LMFDB - Embedded newform 192.8.c.f.191.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,8,Mod(191,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("192.191");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	192.c (of order $2$, degree $1$, not 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:	$59.9779248930$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	no (minimal twist has level 96)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			191.13
Character	$\chi$	$=$	192.191
Dual form			192.8.c.f.191.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.85395 - 46.3975i) q^{3} -192.070i q^{5} +198.065i q^{7} +(-2118.46 + 543.217i) q^{9} +O(q^{10})$	\(q+(-5.85395 - 46.3975i) q^{3} -192.070i q^{5} +198.065i q^{7} +(-2118.46 + 543.217i) q^{9} +4238.13 q^{11} -1211.56 q^{13} +(-8911.59 + 1124.37i) q^{15} +18241.3i q^{17} +15245.3i q^{19} +(9189.73 - 1159.46i) q^{21} -48478.4 q^{23} +41234.0 q^{25} +(37605.3 + 95111.5i) q^{27} +175265. i q^{29} +211071. i q^{31} +(-24809.8 - 196639. i) q^{33} +38042.4 q^{35} -13673.8 q^{37} +(7092.39 + 56213.2i) q^{39} -662174. i q^{41} +377169. i q^{43} +(104336. + 406894. i) q^{45} -1.35766e6 q^{47} +784313. q^{49} +(846349. - 106783. i) q^{51} +488774. i q^{53} -814019. i q^{55} +(707346. - 89245.3i) q^{57} +2.13090e6 q^{59} +2.36809e6 q^{61} +(-107592. - 419594. i) q^{63} +232704. i q^{65} -1.34414e6i q^{67} +(283790. + 2.24928e6i) q^{69} -1.34993e6 q^{71} +1.65756e6 q^{73} +(-241382. - 1.91316e6i) q^{75} +839426. i q^{77} -2.14515e6i q^{79} +(4.19280e6 - 2.30157e6i) q^{81} -4.36234e6 q^{83} +3.50360e6 q^{85} +(8.13185e6 - 1.02599e6i) q^{87} +5.97323e6i q^{89} -239967. i q^{91} +(9.79317e6 - 1.23560e6i) q^{93} +2.92817e6 q^{95} +1.69750e7 q^{97} +(-8.97832e6 + 2.30223e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 2236 q^{9}+O(q^{10}) $ 28 * q + 2236 * q^9	$ 28 q + 2236 q^{9} + 7064 q^{13} - 2344 q^{21} - 417012 q^{25} + 278672 q^{33} + 965112 q^{37} + 2114464 q^{45} - 4821612 q^{49} - 3683352 q^{57} - 402664 q^{61} + 1987424 q^{69} + 223128 q^{73} - 6688900 q^{81} - 7477248 q^{85} - 34969576 q^{93} + 12115480 q^{97}+O(q^{100}) $ 28 * q + 2236 * q^9 + 7064 * q^13 - 2344 * q^21 - 417012 * q^25 + 278672 * q^33 + 965112 * q^37 + 2114464 * q^45 - 4821612 * q^49 - 3683352 * q^57 - 402664 * q^61 + 1987424 * q^69 + 223128 * q^73 - 6688900 * q^81 - 7477248 * q^85 - 34969576 * q^93 + 12115480 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−5.85395	−	46.3975i	−0.125177	−	0.992134i
$3$	−5.85395	−	46.3975i	−0.125177	−	0.992134i
$4$		0			0
$5$		−	192.070i		−	0.687171i	−0.939121	−	0.343586i	$-0.888358\pi$
$5$		−	192.070i		−	0.687171i	0.939121	−	0.343586i	$-0.111642\pi$
$6$		0			0
$7$			198.065i			0.218255i	0.994028	+	0.109128i	$0.0348057\pi$
$7$			198.065i			0.218255i	−0.994028	+	0.109128i	$0.965194\pi$
$8$		0			0
$9$	−2118.46	+	543.217i	−0.968661	+	0.248385i
$10$		0			0
$11$	4238.13			0.960063			0.480032	−	0.877251i	$-0.340625\pi$
$11$	4238.13			0.960063			0.480032	+	0.877251i	$0.340625\pi$
$12$		0			0
$13$	−1211.56			−0.152947			−0.0764737	−	0.997072i	$-0.524366\pi$
$13$	−1211.56			−0.152947			−0.0764737	+	0.997072i	$0.524366\pi$
$14$		0			0
$15$	−8911.59	+	1124.37i	−0.681766	+	0.0860180i
$16$		0			0
$17$			18241.3i			0.900499i	0.892903	+	0.450250i	$0.148665\pi$
$17$			18241.3i			0.900499i	−0.892903	+	0.450250i	$0.851335\pi$
$18$		0			0
$19$			15245.3i			0.509917i	0.966952	+	0.254958i	$0.0820618\pi$
$19$			15245.3i			0.509917i	−0.966952	+	0.254958i	$0.917938\pi$
$20$		0			0
$21$	9189.73	−	1159.46i	0.216539	−	0.0273205i
$22$		0			0
$23$	−48478.4			−0.830808			−0.415404	−	0.909637i	$-0.636360\pi$
$23$	−48478.4			−0.830808			−0.415404	+	0.909637i	$0.636360\pi$
$24$		0			0
$25$	41234.0			0.527795
$26$		0			0
$27$	37605.3	+	95111.5i	0.367685	+	0.929950i
$28$		0			0
$29$			175265.i			1.33445i	0.744857	+	0.667224i	$0.232518\pi$
$29$			175265.i			1.33445i	−0.744857	+	0.667224i	$0.767482\pi$
$30$		0			0
$31$			211071.i			1.27251i	0.771477	+	0.636257i	$0.219518\pi$
$31$			211071.i			1.27251i	−0.771477	+	0.636257i	$0.780482\pi$
$32$		0			0
$33$	−24809.8	−	196639.i	−0.120178	−	0.952512i
$34$		0			0
$35$	38042.4			0.149979
$36$		0			0
$37$	−13673.8			−0.0443794			−0.0221897	−	0.999754i	$-0.507064\pi$
$37$	−13673.8			−0.0443794			−0.0221897	+	0.999754i	$0.507064\pi$
$38$		0			0
$39$	7092.39	+	56213.2i	0.0191455	+	0.151744i
$40$		0			0
$41$		−	662174.i		−	1.50047i	−0.661169	−	0.750237i	$-0.729939\pi$
$41$		−	662174.i		−	1.50047i	0.661169	−	0.750237i	$-0.270061\pi$
$42$		0			0
$43$			377169.i			0.723430i	0.932289	+	0.361715i	$0.117809\pi$
$43$			377169.i			0.723430i	−0.932289	+	0.361715i	$0.882191\pi$
$44$		0			0
$45$	104336.	+	406894.i	0.170683	+	0.665636i
$46$		0			0
$47$	−1.35766e6			−1.90743			−0.953717	−	0.300707i	$-0.902777\pi$
$47$	−1.35766e6			−1.90743			−0.953717	+	0.300707i	$0.902777\pi$
$48$		0			0
$49$	784313.			0.952365
$50$		0			0
$51$	846349.	−	106783.i	0.893416	−	0.112722i
$52$		0			0
$53$			488774.i			0.450965i	0.974247	+	0.225482i	$0.0723958\pi$
$53$			488774.i			0.450965i	−0.974247	+	0.225482i	$0.927604\pi$
$54$		0			0
$55$		−	814019.i		−	0.659728i
$56$		0			0
$57$	707346.	−	89245.3i	0.505906	−	0.0638298i
$58$		0			0
$59$	2.13090e6			1.35077			0.675384	−	0.737467i	$-0.263978\pi$
$59$	2.13090e6			1.35077			0.675384	+	0.737467i	$0.263978\pi$
$60$		0			0
$61$	2.36809e6			1.33581			0.667905	−	0.744247i	$-0.267191\pi$
$61$	2.36809e6			1.33581			0.667905	+	0.744247i	$0.267191\pi$
$62$		0			0
$63$	−107592.	−	419594.i	−0.0542113	−	0.211416i
$64$		0			0
$65$			232704.i			0.105101i
$66$		0			0
$67$		−	1.34414e6i		−	0.545989i	−0.962016	−	0.272995i	$-0.911986\pi$
$67$		−	1.34414e6i		−	0.545989i	0.962016	−	0.272995i	$-0.0880141\pi$
$68$		0			0
$69$	283790.	+	2.24928e6i	0.103998	+	0.824273i
$70$		0			0
$71$	−1.34993e6			−0.447617			−0.223809	−	0.974633i	$-0.571849\pi$
$71$	−1.34993e6			−0.447617			−0.223809	+	0.974633i	$0.571849\pi$
$72$		0			0
$73$	1.65756e6			0.498701			0.249350	−	0.968413i	$-0.419783\pi$
$73$	1.65756e6			0.498701			0.249350	+	0.968413i	$0.419783\pi$
$74$		0			0
$75$	−241382.	−	1.91316e6i	−0.0660678	−	0.523644i
$76$		0			0
$77$			839426.i			0.209539i
$78$		0			0
$79$		−	2.14515e6i		−	0.489511i	−0.969585	−	0.244756i	$-0.921292\pi$
$79$		−	2.14515e6i		−	0.489511i	0.969585	−	0.244756i	$-0.0787078\pi$
$80$		0			0
$81$	4.19280e6	−	2.30157e6i	0.876610	−	0.481201i
$82$		0			0
$83$	−4.36234e6			−0.837425			−0.418712	−	0.908119i	$-0.637518\pi$
$83$	−4.36234e6			−0.837425			−0.418712	+	0.908119i	$0.637518\pi$
$84$		0			0
$85$	3.50360e6			0.618797
$86$		0			0
$87$	8.13185e6	−	1.02599e6i	1.32395	−	0.167042i
$88$		0			0
$89$			5.97323e6i			0.898141i	0.893496	+	0.449070i	$0.148245\pi$
$89$			5.97323e6i			0.898141i	−0.893496	+	0.449070i	$0.851755\pi$
$90$		0			0
$91$		−	239967.i		−	0.0333816i
$92$		0			0
$93$	9.79317e6	−	1.23560e6i	1.26251	−	0.159289i
$94$		0			0
$95$	2.92817e6			0.350400
$96$		0			0
$97$	1.69750e7			1.88846			0.944232	−	0.329280i	$-0.106806\pi$
$97$	1.69750e7			1.88846			0.944232	+	0.329280i	$0.106806\pi$
$98$		0			0
$99$	−8.97832e6	+	2.30223e6i	−0.929976	+	0.238465i
$100$		0			0
$101$		−	1.47334e7i		−	1.42291i	−0.702733	−	0.711454i	$-0.748037\pi$
$101$		−	1.47334e7i		−	1.42291i	0.702733	−	0.711454i	$-0.251963\pi$
$102$		0			0
$103$			1.09651e7i			0.988743i	0.869251	+	0.494371i	$0.164602\pi$
$103$			1.09651e7i			0.988743i	−0.869251	+	0.494371i	$0.835398\pi$
$104$		0			0
$105$	−222698.	−	1.76507e6i	−0.0187739	−	0.148799i
$106$		0			0
$107$	6.36626e6			0.502390			0.251195	−	0.967936i	$-0.419176\pi$
$107$	6.36626e6			0.502390			0.251195	+	0.967936i	$0.419176\pi$
$108$		0			0
$109$	2.19489e7			1.62338			0.811689	−	0.584089i	$-0.198548\pi$
$109$	2.19489e7			1.62338			0.811689	+	0.584089i	$0.198548\pi$
$110$		0			0
$111$	80045.4	+	634429.i	0.00555528	+	0.0440304i
$112$		0			0
$113$			2.95024e7i			1.92346i	0.274006	+	0.961728i	$0.411651\pi$
$113$			2.95024e7i			1.92346i	−0.274006	+	0.961728i	$0.588349\pi$
$114$		0			0
$115$			9.31125e6i			0.570907i
$116$		0			0
$117$	2.56664e6	−	658138.i	0.148154	−	0.0379898i
$118$		0			0
$119$	−3.61296e6			−0.196539
$120$		0			0
$121$	−1.52543e6			−0.0782786
$122$		0			0
$123$	−3.07232e7	+	3.87633e6i	−1.48867	+	0.187825i
$124$		0			0
$125$		−	2.29253e7i		−	1.04986i
$126$		0			0
$127$			1.83979e7i			0.796994i	0.917170	+	0.398497i	$0.130468\pi$
$127$			1.83979e7i			0.796994i	−0.917170	+	0.398497i	$0.869532\pi$
$128$		0			0
$129$	1.74997e7	−	2.20793e6i	0.717740	−	0.0905568i
$130$		0			0
$131$	1.29770e7			0.504343			0.252172	−	0.967683i	$-0.418855\pi$
$131$	1.29770e7			0.504343			0.252172	+	0.967683i	$0.418855\pi$
$132$		0			0
$133$	−3.01957e6			−0.111292
$134$		0			0
$135$	1.82681e7	−	7.22286e6i	0.639035	−	0.252663i
$136$		0			0
$137$			661112.i			0.0219661i	0.999940	+	0.0109830i	$0.00349608\pi$
$137$			661112.i			0.0219661i	−0.999940	+	0.0109830i	$0.996504\pi$
$138$		0			0
$139$			2.01409e7i			0.636101i	0.948074	+	0.318051i	$0.103028\pi$
$139$			2.01409e7i			0.636101i	−0.948074	+	0.318051i	$0.896972\pi$
$140$		0			0
$141$	7.94768e6	+	6.29922e7i	0.238767	+	1.89243i
$142$		0			0
$143$	−5.13473e6			−0.146839
$144$		0			0
$145$	3.36631e7			0.916994
$146$		0			0
$147$	−4.59133e6	−	3.63902e7i	−0.119214	−	0.944874i
$148$		0			0
$149$			1.57666e7i			0.390470i	0.980757	+	0.195235i	$0.0625469\pi$
$149$			1.57666e7i			0.390470i	−0.980757	+	0.195235i	$0.937453\pi$
$150$		0			0
$151$		−	3.46192e7i		−	0.818273i	−0.912473	−	0.409137i	$-0.865830\pi$
$151$		−	3.46192e7i		−	0.818273i	0.912473	−	0.409137i	$-0.134170\pi$
$152$		0			0
$153$	−9.90896e6	−	3.86434e7i	−0.223670	−	0.872279i
$154$		0			0
$155$	4.05405e7			0.874435
$156$		0			0
$157$	2.90767e7			0.599648			0.299824	−	0.953995i	$-0.403072\pi$
$157$	2.90767e7			0.599648			0.299824	+	0.953995i	$0.403072\pi$
$158$		0			0
$159$	2.26779e7	−	2.86126e6i	0.447418	−	0.0564504i
$160$		0			0
$161$		−	9.60187e6i		−	0.181328i
$162$		0			0
$163$		−	3.43986e7i		−	0.622135i	−0.950388	−	0.311067i	$-0.899314\pi$
$163$		−	3.43986e7i		−	0.622135i	0.950388	−	0.311067i	$-0.100686\pi$
$164$		0			0
$165$	−3.77685e7	+	4.76522e6i	−0.654539	+	0.0825827i
$166$		0			0
$167$	−9.12473e7			−1.51605			−0.758023	−	0.652228i	$-0.773835\pi$
$167$	−9.12473e7			−1.51605			−0.758023	+	0.652228i	$0.773835\pi$
$168$		0			0
$169$	−6.12806e7			−0.976607
$170$		0			0
$171$	−8.28153e6	−	3.22967e7i	−0.126656	−	0.493937i
$172$		0			0
$173$		−	2.44193e7i		−	0.358568i	−0.983797	−	0.179284i	$-0.942622\pi$
$173$		−	2.44193e7i		−	0.358568i	0.983797	−	0.179284i	$-0.0573782\pi$
$174$		0			0
$175$			8.16702e6i			0.115194i
$176$		0			0
$177$	−1.24742e7	−	9.88684e7i	−0.169085	−	1.34014i
$178$		0			0
$179$	1.35553e8			1.76654			0.883269	−	0.468866i	$-0.155337\pi$
$179$	1.35553e8			1.76654			0.883269	+	0.468866i	$0.155337\pi$
$180$		0			0
$181$	−1.01395e8			−1.27099			−0.635495	−	0.772105i	$-0.719204\pi$
$181$	−1.01395e8			−1.27099			−0.635495	+	0.772105i	$0.719204\pi$
$182$		0			0
$183$	−1.38627e7	−	1.09874e8i	−0.167213	−	1.32530i
$184$		0			0
$185$			2.62632e6i			0.0304963i
$186$		0			0
$187$			7.73088e7i			0.864536i
$188$		0			0
$189$	−1.88383e7	+	7.44830e6i	−0.202967	+	0.0802492i
$190$		0			0
$191$	−1.13998e8			−1.18381			−0.591905	−	0.806007i	$-0.701624\pi$
$191$	−1.13998e8			−1.18381			−0.591905	+	0.806007i	$0.701624\pi$
$192$		0			0
$193$	−6.60552e7			−0.661388			−0.330694	−	0.943738i	$-0.607283\pi$
$193$	−6.60552e7			−0.661388			−0.330694	+	0.943738i	$0.607283\pi$
$194$		0			0
$195$	1.07969e7	−	1.36224e6i	0.104274	−	0.0131562i
$196$		0			0
$197$		−	531661.i		−	0.00495453i	−0.999997	−	0.00247727i	$-0.999211\pi$
$197$		−	531661.i		−	0.00495453i	0.999997	−	0.00247727i	$-0.000788540\pi$
$198$		0			0
$199$			9.64727e7i			0.867798i	0.900961	+	0.433899i	$0.142863\pi$
$199$			9.64727e7i			0.867798i	−0.900961	+	0.433899i	$0.857137\pi$
$200$		0			0
$201$	−6.23650e7	+	7.86854e6i	−0.541694	+	0.0683452i
$202$		0			0
$203$	−3.47138e7			−0.291250
$204$		0			0
$205$	−1.27184e8			−1.03108
$206$		0			0
$207$	1.02700e8	−	2.63343e7i	0.804771	−	0.206360i
$208$		0			0
$209$			6.46117e7i			0.489552i
$210$		0			0
$211$			6.22023e7i			0.455845i	0.973679	+	0.227923i	$0.0731933\pi$
$211$			6.22023e7i			0.455845i	−0.973679	+	0.227923i	$0.926807\pi$
$212$		0			0
$213$	7.90241e6	+	6.26334e7i	0.0560313	+	0.444096i
$214$		0			0
$215$	7.24430e7			0.497121
$216$		0			0
$217$	−4.18058e7			−0.277733
$218$		0			0
$219$	−9.70329e6	−	7.69069e7i	−0.0624258	−	0.494778i
$220$		0			0
$221$		−	2.21003e7i		−	0.137729i
$222$		0			0
$223$			2.55941e8i			1.54552i	0.634700	+	0.772758i	$0.281124\pi$
$223$			2.55941e8i			1.54552i	−0.634700	+	0.772758i	$0.718876\pi$
$224$		0			0
$225$	−8.73527e7	+	2.23990e7i	−0.511255	+	0.131096i
$226$		0			0
$227$	−2.25437e8			−1.27919			−0.639594	−	0.768713i	$-0.720897\pi$
$227$	−2.25437e8			−1.27919			−0.639594	+	0.768713i	$0.720897\pi$
$228$		0			0
$229$	−7.98610e7			−0.439451			−0.219725	−	0.975562i	$-0.570516\pi$
$229$	−7.98610e7			−0.439451			−0.219725	+	0.975562i	$0.570516\pi$
$230$		0			0
$231$	3.89473e7	−	4.91395e6i	0.207891	−	0.0262294i
$232$		0			0
$233$		−	7.68048e7i		−	0.397780i	−0.980022	−	0.198890i	$-0.936266\pi$
$233$		−	7.68048e7i		−	0.397780i	0.980022	−	0.198890i	$-0.0637336\pi$
$234$		0			0
$235$			2.60767e8i			1.31073i
$236$		0			0
$237$	−9.95297e7	+	1.25576e7i	−0.485661	+	0.0612755i
$238$		0			0
$239$	7.79208e7			0.369199			0.184600	−	0.982814i	$-0.440901\pi$
$239$	7.79208e7			0.369199			0.184600	+	0.982814i	$0.440901\pi$
$240$		0			0
$241$	−3.14267e8			−1.44624			−0.723119	−	0.690724i	$-0.757292\pi$
$241$	−3.14267e8			−1.44624			−0.723119	+	0.690724i	$0.757292\pi$
$242$		0			0
$243$	−1.31332e8	−	1.81062e8i	−0.587148	−	0.809480i
$244$		0			0
$245$		−	1.50643e8i		−	0.654438i
$246$		0			0
$247$		−	1.84706e7i		−	0.0779904i
$248$		0			0
$249$	2.55369e7	+	2.02402e8i	0.104826	+	0.830838i
$250$		0			0
$251$	−2.34756e8			−0.937043			−0.468522	−	0.883452i	$-0.655213\pi$
$251$	−2.34756e8			−0.937043			−0.468522	+	0.883452i	$0.655213\pi$
$252$		0			0
$253$	−2.05458e8			−0.797628
$254$		0			0
$255$	−2.05099e7	−	1.62558e8i	−0.0774592	−	0.613930i
$256$		0			0
$257$			2.21399e8i			0.813597i	0.913518	+	0.406798i	$0.133355\pi$
$257$			2.21399e8i			0.813597i	−0.913518	+	0.406798i	$0.866645\pi$
$258$		0			0
$259$		−	2.70829e6i		−	0.00968605i
$260$		0			0
$261$	−9.52068e7	−	3.71292e8i	−0.331456	−	1.29263i
$262$		0			0
$263$	2.79324e8			0.946810			0.473405	−	0.880845i	$-0.343025\pi$
$263$	2.79324e8			0.946810			0.473405	+	0.880845i	$0.343025\pi$
$264$		0			0
$265$	9.38789e7			0.309890
$266$		0			0
$267$	2.77143e8	−	3.49670e7i	0.891077	−	0.112427i
$268$		0			0
$269$		−	3.53445e8i		−	1.10711i	−0.832814	−	0.553553i	$-0.813272\pi$
$269$		−	3.53445e8i		−	1.10711i	0.832814	−	0.553553i	$-0.186728\pi$
$270$		0			0
$271$			3.68128e8i			1.12359i	0.827278	+	0.561793i	$0.189888\pi$
$271$			3.68128e8i			1.12359i	−0.827278	+	0.561793i	$0.810112\pi$
$272$		0			0
$273$	−1.11339e7	+	1.40475e6i	−0.0331190	+	0.00417860i
$274$		0			0
$275$	1.74755e8			0.506717
$276$		0			0
$277$	5.93804e8			1.67866			0.839332	−	0.543620i	$-0.182947\pi$
$277$	5.93804e8			1.67866			0.839332	+	0.543620i	$0.182947\pi$
$278$		0			0
$279$	−1.14657e8	−	4.47146e8i	−0.316073	−	1.23264i
$280$		0			0
$281$		−	1.37023e8i		−	0.368401i	−0.982889	−	0.184201i	$-0.941030\pi$
$281$		−	1.37023e8i		−	0.368401i	0.982889	−	0.184201i	$-0.0589696\pi$
$282$		0			0
$283$			4.21823e8i			1.10631i	0.833078	+	0.553156i	$0.186577\pi$
$283$			4.21823e8i			1.10631i	−0.833078	+	0.553156i	$0.813423\pi$
$284$		0			0
$285$	−1.71414e7	−	1.35860e8i	−0.0438620	−	0.347644i
$286$		0			0
$287$	1.31154e8			0.327486
$288$		0			0
$289$	7.75954e7			0.189101
$290$		0			0
$291$	−9.93708e7	−	7.87598e8i	−0.236392	−	1.87361i
$292$		0			0
$293$			6.66503e8i			1.54798i	0.633198	+	0.773990i	$0.281742\pi$
$293$			6.66503e8i			1.54798i	−0.633198	+	0.773990i	$0.718258\pi$
$294$		0			0
$295$		−	4.09282e8i		−	0.928209i
$296$		0			0
$297$	1.59376e8	+	4.03095e8i	0.353001	+	0.892811i
$298$		0			0
$299$	5.87343e7			0.127070
$300$		0			0
$301$	−7.47041e7			−0.157893
$302$		0			0
$303$	−6.83591e8	+	8.62483e7i	−1.41172	+	0.178115i
$304$		0			0
$305$		−	4.54841e8i		−	0.917930i
$306$		0			0
$307$		−	4.64843e8i		−	0.916899i	−0.888720	−	0.458450i	$-0.848405\pi$
$307$		−	4.64843e8i		−	0.916899i	0.888720	−	0.458450i	$-0.151595\pi$
$308$		0			0
$309$	5.08755e8	−	6.41893e7i	0.980966	−	0.123768i
$310$		0			0
$311$	5.32696e8			1.00420			0.502098	−	0.864811i	$-0.332562\pi$
$311$	5.32696e8			1.00420			0.502098	+	0.864811i	$0.332562\pi$
$312$		0			0
$313$	6.08243e8			1.12117			0.560586	−	0.828096i	$-0.310576\pi$
$313$	6.08243e8			1.12117			0.560586	+	0.828096i	$0.310576\pi$
$314$		0			0
$315$	−8.05915e7	+	2.06653e7i	−0.145279	+	0.0372524i
$316$		0			0
$317$			8.48915e8i			1.49678i	0.663262	+	0.748388i	$0.269172\pi$
$317$			8.48915e8i			1.49678i	−0.663262	+	0.748388i	$0.730828\pi$
$318$		0			0
$319$			7.42795e8i			1.28115i
$320$		0			0
$321$	−3.72678e7	−	2.95379e8i	−0.0628877	−	0.498439i
$322$		0			0
$323$	−2.78094e8			−0.459180
$324$		0			0
$325$	−4.99573e7			−0.0807249
$326$		0			0
$327$	−1.28488e8	−	1.01837e9i	−0.203210	−	1.61061i
$328$		0			0
$329$		−	2.68906e8i		−	0.416307i
$330$		0			0
$331$			9.67477e8i			1.46637i	0.680031	+	0.733184i	$0.261967\pi$
$331$			9.67477e8i			1.46637i	−0.680031	+	0.733184i	$0.738033\pi$
$332$		0			0
$333$	2.89673e7	−	7.42782e6i	0.0429887	−	0.0110232i
$334$		0			0
$335$	−2.58170e8			−0.375188
$336$		0			0
$337$	4.84379e8			0.689415			0.344708	−	0.938710i	$-0.387978\pi$
$337$	4.84379e8			0.689415			0.344708	+	0.938710i	$0.387978\pi$
$338$		0			0
$339$	1.36884e9	−	1.72705e8i	1.90833	−	0.240772i
$340$		0			0
$341$			8.94546e8i			1.22169i
$342$		0			0
$343$			3.18460e8i			0.426114i
$344$		0			0
$345$	4.32019e8	−	5.45076e7i	0.566417	−	0.0714644i
$346$		0			0
$347$	1.96361e8			0.252291			0.126145	−	0.992012i	$-0.459739\pi$
$347$	1.96361e8			0.252291			0.126145	+	0.992012i	$0.459739\pi$
$348$		0			0
$349$	6.27273e8			0.789891			0.394946	−	0.918704i	$-0.370763\pi$
$349$	6.27273e8			0.789891			0.394946	+	0.918704i	$0.370763\pi$
$350$		0			0
$351$	−4.55610e7	−	1.15233e8i	−0.0562365	−	0.142233i
$352$		0			0
$353$		−	7.80693e8i		−	0.944645i	−0.881426	−	0.472323i	$-0.843416\pi$
$353$		−	7.80693e8i		−	0.944645i	0.881426	−	0.472323i	$-0.156584\pi$
$354$		0			0
$355$			2.59281e8i			0.307590i
$356$		0			0
$357$	2.11500e7	+	1.67632e8i	0.0246021	+	0.194993i
$358$		0			0
$359$	−8.69020e8			−0.991286			−0.495643	−	0.868526i	$-0.665068\pi$
$359$	−8.69020e8			−0.991286			−0.495643	+	0.868526i	$0.665068\pi$
$360$		0			0
$361$	6.61452e8			0.739985
$362$		0			0
$363$	8.92977e6	+	7.07761e7i	0.00979867	+	0.0776629i
$364$		0			0
$365$		−	3.18369e8i		−	0.342693i
$366$		0			0
$367$			1.53891e9i			1.62510i	0.582890	+	0.812551i	$0.301922\pi$
$367$			1.53891e9i			1.62510i	−0.582890	+	0.812551i	$0.698078\pi$
$368$		0			0
$369$	3.59704e8	+	1.40279e9i	0.372695	+	1.45345i
$370$		0			0
$371$	−9.68091e7			−0.0984255
$372$		0			0
$373$	1.38373e9			1.38061			0.690303	−	0.723521i	$-0.257477\pi$
$373$	1.38373e9			1.38061			0.690303	+	0.723521i	$0.257477\pi$
$374$		0			0
$375$	−1.06368e9	+	1.34204e8i	−1.04160	+	0.131418i
$376$		0			0
$377$		−	2.12343e8i		−	0.204100i
$378$		0			0
$379$			1.45015e9i			1.36828i	0.729351	+	0.684140i	$0.239822\pi$
$379$			1.45015e9i			1.36828i	−0.729351	+	0.684140i	$0.760178\pi$
$380$		0			0
$381$	8.53617e8	−	1.07700e8i	0.790725	−	0.0997653i
$382$		0			0
$383$	4.13034e8			0.375655			0.187828	−	0.982202i	$-0.439855\pi$
$383$	4.13034e8			0.375655			0.187828	+	0.982202i	$0.439855\pi$
$384$		0			0
$385$	1.61229e8			0.143989
$386$		0			0
$387$	−2.04885e8	−	7.99019e8i	−0.179689	−	0.700759i
$388$		0			0
$389$		−	9.97406e8i		−	0.859109i	−0.903041	−	0.429555i	$-0.858671\pi$
$389$		−	9.97406e8i		−	0.859109i	0.903041	−	0.429555i	$-0.141329\pi$
$390$		0			0
$391$		−	8.84306e8i		−	0.748142i
$392$		0			0
$393$	−7.59669e7	−	6.02103e8i	−0.0631321	−	0.500376i
$394$		0			0
$395$	−4.12019e8			−0.336378
$396$		0			0
$397$	3.46714e6			0.00278102			0.00139051	−	0.999999i	$-0.499557\pi$
$397$	3.46714e6			0.00278102			0.00139051	+	0.999999i	$0.499557\pi$
$398$		0			0
$399$	1.76764e7	+	1.40101e8i	0.0139312	+	0.110417i
$400$		0			0
$401$			2.26679e8i			0.175552i	0.996140	+	0.0877760i	$0.0279760\pi$
$401$			2.26679e8i			0.175552i	−0.996140	+	0.0877760i	$0.972024\pi$
$402$		0			0
$403$		−	2.55724e8i		−	0.194628i
$404$		0			0
$405$	−4.42063e8	−	8.05312e8i	−0.330668	−	0.602381i
$406$		0			0
$407$	−5.79511e7			−0.0426071
$408$		0			0
$409$	−6.49242e8			−0.469218			−0.234609	−	0.972090i	$-0.575381\pi$
$409$	−6.49242e8			−0.469218			−0.234609	+	0.972090i	$0.575381\pi$
$410$		0			0
$411$	3.06739e7	−	3.87011e6i	0.0217933	−	0.00274965i
$412$		0			0
$413$			4.22056e8i			0.294812i
$414$		0			0
$415$			8.37875e8i			0.575454i
$416$		0			0
$417$	9.34487e8	−	1.17904e8i	0.631098	−	0.0796252i
$418$		0			0
$419$	−4.60966e8			−0.306140			−0.153070	−	0.988215i	$-0.548916\pi$
$419$	−4.60966e8			−0.306140			−0.153070	+	0.988215i	$0.548916\pi$
$420$		0			0
$421$	−2.23723e9			−1.46125			−0.730624	−	0.682780i	$-0.760771\pi$
$421$	−2.23723e9			−1.46125			−0.730624	+	0.682780i	$0.760771\pi$
$422$		0			0
$423$	2.87616e9	−	7.37506e8i	1.84766	−	0.473777i
$424$		0			0
$425$			7.52160e8i			0.475279i
$426$		0			0
$427$			4.69037e8i			0.291548i
$428$		0			0
$429$	3.00584e7	+	2.38239e8i	0.0183809	+	0.145684i
$430$		0			0
$431$	1.91204e9			1.15034			0.575170	−	0.818034i	$-0.304936\pi$
$431$	1.91204e9			1.15034			0.575170	+	0.818034i	$0.304936\pi$
$432$		0			0
$433$	−3.36278e8			−0.199063			−0.0995317	−	0.995034i	$-0.531734\pi$
$433$	−3.36278e8			−0.199063			−0.0995317	+	0.995034i	$0.531734\pi$
$434$		0			0
$435$	−1.97062e8	−	1.56189e9i	−0.114787	−	0.909782i
$436$		0			0
$437$		−	7.39069e8i		−	0.423643i
$438$		0			0
$439$		−	2.00530e9i		−	1.13124i	−0.824668	−	0.565618i	$-0.808638\pi$
$439$		−	2.00530e9i		−	1.13124i	0.824668	−	0.565618i	$-0.191362\pi$
$440$		0			0
$441$	−1.66154e9	+	4.26052e8i	−0.922519	+	0.236553i
$442$		0			0
$443$	−2.58805e9			−1.41436			−0.707178	−	0.707035i	$-0.750032\pi$
$443$	−2.58805e9			−1.41436			−0.707178	+	0.707035i	$0.750032\pi$
$444$		0			0
$445$	1.14728e9			0.617177
$446$		0			0
$447$	7.31533e8	−	9.22971e7i	0.387398	−	0.0488778i
$448$		0			0
$449$			2.67269e9i			1.39343i	0.717347	+	0.696716i	$0.245356\pi$
$449$			2.67269e9i			1.39343i	−0.717347	+	0.696716i	$0.754644\pi$
$450$		0			0
$451$		−	2.80638e9i		−	1.44055i
$452$		0			0
$453$	−1.60625e9	+	2.02659e8i	−0.811837	+	0.102429i
$454$		0			0
$455$	−4.60905e7			−0.0229389
$456$		0			0
$457$	−1.46748e9			−0.719228			−0.359614	−	0.933101i	$-0.617092\pi$
$457$	−1.46748e9			−0.719228			−0.359614	+	0.933101i	$0.617092\pi$
$458$		0			0
$459$	−1.73495e9	+	6.85968e8i	−0.837420	+	0.331100i
$460$		0			0
$461$			1.84277e8i			0.0876026i	0.999040	+	0.0438013i	$0.0139468\pi$
$461$			1.84277e8i			0.0876026i	−0.999040	+	0.0438013i	$0.986053\pi$
$462$		0			0
$463$			2.14254e9i			1.00322i	0.865094	+	0.501609i	$0.167258\pi$
$463$			2.14254e9i			1.00322i	−0.865094	+	0.501609i	$0.832742\pi$
$464$		0			0
$465$	−2.37322e8	−	1.88098e9i	−0.109459	−	0.867557i
$466$		0			0
$467$	1.46950e9			0.667668			0.333834	−	0.942632i	$-0.391658\pi$
$467$	1.46950e9			0.667668			0.333834	+	0.942632i	$0.391658\pi$
$468$		0			0
$469$	2.66228e8			0.119165
$470$		0			0
$471$	−1.70213e8	−	1.34909e9i	−0.0750621	−	0.594931i
$472$		0			0
$473$			1.59849e9i			0.694539i
$474$		0			0
$475$			6.28626e8i			0.269132i
$476$		0			0
$477$	−2.65510e8	−	1.03545e9i	−0.112013	−	0.436832i
$478$		0			0
$479$	−2.97800e9			−1.23809			−0.619043	−	0.785357i	$-0.712479\pi$
$479$	−2.97800e9			−1.23809			−0.619043	+	0.785357i	$0.712479\pi$
$480$		0			0
$481$	1.65665e7			0.00678772
$482$		0			0
$483$	−4.45503e8	+	5.62088e7i	−0.179902	+	0.0226981i
$484$		0			0
$485$		−	3.26039e9i		−	1.29770i
$486$		0			0
$487$		−	2.07191e9i		−	0.812865i	−0.913681	−	0.406433i	$-0.866773\pi$
$487$		−	2.07191e9i		−	0.812865i	0.913681	−	0.406433i	$-0.133227\pi$
$488$		0			0
$489$	−1.59601e9	+	2.01368e8i	−0.617241	+	0.0778769i
$490$		0			0
$491$	3.41609e9			1.30240			0.651200	−	0.758906i	$-0.274266\pi$
$491$	3.41609e9			1.30240			0.651200	+	0.758906i	$0.274266\pi$
$492$		0			0
$493$	−3.19705e9			−1.20167
$494$		0			0
$495$	4.42189e8	+	1.72447e9i	0.163866	+	0.639053i
$496$		0			0
$497$		−	2.67374e8i		−	0.0976948i
$498$		0			0
$499$		−	2.35894e9i		−	0.849893i	−0.905218	−	0.424946i	$-0.860293\pi$
$499$		−	2.35894e9i		−	0.849893i	0.905218	−	0.424946i	$-0.139707\pi$
$500$		0			0
$501$	5.34157e8	+	4.23365e9i	0.189774	+	1.50412i
$502$		0			0
$503$	1.81179e9			0.634776			0.317388	−	0.948296i	$-0.397194\pi$
$503$	1.81179e9			0.634776			0.317388	+	0.948296i	$0.397194\pi$
$504$		0			0
$505$	−2.82984e9			−0.977782
$506$		0			0
$507$	3.58734e8	+	2.84327e9i	0.122249	+	0.968926i
$508$		0			0
$509$		−	3.64929e9i		−	1.22658i	−0.789858	−	0.613290i	$-0.789846\pi$
$509$		−	3.64929e9i		−	1.22658i	0.789858	−	0.613290i	$-0.210154\pi$
$510$		0			0
$511$			3.28306e8i			0.108844i
$512$		0			0
$513$	−1.45001e9	+	5.73305e8i	−0.474197	+	0.187489i
$514$		0			0
$515$	2.10607e9			0.679436
$516$		0			0
$517$	−5.75395e9			−1.83126
$518$		0			0
$519$	−1.13300e9	+	1.42949e8i	−0.355748	+	0.0448845i
$520$		0			0
$521$		−	2.05245e9i		−	0.635831i	−0.948119	−	0.317915i	$-0.897017\pi$
$521$		−	2.05245e9i		−	0.635831i	0.948119	−	0.317915i	$-0.102983\pi$
$522$		0			0
$523$			4.19657e9i			1.28274i	0.767232	+	0.641370i	$0.221634\pi$
$523$			4.19657e9i			1.28274i	−0.767232	+	0.641370i	$0.778366\pi$
$524$		0			0
$525$	3.78930e8	−	4.78093e7i	0.114288	−	0.0144197i
$526$		0			0
$527$	−3.85020e9			−1.14590
$528$		0			0
$529$	−1.05467e9			−0.309759
$530$		0			0
$531$	−4.51423e9	+	1.15754e9i	−1.30844	+	0.335510i
$532$		0			0
$533$			8.02261e8i			0.229493i
$534$		0			0
$535$		−	1.22277e9i		−	0.345228i
$536$		0			0
$537$	−7.93519e8	−	6.28932e9i	−0.221130	−	1.75264i
$538$		0			0
$539$	3.32402e9			0.914330
$540$		0			0
$541$	4.02521e8			0.109294			0.0546472	−	0.998506i	$-0.482597\pi$
$541$	4.02521e8			0.109294			0.0546472	+	0.998506i	$0.482597\pi$
$542$		0			0
$543$	5.93562e8	+	4.70449e9i	0.159099	+	1.26099i
$544$		0			0
$545$		−	4.21573e9i		−	1.11554i
$546$		0			0
$547$		−	1.81029e9i		−	0.472925i	−0.971641	−	0.236462i	$-0.924012\pi$
$547$		−	1.81029e9i		−	0.472925i	0.971641	−	0.236462i	$-0.0759880\pi$
$548$		0			0
$549$	−5.01672e9	+	1.28639e9i	−1.29395	+	0.331795i
$550$		0			0
$551$	−2.67197e9			−0.680457
$552$		0			0
$553$	4.24879e8			0.106838
$554$		0			0
$555$	1.21855e8	−	1.53743e7i	0.0302564	−	0.00381743i
$556$		0			0
$557$			6.46591e9i			1.58539i	0.609618	+	0.792696i	$0.291323\pi$
$557$			6.46591e9i			1.58539i	−0.609618	+	0.792696i	$0.708677\pi$
$558$		0			0
$559$		−	4.56962e8i		−	0.110647i
$560$		0			0
$561$	3.58694e9	−	4.52561e8i	0.857736	−	0.108220i
$562$		0			0
$563$	1.90280e9			0.449380			0.224690	−	0.974430i	$-0.427863\pi$
$563$	1.90280e9			0.449380			0.224690	+	0.974430i	$0.427863\pi$
$564$		0			0
$565$	5.66653e9			1.32174
$566$		0			0
$567$	4.55861e8	+	8.30447e8i	0.105025	+	0.191325i
$568$		0			0
$569$			2.87094e9i			0.653327i	0.945141	+	0.326664i	$0.105924\pi$
$569$			2.87094e9i			0.653327i	−0.945141	+	0.326664i	$0.894076\pi$
$570$		0			0
$571$		−	2.35214e9i		−	0.528735i	−0.964422	−	0.264367i	$-0.914837\pi$
$571$		−	2.35214e9i		−	0.528735i	0.964422	−	0.264367i	$-0.0851631\pi$
$572$		0			0
$573$	6.67341e8	+	5.28925e9i	0.148186	+	1.17450i
$574$		0			0
$575$	−1.99896e9			−0.438496
$576$		0			0
$577$	−3.38752e9			−0.734118			−0.367059	−	0.930198i	$-0.619635\pi$
$577$	−3.38752e9			−0.734118			−0.367059	+	0.930198i	$0.619635\pi$
$578$		0			0
$579$	3.86683e8	+	3.06480e9i	0.0827905	+	0.656186i
$580$		0			0
$581$		−	8.64027e8i		−	0.182772i
$582$		0			0
$583$			2.07149e9i			0.432955i
$584$		0			0
$585$	−1.26409e8	−	4.92975e8i	−0.0261055	−	0.101807i
$586$		0			0
$587$	−1.95816e9			−0.399590			−0.199795	−	0.979838i	$-0.564028\pi$
$587$	−1.95816e9			−0.399590			−0.199795	+	0.979838i	$0.564028\pi$
$588$		0			0
$589$	−3.21785e9			−0.648876
$590$		0			0
$591$	−2.46678e7	+	3.11231e6i	−0.00491556	+	0.000620193i
$592$		0			0
$593$			5.77669e8i			0.113759i	0.998381	+	0.0568797i	$0.0181152\pi$
$593$			5.77669e8i			0.113759i	−0.998381	+	0.0568797i	$0.981885\pi$
$594$		0			0
$595$			6.93941e8i			0.135056i
$596$		0			0
$597$	4.47610e9	−	5.64746e8i	0.860973	−	0.108628i
$598$		0			0
$599$	7.18711e8			0.136635			0.0683173	−	0.997664i	$-0.478237\pi$
$599$	7.18711e8			0.136635			0.0683173	+	0.997664i	$0.478237\pi$
$600$		0			0
$601$	5.03355e9			0.945831			0.472915	−	0.881108i	$-0.343202\pi$
$601$	5.03355e9			0.945831			0.472915	+	0.881108i	$0.343202\pi$
$602$		0			0
$603$	7.30162e8	+	2.84752e9i	0.135615	+	0.528879i
$604$		0			0
$605$			2.92989e8i			0.0537908i
$606$		0			0
$607$		−	8.20419e9i		−	1.48893i	−0.667660	−	0.744466i	$-0.732704\pi$
$607$		−	8.20419e9i		−	1.48893i	0.667660	−	0.744466i	$-0.267296\pi$
$608$		0			0
$609$	2.03213e8	+	1.61064e9i	0.0364578	+	0.288960i
$610$		0			0
$611$	1.64488e9			0.291737
$612$		0			0
$613$	2.30941e9			0.404940			0.202470	−	0.979289i	$-0.435103\pi$
$613$	2.30941e9			0.404940			0.202470	+	0.979289i	$0.435103\pi$
$614$		0			0
$615$	7.44528e8	+	5.90102e9i	0.129068	+	1.02297i
$616$		0			0
$617$			3.95552e9i			0.677962i	0.940793	+	0.338981i	$0.110082\pi$
$617$			3.95552e9i			0.677962i	−0.940793	+	0.338981i	$0.889918\pi$
$618$		0			0
$619$		−	7.21623e9i		−	1.22291i	−0.791281	−	0.611453i	$-0.790585\pi$
$619$		−	7.21623e9i		−	1.22291i	0.791281	−	0.611453i	$-0.209415\pi$
$620$		0			0
$621$	−1.82304e9	−	4.61085e9i	−0.305476	−	0.772610i
$622$		0			0
$623$	−1.18309e9			−0.196024
$624$		0			0
$625$	−1.18186e9			−0.193637
$626$		0			0
$627$	2.99782e9	−	3.78233e8i	0.485702	−	0.0612807i
$628$		0			0
$629$		−	2.49426e8i		−	0.0399637i
$630$		0			0
$631$		−	9.06668e9i		−	1.43663i	−0.695717	−	0.718316i	$-0.744913\pi$
$631$		−	9.06668e9i		−	1.43663i	0.695717	−	0.718316i	$-0.255087\pi$
$632$		0			0
$633$	2.88603e9	−	3.64129e8i	0.452260	−	0.0570613i
$634$		0			0
$635$	3.53369e9			0.547672
$636$		0			0
$637$	−9.50240e8			−0.145662
$638$		0			0
$639$	2.85977e9	−	7.33305e8i	0.433589	−	0.111181i
$640$		0			0
$641$			3.32334e9i			0.498393i	0.968453	+	0.249196i	$0.0801664\pi$
$641$			3.32334e9i			0.498393i	−0.968453	+	0.249196i	$0.919834\pi$
$642$		0			0
$643$		−	2.13723e9i		−	0.317040i	−0.987356	−	0.158520i	$-0.949328\pi$
$643$		−	2.13723e9i		−	0.317040i	0.987356	−	0.158520i	$-0.0506722\pi$
$644$		0			0
$645$	−4.24077e8	−	3.36118e9i	−0.0622280	−	0.493211i
$646$		0			0
$647$	1.08381e9			0.157322			0.0786608	−	0.996901i	$-0.474936\pi$
$647$	1.08381e9			0.157322			0.0786608	+	0.996901i	$0.474936\pi$
$648$		0			0
$649$	9.03102e9			1.29682
$650$		0			0
$651$	2.44729e8	+	1.93969e9i	0.0347658	+	0.275549i
$652$		0			0
$653$		−	9.68847e9i		−	1.36163i	−0.732455	−	0.680815i	$-0.761626\pi$
$653$		−	9.68847e9i		−	1.36163i	0.732455	−	0.680815i	$-0.238374\pi$
$654$		0			0
$655$		−	2.49250e9i		−	0.346570i
$656$		0			0
$657$	−3.51149e9	+	9.00417e8i	−0.483072	+	0.123870i
$658$		0			0
$659$	−1.16595e10			−1.58701			−0.793505	−	0.608564i	$-0.791746\pi$
$659$	−1.16595e10			−1.58701			−0.793505	+	0.608564i	$0.791746\pi$
$660$		0			0
$661$	1.34992e10			1.81804			0.909021	−	0.416751i	$-0.136831\pi$
$661$	1.34992e10			1.81804			0.909021	+	0.416751i	$0.136831\pi$
$662$		0			0
$663$	−1.02540e9	+	1.29374e8i	−0.136646	+	0.0172405i
$664$		0			0
$665$			5.79969e8i			0.0764767i
$666$		0			0
$667$		−	8.49655e9i		−	1.10867i
$668$		0			0
$669$	1.18751e10	−	1.49827e9i	1.53336	−	0.193463i
$670$		0			0
$671$	1.00363e10			1.28246
$672$		0			0
$673$	6.74898e8			0.0853464			0.0426732	−	0.999089i	$-0.486413\pi$
$673$	6.74898e8			0.0853464			0.0426732	+	0.999089i	$0.486413\pi$
$674$		0			0
$675$	1.55062e9	+	3.92183e9i	0.194062	+	0.490824i
$676$		0			0
$677$			3.63709e9i			0.450499i	0.974301	+	0.225249i	$0.0723197\pi$
$677$			3.63709e9i			0.450499i	−0.974301	+	0.225249i	$0.927680\pi$
$678$		0			0
$679$			3.36216e9i			0.412168i
$680$		0			0
$681$	1.31969e9	+	1.04597e10i	0.160125	+	1.26913i
$682$		0			0
$683$	−1.38112e10			−1.65866			−0.829331	−	0.558758i	$-0.811278\pi$
$683$	−1.38112e10			−1.65866			−0.829331	+	0.558758i	$0.811278\pi$
$684$		0			0
$685$	1.26980e8			0.0150945
$686$		0			0
$687$	4.67502e8	+	3.70535e9i	0.0550091	+	0.435994i
$688$		0			0
$689$		−	5.92177e8i		−	0.0689738i
$690$		0			0
$691$		−	8.97865e9i		−	1.03523i	−0.855613	−	0.517616i	$-0.826820\pi$
$691$		−	8.97865e9i		−	1.03523i	0.855613	−	0.517616i	$-0.173180\pi$
$692$		0			0
$693$	−4.55991e8	−	1.77829e9i	−0.0520463	−	0.202972i
$694$		0			0
$695$	3.86846e9			0.437111
$696$		0			0
$697$	1.20789e10			1.35118
$698$		0			0
$699$	−3.56355e9	+	4.49611e8i	−0.394651	+	0.0497928i
$700$		0			0
$701$			1.27725e9i			0.140043i	0.997545	+	0.0700215i	$0.0223068\pi$
$701$			1.27725e9i			0.140043i	−0.997545	+	0.0700215i	$0.977693\pi$
$702$		0			0
$703$		−	2.08461e8i		−	0.0226298i
$704$		0			0
$705$	1.20989e10	−	1.52651e9i	1.30042	−	0.164074i
$706$		0			0
$707$	2.91816e9			0.310557
$708$		0			0
$709$	6.47248e9			0.682038			0.341019	−	0.940056i	$-0.389228\pi$
$709$	6.47248e9			0.682038			0.341019	+	0.940056i	$0.389228\pi$
$710$		0			0
$711$	1.16528e9	+	4.54442e9i	0.121587	+	0.474171i
$712$		0			0
$713$		−	1.02324e10i		−	1.05721i
$714$		0			0
$715$			9.86230e8i			0.100904i
$716$		0			0
$717$	−4.56144e8	−	3.61534e9i	−0.0462152	−	0.366295i
$718$		0			0
$719$	1.36453e10			1.36909			0.684544	−	0.728972i	$-0.260001\pi$
$719$	1.36453e10			1.36909			0.684544	+	0.728972i	$0.260001\pi$
$720$		0			0
$721$	−2.17181e9			−0.215798
$722$		0			0
$723$	1.83970e9	+	1.45812e10i	0.181036	+	1.43486i
$724$		0			0
$725$			7.22687e9i			0.704315i
$726$		0			0
$727$			1.62586e8i			0.0156933i	0.999969	+	0.00784664i	$0.00249769\pi$
$727$			1.62586e8i			0.0156933i	−0.999969	+	0.00784664i	$0.997502\pi$
$728$		0			0
$729$	−7.63203e9	+	7.15339e9i	−0.729615	+	0.683858i
$730$		0			0
$731$	−6.88004e9			−0.651449
$732$		0			0
$733$	−2.55266e9			−0.239402			−0.119701	−	0.992810i	$-0.538194\pi$
$733$	−2.55266e9			−0.239402			−0.119701	+	0.992810i	$0.538194\pi$
$734$		0			0
$735$	−6.98947e9	+	8.81857e8i	−0.649290	+	0.0819205i
$736$		0			0
$737$		−	5.69666e9i		−	0.524184i
$738$		0			0
$739$			9.87241e9i			0.899844i	0.893068	+	0.449922i	$0.148548\pi$
$739$			9.87241e9i			0.899844i	−0.893068	+	0.449922i	$0.851452\pi$
$740$		0			0
$741$	−8.56989e8	+	1.08126e8i	−0.0773770	+	0.00976260i
$742$		0			0
$743$	−1.03822e10			−0.928595			−0.464298	−	0.885679i	$-0.653693\pi$
$743$	−1.03822e10			−0.928595			−0.464298	+	0.885679i	$0.653693\pi$
$744$		0			0
$745$	3.02830e9			0.268320
$746$		0			0
$747$	9.24145e9	−	2.36970e9i	0.811181	−	0.208003i
$748$		0			0
$749$			1.26093e9i			0.109649i
$750$		0			0
$751$		−	3.50680e9i		−	0.302114i	−0.988525	−	0.151057i	$-0.951732\pi$
$751$		−	3.50680e9i		−	0.302114i	0.988525	−	0.151057i	$-0.0482677\pi$
$752$		0			0
$753$	1.37425e9	+	1.08921e10i	0.117296	+	0.929673i
$754$		0			0
$755$	−6.64933e9			−0.562294
$756$		0			0
$757$	5.55090e9			0.465080			0.232540	−	0.972587i	$-0.425296\pi$
$757$	5.55090e9			0.465080			0.232540	+	0.972587i	$0.425296\pi$
$758$		0			0
$759$	1.20274e9	+	9.53272e9i	0.0998446	+	0.791354i
$760$		0			0
$761$			1.01439e10i			0.834372i	0.908821	+	0.417186i	$0.136984\pi$
$761$			1.01439e10i			0.834372i	−0.908821	+	0.417186i	$0.863016\pi$
$762$		0			0
$763$			4.34731e9i			0.354311i
$764$		0			0
$765$	−7.42225e9	+	1.90322e9i	−0.599405	+	0.153700i
$766$		0			0
$767$	−2.58170e9			−0.206596
$768$		0			0
$769$	−7.14242e9			−0.566374			−0.283187	−	0.959065i	$-0.591392\pi$
$769$	−7.14242e9			−0.566374			−0.283187	+	0.959065i	$0.591392\pi$
$770$		0			0
$771$	1.02724e10	−	1.29606e9i	0.807197	−	0.101844i
$772$		0			0
$773$			3.43016e9i			0.267108i	0.991042	+	0.133554i	$0.0426389\pi$
$773$			3.43016e9i			0.267108i	−0.991042	+	0.133554i	$0.957361\pi$
$774$		0			0
$775$			8.70331e9i			0.671627i
$776$		0			0
$777$	−1.25658e8	+	1.58542e7i	−0.00960986	+	0.00121247i
$778$		0			0
$779$	1.00951e10			0.765117
$780$		0			0
$781$	−5.72117e9			−0.429741
$782$		0			0
$783$	−1.66697e10	+	6.59089e9i	−1.24097	+	0.490657i
$784$		0			0
$785$		−	5.58477e9i		−	0.412061i
$786$		0			0
$787$			9.93120e9i			0.726257i	0.931739	+	0.363128i	$0.118291\pi$
$787$			9.93120e9i			0.726257i	−0.931739	+	0.363128i	$0.881709\pi$
$788$		0			0
$789$	−1.63515e9	−	1.29599e10i	−0.118519	−	0.939362i
$790$		0			0
$791$	−5.84339e9			−0.419805
$792$		0			0
$793$	−2.86908e9			−0.204309
$794$		0			0
$795$	−5.49562e8	−	4.35575e9i	−0.0387911	−	0.307453i
$796$		0			0
$797$			1.88852e10i			1.32135i	0.750673	+	0.660674i	$0.229729\pi$
$797$			1.88852e10i			1.32135i	−0.750673	+	0.660674i	$0.770271\pi$
$798$		0			0
$799$		−	2.47655e10i		−	1.71764i
$800$		0			0
$801$	−3.24476e9	−	1.26541e10i	−0.223084	−	0.869995i
$802$		0			0
$803$	7.02497e9			0.478784
$804$		0			0
$805$	−1.84423e9			−0.124604
$806$		0			0
$807$	−1.63990e10	+	2.06905e9i	−1.09840	+	0.138584i
$808$		0			0
$809$		−	2.30353e10i		−	1.52959i	−0.644274	−	0.764794i	$-0.722841\pi$
$809$		−	2.30353e10i		−	1.52959i	0.644274	−	0.764794i	$-0.277159\pi$
$810$		0			0
$811$		−	2.21173e10i		−	1.45599i	−0.685581	−	0.727996i	$-0.740452\pi$
$811$		−	2.21173e10i		−	1.45599i	0.685581	−	0.727996i	$-0.259548\pi$
$812$		0			0
$813$	1.70802e10	−	2.15500e9i	1.11475	−	0.140647i
$814$		0			0
$815$	−6.60695e9			−0.427513
$816$		0			0
$817$	−5.75007e9			−0.368889
$818$		0			0
$819$	1.30354e8	+	5.08361e8i	0.00829147	+	0.0323354i
$820$		0			0
$821$			4.88696e9i			0.308204i	0.988055	+	0.154102i	$0.0492484\pi$
$821$			4.88696e9i			0.308204i	−0.988055	+	0.154102i	$0.950752\pi$
$822$		0			0
$823$			1.54834e10i			0.968205i	0.875011	+	0.484102i	$0.160854\pi$
$823$			1.54834e10i			0.968205i	−0.875011	+	0.484102i	$0.839146\pi$
$824$		0			0
$825$	−1.02301e9	−	8.10821e9i	−0.0634293	−	0.502731i
$826$		0			0
$827$	1.75468e10			1.07877			0.539385	−	0.842059i	$-0.318657\pi$
$827$	1.75468e10			1.07877			0.539385	+	0.842059i	$0.318657\pi$
$828$		0			0
$829$	−9.52705e9			−0.580788			−0.290394	−	0.956907i	$-0.593786\pi$
$829$	−9.52705e9			−0.580788			−0.290394	+	0.956907i	$0.593786\pi$
$830$		0			0
$831$	−3.47609e9	−	2.75510e10i	−0.210130	−	1.66546i
$832$		0			0
$833$			1.43069e10i			0.857604i
$834$		0			0
$835$			1.75259e10i			1.04178i
$836$		0			0
$837$	−2.00753e10	+	7.93739e9i	−1.18338	+	0.467884i
$838$		0			0
$839$	3.26369e10			1.90784			0.953919	−	0.300063i	$-0.0970078\pi$
$839$	3.26369e10			1.90784			0.953919	+	0.300063i	$0.0970078\pi$
$840$		0			0
$841$	−1.34679e10			−0.780751
$842$		0			0
$843$	−6.35753e9	+	8.02125e8i	−0.365504	+	0.0461154i
$844$		0			0
$845$			1.17702e10i			0.671097i
$846$		0			0
$847$		−	3.02134e8i		−	0.0170847i
$848$		0			0
$849$	1.95715e10	−	2.46933e9i	1.09761	−	0.138485i
$850$		0			0
$851$	6.62881e8			0.0368708
$852$		0			0
$853$	−1.83694e10			−1.01338			−0.506691	−	0.862128i	$-0.669132\pi$
$853$	−1.83694e10			−1.01338			−0.506691	+	0.862128i	$0.669132\pi$
$854$		0			0
$855$	−6.20323e9	+	1.59064e9i	−0.339419	+	0.0870340i
$856$		0			0
$857$		−	2.92167e10i		−	1.58562i	−0.609471	−	0.792808i	$-0.708618\pi$
$857$		−	2.92167e10i		−	1.58562i	0.609471	−	0.792808i	$-0.291382\pi$
$858$		0			0
$859$		−	3.07620e10i		−	1.65592i	−0.560788	−	0.827959i	$-0.689502\pi$
$859$		−	3.07620e10i		−	1.65592i	0.560788	−	0.827959i	$-0.310498\pi$
$860$		0			0
$861$	−7.67766e8	−	6.08520e9i	−0.0409938	−	0.324911i
$862$		0			0
$863$	7.08404e9			0.375183			0.187591	−	0.982247i	$-0.439932\pi$
$863$	7.08404e9			0.375183			0.187591	+	0.982247i	$0.439932\pi$
$864$		0			0
$865$	−4.69022e9			−0.246398
$866$		0			0
$867$	−4.54240e8	−	3.60024e9i	−0.0236711	−	0.187614i
$868$		0			0
$869$		−	9.09142e9i		−	0.469962i
$870$		0			0
$871$			1.62851e9i			0.0835076i
$872$		0			0
$873$	−3.59609e10	+	9.22112e9i	−1.82928	+	0.469066i
$874$		0			0
$875$	4.54071e9			0.229137
$876$		0			0
$877$	−1.53321e10			−0.767541			−0.383771	−	0.923428i	$-0.625375\pi$
$877$	−1.53321e10			−0.767541			−0.383771	+	0.923428i	$0.625375\pi$
$878$		0			0
$879$	3.09241e10	−	3.90167e9i	1.53580	−	0.193771i
$880$		0			0
$881$		−	1.80112e10i		−	0.887417i	−0.896171	−	0.443709i	$-0.853662\pi$
$881$		−	1.80112e10i		−	0.887417i	0.896171	−	0.443709i	$-0.146338\pi$
$882$		0			0
$883$			1.62094e10i			0.792326i	0.918180	+	0.396163i	$0.129658\pi$
$883$			1.62094e10i			0.792326i	−0.918180	+	0.396163i	$0.870342\pi$
$884$		0			0
$885$	−1.89897e10	+	2.39591e9i	−0.920908	+	0.116190i
$886$		0			0
$887$	−2.67966e10			−1.28928			−0.644640	−	0.764487i	$-0.722993\pi$
$887$	−2.67966e10			−1.28928			−0.644640	+	0.764487i	$0.722993\pi$
$888$		0			0
$889$	−3.64398e9			−0.173948
$890$		0			0
$891$	1.77696e10	−	9.75436e9i	0.841601	−	0.461984i
$892$		0			0
$893$		−	2.06980e10i		−	0.972632i
$894$		0			0
$895$		−	2.60357e10i		−	1.21391i
$896$		0			0
$897$	−3.43827e8	−	2.72512e9i	−0.0159062	−	0.126070i
$898$		0			0
$899$	−3.69933e10			−1.69810
$900$		0			0
$901$	−8.91585e9			−0.406093
$902$		0			0
$903$	4.37314e8	+	3.46609e9i	0.0197645	+	0.156651i
$904$		0			0
$905$			1.94750e10i			0.873388i
$906$		0			0
$907$		−	5.16221e9i		−	0.229726i	−0.993381	−	0.114863i	$-0.963357\pi$
$907$		−	5.16221e9i		−	0.229726i	0.993381	−	0.114863i	$-0.0366429\pi$
$908$		0			0
$909$	8.00341e9	+	3.12121e10i	0.353429	+	1.37832i
$910$		0			0
$911$	−1.82945e10			−0.801690			−0.400845	−	0.916146i	$-0.631283\pi$
$911$	−1.82945e10			−0.801690			−0.400845	+	0.916146i	$0.631283\pi$
$912$		0			0
$913$	−1.84881e10			−0.803981
$914$		0			0
$915$	−2.11035e10	+	2.66261e9i	−0.910710	+	0.114904i
$916$		0			0
$917$			2.57030e9i			0.110076i
$918$		0			0
$919$			3.10441e10i			1.31939i	0.751531	+	0.659697i	$0.229316\pi$
$919$			3.10441e10i			1.31939i	−0.751531	+	0.659697i	$0.770684\pi$
$920$		0			0
$921$	−2.15676e10	+	2.72116e9i	−0.909687	+	0.114775i
$922$		0			0
$923$	1.63551e9			0.0684618
$924$		0			0
$925$	−5.63824e8			−0.0234233
$926$		0			0
$927$	−5.95645e9	−	2.32292e10i	−0.245589	−	0.957757i
$928$		0			0
$929$			3.04468e10i			1.24591i	0.782258	+	0.622954i	$0.214068\pi$
$929$			3.04468e10i			1.24591i	−0.782258	+	0.622954i	$0.785932\pi$
$930$		0			0
$931$			1.19571e10i			0.485627i
$932$		0			0
$933$	−3.11838e9	−	2.47158e10i	−0.125702	−	0.996297i
$934$		0			0
$935$	1.48487e10			0.594085
$936$		0			0
$937$	1.04555e10			0.415200			0.207600	−	0.978214i	$-0.433435\pi$
$937$	1.04555e10			0.415200			0.207600	+	0.978214i	$0.433435\pi$
$938$		0			0
$939$	−3.56062e9	−	2.82210e10i	−0.140345	−	1.11235i
$940$		0			0
$941$		−	4.73322e10i		−	1.85179i	−0.377775	−	0.925897i	$-0.623311\pi$
$941$		−	4.73322e10i		−	1.85179i	0.377775	−	0.925897i	$-0.376689\pi$
$942$		0			0
$943$			3.21011e10i			1.24661i
$944$		0			0
$945$	1.43060e9	+	3.61827e9i	0.0551450	+	0.139473i
$946$		0			0
$947$	2.91906e10			1.11691			0.558455	−	0.829535i	$-0.311394\pi$
$947$	2.91906e10			1.11691			0.558455	+	0.829535i	$0.311394\pi$
$948$		0			0
$949$	−2.00823e9			−0.0762750
$950$		0			0
$951$	3.93875e10	−	4.96950e9i	1.48500	−	0.187362i
$952$		0			0
$953$			3.96077e10i			1.48236i	0.671304	+	0.741182i	$0.265734\pi$
$953$			3.96077e10i			1.48236i	−0.671304	+	0.741182i	$0.734266\pi$
$954$		0			0
$955$			2.18957e10i			0.813481i
$956$		0			0
$957$	3.44638e10	−	4.34828e9i	1.27108	−	0.160371i
$958$		0			0
$959$	−1.30943e8			−0.00479422
$960$		0			0
$961$	−1.70384e10			−0.619292
$962$		0			0
$963$	−1.34867e10	+	3.45826e9i	−0.486646	+	0.124786i
$964$		0			0
$965$			1.26872e10i			0.454487i
$966$		0			0
$967$			1.79425e10i			0.638103i	0.947737	+	0.319051i	$0.103364\pi$
$967$			1.79425e10i			0.638103i	−0.947737	+	0.319051i	$0.896636\pi$
$968$		0			0
$969$	1.62795e9	+	1.29029e10i	0.0574787	+	0.455568i
$970$		0			0
$971$	−1.71339e10			−0.600606			−0.300303	−	0.953844i	$-0.597088\pi$
$971$	−1.71339e10			−0.600606			−0.300303	+	0.953844i	$0.597088\pi$
$972$		0			0
$973$	−3.98920e9			−0.138833
$974$		0			0
$975$	2.92448e8	+	2.31790e9i	0.0101049	+	0.0800900i
$976$		0			0
$977$			2.56309e10i			0.879291i	0.898171	+	0.439645i	$0.144896\pi$
$977$			2.56309e10i			0.879291i	−0.898171	+	0.439645i	$0.855104\pi$
$978$		0			0
$979$			2.53153e10i			0.862272i
$980$		0			0
$981$	−4.64979e10	+	1.19230e10i	−1.57250	+	0.403222i
$982$		0			0
$983$	4.65121e9			0.156181			0.0780906	−	0.996946i	$-0.475118\pi$
$983$	4.65121e9			0.156181			0.0780906	+	0.996946i	$0.475118\pi$
$984$		0			0
$985$	−1.02116e8			−0.00340461
$986$		0			0
$987$	−1.24766e10	+	1.57416e9i	−0.413033	+	0.0521121i
$988$		0			0
$989$		−	1.82845e10i		−	0.601031i
$990$		0			0
$991$		−	5.59663e9i		−	0.182671i	−0.995820	−	0.0913353i	$-0.970887\pi$
$991$		−	5.59663e9i		−	0.182671i	0.995820	−	0.0913353i	$-0.0291135\pi$
$992$		0			0
$993$	4.48886e10	−	5.66356e9i	1.45483	−	0.183555i
$994$		0			0
$995$	1.85295e10			0.596326
$996$		0			0
$997$	4.54754e10			1.45326			0.726631	−	0.687028i	$-0.241085\pi$
$997$	4.54754e10			1.45326			0.726631	+	0.687028i	$0.241085\pi$
$998$		0			0
$999$	−5.14206e8	−	1.30053e9i	−0.0163177	−	0.0412707i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.8.c.f.191.13		28
3.2	odd	2	inner	192.8.c.f.191.15		28
4.3	odd	2	inner	192.8.c.f.191.16		28
8.3	odd	2		96.8.c.a.95.13	✓	28
8.5	even	2		96.8.c.a.95.16	yes	28
12.11	even	2	inner	192.8.c.f.191.14		28
24.5	odd	2		96.8.c.a.95.14	yes	28
24.11	even	2		96.8.c.a.95.15	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.8.c.a.95.13	✓	28	8.3	odd	2
96.8.c.a.95.14	yes	28	24.5	odd	2
96.8.c.a.95.15	yes	28	24.11	even	2
96.8.c.a.95.16	yes	28	8.5	even	2
192.8.c.f.191.13		28	1.1	even	1	trivial
192.8.c.f.191.14		28	12.11	even	2	inner
192.8.c.f.191.15		28	3.2	odd	2	inner
192.8.c.f.191.16		28	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	192.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-5.85395 - 46.3975i) q^{3} -192.070i q^{5} +198.065i q^{7} +(-2118.46 + 543.217i) q^{9} +O(q^{10})\)	\(q+(-5.85395 - 46.3975i) q^{3} -192.070i q^{5} +198.065i q^{7} +(-2118.46 + 543.217i) q^{9} +4238.13 q^{11} -1211.56 q^{13} +(-8911.59 + 1124.37i) q^{15} +18241.3i q^{17} +15245.3i q^{19} +(9189.73 - 1159.46i) q^{21} -48478.4 q^{23} +41234.0 q^{25} +(37605.3 + 95111.5i) q^{27} +175265. i q^{29} +211071. i q^{31} +(-24809.8 - 196639. i) q^{33} +38042.4 q^{35} -13673.8 q^{37} +(7092.39 + 56213.2i) q^{39} -662174. i q^{41} +377169. i q^{43} +(104336. + 406894. i) q^{45} -1.35766e6 q^{47} +784313. q^{49} +(846349. - 106783. i) q^{51} +488774. i q^{53} -814019. i q^{55} +(707346. - 89245.3i) q^{57} +2.13090e6 q^{59} +2.36809e6 q^{61} +(-107592. - 419594. i) q^{63} +232704. i q^{65} -1.34414e6i q^{67} +(283790. + 2.24928e6i) q^{69} -1.34993e6 q^{71} +1.65756e6 q^{73} +(-241382. - 1.91316e6i) q^{75} +839426. i q^{77} -2.14515e6i q^{79} +(4.19280e6 - 2.30157e6i) q^{81} -4.36234e6 q^{83} +3.50360e6 q^{85} +(8.13185e6 - 1.02599e6i) q^{87} +5.97323e6i q^{89} -239967. i q^{91} +(9.79317e6 - 1.23560e6i) q^{93} +2.92817e6 q^{95} +1.69750e7 q^{97} +(-8.97832e6 + 2.30223e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2236 q^{9}+O(q^{10}) \) 28 * q + 2236 * q^9	\( 28 q + 2236 q^{9} + 7064 q^{13} - 2344 q^{21} - 417012 q^{25} + 278672 q^{33} + 965112 q^{37} + 2114464 q^{45} - 4821612 q^{49} - 3683352 q^{57} - 402664 q^{61} + 1987424 q^{69} + 223128 q^{73} - 6688900 q^{81} - 7477248 q^{85} - 34969576 q^{93} + 12115480 q^{97}+O(q^{100}) \) 28 * q + 2236 * q^9 + 7064 * q^13 - 2344 * q^21 - 417012 * q^25 + 278672 * q^33 + 965112 * q^37 + 2114464 * q^45 - 4821612 * q^49 - 3683352 * q^57 - 402664 * q^61 + 1987424 * q^69 + 223128 * q^73 - 6688900 * q^81 - 7477248 * q^85 - 34969576 * q^93 + 12115480 * q^97

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