LMFDB - Embedded newform 63.8.e.c.37.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,8,Mod(37,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("63.37");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	63.e (of order $3$, degree $2$, 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:	$19.6802566055$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
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} - 4x^{7} + 362x^{6} - 1072x^{5} + 36131x^{4} - 70480x^{3} + 698554x^{2} - 663492x + 2868273 $ x^8 - 4x^7 + 362x^6 - 1072x^5 + 36131x^4 - 70480x^3 + 698554x^2 - 663492*x + 2868273
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{3}\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.2
Root			$0.500000 - 12.0633i$ of defining polynomial
Character	$\chi$	$=$	63.37
Dual form			63.8.e.c.46.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.81424 + 4.87440i) q^{2} +(48.1601 + 83.4158i) q^{4} +(251.471 - 435.561i) q^{5} +(854.822 - 304.667i) q^{7} -1262.58 q^{8} +O(q^{10})$	\(q+(-2.81424 + 4.87440i) q^{2} +(48.1601 + 83.4158i) q^{4} +(251.471 - 435.561i) q^{5} +(854.822 - 304.667i) q^{7} -1262.58 q^{8} +(1415.40 + 2451.54i) q^{10} +(-3100.89 - 5370.90i) q^{11} -9719.32 q^{13} +(-920.606 + 5024.15i) q^{14} +(-2611.29 + 4522.89i) q^{16} +(-6954.71 - 12045.9i) q^{17} +(5914.28 - 10243.8i) q^{19} +48443.5 q^{20} +34906.6 q^{22} +(-1418.72 + 2457.30i) q^{23} +(-87412.9 - 151404. i) q^{25} +(27352.5 - 47375.9i) q^{26} +(66582.4 + 56632.9i) q^{28} +48836.2 q^{29} +(-63.0218 - 109.157i) q^{31} +(-95502.8 - 165416. i) q^{32} +78288.8 q^{34} +(82262.3 - 448942. i) q^{35} +(183727. - 318225. i) q^{37} +(33288.4 + 57657.2i) q^{38} +(-317503. + 549931. i) q^{40} +133287. q^{41} +812254. q^{43} +(298678. - 517326. i) q^{44} +(-7985.25 - 13830.9i) q^{46} +(-552403. + 956790. i) q^{47} +(637900. - 520872. i) q^{49} +984003. q^{50} +(-468084. - 810745. i) q^{52} +(-386165. - 668858. i) q^{53} -3.11914e6 q^{55} +(-1.07928e6 + 384666. i) q^{56} +(-137437. + 238047. i) q^{58} +(356333. + 617187. i) q^{59} +(-626610. + 1.08532e6i) q^{61} +709.434 q^{62} +406580. q^{64} +(-2.44413e6 + 4.23335e6i) q^{65} +(375109. + 649707. i) q^{67} +(669879. - 1.16026e6i) q^{68} +(1.95682e6 + 1.66441e6i) q^{70} +1.13668e6 q^{71} +(2.08563e6 + 3.61241e6i) q^{73} +(1.03410e6 + 1.79112e6i) q^{74} +1.13933e6 q^{76} +(-4.28704e6 - 3.64643e6i) q^{77} +(3.21980e6 - 5.57686e6i) q^{79} +(1.31333e6 + 2.27475e6i) q^{80} +(-375101. + 649694. i) q^{82} +1.83464e6 q^{83} -6.99563e6 q^{85} +(-2.28588e6 + 3.95925e6i) q^{86} +(3.91513e6 + 6.78120e6i) q^{88} +(702126. - 1.21612e6i) q^{89} +(-8.30829e6 + 2.96115e6i) q^{91} -273303. q^{92} +(-3.10919e6 - 5.38527e6i) q^{94} +(-2.97454e6 - 5.15206e6i) q^{95} -6.70215e6 q^{97} +(743737. + 4.57524e6i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} - 101 q^{4} + 196 q^{5} + 154 q^{7} + 2694 q^{8}+O(q^{10}) $ 8 * q - q^2 - 101 * q^4 + 196 * q^5 + 154 * q^7 + 2694 * q^8	\( 8 q - q^{2} - 101 q^{4} + 196 q^{5} + 154 q^{7} + 2694 q^{8} + 5185 q^{10} - 5210 q^{11} - 7588 q^{13} + 29932 q^{14} + 21055 q^{16} - 11436 q^{17} + 69158 q^{19} + 175982 q^{20} + 114526 q^{22} - 146220 q^{23} - 6230 q^{25} + 107696 q^{26} - 19201 q^{28} + 141328 q^{29} + 288618 q^{31} + 2653 q^{32} - 991992 q^{34} + 66164 q^{35} + 448902 q^{37} + 528944 q^{38} - 767361 q^{40} + 1326632 q^{41} + 1108 q^{43} - 686635 q^{44} + 1064964 q^{46} + 762180 q^{47} + 5310620 q^{49} + 1050856 q^{50} - 3423848 q^{52} - 2761920 q^{53} - 3930112 q^{55} - 5341077 q^{56} + 4451395 q^{58} + 3410898 q^{59} - 300892 q^{61} + 4132350 q^{62} - 5833102 q^{64} - 8019032 q^{65} + 4222478 q^{67} + 5770500 q^{68} + 7703801 q^{70} + 761928 q^{71} + 451674 q^{73} - 10091220 q^{74} - 29495312 q^{76} - 16516528 q^{77} + 12154822 q^{79} + 7870085 q^{80} - 8814904 q^{82} + 24175956 q^{83} - 14751000 q^{85} - 32881826 q^{86} + 14439051 q^{88} + 4955752 q^{89} + 14146174 q^{91} - 413784 q^{92} - 5960646 q^{94} + 8460784 q^{95} - 45681228 q^{97} - 8665405 q^{98}+O(q^{100}) \) 8 * q - q^2 - 101 * q^4 + 196 * q^5 + 154 * q^7 + 2694 * q^8 + 5185 * q^10 - 5210 * q^11 - 7588 * q^13 + 29932 * q^14 + 21055 * q^16 - 11436 * q^17 + 69158 * q^19 + 175982 * q^20 + 114526 * q^22 - 146220 * q^23 - 6230 * q^25 + 107696 * q^26 - 19201 * q^28 + 141328 * q^29 + 288618 * q^31 + 2653 * q^32 - 991992 * q^34 + 66164 * q^35 + 448902 * q^37 + 528944 * q^38 - 767361 * q^40 + 1326632 * q^41 + 1108 * q^43 - 686635 * q^44 + 1064964 * q^46 + 762180 * q^47 + 5310620 * q^49 + 1050856 * q^50 - 3423848 * q^52 - 2761920 * q^53 - 3930112 * q^55 - 5341077 * q^56 + 4451395 * q^58 + 3410898 * q^59 - 300892 * q^61 + 4132350 * q^62 - 5833102 * q^64 - 8019032 * q^65 + 4222478 * q^67 + 5770500 * q^68 + 7703801 * q^70 + 761928 * q^71 + 451674 * q^73 - 10091220 * q^74 - 29495312 * q^76 - 16516528 * q^77 + 12154822 * q^79 + 7870085 * q^80 - 8814904 * q^82 + 24175956 * q^83 - 14751000 * q^85 - 32881826 * q^86 + 14439051 * q^88 + 4955752 * q^89 + 14146174 * q^91 - 413784 * q^92 - 5960646 * q^94 + 8460784 * q^95 - 45681228 * q^97 - 8665405 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−2.81424	+	4.87440i	−0.248746	+	0.430841i	−0.963178	−	0.268864i	$-0.913352\pi$
$2$	−2.81424	+	4.87440i	−0.248746	+	0.430841i	0.714432	+	0.699705i	$0.246685\pi$
$3$		0			0
$3$		0			0
$4$	48.1601	+	83.4158i	0.376251	+	0.651686i
$5$	251.471	−	435.561i	0.899690	−	1.55831i	0.0717998	−	0.997419i	$-0.477126\pi$
$5$	251.471	−	435.561i	0.899690	−	1.55831i	0.827890	−	0.560890i	$-0.189541\pi$
$6$		0			0
$7$	854.822	−	304.667i	0.941961	−	0.335723i
$7$	854.822	−	304.667i	0.941961	−	0.335723i
$8$	−1262.58			−0.871855
$9$		0			0
$10$	1415.40	+	2451.54i	0.447588	+	0.775246i
$11$	−3100.89	−	5370.90i	−0.702444	−	1.21667i	−0.967606	−	0.252465i	$-0.918759\pi$
$11$	−3100.89	−	5370.90i	−0.702444	−	1.21667i	0.265162	−	0.964204i	$-0.414575\pi$
$12$		0			0
$13$	−9719.32			−1.22697			−0.613485	−	0.789706i	$-0.710233\pi$
$13$	−9719.32			−1.22697			−0.613485	+	0.789706i	$0.710233\pi$
$14$	−920.606	+	5024.15i	−0.0896656	+	0.489345i
$15$		0			0
$16$	−2611.29	+	4522.89i	−0.159381	+	0.276055i
$17$	−6954.71	−	12045.9i	−0.343327	−	0.594659i	0.641722	−	0.766938i	$-0.278220\pi$
$17$	−6954.71	−	12045.9i	−0.343327	−	0.594659i	−0.985048	+	0.172278i	$0.944887\pi$
$18$		0			0
$19$	5914.28	−	10243.8i	0.197817	−	0.342630i	−0.750003	−	0.661434i	$-0.769948\pi$
$19$	5914.28	−	10243.8i	0.197817	−	0.342630i	0.947820	+	0.318805i	$0.103281\pi$
$20$	48443.5			1.35404
$21$		0			0
$22$	34906.6			0.698921
$23$	−1418.72	+	2457.30i	−0.0243136	+	0.0421125i	−0.877926	−	0.478796i	$-0.841073\pi$
$23$	−1418.72	+	2457.30i	−0.0243136	+	0.0421125i	0.853613	+	0.520908i	$0.174407\pi$
$24$		0			0
$25$	−87412.9	−	151404.i	−1.11888	−	1.93797i
$26$	27352.5	−	47375.9i	0.305204	−	0.528629i
$27$		0			0
$28$	66582.4	+	56632.9i	0.573200	+	0.487546i
$29$	48836.2			0.371834			0.185917	−	0.982565i	$-0.440474\pi$
$29$	48836.2			0.371834			0.185917	+	0.982565i	$0.440474\pi$
$30$		0			0
$31$	−63.0218	−	109.157i	−0.000379949	−	0.000658091i	0.865835	−	0.500329i	$-0.166788\pi$
$31$	−63.0218	−	109.157i	−0.000379949	−	0.000658091i	−0.866215	+	0.499671i	$0.833454\pi$
$32$	−95502.8	−	165416.i	−0.515218	−	0.892384i
$33$		0			0
$34$	78288.8			0.341604
$35$	82262.3	−	448942.i	0.324312	−	1.76991i
$36$		0			0
$37$	183727.	−	318225.i	0.596303	−	1.03283i	−0.397058	−	0.917793i	$-0.629969\pi$
$37$	183727.	−	318225.i	0.596303	−	1.03283i	0.993362	−	0.115034i	$-0.0366977\pi$
$38$	33288.4	+	57657.2i	0.0984125	+	0.170455i
$39$		0			0
$40$	−317503.	+	549931.i	−0.784400	+	1.35862i
$41$	133287.			0.302026			0.151013	−	0.988532i	$-0.451747\pi$
$41$	133287.			0.302026			0.151013	+	0.988532i	$0.451747\pi$
$42$		0			0
$43$	812254.			1.55795			0.778973	−	0.627058i	$-0.215741\pi$
$43$	812254.			1.55795			0.778973	+	0.627058i	$0.215741\pi$
$44$	298678.	−	517326.i	0.528591	−	0.915546i
$45$		0			0
$46$	−7985.25	−	13830.9i	−0.0120958	−	0.0209506i
$47$	−552403.	+	956790.i	−0.776093	+	1.34423i	0.158085	+	0.987425i	$0.449468\pi$
$47$	−552403.	+	956790.i	−0.776093	+	1.34423i	−0.934178	+	0.356807i	$0.883865\pi$
$48$		0			0
$49$	637900.	−	520872.i	0.774580	−	0.632477i
$50$	984003.			1.11327
$51$		0			0
$52$	−468084.	−	810745.i	−0.461649	−	0.799599i
$53$	−386165.	−	668858.i	−0.356293	−	0.617118i	0.631045	−	0.775746i	$-0.282626\pi$
$53$	−386165.	−	668858.i	−0.356293	−	0.617118i	−0.987338	+	0.158628i	$0.949293\pi$
$54$		0			0
$55$	−3.11914e6			−2.52793
$56$	−1.07928e6	+	384666.i	−0.821253	+	0.292702i
$57$		0			0
$58$	−137437.	+	238047.i	−0.0924922	+	0.160201i
$59$	356333.	+	617187.i	0.225878	+	0.391232i	0.956582	−	0.291462i	$-0.0941416\pi$
$59$	356333.	+	617187.i	0.225878	+	0.391232i	−0.730704	+	0.682694i	$0.760808\pi$
$60$		0			0
$61$	−626610.	+	1.08532e6i	−0.353462	+	0.612214i	−0.986854	−	0.161617i	$-0.948329\pi$
$61$	−626610.	+	1.08532e6i	−0.353462	+	0.612214i	0.633391	+	0.773832i	$0.281662\pi$
$62$	709.434			0.000378043
$63$		0			0
$64$	406580.			0.193873
$65$	−2.44413e6	+	4.23335e6i	−1.10389	+	1.91200i
$66$		0			0
$67$	375109.	+	649707.i	0.152369	+	0.263910i	0.932098	−	0.362207i	$-0.117977\pi$
$67$	375109.	+	649707.i	0.152369	+	0.263910i	−0.779729	+	0.626117i	$0.784643\pi$
$68$	669879.	−	1.16026e6i	0.258354	−	0.447482i
$69$		0			0
$70$	1.95682e6	+	1.66441e6i	0.681879	+	0.579985i
$71$	1.13668e6			0.376908			0.188454	−	0.982082i	$-0.439652\pi$
$71$	1.13668e6			0.376908			0.188454	+	0.982082i	$0.439652\pi$
$72$		0			0
$73$	2.08563e6	+	3.61241e6i	0.627489	+	1.08684i	0.988054	+	0.154109i	$0.0492507\pi$
$73$	2.08563e6	+	3.61241e6i	0.627489	+	1.08684i	−0.360565	+	0.932734i	$0.617416\pi$
$74$	1.03410e6	+	1.79112e6i	0.296656	+	0.513823i
$75$		0			0
$76$	1.13933e6			0.297716
$77$	−4.28704e6	−	3.64643e6i	−1.07014	−	0.910227i
$78$		0			0
$79$	3.21980e6	−	5.57686e6i	0.734741	−	1.27261i	−0.220096	−	0.975478i	$-0.570637\pi$
$79$	3.21980e6	−	5.57686e6i	0.734741	−	1.27261i	0.954837	−	0.297130i	$-0.0960295\pi$
$80$	1.31333e6	+	2.27475e6i	0.286786	+	0.496728i
$81$		0			0
$82$	−375101.	+	649694.i	−0.0751276	+	0.130125i
$83$	1.83464e6			0.352191			0.176095	−	0.984373i	$-0.443653\pi$
$83$	1.83464e6			0.352191			0.176095	+	0.984373i	$0.443653\pi$
$84$		0			0
$85$	−6.99563e6			−1.23555
$86$	−2.28588e6	+	3.95925e6i	−0.387533	+	0.671226i
$87$		0			0
$88$	3.91513e6	+	6.78120e6i	0.612430	+	1.06076i
$89$	702126.	−	1.21612e6i	0.105572	−	0.182857i	−0.808400	−	0.588634i	$-0.799666\pi$
$89$	702126.	−	1.21612e6i	0.105572	−	0.182857i	0.913972	+	0.405778i	$0.132999\pi$
$90$		0			0
$91$	−8.30829e6	+	2.96115e6i	−1.15576	+	0.411923i
$92$	−273303.			−0.0365921
$93$		0			0
$94$	−3.10919e6	−	5.38527e6i	−0.386100	−	0.668745i
$95$	−2.97454e6	−	5.15206e6i	−0.355949	−	0.616521i
$96$		0			0
$97$	−6.70215e6			−0.745612			−0.372806	−	0.927909i	$-0.621604\pi$
$97$	−6.70215e6			−0.745612			−0.372806	+	0.927909i	$0.621604\pi$
$98$	743737.	+	4.57524e6i	0.0798231	+	0.491046i
$99$		0			0
$100$	8.41963e6	−	1.45832e7i	0.841963	−	1.45832i
$101$	191713.	+	332057.i	0.0185152	+	0.0320692i	0.875135	−	0.483880i	$-0.160773\pi$
$101$	191713.	+	332057.i	0.0185152	+	0.0320692i	−0.856619	+	0.515949i	$0.827439\pi$
$102$		0			0
$103$	7.52010e6	−	1.30252e7i	0.678099	−	1.17450i	−0.297453	−	0.954736i	$-0.596137\pi$
$103$	7.52010e6	−	1.30252e7i	0.678099	−	1.17450i	0.975553	−	0.219766i	$-0.0705295\pi$
$104$	1.22714e7			1.06974
$105$		0			0
$106$	4.34705e6			0.354506
$107$	3.65923e6	−	6.33797e6i	0.288766	−	0.500158i	−0.684749	−	0.728779i	$-0.740088\pi$
$107$	3.65923e6	−	6.33797e6i	0.288766	−	0.500158i	0.973516	+	0.228621i	$0.0734217\pi$
$108$		0			0
$109$	6.43172e6	+	1.11401e7i	0.475701	+	0.823938i	0.999613	−	0.0278344i	$-0.00886110\pi$
$109$	6.43172e6	+	1.11401e7i	0.475701	+	0.823938i	−0.523912	+	0.851773i	$0.675528\pi$
$110$	8.77799e6	−	1.52039e7i	0.628812	−	1.08913i
$111$		0			0
$112$	−854217.	+	4.66184e6i	−0.0574520	+	0.313541i
$113$	900842.			0.0587319			0.0293660	−	0.999569i	$-0.490651\pi$
$113$	900842.			0.0587319			0.0293660	+	0.999569i	$0.490651\pi$
$114$		0			0
$115$	713535.	+	1.23588e6i	0.0437495	+	0.0757763i
$116$	2.35196e6	+	4.07371e6i	0.139903	+	0.242319i
$117$		0			0
$118$	−4.01122e6			−0.224745
$119$	−9.61503e6	−	8.17824e6i	−0.523041	−	0.444883i
$120$		0			0
$121$	−9.48744e6	+	1.64327e7i	−0.486856	+	0.843259i
$122$	−3.52686e6	−	6.10870e6i	−0.175844	−	0.304572i
$123$		0			0
$124$	6070.28	−	10514.0i	0.000285912	−	0.000495215i
$125$	−4.86349e7			−2.22722
$126$		0			0
$127$	2.48188e6			0.107515			0.0537573	−	0.998554i	$-0.482880\pi$
$127$	2.48188e6			0.107515			0.0537573	+	0.998554i	$0.482880\pi$
$128$	1.10801e7	−	1.91914e7i	0.466993	−	0.808856i
$129$		0			0
$130$	−1.37567e7	−	2.38273e7i	−0.549178	−	0.951204i
$131$	1.40374e7	−	2.43134e7i	0.545552	−	0.944923i	−0.453020	−	0.891500i	$-0.649654\pi$
$131$	1.40374e7	−	2.43134e7i	0.545552	−	0.944923i	0.998572	−	0.0534229i	$-0.0170131\pi$
$132$		0			0
$133$	1.93471e6	−	1.05585e7i	0.0713073	−	0.389156i
$134$	−4.22258e6			−0.151604
$135$		0			0
$136$	8.78088e6	+	1.52089e7i	0.299331	+	0.518457i
$137$	1.09882e7	+	1.90322e7i	0.365095	+	0.632364i	0.988791	−	0.149303i	$-0.0477031\pi$
$137$	1.09882e7	+	1.90322e7i	0.365095	+	0.632364i	−0.623696	+	0.781667i	$0.714370\pi$
$138$		0			0
$139$	7.55942e6			0.238746			0.119373	−	0.992849i	$-0.461912\pi$
$139$	7.55942e6			0.238746			0.119373	+	0.992849i	$0.461912\pi$
$140$	4.14106e7	−	1.47591e7i	1.27545	−	0.454582i
$141$		0			0
$142$	−3.19890e6	+	5.54065e6i	−0.0937542	+	0.162387i
$143$	3.01385e7	+	5.22015e7i	0.861879	+	1.49282i
$144$		0			0
$145$	1.22809e7	−	2.12711e7i	0.334535	−	0.579432i
$146$	−2.34778e7			−0.624341
$147$		0			0
$148$	3.53933e7			0.897439
$149$	−2.35900e7	+	4.08591e7i	−0.584220	+	1.01190i	0.410752	+	0.911747i	$0.365266\pi$
$149$	−2.35900e7	+	4.08591e7i	−0.584220	+	1.01190i	−0.994972	+	0.100152i	$0.968067\pi$
$150$		0			0
$151$	−2.66686e7	−	4.61913e7i	−0.630348	−	1.09179i	−0.987480	−	0.157741i	$-0.949579\pi$
$151$	−2.66686e7	−	4.61913e7i	−0.630348	−	1.09179i	0.357132	−	0.934054i	$-0.383755\pi$
$152$	−7.46726e6	+	1.29337e7i	−0.172468	+	0.298724i
$153$		0			0
$154$	2.98389e7	−	1.06349e7i	0.658356	−	0.234644i
$155$	−63392.7			−0.00136735
$156$		0			0
$157$	3.54801e7	+	6.14533e7i	0.731705	+	1.26735i	0.956154	+	0.292864i	$0.0946083\pi$
$157$	3.54801e7	+	6.14533e7i	0.731705	+	1.26735i	−0.224449	+	0.974486i	$0.572058\pi$
$158$	1.81226e7	+	3.13892e7i	0.365527	+	0.633112i
$159$		0			0
$160$	−9.60648e7			−1.85415
$161$	−464099.	+	2.53279e6i	−0.00876435	+	0.0478309i
$162$		0			0
$163$	−4.91690e7	+	8.51632e7i	−0.889272	+	1.54026i	−0.0485345	+	0.998822i	$0.515455\pi$
$163$	−4.91690e7	+	8.51632e7i	−0.889272	+	1.54026i	−0.840738	+	0.541443i	$0.817878\pi$
$164$	6.41911e6	+	1.11182e7i	0.113637	+	0.196826i
$165$		0			0
$166$	−5.16312e6	+	8.94279e6i	−0.0876060	+	0.151738i
$167$	−7.36791e7			−1.22416			−0.612078	−	0.790797i	$-0.709666\pi$
$167$	−7.36791e7			−1.22416			−0.612078	+	0.790797i	$0.709666\pi$
$168$		0			0
$169$	3.17167e7			0.505458
$170$	1.96874e7	−	3.40995e7i	0.307338	−	0.532325i
$171$		0			0
$172$	3.91182e7	+	6.77548e7i	0.586178	+	1.01529i
$173$	−5.56725e7	+	9.64275e7i	−0.817484	+	1.41592i	0.0900473	+	0.995937i	$0.471298\pi$
$173$	−5.56725e7	+	9.64275e7i	−0.817484	+	1.41592i	−0.907531	+	0.419986i	$0.862035\pi$
$174$		0			0
$175$	−1.20850e8	−	1.02791e8i	−1.70457	−	1.44985i
$176$	3.23893e7			0.447824
$177$		0			0
$178$	3.95190e6	+	6.84489e6i	0.0525213	+	0.0909696i
$179$	2.36590e6	+	4.09786e6i	0.0308326	+	0.0534037i	0.881030	−	0.473060i	$-0.156851\pi$
$179$	2.36590e6	+	4.09786e6i	0.0308326	+	0.0534037i	−0.850197	+	0.526464i	$0.823517\pi$
$180$		0			0
$181$	1.00313e8			1.25742			0.628710	−	0.777640i	$-0.283583\pi$
$181$	1.00313e8			1.25742			0.628710	+	0.777640i	$0.283583\pi$
$182$	8.94767e6	−	4.88314e7i	0.110017	−	0.600412i
$183$		0			0
$184$	1.79125e6	−	3.10254e6i	0.0211980	−	0.0367160i
$185$	−9.24041e7	−	1.60049e8i	−1.07298	−	1.85845i
$186$		0			0
$187$	−4.31316e7	+	7.47060e7i	−0.482336	+	0.835430i
$188$	−1.06415e8			−1.16802
$189$		0			0
$190$	3.34843e7			0.354163
$191$	−3.23791e7	+	5.60822e7i	−0.336238	+	0.582382i	−0.983722	−	0.179697i	$-0.942488\pi$
$191$	−3.23791e7	+	5.60822e7i	−0.336238	+	0.582382i	0.647483	+	0.762079i	$0.275821\pi$
$192$		0			0
$193$	−3.83075e7	−	6.63506e7i	−0.383560	−	0.664346i	0.608008	−	0.793931i	$-0.291969\pi$
$193$	−3.83075e7	−	6.63506e7i	−0.383560	−	0.664346i	−0.991568	+	0.129585i	$0.958636\pi$
$194$	1.88614e7	−	3.26690e7i	0.185468	−	0.321240i
$195$		0			0
$196$	7.41702e7	+	2.81256e7i	0.703612	+	0.266813i
$197$	1.47076e8			1.37060			0.685301	−	0.728260i	$-0.259671\pi$
$197$	1.47076e8			1.37060			0.685301	+	0.728260i	$0.259671\pi$
$198$		0			0
$199$	147032.	+	254667.i	0.00132259	+	0.00229080i	0.866686	−	0.498854i	$-0.166246\pi$
$199$	147032.	+	254667.i	0.00132259	+	0.00229080i	−0.865363	+	0.501145i	$0.832912\pi$
$200$	1.10366e8	+	1.91159e8i	0.975506	+	1.68963i
$201$		0			0
$202$	−2.15811e6			−0.0184223
$203$	4.17463e7	−	1.48788e7i	0.350253	−	0.124833i
$204$		0			0
$205$	3.35178e7	−	5.80545e7i	0.271729	−	0.470649i
$206$	4.23267e7	+	7.33120e7i	0.337349	+	0.584305i
$207$		0			0
$208$	2.53800e7	−	4.39594e7i	0.195555	−	0.338712i
$209$	−7.33581e7			−0.555823
$210$		0			0
$211$	−1.05229e8			−0.771163			−0.385582	−	0.922674i	$-0.625999\pi$
$211$	−1.05229e8			−0.771163			−0.385582	+	0.922674i	$0.625999\pi$
$212$	3.71955e7	−	6.44246e7i	0.268111	−	0.464383i
$213$		0			0
$214$	2.05959e7	+	3.56731e7i	0.143659	+	0.248824i
$215$	2.04258e8	−	3.53786e8i	1.40167	−	2.42776i
$216$		0			0
$217$	−87129.0	−	74109.2i	−0.000578833	−	0.000492338i
$218$	−7.24015e7			−0.473315
$219$		0			0
$220$	−1.50218e8	−	2.60185e8i	−0.951136	−	1.64742i
$221$	6.75950e7	+	1.17078e8i	0.421252	+	0.729630i
$222$		0			0
$223$	3.68334e6			0.0222420			0.0111210	−	0.999938i	$-0.496460\pi$
$223$	3.68334e6			0.0222420			0.0111210	+	0.999938i	$0.496460\pi$
$224$	−1.32035e8	−	1.12305e8i	−0.784909	−	0.667620i
$225$		0			0
$226$	−2.53518e6	+	4.39107e6i	−0.0146093	+	0.0253041i
$227$	−3.86092e6	−	6.68731e6i	−0.0219079	−	0.0379455i	0.854864	−	0.518853i	$-0.173641\pi$
$227$	−3.86092e6	−	6.68731e6i	−0.0219079	−	0.0379455i	−0.876771	+	0.480907i	$0.840307\pi$
$228$		0			0
$229$	1.47549e8	−	2.55563e8i	0.811920	−	1.40629i	−0.0995986	−	0.995028i	$-0.531756\pi$
$229$	1.47549e8	−	2.55563e8i	0.811920	−	1.40629i	0.911519	−	0.411259i	$-0.134911\pi$
$230$	−8.03223e6			−0.0435300
$231$		0			0
$232$	−6.16597e7			−0.324185
$233$	−4.98957e7	+	8.64219e7i	−0.258415	+	0.447588i	−0.965817	−	0.259223i	$-0.916533\pi$
$233$	−4.98957e7	+	8.64219e7i	−0.258415	+	0.447588i	0.707403	+	0.706811i	$0.249867\pi$
$234$		0			0
$235$	2.77827e8	+	4.81210e8i	1.39649	+	2.41879i
$236$	−3.43221e7	+	5.94476e7i	−0.169974	+	0.294403i
$237$		0			0
$238$	6.69230e7	−	2.38520e7i	0.321778	−	0.114685i
$239$	1.79058e8			0.848402			0.424201	−	0.905568i	$-0.360555\pi$
$239$	1.79058e8			0.848402			0.424201	+	0.905568i	$0.360555\pi$
$240$		0			0
$241$	3.55400e7	+	6.15570e7i	0.163553	+	0.283281i	0.936140	−	0.351627i	$-0.114371\pi$
$241$	3.55400e7	+	6.15570e7i	0.163553	+	0.283281i	−0.772588	+	0.634908i	$0.781038\pi$
$242$	−5.33999e7	−	9.24913e7i	−0.242207	−	0.419514i
$243$		0			0
$244$	−1.20710e8			−0.531962
$245$	−6.64579e7	−	4.08828e8i	−0.288712	−	1.77607i
$246$		0			0
$247$	−5.74828e7	+	9.95632e7i	−0.242716	+	0.420397i
$248$	79570.2	+	137820.i	0.000331260	+	0.000573760i
$249$		0			0
$250$	1.36870e8	−	2.37066e8i	0.554011	−	0.959576i
$251$	5.85579e7			0.233737			0.116868	−	0.993147i	$-0.462714\pi$
$251$	5.85579e7			0.233737			0.116868	+	0.993147i	$0.462714\pi$
$252$		0			0
$253$	1.75972e7			0.0683159
$254$	−6.98460e6	+	1.20977e7i	−0.0267438	+	0.0463217i
$255$		0			0
$256$	8.83855e7	+	1.53088e8i	0.329262	+	0.570298i
$257$	1.39244e8	−	2.41178e8i	0.511694	−	0.886280i	−0.488214	−	0.872724i	$-0.662351\pi$
$257$	1.39244e8	−	2.41178e8i	0.511694	−	0.886280i	0.999908	−	0.0135561i	$-0.00431519\pi$
$258$		0			0
$259$	6.01016e7	−	3.28001e8i	0.214950	−	1.17308i
$260$	−4.70838e8			−1.66136
$261$		0			0
$262$	7.90089e7	+	1.36848e8i	0.271407	+	0.470091i
$263$	1.24380e7	+	2.15433e7i	0.0421605	+	0.0730242i	0.886336	−	0.463043i	$-0.153243\pi$
$263$	1.24380e7	+	2.15433e7i	0.0421605	+	0.0730242i	−0.844175	+	0.536068i	$0.819909\pi$
$264$		0			0
$265$	−3.88438e8			−1.28221
$266$	4.60219e7	+	3.91448e7i	0.149927	+	0.127523i
$267$		0			0
$268$	−3.61306e7	+	6.25800e7i	−0.114658	+	0.198593i
$269$	2.27489e8	+	3.94022e8i	0.712569	+	1.23421i	0.963890	+	0.266302i	$0.0858020\pi$
$269$	2.27489e8	+	3.94022e8i	0.712569	+	1.23421i	−0.251320	+	0.967904i	$0.580865\pi$
$270$		0			0
$271$	−1.37286e8	+	2.37787e8i	−0.419020	+	0.725765i	−0.995841	−	0.0911060i	$-0.970960\pi$
$271$	−1.37286e8	+	2.37787e8i	−0.419020	+	0.725765i	0.576821	+	0.816871i	$0.304293\pi$
$272$	7.26430e7			0.218878
$273$		0			0
$274$	−1.23694e8			−0.363264
$275$	−5.42115e8	+	9.38971e8i	−1.57191	+	2.72262i
$276$		0			0
$277$	−2.04311e7	−	3.53877e7i	−0.0577581	−	0.100040i	0.835701	−	0.549185i	$-0.185062\pi$
$277$	−2.04311e7	−	3.53877e7i	−0.0577581	−	0.100040i	−0.893459	+	0.449145i	$0.851729\pi$
$278$	−2.12740e7	+	3.68477e7i	−0.0593872	+	0.102862i
$279$		0			0
$280$	−1.03863e8	+	5.66826e8i	−0.282753	+	1.54311i
$281$	4.08644e8			1.09868			0.549342	−	0.835598i	$-0.314878\pi$
$281$	4.08644e8			1.09868			0.549342	+	0.835598i	$0.314878\pi$
$282$		0			0
$283$	−3.30085e8	−	5.71725e8i	−0.865713	−	1.49946i	−0.866338	−	0.499459i	$-0.833532\pi$
$283$	−3.30085e8	−	5.71725e8i	−0.865713	−	1.49946i	0.000625156	−	1.00000i	$-0.499801\pi$
$284$	5.47428e7	+	9.48173e7i	0.141812	+	0.245625i
$285$		0			0
$286$	−3.39268e8			−0.857555
$287$	1.13937e8	−	4.06080e7i	0.284496	−	0.101397i
$288$		0			0
$289$	1.08433e8	−	1.87812e8i	0.264253	−	0.457700i
$290$	6.91227e7	+	1.19724e8i	0.166429	+	0.288263i
$291$		0			0
$292$	−2.00888e8	+	3.47948e8i	−0.472187	+	0.817852i
$293$	−6.57223e8			−1.52643			−0.763213	−	0.646147i	$-0.776379\pi$
$293$	−6.57223e8			−1.52643			−0.763213	+	0.646147i	$0.776379\pi$
$294$		0			0
$295$	3.58430e8			0.812881
$296$	−2.31970e8	+	4.01784e8i	−0.519890	+	0.900476i
$297$		0			0
$298$	−1.32776e8	−	2.29975e8i	−0.290645	−	0.503411i
$299$	1.37890e7	−	2.38833e7i	0.0298321	−	0.0516708i
$300$		0			0
$301$	6.94333e8	−	2.47467e8i	1.46752	−	0.523039i
$302$	3.00207e8			0.627186
$303$		0			0
$304$	3.08878e7	+	5.34993e7i	0.0630565	+	0.109217i
$305$	3.15148e8	+	5.45853e8i	0.636013	+	1.10161i
$306$		0			0
$307$	2.21654e8			0.437211			0.218606	−	0.975813i	$-0.429849\pi$
$307$	2.21654e8			0.437211			0.218606	+	0.975813i	$0.429849\pi$
$308$	9.77050e7	−	5.33219e8i	0.190541	−	1.03987i
$309$		0			0
$310$	178402.	−	309002.i	0.000340121	−	0.000589108i
$311$	−2.22992e8	−	3.86234e8i	−0.420367	−	0.728097i	0.575608	−	0.817726i	$-0.304765\pi$
$311$	−2.22992e8	−	3.86234e8i	−0.420367	−	0.728097i	−0.995975	+	0.0896286i	$0.971432\pi$
$312$		0			0
$313$	−2.69303e8	+	4.66446e8i	−0.496404	+	0.859797i	−0.999991	−	0.00414734i	$-0.998680\pi$
$313$	−2.69303e8	+	4.66446e8i	−0.496404	+	0.859797i	0.503587	+	0.863944i	$0.332013\pi$
$314$	−3.99398e8			−0.728034
$315$		0			0
$316$	6.20264e8			1.10579
$317$	5.40113e8	−	9.35503e8i	0.952307	−	1.64944i	0.211894	−	0.977293i	$-0.432037\pi$
$317$	5.40113e8	−	9.35503e8i	0.952307	−	1.64944i	0.740413	−	0.672152i	$-0.234630\pi$
$318$		0			0
$319$	−1.51436e8	−	2.62294e8i	−0.261193	−	0.452399i
$320$	1.02243e8	−	1.77090e8i	0.174425	−	0.302113i
$321$		0			0
$322$	−1.10398e7	−	9.39008e6i	−0.0184274	−	0.0156738i
$323$	−1.64528e8			−0.271664
$324$		0			0
$325$	8.49594e8	+	1.47154e9i	1.37284	+	2.37783i
$326$	−2.76747e8	−	4.79339e8i	−0.442406	−	0.766269i
$327$		0			0
$328$	−1.68285e8			−0.263323
$329$	−1.80705e8	+	9.86185e8i	−0.279759	+	1.52677i
$330$		0			0
$331$	3.86056e7	−	6.68668e7i	0.0585130	−	0.101347i	−0.835285	−	0.549817i	$-0.814697\pi$
$331$	3.86056e7	−	6.68668e7i	0.0585130	−	0.101347i	0.893798	+	0.448470i	$0.148031\pi$
$332$	8.83566e7	+	1.53038e8i	0.132512	+	0.229518i
$333$		0			0
$334$	2.07351e8	−	3.59142e8i	0.304504	−	0.527416i
$335$	3.77316e8			0.548338
$336$		0			0
$337$	−1.16026e9			−1.65139			−0.825697	−	0.564114i	$-0.809218\pi$
$337$	−1.16026e9			−1.65139			−0.825697	+	0.564114i	$0.809218\pi$
$338$	−8.92584e7	+	1.54600e8i	−0.125731	+	0.217772i
$339$		0			0
$340$	−3.36910e8	−	5.83546e8i	−0.464877	−	0.805191i
$341$	−390848.	+	676968.i	−0.000533786	+	0.000924544i
$342$		0			0
$343$	3.86599e8	−	6.39599e8i	0.517286	−	0.855813i
$344$	−1.02554e9			−1.35830
$345$		0			0
$346$	−3.13351e8	−	5.42740e8i	−0.406691	−	0.704410i
$347$	−4.28904e8	−	7.42883e8i	−0.551070	−	0.954481i	−0.998198	−	0.0600112i	$-0.980886\pi$
$347$	−4.28904e8	−	7.42883e8i	−0.551070	−	0.954481i	0.447128	−	0.894470i	$-0.352447\pi$
$348$		0			0
$349$	−2.41142e7			−0.0303657			−0.0151829	−	0.999885i	$-0.504833\pi$
$349$	−2.41142e7			−0.0303657			−0.0151829	+	0.999885i	$0.504833\pi$
$350$	8.41147e8	−	2.99793e8i	1.04866	−	0.373752i
$351$		0			0
$352$	−5.92287e8	+	1.02587e9i	−0.723824	+	1.25370i
$353$	3.19711e8	+	5.53755e8i	0.386853	+	0.670048i	0.992024	−	0.126047i	$-0.0402289\pi$
$353$	3.19711e8	+	5.53755e8i	0.386853	+	0.670048i	−0.605172	+	0.796095i	$0.706896\pi$
$354$		0			0
$355$	2.85843e8	−	4.95094e8i	0.339100	−	0.587339i
$356$	1.35258e8			0.158887
$357$		0			0
$358$	−2.66328e7			−0.0306779
$359$	5.24301e8	−	9.08117e8i	0.598068	−	1.03588i	−0.395038	−	0.918665i	$-0.629269\pi$
$359$	5.24301e8	−	9.08117e8i	0.598068	−	1.03588i	0.993106	−	0.117219i	$-0.0373980\pi$
$360$		0			0
$361$	3.76978e8	+	6.52946e8i	0.421737	+	0.730469i
$362$	−2.82304e8	+	4.88964e8i	−0.312778	+	0.541748i
$363$		0			0
$364$	−6.47135e8	−	5.50433e8i	−0.703299	−	0.598205i
$365$	2.09790e9			2.25818
$366$		0			0
$367$	−4.54436e7	−	7.87106e7i	−0.0479889	−	0.0831193i	0.841033	−	0.540984i	$-0.181948\pi$
$367$	−4.54436e7	−	7.87106e7i	−0.0479889	−	0.0831193i	−0.889022	+	0.457864i	$0.848615\pi$
$368$	−7.40939e6	−	1.28334e7i	−0.00775024	−	0.0134238i
$369$		0			0
$370$	1.04019e9			1.06759
$371$	−5.33882e8	−	4.54103e8i	−0.542795	−	0.461685i
$372$		0			0
$373$	6.25483e8	−	1.08337e9i	0.624072	−	1.08092i	−0.364648	−	0.931145i	$-0.618811\pi$
$373$	6.25483e8	−	1.08337e9i	0.624072	−	1.08092i	0.988720	−	0.149778i	$-0.0478560\pi$
$374$	−2.42765e8	−	4.20481e8i	−0.239958	−	0.415620i
$375$		0			0
$376$	6.97454e8	−	1.20803e9i	0.676641	−	1.17198i
$377$	−4.74655e8			−0.456229
$378$		0			0
$379$	7.56067e8			0.713384			0.356692	−	0.934222i	$-0.383905\pi$
$379$	7.56067e8			0.713384			0.356692	+	0.934222i	$0.383905\pi$
$380$	2.86509e8	−	4.96247e8i	0.267852	−	0.463933i
$381$		0			0
$382$	−1.82245e8	−	3.15657e8i	−0.167276	−	0.289730i
$383$	2.86932e8	−	4.96980e8i	0.260965	−	0.452005i	−0.705533	−	0.708677i	$-0.749293\pi$
$383$	2.86932e8	−	4.96980e8i	0.260965	−	0.452005i	0.966499	+	0.256671i	$0.0826258\pi$
$384$		0			0
$385$	−2.66631e9	+	9.50296e8i	−2.38121	+	0.848685i
$386$	4.31226e8			0.381636
$387$		0			0
$388$	−3.22776e8	−	5.59065e8i	−0.280537	−	0.485905i
$389$	1.05986e9	+	1.83572e9i	0.912899	+	1.58119i	0.809948	+	0.586502i	$0.199495\pi$
$389$	1.05986e9	+	1.83572e9i	0.912899	+	1.58119i	0.102952	+	0.994686i	$0.467171\pi$
$390$		0			0
$391$	3.94672e7			0.0333901
$392$	−8.05400e8	+	6.57643e8i	−0.675321	+	0.551428i
$393$		0			0
$394$	−4.13908e8	+	7.16910e8i	−0.340932	+	0.590511i
$395$	−1.61937e9	−	2.80484e9i	−1.32208	−	2.28991i
$396$		0			0
$397$	−6.92743e8	+	1.19987e9i	−0.555655	+	0.962423i	0.442197	+	0.896918i	$0.354199\pi$
$397$	−6.92743e8	+	1.19987e9i	−0.555655	+	0.962423i	−0.997852	+	0.0655049i	$0.979134\pi$
$398$	−1.65513e6			−0.00131596
$399$		0			0
$400$	9.13042e8			0.713314
$401$	2.20004e8	−	3.81058e8i	0.170382	−	0.295111i	−0.768171	−	0.640245i	$-0.778833\pi$
$401$	2.20004e8	−	3.81058e8i	0.170382	−	0.295111i	0.938554	+	0.345133i	$0.112166\pi$
$402$		0			0
$403$	612530.	+	1.06093e6i	0.000466186	+	0.000807458i
$404$	−1.84659e7	+	3.19838e7i	−0.0139327	+	0.0241321i
$405$		0			0
$406$	−4.49589e7	+	2.45361e8i	−0.0333407	+	0.181955i
$407$	−2.27887e9			−1.67548
$408$		0			0
$409$	3.60756e7	+	6.24848e7i	0.0260725	+	0.0451589i	0.878767	−	0.477251i	$-0.158367\pi$
$409$	3.60756e7	+	6.24848e7i	0.0260725	+	0.0451589i	−0.852695	+	0.522409i	$0.825033\pi$
$410$	1.88654e8	+	3.26758e8i	0.135183	+	0.234144i
$411$		0			0
$412$	1.44868e9			1.02054
$413$	4.92638e8	+	4.19022e8i	0.344114	+	0.292693i
$414$		0			0
$415$	4.61359e8	−	7.99098e8i	0.316863	−	0.548822i
$416$	9.28223e8	+	1.60773e9i	0.632158	+	1.09493i
$417$		0			0
$418$	2.06447e8	−	3.57577e8i	0.138259	−	0.239471i
$419$	−1.18463e9			−0.786745			−0.393373	−	0.919379i	$-0.628692\pi$
$419$	−1.18463e9			−0.786745			−0.393373	+	0.919379i	$0.628692\pi$
$420$		0			0
$421$	−2.28422e8			−0.149194			−0.0745969	−	0.997214i	$-0.523767\pi$
$421$	−2.28422e8			−0.149194			−0.0745969	+	0.997214i	$0.523767\pi$
$422$	2.96139e8	−	5.12928e8i	0.191824	−	0.332248i
$423$		0			0
$424$	4.87565e8	+	8.44488e8i	0.310636	+	0.538038i
$425$	−1.21586e9	+	2.10593e9i	−0.768286	+	1.33071i
$426$		0			0
$427$	−2.04979e8	+	1.11866e9i	−0.127413	+	0.695347i
$428$	7.04916e8			0.434594
$429$		0			0
$430$	1.14966e9	+	1.99128e9i	0.697318	+	1.20779i
$431$	−2.66068e8	−	4.60843e8i	−0.160074	−	0.277257i	0.774821	−	0.632181i	$-0.217840\pi$
$431$	−2.66068e8	−	4.60843e8i	−0.160074	−	0.277257i	−0.934895	+	0.354924i	$0.884507\pi$
$432$		0			0
$433$	−3.55195e8			−0.210261			−0.105131	−	0.994458i	$-0.533526\pi$
$433$	−3.55195e8			−0.210261			−0.105131	+	0.994458i	$0.533526\pi$
$434$	606440.	−	216141.i	0.000356102	−	0.000126918i
$435$		0			0
$436$	−6.19504e8	+	1.07301e9i	−0.357966	+	0.620015i
$437$	1.67814e7	+	2.90663e7i	0.00961932	+	0.0166612i
$438$		0			0
$439$	2.86605e8	−	4.96415e8i	0.161681	−	0.280039i	−0.773791	−	0.633441i	$-0.781642\pi$
$439$	2.86605e8	−	4.96415e8i	0.161681	−	0.280039i	0.935472	+	0.353402i	$0.114975\pi$
$440$	3.93816e9			2.20399
$441$		0			0
$442$	−7.60914e8			−0.419139
$443$	8.04540e8	−	1.39350e9i	0.439678	−	0.761544i	−0.557987	−	0.829850i	$-0.688426\pi$
$443$	8.04540e8	−	1.39350e9i	0.439678	−	0.761544i	0.997664	+	0.0683058i	$0.0217594\pi$
$444$		0			0
$445$	−3.53129e8	−	6.11637e8i	−0.189965	−	0.329028i
$446$	−1.03658e7	+	1.79541e7i	−0.00553262	+	0.00958277i
$447$		0			0
$448$	3.47554e8	−	1.23871e8i	0.182620	−	0.0650876i
$449$	−2.60121e9			−1.35616			−0.678082	−	0.734986i	$-0.737189\pi$
$449$	−2.60121e9			−1.35616			−0.678082	+	0.734986i	$0.737189\pi$
$450$		0			0
$451$	−4.13308e8	−	7.15870e8i	−0.212156	−	0.367465i
$452$	4.33847e7	+	7.51444e7i	0.0220979	+	0.0382747i
$453$		0			0
$454$	4.34622e7			0.0217980
$455$	−7.99534e8	+	4.36341e9i	−0.397921	+	2.17163i
$456$		0			0
$457$	1.39615e9	−	2.41820e9i	0.684267	−	1.18519i	−0.289400	−	0.957208i	$-0.593456\pi$
$457$	1.39615e9	−	2.41820e9i	0.684267	−	1.18519i	0.973667	−	0.227977i	$-0.0732110\pi$
$458$	8.30478e8	+	1.43843e9i	0.403924	+	0.699616i
$459$		0			0
$460$	−6.87279e7	+	1.19040e8i	−0.0329216	+	0.0570218i
$461$	2.44371e9			1.16171			0.580854	−	0.814008i	$-0.302719\pi$
$461$	2.44371e9			1.16171			0.580854	+	0.814008i	$0.302719\pi$
$462$		0			0
$463$	−5.78623e8			−0.270933			−0.135467	−	0.990782i	$-0.543253\pi$
$463$	−5.78623e8			−0.270933			−0.135467	+	0.990782i	$0.543253\pi$
$464$	−1.27526e8	+	2.20881e8i	−0.0592631	+	0.102647i
$465$		0			0
$466$	−2.80837e8	−	4.86424e8i	−0.128559	−	0.222671i
$467$	−1.93660e9	+	3.35430e9i	−0.879897	+	1.52403i	−0.0284440	+	0.999595i	$0.509055\pi$
$467$	−1.93660e9	+	3.35430e9i	−0.879897	+	1.52403i	−0.851453	+	0.524431i	$0.824278\pi$
$468$		0			0
$469$	5.18595e8	+	4.41101e8i	0.232126	+	0.197439i
$470$	−3.12748e9			−1.38948
$471$		0			0
$472$	−4.49899e8	−	7.79249e8i	−0.196933	−	0.341098i
$473$	−2.51871e9	−	4.36253e9i	−1.09437	−	1.89550i
$474$		0			0
$475$	−2.06794e9			−0.885339
$476$	2.19134e8	−	1.19591e9i	0.0931290	−	0.508246i
$477$		0			0
$478$	−5.03913e8	+	8.72803e8i	−0.211037	+	0.365526i
$479$	1.00117e9	+	1.73408e9i	0.416232	+	0.720935i	0.995557	−	0.0941618i	$-0.0300171\pi$
$479$	1.00117e9	+	1.73408e9i	0.416232	+	0.720935i	−0.579325	+	0.815097i	$0.696684\pi$
$480$		0			0
$481$	−1.78570e9	+	3.09293e9i	−0.731647	+	1.26725i
$482$	−4.00072e8			−0.162732
$483$		0			0
$484$	−1.82767e9			−0.732720
$485$	−1.68540e9	+	2.91919e9i	−0.670820	+	1.16189i
$486$		0			0
$487$	−2.16847e9	−	3.75591e9i	−0.850751	−	1.47354i	−0.880531	−	0.473988i	$-0.842814\pi$
$487$	−2.16847e9	−	3.75591e9i	−0.850751	−	1.47354i	0.0297798	−	0.999556i	$-0.490519\pi$
$488$	7.91146e8	−	1.37030e9i	0.308168	−	0.533762i
$489$		0			0
$490$	2.17982e9	+	8.26597e8i	0.837018	+	0.317400i
$491$	4.62835e9			1.76458			0.882289	−	0.470709i	$-0.156002\pi$
$491$	4.62835e9			1.76458			0.882289	+	0.470709i	$0.156002\pi$
$492$		0			0
$493$	−3.39642e8	−	5.88277e8i	−0.127661	−	0.221115i
$494$	−3.23541e8	−	5.60389e8i	−0.120749	−	0.209144i
$495$		0			0
$496$	658273.			0.000242226
$497$	9.71662e8	−	3.46309e8i	0.355032	−	0.126537i
$498$		0			0
$499$	−1.25641e9	+	2.17616e9i	−0.452666	+	0.784041i	−0.998551	−	0.0538194i	$-0.982860\pi$
$499$	−1.25641e9	+	2.17616e9i	−0.452666	+	0.784041i	0.545884	+	0.837861i	$0.316194\pi$
$500$	−2.34226e9	−	4.05692e9i	−0.837993	−	1.45145i
$501$		0			0
$502$	−1.64796e8	+	2.85435e8i	−0.0581411	+	0.100703i
$503$	−1.12749e9			−0.395025			−0.197512	−	0.980300i	$-0.563286\pi$
$503$	−1.12749e9			−0.395025			−0.197512	+	0.980300i	$0.563286\pi$
$504$		0			0
$505$	1.92841e8			0.0666316
$506$	−4.95227e7	+	8.57759e7i	−0.0169933	+	0.0294333i
$507$		0			0
$508$	1.19528e8	+	2.07028e8i	0.0404525	+	0.0700658i
$509$	1.32335e9	−	2.29211e9i	0.444798	−	0.770413i	−0.553240	−	0.833022i	$-0.686609\pi$
$509$	1.32335e9	−	2.29211e9i	0.444798	−	0.770413i	0.998038	+	0.0626088i	$0.0199421\pi$
$510$		0			0
$511$	2.88342e9	+	2.45255e9i	0.955949	+	0.813101i
$512$	1.84157e9			0.606376
$513$		0			0
$514$	7.83731e8	+	1.35746e9i	0.254564	+	0.440917i
$515$	−3.78218e9	−	6.55092e9i	−1.22016	−	2.11338i
$516$		0			0
$517$	6.85177e9			2.18065
$518$	1.42967e9	+	1.21603e9i	0.451941	+	0.384407i
$519$		0			0
$520$	3.08591e9	−	5.34495e9i	0.962436	−	1.66699i
$521$	2.49556e9	+	4.32244e9i	0.773101	+	1.33905i	0.935856	+	0.352384i	$0.114629\pi$
$521$	2.49556e9	+	4.32244e9i	0.773101	+	1.33905i	−0.162755	+	0.986667i	$0.552038\pi$
$522$		0			0
$523$	−9.79195e8	+	1.69602e9i	−0.299304	+	0.518411i	−0.975977	−	0.217874i	$-0.930088\pi$
$523$	−9.79195e8	+	1.69602e9i	−0.299304	+	0.518411i	0.676673	+	0.736284i	$0.263421\pi$
$524$	2.70416e9			0.821057
$525$		0			0
$526$	−1.40014e8			−0.0419490
$527$	−876597.	+	1.51831e6i	−0.000260893	+	0.000451880i
$528$		0			0
$529$	1.69839e9	+	2.94169e9i	0.498818	+	0.863978i
$530$	1.09316e9	−	1.89340e9i	0.318946	−	0.552430i
$531$		0			0
$532$	9.73925e8	−	3.47116e8i	0.280437	−	0.0999502i
$533$	−1.29546e9			−0.370577
$534$		0			0
$535$	−1.84038e9	−	3.18763e9i	−0.519600	−	0.899974i
$536$	−4.73605e8	−	8.20308e8i	−0.132843	−	0.230091i
$537$		0			0
$538$	−2.56083e9			−0.708995
$539$	−4.77560e9	−	1.81093e9i	−1.31361	−	0.498127i
$540$		0			0
$541$	2.02416e9	−	3.50595e9i	0.549610	−	0.951952i	−0.448692	−	0.893687i	$-0.648110\pi$
$541$	2.02416e9	−	3.50595e9i	0.549610	−	0.951952i	0.998301	−	0.0582650i	$-0.0185568\pi$
$542$	−7.72714e8	−	1.33838e9i	−0.208459	−	0.361062i
$543$		0			0
$544$	−1.32839e9	+	2.30084e9i	−0.353776	+	0.612759i
$545$	6.46956e9			1.71193
$546$		0			0
$547$	3.15001e9			0.822917			0.411458	−	0.911429i	$-0.365020\pi$
$547$	3.15001e9			0.822917			0.411458	+	0.911429i	$0.365020\pi$
$548$	−1.05839e9	+	1.83319e9i	−0.274735	+	0.475855i
$549$		0			0
$550$	−3.05128e9	−	5.28498e9i	−0.782011	−	1.35448i
$551$	2.88831e8	−	5.00270e8i	0.0735552	−	0.127401i
$552$		0			0
$553$	1.05327e9	−	5.74819e9i	0.264852	−	1.44542i
$554$	2.29992e8			0.0574683
$555$		0			0
$556$	3.64063e8	+	6.30575e8i	0.0898285	+	0.155588i
$557$	1.28499e8	+	2.22567e8i	0.0315071	+	0.0545718i	0.881349	−	0.472466i	$-0.156636\pi$
$557$	1.28499e8	+	2.22567e8i	0.0315071	+	0.0545718i	−0.849842	+	0.527038i	$0.823303\pi$
$558$		0			0
$559$	−7.89456e9			−1.91155
$560$	1.81570e9	+	1.54438e9i	0.436905	+	0.371618i
$561$		0			0
$562$	−1.15002e9	+	1.99190e9i	−0.273293	+	0.473358i
$563$	−2.33078e9	−	4.03703e9i	−0.550455	−	0.953415i	−0.998242	−	0.0592751i	$-0.981121\pi$
$563$	−2.33078e9	−	4.03703e9i	−0.550455	−	0.953415i	0.447787	−	0.894140i	$-0.352212\pi$
$564$		0			0
$565$	2.26536e8	−	3.92371e8i	0.0528405	−	0.0915225i
$566$	3.71576e9			0.861370
$567$		0			0
$568$	−1.43515e9			−0.328609
$569$	1.41323e9	−	2.44779e9i	0.321604	−	0.557034i	−0.659215	−	0.751954i	$-0.729111\pi$
$569$	1.41323e9	−	2.44779e9i	0.321604	−	0.557034i	0.980819	+	0.194920i	$0.0624447\pi$
$570$		0			0
$571$	2.18958e9	+	3.79246e9i	0.492191	+	0.852500i	0.999960	−	0.00899348i	$-0.00286275\pi$
$571$	2.18958e9	+	3.79246e9i	0.492191	+	0.852500i	−0.507768	+	0.861494i	$0.669529\pi$
$572$	−2.90295e9	+	5.02806e9i	−0.648565	+	1.12335i
$573$		0			0
$574$	−1.22705e8	+	6.69653e8i	−0.0270813	+	0.147795i
$575$	4.96058e8			0.108817
$576$		0			0
$577$	−1.27067e9	−	2.20087e9i	−0.275371	−	0.476957i	0.694857	−	0.719148i	$-0.255467\pi$
$577$	−1.27067e9	−	2.20087e9i	−0.275371	−	0.476957i	−0.970229	+	0.242190i	$0.922134\pi$
$578$	6.10315e8	+	1.05710e9i	0.131464	+	0.227702i
$579$		0			0
$580$	2.36580e9			0.503477
$581$	1.56829e9	−	5.58954e8i	0.331750	−	0.118239i
$582$		0			0
$583$	−2.39491e9	+	4.14811e9i	−0.500553	+	0.866982i
$584$	−2.63327e9	−	4.56096e9i	−0.547080	−	0.947570i
$585$		0			0
$586$	1.84958e9	−	3.20357e9i	0.379692	−	0.657646i
$587$	1.61818e9			0.330213			0.165106	−	0.986276i	$-0.447203\pi$
$587$	1.61818e9			0.330213			0.165106	+	0.986276i	$0.447203\pi$
$588$		0			0
$589$	−1.49092e6			−0.000300642
$590$	−1.00871e9	+	1.74713e9i	−0.202201	+	0.350222i
$591$		0			0
$592$	9.59529e8	+	1.66195e9i	0.190078	+	0.329225i
$593$	−1.13749e9	+	1.97018e9i	−0.224003	+	0.387985i	−0.956020	−	0.293302i	$-0.905246\pi$
$593$	−1.13749e9	+	1.97018e9i	−0.224003	+	0.387985i	0.732017	+	0.681287i	$0.238579\pi$
$594$		0			0
$595$	−5.98002e9	+	2.13133e9i	−1.16384	+	0.414803i
$596$	−4.54439e9			−0.879253
$597$		0			0
$598$	7.76112e7	+	1.34427e8i	0.0148412	+	0.0257058i
$599$	2.61737e9	+	4.53342e9i	0.497589	+	0.861850i	0.999996	−	0.00278122i	$-0.000885290\pi$
$599$	2.61737e9	+	4.53342e9i	0.497589	+	0.861850i	−0.502407	+	0.864631i	$0.667552\pi$
$600$		0			0
$601$	5.20968e9			0.978926			0.489463	−	0.872024i	$-0.337193\pi$
$601$	5.20968e9			0.978926			0.489463	+	0.872024i	$0.337193\pi$
$602$	−7.47766e8	+	4.08089e9i	−0.139694	+	0.762372i
$603$		0			0
$604$	2.56872e9	−	4.44916e9i	0.474338	−	0.821578i
$605$	4.77163e9	+	8.26471e9i	0.876039	+	1.51734i
$606$		0			0
$607$	3.04091e9	−	5.26701e9i	0.551878	−	0.955881i	−0.446261	−	0.894903i	$-0.647245\pi$
$607$	3.04091e9	−	5.26701e9i	0.551878	−	0.955881i	0.998139	−	0.0609780i	$-0.0194219\pi$
$608$	−2.25932e9			−0.407676
$609$		0			0
$610$	−3.54761e9			−0.632822
$611$	5.36899e9	−	9.29936e9i	0.952243	−	1.64933i
$612$		0			0
$613$	2.69788e9	+	4.67287e9i	0.473055	+	0.819355i	0.999524	−	0.0308387i	$-0.00981783\pi$
$613$	2.69788e9	+	4.67287e9i	0.473055	+	0.819355i	−0.526469	+	0.850194i	$0.676484\pi$
$614$	−6.23787e8	+	1.08043e9i	−0.108754	+	0.188368i
$615$		0			0
$616$	5.41274e9	+	4.60391e9i	0.933007	+	0.793587i
$617$	−9.38467e9			−1.60850			−0.804249	−	0.594292i	$-0.797432\pi$
$617$	−9.38467e9			−1.60850			−0.804249	+	0.594292i	$0.797432\pi$
$618$		0			0
$619$	1.03338e9	+	1.78987e9i	0.175123	+	0.303322i	0.940204	−	0.340613i	$-0.110634\pi$
$619$	1.03338e9	+	1.78987e9i	0.175123	+	0.303322i	−0.765081	+	0.643934i	$0.777301\pi$
$620$	−3.05300e6	−	5.28795e6i	−0.000514465	−	0.000891079i
$621$		0			0
$622$	2.51021e9			0.418258
$623$	2.29682e8	−	1.25348e9i	0.0380557	−	0.207687i
$624$		0			0
$625$	−5.40113e9	+	9.35503e9i	−0.884921	+	1.53273i
$626$	−1.51576e9	−	2.62538e9i	−0.246957	−	0.427742i
$627$		0			0
$628$	−3.41745e9	+	5.91920e9i	−0.550609	+	0.953683i
$629$	−5.11107e9			−0.818907
$630$		0			0
$631$	−2.45121e9			−0.388399			−0.194200	−	0.980962i	$-0.562211\pi$
$631$	−2.45121e9			−0.388399			−0.194200	+	0.980962i	$0.562211\pi$
$632$	−4.06526e9	+	7.04124e9i	−0.640588	+	1.10953i
$633$		0			0
$634$	3.04001e9	+	5.26546e9i	0.473765	+	0.820585i
$635$	6.24121e8	−	1.08101e9i	0.0967299	−	0.167541i
$636$		0			0
$637$	−6.19995e9	+	5.06252e9i	−0.950387	+	0.776030i
$638$	1.70470e9			0.259882
$639$		0			0
$640$	−5.57267e9	−	9.65215e9i	−0.840298	−	1.45544i
$641$	3.63409e9	+	6.29443e9i	0.544995	+	0.943959i	0.998607	+	0.0527601i	$0.0168019\pi$
$641$	3.63409e9	+	6.29443e9i	0.544995	+	0.943959i	−0.453612	+	0.891199i	$0.649865\pi$
$642$		0			0
$643$	8.55284e9			1.26874			0.634369	−	0.773030i	$-0.281260\pi$
$643$	8.55284e9			1.26874			0.634369	+	0.773030i	$0.281260\pi$
$644$	−2.33626e8	+	8.32664e7i	−0.0344683	+	0.0122848i
$645$		0			0
$646$	4.63022e8	−	8.01978e8i	0.0675753	−	0.117044i
$647$	−3.30445e8	−	5.72348e8i	−0.0479661	−	0.0830797i	0.841046	−	0.540964i	$-0.181941\pi$
$647$	−3.30445e8	−	5.72348e8i	−0.0479661	−	0.0830797i	−0.889012	+	0.457885i	$0.848607\pi$
$648$		0			0
$649$	2.20990e9	−	3.82766e9i	0.317333	−	0.549638i
$650$	−9.56384e9			−1.36595
$651$		0			0
$652$	−9.47194e9			−1.33836
$653$	−8.64218e8	+	1.49687e9i	−0.121458	+	0.210372i	−0.920343	−	0.391112i	$-0.872090\pi$
$653$	−8.64218e8	+	1.49687e9i	−0.121458	+	0.210372i	0.798885	+	0.601484i	$0.205424\pi$
$654$		0			0
$655$	−7.05998e9	−	1.22282e10i	−0.981655	−	1.70028i
$656$	−3.48051e8	+	6.02841e8i	−0.0481370	+	0.0833757i
$657$		0			0
$658$	−4.29852e9	−	3.65619e9i	−0.588204	−	0.500308i
$659$	4.19192e9			0.570576			0.285288	−	0.958442i	$-0.407911\pi$
$659$	4.19192e9			0.570576			0.285288	+	0.958442i	$0.407911\pi$
$660$		0			0
$661$	3.78878e9	+	6.56236e9i	0.510263	+	0.883802i	0.999929	+	0.0118920i	$0.00378543\pi$
$661$	3.78878e9	+	6.56236e9i	0.510263	+	0.883802i	−0.489666	+	0.871910i	$0.662881\pi$
$662$	2.17291e8	+	3.76358e8i	0.0291097	+	0.0504195i
$663$		0			0
$664$	−2.31639e9			−0.307059
$665$	−4.11236e9	−	3.49785e9i	−0.542270	−	0.461238i
$666$		0			0
$667$	−6.92850e7	+	1.20005e8i	−0.00904064	+	0.0156588i
$668$	−3.54840e9	−	6.14600e9i	−0.460590	−	0.797765i
$669$		0			0
$670$	−1.06186e9	+	1.83919e9i	−0.136397	+	0.236246i
$671$	7.77219e9			0.993149
$672$		0			0
$673$	5.50701e9			0.696407			0.348203	−	0.937419i	$-0.386792\pi$
$673$	5.50701e9			0.696407			0.348203	+	0.937419i	$0.386792\pi$
$674$	3.26525e9	−	5.65558e9i	0.410777	−	0.711487i
$675$		0			0
$676$	1.52748e9	+	2.64567e9i	0.190179	+	0.329400i
$677$	−4.86653e9	+	8.42908e9i	−0.602781	+	1.04405i	0.389617	+	0.920977i	$0.372607\pi$
$677$	−4.86653e9	+	8.42908e9i	−0.602781	+	1.04405i	−0.992398	+	0.123070i	$0.960726\pi$
$678$		0			0
$679$	−5.72914e9	+	2.04192e9i	−0.702337	+	0.250319i
$680$	8.83255e9			1.07722
$681$		0			0
$682$	−2.19988e6	−	3.81030e6i	−0.000265554	−	0.000459953i
$683$	4.84040e9	+	8.38382e9i	0.581311	+	1.00686i	0.995324	+	0.0965899i	$0.0307935\pi$
$683$	4.84040e9	+	8.38382e9i	0.581311	+	1.00686i	−0.414013	+	0.910271i	$0.635873\pi$
$684$		0			0
$685$	1.10529e10			1.31389
$686$	2.02969e9	+	3.68442e9i	0.240046	+	0.435748i
$687$		0			0
$688$	−2.12103e9	+	3.67373e9i	−0.248306	+	0.430079i
$689$	3.75327e9	+	6.50085e9i	0.437162	+	0.757186i
$690$		0			0
$691$	2.76919e9	−	4.79637e9i	0.319285	−	0.553019i	−0.661054	−	0.750339i	$-0.729890\pi$
$691$	2.76919e9	−	4.79637e9i	0.319285	−	0.553019i	0.980339	+	0.197320i	$0.0632238\pi$
$692$	−1.07248e10			−1.23032
$693$		0			0
$694$	4.82815e9			0.548306
$695$	1.90097e9	−	3.29258e9i	0.214798	−	0.372040i
$696$		0			0
$697$	−9.26971e8	−	1.60556e9i	−0.103693	−	0.179602i
$698$	6.78631e7	−	1.17542e8i	0.00755335	−	0.0130828i
$699$		0			0
$700$	2.75427e9	−	1.50312e10i	0.303503	−	1.65635i
$701$	1.27820e10			1.40148			0.700738	−	0.713419i	$-0.252854\pi$
$701$	1.27820e10			1.40148			0.700738	+	0.713419i	$0.252854\pi$
$702$		0			0
$703$	−2.17323e9	−	3.76414e9i	−0.235918	−	0.408622i
$704$	−1.26076e9	−	2.18370e9i	−0.136185	−	0.235879i
$705$		0			0
$706$	−3.59897e9			−0.384912
$707$	2.65048e8	+	2.25441e8i	0.0282069	+	0.0239920i
$708$		0			0
$709$	−1.87549e9	+	3.24845e9i	−0.197630	+	0.342306i	−0.947760	−	0.318985i	$-0.896658\pi$
$709$	−1.87549e9	+	3.24845e9i	−0.197630	+	0.342306i	0.750129	+	0.661291i	$0.229991\pi$
$710$	1.60886e9	+	2.78663e9i	0.168700	+	0.292196i
$711$		0			0
$712$	−8.86491e8	+	1.53545e9i	−0.0920437	+	0.159424i
$713$	357642.			3.69518e−5
$714$		0			0
$715$	3.03159e10			3.10169
$716$	−2.27884e8	+	3.94706e8i	−0.0232016	+	0.0401864i
$717$		0			0
$718$	2.95102e9	+	5.11131e9i	0.297534	+	0.515344i
$719$	7.78801e9	−	1.34892e10i	0.781403	−	1.35343i	−0.149721	−	0.988728i	$-0.547838\pi$
$719$	7.78801e9	−	1.34892e10i	0.781403	−	1.35343i	0.931124	−	0.364702i	$-0.118829\pi$
$720$		0			0
$721$	2.46001e9	−	1.34254e10i	0.244435	−	1.33399i
$722$	−4.24363e9			−0.419621
$723$		0			0
$724$	4.83107e9	+	8.36766e9i	0.473106	+	0.819443i
$725$	−4.26891e9	−	7.39398e9i	−0.416039	−	0.720601i
$726$		0			0
$727$	−2.04219e10			−1.97118			−0.985589	−	0.169158i	$-0.945895\pi$
$727$	−2.04219e10			−1.97118			−0.985589	+	0.169158i	$0.945895\pi$
$728$	1.04899e10	−	3.73870e9i	1.00765	−	0.359137i
$729$		0			0
$730$	−5.90398e9	+	1.02260e10i	−0.561714	+	0.972917i
$731$	−5.64899e9	−	9.78433e9i	−0.534884	−	0.926447i
$732$		0			0
$733$	−1.13462e9	+	1.96521e9i	−0.106411	+	0.184309i	−0.914314	−	0.405007i	$-0.867269\pi$
$733$	−1.13462e9	+	1.96521e9i	−0.106411	+	0.184309i	0.807903	+	0.589315i	$0.200602\pi$
$734$	5.11556e8			0.0477482
$735$		0			0
$736$	5.41968e8			0.0501073
$737$	2.32634e9	−	4.02934e9i	0.214061	−	0.370764i
$738$		0			0
$739$	−9.23031e9	−	1.59874e10i	−0.841319	−	1.45721i	−0.888780	−	0.458334i	$-0.848446\pi$
$739$	−9.23031e9	−	1.59874e10i	−0.841319	−	1.45721i	0.0474611	−	0.998873i	$-0.484887\pi$
$740$	8.90038e9	−	1.54159e10i	0.807417	−	1.39849i
$741$		0			0
$742$	3.71595e9	−	1.32440e9i	0.333931	−	0.119016i
$743$	−1.77069e10			−1.58373			−0.791866	−	0.610695i	$-0.790890\pi$
$743$	−1.77069e10			−1.58373			−0.791866	+	0.610695i	$0.790890\pi$
$744$		0			0
$745$	1.18644e10	+	2.05498e10i	1.05123	+	1.82079i
$746$	3.52052e9	+	6.09771e9i	0.310471	+	0.537751i
$747$		0			0
$748$	−8.30888e9			−0.725917
$749$	1.19702e9	−	6.53268e9i	0.104092	−	0.568074i
$750$		0			0
$751$	8.13389e9	−	1.40883e10i	0.700742	−	1.21372i	−0.267464	−	0.963568i	$-0.586186\pi$
$751$	8.13389e9	−	1.40883e10i	0.700742	−	1.21372i	0.968206	−	0.250153i	$-0.0804810\pi$
$752$	−2.88497e9	−	4.99692e9i	−0.247388	−	0.428489i
$753$		0			0
$754$	1.33579e9	−	2.31366e9i	0.113485	−	0.196562i
$755$	−2.68255e10			−2.26847
$756$		0			0
$757$	−2.16032e10			−1.81002			−0.905008	−	0.425394i	$-0.860135\pi$
$757$	−2.16032e10			−1.81002			−0.905008	+	0.425394i	$0.860135\pi$
$758$	−2.12775e9	+	3.68538e9i	−0.177451	+	0.307355i
$759$		0			0
$760$	3.75560e9	+	6.50489e9i	0.310336	+	0.537517i
$761$	−2.78515e9	+	4.82401e9i	−0.229088	+	0.396791i	−0.957538	−	0.288307i	$-0.906908\pi$
$761$	−2.78515e9	+	4.82401e9i	−0.229088	+	0.396791i	0.728450	+	0.685099i	$0.240241\pi$
$762$		0			0
$763$	8.89198e9	+	7.56324e9i	0.724707	+	0.616413i
$764$	−6.23752e9			−0.506040
$765$		0			0
$766$	1.61499e9	+	2.79724e9i	0.129828	+	0.224869i
$767$	−3.46331e9	−	5.99864e9i	−0.277146	−	0.480031i
$768$		0			0
$769$	−2.06958e10			−1.64112			−0.820558	−	0.571563i	$-0.806337\pi$
$769$	−2.06958e10			−1.64112			−0.820558	+	0.571563i	$0.806337\pi$
$770$	2.87149e9	−	1.56710e10i	0.226668	−	1.23703i
$771$		0			0
$772$	3.68979e9	−	6.39091e9i	0.288630	−	0.499922i
$773$	8.11373e9	+	1.40534e10i	0.631819	+	1.09434i	0.987180	+	0.159613i	$0.0510247\pi$
$773$	8.11373e9	+	1.40534e10i	0.631819	+	1.09434i	−0.355361	+	0.934729i	$0.615642\pi$
$774$		0			0
$775$	−1.10178e7	+	1.90835e7i	−0.000850238	+	0.00147266i
$776$	8.46200e9			0.650066
$777$		0			0
$778$	−1.19307e10			−0.908320
$779$	7.88296e8	−	1.36537e9i	0.0597459	−	0.103483i
$780$		0			0
$781$	−3.52473e9	−	6.10501e9i	−0.264757	−	0.458572i
$782$	−1.11070e8	+	1.92379e8i	−0.00830565	+	0.0143858i
$783$		0			0
$784$	6.90103e8	+	4.24529e9i	0.0511455	+	0.314631i
$785$	3.56889e10			2.63323
$786$		0			0
$787$	−4.10073e9	−	7.10268e9i	−0.299882	−	0.519410i	0.676227	−	0.736693i	$-0.263614\pi$
$787$	−4.10073e9	−	7.10268e9i	−0.299882	−	0.519410i	−0.976109	+	0.217283i	$0.930281\pi$
$788$	7.08322e9	+	1.22685e10i	0.515690	+	0.893202i
$789$		0			0
$790$	1.82292e10			1.31545
$791$	7.70060e8	−	2.74456e8i	0.0553231	−	0.0197177i
$792$		0			0
$793$	6.09022e9	−	1.05486e10i	0.433688	−	0.751169i
$794$	−3.89909e9	−	6.75342e9i	−0.276434	−	0.478797i
$795$		0			0
$796$	−1.41621e7	+	2.45296e7i	−0.000995253	+	0.00172383i
$797$	−1.97600e10			−1.38255			−0.691276	−	0.722590i	$-0.742951\pi$
$797$	−1.97600e10			−1.38255			−0.691276	+	0.722590i	$0.742951\pi$
$798$		0			0
$799$	1.53672e10			1.06581
$800$	−1.66963e10	+	2.89189e10i	−1.15294	+	1.99695i
$801$		0			0
$802$	1.23829e9	+	2.14478e9i	0.0847639	+	0.146815i
$803$	1.29346e10	−	2.24034e10i	0.881552	−	1.52689i
$804$		0			0
$805$	9.86477e8	+	8.39067e8i	0.0666502	+	0.0566906i
$806$	−6.89522e6			−0.000463848
$807$		0			0
$808$	−2.42054e8	−	4.19249e8i	−0.0161425	−	0.0279597i
$809$	−5.83956e8	−	1.01144e9i	−0.0387757	−	0.0671615i	0.845986	−	0.533205i	$-0.179012\pi$
$809$	−5.83956e8	−	1.01144e9i	−0.0387757	−	0.0671615i	−0.884762	+	0.466043i	$0.845679\pi$
$810$		0			0
$811$	−1.21328e10			−0.798711			−0.399356	−	0.916796i	$-0.630766\pi$
$811$	−1.21328e10			−0.798711			−0.399356	+	0.916796i	$0.630766\pi$
$812$	3.25163e9	+	2.76574e9i	0.213135	+	0.181286i
$813$		0			0
$814$	6.41328e9	−	1.11081e10i	0.416769	−	0.721864i
$815$	2.47292e10	+	4.28321e10i	1.60014	+	2.77152i
$816$		0			0
$817$	4.80390e9	−	8.32060e9i	0.308189	−	0.533798i
$818$	−4.06102e8			−0.0259417
$819$		0			0
$820$	6.45688e9			0.408954
$821$	9.54695e7	−	1.65358e8i	0.00602093	−	0.0104286i	−0.862999	−	0.505205i	$-0.831417\pi$
$821$	9.54695e7	−	1.65358e8i	0.00602093	−	0.0104286i	0.869020	+	0.494777i	$0.164750\pi$
$822$		0			0
$823$	5.70929e9	+	9.88878e9i	0.357012	+	0.618362i	0.987460	−	0.157869i	$-0.0504623\pi$
$823$	5.70929e9	+	9.88878e9i	0.357012	+	0.618362i	−0.630448	+	0.776231i	$0.717129\pi$
$824$	−9.49474e9	+	1.64454e10i	−0.591205	+	1.02400i
$825$		0			0
$826$	−3.42888e9	+	1.22209e9i	−0.211701	+	0.0754521i
$827$	1.33839e9			0.0822834			0.0411417	−	0.999153i	$-0.486900\pi$
$827$	1.33839e9			0.0822834			0.0411417	+	0.999153i	$0.486900\pi$
$828$		0			0
$829$	1.01269e8	+	1.75402e8i	0.00617353	+	0.0106929i	0.869096	−	0.494644i	$-0.164702\pi$
$829$	1.01269e8	+	1.75402e8i	0.00617353	+	0.0106929i	−0.862922	+	0.505337i	$0.831368\pi$
$830$	2.59675e9	+	4.49770e9i	0.157637	+	0.273035i
$831$		0			0
$832$	−3.95169e9			−0.237876
$833$	−1.07108e10	−	4.06157e9i	−0.642042	−	0.243465i
$834$		0			0
$835$	−1.85282e10	+	3.20917e10i	−1.10136	+	1.90761i
$836$	−3.53294e9	−	6.11923e9i	−0.209129	−	0.362222i
$837$		0			0
$838$	3.33384e9	−	5.77437e9i	0.195700	−	0.338962i
$839$	−2.24187e10			−1.31052			−0.655259	−	0.755405i	$-0.727440\pi$
$839$	−2.24187e10			−1.31052			−0.655259	+	0.755405i	$0.727440\pi$
$840$		0			0
$841$	−1.48649e10			−0.861739
$842$	6.42834e8	−	1.11342e9i	0.0371113	−	0.0642787i
$843$		0			0
$844$	−5.06784e9	−	8.77775e9i	−0.290151	−	0.502556i
$845$	7.97584e9	−	1.38146e10i	0.454755	−	0.787659i
$846$		0			0
$847$	−3.10357e9	+	1.69376e10i	−0.175497	+	0.957766i
$848$	4.03356e9			0.227145
$849$		0			0
$850$	−6.84345e9	−	1.18532e10i	−0.382216	−	0.662018i
$851$	5.21315e8	+	9.02945e8i	0.0289966	+	0.0502236i
$852$		0			0
$853$	−1.43556e10			−0.791952			−0.395976	−	0.918261i	$-0.629594\pi$
$853$	−1.43556e10			−0.791952			−0.395976	+	0.918261i	$0.629594\pi$
$854$	−4.87595e9	−	4.14734e9i	−0.267890	−	0.227859i
$855$		0			0
$856$	−4.62007e9	+	8.00220e9i	−0.251762	+	0.436065i
$857$	−4.29142e9	−	7.43295e9i	−0.232899	−	0.403393i	0.725761	−	0.687947i	$-0.241488\pi$
$857$	−4.29142e9	−	7.43295e9i	−0.232899	−	0.403393i	−0.958660	+	0.284554i	$0.908155\pi$
$858$		0			0
$859$	−5.04094e9	+	8.73117e9i	−0.271354	+	0.469998i	−0.969209	−	0.246241i	$-0.920805\pi$
$859$	−5.04094e9	+	8.73117e9i	−0.271354	+	0.469998i	0.697855	+	0.716239i	$0.254138\pi$
$860$	3.93484e10			2.10952
$861$		0			0
$862$	2.99511e9			0.159271
$863$	−1.70490e10	+	2.95298e10i	−0.902946	+	1.56395i	−0.0792950	+	0.996851i	$0.525267\pi$
$863$	−1.70490e10	+	2.95298e10i	−0.902946	+	1.56395i	−0.823651	+	0.567097i	$0.808066\pi$
$864$		0			0
$865$	2.80000e10	+	4.84975e10i	1.47096	+	2.54778i
$866$	9.99604e8	−	1.73136e9i	0.0523016	−	0.0905891i
$867$		0			0
$868$	1.98574e6	−	1.08370e7i	0.000103063	−	0.000562460i
$869$	−3.99370e10			−2.06446
$870$		0			0
$871$	−3.64580e9	−	6.31471e9i	−0.186952	−	0.323810i
$872$	−8.12056e9	−	1.40652e10i	−0.414742	−	0.718355i
$873$		0			0
$874$	−1.88908e8			−0.00957107
$875$	−4.15742e10	+	1.48174e10i	−2.09795	+	0.747729i
$876$		0			0
$877$	1.38568e10	−	2.40006e10i	0.693687	−	1.20150i	−0.276934	−	0.960889i	$-0.589318\pi$
$877$	1.38568e10	−	2.40006e10i	0.693687	−	1.20150i	0.970621	−	0.240612i	$-0.0773483\pi$
$878$	1.61315e9	+	2.79406e9i	0.0804349	+	0.139317i
$879$		0			0
$880$	8.14497e9	−	1.41075e10i	0.402903	−	0.697848i
$881$	1.61765e10			0.797020			0.398510	−	0.917164i	$-0.369527\pi$
$881$	1.61765e10			0.797020			0.398510	+	0.917164i	$0.369527\pi$
$882$		0			0
$883$	2.67909e10			1.30956			0.654780	−	0.755820i	$-0.272761\pi$
$883$	2.67909e10			1.30956			0.654780	+	0.755820i	$0.272761\pi$
$884$	−6.51077e9	+	1.12770e10i	−0.316993	+	0.549048i
$885$		0			0
$886$	4.52833e9	+	7.84330e9i	0.218736	+	0.378862i
$887$	1.74706e9	−	3.02600e9i	0.0840573	−	0.145591i	−0.820932	−	0.571026i	$-0.806545\pi$
$887$	1.74706e9	−	3.02600e9i	0.0840573	−	0.145591i	0.904989	+	0.425435i	$0.139879\pi$
$888$		0			0
$889$	2.12157e9	−	7.56146e8i	0.101275	−	0.0360952i
$890$	3.97515e9			0.189012
$891$		0			0
$892$	1.77390e8	+	3.07249e8i	0.00836859	+	0.0144948i
$893$	6.53414e9	+	1.13175e10i	0.307049	+	0.531825i
$894$		0			0
$895$	2.37982e9			0.110959
$896$	3.62458e9	−	1.97810e10i	0.168337	−	0.918691i
$897$		0			0
$898$	7.32041e9	−	1.26793e10i	0.337340	−	0.584291i
$899$	−3.07775e6	−	5.33082e6i	−0.000141278	−	0.000244701i
$900$		0			0
$901$	−5.37133e9	+	9.30342e9i	−0.244650	+	0.423746i
$902$	4.65259e9			0.211092
$903$		0			0
$904$	−1.13739e9			−0.0512057
$905$	2.52257e10	−	4.36922e10i	1.13129	−	1.95945i
$906$		0			0
$907$	1.40268e10	+	2.42952e10i	0.624215	+	1.08117i	0.988692	+	0.149959i	$0.0479143\pi$
$907$	1.40268e10	+	2.42952e10i	0.624215	+	1.08117i	−0.364477	+	0.931212i	$0.618752\pi$
$908$	3.71885e8	−	6.44123e8i	0.0164857	−	0.0285541i
$909$		0			0
$910$	−1.90189e10	−	1.61769e10i	−0.836646	−	0.711625i
$911$	2.81753e10			1.23468			0.617341	−	0.786696i	$-0.288210\pi$
$911$	2.81753e10			1.23468			0.617341	+	0.786696i	$0.288210\pi$
$912$		0			0
$913$	−5.68902e9	−	9.85368e9i	−0.247394	−	0.428500i
$914$	7.85820e9	+	1.36108e10i	0.340417	+	0.589620i
$915$		0			0
$916$	2.84240e10			1.22194
$917$	4.59196e9	−	2.50604e10i	0.196655	−	1.07323i
$918$		0			0
$919$	1.41657e10	−	2.45357e10i	0.602052	−	1.04278i	−0.390458	−	0.920621i	$-0.627683\pi$
$919$	1.41657e10	−	2.45357e10i	0.602052	−	1.04278i	0.992510	−	0.122163i	$-0.0389832\pi$
$920$	−9.00896e8	−	1.56040e9i	−0.0381432	−	0.0660660i
$921$		0			0
$922$	−6.87719e9	+	1.19116e10i	−0.288970	+	0.500511i
$923$	−1.10478e10			−0.462455
$924$		0			0
$925$	−6.42404e10			−2.66878
$926$	1.62838e9	−	2.82044e9i	0.0673935	−	0.116729i
$927$		0			0
$928$	−4.66400e9	−	8.07828e9i	−0.191576	−	0.331819i
$929$	−2.01385e10	+	3.48810e10i	−0.824086	+	1.42736i	0.0785291	+	0.996912i	$0.474978\pi$
$929$	−2.01385e10	+	3.48810e10i	−0.824086	+	1.42736i	−0.902616	+	0.430448i	$0.858356\pi$
$930$		0			0
$931$	−1.56301e9	−	9.61512e9i	−0.0634800	−	0.390509i
$932$	−9.61193e9			−0.388915
$933$		0			0
$934$	−1.09001e10	−	1.88796e10i	−0.437742	−	0.758191i
$935$	2.16927e10	+	3.75728e10i	0.867906	+	1.50326i
$936$		0			0
$937$	−2.09269e10			−0.831029			−0.415514	−	0.909587i	$-0.636398\pi$
$937$	−2.09269e10			−0.831029			−0.415514	+	0.909587i	$0.636398\pi$
$938$	−3.60956e9	+	1.28648e9i	−0.142805	+	0.0508971i
$939$		0			0
$940$	−2.67603e10	+	4.63503e10i	−1.05086	+	1.82014i
$941$	−8.70847e8	−	1.50835e9i	−0.0340705	−	0.0590118i	0.848487	−	0.529216i	$-0.177514\pi$
$941$	−8.70847e8	−	1.50835e9i	−0.0340705	−	0.0590118i	−0.882558	+	0.470204i	$0.844180\pi$
$942$		0			0
$943$	−1.89097e8	+	3.27526e8i	−0.00734334	+	0.0127190i
$944$	−3.72196e9			−0.144002
$945$		0			0
$946$	2.83530e10			1.08888
$947$	−1.29476e10	+	2.24258e10i	−0.495408	+	0.858072i	−0.999986	−	0.00529407i	$-0.998315\pi$
$947$	−1.29476e10	+	2.24258e10i	−0.495408	+	0.858072i	0.504578	+	0.863366i	$0.331648\pi$
$948$		0			0
$949$	−2.02709e10	−	3.51102e10i	−0.769911	−	1.33352i
$950$	5.81967e9	−	1.00800e10i	0.220225	−	0.381440i
$951$		0			0
$952$	1.21398e10	+	1.03257e10i	0.456016	+	0.387873i
$953$	3.87113e9			0.144881			0.0724407	−	0.997373i	$-0.476921\pi$
$953$	3.87113e9			0.144881			0.0724407	+	0.997373i	$0.476921\pi$
$954$		0			0
$955$	1.62848e10	+	2.82061e10i	0.605021	+	1.04793i
$956$	8.62347e9	+	1.49363e10i	0.319212	+	0.552892i
$957$		0			0
$958$	−1.12702e10			−0.414144
$959$	1.51915e10	+	1.29214e10i	0.556205	+	0.473091i
$960$		0			0
$961$	1.37563e10	−	2.38266e10i	0.500000	−	0.866025i
$962$	−1.00508e10	−	1.74085e10i	−0.363988	−	0.630446i
$963$		0			0
$964$	−3.42322e9	+	5.92919e9i	−0.123074	+	0.213170i
$965$	−3.85329e10			−1.38034
$966$		0			0
$967$	−1.34763e9			−0.0479266			−0.0239633	−	0.999713i	$-0.507628\pi$
$967$	−1.34763e9			−0.0479266			−0.0239633	+	0.999713i	$0.507628\pi$
$968$	1.19787e10	−	2.07477e10i	0.424468	−	0.735200i
$969$		0			0
$970$	−9.48621e9	−	1.64306e10i	−0.333727	−	0.578033i
$971$	2.62011e10	−	4.53816e10i	0.918443	−	1.59079i	0.116662	−	0.993172i	$-0.462780\pi$
$971$	2.62011e10	−	4.53816e10i	0.918443	−	1.59079i	0.801781	−	0.597618i	$-0.203886\pi$
$972$		0			0
$973$	6.46196e9	−	2.30310e9i	0.224890	−	0.0801527i
$974$	2.44104e10			0.846484
$975$		0			0
$976$	−3.27252e9	−	5.66817e9i	−0.112670	−	0.195150i
$977$	−2.55095e10	−	4.41838e10i	−0.875128	−	1.51577i	−0.856626	−	0.515938i	$-0.827444\pi$
$977$	−2.55095e10	−	4.41838e10i	−0.875128	−	1.51577i	−0.0185021	−	0.999829i	$-0.505890\pi$
$978$		0			0
$979$	−8.70886e9			−0.296635
$980$	3.09021e10	−	2.52328e10i	1.04881	−	0.856397i
$981$		0			0
$982$	−1.30253e10	+	2.25604e10i	−0.438931	+	0.760251i
$983$	−2.19807e10	−	3.80717e10i	−0.738082	−	1.27840i	−0.953358	−	0.301842i	$-0.902398\pi$
$983$	−2.19807e10	−	3.80717e10i	−0.738082	−	1.27840i	0.215276	−	0.976553i	$-0.430935\pi$
$984$		0			0
$985$	3.69855e10	−	6.40607e10i	1.23312	−	2.13582i
$986$	3.82333e9			0.127020
$987$		0			0
$988$	−1.10735e10			−0.365289
$989$	−1.15236e9	+	1.99595e9i	−0.0378793	+	0.0656089i
$990$		0			0
$991$	−6.08355e9	−	1.05370e10i	−0.198563	−	0.343922i	0.749500	−	0.662005i	$-0.230294\pi$
$991$	−6.08355e9	−	1.05370e10i	−0.198563	−	0.343922i	−0.948063	+	0.318083i	$0.896961\pi$
$992$	−1.20375e7	+	2.08496e7i	−0.000391513	+	0.000678121i
$993$		0			0
$994$	−1.04644e9	+	5.71087e9i	−0.0337956	+	0.184438i
$995$	1.47897e8			0.00475969
$996$		0			0
$997$	2.00273e9	+	3.46883e9i	0.0640013	+	0.110853i	0.896251	−	0.443548i	$-0.146280\pi$
$997$	2.00273e9	+	3.46883e9i	0.0640013	+	0.110853i	−0.832249	+	0.554402i	$0.812947\pi$
$998$	−7.07165e9	−	1.22485e10i	−0.225198	−	0.390054i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.8.e.c.37.2		8
3.2	odd	2		21.8.e.a.16.3	yes	8
7.2	even	3		441.8.a.q.1.3		4
7.4	even	3	inner	63.8.e.c.46.2		8
7.5	odd	6		441.8.a.r.1.3		4
21.2	odd	6		147.8.a.i.1.2		4
21.5	even	6		147.8.a.h.1.2		4
21.11	odd	6		21.8.e.a.4.3	✓	8
21.17	even	6		147.8.e.k.67.3		8
21.20	even	2		147.8.e.k.79.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.8.e.a.4.3	✓	8	21.11	odd	6
21.8.e.a.16.3	yes	8	3.2	odd	2
63.8.e.c.37.2		8	1.1	even	1	trivial
63.8.e.c.46.2		8	7.4	even	3	inner
147.8.a.h.1.2		4	21.5	even	6
147.8.a.i.1.2		4	21.2	odd	6
147.8.e.k.67.3		8	21.17	even	6
147.8.e.k.79.3		8	21.20	even	2
441.8.a.q.1.3		4	7.2	even	3
441.8.a.r.1.3		4	7.5	odd	6

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	63.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.81424 + 4.87440i) q^{2} +(48.1601 + 83.4158i) q^{4} +(251.471 - 435.561i) q^{5} +(854.822 - 304.667i) q^{7} -1262.58 q^{8} +O(q^{10})\)	\(q+(-2.81424 + 4.87440i) q^{2} +(48.1601 + 83.4158i) q^{4} +(251.471 - 435.561i) q^{5} +(854.822 - 304.667i) q^{7} -1262.58 q^{8} +(1415.40 + 2451.54i) q^{10} +(-3100.89 - 5370.90i) q^{11} -9719.32 q^{13} +(-920.606 + 5024.15i) q^{14} +(-2611.29 + 4522.89i) q^{16} +(-6954.71 - 12045.9i) q^{17} +(5914.28 - 10243.8i) q^{19} +48443.5 q^{20} +34906.6 q^{22} +(-1418.72 + 2457.30i) q^{23} +(-87412.9 - 151404. i) q^{25} +(27352.5 - 47375.9i) q^{26} +(66582.4 + 56632.9i) q^{28} +48836.2 q^{29} +(-63.0218 - 109.157i) q^{31} +(-95502.8 - 165416. i) q^{32} +78288.8 q^{34} +(82262.3 - 448942. i) q^{35} +(183727. - 318225. i) q^{37} +(33288.4 + 57657.2i) q^{38} +(-317503. + 549931. i) q^{40} +133287. q^{41} +812254. q^{43} +(298678. - 517326. i) q^{44} +(-7985.25 - 13830.9i) q^{46} +(-552403. + 956790. i) q^{47} +(637900. - 520872. i) q^{49} +984003. q^{50} +(-468084. - 810745. i) q^{52} +(-386165. - 668858. i) q^{53} -3.11914e6 q^{55} +(-1.07928e6 + 384666. i) q^{56} +(-137437. + 238047. i) q^{58} +(356333. + 617187. i) q^{59} +(-626610. + 1.08532e6i) q^{61} +709.434 q^{62} +406580. q^{64} +(-2.44413e6 + 4.23335e6i) q^{65} +(375109. + 649707. i) q^{67} +(669879. - 1.16026e6i) q^{68} +(1.95682e6 + 1.66441e6i) q^{70} +1.13668e6 q^{71} +(2.08563e6 + 3.61241e6i) q^{73} +(1.03410e6 + 1.79112e6i) q^{74} +1.13933e6 q^{76} +(-4.28704e6 - 3.64643e6i) q^{77} +(3.21980e6 - 5.57686e6i) q^{79} +(1.31333e6 + 2.27475e6i) q^{80} +(-375101. + 649694. i) q^{82} +1.83464e6 q^{83} -6.99563e6 q^{85} +(-2.28588e6 + 3.95925e6i) q^{86} +(3.91513e6 + 6.78120e6i) q^{88} +(702126. - 1.21612e6i) q^{89} +(-8.30829e6 + 2.96115e6i) q^{91} -273303. q^{92} +(-3.10919e6 - 5.38527e6i) q^{94} +(-2.97454e6 - 5.15206e6i) q^{95} -6.70215e6 q^{97} +(743737. + 4.57524e6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} - 101 q^{4} + 196 q^{5} + 154 q^{7} + 2694 q^{8}+O(q^{10}) \) 8 * q - q^2 - 101 * q^4 + 196 * q^5 + 154 * q^7 + 2694 * q^8	\( 8 q - q^{2} - 101 q^{4} + 196 q^{5} + 154 q^{7} + 2694 q^{8} + 5185 q^{10} - 5210 q^{11} - 7588 q^{13} + 29932 q^{14} + 21055 q^{16} - 11436 q^{17} + 69158 q^{19} + 175982 q^{20} + 114526 q^{22} - 146220 q^{23} - 6230 q^{25} + 107696 q^{26} - 19201 q^{28} + 141328 q^{29} + 288618 q^{31} + 2653 q^{32} - 991992 q^{34} + 66164 q^{35} + 448902 q^{37} + 528944 q^{38} - 767361 q^{40} + 1326632 q^{41} + 1108 q^{43} - 686635 q^{44} + 1064964 q^{46} + 762180 q^{47} + 5310620 q^{49} + 1050856 q^{50} - 3423848 q^{52} - 2761920 q^{53} - 3930112 q^{55} - 5341077 q^{56} + 4451395 q^{58} + 3410898 q^{59} - 300892 q^{61} + 4132350 q^{62} - 5833102 q^{64} - 8019032 q^{65} + 4222478 q^{67} + 5770500 q^{68} + 7703801 q^{70} + 761928 q^{71} + 451674 q^{73} - 10091220 q^{74} - 29495312 q^{76} - 16516528 q^{77} + 12154822 q^{79} + 7870085 q^{80} - 8814904 q^{82} + 24175956 q^{83} - 14751000 q^{85} - 32881826 q^{86} + 14439051 q^{88} + 4955752 q^{89} + 14146174 q^{91} - 413784 q^{92} - 5960646 q^{94} + 8460784 q^{95} - 45681228 q^{97} - 8665405 q^{98}+O(q^{100}) \) 8 * q - q^2 - 101 * q^4 + 196 * q^5 + 154 * q^7 + 2694 * q^8 + 5185 * q^10 - 5210 * q^11 - 7588 * q^13 + 29932 * q^14 + 21055 * q^16 - 11436 * q^17 + 69158 * q^19 + 175982 * q^20 + 114526 * q^22 - 146220 * q^23 - 6230 * q^25 + 107696 * q^26 - 19201 * q^28 + 141328 * q^29 + 288618 * q^31 + 2653 * q^32 - 991992 * q^34 + 66164 * q^35 + 448902 * q^37 + 528944 * q^38 - 767361 * q^40 + 1326632 * q^41 + 1108 * q^43 - 686635 * q^44 + 1064964 * q^46 + 762180 * q^47 + 5310620 * q^49 + 1050856 * q^50 - 3423848 * q^52 - 2761920 * q^53 - 3930112 * q^55 - 5341077 * q^56 + 4451395 * q^58 + 3410898 * q^59 - 300892 * q^61 + 4132350 * q^62 - 5833102 * q^64 - 8019032 * q^65 + 4222478 * q^67 + 5770500 * q^68 + 7703801 * q^70 + 761928 * q^71 + 451674 * q^73 - 10091220 * q^74 - 29495312 * q^76 - 16516528 * q^77 + 12154822 * q^79 + 7870085 * q^80 - 8814904 * q^82 + 24175956 * q^83 - 14751000 * q^85 - 32881826 * q^86 + 14439051 * q^88 + 4955752 * q^89 + 14146174 * q^91 - 413784 * q^92 - 5960646 * q^94 + 8460784 * q^95 - 45681228 * q^97 - 8665405 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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