LMFDB - Embedded newform 63.6.e.e.46.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,6,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, 6, names="a")

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

chi := DirichletCharacter("63.37");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
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:	$10.1041806482$
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} + 98x^{6} + 83x^{5} + 9122x^{4} - 91x^{3} + 28567x^{2} + 2058x + 86436 $ x^8 - x^7 + 98x^6 + 83x^5 + 9122x^4 - 91x^3 + 28567x^2 + 2058x + 86436
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			46.1
Root			$5.09061 + 8.81720i$ of defining polynomial
Character	$\chi$	$=$	63.46
Dual form			63.6.e.e.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.59061 - 7.95118i) q^{2} +(-26.1475 + 45.2888i) q^{4} +(11.0358 + 19.1146i) q^{5} +(126.882 + 26.6059i) q^{7} +186.333 q^{8} +O(q^{10})$	\(q+(-4.59061 - 7.95118i) q^{2} +(-26.1475 + 45.2888i) q^{4} +(11.0358 + 19.1146i) q^{5} +(126.882 + 26.6059i) q^{7} +186.333 q^{8} +(101.322 - 175.495i) q^{10} +(208.355 - 360.881i) q^{11} +797.918 q^{13} +(-370.920 - 1131.00i) q^{14} +(-18.6623 - 32.3240i) q^{16} +(-687.775 + 1191.26i) q^{17} +(-1156.51 - 2003.14i) q^{19} -1154.23 q^{20} -3825.91 q^{22} +(-477.701 - 827.402i) q^{23} +(1318.92 - 2284.44i) q^{25} +(-3662.93 - 6344.39i) q^{26} +(-4522.60 + 5050.67i) q^{28} +7035.29 q^{29} +(-630.596 + 1092.22i) q^{31} +(2809.98 - 4867.03i) q^{32} +12629.2 q^{34} +(891.689 + 2718.92i) q^{35} +(-4888.22 - 8466.65i) q^{37} +(-10618.2 + 18391.3i) q^{38} +(2056.33 + 3561.67i) q^{40} +5400.95 q^{41} +19686.6 q^{43} +(10895.9 + 18872.3i) q^{44} +(-4385.88 + 7596.57i) q^{46} +(1028.28 + 1781.04i) q^{47} +(15391.3 + 6751.63i) q^{49} -24218.7 q^{50} +(-20863.5 + 36136.7i) q^{52} +(9011.37 - 15608.2i) q^{53} +9197.45 q^{55} +(23642.3 + 4957.54i) q^{56} +(-32296.3 - 55938.8i) q^{58} +(3717.84 - 6439.49i) q^{59} +(-1747.69 - 3027.09i) q^{61} +11579.3 q^{62} -52792.5 q^{64} +(8805.67 + 15251.9i) q^{65} +(-7928.21 + 13732.1i) q^{67} +(-35967.2 - 62297.0i) q^{68} +(17525.2 - 19571.5i) q^{70} -58133.5 q^{71} +(-19555.3 + 33870.8i) q^{73} +(-44879.9 + 77734.2i) q^{74} +120960. q^{76} +(36038.1 - 40246.0i) q^{77} +(-4880.35 - 8453.01i) q^{79} +(411.906 - 713.442i) q^{80} +(-24793.7 - 42943.9i) q^{82} +70395.7 q^{83} -30360.6 q^{85} +(-90373.4 - 156531. i) q^{86} +(38823.3 - 67243.9i) q^{88} +(72153.1 + 124973. i) q^{89} +(101242. + 21229.3i) q^{91} +49962.7 q^{92} +(9440.90 - 16352.1i) q^{94} +(25526.1 - 44212.5i) q^{95} -79328.7 q^{97} +(-16971.9 - 153373. i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} - 69 q^{4} + 258 q^{7} - 246 q^{8}+O(q^{10}) $ 8 * q + 3 * q^2 - 69 * q^4 + 258 * q^7 - 246 * q^8	$ 8 q + 3 q^{2} - 69 q^{4} + 258 q^{7} - 246 q^{8} - 283 q^{10} + 402 q^{11} + 924 q^{13} - 1926 q^{14} - 3273 q^{16} + 276 q^{17} - 510 q^{19} - 9438 q^{20} + 2750 q^{22} + 6900 q^{23} - 2814 q^{25} - 15138 q^{26} - 26221 q^{28} - 1080 q^{29} + 6410 q^{31} + 15519 q^{32} + 42288 q^{34} + 33108 q^{35} - 15250 q^{37} - 41250 q^{38} + 8547 q^{40} - 8616 q^{41} + 58396 q^{43} + 70743 q^{44} - 61800 q^{46} - 15060 q^{47} - 64252 q^{49} + 14604 q^{50} + 47476 q^{52} + 13692 q^{53} + 146248 q^{55} + 15921 q^{56} - 52309 q^{58} + 34830 q^{59} + 5364 q^{61} - 32058 q^{62} - 146974 q^{64} + 66864 q^{65} + 5994 q^{67} - 58272 q^{68} - 4307 q^{70} - 178536 q^{71} - 59638 q^{73} - 185442 q^{74} + 42616 q^{76} + 75660 q^{77} + 44062 q^{79} - 33381 q^{80} - 57596 q^{82} + 416892 q^{83} + 72648 q^{85} - 136968 q^{86} - 87597 q^{88} - 77520 q^{89} + 104722 q^{91} - 316512 q^{92} + 73722 q^{94} - 221376 q^{95} - 377260 q^{97} - 382479 q^{98}+O(q^{100}) $ 8 * q + 3 * q^2 - 69 * q^4 + 258 * q^7 - 246 * q^8 - 283 * q^10 + 402 * q^11 + 924 * q^13 - 1926 * q^14 - 3273 * q^16 + 276 * q^17 - 510 * q^19 - 9438 * q^20 + 2750 * q^22 + 6900 * q^23 - 2814 * q^25 - 15138 * q^26 - 26221 * q^28 - 1080 * q^29 + 6410 * q^31 + 15519 * q^32 + 42288 * q^34 + 33108 * q^35 - 15250 * q^37 - 41250 * q^38 + 8547 * q^40 - 8616 * q^41 + 58396 * q^43 + 70743 * q^44 - 61800 * q^46 - 15060 * q^47 - 64252 * q^49 + 14604 * q^50 + 47476 * q^52 + 13692 * q^53 + 146248 * q^55 + 15921 * q^56 - 52309 * q^58 + 34830 * q^59 + 5364 * q^61 - 32058 * q^62 - 146974 * q^64 + 66864 * q^65 + 5994 * q^67 - 58272 * q^68 - 4307 * q^70 - 178536 * q^71 - 59638 * q^73 - 185442 * q^74 + 42616 * q^76 + 75660 * q^77 + 44062 * q^79 - 33381 * q^80 - 57596 * q^82 + 416892 * q^83 + 72648 * q^85 - 136968 * q^86 - 87597 * q^88 - 77520 * q^89 + 104722 * q^91 - 316512 * q^92 + 73722 * q^94 - 221376 * q^95 - 377260 * q^97 - 382479 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−4.59061	−	7.95118i	−0.811514	−	1.40558i	−0.911804	−	0.410625i	$-0.865311\pi$
$2$	−4.59061	−	7.95118i	−0.811514	−	1.40558i	0.100291	−	0.994958i	$-0.468023\pi$
$3$		0			0
$3$		0			0
$4$	−26.1475	+	45.2888i	−0.817109	+	1.41527i
$5$	11.0358	+	19.1146i	0.197414	+	0.341932i	0.947689	−	0.319194i	$-0.103412\pi$
$5$	11.0358	+	19.1146i	0.197414	+	0.341932i	−0.750275	+	0.661126i	$0.770079\pi$
$6$		0			0
$7$	126.882	+	26.6059i	0.978715	+	0.205226i
$7$	126.882	+	26.6059i	0.978715	+	0.205226i
$8$	186.333			1.02935
$9$		0			0
$10$	101.322	−	175.495i	0.320409	−	0.554965i
$11$	208.355	−	360.881i	0.519184	−	0.899254i	−0.480567	−	0.876958i	$-0.659569\pi$
$11$	208.355	−	360.881i	0.519184	−	0.899254i	0.999751	−	0.0222959i	$-0.00709758\pi$
$12$		0			0
$13$	797.918			1.30948			0.654742	−	0.755853i	$-0.272777\pi$
$13$	797.918			1.30948			0.654742	+	0.755853i	$0.272777\pi$
$14$	−370.920	−	1131.00i	−0.505778	−	1.54221i
$15$		0			0
$16$	−18.6623	−	32.3240i	−0.0182249	−	0.0315664i
$17$	−687.775	+	1191.26i	−0.577197	+	0.999735i	0.418602	+	0.908170i	$0.362520\pi$
$17$	−687.775	+	1191.26i	−0.577197	+	0.999735i	−0.995799	+	0.0915652i	$0.970813\pi$
$18$		0			0
$19$	−1156.51	−	2003.14i	−0.734965	−	1.27300i	−0.954739	−	0.297446i	$-0.903865\pi$
$19$	−1156.51	−	2003.14i	−0.734965	−	1.27300i	0.219774	−	0.975551i	$-0.429468\pi$
$20$	−1154.23			−0.645236
$21$		0			0
$22$	−3825.91			−1.68530
$23$	−477.701	−	827.402i	−0.188294	−	0.326135i	0.756388	−	0.654124i	$-0.226962\pi$
$23$	−477.701	−	827.402i	−0.188294	−	0.326135i	−0.944682	+	0.327989i	$0.893629\pi$
$24$		0			0
$25$	1318.92	−	2284.44i	0.422055	−	0.731021i
$26$	−3662.93	−	6344.39i	−1.06266	−	1.84059i
$27$		0			0
$28$	−4522.60	+	5050.67i	−1.09017	+	1.21746i
$29$	7035.29			1.55341			0.776707	−	0.629862i	$-0.216889\pi$
$29$	7035.29			1.55341			0.776707	+	0.629862i	$0.216889\pi$
$30$		0			0
$31$	−630.596	+	1092.22i	−0.117855	+	0.204130i	−0.918917	−	0.394450i	$-0.870935\pi$
$31$	−630.596	+	1092.22i	−0.117855	+	0.204130i	0.801063	+	0.598581i	$0.204268\pi$
$32$	2809.98	−	4867.03i	0.485097	−	0.840212i
$33$		0			0
$34$	12629.2			1.87361
$35$	891.689	+	2718.92i	0.123039	+	0.375168i
$36$		0			0
$37$	−4888.22	−	8466.65i	−0.587012	−	1.01673i	−0.994621	−	0.103578i	$-0.966971\pi$
$37$	−4888.22	−	8466.65i	−0.587012	−	1.01673i	0.407610	−	0.913156i	$-0.366362\pi$
$38$	−10618.2	+	18391.3i	−1.19287	+	2.06611i
$39$		0			0
$40$	2056.33	+	3561.67i	0.203209	+	0.351968i
$41$	5400.95			0.501777			0.250888	−	0.968016i	$-0.419277\pi$
$41$	5400.95			0.501777			0.250888	+	0.968016i	$0.419277\pi$
$42$		0			0
$43$	19686.6			1.62367			0.811837	−	0.583885i	$-0.198468\pi$
$43$	19686.6			1.62367			0.811837	+	0.583885i	$0.198468\pi$
$44$	10895.9	+	18872.3i	0.848460	+	1.46958i
$45$		0			0
$46$	−4385.88	+	7596.57i	−0.305606	+	0.529326i
$47$	1028.28	+	1781.04i	0.0678997	+	0.117606i	0.897977	−	0.440043i	$-0.145037\pi$
$47$	1028.28	+	1781.04i	0.0678997	+	0.117606i	−0.830077	+	0.557649i	$0.811704\pi$
$48$		0			0
$49$	15391.3	+	6751.63i	0.915765	+	0.401715i
$50$	−24218.7			−1.37001
$51$		0			0
$52$	−20863.5	+	36136.7i	−1.06999	+	1.85328i
$53$	9011.37	−	15608.2i	0.440658	−	0.763241i	−0.557081	−	0.830458i	$-0.688079\pi$
$53$	9011.37	−	15608.2i	0.440658	−	0.763241i	0.997738	+	0.0672170i	$0.0214120\pi$
$54$		0			0
$55$	9197.45			0.409978
$56$	23642.3	+	4957.54i	1.00744	+	0.211250i
$57$		0			0
$58$	−32296.3	−	55938.8i	−1.26062	−	2.18345i
$59$	3717.84	−	6439.49i	0.139047	−	0.240836i	−0.788089	−	0.615561i	$-0.788930\pi$
$59$	3717.84	−	6439.49i	0.139047	−	0.240836i	0.927136	+	0.374725i	$0.122263\pi$
$60$		0			0
$61$	−1747.69	−	3027.09i	−0.0601368	−	0.104160i	0.834390	−	0.551175i	$-0.185820\pi$
$61$	−1747.69	−	3027.09i	−0.0601368	−	0.104160i	−0.894526	+	0.447015i	$0.852487\pi$
$62$	11579.3			0.382563
$63$		0			0
$64$	−52792.5			−1.61110
$65$	8805.67	+	15251.9i	0.258511	+	0.447754i
$66$		0			0
$67$	−7928.21	+	13732.1i	−0.215769	+	0.373722i	−0.953510	−	0.301361i	$-0.902559\pi$
$67$	−7928.21	+	13732.1i	−0.215769	+	0.373722i	0.737741	+	0.675083i	$0.235892\pi$
$68$	−35967.2	−	62297.0i	−0.943266	−	1.63378i
$69$		0			0
$70$	17525.2	−	19571.5i	0.427482	−	0.477396i
$71$	−58133.5			−1.36861			−0.684306	−	0.729195i	$-0.739895\pi$
$71$	−58133.5			−1.36861			−0.684306	+	0.729195i	$0.739895\pi$
$72$		0			0
$73$	−19555.3	+	33870.8i	−0.429495	+	0.743907i	−0.996828	−	0.0795812i	$-0.974642\pi$
$73$	−19555.3	+	33870.8i	−0.429495	+	0.743907i	0.567334	+	0.823488i	$0.307975\pi$
$74$	−44879.9	+	77734.2i	−0.952736	+	1.65019i
$75$		0			0
$76$	120960.			2.40218
$77$	36038.1	−	40246.0i	0.692684	−	0.773563i
$78$		0			0
$79$	−4880.35	−	8453.01i	−0.0879798	−	0.152385i	0.818677	−	0.574254i	$-0.194708\pi$
$79$	−4880.35	−	8453.01i	−0.0879798	−	0.152385i	−0.906657	+	0.421868i	$0.861374\pi$
$80$	411.906	−	713.442i	0.00719570	−	0.0124633i
$81$		0			0
$82$	−24793.7	−	42943.9i	−0.407199	−	0.705289i
$83$	70395.7			1.12163			0.560816	−	0.827940i	$-0.310487\pi$
$83$	70395.7			1.12163			0.560816	+	0.827940i	$0.310487\pi$
$84$		0			0
$85$	−30360.6			−0.455788
$86$	−90373.4	−	156531.i	−1.31763	−	2.28221i
$87$		0			0
$88$	38823.3	−	67243.9i	0.534424	−	0.925649i
$89$	72153.1	+	124973.i	0.965562	+	1.67240i	0.708098	+	0.706115i	$0.249554\pi$
$89$	72153.1	+	124973.i	0.965562	+	1.67240i	0.257464	+	0.966288i	$0.417113\pi$
$90$		0			0
$91$	101242.	+	21229.3i	1.28161	+	0.268740i
$92$	49962.7			0.615427
$93$		0			0
$94$	9440.90	−	16352.1i	0.110203	−	0.190877i
$95$	25526.1	−	44212.5i	0.290185	−	0.502616i
$96$		0			0
$97$	−79328.7			−0.856053			−0.428027	−	0.903766i	$-0.640791\pi$
$97$	−79328.7			−0.856053			−0.428027	+	0.903766i	$0.640791\pi$
$98$	−16971.9	−	153373.i	−0.178511	−	1.61318i
$99$		0			0
$100$	68973.0	+	119465.i	0.689730	+	1.19465i
$101$	−42416.9	+	73468.2i	−0.413747	+	0.716631i	−0.995296	−	0.0968802i	$-0.969114\pi$
$101$	−42416.9	+	73468.2i	−0.413747	+	0.716631i	0.581549	+	0.813512i	$0.302447\pi$
$102$		0			0
$103$	−10166.1	−	17608.3i	−0.0944197	−	0.163540i	0.814947	−	0.579536i	$-0.196766\pi$
$103$	−10166.1	−	17608.3i	−0.0944197	−	0.163540i	−0.909366	+	0.415996i	$0.863433\pi$
$104$	148678.			1.34792
$105$		0			0
$106$	−165471.			−1.43040
$107$	3481.09	+	6029.43i	0.0293938	+	0.0509116i	0.880348	−	0.474328i	$-0.157309\pi$
$107$	3481.09	+	6029.43i	0.0293938	+	0.0509116i	−0.850954	+	0.525240i	$0.823976\pi$
$108$		0			0
$109$	−56325.7	+	97559.0i	−0.454088	+	0.786504i	−0.998635	−	0.0522262i	$-0.983368\pi$
$109$	−56325.7	+	97559.0i	−0.454088	+	0.786504i	0.544547	+	0.838730i	$0.316702\pi$
$110$	−42221.9	−	73130.5i	−0.332703	−	0.576258i
$111$		0			0
$112$	−1507.90	−	4597.87i	−0.0113587	−	0.0346347i
$113$	−112005.			−0.825167			−0.412583	−	0.910920i	$-0.635373\pi$
$113$	−112005.			−0.825167			−0.412583	+	0.910920i	$0.635373\pi$
$114$		0			0
$115$	10543.6	−	18262.1i	0.0743439	−	0.128767i
$116$	−183955.	+	318620.i	−1.26931	+	2.19851i
$117$		0			0
$118$	−68268.7			−0.451353
$119$	−118961.	+	132851.i	−0.770083	+	0.860000i
$120$		0			0
$121$	−6297.91	−	10908.3i	−0.0391051	−	0.0677320i
$122$	−16046.0	+	27792.4i	−0.0976037	+	0.169055i
$123$		0			0
$124$	−32977.0	−	57117.8i	−0.192600	−	0.333593i
$125$	127195.			0.728108
$126$		0			0
$127$	82224.5			0.452368			0.226184	−	0.974085i	$-0.427375\pi$
$127$	82224.5			0.452368			0.226184	+	0.974085i	$0.427375\pi$
$128$	152431.	+	264018.i	0.822333	+	1.42432i
$129$		0			0
$130$	80846.8	−	140031.i	0.419570	−	0.726717i
$131$	−87905.9	−	152258.i	−0.447548	−	0.775176i	0.550677	−	0.834718i	$-0.314369\pi$
$131$	−87905.9	−	152258.i	−0.447548	−	0.775176i	−0.998226	+	0.0595417i	$0.981036\pi$
$132$		0			0
$133$	−93445.8	−	284933.i	−0.458069	−	1.39673i
$134$	145581.			0.700397
$135$		0			0
$136$	−128155.	+	221971.i	−0.594140	+	1.02908i
$137$	15665.2	−	27132.9i	0.0713072	−	0.123508i	−0.828167	−	0.560481i	$-0.810616\pi$
$137$	15665.2	−	27132.9i	0.0713072	−	0.123508i	0.899474	+	0.436973i	$0.143950\pi$
$138$		0			0
$139$	152234.			0.668305			0.334152	−	0.942519i	$-0.391550\pi$
$139$	152234.			0.668305			0.334152	+	0.942519i	$0.391550\pi$
$140$	−146452.	−	30709.4i	−0.631502	−	0.132419i
$141$		0			0
$142$	266868.	+	462229.i	1.11065	+	1.92370i
$143$	166250.	−	287953.i	0.679863	−	1.17756i
$144$		0			0
$145$	77640.1	+	134477.i	0.306666	+	0.531162i
$146$	359084.			1.39416
$147$		0			0
$148$	511259.			1.91861
$149$	181430.	+	314246.i	0.669489	+	1.15959i	0.978047	+	0.208384i	$0.0668203\pi$
$149$	181430.	+	314246.i	0.669489	+	1.15959i	−0.308558	+	0.951206i	$0.599846\pi$
$150$		0			0
$151$	−102563.	+	177644.i	−0.366056	+	0.634027i	−0.988945	−	0.148283i	$-0.952625\pi$
$151$	−102563.	+	177644.i	−0.366056	+	0.634027i	0.622889	+	0.782310i	$0.285959\pi$
$152$	−215496.	−	373250.i	−0.756538	−	1.31036i
$153$		0			0
$154$	−485440.	−	101792.i	−1.64943	−	0.345868i
$155$	−27836.5			−0.0930648
$156$		0			0
$157$	38636.0	−	66919.5i	0.125096	−	0.216672i	−0.796675	−	0.604409i	$-0.793409\pi$
$157$	38636.0	−	66919.5i	0.125096	−	0.216672i	0.921770	+	0.387736i	$0.126743\pi$
$158$	−44807.6	+	77609.0i	−0.142794	+	0.247326i
$159$		0			0
$160$	124042.			0.383060
$161$	−38598.1	−	117692.i	−0.117355	−	0.357836i
$162$		0			0
$163$	−92465.7	−	160155.i	−0.272591	−	0.472141i	0.696934	−	0.717136i	$-0.254547\pi$
$163$	−92465.7	−	160155.i	−0.272591	−	0.472141i	−0.969525	+	0.244994i	$0.921214\pi$
$164$	−141221.	+	244602.i	−0.410006	+	0.710152i
$165$		0			0
$166$	−323159.	−	559728.i	−0.910220	−	1.57655i
$167$	−129262.			−0.358657			−0.179329	−	0.983789i	$-0.557393\pi$
$167$	−129262.			−0.358657			−0.179329	+	0.983789i	$0.557393\pi$
$168$		0			0
$169$	265380.			0.714746
$170$	139374.	+	241403.i	0.369878	+	0.640648i
$171$		0			0
$172$	−514754.	+	891580.i	−1.32672	+	2.29794i
$173$	−253934.	−	439826.i	−0.645067	−	1.11729i	−0.984286	−	0.176582i	$-0.943496\pi$
$173$	−253934.	−	439826.i	−0.645067	−	1.11729i	0.339219	−	0.940707i	$-0.389837\pi$
$174$		0			0
$175$	228127.	−	254764.i	0.563096	−	0.628844i
$176$	−15553.5			−0.0378483
$177$		0			0
$178$	662454.	−	1.14740e6i	1.56713	−	2.71435i
$179$	−66294.5	+	114825.i	−0.154648	+	0.267859i	−0.932931	−	0.360056i	$-0.882758\pi$
$179$	−66294.5	+	114825.i	−0.154648	+	0.267859i	0.778283	+	0.627914i	$0.216091\pi$
$180$		0			0
$181$	−740060.			−1.67908			−0.839538	−	0.543301i	$-0.817174\pi$
$181$	−740060.			−1.67908			−0.839538	+	0.543301i	$0.817174\pi$
$182$	−295964.	−	902446.i	−0.662308	−	2.01950i
$183$		0			0
$184$	−89011.3	−	154172.i	−0.193821	−	0.335708i
$185$	107891.	−	186873.i	0.231769	−	0.401436i
$186$		0			0
$187$	286603.	+	496410.i	0.599344	+	1.03809i
$188$	−107548.			−0.221926
$189$		0			0
$190$	−468722.			−0.941957
$191$	−291366.	−	504661.i	−0.577904	−	1.00096i	−0.995719	−	0.0924273i	$-0.970537\pi$
$191$	−291366.	−	504661.i	−0.577904	−	1.00096i	0.417815	−	0.908532i	$-0.362796\pi$
$192$		0			0
$193$	200452.	−	347193.i	0.387362	−	0.670931i	−0.604731	−	0.796429i	$-0.706720\pi$
$193$	200452.	−	347193.i	0.387362	−	0.670931i	0.992094	+	0.125498i	$0.0400529\pi$
$194$	364167.	+	630756.i	0.694699	+	1.20325i
$195$		0			0
$196$	−708216.	+	520513.i	−1.31682	+	0.967813i
$197$	−671589.			−1.23293			−0.616464	−	0.787383i	$-0.711436\pi$
$197$	−671589.			−1.23293			−0.616464	+	0.787383i	$0.711436\pi$
$198$		0			0
$199$	227511.	−	394060.i	0.407258	−	0.705391i	−0.587324	−	0.809352i	$-0.699818\pi$
$199$	227511.	−	394060.i	0.407258	−	0.705391i	0.994581	+	0.103961i	$0.0331518\pi$
$200$	245758.	−	425666.i	0.434443	−	0.752478i
$201$		0			0
$202$	778878.			1.34305
$203$	892654.	+	187180.i	1.52035	+	0.318801i
$204$		0			0
$205$	59603.8	+	103237.i	0.0990580	+	0.171573i
$206$	−93337.6	+	161665.i	−0.153246	+	0.265430i
$207$		0			0
$208$	−14891.0	−	25791.9i	−0.0238652	−	0.0413357i
$209$	−963860.			−1.52633
$210$		0			0
$211$	−1.19545e6			−1.84852			−0.924260	−	0.381764i	$-0.875317\pi$
$211$	−1.19545e6			−1.84852			−0.924260	+	0.381764i	$0.875317\pi$
$212$	471249.	+	816228.i	0.720130	+	1.24730i
$213$		0			0
$214$	31960.7	−	55357.6i	0.0477070	−	0.0826310i
$215$	217257.	+	376300.i	0.320537	+	0.555186i
$216$		0			0
$217$	−109071.	+	121806.i	−0.157239	+	0.175598i
$218$	1.03428e6			1.47400
$219$		0			0
$220$	−240490.	+	416541.i	−0.334997	+	0.580231i
$221$	−548788.	+	950529.i	−0.755830	+	1.30914i
$222$		0			0
$223$	296529.			0.399305			0.199653	−	0.979867i	$-0.436019\pi$
$223$	296529.			0.399305			0.199653	+	0.979867i	$0.436019\pi$
$224$	486029.	−	542778.i	0.647205	−	0.722774i
$225$		0			0
$226$	514172.	+	890573.i	0.669634	+	1.15984i
$227$	109073.	−	188920.i	0.140492	−	0.243340i	−0.787190	−	0.616711i	$-0.788465\pi$
$227$	109073.	−	188920.i	0.140492	−	0.243340i	0.927682	+	0.373371i	$0.121798\pi$
$228$		0			0
$229$	614602.	+	1.06452e6i	0.774471	+	1.34142i	0.935091	+	0.354407i	$0.115317\pi$
$229$	614602.	+	1.06452e6i	0.774471	+	1.34142i	−0.160620	+	0.987016i	$0.551349\pi$
$230$	−193607.			−0.241324
$231$		0			0
$232$	1.31090e6			1.59901
$233$	−31472.1	−	54511.3i	−0.0379784	−	0.0657805i	0.846411	−	0.532530i	$-0.178758\pi$
$233$	−31472.1	−	54511.3i	−0.0379784	−	0.0657805i	−0.884390	+	0.466749i	$0.845425\pi$
$234$		0			0
$235$	−22695.8	+	39310.4i	−0.0268088	+	0.0464341i
$236$	194424.	+	336753.i	0.227233	+	0.393578i
$237$		0			0
$238$	1.60243e6	+	336012.i	1.83373	+	0.384514i
$239$	−219330.			−0.248372			−0.124186	−	0.992259i	$-0.539632\pi$
$239$	−219330.			−0.248372			−0.124186	+	0.992259i	$0.539632\pi$
$240$		0			0
$241$	−216932.	+	375737.i	−0.240592	+	0.416717i	−0.960883	−	0.276955i	$-0.910675\pi$
$241$	−216932.	+	375737.i	−0.240592	+	0.416717i	0.720291	+	0.693672i	$0.244008\pi$
$242$	−57822.6	+	100152.i	−0.0634686	+	0.109931i
$243$		0			0
$244$	182791.			0.196553
$245$	40800.4	+	368707.i	0.0434259	+	0.392433i
$246$		0			0
$247$	−922803.	−	1.59834e6i	−0.962424	−	1.66697i
$248$	−117501.	+	203517.i	−0.121314	+	0.210122i
$249$		0			0
$250$	−583904.	−	1.01135e6i	−0.590870	−	1.02342i
$251$	1.71109e6			1.71431			0.857155	−	0.515059i	$-0.172230\pi$
$251$	1.71109e6			1.71431			0.857155	+	0.515059i	$0.172230\pi$
$252$		0			0
$253$	−398125.			−0.391037
$254$	−377461.	−	653782.i	−0.367103	−	0.635841i
$255$		0			0
$256$	554822.	−	960979.i	0.529119	−	0.916461i
$257$	492029.	+	852219.i	0.464684	+	0.804856i	0.999187	−	0.0403103i	$-0.0128346\pi$
$257$	492029.	+	852219.i	0.464684	+	0.804856i	−0.534503	+	0.845166i	$0.679501\pi$
$258$		0			0
$259$	−394967.	−	1.20432e6i	−0.365857	−	1.11556i
$260$	−920984.			−0.844926
$261$		0			0
$262$	−807084.	+	1.39791e6i	−0.726383	+	1.25813i
$263$	273548.	−	473799.i	0.243862	−	0.422381i	−0.717949	−	0.696096i	$-0.754919\pi$
$263$	273548.	−	473799.i	0.243862	−	0.422381i	0.961811	+	0.273714i	$0.0882523\pi$
$264$		0			0
$265$	397791.			0.347969
$266$	−1.83658e6	+	2.05102e6i	−1.59150	+	1.77732i
$267$		0			0
$268$	−414605.	−	718118.i	−0.352613	−	0.610743i
$269$	−320556.	+	555219.i	−0.270099	+	0.467825i	−0.968887	−	0.247504i	$-0.920390\pi$
$269$	−320556.	+	555219.i	−0.270099	+	0.467825i	0.698788	+	0.715329i	$0.253723\pi$
$270$		0			0
$271$	274006.	+	474593.i	0.226640	+	0.392552i	0.956810	−	0.290713i	$-0.0938925\pi$
$271$	274006.	+	474593.i	0.226640	+	0.392552i	−0.730170	+	0.683265i	$0.760559\pi$
$272$	51341.8			0.0420774
$273$		0			0
$274$	−287651.			−0.231467
$275$	−549607.	−	951948.i	−0.438249	−	0.759069i
$276$		0			0
$277$	−837070.	+	1.44985e6i	−0.655485	+	1.13533i	0.326287	+	0.945271i	$0.394202\pi$
$277$	−837070.	+	1.44985e6i	−0.655485	+	1.13533i	−0.981772	+	0.190062i	$0.939131\pi$
$278$	−698847.	−	1.21044e6i	−0.542338	−	0.939358i
$279$		0			0
$280$	166151.	+	506623.i	0.126651	+	0.386180i
$281$	−1.81078e6			−1.36804			−0.684021	−	0.729462i	$-0.739770\pi$
$281$	−1.81078e6			−1.36804			−0.684021	+	0.729462i	$0.739770\pi$
$282$		0			0
$283$	−1.25657e6	+	2.17645e6i	−0.932657	+	1.61541i	−0.153898	+	0.988087i	$0.549183\pi$
$283$	−1.25657e6	+	2.17645e6i	−0.932657	+	1.61541i	−0.778759	+	0.627323i	$0.784151\pi$
$284$	1.52004e6	−	2.63279e6i	1.11830	−	1.93696i
$285$		0			0
$286$	−3.05276e6			−2.20687
$287$	685285.	+	143697.i	0.491096	+	0.102978i
$288$		0			0
$289$	−236142.	−	409009.i	−0.166314	−	0.288064i
$290$	712831.	−	1.23466e6i	0.497728	−	0.862090i
$291$		0			0
$292$	−1.02265e6	−	1.77127e6i	−0.701888	−	1.21571i
$293$	−107228.			−0.0729691			−0.0364845	−	0.999334i	$-0.511616\pi$
$293$	−107228.			−0.0729691			−0.0364845	+	0.999334i	$0.511616\pi$
$294$		0			0
$295$	164117.			0.109799
$296$	−910836.	−	1.57761e6i	−0.604242	−	1.04658i
$297$		0			0
$298$	1.66575e6	−	2.88517e6i	1.08660	−	1.88205i
$299$	−381166.	−	660199.i	−0.246568	−	0.427068i
$300$		0			0
$301$	2.49788e6	+	523778.i	1.58911	+	0.333220i
$302$	1.88330e6			1.18824
$303$		0			0
$304$	−43166.3	+	74766.2i	−0.0267893	+	0.0464004i
$305$	38574.4	−	66812.8i	0.0237437	−	0.0411254i
$306$		0			0
$307$	1.49622e6			0.906042			0.453021	−	0.891500i	$-0.350346\pi$
$307$	1.49622e6			0.906042			0.453021	+	0.891500i	$0.350346\pi$
$308$	880385.	+	2.68445e6i	0.528805	+	1.61242i
$309$		0			0
$310$	127787.	+	221333.i	0.0755234	+	0.130810i
$311$	430601.	−	745823.i	0.252449	−	0.437255i	−0.711750	−	0.702433i	$-0.752097\pi$
$311$	430601.	−	745823.i	0.252449	−	0.437255i	0.964200	+	0.265178i	$0.0854306\pi$
$312$		0			0
$313$	251969.	+	436422.i	0.145374	+	0.251794i	0.929512	−	0.368791i	$-0.120228\pi$
$313$	251969.	+	436422.i	0.145374	+	0.251794i	−0.784139	+	0.620586i	$0.786895\pi$
$314$	−709452.			−0.406068
$315$		0			0
$316$	510435.			0.287556
$317$	−240004.	−	415700.i	−0.134144	−	0.232344i	0.791126	−	0.611653i	$-0.209495\pi$
$317$	−240004.	−	415700.i	−0.134144	−	0.232344i	−0.925270	+	0.379309i	$0.876162\pi$
$318$		0			0
$319$	1.46584e6	−	2.53890e6i	0.806508	−	1.39691i
$320$	−582608.	−	1.00911e6i	−0.318055	−	0.550887i
$321$		0			0
$322$	−758604.	+	847180.i	−0.407733	+	0.455340i
$323$	3.18168e6			1.69688
$324$		0			0
$325$	1.05239e6	−	1.82280e6i	0.552674	−	0.957259i
$326$	−848948.	+	1.47042e6i	−0.442423	+	0.766298i
$327$		0			0
$328$	1.00637e6			0.516505
$329$	83084.8	+	253341.i	0.0423187	+	0.129037i
$330$		0			0
$331$	1.09961e6	+	1.90458e6i	0.551656	+	0.955497i	0.998155	+	0.0607125i	$0.0193373\pi$
$331$	1.09961e6	+	1.90458e6i	0.551656	+	0.955497i	−0.446499	+	0.894784i	$0.647329\pi$
$332$	−1.84067e6	+	3.18813e6i	−0.916496	+	1.58742i
$333$		0			0
$334$	593392.	+	1.02778e6i	0.291055	+	0.504122i
$335$	−349977.			−0.170383
$336$		0			0
$337$	−1.35725e6			−0.651008			−0.325504	−	0.945541i	$-0.605534\pi$
$337$	−1.35725e6			−0.651008			−0.325504	+	0.945541i	$0.605534\pi$
$338$	−1.21826e6	−	2.11008e6i	−0.580026	−	1.00463i
$339$		0			0
$340$	793854.	−	1.37499e6i	0.372429	−	0.645065i
$341$	262775.	+	455140.i	0.122377	+	0.211963i
$342$		0			0
$343$	1.77325e6	+	1.26616e6i	0.813830	+	0.581103i
$344$	3.66825e6			1.67133
$345$		0			0
$346$	−2.33142e6	+	4.03814e6i	−1.04696	+	1.81339i
$347$	1.89970e6	−	3.29038e6i	0.846959	−	1.46698i	−0.0369507	−	0.999317i	$-0.511764\pi$
$347$	1.89970e6	−	3.29038e6i	0.846959	−	1.46698i	0.883909	−	0.467658i	$-0.154902\pi$
$348$		0			0
$349$	−1.31753e6			−0.579024			−0.289512	−	0.957174i	$-0.593493\pi$
$349$	−1.31753e6			−0.579024			−0.289512	+	0.957174i	$0.593493\pi$
$350$	−3.07292e6	−	644358.i	−1.34085	−	0.281162i
$351$		0			0
$352$	−1.17095e6	−	2.02814e6i	−0.503710	−	0.872451i
$353$	−1.71253e6	+	2.96618e6i	−0.731477	+	1.26695i	0.224775	+	0.974411i	$0.427835\pi$
$353$	−1.71253e6	+	2.96618e6i	−0.731477	+	1.26695i	−0.956252	+	0.292544i	$0.905498\pi$
$354$		0			0
$355$	−641549.	−	1.11120e6i	−0.270184	−	0.467972i
$356$	−7.54649e6			−3.15588
$357$		0			0
$358$	1.21733e6			0.501997
$359$	735419.	+	1.27378e6i	0.301161	+	0.521626i	0.976399	−	0.215974i	$-0.0692925\pi$
$359$	735419.	+	1.27378e6i	0.301161	+	0.521626i	−0.675238	+	0.737600i	$0.735959\pi$
$360$		0			0
$361$	−1.43700e6	+	2.48895e6i	−0.580347	+	1.00519i
$362$	3.39733e6	+	5.88435e6i	1.36259	+	2.36008i
$363$		0			0
$364$	−3.60866e6	+	4.03002e6i	−1.42756	+	1.59424i
$365$	−863235.			−0.339154
$366$		0			0
$367$	2.49039e6	−	4.31349e6i	0.965168	−	1.67172i	0.256006	−	0.966675i	$-0.417593\pi$
$367$	2.49039e6	−	4.31349e6i	0.965168	−	1.67172i	0.709163	−	0.705045i	$-0.249073\pi$
$368$	−17830.0	+	30882.4i	−0.00686326	+	0.0118875i
$369$		0			0
$370$	−1.98114e6			−0.752335
$371$	1.55865e6	−	1.74064e6i	0.587915	−	0.656561i
$372$		0			0
$373$	−1.98024e6	−	3.42987e6i	−0.736962	−	1.27646i	−0.953857	−	0.300261i	$-0.902926\pi$
$373$	−1.98024e6	−	3.42987e6i	−0.736962	−	1.27646i	0.216895	−	0.976195i	$-0.430407\pi$
$374$	2.63136e6	−	4.55766e6i	0.972751	−	1.68485i
$375$		0			0
$376$	191603.	+	331866.i	0.0698927	+	0.121058i
$377$	5.61359e6			2.03417
$378$		0			0
$379$	−1.75155e6			−0.626359			−0.313179	−	0.949694i	$-0.601394\pi$
$379$	−1.75155e6			−0.626359			−0.313179	+	0.949694i	$0.601394\pi$
$380$	1.33489e6	+	2.31209e6i	0.474226	+	0.821384i
$381$		0			0
$382$	−2.67510e6	+	4.63341e6i	−0.937954	+	1.62458i
$383$	1.56917e6	+	2.71788e6i	0.546604	+	0.946745i	0.998504	+	0.0546771i	$0.0174129\pi$
$383$	1.56917e6	+	2.71788e6i	0.546604	+	0.946745i	−0.451900	+	0.892068i	$0.649254\pi$
$384$		0			0
$385$	1.16699e6	+	244706.i	0.401252	+	0.0841381i
$386$	−3.68079e6			−1.25740
$387$		0			0
$388$	2.07425e6	−	3.59270e6i	0.699489	−	1.21155i
$389$	−526262.	+	911512.i	−0.176331	+	0.305414i	−0.940621	−	0.339459i	$-0.889756\pi$
$389$	−526262.	+	911512.i	−0.176331	+	0.305414i	0.764290	+	0.644872i	$0.223089\pi$
$390$		0			0
$391$	1.31420e6			0.434731
$392$	2.86789e6	+	1.25805e6i	0.942645	+	0.413507i
$393$		0			0
$394$	3.08301e6	+	5.33992e6i	1.00054	+	1.73298i
$395$	107717.	−	186571.i	0.0347370	−	0.0601662i
$396$		0			0
$397$	−227362.	−	393803.i	−0.0724005	−	0.125401i	0.827552	−	0.561389i	$-0.189733\pi$
$397$	−227362.	−	393803.i	−0.0724005	−	0.125401i	−0.899953	+	0.435987i	$0.856399\pi$
$398$	−4.17766e6			−1.32198
$399$		0			0
$400$	−98456.3			−0.0307676
$401$	−1.44216e6	−	2.49789e6i	−0.447870	−	0.775733i	0.550378	−	0.834916i	$-0.314484\pi$
$401$	−1.44216e6	−	2.49789e6i	−0.447870	−	0.775733i	−0.998247	+	0.0591831i	$0.981150\pi$
$402$		0			0
$403$	−503164.	+	871505.i	−0.154329	+	0.267305i
$404$	−2.21819e6	−	3.84202e6i	−0.676153	−	1.17113i
$405$		0			0
$406$	−2.60953e6	−	7.95692e6i	−0.785683	−	2.39569i
$407$	−4.07394e6			−1.21907
$408$		0			0
$409$	112957.	−	195647.i	0.0333891	−	0.0578317i	−0.848848	−	0.528637i	$-0.822703\pi$
$409$	112957.	−	195647.i	0.0333891	−	0.0578317i	0.882237	+	0.470805i	$0.156037\pi$
$410$	547236.	−	947841.i	0.160774	−	0.278468i
$411$		0			0
$412$	1.06328e6			0.308605
$413$	643056.	−	718141.i	0.185513	−	0.207174i
$414$		0			0
$415$	776873.	+	1.34558e6i	0.221426	+	0.383522i
$416$	2.24213e6	−	3.88349e6i	0.635226	−	1.10024i
$417$		0			0
$418$	4.42471e6	+	7.66382e6i	1.23864	+	2.14538i
$419$	−4.31027e6			−1.19941			−0.599707	−	0.800220i	$-0.704716\pi$
$419$	−4.31027e6			−1.19941			−0.599707	+	0.800220i	$0.704716\pi$
$420$		0			0
$421$	1.25088e6			0.343962			0.171981	−	0.985100i	$-0.444983\pi$
$421$	1.25088e6			0.343962			0.171981	+	0.985100i	$0.444983\pi$
$422$	5.48784e6	+	9.50521e6i	1.50010	+	2.59825i
$423$		0			0
$424$	1.67911e6	−	2.90831e6i	0.453592	−	0.785644i
$425$	1.81424e6	+	3.14236e6i	0.487218	+	0.843887i
$426$		0			0
$427$	−141213.	−	430583.i	−0.0374804	−	0.114285i
$428$	−364087.			−0.0960719
$429$		0			0
$430$	1.99469e6	−	3.45490e6i	0.520240	−	0.901081i
$431$	−2.20397e6	+	3.81738e6i	−0.571494	+	0.989857i	0.424919	+	0.905231i	$0.360303\pi$
$431$	−2.20397e6	+	3.81738e6i	−0.571494	+	0.989857i	−0.996413	+	0.0846252i	$0.973031\pi$
$432$		0			0
$433$	−1.60951e6			−0.412549			−0.206274	−	0.978494i	$-0.566134\pi$
$433$	−1.60951e6			−0.412549			−0.206274	+	0.978494i	$0.566134\pi$
$434$	1.46921e6	+	308077.i	0.374420	+	0.0785118i
$435$		0			0
$436$	−2.94555e6	−	5.10184e6i	−0.742079	−	1.28532i
$437$	−1.10493e6	+	1.91380e6i	−0.276779	+	0.479395i
$438$		0			0
$439$	2.21226e6	+	3.83175e6i	0.547867	+	0.948933i	0.998420	+	0.0561836i	$0.0178932\pi$
$439$	2.21226e6	+	3.83175e6i	0.547867	+	0.948933i	−0.450554	+	0.892749i	$0.648773\pi$
$440$	1.71379e6			0.422012
$441$		0			0
$442$	1.00771e7			2.45347
$443$	−1.80719e6	−	3.13015e6i	−0.437517	−	0.757801i	0.559980	−	0.828506i	$-0.310809\pi$
$443$	−1.80719e6	−	3.13015e6i	−0.437517	−	0.757801i	−0.997497	+	0.0707044i	$0.977475\pi$
$444$		0			0
$445$	−1.59254e6	+	2.75835e6i	−0.381232	+	0.660313i
$446$	−1.36125e6	−	2.35776e6i	−0.324042	−	0.561257i
$447$		0			0
$448$	−6.69844e6	−	1.40459e6i	−1.57681	−	0.330640i
$449$	467024.			0.109326			0.0546630	−	0.998505i	$-0.482592\pi$
$449$	467024.			0.109326			0.0546630	+	0.998505i	$0.482592\pi$
$450$		0			0
$451$	1.12531e6	−	1.94910e6i	0.260515	−	0.451225i
$452$	2.92865e6	−	5.07257e6i	0.674251	−	1.16784i
$453$		0			0
$454$	−2.00285e6			−0.456046
$455$	711495.	+	2.16947e6i	0.161118	+	0.491276i
$456$		0			0
$457$	300626.	+	520699.i	0.0673342	+	0.116626i	0.897727	−	0.440552i	$-0.145217\pi$
$457$	300626.	+	520699.i	0.0673342	+	0.116626i	−0.830393	+	0.557178i	$0.811884\pi$
$458$	5.64280e6	−	9.77362e6i	1.25699	−	2.17717i
$459$		0			0
$460$	551379.	+	955016.i	0.121494	+	0.210434i
$461$	−2.87193e6			−0.629392			−0.314696	−	0.949192i	$-0.601903\pi$
$461$	−2.87193e6			−0.629392			−0.314696	+	0.949192i	$0.601903\pi$
$462$		0			0
$463$	−2.91502e6			−0.631959			−0.315979	−	0.948766i	$-0.602333\pi$
$463$	−2.91502e6			−0.631959			−0.315979	+	0.948766i	$0.602333\pi$
$464$	−131294.	−	227409.i	−0.0283107	−	0.0490357i
$465$		0			0
$466$	−288953.	+	500481.i	−0.0616399	+	0.106763i
$467$	−3.59688e6	−	6.22998e6i	−0.763192	−	1.32189i	−0.941197	−	0.337857i	$-0.890298\pi$
$467$	−3.59688e6	−	6.22998e6i	−0.763192	−	1.32189i	0.178006	−	0.984029i	$-0.443035\pi$
$468$		0			0
$469$	−1.37130e6	+	1.53142e6i	−0.287873	+	0.321486i
$470$	416751.			0.0870227
$471$		0			0
$472$	692755.	−	1.19989e6i	0.143128	−	0.247905i
$473$	4.10179e6	−	7.10451e6i	0.842986	−	1.46009i
$474$		0			0
$475$	−6.10140e6			−1.24078
$476$	−2.90614e6	−	8.86133e6i	−0.587893	−	1.79259i
$477$		0			0
$478$	1.00686e6	+	1.74393e6i	0.201557	+	0.349108i
$479$	−1.39824e6	+	2.42183e6i	−0.278448	+	0.482286i	−0.970999	−	0.239083i	$-0.923153\pi$
$479$	−1.39824e6	+	2.42183e6i	−0.278448	+	0.482286i	0.692551	+	0.721369i	$0.256487\pi$
$480$		0			0
$481$	−3.90040e6	−	6.75569e6i	−0.768682	−	1.33140i
$482$	3.98340e6			0.780974
$483$		0			0
$484$	658698.			0.127812
$485$	−875456.	−	1.51633e6i	−0.168997	−	0.292712i
$486$		0			0
$487$	1.46624e6	−	2.53960e6i	0.280144	−	0.485224i	−0.691276	−	0.722591i	$-0.742951\pi$
$487$	1.46624e6	−	2.53960e6i	0.280144	−	0.485224i	0.971420	+	0.237367i	$0.0762843\pi$
$488$	−325652.	−	564046.i	−0.0619020	−	0.107217i
$489$		0			0
$490$	2.74436e6	−	2.01700e6i	0.516357	−	0.379504i
$491$	3.06121e6			0.573046			0.286523	−	0.958073i	$-0.407501\pi$
$491$	3.06121e6			0.573046			0.286523	+	0.958073i	$0.407501\pi$
$492$		0			0
$493$	−4.83870e6	+	8.38087e6i	−0.896626	+	1.55300i
$494$	−8.47246e6	+	1.46747e7i	−1.56204	+	2.70553i
$495$		0			0
$496$	47073.4			0.00859154
$497$	−7.37611e6	−	1.54669e6i	−1.33948	−	0.280875i
$498$		0			0
$499$	3.27577e6	+	5.67380e6i	0.588928	+	1.02005i	0.994373	+	0.105934i	$0.0337831\pi$
$499$	3.27577e6	+	5.67380e6i	0.588928	+	1.02005i	−0.405445	+	0.914119i	$0.632884\pi$
$500$	−3.32583e6	+	5.76052e6i	−0.594943	+	1.03047i
$501$		0			0
$502$	−7.85497e6	−	1.36052e7i	−1.39119	−	2.40960i
$503$	1.58524e6			0.279367			0.139684	−	0.990196i	$-0.455391\pi$
$503$	1.58524e6			0.279367			0.139684	+	0.990196i	$0.455391\pi$
$504$		0			0
$505$	−1.87242e6			−0.326719
$506$	1.82764e6	+	3.16556e6i	0.317332	+	0.549635i
$507$		0			0
$508$	−2.14996e6	+	3.72385e6i	−0.369634	+	0.640225i
$509$	3.38991e6	+	5.87149e6i	0.579953	+	1.00451i	0.995484	+	0.0949297i	$0.0302626\pi$
$509$	3.38991e6	+	5.87149e6i	0.579953	+	1.00451i	−0.415530	+	0.909579i	$0.636404\pi$
$510$		0			0
$511$	−3.38239e6	+	3.77732e6i	−0.573022	+	0.639929i
$512$	−432315.			−0.0728829
$513$		0			0
$514$	4.51743e6	−	7.82441e6i	0.754195	−	1.30630i
$515$	224383.	−	388643.i	0.0372796	−	0.0645702i
$516$		0			0
$517$	856990.			0.141010
$518$	−7.76265e6	+	8.66903e6i	−1.27112	+	1.41954i
$519$		0			0
$520$	1.64078e6	+	2.84192e6i	0.266099	+	0.460897i
$521$	−5.06918e6	+	8.78008e6i	−0.818170	+	1.41711i	0.0888599	+	0.996044i	$0.471678\pi$
$521$	−5.06918e6	+	8.78008e6i	−0.818170	+	1.41711i	−0.907029	+	0.421067i	$0.861656\pi$
$522$		0			0
$523$	−49998.6	−	86600.2i	−0.00799289	−	0.0138441i	0.862001	−	0.506906i	$-0.169211\pi$
$523$	−49998.6	−	86600.2i	−0.00799289	−	0.0138441i	−0.869994	+	0.493062i	$0.835878\pi$
$524$	9.19408e6			1.46278
$525$		0			0
$526$	−5.02301e6			−0.791589
$527$	−867416.	−	1.50241e6i	−0.136051	−	0.235647i
$528$		0			0
$529$	2.76178e6	−	4.78354e6i	0.429091	−	0.743207i
$530$	−1.82610e6	−	3.16291e6i	−0.282381	−	0.489099i
$531$		0			0
$532$	1.53476e7	+	3.21824e6i	2.35105	+	0.492991i
$533$	4.30952e6			0.657068
$534$		0			0
$535$	−76833.3	+	133079.i	−0.0116055	+	0.0201014i
$536$	−1.47729e6	+	2.55873e6i	−0.222102	+	0.384692i
$537$		0			0
$538$	5.88620e6			0.876756
$539$	5.64338e6	−	4.14768e6i	0.836695	−	0.614941i
$540$		0			0
$541$	59871.4	+	103700.i	0.00879481	+	0.0152331i	0.870389	−	0.492364i	$-0.163867\pi$
$541$	59871.4	+	103700.i	0.00879481	+	0.0152331i	−0.861595	+	0.507597i	$0.830534\pi$
$542$	2.51571e6	−	4.35734e6i	0.367843	−	0.637123i
$543$		0			0
$544$	3.86527e6	+	6.69485e6i	0.559993	+	0.969937i
$545$	−2.48640e6			−0.358574
$546$		0			0
$547$	236568.			0.0338056			0.0169028	−	0.999857i	$-0.494619\pi$
$547$	236568.			0.0338056			0.0169028	+	0.999857i	$0.494619\pi$
$548$	819209.	+	1.41891e6i	0.116531	+	0.201838i
$549$		0			0
$550$	−5.04607e6	+	8.74005e6i	−0.711290	+	1.23199i
$551$	−8.13641e6	−	1.40927e7i	−1.14170	−	1.97749i
$552$		0			0
$553$	−394330.	−	1.20238e6i	−0.0548336	−	0.167198i
$554$	1.53707e7			2.12774
$555$		0			0
$556$	−3.98054e6	+	6.89449e6i	−0.546078	+	0.945834i
$557$	−2.41833e6	+	4.18867e6i	−0.330277	+	0.572056i	−0.982566	−	0.185914i	$-0.940475\pi$
$557$	−2.41833e6	+	4.18867e6i	−0.330277	+	0.572056i	0.652289	+	0.757970i	$0.273809\pi$
$558$		0			0
$559$	1.57083e7			2.12617
$560$	71245.3	−	79564.1i	0.00960034	−	0.0107213i
$561$		0			0
$562$	8.31258e6	+	1.43978e7i	1.11018	+	1.92290i
$563$	−2.74147e6	+	4.74837e6i	−0.364513	+	0.631355i	−0.988698	−	0.149922i	$-0.952098\pi$
$563$	−2.74147e6	+	4.74837e6i	−0.364513	+	0.631355i	0.624185	+	0.781277i	$0.285431\pi$
$564$		0			0
$565$	−1.23607e6	−	2.14093e6i	−0.162900	−	0.282151i
$566$	2.30738e7			3.02746
$567$		0			0
$568$	−1.08322e7			−1.40878
$569$	−3.48830e6	−	6.04191e6i	−0.451682	−	0.782336i	0.546809	−	0.837258i	$-0.315843\pi$
$569$	−3.48830e6	−	6.04191e6i	−0.451682	−	0.782336i	−0.998491	+	0.0549213i	$0.982509\pi$
$570$		0			0
$571$	5.88573e6	−	1.01944e7i	0.755458	−	1.30849i	−0.189689	−	0.981844i	$-0.560748\pi$
$571$	5.88573e6	−	1.01944e7i	0.755458	−	1.30849i	0.945146	−	0.326647i	$-0.105919\pi$
$572$	8.69404e6	+	1.50585e7i	1.11104	+	1.92439i
$573$		0			0
$574$	−2.00332e6	−	6.10848e6i	−0.253788	−	0.773844i
$575$	−2.52020e6			−0.317882
$576$		0			0
$577$	−3.38646e6	+	5.86552e6i	−0.423454	+	0.733444i	−0.996275	−	0.0862365i	$-0.972516\pi$
$577$	−3.38646e6	+	5.86552e6i	−0.423454	+	0.733444i	0.572820	+	0.819681i	$0.305849\pi$
$578$	−2.16807e6	+	3.75521e6i	−0.269932	+	0.467535i
$579$		0			0
$580$	−8.12037e6			−1.00232
$581$	8.93197e6	+	1.87294e6i	1.09776	+	0.230188i
$582$		0			0
$583$	−3.75512e6	−	6.50407e6i	−0.457565	−	0.792526i
$584$	−3.64380e6	+	6.31124e6i	−0.442102	+	0.765743i
$585$		0			0
$586$	492242.	+	852588.i	0.0592154	+	0.102564i
$587$	1.05020e7			1.25799			0.628996	−	0.777408i	$-0.283466\pi$
$587$	1.05020e7			1.25799			0.628996	+	0.777408i	$0.283466\pi$
$588$		0			0
$589$	2.91717e6			0.346476
$590$	−753400.	−	1.30493e6i	−0.0891036	−	0.154332i
$591$		0			0
$592$	−182451.	+	316014.i	−0.0213964	+	0.0370597i
$593$	−3.79537e6	−	6.57378e6i	−0.443218	−	0.767676i	0.554708	−	0.832045i	$-0.312830\pi$
$593$	−3.79537e6	−	6.57378e6i	−0.443218	−	0.767676i	−0.997926	+	0.0643687i	$0.979497\pi$
$594$		0			0
$595$	−3.85223e6	−	807770.i	−0.446087	−	0.0935396i
$596$	−1.89758e7			−2.18818
$597$		0			0
$598$	−3.49957e6	+	6.06144e6i	−0.400186	+	0.693143i
$599$	−6.50992e6	+	1.12755e7i	−0.741325	+	1.28401i	0.210567	+	0.977580i	$0.432469\pi$
$599$	−6.50992e6	+	1.12755e7i	−0.741325	+	1.28401i	−0.951892	+	0.306434i	$0.900864\pi$
$600$		0			0
$601$	1.41821e7			1.60160			0.800801	−	0.598931i	$-0.204408\pi$
$601$	1.41821e7			1.60160			0.800801	+	0.598931i	$0.204408\pi$
$602$	−7.30214e6	−	2.22655e7i	−0.821219	−	2.50404i
$603$		0			0
$604$	−5.36352e6	−	9.28988e6i	−0.598215	−	1.03614i
$605$	139005.	−	240764.i	0.0154398	−	0.0267426i
$606$		0			0
$607$	−6.03862e6	−	1.04592e7i	−0.665221	−	1.15220i	−0.979225	−	0.202775i	$-0.935004\pi$
$607$	−6.03862e6	−	1.04592e7i	−0.665221	−	1.15220i	0.314004	−	0.949422i	$-0.398329\pi$
$608$	−1.29991e7			−1.42612
$609$		0			0
$610$	−708320.			−0.0770735
$611$	820485.	+	1.42112e6i	0.0889135	+	0.154003i
$612$		0			0
$613$	1.36265e6	−	2.36018e6i	0.146465	−	0.253684i	−0.783454	−	0.621450i	$-0.786544\pi$
$613$	1.36265e6	−	2.36018e6i	0.146465	−	0.253684i	0.929918	+	0.367766i	$0.119877\pi$
$614$	−6.86855e6	−	1.18967e7i	−0.735266	−	1.27352i
$615$		0			0
$616$	6.71508e6	−	7.49914e6i	0.713016	−	0.796269i
$617$	−8.47094e6			−0.895816			−0.447908	−	0.894080i	$-0.647831\pi$
$617$	−8.47094e6			−0.895816			−0.447908	+	0.894080i	$0.647831\pi$
$618$		0			0
$619$	−8.69174e6	+	1.50545e7i	−0.911759	+	1.57921i	−0.100180	+	0.994969i	$0.531942\pi$
$619$	−8.69174e6	+	1.50545e7i	−0.911759	+	1.57921i	−0.811578	+	0.584243i	$0.801391\pi$
$620$	727855.	−	1.26068e6i	0.0760441	−	0.131712i
$621$		0			0
$622$	−7.90690e6			−0.819464
$623$	5.82995e6	+	1.77765e7i	0.601789	+	1.83496i
$624$		0			0
$625$	−2.71793e6	−	4.70759e6i	−0.278316	−	0.482058i
$626$	2.31338e6	−	4.00689e6i	0.235945	−	0.408669i
$627$		0			0
$628$	2.02047e6	+	3.49955e6i	0.204434	+	0.354090i
$629$	1.34480e7			1.35529
$630$		0			0
$631$	−6.45149e6			−0.645040			−0.322520	−	0.946563i	$-0.604530\pi$
$631$	−6.45149e6			−0.645040			−0.322520	+	0.946563i	$0.604530\pi$
$632$	−909368.	−	1.57507e6i	−0.0905622	−	0.156858i
$633$		0			0
$634$	−2.20353e6	+	3.81663e6i	−0.217719	+	0.377101i
$635$	907413.	+	1.57169e6i	0.0893040	+	0.154679i
$636$		0			0
$637$	1.22810e7	+	5.38725e6i	1.19918	+	0.526039i
$638$	−2.69164e7			−2.61797
$639$		0			0
$640$	−3.36439e6	+	5.82730e6i	−0.324681	+	0.562364i
$641$	8.88581e6	−	1.53907e7i	0.854185	−	1.47949i	−0.0232142	−	0.999731i	$-0.507390\pi$
$641$	8.88581e6	−	1.53907e7i	0.854185	−	1.47949i	0.877399	−	0.479761i	$-0.159277\pi$
$642$		0			0
$643$	−9.34806e6			−0.891649			−0.445825	−	0.895120i	$-0.647090\pi$
$643$	−9.34806e6			−0.891649			−0.445825	+	0.895120i	$0.647090\pi$
$644$	6.33938e6	+	1.32930e6i	0.602327	+	0.126302i
$645$		0			0
$646$	−1.46059e7	−	2.52981e7i	−1.37704	−	2.38510i
$647$	2.67193e6	−	4.62792e6i	0.250937	−	0.434635i	−0.712847	−	0.701319i	$-0.752595\pi$
$647$	2.67193e6	−	4.62792e6i	0.250937	−	0.434635i	0.963784	+	0.266684i	$0.0859280\pi$
$648$		0			0
$649$	−1.54926e6	−	2.68340e6i	−0.144382	−	0.250077i
$650$	−1.93245e7			−1.79401
$651$		0			0
$652$	9.67098e6			0.890946
$653$	−598506.	−	1.03664e6i	−0.0549270	−	0.0951363i	0.837255	−	0.546813i	$-0.184159\pi$
$653$	−598506.	−	1.03664e6i	−0.0549270	−	0.0951363i	−0.892182	+	0.451677i	$0.850826\pi$
$654$		0			0
$655$	1.94022e6	−	3.36057e6i	0.176705	−	0.306062i
$656$	−100794.	−	174580.i	−0.00914481	−	0.0158393i
$657$		0			0
$658$	1.63295e6	−	1.82361e6i	0.147030	−	0.164198i
$659$	1.17541e7			1.05433			0.527163	−	0.849764i	$-0.323256\pi$
$659$	1.17541e7			1.05433			0.527163	+	0.849764i	$0.323256\pi$
$660$		0			0
$661$	9.00573e6	−	1.55984e7i	0.801706	−	1.38860i	−0.116787	−	0.993157i	$-0.537259\pi$
$661$	9.00573e6	−	1.55984e7i	0.801706	−	1.38860i	0.918493	−	0.395438i	$-0.129407\pi$
$662$	1.00958e7	−	1.74864e7i	0.895353	−	1.55080i
$663$		0			0
$664$	1.31170e7			1.15456
$665$	4.41512e6	−	4.93064e6i	0.387158	−	0.432364i
$666$		0			0
$667$	−3.36076e6	−	5.82102e6i	−0.292498	−	0.506622i
$668$	3.37987e6	−	5.85411e6i	0.293062	−	0.507598i
$669$		0			0
$670$	1.60661e6	+	2.78273e6i	0.138268	+	0.239488i
$671$	−1.45656e6			−0.124888
$672$		0			0
$673$	1.40977e7			1.19981			0.599904	−	0.800072i	$-0.295206\pi$
$673$	1.40977e7			1.19981			0.599904	+	0.800072i	$0.295206\pi$
$674$	6.23063e6	+	1.07918e7i	0.528302	+	0.915046i
$675$		0			0
$676$	−6.93902e6	+	1.20187e7i	−0.584025	+	1.01156i
$677$	3.82793e6	+	6.63018e6i	0.320991	+	0.555973i	0.980693	−	0.195555i	$-0.0626507\pi$
$677$	3.82793e6	+	6.63018e6i	0.320991	+	0.555973i	−0.659702	+	0.751527i	$0.729317\pi$
$678$		0			0
$679$	−1.00654e7	−	2.11061e6i	−0.837832	−	0.175684i
$680$	−5.65718e6			−0.469167
$681$		0			0
$682$	2.41260e6	−	4.17874e6i	0.198621	−	0.344021i
$683$	−5.43378e6	+	9.41158e6i	−0.445708	+	0.771988i	−0.998101	−	0.0615953i	$-0.980381\pi$
$683$	−5.43378e6	+	9.41158e6i	−0.445708	+	0.771988i	0.552394	+	0.833583i	$0.313715\pi$
$684$		0			0
$685$	691510.			0.0563083
$686$	1.92718e6	−	1.99118e7i	0.156355	−	1.61548i
$687$		0			0
$688$	−367396.	−	636348.i	−0.0295912	−	0.0512535i
$689$	7.19034e6	−	1.24540e7i	0.577034	−	0.999452i
$690$		0			0
$691$	7.30588e6	+	1.26542e7i	0.582073	+	1.00818i	0.995233	+	0.0975219i	$0.0310916\pi$
$691$	7.30588e6	+	1.26542e7i	0.582073	+	1.00818i	−0.413160	+	0.910658i	$0.635575\pi$
$692$	2.65589e7			2.10836
$693$		0			0
$694$	−3.48832e7			−2.74927
$695$	1.68002e6	+	2.90989e6i	0.131933	+	0.228515i
$696$		0			0
$697$	−3.71464e6	+	6.43395e6i	−0.289624	+	0.501644i
$698$	6.04827e6	+	1.04759e7i	0.469886	+	0.813867i
$699$		0			0
$700$	5.57299e6	+	1.69930e7i	0.429876	+	1.31077i
$701$	−1.90104e7			−1.46115			−0.730577	−	0.682830i	$-0.760749\pi$
$701$	−1.90104e7			−1.46115			−0.730577	+	0.682830i	$0.760749\pi$
$702$		0			0
$703$	−1.13066e7	+	1.95836e7i	−0.862866	+	1.49453i
$704$	−1.09996e7	+	1.90518e7i	−0.836458	+	1.44879i
$705$		0			0
$706$	3.14462e7			2.37441
$707$	−7.33664e6	+	8.19328e6i	−0.552012	+	0.616466i
$708$		0			0
$709$	5.79644e6	+	1.00397e7i	0.433058	+	0.750078i	0.997135	−	0.0756440i	$-0.0241013\pi$
$709$	5.79644e6	+	1.00397e7i	0.433058	+	0.750078i	−0.564077	+	0.825722i	$0.690768\pi$
$710$	−5.89021e6	+	1.02021e7i	−0.438516	+	0.759531i
$711$		0			0
$712$	1.34445e7	+	2.32865e7i	0.993904	+	1.72149i
$713$	1.20494e6			0.0887653
$714$		0			0
$715$	7.33881e6			0.536859
$716$	−3.46687e6	−	6.00479e6i	−0.252729	−	0.437739i
$717$		0			0
$718$	6.75205e6	−	1.16949e7i	0.488792	−	0.846613i
$719$	−5.14304e6	−	8.90800e6i	−0.371020	−	0.642626i	0.618703	−	0.785625i	$-0.287659\pi$
$719$	−5.14304e6	−	8.90800e6i	−0.371020	−	0.642626i	−0.989723	+	0.142999i	$0.954325\pi$
$720$		0			0
$721$	−821420.	−	2.50466e6i	−0.0588474	−	0.179436i
$722$	2.63868e7			1.88384
$723$		0			0
$724$	1.93507e7	−	3.35164e7i	1.37199	−	2.37635i
$725$	9.27900e6	−	1.60717e7i	0.655626	−	1.13558i
$726$		0			0
$727$	1.00970e7			0.708526			0.354263	−	0.935146i	$-0.384732\pi$
$727$	1.00970e7			0.708526			0.354263	+	0.935146i	$0.384732\pi$
$728$	1.88646e7	+	3.95571e6i	1.31923	+	0.276628i
$729$		0			0
$730$	3.96278e6	+	6.86373e6i	0.275228	+	0.476709i
$731$	−1.35399e7	+	2.34518e7i	−0.937180	+	1.62324i
$732$		0			0
$733$	−962010.	−	1.66625e6i	−0.0661332	−	0.114546i	0.831063	−	0.556178i	$-0.187733\pi$
$733$	−962010.	−	1.66625e6i	−0.0661332	−	0.114546i	−0.897196	+	0.441632i	$0.854400\pi$
$734$	−4.57298e7			−3.13299
$735$		0			0
$736$	−5.36932e6			−0.365363
$737$	3.30376e6	+	5.72228e6i	0.224047	+	0.388061i
$738$		0			0
$739$	−2.10136e6	+	3.63967e6i	−0.141543	+	0.245161i	−0.928078	−	0.372386i	$-0.878540\pi$
$739$	−2.10136e6	+	3.63967e6i	−0.141543	+	0.245161i	0.786535	+	0.617546i	$0.211873\pi$
$740$	5.64215e6	+	9.77249e6i	0.378761	+	0.656034i
$741$		0			0
$742$	−2.09953e7	−	4.40250e6i	−1.39995	−	0.293555i
$743$	1.99659e7			1.32684			0.663418	−	0.748249i	$-0.269105\pi$
$743$	1.99659e7			1.32684			0.663418	+	0.748249i	$0.269105\pi$
$744$		0			0
$745$	−4.00445e6	+	6.93592e6i	−0.264334	+	0.457839i
$746$	−1.81810e7	+	3.14904e7i	−1.19611	+	2.07172i
$747$		0			0
$748$	−2.99757e7			−1.95892
$749$	281271.	+	857646.i	0.0183198	+	0.0558603i
$750$		0			0
$751$	1.81988e6	+	3.15212e6i	0.117745	+	0.203940i	0.918874	−	0.394552i	$-0.129100\pi$
$751$	1.81988e6	+	3.15212e6i	0.117745	+	0.203940i	−0.801129	+	0.598492i	$0.795767\pi$
$752$	38380.1	−	66476.4i	0.00247492	−	0.00428670i
$753$		0			0
$754$	−2.57698e7	−	4.46346e7i	−1.65076	−	2.85919i
$755$	−4.52745e6			−0.289059
$756$		0			0
$757$	1.73429e7			1.09997			0.549986	−	0.835174i	$-0.314633\pi$
$757$	1.73429e7			1.09997			0.549986	+	0.835174i	$0.314633\pi$
$758$	8.04067e6	+	1.39268e7i	0.508299	+	0.880399i
$759$		0			0
$760$	4.75635e6	−	8.23824e6i	0.298703	−	0.517369i
$761$	−5.17841e6	−	8.96927e6i	−0.324142	−	0.561430i	0.657196	−	0.753719i	$-0.271742\pi$
$761$	−5.17841e6	−	8.96927e6i	−0.324142	−	0.561430i	−0.981338	+	0.192289i	$0.938409\pi$
$762$		0			0
$763$	−9.74238e6	+	1.08799e7i	−0.605834	+	0.676572i
$764$	3.04740e7			1.88884
$765$		0			0
$766$	1.44069e7	−	2.49535e7i	0.887153	−	1.53659i
$767$	2.96653e6	−	5.13818e6i	0.182079	−	0.315371i
$768$		0			0
$769$	−1.81548e7			−1.10707			−0.553534	−	0.832826i	$-0.686721\pi$
$769$	−1.81548e7			−1.10707			−0.553534	+	0.832826i	$0.686721\pi$
$770$	−3.41152e6	−	1.04023e7i	−0.207358	−	0.632272i
$771$		0			0
$772$	1.04826e7	+	1.81565e7i	0.633034	+	1.09645i
$773$	−8.17830e6	+	1.41652e7i	−0.492282	+	0.852658i	−0.999960	−	0.00888861i	$-0.997171\pi$
$773$	−8.17830e6	+	1.41652e7i	−0.492282	+	0.852658i	0.507678	+	0.861547i	$0.330504\pi$
$774$		0			0
$775$	1.66341e6	+	2.88112e6i	0.0994823	+	0.172308i
$776$	−1.47815e7			−0.881181
$777$		0			0
$778$	9.66346e6			0.572379
$779$	−6.24627e6	−	1.08189e7i	−0.368788	−	0.638760i
$780$		0			0
$781$	−1.21124e7	+	2.09793e7i	−0.710562	+	1.23073i
$782$	−6.03300e6	−	1.04495e7i	−0.352790	−	0.611051i
$783$		0			0
$784$	−68996.1	−	623507.i	−0.00400898	−	0.0362286i
$785$	1.70552e6			0.0987829
$786$		0			0
$787$	2.22364e6	−	3.85146e6i	0.127976	−	0.221661i	−0.794916	−	0.606719i	$-0.792485\pi$
$787$	2.22364e6	−	3.85146e6i	0.127976	−	0.221661i	0.922892	+	0.385058i	$0.125819\pi$
$788$	1.75604e7	−	3.04154e7i	1.00744	−	1.74493i
$789$		0			0
$790$	−1.97795e6			−0.112758
$791$	−1.42115e7	−	2.97999e6i	−0.807603	−	0.169346i
$792$		0			0
$793$	−1.39452e6	−	2.41537e6i	−0.0787481	−	0.136396i
$794$	−2.08746e6	+	3.61559e6i	−0.117508	+	0.203530i
$795$		0			0
$796$	1.18977e7	+	2.06074e7i	0.665548	+	1.15276i
$797$	9.15303e6			0.510410			0.255205	−	0.966887i	$-0.417857\pi$
$797$	9.15303e6			0.510410			0.255205	+	0.966887i	$0.417857\pi$
$798$		0			0
$799$	−2.82891e6			−0.156766
$800$	−7.41229e6	−	1.28385e7i	−0.409475	−	0.709232i
$801$		0			0
$802$	−1.32408e7	+	2.29337e7i	−0.726905	+	1.25904i
$803$	8.14889e6	+	1.41143e7i	0.445974	+	0.772450i
$804$		0			0
$805$	1.82368e6	−	2.03662e6i	0.0991879	−	0.110769i
$806$	9.23932e6			0.500959
$807$		0			0
$808$	−7.90365e6	+	1.36895e7i	−0.425892	+	0.737666i
$809$	1.25962e7	−	2.18172e7i	0.676654	−	1.17200i	−0.299328	−	0.954150i	$-0.596763\pi$
$809$	1.25962e7	−	2.18172e7i	0.676654	−	1.17200i	0.975982	−	0.217849i	$-0.0699041\pi$
$810$		0			0
$811$	−8.90585e6			−0.475470			−0.237735	−	0.971330i	$-0.576405\pi$
$811$	−8.90585e6			−0.475470			−0.237735	+	0.971330i	$0.576405\pi$
$812$	−3.18178e7	+	3.55329e7i	−1.69348	+	1.89121i
$813$		0			0
$814$	1.87019e7	+	3.23926e7i	0.989291	+	1.71350i
$815$	2.04087e6	−	3.53488e6i	0.107627	−	0.186415i
$816$		0			0
$817$	−2.27678e7	−	3.94349e7i	−1.19334	−	2.06693i
$818$	−2.07417e6			−0.108383
$819$		0			0
$820$	−6.23396e6			−0.323765
$821$	1.67745e7	+	2.90543e7i	0.868543	+	1.50436i	0.863485	+	0.504374i	$0.168277\pi$
$821$	1.67745e7	+	2.90543e7i	0.868543	+	1.50436i	0.00505812	+	0.999987i	$0.498390\pi$
$822$		0			0
$823$	7.30006e6	−	1.26441e7i	0.375688	−	0.650710i	−0.614742	−	0.788728i	$-0.710740\pi$
$823$	7.30006e6	−	1.26441e7i	0.375688	−	0.650710i	0.990430	+	0.138018i	$0.0440732\pi$
$824$	−1.89428e6	−	3.28100e6i	−0.0971912	−	0.168340i
$825$		0			0
$826$	−8.66209e6	−	1.81635e6i	−0.441746	−	0.0926294i
$827$	−1.97530e7			−1.00431			−0.502156	−	0.864777i	$-0.667460\pi$
$827$	−1.97530e7			−1.00431			−0.502156	+	0.864777i	$0.667460\pi$
$828$		0			0
$829$	2.03127e6	−	3.51827e6i	0.102655	−	0.177804i	−0.810122	−	0.586261i	$-0.800599\pi$
$829$	2.03127e6	−	3.51827e6i	0.102655	−	0.177804i	0.912778	+	0.408456i	$0.133933\pi$
$830$	7.13264e6	−	1.23541e7i	0.359381	−	0.622467i
$831$		0			0
$832$	−4.21241e7			−2.10971
$833$	−1.86287e7	+	1.36914e7i	−0.930186	+	0.683653i
$834$		0			0
$835$	−1.42651e6	−	2.47079e6i	−0.0708041	−	0.122636i
$836$	2.52025e7	−	4.36520e7i	1.24718	−	2.16017i
$837$		0			0
$838$	1.97868e7	+	3.42717e7i	0.973341	+	1.68588i
$839$	1.60509e7			0.787217			0.393609	−	0.919278i	$-0.371227\pi$
$839$	1.60509e7			0.787217			0.393609	+	0.919278i	$0.371227\pi$
$840$		0			0
$841$	2.89842e7			1.41309
$842$	−5.74231e6	−	9.94597e6i	−0.279130	−	0.483467i
$843$		0			0
$844$	3.12579e7	−	5.41403e7i	1.51044	−	2.61616i
$845$	2.92868e6	+	5.07263e6i	0.141101	+	0.244394i
$846$		0			0
$847$	−508869.	−	1.55163e6i	−0.0243724	−	0.0743157i
$848$	−672690.			−0.0321237
$849$		0			0
$850$	1.66570e7	−	2.88508e7i	0.790768	−	1.36965i
$851$	−4.67022e6	+	8.08905e6i	−0.221061	+	0.382890i
$852$		0			0
$853$	−1.23887e7			−0.582979			−0.291489	−	0.956574i	$-0.594151\pi$
$853$	−1.23887e7			−0.582979			−0.291489	+	0.956574i	$0.594151\pi$
$854$	−2.77539e6	+	3.09945e6i	−0.130221	+	0.145425i
$855$		0			0
$856$	648642.	+	1.12348e6i	0.0302566	+	0.0524060i
$857$	1.31760e7	−	2.28214e7i	0.612816	−	1.06143i	−0.377948	−	0.925827i	$-0.623370\pi$
$857$	1.31760e7	−	2.28214e7i	0.612816	−	1.06143i	0.990764	−	0.135601i	$-0.0432966\pi$
$858$		0			0
$859$	6.06245e6	+	1.05005e7i	0.280327	+	0.485541i	0.971465	−	0.237182i	$-0.0762237\pi$
$859$	6.06245e6	+	1.05005e7i	0.280327	+	0.485541i	−0.691138	+	0.722723i	$0.742890\pi$
$860$	−2.27229e7			−1.04765
$861$		0			0
$862$	4.04702e7			1.85510
$863$	1.27976e6	+	2.21661e6i	0.0584927	+	0.101312i	0.893789	−	0.448488i	$-0.148037\pi$
$863$	1.27976e6	+	2.21661e6i	0.0584927	+	0.101312i	−0.835296	+	0.549800i	$0.814704\pi$
$864$		0			0
$865$	5.60472e6	−	9.70766e6i	0.254691	−	0.441138i
$866$	7.38866e6	+	1.27975e7i	0.334789	+	0.579871i
$867$		0			0
$868$	−2.66453e6	−	8.12462e6i	−0.120039	−	0.366019i
$869$	−4.06737e6			−0.182711
$870$		0			0
$871$	−6.32606e6	+	1.09571e7i	−0.282545	+	0.489383i
$872$	−1.04953e7	+	1.81784e7i	−0.467417	+	0.809590i
$873$		0			0
$874$	2.02893e7			0.898439
$875$	1.61388e7	+	3.38414e6i	0.712610	+	0.149427i
$876$		0			0
$877$	−1.32910e7	−	2.30207e7i	−0.583523	−	1.01069i	−0.995058	−	0.0992977i	$-0.968340\pi$
$877$	−1.32910e7	−	2.30207e7i	−0.583523	−	1.01069i	0.411535	−	0.911394i	$-0.364993\pi$
$878$	2.03113e7	−	3.51801e7i	0.889203	−	1.54014i
$879$		0			0
$880$	−171645.	−	297298.i	−0.00747179	−	0.0129415i
$881$	8.32262e6			0.361260			0.180630	−	0.983551i	$-0.442186\pi$
$881$	8.32262e6			0.361260			0.180630	+	0.983551i	$0.442186\pi$
$882$		0			0
$883$	1.81133e7			0.781798			0.390899	−	0.920434i	$-0.372164\pi$
$883$	1.81133e7			0.781798			0.390899	+	0.920434i	$0.372164\pi$
$884$	−2.86989e7	−	4.97079e7i	−1.23519	−	2.13941i
$885$		0			0
$886$	−1.65922e7	+	2.87386e7i	−0.710102	+	1.22993i
$887$	−1.02128e7	−	1.76890e7i	−0.435847	−	0.754909i	0.561517	−	0.827465i	$-0.310218\pi$
$887$	−1.02128e7	−	1.76890e7i	−0.435847	−	0.754909i	−0.997364	+	0.0725558i	$0.976884\pi$
$888$		0			0
$889$	1.04328e7	+	2.18765e6i	0.442739	+	0.0928377i
$890$	2.92429e7			1.23750
$891$		0			0
$892$	−7.75349e6	+	1.34294e7i	−0.326276	+	0.565127i
$893$	2.37844e6	−	4.11959e6i	0.0998078	−	0.172872i
$894$		0			0
$895$	−2.92645e6			−0.122119
$896$	1.23164e7	+	3.75548e7i	0.512522	+	1.56277i
$897$		0			0
$898$	−2.14393e6	−	3.71339e6i	−0.0887195	−	0.153667i
$899$	−4.43642e6	+	7.68411e6i	−0.183077	+	0.317099i
$900$		0			0
$901$	1.23956e7	+	2.14698e7i	0.508693	+	0.881082i
$902$	−2.06635e7			−0.845645
$903$		0			0
$904$	−2.08702e7			−0.849388
$905$	−8.16715e6	−	1.41459e7i	−0.331474	−	0.574130i
$906$		0			0
$907$	1.00599e7	−	1.74242e7i	0.406044	−	0.703290i	−0.588398	−	0.808571i	$-0.700241\pi$
$907$	1.00599e7	−	1.74242e7i	0.406044	−	0.703290i	0.994442	+	0.105282i	$0.0335745\pi$
$908$	5.70397e6	+	9.87957e6i	0.229595	+	0.397670i
$909$		0			0
$910$	1.39837e7	−	1.56164e7i	0.559781	−	0.625142i
$911$	−3.17075e7			−1.26580			−0.632902	−	0.774232i	$-0.718137\pi$
$911$	−3.17075e7			−1.26580			−0.632902	+	0.774232i	$0.718137\pi$
$912$		0			0
$913$	1.46673e7	−	2.54045e7i	0.582334	−	1.00863i
$914$	2.76012e6	−	4.78066e6i	0.109285	−	0.189288i
$915$		0			0
$916$	−6.42812e7			−2.53131
$917$	−7.10277e6	−	2.16576e7i	−0.278936	−	0.850525i
$918$		0			0
$919$	4.35364e6	+	7.54072e6i	0.170045	+	0.294526i	0.938435	−	0.345455i	$-0.112275\pi$
$919$	4.35364e6	+	7.54072e6i	0.170045	+	0.294526i	−0.768390	+	0.639981i	$0.778942\pi$
$920$	1.96462e6	−	3.40283e6i	0.0765261	−	0.132547i
$921$		0			0
$922$	1.31839e7	+	2.28352e7i	0.510760	+	0.884663i
$923$	−4.63857e7			−1.79217
$924$		0			0
$925$	−2.57887e7			−0.991005
$926$	1.33817e7	+	2.31778e7i	0.512843	+	0.888270i
$927$		0			0
$928$	1.97690e7	−	3.42410e7i	0.753556	−	1.30520i
$929$	1.62021e7	+	2.80629e7i	0.615931	+	1.06682i	0.990220	+	0.139512i	$0.0445534\pi$
$929$	1.62021e7	+	2.80629e7i	0.615931	+	1.06682i	−0.374289	+	0.927312i	$0.622113\pi$
$930$		0			0
$931$	−4.27574e6	−	3.86392e7i	−0.161673	−	1.46101i
$932$	3.29167e6			0.124130
$933$		0			0
$934$	−3.30238e7	+	5.71988e7i	−1.23868	+	2.14546i
$935$	−6.32578e6	+	1.09566e7i	−0.236638	+	0.409869i
$936$		0			0
$937$	−2.19155e7			−0.815458			−0.407729	−	0.913103i	$-0.633679\pi$
$937$	−2.19155e7			−0.815458			−0.407729	+	0.913103i	$0.633679\pi$
$938$	1.84717e7	+	3.87332e6i	0.685488	+	0.143740i
$939$		0			0
$940$	−1.18688e6	−	2.05573e6i	−0.0438113	−	0.0758835i
$941$	7.30095e6	−	1.26456e7i	0.268785	−	0.465550i	−0.699763	−	0.714375i	$-0.746711\pi$
$941$	7.30095e6	−	1.26456e7i	0.268785	−	0.465550i	0.968548	+	0.248825i	$0.0800444\pi$
$942$		0			0
$943$	−2.58004e6	−	4.46876e6i	−0.0944815	−	0.163647i
$944$	−277533.			−0.0101364
$945$		0			0
$946$	−7.53189e7			−2.73638
$947$	−1.04189e7	−	1.80461e7i	−0.377527	−	0.653895i	0.613175	−	0.789947i	$-0.289892\pi$
$947$	−1.04189e7	−	1.80461e7i	−0.377527	−	0.653895i	−0.990702	+	0.136052i	$0.956559\pi$
$948$		0			0
$949$	−1.56035e7	+	2.70261e7i	−0.562416	+	0.974134i
$950$	2.80092e7	+	4.85133e7i	1.00691	+	1.74402i
$951$		0			0
$952$	−2.21663e7	+	2.47545e7i	−0.792687	+	0.885243i
$953$	942012.			0.0335988			0.0167994	−	0.999859i	$-0.494652\pi$
$953$	942012.			0.0335988			0.0167994	+	0.999859i	$0.494652\pi$
$954$		0			0
$955$	6.43092e6	−	1.11387e7i	0.228173	−	0.395208i
$956$	5.73492e6	−	9.93318e6i	0.202947	−	0.351515i
$957$		0			0
$958$	2.56752e7			0.903857
$959$	2.70953e6	−	3.02589e6i	0.0951364	−	0.106245i
$960$		0			0
$961$	1.35193e7	+	2.34161e7i	0.472221	+	0.817910i
$962$	−3.58105e7	+	6.20256e7i	−1.24759	+	2.16089i
$963$		0			0
$964$	−1.13444e7	−	1.96492e7i	−0.393179	−	0.681006i
$965$	8.84860e6			0.305884
$966$		0			0
$967$	−2.56570e7			−0.882346			−0.441173	−	0.897422i	$-0.645438\pi$
$967$	−2.56570e7			−0.882346			−0.441173	+	0.897422i	$0.645438\pi$
$968$	−1.17351e6	−	2.03257e6i	−0.0402529	−	0.0697201i
$969$		0			0
$970$	−8.03776e6	+	1.39218e7i	−0.274287	+	0.475079i
$971$	−1.07137e7	−	1.85566e7i	−0.364662	−	0.631613i	0.624060	−	0.781377i	$-0.285482\pi$
$971$	−1.07137e7	−	1.85566e7i	−0.364662	−	0.631613i	−0.988722	+	0.149763i	$0.952149\pi$
$972$		0			0
$973$	1.93158e7	+	4.05032e6i	0.654080	+	0.137153i
$974$	−2.69237e7			−0.909364
$975$		0			0
$976$	−65231.8	+	112985.i	−0.00219197	+	0.00379660i
$977$	−1.02420e7	+	1.77397e7i	−0.343281	+	0.594580i	−0.985040	−	0.172326i	$-0.944872\pi$
$977$	−1.02420e7	+	1.77397e7i	−0.343281	+	0.594580i	0.641759	+	0.766906i	$0.278205\pi$
$978$		0			0
$979$	6.01338e7			2.00522
$980$	−1.77651e7	−	7.79296e6i	−0.590885	−	0.259201i
$981$		0			0
$982$	−1.40528e7	−	2.43402e7i	−0.465035	−	0.805464i
$983$	1.38825e7	−	2.40452e7i	0.458230	−	0.793677i	−0.540638	−	0.841255i	$-0.681817\pi$
$983$	1.38825e7	−	2.40452e7i	0.458230	−	0.793677i	0.998868	+	0.0475784i	$0.0151504\pi$
$984$		0			0
$985$	−7.41152e6	−	1.28371e7i	−0.243398	−	0.421578i
$986$	8.88504e7			2.91050
$987$		0			0
$988$	9.65159e7			3.14562
$989$	−9.40429e6	−	1.62887e7i	−0.305728	−	0.529536i
$990$		0			0
$991$	−1.73416e7	+	3.00366e7i	−0.560926	+	0.971552i	0.436490	+	0.899709i	$0.356221\pi$
$991$	−1.73416e7	+	3.00366e7i	−0.560926	+	0.971552i	−0.997416	+	0.0718429i	$0.977112\pi$
$992$	3.54392e6	+	6.13826e6i	0.114342	+	0.198046i
$993$		0			0
$994$	2.15629e7	+	6.57490e7i	0.692214	+	2.11068i
$995$	1.00431e7			0.321594
$996$		0			0
$997$	7.42861e6	−	1.28667e7i	0.236685	−	0.409950i	−0.723076	−	0.690768i	$-0.757273\pi$
$997$	7.42861e6	−	1.28667e7i	0.236685	−	0.409950i	0.959761	+	0.280818i	$0.0906059\pi$
$998$	3.00756e7	−	5.20925e7i	0.955846	−	1.65557i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.6.e.e.46.1		8
3.2	odd	2		21.6.e.c.4.4	✓	8
7.2	even	3	inner	63.6.e.e.37.1		8
7.3	odd	6		441.6.a.v.1.4		4
7.4	even	3		441.6.a.w.1.4		4
12.11	even	2		336.6.q.j.193.3		8
21.2	odd	6		21.6.e.c.16.4	yes	8
21.5	even	6		147.6.e.o.79.4		8
21.11	odd	6		147.6.a.m.1.1		4
21.17	even	6		147.6.a.l.1.1		4
21.20	even	2		147.6.e.o.67.4		8
84.23	even	6		336.6.q.j.289.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.6.e.c.4.4	✓	8	3.2	odd	2
21.6.e.c.16.4	yes	8	21.2	odd	6
63.6.e.e.37.1		8	7.2	even	3	inner
63.6.e.e.46.1		8	1.1	even	1	trivial
147.6.a.l.1.1		4	21.17	even	6
147.6.a.m.1.1		4	21.11	odd	6
147.6.e.o.67.4		8	21.20	even	2
147.6.e.o.79.4		8	21.5	even	6
336.6.q.j.193.3		8	12.11	even	2
336.6.q.j.289.3		8	84.23	even	6
441.6.a.v.1.4		4	7.3	odd	6
441.6.a.w.1.4		4	7.4	even	3

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:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	63.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.59061 - 7.95118i) q^{2} +(-26.1475 + 45.2888i) q^{4} +(11.0358 + 19.1146i) q^{5} +(126.882 + 26.6059i) q^{7} +186.333 q^{8} +O(q^{10})\)	\(q+(-4.59061 - 7.95118i) q^{2} +(-26.1475 + 45.2888i) q^{4} +(11.0358 + 19.1146i) q^{5} +(126.882 + 26.6059i) q^{7} +186.333 q^{8} +(101.322 - 175.495i) q^{10} +(208.355 - 360.881i) q^{11} +797.918 q^{13} +(-370.920 - 1131.00i) q^{14} +(-18.6623 - 32.3240i) q^{16} +(-687.775 + 1191.26i) q^{17} +(-1156.51 - 2003.14i) q^{19} -1154.23 q^{20} -3825.91 q^{22} +(-477.701 - 827.402i) q^{23} +(1318.92 - 2284.44i) q^{25} +(-3662.93 - 6344.39i) q^{26} +(-4522.60 + 5050.67i) q^{28} +7035.29 q^{29} +(-630.596 + 1092.22i) q^{31} +(2809.98 - 4867.03i) q^{32} +12629.2 q^{34} +(891.689 + 2718.92i) q^{35} +(-4888.22 - 8466.65i) q^{37} +(-10618.2 + 18391.3i) q^{38} +(2056.33 + 3561.67i) q^{40} +5400.95 q^{41} +19686.6 q^{43} +(10895.9 + 18872.3i) q^{44} +(-4385.88 + 7596.57i) q^{46} +(1028.28 + 1781.04i) q^{47} +(15391.3 + 6751.63i) q^{49} -24218.7 q^{50} +(-20863.5 + 36136.7i) q^{52} +(9011.37 - 15608.2i) q^{53} +9197.45 q^{55} +(23642.3 + 4957.54i) q^{56} +(-32296.3 - 55938.8i) q^{58} +(3717.84 - 6439.49i) q^{59} +(-1747.69 - 3027.09i) q^{61} +11579.3 q^{62} -52792.5 q^{64} +(8805.67 + 15251.9i) q^{65} +(-7928.21 + 13732.1i) q^{67} +(-35967.2 - 62297.0i) q^{68} +(17525.2 - 19571.5i) q^{70} -58133.5 q^{71} +(-19555.3 + 33870.8i) q^{73} +(-44879.9 + 77734.2i) q^{74} +120960. q^{76} +(36038.1 - 40246.0i) q^{77} +(-4880.35 - 8453.01i) q^{79} +(411.906 - 713.442i) q^{80} +(-24793.7 - 42943.9i) q^{82} +70395.7 q^{83} -30360.6 q^{85} +(-90373.4 - 156531. i) q^{86} +(38823.3 - 67243.9i) q^{88} +(72153.1 + 124973. i) q^{89} +(101242. + 21229.3i) q^{91} +49962.7 q^{92} +(9440.90 - 16352.1i) q^{94} +(25526.1 - 44212.5i) q^{95} -79328.7 q^{97} +(-16971.9 - 153373. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} - 69 q^{4} + 258 q^{7} - 246 q^{8}+O(q^{10}) \) 8 * q + 3 * q^2 - 69 * q^4 + 258 * q^7 - 246 * q^8	\( 8 q + 3 q^{2} - 69 q^{4} + 258 q^{7} - 246 q^{8} - 283 q^{10} + 402 q^{11} + 924 q^{13} - 1926 q^{14} - 3273 q^{16} + 276 q^{17} - 510 q^{19} - 9438 q^{20} + 2750 q^{22} + 6900 q^{23} - 2814 q^{25} - 15138 q^{26} - 26221 q^{28} - 1080 q^{29} + 6410 q^{31} + 15519 q^{32} + 42288 q^{34} + 33108 q^{35} - 15250 q^{37} - 41250 q^{38} + 8547 q^{40} - 8616 q^{41} + 58396 q^{43} + 70743 q^{44} - 61800 q^{46} - 15060 q^{47} - 64252 q^{49} + 14604 q^{50} + 47476 q^{52} + 13692 q^{53} + 146248 q^{55} + 15921 q^{56} - 52309 q^{58} + 34830 q^{59} + 5364 q^{61} - 32058 q^{62} - 146974 q^{64} + 66864 q^{65} + 5994 q^{67} - 58272 q^{68} - 4307 q^{70} - 178536 q^{71} - 59638 q^{73} - 185442 q^{74} + 42616 q^{76} + 75660 q^{77} + 44062 q^{79} - 33381 q^{80} - 57596 q^{82} + 416892 q^{83} + 72648 q^{85} - 136968 q^{86} - 87597 q^{88} - 77520 q^{89} + 104722 q^{91} - 316512 q^{92} + 73722 q^{94} - 221376 q^{95} - 377260 q^{97} - 382479 q^{98}+O(q^{100}) \) 8 * q + 3 * q^2 - 69 * q^4 + 258 * q^7 - 246 * q^8 - 283 * q^10 + 402 * q^11 + 924 * q^13 - 1926 * q^14 - 3273 * q^16 + 276 * q^17 - 510 * q^19 - 9438 * q^20 + 2750 * q^22 + 6900 * q^23 - 2814 * q^25 - 15138 * q^26 - 26221 * q^28 - 1080 * q^29 + 6410 * q^31 + 15519 * q^32 + 42288 * q^34 + 33108 * q^35 - 15250 * q^37 - 41250 * q^38 + 8547 * q^40 - 8616 * q^41 + 58396 * q^43 + 70743 * q^44 - 61800 * q^46 - 15060 * q^47 - 64252 * q^49 + 14604 * q^50 + 47476 * q^52 + 13692 * q^53 + 146248 * q^55 + 15921 * q^56 - 52309 * q^58 + 34830 * q^59 + 5364 * q^61 - 32058 * q^62 - 146974 * q^64 + 66864 * q^65 + 5994 * q^67 - 58272 * q^68 - 4307 * q^70 - 178536 * q^71 - 59638 * q^73 - 185442 * q^74 + 42616 * q^76 + 75660 * q^77 + 44062 * q^79 - 33381 * q^80 - 57596 * q^82 + 416892 * q^83 + 72648 * q^85 - 136968 * q^86 - 87597 * q^88 - 77520 * q^89 + 104722 * q^91 - 316512 * q^92 + 73722 * q^94 - 221376 * q^95 - 377260 * q^97 - 382479 * q^98

Introduction

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