LMFDB - Embedded newform 983.6.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [983,6,Mod(1,983)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(983, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("983.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 983 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	983.a (trivial)

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:	yes
Analytic conductor:	$157.657294876$
Analytic rank:	$0$
Dimension:	$218$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	983.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-11.0647 q^{2} -25.4268 q^{3} +90.4285 q^{4} +75.4706 q^{5} +281.341 q^{6} +155.090 q^{7} -646.496 q^{8} +403.521 q^{9} -835.063 q^{10} +730.527 q^{11} -2299.30 q^{12} +1160.58 q^{13} -1716.03 q^{14} -1918.97 q^{15} +4259.60 q^{16} +1432.06 q^{17} -4464.85 q^{18} -656.774 q^{19} +6824.69 q^{20} -3943.44 q^{21} -8083.09 q^{22} -3481.34 q^{23} +16438.3 q^{24} +2570.81 q^{25} -12841.5 q^{26} -4081.52 q^{27} +14024.6 q^{28} -6099.65 q^{29} +21232.9 q^{30} -83.1421 q^{31} -26443.5 q^{32} -18574.9 q^{33} -15845.4 q^{34} +11704.7 q^{35} +36489.8 q^{36} +9096.57 q^{37} +7267.03 q^{38} -29509.8 q^{39} -48791.4 q^{40} +2700.14 q^{41} +43633.1 q^{42} +15196.3 q^{43} +66060.5 q^{44} +30453.9 q^{45} +38520.1 q^{46} +2152.66 q^{47} -108308. q^{48} +7245.91 q^{49} -28445.3 q^{50} -36412.6 q^{51} +104949. q^{52} -7656.38 q^{53} +45161.0 q^{54} +55133.3 q^{55} -100265. q^{56} +16699.6 q^{57} +67491.0 q^{58} +13421.9 q^{59} -173530. q^{60} +10176.0 q^{61} +919.946 q^{62} +62582.0 q^{63} +156283. q^{64} +87589.6 q^{65} +205527. q^{66} +43115.3 q^{67} +129499. q^{68} +88519.1 q^{69} -129510. q^{70} -11880.4 q^{71} -260875. q^{72} -41114.5 q^{73} -100651. q^{74} -65367.4 q^{75} -59391.1 q^{76} +113297. q^{77} +326518. q^{78} -87727.1 q^{79} +321475. q^{80} +5724.46 q^{81} -29876.3 q^{82} +52213.8 q^{83} -356599. q^{84} +108078. q^{85} -168143. q^{86} +155094. q^{87} -472283. q^{88} +53416.4 q^{89} -336965. q^{90} +179994. q^{91} -314812. q^{92} +2114.04 q^{93} -23818.7 q^{94} -49567.1 q^{95} +672373. q^{96} +11570.9 q^{97} -80174.2 q^{98} +294783. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 218 q + 35 q^{2} + 70 q^{3} + 3685 q^{4} + 253 q^{5} + 529 q^{6} + 1567 q^{7} + 1695 q^{8} + 19812 q^{9} + 2133 q^{10} + 1752 q^{11} + 3512 q^{12} + 5990 q^{13} + 2319 q^{14} + 4639 q^{15} + 66105 q^{16}+ \cdots + 627643 q^{99}+O(q^{100}) $ 218 * q + 35 * q^2 + 70 * q^3 + 3685 * q^4 + 253 * q^5 + 529 * q^6 + 1567 * q^7 + 1695 * q^8 + 19812 * q^9 + 2133 * q^10 + 1752 * q^11 + 3512 * q^12 + 5990 * q^13 + 2319 * q^14 + 4639 * q^15 + 66105 * q^16 + 10656 * q^17 + 11911 * q^18 + 11511 * q^19 + 10012 * q^20 + 12225 * q^21 + 19401 * q^22 + 9767 * q^23 + 21725 * q^24 + 185207 * q^25 + 7708 * q^26 + 23764 * q^27 + 77808 * q^28 + 25772 * q^29 + 15736 * q^30 + 35900 * q^31 + 60155 * q^32 + 70026 * q^33 + 17236 * q^34 + 28782 * q^35 + 382874 * q^36 + 126082 * q^37 + 62164 * q^38 + 54264 * q^39 + 102846 * q^40 + 70480 * q^41 + 102244 * q^42 + 137413 * q^43 + 116278 * q^44 + 93481 * q^45 + 126122 * q^46 + 63218 * q^47 + 124701 * q^48 + 732031 * q^49 + 131089 * q^50 + 109902 * q^51 + 229519 * q^52 + 102608 * q^53 + 149130 * q^54 + 167596 * q^55 + 87868 * q^56 + 408318 * q^57 + 304579 * q^58 + 67460 * q^59 + 150523 * q^60 + 195132 * q^61 + 132294 * q^62 + 374425 * q^63 + 1296639 * q^64 + 347092 * q^65 + 147397 * q^66 + 381238 * q^67 + 296321 * q^68 + 139362 * q^69 + 325675 * q^70 + 147818 * q^71 + 646059 * q^72 + 961992 * q^73 + 167410 * q^74 + 167324 * q^75 + 504875 * q^76 + 284328 * q^77 + 284295 * q^78 + 285792 * q^79 + 444932 * q^80 + 1980282 * q^81 + 336676 * q^82 + 276734 * q^83 + 378474 * q^84 + 1021245 * q^85 + 156051 * q^86 + 500457 * q^87 + 1068101 * q^88 + 398983 * q^89 + 463961 * q^90 + 273517 * q^91 + 577884 * q^92 + 967833 * q^93 + 224775 * q^94 + 482817 * q^95 + 780445 * q^96 + 1636277 * q^97 + 495958 * q^98 + 627643 * q^99

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 $

$2$	−11.0647	−1.95599	−0.977994	−	0.208632i	$-0.933099\pi$
$2$	−11.0647	−1.95599	−0.977994	+	0.208632i	$0.933099\pi$
$3$	−25.4268	−1.63113	−0.815564	−	0.578667i	$-0.803573\pi$
$3$	−25.4268	−1.63113	−0.815564	+	0.578667i	$0.803573\pi$
$4$	90.4285	2.82589
$5$	75.4706	1.35006	0.675029	−	0.737791i	$-0.264131\pi$
$5$	75.4706	1.35006	0.675029	+	0.737791i	$0.264131\pi$
$6$	281.341	3.19047
$7$	155.090	1.19630	0.598148	−	0.801386i	$-0.295903\pi$
$7$	155.090	1.19630	0.598148	+	0.801386i	$0.295903\pi$
$8$	−646.496	−3.57142
$9$	403.521	1.66058
$10$	−835.063	−2.64070
$11$	730.527	1.82035	0.910174	−	0.414225i	$-0.135947\pi$
$11$	730.527	1.82035	0.910174	+	0.414225i	$0.135947\pi$
$12$	−2299.30	−4.60939
$13$	1160.58	1.90466	0.952328	−	0.305076i	$-0.0986820\pi$
$13$	1160.58	1.90466	0.952328	+	0.305076i	$0.0986820\pi$
$14$	−1716.03	−2.33994
$15$	−1918.97	−2.20212
$16$	4259.60	4.15977
$17$	1432.06	1.20182	0.600908	−	0.799318i	$-0.294806\pi$
$17$	1432.06	1.20182	0.600908	+	0.799318i	$0.294806\pi$
$18$	−4464.85	−3.24807
$19$	−656.774	−0.417380	−0.208690	−	0.977982i	$-0.566920\pi$
$19$	−656.774	−0.417380	−0.208690	+	0.977982i	$0.566920\pi$
$20$	6824.69	3.81512
$21$	−3943.44	−1.95131
$22$	−8083.09	−3.56058
$23$	−3481.34	−1.37223	−0.686114	−	0.727494i	$-0.740685\pi$
$23$	−3481.34	−1.37223	−0.686114	+	0.727494i	$0.740685\pi$
$24$	16438.3	5.82544
$25$	2570.81	0.822659
$26$	−12841.5	−3.72548
$27$	−4081.52	−1.07749
$28$	14024.6	3.38060
$29$	−6099.65	−1.34682	−0.673410	−	0.739269i	$-0.735171\pi$
$29$	−6099.65	−1.34682	−0.673410	+	0.739269i	$0.735171\pi$
$30$	21232.9	4.30732
$31$	−83.1421	−0.0155388	−0.00776939	−	0.999970i	$-0.502473\pi$
$31$	−83.1421	−0.0155388	−0.00776939	+	0.999970i	$0.502473\pi$
$32$	−26443.5	−4.56503
$33$	−18574.9	−2.96922
$34$	−15845.4	−2.35074
$35$	11704.7	1.61507
$36$	36489.8	4.69261
$37$	9096.57	1.09238	0.546190	−	0.837662i	$-0.316078\pi$
$37$	9096.57	1.09238	0.546190	+	0.837662i	$0.316078\pi$
$38$	7267.03	0.816391
$39$	−29509.8	−3.10674
$40$	−48791.4	−4.82163
$41$	2700.14	0.250857	0.125428	−	0.992103i	$-0.459969\pi$
$41$	2700.14	0.250857	0.125428	+	0.992103i	$0.459969\pi$
$42$	43633.1	3.81674
$43$	15196.3	1.25334	0.626668	−	0.779286i	$-0.284418\pi$
$43$	15196.3	1.25334	0.626668	+	0.779286i	$0.284418\pi$
$44$	66060.5	5.14411
$45$	30453.9	2.24188
$46$	38520.1	2.68406
$47$	2152.66	0.142145	0.0710725	−	0.997471i	$-0.477358\pi$
$47$	2152.66	0.142145	0.0710725	+	0.997471i	$0.477358\pi$
$48$	−108308.	−6.78511
$49$	7245.91	0.431125
$50$	−28445.3	−1.60911
$51$	−36412.6	−1.96032
$52$	104949.	5.38235
$53$	−7656.38	−0.374398	−0.187199	−	0.982322i	$-0.559941\pi$
$53$	−7656.38	−0.374398	−0.187199	+	0.982322i	$0.559941\pi$
$54$	45161.0	2.10756
$55$	55133.3	2.45758
$56$	−100265.	−4.27248
$57$	16699.6	0.680801
$58$	67491.0	2.63436
$59$	13421.9	0.501976	0.250988	−	0.967990i	$-0.419245\pi$
$59$	13421.9	0.501976	0.250988	+	0.967990i	$0.419245\pi$
$60$	−173530.	−6.22295
$61$	10176.0	0.350149	0.175074	−	0.984555i	$-0.443983\pi$
$61$	10176.0	0.350149	0.175074	+	0.984555i	$0.443983\pi$
$62$	919.946	0.0303937
$63$	62582.0	1.98654
$64$	156283.	4.76939
$65$	87589.6	2.57140
$66$	205527.	5.80776
$67$	43115.3	1.17339	0.586697	−	0.809806i	$-0.300428\pi$
$67$	43115.3	1.17339	0.586697	+	0.809806i	$0.300428\pi$
$68$	129499.	3.39620
$69$	88519.1	2.23828
$70$	−129510.	−3.15906
$71$	−11880.4	−0.279696	−0.139848	−	0.990173i	$-0.544661\pi$
$71$	−11880.4	−0.279696	−0.139848	+	0.990173i	$0.544661\pi$
$72$	−260875.	−5.93063
$73$	−41114.5	−0.902999	−0.451500	−	0.892271i	$-0.649111\pi$
$73$	−41114.5	−0.902999	−0.451500	+	0.892271i	$0.649111\pi$
$74$	−100651.	−2.13668
$75$	−65367.4	−1.34186
$76$	−59391.1	−1.17947
$77$	113297.	2.17768
$78$	326518.	6.07674
$79$	−87727.1	−1.58149	−0.790744	−	0.612147i	$-0.790306\pi$
$79$	−87727.1	−1.58149	−0.790744	+	0.612147i	$0.790306\pi$
$80$	321475.	5.61593
$81$	5724.46	0.0969442
$82$	−29876.3	−0.490673
$83$	52213.8	0.831937	0.415969	−	0.909379i	$-0.363443\pi$
$83$	52213.8	0.831937	0.415969	+	0.909379i	$0.363443\pi$
$84$	−356599.	−5.51420
$85$	108078.	1.62252
$86$	−168143.	−2.45151
$87$	155094.	2.19684
$88$	−472283.	−6.50123
$89$	53416.4	0.714824	0.357412	−	0.933947i	$-0.383659\pi$
$89$	53416.4	0.714824	0.357412	+	0.933947i	$0.383659\pi$
$90$	−336965.	−4.38509
$91$	179994.	2.27853
$92$	−314812.	−3.87777
$93$	2114.04	0.0253457
$94$	−23818.7	−0.278034
$95$	−49567.1	−0.563488
$96$	672373.	7.44615
$97$	11570.9	0.124864	0.0624322	−	0.998049i	$-0.480114\pi$
$97$	11570.9	0.124864	0.0624322	+	0.998049i	$0.480114\pi$
$98$	−80174.2	−0.843275
$99$	294783.	3.02283
$100$	232474.	2.32474
$101$	8269.40	0.0806623	0.0403311	−	0.999186i	$-0.487159\pi$
$101$	8269.40	0.0806623	0.0403311	+	0.999186i	$0.487159\pi$
$102$	402896.	3.83436
$103$	−168757.	−1.56736	−0.783679	−	0.621166i	$-0.786659\pi$
$103$	−168757.	−1.56736	−0.783679	+	0.621166i	$0.786659\pi$
$104$	−750310.	−6.80233
$105$	−297614.	−2.63439
$106$	84715.9	0.732319
$107$	66323.7	0.560028	0.280014	−	0.959996i	$-0.409661\pi$
$107$	66323.7	0.560028	0.280014	+	0.959996i	$0.409661\pi$
$108$	−369086.	−3.04487
$109$	129009.	1.04004	0.520022	−	0.854153i	$-0.325924\pi$
$109$	129009.	1.04004	0.520022	+	0.854153i	$0.325924\pi$
$110$	−610036.	−4.80699
$111$	−231296.	−1.78181
$112$	660621.	4.97631
$113$	36639.3	0.269930	0.134965	−	0.990850i	$-0.456908\pi$
$113$	36639.3	0.269930	0.134965	+	0.990850i	$0.456908\pi$
$114$	−184777.	−1.33164
$115$	−262738.	−1.85259
$116$	−551582.	−3.80597
$117$	468318.	3.16283
$118$	−148509.	−0.981859
$119$	222098.	1.43773
$120$	1.24061e6	7.86469
$121$	372619.	2.31367
$122$	−112595.	−0.684887
$123$	−68655.7	−0.409180
$124$	−7518.41	−0.0439109
$125$	−41825.1	−0.239421
$126$	−692454.	−3.88566
$127$	172600.	0.949580	0.474790	−	0.880099i	$-0.342524\pi$
$127$	172600.	0.949580	0.474790	+	0.880099i	$0.342524\pi$
$128$	−883041.	−4.76383
$129$	−386394.	−2.04435
$130$	−969156.	−5.02962
$131$	−104664.	−0.532867	−0.266434	−	0.963853i	$-0.585845\pi$
$131$	−104664.	−0.532867	−0.266434	+	0.963853i	$0.585845\pi$
$132$	−1.67970e6	−8.39070
$133$	−101859.	−0.499310
$134$	−477059.	−2.29515
$135$	−308035.	−1.45467
$136$	−925820.	−4.29219
$137$	−211.703	−0.000963662 0	−0.000481831	−	1.00000i	$-0.500153\pi$
$137$	−211.703	−0.000963662 0	−0.000481831		1.00000i	$0.500153\pi$
$138$	−979441.	−4.37805
$139$	−215330.	−0.945294	−0.472647	−	0.881252i	$-0.656701\pi$
$139$	−215330.	−0.945294	−0.472647	+	0.881252i	$0.656701\pi$
$140$	1.05844e6	4.56401
$141$	−54735.3	−0.231857
$142$	131454.	0.547082
$143$	847835.	3.46714
$144$	1.71884e6	6.90762
$145$	−460344.	−1.81829
$146$	454921.	1.76626
$147$	−184240.	−0.703220
$148$	822589.	3.08694
$149$	218905.	0.807773	0.403886	−	0.914809i	$-0.367659\pi$
$149$	218905.	0.807773	0.403886	+	0.914809i	$0.367659\pi$
$150$	723273.	2.62467
$151$	−540652.	−1.92964	−0.964818	−	0.262918i	$-0.915315\pi$
$151$	−540652.	−1.92964	−0.964818	+	0.262918i	$0.915315\pi$
$152$	424602.	1.49064
$153$	577865.	1.99571
$154$	−1.25361e6	−4.25951
$155$	−6274.78	−0.0209783
$156$	−2.66853e6	−8.77930
$157$	313069.	1.01366	0.506829	−	0.862047i	$-0.330818\pi$
$157$	313069.	1.01366	0.506829	+	0.862047i	$0.330818\pi$
$158$	970677.	3.09337
$159$	194677.	0.610692
$160$	−1.99571e6	−6.16306
$161$	−539920.	−1.64159
$162$	−63339.7	−0.189622
$163$	247760.	0.730401	0.365201	−	0.930929i	$-0.381000\pi$
$163$	247760.	0.730401	0.365201	+	0.930929i	$0.381000\pi$
$164$	244169.	0.708894
$165$	−1.40186e6	−4.00862
$166$	−577733.	−1.62726
$167$	32056.3	0.0889451	0.0444725	−	0.999011i	$-0.485839\pi$
$167$	32056.3	0.0889451	0.0444725	+	0.999011i	$0.485839\pi$
$168$	2.54942e6	6.96896
$169$	975652.	2.62771
$170$	−1.19586e6	−3.17364
$171$	−265022.	−0.693093
$172$	1.37418e6	3.54179
$173$	200155.	0.508453	0.254227	−	0.967145i	$-0.418179\pi$
$173$	200155.	0.508453	0.254227	+	0.967145i	$0.418179\pi$
$174$	−1.71608e6	−4.29699
$175$	398707.	0.984144
$176$	3.11175e6	7.57222
$177$	−341275.	−0.818787
$178$	−591038.	−1.39819
$179$	−654052.	−1.52574	−0.762868	−	0.646554i	$-0.776210\pi$
$179$	−654052.	−1.52574	−0.762868	+	0.646554i	$0.776210\pi$
$180$	2.75390e6	6.33531
$181$	−449550.	−1.01996	−0.509978	−	0.860188i	$-0.670346\pi$
$181$	−449550.	−1.01996	−0.509978	+	0.860188i	$0.670346\pi$
$182$	−1.99159e6	−4.45678
$183$	−258743.	−0.571138
$184$	2.25067e6	4.90080
$185$	686524.	1.47478
$186$	−23391.2	−0.0495760
$187$	1.04616e6	2.18773
$188$	194662.	0.401686
$189$	−633004.	−1.28900
$190$	548447.	1.10218
$191$	695859.	1.38019	0.690094	−	0.723720i	$-0.257569\pi$
$191$	695859.	1.38019	0.690094	+	0.723720i	$0.257569\pi$
$192$	−3.97378e6	−7.77948
$193$	767460.	1.48307	0.741536	−	0.670913i	$-0.234098\pi$
$193$	767460.	1.48307	0.741536	+	0.670913i	$0.234098\pi$
$194$	−128029.	−0.244233
$195$	−2.22712e6	−4.19428
$196$	655237.	1.21831
$197$	−435982.	−0.800392	−0.400196	−	0.916430i	$-0.631058\pi$
$197$	−435982.	−0.800392	−0.400196	+	0.916430i	$0.631058\pi$
$198$	−3.26170e6	−5.91263
$199$	−161876.	−0.289767	−0.144883	−	0.989449i	$-0.546281\pi$
$199$	−161876.	−0.289767	−0.144883	+	0.989449i	$0.546281\pi$
$200$	−1.66202e6	−2.93806
$201$	−1.09628e6	−1.91396
$202$	−91498.7	−0.157774
$203$	−945994.	−1.61120
$204$	−3.29274e6	−5.53964
$205$	203781.	0.338671
$206$	1.86725e6	3.06574
$207$	−1.40479e6	−2.27869
$208$	4.94360e6	7.92292
$209$	−479791.	−0.759777
$210$	3.29302e6	5.15283
$211$	1.12669e6	1.74220	0.871101	−	0.491104i	$-0.163406\pi$
$211$	1.12669e6	1.74220	0.871101	+	0.491104i	$0.163406\pi$
$212$	−692355.	−1.05801
$213$	302081.	0.456220
$214$	−733855.	−1.09541
$215$	1.14688e6	1.69208
$216$	2.63869e6	3.84817
$217$	−12894.5	−0.0185890
$218$	−1.42745e6	−2.03432
$219$	1.04541e6	1.47291
$220$	4.98562e6	6.94485
$221$	1.66202e6	2.28905
$222$	2.55924e6	3.48520
$223$	−249475.	−0.335942	−0.167971	−	0.985792i	$-0.553721\pi$
$223$	−249475.	−0.335942	−0.167971	+	0.985792i	$0.553721\pi$
$224$	−4.10112e6	−5.46113
$225$	1.03738e6	1.36609
$226$	−405404.	−0.527979
$227$	−944371.	−1.21640	−0.608202	−	0.793782i	$-0.708109\pi$
$227$	−944371.	−1.21640	−0.608202	+	0.793782i	$0.708109\pi$
$228$	1.51012e6	1.92387
$229$	1.27171e6	1.60251	0.801255	−	0.598323i	$-0.204166\pi$
$229$	1.27171e6	1.60251	0.801255	+	0.598323i	$0.204166\pi$
$230$	2.90713e6	3.62364
$231$	−2.88079e6	−3.55207
$232$	3.94340e6	4.81006
$233$	−544346.	−0.656879	−0.328440	−	0.944525i	$-0.606523\pi$
$233$	−544346.	−0.656879	−0.328440	+	0.944525i	$0.606523\pi$
$234$	−5.18182e6	−6.18646
$235$	162463.	0.191904
$236$	1.21372e6	1.41853
$237$	2.23062e6	2.57961
$238$	−2.45746e6	−2.81218
$239$	−944980.	−1.07011	−0.535054	−	0.844818i	$-0.679709\pi$
$239$	−944980.	−1.07011	−0.535054	+	0.844818i	$0.679709\pi$
$240$	−8.17406e6	−9.16030
$241$	−1.13442e6	−1.25815	−0.629074	−	0.777345i	$-0.716566\pi$
$241$	−1.13442e6	−1.25815	−0.629074	+	0.777345i	$0.716566\pi$
$242$	−4.12293e6	−4.52551
$243$	846256.	0.919361
$244$	920201.	0.989482
$245$	546853.	0.582044
$246$	759658.	0.800351
$247$	−762238.	−0.794966
$248$	53751.0	0.0554955
$249$	−1.32763e6	−1.35700
$250$	462783.	0.468304
$251$	184083.	0.184429	0.0922144	−	0.995739i	$-0.470605\pi$
$251$	184083.	0.184429	0.0922144	+	0.995739i	$0.470605\pi$
$252$	5.65920e6	5.61376
$253$	−2.54321e6	−2.49793
$254$	−1.90978e6	−1.85737
$255$	−2.74808e6	−2.64654
$256$	4.76956e6	4.54861
$257$	−1.02968e6	−0.972458	−0.486229	−	0.873831i	$-0.661628\pi$
$257$	−1.02968e6	−0.972458	−0.486229	+	0.873831i	$0.661628\pi$
$258$	4.27534e6	3.99873
$259$	1.41079e6	1.30681
$260$	7.92060e6	7.26649
$261$	−2.46133e6	−2.23650
$262$	1.15808e6	1.04228
$263$	592032.	0.527784	0.263892	−	0.964552i	$-0.414994\pi$
$263$	592032.	0.527784	0.263892	+	0.964552i	$0.414994\pi$
$264$	1.20086e7	10.6043
$265$	−577832.	−0.505460
$266$	1.12704e6	0.976645
$267$	−1.35821e6	−1.16597
$268$	3.89885e6	3.31588
$269$	673258.	0.567285	0.283642	−	0.958930i	$-0.408457\pi$
$269$	673258.	0.567285	0.283642	+	0.958930i	$0.408457\pi$
$270$	3.40833e6	2.84533
$271$	197982.	0.163758	0.0818788	−	0.996642i	$-0.473908\pi$
$271$	197982.	0.163758	0.0818788	+	0.996642i	$0.473908\pi$
$272$	6.09999e6	4.99928
$273$	−4.57667e6	−3.71658
$274$	2342.43	0.00188491
$275$	1.87805e6	1.49753
$276$	8.00465e6	6.32513
$277$	1.33385e6	1.04449	0.522247	−	0.852794i	$-0.325094\pi$
$277$	1.33385e6	1.04449	0.522247	+	0.852794i	$0.325094\pi$
$278$	2.38257e6	1.84898
$279$	−33549.6	−0.0258034
$280$	−7.56707e6	−5.76810
$281$	−987920.	−0.746373	−0.373187	−	0.927756i	$-0.621735\pi$
$281$	−987920.	−0.746373	−0.373187	+	0.927756i	$0.621735\pi$
$282$	605632.	0.453509
$283$	1.56125e6	1.15879	0.579395	−	0.815047i	$-0.303289\pi$
$283$	1.56125e6	1.15879	0.579395	+	0.815047i	$0.303289\pi$
$284$	−1.07433e6	−0.790390
$285$	1.26033e6	0.919121
$286$	−9.38107e6	−6.78168
$287$	418764.	0.300099
$288$	−1.06705e7	−7.58060
$289$	630933.	0.444364
$290$	5.09359e6	3.55655
$291$	−294211.	−0.203670
$292$	−3.71792e6	−2.55178
$293$	2.22674e6	1.51531	0.757653	−	0.652658i	$-0.226346\pi$
$293$	2.22674e6	1.51531	0.757653	+	0.652658i	$0.226346\pi$
$294$	2.03857e6	1.37549
$295$	1.01296e6	0.677697
$296$	−5.88090e6	−3.90135
$297$	−2.98166e6	−1.96141
$298$	−2.42212e6	−1.57999
$299$	−4.04037e6	−2.61362
$300$	−5.91108e6	−3.79196
$301$	2.35680e6	1.49936
$302$	5.98217e6	3.77435
$303$	−210264.	−0.131570
$304$	−2.79759e6	−1.73620
$305$	767989.	0.472722
$306$	−6.39393e6	−3.90359
$307$	1.57737e6	0.955186	0.477593	−	0.878581i	$-0.341509\pi$
$307$	1.57737e6	0.955186	0.477593	+	0.878581i	$0.341509\pi$
$308$	1.02453e7	6.15387
$309$	4.29094e6	2.55656
$310$	69428.8	0.0410332
$311$	−3.06767e6	−1.79849	−0.899243	−	0.437449i	$-0.855882\pi$
$311$	−3.06767e6	−1.79849	−0.899243	+	0.437449i	$0.855882\pi$
$312$	1.90780e7	11.0955
$313$	2.14600e6	1.23814	0.619069	−	0.785336i	$-0.287510\pi$
$313$	2.14600e6	1.23814	0.619069	+	0.785336i	$0.287510\pi$
$314$	−3.46403e6	−1.98270
$315$	4.72310e6	2.68195
$316$	−7.93303e6	−4.46911
$317$	−639373.	−0.357360	−0.178680	−	0.983907i	$-0.557183\pi$
$317$	−639373.	−0.357360	−0.178680	+	0.983907i	$0.557183\pi$
$318$	−2.15405e6	−1.19451
$319$	−4.45596e6	−2.45168
$320$	1.17948e7	6.43895
$321$	−1.68640e6	−0.913477
$322$	5.97408e6	3.21093
$323$	−940538.	−0.501614
$324$	517654.	0.273954
$325$	2.98363e6	1.56688
$326$	−2.74140e6	−1.42866
$327$	−3.28027e6	−1.69645
$328$	−1.74563e6	−0.895915
$329$	333857.	0.170047
$330$	1.55112e7	7.84082
$331$	−2.42599e6	−1.21708	−0.608539	−	0.793524i	$-0.708244\pi$
$331$	−2.42599e6	−1.21708	−0.608539	+	0.793524i	$0.708244\pi$
$332$	4.72162e6	2.35096
$333$	3.67066e6	1.81398
$334$	−354694.	−0.173976
$335$	3.25394e6	1.58415
$336$	−1.67975e7	−8.11700
$337$	−1.36274e6	−0.653640	−0.326820	−	0.945087i	$-0.605977\pi$
$337$	−1.36274e6	−0.653640	−0.326820	+	0.945087i	$0.605977\pi$
$338$	−1.07953e7	−5.13978
$339$	−931618.	−0.440290
$340$	9.77335e6	4.58507
$341$	−60737.5	−0.0282860
$342$	2.93240e6	1.35568
$343$	−1.48283e6	−0.680543
$344$	−9.82436e6	−4.47619
$345$	6.68059e6	3.02181
$346$	−2.21466e6	−0.994529
$347$	−3.73097e6	−1.66340	−0.831702	−	0.555223i	$-0.812633\pi$
$347$	−3.73097e6	−1.66340	−0.831702	+	0.555223i	$0.812633\pi$
$348$	1.40249e7	6.20802
$349$	2.45026e6	1.07683	0.538416	−	0.842679i	$-0.319023\pi$
$349$	2.45026e6	1.07683	0.538416	+	0.842679i	$0.319023\pi$
$350$	−4.41159e6	−1.92497
$351$	−4.73693e6	−2.05225
$352$	−1.93177e7	−8.30995
$353$	2.98364e6	1.27441	0.637206	−	0.770693i	$-0.280090\pi$
$353$	2.98364e6	1.27441	0.637206	+	0.770693i	$0.280090\pi$
$354$	3.77612e6	1.60154
$355$	−896623.	−0.377606
$356$	4.83036e6	2.02002
$357$	−5.64723e6	−2.34512
$358$	7.23691e6	2.98432
$359$	328419.	0.134491	0.0672453	−	0.997736i	$-0.478579\pi$
$359$	328419.	0.134491	0.0672453	+	0.997736i	$0.478579\pi$
$360$	−1.96884e7	−8.00669
$361$	−2.04475e6	−0.825794
$362$	4.97415e6	1.99502
$363$	−9.47449e6	−3.77389
$364$	1.62766e7	6.43888
$365$	−3.10293e6	−1.21910
$366$	2.86292e6	1.11714
$367$	−1.33487e6	−0.517337	−0.258669	−	0.965966i	$-0.583284\pi$
$367$	−1.33487e6	−0.517337	−0.258669	+	0.965966i	$0.583284\pi$
$368$	−1.48291e7	−5.70815
$369$	1.08956e6	0.416568
$370$	−7.59621e6	−2.88465
$371$	−1.18743e6	−0.447891
$372$	191169.	0.0716243
$373$	4.10183e6	1.52653	0.763266	−	0.646084i	$-0.223595\pi$
$373$	4.10183e6	1.52653	0.763266	+	0.646084i	$0.223595\pi$
$374$	−1.15755e7	−4.27917
$375$	1.06348e6	0.390526
$376$	−1.39169e6	−0.507659
$377$	−7.07912e6	−2.56523
$378$	7.00402e6	2.52126
$379$	4.09936e6	1.46595	0.732974	−	0.680257i	$-0.238132\pi$
$379$	4.09936e6	1.46595	0.732974	+	0.680257i	$0.238132\pi$
$380$	−4.48228e6	−1.59235
$381$	−4.38866e6	−1.54889
$382$	−7.69950e6	−2.69963
$383$	−1.07809e6	−0.375540	−0.187770	−	0.982213i	$-0.560126\pi$
$383$	−1.07809e6	−0.375540	−0.187770	+	0.982213i	$0.560126\pi$
$384$	2.24529e7	7.77042
$385$	8.55063e6	2.93999
$386$	−8.49174e6	−2.90087
$387$	6.13203e6	2.08126
$388$	1.04634e6	0.352853
$389$	−3.56473e6	−1.19441	−0.597204	−	0.802089i	$-0.703722\pi$
$389$	−3.56473e6	−1.19441	−0.597204	+	0.802089i	$0.703722\pi$
$390$	2.46425e7	8.20396
$391$	−4.98547e6	−1.64917
$392$	−4.68446e6	−1.53973
$393$	2.66127e6	0.869175
$394$	4.82402e6	1.56556
$395$	−6.62081e6	−2.13510
$396$	2.66568e7	8.54220
$397$	995607.	0.317038	0.158519	−	0.987356i	$-0.449328\pi$
$397$	995607.	0.317038	0.158519	+	0.987356i	$0.449328\pi$
$398$	1.79111e6	0.566780
$399$	2.58995e6	0.814439
$400$	1.09506e7	3.42207
$401$	−1.08351e6	−0.336491	−0.168245	−	0.985745i	$-0.553810\pi$
$401$	−1.08351e6	−0.336491	−0.168245	+	0.985745i	$0.553810\pi$
$402$	1.21301e7	3.74368
$403$	−96493.0	−0.0295960
$404$	747789.	0.227943
$405$	432028.	0.130880
$406$	1.04672e7	3.15148
$407$	6.64529e6	1.98851
$408$	2.35406e7	7.00112
$409$	−3.02898e6	−0.895340	−0.447670	−	0.894199i	$-0.647746\pi$
$409$	−3.02898e6	−0.895340	−0.447670	+	0.894199i	$0.647746\pi$
$410$	−2.25478e6	−0.662437
$411$	5382.91	0.00157186
$412$	−1.52604e7	−4.42918
$413$	2.08160e6	0.600512
$414$	1.55437e7	4.45710
$415$	3.94061e6	1.12316
$416$	−3.06898e7	−8.69482
$417$	5.47514e6	1.54190
$418$	5.30876e6	1.48612
$419$	3.54514e6	0.986503	0.493252	−	0.869887i	$-0.335808\pi$
$419$	3.54514e6	0.986503	0.493252	+	0.869887i	$0.335808\pi$
$420$	−2.69128e7	−7.44449
$421$	−332195.	−0.0913457	−0.0456728	−	0.998956i	$-0.514543\pi$
$421$	−332195.	−0.0913457	−0.0456728	+	0.998956i	$0.514543\pi$
$422$	−1.24665e7	−3.40773
$423$	868644.	0.236043
$424$	4.94982e6	1.33713
$425$	3.68155e6	0.988686
$426$	−3.34245e6	−0.892361
$427$	1.57820e6	0.418882
$428$	5.99756e6	1.58258
$429$	−2.15577e7	−5.65535
$430$	−1.26899e7	−3.30968
$431$	−2.53175e6	−0.656489	−0.328245	−	0.944593i	$-0.606457\pi$
$431$	−2.53175e6	−0.656489	−0.328245	+	0.944593i	$0.606457\pi$
$432$	−1.73857e7	−4.48210
$433$	6.52861e6	1.67341	0.836703	−	0.547657i	$-0.184480\pi$
$433$	6.52861e6	1.67341	0.836703	+	0.547657i	$0.184480\pi$
$434$	142674.	0.0363598
$435$	1.17051e7	2.96586
$436$	1.16660e7	2.93905
$437$	2.28645e6	0.572741
$438$	−1.15672e7	−2.88099
$439$	−209629.	−0.0519147	−0.0259573	−	0.999663i	$-0.508263\pi$
$439$	−209629.	−0.0519147	−0.0259573	+	0.999663i	$0.508263\pi$
$440$	−3.56435e7	−8.77704
$441$	2.92388e6	0.715917
$442$	−1.83898e7	−4.47735
$443$	6.35203e6	1.53781	0.768906	−	0.639362i	$-0.220801\pi$
$443$	6.35203e6	1.53781	0.768906	+	0.639362i	$0.220801\pi$
$444$	−2.09158e7	−5.03520
$445$	4.03137e6	0.965055
$446$	2.76037e6	0.657099
$447$	−5.56604e6	−1.31758
$448$	2.42380e7	5.70560
$449$	3.20539e6	0.750352	0.375176	−	0.926954i	$-0.377582\pi$
$449$	3.20539e6	0.750352	0.375176	+	0.926954i	$0.377582\pi$
$450$	−1.14783e7	−2.67206
$451$	1.97252e6	0.456647
$452$	3.31323e6	0.762792
$453$	1.37470e7	3.14748
$454$	1.04492e7	2.37927
$455$	1.35843e7	3.07615
$456$	−1.07962e7	−2.43142
$457$	4.05919e6	0.909177	0.454589	−	0.890702i	$-0.349786\pi$
$457$	4.05919e6	0.909177	0.454589	+	0.890702i	$0.349786\pi$
$458$	−1.40712e7	−3.13449
$459$	−5.84498e6	−1.29495
$460$	−2.37590e7	−5.23521
$461$	2.01866e6	0.442396	0.221198	−	0.975229i	$-0.429003\pi$
$461$	2.01866e6	0.442396	0.221198	+	0.975229i	$0.429003\pi$
$462$	3.18752e7	6.94781
$463$	−4.53189e6	−0.982487	−0.491243	−	0.871022i	$-0.663457\pi$
$463$	−4.53189e6	−0.982487	−0.491243	+	0.871022i	$0.663457\pi$
$464$	−2.59821e7	−5.60246
$465$	159547.	0.0342182
$466$	6.02305e6	1.28485
$467$	1.09563e6	0.232473	0.116236	−	0.993222i	$-0.462917\pi$
$467$	1.09563e6	0.232473	0.116236	+	0.993222i	$0.462917\pi$
$468$	4.23493e7	8.93782
$469$	6.68675e6	1.40373
$470$	−1.79761e6	−0.375362
$471$	−7.96035e6	−1.65341
$472$	−8.67718e6	−1.79277
$473$	1.11013e7	2.28151
$474$	−2.46812e7	−5.04569
$475$	−1.68844e6	−0.343362
$476$	2.00840e7	4.06286
$477$	−3.08951e6	−0.621718
$478$	1.04560e7	2.09312
$479$	1.73610e6	0.345729	0.172864	−	0.984946i	$-0.444698\pi$
$479$	1.73610e6	0.345729	0.172864	+	0.984946i	$0.444698\pi$
$480$	5.07444e7	10.0527
$481$	1.05573e7	2.08061
$482$	1.25521e7	2.46092
$483$	1.37284e7	2.67765
$484$	3.36954e7	6.53818
$485$	873265.	0.168574
$486$	−9.36360e6	−1.79826
$487$	1.18222e6	0.225880	0.112940	−	0.993602i	$-0.463973\pi$
$487$	1.18222e6	0.225880	0.112940	+	0.993602i	$0.463973\pi$
$488$	−6.57875e6	−1.25053
$489$	−6.29973e6	−1.19138
$490$	−6.05079e6	−1.13847
$491$	−1.43596e6	−0.268805	−0.134403	−	0.990927i	$-0.542912\pi$
$491$	−1.43596e6	−0.268805	−0.134403	+	0.990927i	$0.542912\pi$
$492$	−6.20843e6	−1.15630
$493$	−8.73505e6	−1.61863
$494$	8.43397e6	1.55494
$495$	2.22474e7	4.08100
$496$	−354152.	−0.0646376
$497$	−1.84254e6	−0.334599
$498$	1.46899e7	2.65427
$499$	1.91752e6	0.344738	0.172369	−	0.985032i	$-0.444858\pi$
$499$	1.91752e6	0.344738	0.172369	+	0.985032i	$0.444858\pi$
$500$	−3.78218e6	−0.676576
$501$	−815088.	−0.145081
$502$	−2.03683e6	−0.360741
$503$	−2.54851e6	−0.449124	−0.224562	−	0.974460i	$-0.572095\pi$
$503$	−2.54851e6	−0.449124	−0.224562	+	0.974460i	$0.572095\pi$
$504$	−4.04590e7	−7.09479
$505$	624096.	0.108899
$506$	2.81400e7	4.88593
$507$	−2.48077e7	−4.28614
$508$	1.56080e7	2.68341
$509$	9.24661e6	1.58193	0.790967	−	0.611859i	$-0.209578\pi$
$509$	9.24661e6	1.58193	0.790967	+	0.611859i	$0.209578\pi$
$510$	3.04068e7	5.17661
$511$	−6.37644e6	−1.08025
$512$	−2.45166e7	−4.13320
$513$	2.68064e6	0.449723
$514$	1.13932e7	1.90212
$515$	−1.27362e7	−2.11603
$516$	−3.49410e7	−5.77711
$517$	1.57258e6	0.258753
$518$	−1.56100e7	−2.55610
$519$	−5.08930e6	−0.829353
$520$	−5.66263e7	−9.18354
$521$	−7.15171e6	−1.15429	−0.577146	−	0.816641i	$-0.695834\pi$
$521$	−7.15171e6	−1.15429	−0.577146	+	0.816641i	$0.695834\pi$
$522$	2.72340e7	4.37457
$523$	−6.11568e6	−0.977666	−0.488833	−	0.872377i	$-0.662577\pi$
$523$	−6.11568e6	−0.977666	−0.488833	+	0.872377i	$0.662577\pi$
$524$	−9.46460e6	−1.50582
$525$	−1.01378e7	−1.60527
$526$	−6.55068e6	−1.03234
$527$	−119064.	−0.0186748
$528$	−7.91218e7	−12.3513
$529$	5.68336e6	0.883010
$530$	6.39356e6	0.988673
$531$	5.41600e6	0.833571
$532$	−9.21096e6	−1.41100
$533$	3.13372e6	0.477796
$534$	1.50282e7	2.28062
$535$	5.00549e6	0.756071
$536$	−2.78739e7	−4.19069
$537$	1.66304e7	2.48867
$538$	−7.44943e6	−1.10960
$539$	5.29334e6	0.784798
$540$	−2.78551e7	−4.11075
$541$	−4.13146e6	−0.606891	−0.303446	−	0.952849i	$-0.598137\pi$
$541$	−4.13146e6	−0.606891	−0.303446	+	0.952849i	$0.598137\pi$
$542$	−2.19062e6	−0.320308
$543$	1.14306e7	1.66368
$544$	−3.78686e7	−5.48633
$545$	9.73635e6	1.40412
$546$	5.06397e7	7.26958
$547$	2.49721e6	0.356850	0.178425	−	0.983953i	$-0.442900\pi$
$547$	2.49721e6	0.356850	0.178425	+	0.983953i	$0.442900\pi$
$548$	−19143.9	−0.00272320
$549$	4.10623e6	0.581450
$550$	−2.07801e7	−2.92914
$551$	4.00609e6	0.562136
$552$	−5.72273e7	−7.99384
$553$	−1.36056e7	−1.89193
$554$	−1.47587e7	−2.04302
$555$	−1.74561e7	−2.40555
$556$	−1.94719e7	−2.67130
$557$	−1.15932e7	−1.58331	−0.791653	−	0.610971i	$-0.790779\pi$
$557$	−1.15932e7	−1.58331	−0.791653	+	0.610971i	$0.790779\pi$
$558$	371217.	0.0504711
$559$	1.76365e7	2.38717
$560$	4.98575e7	6.71831
$561$	−2.66004e7	−3.56846
$562$	1.09311e7	1.45990
$563$	−1.47514e6	−0.196138	−0.0980692	−	0.995180i	$-0.531267\pi$
$563$	−1.47514e6	−0.196138	−0.0980692	+	0.995180i	$0.531267\pi$
$564$	−4.94963e6	−0.655201
$565$	2.76519e6	0.364421
$566$	−1.72748e7	−2.26658
$567$	887806.	0.115974
$568$	7.68065e6	0.998912
$569$	2.31512e6	0.299774	0.149887	−	0.988703i	$-0.452109\pi$
$569$	2.31512e6	0.299774	0.149887	+	0.988703i	$0.452109\pi$
$570$	−1.39452e7	−1.79779
$571$	4.83634e6	0.620764	0.310382	−	0.950612i	$-0.399543\pi$
$571$	4.83634e6	0.620764	0.310382	+	0.950612i	$0.399543\pi$
$572$	7.66684e7	9.79775
$573$	−1.76935e7	−2.25126
$574$	−4.63352e6	−0.586990
$575$	−8.94985e6	−1.12888
$576$	6.30635e7	7.91994
$577$	1.43904e7	1.79942	0.899712	−	0.436484i	$-0.143777\pi$
$577$	1.43904e7	1.79942	0.899712	+	0.436484i	$0.143777\pi$
$578$	−6.98111e6	−0.869170
$579$	−1.95140e7	−2.41908
$580$	−4.16282e7	−5.13828
$581$	8.09785e6	0.995243
$582$	3.25537e6	0.398376
$583$	−5.59319e6	−0.681535
$584$	2.65803e7	3.22499
$585$	3.53442e7	4.27001
$586$	−2.46383e7	−2.96392
$587$	−2.04026e6	−0.244394	−0.122197	−	0.992506i	$-0.538994\pi$
$587$	−2.04026e6	−0.244394	−0.122197	+	0.992506i	$0.538994\pi$
$588$	−1.66606e7	−1.98722
$589$	54605.5	0.00648558
$590$	−1.12081e7	−1.32557
$591$	1.10856e7	1.30554
$592$	3.87478e7	4.54404
$593$	−1.54777e7	−1.80747	−0.903734	−	0.428094i	$-0.859185\pi$
$593$	−1.54777e7	−1.80747	−0.903734	+	0.428094i	$0.859185\pi$
$594$	3.29913e7	3.83649
$595$	1.67619e7	1.94102
$596$	1.97952e7	2.28268
$597$	4.11597e6	0.472647
$598$	4.47056e7	5.11221
$599$	−4.14734e6	−0.472284	−0.236142	−	0.971719i	$-0.575883\pi$
$599$	−4.14734e6	−0.472284	−0.236142	+	0.971719i	$0.575883\pi$
$600$	4.22598e7	4.79235
$601$	−5.56253e6	−0.628183	−0.314091	−	0.949393i	$-0.601700\pi$
$601$	−5.56253e6	−0.628183	−0.314091	+	0.949393i	$0.601700\pi$
$602$	−2.60774e7	−2.93273
$603$	1.73979e7	1.94852
$604$	−4.88903e7	−5.45294
$605$	2.81218e7	3.12359
$606$	2.32652e6	0.257350
$607$	−3.30134e6	−0.363679	−0.181840	−	0.983328i	$-0.558205\pi$
$607$	−3.30134e6	−0.363679	−0.181840	+	0.983328i	$0.558205\pi$
$608$	1.73674e7	1.90535
$609$	2.40536e7	2.62807
$610$	−8.49760e6	−0.924638
$611$	2.49834e6	0.270737
$612$	5.22555e7	5.63966
$613$	−575423.	−0.0618494	−0.0309247	−	0.999522i	$-0.509845\pi$
$613$	−575423.	−0.0618494	−0.0309247	+	0.999522i	$0.509845\pi$
$614$	−1.74532e7	−1.86833
$615$	−5.18149e6	−0.552417
$616$	−7.32464e7	−7.77740
$617$	−1.10421e6	−0.116772	−0.0583861	−	0.998294i	$-0.518595\pi$
$617$	−1.10421e6	−0.116772	−0.0583861	+	0.998294i	$0.518595\pi$
$618$	−4.74782e7	−5.00061
$619$	6.21571e6	0.652025	0.326013	−	0.945365i	$-0.394295\pi$
$619$	6.21571e6	0.652025	0.326013	+	0.945365i	$0.394295\pi$
$620$	−567419.	−0.0592823
$621$	1.42092e7	1.47856
$622$	3.39429e7	3.51782
$623$	8.28435e6	0.855142
$624$	−1.25700e8	−12.9233
$625$	−1.11903e7	−1.14589
$626$	−2.37450e7	−2.42178
$627$	1.21995e7	1.23929
$628$	2.83104e7	2.86449
$629$	1.30268e7	1.31284
$630$	−5.22599e7	−5.24587
$631$	−1.20875e7	−1.20855	−0.604274	−	0.796777i	$-0.706537\pi$
$631$	−1.20875e7	−1.20855	−0.604274	+	0.796777i	$0.706537\pi$
$632$	5.67152e7	5.64816
$633$	−2.86481e7	−2.84175
$634$	7.07450e6	0.698993
$635$	1.30262e7	1.28199
$636$	1.76044e7	1.72575
$637$	8.40946e6	0.821144
$638$	4.93040e7	4.79546
$639$	−4.79400e6	−0.464457
$640$	−6.66437e7	−6.43145
$641$	−1.36080e7	−1.30812	−0.654061	−	0.756442i	$-0.726936\pi$
$641$	−1.36080e7	−1.30812	−0.654061	+	0.756442i	$0.726936\pi$
$642$	1.86596e7	1.78675
$643$	−1.06912e6	−0.101976	−0.0509882	−	0.998699i	$-0.516237\pi$
$643$	−1.06912e6	−0.101976	−0.0509882	+	0.998699i	$0.516237\pi$
$644$	−4.88242e7	−4.63896
$645$	−2.91613e7	−2.75999
$646$	1.04068e7	0.981152
$647$	−1.08015e6	−0.101443	−0.0507215	−	0.998713i	$-0.516152\pi$
$647$	−1.08015e6	−0.101443	−0.0507215	+	0.998713i	$0.516152\pi$
$648$	−3.70084e6	−0.346228
$649$	9.80503e6	0.913771
$650$	−3.30131e7	−3.06480
$651$	327866.	0.0303210
$652$	2.24045e7	2.06403
$653$	−1.32910e7	−1.21976	−0.609882	−	0.792492i	$-0.708783\pi$
$653$	−1.32910e7	−1.21976	−0.609882	+	0.792492i	$0.708783\pi$
$654$	3.62953e7	3.31823
$655$	−7.89905e6	−0.719402
$656$	1.15015e7	1.04351
$657$	−1.65905e7	−1.49950
$658$	−3.69404e6	−0.332611
$659$	−4.81790e6	−0.432159	−0.216080	−	0.976376i	$-0.569327\pi$
$659$	−4.81790e6	−0.432159	−0.216080	+	0.976376i	$0.569327\pi$
$660$	−1.26768e8	−11.3279
$661$	1.03864e7	0.924615	0.462308	−	0.886720i	$-0.347022\pi$
$661$	1.03864e7	0.924615	0.462308	+	0.886720i	$0.347022\pi$
$662$	2.68429e7	2.38059
$663$	−4.22597e7	−3.73373
$664$	−3.37560e7	−2.97120
$665$	−7.68736e6	−0.674098
$666$	−4.06149e7	−3.54813
$667$	2.12349e7	1.84814
$668$	2.89880e6	0.251349
$669$	6.34334e6	0.547964
$670$	−3.60039e7	−3.09858
$671$	7.43385e6	0.637393
$672$	1.04278e8	8.90781
$673$	−2.21233e7	−1.88284	−0.941418	−	0.337242i	$-0.890506\pi$
$673$	−2.21233e7	−1.88284	−0.941418	+	0.337242i	$0.890506\pi$
$674$	1.50784e7	1.27851
$675$	−1.04928e7	−0.886407
$676$	8.82267e7	7.42563
$677$	1.50664e6	0.126339	0.0631697	−	0.998003i	$-0.479879\pi$
$677$	1.50664e6	0.126339	0.0631697	+	0.998003i	$0.479879\pi$
$678$	1.03081e7	0.861202
$679$	1.79454e6	0.149375
$680$	−6.98722e7	−5.79471
$681$	2.40123e7	1.98411
$682$	672045.	0.0553271
$683$	−5.74161e6	−0.470958	−0.235479	−	0.971879i	$-0.575666\pi$
$683$	−5.74161e6	−0.470958	−0.235479	+	0.971879i	$0.575666\pi$
$684$	−2.39655e7	−1.95860
$685$	−15977.3	−0.00130100
$686$	1.64071e7	1.33113
$687$	−3.23356e7	−2.61390
$688$	6.47303e7	5.21358
$689$	−8.88584e6	−0.713100
$690$	−7.39190e7	−5.91063
$691$	1.54380e7	1.22997	0.614986	−	0.788538i	$-0.289162\pi$
$691$	1.54380e7	1.22997	0.614986	+	0.788538i	$0.289162\pi$
$692$	1.80997e7	1.43683
$693$	4.57179e7	3.61620
$694$	4.12822e7	3.25360
$695$	−1.62511e7	−1.27620
$696$	−1.00268e8	−7.84583
$697$	3.86675e6	0.301484
$698$	−2.71115e7	−2.10627
$699$	1.38410e7	1.07145
$700$	3.60545e7	2.78108
$701$	−1.38936e7	−1.06787	−0.533935	−	0.845525i	$-0.679287\pi$
$701$	−1.38936e7	−1.06787	−0.533935	+	0.845525i	$0.679287\pi$
$702$	5.24129e7	4.01417
$703$	−5.97439e6	−0.455937
$704$	1.14169e8	8.68194
$705$	−4.13090e6	−0.313020
$706$	−3.30132e7	−2.49274
$707$	1.28250e6	0.0964960
$708$	−3.08610e7	−2.31380
$709$	−2.27952e7	−1.70305	−0.851527	−	0.524311i	$-0.824323\pi$
$709$	−2.27952e7	−1.70305	−0.851527	+	0.524311i	$0.824323\pi$
$710$	9.92090e6	0.738593
$711$	−3.53997e7	−2.62619
$712$	−3.45335e7	−2.55294
$713$	289446.	0.0213227
$714$	6.24852e7	4.58703
$715$	6.39866e7	4.68084
$716$	−5.91449e7	−4.31156
$717$	2.40278e7	1.74548
$718$	−3.63387e6	−0.263062
$719$	7.68599e6	0.554470	0.277235	−	0.960802i	$-0.410582\pi$
$719$	7.68599e6	0.554470	0.277235	+	0.960802i	$0.410582\pi$
$720$	1.29722e8	9.32569
$721$	−2.61725e7	−1.87503
$722$	2.26246e7	1.61524
$723$	2.88447e7	2.05220
$724$	−4.06521e7	−2.88228
$725$	−1.56810e7	−1.10797
$726$	1.04833e8	7.38169
$727$	−927911.	−0.0651134	−0.0325567	−	0.999470i	$-0.510365\pi$
$727$	−927911.	−0.0651134	−0.0325567	+	0.999470i	$0.510365\pi$
$728$	−1.16366e8	−8.13760
$729$	−2.29086e7	−1.59654
$730$	3.43331e7	2.38455
$731$	2.17620e7	1.50628
$732$	−2.33977e7	−1.61397
$733$	−2.24820e7	−1.54552	−0.772761	−	0.634697i	$-0.781125\pi$
$733$	−2.24820e7	−1.54552	−0.772761	+	0.634697i	$0.781125\pi$
$734$	1.47700e7	1.01191
$735$	−1.39047e7	−0.949388
$736$	9.20587e7	6.26427
$737$	3.14969e7	2.13599
$738$	−1.20557e7	−0.814801
$739$	5.65024e6	0.380589	0.190294	−	0.981727i	$-0.439056\pi$
$739$	5.65024e6	0.380589	0.190294	+	0.981727i	$0.439056\pi$
$740$	6.20813e7	4.16756
$741$	1.93813e7	1.29669
$742$	1.31386e7	0.876070
$743$	3.79179e6	0.251983	0.125992	−	0.992031i	$-0.459789\pi$
$743$	3.79179e6	0.251983	0.125992	+	0.992031i	$0.459789\pi$
$744$	−1.36672e6	−0.0905202
$745$	1.65209e7	1.09054
$746$	−4.53857e7	−2.98588
$747$	2.10694e7	1.38150
$748$	9.46024e7	6.18227
$749$	1.02862e7	0.669959
$750$	−1.17671e7	−0.763864
$751$	−8.27350e6	−0.535290	−0.267645	−	0.963518i	$-0.586246\pi$
$751$	−8.27350e6	−0.535290	−0.267645	+	0.963518i	$0.586246\pi$
$752$	9.16948e6	0.591290
$753$	−4.68063e6	−0.300827
$754$	7.83287e7	5.01756
$755$	−4.08033e7	−2.60512
$756$	−5.72416e7	−3.64256
$757$	−1.78122e7	−1.12974	−0.564868	−	0.825181i	$-0.691073\pi$
$757$	−1.78122e7	−1.12974	−0.564868	+	0.825181i	$0.691073\pi$
$758$	−4.53584e7	−2.86738
$759$	6.46656e7	4.07445
$760$	3.20449e7	2.01245
$761$	2.55877e7	1.60166	0.800830	−	0.598892i	$-0.204392\pi$
$761$	2.55877e7	1.60166	0.800830	+	0.598892i	$0.204392\pi$
$762$	4.85594e7	3.02961
$763$	2.00079e7	1.24420
$764$	6.29255e7	3.90026
$765$	4.36118e7	2.69433
$766$	1.19287e7	0.734552
$767$	1.55771e7	0.956091
$768$	−1.21275e8	−7.41936
$769$	−1.66349e7	−1.01439	−0.507194	−	0.861832i	$-0.669317\pi$
$769$	−1.66349e7	−1.01439	−0.507194	+	0.861832i	$0.669317\pi$
$770$	−9.46105e7	−5.75059
$771$	2.61815e7	1.58620
$772$	6.94002e7	4.19100
$773$	−2.40857e7	−1.44981	−0.724905	−	0.688849i	$-0.758116\pi$
$773$	−2.40857e7	−1.44981	−0.724905	+	0.688849i	$0.758116\pi$
$774$	−6.78494e7	−4.07093
$775$	−213743.	−0.0127831
$776$	−7.48056e6	−0.445943
$777$	−3.58718e7	−2.13157
$778$	3.94429e7	2.33625
$779$	−1.77338e6	−0.104703
$780$	−2.01395e8	−11.8526
$781$	−8.67897e6	−0.509144
$782$	5.51630e7	3.22575
$783$	2.48959e7	1.45118
$784$	3.08647e7	1.79338
$785$	2.36275e7	1.36850
$786$	−2.94462e7	−1.70010
$787$	2.07430e7	1.19381	0.596905	−	0.802312i	$-0.296397\pi$
$787$	2.07430e7	1.19381	0.596905	+	0.802312i	$0.296397\pi$
$788$	−3.94252e7	−2.26182
$789$	−1.50535e7	−0.860883
$790$	7.32576e7	4.17623
$791$	5.68238e6	0.322916
$792$	−1.90576e8	−10.7958
$793$	1.18101e7	0.666913
$794$	−1.10161e7	−0.620123
$795$	1.46924e7	0.824470
$796$	−1.46382e7	−0.818849
$797$	−2.95236e7	−1.64635	−0.823176	−	0.567786i	$-0.807800\pi$
$797$	−2.95236e7	−1.64635	−0.823176	+	0.567786i	$0.807800\pi$
$798$	−2.86571e7	−1.59303
$799$	3.08274e6	0.170832
$800$	−6.79812e7	−3.75547
$801$	2.15546e7	1.18702
$802$	1.19888e7	0.658172
$803$	−3.00352e7	−1.64377
$804$	−9.91351e7	−5.40863
$805$	−4.07481e7	−2.21625
$806$	1.06767e6	0.0578895
$807$	−1.71188e7	−0.925314
$808$	−5.34613e6	−0.288079
$809$	−4.63037e6	−0.248739	−0.124370	−	0.992236i	$-0.539691\pi$
$809$	−4.63037e6	−0.248739	−0.124370	+	0.992236i	$0.539691\pi$
$810$	−4.78028e6	−0.256001
$811$	−1.81998e7	−0.971662	−0.485831	−	0.874053i	$-0.661483\pi$
$811$	−1.81998e7	−0.971662	−0.485831	+	0.874053i	$0.661483\pi$
$812$	−8.55448e7	−4.55306
$813$	−5.03403e6	−0.267110
$814$	−7.35284e7	−3.88950
$815$	1.86986e7	0.986085
$816$	−1.55103e8	−8.15446
$817$	−9.98055e6	−0.523117
$818$	3.35148e7	1.75127
$819$	7.26314e7	3.78368
$820$	1.84276e7	0.957048
$821$	6.39282e6	0.331005	0.165503	−	0.986209i	$-0.447075\pi$
$821$	6.39282e6	0.331005	0.165503	+	0.986209i	$0.447075\pi$
$822$	−59560.5	−0.00307453
$823$	−127076.	−0.00653980	−0.00326990	−	0.999995i	$-0.501041\pi$
$823$	−127076.	−0.00653980	−0.00326990	+	0.999995i	$0.501041\pi$
$824$	1.09101e8	5.59770
$825$	−4.77527e7	−2.44266
$826$	−2.30323e7	−1.17459
$827$	4.24888e6	0.216028	0.108014	−	0.994149i	$-0.465551\pi$
$827$	4.24888e6	0.216028	0.108014	+	0.994149i	$0.465551\pi$
$828$	−1.27033e8	−6.43934
$829$	−3.46104e6	−0.174912	−0.0874561	−	0.996168i	$-0.527874\pi$
$829$	−3.46104e6	−0.174912	−0.0874561	+	0.996168i	$0.527874\pi$
$830$	−4.36018e7	−2.19690
$831$	−3.39154e7	−1.70371
$832$	1.81379e8	9.08404
$833$	1.03766e7	0.518133
$834$	−6.05810e7	−3.01593
$835$	2.41931e6	0.120081
$836$	−4.33868e7	−2.14705
$837$	339347.	0.0167429
$838$	−3.92261e7	−1.92959
$839$	1.68394e7	0.825890	0.412945	−	0.910756i	$-0.364500\pi$
$839$	1.68394e7	0.825890	0.412945	+	0.910756i	$0.364500\pi$
$840$	1.92406e8	9.40850
$841$	1.66945e7	0.813925
$842$	3.67565e6	0.178671
$843$	2.51196e7	1.21743
$844$	1.01885e8	4.92327
$845$	7.36330e7	3.54757
$846$	−9.61132e6	−0.461697
$847$	5.77895e7	2.76783
$848$	−3.26131e7	−1.55741
$849$	−3.96974e7	−1.89014
$850$	−4.07354e7	−1.93386
$851$	−3.16682e7	−1.49899
$852$	2.73167e7	1.28923
$853$	−1.24365e7	−0.585228	−0.292614	−	0.956231i	$-0.594525\pi$
$853$	−1.24365e7	−0.585228	−0.292614	+	0.956231i	$0.594525\pi$
$854$	−1.74623e7	−0.819328
$855$	−2.00014e7	−0.935716
$856$	−4.28780e7	−2.00009
$857$	2.69566e7	1.25376	0.626878	−	0.779117i	$-0.284332\pi$
$857$	2.69566e7	1.25376	0.626878	+	0.779117i	$0.284332\pi$
$858$	2.38530e8	11.0618
$859$	2.17326e6	0.100491	0.0502457	−	0.998737i	$-0.484000\pi$
$859$	2.17326e6	0.100491	0.0502457	+	0.998737i	$0.484000\pi$
$860$	1.03710e8	4.78162
$861$	−1.06478e7	−0.489500
$862$	2.80131e7	1.28408
$863$	−1.24536e7	−0.569203	−0.284602	−	0.958646i	$-0.591861\pi$
$863$	−1.24536e7	−0.569203	−0.284602	+	0.958646i	$0.591861\pi$
$864$	1.07930e8	4.91877
$865$	1.51058e7	0.686442
$866$	−7.22374e7	−3.27316
$867$	−1.60426e7	−0.724814
$868$	−1.16603e6	−0.0525304
$869$	−6.40870e7	−2.87886
$870$	−1.29513e8	−5.80119
$871$	5.00387e7	2.23491
$872$	−8.34035e7	−3.71444
$873$	4.66911e6	0.207347
$874$	−2.52990e7	−1.12027
$875$	−6.48665e6	−0.286418
$876$	9.45347e7	4.16228
$877$	2.25143e7	0.988462	0.494231	−	0.869331i	$-0.335450\pi$
$877$	2.25143e7	0.988462	0.494231	+	0.869331i	$0.335450\pi$
$878$	2.31949e6	0.101544
$879$	−5.66188e7	−2.47166
$880$	2.34846e8	10.2229
$881$	−6.76746e6	−0.293756	−0.146878	−	0.989155i	$-0.546922\pi$
$881$	−6.76746e6	−0.293756	−0.146878	+	0.989155i	$0.546922\pi$
$882$	−3.23519e7	−1.40033
$883$	1.92170e7	0.829438	0.414719	−	0.909949i	$-0.363880\pi$
$883$	1.92170e7	0.829438	0.414719	+	0.909949i	$0.363880\pi$
$884$	1.50294e8	6.46860
$885$	−2.57562e7	−1.10541
$886$	−7.02836e7	−3.00794
$887$	−2.53907e7	−1.08359	−0.541795	−	0.840511i	$-0.682255\pi$
$887$	−2.53907e7	−1.08359	−0.541795	+	0.840511i	$0.682255\pi$
$888$	1.49532e8	6.36359
$889$	2.67686e7	1.13598
$890$	−4.46060e7	−1.88764
$891$	4.18187e6	0.176472
$892$	−2.25596e7	−0.949335
$893$	−1.41381e6	−0.0593285
$894$	6.15868e7	2.57717
$895$	−4.93617e7	−2.05983
$896$	−1.36951e8	−5.69895
$897$	1.02733e8	4.26315
$898$	−3.54668e7	−1.46768
$899$	507137.	0.0209279
$900$	9.38083e7	3.86042
$901$	−1.09644e7	−0.449958
$902$	−2.18254e7	−0.893196
$903$	−5.99258e7	−2.44565
$904$	−2.36871e7	−0.964032
$905$	−3.39278e7	−1.37700
$906$	−1.52107e8	−6.15644
$907$	−4.87489e6	−0.196764	−0.0983822	−	0.995149i	$-0.531367\pi$
$907$	−4.87489e6	−0.196764	−0.0983822	+	0.995149i	$0.531367\pi$
$908$	−8.53981e7	−3.43743
$909$	3.33687e6	0.133946
$910$	−1.50306e8	−6.01692
$911$	−3.11620e7	−1.24403	−0.622013	−	0.783007i	$-0.713685\pi$
$911$	−3.11620e7	−1.24403	−0.622013	+	0.783007i	$0.713685\pi$
$912$	7.11338e7	2.83197
$913$	3.81436e7	1.51442
$914$	−4.49139e7	−1.77834
$915$	−1.95275e7	−0.771070
$916$	1.14999e8	4.52852
$917$	−1.62323e7	−0.637467
$918$	6.46732e7	2.53290
$919$	−2.86685e7	−1.11974	−0.559869	−	0.828581i	$-0.689149\pi$
$919$	−2.86685e7	−1.11974	−0.559869	+	0.828581i	$0.689149\pi$
$920$	1.69859e8	6.61637
$921$	−4.01074e7	−1.55803
$922$	−2.23360e7	−0.865321
$923$	−1.37882e7	−0.532725
$924$	−2.60505e8	−10.0378
$925$	2.33856e7	0.898656
$926$	5.01442e7	1.92173
$927$	−6.80969e7	−2.60272
$928$	1.61296e8	6.14828
$929$	1.63668e7	0.622194	0.311097	−	0.950378i	$-0.399304\pi$
$929$	1.63668e7	0.622194	0.311097	+	0.950378i	$0.399304\pi$
$930$	−1.76535e6	−0.0669305
$931$	−4.75893e6	−0.179943
$932$	−4.92244e7	−1.85627
$933$	7.80009e7	2.93356
$934$	−1.21229e7	−0.454714
$935$	7.89541e7	2.95356
$936$	−3.02766e8	−11.2958
$937$	4.98243e7	1.85393	0.926963	−	0.375152i	$-0.122410\pi$
$937$	4.98243e7	1.85393	0.926963	+	0.375152i	$0.122410\pi$
$938$	−7.39871e7	−2.74568
$939$	−5.45659e7	−2.01956
$940$	1.46913e7	0.542300
$941$	2.78313e7	1.02461	0.512306	−	0.858803i	$-0.328791\pi$
$941$	2.78313e7	1.02461	0.512306	+	0.858803i	$0.328791\pi$
$942$	8.80792e7	3.23404
$943$	−9.40008e6	−0.344233
$944$	5.71718e7	2.08810
$945$	−4.77732e7	−1.74022
$946$	−1.22833e8	−4.46260
$947$	−1.53221e7	−0.555193	−0.277597	−	0.960698i	$-0.589538\pi$
$947$	−1.53221e7	−0.555193	−0.277597	+	0.960698i	$0.589538\pi$
$948$	2.01711e8	7.28969
$949$	−4.77166e7	−1.71990
$950$	1.86822e7	0.671611
$951$	1.62572e7	0.582900
$952$	−1.43585e8	−5.13473
$953$	1.44956e7	0.517017	0.258509	−	0.966009i	$-0.416769\pi$
$953$	1.44956e7	0.517017	0.258509	+	0.966009i	$0.416769\pi$
$954$	3.41846e7	1.21607
$955$	5.25169e7	1.86333
$956$	−8.54531e7	−3.02401
$957$	1.13301e8	3.99901
$958$	−1.92095e7	−0.676241
$959$	−32833.0	−0.00115283
$960$	−2.99903e8	−10.5028
$961$	−2.86222e7	−0.999759
$962$	−1.16814e8	−4.06964
$963$	2.67630e7	0.929971
$964$	−1.02584e8	−3.55539
$965$	5.79206e7	2.00224
$966$	−1.51902e8	−5.23744
$967$	−5.44771e7	−1.87348	−0.936738	−	0.350031i	$-0.886171\pi$
$967$	−5.44771e7	−1.87348	−0.936738	+	0.350031i	$0.886171\pi$
$968$	−2.40897e8	−8.26308
$969$	2.39148e7	0.818198
$970$	−9.66245e6	−0.329730
$971$	2.47508e7	0.842446	0.421223	−	0.906957i	$-0.361601\pi$
$971$	2.47508e7	0.842446	0.421223	+	0.906957i	$0.361601\pi$
$972$	7.65257e7	2.59801
$973$	−3.33955e7	−1.13085
$974$	−1.30810e7	−0.441818
$975$	−7.58641e7	−2.55579
$976$	4.33457e7	1.45654
$977$	−2.17743e7	−0.729808	−0.364904	−	0.931045i	$-0.618898\pi$
$977$	−2.17743e7	−0.729808	−0.364904	+	0.931045i	$0.618898\pi$
$978$	6.97049e7	2.33032
$979$	3.90221e7	1.30123
$980$	4.94511e7	1.64479
$981$	5.20576e7	1.72708
$982$	1.58885e7	0.525779
$983$	966289.	0.0318950
$983$	966289.	0.0318950
$984$	4.43857e7	1.46135
$985$	−3.29038e7	−1.08058
$986$	9.66510e7	3.16602
$987$	−8.48889e6	−0.277369
$988$	−6.89280e7	−2.24649
$989$	−5.29035e7	−1.71986
$990$	−2.46162e8	−7.98239
$991$	−3.51306e7	−1.13632	−0.568160	−	0.822918i	$-0.692345\pi$
$991$	−3.51306e7	−1.13632	−0.568160	+	0.822918i	$0.692345\pi$
$992$	2.19857e6	0.0709350
$993$	6.16850e7	1.98521
$994$	2.03872e7	0.654472
$995$	−1.22168e7	−0.391202
$996$	−1.20056e8	−3.83472
$997$	1.05045e7	0.334685	0.167343	−	0.985899i	$-0.446481\pi$
$997$	1.05045e7	0.334685	0.167343	+	0.985899i	$0.446481\pi$
$998$	−2.12169e7	−0.674303
$999$	−3.71279e7	−1.17703

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.6.a.b.1.2	✓	218

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.6.a.b.1.2	✓	218	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 983 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	983.a (trivial)

\(f(q)\)	\(=\)	\(q-11.0647 q^{2} -25.4268 q^{3} +90.4285 q^{4} +75.4706 q^{5} +281.341 q^{6} +155.090 q^{7} -646.496 q^{8} +403.521 q^{9} -835.063 q^{10} +730.527 q^{11} -2299.30 q^{12} +1160.58 q^{13} -1716.03 q^{14} -1918.97 q^{15} +4259.60 q^{16} +1432.06 q^{17} -4464.85 q^{18} -656.774 q^{19} +6824.69 q^{20} -3943.44 q^{21} -8083.09 q^{22} -3481.34 q^{23} +16438.3 q^{24} +2570.81 q^{25} -12841.5 q^{26} -4081.52 q^{27} +14024.6 q^{28} -6099.65 q^{29} +21232.9 q^{30} -83.1421 q^{31} -26443.5 q^{32} -18574.9 q^{33} -15845.4 q^{34} +11704.7 q^{35} +36489.8 q^{36} +9096.57 q^{37} +7267.03 q^{38} -29509.8 q^{39} -48791.4 q^{40} +2700.14 q^{41} +43633.1 q^{42} +15196.3 q^{43} +66060.5 q^{44} +30453.9 q^{45} +38520.1 q^{46} +2152.66 q^{47} -108308. q^{48} +7245.91 q^{49} -28445.3 q^{50} -36412.6 q^{51} +104949. q^{52} -7656.38 q^{53} +45161.0 q^{54} +55133.3 q^{55} -100265. q^{56} +16699.6 q^{57} +67491.0 q^{58} +13421.9 q^{59} -173530. q^{60} +10176.0 q^{61} +919.946 q^{62} +62582.0 q^{63} +156283. q^{64} +87589.6 q^{65} +205527. q^{66} +43115.3 q^{67} +129499. q^{68} +88519.1 q^{69} -129510. q^{70} -11880.4 q^{71} -260875. q^{72} -41114.5 q^{73} -100651. q^{74} -65367.4 q^{75} -59391.1 q^{76} +113297. q^{77} +326518. q^{78} -87727.1 q^{79} +321475. q^{80} +5724.46 q^{81} -29876.3 q^{82} +52213.8 q^{83} -356599. q^{84} +108078. q^{85} -168143. q^{86} +155094. q^{87} -472283. q^{88} +53416.4 q^{89} -336965. q^{90} +179994. q^{91} -314812. q^{92} +2114.04 q^{93} -23818.7 q^{94} -49567.1 q^{95} +672373. q^{96} +11570.9 q^{97} -80174.2 q^{98} +294783. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 218 q + 35 q^{2} + 70 q^{3} + 3685 q^{4} + 253 q^{5} + 529 q^{6} + 1567 q^{7} + 1695 q^{8} + 19812 q^{9} + 2133 q^{10} + 1752 q^{11} + 3512 q^{12} + 5990 q^{13} + 2319 q^{14} + 4639 q^{15} + 66105 q^{16}+ \cdots + 627643 q^{99}+O(q^{100}) \) 218 * q + 35 * q^2 + 70 * q^3 + 3685 * q^4 + 253 * q^5 + 529 * q^6 + 1567 * q^7 + 1695 * q^8 + 19812 * q^9 + 2133 * q^10 + 1752 * q^11 + 3512 * q^12 + 5990 * q^13 + 2319 * q^14 + 4639 * q^15 + 66105 * q^16 + 10656 * q^17 + 11911 * q^18 + 11511 * q^19 + 10012 * q^20 + 12225 * q^21 + 19401 * q^22 + 9767 * q^23 + 21725 * q^24 + 185207 * q^25 + 7708 * q^26 + 23764 * q^27 + 77808 * q^28 + 25772 * q^29 + 15736 * q^30 + 35900 * q^31 + 60155 * q^32 + 70026 * q^33 + 17236 * q^34 + 28782 * q^35 + 382874 * q^36 + 126082 * q^37 + 62164 * q^38 + 54264 * q^39 + 102846 * q^40 + 70480 * q^41 + 102244 * q^42 + 137413 * q^43 + 116278 * q^44 + 93481 * q^45 + 126122 * q^46 + 63218 * q^47 + 124701 * q^48 + 732031 * q^49 + 131089 * q^50 + 109902 * q^51 + 229519 * q^52 + 102608 * q^53 + 149130 * q^54 + 167596 * q^55 + 87868 * q^56 + 408318 * q^57 + 304579 * q^58 + 67460 * q^59 + 150523 * q^60 + 195132 * q^61 + 132294 * q^62 + 374425 * q^63 + 1296639 * q^64 + 347092 * q^65 + 147397 * q^66 + 381238 * q^67 + 296321 * q^68 + 139362 * q^69 + 325675 * q^70 + 147818 * q^71 + 646059 * q^72 + 961992 * q^73 + 167410 * q^74 + 167324 * q^75 + 504875 * q^76 + 284328 * q^77 + 284295 * q^78 + 285792 * q^79 + 444932 * q^80 + 1980282 * q^81 + 336676 * q^82 + 276734 * q^83 + 378474 * q^84 + 1021245 * q^85 + 156051 * q^86 + 500457 * q^87 + 1068101 * q^88 + 398983 * q^89 + 463961 * q^90 + 273517 * q^91 + 577884 * q^92 + 967833 * q^93 + 224775 * q^94 + 482817 * q^95 + 780445 * q^96 + 1636277 * q^97 + 495958 * q^98 + 627643 * q^99

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