LMFDB - Embedded newform 825.6.a.j.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:	3.3.34253.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 52x + 48 $ x^3 - x^2 - 52*x + 48
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{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			$7.25531$ 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)

$f(q)$	$=$	$q+9.25531 q^{2} -9.00000 q^{3} +53.6607 q^{4} -83.2977 q^{6} -36.4478 q^{7} +200.476 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+9.25531 q^{2} -9.00000 q^{3} +53.6607 q^{4} -83.2977 q^{6} -36.4478 q^{7} +200.476 q^{8} +81.0000 q^{9} -121.000 q^{11} -482.946 q^{12} +878.032 q^{13} -337.336 q^{14} +138.327 q^{16} -155.385 q^{17} +749.680 q^{18} -1932.65 q^{19} +328.030 q^{21} -1119.89 q^{22} -1927.38 q^{23} -1804.29 q^{24} +8126.46 q^{26} -729.000 q^{27} -1955.81 q^{28} -480.444 q^{29} +1759.49 q^{31} -5134.98 q^{32} +1089.00 q^{33} -1438.14 q^{34} +4346.51 q^{36} +1898.87 q^{37} -17887.3 q^{38} -7902.29 q^{39} -4500.03 q^{41} +3036.02 q^{42} +4475.49 q^{43} -6492.94 q^{44} -17838.5 q^{46} +12371.2 q^{47} -1244.94 q^{48} -15478.6 q^{49} +1398.47 q^{51} +47115.8 q^{52} -2145.12 q^{53} -6747.12 q^{54} -7306.92 q^{56} +17393.8 q^{57} -4446.66 q^{58} -15857.9 q^{59} -36447.7 q^{61} +16284.6 q^{62} -2952.27 q^{63} -51952.3 q^{64} +10079.0 q^{66} +15668.5 q^{67} -8338.07 q^{68} +17346.4 q^{69} +10689.5 q^{71} +16238.6 q^{72} -12172.6 q^{73} +17574.6 q^{74} -103707. q^{76} +4410.19 q^{77} -73138.1 q^{78} -87205.6 q^{79} +6561.00 q^{81} -41649.2 q^{82} -97230.6 q^{83} +17602.3 q^{84} +41422.0 q^{86} +4324.00 q^{87} -24257.6 q^{88} +38639.2 q^{89} -32002.4 q^{91} -103424. q^{92} -15835.4 q^{93} +114499. q^{94} +46214.8 q^{96} +36754.5 q^{97} -143259. q^{98} -9801.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 7 q^{2} - 27 q^{3} + 25 q^{4} - 63 q^{6} + 172 q^{7} + 231 q^{8} + 243 q^{9}+O(q^{10}) $ 3 * q + 7 * q^2 - 27 * q^3 + 25 * q^4 - 63 * q^6 + 172 * q^7 + 231 * q^8 + 243 * q^9	\( 3 q + 7 q^{2} - 27 q^{3} + 25 q^{4} - 63 q^{6} + 172 q^{7} + 231 q^{8} + 243 q^{9} - 363 q^{11} - 225 q^{12} + 654 q^{13} - 728 q^{14} - 415 q^{16} + 2366 q^{17} + 567 q^{18} - 2872 q^{19} - 1548 q^{21} - 847 q^{22} - 2272 q^{23} - 2079 q^{24} + 3422 q^{26} - 2187 q^{27} - 4592 q^{28} - 7738 q^{29} + 568 q^{31} - 1001 q^{32} + 3267 q^{33} + 2506 q^{34} + 2025 q^{36} + 9126 q^{37} - 13076 q^{38} - 5886 q^{39} - 8758 q^{41} + 6552 q^{42} + 14672 q^{43} - 3025 q^{44} - 28768 q^{46} + 19392 q^{47} + 3735 q^{48} - 26629 q^{49} - 21294 q^{51} + 61506 q^{52} + 4598 q^{53} - 5103 q^{54} + 2688 q^{56} + 25848 q^{57} - 8550 q^{58} - 9348 q^{59} - 60078 q^{61} + 14096 q^{62} + 13932 q^{63} - 7087 q^{64} + 7623 q^{66} + 38468 q^{67} - 59778 q^{68} + 20448 q^{69} - 74032 q^{71} + 18711 q^{72} + 44442 q^{73} + 82542 q^{74} - 98708 q^{76} - 20812 q^{77} - 30798 q^{78} - 108116 q^{79} + 19683 q^{81} + 92230 q^{82} + 81892 q^{83} + 41328 q^{84} + 126412 q^{86} + 69642 q^{87} - 27951 q^{88} + 167342 q^{89} - 31832 q^{91} - 72960 q^{92} - 5112 q^{93} + 12728 q^{94} + 9009 q^{96} - 159702 q^{97} - 163121 q^{98} - 29403 q^{99}+O(q^{100}) \) 3 * q + 7 * q^2 - 27 * q^3 + 25 * q^4 - 63 * q^6 + 172 * q^7 + 231 * q^8 + 243 * q^9 - 363 * q^11 - 225 * q^12 + 654 * q^13 - 728 * q^14 - 415 * q^16 + 2366 * q^17 + 567 * q^18 - 2872 * q^19 - 1548 * q^21 - 847 * q^22 - 2272 * q^23 - 2079 * q^24 + 3422 * q^26 - 2187 * q^27 - 4592 * q^28 - 7738 * q^29 + 568 * q^31 - 1001 * q^32 + 3267 * q^33 + 2506 * q^34 + 2025 * q^36 + 9126 * q^37 - 13076 * q^38 - 5886 * q^39 - 8758 * q^41 + 6552 * q^42 + 14672 * q^43 - 3025 * q^44 - 28768 * q^46 + 19392 * q^47 + 3735 * q^48 - 26629 * q^49 - 21294 * q^51 + 61506 * q^52 + 4598 * q^53 - 5103 * q^54 + 2688 * q^56 + 25848 * q^57 - 8550 * q^58 - 9348 * q^59 - 60078 * q^61 + 14096 * q^62 + 13932 * q^63 - 7087 * q^64 + 7623 * q^66 + 38468 * q^67 - 59778 * q^68 + 20448 * q^69 - 74032 * q^71 + 18711 * q^72 + 44442 * q^73 + 82542 * q^74 - 98708 * q^76 - 20812 * q^77 - 30798 * q^78 - 108116 * q^79 + 19683 * q^81 + 92230 * q^82 + 81892 * q^83 + 41328 * q^84 + 126412 * q^86 + 69642 * q^87 - 27951 * q^88 + 167342 * q^89 - 31832 * q^91 - 72960 * q^92 - 5112 * q^93 + 12728 * q^94 + 9009 * q^96 - 159702 * q^97 - 163121 * 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 $

$2$	9.25531	1.63612	0.818061	−	0.575131i	$-0.195049\pi$
$2$	9.25531	1.63612	0.818061	+	0.575131i	$0.195049\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	53.6607	1.67690
$5$	0	0
$5$	0	0
$6$	−83.2977	−0.944616
$7$	−36.4478	−0.281142	−0.140571	−	0.990071i	$-0.544894\pi$
$7$	−36.4478	−0.281142	−0.140571	+	0.990071i	$0.544894\pi$
$8$	200.476	1.10749
$9$	81.0000	0.333333
$10$	0	0
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	−482.946	−0.968156
$13$	878.032	1.44096	0.720480	−	0.693476i	$-0.243921\pi$
$13$	878.032	1.44096	0.720480	+	0.693476i	$0.243921\pi$
$14$	−337.336	−0.459983
$15$	0	0
$16$	138.327	0.135085
$17$	−155.385	−0.130403	−0.0652014	−	0.997872i	$-0.520769\pi$
$17$	−155.385	−0.130403	−0.0652014	+	0.997872i	$0.520769\pi$
$18$	749.680	0.545374
$19$	−1932.65	−1.22820	−0.614100	−	0.789228i	$-0.710481\pi$
$19$	−1932.65	−1.22820	−0.614100	+	0.789228i	$0.710481\pi$
$20$	0	0
$21$	328.030	0.162318
$22$	−1119.89	−0.493309
$23$	−1927.38	−0.759709	−0.379855	−	0.925046i	$-0.624026\pi$
$23$	−1927.38	−0.759709	−0.379855	+	0.925046i	$0.624026\pi$
$24$	−1804.29	−0.639407
$25$	0	0
$26$	8126.46	2.35759
$27$	−729.000	−0.192450
$28$	−1955.81	−0.471447
$29$	−480.444	−0.106084	−0.0530418	−	0.998592i	$-0.516892\pi$
$29$	−480.444	−0.106084	−0.0530418	+	0.998592i	$0.516892\pi$
$30$	0	0
$31$	1759.49	0.328838	0.164419	−	0.986391i	$-0.447425\pi$
$31$	1759.49	0.328838	0.164419	+	0.986391i	$0.447425\pi$
$32$	−5134.98	−0.886470
$33$	1089.00	0.174078
$34$	−1438.14	−0.213355
$35$	0	0
$36$	4346.51	0.558965
$37$	1898.87	0.228029	0.114015	−	0.993479i	$-0.463629\pi$
$37$	1898.87	0.228029	0.114015	+	0.993479i	$0.463629\pi$
$38$	−17887.3	−2.00949
$39$	−7902.29	−0.831939
$40$	0	0
$41$	−4500.03	−0.418076	−0.209038	−	0.977907i	$-0.567033\pi$
$41$	−4500.03	−0.418076	−0.209038	+	0.977907i	$0.567033\pi$
$42$	3036.02	0.265572
$43$	4475.49	0.369121	0.184561	−	0.982821i	$-0.440914\pi$
$43$	4475.49	0.369121	0.184561	+	0.982821i	$0.440914\pi$
$44$	−6492.94	−0.505603
$45$	0	0
$46$	−17838.5	−1.24298
$47$	12371.2	0.816895	0.408448	−	0.912782i	$-0.366070\pi$
$47$	12371.2	0.816895	0.408448	+	0.912782i	$0.366070\pi$
$48$	−1244.94	−0.0779912
$49$	−15478.6	−0.920959
$50$	0	0
$51$	1398.47	0.0752881
$52$	47115.8	2.41634
$53$	−2145.12	−0.104897	−0.0524483	−	0.998624i	$-0.516702\pi$
$53$	−2145.12	−0.104897	−0.0524483	+	0.998624i	$0.516702\pi$
$54$	−6747.12	−0.314872
$55$	0	0
$56$	−7306.92	−0.311361
$57$	17393.8	0.709102
$58$	−4446.66	−0.173566
$59$	−15857.9	−0.593084	−0.296542	−	0.955020i	$-0.595834\pi$
$59$	−15857.9	−0.593084	−0.296542	+	0.955020i	$0.595834\pi$
$60$	0	0
$61$	−36447.7	−1.25414	−0.627070	−	0.778963i	$-0.715746\pi$
$61$	−36447.7	−1.25414	−0.627070	+	0.778963i	$0.715746\pi$
$62$	16284.6	0.538020
$63$	−2952.27	−0.0937141
$64$	−51952.3	−1.58546
$65$	0	0
$66$	10079.0	0.284812
$67$	15668.5	0.426424	0.213212	−	0.977006i	$-0.431607\pi$
$67$	15668.5	0.426424	0.213212	+	0.977006i	$0.431607\pi$
$68$	−8338.07	−0.218672
$69$	17346.4	0.438618
$70$	0	0
$71$	10689.5	0.251659	0.125830	−	0.992052i	$-0.459841\pi$
$71$	10689.5	0.251659	0.125830	+	0.992052i	$0.459841\pi$
$72$	16238.6	0.369162
$73$	−12172.6	−0.267347	−0.133674	−	0.991025i	$-0.542677\pi$
$73$	−12172.6	−0.267347	−0.133674	+	0.991025i	$0.542677\pi$
$74$	17574.6	0.373084
$75$	0	0
$76$	−103707.	−2.05956
$77$	4410.19	0.0847676
$78$	−73138.1	−1.36115
$79$	−87205.6	−1.57209	−0.786043	−	0.618171i	$-0.787874\pi$
$79$	−87205.6	−1.57209	−0.786043	+	0.618171i	$0.787874\pi$
$80$	0	0
$81$	6561.00	0.111111
$82$	−41649.2	−0.684024
$83$	−97230.6	−1.54920	−0.774600	−	0.632451i	$-0.782049\pi$
$83$	−97230.6	−1.54920	−0.774600	+	0.632451i	$0.782049\pi$
$84$	17602.3	0.272190
$85$	0	0
$86$	41422.0	0.603928
$87$	4324.00	0.0612473
$88$	−24257.6	−0.333919
$89$	38639.2	0.517075	0.258537	−	0.966001i	$-0.416759\pi$
$89$	38639.2	0.517075	0.258537	+	0.966001i	$0.416759\pi$
$90$	0	0
$91$	−32002.4	−0.405115
$92$	−103424.	−1.27395
$93$	−15835.4	−0.189855
$94$	114499.	1.33654
$95$	0	0
$96$	46214.8	0.511804
$97$	36754.5	0.396626	0.198313	−	0.980139i	$-0.436454\pi$
$97$	36754.5	0.396626	0.198313	+	0.980139i	$0.436454\pi$
$98$	−143259.	−1.50680
$99$	−9801.00	−0.100504
$100$	0	0
$101$	−185487.	−1.80929	−0.904647	−	0.426161i	$-0.859866\pi$
$101$	−185487.	−1.80929	−0.904647	+	0.426161i	$0.859866\pi$
$102$	12943.2	0.123181
$103$	−36890.7	−0.342629	−0.171315	−	0.985216i	$-0.554801\pi$
$103$	−36890.7	−0.342629	−0.171315	+	0.985216i	$0.554801\pi$
$104$	176025.	1.59584
$105$	0	0
$106$	−19853.7	−0.171624
$107$	124996.	1.05545	0.527725	−	0.849415i	$-0.323045\pi$
$107$	124996.	1.05545	0.527725	+	0.849415i	$0.323045\pi$
$108$	−39118.6	−0.322719
$109$	−150975.	−1.21714	−0.608568	−	0.793502i	$-0.708256\pi$
$109$	−150975.	−1.21714	−0.608568	+	0.793502i	$0.708256\pi$
$110$	0	0
$111$	−17089.8	−0.131653
$112$	−5041.71	−0.0379780
$113$	−157970.	−1.16380	−0.581899	−	0.813261i	$-0.697690\pi$
$113$	−157970.	−1.16380	−0.581899	+	0.813261i	$0.697690\pi$
$114$	160985.	1.16018
$115$	0	0
$116$	−25781.0	−0.177891
$117$	71120.6	0.480320
$118$	−146770.	−0.970359
$119$	5663.45	0.0366618
$120$	0	0
$121$	14641.0	0.0909091
$122$	−337335.	−2.05193
$123$	40500.3	0.241377
$124$	94415.4	0.551428
$125$	0	0
$126$	−27324.2	−0.153328
$127$	−268814.	−1.47891	−0.739457	−	0.673204i	$-0.764918\pi$
$127$	−268814.	−1.47891	−0.739457	+	0.673204i	$0.764918\pi$
$128$	−316515.	−1.70753
$129$	−40279.4	−0.213112
$130$	0	0
$131$	−366914.	−1.86804	−0.934020	−	0.357220i	$-0.883725\pi$
$131$	−366914.	−1.86804	−0.934020	+	0.357220i	$0.883725\pi$
$132$	58436.5	0.291910
$133$	70440.9	0.345299
$134$	145017.	0.697682
$135$	0	0
$136$	−31151.0	−0.144419
$137$	182927.	0.832678	0.416339	−	0.909209i	$-0.363313\pi$
$137$	182927.	0.832678	0.416339	+	0.909209i	$0.363313\pi$
$138$	160546.	0.717633
$139$	8429.85	0.0370069	0.0185035	−	0.999829i	$-0.494110\pi$
$139$	8429.85	0.0370069	0.0185035	+	0.999829i	$0.494110\pi$
$140$	0	0
$141$	−111341.	−0.471635
$142$	98934.8	0.411745
$143$	−106242.	−0.434466
$144$	11204.5	0.0450282
$145$	0	0
$146$	−112661.	−0.437413
$147$	139307.	0.531716
$148$	101895.	0.382381
$149$	271810.	1.00300	0.501499	−	0.865158i	$-0.332782\pi$
$149$	271810.	1.00300	0.501499	+	0.865158i	$0.332782\pi$
$150$	0	0
$151$	−236565.	−0.844322	−0.422161	−	0.906521i	$-0.638728\pi$
$151$	−236565.	−0.844322	−0.422161	+	0.906521i	$0.638728\pi$
$152$	−387450.	−1.36021
$153$	−12586.2	−0.0434676
$154$	40817.6	0.138690
$155$	0	0
$156$	−424042.	−1.39508
$157$	−211824.	−0.685846	−0.342923	−	0.939364i	$-0.611417\pi$
$157$	−211824.	−0.685846	−0.342923	+	0.939364i	$0.611417\pi$
$158$	−807114.	−2.57213
$159$	19306.1	0.0605621
$160$	0	0
$161$	70248.7	0.213586
$162$	60724.1	0.181791
$163$	341315.	1.00620	0.503102	−	0.864227i	$-0.332192\pi$
$163$	341315.	1.00620	0.503102	+	0.864227i	$0.332192\pi$
$164$	−241475.	−0.701071
$165$	0	0
$166$	−899899.	−2.53468
$167$	180548.	0.500958	0.250479	−	0.968122i	$-0.419412\pi$
$167$	180548.	0.500958	0.250479	+	0.968122i	$0.419412\pi$
$168$	65762.3	0.179764
$169$	399647.	1.07637
$170$	0	0
$171$	−156545.	−0.409400
$172$	240158.	0.618978
$173$	643322.	1.63423	0.817114	−	0.576476i	$-0.195572\pi$
$173$	643322.	1.63423	0.817114	+	0.576476i	$0.195572\pi$
$174$	40019.9	0.100208
$175$	0	0
$176$	−16737.5	−0.0407296
$177$	142721.	0.342417
$178$	357618.	0.845998
$179$	−266922.	−0.622662	−0.311331	−	0.950302i	$-0.600775\pi$
$179$	−266922.	−0.622662	−0.311331	+	0.950302i	$0.600775\pi$
$180$	0	0
$181$	281529.	0.638745	0.319372	−	0.947629i	$-0.396528\pi$
$181$	281529.	0.638745	0.319372	+	0.947629i	$0.396528\pi$
$182$	−296192.	−0.662818
$183$	328030.	0.724078
$184$	−386393.	−0.841366
$185$	0	0
$186$	−146561.	−0.310626
$187$	18801.6	0.0393179
$188$	663846.	1.36985
$189$	26570.5	0.0541059
$190$	0	0
$191$	933723.	1.85197	0.925987	−	0.377556i	$-0.123235\pi$
$191$	933723.	1.85197	0.925987	+	0.377556i	$0.123235\pi$
$192$	467571.	0.915365
$193$	−300124.	−0.579973	−0.289986	−	0.957031i	$-0.593651\pi$
$193$	−300124.	−0.579973	−0.289986	+	0.957031i	$0.593651\pi$
$194$	340174.	0.648929
$195$	0	0
$196$	−830590.	−1.54435
$197$	944940.	1.73476	0.867378	−	0.497649i	$-0.165803\pi$
$197$	944940.	1.73476	0.867378	+	0.497649i	$0.165803\pi$
$198$	−90711.2	−0.164436
$199$	−1.00821e6	−1.80475	−0.902374	−	0.430954i	$-0.858177\pi$
$199$	−1.00821e6	−1.80475	−0.902374	+	0.430954i	$0.858177\pi$
$200$	0	0
$201$	−141017.	−0.246196
$202$	−1.71674e6	−2.96023
$203$	17511.1	0.0298246
$204$	75042.6	0.126250
$205$	0	0
$206$	−341435.	−0.560583
$207$	−156118.	−0.253236
$208$	121455.	0.194652
$209$	233851.	0.370316
$210$	0	0
$211$	497479.	0.769253	0.384626	−	0.923072i	$-0.374330\pi$
$211$	497479.	0.769253	0.384626	+	0.923072i	$0.374330\pi$
$212$	−115108.	−0.175901
$213$	−96205.7	−0.145295
$214$	1.15688e6	1.72684
$215$	0	0
$216$	−146147.	−0.213136
$217$	−64129.5	−0.0924504
$218$	−1.39732e6	−1.99138
$219$	109553.	0.154353
$220$	0	0
$221$	−136433.	−0.187905
$222$	−158172.	−0.215400
$223$	−1.14136e6	−1.53695	−0.768477	−	0.639878i	$-0.778985\pi$
$223$	−1.14136e6	−1.53695	−0.768477	+	0.639878i	$0.778985\pi$
$224$	187159.	0.249224
$225$	0	0
$226$	−1.46206e6	−1.90411
$227$	−669451.	−0.862292	−0.431146	−	0.902282i	$-0.641891\pi$
$227$	−669451.	−0.862292	−0.431146	+	0.902282i	$0.641891\pi$
$228$	933366.	1.18909
$229$	588061.	0.741026	0.370513	−	0.928827i	$-0.379182\pi$
$229$	588061.	0.741026	0.370513	+	0.928827i	$0.379182\pi$
$230$	0	0
$231$	−39691.7	−0.0489406
$232$	−96317.6	−0.117486
$233$	−199417.	−0.240642	−0.120321	−	0.992735i	$-0.538392\pi$
$233$	−199417.	−0.240642	−0.120321	+	0.992735i	$0.538392\pi$
$234$	658243.	0.785862
$235$	0	0
$236$	−850947.	−0.994541
$237$	784850.	0.907645
$238$	52416.9	0.0599832
$239$	−408055.	−0.462088	−0.231044	−	0.972943i	$-0.574214\pi$
$239$	−408055.	−0.462088	−0.231044	+	0.972943i	$0.574214\pi$
$240$	0	0
$241$	1.24022e6	1.37548	0.687742	−	0.725956i	$-0.258602\pi$
$241$	1.24022e6	1.37548	0.687742	+	0.725956i	$0.258602\pi$
$242$	135507.	0.148738
$243$	−59049.0	−0.0641500
$244$	−1.95581e6	−2.10306
$245$	0	0
$246$	374842.	0.394922
$247$	−1.69693e6	−1.76979
$248$	352736.	0.364183
$249$	875075.	0.894431
$250$	0	0
$251$	30660.6	0.0307183	0.0153591	−	0.999882i	$-0.495111\pi$
$251$	30660.6	0.0307183	0.0153591	+	0.999882i	$0.495111\pi$
$252$	−158421.	−0.157149
$253$	233213.	0.229061
$254$	−2.48796e6	−2.41968
$255$	0	0
$256$	−1.26697e6	−1.20828
$257$	687971.	0.649737	0.324868	−	0.945759i	$-0.394680\pi$
$257$	687971.	0.649737	0.324868	+	0.945759i	$0.394680\pi$
$258$	−372798.	−0.348678
$259$	−69209.6	−0.0641087
$260$	0	0
$261$	−38916.0	−0.0353612
$262$	−3.39590e6	−3.05634
$263$	−1.70103e6	−1.51643	−0.758216	−	0.652004i	$-0.773929\pi$
$263$	−1.70103e6	−1.51643	−0.758216	+	0.652004i	$0.773929\pi$
$264$	218319.	0.192788
$265$	0	0
$266$	651952.	0.564952
$267$	−347753.	−0.298533
$268$	840785.	0.715069
$269$	−982644.	−0.827972	−0.413986	−	0.910283i	$-0.635864\pi$
$269$	−982644.	−0.827972	−0.413986	+	0.910283i	$0.635864\pi$
$270$	0	0
$271$	−276206.	−0.228459	−0.114230	−	0.993454i	$-0.536440\pi$
$271$	−276206.	−0.228459	−0.114230	+	0.993454i	$0.536440\pi$
$272$	−21493.9	−0.0176154
$273$	288021.	0.233893
$274$	1.69305e6	1.36236
$275$	0	0
$276$	930820.	0.735517
$277$	−148776.	−0.116502	−0.0582509	−	0.998302i	$-0.518552\pi$
$277$	−148776.	−0.116502	−0.0582509	+	0.998302i	$0.518552\pi$
$278$	78020.8	0.0605478
$279$	142519.	0.109613
$280$	0	0
$281$	357772.	0.270297	0.135148	−	0.990825i	$-0.456849\pi$
$281$	357772.	0.270297	0.135148	+	0.990825i	$0.456849\pi$
$282$	−1.03049e6	−0.771652
$283$	492090.	0.365240	0.182620	−	0.983184i	$-0.441542\pi$
$283$	492090.	0.365240	0.182620	+	0.983184i	$0.441542\pi$
$284$	573607.	0.422006
$285$	0	0
$286$	−983301.	−0.710839
$287$	164016.	0.117539
$288$	−415934.	−0.295490
$289$	−1.39571e6	−0.982995
$290$	0	0
$291$	−330791.	−0.228992
$292$	−653189.	−0.448314
$293$	−498120.	−0.338973	−0.169487	−	0.985532i	$-0.554211\pi$
$293$	−498120.	−0.338973	−0.169487	+	0.985532i	$0.554211\pi$
$294$	1.28933e6	0.869952
$295$	0	0
$296$	380678.	0.252539
$297$	88209.0	0.0580259
$298$	2.51568e6	1.64103
$299$	−1.69230e6	−1.09471
$300$	0	0
$301$	−163122.	−0.103776
$302$	−2.18948e6	−1.38141
$303$	1.66938e6	1.04460
$304$	−267337.	−0.165911
$305$	0	0
$306$	−116489.	−0.0711183
$307$	998760.	0.604805	0.302402	−	0.953180i	$-0.402211\pi$
$307$	998760.	0.604805	0.302402	+	0.953180i	$0.402211\pi$
$308$	236654.	0.142147
$309$	332017.	0.197817
$310$	0	0
$311$	1.88783e6	1.10678	0.553389	−	0.832923i	$-0.313334\pi$
$311$	1.88783e6	1.10678	0.553389	+	0.832923i	$0.313334\pi$
$312$	−1.58422e6	−0.921360
$313$	2.34787e6	1.35461	0.677303	−	0.735704i	$-0.263149\pi$
$313$	2.34787e6	1.35461	0.677303	+	0.735704i	$0.263149\pi$
$314$	−1.96050e6	−1.12213
$315$	0	0
$316$	−4.67951e6	−2.63623
$317$	−562721.	−0.314518	−0.157259	−	0.987557i	$-0.550266\pi$
$317$	−562721.	−0.314518	−0.157259	+	0.987557i	$0.550266\pi$
$318$	178684.	0.0990870
$319$	58133.7	0.0319854
$320$	0	0
$321$	−1.12497e6	−0.609364
$322$	650173.	0.349454
$323$	300305.	0.160161
$324$	352068.	0.186322
$325$	0	0
$326$	3.15897e6	1.64627
$327$	1.35878e6	0.702713
$328$	−902149.	−0.463013
$329$	−450902.	−0.229664
$330$	0	0
$331$	−1.00593e6	−0.504657	−0.252328	−	0.967642i	$-0.581196\pi$
$331$	−1.00593e6	−0.504657	−0.252328	+	0.967642i	$0.581196\pi$
$332$	−5.21746e6	−2.59785
$333$	153808.	0.0760098
$334$	1.67103e6	0.819628
$335$	0	0
$336$	45375.4	0.0219266
$337$	280192.	0.134394	0.0671971	−	0.997740i	$-0.478594\pi$
$337$	280192.	0.134394	0.0671971	+	0.997740i	$0.478594\pi$
$338$	3.69886e6	1.76107
$339$	1.42173e6	0.671919
$340$	0	0
$341$	−212898.	−0.0991485
$342$	−1.44887e6	−0.669829
$343$	1.17674e6	0.540063
$344$	897229.	0.408796
$345$	0	0
$346$	5.95414e6	2.67380
$347$	−2.10913e6	−0.940328	−0.470164	−	0.882579i	$-0.655805\pi$
$347$	−2.10913e6	−0.940328	−0.470164	+	0.882579i	$0.655805\pi$
$348$	232029.	0.102705
$349$	3.88469e6	1.70723	0.853617	−	0.520901i	$-0.174404\pi$
$349$	3.88469e6	1.70723	0.853617	+	0.520901i	$0.174404\pi$
$350$	0	0
$351$	−640085.	−0.277313
$352$	621333.	0.267281
$353$	−1.35663e6	−0.579463	−0.289732	−	0.957108i	$-0.593566\pi$
$353$	−1.35663e6	−0.579463	−0.289732	+	0.957108i	$0.593566\pi$
$354$	1.32093e6	0.560237
$355$	0	0
$356$	2.07341e6	0.867081
$357$	−50971.0	−0.0211667
$358$	−2.47045e6	−1.01875
$359$	3.93436e6	1.61116	0.805579	−	0.592488i	$-0.201854\pi$
$359$	3.93436e6	1.61116	0.805579	+	0.592488i	$0.201854\pi$
$360$	0	0
$361$	1.25904e6	0.508476
$362$	2.60564e6	1.04506
$363$	−131769.	−0.0524864
$364$	−1.71727e6	−0.679336
$365$	0	0
$366$	3.03602e6	1.18468
$367$	2.82588e6	1.09519	0.547594	−	0.836744i	$-0.315544\pi$
$367$	2.82588e6	1.09519	0.547594	+	0.836744i	$0.315544\pi$
$368$	−266608.	−0.102625
$369$	−364502.	−0.139359
$370$	0	0
$371$	78184.9	0.0294909
$372$	−849738.	−0.318367
$373$	−4.58790e6	−1.70743	−0.853713	−	0.520744i	$-0.825655\pi$
$373$	−4.58790e6	−1.70743	−0.853713	+	0.520744i	$0.825655\pi$
$374$	174015.	0.0643290
$375$	0	0
$376$	2.48013e6	0.904699
$377$	−421845.	−0.152862
$378$	245918.	0.0885239
$379$	2.84827e6	1.01855	0.509277	−	0.860603i	$-0.329913\pi$
$379$	2.84827e6	1.01855	0.509277	+	0.860603i	$0.329913\pi$
$380$	0	0
$381$	2.41933e6	0.853852
$382$	8.64190e6	3.03006
$383$	2.78467e6	0.970013	0.485006	−	0.874511i	$-0.338817\pi$
$383$	2.78467e6	0.970013	0.485006	+	0.874511i	$0.338817\pi$
$384$	2.84863e6	0.985845
$385$	0	0
$386$	−2.77774e6	−0.948906
$387$	362514.	0.123040
$388$	1.97227e6	0.665101
$389$	3.95277e6	1.32442	0.662212	−	0.749316i	$-0.269618\pi$
$389$	3.95277e6	1.32442	0.662212	+	0.749316i	$0.269618\pi$
$390$	0	0
$391$	299486.	0.0990682
$392$	−3.10308e6	−1.01995
$393$	3.30223e6	1.07851
$394$	8.74571e6	2.83827
$395$	0	0
$396$	−525928.	−0.168534
$397$	5.55351e6	1.76844	0.884221	−	0.467068i	$-0.154690\pi$
$397$	5.55351e6	1.76844	0.884221	+	0.467068i	$0.154690\pi$
$398$	−9.33125e6	−2.95279
$399$	−633968.	−0.199359
$400$	0	0
$401$	−279266.	−0.0867277	−0.0433639	−	0.999059i	$-0.513807\pi$
$401$	−279266.	−0.0867277	−0.0433639	+	0.999059i	$0.513807\pi$
$402$	−1.30515e6	−0.402807
$403$	1.54489e6	0.473843
$404$	−9.95334e6	−3.03400
$405$	0	0
$406$	162071.	0.0487967
$407$	−229763.	−0.0687534
$408$	280359.	0.0833805
$409$	5.17128e6	1.52859	0.764293	−	0.644869i	$-0.223088\pi$
$409$	5.17128e6	1.52859	0.764293	+	0.644869i	$0.223088\pi$
$410$	0	0
$411$	−1.64635e6	−0.480747
$412$	−1.97958e6	−0.574554
$413$	577987.	0.166741
$414$	−1.44492e6	−0.414326
$415$	0	0
$416$	−4.50868e6	−1.27737
$417$	−75868.7	−0.0213660
$418$	2.16436e6	0.605883
$419$	−6.04152e6	−1.68117	−0.840585	−	0.541680i	$-0.817788\pi$
$419$	−6.04152e6	−1.68117	−0.840585	+	0.541680i	$0.817788\pi$
$420$	0	0
$421$	−895386.	−0.246210	−0.123105	−	0.992394i	$-0.539285\pi$
$421$	−895386.	−0.246210	−0.123105	+	0.992394i	$0.539285\pi$
$422$	4.60432e6	1.25859
$423$	1.00207e6	0.272298
$424$	−430045.	−0.116171
$425$	0	0
$426$	−890413.	−0.237721
$427$	1.32844e6	0.352592
$428$	6.70738e6	1.76988
$429$	956177.	0.250839
$430$	0	0
$431$	−1.60867e6	−0.417132	−0.208566	−	0.978008i	$-0.566880\pi$
$431$	−1.60867e6	−0.417132	−0.208566	+	0.978008i	$0.566880\pi$
$432$	−100840.	−0.0259971
$433$	−1.86039e6	−0.476853	−0.238427	−	0.971161i	$-0.576632\pi$
$433$	−1.86039e6	−0.476853	−0.238427	+	0.971161i	$0.576632\pi$
$434$	−593538.	−0.151260
$435$	0	0
$436$	−8.10142e6	−2.04101
$437$	3.72495e6	0.933075
$438$	1.01395e6	0.252540
$439$	2.75051e6	0.681164	0.340582	−	0.940215i	$-0.389376\pi$
$439$	2.75051e6	0.681164	0.340582	+	0.940215i	$0.389376\pi$
$440$	0	0
$441$	−1.25376e6	−0.306986
$442$	−1.26273e6	−0.307436
$443$	−3.15804e6	−0.764555	−0.382278	−	0.924048i	$-0.624860\pi$
$443$	−3.15804e6	−0.764555	−0.382278	+	0.924048i	$0.624860\pi$
$444$	−917051.	−0.220768
$445$	0	0
$446$	−1.05636e7	−2.51464
$447$	−2.44629e6	−0.579081
$448$	1.89355e6	0.445740
$449$	−127508.	−0.0298484	−0.0149242	−	0.999889i	$-0.504751\pi$
$449$	−127508.	−0.0298484	−0.0149242	+	0.999889i	$0.504751\pi$
$450$	0	0
$451$	544504.	0.126055
$452$	−8.47675e6	−1.95157
$453$	2.12908e6	0.487469
$454$	−6.19598e6	−1.41082
$455$	0	0
$456$	3.48705e6	0.785319
$457$	−2.19209e6	−0.490984	−0.245492	−	0.969399i	$-0.578950\pi$
$457$	−2.19209e6	−0.490984	−0.245492	+	0.969399i	$0.578950\pi$
$458$	5.44268e6	1.21241
$459$	113276.	0.0250960
$460$	0	0
$461$	5.20229e6	1.14010	0.570050	−	0.821610i	$-0.306924\pi$
$461$	5.20229e6	1.14010	0.570050	+	0.821610i	$0.306924\pi$
$462$	−367359.	−0.0800728
$463$	−2.66624e6	−0.578025	−0.289013	−	0.957325i	$-0.593327\pi$
$463$	−2.66624e6	−0.578025	−0.289013	+	0.957325i	$0.593327\pi$
$464$	−66458.3	−0.0143303
$465$	0	0
$466$	−1.84566e6	−0.393720
$467$	2.35578e6	0.499853	0.249926	−	0.968265i	$-0.419594\pi$
$467$	2.35578e6	0.499853	0.249926	+	0.968265i	$0.419594\pi$
$468$	3.81638e6	0.805447
$469$	−571084.	−0.119886
$470$	0	0
$471$	1.90642e6	0.395973
$472$	−3.17914e6	−0.656832
$473$	−541534.	−0.111294
$474$	7.26403e6	1.48502
$475$	0	0
$476$	303905.	0.0614780
$477$	−173755.	−0.0349655
$478$	−3.77668e6	−0.756032
$479$	−4.78329e6	−0.952551	−0.476276	−	0.879296i	$-0.658014\pi$
$479$	−4.78329e6	−0.952551	−0.476276	+	0.879296i	$0.658014\pi$
$480$	0	0
$481$	1.66727e6	0.328581
$482$	1.14786e7	2.25046
$483$	−632239.	−0.123314
$484$	785646.	0.152445
$485$	0	0
$486$	−546517.	−0.104957
$487$	3.31515e6	0.633405	0.316702	−	0.948525i	$-0.397424\pi$
$487$	3.31515e6	0.633405	0.316702	+	0.948525i	$0.397424\pi$
$488$	−7.30691e6	−1.38894
$489$	−3.07183e6	−0.580932
$490$	0	0
$491$	−3.02276e6	−0.565847	−0.282924	−	0.959142i	$-0.591304\pi$
$491$	−3.02276e6	−0.565847	−0.282924	+	0.959142i	$0.591304\pi$
$492$	2.17327e6	0.404763
$493$	74653.9	0.0138336
$494$	−1.57056e7	−2.89559
$495$	0	0
$496$	243384.	0.0444210
$497$	−389610.	−0.0707520
$498$	8.09909e6	1.46340
$499$	4.46530e6	0.802785	0.401392	−	0.915906i	$-0.368526\pi$
$499$	4.46530e6	0.802785	0.401392	+	0.915906i	$0.368526\pi$
$500$	0	0
$501$	−1.62493e6	−0.289228
$502$	283774.	0.0502589
$503$	1.77528e6	0.312858	0.156429	−	0.987689i	$-0.450002\pi$
$503$	1.77528e6	0.312858	0.156429	+	0.987689i	$0.450002\pi$
$504$	−591861.	−0.103787
$505$	0	0
$506$	2.15846e6	0.374772
$507$	−3.59683e6	−0.621441
$508$	−1.44248e7	−2.47999
$509$	−485180.	−0.0830058	−0.0415029	−	0.999138i	$-0.513215\pi$
$509$	−485180.	−0.0830058	−0.0415029	+	0.999138i	$0.513215\pi$
$510$	0	0
$511$	443664.	0.0751627
$512$	−1.59770e6	−0.269353
$513$	1.40890e6	0.236367
$514$	6.36739e6	1.06305
$515$	0	0
$516$	−2.16142e6	−0.357367
$517$	−1.49691e6	−0.246303
$518$	−640556.	−0.104890
$519$	−5.78989e6	−0.943522
$520$	0	0
$521$	9.92932e6	1.60260	0.801300	−	0.598262i	$-0.204142\pi$
$521$	9.92932e6	1.60260	0.801300	+	0.598262i	$0.204142\pi$
$522$	−360179.	−0.0578552
$523$	−5.04767e6	−0.806931	−0.403466	−	0.914995i	$-0.632195\pi$
$523$	−5.04767e6	−0.806931	−0.403466	+	0.914995i	$0.632195\pi$
$524$	−1.96889e7	−3.13251
$525$	0	0
$526$	−1.57436e7	−2.48107
$527$	−273398.	−0.0428815
$528$	150638.	0.0235152
$529$	−2.72156e6	−0.422842
$530$	0	0
$531$	−1.28449e6	−0.197695
$532$	3.77990e6	0.579031
$533$	−3.95117e6	−0.602432
$534$	−3.21856e6	−0.488437
$535$	0	0
$536$	3.14117e6	0.472258
$537$	2.40230e6	0.359494
$538$	−9.09467e6	−1.35466
$539$	1.87291e6	0.277680
$540$	0	0
$541$	−4.46393e6	−0.655729	−0.327864	−	0.944725i	$-0.606329\pi$
$541$	−4.46393e6	−0.655729	−0.327864	+	0.944725i	$0.606329\pi$
$542$	−2.55637e6	−0.373788
$543$	−2.53376e6	−0.368779
$544$	797900.	0.115598
$545$	0	0
$546$	2.66572e6	0.382678
$547$	6.62530e6	0.946755	0.473377	−	0.880860i	$-0.343035\pi$
$547$	6.62530e6	0.946755	0.473377	+	0.880860i	$0.343035\pi$
$548$	9.81601e6	1.39632
$549$	−2.95227e6	−0.418047
$550$	0	0
$551$	928530.	0.130292
$552$	3.47754e6	0.485763
$553$	3.17845e6	0.441980
$554$	−1.37696e6	−0.190611
$555$	0	0
$556$	452351.	0.0620568
$557$	717580.	0.0980014	0.0490007	−	0.998799i	$-0.484396\pi$
$557$	717580.	0.0980014	0.0490007	+	0.998799i	$0.484396\pi$
$558$	1.31905e6	0.179340
$559$	3.92962e6	0.531889
$560$	0	0
$561$	−169214.	−0.0227002
$562$	3.31129e6	0.442238
$563$	−1.35097e7	−1.79629	−0.898143	−	0.439703i	$-0.855084\pi$
$563$	−1.35097e7	−1.79629	−0.898143	+	0.439703i	$0.855084\pi$
$564$	−5.97461e6	−0.790882
$565$	0	0
$566$	4.55444e6	0.597577
$567$	−239134.	−0.0312380
$568$	2.14300e6	0.278709
$569$	1.35535e7	1.75498	0.877488	−	0.479598i	$-0.159218\pi$
$569$	1.35535e7	1.75498	0.877488	+	0.479598i	$0.159218\pi$
$570$	0	0
$571$	7.82130e6	1.00390	0.501948	−	0.864898i	$-0.332617\pi$
$571$	7.82130e6	1.00390	0.501948	+	0.864898i	$0.332617\pi$
$572$	−5.70101e6	−0.728554
$573$	−8.40351e6	−1.06924
$574$	1.51802e6	0.192308
$575$	0	0
$576$	−4.20814e6	−0.528486
$577$	−218443.	−0.0273149	−0.0136574	−	0.999907i	$-0.504347\pi$
$577$	−218443.	−0.0273149	−0.0136574	+	0.999907i	$0.504347\pi$
$578$	−1.29177e7	−1.60830
$579$	2.70112e6	0.334847
$580$	0	0
$581$	3.54384e6	0.435546
$582$	−3.06157e6	−0.374659
$583$	259559.	0.0316275
$584$	−2.44031e6	−0.296083
$585$	0	0
$586$	−4.61026e6	−0.554602
$587$	5.46003e6	0.654033	0.327017	−	0.945019i	$-0.393957\pi$
$587$	5.46003e6	0.654033	0.327017	+	0.945019i	$0.393957\pi$
$588$	7.47531e6	0.891632
$589$	−3.40048e6	−0.403879
$590$	0	0
$591$	−8.50446e6	−1.00156
$592$	262664.	0.0308033
$593$	−1.41186e7	−1.64875	−0.824375	−	0.566044i	$-0.808473\pi$
$593$	−1.41186e7	−1.64875	−0.824375	+	0.566044i	$0.808473\pi$
$594$	816401.	0.0949374
$595$	0	0
$596$	1.45855e7	1.68192
$597$	9.07385e6	1.04197
$598$	−1.56628e7	−1.79108
$599$	8.02044e6	0.913338	0.456669	−	0.889637i	$-0.349042\pi$
$599$	8.02044e6	0.913338	0.456669	+	0.889637i	$0.349042\pi$
$600$	0	0
$601$	−1.20301e7	−1.35857	−0.679286	−	0.733874i	$-0.737710\pi$
$601$	−1.20301e7	−1.35857	−0.679286	+	0.733874i	$0.737710\pi$
$602$	−1.50974e6	−0.169790
$603$	1.26915e6	0.142141
$604$	−1.26942e7	−1.41584
$605$	0	0
$606$	1.54506e7	1.70909
$607$	1.58863e7	1.75005	0.875025	−	0.484078i	$-0.160845\pi$
$607$	1.58863e7	1.75005	0.875025	+	0.484078i	$0.160845\pi$
$608$	9.92412e6	1.08876
$609$	−157600.	−0.0172192
$610$	0	0
$611$	1.08623e7	1.17711
$612$	−675384.	−0.0728907
$613$	−1.27701e7	−1.37260	−0.686301	−	0.727318i	$-0.740767\pi$
$613$	−1.27701e7	−1.37260	−0.686301	+	0.727318i	$0.740767\pi$
$614$	9.24383e6	0.989535
$615$	0	0
$616$	884137.	0.0938789
$617$	−5.32363e6	−0.562982	−0.281491	−	0.959564i	$-0.590829\pi$
$617$	−5.32363e6	−0.562982	−0.281491	+	0.959564i	$0.590829\pi$
$618$	3.07292e6	0.323653
$619$	−5.79882e6	−0.608293	−0.304147	−	0.952625i	$-0.598371\pi$
$619$	−5.79882e6	−0.608293	−0.304147	+	0.952625i	$0.598371\pi$
$620$	0	0
$621$	1.40506e6	0.146206
$622$	1.74724e7	1.81083
$623$	−1.40832e6	−0.145372
$624$	−1.09310e6	−0.112382
$625$	0	0
$626$	2.17302e7	2.21630
$627$	−2.10466e6	−0.213802
$628$	−1.13666e7	−1.15009
$629$	−295056.	−0.0297357
$630$	0	0
$631$	−8.25264e6	−0.825124	−0.412562	−	0.910929i	$-0.635366\pi$
$631$	−8.25264e6	−0.825124	−0.412562	+	0.910929i	$0.635366\pi$
$632$	−1.74826e7	−1.74106
$633$	−4.47731e6	−0.444128
$634$	−5.20816e6	−0.514590
$635$	0	0
$636$	1.03598e6	0.101556
$637$	−1.35907e7	−1.32707
$638$	538045.	0.0523320
$639$	865852.	0.0838864
$640$	0	0
$641$	1.14111e7	1.09694	0.548471	−	0.836169i	$-0.315210\pi$
$641$	1.14111e7	1.09694	0.548471	+	0.836169i	$0.315210\pi$
$642$	−1.04119e7	−0.996994
$643$	3.26961e6	0.311866	0.155933	−	0.987768i	$-0.450162\pi$
$643$	3.26961e6	0.311866	0.155933	+	0.987768i	$0.450162\pi$
$644$	3.76959e6	0.358162
$645$	0	0
$646$	2.77941e6	0.262043
$647$	9.95068e6	0.934527	0.467264	−	0.884118i	$-0.345240\pi$
$647$	9.95068e6	0.934527	0.467264	+	0.884118i	$0.345240\pi$
$648$	1.31532e6	0.123054
$649$	1.91881e6	0.178822
$650$	0	0
$651$	577166.	0.0533763
$652$	1.83152e7	1.68730
$653$	−1.52022e7	−1.39515	−0.697577	−	0.716509i	$-0.745739\pi$
$653$	−1.52022e7	−1.39515	−0.697577	+	0.716509i	$0.745739\pi$
$654$	1.25759e7	1.14973
$655$	0	0
$656$	−622474.	−0.0564757
$657$	−985979.	−0.0891157
$658$	−4.17324e6	−0.375758
$659$	−9.63232e6	−0.864007	−0.432004	−	0.901872i	$-0.642193\pi$
$659$	−9.63232e6	−0.864007	−0.432004	+	0.901872i	$0.642193\pi$
$660$	0	0
$661$	2.04631e7	1.82166	0.910832	−	0.412778i	$-0.135442\pi$
$661$	2.04631e7	1.82166	0.910832	+	0.412778i	$0.135442\pi$
$662$	−9.31016e6	−0.825681
$663$	1.22790e6	0.108487
$664$	−1.94924e7	−1.71572
$665$	0	0
$666$	1.42354e6	0.124361
$667$	925997.	0.0805926
$668$	9.68832e6	0.840054
$669$	1.02722e7	0.887361
$670$	0	0
$671$	4.41018e6	0.378137
$672$	−1.68443e6	−0.143890
$673$	−1.57773e6	−0.134275	−0.0671376	−	0.997744i	$-0.521387\pi$
$673$	−1.57773e6	−0.134275	−0.0671376	+	0.997744i	$0.521387\pi$
$674$	2.59326e6	0.219885
$675$	0	0
$676$	2.14454e7	1.80496
$677$	−6.92750e6	−0.580904	−0.290452	−	0.956890i	$-0.593806\pi$
$677$	−6.92750e6	−0.580904	−0.290452	+	0.956890i	$0.593806\pi$
$678$	1.31585e7	1.09934
$679$	−1.33962e6	−0.111509
$680$	0	0
$681$	6.02506e6	0.497845
$682$	−1.97044e6	−0.162219
$683$	277554.	0.0227665	0.0113833	−	0.999935i	$-0.496377\pi$
$683$	277554.	0.0227665	0.0113833	+	0.999935i	$0.496377\pi$
$684$	−8.40029e6	−0.686521
$685$	0	0
$686$	1.08911e7	0.883609
$687$	−5.29255e6	−0.427832
$688$	619080.	0.0498627
$689$	−1.88348e6	−0.151152
$690$	0	0
$691$	−2.12446e7	−1.69259	−0.846297	−	0.532712i	$-0.821173\pi$
$691$	−2.12446e7	−1.69259	−0.846297	+	0.532712i	$0.821173\pi$
$692$	3.45211e7	2.74043
$693$	357225.	0.0282559
$694$	−1.95206e7	−1.53849
$695$	0	0
$696$	866858.	0.0678305
$697$	699238.	0.0545184
$698$	3.59540e7	2.79324
$699$	1.79475e6	0.138935
$700$	0	0
$701$	−1.06971e7	−0.822184	−0.411092	−	0.911594i	$-0.634853\pi$
$701$	−1.06971e7	−0.822184	−0.411092	+	0.911594i	$0.634853\pi$
$702$	−5.92419e6	−0.453718
$703$	−3.66985e6	−0.280066
$704$	6.28623e6	0.478034
$705$	0	0
$706$	−1.25561e7	−0.948072
$707$	6.76058e6	0.508669
$708$	7.65853e6	0.574199
$709$	6.52521e6	0.487505	0.243752	−	0.969838i	$-0.421622\pi$
$709$	6.52521e6	0.487505	0.243752	+	0.969838i	$0.421622\pi$
$710$	0	0
$711$	−7.06365e6	−0.524029
$712$	7.74625e6	0.572653
$713$	−3.39120e6	−0.249821
$714$	−471753.	−0.0346313
$715$	0	0
$716$	−1.43232e7	−1.04414
$717$	3.67250e6	0.266786
$718$	3.64137e7	2.63605
$719$	−2.12413e7	−1.53235	−0.766176	−	0.642631i	$-0.777843\pi$
$719$	−2.12413e7	−1.53235	−0.766176	+	0.642631i	$0.777843\pi$
$720$	0	0
$721$	1.34459e6	0.0963276
$722$	1.16528e7	0.831928
$723$	−1.11620e7	−0.794135
$724$	1.51071e7	1.07111
$725$	0	0
$726$	−1.21956e6	−0.0858742
$727$	1.06687e7	0.748646	0.374323	−	0.927298i	$-0.377875\pi$
$727$	1.06687e7	0.748646	0.374323	+	0.927298i	$0.377875\pi$
$728$	−6.41571e6	−0.448659
$729$	531441.	0.0370370
$730$	0	0
$731$	−695424.	−0.0481345
$732$	1.76023e7	1.21420
$733$	2.30788e7	1.58655	0.793274	−	0.608864i	$-0.208375\pi$
$733$	2.30788e7	1.58655	0.793274	+	0.608864i	$0.208375\pi$
$734$	2.61544e7	1.79186
$735$	0	0
$736$	9.89705e6	0.673459
$737$	−1.89589e6	−0.128572
$738$	−3.37358e6	−0.228008
$739$	−2.27313e7	−1.53113	−0.765566	−	0.643358i	$-0.777541\pi$
$739$	−2.27313e7	−1.53113	−0.765566	+	0.643358i	$0.777541\pi$
$740$	0	0
$741$	1.52724e7	1.02179
$742$	723625.	0.0482507
$743$	1.49328e7	0.992360	0.496180	−	0.868220i	$-0.334736\pi$
$743$	1.49328e7	0.992360	0.496180	+	0.868220i	$0.334736\pi$
$744$	−3.17462e6	−0.210261
$745$	0	0
$746$	−4.24624e7	−2.79356
$747$	−7.87568e6	−0.516400
$748$	1.00891e6	0.0659321
$749$	−4.55584e6	−0.296732
$750$	0	0
$751$	−1.92964e7	−1.24846	−0.624232	−	0.781239i	$-0.714588\pi$
$751$	−1.92964e7	−1.24846	−0.624232	+	0.781239i	$0.714588\pi$
$752$	1.71126e6	0.110350
$753$	−275946.	−0.0177352
$754$	−3.90431e6	−0.250101
$755$	0	0
$756$	1.42579e6	0.0907300
$757$	−1.35397e7	−0.858756	−0.429378	−	0.903125i	$-0.641267\pi$
$757$	−1.35397e7	−0.858756	−0.429378	+	0.903125i	$0.641267\pi$
$758$	2.63616e7	1.66648
$759$	−2.09891e6	−0.132248
$760$	0	0
$761$	2.60669e7	1.63165	0.815825	−	0.578299i	$-0.196283\pi$
$761$	2.60669e7	1.63165	0.815825	+	0.578299i	$0.196283\pi$
$762$	2.23916e7	1.39701
$763$	5.50271e6	0.342188
$764$	5.01042e7	3.10557
$765$	0	0
$766$	2.57730e7	1.58706
$767$	−1.39238e7	−0.854611
$768$	1.14027e7	0.697598
$769$	−1.65354e7	−1.00832	−0.504162	−	0.863609i	$-0.668199\pi$
$769$	−1.65354e7	−1.00832	−0.504162	+	0.863609i	$0.668199\pi$
$770$	0	0
$771$	−6.19174e6	−0.375126
$772$	−1.61049e7	−0.972554
$773$	−8.95978e6	−0.539323	−0.269661	−	0.962955i	$-0.586912\pi$
$773$	−8.95978e6	−0.539323	−0.269661	+	0.962955i	$0.586912\pi$
$774$	3.35518e6	0.201309
$775$	0	0
$776$	7.36841e6	0.439258
$777$	622887.	0.0370132
$778$	3.65841e7	2.16692
$779$	8.69698e6	0.513482
$780$	0	0
$781$	−1.29343e6	−0.0758781
$782$	2.77183e6	0.162088
$783$	350244.	0.0204158
$784$	−2.14110e6	−0.124407
$785$	0	0
$786$	3.05631e7	1.76458
$787$	2.31723e7	1.33362	0.666812	−	0.745226i	$-0.267659\pi$
$787$	2.31723e7	1.33362	0.666812	+	0.745226i	$0.267659\pi$
$788$	5.07061e7	2.90901
$789$	1.53093e7	0.875512
$790$	0	0
$791$	5.75765e6	0.327193
$792$	−1.96487e6	−0.111306
$793$	−3.20023e7	−1.80717
$794$	5.13994e7	2.89339
$795$	0	0
$796$	−5.41010e7	−3.02638
$797$	3.40811e7	1.90050	0.950250	−	0.311489i	$-0.100828\pi$
$797$	3.40811e7	1.90050	0.950250	+	0.311489i	$0.100828\pi$
$798$	−5.86757e6	−0.326175
$799$	−1.92230e6	−0.106525
$800$	0	0
$801$	3.12978e6	0.172358
$802$	−2.58470e6	−0.141897
$803$	1.47288e6	0.0806082
$804$	−7.56706e6	−0.412845
$805$	0	0
$806$	1.42984e7	0.775265
$807$	8.84380e6	0.478030
$808$	−3.71857e7	−2.00377
$809$	1.77957e6	0.0955969	0.0477985	−	0.998857i	$-0.484779\pi$
$809$	1.77957e6	0.0955969	0.0477985	+	0.998857i	$0.484779\pi$
$810$	0	0
$811$	1.28099e7	0.683900	0.341950	−	0.939718i	$-0.388913\pi$
$811$	1.28099e7	0.683900	0.341950	+	0.939718i	$0.388913\pi$
$812$	939660.	0.0500127
$813$	2.48585e6	0.131901
$814$	−2.12653e6	−0.112489
$815$	0	0
$816$	193445.	0.0101703
$817$	−8.64955e6	−0.453355
$818$	4.78618e7	2.50095
$819$	−2.59219e6	−0.135038
$820$	0	0
$821$	1.47980e7	0.766205	0.383102	−	0.923706i	$-0.374856\pi$
$821$	1.47980e7	0.766205	0.383102	+	0.923706i	$0.374856\pi$
$822$	−1.52374e7	−0.786561
$823$	1.17405e7	0.604207	0.302103	−	0.953275i	$-0.402311\pi$
$823$	1.17405e7	0.604207	0.302103	+	0.953275i	$0.402311\pi$
$824$	−7.39572e6	−0.379457
$825$	0	0
$826$	5.34945e6	0.272809
$827$	−1.61763e7	−0.822461	−0.411231	−	0.911531i	$-0.634901\pi$
$827$	−1.61763e7	−0.822461	−0.411231	+	0.911531i	$0.634901\pi$
$828$	−8.37738e6	−0.424651
$829$	−1.56514e7	−0.790984	−0.395492	−	0.918470i	$-0.629426\pi$
$829$	−1.56514e7	−0.790984	−0.395492	+	0.918470i	$0.629426\pi$
$830$	0	0
$831$	1.33898e6	0.0672623
$832$	−4.56158e7	−2.28458
$833$	2.40514e6	0.120096
$834$	−702188.	−0.0349573
$835$	0	0
$836$	1.25486e7	0.620982
$837$	−1.28267e6	−0.0632850
$838$	−5.59161e7	−2.75060
$839$	2.70692e7	1.32761	0.663806	−	0.747905i	$-0.268940\pi$
$839$	2.70692e7	1.32761	0.663806	+	0.747905i	$0.268940\pi$
$840$	0	0
$841$	−2.02803e7	−0.988746
$842$	−8.28707e6	−0.402829
$843$	−3.21995e6	−0.156056
$844$	2.66951e7	1.28996
$845$	0	0
$846$	9.27442e6	0.445513
$847$	−533632.	−0.0255584
$848$	−296727.	−0.0141699
$849$	−4.42881e6	−0.210871
$850$	0	0
$851$	−3.65984e6	−0.173236
$852$	−5.16246e6	−0.243645
$853$	2.43979e7	1.14810	0.574050	−	0.818820i	$-0.305371\pi$
$853$	2.43979e7	1.14810	0.574050	+	0.818820i	$0.305371\pi$
$854$	1.22951e7	0.576884
$855$	0	0
$856$	2.50588e7	1.16889
$857$	−1.33841e7	−0.622496	−0.311248	−	0.950329i	$-0.600747\pi$
$857$	−1.33841e7	−0.622496	−0.311248	+	0.950329i	$0.600747\pi$
$858$	8.84971e6	0.410403
$859$	−2.60324e7	−1.20374	−0.601869	−	0.798595i	$-0.705577\pi$
$859$	−2.60324e7	−1.20374	−0.601869	+	0.798595i	$0.705577\pi$
$860$	0	0
$861$	−1.47615e6	−0.0678612
$862$	−1.48887e7	−0.682479
$863$	2.45378e7	1.12152	0.560762	−	0.827977i	$-0.310508\pi$
$863$	2.45378e7	1.12152	0.560762	+	0.827977i	$0.310508\pi$
$864$	3.74340e6	0.170601
$865$	0	0
$866$	−1.72185e7	−0.780190
$867$	1.25614e7	0.567532
$868$	−3.44123e6	−0.155030
$869$	1.05519e7	0.474002
$870$	0	0
$871$	1.37575e7	0.614460
$872$	−3.02669e7	−1.34796
$873$	2.97712e6	0.132209
$874$	3.44755e7	1.52662
$875$	0	0
$876$	5.87870e6	0.258834
$877$	−1.99034e7	−0.873833	−0.436917	−	0.899502i	$-0.643930\pi$
$877$	−1.99034e7	−0.873833	−0.436917	+	0.899502i	$0.643930\pi$
$878$	2.54568e7	1.11447
$879$	4.48308e6	0.195706
$880$	0	0
$881$	−3.90880e7	−1.69669	−0.848346	−	0.529442i	$-0.822401\pi$
$881$	−3.90880e7	−1.69669	−0.848346	+	0.529442i	$0.822401\pi$
$882$	−1.16040e7	−0.502267
$883$	−2.14490e7	−0.925776	−0.462888	−	0.886417i	$-0.653187\pi$
$883$	−2.14490e7	−0.925776	−0.462888	+	0.886417i	$0.653187\pi$
$884$	−7.32109e6	−0.315098
$885$	0	0
$886$	−2.92287e7	−1.25091
$887$	−6.08624e6	−0.259741	−0.129870	−	0.991531i	$-0.541456\pi$
$887$	−6.08624e6	−0.259741	−0.129870	+	0.991531i	$0.541456\pi$
$888$	−3.42610e6	−0.145803
$889$	9.79769e6	0.415786
$890$	0	0
$891$	−793881.	−0.0335013
$892$	−6.12462e7	−2.57731
$893$	−2.39091e7	−1.00331
$894$	−2.26412e7	−0.947447
$895$	0	0
$896$	1.15363e7	0.480060
$897$	1.52307e7	0.632031
$898$	−1.18012e6	−0.0488356
$899$	−845336.	−0.0348843
$900$	0	0
$901$	333319.	0.0136788
$902$	5.03955e6	0.206241
$903$	1.46810e6	0.0599149
$904$	−3.16691e7	−1.28889
$905$	0	0
$906$	1.97053e7	0.797560
$907$	2.14459e7	0.865618	0.432809	−	0.901486i	$-0.357523\pi$
$907$	2.14459e7	0.865618	0.432809	+	0.901486i	$0.357523\pi$
$908$	−3.59232e7	−1.44597
$909$	−1.50244e7	−0.603098
$910$	0	0
$911$	1.03374e7	0.412682	0.206341	−	0.978480i	$-0.433844\pi$
$911$	1.03374e7	0.412682	0.206341	+	0.978480i	$0.433844\pi$
$912$	2.40603e6	0.0957888
$913$	1.17649e7	0.467102
$914$	−2.02884e7	−0.803310
$915$	0	0
$916$	3.15557e7	1.24262
$917$	1.33732e7	0.525185
$918$	1.04840e6	0.0410602
$919$	−4.75142e7	−1.85581	−0.927907	−	0.372811i	$-0.878394\pi$
$919$	−4.75142e7	−1.85581	−0.927907	+	0.372811i	$0.878394\pi$
$920$	0	0
$921$	−8.98884e6	−0.349184
$922$	4.81488e7	1.86534
$923$	9.38575e6	0.362631
$924$	−2.12988e6	−0.0820683
$925$	0	0
$926$	−2.46769e7	−0.945720
$927$	−2.98815e6	−0.114210
$928$	2.46707e6	0.0940398
$929$	6.08962e6	0.231500	0.115750	−	0.993278i	$-0.463073\pi$
$929$	6.08962e6	0.231500	0.115750	+	0.993278i	$0.463073\pi$
$930$	0	0
$931$	2.99146e7	1.13112
$932$	−1.07008e7	−0.403532
$933$	−1.69904e7	−0.638999
$934$	2.18034e7	0.817820
$935$	0	0
$936$	1.42580e7	0.531947
$937$	2.73781e6	0.101872	0.0509360	−	0.998702i	$-0.483780\pi$
$937$	2.73781e6	0.101872	0.0509360	+	0.998702i	$0.483780\pi$
$938$	−5.28556e6	−0.196148
$939$	−2.11308e7	−0.782082
$940$	0	0
$941$	3.73849e7	1.37633	0.688165	−	0.725554i	$-0.258417\pi$
$941$	3.73849e7	1.37633	0.688165	+	0.725554i	$0.258417\pi$
$942$	1.76445e7	0.647861
$943$	8.67326e6	0.317617
$944$	−2.19358e6	−0.0801166
$945$	0	0
$946$	−5.01206e6	−0.182091
$947$	4.08261e7	1.47932	0.739661	−	0.672979i	$-0.234986\pi$
$947$	4.08261e7	1.47932	0.739661	+	0.672979i	$0.234986\pi$
$948$	4.21156e7	1.52203
$949$	−1.06879e7	−0.385237
$950$	0	0
$951$	5.06449e6	0.181587
$952$	1.13539e6	0.0406024
$953$	4.60553e7	1.64266	0.821330	−	0.570453i	$-0.193232\pi$
$953$	4.60553e7	1.64266	0.821330	+	0.570453i	$0.193232\pi$
$954$	−1.60815e6	−0.0572079
$955$	0	0
$956$	−2.18965e7	−0.774873
$957$	−523204.	−0.0184668
$958$	−4.42709e7	−1.55849
$959$	−6.66730e6	−0.234101
$960$	0	0
$961$	−2.55333e7	−0.891865
$962$	1.54311e7	0.537599
$963$	1.01247e7	0.351817
$964$	6.65509e7	2.30654
$965$	0	0
$966$	−5.85156e6	−0.201757
$967$	−1.48162e7	−0.509532	−0.254766	−	0.967003i	$-0.581998\pi$
$967$	−1.48162e7	−0.509532	−0.254766	+	0.967003i	$0.581998\pi$
$968$	2.93517e6	0.100680
$969$	−2.70275e6	−0.0924689
$970$	0	0
$971$	−3.27641e7	−1.11519	−0.557597	−	0.830112i	$-0.688277\pi$
$971$	−3.27641e7	−1.11519	−0.557597	+	0.830112i	$0.688277\pi$
$972$	−3.16861e6	−0.107573
$973$	−307250.	−0.0104042
$974$	3.06828e7	1.03633
$975$	0	0
$976$	−5.04170e6	−0.169415
$977$	4.06772e6	0.136337	0.0681686	−	0.997674i	$-0.478284\pi$
$977$	4.06772e6	0.136337	0.0681686	+	0.997674i	$0.478284\pi$
$978$	−2.84307e7	−0.950476
$979$	−4.67535e6	−0.155904
$980$	0	0
$981$	−1.22290e7	−0.405712
$982$	−2.79765e7	−0.925795
$983$	−3.76095e7	−1.24141	−0.620704	−	0.784045i	$-0.713153\pi$
$983$	−3.76095e7	−1.24141	−0.620704	+	0.784045i	$0.713153\pi$
$984$	8.11934e6	0.267321
$985$	0	0
$986$	690944.	0.0226335
$987$	4.05812e6	0.132596
$988$	−9.10583e7	−2.96775
$989$	−8.62596e6	−0.280425
$990$	0	0
$991$	1.02888e7	0.332797	0.166399	−	0.986059i	$-0.446786\pi$
$991$	1.02888e7	0.332797	0.166399	+	0.986059i	$0.446786\pi$
$992$	−9.03495e6	−0.291505
$993$	9.05334e6	0.291364
$994$	−3.60596e6	−0.115759
$995$	0	0
$996$	4.69571e7	1.49987
$997$	−4.37776e7	−1.39481	−0.697403	−	0.716680i	$-0.745661\pi$
$997$	−4.37776e7	−1.39481	−0.697403	+	0.716680i	$0.745661\pi$
$998$	4.13277e7	1.31345
$999$	−1.38428e6	−0.0438843

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.6.a.a.1.1	✓	3	5.4	even	2
495.6.a.e.1.3		3	15.14	odd	2
825.6.a.j.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)

\(f(q)\)	\(=\)	\(q+9.25531 q^{2} -9.00000 q^{3} +53.6607 q^{4} -83.2977 q^{6} -36.4478 q^{7} +200.476 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+9.25531 q^{2} -9.00000 q^{3} +53.6607 q^{4} -83.2977 q^{6} -36.4478 q^{7} +200.476 q^{8} +81.0000 q^{9} -121.000 q^{11} -482.946 q^{12} +878.032 q^{13} -337.336 q^{14} +138.327 q^{16} -155.385 q^{17} +749.680 q^{18} -1932.65 q^{19} +328.030 q^{21} -1119.89 q^{22} -1927.38 q^{23} -1804.29 q^{24} +8126.46 q^{26} -729.000 q^{27} -1955.81 q^{28} -480.444 q^{29} +1759.49 q^{31} -5134.98 q^{32} +1089.00 q^{33} -1438.14 q^{34} +4346.51 q^{36} +1898.87 q^{37} -17887.3 q^{38} -7902.29 q^{39} -4500.03 q^{41} +3036.02 q^{42} +4475.49 q^{43} -6492.94 q^{44} -17838.5 q^{46} +12371.2 q^{47} -1244.94 q^{48} -15478.6 q^{49} +1398.47 q^{51} +47115.8 q^{52} -2145.12 q^{53} -6747.12 q^{54} -7306.92 q^{56} +17393.8 q^{57} -4446.66 q^{58} -15857.9 q^{59} -36447.7 q^{61} +16284.6 q^{62} -2952.27 q^{63} -51952.3 q^{64} +10079.0 q^{66} +15668.5 q^{67} -8338.07 q^{68} +17346.4 q^{69} +10689.5 q^{71} +16238.6 q^{72} -12172.6 q^{73} +17574.6 q^{74} -103707. q^{76} +4410.19 q^{77} -73138.1 q^{78} -87205.6 q^{79} +6561.00 q^{81} -41649.2 q^{82} -97230.6 q^{83} +17602.3 q^{84} +41422.0 q^{86} +4324.00 q^{87} -24257.6 q^{88} +38639.2 q^{89} -32002.4 q^{91} -103424. q^{92} -15835.4 q^{93} +114499. q^{94} +46214.8 q^{96} +36754.5 q^{97} -143259. q^{98} -9801.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 7 q^{2} - 27 q^{3} + 25 q^{4} - 63 q^{6} + 172 q^{7} + 231 q^{8} + 243 q^{9}+O(q^{10}) \) 3 * q + 7 * q^2 - 27 * q^3 + 25 * q^4 - 63 * q^6 + 172 * q^7 + 231 * q^8 + 243 * q^9	\( 3 q + 7 q^{2} - 27 q^{3} + 25 q^{4} - 63 q^{6} + 172 q^{7} + 231 q^{8} + 243 q^{9} - 363 q^{11} - 225 q^{12} + 654 q^{13} - 728 q^{14} - 415 q^{16} + 2366 q^{17} + 567 q^{18} - 2872 q^{19} - 1548 q^{21} - 847 q^{22} - 2272 q^{23} - 2079 q^{24} + 3422 q^{26} - 2187 q^{27} - 4592 q^{28} - 7738 q^{29} + 568 q^{31} - 1001 q^{32} + 3267 q^{33} + 2506 q^{34} + 2025 q^{36} + 9126 q^{37} - 13076 q^{38} - 5886 q^{39} - 8758 q^{41} + 6552 q^{42} + 14672 q^{43} - 3025 q^{44} - 28768 q^{46} + 19392 q^{47} + 3735 q^{48} - 26629 q^{49} - 21294 q^{51} + 61506 q^{52} + 4598 q^{53} - 5103 q^{54} + 2688 q^{56} + 25848 q^{57} - 8550 q^{58} - 9348 q^{59} - 60078 q^{61} + 14096 q^{62} + 13932 q^{63} - 7087 q^{64} + 7623 q^{66} + 38468 q^{67} - 59778 q^{68} + 20448 q^{69} - 74032 q^{71} + 18711 q^{72} + 44442 q^{73} + 82542 q^{74} - 98708 q^{76} - 20812 q^{77} - 30798 q^{78} - 108116 q^{79} + 19683 q^{81} + 92230 q^{82} + 81892 q^{83} + 41328 q^{84} + 126412 q^{86} + 69642 q^{87} - 27951 q^{88} + 167342 q^{89} - 31832 q^{91} - 72960 q^{92} - 5112 q^{93} + 12728 q^{94} + 9009 q^{96} - 159702 q^{97} - 163121 q^{98} - 29403 q^{99}+O(q^{100}) \) 3 * q + 7 * q^2 - 27 * q^3 + 25 * q^4 - 63 * q^6 + 172 * q^7 + 231 * q^8 + 243 * q^9 - 363 * q^11 - 225 * q^12 + 654 * q^13 - 728 * q^14 - 415 * q^16 + 2366 * q^17 + 567 * q^18 - 2872 * q^19 - 1548 * q^21 - 847 * q^22 - 2272 * q^23 - 2079 * q^24 + 3422 * q^26 - 2187 * q^27 - 4592 * q^28 - 7738 * q^29 + 568 * q^31 - 1001 * q^32 + 3267 * q^33 + 2506 * q^34 + 2025 * q^36 + 9126 * q^37 - 13076 * q^38 - 5886 * q^39 - 8758 * q^41 + 6552 * q^42 + 14672 * q^43 - 3025 * q^44 - 28768 * q^46 + 19392 * q^47 + 3735 * q^48 - 26629 * q^49 - 21294 * q^51 + 61506 * q^52 + 4598 * q^53 - 5103 * q^54 + 2688 * q^56 + 25848 * q^57 - 8550 * q^58 - 9348 * q^59 - 60078 * q^61 + 14096 * q^62 + 13932 * q^63 - 7087 * q^64 + 7623 * q^66 + 38468 * q^67 - 59778 * q^68 + 20448 * q^69 - 74032 * q^71 + 18711 * q^72 + 44442 * q^73 + 82542 * q^74 - 98708 * q^76 - 20812 * q^77 - 30798 * q^78 - 108116 * q^79 + 19683 * q^81 + 92230 * q^82 + 81892 * q^83 + 41328 * q^84 + 126412 * q^86 + 69642 * q^87 - 27951 * q^88 + 167342 * q^89 - 31832 * q^91 - 72960 * q^92 - 5112 * q^93 + 12728 * q^94 + 9009 * q^96 - 159702 * q^97 - 163121 * q^98 - 29403 * q^99

Introduction

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Database

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