	2.76426e10i	−0.372858	+	1.79636i
$815$	−1.17153e10			−0.758059
$816$	8.65942e8	+	2.24452e9i	0.0557922	+	0.144613i
$817$	−7.18219e9			−0.460765
$818$	−1.25942e9	+	6.06766e9i	−0.0804516	+	0.387601i
$819$	−7.57664e9	+	7.84624e9i	−0.481929	+	0.499077i
$820$	5.75780e9	+	2.49782e9i	0.364677	+	0.158203i
$821$			6.81807e9i			0.429992i	0.976615	+	0.214996i	$0.0689739\pi$
$821$			6.81807e9i			0.429992i	−0.976615	+	0.214996i	$0.931026\pi$
$822$	−1.54232e9	+	2.31041e9i	−0.0968555	+	0.145090i
$823$		−	8.14880e9i		−	0.509559i	−0.966999	−	0.254779i	$-0.917997\pi$
$823$		−	8.14880e9i		−	0.509559i	0.966999	−	0.254779i	$-0.0820028\pi$
$824$	−1.18270e10	−	8.33623e9i	−0.736428	−	0.519068i
$825$	7.41967e9	−	1.83650e10i	0.460040	−	1.13868i
$826$	1.91783e10	+	3.98071e9i	1.18408	+	0.245771i
$827$	5.75610e9			0.353883			0.176941	−	0.984221i	$-0.443380\pi$
$827$	5.75610e9			0.353883			0.176941	+	0.984221i	$0.443380\pi$
$828$	−5.14076e9	−	1.23806e10i	−0.314718	−	0.757944i
$829$	1.37897e10			0.840645			0.420322	−	0.907375i	$-0.361917\pi$
$829$	1.37897e10			0.840645			0.420322	+	0.907375i	$0.361917\pi$
$830$	3.80147e9	+	7.89044e8i	0.230769	+	0.0478992i
$831$	1.83221e9	−	4.53505e9i	0.110757	−	0.274144i
$832$	−3.93621e9	−	1.10273e10i	−0.236945	−	0.663801i
$833$			8.03727e7i			0.00481783i
$834$	−1.57368e10	+	2.35738e10i	−0.939366	+	1.40718i
$835$		−	1.16546e10i		−	0.692781i
$836$	−6.72930e9	+	1.55119e10i	−0.398335	+	0.918211i
$837$	−5.36246e9	−	1.20430e10i	−0.316100	−	0.709900i
$838$	7.28045e8	−	3.50759e9i	0.0427370	−	0.205899i
$839$	2.11457e10			1.23610			0.618052	−	0.786138i	$-0.287922\pi$
$839$	2.11457e10			1.23610			0.618052	+	0.786138i	$0.287922\pi$
$840$	4.98132e9	+	7.72275e9i	0.289979	+	0.449567i
$841$	−2.46267e10			−1.42765
$842$	1.96674e9	−	9.47540e9i	0.113542	−	0.547023i
$843$	2.85494e9	+	1.15343e9i	0.164134	+	0.0663122i
$844$	7.35345e9	−	1.69506e10i	0.421010	−	0.970482i
$845$		−	4.79679e9i		−	0.273497i
$846$	−1.33802e10	+	9.11897e9i	−0.759743	+	0.517785i
$847$		−	3.54727e10i		−	2.00587i
$848$	6.06133e8	−	5.67132e8i	0.0341337	−	0.0319373i
$849$	−2.93543e10	−	1.18595e10i	−1.64625	−	0.665102i
$850$	1.91470e9	+	3.97420e8i	0.106938	+	0.0221965i
$851$	1.55312e10			0.863875
$852$	−7.16988e8	+	7.05782e8i	−0.0397167	+	0.0390960i
$853$	8.37806e9			0.462191			0.231096	−	0.972931i	$-0.425769\pi$
$853$	8.37806e9			0.462191			0.231096	+	0.972931i	$0.425769\pi$
$854$	−1.35944e10	−	2.82170e9i	−0.746892	−	0.155027i
$855$	−4.10321e9	−	3.96223e9i	−0.224514	−	0.216799i
$856$	1.16907e10	−	1.65862e10i	0.637063	−	0.903833i
$857$			1.46458e10i			0.794842i	0.917636	+	0.397421i	$0.130095\pi$
$857$			1.46458e10i			0.794842i	−0.917636	+	0.397421i	$0.869905\pi$
$858$	−1.89032e10	−	1.26189e10i	−1.02172	−	0.682050i
$859$			2.68364e10i			1.44460i	0.691579	+	0.722301i	$0.256916\pi$
$859$			2.68364e10i			1.44460i	−0.691579	+	0.722301i	$0.743084\pi$
$860$	−7.46212e9	−	3.23719e9i	−0.400053	−	0.173549i
$861$	5.05101e9	−	1.25021e10i	0.269692	−	0.667534i
$862$	−1.98342e9	+	9.55577e9i	−0.105473	+	0.508148i
$863$	1.14962e9			0.0608858			0.0304429	−	0.999537i	$-0.490308\pi$
$863$	1.14962e9			0.0608858			0.0304429	+	0.999537i	$0.490308\pi$
$864$	−1.07729e10	+	1.56000e10i	−0.568242	+	0.822861i
$865$	1.99628e10			1.04873
$866$	−1.35260e8	+	6.51656e8i	−0.00707710	+	0.0340962i
$867$	7.01564e9	−	1.73649e10i	0.365595	−	0.904912i
$868$	−1.35205e10	−	5.86541e9i	−0.701736	−	0.304424i
$869$			2.45508e10i			1.26910i
$870$	1.36795e10	+	9.13184e9i	0.704295	+	0.470155i
$871$		−	1.39896e10i		−	0.717370i
$872$	6.71863e9	−	9.53205e9i	0.343141	−	0.486831i
$873$	8.76676e9	+	8.46553e9i	0.445953	+	0.430630i
$874$	9.10785e9	+	1.89045e9i	0.461451	+	0.0957802i
$875$	1.80713e10			0.911929
$876$	1.45820e9	−	1.43541e9i	0.0732915	−	0.0721460i
$877$	−3.49369e9			−0.174898			−0.0874491	−	0.996169i	$-0.527872\pi$
$877$	−3.49369e9			−0.174898			−0.0874491	+	0.996169i	$0.527872\pi$
$878$	−1.93506e10	−	4.01648e9i	−0.964860	−	0.200269i
$879$	−2.22651e10	−	8.99537e9i	−1.10577	−	0.446743i
$880$	−1.39832e10	+	1.30834e10i	−0.691697	+	0.647190i
$881$			1.01581e10i			0.500493i	0.968182	+	0.250247i	$0.0805117\pi$
$881$			1.01581e10i			0.500493i	−0.968182	+	0.250247i	$0.919488\pi$
$882$	−5.23374e8	+	3.56693e8i	−0.0256846	+	0.0175047i
$883$		−	1.09496e10i		−	0.535222i	−0.963527	−	0.267611i	$-0.913766\pi$
$883$		−	1.09496e10i		−	0.535222i	0.963527	−	0.267611i	$-0.0862342\pi$
$884$	8.93021e8	−	2.05853e9i	0.0434789	−	0.100224i
$885$	−1.27660e10	−	5.15762e9i	−0.619091	−	0.250120i
$886$	2.21431e9	−	1.06682e10i	0.106960	−	0.515313i
$887$	−9.70090e8			−0.0466744			−0.0233372	−	0.999728i	$-0.507429\pi$
$887$	−9.70090e8			−0.0466744			−0.0233372	+	0.999728i	$0.507429\pi$
$888$	−1.19056e10	−	1.84578e10i	−0.570567	−	0.884575i
$889$	1.19579e10			0.570821
$890$	1.62976e9	−	7.85188e9i	0.0774924	−	0.373344i
$891$	1.28616e9	+	3.67778e10i	0.0609150	+	1.74186i
$892$	−5.74506e9	+	1.32431e10i	−0.271030	+	0.624758i
$893$		−	1.12356e10i		−	0.527979i
$894$	5.33809e9	−	7.99649e9i	0.249865	−	0.374299i
$895$			1.88676e8i			0.00879702i
$896$	2.91969e9	+	2.09923e10i	0.135600	+	0.974951i
$897$	−4.68373e9	+	1.15931e10i	−0.216680	+	0.536321i
$898$	3.52833e10	+	7.32352e9i	1.62593	+	0.337484i
$899$	−2.63770e10			−1.21079
$900$	5.90946e9	+	1.42319e10i	0.270209	+	0.650752i
$901$	1.59078e8			0.00724558
$902$	2.75109e10	+	5.71024e9i	1.24819	+	0.259079i
$903$	−6.54612e9	+	1.62028e10i	−0.295854	+	0.732290i
$904$	−2.94240e9	−	2.07394e9i	−0.132469	−	0.0933699i
$905$		−	1.36674e10i		−	0.612937i
$906$	7.71285e9	−	1.15539e10i	0.344561	−	0.516154i
$907$			3.52293e10i			1.56775i	0.620916	+	0.783877i	$0.286761\pi$
$907$			3.52293e10i			1.56775i	−0.620916	+	0.783877i	$0.713239\pi$
$908$	1.37631e10	+	5.97067e9i	0.610123	+	0.264681i
$909$	1.32323e10	−	1.37031e10i	0.584333	−	0.605125i
$910$	1.74200e9	−	8.39264e9i	0.0766309	−	0.369193i
$911$	−2.95570e10			−1.29523			−0.647613	−	0.761970i	$-0.724232\pi$
$911$	−2.95570e10			−1.29523			−0.647613	+	0.761970i	$0.724232\pi$
$912$	−4.73506e9	−	1.22732e10i	−0.206701	−	0.535769i
$913$	1.73810e10			0.755833
$914$	1.60986e9	−	7.75601e9i	0.0697391	−	0.335990i
$915$	9.04911e9	+	3.65594e9i	0.390510	+	0.157771i
$916$	1.08054e10	+	4.68754e9i	0.464521	+	0.201517i
$917$		−	9.68335e9i		−	0.414699i
$918$	−3.55011e9	+	7.72502e8i	−0.151458	+	0.0329572i
$919$			1.44914e10i			0.615894i	0.951403	+	0.307947i	$0.0996420\pi$
$919$			1.44914e10i			0.615894i	−0.951403	+	0.307947i	$0.900358\pi$
$920$	8.61076e9	+	6.06926e9i	0.364573	+	0.256968i
$921$	−5.88645e9	−	2.37820e9i	−0.248282	−	0.100309i
$922$	−4.05046e10	−	8.40725e9i	−1.70195	−	0.353261i
$923$	9.38383e8			0.0392803
$924$	2.88610e10	+	2.93192e10i	1.20354	+	1.22265i
$925$	−1.78536e10			−0.741701
$926$	1.61613e10	+	3.35448e9i	0.668863	+	0.138831i
$927$	1.51793e10	−	1.57194e10i	0.625854	−	0.648124i
$928$	1.97462e10	+	3.23876e10i	0.811086	+	1.33033i
$929$			1.42684e10i			0.583874i	0.956438	+	0.291937i	$0.0942998\pi$
$929$			1.42684e10i			0.583874i	−0.956438	+	0.291937i	$0.905700\pi$
$930$	8.61641e9	+	5.75192e9i	0.351266	+	0.234489i
$931$		−	4.39486e8i		−	0.0178493i
$932$	1.58165e10	−	3.64590e10i	0.639963	−	1.47519i
$933$	−1.76014e10	+	4.35666e10i	−0.709514	+	1.75617i
$934$	7.76981e9	−	3.74335e10i	0.312030	−	1.50330i
$935$	−3.66984e9			−0.146827
$936$	1.73680e10	−	3.32050e9i	0.692284	−	0.132354i
$937$	−6.09581e9			−0.242071			−0.121036	−	0.992648i	$-0.538622\pi$
$937$	−6.09581e9			−0.242071			−0.121036	+	0.992648i	$0.538622\pi$
$938$	−5.14645e9	+	2.47946e10i	−0.203609	+	0.980951i
$939$	5.12605e9	−	1.26879e10i	0.202048	−	0.500103i
$940$	5.06416e9	−	1.16735e10i	0.198866	−	0.458410i
$941$		−	4.06101e10i		−	1.58880i	−0.607392	−	0.794402i	$-0.707784\pi$
$941$		−	4.06101e10i		−	1.58880i	0.607392	−	0.794402i	$-0.292216\pi$
$942$	−1.70536e10	−	1.13842e10i	−0.664717	−	0.443735i
$943$		−	1.54572e10i		−	0.600260i
$944$	−2.16951e10	−	2.31871e10i	−0.839381	−	0.897106i
$945$	−1.26785e10	+	5.64540e9i	−0.488716	+	0.217612i
$946$	−3.56542e10	−	7.40048e9i	−1.36928	−	0.284211i
$947$	−2.26050e10			−0.864928			−0.432464	−	0.901651i	$-0.642356\pi$
$947$	−2.26050e10			−0.864928			−0.432464	+	0.901651i	$0.642356\pi$
$948$	−1.33994e10	−	1.36121e10i	−0.510805	−	0.518915i
$949$	−1.90847e9			−0.0724861
$950$	−1.04698e10	−	2.17314e9i	−0.396191	−	0.0822345i
$951$	−3.20018e10	−	1.29291e10i	−1.20654	−	0.487458i
$952$	−2.34003e9	+	3.31992e9i	−0.0879007	+	0.124709i
$953$		−	2.42990e10i		−	0.909417i	−0.890640	−	0.454708i	$-0.849743\pi$
$953$		−	2.42990e10i		−	0.909417i	0.890640	−	0.454708i	$-0.150257\pi$
$954$	7.05986e8	+	1.03589e9i	0.0263255	+	0.0386273i
$955$		−	6.92514e9i		−	0.257286i
$956$	2.55203e10	+	1.10711e10i	0.944678	+	0.409816i
$957$	6.82702e10	+	2.75820e10i	2.51791	+	1.01726i
$958$	−2.18811e8	+	1.05419e9i	−0.00804063	+	0.0387383i
$959$	−4.69002e9			−0.171716
$960$	6.12236e8	−	1.48858e10i	0.0223342	−	0.543029i
$961$	1.08984e10			0.396123
$962$	−4.16348e9	+	2.00589e10i	−0.150780	+	0.726430i
$963$	2.20449e10	+	2.12874e10i	0.795456	+	0.768124i
$964$	−1.02419e10	−	4.44310e9i	−0.368223	−	0.159741i
$965$			2.43616e10i			0.872690i
$966$	1.25660e10	−	1.88240e10i	0.448517	−	0.671881i
$967$			6.84835e9i			0.243553i	0.992558	+	0.121776i	$0.0388591\pi$
$967$			6.84835e9i			0.243553i	−0.992558	+	0.121776i	$0.961141\pi$
$968$	−3.31309e10	+	4.70045e10i	−1.17401	+	1.66562i
$969$	9.44367e8	−	2.33748e9i	0.0333432	−	0.0825304i
$970$	−9.37727e9	−	1.94637e9i	−0.329895	−	0.0684739i
$971$	6.30800e9			0.221118			0.110559	−	0.993870i	$-0.464736\pi$
$971$	6.30800e9			0.221118			0.110559	+	0.993870i	$0.464736\pi$
$972$	−2.07857e10	−	1.96893e10i	−0.725995	−	0.687700i
$973$	−4.78536e10			−1.66541
$974$	−3.65421e10	−	7.58478e9i	−1.26718	−	0.263019i
$975$	5.38410e9	−	1.33266e10i	0.186036	−	0.460472i
$976$	1.53784e10	+	1.64360e10i	0.529464	+	0.565876i
$977$		−	1.11209e10i		−	0.381512i	−0.981637	−	0.190756i	$-0.938906\pi$
$977$		−	1.11209e10i		−	0.381512i	0.981637	−	0.190756i	$-0.0610939\pi$
$978$	2.26546e10	−	3.39368e10i	0.774411	−	1.16007i
$979$		−	3.59001e10i		−	1.22280i
$980$	1.98087e8	−	4.56616e8i	0.00672303	−	0.0154974i
$981$	1.26692e10	+	1.22338e10i	0.428456	+	0.413734i
$982$	−5.57506e9	+	2.68596e10i	−0.187871	+	0.905127i
$983$	5.16764e10			1.73522			0.867611	−	0.497244i	$-0.165655\pi$
$983$	5.16764e10			1.73522			0.867611	+	0.497244i	$0.165655\pi$
$984$	−1.83699e10	+	1.18489e10i	−0.614643	+	0.396456i
$985$	−7.30432e9			−0.243530
$986$	−1.47737e9	+	7.11771e9i	−0.0490819	+	0.236467i
$987$	−2.53472e10	−	1.02406e10i	−0.839112	−	0.339011i
$988$	−4.88313e9	+	1.12562e10i	−0.161083	+	0.371316i
$989$			2.00325e10i			0.658489i
$990$	−1.62867e10	−	2.38974e10i	−0.533470	−	0.782757i
$991$			2.83889e10i			0.926596i	0.886202	+	0.463298i	$0.153334\pi$
$991$			2.83889e10i			0.926596i	−0.886202	+	0.463298i	$0.846666\pi$
$992$	1.24377e10	+	2.04001e10i	0.404528	+	0.663502i
$993$	−2.28145e10	−	9.21732e9i	−0.739415	−	0.298732i
$994$	−1.66315e9	−	3.45208e8i	−0.0537129	−	0.0111488i
$995$	2.27580e10			0.732408
$996$	−9.63682e9	+	9.48621e9i	−0.309048	+	0.304218i
$997$	−2.70495e10			−0.864422			−0.432211	−	0.901773i	$-0.642266\pi$
$997$	−2.70495e10			−0.864422			−0.432211	+	0.901773i	$0.642266\pi$
$998$	1.99078e10	+	4.13212e9i	0.633966	+	0.131588i
$999$	3.03023e10	−	1.34928e10i	0.961605	−	0.428177i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.8.b.b.11.5	yes	8
3.2	odd	2	inner	12.8.b.b.11.4	yes	8
4.3	odd	2	inner	12.8.b.b.11.3	✓	8
8.3	odd	2		192.8.c.e.191.5		8
8.5	even	2		192.8.c.e.191.4		8
12.11	even	2	inner	12.8.b.b.11.6	yes	8
24.5	odd	2		192.8.c.e.191.6		8
24.11	even	2		192.8.c.e.191.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.8.b.b.11.3	✓	8	4.3	odd	2	inner
12.8.b.b.11.4	yes	8	3.2	odd	2	inner
12.8.b.b.11.5	yes	8	1.1	even	1	trivial
12.8.b.b.11.6	yes	8	12.11	even	2	inner
192.8.c.e.191.3		8	24.11	even	2
192.8.c.e.191.4		8	8.5	even	2
192.8.c.e.191.5		8	8.3	odd	2
192.8.c.e.191.6		8	24.5	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(2.29930 - 11.0776i) q^{2} +(17.5181 - 43.3603i) q^{3} +(-117.426 - 50.9415i) q^{4} +151.910i q^{5} +(-440.049 - 293.757i) q^{6} -893.278i q^{7} +(-834.308 + 1183.67i) q^{8} +(-1573.23 - 1519.18i) q^{9} +O(q^{10})\)	\(q+(2.29930 - 11.0776i) q^{2} +(17.5181 - 43.3603i) q^{3} +(-117.426 - 50.9415i) q^{4} +151.910i q^{5} +(-440.049 - 293.757i) q^{6} -893.278i q^{7} +(-834.308 + 1183.67i) q^{8} +(-1573.23 - 1519.18i) q^{9} +(1682.79 + 349.286i) q^{10} +7694.02 q^{11} +(-4265.92 + 4199.25i) q^{12} +5583.18 q^{13} +(-9895.37 - 2053.91i) q^{14} +(6586.85 + 2661.16i) q^{15} +(11193.9 + 11963.7i) q^{16} +3139.85i q^{17} +(-20446.2 + 13934.6i) q^{18} -17169.0i q^{19} +(7738.49 - 17838.2i) q^{20} +(-38732.8 - 15648.5i) q^{21} +(17690.9 - 85231.2i) q^{22} -47887.8 q^{23} +(36709.0 + 56911.5i) q^{24} +55048.5 q^{25} +(12837.4 - 61848.2i) q^{26} +(-93432.1 + 41602.9i) q^{27} +(-45504.9 + 104894. i) q^{28} +204638. i q^{29} +(44624.4 - 66847.6i) q^{30} +128896. i q^{31} +(158268. - 96493.7i) q^{32} +(134784. - 333615. i) q^{33} +(34782.0 + 7219.46i) q^{34} +135697. q^{35} +(107350. + 258535. i) q^{36} -324324. q^{37} +(-190192. - 39476.8i) q^{38} +(97806.5 - 242088. i) q^{39} +(-179811. - 126739. i) q^{40} +322779. i q^{41} +(-262406. + 393086. i) q^{42} -418323. i q^{43} +(-903481. - 391944. i) q^{44} +(230778. - 238989. i) q^{45} +(-110108. + 530481. i) q^{46} +654411. q^{47} +(714848. - 275791. i) q^{48} +25597.6 q^{49} +(126573. - 609805. i) q^{50} +(136145. + 55004.1i) q^{51} +(-655613. - 284415. i) q^{52} -50664.2i q^{53} +(246032. + 1.13066e6i) q^{54} +1.16879e6i q^{55} +(1.05735e6 + 745269. i) q^{56} +(-744454. - 300768. i) q^{57} +(2.26689e6 + 470524. i) q^{58} -1.93811e6 q^{59} +(-637906. - 648034. i) q^{60} +1.37382e6 q^{61} +(1.42786e6 + 296371. i) q^{62} +(-1.35705e6 + 1.40534e6i) q^{63} +(-705013. - 1.97510e6i) q^{64} +848138. i q^{65} +(-3.38574e6 - 2.26017e6i) q^{66} -2.50568e6i q^{67} +(159949. - 368701. i) q^{68} +(-838901. + 2.07643e6i) q^{69} +(312009. - 1.50320e6i) q^{70} +168073. q^{71} +(3.11077e6 - 594734. i) q^{72} -341826. q^{73} +(-745719. + 3.59274e6i) q^{74} +(964343. - 2.38692e6i) q^{75} +(-874615. + 2.01610e6i) q^{76} -6.87289e6i q^{77} +(-2.45687e6 - 1.64009e6i) q^{78} +3.19089e6i q^{79} +(-1.81741e6 + 1.70047e6i) q^{80} +(167164. + 4.78005e6i) q^{81} +(3.57562e6 + 742166. i) q^{82} +2.25902e6 q^{83} +(3.75110e6 + 3.81065e6i) q^{84} -476973. q^{85} +(-4.63401e6 - 961849. i) q^{86} +(8.87316e6 + 3.58486e6i) q^{87} +(-6.41918e6 + 9.10720e6i) q^{88} -4.66598e6i q^{89} +(-2.11680e6 - 3.10597e6i) q^{90} -4.98733e6i q^{91} +(5.62329e6 + 2.43947e6i) q^{92} +(5.58898e6 + 2.25801e6i) q^{93} +(1.50469e6 - 7.24931e6i) q^{94} +2.60814e6 q^{95} +(-1.41145e6 - 8.55293e6i) q^{96} -5.57244e6 q^{97} +(58856.6 - 283560. i) q^{98} +(-1.21045e7 - 1.16886e7i) 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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