LMFDB - Embedded newform 24.11.b.a.19.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [24,11,Mod(19,24)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([1, 1, 0]))

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("24.19");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 24 = 2^{3} \cdot 3 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	24.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:	$15.2485740642$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6 x^{19} + 27 x^{18} + 30770 x^{17} - 1815282 x^{16} + 57539616 x^{15} - 4088960592 x^{14} + \cdots + 11\!\cdots\!48 $ x^20 - 6x^19 + 27x^18 + 30770x^17 - 1815282x^16 + 57539616x^15 - 4088960592x^14 + 109320120096x^13 + 1004037421632x^12 - 341428986230848x^11 + 26827330518900768x^10 - 213429230128679232x^9 + 4531185171783109696x^8 - 59577783292763180544x^7 + 773109978866563468032x^6 - 10468831046214498872832x^5 + 100515059455192262016768x^4 - 914964727789235676096000x^3 + 10301728460843161719307008x^2 - 23154508515218989319032320*x + 1190449728946943976769371648
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{82}\cdot 3^{38} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.18
Root			$11.7312 - 4.02609i$ of defining polynomial
Character	$\chi$	$=$	24.19
Dual form			24.11.b.a.19.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(30.0501 + 10.9995i) q^{2} -140.296 q^{3} +(782.022 + 661.073i) q^{4} -977.966i q^{5} +(-4215.92 - 1543.19i) q^{6} +13461.7i q^{7} +(16228.4 + 28467.2i) q^{8} +19683.0 q^{9} +O(q^{10})$	\(q+(30.0501 + 10.9995i) q^{2} -140.296 q^{3} +(782.022 + 661.073i) q^{4} -977.966i q^{5} +(-4215.92 - 1543.19i) q^{6} +13461.7i q^{7} +(16228.4 + 28467.2i) q^{8} +19683.0 q^{9} +(10757.1 - 29388.0i) q^{10} -142575. q^{11} +(-109715. - 92745.9i) q^{12} +702952. i q^{13} +(-148072. + 404526. i) q^{14} +137205. i q^{15} +(174542. + 1.03395e6i) q^{16} -735914. q^{17} +(591477. + 216503. i) q^{18} -1.32395e6 q^{19} +(646506. - 764791. i) q^{20} -1.88862e6i q^{21} +(-4.28440e6 - 1.56825e6i) q^{22} +3.17152e6i q^{23} +(-2.27679e6 - 3.99383e6i) q^{24} +8.80921e6 q^{25} +(-7.73211e6 + 2.11238e7i) q^{26} -2.76145e6 q^{27} +(-8.89916e6 + 1.05273e7i) q^{28} +5.57861e6i q^{29} +(-1.50918e6 + 4.12302e6i) q^{30} +6.23033e6i q^{31} +(-6.12787e6 + 3.29901e7i) q^{32} +2.00027e7 q^{33} +(-2.21143e7 - 8.09468e6i) q^{34} +1.31651e7 q^{35} +(1.53925e7 + 1.30119e7i) q^{36} -1.03173e8i q^{37} +(-3.97850e7 - 1.45628e7i) q^{38} -9.86214e7i q^{39} +(2.78399e7 - 1.58708e7i) q^{40} +1.69259e8 q^{41} +(2.07739e7 - 5.67534e7i) q^{42} +7.80098e7 q^{43} +(-1.11497e8 - 9.42523e7i) q^{44} -1.92493e7i q^{45} +(-3.48851e7 + 9.53047e7i) q^{46} -1.72281e8i q^{47} +(-2.44876e7 - 1.45059e8i) q^{48} +1.01258e8 q^{49} +(2.64718e8 + 9.68968e7i) q^{50} +1.03246e8 q^{51} +(-4.64702e8 + 5.49724e8i) q^{52} -6.23238e8i q^{53} +(-8.29819e7 - 3.03745e7i) q^{54} +1.39433e8i q^{55} +(-3.83216e8 + 2.18462e8i) q^{56} +1.85746e8 q^{57} +(-6.13619e7 + 1.67638e8i) q^{58} +3.24932e8 q^{59} +(-9.07023e7 + 1.07297e8i) q^{60} +1.22646e9i q^{61} +(-6.85305e7 + 1.87222e8i) q^{62} +2.64967e8i q^{63} +(-5.47018e8 + 9.23955e8i) q^{64} +6.87463e8 q^{65} +(6.01084e8 + 2.20020e8i) q^{66} -2.38626e9 q^{67} +(-5.75502e8 - 4.86493e8i) q^{68} -4.44952e8i q^{69} +(3.95613e8 + 1.44809e8i) q^{70} +1.19609e8i q^{71} +(3.19424e8 + 5.60319e8i) q^{72} +3.22972e8 q^{73} +(1.13485e9 - 3.10037e9i) q^{74} -1.23590e9 q^{75} +(-1.03536e9 - 8.75229e8i) q^{76} -1.91930e9i q^{77} +(1.08479e9 - 2.96359e9i) q^{78} +5.08004e9i q^{79} +(1.01117e9 - 1.70696e8i) q^{80} +3.87420e8 q^{81} +(5.08627e9 + 1.86177e9i) q^{82} -5.20864e9 q^{83} +(1.24852e9 - 1.47695e9i) q^{84} +7.19699e8i q^{85} +(2.34421e9 + 8.58068e8i) q^{86} -7.82657e8i q^{87} +(-2.31377e9 - 4.05870e9i) q^{88} +9.20987e9 q^{89} +(2.11733e8 - 5.78444e8i) q^{90} -9.46292e9 q^{91} +(-2.09661e9 + 2.48020e9i) q^{92} -8.74091e8i q^{93} +(1.89500e9 - 5.17706e9i) q^{94} +1.29478e9i q^{95} +(8.59717e8 - 4.62839e9i) q^{96} +3.54656e9 q^{97} +(3.04282e9 + 1.11379e9i) q^{98} -2.80630e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 22 q^{2} - 1864 q^{4} - 2430 q^{6} + 118076 q^{8} + 393660 q^{9}+O(q^{10}) $ 20 * q - 22 * q^2 - 1864 * q^4 - 2430 * q^6 + 118076 * q^8 + 393660 * q^9	\( 20 q - 22 q^{2} - 1864 q^{4} - 2430 q^{6} + 118076 q^{8} + 393660 q^{9} - 113028 q^{10} - 91808 q^{11} + 310068 q^{12} - 503244 q^{14} - 545032 q^{16} - 905768 q^{17} - 433026 q^{18} - 5107040 q^{19} - 5944248 q^{20} - 2702288 q^{22} - 6248988 q^{24} - 40539484 q^{25} + 19400160 q^{26} - 19709616 q^{28} - 6556140 q^{30} + 118772648 q^{32} + 155305372 q^{34} - 68411424 q^{35} - 36689112 q^{36} - 119065400 q^{38} + 477325560 q^{40} + 51872200 q^{41} + 315008676 q^{42} - 392685920 q^{43} - 333411776 q^{44} - 1035567720 q^{46} + 520626528 q^{48} - 1130175964 q^{49} + 2330181842 q^{50} + 373209120 q^{51} - 2683888176 q^{52} - 47829690 q^{54} + 4216587096 q^{56} + 563025168 q^{57} + 2827093836 q^{58} - 1499085440 q^{59} - 574187616 q^{60} - 5504139012 q^{62} + 3240358112 q^{64} + 1717119456 q^{65} + 2366318448 q^{66} - 4570092800 q^{67} - 6509360144 q^{68} - 9179287176 q^{70} + 2324089908 q^{72} - 2312358680 q^{73} + 7298736360 q^{74} + 5958608832 q^{75} - 12863545616 q^{76} - 2062821168 q^{78} + 4230593184 q^{80} + 7748409780 q^{81} + 1201856596 q^{82} + 14192131360 q^{83} - 807928344 q^{84} + 11933558200 q^{86} - 12709901024 q^{88} + 8963359000 q^{89} - 2224730124 q^{90} - 401968224 q^{91} + 13243366752 q^{92} + 5851812792 q^{94} - 7654043160 q^{96} + 23275134232 q^{97} - 20615960782 q^{98} - 1807056864 q^{99}+O(q^{100}) \) 20 * q - 22 * q^2 - 1864 * q^4 - 2430 * q^6 + 118076 * q^8 + 393660 * q^9 - 113028 * q^10 - 91808 * q^11 + 310068 * q^12 - 503244 * q^14 - 545032 * q^16 - 905768 * q^17 - 433026 * q^18 - 5107040 * q^19 - 5944248 * q^20 - 2702288 * q^22 - 6248988 * q^24 - 40539484 * q^25 + 19400160 * q^26 - 19709616 * q^28 - 6556140 * q^30 + 118772648 * q^32 + 155305372 * q^34 - 68411424 * q^35 - 36689112 * q^36 - 119065400 * q^38 + 477325560 * q^40 + 51872200 * q^41 + 315008676 * q^42 - 392685920 * q^43 - 333411776 * q^44 - 1035567720 * q^46 + 520626528 * q^48 - 1130175964 * q^49 + 2330181842 * q^50 + 373209120 * q^51 - 2683888176 * q^52 - 47829690 * q^54 + 4216587096 * q^56 + 563025168 * q^57 + 2827093836 * q^58 - 1499085440 * q^59 - 574187616 * q^60 - 5504139012 * q^62 + 3240358112 * q^64 + 1717119456 * q^65 + 2366318448 * q^66 - 4570092800 * q^67 - 6509360144 * q^68 - 9179287176 * q^70 + 2324089908 * q^72 - 2312358680 * q^73 + 7298736360 * q^74 + 5958608832 * q^75 - 12863545616 * q^76 - 2062821168 * q^78 + 4230593184 * q^80 + 7748409780 * q^81 + 1201856596 * q^82 + 14192131360 * q^83 - 807928344 * q^84 + 11933558200 * q^86 - 12709901024 * q^88 + 8963359000 * q^89 - 2224730124 * q^90 - 401968224 * q^91 + 13243366752 * q^92 + 5851812792 * q^94 - 7654043160 * q^96 + 23275134232 * q^97 - 20615960782 * q^98 - 1807056864 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	30.0501	+	10.9995i	0.939067	+	0.343734i
$2$	30.0501	+	10.9995i	0.939067	+	0.343734i
$3$	−140.296			−0.577350
$3$	−140.296			−0.577350
$4$	782.022	+	661.073i	0.763694	+	0.645579i
$5$		−	977.966i		−	0.312949i	−0.987682	−	0.156475i	$-0.949987\pi$
$5$		−	977.966i		−	0.312949i	0.987682	−	0.156475i	$-0.0500129\pi$
$6$	−4215.92	−	1543.19i	−0.542171	−	0.198455i
$7$			13461.7i			0.800958i	0.916306	+	0.400479i	$0.131156\pi$
$7$			13461.7i			0.800958i	−0.916306	+	0.400479i	$0.868844\pi$
$8$	16228.4	+	28467.2i	0.495252	+	0.868749i
$9$	19683.0			0.333333
$10$	10757.1	−	29388.0i	0.107571	−	0.293880i
$11$	−142575.			−0.885278			−0.442639	−	0.896700i	$-0.645958\pi$
$11$	−142575.			−0.885278			−0.442639	+	0.896700i	$0.645958\pi$
$12$	−109715.	−	92745.9i	−0.440919	−	0.372725i
$13$			702952.i			1.89325i	0.322331	+	0.946627i	$0.395533\pi$
$13$			702952.i			1.89325i	−0.322331	+	0.946627i	$0.604467\pi$
$14$	−148072.	+	404526.i	−0.275316	+	0.752153i
$15$			137205.i			0.180681i
$16$	174542.	+	1.03395e6i	0.166456	+	0.986049i
$17$	−735914.			−0.518302			−0.259151	−	0.965837i	$-0.583443\pi$
$17$	−735914.			−0.518302			−0.259151	+	0.965837i	$0.583443\pi$
$18$	591477.	+	216503.i	0.313022	+	0.114578i
$19$	−1.32395e6			−0.534693			−0.267347	−	0.963600i	$-0.586147\pi$
$19$	−1.32395e6			−0.534693			−0.267347	+	0.963600i	$0.586147\pi$
$20$	646506.	−	764791.i	0.202033	−	0.238997i
$21$		−	1.88862e6i		−	0.462433i
$22$	−4.28440e6	−	1.56825e6i	−0.831335	−	0.304300i
$23$			3.17152e6i			0.492752i	0.969174	+	0.246376i	$0.0792399\pi$
$23$			3.17152e6i			0.492752i	−0.969174	+	0.246376i	$0.920760\pi$
$24$	−2.27679e6	−	3.99383e6i	−0.285934	−	0.501573i
$25$	8.80921e6			0.902063
$26$	−7.73211e6	+	2.11238e7i	−0.650776	+	1.77789i
$27$	−2.76145e6			−0.192450
$28$	−8.89916e6	+	1.05273e7i	−0.517081	+	0.611686i
$29$			5.57861e6i			0.271979i	0.990710	+	0.135990i	$0.0434214\pi$
$29$			5.57861e6i			0.271979i	−0.990710	+	0.135990i	$0.956579\pi$
$30$	−1.50918e6	+	4.12302e6i	−0.0621063	+	0.169672i
$31$			6.23033e6i			0.217622i	0.994062	+	0.108811i	$0.0347043\pi$
$31$			6.23033e6i			0.217622i	−0.994062	+	0.108811i	$0.965296\pi$
$32$	−6.12787e6	+	3.29901e7i	−0.182625	+	0.983183i
$33$	2.00027e7			0.511115
$34$	−2.21143e7	−	8.09468e6i	−0.486720	−	0.178158i
$35$	1.31651e7			0.250659
$36$	1.53925e7	+	1.30119e7i	0.254565	+	0.215193i
$37$		−	1.03173e8i		−	1.48785i	−0.668266	−	0.743923i	$-0.732963\pi$
$37$		−	1.03173e8i		−	1.48785i	0.668266	−	0.743923i	$-0.267037\pi$
$38$	−3.97850e7	−	1.45628e7i	−0.502113	−	0.183792i
$39$		−	9.86214e7i		−	1.09307i
$40$	2.78399e7	−	1.58708e7i	0.271874	−	0.154989i
$41$	1.69259e8			1.46094			0.730471	−	0.682943i	$-0.239300\pi$
$41$	1.69259e8			1.46094			0.730471	+	0.682943i	$0.239300\pi$
$42$	2.07739e7	−	5.67534e7i	0.158954	−	0.434256i
$43$	7.80098e7			0.530648			0.265324	−	0.964159i	$-0.414521\pi$
$43$	7.80098e7			0.530648			0.265324	+	0.964159i	$0.414521\pi$
$44$	−1.11497e8	−	9.42523e7i	−0.676081	−	0.571516i
$45$		−	1.92493e7i		−	0.104316i
$46$	−3.48851e7	+	9.53047e7i	−0.169376	+	0.462728i
$47$		−	1.72281e8i		−	0.751186i	−0.926785	−	0.375593i	$-0.877439\pi$
$47$		−	1.72281e8i		−	0.751186i	0.926785	−	0.375593i	$-0.122561\pi$
$48$	−2.44876e7	−	1.45059e8i	−0.0961036	−	0.569296i
$49$	1.01258e8			0.358467
$50$	2.64718e8	+	9.68968e7i	0.847098	+	0.310070i
$51$	1.03246e8			0.299242
$52$	−4.64702e8	+	5.49724e8i	−1.22224	+	1.44587i
$53$		−	6.23238e8i		−	1.49030i	−0.666895	−	0.745151i	$-0.732377\pi$
$53$		−	6.23238e8i		−	1.49030i	0.666895	−	0.745151i	$-0.267623\pi$
$54$	−8.29819e7	−	3.03745e7i	−0.180724	−	0.0661517i
$55$			1.39433e8i			0.277047i
$56$	−3.83216e8	+	2.18462e8i	−0.695831	+	0.396676i
$57$	1.85746e8			0.308705
$58$	−6.13619e7	+	1.67638e8i	−0.0934886	+	0.255407i
$59$	3.24932e8			0.454498			0.227249	−	0.973837i	$-0.427027\pi$
$59$	3.24932e8			0.454498			0.227249	+	0.973837i	$0.427027\pi$
$60$	−9.07023e7	+	1.07297e8i	−0.116644	+	0.137985i
$61$			1.22646e9i			1.45213i	0.687627	+	0.726064i	$0.258652\pi$
$61$			1.22646e9i			1.45213i	−0.687627	+	0.726064i	$0.741348\pi$
$62$	−6.85305e7	+	1.87222e8i	−0.0748041	+	0.204362i
$63$			2.64967e8i			0.266986i
$64$	−5.47018e8	+	9.23955e8i	−0.509450	+	0.860500i
$65$	6.87463e8			0.592492
$66$	6.01084e8	+	2.20020e8i	0.479972	+	0.175688i
$67$	−2.38626e9			−1.76744			−0.883718	−	0.468019i	$-0.844968\pi$
$67$	−2.38626e9			−1.76744			−0.883718	+	0.468019i	$0.844968\pi$
$68$	−5.75502e8	−	4.86493e8i	−0.395824	−	0.334605i
$69$		−	4.44952e8i		−	0.284491i
$70$	3.95613e8	+	1.44809e8i	0.235386	+	0.0861600i
$71$			1.19609e8i			0.0662934i	0.999450	+	0.0331467i	$0.0105529\pi$
$71$			1.19609e8i			0.0662934i	−0.999450	+	0.0331467i	$0.989447\pi$
$72$	3.19424e8	+	5.60319e8i	0.165084	+	0.289583i
$73$	3.22972e8			0.155794			0.0778971	−	0.996961i	$-0.475179\pi$
$73$	3.22972e8			0.155794			0.0778971	+	0.996961i	$0.475179\pi$
$74$	1.13485e9	−	3.10037e9i	0.511423	−	1.39719i
$75$	−1.23590e9			−0.520806
$76$	−1.03536e9	−	8.75229e8i	−0.408342	−	0.345187i
$77$		−	1.91930e9i		−	0.709070i
$78$	1.08479e9	−	2.96359e9i	0.375726	−	1.02647i
$79$			5.08004e9i			1.65094i	0.564446	+	0.825470i	$0.309090\pi$
$79$			5.08004e9i			1.65094i	−0.564446	+	0.825470i	$0.690910\pi$
$80$	1.01117e9	−	1.70696e8i	0.308583	−	0.0520924i
$81$	3.87420e8			0.111111
$82$	5.08627e9	+	1.86177e9i	1.37192	+	0.502176i
$83$	−5.20864e9			−1.32231			−0.661156	−	0.750249i	$-0.729934\pi$
$83$	−5.20864e9			−1.32231			−0.661156	+	0.750249i	$0.729934\pi$
$84$	1.24852e9	−	1.47695e9i	0.298537	−	0.353157i
$85$			7.19699e8i			0.162202i
$86$	2.34421e9	+	8.58068e8i	0.498315	+	0.182402i
$87$		−	7.82657e8i		−	0.157027i
$88$	−2.31377e9	−	4.05870e9i	−0.438436	−	0.769084i
$89$	9.20987e9			1.64932			0.824658	−	0.565632i	$-0.191368\pi$
$89$	9.20987e9			1.64932			0.824658	+	0.565632i	$0.191368\pi$
$90$	2.11733e8	−	5.78444e8i	0.0358571	−	0.0979601i
$91$	−9.46292e9			−1.51642
$92$	−2.09661e9	+	2.48020e9i	−0.318110	+	0.376312i
$93$		−	8.74091e8i		−	0.125644i
$94$	1.89500e9	−	5.17706e9i	0.258208	−	0.705414i
$95$			1.29478e9i			0.167332i
$96$	8.59717e8	−	4.62839e9i	0.105439	−	0.567641i
$97$	3.54656e9			0.412998			0.206499	−	0.978447i	$-0.433793\pi$
$97$	3.54656e9			0.412998			0.206499	+	0.978447i	$0.433793\pi$
$98$	3.04282e9	+	1.11379e9i	0.336624	+	0.123217i
$99$	−2.80630e9			−0.295093
$100$	6.88900e9	+	5.82353e9i	0.688900	+	0.582353i
$101$		−	1.04232e9i		−	0.0991732i	−0.998770	−	0.0495866i	$-0.984210\pi$
$101$		−	1.04232e9i		−	0.0991732i	0.998770	−	0.0495866i	$-0.0157904\pi$
$102$	3.10256e9	+	1.13565e9i	0.281008	+	0.102860i
$103$		−	1.68984e9i		−	0.145767i	−0.997340	−	0.0728834i	$-0.976780\pi$
$103$		−	1.68984e9i		−	0.145767i	0.997340	−	0.0728834i	$-0.0232201\pi$
$104$	−2.00111e10	+	1.14078e10i	−1.64476	+	0.937638i
$105$	−1.84701e9			−0.144718
$106$	6.85530e9	−	1.87284e10i	0.512268	−	1.39949i
$107$	−3.37221e9			−0.240434			−0.120217	−	0.992748i	$-0.538359\pi$
$107$	−3.37221e9			−0.240434			−0.120217	+	0.992748i	$0.538359\pi$
$108$	−2.15951e9	−	1.82552e9i	−0.146973	−	0.124242i
$109$		−	7.49060e9i		−	0.486838i	−0.969921	−	0.243419i	$-0.921731\pi$
$109$		−	7.49060e9i		−	0.486838i	0.969921	−	0.243419i	$-0.0782690\pi$
$110$	−1.53370e9	+	4.18999e9i	−0.0952304	+	0.260166i
$111$			1.44748e10i			0.859008i
$112$	−1.39187e10	+	2.34963e9i	−0.789783	+	0.133325i
$113$	1.51936e10			0.824647			0.412323	−	0.911038i	$-0.364717\pi$
$113$	1.51936e10			0.824647			0.412323	+	0.911038i	$0.364717\pi$
$114$	5.58168e9	+	2.04311e9i	0.289895	+	0.106113i
$115$	3.10164e9			0.154206
$116$	−3.68787e9	+	4.36260e9i	−0.175584	+	0.207709i
$117$			1.38362e10i			0.631085i
$118$	9.76424e9	+	3.57408e9i	0.426804	+	0.156226i
$119$		−	9.90666e9i		−	0.415138i
$120$	−3.90583e9	+	2.22662e9i	−0.156967	+	0.0894828i
$121$	−5.60983e9			−0.216283
$122$	−1.34904e10	+	3.68553e10i	−0.499146	+	1.36364i
$123$	−2.37464e10			−0.843476
$124$	−4.11870e9	+	4.87226e9i	−0.140492	+	0.166197i
$125$		−	1.81656e10i		−	0.595249i
$126$	−2.91450e9	+	7.96228e9i	−0.0917721	+	0.250718i
$127$			9.48989e9i			0.287238i	0.989633	+	0.143619i	$0.0458741\pi$
$127$			9.48989e9i			0.287238i	−0.989633	+	0.143619i	$0.954126\pi$
$128$	−2.66010e10	+	2.17481e10i	−0.774191	+	0.632952i
$129$	−1.09445e10			−0.306370
$130$	2.06584e10	+	7.56174e9i	0.556390	+	0.203660i
$131$	5.99776e10			1.55465			0.777325	−	0.629099i	$-0.216576\pi$
$131$	5.99776e10			1.55465			0.777325	+	0.629099i	$0.216576\pi$
$132$	1.56426e10	+	1.32232e10i	0.390336	+	0.329965i
$133$		−	1.78227e10i		−	0.428267i
$134$	−7.17075e10	−	2.62477e10i	−1.65974	−	0.607528i
$135$			2.70060e9i			0.0602271i
$136$	−1.19427e10	−	2.09494e10i	−0.256690	−	0.450274i
$137$	5.13817e10			1.06465			0.532323	−	0.846541i	$-0.321319\pi$
$137$	5.13817e10			1.06465			0.532323	+	0.846541i	$0.321319\pi$
$138$	4.89425e9	−	1.33709e10i	0.0977892	−	0.267156i
$139$	4.37636e10			0.843411			0.421706	−	0.906733i	$-0.361432\pi$
$139$	4.37636e10			0.843411			0.421706	+	0.906733i	$0.361432\pi$
$140$	1.02954e10	+	8.70307e9i	0.191427	+	0.161820i
$141$			2.41703e10i			0.433697i
$142$	−1.31563e9	+	3.59425e9i	−0.0227873	+	0.0622540i
$143$		−	1.00223e11i		−	1.67606i
$144$	3.43551e9	+	2.03512e10i	0.0554855	+	0.328683i
$145$	5.45569e9			0.0851157
$146$	9.70537e9	+	3.55253e9i	0.146301	+	0.0535517i
$147$	−1.42061e10			−0.206961
$148$	6.82049e10	−	8.06837e10i	0.960521	−	1.13626i
$149$		−	1.03827e11i		−	1.41377i	−0.707329	−	0.706884i	$-0.750100\pi$
$149$		−	1.03827e11i		−	1.41377i	0.707329	−	0.706884i	$-0.249900\pi$
$150$	−3.71389e10	−	1.35942e10i	−0.489072	−	0.179019i
$151$		−	1.06802e11i		−	1.36049i	−0.732987	−	0.680243i	$-0.761874\pi$
$151$		−	1.06802e11i		−	1.36049i	0.732987	−	0.680243i	$-0.238126\pi$
$152$	−2.14857e10	−	3.76892e10i	−0.264808	−	0.464514i
$153$	−1.44850e10			−0.172767
$154$	2.11113e10	−	5.76752e10i	0.243732	−	0.665864i
$155$	6.09305e9			0.0681046
$156$	6.51959e10	−	7.71242e10i	0.705663	−	0.834771i
$157$			1.24321e11i			1.30331i	0.758516	+	0.651654i	$0.225925\pi$
$157$			1.24321e11i			1.30331i	−0.758516	+	0.651654i	$0.774075\pi$
$158$	−5.58778e10	+	1.52656e11i	−0.567484	+	1.55034i
$159$			8.74379e10i			0.860427i
$160$	3.22632e10	+	5.99285e9i	0.307686	+	0.0571523i
$161$	−4.26941e10			−0.394674
$162$	1.16420e10	+	4.26143e9i	0.104341	+	0.0381927i
$163$	2.03301e10			0.176686			0.0883428	−	0.996090i	$-0.471843\pi$
$163$	2.03301e10			0.176686			0.0883428	+	0.996090i	$0.471843\pi$
$164$	1.32365e11	+	1.11893e11i	1.11571	+	0.943154i
$165$		−	1.95620e10i		−	0.159953i
$166$	−1.56520e11	−	5.72924e10i	−1.24174	−	0.454524i
$167$			2.49396e11i			1.92003i	0.279952	+	0.960014i	$0.409682\pi$
$167$			2.49396e11i			1.92003i	−0.279952	+	0.960014i	$0.590318\pi$
$168$	5.37638e10	−	3.06494e10i	0.401738	−	0.229021i
$169$	−3.56283e11			−2.58441
$170$	−7.91633e9	+	2.16271e10i	−0.0557544	+	0.152319i
$171$	−2.60594e10			−0.178231
$172$	6.10054e10	+	5.15701e10i	0.405253	+	0.342575i
$173$			1.71861e11i			1.10904i	0.832170	+	0.554521i	$0.187099\pi$
$173$			1.71861e11i			1.10904i	−0.832170	+	0.554521i	$0.812901\pi$
$174$	8.60883e9	−	2.35190e10i	0.0539757	−	0.147459i
$175$			1.18587e11i			0.722514i
$176$	−2.48853e10	−	1.47415e11i	−0.147360	−	0.872927i
$177$	−4.55866e10			−0.262404
$178$	2.76758e11	+	1.01304e11i	1.54882	+	0.566926i
$179$	1.28864e11			0.701240			0.350620	−	0.936518i	$-0.385971\pi$
$179$	1.28864e11			0.701240			0.350620	+	0.936518i	$0.385971\pi$
$180$	1.27252e10	−	1.50534e10i	0.0673444	−	0.0796658i
$181$			2.23231e11i			1.14911i	0.818465	+	0.574556i	$0.194825\pi$
$181$			2.23231e11i			1.14911i	−0.818465	+	0.574556i	$0.805175\pi$
$182$	−2.84362e11	−	1.04087e11i	−1.42402	−	0.521244i
$183$		−	1.72068e11i		−	0.838386i
$184$	−9.02843e10	+	5.14688e10i	−0.428078	+	0.244037i
$185$	−1.00900e11			−0.465620
$186$	9.61456e9	−	2.62666e10i	0.0431882	−	0.117988i
$187$	1.04923e11			0.458841
$188$	1.13890e11	−	1.34727e11i	0.484949	−	0.573676i
$189$		−	3.71738e10i		−	0.154144i
$190$	−1.42419e10	+	3.89084e10i	−0.0575176	+	0.157136i
$191$		−	4.43473e11i		−	1.74462i	−0.488956	−	0.872308i	$-0.662622\pi$
$191$		−	4.43473e11i		−	1.74462i	0.488956	−	0.872308i	$-0.337378\pi$
$192$	7.67445e10	−	1.29627e11i	0.294131	−	0.496810i
$193$	−3.35726e11			−1.25371			−0.626857	−	0.779134i	$-0.715659\pi$
$193$	−3.35726e11			−1.25371			−0.626857	+	0.779134i	$0.715659\pi$
$194$	1.06575e11	+	3.90103e10i	0.387833	+	0.141962i
$195$	−9.64484e10			−0.342075
$196$	7.91861e10	+	6.69389e10i	0.273759	+	0.231419i
$197$			5.53835e9i			0.0186659i	0.999956	+	0.00933296i	$0.00297082\pi$
$197$			5.53835e9i			0.0186659i	−0.999956	+	0.00933296i	$0.997029\pi$
$198$	−8.43298e10	−	3.08679e10i	−0.277112	−	0.101433i
$199$			2.33142e11i			0.747059i	0.927618	+	0.373529i	$0.121852\pi$
$199$			2.33142e11i			0.747059i	−0.927618	+	0.373529i	$0.878148\pi$
$200$	1.42960e11	+	2.50773e11i	0.446749	+	0.783666i
$201$	3.34783e11			1.02043
$202$	1.14650e10	−	3.13219e10i	0.0340892	−	0.0931303i
$203$	−7.50976e10			−0.217844
$204$	8.07406e10	+	6.82531e10i	0.228529	+	0.193184i
$205$		−	1.65530e11i		−	0.457201i
$206$	1.85873e10	−	5.07798e10i	0.0501050	−	0.136885i
$207$			6.24251e10i			0.164251i
$208$	−7.26815e11	+	1.22695e11i	−1.86684	+	0.315144i
$209$	1.88762e11			0.473352
$210$	−5.55029e10	−	2.03162e10i	−0.135900	−	0.0497445i
$211$	7.74153e11			1.85104			0.925518	−	0.378705i	$-0.123630\pi$
$211$	7.74153e11			1.85104			0.925518	+	0.378705i	$0.123630\pi$
$212$	4.12005e11	−	4.87386e11i	0.962108	−	1.13814i
$213$		−	1.67806e10i		−	0.0382745i
$214$	−1.01336e11	−	3.70926e10i	−0.225784	−	0.0826454i
$215$		−	7.62909e10i		−	0.166066i
$216$	−4.48140e10	−	7.86106e10i	−0.0953113	−	0.167191i
$217$	−8.38708e10			−0.174306
$218$	8.23928e10	−	2.25094e11i	0.167343	−	0.457173i
$219$	−4.53118e10			−0.0899478
$220$	−9.21756e10	+	1.09040e11i	−0.178856	+	0.211579i
$221$		−	5.17312e11i		−	0.981277i
$222$	−1.59215e11	+	4.34969e11i	−0.295270	+	0.806666i
$223$		−	6.34853e11i		−	1.15120i	−0.817733	−	0.575598i	$-0.804769\pi$
$223$		−	6.34853e11i		−	1.15120i	0.817733	−	0.575598i	$-0.195231\pi$
$224$	−4.44103e11	−	8.24916e10i	−0.787488	−	0.146275i
$225$	1.73392e11			0.300688
$226$	4.56569e11	+	1.67122e11i	0.774398	+	0.283459i
$227$	−6.26190e11			−1.03891			−0.519454	−	0.854499i	$-0.673865\pi$
$227$	−6.26190e11			−1.03891			−0.519454	+	0.854499i	$0.673865\pi$
$228$	1.45257e11	+	1.22791e11i	0.235756	+	0.199294i
$229$			2.28454e11i			0.362762i	0.983413	+	0.181381i	$0.0580567\pi$
$229$			2.28454e11i			0.362762i	−0.983413	+	0.181381i	$0.941943\pi$
$230$	9.32048e10	+	3.41165e10i	0.144810	+	0.0530060i
$231$			2.69270e11i			0.409382i
$232$	−1.58807e11	+	9.05321e10i	−0.236282	+	0.134698i
$233$	8.86390e11			1.29076			0.645380	−	0.763862i	$-0.276699\pi$
$233$	8.86390e11			1.29076			0.645380	+	0.763862i	$0.276699\pi$
$234$	−1.52191e11	+	4.15780e11i	−0.216925	+	0.592631i
$235$	−1.68485e11			−0.235083
$236$	2.54104e11	+	2.14803e11i	0.347097	+	0.293414i
$237$		−	7.12709e11i		−	0.953171i
$238$	1.08968e11	−	2.97696e11i	0.142697	−	0.389842i
$239$			1.22869e12i			1.57563i	0.615915	+	0.787813i	$0.288787\pi$
$239$			1.22869e12i			1.57563i	−0.615915	+	0.787813i	$0.711213\pi$
$240$	−1.41863e11	+	2.39480e10i	−0.178161	+	0.0300755i
$241$	7.42014e11			0.912698			0.456349	−	0.889801i	$-0.349157\pi$
$241$	7.42014e11			0.912698			0.456349	+	0.889801i	$0.349157\pi$
$242$	−1.68576e11	−	6.17053e10i	−0.203104	−	0.0743439i
$243$	−5.43536e10			−0.0641500
$244$	−8.10780e11	+	9.59120e11i	−0.937462	+	1.10898i
$245$		−	9.90269e10i		−	0.112182i
$246$	−7.13583e11	−	2.61199e11i	−0.792080	−	0.289931i
$247$		−	9.30675e11i		−	1.01231i
$248$	−1.77360e11	+	1.01108e11i	−0.189059	+	0.107778i
$249$	7.30752e11			0.763437
$250$	1.99812e11	−	5.45878e11i	0.204607	−	0.558979i
$251$	−1.95248e12			−1.95982			−0.979912	−	0.199430i	$-0.936091\pi$
$251$	−1.95248e12			−1.95982			−0.979912	+	0.199430i	$0.936091\pi$
$252$	−1.75162e11	+	2.07210e11i	−0.172360	+	0.203895i
$253$		−	4.52180e11i		−	0.436223i
$254$	−1.04384e11	+	2.85173e11i	−0.0987337	+	0.269736i
$255$		−	1.00971e11i		−	0.0936474i
$256$	−1.03858e12	+	3.60935e11i	−0.944585	+	0.328268i
$257$	9.52879e10			0.0849908			0.0424954	−	0.999097i	$-0.486469\pi$
$257$	9.52879e10			0.0849908			0.0424954	+	0.999097i	$0.486469\pi$
$258$	−3.28883e11	−	1.20384e11i	−0.287702	−	0.105310i
$259$	1.38888e12			1.19170
$260$	5.37611e11	+	4.54463e11i	0.452482	+	0.382500i
$261$			1.09804e11i			0.0906598i
$262$	1.80234e12	+	6.59723e11i	1.45992	+	0.534386i
$263$			1.25599e12i			0.998178i	0.866551	+	0.499089i	$0.166332\pi$
$263$			1.25599e12i			0.998178i	−0.866551	+	0.499089i	$0.833668\pi$
$264$	3.24612e11	+	5.69420e11i	0.253131	+	0.444031i
$265$	−6.09505e11			−0.466389
$266$	1.96040e11	−	5.35573e11i	0.147210	−	0.402171i
$267$	−1.29211e12			−0.952233
$268$	−1.86611e12	−	1.57749e12i	−1.34978	−	1.14102i
$269$			2.52074e12i			1.78964i	0.446426	+	0.894821i	$0.352697\pi$
$269$			2.52074e12i			1.78964i	−0.446426	+	0.894821i	$0.647303\pi$
$270$	−2.97052e10	+	8.11535e10i	−0.0207021	+	0.0565573i
$271$		−	4.14084e11i		−	0.283297i	−0.989917	−	0.141649i	$-0.954760\pi$
$271$		−	4.14084e11i		−	0.283297i	0.989917	−	0.141649i	$-0.0452403\pi$
$272$	−1.28448e11	−	7.60897e11i	−0.0862747	−	0.511071i
$273$	1.32761e12			0.875503
$274$	1.54403e12	+	5.65172e11i	0.999775	+	0.365955i
$275$	−1.25597e12			−0.798576
$276$	2.94146e11	−	3.47963e11i	0.183661	−	0.217264i
$277$		−	1.03516e12i		−	0.634758i	−0.948299	−	0.317379i	$-0.897197\pi$
$277$		−	1.03516e12i		−	0.634758i	0.948299	−	0.317379i	$-0.102803\pi$
$278$	1.31510e12	+	4.81378e11i	0.792020	+	0.289909i
$279$			1.22632e11i			0.0725407i
$280$	2.13649e11	+	3.74773e11i	0.124139	+	0.217760i
$281$	−1.27651e12			−0.728603			−0.364302	−	0.931281i	$-0.618692\pi$
$281$	−1.27651e12			−0.728603			−0.364302	+	0.931281i	$0.618692\pi$
$282$	−2.65861e11	+	7.26321e11i	−0.149077	+	0.407271i
$283$	8.48312e11			0.467330			0.233665	−	0.972317i	$-0.424928\pi$
$283$	8.48312e11			0.467330			0.233665	+	0.972317i	$0.424928\pi$
$284$	−7.90699e10	+	9.35366e10i	−0.0427976	+	0.0506279i
$285$		−	1.81653e11i		−	0.0966090i
$286$	1.10240e12	−	3.01172e12i	0.576117	−	1.57393i
$287$			2.27852e12i			1.17015i
$288$	−1.20615e11	+	6.49345e11i	−0.0608749	+	0.327728i
$289$	−1.47442e12			−0.731363
$290$	1.63944e11	+	6.00098e10i	0.0799294	+	0.0292572i
$291$	−4.97568e11			−0.238445
$292$	2.52572e11	+	2.13508e11i	0.118979	+	0.100577i
$293$		−	1.75145e12i		−	0.811073i	−0.914079	−	0.405537i	$-0.867085\pi$
$293$		−	1.75145e12i		−	0.811073i	0.914079	−	0.405537i	$-0.132915\pi$
$294$	−4.26896e11	−	1.56260e11i	−0.194350	−	0.0711395i
$295$		−	3.17772e11i		−	0.142235i
$296$	2.93705e12	−	1.67434e12i	1.29256	−	0.736859i
$297$	3.93713e11			0.170372
$298$	1.14204e12	−	3.12001e12i	0.485960	−	1.32762i
$299$	−2.22943e12			−0.932905
$300$	−9.66500e11	−	8.17018e11i	−0.397736	−	0.336221i
$301$			1.05014e12i			0.425027i
$302$	1.17477e12	−	3.20941e12i	0.467645	−	1.27759i
$303$			1.46234e11i			0.0572577i
$304$	−2.31086e11	−	1.36890e12i	−0.0890031	−	0.527234i
$305$	1.19944e12			0.454442
$306$	−4.35277e11	−	1.59328e11i	−0.162240	−	0.0593860i
$307$	2.13417e12			0.782594			0.391297	−	0.920264i	$-0.372027\pi$
$307$	2.13417e12			0.782594			0.391297	+	0.920264i	$0.372027\pi$
$308$	1.26880e12	−	1.50094e12i	0.457760	−	0.541512i
$309$			2.37077e11i			0.0841585i
$310$	1.83097e11	+	6.70205e10i	0.0639548	+	0.0234099i
$311$		−	4.03126e12i		−	1.38560i	−0.721128	−	0.692802i	$-0.756376\pi$
$311$		−	4.03126e12i		−	1.38560i	0.721128	−	0.692802i	$-0.243624\pi$
$312$	2.80747e12	−	1.60047e12i	0.949604	−	0.541346i
$313$	−3.22338e12			−1.07298			−0.536488	−	0.843908i	$-0.680249\pi$
$313$	−3.22338e12			−1.07298			−0.536488	+	0.843908i	$0.680249\pi$
$314$	−1.36747e12	+	3.73587e12i	−0.447991	+	1.22389i
$315$	2.59128e11			0.0835530
$316$	−3.35827e12	+	3.97270e12i	−1.06581	+	1.26081i
$317$		−	1.11953e12i		−	0.349736i	−0.984592	−	0.174868i	$-0.944050\pi$
$317$		−	1.11953e12i		−	0.349736i	0.984592	−	0.174868i	$-0.0559499\pi$
$318$	−9.61772e11	+	2.62752e12i	−0.295758	+	0.807998i
$319$		−	7.95370e11i		−	0.240777i
$320$	9.03596e11	+	5.34965e11i	0.269293	+	0.159432i
$321$	4.73108e11			0.138815
$322$	−1.28296e12	−	4.69613e11i	−0.370625	−	0.135663i
$323$	9.74316e11			0.277132
$324$	3.02972e11	+	2.56113e11i	0.0848549	+	0.0717310i
$325$			6.19245e12i			1.70783i
$326$	6.10922e11	+	2.23621e11i	0.165920	+	0.0607329i
$327$			1.05090e12i			0.281076i
$328$	2.74681e12	+	4.81833e12i	0.723535	+	1.26919i
$329$	2.31919e12			0.601668
$330$	2.15172e11	−	5.87840e11i	0.0549813	−	0.150207i
$331$	3.56815e12			0.898057			0.449028	−	0.893518i	$-0.351770\pi$
$331$	3.56815e12			0.898057			0.449028	+	0.893518i	$0.351770\pi$
$332$	−4.07327e12	−	3.44329e12i	−1.00984	−	0.853656i
$333$		−	2.03076e12i		−	0.495948i
$334$	−2.74323e12	+	7.49439e12i	−0.659979	+	1.80304i
$335$			2.33368e12i			0.553118i
$336$	1.95274e12	−	3.29644e11i	0.455982	−	0.0769749i
$337$	−4.87325e12			−1.12117			−0.560583	−	0.828099i	$-0.689423\pi$
$337$	−4.87325e12			−1.12117			−0.560583	+	0.828099i	$0.689423\pi$
$338$	−1.07064e13	−	3.91893e12i	−2.42693	−	0.888350i
$339$	−2.13160e12			−0.476110
$340$	−4.75773e11	+	5.62821e11i	−0.104714	+	0.123873i
$341$		−	8.88289e11i		−	0.192656i
$342$	−7.83088e11	−	2.86640e11i	−0.167371	−	0.0612641i
$343$			5.16570e12i			1.08807i
$344$	1.26598e12	+	2.22072e12i	0.262805	+	0.461000i
$345$	−4.35148e11			−0.0890311
$346$	−1.89039e12	+	5.16446e12i	−0.381216	+	1.04146i
$347$	5.50460e12			1.09415			0.547077	−	0.837083i	$-0.315741\pi$
$347$	5.50460e12			1.09415			0.547077	+	0.837083i	$0.315741\pi$
$348$	5.17393e11	−	6.12056e11i	0.101374	−	0.119921i
$349$		−	2.30550e12i		−	0.445284i	−0.974900	−	0.222642i	$-0.928532\pi$
$349$		−	2.30550e12i		−	0.445284i	0.974900	−	0.222642i	$-0.0714681\pi$
$350$	−1.30440e12	+	3.56355e12i	−0.248353	+	0.678489i
$351$		−	1.94117e12i		−	0.364357i
$352$	8.73681e11	−	4.70356e12i	0.161674	−	0.870390i
$353$	2.40628e12			0.439007			0.219504	−	0.975612i	$-0.429556\pi$
$353$	2.40628e12			0.439007			0.219504	+	0.975612i	$0.429556\pi$
$354$	−1.36988e12	−	5.01430e11i	−0.246415	−	0.0901973i
$355$	1.16973e11			0.0207465
$356$	7.20233e12	+	6.08840e12i	1.25957	+	1.06476i
$357$			1.38987e12i			0.239680i
$358$	3.87239e12	+	1.41744e12i	0.658512	+	0.241040i
$359$		−	9.41295e12i		−	1.57853i	−0.614051	−	0.789267i	$-0.710461\pi$
$359$		−	9.41295e12i		−	1.57853i	0.614051	−	0.789267i	$-0.289539\pi$
$360$	5.47973e11	−	3.12386e11i	0.0906248	−	0.0516629i
$361$	−4.37821e12			−0.714103
$362$	−2.45543e12	+	6.70813e12i	−0.394989	+	1.07909i
$363$	7.87037e11			0.124871
$364$	−7.40022e12	−	6.25568e12i	−1.15808	−	0.978966i
$365$		−	3.15856e11i		−	0.0487556i
$366$	1.89266e12	−	5.17066e12i	0.288182	−	0.787301i
$367$		−	7.63453e12i		−	1.14671i	−0.819309	−	0.573353i	$-0.805642\pi$
$367$		−	7.63453e12i		−	1.14671i	0.819309	−	0.573353i	$-0.194358\pi$
$368$	−3.27919e12	+	5.53565e11i	−0.485878	+	0.0820218i
$369$	3.33153e12			0.486981
$370$	−3.03205e12	−	1.10985e12i	−0.437248	−	0.160049i
$371$	8.38984e12			1.19367
$372$	5.77838e11	−	6.83559e11i	0.0811131	−	0.0959536i
$373$			2.06079e12i			0.285424i	0.989764	+	0.142712i	$0.0455822\pi$
$373$			2.06079e12i			0.285424i	−0.989764	+	0.142712i	$0.954418\pi$
$374$	3.15295e12	+	1.15410e12i	0.430883	+	0.157719i
$375$			2.54856e12i			0.343667i
$376$	4.90434e12	−	2.79584e12i	0.652592	−	0.372026i
$377$	−3.92149e12			−0.514926
$378$	4.08893e11	−	1.11708e12i	0.0529847	−	0.144752i
$379$	6.22090e12			0.795531			0.397766	−	0.917487i	$-0.369786\pi$
$379$	6.22090e12			0.795531			0.397766	+	0.917487i	$0.369786\pi$
$380$	−8.55944e11	+	1.01255e12i	−0.108026	+	0.127790i
$381$		−	1.33139e12i		−	0.165837i
$382$	4.87797e12	−	1.33264e13i	0.599684	−	1.63831i
$383$		−	4.91730e12i		−	0.596668i	−0.954461	−	0.298334i	$-0.903569\pi$
$383$		−	4.91730e12i		−	0.596668i	0.954461	−	0.298334i	$-0.0964310\pi$
$384$	3.73202e12	−	3.05117e12i	0.446980	−	0.365435i
$385$	−1.87701e12			−0.221903
$386$	−1.00886e13	−	3.69282e12i	−1.17732	−	0.430944i
$387$	1.53547e12			0.176883
$388$	2.77349e12	+	2.34453e12i	0.315404	+	0.266623i
$389$		−	6.89625e12i		−	0.774221i	−0.922033	−	0.387110i	$-0.873473\pi$
$389$		−	6.89625e12i		−	0.774221i	0.922033	−	0.387110i	$-0.126527\pi$
$390$	−2.89829e12	−	1.06088e12i	−0.321232	−	0.117583i
$391$		−	2.33397e12i		−	0.255394i
$392$	1.64326e12	+	2.88253e12i	0.177532	+	0.311418i
$393$	−8.41463e12			−0.897578
$394$	−6.09191e10	+	1.66428e11i	−0.00641611	+	0.0175286i
$395$	4.96810e12			0.516660
$396$	−2.19459e12	−	1.85517e12i	−0.225360	−	0.190505i
$397$			6.06778e12i			0.615287i	0.951502	+	0.307643i	$0.0995404\pi$
$397$			6.06778e12i			0.615287i	−0.951502	+	0.307643i	$0.900460\pi$
$398$	−2.56444e12	+	7.00595e12i	−0.256790	+	0.701538i
$399$			2.50045e12i			0.247260i
$400$	1.53758e12	+	9.10825e12i	0.150154	+	0.889478i
$401$	6.77051e12			0.652980			0.326490	−	0.945201i	$-0.394134\pi$
$401$	6.77051e12			0.652980			0.326490	+	0.945201i	$0.394134\pi$
$402$	1.00603e13	+	3.68244e12i	0.958252	+	0.350757i
$403$	−4.37962e12			−0.412014
$404$	6.89049e11	−	8.15118e11i	0.0640241	−	0.0757380i
$405$		−	3.78884e11i		−	0.0347721i
$406$	−2.25669e12	−	8.26035e11i	−0.204570	−	0.0748804i
$407$			1.47099e13i			1.31716i
$408$	1.67552e12	+	2.93912e12i	0.148200	+	0.259966i
$409$	4.65423e12			0.406660			0.203330	−	0.979110i	$-0.434824\pi$
$409$	4.65423e12			0.406660			0.203330	+	0.979110i	$0.434824\pi$
$410$	1.82074e12	−	4.97420e12i	0.157155	−	0.429342i
$411$	−7.20865e12			−0.614674
$412$	1.11710e12	−	1.32149e12i	0.0941039	−	0.111321i
$413$			4.37413e12i			0.364033i
$414$	−6.86644e11	+	1.87588e12i	−0.0564586	+	0.154243i
$415$			5.09387e12i			0.413816i
$416$	−2.31905e13	−	4.30760e12i	−1.86141	−	0.345755i
$417$	−6.13987e12			−0.486944
$418$	5.67234e12	+	2.07629e12i	0.444509	+	0.162707i
$419$	−7.83914e12			−0.607013			−0.303507	−	0.952829i	$-0.598157\pi$
$419$	−7.83914e12			−0.607013			−0.303507	+	0.952829i	$0.598157\pi$
$420$	−1.44440e12	−	1.22101e12i	−0.110520	−	0.0934269i
$421$		−	4.28529e12i		−	0.324018i	−0.986789	−	0.162009i	$-0.948203\pi$
$421$		−	4.28529e12i		−	0.324018i	0.986789	−	0.162009i	$-0.0517974\pi$
$422$	2.32634e13	+	8.51529e12i	1.73825	+	0.636264i
$423$		−	3.39100e12i		−	0.250395i
$424$	1.77418e13	−	1.01142e13i	1.29470	−	0.738076i
$425$	−6.48282e12			−0.467541
$426$	1.84578e11	−	5.04260e11i	0.0131563	−	0.0359423i
$427$	−1.65102e13			−1.16309
$428$	−2.63715e12	−	2.22928e12i	−0.183618	−	0.155219i
$429$			1.40609e13i			0.967671i
$430$	8.39161e11	−	2.29255e12i	0.0570825	−	0.155947i
$431$		−	8.47536e12i		−	0.569865i	−0.958548	−	0.284932i	$-0.908029\pi$
$431$		−	8.47536e12i		−	0.569865i	0.958548	−	0.284932i	$-0.0919712\pi$
$432$	−4.81989e11	−	2.85519e12i	−0.0320345	−	0.189765i
$433$	3.34011e12			0.219443			0.109721	−	0.993962i	$-0.465004\pi$
$433$	3.34011e12			0.219443			0.109721	+	0.993962i	$0.465004\pi$
$434$	−2.52033e12	−	9.22536e11i	−0.163685	−	0.0599149i
$435$	−7.65412e11			−0.0491416
$436$	4.95183e12	−	5.85782e12i	0.314292	−	0.371795i
$437$		−	4.19895e12i		−	0.263471i
$438$	−1.36163e12	−	4.98406e11i	−0.0844670	−	0.0309181i
$439$			1.88324e13i			1.15500i	0.816389	+	0.577502i	$0.195972\pi$
$439$			1.88324e13i			1.15500i	−0.816389	+	0.577502i	$0.804028\pi$
$440$	−3.96927e12	+	2.26278e12i	−0.240684	+	0.137208i
$441$	1.99306e12			0.119489
$442$	5.69017e12	−	1.55453e13i	0.337298	−	0.921485i
$443$	−1.21718e13			−0.713405			−0.356703	−	0.934218i	$-0.616099\pi$
$443$	−1.21718e13			−0.713405			−0.356703	+	0.934218i	$0.616099\pi$
$444$	−9.56888e12	+	1.13196e13i	−0.554557	+	0.656019i
$445$		−	9.00694e12i		−	0.516152i
$446$	6.98306e12	−	1.90774e13i	0.395705	−	1.08105i
$447$			1.45665e13i			0.816240i
$448$	−1.24380e13	−	7.36379e12i	−0.689224	−	0.408048i
$449$	1.38095e13			0.756741			0.378371	−	0.925654i	$-0.376485\pi$
$449$	1.38095e13			0.756741			0.378371	+	0.925654i	$0.376485\pi$
$450$	5.21044e12	+	1.90722e12i	0.282366	+	0.103357i
$451$	−2.41321e13			−1.29334
$452$	1.18817e13	+	1.00441e13i	0.629778	+	0.532374i
$453$			1.49839e13i			0.785477i
$454$	−1.88171e13	−	6.88777e12i	−0.975604	−	0.357108i
$455$			9.25442e12i			0.474561i
$456$	3.01436e12	+	5.28765e12i	0.152887	+	0.268187i
$457$	1.53610e13			0.770615			0.385307	−	0.922788i	$-0.374095\pi$
$457$	1.53610e13			0.770615			0.385307	+	0.922788i	$0.374095\pi$
$458$	−2.51288e12	+	6.86508e12i	−0.124694	+	0.340658i
$459$	2.03219e12			0.0997472
$460$	2.42555e12	+	2.05041e12i	0.117766	+	0.0995524i
$461$			1.73150e13i			0.831605i	0.909455	+	0.415803i	$0.136499\pi$
$461$			1.73150e13i			0.831605i	−0.909455	+	0.415803i	$0.863501\pi$
$462$	−2.96184e12	+	8.09161e12i	−0.140718	+	0.384437i
$463$			9.55093e12i			0.448891i	0.974487	+	0.224445i	$0.0720570\pi$
$463$			9.55093e12i			0.448891i	−0.974487	+	0.224445i	$0.927943\pi$
$464$	−5.76799e12	+	9.73703e11i	−0.268185	+	0.0452727i
$465$	−8.54832e11			−0.0393202
$466$	2.66361e13	+	9.74984e12i	1.21211	+	0.443678i
$467$	−1.97362e13			−0.888546			−0.444273	−	0.895892i	$-0.646538\pi$
$467$	−1.97362e13			−0.888546			−0.444273	+	0.895892i	$0.646538\pi$
$468$	−9.14673e12	+	1.08202e13i	−0.407415	+	0.481955i
$469$		−	3.21231e13i		−	1.41564i
$470$	−5.06299e12	−	1.85325e12i	−0.220759	−	0.0808060i
$471$		−	1.74418e13i		−	0.752465i
$472$	5.27313e12	+	9.24988e12i	0.225091	+	0.394845i
$473$	−1.11222e13			−0.469771
$474$	7.83944e12	−	2.14170e13i	0.327637	−	0.895091i
$475$	−1.16630e13			−0.482327
$476$	6.54902e12	−	7.74723e12i	0.268004	−	0.317038i
$477$		−	1.22672e13i		−	0.496768i
$478$	−1.35150e13	+	3.69223e13i	−0.541596	+	1.47962i
$479$		−	7.37870e12i		−	0.292619i	−0.989239	−	0.146309i	$-0.953260\pi$
$479$		−	7.37870e12i		−	0.292619i	0.989239	−	0.146309i	$-0.0467395\pi$
$480$	−4.52641e12	−	8.40774e11i	−0.177643	−	0.0329969i
$481$	7.25257e13			2.81687
$482$	2.22976e13	+	8.16178e12i	0.857084	+	0.313725i
$483$	5.98981e12			0.227865
$484$	−4.38701e12	−	3.70850e12i	−0.165174	−	0.139628i
$485$		−	3.46841e12i		−	0.129247i
$486$	−1.63333e12	−	5.97862e11i	−0.0602412	−	0.0220506i
$487$		−	3.37911e13i		−	1.23355i	−0.787138	−	0.616777i	$-0.788438\pi$
$487$		−	3.37911e13i		−	1.23355i	0.787138	−	0.616777i	$-0.211562\pi$
$488$	−3.49139e13	+	1.99035e13i	−1.26153	+	0.719169i
$489$	−2.85223e12			−0.102009
$490$	1.08925e12	−	2.97577e12i	0.0385607	−	0.105346i
$491$	4.46299e13			1.56394			0.781968	−	0.623319i	$-0.214216\pi$
$491$	4.46299e13			1.56394			0.781968	+	0.623319i	$0.214216\pi$
$492$	−1.85702e13	−	1.56981e13i	−0.644157	−	0.544530i
$493$		−	4.10538e12i		−	0.140967i
$494$	1.02370e13	−	2.79669e13i	0.347965	−	0.950627i
$495$			2.74447e12i			0.0923490i
$496$	−6.44183e12	+	1.08746e12i	−0.214586	+	0.0362246i
$497$	−1.61013e12			−0.0530982
$498$	2.19592e13	+	8.03790e12i	0.716919	+	0.262419i
$499$	−4.36472e12			−0.141076			−0.0705380	−	0.997509i	$-0.522472\pi$
$499$	−4.36472e12			−0.141076			−0.0705380	+	0.997509i	$0.522472\pi$
$500$	1.20087e13	−	1.42059e13i	0.384280	−	0.454588i
$501$		−	3.49893e13i		−	1.10853i
$502$	−5.86722e13	−	2.14762e13i	−1.84041	−	0.673658i
$503$			1.24766e13i			0.387488i	0.981052	+	0.193744i	$0.0620631\pi$
$503$			1.24766e13i			0.387488i	−0.981052	+	0.193744i	$0.937937\pi$
$504$	−7.54285e12	+	4.29999e12i	−0.231944	+	0.132225i
$505$	−1.01935e12			−0.0310362
$506$	4.97374e12	−	1.35881e13i	0.149945	−	0.409642i
$507$	4.99851e13			1.49211
$508$	−6.27351e12	+	7.42131e12i	−0.185435	+	0.219362i
$509$		−	5.32566e13i		−	1.55878i	−0.626540	−	0.779389i	$-0.715530\pi$
$509$		−	5.32566e13i		−	1.55878i	0.626540	−	0.779389i	$-0.284470\pi$
$510$	1.11063e12	−	3.03419e12i	0.0321898	−	0.0879412i
$511$			4.34775e12i			0.124784i
$512$	−3.51796e13	−	5.77726e11i	−0.999865	−	0.0164200i
$513$	3.65603e12			0.102902
$514$	2.86341e12	+	1.04812e12i	0.0798121	+	0.0292142i
$515$	−1.65260e12			−0.0456176
$516$	−8.55882e12	−	7.23509e12i	−0.233973	−	0.197786i
$517$			2.45629e13i			0.665008i
$518$	4.17362e13	+	1.52770e13i	1.11909	+	0.409628i
$519$		−	2.41115e13i		−	0.640306i
$520$	1.11564e13	+	1.95701e13i	0.293433	+	0.514727i
$521$	−3.92795e13			−1.02324			−0.511619	−	0.859212i	$-0.670954\pi$
$521$	−3.92795e13			−1.02324			−0.511619	+	0.859212i	$0.670954\pi$
$522$	−1.20779e12	+	3.29962e12i	−0.0311629	+	0.0851356i
$523$	−6.47537e12			−0.165484			−0.0827420	−	0.996571i	$-0.526368\pi$
$523$	−6.47537e12			−0.165484			−0.0827420	+	0.996571i	$0.526368\pi$
$524$	4.69038e13	+	3.96496e13i	1.18728	+	1.00365i
$525$		−	1.66373e13i		−	0.417144i
$526$	−1.38153e13	+	3.77427e13i	−0.343108	+	0.937356i
$527$		−	4.58499e12i		−	0.112794i
$528$	3.49132e12	+	2.06817e13i	0.0850784	+	0.503985i
$529$	3.13680e13			0.757195
$530$	−1.83157e13	−	6.70425e12i	−0.437970	−	0.160314i
$531$	6.39563e12			0.151499
$532$	1.17821e13	−	1.39377e13i	0.276480	−	0.327065i
$533$			1.18981e14i			2.76594i
$534$	−3.88281e13	−	1.42125e13i	−0.894210	−	0.327315i
$535$			3.29791e12i			0.0752437i
$536$	−3.87253e13	−	6.79301e13i	−0.875327	−	1.53546i
$537$	−1.80791e13			−0.404861
$538$	−2.77268e13	+	7.57485e13i	−0.615161	+	1.68059i
$539$	−1.44369e13			−0.317343
$540$	−1.78529e12	+	2.11193e12i	−0.0388813	+	0.0459950i
$541$		−	6.51553e12i		−	0.140593i	−0.997526	−	0.0702964i	$-0.977605\pi$
$541$		−	6.51553e12i		−	0.140593i	0.997526	−	0.0702964i	$-0.0223945\pi$
$542$	4.55471e12	−	1.24433e13i	0.0973789	−	0.266035i
$543$		−	3.13185e13i		−	0.663440i
$544$	4.50959e12	−	2.42779e13i	0.0946548	−	0.509585i
$545$	−7.32555e12			−0.152355
$546$	3.98949e13	+	1.46030e13i	0.822156	+	0.300940i
$547$	−2.52100e13			−0.514797			−0.257398	−	0.966305i	$-0.582865\pi$
$547$	−2.52100e13			−0.514797			−0.257398	+	0.966305i	$0.582865\pi$
$548$	4.01816e13	+	3.39670e13i	0.813064	+	0.687313i
$549$			2.41404e13i			0.484042i
$550$	−3.77421e13	−	1.38150e13i	−0.749917	−	0.274498i
$551$		−	7.38582e12i		−	0.145426i
$552$	1.26665e13	−	7.22088e12i	0.247151	−	0.140895i
$553$	−6.83859e13			−1.32233
$554$	1.13862e13	−	3.11067e13i	0.218188	−	0.596080i
$555$	1.41558e13			0.268826
$556$	3.42241e13	+	2.89309e13i	0.644108	+	0.544488i
$557$			2.51724e13i			0.469513i	0.972054	+	0.234757i	$0.0754293\pi$
$557$			2.51724e13i			0.469513i	−0.972054	+	0.234757i	$0.924571\pi$
$558$	−1.34889e12	+	3.68510e12i	−0.0249347	+	0.0681205i
$559$			5.48371e13i			1.00465i
$560$	2.29786e12	+	1.36120e13i	0.0417238	+	0.247162i
$561$	−1.47203e13			−0.264912
$562$	−3.83592e13	−	1.40409e13i	−0.684207	−	0.250446i
$563$	2.63575e13			0.465974			0.232987	−	0.972480i	$-0.425150\pi$
$563$	2.63575e13			0.465974			0.232987	+	0.972480i	$0.425150\pi$
$564$	−1.59783e13	+	1.89017e13i	−0.279986	+	0.331212i
$565$		−	1.48588e13i		−	0.258072i
$566$	2.54919e13	+	9.33100e12i	0.438854	+	0.160637i
$567$			5.21534e12i			0.0889953i
$568$	−3.40492e12	+	1.94106e12i	−0.0575924	+	0.0328320i
$569$	−9.42607e13			−1.58041			−0.790204	−	0.612843i	$-0.790026\pi$
$569$	−9.42607e13			−1.58041			−0.790204	+	0.612843i	$0.790026\pi$
$570$	1.99809e12	−	5.45869e12i	0.0332078	−	0.0907224i
$571$	1.71663e13			0.282810			0.141405	−	0.989952i	$-0.454838\pi$
$571$	1.71663e13			0.282810			0.141405	+	0.989952i	$0.454838\pi$
$572$	6.62549e13	−	7.83768e13i	1.08203	−	1.27999i
$573$			6.22175e13i			1.00725i
$574$	−2.50625e13	+	6.84698e13i	−0.402222	+	1.09885i
$575$			2.79386e13i			0.444494i
$576$	−1.07670e13	+	1.81862e13i	−0.169817	+	0.286833i
$577$	6.21225e13			0.971337			0.485669	−	0.874143i	$-0.338576\pi$
$577$	6.21225e13			0.971337			0.485669	+	0.874143i	$0.338576\pi$
$578$	−4.43066e13	−	1.62179e13i	−0.686799	−	0.251394i
$579$	4.71011e13			0.723833
$580$	4.26647e12	+	3.60661e12i	0.0650023	+	0.0549489i
$581$		−	7.01171e13i		−	1.05912i
$582$	−1.49520e13	−	5.47299e12i	−0.223915	−	0.0819615i
$583$			8.88581e13i			1.31933i
$584$	5.24133e12	+	9.19411e12i	0.0771574	+	0.135346i
$585$	1.35313e13			0.197497
$586$	1.92651e13	−	5.26314e13i	0.278793	−	0.761652i
$587$	−2.82071e13			−0.404732			−0.202366	−	0.979310i	$-0.564863\pi$
$587$	−2.82071e13			−0.404732			−0.202366	+	0.979310i	$0.564863\pi$
$588$	−1.11095e13	−	9.39127e12i	−0.158055	−	0.133610i
$589$		−	8.24867e12i		−	0.116361i
$590$	3.49533e12	−	9.54909e12i	0.0488909	−	0.133568i
$591$		−	7.77009e11i		−	0.0107768i
$592$	1.06676e14	−	1.80081e13i	1.46709	−	0.247661i
$593$	−4.26981e13			−0.582284			−0.291142	−	0.956680i	$-0.594035\pi$
$593$	−4.26981e13			−0.582284			−0.291142	+	0.956680i	$0.594035\pi$
$594$	1.18311e13	+	4.33064e12i	0.159991	+	0.0585626i
$595$	−9.68837e12			−0.129917
$596$	6.86371e13	−	8.11949e13i	0.912699	−	1.07969i
$597$		−	3.27089e13i		−	0.431315i
$598$	−6.69946e13	−	2.45226e13i	−0.876061	−	0.320671i
$599$		−	1.27609e14i		−	1.65481i	−0.561606	−	0.827405i	$-0.689816\pi$
$599$		−	1.27609e14i		−	1.65481i	0.561606	−	0.827405i	$-0.310184\pi$
$600$	−2.00567e13	−	3.51825e13i	−0.257930	−	0.452450i
$601$	−7.93489e13			−1.01197			−0.505986	−	0.862542i	$-0.668871\pi$
$601$	−7.93489e13			−1.01197			−0.505986	+	0.862542i	$0.668871\pi$
$602$	−1.15511e13	+	3.15570e13i	−0.146096	+	0.399129i
$603$	−4.69688e13			−0.589146
$604$	7.06038e13	−	8.35215e13i	0.878301	−	1.03899i
$605$			5.48622e12i			0.0676856i
$606$	−1.60849e12	+	4.39434e12i	−0.0196814	+	0.0537688i
$607$		−	1.38877e14i		−	1.68534i	−0.538434	−	0.842668i	$-0.680984\pi$
$607$		−	1.38877e14i		−	1.68534i	0.538434	−	0.842668i	$-0.319016\pi$
$608$	8.11302e12	−	4.36774e13i	0.0976483	−	0.525701i
$609$	1.05359e13			0.125772
$610$	3.60433e13	+	1.31932e13i	0.426751	+	0.156207i
$611$	1.21105e14			1.42219
$612$	−1.13276e13	−	9.57564e12i	−0.131941	−	0.111535i
$613$			1.03394e13i			0.119452i	0.998215	+	0.0597258i	$0.0190226\pi$
$613$			1.03394e13i			0.119452i	−0.998215	+	0.0597258i	$0.980977\pi$
$614$	6.41320e13	+	2.34747e13i	0.734908	+	0.269004i
$615$			2.32232e13i			0.263965i
$616$	5.46370e13	−	3.11472e13i	0.616004	−	0.351169i
$617$	−1.42712e13			−0.159601			−0.0798006	−	0.996811i	$-0.525428\pi$
$617$	−1.42712e13			−0.159601			−0.0798006	+	0.996811i	$0.525428\pi$
$618$	−2.60773e12	+	7.12421e12i	−0.0289281	+	0.0790304i
$619$	−1.73348e13			−0.190750			−0.0953751	−	0.995441i	$-0.530405\pi$
$619$	−1.73348e13			−0.190750			−0.0953751	+	0.995441i	$0.530405\pi$
$620$	4.76490e12	+	4.02795e12i	0.0520111	+	0.0439669i
$621$		−	8.75800e12i		−	0.0948302i
$622$	4.43418e13	−	1.21140e14i	0.476279	−	1.30117i
$623$			1.23981e14i			1.32103i
$624$	1.01969e14	−	1.72136e13i	1.07782	−	0.181949i
$625$	6.82621e13			0.715780
$626$	−9.68631e13	−	3.54556e13i	−1.00760	−	0.368819i
$627$	−2.64826e13			−0.273290
$628$	−8.21854e13	+	9.72220e13i	−0.841388	+	0.995328i
$629$			7.59266e13i			0.771153i
$630$	7.78684e12	+	2.85028e12i	0.0784619	+	0.0287200i
$631$		−	6.40748e13i		−	0.640532i	−0.947328	−	0.320266i	$-0.896228\pi$
$631$		−	6.40748e13i		−	0.640532i	0.947328	−	0.320266i	$-0.103772\pi$
$632$	−1.44614e14	+	8.24410e13i	−1.43425	+	0.817632i
$633$	−1.08611e14			−1.06870
$634$	1.23143e13	−	3.36421e13i	0.120216	−	0.328426i
$635$	9.28079e12			0.0898910
$636$	−5.78028e13	+	6.83784e13i	−0.555473	+	0.657103i
$637$			7.11795e13i			0.678669i
$638$	8.74866e12	−	2.39010e13i	0.0827634	−	0.226106i
$639$			2.35425e12i			0.0220978i
$640$	2.12689e13	+	2.60149e13i	0.198082	+	0.242282i
$641$	7.87302e13			0.727530			0.363765	−	0.931491i	$-0.381491\pi$
$641$	7.87302e13			0.727530			0.363765	+	0.931491i	$0.381491\pi$
$642$	1.42170e13	+	5.20395e12i	0.130356	+	0.0477153i
$643$	6.96627e13			0.633790			0.316895	−	0.948461i	$-0.397360\pi$
$643$	6.96627e13			0.633790			0.316895	+	0.948461i	$0.397360\pi$
$644$	−3.33877e13	−	2.82239e13i	−0.301410	−	0.254793i
$645$			1.07033e13i			0.0958782i
$646$	2.92784e13	+	1.07170e13i	0.260246	+	0.0952599i
$647$			1.06976e14i			0.943549i	0.881719	+	0.471775i	$0.156386\pi$
$647$			1.06976e14i			0.943549i	−0.881719	+	0.471775i	$0.843614\pi$
$648$	6.28723e12	+	1.10288e13i	0.0550280	+	0.0965277i
$649$	−4.63271e13			−0.402357
$650$	−6.81138e13	+	1.86084e14i	−0.587041	+	1.60377i
$651$	1.17668e13			0.100636
$652$	1.58986e13	+	1.34397e13i	0.134934	+	0.114064i
$653$			5.31296e12i			0.0447477i	0.999750	+	0.0223738i	$0.00712241\pi$
$653$			5.31296e12i			0.0447477i	−0.999750	+	0.0223738i	$0.992878\pi$
$654$	−1.15594e13	+	3.15798e13i	−0.0966154	+	0.263949i
$655$		−	5.86561e13i		−	0.486526i
$656$	2.95429e13	+	1.75005e14i	0.243183	+	1.44056i
$657$	6.35706e12			0.0519314
$658$	6.96920e13	+	2.55099e13i	0.565006	+	0.206814i
$659$	−7.39523e13			−0.595010			−0.297505	−	0.954720i	$-0.596155\pi$
$659$	−7.39523e13			−0.595010			−0.297505	+	0.954720i	$0.596155\pi$
$660$	1.29319e13	−	1.52979e13i	0.103262	−	0.122155i
$661$		−	1.23796e14i		−	0.981070i	−0.871421	−	0.490535i	$-0.836801\pi$
$661$		−	1.23796e14i		−	0.981070i	0.871421	−	0.490535i	$-0.163199\pi$
$662$	1.07224e14	+	3.92479e13i	0.843335	+	0.308693i
$663$			7.25769e13i			0.566540i
$664$	−8.45280e13	−	1.48275e14i	−0.654878	−	1.14876i
$665$	−1.74299e13			−0.134026
$666$	2.23373e13	−	6.10245e13i	0.170474	−	0.465729i
$667$	−1.76927e13			−0.134019
$668$	−1.64869e14	+	1.95033e14i	−1.23953	+	1.46631i
$669$			8.90675e13i			0.664643i
$670$	−2.56693e13	+	7.01275e13i	−0.190125	+	0.519415i
$671$		−	1.74863e14i		−	1.28554i
$672$	6.23059e13	+	1.15732e13i	0.454656	+	0.0844518i
$673$	7.45146e13			0.539717			0.269859	−	0.962900i	$-0.413023\pi$
$673$	7.45146e13			0.539717			0.269859	+	0.962900i	$0.413023\pi$
$674$	−1.46442e14	−	5.36033e13i	−1.05285	−	0.385383i
$675$	−2.43262e13			−0.173602
$676$	−2.78621e14	−	2.35529e14i	−1.97370	−	1.66844i
$677$		−	1.17798e14i		−	0.828314i	−0.910205	−	0.414157i	$-0.864076\pi$
$677$		−	1.17798e14i		−	0.828314i	0.910205	−	0.414157i	$-0.135924\pi$
$678$	−6.40549e13	−	2.34465e13i	−0.447099	−	0.163655i
$679$			4.77427e13i			0.330794i
$680$	−2.04878e13	+	1.16796e13i	−0.140913	+	0.0803310i
$681$	8.78520e13			0.599814
$682$	9.77072e12	−	2.66932e13i	0.0662224	−	0.180917i
$683$	−2.09059e13			−0.140658			−0.0703290	−	0.997524i	$-0.522405\pi$
$683$	−2.09059e13			−0.140658			−0.0703290	+	0.997524i	$0.522405\pi$
$684$	−2.03790e13	−	1.72271e13i	−0.136114	−	0.115062i
$685$		−	5.02495e13i		−	0.333180i
$686$	−5.68201e13	+	1.55230e14i	−0.374008	+	1.02177i
$687$		−	3.20512e13i		−	0.209441i
$688$	1.36160e13	+	8.06580e13i	0.0883298	+	0.523245i
$689$	4.38106e14			2.82152
$690$	−1.30763e13	−	4.78641e12i	−0.0836062	−	0.0306030i
$691$	1.49719e14			0.950360			0.475180	−	0.879889i	$-0.342383\pi$
$691$	1.49719e14			0.950360			0.475180	+	0.879889i	$0.342383\pi$
$692$	−1.13613e14	+	1.34400e14i	−0.715974	+	0.846969i
$693$		−	3.77776e13i		−	0.236357i
$694$	1.65414e14	+	6.05478e13i	1.02748	+	0.376098i
$695$		−	4.27993e13i		−	0.263945i
$696$	2.22800e13	−	1.27013e13i	0.136417	−	0.0777682i
$697$	−1.24560e14			−0.757209
$698$	2.53593e13	−	6.92805e13i	0.153059	−	0.418152i
$699$	−1.24357e14			−0.745220
$700$	−7.83945e13	+	9.27376e13i	−0.466440	+	0.551780i
$701$		−	2.60502e14i		−	1.53894i	−0.638686	−	0.769468i	$-0.720522\pi$
$701$		−	2.60502e14i		−	1.53894i	0.638686	−	0.769468i	$-0.279478\pi$
$702$	2.13518e13	−	5.83323e13i	0.125242	−	0.342156i
$703$			1.36596e14i			0.795541i
$704$	7.79910e13	−	1.31733e14i	0.451005	−	0.761782i
$705$	2.36377e13			0.135725
$706$	7.23089e13	+	2.64678e13i	0.412257	+	0.150902i
$707$	1.40314e13			0.0794335
$708$	−3.56498e13	−	3.01361e13i	−0.200397	−	0.169403i
$709$			1.06641e14i			0.595241i	0.954684	+	0.297621i	$0.0961931\pi$
$709$			1.06641e14i			0.595241i	−0.954684	+	0.297621i	$0.903807\pi$
$710$	3.51506e12	+	1.28664e12i	0.0194823	+	0.00713127i
$711$			9.99903e13i			0.550313i
$712$	1.49462e14	+	2.62179e14i	0.816827	+	1.43284i
$713$	−1.97596e13			−0.107234
$714$	−1.52878e13	+	4.17657e13i	−0.0823862	+	0.225076i
$715$	−9.80149e13			−0.524520
$716$	1.00775e14	+	8.51885e13i	0.535533	+	0.452706i
$717$		−	1.72381e14i		−	0.909688i
$718$	1.03538e14	−	2.82861e14i	0.542596	−	1.48235i
$719$			3.08159e12i			0.0160373i	0.999968	+	0.00801863i	$0.00255244\pi$
$719$			3.08159e12i			0.0160373i	−0.999968	+	0.00801863i	$0.997448\pi$
$720$	1.99028e13	−	3.35982e12i	0.102861	−	0.0173641i
$721$	2.27481e13			0.116753
$722$	−1.31566e14	−	4.81581e13i	−0.670591	−	0.245462i
$723$	−1.04102e14			−0.526946
$724$	−1.47572e14	+	1.74572e14i	−0.741842	+	0.877570i
$725$			4.91431e13i			0.245343i
$726$	2.36506e13	+	8.65701e12i	0.117262	+	0.0429225i
$727$			2.63293e13i			0.129648i	0.997897	+	0.0648242i	$0.0206487\pi$
$727$			2.63293e13i			0.129648i	−0.997897	+	0.0648242i	$0.979351\pi$
$728$	−1.53568e14	−	2.69383e14i	−0.751008	−	1.31739i
$729$	7.62560e12			0.0370370
$730$	3.47425e12	−	9.49152e12i	0.0167590	−	0.0457848i
$731$	−5.74085e13			−0.275036
$732$	1.13749e14	−	1.34561e14i	0.541244	−	0.640270i
$733$			1.08283e14i			0.511729i	0.966713	+	0.255864i	$0.0823601\pi$
$733$			1.08283e14i			0.511729i	−0.966713	+	0.255864i	$0.917640\pi$
$734$	8.39759e13	−	2.29419e14i	0.394162	−	1.07683i
$735$			1.38931e13i			0.0647682i
$736$	−1.04629e14	−	1.94347e13i	−0.484466	−	0.0899888i
$737$	3.40221e14			1.56467
$738$	1.00113e14	+	3.66451e13i	0.457308	+	0.167392i
$739$	−3.20292e14			−1.45319			−0.726597	−	0.687064i	$-0.758899\pi$
$739$	−3.20292e14			−1.45319			−0.726597	+	0.687064i	$0.758899\pi$
$740$	−7.89059e13	−	6.67021e13i	−0.355591	−	0.300594i
$741$			1.30570e14i			0.584457i
$742$	2.52116e14	+	9.22839e13i	1.12094	+	0.410305i
$743$		−	2.20910e14i		−	0.975598i	−0.872956	−	0.487799i	$-0.837800\pi$
$743$		−	2.20910e14i		−	0.975598i	0.872956	−	0.487799i	$-0.162200\pi$
$744$	2.48829e13	−	1.41851e13i	0.109153	−	0.0622255i
$745$	−1.01539e14			−0.442438
$746$	−2.26677e13	+	6.19271e13i	−0.0981098	+	0.268032i
$747$	−1.02522e14			−0.440771
$748$	8.20521e13	+	6.93617e13i	0.350414	+	0.296218i
$749$		−	4.53957e13i		−	0.192578i
$750$	−2.80328e13	+	7.65845e13i	−0.118130	+	0.322726i
$751$			1.87562e13i			0.0785137i	0.999229	+	0.0392569i	$0.0124991\pi$
$751$			1.87562e13i			0.0785137i	−0.999229	+	0.0392569i	$0.987501\pi$
$752$	1.78129e14	−	3.00702e13i	0.740706	−	0.125040i
$753$	2.73925e14			1.13150
$754$	−1.17841e14	−	4.31344e13i	−0.483550	−	0.176998i
$755$	−1.04449e14			−0.425763
$756$	2.45746e13	−	2.90707e13i	0.0995123	−	0.117719i
$757$			2.03301e14i			0.817823i	0.912574	+	0.408912i	$0.134092\pi$
$757$			2.03301e14i			0.817823i	−0.912574	+	0.408912i	$0.865908\pi$
$758$	1.86939e14	+	6.84267e13i	0.747057	+	0.273451i
$759$			6.34390e13i			0.251853i
$760$	−3.68588e13	+	2.10123e13i	−0.145369	+	0.0828714i
$761$	−1.53803e14			−0.602618			−0.301309	−	0.953527i	$-0.597424\pi$
$761$	−1.53803e14			−0.602618			−0.301309	+	0.953527i	$0.597424\pi$
$762$	1.46447e13	−	4.00086e13i	0.0570039	−	0.155732i
$763$	1.00836e14			0.389936
$764$	2.93168e14	−	3.46806e14i	1.12629	−	1.33235i
$765$			1.41658e13i			0.0540674i
$766$	5.40878e13	−	1.47766e14i	0.205095	−	0.560312i
$767$			2.28411e14i			0.860480i
$768$	1.45709e14	−	5.06377e13i	0.545356	−	0.189526i
$769$	−1.00313e14			−0.373013			−0.186506	−	0.982454i	$-0.559717\pi$
$769$	−1.00313e14			−0.373013			−0.186506	+	0.982454i	$0.559717\pi$
$770$	−5.64044e13	−	2.06461e13i	−0.208382	−	0.0762756i
$771$	−1.33685e13			−0.0490695
$772$	−2.62545e14	−	2.21939e14i	−0.957454	−	0.809371i
$773$		−	2.43461e14i		−	0.882127i	−0.897476	−	0.441063i	$-0.854601\pi$
$773$		−	2.43461e14i		−	0.882127i	0.897476	−	0.441063i	$-0.145399\pi$
$774$	4.61410e13	+	1.68894e13i	0.166105	+	0.0608007i
$775$			5.48843e13i			0.196309i
$776$	5.75550e13	+	1.00960e14i	0.204538	+	0.358792i
$777$	−1.94855e14			−0.688029
$778$	7.58552e13	−	2.07233e14i	0.266126	−	0.727045i
$779$	−2.24091e14			−0.781156
$780$	−7.54248e13	−	6.37594e13i	−0.261241	−	0.220837i
$781$		−	1.70532e13i		−	0.0586881i
$782$	2.56725e13	−	7.01361e13i	0.0877878	−	0.239833i
$783$		−	1.54050e13i		−	0.0523425i
$784$	1.76738e13	+	1.04695e14i	0.0596691	+	0.353466i
$785$	1.21582e14			0.407869
$786$	−2.52861e14	−	9.25566e13i	−0.842886	−	0.308528i
$787$	4.40060e14			1.45760			0.728799	−	0.684727i	$-0.240079\pi$
$787$	4.40060e14			1.45760			0.728799	+	0.684727i	$0.240079\pi$
$788$	−3.66125e12	+	4.33112e12i	−0.0120503	+	0.0142550i
$789$		−	1.76211e14i		−	0.576298i
$790$	1.49292e14	+	5.46466e13i	0.485179	+	0.177594i
$791$			2.04531e14i			0.660507i
$792$	−4.55419e13	−	7.98875e13i	−0.146145	−	0.256361i
$793$	−8.62143e14			−2.74925
$794$	−6.67425e13	+	1.82338e14i	−0.211495	+	0.577796i
$795$	8.55112e13			0.269270
$796$	−1.54124e14	+	1.82322e14i	−0.482285	+	0.570524i
$797$			3.74621e14i			1.16493i	0.812855	+	0.582466i	$0.197912\pi$
$797$			3.74621e14i			1.16493i	−0.812855	+	0.582466i	$0.802088\pi$
$798$	−2.75037e13	+	7.51389e13i	−0.0849916	+	0.232194i
$799$			1.26784e14i			0.389341i
$800$	−5.39817e13	+	2.90617e14i	−0.164739	+	0.886893i
$801$	1.81278e14			0.549772
$802$	2.03455e14	+	7.44722e13i	0.613192	+	0.224451i
$803$	−4.60477e13			−0.137921
$804$	2.61808e14	+	2.21316e14i	0.779296	+	0.658768i
$805$			4.17534e13i			0.123513i
$806$	−1.31608e14	−	4.81736e13i	−0.386908	−	0.141623i
$807$		−	3.53650e14i		−	1.03325i
$808$	2.96719e13	−	1.69152e13i	0.0861567	−	0.0491158i
$809$	−3.84132e14			−1.10850			−0.554252	−	0.832349i	$-0.686996\pi$
$809$	−3.84132e14			−1.10850			−0.554252	+	0.832349i	$0.686996\pi$
$810$	4.16753e12	−	1.13855e13i	0.0119524	−	0.0326534i
$811$	3.71463e14			1.05879			0.529397	−	0.848374i	$-0.322418\pi$
$811$	3.71463e14			1.05879			0.529397	+	0.848374i	$0.322418\pi$
$812$	−5.87280e13	−	4.96449e13i	−0.166366	−	0.140635i
$813$			5.80944e13i			0.163562i
$814$	−1.61801e14	+	4.42034e14i	−0.452751	+	1.23690i
$815$		−	1.98821e13i		−	0.0552936i
$816$	1.80208e13	+	1.06751e14i	0.0498107	+	0.295067i
$817$	−1.03281e14			−0.283734
$818$	1.39860e14	+	5.11942e13i	0.381881	+	0.139783i
$819$	−1.86259e14			−0.505472
$820$	1.09427e14	−	1.29448e14i	0.295159	−	0.349161i
$821$			2.32816e14i			0.624162i	0.950056	+	0.312081i	$0.101026\pi$
$821$			2.32816e14i			0.624162i	−0.950056	+	0.312081i	$0.898974\pi$
$822$	−2.16621e14	−	7.92915e13i	−0.577220	−	0.211284i
$823$		−	3.09951e14i		−	0.820907i	−0.911882	−	0.410453i	$-0.865370\pi$
$823$		−	3.09951e14i		−	0.820907i	0.911882	−	0.410453i	$-0.134630\pi$
$824$	4.81049e13	−	2.74234e13i	0.126635	−	0.0721913i
$825$	1.76208e14			0.461058
$826$	−4.81132e13	+	1.31443e14i	−0.125131	+	0.341852i
$827$	−1.61681e14			−0.417957			−0.208979	−	0.977920i	$-0.567014\pi$
$827$	−1.61681e14			−0.417957			−0.208979	+	0.977920i	$0.567014\pi$
$828$	−4.12675e13	+	4.88178e13i	−0.106037	+	0.125437i
$829$			5.14374e14i			1.31373i	0.754008	+	0.656865i	$0.228118\pi$
$829$			5.14374e14i			1.31373i	−0.754008	+	0.656865i	$0.771882\pi$
$830$	−5.60300e13	+	1.53072e14i	−0.142243	+	0.388601i
$831$			1.45229e14i			0.366478i
$832$	−6.49496e14	−	3.84527e14i	−1.62914	−	0.964519i
$833$	−7.45173e13			−0.185794
$834$	−1.84504e14	−	6.75354e13i	−0.457273	−	0.167379i
$835$	2.43901e14			0.600871
$836$	1.47616e14	+	1.24786e14i	0.361496	+	0.305586i
$837$		−	1.72047e13i		−	0.0418814i
$838$	−2.35567e14	−	8.62265e13i	−0.570026	−	0.208651i
$839$			5.07891e14i			1.22169i	0.791750	+	0.610845i	$0.209170\pi$
$839$			5.07891e14i			1.22169i	−0.791750	+	0.610845i	$0.790830\pi$
$840$	−2.99741e13	−	5.25791e13i	−0.0716719	−	0.125724i
$841$	3.89586e14			0.926027
$842$	4.71360e13	−	1.28774e14i	0.111376	−	0.304275i
$843$	1.79089e14			0.420659
$844$	6.05405e14	+	5.11771e14i	1.41362	+	1.19499i
$845$			3.48432e14i			0.808789i
$846$	3.72993e13	−	1.01900e14i	0.0860694	−	0.235138i
$847$		−	7.55178e13i		−	0.173234i
$848$	6.44395e14	−	1.08781e14i	1.46951	−	0.248070i
$849$	−1.19015e14			−0.269813
$850$	−1.94810e14	−	7.13078e13i	−0.439052	−	0.160710i
$851$	3.27216e14			0.733139
$852$	1.10932e13	−	1.31228e13i	0.0247092	−	0.0292300i
$853$		−	4.06168e14i		−	0.899415i	−0.893176	−	0.449708i	$-0.851528\pi$
$853$		−	4.06168e14i		−	0.899415i	0.893176	−	0.449708i	$-0.148472\pi$
$854$	−4.96135e14	−	1.81604e14i	−1.09222	−	0.399794i
$855$			2.54852e13i			0.0557773i
$856$	−5.47257e13	−	9.59974e13i	−0.119076	−	0.208877i
$857$	−6.02775e14			−1.30392			−0.651960	−	0.758253i	$-0.726053\pi$
$857$	−6.02775e14			−1.30392			−0.651960	+	0.758253i	$0.726053\pi$
$858$	−1.54663e14	+	4.22533e14i	−0.332622	+	0.908708i
$859$	4.72406e14			1.01007			0.505033	−	0.863100i	$-0.331480\pi$
$859$	4.72406e14			1.01007			0.505033	+	0.863100i	$0.331480\pi$
$860$	5.04338e13	−	5.96612e13i	0.107209	−	0.126824i
$861$		−	3.19667e14i		−	0.675588i
$862$	9.32247e13	−	2.54686e14i	0.195882	−	0.535141i
$863$		−	5.31971e14i		−	1.11131i	−0.831414	−	0.555653i	$-0.812468\pi$
$863$		−	5.31971e14i		−	1.11131i	0.831414	−	0.555653i	$-0.187532\pi$
$864$	1.69218e13	−	9.11006e13i	0.0351462	−	0.189214i
$865$	1.68075e14			0.347074
$866$	1.00371e14	+	3.67395e13i	0.206071	+	0.0754299i
$867$	2.06856e14			0.422253
$868$	−6.55889e13	−	5.54447e13i	−0.133116	−	0.112528i
$869$		−	7.24285e14i		−	1.46154i
$870$	−2.30007e13	−	8.41914e12i	−0.0461472	−	0.0168916i
$871$		−	1.67743e15i		−	3.34621i
$872$	2.13236e14	−	1.21561e14i	0.422940	−	0.241108i
$873$	6.98069e13			0.137666
$874$	4.61863e13	−	1.26179e14i	0.0905641	−	0.247417i
$875$	2.44539e14			0.476769
$876$	−3.54348e13	−	2.99544e13i	−0.0686926	−	0.0580684i
$877$		−	7.50987e14i		−	1.44755i	−0.690034	−	0.723777i	$-0.742404\pi$
$877$		−	7.50987e14i		−	1.44755i	0.690034	−	0.723777i	$-0.257596\pi$
$878$	−2.07147e14	+	5.65917e14i	−0.397014	+	1.08463i
$879$			2.45722e14i			0.468273i
$880$	−1.44167e14	+	2.43370e13i	−0.273182	+	0.0461162i
$881$	−4.88152e12			−0.00919761			−0.00459881	−	0.999989i	$-0.501464\pi$
$881$	−4.88152e12			−0.00919761			−0.00459881	+	0.999989i	$0.501464\pi$
$882$	5.98918e13	+	2.19227e13i	0.112208	+	0.0410724i
$883$	3.50967e14			0.653827			0.326914	−	0.945054i	$-0.393991\pi$
$883$	3.50967e14			0.653827			0.326914	+	0.945054i	$0.393991\pi$
$884$	3.41981e14	−	4.04550e14i	0.633491	−	0.749395i
$885$			4.45822e13i			0.0821192i
$886$	−3.65764e14	−	1.33884e14i	−0.669935	−	0.245222i
$887$			5.92009e14i			1.07823i	0.842233	+	0.539114i	$0.181241\pi$
$887$			5.92009e14i			1.07823i	−0.842233	+	0.539114i	$0.818759\pi$
$888$	−4.12056e14	+	2.34903e14i	−0.746262	+	0.425426i
$889$	−1.27750e14			−0.230066
$890$	9.90718e13	−	2.70660e14i	0.177419	−	0.484701i
$891$	−5.52364e13			−0.0983642
$892$	4.19684e14	−	4.96470e14i	0.743187	−	0.879161i
$893$			2.28092e14i			0.401654i
$894$	−1.60224e14	+	4.37725e14i	−0.280569	+	0.766504i
$895$		−	1.26025e14i		−	0.219452i
$896$	−2.92766e14	−	3.58095e14i	−0.506968	−	0.620094i
$897$	3.12780e14			0.538613
$898$	4.14979e14	+	1.51898e14i	0.710631	+	0.260118i
$899$	−3.47566e13			−0.0591887
$900$	1.35596e14	+	1.14624e14i	0.229633	+	0.194118i
$901$			4.58650e14i			0.772427i
$902$	−7.25174e14	−	2.65441e14i	−1.21453	−	0.444565i
$903$		−	1.47331e14i		−	0.245389i
$904$	2.46568e14	+	4.32518e14i	0.408408	+	0.716411i
$905$	2.18313e14			0.359614
$906$	−1.64815e14	+	4.50268e14i	−0.269995	+	0.737616i
$907$	3.01474e13			0.0491150			0.0245575	−	0.999698i	$-0.492182\pi$
$907$	3.01474e13			0.0491150			0.0245575	+	0.999698i	$0.492182\pi$
$908$	−4.89695e14	−	4.13957e14i	−0.793407	−	0.670697i
$909$		−	2.05160e13i		−	0.0330577i
$910$	−1.01794e14	+	2.78097e14i	−0.163123	+	0.445645i
$911$		−	5.91325e14i		−	0.942398i	−0.882027	−	0.471199i	$-0.843821\pi$
$911$		−	5.91325e14i		−	0.942398i	0.882027	−	0.471199i	$-0.156179\pi$
$912$	3.24204e13	+	1.92051e14i	0.0513860	+	0.304398i
$913$	7.42621e14			1.17061
$914$	4.61599e14	+	1.68963e14i	0.723659	+	0.264887i
$915$	−1.68276e14			−0.262372
$916$	−1.51025e14	+	1.78656e14i	−0.234191	+	0.277039i
$917$			8.07400e14i			1.24521i
$918$	6.10676e13	+	2.23531e13i	0.0936693	+	0.0342865i
$919$			1.07296e15i			1.63685i	0.574616	+	0.818423i	$0.305151\pi$
$919$			1.07296e15i			1.63685i	−0.574616	+	0.818423i	$0.694849\pi$
$920$	5.03348e13	+	8.82950e13i	0.0763711	+	0.133967i
$921$	−2.99415e14			−0.451831
$922$	−1.90456e14	+	5.20318e14i	−0.285851	+	0.780933i
$923$	−8.40790e13			−0.125510
$924$	−1.78007e14	+	2.10575e14i	−0.264288	+	0.312642i
$925$		−	9.08873e14i		−	1.34213i
$926$	−1.05055e14	+	2.87007e14i	−0.154299	+	0.421538i
$927$		−	3.32610e13i		−	0.0485889i
$928$	−1.84039e14	−	3.41850e13i	−0.267405	−	0.0496702i
$929$	4.15614e14			0.600636			0.300318	−	0.953839i	$-0.402907\pi$
$929$	4.15614e14			0.600636			0.300318	+	0.953839i	$0.402907\pi$
$930$	−2.56878e13	−	9.40271e12i	−0.0369243	−	0.0135157i
$931$	−1.34061e14			−0.191670
$932$	6.93177e14	+	5.85968e14i	0.985745	+	0.833287i
$933$			5.65570e14i			0.799978i
$934$	−5.93077e14	−	2.17088e14i	−0.834404	−	0.305423i
$935$		−	1.02611e14i		−	0.143594i
$936$	−3.93878e14	+	2.24540e14i	−0.548254	+	0.312546i
$937$	−8.97581e14			−1.24273			−0.621364	−	0.783522i	$-0.713421\pi$
$937$	−8.97581e14			−1.24273			−0.621364	+	0.783522i	$0.713421\pi$
$938$	3.53338e14	−	9.65304e14i	0.486604	−	1.32938i
$939$	4.52228e14			0.619483
$940$	−1.31759e14	−	1.11381e14i	−0.179531	−	0.151764i
$941$		−	2.80409e14i		−	0.380053i	−0.981779	−	0.190027i	$-0.939143\pi$
$941$		−	2.80409e14i		−	0.380053i	0.981779	−	0.190027i	$-0.0608574\pi$
$942$	1.91851e14	−	5.24128e14i	0.258648	−	0.706615i
$943$			5.36810e14i			0.719883i
$944$	5.67143e13	+	3.35962e14i	0.0756541	+	0.448157i
$945$	−3.63547e13			−0.0482393
$946$	−3.34225e14	−	1.22339e14i	−0.441147	−	0.161476i
$947$	−1.22495e15			−1.60831			−0.804154	−	0.594421i	$-0.797381\pi$
$947$	−1.22495e15			−1.60831			−0.804154	+	0.594421i	$0.797381\pi$
$948$	4.71153e14	−	5.57355e14i	0.615347	−	0.727931i
$949$			2.27034e14i			0.294958i
$950$	−3.50474e14	−	1.28287e14i	−0.452937	−	0.165792i
$951$			1.57066e14i			0.201920i
$952$	2.82015e14	−	1.60769e14i	0.360651	−	0.205598i
$953$	−6.20230e14			−0.789020			−0.394510	−	0.918892i	$-0.629086\pi$
$953$	−6.20230e14			−0.789020			−0.394510	+	0.918892i	$0.629086\pi$
$954$	1.34933e14	−	3.68631e14i	0.170756	−	0.466498i
$955$	−4.33701e14			−0.545976
$956$	−8.12254e14	+	9.60864e14i	−1.01719	+	1.20330i
$957$			1.11587e14i			0.139013i
$958$	8.11619e13	−	2.21731e14i	0.100583	−	0.274789i
$959$			6.91684e14i			0.852737i
$960$	−1.26771e14	−	7.50535e13i	−0.155476	−	0.0920481i
$961$	7.80811e14			0.952641
$962$	2.17941e15	+	7.97746e14i	2.64523	+	0.968254i
$963$	−6.63753e13			−0.0801447
$964$	5.80272e14	+	4.90525e14i	0.697022	+	0.589218i
$965$			3.28329e14i			0.392349i
$966$	1.79995e14	+	6.58849e13i	0.213981	+	0.0783250i
$967$			1.26262e15i			1.49328i	0.665230	+	0.746639i	$0.268334\pi$
$967$			1.26262e15i			1.49328i	−0.665230	+	0.746639i	$0.731666\pi$
$968$	−9.10387e13	−	1.59696e14i	−0.107115	−	0.187896i
$969$	−1.36693e14			−0.160003
$970$	3.81507e13	−	1.04226e14i	0.0444267	−	0.121372i
$971$	5.65768e13			0.0655454			0.0327727	−	0.999463i	$-0.489566\pi$
$971$	5.65768e13			0.0655454			0.0327727	+	0.999463i	$0.489566\pi$
$972$	−4.25057e13	−	3.59317e13i	−0.0489910	−	0.0414139i
$973$			5.89133e14i			0.675537i
$974$	3.71685e14	−	1.01543e15i	0.424014	−	1.15839i
$975$		−	8.68777e14i		−	0.986018i
$976$	−1.26810e15	+	2.14069e14i	−1.43187	+	0.241716i
$977$	−1.20070e15			−1.34885			−0.674424	−	0.738344i	$-0.735608\pi$
$977$	−1.20070e15			−1.34885			−0.674424	+	0.738344i	$0.735608\pi$
$978$	−8.57100e13	−	3.13731e13i	−0.0957937	−	0.0350641i
$979$	−1.31310e15			−1.46010
$980$	6.54640e13	−	7.74413e13i	0.0724222	−	0.0856726i
$981$		−	1.47438e14i		−	0.162279i
$982$	1.34114e15	+	4.90906e14i	1.46864	+	0.537578i
$983$		−	9.70458e14i		−	1.05733i	−0.848832	−	0.528663i	$-0.822693\pi$
$983$		−	9.70458e14i		−	1.05733i	0.848832	−	0.528663i	$-0.177307\pi$
$984$	−3.85367e14	−	6.75994e14i	−0.417733	−	0.732769i
$985$	5.41632e12			0.00584148
$986$	4.51571e13	−	1.23367e14i	0.0484553	−	0.132378i
$987$	−3.25373e14			−0.347373
$988$	6.15244e14	−	7.27809e14i	0.653526	−	0.773095i
$989$			2.47410e14i			0.261478i
$990$	−3.01877e13	+	8.24716e13i	−0.0317435	+	0.0867219i
$991$			1.64676e14i			0.172291i	0.996283	+	0.0861456i	$0.0274550\pi$
$991$			1.64676e14i			0.172291i	−0.996283	+	0.0861456i	$0.972545\pi$
$992$	−2.05539e14	−	3.81787e13i	−0.213962	−	0.0397432i
$993$	−5.00598e14			−0.518493
$994$	−4.83847e13	−	1.77106e13i	−0.0498628	−	0.0182517i
$995$	2.28005e14			0.233791
$996$	5.71464e14	+	4.83080e14i	0.583032	+	0.492859i
$997$			3.12384e14i			0.317112i	0.987350	+	0.158556i	$0.0506838\pi$
$997$			3.12384e14i			0.317112i	−0.987350	+	0.158556i	$0.949316\pi$
$998$	−1.31160e14	−	4.80097e13i	−0.132480	−	0.0484927i
$999$			2.84907e14i			0.286336i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	24.11.b.a.19.18	yes	20
3.2	odd	2		72.11.b.d.19.3		20
4.3	odd	2		96.11.b.a.79.15		20
8.3	odd	2	inner	24.11.b.a.19.17	✓	20
8.5	even	2		96.11.b.a.79.16		20
12.11	even	2		288.11.b.c.271.11		20
24.5	odd	2		288.11.b.c.271.10		20
24.11	even	2		72.11.b.d.19.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.11.b.a.19.17	✓	20	8.3	odd	2	inner
24.11.b.a.19.18	yes	20	1.1	even	1	trivial
72.11.b.d.19.3		20	3.2	odd	2
72.11.b.d.19.4		20	24.11	even	2
96.11.b.a.79.15		20	4.3	odd	2
96.11.b.a.79.16		20	8.5	even	2
288.11.b.c.271.10		20	24.5	odd	2
288.11.b.c.271.11		20	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	24.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(30.0501 + 10.9995i) q^{2} -140.296 q^{3} +(782.022 + 661.073i) q^{4} -977.966i q^{5} +(-4215.92 - 1543.19i) q^{6} +13461.7i q^{7} +(16228.4 + 28467.2i) q^{8} +19683.0 q^{9} +O(q^{10})\)	\(q+(30.0501 + 10.9995i) q^{2} -140.296 q^{3} +(782.022 + 661.073i) q^{4} -977.966i q^{5} +(-4215.92 - 1543.19i) q^{6} +13461.7i q^{7} +(16228.4 + 28467.2i) q^{8} +19683.0 q^{9} +(10757.1 - 29388.0i) q^{10} -142575. q^{11} +(-109715. - 92745.9i) q^{12} +702952. i q^{13} +(-148072. + 404526. i) q^{14} +137205. i q^{15} +(174542. + 1.03395e6i) q^{16} -735914. q^{17} +(591477. + 216503. i) q^{18} -1.32395e6 q^{19} +(646506. - 764791. i) q^{20} -1.88862e6i q^{21} +(-4.28440e6 - 1.56825e6i) q^{22} +3.17152e6i q^{23} +(-2.27679e6 - 3.99383e6i) q^{24} +8.80921e6 q^{25} +(-7.73211e6 + 2.11238e7i) q^{26} -2.76145e6 q^{27} +(-8.89916e6 + 1.05273e7i) q^{28} +5.57861e6i q^{29} +(-1.50918e6 + 4.12302e6i) q^{30} +6.23033e6i q^{31} +(-6.12787e6 + 3.29901e7i) q^{32} +2.00027e7 q^{33} +(-2.21143e7 - 8.09468e6i) q^{34} +1.31651e7 q^{35} +(1.53925e7 + 1.30119e7i) q^{36} -1.03173e8i q^{37} +(-3.97850e7 - 1.45628e7i) q^{38} -9.86214e7i q^{39} +(2.78399e7 - 1.58708e7i) q^{40} +1.69259e8 q^{41} +(2.07739e7 - 5.67534e7i) q^{42} +7.80098e7 q^{43} +(-1.11497e8 - 9.42523e7i) q^{44} -1.92493e7i q^{45} +(-3.48851e7 + 9.53047e7i) q^{46} -1.72281e8i q^{47} +(-2.44876e7 - 1.45059e8i) q^{48} +1.01258e8 q^{49} +(2.64718e8 + 9.68968e7i) q^{50} +1.03246e8 q^{51} +(-4.64702e8 + 5.49724e8i) q^{52} -6.23238e8i q^{53} +(-8.29819e7 - 3.03745e7i) q^{54} +1.39433e8i q^{55} +(-3.83216e8 + 2.18462e8i) q^{56} +1.85746e8 q^{57} +(-6.13619e7 + 1.67638e8i) q^{58} +3.24932e8 q^{59} +(-9.07023e7 + 1.07297e8i) q^{60} +1.22646e9i q^{61} +(-6.85305e7 + 1.87222e8i) q^{62} +2.64967e8i q^{63} +(-5.47018e8 + 9.23955e8i) q^{64} +6.87463e8 q^{65} +(6.01084e8 + 2.20020e8i) q^{66} -2.38626e9 q^{67} +(-5.75502e8 - 4.86493e8i) q^{68} -4.44952e8i q^{69} +(3.95613e8 + 1.44809e8i) q^{70} +1.19609e8i q^{71} +(3.19424e8 + 5.60319e8i) q^{72} +3.22972e8 q^{73} +(1.13485e9 - 3.10037e9i) q^{74} -1.23590e9 q^{75} +(-1.03536e9 - 8.75229e8i) q^{76} -1.91930e9i q^{77} +(1.08479e9 - 2.96359e9i) q^{78} +5.08004e9i q^{79} +(1.01117e9 - 1.70696e8i) q^{80} +3.87420e8 q^{81} +(5.08627e9 + 1.86177e9i) q^{82} -5.20864e9 q^{83} +(1.24852e9 - 1.47695e9i) q^{84} +7.19699e8i q^{85} +(2.34421e9 + 8.58068e8i) q^{86} -7.82657e8i q^{87} +(-2.31377e9 - 4.05870e9i) q^{88} +9.20987e9 q^{89} +(2.11733e8 - 5.78444e8i) q^{90} -9.46292e9 q^{91} +(-2.09661e9 + 2.48020e9i) q^{92} -8.74091e8i q^{93} +(1.89500e9 - 5.17706e9i) q^{94} +1.29478e9i q^{95} +(8.59717e8 - 4.62839e9i) q^{96} +3.54656e9 q^{97} +(3.04282e9 + 1.11379e9i) q^{98} -2.80630e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 22 q^{2} - 1864 q^{4} - 2430 q^{6} + 118076 q^{8} + 393660 q^{9}+O(q^{10}) \) 20 * q - 22 * q^2 - 1864 * q^4 - 2430 * q^6 + 118076 * q^8 + 393660 * q^9	\( 20 q - 22 q^{2} - 1864 q^{4} - 2430 q^{6} + 118076 q^{8} + 393660 q^{9} - 113028 q^{10} - 91808 q^{11} + 310068 q^{12} - 503244 q^{14} - 545032 q^{16} - 905768 q^{17} - 433026 q^{18} - 5107040 q^{19} - 5944248 q^{20} - 2702288 q^{22} - 6248988 q^{24} - 40539484 q^{25} + 19400160 q^{26} - 19709616 q^{28} - 6556140 q^{30} + 118772648 q^{32} + 155305372 q^{34} - 68411424 q^{35} - 36689112 q^{36} - 119065400 q^{38} + 477325560 q^{40} + 51872200 q^{41} + 315008676 q^{42} - 392685920 q^{43} - 333411776 q^{44} - 1035567720 q^{46} + 520626528 q^{48} - 1130175964 q^{49} + 2330181842 q^{50} + 373209120 q^{51} - 2683888176 q^{52} - 47829690 q^{54} + 4216587096 q^{56} + 563025168 q^{57} + 2827093836 q^{58} - 1499085440 q^{59} - 574187616 q^{60} - 5504139012 q^{62} + 3240358112 q^{64} + 1717119456 q^{65} + 2366318448 q^{66} - 4570092800 q^{67} - 6509360144 q^{68} - 9179287176 q^{70} + 2324089908 q^{72} - 2312358680 q^{73} + 7298736360 q^{74} + 5958608832 q^{75} - 12863545616 q^{76} - 2062821168 q^{78} + 4230593184 q^{80} + 7748409780 q^{81} + 1201856596 q^{82} + 14192131360 q^{83} - 807928344 q^{84} + 11933558200 q^{86} - 12709901024 q^{88} + 8963359000 q^{89} - 2224730124 q^{90} - 401968224 q^{91} + 13243366752 q^{92} + 5851812792 q^{94} - 7654043160 q^{96} + 23275134232 q^{97} - 20615960782 q^{98} - 1807056864 q^{99}+O(q^{100}) \) 20 * q - 22 * q^2 - 1864 * q^4 - 2430 * q^6 + 118076 * q^8 + 393660 * q^9 - 113028 * q^10 - 91808 * q^11 + 310068 * q^12 - 503244 * q^14 - 545032 * q^16 - 905768 * q^17 - 433026 * q^18 - 5107040 * q^19 - 5944248 * q^20 - 2702288 * q^22 - 6248988 * q^24 - 40539484 * q^25 + 19400160 * q^26 - 19709616 * q^28 - 6556140 * q^30 + 118772648 * q^32 + 155305372 * q^34 - 68411424 * q^35 - 36689112 * q^36 - 119065400 * q^38 + 477325560 * q^40 + 51872200 * q^41 + 315008676 * q^42 - 392685920 * q^43 - 333411776 * q^44 - 1035567720 * q^46 + 520626528 * q^48 - 1130175964 * q^49 + 2330181842 * q^50 + 373209120 * q^51 - 2683888176 * q^52 - 47829690 * q^54 + 4216587096 * q^56 + 563025168 * q^57 + 2827093836 * q^58 - 1499085440 * q^59 - 574187616 * q^60 - 5504139012 * q^62 + 3240358112 * q^64 + 1717119456 * q^65 + 2366318448 * q^66 - 4570092800 * q^67 - 6509360144 * q^68 - 9179287176 * q^70 + 2324089908 * q^72 - 2312358680 * q^73 + 7298736360 * q^74 + 5958608832 * q^75 - 12863545616 * q^76 - 2062821168 * q^78 + 4230593184 * q^80 + 7748409780 * q^81 + 1201856596 * q^82 + 14192131360 * q^83 - 807928344 * q^84 + 11933558200 * q^86 - 12709901024 * q^88 + 8963359000 * q^89 - 2224730124 * q^90 - 401968224 * q^91 + 13243366752 * q^92 + 5851812792 * q^94 - 7654043160 * q^96 + 23275134232 * q^97 - 20615960782 * q^98 - 1807056864 * q^99

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