LMFDB - Embedded newform 63.6.c.b.62.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,6,Mod(62,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("63.62");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	63.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.1041806482$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 456x^{6} - 612x^{5} + 66744x^{4} + 32004x^{3} + 3729464x^{2} + 2503804x + 66026577 $ x^8 - 4x^7 + 456x^6 - 612x^5 + 66744x^4 + 32004x^3 + 3729464x^2 + 2503804*x + 66026577
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			62.2
Root			$-0.822876 - 7.29403i$ of defining polynomial
Character	$\chi$	$=$	63.62
Dual form			63.6.c.b.62.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-7.98430i q^{2} -31.7490 q^{4} +67.9227 q^{5} +(25.6863 - 127.072i) q^{7} -2.00393i q^{8} +O(q^{10})$	\(q-7.98430i q^{2} -31.7490 q^{4} +67.9227 q^{5} +(25.6863 - 127.072i) q^{7} -2.00393i q^{8} -542.315i q^{10} +181.337i q^{11} -796.458i q^{13} +(-1014.58 - 205.087i) q^{14} -1031.97 q^{16} -59.3989 q^{17} +966.599i q^{19} -2156.48 q^{20} +1447.85 q^{22} +2491.36i q^{23} +1488.49 q^{25} -6359.16 q^{26} +(-815.514 + 4034.40i) q^{28} -3787.11i q^{29} -7424.40i q^{31} +8175.42i q^{32} +474.259i q^{34} +(1744.68 - 8631.05i) q^{35} -12638.0 q^{37} +7717.61 q^{38} -136.113i q^{40} +19790.5 q^{41} +13783.1 q^{43} -5757.28i q^{44} +19891.8 q^{46} +23475.1 q^{47} +(-15487.4 - 6528.00i) q^{49} -11884.5i q^{50} +25286.8i q^{52} +27061.7i q^{53} +12316.9i q^{55} +(-254.643 - 51.4736i) q^{56} -30237.4 q^{58} -9085.13 q^{59} +22432.7i q^{61} -59278.6 q^{62} +32252.0 q^{64} -54097.6i q^{65} +59524.2 q^{67} +1885.86 q^{68} +(-68912.9 - 13930.0i) q^{70} +11632.3i q^{71} +38939.3i q^{73} +100905. i q^{74} -30688.6i q^{76} +(23042.8 + 4657.88i) q^{77} +15289.7 q^{79} -70094.1 q^{80} -158014. i q^{82} +64568.6 q^{83} -4034.53 q^{85} -110048. i q^{86} +363.388 q^{88} -103895. q^{89} +(-101207. - 20458.0i) q^{91} -79098.3i q^{92} -187433. i q^{94} +65654.0i q^{95} +14530.7i q^{97} +(-52121.5 + 123656. i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 112 q^{7}+O(q^{10}) $ 8 * q - 112 * q^7	$ 8 q - 112 q^{7} - 128 q^{16} + 5360 q^{22} + 9368 q^{25} - 10080 q^{28} - 34304 q^{37} + 32416 q^{43} + 71888 q^{46} - 106120 q^{49} - 115792 q^{58} + 253952 q^{64} + 152608 q^{67} - 260736 q^{70} - 94592 q^{79} + 475200 q^{85} - 26048 q^{88} - 501312 q^{91}+O(q^{100}) $ 8 * q - 112 * q^7 - 128 * q^16 + 5360 * q^22 + 9368 * q^25 - 10080 * q^28 - 34304 * q^37 + 32416 * q^43 + 71888 * q^46 - 106120 * q^49 - 115792 * q^58 + 253952 * q^64 + 152608 * q^67 - 260736 * q^70 - 94592 * q^79 + 475200 * q^85 - 26048 * q^88 - 501312 * q^91

Display 100 coefficients 10 coefficients

Character values

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

$n$	$10$	$29$
$\chi(n)$	$-1$	$-1$

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 $

$2$		−	7.98430i		−	1.41144i	−0.708492	−	0.705719i	$-0.750624\pi$
$2$		−	7.98430i		−	1.41144i	0.708492	−	0.705719i	$-0.249376\pi$
$3$		0			0
$3$		0			0
$4$	−31.7490			−0.992157
$5$	67.9227			1.21504			0.607519	−	0.794305i	$-0.292165\pi$
$5$	67.9227			1.21504			0.607519	+	0.794305i	$0.292165\pi$
$6$		0			0
$7$	25.6863	−	127.072i	0.198133	−	0.980175i
$7$	25.6863	−	127.072i	0.198133	−	0.980175i
$8$		−	2.00393i		−	0.0110703i
$9$		0			0
$10$		−	542.315i		−	1.71495i
$11$			181.337i			0.451862i	0.974143	+	0.225931i	$0.0725423\pi$
$11$			181.337i			0.451862i	−0.974143	+	0.225931i	$0.927458\pi$
$12$		0			0
$13$		−	796.458i		−	1.30709i	−0.756889	−	0.653544i	$-0.773282\pi$
$13$		−	796.458i		−	1.30709i	0.756889	−	0.653544i	$-0.226718\pi$
$14$	−1014.58	−	205.087i	−1.38346	−	0.279652i
$15$		0			0
$16$	−1031.97			−1.00778
$17$	−59.3989			−0.0498490			−0.0249245	−	0.999689i	$-0.507935\pi$
$17$	−59.3989			−0.0498490			−0.0249245	+	0.999689i	$0.507935\pi$
$18$		0			0
$19$			966.599i			0.614274i	0.951665	+	0.307137i	$0.0993710\pi$
$19$			966.599i			0.614274i	−0.951665	+	0.307137i	$0.900629\pi$
$20$	−2156.48			−1.20551
$21$		0			0
$22$	1447.85			0.637774
$23$			2491.36i			0.982014i	0.871156	+	0.491007i	$0.163371\pi$
$23$			2491.36i			0.982014i	−0.871156	+	0.491007i	$0.836629\pi$
$24$		0			0
$25$	1488.49			0.476317
$26$	−6359.16			−1.84487
$27$		0			0
$28$	−815.514	+	4034.40i	−0.196579	+	0.972487i
$29$		−	3787.11i		−	0.836205i	−0.908400	−	0.418102i	$-0.862695\pi$
$29$		−	3787.11i		−	0.836205i	0.908400	−	0.418102i	$-0.137305\pi$
$30$		0			0
$31$		−	7424.40i		−	1.38758i	−0.720178	−	0.693789i	$-0.755940\pi$
$31$		−	7424.40i		−	1.38758i	0.720178	−	0.693789i	$-0.244060\pi$
$32$			8175.42i			1.41135i
$33$		0			0
$34$			474.259i			0.0703587i
$35$	1744.68	−	8631.05i	0.240739	−	1.19095i
$36$		0			0
$37$	−12638.0			−1.51766			−0.758829	−	0.651290i	$-0.774228\pi$
$37$	−12638.0			−1.51766			−0.758829	+	0.651290i	$0.774228\pi$
$38$	7717.61			0.867010
$39$		0			0
$40$		−	136.113i		−	0.0134508i
$41$	19790.5			1.83865			0.919323	−	0.393505i	$-0.128738\pi$
$41$	19790.5			1.83865			0.919323	+	0.393505i	$0.128738\pi$
$42$		0			0
$43$	13783.1			1.13678			0.568388	−	0.822761i	$-0.307567\pi$
$43$	13783.1			1.13678			0.568388	+	0.822761i	$0.307567\pi$
$44$		−	5757.28i		−	0.448317i
$45$		0			0
$46$	19891.8			1.38605
$47$	23475.1			1.55011			0.775057	−	0.631892i	$-0.217721\pi$
$47$	23475.1			1.55011			0.775057	+	0.631892i	$0.217721\pi$
$48$		0			0
$49$	−15487.4	−	6528.00i	−0.921487	−	0.388409i
$50$		−	11884.5i		−	0.672292i
$51$		0			0
$52$			25286.8i			1.29684i
$53$			27061.7i			1.32332i	0.749803	+	0.661661i	$0.230148\pi$
$53$			27061.7i			1.32332i	−0.749803	+	0.661661i	$0.769852\pi$
$54$		0			0
$55$			12316.9i			0.549029i
$56$	−254.643	−	51.4736i	−0.0108508	−	0.00219338i
$57$		0			0
$58$	−30237.4			−1.18025
$59$	−9085.13			−0.339782			−0.169891	−	0.985463i	$-0.554342\pi$
$59$	−9085.13			−0.339782			−0.169891	+	0.985463i	$0.554342\pi$
$60$		0			0
$61$			22432.7i			0.771892i	0.922521	+	0.385946i	$0.126125\pi$
$61$			22432.7i			0.771892i	−0.922521	+	0.385946i	$0.873875\pi$
$62$	−59278.6			−1.95848
$63$		0			0
$64$	32252.0			0.984252
$65$		−	54097.6i		−	1.58816i
$66$		0			0
$67$	59524.2			1.61997			0.809985	−	0.586451i	$-0.199475\pi$
$67$	59524.2			1.61997			0.809985	+	0.586451i	$0.199475\pi$
$68$	1885.86			0.0494580
$69$		0			0
$70$	−68912.9	−	13930.0i	−1.68095	−	0.339788i
$71$			11632.3i			0.273854i	0.990581	+	0.136927i	$0.0437226\pi$
$71$			11632.3i			0.273854i	−0.990581	+	0.136927i	$0.956277\pi$
$72$		0			0
$73$			38939.3i			0.855227i	0.903962	+	0.427613i	$0.140645\pi$
$73$			38939.3i			0.855227i	−0.903962	+	0.427613i	$0.859355\pi$
$74$			100905.i			2.14208i
$75$		0			0
$76$		−	30688.6i		−	0.609456i
$77$	23042.8	+	4657.88i	0.442903	+	0.0895285i
$78$		0			0
$79$	15289.7			0.275632			0.137816	−	0.990458i	$-0.455992\pi$
$79$	15289.7			0.275632			0.137816	+	0.990458i	$0.455992\pi$
$80$	−70094.1			−1.22449
$81$		0			0
$82$		−	158014.i		−	2.59513i
$83$	64568.6			1.02879			0.514395	−	0.857554i	$-0.328017\pi$
$83$	64568.6			1.02879			0.514395	+	0.857554i	$0.328017\pi$
$84$		0			0
$85$	−4034.53			−0.0605684
$86$		−	110048.i		−	1.60449i
$87$		0			0
$88$	363.388			0.00500223
$89$	−103895.			−1.39034			−0.695170	−	0.718845i	$-0.744671\pi$
$89$	−103895.			−1.39034			−0.695170	+	0.718845i	$0.744671\pi$
$90$		0			0
$91$	−101207.	−	20458.0i	−1.28117	−	0.258977i
$92$		−	79098.3i		−	0.974311i
$93$		0			0
$94$		−	187433.i		−	2.18789i
$95$			65654.0i			0.746366i
$96$		0			0
$97$			14530.7i			0.156804i	0.996922	+	0.0784022i	$0.0249818\pi$
$97$			14530.7i			0.156804i	−0.996922	+	0.0784022i	$0.975018\pi$
$98$	−52121.5	+	123656.i	−0.548216	+	1.30062i
$99$		0			0
$100$	−47258.1			−0.472581
$101$	71877.9			0.701119			0.350560	−	0.936540i	$-0.385991\pi$
$101$	71877.9			0.701119			0.350560	+	0.936540i	$0.385991\pi$
$102$		0			0
$103$			199398.i			1.85194i	0.377597	+	0.925970i	$0.376750\pi$
$103$			199398.i			1.85194i	−0.377597	+	0.925970i	$0.623250\pi$
$104$	−1596.05			−0.0144698
$105$		0			0
$106$	216069.			1.86779
$107$		−	6187.77i		−	0.0522486i	−0.999659	−	0.0261243i	$-0.991683\pi$
$107$		−	6187.77i		−	0.0522486i	0.999659	−	0.0261243i	$-0.00831657\pi$
$108$		0			0
$109$	2236.70			0.0180319			0.00901593	−	0.999959i	$-0.497130\pi$
$109$	2236.70			0.0180319			0.00901593	+	0.999959i	$0.497130\pi$
$110$	98341.9			0.774920
$111$		0			0
$112$	−26507.4	+	131134.i	−0.199674	+	0.987803i
$113$		−	159158.i		−	1.17256i	−0.810110	−	0.586278i	$-0.800593\pi$
$113$		−	159158.i		−	1.17256i	0.810110	−	0.586278i	$-0.199407\pi$
$114$		0			0
$115$			169220.i			1.19318i
$116$			120237.i			0.829646i
$117$		0			0
$118$			72538.4i			0.479582i
$119$	−1525.74	+	7547.92i	−0.00987671	+	0.0488607i
$120$		0			0
$121$	128168.			0.795821
$122$	179109.			1.08948
$123$		0			0
$124$			235717.i			1.37669i
$125$	−111156.			−0.636295
$126$		0			0
$127$	50132.9			0.275812			0.137906	−	0.990445i	$-0.455963\pi$
$127$	50132.9			0.275812			0.137906	+	0.990445i	$0.455963\pi$
$128$			4103.93i			0.0221399i
$129$		0			0
$130$	−431931.			−2.24159
$131$	85756.2			0.436604			0.218302	−	0.975881i	$-0.429948\pi$
$131$	85756.2			0.436604			0.218302	+	0.975881i	$0.429948\pi$
$132$		0			0
$133$	122827.	+	24828.3i	0.602096	+	0.121708i
$134$		−	475259.i		−	2.28649i
$135$		0			0
$136$			119.031i			0.000551842i
$137$			76640.4i			0.348864i	0.984669	+	0.174432i	$0.0558089\pi$
$137$			76640.4i			0.348864i	−0.984669	+	0.174432i	$0.944191\pi$
$138$		0			0
$139$		−	306446.i		−	1.34529i	−0.739963	−	0.672647i	$-0.765157\pi$
$139$		−	306446.i		−	1.34529i	0.739963	−	0.672647i	$-0.234843\pi$
$140$	−55391.9	+	274027.i	−0.238850	+	1.18161i
$141$		0			0
$142$	92875.6			0.386528
$143$	144428.			0.590623
$144$		0			0
$145$		−	257230.i		−	1.01602i
$146$	310903.			1.20710
$147$		0			0
$148$	401244.			1.50575
$149$			491067.i			1.81207i	0.423201	+	0.906036i	$0.360906\pi$
$149$			491067.i			1.81207i	−0.423201	+	0.906036i	$0.639094\pi$
$150$		0			0
$151$	−494842.			−1.76614			−0.883068	−	0.469244i	$-0.844526\pi$
$151$	−494842.			−1.76614			−0.883068	+	0.469244i	$0.844526\pi$
$152$	1937.00			0.00680018
$153$		0			0
$154$	37189.9	−	183981.i	0.126364	−	0.625131i
$155$		−	504285.i		−	1.68596i
$156$		0			0
$157$		−	403237.i		−	1.30560i	−0.757529	−	0.652802i	$-0.773593\pi$
$157$		−	403237.i		−	1.30560i	0.757529	−	0.652802i	$-0.226407\pi$
$158$		−	122077.i		−	0.389038i
$159$		0			0
$160$			555296.i			1.71484i
$161$	316582.	+	63993.8i	0.962545	+	0.194569i
$162$		0			0
$163$	334861.			0.987179			0.493589	−	0.869695i	$-0.335685\pi$
$163$	334861.			0.987179			0.493589	+	0.869695i	$0.335685\pi$
$164$	−628330.			−1.82422
$165$		0			0
$166$		−	515535.i		−	1.45207i
$167$	−44898.2			−0.124577			−0.0622885	−	0.998058i	$-0.519840\pi$
$167$	−44898.2			−0.124577			−0.0622885	+	0.998058i	$0.519840\pi$
$168$		0			0
$169$	−263053.			−0.708478
$170$			32212.9i			0.0854885i
$171$		0			0
$172$	−437599.			−1.12786
$173$	−462944.			−1.17601			−0.588007	−	0.808856i	$-0.700087\pi$
$173$	−462944.			−1.17601			−0.588007	+	0.808856i	$0.700087\pi$
$174$		0			0
$175$	38233.8	−	189145.i	0.0943739	−	0.466874i
$176$		−	187134.i		−	0.455378i
$177$		0			0
$178$			829531.i			1.96238i
$179$		−	51366.8i		−	0.119826i	−0.998204	−	0.0599128i	$-0.980918\pi$
$179$		−	51366.8i		−	0.119826i	0.998204	−	0.0599128i	$-0.0190823\pi$
$180$		0			0
$181$		−	230031.i		−	0.521904i	−0.965352	−	0.260952i	$-0.915964\pi$
$181$		−	230031.i		−	0.521904i	0.965352	−	0.260952i	$-0.0840364\pi$
$182$	−163343.	+	808069.i	−0.365529	+	1.80830i
$183$		0			0
$184$	4992.53			0.0108712
$185$	−858406.			−1.84401
$186$		0			0
$187$		−	10771.2i		−	0.0225248i
$188$	−745313.			−1.53796
$189$		0			0
$190$	524201.			1.05345
$191$			16387.3i			0.0325031i	0.999868	+	0.0162516i	$0.00517326\pi$
$191$			16387.3i			0.0325031i	−0.999868	+	0.0162516i	$0.994827\pi$
$192$		0			0
$193$	−649781.			−1.25567			−0.627833	−	0.778348i	$-0.716058\pi$
$193$	−649781.			−1.25567			−0.627833	+	0.778348i	$0.716058\pi$
$194$	116018.			0.221320
$195$		0			0
$196$	491711.	+	207257.i	0.914259	+	0.385363i
$197$			145238.i			0.266634i	0.991073	+	0.133317i	$0.0425629\pi$
$197$			145238.i			0.266634i	−0.991073	+	0.133317i	$0.957437\pi$
$198$		0			0
$199$			48399.3i			0.0866375i	0.999061	+	0.0433188i	$0.0137931\pi$
$199$			48399.3i			0.0866375i	−0.999061	+	0.0433188i	$0.986207\pi$
$200$		−	2982.83i		−	0.00527296i
$201$		0			0
$202$		−	573895.i		−	0.989586i
$203$	−481234.	−	97276.6i	−0.819627	−	0.165679i
$204$		0			0
$205$	1.34423e6			2.23402
$206$	1.59205e6			2.61390
$207$		0			0
$208$			821920.i			1.31726i
$209$	−175280.			−0.277567
$210$		0			0
$211$	−658037.			−1.01752			−0.508761	−	0.860908i	$-0.669896\pi$
$211$	−658037.			−1.01752			−0.508761	+	0.860908i	$0.669896\pi$
$212$		−	859182.i		−	1.31294i
$213$		0			0
$214$	−49405.0			−0.0737457
$215$	936183.			1.38123
$216$		0			0
$217$	−943431.	−	190705.i	−1.36007	−	0.274924i
$218$		−	17858.4i		−	0.0254509i
$219$		0			0
$220$		−	391050.i		−	0.544723i
$221$			47308.8i			0.0651570i
$222$		0			0
$223$			732455.i			0.986322i	0.869938	+	0.493161i	$0.164159\pi$
$223$			732455.i			0.986322i	−0.869938	+	0.493161i	$0.835841\pi$
$224$	1.03886e6	+	209996.i	1.38337	+	0.279635i
$225$		0			0
$226$	−1.27077e6			−1.65499
$227$	202244.			0.260502			0.130251	−	0.991481i	$-0.458422\pi$
$227$	202244.			0.260502			0.130251	+	0.991481i	$0.458422\pi$
$228$		0			0
$229$		−	321111.i		−	0.404637i	−0.979320	−	0.202319i	$-0.935152\pi$
$229$		−	321111.i		−	0.404637i	0.979320	−	0.202319i	$-0.0648477\pi$
$230$	1.35110e6			1.68410
$231$		0			0
$232$	−7589.11			−0.00925701
$233$		−	96874.8i		−	0.116902i	−0.998290	−	0.0584509i	$-0.981384\pi$
$233$		−	96874.8i		−	0.116902i	0.998290	−	0.0584509i	$-0.0186161\pi$
$234$		0			0
$235$	1.59449e6			1.88345
$236$	288444.			0.337117
$237$		0			0
$238$	60264.9	+	12181.9i	0.0689639	+	0.0139404i
$239$			434839.i			0.492418i	0.969217	+	0.246209i	$0.0791849\pi$
$239$			434839.i			0.492418i	−0.969217	+	0.246209i	$0.920815\pi$
$240$		0			0
$241$		−	812484.i		−	0.901098i	−0.892752	−	0.450549i	$-0.851228\pi$
$241$		−	812484.i		−	0.901098i	0.892752	−	0.450549i	$-0.148772\pi$
$242$		−	1.02333e6i		−	1.12325i
$243$		0			0
$244$		−	712215.i		−	0.765838i
$245$	−1.05195e6	−	443399.i	−1.11964	−	0.471932i
$246$		0			0
$247$	769856.			0.802910
$248$	−14878.0			−0.0153609
$249$		0			0
$250$			887504.i			0.898091i
$251$	679893.			0.681171			0.340585	−	0.940214i	$-0.389375\pi$
$251$	679893.			0.681171			0.340585	+	0.940214i	$0.389375\pi$
$252$		0			0
$253$	−451777.			−0.443734
$254$		−	400276.i		−	0.389292i
$255$		0			0
$256$	1.06483e6			1.01550
$257$	−1.25295e6			−1.18332			−0.591658	−	0.806189i	$-0.701526\pi$
$257$	−1.25295e6			−1.18332			−0.591658	+	0.806189i	$0.701526\pi$
$258$		0			0
$259$	−324623.	+	1.60593e6i	−0.300697	+	1.48757i
$260$			1.71754e6i			1.57570i
$261$		0			0
$262$		−	684703.i		−	0.616239i
$263$			1.92848e6i			1.71920i	0.510969	+	0.859599i	$0.329287\pi$
$263$			1.92848e6i			1.71920i	−0.510969	+	0.859599i	$0.670713\pi$
$264$		0			0
$265$			1.83810e6i			1.60789i
$266$	198237.	−	980690.i	0.171783	−	0.849822i
$267$		0			0
$268$	−1.88984e6			−1.60726
$269$	460423.			0.387951			0.193975	−	0.981006i	$-0.437862\pi$
$269$	460423.			0.387951			0.193975	+	0.981006i	$0.437862\pi$
$270$		0			0
$271$			72590.5i			0.0600422i	0.999549	+	0.0300211i	$0.00955745\pi$
$271$			72590.5i			0.0600422i	−0.999549	+	0.0300211i	$0.990443\pi$
$272$	61297.8			0.0502369
$273$		0			0
$274$	611920.			0.492400
$275$			269919.i			0.215229i
$276$		0			0
$277$	331439.			0.259540			0.129770	−	0.991544i	$-0.458576\pi$
$277$	331439.			0.259540			0.129770	+	0.991544i	$0.458576\pi$
$278$	−2.44676e6			−1.89880
$279$		0			0
$280$	−17296.0	−	3496.22i	−0.0131841	−	0.00266504i
$281$		−	978539.i		−	0.739285i	−0.929174	−	0.369643i	$-0.879480\pi$
$281$		−	978539.i		−	0.739285i	0.929174	−	0.369643i	$-0.120520\pi$
$282$		0			0
$283$			2.10266e6i			1.56064i	0.625382	+	0.780319i	$0.284943\pi$
$283$			2.10266e6i			1.56064i	−0.625382	+	0.780319i	$0.715057\pi$
$284$		−	369313.i		−	0.271706i
$285$		0			0
$286$		−	1.15315e6i		−	0.833627i
$287$	508345.	−	2.51482e6i	0.364296	−	1.80219i
$288$		0			0
$289$	−1.41633e6			−0.997515
$290$	−2.05380e6			−1.43405
$291$		0			0
$292$		−	1.23629e6i		−	0.848519i
$293$	−2.32914e6			−1.58499			−0.792495	−	0.609878i	$-0.791218\pi$
$293$	−2.32914e6			−1.58499			−0.792495	+	0.609878i	$0.791218\pi$
$294$		0			0
$295$	−617086.			−0.412849
$296$			25325.7i			0.0168009i
$297$		0			0
$298$	3.92083e6			2.55763
$299$	1.98427e6			1.28358
$300$		0			0
$301$	354036.	−	1.75144e6i	0.225232	−	1.11424i
$302$			3.95097e6i			2.49279i
$303$		0			0
$304$		−	997500.i		−	0.619054i
$305$			1.52369e6i			0.937878i
$306$		0			0
$307$		−	1.81476e6i		−	1.09894i	−0.835514	−	0.549469i	$-0.814830\pi$
$307$		−	1.81476e6i		−	1.09894i	0.835514	−	0.549469i	$-0.185170\pi$
$308$	−731587.	−	147883.i	−0.439430	−	0.0888263i
$309$		0			0
$310$	−4.02636e6			−2.37963
$311$	938205.			0.550043			0.275022	−	0.961438i	$-0.411315\pi$
$311$	938205.			0.550043			0.275022	+	0.961438i	$0.411315\pi$
$312$		0			0
$313$		−	1.33328e6i		−	0.769239i	−0.923075	−	0.384619i	$-0.874333\pi$
$313$		−	1.33328e6i		−	0.769239i	0.923075	−	0.384619i	$-0.125667\pi$
$314$	−3.21957e6			−1.84278
$315$		0			0
$316$	−485432.			−0.273470
$317$			881093.i			0.492463i	0.969211	+	0.246231i	$0.0791923\pi$
$317$			881093.i			0.492463i	−0.969211	+	0.246231i	$0.920808\pi$
$318$		0			0
$319$	686744.			0.377849
$320$	2.19064e6			1.19590
$321$		0			0
$322$	510946.	−	2.52768e6i	0.274622	−	1.35857i
$323$		−	57414.9i		−	0.0306209i
$324$		0			0
$325$		−	1.18552e6i		−	0.622588i
$326$		−	2.67363e6i		−	1.39334i
$327$		0			0
$328$		−	39658.9i		−	0.0203543i
$329$	602989.	−	2.98303e6i	0.307128	−	1.51938i
$330$		0			0
$331$	1.79165e6			0.898843			0.449421	−	0.893320i	$-0.351630\pi$
$331$	1.79165e6			0.898843			0.449421	+	0.893320i	$0.351630\pi$
$332$	−2.04999e6			−1.02072
$333$		0			0
$334$			358481.i			0.175833i
$335$	4.04305e6			1.96832
$336$		0			0
$337$	−1.78122e6			−0.854363			−0.427181	−	0.904166i	$-0.640493\pi$
$337$	−1.78122e6			−0.854363			−0.427181	+	0.904166i	$0.640493\pi$
$338$			2.10029e6i			0.999972i
$339$		0			0
$340$	128092.			0.0600933
$341$	1.34632e6			0.626993
$342$		0			0
$343$	−1.22734e6	+	1.80033e6i	−0.563286	+	0.826262i
$344$		−	27620.4i		−	0.0125844i
$345$		0			0
$346$			3.69628e6i			1.65987i
$347$		−	787729.i		−	0.351199i	−0.984462	−	0.175600i	$-0.943814\pi$
$347$		−	787729.i		−	0.351199i	0.984462	−	0.175600i	$-0.0561864\pi$
$348$		0			0
$349$		−	65065.1i		−	0.0285946i	−0.999898	−	0.0142973i	$-0.995449\pi$
$349$		−	65065.1i		−	0.0285946i	0.999898	−	0.0142973i	$-0.00455113\pi$
$350$	−1.51019e6	−	305270.i	−0.658964	−	0.133203i
$351$		0			0
$352$	−1.48251e6			−0.637735
$353$	1.01928e6			0.435370			0.217685	−	0.976019i	$-0.430149\pi$
$353$	1.01928e6			0.435370			0.217685	+	0.976019i	$0.430149\pi$
$354$		0			0
$355$			790096.i			0.332743i
$356$	3.29857e6			1.37944
$357$		0			0
$358$	−410128.			−0.169126
$359$		−	510797.i		−	0.209176i	−0.994516	−	0.104588i	$-0.966648\pi$
$359$		−	510797.i		−	0.209176i	0.994516	−	0.104588i	$-0.0333524\pi$
$360$		0			0
$361$	1.54179e6			0.622667
$362$	−1.83664e6			−0.736635
$363$		0			0
$364$	3.21323e6	+	649523.i	1.27113	+	0.256945i
$365$			2.64486e6i			1.03913i
$366$		0			0
$367$			1.34928e6i			0.522923i	0.965214	+	0.261462i	$0.0842045\pi$
$367$			1.34928e6i			0.522923i	−0.965214	+	0.261462i	$0.915795\pi$
$368$		−	2.57101e6i		−	0.989655i
$369$		0			0
$370$			6.85377e6i			2.60271i
$371$	3.43878e6	+	695114.i	1.29709	+	0.262193i
$372$		0			0
$373$	3.86645e6			1.43893			0.719466	−	0.694528i	$-0.244387\pi$
$373$	3.86645e6			1.43893			0.719466	+	0.694528i	$0.244387\pi$
$374$	−86000.8			−0.0317924
$375$		0			0
$376$		−	47042.6i		−	0.0171602i
$377$	−3.01627e6			−1.09299
$378$		0			0
$379$	−2.40390e6			−0.859644			−0.429822	−	0.902914i	$-0.641424\pi$
$379$	−2.40390e6			−0.859644			−0.429822	+	0.902914i	$0.641424\pi$
$380$		−	2.08445e6i		−	0.740512i
$381$		0			0
$382$	130841.			0.0458761
$383$	−1.03382e6			−0.360121			−0.180061	−	0.983656i	$-0.557629\pi$
$383$	−1.03382e6			−0.360121			−0.180061	+	0.983656i	$0.557629\pi$
$384$		0			0
$385$	1.56513e6	+	316376.i	0.538144	+	0.108781i
$386$			5.18805e6i			1.77229i
$387$		0			0
$388$		−	461337.i		−	0.155575i
$389$			2.43425e6i			0.815628i	0.913065	+	0.407814i	$0.133709\pi$
$389$			2.43425e6i			0.815628i	−0.913065	+	0.407814i	$0.866291\pi$
$390$		0			0
$391$		−	147984.i		−	0.0489524i
$392$	−13081.7	+	31035.8i	−0.00429980	+	0.0102011i
$393$		0			0
$394$	1.15963e6			0.376338
$395$	1.03851e6			0.334904
$396$		0			0
$397$			1.50463e6i			0.479131i	0.970880	+	0.239566i	$0.0770050\pi$
$397$			1.50463e6i			0.479131i	−0.970880	+	0.239566i	$0.922995\pi$
$398$	386434.			0.122284
$399$		0			0
$400$	−1.53607e6			−0.480023
$401$		−	1.13980e6i		−	0.353972i	−0.984213	−	0.176986i	$-0.943365\pi$
$401$		−	1.13980e6i		−	0.353972i	0.984213	−	0.176986i	$-0.0566348\pi$
$402$		0			0
$403$	−5.91323e6			−1.81369
$404$	−2.28205e6			−0.695620
$405$		0			0
$406$	−776686.	+	3.84232e6i	−0.233846	+	1.15685i
$407$		−	2.29174e6i		−	0.685771i
$408$		0			0
$409$		−	3.41231e6i		−	1.00865i	−0.863514	−	0.504325i	$-0.831741\pi$
$409$		−	3.41231e6i		−	1.00865i	0.863514	−	0.504325i	$-0.168259\pi$
$410$		−	1.07327e7i		−	3.15318i
$411$		0			0
$412$		−	6.33068e6i		−	1.83741i
$413$	−233363.	+	1.15446e6i	−0.0673220	+	0.333046i
$414$		0			0
$415$	4.38567e6			1.25002
$416$	6.51138e6			1.84476
$417$		0			0
$418$			1.39949e6i			0.391768i
$419$	1.79766e6			0.500233			0.250116	−	0.968216i	$-0.419531\pi$
$419$	1.79766e6			0.500233			0.250116	+	0.968216i	$0.419531\pi$
$420$		0			0
$421$	−3.30245e6			−0.908095			−0.454047	−	0.890978i	$-0.650020\pi$
$421$	−3.30245e6			−0.908095			−0.454047	+	0.890978i	$0.650020\pi$
$422$			5.25396e6i			1.43617i
$423$		0			0
$424$	54229.8			0.0146495
$425$	−88414.7			−0.0237439
$426$		0			0
$427$	2.85056e6	+	576212.i	0.756589	+	0.152937i
$428$			196456.i			0.0518388i
$429$		0			0
$430$		−	7.47477e6i		−	1.94951i
$431$		−	3.79786e6i		−	0.984794i	−0.870371	−	0.492397i	$-0.836121\pi$
$431$		−	3.79786e6i		−	0.984794i	0.870371	−	0.492397i	$-0.163879\pi$
$432$		0			0
$433$		−	2.80204e6i		−	0.718215i	−0.933296	−	0.359108i	$-0.883081\pi$
$433$		−	2.80204e6i		−	0.718215i	0.933296	−	0.359108i	$-0.116919\pi$
$434$	−1.52265e6	+	7.53264e6i	−0.388039	+	1.91965i
$435$		0			0
$436$	−71012.9			−0.0178904
$437$	−2.40815e6			−0.603226
$438$		0			0
$439$		−	275441.i		−	0.0682131i	−0.999418	−	0.0341065i	$-0.989141\pi$
$439$		−	275441.i		−	0.0682131i	0.999418	−	0.0341065i	$-0.0108586\pi$
$440$	24682.3			0.00607790
$441$		0			0
$442$	377727.			0.0919650
$443$		−	2.82524e6i		−	0.683985i	−0.939703	−	0.341993i	$-0.888898\pi$
$443$		−	2.82524e6i		−	0.683985i	0.939703	−	0.341993i	$-0.111102\pi$
$444$		0			0
$445$	−7.05685e6			−1.68932
$446$	5.84814e6			1.39213
$447$		0			0
$448$	828433.	−	4.09831e6i	0.195012	−	0.964740i
$449$			3.19212e6i			0.747245i	0.927581	+	0.373622i	$0.121884\pi$
$449$			3.19212e6i			0.747245i	−0.927581	+	0.373622i	$0.878116\pi$
$450$		0			0
$451$			3.58876e6i			0.830813i
$452$			5.05312e6i			1.16336i
$453$		0			0
$454$		−	1.61478e6i		−	0.367683i
$455$	−6.87427e6	−	1.38957e6i	−1.55668	−	0.314666i
$456$		0			0
$457$	3.41224e6			0.764273			0.382137	−	0.924106i	$-0.375188\pi$
$457$	3.41224e6			0.764273			0.382137	+	0.924106i	$0.375188\pi$
$458$	−2.56384e6			−0.571120
$459$		0			0
$460$		−	5.37257e6i		−	1.18383i
$461$	−5.17955e6			−1.13511			−0.567557	−	0.823334i	$-0.692111\pi$
$461$	−5.17955e6			−1.13511			−0.567557	+	0.823334i	$0.692111\pi$
$462$		0			0
$463$	2.95911e6			0.641518			0.320759	−	0.947161i	$-0.396062\pi$
$463$	2.95911e6			0.641518			0.320759	+	0.947161i	$0.396062\pi$
$464$			3.90817e6i			0.842712i
$465$		0			0
$466$	−773477.			−0.165000
$467$	−4.58858e6			−0.973612			−0.486806	−	0.873510i	$-0.661838\pi$
$467$	−4.58858e6			−0.973612			−0.486806	+	0.873510i	$0.661838\pi$
$468$		0			0
$469$	1.52896e6	−	7.56385e6i	0.320969	−	1.58785i
$470$		−	1.27309e7i		−	2.65837i
$471$		0			0
$472$			18206.0i			0.00376148i
$473$			2.49939e6i			0.513665i
$474$		0			0
$475$			1.43877e6i			0.292589i
$476$	48440.6	−	239639.i	0.00979924	−	0.0484775i
$477$		0			0
$478$	3.47188e6			0.695017
$479$	−8.10226e6			−1.61349			−0.806747	−	0.590897i	$-0.798774\pi$
$479$	−8.10226e6			−1.61349			−0.806747	+	0.590897i	$0.798774\pi$
$480$		0			0
$481$			1.00656e7i			1.98371i
$482$	−6.48711e6			−1.27184
$483$		0			0
$484$	−4.06920e6			−0.789579
$485$			986967.i			0.190523i
$486$		0			0
$487$	−5.51573e6			−1.05385			−0.526927	−	0.849910i	$-0.676656\pi$
$487$	−5.51573e6			−1.05385			−0.526927	+	0.849910i	$0.676656\pi$
$488$	44953.6			0.00854505
$489$		0			0
$490$	−3.54023e6	+	8.39906e6i	−0.666103	+	1.58030i
$491$			6.20893e6i			1.16229i	0.813801	+	0.581143i	$0.197394\pi$
$491$			6.20893e6i			1.16229i	−0.813801	+	0.581143i	$0.802606\pi$
$492$		0			0
$493$			224950.i			0.0416839i
$494$		−	6.14676e6i		−	1.13326i
$495$		0			0
$496$			7.66175e6i			1.39838i
$497$	1.47813e6	+	298790.i	0.268425	+	0.0542594i
$498$		0			0
$499$	−1.86845e6			−0.335915			−0.167958	−	0.985794i	$-0.553717\pi$
$499$	−1.86845e6			−0.335915			−0.167958	+	0.985794i	$0.553717\pi$
$500$	3.52910e6			0.631304
$501$		0			0
$502$		−	5.42846e6i		−	0.961430i
$503$	1.10682e7			1.95055			0.975276	−	0.220992i	$-0.0709293\pi$
$503$	1.10682e7			1.95055			0.975276	+	0.220992i	$0.0709293\pi$
$504$		0			0
$505$	4.88214e6			0.851887
$506$			3.60712e6i			0.626303i
$507$		0			0
$508$	−1.59167e6			−0.273649
$509$	−9.62004e6			−1.64582			−0.822910	−	0.568171i	$-0.807651\pi$
$509$	−9.62004e6			−1.64582			−0.822910	+	0.568171i	$0.807651\pi$
$510$		0			0
$511$	4.94809e6	+	1.00021e6i	0.838272	+	0.169448i
$512$		−	8.37060e6i		−	1.41118i
$513$		0			0
$514$			1.00039e7i			1.67018i
$515$			1.35436e7i			2.25018i
$516$		0			0
$517$			4.25692e6i			0.700437i
$518$	1.28222e7	+	2.59189e6i	2.09961	+	0.424416i
$519$		0			0
$520$	−108408.			−0.0175814
$521$	454479.			0.0733533			0.0366766	−	0.999327i	$-0.488323\pi$
$521$	454479.			0.0733533			0.0366766	+	0.999327i	$0.488323\pi$
$522$		0			0
$523$		−	6.69977e6i		−	1.07104i	−0.844523	−	0.535520i	$-0.820116\pi$
$523$		−	6.69977e6i		−	1.07104i	0.844523	−	0.535520i	$-0.179884\pi$
$524$	−2.72268e6			−0.433179
$525$		0			0
$526$	1.53976e7			2.42654
$527$			441002.i			0.0691693i
$528$		0			0
$529$	229452.			0.0356495
$530$	1.46760e7			2.26943
$531$		0			0
$532$	−3.89965e6	−	788275.i	−0.597374	−	0.120753i
$533$		−	1.57623e7i		−	2.40327i
$534$		0			0
$535$		−	420290.i		−	0.0634840i
$536$		−	119283.i		−	0.0179335i
$537$		0			0
$538$		−	3.67616e6i		−	0.547569i
$539$	1.18377e6	−	2.80845e6i	0.175507	−	0.416385i
$540$		0			0
$541$	−7.60730e6			−1.11747			−0.558737	−	0.829345i	$-0.688714\pi$
$541$	−7.60730e6			−1.11747			−0.558737	+	0.829345i	$0.688714\pi$
$542$	579584.			0.0847459
$543$		0			0
$544$		−	485611.i		−	0.0703544i
$545$	151922.			0.0219094
$546$		0			0
$547$	2.09464e6			0.299323			0.149662	−	0.988737i	$-0.452182\pi$
$547$	2.09464e6			0.299323			0.149662	+	0.988737i	$0.452182\pi$
$548$		−	2.43326e6i		−	0.346128i
$549$		0			0
$550$	2.15511e6			0.303783
$551$	3.66061e6			0.513659
$552$		0			0
$553$	392734.	−	1.94288e6i	0.0546117	−	0.270168i
$554$		−	2.64631e6i		−	0.366324i
$555$		0			0
$556$			9.72937e6i			1.33474i
$557$			5.24643e6i			0.716516i	0.933623	+	0.358258i	$0.116629\pi$
$557$			5.24643e6i			0.716516i	−0.933623	+	0.358258i	$0.883371\pi$
$558$		0			0
$559$		−	1.09776e7i		−	1.48587i
$560$	−1.80046e6	+	8.90697e6i	−0.242612	+	1.20022i
$561$		0			0
$562$	−7.81294e6			−1.04346
$563$	3.50851e6			0.466501			0.233250	−	0.972417i	$-0.425064\pi$
$563$	3.50851e6			0.466501			0.233250	+	0.972417i	$0.425064\pi$
$564$		0			0
$565$		−	1.08105e7i		−	1.42470i
$566$	1.67882e7			2.20274
$567$		0			0
$568$	23310.3			0.00303164
$569$		−	1.15451e7i		−	1.49491i	−0.664310	−	0.747457i	$-0.731275\pi$
$569$		−	1.15451e7i		−	1.49491i	0.664310	−	0.747457i	$-0.268725\pi$
$570$		0			0
$571$	2.27200e6			0.291620			0.145810	−	0.989313i	$-0.453421\pi$
$571$	2.27200e6			0.291620			0.145810	+	0.989313i	$0.453421\pi$
$572$	−4.58543e6			−0.585990
$573$		0			0
$574$	−2.00790e7	−	4.05878e6i	−2.54369	−	0.514180i
$575$			3.70837e6i			0.467750i
$576$		0			0
$577$		−	5.36093e6i		−	0.670349i	−0.942156	−	0.335174i	$-0.891205\pi$
$577$		−	5.36093e6i		−	0.670349i	0.942156	−	0.335174i	$-0.108795\pi$
$578$			1.13084e7i			1.40793i
$579$		0			0
$580$			8.16681e6i			1.00805i
$581$	1.65853e6	−	8.20484e6i	0.203837	−	1.00839i
$582$		0			0
$583$	−4.90730e6			−0.597958
$584$	78031.8			0.00946759
$585$		0			0
$586$			1.85966e7i			2.23712i
$587$	−1.16996e7			−1.40145			−0.700725	−	0.713431i	$-0.747140\pi$
$587$	−1.16996e7			−1.40145			−0.700725	+	0.713431i	$0.747140\pi$
$588$		0			0
$589$	7.17642e6			0.852353
$590$			4.92700e6i			0.582710i
$591$		0			0
$592$	1.30420e7			1.52947
$593$	1.25302e7			1.46326			0.731632	−	0.681699i	$-0.238759\pi$
$593$	1.25302e7			1.46326			0.731632	+	0.681699i	$0.238759\pi$
$594$		0			0
$595$	−103632.	+	512675.i	−0.0120006	+	0.0593676i
$596$		−	1.55909e7i		−	1.79786i
$597$		0			0
$598$		−	1.58430e7i		−	1.81169i
$599$			6.68710e6i			0.761502i	0.924678	+	0.380751i	$0.124334\pi$
$599$			6.68710e6i			0.761502i	−0.924678	+	0.380751i	$0.875666\pi$
$600$		0			0
$601$			1.14251e7i			1.29025i	0.764077	+	0.645125i	$0.223195\pi$
$601$			1.14251e7i			1.29025i	−0.764077	+	0.645125i	$0.776805\pi$
$602$	−1.39840e7	−	2.82673e6i	−1.57268	−	0.317902i
$603$		0			0
$604$	1.57108e7			1.75228
$605$	8.70550e6			0.966953
$606$		0			0
$607$			5.02725e6i			0.553807i	0.960898	+	0.276904i	$0.0893083\pi$
$607$			5.02725e6i			0.553807i	−0.960898	+	0.276904i	$0.910692\pi$
$608$	−7.90235e6			−0.866957
$609$		0			0
$610$	1.21656e7			1.32376
$611$		−	1.86970e7i		−	2.02613i
$612$		0			0
$613$	−6.15239e6			−0.661291			−0.330646	−	0.943755i	$-0.607266\pi$
$613$	−6.15239e6			−0.661291			−0.330646	+	0.943755i	$0.607266\pi$
$614$	−1.44896e7			−1.55108
$615$		0			0
$616$	9334.08	−	46176.3i	0.000991105	−	0.00490306i
$617$			1.45928e7i			1.54321i	0.636102	+	0.771605i	$0.280546\pi$
$617$			1.45928e7i			1.54321i	−0.636102	+	0.771605i	$0.719454\pi$
$618$		0			0
$619$			204738.i			0.0214770i	0.999942	+	0.0107385i	$0.00341823\pi$
$619$			204738.i			0.0214770i	−0.999942	+	0.0107385i	$0.996582\pi$
$620$			1.60106e7i			1.67274i
$621$		0			0
$622$		−	7.49091e6i		−	0.776352i
$623$	−2.66868e6	+	1.32022e7i	−0.275472	+	1.36278i
$624$		0			0
$625$	−1.22016e7			−1.24944
$626$	−1.06453e7			−1.08573
$627$		0			0
$628$			1.28024e7i			1.29536i
$629$	750683.			0.0756537
$630$		0			0
$631$	−5.28340e6			−0.528250			−0.264125	−	0.964488i	$-0.585083\pi$
$631$	−5.28340e6			−0.528250			−0.264125	+	0.964488i	$0.585083\pi$
$632$		−	30639.5i		−	0.00305132i
$633$		0			0
$634$	7.03491e6			0.695081
$635$	3.40516e6			0.335122
$636$		0			0
$637$	−5.19928e6	+	1.23351e7i	−0.507685	+	1.20446i
$638$		−	5.48317e6i		−	0.533310i
$639$		0			0
$640$			278750.i			0.0269008i
$641$			1.28390e7i			1.23420i	0.786886	+	0.617099i	$0.211692\pi$
$641$			1.28390e7i			1.23420i	−0.786886	+	0.617099i	$0.788308\pi$
$642$		0			0
$643$		−	1.73194e7i		−	1.65199i	−0.563681	−	0.825993i	$-0.690615\pi$
$643$		−	1.73194e7i		−	1.65199i	0.563681	−	0.825993i	$-0.309385\pi$
$644$	−1.00512e7	−	2.03174e6i	−0.954996	−	0.193043i
$645$		0			0
$646$	−458418.			−0.0432196
$647$	−1.08785e7			−1.02166			−0.510831	−	0.859681i	$-0.670662\pi$
$647$	−1.08785e7			−1.02166			−0.510831	+	0.859681i	$0.670662\pi$
$648$		0			0
$649$		−	1.64747e6i		−	0.153535i
$650$	−9.46555e6			−0.878744
$651$		0			0
$652$	−1.06315e7			−0.979436
$653$		−	1.59790e7i		−	1.46645i	−0.679985	−	0.733226i	$-0.738014\pi$
$653$		−	1.59790e7i		−	1.46645i	0.679985	−	0.733226i	$-0.261986\pi$
$654$		0			0
$655$	5.82479e6			0.530490
$656$	−2.04232e7			−1.85295
$657$		0			0
$658$	−2.38174e7	−	4.81444e6i	−2.14451	−	0.433492i
$659$		−	3.69348e6i		−	0.331300i	−0.986185	−	0.165650i	$-0.947028\pi$
$659$		−	3.69348e6i		−	0.331300i	0.986185	−	0.165650i	$-0.0529722\pi$
$660$		0			0
$661$			1.23687e6i			0.110109i	0.998483	+	0.0550543i	$0.0175332\pi$
$661$			1.23687e6i			0.110109i	−0.998483	+	0.0550543i	$0.982467\pi$
$662$		−	1.43051e7i		−	1.26866i
$663$		0			0
$664$		−	129391.i		−	0.0113890i
$665$	8.34276e6	+	1.68641e6i	0.731570	+	0.147880i
$666$		0			0
$667$	9.43506e6			0.821164
$668$	1.42547e6			0.123600
$669$		0			0
$670$		−	3.22809e7i		−	2.77817i
$671$	−4.06788e6			−0.348788
$672$		0			0
$673$	1.55042e7			1.31951			0.659755	−	0.751481i	$-0.270660\pi$
$673$	1.55042e7			1.31951			0.659755	+	0.751481i	$0.270660\pi$
$674$			1.42218e7i			1.20588i
$675$		0			0
$676$	8.35167e6			0.702921
$677$	−5.05302e6			−0.423721			−0.211860	−	0.977300i	$-0.567952\pi$
$677$	−5.05302e6			−0.423721			−0.211860	+	0.977300i	$0.567952\pi$
$678$		0			0
$679$	1.84645e6	+	373241.i	0.153696	+	0.0310681i
$680$			8084.94i			0.000670508i
$681$		0			0
$682$		−	1.07494e7i		−	0.884962i
$683$			896048.i			0.0734986i	0.999325	+	0.0367493i	$0.0117003\pi$
$683$			896048.i			0.0734986i	−0.999325	+	0.0367493i	$0.988300\pi$
$684$		0			0
$685$			5.20562e6i			0.423883i
$686$	1.43744e7	+	9.79943e6i	1.16622	+	0.795043i
$687$		0			0
$688$	−1.42237e7			−1.14562
$689$	2.15535e7			1.72970
$690$		0			0
$691$			3.91379e6i			0.311819i	0.987771	+	0.155909i	$0.0498308\pi$
$691$			3.91379e6i			0.311819i	−0.987771	+	0.155909i	$0.950169\pi$
$692$	1.46980e7			1.16679
$693$		0			0
$694$	−6.28947e6			−0.495696
$695$		−	2.08146e7i		−	1.63458i
$696$		0			0
$697$	−1.17554e6			−0.0916546
$698$	−519499.			−0.0403595
$699$		0			0
$700$	−1.21388e6	+	6.00517e6i	−0.0936337	+	0.463212i
$701$			1.89526e7i			1.45671i	0.685199	+	0.728356i	$0.259715\pi$
$701$			1.89526e7i			1.45671i	−0.685199	+	0.728356i	$0.740285\pi$
$702$		0			0
$703$		−	1.22159e7i		−	0.932258i
$704$			5.84849e6i			0.444746i
$705$		0			0
$706$		−	8.13826e6i		−	0.614497i
$707$	1.84628e6	−	9.13365e6i	0.138915	−	0.687220i
$708$		0			0
$709$	−890215.			−0.0665088			−0.0332544	−	0.999447i	$-0.510587\pi$
$709$	−890215.			−0.0665088			−0.0332544	+	0.999447i	$0.510587\pi$
$710$	6.30836e6			0.469646
$711$		0			0
$712$			208199.i			0.0153914i
$713$	1.84969e7			1.36262
$714$		0			0
$715$	9.80991e6			0.717629
$716$			1.63084e6i			0.118886i
$717$		0			0
$718$	−4.07835e6			−0.295239
$719$	4.20018e6			0.303002			0.151501	−	0.988457i	$-0.451589\pi$
$719$	4.20018e6			0.303002			0.151501	+	0.988457i	$0.451589\pi$
$720$		0			0
$721$	2.53378e7	+	5.12178e6i	1.81523	+	0.366930i
$722$		−	1.23101e7i		−	0.878856i
$723$		0			0
$724$			7.30327e6i			0.517810i
$725$		−	5.63707e6i		−	0.398298i
$726$		0			0
$727$			2.34586e7i			1.64614i	0.567940	+	0.823070i	$0.307741\pi$
$727$			2.34586e7i			1.64614i	−0.567940	+	0.823070i	$0.692259\pi$
$728$	−40996.6	+	202813.i	−0.00286694	+	0.0141830i
$729$		0			0
$730$	2.11174e7			1.46667
$731$	−818700.			−0.0566671
$732$		0			0
$733$			1.51434e6i			0.104103i	0.998644	+	0.0520517i	$0.0165761\pi$
$733$			1.51434e6i			0.104103i	−0.998644	+	0.0520517i	$0.983424\pi$
$734$	1.07731e7			0.738074
$735$		0			0
$736$	−2.03679e7			−1.38597
$737$			1.07940e7i			0.732002i
$738$		0			0
$739$	−2.26993e7			−1.52898			−0.764488	−	0.644638i	$-0.777008\pi$
$739$	−2.26993e7			−1.52898			−0.764488	+	0.644638i	$0.777008\pi$
$740$	2.72536e7			1.82955
$741$		0			0
$742$	5.55000e6	−	2.74562e7i	0.370069	−	1.83076i
$743$			4.57793e6i			0.304227i	0.988363	+	0.152113i	$0.0486079\pi$
$743$			4.57793e6i			0.304227i	−0.988363	+	0.152113i	$0.951392\pi$
$744$		0			0
$745$			3.33546e7i			2.20174i
$746$		−	3.08709e7i		−	2.03096i
$747$		0			0
$748$			341976.i			0.0223482i
$749$	−786291.	−	158941.i	−0.0512128	−	0.0103522i
$750$		0			0
$751$	−1.86507e7			−1.20669			−0.603346	−	0.797480i	$-0.706166\pi$
$751$	−1.86507e7			−1.20669			−0.603346	+	0.797480i	$0.706166\pi$
$752$	−2.42256e7			−1.56218
$753$		0			0
$754$			2.40828e7i			1.54269i
$755$	−3.36110e7			−2.14592
$756$		0			0
$757$	−1.22971e7			−0.779942			−0.389971	−	0.920827i	$-0.627515\pi$
$757$	−1.22971e7			−0.779942			−0.389971	+	0.920827i	$0.627515\pi$
$758$			1.91935e7i			1.21333i
$759$		0			0
$760$	131566.			0.00826248
$761$	2.15406e7			1.34833			0.674165	−	0.738581i	$-0.264504\pi$
$761$	2.15406e7			1.34833			0.674165	+	0.738581i	$0.264504\pi$
$762$		0			0
$763$	57452.4	−	284221.i	0.00357270	−	0.0176744i
$764$		−	520282.i		−	0.0322482i
$765$		0			0
$766$			8.25434e6i			0.508289i
$767$			7.23592e6i			0.444125i
$768$		0			0
$769$			1.68033e7i			1.02466i	0.858790	+	0.512328i	$0.171217\pi$
$769$			1.68033e7i			1.02466i	−0.858790	+	0.512328i	$0.828783\pi$
$770$	2.52604e6	−	1.24965e7i	0.153537	−	0.759557i
$771$		0			0
$772$	2.06299e7			1.24582
$773$	−2.17234e7			−1.30761			−0.653805	−	0.756663i	$-0.726828\pi$
$773$	−2.17234e7			−1.30761			−0.653805	+	0.756663i	$0.726828\pi$
$774$		0			0
$775$		−	1.10512e7i		−	0.660927i
$776$	29118.6			0.00173587
$777$		0			0
$778$	1.94358e7			1.15121
$779$			1.91295e7i			1.12943i
$780$		0			0
$781$	−2.10937e6			−0.123744
$782$	−1.18155e6			−0.0690932
$783$		0			0
$784$	1.59825e7	+	6.73669e6i	0.928658	+	0.391432i
$785$		−	2.73889e7i		−	1.58636i
$786$		0			0
$787$			2.36452e7i			1.36084i	0.732824	+	0.680418i	$0.238202\pi$
$787$			2.36452e7i			1.36084i	−0.732824	+	0.680418i	$0.761798\pi$
$788$		−	4.61117e6i		−	0.264543i
$789$		0			0
$790$		−	8.29181e6i		−	0.472696i
$791$	−2.02245e7	−	4.08819e6i	−1.14931	−	0.232321i
$792$		0			0
$793$	1.78667e7			1.00893
$794$	1.20134e7			0.676264
$795$		0			0
$796$		−	1.53663e6i		−	0.0859580i
$797$	2.09606e7			1.16885			0.584425	−	0.811448i	$-0.301320\pi$
$797$	2.09606e7			1.16885			0.584425	+	0.811448i	$0.301320\pi$
$798$		0			0
$799$	−1.39440e6			−0.0772716
$800$			1.21690e7i			0.672250i
$801$		0			0
$802$	−9.10053e6			−0.499610
$803$	−7.06115e6			−0.386444
$804$		0			0
$805$	2.15031e7	+	4.34663e6i	1.16953	+	0.236409i
$806$			4.72130e7i			2.55990i
$807$		0			0
$808$		−	144039.i		−	0.00776158i
$809$		−	2.37033e7i		−	1.27332i	−0.771144	−	0.636661i	$-0.780315\pi$
$809$		−	2.37033e7i		−	1.27332i	0.771144	−	0.636661i	$-0.219685\pi$
$810$		0			0
$811$		−	4.53235e6i		−	0.241976i	−0.992654	−	0.120988i	$-0.961394\pi$
$811$		−	4.53235e6i		−	0.241976i	0.992654	−	0.120988i	$-0.0386062\pi$
$812$	1.52787e7	+	3.08844e6i	0.813198	+	0.164380i
$813$		0			0
$814$	−1.82979e7			−0.967923
$815$	2.27447e7			1.19946
$816$		0			0
$817$			1.33227e7i			0.698292i
$818$	−2.72449e7			−1.42365
$819$		0			0
$820$	−4.26779e7			−2.21650
$821$			1.66553e7i			0.862374i	0.902263	+	0.431187i	$0.141905\pi$
$821$			1.66553e7i			0.862374i	−0.902263	+	0.431187i	$0.858095\pi$
$822$		0			0
$823$	−1.61928e7			−0.833339			−0.416669	−	0.909058i	$-0.636803\pi$
$823$	−1.61928e7			−0.833339			−0.416669	+	0.909058i	$0.636803\pi$
$824$	399579.			0.0205015
$825$		0			0
$826$	9.21757e6	+	1.86324e6i	0.470074	+	0.0950208i
$827$			1.61246e7i			0.819834i	0.912123	+	0.409917i	$0.134442\pi$
$827$			1.61246e7i			0.819834i	−0.912123	+	0.409917i	$0.865558\pi$
$828$		0			0
$829$		−	3.36056e7i		−	1.69834i	−0.528118	−	0.849171i	$-0.677102\pi$
$829$		−	3.36056e7i		−	1.69834i	0.528118	−	0.849171i	$-0.322898\pi$
$830$		−	3.50165e7i		−	1.76432i
$831$		0			0
$832$		−	2.56874e7i		−	1.28650i
$833$	919937.	+	387756.i	0.0459352	+	0.0193618i
$834$		0			0
$835$	−3.04961e6			−0.151366
$836$	5.56498e6			0.275390
$837$		0			0
$838$		−	1.43530e7i		−	0.706047i
$839$	7.40633e6			0.363244			0.181622	−	0.983368i	$-0.441865\pi$
$839$	7.40633e6			0.363244			0.181622	+	0.983368i	$0.441865\pi$
$840$		0			0
$841$	6.16897e6			0.300762
$842$			2.63677e7i			1.28172i
$843$		0			0
$844$	2.08920e7			1.00954
$845$	−1.78673e7			−0.860827
$846$		0			0
$847$	3.29215e6	−	1.62865e7i	0.157678	−	0.780044i
$848$		−	2.79268e7i		−	1.33362i
$849$		0			0
$850$			705929.i			0.0335130i
$851$		−	3.14858e7i		−	1.49036i
$852$		0			0
$853$		−	1.39804e7i		−	0.657880i	−0.944351	−	0.328940i	$-0.893309\pi$
$853$		−	1.39804e7i		−	0.657880i	0.944351	−	0.328940i	$-0.106691\pi$
$854$	4.60065e6	−	2.27597e7i	0.215861	−	1.06788i
$855$		0			0
$856$	−12399.9			−0.000578406
$857$	−6.23872e6			−0.290164			−0.145082	−	0.989420i	$-0.546345\pi$
$857$	−6.23872e6			−0.290164			−0.145082	+	0.989420i	$0.546345\pi$
$858$		0			0
$859$		−	3.06879e7i		−	1.41901i	−0.704701	−	0.709504i	$-0.748919\pi$
$859$		−	3.06879e7i		−	1.41901i	0.704701	−	0.709504i	$-0.251081\pi$
$860$	−2.97229e7			−1.37039
$861$		0			0
$862$	−3.03232e7			−1.38998
$863$			3.33384e6i			0.152376i	0.997093	+	0.0761882i	$0.0242750\pi$
$863$			3.33384e6i			0.152376i	−0.997093	+	0.0761882i	$0.975725\pi$
$864$		0			0
$865$	−3.14444e7			−1.42890
$866$	−2.23723e7			−1.01372
$867$		0			0
$868$	2.99530e7	+	6.05470e6i	1.34940	+	0.272768i
$869$			2.77259e6i			0.124548i
$870$		0			0
$871$		−	4.74086e7i		−	2.11744i
$872$		−	4482.19i		−	0.000199618i
$873$		0			0
$874$			1.92274e7i			0.851415i
$875$	−2.85519e6	+	1.41248e7i	−0.126071	+	0.623680i
$876$		0			0
$877$	389154.			0.0170853			0.00854266	−	0.999964i	$-0.497281\pi$
$877$	389154.			0.0170853			0.00854266	+	0.999964i	$0.497281\pi$
$878$	−2.19921e6			−0.0962785
$879$		0			0
$880$		−	1.27107e7i		−	0.553301i
$881$	2.09290e7			0.908465			0.454232	−	0.890883i	$-0.349914\pi$
$881$	2.09290e7			0.908465			0.454232	+	0.890883i	$0.349914\pi$
$882$		0			0
$883$	−9.39508e6			−0.405507			−0.202754	−	0.979230i	$-0.564989\pi$
$883$	−9.39508e6			−0.405507			−0.202754	+	0.979230i	$0.564989\pi$
$884$		−	1.50201e6i		−	0.0646459i
$885$		0			0
$886$	−2.25576e7			−0.965402
$887$	−3.01808e7			−1.28802			−0.644008	−	0.765019i	$-0.722730\pi$
$887$	−3.01808e7			−1.28802			−0.644008	+	0.765019i	$0.722730\pi$
$888$		0			0
$889$	1.28773e6	−	6.37048e6i	0.0546474	−	0.270344i
$890$			5.63440e7i			2.38436i
$891$		0			0
$892$		−	2.32547e7i		−	0.978586i
$893$			2.26910e7i			0.952195i
$894$		0			0
$895$		−	3.48897e6i		−	0.145593i
$896$	521493.	+	105415.i	0.0217009	+	0.00438663i
$897$		0			0
$898$	2.54868e7			1.05469
$899$	−2.81170e7			−1.16030
$900$		0			0
$901$		−	1.60744e6i		−	0.0659662i
$902$	2.86537e7			1.17264
$903$		0			0
$904$	−318943.			−0.0129805
$905$		−	1.56243e7i		−	0.634133i
$906$		0			0
$907$	2.72280e7			1.09900			0.549499	−	0.835494i	$-0.314819\pi$
$907$	2.72280e7			1.09900			0.549499	+	0.835494i	$0.314819\pi$
$908$	−6.42106e6			−0.258459
$909$		0			0
$910$	−1.10947e7	+	5.48862e7i	−0.444132	+	2.19715i
$911$			4.64974e7i			1.85623i	0.372290	+	0.928117i	$0.378573\pi$
$911$			4.64974e7i			1.85623i	−0.372290	+	0.928117i	$0.621427\pi$
$912$		0			0
$913$			1.17087e7i			0.464870i
$914$		−	2.72443e7i		−	1.07872i
$915$		0			0
$916$			1.01949e7i			0.401464i
$917$	2.20276e6	−	1.08972e7i	0.0865054	−	0.427948i
$918$		0			0
$919$	2.94344e7			1.14965			0.574826	−	0.818276i	$-0.305070\pi$
$919$	2.94344e7			1.14965			0.574826	+	0.818276i	$0.305070\pi$
$920$	339106.			0.0132089
$921$		0			0
$922$			4.13551e7i			1.60214i
$923$	9.26463e6			0.357951
$924$		0			0
$925$	−1.88115e7			−0.722886
$926$		−	2.36264e7i		−	0.905463i
$927$		0			0
$928$	3.09612e7			1.18018
$929$	2.33163e7			0.886381			0.443191	−	0.896427i	$-0.353846\pi$
$929$	2.33163e7			0.886381			0.443191	+	0.896427i	$0.353846\pi$
$930$		0			0
$931$	6.30995e6	−	1.49701e7i	0.238590	−	0.566046i
$932$			3.07568e6i			0.115985i
$933$		0			0
$934$			3.66366e7i			1.37419i
$935$		−	731611.i		−	0.0273685i
$936$		0			0
$937$		−	2.49449e7i		−	0.928182i	−0.885788	−	0.464091i	$-0.846381\pi$
$937$		−	2.49449e7i		−	0.928182i	0.885788	−	0.464091i	$-0.153619\pi$
$938$	−6.03920e7	−	1.22076e7i	−2.24116	−	0.453028i
$939$		0			0
$940$	−5.06236e7			−1.86867
$941$	−1.72759e6			−0.0636013			−0.0318007	−	0.999494i	$-0.510124\pi$
$941$	−1.72759e6			−0.0636013			−0.0318007	+	0.999494i	$0.510124\pi$
$942$		0			0
$943$			4.93054e7i			1.80557i
$944$	9.37556e6			0.342427
$945$		0			0
$946$	1.99558e7			0.725007
$947$		−	2.40722e7i		−	0.872251i	−0.899886	−	0.436126i	$-0.856350\pi$
$947$		−	2.40722e7i		−	0.872251i	0.899886	−	0.436126i	$-0.143650\pi$
$948$		0			0
$949$	3.10135e7			1.11786
$950$	1.14876e7			0.412971
$951$		0			0
$952$	15125.5	+	3057.47i	0.000540902	+	0.000109338i
$953$		−	2.66088e7i		−	0.949059i	−0.880240	−	0.474529i	$-0.842618\pi$
$953$		−	2.66088e7i		−	0.949059i	0.880240	−	0.474529i	$-0.157382\pi$
$954$		0			0
$955$			1.11307e6i			0.0394925i
$956$		−	1.38057e7i		−	0.488556i
$957$		0			0
$958$			6.46909e7i			2.27735i
$959$	9.73883e6	+	1.96861e6i	0.341948	+	0.0691214i
$960$		0			0
$961$	−2.64926e7			−0.925372
$962$	8.03670e7			2.79988
$963$		0			0
$964$			2.57956e7i			0.894031i
$965$	−4.41349e7			−1.52568
$966$		0			0
$967$	−3.13663e7			−1.07869			−0.539346	−	0.842084i	$-0.681328\pi$
$967$	−3.13663e7			−1.07869			−0.539346	+	0.842084i	$0.681328\pi$
$968$		−	256840.i		−	0.00880996i
$969$		0			0
$970$	7.88024e6			0.268912
$971$	5.86276e6			0.199551			0.0997756	−	0.995010i	$-0.468188\pi$
$971$	5.86276e6			0.199551			0.0997756	+	0.995010i	$0.468188\pi$
$972$		0			0
$973$	−3.89406e7	−	7.87146e6i	−1.31862	−	0.266547i
$974$			4.40393e7i			1.48745i
$975$		0			0
$976$		−	2.31498e7i		−	0.777899i
$977$		−	7.41259e6i		−	0.248447i	−0.992254	−	0.124224i	$-0.960356\pi$
$977$		−	7.41259e6i		−	0.248447i	0.992254	−	0.124224i	$-0.0396440\pi$
$978$		0			0
$979$		−	1.88401e7i		−	0.628241i
$980$	3.33983e7	+	1.40775e7i	1.11086	+	0.468231i
$981$		0			0
$982$	4.95740e7			1.64049
$983$	−7.22864e6			−0.238601			−0.119301	−	0.992858i	$-0.538065\pi$
$983$	−7.22864e6			−0.238601			−0.119301	+	0.992858i	$0.538065\pi$
$984$		0			0
$985$			9.86498e6i			0.323971i
$986$	1.79607e6			0.0588343
$987$		0			0
$988$	−2.44422e7			−0.796613
$989$			3.43386e7i			1.11633i
$990$		0			0
$991$	4.40025e7			1.42329			0.711645	−	0.702539i	$-0.247950\pi$
$991$	4.40025e7			1.42329			0.711645	+	0.702539i	$0.247950\pi$
$992$	6.06976e7			1.95836
$993$		0			0
$994$	2.38563e6	−	1.18019e7i	0.0765838	−	0.378865i
$995$			3.28741e6i			0.105268i
$996$		0			0
$997$			2.90225e7i			0.924690i	0.886700	+	0.462345i	$0.152992\pi$
$997$			2.90225e7i			0.924690i	−0.886700	+	0.462345i	$0.847008\pi$
$998$			1.49182e7i			0.474123i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.6.c.b.62.2	yes	8
3.2	odd	2	inner	63.6.c.b.62.7	yes	8
4.3	odd	2		1008.6.k.b.881.8		8
7.6	odd	2	inner	63.6.c.b.62.1	✓	8
12.11	even	2		1008.6.k.b.881.2		8
21.20	even	2	inner	63.6.c.b.62.8	yes	8
28.27	even	2		1008.6.k.b.881.1		8
84.83	odd	2		1008.6.k.b.881.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.6.c.b.62.1	✓	8	7.6	odd	2	inner
63.6.c.b.62.2	yes	8	1.1	even	1	trivial
63.6.c.b.62.7	yes	8	3.2	odd	2	inner
63.6.c.b.62.8	yes	8	21.20	even	2	inner
1008.6.k.b.881.1		8	28.27	even	2
1008.6.k.b.881.2		8	12.11	even	2
1008.6.k.b.881.7		8	84.83	odd	2
1008.6.k.b.881.8		8	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	63.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-7.98430i q^{2} -31.7490 q^{4} +67.9227 q^{5} +(25.6863 - 127.072i) q^{7} -2.00393i q^{8} +O(q^{10})\)	\(q-7.98430i q^{2} -31.7490 q^{4} +67.9227 q^{5} +(25.6863 - 127.072i) q^{7} -2.00393i q^{8} -542.315i q^{10} +181.337i q^{11} -796.458i q^{13} +(-1014.58 - 205.087i) q^{14} -1031.97 q^{16} -59.3989 q^{17} +966.599i q^{19} -2156.48 q^{20} +1447.85 q^{22} +2491.36i q^{23} +1488.49 q^{25} -6359.16 q^{26} +(-815.514 + 4034.40i) q^{28} -3787.11i q^{29} -7424.40i q^{31} +8175.42i q^{32} +474.259i q^{34} +(1744.68 - 8631.05i) q^{35} -12638.0 q^{37} +7717.61 q^{38} -136.113i q^{40} +19790.5 q^{41} +13783.1 q^{43} -5757.28i q^{44} +19891.8 q^{46} +23475.1 q^{47} +(-15487.4 - 6528.00i) q^{49} -11884.5i q^{50} +25286.8i q^{52} +27061.7i q^{53} +12316.9i q^{55} +(-254.643 - 51.4736i) q^{56} -30237.4 q^{58} -9085.13 q^{59} +22432.7i q^{61} -59278.6 q^{62} +32252.0 q^{64} -54097.6i q^{65} +59524.2 q^{67} +1885.86 q^{68} +(-68912.9 - 13930.0i) q^{70} +11632.3i q^{71} +38939.3i q^{73} +100905. i q^{74} -30688.6i q^{76} +(23042.8 + 4657.88i) q^{77} +15289.7 q^{79} -70094.1 q^{80} -158014. i q^{82} +64568.6 q^{83} -4034.53 q^{85} -110048. i q^{86} +363.388 q^{88} -103895. q^{89} +(-101207. - 20458.0i) q^{91} -79098.3i q^{92} -187433. i q^{94} +65654.0i q^{95} +14530.7i q^{97} +(-52121.5 + 123656. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 112 q^{7}+O(q^{10}) \) 8 * q - 112 * q^7	\( 8 q - 112 q^{7} - 128 q^{16} + 5360 q^{22} + 9368 q^{25} - 10080 q^{28} - 34304 q^{37} + 32416 q^{43} + 71888 q^{46} - 106120 q^{49} - 115792 q^{58} + 253952 q^{64} + 152608 q^{67} - 260736 q^{70} - 94592 q^{79} + 475200 q^{85} - 26048 q^{88} - 501312 q^{91}+O(q^{100}) \) 8 * q - 112 * q^7 - 128 * q^16 + 5360 * q^22 + 9368 * q^25 - 10080 * q^28 - 34304 * q^37 + 32416 * q^43 + 71888 * q^46 - 106120 * q^49 - 115792 * q^58 + 253952 * q^64 + 152608 * q^67 - 260736 * q^70 - 94592 * q^79 + 475200 * q^85 - 26048 * q^88 - 501312 * q^91

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