LMFDB - Embedded newform 22.15.b.a.21.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,15,Mod(21,22)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(22, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 15, names="a")

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

chi := DirichletCharacter("22.21");

S:= CuspForms(chi, 15);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 15 $
Character orbit:	$[\chi]$	$=$	22.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:	$27.3523729934$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} - 38299509 x^{12} + 1255603312 x^{11} + 548839279225666 x^{10} + \cdots + 61\!\cdots\!00 $ x^14 - 2x^13 - 38299509x^12 + 1255603312x^11 + 548839279225666x^10 - 62614853719962708x^9 - 3647746096331338780406x^8 + 909709401522475794317032x^7 + 11341528896592004854718535645x^6 - 4608641836922062401823748151666x^5 - 14199433672677462467950659880576257x^4 + 7648786246750765008517429480227297240x^3 + 5468207905418692926727112276614665574080x^2 - 3973529610997293170696151713639263984312200*x + 613220922939245616829253347741252697812260300
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{56}\cdot 3^{6}\cdot 11^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			21.1
Root			$3563.38 - 1.41421i$ of defining polynomial
Character	$\chi$	$=$	22.21
Dual form			22.15.b.a.21.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-90.5097i q^{2} -3249.38 q^{3} -8192.00 q^{4} -6683.13 q^{5} +294100. i q^{6} +286020. i q^{7} +741455. i q^{8} +5.77548e6 q^{9} +O(q^{10})$	\(q-90.5097i q^{2} -3249.38 q^{3} -8192.00 q^{4} -6683.13 q^{5} +294100. i q^{6} +286020. i q^{7} +741455. i q^{8} +5.77548e6 q^{9} +604888. i q^{10} +(1.47323e7 + 1.27557e7i) q^{11} +2.66189e7 q^{12} +5.04236e7i q^{13} +2.58875e7 q^{14} +2.17160e7 q^{15} +6.71089e7 q^{16} -1.90608e8i q^{17} -5.22737e8i q^{18} -4.06180e8i q^{19} +5.47482e7 q^{20} -9.29385e8i q^{21} +(1.15451e9 - 1.33342e9i) q^{22} -2.91861e9 q^{23} -2.40927e9i q^{24} -6.05885e9 q^{25} +4.56382e9 q^{26} -3.22504e9 q^{27} -2.34307e9i q^{28} +1.38634e10i q^{29} -1.96551e9i q^{30} +4.01389e7 q^{31} -6.07400e9i q^{32} +(-4.78709e10 - 4.14481e10i) q^{33} -1.72519e10 q^{34} -1.91151e9i q^{35} -4.73127e10 q^{36} -7.99941e10 q^{37} -3.67632e10 q^{38} -1.63845e11i q^{39} -4.95524e9i q^{40} -2.73523e11i q^{41} -8.41183e10 q^{42} -3.24071e11i q^{43} +(-1.20687e11 - 1.04495e11i) q^{44} -3.85983e10 q^{45} +2.64163e11i q^{46} +3.95866e11 q^{47} -2.18062e11 q^{48} +5.96416e11 q^{49} +5.48385e11i q^{50} +6.19358e11i q^{51} -4.13070e11i q^{52} +2.76319e10 q^{53} +2.91897e11i q^{54} +(-9.84582e10 - 8.52480e10i) q^{55} -2.12071e11 q^{56} +1.31983e12i q^{57} +1.25477e12 q^{58} -8.11184e11 q^{59} -1.77898e11 q^{60} +1.19568e11i q^{61} -3.63296e9i q^{62} +1.65190e12i q^{63} -5.49756e11 q^{64} -3.36987e11i q^{65} +(-3.75145e12 + 4.33278e12i) q^{66} +9.97912e11 q^{67} +1.56146e12i q^{68} +9.48367e12 q^{69} -1.73010e11 q^{70} +1.53918e13 q^{71} +4.28226e12i q^{72} -1.29975e12i q^{73} +7.24024e12i q^{74} +1.96875e13 q^{75} +3.32743e12i q^{76} +(-3.64838e12 + 4.21374e12i) q^{77} -1.48296e13 q^{78} -2.71264e13i q^{79} -4.48497e11 q^{80} -1.71446e13 q^{81} -2.47565e13 q^{82} -4.12561e13i q^{83} +7.61352e12i q^{84} +1.27386e12i q^{85} -2.93315e13 q^{86} -4.50475e13i q^{87} +(-9.45778e12 + 1.09234e13i) q^{88} -4.41203e13 q^{89} +3.49352e12i q^{90} -1.44221e13 q^{91} +2.39093e13 q^{92} -1.30426e11 q^{93} -3.58297e13i q^{94} +2.71455e12i q^{95} +1.97367e13i q^{96} -5.84147e13 q^{97} -5.39814e13i q^{98} +(8.50864e13 + 7.36702e13i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 4394 q^{3} - 114688 q^{4} + 69758 q^{5} + 11016572 q^{9}+O(q^{10}) $ 14 * q + 4394 * q^3 - 114688 * q^4 + 69758 * q^5 + 11016572 * q^9	\( 14 q + 4394 q^{3} - 114688 q^{4} + 69758 q^{5} + 11016572 q^{9} + 20143042 q^{11} - 35995648 q^{12} + 62814720 q^{14} - 1359602 q^{15} + 939524096 q^{16} - 571457536 q^{20} - 2107666944 q^{22} - 7305755542 q^{23} + 19291879452 q^{25} - 6388480512 q^{26} + 34093422830 q^{27} - 33569873942 q^{31} + 2885838062 q^{33} + 167764701696 q^{34} - 90247757824 q^{36} + 73167823966 q^{37} + 71236111872 q^{38} - 222695314944 q^{42} - 165011800064 q^{44} + 2000205168616 q^{45} - 1612717386124 q^{47} + 294876348416 q^{48} + 3424602524990 q^{49} - 3530064068164 q^{53} - 3715439610854 q^{55} - 514578186240 q^{56} - 1374208002048 q^{58} - 818496564070 q^{59} + 11137859584 q^{60} - 7696581394432 q^{64} - 5938395621888 q^{66} + 16485465276922 q^{67} - 11394452631206 q^{69} - 392146020864 q^{70} - 19380879179878 q^{71} + 23016770893992 q^{75} + 60534793808304 q^{77} + 17335823992320 q^{78} + 4681380134912 q^{80} - 10394309810662 q^{81} - 79417078012416 q^{82} + 6375532305408 q^{86} + 17266007605248 q^{88} - 117770741987650 q^{89} + 150621364097712 q^{91} + 59848749400064 q^{92} + 27345122803162 q^{93} + 123398138843566 q^{97} + 118861332531788 q^{99}+O(q^{100}) \) 14 * q + 4394 * q^3 - 114688 * q^4 + 69758 * q^5 + 11016572 * q^9 + 20143042 * q^11 - 35995648 * q^12 + 62814720 * q^14 - 1359602 * q^15 + 939524096 * q^16 - 571457536 * q^20 - 2107666944 * q^22 - 7305755542 * q^23 + 19291879452 * q^25 - 6388480512 * q^26 + 34093422830 * q^27 - 33569873942 * q^31 + 2885838062 * q^33 + 167764701696 * q^34 - 90247757824 * q^36 + 73167823966 * q^37 + 71236111872 * q^38 - 222695314944 * q^42 - 165011800064 * q^44 + 2000205168616 * q^45 - 1612717386124 * q^47 + 294876348416 * q^48 + 3424602524990 * q^49 - 3530064068164 * q^53 - 3715439610854 * q^55 - 514578186240 * q^56 - 1374208002048 * q^58 - 818496564070 * q^59 + 11137859584 * q^60 - 7696581394432 * q^64 - 5938395621888 * q^66 + 16485465276922 * q^67 - 11394452631206 * q^69 - 392146020864 * q^70 - 19380879179878 * q^71 + 23016770893992 * q^75 + 60534793808304 * q^77 + 17335823992320 * q^78 + 4681380134912 * q^80 - 10394309810662 * q^81 - 79417078012416 * q^82 + 6375532305408 * q^86 + 17266007605248 * q^88 - 117770741987650 * q^89 + 150621364097712 * q^91 + 59848749400064 * q^92 + 27345122803162 * q^93 + 123398138843566 * q^97 + 118861332531788 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/22\mathbb{Z}\right)^\times$.

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

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 $

$2$		−	90.5097i		−	0.707107i
$2$		−	90.5097i		−	0.707107i
$3$	−3249.38			−1.48577			−0.742884	−	0.669420i	$-0.766543\pi$
$3$	−3249.38			−1.48577			−0.742884	+	0.669420i	$0.766543\pi$
$4$	−8192.00			−0.500000
$5$	−6683.13			−0.0855441			−0.0427720	−	0.999085i	$-0.513619\pi$
$5$	−6683.13			−0.0855441			−0.0427720	+	0.999085i	$0.513619\pi$
$6$			294100.i			1.05060i
$7$			286020.i			0.347304i	0.984807	+	0.173652i	$0.0555567\pi$
$7$			286020.i			0.347304i	−0.984807	+	0.173652i	$0.944443\pi$
$8$			741455.i			0.353553i
$9$	5.77548e6			1.20751
$10$			604888.i			0.0604888i
$11$	1.47323e7	+	1.27557e7i	0.756002	+	0.654569i
$11$	1.47323e7	+	1.27557e7i	0.756002	+	0.654569i
$12$	2.66189e7			0.742884
$13$			5.04236e7i			0.803582i	0.915731	+	0.401791i	$0.131612\pi$
$13$			5.04236e7i			0.803582i	−0.915731	+	0.401791i	$0.868388\pi$
$14$	2.58875e7			0.245581
$15$	2.17160e7			0.127099
$16$	6.71089e7			0.250000
$17$		−	1.90608e8i		−	0.464514i	−0.972654	−	0.232257i	$-0.925389\pi$
$17$		−	1.90608e8i		−	0.464514i	0.972654	−	0.232257i	$-0.0746111\pi$
$18$		−	5.22737e8i		−	0.853838i
$19$		−	4.06180e8i		−	0.454405i	−0.973848	−	0.227203i	$-0.927042\pi$
$19$		−	4.06180e8i		−	0.454405i	0.973848	−	0.227203i	$-0.0729580\pi$
$20$	5.47482e7			0.0427720
$21$		−	9.29385e8i		−	0.516013i
$22$	1.15451e9	−	1.33342e9i	0.462850	−	0.534574i
$23$	−2.91861e9			−0.857199			−0.428599	−	0.903495i	$-0.640993\pi$
$23$	−2.91861e9			−0.857199			−0.428599	+	0.903495i	$0.640993\pi$
$24$		−	2.40927e9i		−	0.525299i
$25$	−6.05885e9			−0.992682
$26$	4.56382e9			0.568218
$27$	−3.22504e9			−0.308310
$28$		−	2.34307e9i		−	0.173652i
$29$			1.38634e10i			0.803683i	0.915709	+	0.401841i	$0.131630\pi$
$29$			1.38634e10i			0.803683i	−0.915709	+	0.401841i	$0.868370\pi$
$30$		−	1.96551e9i		−	0.0898724i
$31$	4.01389e7			0.00145893			0.000729463	−	1.00000i	$-0.499768\pi$
$31$	4.01389e7			0.00145893			0.000729463		1.00000i	$0.499768\pi$
$32$		−	6.07400e9i		−	0.176777i
$33$	−4.78709e10	−	4.14481e10i	−1.12324	−	0.972538i
$34$	−1.72519e10			−0.328461
$35$		−	1.91151e9i		−	0.0297098i
$36$	−4.73127e10			−0.603755
$37$	−7.99941e10			−0.842647			−0.421324	−	0.906910i	$-0.638434\pi$
$37$	−7.99941e10			−0.842647			−0.421324	+	0.906910i	$0.638434\pi$
$38$	−3.67632e10			−0.321313
$39$		−	1.63845e11i		−	1.19394i
$40$		−	4.95524e9i		−	0.0302444i
$41$		−	2.73523e11i		−	1.40445i	−0.711955	−	0.702226i	$-0.752190\pi$
$41$		−	2.73523e11i		−	1.40445i	0.711955	−	0.702226i	$-0.247810\pi$
$42$	−8.41183e10			−0.364876
$43$		−	3.24071e11i		−	1.19223i	−0.802899	−	0.596116i	$-0.796710\pi$
$43$		−	3.24071e11i		−	1.19223i	0.802899	−	0.596116i	$-0.203290\pi$
$44$	−1.20687e11	−	1.04495e11i	−0.378001	−	0.327284i
$45$	−3.85983e10			−0.103295
$46$			2.64163e11i			0.606131i
$47$	3.95866e11			0.781382			0.390691	−	0.920522i	$-0.372236\pi$
$47$	3.95866e11			0.781382			0.390691	+	0.920522i	$0.372236\pi$
$48$	−2.18062e11			−0.371442
$49$	5.96416e11			0.879380
$50$			5.48385e11i			0.701932i
$51$			6.19358e11i			0.690161i
$52$		−	4.13070e11i		−	0.401791i
$53$	2.76319e10			0.0235223			0.0117612	−	0.999931i	$-0.496256\pi$
$53$	2.76319e10			0.0235223			0.0117612	+	0.999931i	$0.496256\pi$
$54$			2.91897e11i			0.218008i
$55$	−9.84582e10	−	8.52480e10i	−0.0646715	−	0.0559945i
$56$	−2.12071e11			−0.122790
$57$			1.31983e12i			0.675141i
$58$	1.25477e12			0.568290
$59$	−8.11184e11			−0.325953			−0.162977	−	0.986630i	$-0.552109\pi$
$59$	−8.11184e11			−0.325953			−0.162977	+	0.986630i	$0.552109\pi$
$60$	−1.77898e11			−0.0635494
$61$			1.19568e11i			0.0380458i	0.999819	+	0.0190229i	$0.00605555\pi$
$61$			1.19568e11i			0.0380458i	−0.999819	+	0.0190229i	$0.993944\pi$
$62$		−	3.63296e9i		−	0.00103162i
$63$			1.65190e12i			0.419372i
$64$	−5.49756e11			−0.125000
$65$		−	3.36987e11i		−	0.0687417i
$66$	−3.75145e12	+	4.33278e12i	−0.687688	+	0.794254i
$67$	9.97912e11			0.164653			0.0823263	−	0.996605i	$-0.473765\pi$
$67$	9.97912e11			0.164653			0.0823263	+	0.996605i	$0.473765\pi$
$68$			1.56146e12i			0.232257i
$69$	9.48367e12			1.27360
$70$	−1.73010e11			−0.0210080
$71$	1.53918e13			1.69231			0.846154	−	0.532938i	$-0.178912\pi$
$71$	1.53918e13			1.69231			0.846154	+	0.532938i	$0.178912\pi$
$72$			4.28226e12i			0.426919i
$73$		−	1.29975e12i		−	0.117653i	−0.998268	−	0.0588263i	$-0.981264\pi$
$73$		−	1.29975e12i		−	0.117653i	0.998268	−	0.0588263i	$-0.0187358\pi$
$74$			7.24024e12i			0.595841i
$75$	1.96875e13			1.47490
$76$			3.32743e12i			0.227203i
$77$	−3.64838e12	+	4.21374e12i	−0.227334	+	0.262562i
$78$	−1.48296e13			−0.844241
$79$		−	2.71264e13i		−	1.41254i	−0.707940	−	0.706272i	$-0.750376\pi$
$79$		−	2.71264e13i		−	1.41254i	0.707940	−	0.706272i	$-0.249624\pi$
$80$	−4.48497e11			−0.0213860
$81$	−1.71446e13			−0.749431
$82$	−2.47565e13			−0.993097
$83$		−	4.12561e13i		−	1.52034i	−0.649722	−	0.760172i	$-0.725115\pi$
$83$		−	4.12561e13i		−	1.52034i	0.649722	−	0.760172i	$-0.274885\pi$
$84$			7.61352e12i			0.258007i
$85$			1.27386e12i			0.0397364i
$86$	−2.93315e13			−0.843035
$87$		−	4.50475e13i		−	1.19409i
$88$	−9.45778e12	+	1.09234e13i	−0.231425	+	0.267287i
$89$	−4.41203e13			−0.997490			−0.498745	−	0.866749i	$-0.666206\pi$
$89$	−4.41203e13			−0.997490			−0.498745	+	0.866749i	$0.666206\pi$
$90$			3.49352e12i			0.0730408i
$91$	−1.44221e13			−0.279087
$92$	2.39093e13			0.428599
$93$	−1.30426e11			−0.00216763
$94$		−	3.58297e13i		−	0.552520i
$95$			2.71455e12i			0.0388717i
$96$			1.97367e13i			0.262649i
$97$	−5.84147e13			−0.722970			−0.361485	−	0.932378i	$-0.617730\pi$
$97$	−5.84147e13			−0.722970			−0.361485	+	0.932378i	$0.617730\pi$
$98$		−	5.39814e13i		−	0.621816i
$99$	8.50864e13	+	7.36702e13i	0.912880	+	0.790398i
$100$	4.96341e13			0.496341
$101$			1.72813e14i			1.61186i	0.592013	+	0.805928i	$0.298333\pi$
$101$			1.72813e14i			1.61186i	−0.592013	+	0.805928i	$0.701667\pi$
$102$	5.60578e13			0.488017
$103$	−2.59351e13			−0.210876			−0.105438	−	0.994426i	$-0.533625\pi$
$103$	−2.59351e13			−0.210876			−0.105438	+	0.994426i	$0.533625\pi$
$104$	−3.73868e13			−0.284109
$105$			6.21120e12i			0.0441419i
$106$		−	2.50096e12i		−	0.0166328i
$107$		−	1.00010e14i		−	0.622812i	−0.950277	−	0.311406i	$-0.899200\pi$
$107$		−	1.00010e14i		−	0.622812i	0.950277	−	0.311406i	$-0.100800\pi$
$108$	2.64195e13			0.154155
$109$		−	2.99273e14i		−	1.63712i	−0.574418	−	0.818562i	$-0.694772\pi$
$109$		−	2.99273e14i		−	1.63712i	0.574418	−	0.818562i	$-0.305228\pi$
$110$	−7.71577e12	+	8.91142e12i	−0.0395941	+	0.0457297i
$111$	2.59931e14			1.25198
$112$			1.91944e13i			0.0868259i
$113$	−2.06047e14			−0.875825			−0.437913	−	0.899018i	$-0.644282\pi$
$113$	−2.06047e14			−0.875825			−0.437913	+	0.899018i	$0.644282\pi$
$114$	1.19458e14			0.477397
$115$	1.95055e13			0.0733283
$116$		−	1.13569e14i		−	0.401841i
$117$			2.91220e14i			0.970332i
$118$			7.34200e13i			0.230484i
$119$	5.45177e13			0.161328
$120$			1.61014e13i			0.0449362i
$121$	5.43344e13	+	3.75843e14i	0.143079	+	0.989711i
$122$	1.08221e13			0.0269025
$123$			8.88779e14i			2.08669i
$124$	−3.28818e11			−0.000729463
$125$	8.12827e13			0.170462
$126$	1.49513e14			0.296541
$127$		−	7.89612e14i		−	1.48179i	−0.671618	−	0.740897i	$-0.734401\pi$
$127$		−	7.89612e14i		−	1.48179i	0.671618	−	0.740897i	$-0.265599\pi$
$128$			4.97582e13i			0.0883883i
$129$			1.05303e15i			1.77138i
$130$	−3.05006e13			−0.0486077
$131$		−	4.99439e14i		−	0.754369i	−0.926138	−	0.377184i	$-0.876892\pi$
$131$		−	4.99439e14i		−	0.754369i	0.926138	−	0.377184i	$-0.123108\pi$
$132$	3.92159e14	+	3.39542e14i	0.561622	+	0.486269i
$133$	1.16175e14			0.157817
$134$		−	9.03207e13i		−	0.116427i
$135$	2.15533e13			0.0263741
$136$	1.41327e14			0.164231
$137$	−8.77183e14			−0.968380			−0.484190	−	0.874963i	$-0.660886\pi$
$137$	−8.77183e14			−0.968380			−0.484190	+	0.874963i	$0.660886\pi$
$138$		−	8.58364e14i		−	0.900571i
$139$		−	6.29857e14i		−	0.628258i	−0.949380	−	0.314129i	$-0.898288\pi$
$139$		−	6.29857e14i		−	0.628258i	0.949380	−	0.314129i	$-0.101712\pi$
$140$			1.56591e13i			0.0148549i
$141$	−1.28632e15			−1.16095
$142$		−	1.39310e15i		−	1.19664i
$143$	−6.43188e14	+	7.42858e14i	−0.526000	+	0.607510i
$144$	3.87586e14			0.301877
$145$		−	9.26511e13i		−	0.0687503i
$146$	−1.17640e14			−0.0831929
$147$	−1.93798e15			−1.30656
$148$	6.55311e14			0.421324
$149$		−	3.06969e15i		−	1.88274i	−0.337376	−	0.941370i	$-0.609539\pi$
$149$		−	3.06969e15i		−	1.88274i	0.337376	−	0.941370i	$-0.390461\pi$
$150$		−	1.78191e15i		−	1.04291i
$151$			8.37280e14i			0.467770i	0.972264	+	0.233885i	$0.0751439\pi$
$151$			8.37280e14i			0.467770i	−0.972264	+	0.233885i	$0.924856\pi$
$152$	3.01164e14			0.160656
$153$		−	1.10085e15i		−	0.560905i
$154$	3.81384e14	+	3.30213e14i	0.185660	+	0.160750i
$155$	−2.68253e11			−0.000124803
$156$			1.34222e15i			0.596968i
$157$	4.43386e15			1.88575			0.942876	−	0.333145i	$-0.108110\pi$
$157$	4.43386e15			1.88575			0.942876	+	0.333145i	$0.108110\pi$
$158$	−2.45520e15			−0.998820
$159$	−8.97866e13			−0.0349488
$160$			4.05934e13i			0.0151222i
$161$		−	8.34780e14i		−	0.297708i
$162$			1.55175e15i			0.529928i
$163$	−2.71880e14			−0.0889333			−0.0444666	−	0.999011i	$-0.514159\pi$
$163$	−2.71880e14			−0.0889333			−0.0444666	+	0.999011i	$0.514159\pi$
$164$			2.24070e15i			0.702226i
$165$	3.19928e14	+	2.77003e14i	0.0960870	+	0.0831949i
$166$	−3.73408e15			−1.07505
$167$			5.72449e15i			1.58024i	0.612955	+	0.790118i	$0.289981\pi$
$167$			5.72449e15i			1.58024i	−0.612955	+	0.790118i	$0.710019\pi$
$168$	6.89097e14			0.182438
$169$	1.39484e15			0.354256
$170$	1.15297e14			0.0280979
$171$		−	2.34588e15i		−	0.548698i
$172$			2.65479e15i			0.596116i
$173$		−	1.19718e15i		−	0.258130i	−0.991636	−	0.129065i	$-0.958802\pi$
$173$		−	1.19718e15i		−	0.258130i	0.991636	−	0.129065i	$-0.0411975\pi$
$174$	−4.07723e15			−0.844347
$175$		−	1.73295e15i		−	0.344762i
$176$	9.88671e14	+	8.56020e14i	0.189001	+	0.163642i
$177$	2.63584e15			0.484291
$178$			3.99331e15i			0.705332i
$179$	6.21205e15			1.05503			0.527514	−	0.849546i	$-0.323124\pi$
$179$	6.21205e15			1.05503			0.527514	+	0.849546i	$0.323124\pi$
$180$	3.16197e14			0.0516476
$181$	2.67450e15			0.420236			0.210118	−	0.977676i	$-0.432615\pi$
$181$	2.67450e15			0.420236			0.210118	+	0.977676i	$0.432615\pi$
$182$			1.30534e15i			0.197344i
$183$		−	3.88522e14i		−	0.0565273i
$184$		−	2.16402e15i		−	0.303066i
$185$	5.34611e14			0.0720835
$186$			1.18048e13i			0.00153274i
$187$	2.43134e15	−	2.80811e15i	0.304056	−	0.351174i
$188$	−3.24294e15			−0.390691
$189$		−	9.22423e14i		−	0.107077i
$190$	2.45693e14			0.0274864
$191$	−4.39072e15			−0.473481			−0.236741	−	0.971573i	$-0.576079\pi$
$191$	−4.39072e15			−0.473481			−0.236741	+	0.971573i	$0.576079\pi$
$192$	1.78636e15			0.185721
$193$			4.08050e15i			0.409084i	0.978858	+	0.204542i	$0.0655704\pi$
$193$			4.08050e15i			0.409084i	−0.978858	+	0.204542i	$0.934430\pi$
$194$			5.28709e15i			0.511217i
$195$			1.09500e15i			0.102134i
$196$	−4.88584e15			−0.439690
$197$			1.13991e16i			0.989932i	0.868912	+	0.494966i	$0.164819\pi$
$197$			1.13991e16i			0.989932i	−0.868912	+	0.494966i	$0.835181\pi$
$198$	6.66787e15	−	7.70114e15i	0.558896	−	0.645503i
$199$	2.08977e16			1.69093			0.845467	−	0.534027i	$-0.179322\pi$
$199$	2.08977e16			1.69093			0.845467	+	0.534027i	$0.179322\pi$
$200$		−	4.49237e15i		−	0.350966i
$201$	−3.24259e15			−0.244636
$202$	1.56412e16			1.13975
$203$	−3.96521e15			−0.279122
$204$		−	5.07378e15i		−	0.345080i
$205$			1.82799e15i			0.120142i
$206$			2.34738e15i			0.149112i
$207$	−1.68564e16			−1.03508
$208$			3.38387e15i			0.200895i
$209$	5.18111e15	−	5.98398e15i	0.297439	−	0.343531i
$210$	5.62174e14			0.0312130
$211$		−	2.77771e16i		−	1.49180i	−0.666060	−	0.745898i	$-0.732021\pi$
$211$		−	2.77771e16i		−	1.49180i	0.666060	−	0.745898i	$-0.267979\pi$
$212$	−2.26361e14			−0.0117612
$213$	−5.00136e16			−2.51438
$214$	−9.05187e15			−0.440395
$215$			2.16581e15i			0.101988i
$216$		−	2.39122e15i		−	0.109004i
$217$			1.14805e13i			0.000506691i
$218$	−2.70871e16			−1.15762
$219$			4.22339e15i			0.174805i
$220$	8.06570e14	+	6.98352e14i	0.0323358	+	0.0279972i
$221$	9.61114e15			0.373275
$222$		−	2.35263e16i		−	0.885283i
$223$	6.27116e15			0.228672			0.114336	−	0.993442i	$-0.463526\pi$
$223$	6.27116e15			0.228672			0.114336	+	0.993442i	$0.463526\pi$
$224$	1.73728e15			0.0613952
$225$	−3.49928e16			−1.19867
$226$			1.86493e16i			0.619302i
$227$		−	7.84619e15i		−	0.252626i	−0.991990	−	0.126313i	$-0.959686\pi$
$227$		−	7.84619e15i		−	0.252626i	0.991990	−	0.126313i	$-0.0403143\pi$
$228$		−	1.08121e16i		−	0.337571i
$229$	−6.71270e15			−0.203259			−0.101629	−	0.994822i	$-0.532406\pi$
$229$	−6.71270e15			−0.203259			−0.101629	+	0.994822i	$0.532406\pi$
$230$		−	1.76543e15i		−	0.0518509i
$231$	1.18550e16	−	1.36920e16i	0.337766	−	0.390107i
$232$	−1.02791e16			−0.284145
$233$		−	6.42321e16i		−	1.72290i	−0.507840	−	0.861452i	$-0.669556\pi$
$233$		−	6.42321e16i		−	1.72290i	0.507840	−	0.861452i	$-0.330444\pi$
$234$	2.63582e16			0.686129
$235$	−2.64563e15			−0.0668426
$236$	6.64522e15			0.162977
$237$			8.81438e16i			2.09871i
$238$		−	4.93437e15i		−	0.114076i
$239$		−	2.70229e16i		−	0.606661i	−0.952885	−	0.303330i	$-0.901901\pi$
$239$		−	2.70229e16i		−	0.606661i	0.952885	−	0.303330i	$-0.0980986\pi$
$240$	1.45734e15			0.0317747
$241$			7.45366e16i			1.57852i	0.614058	+	0.789261i	$0.289536\pi$
$241$			7.45366e16i			1.57852i	−0.614058	+	0.789261i	$0.710464\pi$
$242$	3.40174e16	−	4.91779e15i	0.699832	−	0.101172i
$243$	7.11344e16			1.42179
$244$		−	9.79503e14i		−	0.0190229i
$245$	−3.98593e15			−0.0752258
$246$	8.04431e16			1.47551
$247$	2.04810e16			0.365152
$248$			2.97612e13i			0.000515808i
$249$			1.34057e17i			2.25888i
$250$		−	7.35687e15i		−	0.120535i
$251$	5.30928e16			0.845901			0.422951	−	0.906153i	$-0.360994\pi$
$251$	5.30928e16			0.845901			0.422951	+	0.906153i	$0.360994\pi$
$252$		−	1.35324e16i		−	0.209686i
$253$	−4.29980e16	−	3.72289e16i	−0.648044	−	0.561096i
$254$	−7.14676e16			−1.04779
$255$		−	4.13925e15i		−	0.0590392i
$256$	4.50360e15			0.0625000
$257$	−1.21724e17			−1.64378			−0.821891	−	0.569645i	$-0.807081\pi$
$257$	−1.21724e17			−1.64378			−0.821891	+	0.569645i	$0.807081\pi$
$258$	9.53092e16			1.25255
$259$		−	2.28799e16i		−	0.292654i
$260$			2.76060e15i			0.0343708i
$261$			8.00679e16i			0.970454i
$262$	−4.52041e16			−0.533419
$263$		−	8.46230e16i		−	0.972295i	−0.873877	−	0.486148i	$-0.838402\pi$
$263$		−	8.46230e16i		−	0.972295i	0.873877	−	0.486148i	$-0.161598\pi$
$264$	3.07319e16	−	3.54942e16i	0.343844	−	0.397127i
$265$	−1.84668e14			−0.00201220
$266$		−	1.05150e16i		−	0.111593i
$267$	1.43363e17			1.48204
$268$	−8.17489e15			−0.0823263
$269$	−1.14473e17			−1.12315			−0.561575	−	0.827426i	$-0.689805\pi$
$269$	−1.14473e17			−1.12315			−0.561575	+	0.827426i	$0.689805\pi$
$270$		−	1.95079e15i		−	0.0186493i
$271$			1.13213e17i			1.05466i	0.849660	+	0.527330i	$0.176807\pi$
$271$			1.13213e17i			1.05466i	−0.849660	+	0.527330i	$0.823193\pi$
$272$		−	1.27915e16i		−	0.116129i
$273$	4.68629e16			0.414659
$274$			7.93935e16i			0.684748i
$275$	−8.92611e16	−	7.72849e16i	−0.750470	−	0.649779i
$276$	−7.76902e16			−0.636800
$277$			4.83020e16i			0.386017i	0.981197	+	0.193008i	$0.0618245\pi$
$277$			4.83020e16i			0.386017i	−0.981197	+	0.193008i	$0.938176\pi$
$278$	−5.70081e16			−0.444246
$279$	2.31821e14			0.00176167
$280$	1.41730e15			0.0105040
$281$		−	1.07006e17i		−	0.773509i	−0.922183	−	0.386754i	$-0.873596\pi$
$281$		−	1.07006e17i		−	0.773509i	0.922183	−	0.386754i	$-0.126404\pi$
$282$			1.16424e17i			0.820918i
$283$		−	3.37734e16i		−	0.232311i	−0.993231	−	0.116156i	$-0.962943\pi$
$283$		−	3.37734e16i		−	0.232311i	0.993231	−	0.116156i	$-0.0370571\pi$
$284$	−1.26089e17			−0.846154
$285$		−	8.82061e15i		−	0.0577543i
$286$	6.72358e16	+	5.82147e16i	0.429574	+	0.371938i
$287$	7.82329e16			0.487771
$288$		−	3.50803e16i		−	0.213459i
$289$	1.32046e17			0.784227
$290$	−8.38582e15			−0.0486138
$291$	1.89811e17			1.07417
$292$			1.06476e16i			0.0588263i
$293$		−	1.78696e17i		−	0.963921i	−0.876193	−	0.481961i	$-0.839925\pi$
$293$		−	1.78696e17i		−	0.963921i	0.876193	−	0.481961i	$-0.160075\pi$
$294$			1.75406e17i			0.923874i
$295$	5.42125e15			0.0278834
$296$		−	5.93120e16i		−	0.297921i
$297$	−4.75124e16	−	4.11376e16i	−0.233083	−	0.201810i
$298$	−2.77836e17			−1.33130
$299$		−	1.47167e17i		−	0.688829i
$300$	−1.61280e17			−0.737448
$301$	9.26905e16			0.414066
$302$	7.57819e16			0.330763
$303$		−	5.61534e17i		−	2.39485i
$304$		−	2.72583e16i		−	0.113601i
$305$		−	7.99090e14i		−	0.00325460i
$306$	−9.96379e16			−0.396620
$307$		−	8.41123e16i		−	0.327259i	−0.986522	−	0.163629i	$-0.947680\pi$
$307$		−	8.41123e16i		−	0.327259i	0.986522	−	0.163629i	$-0.0523201\pi$
$308$	2.98875e16	−	3.45190e16i	0.113667	−	0.131281i
$309$	8.42730e16			0.313313
$310$			2.42795e13i			8.82487e-5i
$311$	−3.87491e17			−1.37702			−0.688508	−	0.725228i	$-0.741734\pi$
$311$	−3.87491e17			−1.37702			−0.688508	+	0.725228i	$0.741734\pi$
$312$	1.21484e17			0.422120
$313$	−4.15385e17			−1.41137			−0.705684	−	0.708527i	$-0.749360\pi$
$313$	−4.15385e17			−1.41137			−0.705684	+	0.708527i	$0.749360\pi$
$314$		−	4.01307e17i		−	1.33343i
$315$		−	1.10399e16i		−	0.0358748i
$316$			2.22219e17i			0.706272i
$317$	3.09963e17			0.963596			0.481798	−	0.876282i	$-0.339984\pi$
$317$	3.09963e17			0.963596			0.481798	+	0.876282i	$0.339984\pi$
$318$			8.12656e15i			0.0247125i
$319$	−1.76838e17	+	2.04241e17i	−0.526066	+	0.607586i
$320$	3.67409e15			0.0106930
$321$			3.24970e17i			0.925355i
$322$	−7.55557e16			−0.210512
$323$	−7.74212e16			−0.211078
$324$	1.40448e17			0.374715
$325$		−	3.05509e17i		−	0.797701i
$326$			2.46078e16i			0.0628853i
$327$			9.72449e17i			2.43239i
$328$	2.02805e17			0.496548
$329$			1.13225e17i			0.271377i
$330$	2.50714e16	−	2.89566e16i	0.0588277	−	0.0679437i
$331$	8.52962e17			1.95945			0.979724	−	0.200351i	$-0.0642083\pi$
$331$	8.52962e17			1.95945			0.979724	+	0.200351i	$0.0642083\pi$
$332$			3.37970e17i			0.760172i
$333$	−4.62004e17			−1.01750
$334$	5.18122e17			1.11739
$335$	−6.66918e15			−0.0140851
$336$		−	6.23700e16i		−	0.129003i
$337$			8.96320e17i			1.81574i	0.419252	+	0.907870i	$0.362292\pi$
$337$			8.96320e17i			1.81574i	−0.419252	+	0.907870i	$0.637708\pi$
$338$		−	1.26246e17i		−	0.250497i
$339$	6.69525e17			1.30127
$340$		−	1.04355e16i		−	0.0198682i
$341$	5.91340e14	+	5.11999e14i	0.00110295	+	0.000954968i
$342$	−2.12325e17			−0.387988
$343$			3.64572e17i			0.652716i
$344$	2.40284e17			0.421517
$345$	−6.33806e16			−0.108949
$346$	−1.08357e17			−0.182525
$347$		−	9.40872e17i		−	1.55319i	−0.630001	−	0.776594i	$-0.716946\pi$
$347$		−	9.40872e17i		−	1.55319i	0.630001	−	0.776594i	$-0.283054\pi$
$348$			3.69029e17i			0.597043i
$349$			5.39921e17i			0.856155i	0.903742	+	0.428077i	$0.140809\pi$
$349$			5.39921e17i			0.856155i	−0.903742	+	0.428077i	$0.859191\pi$
$350$	−1.56849e17			−0.243784
$351$		−	1.62618e17i		−	0.247753i
$352$	7.74781e16	−	8.94843e16i	0.115713	−	0.133644i
$353$	−8.37573e17			−1.22631			−0.613154	−	0.789963i	$-0.710100\pi$
$353$	−8.37573e17			−1.22631			−0.613154	+	0.789963i	$0.710100\pi$
$354$		−	2.38569e17i		−	0.342445i
$355$	−1.02865e17			−0.144767
$356$	3.61433e17			0.498745
$357$	−1.77148e17			−0.239695
$358$		−	5.62251e17i		−	0.746018i
$359$			5.44189e17i			0.708091i	0.935228	+	0.354045i	$0.115194\pi$
$359$			5.44189e17i			0.708091i	−0.935228	+	0.354045i	$0.884806\pi$
$360$		−	2.86189e16i		−	0.0365204i
$361$	6.34025e17			0.793516
$362$		−	2.42068e17i		−	0.297152i
$363$	−1.76553e17	−	1.22125e18i	−0.212583	−	1.47048i
$364$	1.18146e17			0.139543
$365$			8.68643e15i			0.0100645i
$366$	−3.51650e16			−0.0399708
$367$	1.73505e17			0.193486			0.0967428	−	0.995309i	$-0.469158\pi$
$367$	1.73505e17			0.193486			0.0967428	+	0.995309i	$0.469158\pi$
$368$	−1.95865e17			−0.214300
$369$		−	1.57973e18i		−	1.69589i
$370$		−	4.83875e16i		−	0.0509707i
$371$			7.90328e15i			0.00816939i
$372$	1.06845e15			0.00108381
$373$		−	4.60520e16i		−	0.0458444i	−0.999737	−	0.0229222i	$-0.992703\pi$
$373$		−	4.60520e16i		−	0.0458444i	0.999737	−	0.0229222i	$-0.00729700\pi$
$374$	−2.54161e17	−	2.20060e17i	−0.248317	−	0.215000i
$375$	−2.64118e17			−0.253267
$376$			2.93517e17i			0.276260i
$377$	−6.99044e17			−0.645825
$378$	−8.34882e16			−0.0757151
$379$	1.37120e18			1.22075			0.610373	−	0.792114i	$-0.291019\pi$
$379$	1.37120e18			1.22075			0.610373	+	0.792114i	$0.291019\pi$
$380$		−	2.22376e16i		−	0.0194358i
$381$			2.56575e18i			2.20160i
$382$			3.97403e17i			0.334802i
$383$	−1.27993e18			−1.05875			−0.529376	−	0.848387i	$-0.677574\pi$
$383$	−1.27993e18			−1.05875			−0.529376	+	0.848387i	$0.677574\pi$
$384$		−	1.61683e17i		−	0.131325i
$385$	2.43826e16	−	2.81610e16i	0.0194471	−	0.0224607i
$386$	3.69324e17			0.289266
$387$		−	1.87166e18i		−	1.43963i
$388$	4.78533e17			0.361485
$389$	−1.13052e18			−0.838746			−0.419373	−	0.907814i	$-0.637750\pi$
$389$	−1.13052e18			−0.838746			−0.419373	+	0.907814i	$0.637750\pi$
$390$	9.91080e16			0.0722198
$391$			5.56311e17i			0.398181i
$392$			4.42216e17i			0.310908i
$393$			1.62287e18i			1.12082i
$394$	1.03172e18			0.699987
$395$			1.81289e17i			0.120835i
$396$	−6.97027e17	−	6.03507e17i	−0.456440	−	0.395199i
$397$	−2.17037e18			−1.39637			−0.698184	−	0.715919i	$-0.746008\pi$
$397$	−2.17037e18			−1.39637			−0.698184	+	0.715919i	$0.746008\pi$
$398$		−	1.89144e18i		−	1.19567i
$399$	−3.77498e17			−0.234479
$400$	−4.06603e17			−0.248171
$401$	−1.00817e18			−0.604679			−0.302339	−	0.953200i	$-0.597768\pi$
$401$	−1.00817e18			−0.604679			−0.302339	+	0.953200i	$0.597768\pi$
$402$			2.93486e17i			0.172984i
$403$			2.02395e15i			0.00117237i
$404$		−	1.41568e18i		−	0.805928i
$405$	1.14579e17			0.0641094
$406$			3.58890e17i			0.197369i
$407$	−1.17850e18	−	1.02038e18i	−0.637043	−	0.551570i
$408$	−4.59226e17			−0.244009
$409$		−	3.23803e18i		−	1.69129i	−0.533745	−	0.845645i	$-0.679216\pi$
$409$		−	3.23803e18i		−	1.69129i	0.533745	−	0.845645i	$-0.320784\pi$
$410$	1.65451e17			0.0849536
$411$	2.85030e18			1.43879
$412$	2.12461e17			0.105438
$413$		−	2.32014e17i		−	0.113205i
$414$			1.52567e18i			0.731909i
$415$			2.75720e17i			0.130056i
$416$	3.06273e17			0.142055
$417$			2.04664e18i			0.933446i
$418$	−5.41608e17	−	4.68940e17i	−0.242913	−	0.210321i
$419$	2.70654e17			0.119376			0.0596878	−	0.998217i	$-0.480989\pi$
$419$	2.70654e17			0.119376			0.0596878	+	0.998217i	$0.480989\pi$
$420$		−	5.08822e16i		−	0.0220709i
$421$	1.30316e18			0.555935			0.277967	−	0.960591i	$-0.410339\pi$
$421$	1.30316e18			0.555935			0.277967	+	0.960591i	$0.410339\pi$
$422$	−2.51409e18			−1.05486
$423$	2.28632e18			0.943526
$424$			2.04879e16i			0.00831640i
$425$			1.15487e18i			0.461115i
$426$			4.52671e18i			1.77793i
$427$	−3.41989e16			−0.0132135
$428$			8.19282e17i			0.311406i
$429$	2.08996e18	−	2.41382e18i	0.781514	−	0.902619i
$430$	1.96026e17			0.0721166
$431$		−	3.69489e18i		−	1.33740i	−0.743533	−	0.668699i	$-0.766851\pi$
$431$		−	3.69489e18i		−	1.33740i	0.743533	−	0.668699i	$-0.233149\pi$
$432$	−2.16428e17			−0.0770776
$433$	3.60618e18			1.26367			0.631833	−	0.775104i	$-0.282303\pi$
$433$	3.60618e18			1.26367			0.631833	+	0.775104i	$0.282303\pi$
$434$	1.03910e15			0.000358284
$435$			3.01058e17i			0.102147i
$436$			2.45164e18i			0.818562i
$437$			1.18548e18i			0.389516i
$438$	3.82258e17			0.123605
$439$			2.29177e18i			0.729323i	0.931140	+	0.364661i	$0.118815\pi$
$439$			2.29177e18i			0.729323i	−0.931140	+	0.364661i	$0.881185\pi$
$440$	6.32076e16	−	7.30024e16i	0.0197970	−	0.0228648i
$441$	3.44459e18			1.06186
$442$		−	8.69901e17i		−	0.263945i
$443$	2.20357e18			0.658115			0.329057	−	0.944310i	$-0.393269\pi$
$443$	2.20357e18			0.658115			0.329057	+	0.944310i	$0.393269\pi$
$444$	−2.12935e18			−0.625989
$445$	2.94862e17			0.0853293
$446$		−	5.67601e17i		−	0.161696i
$447$			9.97457e18i			2.79732i
$448$		−	1.57241e17i		−	0.0434130i
$449$	−3.84200e17			−0.104432			−0.0522159	−	0.998636i	$-0.516628\pi$
$449$	−3.84200e17			−0.104432			−0.0522159	+	0.998636i	$0.516628\pi$
$450$			3.16718e18i			0.847590i
$451$	3.48897e18	−	4.02963e18i	0.919310	−	1.06177i
$452$	1.68794e18			0.437913
$453$		−	2.72064e18i		−	0.694998i
$454$	−7.10156e17			−0.178633
$455$	9.63850e16			0.0238742
$456$	−9.78596e17			−0.238698
$457$		−	2.48702e18i		−	0.597400i	−0.954347	−	0.298700i	$-0.903447\pi$
$457$		−	2.48702e18i		−	0.597400i	0.954347	−	0.298700i	$-0.0965531\pi$
$458$			6.07565e17i			0.143726i
$459$			6.14718e17i			0.143215i
$460$	−1.59789e17			−0.0366641
$461$		−	1.12211e18i		−	0.253588i	−0.991929	−	0.126794i	$-0.959531\pi$
$461$		−	1.12211e18i		−	0.253588i	0.991929	−	0.126794i	$-0.0404687\pi$
$462$	−1.23926e18	−	1.07299e18i	−0.275847	−	0.238837i
$463$	−2.84181e18			−0.623057			−0.311529	−	0.950237i	$-0.600841\pi$
$463$	−2.84181e18			−0.623057			−0.311529	+	0.950237i	$0.600841\pi$
$464$			9.30359e17i			0.200921i
$465$	8.71657e14			0.000185428
$466$	−5.81363e18			−1.21828
$467$	−7.37244e18			−1.52192			−0.760962	−	0.648796i	$-0.775273\pi$
$467$	−7.37244e18			−1.52192			−0.760962	+	0.648796i	$0.775273\pi$
$468$		−	2.38568e18i		−	0.485166i
$469$			2.85422e17i			0.0571845i
$470$			2.39455e17i			0.0472649i
$471$	−1.44073e19			−2.80179
$472$		−	6.01456e17i		−	0.115242i
$473$	4.13375e18	−	4.77432e18i	0.780397	−	0.901330i
$474$	7.97786e18			1.48401
$475$			2.46098e18i			0.451080i
$476$	−4.46609e17			−0.0806638
$477$	1.59588e17			0.0284034
$478$	−2.44583e18			−0.428974
$479$			9.69431e17i			0.167559i	0.996484	+	0.0837796i	$0.0266992\pi$
$479$			9.69431e17i			0.167559i	−0.996484	+	0.0837796i	$0.973301\pi$
$480$		−	1.31903e17i		−	0.0224681i
$481$		−	4.03359e18i		−	0.677136i
$482$	6.74629e18			1.11618
$483$			2.71251e18i			0.442326i
$484$	−4.45107e17	−	3.07890e18i	−0.0715397	−	0.494856i
$485$	3.90393e17			0.0618458
$486$		−	6.43835e18i		−	1.00536i
$487$	−8.53520e18			−1.31374			−0.656872	−	0.754002i	$-0.728121\pi$
$487$	−8.53520e18			−1.31374			−0.656872	+	0.754002i	$0.728121\pi$
$488$	−8.86545e16			−0.0134512
$489$	8.83441e17			0.132134
$490$			3.60765e17i			0.0531927i
$491$			1.22906e18i			0.178649i	0.996003	+	0.0893247i	$0.0284709\pi$
$491$			1.22906e18i			0.178649i	−0.996003	+	0.0893247i	$0.971529\pi$
$492$		−	7.28088e18i		−	1.04334i
$493$	2.64248e18			0.373322
$494$		−	1.85373e18i		−	0.258201i
$495$	−5.68643e17	−	4.92348e17i	−0.0780915	−	0.0676139i
$496$	2.69368e15			0.000364732
$497$			4.40234e18i			0.587745i
$498$	1.21334e19			1.59727
$499$	−2.92357e18			−0.379498			−0.189749	−	0.981833i	$-0.560767\pi$
$499$	−2.92357e18			−0.379498			−0.189749	+	0.981833i	$0.560767\pi$
$500$	−6.65868e17			−0.0852311
$501$		−	1.86010e19i		−	2.34786i
$502$		−	4.80541e18i		−	0.598143i
$503$			1.48924e19i			1.82805i	0.405659	+	0.914024i	$0.367042\pi$
$503$			1.48924e19i			1.82805i	−0.405659	+	0.914024i	$0.632958\pi$
$504$	−1.22481e18			−0.148271
$505$		−	1.15493e18i		−	0.137885i
$506$	−3.36958e18	+	3.89174e18i	−0.396754	+	0.458237i
$507$	−4.53236e18			−0.526343
$508$			6.46851e18i			0.740897i
$509$	5.81732e18			0.657201			0.328601	−	0.944469i	$-0.393423\pi$
$509$	5.81732e18			0.657201			0.328601	+	0.944469i	$0.393423\pi$
$510$	−3.74642e17			−0.0417470
$511$	3.71755e17			0.0408612
$512$		−	4.07619e17i		−	0.0441942i
$513$			1.30994e18i			0.140098i
$514$			1.10172e19i			1.16233i
$515$	1.73328e17			0.0180392
$516$		−	8.62640e18i		−	0.885690i
$517$	5.83204e18	+	5.04955e18i	0.590727	+	0.511468i
$518$	−2.07085e18			−0.206938
$519$			3.89010e18i			0.383521i
$520$	2.49861e17			0.0243039
$521$	3.80781e18			0.365436			0.182718	−	0.983165i	$-0.441510\pi$
$521$	3.80781e18			0.365436			0.182718	+	0.983165i	$0.441510\pi$
$522$	7.24692e18			0.686215
$523$		−	1.08685e19i		−	1.01544i	−0.861521	−	0.507722i	$-0.830488\pi$
$523$		−	1.08685e19i		−	1.01544i	0.861521	−	0.507722i	$-0.169512\pi$
$524$			4.09141e18i			0.377184i
$525$			5.63101e18i			0.512237i
$526$	−7.65920e18			−0.687516
$527$		−	7.65080e15i		−	0.000677692i
$528$	−3.21256e18	−	2.78153e18i	−0.280811	−	0.243134i
$529$	−3.07454e18			−0.265210
$530$			1.67142e16i			0.00142284i
$531$	−4.68497e18			−0.393591
$532$	−9.51709e17			−0.0789083
$533$	1.37920e19			1.12859
$534$		−	1.29758e19i		−	1.04796i
$535$			6.68380e17i			0.0532779i
$536$			7.39907e17i			0.0582135i
$537$	−2.01853e19			−1.56753
$538$			1.03609e19i			0.794187i
$539$	8.78661e18	+	7.60770e18i	0.664814	+	0.575615i
$540$	−1.76565e17			−0.0131871
$541$		−	3.56690e18i		−	0.262973i	−0.991318	−	0.131486i	$-0.958025\pi$
$541$		−	3.56690e18i		−	0.262973i	0.991318	−	0.131486i	$-0.0419749\pi$
$542$	1.02469e19			0.745758
$543$	−8.69047e18			−0.624373
$544$	−1.15775e18			−0.0821153
$545$			2.00008e18i			0.140046i
$546$		−	4.24155e18i		−	0.293208i
$547$			1.48955e19i			1.01659i	0.861184	+	0.508293i	$0.169723\pi$
$547$			1.48955e19i			1.01659i	−0.861184	+	0.508293i	$0.830277\pi$
$548$	7.18588e18			0.484190
$549$			6.90564e17i			0.0459407i
$550$	−6.99503e18	+	8.07899e18i	−0.459463	+	0.530663i
$551$	5.63105e18			0.365198
$552$			7.03172e18i			0.450285i
$553$	7.75867e18			0.490582
$554$	4.37179e18			0.272955
$555$	−1.73715e18			−0.107099
$556$			5.15978e18i			0.314129i
$557$			4.00286e18i			0.240649i	0.992735	+	0.120325i	$0.0383935\pi$
$557$			4.00286e18i			0.240649i	−0.992735	+	0.120325i	$0.961606\pi$
$558$		−	2.09821e16i		−	0.00124569i
$559$	1.63408e19			0.958055
$560$		−	1.28279e17i		−	0.00742745i
$561$	−7.90034e18	+	9.12459e18i	−0.451758	+	0.521763i
$562$	−9.68511e18			−0.546953
$563$			2.51342e19i			1.40186i	0.713228	+	0.700932i	$0.247232\pi$
$563$			2.51342e19i			1.40186i	−0.713228	+	0.700932i	$0.752768\pi$
$564$	1.05375e19			0.580476
$565$	1.37704e18			0.0749217
$566$	−3.05682e18			−0.164269
$567$		−	4.90368e18i		−	0.260280i
$568$			1.14123e19i			0.598322i
$569$			1.92358e18i			0.0996151i	0.998759	+	0.0498076i	$0.0158608\pi$
$569$			1.92358e18i			0.0996151i	−0.998759	+	0.0498076i	$0.984139\pi$
$570$	−7.98350e17			−0.0408385
$571$		−	2.99035e19i		−	1.51102i	−0.655138	−	0.755509i	$-0.727390\pi$
$571$		−	2.99035e19i		−	1.51102i	0.655138	−	0.755509i	$-0.272610\pi$
$572$	5.26899e18	−	6.08549e18i	0.263000	−	0.303755i
$573$	1.42671e19			0.703483
$574$		−	7.08083e18i		−	0.344906i
$575$	1.76834e19			0.850926
$576$	−3.17510e18			−0.150939
$577$	−6.42637e18			−0.301811			−0.150905	−	0.988548i	$-0.548219\pi$
$577$	−6.42637e18			−0.301811			−0.150905	+	0.988548i	$0.548219\pi$
$578$		−	1.19515e19i		−	0.554532i
$579$		−	1.32591e19i		−	0.607804i
$580$			7.58998e17i			0.0343752i
$581$	1.18001e19			0.528021
$582$		−	1.71798e19i		−	0.759550i
$583$	4.07083e17	+	3.52465e17i	0.0177829	+	0.0153970i
$584$	9.63710e17			0.0415965
$585$		−	1.94626e18i		−	0.0830062i
$586$	−1.61737e19			−0.681595
$587$	3.41897e18			0.142373			0.0711867	−	0.997463i	$-0.477321\pi$
$587$	3.41897e18			0.142373			0.0711867	+	0.997463i	$0.477321\pi$
$588$	1.58759e19			0.653278
$589$		−	1.63036e16i		−	0.000662944i
$590$		−	4.90675e17i		−	0.0197165i
$591$		−	3.70398e19i		−	1.47081i
$592$	−5.36831e18			−0.210662
$593$		−	1.38941e19i		−	0.538825i	−0.963025	−	0.269412i	$-0.913171\pi$
$593$		−	1.38941e19i		−	0.538825i	0.963025	−	0.269412i	$-0.0868295\pi$
$594$	−3.72335e18	+	4.30033e18i	−0.142701	+	0.164815i
$595$	−3.64349e17			−0.0138006
$596$			2.51469e19i			0.941370i
$597$	−6.79045e19			−2.51234
$598$	−1.33200e19			−0.487076
$599$	−3.98002e19			−1.43846			−0.719230	−	0.694772i	$-0.755505\pi$
$599$	−3.98002e19			−1.43846			−0.719230	+	0.694772i	$0.755505\pi$
$600$			1.45974e19i			0.521455i
$601$		−	2.28109e19i		−	0.805416i	−0.915329	−	0.402708i	$-0.868069\pi$
$601$		−	2.28109e19i		−	0.805416i	0.915329	−	0.402708i	$-0.131931\pi$
$602$		−	8.38939e18i		−	0.292789i
$603$	5.76342e18			0.198820
$604$		−	6.85900e18i		−	0.233885i
$605$	−3.63124e17	−	2.51181e18i	−0.0122396	−	0.0846639i
$606$	−5.08243e19			−1.69341
$607$		−	3.02358e19i		−	0.995865i	−0.867216	−	0.497932i	$-0.834093\pi$
$607$		−	3.02358e19i		−	0.995865i	0.867216	−	0.497932i	$-0.165907\pi$
$608$	−2.46714e18			−0.0803282
$609$	1.28845e19			0.414711
$610$	−7.23254e16			−0.00230135
$611$			1.99610e19i			0.627904i
$612$			9.01819e18i			0.280453i
$613$		−	4.77174e19i		−	1.46708i	−0.679646	−	0.733540i	$-0.737867\pi$
$613$		−	4.77174e19i		−	1.46708i	0.679646	−	0.733540i	$-0.262133\pi$
$614$	−7.61298e18			−0.231407
$615$		−	5.93983e18i		−	0.178504i
$616$	−3.12430e18	−	2.70511e18i	−0.0928298	−	0.0803748i
$617$	3.22564e19			0.947587			0.473794	−	0.880636i	$-0.342884\pi$
$617$	3.22564e19			0.947587			0.473794	+	0.880636i	$0.342884\pi$
$618$		−	7.62752e18i		−	0.221546i
$619$	1.12809e18			0.0323972			0.0161986	−	0.999869i	$-0.494844\pi$
$619$	1.12809e18			0.0323972			0.0161986	+	0.999869i	$0.494844\pi$
$620$	2.19753e15			6.24013e−5
$621$	9.41263e18			0.264283
$622$			3.50717e19i			0.973698i
$623$		−	1.26193e19i		−	0.346432i
$624$		−	1.09955e19i		−	0.298484i
$625$	3.64371e19			0.978100
$626$			3.75963e19i			0.997988i
$627$	−1.68354e19	+	1.94442e19i	−0.441926	+	0.510408i
$628$	−3.63222e19			−0.942876
$629$			1.52475e19i			0.391422i
$630$	−9.99214e17			−0.0253673
$631$	5.08147e19			1.27580			0.637902	−	0.770118i	$-0.279803\pi$
$631$	5.08147e19			1.27580			0.637902	+	0.770118i	$0.279803\pi$
$632$	2.01130e19			0.499410
$633$			9.02582e19i			2.21646i
$634$		−	2.80546e19i		−	0.681365i
$635$			5.27708e18i			0.126759i
$636$	7.35532e17			0.0174744
$637$			3.00734e19i			0.706654i
$638$	1.84858e19	+	1.60055e19i	0.429628	+	0.371985i
$639$	8.88947e19			2.04348
$640$		−	3.32541e17i		−	0.00756110i
$641$	−5.41798e19			−1.21852			−0.609258	−	0.792972i	$-0.708532\pi$
$641$	−5.41798e19			−1.21852			−0.609258	+	0.792972i	$0.708532\pi$
$642$	2.94129e19			0.654325
$643$	−8.33971e19			−1.83516			−0.917580	−	0.397551i	$-0.869860\pi$
$643$	−8.33971e19			−1.83516			−0.917580	+	0.397551i	$0.869860\pi$
$644$			6.83852e18i			0.148854i
$645$		−	7.03752e18i		−	0.151531i
$646$			7.00737e18i			0.149254i
$647$	3.79381e19			0.799367			0.399683	−	0.916653i	$-0.369120\pi$
$647$	3.79381e19			0.799367			0.399683	+	0.916653i	$0.369120\pi$
$648$		−	1.27119e19i		−	0.264964i
$649$	−1.19506e19	−	1.03472e19i	−0.246421	−	0.213359i
$650$	−2.76515e19			−0.564060
$651$		−	3.73045e16i		−	0.000752825i
$652$	2.22724e18			0.0444666
$653$	−4.46032e19			−0.880996			−0.440498	−	0.897754i	$-0.645198\pi$
$653$	−4.46032e19			−0.880996			−0.440498	+	0.897754i	$0.645198\pi$
$654$	8.80161e19			1.71996
$655$			3.33782e18i			0.0645318i
$656$		−	1.83558e19i		−	0.351113i
$657$		−	7.50671e18i		−	0.142067i
$658$	1.02480e19			0.191892
$659$			7.97591e19i			1.47769i	0.673877	+	0.738844i	$0.264628\pi$
$659$			7.97591e19i			1.47769i	−0.673877	+	0.738844i	$0.735372\pi$
$660$	−2.62085e18	−	2.26921e18i	−0.0480435	−	0.0415974i
$661$	5.72555e19			1.03850			0.519251	−	0.854622i	$-0.326211\pi$
$661$	5.72555e19			1.03850			0.519251	+	0.854622i	$0.326211\pi$
$662$		−	7.72013e19i		−	1.38554i
$663$	−3.12302e19			−0.554601
$664$	3.05896e19			0.537523
$665$	−7.76416e17			−0.0135003
$666$			4.18158e19i			0.719484i
$667$		−	4.04620e19i		−	0.688916i
$668$		−	4.68950e19i		−	0.790118i
$669$	−2.03774e19			−0.339754
$670$			6.03625e17i			0.00995964i
$671$	−1.52518e18	+	1.76152e18i	−0.0249036	+	0.0287627i
$672$	−5.64509e18			−0.0912191
$673$		−	4.75174e19i		−	0.759884i	−0.925010	−	0.379942i	$-0.875944\pi$
$673$		−	4.75174e19i		−	0.759884i	0.925010	−	0.379942i	$-0.124056\pi$
$674$	8.11256e19			1.28392
$675$	1.95400e19			0.306054
$676$	−1.14265e19			−0.177128
$677$			8.83528e19i			1.35550i	0.735293	+	0.677750i	$0.237045\pi$
$677$			8.83528e19i			1.35550i	−0.735293	+	0.677750i	$0.762955\pi$
$678$		−	6.05985e19i		−	0.920140i
$679$		−	1.67077e19i		−	0.251090i
$680$	−9.44510e17			−0.0140490
$681$			2.54952e19i			0.375344i
$682$	4.63409e16	−	5.35220e16i	0.000675264	−	0.000779905i
$683$	−9.50622e19			−1.37108			−0.685540	−	0.728035i	$-0.740434\pi$
$683$	−9.50622e19			−1.37108			−0.685540	+	0.728035i	$0.740434\pi$
$684$			1.92175e19i			0.274349i
$685$	5.86233e18			0.0828392
$686$	3.29973e19			0.461540
$687$	2.18121e19			0.301995
$688$		−	2.17480e19i		−	0.298058i
$689$			1.39330e18i			0.0189021i
$690$			5.73656e18i			0.0770385i
$691$	2.83606e19			0.377025			0.188512	−	0.982071i	$-0.439633\pi$
$691$	2.83606e19			0.377025			0.188512	+	0.982071i	$0.439633\pi$
$692$			9.80732e18i			0.129065i
$693$	−2.10711e19	+	2.43364e19i	−0.274508	+	0.317047i
$694$	−8.51580e19			−1.09827
$695$			4.20941e18i			0.0537438i
$696$	3.34007e19			0.422173
$697$	−5.21357e19			−0.652387
$698$	4.88681e19			0.605393
$699$			2.08714e20i			2.55984i
$700$			1.41963e19i			0.172381i
$701$		−	4.33905e19i		−	0.521637i	−0.965388	−	0.260818i	$-0.916008\pi$
$701$		−	4.33905e19i		−	0.521637i	0.965388	−	0.260818i	$-0.0839924\pi$
$702$	−1.47185e19			−0.175188
$703$			3.24920e19i			0.382903i
$704$	−8.09919e18	−	7.01252e18i	−0.0945003	−	0.0818211i
$705$	8.59663e18			0.0993127
$706$			7.58085e19i			0.867131i
$707$	−4.94279e19			−0.559804
$708$	−2.15928e19			−0.242145
$709$	4.72412e19			0.524563			0.262281	−	0.964991i	$-0.415525\pi$
$709$	4.72412e19			0.524563			0.262281	+	0.964991i	$0.415525\pi$
$710$			9.31029e18i			0.102366i
$711$		−	1.56668e20i		−	1.70566i
$712$		−	3.27132e19i		−	0.352666i
$713$	−1.17150e17			−0.00125059
$714$			1.60336e19i			0.169490i
$715$	4.29851e18	−	4.96462e18i	0.0449962	−	0.0519689i
$716$	−5.08891e19			−0.527514
$717$			8.78074e19i			0.901358i
$718$	4.92544e19			0.500696
$719$	−1.61052e18			−0.0162130			−0.00810652	−	0.999967i	$-0.502580\pi$
$719$	−1.61052e18			−0.0162130			−0.00810652	+	0.999967i	$0.502580\pi$
$720$	−2.59029e18			−0.0258238
$721$		−	7.41795e18i		−	0.0732381i
$722$		−	5.73854e19i		−	0.561100i
$723$		−	2.42198e20i		−	2.34532i
$724$	−2.19095e19			−0.210118
$725$		−	8.39965e19i		−	0.797802i
$726$	−1.10535e20	+	1.59797e19i	−1.03979	+	0.150319i
$727$	7.40196e19			0.689614			0.344807	−	0.938674i	$-0.387944\pi$
$727$	7.40196e19			0.689614			0.344807	+	0.938674i	$0.387944\pi$
$728$		−	1.06934e19i		−	0.0986721i
$729$	−1.49141e20			−1.36302
$730$	7.86206e17			0.00711666
$731$	−6.17705e19			−0.553808
$732$			3.18277e18i			0.0282637i
$733$		−	1.90949e20i		−	1.67954i	−0.542946	−	0.839768i	$-0.682691\pi$
$733$		−	1.90949e20i		−	1.67954i	0.542946	−	0.839768i	$-0.317309\pi$
$734$		−	1.57038e19i		−	0.136815i
$735$	1.29518e19			0.111768
$736$			1.77277e19i			0.151533i
$737$	1.47016e19	+	1.27291e19i	0.124478	+	0.107776i
$738$	−1.42980e20			−1.19917
$739$			1.11715e20i			0.928112i	0.885806	+	0.464056i	$0.153606\pi$
$739$			1.11715e20i			0.928112i	−0.885806	+	0.464056i	$0.846394\pi$
$740$	−4.37953e18			−0.0360417
$741$	−6.65506e19			−0.542531
$742$	7.15323e17			0.00577663
$743$		−	1.25747e20i		−	1.00595i	−0.864301	−	0.502976i	$-0.832239\pi$
$743$		−	1.25747e20i		−	1.00595i	0.864301	−	0.502976i	$-0.167761\pi$
$744$		−	9.67053e16i		−	0.000766372i
$745$			2.05151e19i			0.161057i
$746$	−4.16815e18			−0.0324169
$747$		−	2.38274e20i		−	1.83583i
$748$	−1.99175e19	+	2.30040e19i	−0.152028	+	0.175587i
$749$	2.86048e19			0.216305
$750$			2.39052e19i			0.179087i
$751$	1.16074e20			0.861501			0.430751	−	0.902471i	$-0.358249\pi$
$751$	1.16074e20			0.861501			0.430751	+	0.902471i	$0.358249\pi$
$752$	2.65661e19			0.195345
$753$	−1.72519e20			−1.25681
$754$			6.32702e19i			0.456667i
$755$		−	5.59565e18i		−	0.0400149i
$756$			7.55649e18i			0.0535387i
$757$	7.10154e19			0.498519			0.249259	−	0.968437i	$-0.419813\pi$
$757$	7.10154e19			0.498519			0.249259	+	0.968437i	$0.419813\pi$
$758$		−	1.24107e20i		−	0.863198i
$759$	1.39717e20	+	1.20971e20i	0.962844	+	0.833658i
$760$	−2.01272e18			−0.0137432
$761$			1.94599e20i			1.31658i	0.752763	+	0.658292i	$0.228721\pi$
$761$			1.94599e20i			1.31658i	−0.752763	+	0.658292i	$0.771279\pi$
$762$	2.32225e20			1.55677
$763$	8.55978e19			0.568579
$764$	3.59688e19			0.236741
$765$			7.35715e18i			0.0479821i
$766$			1.15846e20i			0.748651i
$767$		−	4.09028e19i		−	0.261930i
$768$	−1.46339e19			−0.0928606
$769$			1.77818e20i			1.11813i	0.829124	+	0.559064i	$0.188840\pi$
$769$			1.77818e20i			1.11813i	−0.829124	+	0.559064i	$0.811160\pi$
$770$	−2.54884e18	−	2.20686e18i	−0.0158821	−	0.0137512i
$771$	3.95527e20			2.44228
$772$		−	3.34274e19i		−	0.204542i
$773$	−1.17814e20			−0.714400			−0.357200	−	0.934028i	$-0.616269\pi$
$773$	−1.17814e20			−0.714400			−0.357200	+	0.934028i	$0.616269\pi$
$774$	−1.69404e20			−1.01797
$775$	−2.43196e17			−0.00144825
$776$		−	4.33119e19i		−	0.255608i
$777$			7.43453e19i			0.434817i
$778$			1.02323e20i			0.593083i
$779$	−1.11100e20			−0.638190
$780$		−	8.97023e18i		−	0.0510671i
$781$	2.26757e20	+	1.96332e20i	1.27939	+	1.10773i
$782$	5.03515e19			0.281556
$783$		−	4.47101e19i		−	0.247784i
$784$	4.00248e19			0.219845
$785$	−2.96321e19			−0.161315
$786$	1.46885e20			0.792538
$787$		−	2.37792e19i		−	0.127167i	−0.997977	−	0.0635834i	$-0.979747\pi$
$787$		−	2.37792e19i		−	0.127167i	0.997977	−	0.0635834i	$-0.0202529\pi$
$788$		−	9.33810e19i		−	0.494966i
$789$			2.74972e20i			1.44461i
$790$	1.64084e19			0.0854431
$791$		−	5.89335e19i		−	0.304177i
$792$	−5.46232e19	+	6.30877e19i	−0.279448	+	0.322752i
$793$	−6.02906e18			−0.0305729
$794$			1.96439e20i			0.987381i
$795$	6.00056e17			0.00298966
$796$	−1.71194e20			−0.845467
$797$	−5.93031e19			−0.290315			−0.145157	−	0.989409i	$-0.546369\pi$
$797$	−5.93031e19			−0.290315			−0.145157	+	0.989409i	$0.546369\pi$
$798$			3.41672e19i			0.165802i
$799$		−	7.54553e19i		−	0.362963i
$800$			3.68015e19i			0.175483i
$801$	−2.54816e20			−1.20448
$802$			9.12495e19i			0.427572i
$803$	1.65793e19	−	1.91484e19i	0.0770117	−	0.0889456i
$804$	2.65633e19			0.122318
$805$			5.57895e18i			0.0254672i
$806$	1.83187e17			0.000828989
$807$	3.71967e20			1.66874
$808$	−1.28133e20			−0.569877
$809$		−	1.26549e20i		−	0.557979i	−0.960294	−	0.278990i	$-0.910000\pi$
$809$		−	1.26549e20i		−	0.557979i	0.960294	−	0.278990i	$-0.0899995\pi$
$810$		−	1.03706e19i		−	0.0453322i
$811$			1.85831e20i			0.805327i	0.915348	+	0.402664i	$0.131916\pi$
$811$			1.85831e20i			0.805327i	−0.915348	+	0.402664i	$0.868084\pi$
$812$	3.24830e19			0.139561
$813$		−	3.67873e20i		−	1.56698i
$814$	−9.23542e19	+	1.06666e20i	−0.390019	+	0.450458i
$815$	1.81701e18			0.00760772
$816$			4.15644e19i			0.172540i
$817$	−1.31631e20			−0.541756
$818$	−2.93073e20			−1.19592
$819$	−8.32947e19			−0.337000
$820$		−	1.49749e19i		−	0.0600712i
$821$		−	2.34526e20i		−	0.932802i	−0.884573	−	0.466401i	$-0.845550\pi$
$821$		−	2.34526e20i		−	0.932802i	0.884573	−	0.466401i	$-0.154450\pi$
$822$		−	2.57979e20i		−	1.01738i
$823$	−3.76170e20			−1.47091			−0.735454	−	0.677575i	$-0.763031\pi$
$823$	−3.76170e20			−1.47091			−0.735454	+	0.677575i	$0.763031\pi$
$824$		−	1.92297e19i		−	0.0745560i
$825$	2.90043e20	+	2.51128e20i	1.11503	+	0.965421i
$826$	−2.09995e19			−0.0800478
$827$		−	1.37139e20i		−	0.518350i	−0.965830	−	0.259175i	$-0.916549\pi$
$827$		−	1.37139e20i		−	0.518350i	0.965830	−	0.259175i	$-0.0834507\pi$
$828$	1.38087e20			0.517538
$829$	1.74079e20			0.646942			0.323471	−	0.946238i	$-0.395150\pi$
$829$	1.74079e20			0.646942			0.323471	+	0.946238i	$0.395150\pi$
$830$	2.49553e19			0.0919638
$831$		−	1.56951e20i		−	0.573532i
$832$		−	2.77207e19i		−	0.100448i
$833$		−	1.13682e20i		−	0.408485i
$834$	1.85241e20			0.660046
$835$		−	3.82575e19i		−	0.135180i
$836$	−4.24436e19	+	4.90208e19i	−0.148720	+	0.171766i
$837$	−1.29449e17			−0.000449802
$838$		−	2.44968e19i		−	0.0844113i
$839$	4.85450e18			0.0165886			0.00829431	−	0.999966i	$-0.497360\pi$
$839$	4.85450e18			0.0165886			0.00829431	+	0.999966i	$0.497360\pi$
$840$	−4.60533e18			−0.0156065
$841$	1.05364e20			0.354094
$842$		−	1.17949e20i		−	0.393105i
$843$			3.47704e20i			1.14926i
$844$			2.27550e20i			0.745898i
$845$	−9.32190e18			−0.0303045
$846$		−	2.06934e20i		−	0.667173i
$847$	−1.07498e20	+	1.55407e19i	−0.343730	+	0.0496920i
$848$	1.85435e18			0.00588058
$849$			1.09743e20i			0.345160i
$850$	1.04527e20			0.326058
$851$	2.33472e20			0.722316
$852$	4.09711e20			1.25719
$853$		−	1.37223e20i		−	0.417623i	−0.977956	−	0.208811i	$-0.933041\pi$
$853$		−	1.37223e20i		−	0.417623i	0.977956	−	0.208811i	$-0.0669595\pi$
$854$			3.09533e18i			0.00934333i
$855$			1.56778e19i			0.0469379i
$856$	7.41529e19			0.220197
$857$		−	6.85783e19i		−	0.201986i	−0.994887	−	0.100993i	$-0.967798\pi$
$857$		−	6.85783e19i		−	0.201986i	0.994887	−	0.100993i	$-0.0322020\pi$
$858$	−2.18474e20	−	1.89161e20i	−0.638248	−	0.552614i
$859$	1.00082e20			0.290004			0.145002	−	0.989431i	$-0.453681\pi$
$859$	1.00082e20			0.290004			0.145002	+	0.989431i	$0.453681\pi$
$860$		−	1.77423e19i		−	0.0509942i
$861$	−2.54208e20			−0.724715
$862$	−3.34423e20			−0.945684
$863$	−5.97607e20			−1.67625			−0.838127	−	0.545475i	$-0.816349\pi$
$863$	−5.97607e20			−1.67625			−0.838127	+	0.545475i	$0.816349\pi$
$864$			1.95889e19i			0.0545021i
$865$			8.00093e18i			0.0220815i
$866$		−	3.26394e20i		−	0.893547i
$867$	−4.29068e20			−1.16518
$868$		−	9.40483e16i		−	0.000253345i
$869$	3.46016e20	−	3.99635e20i	0.924607	−	1.06789i
$870$	2.72487e19			0.0722289
$871$			5.03183e19i			0.132312i
$872$	2.21897e20			0.578811
$873$	−3.37373e20			−0.872992
$874$	1.07298e20			0.275429
$875$			2.32484e19i			0.0592022i
$876$		−	3.45980e19i		−	0.0874023i
$877$		−	2.83416e20i		−	0.710275i	−0.934814	−	0.355138i	$-0.884434\pi$
$877$		−	2.83416e20i		−	0.710275i	0.934814	−	0.355138i	$-0.115566\pi$
$878$	2.07428e20			0.515709
$879$			5.80651e20i			1.43216i
$880$	−6.60742e18	−	5.72090e18i	−0.0161679	−	0.0139986i
$881$	−4.86796e20			−1.18172			−0.590861	−	0.806773i	$-0.701212\pi$
$881$	−4.86796e20			−1.18172			−0.590861	+	0.806773i	$0.701212\pi$
$882$		−	3.11768e20i		−	0.750848i
$883$	−2.39197e20			−0.571520			−0.285760	−	0.958301i	$-0.592246\pi$
$883$	−2.39197e20			−0.571520			−0.285760	+	0.958301i	$0.592246\pi$
$884$	−7.87345e19			−0.186638
$885$	−1.76157e19			−0.0414282
$886$		−	1.99445e20i		−	0.465357i
$887$			2.86502e20i			0.663227i	0.943415	+	0.331613i	$0.107593\pi$
$887$			2.86502e20i			0.663227i	−0.943415	+	0.331613i	$0.892407\pi$
$888$			1.92727e20i			0.442641i
$889$	2.25845e20			0.514633
$890$		−	2.66878e19i		−	0.0603370i
$891$	−2.52580e20	−	2.18691e20i	−0.566572	−	0.490554i
$892$	−5.13734e19			−0.114336
$893$		−	1.60793e20i		−	0.355064i
$894$	9.02795e20			1.97800
$895$	−4.15160e19			−0.0902514
$896$	−1.42318e19			−0.0306976
$897$			4.78200e20i			1.02344i
$898$			3.47738e19i			0.0738444i
$899$			5.56463e17i			0.00117251i
$900$	2.86661e20			0.599336
$901$		−	5.26687e18i		−	0.0109265i
$902$	−3.64721e20	−	3.15786e20i	−0.750784	−	0.650050i
$903$	−3.01186e20			−0.615207
$904$		−	1.52775e20i		−	0.309651i
$905$	−1.78741e19			−0.0359487
$906$	−2.46244e20			−0.491437
$907$	9.45672e19			0.187279			0.0936396	−	0.995606i	$-0.470150\pi$
$907$	9.45672e19			0.187279			0.0936396	+	0.995606i	$0.470150\pi$
$908$			6.42760e19i			0.126313i
$909$			9.98077e20i			1.94633i
$910$		−	8.72377e18i		−	0.0168816i
$911$	−7.56532e20			−1.45278			−0.726388	−	0.687285i	$-0.758802\pi$
$911$	−7.56532e20			−1.45278			−0.726388	+	0.687285i	$0.758802\pi$
$912$			8.85724e19i			0.168785i
$913$	5.26250e20	−	6.07799e20i	0.995169	−	1.14938i
$914$	−2.25099e20			−0.422426
$915$			2.59655e18i			0.00483558i
$916$	5.49905e19			0.101629
$917$	1.42849e20			0.261995
$918$	5.56379e19			0.101268
$919$			3.69598e20i			0.667607i	0.942643	+	0.333804i	$0.108332\pi$
$919$			3.69598e20i			0.667607i	−0.942643	+	0.333804i	$0.891668\pi$
$920$			1.44624e19i			0.0259255i
$921$			2.73313e20i			0.486231i
$922$	−1.01562e20			−0.179314
$923$			7.76107e20i			1.35991i
$924$	−9.71158e19	+	1.12165e20i	−0.168883	+	0.195054i
$925$	4.84672e20			0.836481
$926$			2.57211e20i			0.440568i
$927$	−1.49788e20			−0.254635
$928$	8.42065e19			0.142072
$929$	1.12578e21			1.88514			0.942571	−	0.334006i	$-0.108401\pi$
$929$	1.12578e21			1.88514			0.942571	+	0.334006i	$0.108401\pi$
$930$		−	7.88933e16i		−	0.000131117i
$931$		−	2.42252e20i		−	0.399595i
$932$			5.26190e20i			0.861452i
$933$	1.25910e21			2.04593
$934$			6.67277e20i			1.07616i
$935$	−1.62490e19	+	1.87669e19i	−0.0260102	+	0.0300408i
$936$	−2.15927e20			−0.343064
$937$		−	9.47400e20i		−	1.49402i	−0.664813	−	0.747010i	$-0.731489\pi$
$937$		−	9.47400e20i		−	1.49402i	0.664813	−	0.747010i	$-0.268511\pi$
$938$	2.58335e19			0.0404355
$939$	1.34974e21			2.09697
$940$	2.16730e19			0.0334213
$941$		−	7.65539e20i		−	1.17176i	−0.810397	−	0.585882i	$-0.800748\pi$
$941$		−	7.65539e20i		−	1.17176i	0.810397	−	0.585882i	$-0.199252\pi$
$942$			1.30400e21i			1.98116i
$943$			7.98307e20i			1.20389i
$944$	−5.44376e19			−0.0814883
$945$			6.16468e18i			0.00915984i
$946$	−4.32122e20	−	3.74144e20i	−0.637336	−	0.551824i
$947$	5.85443e20			0.857107			0.428553	−	0.903516i	$-0.359023\pi$
$947$	5.85443e20			0.857107			0.428553	+	0.903516i	$0.359023\pi$
$948$		−	7.22074e20i		−	1.04936i
$949$	6.55383e19			0.0945435
$950$	2.22743e20			0.318962
$951$	−1.00719e21			−1.43168
$952$			4.04224e19i			0.0570379i
$953$		−	2.03940e20i		−	0.285661i	−0.989747	−	0.142831i	$-0.954380\pi$
$953$		−	2.03940e20i		−	0.285661i	0.989747	−	0.142831i	$-0.0456204\pi$
$954$		−	1.44442e19i		−	0.0200843i
$955$	2.93438e19			0.0405035
$956$			2.21371e20i			0.303330i
$957$	5.74612e20	−	6.63656e20i	0.781612	−	0.902733i
$958$	8.77428e19			0.118482
$959$		−	2.50891e20i		−	0.336322i
$960$	−1.19385e19			−0.0158873
$961$	−7.56942e20			−0.999998
$962$	−3.65079e20			−0.478807
$963$		−	5.77606e20i		−	0.752051i
$964$		−	6.10604e20i		−	0.789261i
$965$		−	2.72705e19i		−	0.0349947i
$966$	2.45509e20			0.312772
$967$			6.01669e20i			0.760978i	0.924785	+	0.380489i	$0.124244\pi$
$967$			6.01669e20i			0.760978i	−0.924785	+	0.380489i	$0.875756\pi$
$968$	−2.78671e20	+	4.02865e19i	−0.349916	+	0.0505862i
$969$	2.51571e20			0.313613
$970$		−	3.53344e19i		−	0.0437316i
$971$	−9.30510e20			−1.14337			−0.571684	−	0.820474i	$-0.693710\pi$
$971$	−9.30510e20			−1.14337			−0.571684	+	0.820474i	$0.693710\pi$
$972$	−5.82733e20			−0.710896
$973$	1.80151e20			0.218196
$974$			7.72518e20i			0.928958i
$975$			9.92713e20i			1.18520i
$976$			8.02409e18i			0.00951146i
$977$	6.32034e20			0.743839			0.371919	−	0.928265i	$-0.378700\pi$
$977$	6.32034e20			0.743839			0.371919	+	0.928265i	$0.378700\pi$
$978$		−	7.99599e19i		−	0.0934330i
$979$	−6.49996e20	−	5.62785e20i	−0.754105	−	0.652926i
$980$	3.26527e19			0.0376129
$981$		−	1.72844e21i		−	1.97684i
$982$	1.11242e20			0.126324
$983$	3.55924e20			0.401313			0.200656	−	0.979662i	$-0.435692\pi$
$983$	3.55924e20			0.401313			0.200656	+	0.979662i	$0.435692\pi$
$984$	−6.58990e20			−0.737756
$985$		−	7.61814e19i		−	0.0846828i
$986$		−	2.39170e20i		−	0.263979i
$987$		−	3.67912e20i		−	0.403203i
$988$	−1.67781e20			−0.182576
$989$			9.45836e20i			1.02198i
$990$	−4.45622e19	+	5.14677e19i	−0.0478102	+	0.0552190i
$991$	1.20231e19			0.0128085			0.00640427	−	0.999979i	$-0.497961\pi$
$991$	1.20231e19			0.0128085			0.00640427	+	0.999979i	$0.497961\pi$
$992$		−	2.43804e17i		−	0.000257904i
$993$	−2.77160e21			−2.91129
$994$	3.98455e20			0.415599
$995$	−1.39662e20			−0.144649
$996$		−	1.09819e21i		−	1.12944i
$997$		−	4.29082e20i		−	0.438201i	−0.975702	−	0.219101i	$-0.929688\pi$
$997$		−	4.29082e20i		−	0.438201i	0.975702	−	0.219101i	$-0.0703123\pi$
$998$			2.64611e20i			0.268346i
$999$	2.57984e20			0.259797

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.15.b.a.21.1	✓	14
4.3	odd	2		176.15.h.e.65.13		14
11.10	odd	2	inner	22.15.b.a.21.8	yes	14
44.43	even	2		176.15.h.e.65.14		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.15.b.a.21.1	✓	14	1.1	even	1	trivial
22.15.b.a.21.8	yes	14	11.10	odd	2	inner
176.15.h.e.65.13		14	4.3	odd	2
176.15.h.e.65.14		14	44.43	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:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 15 \)
Character orbit:	\([\chi]\)	\(=\)	22.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-90.5097i q^{2} -3249.38 q^{3} -8192.00 q^{4} -6683.13 q^{5} +294100. i q^{6} +286020. i q^{7} +741455. i q^{8} +5.77548e6 q^{9} +O(q^{10})\)	\(q-90.5097i q^{2} -3249.38 q^{3} -8192.00 q^{4} -6683.13 q^{5} +294100. i q^{6} +286020. i q^{7} +741455. i q^{8} +5.77548e6 q^{9} +604888. i q^{10} +(1.47323e7 + 1.27557e7i) q^{11} +2.66189e7 q^{12} +5.04236e7i q^{13} +2.58875e7 q^{14} +2.17160e7 q^{15} +6.71089e7 q^{16} -1.90608e8i q^{17} -5.22737e8i q^{18} -4.06180e8i q^{19} +5.47482e7 q^{20} -9.29385e8i q^{21} +(1.15451e9 - 1.33342e9i) q^{22} -2.91861e9 q^{23} -2.40927e9i q^{24} -6.05885e9 q^{25} +4.56382e9 q^{26} -3.22504e9 q^{27} -2.34307e9i q^{28} +1.38634e10i q^{29} -1.96551e9i q^{30} +4.01389e7 q^{31} -6.07400e9i q^{32} +(-4.78709e10 - 4.14481e10i) q^{33} -1.72519e10 q^{34} -1.91151e9i q^{35} -4.73127e10 q^{36} -7.99941e10 q^{37} -3.67632e10 q^{38} -1.63845e11i q^{39} -4.95524e9i q^{40} -2.73523e11i q^{41} -8.41183e10 q^{42} -3.24071e11i q^{43} +(-1.20687e11 - 1.04495e11i) q^{44} -3.85983e10 q^{45} +2.64163e11i q^{46} +3.95866e11 q^{47} -2.18062e11 q^{48} +5.96416e11 q^{49} +5.48385e11i q^{50} +6.19358e11i q^{51} -4.13070e11i q^{52} +2.76319e10 q^{53} +2.91897e11i q^{54} +(-9.84582e10 - 8.52480e10i) q^{55} -2.12071e11 q^{56} +1.31983e12i q^{57} +1.25477e12 q^{58} -8.11184e11 q^{59} -1.77898e11 q^{60} +1.19568e11i q^{61} -3.63296e9i q^{62} +1.65190e12i q^{63} -5.49756e11 q^{64} -3.36987e11i q^{65} +(-3.75145e12 + 4.33278e12i) q^{66} +9.97912e11 q^{67} +1.56146e12i q^{68} +9.48367e12 q^{69} -1.73010e11 q^{70} +1.53918e13 q^{71} +4.28226e12i q^{72} -1.29975e12i q^{73} +7.24024e12i q^{74} +1.96875e13 q^{75} +3.32743e12i q^{76} +(-3.64838e12 + 4.21374e12i) q^{77} -1.48296e13 q^{78} -2.71264e13i q^{79} -4.48497e11 q^{80} -1.71446e13 q^{81} -2.47565e13 q^{82} -4.12561e13i q^{83} +7.61352e12i q^{84} +1.27386e12i q^{85} -2.93315e13 q^{86} -4.50475e13i q^{87} +(-9.45778e12 + 1.09234e13i) q^{88} -4.41203e13 q^{89} +3.49352e12i q^{90} -1.44221e13 q^{91} +2.39093e13 q^{92} -1.30426e11 q^{93} -3.58297e13i q^{94} +2.71455e12i q^{95} +1.97367e13i q^{96} -5.84147e13 q^{97} -5.39814e13i q^{98} +(8.50864e13 + 7.36702e13i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 4394 q^{3} - 114688 q^{4} + 69758 q^{5} + 11016572 q^{9}+O(q^{10}) \) 14 * q + 4394 * q^3 - 114688 * q^4 + 69758 * q^5 + 11016572 * q^9	\( 14 q + 4394 q^{3} - 114688 q^{4} + 69758 q^{5} + 11016572 q^{9} + 20143042 q^{11} - 35995648 q^{12} + 62814720 q^{14} - 1359602 q^{15} + 939524096 q^{16} - 571457536 q^{20} - 2107666944 q^{22} - 7305755542 q^{23} + 19291879452 q^{25} - 6388480512 q^{26} + 34093422830 q^{27} - 33569873942 q^{31} + 2885838062 q^{33} + 167764701696 q^{34} - 90247757824 q^{36} + 73167823966 q^{37} + 71236111872 q^{38} - 222695314944 q^{42} - 165011800064 q^{44} + 2000205168616 q^{45} - 1612717386124 q^{47} + 294876348416 q^{48} + 3424602524990 q^{49} - 3530064068164 q^{53} - 3715439610854 q^{55} - 514578186240 q^{56} - 1374208002048 q^{58} - 818496564070 q^{59} + 11137859584 q^{60} - 7696581394432 q^{64} - 5938395621888 q^{66} + 16485465276922 q^{67} - 11394452631206 q^{69} - 392146020864 q^{70} - 19380879179878 q^{71} + 23016770893992 q^{75} + 60534793808304 q^{77} + 17335823992320 q^{78} + 4681380134912 q^{80} - 10394309810662 q^{81} - 79417078012416 q^{82} + 6375532305408 q^{86} + 17266007605248 q^{88} - 117770741987650 q^{89} + 150621364097712 q^{91} + 59848749400064 q^{92} + 27345122803162 q^{93} + 123398138843566 q^{97} + 118861332531788 q^{99}+O(q^{100}) \) 14 * q + 4394 * q^3 - 114688 * q^4 + 69758 * q^5 + 11016572 * q^9 + 20143042 * q^11 - 35995648 * q^12 + 62814720 * q^14 - 1359602 * q^15 + 939524096 * q^16 - 571457536 * q^20 - 2107666944 * q^22 - 7305755542 * q^23 + 19291879452 * q^25 - 6388480512 * q^26 + 34093422830 * q^27 - 33569873942 * q^31 + 2885838062 * q^33 + 167764701696 * q^34 - 90247757824 * q^36 + 73167823966 * q^37 + 71236111872 * q^38 - 222695314944 * q^42 - 165011800064 * q^44 + 2000205168616 * q^45 - 1612717386124 * q^47 + 294876348416 * q^48 + 3424602524990 * q^49 - 3530064068164 * q^53 - 3715439610854 * q^55 - 514578186240 * q^56 - 1374208002048 * q^58 - 818496564070 * q^59 + 11137859584 * q^60 - 7696581394432 * q^64 - 5938395621888 * q^66 + 16485465276922 * q^67 - 11394452631206 * q^69 - 392146020864 * q^70 - 19380879179878 * q^71 + 23016770893992 * q^75 + 60534793808304 * q^77 + 17335823992320 * q^78 + 4681380134912 * q^80 - 10394309810662 * q^81 - 79417078012416 * q^82 + 6375532305408 * q^86 + 17266007605248 * q^88 - 117770741987650 * q^89 + 150621364097712 * q^91 + 59848749400064 * q^92 + 27345122803162 * q^93 + 123398138843566 * q^97 + 118861332531788 * q^99

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