LMFDB - Embedded newform 63.8.e.b.46.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [63,8,Mod(37,63)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [8,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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} - x^{7} + 103x^{6} - 378x^{5} + 9744x^{4} - 22680x^{3} + 149400x^{2} + 216000x + 810000 $ x^8 - x^7 + 103x^6 - 378x^5 + 9744x^4 - 22680x^3 + 149400x^2 + 216000x + 810000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 7)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			46.3
Root			$4.11776 - 7.13217i$ of defining polynomial
Character	$\chi$	$=$	63.46
Dual form			63.8.e.b.37.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.59276 + 2.75874i) q^{2} +(58.9262 - 102.063i) q^{4} +(-0.294487 - 0.510067i) q^{5} +(31.8040 + 906.935i) q^{7} +783.169 q^{8} +(0.938097 - 1.62483i) q^{10} +(-599.771 + 1038.83i) q^{11} +7651.01 q^{13} +(-2451.35 + 1532.27i) q^{14} +(-6295.16 - 10903.5i) q^{16} +(17592.9 - 30471.9i) q^{17} +(4286.72 + 7424.82i) q^{19} -69.4121 q^{20} -3821.17 q^{22} +(39366.9 + 68185.4i) q^{23} +(39062.3 - 67657.9i) q^{25} +(12186.2 + 21107.2i) q^{26} +(94438.8 + 50196.3i) q^{28} +199760. q^{29} +(-68557.2 + 118745. i) q^{31} +(70176.2 - 121549. i) q^{32} +112085. q^{34} +(453.232 - 283.303i) q^{35} +(-45042.1 - 78015.3i) q^{37} +(-13655.4 + 23651.9i) q^{38} +(-230.633 - 399.469i) q^{40} +269601. q^{41} +602901. q^{43} +(70684.5 + 122429. i) q^{44} +(-125404. + 217206. i) q^{46} +(-192458. - 333347. i) q^{47} +(-821520. + 57688.3i) q^{49} +248868. q^{50} +(450845. - 780887. i) q^{52} +(332119. - 575247. i) q^{53} +706.501 q^{55} +(24907.9 + 710283. i) q^{56} +(318170. + 551087. i) q^{58} +(-1.15394e6 + 1.99868e6i) q^{59} +(-449938. - 779316. i) q^{61} -436781. q^{62} -1.16446e6 q^{64} +(-2253.13 - 3902.53i) q^{65} +(-11879.4 + 20575.8i) q^{67} +(-2.07337e6 - 3.59118e6i) q^{68} +(1503.45 + 799.117i) q^{70} -2.52558e6 q^{71} +(-1.76425e6 + 3.05578e6i) q^{73} +(143483. - 248519. i) q^{74} +1.01040e6 q^{76} +(-961231. - 510915. i) q^{77} +(-2.31891e6 - 4.01647e6i) q^{79} +(-3707.69 + 6421.91i) q^{80} +(429410. + 743759. i) q^{82} -7.71353e6 q^{83} -20723.6 q^{85} +(960277. + 1.66325e6i) q^{86} +(-469722. + 813583. i) q^{88} +(4.39050e6 + 7.60457e6i) q^{89} +(243332. + 6.93897e6i) q^{91} +9.27896e6 q^{92} +(613079. - 1.06188e6i) q^{94} +(2524.77 - 4373.03i) q^{95} +4.42347e6 q^{97} +(-1.46763e6 - 2.17448e6i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{2} - 348 q^{4} + 252 q^{5} + 672 q^{7} + 1968 q^{8} - 4774 q^{10} - 3972 q^{11} - 2352 q^{13} - 47502 q^{14} - 57264 q^{16} + 56364 q^{17} - 41748 q^{19} - 324744 q^{20} - 305908 q^{22} + 131748 q^{23}+ \cdots - 60255006 q^{98}+O(q^{100}) $ 8 * q - 6 * q^2 - 348 * q^4 + 252 * q^5 + 672 * q^7 + 1968 * q^8 - 4774 * q^10 - 3972 * q^11 - 2352 * q^13 - 47502 * q^14 - 57264 * q^16 + 56364 * q^17 - 41748 * q^19 - 324744 * q^20 - 305908 * q^22 + 131748 * q^23 + 68016 * q^25 + 113652 * q^26 + 681548 * q^28 - 68112 * q^29 - 401212 * q^31 - 453408 * q^32 + 164220 * q^34 - 40404 * q^35 + 5396 * q^37 + 31794 * q^38 + 443688 * q^40 - 820848 * q^41 + 93088 * q^43 - 1465836 * q^44 - 1379202 * q^46 + 1470084 * q^47 - 2793784 * q^49 - 2791056 * q^50 + 5269768 * q^52 - 642372 * q^53 - 6126680 * q^55 + 6195168 * q^56 + 1972220 * q^58 + 752220 * q^59 - 1325772 * q^61 + 6032628 * q^62 - 1731712 * q^64 - 4868808 * q^65 + 290916 * q^67 + 2453556 * q^68 + 11665990 * q^70 - 6755520 * q^71 - 6706588 * q^73 + 3616878 * q^74 + 5846008 * q^76 + 5310564 * q^77 - 3946244 * q^79 + 10695888 * q^80 + 17563252 * q^82 - 19084128 * q^83 + 14012136 * q^85 + 23237832 * q^86 + 8043336 * q^88 + 16165212 * q^89 - 2414720 * q^91 + 38885256 * q^92 - 5720442 * q^94 - 3268452 * q^95 + 3066224 * q^97 - 60255006 * q^98

Character values

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

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	1.59276	+	2.75874i	0.140782	+	0.243841i	0.927791	−	0.373100i	$-0.121705\pi$
$2$	1.59276	+	2.75874i	0.140782	+	0.243841i	−0.787010	+	0.616941i	$0.788372\pi$
$3$		0			0
$3$		0			0
$4$	58.9262	−	102.063i	0.460361	−	0.797369i
$5$	−0.294487	−	0.510067i	−0.00105359	−	0.00182487i	0.865498	−	0.500912i	$-0.167002\pi$
$5$	−0.294487	−	0.510067i	−0.00105359	−	0.00182487i	−0.866552	+	0.499087i	$0.833669\pi$
$6$		0			0
$7$	31.8040	+	906.935i	0.0350460	+	0.999386i
$7$	31.8040	+	906.935i	0.0350460	+	0.999386i
$8$	783.169			0.540805
$9$		0			0
$10$	0.938097	−	1.62483i	0.000296652	−	0.000513817i
$11$	−599.771	+	1038.83i	−0.135866	+	0.235327i	−0.925928	−	0.377700i	$-0.876715\pi$
$11$	−599.771	+	1038.83i	−0.135866	+	0.235327i	0.790062	+	0.613027i	$0.210048\pi$
$12$		0			0
$13$	7651.01			0.965867			0.482933	−	0.875657i	$-0.339571\pi$
$13$	7651.01			0.965867			0.482933	+	0.875657i	$0.339571\pi$
$14$	−2451.35	+	1532.27i	−0.238757	+	0.149241i
$15$		0			0
$16$	−6295.16	−	10903.5i	−0.384226	−	0.665499i
$17$	17592.9	−	30471.9i	0.868495	−	1.50428i	0.00496047	−	0.999988i	$-0.498421\pi$
$17$	17592.9	−	30471.9i	0.868495	−	1.50428i	0.863535	−	0.504290i	$-0.168246\pi$
$18$		0			0
$19$	4286.72	+	7424.82i	0.143380	+	0.248341i	0.928767	−	0.370663i	$-0.120870\pi$
$19$	4286.72	+	7424.82i	0.143380	+	0.248341i	−0.785388	+	0.619004i	$0.787536\pi$
$20$	−69.4121			−0.00194013
$21$		0			0
$22$	−3821.17			−0.0765098
$23$	39366.9	+	68185.4i	0.674657	+	1.16854i	0.976569	+	0.215205i	$0.0690420\pi$
$23$	39366.9	+	68185.4i	0.674657	+	1.16854i	−0.301911	+	0.953336i	$0.597625\pi$
$24$		0			0
$25$	39062.3	−	67657.9i	0.499998	−	0.866022i
$26$	12186.2	+	21107.2i	0.135976	+	0.235518i
$27$		0			0
$28$	94438.8	+	50196.3i	0.813013	+	0.432134i
$29$	199760.			1.52095			0.760477	−	0.649365i	$-0.224965\pi$
$29$	199760.			1.52095			0.760477	+	0.649365i	$0.224965\pi$
$30$		0			0
$31$	−68557.2	+	118745.i	−0.413321	+	0.715893i	−0.995251	−	0.0973464i	$-0.968965\pi$
$31$	−68557.2	+	118745.i	−0.413321	+	0.715893i	0.581930	+	0.813239i	$0.302298\pi$
$32$	70176.2	−	121549.i	0.378586	−	0.655730i
$33$		0			0
$34$	112085.			0.489072
$35$	453.232	−	283.303i	0.00178683	−	0.00111690i
$36$		0			0
$37$	−45042.1	−	78015.3i	−0.146188	−	0.253206i	0.783627	−	0.621231i	$-0.213367\pi$
$37$	−45042.1	−	78015.3i	−0.146188	−	0.253206i	−0.929816	+	0.368025i	$0.880034\pi$
$38$	−13655.4	+	23651.9i	−0.0403704	+	0.0699236i
$39$		0			0
$40$	−230.633	−	399.469i	−0.000569786	−	0.000986899i
$41$	269601.			0.610911			0.305455	−	0.952206i	$-0.401191\pi$
$41$	269601.			0.610911			0.305455	+	0.952206i	$0.401191\pi$
$42$		0			0
$43$	602901.			1.15640			0.578198	−	0.815897i	$-0.303756\pi$
$43$	602901.			1.15640			0.578198	+	0.815897i	$0.303756\pi$
$44$	70684.5	+	122429.i	0.125095	+	0.216671i
$45$		0			0
$46$	−125404.	+	217206.i	−0.189959	+	0.329018i
$47$	−192458.	−	333347.i	−0.270391	−	0.468332i	0.698571	−	0.715541i	$-0.253820\pi$
$47$	−192458.	−	333347.i	−0.270391	−	0.468332i	−0.968962	+	0.247209i	$0.920486\pi$
$48$		0			0
$49$	−821520.	+	57688.3i	−0.997544	+	0.0700489i
$50$	248868.			0.281562
$51$		0			0
$52$	450845.	−	780887.i	0.444647	−	0.770152i
$53$	332119.	−	575247.i	0.306428	−	0.530748i	−0.671150	−	0.741321i	$-0.734200\pi$
$53$	332119.	−	575247.i	0.306428	−	0.530748i	0.977578	+	0.210573i	$0.0675329\pi$
$54$		0			0
$55$	706.501			0.000572589
$56$	24907.9	+	710283.i	0.0189530	+	0.540472i
$57$		0			0
$58$	318170.	+	551087.i	0.214122	+	0.370870i
$59$	−1.15394e6	+	1.99868e6i	−0.731478	+	1.26696i	0.224774	+	0.974411i	$0.427836\pi$
$59$	−1.15394e6	+	1.99868e6i	−0.731478	+	1.26696i	−0.956252	+	0.292546i	$0.905498\pi$
$60$		0			0
$61$	−449938.	−	779316.i	−0.253804	−	0.439601i	0.710766	−	0.703428i	$-0.248348\pi$
$61$	−449938.	−	779316.i	−0.253804	−	0.439601i	−0.964570	+	0.263827i	$0.915015\pi$
$62$	−436781.			−0.232752
$63$		0			0
$64$	−1.16446e6			−0.555260
$65$	−2253.13	−	3902.53i	−0.00101763	−	0.00176258i
$66$		0			0
$67$	−11879.4	+	20575.8i	−0.00482540	+	0.00835784i	−0.868428	−	0.495815i	$-0.834869\pi$
$67$	−11879.4	+	20575.8i	−0.00482540	+	0.00835784i	0.863603	+	0.504173i	$0.168203\pi$
$68$	−2.07337e6	−	3.59118e6i	−0.799643	−	1.38502i
$69$		0			0
$70$	1503.45	+	799.117i	0.000523898	+	0.000278463i
$71$	−2.52558e6			−0.837446			−0.418723	−	0.908114i	$-0.637522\pi$
$71$	−2.52558e6			−0.837446			−0.418723	+	0.908114i	$0.637522\pi$
$72$		0			0
$73$	−1.76425e6	+	3.05578e6i	−0.530800	+	0.919373i	0.468554	+	0.883435i	$0.344775\pi$
$73$	−1.76425e6	+	3.05578e6i	−0.530800	+	0.919373i	−0.999354	+	0.0359379i	$0.988558\pi$
$74$	143483.	−	248519.i	0.0411613	−	0.0712934i
$75$		0			0
$76$	1.01040e6			0.264026
$77$	−961231.	−	510915.i	−0.239944	−	0.127535i
$78$		0			0
$79$	−2.31891e6	−	4.01647e6i	−0.529162	−	0.916536i	−0.999422	−	0.0340079i	$-0.989173\pi$
$79$	−2.31891e6	−	4.01647e6i	−0.529162	−	0.916536i	0.470259	−	0.882528i	$-0.344160\pi$
$80$	−3707.69	+	6421.91i	−0.000809633	+	0.00140233i
$81$		0			0
$82$	429410.	+	743759.i	0.0860049	+	0.148965i
$83$	−7.71353e6			−1.48074			−0.740372	−	0.672197i	$-0.765351\pi$
$83$	−7.71353e6			−1.48074			−0.740372	+	0.672197i	$0.765351\pi$
$84$		0			0
$85$	−20723.6			−0.00366015
$86$	960277.	+	1.66325e6i	0.162799	+	0.281976i
$87$		0			0
$88$	−469722.	+	813583.i	−0.0734770	+	0.127266i
$89$	4.39050e6	+	7.60457e6i	0.660160	+	1.14343i	0.980573	+	0.196153i	$0.0628448\pi$
$89$	4.39050e6	+	7.60457e6i	0.660160	+	1.14343i	−0.320413	+	0.947278i	$0.603822\pi$
$90$		0			0
$91$	243332.	+	6.93897e6i	0.0338497	+	0.965273i
$92$	9.27896e6			1.24234
$93$		0			0
$94$	613079.	−	1.06188e6i	0.0761322	−	0.131865i
$95$	2524.77	−	4373.03i	0.000302127	−	0.000523299i
$96$		0			0
$97$	4.42347e6			0.492110			0.246055	−	0.969256i	$-0.420866\pi$
$97$	4.42347e6			0.492110			0.246055	+	0.969256i	$0.420866\pi$
$98$	−1.46763e6	−	2.17448e6i	−0.157517	−	0.233380i
$99$		0			0
$100$	−4.60359e6	−	7.97365e6i	−0.460359	−	0.797365i
$101$	2.93551e6	−	5.08446e6i	0.283504	−	0.491043i	−0.688741	−	0.725007i	$-0.741836\pi$
$101$	2.93551e6	−	5.08446e6i	0.283504	−	0.491043i	0.972245	+	0.233964i	$0.0751697\pi$
$102$		0			0
$103$	826811.	+	1.43208e6i	0.0745549	+	0.129133i	0.900893	−	0.434042i	$-0.142913\pi$
$103$	826811.	+	1.43208e6i	0.0745549	+	0.129133i	−0.826338	+	0.563175i	$0.809580\pi$
$104$	5.99203e6			0.522345
$105$		0			0
$106$	2.11594e6			0.172557
$107$	464692.	+	804869.i	0.0366709	+	0.0635159i	0.883778	−	0.467906i	$-0.154991\pi$
$107$	464692.	+	804869.i	0.0366709	+	0.0635159i	−0.847107	+	0.531422i	$0.821658\pi$
$108$		0			0
$109$	4.62545e6	−	8.01151e6i	0.342106	−	0.592545i	−0.642717	−	0.766103i	$-0.722193\pi$
$109$	4.62545e6	−	8.01151e6i	0.342106	−	0.592545i	0.984824	+	0.173558i	$0.0555264\pi$
$110$	1125.29	+	1949.05i	8.06100e−5	+	0.000139621i
$111$		0			0
$112$	9.68858e6	−	6.05607e6i	0.651624	−	0.407313i
$113$	−1.16423e7			−0.759039			−0.379519	−	0.925184i	$-0.623911\pi$
$113$	−1.16423e7			−0.759039			−0.379519	+	0.925184i	$0.623911\pi$
$114$		0			0
$115$	23186.1	−	40159.5i	0.00142163	−	0.00246233i
$116$	1.17711e7	−	2.03882e7i	0.700188	−	1.21276i
$117$		0			0
$118$	−7.35180e6			−0.411914
$119$	2.81955e7	+	1.49865e7i	1.53379	+	0.815243i
$120$		0			0
$121$	9.02413e6	+	1.56303e7i	0.463081	+	0.802079i
$122$	1.43329e6	−	2.48253e6i	0.0714618	−	0.123776i
$123$		0			0
$124$	8.07964e6	+	1.39943e7i	0.380554	+	0.659138i
$125$	−92027.1			−0.00421435
$126$		0			0
$127$	437184.			0.0189387			0.00946937	−	0.999955i	$-0.496986\pi$
$127$	437184.			0.0189387			0.00946937	+	0.999955i	$0.496986\pi$
$128$	−1.08373e7	−	1.87707e7i	−0.456756	−	0.791125i
$129$		0			0
$130$	7177.39	−	12431.6i	0.000286526	−	0.000496278i
$131$	1.45701e7	+	2.52361e7i	0.566255	+	0.980782i	0.996932	+	0.0782760i	$0.0249415\pi$
$131$	1.45701e7	+	2.52361e7i	0.566255	+	0.980782i	−0.430677	+	0.902506i	$0.641725\pi$
$132$		0			0
$133$	−6.59749e6	+	4.12392e6i	−0.243163	+	0.151995i
$134$	−75684.4			−0.00271731
$135$		0			0
$136$	1.37782e7	−	2.38646e7i	0.469686	−	0.813520i
$137$	−1.06024e7	+	1.83639e7i	−0.352275	+	0.610159i	−0.986648	−	0.162869i	$-0.947925\pi$
$137$	−1.06024e7	+	1.83639e7i	−0.352275	+	0.610159i	0.634372	+	0.773028i	$0.281259\pi$
$138$		0			0
$139$	−1.42359e7			−0.449608			−0.224804	−	0.974404i	$-0.572174\pi$
$139$	−1.42359e7			−0.449608			−0.224804	+	0.974404i	$0.572174\pi$
$140$	−2207.58	−	62952.3i	−6.79937e−5	−	0.00193894i
$141$		0			0
$142$	−4.02265e6	−	6.96743e6i	−0.117897	−	0.204204i
$143$	−4.58886e6	+	7.94813e6i	−0.131229	+	0.227295i
$144$		0			0
$145$	−58826.9	−	101891.i	−0.00160246	−	0.00277555i
$146$	−1.12401e7			−0.298907
$147$		0			0
$148$	−1.06167e7			−0.269198
$149$	−1.78193e7	−	3.08640e7i	−0.441306	−	0.764364i	0.556481	−	0.830860i	$-0.312151\pi$
$149$	−1.78193e7	−	3.08640e7i	−0.441306	−	0.764364i	−0.997787	+	0.0664967i	$0.978818\pi$
$150$		0			0
$151$	−6.50467e6	+	1.12664e7i	−0.153747	+	0.266297i	−0.932602	−	0.360907i	$-0.882467\pi$
$151$	−6.50467e6	+	1.12664e7i	−0.153747	+	0.266297i	0.778855	+	0.627204i	$0.215801\pi$
$152$	3.35723e6	+	5.81488e6i	0.0775404	+	0.134304i
$153$		0			0
$154$	−121528.	−	3.46555e6i	−0.00268136	−	0.0764628i
$155$	80757.0			0.00174188
$156$		0			0
$157$	−3.30862e7	+	5.73070e7i	−0.682337	+	1.18184i	0.291929	+	0.956440i	$0.405703\pi$
$157$	−3.30862e7	+	5.73070e7i	−0.682337	+	1.18184i	−0.974266	+	0.225402i	$0.927631\pi$
$158$	7.38694e6	−	1.27946e7i	0.148993	−	0.258063i
$159$		0			0
$160$	−82664.0			−0.00159550
$161$	−6.05877e7	+	3.78718e7i	−1.14418	+	0.715196i
$162$		0			0
$163$	−2.77170e7	−	4.80073e7i	−0.501292	−	0.868262i	−0.999999	−	0.00149200i	$-0.999525\pi$
$163$	−2.77170e7	−	4.80073e7i	−0.501292	−	0.868262i	0.498707	−	0.866770i	$-0.333808\pi$
$164$	1.58866e7	−	2.75163e7i	0.281239	−	0.487121i
$165$		0			0
$166$	−1.22858e7	−	2.12797e7i	−0.208461	−	0.361066i
$167$	−1.10649e8			−1.83840			−0.919201	−	0.393788i	$-0.871164\pi$
$167$	−1.10649e8			−1.83840			−0.919201	+	0.393788i	$0.871164\pi$
$168$		0			0
$169$	−4.21054e6			−0.0671019
$170$	−33007.8	−	57171.1i	−0.000515282	−	0.000892494i
$171$		0			0
$172$	3.55267e7	−	6.15340e7i	0.532359	−	0.922074i
$173$	9.07141e6	+	1.57121e7i	0.133203	+	0.230714i	0.924909	−	0.380187i	$-0.124141\pi$
$173$	9.07141e6	+	1.57121e7i	0.133203	+	0.230714i	−0.791707	+	0.610901i	$0.790807\pi$
$174$		0			0
$175$	6.26037e7	+	3.32752e7i	0.883012	+	0.469340i
$176$	1.51026e7			0.208813
$177$		0			0
$178$	−1.39860e7	+	2.42245e7i	−0.185877	+	0.321948i
$179$	2.85557e7	−	4.94599e7i	0.372141	−	0.644567i	−0.617754	−	0.786372i	$-0.711957\pi$
$179$	2.85557e7	−	4.94599e7i	0.372141	−	0.644567i	0.989895	+	0.141805i	$0.0452905\pi$
$180$		0			0
$181$	−9.95371e7			−1.24770			−0.623850	−	0.781544i	$-0.714432\pi$
$181$	−9.95371e7			−1.24770			−0.623850	+	0.781544i	$0.714432\pi$
$182$	−1.87553e7	+	1.17234e7i	−0.230608	+	0.144147i
$183$		0			0
$184$	3.08309e7	+	5.34007e7i	0.364858	+	0.631952i
$185$	−26528.7	+	45949.1i	−0.000308046	+	0.000533550i
$186$		0			0
$187$	2.11035e7	+	3.65523e7i	0.235998	+	0.408761i
$188$	−4.53632e7			−0.497911
$189$		0			0
$190$	16085.4			0.000170136
$191$	−2.30643e6	−	3.99486e6i	−0.0239510	−	0.0414844i	0.853801	−	0.520599i	$-0.174291\pi$
$191$	−2.30643e6	−	3.99486e6i	−0.0239510	−	0.0414844i	−0.877752	+	0.479114i	$0.840958\pi$
$192$		0			0
$193$	3.93262e7	−	6.81151e7i	0.393760	−	0.682013i	−0.599182	−	0.800613i	$-0.704507\pi$
$193$	3.93262e7	−	6.81151e7i	0.393760	−	0.682013i	0.992942	+	0.118600i	$0.0378407\pi$
$194$	7.04554e6	+	1.22032e7i	0.0692800	+	0.119997i
$195$		0			0
$196$	−4.25212e7	+	8.72463e7i	−0.403375	+	0.827658i
$197$	1.37253e8			1.27906			0.639531	−	0.768765i	$-0.279129\pi$
$197$	1.37253e8			1.27906			0.639531	+	0.768765i	$0.279129\pi$
$198$		0			0
$199$	4.46296e7	−	7.73007e7i	0.401455	−	0.695341i	−0.592447	−	0.805610i	$-0.701838\pi$
$199$	4.46296e7	−	7.73007e7i	0.401455	−	0.695341i	0.993902	+	0.110269i	$0.0351712\pi$
$200$	3.05924e7	−	5.29876e7i	0.270401	−	0.468348i
$201$		0			0
$202$	1.87023e7			0.159649
$203$	6.35316e6	+	1.81170e8i	0.0533033	+	1.52002i
$204$		0			0
$205$	−79394.1	−	137515.i	−0.000643650	−	0.00111483i
$206$	−2.63383e6	+	4.56192e6i	−0.0209919	+	0.0363590i
$207$		0			0
$208$	−4.81643e7	−	8.34230e7i	−0.371111	−	0.642783i
$209$	−1.02842e7			−0.0779218
$210$		0			0
$211$	1.16809e8			0.856031			0.428016	−	0.903771i	$-0.359213\pi$
$211$	1.16809e8			0.856031			0.428016	+	0.903771i	$0.359213\pi$
$212$	−3.91410e7	−	6.77942e7i	−0.282135	−	0.488672i
$213$		0			0
$214$	−1.48029e6	+	2.56393e6i	−0.0103252	+	0.0178837i
$215$	−177547.	−	307520.i	−0.00121837	−	0.00211027i
$216$		0			0
$217$	−1.09874e8	−	5.84004e7i	−0.729938	−	0.387978i
$218$	2.94689e7			0.192649
$219$		0			0
$220$	41631.4	−	72107.7i	0.000263598	−	0.000456565i
$221$	1.34604e8	−	2.33141e8i	0.838850	−	1.45293i
$222$		0			0
$223$	−8.22050e7			−0.496399			−0.248200	−	0.968709i	$-0.579839\pi$
$223$	−8.22050e7			−0.496399			−0.248200	+	0.968709i	$0.579839\pi$
$224$	1.12469e8	+	5.97795e7i	0.668595	+	0.355373i
$225$		0			0
$226$	−1.85434e7	−	3.21181e7i	−0.106859	−	0.185085i
$227$	1.05432e7	−	1.82613e7i	0.0598247	−	0.103619i	−0.834562	−	0.550914i	$-0.814279\pi$
$227$	1.05432e7	−	1.82613e7i	0.0598247	−	0.103619i	0.894387	+	0.447295i	$0.147612\pi$
$228$		0			0
$229$	1.73315e8	+	3.00190e8i	0.953698	+	1.65185i	0.737319	+	0.675544i	$0.236091\pi$
$229$	1.73315e8	+	3.00190e8i	0.953698	+	1.65185i	0.216379	+	0.976309i	$0.430575\pi$
$230$	147720.			0.000800554
$231$		0			0
$232$	1.56446e8			0.822538
$233$	−1.66368e7	−	2.88158e7i	−0.0861638	−	0.149240i	0.819723	−	0.572761i	$-0.194127\pi$
$233$	−1.66368e7	−	2.88158e7i	−0.0861638	−	0.149240i	−0.905887	+	0.423520i	$0.860794\pi$
$234$		0			0
$235$	−113353.	+	196333.i	−0.000569764	+	0.000986859i
$236$	1.35995e8	+	2.35550e8i	0.673488	+	1.16652i
$237$		0			0
$238$	3.56476e6	+	1.01654e8i	0.0171400	+	0.488772i
$239$	1.74413e8			0.826394			0.413197	−	0.910642i	$-0.364412\pi$
$239$	1.74413e8			0.826394			0.413197	+	0.910642i	$0.364412\pi$
$240$		0			0
$241$	1.42610e8	−	2.47007e8i	0.656280	−	1.13671i	−0.325291	−	0.945614i	$-0.605462\pi$
$241$	1.42610e8	−	2.47007e8i	0.656280	−	1.13671i	0.981571	−	0.191096i	$-0.0612043\pi$
$242$	−2.87466e7	+	4.97905e7i	−0.130386	+	0.225836i
$243$		0			0
$244$	−1.06053e8			−0.467366
$245$	271352.	+	402042.i	0.00117883	+	0.00174659i
$246$		0			0
$247$	3.27977e7	+	5.68074e7i	0.138486	+	0.239864i
$248$	−5.36919e7	+	9.29970e7i	−0.223526	+	0.387158i
$249$		0			0
$250$	−146577.	−	253879.i	−0.000593303	−	0.00102763i
$251$	−3.46951e8			−1.38487			−0.692437	−	0.721478i	$-0.743463\pi$
$251$	−3.46951e8			−1.38487			−0.692437	+	0.721478i	$0.743463\pi$
$252$		0			0
$253$	−9.44445e7			−0.366652
$254$	696330.	+	1.20608e6i	0.00266623	+	0.00461804i
$255$		0			0
$256$	−4.00034e7	+	6.92879e7i	−0.149024	+	0.258117i
$257$	1.98591e7	+	3.43971e7i	0.0729785	+	0.126402i	0.900205	−	0.435466i	$-0.143416\pi$
$257$	1.98591e7	+	3.43971e7i	0.0729785	+	0.126402i	−0.827227	+	0.561868i	$0.810083\pi$
$258$		0			0
$259$	6.93223e7	−	4.33315e7i	0.247927	−	0.154972i
$260$	−531073.			−0.00187390
$261$		0			0
$262$	−4.64133e7	+	8.03902e7i	−0.159436	+	0.276152i
$263$	1.98988e8	−	3.44657e8i	0.674499	−	1.16827i	−0.302116	−	0.953271i	$-0.597693\pi$
$263$	1.98988e8	−	3.44657e8i	0.674499	−	1.16827i	0.976615	−	0.214996i	$-0.0689738\pi$
$264$		0			0
$265$	−391219.			−0.00129140
$266$	−2.18851e7	−	1.16324e7i	−0.0712955	−	0.0378951i
$267$		0			0
$268$	1.40002e6	+	2.42490e6i	0.00444286	+	0.00769525i
$269$	1.97301e8	−	3.41735e8i	0.618011	−	1.07043i	−0.371837	−	0.928298i	$-0.621272\pi$
$269$	1.97301e8	−	3.41735e8i	0.618011	−	1.07043i	0.989848	−	0.142129i	$-0.0453947\pi$
$270$		0			0
$271$	−1.61539e8	−	2.79794e8i	−0.493043	−	0.853975i	0.506925	−	0.861990i	$-0.330782\pi$
$271$	−1.61539e8	−	2.79794e8i	−0.493043	−	0.853975i	−0.999968	+	0.00801501i	$0.997449\pi$
$272$	−4.43001e8			−1.33479
$273$		0			0
$274$	−6.75484e7			−0.198375
$275$	4.68569e7	+	8.11586e7i	0.135866	+	0.235326i
$276$		0			0
$277$	7.84594e7	−	1.35896e8i	0.221802	−	0.384173i	−0.733553	−	0.679632i	$-0.762139\pi$
$277$	7.84594e7	−	1.35896e8i	0.221802	−	0.384173i	0.955355	+	0.295460i	$0.0954728\pi$
$278$	−2.26744e7	−	3.92733e7i	−0.0632965	−	0.109633i
$279$		0			0
$280$	354957.	−	221874.i	0.000966324	−	0.000604023i
$281$	−4.96958e8			−1.33613			−0.668063	−	0.744105i	$-0.732876\pi$
$281$	−4.96958e8			−1.33613			−0.668063	+	0.744105i	$0.732876\pi$
$282$		0			0
$283$	−1.41773e8	+	2.45558e8i	−0.371828	+	0.644025i	−0.989847	−	0.142139i	$-0.954602\pi$
$283$	−1.41773e8	+	2.45558e8i	−0.371828	+	0.644025i	0.618019	+	0.786163i	$0.287935\pi$
$284$	−1.48823e8	+	2.57769e8i	−0.385528	+	0.667753i
$285$		0			0
$286$	−2.92358e7			−0.0738983
$287$	8.57437e6	+	2.44510e8i	0.0214100	+	0.610535i
$288$		0			0
$289$	−4.13854e8	−	7.16816e8i	−1.00857	−	1.74689i
$290$	187394.	−	324576.i	0.000451194	−	0.000781491i
$291$		0			0
$292$	2.07922e8	+	3.60131e8i	0.488719	+	0.846487i
$293$	−3.75616e8			−0.872384			−0.436192	−	0.899854i	$-0.643673\pi$
$293$	−3.75616e8			−0.872384			−0.436192	+	0.899854i	$0.643673\pi$
$294$		0			0
$295$	1.35928e6			0.00308271
$296$	−3.52756e7	−	6.10991e7i	−0.0790594	−	0.136935i
$297$		0			0
$298$	5.67639e7	−	9.83179e7i	0.124255	−	0.215217i
$299$	3.01196e8	+	5.21687e8i	0.651629	+	1.12865i
$300$		0			0
$301$	1.91746e7	+	5.46792e8i	0.0405270	+	1.15568i
$302$	−4.14415e7			−0.0865788
$303$		0			0
$304$	5.39711e7	−	9.34808e7i	0.110180	−	0.190838i
$305$	−265002.	+	458997.i	−0.000534811	+	0.000926319i
$306$		0			0
$307$	−2.34442e8			−0.462435			−0.231217	−	0.972902i	$-0.574271\pi$
$307$	−2.34442e8			−0.462435			−0.231217	+	0.972902i	$0.574271\pi$
$308$	−1.08787e8	+	6.80000e7i	−0.212154	+	0.132612i
$309$		0			0
$310$	128627.	+	222788.i	0.000245225	+	0.000424742i
$311$	2.31126e8	−	4.00322e8i	0.435700	−	0.754655i	−0.561652	−	0.827373i	$-0.689834\pi$
$311$	2.31126e8	−	4.00322e8i	0.435700	−	0.754655i	0.997353	+	0.0727184i	$0.0231674\pi$
$312$		0			0
$313$	2.38609e8	+	4.13283e8i	0.439827	+	0.761803i	0.997676	−	0.0681396i	$-0.0217063\pi$
$313$	2.38609e8	+	4.13283e8i	0.439827	+	0.761803i	−0.557848	+	0.829943i	$0.688373\pi$
$314$	−2.10794e8			−0.384242
$315$		0			0
$316$	−5.46578e8			−0.974423
$317$	−2.52154e8	−	4.36743e8i	−0.444588	−	0.770050i	0.553435	−	0.832892i	$-0.313317\pi$
$317$	−2.52154e8	−	4.36743e8i	−0.444588	−	0.770050i	−0.998023	+	0.0628427i	$0.979983\pi$
$318$		0			0
$319$	−1.19810e8	+	2.07518e8i	−0.206646	+	0.357922i
$320$	342920.	+	593955.i	0.000585016	+	0.00101328i
$321$		0			0
$322$	−2.00980e8	−	1.06825e8i	−0.335473	−	0.178311i
$323$	3.01664e8			0.498098
$324$		0			0
$325$	2.98866e8	−	5.17652e8i	0.482931	−	0.836461i
$326$	8.82933e7	−	1.52928e8i	0.141145	−	0.244471i
$327$		0			0
$328$	2.11143e8			0.330383
$329$	2.96203e8	−	1.85148e8i	0.458568	−	0.286638i
$330$		0			0
$331$	4.89244e8	+	8.47396e8i	0.741528	+	1.28436i	0.951799	+	0.306721i	$0.0992320\pi$
$331$	4.89244e8	+	8.47396e8i	0.741528	+	1.28436i	−0.210271	+	0.977643i	$0.567435\pi$
$332$	−4.54529e8	+	7.87268e8i	−0.681677	+	1.18070i
$333$		0			0
$334$	−1.76238e8	−	3.05253e8i	−0.258813	−	0.448278i
$335$	13993.4			2.03360e−5
$336$		0			0
$337$	8.99273e8			1.27993			0.639966	−	0.768403i	$-0.278948\pi$
$337$	8.99273e8			1.27993			0.639966	+	0.768403i	$0.278948\pi$
$338$	−6.70639e6	−	1.16158e7i	−0.00944671	−	0.0163622i
$339$		0			0
$340$	−1.22116e6	+	2.11512e6i	−0.00168499	+	0.00291849i
$341$	−8.22373e7	−	1.42439e8i	−0.112313	−	0.194531i
$342$		0			0
$343$	−7.84471e7	−	7.43231e8i	−0.104966	−	0.994476i
$344$	4.72173e8			0.625384
$345$		0			0
$346$	−2.88972e7	+	5.00514e7i	−0.0375050	+	0.0649605i
$347$	1.19589e8	−	2.07135e8i	0.153652	−	0.266134i	−0.778915	−	0.627129i	$-0.784230\pi$
$347$	1.19589e8	−	2.07135e8i	0.153652	−	0.266134i	0.932568	+	0.360996i	$0.117563\pi$
$348$		0			0
$349$	−9.79547e8			−1.23349			−0.616746	−	0.787162i	$-0.711549\pi$
$349$	−9.79547e8			−1.23349			−0.616746	+	0.787162i	$0.711549\pi$
$350$	7.91498e6	+	2.25707e8i	0.00986761	+	0.281389i
$351$		0			0
$352$	8.41793e7	+	1.45803e8i	0.102874	+	0.178183i
$353$	7.20543e6	−	1.24802e7i	0.00871864	−	0.0151011i	−0.861633	−	0.507532i	$-0.830558\pi$
$353$	7.20543e6	−	1.24802e7i	0.00871864	−	0.0151011i	0.870352	+	0.492430i	$0.163891\pi$
$354$		0			0
$355$	743752.	+	1.28822e6i	0.000882325	+	0.00152823i
$356$	1.03486e9			1.21565
$357$		0			0
$358$	1.81930e8			0.209562
$359$	−5.55424e6	−	9.62023e6i	−0.00633569	−	0.0109737i	0.862840	−	0.505477i	$-0.168683\pi$
$359$	−5.55424e6	−	9.62023e6i	−0.00633569	−	0.0109737i	−0.869176	+	0.494503i	$0.835350\pi$
$360$		0			0
$361$	4.10184e8	−	7.10459e8i	0.458885	−	0.794811i
$362$	−1.58539e8	−	2.74597e8i	−0.175653	−	0.304240i
$363$		0			0
$364$	7.22552e8	+	3.84052e8i	0.785262	+	0.417384i
$365$	2.07820e6			0.00223698
$366$		0			0
$367$	−3.07437e8	+	5.32497e8i	−0.324658	+	0.562324i	−0.981443	−	0.191754i	$-0.938582\pi$
$367$	−3.07437e8	+	5.32497e8i	−0.324658	+	0.562324i	0.656785	+	0.754078i	$0.271916\pi$
$368$	4.95641e8	−	8.58475e8i	0.518442	−	0.897967i
$369$		0			0
$370$	−169016.			−0.000173469
$371$	5.32274e8	+	2.82915e8i	0.541161	+	0.287639i
$372$		0			0
$373$	−2.01411e8	−	3.48854e8i	−0.200957	−	0.348067i	0.747880	−	0.663834i	$-0.231072\pi$
$373$	−2.01411e8	−	3.48854e8i	−0.200957	−	0.348067i	−0.948837	+	0.315766i	$0.897738\pi$
$374$	−6.72256e7	+	1.16438e8i	−0.0664484	+	0.115092i
$375$		0			0
$376$	−1.50727e8	−	2.61067e8i	−0.146229	−	0.253276i
$377$	1.52837e9			1.46904
$378$		0			0
$379$	5.93933e7			0.0560403			0.0280201	−	0.999607i	$-0.491080\pi$
$379$	5.93933e7			0.0560403			0.0280201	+	0.999607i	$0.491080\pi$
$380$	−297550.	−	515372.i	−0.000278175	−	0.000481813i
$381$		0			0
$382$	7.34720e6	−	1.27257e7i	0.00674373	−	0.0116805i
$383$	1.80200e8	+	3.12116e8i	0.163893	+	0.283871i	0.936262	−	0.351304i	$-0.114262\pi$
$383$	1.80200e8	+	3.12116e8i	0.163893	+	0.283871i	−0.772369	+	0.635175i	$0.780928\pi$
$384$		0			0
$385$	22469.5	+	640750.i	2.00669e−5	+	0.000572237i
$386$	2.50549e8			0.221737
$387$		0			0
$388$	2.60658e8	−	4.51474e8i	0.226548	−	0.392393i
$389$	−8.50960e8	+	1.47391e9i	−0.732969	+	1.26954i	0.222640	+	0.974901i	$0.428532\pi$
$389$	−8.50960e8	+	1.47391e9i	−0.732969	+	1.26954i	−0.955609	+	0.294638i	$0.904801\pi$
$390$		0			0
$391$	2.77032e9			2.34375
$392$	−6.43389e8	+	4.51796e7i	−0.539476	+	0.0378828i
$393$		0			0
$394$	2.18612e8	+	3.78647e8i	0.180068	+	0.311887i
$395$	−1.36578e6	+	2.36560e6i	−0.00111504	+	0.00193131i
$396$		0			0
$397$	−6.50134e8	−	1.12606e9i	−0.521478	−	0.903226i	−0.999688	−	0.0249808i	$-0.992048\pi$
$397$	−6.50134e8	−	1.12606e9i	−0.521478	−	0.903226i	0.478210	−	0.878246i	$-0.341286\pi$
$398$	2.84337e8			0.226070
$399$		0			0
$400$	−9.83614e8			−0.768448
$401$	3.36277e8	+	5.82449e8i	0.260431	+	0.451079i	0.966356	−	0.257207i	$-0.0828021\pi$
$401$	3.36277e8	+	5.82449e8i	0.260431	+	0.451079i	−0.705926	+	0.708286i	$0.749469\pi$
$402$		0			0
$403$	−5.24532e8	+	9.08516e8i	−0.399213	+	0.691457i
$404$	−3.45957e8	−	5.99216e8i	−0.261028	−	0.452115i
$405$		0			0
$406$	−4.89681e8	+	3.06087e8i	−0.363139	+	0.226988i
$407$	1.08060e8			0.0794483
$408$		0			0
$409$	−1.14685e9	+	1.98640e9i	−0.828846	+	1.43560i	0.0700984	+	0.997540i	$0.477669\pi$
$409$	−1.14685e9	+	1.98640e9i	−0.828846	+	1.43560i	−0.898944	+	0.438063i	$0.855665\pi$
$410$	252912.	−	438056.i	0.000181228	−	0.000313896i
$411$		0			0
$412$	1.94883e8			0.137289
$413$	−1.84938e9	−	9.82983e8i	−1.29181	−	0.686627i
$414$		0			0
$415$	2.27154e6	+	3.93442e6i	0.00156010	+	0.00270217i
$416$	5.36919e8	−	9.29970e8i	0.365664	−	0.633348i
$417$		0			0
$418$	−1.63803e7	−	2.83715e7i	−0.0109700	−	0.0190005i
$419$	−8.65006e8			−0.574473			−0.287237	−	0.957860i	$-0.592737\pi$
$419$	−8.65006e8			−0.574473			−0.287237	+	0.957860i	$0.592737\pi$
$420$		0			0
$421$	−3.17458e8			−0.207347			−0.103674	−	0.994611i	$-0.533060\pi$
$421$	−3.17458e8			−0.207347			−0.103674	+	0.994611i	$0.533060\pi$
$422$	1.86050e8	+	3.22247e8i	0.120513	+	0.208735i
$423$		0			0
$424$	2.60105e8	−	4.50515e8i	0.165717	−	0.287031i
$425$	−1.37444e9	−	2.38060e9i	−0.868491	−	1.50427i
$426$		0			0
$427$	6.92479e8	−	4.32850e8i	0.430436	−	0.269054i
$428$	1.09530e8			0.0675274
$429$		0			0
$430$	565579.	−	979612.i	0.000343047	−	0.000594175i
$431$	−6.69176e8	+	1.15905e9i	−0.402596	+	0.697318i	−0.994038	−	0.109030i	$-0.965226\pi$
$431$	−6.69176e8	+	1.15905e9i	−0.402596	+	0.697318i	0.591442	+	0.806348i	$0.298559\pi$
$432$		0			0
$433$	−1.76343e9			−1.04388			−0.521939	−	0.852983i	$-0.674791\pi$
$433$	−1.76343e9			−1.04388			−0.521939	+	0.852983i	$0.674791\pi$
$434$	−1.38914e7	−	3.96132e8i	−0.00815701	−	0.232609i
$435$		0			0
$436$	−5.45120e8	−	9.44176e8i	−0.314985	−	0.545570i
$437$	−3.37509e8	+	5.84583e8i	−0.193464	+	0.335090i
$438$		0			0
$439$	1.45826e8	+	2.52578e8i	0.0822640	+	0.142485i	0.904222	−	0.427063i	$-0.140452\pi$
$439$	1.45826e8	+	2.52578e8i	0.0822640	+	0.142485i	−0.821958	+	0.569548i	$0.807118\pi$
$440$	553309.			0.000309659
$441$		0			0
$442$	8.57567e8			0.472379
$443$	8.44711e8	+	1.46308e9i	0.461631	+	0.799569i	0.999042	−	0.0437514i	$-0.0139310\pi$
$443$	8.44711e8	+	1.46308e9i	0.461631	+	0.799569i	−0.537411	+	0.843320i	$0.680598\pi$
$444$		0			0
$445$	2.58590e6	−	4.47890e6i	0.00139108	−	0.00240941i
$446$	−1.30933e8	−	2.26782e8i	−0.0698838	−	0.121042i
$447$		0			0
$448$	−3.70346e7	−	1.05609e9i	−0.0194596	−	0.554919i
$449$	−2.63133e9			−1.37187			−0.685936	−	0.727662i	$-0.740607\pi$
$449$	−2.63133e9			−1.37187			−0.685936	+	0.727662i	$0.740607\pi$
$450$		0			0
$451$	−1.61699e8	+	2.80071e8i	−0.0830021	+	0.143764i
$452$	−6.86036e8	+	1.18825e9i	−0.349432	+	0.605234i
$453$		0			0
$454$	6.71710e7			0.0336889
$455$	3.46768e6	−	2.16756e6i	0.00172584	−	0.00107877i
$456$		0			0
$457$	3.04790e8	+	5.27911e8i	0.149380	+	0.258734i	0.930999	−	0.365023i	$-0.118939\pi$
$457$	3.04790e8	+	5.27911e8i	0.149380	+	0.258734i	−0.781618	+	0.623757i	$0.785605\pi$
$458$	−5.52098e8	+	9.56261e8i	−0.268526	+	0.465101i
$459$		0			0
$460$	−2.73254e6	−	4.73289e6i	−0.00130892	−	0.00226712i
$461$	1.07374e9			0.510440			0.255220	−	0.966883i	$-0.417852\pi$
$461$	1.07374e9			0.510440			0.255220	+	0.966883i	$0.417852\pi$
$462$		0			0
$463$	−3.10301e9			−1.45295			−0.726474	−	0.687194i	$-0.758842\pi$
$463$	−3.10301e9			−1.45295			−0.726474	+	0.687194i	$0.758842\pi$
$464$	−1.25752e9	−	2.17809e9i	−0.584389	−	1.01219i
$465$		0			0
$466$	5.29970e7	−	9.17935e7i	0.0242605	−	0.0420205i
$467$	1.06496e9	+	1.84456e9i	0.483864	+	0.838077i	0.999828	−	0.0185329i	$-0.00589956\pi$
$467$	1.06496e9	+	1.84456e9i	0.483864	+	0.838077i	−0.515964	+	0.856610i	$0.672566\pi$
$468$		0			0
$469$	−1.90387e7	−	1.01195e7i	−0.00852182	−	0.00452953i
$470$	−722176.			−0.000320849
$471$		0			0
$472$	−9.03729e8	+	1.56531e9i	−0.395586	+	0.685176i
$473$	−3.61603e8	+	6.26314e8i	−0.157115	+	0.272131i
$474$		0			0
$475$	6.69797e8			0.286758
$476$	3.19103e9	−	1.99463e9i	1.35615	−	0.847691i
$477$		0			0
$478$	2.77799e8	+	4.81162e8i	0.116341	+	0.201509i
$479$	−1.28729e9	+	2.22965e9i	−0.535183	+	0.926964i	0.463972	+	0.885850i	$0.346424\pi$
$479$	−1.28729e9	+	2.22965e9i	−0.535183	+	0.926964i	−0.999154	+	0.0411137i	$0.986909\pi$
$480$		0			0
$481$	−3.44618e8	−	5.96896e8i	−0.141199	−	0.244563i
$482$	9.08572e8			0.369568
$483$		0			0
$484$	2.12703e9			0.852738
$485$	−1.30266e6	−	2.25627e6i	−0.000518482	−	0.000898038i
$486$		0			0
$487$	−1.70510e9	+	2.95332e9i	−0.668958	+	1.15867i	0.309238	+	0.950985i	$0.399926\pi$
$487$	−1.70510e9	+	2.95332e9i	−0.668958	+	1.15867i	−0.978196	+	0.207684i	$0.933407\pi$
$488$	−3.52377e8	−	6.10335e8i	−0.137258	−	0.237738i
$489$		0			0
$490$	−676931.	+	1.38895e6i	−0.000259931	+	0.000533335i
$491$	−1.34263e9			−0.511884			−0.255942	−	0.966692i	$-0.582386\pi$
$491$	−1.34263e9			−0.511884			−0.255942	+	0.966692i	$0.582386\pi$
$492$		0			0
$493$	3.51437e9	−	6.08707e9i	1.32094	−	2.28794i
$494$	−1.04478e8	+	1.80961e8i	−0.0389924	+	0.0675369i
$495$		0			0
$496$	1.72631e9			0.635234
$497$	−8.03235e7	−	2.29054e9i	−0.0293491	−	0.836932i
$498$		0			0
$499$	2.15852e7	+	3.73867e7i	0.00777686	+	0.0134699i	0.869888	−	0.493250i	$-0.164191\pi$
$499$	2.15852e7	+	3.73867e7i	0.00777686	+	0.0134699i	−0.862111	+	0.506720i	$0.830858\pi$
$500$	−5.42281e6	+	9.39258e6i	−0.00194012	+	0.00336039i
$501$		0			0
$502$	−5.52610e8	−	9.57149e8i	−0.194965	−	0.337689i
$503$	3.15009e9			1.10366			0.551829	−	0.833957i	$-0.313930\pi$
$503$	3.15009e9			1.10366			0.551829	+	0.833957i	$0.313930\pi$
$504$		0			0
$505$	−3.45789e6			−0.00119479
$506$	−1.50427e8	−	2.60548e8i	−0.0516179	−	0.0894048i
$507$		0			0
$508$	2.57616e7	−	4.46204e7i	0.00871866	−	0.0151012i
$509$	−1.14847e9	−	1.98921e9i	−0.386019	−	0.668604i	0.605891	−	0.795547i	$-0.292817\pi$
$509$	−1.14847e9	−	1.98921e9i	−0.386019	−	0.668604i	−0.991910	+	0.126944i	$0.959483\pi$
$510$		0			0
$511$	−2.82750e9	−	1.50288e9i	−0.937410	−	0.498254i
$512$	−3.02920e9			−0.997432
$513$		0			0
$514$	−6.32618e7	+	1.09573e8i	−0.0205480	+	0.0355903i
$515$	486971.	−	843458.i	0.000157101	−	0.000272106i
$516$		0			0
$517$	4.61723e8			0.146948
$518$	2.29954e8	+	1.22226e8i	0.0726922	+	0.0386374i
$519$		0			0
$520$	−1.76458e6	−	3.05634e6i	−0.000550338	−	0.000953213i
$521$	1.96651e9	−	3.40610e9i	0.609207	−	1.05518i	−0.382164	−	0.924095i	$-0.624821\pi$
$521$	1.96651e9	−	3.40610e9i	0.609207	−	1.05518i	0.991371	−	0.131083i	$-0.0418456\pi$
$522$		0			0
$523$	2.95988e9	+	5.12666e9i	0.904729	+	1.56704i	0.821281	+	0.570524i	$0.193260\pi$
$523$	2.95988e9	+	5.12666e9i	0.904729	+	1.56704i	0.0834478	+	0.996512i	$0.473407\pi$
$524$	3.43424e9			1.04273
$525$		0			0
$526$	1.26776e9			0.379828
$527$	2.41225e9	+	4.17813e9i	0.717934	+	1.24350i
$528$		0			0
$529$	−1.39709e9	+	2.41982e9i	−0.410325	+	0.710704i
$530$	−623119.	−	1.07927e6i	−0.000181805	−	0.000314895i
$531$		0			0
$532$	3.21348e7	+	9.16368e8i	0.00925304	+	0.263864i
$533$	2.06272e9			0.590058
$534$		0			0
$535$	273692.	−	474048.i	7.72722e−5	−	0.000133839i
$536$	−9.30359e6	+	1.61143e7i	−0.00260960	+	0.00451996i
$537$		0			0
$538$	1.25701e9			0.348018
$539$	4.32796e8	−	8.88023e8i	0.119048	−	0.244266i
$540$		0			0
$541$	1.03313e9	+	1.78943e9i	0.280520	+	0.485876i	0.971513	−	0.236986i	$-0.0761596\pi$
$541$	1.03313e9	+	1.78943e9i	0.280520	+	0.485876i	−0.690993	+	0.722862i	$0.742826\pi$
$542$	5.14586e8	−	8.91289e8i	0.138823	−	0.240448i
$543$		0			0
$544$	−2.46921e9	−	4.27680e9i	−0.657600	−	1.13900i
$545$	−5.44854e6			−0.00144176
$546$		0			0
$547$	−1.44090e9			−0.376425			−0.188213	−	0.982128i	$-0.560269\pi$
$547$	−1.44090e9			−0.376425			−0.188213	+	0.982128i	$0.560269\pi$
$548$	1.24952e9	+	2.16423e9i	0.324348	+	0.561787i
$549$		0			0
$550$	−1.49264e8	+	2.58533e8i	−0.0382547	+	0.0662591i
$551$	8.56316e8	+	1.48318e9i	0.218074	+	0.377715i
$552$		0			0
$553$	3.56893e9	−	2.23084e9i	0.897428	−	0.560958i
$554$	4.99868e8			0.124903
$555$		0			0
$556$	−8.38869e8	+	1.45296e9i	−0.206982	+	0.358503i
$557$	−2.75670e9	+	4.77475e9i	−0.675922	+	1.17073i	0.300277	+	0.953852i	$0.402921\pi$
$557$	−2.75670e9	+	4.77475e9i	−0.675922	+	1.17073i	−0.976199	+	0.216879i	$0.930412\pi$
$558$		0			0
$559$	4.61280e9			1.11692
$560$	−5.94217e6	−	3.15839e6i	−0.00142984	−	0.000759990i
$561$		0			0
$562$	−7.91535e8	−	1.37098e9i	−0.188102	−	0.325802i
$563$	3.49097e8	−	6.04655e8i	0.0824456	−	0.142800i	−0.821854	−	0.569698i	$-0.807060\pi$
$563$	3.49097e8	−	6.04655e8i	0.0824456	−	0.142800i	0.904300	+	0.426898i	$0.140394\pi$
$564$		0			0
$565$	3.42851e6	+	5.93835e6i	0.000799716	+	0.00138515i
$566$	−9.03244e8			−0.209386
$567$		0			0
$568$	−1.97795e9			−0.452895
$569$	1.42595e9	+	2.46982e9i	0.324497	+	0.562046i	0.981410	−	0.191920i	$-0.0614716\pi$
$569$	1.42595e9	+	2.46982e9i	0.324497	+	0.562046i	−0.656913	+	0.753966i	$0.728138\pi$
$570$		0			0
$571$	1.99936e9	−	3.46299e9i	0.449433	−	0.778440i	−0.548917	−	0.835877i	$-0.684960\pi$
$571$	1.99936e9	−	3.46299e9i	0.449433	−	0.778440i	0.998349	+	0.0574372i	$0.0182929\pi$
$572$	5.40808e8	+	9.36707e8i	0.120825	+	0.209275i
$573$		0			0
$574$	−6.60885e8	+	4.13101e8i	−0.145859	+	0.0911727i
$575$	6.15104e9			1.34931
$576$		0			0
$577$	−1.84639e9	+	3.19804e9i	−0.400136	+	0.693056i	−0.993742	−	0.111700i	$-0.964370\pi$
$577$	−1.84639e9	+	3.19804e9i	−0.400136	+	0.693056i	0.593606	+	0.804756i	$0.297704\pi$
$578$	1.31834e9	−	2.28343e9i	0.283975	−	0.491860i
$579$		0			0
$580$	−1.38658e7			−0.00295084
$581$	−2.45321e8	−	6.99567e9i	−0.0518941	−	1.47983i
$582$		0			0
$583$	3.98391e8	+	6.90033e8i	0.0832663	+	0.144221i
$584$	−1.38171e9	+	2.39319e9i	−0.287059	+	0.497201i
$585$		0			0
$586$	−5.98267e8	−	1.03623e9i	−0.122816	−	0.212723i
$587$	−1.47103e9			−0.300184			−0.150092	−	0.988672i	$-0.547957\pi$
$587$	−1.47103e9			−0.300184			−0.150092	+	0.988672i	$0.547957\pi$
$588$		0			0
$589$	−1.17554e9			−0.237047
$590$	2.16501e6	+	3.74991e6i	0.000433989	+	0.000751691i
$591$		0			0
$592$	−5.67095e8	+	9.82237e8i	−0.112339	+	0.194576i
$593$	−3.39731e9	−	5.88431e9i	−0.669027	−	1.15879i	−0.978177	−	0.207776i	$-0.933378\pi$
$593$	−3.39731e9	−	5.88431e9i	−0.669027	−	1.15879i	0.309149	−	0.951014i	$-0.399956\pi$
$594$		0			0
$595$	−659093.	−	1.87950e7i	−0.000128274	−	0.00365790i
$596$	−4.20010e9			−0.812640
$597$		0			0
$598$	−9.59468e8	+	1.66185e9i	−0.183475	+	0.317787i
$599$	−2.08411e9	+	3.60979e9i	−0.396211	+	0.686258i	−0.993255	−	0.115951i	$-0.963009\pi$
$599$	−2.08411e9	+	3.60979e9i	−0.396211	+	0.686258i	0.597044	+	0.802209i	$0.296342\pi$
$600$		0			0
$601$	−3.48946e9			−0.655689			−0.327845	−	0.944732i	$-0.606322\pi$
$601$	−3.48946e9			−0.655689			−0.327845	+	0.944732i	$0.606322\pi$
$602$	−1.47792e9	+	9.23807e8i	−0.276098	+	0.172581i
$603$		0			0
$604$	7.66591e8	+	1.32777e9i	0.141558	+	0.245186i
$605$	5.31499e6	−	9.20583e6i	0.000975795	−	0.00169013i
$606$		0			0
$607$	−2.29268e9	−	3.97104e9i	−0.416086	−	0.720682i	0.579456	−	0.815004i	$-0.303265\pi$
$607$	−2.29268e9	−	3.97104e9i	−0.416086	−	0.720682i	−0.995542	+	0.0943215i	$0.969932\pi$
$608$	1.20330e9			0.217126
$609$		0			0
$610$	−1.68834e6			−0.000301166
$611$	−1.47250e9	−	2.55044e9i	−0.261162	−	0.452346i
$612$		0			0
$613$	−1.53799e9	+	2.66388e9i	−0.269676	+	0.467093i	−0.968778	−	0.247929i	$-0.920250\pi$
$613$	−1.53799e9	+	2.66388e9i	−0.269676	+	0.467093i	0.699102	+	0.715022i	$0.253583\pi$
$614$	−3.73410e8	−	6.46764e8i	−0.0651023	−	0.112760i
$615$		0			0
$616$	−7.52806e8	−	4.00132e8i	−0.129763	−	0.0689717i
$617$	−2.75456e9			−0.472123			−0.236061	−	0.971738i	$-0.575857\pi$
$617$	−2.75456e9			−0.472123			−0.236061	+	0.971738i	$0.575857\pi$
$618$		0			0
$619$	2.20839e9	−	3.82504e9i	0.374247	−	0.648215i	−0.615967	−	0.787772i	$-0.711235\pi$
$619$	2.20839e9	−	3.82504e9i	0.374247	−	0.648215i	0.990214	+	0.139557i	$0.0445679\pi$
$620$	4.75870e6	−	8.24232e6i	0.000801895	−	0.00138892i
$621$		0			0
$622$	1.47252e9			0.245354
$623$	−6.75722e9	+	4.22376e9i	−1.11959	+	0.699827i
$624$		0			0
$625$	−3.05172e9	−	5.28573e9i	−0.499993	−	0.866014i
$626$	−7.60095e8	+	1.31652e9i	−0.123839	+	0.214496i
$627$		0			0
$628$	3.89929e9	+	6.75378e9i	0.628242	+	1.08815i
$629$	−3.16970e9			−0.507856
$630$		0			0
$631$	1.17209e10			1.85720			0.928598	−	0.371087i	$-0.121015\pi$
$631$	1.17209e10			1.85720			0.928598	+	0.371087i	$0.121015\pi$
$632$	−1.81610e9	−	3.14557e9i	−0.286173	−	0.495667i
$633$		0			0
$634$	8.03242e8	−	1.39126e9i	0.125180	−	0.216818i
$635$	−128745.	−	222993.i	−1.99537e−5	−	3.45608e-5i
$636$		0			0
$637$	−6.28546e9	+	4.41374e8i	−0.963494	+	0.0676579i
$638$	−7.63318e8			−0.116368
$639$		0			0
$640$	−6.38288e6	+	1.10555e7i	−0.000962468	+	0.00166704i
$641$	4.44754e9	−	7.70336e9i	0.666986	−	1.15525i	−0.311757	−	0.950162i	$-0.600918\pi$
$641$	4.44754e9	−	7.70336e9i	0.666986	−	1.15525i	0.978743	−	0.205091i	$-0.0657492\pi$
$642$		0			0
$643$	−7.02222e9			−1.04168			−0.520842	−	0.853653i	$-0.674382\pi$
$643$	−7.02222e9			−1.04168			−0.520842	+	0.853653i	$0.674382\pi$
$644$	2.95108e8	+	8.41542e9i	0.0435392	+	1.24158i
$645$		0			0
$646$	4.80479e8	+	8.32214e8i	0.0701230	+	0.121457i
$647$	1.12003e9	−	1.93995e9i	0.162579	−	0.281596i	−0.773214	−	0.634146i	$-0.781352\pi$
$647$	1.12003e9	−	1.93995e9i	0.162579	−	0.281596i	0.935793	+	0.352550i	$0.114685\pi$
$648$		0			0
$649$	−1.38420e9	−	2.39750e9i	−0.198766	−	0.344273i
$650$	1.90409e9			0.271951
$651$		0			0
$652$	−6.53304e9			−0.923101
$653$	−2.34366e9	−	4.05934e9i	−0.329381	−	0.570504i	0.653008	−	0.757351i	$-0.273507\pi$
$653$	−2.34366e9	−	4.05934e9i	−0.329381	−	0.570504i	−0.982389	+	0.186847i	$0.940173\pi$
$654$		0			0
$655$	8.58140e6	−	1.48634e7i	0.00119320	−	0.00206669i
$656$	−1.69718e9	−	2.93960e9i	−0.234728	−	0.406560i
$657$		0			0
$658$	9.82558e8	+	5.22250e8i	0.134452	+	0.0714641i
$659$	1.65220e9			0.224886			0.112443	−	0.993658i	$-0.464132\pi$
$659$	1.65220e9			0.224886			0.112443	+	0.993658i	$0.464132\pi$
$660$		0			0
$661$	1.64924e9	−	2.85657e9i	0.222116	−	0.384715i	−0.733335	−	0.679868i	$-0.762037\pi$
$661$	1.64924e9	−	2.85657e9i	0.222116	−	0.384715i	0.955450	+	0.295153i	$0.0953705\pi$
$662$	−1.55850e9	+	2.69940e9i	−0.208787	+	0.361630i
$663$		0			0
$664$	−6.04100e9			−0.800793
$665$	4.04635e6	+	2.15072e6i	0.000533566	+	0.000283602i
$666$		0			0
$667$	7.86393e9	+	1.36207e10i	1.02612	+	1.77730i
$668$	−6.52014e9	+	1.12932e10i	−0.846329	+	1.46588i
$669$		0			0
$670$	22288.1	+	38604.1i	2.86293e−6	+	4.95875e-6i
$671$	1.07944e9			0.137933
$672$		0			0
$673$	−3.03240e9			−0.383472			−0.191736	−	0.981447i	$-0.561412\pi$
$673$	−3.03240e9			−0.383472			−0.191736	+	0.981447i	$0.561412\pi$
$674$	1.43233e9	+	2.48086e9i	0.180191	+	0.312100i
$675$		0			0
$676$	−2.48111e8	+	4.29742e8i	−0.0308911	+	0.0535050i
$677$	2.57174e9	+	4.45439e9i	0.318542	+	0.551732i	0.980184	−	0.198088i	$-0.0634733\pi$
$677$	2.57174e9	+	4.45439e9i	0.318542	+	0.551732i	−0.661642	+	0.749820i	$0.730140\pi$
$678$		0			0
$679$	1.40684e8	+	4.01180e9i	0.0172465	+	0.491808i
$680$	−1.62301e7			−0.00197943
$681$		0			0
$682$	2.61969e8	−	4.53743e8i	0.0316231	−	0.0547728i
$683$	−6.78419e8	+	1.17506e9i	−0.0814752	+	0.141119i	−0.903884	−	0.427778i	$-0.859296\pi$
$683$	−6.78419e8	+	1.17506e9i	−0.0814752	+	0.141119i	0.822409	+	0.568897i	$0.192630\pi$
$684$		0			0
$685$	1.24891e7			0.00148462
$686$	1.92544e9	−	1.40020e9i	0.227717	−	0.165599i
$687$		0			0
$688$	−3.79535e9	−	6.57375e9i	−0.444317	−	0.769579i
$689$	2.54105e9	−	4.40122e9i	0.295968	−	0.512632i
$690$		0			0
$691$	−3.81213e9	−	6.60280e9i	−0.439536	−	0.761299i	0.558118	−	0.829762i	$-0.311524\pi$
$691$	−3.81213e9	−	6.60280e9i	−0.439536	−	0.761299i	−0.997654	+	0.0684630i	$0.978190\pi$
$692$	2.13817e9			0.245286
$693$		0			0
$694$	7.61909e8			0.0865257
$695$	4.19230e6	+	7.26128e6i	0.000473703	+	0.000820477i
$696$		0			0
$697$	4.74307e9	−	8.21524e9i	0.530573	−	0.918979i
$698$	−1.56018e9	−	2.70232e9i	−0.173653	−	0.300776i
$699$		0			0
$700$	7.08517e9	−	4.42875e9i	0.780742	−	0.488021i
$701$	2.55816e9			0.280489			0.140244	−	0.990117i	$-0.455211\pi$
$701$	2.55816e9			0.280489			0.140244	+	0.990117i	$0.455211\pi$
$702$		0			0
$703$	3.86166e8	−	6.68860e8i	0.0419209	−	0.0726091i
$704$	6.98412e8	−	1.20969e9i	0.0754410	−	0.130668i
$705$		0			0
$706$	4.59062e7			0.00490969
$707$	4.70464e9	+	2.50061e9i	0.500677	+	0.266121i
$708$		0			0
$709$	2.31182e9	+	4.00419e9i	0.243608	+	0.421942i	0.961739	−	0.273966i	$-0.0883356\pi$
$709$	2.31182e9	+	4.00419e9i	0.243608	+	0.421942i	−0.718131	+	0.695908i	$0.755002\pi$
$710$	−2.36924e6	+	4.10364e6i	−0.000248430	+	0.000430294i
$711$		0			0
$712$	3.43850e9	+	5.95566e9i	0.357017	+	0.618372i
$713$	−1.07955e10			−1.11540
$714$		0			0
$715$	5.40544e6			0.000553045
$716$	−3.36536e9	−	5.82897e9i	−0.342638	−	0.593467i
$717$		0			0
$718$	1.76932e7	−	3.06455e7i	0.00178390	−	0.00308980i
$719$	5.37972e9	+	9.31795e9i	0.539770	+	0.934909i	0.998916	+	0.0465481i	$0.0148221\pi$
$719$	5.37972e9	+	9.31795e9i	0.539770	+	0.934909i	−0.459146	+	0.888361i	$0.651845\pi$
$720$		0			0
$721$	−1.27251e9	+	7.95410e8i	−0.126441	+	0.0790346i
$722$	2.61330e9			0.258410
$723$		0			0
$724$	−5.86534e9	+	1.01591e10i	−0.574392	+	0.994876i
$725$	7.80310e9	−	1.35154e10i	0.760473	−	1.31718i
$726$		0			0
$727$	−2.05793e9			−0.198637			−0.0993183	−	0.995056i	$-0.531666\pi$
$727$	−2.05793e9			−0.198637			−0.0993183	+	0.995056i	$0.531666\pi$
$728$	1.90570e8	+	5.43438e9i	0.0183061	+	0.522024i
$729$		0			0
$730$	3.31008e6	+	5.73323e6i	0.000314926	+	0.000545468i
$731$	1.06068e10	−	1.83715e10i	1.00432	−	1.73954i
$732$		0			0
$733$	1.40822e9	+	2.43911e9i	0.132071	+	0.228753i	0.924475	−	0.381244i	$-0.124504\pi$
$733$	1.40822e9	+	2.43911e9i	0.132071	+	0.228753i	−0.792404	+	0.609997i	$0.791171\pi$
$734$	−1.95870e9			−0.182823
$735$		0			0
$736$	1.10505e10			1.02166
$737$	−1.42499e7	−	2.46815e7i	−0.00131122	−	0.00227110i
$738$		0			0
$739$	2.32868e9	−	4.03340e9i	0.212254	−	0.367634i	−0.740166	−	0.672424i	$-0.765253\pi$
$739$	2.32868e9	−	4.03340e9i	0.212254	−	0.367634i	0.952419	+	0.304790i	$0.0985864\pi$
$740$	3.12647e6	+	5.41521e6i	0.000283624	+	0.000491252i
$741$		0			0
$742$	6.72954e7	+	1.91902e9i	0.00604744	+	0.172451i
$743$	1.44668e10			1.29393			0.646964	−	0.762520i	$-0.276038\pi$
$743$	1.44668e10			1.29393			0.646964	+	0.762520i	$0.276038\pi$
$744$		0			0
$745$	−1.04951e7	+	1.81781e7i	−0.000929911	+	0.00161065i
$746$	6.41600e8	−	1.11128e9i	0.0565820	−	0.0980029i
$747$		0			0
$748$	4.97420e9			0.434578
$749$	−7.15185e8	+	4.47043e8i	−0.0621917	+	0.0388743i
$750$		0			0
$751$	−6.87875e9	−	1.19143e10i	−0.592611	−	1.02643i	−0.993879	−	0.110471i	$-0.964764\pi$
$751$	−6.87875e9	−	1.19143e10i	−0.592611	−	1.02643i	0.401269	−	0.915960i	$-0.368569\pi$
$752$	−2.42310e9	+	4.19694e9i	−0.207783	+	0.359890i
$753$		0			0
$754$	2.43432e9	+	4.21637e9i	0.206813	+	0.358211i
$755$	7.66217e6			0.000647944
$756$		0			0
$757$	−4.61358e9			−0.386547			−0.193273	−	0.981145i	$-0.561910\pi$
$757$	−4.61358e9			−0.386547			−0.193273	+	0.981145i	$0.561910\pi$
$758$	9.45994e7	+	1.63851e8i	0.00788944	+	0.0136649i
$759$		0			0
$760$	1.97732e6	−	3.42482e6i	0.000163392	−	0.000283003i
$761$	1.09777e10	+	1.90139e10i	0.902951	+	1.56396i	0.823644	+	0.567108i	$0.191938\pi$
$761$	1.09777e10	+	1.90139e10i	0.902951	+	1.56396i	0.0793078	+	0.996850i	$0.474729\pi$
$762$		0			0
$763$	7.41303e9	+	3.94018e9i	0.604171	+	0.321130i
$764$	−5.43638e8			−0.0441045
$765$		0			0
$766$	−5.74033e8	+	9.94254e8i	−0.0461462	+	0.0799276i
$767$	−8.82881e9	+	1.52919e10i	−0.706510	+	1.22371i
$768$		0			0
$769$	1.61256e10			1.27871			0.639357	−	0.768910i	$-0.279201\pi$
$769$	1.61256e10			1.27871			0.639357	+	0.768910i	$0.279201\pi$
$770$	−1.73188e6	+	1.08255e6i	−0.000136710	+	8.54536e-5i
$771$		0			0
$772$	−4.63469e9	−	8.02753e9i	−0.362544	−	0.627944i
$773$	1.59062e9	−	2.75504e9i	0.123862	−	0.214535i	−0.797425	−	0.603417i	$-0.793805\pi$
$773$	1.59062e9	−	2.75504e9i	0.123862	−	0.214535i	0.921288	+	0.388882i	$0.127139\pi$
$774$		0			0
$775$	5.35601e9	+	9.27688e9i	0.413319	+	0.715889i
$776$	3.46432e9			0.266135
$777$		0			0
$778$	−5.42150e9			−0.412754
$779$	1.15570e9	+	2.00174e9i	0.0875922	+	0.151714i
$780$		0			0
$781$	1.51477e9	−	2.62366e9i	0.113781	−	0.197074i
$782$	4.41245e9	+	7.64259e9i	0.329956	+	0.571501i
$783$		0			0
$784$	5.80060e9	+	8.59431e9i	0.429899	+	0.636949i
$785$	3.89739e7			0.00287561
$786$		0			0
$787$	3.77490e9	−	6.53832e9i	0.276054	−	0.478139i	−0.694347	−	0.719641i	$-0.744307\pi$
$787$	3.77490e9	−	6.53832e9i	0.276054	−	0.478139i	0.970400	+	0.241501i	$0.0776399\pi$
$788$	8.08783e9	−	1.40085e10i	0.588830	−	1.01988i
$789$		0			0
$790$	−8.70145e6			−0.000627909
$791$	−3.70271e8	−	1.05588e10i	−0.0266012	−	0.758572i
$792$		0			0
$793$	−3.44248e9	−	5.96255e9i	−0.245141	−	0.424596i
$794$	2.07102e9	−	3.58711e9i	0.146829	−	0.254315i
$795$		0			0
$796$	−5.25971e9	−	9.11008e9i	−0.369629	−	0.640216i
$797$	−2.52925e10			−1.76965			−0.884824	−	0.465926i	$-0.845721\pi$
$797$	−2.52925e10			−1.76965			−0.884824	+	0.465926i	$0.845721\pi$
$798$		0			0
$799$	−1.35436e10			−0.939334
$800$	−5.48249e9	−	9.49595e9i	−0.378584	−	0.655727i
$801$		0			0
$802$	−1.07122e9	+	1.85541e9i	−0.0733277	+	0.127007i
$803$	−2.11630e9	−	3.66554e9i	−0.144236	−	0.249823i
$804$		0			0
$805$	3.71595e7	+	1.97511e7i	0.00251064	+	0.00133446i
$806$	−3.34182e9			−0.224807
$807$		0			0
$808$	2.29900e9	−	3.98199e9i	0.153320	−	0.265558i
$809$	7.43299e9	−	1.28743e10i	0.493564	−	0.854878i	−0.506408	−	0.862294i	$-0.669027\pi$
$809$	7.43299e9	−	1.28743e10i	0.493564	−	0.854878i	0.999973	+	0.00741559i	$0.00236048\pi$
$810$		0			0
$811$	−2.03817e10			−1.34174			−0.670868	−	0.741577i	$-0.734078\pi$
$811$	−2.03817e10			−1.34174			−0.670868	+	0.741577i	$0.734078\pi$
$812$	1.88651e10	+	1.00272e10i	1.23655	+	0.657255i
$813$		0			0
$814$	1.72114e8	+	2.98110e8i	0.0111848	+	0.0193727i
$815$	−1.63246e7	+	2.82751e7i	−0.00105631	+	0.00182959i
$816$		0			0
$817$	2.58447e9	+	4.47643e9i	0.165804	+	0.287180i
$818$	−7.30661e9			−0.466745
$819$		0			0
$820$	−1.87136e7			−0.00118524
$821$	−1.90319e9	−	3.29642e9i	−0.120028	−	0.207894i	0.799751	−	0.600332i	$-0.204965\pi$
$821$	−1.90319e9	−	3.29642e9i	−0.120028	−	0.207894i	−0.919778	+	0.392438i	$0.871632\pi$
$822$		0			0
$823$	−4.24519e9	+	7.35289e9i	−0.265459	+	0.459789i	−0.967684	−	0.252166i	$-0.918857\pi$
$823$	−4.24519e9	+	7.35289e9i	−0.265459	+	0.459789i	0.702224	+	0.711956i	$0.252190\pi$
$824$	6.47532e8	+	1.12156e9i	0.0403196	+	0.0698356i
$825$		0			0
$826$	−2.33816e8	−	6.66761e9i	−0.0144359	−	0.411661i
$827$	−2.17143e10			−1.33499			−0.667494	−	0.744615i	$-0.732633\pi$
$827$	−2.17143e10			−1.33499			−0.667494	+	0.744615i	$0.732633\pi$
$828$		0			0
$829$	−1.49181e9	+	2.58389e9i	−0.0909438	+	0.157519i	−0.907909	−	0.419168i	$-0.862322\pi$
$829$	−1.49181e9	+	2.58389e9i	−0.0909438	+	0.157519i	0.816965	+	0.576688i	$0.195655\pi$
$830$	−7.23604e6	+	1.25332e7i	−0.000439266	+	0.000760831i
$831$		0			0
$832$	−8.90933e9			−0.536307
$833$	−1.26951e10	+	2.60482e10i	−0.760989	+	1.56142i
$834$		0			0
$835$	3.25848e7	+	5.64385e7i	0.00193692	+	0.00335485i
$836$	−6.06010e8	+	1.04964e9i	−0.0358722	+	0.0621324i
$837$		0			0
$838$	−1.37775e9	−	2.38633e9i	−0.0808752	−	0.140080i
$839$	−2.09807e10			−1.22646			−0.613230	−	0.789905i	$-0.710130\pi$
$839$	−2.09807e10			−1.22646			−0.613230	+	0.789905i	$0.710130\pi$
$840$		0			0
$841$	2.26542e10			1.31330
$842$	−5.05635e8	−	8.75785e8i	−0.0291907	−	0.0505598i
$843$		0			0
$844$	6.88314e9	−	1.19220e10i	0.394083	−	0.682573i
$845$	1.23995e6	+	2.14766e6i	7.06979e−5	+	0.000122452i
$846$		0			0
$847$	−1.38886e10	+	8.68141e9i	−0.785358	+	0.490906i
$848$	−8.36296e9			−0.470950
$849$		0			0
$850$	4.37832e9	−	7.58347e9i	0.244535	−	0.423547i
$851$	3.54634e9	−	6.14243e9i	0.197254	−	0.341654i
$852$		0			0
$853$	−2.23064e10			−1.23058			−0.615288	−	0.788303i	$-0.710960\pi$
$853$	−2.23064e10			−1.23058			−0.615288	+	0.788303i	$0.710960\pi$
$854$	2.29708e9	+	1.22095e9i	0.126204	+	0.0670801i
$855$		0			0
$856$	3.63932e8	+	6.30348e8i	0.0198318	+	0.0343497i
$857$	−8.55100e9	+	1.48108e10i	−0.464070	+	0.803793i	−0.999159	−	0.0410024i	$-0.986945\pi$
$857$	−8.55100e9	+	1.48108e10i	−0.464070	+	0.803793i	0.535089	+	0.844796i	$0.320278\pi$
$858$		0			0
$859$	1.13049e10	+	1.95806e10i	0.608541	+	1.05402i	0.991481	+	0.130251i	$0.0415782\pi$
$859$	1.13049e10	+	1.95806e10i	0.608541	+	1.05402i	−0.382940	+	0.923773i	$0.625088\pi$
$860$	−4.18486e7			−0.00224356
$861$		0			0
$862$	−4.26335e9			−0.226713
$863$	6.89976e9	+	1.19507e10i	0.365423	+	0.632932i	0.988844	−	0.148955i	$-0.0475909\pi$
$863$	6.89976e9	+	1.19507e10i	0.365423	+	0.632932i	−0.623421	+	0.781887i	$0.714258\pi$
$864$		0			0
$865$	5.34283e6	−	9.25406e6i	0.000280682	−	0.000486156i
$866$	−2.80872e9	−	4.86484e9i	−0.146959	−	0.254540i
$867$		0			0
$868$	−1.24350e10	+	7.77278e9i	−0.645396	+	0.403420i
$869$	5.56326e9			0.287581
$870$		0			0
$871$	−9.08896e7	+	1.57425e8i	−0.00466070	+	0.00807256i
$872$	3.62250e9	−	6.27436e9i	0.185013	−	0.320451i
$873$		0			0
$874$	−2.15029e9			−0.108945
$875$	−2.92683e6	−	8.34626e7i	−0.000147696	−	0.00421176i
$876$		0			0
$877$	1.07693e10	+	1.86530e10i	0.539125	+	0.933792i	0.998951	+	0.0457828i	$0.0145782\pi$
$877$	1.07693e10	+	1.86530e10i	0.539125	+	0.933792i	−0.459827	+	0.888009i	$0.652088\pi$
$878$	−4.64533e8	+	8.04594e8i	−0.0231625	+	0.0401186i
$879$		0			0
$880$	−4.44753e6	−	7.70335e6i	−0.000220004	−	0.000381057i
$881$	9.50136e8			0.0468134			0.0234067	−	0.999726i	$-0.492549\pi$
$881$	9.50136e8			0.0468134			0.0234067	+	0.999726i	$0.492549\pi$
$882$		0			0
$883$	1.42541e10			0.696751			0.348376	−	0.937355i	$-0.386733\pi$
$883$	1.42541e10			0.696751			0.348376	+	0.937355i	$0.386733\pi$
$884$	−1.58634e10	−	2.74762e10i	−0.772348	−	1.33775i
$885$		0			0
$886$	−2.69085e9	+	4.66068e9i	−0.129978	+	0.225129i
$887$	−5.16456e9	−	8.94529e9i	−0.248486	−	0.430390i	0.714620	−	0.699513i	$-0.246600\pi$
$887$	−5.16456e9	−	8.94529e9i	−0.248486	−	0.430390i	−0.963106	+	0.269123i	$0.913266\pi$
$888$		0			0
$889$	1.39042e7	+	3.96497e8i	0.000663727	+	0.0189271i
$890$	1.64749e7			0.000783352
$891$		0			0
$892$	−4.84403e9	+	8.39010e9i	−0.228523	+	0.395813i
$893$	1.65003e9	−	2.85793e9i	0.0775373	−	0.134298i
$894$		0			0
$895$	−3.36372e7			−0.00156834
$896$	1.66791e10	−	1.04257e10i	0.774632	−	0.484202i
$897$		0			0
$898$	−4.19108e9	−	7.25917e9i	−0.193134	−	0.334518i
$899$	−1.36950e10	+	2.37204e10i	−0.628642	+	1.08884i
$900$		0			0
$901$	−1.16859e10	−	2.02406e10i	−0.532262	−	0.921905i
$902$	−1.03019e9			−0.0467406
$903$		0			0
$904$	−9.11788e9			−0.410492
$905$	2.93124e7	+	5.07706e7i	0.00131456	+	0.00227689i
$906$		0			0
$907$	−2.39760e9	+	4.15277e9i	−0.106697	+	0.184804i	−0.914430	−	0.404744i	$-0.867361\pi$
$907$	−2.39760e9	+	4.15277e9i	−0.106697	+	0.184804i	0.807733	+	0.589548i	$0.200694\pi$
$908$	−1.24254e9	−	2.15214e9i	−0.0550819	−	0.0954047i
$909$		0			0
$910$	1.15029e7	+	6.11405e6i	0.000506015	+	0.000268958i
$911$	2.81747e10			1.23465			0.617326	−	0.786707i	$-0.288216\pi$
$911$	2.81747e10			1.23465			0.617326	+	0.786707i	$0.288216\pi$
$912$		0			0
$913$	4.62636e9	−	8.01308e9i	0.201183	−	0.348459i
$914$	−9.70914e8	+	1.68167e9i	−0.0420600	+	0.0728500i
$915$		0			0
$916$	4.08511e10			1.75618
$917$	−2.24241e10	+	1.40167e10i	−0.960335	+	0.600279i
$918$		0			0
$919$	−1.80005e10	−	3.11777e10i	−0.765032	−	1.32507i	−0.940230	−	0.340541i	$-0.889390\pi$
$919$	−1.80005e10	−	3.11777e10i	−0.765032	−	1.32507i	0.175198	−	0.984533i	$-0.443944\pi$
$920$	1.81586e7	−	3.14517e7i	0.000768821	−	0.00133164i
$921$		0			0
$922$	1.71021e9	+	2.96216e9i	0.0718605	+	0.124466i
$923$	−1.93232e10			−0.808861
$924$		0			0
$925$	−7.03780e9			−0.292376
$926$	−4.94236e9	−	8.56042e9i	−0.204548	−	0.354288i
$927$		0			0
$928$	1.40184e10	−	2.42806e10i	0.575812	−	0.997335i
$929$	1.12664e10	+	1.95140e10i	0.461032	+	0.798530i	0.999013	−	0.0444266i	$-0.0141461\pi$
$929$	1.12664e10	+	1.95140e10i	0.461032	+	0.798530i	−0.537981	+	0.842957i	$0.680813\pi$
$930$		0			0
$931$	−3.94995e9	−	5.85234e9i	−0.160423	−	0.237687i
$932$	−3.92138e9			−0.158666
$933$		0			0
$934$	−3.39245e9	+	5.87589e9i	−0.136238	+	0.235972i
$935$	1.24294e7	−	2.15284e7i	0.000497291	−	0.000861333i
$936$		0			0
$937$	6.17708e9			0.245298			0.122649	−	0.992450i	$-0.460861\pi$
$937$	6.17708e9			0.245298			0.122649	+	0.992450i	$0.460861\pi$
$938$	−2.40706e6	−	6.86408e7i	−9.52308e−5	−	0.00271564i
$939$		0			0
$940$	1.33589e7	+	2.31383e7i	0.000524594	+	0.000908623i
$941$	1.88459e10	−	3.26421e10i	0.737316	−	1.27707i	−0.216384	−	0.976308i	$-0.569426\pi$
$941$	1.88459e10	−	3.26421e10i	0.737316	−	1.27707i	0.953700	−	0.300761i	$-0.0972405\pi$
$942$		0			0
$943$	1.06133e10	+	1.83828e10i	0.412155	+	0.713874i
$944$	2.90569e10			1.12421
$945$		0			0
$946$	−2.30379e9			−0.0884756
$947$	1.88281e10	+	3.26112e10i	0.720412	+	1.24779i	0.960835	+	0.277122i	$0.0893806\pi$
$947$	1.88281e10	+	3.26112e10i	0.720412	+	1.24779i	−0.240423	+	0.970668i	$0.577286\pi$
$948$		0			0
$949$	−1.34983e10	+	2.33798e10i	−0.512682	+	0.887991i
$950$	1.06683e9	+	1.84780e9i	0.0403702	+	0.0699233i
$951$		0			0
$952$	2.20819e10	+	1.17370e10i	0.829481	+	0.440887i
$953$	5.18903e10			1.94205			0.971027	−	0.238971i	$-0.0768100\pi$
$953$	5.18903e10			1.94205			0.971027	+	0.238971i	$0.0768100\pi$
$954$		0			0
$955$	−1.35843e6	+	2.35287e6i	−5.04691e−5	+	8.74151e-5i
$956$	1.02775e10	−	1.78012e10i	0.380440	−	0.658941i
$957$		0			0
$958$	−8.20138e9			−0.301375
$959$	−1.69921e10	−	9.03164e9i	−0.622130	−	0.330675i
$960$		0			0
$961$	4.35612e9	+	7.54502e9i	0.158332	+	0.274239i
$962$	1.09779e9	−	1.90143e9i	0.0397563	−	0.0688599i
$963$		0			0
$964$	−1.68069e10	−	2.91104e10i	−0.604251	−	1.04659i
$965$	−4.63243e7			−0.00165945
$966$		0			0
$967$	2.54614e10			0.905501			0.452751	−	0.891637i	$-0.350443\pi$
$967$	2.54614e10			0.905501			0.452751	+	0.891637i	$0.350443\pi$
$968$	7.06742e9	+	1.22411e10i	0.250436	+	0.433768i
$969$		0			0
$970$	4.14964e6	−	7.18739e6i	0.000145986	−	0.000252854i
$971$	−2.60193e10	−	4.50667e10i	−0.912070	−	1.57975i	−0.811136	−	0.584858i	$-0.801150\pi$
$971$	−2.60193e10	−	4.50667e10i	−0.912070	−	1.57975i	−0.100934	−	0.994893i	$-0.532183\pi$
$972$		0			0
$973$	−4.52759e8	−	1.29111e10i	−0.0157569	−	0.449332i
$974$	−1.08633e10			−0.376708
$975$		0			0
$976$	−5.66486e9	+	9.81183e9i	−0.195036	+	0.337812i
$977$	−1.44388e10	+	2.50087e10i	−0.495336	+	0.857948i	−0.999986	−	0.00537679i	$-0.998289\pi$
$977$	−1.44388e10	+	2.50087e10i	−0.495336	+	0.857948i	0.504649	+	0.863324i	$0.331622\pi$
$978$		0			0
$979$	−1.05332e10			−0.358774
$980$	5.70235e7	−	4.00427e6i	0.00193536	−	0.000135904i
$981$		0			0
$982$	−2.13849e9	−	3.70397e9i	−0.0720638	−	0.124818i
$983$	2.21233e10	−	3.83187e10i	0.742870	−	1.28669i	−0.208313	−	0.978062i	$-0.566797\pi$
$983$	2.21233e10	−	3.83187e10i	0.742870	−	1.28669i	0.951183	−	0.308627i	$-0.0998694\pi$
$984$		0			0
$985$	−4.04194e7	−	7.00085e7i	−0.00134761	−	0.00233412i
$986$	2.23902e10			0.743856
$987$		0			0
$988$	7.73059e9			0.255014
$989$	2.37343e10	+	4.11090e10i	0.780171	+	1.35130i
$990$		0			0
$991$	2.19178e10	−	3.79627e10i	0.715383	−	1.23908i	−0.247429	−	0.968906i	$-0.579586\pi$
$991$	2.19178e10	−	3.79627e10i	0.715383	−	1.23908i	0.962812	−	0.270174i	$-0.0870811\pi$
$992$	9.62216e9	+	1.66661e10i	0.312955	+	0.542054i
$993$		0			0
$994$	6.19107e9	−	3.86987e9i	0.199946	−	0.124981i
$995$	−5.25714e7			−0.00169188
$996$		0			0
$997$	−3.01677e9	+	5.22519e9i	−0.0964070	+	0.166982i	−0.910195	−	0.414180i	$-0.864068\pi$
$997$	−3.01677e9	+	5.22519e9i	−0.0964070	+	0.166982i	0.813788	+	0.581162i	$0.197402\pi$
$998$	−6.87602e7	+	1.19096e8i	−0.00218968	+	0.00379263i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.8.e.b.46.3		8
3.2	odd	2		7.8.c.a.4.2	yes	8
7.2	even	3	inner	63.8.e.b.37.3		8
7.3	odd	6		441.8.a.t.1.2		4
7.4	even	3		441.8.a.s.1.2		4
12.11	even	2		112.8.i.c.81.2		8
21.2	odd	6		7.8.c.a.2.2	✓	8
21.5	even	6		49.8.c.g.30.2		8
21.11	odd	6		49.8.a.f.1.3		4
21.17	even	6		49.8.a.e.1.3		4
21.20	even	2		49.8.c.g.18.2		8
84.23	even	6		112.8.i.c.65.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.8.c.a.2.2	✓	8	21.2	odd	6
7.8.c.a.4.2	yes	8	3.2	odd	2
49.8.a.e.1.3		4	21.17	even	6
49.8.a.f.1.3		4	21.11	odd	6
49.8.c.g.18.2		8	21.20	even	2
49.8.c.g.30.2		8	21.5	even	6
63.8.e.b.37.3		8	7.2	even	3	inner
63.8.e.b.46.3		8	1.1	even	1	trivial
112.8.i.c.65.2		8	84.23	even	6
112.8.i.c.81.2		8	12.11	even	2
441.8.a.s.1.2		4	7.4	even	3
441.8.a.t.1.2		4	7.3	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(1.59276 + 2.75874i) q^{2} +(58.9262 - 102.063i) q^{4} +(-0.294487 - 0.510067i) q^{5} +(31.8040 + 906.935i) q^{7} +783.169 q^{8} +(0.938097 - 1.62483i) q^{10} +(-599.771 + 1038.83i) q^{11} +7651.01 q^{13} +(-2451.35 + 1532.27i) q^{14} +(-6295.16 - 10903.5i) q^{16} +(17592.9 - 30471.9i) q^{17} +(4286.72 + 7424.82i) q^{19} -69.4121 q^{20} -3821.17 q^{22} +(39366.9 + 68185.4i) q^{23} +(39062.3 - 67657.9i) q^{25} +(12186.2 + 21107.2i) q^{26} +(94438.8 + 50196.3i) q^{28} +199760. q^{29} +(-68557.2 + 118745. i) q^{31} +(70176.2 - 121549. i) q^{32} +112085. q^{34} +(453.232 - 283.303i) q^{35} +(-45042.1 - 78015.3i) q^{37} +(-13655.4 + 23651.9i) q^{38} +(-230.633 - 399.469i) q^{40} +269601. q^{41} +602901. q^{43} +(70684.5 + 122429. i) q^{44} +(-125404. + 217206. i) q^{46} +(-192458. - 333347. i) q^{47} +(-821520. + 57688.3i) q^{49} +248868. q^{50} +(450845. - 780887. i) q^{52} +(332119. - 575247. i) q^{53} +706.501 q^{55} +(24907.9 + 710283. i) q^{56} +(318170. + 551087. i) q^{58} +(-1.15394e6 + 1.99868e6i) q^{59} +(-449938. - 779316. i) q^{61} -436781. q^{62} -1.16446e6 q^{64} +(-2253.13 - 3902.53i) q^{65} +(-11879.4 + 20575.8i) q^{67} +(-2.07337e6 - 3.59118e6i) q^{68} +(1503.45 + 799.117i) q^{70} -2.52558e6 q^{71} +(-1.76425e6 + 3.05578e6i) q^{73} +(143483. - 248519. i) q^{74} +1.01040e6 q^{76} +(-961231. - 510915. i) q^{77} +(-2.31891e6 - 4.01647e6i) q^{79} +(-3707.69 + 6421.91i) q^{80} +(429410. + 743759. i) q^{82} -7.71353e6 q^{83} -20723.6 q^{85} +(960277. + 1.66325e6i) q^{86} +(-469722. + 813583. i) q^{88} +(4.39050e6 + 7.60457e6i) q^{89} +(243332. + 6.93897e6i) q^{91} +9.27896e6 q^{92} +(613079. - 1.06188e6i) q^{94} +(2524.77 - 4373.03i) q^{95} +4.42347e6 q^{97} +(-1.46763e6 - 2.17448e6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{2} - 348 q^{4} + 252 q^{5} + 672 q^{7} + 1968 q^{8} - 4774 q^{10} - 3972 q^{11} - 2352 q^{13} - 47502 q^{14} - 57264 q^{16} + 56364 q^{17} - 41748 q^{19} - 324744 q^{20} - 305908 q^{22} + 131748 q^{23}+ \cdots - 60255006 q^{98}+O(q^{100}) \) 8 * q - 6 * q^2 - 348 * q^4 + 252 * q^5 + 672 * q^7 + 1968 * q^8 - 4774 * q^10 - 3972 * q^11 - 2352 * q^13 - 47502 * q^14 - 57264 * q^16 + 56364 * q^17 - 41748 * q^19 - 324744 * q^20 - 305908 * q^22 + 131748 * q^23 + 68016 * q^25 + 113652 * q^26 + 681548 * q^28 - 68112 * q^29 - 401212 * q^31 - 453408 * q^32 + 164220 * q^34 - 40404 * q^35 + 5396 * q^37 + 31794 * q^38 + 443688 * q^40 - 820848 * q^41 + 93088 * q^43 - 1465836 * q^44 - 1379202 * q^46 + 1470084 * q^47 - 2793784 * q^49 - 2791056 * q^50 + 5269768 * q^52 - 642372 * q^53 - 6126680 * q^55 + 6195168 * q^56 + 1972220 * q^58 + 752220 * q^59 - 1325772 * q^61 + 6032628 * q^62 - 1731712 * q^64 - 4868808 * q^65 + 290916 * q^67 + 2453556 * q^68 + 11665990 * q^70 - 6755520 * q^71 - 6706588 * q^73 + 3616878 * q^74 + 5846008 * q^76 + 5310564 * q^77 - 3946244 * q^79 + 10695888 * q^80 + 17563252 * q^82 - 19084128 * q^83 + 14012136 * q^85 + 23237832 * q^86 + 8043336 * q^88 + 16165212 * q^89 - 2414720 * q^91 + 38885256 * q^92 - 5720442 * q^94 - 3268452 * q^95 + 3066224 * q^97 - 60255006 * q^98

Introduction

L-functions

Modular forms

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Database

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