LMFDB - Embedded newform 6.19.b.a.5.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6,19,Mod(5,6)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 19, names="a")

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

chi := DirichletCharacter("6.5");

S:= CuspForms(chi, 19);

N := Newforms(S);

Level:	$ N $	$=$	$ 6 = 2 \cdot 3 $
Weight:	$ k $	$=$	$ 19 $
Character orbit:	$[\chi]$	$=$	6.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:	$12.3231682626$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 8797x^{4} + 1809980x^{3} + 107861490x^{2} - 7180095600x + 788142376800 $ x^6 - 2x^5 - 8797x^4 + 1809980x^3 + 107861490x^2 - 7180095600*x + 788142376800
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{31}\cdot 3^{14} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.6
Root			$-112.126 + 31.1763i$ of defining polynomial
Character	$\chi$	$=$	6.5
Dual form			6.19.b.a.5.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+362.039i q^{2} +(19502.4 - 2660.56i) q^{3} -131072. q^{4} +1.30525e6i q^{5} +(963226. + 7.06061e6i) q^{6} +3.15845e7 q^{7} -4.74531e7i q^{8} +(3.73263e8 - 1.03774e8i) q^{9} +O(q^{10})$	\(q+362.039i q^{2} +(19502.4 - 2660.56i) q^{3} -131072. q^{4} +1.30525e6i q^{5} +(963226. + 7.06061e6i) q^{6} +3.15845e7 q^{7} -4.74531e7i q^{8} +(3.73263e8 - 1.03774e8i) q^{9} -4.72550e8 q^{10} +3.81148e9i q^{11} +(-2.55621e9 + 3.48725e8i) q^{12} -5.50456e9 q^{13} +1.14348e10i q^{14} +(3.47269e9 + 2.54554e10i) q^{15} +1.71799e10 q^{16} +1.95721e11i q^{17} +(3.75704e10 + 1.35136e11i) q^{18} -1.56485e11 q^{19} -1.71081e11i q^{20} +(6.15971e11 - 8.40324e10i) q^{21} -1.37990e12 q^{22} -1.49039e12i q^{23} +(-1.26252e11 - 9.25448e11i) q^{24} +2.11102e12 q^{25} -1.99286e12i q^{26} +(7.00342e12 - 3.01694e12i) q^{27} -4.13984e12 q^{28} -7.21871e12i q^{29} +(-9.21584e12 + 1.25725e12i) q^{30} +3.81624e12 q^{31} +6.21978e12i q^{32} +(1.01407e13 + 7.43328e13i) q^{33} -7.08587e13 q^{34} +4.12256e13i q^{35} +(-4.89244e13 + 1.36019e13i) q^{36} +2.50324e14 q^{37} -5.66536e13i q^{38} +(-1.07352e14 + 1.46452e13i) q^{39} +6.19381e13 q^{40} -4.39043e14i q^{41} +(3.04230e13 + 2.23005e14i) q^{42} -5.41174e14 q^{43} -4.99578e14i q^{44} +(1.35451e14 + 4.87201e14i) q^{45} +5.39578e14 q^{46} -1.94037e15i q^{47} +(3.35048e14 - 4.57081e13i) q^{48} -6.30835e14 q^{49} +7.64273e14i q^{50} +(5.20729e14 + 3.81703e15i) q^{51} +7.21494e14 q^{52} +1.53546e15i q^{53} +(1.09225e15 + 2.53551e15i) q^{54} -4.97492e15 q^{55} -1.49878e15i q^{56} +(-3.05182e15 + 4.16338e14i) q^{57} +2.61345e15 q^{58} -6.50072e15i q^{59} +(-4.55173e14 - 3.33649e15i) q^{60} +3.87413e15 q^{61} +1.38163e15i q^{62} +(1.17893e16 - 3.27766e15i) q^{63} -2.25180e15 q^{64} -7.18482e15i q^{65} +(-2.69113e16 + 3.67131e15i) q^{66} +3.71114e16 q^{67} -2.56536e16i q^{68} +(-3.96527e15 - 2.90661e16i) q^{69} -1.49252e16 q^{70} +6.33282e16i q^{71} +(-4.92442e15 - 1.77125e16i) q^{72} -5.51216e16 q^{73} +9.06269e16i q^{74} +(4.11700e16 - 5.61651e15i) q^{75} +2.05108e16 q^{76} +1.20383e17i q^{77} +(-5.30214e15 - 3.88655e16i) q^{78} -7.16429e16 q^{79} +2.24240e16i q^{80} +(1.28556e17 - 7.74704e16i) q^{81} +1.58951e17 q^{82} -1.18877e17i q^{83} +(-8.07366e16 + 1.10143e16i) q^{84} -2.55465e17 q^{85} -1.95926e17i q^{86} +(-1.92058e16 - 1.40782e17i) q^{87} +1.80867e17 q^{88} -9.49218e16i q^{89} +(-1.76386e17 + 4.90386e16i) q^{90} -1.73859e17 q^{91} +1.95348e17i q^{92} +(7.44258e16 - 1.01534e16i) q^{93} +7.02490e17 q^{94} -2.04252e17i q^{95} +(1.65481e16 + 1.21300e17i) q^{96} -3.38927e17 q^{97} -2.28387e17i q^{98} +(3.95534e17 + 1.42268e18i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6258 q^{3} - 786432 q^{4} - 15753216 q^{6} + 28233804 q^{7} + 695971638 q^{9}+O(q^{10}) $ 6 * q - 6258 * q^3 - 786432 * q^4 - 15753216 * q^6 + 28233804 * q^7 + 695971638 * q^9	$ 6 q - 6258 q^{3} - 786432 q^{4} - 15753216 q^{6} + 28233804 q^{7} + 695971638 q^{9} - 434257920 q^{10} + 820248576 q^{12} + 29566196220 q^{13} + 119627095680 q^{15} + 103079215104 q^{16} + 315939373056 q^{18} - 438814047012 q^{19} + 2876527406172 q^{21} - 2844452929536 q^{22} + 2064805527552 q^{24} - 25696048717290 q^{25} + 11197265522814 q^{27} - 3700661157888 q^{28} + 13072787619840 q^{30} + 21775814927148 q^{31} - 962560003968 q^{33} + 99067611119616 q^{34} - 91222394535936 q^{36} + 638446564817436 q^{37} - 736541155104180 q^{39} + 56919054090240 q^{40} - 203954622480384 q^{42} - 16\!\cdots\!52 q^{43}+ \cdots + 76\!\cdots\!72 q^{99}+O(q^{100}) $ 6 * q - 6258 * q^3 - 786432 * q^4 - 15753216 * q^6 + 28233804 * q^7 + 695971638 * q^9 - 434257920 * q^10 + 820248576 * q^12 + 29566196220 * q^13 + 119627095680 * q^15 + 103079215104 * q^16 + 315939373056 * q^18 - 438814047012 * q^19 + 2876527406172 * q^21 - 2844452929536 * q^22 + 2064805527552 * q^24 - 25696048717290 * q^25 + 11197265522814 * q^27 - 3700661157888 * q^28 + 13072787619840 * q^30 + 21775814927148 * q^31 - 962560003968 * q^33 + 99067611119616 * q^34 - 91222394535936 * q^36 + 638446564817436 * q^37 - 736541155104180 * q^39 + 56919054090240 * q^40 - 203954622480384 * q^42 - 1688313718883652 * q^43 + 390590504075520 * q^45 + 1979247919104 * q^46 - 107511621353472 * q^48 - 895767896448270 * q^49 + 9636273526722048 * q^51 - 3875300470947840 * q^52 + 2993011804200960 * q^54 - 1259959207783680 * q^55 + 4023767318253996 * q^57 + 21251172660756480 * q^58 - 15679762684968960 * q^60 - 16279597277700036 * q^61 - 32525159214131028 * q^63 - 13510798882111488 * q^64 - 60047751762690048 * q^66 + 11153724314613276 * q^67 + 3612037794746112 * q^69 + 161904998736691200 * q^70 - 41410805505196032 * q^72 - 78910243347781140 * q^73 + 348225828845090910 * q^75 + 57516234769956864 * q^76 - 168903906208235520 * q^78 - 476518976428926228 * q^79 + 630680446106425062 * q^81 + 396536393269149696 * q^82 - 377032200181776384 * q^84 - 967978669078932480 * q^85 + 419256510981966720 * q^87 + 372828134380142592 * q^88 - 2046848246643179520 * q^90 - 1032060167365562760 * q^91 + 764294136047005116 * q^93 + 2566175766871080960 * q^94 - 270638190107295744 * q^96 + 834695417243310348 * q^97 + 761688154713814272 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/6\mathbb{Z}\right)^\times$.

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

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 $

$2$			362.039i			0.707107i
$2$			362.039i			0.707107i
$3$	19502.4	−	2660.56i	0.990822	−	0.135171i
$3$	19502.4	−	2660.56i	0.990822	−	0.135171i
$4$	−131072.			−0.500000
$5$			1.30525e6i			0.668287i	0.942522	+	0.334143i	$0.108447\pi$
$5$			1.30525e6i			0.668287i	−0.942522	+	0.334143i	$0.891553\pi$
$6$	963226.	+	7.06061e6i	0.0955800	+	0.700617i
$7$	3.15845e7			0.782692			0.391346	−	0.920244i	$-0.372009\pi$
$7$	3.15845e7			0.782692			0.391346	+	0.920244i	$0.372009\pi$
$8$		−	4.74531e7i		−	0.353553i
$9$	3.73263e8	−	1.03774e8i	0.963458	−	0.267860i
$10$	−4.72550e8			−0.472550
$11$			3.81148e9i			1.61644i	0.588882	+	0.808219i	$0.299568\pi$
$11$			3.81148e9i			1.61644i	−0.588882	+	0.808219i	$0.700432\pi$
$12$	−2.55621e9	+	3.48725e8i	−0.495411	+	0.0675853i
$13$	−5.50456e9			−0.519078			−0.259539	−	0.965733i	$-0.583571\pi$
$13$	−5.50456e9			−0.519078			−0.259539	+	0.965733i	$0.583571\pi$
$14$			1.14348e10i			0.553447i
$15$	3.47269e9	+	2.54554e10i	0.0903327	+	0.662154i
$16$	1.71799e10			0.250000
$17$			1.95721e11i			1.65043i	0.564816	+	0.825217i	$0.308947\pi$
$17$			1.95721e11i			1.65043i	−0.564816	+	0.825217i	$0.691053\pi$
$18$	3.75704e10	+	1.35136e11i	0.189406	+	0.681268i
$19$	−1.56485e11			−0.484942			−0.242471	−	0.970159i	$-0.577958\pi$
$19$	−1.56485e11			−0.484942			−0.242471	+	0.970159i	$0.577958\pi$
$20$		−	1.71081e11i		−	0.334143i
$21$	6.15971e11	−	8.40324e10i	0.775509	−	0.105797i
$22$	−1.37990e12			−1.14299
$23$		−	1.49039e12i		−	0.827463i	−0.910399	−	0.413732i	$-0.864225\pi$
$23$		−	1.49039e12i		−	0.827463i	0.910399	−	0.413732i	$-0.135775\pi$
$24$	−1.26252e11	−	9.25448e11i	−0.0477900	−	0.350309i
$25$	2.11102e12			0.553392
$26$		−	1.99286e12i		−	0.367044i
$27$	7.00342e12	−	3.01694e12i	0.918409	−	0.395633i
$28$	−4.13984e12			−0.391346
$29$		−	7.21871e12i		−	0.497597i	−0.968555	−	0.248799i	$-0.919964\pi$
$29$		−	7.21871e12i		−	0.497597i	0.968555	−	0.248799i	$-0.0800357\pi$
$30$	−9.21584e12	+	1.25725e12i	−0.468213	+	0.0638749i
$31$	3.81624e12			0.144338			0.0721690	−	0.997392i	$-0.477008\pi$
$31$	3.81624e12			0.144338			0.0721690	+	0.997392i	$0.477008\pi$
$32$			6.21978e12i			0.176777i
$33$	1.01407e13	+	7.43328e13i	0.218495	+	1.60160i
$34$	−7.08587e13			−1.16703
$35$			4.12256e13i			0.523063i
$36$	−4.89244e13	+	1.36019e13i	−0.481729	+	0.133930i
$37$	2.50324e14			1.92614			0.963068	−	0.269260i	$-0.0867791\pi$
$37$	2.50324e14			1.92614			0.963068	+	0.269260i	$0.0867791\pi$
$38$		−	5.66536e13i		−	0.342906i
$39$	−1.07352e14	+	1.46452e13i	−0.514314	+	0.0701641i
$40$	6.19381e13			0.236275
$41$		−	4.39043e14i		−	1.34107i	−0.741876	−	0.670537i	$-0.766064\pi$
$41$		−	4.39043e14i		−	1.34107i	0.741876	−	0.670537i	$-0.233936\pi$
$42$	3.04230e13	+	2.23005e14i	0.0748098	+	0.548368i
$43$	−5.41174e14			−1.07676			−0.538382	−	0.842701i	$-0.680964\pi$
$43$	−5.41174e14			−1.07676			−0.538382	+	0.842701i	$0.680964\pi$
$44$		−	4.99578e14i		−	0.808219i
$45$	1.35451e14	+	4.87201e14i	0.179007	+	0.643866i
$46$	5.39578e14			0.585105
$47$		−	1.94037e15i		−	1.73382i	−0.498464	−	0.866911i	$-0.666102\pi$
$47$		−	1.94037e15i		−	1.73382i	0.498464	−	0.866911i	$-0.333898\pi$
$48$	3.35048e14	−	4.57081e13i	0.247706	−	0.0337926i
$49$	−6.30835e14			−0.387392
$50$			7.64273e14i			0.391308i
$51$	5.20729e14	+	3.81703e15i	0.223090	+	1.63529i
$52$	7.21494e14			0.259539
$53$			1.53546e15i			0.465325i	0.972558	+	0.232663i	$0.0747438\pi$
$53$			1.53546e15i			0.465325i	−0.972558	+	0.232663i	$0.925256\pi$
$54$	1.09225e15	+	2.53551e15i	0.279755	+	0.649413i
$55$	−4.97492e15			−1.08024
$56$		−	1.49878e15i		−	0.276724i
$57$	−3.05182e15	+	4.16338e14i	−0.480492	+	0.0655499i
$58$	2.61345e15			0.351854
$59$		−	6.50072e15i		−	0.750401i	−0.926944	−	0.375201i	$-0.877574\pi$
$59$		−	6.50072e15i		−	0.750401i	0.926944	−	0.375201i	$-0.122426\pi$
$60$	−4.55173e14	−	3.33649e15i	−0.0451664	−	0.331077i
$61$	3.87413e15			0.331288			0.165644	−	0.986186i	$-0.447030\pi$
$61$	3.87413e15			0.331288			0.165644	+	0.986186i	$0.447030\pi$
$62$			1.38163e15i			0.102062i
$63$	1.17893e16	−	3.27766e15i	0.754091	−	0.209652i
$64$	−2.25180e15			−0.125000
$65$		−	7.18482e15i		−	0.346893i
$66$	−2.69113e16	+	3.67131e15i	−1.13250	+	0.154499i
$67$	3.71114e16			1.36406			0.682032	−	0.731322i	$-0.261097\pi$
$67$	3.71114e16			1.36406			0.682032	+	0.731322i	$0.261097\pi$
$68$		−	2.56536e16i		−	0.825217i
$69$	−3.96527e15	−	2.90661e16i	−0.111849	−	0.819869i
$70$	−1.49252e16			−0.369862
$71$			6.33282e16i			1.38125i	0.723214	+	0.690624i	$0.242664\pi$
$71$			6.33282e16i			1.38125i	−0.723214	+	0.690624i	$0.757336\pi$
$72$	−4.92442e15	−	1.77125e16i	−0.0947028	−	0.340634i
$73$	−5.51216e16			−0.936302			−0.468151	−	0.883648i	$-0.655080\pi$
$73$	−5.51216e16			−0.936302			−0.468151	+	0.883648i	$0.655080\pi$
$74$			9.06269e16i			1.36198i
$75$	4.11700e16	−	5.61651e15i	0.548314	−	0.0748024i
$76$	2.05108e16			0.242471
$77$			1.20383e17i			1.26517i
$78$	−5.30214e15	−	3.88655e16i	−0.0496135	−	0.363675i
$79$	−7.16429e16			−0.597763			−0.298882	−	0.954290i	$-0.596614\pi$
$79$	−7.16429e16			−0.597763			−0.298882	+	0.954290i	$0.596614\pi$
$80$			2.24240e16i			0.167072i
$81$	1.28556e17	−	7.74704e16i	0.856502	−	0.516144i
$82$	1.58951e17			0.948283
$83$		−	1.18877e17i		−	0.635911i	−0.948106	−	0.317956i	$-0.897004\pi$
$83$		−	1.18877e17i		−	0.635911i	0.948106	−	0.317956i	$-0.102996\pi$
$84$	−8.07366e16	+	1.10143e16i	−0.387755	+	0.0528985i
$85$	−2.55465e17			−1.10296
$86$		−	1.95926e17i		−	0.761388i
$87$	−1.92058e16	−	1.40782e17i	−0.0672605	−	0.493030i
$88$	1.80867e17			0.571497
$89$		−	9.49218e16i		−	0.270929i	−0.990782	−	0.135465i	$-0.956747\pi$
$89$		−	9.49218e16i		−	0.270929i	0.990782	−	0.135465i	$-0.0432527\pi$
$90$	−1.76386e17	+	4.90386e16i	−0.455282	+	0.126577i
$91$	−1.73859e17			−0.406278
$92$			1.95348e17i			0.413732i
$93$	7.44258e16	−	1.01534e16i	0.143013	−	0.0195103i
$94$	7.02490e17			1.22600
$95$		−	2.04252e17i		−	0.324081i
$96$	1.65481e16	+	1.21300e17i	0.0238950	+	0.175154i
$97$	−3.38927e17			−0.445821			−0.222910	−	0.974839i	$-0.571556\pi$
$97$	−3.38927e17			−0.445821			−0.222910	+	0.974839i	$0.571556\pi$
$98$		−	2.28387e17i		−	0.273928i
$99$	3.95534e17	+	1.42268e18i	0.432979	+	1.55737i
$100$	−2.76696e17			−0.276696
$101$			2.06526e17i			0.188835i	0.995533	+	0.0944176i	$0.0300989\pi$
$101$			2.06526e17i			0.188835i	−0.995533	+	0.0944176i	$0.969901\pi$
$102$	−1.38191e18	+	1.88524e17i	−1.15632	+	0.157748i
$103$	1.06701e18			0.817772			0.408886	−	0.912585i	$-0.365917\pi$
$103$	1.06701e18			0.817772			0.408886	+	0.912585i	$0.365917\pi$
$104$			2.61209e17i			0.183522i
$105$	1.09683e17	+	8.03996e17i	0.0707027	+	0.518263i
$106$	−5.55897e17			−0.329035
$107$		−	8.00886e17i		−	0.435629i	−0.975990	−	0.217814i	$-0.930107\pi$
$107$		−	8.00886e17i		−	0.435629i	0.975990	−	0.217814i	$-0.0698928\pi$
$108$	−9.17952e17	+	3.95436e17i	−0.459204	+	0.197816i
$109$	−2.27655e18			−1.04819			−0.524094	−	0.851660i	$-0.675596\pi$
$109$	−2.27655e18			−1.04819			−0.524094	+	0.851660i	$0.675596\pi$
$110$		−	1.80111e18i		−	0.763848i
$111$	4.88191e18	−	6.66002e17i	1.90846	−	0.260357i
$112$	5.42617e17			0.195673
$113$		−	5.22481e18i		−	1.73926i	−0.493703	−	0.869630i	$-0.664357\pi$
$113$		−	5.22481e18i		−	1.73926i	0.493703	−	0.869630i	$-0.335643\pi$
$114$	−1.50730e17	−	1.10488e18i	−0.0463508	−	0.339759i
$115$	1.94533e18			0.552983
$116$			9.46171e17i			0.248799i
$117$	−2.05465e18	+	5.71233e17i	−0.500110	+	0.139040i
$118$	2.35351e18			0.530614
$119$			6.18176e18i			1.29178i
$120$	1.20794e18	−	1.64790e17i	0.234107	−	0.0319374i
$121$	−8.96744e18			−1.61287
$122$			1.40258e18i			0.234256i
$123$	−1.16810e18	−	8.56238e18i	−0.181274	−	1.32877i
$124$	−5.00203e17			−0.0721690
$125$			7.73454e18i			1.03811i
$126$	1.18664e18	+	4.26819e18i	0.148246	+	0.533223i
$127$	1.03674e19			1.20625			0.603123	−	0.797648i	$-0.293923\pi$
$127$	1.03674e19			1.20625			0.603123	+	0.797648i	$0.293923\pi$
$128$		−	8.15239e17i		−	0.0883883i
$129$	−1.05542e19	+	1.43983e18i	−1.06688	+	0.145547i
$130$	2.60118e18			0.245290
$131$			7.19901e18i			0.633623i	0.948488	+	0.316812i	$0.102612\pi$
$131$			7.19901e18i			0.633623i	−0.948488	+	0.316812i	$0.897388\pi$
$132$	−1.32916e18	−	9.74295e18i	−0.109247	−	0.800802i
$133$	−4.94249e18			−0.379561
$134$			1.34358e19i			0.964539i
$135$	3.93785e18	+	9.14119e18i	0.264396	+	0.613761i
$136$	9.28760e18			0.583516
$137$		−	3.99891e18i		−	0.235210i	−0.993060	−	0.117605i	$-0.962478\pi$
$137$		−	3.99891e18i		−	0.235210i	0.993060	−	0.117605i	$-0.0375217\pi$
$138$	1.05230e19	−	1.43558e18i	0.579735	−	0.0790889i
$139$	2.78138e18			0.143591			0.0717956	−	0.997419i	$-0.477127\pi$
$139$	2.78138e18			0.143591			0.0717956	+	0.997419i	$0.477127\pi$
$140$		−	5.40352e18i		−	0.261532i
$141$	−5.16248e18	−	3.78418e19i	−0.234362	−	1.71791i
$142$	−2.29272e19			−0.976690
$143$		−	2.09805e19i		−	0.839057i
$144$	6.41261e18	−	1.78283e18i	0.240864	−	0.0669650i
$145$	9.42221e18			0.332538
$146$		−	1.99561e19i		−	0.662066i
$147$	−1.23028e19	+	1.67838e18i	−0.383837	+	0.0523641i
$148$	−3.28104e19			−0.963068
$149$			1.35043e19i			0.373074i	0.982448	+	0.186537i	$0.0597264\pi$
$149$			1.35043e19i			0.373074i	−0.982448	+	0.186537i	$0.940274\pi$
$150$	2.03339e18	+	1.49051e19i	0.0528933	+	0.387716i
$151$	6.29355e19			1.54207			0.771034	−	0.636794i	$-0.219740\pi$
$151$	6.29355e19			1.54207			0.771034	+	0.636794i	$0.219740\pi$
$152$			7.42570e18i			0.171453i
$153$	2.03109e19	+	7.30556e19i	0.442085	+	1.59012i
$154$	−4.35835e19			−0.894613
$155$			4.98115e18i			0.0964593i
$156$	1.40708e19	−	1.91958e18i	0.257157	−	0.0350820i
$157$	−1.52297e19			−0.262781			−0.131391	−	0.991331i	$-0.541944\pi$
$157$	−1.52297e19			−0.262781			−0.131391	+	0.991331i	$0.541944\pi$
$158$		−	2.59375e19i		−	0.422683i
$159$	4.08519e18	+	2.99451e19i	0.0628983	+	0.461055i
$160$	−8.11835e18			−0.118138
$161$		−	4.70731e19i		−	0.647649i
$162$	2.80473e19	+	4.65424e19i	0.364969	+	0.605638i
$163$	2.05524e19			0.253032			0.126516	−	0.991965i	$-0.459621\pi$
$163$	2.05524e19			0.253032			0.126516	+	0.991965i	$0.459621\pi$
$164$			5.75463e19i			0.670537i
$165$	−9.70227e19	+	1.32361e19i	−1.07033	+	0.146017i
$166$	4.30382e19			0.449657
$167$		−	9.65270e18i		−	0.0955434i	−0.998858	−	0.0477717i	$-0.984788\pi$
$167$		−	9.65270e18i		−	0.0955434i	0.998858	−	0.0477717i	$-0.0152120\pi$
$168$	−3.98760e18	−	2.92298e19i	−0.0374049	−	0.274184i
$169$	−8.21552e19			−0.730558
$170$		−	9.24882e19i		−	0.779913i
$171$	−5.84101e19	+	1.62391e19i	−0.467221	+	0.129897i
$172$	7.09328e19			0.538382
$173$		−	8.60111e19i		−	0.619640i	−0.950795	−	0.309820i	$-0.899731\pi$
$173$		−	8.60111e19i		−	0.619640i	0.950795	−	0.309820i	$-0.100269\pi$
$174$	5.09685e19	−	6.95326e18i	0.348625	−	0.0475603i
$175$	6.66756e19			0.433136
$176$			6.54807e19i			0.404110i
$177$	−1.72956e19	−	1.26779e20i	−0.101432	−	0.743514i
$178$	3.43654e19			0.191576
$179$		−	1.49036e20i		−	0.789977i	−0.918686	−	0.394988i	$-0.870749\pi$
$179$		−	1.49036e20i		−	0.789977i	0.918686	−	0.394988i	$-0.129251\pi$
$180$	−1.77539e19	−	6.38584e19i	−0.0895037	−	0.321933i
$181$	2.50765e20			1.20271			0.601354	−	0.798983i	$-0.294628\pi$
$181$	2.50765e20			1.20271			0.601354	+	0.798983i	$0.294628\pi$
$182$		−	6.29436e19i		−	0.287282i
$183$	7.55547e19	−	1.03074e19i	0.328248	−	0.0447804i
$184$	−7.07235e19			−0.292552
$185$			3.26735e20i			1.28721i
$186$	3.67591e18	+	2.69450e19i	0.0137958	+	0.101126i
$187$	−7.45988e20			−2.66782
$188$			2.54328e20i			0.866911i
$189$	2.21199e20	−	9.52883e19i	0.718832	−	0.309659i
$190$	7.39470e19			0.229160
$191$			4.59540e20i			1.35839i	0.733959	+	0.679193i	$0.237670\pi$
$191$			4.59540e20i			1.35839i	−0.733959	+	0.679193i	$0.762330\pi$
$192$	−4.39154e19	+	5.99105e18i	−0.123853	+	0.0168963i
$193$	7.00243e19			0.188466			0.0942330	−	0.995550i	$-0.469960\pi$
$193$	7.00243e19			0.188466			0.0942330	+	0.995550i	$0.469960\pi$
$194$		−	1.22705e20i		−	0.315243i
$195$	−1.91157e19	−	1.40121e20i	−0.0468897	−	0.343709i
$196$	8.26848e19			0.193696
$197$			3.14404e20i			0.703545i	0.936086	+	0.351772i	$0.114421\pi$
$197$			3.14404e20i			0.703545i	−0.936086	+	0.351772i	$0.885579\pi$
$198$	−5.15067e20	+	1.43199e20i	−1.10123	+	0.306162i
$199$	1.46711e20			0.299768			0.149884	−	0.988704i	$-0.452110\pi$
$199$	1.46711e20			0.299768			0.149884	+	0.988704i	$0.452110\pi$
$200$		−	1.00175e20i		−	0.195654i
$201$	7.23761e20	−	9.87373e19i	1.35154	−	0.184381i
$202$	−7.47705e19			−0.133527
$203$		−	2.27999e20i		−	0.389466i
$204$	−6.82530e19	−	5.00306e20i	−0.111545	−	0.817643i
$205$	5.73061e20			0.896222
$206$			3.86298e20i			0.578252i
$207$	−1.54664e20	−	5.56307e20i	−0.221644	−	0.797226i
$208$	−9.45677e19			−0.129769
$209$		−	5.96438e20i		−	0.783879i
$210$	−2.91077e20	+	3.97095e19i	−0.366467	+	0.0499944i
$211$	−5.46493e20			−0.659239			−0.329619	−	0.944114i	$-0.606920\pi$
$211$	−5.46493e20			−0.659239			−0.329619	+	0.944114i	$0.606920\pi$
$212$		−	2.01256e20i		−	0.232663i
$213$	1.68488e20	+	1.23505e21i	0.186704	+	1.36857i
$214$	2.89952e20			0.308036
$215$		−	7.06366e20i		−	0.719588i
$216$	−1.43163e20	−	3.32334e20i	−0.139877	−	0.324707i
$217$	1.20534e20			0.112972
$218$		−	8.24200e20i		−	0.741181i
$219$	−1.07500e21	+	1.46654e20i	−0.927709	+	0.126560i
$220$	6.52073e20			0.540122
$221$		−	1.07736e21i		−	0.856704i
$222$	2.41119e20	+	1.76744e21i	0.184100	+	1.34948i
$223$	−1.21601e21			−0.891648			−0.445824	−	0.895121i	$-0.647089\pi$
$223$	−1.21601e21			−0.891648			−0.445824	+	0.895121i	$0.647089\pi$
$224$			1.96448e20i			0.138362i
$225$	7.87968e20	−	2.19070e20i	0.533170	−	0.148232i
$226$	1.89158e21			1.22984
$227$			1.82295e21i			1.13905i	0.821974	+	0.569524i	$0.192873\pi$
$227$			1.82295e21i			1.13905i	−0.821974	+	0.569524i	$0.807127\pi$
$228$	4.00009e20	−	5.45702e19i	0.240246	−	0.0327749i
$229$	−1.70915e21			−0.986872			−0.493436	−	0.869782i	$-0.664259\pi$
$229$	−1.70915e21			−0.986872			−0.493436	+	0.869782i	$0.664259\pi$
$230$			7.04283e20i			0.391018i
$231$	3.20288e20	+	2.34776e21i	0.171014	+	1.25356i
$232$	−3.42551e20			−0.175927
$233$			7.67655e20i			0.379283i	0.981853	+	0.189641i	$0.0607325\pi$
$233$			7.67655e20i			0.379283i	−0.981853	+	0.189641i	$0.939267\pi$
$234$	−2.06808e20	−	7.43863e20i	−0.0983163	−	0.353631i
$235$	2.53267e21			1.15869
$236$			8.52063e20i			0.375201i
$237$	−1.39721e21	+	1.90610e20i	−0.592277	+	0.0808000i
$238$	−2.23804e21			−0.913428
$239$		−	2.79282e21i		−	1.09765i	−0.835938	−	0.548823i	$-0.815076\pi$
$239$		−	2.79282e21i		−	1.09765i	0.835938	−	0.548823i	$-0.184924\pi$
$240$	5.96604e19	+	4.37321e20i	0.0225832	+	0.165538i
$241$	−2.42709e21			−0.884979			−0.442490	−	0.896774i	$-0.645905\pi$
$241$	−2.42709e21			−0.884979			−0.442490	+	0.896774i	$0.645905\pi$
$242$		−	3.24656e21i		−	1.14047i
$243$	2.30104e21	−	1.85289e21i	0.778874	−	0.627180i
$244$	−5.07790e20			−0.165644
$245$		−	8.23396e20i		−	0.258889i
$246$	3.09991e21	−	4.22898e20i	0.939580	−	0.128180i
$247$	8.61381e20			0.251723
$248$		−	1.81093e20i		−	0.0510312i
$249$	−3.16281e20	−	2.31839e21i	−0.0859565	−	0.630075i
$250$	−2.80020e21			−0.734056
$251$		−	6.90800e20i		−	0.174698i	−0.996178	−	0.0873492i	$-0.972160\pi$
$251$		−	6.90800e20i		−	0.174698i	0.996178	−	0.0873492i	$-0.0278396\pi$
$252$	−1.54525e21	+	4.29610e20i	−0.377046	+	0.104826i
$253$	5.68058e21			1.33754
$254$			3.75340e21i			0.852945i
$255$	−4.98217e21	+	6.79680e20i	−1.09284	+	0.149088i
$256$	2.95148e20			0.0625000
$257$			4.00679e21i			0.819216i	0.912262	+	0.409608i	$0.134334\pi$
$257$			4.00679e21i			0.819216i	−0.912262	+	0.409608i	$0.865666\pi$
$258$	−5.21273e20	−	3.82102e21i	−0.102917	−	0.754400i
$259$	7.90635e21			1.50757
$260$			9.41729e20i			0.173447i
$261$	−7.49118e20	−	2.69448e21i	−0.133286	−	0.479414i
$262$	−2.60632e21			−0.448039
$263$			3.40224e21i			0.565149i	0.959245	+	0.282575i	$0.0911885\pi$
$263$			3.40224e21i			0.565149i	−0.959245	+	0.282575i	$0.908812\pi$
$264$	3.52732e21	−	4.81207e20i	0.566252	−	0.0772496i
$265$	−2.00416e21			−0.310971
$266$		−	1.78937e21i		−	0.268390i
$267$	−2.52545e20	−	1.85120e21i	−0.0366217	−	0.268443i
$268$	−4.86427e21			−0.682032
$269$			8.26566e21i			1.12075i	0.828241	+	0.560373i	$0.189342\pi$
$269$			8.26566e21i			1.12075i	−0.828241	+	0.560373i	$0.810658\pi$
$270$	−3.30947e21	+	1.42565e21i	−0.433994	+	0.186956i
$271$	−6.07257e20			−0.0770280			−0.0385140	−	0.999258i	$-0.512262\pi$
$271$	−6.07257e20			−0.0770280			−0.0385140	+	0.999258i	$0.512262\pi$
$272$			3.36247e21i			0.412608i
$273$	−3.39065e21	+	4.62562e20i	−0.402550	+	0.0549169i
$274$	1.44776e21			0.166319
$275$			8.04612e21i			0.894525i
$276$	5.19736e20	+	3.80975e21i	0.0559243	+	0.409934i
$277$	−7.76370e21			−0.808632			−0.404316	−	0.914619i	$-0.632490\pi$
$277$	−7.76370e21			−0.808632			−0.404316	+	0.914619i	$0.632490\pi$
$278$			1.00697e21i			0.101534i
$279$	1.42446e21	−	3.96029e20i	0.139064	−	0.0386624i
$280$	1.95628e21			0.184931
$281$		−	1.12811e22i		−	1.03274i	−0.856364	−	0.516372i	$-0.827282\pi$
$281$		−	1.12811e22i		−	1.03274i	0.856364	−	0.516372i	$-0.172718\pi$
$282$	1.37002e22	−	1.86902e21i	1.21474	−	0.165719i
$283$	1.16922e22			1.00419			0.502096	−	0.864812i	$-0.332562\pi$
$283$	1.16922e22			1.00419			0.502096	+	0.864812i	$0.332562\pi$
$284$		−	8.30055e21i		−	0.690624i
$285$	−5.43424e20	−	3.98339e21i	−0.0438061	−	0.321106i
$286$	7.59576e21			0.593303
$287$		−	1.38670e22i		−	1.04965i
$288$	6.45454e20	+	2.32161e21i	0.0473514	+	0.170317i
$289$	−2.42438e22			−1.72393
$290$			3.41121e21i			0.235140i
$291$	−6.60987e21	+	9.01735e20i	−0.441729	+	0.0602618i
$292$	7.22490e21			0.468151
$293$		−	2.56349e22i		−	1.61073i	−0.592777	−	0.805367i	$-0.701968\pi$
$293$		−	2.56349e22i		−	1.61073i	0.592777	−	0.805367i	$-0.298032\pi$
$294$	−6.07637e20	−	4.45408e21i	−0.0370270	−	0.271414i
$295$	8.48505e21			0.501483
$296$		−	1.18787e22i		−	0.680992i
$297$	1.14990e22	+	2.66934e22i	0.639516	+	1.48455i
$298$	−4.88907e21			−0.263803
$299$			8.20393e21i			0.429518i
$300$	−5.39623e21	+	7.36167e20i	−0.274157	+	0.0374012i
$301$	−1.70927e22			−0.842776
$302$			2.27851e22i			1.09041i
$303$	5.49476e20	+	4.02775e21i	0.0255250	+	0.187102i
$304$	−2.68839e21			−0.121236
$305$			5.05670e21i			0.221395i
$306$	−2.64490e22	+	7.35333e21i	−1.12439	+	0.312601i
$307$	1.11726e22			0.461221			0.230610	−	0.973046i	$-0.425928\pi$
$307$	1.11726e22			0.461221			0.230610	+	0.973046i	$0.425928\pi$
$308$		−	1.57789e22i		−	0.632587i
$309$	2.08092e22	−	2.83884e21i	0.810267	−	0.110539i
$310$	−1.80337e21			−0.0682070
$311$		−	2.40165e21i		−	0.0882403i	−0.999026	−	0.0441202i	$-0.985952\pi$
$311$		−	2.40165e21i		−	0.0882403i	0.999026	−	0.0441202i	$-0.0140484\pi$
$312$	6.94962e20	+	5.09419e21i	0.0248067	+	0.181837i
$313$	7.63802e21			0.264900			0.132450	−	0.991190i	$-0.457716\pi$
$313$	7.63802e21			0.264900			0.132450	+	0.991190i	$0.457716\pi$
$314$		−	5.51374e21i		−	0.185815i
$315$	4.27816e21	+	1.53880e22i	0.140108	+	0.503949i
$316$	9.39038e21			0.298882
$317$			5.61795e22i			1.73798i	0.494830	+	0.868990i	$0.335230\pi$
$317$			5.61795e22i			1.73798i	−0.494830	+	0.868990i	$0.664770\pi$
$318$	−1.08413e22	+	1.47900e21i	−0.326015	+	0.0444758i
$319$	2.75140e22			0.804335
$320$		−	2.93916e21i		−	0.0835359i
$321$	−2.13081e21	−	1.56192e22i	−0.0588842	−	0.431631i
$322$	1.70423e22			0.457957
$323$		−	3.06274e22i		−	0.800365i
$324$	−1.68501e22	+	1.01542e22i	−0.428251	+	0.258072i
$325$	−1.16203e22			−0.287254
$326$			7.44077e21i			0.178920i
$327$	−4.43981e22	+	6.05691e21i	−1.03857	+	0.141684i
$328$	−2.08340e22			−0.474141
$329$		−	6.12856e22i		−	1.35705i
$330$	−4.79198e21	−	3.51260e22i	−0.103250	−	0.756838i
$331$	−4.49114e22			−0.941684			−0.470842	−	0.882218i	$-0.656050\pi$
$331$	−4.49114e22			−0.941684			−0.470842	+	0.882218i	$0.656050\pi$
$332$			1.55815e22i			0.317956i
$333$	9.34367e22	−	2.59772e22i	1.85575	−	0.515935i
$334$	3.49465e21			0.0675594
$335$			4.84396e22i			0.911586i
$336$	1.05823e22	−	1.44367e21i	0.193877	−	0.0264492i
$337$	1.02040e22			0.182012			0.0910061	−	0.995850i	$-0.470992\pi$
$337$	1.02040e22			0.182012			0.0910061	+	0.995850i	$0.470992\pi$
$338$		−	2.97434e22i		−	0.516583i
$339$	−1.39009e22	−	1.01896e23i	−0.235097	−	1.72330i
$340$	3.34843e22			0.551482
$341$			1.45455e22i			0.233314i
$342$	−5.87919e21	−	2.11467e22i	−0.0918508	−	0.330375i
$343$	−7.13572e22			−1.08590
$344$			2.56804e22i			0.380694i
$345$	3.79384e22	−	5.17566e21i	0.547908	−	0.0747470i
$346$	3.11394e22			0.438152
$347$			6.29266e22i			0.862718i	0.902180	+	0.431359i	$0.141966\pi$
$347$			6.29266e22i			0.862718i	−0.902180	+	0.431359i	$0.858034\pi$
$348$	2.51735e21	+	1.84526e22i	0.0336302	+	0.246515i
$349$	4.44746e22			0.579006			0.289503	−	0.957177i	$-0.406510\pi$
$349$	4.44746e22			0.579006			0.289503	+	0.957177i	$0.406510\pi$
$350$			2.41391e22i			0.306274i
$351$	−3.85507e22	+	1.66069e22i	−0.476726	+	0.205364i
$352$	−2.37065e22			−0.285749
$353$			1.05940e23i			1.24476i	0.782715	+	0.622380i	$0.213834\pi$
$353$			1.05940e23i			1.24476i	−0.782715	+	0.622380i	$0.786166\pi$
$354$	4.58990e22	−	6.26167e21i	0.525744	−	0.0717233i
$355$	−8.26590e22			−0.923070
$356$			1.24416e22i			0.135465i
$357$	1.64469e22	+	1.20559e23i	0.174611	+	1.27993i
$358$	5.39568e22			0.558598
$359$		−	1.13366e23i		−	1.14455i	−0.820063	−	0.572273i	$-0.806062\pi$
$359$		−	1.13366e23i		−	1.14455i	0.820063	−	0.572273i	$-0.193938\pi$
$360$	2.31192e22	−	6.42759e21i	0.227641	−	0.0632887i
$361$	−7.96398e22			−0.764831
$362$			9.07867e22i			0.850443i
$363$	−1.74886e23	+	2.38584e22i	−1.59807	+	0.218013i
$364$	2.27880e22			0.203139
$365$		−	7.19474e22i		−	0.625719i
$366$	3.73166e21	+	2.73537e22i	0.0316645	+	0.232106i
$367$	1.89333e23			1.56759			0.783795	−	0.621019i	$-0.213281\pi$
$367$	1.89333e23			1.56759			0.783795	+	0.621019i	$0.213281\pi$
$368$		−	2.56047e22i		−	0.206866i
$369$	−4.55615e22	−	1.63879e23i	−0.359220	−	1.29207i
$370$	−1.18291e23			−0.910196
$371$			4.84968e22i			0.364207i
$372$	−9.75513e21	+	1.33082e21i	−0.0715067	+	0.00975513i
$373$	9.21191e22			0.659128			0.329564	−	0.944133i	$-0.393098\pi$
$373$	9.21191e22			0.659128			0.329564	+	0.944133i	$0.393098\pi$
$374$		−	2.70076e23i		−	1.88644i
$375$	2.05782e22	+	1.50842e23i	0.140322	+	1.02858i
$376$	−9.20767e22			−0.612998
$377$			3.97359e22i			0.258292i
$378$	3.44981e22	+	8.00826e22i	0.218962	+	0.508291i
$379$	2.72704e23			1.69020			0.845102	−	0.534605i	$-0.179540\pi$
$379$	2.72704e23			1.69020			0.845102	+	0.534605i	$0.179540\pi$
$380$			2.67717e22i			0.162040i
$381$	2.02189e23	−	2.75831e22i	1.19518	−	0.163049i
$382$	−1.66371e23			−0.960524
$383$		−	3.04293e23i		−	1.71595i	−0.513696	−	0.857973i	$-0.671724\pi$
$383$		−	3.04293e23i		−	1.71595i	0.513696	−	0.857973i	$-0.328276\pi$
$384$	−2.16899e21	−	1.58991e22i	−0.0119475	−	0.0875772i
$385$	−1.57130e23			−0.845499
$386$			2.53515e22i			0.133266i
$387$	−2.02000e23	+	5.61600e22i	−1.03742	+	0.288422i
$388$	4.44238e22			0.222910
$389$		−	5.34134e22i		−	0.261881i	−0.991390	−	0.130940i	$-0.958200\pi$
$389$		−	5.34134e22i		−	0.261881i	0.991390	−	0.130940i	$-0.0417997\pi$
$390$	5.07292e22	−	6.92061e21i	0.243039	−	0.0331560i
$391$	2.91701e23			1.36567
$392$			2.99351e22i			0.136964i
$393$	1.91534e22	+	1.40398e23i	0.0856472	+	0.627808i
$394$	−1.13826e23			−0.497481
$395$		−	9.35117e22i		−	0.399477i
$396$	−5.18434e22	−	1.86474e23i	−0.216490	−	0.778685i
$397$	−2.54444e23			−1.03867			−0.519334	−	0.854571i	$-0.673820\pi$
$397$	−2.54444e23			−1.03867			−0.519334	+	0.854571i	$0.673820\pi$
$398$			5.31151e22i			0.211968i
$399$	−9.63902e22	+	1.31498e22i	−0.376077	+	0.0513054i
$400$	3.62671e22			0.138348
$401$		−	1.36946e23i		−	0.510799i	−0.966836	−	0.255400i	$-0.917793\pi$
$401$		−	1.36946e23i		−	0.510799i	0.966836	−	0.255400i	$-0.0822071\pi$
$402$	3.57467e22	+	2.62029e23i	0.130377	+	0.955687i
$403$	−2.10068e22			−0.0749227
$404$		−	2.70698e22i		−	0.0944176i
$405$	1.01118e23	+	1.67798e23i	0.344932	+	0.572389i
$406$	8.25445e22			0.275394
$407$			9.54104e23i			3.11348i
$408$	1.81130e23	−	2.47102e22i	0.578161	−	0.0788742i
$409$	−3.94768e23			−1.23263			−0.616314	−	0.787501i	$-0.711375\pi$
$409$	−3.94768e23			−1.23263			−0.616314	+	0.787501i	$0.711375\pi$
$410$			2.07470e23i			0.633725i
$411$	−1.06393e22	−	7.79881e22i	−0.0317935	−	0.233052i
$412$	−1.39855e23			−0.408886
$413$		−	2.05322e23i		−	0.587333i
$414$	2.01405e23	−	5.59944e22i	0.563724	−	0.156726i
$415$	1.55165e23			0.424971
$416$		−	3.42371e22i		−	0.0917609i
$417$	5.42435e22	−	7.40004e21i	0.142273	−	0.0194093i
$418$	2.15934e23			0.554286
$419$		−	3.47824e23i		−	0.873843i	−0.899500	−	0.436922i	$-0.856069\pi$
$419$		−	3.47824e23i		−	0.873843i	0.899500	−	0.436922i	$-0.143931\pi$
$420$	−1.43764e22	−	1.05381e23i	−0.0353514	−	0.259131i
$421$	2.83789e23			0.683056			0.341528	−	0.939872i	$-0.389056\pi$
$421$	2.83789e23			0.683056			0.341528	+	0.939872i	$0.389056\pi$
$422$		−	1.97852e23i		−	0.466152i
$423$	−2.01361e23	−	7.24270e23i	−0.464421	−	1.67046i
$424$	7.28625e22			0.164517
$425$			4.13173e23i			0.913338i
$426$	−4.47135e23	+	6.09993e22i	−0.967726	+	0.132020i
$427$	1.22362e23			0.259297
$428$			1.04974e23i			0.217814i
$429$	−5.58199e22	−	4.09169e23i	−0.113416	−	0.831357i
$430$	2.55732e23			0.508825
$431$		−	2.66986e23i		−	0.520228i	−0.965578	−	0.260114i	$-0.916240\pi$
$431$		−	2.66986e23i		−	0.520228i	0.965578	−	0.260114i	$-0.0837601\pi$
$432$	1.20318e23	−	5.18306e22i	0.229602	−	0.0989082i
$433$	−9.50235e23			−1.77599			−0.887994	−	0.459856i	$-0.847901\pi$
$433$	−9.50235e23			−1.77599			−0.887994	+	0.459856i	$0.847901\pi$
$434$			4.36380e22i			0.0798835i
$435$	1.83755e23	−	2.50684e22i	0.329486	−	0.0449493i
$436$	2.98392e23			0.524094
$437$			2.33223e23i			0.401272i
$438$	−5.30946e22	−	3.89192e23i	−0.0894918	−	0.655989i
$439$	−8.77998e22			−0.144982			−0.0724908	−	0.997369i	$-0.523095\pi$
$439$	−8.77998e22			−0.144982			−0.0724908	+	0.997369i	$0.523095\pi$
$440$			2.36076e23i			0.381924i
$441$	−2.35468e23	+	6.54646e22i	−0.373236	+	0.103767i
$442$	3.90046e23			0.605781
$443$			5.17374e23i			0.787356i	0.919248	+	0.393678i	$0.128797\pi$
$443$			5.17374e23i			0.787356i	−0.919248	+	0.393678i	$0.871203\pi$
$444$	−6.39881e23	+	8.72942e22i	−0.954229	+	0.130178i
$445$	1.23897e23			0.181059
$446$		−	4.40243e23i		−	0.630490i
$447$	3.59290e22	+	2.63365e23i	0.0504286	+	0.369650i
$448$	−7.11219e22			−0.0978366
$449$		−	6.77346e23i		−	0.913258i	−0.889657	−	0.456629i	$-0.849057\pi$
$449$		−	6.77346e23i		−	0.913258i	0.889657	−	0.456629i	$-0.150943\pi$
$450$	7.93120e22	+	2.85275e23i	0.104816	+	0.377008i
$451$	1.67340e24			2.16776
$452$			6.84827e23i			0.869630i
$453$	1.22739e24	−	1.67444e23i	1.52791	−	0.208442i
$454$	−6.59979e23			−0.805429
$455$		−	2.26929e23i		−	0.271511i
$456$	1.97565e22	+	1.44819e23i	0.0231754	+	0.169879i
$457$	−1.62058e24			−1.86391			−0.931956	−	0.362571i	$-0.881899\pi$
$457$	−1.62058e24			−1.86391			−0.931956	+	0.362571i	$0.881899\pi$
$458$		−	6.18778e23i		−	0.697824i
$459$	5.90479e23	+	1.37072e24i	0.652966	+	1.51577i
$460$	−2.54978e23			−0.276491
$461$			1.38120e24i			1.46876i	0.678741	+	0.734378i	$0.262526\pi$
$461$			1.38120e24i			1.46876i	−0.678741	+	0.734378i	$0.737474\pi$
$462$	−8.49980e23	+	1.15957e23i	−0.886403	+	0.120925i
$463$	−6.56869e23			−0.671815			−0.335908	−	0.941895i	$-0.609043\pi$
$463$	−6.56869e23			−0.671815			−0.335908	+	0.941895i	$0.609043\pi$
$464$		−	1.24017e23i		−	0.124399i
$465$	1.32526e22	+	9.71441e22i	0.0130385	+	0.0955740i
$466$	−2.77921e23			−0.268193
$467$			2.48434e23i			0.235158i	0.993064	+	0.117579i	$0.0375133\pi$
$467$			2.48434e23i			0.235158i	−0.993064	+	0.117579i	$0.962487\pi$
$468$	2.69307e23	−	7.48726e22i	0.250055	−	0.0695201i
$469$	1.17215e24			1.06764
$470$			9.16923e23i			0.819318i
$471$	−2.97015e23	+	4.05196e22i	−0.260370	+	0.0355203i
$472$	−3.08480e23			−0.265307
$473$		−	2.06267e24i		−	1.74052i
$474$	−6.90083e22	−	5.05842e23i	−0.0571342	−	0.418803i
$475$	−3.30343e23			−0.268363
$476$		−	8.10255e23i		−	0.645891i
$477$	1.59342e23	+	5.73132e23i	0.124642	+	0.448321i
$478$	1.01111e24			0.776153
$479$		−	1.29607e24i		−	0.976359i	−0.872743	−	0.488180i	$-0.837661\pi$
$479$		−	1.29607e24i		−	0.976359i	0.872743	−	0.488180i	$-0.162339\pi$
$480$	−1.58327e23	+	2.15994e22i	−0.117053	+	0.0159687i
$481$	−1.37792e24			−0.999814
$482$		−	8.78701e23i		−	0.625775i
$483$	−1.25241e23	−	9.18036e23i	−0.0875431	−	0.641705i
$484$	1.17538e24			0.806436
$485$		−	4.42383e23i		−	0.297936i
$486$	6.70817e23	+	8.33064e23i	0.443484	+	0.550747i
$487$	9.72420e22			0.0631093			0.0315547	−	0.999502i	$-0.489954\pi$
$487$	9.72420e22			0.0631093			0.0315547	+	0.999502i	$0.489954\pi$
$488$		−	1.83840e23i		−	0.117128i
$489$	4.00821e23	−	5.46810e22i	0.250709	−	0.0342024i
$490$	2.98101e23			0.183062
$491$		−	1.80548e24i		−	1.08858i	−0.838898	−	0.544289i	$-0.816799\pi$
$491$		−	1.80548e24i		−	1.08858i	0.838898	−	0.544289i	$-0.183201\pi$
$492$	1.53105e23	+	1.12229e24i	0.0906369	+	0.664383i
$493$	1.41286e24			0.821251
$494$			3.11853e23i			0.177995i
$495$	−1.85696e24	+	5.16270e23i	−1.04077	+	0.289354i
$496$	6.55626e22			0.0360845
$497$			2.00019e24i			1.08109i
$498$	8.39347e23	−	1.14506e23i	0.445531	−	0.0607804i
$499$	−6.98251e23			−0.364004			−0.182002	−	0.983298i	$-0.558258\pi$
$499$	−6.98251e23			−0.364004			−0.182002	+	0.983298i	$0.558258\pi$
$500$		−	1.01378e24i		−	0.519056i
$501$	−2.56816e22	−	1.88250e23i	−0.0129146	−	0.0946665i
$502$	2.50096e23			0.123530
$503$			2.15858e24i			1.04726i	0.851945	+	0.523632i	$0.175423\pi$
$503$			2.15858e24i			1.04726i	−0.851945	+	0.523632i	$0.824577\pi$
$504$	−1.55535e23	−	5.59440e23i	−0.0741232	−	0.266612i
$505$	−2.69568e23			−0.126196
$506$			2.05659e24i			0.945786i
$507$	−1.60222e24	+	2.18579e23i	−0.723853	+	0.0987499i
$508$	−1.35887e24			−0.603123
$509$			2.38712e23i			0.104091i	0.998645	+	0.0520456i	$0.0165741\pi$
$509$			2.38712e23i			0.104091i	−0.998645	+	0.0520456i	$0.983426\pi$
$510$	−2.46071e23	−	1.80374e24i	−0.105421	−	0.772755i
$511$	−1.74099e24			−0.732837
$512$			1.06855e23i			0.0441942i
$513$	−1.09593e24	+	4.72105e23i	−0.445375	+	0.191859i
$514$	−1.45061e24			−0.579273
$515$			1.39271e24i			0.546506i
$516$	1.38336e24	−	1.88721e23i	0.533441	−	0.0727734i
$517$	7.39568e24			2.80261
$518$			2.86240e24i			1.06601i
$519$	−2.28838e23	−	1.67742e24i	−0.0837571	−	0.613953i
$520$	−3.40942e23			−0.122645
$521$			6.08131e23i			0.215010i	0.994205	+	0.107505i	$0.0342861\pi$
$521$			6.08131e23i			0.215010i	−0.994205	+	0.107505i	$0.965714\pi$
$522$	9.75506e23	−	2.71210e23i	0.338997	−	0.0942477i
$523$	−3.17661e24			−1.08505			−0.542523	−	0.840041i	$-0.682531\pi$
$523$	−3.17661e24			−1.08505			−0.542523	+	0.840041i	$0.682531\pi$
$524$		−	9.43589e23i		−	0.316812i
$525$	1.30033e24	−	1.77395e23i	0.429161	−	0.0585472i
$526$	−1.23174e24			−0.399621
$527$			7.46921e23i			0.238220i
$528$	1.74215e23	+	1.27703e24i	0.0546237	+	0.400401i
$529$	1.02290e24			0.315305
$530$		−	7.25584e23i		−	0.219890i
$531$	−6.74609e23	−	2.42648e24i	−0.201002	−	0.722980i
$532$	6.47822e23			0.189780
$533$			2.41674e24i			0.696122i
$534$	6.70206e23	−	9.14312e22i	0.189818	−	0.0258954i
$535$	1.04535e24			0.291125
$536$		−	1.76105e24i		−	0.482269i
$537$	−3.96520e23	−	2.90656e24i	−0.106782	−	0.782726i
$538$	−2.99249e24			−0.792487
$539$		−	2.40441e24i		−	0.626196i
$540$	−5.16142e23	−	1.19815e24i	−0.132198	−	0.306880i
$541$	9.87736e23			0.248809			0.124404	−	0.992232i	$-0.460298\pi$
$541$	9.87736e23			0.248809			0.124404	+	0.992232i	$0.460298\pi$
$542$		−	2.19850e23i		−	0.0544670i
$543$	4.89051e24	−	6.67176e23i	1.19167	−	0.162571i
$544$	−1.21734e24			−0.291758
$545$		−	2.97147e24i		−	0.700490i
$546$	−1.67465e23	−	1.22755e24i	−0.0388321	−	0.284646i
$547$	−6.90954e23			−0.157603			−0.0788013	−	0.996890i	$-0.525109\pi$
$547$	−6.90954e23			−0.157603			−0.0788013	+	0.996890i	$0.525109\pi$
$548$			5.24145e23i			0.117605i
$549$	1.44607e24	−	4.02036e23i	0.319182	−	0.0887388i
$550$	−2.91301e24			−0.632525
$551$			1.12962e24i			0.241306i
$552$	−1.37928e24	+	1.88164e23i	−0.289867	+	0.0395445i
$553$	−2.26280e24			−0.467865
$554$		−	2.81076e24i		−	0.571789i
$555$	8.69298e23	+	6.37210e24i	0.173993	+	1.27540i
$556$	−3.64561e23			−0.0717956
$557$		−	5.42846e24i		−	1.05191i	−0.850512	−	0.525956i	$-0.823708\pi$
$557$		−	5.42846e24i		−	1.05191i	0.850512	−	0.525956i	$-0.176292\pi$
$558$	1.43378e23	+	5.15711e23i	0.0273384	+	0.0983329i
$559$	2.97893e24			0.558925
$560$			7.08250e23i			0.130766i
$561$	−1.45485e25	+	1.98475e24i	−2.64334	+	0.360611i
$562$	4.08418e24			0.730261
$563$			4.18442e24i			0.736308i	0.929765	+	0.368154i	$0.120010\pi$
$563$			4.18442e24i			0.736308i	−0.929765	+	0.368154i	$0.879990\pi$
$564$	6.76657e23	+	4.96000e24i	0.117181	+	0.858954i
$565$	6.81968e24			1.16233
$566$			4.23301e24i			0.710071i
$567$	4.06038e24	−	2.44686e24i	0.670378	−	0.403982i
$568$	3.00512e24			0.488345
$569$			7.47092e24i			1.19499i	0.801873	+	0.597494i	$0.203837\pi$
$569$			7.47092e24i			1.19499i	−0.801873	+	0.597494i	$0.796163\pi$
$570$	1.44214e24	−	1.96740e23i	0.227056	−	0.0309756i
$571$	−3.78796e23			−0.0587057			−0.0293528	−	0.999569i	$-0.509345\pi$
$571$	−3.78796e23			−0.0587057			−0.0293528	+	0.999569i	$0.509345\pi$
$572$			2.74996e24i			0.419529i
$573$	1.22264e24	+	8.96212e24i	0.183614	+	1.34592i
$574$	5.02037e24			0.742214
$575$		−	3.14624e24i		−	0.457912i
$576$	−8.40514e23	+	2.33679e23i	−0.120432	+	0.0334825i
$577$	−1.36291e25			−1.92258			−0.961291	−	0.275534i	$-0.911145\pi$
$577$	−1.36291e25			−1.92258			−0.961291	+	0.275534i	$0.911145\pi$
$578$		−	8.77719e24i		−	1.21900i
$579$	1.36564e24	−	1.86304e23i	0.186736	−	0.0254750i
$580$	−1.23499e24			−0.166269
$581$		−	3.75468e24i		−	0.497723i
$582$	−3.26463e23	−	2.39303e24i	−0.0426115	−	0.312350i
$583$	−5.85238e24			−0.752169
$584$			2.61569e24i			0.331033i
$585$	−7.45601e23	−	2.68183e24i	−0.0929188	−	0.334217i
$586$	9.28084e24			1.13896
$587$		−	1.35788e25i		−	1.64104i	−0.571617	−	0.820520i	$-0.693684\pi$
$587$		−	1.35788e25i		−	1.64104i	0.571617	−	0.820520i	$-0.306316\pi$
$588$	1.61255e24	−	2.19988e23i	0.191919	−	0.0261820i
$589$	−5.97184e23			−0.0699956
$590$			3.07192e24i			0.354602i
$591$	8.36491e23	+	6.13161e24i	0.0950985	+	0.697088i
$592$	4.30053e24			0.481534
$593$		−	6.16432e24i		−	0.679819i	−0.940458	−	0.339909i	$-0.889604\pi$
$593$		−	6.16432e24i		−	0.679819i	0.940458	−	0.339909i	$-0.110396\pi$
$594$	−9.66403e24	+	4.16308e24i	−1.04974	+	0.452206i
$595$	−8.06873e24			−0.863281
$596$		−	1.77003e24i		−	0.186537i
$597$	2.86121e24	−	3.90334e23i	0.297017	−	0.0405198i
$598$	−2.97014e24			−0.303715
$599$			8.55875e24i			0.862122i	0.902323	+	0.431061i	$0.141861\pi$
$599$			8.55875e24i			0.862122i	−0.902323	+	0.431061i	$0.858139\pi$
$600$	−2.66521e23	−	1.95364e24i	−0.0264466	−	0.193858i
$601$	6.20429e24			0.606488			0.303244	−	0.952913i	$-0.401930\pi$
$601$	6.20429e24			0.606488			0.303244	+	0.952913i	$0.401930\pi$
$602$		−	6.18821e24i		−	0.595932i
$603$	1.38523e25	−	3.85122e24i	1.31422	−	0.365378i
$604$	−8.24909e24			−0.771034
$605$		−	1.17047e25i		−	1.07786i
$606$	−1.45820e24	+	1.98932e23i	−0.132301	+	0.0180489i
$607$	7.07816e24			0.632735			0.316368	−	0.948637i	$-0.397537\pi$
$607$	7.07816e24			0.632735			0.316368	+	0.948637i	$0.397537\pi$
$608$		−	9.73301e23i		−	0.0857265i
$609$	−6.06606e23	−	4.44652e24i	−0.0526443	−	0.385891i
$610$	−1.83072e24			−0.156550
$611$			1.06809e25i			0.899988i
$612$	−2.66219e24	−	9.57555e24i	−0.221043	−	0.795062i
$613$	−4.11449e24			−0.336644			−0.168322	−	0.985732i	$-0.553835\pi$
$613$	−4.11449e24			−0.336644			−0.168322	+	0.985732i	$0.553835\pi$
$614$			4.04491e24i			0.326132i
$615$	1.11760e25	−	1.52466e24i	0.887997	−	0.121143i
$616$	5.71257e24			0.447307
$617$			9.81674e24i			0.757532i	0.925493	+	0.378766i	$0.123651\pi$
$617$			9.81674e24i			0.757532i	−0.925493	+	0.378766i	$0.876349\pi$
$618$	1.02777e24	+	7.53372e24i	0.0781627	+	0.572945i
$619$	3.40269e24			0.255039			0.127519	−	0.991836i	$-0.459299\pi$
$619$	3.40269e24			0.255039			0.127519	+	0.991836i	$0.459299\pi$
$620$		−	6.52889e23i		−	0.0482296i
$621$	−4.49640e24	−	1.04378e25i	−0.327372	−	0.759949i
$622$	8.69492e23			0.0623953
$623$		−	2.99805e24i		−	0.212054i
$624$	−1.84429e24	+	2.51603e23i	−0.128579	+	0.0175410i
$625$	−2.04257e24			−0.140364
$626$			2.76526e24i			0.187312i
$627$	−1.58686e24	−	1.16320e25i	−0.105957	−	0.776685i
$628$	1.99619e24			0.131391
$629$			4.89937e25i			3.17896i
$630$	−5.57105e24	+	1.54886e24i	−0.356346	+	0.0990711i
$631$	−7.72031e24			−0.486822			−0.243411	−	0.969923i	$-0.578266\pi$
$631$	−7.72031e24			−0.486822			−0.243411	+	0.969923i	$0.578266\pi$
$632$			3.39968e24i			0.211341i
$633$	−1.06579e25	+	1.45398e24i	−0.653188	+	0.0891097i
$634$	−2.03392e25			−1.22894
$635$			1.35320e25i			0.806119i
$636$	−5.35455e23	−	3.92497e24i	−0.0314491	−	0.230527i
$637$	3.47247e24			0.201087
$638$			9.96112e24i			0.568751i
$639$	6.57185e24	+	2.36381e25i	0.369981	+	1.33077i
$640$	1.06409e24			0.0590688
$641$		−	2.62444e25i		−	1.43653i	−0.695770	−	0.718265i	$-0.744937\pi$
$641$		−	2.62444e25i		−	1.43653i	0.695770	−	0.718265i	$-0.255063\pi$
$642$	5.65474e24	−	7.71434e23i	0.305209	−	0.0416374i
$643$	4.38088e23			0.0233164			0.0116582	−	0.999932i	$-0.496289\pi$
$643$	4.38088e23			0.0233164			0.0116582	+	0.999932i	$0.496289\pi$
$644$			6.16996e24i			0.323825i
$645$	−1.87933e24	−	1.37758e25i	−0.0972671	−	0.712984i
$646$	1.10883e25			0.565943
$647$		−	3.47092e25i		−	1.74705i	−0.486776	−	0.873527i	$-0.661827\pi$
$647$		−	3.47092e25i		−	1.74705i	0.486776	−	0.873527i	$-0.338173\pi$
$648$	−3.67621e24	−	6.10040e24i	−0.182484	−	0.302819i
$649$	2.47773e25			1.21298
$650$		−	4.20699e24i		−	0.203119i
$651$	2.35070e24	−	3.20688e23i	0.111936	−	0.0152705i
$652$	−2.69385e24			−0.126516
$653$			2.96983e24i			0.137567i	0.997632	+	0.0687833i	$0.0219117\pi$
$653$			2.96983e24i			0.137567i	−0.997632	+	0.0687833i	$0.978088\pi$
$654$	−2.19283e24	−	1.60738e25i	−0.100186	−	0.734379i
$655$	−9.39650e24			−0.423442
$656$		−	7.54271e24i		−	0.335269i
$657$	−2.05749e25	+	5.72021e24i	−0.902088	+	0.250798i
$658$	2.21878e25			0.959578
$659$			5.37440e24i			0.229277i	0.993407	+	0.114639i	$0.0365710\pi$
$659$			5.37440e24i			0.229277i	−0.993407	+	0.114639i	$0.963429\pi$
$660$	1.27170e25	−	1.73488e24i	0.535165	−	0.0730086i
$661$	3.04882e25			1.26566			0.632831	−	0.774290i	$-0.281893\pi$
$661$	3.04882e25			1.26566			0.632831	+	0.774290i	$0.281893\pi$
$662$		−	1.62597e25i		−	0.665871i
$663$	−2.86638e24	−	2.10111e25i	−0.115801	−	0.848841i
$664$	−5.64111e24			−0.224829
$665$		−	6.45118e24i		−	0.253655i
$666$	9.40476e24	+	3.38277e25i	0.364821	+	1.31221i
$667$	−1.07587e25			−0.411743
$668$			1.26520e24i			0.0477717i
$669$	−2.37151e25	+	3.23527e24i	−0.883464	+	0.120525i
$670$	−1.75370e25			−0.644589
$671$			1.47662e25i			0.535507i
$672$	5.22663e23	+	3.83121e24i	0.0187024	+	0.137092i
$673$	−4.74754e25			−1.67623			−0.838114	−	0.545495i	$-0.816342\pi$
$673$	−4.74754e25			−1.67623			−0.838114	+	0.545495i	$0.816342\pi$
$674$			3.69423e24i			0.128702i
$675$	1.47844e25	−	6.36883e24i	0.508241	−	0.218940i
$676$	1.07682e25			0.365279
$677$		−	5.46641e25i		−	1.82980i	−0.403678	−	0.914901i	$-0.632268\pi$
$677$		−	5.46641e25i		−	1.82980i	0.403678	−	0.914901i	$-0.367732\pi$
$678$	3.68904e25	−	5.03268e24i	1.21856	−	0.166239i
$679$	−1.07048e25			−0.348940
$680$			1.21226e25i			0.389956i
$681$	4.85007e24	+	3.55518e25i	0.153966	+	1.12859i
$682$	−5.26604e24			−0.164978
$683$			1.33062e25i			0.411404i	0.978615	+	0.205702i	$0.0659478\pi$
$683$			1.33062e25i			0.411404i	−0.978615	+	0.205702i	$0.934052\pi$
$684$	7.65592e24	−	2.12850e24i	0.233611	−	0.0649483i
$685$	5.21956e24			0.157188
$686$		−	2.58341e25i		−	0.767848i
$687$	−3.33324e25	+	4.54730e24i	−0.977814	+	0.133396i
$688$	−9.29730e24			−0.269191
$689$		−	8.45205e24i		−	0.241540i
$690$	1.87379e24	+	1.37352e25i	0.0528541	+	0.387429i
$691$	−2.30153e24			−0.0640787			−0.0320393	−	0.999487i	$-0.510200\pi$
$691$	−2.30153e24			−0.0640787			−0.0320393	+	0.999487i	$0.510200\pi$
$692$			1.12736e25i			0.309820i
$693$	1.24927e25	+	4.49347e25i	0.338890	+	1.21894i
$694$	−2.27818e25			−0.610034
$695$			3.63040e24i			0.0959601i
$696$	−6.68054e24	+	9.11377e23i	−0.174313	+	0.0237802i
$697$	8.59302e25			2.21335
$698$			1.61015e25i			0.409419i
$699$	2.04239e24	+	1.49711e25i	0.0512678	+	0.375802i
$700$	−8.73930e24			−0.216568
$701$			4.35484e25i			1.06539i	0.846306	+	0.532697i	$0.178822\pi$
$701$			4.35484e25i			1.06539i	−0.846306	+	0.532697i	$0.821178\pi$
$702$	−6.01234e24	−	1.39569e25i	−0.145214	−	0.337096i
$703$	−3.91719e25			−0.934064
$704$		−	8.58268e24i		−	0.202055i
$705$	4.93930e25	−	6.73832e24i	1.14806	−	0.156621i
$706$	−3.83542e25			−0.880179
$707$			6.52302e24i			0.147800i
$708$	2.26697e24	+	1.66172e25i	0.0507161	+	0.371757i
$709$	3.77583e25			0.834059			0.417030	−	0.908893i	$-0.363071\pi$
$709$	3.77583e25			0.834059			0.417030	+	0.908893i	$0.363071\pi$
$710$		−	2.99257e25i		−	0.652709i
$711$	−2.67417e25	+	7.43470e24i	−0.575920	+	0.160117i
$712$	−4.50434e24			−0.0957880
$713$		−	5.68768e24i		−	0.119434i
$714$	−4.36470e25	+	5.95443e24i	−0.905045	+	0.123469i
$715$	2.73848e25			0.560731
$716$			1.95345e25i			0.394988i
$717$	−7.43048e24	−	5.44666e25i	−0.148369	−	1.08757i
$718$	4.10429e25			0.809316
$719$		−	5.42700e25i		−	1.05682i	−0.848990	−	0.528408i	$-0.822789\pi$
$719$		−	5.42700e25i		−	1.05682i	0.848990	−	0.528408i	$-0.177211\pi$
$720$	2.32704e24	+	8.37005e24i	0.0447518	+	0.160967i
$721$	3.37009e25			0.640064
$722$		−	2.88327e25i		−	0.540817i
$723$	−4.73340e25	+	6.45743e24i	−0.876857	+	0.119623i
$724$	−3.28683e25			−0.601354
$725$		−	1.52389e25i		−	0.275367i
$726$	−8.63767e24	−	6.33156e25i	−0.154158	−	1.13001i
$727$	−3.54138e25			−0.624257			−0.312128	−	0.950040i	$-0.601042\pi$
$727$	−3.54138e25			−0.624257			−0.312128	+	0.950040i	$0.601042\pi$
$728$			8.25014e24i			0.143641i
$729$	3.99459e25	−	4.22577e25i	0.686949	−	0.726705i
$730$	2.60477e25			0.442450
$731$		−	1.05919e26i		−	1.77713i
$732$	−9.90310e24	+	1.35101e24i	−0.164124	+	0.0223902i
$733$	−7.56671e25			−1.23872			−0.619358	−	0.785109i	$-0.712607\pi$
$733$	−7.56671e25			−1.23872			−0.619358	+	0.785109i	$0.712607\pi$
$734$			6.85460e25i			1.10845i
$735$	−2.19070e24	−	1.60582e25i	−0.0349942	−	0.256513i
$736$	9.26988e24			0.146276
$737$			1.41449e26i			2.20492i
$738$	5.93305e25	−	1.64950e25i	0.913630	−	0.254007i
$739$	5.97970e25			0.909660			0.454830	−	0.890578i	$-0.349700\pi$
$739$	5.97970e25			0.909660			0.454830	+	0.890578i	$0.349700\pi$
$740$		−	4.28258e25i		−	0.643606i
$741$	1.67990e25	−	2.29176e24i	0.249413	−	0.0340255i
$742$	−1.75577e25			−0.257533
$743$			1.08144e26i			1.56713i	0.621311	+	0.783564i	$0.286601\pi$
$743$			1.08144e26i			1.56713i	−0.621311	+	0.783564i	$0.713399\pi$
$744$	−4.81808e23	−	3.53174e24i	−0.00689792	−	0.0505629i
$745$	−1.76264e25			−0.249321
$746$			3.33507e25i			0.466074i
$747$	−1.23364e25	−	4.43726e25i	−0.170335	−	0.612674i
$748$	9.77781e25			1.33391
$749$		−	2.52956e25i		−	0.340963i
$750$	−5.46105e25	+	7.45011e24i	−0.727319	+	0.0992228i
$751$	1.63334e25			0.214940			0.107470	−	0.994208i	$-0.465725\pi$
$751$	1.63334e25			0.214940			0.107470	+	0.994208i	$0.465725\pi$
$752$		−	3.33353e25i		−	0.433455i
$753$	−1.83792e24	−	1.34722e25i	−0.0236141	−	0.173095i
$754$	−1.43859e25			−0.182640
$755$			8.21465e25i			1.03054i
$756$	−2.89930e25	+	1.24896e25i	−0.359416	+	0.154829i
$757$	−9.00151e25			−1.10269			−0.551344	−	0.834278i	$-0.685885\pi$
$757$	−9.00151e25			−1.10269			−0.551344	+	0.834278i	$0.685885\pi$
$758$			9.87295e25i			1.19515i
$759$	1.10785e26	−	1.51135e25i	1.32527	−	0.180796i
$760$	−9.69238e24			−0.114580
$761$			1.56524e25i			0.182860i	0.995811	+	0.0914302i	$0.0291438\pi$
$761$			1.56524e25i			0.182860i	−0.995811	+	0.0914302i	$0.970856\pi$
$762$	9.98614e24	+	7.32001e25i	0.115293	+	0.845117i
$763$	−7.19037e25			−0.820409
$764$		−	6.02329e25i		−	0.679193i
$765$	−9.53557e25	+	2.65107e25i	−1.06266	+	0.295440i
$766$	1.10166e26			1.21336
$767$			3.57836e25i			0.389517i
$768$	5.75608e24	−	7.85259e23i	0.0619264	−	0.00844816i
$769$	−4.92978e25			−0.524192			−0.262096	−	0.965042i	$-0.584414\pi$
$769$	−4.92978e25			−0.524192			−0.262096	+	0.965042i	$0.584414\pi$
$770$		−	5.68872e25i		−	0.597858i
$771$	1.06603e25	+	7.81418e25i	0.110734	+	0.811697i
$772$	−9.17822e24			−0.0942330
$773$		−	1.44380e26i		−	1.46518i	−0.680670	−	0.732590i	$-0.738311\pi$
$773$		−	1.44380e26i		−	1.46518i	0.680670	−	0.732590i	$-0.261689\pi$
$774$	−2.03321e25	−	7.31319e25i	−0.203945	−	0.733565i
$775$	8.05619e24			0.0798756
$776$			1.60831e25i			0.157621i
$777$	1.54192e26	−	2.10353e25i	1.49374	−	0.203779i
$778$	1.93377e25			0.185178
$779$			6.87037e25i			0.650343i
$780$	2.50553e24	+	1.83659e25i	0.0234449	+	0.171855i
$781$	−2.41374e26			−2.23270
$782$			1.05607e26i			0.965677i
$783$	−2.17784e25	−	5.05557e25i	−0.196866	−	0.456998i
$784$	−1.08377e25			−0.0968481
$785$		−	1.98785e25i		−	0.175613i
$786$	−5.08294e25	+	6.93428e24i	−0.443927	+	0.0605617i
$787$	9.40272e25			0.811860			0.405930	−	0.913904i	$-0.366948\pi$
$787$	9.40272e25			0.811860			0.405930	+	0.913904i	$0.366948\pi$
$788$		−	4.12095e25i		−	0.351772i
$789$	9.05187e24	+	6.63517e25i	0.0763915	+	0.559963i
$790$	3.38549e25			0.282473
$791$		−	1.65023e26i		−	1.36131i
$792$	6.75108e25	−	1.87693e25i	0.550613	−	0.153081i
$793$	−2.13254e25			−0.171964
$794$		−	9.21184e25i		−	0.734450i
$795$	−3.90858e25	+	5.33219e24i	−0.308117	+	0.0420341i
$796$	−1.92297e25			−0.149884
$797$			1.37212e25i			0.105746i	0.998601	+	0.0528732i	$0.0168379\pi$
$797$			1.37212e25i			0.105746i	−0.998601	+	0.0528732i	$0.983162\pi$
$798$	−4.76074e24	−	3.48970e25i	−0.0362784	−	0.265927i
$799$	3.79772e26			2.86156
$800$			1.31301e25i			0.0978269i
$801$	−9.85046e24	−	3.54308e25i	−0.0725711	−	0.261029i
$802$	4.95798e25			0.361190
$803$		−	2.10095e26i		−	1.51347i
$804$	−9.48648e25	+	1.29417e25i	−0.675772	+	0.0921906i
$805$	6.14421e25			0.432816
$806$		−	7.60526e24i		−	0.0529784i
$807$	2.19913e25	+	1.61200e26i	0.151492	+	1.11046i
$808$	9.80032e24			0.0667634
$809$		−	1.50535e26i		−	1.01415i	−0.861903	−	0.507074i	$-0.830727\pi$
$809$		−	1.50535e26i		−	1.01415i	0.861903	−	0.507074i	$-0.169273\pi$
$810$	−6.07493e25	+	3.66087e25i	−0.404740	+	0.243904i
$811$	−1.38926e26			−0.915367			−0.457683	−	0.889115i	$-0.651321\pi$
$811$	−1.38926e26			−0.915367			−0.457683	+	0.889115i	$0.651321\pi$
$812$			2.98843e25i			0.194733i
$813$	−1.18429e25	+	1.61564e24i	−0.0763211	+	0.0104119i
$814$	−3.45422e26			−2.20156
$815$			2.68260e25i			0.169098i
$816$	8.94606e24	+	6.55761e25i	0.0557725	+	0.408822i
$817$	8.46855e25			0.522169
$818$		−	1.42921e26i		−	0.871599i
$819$	−6.48951e25	+	1.80421e25i	−0.391432	+	0.108826i
$820$	−7.51122e25			−0.448111
$821$			3.07155e26i			1.81246i	0.422782	+	0.906231i	$0.361054\pi$
$821$			3.07155e26i			1.81246i	−0.422782	+	0.906231i	$0.638946\pi$
$822$	2.82347e25	−	3.85185e24i	0.164792	−	0.0224814i
$823$	2.44832e26			1.41342			0.706708	−	0.707505i	$-0.250179\pi$
$823$	2.44832e26			1.41342			0.706708	+	0.707505i	$0.250179\pi$
$824$		−	5.06328e25i		−	0.289126i
$825$	2.14072e25	+	1.56918e26i	0.120913	+	0.886315i
$826$	7.43344e25			0.415307
$827$			2.20127e26i			1.21653i	0.793732	+	0.608267i	$0.208135\pi$
$827$			2.20127e26i			1.21653i	−0.793732	+	0.608267i	$0.791865\pi$
$828$	2.02721e25	+	7.29163e25i	0.110822	+	0.398613i
$829$	−2.47819e26			−1.34012			−0.670061	−	0.742306i	$-0.733732\pi$
$829$	−2.47819e26			−1.34012			−0.670061	+	0.742306i	$0.733732\pi$
$830$			5.61756e25i			0.300500i
$831$	−1.51410e26	+	2.06558e25i	−0.801210	+	0.109303i
$832$	1.23952e25			0.0648847
$833$		−	1.23468e26i		−	0.639366i
$834$	2.67910e24	+	1.96383e25i	0.0137244	+	0.100602i
$835$	1.25992e25			0.0638504
$836$			7.81764e25i			0.391940i
$837$	2.67267e25	−	1.15134e25i	0.132561	−	0.0571049i
$838$	1.25926e26			0.617900
$839$			1.51315e26i			0.734557i	0.930111	+	0.367278i	$0.119710\pi$
$839$			1.51315e26i			0.734557i	−0.930111	+	0.367278i	$0.880290\pi$
$840$	3.81521e25	−	5.20481e24i	0.183234	−	0.0249972i
$841$	1.58347e26			0.752397
$842$			1.02742e26i			0.482993i
$843$	−3.00139e25	−	2.20007e26i	−0.139597	−	1.02327i
$844$	7.16300e25			0.329619
$845$		−	1.07233e26i		−	0.488222i
$846$	2.62214e26	−	7.29005e25i	1.18120	−	0.328395i
$847$	−2.83232e26			−1.26238
$848$			2.63791e25i			0.116331i
$849$	2.28025e26	−	3.11077e25i	0.994976	−	0.135737i
$850$	−1.49585e26			−0.645827
$851$		−	3.73080e26i		−	1.59381i
$852$	−2.20841e25	−	1.61880e26i	−0.0933520	−	0.684286i
$853$	−3.47086e26			−1.45176			−0.725881	−	0.687821i	$-0.758568\pi$
$853$	−3.47086e26			−1.45176			−0.725881	+	0.687821i	$0.758568\pi$
$854$			4.42999e25i			0.183350i
$855$	−2.11961e25	−	7.62396e25i	−0.0868082	−	0.312238i
$856$	−3.80045e25			−0.154018
$857$			3.05940e26i			1.22690i	0.789733	+	0.613451i	$0.210219\pi$
$857$			3.05940e26i			1.22690i	−0.789733	+	0.613451i	$0.789781\pi$
$858$	1.48135e26	−	2.02090e25i	0.587858	−	0.0801971i
$859$	4.26960e26			1.67667			0.838336	−	0.545153i	$-0.183529\pi$
$859$	4.26960e26			1.67667			0.838336	+	0.545153i	$0.183529\pi$
$860$			9.25848e25i			0.359794i
$861$	−3.68939e25	−	2.70438e26i	−0.141882	−	1.04002i
$862$	9.66594e25			0.367857
$863$			2.75377e26i			1.03712i	0.855040	+	0.518562i	$0.173532\pi$
$863$			2.75377e26i			1.03712i	−0.855040	+	0.518562i	$0.826468\pi$
$864$	1.87647e25	+	4.35597e25i	0.0699387	+	0.162353i
$865$	1.12266e26			0.414098
$866$		−	3.44022e26i		−	1.25581i
$867$	−4.72811e26	+	6.45021e25i	−1.70811	+	0.233025i
$868$	−1.57986e25			−0.0564862
$869$		−	2.73065e26i		−	0.966247i
$870$	9.07572e24	+	6.65265e25i	0.0317840	+	0.232982i
$871$	−2.04282e26			−0.708055
$872$			1.08030e26i			0.370590i
$873$	−1.26509e26	+	3.51719e25i	−0.429529	+	0.119417i
$874$	−8.44358e25			−0.283742
$875$			2.44291e26i			0.812522i
$876$	1.40903e26	−	1.92223e25i	0.463855	−	0.0632802i
$877$	−3.39070e25			−0.110482			−0.0552411	−	0.998473i	$-0.517593\pi$
$877$	−3.39070e25			−0.110482			−0.0552411	+	0.998473i	$0.517593\pi$
$878$		−	3.17869e25i		−	0.102517i
$879$	−6.82033e25	−	4.99942e26i	−0.217724	−	1.59595i
$880$	−8.54685e25			−0.270061
$881$		−	2.34511e26i		−	0.733466i	−0.930326	−	0.366733i	$-0.880476\pi$
$881$		−	2.34511e26i		−	0.733466i	0.930326	−	0.366733i	$-0.119524\pi$
$882$	−2.37007e25	−	8.52484e25i	−0.0733743	−	0.263918i
$883$	1.50498e26			0.461194			0.230597	−	0.973049i	$-0.425932\pi$
$883$	1.50498e26			0.461194			0.230597	+	0.973049i	$0.425932\pi$
$884$			1.41212e26i			0.428352i
$885$	1.65479e26	−	2.25750e25i	0.496881	−	0.0677858i
$886$	−1.87309e26			−0.556745
$887$		−	6.20499e25i		−	0.182570i	−0.995825	−	0.0912848i	$-0.970903\pi$
$887$		−	6.20499e25i		−	0.182570i	0.995825	−	0.0912848i	$-0.0290974\pi$
$888$	−3.16039e25	−	2.31662e26i	−0.0920500	−	0.674742i
$889$	3.27449e26			0.944120
$890$			4.48553e25i			0.128028i
$891$	2.95277e26	+	4.89990e26i	0.834314	+	1.38448i
$892$	1.59385e26			0.445824
$893$			3.03639e26i			0.840803i
$894$	−9.53484e25	+	1.30077e25i	−0.261382	+	0.0356584i
$895$	1.94529e26			0.527931
$896$		−	2.57489e25i		−	0.0691809i
$897$	2.18271e25	+	1.59996e26i	0.0580582	+	0.425576i
$898$	2.45226e26			0.645771
$899$		−	2.75484e25i		−	0.0718222i
$900$	−1.03281e26	+	2.87140e25i	−0.266585	+	0.0741159i
$901$	−3.00523e26			−0.767988
$902$			6.05837e26i			1.53284i
$903$	−3.33348e26	+	4.54762e25i	−0.835041	+	0.113918i
$904$	−2.47934e26			−0.614922
$905$			3.27311e26i			0.803754i
$906$	6.06212e25	+	4.44363e26i	0.147391	+	1.08040i
$907$	−1.76420e26			−0.424699			−0.212349	−	0.977194i	$-0.568112\pi$
$907$	−1.76420e26			−0.424699			−0.212349	+	0.977194i	$0.568112\pi$
$908$		−	2.38938e26i		−	0.569524i
$909$	2.14322e25	+	7.70887e25i	0.0505814	+	0.181935i
$910$	8.21569e25			0.191987
$911$			4.89283e25i			0.113213i	0.998397	+	0.0566063i	$0.0180280\pi$
$911$			4.89283e25i			0.113213i	−0.998397	+	0.0566063i	$0.981972\pi$
$912$	−5.24299e25	+	7.15263e24i	−0.120123	+	0.0163875i
$913$	4.53099e26			1.02791
$914$		−	5.86714e26i		−	1.31798i
$915$	1.34537e25	+	9.86176e25i	0.0299261	+	0.219364i
$916$	2.24022e26			0.493436
$917$			2.27377e26i			0.495932i
$918$	−4.96253e26	+	2.13776e26i	−1.07181	+	0.461716i
$919$	−5.67137e26			−1.21296			−0.606482	−	0.795097i	$-0.707420\pi$
$919$	−5.67137e26			−1.21296			−0.606482	+	0.795097i	$0.707420\pi$
$920$		−	9.23118e25i		−	0.195509i
$921$	2.17892e26	−	2.97254e25i	0.456988	−	0.0623435i
$922$	−5.00049e26			−1.03857
$923$		−	3.48594e26i		−	0.716976i
$924$	−4.19807e25	−	3.07726e26i	−0.0855071	−	0.626781i
$925$	5.28440e26			1.06591
$926$		−	2.37812e26i		−	0.475045i
$927$	3.98275e26	−	1.10728e26i	0.787889	−	0.219048i
$928$	4.48988e25			0.0879636
$929$		−	1.93301e26i		−	0.375053i	−0.982260	−	0.187527i	$-0.939953\pi$
$929$		−	1.93301e26i		−	0.375053i	0.982260	−	0.187527i	$-0.0600471\pi$
$930$	−3.51699e25	+	4.79797e24i	−0.0675810	+	0.00921958i
$931$	9.87162e25			0.187863
$932$		−	1.00618e26i		−	0.189641i
$933$	−6.38975e24	−	4.68379e25i	−0.0119275	−	0.0874305i
$934$	−8.99429e25			−0.166282
$935$		−	9.73699e26i		−	1.78287i
$936$	2.71068e25	+	9.74996e25i	0.0491581	+	0.176815i
$937$	−3.34473e25			−0.0600765			−0.0300383	−	0.999549i	$-0.509563\pi$
$937$	−3.34473e25			−0.0600765			−0.0300383	+	0.999549i	$0.509563\pi$
$938$			4.24362e26i			0.754937i
$939$	1.48959e26	−	2.03214e25i	0.262469	−	0.0358067i
$940$	−3.31962e26			−0.579345
$941$		−	7.15034e26i		−	1.23600i	−0.786176	−	0.618002i	$-0.787942\pi$
$941$		−	7.15034e26i		−	1.23600i	0.786176	−	0.618002i	$-0.212058\pi$
$942$	−1.46697e25	−	1.07531e26i	−0.0251166	−	0.184109i
$943$	−6.54345e26			−1.10969
$944$		−	1.11682e26i		−	0.187600i
$945$	1.24375e26	+	2.88720e26i	0.206941	+	0.480386i
$946$	7.46767e26			1.23074
$947$			2.50281e26i			0.408581i	0.978910	+	0.204291i	$0.0654888\pi$
$947$			2.50281e26i			0.408581i	−0.978910	+	0.204291i	$0.934511\pi$
$948$	1.83134e26	−	2.49837e25i	0.296139	−	0.0404000i
$949$	3.03420e26			0.486014
$950$		−	1.19597e26i		−	0.189762i
$951$	1.49469e26	+	1.09563e27i	0.234924	+	1.72203i
$952$	2.93344e26			0.456714
$953$		−	1.23347e26i		−	0.190236i	−0.995466	−	0.0951180i	$-0.969677\pi$
$953$		−	1.23347e26i		−	0.190236i	0.995466	−	0.0951180i	$-0.0303229\pi$
$954$	−2.07496e26	+	5.76879e25i	−0.317011	+	0.0881352i
$955$	−5.99814e26			−0.907792
$956$			3.66061e26i			0.548823i
$957$	5.36587e26	−	7.32026e25i	0.796953	−	0.108722i
$958$	4.69228e26			0.690390
$959$		−	1.26303e26i		−	0.184097i
$960$	−7.81981e24	−	5.73205e25i	−0.0112916	−	0.0827692i
$961$	−6.84490e26			−0.979167
$962$		−	4.98861e26i		−	0.706975i
$963$	−8.31115e25	−	2.98941e26i	−0.116688	−	0.419710i
$964$	3.18124e26			0.442490
$965$			9.13991e25i			0.125949i
$966$	3.32365e26	−	4.53420e25i	0.453754	−	0.0619023i
$967$	−1.07798e27			−1.45805			−0.729027	−	0.684485i	$-0.760027\pi$
$967$	−1.07798e27			−1.45805			−0.729027	+	0.684485i	$0.760027\pi$
$968$			4.25533e26i			0.570237i
$969$	−8.14862e25	−	5.97307e26i	−0.108186	−	0.793019i
$970$	1.60160e26			0.210673
$971$			1.59421e26i			0.207765i	0.994590	+	0.103882i	$0.0331265\pi$
$971$			1.59421e26i			0.207765i	−0.994590	+	0.103882i	$0.966873\pi$
$972$	−3.01602e26	+	2.42862e26i	−0.389437	+	0.313590i
$973$	8.78485e25			0.112388
$974$			3.52054e25i			0.0446250i
$975$	−2.26623e26	+	3.09164e25i	−0.284618	+	0.0388283i
$976$	6.65571e25			0.0828220
$977$			9.18709e26i			1.13273i	0.824154	+	0.566366i	$0.191651\pi$
$977$			9.18709e26i			1.13273i	−0.824154	+	0.566366i	$0.808349\pi$
$978$	1.97966e25	+	1.45113e26i	0.0241848	+	0.177278i
$979$	3.61792e26			0.437940
$980$			1.07924e26i			0.129445i
$981$	−8.49753e26	+	2.36248e26i	−1.00988	+	0.280768i
$982$	6.53654e26			0.769741
$983$			1.27925e27i			1.49270i	0.665552	+	0.746351i	$0.268196\pi$
$983$			1.27925e27i			1.49270i	−0.665552	+	0.746351i	$0.731804\pi$
$984$	−4.06312e26	+	5.54301e25i	−0.469790	+	0.0640899i
$985$	−4.10375e26			−0.470170
$986$			5.11509e26i			0.580712i
$987$	−1.63054e26	−	1.19521e27i	−0.183433	−	1.34459i
$988$	−1.12903e26			−0.125861
$989$			8.06559e26i			0.890983i
$990$	−1.86910e26	−	6.72290e26i	−0.204604	−	0.735936i
$991$	1.34771e27			1.46195			0.730975	−	0.682404i	$-0.239065\pi$
$991$	1.34771e27			1.46195			0.730975	+	0.682404i	$0.239065\pi$
$992$			2.37362e25i			0.0255156i
$993$	−8.75879e26	+	1.19490e26i	−0.933041	+	0.127288i
$994$	−7.24145e26			−0.764448
$995$			1.91494e26i			0.200331i
$996$	4.14556e25	+	3.03876e26i	0.0429782	+	0.315038i
$997$	−4.03504e25			−0.0414564			−0.0207282	−	0.999785i	$-0.506598\pi$
$997$	−4.03504e25			−0.0414564			−0.0207282	+	0.999785i	$0.506598\pi$
$998$		−	2.52794e26i		−	0.257390i
$999$	1.75312e27	−	7.55211e26i	1.76898	−	0.762042i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6.19.b.a.5.6	yes	6
3.2	odd	2	inner	6.19.b.a.5.3	✓	6
4.3	odd	2		48.19.e.d.17.2		6
12.11	even	2		48.19.e.d.17.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.19.b.a.5.3	✓	6	3.2	odd	2	inner
6.19.b.a.5.6	yes	6	1.1	even	1	trivial
48.19.e.d.17.1		6	12.11	even	2
48.19.e.d.17.2		6	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6 = 2 \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 19 \)
Character orbit:	\([\chi]\)	\(=\)	6.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+362.039i q^{2} +(19502.4 - 2660.56i) q^{3} -131072. q^{4} +1.30525e6i q^{5} +(963226. + 7.06061e6i) q^{6} +3.15845e7 q^{7} -4.74531e7i q^{8} +(3.73263e8 - 1.03774e8i) q^{9} +O(q^{10})\)	\(q+362.039i q^{2} +(19502.4 - 2660.56i) q^{3} -131072. q^{4} +1.30525e6i q^{5} +(963226. + 7.06061e6i) q^{6} +3.15845e7 q^{7} -4.74531e7i q^{8} +(3.73263e8 - 1.03774e8i) q^{9} -4.72550e8 q^{10} +3.81148e9i q^{11} +(-2.55621e9 + 3.48725e8i) q^{12} -5.50456e9 q^{13} +1.14348e10i q^{14} +(3.47269e9 + 2.54554e10i) q^{15} +1.71799e10 q^{16} +1.95721e11i q^{17} +(3.75704e10 + 1.35136e11i) q^{18} -1.56485e11 q^{19} -1.71081e11i q^{20} +(6.15971e11 - 8.40324e10i) q^{21} -1.37990e12 q^{22} -1.49039e12i q^{23} +(-1.26252e11 - 9.25448e11i) q^{24} +2.11102e12 q^{25} -1.99286e12i q^{26} +(7.00342e12 - 3.01694e12i) q^{27} -4.13984e12 q^{28} -7.21871e12i q^{29} +(-9.21584e12 + 1.25725e12i) q^{30} +3.81624e12 q^{31} +6.21978e12i q^{32} +(1.01407e13 + 7.43328e13i) q^{33} -7.08587e13 q^{34} +4.12256e13i q^{35} +(-4.89244e13 + 1.36019e13i) q^{36} +2.50324e14 q^{37} -5.66536e13i q^{38} +(-1.07352e14 + 1.46452e13i) q^{39} +6.19381e13 q^{40} -4.39043e14i q^{41} +(3.04230e13 + 2.23005e14i) q^{42} -5.41174e14 q^{43} -4.99578e14i q^{44} +(1.35451e14 + 4.87201e14i) q^{45} +5.39578e14 q^{46} -1.94037e15i q^{47} +(3.35048e14 - 4.57081e13i) q^{48} -6.30835e14 q^{49} +7.64273e14i q^{50} +(5.20729e14 + 3.81703e15i) q^{51} +7.21494e14 q^{52} +1.53546e15i q^{53} +(1.09225e15 + 2.53551e15i) q^{54} -4.97492e15 q^{55} -1.49878e15i q^{56} +(-3.05182e15 + 4.16338e14i) q^{57} +2.61345e15 q^{58} -6.50072e15i q^{59} +(-4.55173e14 - 3.33649e15i) q^{60} +3.87413e15 q^{61} +1.38163e15i q^{62} +(1.17893e16 - 3.27766e15i) q^{63} -2.25180e15 q^{64} -7.18482e15i q^{65} +(-2.69113e16 + 3.67131e15i) q^{66} +3.71114e16 q^{67} -2.56536e16i q^{68} +(-3.96527e15 - 2.90661e16i) q^{69} -1.49252e16 q^{70} +6.33282e16i q^{71} +(-4.92442e15 - 1.77125e16i) q^{72} -5.51216e16 q^{73} +9.06269e16i q^{74} +(4.11700e16 - 5.61651e15i) q^{75} +2.05108e16 q^{76} +1.20383e17i q^{77} +(-5.30214e15 - 3.88655e16i) q^{78} -7.16429e16 q^{79} +2.24240e16i q^{80} +(1.28556e17 - 7.74704e16i) q^{81} +1.58951e17 q^{82} -1.18877e17i q^{83} +(-8.07366e16 + 1.10143e16i) q^{84} -2.55465e17 q^{85} -1.95926e17i q^{86} +(-1.92058e16 - 1.40782e17i) q^{87} +1.80867e17 q^{88} -9.49218e16i q^{89} +(-1.76386e17 + 4.90386e16i) q^{90} -1.73859e17 q^{91} +1.95348e17i q^{92} +(7.44258e16 - 1.01534e16i) q^{93} +7.02490e17 q^{94} -2.04252e17i q^{95} +(1.65481e16 + 1.21300e17i) q^{96} -3.38927e17 q^{97} -2.28387e17i q^{98} +(3.95534e17 + 1.42268e18i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6258 q^{3} - 786432 q^{4} - 15753216 q^{6} + 28233804 q^{7} + 695971638 q^{9}+O(q^{10}) \) 6 * q - 6258 * q^3 - 786432 * q^4 - 15753216 * q^6 + 28233804 * q^7 + 695971638 * q^9	\( 6 q - 6258 q^{3} - 786432 q^{4} - 15753216 q^{6} + 28233804 q^{7} + 695971638 q^{9} - 434257920 q^{10} + 820248576 q^{12} + 29566196220 q^{13} + 119627095680 q^{15} + 103079215104 q^{16} + 315939373056 q^{18} - 438814047012 q^{19} + 2876527406172 q^{21} - 2844452929536 q^{22} + 2064805527552 q^{24} - 25696048717290 q^{25} + 11197265522814 q^{27} - 3700661157888 q^{28} + 13072787619840 q^{30} + 21775814927148 q^{31} - 962560003968 q^{33} + 99067611119616 q^{34} - 91222394535936 q^{36} + 638446564817436 q^{37} - 736541155104180 q^{39} + 56919054090240 q^{40} - 203954622480384 q^{42} - 16\!\cdots\!52 q^{43}+ \cdots + 76\!\cdots\!72 q^{99}+O(q^{100}) \) 6 * q - 6258 * q^3 - 786432 * q^4 - 15753216 * q^6 + 28233804 * q^7 + 695971638 * q^9 - 434257920 * q^10 + 820248576 * q^12 + 29566196220 * q^13 + 119627095680 * q^15 + 103079215104 * q^16 + 315939373056 * q^18 - 438814047012 * q^19 + 2876527406172 * q^21 - 2844452929536 * q^22 + 2064805527552 * q^24 - 25696048717290 * q^25 + 11197265522814 * q^27 - 3700661157888 * q^28 + 13072787619840 * q^30 + 21775814927148 * q^31 - 962560003968 * q^33 + 99067611119616 * q^34 - 91222394535936 * q^36 + 638446564817436 * q^37 - 736541155104180 * q^39 + 56919054090240 * q^40 - 203954622480384 * q^42 - 1688313718883652 * q^43 + 390590504075520 * q^45 + 1979247919104 * q^46 - 107511621353472 * q^48 - 895767896448270 * q^49 + 9636273526722048 * q^51 - 3875300470947840 * q^52 + 2993011804200960 * q^54 - 1259959207783680 * q^55 + 4023767318253996 * q^57 + 21251172660756480 * q^58 - 15679762684968960 * q^60 - 16279597277700036 * q^61 - 32525159214131028 * q^63 - 13510798882111488 * q^64 - 60047751762690048 * q^66 + 11153724314613276 * q^67 + 3612037794746112 * q^69 + 161904998736691200 * q^70 - 41410805505196032 * q^72 - 78910243347781140 * q^73 + 348225828845090910 * q^75 + 57516234769956864 * q^76 - 168903906208235520 * q^78 - 476518976428926228 * q^79 + 630680446106425062 * q^81 + 396536393269149696 * q^82 - 377032200181776384 * q^84 - 967978669078932480 * q^85 + 419256510981966720 * q^87 + 372828134380142592 * q^88 - 2046848246643179520 * q^90 - 1032060167365562760 * q^91 + 764294136047005116 * q^93 + 2566175766871080960 * q^94 - 270638190107295744 * q^96 + 834695417243310348 * q^97 + 761688154713814272 * q^99

Introduction

L-functions

Modular forms

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