LMFDB - Embedded newform 1014.6.a.o.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,6,Mod(1,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1014.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	1014.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:	$162.629193290$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 727x - 6617 $ x^3 - x^2 - 727*x - 6617
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	no (minimal twist has level 78)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-18.9385$ of defining polynomial
Character	$\chi$	$=$	1014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +86.8538 q^{5} +36.0000 q^{6} +98.7774 q^{7} -64.0000 q^{8} +81.0000 q^{9} -347.415 q^{10} +610.754 q^{11} -144.000 q^{12} -395.109 q^{14} -781.684 q^{15} +256.000 q^{16} +1148.60 q^{17} -324.000 q^{18} -2267.14 q^{19} +1389.66 q^{20} -888.996 q^{21} -2443.02 q^{22} -433.224 q^{23} +576.000 q^{24} +4418.59 q^{25} -729.000 q^{27} +1580.44 q^{28} +7669.59 q^{29} +3126.74 q^{30} -7367.13 q^{31} -1024.00 q^{32} -5496.79 q^{33} -4594.42 q^{34} +8579.19 q^{35} +1296.00 q^{36} +10575.0 q^{37} +9068.57 q^{38} -5558.65 q^{40} +3699.17 q^{41} +3555.98 q^{42} +6061.57 q^{43} +9772.07 q^{44} +7035.16 q^{45} +1732.89 q^{46} +8740.69 q^{47} -2304.00 q^{48} -7050.03 q^{49} -17674.4 q^{50} -10337.4 q^{51} +34784.8 q^{53} +2916.00 q^{54} +53046.3 q^{55} -6321.75 q^{56} +20404.3 q^{57} -30678.4 q^{58} -11949.6 q^{59} -12507.0 q^{60} -45400.2 q^{61} +29468.5 q^{62} +8000.97 q^{63} +4096.00 q^{64} +21987.2 q^{66} +45698.1 q^{67} +18377.7 q^{68} +3899.01 q^{69} -34316.8 q^{70} +23826.9 q^{71} -5184.00 q^{72} +37759.1 q^{73} -42299.9 q^{74} -39767.3 q^{75} -36274.3 q^{76} +60328.7 q^{77} -35307.0 q^{79} +22234.6 q^{80} +6561.00 q^{81} -14796.7 q^{82} -31484.4 q^{83} -14223.9 q^{84} +99760.7 q^{85} -24246.3 q^{86} -69026.3 q^{87} -39088.3 q^{88} +59051.5 q^{89} -28140.6 q^{90} -6931.58 q^{92} +66304.2 q^{93} -34962.7 q^{94} -196910. q^{95} +9216.00 q^{96} -4965.78 q^{97} +28200.1 q^{98} +49471.1 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 12 q^{2} - 27 q^{3} + 48 q^{4} + 40 q^{5} + 108 q^{6} + 170 q^{7} - 192 q^{8} + 243 q^{9} - 160 q^{10} + 162 q^{11} - 432 q^{12} - 680 q^{14} - 360 q^{15} + 768 q^{16} + 418 q^{17} - 972 q^{18} + 66 q^{19}+ \cdots + 13122 q^{99}+O(q^{100}) $ 3 * q - 12 * q^2 - 27 * q^3 + 48 * q^4 + 40 * q^5 + 108 * q^6 + 170 * q^7 - 192 * q^8 + 243 * q^9 - 160 * q^10 + 162 * q^11 - 432 * q^12 - 680 * q^14 - 360 * q^15 + 768 * q^16 + 418 * q^17 - 972 * q^18 + 66 * q^19 + 640 * q^20 - 1530 * q^21 - 648 * q^22 + 208 * q^23 + 1728 * q^24 - 359 * q^25 - 2187 * q^27 + 2720 * q^28 + 9394 * q^29 + 1440 * q^30 - 7418 * q^31 - 3072 * q^32 - 1458 * q^33 - 1672 * q^34 + 3056 * q^35 + 3888 * q^36 + 7780 * q^37 - 264 * q^38 - 2560 * q^40 + 18140 * q^41 + 6120 * q^42 + 12100 * q^43 + 2592 * q^44 + 3240 * q^45 - 832 * q^46 + 4086 * q^47 - 6912 * q^48 + 1519 * q^49 + 1436 * q^50 - 3762 * q^51 - 21198 * q^53 + 8748 * q^54 + 62328 * q^55 - 10880 * q^56 - 594 * q^57 - 37576 * q^58 - 1718 * q^59 - 5760 * q^60 - 1598 * q^61 + 29672 * q^62 + 13770 * q^63 + 12288 * q^64 + 5832 * q^66 + 106810 * q^67 + 6688 * q^68 - 1872 * q^69 - 12224 * q^70 - 68694 * q^71 - 15552 * q^72 + 66976 * q^73 - 31120 * q^74 + 3231 * q^75 + 1056 * q^76 + 57012 * q^77 - 84664 * q^79 + 10240 * q^80 + 19683 * q^81 - 72560 * q^82 - 40898 * q^83 - 24480 * q^84 + 81328 * q^85 - 48400 * q^86 - 84546 * q^87 - 10368 * q^88 + 13524 * q^89 - 12960 * q^90 + 3328 * q^92 + 66762 * q^93 - 16344 * q^94 - 283584 * q^95 + 27648 * q^96 - 103224 * q^97 - 6076 * q^98 + 13122 * 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 $

$2$	−4.00000	−0.707107
$2$	−4.00000	−0.707107
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	16.0000	0.500000
$5$	86.8538	1.55369	0.776844	−	0.629693i	$-0.216819\pi$
$5$	86.8538	1.55369	0.776844	+	0.629693i	$0.216819\pi$
$6$	36.0000	0.408248
$7$	98.7774	0.761925	0.380963	−	0.924590i	$-0.375593\pi$
$7$	98.7774	0.761925	0.380963	+	0.924590i	$0.375593\pi$
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	−347.415	−1.09862
$11$	610.754	1.52190	0.760948	−	0.648813i	$-0.224734\pi$
$11$	610.754	1.52190	0.760948	+	0.648813i	$0.224734\pi$
$12$	−144.000	−0.288675
$13$	0	0
$13$	0	0
$14$	−395.109	−0.538762
$15$	−781.684	−0.897023
$16$	256.000	0.250000
$17$	1148.60	0.963936	0.481968	−	0.876189i	$-0.339922\pi$
$17$	1148.60	0.963936	0.481968	+	0.876189i	$0.339922\pi$
$18$	−324.000	−0.235702
$19$	−2267.14	−1.44077	−0.720386	−	0.693574i	$-0.756035\pi$
$19$	−2267.14	−1.44077	−0.720386	+	0.693574i	$0.756035\pi$
$20$	1389.66	0.776844
$21$	−888.996	−0.439898
$22$	−2443.02	−1.07614
$23$	−433.224	−0.170763	−0.0853813	−	0.996348i	$-0.527211\pi$
$23$	−433.224	−0.170763	−0.0853813	+	0.996348i	$0.527211\pi$
$24$	576.000	0.204124
$25$	4418.59	1.41395
$26$	0	0
$27$	−729.000	−0.192450
$28$	1580.44	0.380963
$29$	7669.59	1.69347	0.846734	−	0.532016i	$-0.178566\pi$
$29$	7669.59	1.69347	0.846734	+	0.532016i	$0.178566\pi$
$30$	3126.74	0.634291
$31$	−7367.13	−1.37687	−0.688437	−	0.725296i	$-0.741703\pi$
$31$	−7367.13	−1.37687	−0.688437	+	0.725296i	$0.741703\pi$
$32$	−1024.00	−0.176777
$33$	−5496.79	−0.878667
$34$	−4594.42	−0.681606
$35$	8579.19	1.18379
$36$	1296.00	0.166667
$37$	10575.0	1.26991	0.634957	−	0.772547i	$-0.281018\pi$
$37$	10575.0	1.26991	0.634957	+	0.772547i	$0.281018\pi$
$38$	9068.57	1.01878
$39$	0	0
$40$	−5558.65	−0.549312
$41$	3699.17	0.343672	0.171836	−	0.985126i	$-0.445030\pi$
$41$	3699.17	0.343672	0.171836	+	0.985126i	$0.445030\pi$
$42$	3555.98	0.311055
$43$	6061.57	0.499936	0.249968	−	0.968254i	$-0.419580\pi$
$43$	6061.57	0.499936	0.249968	+	0.968254i	$0.419580\pi$
$44$	9772.07	0.760948
$45$	7035.16	0.517896
$46$	1732.89	0.120747
$47$	8740.69	0.577166	0.288583	−	0.957455i	$-0.406816\pi$
$47$	8740.69	0.577166	0.288583	+	0.957455i	$0.406816\pi$
$48$	−2304.00	−0.144338
$49$	−7050.03	−0.419470
$50$	−17674.4	−0.999812
$51$	−10337.4	−0.556529
$52$	0	0
$53$	34784.8	1.70098	0.850491	−	0.525990i	$-0.176305\pi$
$53$	34784.8	1.70098	0.850491	+	0.525990i	$0.176305\pi$
$54$	2916.00	0.136083
$55$	53046.3	2.36455
$56$	−6321.75	−0.269381
$57$	20404.3	0.831830
$58$	−30678.4	−1.19746
$59$	−11949.6	−0.446915	−0.223457	−	0.974714i	$-0.571734\pi$
$59$	−11949.6	−0.446915	−0.223457	+	0.974714i	$0.571734\pi$
$60$	−12507.0	−0.448511
$61$	−45400.2	−1.56219	−0.781094	−	0.624414i	$-0.785338\pi$
$61$	−45400.2	−1.56219	−0.781094	+	0.624414i	$0.785338\pi$
$62$	29468.5	0.973597
$63$	8000.97	0.253975
$64$	4096.00	0.125000
$65$	0	0
$66$	21987.2	0.621311
$67$	45698.1	1.24369	0.621844	−	0.783141i	$-0.286384\pi$
$67$	45698.1	1.24369	0.621844	+	0.783141i	$0.286384\pi$
$68$	18377.7	0.481968
$69$	3899.01	0.0985898
$70$	−34316.8	−0.837069
$71$	23826.9	0.560946	0.280473	−	0.959862i	$-0.409509\pi$
$71$	23826.9	0.560946	0.280473	+	0.959862i	$0.409509\pi$
$72$	−5184.00	−0.117851
$73$	37759.1	0.829305	0.414653	−	0.909980i	$-0.363903\pi$
$73$	37759.1	0.829305	0.414653	+	0.909980i	$0.363903\pi$
$74$	−42299.9	−0.897965
$75$	−39767.3	−0.816343
$76$	−36274.3	−0.720386
$77$	60328.7	1.15957
$78$	0	0
$79$	−35307.0	−0.636492	−0.318246	−	0.948008i	$-0.603094\pi$
$79$	−35307.0	−0.636492	−0.318246	+	0.948008i	$0.603094\pi$
$80$	22234.6	0.388422
$81$	6561.00	0.111111
$82$	−14796.7	−0.243013
$83$	−31484.4	−0.501649	−0.250824	−	0.968033i	$-0.580702\pi$
$83$	−31484.4	−0.501649	−0.250824	+	0.968033i	$0.580702\pi$
$84$	−14223.9	−0.219949
$85$	99760.7	1.49766
$86$	−24246.3	−0.353508
$87$	−69026.3	−0.977724
$88$	−39088.3	−0.538071
$89$	59051.5	0.790235	0.395117	−	0.918631i	$-0.370704\pi$
$89$	59051.5	0.790235	0.395117	+	0.918631i	$0.370704\pi$
$90$	−28140.6	−0.366208
$91$	0	0
$92$	−6931.58	−0.0853813
$93$	66304.2	0.794938
$94$	−34962.7	−0.408118
$95$	−196910.	−2.23851
$96$	9216.00	0.102062
$97$	−4965.78	−0.0535868	−0.0267934	−	0.999641i	$-0.508530\pi$
$97$	−4965.78	−0.0535868	−0.0267934	+	0.999641i	$0.508530\pi$
$98$	28200.1	0.296610
$99$	49471.1	0.507298
$100$	70697.4	0.706974
$101$	125605.	1.22519	0.612596	−	0.790396i	$-0.290125\pi$
$101$	125605.	1.22519	0.612596	+	0.790396i	$0.290125\pi$
$102$	41349.8	0.393525
$103$	126352.	1.17351	0.586756	−	0.809764i	$-0.300405\pi$
$103$	126352.	1.17351	0.586756	+	0.809764i	$0.300405\pi$
$104$	0	0
$105$	−77212.7	−0.683464
$106$	−139139.	−1.20278
$107$	33067.8	0.279219	0.139610	−	0.990207i	$-0.455415\pi$
$107$	33067.8	0.279219	0.139610	+	0.990207i	$0.455415\pi$
$108$	−11664.0	−0.0962250
$109$	−147666.	−1.19046	−0.595230	−	0.803555i	$-0.702939\pi$
$109$	−147666.	−1.19046	−0.595230	+	0.803555i	$0.702939\pi$
$110$	−212185.	−1.67199
$111$	−95174.7	−0.733186
$112$	25287.0	0.190481
$113$	118111.	0.870152	0.435076	−	0.900394i	$-0.356722\pi$
$113$	118111.	0.870152	0.435076	+	0.900394i	$0.356722\pi$
$114$	−81617.2	−0.588192
$115$	−37627.1	−0.265312
$116$	122713.	0.846734
$117$	0	0
$118$	47798.6	0.316016
$119$	113456.	0.734447
$120$	50027.8	0.317145
$121$	211970.	1.31616
$122$	181601.	1.10463
$123$	−33292.5	−0.198419
$124$	−117874.	−0.688437
$125$	112353.	0.643147
$126$	−32003.9	−0.179587
$127$	−322666.	−1.77518	−0.887592	−	0.460631i	$-0.847623\pi$
$127$	−322666.	−1.77518	−0.887592	+	0.460631i	$0.847623\pi$
$128$	−16384.0	−0.0883883
$129$	−54554.2	−0.288638
$130$	0	0
$131$	−357874.	−1.82202	−0.911008	−	0.412390i	$-0.864694\pi$
$131$	−357874.	−1.82202	−0.911008	+	0.412390i	$0.864694\pi$
$132$	−87948.6	−0.439333
$133$	−223942.	−1.09776
$134$	−182792.	−0.879420
$135$	−63316.4	−0.299008
$136$	−73510.7	−0.340803
$137$	−347064.	−1.57982	−0.789912	−	0.613221i	$-0.789874\pi$
$137$	−347064.	−1.57982	−0.789912	+	0.613221i	$0.789874\pi$
$138$	−15596.1	−0.0697135
$139$	−103030.	−0.452299	−0.226149	−	0.974093i	$-0.572614\pi$
$139$	−103030.	−0.452299	−0.226149	+	0.974093i	$0.572614\pi$
$140$	137267.	0.591897
$141$	−78666.2	−0.333227
$142$	−95307.4	−0.396649
$143$	0	0
$144$	20736.0	0.0833333
$145$	666133.	2.63112
$146$	−151036.	−0.586407
$147$	63450.3	0.242181
$148$	169199.	0.634957
$149$	−90695.3	−0.334672	−0.167336	−	0.985900i	$-0.553516\pi$
$149$	−90695.3	−0.334672	−0.167336	+	0.985900i	$0.553516\pi$
$150$	159069.	0.577242
$151$	−104288.	−0.372215	−0.186107	−	0.982529i	$-0.559587\pi$
$151$	−104288.	−0.372215	−0.186107	+	0.982529i	$0.559587\pi$
$152$	145097.	0.509390
$153$	93036.9	0.321312
$154$	−241315.	−0.819940
$155$	−639863.	−2.13923
$156$	0	0
$157$	−314419.	−1.01803	−0.509014	−	0.860758i	$-0.669990\pi$
$157$	−314419.	−1.01803	−0.509014	+	0.860758i	$0.669990\pi$
$158$	141228.	0.450068
$159$	−313063.	−0.982062
$160$	−88938.3	−0.274656
$161$	−42792.7	−0.130108
$162$	−26244.0	−0.0785674
$163$	140732.	0.414881	0.207441	−	0.978248i	$-0.433487\pi$
$163$	140732.	0.414881	0.207441	+	0.978248i	$0.433487\pi$
$164$	59186.7	0.171836
$165$	−477417.	−1.36517
$166$	125937.	0.354719
$167$	108944.	0.302281	0.151141	−	0.988512i	$-0.451705\pi$
$167$	108944.	0.302281	0.151141	+	0.988512i	$0.451705\pi$
$168$	56895.8	0.155527
$169$	0	0
$170$	−399043.	−1.05900
$171$	−183639.	−0.480257
$172$	96985.2	0.249968
$173$	−401188.	−1.01914	−0.509569	−	0.860430i	$-0.670195\pi$
$173$	−401188.	−1.01914	−0.509569	+	0.860430i	$0.670195\pi$
$174$	276105.	0.691355
$175$	436456.	1.07732
$176$	156353.	0.380474
$177$	107547.	0.258026
$178$	−236206.	−0.558780
$179$	209535.	0.488792	0.244396	−	0.969676i	$-0.421410\pi$
$179$	209535.	0.488792	0.244396	+	0.969676i	$0.421410\pi$
$180$	112563.	0.258948
$181$	−236277.	−0.536075	−0.268038	−	0.963408i	$-0.586375\pi$
$181$	−236277.	−0.536075	−0.268038	+	0.963408i	$0.586375\pi$
$182$	0	0
$183$	408602.	0.901929
$184$	27726.3	0.0603737
$185$	918476.	1.97305
$186$	−265217.	−0.562106
$187$	701515.	1.46701
$188$	139851.	0.288583
$189$	−72008.7	−0.146633
$190$	787640.	1.58287
$191$	509719.	1.01099	0.505496	−	0.862829i	$-0.331310\pi$
$191$	509719.	1.01099	0.505496	+	0.862829i	$0.331310\pi$
$192$	−36864.0	−0.0721688
$193$	−58146.8	−0.112365	−0.0561827	−	0.998421i	$-0.517893\pi$
$193$	−58146.8	−0.112365	−0.0561827	+	0.998421i	$0.517893\pi$
$194$	19863.1	0.0378916
$195$	0	0
$196$	−112801.	−0.209735
$197$	−91830.0	−0.168585	−0.0842925	−	0.996441i	$-0.526863\pi$
$197$	−91830.0	−0.168585	−0.0842925	+	0.996441i	$0.526863\pi$
$198$	−197884.	−0.358714
$199$	−562291.	−1.00653	−0.503267	−	0.864131i	$-0.667869\pi$
$199$	−562291.	−1.00653	−0.503267	+	0.864131i	$0.667869\pi$
$200$	−282790.	−0.499906
$201$	−411283.	−0.718043
$202$	−502421.	−0.866341
$203$	757582.	1.29030
$204$	−165399.	−0.278264
$205$	321287.	0.533960
$206$	−505406.	−0.829798
$207$	−35091.1	−0.0569208
$208$	0	0
$209$	−1.38467e6	−2.19270
$210$	308851.	0.483282
$211$	650662.	1.00612	0.503059	−	0.864252i	$-0.332208\pi$
$211$	650662.	1.00612	0.503059	+	0.864252i	$0.332208\pi$
$212$	556557.	0.850491
$213$	−214442.	−0.323862
$214$	−132271.	−0.197438
$215$	526471.	0.776745
$216$	46656.0	0.0680414
$217$	−727706.	−1.04907
$218$	590665.	0.841782
$219$	−339832.	−0.478800
$220$	848741.	1.18228
$221$	0	0
$222$	380699.	0.518441
$223$	−302795.	−0.407743	−0.203871	−	0.978998i	$-0.565352\pi$
$223$	−302795.	−0.407743	−0.203871	+	0.978998i	$0.565352\pi$
$224$	−101148.	−0.134691
$225$	357906.	0.471316
$226$	−472445.	−0.615290
$227$	−723191.	−0.931512	−0.465756	−	0.884913i	$-0.654218\pi$
$227$	−723191.	−0.931512	−0.465756	+	0.884913i	$0.654218\pi$
$228$	326469.	0.415915
$229$	1.39378e6	1.75633	0.878166	−	0.478356i	$-0.158767\pi$
$229$	1.39378e6	1.75633	0.878166	+	0.478356i	$0.158767\pi$
$230$	150509.	0.187604
$231$	−542958.	−0.669478
$232$	−490854.	−0.598731
$233$	319385.	0.385411	0.192706	−	0.981257i	$-0.438274\pi$
$233$	319385.	0.385411	0.192706	+	0.981257i	$0.438274\pi$
$234$	0	0
$235$	759162.	0.896736
$236$	−191194.	−0.223457
$237$	317763.	0.367479
$238$	−453824.	−0.519332
$239$	1.52265e6	1.72427	0.862133	−	0.506682i	$-0.169128\pi$
$239$	1.52265e6	1.72427	0.862133	+	0.506682i	$0.169128\pi$
$240$	−200111.	−0.224256
$241$	607839.	0.674134	0.337067	−	0.941481i	$-0.390565\pi$
$241$	607839.	0.674134	0.337067	+	0.941481i	$0.390565\pi$
$242$	−847879.	−0.930669
$243$	−59049.0	−0.0641500
$244$	−726403.	−0.781094
$245$	−612323.	−0.651726
$246$	133170.	0.140304
$247$	0	0
$248$	471496.	0.486798
$249$	283359.	0.289627
$250$	−449412.	−0.454773
$251$	1.05049e6	1.05247	0.526234	−	0.850340i	$-0.323604\pi$
$251$	1.05049e6	1.05247	0.526234	+	0.850340i	$0.323604\pi$
$252$	128015.	0.126988
$253$	−264593.	−0.259883
$254$	1.29066e6	1.25524
$255$	−897846.	−0.864672
$256$	65536.0	0.0625000
$257$	−236240.	−0.223111	−0.111555	−	0.993758i	$-0.535583\pi$
$257$	−236240.	−0.223111	−0.111555	+	0.993758i	$0.535583\pi$
$258$	218217.	0.204098
$259$	1.04457e6	0.967580
$260$	0	0
$261$	621237.	0.564489
$262$	1.43150e6	1.28836
$263$	928964.	0.828151	0.414076	−	0.910242i	$-0.364105\pi$
$263$	928964.	0.828151	0.414076	+	0.910242i	$0.364105\pi$
$264$	351794.	0.310656
$265$	3.02119e6	2.64280
$266$	895770.	0.776233
$267$	−531464.	−0.456242
$268$	731170.	0.621844
$269$	827650.	0.697374	0.348687	−	0.937239i	$-0.386628\pi$
$269$	827650.	0.697374	0.348687	+	0.937239i	$0.386628\pi$
$270$	253266.	0.211430
$271$	660781.	0.546555	0.273278	−	0.961935i	$-0.411892\pi$
$271$	660781.	0.546555	0.273278	+	0.961935i	$0.411892\pi$
$272$	294043.	0.240984
$273$	0	0
$274$	1.38826e6	1.11710
$275$	2.69867e6	2.15188
$276$	62384.2	0.0492949
$277$	1.38275e6	1.08279	0.541395	−	0.840769i	$-0.317896\pi$
$277$	1.38275e6	1.08279	0.541395	+	0.840769i	$0.317896\pi$
$278$	412119.	0.319823
$279$	−596738.	−0.458958
$280$	−549068.	−0.418534
$281$	1.44893e6	1.09467	0.547333	−	0.836915i	$-0.315643\pi$
$281$	1.44893e6	1.09467	0.547333	+	0.836915i	$0.315643\pi$
$282$	314665.	0.235627
$283$	−1.22044e6	−0.905841	−0.452921	−	0.891551i	$-0.649618\pi$
$283$	−1.22044e6	−0.905841	−0.452921	+	0.891551i	$0.649618\pi$
$284$	381230.	0.280473
$285$	1.77219e6	1.29240
$286$	0	0
$287$	365394.	0.261853
$288$	−82944.0	−0.0589256
$289$	−100565.	−0.0708279
$290$	−2.66453e6	−1.86048
$291$	44692.0	0.0309384
$292$	604146.	0.414653
$293$	−2.19465e6	−1.49347	−0.746734	−	0.665123i	$-0.768379\pi$
$293$	−2.19465e6	−1.49347	−0.746734	+	0.665123i	$0.768379\pi$
$294$	−253801.	−0.171248
$295$	−1.03787e6	−0.694366
$296$	−676798.	−0.448983
$297$	−445240.	−0.292889
$298$	362781.	0.236649
$299$	0	0
$300$	−636277.	−0.408172
$301$	598746.	0.380914
$302$	417154.	0.263196
$303$	−1.13045e6	−0.707365
$304$	−580389.	−0.360193
$305$	−3.94318e6	−2.42715
$306$	−372148.	−0.227202
$307$	−83619.1	−0.0506360	−0.0253180	−	0.999679i	$-0.508060\pi$
$307$	−83619.1	−0.0506360	−0.0253180	+	0.999679i	$0.508060\pi$
$308$	965259.	0.579785
$309$	−1.13716e6	−0.677528
$310$	2.55945e6	1.51267
$311$	−491767.	−0.288309	−0.144155	−	0.989555i	$-0.546046\pi$
$311$	−491767.	−0.288309	−0.144155	+	0.989555i	$0.546046\pi$
$312$	0	0
$313$	896969.	0.517508	0.258754	−	0.965943i	$-0.416688\pi$
$313$	896969.	0.517508	0.258754	+	0.965943i	$0.416688\pi$
$314$	1.25768e6	0.719854
$315$	694915.	0.394598
$316$	−564912.	−0.318246
$317$	3.15449e6	1.76312	0.881559	−	0.472074i	$-0.156494\pi$
$317$	3.15449e6	1.76312	0.881559	+	0.472074i	$0.156494\pi$
$318$	1.25225e6	0.694423
$319$	4.68423e6	2.57728
$320$	355753.	0.194211
$321$	−297610.	−0.161207
$322$	171171.	0.0920004
$323$	−2.60405e6	−1.38881
$324$	104976.	0.0555556
$325$	0	0
$326$	−562928.	−0.293365
$327$	1.32900e6	0.687312
$328$	−236747.	−0.121507
$329$	863382.	0.439757
$330$	1.90967e6	0.965324
$331$	597196.	0.299604	0.149802	−	0.988716i	$-0.452136\pi$
$331$	597196.	0.299604	0.149802	+	0.988716i	$0.452136\pi$
$332$	−503750.	−0.250824
$333$	856572.	0.423305
$334$	−435775.	−0.213745
$335$	3.96906e6	1.93230
$336$	−227583.	−0.109974
$337$	−3.61808e6	−1.73541	−0.867707	−	0.497077i	$-0.834407\pi$
$337$	−3.61808e6	−1.73541	−0.867707	+	0.497077i	$0.834407\pi$
$338$	0	0
$339$	−1.06300e6	−0.502382
$340$	1.59617e6	0.748828
$341$	−4.49951e6	−2.09546
$342$	734555.	0.339593
$343$	−2.35653e6	−1.08153
$344$	−387941.	−0.176754
$345$	338644.	0.153178
$346$	1.60475e6	0.720639
$347$	−1.62893e6	−0.726236	−0.363118	−	0.931743i	$-0.618288\pi$
$347$	−1.62893e6	−0.726236	−0.363118	+	0.931743i	$0.618288\pi$
$348$	−1.10442e6	−0.488862
$349$	−2.60140e6	−1.14326	−0.571628	−	0.820513i	$-0.693688\pi$
$349$	−2.60140e6	−1.14326	−0.571628	+	0.820513i	$0.693688\pi$
$350$	−1.74583e6	−0.761782
$351$	0	0
$352$	−625412.	−0.269036
$353$	−1.30441e6	−0.557155	−0.278578	−	0.960414i	$-0.589863\pi$
$353$	−1.30441e6	−0.557155	−0.278578	+	0.960414i	$0.589863\pi$
$354$	−430187.	−0.182452
$355$	2.06945e6	0.871535
$356$	944824.	0.395117
$357$	−1.02110e6	−0.424033
$358$	−838140.	−0.345628
$359$	213674.	0.0875013	0.0437507	−	0.999042i	$-0.486069\pi$
$359$	213674.	0.0875013	0.0437507	+	0.999042i	$0.486069\pi$
$360$	−450250.	−0.183104
$361$	2.66384e6	1.07582
$362$	945110.	0.379062
$363$	−1.90773e6	−0.759888
$364$	0	0
$365$	3.27952e6	1.28848
$366$	−1.63441e6	−0.637760
$367$	1.15670e6	0.448285	0.224142	−	0.974556i	$-0.428042\pi$
$367$	1.15670e6	0.448285	0.224142	+	0.974556i	$0.428042\pi$
$368$	−110905.	−0.0426906
$369$	299633.	0.114557
$370$	−3.67390e6	−1.39516
$371$	3.43595e6	1.29602
$372$	1.06087e6	0.397469
$373$	1.97983e6	0.736810	0.368405	−	0.929665i	$-0.379904\pi$
$373$	1.97983e6	0.736810	0.368405	+	0.929665i	$0.379904\pi$
$374$	−2.80606e6	−1.03733
$375$	−1.01118e6	−0.371321
$376$	−559404.	−0.204059
$377$	0	0
$378$	288035.	0.103685
$379$	3.86155e6	1.38090	0.690451	−	0.723379i	$-0.257412\pi$
$379$	3.86155e6	1.38090	0.690451	+	0.723379i	$0.257412\pi$
$380$	−3.15056e6	−1.11925
$381$	2.90399e6	1.02490
$382$	−2.03888e6	−0.714879
$383$	1.55518e6	0.541731	0.270866	−	0.962617i	$-0.412690\pi$
$383$	1.55518e6	0.541731	0.270866	+	0.962617i	$0.412690\pi$
$384$	147456.	0.0510310
$385$	5.23978e6	1.80161
$386$	232587.	0.0794544
$387$	490988.	0.166645
$388$	−79452.4	−0.0267934
$389$	−2.85249e6	−0.955763	−0.477881	−	0.878424i	$-0.658595\pi$
$389$	−2.85249e6	−0.955763	−0.477881	+	0.878424i	$0.658595\pi$
$390$	0	0
$391$	−497603.	−0.164604
$392$	451202.	0.148305
$393$	3.22087e6	1.05194
$394$	367320.	0.119208
$395$	−3.06655e6	−0.988911
$396$	791537.	0.253649
$397$	−1.25222e6	−0.398752	−0.199376	−	0.979923i	$-0.563891\pi$
$397$	−1.25222e6	−0.398752	−0.199376	+	0.979923i	$0.563891\pi$
$398$	2.24917e6	0.711727
$399$	2.01548e6	0.633792
$400$	1.13116e6	0.353487
$401$	4.20050e6	1.30449	0.652244	−	0.758009i	$-0.273828\pi$
$401$	4.20050e6	1.30449	0.652244	+	0.758009i	$0.273828\pi$
$402$	1.64513e6	0.507733
$403$	0	0
$404$	2.00968e6	0.612596
$405$	569848.	0.172632
$406$	−3.03033e6	−0.912377
$407$	6.45870e6	1.93268
$408$	661596.	0.196763
$409$	650694.	0.192340	0.0961698	−	0.995365i	$-0.469341\pi$
$409$	650694.	0.192340	0.0961698	+	0.995365i	$0.469341\pi$
$410$	−1.28515e6	−0.377567
$411$	3.12358e6	0.912111
$412$	2.02163e6	0.586756
$413$	−1.18035e6	−0.340516
$414$	140364.	0.0402491
$415$	−2.73454e6	−0.779406
$416$	0	0
$417$	927267.	0.261135
$418$	5.53867e6	1.55047
$419$	−6.82010e6	−1.89782	−0.948912	−	0.315541i	$-0.897814\pi$
$419$	−6.82010e6	−1.89782	−0.948912	+	0.315541i	$0.897814\pi$
$420$	−1.23540e6	−0.341732
$421$	3.11659e6	0.856988	0.428494	−	0.903545i	$-0.359044\pi$
$421$	3.11659e6	0.856988	0.428494	+	0.903545i	$0.359044\pi$
$422$	−2.60265e6	−0.711433
$423$	707996.	0.192389
$424$	−2.22623e6	−0.601388
$425$	5.07521e6	1.36296
$426$	857767.	0.229005
$427$	−4.48451e6	−1.19027
$428$	529084.	0.139610
$429$	0	0
$430$	−2.10588e6	−0.549241
$431$	4.88213e6	1.26595	0.632974	−	0.774173i	$-0.281834\pi$
$431$	4.88213e6	1.26595	0.632974	+	0.774173i	$0.281834\pi$
$432$	−186624.	−0.0481125
$433$	−3.64275e6	−0.933705	−0.466852	−	0.884335i	$-0.654612\pi$
$433$	−3.64275e6	−0.933705	−0.466852	+	0.884335i	$0.654612\pi$
$434$	2.91082e6	0.741808
$435$	−5.99520e6	−1.51908
$436$	−2.36266e6	−0.595230
$437$	982180.	0.246030
$438$	1.35933e6	0.338562
$439$	1.70122e6	0.421308	0.210654	−	0.977561i	$-0.432441\pi$
$439$	1.70122e6	0.421308	0.210654	+	0.977561i	$0.432441\pi$
$440$	−3.39497e6	−0.835995
$441$	−571053.	−0.139823
$442$	0	0
$443$	−5.85057e6	−1.41641	−0.708205	−	0.706007i	$-0.750495\pi$
$443$	−5.85057e6	−1.41641	−0.708205	+	0.706007i	$0.750495\pi$
$444$	−1.52279e6	−0.366593
$445$	5.12885e6	1.22778
$446$	1.21118e6	0.288318
$447$	816258.	0.193223
$448$	404592.	0.0952406
$449$	−1.56399e6	−0.366115	−0.183058	−	0.983102i	$-0.558599\pi$
$449$	−1.56399e6	−0.366115	−0.183058	+	0.983102i	$0.558599\pi$
$450$	−1.43162e6	−0.333271
$451$	2.25928e6	0.523033
$452$	1.88978e6	0.435076
$453$	938596.	0.214898
$454$	2.89276e6	0.658678
$455$	0	0
$456$	−1.30587e6	−0.294096
$457$	−336948.	−0.0754697	−0.0377349	−	0.999288i	$-0.512014\pi$
$457$	−336948.	−0.0754697	−0.0377349	+	0.999288i	$0.512014\pi$
$458$	−5.57513e6	−1.24191
$459$	−837332.	−0.185510
$460$	−602034.	−0.132656
$461$	−3.89174e6	−0.852887	−0.426444	−	0.904514i	$-0.640234\pi$
$461$	−3.89174e6	−0.852887	−0.426444	+	0.904514i	$0.640234\pi$
$462$	2.17183e6	0.473393
$463$	−6.34214e6	−1.37494	−0.687470	−	0.726213i	$-0.741279\pi$
$463$	−6.34214e6	−1.37494	−0.687470	+	0.726213i	$0.741279\pi$
$464$	1.96341e6	0.423367
$465$	5.75877e6	1.23509
$466$	−1.27754e6	−0.272527
$467$	−2.48691e6	−0.527677	−0.263839	−	0.964567i	$-0.584989\pi$
$467$	−2.48691e6	−0.527677	−0.263839	+	0.964567i	$0.584989\pi$
$468$	0	0
$469$	4.51394e6	0.947597
$470$	−3.03665e6	−0.634088
$471$	2.82977e6	0.587759
$472$	764777.	0.158008
$473$	3.70213e6	0.760850
$474$	−1.27105e6	−0.259847
$475$	−1.00176e7	−2.03718
$476$	1.81530e6	0.367223
$477$	2.81757e6	0.566994
$478$	−6.09058e6	−1.21924
$479$	−5.31079e6	−1.05760	−0.528798	−	0.848747i	$-0.677357\pi$
$479$	−5.31079e6	−1.05760	−0.528798	+	0.848747i	$0.677357\pi$
$480$	800445.	0.158573
$481$	0	0
$482$	−2.43136e6	−0.476685
$483$	385134.	0.0751180
$484$	3.39151e6	0.658082
$485$	−431297.	−0.0832572
$486$	236196.	0.0453609
$487$	7.73506e6	1.47789	0.738944	−	0.673767i	$-0.235325\pi$
$487$	7.73506e6	1.47789	0.738944	+	0.673767i	$0.235325\pi$
$488$	2.90561e6	0.552317
$489$	−1.26659e6	−0.239532
$490$	2.44929e6	0.460840
$491$	322490.	0.0603689	0.0301844	−	0.999544i	$-0.490391\pi$
$491$	322490.	0.0603689	0.0301844	+	0.999544i	$0.490391\pi$
$492$	−532680.	−0.0992097
$493$	8.80932e6	1.63239
$494$	0	0
$495$	4.29675e6	0.788184
$496$	−1.88599e6	−0.344218
$497$	2.35355e6	0.427399
$498$	−1.13344e6	−0.204797
$499$	−414653.	−0.0745476	−0.0372738	−	0.999305i	$-0.511867\pi$
$499$	−414653.	−0.0745476	−0.0372738	+	0.999305i	$0.511867\pi$
$500$	1.79765e6	0.321573
$501$	−980493.	−0.174522
$502$	−4.20197e6	−0.744207
$503$	−1.11227e7	−1.96016	−0.980080	−	0.198604i	$-0.936359\pi$
$503$	−1.11227e7	−1.96016	−0.980080	+	0.198604i	$0.936359\pi$
$504$	−512062.	−0.0897937
$505$	1.09093e7	1.90357
$506$	1.05837e6	0.183765
$507$	0	0
$508$	−5.16265e6	−0.887592
$509$	754143.	0.129021	0.0645103	−	0.997917i	$-0.479451\pi$
$509$	754143.	0.129021	0.0645103	+	0.997917i	$0.479451\pi$
$510$	3.59138e6	0.611415
$511$	3.72974e6	0.631869
$512$	−262144.	−0.0441942
$513$	1.65275e6	0.277277
$514$	944959.	0.157763
$515$	1.09741e7	1.82327
$516$	−872867.	−0.144319
$517$	5.33841e6	0.878386
$518$	−4.17827e6	−0.684182
$519$	3.61069e6	0.588399
$520$	0	0
$521$	6.34188e6	1.02358	0.511792	−	0.859109i	$-0.328982\pi$
$521$	6.34188e6	1.02358	0.511792	+	0.859109i	$0.328982\pi$
$522$	−2.48495e6	−0.399154
$523$	7.64810e6	1.22264	0.611321	−	0.791382i	$-0.290638\pi$
$523$	7.64810e6	1.22264	0.611321	+	0.791382i	$0.290638\pi$
$524$	−5.72599e6	−0.911008
$525$	−3.92811e6	−0.621993
$526$	−3.71586e6	−0.585591
$527$	−8.46192e6	−1.32722
$528$	−1.40718e6	−0.219667
$529$	−6.24866e6	−0.970840
$530$	−1.20848e7	−1.86874
$531$	−967921.	−0.148972
$532$	−3.58308e6	−0.548880
$533$	0	0
$534$	2.12585e6	0.322612
$535$	2.87206e6	0.433820
$536$	−2.92468e6	−0.439710
$537$	−1.88581e6	−0.282204
$538$	−3.31060e6	−0.493118
$539$	−4.30584e6	−0.638390
$540$	−1.01306e6	−0.149504
$541$	5.40473e6	0.793927	0.396964	−	0.917834i	$-0.370064\pi$
$541$	5.40473e6	0.793927	0.396964	+	0.917834i	$0.370064\pi$
$542$	−2.64312e6	−0.386473
$543$	2.12650e6	0.309503
$544$	−1.17617e6	−0.170401
$545$	−1.28254e7	−1.84960
$546$	0	0
$547$	6.06535e6	0.866737	0.433368	−	0.901217i	$-0.357325\pi$
$547$	6.06535e6	0.866737	0.433368	+	0.901217i	$0.357325\pi$
$548$	−5.55303e6	−0.789912
$549$	−3.67742e6	−0.520729
$550$	−1.07947e7	−1.52161
$551$	−1.73881e7	−2.43990
$552$	−249537.	−0.0348568
$553$	−3.48753e6	−0.484960
$554$	−5.53100e6	−0.765648
$555$	−8.26629e6	−1.13914
$556$	−1.64847e6	−0.226149
$557$	6.81169e6	0.930287	0.465143	−	0.885235i	$-0.346003\pi$
$557$	6.81169e6	0.930287	0.465143	+	0.885235i	$0.346003\pi$
$558$	2.38695e6	0.324532
$559$	0	0
$560$	2.19627e6	0.295949
$561$	−6.31363e6	−0.846978
$562$	−5.79572e6	−0.774046
$563$	−4.93741e6	−0.656491	−0.328245	−	0.944593i	$-0.606457\pi$
$563$	−4.93741e6	−0.656491	−0.328245	+	0.944593i	$0.606457\pi$
$564$	−1.25866e6	−0.166614
$565$	1.02584e7	1.35194
$566$	4.88178e6	0.640526
$567$	648078.	0.0846583
$568$	−1.52492e6	−0.198324
$569$	−9.18371e6	−1.18915	−0.594576	−	0.804039i	$-0.702680\pi$
$569$	−9.18371e6	−1.18915	−0.594576	+	0.804039i	$0.702680\pi$
$570$	−7.08876e6	−0.913868
$571$	1.11741e7	1.43424	0.717120	−	0.696949i	$-0.245460\pi$
$571$	1.11741e7	1.43424	0.717120	+	0.696949i	$0.245460\pi$
$572$	0	0
$573$	−4.58748e6	−0.583697
$574$	−1.46158e6	−0.185158
$575$	−1.91424e6	−0.241449
$576$	331776.	0.0416667
$577$	8.62732e6	1.07879	0.539394	−	0.842053i	$-0.318653\pi$
$577$	8.62732e6	1.07879	0.539394	+	0.842053i	$0.318653\pi$
$578$	402262.	0.0500829
$579$	523322.	0.0648742
$580$	1.06581e7	1.31556
$581$	−3.10994e6	−0.382219
$582$	−178768.	−0.0218767
$583$	2.12450e7	2.58872
$584$	−2.41658e6	−0.293204
$585$	0	0
$586$	8.77859e6	1.05604
$587$	−5.86783e6	−0.702882	−0.351441	−	0.936210i	$-0.614308\pi$
$587$	−5.86783e6	−0.702882	−0.351441	+	0.936210i	$0.614308\pi$
$588$	1.01520e6	0.121091
$589$	1.67023e7	1.98376
$590$	4.15149e6	0.490991
$591$	826470.	0.0973326
$592$	2.70719e6	0.317479
$593$	−1.28187e7	−1.49694	−0.748472	−	0.663166i	$-0.769212\pi$
$593$	−1.28187e7	−1.49694	−0.748472	+	0.663166i	$0.769212\pi$
$594$	1.78096e6	0.207104
$595$	9.85410e6	1.14110
$596$	−1.45112e6	−0.167336
$597$	5.06062e6	0.581123
$598$	0	0
$599$	−8.82262e6	−1.00469	−0.502343	−	0.864668i	$-0.667529\pi$
$599$	−8.82262e6	−1.00469	−0.502343	+	0.864668i	$0.667529\pi$
$600$	2.54511e6	0.288621
$601$	8.16061e6	0.921587	0.460793	−	0.887507i	$-0.347565\pi$
$601$	8.16061e6	0.921587	0.460793	+	0.887507i	$0.347565\pi$
$602$	−2.39499e6	−0.269347
$603$	3.70155e6	0.414563
$604$	−1.66862e6	−0.186107
$605$	1.84104e7	2.04491
$606$	4.52179e6	0.500182
$607$	8.03055e6	0.884654	0.442327	−	0.896854i	$-0.354153\pi$
$607$	8.03055e6	0.884654	0.442327	+	0.896854i	$0.354153\pi$
$608$	2.32155e6	0.254695
$609$	−6.81823e6	−0.744953
$610$	1.57727e7	1.71626
$611$	0	0
$612$	1.48859e6	0.160656
$613$	3.99383e6	0.429278	0.214639	−	0.976693i	$-0.431143\pi$
$613$	3.99383e6	0.429278	0.214639	+	0.976693i	$0.431143\pi$
$614$	334476.	0.0358051
$615$	−2.89158e6	−0.308282
$616$	−3.86104e6	−0.409970
$617$	1.20933e7	1.27888	0.639442	−	0.768840i	$-0.279166\pi$
$617$	1.20933e7	1.27888	0.639442	+	0.768840i	$0.279166\pi$
$618$	4.54866e6	0.479084
$619$	−1.31953e7	−1.38418	−0.692088	−	0.721813i	$-0.743309\pi$
$619$	−1.31953e7	−1.38418	−0.692088	+	0.721813i	$0.743309\pi$
$620$	−1.02378e7	−1.06962
$621$	315820.	0.0328633
$622$	1.96707e6	0.203865
$623$	5.83295e6	0.602100
$624$	0	0
$625$	−4.04979e6	−0.414699
$626$	−3.58788e6	−0.365933
$627$	1.24620e7	1.26596
$628$	−5.03070e6	−0.509014
$629$	1.21464e7	1.22412
$630$	−2.77966e6	−0.279023
$631$	1.16207e7	1.16188	0.580939	−	0.813947i	$-0.302686\pi$
$631$	1.16207e7	1.16188	0.580939	+	0.813947i	$0.302686\pi$
$632$	2.25965e6	0.225034
$633$	−5.85595e6	−0.580883
$634$	−1.26180e7	−1.24671
$635$	−2.80247e7	−2.75808
$636$	−5.00901e6	−0.491031
$637$	0	0
$638$	−1.87369e7	−1.82241
$639$	1.92998e6	0.186982
$640$	−1.42301e6	−0.137328
$641$	1.15298e7	1.10835	0.554173	−	0.832402i	$-0.313035\pi$
$641$	1.15298e7	1.10835	0.554173	+	0.832402i	$0.313035\pi$
$642$	1.19044e6	0.113991
$643$	2.90732e6	0.277310	0.138655	−	0.990341i	$-0.455722\pi$
$643$	2.90732e6	0.277310	0.138655	+	0.990341i	$0.455722\pi$
$644$	−684683.	−0.0650541
$645$	−4.73824e6	−0.448454
$646$	1.04162e7	0.982038
$647$	4.58122e6	0.430249	0.215125	−	0.976587i	$-0.430984\pi$
$647$	4.58122e6	0.430249	0.215125	+	0.976587i	$0.430984\pi$
$648$	−419904.	−0.0392837
$649$	−7.29829e6	−0.680157
$650$	0	0
$651$	6.54935e6	0.605684
$652$	2.25171e6	0.207441
$653$	1.95066e7	1.79019	0.895096	−	0.445874i	$-0.147107\pi$
$653$	1.95066e7	1.79019	0.895096	+	0.445874i	$0.147107\pi$
$654$	−5.31598e6	−0.486003
$655$	−3.10827e7	−2.83084
$656$	946987.	0.0859181
$657$	3.05849e6	0.276435
$658$	−3.45353e6	−0.310955
$659$	8.41225e6	0.754568	0.377284	−	0.926098i	$-0.376858\pi$
$659$	8.41225e6	0.754568	0.377284	+	0.926098i	$0.376858\pi$
$660$	−7.63867e6	−0.682587
$661$	1.64620e7	1.46548	0.732739	−	0.680510i	$-0.238242\pi$
$661$	1.64620e7	1.46548	0.732739	+	0.680510i	$0.238242\pi$
$662$	−2.38879e6	−0.211852
$663$	0	0
$664$	2.01500e6	0.177360
$665$	−1.94503e7	−1.70558
$666$	−3.42629e6	−0.299322
$667$	−3.32265e6	−0.289181
$668$	1.74310e6	0.151141
$669$	2.72515e6	0.235410
$670$	−1.58762e7	−1.36634
$671$	−2.77284e7	−2.37748
$672$	910332.	0.0777637
$673$	−9.88194e6	−0.841016	−0.420508	−	0.907289i	$-0.638148\pi$
$673$	−9.88194e6	−0.841016	−0.420508	+	0.907289i	$0.638148\pi$
$674$	1.44723e7	1.22712
$675$	−3.22115e6	−0.272114
$676$	0	0
$677$	−731933.	−0.0613761	−0.0306881	−	0.999529i	$-0.509770\pi$
$677$	−731933.	−0.0613761	−0.0306881	+	0.999529i	$0.509770\pi$
$678$	4.25200e6	0.355238
$679$	−490506.	−0.0408291
$680$	−6.38468e6	−0.529501
$681$	6.50872e6	0.537809
$682$	1.79980e7	1.48171
$683$	−6.46151e6	−0.530008	−0.265004	−	0.964247i	$-0.585373\pi$
$683$	−6.46151e6	−0.530008	−0.265004	+	0.964247i	$0.585373\pi$
$684$	−2.93822e6	−0.240129
$685$	−3.01439e7	−2.45455
$686$	9.42614e6	0.764757
$687$	−1.25440e7	−1.01402
$688$	1.55176e6	0.124984
$689$	0	0
$690$	−1.35458e6	−0.108313
$691$	−1.16211e7	−0.925877	−0.462939	−	0.886390i	$-0.653205\pi$
$691$	−1.16211e7	−0.925877	−0.462939	+	0.886390i	$0.653205\pi$
$692$	−6.41901e6	−0.509569
$693$	4.88662e6	0.386523
$694$	6.51570e6	0.513526
$695$	−8.94852e6	−0.702731
$696$	4.41768e6	0.345678
$697$	4.24888e6	0.331278
$698$	1.04056e7	0.808404
$699$	−2.87446e6	−0.222517
$700$	6.98330e6	0.538661
$701$	1.39904e6	0.107531	0.0537655	−	0.998554i	$-0.482878\pi$
$701$	1.39904e6	0.107531	0.0537655	+	0.998554i	$0.482878\pi$
$702$	0	0
$703$	−2.39750e7	−1.82966
$704$	2.50165e6	0.190237
$705$	−6.83246e6	−0.517731
$706$	5.21763e6	0.393968
$707$	1.24069e7	0.933504
$708$	1.72075e6	0.129013
$709$	−1.84802e7	−1.38067	−0.690336	−	0.723489i	$-0.742537\pi$
$709$	−1.84802e7	−1.38067	−0.690336	+	0.723489i	$0.742537\pi$
$710$	−8.27781e6	−0.616268
$711$	−2.85987e6	−0.212164
$712$	−3.77930e6	−0.279390
$713$	3.19162e6	0.235118
$714$	4.08442e6	0.299837
$715$	0	0
$716$	3.35256e6	0.244396
$717$	−1.37038e7	−0.995505
$718$	−854694.	−0.0618728
$719$	−7.61846e6	−0.549598	−0.274799	−	0.961502i	$-0.588611\pi$
$719$	−7.61846e6	−0.549598	−0.274799	+	0.961502i	$0.588611\pi$
$720$	1.80100e6	0.129474
$721$	1.24807e7	0.894128
$722$	−1.06554e7	−0.760721
$723$	−5.47055e6	−0.389211
$724$	−3.78044e6	−0.268038
$725$	3.38888e7	2.39448
$726$	7.63091e6	0.537322
$727$	−2.55002e7	−1.78940	−0.894699	−	0.446670i	$-0.852610\pi$
$727$	−2.55002e7	−1.78940	−0.894699	+	0.446670i	$0.852610\pi$
$728$	0	0
$729$	531441.	0.0370370
$730$	−1.31181e7	−0.911094
$731$	6.96235e6	0.481906
$732$	6.53763e6	0.450965
$733$	−1.27470e7	−0.876293	−0.438147	−	0.898903i	$-0.644365\pi$
$733$	−1.27470e7	−0.876293	−0.438147	+	0.898903i	$0.644365\pi$
$734$	−4.62678e6	−0.316985
$735$	5.51090e6	0.376274
$736$	443621.	0.0301868
$737$	2.79103e7	1.89276
$738$	−1.19853e6	−0.0810043
$739$	1.54752e7	1.04238	0.521190	−	0.853441i	$-0.325488\pi$
$739$	1.54752e7	1.04238	0.521190	+	0.853441i	$0.325488\pi$
$740$	1.46956e7	0.986526
$741$	0	0
$742$	−1.37438e7	−0.916425
$743$	−3.52596e6	−0.234318	−0.117159	−	0.993113i	$-0.537379\pi$
$743$	−3.52596e6	−0.234318	−0.117159	+	0.993113i	$0.537379\pi$
$744$	−4.24347e6	−0.281053
$745$	−7.87723e6	−0.519976
$746$	−7.91931e6	−0.521003
$747$	−2.55023e6	−0.167216
$748$	1.12242e7	0.733505
$749$	3.26635e6	0.212744
$750$	4.04471e6	0.262563
$751$	−8.20700e6	−0.530988	−0.265494	−	0.964113i	$-0.585535\pi$
$751$	−8.20700e6	−0.530988	−0.265494	+	0.964113i	$0.585535\pi$
$752$	2.23762e6	0.144292
$753$	−9.45443e6	−0.607642
$754$	0	0
$755$	−9.05785e6	−0.578306
$756$	−1.15214e6	−0.0733163
$757$	−1.27038e7	−0.805736	−0.402868	−	0.915258i	$-0.631987\pi$
$757$	−1.27038e7	−0.805736	−0.402868	+	0.915258i	$0.631987\pi$
$758$	−1.54462e7	−0.976446
$759$	2.38134e6	0.150043
$760$	1.26022e7	0.791433
$761$	1.41876e7	0.888073	0.444037	−	0.896009i	$-0.353546\pi$
$761$	1.41876e7	0.888073	0.444037	+	0.896009i	$0.353546\pi$
$762$	−1.16160e7	−0.724716
$763$	−1.45861e7	−0.907041
$764$	8.15551e6	0.505496
$765$	8.08061e6	0.499219
$766$	−6.22072e6	−0.383062
$767$	0	0
$768$	−589824.	−0.0360844
$769$	1.10700e7	0.675045	0.337522	−	0.941318i	$-0.390411\pi$
$769$	1.10700e7	0.675045	0.337522	+	0.941318i	$0.390411\pi$
$770$	−2.09591e7	−1.27393
$771$	2.12616e6	0.128813
$772$	−930349.	−0.0561827
$773$	−5.17639e6	−0.311586	−0.155793	−	0.987790i	$-0.549793\pi$
$773$	−5.17639e6	−0.311586	−0.155793	+	0.987790i	$0.549793\pi$
$774$	−1.96395e6	−0.117836
$775$	−3.25523e7	−1.94683
$776$	317810.	0.0189458
$777$	−9.40110e6	−0.558633
$778$	1.14100e7	0.675826
$779$	−8.38655e6	−0.495153
$780$	0	0
$781$	1.45524e7	0.853701
$782$	1.99041e6	0.116393
$783$	−5.59113e6	−0.325908
$784$	−1.80481e6	−0.104868
$785$	−2.73085e7	−1.58170
$786$	−1.28835e7	−0.743835
$787$	1.43044e7	0.823252	0.411626	−	0.911353i	$-0.364961\pi$
$787$	1.43044e7	0.823252	0.411626	+	0.911353i	$0.364961\pi$
$788$	−1.46928e6	−0.0842925
$789$	−8.36068e6	−0.478133
$790$	1.22662e7	0.699266
$791$	1.16667e7	0.662990
$792$	−3.16615e6	−0.179357
$793$	0	0
$794$	5.00886e6	0.281960
$795$	−2.71907e7	−1.52582
$796$	−8.99666e6	−0.503267
$797$	1.27192e7	0.709275	0.354638	−	0.935004i	$-0.384604\pi$
$797$	1.27192e7	0.709275	0.354638	+	0.935004i	$0.384604\pi$
$798$	−8.06193e6	−0.448159
$799$	1.00396e7	0.556351
$800$	−4.52463e6	−0.249953
$801$	4.78317e6	0.263412
$802$	−1.68020e7	−0.922412
$803$	2.30615e7	1.26212
$804$	−6.58053e6	−0.359022
$805$	−3.71671e6	−0.202148
$806$	0	0
$807$	−7.44885e6	−0.402629
$808$	−8.03873e6	−0.433171
$809$	5.39790e6	0.289970	0.144985	−	0.989434i	$-0.453687\pi$
$809$	5.39790e6	0.289970	0.144985	+	0.989434i	$0.453687\pi$
$810$	−2.27939e6	−0.122069
$811$	−1.46019e7	−0.779576	−0.389788	−	0.920905i	$-0.627452\pi$
$811$	−1.46019e7	−0.779576	−0.389788	+	0.920905i	$0.627452\pi$
$812$	1.21213e7	0.645148
$813$	−5.94703e6	−0.315554
$814$	−2.58348e7	−1.36661
$815$	1.22231e7	0.644597
$816$	−2.64638e6	−0.139132
$817$	−1.37425e7	−0.720293
$818$	−2.60278e6	−0.136005
$819$	0	0
$820$	5.14059e6	0.266980
$821$	−2.73956e7	−1.41848	−0.709240	−	0.704967i	$-0.750962\pi$
$821$	−2.73956e7	−1.41848	−0.709240	+	0.704967i	$0.750962\pi$
$822$	−1.24943e7	−0.644960
$823$	−2.28175e7	−1.17427	−0.587136	−	0.809488i	$-0.699745\pi$
$823$	−2.28175e7	−1.17427	−0.587136	+	0.809488i	$0.699745\pi$
$824$	−8.08650e6	−0.414899
$825$	−2.42880e7	−1.24239
$826$	4.72141e6	0.240781
$827$	1.17556e7	0.597698	0.298849	−	0.954300i	$-0.403397\pi$
$827$	1.17556e7	0.597698	0.298849	+	0.954300i	$0.403397\pi$
$828$	−561458.	−0.0284604
$829$	2.04885e7	1.03544	0.517718	−	0.855551i	$-0.326781\pi$
$829$	2.04885e7	1.03544	0.517718	+	0.855551i	$0.326781\pi$
$830$	1.09382e7	0.551123
$831$	−1.24447e7	−0.625149
$832$	0	0
$833$	−8.09770e6	−0.404342
$834$	−3.70907e6	−0.184650
$835$	9.46218e6	0.469651
$836$	−2.21547e7	−1.09635
$837$	5.37064e6	0.264979
$838$	2.72804e7	1.34196
$839$	2.38084e7	1.16769	0.583843	−	0.811867i	$-0.301549\pi$
$839$	2.38084e7	1.16769	0.583843	+	0.811867i	$0.301549\pi$
$840$	4.94161e6	0.241641
$841$	3.83114e7	1.86783
$842$	−1.24664e7	−0.605982
$843$	−1.30404e7	−0.632006
$844$	1.04106e7	0.503059
$845$	0	0
$846$	−2.83198e6	−0.136039
$847$	2.09378e7	1.00282
$848$	8.90491e6	0.425246
$849$	1.09840e7	0.522988
$850$	−2.03008e7	−0.963755
$851$	−4.58133e6	−0.216854
$852$	−3.43107e6	−0.161931
$853$	9.87851e6	0.464857	0.232428	−	0.972614i	$-0.425333\pi$
$853$	9.87851e6	0.464857	0.232428	+	0.972614i	$0.425333\pi$
$854$	1.79380e7	0.841648
$855$	−1.59497e7	−0.746170
$856$	−2.11634e6	−0.0987189
$857$	1.97784e6	0.0919898	0.0459949	−	0.998942i	$-0.485354\pi$
$857$	1.97784e6	0.0919898	0.0459949	+	0.998942i	$0.485354\pi$
$858$	0	0
$859$	−5.87858e6	−0.271825	−0.135913	−	0.990721i	$-0.543397\pi$
$859$	−5.87858e6	−0.271825	−0.135913	+	0.990721i	$0.543397\pi$
$860$	8.42354e6	0.388372
$861$	−3.28855e6	−0.151181
$862$	−1.95285e7	−0.895160
$863$	1.96178e7	0.896651	0.448325	−	0.893870i	$-0.352021\pi$
$863$	1.96178e7	0.896651	0.448325	+	0.893870i	$0.352021\pi$
$864$	746496.	0.0340207
$865$	−3.48447e7	−1.58342
$866$	1.45710e7	0.660229
$867$	905089.	0.0408925
$868$	−1.16433e7	−0.524537
$869$	−2.15639e7	−0.968675
$870$	2.39808e7	1.07415
$871$	0	0
$872$	9.45063e6	0.420891
$873$	−402228.	−0.0178623
$874$	−3.92872e6	−0.173969
$875$	1.10979e7	0.490030
$876$	−5.43731e6	−0.239400
$877$	1.90004e7	0.834189	0.417095	−	0.908863i	$-0.363048\pi$
$877$	1.90004e7	0.834189	0.417095	+	0.908863i	$0.363048\pi$
$878$	−6.80489e6	−0.297910
$879$	1.97518e7	0.862254
$880$	1.35799e7	0.591138
$881$	−6.81302e6	−0.295733	−0.147866	−	0.989007i	$-0.547241\pi$
$881$	−6.81302e6	−0.295733	−0.147866	+	0.989007i	$0.547241\pi$
$882$	2.28421e6	0.0988701
$883$	−2.84750e7	−1.22903	−0.614513	−	0.788906i	$-0.710648\pi$
$883$	−2.84750e7	−1.22903	−0.614513	+	0.788906i	$0.710648\pi$
$884$	0	0
$885$	9.34085e6	0.400893
$886$	2.34023e7	1.00155
$887$	3.43992e7	1.46804	0.734022	−	0.679126i	$-0.237641\pi$
$887$	3.43992e7	1.46804	0.734022	+	0.679126i	$0.237641\pi$
$888$	6.09118e6	0.259220
$889$	−3.18721e7	−1.35256
$890$	−2.05154e7	−0.868170
$891$	4.00716e6	0.169099
$892$	−4.84472e6	−0.203871
$893$	−1.98164e7	−0.831564
$894$	−3.26503e6	−0.136629
$895$	1.81989e7	0.759430
$896$	−1.61837e6	−0.0673453
$897$	0	0
$898$	6.25596e6	0.258883
$899$	−5.65029e7	−2.33169
$900$	5.72649e6	0.235658
$901$	3.99540e7	1.63964
$902$	−9.03713e6	−0.369840
$903$	−5.38872e6	−0.219921
$904$	−7.55912e6	−0.307645
$905$	−2.05216e7	−0.832894
$906$	−3.75438e6	−0.151956
$907$	−2.13493e7	−0.861719	−0.430859	−	0.902419i	$-0.641789\pi$
$907$	−2.13493e7	−0.861719	−0.430859	+	0.902419i	$0.641789\pi$
$908$	−1.15711e7	−0.465756
$909$	1.01740e7	0.408397
$910$	0	0
$911$	−7.55882e6	−0.301758	−0.150879	−	0.988552i	$-0.548210\pi$
$911$	−7.55882e6	−0.301758	−0.150879	+	0.988552i	$0.548210\pi$
$912$	5.22350e6	0.207957
$913$	−1.92292e7	−0.763457
$914$	1.34779e6	0.0533651
$915$	3.54886e7	1.40132
$916$	2.23005e7	0.878166
$917$	−3.53499e7	−1.38824
$918$	3.34933e6	0.131175
$919$	−4.56027e7	−1.78115	−0.890577	−	0.454832i	$-0.849699\pi$
$919$	−4.56027e7	−1.78115	−0.890577	+	0.454832i	$0.849699\pi$
$920$	2.40814e6	0.0938019
$921$	752572.	0.0292347
$922$	1.55670e7	0.603082
$923$	0	0
$924$	−8.68733e6	−0.334739
$925$	4.67264e7	1.79559
$926$	2.53686e7	0.972229
$927$	1.02345e7	0.391171
$928$	−7.85366e6	−0.299366
$929$	4.74157e7	1.80253	0.901266	−	0.433267i	$-0.142639\pi$
$929$	4.74157e7	1.80253	0.901266	+	0.433267i	$0.142639\pi$
$930$	−2.30351e7	−0.873338
$931$	1.59834e7	0.604360
$932$	5.11016e6	0.192706
$933$	4.42590e6	0.166455
$934$	9.94765e6	0.373124
$935$	6.09292e7	2.27928
$936$	0	0
$937$	4.02496e7	1.49766	0.748829	−	0.662764i	$-0.230617\pi$
$937$	4.02496e7	1.49766	0.748829	+	0.662764i	$0.230617\pi$
$938$	−1.80558e7	−0.670052
$939$	−8.07272e6	−0.298783
$940$	1.21466e7	0.448368
$941$	−8.70389e6	−0.320434	−0.160217	−	0.987082i	$-0.551219\pi$
$941$	−8.70389e6	−0.320434	−0.160217	+	0.987082i	$0.551219\pi$
$942$	−1.13191e7	−0.415608
$943$	−1.60257e6	−0.0586864
$944$	−3.05911e6	−0.111729
$945$	−6.25423e6	−0.227821
$946$	−1.48085e7	−0.538002
$947$	−9.78178e6	−0.354440	−0.177220	−	0.984171i	$-0.556710\pi$
$947$	−9.78178e6	−0.354440	−0.177220	+	0.984171i	$0.556710\pi$
$948$	5.08421e6	0.183740
$949$	0	0
$950$	4.00703e7	1.44050
$951$	−2.83904e7	−1.01794
$952$	−7.26119e6	−0.259666
$953$	1.18962e7	0.424303	0.212151	−	0.977237i	$-0.431953\pi$
$953$	1.18962e7	0.424303	0.212151	+	0.977237i	$0.431953\pi$
$954$	−1.12703e7	−0.400925
$955$	4.42711e7	1.57077
$956$	2.43623e7	0.862133
$957$	−4.21581e7	−1.48799
$958$	2.12431e7	0.747834
$959$	−3.42821e7	−1.20371
$960$	−3.20178e6	−0.112128
$961$	2.56455e7	0.895781
$962$	0	0
$963$	2.67849e6	0.0930731
$964$	9.72543e6	0.337067
$965$	−5.05028e6	−0.174581
$966$	−1.54054e6	−0.0531165
$967$	−7.21381e6	−0.248084	−0.124042	−	0.992277i	$-0.539586\pi$
$967$	−7.21381e6	−0.248084	−0.124042	+	0.992277i	$0.539586\pi$
$968$	−1.35661e7	−0.465335
$969$	2.34365e7	0.801830
$970$	1.72519e6	0.0588717
$971$	9.17081e6	0.312147	0.156074	−	0.987745i	$-0.450116\pi$
$971$	9.17081e6	0.312147	0.156074	+	0.987745i	$0.450116\pi$
$972$	−944784.	−0.0320750
$973$	−1.01770e7	−0.344618
$974$	−3.09402e7	−1.04502
$975$	0	0
$976$	−1.16224e7	−0.390547
$977$	−2.18053e7	−0.730845	−0.365423	−	0.930842i	$-0.619076\pi$
$977$	−2.18053e7	−0.730845	−0.365423	+	0.930842i	$0.619076\pi$
$978$	5.06635e6	0.169375
$979$	3.60660e7	1.20265
$980$	−9.79716e6	−0.325863
$981$	−1.19610e7	−0.396820
$982$	−1.28996e6	−0.0426872
$983$	−1.96569e7	−0.648831	−0.324415	−	0.945915i	$-0.605168\pi$
$983$	−1.96569e7	−0.648831	−0.324415	+	0.945915i	$0.605168\pi$
$984$	2.13072e6	0.0701518
$985$	−7.97579e6	−0.261929
$986$	−3.52373e7	−1.15428
$987$	−7.77044e6	−0.253894
$988$	0	0
$989$	−2.62602e6	−0.0853703
$990$	−1.71870e7	−0.557330
$991$	2.15229e7	0.696173	0.348087	−	0.937462i	$-0.386832\pi$
$991$	2.15229e7	0.696173	0.348087	+	0.937462i	$0.386832\pi$
$992$	7.54394e6	0.243399
$993$	−5.37477e6	−0.172976
$994$	−9.41421e6	−0.302216
$995$	−4.88372e7	−1.56384
$996$	4.53375e6	0.144814
$997$	−1.16375e6	−0.0370783	−0.0185392	−	0.999828i	$-0.505902\pi$
$997$	−1.16375e6	−0.0370783	−0.0185392	+	0.999828i	$0.505902\pi$
$998$	1.65861e6	0.0527131
$999$	−7.70915e6	−0.244395

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.6.a.o.1.3		3
13.5	odd	4		78.6.b.a.25.4	yes	6
13.8	odd	4		78.6.b.a.25.3	✓	6
13.12	even	2		1014.6.a.q.1.1		3
39.5	even	4		234.6.b.c.181.3		6
39.8	even	4		234.6.b.c.181.4		6
52.31	even	4		624.6.c.d.337.1		6
52.47	even	4		624.6.c.d.337.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.6.b.a.25.3	✓	6	13.8	odd	4
78.6.b.a.25.4	yes	6	13.5	odd	4
234.6.b.c.181.3		6	39.5	even	4
234.6.b.c.181.4		6	39.8	even	4
624.6.c.d.337.1		6	52.31	even	4
624.6.c.d.337.6		6	52.47	even	4
1014.6.a.o.1.3		3	1.1	even	1	trivial
1014.6.a.q.1.1		3	13.12	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1014.a (trivial)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +86.8538 q^{5} +36.0000 q^{6} +98.7774 q^{7} -64.0000 q^{8} +81.0000 q^{9} -347.415 q^{10} +610.754 q^{11} -144.000 q^{12} -395.109 q^{14} -781.684 q^{15} +256.000 q^{16} +1148.60 q^{17} -324.000 q^{18} -2267.14 q^{19} +1389.66 q^{20} -888.996 q^{21} -2443.02 q^{22} -433.224 q^{23} +576.000 q^{24} +4418.59 q^{25} -729.000 q^{27} +1580.44 q^{28} +7669.59 q^{29} +3126.74 q^{30} -7367.13 q^{31} -1024.00 q^{32} -5496.79 q^{33} -4594.42 q^{34} +8579.19 q^{35} +1296.00 q^{36} +10575.0 q^{37} +9068.57 q^{38} -5558.65 q^{40} +3699.17 q^{41} +3555.98 q^{42} +6061.57 q^{43} +9772.07 q^{44} +7035.16 q^{45} +1732.89 q^{46} +8740.69 q^{47} -2304.00 q^{48} -7050.03 q^{49} -17674.4 q^{50} -10337.4 q^{51} +34784.8 q^{53} +2916.00 q^{54} +53046.3 q^{55} -6321.75 q^{56} +20404.3 q^{57} -30678.4 q^{58} -11949.6 q^{59} -12507.0 q^{60} -45400.2 q^{61} +29468.5 q^{62} +8000.97 q^{63} +4096.00 q^{64} +21987.2 q^{66} +45698.1 q^{67} +18377.7 q^{68} +3899.01 q^{69} -34316.8 q^{70} +23826.9 q^{71} -5184.00 q^{72} +37759.1 q^{73} -42299.9 q^{74} -39767.3 q^{75} -36274.3 q^{76} +60328.7 q^{77} -35307.0 q^{79} +22234.6 q^{80} +6561.00 q^{81} -14796.7 q^{82} -31484.4 q^{83} -14223.9 q^{84} +99760.7 q^{85} -24246.3 q^{86} -69026.3 q^{87} -39088.3 q^{88} +59051.5 q^{89} -28140.6 q^{90} -6931.58 q^{92} +66304.2 q^{93} -34962.7 q^{94} -196910. q^{95} +9216.00 q^{96} -4965.78 q^{97} +28200.1 q^{98} +49471.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 12 q^{2} - 27 q^{3} + 48 q^{4} + 40 q^{5} + 108 q^{6} + 170 q^{7} - 192 q^{8} + 243 q^{9} - 160 q^{10} + 162 q^{11} - 432 q^{12} - 680 q^{14} - 360 q^{15} + 768 q^{16} + 418 q^{17} - 972 q^{18} + 66 q^{19}+ \cdots + 13122 q^{99}+O(q^{100}) \) 3 * q - 12 * q^2 - 27 * q^3 + 48 * q^4 + 40 * q^5 + 108 * q^6 + 170 * q^7 - 192 * q^8 + 243 * q^9 - 160 * q^10 + 162 * q^11 - 432 * q^12 - 680 * q^14 - 360 * q^15 + 768 * q^16 + 418 * q^17 - 972 * q^18 + 66 * q^19 + 640 * q^20 - 1530 * q^21 - 648 * q^22 + 208 * q^23 + 1728 * q^24 - 359 * q^25 - 2187 * q^27 + 2720 * q^28 + 9394 * q^29 + 1440 * q^30 - 7418 * q^31 - 3072 * q^32 - 1458 * q^33 - 1672 * q^34 + 3056 * q^35 + 3888 * q^36 + 7780 * q^37 - 264 * q^38 - 2560 * q^40 + 18140 * q^41 + 6120 * q^42 + 12100 * q^43 + 2592 * q^44 + 3240 * q^45 - 832 * q^46 + 4086 * q^47 - 6912 * q^48 + 1519 * q^49 + 1436 * q^50 - 3762 * q^51 - 21198 * q^53 + 8748 * q^54 + 62328 * q^55 - 10880 * q^56 - 594 * q^57 - 37576 * q^58 - 1718 * q^59 - 5760 * q^60 - 1598 * q^61 + 29672 * q^62 + 13770 * q^63 + 12288 * q^64 + 5832 * q^66 + 106810 * q^67 + 6688 * q^68 - 1872 * q^69 - 12224 * q^70 - 68694 * q^71 - 15552 * q^72 + 66976 * q^73 - 31120 * q^74 + 3231 * q^75 + 1056 * q^76 + 57012 * q^77 - 84664 * q^79 + 10240 * q^80 + 19683 * q^81 - 72560 * q^82 - 40898 * q^83 - 24480 * q^84 + 81328 * q^85 - 48400 * q^86 - 84546 * q^87 - 10368 * q^88 + 13524 * q^89 - 12960 * q^90 + 3328 * q^92 + 66762 * q^93 - 16344 * q^94 - 283584 * q^95 + 27648 * q^96 - 103224 * q^97 - 6076 * q^98 + 13122 * q^99

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