LMFDB - Embedded newform 400.6.n.f.143.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,6,Mod(143,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("400.143");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	400.n (of order $4$, degree $2$, 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:	$64.1535279252$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 12 x^{14} - 100 x^{13} + 524 x^{12} - 400 x^{11} + 3746 x^{10} - 42400 x^{9} + \cdots + 1540307025 $ x^16 + 12x^14 - 100x^13 + 524x^12 - 400x^11 + 3746x^10 - 42400x^9 + 111549x^8 + 256200x^7 - 966658x^6 - 8816000x^5 + 21164416x^4 + 39337200x^3 + 22584690x^2 - 776398500x + 1540307025
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{44}\cdot 5^{16} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			143.8
Root			$1.96154 - 1.56825i$ of defining polynomial
Character	$\chi$	$=$	400.143
Dual form			400.6.n.f.207.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(20.4551 - 20.4551i) q^{3} +(7.62217 + 7.62217i) q^{7} -593.825i q^{9} +O(q^{10})$	$q+(20.4551 - 20.4551i) q^{3} +(7.62217 + 7.62217i) q^{7} -593.825i q^{9} +406.744i q^{11} +(-712.587 - 712.587i) q^{13} +(-804.443 + 804.443i) q^{17} -2380.45 q^{19} +311.825 q^{21} +(476.455 - 476.455i) q^{23} +(-7176.18 - 7176.18i) q^{27} +5020.43i q^{29} +7016.55i q^{31} +(8320.00 + 8320.00i) q^{33} +(5205.26 - 5205.26i) q^{37} -29152.1 q^{39} -12768.9 q^{41} +(6352.93 - 6352.93i) q^{43} +(-17012.4 - 17012.4i) q^{47} -16690.8i q^{49} +32910.0i q^{51} +(-17430.6 - 17430.6i) q^{53} +(-48692.3 + 48692.3i) q^{57} -12493.8 q^{59} +6022.04 q^{61} +(4526.24 - 4526.24i) q^{63} +(-9149.24 - 9149.24i) q^{67} -19491.9i q^{69} -60841.9i q^{71} +(42123.1 + 42123.1i) q^{73} +(-3100.27 + 3100.27i) q^{77} +61442.1 q^{79} -149280. q^{81} +(-58413.1 + 58413.1i) q^{83} +(102694. + 102694. i) q^{87} +66206.4i q^{89} -10862.9i q^{91} +(143525. + 143525. i) q^{93} +(-41495.9 + 41495.9i) q^{97} +241535. q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 1600 q^{21} - 125232 q^{41} - 279232 q^{61} - 1591184 q^{81}+O(q^{100}) $ 16 * q - 1600 * q^21 - 125232 * q^41 - 279232 * q^61 - 1591184 * q^81

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	20.4551	−	20.4551i	1.31220	−	1.31220i	0.392405	−	0.919792i	$-0.371643\pi$
$3$	20.4551	−	20.4551i	1.31220	−	1.31220i	0.919792	−	0.392405i	$-0.128357\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	7.62217	+	7.62217i	0.0587941	+	0.0587941i	0.735892	−	0.677098i	$-0.236763\pi$
$7$	7.62217	+	7.62217i	0.0587941	+	0.0587941i	−0.677098	+	0.735892i	$0.736763\pi$
$8$		0			0
$9$		−	593.825i		−	2.44373i
$10$		0			0
$11$			406.744i			1.01354i	0.862082	+	0.506768i	$0.169160\pi$
$11$			406.744i			1.01354i	−0.862082	+	0.506768i	$0.830840\pi$
$12$		0			0
$13$	−712.587	−	712.587i	−1.16944	−	1.16944i	−0.982340	−	0.187105i	$-0.940090\pi$
$13$	−712.587	−	712.587i	−1.16944	−	1.16944i	−0.187105	−	0.982340i	$-0.559910\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−804.443	+	804.443i	−0.675108	+	0.675108i	−0.958889	−	0.283781i	$-0.908411\pi$
$17$	−804.443	+	804.443i	−0.675108	+	0.675108i	0.283781	+	0.958889i	$0.408411\pi$
$18$		0			0
$19$	−2380.45			−1.51277			−0.756387	−	0.654124i	$-0.773038\pi$
$19$	−2380.45			−1.51277			−0.756387	+	0.654124i	$0.773038\pi$
$20$		0			0
$21$	311.825			0.154299
$22$		0			0
$23$	476.455	−	476.455i	0.187803	−	0.187803i	−0.606943	−	0.794746i	$-0.707604\pi$
$23$	476.455	−	476.455i	0.187803	−	0.187803i	0.794746	+	0.606943i	$0.207604\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−7176.18	−	7176.18i	−1.89445	−	1.89445i
$28$		0			0
$29$			5020.43i			1.10853i	0.832342	+	0.554263i	$0.187000\pi$
$29$			5020.43i			1.10853i	−0.832342	+	0.554263i	$0.813000\pi$
$30$		0			0
$31$			7016.55i			1.31135i	0.755042	+	0.655676i	$0.227616\pi$
$31$			7016.55i			1.31135i	−0.755042	+	0.655676i	$0.772384\pi$
$32$		0			0
$33$	8320.00	+	8320.00i	1.32996	+	1.32996i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	5205.26	−	5205.26i	0.625084	−	0.625084i	−0.321743	−	0.946827i	$-0.604269\pi$
$37$	5205.26	−	5205.26i	0.625084	−	0.625084i	0.946827	+	0.321743i	$0.104269\pi$
$38$		0			0
$39$	−29152.1			−3.06909
$40$		0			0
$41$	−12768.9			−1.18630			−0.593149	−	0.805093i	$-0.702116\pi$
$41$	−12768.9			−1.18630			−0.593149	+	0.805093i	$0.702116\pi$
$42$		0			0
$43$	6352.93	−	6352.93i	0.523966	−	0.523966i	−0.394801	−	0.918767i	$-0.629186\pi$
$43$	6352.93	−	6352.93i	0.523966	−	0.523966i	0.918767	+	0.394801i	$0.129186\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−17012.4	−	17012.4i	−1.12337	−	1.12337i	−0.991232	−	0.132136i	$-0.957816\pi$
$47$	−17012.4	−	17012.4i	−1.12337	−	1.12337i	−0.132136	−	0.991232i	$-0.542184\pi$
$48$		0			0
$49$		−	16690.8i		−	0.993087i
$50$		0			0
$51$			32910.0i			1.77175i
$52$		0			0
$53$	−17430.6	−	17430.6i	−0.852361	−	0.852361i	0.138062	−	0.990424i	$-0.455913\pi$
$53$	−17430.6	−	17430.6i	−0.852361	−	0.852361i	−0.990424	+	0.138062i	$0.955913\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−48692.3	+	48692.3i	−1.98506	+	1.98506i
$58$		0			0
$59$	−12493.8			−0.467266			−0.233633	−	0.972325i	$-0.575061\pi$
$59$	−12493.8			−0.467266			−0.233633	+	0.972325i	$0.575061\pi$
$60$		0			0
$61$	6022.04			0.207214			0.103607	−	0.994618i	$-0.466962\pi$
$61$	6022.04			0.207214			0.103607	+	0.994618i	$0.466962\pi$
$62$		0			0
$63$	4526.24	−	4526.24i	0.143677	−	0.143677i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−9149.24	−	9149.24i	−0.248999	−	0.248999i	0.571561	−	0.820560i	$-0.306338\pi$
$67$	−9149.24	−	9149.24i	−0.248999	−	0.248999i	−0.820560	+	0.571561i	$0.806338\pi$
$68$		0			0
$69$		−	19491.9i		−	0.492869i
$70$		0			0
$71$		−	60841.9i		−	1.43238i	−0.697908	−	0.716188i	$-0.745885\pi$
$71$		−	60841.9i		−	1.43238i	0.697908	−	0.716188i	$-0.254115\pi$
$72$		0			0
$73$	42123.1	+	42123.1i	0.925151	+	0.925151i	0.997388	−	0.0722364i	$-0.0230136\pi$
$73$	42123.1	+	42123.1i	0.925151	+	0.925151i	−0.0722364	+	0.997388i	$0.523014\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−3100.27	+	3100.27i	−0.0595899	+	0.0595899i
$78$		0			0
$79$	61442.1			1.10764			0.553819	−	0.832637i	$-0.313170\pi$
$79$	61442.1			1.10764			0.553819	+	0.832637i	$0.313170\pi$
$80$		0			0
$81$	−149280.			−2.52807
$82$		0			0
$83$	−58413.1	+	58413.1i	−0.930712	+	0.930712i	−0.997750	−	0.0670385i	$-0.978645\pi$
$83$	−58413.1	+	58413.1i	−0.930712	+	0.930712i	0.0670385	+	0.997750i	$0.478645\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	102694.	+	102694.i	1.45460	+	1.45460i
$88$		0			0
$89$			66206.4i			0.885982i	0.896526	+	0.442991i	$0.146083\pi$
$89$			66206.4i			0.885982i	−0.896526	+	0.442991i	$0.853917\pi$
$90$		0			0
$91$		−	10862.9i		−	0.137513i
$92$		0			0
$93$	143525.	+	143525.i	1.72075	+	1.72075i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−41495.9	+	41495.9i	−0.447792	+	0.447792i	−0.894620	−	0.446828i	$-0.852554\pi$
$97$	−41495.9	+	41495.9i	−0.447792	+	0.447792i	0.446828	+	0.894620i	$0.352554\pi$
$98$		0			0
$99$	241535.			2.47680
$100$		0			0
$101$	−126258.			−1.23156			−0.615779	−	0.787919i	$-0.711158\pi$
$101$	−126258.			−1.23156			−0.615779	+	0.787919i	$0.711158\pi$
$102$		0			0
$103$	110361.	−	110361.i	1.02500	−	1.02500i	0.0253215	−	0.999679i	$-0.491939\pi$
$103$	110361.	−	110361.i	1.02500	−	1.02500i	0.999679	−	0.0253215i	$-0.00806094\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	146564.	+	146564.i	1.23756	+	1.23756i	0.960994	+	0.276569i	$0.0891973\pi$
$107$	146564.	+	146564.i	1.23756	+	1.23756i	0.276569	+	0.960994i	$0.410803\pi$
$108$		0			0
$109$		−	99679.9i		−	0.803603i	−0.915727	−	0.401801i	$-0.868384\pi$
$109$		−	99679.9i		−	0.803603i	0.915727	−	0.401801i	$-0.131616\pi$
$110$		0			0
$111$		−	212949.i		−	1.64047i
$112$		0			0
$113$	−61798.7	−	61798.7i	−0.455285	−	0.455285i	0.441819	−	0.897104i	$-0.354333\pi$
$113$	−61798.7	−	61798.7i	−0.455285	−	0.455285i	−0.897104	+	0.441819i	$0.854333\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−423152.	+	423152.i	−2.85780	+	2.85780i
$118$		0			0
$119$	−12263.2			−0.0793847
$120$		0			0
$121$	−4389.55			−0.0272556
$122$		0			0
$123$	−261190.	+	261190.i	−1.55666	+	1.55666i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−9601.33	−	9601.33i	−0.0528229	−	0.0528229i	0.680202	−	0.733025i	$-0.261892\pi$
$127$	−9601.33	−	9601.33i	−0.0528229	−	0.0528229i	−0.733025	+	0.680202i	$0.761892\pi$
$128$		0			0
$129$		−	259900.i		−	1.37509i
$130$		0			0
$131$			164873.i			0.839402i	0.907662	+	0.419701i	$0.137865\pi$
$131$			164873.i			0.839402i	−0.907662	+	0.419701i	$0.862135\pi$
$132$		0			0
$133$	−18144.2	−	18144.2i	−0.0889422	−	0.0889422i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	16489.0	−	16489.0i	0.0750572	−	0.0750572i	−0.668582	−	0.743639i	$-0.733098\pi$
$137$	16489.0	−	16489.0i	0.0750572	−	0.0750572i	0.743639	+	0.668582i	$0.233098\pi$
$138$		0			0
$139$	32797.7			0.143981			0.0719907	−	0.997405i	$-0.477065\pi$
$139$	32797.7			0.143981			0.0719907	+	0.997405i	$0.477065\pi$
$140$		0			0
$141$	−695983.			−2.94816
$142$		0			0
$143$	289841.	−	289841.i	1.18527	−	1.18527i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−341413.	−	341413.i	−1.30313	−	1.30313i
$148$		0			0
$149$		−	31288.5i		−	0.115457i	−0.998332	−	0.0577284i	$-0.981614\pi$
$149$		−	31288.5i		−	0.115457i	0.998332	−	0.0577284i	$-0.0183858\pi$
$150$		0			0
$151$		−	222531.i		−	0.794233i	−0.917768	−	0.397117i	$-0.870011\pi$
$151$		−	222531.i		−	0.794233i	0.917768	−	0.397117i	$-0.129989\pi$
$152$		0			0
$153$	477699.	+	477699.i	1.64978	+	1.64978i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−35064.3	+	35064.3i	−0.113531	+	0.113531i	−0.761590	−	0.648059i	$-0.775581\pi$
$157$	−35064.3	+	35064.3i	−0.113531	+	0.113531i	0.648059	+	0.761590i	$0.275581\pi$
$158$		0			0
$159$	−713092.			−2.23693
$160$		0			0
$161$	7263.25			0.0220834
$162$		0			0
$163$	−44749.2	+	44749.2i	−0.131922	+	0.131922i	−0.769984	−	0.638063i	$-0.779736\pi$
$163$	−44749.2	+	44749.2i	−0.131922	+	0.131922i	0.638063	+	0.769984i	$0.279736\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−153868.	−	153868.i	−0.426930	−	0.426930i	0.460651	−	0.887581i	$-0.347616\pi$
$167$	−153868.	−	153868.i	−0.426930	−	0.426930i	−0.887581	+	0.460651i	$0.847616\pi$
$168$		0			0
$169$			644269.i			1.73520i
$170$		0			0
$171$			1.41357e6i			3.69681i
$172$		0			0
$173$	305644.	+	305644.i	0.776427	+	0.776427i	0.979221	−	0.202795i	$-0.0650023\pi$
$173$	305644.	+	305644.i	0.776427	+	0.776427i	−0.202795	+	0.979221i	$0.565002\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−255562.	+	255562.i	−0.613145	+	0.613145i
$178$		0			0
$179$	−414707.			−0.967406			−0.483703	−	0.875232i	$-0.660708\pi$
$179$	−414707.			−0.967406			−0.483703	+	0.875232i	$0.660708\pi$
$180$		0			0
$181$	36827.2			0.0835550			0.0417775	−	0.999127i	$-0.486698\pi$
$181$	36827.2			0.0835550			0.0417775	+	0.999127i	$0.486698\pi$
$182$		0			0
$183$	123182.	−	123182.i	0.271906	−	0.271906i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−327202.	−	327202.i	−0.684246	−	0.684246i
$188$		0			0
$189$		−	109396.i		−	0.222765i
$190$		0			0
$191$		−	589465.i		−	1.16916i	−0.811335	−	0.584581i	$-0.801259\pi$
$191$		−	589465.i		−	1.16916i	0.811335	−	0.584581i	$-0.198741\pi$
$192$		0			0
$193$	−263533.	−	263533.i	−0.509263	−	0.509263i	0.405037	−	0.914300i	$-0.367259\pi$
$193$	−263533.	−	263533.i	−0.509263	−	0.509263i	−0.914300	+	0.405037i	$0.867259\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−169645.	+	169645.i	−0.311442	+	0.311442i	−0.845468	−	0.534026i	$-0.820678\pi$
$197$	−169645.	+	169645.i	−0.311442	+	0.311442i	0.534026	+	0.845468i	$0.320678\pi$
$198$		0			0
$199$	−958493.			−1.71576			−0.857880	−	0.513850i	$-0.828219\pi$
$199$	−958493.			−1.71576			−0.857880	+	0.513850i	$0.828219\pi$
$200$		0			0
$201$	−374298.			−0.653472
$202$		0			0
$203$	−38266.6	+	38266.6i	−0.0651748	+	0.0651748i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−282931.	−	282931.i	−0.458939	−	0.458939i
$208$		0			0
$209$		−	968232.i		−	1.53325i
$210$		0			0
$211$		−	220585.i		−	0.341090i	−0.985350	−	0.170545i	$-0.945447\pi$
$211$		−	220585.i		−	0.341090i	0.985350	−	0.170545i	$-0.0545528\pi$
$212$		0			0
$213$	−1.24453e6	−	1.24453e6i	−1.87956	−	1.87956i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−53481.4	+	53481.4i	−0.0770998	+	0.0770998i
$218$		0			0
$219$	1.72327e6			2.42796
$220$		0			0
$221$	1.14647e6			1.57900
$222$		0			0
$223$	333226.	−	333226.i	0.448721	−	0.448721i	−0.446208	−	0.894929i	$-0.647226\pi$
$223$	333226.	−	333226.i	0.448721	−	0.448721i	0.894929	+	0.446208i	$0.147226\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	108690.	+	108690.i	0.139999	+	0.139999i	0.773633	−	0.633634i	$-0.218437\pi$
$227$	108690.	+	108690.i	0.139999	+	0.139999i	−0.633634	+	0.773633i	$0.718437\pi$
$228$		0			0
$229$		−	1.06177e6i		−	1.33796i	−0.743280	−	0.668981i	$-0.766731\pi$
$229$		−	1.06177e6i		−	1.33796i	0.743280	−	0.668981i	$-0.233269\pi$
$230$		0			0
$231$			126833.i			0.156388i
$232$		0			0
$233$	722161.	+	722161.i	0.871454	+	0.871454i	0.992631	−	0.121177i	$-0.0386669\pi$
$233$	722161.	+	722161.i	0.871454	+	0.871454i	−0.121177	+	0.992631i	$0.538667\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	1.25681e6	−	1.25681e6i	1.45344	−	1.45344i
$238$		0			0
$239$	447940.			0.507254			0.253627	−	0.967302i	$-0.418376\pi$
$239$	447940.			0.507254			0.253627	+	0.967302i	$0.418376\pi$
$240$		0			0
$241$	−666714.			−0.739430			−0.369715	−	0.929145i	$-0.620545\pi$
$241$	−666714.			−0.739430			−0.369715	+	0.929145i	$0.620545\pi$
$242$		0			0
$243$	−1.30973e6	+	1.30973e6i	−1.42287	+	1.42287i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	1.69628e6	+	1.69628e6i	1.76911	+	1.76911i
$248$		0			0
$249$			2.38970e6i			2.44256i
$250$		0			0
$251$		−	1.35917e6i		−	1.36173i	−0.732409	−	0.680865i	$-0.761604\pi$
$251$		−	1.35917e6i		−	1.36173i	0.732409	−	0.680865i	$-0.238396\pi$
$252$		0			0
$253$	193795.	+	193795.i	0.190345	+	0.190345i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	559279.	−	559279.i	0.528196	−	0.528196i	−0.391838	−	0.920034i	$-0.628161\pi$
$257$	559279.	−	559279.i	0.528196	−	0.528196i	0.920034	+	0.391838i	$0.128161\pi$
$258$		0			0
$259$	79350.8			0.0735025
$260$		0			0
$261$	2.98126e6			2.70893
$262$		0			0
$263$	792250.	−	792250.i	0.706274	−	0.706274i	−0.259476	−	0.965750i	$-0.583550\pi$
$263$	792250.	−	792250.i	0.706274	−	0.706274i	0.965750	+	0.259476i	$0.0835498\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	1.35426e6	+	1.35426e6i	1.16258	+	1.16258i
$268$		0			0
$269$			2.25887e6i			1.90332i	0.307158	+	0.951659i	$0.400622\pi$
$269$			2.25887e6i			1.90332i	−0.307158	+	0.951659i	$0.599378\pi$
$270$		0			0
$271$		−	1.13559e6i		−	0.939289i	−0.882856	−	0.469645i	$-0.844382\pi$
$271$		−	1.13559e6i		−	0.939289i	0.882856	−	0.469645i	$-0.155618\pi$
$272$		0			0
$273$	−222203.	−	222203.i	−0.180444	−	0.180444i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	371729.	−	371729.i	0.291090	−	0.291090i	−0.546421	−	0.837511i	$-0.684010\pi$
$277$	371729.	−	371729.i	0.291090	−	0.291090i	0.837511	+	0.546421i	$0.184010\pi$
$278$		0			0
$279$	4.16661e6			3.20459
$280$		0			0
$281$	−119919.			−0.0905989			−0.0452995	−	0.998973i	$-0.514424\pi$
$281$	−119919.			−0.0905989			−0.0452995	+	0.998973i	$0.514424\pi$
$282$		0			0
$283$	647984.	−	647984.i	0.480948	−	0.480948i	−0.424486	−	0.905434i	$-0.639545\pi$
$283$	647984.	−	647984.i	0.480948	−	0.480948i	0.905434	+	0.424486i	$0.139545\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−97326.8	−	97326.8i	−0.0697473	−	0.0697473i
$288$		0			0
$289$			125599.i			0.0884589i
$290$		0			0
$291$			1.69761e6i			1.17518i
$292$		0			0
$293$	−1.53617e6	−	1.53617e6i	−1.04537	−	1.04537i	−0.998920	−	0.0464532i	$-0.985208\pi$
$293$	−1.53617e6	−	1.53617e6i	−1.04537	−	1.04537i	−0.0464532	−	0.998920i	$-0.514792\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	2.91887e6	−	2.91887e6i	1.92010	−	1.92010i
$298$		0			0
$299$	−679032.			−0.439250
$300$		0			0
$301$	96846.2			0.0616122
$302$		0			0
$303$	−2.58262e6	+	2.58262e6i	−1.61605	+	1.61605i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−153306.	−	153306.i	−0.0928351	−	0.0928351i	0.659164	−	0.751999i	$-0.270910\pi$
$307$	−153306.	−	153306.i	−0.0928351	−	0.0928351i	−0.751999	+	0.659164i	$0.770910\pi$
$308$		0			0
$309$		−	4.51492e6i		−	2.69001i
$310$		0			0
$311$		−	1.53907e6i		−	0.902314i	−0.892445	−	0.451157i	$-0.851011\pi$
$311$		−	1.53907e6i		−	0.902314i	0.892445	−	0.451157i	$-0.148989\pi$
$312$		0			0
$313$	−707822.	−	707822.i	−0.408379	−	0.408379i	0.472794	−	0.881173i	$-0.343245\pi$
$313$	−707822.	−	707822.i	−0.408379	−	0.408379i	−0.881173	+	0.472794i	$0.843245\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−891690.	+	891690.i	−0.498386	+	0.498386i	−0.910935	−	0.412550i	$-0.864638\pi$
$317$	−891690.	+	891690.i	−0.498386	+	0.498386i	0.412550	+	0.910935i	$0.364638\pi$
$318$		0			0
$319$	−2.04203e6			−1.12353
$320$		0			0
$321$	5.99596e6			3.24785
$322$		0			0
$323$	1.91493e6	−	1.91493e6i	1.02129	−	1.02129i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−2.03897e6	−	2.03897e6i	−1.05449	−	1.05449i
$328$		0			0
$329$		−	259343.i		−	0.132095i
$330$		0			0
$331$		−	3.68173e6i		−	1.84706i	−0.383522	−	0.923532i	$-0.625289\pi$
$331$		−	3.68173e6i		−	1.84706i	0.383522	−	0.923532i	$-0.374711\pi$
$332$		0			0
$333$	−3.09101e6	−	3.09101e6i	−1.52753	−	1.52753i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	904485.	−	904485.i	0.433837	−	0.433837i	−0.456094	−	0.889931i	$-0.650752\pi$
$337$	904485.	−	904485.i	0.433837	−	0.433837i	0.889931	+	0.456094i	$0.150752\pi$
$338$		0			0
$339$	−2.52820e6			−1.19485
$340$		0			0
$341$	−2.85394e6			−1.32910
$342$		0			0
$343$	255326.	−	255326.i	0.117182	−	0.117182i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	88986.1	+	88986.1i	0.0396733	+	0.0396733i	0.726665	−	0.686992i	$-0.241069\pi$
$347$	88986.1	+	88986.1i	0.0396733	+	0.0396733i	−0.686992	+	0.726665i	$0.741069\pi$
$348$		0			0
$349$			138062.i			0.0606750i	0.999540	+	0.0303375i	$0.00965821\pi$
$349$			138062.i			0.0606750i	−0.999540	+	0.0303375i	$0.990342\pi$
$350$		0			0
$351$			1.02273e7i			4.43092i
$352$		0			0
$353$	800599.	+	800599.i	0.341962	+	0.341962i	0.857105	−	0.515142i	$-0.172261\pi$
$353$	800599.	+	800599.i	0.341962	+	0.341962i	−0.515142	+	0.857105i	$0.672261\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−250846.	+	250846.i	−0.104168	+	0.104168i
$358$		0			0
$359$	−2.38988e6			−0.978680			−0.489340	−	0.872093i	$-0.662762\pi$
$359$	−2.38988e6			−0.978680			−0.489340	+	0.872093i	$0.662762\pi$
$360$		0			0
$361$	3.19042e6			1.28849
$362$		0			0
$363$	−89788.8	+	89788.8i	−0.0357648	+	0.0357648i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−2.47079e6	−	2.47079e6i	−0.957571	−	0.957571i	0.0415643	−	0.999136i	$-0.486766\pi$
$367$	−2.47079e6	−	2.47079e6i	−0.957571	−	0.957571i	−0.999136	+	0.0415643i	$0.986766\pi$
$368$		0			0
$369$			7.58250e6i			2.89899i
$370$		0			0
$371$		−	265719.i		−	0.100228i
$372$		0			0
$373$	1.07325e6	+	1.07325e6i	0.399420	+	0.399420i	0.878029	−	0.478608i	$-0.158859\pi$
$373$	1.07325e6	+	1.07325e6i	0.399420	+	0.399420i	−0.478608	+	0.878029i	$0.658859\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	3.57749e6	−	3.57749e6i	1.29636	−	1.29636i
$378$		0			0
$379$	−2.96021e6			−1.05858			−0.529292	−	0.848440i	$-0.677542\pi$
$379$	−2.96021e6			−1.05858			−0.529292	+	0.848440i	$0.677542\pi$
$380$		0			0
$381$	−392793.			−0.138628
$382$		0			0
$383$	1.15833e6	−	1.15833e6i	0.403493	−	0.403493i	−0.475969	−	0.879462i	$-0.657902\pi$
$383$	1.15833e6	−	1.15833e6i	0.403493	−	0.403493i	0.879462	+	0.475969i	$0.157902\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−3.77253e6	−	3.77253e6i	−1.28043	−	1.28043i
$388$		0			0
$389$			2.07790e6i			0.696228i	0.937452	+	0.348114i	$0.113178\pi$
$389$			2.07790e6i			0.696228i	−0.937452	+	0.348114i	$0.886822\pi$
$390$		0			0
$391$			766562.i			0.253574i
$392$		0			0
$393$	3.37249e6	+	3.37249e6i	1.10146	+	1.10146i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−1.69118e6	+	1.69118e6i	−0.538535	+	0.538535i	−0.923099	−	0.384564i	$-0.874352\pi$
$397$	−1.69118e6	+	1.69118e6i	−0.538535	+	0.538535i	0.384564	+	0.923099i	$0.374352\pi$
$398$		0			0
$399$	−742283.			−0.233420
$400$		0			0
$401$	−3.15441e6			−0.979618			−0.489809	−	0.871830i	$-0.662933\pi$
$401$	−3.15441e6			−0.979618			−0.489809	+	0.871830i	$0.662933\pi$
$402$		0			0
$403$	4.99991e6	−	4.99991e6i	1.53355	−	1.53355i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	2.11721e6	+	2.11721e6i	0.633545	+	0.633545i
$408$		0			0
$409$		−	2.29208e6i		−	0.677518i	−0.940873	−	0.338759i	$-0.889993\pi$
$409$		−	2.29208e6i		−	0.677518i	0.940873	−	0.338759i	$-0.110007\pi$
$410$		0			0
$411$		−	674569.i		−	0.196980i
$412$		0			0
$413$	−95229.7	−	95229.7i	−0.0274725	−	0.0274725i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	670881.	−	670881.i	0.188932	−	0.188932i
$418$		0			0
$419$	−6.15646e6			−1.71315			−0.856576	−	0.516021i	$-0.827413\pi$
$419$	−6.15646e6			−1.71315			−0.856576	+	0.516021i	$0.827413\pi$
$420$		0			0
$421$	2.49505e6			0.686078			0.343039	−	0.939321i	$-0.388544\pi$
$421$	2.49505e6			0.686078			0.343039	+	0.939321i	$0.388544\pi$
$422$		0			0
$423$	−1.01024e7	+	1.01024e7i	−2.74520	+	2.74520i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	45901.0	+	45901.0i	0.0121830	+	0.0121830i
$428$		0			0
$429$		−	1.18575e7i		−	3.11063i
$430$		0			0
$431$		−	243250.i		−	0.0630754i	−0.999503	−	0.0315377i	$-0.989960\pi$
$431$		−	243250.i		−	0.0630754i	0.999503	−	0.0315377i	$-0.0100404\pi$
$432$		0			0
$433$	−248812.	−	248812.i	−0.0637752	−	0.0637752i	0.674500	−	0.738275i	$-0.264359\pi$
$433$	−248812.	−	248812.i	−0.0637752	−	0.0637752i	−0.738275	+	0.674500i	$0.764359\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.13418e6	+	1.13418e6i	−0.284104	+	0.284104i
$438$		0			0
$439$	7.50553e6			1.85875			0.929373	−	0.369141i	$-0.120348\pi$
$439$	7.50553e6			1.85875			0.929373	+	0.369141i	$0.120348\pi$
$440$		0			0
$441$	−9.91142e6			−2.42683
$442$		0			0
$443$	1.54032e6	−	1.54032e6i	0.372908	−	0.372908i	−0.495627	−	0.868535i	$-0.665062\pi$
$443$	1.54032e6	−	1.54032e6i	0.372908	−	0.372908i	0.868535	+	0.495627i	$0.165062\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−640012.	−	640012.i	−0.151502	−	0.151502i
$448$		0			0
$449$			2.84010e6i			0.664841i	0.943131	+	0.332420i	$0.107865\pi$
$449$			2.84010e6i			0.664841i	−0.943131	+	0.332420i	$0.892135\pi$
$450$		0			0
$451$		−	5.19367e6i		−	1.20236i
$452$		0			0
$453$	−4.55190e6	−	4.55190e6i	−1.04219	−	1.04219i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−6.14292e6	+	6.14292e6i	−1.37589	+	1.37589i	−0.524454	+	0.851439i	$0.675730\pi$
$457$	−6.14292e6	+	6.14292e6i	−1.37589	+	1.37589i	−0.851439	+	0.524454i	$0.824270\pi$
$458$		0			0
$459$	1.15457e7			2.55792
$460$		0			0
$461$	6.75343e6			1.48003			0.740017	−	0.672588i	$-0.234817\pi$
$461$	6.75343e6			1.48003			0.740017	+	0.672588i	$0.234817\pi$
$462$		0			0
$463$	4.06006e6	−	4.06006e6i	0.880197	−	0.880197i	−0.113358	−	0.993554i	$-0.536161\pi$
$463$	4.06006e6	−	4.06006e6i	0.880197	−	0.880197i	0.993554	+	0.113358i	$0.0361605\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	3.18292e6	+	3.18292e6i	0.675357	+	0.675357i	0.958946	−	0.283589i	$-0.0915252\pi$
$467$	3.18292e6	+	3.18292e6i	0.675357	+	0.675357i	−0.283589	+	0.958946i	$0.591525\pi$
$468$		0			0
$469$		−	139474.i		−	0.0292794i
$470$		0			0
$471$			1.43449e6i			0.297951i
$472$		0			0
$473$	2.58401e6	+	2.58401e6i	0.531058	+	0.531058i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−1.03508e7	+	1.03508e7i	−2.08294	+	2.08294i
$478$		0			0
$479$	892421.			0.177718			0.0888590	−	0.996044i	$-0.471678\pi$
$479$	892421.			0.177718			0.0888590	+	0.996044i	$0.471678\pi$
$480$		0			0
$481$	−7.41841e6			−1.46200
$482$		0			0
$483$	148571.	−	148571.i	0.0289778	−	0.0289778i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	6.25745e6	+	6.25745e6i	1.19557	+	1.19557i	0.975480	+	0.220089i	$0.0706349\pi$
$487$	6.25745e6	+	6.25745e6i	1.19557	+	1.19557i	0.220089	+	0.975480i	$0.429365\pi$
$488$		0			0
$489$			1.83070e6i			0.346215i
$490$		0			0
$491$		−	9.81255e6i		−	1.83687i	−0.395574	−	0.918434i	$-0.629454\pi$
$491$		−	9.81255e6i		−	1.83687i	0.395574	−	0.918434i	$-0.370546\pi$
$492$		0			0
$493$	−4.03865e6	−	4.03865e6i	−0.748374	−	0.748374i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	463748.	−	463748.i	0.0842152	−	0.0842152i
$498$		0			0
$499$	−2.89414e6			−0.520317			−0.260159	−	0.965566i	$-0.583775\pi$
$499$	−2.89414e6			−0.520317			−0.260159	+	0.965566i	$0.583775\pi$
$500$		0			0
$501$	−6.29477e6			−1.12043
$502$		0			0
$503$	−1.78816e6	+	1.78816e6i	−0.315128	+	0.315128i	−0.846892	−	0.531765i	$-0.821529\pi$
$503$	−1.78816e6	+	1.78816e6i	−0.315128	+	0.315128i	0.531765	+	0.846892i	$0.321529\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	1.31786e7	+	1.31786e7i	2.27693	+	2.27693i
$508$		0			0
$509$		−	972151.i		−	0.166318i	−0.996536	−	0.0831590i	$-0.973499\pi$
$509$		−	972151.i		−	0.166318i	0.996536	−	0.0831590i	$-0.0265009\pi$
$510$		0			0
$511$			642138.i			0.108787i
$512$		0			0
$513$	1.70825e7	+	1.70825e7i	2.86588	+	2.86588i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	6.91970e6	−	6.91970e6i	1.13857	−	1.13857i
$518$		0			0
$519$	1.25040e7			2.03765
$520$		0			0
$521$	−3.44776e6			−0.556471			−0.278235	−	0.960513i	$-0.589750\pi$
$521$	−3.44776e6			−0.556471			−0.278235	+	0.960513i	$0.589750\pi$
$522$		0			0
$523$	−5.91328e6	+	5.91328e6i	−0.945310	+	0.945310i	−0.998580	−	0.0532699i	$-0.983036\pi$
$523$	−5.91328e6	+	5.91328e6i	−0.945310	+	0.945310i	0.0532699	+	0.998580i	$0.483036\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−5.64442e6	−	5.64442e6i	−0.885304	−	0.885304i
$528$		0			0
$529$			5.98232e6i			0.929460i
$530$		0			0
$531$			7.41912e6i			1.14187i
$532$		0			0
$533$	9.09896e6	+	9.09896e6i	1.38731	+	1.38731i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−8.48288e6	+	8.48288e6i	−1.26943	+	1.26943i
$538$		0			0
$539$	6.78888e6			1.00653
$540$		0			0
$541$	−6.56403e6			−0.964223			−0.482111	−	0.876110i	$-0.660130\pi$
$541$	−6.56403e6			−0.964223			−0.482111	+	0.876110i	$0.660130\pi$
$542$		0			0
$543$	753305.	−	753305.i	0.109641	−	0.109641i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−3.79769e6	−	3.79769e6i	−0.542690	−	0.542690i	0.381627	−	0.924316i	$-0.375364\pi$
$547$	−3.79769e6	−	3.79769e6i	−0.542690	−	0.542690i	−0.924316	+	0.381627i	$0.875364\pi$
$548$		0			0
$549$		−	3.57604e6i		−	0.506374i
$550$		0			0
$551$		−	1.19509e7i		−	1.67695i
$552$		0			0
$553$	468322.	+	468322.i	0.0651226	+	0.0651226i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	1.14329e6	−	1.14329e6i	0.156142	−	0.156142i	−0.624713	−	0.780855i	$-0.714784\pi$
$557$	1.14329e6	−	1.14329e6i	0.156142	−	0.156142i	0.780855	+	0.624713i	$0.214784\pi$
$558$		0			0
$559$	−9.05403e6			−1.22550
$560$		0			0
$561$	−1.33859e7			−1.79573
$562$		0			0
$563$	2.71925e6	−	2.71925e6i	0.361558	−	0.361558i	−0.502828	−	0.864386i	$-0.667707\pi$
$563$	2.71925e6	−	2.71925e6i	0.361558	−	0.361558i	0.864386	+	0.502828i	$0.167707\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−1.13784e6	−	1.13784e6i	−0.148635	−	0.148635i
$568$		0			0
$569$			1.41869e6i			0.183700i	0.995773	+	0.0918498i	$0.0292780\pi$
$569$			1.41869e6i			0.183700i	−0.995773	+	0.0918498i	$0.970722\pi$
$570$		0			0
$571$		−	3.00296e6i		−	0.385442i	−0.981254	−	0.192721i	$-0.938269\pi$
$571$		−	3.00296e6i		−	0.385442i	0.981254	−	0.192721i	$-0.0617313\pi$
$572$		0			0
$573$	−1.20576e7	−	1.20576e7i	−1.53417	−	1.53417i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	1.58698e6	−	1.58698e6i	0.198441	−	0.198441i	−0.600890	−	0.799332i	$-0.705187\pi$
$577$	1.58698e6	−	1.58698e6i	0.198441	−	0.198441i	0.799332	+	0.600890i	$0.205187\pi$
$578$		0			0
$579$	−1.07812e7			−1.33651
$580$		0			0
$581$	−890470.			−0.109441
$582$		0			0
$583$	7.08980e6	−	7.08980e6i	0.863899	−	0.863899i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−7.77055e6	−	7.77055e6i	−0.930800	−	0.930800i	0.0669557	−	0.997756i	$-0.478671\pi$
$587$	−7.77055e6	−	7.77055e6i	−0.930800	−	0.930800i	−0.997756	+	0.0669557i	$0.978671\pi$
$588$		0			0
$589$		−	1.67025e7i		−	1.98378i
$590$		0			0
$591$			6.94024e6i			0.817346i
$592$		0			0
$593$	4.31542e6	+	4.31542e6i	0.503949	+	0.503949i	0.912663	−	0.408714i	$-0.134023\pi$
$593$	4.31542e6	+	4.31542e6i	0.503949	+	0.503949i	−0.408714	+	0.912663i	$0.634023\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−1.96061e7	+	1.96061e7i	−2.25142	+	2.25142i
$598$		0			0
$599$	125665.			0.0143103			0.00715515	−	0.999974i	$-0.497722\pi$
$599$	125665.			0.0143103			0.00715515	+	0.999974i	$0.497722\pi$
$600$		0			0
$601$	1.32263e7			1.49366			0.746829	−	0.665016i	$-0.231575\pi$
$601$	1.32263e7			1.49366			0.746829	+	0.665016i	$0.231575\pi$
$602$		0			0
$603$	−5.43305e6	+	5.43305e6i	−0.608486	+	0.608486i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−263218.	−	263218.i	−0.0289964	−	0.0289964i	0.692460	−	0.721456i	$-0.256527\pi$
$607$	−263218.	−	263218.i	−0.0289964	−	0.0289964i	−0.721456	+	0.692460i	$0.756527\pi$
$608$		0			0
$609$			1.56550e6i			0.171044i
$610$		0			0
$611$			2.42457e7i			2.62743i
$612$		0			0
$613$	−8.60910e6	−	8.60910e6i	−0.925351	−	0.925351i	0.0720496	−	0.997401i	$-0.477046\pi$
$613$	−8.60910e6	−	8.60910e6i	−0.925351	−	0.925351i	−0.997401	+	0.0720496i	$0.977046\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1.09363e6	+	1.09363e6i	−0.115653	+	0.115653i	−0.762565	−	0.646912i	$-0.776060\pi$
$617$	−1.09363e6	+	1.09363e6i	−0.115653	+	0.115653i	0.646912	+	0.762565i	$0.276060\pi$
$618$		0			0
$619$	−2.29345e6			−0.240581			−0.120291	−	0.992739i	$-0.538383\pi$
$619$	−2.29345e6			−0.240581			−0.120291	+	0.992739i	$0.538383\pi$
$620$		0			0
$621$	−6.83825e6			−0.711567
$622$		0			0
$623$	−504636.	+	504636.i	−0.0520905	+	0.0520905i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−1.98053e7	−	1.98053e7i	−2.01193	−	2.01193i
$628$		0			0
$629$			8.37467e6i			0.843998i
$630$		0			0
$631$		−	606243.i		−	0.0606140i	−0.999541	−	0.0303070i	$-0.990351\pi$
$631$		−	606243.i		−	0.0606140i	0.999541	−	0.0303070i	$-0.00964850\pi$
$632$		0			0
$633$	−4.51209e6	−	4.51209e6i	−0.447577	−	0.447577i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−1.18937e7	+	1.18937e7i	−1.16136	+	1.16136i
$638$		0			0
$639$	−3.61295e7			−3.50033
$640$		0			0
$641$	1.32752e7			1.27614			0.638068	−	0.769980i	$-0.279734\pi$
$641$	1.32752e7			1.27614			0.638068	+	0.769980i	$0.279734\pi$
$642$		0			0
$643$	−8.12358e6	+	8.12358e6i	−0.774854	+	0.774854i	−0.978951	−	0.204096i	$-0.934574\pi$
$643$	−8.12358e6	+	8.12358e6i	−0.774854	+	0.774854i	0.204096	+	0.978951i	$0.434574\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1.19518e7	+	1.19518e7i	1.12246	+	1.12246i	0.991370	+	0.131091i	$0.0418480\pi$
$647$	1.19518e7	+	1.19518e7i	1.12246	+	1.12246i	0.131091	+	0.991370i	$0.458152\pi$
$648$		0			0
$649$		−	5.08177e6i		−	0.473591i
$650$		0			0
$651$			2.18794e6i			0.202340i
$652$		0			0
$653$	1.04541e7	+	1.04541e7i	0.959410	+	0.959410i	0.999208	−	0.0397980i	$-0.0126714\pi$
$653$	1.04541e7	+	1.04541e7i	0.959410	+	0.959410i	−0.0397980	+	0.999208i	$0.512671\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	2.50137e7	−	2.50137e7i	2.26082	−	2.26082i
$658$		0			0
$659$	−6.35607e6			−0.570131			−0.285066	−	0.958508i	$-0.592015\pi$
$659$	−6.35607e6			−0.570131			−0.285066	+	0.958508i	$0.592015\pi$
$660$		0			0
$661$	−7.61056e6			−0.677506			−0.338753	−	0.940875i	$-0.610005\pi$
$661$	−7.61056e6			−0.677506			−0.338753	+	0.940875i	$0.610005\pi$
$662$		0			0
$663$	2.34512e7	−	2.34512e7i	2.07196	−	2.07196i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	2.39201e6	+	2.39201e6i	0.208184	+	0.208184i
$668$		0			0
$669$		−	1.36324e7i		−	1.17762i
$670$		0			0
$671$			2.44943e6i			0.210019i
$672$		0			0
$673$	2.78078e6	+	2.78078e6i	0.236662	+	0.236662i	0.815466	−	0.578804i	$-0.196480\pi$
$673$	2.78078e6	+	2.78078e6i	0.236662	+	0.236662i	−0.578804	+	0.815466i	$0.696480\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	1.08002e7	−	1.08002e7i	0.905649	−	0.905649i	−0.0902683	−	0.995917i	$-0.528772\pi$
$677$	1.08002e7	−	1.08002e7i	0.905649	−	0.905649i	0.995917	+	0.0902683i	$0.0287725\pi$
$678$		0			0
$679$	−632578.			−0.0526550
$680$		0			0
$681$	4.44655e6			0.367414
$682$		0			0
$683$	7.14651e6	−	7.14651e6i	0.586195	−	0.586195i	−0.350404	−	0.936599i	$-0.613956\pi$
$683$	7.14651e6	−	7.14651e6i	0.586195	−	0.586195i	0.936599	+	0.350404i	$0.113956\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−2.17187e7	−	2.17187e7i	−1.75567	−	1.75567i
$688$		0			0
$689$			2.48417e7i			1.99358i
$690$		0			0
$691$			1.88887e7i			1.50490i	0.658651	+	0.752449i	$0.271128\pi$
$691$			1.88887e7i			1.50490i	−0.658651	+	0.752449i	$0.728872\pi$
$692$		0			0
$693$	1.84102e6	+	1.84102e6i	0.145621	+	0.145621i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	1.02719e7	−	1.02719e7i	0.800879	−	0.800879i
$698$		0			0
$699$	2.95438e7			2.28704
$700$		0			0
$701$	−1.43661e7			−1.10419			−0.552094	−	0.833782i	$-0.686171\pi$
$701$	−1.43661e7			−1.10419			−0.552094	+	0.833782i	$0.686171\pi$
$702$		0			0
$703$	−1.23908e7	+	1.23908e7i	−0.945611	+	0.945611i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−962359.	−	962359.i	−0.0724083	−	0.0724083i
$708$		0			0
$709$			1.10916e7i			0.828665i	0.910126	+	0.414332i	$0.135985\pi$
$709$			1.10916e7i			0.828665i	−0.910126	+	0.414332i	$0.864015\pi$
$710$		0			0
$711$		−	3.64859e7i		−	2.70676i
$712$		0			0
$713$	3.34307e6	+	3.34307e6i	0.246276	+	0.246276i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	9.16268e6	−	9.16268e6i	0.665617	−	0.665617i
$718$		0			0
$719$	−6.35957e6			−0.458781			−0.229391	−	0.973334i	$-0.573673\pi$
$719$	−6.35957e6			−0.458781			−0.229391	+	0.973334i	$0.573673\pi$
$720$		0			0
$721$	1.68239e6			0.120528
$722$		0			0
$723$	−1.36377e7	+	1.36377e7i	−0.970279	+	0.970279i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	1.96255e6	+	1.96255e6i	0.137716	+	0.137716i	0.772604	−	0.634888i	$-0.218954\pi$
$727$	1.96255e6	+	1.96255e6i	0.137716	+	0.137716i	−0.634888	+	0.772604i	$0.718954\pi$
$728$		0			0
$729$			1.73063e7i			1.20611i
$730$		0			0
$731$			1.02211e7i			0.707467i
$732$		0			0
$733$	−1.23035e6	−	1.23035e6i	−0.0845803	−	0.0845803i	0.663551	−	0.748131i	$-0.269049\pi$
$733$	−1.23035e6	−	1.23035e6i	−0.0845803	−	0.0845803i	−0.748131	+	0.663551i	$0.769049\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	3.72140e6	−	3.72140e6i	0.252370	−	0.252370i
$738$		0			0
$739$	3.51888e6			0.237024			0.118512	−	0.992953i	$-0.462188\pi$
$739$	3.51888e6			0.237024			0.118512	+	0.992953i	$0.462188\pi$
$740$		0			0
$741$	6.93951e7			4.64284
$742$		0			0
$743$	−1.13866e7	+	1.13866e7i	−0.756700	+	0.756700i	−0.975720	−	0.219020i	$-0.929714\pi$
$743$	−1.13866e7	+	1.13866e7i	−0.756700	+	0.756700i	0.219020	+	0.975720i	$0.429714\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	3.46872e7	+	3.46872e7i	2.27440	+	2.27440i
$748$		0			0
$749$			2.23427e6i			0.145523i
$750$		0			0
$751$		−	1.51880e7i		−	0.982657i	−0.870974	−	0.491329i	$-0.836511\pi$
$751$		−	1.51880e7i		−	0.982657i	0.870974	−	0.491329i	$-0.163489\pi$
$752$		0			0
$753$	−2.78021e7	−	2.78021e7i	−1.78686	−	1.78686i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−1.34745e7	+	1.34745e7i	−0.854619	+	0.854619i	−0.990698	−	0.136079i	$-0.956550\pi$
$757$	−1.34745e7	+	1.34745e7i	−0.854619	+	0.854619i	0.136079	+	0.990698i	$0.456550\pi$
$758$		0			0
$759$	7.92821e6			0.499541
$760$		0			0
$761$	−2.19416e7			−1.37343			−0.686716	−	0.726926i	$-0.740948\pi$
$761$	−2.19416e7			−1.37343			−0.686716	+	0.726926i	$0.740948\pi$
$762$		0			0
$763$	759778.	−	759778.i	0.0472471	−	0.0472471i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	8.90291e6	+	8.90291e6i	0.546441	+	0.546441i
$768$		0			0
$769$		−	3.24691e7i		−	1.97995i	−0.141244	−	0.989975i	$-0.545110\pi$
$769$		−	3.24691e7i		−	1.97995i	0.141244	−	0.989975i	$-0.454890\pi$
$770$		0			0
$771$		−	2.28802e7i		−	1.38620i
$772$		0			0
$773$	−1.40880e7	−	1.40880e7i	−0.848011	−	0.848011i	0.141874	−	0.989885i	$-0.454687\pi$
$773$	−1.40880e7	−	1.40880e7i	−0.848011	−	0.848011i	−0.989885	+	0.141874i	$0.954687\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	1.62313e6	−	1.62313e6i	0.0964498	−	0.0964498i
$778$		0			0
$779$	3.03957e7			1.79460
$780$		0			0
$781$	2.47471e7			1.45176
$782$		0			0
$783$	3.60275e7	−	3.60275e7i	2.10005	−	2.10005i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−1.41156e7	−	1.41156e7i	−0.812384	−	0.812384i	0.172606	−	0.984991i	$-0.444781\pi$
$787$	−1.41156e7	−	1.41156e7i	−0.812384	−	0.812384i	−0.984991	+	0.172606i	$0.944781\pi$
$788$		0			0
$789$		−	3.24112e7i		−	1.85354i
$790$		0			0
$791$		−	942081.i		−	0.0535362i
$792$		0			0
$793$	−4.29123e6	−	4.29123e6i	−0.242325	−	0.242325i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	2.30674e7	−	2.30674e7i	1.28633	−	1.28633i	0.349330	−	0.937000i	$-0.386409\pi$
$797$	2.30674e7	−	2.30674e7i	1.28633	−	1.28633i	0.937000	−	0.349330i	$-0.113591\pi$
$798$		0			0
$799$	2.73711e7			1.51679
$800$		0			0
$801$	3.93150e7			2.16510
$802$		0			0
$803$	−1.71333e7	+	1.71333e7i	−0.937674	+	0.937674i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	4.62056e7	+	4.62056e7i	2.49753	+	2.49753i
$808$		0			0
$809$			2.89763e7i			1.55658i	0.627903	+	0.778291i	$0.283913\pi$
$809$			2.89763e7i			1.55658i	−0.627903	+	0.778291i	$0.716087\pi$
$810$		0			0
$811$			2.02186e7i			1.07944i	0.841844	+	0.539721i	$0.181470\pi$
$811$			2.02186e7i			1.07944i	−0.841844	+	0.539721i	$0.818530\pi$
$812$		0			0
$813$	−2.32287e7	−	2.32287e7i	−1.23253	−	1.23253i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−1.51228e7	+	1.51228e7i	−0.792642	+	0.792642i
$818$		0			0
$819$	−6.45068e6			−0.336044
$820$		0			0
$821$	−2.37780e7			−1.23117			−0.615585	−	0.788070i	$-0.711080\pi$
$821$	−2.37780e7			−1.23117			−0.615585	+	0.788070i	$0.711080\pi$
$822$		0			0
$823$	−1.91500e7	+	1.91500e7i	−0.985530	+	0.985530i	−0.999897	−	0.0143670i	$-0.995427\pi$
$823$	−1.91500e7	+	1.91500e7i	−0.985530	+	0.985530i	0.0143670	+	0.999897i	$0.495427\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−8.17984e6	−	8.17984e6i	−0.415892	−	0.415892i	0.467893	−	0.883785i	$-0.345013\pi$
$827$	−8.17984e6	−	8.17984e6i	−0.415892	−	0.415892i	−0.883785	+	0.467893i	$0.845013\pi$
$828$		0			0
$829$			1.92400e7i			0.972339i	0.873865	+	0.486170i	$0.161606\pi$
$829$			1.92400e7i			0.972339i	−0.873865	+	0.486170i	$0.838394\pi$
$830$		0			0
$831$		−	1.52076e7i		−	0.763936i
$832$		0			0
$833$	1.34268e7	+	1.34268e7i	0.670440	+	0.670440i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	5.03520e7	−	5.03520e7i	2.48430	−	2.48430i
$838$		0			0
$839$	3.57749e7			1.75458			0.877291	−	0.479959i	$-0.159349\pi$
$839$	3.57749e7			1.75458			0.877291	+	0.479959i	$0.159349\pi$
$840$		0			0
$841$	−4.69354e6			−0.228829
$842$		0			0
$843$	−2.45296e6	+	2.45296e6i	−0.118884	+	0.118884i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−33457.9	−	33457.9i	−0.00160247	−	0.00160247i
$848$		0			0
$849$		−	2.65092e7i		−	1.26220i
$850$		0			0
$851$		−	4.96014e6i		−	0.234785i
$852$		0			0
$853$	−1.23154e7	−	1.23154e7i	−0.579529	−	0.579529i	0.355244	−	0.934774i	$-0.384398\pi$
$853$	−1.23154e7	−	1.23154e7i	−0.579529	−	0.579529i	−0.934774	+	0.355244i	$0.884398\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1.12779e7	−	1.12779e7i	0.524539	−	0.524539i	−0.394400	−	0.918939i	$-0.629048\pi$
$857$	1.12779e7	−	1.12779e7i	0.524539	−	0.524539i	0.918939	+	0.394400i	$0.129048\pi$
$858$		0			0
$859$	7.35211e6			0.339961			0.169980	−	0.985447i	$-0.445630\pi$
$859$	7.35211e6			0.339961			0.169980	+	0.985447i	$0.445630\pi$
$860$		0			0
$861$	−3.98167e6			−0.183045
$862$		0			0
$863$	8.13326e6	−	8.13326e6i	0.371739	−	0.371739i	−0.496372	−	0.868110i	$-0.665335\pi$
$863$	8.13326e6	−	8.13326e6i	0.371739	−	0.371739i	0.868110	+	0.496372i	$0.165335\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	2.56914e6	+	2.56914e6i	0.116076	+	0.116076i
$868$		0			0
$869$			2.49912e7i			1.12263i
$870$		0			0
$871$			1.30393e7i			0.582382i
$872$		0			0
$873$	2.46413e7	+	2.46413e7i	1.09428	+	1.09428i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	8.47946e6	−	8.47946e6i	0.372280	−	0.372280i	−0.496027	−	0.868307i	$-0.665208\pi$
$877$	8.47946e6	−	8.47946e6i	0.372280	−	0.372280i	0.868307	+	0.496027i	$0.165208\pi$
$878$		0			0
$879$	−6.28453e7			−2.74347
$880$		0			0
$881$	1.68347e7			0.730746			0.365373	−	0.930861i	$-0.380941\pi$
$881$	1.68347e7			0.730746			0.365373	+	0.930861i	$0.380941\pi$
$882$		0			0
$883$	1.77667e7	−	1.77667e7i	0.766842	−	0.766842i	−0.210708	−	0.977549i	$-0.567577\pi$
$883$	1.77667e7	−	1.77667e7i	0.766842	−	0.766842i	0.977549	+	0.210708i	$0.0675768\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−2.48114e7	−	2.48114e7i	−1.05887	−	1.05887i	−0.998155	−	0.0607123i	$-0.980663\pi$
$887$	−2.48114e7	−	2.48114e7i	−1.05887	−	1.05887i	−0.0607123	−	0.998155i	$-0.519337\pi$
$888$		0			0
$889$		−	146366.i		−	0.00621135i
$890$		0			0
$891$		−	6.07187e7i		−	2.56229i
$892$		0			0
$893$	4.04972e7	+	4.04972e7i	1.69940	+	1.69940i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−1.38897e7	+	1.38897e7i	−0.576383	+	0.576383i
$898$		0			0
$899$	−3.52261e7			−1.45367
$900$		0			0
$901$	2.80439e7			1.15087
$902$		0			0
$903$	1.98100e6	−	1.98100e6i	0.0808473	−	0.0808473i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	1.69766e7	+	1.69766e7i	0.685223	+	0.685223i	0.961172	−	0.275950i	$-0.0889923\pi$
$907$	1.69766e7	+	1.69766e7i	0.685223	+	0.685223i	−0.275950	+	0.961172i	$0.588992\pi$
$908$		0			0
$909$			7.49750e7i			3.00959i
$910$		0			0
$911$			3.88671e7i			1.55162i	0.630964	+	0.775812i	$0.282659\pi$
$911$			3.88671e7i			1.55162i	−0.630964	+	0.775812i	$0.717341\pi$
$912$		0			0
$913$	−2.37592e7	−	2.37592e7i	−0.943310	−	0.943310i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1.25669e6	+	1.25669e6i	−0.0493519	+	0.0493519i
$918$		0			0
$919$	2.28441e7			0.892248			0.446124	−	0.894971i	$-0.352804\pi$
$919$	2.28441e7			0.892248			0.446124	+	0.894971i	$0.352804\pi$
$920$		0			0
$921$	−6.27178e6			−0.243636
$922$		0			0
$923$	−4.33552e7	+	4.33552e7i	−1.67508	+	1.67508i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−6.55354e7	−	6.55354e7i	−2.50482	−	2.50482i
$928$		0			0
$929$			2.09188e7i			0.795239i	0.917550	+	0.397620i	$0.130164\pi$
$929$			2.09188e7i			0.795239i	−0.917550	+	0.397620i	$0.869836\pi$
$930$		0			0
$931$			3.97316e7i			1.50232i
$932$		0			0
$933$	−3.14819e7	−	3.14819e7i	−1.18401	−	1.18401i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−24574.3	+	24574.3i	−0.000914390	+	0.000914390i	−0.707564	−	0.706649i	$-0.750206\pi$
$937$	−24574.3	+	24574.3i	−0.000914390	+	0.000914390i	0.706649	+	0.707564i	$0.250206\pi$
$938$		0			0
$939$	−2.89572e7			−1.07175
$940$		0			0
$941$	1.97651e7			0.727656			0.363828	−	0.931466i	$-0.381470\pi$
$941$	1.97651e7			0.727656			0.363828	+	0.931466i	$0.381470\pi$
$942$		0			0
$943$	−6.08381e6	+	6.08381e6i	−0.222790	+	0.222790i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.24170e7	−	1.24170e7i	−0.449926	−	0.449926i	0.445404	−	0.895330i	$-0.353060\pi$
$947$	−1.24170e7	−	1.24170e7i	−0.449926	−	0.449926i	−0.895330	+	0.445404i	$0.853060\pi$
$948$		0			0
$949$		−	6.00327e7i		−	2.16383i
$950$		0			0
$951$			3.64793e7i			1.30796i
$952$		0			0
$953$	2.54577e7	+	2.54577e7i	0.908001	+	0.908001i	0.996111	−	0.0881096i	$-0.0280826\pi$
$953$	2.54577e7	+	2.54577e7i	0.908001	+	0.908001i	−0.0881096	+	0.996111i	$0.528083\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−4.17700e7	+	4.17700e7i	−1.47429	+	1.47429i
$958$		0			0
$959$	251364.			0.00882585
$960$		0			0
$961$	−2.06028e7			−0.719646
$962$		0			0
$963$	8.70333e7	−	8.70333e7i	3.02426	−	3.02426i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−7.40159e6	−	7.40159e6i	−0.254542	−	0.254542i	0.568288	−	0.822830i	$-0.307606\pi$
$967$	−7.40159e6	−	7.40159e6i	−0.254542	−	0.254542i	−0.822830	+	0.568288i	$0.807606\pi$
$968$		0			0
$969$		−	7.83405e7i		−	2.68026i
$970$		0			0
$971$			1.51501e7i			0.515666i	0.966189	+	0.257833i	$0.0830085\pi$
$971$			1.51501e7i			0.515666i	−0.966189	+	0.257833i	$0.916992\pi$
$972$		0			0
$973$	249990.	+	249990.i	0.00846526	+	0.00846526i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	7.88379e6	−	7.88379e6i	0.264240	−	0.264240i	−0.562534	−	0.826774i	$-0.690174\pi$
$977$	7.88379e6	−	7.88379e6i	0.264240	−	0.264240i	0.826774	+	0.562534i	$0.190174\pi$
$978$		0			0
$979$	−2.69290e7			−0.897974
$980$		0			0
$981$	−5.91925e7			−1.96378
$982$		0			0
$983$	−6.76370e6	+	6.76370e6i	−0.223255	+	0.223255i	−0.809867	−	0.586613i	$-0.800461\pi$
$983$	−6.76370e6	+	6.76370e6i	−0.223255	+	0.223255i	0.586613	+	0.809867i	$0.300461\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−5.30491e6	−	5.30491e6i	−0.173334	−	0.173334i
$988$		0			0
$989$		−	6.05377e6i		−	0.196805i
$990$		0			0
$991$			3.26800e7i			1.05706i	0.848916	+	0.528528i	$0.177256\pi$
$991$			3.26800e7i			1.05706i	−0.848916	+	0.528528i	$0.822744\pi$
$992$		0			0
$993$	−7.53103e7	−	7.53103e7i	−2.42371	−	2.42371i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	594875.	−	594875.i	0.0189534	−	0.0189534i	−0.697567	−	0.716520i	$-0.745734\pi$
$997$	594875.	−	594875.i	0.0189534	−	0.0189534i	0.716520	+	0.697567i	$0.245734\pi$
$998$		0			0
$999$	−7.47077e7			−2.36838

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.6.n.f.143.8	yes	16
4.3	odd	2	inner	400.6.n.f.143.1	✓	16
5.2	odd	4	inner	400.6.n.f.207.2	yes	16
5.3	odd	4	inner	400.6.n.f.207.8	yes	16
5.4	even	2	inner	400.6.n.f.143.2	yes	16
20.3	even	4	inner	400.6.n.f.207.1	yes	16
20.7	even	4	inner	400.6.n.f.207.7	yes	16
20.19	odd	2	inner	400.6.n.f.143.7	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.6.n.f.143.1	✓	16	4.3	odd	2	inner
400.6.n.f.143.2	yes	16	5.4	even	2	inner
400.6.n.f.143.7	yes	16	20.19	odd	2	inner
400.6.n.f.143.8	yes	16	1.1	even	1	trivial
400.6.n.f.207.1	yes	16	20.3	even	4	inner
400.6.n.f.207.2	yes	16	5.2	odd	4	inner
400.6.n.f.207.7	yes	16	20.7	even	4	inner
400.6.n.f.207.8	yes	16	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	400.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(20.4551 - 20.4551i) q^{3} +(7.62217 + 7.62217i) q^{7} -593.825i q^{9} +O(q^{10})\)	\(q+(20.4551 - 20.4551i) q^{3} +(7.62217 + 7.62217i) q^{7} -593.825i q^{9} +406.744i q^{11} +(-712.587 - 712.587i) q^{13} +(-804.443 + 804.443i) q^{17} -2380.45 q^{19} +311.825 q^{21} +(476.455 - 476.455i) q^{23} +(-7176.18 - 7176.18i) q^{27} +5020.43i q^{29} +7016.55i q^{31} +(8320.00 + 8320.00i) q^{33} +(5205.26 - 5205.26i) q^{37} -29152.1 q^{39} -12768.9 q^{41} +(6352.93 - 6352.93i) q^{43} +(-17012.4 - 17012.4i) q^{47} -16690.8i q^{49} +32910.0i q^{51} +(-17430.6 - 17430.6i) q^{53} +(-48692.3 + 48692.3i) q^{57} -12493.8 q^{59} +6022.04 q^{61} +(4526.24 - 4526.24i) q^{63} +(-9149.24 - 9149.24i) q^{67} -19491.9i q^{69} -60841.9i q^{71} +(42123.1 + 42123.1i) q^{73} +(-3100.27 + 3100.27i) q^{77} +61442.1 q^{79} -149280. q^{81} +(-58413.1 + 58413.1i) q^{83} +(102694. + 102694. i) q^{87} +66206.4i q^{89} -10862.9i q^{91} +(143525. + 143525. i) q^{93} +(-41495.9 + 41495.9i) q^{97} +241535. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 1600 q^{21} - 125232 q^{41} - 279232 q^{61} - 1591184 q^{81}+O(q^{100}) \) 16 * q - 1600 * q^21 - 125232 * q^41 - 279232 * q^61 - 1591184 * q^81

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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