LMFDB - Embedded newform 6.23.b.a.5.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6,23,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, 23, names="a")

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

chi := DirichletCharacter("6.5");

S:= CuspForms(chi, 23);

N := Newforms(S);

Level:	$ N $	$=$	$ 6 = 2 \cdot 3 $
Weight:	$ k $	$=$	$ 23 $
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:	$18.4024460905$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4 x^{7} - 12878974 x^{6} - 2567056924 x^{5} + 47744458496177 x^{4} + \cdots + 98\!\cdots\!84 $ x^8 - 4x^7 - 12878974x^6 - 2567056924x^5 + 47744458496177x^4 + 16683879235776608x^3 - 38709208854294504224x^2 - 8131330234969024044480*x + 9835296816172879412979984
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{53}\cdot 3^{29} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.1
Root			$-865.062 + 1.41421i$ of defining polynomial
Character	$\chi$	$=$	6.5
Dual form			6.23.b.a.5.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1448.15i q^{2} +(-128493. + 121945. i) q^{3} -2.09715e6 q^{4} -8.15211e7i q^{5} +(1.76595e8 + 1.86078e8i) q^{6} +2.43000e9 q^{7} +3.03700e9i q^{8} +(1.64002e9 - 3.13382e10i) q^{9} +O(q^{10})$	\(q-1448.15i q^{2} +(-128493. + 121945. i) q^{3} -2.09715e6 q^{4} -8.15211e7i q^{5} +(1.76595e8 + 1.86078e8i) q^{6} +2.43000e9 q^{7} +3.03700e9i q^{8} +(1.64002e9 - 3.13382e10i) q^{9} -1.18055e11 q^{10} +6.25607e9i q^{11} +(2.69470e11 - 2.55737e11i) q^{12} -3.34030e12 q^{13} -3.51901e12i q^{14} +(9.94107e12 + 1.04749e13i) q^{15} +4.39805e12 q^{16} +2.70899e13i q^{17} +(-4.53825e13 - 2.37500e12i) q^{18} -9.29168e13 q^{19} +1.70962e14i q^{20} +(-3.12239e14 + 2.96325e14i) q^{21} +9.05975e12 q^{22} +1.49571e14i q^{23} +(-3.70346e14 - 3.90234e14i) q^{24} -4.26151e15 q^{25} +4.83727e15i q^{26} +(3.61079e15 + 4.22674e15i) q^{27} -5.09607e15 q^{28} -2.50044e14i q^{29} +(1.51693e16 - 1.43962e16i) q^{30} +8.84301e15 q^{31} -6.36905e15i q^{32} +(-7.62894e14 - 8.03863e14i) q^{33} +3.92304e16 q^{34} -1.98096e17i q^{35} +(-3.43937e15 + 6.57209e16i) q^{36} -1.23534e17 q^{37} +1.34558e17i q^{38} +(4.29206e17 - 4.07332e17i) q^{39} +2.47580e17 q^{40} +7.10953e17i q^{41} +(4.29125e17 + 4.52170e17i) q^{42} -1.56221e18 q^{43} -1.31199e16i q^{44} +(-2.55472e18 - 1.33696e17i) q^{45} +2.16603e17 q^{46} +9.63200e15i q^{47} +(-5.65120e17 + 5.36319e17i) q^{48} +1.99507e18 q^{49} +6.17133e18i q^{50} +(-3.30347e18 - 3.48088e18i) q^{51} +7.00511e18 q^{52} -6.22288e18i q^{53} +(6.12097e18 - 5.22899e18i) q^{54} +5.10002e17 q^{55} +7.37990e18i q^{56} +(1.19392e19 - 1.13307e19i) q^{57} -3.62103e17 q^{58} -1.73109e18i q^{59} +(-2.08479e19 - 2.19675e19i) q^{60} +1.43862e19 q^{61} -1.28061e19i q^{62} +(3.98524e18 - 7.61517e19i) q^{63} -9.22337e18 q^{64} +2.72305e20i q^{65} +(-1.16412e18 + 1.10479e18i) q^{66} -4.19715e19 q^{67} -5.68117e19i q^{68} +(-1.82394e19 - 1.92189e19i) q^{69} -2.86874e20 q^{70} +2.15220e20i q^{71} +(9.51741e19 + 4.98074e18i) q^{72} -9.65337e18 q^{73} +1.78897e20i q^{74} +(5.47576e20 - 5.19669e20i) q^{75} +1.94861e20 q^{76} +1.52022e19i q^{77} +(-5.89879e20 - 6.21556e20i) q^{78} +1.87187e20 q^{79} -3.58534e20i q^{80} +(-9.79392e20 - 1.02790e20i) q^{81} +1.02957e21 q^{82} +6.23141e20i q^{83} +(6.54812e20 - 6.21440e20i) q^{84} +2.20840e21 q^{85} +2.26233e21i q^{86} +(3.04916e19 + 3.21290e19i) q^{87} -1.89997e19 q^{88} -5.00057e21i q^{89} +(-1.93613e20 + 3.69964e21i) q^{90} -8.11691e21 q^{91} -3.13674e20i q^{92} +(-1.13627e21 + 1.07836e21i) q^{93} +1.39486e19 q^{94} +7.57469e21i q^{95} +(7.76672e20 + 8.18381e20i) q^{96} -4.47780e21 q^{97} -2.88917e21i q^{98} +(1.96054e20 + 1.02601e19i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 69720 q^{3} - 16777216 q^{4} + 156352512 q^{6} + 5645581840 q^{7} - 53592329016 q^{9}+O(q^{10}) $ 8 * q - 69720 * q^3 - 16777216 * q^4 + 156352512 * q^6 + 5645581840 * q^7 - 53592329016 * q^9	$ 8 q - 69720 q^{3} - 16777216 q^{4} + 156352512 q^{6} + 5645581840 q^{7} - 53592329016 q^{9} + 46180761600 q^{10} + 146213437440 q^{12} - 2875682381360 q^{13} - 731868641280 q^{15} + 35184372088832 q^{16} - 55595702845440 q^{18} - 314803957551536 q^{19} + 661593766080336 q^{21} - 511896111513600 q^{22} - 327894983245824 q^{24} - 62\!\cdots\!20 q^{25}+ \cdots + 36\!\cdots\!76 q^{99}+O(q^{100}) $ 8 * q - 69720 * q^3 - 16777216 * q^4 + 156352512 * q^6 + 5645581840 * q^7 - 53592329016 * q^9 + 46180761600 * q^10 + 146213437440 * q^12 - 2875682381360 * q^13 - 731868641280 * q^15 + 35184372088832 * q^16 - 55595702845440 * q^18 - 314803957551536 * q^19 + 661593766080336 * q^21 - 511896111513600 * q^22 - 327894983245824 * q^24 - 6264418212884920 * q^25 + 11756777174853480 * q^27 - 11839643246919680 * q^28 + 51661456814407680 * q^30 - 110293228249214576 * q^31 + 256091518967454720 * q^33 - 100789882794934272 * q^34 + 112391259980562432 * q^36 - 752490366563284400 * q^37 + 1437242122292286480 * q^39 - 96848076550963200 * q^40 + 255515905807319040 * q^42 - 1301015563442074160 * q^43 - 4916408514089748480 * q^45 + 1601638996847296512 * q^46 - 306631802754170880 * q^48 + 12029391373660580760 * q^49 - 18532151948158119936 * q^51 + 6030743057433886720 * q^52 - 18559682184349532160 * q^54 + 56456085576783974400 * q^55 - 35832783024333133680 * q^57 + 34659140078143242240 * q^58 + 1534839784797634560 * q^60 - 124415281411828286768 * q^61 + 223305694023597186960 * q^63 - 73786976294838206464 * q^64 + 122984956040514011136 * q^66 - 349673137262790165680 * q^67 + 217762533639160621056 * q^69 - 485339414077397729280 * q^70 + 116592639413720186880 * q^72 - 65576379188480063600 * q^73 + 923803988759061007080 * q^75 + 660191749187118825472 * q^76 - 1049693699266563440640 * q^78 - 325232563432330354544 * q^79 - 2780170203320395644024 * q^81 + 2935193462963889438720 * q^82 - 1387462689722908803072 * q^84 + 6970706743345629511680 * q^85 - 3070393070764643665920 * q^87 + 1073523954052969267200 * q^88 - 4943089610251404410880 * q^90 - 6363735561736496595040 * q^91 + 3617627578345665462480 * q^93 + 2855373122028803850240 * q^94 + 687645619903946293248 * q^96 - 23922503524683181095920 * q^97 + 36535312526138292658176 * 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 $

$2$		−	1448.15i		−	0.707107i
$2$		−	1448.15i		−	0.707107i
$3$	−128493.	+	121945.i	−0.725349	+	0.688382i
$3$	−128493.	+	121945.i	−0.725349	+	0.688382i
$4$	−2.09715e6			−0.500000
$5$		−	8.15211e7i		−	1.66955i	−0.550589	−	0.834777i	$-0.685597\pi$
$5$		−	8.15211e7i		−	1.66955i	0.550589	−	0.834777i	$-0.314403\pi$
$6$	1.76595e8	+	1.86078e8i	0.486759	+	0.512899i
$7$	2.43000e9			1.22893			0.614465	−	0.788944i	$-0.289372\pi$
$7$	2.43000e9			1.22893			0.614465	+	0.788944i	$0.289372\pi$
$8$			3.03700e9i			0.353553i
$9$	1.64002e9	−	3.13382e10i	0.0522615	−	0.998633i
$10$	−1.18055e11			−1.18055
$11$			6.25607e9i			0.0219271i	0.999940	+	0.0109636i	$0.00348988\pi$
$11$			6.25607e9i			0.0219271i	−0.999940	+	0.0109636i	$0.996510\pi$
$12$	2.69470e11	−	2.55737e11i	0.362674	−	0.344191i
$13$	−3.34030e12			−1.86384			−0.931919	−	0.362667i	$-0.881866\pi$
$13$	−3.34030e12			−1.86384			−0.931919	+	0.362667i	$0.881866\pi$
$14$		−	3.51901e12i		−	0.868985i
$15$	9.94107e12	+	1.04749e13i	1.14929	+	1.21101i
$16$	4.39805e12			0.250000
$17$			2.70899e13i			0.790442i	0.918586	+	0.395221i	$0.129332\pi$
$17$			2.70899e13i			0.790442i	−0.918586	+	0.395221i	$0.870668\pi$
$18$	−4.53825e13	−	2.37500e12i	−0.706140	−	0.0369544i
$19$	−9.29168e13			−0.797636			−0.398818	−	0.917030i	$-0.630579\pi$
$19$	−9.29168e13			−0.797636			−0.398818	+	0.917030i	$0.630579\pi$
$20$			1.70962e14i			0.834777i
$21$	−3.12239e14	+	2.96325e14i	−0.891403	+	0.845973i
$22$	9.05975e12			0.0155048
$23$			1.49571e14i			0.156979i	0.996915	+	0.0784896i	$0.0250098\pi$
$23$			1.49571e14i			0.156979i	−0.996915	+	0.0784896i	$0.974990\pi$
$24$	−3.70346e14	−	3.90234e14i	−0.243380	−	0.256449i
$25$	−4.26151e15			−1.78741
$26$			4.83727e15i			1.31793i
$27$	3.61079e15	+	4.22674e15i	0.649533	+	0.760333i
$28$	−5.09607e15			−0.614465
$29$		−	2.50044e14i		−	0.0204946i	−0.999947	−	0.0102473i	$-0.996738\pi$
$29$		−	2.50044e14i		−	0.0204946i	0.999947	−	0.0102473i	$-0.00326187\pi$
$30$	1.51693e16	−	1.43962e16i	0.856312	−	0.812671i
$31$	8.84301e15			0.348034			0.174017	−	0.984743i	$-0.444325\pi$
$31$	8.84301e15			0.348034			0.174017	+	0.984743i	$0.444325\pi$
$32$		−	6.36905e15i		−	0.176777i
$33$	−7.62894e14	−	8.03863e14i	−0.0150942	−	0.0159048i
$34$	3.92304e16			0.558927
$35$		−	1.98096e17i		−	2.05177i
$36$	−3.43937e15	+	6.57209e16i	−0.0261307	+	0.499317i
$37$	−1.23534e17			−0.694334			−0.347167	−	0.937803i	$-0.612856\pi$
$37$	−1.23534e17			−0.694334			−0.347167	+	0.937803i	$0.612856\pi$
$38$			1.34558e17i			0.564014i
$39$	4.29206e17	−	4.07332e17i	1.35193	−	1.28303i
$40$	2.47580e17			0.590276
$41$			7.10953e17i			1.29187i	0.763393	+	0.645935i	$0.223532\pi$
$41$			7.10953e17i			1.29187i	−0.763393	+	0.645935i	$0.776468\pi$
$42$	4.29125e17	+	4.52170e17i	0.598194	+	0.630317i
$43$	−1.56221e18			−1.68108			−0.840539	−	0.541751i	$-0.817761\pi$
$43$	−1.56221e18			−1.68108			−0.840539	+	0.541751i	$0.817761\pi$
$44$		−	1.31199e16i		−	0.0109636i
$45$	−2.55472e18	−	1.33696e17i	−1.66727	−	0.0872533i
$46$	2.16603e17			0.111001
$47$			9.63200e15i			0.00389619i	0.999998	+	0.00194809i	$0.000620098\pi$
$47$			9.63200e15i			0.00389619i	−0.999998	+	0.00194809i	$0.999380\pi$
$48$	−5.65120e17	+	5.36319e17i	−0.181337	+	0.172095i
$49$	1.99507e18			0.510271
$50$			6.17133e18i			1.26389i
$51$	−3.30347e18	−	3.48088e18i	−0.544125	−	0.573346i
$52$	7.00511e18			0.931919
$53$		−	6.22288e18i		−	0.671363i	−0.941976	−	0.335681i	$-0.891033\pi$
$53$		−	6.22288e18i		−	0.671363i	0.941976	−	0.335681i	$-0.108967\pi$
$54$	6.12097e18	−	5.22899e18i	0.537637	−	0.459289i
$55$	5.10002e17			0.0366085
$56$			7.37990e18i			0.434493i
$57$	1.19392e19	−	1.13307e19i	0.578564	−	0.549078i
$58$	−3.62103e17			−0.0144919
$59$		−	1.73109e18i		−	0.0574048i	−0.999588	−	0.0287024i	$-0.990862\pi$
$59$		−	1.73109e18i		−	0.0574048i	0.999588	−	0.0287024i	$-0.00913751\pi$
$60$	−2.08479e19	−	2.19675e19i	−0.574645	−	0.605504i
$61$	1.43862e19			0.330611			0.165305	−	0.986242i	$-0.447139\pi$
$61$	1.43862e19			0.330611			0.165305	+	0.986242i	$0.447139\pi$
$62$		−	1.28061e19i		−	0.246097i
$63$	3.98524e18	−	7.61517e19i	0.0642257	−	1.22725i
$64$	−9.22337e18			−0.125000
$65$			2.72305e20i			3.11178i
$66$	−1.16412e18	+	1.10479e18i	−0.0112464	+	0.0106732i
$67$	−4.19715e19			−0.343662			−0.171831	−	0.985126i	$-0.554968\pi$
$67$	−4.19715e19			−0.343662			−0.171831	+	0.985126i	$0.554968\pi$
$68$		−	5.68117e19i		−	0.395221i
$69$	−1.82394e19	−	1.92189e19i	−0.108062	−	0.113865i
$70$	−2.86874e20			−1.45082
$71$			2.15220e20i			0.931194i	0.884997	+	0.465597i	$0.154160\pi$
$71$			2.15220e20i			0.931194i	−0.884997	+	0.465597i	$0.845840\pi$
$72$	9.51741e19	+	4.98074e18i	0.353070	+	0.0184772i
$73$	−9.65337e18			−0.0307700			−0.0153850	−	0.999882i	$-0.504897\pi$
$73$	−9.65337e18			−0.0307700			−0.0153850	+	0.999882i	$0.504897\pi$
$74$			1.78897e20i			0.490968i
$75$	5.47576e20	−	5.19669e20i	1.29649	−	1.23042i
$76$	1.94861e20			0.398818
$77$			1.52022e19i			0.0269469i
$78$	−5.89879e20	−	6.21556e20i	−0.907240	−	0.955961i
$79$	1.87187e20			0.250253			0.125126	−	0.992141i	$-0.460066\pi$
$79$	1.87187e20			0.250253			0.125126	+	0.992141i	$0.460066\pi$
$80$		−	3.58534e20i		−	0.417388i
$81$	−9.79392e20	−	1.02790e20i	−0.994537	−	0.104380i
$82$	1.02957e21			0.913490
$83$			6.23141e20i			0.483868i	0.970293	+	0.241934i	$0.0777818\pi$
$83$			6.23141e20i			0.483868i	−0.970293	+	0.241934i	$0.922218\pi$
$84$	6.54812e20	−	6.21440e20i	0.445702	−	0.422987i
$85$	2.20840e21			1.31968
$86$			2.26233e21i			1.18870i
$87$	3.04916e19	+	3.21290e19i	0.0141081	+	0.0148657i
$88$	−1.89997e19			−0.00775241
$89$		−	5.00057e21i		−	1.80189i	−0.433929	−	0.900947i	$-0.642873\pi$
$89$		−	5.00057e21i		−	1.80189i	0.433929	−	0.900947i	$-0.357127\pi$
$90$	−1.93613e20	+	3.69964e21i	−0.0616974	+	1.17894i
$91$	−8.11691e21			−2.29053
$92$		−	3.13674e20i		−	0.0784896i
$93$	−1.13627e21	+	1.07836e21i	−0.252446	+	0.239580i
$94$	1.39486e19			0.00275502
$95$			7.57469e21i			1.33170i
$96$	7.76672e20	+	8.18381e20i	0.121690	+	0.128225i
$97$	−4.47780e21			−0.626002			−0.313001	−	0.949753i	$-0.601334\pi$
$97$	−4.47780e21			−0.626002			−0.313001	+	0.949753i	$0.601334\pi$
$98$		−	2.88917e21i		−	0.360816i
$99$	1.96054e20	+	1.02601e19i	0.0218972	+	0.00114594i
$100$	8.93704e21			0.893704
$101$		−	1.21971e22i		−	1.09325i	−0.837377	−	0.546625i	$-0.815912\pi$
$101$		−	1.21971e22i		−	1.09325i	0.837377	−	0.546625i	$-0.184088\pi$
$102$	−5.04085e21	+	4.78394e21i	−0.405417	+	0.384755i
$103$	1.78306e22			1.28812			0.644061	−	0.764975i	$-0.277248\pi$
$103$	1.78306e22			1.28812			0.644061	+	0.764975i	$0.277248\pi$
$104$		−	1.01445e22i		−	0.658966i
$105$	2.41568e22	+	2.54540e22i	1.41240	+	1.48825i
$106$	−9.01170e21			−0.474725
$107$		−	2.25812e22i		−	1.07282i	−0.843958	−	0.536409i	$-0.819780\pi$
$107$		−	2.25812e22i		−	1.07282i	0.843958	−	0.536409i	$-0.180220\pi$
$108$	−7.57238e21	−	8.86411e21i	−0.324767	−	0.380167i
$109$	−3.14292e22			−1.21798			−0.608992	−	0.793177i	$-0.708426\pi$
$109$	−3.14292e22			−1.21798			−0.608992	+	0.793177i	$0.708426\pi$
$110$		−	7.38561e20i		−	0.0258861i
$111$	1.58733e22	−	1.50643e22i	0.503634	−	0.477967i
$112$	1.06872e22			0.307233
$113$		−	2.55953e22i		−	0.667264i	−0.942703	−	0.333632i	$-0.891726\pi$
$113$		−	2.55953e22i		−	0.667264i	0.942703	−	0.333632i	$-0.108274\pi$
$114$	−1.64086e22	−	1.72898e22i	−0.388257	−	0.409107i
$115$	1.21932e22			0.262085
$116$			5.24381e20i			0.0102473i
$117$	−5.47815e21	+	1.04679e23i	−0.0974069	+	1.86129i
$118$	−2.50689e21			−0.0405913
$119$			6.58285e22i			0.971398i
$120$	−3.18124e22	+	3.01910e22i	−0.428156	+	0.406335i
$121$	8.13636e22			0.999519
$122$		−	2.08334e22i		−	0.233777i
$123$	−8.66970e22	−	9.13528e22i	−0.889299	−	0.937056i
$124$	−1.85451e22			−0.174017
$125$			1.53042e23i			1.31462i
$126$	−1.10279e23	−	5.77125e21i	−0.867798	−	0.0454144i
$127$	−2.54447e23			−1.83551			−0.917753	−	0.397151i	$-0.869999\pi$
$127$	−2.54447e23			−1.83551			−0.917753	+	0.397151i	$0.869999\pi$
$128$			1.33569e22i			0.0883883i
$129$	2.00734e23	−	1.90504e23i	1.21937	−	1.15722i
$130$	3.94339e23			2.20036
$131$			7.58864e21i			0.0389206i	0.999811	+	0.0194603i	$0.00619480\pi$
$131$			7.58864e21i			0.0389206i	−0.999811	+	0.0194603i	$0.993805\pi$
$132$	1.59991e21	+	1.68582e21i	0.00754712	+	0.00795241i
$133$	−2.25788e23			−0.980239
$134$			6.07813e22i			0.243006i
$135$	3.44569e23	−	2.94356e23i	1.26942	−	1.08443i
$136$	−8.22721e22			−0.279463
$137$		−	3.35740e23i		−	1.05215i	−0.850438	−	0.526075i	$-0.823663\pi$
$137$		−	3.35740e23i		−	1.05215i	0.850438	−	0.526075i	$-0.176337\pi$
$138$	−2.78320e22	+	2.64135e22i	−0.0805145	+	0.0764111i
$139$	−8.70159e21			−0.0232507			−0.0116253	−	0.999932i	$-0.503701\pi$
$139$	−8.70159e21			−0.0232507			−0.0116253	+	0.999932i	$0.503701\pi$
$140$			4.15438e23i			1.02588i
$141$	−1.17457e21	−	1.23765e21i	−0.00268207	−	0.00282610i
$142$	3.11671e23			0.658454
$143$		−	2.08971e22i		−	0.0408686i
$144$	7.21288e21	−	1.37827e23i	0.0130654	−	0.249658i
$145$	−2.03839e22			−0.0342168
$146$			1.39796e22i			0.0217577i
$147$	−2.56353e23	+	2.43288e23i	−0.370124	+	0.351261i
$148$	2.59070e23			0.347167
$149$			1.47004e24i			1.82928i	0.404271	+	0.914639i	$0.367525\pi$
$149$			1.47004e24i			1.82928i	−0.404271	+	0.914639i	$0.632475\pi$
$150$	−7.52561e23	−	7.92975e23i	−0.870037	−	0.916759i
$151$	−1.33826e24			−1.43811			−0.719057	−	0.694951i	$-0.755426\pi$
$151$	−1.33826e24			−1.43811			−0.719057	+	0.694951i	$0.755426\pi$
$152$		−	2.82188e23i		−	0.282007i
$153$	8.48949e23	+	4.44280e22i	0.789361	+	0.0413096i
$154$	2.20152e22			0.0190544
$155$		−	7.20893e23i		−	0.581061i
$156$	−9.00110e23	+	8.54236e23i	−0.675966	+	0.641516i
$157$	1.57598e23			0.110320			0.0551599	−	0.998478i	$-0.482433\pi$
$157$	1.57598e23			0.110320			0.0551599	+	0.998478i	$0.482433\pi$
$158$		−	2.71076e23i		−	0.176955i
$159$	7.58848e23	+	7.99599e23i	0.462154	+	0.486972i
$160$	−5.19212e23			−0.295138
$161$			3.63458e23i			0.192917i
$162$	−1.48856e23	+	1.41831e24i	−0.0738079	+	0.703244i
$163$	5.35890e23			0.248320			0.124160	−	0.992262i	$-0.460376\pi$
$163$	5.35890e23			0.248320			0.124160	+	0.992262i	$0.460376\pi$
$164$		−	1.49098e24i		−	0.645935i
$165$	−6.55318e22	+	6.21920e22i	−0.0265539	+	0.0252006i
$166$	9.02404e23			0.342147
$167$		−	3.92922e24i		−	1.39452i	−0.716817	−	0.697261i	$-0.754402\pi$
$167$		−	3.92922e24i		−	1.39452i	0.716817	−	0.697261i	$-0.245598\pi$
$168$	−8.99941e23	−	9.48269e23i	−0.299097	−	0.315159i
$169$	7.94574e24			2.47389
$170$		−	3.19811e24i		−	0.933158i
$171$	−1.52385e23	+	2.91184e24i	−0.0416856	+	0.796546i
$172$	3.27620e24			0.840539
$173$			2.12608e24i			0.511768i	0.966707	+	0.255884i	$0.0823665\pi$
$173$			2.12608e24i			0.511768i	−0.966707	+	0.255884i	$0.917633\pi$
$174$	4.65278e22	−	4.41566e22i	0.0105117	−	0.00997593i
$175$	−1.03555e25			−2.19660
$176$			2.75145e22i			0.00548178i
$177$	2.11097e23	+	2.22434e23i	0.0395164	+	0.0416385i
$178$	−7.24160e24			−1.27413
$179$		−	1.09737e25i		−	1.81539i	−0.419629	−	0.907696i	$-0.637840\pi$
$179$		−	1.09737e25i		−	1.81539i	0.419629	−	0.907696i	$-0.362160\pi$
$180$	5.35764e24	+	2.80381e23i	0.833636	+	0.0436266i
$181$	−3.30046e24			−0.483181			−0.241590	−	0.970378i	$-0.577669\pi$
$181$	−3.30046e24			−0.483181			−0.241590	+	0.970378i	$0.577669\pi$
$182$			1.17545e25i			1.61965i
$183$	−1.84853e24	+	1.75432e24i	−0.239808	+	0.227586i
$184$	−4.54248e23			−0.0555006
$185$			1.00707e25i			1.15923i
$186$	1.56163e24	+	1.64549e24i	0.169409	+	0.178506i
$187$	−1.69476e23			−0.0173321
$188$		−	2.01998e22i		−	0.00194809i
$189$	8.77422e24	+	1.02710e25i	0.798231	+	0.934397i
$190$	1.09693e25			0.941651
$191$		−	6.88290e24i		−	0.557705i	−0.960334	−	0.278852i	$-0.910046\pi$
$191$		−	6.88290e24i		−	0.557705i	0.960334	−	0.278852i	$-0.0899540\pi$
$192$	1.18514e24	−	1.12474e24i	0.0906686	−	0.0860477i
$193$	−1.02055e25			−0.737401			−0.368700	−	0.929548i	$-0.620197\pi$
$193$	−1.02055e25			−0.737401			−0.368700	+	0.929548i	$0.620197\pi$
$194$			6.48455e24i			0.442650i
$195$	−3.32061e25	−	3.49894e25i	−2.14209	−	2.25712i
$196$	−4.18396e24			−0.255135
$197$			1.83021e25i			1.05529i	0.849464	+	0.527647i	$0.176926\pi$
$197$			1.83021e25i			1.05529i	−0.849464	+	0.527647i	$0.823074\pi$
$198$	1.48582e22	−	2.83916e23i	0.000810305	−	0.0154836i
$199$	2.64799e25			1.36626			0.683130	−	0.730297i	$-0.260618\pi$
$199$	2.64799e25			1.36626			0.683130	+	0.730297i	$0.260618\pi$
$200$		−	1.29422e25i		−	0.631944i
$201$	5.39306e24	−	5.11821e24i	0.249275	−	0.236571i
$202$	−1.76632e25			−0.773045
$203$		−	6.07607e23i		−	0.0251864i
$204$	6.92789e24	+	7.29993e24i	0.272063	+	0.286673i
$205$	5.79577e25			2.15685
$206$		−	2.58215e25i		−	0.910839i
$207$	4.68729e24	+	2.45300e23i	0.156765	+	0.00820397i
$208$	−1.46908e25			−0.465959
$209$		−	5.81294e23i		−	0.0174899i
$210$	3.68614e25	−	3.49828e25i	1.05235	−	0.998716i
$211$	−9.96760e24			−0.270074			−0.135037	−	0.990841i	$-0.543115\pi$
$211$	−9.96760e24			−0.270074			−0.135037	+	0.990841i	$0.543115\pi$
$212$			1.30503e25i			0.335681i
$213$	−2.62449e25	−	2.76543e25i	−0.641017	−	0.675440i
$214$	−3.27011e25			−0.758597
$215$			1.27354e26i			2.80665i
$216$	−1.28366e25	+	1.09660e25i	−0.268818	+	0.229645i
$217$	2.14885e25			0.427710
$218$			4.55143e25i			0.861244i
$219$	1.24039e24	−	1.17718e24i	0.0223190	−	0.0211815i
$220$	−1.06955e24			−0.0183043
$221$		−	9.04884e25i		−	1.47325i
$222$	−2.18155e25	−	2.29870e25i	−0.337973	−	0.356123i
$223$	−9.49048e25			−1.39938			−0.699689	−	0.714448i	$-0.746678\pi$
$223$	−9.49048e25			−1.39938			−0.699689	+	0.714448i	$0.746678\pi$
$224$		−	1.54768e25i		−	0.217246i
$225$	−6.98896e24	+	1.33548e26i	−0.0934125	+	1.78496i
$226$	−3.70660e25			−0.471827
$227$		−	1.04526e26i		−	1.26748i	−0.773548	−	0.633738i	$-0.781520\pi$
$227$		−	1.04526e26i		−	1.26748i	0.773548	−	0.633738i	$-0.218480\pi$
$228$	−2.50383e25	+	2.37622e25i	−0.289282	+	0.274539i
$229$	8.27122e25			0.910709			0.455354	−	0.890310i	$-0.349513\pi$
$229$	8.27122e25			0.910709			0.455354	+	0.890310i	$0.349513\pi$
$230$		−	1.76577e25i		−	0.185322i
$231$	−1.85383e24	−	1.95339e24i	−0.0185498	−	0.0195459i
$232$	7.59385e23			0.00724593
$233$			7.15811e25i			0.651453i	0.945464	+	0.325727i	$0.105609\pi$
$233$			7.15811e25i			0.651453i	−0.945464	+	0.325727i	$0.894391\pi$
$234$	1.51591e26	+	7.93321e24i	1.31613	+	0.0688771i
$235$	7.85212e23			0.00650489
$236$			3.63036e24i			0.0287024i
$237$	−2.40523e25	+	2.28265e25i	−0.181520	+	0.172269i
$238$	9.53298e25			0.686882
$239$		−	1.10361e26i		−	0.759346i	−0.925121	−	0.379673i	$-0.876037\pi$
$239$		−	1.10361e26i		−	0.759346i	0.925121	−	0.379673i	$-0.123963\pi$
$240$	4.37213e25	+	4.60692e25i	0.287322	+	0.302752i
$241$	−2.16586e26			−1.35970			−0.679849	−	0.733352i	$-0.737955\pi$
$241$	−2.16586e26			−1.35970			−0.679849	+	0.733352i	$0.737955\pi$
$242$		−	1.17827e26i		−	0.706767i
$243$	1.38380e26	−	1.06224e26i	0.793240	−	0.608909i
$244$	−3.01700e25			−0.165305
$245$		−	1.62640e26i		−	0.851924i
$246$	−1.32293e26	+	1.25551e26i	−0.662599	+	0.628830i
$247$	3.10370e26			1.48666
$248$			2.68562e25i			0.123049i
$249$	−7.59888e25	−	8.00695e25i	−0.333086	−	0.350973i
$250$	2.21628e26			0.929576
$251$		−	2.26728e26i		−	0.910109i	−0.890464	−	0.455054i	$-0.849620\pi$
$251$		−	2.26728e26i		−	0.910109i	0.890464	−	0.455054i	$-0.150380\pi$
$252$	−8.35766e24	+	1.59702e26i	−0.0321129	+	0.613626i
$253$	−9.35729e23			−0.00344211
$254$			3.68478e26i			1.29790i
$255$	−2.83765e26	+	2.69303e26i	−0.957231	+	0.908446i
$256$	1.93428e25			0.0625000
$257$			5.65076e25i			0.174921i	0.996168	+	0.0874607i	$0.0278752\pi$
$257$			5.65076e25i			0.174921i	−0.996168	+	0.0874607i	$0.972125\pi$
$258$	−2.75879e26	−	2.90694e26i	−0.818280	−	0.862223i
$259$	−3.00188e26			−0.853288
$260$		−	5.71065e26i		−	1.55589i
$261$	−7.83594e24	−	4.10078e23i	−0.0204666	−	0.00107108i
$262$	1.09895e25			0.0275210
$263$			6.09160e26i			1.46291i	0.681888	+	0.731456i	$0.261159\pi$
$263$			6.09160e26i			1.46291i	−0.681888	+	0.731456i	$0.738841\pi$
$264$	2.44133e24	−	2.31691e24i	0.00562320	−	0.00533662i
$265$	−5.07297e26			−1.12088
$266$			3.26975e26i			0.693134i
$267$	6.09793e26	+	6.42540e26i	1.24039	+	1.30700i
$268$	8.80207e25			0.171831
$269$			5.69197e26i			1.06657i	0.845937	+	0.533283i	$0.179042\pi$
$269$			5.69197e26i			1.06657i	−0.845937	+	0.533283i	$0.820958\pi$
$270$	−4.26273e26	−	4.98989e26i	−0.766808	−	0.897613i
$271$	3.92320e26			0.677608			0.338804	−	0.940857i	$-0.389978\pi$
$271$	3.92320e26			0.677608			0.338804	+	0.940857i	$0.389978\pi$
$272$			1.19143e26i			0.197610i
$273$	1.04297e27	−	9.89815e26i	1.66143	−	1.57676i
$274$	−4.86204e26			−0.743982
$275$		−	2.66603e25i		−	0.0391927i
$276$	3.82509e25	+	4.03050e25i	0.0540308	+	0.0569324i
$277$	−4.68221e26			−0.635585			−0.317793	−	0.948160i	$-0.602942\pi$
$277$	−4.68221e26			−0.635585			−0.317793	+	0.948160i	$0.602942\pi$
$278$			1.26012e25i			0.0164407i
$279$	1.45027e25	−	2.77124e26i	0.0181888	−	0.347558i
$280$	6.01618e26			0.725409
$281$		−	1.18275e27i		−	1.37127i	−0.727945	−	0.685636i	$-0.759524\pi$
$281$		−	1.18275e27i		−	1.37127i	0.727945	−	0.685636i	$-0.240476\pi$
$282$	−1.79231e24	+	1.70096e24i	−0.00199835	+	0.00189651i
$283$	4.88882e26			0.524268			0.262134	−	0.965031i	$-0.415574\pi$
$283$	4.88882e26			0.524268			0.262134	+	0.965031i	$0.415574\pi$
$284$		−	4.51348e26i		−	0.465597i
$285$	−9.23693e26	−	9.73297e26i	−0.916715	−	0.965944i
$286$	−3.02623e25			−0.0288985
$287$			1.72762e27i			1.58762i
$288$	−1.99594e26	−	1.04454e25i	−0.176535	−	0.00923861i
$289$	4.40698e26			0.375202
$290$			2.95191e25i			0.0241949i
$291$	5.75368e26	−	5.46044e26i	0.454070	−	0.430928i
$292$	2.02446e25			0.0153850
$293$			7.47089e26i			0.546800i	0.961900	+	0.273400i	$0.0881482\pi$
$293$			7.47089e26i			0.546800i	−0.961900	+	0.273400i	$0.911852\pi$
$294$	3.52319e26	+	3.71239e26i	0.248379	+	0.261717i
$295$	−1.41121e26			−0.0958403
$296$		−	3.75173e26i		−	0.245484i
$297$	−2.64428e25	+	2.25894e25i	−0.0166719	+	0.0142424i
$298$	2.12884e27			1.29350
$299$		−	4.99613e26i		−	0.292584i
$300$	−1.14835e27	+	1.08982e27i	−0.648247	+	0.615209i
$301$	−3.79618e27			−2.06593
$302$			1.93800e27i			1.01690i
$303$	1.48737e27	+	1.56724e27i	0.752574	+	0.792988i
$304$	−4.08652e26			−0.199409
$305$		−	1.17278e27i		−	0.551972i
$306$	6.43387e25	−	1.22941e27i	0.0292103	−	0.558163i
$307$	1.44713e27			0.633849			0.316924	−	0.948451i	$-0.397350\pi$
$307$	1.44713e27			0.633849			0.316924	+	0.948451i	$0.397350\pi$
$308$		−	3.18814e25i		−	0.0134735i
$309$	−2.29111e27	+	2.17435e27i	−0.934337	+	0.886719i
$310$	−1.04396e27			−0.410872
$311$		−	1.31713e27i		−	0.500338i	−0.968202	−	0.250169i	$-0.919514\pi$
$311$		−	1.31713e27i		−	0.500338i	0.968202	−	0.250169i	$-0.0804862\pi$
$312$	1.23707e27	+	1.30350e27i	0.453620	+	0.477980i
$313$	−7.65076e26			−0.270842			−0.135421	−	0.990788i	$-0.543239\pi$
$313$	−7.65076e26			−0.270842			−0.135421	+	0.990788i	$0.543239\pi$
$314$		−	2.28226e26i		−	0.0780079i
$315$	−6.20797e27	−	3.24882e26i	−2.04896	−	0.107228i
$316$	−3.92560e26			−0.125126
$317$		−	3.31997e27i		−	1.02207i	−0.859559	−	0.511037i	$-0.829262\pi$
$317$		−	3.31997e27i		−	1.02207i	0.859559	−	0.511037i	$-0.170738\pi$
$318$	1.15794e27	−	1.09893e27i	0.344341	−	0.326792i
$319$	1.56429e24			0.000449388
$320$			7.51900e26i			0.208694i
$321$	2.75366e27	+	2.90154e27i	0.738508	+	0.778167i
$322$	5.26344e26			0.136413
$323$		−	2.51711e27i		−	0.630485i
$324$	2.05393e27	+	2.15567e26i	0.497269	+	0.0521900i
$325$	1.42347e28			3.33144
$326$		−	7.76052e26i		−	0.175589i
$327$	4.03844e27	−	3.83262e27i	0.883463	−	0.838437i
$328$	−2.15917e27			−0.456745
$329$			2.34057e25i			0.00478815i
$330$	9.00637e25	+	9.49002e25i	0.0178195	+	0.0187765i
$331$	−2.97386e27			−0.569131			−0.284566	−	0.958657i	$-0.591849\pi$
$331$	−2.97386e27			−0.569131			−0.284566	+	0.958657i	$0.591849\pi$
$332$		−	1.30682e27i		−	0.241934i
$333$	−2.02599e26	+	3.87134e27i	−0.0362869	+	0.693385i
$334$	−5.69012e27			−0.986076
$335$			3.42157e27i			0.573763i
$336$	−1.37324e27	+	1.30325e27i	−0.222851	+	0.211493i
$337$	−6.71977e27			−1.05542			−0.527710	−	0.849425i	$-0.676949\pi$
$337$	−6.71977e27			−1.05542			−0.527710	+	0.849425i	$0.676949\pi$
$338$		−	1.15067e28i		−	1.74931i
$339$	3.12122e27	+	3.28883e27i	0.459332	+	0.483999i
$340$	−4.63136e27			−0.659842
$341$			5.53225e25i			0.00763139i
$342$	4.21680e27	+	2.20678e26i	0.563243	+	0.0294762i
$343$	−4.65285e27			−0.601843
$344$		−	4.74445e27i		−	0.594351i
$345$	−1.56675e27	+	1.48690e27i	−0.190103	+	0.180415i
$346$	3.07890e27			0.361875
$347$			8.45322e27i			0.962494i	0.876585	+	0.481247i	$0.159816\pi$
$347$			8.45322e27i			0.962494i	−0.876585	+	0.481247i	$0.840184\pi$
$348$	−6.39455e25	−	6.73795e25i	−0.00705405	−	0.00743286i
$349$	6.08370e27			0.650262			0.325131	−	0.945669i	$-0.394592\pi$
$349$	6.08370e27			0.650262			0.325131	+	0.945669i	$0.394592\pi$
$350$			1.49963e28i			1.55323i
$351$	−1.20611e28	−	1.41186e28i	−1.21062	−	1.41714i
$352$	3.98452e25			0.00387621
$353$			1.71337e28i			1.61558i	0.589471	+	0.807790i	$0.299336\pi$
$353$			1.71337e28i			1.61558i	−0.589471	+	0.807790i	$0.700664\pi$
$354$	3.22118e26	−	3.05702e26i	0.0294428	−	0.0279423i
$355$	1.75450e28			1.55468
$356$			1.04870e28i			0.900947i
$357$	−8.02744e27	−	8.45852e27i	−0.668693	−	0.704602i
$358$	−1.58916e28			−1.28368
$359$		−	1.32701e28i		−	1.03953i	−0.854311	−	0.519763i	$-0.826020\pi$
$359$		−	1.32701e28i		−	1.03953i	0.854311	−	0.519763i	$-0.173980\pi$
$360$	4.06036e26	−	7.75870e27i	0.0308487	−	0.589469i
$361$	−4.93645e27			−0.363777
$362$			4.77957e27i			0.341660i
$363$	−1.04547e28	+	9.92186e27i	−0.725000	+	0.688051i
$364$	1.70224e28			1.14526
$365$			7.86954e26i			0.0513722i
$366$	2.54052e27	+	2.67695e27i	0.160928	+	0.169570i
$367$	−4.06121e27			−0.249649			−0.124824	−	0.992179i	$-0.539837\pi$
$367$	−4.06121e27			−0.249649			−0.124824	+	0.992179i	$0.539837\pi$
$368$			6.57822e26i			0.0392448i
$369$	2.22800e28	+	1.16598e27i	1.29010	+	0.0675150i
$370$	1.45839e28			0.819697
$371$		−	1.51216e28i		−	0.825058i
$372$	2.38293e27	−	2.26148e27i	0.126223	−	0.119790i
$373$	2.81315e27			0.144676			0.0723378	−	0.997380i	$-0.476954\pi$
$373$	2.81315e27			0.144676			0.0723378	+	0.997380i	$0.476954\pi$
$374$			2.45428e26i			0.0122557i
$375$	−1.86626e28	−	1.96648e28i	−0.904959	−	0.953557i
$376$	−2.92524e25			−0.00137751
$377$			8.35222e26i			0.0381986i
$378$	1.48739e28	−	1.27064e28i	0.660718	−	0.564435i
$379$	−1.84723e28			−0.797057			−0.398529	−	0.917156i	$-0.630479\pi$
$379$	−1.84723e28			−0.797057			−0.398529	+	0.917156i	$0.630479\pi$
$380$		−	1.58853e28i		−	0.665848i
$381$	3.26947e28	−	3.10284e28i	1.33138	−	1.26353i
$382$	−9.96750e27			−0.394357
$383$		−	9.71325e26i		−	0.0373403i	−0.999826	−	0.0186702i	$-0.994057\pi$
$383$		−	9.71325e26i		−	0.0373403i	0.999826	−	0.0186702i	$-0.00594324\pi$
$384$	−1.62880e27	−	1.71627e27i	−0.0608449	−	0.0641124i
$385$	1.23930e27			0.0449893
$386$			1.47791e28i			0.521421i
$387$	−2.56206e27	+	4.89570e28i	−0.0878556	+	1.67878i
$388$	9.39063e27			0.313001
$389$			1.69345e28i			0.548689i	0.961631	+	0.274345i	$0.0884609\pi$
$389$			1.69345e28i			0.548689i	−0.961631	+	0.274345i	$0.911539\pi$
$390$	−5.06700e28	+	4.80876e28i	−1.59603	+	1.51469i
$391$	−4.05188e27			−0.124083
$392$			6.05902e27i			0.180408i
$393$	−9.25394e26	−	9.75089e26i	−0.0267922	−	0.0282310i
$394$	2.65043e28			0.746206
$395$		−	1.52597e28i		−	0.417810i
$396$	−4.11154e26	−	2.15169e25i	−0.0109486	−	0.000572972i
$397$	−2.59381e28			−0.671804			−0.335902	−	0.941897i	$-0.609041\pi$
$397$	−2.59381e28			−0.671804			−0.335902	+	0.941897i	$0.609041\pi$
$398$		−	3.83471e28i		−	0.966092i
$399$	2.90122e28	−	2.75336e28i	0.711015	−	0.674779i
$400$	−1.87423e28			−0.446852
$401$			3.52251e28i			0.817080i	0.912740	+	0.408540i	$0.133962\pi$
$401$			3.52251e28i			0.817080i	−0.912740	+	0.408540i	$0.866038\pi$
$402$	−7.41196e27	−	7.80999e27i	−0.167281	−	0.176264i
$403$	−2.95383e28			−0.648679
$404$			2.55791e28i			0.546625i
$405$	−8.37960e27	+	7.98411e28i	−0.174268	+	1.66043i
$406$	−8.79909e26			−0.0178095
$407$		−	7.72838e26i		−	0.0152247i
$408$	1.05714e28	−	1.00327e28i	0.202708	−	0.192377i
$409$	−1.88501e27			−0.0351849			−0.0175925	−	0.999845i	$-0.505600\pi$
$409$	−1.88501e27			−0.0351849			−0.0175925	+	0.999845i	$0.505600\pi$
$410$		−	8.39318e28i		−	1.52512i
$411$	4.09418e28	+	4.31404e28i	0.724280	+	0.763175i
$412$	−3.73935e28			−0.644061
$413$		−	4.20655e27i		−	0.0705465i
$414$	3.55232e26	−	6.78793e27i	0.00580108	−	0.110849i
$415$	5.07992e28			0.807844
$416$			2.12745e28i			0.329483i
$417$	1.11810e27	−	1.06111e27i	0.0168648	−	0.0160053i
$418$	−8.41803e26			−0.0123672
$419$		−	1.12689e29i		−	1.61260i	−0.591508	−	0.806299i	$-0.701467\pi$
$419$		−	1.12689e29i		−	1.61260i	0.591508	−	0.806299i	$-0.298533\pi$
$420$	−5.06605e28	−	5.33810e28i	−0.706199	−	0.744123i
$421$	−1.63590e27			−0.0222154			−0.0111077	−	0.999938i	$-0.503536\pi$
$421$	−1.63590e27			−0.0222154			−0.0111077	+	0.999938i	$0.503536\pi$
$422$			1.44346e28i			0.190971i
$423$	3.01849e26	+	1.57967e25i	0.00389086	+	0.000203621i
$424$	1.88989e28			0.237363
$425$		−	1.15444e29i		−	1.41284i
$426$	−4.00477e28	+	3.80067e28i	−0.477608	+	0.453267i
$427$	3.49584e28			0.406298
$428$			4.73563e28i			0.536409i
$429$	2.54829e27	+	2.68514e27i	0.0281332	+	0.0296440i
$430$	1.84428e29			1.98460
$431$			1.25299e29i			1.31431i	0.753757	+	0.657154i	$0.228240\pi$
$431$			1.25299e29i			1.31431i	−0.753757	+	0.657154i	$0.771760\pi$
$432$	1.58804e28	+	1.85894e28i	0.162383	+	0.190083i
$433$	2.99363e28			0.298422			0.149211	−	0.988805i	$-0.452327\pi$
$433$	2.99363e28			0.298422			0.149211	+	0.988805i	$0.452327\pi$
$434$		−	3.11187e28i		−	0.302436i
$435$	2.61920e27	−	2.48571e27i	0.0248191	−	0.0235542i
$436$	6.59117e28			0.608992
$437$		−	1.38977e28i		−	0.125212i
$438$	−1.70474e27	−	1.79628e27i	−0.0149776	−	0.0157819i
$439$	6.93279e28			0.594016			0.297008	−	0.954875i	$-0.404011\pi$
$439$	6.93279e28			0.594016			0.297008	+	0.954875i	$0.404011\pi$
$440$			1.54888e27i			0.0129431i
$441$	3.27195e27	−	6.25218e28i	0.0266675	−	0.509574i
$442$	−1.31041e29			−1.04175
$443$			6.10344e28i			0.473297i	0.971595	+	0.236649i	$0.0760490\pi$
$443$			6.10344e28i			0.473297i	−0.971595	+	0.236649i	$0.923951\pi$
$444$	−3.32888e28	+	3.15922e28i	−0.251817	+	0.238983i
$445$	−4.07652e29			−3.00836
$446$			1.37437e29i			0.989509i
$447$	−1.79263e29	−	1.88890e29i	−1.25924	−	1.32686i
$448$	−2.24128e28			−0.153616
$449$		−	1.05434e29i		−	0.705135i	−0.935786	−	0.352567i	$-0.885309\pi$
$449$		−	1.05434e29i		−	0.705135i	0.935786	−	0.352567i	$-0.114691\pi$
$450$	1.93398e29	+	1.01211e28i	1.26216	+	0.0660526i
$451$	−4.44777e27			−0.0283270
$452$			5.36773e28i			0.333632i
$453$	1.71957e29	−	1.63193e29i	1.04313	−	0.989971i
$454$	−1.51370e29			−0.896240
$455$			6.61700e29i			3.82416i
$456$	3.44114e28	+	3.62593e28i	0.194128	+	0.204553i
$457$	−9.15845e28			−0.504363			−0.252182	−	0.967680i	$-0.581148\pi$
$457$	−9.15845e28			−0.504363			−0.252182	+	0.967680i	$0.581148\pi$
$458$		−	1.19780e29i		−	0.643968i
$459$	−1.14502e29	+	9.78162e28i	−0.600999	+	0.513418i
$460$	−2.55711e28			−0.131043
$461$		−	2.43448e29i		−	1.21813i	−0.793119	−	0.609067i	$-0.791544\pi$
$461$		−	2.43448e29i		−	1.21813i	0.793119	−	0.609067i	$-0.208456\pi$
$462$	−2.82880e27	+	2.68464e27i	−0.0138211	+	0.0131167i
$463$	3.88463e29			1.85335			0.926677	−	0.375859i	$-0.122652\pi$
$463$	3.88463e29			1.85335			0.926677	+	0.375859i	$0.122652\pi$
$464$		−	1.09971e27i		−	0.00512365i
$465$	8.79091e28	+	9.26299e28i	0.399992	+	0.421472i
$466$	1.03660e29			0.460647
$467$		−	2.67460e28i		−	0.116084i	−0.998314	−	0.0580420i	$-0.981514\pi$
$467$		−	2.67460e28i		−	0.116084i	0.998314	−	0.0580420i	$-0.0184857\pi$
$468$	1.14885e28	−	2.19527e29i	0.0487034	−	0.930645i
$469$	−1.01991e29			−0.422337
$470$		−	1.13711e27i		−	0.00459966i
$471$	−2.02502e28	+	1.92182e28i	−0.0800203	+	0.0759421i
$472$	5.25733e27			0.0202956
$473$		−	9.77332e27i		−	0.0368612i
$474$	3.30563e28	+	3.48315e28i	0.121813	+	0.128354i
$475$	3.95966e29			1.42570
$476$		−	1.38052e29i		−	0.485699i
$477$	−1.95014e29	−	1.02057e28i	−0.670445	−	0.0350864i
$478$	−1.59820e29			−0.536939
$479$		−	5.17851e29i		−	1.70026i	−0.526576	−	0.850128i	$-0.676525\pi$
$479$		−	5.17851e29i		−	1.70026i	0.526576	−	0.850128i	$-0.323475\pi$
$480$	6.67153e28	−	6.33152e28i	0.214078	−	0.203168i
$481$	4.12641e29			1.29413
$482$			3.13650e29i			0.961452i
$483$	−4.43218e28	−	4.67020e28i	−0.132800	−	0.139932i
$484$	−1.70632e29			−0.499760
$485$			3.65036e29i			1.04514i
$486$	−1.53828e29	−	2.00396e29i	−0.430564	−	0.560905i
$487$	−2.51685e29			−0.688714			−0.344357	−	0.938839i	$-0.611903\pi$
$487$	−2.51685e29			−0.688714			−0.344357	+	0.938839i	$0.611903\pi$
$488$			4.36908e28i			0.116889i
$489$	−6.88583e28	+	6.53490e28i	−0.180119	+	0.170939i
$490$	−2.35528e29			−0.602402
$491$		−	5.88907e29i		−	1.47282i	−0.676535	−	0.736411i	$-0.736519\pi$
$491$		−	5.88907e29i		−	1.47282i	0.676535	−	0.736411i	$-0.263481\pi$
$492$	1.81817e29	+	1.91581e29i	0.444650	+	0.468528i
$493$	6.77369e27			0.0161998
$494$		−	4.49463e29i		−	1.05123i
$495$	8.36413e26	−	1.59825e28i	0.00191321	−	0.0365585i
$496$	3.88920e28			0.0870085
$497$			5.22983e29i			1.14437i
$498$	−1.15953e29	+	1.10043e29i	−0.248176	+	0.235527i
$499$	7.36099e29			1.54110			0.770549	−	0.637381i	$-0.219982\pi$
$499$	7.36099e29			1.54110			0.770549	+	0.637381i	$0.219982\pi$
$500$		−	3.20952e29i		−	0.657309i
$501$	4.79148e29	+	5.04879e29i	0.959964	+	1.01152i
$502$	−3.28337e29			−0.643544
$503$			6.61522e29i			1.26852i	0.773121	+	0.634258i	$0.218694\pi$
$503$			6.61522e29i			1.26852i	−0.773121	+	0.634258i	$0.781306\pi$
$504$	2.31273e29	+	1.21032e28i	0.433899	+	0.0227072i
$505$	−9.94318e29			−1.82524
$506$			1.35508e27i			0.00243394i
$507$	−1.02097e30	+	9.68941e29i	−1.79443	+	1.70298i
$508$	5.33613e29			0.917753
$509$		−	1.68144e29i		−	0.283000i	−0.989938	−	0.141500i	$-0.954807\pi$
$509$		−	1.68144e29i		−	0.283000i	0.989938	−	0.141500i	$-0.0451925\pi$
$510$	3.89992e29	+	4.10936e29i	0.642369	+	0.676865i
$511$	−2.34577e28			−0.0378142
$512$		−	2.80114e28i		−	0.0441942i
$513$	−3.35503e29	−	3.92735e29i	−0.518091	−	0.606469i
$514$	8.18318e28			0.123688
$515$		−	1.45357e30i		−	2.15059i
$516$	−4.20970e29	+	3.99516e29i	−0.609684	+	0.578611i
$517$	−6.02584e25			−8.54323e−5
$518$			4.34718e29i			0.603366i
$519$	−2.59265e29	−	2.73188e29i	−0.352292	−	0.371210i
$520$	−8.26990e29			−1.10018
$521$			3.58985e29i			0.467586i	0.972286	+	0.233793i	$0.0751138\pi$
$521$			3.58985e29i			0.467586i	−0.972286	+	0.233793i	$0.924886\pi$
$522$	−5.93856e26	+	1.13476e28i	−0.000757366	+	0.0144721i
$523$	−1.39459e29			−0.174152			−0.0870759	−	0.996202i	$-0.527752\pi$
$523$	−1.39459e29			−0.174152			−0.0870759	+	0.996202i	$0.527752\pi$
$524$		−	1.59145e28i		−	0.0194603i
$525$	1.33061e30	−	1.26279e30i	1.59330	−	1.51210i
$526$	8.82159e29			1.03444
$527$			2.39557e29i			0.275101i
$528$	−3.35525e27	−	3.53543e27i	−0.00377356	−	0.00397620i
$529$	8.85475e29			0.975358
$530$			7.34644e29i			0.792579i
$531$	−5.42492e28	−	2.83902e27i	−0.0573263	−	0.00300006i
$532$	4.73511e29			0.490120
$533$		−	2.37480e30i		−	2.40784i
$534$	9.30497e29	−	8.83075e29i	0.924190	−	0.877089i
$535$	−1.84085e30			−1.79113
$536$		−	1.27468e29i		−	0.121503i
$537$	1.33819e30	+	1.41005e30i	1.24968	+	1.31679i
$538$	8.24286e29			0.754176
$539$			1.24813e28i			0.0111888i
$540$	−7.22613e29	+	6.17309e29i	−0.634708	+	0.542215i
$541$	−1.08758e30			−0.936030			−0.468015	−	0.883720i	$-0.655031\pi$
$541$	−1.08758e30			−0.936030			−0.468015	+	0.883720i	$0.655031\pi$
$542$		−	5.68141e29i		−	0.479141i
$543$	4.24087e29	−	4.02473e29i	0.350474	−	0.332613i
$544$	1.72537e29			0.139732
$545$			2.56214e30i			2.03349i
$546$	−1.43340e30	−	1.51038e30i	−1.11494	−	1.17481i
$547$	−1.88013e29			−0.143327			−0.0716635	−	0.997429i	$-0.522831\pi$
$547$	−1.88013e29			−0.143327			−0.0716635	+	0.997429i	$0.522831\pi$
$548$			7.04099e29i			0.526075i
$549$	2.35936e28	−	4.50836e29i	0.0172782	−	0.330159i
$550$	−3.86082e28			−0.0277134
$551$			2.32333e28i			0.0163472i
$552$	5.83679e28	−	5.53932e28i	0.0402573	−	0.0382056i
$553$	4.54865e29			0.307543
$554$			6.78057e29i			0.449427i
$555$	−1.22806e30	−	1.29401e30i	−0.797991	−	0.840844i
$556$	1.82485e28			0.0116253
$557$			2.83210e30i			1.76889i	0.466640	+	0.884447i	$0.345464\pi$
$557$			2.83210e30i			1.76889i	−0.466640	+	0.884447i	$0.654536\pi$
$558$	−4.01318e29	−	2.10022e28i	−0.245761	−	0.0128614i
$559$	5.21826e30			3.13326
$560$		−	8.71236e29i		−	0.512941i
$561$	2.17766e28	−	2.06668e28i	0.0125718	−	0.0119311i
$562$	−1.71281e30			−0.969636
$563$			1.38770e30i			0.770379i	0.922837	+	0.385190i	$0.125864\pi$
$563$			1.38770e30i			0.770379i	−0.922837	+	0.385190i	$0.874136\pi$
$564$	2.46326e27	+	2.59554e27i	0.00134103	+	0.00141305i
$565$	−2.08656e30			−1.11403
$566$		−	7.07977e29i		−	0.370714i
$567$	−2.37992e30	−	2.49781e29i	−1.22222	−	0.128276i
$568$	−6.53622e29			−0.329227
$569$		−	1.15851e30i		−	0.572354i	−0.958177	−	0.286177i	$-0.907616\pi$
$569$		−	1.15851e30i		−	0.572354i	0.958177	−	0.286177i	$-0.0923845\pi$
$570$	−1.40948e30	+	1.33765e30i	−0.683025	+	0.648215i
$571$	−2.95736e30			−1.40575			−0.702873	−	0.711315i	$-0.748100\pi$
$571$	−2.95736e30			−1.40575			−0.702873	+	0.711315i	$0.748100\pi$
$572$			4.38244e28i			0.0204343i
$573$	8.39333e29	+	8.84406e29i	0.383914	+	0.404530i
$574$	2.50185e30			1.12262
$575$		−	6.37400e29i		−	0.280586i
$576$	−1.51265e28	+	2.89044e29i	−0.00653268	+	0.124829i
$577$	−1.38283e30			−0.585914			−0.292957	−	0.956126i	$-0.594639\pi$
$577$	−1.38283e30			−0.585914			−0.292957	+	0.956126i	$0.594639\pi$
$578$		−	6.38200e29i		−	0.265308i
$579$	1.31134e30	−	1.24451e30i	0.534873	−	0.507613i
$580$	4.27482e28			0.0171084
$581$			1.51423e30i			0.594641i
$582$	−7.90757e29	−	8.33221e29i	−0.304712	−	0.321076i
$583$	3.89308e28			0.0147211
$584$		−	2.93173e28i		−	0.0108788i
$585$	8.53353e30	+	4.46585e29i	3.10752	+	0.162626i
$586$	1.08190e30			0.386646
$587$			3.03148e30i			1.06325i	0.846980	+	0.531625i	$0.178419\pi$
$587$			3.03148e30i			1.06325i	−0.846980	+	0.531625i	$0.821581\pi$
$588$	5.37611e29	−	5.10212e29i	0.185062	−	0.175631i
$589$	−8.21665e29			−0.277604
$590$			2.04364e29i			0.0677693i
$591$	−2.23185e30	−	2.35170e30i	−0.726445	−	0.765456i
$592$	−5.43309e29			−0.173583
$593$		−	5.60572e30i		−	1.75804i	−0.476782	−	0.879021i	$-0.658197\pi$
$593$		−	5.60572e30i		−	1.75804i	0.476782	−	0.879021i	$-0.341803\pi$
$594$	3.27129e28	+	3.82932e28i	0.0100709	+	0.0117888i
$595$	5.36641e30			1.62180
$596$		−	3.08289e30i		−	0.914639i
$597$	−3.40250e30	+	3.22909e30i	−0.991015	+	0.940508i
$598$	−7.23517e29			−0.206888
$599$		−	3.48458e30i		−	0.978263i	−0.872210	−	0.489131i	$-0.837314\pi$
$599$		−	3.48458e30i		−	0.978263i	0.872210	−	0.489131i	$-0.162686\pi$
$600$	1.57823e30	+	1.66299e30i	0.435019	+	0.458380i
$601$	−7.67603e29			−0.207739			−0.103869	−	0.994591i	$-0.533122\pi$
$601$	−7.67603e29			−0.207739			−0.103869	+	0.994591i	$0.533122\pi$
$602$			5.49745e30i			1.46083i
$603$	−6.88342e28	+	1.31531e30i	−0.0179603	+	0.343193i
$604$	2.80653e30			0.719057
$605$		−	6.63285e30i		−	1.66875i
$606$	2.26961e30	−	2.15394e30i	0.560727	−	0.532150i
$607$	−1.21587e30			−0.294993			−0.147497	−	0.989063i	$-0.547122\pi$
$607$	−1.21587e30			−0.294993			−0.147497	+	0.989063i	$0.547122\pi$
$608$			5.91792e29i			0.141003i
$609$	7.40945e28	+	7.80735e28i	0.0173379	+	0.0182689i
$610$	−1.69836e30			−0.390303
$611$		−	3.21737e28i		−	0.00726186i
$612$	−1.78038e30	−	9.31723e28i	−0.394681	−	0.0206548i
$613$	−5.96084e30			−1.29790			−0.648951	−	0.760830i	$-0.724792\pi$
$613$	−5.96084e30			−1.29790			−0.648951	+	0.760830i	$0.724792\pi$
$614$		−	2.09567e30i		−	0.448199i
$615$	−7.44718e30	+	7.06764e30i	−1.56446	+	1.48473i
$616$	−4.61692e28			−0.00952718
$617$			7.40435e30i			1.50090i	0.660930	+	0.750448i	$0.270162\pi$
$617$			7.40435e30i			1.50090i	−0.660930	+	0.750448i	$0.729838\pi$
$618$	3.14879e30	+	3.31789e30i	0.627005	+	0.660676i
$619$	−1.30025e30			−0.254349			−0.127174	−	0.991880i	$-0.540591\pi$
$619$	−1.30025e30			−0.254349			−0.127174	+	0.991880i	$0.540591\pi$
$620$			1.51182e30i			0.290531i
$621$	−6.32199e29	+	5.40072e29i	−0.119357	+	0.101963i
$622$	−1.90740e30			−0.353792
$623$		−	1.21514e31i		−	2.21440i
$624$	1.88767e30	−	1.79146e30i	0.337983	−	0.320758i
$625$	2.31590e30			0.407418
$626$			1.10795e30i			0.191515i
$627$	7.08857e28	+	7.46924e28i	0.0120397	+	0.0126863i
$628$	−3.30506e29			−0.0551599
$629$		−	3.34653e30i		−	0.548830i
$630$	−4.70479e29	+	8.99011e30i	−0.0758218	+	1.44883i
$631$	8.75982e30			1.38731			0.693653	−	0.720309i	$-0.256000\pi$
$631$	8.75982e30			1.38731			0.693653	+	0.720309i	$0.256000\pi$
$632$			5.68488e29i			0.0884776i
$633$	1.28077e30	−	1.21550e30i	0.195898	−	0.185914i
$634$	−4.80783e30			−0.722715
$635$			2.07428e31i			3.06448i
$636$	−1.59142e30	−	1.67688e30i	−0.231077	−	0.243486i
$637$	−6.66412e30			−0.951062
$638$		−	2.26534e27i		−	0.000317765i
$639$	6.74459e30	+	3.52965e29i	0.929921	+	0.0486655i
$640$	1.08887e30			0.147569
$641$		−	1.38460e30i		−	0.184453i	−0.995738	−	0.0922263i	$-0.970602\pi$
$641$		−	1.38460e30i		−	0.184453i	0.995738	−	0.0922263i	$-0.0293983\pi$
$642$	4.20188e30	−	3.98773e30i	0.550247	−	0.522204i
$643$	1.46506e31			1.88596			0.942982	−	0.332844i	$-0.108008\pi$
$643$	1.46506e31			1.88596			0.942982	+	0.332844i	$0.108008\pi$
$644$		−	7.62227e29i		−	0.0964583i
$645$	−1.55301e31	−	1.63641e31i	−1.93204	−	2.03580i
$646$	−3.64516e30			−0.445820
$647$			6.52633e30i			0.784733i	0.919809	+	0.392367i	$0.128344\pi$
$647$			6.52633e30i			0.784733i	−0.919809	+	0.392367i	$0.871656\pi$
$648$	3.12175e29	−	2.97441e30i	0.0369039	−	0.351622i
$649$	1.08298e28			0.00125872
$650$		−	2.06141e31i		−	2.35568i
$651$	−2.76113e30	+	2.62041e30i	−0.310239	+	0.294428i
$652$	−1.12384e30			−0.124160
$653$		−	2.21687e30i		−	0.240821i	−0.992724	−	0.120411i	$-0.961579\pi$
$653$		−	2.21687e30i		−	0.240821i	0.992724	−	0.120411i	$-0.0384211\pi$
$654$	−5.55023e30	−	5.84828e30i	−0.592865	−	0.624702i
$655$	6.18634e29			0.0649800
$656$			3.12681e30i			0.322967i
$657$	−1.58317e28	+	3.02519e29i	−0.00160809	+	0.0307280i
$658$	3.38951e28			0.00338573
$659$		−	1.13807e31i		−	1.11797i	−0.829179	−	0.558983i	$-0.811192\pi$
$659$		−	1.13807e31i		−	1.11797i	0.829179	−	0.558983i	$-0.188808\pi$
$660$	1.37430e29	−	1.30426e29i	0.0132770	−	0.0126003i
$661$	1.34060e31			1.27375			0.636873	−	0.770969i	$-0.280227\pi$
$661$	1.34060e31			1.27375			0.636873	+	0.770969i	$0.280227\pi$
$662$			4.30661e30i			0.402437i
$663$	1.10346e31	+	1.16272e31i	1.01416	+	1.06862i
$664$	−1.89248e30			−0.171073
$665$			1.84065e31i			1.63656i
$666$	5.60629e30	+	2.93394e29i	0.490297	+	0.0256587i
$667$	3.73995e28			0.00321723
$668$			8.24018e30i			0.697261i
$669$	1.21946e31	−	1.15731e31i	1.01504	−	0.963305i
$670$	4.95496e30			0.405712
$671$			9.00008e28i			0.00724934i
$672$	1.88731e30	+	1.98866e30i	0.149548	+	0.157579i
$673$	−3.17018e29			−0.0247126			−0.0123563	−	0.999924i	$-0.503933\pi$
$673$	−3.17018e29			−0.0247126			−0.0123563	+	0.999924i	$0.503933\pi$
$674$			9.73126e30i			0.746295i
$675$	−1.53874e31	−	1.80123e31i	−1.16098	−	1.35903i
$676$	−1.66634e31			−1.23695
$677$		−	1.91763e31i		−	1.40052i	−0.713887	−	0.700261i	$-0.753067\pi$
$677$		−	1.91763e31i		−	1.40052i	0.713887	−	0.700261i	$-0.246933\pi$
$678$	4.76273e30	−	4.52000e30i	0.342239	−	0.324797i
$679$	−1.08810e31			−0.769313
$680$			6.70692e30i			0.466579i
$681$	1.27464e31	+	1.34309e31i	0.872507	+	0.919361i
$682$	8.01155e28			0.00539621
$683$			1.56555e31i			1.03762i	0.854889	+	0.518812i	$0.173625\pi$
$683$			1.56555e31i			1.03762i	−0.854889	+	0.518812i	$0.826375\pi$
$684$	3.19575e29	−	6.10658e30i	0.0208428	−	0.398273i
$685$	−2.73699e31			−1.75662
$686$			6.73804e30i			0.425567i
$687$	−1.06280e31	+	1.00863e31i	−0.660581	+	0.626915i
$688$	−6.87069e30			−0.420269
$689$			2.07863e31i			1.25131i
$690$	2.15326e30	+	2.26890e30i	0.127572	+	0.134423i
$691$	1.45653e30			0.0849301			0.0424651	−	0.999098i	$-0.486479\pi$
$691$	1.45653e30			0.0849301			0.0424651	+	0.999098i	$0.486479\pi$
$692$		−	4.45872e30i		−	0.255884i
$693$	4.76410e29	+	2.49320e28i	0.0269101	+	0.00140829i
$694$	1.22416e31			0.680586
$695$			7.09363e29i			0.0388182i
$696$	−9.75759e28	+	9.26030e28i	−0.00525583	+	0.00498797i
$697$	−1.92597e31			−1.02115
$698$		−	8.81014e30i		−	0.459805i
$699$	−8.72894e30	−	9.19769e30i	−0.448448	−	0.472531i
$700$	2.17170e31			1.09830
$701$		−	1.44651e31i		−	0.720150i	−0.932923	−	0.360075i	$-0.882751\pi$
$701$		−	1.44651e31i		−	0.720150i	0.932923	−	0.360075i	$-0.117249\pi$
$702$	−2.04459e31	+	1.74664e31i	−1.00207	+	0.856041i
$703$	1.14784e31			0.553826
$704$		−	5.77020e28i		−	0.00274089i
$705$	−1.00894e29	+	9.57524e28i	−0.00471832	+	0.00447785i
$706$	2.48122e31			1.14239
$707$		−	2.96388e31i		−	1.34353i
$708$	−4.42704e29	−	4.66477e29i	−0.0197582	−	0.0208192i
$709$	6.60398e30			0.290200			0.145100	−	0.989417i	$-0.453650\pi$
$709$	6.60398e30			0.290200			0.145100	+	0.989417i	$0.453650\pi$
$710$		−	2.54078e31i		−	1.09932i
$711$	3.06991e29	−	5.86611e30i	0.0130786	−	0.249911i
$712$	1.51867e31			0.637066
$713$			1.32266e30i			0.0546341i
$714$	−1.22492e31	+	1.16250e31i	−0.498229	+	0.472837i
$715$	−1.70356e30			−0.0682323
$716$			2.30135e31i			0.907696i
$717$	1.34580e31	+	1.41807e31i	0.522720	+	0.550790i
$718$	−1.92172e31			−0.735056
$719$		−	8.90367e30i		−	0.335391i	−0.985839	−	0.167695i	$-0.946368\pi$
$719$		−	8.90367e30i		−	0.335391i	0.985839	−	0.167695i	$-0.0536325\pi$
$720$	−1.12358e31	−	5.88002e29i	−0.416818	−	0.0218133i
$721$	4.33283e31			1.58301
$722$			7.14874e30i			0.257229i
$723$	2.78298e31	−	2.64115e31i	0.986256	−	0.935992i
$724$	6.92156e30			0.241590
$725$			1.06557e30i			0.0366322i
$726$	1.43684e31	+	1.51400e31i	0.486525	+	0.512652i
$727$	−1.29208e31			−0.430933			−0.215467	−	0.976511i	$-0.569127\pi$
$727$	−1.29208e31			−0.430933			−0.215467	+	0.976511i	$0.569127\pi$
$728$		−	2.46511e31i		−	0.809824i
$729$	−4.82749e30	+	3.05238e31i	−0.156213	+	0.987723i
$730$	1.13963e30			0.0363256
$731$		−	4.23203e31i		−	1.32879i
$732$	3.87664e30	−	3.67907e30i	0.119904	−	0.113793i
$733$	−4.83812e31			−1.47412			−0.737060	−	0.675827i	$-0.763787\pi$
$733$	−4.83812e31			−1.47412			−0.737060	+	0.675827i	$0.763787\pi$
$734$			5.88126e30i			0.176528i
$735$	1.98331e31	+	2.08982e31i	0.586449	+	0.617942i
$736$	9.52628e29			0.0277503
$737$		−	2.62577e29i		−	0.00753553i
$738$	1.68852e30	−	3.22649e31i	0.0477403	−	0.912242i
$739$	−4.94638e31			−1.37784			−0.688919	−	0.724838i	$-0.741915\pi$
$739$	−4.94638e31			−1.37784			−0.688919	+	0.724838i	$0.741915\pi$
$740$		−	2.11197e31i		−	0.579614i
$741$	−3.98804e31	+	3.78480e31i	−1.07835	+	1.02339i
$742$	−2.18984e31			−0.583404
$743$			1.54838e31i			0.406445i	0.979133	+	0.203222i	$0.0651414\pi$
$743$			1.54838e31i			0.406445i	−0.979133	+	0.203222i	$0.934859\pi$
$744$	−3.27498e30	−	3.45085e30i	−0.0847044	−	0.0892531i
$745$	1.19839e32			3.05408
$746$		−	4.07387e30i		−	0.102301i
$747$	1.95281e31	+	1.02196e30i	0.483207	+	0.0252877i
$748$	3.55418e29			0.00866606
$749$		−	5.48723e31i		−	1.31842i
$750$	−2.84777e31	+	2.70264e31i	−0.674266	+	0.639903i
$751$	−3.61372e31			−0.843171			−0.421586	−	0.906789i	$-0.638526\pi$
$751$	−3.61372e31			−0.843171			−0.421586	+	0.906789i	$0.638526\pi$
$752$			4.23620e28i			0.000974047i
$753$	2.76482e31	+	2.91330e31i	0.626502	+	0.660146i
$754$	1.20953e30			0.0270105
$755$			1.09096e32i			2.40101i
$756$	−1.84009e31	−	2.15398e31i	−0.399116	−	0.467199i
$757$	−4.28262e31			−0.915493			−0.457746	−	0.889083i	$-0.651343\pi$
$757$	−4.28262e31			−0.915493			−0.457746	+	0.889083i	$0.651343\pi$
$758$			2.67507e31i			0.563605i
$759$	1.20235e29	−	1.14107e29i	0.00249673	−	0.00236948i
$760$	−2.30043e31			−0.470825
$761$			5.59183e31i			1.12804i	0.825763	+	0.564018i	$0.190745\pi$
$761$			5.59183e31i			1.12804i	−0.825763	+	0.564018i	$0.809255\pi$
$762$	−4.49340e31	−	4.73470e31i	−0.893450	−	0.941429i
$763$	−7.63728e31			−1.49682
$764$			1.44345e31i			0.278852i
$765$	3.62182e30	−	6.92073e31i	0.0689686	−	1.31788i
$766$	−1.40663e30			−0.0264036
$767$			5.78236e30i			0.106993i
$768$	−2.48542e30	+	2.35875e30i	−0.0453343	+	0.0430239i
$769$	9.27501e31			1.66773			0.833863	−	0.551972i	$-0.186125\pi$
$769$	9.27501e31			1.66773			0.833863	+	0.551972i	$0.186125\pi$
$770$		−	1.79470e30i		−	0.0318123i
$771$	−6.89081e30	−	7.26086e30i	−0.120413	−	0.126879i
$772$	2.14025e31			0.368700
$773$			3.19744e31i			0.543035i	0.962434	+	0.271517i	$0.0875255\pi$
$773$			3.19744e31i			0.543035i	−0.962434	+	0.271517i	$0.912475\pi$
$774$	7.08973e31	+	3.71026e30i	1.18708	+	0.0621233i
$775$	−3.76846e31			−0.622079
$776$		−	1.35991e31i		−	0.221325i
$777$	3.85721e31	−	3.66063e31i	0.618931	−	0.587388i
$778$	2.45238e31			0.387982
$779$		−	6.60595e31i		−	1.03044i
$780$	6.96383e31	+	7.33780e31i	1.07104	+	1.12856i
$781$	−1.34643e30			−0.0204184
$782$			5.86775e30i			0.0877399i
$783$	1.05687e30	−	9.02859e29i	0.0155827	−	0.0133119i
$784$	8.77440e30			0.127568
$785$		−	1.28475e31i		−	0.184185i
$786$	−1.41208e30	+	1.34011e30i	−0.0199623	+	0.0189450i
$787$	1.12073e32			1.56235			0.781173	−	0.624315i	$-0.214622\pi$
$787$	1.12073e32			1.56235			0.781173	+	0.624315i	$0.214622\pi$
$788$		−	3.83824e31i		−	0.527647i
$789$	−7.42839e31	−	7.82731e31i	−1.00704	−	1.06112i
$790$	−2.20984e31			−0.295436
$791$		−	6.21966e31i		−	0.820021i
$792$	−3.11598e28	+	5.95415e29i	−0.000405152	+	0.00774182i
$793$	−4.80541e31			−0.616205
$794$			3.75624e31i			0.475037i
$795$	6.51842e31	−	6.18622e31i	0.813026	−	0.771590i
$796$	−5.55325e31			−0.683130
$797$			3.03484e31i			0.368209i	0.982907	+	0.184105i	$0.0589385\pi$
$797$			3.03484e31i			0.368209i	−0.982907	+	0.184105i	$0.941061\pi$
$798$	−3.98729e31	−	4.20142e31i	−0.477141	−	0.502764i
$799$	−2.60930e29			−0.00307971
$800$			2.71418e31i			0.315972i
$801$	−1.56709e32	−	8.20103e30i	−1.79943	−	0.0941696i
$802$	5.10115e31			0.577763
$803$		−	6.03921e28i		−	0.000674698i
$804$	−1.13101e31	+	1.07337e31i	−0.124638	+	0.118285i
$805$	2.96295e31			0.322085
$806$			4.27760e31i			0.458685i
$807$	−6.94106e31	−	7.31381e31i	−0.734204	−	0.773632i
$808$	3.70425e31			0.386522
$809$			1.14120e32i			1.17470i	0.809333	+	0.587349i	$0.199829\pi$
$809$			1.14120e32i			1.17470i	−0.809333	+	0.587349i	$0.800171\pi$
$810$	1.15622e32	+	1.21350e31i	1.17410	+	0.123226i
$811$	3.53046e31			0.353673			0.176836	−	0.984240i	$-0.443414\pi$
$811$	3.53046e31			0.353673			0.176836	+	0.984240i	$0.443414\pi$
$812$			1.27425e30i			0.0125932i
$813$	−5.04106e31	+	4.78414e31i	−0.491502	+	0.466453i
$814$	−1.11919e30			−0.0107655
$815$		−	4.36864e31i		−	0.414584i
$816$	−1.45288e31	−	1.53091e31i	−0.136031	−	0.143336i
$817$	1.45156e32			1.34089
$818$			2.72978e30i			0.0248795i
$819$	−1.33119e31	+	2.54369e32i	−0.119706	+	2.28740i
$820$	−1.21546e32			−1.07842
$821$			1.09798e32i			0.961211i	0.876937	+	0.480606i	$0.159583\pi$
$821$			1.09798e32i			0.961211i	−0.876937	+	0.480606i	$0.840417\pi$
$822$	6.24740e31	−	5.92900e31i	0.539646	−	0.512144i
$823$	2.58120e31			0.220001			0.110000	−	0.993932i	$-0.464915\pi$
$823$	2.58120e31			0.220001			0.110000	+	0.993932i	$0.464915\pi$
$824$			5.41516e31i			0.455420i
$825$	3.25108e30	+	3.42567e30i	0.0269795	+	0.0284284i
$826$	−6.09173e30			−0.0498839
$827$		−	1.47626e32i		−	1.19289i	−0.802653	−	0.596447i	$-0.796579\pi$
$827$		−	1.47626e32i		−	1.19289i	0.802653	−	0.596447i	$-0.203421\pi$
$828$	−9.82997e30	−	5.14431e29i	−0.0783824	−	0.00410198i
$829$	−1.70341e32			−1.34035			−0.670177	−	0.742201i	$-0.733782\pi$
$829$	−1.70341e32			−1.34035			−0.670177	+	0.742201i	$0.733782\pi$
$830$		−	7.35650e31i		−	0.571232i
$831$	6.01633e31	−	5.70971e31i	0.461021	−	0.437525i
$832$	3.08088e31			0.232980
$833$			5.40463e31i			0.403339i
$834$	−1.53666e30	−	1.61918e30i	−0.0113175	−	0.0119252i
$835$	−3.20315e32			−2.32823
$836$			1.21906e30i			0.00874493i
$837$	3.19303e31	+	3.73771e31i	0.226060	+	0.264622i
$838$	−1.63191e32			−1.14028
$839$			1.84528e32i			1.27256i	0.771456	+	0.636282i	$0.219529\pi$
$839$			1.84528e32i			1.27256i	−0.771456	+	0.636282i	$0.780471\pi$
$840$	−7.73039e31	+	7.33642e31i	−0.526174	+	0.499358i
$841$	1.48790e32			0.999580
$842$			2.36904e30i			0.0157087i
$843$	1.44230e32	+	1.51976e32i	0.943958	+	0.994650i
$844$	2.09036e31			0.135037
$845$		−	6.47746e32i		−	4.13029i
$846$	2.28760e28	−	4.37124e29i	0.000143981	−	0.00275126i
$847$	1.97713e32			1.22834
$848$		−	2.73685e31i		−	0.167841i
$849$	−6.28181e31	+	5.96166e31i	−0.380277	+	0.360897i
$850$	−1.67181e32			−0.999030
$851$		−	1.84772e31i		−	0.108996i
$852$	5.50396e31	+	5.79953e31i	0.320508	+	0.337720i
$853$	−2.18762e31			−0.125757			−0.0628784	−	0.998021i	$-0.520028\pi$
$853$	−2.18762e31			−0.125757			−0.0628784	+	0.998021i	$0.520028\pi$
$854$		−	5.06251e31i		−	0.287296i
$855$	2.37377e32	+	1.24226e31i	1.32988	+	0.0695963i
$856$	6.85792e31			0.379298
$857$			2.06327e31i			0.112660i	0.998412	+	0.0563298i	$0.0179398\pi$
$857$			2.06327e31i			0.112660i	−0.998412	+	0.0563298i	$0.982060\pi$
$858$	3.88850e30	−	3.69032e30i	0.0209615	−	0.0198932i
$859$	1.35417e32			0.720688			0.360344	−	0.932820i	$-0.382659\pi$
$859$	1.35417e32			0.720688			0.360344	+	0.932820i	$0.382659\pi$
$860$		−	2.67080e32i		−	1.40332i
$861$	−2.10674e32	−	2.21987e32i	−1.09289	−	1.15158i
$862$	1.81452e32			0.929355
$863$			3.40137e32i			1.72003i	0.510270	+	0.860014i	$0.329546\pi$
$863$			3.40137e32i			1.72003i	−0.510270	+	0.860014i	$0.670454\pi$
$864$	2.69203e31	−	2.29973e31i	0.134409	−	0.114822i
$865$	1.73321e32			0.854424
$866$		−	4.33524e31i		−	0.211016i
$867$	−5.66268e31	+	5.37409e31i	−0.272152	+	0.258282i
$868$	−4.50647e31			−0.213855
$869$			1.17106e30i			0.00548732i
$870$	−3.59969e30	−	3.79300e30i	−0.0166553	−	0.0175498i
$871$	1.40197e32			0.640531
$872$		−	9.54504e31i		−	0.430622i
$873$	−7.34368e30	+	1.40326e32i	−0.0327158	+	0.625147i
$874$	−2.01260e31			−0.0885385
$875$			3.71891e32i			1.61557i
$876$	−2.60130e30	+	2.46872e30i	−0.0111595	+	0.0105908i
$877$	7.22813e31			0.306218			0.153109	−	0.988209i	$-0.451071\pi$
$877$	7.22813e31			0.306218			0.153109	+	0.988209i	$0.451071\pi$
$878$		−	1.00397e32i		−	0.420033i
$879$	−9.11035e31	−	9.59959e31i	−0.376407	−	0.396621i
$880$	2.24301e30			0.00915213
$881$		−	1.95541e32i		−	0.787957i	−0.919120	−	0.393979i	$-0.871098\pi$
$881$		−	1.95541e32i		−	0.787957i	0.919120	−	0.393979i	$-0.128902\pi$
$882$	−9.05412e31	−	4.73829e30i	−0.360323	−	0.0188568i
$883$	−8.63196e30			−0.0339267			−0.0169634	−	0.999856i	$-0.505400\pi$
$883$	−8.63196e30			−0.0339267			−0.0169634	+	0.999856i	$0.505400\pi$
$884$			1.89768e32i			0.736627i
$885$	1.81331e31	−	1.72089e31i	0.0695176	−	0.0659747i
$886$	8.83873e31			0.334672
$887$		−	4.69289e32i		−	1.75502i	−0.479562	−	0.877508i	$-0.659205\pi$
$887$		−	4.69289e32i		−	1.75502i	0.479562	−	0.877508i	$-0.340795\pi$
$888$	4.57504e31	+	4.82073e31i	0.168987	+	0.178062i
$889$	−6.18305e32			−2.25571
$890$			5.90343e32i			2.12723i
$891$	6.43064e29	−	6.12714e30i	0.00228876	−	0.0218074i
$892$	1.99030e32			0.699689
$893$		−	8.94975e29i		−	0.00310774i
$894$	−2.73542e32	+	2.59601e32i	−0.938235	+	0.890418i
$895$	−8.94590e32			−3.03089
$896$			3.24572e31i			0.108623i
$897$	6.09252e31	+	6.41969e31i	0.201409	+	0.212225i
$898$	−1.52685e32			−0.498606
$899$		−	2.21115e30i		−	0.00713281i
$900$	1.46569e31	−	2.80070e32i	0.0467063	−	0.892482i
$901$	1.68578e32			0.530673
$902$			6.44106e30i			0.0200302i
$903$	4.87784e32	−	4.62924e32i	1.49852	−	1.42215i
$904$	7.77330e31			0.235913
$905$			2.69057e32i			0.806696i
$906$	−2.36329e32	−	2.49021e32i	−0.700015	−	0.737607i
$907$	3.98603e32			1.16643			0.583217	−	0.812316i	$-0.301794\pi$
$907$	3.98603e32			1.16643			0.583217	+	0.812316i	$0.301794\pi$
$908$			2.19207e32i			0.633738i
$909$	−3.82233e32	−	2.00034e31i	−1.09176	−	0.0571349i
$910$	9.58244e32			2.70409
$911$			6.46638e32i			1.80285i	0.432937	+	0.901424i	$0.357477\pi$
$911$			6.46638e32i			1.80285i	−0.432937	+	0.901424i	$0.642523\pi$
$912$	5.25091e31	−	4.98330e31i	0.144641	−	0.137269i
$913$	−3.89841e30			−0.0106098
$914$			1.32628e32i			0.356639i
$915$	1.43014e32	+	1.50694e32i	0.379967	+	0.400372i
$916$	−1.73460e32			−0.455354
$917$			1.84404e31i			0.0478307i
$918$	1.41653e32	+	1.65817e32i	0.363041	+	0.424971i
$919$	−3.77545e32			−0.956088			−0.478044	−	0.878336i	$-0.658654\pi$
$919$	−3.77545e32			−0.956088			−0.478044	+	0.878336i	$0.658654\pi$
$920$			3.70309e31i			0.0926611i
$921$	−1.85947e32	+	1.76470e32i	−0.459761	+	0.436330i
$922$	−3.52550e32			−0.861351
$923$		−	7.18897e32i		−	1.73559i
$924$	3.88777e30	+	4.09655e30i	0.00927488	+	0.00977296i
$925$	5.26442e32			1.24106
$926$		−	5.62554e32i		−	1.31052i
$927$	2.92426e31	−	5.58779e32i	0.0673191	−	1.28636i
$928$	−1.59255e30			−0.00362297
$929$			5.76621e31i			0.129634i	0.997897	+	0.0648168i	$0.0206463\pi$
$929$			5.76621e31i			0.129634i	−0.997897	+	0.0648168i	$0.979354\pi$
$930$	1.34142e32	−	1.27306e32i	0.298026	−	0.282837i
$931$	−1.85375e32			−0.407010
$932$		−	1.50116e32i		−	0.325727i
$933$	1.60617e32	+	1.69242e32i	0.344424	+	0.362920i
$934$	−3.87323e31			−0.0820838
$935$			1.38159e31i			0.0289369i
$936$	−3.17910e32	−	1.66372e31i	−0.658066	−	0.0344385i
$937$	4.02717e32			0.823880			0.411940	−	0.911211i	$-0.364851\pi$
$937$	4.02717e32			0.823880			0.411940	+	0.911211i	$0.364851\pi$
$938$			1.47698e32i			0.298638i
$939$	9.83072e31	−	9.32970e31i	0.196455	−	0.186443i
$940$	−1.64671e30			−0.00325245
$941$			3.33355e32i			0.650760i	0.945583	+	0.325380i	$0.105492\pi$
$941$			3.33355e32i			0.650760i	−0.945583	+	0.325380i	$0.894508\pi$
$942$	2.78309e31	+	2.93255e31i	0.0536992	+	0.0565829i
$943$	−1.06338e32			−0.202797
$944$		−	7.61342e30i		−	0.0143512i
$945$	8.37301e32	−	7.15285e32i	1.56003	−	1.33269i
$946$	−1.41533e31			−0.0260648
$947$			3.75870e32i			0.684207i	0.939662	+	0.342103i	$0.111139\pi$
$947$			3.75870e32i			0.684207i	−0.939662	+	0.342103i	$0.888861\pi$
$948$	5.04414e31	−	4.78707e31i	0.0907602	−	0.0861346i
$949$	3.22451e31			0.0573503
$950$		−	5.73420e32i		−	1.00812i
$951$	4.04853e32	+	4.26594e32i	0.703576	+	0.741360i
$952$	−1.99921e32			−0.343441
$953$			2.96604e32i			0.503680i	0.967769	+	0.251840i	$0.0810357\pi$
$953$			2.96604e32i			0.503680i	−0.967769	+	0.251840i	$0.918964\pi$
$954$	−1.47794e31	+	2.82410e32i	−0.0248098	+	0.474076i
$955$	−5.61102e32			−0.931117
$956$			2.31444e32i			0.379673i
$957$	−2.01001e29	+	1.90757e29i	−0.000325963	+	0.000309350i
$958$	−7.49928e32			−1.20226
$959$		−	8.15848e32i		−	1.29302i
$960$	−9.16902e31	−	9.66141e31i	−0.143661	−	0.151376i
$961$	−5.67392e32			−0.878872
$962$		−	5.97568e32i		−	0.915085i
$963$	−7.07655e32	−	3.70337e31i	−1.07135	−	0.0560670i
$964$	4.54213e32			0.679849
$965$			8.31963e32i			1.23113i
$966$	−6.76317e31	+	6.41848e31i	−0.0989468	+	0.0939040i
$967$	7.15946e32			1.03559			0.517796	−	0.855504i	$-0.326753\pi$
$967$	7.15946e32			1.03559			0.517796	+	0.855504i	$0.326753\pi$
$968$			2.47101e32i			0.353383i
$969$	3.06948e32	+	3.23432e32i	0.434014	+	0.457321i
$970$	5.28628e32			0.739028
$971$		−	2.32402e32i		−	0.321239i	−0.987016	−	0.160619i	$-0.948651\pi$
$971$		−	2.32402e32i		−	0.321239i	0.987016	−	0.160619i	$-0.0513491\pi$
$972$	−2.90204e32	+	2.22767e32i	−0.396620	+	0.304455i
$973$	−2.11448e31			−0.0285735
$974$			3.64479e32i			0.486995i
$975$	−1.82907e33	+	1.73585e33i	−2.41645	+	2.29330i
$976$	6.32710e31			0.0826527
$977$		−	4.69586e32i		−	0.606562i	−0.952901	−	0.303281i	$-0.901918\pi$
$977$		−	4.69586e32i		−	0.606562i	0.952901	−	0.303281i	$-0.0980821\pi$
$978$	9.46354e31	+	9.97175e31i	0.120872	+	0.127363i
$979$	3.12839e31			0.0395104
$980$			3.41081e32i			0.425962i
$981$	−5.15445e31	+	9.84933e32i	−0.0636536	+	1.21632i
$982$	−8.52828e32			−1.04144
$983$		−	2.33933e32i		−	0.282490i	−0.989975	−	0.141245i	$-0.954889\pi$
$983$		−	2.33933e32i		−	0.282490i	0.989975	−	0.141245i	$-0.0451105\pi$
$984$	2.77438e32	−	2.63299e32i	0.331299	−	0.314415i
$985$	1.49201e33			1.76187
$986$		−	9.80935e30i		−	0.0114550i
$987$	−2.85421e30	−	3.00748e30i	−0.00329607	−	0.00347308i
$988$	−6.50892e32			−0.743332
$989$		−	2.33663e32i		−	0.263894i
$990$	−2.31452e31	−	1.21126e30i	−0.0258507	−	0.00135285i
$991$	1.06857e33			1.18030			0.590149	−	0.807294i	$-0.299069\pi$
$991$	1.06857e33			1.18030			0.590149	+	0.807294i	$0.299069\pi$
$992$		−	5.63216e31i		−	0.0615243i
$993$	3.82121e32	−	3.62646e32i	0.412819	−	0.391779i
$994$	7.57361e32			0.809194
$995$		−	2.15868e33i		−	2.28104i
$996$	1.59360e32	+	1.67918e32i	0.166543	+	0.175487i
$997$	−1.04461e33			−1.07971			−0.539856	−	0.841757i	$-0.681521\pi$
$997$	−1.04461e33			−1.07971			−0.539856	+	0.841757i	$0.681521\pi$
$998$		−	1.06598e33i		−	1.08972i
$999$	−4.46057e32	−	5.22147e32i	−0.450993	−	0.527925i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6.23.b.a.5.1	✓	8
3.2	odd	2	inner	6.23.b.a.5.5	yes	8
4.3	odd	2		48.23.e.d.17.7		8
12.11	even	2		48.23.e.d.17.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.23.b.a.5.1	✓	8	1.1	even	1	trivial
6.23.b.a.5.5	yes	8	3.2	odd	2	inner
48.23.e.d.17.7		8	4.3	odd	2
48.23.e.d.17.8		8	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6 = 2 \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 23 \)
Character orbit:	\([\chi]\)	\(=\)	6.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1448.15i q^{2} +(-128493. + 121945. i) q^{3} -2.09715e6 q^{4} -8.15211e7i q^{5} +(1.76595e8 + 1.86078e8i) q^{6} +2.43000e9 q^{7} +3.03700e9i q^{8} +(1.64002e9 - 3.13382e10i) q^{9} +O(q^{10})\)	\(q-1448.15i q^{2} +(-128493. + 121945. i) q^{3} -2.09715e6 q^{4} -8.15211e7i q^{5} +(1.76595e8 + 1.86078e8i) q^{6} +2.43000e9 q^{7} +3.03700e9i q^{8} +(1.64002e9 - 3.13382e10i) q^{9} -1.18055e11 q^{10} +6.25607e9i q^{11} +(2.69470e11 - 2.55737e11i) q^{12} -3.34030e12 q^{13} -3.51901e12i q^{14} +(9.94107e12 + 1.04749e13i) q^{15} +4.39805e12 q^{16} +2.70899e13i q^{17} +(-4.53825e13 - 2.37500e12i) q^{18} -9.29168e13 q^{19} +1.70962e14i q^{20} +(-3.12239e14 + 2.96325e14i) q^{21} +9.05975e12 q^{22} +1.49571e14i q^{23} +(-3.70346e14 - 3.90234e14i) q^{24} -4.26151e15 q^{25} +4.83727e15i q^{26} +(3.61079e15 + 4.22674e15i) q^{27} -5.09607e15 q^{28} -2.50044e14i q^{29} +(1.51693e16 - 1.43962e16i) q^{30} +8.84301e15 q^{31} -6.36905e15i q^{32} +(-7.62894e14 - 8.03863e14i) q^{33} +3.92304e16 q^{34} -1.98096e17i q^{35} +(-3.43937e15 + 6.57209e16i) q^{36} -1.23534e17 q^{37} +1.34558e17i q^{38} +(4.29206e17 - 4.07332e17i) q^{39} +2.47580e17 q^{40} +7.10953e17i q^{41} +(4.29125e17 + 4.52170e17i) q^{42} -1.56221e18 q^{43} -1.31199e16i q^{44} +(-2.55472e18 - 1.33696e17i) q^{45} +2.16603e17 q^{46} +9.63200e15i q^{47} +(-5.65120e17 + 5.36319e17i) q^{48} +1.99507e18 q^{49} +6.17133e18i q^{50} +(-3.30347e18 - 3.48088e18i) q^{51} +7.00511e18 q^{52} -6.22288e18i q^{53} +(6.12097e18 - 5.22899e18i) q^{54} +5.10002e17 q^{55} +7.37990e18i q^{56} +(1.19392e19 - 1.13307e19i) q^{57} -3.62103e17 q^{58} -1.73109e18i q^{59} +(-2.08479e19 - 2.19675e19i) q^{60} +1.43862e19 q^{61} -1.28061e19i q^{62} +(3.98524e18 - 7.61517e19i) q^{63} -9.22337e18 q^{64} +2.72305e20i q^{65} +(-1.16412e18 + 1.10479e18i) q^{66} -4.19715e19 q^{67} -5.68117e19i q^{68} +(-1.82394e19 - 1.92189e19i) q^{69} -2.86874e20 q^{70} +2.15220e20i q^{71} +(9.51741e19 + 4.98074e18i) q^{72} -9.65337e18 q^{73} +1.78897e20i q^{74} +(5.47576e20 - 5.19669e20i) q^{75} +1.94861e20 q^{76} +1.52022e19i q^{77} +(-5.89879e20 - 6.21556e20i) q^{78} +1.87187e20 q^{79} -3.58534e20i q^{80} +(-9.79392e20 - 1.02790e20i) q^{81} +1.02957e21 q^{82} +6.23141e20i q^{83} +(6.54812e20 - 6.21440e20i) q^{84} +2.20840e21 q^{85} +2.26233e21i q^{86} +(3.04916e19 + 3.21290e19i) q^{87} -1.89997e19 q^{88} -5.00057e21i q^{89} +(-1.93613e20 + 3.69964e21i) q^{90} -8.11691e21 q^{91} -3.13674e20i q^{92} +(-1.13627e21 + 1.07836e21i) q^{93} +1.39486e19 q^{94} +7.57469e21i q^{95} +(7.76672e20 + 8.18381e20i) q^{96} -4.47780e21 q^{97} -2.88917e21i q^{98} +(1.96054e20 + 1.02601e19i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 69720 q^{3} - 16777216 q^{4} + 156352512 q^{6} + 5645581840 q^{7} - 53592329016 q^{9}+O(q^{10}) \) 8 * q - 69720 * q^3 - 16777216 * q^4 + 156352512 * q^6 + 5645581840 * q^7 - 53592329016 * q^9	\( 8 q - 69720 q^{3} - 16777216 q^{4} + 156352512 q^{6} + 5645581840 q^{7} - 53592329016 q^{9} + 46180761600 q^{10} + 146213437440 q^{12} - 2875682381360 q^{13} - 731868641280 q^{15} + 35184372088832 q^{16} - 55595702845440 q^{18} - 314803957551536 q^{19} + 661593766080336 q^{21} - 511896111513600 q^{22} - 327894983245824 q^{24} - 62\!\cdots\!20 q^{25}+ \cdots + 36\!\cdots\!76 q^{99}+O(q^{100}) \) 8 * q - 69720 * q^3 - 16777216 * q^4 + 156352512 * q^6 + 5645581840 * q^7 - 53592329016 * q^9 + 46180761600 * q^10 + 146213437440 * q^12 - 2875682381360 * q^13 - 731868641280 * q^15 + 35184372088832 * q^16 - 55595702845440 * q^18 - 314803957551536 * q^19 + 661593766080336 * q^21 - 511896111513600 * q^22 - 327894983245824 * q^24 - 6264418212884920 * q^25 + 11756777174853480 * q^27 - 11839643246919680 * q^28 + 51661456814407680 * q^30 - 110293228249214576 * q^31 + 256091518967454720 * q^33 - 100789882794934272 * q^34 + 112391259980562432 * q^36 - 752490366563284400 * q^37 + 1437242122292286480 * q^39 - 96848076550963200 * q^40 + 255515905807319040 * q^42 - 1301015563442074160 * q^43 - 4916408514089748480 * q^45 + 1601638996847296512 * q^46 - 306631802754170880 * q^48 + 12029391373660580760 * q^49 - 18532151948158119936 * q^51 + 6030743057433886720 * q^52 - 18559682184349532160 * q^54 + 56456085576783974400 * q^55 - 35832783024333133680 * q^57 + 34659140078143242240 * q^58 + 1534839784797634560 * q^60 - 124415281411828286768 * q^61 + 223305694023597186960 * q^63 - 73786976294838206464 * q^64 + 122984956040514011136 * q^66 - 349673137262790165680 * q^67 + 217762533639160621056 * q^69 - 485339414077397729280 * q^70 + 116592639413720186880 * q^72 - 65576379188480063600 * q^73 + 923803988759061007080 * q^75 + 660191749187118825472 * q^76 - 1049693699266563440640 * q^78 - 325232563432330354544 * q^79 - 2780170203320395644024 * q^81 + 2935193462963889438720 * q^82 - 1387462689722908803072 * q^84 + 6970706743345629511680 * q^85 - 3070393070764643665920 * q^87 + 1073523954052969267200 * q^88 - 4943089610251404410880 * q^90 - 6363735561736496595040 * q^91 + 3617627578345665462480 * q^93 + 2855373122028803850240 * q^94 + 687645619903946293248 * q^96 - 23922503524683181095920 * q^97 + 36535312526138292658176 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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