LMFDB - Embedded newform 726.3.d.e.241.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [726,3,Mod(241,726)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("726.241"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(726, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 726 = 2 \cdot 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	726.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,-32,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$19.7820671926$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	16.0.6879707136000000000000.7
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 15x^{12} - 56x^{10} + 209x^{8} - 56x^{6} + 15x^{4} - 4x^{2} + 1 $ x^16 - 4x^14 + 15x^12 - 56x^10 + 209x^8 - 56x^6 + 15x^4 - 4*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12}\cdot 11^{2} $
Twist minimal:	no (minimal twist has level 66)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			241.11
Root			$-0.492303 + 0.159959i$ of defining polynomial
Character	$\chi$	$=$	726.241
Dual form			726.3.d.e.241.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.41421i q^{2} -1.73205 q^{3} -2.00000 q^{4} +6.34678 q^{5} -2.44949i q^{6} -10.0669i q^{7} -2.82843i q^{8} +3.00000 q^{9} +8.97571i q^{10} +3.46410 q^{12} +1.12617i q^{13} +14.2368 q^{14} -10.9930 q^{15} +4.00000 q^{16} -19.8215i q^{17} +4.24264i q^{18} +1.47626i q^{19} -12.6936 q^{20} +17.4364i q^{21} -38.3012 q^{23} +4.89898i q^{24} +15.2817 q^{25} -1.59265 q^{26} -5.19615 q^{27} +20.1338i q^{28} -17.2267i q^{29} -15.5464i q^{30} -60.1240 q^{31} +5.65685i q^{32} +28.0319 q^{34} -63.8925i q^{35} -6.00000 q^{36} +24.1590 q^{37} -2.08775 q^{38} -1.95059i q^{39} -17.9514i q^{40} -33.4750i q^{41} -24.6588 q^{42} +42.3015i q^{43} +19.0404 q^{45} -54.1661i q^{46} -59.7137 q^{47} -6.92820 q^{48} -52.3426 q^{49} +21.6115i q^{50} +34.3319i q^{51} -2.25235i q^{52} -23.9733 q^{53} -7.34847i q^{54} -28.4735 q^{56} -2.55696i q^{57} +24.3623 q^{58} +43.3596 q^{59} +21.9859 q^{60} -102.060i q^{61} -85.0282i q^{62} -30.2007i q^{63} -8.00000 q^{64} +7.14758i q^{65} +110.204 q^{67} +39.6431i q^{68} +66.3396 q^{69} +90.3576 q^{70} +33.2457 q^{71} -8.48528i q^{72} +45.7529i q^{73} +34.1659i q^{74} -26.4686 q^{75} -2.95253i q^{76} +2.75855 q^{78} -76.8219i q^{79} +25.3871 q^{80} +9.00000 q^{81} +47.3408 q^{82} -70.6453i q^{83} -34.8728i q^{84} -125.803i q^{85} -59.8233 q^{86} +29.8376i q^{87} +53.1788 q^{89} +26.9271i q^{90} +11.3371 q^{91} +76.6024 q^{92} +104.138 q^{93} -84.4479i q^{94} +9.36952i q^{95} -9.79796i q^{96} +108.152 q^{97} -74.0236i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 32 q^{4} + 8 q^{5} + 48 q^{9} + 48 q^{14} - 48 q^{15} + 64 q^{16} - 16 q^{20} - 8 q^{23} - 8 q^{25} + 128 q^{26} - 8 q^{31} - 64 q^{34} - 96 q^{36} + 96 q^{37} - 208 q^{38} - 144 q^{42} + 24 q^{45}+ \cdots + 184 q^{97}+O(q^{100}) $ 16 * q - 32 * q^4 + 8 * q^5 + 48 * q^9 + 48 * q^14 - 48 * q^15 + 64 * q^16 - 16 * q^20 - 8 * q^23 - 8 * q^25 + 128 * q^26 - 8 * q^31 - 64 * q^34 - 96 * q^36 + 96 * q^37 - 208 * q^38 - 144 * q^42 + 24 * q^45 - 128 * q^47 - 64 * q^49 + 16 * q^53 - 96 * q^56 + 64 * q^58 - 152 * q^59 + 96 * q^60 - 128 * q^64 + 248 * q^67 + 168 * q^69 - 32 * q^70 - 72 * q^71 - 48 * q^75 + 32 * q^80 + 144 * q^81 + 176 * q^82 + 464 * q^86 - 360 * q^89 - 32 * q^91 + 16 * q^92 + 336 * q^93 + 184 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/726\mathbb{Z}\right)^\times$.

$n$	$485$	$607$
$\chi(n)$	$1$	$-1$

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 $

$2$	1.41421i	0.707107i
$2$	1.41421i	0.707107i
$3$	−1.73205	−0.577350
$3$	−1.73205	−0.577350
$4$	−2.00000	−0.500000
$5$	6.34678	1.26936	0.634678	−	0.772776i	$-0.281133\pi$
$5$	6.34678	1.26936	0.634678	+	0.772776i	$0.281133\pi$
$6$	− 2.44949i	− 0.408248i
$7$	− 10.0669i	− 1.43813i	−0.694943	−	0.719065i	$-0.744570\pi$
$7$	− 10.0669i	− 1.43813i	0.694943	−	0.719065i	$-0.255430\pi$
$8$	− 2.82843i	− 0.353553i
$9$	3.00000	0.333333
$10$	8.97571i	0.897571i
$11$	0	0
$11$	0	0
$12$	3.46410	0.288675
$13$	1.12617i	0.0866288i	0.999061	+	0.0433144i	$0.0137917\pi$
$13$	1.12617i	0.0866288i	−0.999061	+	0.0433144i	$0.986208\pi$
$14$	14.2368	1.01691
$15$	−10.9930	−0.732863
$16$	4.00000	0.250000
$17$	− 19.8215i	− 1.16597i	−0.812482	−	0.582986i	$-0.801884\pi$
$17$	− 19.8215i	− 1.16597i	0.812482	−	0.582986i	$-0.198116\pi$
$18$	4.24264i	0.235702i
$19$	1.47626i	0.0776981i	0.999245	+	0.0388490i	$0.0123691\pi$
$19$	1.47626i	0.0776981i	−0.999245	+	0.0388490i	$0.987631\pi$
$20$	−12.6936	−0.634678
$21$	17.4364i	0.830304i
$22$	0	0
$23$	−38.3012	−1.66527	−0.832635	−	0.553823i	$-0.813169\pi$
$23$	−38.3012	−1.66527	−0.832635	+	0.553823i	$0.813169\pi$
$24$	4.89898i	0.204124i
$25$	15.2817	0.611266
$26$	−1.59265	−0.0612558
$27$	−5.19615	−0.192450
$28$	20.1338i	0.719065i
$29$	− 17.2267i	− 0.594025i	−0.954874	−	0.297013i	$-0.904010\pi$
$29$	− 17.2267i	− 0.594025i	0.954874	−	0.297013i	$-0.0959903\pi$
$30$	− 15.5464i	− 0.518213i
$31$	−60.1240	−1.93948	−0.969742	−	0.244130i	$-0.921498\pi$
$31$	−60.1240	−1.93948	−0.969742	+	0.244130i	$0.921498\pi$
$32$	5.65685i	0.176777i
$33$	0	0
$34$	28.0319	0.824467
$35$	− 63.8925i	− 1.82550i
$36$	−6.00000	−0.166667
$37$	24.1590	0.652945	0.326472	−	0.945207i	$-0.394140\pi$
$37$	24.1590	0.652945	0.326472	+	0.945207i	$0.394140\pi$
$38$	−2.08775	−0.0549408
$39$	− 1.95059i	− 0.0500151i
$40$	− 17.9514i	− 0.448785i
$41$	− 33.4750i	− 0.816463i	−0.912878	−	0.408231i	$-0.866146\pi$
$41$	− 33.4750i	− 0.816463i	0.912878	−	0.408231i	$-0.133854\pi$
$42$	−24.6588	−0.587114
$43$	42.3015i	0.983755i	0.870664	+	0.491877i	$0.163689\pi$
$43$	42.3015i	0.983755i	−0.870664	+	0.491877i	$0.836311\pi$
$44$	0	0
$45$	19.0404	0.423119
$46$	− 54.1661i	− 1.17752i
$47$	−59.7137	−1.27050	−0.635252	−	0.772305i	$-0.719104\pi$
$47$	−59.7137	−1.27050	−0.635252	+	0.772305i	$0.719104\pi$
$48$	−6.92820	−0.144338
$49$	−52.3426	−1.06822
$50$	21.6115i	0.432231i
$51$	34.3319i	0.673174i
$52$	− 2.25235i	− 0.0433144i
$53$	−23.9733	−0.452327	−0.226163	−	0.974089i	$-0.572618\pi$
$53$	−23.9733	−0.452327	−0.226163	+	0.974089i	$0.572618\pi$
$54$	− 7.34847i	− 0.136083i
$55$	0	0
$56$	−28.4735	−0.508456
$57$	− 2.55696i	− 0.0448590i
$58$	24.3623	0.420039
$59$	43.3596	0.734909	0.367455	−	0.930041i	$-0.380229\pi$
$59$	43.3596	0.734909	0.367455	+	0.930041i	$0.380229\pi$
$60$	21.9859	0.366432
$61$	− 102.060i	− 1.67312i	−0.547875	−	0.836561i	$-0.684563\pi$
$61$	− 102.060i	− 1.67312i	0.547875	−	0.836561i	$-0.315437\pi$
$62$	− 85.0282i	− 1.37142i
$63$	− 30.2007i	− 0.479376i
$64$	−8.00000	−0.125000
$65$	7.14758i	0.109963i
$66$	0	0
$67$	110.204	1.64483	0.822417	−	0.568884i	$-0.192625\pi$
$67$	110.204	1.64483	0.822417	+	0.568884i	$0.192625\pi$
$68$	39.6431i	0.582986i
$69$	66.3396	0.961444
$70$	90.3576	1.29082
$71$	33.2457	0.468250	0.234125	−	0.972207i	$-0.424778\pi$
$71$	33.2457	0.468250	0.234125	+	0.972207i	$0.424778\pi$
$72$	− 8.48528i	− 0.117851i
$73$	45.7529i	0.626752i	0.949629	+	0.313376i	$0.101460\pi$
$73$	45.7529i	0.626752i	−0.949629	+	0.313376i	$0.898540\pi$
$74$	34.1659i	0.461702i
$75$	−26.4686	−0.352915
$76$	− 2.95253i	− 0.0388490i
$77$	0	0
$78$	2.75855	0.0353660
$79$	− 76.8219i	− 0.972429i	−0.873840	−	0.486214i	$-0.838377\pi$
$79$	− 76.8219i	− 0.972429i	0.873840	−	0.486214i	$-0.161623\pi$
$80$	25.3871	0.317339
$81$	9.00000	0.111111
$82$	47.3408	0.577326
$83$	− 70.6453i	− 0.851148i	−0.904924	−	0.425574i	$-0.860072\pi$
$83$	− 70.6453i	− 0.851148i	0.904924	−	0.425574i	$-0.139928\pi$
$84$	− 34.8728i	− 0.415152i
$85$	− 125.803i	− 1.48003i
$86$	−59.8233	−0.695620
$87$	29.8376i	0.342961i
$88$	0	0
$89$	53.1788	0.597514	0.298757	−	0.954329i	$-0.403428\pi$
$89$	53.1788	0.597514	0.298757	+	0.954329i	$0.403428\pi$
$90$	26.9271i	0.299190i
$91$	11.3371	0.124583
$92$	76.6024	0.832635
$93$	104.138	1.11976
$94$	− 84.4479i	− 0.898382i
$95$	9.36952i	0.0986266i
$96$	− 9.79796i	− 0.102062i
$97$	108.152	1.11496	0.557482	−	0.830189i	$-0.311767\pi$
$97$	108.152	1.11496	0.557482	+	0.830189i	$0.311767\pi$
$98$	− 74.0236i	− 0.755343i
$99$	0	0
$100$	−30.5633	−0.305633
$101$	− 3.37711i	− 0.0334367i	−0.999860	−	0.0167183i	$-0.994678\pi$
$101$	− 3.37711i	− 0.0334367i	0.999860	−	0.0167183i	$-0.00532186\pi$
$102$	−48.5526	−0.476006
$103$	−117.064	−1.13655	−0.568274	−	0.822840i	$-0.692388\pi$
$103$	−117.064	−1.13655	−0.568274	+	0.822840i	$0.692388\pi$
$104$	3.18530	0.0306279
$105$	110.665i	1.05395i
$106$	− 33.9034i	− 0.319843i
$107$	− 59.6388i	− 0.557372i	−0.960382	−	0.278686i	$-0.910101\pi$
$107$	− 59.6388i	− 0.557372i	0.960382	−	0.278686i	$-0.0898988\pi$
$108$	10.3923	0.0962250
$109$	− 188.343i	− 1.72792i	−0.503560	−	0.863961i	$-0.667977\pi$
$109$	− 188.343i	− 1.72792i	0.503560	−	0.863961i	$-0.332023\pi$
$110$	0	0
$111$	−41.8445	−0.376978
$112$	− 40.2676i	− 0.359532i
$113$	8.30017	0.0734529	0.0367264	−	0.999325i	$-0.488307\pi$
$113$	8.30017	0.0734529	0.0367264	+	0.999325i	$0.488307\pi$
$114$	3.61609	0.0317201
$115$	−243.089	−2.11382
$116$	34.4535i	0.297013i
$117$	3.37852i	0.0288763i
$118$	61.3198i	0.519659i
$119$	−199.541	−1.67682
$120$	31.0928i	0.259106i
$121$	0	0
$122$	144.335	1.18308
$123$	57.9804i	0.471385i
$124$	120.248	0.969742
$125$	−61.6802	−0.493442
$126$	42.7103	0.338970
$127$	124.892i	0.983404i	0.870764	+	0.491702i	$0.163625\pi$
$127$	124.892i	0.983404i	−0.870764	+	0.491702i	$0.836375\pi$
$128$	− 11.3137i	− 0.0883883i
$129$	− 73.2683i	− 0.567971i
$130$	−10.1082	−0.0777554
$131$	43.0571i	0.328680i	0.986404	+	0.164340i	$0.0525494\pi$
$131$	43.0571i	0.328680i	−0.986404	+	0.164340i	$0.947451\pi$
$132$	0	0
$133$	14.8614	0.111740
$134$	155.852i	1.16307i
$135$	−32.9789	−0.244288
$136$	−56.0638	−0.412233
$137$	−17.3563	−0.126689	−0.0633443	−	0.997992i	$-0.520177\pi$
$137$	−17.3563	−0.126689	−0.0633443	+	0.997992i	$0.520177\pi$
$138$	93.8184i	0.679843i
$139$	− 35.7025i	− 0.256852i	−0.991719	−	0.128426i	$-0.959007\pi$
$139$	− 35.7025i	− 0.256852i	0.991719	−	0.128426i	$-0.0409925\pi$
$140$	127.785i	0.912750i
$141$	103.427	0.733526
$142$	47.0165i	0.331102i
$143$	0	0
$144$	12.0000	0.0833333
$145$	− 109.334i	− 0.754030i
$146$	−64.7043	−0.443180
$147$	90.6600	0.616735
$148$	−48.3179	−0.326472
$149$	0.213896i	0.00143555i	1.00000		0.000717773i	$0.000228474\pi$
$149$	0.213896i	0.00143555i	−1.00000		0.000717773i	$0.999772\pi$
$150$	− 37.4323i	− 0.249548i
$151$	− 102.942i	− 0.681733i	−0.940112	−	0.340867i	$-0.889280\pi$
$151$	− 102.942i	− 0.681733i	0.940112	−	0.340867i	$-0.110720\pi$
$152$	4.17550	0.0274704
$153$	− 59.4646i	− 0.388657i
$154$	0	0
$155$	−381.594	−2.46190
$156$	3.90118i	0.0250076i
$157$	75.2317	0.479183	0.239591	−	0.970874i	$-0.422987\pi$
$157$	75.2317	0.479183	0.239591	+	0.970874i	$0.422987\pi$
$158$	108.643	0.687611
$159$	41.5230	0.261151
$160$	35.9028i	0.224393i
$161$	385.575i	2.39487i
$162$	12.7279i	0.0785674i
$163$	192.115	1.17862	0.589311	−	0.807907i	$-0.299399\pi$
$163$	192.115	1.17862	0.589311	+	0.807907i	$0.299399\pi$
$164$	66.9500i	0.408231i
$165$	0	0
$166$	99.9076	0.601853
$167$	153.948i	0.921845i	0.887440	+	0.460923i	$0.152481\pi$
$167$	153.948i	0.921845i	−0.887440	+	0.460923i	$0.847519\pi$
$168$	49.3176	0.293557
$169$	167.732	0.992495
$170$	177.912	1.04654
$171$	4.42879i	0.0258994i
$172$	− 84.6029i	− 0.491877i
$173$	328.775i	1.90044i	0.311586	+	0.950218i	$0.399140\pi$
$173$	328.775i	1.90044i	−0.311586	+	0.950218i	$0.600860\pi$
$174$	−42.1967	−0.242510
$175$	− 153.839i	− 0.879080i
$176$	0	0
$177$	−75.1011	−0.424300
$178$	75.2062i	0.422507i
$179$	−125.172	−0.699284	−0.349642	−	0.936883i	$-0.613697\pi$
$179$	−125.172	−0.699284	−0.349642	+	0.936883i	$0.613697\pi$
$180$	−38.0807	−0.211559
$181$	−161.245	−0.890857	−0.445428	−	0.895318i	$-0.646949\pi$
$181$	−161.245	−0.890857	−0.445428	+	0.895318i	$0.646949\pi$
$182$	16.0331i	0.0880937i
$183$	176.774i	0.965977i
$184$	108.332i	0.588762i
$185$	153.332	0.828820
$186$	147.273i	0.791791i
$187$	0	0
$188$	119.427	0.635252
$189$	52.3092i	0.276768i
$190$	−13.2505	−0.0697395
$191$	−246.391	−1.29001	−0.645004	−	0.764179i	$-0.723144\pi$
$191$	−246.391	−1.29001	−0.645004	+	0.764179i	$0.723144\pi$
$192$	13.8564	0.0721688
$193$	− 271.845i	− 1.40853i	−0.709939	−	0.704263i	$-0.751278\pi$
$193$	− 271.845i	− 1.40853i	0.709939	−	0.704263i	$-0.248722\pi$
$194$	152.949i	0.788399i
$195$	− 12.3800i	− 0.0634871i
$196$	104.685	0.534108
$197$	371.771i	1.88716i	0.331139	+	0.943582i	$0.392567\pi$
$197$	371.771i	1.88716i	−0.331139	+	0.943582i	$0.607433\pi$
$198$	0	0
$199$	113.221	0.568951	0.284476	−	0.958683i	$-0.408180\pi$
$199$	113.221	0.568951	0.284476	+	0.958683i	$0.408180\pi$
$200$	− 43.2231i	− 0.216115i
$201$	−190.879	−0.949646
$202$	4.77595	0.0236433
$203$	−173.420	−0.854285
$204$	− 68.6638i	− 0.336587i
$205$	− 212.458i	− 1.03638i
$206$	− 165.554i	− 0.803660i
$207$	−114.904	−0.555090
$208$	4.50470i	0.0216572i
$209$	0	0
$210$	−156.504	−0.745257
$211$	− 132.371i	− 0.627351i	−0.949530	−	0.313675i	$-0.898440\pi$
$211$	− 132.371i	− 0.627351i	0.949530	−	0.313675i	$-0.101560\pi$
$212$	47.9466	0.226163
$213$	−57.5833	−0.270344
$214$	84.3419	0.394121
$215$	268.478i	1.24874i
$216$	14.6969i	0.0680414i
$217$	605.263i	2.78923i
$218$	266.358	1.22182
$219$	− 79.2463i	− 0.361855i
$220$	0	0
$221$	22.3225	0.101007
$222$	− 59.1771i	− 0.266564i
$223$	133.907	0.600479	0.300239	−	0.953864i	$-0.402933\pi$
$223$	133.907	0.600479	0.300239	+	0.953864i	$0.402933\pi$
$224$	56.9470	0.254228
$225$	45.8450	0.203755
$226$	11.7382i	0.0519390i
$227$	− 383.459i	− 1.68925i	−0.535361	−	0.844623i	$-0.679824\pi$
$227$	− 383.459i	− 1.68925i	0.535361	−	0.844623i	$-0.320176\pi$
$228$	5.11393i	0.0224295i
$229$	101.557	0.443479	0.221739	−	0.975106i	$-0.428827\pi$
$229$	101.557	0.443479	0.221739	+	0.975106i	$0.428827\pi$
$230$	− 343.780i	− 1.49470i
$231$	0	0
$232$	−48.7246	−0.210020
$233$	− 37.6592i	− 0.161628i	−0.996729	−	0.0808138i	$-0.974248\pi$
$233$	− 37.6592i	− 0.161628i	0.996729	−	0.0808138i	$-0.0257519\pi$
$234$	−4.77795	−0.0204186
$235$	−378.990	−1.61272
$236$	−86.7193	−0.367455
$237$	133.059i	0.561432i
$238$	− 282.194i	− 1.18569i
$239$	− 121.026i	− 0.506384i	−0.967416	−	0.253192i	$-0.918520\pi$
$239$	− 121.026i	− 0.506384i	0.967416	−	0.253192i	$-0.0814805\pi$
$240$	−43.9718	−0.183216
$241$	− 25.2413i	− 0.104736i	−0.998628	−	0.0523679i	$-0.983323\pi$
$241$	− 25.2413i	− 0.104736i	0.998628	−	0.0523679i	$-0.0166768\pi$
$242$	0	0
$243$	−15.5885	−0.0641500
$244$	204.121i	0.836561i
$245$	−332.207	−1.35595
$246$	−81.9966	−0.333320
$247$	−1.66253	−0.00673089
$248$	170.056i	0.685711i
$249$	122.361i	0.491411i
$250$	− 87.2290i	− 0.348916i
$251$	149.794	0.596787	0.298394	−	0.954443i	$-0.403549\pi$
$251$	149.794	0.596787	0.298394	+	0.954443i	$0.403549\pi$
$252$	60.4014i	0.239688i
$253$	0	0
$254$	−176.624	−0.695371
$255$	217.897i	0.854498i
$256$	16.0000	0.0625000
$257$	−403.749	−1.57101	−0.785504	−	0.618856i	$-0.787596\pi$
$257$	−403.749	−1.57101	−0.785504	+	0.618856i	$0.787596\pi$
$258$	103.617	0.401616
$259$	− 243.206i	− 0.939019i
$260$	− 14.2952i	− 0.0549814i
$261$	− 51.6802i	− 0.198008i
$262$	−60.8919	−0.232412
$263$	− 163.005i	− 0.619790i	−0.950771	−	0.309895i	$-0.899706\pi$
$263$	− 163.005i	− 0.619790i	0.950771	−	0.309895i	$-0.100294\pi$
$264$	0	0
$265$	−152.153	−0.574164
$266$	21.0172i	0.0790120i
$267$	−92.1084	−0.344975
$268$	−220.408	−0.822417
$269$	355.540	1.32171	0.660855	−	0.750514i	$-0.270194\pi$
$269$	355.540	1.32171	0.660855	+	0.750514i	$0.270194\pi$
$270$	− 46.6391i	− 0.172738i
$271$	445.111i	1.64248i	0.570584	+	0.821239i	$0.306717\pi$
$271$	445.111i	1.64248i	−0.570584	+	0.821239i	$0.693283\pi$
$272$	− 79.2861i	− 0.291493i
$273$	−19.6364	−0.0719282
$274$	− 24.5456i	− 0.0895823i
$275$	0	0
$276$	−132.679	−0.480722
$277$	102.471i	0.369932i	0.982745	+	0.184966i	$0.0592174\pi$
$277$	102.471i	0.369932i	−0.982745	+	0.184966i	$0.940783\pi$
$278$	50.4909	0.181622
$279$	−180.372	−0.646495
$280$	−180.715	−0.645411
$281$	− 146.819i	− 0.522488i	−0.965273	−	0.261244i	$-0.915867\pi$
$281$	− 146.819i	− 0.522488i	0.965273	−	0.261244i	$-0.0841327\pi$
$282$	146.268i	0.518681i
$283$	− 128.949i	− 0.455650i	−0.973702	−	0.227825i	$-0.926839\pi$
$283$	− 128.949i	− 0.455650i	0.973702	−	0.227825i	$-0.0731614\pi$
$284$	−66.4914	−0.234125
$285$	− 16.2285i	− 0.0569421i
$286$	0	0
$287$	−336.989	−1.17418
$288$	16.9706i	0.0589256i
$289$	−103.893	−0.359491
$290$	154.622	0.533180
$291$	−187.324	−0.643725
$292$	− 91.5058i	− 0.313376i
$293$	72.9305i	0.248909i	0.992225	+	0.124455i	$0.0397181\pi$
$293$	72.9305i	0.248909i	−0.992225	+	0.124455i	$0.960282\pi$
$294$	128.213i	0.436097i
$295$	275.194	0.932862
$296$	− 68.3318i	− 0.230851i
$297$	0	0
$298$	−0.302495	−0.00101508
$299$	− 43.1338i	− 0.144260i
$300$	52.9372	0.176457
$301$	425.845	1.41477
$302$	145.582	0.482058
$303$	5.84932i	0.0193047i
$304$	5.90505i	0.0194245i
$305$	− 647.755i	− 2.12379i
$306$	84.0956	0.274822
$307$	− 243.270i	− 0.792409i	−0.918162	−	0.396204i	$-0.870327\pi$
$307$	− 243.270i	− 0.792409i	0.918162	−	0.396204i	$-0.129673\pi$
$308$	0	0
$309$	202.761	0.656186
$310$	− 539.656i	− 1.74082i
$311$	158.095	0.508343	0.254172	−	0.967159i	$-0.418197\pi$
$311$	158.095	0.508343	0.254172	+	0.967159i	$0.418197\pi$
$312$	−5.51710	−0.0176830
$313$	−17.4297	−0.0556858	−0.0278429	−	0.999612i	$-0.508864\pi$
$313$	−17.4297	−0.0556858	−0.0278429	+	0.999612i	$0.508864\pi$
$314$	106.394i	0.338833i
$315$	− 191.677i	− 0.608500i
$316$	153.644i	0.486214i
$317$	−73.8869	−0.233082	−0.116541	−	0.993186i	$-0.537181\pi$
$317$	−73.8869	−0.233082	−0.116541	+	0.993186i	$0.537181\pi$
$318$	58.7224i	0.184662i
$319$	0	0
$320$	−50.7743	−0.158670
$321$	103.297i	0.321799i
$322$	−545.285	−1.69343
$323$	29.2618	0.0905938
$324$	−18.0000	−0.0555556
$325$	17.2098i	0.0529533i
$326$	271.692i	0.833411i
$327$	326.220i	0.997616i
$328$	−94.6815	−0.288663
$329$	601.132i	1.82715i
$330$	0	0
$331$	418.904	1.26557	0.632786	−	0.774327i	$-0.281911\pi$
$331$	418.904	1.26557	0.632786	+	0.774327i	$0.281911\pi$
$332$	141.291i	0.425574i
$333$	72.4769	0.217648
$334$	−217.716	−0.651843
$335$	699.441	2.08788
$336$	69.7456i	0.207576i
$337$	153.173i	0.454518i	0.973834	+	0.227259i	$0.0729764\pi$
$337$	153.173i	0.454518i	−0.973834	+	0.227259i	$0.927024\pi$
$338$	237.208i	0.701800i
$339$	−14.3763	−0.0424080
$340$	251.606i	0.740017i
$341$	0	0
$342$	−6.26325	−0.0183136
$343$	33.6495i	0.0981035i
$344$	119.647	0.347810
$345$	421.043	1.22042
$346$	−464.959	−1.34381
$347$	303.564i	0.874823i	0.899261	+	0.437411i	$0.144105\pi$
$347$	303.564i	0.874823i	−0.899261	+	0.437411i	$0.855895\pi$
$348$	− 59.6751i	− 0.171480i
$349$	459.785i	1.31744i	0.752390	+	0.658718i	$0.228901\pi$
$349$	459.785i	1.31744i	−0.752390	+	0.658718i	$0.771099\pi$
$350$	217.561	0.621604
$351$	− 5.85177i	− 0.0166717i
$352$	0	0
$353$	−35.2031	−0.0997256	−0.0498628	−	0.998756i	$-0.515878\pi$
$353$	−35.2031	−0.0997256	−0.0498628	+	0.998756i	$0.515878\pi$
$354$	− 106.209i	− 0.300025i
$355$	211.003	0.594376
$356$	−106.358	−0.298757
$357$	345.616	0.968112
$358$	− 177.020i	− 0.494468i
$359$	− 209.848i	− 0.584534i	−0.956337	−	0.292267i	$-0.905590\pi$
$359$	− 209.848i	− 0.584534i	0.956337	−	0.292267i	$-0.0944096\pi$
$360$	− 53.8542i	− 0.149595i
$361$	358.821	0.993963
$362$	− 228.035i	− 0.629931i
$363$	0	0
$364$	−22.6742	−0.0622917
$365$	290.384i	0.795572i
$366$	−249.996	−0.683049
$367$	391.558	1.06692	0.533458	−	0.845826i	$-0.320892\pi$
$367$	391.558	1.06692	0.533458	+	0.845826i	$0.320892\pi$
$368$	−153.205	−0.416317
$369$	− 100.425i	− 0.272154i
$370$	216.844i	0.586064i
$371$	241.337i	0.650504i
$372$	−208.276	−0.559881
$373$	352.395i	0.944758i	0.881395	+	0.472379i	$0.156605\pi$
$373$	352.395i	0.944758i	−0.881395	+	0.472379i	$0.843395\pi$
$374$	0	0
$375$	106.833	0.284889
$376$	168.896i	0.449191i
$377$	19.4003	0.0514597
$378$	−73.9763	−0.195705
$379$	−555.910	−1.46678	−0.733390	−	0.679808i	$-0.762063\pi$
$379$	−555.910	−1.46678	−0.733390	+	0.679808i	$0.762063\pi$
$380$	− 18.7390i	− 0.0493133i
$381$	− 216.320i	− 0.567768i
$382$	− 348.450i	− 0.912173i
$383$	−203.493	−0.531313	−0.265657	−	0.964068i	$-0.585589\pi$
$383$	−203.493	−0.531313	−0.265657	+	0.964068i	$0.585589\pi$
$384$	19.5959i	0.0510310i
$385$	0	0
$386$	384.448	0.995978
$387$	126.904i	0.327918i
$388$	−216.303	−0.557482
$389$	432.943	1.11296	0.556482	−	0.830860i	$-0.312151\pi$
$389$	432.943	1.11296	0.556482	+	0.830860i	$0.312151\pi$
$390$	17.5079	0.0448921
$391$	759.188i	1.94166i
$392$	148.047i	0.377671i
$393$	− 74.5770i	− 0.189763i
$394$	−525.764	−1.33443
$395$	− 487.572i	− 1.23436i
$396$	0	0
$397$	−216.304	−0.544847	−0.272423	−	0.962177i	$-0.587825\pi$
$397$	−216.304	−0.544847	−0.272423	+	0.962177i	$0.587825\pi$
$398$	160.119i	0.402309i
$399$	−25.7407	−0.0645130
$400$	61.1266	0.152817
$401$	79.2577	0.197650	0.0988251	−	0.995105i	$-0.468492\pi$
$401$	79.2577	0.197650	0.0988251	+	0.995105i	$0.468492\pi$
$402$	− 269.943i	− 0.671501i
$403$	− 67.7101i	− 0.168015i
$404$	6.75421i	0.0167183i
$405$	57.1211	0.141040
$406$	− 245.253i	− 0.604071i
$407$	0	0
$408$	97.1053	0.238003
$409$	− 322.622i	− 0.788808i	−0.918937	−	0.394404i	$-0.870951\pi$
$409$	− 322.622i	− 0.788808i	0.918937	−	0.394404i	$-0.129049\pi$
$410$	300.462	0.732833
$411$	30.0620	0.0731437
$412$	234.129	0.568274
$413$	− 436.497i	− 1.05689i
$414$	− 162.498i	− 0.392508i
$415$	− 448.371i	− 1.08041i
$416$	−6.37060	−0.0153139
$417$	61.8385i	0.148294i
$418$	0	0
$419$	609.683	1.45509	0.727546	−	0.686059i	$-0.240661\pi$
$419$	609.683	1.45509	0.727546	+	0.686059i	$0.240661\pi$
$420$	− 221.330i	− 0.526976i
$421$	31.3509	0.0744678	0.0372339	−	0.999307i	$-0.488145\pi$
$421$	31.3509	0.0744678	0.0372339	+	0.999307i	$0.488145\pi$
$422$	187.201	0.443604
$423$	−179.141	−0.423501
$424$	67.8067i	0.159922i
$425$	− 302.906i	− 0.712720i
$426$	− 81.4350i	− 0.191162i
$427$	−1027.43	−2.40616
$428$	119.278i	0.278686i
$429$	0	0
$430$	−379.686	−0.882990
$431$	− 362.761i	− 0.841672i	−0.907137	−	0.420836i	$-0.861737\pi$
$431$	− 362.761i	− 0.841672i	0.907137	−	0.420836i	$-0.138263\pi$
$432$	−20.7846	−0.0481125
$433$	−88.6628	−0.204764	−0.102382	−	0.994745i	$-0.532646\pi$
$433$	−88.6628	−0.204764	−0.102382	+	0.994745i	$0.532646\pi$
$434$	−855.971	−1.97228
$435$	189.373i	0.435339i
$436$	376.687i	0.863961i
$437$	− 56.5426i	− 0.129388i
$438$	112.071	0.255870
$439$	− 373.125i	− 0.849944i	−0.905207	−	0.424972i	$-0.860284\pi$
$439$	− 373.125i	− 0.849944i	0.905207	−	0.424972i	$-0.139716\pi$
$440$	0	0
$441$	−157.028	−0.356072
$442$	31.5688i	0.0714226i
$443$	544.498	1.22912	0.614558	−	0.788872i	$-0.289335\pi$
$443$	544.498	1.22912	0.614558	+	0.788872i	$0.289335\pi$
$444$	83.6891	0.188489
$445$	337.514	0.758459
$446$	189.373i	0.424603i
$447$	− 0.370479i	0 0.000828813i
$448$	80.5352i	0.179766i
$449$	86.0956	0.191750	0.0958748	−	0.995393i	$-0.469435\pi$
$449$	86.0956	0.191750	0.0958748	+	0.995393i	$0.469435\pi$
$450$	64.8346i	0.144077i
$451$	0	0
$452$	−16.6003	−0.0367264
$453$	178.300i	0.393599i
$454$	542.293	1.19448
$455$	71.9540	0.158141
$456$	−7.23218	−0.0158601
$457$	− 420.181i	− 0.919434i	−0.888065	−	0.459717i	$-0.847951\pi$
$457$	− 420.181i	− 0.919434i	0.888065	−	0.459717i	$-0.152049\pi$
$458$	143.623i	0.313587i
$459$	102.996i	0.224391i
$460$	486.179	1.05691
$461$	169.900i	0.368546i	0.982875	+	0.184273i	$0.0589930\pi$
$461$	169.900i	0.368546i	−0.982875	+	0.184273i	$0.941007\pi$
$462$	0	0
$463$	23.1381	0.0499743	0.0249872	−	0.999688i	$-0.492046\pi$
$463$	23.1381	0.0499743	0.0249872	+	0.999688i	$0.492046\pi$
$464$	− 68.9069i	− 0.148506i
$465$	660.941	1.42138
$466$	53.2582	0.114288
$467$	−280.938	−0.601581	−0.300790	−	0.953690i	$-0.597250\pi$
$467$	−280.938	−0.601581	−0.300790	+	0.953690i	$0.597250\pi$
$468$	− 6.75704i	− 0.0144381i
$469$	− 1109.41i	− 2.36549i
$470$	− 535.973i	− 1.14037i
$471$	−130.305	−0.276656
$472$	− 122.640i	− 0.259830i
$473$	0	0
$474$	−188.174	−0.396992
$475$	22.5598i	0.0474942i
$476$	399.083	0.838410
$477$	−71.9199	−0.150776
$478$	171.156	0.358068
$479$	249.584i	0.521053i	0.965467	+	0.260526i	$0.0838961\pi$
$479$	249.584i	0.521053i	−0.965467	+	0.260526i	$0.916104\pi$
$480$	− 62.1855i	− 0.129553i
$481$	27.2072i	0.0565638i
$482$	35.6966	0.0740593
$483$	− 667.835i	− 1.38268i
$484$	0	0
$485$	686.415	1.41529
$486$	− 22.0454i	− 0.0453609i
$487$	574.028	1.17870	0.589351	−	0.807877i	$-0.299383\pi$
$487$	574.028	1.17870	0.589351	+	0.807877i	$0.299383\pi$
$488$	−288.670	−0.591538
$489$	−332.753	−0.680477
$490$	− 469.812i	− 0.958799i
$491$	− 60.7276i	− 0.123682i	−0.998086	−	0.0618408i	$-0.980303\pi$
$491$	− 60.7276i	− 0.123682i	0.998086	−	0.0618408i	$-0.0196971\pi$
$492$	− 115.961i	− 0.235693i
$493$	−341.460	−0.692617
$494$	− 2.35117i	− 0.00475946i
$495$	0	0
$496$	−240.496	−0.484871
$497$	− 334.681i	− 0.673403i
$498$	−173.045	−0.347480
$499$	570.616	1.14352	0.571759	−	0.820422i	$-0.306261\pi$
$499$	570.616	1.14352	0.571759	+	0.820422i	$0.306261\pi$
$500$	123.360	0.246721
$501$	− 266.646i	− 0.532228i
$502$	211.840i	0.421992i
$503$	− 188.776i	− 0.375299i	−0.982236	−	0.187650i	$-0.939913\pi$
$503$	− 188.776i	− 0.375299i	0.982236	−	0.187650i	$-0.0600870\pi$
$504$	−85.4205	−0.169485
$505$	− 21.4338i	− 0.0424431i
$506$	0	0
$507$	−290.520	−0.573018
$508$	− 249.784i	− 0.491702i
$509$	−114.710	−0.225364	−0.112682	−	0.993631i	$-0.535944\pi$
$509$	−114.710	−0.225364	−0.112682	+	0.993631i	$0.535944\pi$
$510$	−308.153	−0.604222
$511$	460.590	0.901350
$512$	22.6274i	0.0441942i
$513$	− 7.67089i	− 0.0149530i
$514$	− 570.988i	− 1.11087i
$515$	−742.982	−1.44268
$516$	146.537i	0.283986i
$517$	0	0
$518$	343.945	0.663987
$519$	− 569.456i	− 1.09722i
$520$	20.2164	0.0388777
$521$	−499.055	−0.957878	−0.478939	−	0.877848i	$-0.658979\pi$
$521$	−499.055	−0.957878	−0.478939	+	0.877848i	$0.658979\pi$
$522$	73.0868	0.140013
$523$	509.331i	0.973865i	0.873440	+	0.486933i	$0.161884\pi$
$523$	509.331i	0.973865i	−0.873440	+	0.486933i	$0.838116\pi$
$524$	− 86.1141i	− 0.164340i
$525$	266.457i	0.507537i
$526$	230.524	0.438258
$527$	1191.75i	2.26139i
$528$	0	0
$529$	937.982	1.77312
$530$	− 215.177i	− 0.405995i
$531$	130.079	0.244970
$532$	−29.7228	−0.0558699
$533$	37.6986	0.0707292
$534$	− 130.261i	− 0.243934i
$535$	− 378.514i	− 0.707503i
$536$	− 311.704i	− 0.581537i
$537$	216.804	0.403732
$538$	502.809i	0.934590i
$539$	0	0
$540$	65.9577	0.122144
$541$	1055.03i	1.95014i	0.221897	+	0.975070i	$0.428775\pi$
$541$	1055.03i	1.95014i	−0.221897	+	0.975070i	$0.571225\pi$
$542$	−629.483	−1.16141
$543$	279.285	0.514336
$544$	112.128	0.206117
$545$	− 1195.37i	− 2.19335i
$546$	− 27.7701i	− 0.0508609i
$547$	153.341i	0.280331i	0.990128	+	0.140165i	$0.0447634\pi$
$547$	153.341i	0.280331i	−0.990128	+	0.140165i	$0.955237\pi$
$548$	34.7127	0.0633443
$549$	− 306.181i	− 0.557707i
$550$	0	0
$551$	25.4312	0.0461546
$552$	− 187.637i	− 0.339922i
$553$	−773.359	−1.39848
$554$	−144.916	−0.261581
$555$	−265.578	−0.478519
$556$	71.4049i	0.128426i
$557$	165.728i	0.297537i	0.988872	+	0.148769i	$0.0475309\pi$
$557$	165.728i	0.297537i	−0.988872	+	0.148769i	$0.952469\pi$
$558$	− 255.085i	− 0.457141i
$559$	−47.6388	−0.0852215
$560$	− 255.570i	− 0.456375i
$561$	0	0
$562$	207.633	0.369455
$563$	− 538.007i	− 0.955608i	−0.878467	−	0.477804i	$-0.841433\pi$
$563$	− 538.007i	− 0.955608i	0.878467	−	0.477804i	$-0.158567\pi$
$564$	−206.854	−0.366763
$565$	52.6794	0.0932379
$566$	182.361	0.322193
$567$	− 90.6021i	− 0.159792i
$568$	− 94.0331i	− 0.165551i
$569$	− 27.2038i	− 0.0478098i	−0.999714	−	0.0239049i	$-0.992390\pi$
$569$	− 27.2038i	− 0.0478098i	0.999714	−	0.0239049i	$-0.00760989\pi$
$570$	22.9506	0.0402641
$571$	372.459i	0.652292i	0.945319	+	0.326146i	$0.105750\pi$
$571$	372.459i	0.652292i	−0.945319	+	0.326146i	$0.894250\pi$
$572$	0	0
$573$	426.762	0.744786
$574$	− 476.575i	− 0.830270i
$575$	−585.306	−1.01792
$576$	−24.0000	−0.0416667
$577$	1065.87	1.84727	0.923634	−	0.383276i	$-0.125204\pi$
$577$	1065.87	1.84727	0.923634	+	0.383276i	$0.125204\pi$
$578$	− 146.927i	− 0.254199i
$579$	470.850i	0.813213i
$580$	218.669i	0.377015i
$581$	−711.180	−1.22406
$582$	− 264.916i	− 0.455183i
$583$	0	0
$584$	129.409	0.221590
$585$	21.4427i	0.0366543i
$586$	−103.139	−0.176006
$587$	586.748	0.999571	0.499785	−	0.866149i	$-0.333412\pi$
$587$	586.748	0.999571	0.499785	+	0.866149i	$0.333412\pi$
$588$	−181.320	−0.308367
$589$	− 88.7589i	− 0.150694i
$590$	389.184i	0.659633i
$591$	− 643.927i	− 1.08955i
$592$	96.6358	0.163236
$593$	− 173.493i	− 0.292568i	−0.989243	−	0.146284i	$-0.953269\pi$
$593$	− 173.493i	− 0.292568i	0.989243	−	0.146284i	$-0.0467314\pi$
$594$	0	0
$595$	−1266.45	−2.12848
$596$	− 0.427793i	0 0.000717773i
$597$	−196.105	−0.328484
$598$	61.0004	0.102007
$599$	−912.403	−1.52321	−0.761606	−	0.648041i	$-0.775589\pi$
$599$	−912.403	−1.52321	−0.761606	+	0.648041i	$0.775589\pi$
$600$	74.8645i	0.124774i
$601$	97.1029i	0.161569i	0.996732	+	0.0807844i	$0.0257425\pi$
$601$	97.1029i	0.161569i	−0.996732	+	0.0807844i	$0.974257\pi$
$602$	602.236i	1.00039i
$603$	330.612	0.548278
$604$	205.884i	0.340867i
$605$	0	0
$606$	−8.27219	−0.0136505
$607$	970.427i	1.59873i	0.600848	+	0.799363i	$0.294830\pi$
$607$	970.427i	1.59873i	−0.600848	+	0.799363i	$0.705170\pi$
$608$	−8.35101	−0.0137352
$609$	300.372	0.493222
$610$	916.064	1.50174
$611$	− 67.2480i	− 0.110062i
$612$	118.929i	0.194329i
$613$	− 459.111i	− 0.748958i	−0.927235	−	0.374479i	$-0.877822\pi$
$613$	− 459.111i	− 0.748958i	0.927235	−	0.374479i	$-0.122178\pi$
$614$	344.035	0.560318
$615$	367.989i	0.598356i
$616$	0	0
$617$	−836.518	−1.35578	−0.677891	−	0.735162i	$-0.737106\pi$
$617$	−836.518	−1.35578	−0.677891	+	0.735162i	$0.737106\pi$
$618$	286.748i	0.463993i
$619$	−190.677	−0.308041	−0.154020	−	0.988068i	$-0.549222\pi$
$619$	−190.677	−0.308041	−0.154020	+	0.988068i	$0.549222\pi$
$620$	763.188	1.23095
$621$	199.019	0.320481
$622$	223.580i	0.359453i
$623$	− 535.346i	− 0.859303i
$624$	− 7.80236i	− 0.0125038i
$625$	−773.512	−1.23762
$626$	− 24.6493i	− 0.0393758i
$627$	0	0
$628$	−150.463	−0.239591
$629$	− 478.867i	− 0.761315i
$630$	271.073	0.430274
$631$	282.476	0.447664	0.223832	−	0.974628i	$-0.428143\pi$
$631$	282.476	0.447664	0.223832	+	0.974628i	$0.428143\pi$
$632$	−217.285	−0.343806
$633$	229.273i	0.362201i
$634$	− 104.492i	− 0.164814i
$635$	792.664i	1.24829i
$636$	−83.0460	−0.130575
$637$	− 58.9469i	− 0.0925382i
$638$	0	0
$639$	99.7372	0.156083
$640$	− 71.8057i	− 0.112196i
$641$	657.572	1.02585	0.512927	−	0.858432i	$-0.328561\pi$
$641$	657.572	1.02585	0.512927	+	0.858432i	$0.328561\pi$
$642$	−146.085	−0.227546
$643$	554.534	0.862417	0.431209	−	0.902252i	$-0.358087\pi$
$643$	554.534	0.862417	0.431209	+	0.902252i	$0.358087\pi$
$644$	− 771.149i	− 1.19744i
$645$	− 465.018i	− 0.720958i
$646$	41.3824i	0.0640595i
$647$	−704.426	−1.08876	−0.544378	−	0.838840i	$-0.683234\pi$
$647$	−704.426	−1.08876	−0.544378	+	0.838840i	$0.683234\pi$
$648$	− 25.4558i	− 0.0392837i
$649$	0	0
$650$	−24.3383	−0.0374436
$651$	− 1048.35i	− 1.61036i
$652$	−384.231	−0.589311
$653$	−141.023	−0.215961	−0.107980	−	0.994153i	$-0.534438\pi$
$653$	−141.023	−0.215961	−0.107980	+	0.994153i	$0.534438\pi$
$654$	−461.345	−0.705421
$655$	273.274i	0.417212i
$656$	− 133.900i	− 0.204116i
$657$	137.259i	0.208917i
$658$	−850.129	−1.29199
$659$	− 346.909i	− 0.526418i	−0.964739	−	0.263209i	$-0.915219\pi$
$659$	− 346.909i	− 0.526418i	0.964739	−	0.263209i	$-0.0847808\pi$
$660$	0	0
$661$	527.348	0.797803	0.398902	−	0.916994i	$-0.369392\pi$
$661$	527.348	0.797803	0.398902	+	0.916994i	$0.369392\pi$
$662$	592.420i	0.894894i
$663$	−38.6637	−0.0583163
$664$	−199.815	−0.300926
$665$	94.3221	0.141838
$666$	102.498i	0.153901i
$667$	659.804i	0.989212i
$668$	− 307.896i	− 0.460923i
$669$	−231.933	−0.346687
$670$	989.158i	1.47636i
$671$	0	0
$672$	−98.6351	−0.146778
$673$	− 165.894i	− 0.246500i	−0.992376	−	0.123250i	$-0.960668\pi$
$673$	− 165.894i	− 0.246500i	0.992376	−	0.123250i	$-0.0393316\pi$
$674$	−216.619	−0.321393
$675$	−79.4058	−0.117638
$676$	−335.463	−0.496248
$677$	821.518i	1.21347i	0.794905	+	0.606734i	$0.207521\pi$
$677$	821.518i	1.21347i	−0.794905	+	0.606734i	$0.792479\pi$
$678$	− 20.3312i	− 0.0299870i
$679$	− 1088.75i	− 1.60346i
$680$	−355.824	−0.523271
$681$	664.171i	0.975287i
$682$	0	0
$683$	−674.547	−0.987623	−0.493812	−	0.869569i	$-0.664397\pi$
$683$	−674.547	−0.987623	−0.493812	+	0.869569i	$0.664397\pi$
$684$	− 8.85758i	− 0.0129497i
$685$	−110.157	−0.160813
$686$	−47.5876	−0.0693697
$687$	−175.901	−0.256043
$688$	169.206i	0.245939i
$689$	− 26.9981i	− 0.0391845i
$690$	595.445i	0.862964i
$691$	241.760	0.349870	0.174935	−	0.984580i	$-0.444029\pi$
$691$	241.760	0.349870	0.174935	+	0.984580i	$0.444029\pi$
$692$	− 657.551i	− 0.950218i
$693$	0	0
$694$	−429.304	−0.618593
$695$	− 226.596i	− 0.326037i
$696$	84.3934	0.121255
$697$	−663.525	−0.951973
$698$	−650.234	−0.931567
$699$	65.2277i	0.0933157i
$700$	307.678i	0.439540i
$701$	453.896i	0.647498i	0.946143	+	0.323749i	$0.104943\pi$
$701$	453.896i	0.647498i	−0.946143	+	0.323749i	$0.895057\pi$
$702$	8.27565	0.0117887
$703$	35.6650i	0.0507325i
$704$	0	0
$705$	656.430	0.931106
$706$	− 49.7847i	− 0.0705166i
$707$	−33.9970	−0.0480863
$708$	150.202	0.212150
$709$	432.374	0.609836	0.304918	−	0.952379i	$-0.401371\pi$
$709$	432.374	0.609836	0.304918	+	0.952379i	$0.401371\pi$
$710$	298.404i	0.420287i
$711$	− 230.466i	− 0.324143i
$712$	− 150.412i	− 0.211253i
$713$	2302.82	3.22976
$714$	488.775i	0.684559i
$715$	0	0
$716$	250.344	0.349642
$717$	209.623i	0.292361i
$718$	296.770	0.413328
$719$	−406.442	−0.565289	−0.282644	−	0.959225i	$-0.591212\pi$
$719$	−406.442	−0.565289	−0.282644	+	0.959225i	$0.591212\pi$
$720$	76.1614	0.105780
$721$	1178.48i	1.63450i
$722$	507.449i	0.702838i
$723$	43.7192i	0.0604692i
$724$	322.490	0.445428
$725$	− 263.253i	− 0.363108i
$726$	0	0
$727$	−710.158	−0.976834	−0.488417	−	0.872610i	$-0.662425\pi$
$727$	−710.158	−0.976834	−0.488417	+	0.872610i	$0.662425\pi$
$728$	− 32.0661i	− 0.0440469i
$729$	27.0000	0.0370370
$730$	−410.664	−0.562554
$731$	838.480	1.14703
$732$	− 353.548i	− 0.482988i
$733$	404.685i	0.552095i	0.961144	+	0.276047i	$0.0890247\pi$
$733$	404.685i	0.552095i	−0.961144	+	0.276047i	$0.910975\pi$
$734$	553.747i	0.754424i
$735$	575.400	0.782856
$736$	− 216.664i	− 0.294381i
$737$	0	0
$738$	142.022	0.192442
$739$	− 1002.85i	− 1.35704i	−0.734584	−	0.678518i	$-0.762623\pi$
$739$	− 1002.85i	− 1.35704i	0.734584	−	0.678518i	$-0.237377\pi$
$740$	−306.663	−0.414410
$741$	2.87959	0.00388608
$742$	−341.302	−0.459976
$743$	139.721i	0.188050i	0.995570	+	0.0940249i	$0.0299733\pi$
$743$	139.721i	0.188050i	−0.995570	+	0.0940249i	$0.970027\pi$
$744$	− 294.546i	− 0.395896i
$745$	1.35755i	0.00182222i
$746$	−498.362	−0.668045
$747$	− 211.936i	− 0.283716i
$748$	0	0
$749$	−600.378	−0.801572
$750$	151.085i	0.201447i
$751$	−29.6933	−0.0395384	−0.0197692	−	0.999805i	$-0.506293\pi$
$751$	−29.6933	−0.0395384	−0.0197692	+	0.999805i	$0.506293\pi$
$752$	−238.855	−0.317626
$753$	−259.450	−0.344555
$754$	27.4362i	0.0363875i
$755$	− 653.349i	− 0.865363i
$756$	− 104.618i	− 0.138384i
$757$	386.576	0.510668	0.255334	−	0.966853i	$-0.417815\pi$
$757$	386.576	0.510668	0.255334	+	0.966853i	$0.417815\pi$
$758$	− 786.175i	− 1.03717i
$759$	0	0
$760$	26.5010	0.0348698
$761$	328.708i	0.431942i	0.976400	+	0.215971i	$0.0692916\pi$
$761$	328.708i	0.431942i	−0.976400	+	0.215971i	$0.930708\pi$
$762$	305.922	0.401473
$763$	−1896.04	−2.48497
$764$	492.783	0.645004
$765$	− 377.409i	− 0.493345i
$766$	− 287.783i	− 0.375695i
$767$	48.8305i	0.0636643i
$768$	−27.7128	−0.0360844
$769$	− 240.314i	− 0.312502i	−0.987717	−	0.156251i	$-0.950059\pi$
$769$	− 240.314i	− 0.312502i	0.987717	−	0.156251i	$-0.0499409\pi$
$770$	0	0
$771$	699.314	0.907022
$772$	543.691i	0.704263i
$773$	−634.877	−0.821315	−0.410658	−	0.911790i	$-0.634701\pi$
$773$	−634.877	−0.821315	−0.410658	+	0.911790i	$0.634701\pi$
$774$	−179.470	−0.231873
$775$	−918.795	−1.18554
$776$	− 305.899i	− 0.394200i
$777$	421.245i	0.542143i
$778$	612.274i	0.786984i
$779$	49.4179	0.0634376
$780$	24.7600i	0.0317435i
$781$	0	0
$782$	−1073.65	−1.37296
$783$	89.5127i	0.114320i
$784$	−209.370	−0.267054
$785$	477.479	0.608254
$786$	105.468	0.134183
$787$	22.3959i	0.0284573i	0.999899	+	0.0142287i	$0.00452927\pi$
$787$	22.3959i	0.0284573i	−0.999899	+	0.0142287i	$0.995471\pi$
$788$	− 743.543i	− 0.943582i
$789$	282.333i	0.357836i
$790$	689.531	0.872824
$791$	− 83.5571i	− 0.105635i
$792$	0	0
$793$	114.938	0.144940
$794$	− 305.900i	− 0.385265i
$795$	263.537	0.331494
$796$	−226.443	−0.284476
$797$	−1027.82	−1.28961	−0.644803	−	0.764349i	$-0.723061\pi$
$797$	−1027.82	−1.28961	−0.644803	+	0.764349i	$0.723061\pi$
$798$	− 36.4029i	− 0.0456176i
$799$	1183.62i	1.48137i
$800$	86.4461i	0.108058i
$801$	159.536	0.199171
$802$	112.087i	0.139760i
$803$	0	0
$804$	381.758	0.474823
$805$	2447.16i	3.03995i
$806$	95.7566	0.118805
$807$	−615.813	−0.763089
$808$	−9.55190	−0.0118217
$809$	− 1476.24i	− 1.82477i	−0.409331	−	0.912386i	$-0.634238\pi$
$809$	− 1476.24i	− 1.82477i	0.409331	−	0.912386i	$-0.365762\pi$
$810$	80.7814i	0.0997301i
$811$	− 277.810i	− 0.342552i	−0.985223	−	0.171276i	$-0.945211\pi$
$811$	− 277.810i	− 0.342552i	0.985223	−	0.171276i	$-0.0547890\pi$
$812$	346.840	0.427143
$813$	− 770.956i	− 0.948285i
$814$	0	0
$815$	1219.31	1.49609
$816$	137.328i	0.168294i
$817$	−62.4481	−0.0764359
$818$	456.257	0.557771
$819$	34.0113	0.0415278
$820$	424.917i	0.518191i
$821$	− 1012.05i	− 1.23270i	−0.787471	−	0.616352i	$-0.788610\pi$
$821$	− 1012.05i	− 1.23270i	0.787471	−	0.616352i	$-0.211390\pi$
$822$	42.5142i	0.0517204i
$823$	561.875	0.682715	0.341358	−	0.939933i	$-0.389113\pi$
$823$	561.875	0.682715	0.341358	+	0.939933i	$0.389113\pi$
$824$	331.108i	0.401830i
$825$	0	0
$826$	617.301	0.747337
$827$	743.913i	0.899532i	0.893146	+	0.449766i	$0.148493\pi$
$827$	743.913i	0.899532i	−0.893146	+	0.449766i	$0.851507\pi$
$828$	229.807	0.277545
$829$	319.318	0.385184	0.192592	−	0.981279i	$-0.438311\pi$
$829$	319.318	0.385184	0.192592	+	0.981279i	$0.438311\pi$
$830$	634.092	0.763966
$831$	− 177.485i	− 0.213580i
$832$	− 9.00939i	− 0.0108286i
$833$	1037.51i	1.24551i
$834$	−87.4528	−0.104859
$835$	977.075i	1.17015i
$836$	0	0
$837$	312.414	0.373254
$838$	862.223i	1.02891i
$839$	1403.15	1.67241	0.836204	−	0.548419i	$-0.184770\pi$
$839$	1403.15	1.67241	0.836204	+	0.548419i	$0.184770\pi$
$840$	313.008	0.372628
$841$	544.240	0.647134
$842$	44.3369i	0.0526567i
$843$	254.298i	0.301658i
$844$	264.742i	0.313675i
$845$	1064.56	1.25983
$846$	− 253.344i	− 0.299461i
$847$	0	0
$848$	−95.8932	−0.113082
$849$	223.346i	0.263069i
$850$	428.374	0.503969
$851$	−925.317	−1.08733
$852$	115.167	0.135172
$853$	− 1451.36i	− 1.70148i	−0.525585	−	0.850741i	$-0.676153\pi$
$853$	− 1451.36i	− 1.70148i	0.525585	−	0.850741i	$-0.323847\pi$
$854$	− 1453.01i	− 1.70142i
$855$	28.1086i	0.0328755i
$856$	−168.684	−0.197061
$857$	− 598.032i	− 0.697820i	−0.937156	−	0.348910i	$-0.886552\pi$
$857$	− 598.032i	− 0.697820i	0.937156	−	0.348910i	$-0.113448\pi$
$858$	0	0
$859$	−1338.18	−1.55784	−0.778919	−	0.627125i	$-0.784232\pi$
$859$	−1338.18	−1.55784	−0.778919	+	0.627125i	$0.784232\pi$
$860$	− 536.956i	− 0.624368i
$861$	583.683	0.677913
$862$	513.021	0.595152
$863$	−1062.16	−1.23078	−0.615389	−	0.788224i	$-0.711001\pi$
$863$	−1062.16	−1.23078	−0.615389	+	0.788224i	$0.711001\pi$
$864$	− 29.3939i	− 0.0340207i
$865$	2086.67i	2.41233i
$866$	− 125.388i	− 0.144790i
$867$	179.948	0.207553
$868$	− 1210.53i	− 1.39462i
$869$	0	0
$870$	−267.813	−0.307831
$871$	124.109i	0.142490i
$872$	−532.716	−0.610912
$873$	324.455	0.371655
$874$	79.9634	0.0914913
$875$	620.929i	0.709633i
$876$	158.493i	0.180928i
$877$	166.881i	0.190287i	0.995464	+	0.0951434i	$0.0303310\pi$
$877$	166.881i	0.190287i	−0.995464	+	0.0951434i	$0.969669\pi$
$878$	527.679	0.601001
$879$	− 126.319i	− 0.143708i
$880$	0	0
$881$	−1345.57	−1.52732	−0.763662	−	0.645616i	$-0.776601\pi$
$881$	−1345.57	−1.52732	−0.763662	+	0.645616i	$0.776601\pi$
$882$	− 222.071i	− 0.251781i
$883$	−1021.04	−1.15633	−0.578166	−	0.815919i	$-0.696232\pi$
$883$	−1021.04	−1.15633	−0.578166	+	0.815919i	$0.696232\pi$
$884$	−44.6450	−0.0505034
$885$	−476.651	−0.538588
$886$	770.037i	0.869116i
$887$	680.244i	0.766904i	0.923561	+	0.383452i	$0.125265\pi$
$887$	680.244i	0.766904i	−0.923561	+	0.383452i	$0.874735\pi$
$888$	118.354i	0.133282i
$889$	1257.28	1.41426
$890$	477.317i	0.536311i
$891$	0	0
$892$	−267.814	−0.300239
$893$	− 88.1531i	− 0.0987157i
$894$	0.523937	0.000586059 0
$895$	−794.438	−0.887640
$896$	−113.894	−0.127114
$897$	74.7100i	0.0832887i
$898$	121.758i	0.135587i
$899$	1035.74i	1.15210i
$900$	−91.6900	−0.101878
$901$	475.188i	0.527400i
$902$	0	0
$903$	−737.585	−0.816816
$904$	− 23.4764i	− 0.0259695i
$905$	−1023.39	−1.13082
$906$	−252.155	−0.278317
$907$	831.611	0.916881	0.458440	−	0.888725i	$-0.348408\pi$
$907$	831.611	0.916881	0.458440	+	0.888725i	$0.348408\pi$
$908$	766.918i	0.844623i
$909$	− 10.1313i	− 0.0111456i
$910$	101.758i	0.111822i
$911$	857.147	0.940886	0.470443	−	0.882430i	$-0.344094\pi$
$911$	857.147	0.940886	0.470443	+	0.882430i	$0.344094\pi$
$912$	− 10.2279i	− 0.0112147i
$913$	0	0
$914$	594.226	0.650138
$915$	1121.94i	1.22617i
$916$	−203.113	−0.221739
$917$	433.451	0.472684
$918$	−145.658	−0.158669
$919$	203.278i	0.221195i	0.993865	+	0.110597i	$0.0352764\pi$
$919$	203.278i	0.221195i	−0.993865	+	0.110597i	$0.964724\pi$
$920$	687.561i	0.747349i
$921$	421.355i	0.457497i
$922$	−240.274	−0.260601
$923$	37.4405i	0.0405639i
$924$	0	0
$925$	369.189	0.399123
$926$	32.7222i	0.0353372i
$927$	−351.193	−0.378849
$928$	97.4491	0.105010
$929$	−1050.34	−1.13061	−0.565305	−	0.824882i	$-0.691242\pi$
$929$	−1050.34	−1.13061	−0.565305	+	0.824882i	$0.691242\pi$
$930$	934.711i	1.00507i
$931$	− 77.2714i	− 0.0829983i
$932$	75.3184i	0.0808138i
$933$	−273.828	−0.293492
$934$	− 397.307i	− 0.425382i
$935$	0	0
$936$	9.55590	0.0102093
$937$	− 605.851i	− 0.646586i	−0.946299	−	0.323293i	$-0.895210\pi$
$937$	− 605.851i	− 0.646586i	0.946299	−	0.323293i	$-0.104790\pi$
$938$	1568.95	1.67265
$939$	30.1891	0.0321502
$940$	757.980	0.806361
$941$	593.739i	0.630966i	0.948931	+	0.315483i	$0.102167\pi$
$941$	593.739i	0.630966i	−0.948931	+	0.315483i	$0.897833\pi$
$942$	− 184.279i	− 0.195626i
$943$	1282.13i	1.35963i
$944$	173.439	0.183727
$945$	331.995i	0.351317i
$946$	0	0
$947$	141.939	0.149883	0.0749413	−	0.997188i	$-0.476123\pi$
$947$	141.939	0.149883	0.0749413	+	0.997188i	$0.476123\pi$
$948$	− 266.119i	− 0.280716i
$949$	−51.5257	−0.0542947
$950$	−31.9043	−0.0335835
$951$	127.976	0.134570
$952$	564.388i	0.592845i
$953$	1694.64i	1.77822i	0.457694	+	0.889110i	$0.348675\pi$
$953$	1694.64i	1.77822i	−0.457694	+	0.889110i	$0.651325\pi$
$954$	− 101.710i	− 0.106614i
$955$	−1563.79	−1.63748
$956$	242.052i	0.253192i
$957$	0	0
$958$	−352.966	−0.368440
$959$	174.725i	0.182195i
$960$	87.9436	0.0916079
$961$	2653.90	2.76160
$962$	−38.4768	−0.0399966
$963$	− 178.916i	− 0.185791i
$964$	50.4826i	0.0523679i
$965$	− 1725.34i	− 1.78792i
$966$	944.461	0.977703
$967$	− 1285.89i	− 1.32978i	−0.746943	−	0.664888i	$-0.768479\pi$
$967$	− 1285.89i	− 1.32978i	0.746943	−	0.664888i	$-0.231521\pi$
$968$	0	0
$969$	−50.6829	−0.0523044
$970$	970.737i	1.00076i
$971$	−407.768	−0.419947	−0.209973	−	0.977707i	$-0.567338\pi$
$971$	−407.768	−0.419947	−0.209973	+	0.977707i	$0.567338\pi$
$972$	31.1769	0.0320750
$973$	−359.413	−0.369387
$974$	811.798i	0.833468i
$975$	− 29.8083i	− 0.0305726i
$976$	− 408.242i	− 0.418280i
$977$	−1047.71	−1.07238	−0.536190	−	0.844098i	$-0.680137\pi$
$977$	−1047.71	−1.07238	−0.536190	+	0.844098i	$0.680137\pi$
$978$	− 470.584i	− 0.481170i
$979$	0	0
$980$	664.414	0.677974
$981$	− 565.030i	− 0.575974i
$982$	85.8818	0.0874561
$983$	72.4020	0.0736541	0.0368271	−	0.999322i	$-0.488275\pi$
$983$	72.4020	0.0736541	0.0368271	+	0.999322i	$0.488275\pi$
$984$	163.993	0.166660
$985$	2359.55i	2.39548i
$986$	− 482.898i	− 0.489754i
$987$	− 1041.19i	− 1.05490i
$988$	3.32506	0.00336544
$989$	− 1620.20i	− 1.63822i
$990$	0	0
$991$	1335.55	1.34768	0.673838	−	0.738879i	$-0.264644\pi$
$991$	1335.55	1.34768	0.673838	+	0.738879i	$0.264644\pi$
$992$	− 340.113i	− 0.342856i
$993$	−725.563	−0.730678
$994$	473.311	0.476168
$995$	718.591	0.722202
$996$	− 244.723i	− 0.245705i
$997$	− 511.127i	− 0.512665i	−0.966589	−	0.256332i	$-0.917486\pi$
$997$	− 511.127i	− 0.512665i	0.966589	−	0.256332i	$-0.0825142\pi$
$998$	806.972i	0.808589i
$999$	−125.534	−0.125659

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	726.3.d.e.241.11		16
3.2	odd	2		2178.3.d.m.1693.2		16
11.4	even	5		66.3.f.a.61.2	yes	16
11.8	odd	10		66.3.f.a.13.2	✓	16
11.10	odd	2	inner	726.3.d.e.241.3		16
33.8	even	10		198.3.j.b.145.3		16
33.26	odd	10		198.3.j.b.127.3		16
33.32	even	2		2178.3.d.m.1693.10		16
44.15	odd	10		528.3.bf.c.193.2		16
44.19	even	10		528.3.bf.c.145.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.3.f.a.13.2	✓	16	11.8	odd	10
66.3.f.a.61.2	yes	16	11.4	even	5
198.3.j.b.127.3		16	33.26	odd	10
198.3.j.b.145.3		16	33.8	even	10
528.3.bf.c.145.2		16	44.19	even	10
528.3.bf.c.193.2		16	44.15	odd	10
726.3.d.e.241.3		16	11.10	odd	2	inner
726.3.d.e.241.11		16	1.1	even	1	trivial
2178.3.d.m.1693.2		16	3.2	odd	2
2178.3.d.m.1693.10		16	33.32	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	726.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} -1.73205 q^{3} -2.00000 q^{4} +6.34678 q^{5} -2.44949i q^{6} -10.0669i q^{7} -2.82843i q^{8} +3.00000 q^{9} +8.97571i q^{10} +3.46410 q^{12} +1.12617i q^{13} +14.2368 q^{14} -10.9930 q^{15} +4.00000 q^{16} -19.8215i q^{17} +4.24264i q^{18} +1.47626i q^{19} -12.6936 q^{20} +17.4364i q^{21} -38.3012 q^{23} +4.89898i q^{24} +15.2817 q^{25} -1.59265 q^{26} -5.19615 q^{27} +20.1338i q^{28} -17.2267i q^{29} -15.5464i q^{30} -60.1240 q^{31} +5.65685i q^{32} +28.0319 q^{34} -63.8925i q^{35} -6.00000 q^{36} +24.1590 q^{37} -2.08775 q^{38} -1.95059i q^{39} -17.9514i q^{40} -33.4750i q^{41} -24.6588 q^{42} +42.3015i q^{43} +19.0404 q^{45} -54.1661i q^{46} -59.7137 q^{47} -6.92820 q^{48} -52.3426 q^{49} +21.6115i q^{50} +34.3319i q^{51} -2.25235i q^{52} -23.9733 q^{53} -7.34847i q^{54} -28.4735 q^{56} -2.55696i q^{57} +24.3623 q^{58} +43.3596 q^{59} +21.9859 q^{60} -102.060i q^{61} -85.0282i q^{62} -30.2007i q^{63} -8.00000 q^{64} +7.14758i q^{65} +110.204 q^{67} +39.6431i q^{68} +66.3396 q^{69} +90.3576 q^{70} +33.2457 q^{71} -8.48528i q^{72} +45.7529i q^{73} +34.1659i q^{74} -26.4686 q^{75} -2.95253i q^{76} +2.75855 q^{78} -76.8219i q^{79} +25.3871 q^{80} +9.00000 q^{81} +47.3408 q^{82} -70.6453i q^{83} -34.8728i q^{84} -125.803i q^{85} -59.8233 q^{86} +29.8376i q^{87} +53.1788 q^{89} +26.9271i q^{90} +11.3371 q^{91} +76.6024 q^{92} +104.138 q^{93} -84.4479i q^{94} +9.36952i q^{95} -9.79796i q^{96} +108.152 q^{97} -74.0236i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 32 q^{4} + 8 q^{5} + 48 q^{9} + 48 q^{14} - 48 q^{15} + 64 q^{16} - 16 q^{20} - 8 q^{23} - 8 q^{25} + 128 q^{26} - 8 q^{31} - 64 q^{34} - 96 q^{36} + 96 q^{37} - 208 q^{38} - 144 q^{42} + 24 q^{45}+ \cdots + 184 q^{97}+O(q^{100}) \) 16 * q - 32 * q^4 + 8 * q^5 + 48 * q^9 + 48 * q^14 - 48 * q^15 + 64 * q^16 - 16 * q^20 - 8 * q^23 - 8 * q^25 + 128 * q^26 - 8 * q^31 - 64 * q^34 - 96 * q^36 + 96 * q^37 - 208 * q^38 - 144 * q^42 + 24 * q^45 - 128 * q^47 - 64 * q^49 + 16 * q^53 - 96 * q^56 + 64 * q^58 - 152 * q^59 + 96 * q^60 - 128 * q^64 + 248 * q^67 + 168 * q^69 - 32 * q^70 - 72 * q^71 - 48 * q^75 + 32 * q^80 + 144 * q^81 + 176 * q^82 + 464 * q^86 - 360 * q^89 - 32 * q^91 + 16 * q^92 + 336 * q^93 + 184 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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