LMFDB - Embedded newform 650.6.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,6,Mod(1,650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(650, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("650.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	650.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:	$104.249482878$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{14}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 14 $ x^2 - 14
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$3.74166$ of defining polynomial
Character	$\chi$	$=$	650.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000 q^{2} +19.2250 q^{3} +16.0000 q^{4} -76.8999 q^{6} +51.1669 q^{7} -64.0000 q^{8} +126.600 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} +19.2250 q^{3} +16.0000 q^{4} -76.8999 q^{6} +51.1669 q^{7} -64.0000 q^{8} +126.600 q^{9} +494.607 q^{11} +307.600 q^{12} +169.000 q^{13} -204.667 q^{14} +256.000 q^{16} +2364.88 q^{17} -506.398 q^{18} -699.408 q^{19} +983.681 q^{21} -1978.43 q^{22} +3809.57 q^{23} -1230.40 q^{24} -676.000 q^{26} -2237.80 q^{27} +818.670 q^{28} +2263.52 q^{29} -9088.51 q^{31} -1024.00 q^{32} +9508.81 q^{33} -9459.52 q^{34} +2025.59 q^{36} +4487.29 q^{37} +2797.63 q^{38} +3249.02 q^{39} -12430.1 q^{41} -3934.73 q^{42} +12572.6 q^{43} +7913.71 q^{44} -15238.3 q^{46} -3601.31 q^{47} +4921.59 q^{48} -14189.0 q^{49} +45464.8 q^{51} +2704.00 q^{52} -7547.01 q^{53} +8951.18 q^{54} -3274.68 q^{56} -13446.1 q^{57} -9054.09 q^{58} +50069.9 q^{59} -24756.7 q^{61} +36354.0 q^{62} +6477.70 q^{63} +4096.00 q^{64} -38035.2 q^{66} -43724.6 q^{67} +37838.1 q^{68} +73238.8 q^{69} +7603.34 q^{71} -8102.37 q^{72} +21623.2 q^{73} -17949.2 q^{74} -11190.5 q^{76} +25307.5 q^{77} -12996.1 q^{78} +103537. q^{79} -73785.2 q^{81} +49720.3 q^{82} +80394.0 q^{83} +15738.9 q^{84} -50290.4 q^{86} +43516.1 q^{87} -31654.9 q^{88} +59301.0 q^{89} +8647.20 q^{91} +60953.1 q^{92} -174726. q^{93} +14405.2 q^{94} -19686.4 q^{96} +73477.5 q^{97} +56755.8 q^{98} +62617.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8 q^{2} + 16 q^{3} + 32 q^{4} - 64 q^{6} + 252 q^{7} - 128 q^{8} - 106 q^{9}+O(q^{10}) $ 2 * q - 8 * q^2 + 16 * q^3 + 32 * q^4 - 64 * q^6 + 252 * q^7 - 128 * q^8 - 106 * q^9	\( 2 q - 8 q^{2} + 16 q^{3} + 32 q^{4} - 64 q^{6} + 252 q^{7} - 128 q^{8} - 106 q^{9} - 36 q^{11} + 256 q^{12} + 338 q^{13} - 1008 q^{14} + 512 q^{16} + 2380 q^{17} + 424 q^{18} - 1092 q^{19} + 336 q^{21} + 144 q^{22} + 1176 q^{23} - 1024 q^{24} - 1352 q^{26} - 704 q^{27} + 4032 q^{28} - 4872 q^{29} - 2260 q^{31} - 2048 q^{32} + 11220 q^{33} - 9520 q^{34} - 1696 q^{36} + 17760 q^{37} + 4368 q^{38} + 2704 q^{39} - 9220 q^{41} - 1344 q^{42} + 23656 q^{43} - 576 q^{44} - 4704 q^{46} - 12860 q^{47} + 4096 q^{48} + 9338 q^{49} + 45416 q^{51} + 5408 q^{52} - 11068 q^{53} + 2816 q^{54} - 16128 q^{56} - 12180 q^{57} + 19488 q^{58} + 90404 q^{59} - 69000 q^{61} + 9040 q^{62} - 40236 q^{63} + 8192 q^{64} - 44880 q^{66} - 50796 q^{67} + 38080 q^{68} + 81732 q^{69} - 28668 q^{71} + 6784 q^{72} + 62688 q^{73} - 71040 q^{74} - 17472 q^{76} - 81256 q^{77} - 10816 q^{78} + 84064 q^{79} - 22210 q^{81} + 36880 q^{82} + 12828 q^{83} + 5376 q^{84} - 94624 q^{86} + 66528 q^{87} + 2304 q^{88} + 92620 q^{89} + 42588 q^{91} + 18816 q^{92} - 196748 q^{93} + 51440 q^{94} - 16384 q^{96} + 75684 q^{97} - 37352 q^{98} + 186036 q^{99}+O(q^{100}) \) 2 * q - 8 * q^2 + 16 * q^3 + 32 * q^4 - 64 * q^6 + 252 * q^7 - 128 * q^8 - 106 * q^9 - 36 * q^11 + 256 * q^12 + 338 * q^13 - 1008 * q^14 + 512 * q^16 + 2380 * q^17 + 424 * q^18 - 1092 * q^19 + 336 * q^21 + 144 * q^22 + 1176 * q^23 - 1024 * q^24 - 1352 * q^26 - 704 * q^27 + 4032 * q^28 - 4872 * q^29 - 2260 * q^31 - 2048 * q^32 + 11220 * q^33 - 9520 * q^34 - 1696 * q^36 + 17760 * q^37 + 4368 * q^38 + 2704 * q^39 - 9220 * q^41 - 1344 * q^42 + 23656 * q^43 - 576 * q^44 - 4704 * q^46 - 12860 * q^47 + 4096 * q^48 + 9338 * q^49 + 45416 * q^51 + 5408 * q^52 - 11068 * q^53 + 2816 * q^54 - 16128 * q^56 - 12180 * q^57 + 19488 * q^58 + 90404 * q^59 - 69000 * q^61 + 9040 * q^62 - 40236 * q^63 + 8192 * q^64 - 44880 * q^66 - 50796 * q^67 + 38080 * q^68 + 81732 * q^69 - 28668 * q^71 + 6784 * q^72 + 62688 * q^73 - 71040 * q^74 - 17472 * q^76 - 81256 * q^77 - 10816 * q^78 + 84064 * q^79 - 22210 * q^81 + 36880 * q^82 + 12828 * q^83 + 5376 * q^84 - 94624 * q^86 + 66528 * q^87 + 2304 * q^88 + 92620 * q^89 + 42588 * q^91 + 18816 * q^92 - 196748 * q^93 + 51440 * q^94 - 16384 * q^96 + 75684 * q^97 - 37352 * q^98 + 186036 * 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 $

$2$	−4.00000	−0.707107
$2$	−4.00000	−0.707107
$3$	19.2250	1.23328	0.616641	−	0.787244i	$-0.288493\pi$
$3$	19.2250	1.23328	0.616641	+	0.787244i	$0.288493\pi$
$4$	16.0000	0.500000
$5$	0	0
$5$	0	0
$6$	−76.8999	−0.872062
$7$	51.1669	0.394679	0.197339	−	0.980335i	$-0.436770\pi$
$7$	51.1669	0.394679	0.197339	+	0.980335i	$0.436770\pi$
$8$	−64.0000	−0.353553
$9$	126.600	0.520986
$10$	0	0
$11$	494.607	1.23248	0.616238	−	0.787560i	$-0.288656\pi$
$11$	494.607	1.23248	0.616238	+	0.787560i	$0.288656\pi$
$12$	307.600	0.616641
$13$	169.000	0.277350
$13$	169.000	0.277350
$14$	−204.667	−0.279080
$15$	0	0
$16$	256.000	0.250000
$17$	2364.88	1.98466	0.992332	−	0.123603i	$-0.0394449\pi$
$17$	2364.88	1.98466	0.992332	+	0.123603i	$0.0394449\pi$
$18$	−506.398	−0.368393
$19$	−699.408	−0.444474	−0.222237	−	0.974993i	$-0.571336\pi$
$19$	−699.408	−0.444474	−0.222237	+	0.974993i	$0.571336\pi$
$20$	0	0
$21$	983.681	0.486750
$22$	−1978.43	−0.871492
$23$	3809.57	1.50161	0.750803	−	0.660526i	$-0.229667\pi$
$23$	3809.57	1.50161	0.750803	+	0.660526i	$0.229667\pi$
$24$	−1230.40	−0.436031
$25$	0	0
$26$	−676.000	−0.196116
$27$	−2237.80	−0.590760
$28$	818.670	0.197339
$29$	2263.52	0.499792	0.249896	−	0.968273i	$-0.419603\pi$
$29$	2263.52	0.499792	0.249896	+	0.968273i	$0.419603\pi$
$30$	0	0
$31$	−9088.51	−1.69859	−0.849294	−	0.527920i	$-0.822972\pi$
$31$	−9088.51	−1.69859	−0.849294	+	0.527920i	$0.822972\pi$
$32$	−1024.00	−0.176777
$33$	9508.81	1.51999
$34$	−9459.52	−1.40337
$35$	0	0
$36$	2025.59	0.260493
$37$	4487.29	0.538865	0.269433	−	0.963019i	$-0.413164\pi$
$37$	4487.29	0.538865	0.269433	+	0.963019i	$0.413164\pi$
$38$	2797.63	0.314291
$39$	3249.02	0.342051
$40$	0	0
$41$	−12430.1	−1.15482	−0.577409	−	0.816455i	$-0.695936\pi$
$41$	−12430.1	−1.15482	−0.577409	+	0.816455i	$0.695936\pi$
$42$	−3934.73	−0.344184
$43$	12572.6	1.03694	0.518470	−	0.855096i	$-0.326502\pi$
$43$	12572.6	1.03694	0.518470	+	0.855096i	$0.326502\pi$
$44$	7913.71	0.616238
$45$	0	0
$46$	−15238.3	−1.06180
$47$	−3601.31	−0.237802	−0.118901	−	0.992906i	$-0.537937\pi$
$47$	−3601.31	−0.237802	−0.118901	+	0.992906i	$0.537937\pi$
$48$	4921.59	0.308321
$49$	−14189.0	−0.844229
$50$	0	0
$51$	45464.8	2.44765
$52$	2704.00	0.138675
$53$	−7547.01	−0.369050	−0.184525	−	0.982828i	$-0.559075\pi$
$53$	−7547.01	−0.369050	−0.184525	+	0.982828i	$0.559075\pi$
$54$	8951.18	0.417730
$55$	0	0
$56$	−3274.68	−0.139540
$57$	−13446.1	−0.548162
$58$	−9054.09	−0.353407
$59$	50069.9	1.87261	0.936304	−	0.351192i	$-0.114223\pi$
$59$	50069.9	1.87261	0.936304	+	0.351192i	$0.114223\pi$
$60$	0	0
$61$	−24756.7	−0.851861	−0.425930	−	0.904756i	$-0.640053\pi$
$61$	−24756.7	−0.851861	−0.425930	+	0.904756i	$0.640053\pi$
$62$	36354.0	1.20108
$63$	6477.70	0.205622
$64$	4096.00	0.125000
$65$	0	0
$66$	−38035.2	−1.07480
$67$	−43724.6	−1.18998	−0.594989	−	0.803734i	$-0.702844\pi$
$67$	−43724.6	−1.18998	−0.594989	+	0.803734i	$0.702844\pi$
$68$	37838.1	0.992332
$69$	73238.8	1.85190
$70$	0	0
$71$	7603.34	0.179002	0.0895011	−	0.995987i	$-0.471473\pi$
$71$	7603.34	0.179002	0.0895011	+	0.995987i	$0.471473\pi$
$72$	−8102.37	−0.184196
$73$	21623.2	0.474911	0.237456	−	0.971398i	$-0.423687\pi$
$73$	21623.2	0.474911	0.237456	+	0.971398i	$0.423687\pi$
$74$	−17949.2	−0.381035
$75$	0	0
$76$	−11190.5	−0.222237
$77$	25307.5	0.486432
$78$	−12996.1	−0.241867
$79$	103537.	1.86651	0.933253	−	0.359220i	$-0.116957\pi$
$79$	103537.	1.86651	0.933253	+	0.359220i	$0.116957\pi$
$80$	0	0
$81$	−73785.2	−1.24956
$82$	49720.3	0.816580
$83$	80394.0	1.28094	0.640470	−	0.767983i	$-0.278740\pi$
$83$	80394.0	1.28094	0.640470	+	0.767983i	$0.278740\pi$
$84$	15738.9	0.243375
$85$	0	0
$86$	−50290.4	−0.733227
$87$	43516.1	0.616385
$88$	−31654.9	−0.435746
$89$	59301.0	0.793574	0.396787	−	0.917911i	$-0.370125\pi$
$89$	59301.0	0.793574	0.396787	+	0.917911i	$0.370125\pi$
$90$	0	0
$91$	8647.20	0.109464
$92$	60953.1	0.750803
$93$	−174726.	−2.09484
$94$	14405.2	0.168151
$95$	0	0
$96$	−19686.4	−0.218016
$97$	73477.5	0.792913	0.396456	−	0.918054i	$-0.370240\pi$
$97$	73477.5	0.792913	0.396456	+	0.918054i	$0.370240\pi$
$98$	56755.8	0.596960
$99$	62617.0	0.642103
$100$	0	0
$101$	97567.8	0.951707	0.475853	−	0.879525i	$-0.342139\pi$
$101$	97567.8	0.951707	0.475853	+	0.879525i	$0.342139\pi$
$102$	−181859.	−1.73075
$103$	−30991.0	−0.287835	−0.143917	−	0.989590i	$-0.545970\pi$
$103$	−30991.0	−0.287835	−0.143917	+	0.989590i	$0.545970\pi$
$104$	−10816.0	−0.0980581
$105$	0	0
$106$	30188.0	0.260958
$107$	−202039.	−1.70599	−0.852993	−	0.521923i	$-0.825215\pi$
$107$	−202039.	−1.70599	−0.852993	+	0.521923i	$0.825215\pi$
$108$	−35804.7	−0.295380
$109$	−171150.	−1.37978	−0.689890	−	0.723914i	$-0.742341\pi$
$109$	−171150.	−1.37978	−0.689890	+	0.723914i	$0.742341\pi$
$110$	0	0
$111$	86268.1	0.664573
$112$	13098.7	0.0986697
$113$	138118.	1.01755	0.508774	−	0.860900i	$-0.330099\pi$
$113$	138118.	1.01755	0.508774	+	0.860900i	$0.330099\pi$
$114$	53784.4	0.387609
$115$	0	0
$116$	36216.3	0.249896
$117$	21395.3	0.144495
$118$	−200280.	−1.32413
$119$	121003.	0.783304
$120$	0	0
$121$	83585.1	0.518998
$122$	99026.9	0.602356
$123$	−238968.	−1.42422
$124$	−145416.	−0.849294
$125$	0	0
$126$	−25910.8	−0.145397
$127$	−86030.1	−0.473305	−0.236653	−	0.971594i	$-0.576050\pi$
$127$	−86030.1	−0.473305	−0.236653	+	0.971594i	$0.576050\pi$
$128$	−16384.0	−0.0883883
$129$	241708.	1.27884
$130$	0	0
$131$	−297647.	−1.51538	−0.757692	−	0.652612i	$-0.773673\pi$
$131$	−297647.	−1.51538	−0.757692	+	0.652612i	$0.773673\pi$
$132$	152141.	0.759996
$133$	−35786.5	−0.175424
$134$	174899.	0.841442
$135$	0	0
$136$	−151352.	−0.701685
$137$	75631.0	0.344269	0.172135	−	0.985073i	$-0.444934\pi$
$137$	75631.0	0.344269	0.172135	+	0.985073i	$0.444934\pi$
$138$	−292955.	−1.30949
$139$	58569.2	0.257118	0.128559	−	0.991702i	$-0.458965\pi$
$139$	58569.2	0.257118	0.128559	+	0.991702i	$0.458965\pi$
$140$	0	0
$141$	−69235.0	−0.293277
$142$	−30413.3	−0.126574
$143$	83588.6	0.341827
$144$	32409.5	0.130246
$145$	0	0
$146$	−86492.7	−0.335813
$147$	−272782.	−1.04117
$148$	71796.7	0.269433
$149$	−344984.	−1.27301	−0.636507	−	0.771271i	$-0.719621\pi$
$149$	−344984.	−1.27301	−0.636507	+	0.771271i	$0.719621\pi$
$150$	0	0
$151$	12433.7	0.0443770	0.0221885	−	0.999754i	$-0.492937\pi$
$151$	12433.7	0.0443770	0.0221885	+	0.999754i	$0.492937\pi$
$152$	44762.1	0.157145
$153$	299393.	1.03398
$154$	−101230.	−0.343959
$155$	0	0
$156$	51984.3	0.171026
$157$	416674.	1.34911	0.674555	−	0.738225i	$-0.264336\pi$
$157$	416674.	1.34911	0.674555	+	0.738225i	$0.264336\pi$
$158$	−414149.	−1.31982
$159$	−145091.	−0.455143
$160$	0	0
$161$	194924.	0.592652
$162$	295141.	0.883572
$163$	225121.	0.663661	0.331831	−	0.943339i	$-0.392334\pi$
$163$	225121.	0.663661	0.331831	+	0.943339i	$0.392334\pi$
$164$	−198881.	−0.577409
$165$	0	0
$166$	−321576.	−0.905761
$167$	94547.0	0.262335	0.131168	−	0.991360i	$-0.458127\pi$
$167$	94547.0	0.262335	0.131168	+	0.991360i	$0.458127\pi$
$168$	−62955.6	−0.172092
$169$	28561.0	0.0769231
$170$	0	0
$171$	−88544.7	−0.231565
$172$	201161.	0.518470
$173$	92745.6	0.235602	0.117801	−	0.993037i	$-0.462416\pi$
$173$	92745.6	0.235602	0.117801	+	0.993037i	$0.462416\pi$
$174$	−174065.	−0.435850
$175$	0	0
$176$	126619.	0.308119
$177$	962592.	2.30945
$178$	−237204.	−0.561141
$179$	226852.	0.529187	0.264594	−	0.964360i	$-0.414762\pi$
$179$	226852.	0.529187	0.264594	+	0.964360i	$0.414762\pi$
$180$	0	0
$181$	691487.	1.56887	0.784436	−	0.620210i	$-0.212953\pi$
$181$	691487.	1.56887	0.784436	+	0.620210i	$0.212953\pi$
$182$	−34588.8	−0.0774028
$183$	−475947.	−1.05058
$184$	−243812.	−0.530898
$185$	0	0
$186$	698905.	1.48128
$187$	1.16969e6	2.44605
$188$	−57620.9	−0.118901
$189$	−114501.	−0.233160
$190$	0	0
$191$	−340612.	−0.675579	−0.337790	−	0.941222i	$-0.609679\pi$
$191$	−340612.	−0.675579	−0.337790	+	0.941222i	$0.609679\pi$
$192$	78745.5	0.154160
$193$	479839.	0.927262	0.463631	−	0.886028i	$-0.346546\pi$
$193$	479839.	0.927262	0.463631	+	0.886028i	$0.346546\pi$
$194$	−293910.	−0.560674
$195$	0	0
$196$	−227023.	−0.422114
$197$	−775437.	−1.42358	−0.711789	−	0.702394i	$-0.752115\pi$
$197$	−775437.	−1.42358	−0.711789	+	0.702394i	$0.752115\pi$
$198$	−250468.	−0.454035
$199$	960804.	1.71990	0.859948	−	0.510382i	$-0.170496\pi$
$199$	960804.	1.71990	0.859948	+	0.510382i	$0.170496\pi$
$200$	0	0
$201$	−840605.	−1.46758
$202$	−390271.	−0.672958
$203$	115817.	0.197257
$204$	727436.	1.22383
$205$	0	0
$206$	123964.	0.203530
$207$	482289.	0.782315
$208$	43264.0	0.0693375
$209$	−345932.	−0.547804
$210$	0	0
$211$	1.00406e6	1.55258	0.776289	−	0.630377i	$-0.217100\pi$
$211$	1.00406e6	1.55258	0.776289	+	0.630377i	$0.217100\pi$
$212$	−120752.	−0.184525
$213$	146174.	0.220760
$214$	808155.	1.20631
$215$	0	0
$216$	143219.	0.208865
$217$	−465030.	−0.670397
$218$	684599.	0.975652
$219$	415705.	0.585700
$220$	0	0
$221$	399665.	0.550447
$222$	−345072.	−0.469924
$223$	−369742.	−0.497893	−0.248947	−	0.968517i	$-0.580084\pi$
$223$	−369742.	−0.497893	−0.248947	+	0.968517i	$0.580084\pi$
$224$	−52394.9	−0.0697700
$225$	0	0
$226$	−552473.	−0.719515
$227$	622238.	0.801479	0.400740	−	0.916192i	$-0.368753\pi$
$227$	622238.	0.801479	0.400740	+	0.916192i	$0.368753\pi$
$228$	−215138.	−0.274081
$229$	328149.	0.413506	0.206753	−	0.978393i	$-0.433710\pi$
$229$	328149.	0.413506	0.206753	+	0.978393i	$0.433710\pi$
$230$	0	0
$231$	486536.	0.599908
$232$	−144865.	−0.176703
$233$	−1.25086e6	−1.50945	−0.754723	−	0.656044i	$-0.772229\pi$
$233$	−1.25086e6	−1.50945	−0.754723	+	0.656044i	$0.772229\pi$
$234$	−85581.3	−0.102174
$235$	0	0
$236$	801118.	0.936304
$237$	1.99050e6	2.30193
$238$	−484014.	−0.553880
$239$	14131.5	0.0160027	0.00800134	−	0.999968i	$-0.497453\pi$
$239$	14131.5	0.0160027	0.00800134	+	0.999968i	$0.497453\pi$
$240$	0	0
$241$	61638.0	0.0683606	0.0341803	−	0.999416i	$-0.489118\pi$
$241$	61638.0	0.0683606	0.0341803	+	0.999416i	$0.489118\pi$
$242$	−334341.	−0.366987
$243$	−874735.	−0.950300
$244$	−396108.	−0.425930
$245$	0	0
$246$	955871.	1.00707
$247$	−118200.	−0.123275
$248$	581664.	0.600542
$249$	1.54557e6	1.57976
$250$	0	0
$251$	−66537.0	−0.0666621	−0.0333310	−	0.999444i	$-0.510612\pi$
$251$	−66537.0	−0.0666621	−0.0333310	+	0.999444i	$0.510612\pi$
$252$	103643.	0.102811
$253$	1.88424e6	1.85069
$254$	344121.	0.334677
$255$	0	0
$256$	65536.0	0.0625000
$257$	270539.	0.255504	0.127752	−	0.991806i	$-0.459224\pi$
$257$	270539.	0.255504	0.127752	+	0.991806i	$0.459224\pi$
$258$	−966831.	−0.904276
$259$	229601.	0.212679
$260$	0	0
$261$	286561.	0.260385
$262$	1.19059e6	1.07154
$263$	1.11803e6	0.996698	0.498349	−	0.866976i	$-0.333940\pi$
$263$	1.11803e6	0.996698	0.498349	+	0.866976i	$0.333940\pi$
$264$	−608564.	−0.537398
$265$	0	0
$266$	143146.	0.124044
$267$	1.14006e6	0.978701
$268$	−699594.	−0.594989
$269$	947186.	0.798095	0.399047	−	0.916930i	$-0.369341\pi$
$269$	947186.	0.798095	0.399047	+	0.916930i	$0.369341\pi$
$270$	0	0
$271$	−2.13848e6	−1.76881	−0.884405	−	0.466720i	$-0.845436\pi$
$271$	−2.13848e6	−1.76881	−0.884405	+	0.466720i	$0.845436\pi$
$272$	605409.	0.496166
$273$	166242.	0.135000
$274$	−302524.	−0.243435
$275$	0	0
$276$	1.17182e6	0.925952
$277$	1.34126e6	1.05030	0.525151	−	0.851009i	$-0.324009\pi$
$277$	1.34126e6	1.05030	0.525151	+	0.851009i	$0.324009\pi$
$278$	−234277.	−0.181810
$279$	−1.15060e6	−0.884941
$280$	0	0
$281$	1.64581e6	1.24341	0.621705	−	0.783252i	$-0.286440\pi$
$281$	1.64581e6	1.24341	0.621705	+	0.783252i	$0.286440\pi$
$282$	276940.	0.207378
$283$	−444740.	−0.330096	−0.165048	−	0.986286i	$-0.552778\pi$
$283$	−444740.	−0.330096	−0.165048	+	0.986286i	$0.552778\pi$
$284$	121653.	0.0895011
$285$	0	0
$286$	−334354.	−0.241709
$287$	−636007.	−0.455782
$288$	−129638.	−0.0920982
$289$	4.17280e6	2.93889
$290$	0	0
$291$	1.41260e6	0.977885
$292$	345971.	0.237456
$293$	−458582.	−0.312067	−0.156033	−	0.987752i	$-0.549871\pi$
$293$	−458582.	−0.312067	−0.156033	+	0.987752i	$0.549871\pi$
$294$	1.09113e6	0.736220
$295$	0	0
$296$	−287187.	−0.190518
$297$	−1.10683e6	−0.728098
$298$	1.37994e6	0.900157
$299$	643817.	0.416471
$300$	0	0
$301$	643300.	0.409258
$302$	−49734.8	−0.0313793
$303$	1.87574e6	1.17372
$304$	−179048.	−0.111119
$305$	0	0
$306$	−1.19757e6	−0.731135
$307$	−2.49374e6	−1.51010	−0.755050	−	0.655668i	$-0.772387\pi$
$307$	−2.49374e6	−1.51010	−0.755050	+	0.655668i	$0.772387\pi$
$308$	404920.	0.243216
$309$	−595802.	−0.354982
$310$	0	0
$311$	−1.74516e6	−1.02314	−0.511569	−	0.859242i	$-0.670935\pi$
$311$	−1.74516e6	−1.02314	−0.511569	+	0.859242i	$0.670935\pi$
$312$	−207937.	−0.120933
$313$	−791926.	−0.456903	−0.228451	−	0.973555i	$-0.573366\pi$
$313$	−791926.	−0.456903	−0.228451	+	0.973555i	$0.573366\pi$
$314$	−1.66670e6	−0.953965
$315$	0	0
$316$	1.65660e6	0.933253
$317$	2.73806e6	1.53037	0.765183	−	0.643813i	$-0.222648\pi$
$317$	2.73806e6	1.53037	0.765183	+	0.643813i	$0.222648\pi$
$318$	580364.	0.321835
$319$	1.11955e6	0.615982
$320$	0	0
$321$	−3.88419e6	−2.10396
$322$	−779694.	−0.419068
$323$	−1.65402e6	−0.882132
$324$	−1.18056e6	−0.624780
$325$	0	0
$326$	−900483.	−0.469279
$327$	−3.29035e6	−1.70166
$328$	795524.	0.408290
$329$	−184268.	−0.0938554
$330$	0	0
$331$	134538.	0.0674954	0.0337477	−	0.999430i	$-0.489256\pi$
$331$	134538.	0.0674954	0.0337477	+	0.999430i	$0.489256\pi$
$332$	1.28630e6	0.640470
$333$	568089.	0.280741
$334$	−378188.	−0.185499
$335$	0	0
$336$	251822.	0.121688
$337$	393396.	0.188693	0.0943463	−	0.995539i	$-0.469924\pi$
$337$	393396.	0.188693	0.0943463	+	0.995539i	$0.469924\pi$
$338$	−114244.	−0.0543928
$339$	2.65532e6	1.25492
$340$	0	0
$341$	−4.49524e6	−2.09347
$342$	354179.	0.163741
$343$	−1.58597e6	−0.727878
$344$	−804646.	−0.366614
$345$	0	0
$346$	−370982.	−0.166595
$347$	409410.	0.182530	0.0912651	−	0.995827i	$-0.470909\pi$
$347$	409410.	0.182530	0.0912651	+	0.995827i	$0.470909\pi$
$348$	696258.	0.308193
$349$	862372.	0.378993	0.189497	−	0.981881i	$-0.439314\pi$
$349$	862372.	0.378993	0.189497	+	0.981881i	$0.439314\pi$
$350$	0	0
$351$	−378187.	−0.163847
$352$	−506478.	−0.217873
$353$	967902.	0.413423	0.206711	−	0.978402i	$-0.433724\pi$
$353$	967902.	0.413423	0.206711	+	0.978402i	$0.433724\pi$
$354$	−3.85037e6	−1.63303
$355$	0	0
$356$	948817.	0.396787
$357$	2.32629e6	0.966035
$358$	−907407.	−0.374192
$359$	−2.87414e6	−1.17699	−0.588493	−	0.808502i	$-0.700279\pi$
$359$	−2.87414e6	−1.17699	−0.588493	+	0.808502i	$0.700279\pi$
$360$	0	0
$361$	−1.98693e6	−0.802443
$362$	−2.76595e6	−1.10936
$363$	1.60692e6	0.640071
$364$	138355.	0.0547321
$365$	0	0
$366$	1.90379e6	0.742876
$367$	−2.80197e6	−1.08592	−0.542961	−	0.839758i	$-0.682697\pi$
$367$	−2.80197e6	−1.08592	−0.542961	+	0.839758i	$0.682697\pi$
$368$	975249.	0.375402
$369$	−1.57364e6	−0.601644
$370$	0	0
$371$	−386157.	−0.145656
$372$	−2.79562e6	−1.04742
$373$	508739.	0.189331	0.0946657	−	0.995509i	$-0.469822\pi$
$373$	508739.	0.189331	0.0946657	+	0.995509i	$0.469822\pi$
$374$	−4.67875e6	−1.72962
$375$	0	0
$376$	230484.	0.0840757
$377$	382535.	0.138617
$378$	458004.	0.164869
$379$	26753.7	0.00956722	0.00478361	−	0.999989i	$-0.498477\pi$
$379$	26753.7	0.00956722	0.00478361	+	0.999989i	$0.498477\pi$
$380$	0	0
$381$	−1.65393e6	−0.583719
$382$	1.36245e6	0.477707
$383$	4.57628e6	1.59410	0.797049	−	0.603914i	$-0.206393\pi$
$383$	4.57628e6	1.59410	0.797049	+	0.603914i	$0.206393\pi$
$384$	−314982.	−0.109008
$385$	0	0
$386$	−1.91936e6	−0.655673
$387$	1.59168e6	0.540231
$388$	1.17564e6	0.396456
$389$	−905452.	−0.303383	−0.151692	−	0.988428i	$-0.548472\pi$
$389$	−905452.	−0.303383	−0.151692	+	0.988428i	$0.548472\pi$
$390$	0	0
$391$	9.00917e6	2.98018
$392$	908093.	0.298480
$393$	−5.72225e6	−1.86890
$394$	3.10175e6	1.00662
$395$	0	0
$396$	1.00187e6	0.321051
$397$	−2.20323e6	−0.701590	−0.350795	−	0.936452i	$-0.614089\pi$
$397$	−2.20323e6	−0.701590	−0.350795	+	0.936452i	$0.614089\pi$
$398$	−3.84322e6	−1.21615
$399$	−687995.	−0.216348
$400$	0	0
$401$	−1.12383e6	−0.349011	−0.174505	−	0.984656i	$-0.555833\pi$
$401$	−1.12383e6	−0.349011	−0.174505	+	0.984656i	$0.555833\pi$
$402$	3.36242e6	1.03774
$403$	−1.53596e6	−0.471104
$404$	1.56108e6	0.475853
$405$	0	0
$406$	−463269.	−0.139482
$407$	2.21945e6	0.664139
$408$	−2.90974e6	−0.865375
$409$	1.00525e6	0.297143	0.148572	−	0.988902i	$-0.452532\pi$
$409$	1.00525e6	0.297143	0.148572	+	0.988902i	$0.452532\pi$
$410$	0	0
$411$	1.45400e6	0.424581
$412$	−495857.	−0.143917
$413$	2.56192e6	0.739078
$414$	−1.92916e6	−0.553181
$415$	0	0
$416$	−173056.	−0.0490290
$417$	1.12599e6	0.317099
$418$	1.38373e6	0.387356
$419$	1.52964e6	0.425653	0.212826	−	0.977090i	$-0.431733\pi$
$419$	1.52964e6	0.425653	0.212826	+	0.977090i	$0.431733\pi$
$420$	0	0
$421$	2.29967e6	0.632354	0.316177	−	0.948700i	$-0.397601\pi$
$421$	2.29967e6	0.632354	0.316177	+	0.948700i	$0.397601\pi$
$422$	−4.01624e6	−1.09784
$423$	−455924.	−0.123891
$424$	483009.	0.130479
$425$	0	0
$426$	−584696.	−0.156101
$427$	−1.26672e6	−0.336211
$428$	−3.23262e6	−0.852993
$429$	1.60699e6	0.421570
$430$	0	0
$431$	−2.62082e6	−0.679585	−0.339793	−	0.940500i	$-0.610357\pi$
$431$	−2.62082e6	−0.679585	−0.339793	+	0.940500i	$0.610357\pi$
$432$	−572876.	−0.147690
$433$	591237.	0.151545	0.0757726	−	0.997125i	$-0.475858\pi$
$433$	591237.	0.151545	0.0757726	+	0.997125i	$0.475858\pi$
$434$	1.86012e6	0.474042
$435$	0	0
$436$	−2.73840e6	−0.689890
$437$	−2.66444e6	−0.667425
$438$	−1.66282e6	−0.414152
$439$	−5.86023e6	−1.45129	−0.725644	−	0.688070i	$-0.758458\pi$
$439$	−5.86023e6	−1.45129	−0.725644	+	0.688070i	$0.758458\pi$
$440$	0	0
$441$	−1.79632e6	−0.439831
$442$	−1.59866e6	−0.389225
$443$	−1.49526e6	−0.361998	−0.180999	−	0.983483i	$-0.557933\pi$
$443$	−1.49526e6	−0.361998	−0.180999	+	0.983483i	$0.557933\pi$
$444$	1.38029e6	0.332287
$445$	0	0
$446$	1.47897e6	0.352064
$447$	−6.63231e6	−1.56999
$448$	209579.	0.0493348
$449$	−3.87629e6	−0.907404	−0.453702	−	0.891154i	$-0.649897\pi$
$449$	−3.87629e6	−0.907404	−0.453702	+	0.891154i	$0.649897\pi$
$450$	0	0
$451$	−6.14800e6	−1.42329
$452$	2.20989e6	0.508774
$453$	239038.	0.0547294
$454$	−2.48895e6	−0.566731
$455$	0	0
$456$	860550.	0.193805
$457$	−6.46622e6	−1.44830	−0.724152	−	0.689640i	$-0.757769\pi$
$457$	−6.46622e6	−1.44830	−0.724152	+	0.689640i	$0.757769\pi$
$458$	−1.31260e6	−0.292393
$459$	−5.29212e6	−1.17246
$460$	0	0
$461$	−7.26166e6	−1.59141	−0.795707	−	0.605681i	$-0.792901\pi$
$461$	−7.26166e6	−1.59141	−0.795707	+	0.605681i	$0.792901\pi$
$462$	−1.94614e6	−0.424199
$463$	−4.81594e6	−1.04407	−0.522034	−	0.852925i	$-0.674827\pi$
$463$	−4.81594e6	−1.04407	−0.522034	+	0.852925i	$0.674827\pi$
$464$	579462.	0.124948
$465$	0	0
$466$	5.00342e6	1.06734
$467$	−231914.	−0.0492078	−0.0246039	−	0.999697i	$-0.507832\pi$
$467$	−231914.	−0.0492078	−0.0246039	+	0.999697i	$0.507832\pi$
$468$	342325.	0.0722477
$469$	−2.23725e6	−0.469659
$470$	0	0
$471$	8.01055e6	1.66383
$472$	−3.20447e6	−0.662067
$473$	6.21849e6	1.27800
$474$	−7.96201e6	−1.62771
$475$	0	0
$476$	1.93606e6	0.391652
$477$	−955448.	−0.192270
$478$	−56525.9	−0.0113156
$479$	3.25748e6	0.648700	0.324350	−	0.945937i	$-0.394855\pi$
$479$	3.25748e6	0.648700	0.324350	+	0.945937i	$0.394855\pi$
$480$	0	0
$481$	758353.	0.149454
$482$	−246552.	−0.0483382
$483$	3.74740e6	0.730907
$484$	1.33736e6	0.259499
$485$	0	0
$486$	3.49894e6	0.671964
$487$	−7.51626e6	−1.43608	−0.718042	−	0.696000i	$-0.754961\pi$
$487$	−7.51626e6	−1.43608	−0.718042	+	0.696000i	$0.754961\pi$
$488$	1.58443e6	0.301178
$489$	4.32794e6	0.818482
$490$	0	0
$491$	−456011.	−0.0853634	−0.0426817	−	0.999089i	$-0.513590\pi$
$491$	−456011.	−0.0853634	−0.0426817	+	0.999089i	$0.513590\pi$
$492$	−3.82348e6	−0.712109
$493$	5.35296e6	0.991920
$494$	472800.	0.0871686
$495$	0	0
$496$	−2.32666e6	−0.424647
$497$	389039.	0.0706483
$498$	−6.18229e6	−1.11706
$499$	3.33321e6	0.599255	0.299627	−	0.954056i	$-0.403138\pi$
$499$	3.33321e6	0.599255	0.299627	+	0.954056i	$0.403138\pi$
$500$	0	0
$501$	1.81766e6	0.323534
$502$	266148.	0.0471372
$503$	3.46235e6	0.610171	0.305085	−	0.952325i	$-0.401315\pi$
$503$	3.46235e6	0.610171	0.305085	+	0.952325i	$0.401315\pi$
$504$	−414573.	−0.0726983
$505$	0	0
$506$	−7.53695e6	−1.30864
$507$	549084.	0.0948679
$508$	−1.37648e6	−0.236653
$509$	−7.66998e6	−1.31220	−0.656100	−	0.754674i	$-0.727795\pi$
$509$	−7.66998e6	−1.31220	−0.656100	+	0.754674i	$0.727795\pi$
$510$	0	0
$511$	1.10639e6	0.187437
$512$	−262144.	−0.0441942
$513$	1.56513e6	0.262578
$514$	−1.08216e6	−0.180668
$515$	0	0
$516$	3.86732e6	0.639420
$517$	−1.78123e6	−0.293085
$518$	−918403.	−0.150386
$519$	1.78303e6	0.290563
$520$	0	0
$521$	−7.45075e6	−1.20256	−0.601278	−	0.799040i	$-0.705342\pi$
$521$	−7.45075e6	−1.20256	−0.601278	+	0.799040i	$0.705342\pi$
$522$	−1.14624e6	−0.184120
$523$	3.50008e6	0.559530	0.279765	−	0.960068i	$-0.409743\pi$
$523$	3.50008e6	0.559530	0.279765	+	0.960068i	$0.409743\pi$
$524$	−4.76235e6	−0.757692
$525$	0	0
$526$	−4.47212e6	−0.704772
$527$	−2.14932e7	−3.37113
$528$	2.43425e6	0.379998
$529$	8.07646e6	1.25482
$530$	0	0
$531$	6.33883e6	0.975602
$532$	−572584.	−0.0877122
$533$	−2.10068e6	−0.320289
$534$	−4.56024e6	−0.692046
$535$	0	0
$536$	2.79838e6	0.420721
$537$	4.36122e6	0.652638
$538$	−3.78874e6	−0.564338
$539$	−7.01796e6	−1.04049
$540$	0	0
$541$	−6.76874e6	−0.994294	−0.497147	−	0.867666i	$-0.665619\pi$
$541$	−6.76874e6	−0.994294	−0.497147	+	0.867666i	$0.665619\pi$
$542$	8.55391e6	1.25074
$543$	1.32938e7	1.93486
$544$	−2.42164e6	−0.350842
$545$	0	0
$546$	−664969.	−0.0954596
$547$	1.19664e7	1.71000	0.855001	−	0.518627i	$-0.173557\pi$
$547$	1.19664e7	1.71000	0.855001	+	0.518627i	$0.173557\pi$
$548$	1.21010e6	0.172135
$549$	−3.13419e6	−0.443807
$550$	0	0
$551$	−1.58313e6	−0.222145
$552$	−4.68728e6	−0.654747
$553$	5.29768e6	0.736670
$554$	−5.36504e6	−0.742675
$555$	0	0
$556$	937108.	0.128559
$557$	−445095.	−0.0607875	−0.0303938	−	0.999538i	$-0.509676\pi$
$557$	−445095.	−0.0607875	−0.0303938	+	0.999538i	$0.509676\pi$
$558$	4.60240e6	0.625748
$559$	2.12477e6	0.287595
$560$	0	0
$561$	2.24872e7	3.01667
$562$	−6.58324e6	−0.879223
$563$	9.94384e6	1.32216	0.661078	−	0.750317i	$-0.270099\pi$
$563$	9.94384e6	1.32216	0.661078	+	0.750317i	$0.270099\pi$
$564$	−1.10776e6	−0.146639
$565$	0	0
$566$	1.77896e6	0.233413
$567$	−3.77536e6	−0.493174
$568$	−486614.	−0.0632868
$569$	6.04270e6	0.782439	0.391220	−	0.920297i	$-0.372053\pi$
$569$	6.04270e6	0.782439	0.391220	+	0.920297i	$0.372053\pi$
$570$	0	0
$571$	−5.12993e6	−0.658447	−0.329224	−	0.944252i	$-0.606787\pi$
$571$	−5.12993e6	−0.658447	−0.329224	+	0.944252i	$0.606787\pi$
$572$	1.33742e6	0.170914
$573$	−6.54825e6	−0.833180
$574$	2.54403e6	0.322287
$575$	0	0
$576$	518552.	0.0651232
$577$	5.30151e6	0.662918	0.331459	−	0.943470i	$-0.392459\pi$
$577$	5.30151e6	0.662918	0.331459	+	0.943470i	$0.392459\pi$
$578$	−1.66912e7	−2.07811
$579$	9.22489e6	1.14358
$580$	0	0
$581$	4.11351e6	0.505560
$582$	−5.65042e6	−0.691469
$583$	−3.73281e6	−0.454846
$584$	−1.38388e6	−0.167906
$585$	0	0
$586$	1.83433e6	0.220665
$587$	−9.26443e6	−1.10975	−0.554873	−	0.831935i	$-0.687233\pi$
$587$	−9.26443e6	−1.10975	−0.554873	+	0.831935i	$0.687233\pi$
$588$	−4.36452e6	−0.520586
$589$	6.35657e6	0.754979
$590$	0	0
$591$	−1.49078e7	−1.75567
$592$	1.14875e6	0.134716
$593$	4.97831e6	0.581360	0.290680	−	0.956820i	$-0.406118\pi$
$593$	4.97831e6	0.581360	0.290680	+	0.956820i	$0.406118\pi$
$594$	4.42732e6	0.514843
$595$	0	0
$596$	−5.51974e6	−0.636507
$597$	1.84714e7	2.12112
$598$	−2.57527e6	−0.294489
$599$	−9.54062e6	−1.08645	−0.543225	−	0.839587i	$-0.682797\pi$
$599$	−9.54062e6	−1.08645	−0.543225	+	0.839587i	$0.682797\pi$
$600$	0	0
$601$	−3.23751e6	−0.365615	−0.182808	−	0.983149i	$-0.558519\pi$
$601$	−3.23751e6	−0.365615	−0.182808	+	0.983149i	$0.558519\pi$
$602$	−2.57320e6	−0.289389
$603$	−5.53552e6	−0.619962
$604$	198939.	0.0221885
$605$	0	0
$606$	−7.50295e6	−0.829948
$607$	1.01617e7	1.11942	0.559711	−	0.828688i	$-0.310912\pi$
$607$	1.01617e7	1.11942	0.559711	+	0.828688i	$0.310912\pi$
$608$	716194.	0.0785727
$609$	2.22658e6	0.243274
$610$	0	0
$611$	−608621.	−0.0659544
$612$	4.79028e6	0.516991
$613$	−2.31456e6	−0.248781	−0.124391	−	0.992233i	$-0.539698\pi$
$613$	−2.31456e6	−0.248781	−0.124391	+	0.992233i	$0.539698\pi$
$614$	9.97496e6	1.06780
$615$	0	0
$616$	−1.61968e6	−0.171980
$617$	6.41200e6	0.678079	0.339040	−	0.940772i	$-0.389898\pi$
$617$	6.41200e6	0.678079	0.339040	+	0.940772i	$0.389898\pi$
$618$	2.38321e6	0.251010
$619$	−1.37209e7	−1.43932	−0.719659	−	0.694327i	$-0.755702\pi$
$619$	−1.37209e7	−1.43932	−0.719659	+	0.694327i	$0.755702\pi$
$620$	0	0
$621$	−8.52503e6	−0.887089
$622$	6.98064e6	0.723467
$623$	3.03425e6	0.313207
$624$	831749.	0.0855128
$625$	0	0
$626$	3.16770e6	0.323079
$627$	−6.65054e6	−0.675597
$628$	6.66678e6	0.674555
$629$	1.06119e7	1.06947
$630$	0	0
$631$	−3.42813e6	−0.342755	−0.171378	−	0.985205i	$-0.554822\pi$
$631$	−3.42813e6	−0.342755	−0.171378	+	0.985205i	$0.554822\pi$
$632$	−6.62639e6	−0.659910
$633$	1.93030e7	1.91477
$634$	−1.09523e7	−1.08213
$635$	0	0
$636$	−2.32146e6	−0.227572
$637$	−2.39793e6	−0.234147
$638$	−4.47822e6	−0.435565
$639$	962579.	0.0932576
$640$	0	0
$641$	1.19999e7	1.15354	0.576770	−	0.816906i	$-0.304313\pi$
$641$	1.19999e7	1.15354	0.576770	+	0.816906i	$0.304313\pi$
$642$	1.55368e7	1.48773
$643$	−39448.9	−0.00376277	−0.00188139	−	0.999998i	$-0.500599\pi$
$643$	−39448.9	−0.00376277	−0.00188139	+	0.999998i	$0.500599\pi$
$644$	3.11878e6	0.296326
$645$	0	0
$646$	6.61606e6	0.623761
$647$	3.43534e6	0.322633	0.161317	−	0.986903i	$-0.448426\pi$
$647$	3.43534e6	0.322633	0.161317	+	0.986903i	$0.448426\pi$
$648$	4.72226e6	0.441786
$649$	2.47649e7	2.30794
$650$	0	0
$651$	−8.94019e6	−0.826788
$652$	3.60193e6	0.331831
$653$	−1.35146e7	−1.24028	−0.620142	−	0.784490i	$-0.712925\pi$
$653$	−1.35146e7	−1.24028	−0.620142	+	0.784490i	$0.712925\pi$
$654$	1.31614e7	1.20325
$655$	0	0
$656$	−3.18210e6	−0.288705
$657$	2.73748e6	0.247422
$658$	737070.	0.0663658
$659$	−2.17250e7	−1.94871	−0.974355	−	0.225018i	$-0.927756\pi$
$659$	−2.17250e7	−1.94871	−0.974355	+	0.225018i	$0.927756\pi$
$660$	0	0
$661$	3.12575e6	0.278260	0.139130	−	0.990274i	$-0.455569\pi$
$661$	3.12575e6	0.278260	0.139130	+	0.990274i	$0.455569\pi$
$662$	−538151.	−0.0477265
$663$	7.68354e6	0.678856
$664$	−5.14522e6	−0.452881
$665$	0	0
$666$	−2.27236e6	−0.198514
$667$	8.62304e6	0.750491
$668$	1.51275e6	0.131168
$669$	−7.10827e6	−0.614043
$670$	0	0
$671$	−1.22449e7	−1.04990
$672$	−1.00729e6	−0.0860461
$673$	1.26422e7	1.07594	0.537968	−	0.842965i	$-0.319192\pi$
$673$	1.26422e7	1.07594	0.537968	+	0.842965i	$0.319192\pi$
$674$	−1.57358e6	−0.133426
$675$	0	0
$676$	456976.	0.0384615
$677$	1.82316e7	1.52881	0.764404	−	0.644737i	$-0.223033\pi$
$677$	1.82316e7	1.52881	0.764404	+	0.644737i	$0.223033\pi$
$678$	−1.06213e7	−0.887366
$679$	3.75961e6	0.312946
$680$	0	0
$681$	1.19625e7	0.988450
$682$	1.79810e7	1.48031
$683$	1.60919e7	1.31994	0.659972	−	0.751290i	$-0.270568\pi$
$683$	1.60919e7	1.31994	0.659972	+	0.751290i	$0.270568\pi$
$684$	−1.41672e6	−0.115782
$685$	0	0
$686$	6.34386e6	0.514687
$687$	6.30865e6	0.509970
$688$	3.21858e6	0.259235
$689$	−1.27544e6	−0.102356
$690$	0	0
$691$	1.96555e6	0.156599	0.0782994	−	0.996930i	$-0.475051\pi$
$691$	1.96555e6	0.156599	0.0782994	+	0.996930i	$0.475051\pi$
$692$	1.48393e6	0.117801
$693$	3.20392e6	0.253424
$694$	−1.63764e6	−0.129068
$695$	0	0
$696$	−2.78503e6	−0.217925
$697$	−2.93956e7	−2.29193
$698$	−3.44949e6	−0.267989
$699$	−2.40477e7	−1.86157
$700$	0	0
$701$	2.38464e7	1.83285	0.916426	−	0.400204i	$-0.131061\pi$
$701$	2.38464e7	1.83285	0.916426	+	0.400204i	$0.131061\pi$
$702$	1.51275e6	0.115858
$703$	−3.13845e6	−0.239512
$704$	2.02591e6	0.154060
$705$	0	0
$706$	−3.87161e6	−0.292334
$707$	4.99224e6	0.375618
$708$	1.54015e7	1.15473
$709$	−6.90141e6	−0.515611	−0.257805	−	0.966197i	$-0.582999\pi$
$709$	−6.90141e6	−0.515611	−0.257805	+	0.966197i	$0.582999\pi$
$710$	0	0
$711$	1.31078e7	0.972423
$712$	−3.79527e6	−0.280571
$713$	−3.46233e7	−2.55061
$714$	−9.30515e6	−0.683090
$715$	0	0
$716$	3.62963e6	0.264594
$717$	271677.	0.0197358
$718$	1.14966e7	0.832255
$719$	−1.72590e6	−0.124507	−0.0622533	−	0.998060i	$-0.519829\pi$
$719$	−1.72590e6	−0.124507	−0.0622533	+	0.998060i	$0.519829\pi$
$720$	0	0
$721$	−1.58571e6	−0.113602
$722$	7.94771e6	0.567413
$723$	1.18499e6	0.0843079
$724$	1.10638e7	0.784436
$725$	0	0
$726$	−6.42769e6	−0.452599
$727$	−4.93378e6	−0.346213	−0.173107	−	0.984903i	$-0.555381\pi$
$727$	−4.93378e6	−0.346213	−0.173107	+	0.984903i	$0.555381\pi$
$728$	−553421.	−0.0387014
$729$	1.11306e6	0.0775709
$730$	0	0
$731$	2.97327e7	2.05798
$732$	−7.61516e6	−0.525292
$733$	−1.95099e7	−1.34120	−0.670601	−	0.741818i	$-0.733964\pi$
$733$	−1.95099e7	−1.34120	−0.670601	+	0.741818i	$0.733964\pi$
$734$	1.12079e7	0.767863
$735$	0	0
$736$	−3.90100e6	−0.265449
$737$	−2.16265e7	−1.46662
$738$	6.29456e6	0.425427
$739$	1.62743e7	1.09621	0.548103	−	0.836411i	$-0.315350\pi$
$739$	1.62743e7	1.09621	0.548103	+	0.836411i	$0.315350\pi$
$740$	0	0
$741$	−2.27239e6	−0.152033
$742$	1.54463e6	0.102994
$743$	−1.79935e7	−1.19576	−0.597878	−	0.801587i	$-0.703989\pi$
$743$	−1.79935e7	−1.19576	−0.597878	+	0.801587i	$0.703989\pi$
$744$	1.11825e7	0.740638
$745$	0	0
$746$	−2.03495e6	−0.133877
$747$	1.01779e7	0.667351
$748$	1.87150e7	1.22303
$749$	−1.03377e7	−0.673316
$750$	0	0
$751$	1.05276e7	0.681130	0.340565	−	0.940221i	$-0.389382\pi$
$751$	1.05276e7	0.681130	0.340565	+	0.940221i	$0.389382\pi$
$752$	−921935.	−0.0594505
$753$	−1.27917e6	−0.0822132
$754$	−1.53014e6	−0.0980174
$755$	0	0
$756$	−1.83202e6	−0.116580
$757$	−7.81642e6	−0.495756	−0.247878	−	0.968791i	$-0.579733\pi$
$757$	−7.81642e6	−0.495756	−0.247878	+	0.968791i	$0.579733\pi$
$758$	−107015.	−0.00676505
$759$	3.62244e7	2.28243
$760$	0	0
$761$	−6.86800e6	−0.429901	−0.214951	−	0.976625i	$-0.568959\pi$
$761$	−6.86800e6	−0.429901	−0.214951	+	0.976625i	$0.568959\pi$
$762$	6.61571e6	0.412752
$763$	−8.75719e6	−0.544570
$764$	−5.44979e6	−0.337790
$765$	0	0
$766$	−1.83051e7	−1.12720
$767$	8.46181e6	0.519368
$768$	1.25993e6	0.0770802
$769$	1.29868e7	0.791928	0.395964	−	0.918266i	$-0.370410\pi$
$769$	1.29868e7	0.791928	0.395964	+	0.918266i	$0.370410\pi$
$770$	0	0
$771$	5.20111e6	0.315108
$772$	7.67743e6	0.463631
$773$	−2.61945e7	−1.57674	−0.788371	−	0.615200i	$-0.789075\pi$
$773$	−2.61945e7	−1.57674	−0.788371	+	0.615200i	$0.789075\pi$
$774$	−6.36674e6	−0.382001
$775$	0	0
$776$	−4.70256e6	−0.280337
$777$	4.41407e6	0.262293
$778$	3.62181e6	0.214524
$779$	8.69369e6	0.513287
$780$	0	0
$781$	3.76066e6	0.220616
$782$	−3.60367e7	−2.10731
$783$	−5.06530e6	−0.295257
$784$	−3.63237e6	−0.211057
$785$	0	0
$786$	2.28890e7	1.32151
$787$	−2.55783e6	−0.147209	−0.0736046	−	0.997288i	$-0.523450\pi$
$787$	−2.55783e6	−0.147209	−0.0736046	+	0.997288i	$0.523450\pi$
$788$	−1.24070e7	−0.711789
$789$	2.14941e7	1.22921
$790$	0	0
$791$	7.06708e6	0.401605
$792$	−4.00749e6	−0.227018
$793$	−4.18389e6	−0.236264
$794$	8.81291e6	0.496099
$795$	0	0
$796$	1.53729e7	0.859948
$797$	−2.70410e7	−1.50792	−0.753958	−	0.656923i	$-0.771858\pi$
$797$	−2.70410e7	−1.50792	−0.753958	+	0.656923i	$0.771858\pi$
$798$	2.75198e6	0.152981
$799$	−8.51666e6	−0.471957
$800$	0	0
$801$	7.50748e6	0.413441
$802$	4.49531e6	0.246788
$803$	1.06950e7	0.585317
$804$	−1.34497e7	−0.733790
$805$	0	0
$806$	6.14383e6	0.333121
$807$	1.82096e7	0.984276
$808$	−6.24434e6	−0.336479
$809$	−7.14004e6	−0.383557	−0.191778	−	0.981438i	$-0.561425\pi$
$809$	−7.14004e6	−0.383557	−0.191778	+	0.981438i	$0.561425\pi$
$810$	0	0
$811$	−3.49368e7	−1.86522	−0.932612	−	0.360882i	$-0.882476\pi$
$811$	−3.49368e7	−1.86522	−0.932612	+	0.360882i	$0.882476\pi$
$812$	1.85308e6	0.0986287
$813$	−4.11122e7	−2.18144
$814$	−8.87779e6	−0.469617
$815$	0	0
$816$	1.16390e7	0.611913
$817$	−8.79337e6	−0.460893
$818$	−4.02100e6	−0.210112
$819$	1.09473e6	0.0570293
$820$	0	0
$821$	−5.14344e6	−0.266315	−0.133158	−	0.991095i	$-0.542512\pi$
$821$	−5.14344e6	−0.266315	−0.133158	+	0.991095i	$0.542512\pi$
$822$	−5.81601e6	−0.300224
$823$	−4.85712e6	−0.249965	−0.124982	−	0.992159i	$-0.539887\pi$
$823$	−4.85712e6	−0.249965	−0.124982	+	0.992159i	$0.539887\pi$
$824$	1.98343e6	0.101765
$825$	0	0
$826$	−1.02477e7	−0.522607
$827$	−1.70403e7	−0.866391	−0.433196	−	0.901300i	$-0.642614\pi$
$827$	−1.70403e7	−0.866391	−0.433196	+	0.901300i	$0.642614\pi$
$828$	7.71663e6	0.391158
$829$	−2.27045e7	−1.14743	−0.573715	−	0.819055i	$-0.694498\pi$
$829$	−2.27045e7	−1.14743	−0.573715	+	0.819055i	$0.694498\pi$
$830$	0	0
$831$	2.57857e7	1.29532
$832$	692224.	0.0346688
$833$	−3.35552e7	−1.67551
$834$	−4.50397e6	−0.224223
$835$	0	0
$836$	−5.53491e6	−0.273902
$837$	2.03382e7	1.00346
$838$	−6.11858e6	−0.300982
$839$	−1.63556e7	−0.802159	−0.401080	−	0.916043i	$-0.631365\pi$
$839$	−1.63556e7	−0.802159	−0.401080	+	0.916043i	$0.631365\pi$
$840$	0	0
$841$	−1.53876e7	−0.750208
$842$	−9.19868e6	−0.447142
$843$	3.16407e7	1.53347
$844$	1.60650e7	0.776289
$845$	0	0
$846$	1.82370e6	0.0876045
$847$	4.27679e6	0.204837
$848$	−1.93203e6	−0.0922625
$849$	−8.55012e6	−0.407102
$850$	0	0
$851$	1.70946e7	0.809163
$852$	2.33878e6	0.110380
$853$	4.52879e6	0.213113	0.106556	−	0.994307i	$-0.466018\pi$
$853$	4.52879e6	0.213113	0.106556	+	0.994307i	$0.466018\pi$
$854$	5.06689e6	0.237737
$855$	0	0
$856$	1.29305e7	0.603157
$857$	3.52177e7	1.63798	0.818990	−	0.573807i	$-0.194534\pi$
$857$	3.52177e7	1.63798	0.818990	+	0.573807i	$0.194534\pi$
$858$	−6.42795e6	−0.298095
$859$	−3.55901e7	−1.64568	−0.822841	−	0.568271i	$-0.807612\pi$
$859$	−3.55901e7	−1.64568	−0.822841	+	0.568271i	$0.807612\pi$
$860$	0	0
$861$	−1.22272e7	−0.562108
$862$	1.04833e7	0.480539
$863$	−2.78981e7	−1.27511	−0.637555	−	0.770405i	$-0.720054\pi$
$863$	−2.78981e7	−1.27511	−0.637555	+	0.770405i	$0.720054\pi$
$864$	2.29150e6	0.104433
$865$	0	0
$866$	−2.36495e6	−0.107159
$867$	8.02220e7	3.62448
$868$	−7.44048e6	−0.335198
$869$	5.12103e7	2.30042
$870$	0	0
$871$	−7.38946e6	−0.330041
$872$	1.09536e7	0.487826
$873$	9.30222e6	0.413096
$874$	1.06578e7	0.471941
$875$	0	0
$876$	6.65128e6	0.292850
$877$	−6.79883e6	−0.298494	−0.149247	−	0.988800i	$-0.547685\pi$
$877$	−6.79883e6	−0.298494	−0.149247	+	0.988800i	$0.547685\pi$
$878$	2.34409e7	1.02622
$879$	−8.81622e6	−0.384867
$880$	0	0
$881$	−4.02331e7	−1.74640	−0.873201	−	0.487360i	$-0.837960\pi$
$881$	−4.02331e7	−1.74640	−0.873201	+	0.487360i	$0.837960\pi$
$882$	7.18526e6	0.311008
$883$	−7.81137e6	−0.337152	−0.168576	−	0.985689i	$-0.553917\pi$
$883$	−7.81137e6	−0.337152	−0.168576	+	0.985689i	$0.553917\pi$
$884$	6.39464e6	0.275223
$885$	0	0
$886$	5.98103e6	0.255971
$887$	2.69396e7	1.14970	0.574848	−	0.818260i	$-0.305061\pi$
$887$	2.69396e7	1.14970	0.574848	+	0.818260i	$0.305061\pi$
$888$	−5.52116e6	−0.234962
$889$	−4.40189e6	−0.186803
$890$	0	0
$891$	−3.64947e7	−1.54005
$892$	−5.91587e6	−0.248947
$893$	2.51878e6	0.105697
$894$	2.65292e7	1.11015
$895$	0	0
$896$	−838318.	−0.0348850
$897$	1.23774e7	0.513626
$898$	1.55052e7	0.641631
$899$	−2.05720e7	−0.848942
$900$	0	0
$901$	−1.78478e7	−0.732440
$902$	2.45920e7	1.00642
$903$	1.23674e7	0.504731
$904$	−8.83957e6	−0.359758
$905$	0	0
$906$	−956151.	−0.0386995
$907$	−3.66946e7	−1.48110	−0.740549	−	0.672002i	$-0.765435\pi$
$907$	−3.66946e7	−1.48110	−0.740549	+	0.672002i	$0.765435\pi$
$908$	9.95582e6	0.400740
$909$	1.23520e7	0.495826
$910$	0	0
$911$	−1.68568e7	−0.672945	−0.336473	−	0.941693i	$-0.609234\pi$
$911$	−1.68568e7	−0.672945	−0.336473	+	0.941693i	$0.609234\pi$
$912$	−3.44220e6	−0.137041
$913$	3.97635e7	1.57873
$914$	2.58649e7	1.02411
$915$	0	0
$916$	5.25038e6	0.206753
$917$	−1.52296e7	−0.598090
$918$	2.11685e7	0.829054
$919$	3.12525e7	1.22066	0.610332	−	0.792146i	$-0.291036\pi$
$919$	3.12525e7	1.22066	0.610332	+	0.792146i	$0.291036\pi$
$920$	0	0
$921$	−4.79421e7	−1.86238
$922$	2.90466e7	1.12530
$923$	1.28496e6	0.0496463
$924$	7.78457e6	0.299954
$925$	0	0
$926$	1.92638e7	0.738267
$927$	−3.92345e6	−0.149958
$928$	−2.31785e6	−0.0883517
$929$	−3.27128e7	−1.24359	−0.621797	−	0.783178i	$-0.713597\pi$
$929$	−3.27128e7	−1.24359	−0.621797	+	0.783178i	$0.713597\pi$
$930$	0	0
$931$	9.92387e6	0.375238
$932$	−2.00137e7	−0.754723
$933$	−3.35506e7	−1.26182
$934$	927655.	0.0347952
$935$	0	0
$936$	−1.36930e6	−0.0510869
$937$	−4.53506e7	−1.68746	−0.843731	−	0.536767i	$-0.819645\pi$
$937$	−4.53506e7	−1.68746	−0.843731	+	0.536767i	$0.819645\pi$
$938$	8.94901e6	0.332099
$939$	−1.52247e7	−0.563490
$940$	0	0
$941$	−4.45649e7	−1.64066	−0.820331	−	0.571890i	$-0.806211\pi$
$941$	−4.45649e7	−1.64066	−0.820331	+	0.571890i	$0.806211\pi$
$942$	−3.20422e7	−1.17651
$943$	−4.73532e7	−1.73408
$944$	1.28179e7	0.468152
$945$	0	0
$946$	−2.48740e7	−0.903685
$947$	−1.90646e7	−0.690800	−0.345400	−	0.938456i	$-0.612257\pi$
$947$	−1.90646e7	−0.690800	−0.345400	+	0.938456i	$0.612257\pi$
$948$	3.18480e7	1.15096
$949$	3.65432e6	0.131717
$950$	0	0
$951$	5.26392e7	1.88737
$952$	−7.74422e6	−0.276940
$953$	−4.22576e6	−0.150721	−0.0753603	−	0.997156i	$-0.524011\pi$
$953$	−4.22576e6	−0.150721	−0.0753603	+	0.997156i	$0.524011\pi$
$954$	3.82179e6	0.135955
$955$	0	0
$956$	226104.	0.00800134
$957$	2.15234e7	0.759680
$958$	−1.30299e7	−0.458700
$959$	3.86980e6	0.135876
$960$	0	0
$961$	5.39718e7	1.88520
$962$	−3.03341e6	−0.105680
$963$	−2.55780e7	−0.888794
$964$	986207.	0.0341803
$965$	0	0
$966$	−1.49896e7	−0.516829
$967$	3.50435e7	1.20515	0.602575	−	0.798062i	$-0.294141\pi$
$967$	3.50435e7	1.20515	0.602575	+	0.798062i	$0.294141\pi$
$968$	−5.34945e6	−0.183494
$969$	−3.17984e7	−1.08792
$970$	0	0
$971$	7.67176e6	0.261124	0.130562	−	0.991440i	$-0.458322\pi$
$971$	7.67176e6	0.261124	0.130562	+	0.991440i	$0.458322\pi$
$972$	−1.39958e7	−0.475150
$973$	2.99680e6	0.101479
$974$	3.00651e7	1.01546
$975$	0	0
$976$	−6.33772e6	−0.212965
$977$	4.64539e7	1.55699	0.778494	−	0.627652i	$-0.215984\pi$
$977$	4.64539e7	1.55699	0.778494	+	0.627652i	$0.215984\pi$
$978$	−1.73118e7	−0.578754
$979$	2.93307e7	0.978061
$980$	0	0
$981$	−2.16675e7	−0.718846
$982$	1.82404e6	0.0603611
$983$	−1.52982e7	−0.504959	−0.252480	−	0.967602i	$-0.581246\pi$
$983$	−1.52982e7	−0.504959	−0.252480	+	0.967602i	$0.581246\pi$
$984$	1.52939e7	0.503537
$985$	0	0
$986$	−2.14118e7	−0.701393
$987$	−3.54254e6	−0.115750
$988$	−1.89120e6	−0.0616375
$989$	4.78961e7	1.55708
$990$	0	0
$991$	−8.70500e6	−0.281569	−0.140784	−	0.990040i	$-0.544962\pi$
$991$	−8.70500e6	−0.281569	−0.140784	+	0.990040i	$0.544962\pi$
$992$	9.30663e6	0.300271
$993$	2.58649e6	0.0832409
$994$	−1.55616e6	−0.0499559
$995$	0	0
$996$	2.47292e7	0.789880
$997$	4.01903e7	1.28051	0.640256	−	0.768162i	$-0.278828\pi$
$997$	4.01903e7	1.28051	0.640256	+	0.768162i	$0.278828\pi$
$998$	−1.33328e7	−0.423737
$999$	−1.00416e7	−0.318340

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.6.a.c.1.2		2
5.2	odd	4		650.6.b.c.599.1		4
5.3	odd	4		650.6.b.c.599.4		4
5.4	even	2		130.6.a.e.1.1	✓	2
20.19	odd	2		1040.6.a.h.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.6.a.e.1.1	✓	2	5.4	even	2
650.6.a.c.1.2		2	1.1	even	1	trivial
650.6.b.c.599.1		4	5.2	odd	4
650.6.b.c.599.4		4	5.3	odd	4
1040.6.a.h.1.2		2	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	650.a (trivial)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +19.2250 q^{3} +16.0000 q^{4} -76.8999 q^{6} +51.1669 q^{7} -64.0000 q^{8} +126.600 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} +19.2250 q^{3} +16.0000 q^{4} -76.8999 q^{6} +51.1669 q^{7} -64.0000 q^{8} +126.600 q^{9} +494.607 q^{11} +307.600 q^{12} +169.000 q^{13} -204.667 q^{14} +256.000 q^{16} +2364.88 q^{17} -506.398 q^{18} -699.408 q^{19} +983.681 q^{21} -1978.43 q^{22} +3809.57 q^{23} -1230.40 q^{24} -676.000 q^{26} -2237.80 q^{27} +818.670 q^{28} +2263.52 q^{29} -9088.51 q^{31} -1024.00 q^{32} +9508.81 q^{33} -9459.52 q^{34} +2025.59 q^{36} +4487.29 q^{37} +2797.63 q^{38} +3249.02 q^{39} -12430.1 q^{41} -3934.73 q^{42} +12572.6 q^{43} +7913.71 q^{44} -15238.3 q^{46} -3601.31 q^{47} +4921.59 q^{48} -14189.0 q^{49} +45464.8 q^{51} +2704.00 q^{52} -7547.01 q^{53} +8951.18 q^{54} -3274.68 q^{56} -13446.1 q^{57} -9054.09 q^{58} +50069.9 q^{59} -24756.7 q^{61} +36354.0 q^{62} +6477.70 q^{63} +4096.00 q^{64} -38035.2 q^{66} -43724.6 q^{67} +37838.1 q^{68} +73238.8 q^{69} +7603.34 q^{71} -8102.37 q^{72} +21623.2 q^{73} -17949.2 q^{74} -11190.5 q^{76} +25307.5 q^{77} -12996.1 q^{78} +103537. q^{79} -73785.2 q^{81} +49720.3 q^{82} +80394.0 q^{83} +15738.9 q^{84} -50290.4 q^{86} +43516.1 q^{87} -31654.9 q^{88} +59301.0 q^{89} +8647.20 q^{91} +60953.1 q^{92} -174726. q^{93} +14405.2 q^{94} -19686.4 q^{96} +73477.5 q^{97} +56755.8 q^{98} +62617.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8 q^{2} + 16 q^{3} + 32 q^{4} - 64 q^{6} + 252 q^{7} - 128 q^{8} - 106 q^{9}+O(q^{10}) \) 2 * q - 8 * q^2 + 16 * q^3 + 32 * q^4 - 64 * q^6 + 252 * q^7 - 128 * q^8 - 106 * q^9	\( 2 q - 8 q^{2} + 16 q^{3} + 32 q^{4} - 64 q^{6} + 252 q^{7} - 128 q^{8} - 106 q^{9} - 36 q^{11} + 256 q^{12} + 338 q^{13} - 1008 q^{14} + 512 q^{16} + 2380 q^{17} + 424 q^{18} - 1092 q^{19} + 336 q^{21} + 144 q^{22} + 1176 q^{23} - 1024 q^{24} - 1352 q^{26} - 704 q^{27} + 4032 q^{28} - 4872 q^{29} - 2260 q^{31} - 2048 q^{32} + 11220 q^{33} - 9520 q^{34} - 1696 q^{36} + 17760 q^{37} + 4368 q^{38} + 2704 q^{39} - 9220 q^{41} - 1344 q^{42} + 23656 q^{43} - 576 q^{44} - 4704 q^{46} - 12860 q^{47} + 4096 q^{48} + 9338 q^{49} + 45416 q^{51} + 5408 q^{52} - 11068 q^{53} + 2816 q^{54} - 16128 q^{56} - 12180 q^{57} + 19488 q^{58} + 90404 q^{59} - 69000 q^{61} + 9040 q^{62} - 40236 q^{63} + 8192 q^{64} - 44880 q^{66} - 50796 q^{67} + 38080 q^{68} + 81732 q^{69} - 28668 q^{71} + 6784 q^{72} + 62688 q^{73} - 71040 q^{74} - 17472 q^{76} - 81256 q^{77} - 10816 q^{78} + 84064 q^{79} - 22210 q^{81} + 36880 q^{82} + 12828 q^{83} + 5376 q^{84} - 94624 q^{86} + 66528 q^{87} + 2304 q^{88} + 92620 q^{89} + 42588 q^{91} + 18816 q^{92} - 196748 q^{93} + 51440 q^{94} - 16384 q^{96} + 75684 q^{97} - 37352 q^{98} + 186036 q^{99}+O(q^{100}) \) 2 * q - 8 * q^2 + 16 * q^3 + 32 * q^4 - 64 * q^6 + 252 * q^7 - 128 * q^8 - 106 * q^9 - 36 * q^11 + 256 * q^12 + 338 * q^13 - 1008 * q^14 + 512 * q^16 + 2380 * q^17 + 424 * q^18 - 1092 * q^19 + 336 * q^21 + 144 * q^22 + 1176 * q^23 - 1024 * q^24 - 1352 * q^26 - 704 * q^27 + 4032 * q^28 - 4872 * q^29 - 2260 * q^31 - 2048 * q^32 + 11220 * q^33 - 9520 * q^34 - 1696 * q^36 + 17760 * q^37 + 4368 * q^38 + 2704 * q^39 - 9220 * q^41 - 1344 * q^42 + 23656 * q^43 - 576 * q^44 - 4704 * q^46 - 12860 * q^47 + 4096 * q^48 + 9338 * q^49 + 45416 * q^51 + 5408 * q^52 - 11068 * q^53 + 2816 * q^54 - 16128 * q^56 - 12180 * q^57 + 19488 * q^58 + 90404 * q^59 - 69000 * q^61 + 9040 * q^62 - 40236 * q^63 + 8192 * q^64 - 44880 * q^66 - 50796 * q^67 + 38080 * q^68 + 81732 * q^69 - 28668 * q^71 + 6784 * q^72 + 62688 * q^73 - 71040 * q^74 - 17472 * q^76 - 81256 * q^77 - 10816 * q^78 + 84064 * q^79 - 22210 * q^81 + 36880 * q^82 + 12828 * q^83 + 5376 * q^84 - 94624 * q^86 + 66528 * q^87 + 2304 * q^88 + 92620 * q^89 + 42588 * q^91 + 18816 * q^92 - 196748 * q^93 + 51440 * q^94 - 16384 * q^96 + 75684 * q^97 - 37352 * q^98 + 186036 * q^99

Introduction

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