LMFDB - Embedded newform 825.6.a.f.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,6,Mod(1,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("825.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	825.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:	$132.316651346$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.307532.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 76x + 168 $ x^3 - x^2 - 76*x + 168
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 165)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-9.21967$ of defining polynomial
Character	$\chi$	$=$	825.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+7.21967 q^{2} +9.00000 q^{3} +20.1236 q^{4} +64.9770 q^{6} -147.570 q^{7} -85.7438 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+7.21967 q^{2} +9.00000 q^{3} +20.1236 q^{4} +64.9770 q^{6} -147.570 q^{7} -85.7438 q^{8} +81.0000 q^{9} +121.000 q^{11} +181.112 q^{12} +1124.39 q^{13} -1065.40 q^{14} -1263.00 q^{16} -1019.99 q^{17} +584.793 q^{18} -13.7131 q^{19} -1328.13 q^{21} +873.580 q^{22} +2116.94 q^{23} -771.694 q^{24} +8117.69 q^{26} +729.000 q^{27} -2969.63 q^{28} +3120.98 q^{29} -9628.99 q^{31} -6374.61 q^{32} +1089.00 q^{33} -7363.96 q^{34} +1630.01 q^{36} +3121.52 q^{37} -99.0039 q^{38} +10119.5 q^{39} -5884.38 q^{41} -9588.63 q^{42} -20522.3 q^{43} +2434.95 q^{44} +15283.6 q^{46} -24718.5 q^{47} -11367.0 q^{48} +4969.81 q^{49} -9179.87 q^{51} +22626.7 q^{52} -22761.1 q^{53} +5263.14 q^{54} +12653.2 q^{56} -123.418 q^{57} +22532.4 q^{58} -14533.5 q^{59} +43984.9 q^{61} -69518.1 q^{62} -11953.1 q^{63} -5606.68 q^{64} +7862.22 q^{66} +31488.3 q^{67} -20525.8 q^{68} +19052.5 q^{69} -29173.2 q^{71} -6945.24 q^{72} -49583.0 q^{73} +22536.3 q^{74} -275.956 q^{76} -17855.9 q^{77} +73059.2 q^{78} -85075.4 q^{79} +6561.00 q^{81} -42483.3 q^{82} -77321.9 q^{83} -26726.7 q^{84} -148164. q^{86} +28088.8 q^{87} -10375.0 q^{88} +70217.7 q^{89} -165925. q^{91} +42600.5 q^{92} -86660.9 q^{93} -178459. q^{94} -57371.5 q^{96} +21080.0 q^{97} +35880.4 q^{98} +9801.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 7 q^{2} + 27 q^{3} + 73 q^{4} - 63 q^{6} - 92 q^{7} - 231 q^{8} + 243 q^{9}+O(q^{10}) $ 3 * q - 7 * q^2 + 27 * q^3 + 73 * q^4 - 63 * q^6 - 92 * q^7 - 231 * q^8 + 243 * q^9	\( 3 q - 7 q^{2} + 27 q^{3} + 73 q^{4} - 63 q^{6} - 92 q^{7} - 231 q^{8} + 243 q^{9} + 363 q^{11} + 657 q^{12} + 90 q^{13} - 784 q^{14} - 415 q^{16} - 1934 q^{17} - 567 q^{18} + 2084 q^{19} - 828 q^{21} - 847 q^{22} - 1220 q^{23} - 2079 q^{24} + 17062 q^{26} + 2187 q^{27} - 11120 q^{28} + 4402 q^{29} - 10688 q^{31} - 12439 q^{32} + 3267 q^{33} - 4094 q^{34} + 5913 q^{36} + 8190 q^{37} - 13792 q^{38} + 810 q^{39} + 5974 q^{41} - 7056 q^{42} - 18868 q^{43} + 8833 q^{44} + 46220 q^{46} - 55500 q^{47} - 3735 q^{48} + 1907 q^{49} - 17406 q^{51} - 27330 q^{52} - 9206 q^{53} - 5103 q^{54} + 73248 q^{56} + 18756 q^{57} - 15366 q^{58} - 59196 q^{59} + 79902 q^{61} - 64616 q^{62} - 7452 q^{63} + 2129 q^{64} - 7623 q^{66} - 4468 q^{67} + 1218 q^{68} - 10980 q^{69} - 75164 q^{71} - 18711 q^{72} + 61290 q^{73} - 56766 q^{74} + 37816 q^{76} - 11132 q^{77} + 153558 q^{78} - 83564 q^{79} + 19683 q^{81} - 147410 q^{82} - 74764 q^{83} - 100080 q^{84} - 253432 q^{86} + 39618 q^{87} - 27951 q^{88} + 37342 q^{89} - 126488 q^{91} - 148164 q^{92} - 96192 q^{93} + 59252 q^{94} - 111951 q^{96} - 33486 q^{97} + 95249 q^{98} + 29403 q^{99}+O(q^{100}) \) 3 * q - 7 * q^2 + 27 * q^3 + 73 * q^4 - 63 * q^6 - 92 * q^7 - 231 * q^8 + 243 * q^9 + 363 * q^11 + 657 * q^12 + 90 * q^13 - 784 * q^14 - 415 * q^16 - 1934 * q^17 - 567 * q^18 + 2084 * q^19 - 828 * q^21 - 847 * q^22 - 1220 * q^23 - 2079 * q^24 + 17062 * q^26 + 2187 * q^27 - 11120 * q^28 + 4402 * q^29 - 10688 * q^31 - 12439 * q^32 + 3267 * q^33 - 4094 * q^34 + 5913 * q^36 + 8190 * q^37 - 13792 * q^38 + 810 * q^39 + 5974 * q^41 - 7056 * q^42 - 18868 * q^43 + 8833 * q^44 + 46220 * q^46 - 55500 * q^47 - 3735 * q^48 + 1907 * q^49 - 17406 * q^51 - 27330 * q^52 - 9206 * q^53 - 5103 * q^54 + 73248 * q^56 + 18756 * q^57 - 15366 * q^58 - 59196 * q^59 + 79902 * q^61 - 64616 * q^62 - 7452 * q^63 + 2129 * q^64 - 7623 * q^66 - 4468 * q^67 + 1218 * q^68 - 10980 * q^69 - 75164 * q^71 - 18711 * q^72 + 61290 * q^73 - 56766 * q^74 + 37816 * q^76 - 11132 * q^77 + 153558 * q^78 - 83564 * q^79 + 19683 * q^81 - 147410 * q^82 - 74764 * q^83 - 100080 * q^84 - 253432 * q^86 + 39618 * q^87 - 27951 * q^88 + 37342 * q^89 - 126488 * q^91 - 148164 * q^92 - 96192 * q^93 + 59252 * q^94 - 111951 * q^96 - 33486 * q^97 + 95249 * q^98 + 29403 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	7.21967	1.27627	0.638134	−	0.769925i	$-0.279706\pi$
$2$	7.21967	1.27627	0.638134	+	0.769925i	$0.279706\pi$
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	20.1236	0.628862
$5$	0	0
$5$	0	0
$6$	64.9770	0.736854
$7$	−147.570	−1.13829	−0.569144	−	0.822238i	$-0.692725\pi$
$7$	−147.570	−1.13829	−0.569144	+	0.822238i	$0.692725\pi$
$8$	−85.7438	−0.473672
$9$	81.0000	0.333333
$10$	0	0
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	181.112	0.363074
$13$	1124.39	1.84526	0.922628	−	0.385690i	$-0.126037\pi$
$13$	1124.39	1.84526	0.922628	+	0.385690i	$0.126037\pi$
$14$	−1065.40	−1.45276
$15$	0	0
$16$	−1263.00	−1.23339
$17$	−1019.99	−0.855996	−0.427998	−	0.903780i	$-0.640781\pi$
$17$	−1019.99	−0.855996	−0.427998	+	0.903780i	$0.640781\pi$
$18$	584.793	0.425423
$19$	−13.7131	−0.00871467	−0.00435734	−	0.999991i	$-0.501387\pi$
$19$	−13.7131	−0.00871467	−0.00435734	+	0.999991i	$0.501387\pi$
$20$	0	0
$21$	−1328.13	−0.657191
$22$	873.580	0.384810
$23$	2116.94	0.834430	0.417215	−	0.908808i	$-0.363006\pi$
$23$	2116.94	0.834430	0.417215	+	0.908808i	$0.363006\pi$
$24$	−771.694	−0.273475
$25$	0	0
$26$	8117.69	2.35504
$27$	729.000	0.192450
$28$	−2969.63	−0.715826
$29$	3120.98	0.689122	0.344561	−	0.938764i	$-0.388028\pi$
$29$	3120.98	0.689122	0.344561	+	0.938764i	$0.388028\pi$
$30$	0	0
$31$	−9628.99	−1.79960	−0.899801	−	0.436301i	$-0.856288\pi$
$31$	−9628.99	−1.79960	−0.899801	+	0.436301i	$0.856288\pi$
$32$	−6374.61	−1.10047
$33$	1089.00	0.174078
$34$	−7363.96	−1.09248
$35$	0	0
$36$	1630.01	0.209621
$37$	3121.52	0.374854	0.187427	−	0.982279i	$-0.439985\pi$
$37$	3121.52	0.374854	0.187427	+	0.982279i	$0.439985\pi$
$38$	−99.0039	−0.0111223
$39$	10119.5	1.06536
$40$	0	0
$41$	−5884.38	−0.546690	−0.273345	−	0.961916i	$-0.588130\pi$
$41$	−5884.38	−0.546690	−0.273345	+	0.961916i	$0.588130\pi$
$42$	−9588.63	−0.838752
$43$	−20522.3	−1.69260	−0.846302	−	0.532704i	$-0.821176\pi$
$43$	−20522.3	−1.69260	−0.846302	+	0.532704i	$0.821176\pi$
$44$	2434.95	0.189609
$45$	0	0
$46$	15283.6	1.06496
$47$	−24718.5	−1.63222	−0.816108	−	0.577899i	$-0.803873\pi$
$47$	−24718.5	−1.63222	−0.816108	+	0.577899i	$0.803873\pi$
$48$	−11367.0	−0.712101
$49$	4969.81	0.295699
$50$	0	0
$51$	−9179.87	−0.494210
$52$	22626.7	1.16041
$53$	−22761.1	−1.11302	−0.556511	−	0.830840i	$-0.687860\pi$
$53$	−22761.1	−1.11302	−0.556511	+	0.830840i	$0.687860\pi$
$54$	5263.14	0.245618
$55$	0	0
$56$	12653.2	0.539175
$57$	−123.418	−0.00503142
$58$	22532.4	0.879505
$59$	−14533.5	−0.543553	−0.271776	−	0.962360i	$-0.587611\pi$
$59$	−14533.5	−0.543553	−0.271776	+	0.962360i	$0.587611\pi$
$60$	0	0
$61$	43984.9	1.51349	0.756743	−	0.653712i	$-0.226789\pi$
$61$	43984.9	1.51349	0.756743	+	0.653712i	$0.226789\pi$
$62$	−69518.1	−2.29677
$63$	−11953.1	−0.379429
$64$	−5606.68	−0.171102
$65$	0	0
$66$	7862.22	0.222170
$67$	31488.3	0.856964	0.428482	−	0.903550i	$-0.359049\pi$
$67$	31488.3	0.856964	0.428482	+	0.903550i	$0.359049\pi$
$68$	−20525.8	−0.538303
$69$	19052.5	0.481758
$70$	0	0
$71$	−29173.2	−0.686812	−0.343406	−	0.939187i	$-0.611581\pi$
$71$	−29173.2	−0.686812	−0.343406	+	0.939187i	$0.611581\pi$
$72$	−6945.24	−0.157891
$73$	−49583.0	−1.08899	−0.544497	−	0.838763i	$-0.683279\pi$
$73$	−49583.0	−1.08899	−0.544497	+	0.838763i	$0.683279\pi$
$74$	22536.3	0.478414
$75$	0	0
$76$	−275.956	−0.00548033
$77$	−17855.9	−0.343207
$78$	73059.2	1.35968
$79$	−85075.4	−1.53369	−0.766843	−	0.641835i	$-0.778174\pi$
$79$	−85075.4	−1.53369	−0.766843	+	0.641835i	$0.778174\pi$
$80$	0	0
$81$	6561.00	0.111111
$82$	−42483.3	−0.697724
$83$	−77321.9	−1.23199	−0.615995	−	0.787750i	$-0.711246\pi$
$83$	−77321.9	−1.23199	−0.615995	+	0.787750i	$0.711246\pi$
$84$	−26726.7	−0.413282
$85$	0	0
$86$	−148164.	−2.16022
$87$	28088.8	0.397865
$88$	−10375.0	−0.142817
$89$	70217.7	0.939661	0.469831	−	0.882757i	$-0.344315\pi$
$89$	70217.7	0.939661	0.469831	+	0.882757i	$0.344315\pi$
$90$	0	0
$91$	−165925.	−2.10043
$92$	42600.5	0.524741
$93$	−86660.9	−1.03900
$94$	−178459.	−2.08315
$95$	0	0
$96$	−57371.5	−0.635357
$97$	21080.0	0.227479	0.113739	−	0.993511i	$-0.463717\pi$
$97$	21080.0	0.227479	0.113739	+	0.993511i	$0.463717\pi$
$98$	35880.4	0.377391
$99$	9801.00	0.100504
$100$	0	0
$101$	−60279.4	−0.587984	−0.293992	−	0.955808i	$-0.594984\pi$
$101$	−60279.4	−0.587984	−0.293992	+	0.955808i	$0.594984\pi$
$102$	−66275.6	−0.630744
$103$	−83535.5	−0.775851	−0.387925	−	0.921691i	$-0.626808\pi$
$103$	−83535.5	−0.775851	−0.387925	+	0.921691i	$0.626808\pi$
$104$	−96409.0	−0.874046
$105$	0	0
$106$	−164328.	−1.42052
$107$	−159288.	−1.34500	−0.672502	−	0.740095i	$-0.734781\pi$
$107$	−159288.	−1.34500	−0.672502	+	0.740095i	$0.734781\pi$
$108$	14670.1	0.121025
$109$	−31166.3	−0.251258	−0.125629	−	0.992077i	$-0.540095\pi$
$109$	−31166.3	−0.251258	−0.125629	+	0.992077i	$0.540095\pi$
$110$	0	0
$111$	28093.7	0.216422
$112$	186380.	1.40396
$113$	−141850.	−1.04504	−0.522521	−	0.852626i	$-0.675008\pi$
$113$	−141850.	−1.04504	−0.522521	+	0.852626i	$0.675008\pi$
$114$	−891.035	−0.00642144
$115$	0	0
$116$	62805.3	0.433363
$117$	91075.2	0.615086
$118$	−104927.	−0.693719
$119$	150519.	0.974370
$120$	0	0
$121$	14641.0	0.0909091
$122$	317556.	1.93162
$123$	−52959.5	−0.315632
$124$	−193770.	−1.13170
$125$	0	0
$126$	−86297.7	−0.484254
$127$	92350.0	0.508075	0.254037	−	0.967194i	$-0.418241\pi$
$127$	92350.0	0.508075	0.254037	+	0.967194i	$0.418241\pi$
$128$	163509.	0.882098
$129$	−184701.	−0.977225
$130$	0	0
$131$	210539.	1.07190	0.535949	−	0.844250i	$-0.319954\pi$
$131$	210539.	1.07190	0.535949	+	0.844250i	$0.319954\pi$
$132$	21914.6	0.109471
$133$	2023.64	0.00991981
$134$	227335.	1.09372
$135$	0	0
$136$	87457.4	0.405461
$137$	−23859.0	−0.108605	−0.0543027	−	0.998525i	$-0.517294\pi$
$137$	−23859.0	−0.108605	−0.0543027	+	0.998525i	$0.517294\pi$
$138$	137553.	0.614853
$139$	292430.	1.28377	0.641883	−	0.766803i	$-0.278154\pi$
$139$	292430.	1.28377	0.641883	+	0.766803i	$0.278154\pi$
$140$	0	0
$141$	−222467.	−0.942361
$142$	−210621.	−0.876557
$143$	136051.	0.556366
$144$	−102303.	−0.411132
$145$	0	0
$146$	−357973.	−1.38985
$147$	44728.3	0.170722
$148$	62816.2	0.235731
$149$	350530.	1.29348	0.646740	−	0.762710i	$-0.276132\pi$
$149$	350530.	1.29348	0.646740	+	0.762710i	$0.276132\pi$
$150$	0	0
$151$	−513284.	−1.83196	−0.915979	−	0.401225i	$-0.868584\pi$
$151$	−513284.	−1.83196	−0.915979	+	0.401225i	$0.868584\pi$
$152$	1175.81	0.00412790
$153$	−82618.8	−0.285332
$154$	−128914.	−0.438024
$155$	0	0
$156$	203640.	0.669964
$157$	−154810.	−0.501244	−0.250622	−	0.968085i	$-0.580635\pi$
$157$	−154810.	−0.501244	−0.250622	+	0.968085i	$0.580635\pi$
$158$	−614216.	−1.95740
$159$	−204850.	−0.642604
$160$	0	0
$161$	−312397.	−0.949821
$162$	47368.2	0.141808
$163$	−184152.	−0.542883	−0.271442	−	0.962455i	$-0.587500\pi$
$163$	−184152.	−0.542883	−0.271442	+	0.962455i	$0.587500\pi$
$164$	−118415.	−0.343793
$165$	0	0
$166$	−558238.	−1.57235
$167$	72082.3	0.200003	0.100002	−	0.994987i	$-0.468115\pi$
$167$	72082.3	0.200003	0.100002	+	0.994987i	$0.468115\pi$
$168$	113879.	0.311293
$169$	892949.	2.40497
$170$	0	0
$171$	−1110.76	−0.00290489
$172$	−412983.	−1.06441
$173$	374895.	0.952345	0.476173	−	0.879352i	$-0.342024\pi$
$173$	374895.	0.952345	0.476173	+	0.879352i	$0.342024\pi$
$174$	202792.	0.507782
$175$	0	0
$176$	−152823.	−0.371882
$177$	−130802.	−0.313820
$178$	506948.	1.19926
$179$	354545.	0.827064	0.413532	−	0.910490i	$-0.364295\pi$
$179$	354545.	0.827064	0.413532	+	0.910490i	$0.364295\pi$
$180$	0	0
$181$	403999.	0.916609	0.458305	−	0.888795i	$-0.348457\pi$
$181$	403999.	0.916609	0.458305	+	0.888795i	$0.348457\pi$
$182$	−1.19792e6	−2.68072
$183$	395864.	0.873812
$184$	−181515.	−0.395246
$185$	0	0
$186$	−625663.	−1.32604
$187$	−123418.	−0.258093
$188$	−497425.	−1.02644
$189$	−107578.	−0.219064
$190$	0	0
$191$	181282.	0.359560	0.179780	−	0.983707i	$-0.442461\pi$
$191$	181282.	0.359560	0.179780	+	0.983707i	$0.442461\pi$
$192$	−50460.2	−0.0987860
$193$	−683762.	−1.32133	−0.660665	−	0.750681i	$-0.729726\pi$
$193$	−683762.	−1.32133	−0.660665	+	0.750681i	$0.729726\pi$
$194$	152190.	0.290324
$195$	0	0
$196$	100010.	0.185954
$197$	442098.	0.811620	0.405810	−	0.913958i	$-0.366990\pi$
$197$	442098.	0.811620	0.405810	+	0.913958i	$0.366990\pi$
$198$	70760.0	0.128270
$199$	925615.	1.65691	0.828453	−	0.560059i	$-0.189222\pi$
$199$	925615.	1.65691	0.828453	+	0.560059i	$0.189222\pi$
$200$	0	0
$201$	283395.	0.494768
$202$	−435197.	−0.750425
$203$	−460562.	−0.784419
$204$	−184732.	−0.310790
$205$	0	0
$206$	−603099.	−0.990194
$207$	171472.	0.278143
$208$	−1.42009e6	−2.27593
$209$	−1659.28	−0.00262757
$210$	0	0
$211$	605880.	0.936873	0.468436	−	0.883497i	$-0.344818\pi$
$211$	605880.	0.936873	0.468436	+	0.883497i	$0.344818\pi$
$212$	−458035.	−0.699938
$213$	−262559.	−0.396531
$214$	−1.15001e6	−1.71659
$215$	0	0
$216$	−62507.2	−0.0911582
$217$	1.42095e6	2.04846
$218$	−225011.	−0.320673
$219$	−446247.	−0.628731
$220$	0	0
$221$	−1.14686e6	−1.57953
$222$	202827.	0.276213
$223$	−581147.	−0.782571	−0.391286	−	0.920269i	$-0.627970\pi$
$223$	−581147.	−0.782571	−0.391286	+	0.920269i	$0.627970\pi$
$224$	940699.	1.25265
$225$	0	0
$226$	−1.02411e6	−1.33376
$227$	−1.51651e6	−1.95335	−0.976674	−	0.214726i	$-0.931114\pi$
$227$	−1.51651e6	−1.95335	−0.976674	+	0.214726i	$0.931114\pi$
$228$	−2483.61	−0.00316407
$229$	916540.	1.15495	0.577474	−	0.816409i	$-0.304038\pi$
$229$	916540.	1.15495	0.577474	+	0.816409i	$0.304038\pi$
$230$	0	0
$231$	−160703.	−0.198150
$232$	−267605.	−0.326418
$233$	650940.	0.785509	0.392755	−	0.919643i	$-0.371522\pi$
$233$	650940.	0.785509	0.392755	+	0.919643i	$0.371522\pi$
$234$	657533.	0.785014
$235$	0	0
$236$	−292467.	−0.341820
$237$	−765679.	−0.885474
$238$	1.08670e6	1.24356
$239$	−1.06473e6	−1.20572	−0.602860	−	0.797847i	$-0.705972\pi$
$239$	−1.06473e6	−1.20572	−0.602860	+	0.797847i	$0.705972\pi$
$240$	0	0
$241$	−1.21958e6	−1.35259	−0.676297	−	0.736629i	$-0.736417\pi$
$241$	−1.21958e6	−1.35259	−0.676297	+	0.736629i	$0.736417\pi$
$242$	105703.	0.116024
$243$	59049.0	0.0641500
$244$	885133.	0.951774
$245$	0	0
$246$	−382350.	−0.402831
$247$	−15418.8	−0.0160808
$248$	825625.	0.852420
$249$	−695897.	−0.711290
$250$	0	0
$251$	1.82454e6	1.82797	0.913987	−	0.405743i	$-0.132987\pi$
$251$	1.82454e6	1.82797	0.913987	+	0.405743i	$0.132987\pi$
$252$	−240540.	−0.238609
$253$	256150.	0.251590
$254$	666736.	0.648440
$255$	0	0
$256$	1.35990e6	1.29690
$257$	475038.	0.448637	0.224319	−	0.974516i	$-0.427984\pi$
$257$	475038.	0.448637	0.224319	+	0.974516i	$0.427984\pi$
$258$	−1.33348e6	−1.24720
$259$	−460642.	−0.426691
$260$	0	0
$261$	252799.	0.229707
$262$	1.52002e6	1.36803
$263$	1.07504e6	0.958376	0.479188	−	0.877712i	$-0.340931\pi$
$263$	1.07504e6	0.958376	0.479188	+	0.877712i	$0.340931\pi$
$264$	−93375.0	−0.0824557
$265$	0	0
$266$	14610.0	0.0126603
$267$	631959.	0.542514
$268$	633658.	0.538912
$269$	180662.	0.152225	0.0761126	−	0.997099i	$-0.475749\pi$
$269$	180662.	0.152225	0.0761126	+	0.997099i	$0.475749\pi$
$270$	0	0
$271$	302884.	0.250526	0.125263	−	0.992124i	$-0.460023\pi$
$271$	302884.	0.250526	0.125263	+	0.992124i	$0.460023\pi$
$272$	1.28824e6	1.05578
$273$	−1.49333e6	−1.21269
$274$	−172254.	−0.138610
$275$	0	0
$276$	383404.	0.302959
$277$	−1.08898e6	−0.852745	−0.426372	−	0.904548i	$-0.640209\pi$
$277$	−1.08898e6	−0.852745	−0.426372	+	0.904548i	$0.640209\pi$
$278$	2.11125e6	1.63843
$279$	−779948.	−0.599867
$280$	0	0
$281$	−942590.	−0.712127	−0.356063	−	0.934462i	$-0.615881\pi$
$281$	−942590.	−0.712127	−0.356063	+	0.934462i	$0.615881\pi$
$282$	−1.60614e6	−1.20271
$283$	−848952.	−0.630111	−0.315055	−	0.949073i	$-0.602023\pi$
$283$	−848952.	−0.630111	−0.315055	+	0.949073i	$0.602023\pi$
$284$	−587069.	−0.431910
$285$	0	0
$286$	982240.	0.710072
$287$	868357.	0.622291
$288$	−516343.	−0.366824
$289$	−379486.	−0.267271
$290$	0	0
$291$	189720.	0.131335
$292$	−997788.	−0.684827
$293$	−628367.	−0.427606	−0.213803	−	0.976877i	$-0.568585\pi$
$293$	−628367.	−0.427606	−0.213803	+	0.976877i	$0.568585\pi$
$294$	322923.	0.217887
$295$	0	0
$296$	−267651.	−0.177558
$297$	88209.0	0.0580259
$298$	2.53071e6	1.65083
$299$	2.38026e6	1.53974
$300$	0	0
$301$	3.02847e6	1.92667
$302$	−3.70574e6	−2.33807
$303$	−542514.	−0.339473
$304$	17319.6	0.0107486
$305$	0	0
$306$	−596480.	−0.364160
$307$	−1.88248e6	−1.13994	−0.569972	−	0.821664i	$-0.693046\pi$
$307$	−1.88248e6	−1.13994	−0.569972	+	0.821664i	$0.693046\pi$
$308$	−359325.	−0.215830
$309$	−751820.	−0.447938
$310$	0	0
$311$	−1.53497e6	−0.899908	−0.449954	−	0.893052i	$-0.648560\pi$
$311$	−1.53497e6	−0.899908	−0.449954	+	0.893052i	$0.648560\pi$
$312$	−867681.	−0.504631
$313$	2.22901e6	1.28603	0.643015	−	0.765854i	$-0.277683\pi$
$313$	2.22901e6	1.28603	0.643015	+	0.765854i	$0.277683\pi$
$314$	−1.11767e6	−0.639722
$315$	0	0
$316$	−1.71202e6	−0.964477
$317$	−1.00659e6	−0.562605	−0.281303	−	0.959619i	$-0.590766\pi$
$317$	−1.00659e6	−0.562605	−0.281303	+	0.959619i	$0.590766\pi$
$318$	−1.47895e6	−0.820135
$319$	377639.	0.207778
$320$	0	0
$321$	−1.43359e6	−0.776539
$322$	−2.25540e6	−1.21223
$323$	13987.2	0.00745973
$324$	132031.	0.0698736
$325$	0	0
$326$	−1.32951e6	−0.692865
$327$	−280497.	−0.145064
$328$	504549.	0.258952
$329$	3.64770e6	1.85793
$330$	0	0
$331$	−2.96963e6	−1.48982	−0.744908	−	0.667167i	$-0.767507\pi$
$331$	−2.96963e6	−1.48982	−0.744908	+	0.667167i	$0.767507\pi$
$332$	−1.55599e6	−0.774752
$333$	252843.	0.124951
$334$	520410.	0.255258
$335$	0	0
$336$	1.67742e6	0.810575
$337$	−69782.5	−0.0334712	−0.0167356	−	0.999860i	$-0.505327\pi$
$337$	−69782.5	−0.0334712	−0.0167356	+	0.999860i	$0.505327\pi$
$338$	6.44680e6	3.06939
$339$	−1.27665e6	−0.603356
$340$	0	0
$341$	−1.16511e6	−0.542600
$342$	−8019.32	−0.00370742
$343$	1.74681e6	0.801697
$344$	1.75966e6	0.801739
$345$	0	0
$346$	2.70662e6	1.21545
$347$	1.04233e6	0.464708	0.232354	−	0.972631i	$-0.425357\pi$
$347$	1.04233e6	0.464708	0.232354	+	0.972631i	$0.425357\pi$
$348$	565248.	0.250202
$349$	−3.75012e6	−1.64809	−0.824047	−	0.566522i	$-0.808289\pi$
$349$	−3.75012e6	−1.64809	−0.824047	+	0.566522i	$0.808289\pi$
$350$	0	0
$351$	819677.	0.355120
$352$	−771328.	−0.331805
$353$	−800792.	−0.342045	−0.171022	−	0.985267i	$-0.554707\pi$
$353$	−800792.	−0.342045	−0.171022	+	0.985267i	$0.554707\pi$
$354$	−944346.	−0.400519
$355$	0	0
$356$	1.41303e6	0.590917
$357$	1.35467e6	0.562553
$358$	2.55970e6	1.05556
$359$	267422.	0.109512	0.0547559	−	0.998500i	$-0.482562\pi$
$359$	267422.	0.109512	0.0547559	+	0.998500i	$0.482562\pi$
$360$	0	0
$361$	−2.47591e6	−0.999924
$362$	2.91674e6	1.16984
$363$	131769.	0.0524864
$364$	−3.33901e6	−1.32088
$365$	0	0
$366$	2.85800e6	1.11522
$367$	−2.63334e6	−1.02057	−0.510283	−	0.860007i	$-0.670459\pi$
$367$	−2.63334e6	−1.02057	−0.510283	+	0.860007i	$0.670459\pi$
$368$	−2.67369e6	−1.02918
$369$	−476635.	−0.182230
$370$	0	0
$371$	3.35885e6	1.26694
$372$	−1.74393e6	−0.653388
$373$	3.93389e6	1.46403	0.732015	−	0.681289i	$-0.238580\pi$
$373$	3.93389e6	1.46403	0.732015	+	0.681289i	$0.238580\pi$
$374$	−891039.	−0.329395
$375$	0	0
$376$	2.11946e6	0.773135
$377$	3.50918e6	1.27161
$378$	−776679.	−0.279584
$379$	−1.80355e6	−0.644956	−0.322478	−	0.946577i	$-0.604516\pi$
$379$	−1.80355e6	−0.644956	−0.322478	+	0.946577i	$0.604516\pi$
$380$	0	0
$381$	831150.	0.293337
$382$	1.30880e6	0.458895
$383$	−2.19398e6	−0.764252	−0.382126	−	0.924110i	$-0.624808\pi$
$383$	−2.19398e6	−0.764252	−0.382126	+	0.924110i	$0.624808\pi$
$384$	1.47158e6	0.509280
$385$	0	0
$386$	−4.93653e6	−1.68637
$387$	−1.66231e6	−0.564201
$388$	424204.	0.143053
$389$	354221.	0.118686	0.0593430	−	0.998238i	$-0.481099\pi$
$389$	354221.	0.118686	0.0593430	+	0.998238i	$0.481099\pi$
$390$	0	0
$391$	−2.15925e6	−0.714268
$392$	−426130.	−0.140064
$393$	1.89485e6	0.618861
$394$	3.19180e6	1.03584
$395$	0	0
$396$	197231.	0.0632030
$397$	−168373.	−0.0536162	−0.0268081	−	0.999641i	$-0.508534\pi$
$397$	−168373.	−0.0536162	−0.0268081	+	0.999641i	$0.508534\pi$
$398$	6.68263e6	2.11466
$399$	18212.7	0.00572720
$400$	0	0
$401$	−4.59458e6	−1.42687	−0.713436	−	0.700721i	$-0.752862\pi$
$401$	−4.59458e6	−1.42687	−0.713436	+	0.700721i	$0.752862\pi$
$402$	2.04602e6	0.631457
$403$	−1.08267e7	−3.32073
$404$	−1.21304e6	−0.369761
$405$	0	0
$406$	−3.32510e6	−1.00113
$407$	377704.	0.113023
$408$	787117.	0.234093
$409$	3.59299e6	1.06206	0.531028	−	0.847354i	$-0.321806\pi$
$409$	3.59299e6	1.06206	0.531028	+	0.847354i	$0.321806\pi$
$410$	0	0
$411$	−214731.	−0.0627033
$412$	−1.68103e6	−0.487903
$413$	2.14471e6	0.618719
$414$	1.23797e6	0.354986
$415$	0	0
$416$	−7.16752e6	−2.03065
$417$	2.63187e6	0.741182
$418$	−11979.5	−0.00335349
$419$	−4.10701e6	−1.14285	−0.571427	−	0.820653i	$-0.693610\pi$
$419$	−4.10701e6	−1.14285	−0.571427	+	0.820653i	$0.693610\pi$
$420$	0	0
$421$	5.36278e6	1.47464	0.737318	−	0.675546i	$-0.236092\pi$
$421$	5.36278e6	1.47464	0.737318	+	0.675546i	$0.236092\pi$
$422$	4.37425e6	1.19570
$423$	−2.00220e6	−0.544072
$424$	1.95162e6	0.527208
$425$	0	0
$426$	−1.89559e6	−0.506081
$427$	−6.49083e6	−1.72278
$428$	−3.20545e6	−0.845822
$429$	1.22446e6	0.321218
$430$	0	0
$431$	2.52160e6	0.653857	0.326929	−	0.945049i	$-0.393986\pi$
$431$	2.52160e6	0.653857	0.326929	+	0.945049i	$0.393986\pi$
$432$	−920724.	−0.237367
$433$	−2.99694e6	−0.768171	−0.384085	−	0.923298i	$-0.625483\pi$
$433$	−2.99694e6	−0.768171	−0.384085	+	0.923298i	$0.625483\pi$
$434$	1.02588e7	2.61439
$435$	0	0
$436$	−627179.	−0.158007
$437$	−29029.8	−0.00727178
$438$	−3.22175e6	−0.802430
$439$	1.93618e6	0.479495	0.239748	−	0.970835i	$-0.422935\pi$
$439$	1.93618e6	0.479495	0.239748	+	0.970835i	$0.422935\pi$
$440$	0	0
$441$	402554.	0.0985662
$442$	−8.27992e6	−2.01591
$443$	7.28132e6	1.76279	0.881395	−	0.472380i	$-0.156605\pi$
$443$	7.28132e6	1.76279	0.881395	+	0.472380i	$0.156605\pi$
$444$	565346.	0.136100
$445$	0	0
$446$	−4.19569e6	−0.998771
$447$	3.15477e6	0.746791
$448$	827377.	0.194764
$449$	6.15007e6	1.43967	0.719837	−	0.694143i	$-0.244216\pi$
$449$	6.15007e6	1.43967	0.719837	+	0.694143i	$0.244216\pi$
$450$	0	0
$451$	−712011.	−0.164833
$452$	−2.85454e6	−0.657188
$453$	−4.61956e6	−1.05768
$454$	−1.09487e7	−2.49300
$455$	0	0
$456$	10582.3	0.00238324
$457$	5.60231e6	1.25481	0.627403	−	0.778695i	$-0.284118\pi$
$457$	5.60231e6	1.25481	0.627403	+	0.778695i	$0.284118\pi$
$458$	6.61711e6	1.47402
$459$	−743570.	−0.164737
$460$	0	0
$461$	2.85697e6	0.626113	0.313057	−	0.949734i	$-0.398647\pi$
$461$	2.85697e6	0.626113	0.313057	+	0.949734i	$0.398647\pi$
$462$	−1.16022e6	−0.252893
$463$	−2.42615e6	−0.525976	−0.262988	−	0.964799i	$-0.584708\pi$
$463$	−2.42615e6	−0.525976	−0.262988	+	0.964799i	$0.584708\pi$
$464$	−3.94179e6	−0.849959
$465$	0	0
$466$	4.69957e6	1.00252
$467$	−167522.	−0.0355451	−0.0177726	−	0.999842i	$-0.505657\pi$
$467$	−167522.	−0.0355451	−0.0177726	+	0.999842i	$0.505657\pi$
$468$	1.83276e6	0.386804
$469$	−4.64672e6	−0.975471
$470$	0	0
$471$	−1.39329e6	−0.289393
$472$	1.24616e6	0.257466
$473$	−2.48320e6	−0.510339
$474$	−5.52795e6	−1.13010
$475$	0	0
$476$	3.02898e6	0.612744
$477$	−1.84365e6	−0.371008
$478$	−7.68702e6	−1.53882
$479$	5.39034e6	1.07344	0.536719	−	0.843761i	$-0.319663\pi$
$479$	5.39034e6	1.07344	0.536719	+	0.843761i	$0.319663\pi$
$480$	0	0
$481$	3.50979e6	0.691701
$482$	−8.80496e6	−1.72627
$483$	−2.81157e6	−0.548379
$484$	294629.	0.0571693
$485$	0	0
$486$	426314.	0.0818727
$487$	−1.38574e6	−0.264764	−0.132382	−	0.991199i	$-0.542263\pi$
$487$	−1.38574e6	−0.264764	−0.132382	+	0.991199i	$0.542263\pi$
$488$	−3.77143e6	−0.716896
$489$	−1.65736e6	−0.313434
$490$	0	0
$491$	−3.39592e6	−0.635703	−0.317851	−	0.948141i	$-0.602961\pi$
$491$	−3.39592e6	−0.635703	−0.317851	+	0.948141i	$0.602961\pi$
$492$	−1.06573e6	−0.198489
$493$	−3.18336e6	−0.589886
$494$	−111319.	−0.0205234
$495$	0	0
$496$	1.21614e7	2.21962
$497$	4.30508e6	0.781790
$498$	−5.02414e6	−0.907797
$499$	2.83293e6	0.509313	0.254657	−	0.967032i	$-0.418038\pi$
$499$	2.83293e6	0.509313	0.254657	+	0.967032i	$0.418038\pi$
$500$	0	0
$501$	648741.	0.115472
$502$	1.31726e7	2.33299
$503$	−9.23328e6	−1.62718	−0.813591	−	0.581437i	$-0.802491\pi$
$503$	−9.23328e6	−1.62718	−0.813591	+	0.581437i	$0.802491\pi$
$504$	1.02491e6	0.179725
$505$	0	0
$506$	1.84932e6	0.321096
$507$	8.03654e6	1.38851
$508$	1.85841e6	0.319509
$509$	−5.70039e6	−0.975238	−0.487619	−	0.873057i	$-0.662134\pi$
$509$	−5.70039e6	−0.975238	−0.487619	+	0.873057i	$0.662134\pi$
$510$	0	0
$511$	7.31695e6	1.23959
$512$	4.58570e6	0.773091
$513$	−9996.84	−0.00167714
$514$	3.42961e6	0.572582
$515$	0	0
$516$	−3.71684e6	−0.614540
$517$	−2.99094e6	−0.492132
$518$	−3.32568e6	−0.544573
$519$	3.37406e6	0.549837
$520$	0	0
$521$	−1.35063e6	−0.217994	−0.108997	−	0.994042i	$-0.534764\pi$
$521$	−1.35063e6	−0.217994	−0.108997	+	0.994042i	$0.534764\pi$
$522$	1.82513e6	0.293168
$523$	−440837.	−0.0704731	−0.0352366	−	0.999379i	$-0.511218\pi$
$523$	−440837.	−0.0704731	−0.0352366	+	0.999379i	$0.511218\pi$
$524$	4.23679e6	0.674076
$525$	0	0
$526$	7.76144e6	1.22314
$527$	9.82143e6	1.54045
$528$	−1.37540e6	−0.214706
$529$	−1.95489e6	−0.303727
$530$	0	0
$531$	−1.17722e6	−0.181184
$532$	40722.8	0.00623819
$533$	−6.61632e6	−1.00878
$534$	4.56253e6	0.692393
$535$	0	0
$536$	−2.69993e6	−0.405919
$537$	3.19091e6	0.477506
$538$	1.30432e6	0.194280
$539$	601347.	0.0891565
$540$	0	0
$541$	7.01375e6	1.03028	0.515142	−	0.857105i	$-0.327739\pi$
$541$	7.01375e6	1.03028	0.515142	+	0.857105i	$0.327739\pi$
$542$	2.18672e6	0.319738
$543$	3.63599e6	0.529205
$544$	6.50201e6	0.941999
$545$	0	0
$546$	−1.07813e7	−1.54771
$547$	1.01822e7	1.45503	0.727517	−	0.686090i	$-0.240674\pi$
$547$	1.01822e7	1.45503	0.727517	+	0.686090i	$0.240674\pi$
$548$	−480129.	−0.0682978
$549$	3.56277e6	0.504496
$550$	0	0
$551$	−42798.3	−0.00600547
$552$	−1.63363e6	−0.228195
$553$	1.25546e7	1.74578
$554$	−7.86205e6	−1.08833
$555$	0	0
$556$	5.88475e6	0.807311
$557$	1.09154e7	1.49074	0.745371	−	0.666650i	$-0.232272\pi$
$557$	1.09154e7	1.49074	0.745371	+	0.666650i	$0.232272\pi$
$558$	−5.63096e6	−0.765592
$559$	−2.30750e7	−3.12329
$560$	0	0
$561$	−1.11076e6	−0.149010
$562$	−6.80519e6	−0.908865
$563$	−1.25187e6	−0.166452	−0.0832261	−	0.996531i	$-0.526522\pi$
$563$	−1.25187e6	−0.166452	−0.0832261	+	0.996531i	$0.526522\pi$
$564$	−4.47683e6	−0.592615
$565$	0	0
$566$	−6.12915e6	−0.804191
$567$	−968205.	−0.126476
$568$	2.50142e6	0.325324
$569$	3.75381e6	0.486061	0.243031	−	0.970019i	$-0.421858\pi$
$569$	3.75381e6	0.486061	0.243031	+	0.970019i	$0.421858\pi$
$570$	0	0
$571$	−7.39573e6	−0.949273	−0.474636	−	0.880182i	$-0.657420\pi$
$571$	−7.39573e6	−0.949273	−0.474636	+	0.880182i	$0.657420\pi$
$572$	2.73783e6	0.349877
$573$	1.63154e6	0.207592
$574$	6.26925e6	0.794210
$575$	0	0
$576$	−454141.	−0.0570341
$577$	6.45181e6	0.806755	0.403378	−	0.915034i	$-0.367836\pi$
$577$	6.45181e6	0.806755	0.403378	+	0.915034i	$0.367836\pi$
$578$	−2.73976e6	−0.341109
$579$	−6.15386e6	−0.762871
$580$	0	0
$581$	1.14104e7	1.40236
$582$	1.36971e6	0.167619
$583$	−2.75410e6	−0.335589
$584$	4.25143e6	0.515826
$585$	0	0
$586$	−4.53660e6	−0.545741
$587$	−5.91956e6	−0.709078	−0.354539	−	0.935041i	$-0.615362\pi$
$587$	−5.91956e6	−0.709078	−0.354539	+	0.935041i	$0.615362\pi$
$588$	900093.	0.107360
$589$	132043.	0.0156829
$590$	0	0
$591$	3.97888e6	0.468589
$592$	−3.94247e6	−0.462343
$593$	2.54171e6	0.296817	0.148409	−	0.988926i	$-0.452585\pi$
$593$	2.54171e6	0.296817	0.148409	+	0.988926i	$0.452585\pi$
$594$	636840.	0.0740566
$595$	0	0
$596$	7.05393e6	0.813421
$597$	8.33053e6	0.956615
$598$	1.71847e7	1.96512
$599$	1.17309e7	1.33587	0.667935	−	0.744220i	$-0.267179\pi$
$599$	1.17309e7	1.33587	0.667935	+	0.744220i	$0.267179\pi$
$600$	0	0
$601$	−2.88018e6	−0.325262	−0.162631	−	0.986687i	$-0.551998\pi$
$601$	−2.88018e6	−0.325262	−0.162631	+	0.986687i	$0.551998\pi$
$602$	2.18646e7	2.45895
$603$	2.55055e6	0.285655
$604$	−1.03291e7	−1.15205
$605$	0	0
$606$	−3.91677e6	−0.433258
$607$	1.33207e7	1.46742	0.733712	−	0.679460i	$-0.237786\pi$
$607$	1.33207e7	1.46742	0.733712	+	0.679460i	$0.237786\pi$
$608$	87415.6	0.00959025
$609$	−4.14506e6	−0.452885
$610$	0	0
$611$	−2.77931e7	−3.01186
$612$	−1.66259e6	−0.179434
$613$	8.85926e6	0.952239	0.476120	−	0.879381i	$-0.342043\pi$
$613$	8.85926e6	0.952239	0.476120	+	0.879381i	$0.342043\pi$
$614$	−1.35908e7	−1.45487
$615$	0	0
$616$	1.53103e6	0.162567
$617$	−1.75148e7	−1.85222	−0.926110	−	0.377253i	$-0.876869\pi$
$617$	−1.75148e7	−1.85222	−0.926110	+	0.377253i	$0.876869\pi$
$618$	−5.42789e6	−0.571689
$619$	3.94768e6	0.414109	0.207055	−	0.978329i	$-0.433612\pi$
$619$	3.94768e6	0.414109	0.207055	+	0.978329i	$0.433612\pi$
$620$	0	0
$621$	1.54325e6	0.160586
$622$	−1.10820e7	−1.14852
$623$	−1.03620e7	−1.06960
$624$	−1.27808e7	−1.31401
$625$	0	0
$626$	1.60927e7	1.64132
$627$	−14933.6	−0.00151703
$628$	−3.11533e6	−0.315213
$629$	−3.18391e6	−0.320873
$630$	0	0
$631$	−5.78181e6	−0.578083	−0.289042	−	0.957317i	$-0.593337\pi$
$631$	−5.78181e6	−0.578083	−0.289042	+	0.957317i	$0.593337\pi$
$632$	7.29469e6	0.726464
$633$	5.45292e6	0.540904
$634$	−7.26723e6	−0.718035
$635$	0	0
$636$	−4.12232e6	−0.404109
$637$	5.58798e6	0.545640
$638$	2.72643e6	0.265181
$639$	−2.36303e6	−0.228937
$640$	0	0
$641$	−4.31966e6	−0.415245	−0.207623	−	0.978209i	$-0.566573\pi$
$641$	−4.31966e6	−0.415245	−0.207623	+	0.978209i	$0.566573\pi$
$642$	−1.03501e7	−0.991072
$643$	−1.95083e7	−1.86076	−0.930381	−	0.366593i	$-0.880524\pi$
$643$	−1.95083e7	−1.86076	−0.930381	+	0.366593i	$0.880524\pi$
$644$	−6.28654e6	−0.597306
$645$	0	0
$646$	100983.	0.00952062
$647$	1.08322e7	1.01732	0.508660	−	0.860967i	$-0.330141\pi$
$647$	1.08322e7	1.01732	0.508660	+	0.860967i	$0.330141\pi$
$648$	−562565.	−0.0526302
$649$	−1.75856e6	−0.163887
$650$	0	0
$651$	1.27885e7	1.18268
$652$	−3.70579e6	−0.341399
$653$	−1.83320e6	−0.168239	−0.0841197	−	0.996456i	$-0.526808\pi$
$653$	−1.83320e6	−0.168239	−0.0841197	+	0.996456i	$0.526808\pi$
$654$	−2.02510e6	−0.185140
$655$	0	0
$656$	7.43195e6	0.674285
$657$	−4.01622e6	−0.362998
$658$	2.63352e7	2.37122
$659$	1.77259e7	1.58999	0.794994	−	0.606618i	$-0.207474\pi$
$659$	1.77259e7	1.58999	0.794994	+	0.606618i	$0.207474\pi$
$660$	0	0
$661$	−5.89810e6	−0.525060	−0.262530	−	0.964924i	$-0.584557\pi$
$661$	−5.89810e6	−0.525060	−0.262530	+	0.964924i	$0.584557\pi$
$662$	−2.14398e7	−1.90141
$663$	−1.03217e7	−0.911943
$664$	6.62987e6	0.583559
$665$	0	0
$666$	1.82544e6	0.159471
$667$	6.60694e6	0.575024
$668$	1.45055e6	0.125775
$669$	−5.23032e6	−0.451818
$670$	0	0
$671$	5.32217e6	0.456333
$672$	8.46629e6	0.723219
$673$	6.98177e6	0.594193	0.297097	−	0.954847i	$-0.403982\pi$
$673$	6.98177e6	0.594193	0.297097	+	0.954847i	$0.403982\pi$
$674$	−503806.	−0.0427183
$675$	0	0
$676$	1.79693e7	1.51240
$677$	−5.68896e6	−0.477047	−0.238524	−	0.971137i	$-0.576663\pi$
$677$	−5.68896e6	−0.477047	−0.238524	+	0.971137i	$0.576663\pi$
$678$	−9.21700e6	−0.770044
$679$	−3.11076e6	−0.258936
$680$	0	0
$681$	−1.36486e7	−1.12777
$682$	−8.41169e6	−0.692504
$683$	−1.65539e6	−0.135784	−0.0678920	−	0.997693i	$-0.521627\pi$
$683$	−1.65539e6	−0.135784	−0.0678920	+	0.997693i	$0.521627\pi$
$684$	−22352.5	−0.00182678
$685$	0	0
$686$	1.26114e7	1.02318
$687$	8.24886e6	0.666810
$688$	2.59196e7	2.08765
$689$	−2.55923e7	−2.05381
$690$	0	0
$691$	−8.36041e6	−0.666090	−0.333045	−	0.942911i	$-0.608076\pi$
$691$	−8.36041e6	−0.666090	−0.333045	+	0.942911i	$0.608076\pi$
$692$	7.54423e6	0.598894
$693$	−1.44633e6	−0.114402
$694$	7.52524e6	0.593092
$695$	0	0
$696$	−2.40844e6	−0.188457
$697$	6.00199e6	0.467965
$698$	−2.70746e7	−2.10341
$699$	5.85846e6	0.453514
$700$	0	0
$701$	1.07851e7	0.828948	0.414474	−	0.910061i	$-0.363966\pi$
$701$	1.07851e7	0.828948	0.414474	+	0.910061i	$0.363966\pi$
$702$	5.91779e6	0.453228
$703$	−42805.7	−0.00326673
$704$	−678409.	−0.0515893
$705$	0	0
$706$	−5.78145e6	−0.436541
$707$	8.89541e6	0.669295
$708$	−2.63220e6	−0.197350
$709$	−1.37457e7	−1.02695	−0.513476	−	0.858104i	$-0.671642\pi$
$709$	−1.37457e7	−1.02695	−0.513476	+	0.858104i	$0.671642\pi$
$710$	0	0
$711$	−6.89111e6	−0.511229
$712$	−6.02073e6	−0.445091
$713$	−2.03840e7	−1.50164
$714$	9.78027e6	0.717968
$715$	0	0
$716$	7.13472e6	0.520109
$717$	−9.58260e6	−0.696122
$718$	1.93070e6	0.139767
$719$	2.23290e6	0.161082	0.0805409	−	0.996751i	$-0.474335\pi$
$719$	2.23290e6	0.161082	0.0805409	+	0.996751i	$0.474335\pi$
$720$	0	0
$721$	1.23273e7	0.883141
$722$	−1.78753e7	−1.27617
$723$	−1.09762e7	−0.780921
$724$	8.12991e6	0.576421
$725$	0	0
$726$	951328.	0.0669867
$727$	−7.70500e6	−0.540675	−0.270338	−	0.962766i	$-0.587135\pi$
$727$	−7.70500e6	−0.540675	−0.270338	+	0.962766i	$0.587135\pi$
$728$	1.42270e7	0.994916
$729$	531441.	0.0370370
$730$	0	0
$731$	2.09325e7	1.44886
$732$	7.96620e6	0.549507
$733$	5.23205e6	0.359676	0.179838	−	0.983696i	$-0.442443\pi$
$733$	5.23205e6	0.359676	0.179838	+	0.983696i	$0.442443\pi$
$734$	−1.90118e7	−1.30252
$735$	0	0
$736$	−1.34947e7	−0.918266
$737$	3.81009e6	0.258384
$738$	−3.44115e6	−0.232575
$739$	1.90698e7	1.28450	0.642252	−	0.766494i	$-0.278000\pi$
$739$	1.90698e7	1.28450	0.642252	+	0.766494i	$0.278000\pi$
$740$	0	0
$741$	−138769.	−0.00928426
$742$	2.42498e7	1.61696
$743$	−2.31407e7	−1.53781	−0.768907	−	0.639361i	$-0.779199\pi$
$743$	−2.31407e7	−1.53781	−0.768907	+	0.639361i	$0.779199\pi$
$744$	7.43063e6	0.492145
$745$	0	0
$746$	2.84013e7	1.86849
$747$	−6.26307e6	−0.410663
$748$	−2.48362e6	−0.162305
$749$	2.35061e7	1.53100
$750$	0	0
$751$	1.96879e7	1.27380	0.636898	−	0.770948i	$-0.280217\pi$
$751$	1.96879e7	1.27380	0.636898	+	0.770948i	$0.280217\pi$
$752$	3.12194e7	2.01317
$753$	1.64209e7	1.05538
$754$	2.53351e7	1.62291
$755$	0	0
$756$	−2.16486e6	−0.137761
$757$	8.22162e6	0.521456	0.260728	−	0.965412i	$-0.416037\pi$
$757$	8.22162e6	0.521456	0.260728	+	0.965412i	$0.416037\pi$
$758$	−1.30210e7	−0.823137
$759$	2.30535e6	0.145256
$760$	0	0
$761$	2.18719e6	0.136907	0.0684534	−	0.997654i	$-0.478194\pi$
$761$	2.18719e6	0.136907	0.0684534	+	0.997654i	$0.478194\pi$
$762$	6.00063e6	0.374377
$763$	4.59921e6	0.286004
$764$	3.64805e6	0.226114
$765$	0	0
$766$	−1.58398e7	−0.975391
$767$	−1.63413e7	−1.00299
$768$	1.22391e7	0.748764
$769$	3.97950e6	0.242668	0.121334	−	0.992612i	$-0.461283\pi$
$769$	3.97950e6	0.242668	0.121334	+	0.992612i	$0.461283\pi$
$770$	0	0
$771$	4.27534e6	0.259021
$772$	−1.37597e7	−0.830935
$773$	1.92979e7	1.16161	0.580807	−	0.814042i	$-0.302737\pi$
$773$	1.92979e7	1.16161	0.580807	+	0.814042i	$0.302737\pi$
$774$	−1.20013e7	−0.720072
$775$	0	0
$776$	−1.80748e6	−0.107750
$777$	−4.14578e6	−0.246350
$778$	2.55735e6	0.151475
$779$	80693.1	0.00476423
$780$	0	0
$781$	−3.52996e6	−0.207082
$782$	−1.55891e7	−0.911599
$783$	2.27519e6	0.132622
$784$	−6.27685e6	−0.364713
$785$	0	0
$786$	1.36802e7	0.789832
$787$	1.54391e7	0.888556	0.444278	−	0.895889i	$-0.353460\pi$
$787$	1.54391e7	0.888556	0.444278	+	0.895889i	$0.353460\pi$
$788$	8.89659e6	0.510397
$789$	9.67537e6	0.553318
$790$	0	0
$791$	2.09328e7	1.18956
$792$	−840375.	−0.0476058
$793$	4.94559e7	2.79277
$794$	−1.21560e6	−0.0684287
$795$	0	0
$796$	1.86267e7	1.04196
$797$	−2.66071e7	−1.48372	−0.741860	−	0.670555i	$-0.766056\pi$
$797$	−2.66071e7	−1.48372	−0.741860	+	0.670555i	$0.766056\pi$
$798$	131490.	0.00730945
$799$	2.52125e7	1.39717
$800$	0	0
$801$	5.68763e6	0.313220
$802$	−3.31713e7	−1.82107
$803$	−5.99954e6	−0.328344
$804$	5.70292e6	0.311141
$805$	0	0
$806$	−7.81651e7	−4.23814
$807$	1.62596e6	0.0878872
$808$	5.16858e6	0.278511
$809$	−3.15651e7	−1.69565	−0.847825	−	0.530276i	$-0.822088\pi$
$809$	−3.15651e7	−1.69565	−0.847825	+	0.530276i	$0.822088\pi$
$810$	0	0
$811$	3.50230e7	1.86982	0.934912	−	0.354880i	$-0.115478\pi$
$811$	3.50230e7	1.86982	0.934912	+	0.354880i	$0.115478\pi$
$812$	−9.26816e6	−0.493291
$813$	2.72595e6	0.144641
$814$	2.72690e6	0.144247
$815$	0	0
$816$	1.15941e7	0.609555
$817$	281424.	0.0147505
$818$	2.59402e7	1.35547
$819$	−1.34399e7	−0.700144
$820$	0	0
$821$	−6.00202e6	−0.310770	−0.155385	−	0.987854i	$-0.549662\pi$
$821$	−6.00202e6	−0.310770	−0.155385	+	0.987854i	$0.549662\pi$
$822$	−1.55029e6	−0.0800263
$823$	2.98462e7	1.53599	0.767996	−	0.640455i	$-0.221254\pi$
$823$	2.98462e7	1.53599	0.767996	+	0.640455i	$0.221254\pi$
$824$	7.16265e6	0.367499
$825$	0	0
$826$	1.54841e7	0.789652
$827$	3.81477e6	0.193956	0.0969782	−	0.995287i	$-0.469082\pi$
$827$	3.81477e6	0.193956	0.0969782	+	0.995287i	$0.469082\pi$
$828$	3.45064e6	0.174914
$829$	7.23404e6	0.365590	0.182795	−	0.983151i	$-0.441486\pi$
$829$	7.23404e6	0.365590	0.182795	+	0.983151i	$0.441486\pi$
$830$	0	0
$831$	−9.80079e6	−0.492332
$832$	−6.30407e6	−0.315728
$833$	−5.06913e6	−0.253117
$834$	1.90013e7	0.945948
$835$	0	0
$836$	−33390.7	−0.00165238
$837$	−7.01953e6	−0.346333
$838$	−2.96512e7	−1.45859
$839$	−2.18515e6	−0.107171	−0.0535853	−	0.998563i	$-0.517065\pi$
$839$	−2.18515e6	−0.107171	−0.0535853	+	0.998563i	$0.517065\pi$
$840$	0	0
$841$	−1.07706e7	−0.525111
$842$	3.87175e7	1.88203
$843$	−8.48331e6	−0.411146
$844$	1.21925e7	0.589164
$845$	0	0
$846$	−1.44552e7	−0.694383
$847$	−2.16057e6	−0.103481
$848$	2.87472e7	1.37280
$849$	−7.64056e6	−0.363795
$850$	0	0
$851$	6.60808e6	0.312789
$852$	−5.28362e6	−0.249363
$853$	1.41107e7	0.664014	0.332007	−	0.943277i	$-0.392274\pi$
$853$	1.41107e7	0.664014	0.332007	+	0.943277i	$0.392274\pi$
$854$	−4.68616e7	−2.19873
$855$	0	0
$856$	1.36580e7	0.637091
$857$	−3.50068e7	−1.62817	−0.814087	−	0.580743i	$-0.802762\pi$
$857$	−3.50068e7	−1.62817	−0.814087	+	0.580743i	$0.802762\pi$
$858$	8.84016e6	0.409960
$859$	2.72242e6	0.125885	0.0629423	−	0.998017i	$-0.479952\pi$
$859$	2.72242e6	0.125885	0.0629423	+	0.998017i	$0.479952\pi$
$860$	0	0
$861$	7.81521e6	0.359280
$862$	1.82051e7	0.834498
$863$	−976336.	−0.0446244	−0.0223122	−	0.999751i	$-0.507103\pi$
$863$	−976336.	−0.0446244	−0.0223122	+	0.999751i	$0.507103\pi$
$864$	−4.64709e6	−0.211786
$865$	0	0
$866$	−2.16369e7	−0.980392
$867$	−3.41538e6	−0.154309
$868$	2.85945e7	1.28820
$869$	−1.02941e7	−0.462424
$870$	0	0
$871$	3.54050e7	1.58132
$872$	2.67232e6	0.119014
$873$	1.70748e6	0.0758262
$874$	−209586.	−0.00928075
$875$	0	0
$876$	−8.98009e6	−0.395385
$877$	−3.04885e7	−1.33856	−0.669279	−	0.743011i	$-0.733397\pi$
$877$	−3.04885e7	−1.33856	−0.669279	+	0.743011i	$0.733397\pi$
$878$	1.39786e7	0.611965
$879$	−5.65530e6	−0.246879
$880$	0	0
$881$	3.54112e7	1.53710	0.768548	−	0.639792i	$-0.220980\pi$
$881$	3.54112e7	1.53710	0.768548	+	0.639792i	$0.220980\pi$
$882$	2.90631e6	0.125797
$883$	−7.34069e6	−0.316836	−0.158418	−	0.987372i	$-0.550639\pi$
$883$	−7.34069e6	−0.316836	−0.158418	+	0.987372i	$0.550639\pi$
$884$	−2.30789e7	−0.993308
$885$	0	0
$886$	5.25687e7	2.24979
$887$	−8.51565e6	−0.363420	−0.181710	−	0.983352i	$-0.558163\pi$
$887$	−8.51565e6	−0.363420	−0.181710	+	0.983352i	$0.558163\pi$
$888$	−2.40886e6	−0.102513
$889$	−1.36281e7	−0.578335
$890$	0	0
$891$	793881.	0.0335013
$892$	−1.16948e7	−0.492129
$893$	338967.	0.0142242
$894$	2.27764e7	0.953107
$895$	0	0
$896$	−2.41290e7	−1.00408
$897$	2.14223e7	0.888967
$898$	4.44015e7	1.83741
$899$	−3.00519e7	−1.24014
$900$	0	0
$901$	2.32160e7	0.952743
$902$	−5.14048e6	−0.210372
$903$	2.72562e7	1.11236
$904$	1.21628e7	0.495007
$905$	0	0
$906$	−3.33517e7	−1.34989
$907$	−1.84383e7	−0.744224	−0.372112	−	0.928188i	$-0.621366\pi$
$907$	−1.84383e7	−0.744224	−0.372112	+	0.928188i	$0.621366\pi$
$908$	−3.05176e7	−1.22839
$909$	−4.88263e6	−0.195995
$910$	0	0
$911$	3.20540e7	1.27964	0.639819	−	0.768526i	$-0.279009\pi$
$911$	3.20540e7	1.27964	0.639819	+	0.768526i	$0.279009\pi$
$912$	155876.	0.00620573
$913$	−9.35595e6	−0.371459
$914$	4.04468e7	1.60147
$915$	0	0
$916$	1.84441e7	0.726303
$917$	−3.10691e7	−1.22013
$918$	−5.36832e6	−0.210248
$919$	2.41323e7	0.942563	0.471282	−	0.881983i	$-0.343792\pi$
$919$	2.41323e7	0.942563	0.471282	+	0.881983i	$0.343792\pi$
$920$	0	0
$921$	−1.69423e7	−0.658147
$922$	2.06264e7	0.799089
$923$	−3.28019e7	−1.26735
$924$	−3.23393e6	−0.124609
$925$	0	0
$926$	−1.75160e7	−0.671287
$927$	−6.76638e6	−0.258617
$928$	−1.98950e7	−0.758359
$929$	−2.12500e7	−0.807828	−0.403914	−	0.914797i	$-0.632350\pi$
$929$	−2.12500e7	−0.807828	−0.403914	+	0.914797i	$0.632350\pi$
$930$	0	0
$931$	−68151.4	−0.00257692
$932$	1.30993e7	0.493977
$933$	−1.38147e7	−0.519562
$934$	−1.20945e6	−0.0453652
$935$	0	0
$936$	−7.80913e6	−0.291349
$937$	2.96484e7	1.10320	0.551598	−	0.834110i	$-0.314018\pi$
$937$	2.96484e7	1.10320	0.551598	+	0.834110i	$0.314018\pi$
$938$	−3.35478e7	−1.24496
$939$	2.00611e7	0.742490
$940$	0	0
$941$	−4.32235e7	−1.59128	−0.795638	−	0.605772i	$-0.792864\pi$
$941$	−4.32235e7	−1.59128	−0.795638	+	0.605772i	$0.792864\pi$
$942$	−1.00591e7	−0.369344
$943$	−1.24569e7	−0.456175
$944$	1.83558e7	0.670415
$945$	0	0
$946$	−1.79279e7	−0.651330
$947$	−1.03051e7	−0.373402	−0.186701	−	0.982417i	$-0.559780\pi$
$947$	−1.03051e7	−0.373402	−0.186701	+	0.982417i	$0.559780\pi$
$948$	−1.54082e7	−0.556841
$949$	−5.57504e7	−2.00947
$950$	0	0
$951$	−9.05929e6	−0.324820
$952$	−1.29061e7	−0.461531
$953$	−2.76302e7	−0.985488	−0.492744	−	0.870174i	$-0.664006\pi$
$953$	−2.76302e7	−0.985488	−0.492744	+	0.870174i	$0.664006\pi$
$954$	−1.33105e7	−0.473505
$955$	0	0
$956$	−2.14263e7	−0.758231
$957$	3.39875e6	0.119961
$958$	3.89164e7	1.37000
$959$	3.52087e6	0.123624
$960$	0	0
$961$	6.40882e7	2.23856
$962$	2.53395e7	0.882797
$963$	−1.29023e7	−0.448335
$964$	−2.45423e7	−0.850596
$965$	0	0
$966$	−2.02986e7	−0.699879
$967$	1.92779e7	0.662968	0.331484	−	0.943461i	$-0.392451\pi$
$967$	1.92779e7	0.662968	0.331484	+	0.943461i	$0.392451\pi$
$968$	−1.25537e6	−0.0430611
$969$	125884.	0.00430688
$970$	0	0
$971$	−2.79869e7	−0.952592	−0.476296	−	0.879285i	$-0.658021\pi$
$971$	−2.79869e7	−0.952592	−0.476296	+	0.879285i	$0.658021\pi$
$972$	1.18828e6	0.0403415
$973$	−4.31539e7	−1.46129
$974$	−1.00046e7	−0.337910
$975$	0	0
$976$	−5.55527e7	−1.86673
$977$	−3.40783e7	−1.14220	−0.571099	−	0.820881i	$-0.693483\pi$
$977$	−3.40783e7	−1.14220	−0.571099	+	0.820881i	$0.693483\pi$
$978$	−1.19656e7	−0.400026
$979$	8.49634e6	0.283319
$980$	0	0
$981$	−2.52447e6	−0.0837526
$982$	−2.45174e7	−0.811328
$983$	5.50760e7	1.81794	0.908968	−	0.416866i	$-0.136872\pi$
$983$	5.50760e7	1.81794	0.908968	+	0.416866i	$0.136872\pi$
$984$	4.54094e6	0.149506
$985$	0	0
$986$	−2.29828e7	−0.752853
$987$	3.28293e7	1.07268
$988$	−310281.	−0.0101126
$989$	−4.34446e7	−1.41236
$990$	0	0
$991$	−6.15387e6	−0.199051	−0.0995255	−	0.995035i	$-0.531732\pi$
$991$	−6.15387e6	−0.199051	−0.0995255	+	0.995035i	$0.531732\pi$
$992$	6.13810e7	1.98041
$993$	−2.67267e7	−0.860146
$994$	3.10812e7	0.997774
$995$	0	0
$996$	−1.40039e7	−0.447303
$997$	−1.41497e7	−0.450828	−0.225414	−	0.974263i	$-0.572373\pi$
$997$	−1.41497e7	−0.450828	−0.225414	+	0.974263i	$0.572373\pi$
$998$	2.04528e7	0.650021
$999$	2.27559e6	0.0721406

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.6.a.f.1.3		3
5.4	even	2		165.6.a.e.1.1	✓	3
15.14	odd	2		495.6.a.a.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.6.a.e.1.1	✓	3	5.4	even	2
495.6.a.a.1.3		3	15.14	odd	2
825.6.a.f.1.3		3	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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	825.a (trivial)

\(f(q)\)	\(=\)	\(q+7.21967 q^{2} +9.00000 q^{3} +20.1236 q^{4} +64.9770 q^{6} -147.570 q^{7} -85.7438 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+7.21967 q^{2} +9.00000 q^{3} +20.1236 q^{4} +64.9770 q^{6} -147.570 q^{7} -85.7438 q^{8} +81.0000 q^{9} +121.000 q^{11} +181.112 q^{12} +1124.39 q^{13} -1065.40 q^{14} -1263.00 q^{16} -1019.99 q^{17} +584.793 q^{18} -13.7131 q^{19} -1328.13 q^{21} +873.580 q^{22} +2116.94 q^{23} -771.694 q^{24} +8117.69 q^{26} +729.000 q^{27} -2969.63 q^{28} +3120.98 q^{29} -9628.99 q^{31} -6374.61 q^{32} +1089.00 q^{33} -7363.96 q^{34} +1630.01 q^{36} +3121.52 q^{37} -99.0039 q^{38} +10119.5 q^{39} -5884.38 q^{41} -9588.63 q^{42} -20522.3 q^{43} +2434.95 q^{44} +15283.6 q^{46} -24718.5 q^{47} -11367.0 q^{48} +4969.81 q^{49} -9179.87 q^{51} +22626.7 q^{52} -22761.1 q^{53} +5263.14 q^{54} +12653.2 q^{56} -123.418 q^{57} +22532.4 q^{58} -14533.5 q^{59} +43984.9 q^{61} -69518.1 q^{62} -11953.1 q^{63} -5606.68 q^{64} +7862.22 q^{66} +31488.3 q^{67} -20525.8 q^{68} +19052.5 q^{69} -29173.2 q^{71} -6945.24 q^{72} -49583.0 q^{73} +22536.3 q^{74} -275.956 q^{76} -17855.9 q^{77} +73059.2 q^{78} -85075.4 q^{79} +6561.00 q^{81} -42483.3 q^{82} -77321.9 q^{83} -26726.7 q^{84} -148164. q^{86} +28088.8 q^{87} -10375.0 q^{88} +70217.7 q^{89} -165925. q^{91} +42600.5 q^{92} -86660.9 q^{93} -178459. q^{94} -57371.5 q^{96} +21080.0 q^{97} +35880.4 q^{98} +9801.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 7 q^{2} + 27 q^{3} + 73 q^{4} - 63 q^{6} - 92 q^{7} - 231 q^{8} + 243 q^{9}+O(q^{10}) \) 3 * q - 7 * q^2 + 27 * q^3 + 73 * q^4 - 63 * q^6 - 92 * q^7 - 231 * q^8 + 243 * q^9	\( 3 q - 7 q^{2} + 27 q^{3} + 73 q^{4} - 63 q^{6} - 92 q^{7} - 231 q^{8} + 243 q^{9} + 363 q^{11} + 657 q^{12} + 90 q^{13} - 784 q^{14} - 415 q^{16} - 1934 q^{17} - 567 q^{18} + 2084 q^{19} - 828 q^{21} - 847 q^{22} - 1220 q^{23} - 2079 q^{24} + 17062 q^{26} + 2187 q^{27} - 11120 q^{28} + 4402 q^{29} - 10688 q^{31} - 12439 q^{32} + 3267 q^{33} - 4094 q^{34} + 5913 q^{36} + 8190 q^{37} - 13792 q^{38} + 810 q^{39} + 5974 q^{41} - 7056 q^{42} - 18868 q^{43} + 8833 q^{44} + 46220 q^{46} - 55500 q^{47} - 3735 q^{48} + 1907 q^{49} - 17406 q^{51} - 27330 q^{52} - 9206 q^{53} - 5103 q^{54} + 73248 q^{56} + 18756 q^{57} - 15366 q^{58} - 59196 q^{59} + 79902 q^{61} - 64616 q^{62} - 7452 q^{63} + 2129 q^{64} - 7623 q^{66} - 4468 q^{67} + 1218 q^{68} - 10980 q^{69} - 75164 q^{71} - 18711 q^{72} + 61290 q^{73} - 56766 q^{74} + 37816 q^{76} - 11132 q^{77} + 153558 q^{78} - 83564 q^{79} + 19683 q^{81} - 147410 q^{82} - 74764 q^{83} - 100080 q^{84} - 253432 q^{86} + 39618 q^{87} - 27951 q^{88} + 37342 q^{89} - 126488 q^{91} - 148164 q^{92} - 96192 q^{93} + 59252 q^{94} - 111951 q^{96} - 33486 q^{97} + 95249 q^{98} + 29403 q^{99}+O(q^{100}) \) 3 * q - 7 * q^2 + 27 * q^3 + 73 * q^4 - 63 * q^6 - 92 * q^7 - 231 * q^8 + 243 * q^9 + 363 * q^11 + 657 * q^12 + 90 * q^13 - 784 * q^14 - 415 * q^16 - 1934 * q^17 - 567 * q^18 + 2084 * q^19 - 828 * q^21 - 847 * q^22 - 1220 * q^23 - 2079 * q^24 + 17062 * q^26 + 2187 * q^27 - 11120 * q^28 + 4402 * q^29 - 10688 * q^31 - 12439 * q^32 + 3267 * q^33 - 4094 * q^34 + 5913 * q^36 + 8190 * q^37 - 13792 * q^38 + 810 * q^39 + 5974 * q^41 - 7056 * q^42 - 18868 * q^43 + 8833 * q^44 + 46220 * q^46 - 55500 * q^47 - 3735 * q^48 + 1907 * q^49 - 17406 * q^51 - 27330 * q^52 - 9206 * q^53 - 5103 * q^54 + 73248 * q^56 + 18756 * q^57 - 15366 * q^58 - 59196 * q^59 + 79902 * q^61 - 64616 * q^62 - 7452 * q^63 + 2129 * q^64 - 7623 * q^66 - 4468 * q^67 + 1218 * q^68 - 10980 * q^69 - 75164 * q^71 - 18711 * q^72 + 61290 * q^73 - 56766 * q^74 + 37816 * q^76 - 11132 * q^77 + 153558 * q^78 - 83564 * q^79 + 19683 * q^81 - 147410 * q^82 - 74764 * q^83 - 100080 * q^84 - 253432 * q^86 + 39618 * q^87 - 27951 * q^88 + 37342 * q^89 - 126488 * q^91 - 148164 * q^92 - 96192 * q^93 + 59252 * q^94 - 111951 * q^96 - 33486 * q^97 + 95249 * q^98 + 29403 * q^99

Introduction

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Database

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