LMFDB - Embedded newform 147.6.a.h.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,6,Mod(1,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, 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("147.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	147.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:	$23.5764215125$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{193}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 48 $ x^2 - x - 48
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-6.44622$ of defining polynomial
Character	$\chi$	$=$	147.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+5.44622 q^{2} -9.00000 q^{3} -2.33867 q^{4} +36.0000 q^{5} -49.0160 q^{6} -187.016 q^{8} +81.0000 q^{9} +196.064 q^{10} +184.430 q^{11} +21.0480 q^{12} +147.872 q^{13} -324.000 q^{15} -943.693 q^{16} +1968.38 q^{17} +441.144 q^{18} +1892.51 q^{19} -84.1920 q^{20} +1004.45 q^{22} +136.988 q^{23} +1683.14 q^{24} -1829.00 q^{25} +805.344 q^{26} -729.000 q^{27} -1259.58 q^{29} -1764.58 q^{30} +8969.02 q^{31} +844.949 q^{32} -1659.87 q^{33} +10720.3 q^{34} -189.432 q^{36} +12897.2 q^{37} +10307.0 q^{38} -1330.85 q^{39} -6732.58 q^{40} +8975.62 q^{41} +13538.9 q^{43} -431.321 q^{44} +2916.00 q^{45} +746.069 q^{46} -20046.1 q^{47} +8493.24 q^{48} -9961.14 q^{50} -17715.5 q^{51} -345.823 q^{52} +9334.33 q^{53} -3970.30 q^{54} +6639.49 q^{55} -17032.6 q^{57} -6859.96 q^{58} +8866.46 q^{59} +757.728 q^{60} -41148.3 q^{61} +48847.3 q^{62} +34800.0 q^{64} +5323.39 q^{65} -9040.03 q^{66} -55351.5 q^{67} -4603.39 q^{68} -1232.90 q^{69} -63866.8 q^{71} -15148.3 q^{72} +41299.3 q^{73} +70241.1 q^{74} +16461.0 q^{75} -4425.95 q^{76} -7248.09 q^{78} +16963.5 q^{79} -33973.0 q^{80} +6561.00 q^{81} +48883.2 q^{82} -101693. q^{83} +70861.8 q^{85} +73736.0 q^{86} +11336.2 q^{87} -34491.4 q^{88} +87102.5 q^{89} +15881.2 q^{90} -320.370 q^{92} -80721.2 q^{93} -109176. q^{94} +68130.4 q^{95} -7604.54 q^{96} -118107. q^{97} +14938.8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{2} - 18 q^{3} + 37 q^{4} + 72 q^{5} + 27 q^{6} - 249 q^{8} + 162 q^{9} - 108 q^{10} + 480 q^{11} - 333 q^{12} + 1296 q^{13} - 648 q^{15} - 1679 q^{16} + 936 q^{17} - 243 q^{18} - 216 q^{19} + 1332 q^{20}+ \cdots + 38880 q^{99}+O(q^{100}) $ 2 * q - 3 * q^2 - 18 * q^3 + 37 * q^4 + 72 * q^5 + 27 * q^6 - 249 * q^8 + 162 * q^9 - 108 * q^10 + 480 * q^11 - 333 * q^12 + 1296 * q^13 - 648 * q^15 - 1679 * q^16 + 936 * q^17 - 243 * q^18 - 216 * q^19 + 1332 * q^20 - 1492 * q^22 - 504 * q^23 + 2241 * q^24 - 3658 * q^25 - 8892 * q^26 - 1458 * q^27 + 6372 * q^29 + 972 * q^30 + 9936 * q^31 + 9039 * q^32 - 4320 * q^33 + 19440 * q^34 + 2997 * q^36 + 11124 * q^37 + 28116 * q^38 - 11664 * q^39 - 8964 * q^40 + 20952 * q^41 - 6264 * q^43 + 11196 * q^44 + 5832 * q^45 + 6160 * q^46 + 7920 * q^47 + 15111 * q^48 + 5487 * q^50 - 8424 * q^51 + 44820 * q^52 + 2220 * q^53 + 2187 * q^54 + 17280 * q^55 + 1944 * q^57 - 71318 * q^58 + 29736 * q^59 - 11988 * q^60 - 17280 * q^61 + 40680 * q^62 - 10879 * q^64 + 46656 * q^65 + 13428 * q^66 - 20680 * q^67 - 45216 * q^68 + 4536 * q^69 - 92280 * q^71 - 20169 * q^72 + 56592 * q^73 + 85218 * q^74 + 32922 * q^75 - 87372 * q^76 + 80028 * q^78 - 56096 * q^79 - 60444 * q^80 + 13122 * q^81 - 52272 * q^82 - 71352 * q^83 + 33696 * q^85 + 240996 * q^86 - 57348 * q^87 - 52812 * q^88 + 123192 * q^89 - 8748 * q^90 - 25536 * q^92 - 89424 * q^93 - 345384 * q^94 - 7776 * q^95 - 81351 * q^96 + 35856 * q^97 + 38880 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	5.44622	0.962765	0.481383	−	0.876511i	$-0.340135\pi$
$2$	5.44622	0.962765	0.481383	+	0.876511i	$0.340135\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	−2.33867	−0.0730833
$5$	36.0000	0.643988	0.321994	−	0.946742i	$-0.395647\pi$
$5$	36.0000	0.643988	0.321994	+	0.946742i	$0.395647\pi$
$6$	−49.0160	−0.555853
$7$	0	0
$7$	0	0
$8$	−187.016	−1.03313
$9$	81.0000	0.333333
$10$	196.064	0.620009
$11$	184.430	0.459569	0.229784	−	0.973242i	$-0.426198\pi$
$11$	184.430	0.459569	0.229784	+	0.973242i	$0.426198\pi$
$12$	21.0480	0.0421947
$13$	147.872	0.242676	0.121338	−	0.992611i	$-0.461281\pi$
$13$	147.872	0.242676	0.121338	+	0.992611i	$0.461281\pi$
$14$	0	0
$15$	−324.000	−0.371806
$16$	−943.693	−0.921576
$17$	1968.38	1.65191	0.825957	−	0.563733i	$-0.190635\pi$
$17$	1968.38	1.65191	0.825957	+	0.563733i	$0.190635\pi$
$18$	441.144	0.320922
$19$	1892.51	1.20269	0.601346	−	0.798989i	$-0.294631\pi$
$19$	1892.51	1.20269	0.601346	+	0.798989i	$0.294631\pi$
$20$	−84.1920	−0.0470647
$21$	0	0
$22$	1004.45	0.442457
$23$	136.988	0.0539963	0.0269982	−	0.999635i	$-0.491405\pi$
$23$	136.988	0.0539963	0.0269982	+	0.999635i	$0.491405\pi$
$24$	1683.14	0.596476
$25$	−1829.00	−0.585280
$26$	805.344	0.233640
$27$	−729.000	−0.192450
$28$	0	0
$29$	−1259.58	−0.278120	−0.139060	−	0.990284i	$-0.544408\pi$
$29$	−1259.58	−0.278120	−0.139060	+	0.990284i	$0.544408\pi$
$30$	−1764.58	−0.357962
$31$	8969.02	1.67626	0.838129	−	0.545472i	$-0.183650\pi$
$31$	8969.02	1.67626	0.838129	+	0.545472i	$0.183650\pi$
$32$	844.949	0.145866
$33$	−1659.87	−0.265332
$34$	10720.3	1.59041
$35$	0	0
$36$	−189.432	−0.0243611
$37$	12897.2	1.54879	0.774393	−	0.632705i	$-0.218055\pi$
$37$	12897.2	1.54879	0.774393	+	0.632705i	$0.218055\pi$
$38$	10307.0	1.15791
$39$	−1330.85	−0.140109
$40$	−6732.58	−0.665321
$41$	8975.62	0.833882	0.416941	−	0.908934i	$-0.363102\pi$
$41$	8975.62	0.833882	0.416941	+	0.908934i	$0.363102\pi$
$42$	0	0
$43$	13538.9	1.11664	0.558320	−	0.829626i	$-0.311446\pi$
$43$	13538.9	1.11664	0.558320	+	0.829626i	$0.311446\pi$
$44$	−431.321	−0.0335868
$45$	2916.00	0.214663
$46$	746.069	0.0519858
$47$	−20046.1	−1.32369	−0.661845	−	0.749641i	$-0.730226\pi$
$47$	−20046.1	−1.32369	−0.661845	+	0.749641i	$0.730226\pi$
$48$	8493.24	0.532072
$49$	0	0
$50$	−9961.14	−0.563487
$51$	−17715.5	−0.953733
$52$	−345.823	−0.0177356
$53$	9334.33	0.456450	0.228225	−	0.973608i	$-0.426708\pi$
$53$	9334.33	0.456450	0.228225	+	0.973608i	$0.426708\pi$
$54$	−3970.30	−0.185284
$55$	6639.49	0.295956
$56$	0	0
$57$	−17032.6	−0.694375
$58$	−6859.96	−0.267764
$59$	8866.46	0.331605	0.165802	−	0.986159i	$-0.446979\pi$
$59$	8866.46	0.331605	0.165802	+	0.986159i	$0.446979\pi$
$60$	757.728	0.0271728
$61$	−41148.3	−1.41588	−0.707942	−	0.706271i	$-0.750376\pi$
$61$	−41148.3	−1.41588	−0.707942	+	0.706271i	$0.750376\pi$
$62$	48847.3	1.61384
$63$	0	0
$64$	34800.0	1.06201
$65$	5323.39	0.156281
$66$	−9040.03	−0.255452
$67$	−55351.5	−1.50641	−0.753204	−	0.657787i	$-0.771493\pi$
$67$	−55351.5	−1.50641	−0.753204	+	0.657787i	$0.771493\pi$
$68$	−4603.39	−0.120727
$69$	−1232.90	−0.0311748
$70$	0	0
$71$	−63866.8	−1.50359	−0.751794	−	0.659398i	$-0.770811\pi$
$71$	−63866.8	−1.50359	−0.751794	+	0.659398i	$0.770811\pi$
$72$	−15148.3	−0.344376
$73$	41299.3	0.907060	0.453530	−	0.891241i	$-0.350165\pi$
$73$	41299.3	0.907060	0.453530	+	0.891241i	$0.350165\pi$
$74$	70241.1	1.49112
$75$	16461.0	0.337912
$76$	−4425.95	−0.0878968
$77$	0	0
$78$	−7248.09	−0.134892
$79$	16963.5	0.305808	0.152904	−	0.988241i	$-0.451138\pi$
$79$	16963.5	0.305808	0.152904	+	0.988241i	$0.451138\pi$
$80$	−33973.0	−0.593483
$81$	6561.00	0.111111
$82$	48883.2	0.802833
$83$	−101693.	−1.62030	−0.810150	−	0.586223i	$-0.800614\pi$
$83$	−101693.	−1.62030	−0.810150	+	0.586223i	$0.800614\pi$
$84$	0	0
$85$	70861.8	1.06381
$86$	73736.0	1.07506
$87$	11336.2	0.160572
$88$	−34491.4	−0.474793
$89$	87102.5	1.16562	0.582808	−	0.812610i	$-0.301954\pi$
$89$	87102.5	1.16562	0.582808	+	0.812610i	$0.301954\pi$
$90$	15881.2	0.206670
$91$	0	0
$92$	−320.370	−0.00394623
$93$	−80721.2	−0.967788
$94$	−109176.	−1.27440
$95$	68130.4	0.774519
$96$	−7604.54	−0.0842160
$97$	−118107.	−1.27452	−0.637258	−	0.770650i	$-0.719932\pi$
$97$	−118107.	−1.27452	−0.637258	+	0.770650i	$0.719932\pi$
$98$	0	0
$99$	14938.8	0.153190
$100$	4277.42	0.0427742
$101$	22232.7	0.216865	0.108432	−	0.994104i	$-0.465417\pi$
$101$	22232.7	0.216865	0.108432	+	0.994104i	$0.465417\pi$
$102$	−96482.3	−0.918221
$103$	135931.	1.26248	0.631239	−	0.775588i	$-0.282547\pi$
$103$	135931.	1.26248	0.631239	+	0.775588i	$0.282547\pi$
$104$	−27654.4	−0.250716
$105$	0	0
$106$	50836.8	0.439454
$107$	117626.	0.993218	0.496609	−	0.867974i	$-0.334578\pi$
$107$	117626.	0.993218	0.496609	+	0.867974i	$0.334578\pi$
$108$	1704.89	0.0140649
$109$	−34664.2	−0.279457	−0.139729	−	0.990190i	$-0.544623\pi$
$109$	−34664.2	−0.279457	−0.139729	+	0.990190i	$0.544623\pi$
$110$	36160.1	0.284937
$111$	−116075.	−0.894192
$112$	0	0
$113$	−26584.5	−0.195854	−0.0979269	−	0.995194i	$-0.531221\pi$
$113$	−26584.5	−0.195854	−0.0979269	+	0.995194i	$0.531221\pi$
$114$	−92763.4	−0.668520
$115$	4931.58	0.0347730
$116$	2945.74	0.0203259
$117$	11977.6	0.0808921
$118$	48288.7	0.319257
$119$	0	0
$120$	60593.2	0.384123
$121$	−127036.	−0.788797
$122$	−224103.	−1.36316
$123$	−80780.5	−0.481442
$124$	−20975.6	−0.122507
$125$	−178344.	−1.02090
$126$	0	0
$127$	−137111.	−0.754334	−0.377167	−	0.926145i	$-0.623102\pi$
$127$	−137111.	−0.754334	−0.377167	+	0.926145i	$0.623102\pi$
$128$	162490.	0.876600
$129$	−121850.	−0.644693
$130$	28992.4	0.150462
$131$	−54089.2	−0.275380	−0.137690	−	0.990475i	$-0.543968\pi$
$131$	−54089.2	−0.275380	−0.137690	+	0.990475i	$0.543968\pi$
$132$	3881.89	0.0193913
$133$	0	0
$134$	−301457.	−1.45032
$135$	−26244.0	−0.123935
$136$	−368119.	−1.70664
$137$	422849.	1.92479	0.962395	−	0.271653i	$-0.0875703\pi$
$137$	422849.	1.92479	0.962395	+	0.271653i	$0.0875703\pi$
$138$	−6714.62	−0.0300140
$139$	−9913.38	−0.0435196	−0.0217598	−	0.999763i	$-0.506927\pi$
$139$	−9913.38	−0.0435196	−0.0217598	+	0.999763i	$0.506927\pi$
$140$	0	0
$141$	180415.	0.764233
$142$	−347833.	−1.44760
$143$	27272.1	0.111526
$144$	−76439.2	−0.307192
$145$	−45345.0	−0.179106
$146$	224925.	0.873285
$147$	0	0
$148$	−30162.3	−0.113190
$149$	505462.	1.86519	0.932595	−	0.360925i	$-0.117539\pi$
$149$	505462.	1.86519	0.932595	+	0.360925i	$0.117539\pi$
$150$	89650.3	0.325329
$151$	−193103.	−0.689201	−0.344601	−	0.938749i	$-0.611986\pi$
$151$	−193103.	−0.689201	−0.344601	+	0.938749i	$0.611986\pi$
$152$	−353930.	−1.24253
$153$	159439.	0.550638
$154$	0	0
$155$	322885.	1.07949
$156$	3112.41	0.0102397
$157$	264923.	0.857770	0.428885	−	0.903359i	$-0.358907\pi$
$157$	264923.	0.857770	0.428885	+	0.903359i	$0.358907\pi$
$158$	92387.1	0.294421
$159$	−84008.9	−0.263532
$160$	30418.1	0.0939362
$161$	0	0
$162$	35732.7	0.106974
$163$	−539093.	−1.58926	−0.794629	−	0.607095i	$-0.792335\pi$
$163$	−539093.	−1.58926	−0.794629	+	0.607095i	$0.792335\pi$
$164$	−20991.0	−0.0609429
$165$	−59755.4	−0.170871
$166$	−553842.	−1.55997
$167$	218748.	0.606949	0.303475	−	0.952840i	$-0.401853\pi$
$167$	218748.	0.606949	0.303475	+	0.952840i	$0.401853\pi$
$168$	0	0
$169$	−349427.	−0.941108
$170$	385929.	1.02420
$171$	153293.	0.400898
$172$	−31663.0	−0.0816078
$173$	590201.	1.49929	0.749644	−	0.661842i	$-0.230225\pi$
$173$	590201.	1.49929	0.749644	+	0.661842i	$0.230225\pi$
$174$	61739.7	0.154593
$175$	0	0
$176$	−174046.	−0.423527
$177$	−79798.2	−0.191452
$178$	474380.	1.12222
$179$	−217352.	−0.507026	−0.253513	−	0.967332i	$-0.581586\pi$
$179$	−217352.	−0.507026	−0.253513	+	0.967332i	$0.581586\pi$
$180$	−6819.55	−0.0156882
$181$	188109.	0.426790	0.213395	−	0.976966i	$-0.431548\pi$
$181$	188109.	0.426790	0.213395	+	0.976966i	$0.431548\pi$
$182$	0	0
$183$	370335.	0.817461
$184$	−25619.0	−0.0557851
$185$	464300.	0.997399
$186$	−439626.	−0.931753
$187$	363029.	0.759168
$188$	46881.2	0.0967396
$189$	0	0
$190$	371053.	0.745680
$191$	173523.	0.344170	0.172085	−	0.985082i	$-0.444950\pi$
$191$	173523.	0.344170	0.172085	+	0.985082i	$0.444950\pi$
$192$	−313200.	−0.613152
$193$	117781.	0.227606	0.113803	−	0.993503i	$-0.463697\pi$
$193$	117781.	0.227606	0.113803	+	0.993503i	$0.463697\pi$
$194$	−643236.	−1.22706
$195$	−47910.5	−0.0902287
$196$	0	0
$197$	224734.	0.412575	0.206288	−	0.978491i	$-0.433862\pi$
$197$	224734.	0.412575	0.206288	+	0.978491i	$0.433862\pi$
$198$	81360.3	0.147486
$199$	740273.	1.32513	0.662567	−	0.749003i	$-0.269467\pi$
$199$	740273.	1.32513	0.662567	+	0.749003i	$0.269467\pi$
$200$	342052.	0.604669
$201$	498164.	0.869725
$202$	121084.	0.208790
$203$	0	0
$204$	41430.5	0.0697020
$205$	323122.	0.537010
$206$	740308.	1.21547
$207$	11096.1	0.0179988
$208$	−139546.	−0.223645
$209$	349036.	0.552720
$210$	0	0
$211$	−705896.	−1.09153	−0.545763	−	0.837939i	$-0.683760\pi$
$211$	−705896.	−1.09153	−0.545763	+	0.837939i	$0.683760\pi$
$212$	−21829.9	−0.0333589
$213$	574801.	0.868097
$214$	640618.	0.956236
$215$	487402.	0.719102
$216$	136335.	0.198825
$217$	0	0
$218$	−188789.	−0.269052
$219$	−371694.	−0.523691
$220$	−15527.5	−0.0216295
$221$	291069.	0.400881
$222$	−632170.	−0.860897
$223$	42214.3	0.0568456	0.0284228	−	0.999596i	$-0.490952\pi$
$223$	42214.3	0.0568456	0.0284228	+	0.999596i	$0.490952\pi$
$224$	0	0
$225$	−148149.	−0.195093
$226$	−144785.	−0.188561
$227$	742403.	0.956258	0.478129	−	0.878290i	$-0.341315\pi$
$227$	742403.	0.956258	0.478129	+	0.878290i	$0.341315\pi$
$228$	39833.6	0.0507472
$229$	941236.	1.18607	0.593034	−	0.805177i	$-0.297930\pi$
$229$	941236.	1.18607	0.593034	+	0.805177i	$0.297930\pi$
$230$	26858.5	0.0334782
$231$	0	0
$232$	235562.	0.287333
$233$	−512331.	−0.618246	−0.309123	−	0.951022i	$-0.600035\pi$
$233$	−512331.	−0.618246	−0.309123	+	0.951022i	$0.600035\pi$
$234$	65232.9	0.0778801
$235$	−721661.	−0.852440
$236$	−20735.7	−0.0242348
$237$	−152672.	−0.176558
$238$	0	0
$239$	−115323.	−0.130593	−0.0652966	−	0.997866i	$-0.520799\pi$
$239$	−115323.	−0.130593	−0.0652966	+	0.997866i	$0.520799\pi$
$240$	305757.	0.342648
$241$	−909864.	−1.00910	−0.504549	−	0.863383i	$-0.668341\pi$
$241$	−909864.	−1.00910	−0.504549	+	0.863383i	$0.668341\pi$
$242$	−691869.	−0.759426
$243$	−59049.0	−0.0641500
$244$	96232.2	0.103477
$245$	0	0
$246$	−439949.	−0.463516
$247$	279850.	0.291865
$248$	−1.67735e6	−1.73179
$249$	915236.	0.935481
$250$	−971301.	−0.982888
$251$	−321264.	−0.321868	−0.160934	−	0.986965i	$-0.551451\pi$
$251$	−321264.	−0.321868	−0.160934	+	0.986965i	$0.551451\pi$
$252$	0	0
$253$	25264.8	0.0248150
$254$	−746738.	−0.726246
$255$	−637756.	−0.614192
$256$	−228642.	−0.218050
$257$	−556492.	−0.525565	−0.262782	−	0.964855i	$-0.584640\pi$
$257$	−556492.	−0.525565	−0.262782	+	0.964855i	$0.584640\pi$
$258$	−663624.	−0.620688
$259$	0	0
$260$	−12449.6	−0.0114215
$261$	−102026.	−0.0927065
$262$	−294582.	−0.265126
$263$	−233379.	−0.208052	−0.104026	−	0.994575i	$-0.533173\pi$
$263$	−233379.	−0.208052	−0.104026	+	0.994575i	$0.533173\pi$
$264$	310423.	0.274122
$265$	336036.	0.293948
$266$	0	0
$267$	−783923.	−0.672969
$268$	129449.	0.110093
$269$	−1.47857e6	−1.24584	−0.622919	−	0.782286i	$-0.714053\pi$
$269$	−1.47857e6	−1.24584	−0.622919	+	0.782286i	$0.714053\pi$
$270$	−142931.	−0.119321
$271$	177762.	0.147033	0.0735165	−	0.997294i	$-0.476578\pi$
$271$	177762.	0.147033	0.0735165	+	0.997294i	$0.476578\pi$
$272$	−1.85755e6	−1.52236
$273$	0	0
$274$	2.30293e6	1.85312
$275$	−337323.	−0.268976
$276$	2883.33	0.00227836
$277$	−1.22252e6	−0.957318	−0.478659	−	0.878001i	$-0.658877\pi$
$277$	−1.22252e6	−0.957318	−0.478659	+	0.878001i	$0.658877\pi$
$278$	−53990.5	−0.0418991
$279$	726491.	0.558753
$280$	0	0
$281$	177799.	0.134327	0.0671636	−	0.997742i	$-0.478605\pi$
$281$	177799.	0.134327	0.0671636	+	0.997742i	$0.478605\pi$
$282$	982582.	0.735776
$283$	−1.09052e6	−0.809406	−0.404703	−	0.914448i	$-0.632625\pi$
$283$	−1.09052e6	−0.809406	−0.404703	+	0.914448i	$0.632625\pi$
$284$	149363.	0.109887
$285$	−613174.	−0.447169
$286$	148530.	0.107374
$287$	0	0
$288$	68440.8	0.0486221
$289$	2.45468e6	1.72882
$290$	−246959.	−0.172437
$291$	1.06296e6	0.735843
$292$	−96585.3	−0.0662909
$293$	545742.	0.371380	0.185690	−	0.982608i	$-0.440548\pi$
$293$	545742.	0.371380	0.185690	+	0.982608i	$0.440548\pi$
$294$	0	0
$295$	319193.	0.213549
$296$	−2.41198e6	−1.60009
$297$	−134450.	−0.0884440
$298$	2.75286e6	1.79574
$299$	20256.8	0.0131036
$300$	−38496.8	−0.0246957
$301$	0	0
$302$	−1.05168e6	−0.663539
$303$	−200095.	−0.125207
$304$	−1.78595e6	−1.10837
$305$	−1.48134e6	−0.911811
$306$	868341.	0.530135
$307$	−3.29000e6	−1.99228	−0.996138	−	0.0878052i	$-0.972015\pi$
$307$	−3.29000e6	−1.99228	−0.996138	+	0.0878052i	$0.972015\pi$
$308$	0	0
$309$	−1.22338e6	−0.728892
$310$	1.75850e6	1.03929
$311$	−699712.	−0.410221	−0.205111	−	0.978739i	$-0.565755\pi$
$311$	−699712.	−0.410221	−0.205111	+	0.978739i	$0.565755\pi$
$312$	248890.	0.144751
$313$	623219.	0.359567	0.179783	−	0.983706i	$-0.442460\pi$
$313$	623219.	0.359567	0.179783	+	0.983706i	$0.442460\pi$
$314$	1.44283e6	0.825831
$315$	0	0
$316$	−39672.0	−0.0223494
$317$	−639244.	−0.357288	−0.178644	−	0.983914i	$-0.557171\pi$
$317$	−639244.	−0.357288	−0.178644	+	0.983914i	$0.557171\pi$
$318$	−457531.	−0.253719
$319$	−232305.	−0.127815
$320$	1.25280e6	0.683922
$321$	−1.05864e6	−0.573435
$322$	0	0
$323$	3.72519e6	1.98675
$324$	−15344.0	−0.00812037
$325$	−270458.	−0.142034
$326$	−2.93602e6	−1.53008
$327$	311978.	0.161345
$328$	−1.67858e6	−0.861506
$329$	0	0
$330$	−325441.	−0.164508
$331$	1.40963e6	0.707190	0.353595	−	0.935399i	$-0.384959\pi$
$331$	1.40963e6	0.707190	0.353595	+	0.935399i	$0.384959\pi$
$332$	237826.	0.118417
$333$	1.04467e6	0.516262
$334$	1.19135e6	0.584350
$335$	−1.99265e6	−0.970108
$336$	0	0
$337$	−1.55677e6	−0.746704	−0.373352	−	0.927690i	$-0.621792\pi$
$337$	−1.55677e6	−0.746704	−0.373352	+	0.927690i	$0.621792\pi$
$338$	−1.90306e6	−0.906066
$339$	239260.	0.113076
$340$	−165722.	−0.0777469
$341$	1.65416e6	0.770356
$342$	834870.	0.385970
$343$	0	0
$344$	−2.53200e6	−1.15363
$345$	−44384.3	−0.0200762
$346$	3.21437e6	1.44346
$347$	248297.	0.110700	0.0553500	−	0.998467i	$-0.482373\pi$
$347$	248297.	0.110700	0.0553500	+	0.998467i	$0.482373\pi$
$348$	−26511.7	−0.0117352
$349$	1.86169e6	0.818171	0.409086	−	0.912496i	$-0.365848\pi$
$349$	1.86169e6	0.818171	0.409086	+	0.912496i	$0.365848\pi$
$350$	0	0
$351$	−107799.	−0.0467031
$352$	155834.	0.0670356
$353$	1.77128e6	0.756574	0.378287	−	0.925688i	$-0.376513\pi$
$353$	1.77128e6	0.756574	0.378287	+	0.925688i	$0.376513\pi$
$354$	−434599.	−0.184323
$355$	−2.29920e6	−0.968292
$356$	−203704.	−0.0851871
$357$	0	0
$358$	−1.18375e6	−0.488147
$359$	−4.47560e6	−1.83280	−0.916401	−	0.400262i	$-0.868919\pi$
$359$	−4.47560e6	−1.83280	−0.916401	+	0.400262i	$0.868919\pi$
$360$	−545339.	−0.221774
$361$	1.10550e6	0.446469
$362$	1.02449e6	0.410898
$363$	1.14333e6	0.455412
$364$	0	0
$365$	1.48678e6	0.584135
$366$	2.01693e6	0.787023
$367$	3.17097e6	1.22893	0.614465	−	0.788944i	$-0.289372\pi$
$367$	3.17097e6	1.22893	0.614465	+	0.788944i	$0.289372\pi$
$368$	−129275.	−0.0497617
$369$	727025.	0.277961
$370$	2.52868e6	0.960261
$371$	0	0
$372$	188780.	0.0707292
$373$	−2.31179e6	−0.860353	−0.430177	−	0.902745i	$-0.641549\pi$
$373$	−2.31179e6	−0.860353	−0.430177	+	0.902745i	$0.641549\pi$
$374$	1.97714e6	0.730900
$375$	1.60510e6	0.589417
$376$	3.74895e6	1.36754
$377$	−186257.	−0.0674931
$378$	0	0
$379$	−591840.	−0.211644	−0.105822	−	0.994385i	$-0.533747\pi$
$379$	−591840.	−0.211644	−0.105822	+	0.994385i	$0.533747\pi$
$380$	−159334.	−0.0566044
$381$	1.23400e6	0.435515
$382$	945042.	0.331354
$383$	−3.59766e6	−1.25321	−0.626605	−	0.779337i	$-0.715556\pi$
$383$	−3.59766e6	−1.25321	−0.626605	+	0.779337i	$0.715556\pi$
$384$	−1.46241e6	−0.506105
$385$	0	0
$386$	641464.	0.219131
$387$	1.09665e6	0.372213
$388$	276212.	0.0931459
$389$	−2.24746e6	−0.753040	−0.376520	−	0.926409i	$-0.622879\pi$
$389$	−2.24746e6	−0.753040	−0.376520	+	0.926409i	$0.622879\pi$
$390$	−260931.	−0.0868690
$391$	269646.	0.0891973
$392$	0	0
$393$	486803.	0.158991
$394$	1.22395e6	0.397213
$395$	610687.	0.196936
$396$	−34937.0	−0.0111956
$397$	−4.58670e6	−1.46058	−0.730288	−	0.683139i	$-0.760614\pi$
$397$	−4.58670e6	−1.46058	−0.730288	+	0.683139i	$0.760614\pi$
$398$	4.03169e6	1.27579
$399$	0	0
$400$	1.72602e6	0.539380
$401$	6.00432e6	1.86468	0.932338	−	0.361589i	$-0.117766\pi$
$401$	6.00432e6	1.86468	0.932338	+	0.361589i	$0.117766\pi$
$402$	2.71311e6	0.837341
$403$	1.32627e6	0.406788
$404$	−51994.9	−0.0158492
$405$	236196.	0.0715542
$406$	0	0
$407$	2.37864e6	0.711774
$408$	3.31307e6	0.985328
$409$	−3.55340e6	−1.05035	−0.525177	−	0.850993i	$-0.676001\pi$
$409$	−3.55340e6	−1.05035	−0.525177	+	0.850993i	$0.676001\pi$
$410$	1.75980e6	0.517014
$411$	−3.80564e6	−1.11128
$412$	−317896.	−0.0922661
$413$	0	0
$414$	60431.6	0.0173286
$415$	−3.66094e6	−1.04345
$416$	124944.	0.0353983
$417$	89220.4	0.0251260
$418$	1.90093e6	0.532139
$419$	2.01375e6	0.560365	0.280182	−	0.959947i	$-0.409605\pi$
$419$	2.01375e6	0.560365	0.280182	+	0.959947i	$0.409605\pi$
$420$	0	0
$421$	−5.89987e6	−1.62232	−0.811161	−	0.584823i	$-0.801164\pi$
$421$	−5.89987e6	−1.62232	−0.811161	+	0.584823i	$0.801164\pi$
$422$	−3.84446e6	−1.05088
$423$	−1.62374e6	−0.441230
$424$	−1.74567e6	−0.471571
$425$	−3.60017e6	−0.966832
$426$	3.13049e6	0.835774
$427$	0	0
$428$	−275088.	−0.0725877
$429$	−245449.	−0.0643898
$430$	2.65450e6	0.692327
$431$	−3.81048e6	−0.988066	−0.494033	−	0.869443i	$-0.664478\pi$
$431$	−3.81048e6	−0.988066	−0.494033	+	0.869443i	$0.664478\pi$
$432$	687952.	0.177357
$433$	6.59449e6	1.69029	0.845146	−	0.534536i	$-0.179513\pi$
$433$	6.59449e6	1.69029	0.845146	+	0.534536i	$0.179513\pi$
$434$	0	0
$435$	408105.	0.103407
$436$	81068.1	0.0204237
$437$	259252.	0.0649410
$438$	−2.02433e6	−0.504192
$439$	−4.55028e6	−1.12688	−0.563438	−	0.826158i	$-0.690522\pi$
$439$	−4.55028e6	−1.12688	−0.563438	+	0.826158i	$0.690522\pi$
$440$	−1.24169e6	−0.305761
$441$	0	0
$442$	1.58523e6	0.385954
$443$	5.11537e6	1.23842	0.619210	−	0.785225i	$-0.287453\pi$
$443$	5.11537e6	1.23842	0.619210	+	0.785225i	$0.287453\pi$
$444$	271460.	0.0653505
$445$	3.13569e6	0.750643
$446$	229908.	0.0547290
$447$	−4.54916e6	−1.07687
$448$	0	0
$449$	5.95600e6	1.39424	0.697122	−	0.716953i	$-0.254464\pi$
$449$	5.95600e6	1.39424	0.697122	+	0.716953i	$0.254464\pi$
$450$	−806852.	−0.187829
$451$	1.65537e6	0.383226
$452$	62172.2	0.0143136
$453$	1.73792e6	0.397911
$454$	4.04329e6	0.920652
$455$	0	0
$456$	3.18537e6	0.717378
$457$	−2.59834e6	−0.581976	−0.290988	−	0.956727i	$-0.593984\pi$
$457$	−2.59834e6	−0.581976	−0.290988	+	0.956727i	$0.593984\pi$
$458$	5.12618e6	1.14191
$459$	−1.43495e6	−0.317911
$460$	−11533.3	−0.00254132
$461$	4.51513e6	0.989505	0.494752	−	0.869034i	$-0.335259\pi$
$461$	4.51513e6	0.989505	0.494752	+	0.869034i	$0.335259\pi$
$462$	0	0
$463$	−5.55129e6	−1.20349	−0.601744	−	0.798689i	$-0.705527\pi$
$463$	−5.55129e6	−1.20349	−0.601744	+	0.798689i	$0.705527\pi$
$464$	1.18866e6	0.256308
$465$	−2.90596e6	−0.623244
$466$	−2.79027e6	−0.595225
$467$	−7.95350e6	−1.68759	−0.843794	−	0.536668i	$-0.819683\pi$
$467$	−7.95350e6	−1.68759	−0.843794	+	0.536668i	$0.819683\pi$
$468$	−28011.7	−0.00591187
$469$	0	0
$470$	−3.93033e6	−0.820699
$471$	−2.38431e6	−0.495233
$472$	−1.65817e6	−0.342590
$473$	2.49699e6	0.513173
$474$	−831484.	−0.169984
$475$	−3.46140e6	−0.703912
$476$	0	0
$477$	756080.	0.152150
$478$	−628074.	−0.125731
$479$	−6.56370e6	−1.30710	−0.653552	−	0.756882i	$-0.726722\pi$
$479$	−6.56370e6	−1.30710	−0.653552	+	0.756882i	$0.726722\pi$
$480$	−273763.	−0.0542341
$481$	1.90714e6	0.375854
$482$	−4.95532e6	−0.971525
$483$	0	0
$484$	297096.	0.0576479
$485$	−4.25185e6	−0.820773
$486$	−321594.	−0.0617614
$487$	4.66370e6	0.891062	0.445531	−	0.895266i	$-0.353015\pi$
$487$	4.66370e6	0.891062	0.445531	+	0.895266i	$0.353015\pi$
$488$	7.69539e6	1.46279
$489$	4.85183e6	0.917558
$490$	0	0
$491$	−917227.	−0.171701	−0.0858506	−	0.996308i	$-0.527361\pi$
$491$	−917227.	−0.171701	−0.0858506	+	0.996308i	$0.527361\pi$
$492$	188919.	0.0351854
$493$	−2.47934e6	−0.459430
$494$	1.52412e6	0.280998
$495$	537799.	0.0986522
$496$	−8.46401e6	−1.54480
$497$	0	0
$498$	4.98458e6	0.900648
$499$	313436.	0.0563504	0.0281752	−	0.999603i	$-0.491030\pi$
$499$	313436.	0.0563504	0.0281752	+	0.999603i	$0.491030\pi$
$500$	417087.	0.0746108
$501$	−1.96873e6	−0.350422
$502$	−1.74967e6	−0.309883
$503$	−3.74110e6	−0.659294	−0.329647	−	0.944104i	$-0.606930\pi$
$503$	−3.74110e6	−0.659294	−0.329647	+	0.944104i	$0.606930\pi$
$504$	0	0
$505$	800378.	0.139658
$506$	137598.	0.0238910
$507$	3.14484e6	0.543349
$508$	320657.	0.0551292
$509$	1.03017e7	1.76244	0.881220	−	0.472707i	$-0.156723\pi$
$509$	1.03017e7	1.76244	0.881220	+	0.472707i	$0.156723\pi$
$510$	−3.47336e6	−0.591323
$511$	0	0
$512$	−6.44492e6	−1.08653
$513$	−1.37964e6	−0.231458
$514$	−3.03078e6	−0.505995
$515$	4.89350e6	0.813021
$516$	284967.	0.0471163
$517$	−3.69711e6	−0.608326
$518$	0	0
$519$	−5.31181e6	−0.865614
$520$	−995560.	−0.161458
$521$	−6.57325e6	−1.06093	−0.530464	−	0.847707i	$-0.677982\pi$
$521$	−6.57325e6	−1.06093	−0.530464	+	0.847707i	$0.677982\pi$
$522$	−555657.	−0.0892546
$523$	8.36532e6	1.33730	0.668650	−	0.743578i	$-0.266873\pi$
$523$	8.36532e6	1.33730	0.668650	+	0.743578i	$0.266873\pi$
$524$	126497.	0.0201257
$525$	0	0
$526$	−1.27103e6	−0.200306
$527$	1.76545e7	2.76904
$528$	1.56641e6	0.244524
$529$	−6.41758e6	−0.997084
$530$	1.83013e6	0.283003
$531$	718184.	0.110535
$532$	0	0
$533$	1.32724e6	0.202364
$534$	−4.26942e6	−0.647911
$535$	4.23454e6	0.639620
$536$	1.03516e7	1.55631
$537$	1.95617e6	0.292732
$538$	−8.05263e6	−1.19945
$539$	0	0
$540$	61376.0	0.00905761
$541$	−8.06623e6	−1.18489	−0.592444	−	0.805612i	$-0.701837\pi$
$541$	−8.06623e6	−1.18489	−0.592444	+	0.805612i	$0.701837\pi$
$542$	968129.	0.141558
$543$	−1.69298e6	−0.246407
$544$	1.66318e6	0.240959
$545$	−1.24791e6	−0.179967
$546$	0	0
$547$	3.90775e6	0.558416	0.279208	−	0.960231i	$-0.409928\pi$
$547$	3.90775e6	0.558416	0.279208	+	0.960231i	$0.409928\pi$
$548$	−988902.	−0.140670
$549$	−3.33301e6	−0.471961
$550$	−1.83714e6	−0.258961
$551$	−2.38377e6	−0.334492
$552$	230571.	0.0322075
$553$	0	0
$554$	−6.65811e6	−0.921672
$555$	−4.17870e6	−0.575849
$556$	23184.1	0.00318056
$557$	−1.15862e7	−1.58235	−0.791177	−	0.611588i	$-0.790531\pi$
$557$	−1.15862e7	−1.58235	−0.791177	+	0.611588i	$0.790531\pi$
$558$	3.95663e6	0.537948
$559$	2.00203e6	0.270982
$560$	0	0
$561$	−3.26727e6	−0.438306
$562$	968334.	0.129326
$563$	1.91176e6	0.254192	0.127096	−	0.991890i	$-0.459434\pi$
$563$	1.91176e6	0.254192	0.127096	+	0.991890i	$0.459434\pi$
$564$	−421931.	−0.0558526
$565$	−957041.	−0.126127
$566$	−5.93920e6	−0.779268
$567$	0	0
$568$	1.19441e7	1.55340
$569$	8.16817e6	1.05766	0.528828	−	0.848729i	$-0.322632\pi$
$569$	8.16817e6	1.05766	0.528828	+	0.848729i	$0.322632\pi$
$570$	−3.33948e6	−0.430519
$571$	−7.46593e6	−0.958283	−0.479141	−	0.877738i	$-0.659052\pi$
$571$	−7.46593e6	−0.958283	−0.479141	+	0.877738i	$0.659052\pi$
$572$	−63780.3	−0.00815072
$573$	−1.56170e6	−0.198706
$574$	0	0
$575$	−250552.	−0.0316030
$576$	2.81880e6	0.354004
$577$	−6.88438e6	−0.860845	−0.430423	−	0.902627i	$-0.641635\pi$
$577$	−6.88438e6	−0.860845	−0.430423	+	0.902627i	$0.641635\pi$
$578$	1.33687e7	1.66445
$579$	−1.06003e6	−0.131408
$580$	106047.	0.0130896
$581$	0	0
$582$	5.78912e6	0.708444
$583$	1.72153e6	0.209770
$584$	−7.72363e6	−0.937108
$585$	431195.	0.0520935
$586$	2.97223e6	0.357551
$587$	−8.91086e6	−1.06739	−0.533696	−	0.845676i	$-0.679197\pi$
$587$	−8.91086e6	−1.06739	−0.533696	+	0.845676i	$0.679197\pi$
$588$	0	0
$589$	1.69740e7	2.01602
$590$	1.73839e6	0.205598
$591$	−2.02261e6	−0.238200
$592$	−1.21710e7	−1.42732
$593$	1.23430e7	1.44140	0.720700	−	0.693247i	$-0.243820\pi$
$593$	1.23430e7	1.44140	0.720700	+	0.693247i	$0.243820\pi$
$594$	−732243.	−0.0851508
$595$	0	0
$596$	−1.18211e6	−0.136314
$597$	−6.66246e6	−0.765066
$598$	110323.	0.0126157
$599$	9.05732e6	1.03141	0.515707	−	0.856765i	$-0.327529\pi$
$599$	9.05732e6	1.03141	0.515707	+	0.856765i	$0.327529\pi$
$600$	−3.07847e6	−0.349106
$601$	7.41700e6	0.837611	0.418805	−	0.908076i	$-0.362449\pi$
$601$	7.41700e6	0.837611	0.418805	+	0.908076i	$0.362449\pi$
$602$	0	0
$603$	−4.48347e6	−0.502136
$604$	451603.	0.0503691
$605$	−4.57331e6	−0.507975
$606$	−1.08976e6	−0.120545
$607$	−5.77813e6	−0.636525	−0.318263	−	0.948003i	$-0.603099\pi$
$607$	−5.77813e6	−0.636525	−0.318263	+	0.948003i	$0.603099\pi$
$608$	1.59908e6	0.175432
$609$	0	0
$610$	−8.06770e6	−0.877860
$611$	−2.96426e6	−0.321228
$612$	−372875.	−0.0402425
$613$	6.29264e6	0.676366	0.338183	−	0.941080i	$-0.390188\pi$
$613$	6.29264e6	0.676366	0.338183	+	0.941080i	$0.390188\pi$
$614$	−1.79180e7	−1.91809
$615$	−2.90810e6	−0.310043
$616$	0	0
$617$	−9.79133e6	−1.03545	−0.517725	−	0.855547i	$-0.673221\pi$
$617$	−9.79133e6	−1.03545	−0.517725	+	0.855547i	$0.673221\pi$
$618$	−6.66277e6	−0.701752
$619$	−1.32677e7	−1.39178	−0.695889	−	0.718150i	$-0.744989\pi$
$619$	−1.32677e7	−1.39178	−0.695889	+	0.718150i	$0.744989\pi$
$620$	−755120.	−0.0788927
$621$	−99864.6	−0.0103916
$622$	−3.81079e6	−0.394947
$623$	0	0
$624$	1.25591e6	0.129121
$625$	−704759.	−0.0721673
$626$	3.39419e6	0.346178
$627$	−3.14133e6	−0.319113
$628$	−619567.	−0.0626886
$629$	2.53867e7	2.55846
$630$	0	0
$631$	4.41233e6	0.441158	0.220579	−	0.975369i	$-0.429205\pi$
$631$	4.41233e6	0.441158	0.220579	+	0.975369i	$0.429205\pi$
$632$	−3.17245e6	−0.315938
$633$	6.35306e6	0.630193
$634$	−3.48146e6	−0.343984
$635$	−4.93600e6	−0.485782
$636$	196469.	0.0192598
$637$	0	0
$638$	−1.26518e6	−0.123056
$639$	−5.17321e6	−0.501196
$640$	5.84964e6	0.564520
$641$	8.13035e6	0.781564	0.390782	−	0.920483i	$-0.372205\pi$
$641$	8.13035e6	0.781564	0.390782	+	0.920483i	$0.372205\pi$
$642$	−5.76557e6	−0.552083
$643$	−3.12961e6	−0.298513	−0.149256	−	0.988799i	$-0.547688\pi$
$643$	−3.12961e6	−0.298513	−0.149256	+	0.988799i	$0.547688\pi$
$644$	0	0
$645$	−4.38661e6	−0.415174
$646$	2.02882e7	1.91277
$647$	1.34660e7	1.26467	0.632336	−	0.774695i	$-0.282096\pi$
$647$	1.34660e7	1.26467	0.632336	+	0.774695i	$0.282096\pi$
$648$	−1.22701e6	−0.114792
$649$	1.63524e6	0.152395
$650$	−1.47297e6	−0.136745
$651$	0	0
$652$	1.26076e6	0.116148
$653$	1.44772e7	1.32862	0.664312	−	0.747455i	$-0.268725\pi$
$653$	1.44772e7	1.32862	0.664312	+	0.747455i	$0.268725\pi$
$654$	1.69910e6	0.155337
$655$	−1.94721e6	−0.177341
$656$	−8.47023e6	−0.768485
$657$	3.34525e6	0.302353
$658$	0	0
$659$	432708.	0.0388134	0.0194067	−	0.999812i	$-0.493822\pi$
$659$	432708.	0.0388134	0.0194067	+	0.999812i	$0.493822\pi$
$660$	139748.	0.0124878
$661$	−29965.2	−0.00266756	−0.00133378	−	0.999999i	$-0.500425\pi$
$661$	−29965.2	−0.00266756	−0.00133378	+	0.999999i	$0.500425\pi$
$662$	7.67718e6	0.680858
$663$	−2.61962e6	−0.231449
$664$	1.90182e7	1.67398
$665$	0	0
$666$	5.68953e6	0.497039
$667$	−172548.	−0.0150174
$668$	−511578.	−0.0443579
$669$	−379928.	−0.0328198
$670$	−1.08524e7	−0.933986
$671$	−7.58899e6	−0.650696
$672$	0	0
$673$	−6.71329e6	−0.571344	−0.285672	−	0.958327i	$-0.592217\pi$
$673$	−6.71329e6	−0.571344	−0.285672	+	0.958327i	$0.592217\pi$
$674$	−8.47849e6	−0.718901
$675$	1.33334e6	0.112637
$676$	817193.	0.0687793
$677$	−4.45929e6	−0.373933	−0.186967	−	0.982366i	$-0.559866\pi$
$677$	−4.45929e6	−0.373933	−0.186967	+	0.982366i	$0.559866\pi$
$678$	1.30306e6	0.108866
$679$	0	0
$680$	−1.32523e7	−1.09905
$681$	−6.68163e6	−0.552096
$682$	9.00892e6	0.741672
$683$	−1.79839e7	−1.47514	−0.737569	−	0.675272i	$-0.764026\pi$
$683$	−1.79839e7	−1.47514	−0.737569	+	0.675272i	$0.764026\pi$
$684$	−358502.	−0.0292989
$685$	1.52225e7	1.23954
$686$	0	0
$687$	−8.47112e6	−0.684777
$688$	−1.27766e7	−1.02907
$689$	1.38029e6	0.110770
$690$	−241726.	−0.0193286
$691$	2.50935e6	0.199925	0.0999624	−	0.994991i	$-0.468128\pi$
$691$	2.50935e6	0.199925	0.0999624	+	0.994991i	$0.468128\pi$
$692$	−1.38028e6	−0.109573
$693$	0	0
$694$	1.35228e6	0.106578
$695$	−356882.	−0.0280261
$696$	−2.12006e6	−0.165892
$697$	1.76675e7	1.37750
$698$	1.01392e7	0.787707
$699$	4.61098e6	0.356944
$700$	0	0
$701$	9.68649e6	0.744512	0.372256	−	0.928130i	$-0.378584\pi$
$701$	9.68649e6	0.744512	0.372256	+	0.928130i	$0.378584\pi$
$702$	−587096.	−0.0449641
$703$	2.44081e7	1.86271
$704$	6.41817e6	0.488067
$705$	6.49495e6	0.492156
$706$	9.64681e6	0.728403
$707$	0	0
$708$	186621.	0.0139919
$709$	−9.52720e6	−0.711786	−0.355893	−	0.934527i	$-0.615823\pi$
$709$	−9.52720e6	−0.711786	−0.355893	+	0.934527i	$0.615823\pi$
$710$	−1.25220e7	−0.932238
$711$	1.37405e6	0.101936
$712$	−1.62896e7	−1.20423
$713$	1.22865e6	0.0905118
$714$	0	0
$715$	981794.	0.0718217
$716$	508313.	0.0370552
$717$	1.03791e6	0.0753980
$718$	−2.43751e7	−1.76456
$719$	757176.	0.0546229	0.0273114	−	0.999627i	$-0.491305\pi$
$719$	757176.	0.0546229	0.0273114	+	0.999627i	$0.491305\pi$
$720$	−2.75181e6	−0.197828
$721$	0	0
$722$	6.02081e6	0.429845
$723$	8.18877e6	0.582603
$724$	−439925.	−0.0311912
$725$	2.30378e6	0.162778
$726$	6.22682e6	0.438455
$727$	−2.66570e7	−1.87058	−0.935288	−	0.353888i	$-0.884859\pi$
$727$	−2.66570e7	−1.87058	−0.935288	+	0.353888i	$0.884859\pi$
$728$	0	0
$729$	531441.	0.0370370
$730$	8.09731e6	0.562385
$731$	2.66498e7	1.84459
$732$	−866090.	−0.0597427
$733$	2.70857e7	1.86200	0.931001	−	0.365017i	$-0.118937\pi$
$733$	2.70857e7	1.86200	0.931001	+	0.365017i	$0.118937\pi$
$734$	1.72698e7	1.18317
$735$	0	0
$736$	115748.	0.00787625
$737$	−1.02085e7	−0.692298
$738$	3.95954e6	0.267611
$739$	2.19507e7	1.47855	0.739276	−	0.673402i	$-0.235168\pi$
$739$	2.19507e7	1.47855	0.739276	+	0.673402i	$0.235168\pi$
$740$	−1.08584e6	−0.0728932
$741$	−2.51865e6	−0.168508
$742$	0	0
$743$	5.77370e6	0.383691	0.191846	−	0.981425i	$-0.438553\pi$
$743$	5.77370e6	0.383691	0.191846	+	0.981425i	$0.438553\pi$
$744$	1.50962e7	0.999848
$745$	1.81966e7	1.20116
$746$	−1.25905e7	−0.828318
$747$	−8.23712e6	−0.540100
$748$	−849005.	−0.0554825
$749$	0	0
$750$	8.74171e6	0.567470
$751$	−8.37749e6	−0.542018	−0.271009	−	0.962577i	$-0.587357\pi$
$751$	−8.37749e6	−0.542018	−0.271009	+	0.962577i	$0.587357\pi$
$752$	1.89174e7	1.21988
$753$	2.89138e6	0.185831
$754$	−1.01440e6	−0.0649800
$755$	−6.95170e6	−0.443837
$756$	0	0
$757$	1.18828e7	0.753665	0.376833	−	0.926281i	$-0.377013\pi$
$757$	1.18828e7	0.753665	0.376833	+	0.926281i	$0.377013\pi$
$758$	−3.22329e6	−0.203764
$759$	−227383.	−0.0143270
$760$	−1.27415e7	−0.800177
$761$	1.76940e7	1.10755	0.553777	−	0.832665i	$-0.313186\pi$
$761$	1.76940e7	1.10755	0.553777	+	0.832665i	$0.313186\pi$
$762$	6.72064e6	0.419298
$763$	0	0
$764$	−405811.	−0.0251531
$765$	5.73981e6	0.354604
$766$	−1.95937e7	−1.20655
$767$	1.31110e6	0.0804726
$768$	2.05778e6	0.125891
$769$	−4.12006e6	−0.251239	−0.125620	−	0.992078i	$-0.540092\pi$
$769$	−4.12006e6	−0.251239	−0.125620	+	0.992078i	$0.540092\pi$
$770$	0	0
$771$	5.00843e6	0.303435
$772$	−275452.	−0.0166342
$773$	1.26864e7	0.763642	0.381821	−	0.924236i	$-0.375297\pi$
$773$	1.26864e7	0.763642	0.381821	+	0.924236i	$0.375297\pi$
$774$	5.97262e6	0.358354
$775$	−1.64043e7	−0.981080
$776$	2.20879e7	1.31674
$777$	0	0
$778$	−1.22402e7	−0.725001
$779$	1.69865e7	1.00290
$780$	112047.	0.00659421
$781$	−1.17790e7	−0.691002
$782$	1.46855e6	0.0858761
$783$	918235.	0.0535241
$784$	0	0
$785$	9.53723e6	0.552393
$786$	2.65124e6	0.153071
$787$	9.14809e6	0.526494	0.263247	−	0.964728i	$-0.415207\pi$
$787$	9.14809e6	0.526494	0.263247	+	0.964728i	$0.415207\pi$
$788$	−525578.	−0.0301524
$789$	2.10041e6	0.120119
$790$	3.32594e6	0.189603
$791$	0	0
$792$	−2.79380e6	−0.158264
$793$	−6.08468e6	−0.343602
$794$	−2.49802e7	−1.40619
$795$	−3.02432e6	−0.169711
$796$	−1.73125e6	−0.0968451
$797$	−1.10180e7	−0.614408	−0.307204	−	0.951644i	$-0.599393\pi$
$797$	−1.10180e7	−0.614408	−0.307204	+	0.951644i	$0.599393\pi$
$798$	0	0
$799$	−3.94585e7	−2.18662
$800$	−1.54541e6	−0.0853727
$801$	7.05530e6	0.388539
$802$	3.27009e7	1.79524
$803$	7.61684e6	0.416856
$804$	−1.16504e6	−0.0635624
$805$	0	0
$806$	7.22315e6	0.391642
$807$	1.33071e7	0.719285
$808$	−4.15788e6	−0.224049
$809$	−3.10273e7	−1.66676	−0.833378	−	0.552703i	$-0.813596\pi$
$809$	−3.10273e7	−1.66676	−0.833378	+	0.552703i	$0.813596\pi$
$810$	1.28638e6	0.0688899
$811$	−2.94456e7	−1.57206	−0.786028	−	0.618191i	$-0.787866\pi$
$811$	−2.94456e7	−1.57206	−0.786028	+	0.618191i	$0.787866\pi$
$812$	0	0
$813$	−1.59985e6	−0.0848895
$814$	1.29546e7	0.685271
$815$	−1.94073e7	−1.02346
$816$	1.67180e7	0.878937
$817$	2.56226e7	1.34297
$818$	−1.93526e7	−1.01124
$819$	0	0
$820$	−755675.	−0.0392464
$821$	−5.23311e6	−0.270958	−0.135479	−	0.990780i	$-0.543257\pi$
$821$	−5.23311e6	−0.270958	−0.135479	+	0.990780i	$0.543257\pi$
$822$	−2.07263e7	−1.06990
$823$	1.41631e7	0.728884	0.364442	−	0.931226i	$-0.381260\pi$
$823$	1.41631e7	0.728884	0.364442	+	0.931226i	$0.381260\pi$
$824$	−2.54212e7	−1.30430
$825$	3.03591e6	0.155294
$826$	0	0
$827$	2.98006e7	1.51517	0.757585	−	0.652737i	$-0.226379\pi$
$827$	2.98006e7	1.51517	0.757585	+	0.652737i	$0.226379\pi$
$828$	−25950.0	−0.00131541
$829$	−1.99304e7	−1.00723	−0.503617	−	0.863927i	$-0.667998\pi$
$829$	−1.99304e7	−1.00723	−0.503617	+	0.863927i	$0.667998\pi$
$830$	−1.99383e7	−1.00460
$831$	1.10027e7	0.552708
$832$	5.14594e6	0.257725
$833$	0	0
$834$	485914.	0.0241905
$835$	7.87492e6	0.390868
$836$	−816280.	−0.0403946
$837$	−6.53842e6	−0.322596
$838$	1.09673e7	0.539500
$839$	−1.88103e7	−0.922552	−0.461276	−	0.887257i	$-0.652608\pi$
$839$	−1.88103e7	−0.922552	−0.461276	+	0.887257i	$0.652608\pi$
$840$	0	0
$841$	−1.89246e7	−0.922650
$842$	−3.21320e7	−1.56191
$843$	−1.60019e6	−0.0775538
$844$	1.65085e6	0.0797724
$845$	−1.25794e7	−0.606062
$846$	−8.84324e6	−0.424801
$847$	0	0
$848$	−8.80874e6	−0.420653
$849$	9.81466e6	0.467311
$850$	−1.96073e7	−0.930833
$851$	1.76677e6	0.0836288
$852$	−1.34427e6	−0.0634434
$853$	2.05980e7	0.969285	0.484643	−	0.874712i	$-0.338950\pi$
$853$	2.05980e7	0.969285	0.484643	+	0.874712i	$0.338950\pi$
$854$	0	0
$855$	5.51856e6	0.258173
$856$	−2.19980e7	−1.02612
$857$	−2.47572e7	−1.15146	−0.575731	−	0.817639i	$-0.695282\pi$
$857$	−2.47572e7	−1.15146	−0.575731	+	0.817639i	$0.695282\pi$
$858$	−1.33677e6	−0.0619923
$859$	−3.91065e7	−1.80828	−0.904141	−	0.427234i	$-0.859488\pi$
$859$	−3.91065e7	−1.80828	−0.904141	+	0.427234i	$0.859488\pi$
$860$	−1.13987e6	−0.0525544
$861$	0	0
$862$	−2.07527e7	−0.951275
$863$	−3.93363e7	−1.79790	−0.898952	−	0.438048i	$-0.855670\pi$
$863$	−3.93363e7	−1.79790	−0.898952	+	0.438048i	$0.855670\pi$
$864$	−615968.	−0.0280720
$865$	2.12472e7	0.965522
$866$	3.59151e7	1.62735
$867$	−2.20921e7	−0.998135
$868$	0	0
$869$	3.12859e6	0.140540
$870$	2.22263e6	0.0995563
$871$	−8.18494e6	−0.365570
$872$	6.48277e6	0.288715
$873$	−9.56665e6	−0.424839
$874$	1.41195e6	0.0625229
$875$	0	0
$876$	869268.	0.0382731
$877$	8.09253e6	0.355292	0.177646	−	0.984094i	$-0.443152\pi$
$877$	8.09253e6	0.355292	0.177646	+	0.984094i	$0.443152\pi$
$878$	−2.47818e7	−1.08492
$879$	−4.91168e6	−0.214416
$880$	−6.26564e6	−0.272746
$881$	−4.05755e6	−0.176126	−0.0880631	−	0.996115i	$-0.528068\pi$
$881$	−4.05755e6	−0.176126	−0.0880631	+	0.996115i	$0.528068\pi$
$882$	0	0
$883$	1.79813e7	0.776102	0.388051	−	0.921638i	$-0.373148\pi$
$883$	1.79813e7	0.776102	0.388051	+	0.921638i	$0.373148\pi$
$884$	−680713.	−0.0292977
$885$	−2.87273e6	−0.123293
$886$	2.78595e7	1.19231
$887$	−1.53139e7	−0.653547	−0.326773	−	0.945103i	$-0.605961\pi$
$887$	−1.53139e7	−0.653547	−0.326773	+	0.945103i	$0.605961\pi$
$888$	2.17079e7	0.923814
$889$	0	0
$890$	1.70777e7	0.722693
$891$	1.21005e6	0.0510632
$892$	−98725.0	−0.00415447
$893$	−3.79376e7	−1.59199
$894$	−2.47757e7	−1.03677
$895$	−7.82466e6	−0.326519
$896$	0	0
$897$	−182311.	−0.00756539
$898$	3.24377e7	1.34233
$899$	−1.12972e7	−0.466200
$900$	346471.	0.0142581
$901$	1.83735e7	0.754016
$902$	9.01554e6	0.368957
$903$	0	0
$904$	4.97172e6	0.202342
$905$	6.77194e6	0.274847
$906$	9.46512e6	0.383094
$907$	−2.17757e7	−0.878930	−0.439465	−	0.898260i	$-0.644832\pi$
$907$	−2.17757e7	−0.878930	−0.439465	+	0.898260i	$0.644832\pi$
$908$	−1.73623e6	−0.0698865
$909$	1.80085e6	0.0722883
$910$	0	0
$911$	−5.35112e6	−0.213623	−0.106812	−	0.994279i	$-0.534064\pi$
$911$	−5.35112e6	−0.213623	−0.106812	+	0.994279i	$0.534064\pi$
$912$	1.60736e7	0.639919
$913$	−1.87552e7	−0.744639
$914$	−1.41511e7	−0.560306
$915$	1.33321e7	0.526435
$916$	−2.20124e6	−0.0866818
$917$	0	0
$918$	−7.81507e6	−0.306074
$919$	−2.67858e7	−1.04620	−0.523102	−	0.852270i	$-0.675225\pi$
$919$	−2.67858e7	−1.04620	−0.523102	+	0.852270i	$0.675225\pi$
$920$	−922285.	−0.0359249
$921$	2.96100e7	1.15024
$922$	2.45904e7	0.952661
$923$	−9.44411e6	−0.364886
$924$	0	0
$925$	−2.35890e7	−0.906474
$926$	−3.02336e7	−1.15868
$927$	1.10104e7	0.420826
$928$	−1.06428e6	−0.0405683
$929$	739974.	0.0281305	0.0140652	−	0.999901i	$-0.495523\pi$
$929$	739974.	0.0281305	0.0140652	+	0.999901i	$0.495523\pi$
$930$	−1.58265e7	−0.600037
$931$	0	0
$932$	1.19817e6	0.0451834
$933$	6.29741e6	0.236841
$934$	−4.33166e7	−1.62475
$935$	1.30691e7	0.488895
$936$	−2.24001e6	−0.0835719
$937$	−122654.	−0.00456385	−0.00228193	−	0.999997i	$-0.500726\pi$
$937$	−122654.	−0.00456385	−0.00228193	+	0.999997i	$0.500726\pi$
$938$	0	0
$939$	−5.60897e6	−0.207596
$940$	1.68772e6	0.0622991
$941$	1.22466e7	0.450861	0.225431	−	0.974259i	$-0.427621\pi$
$941$	1.22466e7	0.450861	0.225431	+	0.974259i	$0.427621\pi$
$942$	−1.29855e7	−0.476794
$943$	1.22956e6	0.0450266
$944$	−8.36722e6	−0.305599
$945$	0	0
$946$	1.35992e7	0.494065
$947$	−3.71174e6	−0.134494	−0.0672470	−	0.997736i	$-0.521422\pi$
$947$	−3.71174e6	−0.134494	−0.0672470	+	0.997736i	$0.521422\pi$
$948$	357048.	0.0129034
$949$	6.10701e6	0.220122
$950$	−1.88516e7	−0.677702
$951$	5.75319e6	0.206280
$952$	0	0
$953$	−2.32857e7	−0.830533	−0.415266	−	0.909700i	$-0.636312\pi$
$953$	−2.32857e7	−0.830533	−0.415266	+	0.909700i	$0.636312\pi$
$954$	4.11778e6	0.146485
$955$	6.24681e6	0.221641
$956$	269702.	0.00954418
$957$	2.09075e6	0.0737940
$958$	−3.57474e7	−1.25843
$959$	0	0
$960$	−1.12752e7	−0.394862
$961$	5.18142e7	1.80984
$962$	1.03867e7	0.361859
$963$	9.52772e6	0.331073
$964$	2.12787e6	0.0737483
$965$	4.24013e6	0.146575
$966$	0	0
$967$	2.25257e7	0.774661	0.387330	−	0.921941i	$-0.373397\pi$
$967$	2.25257e7	0.774661	0.387330	+	0.921941i	$0.373397\pi$
$968$	2.37579e7	0.814927
$969$	−3.35267e7	−1.14705
$970$	−2.31565e7	−0.790212
$971$	1.99456e7	0.678890	0.339445	−	0.940626i	$-0.389761\pi$
$971$	1.99456e7	0.678890	0.339445	+	0.940626i	$0.389761\pi$
$972$	138096.	0.00468830
$973$	0	0
$974$	2.53995e7	0.857884
$975$	2.43412e6	0.0820032
$976$	3.88314e7	1.30484
$977$	−959342.	−0.0321542	−0.0160771	−	0.999871i	$-0.505118\pi$
$977$	−959342.	−0.0321542	−0.0160771	+	0.999871i	$0.505118\pi$
$978$	2.64242e7	0.883393
$979$	1.60643e7	0.535681
$980$	0	0
$981$	−2.80780e6	−0.0931524
$982$	−4.99542e6	−0.165308
$983$	5.22097e7	1.72333	0.861663	−	0.507481i	$-0.169423\pi$
$983$	5.22097e7	1.72333	0.861663	+	0.507481i	$0.169423\pi$
$984$	1.51073e7	0.497391
$985$	8.09042e6	0.265693
$986$	−1.35030e7	−0.442323
$987$	0	0
$988$	−654475.	−0.0213305
$989$	1.85468e6	0.0602945
$990$	2.92897e6	0.0949789
$991$	−1.76305e7	−0.570269	−0.285134	−	0.958488i	$-0.592038\pi$
$991$	−1.76305e7	−0.570269	−0.285134	+	0.958488i	$0.592038\pi$
$992$	7.57836e6	0.244510
$993$	−1.26867e7	−0.408296
$994$	0	0
$995$	2.66498e7	0.853369
$996$	−2.14043e6	−0.0683680
$997$	4.04875e7	1.28998	0.644990	−	0.764191i	$-0.276862\pi$
$997$	4.04875e7	1.28998	0.644990	+	0.764191i	$0.276862\pi$
$998$	1.70704e6	0.0542522
$999$	−9.40207e6	−0.298064

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.6.a.h.1.2	✓	2
3.2	odd	2		441.6.a.q.1.1		2
7.2	even	3		147.6.e.n.67.1		4
7.3	odd	6		147.6.e.m.79.1		4
7.4	even	3		147.6.e.n.79.1		4
7.5	odd	6		147.6.e.m.67.1		4
7.6	odd	2		147.6.a.j.1.2	yes	2
21.20	even	2		441.6.a.r.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.6.a.h.1.2	✓	2	1.1	even	1	trivial
147.6.a.j.1.2	yes	2	7.6	odd	2
147.6.e.m.67.1		4	7.5	odd	6
147.6.e.m.79.1		4	7.3	odd	6
147.6.e.n.67.1		4	7.2	even	3
147.6.e.n.79.1		4	7.4	even	3
441.6.a.q.1.1		2	3.2	odd	2
441.6.a.r.1.1		2	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	147.a (trivial)

\(f(q)\)	\(=\)	\(q+5.44622 q^{2} -9.00000 q^{3} -2.33867 q^{4} +36.0000 q^{5} -49.0160 q^{6} -187.016 q^{8} +81.0000 q^{9} +196.064 q^{10} +184.430 q^{11} +21.0480 q^{12} +147.872 q^{13} -324.000 q^{15} -943.693 q^{16} +1968.38 q^{17} +441.144 q^{18} +1892.51 q^{19} -84.1920 q^{20} +1004.45 q^{22} +136.988 q^{23} +1683.14 q^{24} -1829.00 q^{25} +805.344 q^{26} -729.000 q^{27} -1259.58 q^{29} -1764.58 q^{30} +8969.02 q^{31} +844.949 q^{32} -1659.87 q^{33} +10720.3 q^{34} -189.432 q^{36} +12897.2 q^{37} +10307.0 q^{38} -1330.85 q^{39} -6732.58 q^{40} +8975.62 q^{41} +13538.9 q^{43} -431.321 q^{44} +2916.00 q^{45} +746.069 q^{46} -20046.1 q^{47} +8493.24 q^{48} -9961.14 q^{50} -17715.5 q^{51} -345.823 q^{52} +9334.33 q^{53} -3970.30 q^{54} +6639.49 q^{55} -17032.6 q^{57} -6859.96 q^{58} +8866.46 q^{59} +757.728 q^{60} -41148.3 q^{61} +48847.3 q^{62} +34800.0 q^{64} +5323.39 q^{65} -9040.03 q^{66} -55351.5 q^{67} -4603.39 q^{68} -1232.90 q^{69} -63866.8 q^{71} -15148.3 q^{72} +41299.3 q^{73} +70241.1 q^{74} +16461.0 q^{75} -4425.95 q^{76} -7248.09 q^{78} +16963.5 q^{79} -33973.0 q^{80} +6561.00 q^{81} +48883.2 q^{82} -101693. q^{83} +70861.8 q^{85} +73736.0 q^{86} +11336.2 q^{87} -34491.4 q^{88} +87102.5 q^{89} +15881.2 q^{90} -320.370 q^{92} -80721.2 q^{93} -109176. q^{94} +68130.4 q^{95} -7604.54 q^{96} -118107. q^{97} +14938.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{2} - 18 q^{3} + 37 q^{4} + 72 q^{5} + 27 q^{6} - 249 q^{8} + 162 q^{9} - 108 q^{10} + 480 q^{11} - 333 q^{12} + 1296 q^{13} - 648 q^{15} - 1679 q^{16} + 936 q^{17} - 243 q^{18} - 216 q^{19} + 1332 q^{20}+ \cdots + 38880 q^{99}+O(q^{100}) \) 2 * q - 3 * q^2 - 18 * q^3 + 37 * q^4 + 72 * q^5 + 27 * q^6 - 249 * q^8 + 162 * q^9 - 108 * q^10 + 480 * q^11 - 333 * q^12 + 1296 * q^13 - 648 * q^15 - 1679 * q^16 + 936 * q^17 - 243 * q^18 - 216 * q^19 + 1332 * q^20 - 1492 * q^22 - 504 * q^23 + 2241 * q^24 - 3658 * q^25 - 8892 * q^26 - 1458 * q^27 + 6372 * q^29 + 972 * q^30 + 9936 * q^31 + 9039 * q^32 - 4320 * q^33 + 19440 * q^34 + 2997 * q^36 + 11124 * q^37 + 28116 * q^38 - 11664 * q^39 - 8964 * q^40 + 20952 * q^41 - 6264 * q^43 + 11196 * q^44 + 5832 * q^45 + 6160 * q^46 + 7920 * q^47 + 15111 * q^48 + 5487 * q^50 - 8424 * q^51 + 44820 * q^52 + 2220 * q^53 + 2187 * q^54 + 17280 * q^55 + 1944 * q^57 - 71318 * q^58 + 29736 * q^59 - 11988 * q^60 - 17280 * q^61 + 40680 * q^62 - 10879 * q^64 + 46656 * q^65 + 13428 * q^66 - 20680 * q^67 - 45216 * q^68 + 4536 * q^69 - 92280 * q^71 - 20169 * q^72 + 56592 * q^73 + 85218 * q^74 + 32922 * q^75 - 87372 * q^76 + 80028 * q^78 - 56096 * q^79 - 60444 * q^80 + 13122 * q^81 - 52272 * q^82 - 71352 * q^83 + 33696 * q^85 + 240996 * q^86 - 57348 * q^87 - 52812 * q^88 + 123192 * q^89 - 8748 * q^90 - 25536 * q^92 - 89424 * q^93 - 345384 * q^94 - 7776 * q^95 - 81351 * q^96 + 35856 * q^97 + 38880 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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