LMFDB - Embedded newform 432.6.i.b.145.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,6,Mod(145,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("432.145");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	432.i (of order $3$, degree $2$, 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:	$69.2858101592$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.47347183152.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 118x^{4} - 231x^{3} + 3700x^{2} - 3585x + 32331 $ x^6 - 3x^5 + 118x^4 - 231x^3 + 3700x^2 - 3585*x + 32331
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{9} $
Twist minimal:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			145.3
Root			$0.500000 + 4.03013i$ of defining polynomial
Character	$\chi$	$=$	432.145
Dual form			432.6.i.b.289.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(39.2420 - 67.9691i) q^{5} +(110.566 + 191.505i) q^{7} +O(q^{10})$	$q+(39.2420 - 67.9691i) q^{5} +(110.566 + 191.505i) q^{7} +(-115.144 - 199.436i) q^{11} +(385.793 - 668.213i) q^{13} +769.880 q^{17} +383.367 q^{19} +(-193.178 + 334.594i) q^{23} +(-1517.37 - 2628.15i) q^{25} +(-394.883 - 683.958i) q^{29} +(1609.97 - 2788.54i) q^{31} +17355.2 q^{35} +2465.33 q^{37} +(-4621.73 + 8005.07i) q^{41} +(5315.76 + 9207.16i) q^{43} +(-976.032 - 1690.54i) q^{47} +(-16046.0 + 27792.4i) q^{49} +32589.2 q^{53} -18074.0 q^{55} +(11916.1 - 20639.2i) q^{59} +(-18804.4 - 32570.2i) q^{61} +(-30278.5 - 52444.0i) q^{65} +(-11525.6 + 19962.9i) q^{67} -66050.4 q^{71} +65130.0 q^{73} +(25462.0 - 44101.5i) q^{77} +(-35433.7 - 61373.0i) q^{79} +(-27643.5 - 47880.0i) q^{83} +(30211.6 - 52328.0i) q^{85} -10598.6 q^{89} +170622. q^{91} +(15044.1 - 26057.1i) q^{95} +(41409.9 + 71724.1i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 54 q^{5} + 132 q^{7}+O(q^{10}) $ 6 * q + 54 * q^5 + 132 * q^7	$ 6 q + 54 q^{5} + 132 q^{7} - 315 q^{11} - 744 q^{13} - 2898 q^{17} - 2262 q^{19} - 3168 q^{23} - 2883 q^{25} + 5148 q^{29} + 8610 q^{31} + 2700 q^{35} + 39936 q^{37} - 5049 q^{41} + 31389 q^{43} + 12924 q^{47} - 52857 q^{49} + 96048 q^{53} - 126252 q^{55} + 62955 q^{59} - 75966 q^{61} - 108702 q^{65} + 32991 q^{67} - 129672 q^{71} - 8466 q^{73} - 88740 q^{77} - 89202 q^{79} + 32634 q^{83} + 71388 q^{85} - 66132 q^{89} + 301836 q^{91} - 82944 q^{95} + 46245 q^{97}+O(q^{100}) $ 6 * q + 54 * q^5 + 132 * q^7 - 315 * q^11 - 744 * q^13 - 2898 * q^17 - 2262 * q^19 - 3168 * q^23 - 2883 * q^25 + 5148 * q^29 + 8610 * q^31 + 2700 * q^35 + 39936 * q^37 - 5049 * q^41 + 31389 * q^43 + 12924 * q^47 - 52857 * q^49 + 96048 * q^53 - 126252 * q^55 + 62955 * q^59 - 75966 * q^61 - 108702 * q^65 + 32991 * q^67 - 129672 * q^71 - 8466 * q^73 - 88740 * q^77 - 89202 * q^79 + 32634 * q^83 + 71388 * q^85 - 66132 * q^89 + 301836 * q^91 - 82944 * q^95 + 46245 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$		0			0
$3$		0			0
$4$		0			0
$5$	39.2420	−	67.9691i	0.701982	−	1.21587i	−0.265788	−	0.964032i	$-0.585632\pi$
$5$	39.2420	−	67.9691i	0.701982	−	1.21587i	0.967770	−	0.251837i	$-0.0810346\pi$
$6$		0			0
$7$	110.566	+	191.505i	0.852854	+	1.47719i	0.878622	+	0.477518i	$0.158464\pi$
$7$	110.566	+	191.505i	0.852854	+	1.47719i	−0.0257678	+	0.999668i	$0.508203\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−115.144	−	199.436i	−0.286920	−	0.496960i	0.686153	−	0.727457i	$-0.259298\pi$
$11$	−115.144	−	199.436i	−0.286920	−	0.496960i	−0.973073	+	0.230497i	$0.925965\pi$
$12$		0			0
$13$	385.793	−	668.213i	0.633134	−	1.09662i	−0.353773	−	0.935331i	$-0.615101\pi$
$13$	385.793	−	668.213i	0.633134	−	1.09662i	0.986907	−	0.161289i	$-0.0515652\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	769.880			0.646101			0.323051	−	0.946382i	$-0.395292\pi$
$17$	769.880			0.646101			0.323051	+	0.946382i	$0.395292\pi$
$18$		0			0
$19$	383.367			0.243630			0.121815	−	0.992553i	$-0.461129\pi$
$19$	383.367			0.243630			0.121815	+	0.992553i	$0.461129\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−193.178	+	334.594i	−0.0761444	+	0.131886i	−0.901583	−	0.432605i	$-0.857594\pi$
$23$	−193.178	+	334.594i	−0.0761444	+	0.131886i	0.825439	+	0.564491i	$0.190928\pi$
$24$		0			0
$25$	−1517.37	−	2628.15i	−0.485557	−	0.841009i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−394.883	−	683.958i	−0.0871914	−	0.151020i	0.819131	−	0.573606i	$-0.194456\pi$
$29$	−394.883	−	683.958i	−0.0871914	−	0.151020i	−0.906323	+	0.422586i	$0.861123\pi$
$30$		0			0
$31$	1609.97	−	2788.54i	0.300893	−	0.521163i	−0.675445	−	0.737410i	$-0.736048\pi$
$31$	1609.97	−	2788.54i	0.300893	−	0.521163i	0.976339	+	0.216247i	$0.0693818\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	17355.2			2.39475
$36$		0			0
$37$	2465.33			0.296054			0.148027	−	0.988983i	$-0.452708\pi$
$37$	2465.33			0.296054			0.148027	+	0.988983i	$0.452708\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−4621.73	+	8005.07i	−0.429383	+	0.743713i	−0.996819	−	0.0797047i	$-0.974602\pi$
$41$	−4621.73	+	8005.07i	−0.429383	+	0.743713i	0.567436	+	0.823418i	$0.307936\pi$
$42$		0			0
$43$	5315.76	+	9207.16i	0.438424	+	0.759372i	0.997568	−	0.0696983i	$-0.0222037\pi$
$43$	5315.76	+	9207.16i	0.438424	+	0.759372i	−0.559145	+	0.829070i	$0.688870\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−976.032	−	1690.54i	−0.0644495	−	0.111630i	0.832000	−	0.554775i	$-0.187196\pi$
$47$	−976.032	−	1690.54i	−0.0644495	−	0.111630i	−0.896450	+	0.443146i	$0.853862\pi$
$48$		0			0
$49$	−16046.0	+	27792.4i	−0.954720	+	1.65362i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	32589.2			1.59362			0.796809	−	0.604231i	$-0.206520\pi$
$53$	32589.2			1.59362			0.796809	+	0.604231i	$0.206520\pi$
$54$		0			0
$55$	−18074.0			−0.805651
$56$		0			0
$57$		0			0
$58$		0			0
$59$	11916.1	−	20639.2i	0.445659	−	0.771903i	−0.552439	−	0.833553i	$-0.686303\pi$
$59$	11916.1	−	20639.2i	0.445659	−	0.771903i	0.998098	+	0.0616498i	$0.0196362\pi$
$60$		0			0
$61$	−18804.4	−	32570.2i	−0.647046	−	1.12072i	−0.983825	−	0.179133i	$-0.942671\pi$
$61$	−18804.4	−	32570.2i	−0.647046	−	1.12072i	0.336779	−	0.941584i	$-0.390663\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−30278.5	−	52444.0i	−0.888897	−	1.53962i
$66$		0			0
$67$	−11525.6	+	19962.9i	−0.313672	+	0.543295i	−0.979154	−	0.203118i	$-0.934892\pi$
$67$	−11525.6	+	19962.9i	−0.313672	+	0.543295i	0.665483	+	0.746413i	$0.268226\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−66050.4			−1.55500			−0.777498	−	0.628885i	$-0.783511\pi$
$71$	−66050.4			−1.55500			−0.777498	+	0.628885i	$0.783511\pi$
$72$		0			0
$73$	65130.0			1.43045			0.715227	−	0.698893i	$-0.246324\pi$
$73$	65130.0			1.43045			0.715227	+	0.698893i	$0.246324\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	25462.0	−	44101.5i	0.489402	−	0.847669i
$78$		0			0
$79$	−35433.7	−	61373.0i	−0.638776	−	1.10639i	−0.985702	−	0.168500i	$-0.946108\pi$
$79$	−35433.7	−	61373.0i	−0.638776	−	1.10639i	0.346925	−	0.937893i	$-0.387226\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−27643.5	−	47880.0i	−0.440451	−	0.762884i	0.557272	−	0.830330i	$-0.311848\pi$
$83$	−27643.5	−	47880.0i	−0.440451	−	0.762884i	−0.997723	+	0.0674462i	$0.978515\pi$
$84$		0			0
$85$	30211.6	−	52328.0i	0.453551	−	0.785574i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−10598.6			−0.141831			−0.0709156	−	0.997482i	$-0.522592\pi$
$89$	−10598.6			−0.141831			−0.0709156	+	0.997482i	$0.522592\pi$
$90$		0			0
$91$	170622.			2.15988
$92$		0			0
$93$		0			0
$94$		0			0
$95$	15044.1	−	26057.1i	0.171024	−	0.296222i
$96$		0			0
$97$	41409.9	+	71724.1i	0.446864	+	0.773991i	0.998180	−	0.0603057i	$-0.0192076\pi$
$97$	41409.9	+	71724.1i	0.446864	+	0.773991i	−0.551316	+	0.834296i	$0.685874\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	10604.1	+	18366.9i	0.103436	+	0.179156i	0.913098	−	0.407740i	$-0.133683\pi$
$101$	10604.1	+	18366.9i	0.103436	+	0.179156i	−0.809662	+	0.586896i	$0.800350\pi$
$102$		0			0
$103$	65877.4	−	114103.i	0.611848	−	1.05975i	−0.379081	−	0.925363i	$-0.623760\pi$
$103$	65877.4	−	114103.i	0.611848	−	1.05975i	0.990929	−	0.134388i	$-0.0429068\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	54796.5			0.462693			0.231347	−	0.972871i	$-0.425687\pi$
$107$	54796.5			0.462693			0.231347	+	0.972871i	$0.425687\pi$
$108$		0			0
$109$	160570.			1.29448			0.647242	−	0.762284i	$-0.275922\pi$
$109$	160570.			1.29448			0.647242	+	0.762284i	$0.275922\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−33217.8	+	57534.9i	−0.244723	+	0.423873i	−0.962054	−	0.272860i	$-0.912030\pi$
$113$	−33217.8	+	57534.9i	−0.244723	+	0.423873i	0.717331	+	0.696733i	$0.245364\pi$
$114$		0			0
$115$	15161.4	+	26260.3i	0.106904	+	0.185163i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	85122.2	+	147436.i	0.551030	+	0.954412i
$120$		0			0
$121$	54009.1	−	93546.4i	0.335354	−	0.580850i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	7084.72			0.0405553
$126$		0			0
$127$	299603.			1.64830			0.824152	−	0.566368i	$-0.191652\pi$
$127$	299603.			1.64830			0.824152	+	0.566368i	$0.191652\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	166224.	−	287909.i	0.846283	−	1.46581i	−0.0382189	−	0.999269i	$-0.512168\pi$
$131$	166224.	−	287909.i	0.846283	−	1.46581i	0.884502	−	0.466536i	$-0.154498\pi$
$132$		0			0
$133$	42387.1	+	73416.7i	0.207781	+	0.359887i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−93601.3	−	162122.i	−0.426070	−	0.737974i	0.570450	−	0.821332i	$-0.306769\pi$
$137$	−93601.3	−	162122.i	−0.426070	−	0.737974i	−0.996520	+	0.0833580i	$0.973436\pi$
$138$		0			0
$139$	−105285.	+	182358.i	−0.462198	+	0.800550i	−0.999070	−	0.0431133i	$-0.986272\pi$
$139$	−105285.	+	182358.i	−0.462198	+	0.800550i	0.536872	+	0.843664i	$0.319606\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−177687.			−0.726635
$144$		0			0
$145$	−61984.0			−0.244827
$146$		0			0
$147$		0			0
$148$		0			0
$149$	242872.	−	420667.i	0.896215	−	1.55229i	0.0639212	−	0.997955i	$-0.479639\pi$
$149$	242872.	−	420667.i	0.896215	−	1.55229i	0.832294	−	0.554335i	$-0.187027\pi$
$150$		0			0
$151$	105105.	+	182047.i	0.375130	+	0.649744i	0.990346	−	0.138614i	$-0.0442648\pi$
$151$	105105.	+	182047.i	0.375130	+	0.649744i	−0.615217	+	0.788358i	$0.710931\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−126357.	−	218856.i	−0.422443	−	0.731694i
$156$		0			0
$157$	196123.	−	339696.i	0.635009	−	1.09987i	−0.351504	−	0.936186i	$-0.614330\pi$
$157$	196123.	−	339696.i	0.635009	−	1.09987i	0.986513	−	0.163682i	$-0.0523371\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−85435.3			−0.259760
$162$		0			0
$163$	−190208.			−0.560738			−0.280369	−	0.959892i	$-0.590457\pi$
$163$	−190208.			−0.560738			−0.280369	+	0.959892i	$0.590457\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	200619.	−	347483.i	0.556650	−	0.964145i	−0.441123	−	0.897446i	$-0.645420\pi$
$167$	200619.	−	347483.i	0.556650	−	0.964145i	0.997773	−	0.0666991i	$-0.0212467\pi$
$168$		0			0
$169$	−112026.	−	194034.i	−0.301718	−	0.522590i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	47391.9	+	82085.1i	0.120389	+	0.208521i	0.919921	−	0.392103i	$-0.128252\pi$
$173$	47391.9	+	82085.1i	0.120389	+	0.208521i	−0.799532	+	0.600624i	$0.794919\pi$
$174$		0			0
$175$	335537.	−	581166.i	0.828218	−	1.43452i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−218816.			−0.510442			−0.255221	−	0.966883i	$-0.582148\pi$
$179$	−218816.			−0.510442			−0.255221	+	0.966883i	$0.582148\pi$
$180$		0			0
$181$	−344513.			−0.781645			−0.390823	−	0.920466i	$-0.627809\pi$
$181$	−344513.			−0.781645			−0.390823	+	0.920466i	$0.627809\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	96744.5	−	167566.i	0.207825	−	0.359963i
$186$		0			0
$187$	−88647.3	−	153542.i	−0.185379	−	0.321087i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	67476.5	+	116873.i	0.133835	+	0.231809i	0.925152	−	0.379597i	$-0.123938\pi$
$191$	67476.5	+	116873.i	0.133835	+	0.231809i	−0.791317	+	0.611406i	$0.790604\pi$
$192$		0			0
$193$	−113675.	+	196892.i	−0.219671	+	0.380482i	−0.954707	−	0.297546i	$-0.903832\pi$
$193$	−113675.	+	196892.i	−0.219671	+	0.380482i	0.735036	+	0.678028i	$0.237165\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−430437.			−0.790213			−0.395107	−	0.918635i	$-0.629292\pi$
$197$	−430437.			−0.790213			−0.395107	+	0.918635i	$0.629292\pi$
$198$		0			0
$199$	−719704.			−1.28831			−0.644156	−	0.764894i	$-0.722791\pi$
$199$	−719704.			−1.28831			−0.644156	+	0.764894i	$0.722791\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	87321.0	−	151244.i	0.148723	−	0.257596i
$204$		0			0
$205$	362732.	+	628269.i	0.602838	+	1.04415i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−44142.5	−	76457.1i	−0.0699023	−	0.121074i
$210$		0			0
$211$	30700.0	−	53174.0i	0.0474715	−	0.0822230i	−0.841313	−	0.540548i	$-0.818217\pi$
$211$	30700.0	−	53174.0i	0.0474715	−	0.0822230i	0.888785	+	0.458325i	$0.151550\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	834403.			1.23106
$216$		0			0
$217$	712027.			1.02647
$218$		0			0
$219$		0			0
$220$		0			0
$221$	297014.	−	514443.i	0.409069	−	0.708528i
$222$		0			0
$223$	329013.	+	569868.i	0.443049	+	0.767383i	0.997914	−	0.0645574i	$-0.0205636\pi$
$223$	329013.	+	569868.i	0.443049	+	0.767383i	−0.554865	+	0.831940i	$0.687230\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	5067.16	+	8776.57i	0.00652679	+	0.0113047i	0.869270	−	0.494337i	$-0.164589\pi$
$227$	5067.16	+	8776.57i	0.00652679	+	0.0113047i	−0.862744	+	0.505642i	$0.831256\pi$
$228$		0			0
$229$	−611518.	+	1.05918e6i	−0.770584	+	1.33469i	0.166659	+	0.986015i	$0.446702\pi$
$229$	−611518.	+	1.05918e6i	−0.770584	+	1.33469i	−0.937243	+	0.348677i	$0.886631\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.16513e6			1.40599			0.702996	−	0.711194i	$-0.251845\pi$
$233$	1.16513e6			1.40599			0.702996	+	0.711194i	$0.251845\pi$
$234$		0			0
$235$	−153206.			−0.180969
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−659760.	+	1.14274e6i	−0.747122	+	1.29405i	0.202075	+	0.979370i	$0.435231\pi$
$239$	−659760.	+	1.14274e6i	−0.747122	+	1.29405i	−0.949197	+	0.314683i	$0.898102\pi$
$240$		0			0
$241$	−265905.	−	460560.i	−0.294906	−	0.510792i	0.680057	−	0.733159i	$-0.261955\pi$
$241$	−265905.	−	460560.i	−0.294906	−	0.510792i	−0.974963	+	0.222367i	$0.928622\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	1.25935e6	+	2.18126e6i	1.34039	+	2.32163i
$246$		0			0
$247$	147900.	−	256170.i	0.154250	−	0.267169i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	475.750			0.000476644			0.000238322	−	1.00000i	$-0.499924\pi$
$251$	475.750			0.000476644			0.000238322		1.00000i	$0.499924\pi$
$252$		0			0
$253$	88973.4			0.0873894
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−13603.3	+	23561.6i	−0.0128473	+	0.0222522i	−0.872378	−	0.488833i	$-0.837423\pi$
$257$	−13603.3	+	23561.6i	−0.0128473	+	0.0222522i	0.859530	+	0.511085i	$0.170756\pi$
$258$		0			0
$259$	272581.	+	472124.i	0.252491	+	0.437327i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	69991.2	+	121228.i	0.0623956	+	0.108072i	0.895536	−	0.444990i	$-0.146793\pi$
$263$	69991.2	+	121228.i	0.0623956	+	0.108072i	−0.833140	+	0.553062i	$0.813459\pi$
$264$		0			0
$265$	1.27887e6	−	2.21506e6i	1.11869	−	1.93763i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−1.63842e6			−1.38053			−0.690263	−	0.723558i	$-0.742505\pi$
$269$	−1.63842e6			−1.38053			−0.690263	+	0.723558i	$0.742505\pi$
$270$		0			0
$271$	280791.			0.232252			0.116126	−	0.993234i	$-0.462952\pi$
$271$	280791.			0.232252			0.116126	+	0.993234i	$0.462952\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−349432.	+	605234.i	−0.278632	+	0.482605i
$276$		0			0
$277$	−346404.	−	599989.i	−0.271259	−	0.469834i	0.697926	−	0.716170i	$-0.254107\pi$
$277$	−346404.	−	599989.i	−0.271259	−	0.469834i	−0.969184	+	0.246336i	$0.920773\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−1.05464e6	−	1.82670e6i	−0.796782	−	1.38007i	−0.921701	−	0.387901i	$-0.873200\pi$
$281$	−1.05464e6	−	1.82670e6i	−0.796782	−	1.38007i	0.124919	−	0.992167i	$-0.460133\pi$
$282$		0			0
$283$	−731346.	+	1.26673e6i	−0.542821	+	0.940193i	0.455920	+	0.890021i	$0.349310\pi$
$283$	−731346.	+	1.26673e6i	−0.542821	+	0.940193i	−0.998741	+	0.0501725i	$0.984023\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−2.04402e6			−1.46480
$288$		0			0
$289$	−827142.			−0.582553
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−1.27745e6	+	2.21261e6i	−0.869313	+	1.50569i	−0.00661216	+	0.999978i	$0.502105\pi$
$293$	−1.27745e6	+	2.21261e6i	−0.869313	+	1.50569i	−0.862700	+	0.505715i	$0.831229\pi$
$294$		0			0
$295$	−935219.	−	1.61985e6i	−0.625688	−	1.08372i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	149053.	+	258168.i	0.0964192	+	0.167003i
$300$		0			0
$301$	−1.17548e6	+	2.03599e6i	−0.747822	+	1.29527i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−2.95169e6			−1.81686
$306$		0			0
$307$	2.14982e6			1.30183			0.650917	−	0.759149i	$-0.274385\pi$
$307$	2.14982e6			1.30183			0.650917	+	0.759149i	$0.274385\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	183809.	−	318367.i	0.107762	−	0.186650i	−0.807101	−	0.590413i	$-0.798965\pi$
$311$	183809.	−	318367.i	0.107762	−	0.186650i	0.914863	+	0.403763i	$0.132298\pi$
$312$		0			0
$313$	−91371.8	−	158261.i	−0.0527171	−	0.0913086i	0.838463	−	0.544959i	$-0.183455\pi$
$313$	−91371.8	−	158261.i	−0.0527171	−	0.0913086i	−0.891180	+	0.453650i	$0.850121\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	432482.	+	749081.i	0.241724	+	0.418679i	0.961206	−	0.275833i	$-0.0889538\pi$
$317$	432482.	+	749081.i	0.241724	+	0.418679i	−0.719481	+	0.694512i	$0.755620\pi$
$318$		0			0
$319$	−90937.2	+	157508.i	−0.0500339	+	0.0866613i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	295146.			0.157409
$324$		0			0
$325$	−2.34155e6			−1.22969
$326$		0			0
$327$		0			0
$328$		0			0
$329$	215831.	−	373830.i	0.109932	−	0.190408i
$330$		0			0
$331$	−1.49880e6	−	2.59600e6i	−0.751923	−	1.30237i	−0.946890	−	0.321559i	$-0.895793\pi$
$331$	−1.49880e6	−	2.59600e6i	−0.751923	−	1.30237i	0.194967	−	0.980810i	$-0.437540\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	904572.	+	1.56676e6i	0.440384	+	0.762767i
$336$		0			0
$337$	−359139.	+	622047.i	−0.172261	+	0.298365i	−0.939210	−	0.343343i	$-0.888441\pi$
$337$	−359139.	+	622047.i	−0.172261	+	0.298365i	0.766949	+	0.641708i	$0.221774\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−741514.			−0.345329
$342$		0			0
$343$	−3.37998e6			−1.55124
$344$		0			0
$345$		0			0
$346$		0			0
$347$	1.87463e6	−	3.24695e6i	0.835779	−	1.44761i	−0.0576157	−	0.998339i	$-0.518350\pi$
$347$	1.87463e6	−	3.24695e6i	0.835779	−	1.44761i	0.893395	−	0.449273i	$-0.148317\pi$
$348$		0			0
$349$	1.16679e6	+	2.02094e6i	0.512778	+	0.888157i	0.999890	+	0.0148181i	$0.00471692\pi$
$349$	1.16679e6	+	2.02094e6i	0.512778	+	0.888157i	−0.487112	+	0.873339i	$0.661950\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	2.17285e6	+	3.76348e6i	0.928094	+	1.60751i	0.786508	+	0.617580i	$0.211887\pi$
$353$	2.17285e6	+	3.76348e6i	0.928094	+	1.60751i	0.141586	+	0.989926i	$0.454780\pi$
$354$		0			0
$355$	−2.59195e6	+	4.48938e6i	−1.09158	+	1.89067i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−2.71281e6			−1.11092			−0.555461	−	0.831542i	$-0.687458\pi$
$359$	−2.71281e6			−1.11092			−0.555461	+	0.831542i	$0.687458\pi$
$360$		0			0
$361$	−2.32913e6			−0.940645
$362$		0			0
$363$		0			0
$364$		0			0
$365$	2.55583e6	−	4.42682e6i	1.00415	−	1.73924i
$366$		0			0
$367$	1.95814e6	+	3.39160e6i	0.758889	+	1.31443i	0.943417	+	0.331608i	$0.107591\pi$
$367$	1.95814e6	+	3.39160e6i	0.758889	+	1.31443i	−0.184528	+	0.982827i	$0.559076\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	3.60324e6	+	6.24100e6i	1.35912	+	2.35407i
$372$		0			0
$373$	−890322.	+	1.54208e6i	−0.331341	+	0.573899i	−0.982775	−	0.184806i	$-0.940834\pi$
$373$	−890322.	+	1.54208e6i	−0.331341	+	0.573899i	0.651434	+	0.758705i	$0.274168\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−609373.			−0.220815
$378$		0			0
$379$	631740.			0.225912			0.112956	−	0.993600i	$-0.463968\pi$
$379$	631740.			0.225912			0.112956	+	0.993600i	$0.463968\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−66803.0	+	115706.i	−0.0232701	+	0.0403050i	−0.877426	−	0.479712i	$-0.840741\pi$
$383$	−66803.0	+	115706.i	−0.0232701	+	0.0403050i	0.854156	+	0.520017i	$0.174074\pi$
$384$		0			0
$385$	−1.99836e6	−	3.46126e6i	−0.687102	−	1.19010i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	2.79735e6	+	4.84515e6i	0.937286	+	1.62343i	0.770505	+	0.637434i	$0.220004\pi$
$389$	2.79735e6	+	4.84515e6i	0.937286	+	1.62343i	0.166781	+	0.985994i	$0.446663\pi$
$390$		0			0
$391$	−148724.	+	257597.i	−0.0491970	+	0.0852117i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−5.56195e6			−1.79364
$396$		0			0
$397$	4.19051e6			1.33441			0.667206	−	0.744873i	$-0.267490\pi$
$397$	4.19051e6			1.33441			0.667206	+	0.744873i	$0.267490\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−229109.	+	396829.i	−0.0711511	+	0.123237i	−0.899406	−	0.437114i	$-0.856001\pi$
$401$	−229109.	+	396829.i	−0.0711511	+	0.123237i	0.828255	+	0.560351i	$0.189334\pi$
$402$		0			0
$403$	−1.24223e6	−	2.15160e6i	−0.381012	−	0.659932i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−283869.	−	491675.i	−0.0849438	−	0.147127i
$408$		0			0
$409$	−8467.95	+	14666.9i	−0.00250305	+	0.00433541i	−0.867274	−	0.497831i	$-0.834130\pi$
$409$	−8467.95	+	14666.9i	−0.00250305	+	0.00433541i	0.864771	+	0.502166i	$0.167463\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	5.27002e6			1.52033
$414$		0			0
$415$	−4.33914e6			−1.23676
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−2.24889e6	+	3.89520e6i	−0.625798	+	1.08391i	0.362588	+	0.931949i	$0.381893\pi$
$419$	−2.24889e6	+	3.89520e6i	−0.625798	+	1.08391i	−0.988386	+	0.151964i	$0.951440\pi$
$420$		0			0
$421$	217248.	+	376285.i	0.0597381	+	0.103469i	0.894348	−	0.447372i	$-0.147640\pi$
$421$	217248.	+	376285.i	0.0597381	+	0.103469i	−0.834610	+	0.550842i	$0.814307\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−1.16819e6	−	2.02336e6i	−0.313719	−	0.543377i
$426$		0			0
$427$	4.15824e6	−	7.20229e6i	1.10367	−	1.91162i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	5.16700e6			1.33982			0.669908	−	0.742444i	$-0.266334\pi$
$431$	5.16700e6			1.33982			0.669908	+	0.742444i	$0.266334\pi$
$432$		0			0
$433$	3.95066e6			1.01263			0.506314	−	0.862349i	$-0.331008\pi$
$433$	3.95066e6			1.01263			0.506314	+	0.862349i	$0.331008\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−74058.0	+	128272.i	−0.0185510	+	0.0321313i
$438$		0			0
$439$	−243803.	−	422279.i	−0.0603778	−	0.104577i	0.834257	−	0.551377i	$-0.185897\pi$
$439$	−243803.	−	422279.i	−0.0603778	−	0.104577i	−0.894634	+	0.446799i	$0.852564\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	4027.52	+	6975.87i	0.000975053	+	0.00168884i	0.866513	−	0.499155i	$-0.166356\pi$
$443$	4027.52	+	6975.87i	0.000975053	+	0.00168884i	−0.865537	+	0.500844i	$0.833023\pi$
$444$		0			0
$445$	−415909.	+	720375.i	−0.0995630	+	0.172448i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−6.79644e6			−1.59098			−0.795492	−	0.605964i	$-0.792788\pi$
$449$	−6.79644e6			−1.59098			−0.795492	+	0.605964i	$0.792788\pi$
$450$		0			0
$451$	2.12866e6			0.492794
$452$		0			0
$453$		0			0
$454$		0			0
$455$	6.69553e6	−	1.15970e7i	1.51620	−	2.62613i
$456$		0			0
$457$	−199059.	−	344780.i	−0.0445852	−	0.0772238i	0.842872	−	0.538115i	$-0.180863\pi$
$457$	−199059.	−	344780.i	−0.0445852	−	0.0772238i	−0.887457	+	0.460891i	$0.847530\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−620959.	−	1.07553e6i	−0.136085	−	0.235706i	0.789926	−	0.613202i	$-0.210119\pi$
$461$	−620959.	−	1.07553e6i	−0.136085	−	0.235706i	−0.926011	+	0.377495i	$0.876785\pi$
$462$		0			0
$463$	−1.21707e6	+	2.10802e6i	−0.263853	+	0.457007i	−0.967263	−	0.253778i	$-0.918327\pi$
$463$	−1.21707e6	+	2.10802e6i	−0.263853	+	0.457007i	0.703409	+	0.710785i	$0.251660\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−1.08309e6			−0.229811			−0.114906	−	0.993376i	$-0.536657\pi$
$467$	−1.08309e6			−0.229811			−0.114906	+	0.993376i	$0.536657\pi$
$468$		0			0
$469$	−5.09732e6			−1.07006
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.22416e6	−	2.12030e6i	0.251585	−	0.435758i
$474$		0			0
$475$	−581707.	−	1.00755e6i	−0.118296	−	0.204895i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	1.66906e6	+	2.89090e6i	0.332379	+	0.575698i	0.982978	−	0.183724i	$-0.0588153\pi$
$479$	1.66906e6	+	2.89090e6i	0.332379	+	0.575698i	−0.650599	+	0.759422i	$0.725482\pi$
$480$		0			0
$481$	951107.	−	1.64737e6i	0.187442	−	0.324659i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	6.50003e6			1.25476
$486$		0			0
$487$	5.17210e6			0.988198			0.494099	−	0.869406i	$-0.335498\pi$
$487$	5.17210e6			0.988198			0.494099	+	0.869406i	$0.335498\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−303947.	+	526452.i	−0.0568977	+	0.0985497i	−0.893071	−	0.449915i	$-0.851454\pi$
$491$	−303947.	+	526452.i	−0.0568977	+	0.0985497i	0.836174	+	0.548465i	$0.184788\pi$
$492$		0			0
$493$	−304013.	−	526565.i	−0.0563345	−	0.0975742i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−7.30289e6	−	1.26490e7i	−1.32618	−	2.29702i
$498$		0			0
$499$	1.75645e6	−	3.04226e6i	0.315780	−	0.546947i	−0.663823	−	0.747890i	$-0.731067\pi$
$499$	1.75645e6	−	3.04226e6i	0.315780	−	0.546947i	0.979603	+	0.200943i	$0.0644006\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−8.23500e6			−1.45125			−0.725627	−	0.688088i	$-0.758450\pi$
$503$	−8.23500e6			−1.45125			−0.725627	+	0.688088i	$0.758450\pi$
$504$		0			0
$505$	1.66451e6			0.290440
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−5.30292e6	+	9.18492e6i	−0.907236	+	1.57138i	−0.0893495	+	0.996000i	$0.528479\pi$
$509$	−5.30292e6	+	9.18492e6i	−0.907236	+	1.57138i	−0.817887	+	0.575379i	$0.804855\pi$
$510$		0			0
$511$	7.20113e6	+	1.24727e7i	1.21997	+	2.11305i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−5.17032e6	−	8.95525e6i	−0.859012	−	1.48785i
$516$		0			0
$517$	−224769.	+	389312.i	−0.0369837	+	0.0640576i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−1.03709e7			−1.67388			−0.836939	−	0.547297i	$-0.815657\pi$
$521$	−1.03709e7			−1.67388			−0.836939	+	0.547297i	$0.815657\pi$
$522$		0			0
$523$	−8.86641e6			−1.41740			−0.708702	−	0.705508i	$-0.750719\pi$
$523$	−8.86641e6			−1.41740			−0.708702	+	0.705508i	$0.750719\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.23948e6	−	2.14684e6i	0.194408	−	0.336724i
$528$		0			0
$529$	3.14354e6	+	5.44476e6i	0.488404	+	0.845941i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	3.56606e6	+	6.17660e6i	0.543714	+	0.941740i
$534$		0			0
$535$	2.15032e6	−	3.72447e6i	0.324802	−	0.562574i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	7.39041e6			1.09571
$540$		0			0
$541$	−1.22530e6			−0.179990			−0.0899949	−	0.995942i	$-0.528685\pi$
$541$	−1.22530e6			−0.179990			−0.0899949	+	0.995942i	$0.528685\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	6.30107e6	−	1.09138e7i	0.908705	−	1.57392i
$546$		0			0
$547$	1.34505e6	+	2.32969e6i	0.192207	+	0.332913i	0.945981	−	0.324221i	$-0.105102\pi$
$547$	1.34505e6	+	2.32969e6i	0.192207	+	0.332913i	−0.753774	+	0.657134i	$0.771769\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−151385.	−	262207.i	−0.0212424	−	0.0367930i
$552$		0			0
$553$	7.83549e6	−	1.35715e7i	1.08957	−	1.88718i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	5.82722e6			0.795835			0.397918	−	0.917421i	$-0.369733\pi$
$557$	5.82722e6			0.795835			0.397918	+	0.917421i	$0.369733\pi$
$558$		0			0
$559$	8.20312e6			1.11032
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−4.66117e6	+	8.07338e6i	−0.619760	+	1.07346i	0.369769	+	0.929124i	$0.379437\pi$
$563$	−4.66117e6	+	8.07338e6i	−0.619760	+	1.07346i	−0.989529	+	0.144333i	$0.953896\pi$
$564$		0			0
$565$	2.60707e6	+	4.51557e6i	0.343582	+	0.595102i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	5.38674e6	+	9.33011e6i	0.697502	+	1.20811i	0.969330	+	0.245763i	$0.0790386\pi$
$569$	5.38674e6	+	9.33011e6i	0.697502	+	1.20811i	−0.271828	+	0.962346i	$0.587628\pi$
$570$		0			0
$571$	−1.66600e6	+	2.88559e6i	−0.213838	+	0.370378i	−0.952912	−	0.303246i	$-0.901930\pi$
$571$	−1.66600e6	+	2.88559e6i	−0.213838	+	0.370378i	0.739075	+	0.673623i	$0.235263\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	1.17249e6			0.147890
$576$		0			0
$577$	3.94388e6			0.493156			0.246578	−	0.969123i	$-0.420694\pi$
$577$	3.94388e6			0.493156			0.246578	+	0.969123i	$0.420694\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	6.11284e6	−	1.05877e7i	0.751281	−	1.30126i
$582$		0			0
$583$	−3.75246e6	−	6.49946e6i	−0.457241	−	0.791965i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	817286.	+	1.41558e6i	0.0978991	+	0.169566i	0.910815	−	0.412815i	$-0.135454\pi$
$587$	817286.	+	1.41558e6i	0.0978991	+	0.169566i	−0.812916	+	0.582381i	$0.802121\pi$
$588$		0			0
$589$	617208.	−	1.06904e6i	0.0733066	−	0.126971i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−9.45304e6			−1.10391			−0.551957	−	0.833873i	$-0.686119\pi$
$593$	−9.45304e6			−1.10391			−0.551957	+	0.833873i	$0.686119\pi$
$594$		0			0
$595$	1.33614e7			1.54725
$596$		0			0
$597$		0			0
$598$		0			0
$599$	1.03628e6	−	1.79489e6i	0.118008	−	0.204395i	−0.800970	−	0.598704i	$-0.795683\pi$
$599$	1.03628e6	−	1.79489e6i	0.118008	−	0.204395i	0.918978	+	0.394309i	$0.129016\pi$
$600$		0			0
$601$	−5.30513e6	−	9.18876e6i	−0.599115	−	1.03770i	−0.992952	−	0.118517i	$-0.962186\pi$
$601$	−5.30513e6	−	9.18876e6i	−0.599115	−	1.03770i	0.393838	−	0.919180i	$-0.371147\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−4.23884e6	−	7.34189e6i	−0.470824	−	0.815492i
$606$		0			0
$607$	3.67761e6	−	6.36980e6i	0.405129	−	0.701704i	−0.589207	−	0.807982i	$-0.700560\pi$
$607$	3.67761e6	−	6.36980e6i	0.405129	−	0.701704i	0.994336	+	0.106278i	$0.0338932\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−1.50618e6			−0.163221
$612$		0			0
$613$	1.09586e7			1.17789			0.588946	−	0.808173i	$-0.299543\pi$
$613$	1.09586e7			1.17789			0.588946	+	0.808173i	$0.299543\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.88984e6	−	3.27330e6i	0.199854	−	0.346157i	−0.748627	−	0.662991i	$-0.769287\pi$
$617$	1.88984e6	−	3.27330e6i	0.199854	−	0.346157i	0.948481	+	0.316835i	$0.102620\pi$
$618$		0			0
$619$	−246460.	−	426881.i	−0.0258535	−	0.0447796i	0.852809	−	0.522223i	$-0.174897\pi$
$619$	−246460.	−	426881.i	−0.0258535	−	0.0447796i	−0.878663	+	0.477443i	$0.841564\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−1.17184e6	−	2.02968e6i	−0.120961	−	0.209511i
$624$		0			0
$625$	5.01978e6	−	8.69452e6i	0.514026	−	0.890319i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	1.89801e6			0.191281
$630$		0			0
$631$	1.31134e6			0.131112			0.0655558	−	0.997849i	$-0.479118\pi$
$631$	1.31134e6			0.131112			0.0655558	+	0.997849i	$0.479118\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.17570e7	−	2.03638e7i	1.15708	−	2.00412i
$636$		0			0
$637$	1.23808e7	+	2.14442e7i	1.20893	+	2.09393i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	692306.	+	1.19911e6i	0.0665508	+	0.115269i	0.897381	−	0.441257i	$-0.145467\pi$
$641$	692306.	+	1.19911e6i	0.0665508	+	0.115269i	−0.830830	+	0.556526i	$0.812134\pi$
$642$		0			0
$643$	3.97132e6	−	6.87852e6i	0.378797	−	0.656096i	−0.612090	−	0.790788i	$-0.709671\pi$
$643$	3.97132e6	−	6.87852e6i	0.378797	−	0.656096i	0.990888	+	0.134692i	$0.0430044\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−2.30348e6			−0.216334			−0.108167	−	0.994133i	$-0.534498\pi$
$647$	−2.30348e6			−0.216334			−0.108167	+	0.994133i	$0.534498\pi$
$648$		0			0
$649$	−5.48826e6			−0.511474
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−3.96246e6	+	6.86318e6i	−0.363649	+	0.629858i	−0.988558	−	0.150839i	$-0.951802\pi$
$653$	−3.96246e6	+	6.86318e6i	−0.363649	+	0.629858i	0.624910	+	0.780697i	$0.285136\pi$
$654$		0			0
$655$	−1.30459e7	−	2.25962e7i	−1.18815	−	2.05794i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−4.75895e6	−	8.24275e6i	−0.426872	−	0.739364i	0.569721	−	0.821838i	$-0.307051\pi$
$659$	−4.75895e6	−	8.24275e6i	−0.426872	−	0.739364i	−0.996593	+	0.0824739i	$0.973718\pi$
$660$		0			0
$661$	−6.42742e6	+	1.11326e7i	−0.572181	+	0.991046i	0.424161	+	0.905587i	$0.360569\pi$
$661$	−6.42742e6	+	1.11326e7i	−0.572181	+	0.991046i	−0.996342	+	0.0854592i	$0.972764\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	6.65342e6			0.583433
$666$		0			0
$667$	305131.			0.0265565
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−4.33045e6	+	7.50055e6i	−0.371301	+	0.643112i
$672$		0			0
$673$	−3.27549e6	−	5.67332e6i	−0.278766	−	0.482836i	0.692313	−	0.721598i	$-0.256592\pi$
$673$	−3.27549e6	−	5.67332e6i	−0.278766	−	0.482836i	−0.971078	+	0.238762i	$0.923259\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	4.58192e6	+	7.93613e6i	0.384217	+	0.665483i	0.991660	−	0.128880i	$-0.0411382\pi$
$677$	4.58192e6	+	7.93613e6i	0.384217	+	0.665483i	−0.607443	+	0.794363i	$0.707805\pi$
$678$		0			0
$679$	−9.15702e6	+	1.58604e7i	−0.762219	+	1.32020i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	8.96737e6			0.735552			0.367776	−	0.929914i	$-0.380119\pi$
$683$	8.96737e6			0.735552			0.367776	+	0.929914i	$0.380119\pi$
$684$		0			0
$685$	−1.46924e7			−1.19637
$686$		0			0
$687$		0			0
$688$		0			0
$689$	1.25727e7	−	2.17765e7i	1.00897	−	1.74759i
$690$		0			0
$691$	6.85931e6	+	1.18807e7i	0.546494	+	0.946555i	0.998511	+	0.0545458i	$0.0173711\pi$
$691$	6.85931e6	+	1.18807e7i	0.546494	+	0.946555i	−0.452018	+	0.892009i	$0.649296\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	8.26315e6	+	1.43122e7i	0.648909	+	1.12394i
$696$		0			0
$697$	−3.55818e6	+	6.16294e6i	−0.277425	+	0.480514i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−3.42100e6			−0.262941			−0.131470	−	0.991320i	$-0.541970\pi$
$701$	−3.42100e6			−0.262941			−0.131470	+	0.991320i	$0.541970\pi$
$702$		0			0
$703$	945126.			0.0721276
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−2.34490e6	+	4.06149e6i	−0.176431	+	0.305588i
$708$		0			0
$709$	−6.61125e6	−	1.14510e7i	−0.493933	−	0.855516i	0.506043	−	0.862508i	$-0.331108\pi$
$709$	−6.61125e6	−	1.14510e7i	−0.493933	−	0.855516i	−0.999976	+	0.00699191i	$0.997774\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	622020.	+	1.07737e6i	0.0458227	+	0.0793672i
$714$		0			0
$715$	−6.97281e6	+	1.20773e7i	−0.510085	+	0.883493i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−6.17969e6			−0.445804			−0.222902	−	0.974841i	$-0.571553\pi$
$719$	−6.17969e6			−0.445804			−0.222902	+	0.974841i	$0.571553\pi$
$720$		0			0
$721$	2.91351e7			2.08727
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−1.19836e6	+	2.07563e6i	−0.0846728	+	0.146658i
$726$		0			0
$727$	−4.83384e6	−	8.37245e6i	−0.339200	−	0.587512i	0.645082	−	0.764113i	$-0.276823\pi$
$727$	−4.83384e6	−	8.37245e6i	−0.339200	−	0.587512i	−0.984282	+	0.176601i	$0.943490\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	4.09249e6	+	7.08841e6i	0.283266	+	0.490631i
$732$		0			0
$733$	−1.13678e7	+	1.96895e7i	−0.781475	+	1.35355i	0.149608	+	0.988745i	$0.452199\pi$
$733$	−1.13678e7	+	1.96895e7i	−0.781475	+	1.35355i	−0.931082	+	0.364809i	$0.881134\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	5.30842e6			0.359995
$738$		0			0
$739$	−2.13860e7			−1.44052			−0.720260	−	0.693704i	$-0.755978\pi$
$739$	−2.13860e7			−1.44052			−0.720260	+	0.693704i	$0.755978\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−4.30567e6	+	7.45765e6i	−0.286134	+	0.495598i	−0.972884	−	0.231296i	$-0.925704\pi$
$743$	−4.30567e6	+	7.45765e6i	−0.286134	+	0.495598i	0.686750	+	0.726894i	$0.259037\pi$
$744$		0			0
$745$	−1.90616e7	−	3.30156e7i	−1.25825	−	2.17936i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	6.05860e6	+	1.04938e7i	0.394610	+	0.683484i
$750$		0			0
$751$	−3.62736e6	+	6.28277e6i	−0.234688	+	0.406491i	−0.959182	−	0.282790i	$-0.908740\pi$
$751$	−3.62736e6	+	6.28277e6i	−0.234688	+	0.406491i	0.724494	+	0.689281i	$0.242073\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	1.64981e7			1.05334
$756$		0			0
$757$	−3.04305e6			−0.193005			−0.0965027	−	0.995333i	$-0.530766\pi$
$757$	−3.04305e6			−0.193005			−0.0965027	+	0.995333i	$0.530766\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−1.33530e7	+	2.31282e7i	−0.835832	+	1.44770i	0.0575199	+	0.998344i	$0.481681\pi$
$761$	−1.33530e7	+	2.31282e7i	−0.835832	+	1.44770i	−0.893352	+	0.449359i	$0.851653\pi$
$762$		0			0
$763$	1.77535e7	+	3.07499e7i	1.10401	+	1.91220i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−9.19425e6	−	1.59249e7i	−0.564323	−	0.977437i
$768$		0			0
$769$	−2.45064e6	+	4.24463e6i	−0.149439	+	0.258836i	−0.931020	−	0.364968i	$-0.881080\pi$
$769$	−2.45064e6	+	4.24463e6i	−0.149439	+	0.258836i	0.781581	+	0.623803i	$0.214413\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−5.22612e6			−0.314579			−0.157290	−	0.987552i	$-0.550276\pi$
$773$	−5.22612e6			−0.314579			−0.157290	+	0.987552i	$0.550276\pi$
$774$		0			0
$775$	−9.77163e6			−0.584404
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1.77182e6	+	3.06888e6i	−0.104610	+	0.181191i
$780$		0			0
$781$	7.60532e6	+	1.31728e7i	0.446160	+	0.772771i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−1.53925e7	−	2.66607e7i	−0.891530	−	1.54418i
$786$		0			0
$787$	−272112.	+	471312.i	−0.0156607	+	0.0271251i	−0.873750	−	0.486376i	$-0.838318\pi$
$787$	−272112.	+	471312.i	−0.0156607	+	0.0271251i	0.858089	+	0.513501i	$0.171652\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−1.46910e7			−0.834852
$792$		0			0
$793$	−2.90184e7			−1.63867
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−8.60486e6	+	1.49041e7i	−0.479842	+	0.831110i	−0.999733	−	0.0231224i	$-0.992639\pi$
$797$	−8.60486e6	+	1.49041e7i	−0.479842	+	0.831110i	0.519891	+	0.854233i	$0.325973\pi$
$798$		0			0
$799$	−751427.	−	1.30151e6i	−0.0416409	−	0.0721241i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−7.49935e6	−	1.29892e7i	−0.410426	−	0.710878i
$804$		0			0
$805$	−3.35265e6	+	5.80696e6i	−0.182347	+	0.315834i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	9.72387e6			0.522357			0.261179	−	0.965290i	$-0.415889\pi$
$809$	9.72387e6			0.522357			0.261179	+	0.965290i	$0.415889\pi$
$810$		0			0
$811$	−1.04900e6			−0.0560045			−0.0280023	−	0.999608i	$-0.508915\pi$
$811$	−1.04900e6			−0.0560045			−0.0280023	+	0.999608i	$0.508915\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−7.46414e6	+	1.29283e7i	−0.393628	+	0.681784i
$816$		0			0
$817$	2.03788e6	+	3.52972e6i	0.106813	+	0.185006i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−2.86412e6	−	4.96080e6i	−0.148297	−	0.256858i	0.782301	−	0.622901i	$-0.214046\pi$
$821$	−2.86412e6	−	4.96080e6i	−0.148297	−	0.256858i	−0.930598	+	0.366042i	$0.880713\pi$
$822$		0			0
$823$	1.60427e7	−	2.77868e7i	0.825617	−	1.43001i	−0.0758307	−	0.997121i	$-0.524161\pi$
$823$	1.60427e7	−	2.77868e7i	0.825617	−	1.43001i	0.901447	−	0.432889i	$-0.142506\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−5.90474e6			−0.300218			−0.150109	−	0.988669i	$-0.547963\pi$
$827$	−5.90474e6			−0.300218			−0.150109	+	0.988669i	$0.547963\pi$
$828$		0			0
$829$	−1.24236e6			−0.0627859			−0.0313929	−	0.999507i	$-0.509994\pi$
$829$	−1.24236e6			−0.0627859			−0.0313929	+	0.999507i	$0.509994\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−1.23535e7	+	2.13968e7i	−0.616846	+	1.06841i
$834$		0			0
$835$	−1.57454e7	−	2.72718e7i	−0.781516	−	1.35363i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	9.84453e6	+	1.70512e7i	0.482825	+	0.836278i	0.999806	−	0.0197194i	$-0.00627728\pi$
$839$	9.84453e6	+	1.70512e7i	0.482825	+	0.836278i	−0.516980	+	0.855997i	$0.672944\pi$
$840$		0			0
$841$	9.94371e6	−	1.72230e7i	0.484795	−	0.839690i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−1.75844e7			−0.847201
$846$		0			0
$847$	2.38862e7			1.14403
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−476247.	+	824885.i	−0.0225428	+	0.0390454i
$852$		0			0
$853$	−1.43299e7	−	2.48201e7i	−0.674327	−	1.16797i	−0.976665	−	0.214767i	$-0.931101\pi$
$853$	−1.43299e7	−	2.48201e7i	−0.674327	−	1.16797i	0.302339	−	0.953201i	$-0.402233\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	3.69269e6	+	6.39594e6i	0.171748	+	0.297476i	0.939031	−	0.343832i	$-0.111725\pi$
$857$	3.69269e6	+	6.39594e6i	0.171748	+	0.297476i	−0.767283	+	0.641308i	$0.778392\pi$
$858$		0			0
$859$	3.84152e6	−	6.65370e6i	0.177631	−	0.307667i	−0.763437	−	0.645882i	$-0.776490\pi$
$859$	3.84152e6	−	6.65370e6i	0.177631	−	0.307667i	0.941069	+	0.338215i	$0.109823\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	3.40976e7			1.55846			0.779232	−	0.626735i	$-0.215609\pi$
$863$	3.40976e7			1.55846			0.779232	+	0.626735i	$0.215609\pi$
$864$		0			0
$865$	7.43900e6			0.338045
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−8.15998e6	+	1.41335e7i	−0.366556	+	0.634893i
$870$		0			0
$871$	8.89296e6	+	1.54031e7i	0.397193	+	0.687958i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	783325.	+	1.35676e6i	0.0345877	+	0.0599077i
$876$		0			0
$877$	631848.	−	1.09439e6i	0.0277405	−	0.0480479i	−0.851822	−	0.523832i	$-0.824502\pi$
$877$	631848.	−	1.09439e6i	0.0277405	−	0.0480479i	0.879562	+	0.475784i	$0.157835\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−1.89395e7			−0.822108			−0.411054	−	0.911611i	$-0.634839\pi$
$881$	−1.89395e7			−0.822108			−0.411054	+	0.911611i	$0.634839\pi$
$882$		0			0
$883$	−3.16414e7			−1.36570			−0.682848	−	0.730560i	$-0.739259\pi$
$883$	−3.16414e7			−1.36570			−0.682848	+	0.730560i	$0.739259\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−1.39213e7	+	2.41124e7i	−0.594116	+	1.02904i	0.399555	+	0.916709i	$0.369165\pi$
$887$	−1.39213e7	+	2.41124e7i	−0.594116	+	1.02904i	−0.993671	+	0.112330i	$0.964169\pi$
$888$		0			0
$889$	3.31258e7	+	5.73756e7i	1.40576	+	2.43485i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−374178.	−	648096.i	−0.0157018	−	0.0271963i
$894$		0			0
$895$	−8.58678e6	+	1.48727e7i	−0.358321	+	0.620631i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−2.54300e6			−0.104941
$900$		0			0
$901$	2.50898e7			1.02964
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−1.35194e7	+	2.34163e7i	−0.548701	+	0.950377i
$906$		0			0
$907$	−4.48735e6	−	7.77232e6i	−0.181122	−	0.313713i	0.761141	−	0.648587i	$-0.224640\pi$
$907$	−4.48735e6	−	7.77232e6i	−0.181122	−	0.313713i	−0.942263	+	0.334874i	$0.891306\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	4.43865e6	+	7.68797e6i	0.177196	+	0.306913i	0.940919	−	0.338631i	$-0.109964\pi$
$911$	4.43865e6	+	7.68797e6i	0.177196	+	0.306913i	−0.763723	+	0.645544i	$0.776631\pi$
$912$		0			0
$913$	−6.36599e6	+	1.10262e7i	−0.252749	+	0.437773i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	7.35146e7			2.88702
$918$		0			0
$919$	1.48072e7			0.578343			0.289172	−	0.957277i	$-0.406620\pi$
$919$	1.48072e7			0.578343			0.289172	+	0.957277i	$0.406620\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−2.54818e7	+	4.41357e7i	−0.984521	+	1.70524i
$924$		0			0
$925$	−3.74081e6	−	6.47927e6i	−0.143751	−	0.248984i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−7.13029e6	−	1.23500e7i	−0.271062	−	0.469492i	0.698072	−	0.716027i	$-0.254041\pi$
$929$	−7.13029e6	−	1.23500e7i	−0.271062	−	0.469492i	−0.969134	+	0.246535i	$0.920708\pi$
$930$		0			0
$931$	−6.15149e6	+	1.06547e7i	−0.232598	+	0.402872i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−1.39148e7			−0.520532
$936$		0			0
$937$	−3.54753e7			−1.32001			−0.660006	−	0.751261i	$-0.729446\pi$
$937$	−3.54753e7			−1.32001			−0.660006	+	0.751261i	$0.729446\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	1.30008e7	−	2.25180e7i	0.478624	−	0.829001i	−0.521076	−	0.853511i	$-0.674469\pi$
$941$	1.30008e7	−	2.25180e7i	0.478624	−	0.829001i	0.999700	+	0.0245095i	$0.00780238\pi$
$942$		0			0
$943$	−1.78563e6	−	3.09280e6i	−0.0653902	−	0.113259i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.11889e7	−	1.93797e7i	−0.405426	−	0.702218i	0.588945	−	0.808173i	$-0.299543\pi$
$947$	−1.11889e7	−	1.93797e7i	−0.405426	−	0.702218i	−0.994371	+	0.105955i	$0.966210\pi$
$948$		0			0
$949$	2.51267e7	−	4.35207e7i	0.905669	−	1.56866i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	4.62557e7			1.64981			0.824903	−	0.565275i	$-0.191230\pi$
$953$	4.62557e7			1.64981			0.824903	+	0.565275i	$0.191230\pi$
$954$		0			0
$955$	1.05916e7			0.375798
$956$		0			0
$957$		0			0
$958$		0			0
$959$	2.06982e7	−	3.58503e7i	0.726750	−	1.25877i
$960$		0			0
$961$	9.13059e6	+	1.58146e7i	0.318926	+	0.552396i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	8.92170e6	+	1.54528e7i	0.308411	+	0.534183i
$966$		0			0
$967$	−2.04313e7	+	3.53880e7i	−0.702634	+	1.21700i	0.264905	+	0.964274i	$0.414659\pi$
$967$	−2.04313e7	+	3.53880e7i	−0.702634	+	1.21700i	−0.967539	+	0.252723i	$0.918674\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−3.69663e7			−1.25822			−0.629112	−	0.777315i	$-0.716581\pi$
$971$	−3.69663e7			−1.25822			−0.629112	+	0.777315i	$0.716581\pi$
$972$		0			0
$973$	−4.65634e7			−1.57675
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−2.95829e7	+	5.12390e7i	−0.991525	+	1.71737i	−0.383253	+	0.923643i	$0.625196\pi$
$977$	−2.95829e7	+	5.12390e7i	−0.991525	+	1.71737i	−0.608272	+	0.793729i	$0.708137\pi$
$978$		0			0
$979$	1.22036e6	+	2.11373e6i	0.0406942	+	0.0704845i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	9.12629e6	+	1.58072e7i	0.301238	+	0.521760i	0.976417	−	0.215894i	$-0.0692667\pi$
$983$	9.12629e6	+	1.58072e7i	0.301238	+	0.521760i	−0.675178	+	0.737655i	$0.735933\pi$
$984$		0			0
$985$	−1.68912e7	+	2.92564e7i	−0.554715	+	0.960795i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−4.10755e6			−0.133534
$990$		0			0
$991$	−4.10661e7			−1.32831			−0.664154	−	0.747596i	$-0.731208\pi$
$991$	−4.10661e7			−1.32831			−0.664154	+	0.747596i	$0.731208\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−2.82426e7	+	4.89176e7i	−0.904372	+	1.56642i
$996$		0			0
$997$	−9.35086e6	−	1.61962e7i	−0.297930	−	0.516029i	0.677732	−	0.735309i	$-0.262963\pi$
$997$	−9.35086e6	−	1.61962e7i	−0.297930	−	0.516029i	−0.975662	+	0.219279i	$0.929629\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.6.i.b.145.3		6
3.2	odd	2		144.6.i.b.49.3		6
4.3	odd	2		54.6.c.b.37.3		6
9.2	odd	6		144.6.i.b.97.3		6
9.7	even	3	inner	432.6.i.b.289.3		6
12.11	even	2		18.6.c.b.13.1	yes	6
36.7	odd	6		54.6.c.b.19.3		6
36.11	even	6		18.6.c.b.7.1	✓	6
36.23	even	6		162.6.a.j.1.3		3
36.31	odd	6		162.6.a.i.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.6.c.b.7.1	✓	6	36.11	even	6
18.6.c.b.13.1	yes	6	12.11	even	2
54.6.c.b.19.3		6	36.7	odd	6
54.6.c.b.37.3		6	4.3	odd	2
144.6.i.b.49.3		6	3.2	odd	2
144.6.i.b.97.3		6	9.2	odd	6
162.6.a.i.1.1		3	36.31	odd	6
162.6.a.j.1.3		3	36.23	even	6
432.6.i.b.145.3		6	1.1	even	1	trivial
432.6.i.b.289.3		6	9.7	even	3	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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	432.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(39.2420 - 67.9691i) q^{5} +(110.566 + 191.505i) q^{7} +O(q^{10})\)	\(q+(39.2420 - 67.9691i) q^{5} +(110.566 + 191.505i) q^{7} +(-115.144 - 199.436i) q^{11} +(385.793 - 668.213i) q^{13} +769.880 q^{17} +383.367 q^{19} +(-193.178 + 334.594i) q^{23} +(-1517.37 - 2628.15i) q^{25} +(-394.883 - 683.958i) q^{29} +(1609.97 - 2788.54i) q^{31} +17355.2 q^{35} +2465.33 q^{37} +(-4621.73 + 8005.07i) q^{41} +(5315.76 + 9207.16i) q^{43} +(-976.032 - 1690.54i) q^{47} +(-16046.0 + 27792.4i) q^{49} +32589.2 q^{53} -18074.0 q^{55} +(11916.1 - 20639.2i) q^{59} +(-18804.4 - 32570.2i) q^{61} +(-30278.5 - 52444.0i) q^{65} +(-11525.6 + 19962.9i) q^{67} -66050.4 q^{71} +65130.0 q^{73} +(25462.0 - 44101.5i) q^{77} +(-35433.7 - 61373.0i) q^{79} +(-27643.5 - 47880.0i) q^{83} +(30211.6 - 52328.0i) q^{85} -10598.6 q^{89} +170622. q^{91} +(15044.1 - 26057.1i) q^{95} +(41409.9 + 71724.1i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 54 q^{5} + 132 q^{7}+O(q^{10}) \) 6 * q + 54 * q^5 + 132 * q^7	\( 6 q + 54 q^{5} + 132 q^{7} - 315 q^{11} - 744 q^{13} - 2898 q^{17} - 2262 q^{19} - 3168 q^{23} - 2883 q^{25} + 5148 q^{29} + 8610 q^{31} + 2700 q^{35} + 39936 q^{37} - 5049 q^{41} + 31389 q^{43} + 12924 q^{47} - 52857 q^{49} + 96048 q^{53} - 126252 q^{55} + 62955 q^{59} - 75966 q^{61} - 108702 q^{65} + 32991 q^{67} - 129672 q^{71} - 8466 q^{73} - 88740 q^{77} - 89202 q^{79} + 32634 q^{83} + 71388 q^{85} - 66132 q^{89} + 301836 q^{91} - 82944 q^{95} + 46245 q^{97}+O(q^{100}) \) 6 * q + 54 * q^5 + 132 * q^7 - 315 * q^11 - 744 * q^13 - 2898 * q^17 - 2262 * q^19 - 3168 * q^23 - 2883 * q^25 + 5148 * q^29 + 8610 * q^31 + 2700 * q^35 + 39936 * q^37 - 5049 * q^41 + 31389 * q^43 + 12924 * q^47 - 52857 * q^49 + 96048 * q^53 - 126252 * q^55 + 62955 * q^59 - 75966 * q^61 - 108702 * q^65 + 32991 * q^67 - 129672 * q^71 - 8466 * q^73 - 88740 * q^77 - 89202 * q^79 + 32634 * q^83 + 71388 * q^85 - 66132 * q^89 + 301836 * q^91 - 82944 * q^95 + 46245 * q^97

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