LMFDB - Embedded newform 384.6.c.b.383.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,6,Mod(383,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("384.383");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	384.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:	$61.5873868082$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 306 x^{18} + 37827 x^{16} + 2442168 x^{14} + 88368509 x^{12} + 1774000974 x^{10} + \cdots + 2870280625 $ x^20 + 306x^18 + 37827x^16 + 2442168x^14 + 88368509x^12 + 1774000974x^10 + 18093172325x^8 + 74958811500x^6 + 79355888475x^4 + 28497132750*x^2 + 2870280625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{88}\cdot 3^{14}\cdot 41^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			383.19
Root			$0.852576i$ of defining polynomial
Character	$\chi$	$=$	384.383
Dual form			384.6.c.b.383.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(15.4777 - 1.85457i) q^{3} -55.8580i q^{5} -225.953i q^{7} +(236.121 - 57.4091i) q^{9} +O(q^{10})$	\(q+(15.4777 - 1.85457i) q^{3} -55.8580i q^{5} -225.953i q^{7} +(236.121 - 57.4091i) q^{9} -36.9229 q^{11} -795.597 q^{13} +(-103.593 - 864.557i) q^{15} -129.541i q^{17} -998.033i q^{19} +(-419.046 - 3497.25i) q^{21} -3748.76 q^{23} +4.87856 q^{25} +(3548.15 - 1326.47i) q^{27} -921.479i q^{29} -423.688i q^{31} +(-571.482 + 68.4759i) q^{33} -12621.3 q^{35} +10929.6 q^{37} +(-12314.0 + 1475.49i) q^{39} +14465.5i q^{41} +20897.9i q^{43} +(-3206.76 - 13189.3i) q^{45} +12002.2 q^{47} -34247.9 q^{49} +(-240.242 - 2005.00i) q^{51} +11365.4i q^{53} +2062.44i q^{55} +(-1850.92 - 15447.3i) q^{57} -36606.6 q^{59} -38251.8 q^{61} +(-12971.8 - 53352.4i) q^{63} +44440.5i q^{65} -8975.18i q^{67} +(-58022.3 + 6952.33i) q^{69} +61606.6 q^{71} +2569.04 q^{73} +(75.5091 - 9.04762i) q^{75} +8342.84i q^{77} -61551.9i q^{79} +(52457.4 - 27111.0i) q^{81} +113300. q^{83} -7235.89 q^{85} +(-1708.95 - 14262.4i) q^{87} -125521. i q^{89} +179768. i q^{91} +(-785.759 - 6557.74i) q^{93} -55748.2 q^{95} -156644. q^{97} +(-8718.27 + 2119.71i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{3}+O(q^{10}) $ 20 * q - 2 * q^3	$ 20 q - 2 q^{3} - 948 q^{11} + 852 q^{15} + 1640 q^{21} + 328 q^{23} - 12500 q^{25} - 2030 q^{27} + 2836 q^{33} + 7184 q^{35} + 15056 q^{37} - 12980 q^{39} + 11800 q^{45} + 36640 q^{47} - 33388 q^{49} - 1936 q^{51} + 15404 q^{57} - 62908 q^{59} + 73264 q^{61} + 23608 q^{63} - 84024 q^{69} + 34888 q^{71} + 52568 q^{73} - 115698 q^{75} + 55444 q^{81} + 225172 q^{83} - 30112 q^{85} - 225700 q^{87} - 148016 q^{93} + 418616 q^{95} + 7600 q^{97} - 378260 q^{99}+O(q^{100}) $ 20 * q - 2 * q^3 - 948 * q^11 + 852 * q^15 + 1640 * q^21 + 328 * q^23 - 12500 * q^25 - 2030 * q^27 + 2836 * q^33 + 7184 * q^35 + 15056 * q^37 - 12980 * q^39 + 11800 * q^45 + 36640 * q^47 - 33388 * q^49 - 1936 * q^51 + 15404 * q^57 - 62908 * q^59 + 73264 * q^61 + 23608 * q^63 - 84024 * q^69 + 34888 * q^71 + 52568 * q^73 - 115698 * q^75 + 55444 * q^81 + 225172 * q^83 - 30112 * q^85 - 225700 * q^87 - 148016 * q^93 + 418616 * q^95 + 7600 * q^97 - 378260 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$-1$	$1$	$-1$

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
$3$	15.4777	−	1.85457i	0.992898	−	0.118971i
$3$	15.4777	−	1.85457i	0.992898	−	0.118971i
$4$		0			0
$5$		−	55.8580i		−	0.999219i	−0.866251	−	0.499610i	$-0.833477\pi$
$5$		−	55.8580i		−	0.999219i	0.866251	−	0.499610i	$-0.166523\pi$
$6$		0			0
$7$		−	225.953i		−	1.74290i	−0.490480	−	0.871452i	$-0.663179\pi$
$7$		−	225.953i		−	1.74290i	0.490480	−	0.871452i	$-0.336821\pi$
$8$		0			0
$9$	236.121	−	57.4091i	0.971692	−	0.236251i
$10$		0			0
$11$	−36.9229			−0.0920054			−0.0460027	−	0.998941i	$-0.514648\pi$
$11$	−36.9229			−0.0920054			−0.0460027	+	0.998941i	$0.514648\pi$
$12$		0			0
$13$	−795.597			−1.30567			−0.652837	−	0.757499i	$-0.726421\pi$
$13$	−795.597			−1.30567			−0.652837	+	0.757499i	$0.726421\pi$
$14$		0			0
$15$	−103.593	−	864.557i	−0.118878	−	0.992122i
$16$		0			0
$17$		−	129.541i		−	0.108714i	−0.998522	−	0.0543568i	$-0.982689\pi$
$17$		−	129.541i		−	0.108714i	0.998522	−	0.0543568i	$-0.0173108\pi$
$18$		0			0
$19$		−	998.033i		−	0.634251i	−0.948384	−	0.317125i	$-0.897282\pi$
$19$		−	998.033i		−	0.634251i	0.948384	−	0.317125i	$-0.102718\pi$
$20$		0			0
$21$	−419.046	−	3497.25i	−0.207354	−	1.73053i
$22$		0			0
$23$	−3748.76			−1.47764			−0.738819	−	0.673904i	$-0.764616\pi$
$23$	−3748.76			−1.47764			−0.738819	+	0.673904i	$0.764616\pi$
$24$		0			0
$25$	4.87856			0.00156114
$26$		0			0
$27$	3548.15	−	1326.47i	0.936684	−	0.350176i
$28$		0			0
$29$		−	921.479i		−	0.203465i	−0.994812	−	0.101733i	$-0.967561\pi$
$29$		−	921.479i		−	0.203465i	0.994812	−	0.101733i	$-0.0324386\pi$
$30$		0			0
$31$		−	423.688i		−	0.0791849i	−0.999216	−	0.0395925i	$-0.987394\pi$
$31$		−	423.688i		−	0.0791849i	0.999216	−	0.0395925i	$-0.0126060\pi$
$32$		0			0
$33$	−571.482	+	68.4759i	−0.0913520	+	0.0109459i
$34$		0			0
$35$	−12621.3			−1.74154
$36$		0			0
$37$	10929.6			1.31250			0.656249	−	0.754544i	$-0.272142\pi$
$37$	10929.6			1.31250			0.656249	+	0.754544i	$0.272142\pi$
$38$		0			0
$39$	−12314.0	+	1475.49i	−1.29640	+	0.155337i
$40$		0			0
$41$			14465.5i			1.34392i	0.740586	+	0.671962i	$0.234548\pi$
$41$			14465.5i			1.34392i	−0.740586	+	0.671962i	$0.765452\pi$
$42$		0			0
$43$			20897.9i			1.72358i	0.507268	+	0.861788i	$0.330655\pi$
$43$			20897.9i			1.72358i	−0.507268	+	0.861788i	$0.669345\pi$
$44$		0			0
$45$	−3206.76	−	13189.3i	−0.236067	−	0.970933i
$46$		0			0
$47$	12002.2			0.792534			0.396267	−	0.918135i	$-0.370305\pi$
$47$	12002.2			0.792534			0.396267	+	0.918135i	$0.370305\pi$
$48$		0			0
$49$	−34247.9			−2.03772
$50$		0			0
$51$	−240.242	−	2005.00i	−0.0129337	−	0.107942i
$52$		0			0
$53$			11365.4i			0.555769i	0.960615	+	0.277884i	$0.0896332\pi$
$53$			11365.4i			0.555769i	−0.960615	+	0.277884i	$0.910367\pi$
$54$		0			0
$55$			2062.44i			0.0919336i
$56$		0			0
$57$	−1850.92	−	15447.3i	−0.0754572	−	0.629746i
$58$		0			0
$59$	−36606.6			−1.36908			−0.684542	−	0.728974i	$-0.739998\pi$
$59$	−36606.6			−1.36908			−0.684542	+	0.728974i	$0.739998\pi$
$60$		0			0
$61$	−38251.8			−1.31622			−0.658108	−	0.752923i	$-0.728643\pi$
$61$	−38251.8			−1.31622			−0.658108	+	0.752923i	$0.728643\pi$
$62$		0			0
$63$	−12971.8	−	53352.4i	−0.411763	−	1.69357i
$64$		0			0
$65$			44440.5i			1.30465i
$66$		0			0
$67$		−	8975.18i		−	0.244262i	−0.992514	−	0.122131i	$-0.961027\pi$
$67$		−	8975.18i		−	0.244262i	0.992514	−	0.122131i	$-0.0389728\pi$
$68$		0			0
$69$	−58022.3	+	6952.33i	−1.46714	+	0.175795i
$70$		0			0
$71$	61606.6			1.45038			0.725189	−	0.688549i	$-0.241752\pi$
$71$	61606.6			1.45038			0.725189	+	0.688549i	$0.241752\pi$
$72$		0			0
$73$	2569.04			0.0564240			0.0282120	−	0.999602i	$-0.491019\pi$
$73$	2569.04			0.0564240			0.0282120	+	0.999602i	$0.491019\pi$
$74$		0			0
$75$	75.5091	−	9.04762i	0.00155005	−	0.000185730i
$76$		0			0
$77$			8342.84i			0.160357i
$78$		0			0
$79$		−	61551.9i		−	1.10962i	−0.831978	−	0.554809i	$-0.812791\pi$
$79$		−	61551.9i		−	1.10962i	0.831978	−	0.554809i	$-0.187209\pi$
$80$		0			0
$81$	52457.4	−	27111.0i	0.888371	−	0.459127i
$82$		0			0
$83$	113300.			1.80523			0.902617	−	0.430444i	$-0.141643\pi$
$83$	113300.			1.80523			0.902617	+	0.430444i	$0.141643\pi$
$84$		0			0
$85$	−7235.89			−0.108629
$86$		0			0
$87$	−1708.95	−	14262.4i	−0.0242064	−	0.202020i
$88$		0			0
$89$		−	125521.i		−	1.67974i	−0.542790	−	0.839868i	$-0.682632\pi$
$89$		−	125521.i		−	1.67974i	0.542790	−	0.839868i	$-0.317368\pi$
$90$		0			0
$91$			179768.i			2.27566i
$92$		0			0
$93$	−785.759	−	6557.74i	−0.00942067	−	0.0786225i
$94$		0			0
$95$	−55748.2			−0.633756
$96$		0			0
$97$	−156644.			−1.69038			−0.845191	−	0.534465i	$-0.820513\pi$
$97$	−156644.			−1.69038			−0.845191	+	0.534465i	$0.820513\pi$
$98$		0			0
$99$	−8718.27	+	2119.71i	−0.0894010	+	0.0217364i
$100$		0			0
$101$			34422.0i			0.335763i	0.985807	+	0.167881i	$0.0536926\pi$
$101$			34422.0i			0.335763i	−0.985807	+	0.167881i	$0.946307\pi$
$102$		0			0
$103$			28205.4i			0.261962i	0.991385	+	0.130981i	$0.0418127\pi$
$103$			28205.4i			0.261962i	−0.991385	+	0.130981i	$0.958187\pi$
$104$		0			0
$105$	−195349.	+	23407.1i	−1.72917	+	0.207192i
$106$		0			0
$107$	42182.3			0.356181			0.178090	−	0.984014i	$-0.443008\pi$
$107$	42182.3			0.356181			0.178090	+	0.984014i	$0.443008\pi$
$108$		0			0
$109$	−88788.0			−0.715794			−0.357897	−	0.933761i	$-0.616506\pi$
$109$	−88788.0			−0.715794			−0.357897	+	0.933761i	$0.616506\pi$
$110$		0			0
$111$	169165.	−	20269.6i	1.30318	−	0.156149i
$112$		0			0
$113$		−	238904.i		−	1.76006i	−0.474921	−	0.880028i	$-0.657523\pi$
$113$		−	238904.i		−	1.76006i	0.474921	−	0.880028i	$-0.342477\pi$
$114$		0			0
$115$			209398.i			1.47648i
$116$		0			0
$117$	−187857.	+	45674.5i	−1.26871	+	0.308467i
$118$		0			0
$119$	−29270.2			−0.189477
$120$		0			0
$121$	−159688.			−0.991535
$122$		0			0
$123$	26827.3	+	223894.i	0.159887	+	1.33438i
$124$		0			0
$125$		−	174829.i		−	1.00078i
$126$		0			0
$127$		−	258860.i		−	1.42415i	−0.702105	−	0.712074i	$-0.747756\pi$
$127$		−	258860.i		−	1.42415i	0.702105	−	0.712074i	$-0.252244\pi$
$128$		0			0
$129$	38756.5	+	323452.i	0.205055	+	1.71133i
$130$		0			0
$131$	9462.28			0.0481745			0.0240873	−	0.999710i	$-0.492332\pi$
$131$	9462.28			0.0481745			0.0240873	+	0.999710i	$0.492332\pi$
$132$		0			0
$133$	−225509.			−1.10544
$134$		0			0
$135$	−74093.8	−	198193.i	−0.349903	−	0.935952i
$136$		0			0
$137$		−	146703.i		−	0.667788i	−0.942611	−	0.333894i	$-0.891637\pi$
$137$		−	146703.i		−	0.667788i	0.942611	−	0.333894i	$-0.108363\pi$
$138$		0			0
$139$		−	150825.i		−	0.662119i	−0.943610	−	0.331060i	$-0.892594\pi$
$139$		−	150825.i		−	0.662119i	0.943610	−	0.331060i	$-0.107406\pi$
$140$		0			0
$141$	185768.	−	22259.0i	0.786905	−	0.0942882i
$142$		0			0
$143$	29375.7			0.120129
$144$		0			0
$145$	−51472.0			−0.203306
$146$		0			0
$147$	−530080.	+	63515.1i	−2.02324	+	0.242428i
$148$		0			0
$149$			223409.i			0.824396i	0.911094	+	0.412198i	$0.135239\pi$
$149$			223409.i			0.824396i	−0.911094	+	0.412198i	$0.864761\pi$
$150$		0			0
$151$		−	398109.i		−	1.42089i	−0.703754	−	0.710443i	$-0.748494\pi$
$151$		−	398109.i		−	1.42089i	0.703754	−	0.710443i	$-0.251506\pi$
$152$		0			0
$153$	−7436.81	−	30587.3i	−0.0256837	−	0.105636i
$154$		0			0
$155$	−23666.4			−0.0791231
$156$		0			0
$157$	−457758.			−1.48213			−0.741066	−	0.671432i	$-0.765680\pi$
$157$	−457758.			−1.48213			−0.741066	+	0.671432i	$0.765680\pi$
$158$		0			0
$159$	21077.9	+	175910.i	0.0661202	+	0.551822i
$160$		0			0
$161$			847044.i			2.57538i
$162$		0			0
$163$		−	90580.0i		−	0.267032i	−0.991047	−	0.133516i	$-0.957373\pi$
$163$		−	90580.0i		−	0.267032i	0.991047	−	0.133516i	$-0.0426268\pi$
$164$		0			0
$165$	3824.93	+	31921.9i	0.0109374	+	0.0912807i
$166$		0			0
$167$	160677.			0.445822			0.222911	−	0.974839i	$-0.428444\pi$
$167$	160677.			0.445822			0.222911	+	0.974839i	$0.428444\pi$
$168$		0			0
$169$	261681.			0.704784
$170$		0			0
$171$	−57296.2	−	235657.i	−0.149843	−	0.616296i
$172$		0			0
$173$		−	425382.i		−	1.08060i	−0.841473	−	0.540299i	$-0.818311\pi$
$173$		−	425382.i		−	1.08060i	0.841473	−	0.540299i	$-0.181689\pi$
$174$		0			0
$175$		−	1102.33i		−	0.00272092i
$176$		0			0
$177$	−566588.	+	67889.5i	−1.35936	+	0.162881i
$178$		0			0
$179$	19674.5			0.0458956			0.0229478	−	0.999737i	$-0.492695\pi$
$179$	19674.5			0.0458956			0.0229478	+	0.999737i	$0.492695\pi$
$180$		0			0
$181$	46347.1			0.105154			0.0525771	−	0.998617i	$-0.483256\pi$
$181$	46347.1			0.105154			0.0525771	+	0.998617i	$0.483256\pi$
$182$		0			0
$183$	−592052.	+	70940.6i	−1.30687	+	0.156591i
$184$		0			0
$185$		−	610504.i		−	1.31147i
$186$		0			0
$187$			4783.01i			0.0100022i
$188$		0			0
$189$	−299719.	−	801717.i	−0.610324	−	1.63255i
$190$		0			0
$191$	−57120.9			−0.113295			−0.0566476	−	0.998394i	$-0.518041\pi$
$191$	−57120.9			−0.113295			−0.0566476	+	0.998394i	$0.518041\pi$
$192$		0			0
$193$	−257879.			−0.498336			−0.249168	−	0.968460i	$-0.580157\pi$
$193$	−257879.			−0.498336			−0.249168	+	0.968460i	$0.580157\pi$
$194$		0			0
$195$	82417.9	+	687838.i	0.155215	+	1.29539i
$196$		0			0
$197$			704799.i			1.29390i	0.762534	+	0.646948i	$0.223955\pi$
$197$			704799.i			1.29390i	−0.762534	+	0.646948i	$0.776045\pi$
$198$		0			0
$199$		−	259574.i		−	0.464654i	−0.972638	−	0.232327i	$-0.925366\pi$
$199$		−	259574.i		−	0.464654i	0.972638	−	0.232327i	$-0.0746339\pi$
$200$		0			0
$201$	−16645.1	−	138916.i	−0.0290600	−	0.242527i
$202$		0			0
$203$	−208211.			−0.354621
$204$		0			0
$205$	808016.			1.34287
$206$		0			0
$207$	−885161.	+	215213.i	−1.43581	+	0.349094i
$208$		0			0
$209$			36850.2i			0.0583545i
$210$		0			0
$211$			534281.i			0.826159i	0.910695	+	0.413080i	$0.135547\pi$
$211$			534281.i			0.826159i	−0.910695	+	0.413080i	$0.864453\pi$
$212$		0			0
$213$	953531.	−	114254.i	1.44008	−	0.172552i
$214$		0			0
$215$	1.16731e6			1.72223
$216$		0			0
$217$	−95733.8			−0.138012
$218$		0			0
$219$	39762.9	−	4764.46i	0.0560232	−	0.00671279i
$220$		0			0
$221$			103062.i			0.141945i
$222$		0			0
$223$			864006.i			1.16347i	0.813379	+	0.581734i	$0.197626\pi$
$223$			864006.i			1.16347i	−0.813379	+	0.581734i	$0.802374\pi$
$224$		0			0
$225$	1151.93	−	280.074i	0.00151695	−	0.000368821i
$226$		0			0
$227$	889864.			1.14620			0.573098	−	0.819487i	$-0.305741\pi$
$227$	889864.			1.14620			0.573098	+	0.819487i	$0.305741\pi$
$228$		0			0
$229$	−296508.			−0.373635			−0.186818	−	0.982395i	$-0.559817\pi$
$229$	−296508.			−0.373635			−0.186818	+	0.982395i	$0.559817\pi$
$230$		0			0
$231$	15472.4	+	129128.i	0.0190777	+	0.159218i
$232$		0			0
$233$		−	763288.i		−	0.921083i	−0.887638	−	0.460541i	$-0.847655\pi$
$233$		−	763288.i		−	0.921083i	0.887638	−	0.460541i	$-0.152345\pi$
$234$		0			0
$235$		−	670422.i		−	0.791915i
$236$		0			0
$237$	−114152.	−	952684.i	−0.132012	−	1.10174i
$238$		0			0
$239$	−36450.5			−0.0412771			−0.0206385	−	0.999787i	$-0.506570\pi$
$239$	−36450.5			−0.0412771			−0.0206385	+	0.999787i	$0.506570\pi$
$240$		0			0
$241$	1.29506e6			1.43631			0.718155	−	0.695884i	$-0.244987\pi$
$241$	1.29506e6			1.43631			0.718155	+	0.695884i	$0.244987\pi$
$242$		0			0
$243$	761643.	−	516903.i	0.827439	−	0.561556i
$244$		0			0
$245$			1.91302e6i			2.03613i
$246$		0			0
$247$			794032.i			0.828125i
$248$		0			0
$249$	1.75362e6	−	210122.i	1.79241	−	0.214770i
$250$		0			0
$251$	466045.			0.466921			0.233460	−	0.972366i	$-0.424995\pi$
$251$	466045.			0.466921			0.233460	+	0.972366i	$0.424995\pi$
$252$		0			0
$253$	138415.			0.135951
$254$		0			0
$255$	−111995.	+	13419.5i	−0.107857	+	0.0129236i
$256$		0			0
$257$		−	571612.i		−	0.539844i	−0.962882	−	0.269922i	$-0.913002\pi$
$257$		−	571612.i		−	0.539844i	0.962882	−	0.269922i	$-0.0869979\pi$
$258$		0			0
$259$		−	2.46957e6i		−	2.28756i
$260$		0			0
$261$	−52901.2	−	217581.i	−0.0480689	−	0.197706i
$262$		0			0
$263$	435018.			0.387809			0.193905	−	0.981020i	$-0.437885\pi$
$263$	435018.			0.387809			0.193905	+	0.981020i	$0.437885\pi$
$264$		0			0
$265$	634848.			0.555335
$266$		0			0
$267$	−232787.	−	1.94278e6i	−0.199839	−	1.66781i
$268$		0			0
$269$			1.11982e6i			0.943556i	0.881717	+	0.471778i	$0.156388\pi$
$269$			1.11982e6i			0.943556i	−0.881717	+	0.471778i	$0.843612\pi$
$270$		0			0
$271$			201205.i			0.166424i	0.996532	+	0.0832118i	$0.0265178\pi$
$271$			201205.i			0.166424i	−0.996532	+	0.0832118i	$0.973482\pi$
$272$		0			0
$273$	333392.	+	2.78240e6i	0.270737	+	2.25950i
$274$		0			0
$275$	−180.130			−0.000143633
$276$		0			0
$277$	302438.			0.236830			0.118415	−	0.992964i	$-0.462219\pi$
$277$	302438.			0.236830			0.118415	+	0.992964i	$0.462219\pi$
$278$		0			0
$279$	−24323.6	−	100042.i	−0.0187075	−	0.0769433i
$280$		0			0
$281$		−	1.77044e6i		−	1.33757i	−0.743457	−	0.668784i	$-0.766815\pi$
$281$		−	1.77044e6i		−	1.33757i	0.743457	−	0.668784i	$-0.233185\pi$
$282$		0			0
$283$			809916.i			0.601138i	0.953760	+	0.300569i	$0.0971765\pi$
$283$			809916.i			0.601138i	−0.953760	+	0.300569i	$0.902824\pi$
$284$		0			0
$285$	−862856.	+	103389.i	−0.629255	+	0.0753983i
$286$		0			0
$287$	3.26853e6			2.34233
$288$		0			0
$289$	1.40308e6			0.988181
$290$		0			0
$291$	−2.42450e6	+	290507.i	−1.67838	+	0.201106i
$292$		0			0
$293$			1.73657e6i			1.18174i	0.806767	+	0.590870i	$0.201216\pi$
$293$			1.73657e6i			1.18174i	−0.806767	+	0.590870i	$0.798784\pi$
$294$		0			0
$295$			2.04478e6i			1.36801i
$296$		0			0
$297$	−131008.	+	48976.9i	−0.0861800	+	0.0322181i
$298$		0			0
$299$	2.98250e6			1.92931
$300$		0			0
$301$	4.72194e6			3.00403
$302$		0			0
$303$	63837.9	+	532775.i	0.0399459	+	0.333378i
$304$		0			0
$305$			2.13667e6i			1.31519i
$306$		0			0
$307$			596701.i			0.361335i	0.983544	+	0.180668i	$0.0578259\pi$
$307$			596701.i			0.361335i	−0.983544	+	0.180668i	$0.942174\pi$
$308$		0			0
$309$	52308.8	+	436556.i	0.0311658	+	0.260102i
$310$		0			0
$311$	−2.86268e6			−1.67831			−0.839154	−	0.543894i	$-0.816949\pi$
$311$	−2.86268e6			−1.67831			−0.839154	+	0.543894i	$0.816949\pi$
$312$		0			0
$313$	−1.53442e6			−0.885287			−0.442644	−	0.896698i	$-0.645959\pi$
$313$	−1.53442e6			−0.885287			−0.442644	+	0.896698i	$0.645959\pi$
$314$		0			0
$315$	−2.98016e6	+	724578.i	−1.69224	+	0.411442i
$316$		0			0
$317$		−	3.33250e6i		−	1.86261i	−0.364241	−	0.931305i	$-0.618671\pi$
$317$		−	3.33250e6i		−	1.86261i	0.364241	−	0.931305i	$-0.381329\pi$
$318$		0			0
$319$			34023.6i			0.0187199i
$320$		0			0
$321$	652886.	−	78229.9i	0.353651	−	0.0423750i
$322$		0			0
$323$	−129286.			−0.0689517
$324$		0			0
$325$	−3881.37			−0.00203834
$326$		0			0
$327$	−1.37424e6	+	164663.i	−0.710711	+	0.0851585i
$328$		0			0
$329$		−	2.71195e6i		−	1.38131i
$330$		0			0
$331$			2.02136e6i			1.01408i	0.861922	+	0.507041i	$0.169261\pi$
$331$			2.02136e6i			1.01408i	−0.861922	+	0.507041i	$0.830739\pi$
$332$		0			0
$333$	2.58070e6	−	627456.i	1.27534	−	0.310079i
$334$		0			0
$335$	−501336.			−0.244071
$336$		0			0
$337$	−1.12008e6			−0.537249			−0.268625	−	0.963245i	$-0.586569\pi$
$337$	−1.12008e6			−0.537249			−0.268625	+	0.963245i	$0.586569\pi$
$338$		0			0
$339$	−443063.	−	3.69769e6i	−0.209395	−	1.74756i
$340$		0			0
$341$			15643.8i			0.00728544i
$342$		0			0
$343$			3.94083e6i			1.80864i
$344$		0			0
$345$	388343.	+	3.24101e6i	0.175658	+	1.46600i
$346$		0			0
$347$	2.39720e6			1.06876			0.534380	−	0.845244i	$-0.320545\pi$
$347$	2.39720e6			1.06876			0.534380	+	0.845244i	$0.320545\pi$
$348$		0			0
$349$	−1.86085e6			−0.817801			−0.408900	−	0.912579i	$-0.634088\pi$
$349$	−1.86085e6			−0.817801			−0.408900	+	0.912579i	$0.634088\pi$
$350$		0			0
$351$	−2.82290e6	+	1.05533e6i	−1.22300	+	0.457216i
$352$		0			0
$353$		−	2.14786e6i		−	0.917423i	−0.888585	−	0.458711i	$-0.848311\pi$
$353$		−	2.14786e6i		−	0.917423i	0.888585	−	0.458711i	$-0.151689\pi$
$354$		0			0
$355$		−	3.44122e6i		−	1.44925i
$356$		0			0
$357$	−453036.	+	54283.5i	−0.188132	+	0.0225423i
$358$		0			0
$359$	1.48571e6			0.608412			0.304206	−	0.952606i	$-0.401609\pi$
$359$	1.48571e6			0.608412			0.304206	+	0.952606i	$0.401609\pi$
$360$		0			0
$361$	1.48003e6			0.597726
$362$		0			0
$363$	−2.47161e6	+	296152.i	−0.984493	+	0.117964i
$364$		0			0
$365$		−	143501.i		−	0.0563799i
$366$		0			0
$367$		−	2.58403e6i		−	1.00146i	−0.865604	−	0.500729i	$-0.833065\pi$
$367$		−	2.58403e6i		−	1.00146i	0.865604	−	0.500729i	$-0.166935\pi$
$368$		0			0
$369$	830452.	+	3.41562e6i	0.317504	+	1.30588i
$370$		0			0
$371$	2.56804e6			0.968652
$372$		0			0
$373$	3.75492e6			1.39743			0.698713	−	0.715402i	$-0.253756\pi$
$373$	3.75492e6			1.39743			0.698713	+	0.715402i	$0.253756\pi$
$374$		0			0
$375$	−324232.	−	2.70596e6i	−0.119063	−	0.993671i
$376$		0			0
$377$			733126.i			0.265659i
$378$		0			0
$379$		−	4.37130e6i		−	1.56319i	−0.623784	−	0.781597i	$-0.714405\pi$
$379$		−	4.37130e6i		−	1.56319i	0.623784	−	0.781597i	$-0.285595\pi$
$380$		0			0
$381$	−480073.	−	4.00656e6i	−0.169432	−	1.41403i
$382$		0			0
$383$	−1.26259e6			−0.439812			−0.219906	−	0.975521i	$-0.570575\pi$
$383$	−1.26259e6			−0.439812			−0.219906	+	0.975521i	$0.570575\pi$
$384$		0			0
$385$	466015.			0.160231
$386$		0			0
$387$	1.19973e6	+	4.93442e6i	0.407197	+	1.67479i
$388$		0			0
$389$		−	2.13040e6i		−	0.713817i	−0.934139	−	0.356908i	$-0.883831\pi$
$389$		−	2.13040e6i		−	0.713817i	0.934139	−	0.356908i	$-0.116169\pi$
$390$		0			0
$391$			485617.i			0.160639i
$392$		0			0
$393$	146455.	−	17548.4i	0.0478324	−	0.00573135i
$394$		0			0
$395$	−3.43817e6			−1.10875
$396$		0			0
$397$	−3.68644e6			−1.17390			−0.586950	−	0.809623i	$-0.699672\pi$
$397$	−3.68644e6			−1.17390			−0.586950	+	0.809623i	$0.699672\pi$
$398$		0			0
$399$	−3.49037e6	+	418222.i	−1.09759	+	0.131515i
$400$		0			0
$401$		−	3.06338e6i		−	0.951350i	−0.879621	−	0.475675i	$-0.842204\pi$
$401$		−	3.06338e6i		−	0.951350i	0.879621	−	0.475675i	$-0.157796\pi$
$402$		0			0
$403$			337085.i			0.103390i
$404$		0			0
$405$	−1.51437e6	−	2.93017e6i	−0.458768	−	0.887677i
$406$		0			0
$407$	−403551.			−0.120757
$408$		0			0
$409$	4.44429e6			1.31369			0.656847	−	0.754024i	$-0.271890\pi$
$409$	4.44429e6			1.31369			0.656847	+	0.754024i	$0.271890\pi$
$410$		0			0
$411$	−272071.	−	2.27064e6i	−0.0794472	−	0.663046i
$412$		0			0
$413$			8.27139e6i			2.38618i
$414$		0			0
$415$		−	6.32870e6i		−	1.80382i
$416$		0			0
$417$	−279715.	−	2.33443e6i	−0.0787727	−	0.657417i
$418$		0			0
$419$	1.62681e6			0.452691			0.226346	−	0.974047i	$-0.427322\pi$
$419$	1.62681e6			0.452691			0.226346	+	0.974047i	$0.427322\pi$
$420$		0			0
$421$	−1.43223e6			−0.393828			−0.196914	−	0.980421i	$-0.563092\pi$
$421$	−1.43223e6			−0.393828			−0.196914	+	0.980421i	$0.563092\pi$
$422$		0			0
$423$	2.83398e6	−	689038.i	0.770099	−	0.187237i
$424$		0			0
$425$		−	631.972i		−	0.000169717i
$426$		0			0
$427$			8.64312e6i			2.29404i
$428$		0			0
$429$	454670.	−	54479.2i	0.119276	−	0.0142918i
$430$		0			0
$431$	5.60361e6			1.45303			0.726515	−	0.687151i	$-0.241139\pi$
$431$	5.60361e6			1.45303			0.726515	+	0.687151i	$0.241139\pi$
$432$		0			0
$433$	−4.49780e6			−1.15287			−0.576435	−	0.817143i	$-0.695557\pi$
$433$	−4.49780e6			−1.15287			−0.576435	+	0.817143i	$0.695557\pi$
$434$		0			0
$435$	−796671.	+	95458.3i	−0.201862	+	0.0241875i
$436$		0			0
$437$			3.74139e6i			0.937193i
$438$		0			0
$439$		−	5.39182e6i		−	1.33529i	−0.744481	−	0.667643i	$-0.767303\pi$
$439$		−	5.39182e6i		−	1.33529i	0.744481	−	0.667643i	$-0.232697\pi$
$440$		0			0
$441$	−8.08665e6	+	1.96614e6i	−1.98003	+	0.481413i
$442$		0			0
$443$	697144.			0.168777			0.0843885	−	0.996433i	$-0.473106\pi$
$443$	697144.			0.168777			0.0843885	+	0.996433i	$0.473106\pi$
$444$		0			0
$445$	−7.01136e6			−1.67843
$446$		0			0
$447$	414328.	+	3.45787e6i	0.0980788	+	0.818541i
$448$		0			0
$449$			2.66314e6i			0.623416i	0.950178	+	0.311708i	$0.100901\pi$
$449$			2.66314e6i			0.623416i	−0.950178	+	0.311708i	$0.899099\pi$
$450$		0			0
$451$		−	534108.i		−	0.123648i
$452$		0			0
$453$	−738320.	−	6.16183e6i	−0.169044	−	1.41080i
$454$		0			0
$455$	1.00415e7			2.27389
$456$		0			0
$457$	−2.12657e6			−0.476310			−0.238155	−	0.971227i	$-0.576543\pi$
$457$	−2.12657e6			−0.476310			−0.238155	+	0.971227i	$0.576543\pi$
$458$		0			0
$459$	−171831.	−	459630.i	−0.0380689	−	0.101830i
$460$		0			0
$461$			4.19441e6i			0.919218i	0.888121	+	0.459609i	$0.152011\pi$
$461$			4.19441e6i			0.919218i	−0.888121	+	0.459609i	$0.847989\pi$
$462$		0			0
$463$			4.23099e6i			0.917254i	0.888629	+	0.458627i	$0.151659\pi$
$463$			4.23099e6i			0.917254i	−0.888629	+	0.458627i	$0.848341\pi$
$464$		0			0
$465$	−366303.	+	43891.0i	−0.0785611	+	0.00941332i
$466$		0			0
$467$	−4.90063e6			−1.03982			−0.519912	−	0.854220i	$-0.674035\pi$
$467$	−4.90063e6			−1.03982			−0.519912	+	0.854220i	$0.674035\pi$
$468$		0			0
$469$	−2.02797e6			−0.425726
$470$		0			0
$471$	−7.08506e6	+	848944.i	−1.47161	+	0.176330i
$472$		0			0
$473$		−	771608.i		−	0.158578i
$474$		0			0
$475$		−	4868.97i		−	0.000990154i
$476$		0			0
$477$	652476.	+	2.68361e6i	0.131301	+	0.540036i
$478$		0			0
$479$	3.45294e6			0.687622			0.343811	−	0.939039i	$-0.388282\pi$
$479$	3.45294e6			0.687622			0.343811	+	0.939039i	$0.388282\pi$
$480$		0			0
$481$	−8.69553e6			−1.71369
$482$		0			0
$483$	1.57090e6	+	1.31103e7i	0.306395	+	2.55709i
$484$		0			0
$485$			8.74983e6i			1.68906i
$486$		0			0
$487$		−	1.62872e6i		−	0.311188i	−0.987821	−	0.155594i	$-0.950271\pi$
$487$		−	1.62872e6i		−	0.311188i	0.987821	−	0.155594i	$-0.0497292\pi$
$488$		0			0
$489$	−167987.	−	1.40197e6i	−0.0317690	−	0.265136i
$490$		0			0
$491$	5.79077e6			1.08401			0.542004	−	0.840376i	$-0.317666\pi$
$491$	5.79077e6			1.08401			0.542004	+	0.840376i	$0.317666\pi$
$492$		0			0
$493$	−119369.			−0.0221195
$494$		0			0
$495$	118403.	+	486985.i	0.0217194	+	0.0893311i
$496$		0			0
$497$		−	1.39202e7i		−	2.52787i
$498$		0			0
$499$			4.75964e6i			0.855702i	0.903849	+	0.427851i	$0.140729\pi$
$499$			4.75964e6i			0.855702i	−0.903849	+	0.427851i	$0.859271\pi$
$500$		0			0
$501$	2.48691e6	−	297986.i	0.442656	−	0.0530397i
$502$		0			0
$503$	−55691.2			−0.00981446			−0.00490723	−	0.999988i	$-0.501562\pi$
$503$	−55691.2			−0.00981446			−0.00490723	+	0.999988i	$0.501562\pi$
$504$		0			0
$505$	1.92275e6			0.335501
$506$		0			0
$507$	4.05024e6	−	485306.i	0.699778	−	0.0838486i
$508$		0			0
$509$		−	2.84383e6i		−	0.486530i	−0.969960	−	0.243265i	$-0.921781\pi$
$509$		−	2.84383e6i		−	0.486530i	0.969960	−	0.243265i	$-0.0782185\pi$
$510$		0			0
$511$		−	580483.i		−	0.0983416i
$512$		0			0
$513$	−1.32386e6	−	3.54118e6i	−0.222100	−	0.594093i
$514$		0			0
$515$	1.57550e6			0.261758
$516$		0			0
$517$	−443157.			−0.0729174
$518$		0			0
$519$	−788900.	−	6.58396e6i	−0.128559	−	1.07292i
$520$		0			0
$521$			1.07097e7i			1.72855i	0.503019	+	0.864275i	$0.332223\pi$
$521$			1.07097e7i			1.72855i	−0.503019	+	0.864275i	$0.667777\pi$
$522$		0			0
$523$			4.05988e6i			0.649022i	0.945882	+	0.324511i	$0.105200\pi$
$523$			4.05988e6i			0.649022i	−0.945882	+	0.324511i	$0.894800\pi$
$524$		0			0
$525$	−2044.34	−	17061.5i	−0.000323709	−	0.00270159i
$526$		0			0
$527$	−54884.9			−0.00860848
$528$		0			0
$529$	7.61684e6			1.18341
$530$		0			0
$531$	−8.64360e6	+	2.10155e6i	−1.33033	+	0.323448i
$532$		0			0
$533$		−	1.15087e7i		−	1.75473i
$534$		0			0
$535$		−	2.35622e6i		−	0.355903i
$536$		0			0
$537$	304517.	−	36487.7i	0.0455696	−	0.00546022i
$538$		0			0
$539$	1.26453e6			0.187481
$540$		0			0
$541$	−3.26069e6			−0.478979			−0.239490	−	0.970899i	$-0.576980\pi$
$541$	−3.26069e6			−0.478979			−0.239490	+	0.970899i	$0.576980\pi$
$542$		0			0
$543$	717349.	−	85953.9i	0.104407	−	0.0125102i
$544$		0			0
$545$			4.95953e6i			0.715235i
$546$		0			0
$547$		−	5.81195e6i		−	0.830526i	−0.909701	−	0.415263i	$-0.863690\pi$
$547$		−	5.81195e6i		−	0.830526i	0.909701	−	0.415263i	$-0.136310\pi$
$548$		0			0
$549$	−9.03206e6	+	2.19600e6i	−1.27896	+	0.310958i
$550$		0			0
$551$	−919667.			−0.129048
$552$		0			0
$553$	−1.39078e7			−1.93396
$554$		0			0
$555$	−1.13222e6	−	9.44923e6i	−0.156027	−	1.30216i
$556$		0			0
$557$			5.08607e6i			0.694615i	0.937751	+	0.347308i	$0.112904\pi$
$557$			5.08607e6i			0.694615i	−0.937751	+	0.347308i	$0.887096\pi$
$558$		0			0
$559$		−	1.66263e7i		−	2.25043i
$560$		0			0
$561$	8870.42	+	74030.3i	0.00118997	+	0.00993121i
$562$		0			0
$563$	9.79359e6			1.30218			0.651090	−	0.759001i	$-0.274312\pi$
$563$	9.79359e6			1.30218			0.651090	+	0.759001i	$0.274312\pi$
$564$		0			0
$565$	−1.33447e7			−1.75868
$566$		0			0
$567$	−6.12582e6	−	1.18529e7i	−0.800214	−	1.54835i
$568$		0			0
$569$		−	8.50753e6i		−	1.10160i	−0.834638	−	0.550799i	$-0.814323\pi$
$569$		−	8.50753e6i		−	1.10160i	0.834638	−	0.550799i	$-0.185677\pi$
$570$		0			0
$571$			4.37026e6i			0.560941i	0.959863	+	0.280470i	$0.0904905\pi$
$571$			4.37026e6i			0.560941i	−0.959863	+	0.280470i	$0.909510\pi$
$572$		0			0
$573$	−884103.	+	105935.i	−0.112491	+	0.0134788i
$574$		0			0
$575$	−18288.5			−0.00230680
$576$		0			0
$577$	8.87042e6			1.10919			0.554594	−	0.832121i	$-0.312874\pi$
$577$	8.87042e6			1.10919			0.554594	+	0.832121i	$0.312874\pi$
$578$		0			0
$579$	−3.99138e6	+	478254.i	−0.494797	+	0.0592874i
$580$		0			0
$581$		−	2.56004e7i		−	3.14635i
$582$		0			0
$583$		−	419642.i		−	0.0511338i
$584$		0			0
$585$	2.55129e6	+	1.04933e7i	0.308226	+	1.26772i
$586$		0			0
$587$	−1.40119e6			−0.167842			−0.0839209	−	0.996472i	$-0.526744\pi$
$587$	−1.40119e6			−0.167842			−0.0839209	+	0.996472i	$0.526744\pi$
$588$		0			0
$589$	−422855.			−0.0502231
$590$		0			0
$591$	1.30710e6	+	1.09087e7i	0.153936	+	1.28471i
$592$		0			0
$593$		−	1.59083e7i		−	1.85774i	−0.370401	−	0.928872i	$-0.620780\pi$
$593$		−	1.59083e7i		−	1.85774i	0.370401	−	0.928872i	$-0.379220\pi$
$594$		0			0
$595$			1.63497e6i			0.189330i
$596$		0			0
$597$	−481398.	−	4.01763e6i	−0.0552801	−	0.461353i
$598$		0			0
$599$	−1.27346e7			−1.45017			−0.725085	−	0.688660i	$-0.758199\pi$
$599$	−1.27346e7			−1.45017			−0.725085	+	0.688660i	$0.758199\pi$
$600$		0			0
$601$	−8.53611e6			−0.963992			−0.481996	−	0.876173i	$-0.660088\pi$
$601$	−8.53611e6			−0.963992			−0.481996	+	0.876173i	$0.660088\pi$
$602$		0			0
$603$	−515257.	−	2.11923e6i	−0.0577072	−	0.237348i
$604$		0			0
$605$			8.91984e6i			0.990761i
$606$		0			0
$607$			3.68744e6i			0.406212i	0.979157	+	0.203106i	$0.0651036\pi$
$607$			3.68744e6i			0.406212i	−0.979157	+	0.203106i	$0.934896\pi$
$608$		0			0
$609$	−3.22264e6	+	386142.i	−0.352102	+	0.0421894i
$610$		0			0
$611$	−9.54895e6			−1.03479
$612$		0			0
$613$	5.99314e6			0.644174			0.322087	−	0.946710i	$-0.395616\pi$
$613$	5.99314e6			0.644174			0.322087	+	0.946710i	$0.395616\pi$
$614$		0			0
$615$	1.25063e7	−	1.49852e6i	1.33334	−	0.159762i
$616$		0			0
$617$			1.12913e7i			1.19407i	0.802215	+	0.597035i	$0.203655\pi$
$617$			1.12913e7i			1.19407i	−0.802215	+	0.597035i	$0.796345\pi$
$618$		0			0
$619$			7.53091e6i			0.789989i	0.918684	+	0.394994i	$0.129253\pi$
$619$			7.53091e6i			0.789989i	−0.918684	+	0.394994i	$0.870747\pi$
$620$		0			0
$621$	−1.33012e7	+	4.97260e6i	−1.38408	+	0.517433i
$622$		0			0
$623$	−2.83619e7			−2.92762
$624$		0			0
$625$	−9.75036e6			−0.998436
$626$		0			0
$627$	68341.3	+	570359.i	0.00694247	+	0.0579401i
$628$		0			0
$629$		−	1.41582e6i		−	0.142686i
$630$		0			0
$631$			1.39881e7i			1.39858i	0.714840	+	0.699289i	$0.246500\pi$
$631$			1.39881e7i			1.39858i	−0.714840	+	0.699289i	$0.753500\pi$
$632$		0			0
$633$	990861.	+	8.26947e6i	0.0982887	+	0.820292i
$634$		0			0
$635$	−1.44594e7			−1.42304
$636$		0			0
$637$	2.72475e7			2.66059
$638$		0			0
$639$	1.45466e7	−	3.53678e6i	1.40932	−	0.342654i
$640$		0			0
$641$			9.54988e6i			0.918021i	0.888431	+	0.459011i	$0.151796\pi$
$641$			9.54988e6i			0.918021i	−0.888431	+	0.459011i	$0.848204\pi$
$642$		0			0
$643$		−	1.51800e6i		−	0.144792i	−0.997376	−	0.0723959i	$-0.976935\pi$
$643$		−	1.51800e6i		−	0.144792i	0.997376	−	0.0723959i	$-0.0230645\pi$
$644$		0			0
$645$	1.80674e7	−	2.16486e6i	1.71000	−	0.204895i
$646$		0			0
$647$	1.58617e7			1.48967			0.744834	−	0.667250i	$-0.232529\pi$
$647$	1.58617e7			1.48967			0.744834	+	0.667250i	$0.232529\pi$
$648$		0			0
$649$	1.35162e6			0.125963
$650$		0			0
$651$	−1.48174e6	+	177545.i	−0.137032	+	0.0164193i
$652$		0			0
$653$			543838.i			0.0499099i	0.999689	+	0.0249549i	$0.00794423\pi$
$653$			543838.i			0.0499099i	−0.999689	+	0.0249549i	$0.992056\pi$
$654$		0			0
$655$		−	528544.i		−	0.0481369i
$656$		0			0
$657$	606604.	−	147486.i	0.0548267	−	0.0133302i
$658$		0			0
$659$	1.06321e7			0.953685			0.476843	−	0.878989i	$-0.341781\pi$
$659$	1.06321e7			0.953685			0.476843	+	0.878989i	$0.341781\pi$
$660$		0			0
$661$	1.47871e7			1.31638			0.658189	−	0.752853i	$-0.271323\pi$
$661$	1.47871e7			1.31638			0.658189	+	0.752853i	$0.271323\pi$
$662$		0			0
$663$	191136.	+	1.59517e6i	0.0168872	+	0.140936i
$664$		0			0
$665$			1.25965e7i			1.10458i
$666$		0			0
$667$			3.45440e6i			0.300648i
$668$		0			0
$669$	1.60236e6	+	1.33729e7i	0.138419	+	1.15521i
$670$		0			0
$671$	1.41237e6			0.121099
$672$		0			0
$673$	1.01183e7			0.861129			0.430565	−	0.902560i	$-0.358314\pi$
$673$	1.01183e7			0.861129			0.430565	+	0.902560i	$0.358314\pi$
$674$		0			0
$675$	17309.9	−	6471.24i	0.00146229	−	0.000546674i
$676$		0			0
$677$			9.55270e6i			0.801040i	0.916288	+	0.400520i	$0.131171\pi$
$677$			9.55270e6i			0.801040i	−0.916288	+	0.400520i	$0.868829\pi$
$678$		0			0
$679$			3.53942e7i			2.94617i
$680$		0			0
$681$	1.37731e7	−	1.65031e6i	1.13806	−	0.136364i
$682$		0			0
$683$	−1.31661e7			−1.07995			−0.539975	−	0.841681i	$-0.681566\pi$
$683$	−1.31661e7			−1.07995			−0.539975	+	0.841681i	$0.681566\pi$
$684$		0			0
$685$	−8.19457e6			−0.667267
$686$		0			0
$687$	−4.58928e6	+	549894.i	−0.370982	+	0.0444516i
$688$		0			0
$689$		−	9.04226e6i		−	0.725653i
$690$		0			0
$691$		−	1.90008e7i		−	1.51383i	−0.653516	−	0.756913i	$-0.726707\pi$
$691$		−	1.90008e7i		−	1.51383i	0.653516	−	0.756913i	$-0.273293\pi$
$692$		0			0
$693$	478955.	+	1.96992e6i	0.0378845	+	0.155817i
$694$		0			0
$695$	−8.42479e6			−0.661602
$696$		0			0
$697$	1.87387e6			0.146103
$698$		0			0
$699$	−1.41557e6	−	1.18140e7i	−0.109582	−	0.914541i
$700$		0			0
$701$		−	7.43183e6i		−	0.571216i	−0.958347	−	0.285608i	$-0.907804\pi$
$701$		−	7.43183e6i		−	0.571216i	0.958347	−	0.285608i	$-0.0921956\pi$
$702$		0			0
$703$		−	1.09081e7i		−	0.832453i
$704$		0			0
$705$	−1.24334e6	−	1.03766e7i	−0.0942146	−	0.786291i
$706$		0			0
$707$	7.77776e6			0.585202
$708$		0			0
$709$	−9.49641e6			−0.709486			−0.354743	−	0.934964i	$-0.615432\pi$
$709$	−9.49641e6			−0.709486			−0.354743	+	0.934964i	$0.615432\pi$
$710$		0			0
$711$	−3.53364e6	−	1.45337e7i	−0.262149	−	1.07821i
$712$		0			0
$713$			1.58831e6i			0.117007i
$714$		0			0
$715$		−	1.64087e6i		−	0.120035i
$716$		0			0
$717$	−564172.	+	67600.0i	−0.0409839	+	0.00491076i
$718$		0			0
$719$	2.25267e6			0.162508			0.0812541	−	0.996693i	$-0.474107\pi$
$719$	2.25267e6			0.162508			0.0812541	+	0.996693i	$0.474107\pi$
$720$		0			0
$721$	6.37310e6			0.456575
$722$		0			0
$723$	2.00446e7	−	2.40178e6i	1.42611	−	0.170879i
$724$		0			0
$725$		−	4495.49i		−	0.000317638i
$726$		0			0
$727$			9.23196e6i			0.647825i	0.946087	+	0.323913i	$0.104998\pi$
$727$			9.23196e6i			0.647825i	−0.946087	+	0.323913i	$0.895002\pi$
$728$		0			0
$729$	1.08299e7	−	9.41301e6i	0.754753	−	0.656009i
$730$		0			0
$731$	2.70712e6			0.187376
$732$		0			0
$733$	3.66782e6			0.252143			0.126072	−	0.992021i	$-0.459763\pi$
$733$	3.66782e6			0.252143			0.126072	+	0.992021i	$0.459763\pi$
$734$		0			0
$735$	3.54783e6	+	2.96092e7i	0.242239	+	2.02166i
$736$		0			0
$737$			331389.i			0.0224734i
$738$		0			0
$739$		−	2.25692e7i		−	1.52022i	−0.649795	−	0.760109i	$-0.725145\pi$
$739$		−	2.25692e7i		−	1.52022i	0.649795	−	0.760109i	$-0.274855\pi$
$740$		0			0
$741$	1.47259e6	+	1.22898e7i	0.0985225	+	0.822243i
$742$		0			0
$743$	1.79409e7			1.19226			0.596130	−	0.802888i	$-0.296704\pi$
$743$	1.79409e7			1.19226			0.596130	+	0.802888i	$0.296704\pi$
$744$		0			0
$745$	1.24792e7			0.823752
$746$		0			0
$747$	2.67525e7	−	6.50443e6i	1.75413	−	0.426489i
$748$		0			0
$749$		−	9.53122e6i		−	0.620789i
$750$		0			0
$751$		−	1.43657e7i		−	0.929451i	−0.885455	−	0.464726i	$-0.846153\pi$
$751$		−	1.43657e7i		−	0.929451i	0.885455	−	0.464726i	$-0.153847\pi$
$752$		0			0
$753$	7.21332e6	−	864311.i	0.463605	−	0.0555498i
$754$		0			0
$755$	−2.22376e7			−1.41978
$756$		0			0
$757$	−5.10716e6			−0.323922			−0.161961	−	0.986797i	$-0.551782\pi$
$757$	−5.10716e6			−0.323922			−0.161961	+	0.986797i	$0.551782\pi$
$758$		0			0
$759$	2.14235e6	−	256700.i	0.134985	−	0.0161741i
$760$		0			0
$761$			8.66301e6i			0.542260i	0.962543	+	0.271130i	$0.0873973\pi$
$761$			8.66301e6i			0.542260i	−0.962543	+	0.271130i	$0.912603\pi$
$762$		0			0
$763$			2.00619e7i			1.24756i
$764$		0			0
$765$	−1.70855e6	+	415406.i	−0.105554	+	0.0256637i
$766$		0			0
$767$	2.91241e7			1.78758
$768$		0			0
$769$	1.21621e6			0.0741639			0.0370819	−	0.999312i	$-0.488194\pi$
$769$	1.21621e6			0.0741639			0.0370819	+	0.999312i	$0.488194\pi$
$770$		0			0
$771$	−1.06009e6	−	8.84726e6i	−0.0642256	−	0.536010i
$772$		0			0
$773$			1.17432e6i			0.0706867i	0.999375	+	0.0353434i	$0.0112525\pi$
$773$			1.17432e6i			0.0706867i	−0.999375	+	0.0353434i	$0.988748\pi$
$774$		0			0
$775$		−	2066.99i		−	0.000123619i
$776$		0			0
$777$	−4.57999e6	−	3.82234e7i	−0.272152	−	2.27131i
$778$		0			0
$779$	1.44371e7			0.852384
$780$		0			0
$781$	−2.27469e6			−0.133443
$782$		0			0
$783$	−1.22231e6	−	3.26955e6i	−0.0712487	−	0.190583i
$784$		0			0
$785$			2.55695e7i			1.48098i
$786$		0			0
$787$		−	1.61589e7i		−	0.929983i	−0.885315	−	0.464991i	$-0.846057\pi$
$787$		−	1.61589e7i		−	0.929983i	0.885315	−	0.464991i	$-0.153943\pi$
$788$		0			0
$789$	6.73310e6	−	806771.i	0.385055	−	0.0461379i
$790$		0			0
$791$	−5.39811e7			−3.06761
$792$		0			0
$793$	3.04330e7			1.71855
$794$		0			0
$795$	9.82601e6	−	1.17737e6i	0.551391	−	0.0660685i
$796$		0			0
$797$			1.59354e7i			0.888622i	0.895873	+	0.444311i	$0.146552\pi$
$797$			1.59354e7i			0.888622i	−0.895873	+	0.444311i	$0.853448\pi$
$798$		0			0
$799$		−	1.55478e6i		−	0.0861592i
$800$		0			0
$801$	−7.20604e6	−	2.96382e7i	−0.396840	−	1.63219i
$802$		0			0
$803$	−94856.2			−0.00519131
$804$		0			0
$805$	4.73142e7			2.57337
$806$		0			0
$807$	2.07678e6	+	1.73323e7i	0.112255	+	0.936855i
$808$		0			0
$809$		−	8.21438e6i		−	0.441269i	−0.975357	−	0.220635i	$-0.929187\pi$
$809$		−	8.21438e6i		−	0.441269i	0.975357	−	0.220635i	$-0.0708128\pi$
$810$		0			0
$811$		−	2.18134e7i		−	1.16459i	−0.812979	−	0.582293i	$-0.802156\pi$
$811$		−	2.18134e7i		−	1.16459i	0.812979	−	0.582293i	$-0.197844\pi$
$812$		0			0
$813$	373148.	+	3.11419e6i	0.0197995	+	0.165242i
$814$		0			0
$815$	−5.05962e6			−0.266824
$816$		0			0
$817$	2.08568e7			1.09318
$818$		0			0
$819$	1.03203e7	+	4.24470e7i	0.537629	+	2.21125i
$820$		0			0
$821$		−	8.73324e6i		−	0.452186i	−0.974106	−	0.226093i	$-0.927405\pi$
$821$		−	8.73324e6i		−	0.452186i	0.974106	−	0.226093i	$-0.0725954\pi$
$822$		0			0
$823$			5.88986e6i			0.303114i	0.988449	+	0.151557i	$0.0484287\pi$
$823$			5.88986e6i			0.303114i	−0.988449	+	0.151557i	$0.951571\pi$
$824$		0			0
$825$	−2788.01	+	334.064i	−0.000142613	+	1.70881e-5i
$826$		0			0
$827$	2.33435e7			1.18687			0.593435	−	0.804882i	$-0.297771\pi$
$827$	2.33435e7			1.18687			0.593435	+	0.804882i	$0.297771\pi$
$828$		0			0
$829$	1.06227e7			0.536846			0.268423	−	0.963301i	$-0.413498\pi$
$829$	1.06227e7			0.536846			0.268423	+	0.963301i	$0.413498\pi$
$830$		0			0
$831$	4.68106e6	−	560892.i	0.235148	−	0.0281758i
$832$		0			0
$833$			4.43650e6i			0.221528i
$834$		0			0
$835$		−	8.97508e6i		−	0.445474i
$836$		0			0
$837$	−562008.	−	1.50331e6i	−0.0277287	−	0.0741712i
$838$		0			0
$839$	2.24424e7			1.10069			0.550345	−	0.834937i	$-0.314496\pi$
$839$	2.24424e7			1.10069			0.550345	+	0.834937i	$0.314496\pi$
$840$		0			0
$841$	1.96620e7			0.958602
$842$		0			0
$843$	−3.28341e6	−	2.74025e7i	−0.159131	−	1.32807i
$844$		0			0
$845$		−	1.46170e7i		−	0.704234i
$846$		0			0
$847$			3.60820e7i			1.72815i
$848$		0			0
$849$	1.50204e6	+	1.25357e7i	0.0715177	+	0.596868i
$850$		0			0
$851$	−4.09723e7			−1.93940
$852$		0			0
$853$	−2.61531e7			−1.23070			−0.615348	−	0.788256i	$-0.710985\pi$
$853$	−2.61531e7			−1.23070			−0.615348	+	0.788256i	$0.710985\pi$
$854$		0			0
$855$	−1.31633e7	+	3.20045e6i	−0.615815	+	0.149726i
$856$		0			0
$857$			1.20270e7i			0.559380i	0.960090	+	0.279690i	$0.0902316\pi$
$857$			1.20270e7i			0.559380i	−0.960090	+	0.279690i	$0.909768\pi$
$858$		0			0
$859$			3.12884e7i			1.44677i	0.690443	+	0.723387i	$0.257416\pi$
$859$			3.12884e7i			1.44677i	−0.690443	+	0.723387i	$0.742584\pi$
$860$		0			0
$861$	5.05895e7	−	6.06172e6i	2.32569	−	0.278668i
$862$		0			0
$863$	−1.08600e7			−0.496368			−0.248184	−	0.968713i	$-0.579834\pi$
$863$	−1.08600e7			−0.496368			−0.248184	+	0.968713i	$0.579834\pi$
$864$		0			0
$865$	−2.37610e7			−1.07975
$866$		0			0
$867$	2.17165e7	−	2.60210e6i	0.981163	−	0.117565i
$868$		0			0
$869$			2.27267e6i			0.102091i
$870$		0			0
$871$			7.14063e6i			0.318927i
$872$		0			0
$873$	−3.69870e7	+	8.99279e6i	−1.64253	+	0.399355i
$874$		0			0
$875$	−3.95032e7			−1.74426
$876$		0			0
$877$	−1.30114e7			−0.571248			−0.285624	−	0.958342i	$-0.592201\pi$
$877$	−1.30114e7			−0.571248			−0.285624	+	0.958342i	$0.592201\pi$
$878$		0			0
$879$	3.22058e6	+	2.68781e7i	0.140592	+	1.17335i
$880$		0			0
$881$			4.19604e7i			1.82138i	0.413092	+	0.910689i	$0.364449\pi$
$881$			4.19604e7i			1.82138i	−0.413092	+	0.910689i	$0.635551\pi$
$882$		0			0
$883$		−	2.89203e7i		−	1.24825i	−0.781325	−	0.624124i	$-0.785456\pi$
$883$		−	2.89203e7i		−	1.24825i	0.781325	−	0.624124i	$-0.214544\pi$
$884$		0			0
$885$	3.79218e6	+	3.16485e7i	0.162753	+	1.35830i
$886$		0			0
$887$	−3.04342e7			−1.29883			−0.649415	−	0.760434i	$-0.724986\pi$
$887$	−3.04342e7			−1.29883			−0.649415	+	0.760434i	$0.724986\pi$
$888$		0			0
$889$	−5.84902e7			−2.48215
$890$		0			0
$891$	−1.93688e6	+	1.00102e6i	−0.0817349	+	0.0422422i
$892$		0			0
$893$		−	1.19786e7i		−	0.502665i
$894$		0			0
$895$		−	1.09898e6i		−	0.0458597i
$896$		0			0
$897$	4.61624e7	−	5.53125e6i	1.91561	−	0.229531i
$898$		0			0
$899$	−390420.			−0.0161114
$900$		0			0
$901$	1.47228e6			0.0604197
$902$		0			0
$903$	7.30850e7	−	8.75716e6i	2.98269	−	0.357391i
$904$		0			0
$905$		−	2.58886e6i		−	0.105072i
$906$		0			0
$907$		−	2.69233e7i		−	1.08670i	−0.839506	−	0.543350i	$-0.817156\pi$
$907$		−	2.69233e7i		−	1.08670i	0.839506	−	0.543350i	$-0.182844\pi$
$908$		0			0
$909$	1.97613e6	+	8.12776e6i	0.0793244	+	0.326258i
$910$		0			0
$911$	−3.27099e7			−1.30582			−0.652910	−	0.757435i	$-0.726452\pi$
$911$	−3.27099e7			−1.30582			−0.652910	+	0.757435i	$0.726452\pi$
$912$		0			0
$913$	−4.18335e6			−0.166091
$914$		0			0
$915$	3.96260e6	+	3.30709e7i	0.156469	+	1.30585i
$916$		0			0
$917$		−	2.13803e6i		−	0.0839636i
$918$		0			0
$919$		−	1.99356e7i		−	0.778648i	−0.921101	−	0.389324i	$-0.872709\pi$
$919$		−	1.99356e7i		−	0.778648i	0.921101	−	0.389324i	$-0.127291\pi$
$920$		0			0
$921$	1.10662e6	+	9.23558e6i	0.0429883	+	0.358769i
$922$		0			0
$923$	−4.90140e7			−1.89372
$924$		0			0
$925$	53320.6			0.00204899
$926$		0			0
$927$	1.61924e6	+	6.65989e6i	0.0618889	+	0.254547i
$928$		0			0
$929$		−	6.13766e6i		−	0.233326i	−0.993172	−	0.116663i	$-0.962780\pi$
$929$		−	6.13766e6i		−	0.233326i	0.993172	−	0.116663i	$-0.0372198\pi$
$930$		0			0
$931$			3.41805e7i			1.29242i
$932$		0			0
$933$	−4.43078e7	+	5.30903e6i	−1.66639	+	0.199669i
$934$		0			0
$935$	267170.			0.00999444
$936$		0			0
$937$	2.01876e7			0.751166			0.375583	−	0.926789i	$-0.377443\pi$
$937$	2.01876e7			0.751166			0.375583	+	0.926789i	$0.377443\pi$
$938$		0			0
$939$	−2.37494e7	+	2.84569e6i	−0.879000	+	0.105323i
$940$		0			0
$941$		−	4.23966e7i		−	1.56083i	−0.625259	−	0.780417i	$-0.715007\pi$
$941$		−	4.23966e7i		−	1.56083i	0.625259	−	0.780417i	$-0.284993\pi$
$942$		0			0
$943$		−	5.42277e7i		−	1.98583i
$944$		0			0
$945$	−4.47824e7	+	1.67417e7i	−1.63128	+	0.609847i
$946$		0			0
$947$	−4.58224e6			−0.166036			−0.0830181	−	0.996548i	$-0.526456\pi$
$947$	−4.58224e6			−0.166036			−0.0830181	+	0.996548i	$0.526456\pi$
$948$		0			0
$949$	−2.04392e6			−0.0736713
$950$		0			0
$951$	−6.18035e6	−	5.15796e7i	−0.221596	−	1.84938i
$952$		0			0
$953$		−	2.70977e7i		−	0.966498i	−0.875483	−	0.483249i	$-0.839457\pi$
$953$		−	2.70977e7i		−	0.966498i	0.875483	−	0.483249i	$-0.160543\pi$
$954$		0			0
$955$			3.19066e6i			0.113207i
$956$		0			0
$957$	63099.1	+	526609.i	0.00222712	+	0.0185870i
$958$		0			0
$959$	−3.31481e7			−1.16389
$960$		0			0
$961$	2.84496e7			0.993730
$962$		0			0
$963$	9.96012e6	−	2.42164e6i	0.346098	−	0.0841481i
$964$		0			0
$965$			1.44046e7i			0.497947i
$966$		0			0
$967$		−	2.22367e7i		−	0.764724i	−0.924013	−	0.382362i	$-0.875111\pi$
$967$		−	2.22367e7i		−	0.764724i	0.924013	−	0.382362i	$-0.124889\pi$
$968$		0			0
$969$	−2.00106e6	+	239770.i	−0.0684620	+	0.00820323i
$970$		0			0
$971$	3.88599e7			1.32267			0.661337	−	0.750089i	$-0.269989\pi$
$971$	3.88599e7			1.32267			0.661337	+	0.750089i	$0.269989\pi$
$972$		0			0
$973$	−3.40794e7			−1.15401
$974$		0			0
$975$	−60074.8	+	7198.26i	−0.00202386	+	0.000242502i
$976$		0			0
$977$			3.97266e7i			1.33151i	0.746169	+	0.665756i	$0.231891\pi$
$977$			3.97266e7i			1.33151i	−0.746169	+	0.665756i	$0.768109\pi$
$978$		0			0
$979$			4.63459e6i			0.154545i
$980$		0			0
$981$	−2.09647e7	+	5.09724e6i	−0.695532	+	0.169107i
$982$		0			0
$983$	−7.21692e6			−0.238215			−0.119107	−	0.992881i	$-0.538003\pi$
$983$	−7.21692e6			−0.238215			−0.119107	+	0.992881i	$0.538003\pi$
$984$		0			0
$985$	3.93687e7			1.29289
$986$		0			0
$987$	−5.02949e6	−	4.19748e7i	−0.164335	−	1.37150i
$988$		0			0
$989$		−	7.83410e7i		−	2.54682i
$990$		0			0
$991$		−	2.46570e7i		−	0.797545i	−0.917050	−	0.398773i	$-0.869436\pi$
$991$		−	2.46570e7i		−	0.797545i	0.917050	−	0.398773i	$-0.130564\pi$
$992$		0			0
$993$	3.74875e6	+	3.12861e7i	0.120646	+	1.00688i
$994$		0			0
$995$	−1.44993e7			−0.464291
$996$		0			0
$997$	−1.96664e7			−0.626596			−0.313298	−	0.949655i	$-0.601434\pi$
$997$	−1.96664e7			−0.626596			−0.313298	+	0.949655i	$0.601434\pi$
$998$		0			0
$999$	3.87798e7	−	1.44977e7i	1.22940	−	0.459606i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.6.c.b.383.19	yes	20
3.2	odd	2		384.6.c.c.383.1	yes	20
4.3	odd	2		384.6.c.c.383.2	yes	20
8.3	odd	2		384.6.c.a.383.19	✓	20
8.5	even	2		384.6.c.d.383.2	yes	20
12.11	even	2	inner	384.6.c.b.383.20	yes	20
24.5	odd	2		384.6.c.a.383.20	yes	20
24.11	even	2		384.6.c.d.383.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.6.c.a.383.19	✓	20	8.3	odd	2
384.6.c.a.383.20	yes	20	24.5	odd	2
384.6.c.b.383.19	yes	20	1.1	even	1	trivial
384.6.c.b.383.20	yes	20	12.11	even	2	inner
384.6.c.c.383.1	yes	20	3.2	odd	2
384.6.c.c.383.2	yes	20	4.3	odd	2
384.6.c.d.383.1	yes	20	24.11	even	2
384.6.c.d.383.2	yes	20	8.5	even	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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	384.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(15.4777 - 1.85457i) q^{3} -55.8580i q^{5} -225.953i q^{7} +(236.121 - 57.4091i) q^{9} +O(q^{10})\)	\(q+(15.4777 - 1.85457i) q^{3} -55.8580i q^{5} -225.953i q^{7} +(236.121 - 57.4091i) q^{9} -36.9229 q^{11} -795.597 q^{13} +(-103.593 - 864.557i) q^{15} -129.541i q^{17} -998.033i q^{19} +(-419.046 - 3497.25i) q^{21} -3748.76 q^{23} +4.87856 q^{25} +(3548.15 - 1326.47i) q^{27} -921.479i q^{29} -423.688i q^{31} +(-571.482 + 68.4759i) q^{33} -12621.3 q^{35} +10929.6 q^{37} +(-12314.0 + 1475.49i) q^{39} +14465.5i q^{41} +20897.9i q^{43} +(-3206.76 - 13189.3i) q^{45} +12002.2 q^{47} -34247.9 q^{49} +(-240.242 - 2005.00i) q^{51} +11365.4i q^{53} +2062.44i q^{55} +(-1850.92 - 15447.3i) q^{57} -36606.6 q^{59} -38251.8 q^{61} +(-12971.8 - 53352.4i) q^{63} +44440.5i q^{65} -8975.18i q^{67} +(-58022.3 + 6952.33i) q^{69} +61606.6 q^{71} +2569.04 q^{73} +(75.5091 - 9.04762i) q^{75} +8342.84i q^{77} -61551.9i q^{79} +(52457.4 - 27111.0i) q^{81} +113300. q^{83} -7235.89 q^{85} +(-1708.95 - 14262.4i) q^{87} -125521. i q^{89} +179768. i q^{91} +(-785.759 - 6557.74i) q^{93} -55748.2 q^{95} -156644. q^{97} +(-8718.27 + 2119.71i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{3}+O(q^{10}) \) 20 * q - 2 * q^3	\( 20 q - 2 q^{3} - 948 q^{11} + 852 q^{15} + 1640 q^{21} + 328 q^{23} - 12500 q^{25} - 2030 q^{27} + 2836 q^{33} + 7184 q^{35} + 15056 q^{37} - 12980 q^{39} + 11800 q^{45} + 36640 q^{47} - 33388 q^{49} - 1936 q^{51} + 15404 q^{57} - 62908 q^{59} + 73264 q^{61} + 23608 q^{63} - 84024 q^{69} + 34888 q^{71} + 52568 q^{73} - 115698 q^{75} + 55444 q^{81} + 225172 q^{83} - 30112 q^{85} - 225700 q^{87} - 148016 q^{93} + 418616 q^{95} + 7600 q^{97} - 378260 q^{99}+O(q^{100}) \) 20 * q - 2 * q^3 - 948 * q^11 + 852 * q^15 + 1640 * q^21 + 328 * q^23 - 12500 * q^25 - 2030 * q^27 + 2836 * q^33 + 7184 * q^35 + 15056 * q^37 - 12980 * q^39 + 11800 * q^45 + 36640 * q^47 - 33388 * q^49 - 1936 * q^51 + 15404 * q^57 - 62908 * q^59 + 73264 * q^61 + 23608 * q^63 - 84024 * q^69 + 34888 * q^71 + 52568 * q^73 - 115698 * q^75 + 55444 * q^81 + 225172 * q^83 - 30112 * q^85 - 225700 * q^87 - 148016 * q^93 + 418616 * q^95 + 7600 * q^97 - 378260 * q^99

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