LMFDB - Embedded newform 400.6.n.f.207.2

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			207.2
Root			$1.96154 + 3.80431i$ of defining polynomial
Character	$\chi$	$=$	400.207
Dual form			400.6.n.f.143.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-20.4551 - 20.4551i) q^{3} +(-7.62217 + 7.62217i) q^{7} +593.825i q^{9} +O(q^{10})$	$q+(-20.4551 - 20.4551i) q^{3} +(-7.62217 + 7.62217i) q^{7} +593.825i q^{9} +406.744i q^{11} +(-712.587 + 712.587i) q^{13} +(-804.443 - 804.443i) q^{17} +2380.45 q^{19} +311.825 q^{21} +(-476.455 - 476.455i) q^{23} +(7176.18 - 7176.18i) q^{27} -5020.43i q^{29} +7016.55i q^{31} +(8320.00 - 8320.00i) q^{33} +(5205.26 + 5205.26i) q^{37} +29152.1 q^{39} -12768.9 q^{41} +(-6352.93 - 6352.93i) q^{43} +(17012.4 - 17012.4i) q^{47} +16690.8i q^{49} +32910.0i q^{51} +(-17430.6 + 17430.6i) q^{53} +(-48692.3 - 48692.3i) q^{57} +12493.8 q^{59} +6022.04 q^{61} +(-4526.24 - 4526.24i) q^{63} +(9149.24 - 9149.24i) q^{67} +19491.9i q^{69} -60841.9i q^{71} +(42123.1 - 42123.1i) q^{73} +(-3100.27 - 3100.27i) q^{77} -61442.1 q^{79} -149280. q^{81} +(58413.1 + 58413.1i) q^{83} +(-102694. + 102694. i) q^{87} -66206.4i q^{89} -10862.9i q^{91} +(143525. - 143525. i) q^{93} +(-41495.9 - 41495.9i) q^{97} -241535. q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

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

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	−0.919792	−	0.392405i	$-0.871643\pi$
$3$	−20.4551	−	20.4551i	−1.31220	−	1.31220i	−0.392405	−	0.919792i	$-0.628357\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−7.62217	+	7.62217i	−0.0587941	+	0.0587941i	−0.735892	−	0.677098i	$-0.763237\pi$
$7$	−7.62217	+	7.62217i	−0.0587941	+	0.0587941i	0.677098	+	0.735892i	$0.263237\pi$
$8$		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	−0.187105	+	0.982340i	$0.559910\pi$
$13$	−712.587	+	712.587i	−1.16944	+	1.16944i	−0.982340	+	0.187105i	$0.940090\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−804.443	−	804.443i	−0.675108	−	0.675108i	0.283781	−	0.958889i	$-0.408411\pi$
$17$	−804.443	−	804.443i	−0.675108	−	0.675108i	−0.958889	+	0.283781i	$0.908411\pi$
$18$		0			0
$19$	2380.45			1.51277			0.756387	−	0.654124i	$-0.226962\pi$
$19$	2380.45			1.51277			0.756387	+	0.654124i	$0.226962\pi$
$20$		0			0
$21$	311.825			0.154299
$22$		0			0
$23$	−476.455	−	476.455i	−0.187803	−	0.187803i	0.606943	−	0.794746i	$-0.292396\pi$
$23$	−476.455	−	476.455i	−0.187803	−	0.187803i	−0.794746	+	0.606943i	$0.792396\pi$
$24$		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	$-0.813000\pi$
$29$		−	5020.43i		−	1.10853i	0.832342	−	0.554263i	$-0.187000\pi$
$30$		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	0.946827	−	0.321743i	$-0.104269\pi$
$37$	5205.26	+	5205.26i	0.625084	+	0.625084i	−0.321743	+	0.946827i	$0.604269\pi$
$38$		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	$-0.370814\pi$
$43$	−6352.93	−	6352.93i	−0.523966	−	0.523966i	−0.918767	+	0.394801i	$0.870814\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	17012.4	−	17012.4i	1.12337	−	1.12337i	0.132136	−	0.991232i	$-0.457816\pi$
$47$	17012.4	−	17012.4i	1.12337	−	1.12337i	0.991232	−	0.132136i	$-0.0421835\pi$
$48$		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	−0.990424	−	0.138062i	$-0.955913\pi$
$53$	−17430.6	+	17430.6i	−0.852361	+	0.852361i	0.138062	+	0.990424i	$0.455913\pi$
$54$		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	$-0.424939\pi$
$59$	12493.8			0.467266			0.233633	+	0.972325i	$0.424939\pi$
$60$		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	$-0.693662\pi$
$67$	9149.24	−	9149.24i	0.248999	−	0.248999i	0.820560	+	0.571561i	$0.193662\pi$
$68$		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	−0.0722364	−	0.997388i	$-0.523014\pi$
$73$	42123.1	−	42123.1i	0.925151	−	0.925151i	0.997388	+	0.0722364i	$0.0230136\pi$
$74$		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	$-0.686830\pi$
$79$	−61442.1			−1.10764			−0.553819	+	0.832637i	$0.686830\pi$
$80$		0			0
$81$	−149280.			−2.52807
$82$		0			0
$83$	58413.1	+	58413.1i	0.930712	+	0.930712i	0.997750	−	0.0670385i	$-0.0213550\pi$
$83$	58413.1	+	58413.1i	0.930712	+	0.930712i	−0.0670385	+	0.997750i	$0.521355\pi$
$84$		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	$-0.853917\pi$
$89$		−	66206.4i		−	0.885982i	0.896526	−	0.442991i	$-0.146083\pi$
$90$		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	0.446828	−	0.894620i	$-0.352554\pi$
$97$	−41495.9	−	41495.9i	−0.447792	−	0.447792i	−0.894620	+	0.446828i	$0.852554\pi$
$98$		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	−0.999679	−	0.0253215i	$-0.991939\pi$
$103$	−110361.	−	110361.i	−1.02500	−	1.02500i	−0.0253215	−	0.999679i	$-0.508061\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−146564.	+	146564.i	−1.23756	+	1.23756i	−0.276569	+	0.960994i	$0.589197\pi$
$107$	−146564.	+	146564.i	−1.23756	+	1.23756i	−0.960994	+	0.276569i	$0.910803\pi$
$108$		0			0
$109$			99679.9i			0.803603i	0.915727	+	0.401801i	$0.131616\pi$
$109$			99679.9i			0.803603i	−0.915727	+	0.401801i	$0.868384\pi$
$110$		0			0
$111$		−	212949.i		−	1.64047i
$112$		0			0
$113$	−61798.7	+	61798.7i	−0.455285	+	0.455285i	−0.897104	−	0.441819i	$-0.854333\pi$
$113$	−61798.7	+	61798.7i	−0.455285	+	0.455285i	0.441819	+	0.897104i	$0.354333\pi$
$114$		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	$-0.738108\pi$
$127$	9601.33	−	9601.33i	0.0528229	−	0.0528229i	0.733025	+	0.680202i	$0.238108\pi$
$128$		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	0.743639	−	0.668582i	$-0.233098\pi$
$137$	16489.0	+	16489.0i	0.0750572	+	0.0750572i	−0.668582	+	0.743639i	$0.733098\pi$
$138$		0			0
$139$	−32797.7			−0.143981			−0.0719907	−	0.997405i	$-0.522935\pi$
$139$	−32797.7			−0.143981			−0.0719907	+	0.997405i	$0.522935\pi$
$140$		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	$0.0183858\pi$
$149$			31288.5i			0.115457i	−0.998332	+	0.0577284i	$0.981614\pi$
$150$		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	0.648059	−	0.761590i	$-0.275581\pi$
$157$	−35064.3	−	35064.3i	−0.113531	−	0.113531i	−0.761590	+	0.648059i	$0.775581\pi$
$158$		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	$-0.220264\pi$
$163$	44749.2	+	44749.2i	0.131922	+	0.131922i	−0.638063	+	0.769984i	$0.720264\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	153868.	−	153868.i	0.426930	−	0.426930i	−0.460651	−	0.887581i	$-0.652384\pi$
$167$	153868.	−	153868.i	0.426930	−	0.426930i	0.887581	+	0.460651i	$0.152384\pi$
$168$		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	−0.202795	−	0.979221i	$-0.565002\pi$
$173$	305644.	−	305644.i	0.776427	−	0.776427i	0.979221	+	0.202795i	$0.0650023\pi$
$174$		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	$-0.339292\pi$
$179$	414707.			0.967406			0.483703	+	0.875232i	$0.339292\pi$
$180$		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	−0.914300	−	0.405037i	$-0.867259\pi$
$193$	−263533.	+	263533.i	−0.509263	+	0.509263i	0.405037	+	0.914300i	$0.367259\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−169645.	−	169645.i	−0.311442	−	0.311442i	0.534026	−	0.845468i	$-0.320678\pi$
$197$	−169645.	−	169645.i	−0.311442	−	0.311442i	−0.845468	+	0.534026i	$0.820678\pi$
$198$		0			0
$199$	958493.			1.71576			0.857880	−	0.513850i	$-0.171781\pi$
$199$	958493.			1.71576			0.857880	+	0.513850i	$0.171781\pi$
$200$		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	$-0.352774\pi$
$223$	−333226.	−	333226.i	−0.448721	−	0.448721i	−0.894929	+	0.446208i	$0.852774\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−108690.	+	108690.i	−0.139999	+	0.139999i	−0.773633	−	0.633634i	$-0.781563\pi$
$227$	−108690.	+	108690.i	−0.139999	+	0.139999i	0.633634	+	0.773633i	$0.281563\pi$
$228$		0			0
$229$			1.06177e6i			1.33796i	0.743280	+	0.668981i	$0.233269\pi$
$229$			1.06177e6i			1.33796i	−0.743280	+	0.668981i	$0.766731\pi$
$230$		0			0
$231$			126833.i			0.156388i
$232$		0			0
$233$	722161.	−	722161.i	0.871454	−	0.871454i	−0.121177	−	0.992631i	$-0.538667\pi$
$233$	722161.	−	722161.i	0.871454	−	0.871454i	0.992631	+	0.121177i	$0.0386669\pi$
$234$		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	$-0.581624\pi$
$239$	−447940.			−0.507254			−0.253627	+	0.967302i	$0.581624\pi$
$240$		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	0.920034	−	0.391838i	$-0.128161\pi$
$257$	559279.	+	559279.i	0.528196	+	0.528196i	−0.391838	+	0.920034i	$0.628161\pi$
$258$		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	$-0.416450\pi$
$263$	−792250.	−	792250.i	−0.706274	−	0.706274i	−0.965750	+	0.259476i	$0.916450\pi$
$264$		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	$-0.599378\pi$
$269$		−	2.25887e6i		−	1.90332i	0.307158	−	0.951659i	$-0.400622\pi$
$270$		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	0.837511	−	0.546421i	$-0.184010\pi$
$277$	371729.	+	371729.i	0.291090	+	0.291090i	−0.546421	+	0.837511i	$0.684010\pi$
$278$		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	$-0.360455\pi$
$283$	−647984.	−	647984.i	−0.480948	−	0.480948i	−0.905434	+	0.424486i	$0.860455\pi$
$284$		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	−0.0464532	+	0.998920i	$0.514792\pi$
$293$	−1.53617e6	+	1.53617e6i	−1.04537	+	1.04537i	−0.998920	+	0.0464532i	$0.985208\pi$
$294$		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	$-0.729090\pi$
$307$	153306.	−	153306.i	0.0928351	−	0.0928351i	0.751999	+	0.659164i	$0.229090\pi$
$308$		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	−0.881173	−	0.472794i	$-0.843245\pi$
$313$	−707822.	+	707822.i	−0.408379	+	0.408379i	0.472794	+	0.881173i	$0.343245\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−891690.	−	891690.i	−0.498386	−	0.498386i	0.412550	−	0.910935i	$-0.364638\pi$
$317$	−891690.	−	891690.i	−0.498386	−	0.498386i	−0.910935	+	0.412550i	$0.864638\pi$
$318$		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	0.889931	−	0.456094i	$-0.150752\pi$
$337$	904485.	+	904485.i	0.433837	+	0.433837i	−0.456094	+	0.889931i	$0.650752\pi$
$338$		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	$-0.758931\pi$
$347$	−88986.1	+	88986.1i	−0.0396733	+	0.0396733i	0.686992	+	0.726665i	$0.258931\pi$
$348$		0			0
$349$		−	138062.i		−	0.0606750i	−0.999540	−	0.0303375i	$-0.990342\pi$
$349$		−	138062.i		−	0.0606750i	0.999540	−	0.0303375i	$-0.00965821\pi$
$350$		0			0
$351$			1.02273e7i			4.43092i
$352$		0			0
$353$	800599.	−	800599.i	0.341962	−	0.341962i	−0.515142	−	0.857105i	$-0.672261\pi$
$353$	800599.	−	800599.i	0.341962	−	0.341962i	0.857105	+	0.515142i	$0.172261\pi$
$354$		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	$-0.337238\pi$
$359$	2.38988e6			0.978680			0.489340	+	0.872093i	$0.337238\pi$
$360$		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	$-0.513234\pi$
$367$	2.47079e6	−	2.47079e6i	0.957571	−	0.957571i	0.999136	+	0.0415643i	$0.0132342\pi$
$368$		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	−0.478608	−	0.878029i	$-0.658859\pi$
$373$	1.07325e6	−	1.07325e6i	0.399420	−	0.399420i	0.878029	+	0.478608i	$0.158859\pi$
$374$		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	$-0.322458\pi$
$379$	2.96021e6			1.05858			0.529292	+	0.848440i	$0.322458\pi$
$380$		0			0
$381$	−392793.			−0.138628
$382$		0			0
$383$	−1.15833e6	−	1.15833e6i	−0.403493	−	0.403493i	0.475969	−	0.879462i	$-0.342098\pi$
$383$	−1.15833e6	−	1.15833e6i	−0.403493	−	0.403493i	−0.879462	+	0.475969i	$0.842098\pi$
$384$		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	$-0.886822\pi$
$389$		−	2.07790e6i		−	0.696228i	0.937452	−	0.348114i	$-0.113178\pi$
$390$		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	0.384564	−	0.923099i	$-0.374352\pi$
$397$	−1.69118e6	−	1.69118e6i	−0.538535	−	0.538535i	−0.923099	+	0.384564i	$0.874352\pi$
$398$		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	$0.110007\pi$
$409$			2.29208e6i			0.677518i	−0.940873	+	0.338759i	$0.889993\pi$
$410$		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	$-0.172587\pi$
$419$	6.15646e6			1.71315			0.856576	+	0.516021i	$0.172587\pi$
$420$		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	−0.738275	−	0.674500i	$-0.764359\pi$
$433$	−248812.	+	248812.i	−0.0637752	+	0.0637752i	0.674500	+	0.738275i	$0.264359\pi$
$434$		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	$-0.879652\pi$
$439$	−7.50553e6			−1.85875			−0.929373	+	0.369141i	$0.879652\pi$
$440$		0			0
$441$	−9.91142e6			−2.42683
$442$		0			0
$443$	−1.54032e6	−	1.54032e6i	−0.372908	−	0.372908i	0.495627	−	0.868535i	$-0.334938\pi$
$443$	−1.54032e6	−	1.54032e6i	−0.372908	−	0.372908i	−0.868535	+	0.495627i	$0.834938\pi$
$444$		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	$-0.892135\pi$
$449$		−	2.84010e6i		−	0.664841i	0.943131	−	0.332420i	$-0.107865\pi$
$450$		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	−0.851439	−	0.524454i	$-0.824270\pi$
$457$	−6.14292e6	−	6.14292e6i	−1.37589	−	1.37589i	−0.524454	−	0.851439i	$-0.675730\pi$
$458$		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	$-0.463839\pi$
$463$	−4.06006e6	−	4.06006e6i	−0.880197	−	0.880197i	−0.993554	+	0.113358i	$0.963839\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−3.18292e6	+	3.18292e6i	−0.675357	+	0.675357i	−0.958946	−	0.283589i	$-0.908475\pi$
$467$	−3.18292e6	+	3.18292e6i	−0.675357	+	0.675357i	0.283589	+	0.958946i	$0.408475\pi$
$468$		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	$-0.528322\pi$
$479$	−892421.			−0.177718			−0.0888590	+	0.996044i	$0.528322\pi$
$480$		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	−0.220089	+	0.975480i	$0.570635\pi$
$487$	−6.25745e6	+	6.25745e6i	−1.19557	+	1.19557i	−0.975480	+	0.220089i	$0.929365\pi$
$488$		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	$-0.416225\pi$
$499$	2.89414e6			0.520317			0.260159	+	0.965566i	$0.416225\pi$
$500$		0			0
$501$	−6.29477e6			−1.12043
$502$		0			0
$503$	1.78816e6	+	1.78816e6i	0.315128	+	0.315128i	0.846892	−	0.531765i	$-0.178471\pi$
$503$	1.78816e6	+	1.78816e6i	0.315128	+	0.315128i	−0.531765	+	0.846892i	$0.678471\pi$
$504$		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	$0.0265009\pi$
$509$			972151.i			0.166318i	−0.996536	+	0.0831590i	$0.973499\pi$
$510$		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	$-0.0169644\pi$
$523$	5.91328e6	+	5.91328e6i	0.945310	+	0.945310i	−0.0532699	+	0.998580i	$0.516964\pi$
$524$		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	$-0.624636\pi$
$547$	3.79769e6	−	3.79769e6i	0.542690	−	0.542690i	0.924316	+	0.381627i	$0.124636\pi$
$548$		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	0.780855	−	0.624713i	$-0.214784\pi$
$557$	1.14329e6	+	1.14329e6i	0.156142	+	0.156142i	−0.624713	+	0.780855i	$0.714784\pi$
$558$		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	$-0.332293\pi$
$563$	−2.71925e6	−	2.71925e6i	−0.361558	−	0.361558i	−0.864386	+	0.502828i	$0.832293\pi$
$564$		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	$-0.970722\pi$
$569$		−	1.41869e6i		−	0.183700i	0.995773	−	0.0918498i	$-0.0292780\pi$
$570$		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	0.799332	−	0.600890i	$-0.205187\pi$
$577$	1.58698e6	+	1.58698e6i	0.198441	+	0.198441i	−0.600890	+	0.799332i	$0.705187\pi$
$578$		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	$-0.521329\pi$
$587$	7.77055e6	−	7.77055e6i	0.930800	−	0.930800i	0.997756	+	0.0669557i	$0.0213286\pi$
$588$		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	−0.408714	−	0.912663i	$-0.634023\pi$
$593$	4.31542e6	−	4.31542e6i	0.503949	−	0.503949i	0.912663	+	0.408714i	$0.134023\pi$
$594$		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	$-0.502278\pi$
$599$	−125665.			−0.0143103			−0.00715515	+	0.999974i	$0.502278\pi$
$600$		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	$-0.743473\pi$
$607$	263218.	−	263218.i	0.0289964	−	0.0289964i	0.721456	+	0.692460i	$0.243473\pi$
$608$		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	−0.997401	−	0.0720496i	$-0.977046\pi$
$613$	−8.60910e6	+	8.60910e6i	−0.925351	+	0.925351i	0.0720496	+	0.997401i	$0.477046\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1.09363e6	−	1.09363e6i	−0.115653	−	0.115653i	0.646912	−	0.762565i	$-0.276060\pi$
$617$	−1.09363e6	−	1.09363e6i	−0.115653	−	0.115653i	−0.762565	+	0.646912i	$0.776060\pi$
$618$		0			0
$619$	2.29345e6			0.240581			0.120291	−	0.992739i	$-0.461617\pi$
$619$	2.29345e6			0.240581			0.120291	+	0.992739i	$0.461617\pi$
$620$		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	$-0.0654256\pi$
$643$	8.12358e6	+	8.12358e6i	0.774854	+	0.774854i	−0.204096	+	0.978951i	$0.565426\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.19518e7	+	1.19518e7i	−1.12246	+	1.12246i	−0.131091	+	0.991370i	$0.541848\pi$
$647$	−1.19518e7	+	1.19518e7i	−1.12246	+	1.12246i	−0.991370	+	0.131091i	$0.958152\pi$
$648$		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	−0.0397980	−	0.999208i	$-0.512671\pi$
$653$	1.04541e7	−	1.04541e7i	0.959410	−	0.959410i	0.999208	+	0.0397980i	$0.0126714\pi$
$654$		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	$-0.407985\pi$
$659$	6.35607e6			0.570131			0.285066	+	0.958508i	$0.407985\pi$
$660$		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	−0.578804	−	0.815466i	$-0.696480\pi$
$673$	2.78078e6	−	2.78078e6i	0.236662	−	0.236662i	0.815466	+	0.578804i	$0.196480\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	1.08002e7	+	1.08002e7i	0.905649	+	0.905649i	0.995917	−	0.0902683i	$-0.0287725\pi$
$677$	1.08002e7	+	1.08002e7i	0.905649	+	0.905649i	−0.0902683	+	0.995917i	$0.528772\pi$
$678$		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	$-0.386044\pi$
$683$	−7.14651e6	−	7.14651e6i	−0.586195	−	0.586195i	−0.936599	+	0.350404i	$0.886044\pi$
$684$		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	$-0.864015\pi$
$709$		−	1.10916e7i		−	0.828665i	0.910126	−	0.414332i	$-0.135985\pi$
$710$		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	$-0.426327\pi$
$719$	6.35957e6			0.458781			0.229391	+	0.973334i	$0.426327\pi$
$720$		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	$-0.781046\pi$
$727$	−1.96255e6	+	1.96255e6i	−0.137716	+	0.137716i	0.634888	+	0.772604i	$0.281046\pi$
$728$		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	−0.748131	−	0.663551i	$-0.769049\pi$
$733$	−1.23035e6	+	1.23035e6i	−0.0845803	+	0.0845803i	0.663551	+	0.748131i	$0.269049\pi$
$734$		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	$-0.537812\pi$
$739$	−3.51888e6			−0.237024			−0.118512	+	0.992953i	$0.537812\pi$
$740$		0			0
$741$	6.93951e7			4.64284
$742$		0			0
$743$	1.13866e7	+	1.13866e7i	0.756700	+	0.756700i	0.975720	−	0.219020i	$-0.0702861\pi$
$743$	1.13866e7	+	1.13866e7i	0.756700	+	0.756700i	−0.219020	+	0.975720i	$0.570286\pi$
$744$		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	0.136079	−	0.990698i	$-0.456550\pi$
$757$	−1.34745e7	−	1.34745e7i	−0.854619	−	0.854619i	−0.990698	+	0.136079i	$0.956550\pi$
$758$		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	$0.454890\pi$
$769$			3.24691e7i			1.97995i	−0.141244	+	0.989975i	$0.545110\pi$
$770$		0			0
$771$		−	2.28802e7i		−	1.38620i
$772$		0			0
$773$	−1.40880e7	+	1.40880e7i	−0.848011	+	0.848011i	−0.989885	−	0.141874i	$-0.954687\pi$
$773$	−1.40880e7	+	1.40880e7i	−0.848011	+	0.848011i	0.141874	+	0.989885i	$0.454687\pi$
$774$		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	$-0.555219\pi$
$787$	1.41156e7	−	1.41156e7i	0.812384	−	0.812384i	0.984991	+	0.172606i	$0.0552189\pi$
$788$		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	0.937000	+	0.349330i	$0.113591\pi$
$797$	2.30674e7	+	2.30674e7i	1.28633	+	1.28633i	0.349330	+	0.937000i	$0.386409\pi$
$798$		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	$-0.716087\pi$
$809$		−	2.89763e7i		−	1.55658i	0.627903	−	0.778291i	$-0.283913\pi$
$810$		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	$-0.00457333\pi$
$823$	1.91500e7	+	1.91500e7i	0.985530	+	0.985530i	−0.0143670	+	0.999897i	$0.504573\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	8.17984e6	−	8.17984e6i	0.415892	−	0.415892i	−0.467893	−	0.883785i	$-0.654987\pi$
$827$	8.17984e6	−	8.17984e6i	0.415892	−	0.415892i	0.883785	+	0.467893i	$0.154987\pi$
$828$		0			0
$829$		−	1.92400e7i		−	0.972339i	−0.873865	−	0.486170i	$-0.838394\pi$
$829$		−	1.92400e7i		−	0.972339i	0.873865	−	0.486170i	$-0.161606\pi$
$830$		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	$-0.840651\pi$
$839$	−3.57749e7			−1.75458			−0.877291	+	0.479959i	$0.840651\pi$
$840$		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	−0.934774	−	0.355244i	$-0.884398\pi$
$853$	−1.23154e7	+	1.23154e7i	−0.579529	+	0.579529i	0.355244	+	0.934774i	$0.384398\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1.12779e7	+	1.12779e7i	0.524539	+	0.524539i	0.918939	−	0.394400i	$-0.129048\pi$
$857$	1.12779e7	+	1.12779e7i	0.524539	+	0.524539i	−0.394400	+	0.918939i	$0.629048\pi$
$858$		0			0
$859$	−7.35211e6			−0.339961			−0.169980	−	0.985447i	$-0.554370\pi$
$859$	−7.35211e6			−0.339961			−0.169980	+	0.985447i	$0.554370\pi$
$860$		0			0
$861$	−3.98167e6			−0.183045
$862$		0			0
$863$	−8.13326e6	−	8.13326e6i	−0.371739	−	0.371739i	0.496372	−	0.868110i	$-0.334665\pi$
$863$	−8.13326e6	−	8.13326e6i	−0.371739	−	0.371739i	−0.868110	+	0.496372i	$0.834665\pi$
$864$		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	0.868307	−	0.496027i	$-0.165208\pi$
$877$	8.47946e6	+	8.47946e6i	0.372280	+	0.372280i	−0.496027	+	0.868307i	$0.665208\pi$
$878$		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	$-0.432423\pi$
$883$	−1.77667e7	−	1.77667e7i	−0.766842	−	0.766842i	−0.977549	+	0.210708i	$0.932423\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	2.48114e7	−	2.48114e7i	1.05887	−	1.05887i	0.0607123	−	0.998155i	$-0.480663\pi$
$887$	2.48114e7	−	2.48114e7i	1.05887	−	1.05887i	0.998155	−	0.0607123i	$-0.0193372\pi$
$888$		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	$-0.911008\pi$
$907$	−1.69766e7	+	1.69766e7i	−0.685223	+	0.685223i	0.275950	+	0.961172i	$0.411008\pi$
$908$		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	$-0.647196\pi$
$919$	−2.28441e7			−0.892248			−0.446124	+	0.894971i	$0.647196\pi$
$920$		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	$-0.869836\pi$
$929$		−	2.09188e7i		−	0.795239i	0.917550	−	0.397620i	$-0.130164\pi$
$930$		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	0.706649	−	0.707564i	$-0.250206\pi$
$937$	−24574.3	−	24574.3i	−0.000914390	−	0.000914390i	−0.707564	+	0.706649i	$0.750206\pi$
$938$		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	$-0.646940\pi$
$947$	1.24170e7	−	1.24170e7i	0.449926	−	0.449926i	0.895330	+	0.445404i	$0.146940\pi$
$948$		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	−0.0881096	−	0.996111i	$-0.528083\pi$
$953$	2.54577e7	−	2.54577e7i	0.908001	−	0.908001i	0.996111	+	0.0881096i	$0.0280826\pi$
$954$		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	$-0.692394\pi$
$967$	7.40159e6	−	7.40159e6i	0.254542	−	0.254542i	0.822830	+	0.568288i	$0.192394\pi$
$968$		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	0.826774	−	0.562534i	$-0.190174\pi$
$977$	7.88379e6	+	7.88379e6i	0.264240	+	0.264240i	−0.562534	+	0.826774i	$0.690174\pi$
$978$		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	$-0.199539\pi$
$983$	6.76370e6	+	6.76370e6i	0.223255	+	0.223255i	−0.586613	+	0.809867i	$0.699539\pi$
$984$		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	0.716520	−	0.697567i	$-0.245734\pi$
$997$	594875.	+	594875.i	0.0189534	+	0.0189534i	−0.697567	+	0.716520i	$0.745734\pi$
$998$		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.207.2	yes	16
4.3	odd	2	inner	400.6.n.f.207.7	yes	16
5.2	odd	4	inner	400.6.n.f.143.2	yes	16
5.3	odd	4	inner	400.6.n.f.143.8	yes	16
5.4	even	2	inner	400.6.n.f.207.8	yes	16
20.3	even	4	inner	400.6.n.f.143.1	✓	16
20.7	even	4	inner	400.6.n.f.143.7	yes	16
20.19	odd	2	inner	400.6.n.f.207.1	yes	16

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

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