LMFDB - Embedded newform 324.6.e.e.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,6,Mod(109,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("324.109");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	324.e (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:	$51.9643576194$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{5} $
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			109.1
Root			$1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	324.109
Dual form			324.6.e.e.217.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-44.0908 + 76.3675i) q^{5} +(-14.5000 - 25.1147i) q^{7} +O(q^{10})$	$q+(-44.0908 + 76.3675i) q^{5} +(-14.5000 - 25.1147i) q^{7} +(-44.0908 - 76.3675i) q^{11} +(-164.500 + 284.922i) q^{13} -2204.54 q^{17} +1799.00 q^{19} +(-1807.72 + 3131.07i) q^{23} +(-2325.50 - 4027.88i) q^{25} +(-705.453 - 1221.88i) q^{29} +(-2614.00 + 4527.58i) q^{31} +2557.27 q^{35} +8783.00 q^{37} +(7759.98 - 13440.7i) q^{41} +(-9988.00 - 17299.7i) q^{43} +(5423.17 + 9393.21i) q^{47} +(7983.00 - 13827.0i) q^{49} +29452.7 q^{53} +7776.00 q^{55} +(-2865.90 + 4963.89i) q^{59} +(534.500 + 925.781i) q^{61} +(-14505.9 - 25124.9i) q^{65} +(31038.5 - 53760.3i) q^{67} -46383.5 q^{71} -48079.0 q^{73} +(-1278.63 + 2214.66i) q^{77} +(-24989.5 - 43283.1i) q^{79} +(28835.4 + 49944.4i) q^{83} +(97200.0 - 168355. i) q^{85} -87917.1 q^{89} +9541.00 q^{91} +(-79319.4 + 137385. i) q^{95} +(-6458.50 - 11186.5i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 58 q^{7}+O(q^{10}) $ 4 * q - 58 * q^7	$ 4 q - 58 q^{7} - 658 q^{13} + 7196 q^{19} - 9302 q^{25} - 10456 q^{31} + 35132 q^{37} - 39952 q^{43} + 31932 q^{49} + 31104 q^{55} + 2138 q^{61} + 124154 q^{67} - 192316 q^{73} - 99958 q^{79} + 388800 q^{85} + 38164 q^{91} - 25834 q^{97}+O(q^{100}) $ 4 * q - 58 * q^7 - 658 * q^13 + 7196 * q^19 - 9302 * q^25 - 10456 * q^31 + 35132 * q^37 - 39952 * q^43 + 31932 * q^49 + 31104 * q^55 + 2138 * q^61 + 124154 * q^67 - 192316 * q^73 - 99958 * q^79 + 388800 * q^85 + 38164 * q^91 - 25834 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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
$5$	−44.0908	+	76.3675i	−0.788720	+	1.36610i	0.138031	+	0.990428i	$0.455923\pi$
$5$	−44.0908	+	76.3675i	−0.788720	+	1.36610i	−0.926751	+	0.375676i	$0.877411\pi$
$6$		0			0
$7$	−14.5000	−	25.1147i	−0.111847	−	0.193724i	0.804668	−	0.593725i	$-0.202343\pi$
$7$	−14.5000	−	25.1147i	−0.111847	−	0.193724i	−0.916515	+	0.400001i	$0.869010\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−44.0908	−	76.3675i	−0.109867	−	0.190295i	0.805849	−	0.592121i	$-0.201709\pi$
$11$	−44.0908	−	76.3675i	−0.109867	−	0.190295i	−0.915716	+	0.401826i	$0.868376\pi$
$12$		0			0
$13$	−164.500	+	284.922i	−0.269965	+	0.467593i	−0.968853	−	0.247638i	$-0.920345\pi$
$13$	−164.500	+	284.922i	−0.269965	+	0.467593i	0.698887	+	0.715232i	$0.253679\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2204.54			−1.85010			−0.925051	−	0.379842i	$-0.875978\pi$
$17$	−2204.54			−1.85010			−0.925051	+	0.379842i	$0.875978\pi$
$18$		0			0
$19$	1799.00			1.14327			0.571633	−	0.820510i	$-0.306310\pi$
$19$	1799.00			1.14327			0.571633	+	0.820510i	$0.306310\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1807.72	+	3131.07i	−0.712545	+	1.23416i	0.251354	+	0.967895i	$0.419124\pi$
$23$	−1807.72	+	3131.07i	−0.712545	+	1.23416i	−0.963899	+	0.266269i	$0.914209\pi$
$24$		0			0
$25$	−2325.50	−	4027.88i	−0.744160	−	1.28892i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−705.453	−	1221.88i	−0.155766	−	0.269795i	0.777572	−	0.628794i	$-0.216451\pi$
$29$	−705.453	−	1221.88i	−0.155766	−	0.269795i	−0.933338	+	0.359000i	$0.883118\pi$
$30$		0			0
$31$	−2614.00	+	4527.58i	−0.488541	+	0.846178i	−0.999913	−	0.0131811i	$-0.995804\pi$
$31$	−2614.00	+	4527.58i	−0.488541	+	0.846178i	0.511372	+	0.859360i	$0.329138\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2557.27			0.352863
$36$		0			0
$37$	8783.00			1.05472			0.527362	−	0.849641i	$-0.323181\pi$
$37$	8783.00			1.05472			0.527362	+	0.849641i	$0.323181\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	7759.98	−	13440.7i	0.720943	−	1.24871i	−0.239679	−	0.970852i	$-0.577042\pi$
$41$	7759.98	−	13440.7i	0.720943	−	1.24871i	0.960622	−	0.277858i	$-0.0896246\pi$
$42$		0			0
$43$	−9988.00	−	17299.7i	−0.823773	−	1.42682i	−0.902854	−	0.429948i	$-0.858532\pi$
$43$	−9988.00	−	17299.7i	−0.823773	−	1.42682i	0.0790810	−	0.996868i	$-0.474801\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5423.17	+	9393.21i	0.358104	+	0.620254i	0.987644	−	0.156714i	$-0.0500902\pi$
$47$	5423.17	+	9393.21i	0.358104	+	0.620254i	−0.629540	+	0.776968i	$0.716757\pi$
$48$		0			0
$49$	7983.00	−	13827.0i	0.474981	−	0.822691i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	29452.7			1.44024			0.720120	−	0.693849i	$-0.244087\pi$
$53$	29452.7			1.44024			0.720120	+	0.693849i	$0.244087\pi$
$54$		0			0
$55$	7776.00			0.346617
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2865.90	+	4963.89i	−0.107184	+	0.185649i	−0.914629	−	0.404295i	$-0.867517\pi$
$59$	−2865.90	+	4963.89i	−0.107184	+	0.185649i	0.807444	+	0.589944i	$0.200850\pi$
$60$		0			0
$61$	534.500	+	925.781i	0.0183918	+	0.0318555i	0.875075	−	0.483988i	$-0.160812\pi$
$61$	534.500	+	925.781i	0.0183918	+	0.0318555i	−0.856683	+	0.515843i	$0.827479\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−14505.9	−	25124.9i	−0.425854	−	0.737601i
$66$		0			0
$67$	31038.5	−	53760.3i	0.844722	−	1.46310i	−0.0411407	−	0.999153i	$-0.513099\pi$
$67$	31038.5	−	53760.3i	0.844722	−	1.46310i	0.885863	−	0.463948i	$-0.153567\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−46383.5			−1.09199			−0.545994	−	0.837789i	$-0.683848\pi$
$71$	−46383.5			−1.09199			−0.545994	+	0.837789i	$0.683848\pi$
$72$		0			0
$73$	−48079.0			−1.05596			−0.527981	−	0.849256i	$-0.677051\pi$
$73$	−48079.0			−1.05596			−0.527981	+	0.849256i	$0.677051\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1278.63	+	2214.66i	−0.0245765	+	0.0425677i
$78$		0			0
$79$	−24989.5	−	43283.1i	−0.450495	−	0.780280i	0.547922	−	0.836530i	$-0.315419\pi$
$79$	−24989.5	−	43283.1i	−0.450495	−	0.780280i	−0.998417	+	0.0562495i	$0.982086\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	28835.4	+	49944.4i	0.459442	+	0.795777i	0.998931	−	0.0462155i	$-0.0147161\pi$
$83$	28835.4	+	49944.4i	0.459442	+	0.795777i	−0.539490	+	0.841992i	$0.681383\pi$
$84$		0			0
$85$	97200.0	−	168355.i	1.45921	−	2.52743i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−87917.1			−1.17652			−0.588259	−	0.808673i	$-0.700186\pi$
$89$	−87917.1			−1.17652			−0.588259	+	0.808673i	$0.700186\pi$
$90$		0			0
$91$	9541.00			0.120779
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−79319.4	+	137385.i	−0.901717	+	1.56182i
$96$		0			0
$97$	−6458.50	−	11186.5i	−0.0696951	−	0.120715i	0.829072	−	0.559142i	$-0.188869\pi$
$97$	−6458.50	−	11186.5i	−0.0696951	−	0.120715i	−0.898767	+	0.438426i	$0.855536\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−56436.2	−	97750.4i	−0.550497	−	0.953488i	−0.998239	−	0.0593254i	$-0.981105\pi$
$101$	−56436.2	−	97750.4i	−0.550497	−	0.953488i	0.447742	−	0.894163i	$-0.352228\pi$
$102$		0			0
$103$	38751.5	−	67119.6i	0.359911	−	0.623385i	−0.628034	−	0.778186i	$-0.716140\pi$
$103$	38751.5	−	67119.6i	0.359911	−	0.623385i	0.987946	+	0.154801i	$0.0494736\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	111726.			0.943399			0.471699	−	0.881759i	$-0.343641\pi$
$107$	111726.			0.943399			0.471699	+	0.881759i	$0.343641\pi$
$108$		0			0
$109$	−17710.0			−0.142775			−0.0713875	−	0.997449i	$-0.522743\pi$
$109$	−17710.0			−0.142775			−0.0713875	+	0.997449i	$0.522743\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	125791.	−	217877.i	0.926731	−	1.60515i	0.137978	−	0.990435i	$-0.455940\pi$
$113$	125791.	−	217877.i	0.926731	−	1.60515i	0.788753	−	0.614710i	$-0.210727\pi$
$114$		0			0
$115$	−159408.	−	276103.i	−1.12400	−	1.94682i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	31965.8	+	55366.5i	0.206928	+	0.358409i
$120$		0			0
$121$	76637.5	−	132740.i	0.475859	−	0.824211i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	134565.			0.770296
$126$		0			0
$127$	269444.			1.48238			0.741189	−	0.671296i	$-0.234262\pi$
$127$	269444.			1.48238			0.741189	+	0.671296i	$0.234262\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	77070.7	−	133490.i	0.392384	−	0.679629i	−0.600379	−	0.799715i	$-0.704984\pi$
$131$	77070.7	−	133490.i	0.392384	−	0.679629i	0.992763	+	0.120086i	$0.0383171\pi$
$132$		0			0
$133$	−26085.5	−	45181.4i	−0.127870	−	0.221478i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	135932.	+	235441.i	0.618757	+	1.07172i	0.989713	+	0.143068i	$0.0456968\pi$
$137$	135932.	+	235441.i	0.618757	+	1.07172i	−0.370956	+	0.928651i	$0.620970\pi$
$138$		0			0
$139$	−91352.5	+	158227.i	−0.401036	+	0.694615i	−0.993851	−	0.110724i	$-0.964683\pi$
$139$	−91352.5	+	158227.i	−0.401036	+	0.694615i	0.592815	+	0.805339i	$0.298016\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	29011.8			0.118641
$144$		0			0
$145$	124416.			0.491424
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−173630.	+	300735.i	−0.640705	+	1.10973i	0.344571	+	0.938760i	$0.388025\pi$
$149$	−173630.	+	300735.i	−0.640705	+	1.10973i	−0.985276	+	0.170973i	$0.945309\pi$
$150$		0			0
$151$	−217176.	−	376159.i	−0.775119	−	1.34255i	−0.934727	−	0.355365i	$-0.884356\pi$
$151$	−217176.	−	376159.i	−0.775119	−	1.34255i	0.159608	−	0.987180i	$-0.448977\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−230507.	−	399249.i	−0.770645	−	1.33480i
$156$		0			0
$157$	11489.0	−	19899.5i	0.0371992	−	0.0644308i	−0.846826	−	0.531869i	$-0.821490\pi$
$157$	11489.0	−	19899.5i	0.0371992	−	0.0644308i	0.884026	+	0.467439i	$0.154823\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	104848.			0.318783
$162$		0			0
$163$	109961.			0.324168			0.162084	−	0.986777i	$-0.448179\pi$
$163$	109961.			0.324168			0.162084	+	0.986777i	$0.448179\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	153568.	−	265988.i	0.426099	−	0.738025i	−0.570423	−	0.821351i	$-0.693221\pi$
$167$	153568.	−	265988.i	0.426099	−	0.738025i	0.996522	+	0.0833258i	$0.0265542\pi$
$168$		0			0
$169$	131526.	+	227810.i	0.354238	+	0.613558i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	2116.36	+	3665.64i	0.00537618	+	0.00931182i	0.868701	−	0.495337i	$-0.164955\pi$
$173$	2116.36	+	3665.64i	0.00537618	+	0.00931182i	−0.863325	+	0.504649i	$0.831622\pi$
$174$		0			0
$175$	−67439.5	+	116809.i	−0.166464	+	0.288323i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−831906.			−1.94062			−0.970312	−	0.241856i	$-0.922244\pi$
$179$	−831906.			−1.94062			−0.970312	+	0.241856i	$0.922244\pi$
$180$		0			0
$181$	−327187.			−0.742334			−0.371167	−	0.928566i	$-0.621042\pi$
$181$	−327187.			−0.742334			−0.371167	+	0.928566i	$0.621042\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−387250.	+	670736.i	−0.831882	+	1.44086i
$186$		0			0
$187$	97200.0	+	168355.i	0.203265	+	0.352065i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	234431.	+	406046.i	0.464977	+	0.805364i	0.999200	−	0.0399796i	$-0.0127293\pi$
$191$	234431.	+	406046.i	0.464977	+	0.805364i	−0.534224	+	0.845343i	$0.679396\pi$
$192$		0			0
$193$	−76115.5	+	131836.i	−0.147089	+	0.254765i	−0.930150	−	0.367179i	$-0.880324\pi$
$193$	−76115.5	+	131836.i	−0.147089	+	0.254765i	0.783061	+	0.621944i	$0.213657\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−653514.			−1.19975			−0.599873	−	0.800095i	$-0.704782\pi$
$197$	−653514.			−1.19975			−0.599873	+	0.800095i	$0.704782\pi$
$198$		0			0
$199$	−645895.			−1.15619			−0.578095	−	0.815969i	$-0.696204\pi$
$199$	−645895.			−1.15619			−0.578095	+	0.815969i	$0.696204\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−20458.1	+	35434.5i	−0.0348438	+	0.0603513i
$204$		0			0
$205$	684288.	+	1.18522e6i	1.13725	+	1.96977i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−79319.4	−	137385.i	−0.125607	−	0.217558i
$210$		0			0
$211$	−84818.5	+	146910.i	−0.131155	+	0.227167i	−0.924122	−	0.382097i	$-0.875202\pi$
$211$	−84818.5	+	146910.i	−0.131155	+	0.227167i	0.792967	+	0.609264i	$0.208535\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	1.76152e6			2.59891
$216$		0			0
$217$	151612.			0.218567
$218$		0			0
$219$		0			0
$220$		0			0
$221$	362647.	−	628123.i	0.499463	−	0.865095i
$222$		0			0
$223$	345638.	+	598663.i	0.465435	+	0.806158i	0.999221	−	0.0394622i	$-0.0125645\pi$
$223$	345638.	+	598663.i	0.465435	+	0.806158i	−0.533786	+	0.845620i	$0.679231\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−494963.	−	857302.i	−0.637542	−	1.10425i	−0.985971	−	0.166919i	$-0.946618\pi$
$227$	−494963.	−	857302.i	−0.637542	−	1.10425i	0.348429	−	0.937335i	$-0.386715\pi$
$228$		0			0
$229$	−176125.	+	305057.i	−0.221938	+	0.384408i	−0.955397	−	0.295326i	$-0.904572\pi$
$229$	−176125.	+	305057.i	−0.221938	+	0.384408i	0.733458	+	0.679735i	$0.237905\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	381297.			0.460123			0.230062	−	0.973176i	$-0.426107\pi$
$233$	381297.			0.460123			0.230062	+	0.973176i	$0.426107\pi$
$234$		0			0
$235$	−956448.			−1.12977
$236$		0			0
$237$		0			0
$238$		0			0
$239$	392849.	−	680435.i	0.444868	−	0.770534i	−0.553175	−	0.833065i	$-0.686584\pi$
$239$	392849.	−	680435.i	0.444868	−	0.770534i	0.998043	+	0.0625312i	$0.0199173\pi$
$240$		0			0
$241$	601312.	+	1.04150e6i	0.666894	+	1.15509i	0.978768	+	0.204971i	$0.0657100\pi$
$241$	601312.	+	1.04150e6i	0.666894	+	1.15509i	−0.311874	+	0.950124i	$0.600957\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	703954.	+	1.21928e6i	0.749254	+	1.29775i
$246$		0			0
$247$	−295936.	+	512575.i	−0.308642	+	0.534583i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−416570.			−0.417353			−0.208677	−	0.977985i	$-0.566916\pi$
$251$	−416570.			−0.417353			−0.208677	+	0.977985i	$0.566916\pi$
$252$		0			0
$253$	318816.			0.313140
$254$		0			0
$255$		0			0
$256$		0			0
$257$	22486.3	−	38947.4i	0.0212366	−	0.0367829i	−0.855212	−	0.518279i	$-0.826573\pi$
$257$	22486.3	−	38947.4i	0.0212366	−	0.0367829i	0.876448	+	0.481496i	$0.159906\pi$
$258$		0			0
$259$	−127353.	−	220583.i	−0.117967	−	0.204325i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	257579.	+	446139.i	0.229626	+	0.397723i	0.957697	−	0.287778i	$-0.0929165\pi$
$263$	257579.	+	446139.i	0.229626	+	0.397723i	−0.728072	+	0.685501i	$0.759583\pi$
$264$		0			0
$265$	−1.29859e6	+	2.24923e6i	−1.13595	+	1.96752i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	197439.			0.166361			0.0831805	−	0.996534i	$-0.473492\pi$
$269$	197439.			0.166361			0.0831805	+	0.996534i	$0.473492\pi$
$270$		0			0
$271$	−1.01499e6			−0.839530			−0.419765	−	0.907633i	$-0.637888\pi$
$271$	−1.01499e6			−0.839530			−0.419765	+	0.907633i	$0.637888\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−205066.	+	355185.i	−0.163517	+	0.283220i
$276$		0			0
$277$	189659.	+	328499.i	0.148516	+	0.257238i	0.930679	−	0.365836i	$-0.119217\pi$
$277$	189659.	+	328499.i	0.148516	+	0.257238i	−0.782163	+	0.623074i	$0.785884\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−477944.	−	827824.i	−0.361087	−	0.625421i	0.627053	−	0.778976i	$-0.284261\pi$
$281$	−477944.	−	827824.i	−0.361087	−	0.625421i	−0.988140	+	0.153556i	$0.950928\pi$
$282$		0			0
$283$	−331456.	+	574099.i	−0.246014	+	0.426109i	−0.962416	−	0.271579i	$-0.912454\pi$
$283$	−331456.	+	574099.i	−0.246014	+	0.426109i	0.716402	+	0.697688i	$0.245788\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−450079.			−0.322540
$288$		0			0
$289$	3.44014e6			2.42288
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−223761.	+	387565.i	−0.152270	+	0.263740i	−0.932062	−	0.362300i	$-0.881992\pi$
$293$	−223761.	+	387565.i	−0.152270	+	0.263740i	0.779791	+	0.626039i	$0.215325\pi$
$294$		0			0
$295$	−252720.	−	437724.i	−0.169077	−	0.292850i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−594741.	−	1.03012e6i	−0.384725	−	0.666362i
$300$		0			0
$301$	−289652.	+	501692.i	−0.184272	+	0.319169i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−94266.2			−0.0580238
$306$		0			0
$307$	−1.17362e6			−0.710690			−0.355345	−	0.934735i	$-0.615637\pi$
$307$	−1.17362e6			−0.710690			−0.355345	+	0.934735i	$0.615637\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−1.20610e6	+	2.08903e6i	−0.707105	+	1.22474i	0.258822	+	0.965925i	$0.416666\pi$
$311$	−1.20610e6	+	2.08903e6i	−0.707105	+	1.22474i	−0.965926	+	0.258817i	$0.916667\pi$
$312$		0			0
$313$	−864834.	−	1.49794e6i	−0.498967	−	0.864236i	0.501032	−	0.865428i	$-0.332954\pi$
$313$	−864834.	−	1.49794e6i	−0.498967	−	0.864236i	−0.999999	+	0.00119261i	$0.999620\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−587378.	−	1.01737e6i	−0.328299	−	0.568630i	0.653876	−	0.756602i	$-0.273142\pi$
$317$	−587378.	−	1.01737e6i	−0.328299	−	0.568630i	−0.982174	+	0.187972i	$0.939809\pi$
$318$		0			0
$319$	−62208.0	+	107747.i	−0.0342271	+	0.0592830i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−3.96597e6			−2.11516
$324$		0			0
$325$	1.53018e6			0.803589
$326$		0			0
$327$		0			0
$328$		0			0
$329$	157272.	−	272403.i	0.0801053	−	0.138747i
$330$		0			0
$331$	−225500.	−	390578.i	−0.113130	−	0.195947i	0.803901	−	0.594763i	$-0.202754\pi$
$331$	−225500.	−	390578.i	−0.113130	−	0.195947i	−0.917031	+	0.398817i	$0.869421\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	2.73703e6	+	4.74067e6i	1.33250	+	2.30796i
$336$		0			0
$337$	−1.08969e6	+	1.88739e6i	−0.522669	+	0.905289i	0.476983	+	0.878913i	$0.341730\pi$
$337$	−1.08969e6	+	1.88739e6i	−0.522669	+	0.905289i	−0.999652	+	0.0263769i	$0.991603\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	461014.			0.214698
$342$		0			0
$343$	−950417.			−0.436193
$344$		0			0
$345$		0			0
$346$		0			0
$347$	190737.	−	330366.i	0.0850376	−	0.147289i	−0.820370	−	0.571834i	$-0.806232\pi$
$347$	190737.	−	330366.i	0.0850376	−	0.147289i	0.905407	+	0.424544i	$0.139566\pi$
$348$		0			0
$349$	1.14798e6	+	1.98836e6i	0.504511	+	0.873839i	0.999986	+	0.00521712i	$0.00166067\pi$
$349$	1.14798e6	+	1.98836e6i	0.504511	+	0.873839i	−0.495475	+	0.868622i	$0.665006\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−1.62051e6	−	2.80681e6i	−0.692175	−	1.19888i	−0.971124	−	0.238576i	$-0.923319\pi$
$353$	−1.62051e6	−	2.80681e6i	−0.692175	−	1.19888i	0.278949	−	0.960306i	$-0.410014\pi$
$354$		0			0
$355$	2.04509e6	−	3.54220e6i	0.861274	−	1.49177i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	4.15044e6			1.69965			0.849823	−	0.527068i	$-0.176709\pi$
$359$	4.15044e6			1.69965			0.849823	+	0.527068i	$0.176709\pi$
$360$		0			0
$361$	760302.			0.307056
$362$		0			0
$363$		0			0
$364$		0			0
$365$	2.11984e6	−	3.67167e6i	0.832859	−	1.44255i
$366$		0			0
$367$	−1.69956e6	−	2.94372e6i	−0.658674	−	1.14086i	−0.980959	−	0.194214i	$-0.937784\pi$
$367$	−1.69956e6	−	2.94372e6i	−0.658674	−	1.14086i	0.322285	−	0.946643i	$-0.395549\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−427064.	−	739696.i	−0.161086	−	0.279009i
$372$		0			0
$373$	1.57247e6	−	2.72360e6i	0.585207	−	1.01361i	−0.409642	−	0.912246i	$-0.634346\pi$
$373$	1.57247e6	−	2.72360e6i	0.585207	−	1.01361i	0.994850	−	0.101363i	$-0.0323203\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	464188.			0.168206
$378$		0			0
$379$	−2.76635e6			−0.989257			−0.494628	−	0.869105i	$-0.664696\pi$
$379$	−2.76635e6			−0.989257			−0.494628	+	0.869105i	$0.664696\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−1.12449e6	+	1.94768e6i	−0.391705	+	0.678454i	−0.992675	−	0.120819i	$-0.961448\pi$
$383$	−1.12449e6	+	1.94768e6i	−0.391705	+	0.678454i	0.600969	+	0.799272i	$0.294781\pi$
$384$		0			0
$385$	−112752.	−	195292.i	−0.0387679	−	0.0671480i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−277993.	−	481497.i	−0.0931449	−	0.161332i	0.815688	−	0.578492i	$-0.196359\pi$
$389$	−277993.	−	481497.i	−0.0931449	−	0.161332i	−0.908833	+	0.417160i	$0.863025\pi$
$390$		0			0
$391$	3.98520e6	−	6.90257e6i	1.31828	−	2.28333i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	4.40723e6			1.42126
$396$		0			0
$397$	836174.			0.266269			0.133134	−	0.991098i	$-0.457496\pi$
$397$	836174.			0.266269			0.133134	+	0.991098i	$0.457496\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	1.00642e6	−	1.74317e6i	0.312548	−	0.541349i	−0.666365	−	0.745626i	$-0.732151\pi$
$401$	1.00642e6	−	1.74317e6i	0.312548	−	0.541349i	0.978913	+	0.204276i	$0.0654841\pi$
$402$		0			0
$403$	−860006.	−	1.48957e6i	−0.263778	−	0.456877i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−387250.	−	670736.i	−0.115879	−	0.200708i
$408$		0			0
$409$	686356.	−	1.18880e6i	0.202881	−	0.351400i	−0.746575	−	0.665302i	$-0.768303\pi$
$409$	686356.	−	1.18880e6i	0.202881	−	0.351400i	0.949455	+	0.313902i	$0.101636\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	166222.			0.0479528
$414$		0			0
$415$	−5.08550e6			−1.44949
$416$		0			0
$417$		0			0
$418$		0			0
$419$	1.77152e6	−	3.06837e6i	0.492961	−	0.853833i	−0.507007	−	0.861942i	$-0.669248\pi$
$419$	1.77152e6	−	3.06837e6i	0.492961	−	0.853833i	0.999967	+	0.00810943i	$0.00258134\pi$
$420$		0			0
$421$	1.74442e6	+	3.02142e6i	0.479673	+	0.830819i	0.999728	−	0.0233141i	$-0.00742179\pi$
$421$	1.74442e6	+	3.02142e6i	0.479673	+	0.830819i	−0.520055	+	0.854133i	$0.674088\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	5.12666e6	+	8.87963e6i	1.37677	+	2.38464i
$426$		0			0
$427$	15500.5	−	26847.7i	0.00411411	−	0.00712585i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−5.43754e6			−1.40997			−0.704985	−	0.709223i	$-0.749046\pi$
$431$	−5.43754e6			−1.40997			−0.704985	+	0.709223i	$0.749046\pi$
$432$		0			0
$433$	4.96023e6			1.27140			0.635699	−	0.771937i	$-0.280712\pi$
$433$	4.96023e6			1.27140			0.635699	+	0.771937i	$0.280712\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−3.25209e6	+	5.63279e6i	−0.814628	+	1.41098i
$438$		0			0
$439$	−2.87535e6	−	4.98026e6i	−0.712082	−	1.23336i	−0.964074	−	0.265633i	$-0.914419\pi$
$439$	−2.87535e6	−	4.98026e6i	−0.712082	−	1.23336i	0.251992	−	0.967729i	$-0.418914\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−2.81555e6	−	4.87668e6i	−0.681639	−	1.18063i	−0.974481	−	0.224472i	$-0.927934\pi$
$443$	−2.81555e6	−	4.87668e6i	−0.681639	−	1.18063i	0.292842	−	0.956161i	$-0.405399\pi$
$444$		0			0
$445$	3.87634e6	−	6.71401e6i	0.927943	−	1.60724i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−3.45310e6			−0.808340			−0.404170	−	0.914684i	$-0.632440\pi$
$449$	−3.45310e6			−0.808340			−0.404170	+	0.914684i	$0.632440\pi$
$450$		0			0
$451$	−1.36858e6			−0.316831
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−420670.	+	728623.i	−0.0952606	+	0.164996i
$456$		0			0
$457$	−983995.	−	1.70433e6i	−0.220395	−	0.381736i	0.734533	−	0.678573i	$-0.237401\pi$
$457$	−983995.	−	1.70433e6i	−0.220395	−	0.381736i	−0.954928	+	0.296837i	$0.904068\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−3.31664e6	−	5.74459e6i	−0.726853	−	1.25895i	−0.958207	−	0.286076i	$-0.907649\pi$
$461$	−3.31664e6	−	5.74459e6i	−0.726853	−	1.25895i	0.231354	−	0.972870i	$-0.425684\pi$
$462$		0			0
$463$	812842.	−	1.40788e6i	0.176219	−	0.305221i	−0.764363	−	0.644786i	$-0.776947\pi$
$463$	812842.	−	1.40788e6i	0.176219	−	0.305221i	0.940583	+	0.339565i	$0.110280\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−2.48346e6			−0.526944			−0.263472	−	0.964667i	$-0.584868\pi$
$467$	−2.48346e6			−0.526944			−0.263472	+	0.964667i	$0.584868\pi$
$468$		0			0
$469$	−1.80023e6			−0.377917
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−880758.	+	1.52552e6i	−0.181011	+	0.313519i
$474$		0			0
$475$	−4.18357e6	−	7.24616e6i	−0.850773	−	1.47358i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−798132.	−	1.38241e6i	−0.158941	−	0.275294i	0.775546	−	0.631291i	$-0.217475\pi$
$479$	−798132.	−	1.38241e6i	−0.158941	−	0.275294i	−0.934487	+	0.355997i	$0.884141\pi$
$480$		0			0
$481$	−1.44480e6	+	2.50247e6i	−0.284738	+	0.493181i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1.13904e6			0.219880
$486$		0			0
$487$	7.95245e6			1.51942			0.759712	−	0.650260i	$-0.225340\pi$
$487$	7.95245e6			1.51942			0.759712	+	0.650260i	$0.225340\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−1.02798e6	+	1.78051e6i	−0.192433	+	0.333304i	−0.946056	−	0.324003i	$-0.894971\pi$
$491$	−1.02798e6	+	1.78051e6i	−0.192433	+	0.333304i	0.753623	+	0.657307i	$0.228305\pi$
$492$		0			0
$493$	1.55520e6	+	2.69369e6i	0.288183	+	0.499148i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	672561.	+	1.16491e6i	0.122135	+	0.211544i
$498$		0			0
$499$	−2.46770e6	+	4.27417e6i	−0.443650	+	0.768424i	−0.997957	−	0.0638881i	$-0.979650\pi$
$499$	−2.46770e6	+	4.27417e6i	−0.443650	+	0.768424i	0.554307	+	0.832312i	$0.312983\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	836755.			0.147461			0.0737307	−	0.997278i	$-0.476509\pi$
$503$	836755.			0.147461			0.0737307	+	0.997278i	$0.476509\pi$
$504$		0			0
$505$	9.95328e6			1.73675
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−2.95078e6	+	5.11090e6i	−0.504826	+	0.874385i	0.495158	+	0.868803i	$0.335110\pi$
$509$	−2.95078e6	+	5.11090e6i	−0.504826	+	0.874385i	−0.999984	+	0.00558204i	$0.998223\pi$
$510$		0			0
$511$	697146.	+	1.20749e6i	0.118106	+	0.204565i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	3.41717e6	+	5.91871e6i	0.567739	+	0.983352i
$516$		0			0
$517$	478224.	−	828308.i	0.0786874	−	0.136291i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−163577.			−0.0264014			−0.0132007	−	0.999913i	$-0.504202\pi$
$521$	−163577.			−0.0264014			−0.0132007	+	0.999913i	$0.504202\pi$
$522$		0			0
$523$	−2.95232e6			−0.471965			−0.235983	−	0.971757i	$-0.575831\pi$
$523$	−2.95232e6			−0.471965			−0.235983	+	0.971757i	$0.575831\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	5.76267e6	−	9.98124e6i	0.903852	−	1.56552i
$528$		0			0
$529$	−3.31756e6	−	5.74618e6i	−0.515441	−	0.892770i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	2.55303e6	+	4.42199e6i	0.389259	+	0.674216i
$534$		0			0
$535$	−4.92610e6	+	8.53225e6i	−0.744078	+	1.28878i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−1.40791e6			−0.208738
$540$		0			0
$541$	−9.58390e6			−1.40783			−0.703913	−	0.710286i	$-0.748566\pi$
$541$	−9.58390e6			−1.40783			−0.703913	+	0.710286i	$0.748566\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	780848.	−	1.35247e6i	0.112610	−	0.195046i
$546$		0			0
$547$	−6.08907e6	−	1.05466e7i	−0.870127	−	1.50710i	−0.861864	−	0.507139i	$-0.830703\pi$
$547$	−6.08907e6	−	1.05466e7i	−0.870127	−	1.50710i	−0.00826306	−	0.999966i	$-0.502630\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−1.26911e6	−	2.19816e6i	−0.178082	−	0.308447i
$552$		0			0
$553$	−724695.	+	1.25521e6i	−0.100773	+	0.174543i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	5.32679e6			0.727491			0.363745	−	0.931498i	$-0.381498\pi$
$557$	5.32679e6			0.727491			0.363745	+	0.931498i	$0.381498\pi$
$558$		0			0
$559$	6.57210e6			0.889559
$560$		0			0
$561$		0			0
$562$		0			0
$563$	4.11949e6	−	7.13517e6i	0.547738	−	0.948710i	−0.450691	−	0.892680i	$-0.648822\pi$
$563$	4.11949e6	−	7.13517e6i	0.547738	−	0.948710i	0.998429	−	0.0560299i	$-0.0178442\pi$
$564$		0			0
$565$	1.10925e7	+	1.92127e7i	1.46186	+	2.53202i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−3.71205e6	−	6.42946e6i	−0.480655	−	0.832518i	0.519099	−	0.854714i	$-0.326268\pi$
$569$	−3.71205e6	−	6.42946e6i	−0.480655	−	0.832518i	−0.999754	+	0.0221959i	$0.992934\pi$
$570$		0			0
$571$	144276.	−	249894.i	0.0185185	−	0.0320749i	−0.856618	−	0.515952i	$-0.827438\pi$
$571$	144276.	−	249894.i	0.0185185	−	0.0320749i	0.875136	+	0.483877i	$0.160772\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	1.68154e7			2.12099
$576$		0			0
$577$	933299.			0.116703			0.0583514	−	0.998296i	$-0.481416\pi$
$577$	933299.			0.116703			0.0583514	+	0.998296i	$0.481416\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	836226.	−	1.44839e6i	0.102774	−	0.178010i
$582$		0			0
$583$	−1.29859e6	−	2.24923e6i	−0.158235	−	0.274070i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−4.07712e6	−	7.06178e6i	−0.488381	−	0.845900i	0.511530	−	0.859265i	$-0.329079\pi$
$587$	−4.07712e6	−	7.06178e6i	−0.488381	−	0.845900i	−0.999911	+	0.0133653i	$0.995746\pi$
$588$		0			0
$589$	−4.70259e6	+	8.14512e6i	−0.558533	+	0.967407i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	2.18214e6			0.254828			0.127414	−	0.991850i	$-0.459332\pi$
$593$	2.18214e6			0.254828			0.127414	+	0.991850i	$0.459332\pi$
$594$		0			0
$595$	−5.63760e6			−0.652833
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−1.42995e6	+	2.47675e6i	−0.162838	+	0.282043i	−0.935885	−	0.352305i	$-0.885398\pi$
$599$	−1.42995e6	+	2.47675e6i	−0.162838	+	0.282043i	0.773048	+	0.634348i	$0.218731\pi$
$600$		0			0
$601$	7.63064e6	+	1.32167e7i	0.861737	+	1.49257i	0.870251	+	0.492609i	$0.163957\pi$
$601$	7.63064e6	+	1.32167e7i	0.861737	+	1.49257i	−0.00851319	+	0.999964i	$0.502710\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	6.75802e6	+	1.17052e7i	0.750639	+	1.30014i
$606$		0			0
$607$	−1.18678e6	+	2.05556e6i	−0.130737	+	0.226443i	−0.923961	−	0.382487i	$-0.875068\pi$
$607$	−1.18678e6	+	2.05556e6i	−0.130737	+	0.226443i	0.793224	+	0.608930i	$0.208401\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−3.56845e6			−0.386702
$612$		0			0
$613$	−4.21002e6			−0.452515			−0.226258	−	0.974068i	$-0.572649\pi$
$613$	−4.21002e6			−0.452515			−0.226258	+	0.974068i	$0.572649\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1.59790e6	+	2.76764e6i	−0.168980	+	0.292682i	−0.938062	−	0.346469i	$-0.887381\pi$
$617$	−1.59790e6	+	2.76764e6i	−0.168980	+	0.292682i	0.769081	+	0.639151i	$0.220714\pi$
$618$		0			0
$619$	6.51032e6	+	1.12762e7i	0.682930	+	1.18287i	0.974083	+	0.226192i	$0.0726278\pi$
$619$	6.51032e6	+	1.12762e7i	0.682930	+	1.18287i	−0.291153	+	0.956677i	$0.594039\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	1.27480e6	+	2.20801e6i	0.131589	+	0.227920i
$624$		0			0
$625$	1.33410e6	−	2.31073e6i	0.136612	−	0.236619i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−1.93625e7			−1.95135
$630$		0			0
$631$	−1.44185e7			−1.44161			−0.720803	−	0.693140i	$-0.756227\pi$
$631$	−1.44185e7			−1.44161			−0.720803	+	0.693140i	$0.756227\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−1.18800e7	+	2.05768e7i	−1.16918	+	2.02508i
$636$		0			0
$637$	2.62641e6	+	4.54907e6i	0.256456	+	0.444195i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−1.70411e6	−	2.95161e6i	−0.163815	−	0.283735i	0.772419	−	0.635113i	$-0.219047\pi$
$641$	−1.70411e6	−	2.95161e6i	−0.163815	−	0.283735i	−0.936234	+	0.351378i	$0.885713\pi$
$642$		0			0
$643$	−7.15083e6	+	1.23856e7i	−0.682070	+	1.18138i	0.292278	+	0.956333i	$0.405587\pi$
$643$	−7.15083e6	+	1.23856e7i	−0.682070	+	1.18138i	−0.974348	+	0.225046i	$0.927747\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.59891e7			−1.50163			−0.750815	−	0.660512i	$-0.770339\pi$
$647$	−1.59891e7			−1.50163			−0.750815	+	0.660512i	$0.770339\pi$
$648$		0			0
$649$	505440.			0.0471040
$650$		0			0
$651$		0			0
$652$		0			0
$653$	9.15158e6	−	1.58510e7i	0.839872	−	1.45470i	−0.0501295	−	0.998743i	$-0.515963\pi$
$653$	9.15158e6	−	1.58510e7i	0.839872	−	1.45470i	0.890001	−	0.455958i	$-0.150703\pi$
$654$		0			0
$655$	6.79622e6	+	1.17714e7i	0.618963	+	1.07207i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	2.41362e6	+	4.18051e6i	0.216499	+	0.374987i	0.953735	−	0.300648i	$-0.0972030\pi$
$659$	2.41362e6	+	4.18051e6i	0.216499	+	0.374987i	−0.737236	+	0.675635i	$0.763870\pi$
$660$		0			0
$661$	7.25635e6	−	1.25684e7i	0.645973	−	1.11886i	−0.338103	−	0.941109i	$-0.609785\pi$
$661$	7.25635e6	−	1.25684e7i	0.645973	−	1.11886i	0.984076	−	0.177749i	$-0.0568815\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	4.60052e6			0.403416
$666$		0			0
$667$	5.10106e6			0.443962
$668$		0			0
$669$		0			0
$670$		0			0
$671$	47133.1	−	81636.9i	0.00404129	−	0.00699971i
$672$		0			0
$673$	2.61637e6	+	4.53168e6i	0.222670	+	0.385675i	0.955618	−	0.294609i	$-0.0951896\pi$
$673$	2.61637e6	+	4.53168e6i	0.222670	+	0.385675i	−0.732948	+	0.680285i	$0.761856\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−1.65945e6	−	2.87424e6i	−0.139153	−	0.241019i	0.788023	−	0.615645i	$-0.211105\pi$
$677$	−1.65945e6	−	2.87424e6i	−0.139153	−	0.241019i	−0.927176	+	0.374626i	$0.877771\pi$
$678$		0			0
$679$	−187296.	+	324407.i	−0.0155903	+	0.0270032i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	350257.			0.0287300			0.0143650	−	0.999897i	$-0.495427\pi$
$683$	350257.			0.0287300			0.0143650	+	0.999897i	$0.495427\pi$
$684$		0			0
$685$	−2.39734e7			−1.95211
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−4.84496e6	+	8.39172e6i	−0.388814	+	0.673446i
$690$		0			0
$691$	4.81372e6	+	8.33761e6i	0.383518	+	0.664273i	0.991562	−	0.129630i	$-0.0413790\pi$
$691$	4.81372e6	+	8.33761e6i	0.383518	+	0.664273i	−0.608044	+	0.793903i	$0.708046\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−8.05561e6	−	1.39527e7i	−0.632611	−	1.09571i
$696$		0			0
$697$	−1.71072e7	+	2.96305e7i	−1.33382	+	2.31024i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	1.75325e7			1.34756			0.673782	−	0.738930i	$-0.264668\pi$
$701$	1.75325e7			1.34756			0.673782	+	0.738930i	$0.264668\pi$
$702$		0			0
$703$	1.58006e7			1.20583
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1.63665e6	+	2.83476e6i	−0.123142	+	0.213289i
$708$		0			0
$709$	−2.66079e6	−	4.60863e6i	−0.198790	−	0.344315i	0.749346	−	0.662179i	$-0.230368\pi$
$709$	−2.66079e6	−	4.60863e6i	−0.198790	−	0.344315i	−0.948136	+	0.317863i	$0.897035\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−9.45078e6	−	1.63692e7i	−0.696216	−	1.20588i
$714$		0			0
$715$	−1.27915e6	+	2.21556e6i	−0.0935744	+	0.162076i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−1.74700e7			−1.26029			−0.630146	−	0.776477i	$-0.717005\pi$
$719$	−1.74700e7			−1.26029			−0.630146	+	0.776477i	$0.717005\pi$
$720$		0			0
$721$	−2.24759e6			−0.161019
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−3.28106e6	+	5.68297e6i	−0.231830	+	0.401541i
$726$		0			0
$727$	2.93487e6	+	5.08334e6i	0.205945	+	0.356708i	0.950434	−	0.310928i	$-0.100640\pi$
$727$	2.93487e6	+	5.08334e6i	0.205945	+	0.356708i	−0.744488	+	0.667636i	$0.767306\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	2.20190e7	+	3.81379e7i	1.52406	+	2.63976i
$732$		0			0
$733$	2.80147e6	−	4.85229e6i	0.192587	−	0.333570i	−0.753520	−	0.657425i	$-0.771646\pi$
$733$	2.80147e6	−	4.85229e6i	0.192587	−	0.333570i	0.946107	+	0.323855i	$0.104979\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−5.47405e6			−0.371227
$738$		0			0
$739$	−5.56792e6			−0.375044			−0.187522	−	0.982260i	$-0.560046\pi$
$739$	−5.56792e6			−0.375044			−0.187522	+	0.982260i	$0.560046\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−1.89242e6	+	3.27777e6i	−0.125761	+	0.217824i	−0.922030	−	0.387118i	$-0.873471\pi$
$743$	−1.89242e6	+	3.27777e6i	−0.125761	+	0.217824i	0.796269	+	0.604942i	$0.206804\pi$
$744$		0			0
$745$	−1.53109e7	−	2.65193e7i	−1.01067	−	1.75054i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−1.62003e6	−	2.80597e6i	−0.105516	−	0.182759i
$750$		0			0
$751$	3.38329e6	−	5.86002e6i	0.218897	−	0.379140i	−0.735574	−	0.677444i	$-0.763088\pi$
$751$	3.38329e6	−	5.86002e6i	0.218897	−	0.379140i	0.954471	+	0.298304i	$0.0964209\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	3.83018e7			2.44541
$756$		0			0
$757$	2.46970e7			1.56640			0.783202	−	0.621768i	$-0.213585\pi$
$757$	2.46970e7			1.56640			0.783202	+	0.621768i	$0.213585\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	1.50435e7	−	2.60561e7i	0.941644	−	1.63097i	0.179308	−	0.983793i	$-0.442614\pi$
$761$	1.50435e7	−	2.60561e7i	0.941644	−	1.63097i	0.762336	−	0.647182i	$-0.224053\pi$
$762$		0			0
$763$	256795.	+	444782.i	0.0159689	+	0.0276590i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−942882.	−	1.63312e6i	−0.0578721	−	0.100237i
$768$		0			0
$769$	−1.62559e6	+	2.81561e6i	−0.0991278	+	0.171694i	−0.911324	−	0.411690i	$-0.864939\pi$
$769$	−1.62559e6	+	2.81561e6i	−0.0991278	+	0.171694i	0.812196	+	0.583385i	$0.198272\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−3.30628e6			−0.199017			−0.0995087	−	0.995037i	$-0.531727\pi$
$773$	−3.30628e6			−0.199017			−0.0995087	+	0.995037i	$0.531727\pi$
$774$		0			0
$775$	2.43154e7			1.45421
$776$		0			0
$777$		0			0
$778$		0			0
$779$	1.39602e7	−	2.41798e7i	0.824230	−	1.42761i
$780$		0			0
$781$	2.04509e6	+	3.54220e6i	0.119973	+	0.207800i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	1.01312e6	+	1.75477e6i	0.0586795	+	0.101636i
$786$		0			0
$787$	−8.50778e6	+	1.47359e7i	−0.489643	+	0.848087i	−0.999929	−	0.0119182i	$-0.996206\pi$
$787$	−8.50778e6	+	1.47359e7i	−0.489643	+	0.848087i	0.510286	+	0.860005i	$0.329540\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−7.29588e6			−0.414607
$792$		0			0
$793$	−351701.			−0.0198605
$794$		0			0
$795$		0			0
$796$		0			0
$797$	6.56336e6	−	1.13681e7i	0.365999	−	0.633930i	−0.622937	−	0.782272i	$-0.714061\pi$
$797$	6.56336e6	−	1.13681e7i	0.365999	−	0.633930i	0.988936	+	0.148343i	$0.0473939\pi$
$798$		0			0
$799$	−1.19556e7	−	2.07077e7i	−0.662528	−	1.14753i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	2.11984e6	+	3.67167e6i	0.116015	+	0.200944i
$804$		0			0
$805$	−4.62283e6	+	8.00698e6i	−0.251431	+	0.435491i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	2.90313e7			1.55954			0.779768	−	0.626068i	$-0.215337\pi$
$809$	2.90313e7			1.55954			0.779768	+	0.626068i	$0.215337\pi$
$810$		0			0
$811$	−2.70345e7			−1.44333			−0.721666	−	0.692241i	$-0.756623\pi$
$811$	−2.70345e7			−1.44333			−0.721666	+	0.692241i	$0.756623\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−4.84827e6	+	8.39745e6i	−0.255678	+	0.442847i
$816$		0			0
$817$	−1.79684e7	−	3.11222e7i	−0.941791	−	1.63123i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.07418e7	−	1.86053e7i	−0.556185	−	0.963341i	−0.997810	−	0.0661410i	$-0.978931\pi$
$821$	−1.07418e7	−	1.86053e7i	−0.556185	−	0.963341i	0.441625	−	0.897200i	$-0.354402\pi$
$822$		0			0
$823$	1.23141e7	−	2.13286e7i	0.633727	−	1.09765i	−0.353056	−	0.935602i	$-0.614858\pi$
$823$	1.23141e7	−	2.13286e7i	0.633727	−	1.09765i	0.986783	−	0.162045i	$-0.0518091\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	5.10933e6			0.259777			0.129888	−	0.991529i	$-0.458538\pi$
$827$	5.10933e6			0.259777			0.129888	+	0.991529i	$0.458538\pi$
$828$		0			0
$829$	3.04805e7			1.54041			0.770205	−	0.637797i	$-0.220154\pi$
$829$	3.04805e7			1.54041			0.770205	+	0.637797i	$0.220154\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−1.75988e7	+	3.04821e7i	−0.878763	+	1.52206i
$834$		0			0
$835$	1.35419e7	+	2.34553e7i	0.672146	+	1.16419i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−6.84034e6	−	1.18478e7i	−0.335485	−	0.581076i	0.648093	−	0.761561i	$-0.275567\pi$
$839$	−6.84034e6	−	1.18478e7i	−0.335485	−	0.581076i	−0.983578	+	0.180485i	$0.942233\pi$
$840$		0			0
$841$	9.26025e6	−	1.60392e7i	0.451474	−	0.781976i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−2.31964e7			−1.11758
$846$		0			0
$847$	−4.44498e6			−0.212893
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−1.58772e7	+	2.75002e7i	−0.751538	+	1.30170i
$852$		0			0
$853$	−1.72040e7	−	2.97981e7i	−0.809572	−	1.40222i	−0.913160	−	0.407600i	$-0.866366\pi$
$853$	−1.72040e7	−	2.97981e7i	−0.809572	−	1.40222i	0.103588	−	0.994620i	$-0.466968\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1.36778e7	+	2.36906e7i	0.636155	+	1.10185i	0.986269	+	0.165146i	$0.0528095\pi$
$857$	1.36778e7	+	2.36906e7i	0.636155	+	1.10185i	−0.350114	+	0.936707i	$0.613857\pi$
$858$		0			0
$859$	2.68909e6	−	4.65764e6i	0.124343	−	0.215369i	−0.797133	−	0.603804i	$-0.793651\pi$
$859$	2.68909e6	−	4.65764e6i	0.124343	−	0.215369i	0.921476	+	0.388435i	$0.126984\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−2.64604e7			−1.20940			−0.604699	−	0.796454i	$-0.706707\pi$
$863$	−2.64604e7			−1.20940			−0.604699	+	0.796454i	$0.706707\pi$
$864$		0			0
$865$	−373248.			−0.0169612
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−2.20361e6	+	3.81677e6i	−0.0989888	+	0.171454i
$870$		0			0
$871$	1.02117e7	+	1.76871e7i	0.456091	+	0.789972i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−1.95119e6	−	3.37957e6i	−0.0861550	−	0.149225i
$876$		0			0
$877$	8.85541e6	−	1.53380e7i	0.388785	−	0.673396i	−0.603501	−	0.797362i	$-0.706228\pi$
$877$	8.85541e6	−	1.53380e7i	0.388785	−	0.673396i	0.992286	+	0.123966i	$0.0395615\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−3.04035e7			−1.31973			−0.659864	−	0.751385i	$-0.729386\pi$
$881$	−3.04035e7			−1.31973			−0.659864	+	0.751385i	$0.729386\pi$
$882$		0			0
$883$	2.93557e7			1.26704			0.633521	−	0.773726i	$-0.281609\pi$
$883$	2.93557e7			1.26704			0.633521	+	0.773726i	$0.281609\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1.32281e6	−	2.29118e6i	0.0564533	−	0.0977800i	−0.836418	−	0.548093i	$-0.815354\pi$
$887$	1.32281e6	−	2.29118e6i	0.0564533	−	0.0977800i	0.892871	+	0.450313i	$0.148687\pi$
$888$		0			0
$889$	−3.90694e6	−	6.76702e6i	−0.165799	−	0.287172i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	9.75628e6	+	1.68984e7i	0.409407	+	0.709115i
$894$		0			0
$895$	3.66794e7	−	6.35306e7i	1.53061	−	2.65109i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	7.37622e6			0.304393
$900$		0			0
$901$	−6.49296e7			−2.66459
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.44259e7	−	2.49865e7i	0.585494	−	1.01411i
$906$		0			0
$907$	−1.03696e7	−	1.79607e7i	−0.418548	−	0.724946i	0.577246	−	0.816570i	$-0.304127\pi$
$907$	−1.03696e7	−	1.79607e7i	−0.418548	−	0.724946i	−0.995794	+	0.0916246i	$0.970794\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−2.27546e7	−	3.94121e7i	−0.908390	−	1.57338i	−0.816300	−	0.577628i	$-0.803979\pi$
$911$	−2.27546e7	−	3.94121e7i	−0.908390	−	1.57338i	−0.0920903	−	0.995751i	$-0.529355\pi$
$912$		0			0
$913$	2.54275e6	−	4.40418e6i	0.100955	−	0.174859i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−4.47010e6			−0.175547
$918$		0			0
$919$	1.89012e7			0.738247			0.369123	−	0.929380i	$-0.379658\pi$
$919$	1.89012e7			0.738247			0.369123	+	0.929380i	$0.379658\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	7.63009e6	−	1.32157e7i	0.294799	−	0.510606i
$924$		0			0
$925$	−2.04249e7	−	3.53769e7i	−0.784883	−	1.35946i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.54195e7	+	2.67074e7i	0.586181	+	1.01530i	0.994727	+	0.102558i	$0.0327026\pi$
$929$	1.54195e7	+	2.67074e7i	0.586181	+	1.01530i	−0.408546	+	0.912738i	$0.633964\pi$
$930$		0			0
$931$	1.43614e7	−	2.48747e7i	0.543029	−	0.940554i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−1.71425e7			−0.641277
$936$		0			0
$937$	−5.36296e6			−0.199552			−0.0997758	−	0.995010i	$-0.531813\pi$
$937$	−5.36296e6			−0.199552			−0.0997758	+	0.995010i	$0.531813\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1.88393e7	+	3.26305e7i	−0.693569	+	1.20130i	0.277092	+	0.960843i	$0.410629\pi$
$941$	−1.88393e7	+	3.26305e7i	−0.693569	+	1.20130i	−0.970661	+	0.240453i	$0.922704\pi$
$942$		0			0
$943$	2.80558e7	+	4.85941e7i	1.02741	+	1.77953i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−9.81104e6	−	1.69932e7i	−0.355501	−	0.615745i	0.631703	−	0.775211i	$-0.282356\pi$
$947$	−9.81104e6	−	1.69932e7i	−0.355501	−	0.615745i	−0.987203	+	0.159466i	$0.949023\pi$
$948$		0			0
$949$	7.90900e6	−	1.36988e7i	0.285073	−	0.493761i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	1.36730e7			0.487676			0.243838	−	0.969816i	$-0.421593\pi$
$953$	1.36730e7			0.487676			0.243838	+	0.969816i	$0.421593\pi$
$954$		0			0
$955$	−4.13450e7			−1.46695
$956$		0			0
$957$		0			0
$958$		0			0
$959$	3.94203e6	−	6.82779e6i	0.138412	−	0.239736i
$960$		0			0
$961$	648584.	+	1.12338e6i	0.0226547	+	0.0392390i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−6.71199e6	−	1.16255e7i	−0.232024	−	0.401877i
$966$		0			0
$967$	−1.81912e7	+	3.15081e7i	−0.625597	+	1.08357i	0.362828	+	0.931856i	$0.381811\pi$
$967$	−1.81912e7	+	3.15081e7i	−0.625597	+	1.08357i	−0.988425	+	0.151710i	$0.951522\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	9.46886e6			0.322292			0.161146	−	0.986931i	$-0.448481\pi$
$971$	9.46886e6			0.322292			0.161146	+	0.986931i	$0.448481\pi$
$972$		0			0
$973$	5.29844e6			0.179418
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1.79944e7	+	3.11673e7i	−0.603117	+	1.04463i	0.389229	+	0.921141i	$0.372742\pi$
$977$	−1.79944e7	+	3.11673e7i	−0.603117	+	1.04463i	−0.992346	+	0.123489i	$0.960592\pi$
$978$		0			0
$979$	3.87634e6	+	6.71401e6i	0.129260	+	0.223885i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	1.30278e7	+	2.25648e7i	0.430019	+	0.744815i	0.996874	−	0.0790021i	$-0.0251734\pi$
$983$	1.30278e7	+	2.25648e7i	0.430019	+	0.744815i	−0.566855	+	0.823818i	$0.691840\pi$
$984$		0			0
$985$	2.88140e7	−	4.99073e7i	0.946264	−	1.63898i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	7.22222e7			2.34790
$990$		0			0
$991$	1.92232e7			0.621788			0.310894	−	0.950445i	$-0.399372\pi$
$991$	1.92232e7			0.621788			0.310894	+	0.950445i	$0.399372\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	2.84780e7	−	4.93254e7i	0.911911	−	1.57948i
$996$		0			0
$997$	−1.46644e7	−	2.53994e7i	−0.467224	−	0.809256i	0.532075	−	0.846697i	$-0.321412\pi$
$997$	−1.46644e7	−	2.53994e7i	−0.467224	−	0.809256i	−0.999299	+	0.0374417i	$0.988079\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.6.e.e.109.1		4
3.2	odd	2	inner	324.6.e.e.109.2		4
9.2	odd	6	inner	324.6.e.e.217.2		4
9.4	even	3		108.6.a.d.1.2	yes	2
9.5	odd	6		108.6.a.d.1.1	✓	2
9.7	even	3	inner	324.6.e.e.217.1		4
36.23	even	6		432.6.a.p.1.1		2
36.31	odd	6		432.6.a.p.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.6.a.d.1.1	✓	2	9.5	odd	6
108.6.a.d.1.2	yes	2	9.4	even	3
324.6.e.e.109.1		4	1.1	even	1	trivial
324.6.e.e.109.2		4	3.2	odd	2	inner
324.6.e.e.217.1		4	9.7	even	3	inner
324.6.e.e.217.2		4	9.2	odd	6	inner
432.6.a.p.1.1		2	36.23	even	6
432.6.a.p.1.2		2	36.31	odd	6

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	324.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-44.0908 + 76.3675i) q^{5} +(-14.5000 - 25.1147i) q^{7} +O(q^{10})\)	\(q+(-44.0908 + 76.3675i) q^{5} +(-14.5000 - 25.1147i) q^{7} +(-44.0908 - 76.3675i) q^{11} +(-164.500 + 284.922i) q^{13} -2204.54 q^{17} +1799.00 q^{19} +(-1807.72 + 3131.07i) q^{23} +(-2325.50 - 4027.88i) q^{25} +(-705.453 - 1221.88i) q^{29} +(-2614.00 + 4527.58i) q^{31} +2557.27 q^{35} +8783.00 q^{37} +(7759.98 - 13440.7i) q^{41} +(-9988.00 - 17299.7i) q^{43} +(5423.17 + 9393.21i) q^{47} +(7983.00 - 13827.0i) q^{49} +29452.7 q^{53} +7776.00 q^{55} +(-2865.90 + 4963.89i) q^{59} +(534.500 + 925.781i) q^{61} +(-14505.9 - 25124.9i) q^{65} +(31038.5 - 53760.3i) q^{67} -46383.5 q^{71} -48079.0 q^{73} +(-1278.63 + 2214.66i) q^{77} +(-24989.5 - 43283.1i) q^{79} +(28835.4 + 49944.4i) q^{83} +(97200.0 - 168355. i) q^{85} -87917.1 q^{89} +9541.00 q^{91} +(-79319.4 + 137385. i) q^{95} +(-6458.50 - 11186.5i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 58 q^{7}+O(q^{10}) \) 4 * q - 58 * q^7	\( 4 q - 58 q^{7} - 658 q^{13} + 7196 q^{19} - 9302 q^{25} - 10456 q^{31} + 35132 q^{37} - 39952 q^{43} + 31932 q^{49} + 31104 q^{55} + 2138 q^{61} + 124154 q^{67} - 192316 q^{73} - 99958 q^{79} + 388800 q^{85} + 38164 q^{91} - 25834 q^{97}+O(q^{100}) \) 4 * q - 58 * q^7 - 658 * q^13 + 7196 * q^19 - 9302 * q^25 - 10456 * q^31 + 35132 * q^37 - 39952 * q^43 + 31932 * q^49 + 31104 * q^55 + 2138 * q^61 + 124154 * q^67 - 192316 * q^73 - 99958 * q^79 + 388800 * q^85 + 38164 * q^91 - 25834 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more