LMFDB - Embedded newform 43.9.b.b.42.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,9,Mod(42,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("43.42");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	43.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:	$17.5172802326$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			42.3
Character	$\chi$	$=$	43.42
Dual form			43.9.b.b.42.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-25.4156i q^{2} -123.997i q^{3} -389.955 q^{4} -710.884i q^{5} -3151.46 q^{6} +4245.58i q^{7} +3404.55i q^{8} -8814.20 q^{9} +O(q^{10})$	\(q-25.4156i q^{2} -123.997i q^{3} -389.955 q^{4} -710.884i q^{5} -3151.46 q^{6} +4245.58i q^{7} +3404.55i q^{8} -8814.20 q^{9} -18067.6 q^{10} +19261.7 q^{11} +48353.1i q^{12} -24555.5 q^{13} +107904. q^{14} -88147.3 q^{15} -13299.6 q^{16} -142372. q^{17} +224018. i q^{18} -152283. i q^{19} +277213. i q^{20} +526438. q^{21} -489549. i q^{22} +169711. q^{23} +422153. q^{24} -114731. q^{25} +624094. i q^{26} +279389. i q^{27} -1.65558e6i q^{28} -350183. i q^{29} +2.24032e6i q^{30} -167211. q^{31} +1.20958e6i q^{32} -2.38839e6i q^{33} +3.61848e6i q^{34} +3.01811e6 q^{35} +3.43714e6 q^{36} +965271. i q^{37} -3.87037e6 q^{38} +3.04480e6i q^{39} +2.42024e6 q^{40} -4.61149e6 q^{41} -1.33798e7i q^{42} +(2.23132e6 - 2.59026e6i) q^{43} -7.51120e6 q^{44} +6.26587e6i q^{45} -4.31331e6i q^{46} +2.55322e6 q^{47} +1.64911e6i q^{48} -1.22601e7 q^{49} +2.91596e6i q^{50} +1.76537e7i q^{51} +9.57553e6 q^{52} -121198. q^{53} +7.10085e6 q^{54} -1.36929e7i q^{55} -1.44543e7 q^{56} -1.88826e7 q^{57} -8.90013e6 q^{58} +3.24451e6 q^{59} +3.43735e7 q^{60} -1.17814e7i q^{61} +4.24978e6i q^{62} -3.74214e7i q^{63} +2.73376e7 q^{64} +1.74561e7i q^{65} -6.07025e7 q^{66} -3.62950e7 q^{67} +5.55188e7 q^{68} -2.10436e7i q^{69} -7.67073e7i q^{70} +1.36356e7i q^{71} -3.00084e7i q^{72} -1.61861e7i q^{73} +2.45330e7 q^{74} +1.42262e7i q^{75} +5.93834e7i q^{76} +8.17772e7i q^{77} +7.73856e7 q^{78} +3.75891e7 q^{79} +9.45449e6i q^{80} -2.31866e7 q^{81} +1.17204e8i q^{82} +6.67652e7 q^{83} -2.05287e8 q^{84} +1.01210e8i q^{85} +(-6.58330e7 - 5.67103e7i) q^{86} -4.34216e7 q^{87} +6.55775e7i q^{88} -4.02096e7i q^{89} +1.59251e8 q^{90} -1.04252e8i q^{91} -6.61796e7 q^{92} +2.07336e7i q^{93} -6.48916e7i q^{94} -1.08255e8 q^{95} +1.49984e8 q^{96} +3.96028e6 q^{97} +3.11599e8i q^{98} -1.69777e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4284 q^{4} - 1794 q^{6} - 80754 q^{9}+O(q^{10}) $ 28 * q - 4284 * q^4 - 1794 * q^6 - 80754 * q^9	$ 28 q - 4284 q^{4} - 1794 q^{6} - 80754 q^{9} + 24982 q^{10} + 4538 q^{11} + 22086 q^{13} + 24732 q^{14} + 15388 q^{15} + 525812 q^{16} - 135136 q^{17} - 261352 q^{21} - 184432 q^{23} + 1770326 q^{24} - 2640434 q^{25} - 110272 q^{31} + 10947816 q^{35} + 11602066 q^{36} - 7189158 q^{38} - 21389338 q^{40} + 1301336 q^{41} + 2473420 q^{43} - 8818480 q^{44} + 1983566 q^{47} - 15560936 q^{49} + 12927876 q^{52} + 23942594 q^{53} - 13757972 q^{54} + 34967256 q^{56} + 35225148 q^{57} + 22565734 q^{58} - 5554336 q^{59} - 44902072 q^{60} - 170444572 q^{64} - 48457584 q^{66} - 130953802 q^{67} + 150021122 q^{68} + 205870278 q^{74} + 267860612 q^{78} + 7380250 q^{79} - 57601004 q^{81} - 42603970 q^{83} + 251931292 q^{84} - 45482652 q^{86} - 106687410 q^{87} - 255044692 q^{90} - 409532014 q^{92} + 123322986 q^{95} - 692987086 q^{96} - 318744840 q^{97} - 609707206 q^{99}+O(q^{100}) $ 28 * q - 4284 * q^4 - 1794 * q^6 - 80754 * q^9 + 24982 * q^10 + 4538 * q^11 + 22086 * q^13 + 24732 * q^14 + 15388 * q^15 + 525812 * q^16 - 135136 * q^17 - 261352 * q^21 - 184432 * q^23 + 1770326 * q^24 - 2640434 * q^25 - 110272 * q^31 + 10947816 * q^35 + 11602066 * q^36 - 7189158 * q^38 - 21389338 * q^40 + 1301336 * q^41 + 2473420 * q^43 - 8818480 * q^44 + 1983566 * q^47 - 15560936 * q^49 + 12927876 * q^52 + 23942594 * q^53 - 13757972 * q^54 + 34967256 * q^56 + 35225148 * q^57 + 22565734 * q^58 - 5554336 * q^59 - 44902072 * q^60 - 170444572 * q^64 - 48457584 * q^66 - 130953802 * q^67 + 150021122 * q^68 + 205870278 * q^74 + 267860612 * q^78 + 7380250 * q^79 - 57601004 * q^81 - 42603970 * q^83 + 251931292 * q^84 - 45482652 * q^86 - 106687410 * q^87 - 255044692 * q^90 - 409532014 * q^92 + 123322986 * q^95 - 692987086 * q^96 - 318744840 * q^97 - 609707206 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$		−	25.4156i		−	1.58848i	−0.607606	−	0.794239i	$-0.707870\pi$
$2$		−	25.4156i		−	1.58848i	0.607606	−	0.794239i	$-0.292130\pi$
$3$		−	123.997i		−	1.53082i	−0.643540	−	0.765412i	$-0.722535\pi$
$3$		−	123.997i		−	1.53082i	0.643540	−	0.765412i	$-0.277465\pi$
$4$	−389.955			−1.52326
$5$		−	710.884i		−	1.13741i	−0.822540	−	0.568707i	$-0.807444\pi$
$5$		−	710.884i		−	1.13741i	0.822540	−	0.568707i	$-0.192556\pi$
$6$	−3151.46			−2.43168
$7$			4245.58i			1.76825i	0.467247	+	0.884127i	$0.345246\pi$
$7$			4245.58i			1.76825i	−0.467247	+	0.884127i	$0.654754\pi$
$8$			3404.55i			0.831189i
$9$	−8814.20			−1.34342
$10$	−18067.6			−1.80676
$11$	19261.7			1.31560			0.657801	−	0.753192i	$-0.271487\pi$
$11$	19261.7			1.31560			0.657801	+	0.753192i	$0.271487\pi$
$12$			48353.1i			2.33185i
$13$	−24555.5			−0.859756			−0.429878	−	0.902887i	$-0.641443\pi$
$13$	−24555.5			−0.859756			−0.429878	+	0.902887i	$0.641443\pi$
$14$	107904.			2.80883
$15$	−88147.3			−1.74118
$16$	−13299.6			−0.202936
$17$	−142372.			−1.70463			−0.852314	−	0.523030i	$-0.824802\pi$
$17$	−142372.			−1.70463			−0.852314	+	0.523030i	$0.824802\pi$
$18$			224018.i			2.13400i
$19$		−	152283.i		−	1.16852i	−0.811566	−	0.584261i	$-0.801385\pi$
$19$		−	152283.i		−	1.16852i	0.811566	−	0.584261i	$-0.198615\pi$
$20$			277213.i			1.73258i
$21$	526438.			2.70689
$22$		−	489549.i		−	2.08980i
$23$	169711.			0.606454			0.303227	−	0.952918i	$-0.401936\pi$
$23$	169711.			0.606454			0.303227	+	0.952918i	$0.401936\pi$
$24$	422153.			1.27240
$25$	−114731.			−0.293711
$26$			624094.i			1.36570i
$27$			279389.i			0.525720i
$28$		−	1.65558e6i		−	2.69351i
$29$		−	350183.i		−	0.495112i	−0.968874	−	0.247556i	$-0.920373\pi$
$29$		−	350183.i		−	0.495112i	0.968874	−	0.247556i	$-0.0796274\pi$
$30$			2.24032e6i			2.76583i
$31$	−167211.			−0.181058			−0.0905291	−	0.995894i	$-0.528856\pi$
$31$	−167211.			−0.181058			−0.0905291	+	0.995894i	$0.528856\pi$
$32$			1.20958e6i			1.15355i
$33$		−	2.38839e6i		−	2.01396i
$34$			3.61848e6i			2.70776i
$35$	3.01811e6			2.01124
$36$	3.43714e6			2.04638
$37$			965271.i			0.515042i	0.966273	+	0.257521i	$0.0829056\pi$
$37$			965271.i			0.515042i	−0.966273	+	0.257521i	$0.917094\pi$
$38$	−3.87037e6			−1.85617
$39$			3.04480e6i			1.31614i
$40$	2.42024e6			0.945406
$41$	−4.61149e6			−1.63195			−0.815974	−	0.578089i	$-0.803799\pi$
$41$	−4.61149e6			−1.63195			−0.815974	+	0.578089i	$0.803799\pi$
$42$		−	1.33798e7i		−	4.29983i
$43$	2.23132e6	−	2.59026e6i	0.652661	−	0.757650i
$43$	2.23132e6	−	2.59026e6i	0.652661	−	0.757650i
$44$	−7.51120e6			−2.00401
$45$			6.26587e6i			1.52803i
$46$		−	4.31331e6i		−	0.963339i
$47$	2.55322e6			0.523234			0.261617	−	0.965172i	$-0.415744\pi$
$47$	2.55322e6			0.523234			0.261617	+	0.965172i	$0.415744\pi$
$48$			1.64911e6i			0.310660i
$49$	−1.22601e7			−2.12672
$50$			2.91596e6i			0.466553i
$51$			1.76537e7i			2.60949i
$52$	9.57553e6			1.30963
$53$	−121198.			−0.0153600			−0.00768000	−	0.999971i	$-0.502445\pi$
$53$	−121198.			−0.0153600			−0.00768000	+	0.999971i	$0.502445\pi$
$54$	7.10085e6			0.835094
$55$		−	1.36929e7i		−	1.49638i
$56$	−1.44543e7			−1.46975
$57$	−1.88826e7			−1.78880
$58$	−8.90013e6			−0.786474
$59$	3.24451e6			0.267757			0.133879	−	0.990998i	$-0.457257\pi$
$59$	3.24451e6			0.267757			0.133879	+	0.990998i	$0.457257\pi$
$60$	3.43735e7			2.65227
$61$		−	1.17814e7i		−	0.850900i	−0.904982	−	0.425450i	$-0.860116\pi$
$61$		−	1.17814e7i		−	0.850900i	0.904982	−	0.425450i	$-0.139884\pi$
$62$			4.24978e6i			0.287607i
$63$		−	3.74214e7i		−	2.37551i
$64$	2.73376e7			1.62945
$65$			1.74561e7i			0.977899i
$66$	−6.07025e7			−3.19912
$67$	−3.62950e7			−1.80114			−0.900571	−	0.434708i	$-0.856852\pi$
$67$	−3.62950e7			−1.80114			−0.900571	+	0.434708i	$0.856852\pi$
$68$	5.55188e7			2.59659
$69$		−	2.10436e7i		−	0.928375i
$70$		−	7.67073e7i		−	3.19480i
$71$			1.36356e7i			0.536587i	0.963337	+	0.268294i	$0.0864598\pi$
$71$			1.36356e7i			0.536587i	−0.963337	+	0.268294i	$0.913540\pi$
$72$		−	3.00084e7i		−	1.11664i
$73$		−	1.61861e7i		−	0.569969i	−0.958532	−	0.284985i	$-0.908011\pi$
$73$		−	1.61861e7i		−	0.569969i	0.958532	−	0.284985i	$-0.0919885\pi$
$74$	2.45330e7			0.818132
$75$			1.42262e7i			0.449620i
$76$			5.93834e7i			1.77996i
$77$			8.17772e7i			2.32632i
$78$	7.73856e7			2.09065
$79$	3.75891e7			0.965057			0.482529	−	0.875880i	$-0.339718\pi$
$79$	3.75891e7			0.965057			0.482529	+	0.875880i	$0.339718\pi$
$80$			9.45449e6i			0.230823i
$81$	−2.31866e7			−0.538638
$82$			1.17204e8i			2.59231i
$83$	6.67652e7			1.40682			0.703409	−	0.710785i	$-0.251660\pi$
$83$	6.67652e7			1.40682			0.703409	+	0.710785i	$0.251660\pi$
$84$	−2.05287e8			−4.12329
$85$			1.01210e8i			1.93887i
$86$	−6.58330e7	−	5.67103e7i	−1.20351	−	1.03674i
$87$	−4.34216e7			−0.757929
$88$			6.55775e7i			1.09351i
$89$		−	4.02096e7i		−	0.640869i	−0.947271	−	0.320435i	$-0.896171\pi$
$89$		−	4.02096e7i		−	0.640869i	0.947271	−	0.320435i	$-0.103829\pi$
$90$	1.59251e8			2.42724
$91$		−	1.04252e8i		−	1.52027i
$92$	−6.61796e7			−0.923788
$93$			2.07336e7i			0.277168i
$94$		−	6.48916e7i		−	0.831146i
$95$	−1.08255e8			−1.32909
$96$	1.49984e8			1.76588
$97$	3.96028e6			0.0447341			0.0223671	−	0.999750i	$-0.492880\pi$
$97$	3.96028e6			0.0447341			0.0223671	+	0.999750i	$0.492880\pi$
$98$			3.11599e8i			3.37825i
$99$	−1.69777e8			−1.76741
$100$	4.47398e7			0.447398
$101$	−6.42933e7			−0.617846			−0.308923	−	0.951087i	$-0.599969\pi$
$101$	−6.42933e7			−0.617846			−0.308923	+	0.951087i	$0.599969\pi$
$102$	4.48680e8			4.14511
$103$	−5.70467e7			−0.506852			−0.253426	−	0.967355i	$-0.581557\pi$
$103$	−5.70467e7			−0.506852			−0.253426	+	0.967355i	$0.581557\pi$
$104$		−	8.36004e7i		−	0.714620i
$105$		−	3.74236e8i		−	3.07885i
$106$			3.08032e6i			0.0243990i
$107$	1.77956e8			1.35762			0.678808	−	0.734316i	$-0.262497\pi$
$107$	1.77956e8			1.35762			0.678808	+	0.734316i	$0.262497\pi$
$108$		−	1.08949e8i		−	0.800809i
$109$	1.45829e8			1.03309			0.516546	−	0.856260i	$-0.327218\pi$
$109$	1.45829e8			1.03309			0.516546	+	0.856260i	$0.327218\pi$
$110$	−3.48013e8			−2.37697
$111$	1.19690e8			0.788438
$112$		−	5.64646e7i		−	0.358843i
$113$		−	3.96357e6i		−	0.0243093i	−0.999926	−	0.0121547i	$-0.996131\pi$
$113$		−	3.96357e6i		−	0.0243093i	0.999926	−	0.0121547i	$-0.00386905\pi$
$114$			4.79913e8i			2.84147i
$115$		−	1.20645e8i		−	0.689790i
$116$			1.36556e8i			0.754185i
$117$	2.16437e8			1.15502
$118$		−	8.24614e7i		−	0.425327i
$119$		−	6.04453e8i		−	3.01422i
$120$		−	3.00102e8i		−	1.44725i
$121$	1.56655e8			0.730808
$122$	−2.99432e8			−1.35164
$123$			5.71810e8i			2.49823i
$124$	6.52047e7			0.275799
$125$		−	1.96129e8i		−	0.803343i
$126$	−9.51088e8			−3.77345
$127$	−2.72143e8			−1.04612			−0.523061	−	0.852295i	$-0.675210\pi$
$127$	−2.72143e8			−1.04612			−0.523061	+	0.852295i	$0.675210\pi$
$128$		−	3.85150e8i		−	1.43480i
$129$	−3.21183e8	−	2.76676e8i	−1.15983	−	0.999109i
$130$	4.43658e8			1.55337
$131$			4.60295e7i			0.156297i	0.996942	+	0.0781486i	$0.0249009\pi$
$131$			4.60295e7i			0.156297i	−0.996942	+	0.0781486i	$0.975099\pi$
$132$			9.31365e8i			3.06778i
$133$	6.46529e8			2.06624
$134$			9.22462e8i			2.86108i
$135$	1.98613e8			0.597961
$136$		−	4.84713e8i		−	1.41687i
$137$		−	2.81241e8i		−	0.798357i	−0.916873	−	0.399178i	$-0.869295\pi$
$137$		−	2.81241e8i		−	0.798357i	0.916873	−	0.399178i	$-0.130705\pi$
$138$	−5.34836e8			−1.47470
$139$	−6.05884e8			−1.62304			−0.811522	−	0.584322i	$-0.801360\pi$
$139$	−6.05884e8			−1.62304			−0.811522	+	0.584322i	$0.801360\pi$
$140$	−1.17693e9			−3.06364
$141$		−	3.16591e8i		−	0.800980i
$142$	3.46557e8			0.852357
$143$	−4.72981e8			−1.13110
$144$	1.17226e8			0.272629
$145$	−2.48940e8			−0.563147
$146$	−4.11381e8			−0.905384
$147$			1.52022e9i			3.25564i
$148$		−	3.76412e8i		−	0.784543i
$149$		−	6.51784e8i		−	1.32239i	−0.750215	−	0.661194i	$-0.770050\pi$
$149$		−	6.51784e8i		−	1.32239i	0.750215	−	0.661194i	$-0.229950\pi$
$150$	3.61569e8			0.714211
$151$		−	1.34573e8i		−	0.258852i	−0.991589	−	0.129426i	$-0.958687\pi$
$151$		−	1.34573e8i		−	0.258852i	0.991589	−	0.129426i	$-0.0413135\pi$
$152$	5.18455e8			0.971262
$153$	1.25490e9			2.29004
$154$	2.07842e9			3.69530
$155$			1.18868e8i			0.205938i
$156$		−	1.18734e9i		−	2.00482i
$157$		−	9.79370e7i		−	0.161194i	−0.996747	−	0.0805969i	$-0.974317\pi$
$157$		−	9.79370e7i		−	0.161194i	0.996747	−	0.0805969i	$-0.0256826\pi$
$158$		−	9.55350e8i		−	1.53297i
$159$			1.50281e7i			0.0235135i
$160$	8.59873e8			1.31206
$161$			7.20520e8i			1.07237i
$162$			5.89303e8i			0.855615i
$163$			3.08528e8i			0.437063i	0.975830	+	0.218531i	$0.0701266\pi$
$163$			3.08528e8i			0.437063i	−0.975830	+	0.218531i	$0.929873\pi$
$164$	1.79827e9			2.48588
$165$	−1.69787e9			−2.29070
$166$		−	1.69688e9i		−	2.23470i
$167$	−6.12522e8			−0.787510			−0.393755	−	0.919215i	$-0.628824\pi$
$167$	−6.12522e8			−0.787510			−0.393755	+	0.919215i	$0.628824\pi$
$168$			1.79228e9i			2.24993i
$169$	−2.12759e8			−0.260820
$170$	2.57232e9			3.07985
$171$			1.34225e9i			1.56982i
$172$	−8.70113e8	+	1.01008e9i	−0.994173	+	1.15410i
$173$	−5.69720e7			−0.0636029			−0.0318015	−	0.999494i	$-0.510124\pi$
$173$	−5.69720e7			−0.0636029			−0.0318015	+	0.999494i	$0.510124\pi$
$174$			1.10359e9i			1.20395i
$175$		−	4.87098e8i		−	0.519355i
$176$	−2.56174e8			−0.266983
$177$		−	4.02309e8i		−	0.409890i
$178$	−1.02195e9			−1.01801
$179$		−	3.49206e8i		−	0.340149i	−0.985431	−	0.170074i	$-0.945599\pi$
$179$		−	3.49206e8i		−	0.340149i	0.985431	−	0.170074i	$-0.0544008\pi$
$180$		−	2.44341e9i		−	2.32759i
$181$	7.24881e8			0.675387			0.337693	−	0.941256i	$-0.390353\pi$
$181$	7.24881e8			0.675387			0.337693	+	0.941256i	$0.390353\pi$
$182$	−2.64964e9			−2.41491
$183$	−1.46086e9			−1.30258
$184$			5.77789e8i			0.504078i
$185$	6.86195e8			0.585816
$186$	5.26958e8			0.440275
$187$	−2.74234e9			−2.24261
$188$	−9.95639e8			−0.797023
$189$	−1.18617e9			−0.929606
$190$			2.75138e9i			2.11123i
$191$			1.33591e9i			1.00379i	0.864929	+	0.501894i	$0.167363\pi$
$191$			1.33591e9i			1.00379i	−0.864929	+	0.501894i	$0.832637\pi$
$192$		−	3.38978e9i		−	2.49440i
$193$	1.61824e9			1.16631			0.583155	−	0.812361i	$-0.301818\pi$
$193$	1.61824e9			1.16631			0.583155	+	0.812361i	$0.301818\pi$
$194$		−	1.00653e8i		−	0.0710591i
$195$	2.16450e9			1.49699
$196$	4.78090e9			3.23955
$197$	9.06502e8			0.601872			0.300936	−	0.953644i	$-0.402701\pi$
$197$	9.06502e8			0.601872			0.300936	+	0.953644i	$0.402701\pi$
$198$			4.31498e9i			2.80749i
$199$		−	1.65380e9i		−	1.05456i	−0.849692	−	0.527279i	$-0.823212\pi$
$199$		−	1.65380e9i		−	1.05456i	0.849692	−	0.527279i	$-0.176788\pi$
$200$		−	3.90607e8i		−	0.244129i
$201$			4.50047e9i			2.75723i
$202$			1.63406e9i			0.981434i
$203$	1.48673e9			0.875484
$204$		−	6.88415e9i		−	3.97493i
$205$			3.27824e9i			1.85620i
$206$			1.44988e9i			0.805124i
$207$	−1.49586e9			−0.814725
$208$	3.26579e8			0.174476
$209$		−	2.93323e9i		−	1.53731i
$210$	−9.51145e9			−4.89068
$211$		−	2.92300e9i		−	1.47468i	−0.675520	−	0.737342i	$-0.736081\pi$
$211$		−	2.92300e9i		−	1.47468i	0.675520	−	0.737342i	$-0.263919\pi$
$212$	4.72617e7			0.0233973
$213$	1.69077e9			0.821421
$214$		−	4.52286e9i		−	2.15654i
$215$	−1.84137e9	−	1.58621e9i	−0.861762	−	0.742345i
$216$	−9.51194e8			−0.436972
$217$		−	7.09907e8i		−	0.320157i
$218$		−	3.70634e9i		−	1.64104i
$219$	−2.00703e9			−0.872523
$220$			5.33959e9i			2.27938i
$221$	3.49602e9			1.46556
$222$		−	3.04201e9i		−	1.25242i
$223$			2.27107e9i			0.918356i	0.888344	+	0.459178i	$0.151856\pi$
$223$			2.27107e9i			0.918356i	−0.888344	+	0.459178i	$0.848144\pi$
$224$	−5.13538e9			−2.03977
$225$	1.01126e9			0.394578
$226$	−1.00737e8			−0.0386148
$227$		−	5.65990e8i		−	0.213160i	−0.994304	−	0.106580i	$-0.966010\pi$
$227$		−	5.65990e8i		−	0.213160i	0.994304	−	0.106580i	$-0.0339900\pi$
$228$	7.36335e9			2.72481
$229$	−3.13606e9			−1.14036			−0.570181	−	0.821519i	$-0.693127\pi$
$229$	−3.13606e9			−1.14036			−0.570181	+	0.821519i	$0.693127\pi$
$230$	−3.06626e9			−1.09572
$231$	1.01401e10			3.56118
$232$	1.19222e9			0.411532
$233$			2.14351e9i			0.727281i	0.931539	+	0.363641i	$0.118466\pi$
$233$			2.14351e9i			0.727281i	−0.931539	+	0.363641i	$0.881534\pi$
$234$		−	5.50088e9i		−	1.83472i
$235$		−	1.81504e9i		−	0.595134i
$236$	−1.26521e9			−0.407865
$237$		−	4.66092e9i		−	1.47733i
$238$	−1.53625e10			−4.78801
$239$	4.34656e9			1.33215			0.666077	−	0.745883i	$-0.267972\pi$
$239$	4.34656e9			1.33215			0.666077	+	0.745883i	$0.267972\pi$
$240$	1.17233e9			0.353349
$241$		−	8.68227e8i		−	0.257374i	−0.991685	−	0.128687i	$-0.958924\pi$
$241$		−	8.68227e8i		−	0.257374i	0.991685	−	0.128687i	$-0.0410763\pi$
$242$		−	3.98149e9i		−	1.16087i
$243$			4.70814e9i			1.35028i
$244$			4.59422e9i			1.29614i
$245$			8.71552e9i			2.41896i
$246$	1.45329e10			3.96838
$247$			3.73938e9i			1.00464i
$248$		−	5.69278e8i		−	0.150494i
$249$		−	8.27867e9i		−	2.15359i
$250$	−4.98474e9			−1.27609
$251$	−4.77899e9			−1.20404			−0.602021	−	0.798481i	$-0.705638\pi$
$251$	−4.77899e9			−1.20404			−0.602021	+	0.798481i	$0.705638\pi$
$252$			1.45926e10i			3.61853i
$253$	3.26892e9			0.797853
$254$			6.91669e9i			1.66174i
$255$	1.25497e10			2.96807
$256$	−2.79041e9			−0.649692
$257$		−	4.13081e9i		−	0.946898i	−0.880821	−	0.473449i	$-0.843009\pi$
$257$		−	4.13081e9i		−	0.946898i	0.880821	−	0.473449i	$-0.156991\pi$
$258$	−7.03190e9	+	8.16308e9i	−1.58706	+	1.84236i
$259$	−4.09813e9			−0.910724
$260$		−	6.80709e9i		−	1.48960i
$261$			3.08658e9i			0.665145i
$262$	1.16987e9			0.248275
$263$		−	8.67393e9i		−	1.81298i	−0.422229	−	0.906489i	$-0.638752\pi$
$263$		−	8.67393e9i		−	1.81298i	0.422229	−	0.906489i	$-0.361248\pi$
$264$	8.13140e9			1.67398
$265$			8.61576e7i			0.0174707i
$266$		−	1.64319e10i		−	3.28218i
$267$	−4.98586e9			−0.981058
$268$	1.41534e10			2.74361
$269$	−5.79853e9			−1.10741			−0.553705	−	0.832713i	$-0.686786\pi$
$269$	−5.79853e9			−1.10741			−0.553705	+	0.832713i	$0.686786\pi$
$270$		−	5.04788e9i		−	0.949848i
$271$	−7.28151e8			−0.135003			−0.0675016	−	0.997719i	$-0.521503\pi$
$271$	−7.28151e8			−0.135003			−0.0675016	+	0.997719i	$0.521503\pi$
$272$	1.89350e9			0.345931
$273$	−1.29269e10			−2.32726
$274$	−7.14793e9			−1.26817
$275$	−2.20991e9			−0.386407
$276$			8.20605e9i			1.41416i
$277$			4.67054e9i			0.793319i	0.917966	+	0.396659i	$0.129831\pi$
$277$			4.67054e9i			0.793319i	−0.917966	+	0.396659i	$0.870169\pi$
$278$			1.53989e10i			2.57817i
$279$	1.47383e9			0.243238
$280$			1.02753e10i			1.67172i
$281$	4.09921e9			0.657468			0.328734	−	0.944422i	$-0.393378\pi$
$281$	4.09921e9			0.657468			0.328734	+	0.944422i	$0.393378\pi$
$282$	−8.04635e9			−1.27234
$283$	−3.83506e8			−0.0597898			−0.0298949	−	0.999553i	$-0.509517\pi$
$283$	−3.83506e8			−0.0597898			−0.0298949	+	0.999553i	$0.509517\pi$
$284$		−	5.31726e9i		−	0.817363i
$285$			1.34233e10i			2.03461i
$286$			1.20211e10i			1.79672i
$287$		−	1.95785e10i		−	2.88570i
$288$		−	1.06615e10i		−	1.54970i
$289$	1.32941e10			1.90576
$290$			6.32696e9i			0.894547i
$291$		−	4.91062e8i		−	0.0684800i
$292$			6.31186e9i			0.868212i
$293$	−7.92297e9			−1.07502			−0.537511	−	0.843257i	$-0.680635\pi$
$293$	−7.92297e9			−1.07502			−0.537511	+	0.843257i	$0.680635\pi$
$294$	3.86373e10			5.17151
$295$		−	2.30647e9i		−	0.304551i
$296$	−3.28631e9			−0.428097
$297$			5.38152e9i			0.691638i
$298$	−1.65655e10			−2.10058
$299$	−4.16733e9			−0.521403
$300$		−	5.54759e9i		−	0.684888i
$301$	1.09971e10	+	9.47323e9i	1.33972	+	1.15407i
$302$	−3.42027e9			−0.411181
$303$			7.97216e9i			0.945813i
$304$			2.02531e9i			0.237135i
$305$	−8.37522e9			−0.967825
$306$		−	3.18940e10i		−	3.63767i
$307$	1.17322e10			1.32077			0.660386	−	0.750926i	$-0.270393\pi$
$307$	1.17322e10			1.32077			0.660386	+	0.750926i	$0.270393\pi$
$308$		−	3.18894e10i		−	3.54359i
$309$			7.07360e9i			0.775902i
$310$	3.02110e9			0.327128
$311$	2.02378e9			0.216333			0.108166	−	0.994133i	$-0.465502\pi$
$311$	2.02378e9			0.216333			0.108166	+	0.994133i	$0.465502\pi$
$312$	−1.03662e10			−1.09396
$313$			1.45585e10i			1.51683i	0.651769	+	0.758417i	$0.274027\pi$
$313$			1.45585e10i			1.51683i	−0.651769	+	0.758417i	$0.725973\pi$
$314$	−2.48913e9			−0.256053
$315$	−2.66022e10			−2.70194
$316$	−1.46580e10			−1.47003
$317$	1.69110e10			1.67468			0.837342	−	0.546680i	$-0.184109\pi$
$317$	1.69110e10			1.67468			0.837342	+	0.546680i	$0.184109\pi$
$318$	3.81950e8			0.0373506
$319$		−	6.74514e9i		−	0.651370i
$320$		−	1.94339e10i		−	1.85336i
$321$		−	2.20659e10i		−	2.07827i
$322$	1.83125e10			1.70343
$323$			2.16809e10i			1.99189i
$324$	9.04173e9			0.820487
$325$	2.81727e9			0.252520
$326$	7.84143e9			0.694265
$327$		−	1.80824e10i		−	1.58148i
$328$		−	1.57001e10i		−	1.35646i
$329$			1.08399e10i			0.925211i
$330$			4.31524e10i			3.63873i
$331$		−	2.26514e10i		−	1.88705i	−0.331304	−	0.943524i	$-0.607488\pi$
$331$		−	2.26514e10i		−	1.88705i	0.331304	−	0.943524i	$-0.392512\pi$
$332$	−2.60354e10			−2.14295
$333$		−	8.50809e9i		−	0.691919i
$334$			1.55676e10i			1.25094i
$335$			2.58016e10i			2.04865i
$336$	−7.00143e9			−0.549325
$337$	−2.09936e10			−1.62767			−0.813837	−	0.581093i	$-0.802625\pi$
$337$	−2.09936e10			−1.62767			−0.813837	+	0.581093i	$0.802625\pi$
$338$			5.40740e9i			0.414306i
$339$	−4.91470e8			−0.0372133
$340$		−	3.94674e10i		−	2.95340i
$341$	−3.22077e9			−0.238200
$342$	3.41142e10			2.49362
$343$		−	2.75764e10i		−	1.99233i
$344$	8.81866e9	+	7.59663e9i	0.629751	+	0.542484i
$345$	−1.49595e10			−1.05595
$346$			1.44798e9i			0.101032i
$347$			4.17920e9i			0.288254i	0.989559	+	0.144127i	$0.0460373\pi$
$347$			4.17920e9i			0.288254i	−0.989559	+	0.144127i	$0.953963\pi$
$348$	1.69325e10			1.15452
$349$		−	1.39214e10i		−	0.938387i	−0.883096	−	0.469193i	$-0.844545\pi$
$349$		−	1.39214e10i		−	0.938387i	0.883096	−	0.469193i	$-0.155455\pi$
$350$	−1.23799e10			−0.824984
$351$		−	6.86053e9i		−	0.451991i
$352$			2.32987e10i			1.51761i
$353$	1.37614e10			0.886267			0.443134	−	0.896456i	$-0.353867\pi$
$353$	1.37614e10			0.886267			0.443134	+	0.896456i	$0.353867\pi$
$354$	−1.02249e10			−0.651101
$355$	9.69332e9			0.610322
$356$			1.56799e10i			0.976211i
$357$	−7.49502e10			−4.61423
$358$	−8.87529e9			−0.540319
$359$	3.97968e9			0.239591			0.119795	−	0.992799i	$-0.461776\pi$
$359$	3.97968e9			0.239591			0.119795	+	0.992799i	$0.461776\pi$
$360$	−2.13325e10			−1.27008
$361$	−6.20650e9			−0.365442
$362$		−	1.84233e10i		−	1.07284i
$363$		−	1.94247e10i		−	1.11874i
$364$			4.06537e10i			2.31576i
$365$	−1.15065e10			−0.648291
$366$			3.71286e10i			2.06912i
$367$	3.22905e10			1.77996			0.889981	−	0.455998i	$-0.150718\pi$
$367$	3.22905e10			1.77996			0.889981	+	0.455998i	$0.150718\pi$
$368$	−2.25709e9			−0.123072
$369$	4.06466e10			2.19240
$370$		−	1.74401e10i		−	0.930555i
$371$		−	5.14555e8i		−	0.0271604i
$372$		−	8.08518e9i		−	0.422200i
$373$		−	2.21792e8i		−	0.0114580i	−0.999984	−	0.00572902i	$-0.998176\pi$
$373$		−	2.21792e8i		−	0.0114580i	0.999984	−	0.00572902i	$-0.00182361\pi$
$374$			6.96982e10i			3.56234i
$375$	−2.43193e10			−1.22978
$376$			8.69255e9i			0.434907i
$377$			8.59892e9i			0.425676i
$378$			3.01472e10i			1.47666i
$379$	−1.63002e10			−0.790019			−0.395009	−	0.918677i	$-0.629259\pi$
$379$	−1.63002e10			−0.790019			−0.395009	+	0.918677i	$0.629259\pi$
$380$	4.22147e10			2.02456
$381$			3.37449e10i			1.60143i
$382$	3.39529e10			1.59450
$383$			3.14817e10i			1.46306i	0.681809	+	0.731531i	$0.261194\pi$
$383$			3.14817e10i			1.46306i	−0.681809	+	0.731531i	$0.738806\pi$
$384$	−4.77574e10			−2.19642
$385$	5.81341e10			2.64599
$386$		−	4.11286e10i		−	1.85266i
$387$	−1.96673e10	+	2.28310e10i	−0.876799	+	1.01784i
$388$	−1.54433e9			−0.0681417
$389$		−	2.51872e10i		−	1.09997i	−0.835174	−	0.549986i	$-0.814633\pi$
$389$		−	2.51872e10i		−	1.09997i	0.835174	−	0.549986i	$-0.185367\pi$
$390$		−	5.50122e10i		−	2.37794i
$391$	−2.41621e10			−1.03378
$392$		−	4.17402e10i		−	1.76771i
$393$	5.70751e9			0.239264
$394$		−	2.30393e10i		−	0.956060i
$395$		−	2.67215e10i		−	1.09767i
$396$	6.62052e10			2.69223
$397$	2.97336e10			1.19698			0.598488	−	0.801132i	$-0.295768\pi$
$397$	2.97336e10			1.19698			0.598488	+	0.801132i	$0.295768\pi$
$398$	−4.20324e10			−1.67514
$399$		−	8.01675e10i		−	3.16305i
$400$	1.52588e9			0.0596046
$401$	1.21677e10			0.470576			0.235288	−	0.971926i	$-0.424397\pi$
$401$	1.21677e10			0.470576			0.235288	+	0.971926i	$0.424397\pi$
$402$	1.14382e11			4.37980
$403$	4.10595e9			0.155666
$404$	2.50715e10			0.941141
$405$			1.64830e10i			0.612655i
$406$		−	3.77862e10i		−	1.39069i
$407$			1.85928e10i			0.677590i
$408$	−6.01029e10			−2.16898
$409$		−	2.93025e9i		−	0.104716i	−0.998628	−	0.0523578i	$-0.983326\pi$
$409$		−	2.93025e9i		−	0.104716i	0.998628	−	0.0523578i	$-0.0166736\pi$
$410$	8.33185e10			2.94853
$411$	−3.48730e10			−1.22214
$412$	2.22456e10			0.772069
$413$			1.37748e10i			0.473463i
$414$			3.80184e10i			1.29417i
$415$		−	4.74623e10i		−	1.60013i
$416$		−	2.97019e10i		−	0.991770i
$417$			7.51276e10i			2.48459i
$418$	−7.45499e10			−2.44198
$419$		−	9.01121e9i		−	0.292366i	−0.989258	−	0.146183i	$-0.953301\pi$
$419$		−	9.01121e9i		−	0.292366i	0.989258	−	0.146183i	$-0.0466989\pi$
$420$			1.45935e11i			4.68989i
$421$		−	3.93187e10i		−	1.25161i	−0.779978	−	0.625807i	$-0.784770\pi$
$421$		−	3.93187e10i		−	1.25161i	0.779978	−	0.625807i	$-0.215230\pi$
$422$	−7.42899e10			−2.34250
$423$	−2.25046e10			−0.702925
$424$		−	4.12624e8i		−	0.0127671i
$425$	1.63345e10			0.500668
$426$		−	4.29720e10i		−	1.30481i
$427$	5.00189e10			1.50461
$428$	−6.93947e10			−2.06800
$429$			5.86481e10i			1.73151i
$430$	−4.03145e10	+	4.67996e10i	−1.17920	+	1.36889i
$431$	4.46793e10			1.29478			0.647392	−	0.762157i	$-0.275860\pi$
$431$	4.46793e10			1.29478			0.647392	+	0.762157i	$0.275860\pi$
$432$		−	3.71577e9i		−	0.106688i
$433$		−	3.91721e7i		−	0.00111436i	−1.00000		0.000557180i	$-0.999823\pi$
$433$		−	3.91721e7i		−	0.00111436i	1.00000		0.000557180i	$-0.000177356\pi$
$434$	−1.80427e10			−0.508562
$435$			3.08677e10i			0.862080i
$436$	−5.68668e10			−1.57367
$437$		−	2.58440e10i		−	0.708655i
$438$			5.10099e10i			1.38598i
$439$	3.54045e10			0.953235			0.476618	−	0.879111i	$-0.341863\pi$
$439$	3.54045e10			0.953235			0.476618	+	0.879111i	$0.341863\pi$
$440$	4.66180e10			1.24378
$441$	1.08063e11			2.85709
$442$		−	8.88536e10i		−	2.32802i
$443$	−3.92702e10			−1.01964			−0.509821	−	0.860280i	$-0.670288\pi$
$443$	−3.92702e10			−1.01964			−0.509821	+	0.860280i	$0.670288\pi$
$444$	−4.66739e10			−1.20100
$445$	−2.85843e10			−0.728934
$446$	5.77207e10			1.45879
$447$	−8.08191e10			−2.02434
$448$			1.16064e11i			2.88128i
$449$			3.13621e9i			0.0771650i	0.999255	+	0.0385825i	$0.0122842\pi$
$449$			3.13621e9i			0.0771650i	−0.999255	+	0.0385825i	$0.987716\pi$
$450$		−	2.57018e10i		−	0.626778i
$451$	−8.88254e10			−2.14699
$452$			1.54561e9i			0.0370295i
$453$	−1.66867e10			−0.396257
$454$	−1.43850e10			−0.338600
$455$	−7.41112e10			−1.72917
$456$		−	6.42867e10i		−	1.48683i
$457$		−	1.45128e10i		−	0.332726i	−0.986065	−	0.166363i	$-0.946798\pi$
$457$		−	1.45128e10i		−	0.332726i	0.986065	−	0.166363i	$-0.0532024\pi$
$458$			7.97050e10i			1.81144i
$459$		−	3.97773e10i		−	0.896157i
$460$			4.70460e10i			1.05073i
$461$	6.92222e10			1.53265			0.766323	−	0.642456i	$-0.222084\pi$
$461$	6.92222e10			1.53265			0.766323	+	0.642456i	$0.222084\pi$
$462$		−	2.57717e11i		−	5.65686i
$463$			3.30451e10i			0.719090i	0.933128	+	0.359545i	$0.117068\pi$
$463$			3.30451e10i			0.719090i	−0.933128	+	0.359545i	$0.882932\pi$
$464$			4.65731e9i			0.100476i
$465$	1.47392e10			0.315255
$466$	5.44788e10			1.15527
$467$			2.97268e10i			0.625001i	0.949918	+	0.312501i	$0.101167\pi$
$467$			2.97268e10i			0.625001i	−0.949918	+	0.312501i	$0.898833\pi$
$468$	−8.44006e10			−1.75939
$469$		−	1.54093e11i		−	3.18488i
$470$	−4.61304e10			−0.945357
$471$	−1.21439e10			−0.246759
$472$			1.10461e10i			0.222557i
$473$	4.29790e10	−	4.98928e10i	0.858641	−	0.996766i
$474$	−1.18460e11			−2.34671
$475$			1.74715e10i			0.343207i
$476$			2.35709e11i			4.59144i
$477$	1.06826e9			0.0206350
$478$		−	1.10471e11i		−	2.11610i
$479$	−7.52787e10			−1.42998			−0.714990	−	0.699135i	$-0.753569\pi$
$479$	−7.52787e10			−1.42998			−0.714990	+	0.699135i	$0.753569\pi$
$480$		−	1.06622e11i		−	2.00854i
$481$		−	2.37027e10i		−	0.442810i
$482$	−2.20666e10			−0.408833
$483$	8.93422e10			1.64160
$484$	−6.10885e10			−1.11321
$485$		−	2.81530e9i		−	0.0508812i
$486$	1.19660e11			2.14489
$487$	8.28852e10			1.47354			0.736769	−	0.676145i	$-0.236351\pi$
$487$	8.28852e10			1.47354			0.736769	+	0.676145i	$0.236351\pi$
$488$	4.01104e10			0.707258
$489$	3.82564e10			0.669066
$490$	2.21511e11			3.84247
$491$		−	3.32135e10i		−	0.571464i	−0.958310	−	0.285732i	$-0.907763\pi$
$491$		−	3.32135e10i		−	0.571464i	0.958310	−	0.285732i	$-0.0922367\pi$
$492$		−	2.22980e11i		−	3.80545i
$493$			4.98564e10i			0.843982i
$494$	9.50387e10			1.59585
$495$			1.20691e11i			2.01028i
$496$	2.22385e9			0.0367433
$497$	−5.78909e10			−0.948823
$498$	−2.10408e11			−3.42093
$499$			1.20030e11i			1.93592i	0.251103	+	0.967960i	$0.419207\pi$
$499$			1.20030e11i			1.93592i	−0.251103	+	0.967960i	$0.580793\pi$
$500$			7.64814e10i			1.22370i
$501$			7.59508e10i			1.20554i
$502$			1.21461e11i			1.91259i
$503$		−	4.36030e9i		−	0.0681152i	−0.999420	−	0.0340576i	$-0.989157\pi$
$503$		−	4.36030e9i		−	0.0681152i	0.999420	−	0.0340576i	$-0.0108430\pi$
$504$	1.27403e11			1.97450
$505$			4.57051e10i			0.702747i
$506$		−	8.30818e10i		−	1.26737i
$507$			2.63814e10i			0.399269i
$508$	1.06124e11			1.59352
$509$	−4.13833e10			−0.616530			−0.308265	−	0.951301i	$-0.599748\pi$
$509$	−4.13833e10			−0.616530			−0.308265	+	0.951301i	$0.599748\pi$
$510$		−	3.18959e11i		−	4.71471i
$511$	6.87194e10			1.00785
$512$		−	2.76785e10i		−	0.402775i
$513$	4.25462e10			0.614315
$514$	−1.04987e11			−1.50413
$515$			4.05536e10i			0.576501i
$516$	1.25247e11	+	1.07891e11i	1.76672	+	1.52190i
$517$	4.91794e10			0.688368
$518$			1.04157e11i			1.44667i
$519$			7.06435e9i			0.0973649i
$520$	−5.94302e10			−0.812818
$521$			2.54747e10i			0.345747i	0.984944	+	0.172874i	$0.0553053\pi$
$521$			2.54747e10i			0.345747i	−0.984944	+	0.172874i	$0.944695\pi$
$522$	7.84475e10			1.05657
$523$		−	4.78528e10i		−	0.639588i	−0.947487	−	0.319794i	$-0.896386\pi$
$523$		−	4.78528e10i		−	0.639588i	0.947487	−	0.319794i	$-0.103614\pi$
$524$		−	1.79494e10i		−	0.238082i
$525$	−6.03986e10			−0.795042
$526$	−2.20453e11			−2.87988
$527$	2.38062e10			0.308637
$528$			3.17647e10i			0.408705i
$529$	−4.95092e10			−0.632213
$530$	2.18975e9			0.0277518
$531$	−2.85978e10			−0.359711
$532$	−2.52117e11			−3.14743
$533$	1.13238e11			1.40308
$534$			1.26719e11i			1.55839i
$535$		−	1.26506e11i		−	1.54417i
$536$		−	1.23568e11i		−	1.49709i
$537$	−4.33004e10			−0.520708
$538$			1.47373e11i			1.75910i
$539$	−2.36151e11			−2.79792
$540$	−7.74502e10			−0.910851
$541$	9.62804e10			1.12396			0.561978	−	0.827152i	$-0.310041\pi$
$541$	9.62804e10			1.12396			0.561978	+	0.827152i	$0.310041\pi$
$542$			1.85064e10i			0.214450i
$543$		−	8.98829e10i		−	1.03390i
$544$		−	1.72211e11i		−	1.96637i
$545$		−	1.03668e11i		−	1.17505i
$546$			3.28546e11i			3.69680i
$547$	2.42196e10			0.270531			0.135265	−	0.990809i	$-0.456811\pi$
$547$	2.42196e10			0.270531			0.135265	+	0.990809i	$0.456811\pi$
$548$			1.09671e11i			1.21611i
$549$			1.03844e11i			1.14312i
$550$			5.61664e10i			0.613798i
$551$	−5.33269e10			−0.578549
$552$	7.16439e10			0.771655
$553$			1.59587e11i			1.70647i
$554$	1.18705e11			1.26017
$555$		−	8.50860e10i		−	0.896781i
$556$	2.36267e11			2.47232
$557$	9.97285e10			1.03609			0.518046	−	0.855353i	$-0.326660\pi$
$557$	9.97285e10			1.03609			0.518046	+	0.855353i	$0.326660\pi$
$558$		−	3.74584e10i		−	0.386378i
$559$	−5.47911e10	+	6.36050e10i	−0.561129	+	0.651395i
$560$	−4.01398e10			−0.408153
$561$			3.40041e11i			3.43305i
$562$		−	1.04184e11i		−	1.04437i
$563$	1.38700e11			1.38052			0.690261	−	0.723561i	$-0.257496\pi$
$563$	1.38700e11			1.38052			0.690261	+	0.723561i	$0.257496\pi$
$564$			1.23456e11i			1.22010i
$565$	−2.81764e9			−0.0276498
$566$			9.74706e9i			0.0949747i
$567$		−	9.84405e10i		−	0.952449i
$568$	−4.64230e10			−0.446005
$569$	8.10953e9			0.0773654			0.0386827	−	0.999252i	$-0.487684\pi$
$569$	8.10953e9			0.0773654			0.0386827	+	0.999252i	$0.487684\pi$
$570$	3.41162e11			3.23193
$571$		−	4.34370e10i		−	0.408616i	−0.978907	−	0.204308i	$-0.934506\pi$
$571$		−	4.34370e10i		−	0.408616i	0.978907	−	0.204308i	$-0.0654944\pi$
$572$	1.84441e11			1.72296
$573$	1.65648e11			1.53662
$574$	−4.97599e11			−4.58387
$575$	−1.94711e10			−0.178122
$576$	−2.40959e11			−2.18904
$577$		−	1.29380e11i		−	1.16725i	−0.812024	−	0.583624i	$-0.801634\pi$
$577$		−	1.29380e11i		−	1.16725i	0.812024	−	0.583624i	$-0.198366\pi$
$578$		−	3.37878e11i		−	3.02725i
$579$		−	2.00657e11i		−	1.78542i
$580$	9.70752e10			0.857821
$581$			2.83457e11i			2.48761i
$582$	−1.24806e10			−0.108779
$583$	−2.33448e9			−0.0202076
$584$	5.51065e10			0.473752
$585$		−	1.53861e11i		−	1.31373i
$586$			2.01367e11i			1.70765i
$587$			2.11829e11i			1.78415i	0.451883	+	0.892077i	$0.350752\pi$
$587$			2.11829e11i			1.78415i	−0.451883	+	0.892077i	$0.649248\pi$
$588$		−	5.92816e11i		−	4.95919i
$589$			2.54634e10i			0.211570i
$590$	−5.86205e10			−0.483773
$591$		−	1.12403e11i		−	0.921360i
$592$		−	1.28377e10i		−	0.104521i
$593$		−	9.55395e9i		−	0.0772617i	−0.999254	−	0.0386308i	$-0.987700\pi$
$593$		−	9.55395e9i		−	0.0772617i	0.999254	−	0.0386308i	$-0.0122996\pi$
$594$	1.36775e11			1.09865
$595$	−4.29696e11			−3.42841
$596$			2.54166e11i			2.01434i
$597$	−2.05066e11			−1.61434
$598$			1.05915e11i			0.828237i
$599$	8.88356e8			0.00690048			0.00345024	−	0.999994i	$-0.498902\pi$
$599$	8.88356e8			0.00690048			0.00345024	+	0.999994i	$0.498902\pi$
$600$	−4.84340e10			−0.373719
$601$		−	5.66506e10i		−	0.434217i	−0.976148	−	0.217108i	$-0.930337\pi$
$601$		−	5.66506e10i		−	0.434217i	0.976148	−	0.217108i	$-0.0696625\pi$
$602$	2.40768e11	−	2.79499e11i	1.83321	−	2.12811i
$603$	3.19912e11			2.41970
$604$			5.24776e10i			0.394299i
$605$		−	1.11364e11i		−	0.831232i
$606$	2.02618e11			1.50240
$607$		−	1.71828e10i		−	0.126573i	−0.997995	−	0.0632863i	$-0.979842\pi$
$607$		−	1.71828e10i		−	0.126573i	0.997995	−	0.0632863i	$-0.0201581\pi$
$608$	1.84199e11			1.34795
$609$		−	1.84350e11i		−	1.34021i
$610$			2.12862e11i			1.53737i
$611$	−6.26955e10			−0.449854
$612$	−4.89353e11			−3.48832
$613$	−2.11244e11			−1.49603			−0.748017	−	0.663679i	$-0.768994\pi$
$613$	−2.11244e11			−1.49603			−0.748017	+	0.663679i	$0.768994\pi$
$614$		−	2.98183e11i		−	2.09802i
$615$	4.06491e11			2.84152
$616$	−2.78414e11			−1.93361
$617$	−8.35394e10			−0.576435			−0.288218	−	0.957565i	$-0.593063\pi$
$617$	−8.35394e10			−0.576435			−0.288218	+	0.957565i	$0.593063\pi$
$618$	1.79780e11			1.23250
$619$	6.90104e10			0.470059			0.235029	−	0.971988i	$-0.424481\pi$
$619$	6.90104e10			0.470059			0.235029	+	0.971988i	$0.424481\pi$
$620$		−	4.63530e10i		−	0.313698i
$621$			4.74153e10i			0.318825i
$622$		−	5.14357e10i		−	0.343640i
$623$	1.70713e11			1.13322
$624$		−	4.04947e10i		−	0.267092i
$625$	−1.84241e11			−1.20744
$626$	3.70013e11			2.40946
$627$	−3.63711e11			−2.35335
$628$			3.81910e10i			0.245540i
$629$		−	1.37428e11i		−	0.877955i
$630$			6.76113e11i			4.29197i
$631$		−	1.16433e11i		−	0.734446i	−0.930133	−	0.367223i	$-0.880309\pi$
$631$		−	1.16433e11i		−	0.734446i	0.930133	−	0.367223i	$-0.119691\pi$
$632$			1.27974e11i			0.802145i
$633$	−3.62442e11			−2.25748
$634$		−	4.29804e11i		−	2.66020i
$635$			1.93462e11i			1.18987i
$636$		−	5.86029e9i		−	0.0358171i
$637$	3.01053e11			1.82846
$638$	−1.71432e11			−1.03469
$639$		−	1.20187e11i		−	0.720864i
$640$	−2.73797e11			−1.63196
$641$			2.88483e11i			1.70879i	0.519625	+	0.854395i	$0.326072\pi$
$641$			2.88483e11i			1.70879i	−0.519625	+	0.854395i	$0.673928\pi$
$642$	−5.60820e11			−3.30129
$643$	−2.45488e10			−0.143610			−0.0718052	−	0.997419i	$-0.522876\pi$
$643$	−2.45488e10			−0.143610			−0.0718052	+	0.997419i	$0.522876\pi$
$644$		−	2.80970e11i		−	1.63349i
$645$	−1.96684e11	+	2.28324e11i	−1.13640	+	1.31921i
$646$	5.51033e11			3.16408
$647$			9.34246e9i			0.0533144i	0.999645	+	0.0266572i	$0.00848625\pi$
$647$			9.34246e9i			0.0533144i	−0.999645	+	0.0266572i	$0.991514\pi$
$648$		−	7.89400e10i		−	0.447710i
$649$	6.24949e10			0.352262
$650$		−	7.16028e10i		−	0.401122i
$651$	−8.80262e10			−0.490104
$652$		−	1.20312e11i		−	0.665761i
$653$			2.90231e11i			1.59622i	0.602515	+	0.798108i	$0.294165\pi$
$653$			2.90231e11i			1.59622i	−0.602515	+	0.798108i	$0.705835\pi$
$654$	−4.59575e11			−2.51215
$655$	3.27217e10			0.177775
$656$	6.13312e10			0.331181
$657$			1.42668e11i			0.765710i
$658$	2.75502e11			1.46968
$659$	3.20513e11			1.69943			0.849717	−	0.527239i	$-0.176773\pi$
$659$	3.20513e11			1.69943			0.849717	+	0.527239i	$0.176773\pi$
$660$	6.62092e11			3.48934
$661$	−1.23308e11			−0.645930			−0.322965	−	0.946411i	$-0.604680\pi$
$661$	−1.23308e11			−0.645930			−0.322965	+	0.946411i	$0.604680\pi$
$662$	−5.75700e11			−2.99753
$663$		−	4.33495e11i		−	2.24352i
$664$			2.27305e11i			1.16933i
$665$		−	4.59607e11i		−	2.35017i
$666$	−2.16239e11			−1.09910
$667$		−	5.94299e10i		−	0.300263i
$668$	2.38856e11			1.19958
$669$	2.81605e11			1.40584
$670$	6.55763e11			3.25423
$671$		−	2.26931e11i		−	1.11945i
$672$			6.36770e11i			3.12252i
$673$			1.36670e11i			0.666214i	0.942889	+	0.333107i	$0.108097\pi$
$673$			1.36670e11i			0.666214i	−0.942889	+	0.333107i	$0.891903\pi$
$674$			5.33566e11i			2.58552i
$675$		−	3.20545e10i		−	0.154410i
$676$	8.29663e10			0.397297
$677$			7.59379e10i			0.361496i	0.983529	+	0.180748i	$0.0578519\pi$
$677$			7.59379e10i			0.361496i	−0.983529	+	0.180748i	$0.942148\pi$
$678$			1.24910e10i			0.0591125i
$679$			1.68137e10i			0.0791012i
$680$	−3.44575e11			−1.61157
$681$	−7.01809e10			−0.326310
$682$			8.18580e10i			0.378376i
$683$	2.26713e11			1.04182			0.520911	−	0.853611i	$-0.325592\pi$
$683$	2.26713e11			1.04182			0.520911	+	0.853611i	$0.325592\pi$
$684$		−	5.23417e11i		−	2.39124i
$685$	−1.99930e11			−0.908062
$686$	−7.00872e11			−3.16477
$687$			3.88861e11i			1.74569i
$688$	−2.96757e10	+	3.44495e10i	−0.132449	+	0.153755i
$689$	2.97607e9			0.0132059
$690$			3.80206e11i			1.67735i
$691$		−	2.53902e11i		−	1.11366i	−0.830625	−	0.556832i	$-0.812017\pi$
$691$		−	2.53902e11i		−	1.11366i	0.830625	−	0.556832i	$-0.187983\pi$
$692$	2.22165e10			0.0968839
$693$		−	7.20800e11i		−	3.12523i
$694$	1.06217e11			0.457885
$695$			4.30713e11i			1.84607i
$696$		−	1.47831e11i		−	0.629983i
$697$	6.56549e11			2.78186
$698$	−3.53822e11			−1.49061
$699$	2.65789e11			1.11334
$700$			1.89946e11i			0.791114i
$701$	1.87896e10			0.0778116			0.0389058	−	0.999243i	$-0.487613\pi$
$701$	1.87896e10			0.0778116			0.0389058	+	0.999243i	$0.487613\pi$
$702$	−1.74365e11			−0.717977
$703$	1.46994e11			0.601837
$704$	5.26570e11			2.14371
$705$	−2.25059e11			−0.911046
$706$		−	3.49755e11i		−	1.40782i
$707$		−	2.72962e11i		−	1.09251i
$708$			1.56882e11i			0.624369i
$709$	1.66008e11			0.656969			0.328484	−	0.944509i	$-0.393462\pi$
$709$	1.66008e11			0.656969			0.328484	+	0.944509i	$0.393462\pi$
$710$		−	2.46362e11i		−	0.969483i
$711$	−3.31317e11			−1.29648
$712$	1.36896e11			0.532683
$713$	−2.83775e10			−0.109804
$714$			1.90491e12i			7.32961i
$715$			3.36235e11i			1.28653i
$716$			1.36174e11i			0.518136i
$717$		−	5.38959e11i		−	2.03929i
$718$		−	1.01146e11i		−	0.380585i
$719$	−3.71527e11			−1.39019			−0.695097	−	0.718916i	$-0.744638\pi$
$719$	−3.71527e11			−1.39019			−0.695097	+	0.718916i	$0.744638\pi$
$720$		−	8.33338e10i		−	0.310092i
$721$		−	2.42196e11i		−	0.896244i
$722$			1.57742e11i			0.580496i
$723$	−1.07657e11			−0.393995
$724$	−2.82671e11			−1.02879
$725$			4.01768e10i			0.145420i
$726$	−4.93692e11			−1.77709
$727$		−	2.49562e11i		−	0.893390i	−0.894686	−	0.446695i	$-0.852601\pi$
$727$		−	2.49562e11i		−	0.893390i	0.894686	−	0.446695i	$-0.147399\pi$
$728$	3.54932e11			1.26363
$729$	4.31666e11			1.52840
$730$			2.92444e11i			1.02980i
$731$	−3.17678e11	+	3.68781e11i	−1.11254	+	1.29151i
$732$	5.69669e11			1.98417
$733$		−	3.98663e11i		−	1.38099i	−0.723337	−	0.690495i	$-0.757393\pi$
$733$		−	3.98663e11i		−	1.38099i	0.723337	−	0.690495i	$-0.242607\pi$
$734$		−	8.20684e11i		−	2.82743i
$735$	1.08070e12			3.70301
$736$			2.05279e11i			0.699575i
$737$	−6.99105e11			−2.36959
$738$		−	1.03306e12i		−	3.48257i
$739$		−	2.31276e11i		−	0.775449i	−0.921775	−	0.387724i	$-0.873261\pi$
$739$		−	2.31276e11i		−	0.775449i	0.921775	−	0.387724i	$-0.126739\pi$
$740$	−2.67585e11			−0.892350
$741$	4.63671e11			1.53793
$742$	−1.30777e10			−0.0431437
$743$		−	2.82004e11i		−	0.925336i	−0.886532	−	0.462668i	$-0.846892\pi$
$743$		−	2.82004e11i		−	0.925336i	0.886532	−	0.462668i	$-0.153108\pi$
$744$	−7.05886e10			−0.230379
$745$	−4.63343e11			−1.50410
$746$	−5.63698e9			−0.0182008
$747$	−5.88482e11			−1.88995
$748$	1.06939e12			3.41608
$749$			7.55524e11i			2.40061i
$750$			6.18091e11i			1.95347i
$751$		−	1.06170e11i		−	0.333766i	−0.985977	−	0.166883i	$-0.946630\pi$
$751$		−	1.06170e11i		−	0.333766i	0.985977	−	0.166883i	$-0.0533702\pi$
$752$	−3.39568e10			−0.106183
$753$			5.92579e11i			1.84318i
$754$	2.18547e11			0.676176
$755$	−9.56661e10			−0.294422
$756$	4.62552e11			1.41603
$757$			1.79106e11i			0.545415i	0.962097	+	0.272707i	$0.0879191\pi$
$757$			1.79106e11i			0.545415i	−0.962097	+	0.272707i	$0.912081\pi$
$758$			4.14281e11i			1.25493i
$759$		−	4.05336e11i		−	1.22137i
$760$		−	3.68561e11i		−	1.10473i
$761$		−	2.33012e11i		−	0.694767i	−0.937723	−	0.347383i	$-0.887070\pi$
$761$		−	2.33012e11i		−	0.694767i	0.937723	−	0.347383i	$-0.112930\pi$
$762$	8.57647e11			2.54383
$763$			6.19129e11i			1.82677i
$764$		−	5.20943e11i		−	1.52903i
$765$		−	8.92086e11i		−	2.60472i
$766$	8.00127e11			2.32404
$767$	−7.96706e10			−0.230206
$768$			3.46001e11i			0.994564i
$769$	−8.40202e10			−0.240258			−0.120129	−	0.992758i	$-0.538331\pi$
$769$	−8.40202e10			−0.240258			−0.120129	+	0.992758i	$0.538331\pi$
$770$		−	1.47751e12i		−	4.20309i
$771$	−5.12208e11			−1.44953
$772$	−6.31041e11			−1.77660
$773$		−	3.81824e11i		−	1.06941i	−0.845038	−	0.534706i	$-0.820422\pi$
$773$		−	3.81824e11i		−	1.06941i	0.845038	−	0.534706i	$-0.179578\pi$
$774$	5.80265e11	+	4.99856e11i	1.61682	+	1.39278i
$775$	1.91843e10			0.0531787
$776$			1.34830e10i			0.0371825i
$777$			5.08155e11i			1.39416i
$778$	−6.40149e11			−1.74728
$779$			7.02252e11i			1.90697i
$780$	−8.44057e11			−2.28031
$781$			2.62645e11i			0.705935i
$782$			6.14096e11i			1.64214i
$783$	9.78374e10			0.260290
$784$	1.63055e11			0.431589
$785$	−6.96218e10			−0.183344
$786$		−	1.45060e11i		−	0.380065i
$787$	−4.56793e10			−0.119075			−0.0595376	−	0.998226i	$-0.518963\pi$
$787$	−4.56793e10			−0.119075			−0.0595376	+	0.998226i	$0.518963\pi$
$788$	−3.53495e11			−0.916808
$789$	−1.07554e12			−2.77535
$790$	−6.79143e11			−1.74362
$791$	1.68277e10			0.0429851
$792$		−	5.78013e11i		−	1.46905i
$793$			2.89299e11i			0.731566i
$794$		−	7.55699e11i		−	1.90137i
$795$	1.06833e10			0.0267445
$796$			6.44907e11i			1.60637i
$797$	5.18174e11			1.28423			0.642114	−	0.766609i	$-0.278057\pi$
$797$	5.18174e11			1.28423			0.642114	+	0.766609i	$0.278057\pi$
$798$	−2.03751e12			−5.02444
$799$	−3.63507e11			−0.891920
$800$		−	1.38776e11i		−	0.338810i
$801$			3.54415e11i			0.860958i
$802$		−	3.09249e11i		−	0.747499i
$803$		−	3.11773e11i		−	0.749853i
$804$		−	1.75498e12i		−	4.19999i
$805$	5.12206e11			1.21972
$806$		−	1.04355e11i		−	0.247272i
$807$			7.18998e11i			1.69525i
$808$		−	2.18890e11i		−	0.513547i
$809$	−6.41088e11			−1.49666			−0.748331	−	0.663325i	$-0.769145\pi$
$809$	−6.41088e11			−1.49666			−0.748331	+	0.663325i	$0.769145\pi$
$810$	4.18926e11			0.973188
$811$			7.10605e11i			1.64265i	0.570460	+	0.821325i	$0.306765\pi$
$811$			7.10605e11i			1.64265i	−0.570460	+	0.821325i	$0.693235\pi$
$812$	−5.79758e11			−1.33359
$813$			9.02884e10i			0.206666i
$814$	4.72548e11			1.07634
$815$	2.19327e11			0.497121
$816$		−	2.34788e11i		−	0.529560i
$817$	−3.94452e11	−	3.39791e11i	−0.885331	−	0.762648i
$818$	−7.44742e10			−0.166338
$819$			9.18900e11i			2.04236i
$820$		−	1.27836e12i		−	2.82748i
$821$	1.56152e10			0.0343696			0.0171848	−	0.999852i	$-0.494530\pi$
$821$	1.56152e10			0.0343696			0.0171848	+	0.999852i	$0.494530\pi$
$822$			8.86320e11i			1.94135i
$823$	1.98386e11			0.432425			0.216213	−	0.976346i	$-0.430630\pi$
$823$	1.98386e11			0.432425			0.216213	+	0.976346i	$0.430630\pi$
$824$		−	1.94218e11i		−	0.421290i
$825$			2.74022e11i			0.591520i
$826$	3.50096e11			0.752086
$827$	−1.86067e11			−0.397784			−0.198892	−	0.980021i	$-0.563734\pi$
$827$	−1.86067e11			−0.397784			−0.198892	+	0.980021i	$0.563734\pi$
$828$	5.83320e11			1.24104
$829$		−	5.39340e11i		−	1.14194i	−0.820970	−	0.570972i	$-0.806566\pi$
$829$		−	5.39340e11i		−	1.14194i	0.820970	−	0.570972i	$-0.193434\pi$
$830$	−1.20629e12			−2.54178
$831$	5.79131e11			1.21443
$832$	−6.71289e11			−1.40093
$833$	1.74550e12			3.62527
$834$	1.90942e12			3.94672
$835$			4.35432e11i			0.895725i
$836$			1.14383e12i			2.34172i
$837$		−	4.67169e10i		−	0.0951858i
$838$	−2.29026e11			−0.464417
$839$		−	2.70407e11i		−	0.545721i	−0.962054	−	0.272861i	$-0.912030\pi$
$839$		−	2.70407e11i		−	0.545721i	0.962054	−	0.272861i	$-0.0879698\pi$
$840$	1.27411e12			2.55911
$841$	3.77618e11			0.754864
$842$	−9.99310e11			−1.98816
$843$		−	5.08289e11i		−	1.00647i
$844$			1.13984e12i			2.24633i
$845$			1.51247e11i			0.296660i
$846$			5.71968e11i			1.11658i
$847$			6.65092e11i			1.29225i
$848$	1.61189e9			0.00311710
$849$			4.75535e10i			0.0915276i
$850$		−	4.15151e11i		−	0.795300i
$851$			1.63817e11i			0.312349i
$852$	−6.59324e11			−1.25124
$853$	−2.18981e11			−0.413629			−0.206814	−	0.978380i	$-0.566310\pi$
$853$	−2.18981e11			−0.413629			−0.206814	+	0.978380i	$0.566310\pi$
$854$		−	1.27126e12i		−	2.39003i
$855$	9.54184e11			1.78553
$856$			6.05859e11i			1.12843i
$857$	−3.75880e11			−0.696829			−0.348414	−	0.937341i	$-0.613280\pi$
$857$	−3.75880e11			−0.696829			−0.348414	+	0.937341i	$0.613280\pi$
$858$	1.49058e12			2.75046
$859$		−	3.72052e11i		−	0.683331i	−0.939822	−	0.341665i	$-0.889009\pi$
$859$		−	3.72052e11i		−	0.683331i	0.939822	−	0.341665i	$-0.110991\pi$
$860$	7.18052e11	+	6.18549e11i	1.31269	+	1.13079i
$861$	−2.42767e12			−4.41750
$862$		−	1.13555e12i		−	2.05674i
$863$		−	4.71209e11i		−	0.849514i	−0.905307	−	0.424757i	$-0.860360\pi$
$863$		−	4.71209e11i		−	0.849514i	0.905307	−	0.424757i	$-0.139640\pi$
$864$	−3.37944e11			−0.606443
$865$			4.05005e10i			0.0723429i
$866$	−9.95584e8			−0.00177013
$867$		−	1.64843e12i		−	2.91738i
$868$			2.76832e11i			0.487682i
$869$	7.24030e11			1.26963
$870$	7.84523e11			1.36939
$871$	8.91243e11			1.54854
$872$			4.96483e11i			0.858694i
$873$	−3.49067e10			−0.0600968
$874$	−6.56843e11			−1.12568
$875$	8.32680e11			1.42051
$876$	7.82650e11			1.32908
$877$	−2.44914e11			−0.414014			−0.207007	−	0.978339i	$-0.566372\pi$
$877$	−2.44914e11			−0.414014			−0.207007	+	0.978339i	$0.566372\pi$
$878$		−	8.99828e11i		−	1.51419i
$879$			9.82423e11i			1.64567i
$880$			1.82110e11i			0.303671i
$881$	−8.75648e10			−0.145354			−0.0726768	−	0.997356i	$-0.523154\pi$
$881$	−8.75648e10			−0.145354			−0.0726768	+	0.997356i	$0.523154\pi$
$882$		−	2.74649e12i		−	4.53842i
$883$	−9.16929e11			−1.50832			−0.754159	−	0.656692i	$-0.771955\pi$
$883$	−9.16929e11			−1.50832			−0.754159	+	0.656692i	$0.771955\pi$
$884$	−1.36329e12			−2.23244
$885$	−2.85995e11			−0.466214
$886$			9.98077e11i			1.61968i
$887$		−	7.46646e10i		−	0.120620i	−0.998180	−	0.0603102i	$-0.980791\pi$
$887$		−	7.46646e10i		−	0.120620i	0.998180	−	0.0603102i	$-0.0192090\pi$
$888$			4.07492e11i			0.655341i
$889$		−	1.15540e12i		−	1.84981i
$890$			7.26489e11i			1.15790i
$891$	−4.46614e11			−0.708633
$892$		−	8.85615e11i		−	1.39890i
$893$		−	3.88811e11i		−	0.611410i
$894$			2.05407e12i			3.21562i
$895$	−2.48245e11			−0.386890
$896$	1.63518e12			2.53708
$897$			5.16736e11i			0.798176i
$898$	7.97089e10			0.122575
$899$			5.85545e10i			0.0896441i
$900$	−3.94346e11			−0.601045
$901$	1.72552e10			0.0261831
$902$			2.25755e12i			3.41045i
$903$	1.17465e12	−	1.36361e12i	1.76668	−	2.05087i
$904$	1.34942e10			0.0202056
$905$		−	5.15306e11i		−	0.768195i
$906$			4.24103e11i			0.629446i
$907$	1.94235e11			0.287010			0.143505	−	0.989650i	$-0.454163\pi$
$907$	1.94235e11			0.287010			0.143505	+	0.989650i	$0.454163\pi$
$908$			2.20711e11i			0.324698i
$909$	5.66694e11			0.830028
$910$			1.88358e12i			2.74675i
$911$			3.46102e11i			0.502493i	0.967923	+	0.251247i	$0.0808405\pi$
$911$			3.46102e11i			0.502493i	−0.967923	+	0.251247i	$0.919160\pi$
$912$	2.51131e11			0.363013
$913$	1.28601e12			1.85081
$914$	−3.68853e11			−0.528528
$915$			1.03850e12i			1.48157i
$916$	1.22292e12			1.73707
$917$	−1.95422e11			−0.276373
$918$	−1.01096e12			−1.42353
$919$	−1.24168e12			−1.74080			−0.870400	−	0.492346i	$-0.836140\pi$
$919$	−1.24168e12			−1.74080			−0.870400	+	0.492346i	$0.836140\pi$
$920$	4.10741e11			0.573346
$921$		−	1.45476e12i		−	2.02187i
$922$		−	1.75933e12i		−	2.43457i
$923$		−	3.34829e11i		−	0.461334i
$924$	−3.95418e12			−5.42461
$925$		−	1.10746e11i		−	0.151273i
$926$	8.39862e11			1.14226
$927$	5.02821e11			0.680917
$928$	4.23576e11			0.571136
$929$			1.32743e12i			1.78216i	0.453844	+	0.891081i	$0.350052\pi$
$929$			1.32743e12i			1.78216i	−0.453844	+	0.891081i	$0.649948\pi$
$930$		−	3.74606e11i		−	0.500776i
$931$			1.86701e12i			2.48512i
$932$		−	8.35873e11i		−	1.10784i
$933$		−	2.50943e11i		−	0.331168i
$934$	7.55526e11			0.992801
$935$			1.94948e12i			2.55078i
$936$			7.36870e11i			0.960036i
$937$			8.20440e11i			1.06436i	0.846631	+	0.532180i	$0.178627\pi$
$937$			8.20440e11i			1.06436i	−0.846631	+	0.532180i	$0.821373\pi$
$938$	−3.91638e12			−5.05911
$939$	1.80520e12			2.32201
$940$			7.07784e11i			0.906545i
$941$	9.38938e11			1.19751			0.598754	−	0.800933i	$-0.295663\pi$
$941$	9.38938e11			1.19751			0.598754	+	0.800933i	$0.295663\pi$
$942$			3.08644e11i			0.391972i
$943$	−7.82620e11			−0.989702
$944$	−4.31508e10			−0.0543377
$945$			8.43227e11i			1.05735i
$946$	−1.26806e12	−	1.09234e12i	−1.58334	−	1.36393i
$947$	3.94292e10			0.0490251			0.0245125	−	0.999700i	$-0.492197\pi$
$947$	3.94292e10			0.0490251			0.0245125	+	0.999700i	$0.492197\pi$
$948$			1.81755e12i			2.25036i
$949$			3.97458e11i			0.490035i
$950$	4.44050e11			0.545177
$951$		−	2.09691e12i		−	2.56365i
$952$	2.05789e12			2.50538
$953$			4.94300e11i			0.599265i	0.954055	+	0.299633i	$0.0968641\pi$
$953$			4.94300e11i			0.599265i	−0.954055	+	0.299633i	$0.903136\pi$
$954$		−	2.71505e10i		−	0.0327782i
$955$	9.49674e11			1.14172
$956$	−1.69496e12			−2.02922
$957$	−8.36375e11			−0.997133
$958$			1.91326e12i			2.27149i
$959$	1.19403e12			1.41170
$960$	−2.40974e12			−2.83717
$961$	−8.24932e11			−0.967218
$962$	−6.02419e11			−0.703394
$963$	−1.56854e12			−1.82385
$964$			3.38570e11i			0.392048i
$965$		−	1.15038e12i		−	1.32658i
$966$		−	2.27069e12i		−	2.60765i
$967$	−1.12086e12			−1.28188			−0.640938	−	0.767593i	$-0.721455\pi$
$967$	−1.12086e12			−1.28188			−0.640938	+	0.767593i	$0.721455\pi$
$968$			5.33341e11i			0.607440i
$969$	2.68836e12			3.04924
$970$	−7.15526e10			−0.0808236
$971$	7.14834e11			0.804134			0.402067	−	0.915610i	$-0.368292\pi$
$971$	7.14834e11			0.804134			0.402067	+	0.915610i	$0.368292\pi$
$972$		−	1.83596e12i		−	2.05683i
$973$		−	2.57233e12i		−	2.86995i
$974$		−	2.10658e12i		−	2.34068i
$975$		−	3.49332e11i		−	0.386563i
$976$			1.56689e11i			0.172678i
$977$	1.06800e12			1.17218			0.586088	−	0.810247i	$-0.300667\pi$
$977$	1.06800e12			1.17218			0.586088	+	0.810247i	$0.300667\pi$
$978$		−	9.72312e11i		−	1.06280i
$979$		−	7.74506e11i		−	0.843129i
$980$		−	3.39866e12i		−	3.68471i
$981$	−1.28537e12			−1.38788
$982$	−8.44143e11			−0.907758
$983$			9.30409e11i			0.996460i	0.867045	+	0.498230i	$0.166017\pi$
$983$			9.30409e11i			0.996460i	−0.867045	+	0.498230i	$0.833983\pi$
$984$	−1.94676e12			−2.07650
$985$		−	6.44418e11i		−	0.684577i
$986$	1.26713e12			1.34065
$987$	1.34411e12			1.41634
$988$		−	1.45819e12i		−	1.53033i
$989$	3.78678e11	−	4.39594e11i	0.395809	−	0.459480i
$990$	3.06745e12			3.19328
$991$			7.43172e11i			0.770539i	0.922804	+	0.385269i	$0.125891\pi$
$991$			7.43172e11i			0.770539i	−0.922804	+	0.385269i	$0.874109\pi$
$992$		−	2.02256e11i		−	0.208859i
$993$	−2.80870e12			−2.88874
$994$			1.47134e12i			1.50718i
$995$	−1.17566e12			−1.19947
$996$			3.22831e12i			3.28048i
$997$		−	3.65619e11i		−	0.370039i	−0.982735	−	0.185020i	$-0.940765\pi$
$997$		−	3.65619e11i		−	0.370039i	0.982735	−	0.185020i	$-0.0592349\pi$
$998$	3.05064e12			3.07517
$999$	−2.69686e11			−0.270768

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.9.b.b.42.3	✓	28
43.42	odd	2	inner	43.9.b.b.42.26	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.9.b.b.42.3	✓	28	1.1	even	1	trivial
43.9.b.b.42.26	yes	28	43.42	odd	2	inner

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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	43.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-25.4156i q^{2} -123.997i q^{3} -389.955 q^{4} -710.884i q^{5} -3151.46 q^{6} +4245.58i q^{7} +3404.55i q^{8} -8814.20 q^{9} +O(q^{10})\)	\(q-25.4156i q^{2} -123.997i q^{3} -389.955 q^{4} -710.884i q^{5} -3151.46 q^{6} +4245.58i q^{7} +3404.55i q^{8} -8814.20 q^{9} -18067.6 q^{10} +19261.7 q^{11} +48353.1i q^{12} -24555.5 q^{13} +107904. q^{14} -88147.3 q^{15} -13299.6 q^{16} -142372. q^{17} +224018. i q^{18} -152283. i q^{19} +277213. i q^{20} +526438. q^{21} -489549. i q^{22} +169711. q^{23} +422153. q^{24} -114731. q^{25} +624094. i q^{26} +279389. i q^{27} -1.65558e6i q^{28} -350183. i q^{29} +2.24032e6i q^{30} -167211. q^{31} +1.20958e6i q^{32} -2.38839e6i q^{33} +3.61848e6i q^{34} +3.01811e6 q^{35} +3.43714e6 q^{36} +965271. i q^{37} -3.87037e6 q^{38} +3.04480e6i q^{39} +2.42024e6 q^{40} -4.61149e6 q^{41} -1.33798e7i q^{42} +(2.23132e6 - 2.59026e6i) q^{43} -7.51120e6 q^{44} +6.26587e6i q^{45} -4.31331e6i q^{46} +2.55322e6 q^{47} +1.64911e6i q^{48} -1.22601e7 q^{49} +2.91596e6i q^{50} +1.76537e7i q^{51} +9.57553e6 q^{52} -121198. q^{53} +7.10085e6 q^{54} -1.36929e7i q^{55} -1.44543e7 q^{56} -1.88826e7 q^{57} -8.90013e6 q^{58} +3.24451e6 q^{59} +3.43735e7 q^{60} -1.17814e7i q^{61} +4.24978e6i q^{62} -3.74214e7i q^{63} +2.73376e7 q^{64} +1.74561e7i q^{65} -6.07025e7 q^{66} -3.62950e7 q^{67} +5.55188e7 q^{68} -2.10436e7i q^{69} -7.67073e7i q^{70} +1.36356e7i q^{71} -3.00084e7i q^{72} -1.61861e7i q^{73} +2.45330e7 q^{74} +1.42262e7i q^{75} +5.93834e7i q^{76} +8.17772e7i q^{77} +7.73856e7 q^{78} +3.75891e7 q^{79} +9.45449e6i q^{80} -2.31866e7 q^{81} +1.17204e8i q^{82} +6.67652e7 q^{83} -2.05287e8 q^{84} +1.01210e8i q^{85} +(-6.58330e7 - 5.67103e7i) q^{86} -4.34216e7 q^{87} +6.55775e7i q^{88} -4.02096e7i q^{89} +1.59251e8 q^{90} -1.04252e8i q^{91} -6.61796e7 q^{92} +2.07336e7i q^{93} -6.48916e7i q^{94} -1.08255e8 q^{95} +1.49984e8 q^{96} +3.96028e6 q^{97} +3.11599e8i q^{98} -1.69777e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4284 q^{4} - 1794 q^{6} - 80754 q^{9}+O(q^{10}) \) 28 * q - 4284 * q^4 - 1794 * q^6 - 80754 * q^9	\( 28 q - 4284 q^{4} - 1794 q^{6} - 80754 q^{9} + 24982 q^{10} + 4538 q^{11} + 22086 q^{13} + 24732 q^{14} + 15388 q^{15} + 525812 q^{16} - 135136 q^{17} - 261352 q^{21} - 184432 q^{23} + 1770326 q^{24} - 2640434 q^{25} - 110272 q^{31} + 10947816 q^{35} + 11602066 q^{36} - 7189158 q^{38} - 21389338 q^{40} + 1301336 q^{41} + 2473420 q^{43} - 8818480 q^{44} + 1983566 q^{47} - 15560936 q^{49} + 12927876 q^{52} + 23942594 q^{53} - 13757972 q^{54} + 34967256 q^{56} + 35225148 q^{57} + 22565734 q^{58} - 5554336 q^{59} - 44902072 q^{60} - 170444572 q^{64} - 48457584 q^{66} - 130953802 q^{67} + 150021122 q^{68} + 205870278 q^{74} + 267860612 q^{78} + 7380250 q^{79} - 57601004 q^{81} - 42603970 q^{83} + 251931292 q^{84} - 45482652 q^{86} - 106687410 q^{87} - 255044692 q^{90} - 409532014 q^{92} + 123322986 q^{95} - 692987086 q^{96} - 318744840 q^{97} - 609707206 q^{99}+O(q^{100}) \) 28 * q - 4284 * q^4 - 1794 * q^6 - 80754 * q^9 + 24982 * q^10 + 4538 * q^11 + 22086 * q^13 + 24732 * q^14 + 15388 * q^15 + 525812 * q^16 - 135136 * q^17 - 261352 * q^21 - 184432 * q^23 + 1770326 * q^24 - 2640434 * q^25 - 110272 * q^31 + 10947816 * q^35 + 11602066 * q^36 - 7189158 * q^38 - 21389338 * q^40 + 1301336 * q^41 + 2473420 * q^43 - 8818480 * q^44 + 1983566 * q^47 - 15560936 * q^49 + 12927876 * q^52 + 23942594 * q^53 - 13757972 * q^54 + 34967256 * q^56 + 35225148 * q^57 + 22565734 * q^58 - 5554336 * q^59 - 44902072 * q^60 - 170444572 * q^64 - 48457584 * q^66 - 130953802 * q^67 + 150021122 * q^68 + 205870278 * q^74 + 267860612 * q^78 + 7380250 * q^79 - 57601004 * q^81 - 42603970 * q^83 + 251931292 * q^84 - 45482652 * q^86 - 106687410 * q^87 - 255044692 * q^90 - 409532014 * q^92 + 123322986 * q^95 - 692987086 * q^96 - 318744840 * q^97 - 609707206 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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