LMFDB - Embedded newform 576.6.k.a.145.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,6,Mod(145,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("576.145");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	576.k (of order $4$, 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:	$92.3810802123$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 8 x^{17} - 3867 x^{16} + 20528 x^{15} + 5993890 x^{14} - 12125584 x^{13} + \cdots + 93\!\cdots\!16 $ x^18 - 8x^17 - 3867x^16 + 20528x^15 + 5993890x^14 - 12125584x^13 - 4820441926x^12 - 8265606272x^11 + 2160047956949x^10 + 11904535942584x^9 - 516092236107743x^8 - 4797958060187376x^7 + 51973134198079192x^6 + 743014063051675680x^5 - 75719701558176624x^4 - 27807708117417695360x^3 - 50069849523887397376x^2 + 334053680451369438208*x + 937540826009984214016
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 2^{72}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			145.7
Root			$-13.6637 - 1.00000i$ of defining polynomial
Character	$\chi$	$=$	576.145
Dual form			576.6.k.a.433.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(28.3274 - 28.3274i) q^{5} +55.5494i q^{7} +O(q^{10})$	$q+(28.3274 - 28.3274i) q^{5} +55.5494i q^{7} +(-137.411 + 137.411i) q^{11} +(-574.133 - 574.133i) q^{13} -320.902 q^{17} +(858.068 + 858.068i) q^{19} -825.465i q^{23} +1520.12i q^{25} +(-333.912 - 333.912i) q^{29} +8904.00 q^{31} +(1573.57 + 1573.57i) q^{35} +(-3878.91 + 3878.91i) q^{37} +6546.26i q^{41} +(5620.33 - 5620.33i) q^{43} -3122.27 q^{47} +13721.3 q^{49} +(-18167.5 + 18167.5i) q^{53} +7784.97i q^{55} +(-5538.91 + 5538.91i) q^{59} +(-701.393 - 701.393i) q^{61} -32527.4 q^{65} +(14453.4 + 14453.4i) q^{67} -23608.4i q^{71} -57755.7i q^{73} +(-7633.07 - 7633.07i) q^{77} +57871.5 q^{79} +(78955.3 + 78955.3i) q^{83} +(-9090.32 + 9090.32i) q^{85} -25908.3i q^{89} +(31892.7 - 31892.7i) q^{91} +48613.7 q^{95} +39197.0 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 2 q^{5}+O(q^{10}) $ 18 * q + 2 * q^5	$ 18 q + 2 q^{5} - 606 q^{11} - 2 q^{13} + 4 q^{17} + 2362 q^{19} - 4070 q^{29} + 11536 q^{31} + 8636 q^{35} - 10650 q^{37} + 15382 q^{43} + 44176 q^{47} - 14410 q^{49} - 24726 q^{53} - 29734 q^{59} - 48082 q^{61} - 27684 q^{65} + 75210 q^{67} - 41060 q^{77} + 52864 q^{79} + 227838 q^{83} - 138652 q^{85} + 231164 q^{91} - 250380 q^{95} - 4 q^{97}+O(q^{100}) $ 18 * q + 2 * q^5 - 606 * q^11 - 2 * q^13 + 4 * q^17 + 2362 * q^19 - 4070 * q^29 + 11536 * q^31 + 8636 * q^35 - 10650 * q^37 + 15382 * q^43 + 44176 * q^47 - 14410 * q^49 - 24726 * q^53 - 29734 * q^59 - 48082 * q^61 - 27684 * q^65 + 75210 * q^67 - 41060 * q^77 + 52864 * q^79 + 227838 * q^83 - 138652 * q^85 + 231164 * q^91 - 250380 * q^95 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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
$5$	28.3274	−	28.3274i	0.506736	−	0.506736i	−0.406787	−	0.913523i	$-0.633351\pi$
$5$	28.3274	−	28.3274i	0.506736	−	0.506736i	0.913523	+	0.406787i	$0.133351\pi$
$6$		0			0
$7$			55.5494i			0.428483i	0.976781	+	0.214242i	$0.0687280\pi$
$7$			55.5494i			0.428483i	−0.976781	+	0.214242i	$0.931272\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−137.411	+	137.411i	−0.342404	+	0.342404i	−0.857270	−	0.514867i	$-0.827841\pi$
$11$	−137.411	+	137.411i	−0.342404	+	0.342404i	0.514867	+	0.857270i	$0.327841\pi$
$12$		0			0
$13$	−574.133	−	574.133i	−0.942225	−	0.942225i	0.0561952	−	0.998420i	$-0.482103\pi$
$13$	−574.133	−	574.133i	−0.942225	−	0.942225i	−0.998420	+	0.0561952i	$0.982103\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−320.902			−0.269308			−0.134654	−	0.990893i	$-0.542992\pi$
$17$	−320.902			−0.269308			−0.134654	+	0.990893i	$0.542992\pi$
$18$		0			0
$19$	858.068	+	858.068i	0.545303	+	0.545303i	0.925079	−	0.379776i	$-0.123999\pi$
$19$	858.068	+	858.068i	0.545303	+	0.545303i	−0.379776	+	0.925079i	$0.623999\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		−	825.465i		−	0.325371i	−0.986678	−	0.162686i	$-0.947984\pi$
$23$		−	825.465i		−	0.325371i	0.986678	−	0.162686i	$-0.0520156\pi$
$24$		0			0
$25$			1520.12i			0.486438i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−333.912	−	333.912i	−0.0737288	−	0.0737288i	0.669281	−	0.743010i	$-0.266602\pi$
$29$	−333.912	−	333.912i	−0.0737288	−	0.0737288i	−0.743010	+	0.669281i	$0.766602\pi$
$30$		0			0
$31$	8904.00			1.66411			0.832053	−	0.554697i	$-0.187166\pi$
$31$	8904.00			1.66411			0.832053	+	0.554697i	$0.187166\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1573.57	+	1573.57i	0.217128	+	0.217128i
$36$		0			0
$37$	−3878.91	+	3878.91i	−0.465806	+	0.465806i	−0.900553	−	0.434746i	$-0.856838\pi$
$37$	−3878.91	+	3878.91i	−0.465806	+	0.465806i	0.434746	+	0.900553i	$0.356838\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$			6546.26i			0.608182i	0.952643	+	0.304091i	$0.0983527\pi$
$41$			6546.26i			0.608182i	−0.952643	+	0.304091i	$0.901647\pi$
$42$		0			0
$43$	5620.33	−	5620.33i	0.463544	−	0.463544i	−0.436272	−	0.899815i	$-0.643701\pi$
$43$	5620.33	−	5620.33i	0.463544	−	0.463544i	0.899815	+	0.436272i	$0.143701\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3122.27			−0.206170			−0.103085	−	0.994673i	$-0.532871\pi$
$47$	−3122.27			−0.206170			−0.103085	+	0.994673i	$0.532871\pi$
$48$		0			0
$49$	13721.3			0.816402
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−18167.5	+	18167.5i	−0.888395	+	0.888395i	−0.994369	−	0.105974i	$-0.966204\pi$
$53$	−18167.5	+	18167.5i	−0.888395	+	0.888395i	0.105974	+	0.994369i	$0.466204\pi$
$54$		0			0
$55$			7784.97i			0.347016i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−5538.91	+	5538.91i	−0.207154	+	0.207154i	−0.803057	−	0.595902i	$-0.796794\pi$
$59$	−5538.91	+	5538.91i	−0.207154	+	0.207154i	0.595902	+	0.803057i	$0.296794\pi$
$60$		0			0
$61$	−701.393	−	701.393i	−0.0241344	−	0.0241344i	0.694937	−	0.719071i	$-0.255432\pi$
$61$	−701.393	−	701.393i	−0.0241344	−	0.0241344i	−0.719071	+	0.694937i	$0.755432\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−32527.4			−0.954918
$66$		0			0
$67$	14453.4	+	14453.4i	0.393354	+	0.393354i	0.875881	−	0.482527i	$-0.160281\pi$
$67$	14453.4	+	14453.4i	0.393354	+	0.393354i	−0.482527	+	0.875881i	$0.660281\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	23608.4i		−	0.555802i	−0.960610	−	0.277901i	$-0.910361\pi$
$71$		−	23608.4i		−	0.555802i	0.960610	−	0.277901i	$-0.0896388\pi$
$72$		0			0
$73$		−	57755.7i		−	1.26849i	−0.773131	−	0.634246i	$-0.781311\pi$
$73$		−	57755.7i		−	1.26849i	0.773131	−	0.634246i	$-0.218689\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−7633.07	−	7633.07i	−0.146714	−	0.146714i
$78$		0			0
$79$	57871.5			1.04327			0.521635	−	0.853169i	$-0.325322\pi$
$79$	57871.5			1.04327			0.521635	+	0.853169i	$0.325322\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	78955.3	+	78955.3i	1.25802	+	1.25802i	0.952039	+	0.305976i	$0.0989827\pi$
$83$	78955.3	+	78955.3i	1.25802	+	1.25802i	0.305976	+	0.952039i	$0.401017\pi$
$84$		0			0
$85$	−9090.32	+	9090.32i	−0.136468	+	0.136468i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	25908.3i		−	0.346708i	−0.984860	−	0.173354i	$-0.944540\pi$
$89$		−	25908.3i		−	0.346708i	0.984860	−	0.173354i	$-0.0554605\pi$
$90$		0			0
$91$	31892.7	−	31892.7i	0.403728	−	0.403728i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	48613.7			0.552649
$96$		0			0
$97$	39197.0			0.422983			0.211492	−	0.977380i	$-0.432168\pi$
$97$	39197.0			0.422983			0.211492	+	0.977380i	$0.432168\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	99841.8	−	99841.8i	0.973887	−	0.973887i	−0.0257802	−	0.999668i	$-0.508207\pi$
$101$	99841.8	−	99841.8i	0.973887	−	0.973887i	0.999668	+	0.0257802i	$0.00820701\pi$
$102$		0			0
$103$			154754.i			1.43731i	0.695368	+	0.718654i	$0.255241\pi$
$103$			154754.i			1.43731i	−0.695368	+	0.718654i	$0.744759\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−73018.1	+	73018.1i	−0.616554	+	0.616554i	−0.944646	−	0.328092i	$-0.893594\pi$
$107$	−73018.1	+	73018.1i	−0.616554	+	0.616554i	0.328092	+	0.944646i	$0.393594\pi$
$108$		0			0
$109$	−135654.	−	135654.i	−1.09362	−	1.09362i	−0.995139	−	0.0984792i	$-0.968602\pi$
$109$	−135654.	−	135654.i	−1.09362	−	1.09362i	−0.0984792	−	0.995139i	$-0.531398\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	74503.6			0.548885			0.274442	−	0.961604i	$-0.411507\pi$
$113$	74503.6			0.548885			0.274442	+	0.961604i	$0.411507\pi$
$114$		0			0
$115$	−23383.3	−	23383.3i	−0.164877	−	0.164877i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		−	17825.9i		−	0.115394i
$120$		0			0
$121$			123288.i			0.765519i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	131584.	+	131584.i	0.753231	+	0.753231i
$126$		0			0
$127$	162314.			0.892988			0.446494	−	0.894787i	$-0.352672\pi$
$127$	162314.			0.892988			0.446494	+	0.894787i	$0.352672\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	142911.	+	142911.i	0.727589	+	0.727589i	0.970139	−	0.242550i	$-0.0779839\pi$
$131$	142911.	+	142911.i	0.727589	+	0.727589i	−0.242550	+	0.970139i	$0.577984\pi$
$132$		0			0
$133$	−47665.2	+	47665.2i	−0.233653	+	0.233653i
$134$		0			0
$135$		0			0
$136$		0			0
$137$			286655.i			1.30484i	0.757856	+	0.652422i	$0.226247\pi$
$137$			286655.i			1.30484i	−0.757856	+	0.652422i	$0.773753\pi$
$138$		0			0
$139$	−56704.6	+	56704.6i	−0.248932	+	0.248932i	−0.820532	−	0.571600i	$-0.806323\pi$
$139$	−56704.6	+	56704.6i	−0.248932	+	0.248932i	0.571600	+	0.820532i	$0.306323\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	157784.			0.645242
$144$		0			0
$145$	−18917.7			−0.0747221
$146$		0			0
$147$		0			0
$148$		0			0
$149$	329942.	−	329942.i	1.21751	−	1.21751i	0.249006	−	0.968502i	$-0.419896\pi$
$149$	329942.	−	329942.i	1.21751	−	1.21751i	0.968502	−	0.249006i	$-0.0801037\pi$
$150$		0			0
$151$			200506.i			0.715625i	0.933794	+	0.357812i	$0.116477\pi$
$151$			200506.i			0.715625i	−0.933794	+	0.357812i	$0.883523\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	252227.	−	252227.i	0.843262	−	0.843262i
$156$		0			0
$157$	236335.	+	236335.i	0.765206	+	0.765206i	0.977258	−	0.212053i	$-0.0680148\pi$
$157$	236335.	+	236335.i	0.765206	+	0.765206i	−0.212053	+	0.977258i	$0.568015\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	45854.0			0.139416
$162$		0			0
$163$	−137842.	−	137842.i	−0.406363	−	0.406363i	0.474105	−	0.880468i	$-0.342772\pi$
$163$	−137842.	−	137842.i	−0.406363	−	0.406363i	−0.880468	+	0.474105i	$0.842772\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			324357.i			0.899978i	0.893034	+	0.449989i	$0.148572\pi$
$167$			324357.i			0.899978i	−0.893034	+	0.449989i	$0.851428\pi$
$168$		0			0
$169$			287965.i			0.775574i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	376606.	+	376606.i	0.956691	+	0.956691i	0.999100	−	0.0424095i	$-0.0135034\pi$
$173$	376606.	+	376606.i	0.956691	+	0.956691i	−0.0424095	+	0.999100i	$0.513503\pi$
$174$		0			0
$175$	−84441.6			−0.208430
$176$		0			0
$177$		0			0
$178$		0			0
$179$	166781.	+	166781.i	0.389058	+	0.389058i	0.874351	−	0.485293i	$-0.161287\pi$
$179$	166781.	+	166781.i	0.389058	+	0.389058i	−0.485293	+	0.874351i	$0.661287\pi$
$180$		0			0
$181$	85411.9	−	85411.9i	0.193786	−	0.193786i	−0.603544	−	0.797330i	$-0.706245\pi$
$181$	85411.9	−	85411.9i	0.193786	−	0.193786i	0.797330	+	0.603544i	$0.206245\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$			219759.i			0.472082i
$186$		0			0
$187$	44095.3	−	44095.3i	0.0922122	−	0.0922122i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	804534.			1.59574			0.797868	−	0.602832i	$-0.205961\pi$
$191$	804534.			1.59574			0.797868	+	0.602832i	$0.205961\pi$
$192$		0			0
$193$	247122.			0.477550			0.238775	−	0.971075i	$-0.423254\pi$
$193$	247122.			0.477550			0.238775	+	0.971075i	$0.423254\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−295923.	+	295923.i	−0.543267	+	0.543267i	−0.924485	−	0.381218i	$-0.875505\pi$
$197$	−295923.	+	295923.i	−0.543267	+	0.543267i	0.381218	+	0.924485i	$0.375505\pi$
$198$		0			0
$199$			252267.i			0.451572i	0.974177	+	0.225786i	$0.0724950\pi$
$199$			252267.i			0.451572i	−0.974177	+	0.225786i	$0.927505\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	18548.6	−	18548.6i	0.0315916	−	0.0315916i
$204$		0			0
$205$	185438.	+	185438.i	0.308188	+	0.308188i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−235815.			−0.373428
$210$		0			0
$211$	−517797.	−	517797.i	−0.800670	−	0.800670i	0.182530	−	0.983200i	$-0.441571\pi$
$211$	−517797.	−	517797.i	−0.800670	−	0.800670i	−0.983200	+	0.182530i	$0.941571\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		−	318419.i		−	0.469788i
$216$		0			0
$217$			494611.i			0.713041i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	184241.	+	184241.i	0.253749	+	0.253749i
$222$		0			0
$223$	1.09445e6			1.47379			0.736895	−	0.676007i	$-0.236291\pi$
$223$	1.09445e6			1.47379			0.736895	+	0.676007i	$0.236291\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−775097.	−	775097.i	−0.998370	−	0.998370i	0.00162838	−	0.999999i	$-0.499482\pi$
$227$	−775097.	−	775097.i	−0.998370	−	0.998370i	−0.999999	+	0.00162838i	$0.999482\pi$
$228$		0			0
$229$	951518.	−	951518.i	1.19903	−	1.19903i	0.224567	−	0.974459i	$-0.427903\pi$
$229$	951518.	−	951518.i	1.19903	−	1.19903i	0.974459	−	0.224567i	$-0.0720968\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			652629.i			0.787547i	0.919207	+	0.393774i	$0.128831\pi$
$233$			652629.i			0.787547i	−0.919207	+	0.393774i	$0.871169\pi$
$234$		0			0
$235$	−88445.9	+	88445.9i	−0.104474	+	0.104474i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−99764.8			−0.112975			−0.0564875	−	0.998403i	$-0.517990\pi$
$239$	−99764.8			−0.112975			−0.0564875	+	0.998403i	$0.517990\pi$
$240$		0			0
$241$	274915.			0.304899			0.152449	−	0.988311i	$-0.451284\pi$
$241$	274915.			0.304899			0.152449	+	0.988311i	$0.451284\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	388688.	−	388688.i	0.413700	−	0.413700i
$246$		0			0
$247$		−	985292.i		−	1.02760i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−509257.	+	509257.i	−0.510214	+	0.510214i	−0.914592	−	0.404378i	$-0.867488\pi$
$251$	−509257.	+	509257.i	−0.510214	+	0.510214i	0.404378	+	0.914592i	$0.367488\pi$
$252$		0			0
$253$	113428.	+	113428.i	0.111408	+	0.111408i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1.81164e6			1.71096			0.855480	−	0.517835i	$-0.173262\pi$
$257$	1.81164e6			1.71096			0.855480	+	0.517835i	$0.173262\pi$
$258$		0			0
$259$	−215471.	−	215471.i	−0.199590	−	0.199590i
$260$		0			0
$261$		0			0
$262$		0			0
$263$			1.76822e6i			1.57633i	0.615465	+	0.788164i	$0.288968\pi$
$263$			1.76822e6i			1.57633i	−0.615465	+	0.788164i	$0.711032\pi$
$264$		0			0
$265$			1.02928e6i			0.900363i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−864877.	−	864877.i	−0.728742	−	0.728742i	0.241627	−	0.970369i	$-0.422319\pi$
$269$	−864877.	−	864877.i	−0.728742	−	0.728742i	−0.970369	+	0.241627i	$0.922319\pi$
$270$		0			0
$271$	597062.			0.493851			0.246926	−	0.969034i	$-0.420580\pi$
$271$	597062.			0.493851			0.246926	+	0.969034i	$0.420580\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−208880.	−	208880.i	−0.166558	−	0.166558i
$276$		0			0
$277$	1.20879e6	−	1.20879e6i	0.946564	−	0.946564i	−0.0520791	−	0.998643i	$-0.516585\pi$
$277$	1.20879e6	−	1.20879e6i	0.946564	−	0.946564i	0.998643	+	0.0520791i	$0.0165848\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	174043.i		−	0.131489i	−0.997836	−	0.0657446i	$-0.979058\pi$
$281$		−	174043.i		−	0.131489i	0.997836	−	0.0657446i	$-0.0209423\pi$
$282$		0			0
$283$	−483416.	+	483416.i	−0.358802	+	0.358802i	−0.863371	−	0.504569i	$-0.831651\pi$
$283$	−483416.	+	483416.i	−0.358802	+	0.358802i	0.504569	+	0.863371i	$0.331651\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−363640.			−0.260596
$288$		0			0
$289$	−1.31688e6			−0.927473
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−146105.	+	146105.i	−0.0994252	+	0.0994252i	−0.755070	−	0.655644i	$-0.772397\pi$
$293$	−146105.	+	146105.i	−0.0994252	+	0.0994252i	0.655644	+	0.755070i	$0.272397\pi$
$294$		0			0
$295$			313806.i			0.209945i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−473927.	+	473927.i	−0.306573	+	0.306573i
$300$		0			0
$301$	312206.	+	312206.i	0.198621	+	0.198621i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−39737.3			−0.0244596
$306$		0			0
$307$	887303.	+	887303.i	0.537311	+	0.537311i	0.922738	−	0.385427i	$-0.125946\pi$
$307$	887303.	+	887303.i	0.537311	+	0.537311i	−0.385427	+	0.922738i	$0.625946\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$			273571.i			0.160387i	0.996779	+	0.0801935i	$0.0255538\pi$
$311$			273571.i			0.160387i	−0.996779	+	0.0801935i	$0.974446\pi$
$312$		0			0
$313$			1.86824e6i			1.07788i	0.842343	+	0.538942i	$0.181176\pi$
$313$			1.86824e6i			1.07788i	−0.842343	+	0.538942i	$0.818824\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−202652.	−	202652.i	−0.113267	−	0.113267i	0.648202	−	0.761469i	$-0.275521\pi$
$317$	−202652.	−	202652.i	−0.113267	−	0.113267i	−0.761469	+	0.648202i	$0.775521\pi$
$318$		0			0
$319$	91766.1			0.0504900
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−275356.	−	275356.i	−0.146855	−	0.146855i
$324$		0			0
$325$	872750.	−	872750.i	0.458333	−	0.458333i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		−	173440.i		−	0.0883406i
$330$		0			0
$331$	−895762.	+	895762.i	−0.449389	+	0.449389i	−0.895151	−	0.445762i	$-0.852933\pi$
$331$	−895762.	+	895762.i	−0.449389	+	0.449389i	0.445762	+	0.895151i	$0.352933\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	818854.			0.398653
$336$		0			0
$337$	−2.99915e6			−1.43855			−0.719274	−	0.694727i	$-0.755525\pi$
$337$	−2.99915e6			−1.43855			−0.719274	+	0.694727i	$0.755525\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−1.22350e6	+	1.22350e6i	−0.569796	+	0.569796i
$342$		0			0
$343$			1.69583e6i			0.778298i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	1.04197e6	−	1.04197e6i	0.464548	−	0.464548i	−0.435595	−	0.900143i	$-0.643462\pi$
$347$	1.04197e6	−	1.04197e6i	0.464548	−	0.464548i	0.900143	+	0.435595i	$0.143462\pi$
$348$		0			0
$349$	−2.07045e6	−	2.07045e6i	−0.909918	−	0.909918i	0.0863472	−	0.996265i	$-0.472481\pi$
$349$	−2.07045e6	−	2.07045e6i	−0.909918	−	0.909918i	−0.996265	+	0.0863472i	$0.972481\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−1.99154e6			−0.850655			−0.425327	−	0.905040i	$-0.639841\pi$
$353$	−1.99154e6			−0.850655			−0.425327	+	0.905040i	$0.639841\pi$
$354$		0			0
$355$	−668764.	−	668764.i	−0.281645	−	0.281645i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	603261.i		−	0.247041i	−0.992342	−	0.123520i	$-0.960582\pi$
$359$		−	603261.i		−	0.247041i	0.992342	−	0.123520i	$-0.0394184\pi$
$360$		0			0
$361$		−	1.00354e6i		−	0.405289i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−1.63607e6	−	1.63607e6i	−0.642791	−	0.642791i
$366$		0			0
$367$	946062.			0.366652			0.183326	−	0.983052i	$-0.441314\pi$
$367$	946062.			0.366652			0.183326	+	0.983052i	$0.441314\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−1.00919e6	−	1.00919e6i	−0.380662	−	0.380662i
$372$		0			0
$373$	21095.1	−	21095.1i	0.00785070	−	0.00785070i	−0.703171	−	0.711021i	$-0.748233\pi$
$373$	21095.1	−	21095.1i	0.00785070	−	0.00785070i	0.711021	+	0.703171i	$0.248233\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			383420.i			0.138938i
$378$		0			0
$379$	−576840.	+	576840.i	−0.206280	+	0.206280i	−0.802684	−	0.596404i	$-0.796596\pi$
$379$	−576840.	+	576840.i	−0.206280	+	0.206280i	0.596404	+	0.802684i	$0.296596\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	3.61983e6			1.26093			0.630466	−	0.776217i	$-0.282864\pi$
$383$	3.61983e6			1.26093			0.630466	+	0.776217i	$0.282864\pi$
$384$		0			0
$385$	−432450.			−0.148691
$386$		0			0
$387$		0			0
$388$		0			0
$389$	2.88292e6	−	2.88292e6i	0.965958	−	0.965958i	−0.0334816	−	0.999439i	$-0.510660\pi$
$389$	2.88292e6	−	2.88292e6i	0.965958	−	0.965958i	0.999439	+	0.0334816i	$0.0106595\pi$
$390$		0			0
$391$			264893.i			0.0876252i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	1.63935e6	−	1.63935e6i	0.528662	−	0.528662i
$396$		0			0
$397$	−2.91477e6	−	2.91477e6i	−0.928172	−	0.928172i	0.0694156	−	0.997588i	$-0.477887\pi$
$397$	−2.91477e6	−	2.91477e6i	−0.928172	−	0.928172i	−0.997588	+	0.0694156i	$0.977887\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−2.02162e6			−0.627824			−0.313912	−	0.949452i	$-0.601640\pi$
$401$	−2.02162e6			−0.627824			−0.313912	+	0.949452i	$0.601640\pi$
$402$		0			0
$403$	−5.11208e6	−	5.11208e6i	−1.56796	−	1.56796i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	1.06601e6i		−	0.318988i
$408$		0			0
$409$			3.30579e6i			0.977162i	0.872519	+	0.488581i	$0.162485\pi$
$409$			3.30579e6i			0.977162i	−0.872519	+	0.488581i	$0.837515\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−307683.	−	307683.i	−0.0887622	−	0.0887622i
$414$		0			0
$415$	4.47319e6			1.27496
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−1.85951e6	−	1.85951e6i	−0.517445	−	0.517445i	0.399353	−	0.916797i	$-0.369235\pi$
$419$	−1.85951e6	−	1.85951e6i	−0.517445	−	0.517445i	−0.916797	+	0.399353i	$0.869235\pi$
$420$		0			0
$421$	1.25469e6	−	1.25469e6i	0.345010	−	0.345010i	−0.513237	−	0.858247i	$-0.671554\pi$
$421$	1.25469e6	−	1.25469e6i	0.345010	−	0.345010i	0.858247	+	0.513237i	$0.171554\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		−	487809.i		−	0.131002i
$426$		0			0
$427$	38961.9	−	38961.9i	0.0103412	−	0.0103412i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−129266.			−0.0335191			−0.0167596	−	0.999860i	$-0.505335\pi$
$431$	−129266.			−0.0335191			−0.0167596	+	0.999860i	$0.505335\pi$
$432$		0			0
$433$	−6.66800e6			−1.70913			−0.854567	−	0.519342i	$-0.826177\pi$
$433$	−6.66800e6			−1.70913			−0.854567	+	0.519342i	$0.826177\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	708305.	−	708305.i	0.177426	−	0.177426i
$438$		0			0
$439$		−	378688.i		−	0.0937823i	−0.998900	−	0.0468911i	$-0.985069\pi$
$439$		−	378688.i		−	0.0937823i	0.998900	−	0.0468911i	$-0.0149314\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−4.52584e6	+	4.52584e6i	−1.09570	+	1.09570i	−0.100788	+	0.994908i	$0.532136\pi$
$443$	−4.52584e6	+	4.52584e6i	−1.09570	+	1.09570i	−0.994908	+	0.100788i	$0.967864\pi$
$444$		0			0
$445$	−733915.	−	733915.i	−0.175689	−	0.175689i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−6.64190e6			−1.55481			−0.777404	−	0.629002i	$-0.783464\pi$
$449$	−6.64190e6			−1.55481			−0.777404	+	0.629002i	$0.783464\pi$
$450$		0			0
$451$	−899525.	−	899525.i	−0.208244	−	0.208244i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		−	1.80688e6i		−	0.409166i
$456$		0			0
$457$			1.35265e6i			0.302966i	0.988460	+	0.151483i	$0.0484048\pi$
$457$			1.35265e6i			0.302966i	−0.988460	+	0.151483i	$0.951595\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−2.17241e6	−	2.17241e6i	−0.476090	−	0.476090i	0.427789	−	0.903879i	$-0.359293\pi$
$461$	−2.17241e6	−	2.17241e6i	−0.476090	−	0.476090i	−0.903879	+	0.427789i	$0.859293\pi$
$462$		0			0
$463$	484327.			0.104999			0.0524996	−	0.998621i	$-0.483281\pi$
$463$	484327.			0.104999			0.0524996	+	0.998621i	$0.483281\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−4.84130e6	−	4.84130e6i	−1.02724	−	1.02724i	−0.999619	−	0.0276165i	$-0.991208\pi$
$467$	−4.84130e6	−	4.84130e6i	−1.02724	−	1.02724i	−0.0276165	−	0.999619i	$-0.508792\pi$
$468$		0			0
$469$	−802877.	+	802877.i	−0.168545	+	0.168545i
$470$		0			0
$471$		0			0
$472$		0			0
$473$			1.54458e6i			0.317438i
$474$		0			0
$475$	−1.30436e6	+	1.30436e6i	−0.265256	+	0.265256i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−8.10148e6			−1.61334			−0.806670	−	0.591002i	$-0.798732\pi$
$479$	−8.10148e6			−1.61334			−0.806670	+	0.591002i	$0.798732\pi$
$480$		0			0
$481$	4.45402e6			0.877788
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1.11035e6	−	1.11035e6i	0.214341	−	0.214341i
$486$		0			0
$487$			6.33460e6i			1.21031i	0.796108	+	0.605155i	$0.206889\pi$
$487$			6.33460e6i			1.21031i	−0.796108	+	0.605155i	$0.793111\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	662865.	−	662865.i	0.124086	−	0.124086i	−0.642337	−	0.766422i	$-0.722035\pi$
$491$	662865.	−	662865.i	0.124086	−	0.124086i	0.766422	+	0.642337i	$0.222035\pi$
$492$		0			0
$493$	107153.	+	107153.i	0.0198558	+	0.0198558i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.31143e6			0.238152
$498$		0			0
$499$	−5.01189e6	−	5.01189e6i	−0.901052	−	0.901052i	0.0944754	−	0.995527i	$-0.469883\pi$
$499$	−5.01189e6	−	5.01189e6i	−0.901052	−	0.901052i	−0.995527	+	0.0944754i	$0.969883\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			752594.i			0.132630i	0.997799	+	0.0663149i	$0.0211242\pi$
$503$			752594.i			0.132630i	−0.997799	+	0.0663149i	$0.978876\pi$
$504$		0			0
$505$		−	5.65651e6i		−	0.987007i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	649015.	+	649015.i	0.111035	+	0.111035i	0.760442	−	0.649406i	$-0.224983\pi$
$509$	649015.	+	649015.i	0.111035	+	0.111035i	−0.649406	+	0.760442i	$0.724983\pi$
$510$		0			0
$511$	3.20829e6			0.543528
$512$		0			0
$513$		0			0
$514$		0			0
$515$	4.38379e6	+	4.38379e6i	0.728335	+	0.728335i
$516$		0			0
$517$	429033.	−	429033.i	0.0705935	−	0.0705935i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			5.88783e6i			0.950300i	0.879905	+	0.475150i	$0.157606\pi$
$521$			5.88783e6i			0.950300i	−0.879905	+	0.475150i	$0.842394\pi$
$522$		0			0
$523$	6.82221e6	−	6.82221e6i	1.09061	−	1.09061i	0.0951505	−	0.995463i	$-0.469667\pi$
$523$	6.82221e6	−	6.82221e6i	1.09061	−	1.09061i	0.995463	−	0.0951505i	$-0.0303332\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.85731e6			−0.448158
$528$		0			0
$529$	5.75495e6			0.894134
$530$		0			0
$531$		0			0
$532$		0			0
$533$	3.75842e6	−	3.75842e6i	0.573044	−	0.573044i
$534$		0			0
$535$			4.13683e6i			0.624860i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−1.88545e6	+	1.88545e6i	−0.279539	+	0.279539i
$540$		0			0
$541$	1.05152e6	+	1.05152e6i	0.154463	+	0.154463i	0.780108	−	0.625645i	$-0.215164\pi$
$541$	1.05152e6	+	1.05152e6i	0.154463	+	0.154463i	−0.625645	+	0.780108i	$0.715164\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−7.68544e6			−1.10835
$546$		0			0
$547$	−210027.	−	210027.i	−0.0300128	−	0.0300128i	0.691941	−	0.721954i	$-0.256756\pi$
$547$	−210027.	−	210027.i	−0.0300128	−	0.0300128i	−0.721954	+	0.691941i	$0.756756\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		−	573039.i		−	0.0804091i
$552$		0			0
$553$			3.21472e6i			0.447024i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	644791.	+	644791.i	0.0880604	+	0.0880604i	0.749765	−	0.661704i	$-0.230167\pi$
$557$	644791.	+	644791.i	0.0880604	+	0.0880604i	−0.661704	+	0.749765i	$0.730167\pi$
$558$		0			0
$559$	−6.45364e6			−0.873524
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−1.51267e6	−	1.51267e6i	−0.201128	−	0.201128i	0.599355	−	0.800483i	$-0.295424\pi$
$563$	−1.51267e6	−	1.51267e6i	−0.201128	−	0.201128i	−0.800483	+	0.599355i	$0.795424\pi$
$564$		0			0
$565$	2.11049e6	−	2.11049e6i	0.278140	−	0.278140i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	1.27829e7i		−	1.65520i	−0.561321	−	0.827598i	$-0.689707\pi$
$569$		−	1.27829e7i		−	1.65520i	0.561321	−	0.827598i	$-0.310293\pi$
$570$		0			0
$571$	−4.54358e6	+	4.54358e6i	−0.583187	+	0.583187i	−0.935778	−	0.352591i	$-0.885301\pi$
$571$	−4.54358e6	+	4.54358e6i	−0.583187	+	0.583187i	0.352591	+	0.935778i	$0.385301\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	1.25480e6			0.158273
$576$		0			0
$577$	9.65395e6			1.20716			0.603581	−	0.797302i	$-0.293740\pi$
$577$	9.65395e6			1.20716			0.603581	+	0.797302i	$0.293740\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−4.38591e6	+	4.38591e6i	−0.539039	+	0.539039i
$582$		0			0
$583$		−	4.99282e6i		−	0.608379i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−6.86328e6	+	6.86328e6i	−0.822122	+	0.822122i	−0.986412	−	0.164290i	$-0.947467\pi$
$587$	−6.86328e6	+	6.86328e6i	−0.822122	+	0.822122i	0.164290	+	0.986412i	$0.447467\pi$
$588$		0			0
$589$	7.64024e6	+	7.64024e6i	0.907442	+	0.907442i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−3.03066e6			−0.353916			−0.176958	−	0.984218i	$-0.556626\pi$
$593$	−3.03066e6			−0.353916			−0.176958	+	0.984218i	$0.556626\pi$
$594$		0			0
$595$	−504961.	−	504961.i	−0.0584744	−	0.0584744i
$596$		0			0
$597$		0			0
$598$		0			0
$599$		−	2.59781e6i		−	0.295829i	−0.989000	−	0.147915i	$-0.952744\pi$
$599$		−	2.59781e6i		−	0.295829i	0.989000	−	0.147915i	$-0.0472561\pi$
$600$		0			0
$601$			6.77065e6i			0.764618i	0.924035	+	0.382309i	$0.124871\pi$
$601$			6.77065e6i			0.764618i	−0.924035	+	0.382309i	$0.875129\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	3.49242e6	+	3.49242e6i	0.387916	+	0.387916i
$606$		0			0
$607$	−5.58620e6			−0.615382			−0.307691	−	0.951486i	$-0.599556\pi$
$607$	−5.58620e6			−0.615382			−0.307691	+	0.951486i	$0.599556\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1.79260e6	+	1.79260e6i	0.194259	+	0.194259i
$612$		0			0
$613$	3.01179e6	−	3.01179e6i	0.323723	−	0.323723i	−0.526470	−	0.850193i	$-0.676485\pi$
$613$	3.01179e6	−	3.01179e6i	0.323723	−	0.323723i	0.850193	+	0.526470i	$0.176485\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			1.20095e7i			1.27003i	0.772502	+	0.635013i	$0.219005\pi$
$617$			1.20095e7i			1.27003i	−0.772502	+	0.635013i	$0.780995\pi$
$618$		0			0
$619$	−3.23215e6	+	3.23215e6i	−0.339051	+	0.339051i	−0.856010	−	0.516959i	$-0.827064\pi$
$619$	−3.23215e6	+	3.23215e6i	−0.339051	+	0.339051i	0.516959	+	0.856010i	$0.327064\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	1.43919e6			0.148559
$624$		0			0
$625$	2.70450e6			0.276941
$626$		0			0
$627$		0			0
$628$		0			0
$629$	1.24475e6	−	1.24475e6i	0.125446	−	0.125446i
$630$		0			0
$631$		−	1.24972e7i		−	1.24951i	−0.780821	−	0.624755i	$-0.785199\pi$
$631$		−	1.24972e7i		−	1.24951i	0.780821	−	0.624755i	$-0.214801\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	4.59792e6	−	4.59792e6i	0.452509	−	0.452509i
$636$		0			0
$637$	−7.87784e6	−	7.87784e6i	−0.769234	−	0.769234i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	1.96793e7			1.89176			0.945879	−	0.324520i	$-0.105203\pi$
$641$	1.96793e7			1.89176			0.945879	+	0.324520i	$0.105203\pi$
$642$		0			0
$643$	3.25875e6	+	3.25875e6i	0.310831	+	0.310831i	0.845231	−	0.534401i	$-0.179463\pi$
$643$	3.25875e6	+	3.25875e6i	0.310831	+	0.310831i	−0.534401	+	0.845231i	$0.679463\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	7.75349e6i		−	0.728177i	−0.931364	−	0.364088i	$-0.881381\pi$
$647$		−	7.75349e6i		−	0.728177i	0.931364	−	0.364088i	$-0.118619\pi$
$648$		0			0
$649$		−	1.52221e6i		−	0.141861i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−3.26906e6	−	3.26906e6i	−0.300013	−	0.300013i	0.541006	−	0.841019i	$-0.318044\pi$
$653$	−3.26906e6	−	3.26906e6i	−0.300013	−	0.300013i	−0.841019	+	0.541006i	$0.818044\pi$
$654$		0			0
$655$	8.09657e6			0.737391
$656$		0			0
$657$		0			0
$658$		0			0
$659$	3.61551e6	+	3.61551e6i	0.324307	+	0.324307i	0.850417	−	0.526110i	$-0.176350\pi$
$659$	3.61551e6	+	3.61551e6i	0.324307	+	0.324307i	−0.526110	+	0.850417i	$0.676350\pi$
$660$		0			0
$661$	−1.10992e7	+	1.10992e7i	−0.988068	+	0.988068i	−0.999930	−	0.0118621i	$-0.996224\pi$
$661$	−1.10992e7	+	1.10992e7i	−0.988068	+	0.988068i	0.0118621	+	0.999930i	$0.496224\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$			2.70046e6i			0.236801i
$666$		0			0
$667$	−275633.	+	275633.i	−0.0239892	+	0.0239892i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	192758.			0.0165274
$672$		0			0
$673$	−1.15752e7			−0.985122			−0.492561	−	0.870278i	$-0.663939\pi$
$673$	−1.15752e7			−0.985122			−0.492561	+	0.870278i	$0.663939\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−6.16288e6	+	6.16288e6i	−0.516788	+	0.516788i	−0.916598	−	0.399810i	$-0.869076\pi$
$677$	−6.16288e6	+	6.16288e6i	−0.516788	+	0.516788i	0.399810	+	0.916598i	$0.369076\pi$
$678$		0			0
$679$			2.17737e6i			0.181241i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1.61758e7	−	1.61758e7i	1.32683	−	1.32683i	0.418701	−	0.908124i	$-0.362486\pi$
$683$	1.61758e7	−	1.61758e7i	1.32683	−	1.32683i	0.908124	−	0.418701i	$-0.137514\pi$
$684$		0			0
$685$	8.12020e6	+	8.12020e6i	0.661212	+	0.661212i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	2.08612e7			1.67413
$690$		0			0
$691$	5.55329e6	+	5.55329e6i	0.442441	+	0.442441i	0.892832	−	0.450391i	$-0.148715\pi$
$691$	5.55329e6	+	5.55329e6i	0.442441	+	0.442441i	−0.450391	+	0.892832i	$0.648715\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$			3.21259e6i			0.252286i
$696$		0			0
$697$		−	2.10071e6i		−	0.163789i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	1.27706e7	+	1.27706e7i	0.981556	+	0.981556i	0.999833	−	0.0182770i	$-0.00581807\pi$
$701$	1.27706e7	+	1.27706e7i	0.981556	+	0.981556i	−0.0182770	+	0.999833i	$0.505818\pi$
$702$		0			0
$703$	−6.65674e6			−0.508011
$704$		0			0
$705$		0			0
$706$		0			0
$707$	5.54615e6	+	5.54615e6i	0.417295	+	0.417295i
$708$		0			0
$709$	3.14350e6	−	3.14350e6i	0.234854	−	0.234854i	−0.579861	−	0.814715i	$-0.696893\pi$
$709$	3.14350e6	−	3.14350e6i	0.234854	−	0.234854i	0.814715	+	0.579861i	$0.196893\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		−	7.34994e6i		−	0.541452i
$714$		0			0
$715$	4.46961e6	−	4.46961e6i	0.326967	−	0.326967i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	1.75922e7			1.26911			0.634553	−	0.772879i	$-0.281184\pi$
$719$	1.75922e7			1.26911			0.634553	+	0.772879i	$0.281184\pi$
$720$		0			0
$721$	−8.59650e6			−0.615862
$722$		0			0
$723$		0			0
$724$		0			0
$725$	507586.	−	507586.i	0.0358645	−	0.0358645i
$726$		0			0
$727$		−	1.28421e7i		−	0.901153i	−0.892738	−	0.450576i	$-0.851219\pi$
$727$		−	1.28421e7i		−	0.901153i	0.892738	−	0.450576i	$-0.148781\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−1.80357e6	+	1.80357e6i	−0.124836	+	0.124836i
$732$		0			0
$733$	−4.54419e6	−	4.54419e6i	−0.312389	−	0.312389i	0.533445	−	0.845835i	$-0.320897\pi$
$733$	−4.54419e6	−	4.54419e6i	−0.312389	−	0.312389i	−0.845835	+	0.533445i	$0.820897\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−3.97210e6			−0.269371
$738$		0			0
$739$	1.76573e7	+	1.76573e7i	1.18936	+	1.18936i	0.977245	+	0.212114i	$0.0680349\pi$
$739$	1.76573e7	+	1.76573e7i	1.18936	+	1.18936i	0.212114	+	0.977245i	$0.431965\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$			1.87092e7i			1.24332i	0.783286	+	0.621662i	$0.213542\pi$
$743$			1.87092e7i			1.24332i	−0.783286	+	0.621662i	$0.786458\pi$
$744$		0			0
$745$		−	1.86928e7i		−	1.23391i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−4.05611e6	−	4.05611e6i	−0.264183	−	0.264183i
$750$		0			0
$751$	−1.38400e7			−0.895441			−0.447721	−	0.894174i	$-0.647764\pi$
$751$	−1.38400e7			−0.895441			−0.447721	+	0.894174i	$0.647764\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	5.67982e6	+	5.67982e6i	0.362633	+	0.362633i
$756$		0			0
$757$	−1.49710e7	+	1.49710e7i	−0.949535	+	0.949535i	−0.998786	−	0.0492513i	$-0.984316\pi$
$757$	−1.49710e7	+	1.49710e7i	−0.949535	+	0.949535i	0.0492513	+	0.998786i	$0.484316\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		−	1.28130e7i		−	0.802030i	−0.916072	−	0.401015i	$-0.868658\pi$
$761$		−	1.28130e7i		−	0.802030i	0.916072	−	0.401015i	$-0.131342\pi$
$762$		0			0
$763$	7.53548e6	−	7.53548e6i	0.468597	−	0.468597i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	6.36015e6			0.390372
$768$		0			0
$769$	−4.01336e6			−0.244733			−0.122366	−	0.992485i	$-0.539048\pi$
$769$	−4.01336e6			−0.244733			−0.122366	+	0.992485i	$0.539048\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−1.37735e7	+	1.37735e7i	−0.829081	+	0.829081i	−0.987390	−	0.158309i	$-0.949396\pi$
$773$	−1.37735e7	+	1.37735e7i	−0.829081	+	0.829081i	0.158309	+	0.987390i	$0.449396\pi$
$774$		0			0
$775$			1.35351e7i			0.809483i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−5.61714e6	+	5.61714e6i	−0.331643	+	0.331643i
$780$		0			0
$781$	3.24404e6	+	3.24404e6i	0.190309	+	0.190309i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	1.33895e7			0.775514
$786$		0			0
$787$	1.67606e7	+	1.67606e7i	0.964612	+	0.964612i	0.999395	−	0.0347829i	$-0.0110740\pi$
$787$	1.67606e7	+	1.67606e7i	0.964612	+	0.964612i	−0.0347829	+	0.999395i	$0.511074\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			4.13863e6i			0.235188i
$792$		0			0
$793$			805387.i			0.0454801i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	1.27890e6	+	1.27890e6i	0.0713165	+	0.0713165i	0.741865	−	0.670549i	$-0.233941\pi$
$797$	1.27890e6	+	1.27890e6i	0.0713165	+	0.0713165i	−0.670549	+	0.741865i	$0.733941\pi$
$798$		0			0
$799$	1.00194e6			0.0555234
$800$		0			0
$801$		0			0
$802$		0			0
$803$	7.93625e6	+	7.93625e6i	0.434336	+	0.434336i
$804$		0			0
$805$	1.29893e6	−	1.29893e6i	0.0706471	−	0.0706471i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			2.13057e6i			0.114452i	0.998361	+	0.0572260i	$0.0182256\pi$
$809$			2.13057e6i			0.114452i	−0.998361	+	0.0572260i	$0.981774\pi$
$810$		0			0
$811$	−3.29628e6	+	3.29628e6i	−0.175983	+	0.175983i	−0.789602	−	0.613619i	$-0.789713\pi$
$811$	−3.29628e6	+	3.29628e6i	−0.175983	+	0.175983i	0.613619	+	0.789602i	$0.289713\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−7.80944e6			−0.411837
$816$		0			0
$817$	9.64525e6			0.505543
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1.10250e7	−	1.10250e7i	0.570847	−	0.570847i	−0.361518	−	0.932365i	$-0.617742\pi$
$821$	1.10250e7	−	1.10250e7i	0.570847	−	0.570847i	0.932365	+	0.361518i	$0.117742\pi$
$822$		0			0
$823$			1.19996e7i			0.617545i	0.951136	+	0.308773i	$0.0999182\pi$
$823$			1.19996e7i			0.617545i	−0.951136	+	0.308773i	$0.900082\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	2.02039e7	−	2.02039e7i	1.02724	−	1.02724i	0.0276211	−	0.999618i	$-0.491207\pi$
$827$	2.02039e7	−	2.02039e7i	1.02724	−	1.02724i	0.999618	−	0.0276211i	$-0.00879319\pi$
$828$		0			0
$829$	1.63964e7	+	1.63964e7i	0.828633	+	0.828633i	0.987328	−	0.158695i	$-0.0507285\pi$
$829$	1.63964e7	+	1.63964e7i	0.828633	+	0.828633i	−0.158695	+	0.987328i	$0.550729\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−4.40318e6			−0.219864
$834$		0			0
$835$	9.18819e6	+	9.18819e6i	0.456051	+	0.456051i
$836$		0			0
$837$		0			0
$838$		0			0
$839$			2.67951e7i			1.31417i	0.753819	+	0.657083i	$0.228210\pi$
$839$			2.67951e7i			1.31417i	−0.753819	+	0.657083i	$0.771790\pi$
$840$		0			0
$841$		−	2.02882e7i		−	0.989128i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	8.15731e6	+	8.15731e6i	0.393011	+	0.393011i
$846$		0			0
$847$	−6.84855e6			−0.328012
$848$		0			0
$849$		0			0
$850$		0			0
$851$	3.20190e6	+	3.20190e6i	0.151560	+	0.151560i
$852$		0			0
$853$	9.90761e6	−	9.90761e6i	0.466226	−	0.466226i	−0.434463	−	0.900689i	$-0.643062\pi$
$853$	9.90761e6	−	9.90761e6i	0.466226	−	0.466226i	0.900689	+	0.434463i	$0.143062\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			1.79738e6i			0.0835963i	0.999126	+	0.0417982i	$0.0133086\pi$
$857$			1.79738e6i			0.0835963i	−0.999126	+	0.0417982i	$0.986691\pi$
$858$		0			0
$859$	−8.93866e6	+	8.93866e6i	−0.413323	+	0.413323i	−0.882894	−	0.469572i	$-0.844408\pi$
$859$	−8.93866e6	+	8.93866e6i	−0.413323	+	0.413323i	0.469572	+	0.882894i	$0.344408\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	1.94832e7			0.890498			0.445249	−	0.895407i	$-0.353115\pi$
$863$	1.94832e7			0.890498			0.445249	+	0.895407i	$0.353115\pi$
$864$		0			0
$865$	2.13365e7			0.969579
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−7.95215e6	+	7.95215e6i	−0.357220	+	0.357220i
$870$		0			0
$871$		−	1.65964e7i		−	0.741255i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−7.30941e6	+	7.30941e6i	−0.322747	+	0.322747i
$876$		0			0
$877$	3.95987e6	+	3.95987e6i	0.173853	+	0.173853i	0.788670	−	0.614817i	$-0.210770\pi$
$877$	3.95987e6	+	3.95987e6i	0.173853	+	0.173853i	−0.614817	+	0.788670i	$0.710770\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1.91087e7			0.829453			0.414727	−	0.909946i	$-0.363877\pi$
$881$	1.91087e7			0.829453			0.414727	+	0.909946i	$0.363877\pi$
$882$		0			0
$883$	4.24231e6	+	4.24231e6i	0.183105	+	0.183105i	0.792707	−	0.609602i	$-0.208671\pi$
$883$	4.24231e6	+	4.24231e6i	0.183105	+	0.183105i	−0.609602	+	0.792707i	$0.708671\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		−	1.89345e7i		−	0.808061i	−0.914746	−	0.404030i	$-0.867609\pi$
$887$		−	1.89345e7i		−	0.808061i	0.914746	−	0.404030i	$-0.132391\pi$
$888$		0			0
$889$			9.01642e6i			0.382631i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−2.67912e6	−	2.67912e6i	−0.112425	−	0.112425i
$894$		0			0
$895$	9.44895e6			0.394299
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−2.97315e6	−	2.97315e6i	−0.122693	−	0.122693i
$900$		0			0
$901$	5.82999e6	−	5.82999e6i	0.239252	−	0.239252i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		−	4.83899e6i		−	0.196396i
$906$		0			0
$907$	5.57532e6	−	5.57532e6i	0.225036	−	0.225036i	−0.585579	−	0.810615i	$-0.699133\pi$
$907$	5.57532e6	−	5.57532e6i	0.225036	−	0.225036i	0.810615	+	0.585579i	$0.199133\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−3.30115e7			−1.31786			−0.658929	−	0.752205i	$-0.728990\pi$
$911$	−3.30115e7			−1.31786			−0.658929	+	0.752205i	$0.728990\pi$
$912$		0			0
$913$	−2.16986e7			−0.861498
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−7.93859e6	+	7.93859e6i	−0.311760	+	0.311760i
$918$		0			0
$919$		−	2.94518e7i		−	1.15033i	−0.818037	−	0.575166i	$-0.804938\pi$
$919$		−	2.94518e7i		−	1.15033i	0.818037	−	0.575166i	$-0.195062\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−1.35544e7	+	1.35544e7i	−0.523691	+	0.523691i
$924$		0			0
$925$	−5.89640e6	−	5.89640e6i	−0.226586	−	0.226586i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−3.47221e7			−1.31998			−0.659989	−	0.751275i	$-0.729439\pi$
$929$	−3.47221e7			−1.31998			−0.659989	+	0.751275i	$0.729439\pi$
$930$		0			0
$931$	1.17738e7	+	1.17738e7i	0.445187	+	0.445187i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	2.49821e6i		−	0.0934545i
$936$		0			0
$937$		−	3.02876e7i		−	1.12698i	−0.826123	−	0.563490i	$-0.809458\pi$
$937$		−	3.02876e7i		−	1.12698i	0.826123	−	0.563490i	$-0.190542\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	529526.	+	529526.i	0.0194945	+	0.0194945i	0.716787	−	0.697292i	$-0.245612\pi$
$941$	529526.	+	529526.i	0.0194945	+	0.0194945i	−0.697292	+	0.716787i	$0.745612\pi$
$942$		0			0
$943$	5.40370e6			0.197885
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−9.98574e6	−	9.98574e6i	−0.361831	−	0.361831i	0.502656	−	0.864487i	$-0.332356\pi$
$947$	−9.98574e6	−	9.98574e6i	−0.361831	−	0.361831i	−0.864487	+	0.502656i	$0.832356\pi$
$948$		0			0
$949$	−3.31595e7	+	3.31595e7i	−1.19520	+	1.19520i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	1.77547e7i		−	0.633258i	−0.948549	−	0.316629i	$-0.897449\pi$
$953$		−	1.77547e7i		−	0.633258i	0.948549	−	0.316629i	$-0.102551\pi$
$954$		0			0
$955$	2.27904e7	−	2.27904e7i	0.808617	−	0.808617i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−1.59235e7			−0.559104
$960$		0			0
$961$	5.06520e7			1.76925
$962$		0			0
$963$		0			0
$964$		0			0
$965$	7.00033e6	−	7.00033e6i	0.241992	−	0.241992i
$966$		0			0
$967$			1.67748e7i			0.576888i	0.957497	+	0.288444i	$0.0931378\pi$
$967$			1.67748e7i			0.576888i	−0.957497	+	0.288444i	$0.906862\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−1.02779e7	+	1.02779e7i	−0.349829	+	0.349829i	−0.860046	−	0.510217i	$-0.829565\pi$
$971$	−1.02779e7	+	1.02779e7i	−0.349829	+	0.349829i	0.510217	+	0.860046i	$0.329565\pi$
$972$		0			0
$973$	−3.14990e6	−	3.14990e6i	−0.106663	−	0.106663i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−8.61733e6			−0.288826			−0.144413	−	0.989518i	$-0.546129\pi$
$977$	−8.61733e6			−0.288826			−0.144413	+	0.989518i	$0.546129\pi$
$978$		0			0
$979$	3.56008e6	+	3.56008e6i	0.118714	+	0.118714i
$980$		0			0
$981$		0			0
$982$		0			0
$983$			9.65214e6i			0.318596i	0.987231	+	0.159298i	$0.0509230\pi$
$983$			9.65214e6i			0.318596i	−0.987231	+	0.159298i	$0.949077\pi$
$984$		0			0
$985$			1.67655e7i			0.550586i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−4.63938e6	−	4.63938e6i	−0.150824	−	0.150824i
$990$		0			0
$991$	−3.34127e7			−1.08075			−0.540377	−	0.841423i	$-0.681718\pi$
$991$	−3.34127e7			−1.08075			−0.540377	+	0.841423i	$0.681718\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	7.14606e6	+	7.14606e6i	0.228828	+	0.228828i
$996$		0			0
$997$	−9.62270e6	+	9.62270e6i	−0.306591	+	0.306591i	−0.843586	−	0.536995i	$-0.819559\pi$
$997$	−9.62270e6	+	9.62270e6i	−0.306591	+	0.306591i	0.536995	+	0.843586i	$0.319559\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.6.k.a.145.7		18
3.2	odd	2		64.6.e.a.17.9		18
4.3	odd	2		144.6.k.a.109.4		18
12.11	even	2		16.6.e.a.13.6	yes	18
16.5	even	4	inner	576.6.k.a.433.7		18
16.11	odd	4		144.6.k.a.37.4		18
24.5	odd	2		128.6.e.a.33.1		18
24.11	even	2		128.6.e.b.33.9		18
48.5	odd	4		64.6.e.a.49.9		18
48.11	even	4		16.6.e.a.5.6	✓	18
48.29	odd	4		128.6.e.a.97.1		18
48.35	even	4		128.6.e.b.97.9		18
96.5	odd	8		1024.6.a.l.1.1		18
96.11	even	8		1024.6.a.k.1.1		18
96.53	odd	8		1024.6.a.l.1.18		18
96.59	even	8		1024.6.a.k.1.18		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.6.e.a.5.6	✓	18	48.11	even	4
16.6.e.a.13.6	yes	18	12.11	even	2
64.6.e.a.17.9		18	3.2	odd	2
64.6.e.a.49.9		18	48.5	odd	4
128.6.e.a.33.1		18	24.5	odd	2
128.6.e.a.97.1		18	48.29	odd	4
128.6.e.b.33.9		18	24.11	even	2
128.6.e.b.97.9		18	48.35	even	4
144.6.k.a.37.4		18	16.11	odd	4
144.6.k.a.109.4		18	4.3	odd	2
576.6.k.a.145.7		18	1.1	even	1	trivial
576.6.k.a.433.7		18	16.5	even	4	inner
1024.6.a.k.1.1		18	96.11	even	8
1024.6.a.k.1.18		18	96.59	even	8
1024.6.a.l.1.1		18	96.5	odd	8
1024.6.a.l.1.18		18	96.53	odd	8

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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	576.k (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(28.3274 - 28.3274i) q^{5} +55.5494i q^{7} +O(q^{10})\)	\(q+(28.3274 - 28.3274i) q^{5} +55.5494i q^{7} +(-137.411 + 137.411i) q^{11} +(-574.133 - 574.133i) q^{13} -320.902 q^{17} +(858.068 + 858.068i) q^{19} -825.465i q^{23} +1520.12i q^{25} +(-333.912 - 333.912i) q^{29} +8904.00 q^{31} +(1573.57 + 1573.57i) q^{35} +(-3878.91 + 3878.91i) q^{37} +6546.26i q^{41} +(5620.33 - 5620.33i) q^{43} -3122.27 q^{47} +13721.3 q^{49} +(-18167.5 + 18167.5i) q^{53} +7784.97i q^{55} +(-5538.91 + 5538.91i) q^{59} +(-701.393 - 701.393i) q^{61} -32527.4 q^{65} +(14453.4 + 14453.4i) q^{67} -23608.4i q^{71} -57755.7i q^{73} +(-7633.07 - 7633.07i) q^{77} +57871.5 q^{79} +(78955.3 + 78955.3i) q^{83} +(-9090.32 + 9090.32i) q^{85} -25908.3i q^{89} +(31892.7 - 31892.7i) q^{91} +48613.7 q^{95} +39197.0 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{5}+O(q^{10}) \) 18 * q + 2 * q^5	\( 18 q + 2 q^{5} - 606 q^{11} - 2 q^{13} + 4 q^{17} + 2362 q^{19} - 4070 q^{29} + 11536 q^{31} + 8636 q^{35} - 10650 q^{37} + 15382 q^{43} + 44176 q^{47} - 14410 q^{49} - 24726 q^{53} - 29734 q^{59} - 48082 q^{61} - 27684 q^{65} + 75210 q^{67} - 41060 q^{77} + 52864 q^{79} + 227838 q^{83} - 138652 q^{85} + 231164 q^{91} - 250380 q^{95} - 4 q^{97}+O(q^{100}) \) 18 * q + 2 * q^5 - 606 * q^11 - 2 * q^13 + 4 * q^17 + 2362 * q^19 - 4070 * q^29 + 11536 * q^31 + 8636 * q^35 - 10650 * q^37 + 15382 * q^43 + 44176 * q^47 - 14410 * q^49 - 24726 * q^53 - 29734 * q^59 - 48082 * q^61 - 27684 * q^65 + 75210 * q^67 - 41060 * q^77 + 52864 * q^79 + 227838 * q^83 - 138652 * q^85 + 231164 * q^91 - 250380 * q^95 - 4 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more