LMFDB - Embedded newform 637.4.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,4,Mod(1,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("637.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	637.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:	$37.5842166737$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.5364412.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 27x^{2} - 24x + 76 $ x^4 - 27x^2 - 24x + 76
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.63459$ of defining polynomial
Character	$\chi$	$=$	637.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.63459 q^{2} +5.33748 q^{3} +5.21021 q^{4} -11.0031 q^{5} -19.3995 q^{6} +10.1397 q^{8} +1.48874 q^{9} +O(q^{10})$	\(q-3.63459 q^{2} +5.33748 q^{3} +5.21021 q^{4} -11.0031 q^{5} -19.3995 q^{6} +10.1397 q^{8} +1.48874 q^{9} +39.9917 q^{10} -11.7038 q^{11} +27.8094 q^{12} +13.0000 q^{13} -58.7289 q^{15} -78.5354 q^{16} +102.636 q^{17} -5.41094 q^{18} -43.2825 q^{19} -57.3285 q^{20} +42.5383 q^{22} -25.9576 q^{23} +54.1206 q^{24} -3.93182 q^{25} -47.2496 q^{26} -136.166 q^{27} -272.081 q^{29} +213.455 q^{30} +121.190 q^{31} +204.326 q^{32} -62.4686 q^{33} -373.039 q^{34} +7.75663 q^{36} +168.192 q^{37} +157.314 q^{38} +69.3873 q^{39} -111.568 q^{40} +451.218 q^{41} +94.6309 q^{43} -60.9790 q^{44} -16.3807 q^{45} +94.3450 q^{46} -50.6431 q^{47} -419.181 q^{48} +14.2905 q^{50} +547.817 q^{51} +67.7327 q^{52} -398.509 q^{53} +494.907 q^{54} +128.778 q^{55} -231.020 q^{57} +988.901 q^{58} +686.474 q^{59} -305.990 q^{60} +75.3794 q^{61} -440.476 q^{62} -114.356 q^{64} -143.040 q^{65} +227.047 q^{66} -336.720 q^{67} +534.754 q^{68} -138.548 q^{69} +427.161 q^{71} +15.0954 q^{72} +134.191 q^{73} -611.308 q^{74} -20.9860 q^{75} -225.511 q^{76} -252.194 q^{78} +253.005 q^{79} +864.133 q^{80} -766.980 q^{81} -1639.99 q^{82} +193.536 q^{83} -1129.31 q^{85} -343.944 q^{86} -1452.23 q^{87} -118.673 q^{88} +996.000 q^{89} +59.5371 q^{90} -135.244 q^{92} +646.851 q^{93} +184.067 q^{94} +476.242 q^{95} +1090.59 q^{96} -761.982 q^{97} -17.4238 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 5 q^{3} + 26 q^{4} + 36 q^{5} + 45 q^{6} - 30 q^{8} + 21 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 5 * q^3 + 26 * q^4 + 36 * q^5 + 45 * q^6 - 30 * q^8 + 21 * q^9	\( 4 q - 4 q^{2} + 5 q^{3} + 26 q^{4} + 36 q^{5} + 45 q^{6} - 30 q^{8} + 21 q^{9} + 44 q^{10} - 95 q^{11} + 17 q^{12} + 52 q^{13} - 16 q^{15} + 58 q^{16} + 146 q^{17} + 65 q^{18} + 48 q^{19} + 474 q^{20} - 143 q^{22} - 121 q^{23} + 469 q^{24} + 506 q^{25} - 52 q^{26} + 83 q^{27} - 440 q^{29} + 1548 q^{30} + 283 q^{31} - 114 q^{32} - 227 q^{33} - 1234 q^{34} + 755 q^{36} - 209 q^{37} - 440 q^{38} + 65 q^{39} - 754 q^{40} + 93 q^{41} + 526 q^{43} + 217 q^{44} + 768 q^{45} - 841 q^{46} + 783 q^{47} - 1407 q^{48} + 446 q^{50} - 672 q^{51} + 338 q^{52} - 340 q^{53} + 199 q^{54} - 756 q^{55} - 1014 q^{57} + 1916 q^{58} + 922 q^{59} - 396 q^{60} + 141 q^{61} - 1745 q^{62} - 1510 q^{64} + 468 q^{65} - 503 q^{66} - 523 q^{67} + 1710 q^{68} - 1595 q^{69} + 1468 q^{71} - 9 q^{72} + 47 q^{73} - 2249 q^{74} + 1547 q^{75} + 1382 q^{76} + 585 q^{78} + 1025 q^{79} + 2538 q^{80} - 1772 q^{81} + 1561 q^{82} + 1190 q^{83} - 568 q^{85} + 738 q^{86} - 720 q^{87} - 555 q^{88} + 2962 q^{89} + 1960 q^{90} - 599 q^{92} - 763 q^{93} - 317 q^{94} + 2082 q^{95} + 45 q^{96} - 2715 q^{97} + 586 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 5 * q^3 + 26 * q^4 + 36 * q^5 + 45 * q^6 - 30 * q^8 + 21 * q^9 + 44 * q^10 - 95 * q^11 + 17 * q^12 + 52 * q^13 - 16 * q^15 + 58 * q^16 + 146 * q^17 + 65 * q^18 + 48 * q^19 + 474 * q^20 - 143 * q^22 - 121 * q^23 + 469 * q^24 + 506 * q^25 - 52 * q^26 + 83 * q^27 - 440 * q^29 + 1548 * q^30 + 283 * q^31 - 114 * q^32 - 227 * q^33 - 1234 * q^34 + 755 * q^36 - 209 * q^37 - 440 * q^38 + 65 * q^39 - 754 * q^40 + 93 * q^41 + 526 * q^43 + 217 * q^44 + 768 * q^45 - 841 * q^46 + 783 * q^47 - 1407 * q^48 + 446 * q^50 - 672 * q^51 + 338 * q^52 - 340 * q^53 + 199 * q^54 - 756 * q^55 - 1014 * q^57 + 1916 * q^58 + 922 * q^59 - 396 * q^60 + 141 * q^61 - 1745 * q^62 - 1510 * q^64 + 468 * q^65 - 503 * q^66 - 523 * q^67 + 1710 * q^68 - 1595 * q^69 + 1468 * q^71 - 9 * q^72 + 47 * q^73 - 2249 * q^74 + 1547 * q^75 + 1382 * q^76 + 585 * q^78 + 1025 * q^79 + 2538 * q^80 - 1772 * q^81 + 1561 * q^82 + 1190 * q^83 - 568 * q^85 + 738 * q^86 - 720 * q^87 - 555 * q^88 + 2962 * q^89 + 1960 * q^90 - 599 * q^92 - 763 * q^93 - 317 * q^94 + 2082 * q^95 + 45 * q^96 - 2715 * q^97 + 586 * 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 $

$2$	−3.63459	−1.28502	−0.642510	−	0.766277i	$-0.722107\pi$
$2$	−3.63459	−1.28502	−0.642510	+	0.766277i	$0.722107\pi$
$3$	5.33748	1.02720	0.513600	−	0.858030i	$-0.328312\pi$
$3$	5.33748	1.02720	0.513600	+	0.858030i	$0.328312\pi$
$4$	5.21021	0.651276
$5$	−11.0031	−0.984147	−0.492074	−	0.870554i	$-0.663761\pi$
$5$	−11.0031	−0.984147	−0.492074	+	0.870554i	$0.663761\pi$
$6$	−19.3995	−1.31997
$7$	0	0
$7$	0	0
$8$	10.1397	0.448117
$9$	1.48874	0.0551384
$10$	39.9917	1.26465
$11$	−11.7038	−0.320801	−0.160401	−	0.987052i	$-0.551279\pi$
$11$	−11.7038	−0.320801	−0.160401	+	0.987052i	$0.551279\pi$
$12$	27.8094	0.668991
$13$	13.0000	0.277350
$13$	13.0000	0.277350
$14$	0	0
$15$	−58.7289	−1.01092
$16$	−78.5354	−1.22712
$17$	102.636	1.46429	0.732143	−	0.681151i	$-0.238520\pi$
$17$	102.636	1.46429	0.732143	+	0.681151i	$0.238520\pi$
$18$	−5.41094	−0.0708539
$19$	−43.2825	−0.522616	−0.261308	−	0.965256i	$-0.584154\pi$
$19$	−43.2825	−0.522616	−0.261308	+	0.965256i	$0.584154\pi$
$20$	−57.3285	−0.640952
$21$	0	0
$22$	42.5383	0.412236
$23$	−25.9576	−0.235327	−0.117664	−	0.993054i	$-0.537540\pi$
$23$	−25.9576	−0.235327	−0.117664	+	0.993054i	$0.537540\pi$
$24$	54.1206	0.460305
$25$	−3.93182	−0.0314546
$26$	−47.2496	−0.356400
$27$	−136.166	−0.970561
$28$	0	0
$29$	−272.081	−1.74221	−0.871106	−	0.491095i	$-0.836597\pi$
$29$	−272.081	−1.74221	−0.871106	+	0.491095i	$0.836597\pi$
$30$	213.455	1.29905
$31$	121.190	0.702142	0.351071	−	0.936349i	$-0.385818\pi$
$31$	121.190	0.702142	0.351071	+	0.936349i	$0.385818\pi$
$32$	204.326	1.12875
$33$	−62.4686	−0.329527
$34$	−373.039	−1.88164
$35$	0	0
$36$	7.75663	0.0359103
$37$	168.192	0.747314	0.373657	−	0.927567i	$-0.378104\pi$
$37$	168.192	0.747314	0.373657	+	0.927567i	$0.378104\pi$
$38$	157.314	0.671572
$39$	69.3873	0.284894
$40$	−111.568	−0.441013
$41$	451.218	1.71874	0.859372	−	0.511351i	$-0.170855\pi$
$41$	451.218	1.71874	0.859372	+	0.511351i	$0.170855\pi$
$42$	0	0
$43$	94.6309	0.335606	0.167803	−	0.985821i	$-0.446333\pi$
$43$	94.6309	0.335606	0.167803	+	0.985821i	$0.446333\pi$
$44$	−60.9790	−0.208930
$45$	−16.3807	−0.0542643
$46$	94.3450	0.302400
$47$	−50.6431	−0.157171	−0.0785857	−	0.996907i	$-0.525040\pi$
$47$	−50.6431	−0.157171	−0.0785857	+	0.996907i	$0.525040\pi$
$48$	−419.181	−1.26049
$49$	0	0
$50$	14.2905	0.0404198
$51$	547.817	1.50411
$52$	67.7327	0.180632
$53$	−398.509	−1.03282	−0.516410	−	0.856341i	$-0.672732\pi$
$53$	−398.509	−1.03282	−0.516410	+	0.856341i	$0.672732\pi$
$54$	494.907	1.24719
$55$	128.778	0.315716
$56$	0	0
$57$	−231.020	−0.536830
$58$	988.901	2.23878
$59$	686.474	1.51477	0.757384	−	0.652970i	$-0.226477\pi$
$59$	686.474	1.51477	0.757384	+	0.652970i	$0.226477\pi$
$60$	−305.990	−0.658385
$61$	75.3794	0.158219	0.0791094	−	0.996866i	$-0.474792\pi$
$61$	75.3794	0.158219	0.0791094	+	0.996866i	$0.474792\pi$
$62$	−440.476	−0.902267
$63$	0	0
$64$	−114.356	−0.223352
$65$	−143.040	−0.272953
$66$	227.047	0.423449
$67$	−336.720	−0.613983	−0.306991	−	0.951712i	$-0.599322\pi$
$67$	−336.720	−0.613983	−0.306991	+	0.951712i	$0.599322\pi$
$68$	534.754	0.953654
$69$	−138.548	−0.241728
$70$	0	0
$71$	427.161	0.714009	0.357005	−	0.934103i	$-0.383798\pi$
$71$	427.161	0.714009	0.357005	+	0.934103i	$0.383798\pi$
$72$	15.0954	0.0247084
$73$	134.191	0.215148	0.107574	−	0.994197i	$-0.465692\pi$
$73$	134.191	0.215148	0.107574	+	0.994197i	$0.465692\pi$
$74$	−611.308	−0.960313
$75$	−20.9860	−0.0323101
$76$	−225.511	−0.340367
$77$	0	0
$78$	−252.194	−0.366094
$79$	253.005	0.360319	0.180160	−	0.983637i	$-0.442339\pi$
$79$	253.005	0.360319	0.180160	+	0.983637i	$0.442339\pi$
$80$	864.133	1.20766
$81$	−766.980	−1.05210
$82$	−1639.99	−2.20862
$83$	193.536	0.255944	0.127972	−	0.991778i	$-0.459153\pi$
$83$	193.536	0.255944	0.127972	+	0.991778i	$0.459153\pi$
$84$	0	0
$85$	−1129.31	−1.44107
$86$	−343.944	−0.431261
$87$	−1452.23	−1.78960
$88$	−118.673	−0.143756
$89$	996.000	1.18624	0.593122	−	0.805112i	$-0.297895\pi$
$89$	996.000	1.18624	0.593122	+	0.805112i	$0.297895\pi$
$90$	59.5371	0.0697307
$91$	0	0
$92$	−135.244	−0.153263
$93$	646.851	0.721240
$94$	184.067	0.201968
$95$	476.242	0.514331
$96$	1090.59	1.15945
$97$	−761.982	−0.797604	−0.398802	−	0.917037i	$-0.630574\pi$
$97$	−761.982	−0.797604	−0.398802	+	0.917037i	$0.630574\pi$
$98$	0	0
$99$	−17.4238	−0.0176885
$100$	−20.4856	−0.0204856
$101$	−822.058	−0.809879	−0.404940	−	0.914343i	$-0.632707\pi$
$101$	−822.058	−0.809879	−0.404940	+	0.914343i	$0.632707\pi$
$102$	−1991.09	−1.93282
$103$	−794.608	−0.760146	−0.380073	−	0.924956i	$-0.624101\pi$
$103$	−794.608	−0.760146	−0.380073	+	0.924956i	$0.624101\pi$
$104$	131.816	0.124285
$105$	0	0
$106$	1448.42	1.32719
$107$	2115.28	1.91114	0.955571	−	0.294761i	$-0.0952402\pi$
$107$	2115.28	1.91114	0.955571	+	0.294761i	$0.0952402\pi$
$108$	−709.453	−0.632104
$109$	1364.17	1.19875	0.599377	−	0.800467i	$-0.295415\pi$
$109$	1364.17	1.19875	0.599377	+	0.800467i	$0.295415\pi$
$110$	−468.053	−0.405701
$111$	897.722	0.767640
$112$	0	0
$113$	1277.27	1.06332	0.531660	−	0.846958i	$-0.321568\pi$
$113$	1277.27	1.06332	0.531660	+	0.846958i	$0.321568\pi$
$114$	839.662	0.689838
$115$	285.614	0.231597
$116$	−1417.60	−1.13466
$117$	19.3536	0.0152926
$118$	−2495.05	−1.94651
$119$	0	0
$120$	−595.495	−0.453008
$121$	−1194.02	−0.897087
$122$	−273.973	−0.203314
$123$	2408.37	1.76549
$124$	631.427	0.457289
$125$	1418.65	1.01510
$126$	0	0
$127$	1278.83	0.893526	0.446763	−	0.894652i	$-0.352577\pi$
$127$	1278.83	0.893526	0.446763	+	0.894652i	$0.352577\pi$
$128$	−1218.97	−0.841739
$129$	505.091	0.344735
$130$	519.892	0.350750
$131$	2865.00	1.91081	0.955405	−	0.295297i	$-0.0954187\pi$
$131$	2865.00	1.91081	0.955405	+	0.295297i	$0.0954187\pi$
$132$	−325.475	−0.214613
$133$	0	0
$134$	1223.84	0.788980
$135$	1498.25	0.955175
$136$	1040.70	0.656171
$137$	1494.96	0.932283	0.466141	−	0.884710i	$-0.345644\pi$
$137$	1494.96	0.932283	0.466141	+	0.884710i	$0.345644\pi$
$138$	503.565	0.310625
$139$	1783.85	1.08852	0.544260	−	0.838917i	$-0.316811\pi$
$139$	1783.85	1.08852	0.544260	+	0.838917i	$0.316811\pi$
$140$	0	0
$141$	−270.307	−0.161446
$142$	−1552.55	−0.917516
$143$	−152.149	−0.0889743
$144$	−116.918	−0.0676612
$145$	2993.73	1.71459
$146$	−487.728	−0.276470
$147$	0	0
$148$	876.316	0.486708
$149$	1727.01	0.949547	0.474774	−	0.880108i	$-0.342530\pi$
$149$	1727.01	0.949547	0.474774	+	0.880108i	$0.342530\pi$
$150$	76.2756	0.0415192
$151$	1499.77	0.808277	0.404139	−	0.914698i	$-0.367571\pi$
$151$	1499.77	0.808277	0.404139	+	0.914698i	$0.367571\pi$
$152$	−438.873	−0.234193
$153$	152.798	0.0807383
$154$	0	0
$155$	−1333.47	−0.691011
$156$	361.522	0.185545
$157$	1021.82	0.519430	0.259715	−	0.965685i	$-0.416371\pi$
$157$	1021.82	0.519430	0.259715	+	0.965685i	$0.416371\pi$
$158$	−919.567	−0.463018
$159$	−2127.04	−1.06091
$160$	−2248.22	−1.11086
$161$	0	0
$162$	2787.65	1.35197
$163$	−3847.87	−1.84901	−0.924504	−	0.381172i	$-0.875520\pi$
$163$	−3847.87	−1.84901	−0.924504	+	0.381172i	$0.875520\pi$
$164$	2350.94	1.11938
$165$	687.348	0.324303
$166$	−703.423	−0.328893
$167$	424.130	0.196528	0.0982639	−	0.995160i	$-0.468671\pi$
$167$	424.130	0.196528	0.0982639	+	0.995160i	$0.468671\pi$
$168$	0	0
$169$	169.000	0.0769231
$170$	4104.58	1.85181
$171$	−64.4363	−0.0288162
$172$	493.047	0.218573
$173$	3117.51	1.37006	0.685029	−	0.728516i	$-0.259790\pi$
$173$	3117.51	1.37006	0.685029	+	0.728516i	$0.259790\pi$
$174$	5278.24	2.29967
$175$	0	0
$176$	919.159	0.393660
$177$	3664.05	1.55597
$178$	−3620.05	−1.52435
$179$	2962.21	1.23690	0.618452	−	0.785823i	$-0.287760\pi$
$179$	2962.21	1.23690	0.618452	+	0.785823i	$0.287760\pi$
$180$	−85.3470	−0.0353410
$181$	1198.27	0.492081	0.246041	−	0.969259i	$-0.420870\pi$
$181$	1198.27	0.492081	0.246041	+	0.969259i	$0.420870\pi$
$182$	0	0
$183$	402.336	0.162522
$184$	−263.203	−0.105454
$185$	−1850.63	−0.735466
$186$	−2351.04	−0.926808
$187$	−1201.22	−0.469745
$188$	−263.861	−0.102362
$189$	0	0
$190$	−1730.94	−0.660925
$191$	−3940.99	−1.49298	−0.746492	−	0.665394i	$-0.768263\pi$
$191$	−3940.99	−1.49298	−0.746492	+	0.665394i	$0.768263\pi$
$192$	−610.376	−0.229427
$193$	−1974.13	−0.736276	−0.368138	−	0.929771i	$-0.620005\pi$
$193$	−1974.13	−0.736276	−0.368138	+	0.929771i	$0.620005\pi$
$194$	2769.49	1.02494
$195$	−763.475	−0.280377
$196$	0	0
$197$	2772.61	1.00274	0.501372	−	0.865232i	$-0.332829\pi$
$197$	2772.61	1.00274	0.501372	+	0.865232i	$0.332829\pi$
$198$	63.3283	0.0227300
$199$	919.870	0.327678	0.163839	−	0.986487i	$-0.447612\pi$
$199$	919.870	0.327678	0.163839	+	0.986487i	$0.447612\pi$
$200$	−39.8676	−0.0140953
$201$	−1797.24	−0.630683
$202$	2987.84	1.04071
$203$	0	0
$204$	2854.24	0.979593
$205$	−4964.80	−1.69150
$206$	2888.07	0.976803
$207$	−38.6440	−0.0129756
$208$	−1020.96	−0.340341
$209$	506.568	0.167656
$210$	0	0
$211$	936.550	0.305568	0.152784	−	0.988260i	$-0.451176\pi$
$211$	936.550	0.305568	0.152784	+	0.988260i	$0.451176\pi$
$212$	−2076.32	−0.672651
$213$	2279.96	0.733430
$214$	−7688.18	−2.45586
$215$	−1041.23	−0.330286
$216$	−1380.69	−0.434925
$217$	0	0
$218$	−4958.20	−1.54042
$219$	716.241	0.221000
$220$	670.958	0.205618
$221$	1334.27	0.406120
$222$	−3262.85	−0.986433
$223$	−5243.34	−1.57453	−0.787264	−	0.616616i	$-0.788503\pi$
$223$	−5243.34	−1.57453	−0.787264	+	0.616616i	$0.788503\pi$
$224$	0	0
$225$	−5.85345	−0.00173435
$226$	−4642.34	−1.36639
$227$	3821.36	1.11732	0.558662	−	0.829396i	$-0.311315\pi$
$227$	3821.36	1.11732	0.558662	+	0.829396i	$0.311315\pi$
$228$	−1203.66	−0.349625
$229$	−2144.86	−0.618936	−0.309468	−	0.950910i	$-0.600151\pi$
$229$	−2144.86	−0.618936	−0.309468	+	0.950910i	$0.600151\pi$
$230$	−1038.09	−0.297606
$231$	0	0
$232$	−2758.83	−0.780714
$233$	−3473.06	−0.976513	−0.488257	−	0.872700i	$-0.662367\pi$
$233$	−3473.06	−0.976513	−0.488257	+	0.872700i	$0.662367\pi$
$234$	−70.3422	−0.0196513
$235$	557.231	0.154680
$236$	3576.68	0.986533
$237$	1350.41	0.370120
$238$	0	0
$239$	3691.00	0.998959	0.499479	−	0.866326i	$-0.333525\pi$
$239$	3691.00	0.998959	0.499479	+	0.866326i	$0.333525\pi$
$240$	4612.29	1.24051
$241$	914.807	0.244514	0.122257	−	0.992498i	$-0.460987\pi$
$241$	914.807	0.244514	0.122257	+	0.992498i	$0.460987\pi$
$242$	4339.78	1.15277
$243$	−417.260	−0.110153
$244$	392.743	0.103044
$245$	0	0
$246$	−8753.43	−2.26869
$247$	−562.673	−0.144948
$248$	1228.84	0.314642
$249$	1032.99	0.262905
$250$	−5156.20	−1.30443
$251$	−5817.09	−1.46283	−0.731417	−	0.681930i	$-0.761141\pi$
$251$	−5817.09	−1.46283	−0.731417	+	0.681930i	$0.761141\pi$
$252$	0	0
$253$	303.801	0.0754933
$254$	−4648.02	−1.14820
$255$	−6027.69	−1.48027
$256$	5345.30	1.30500
$257$	−3066.16	−0.744210	−0.372105	−	0.928191i	$-0.621364\pi$
$257$	−3066.16	−0.744210	−0.372105	+	0.928191i	$0.621364\pi$
$258$	−1835.80	−0.442991
$259$	0	0
$260$	−745.270	−0.177768
$261$	−405.057	−0.0960627
$262$	−10413.1	−2.45543
$263$	1215.01	0.284869	0.142435	−	0.989804i	$-0.454507\pi$
$263$	1215.01	0.284869	0.142435	+	0.989804i	$0.454507\pi$
$264$	−633.414	−0.147666
$265$	4384.84	1.01645
$266$	0	0
$267$	5316.13	1.21851
$268$	−1754.38	−0.399873
$269$	−3689.75	−0.836311	−0.418156	−	0.908375i	$-0.637323\pi$
$269$	−3689.75	−0.836311	−0.418156	+	0.908375i	$0.637323\pi$
$270$	−5445.51	−1.22742
$271$	−5672.09	−1.27142	−0.635710	−	0.771928i	$-0.719292\pi$
$271$	−5672.09	−1.27142	−0.635710	+	0.771928i	$0.719292\pi$
$272$	−8060.55	−1.79685
$273$	0	0
$274$	−5433.55	−1.19800
$275$	46.0171	0.0100907
$276$	−721.865	−0.157432
$277$	6266.61	1.35929	0.679647	−	0.733539i	$-0.262133\pi$
$277$	6266.61	1.35929	0.679647	+	0.733539i	$0.262133\pi$
$278$	−6483.56	−1.39877
$279$	180.420	0.0387150
$280$	0	0
$281$	−7122.92	−1.51216	−0.756082	−	0.654477i	$-0.772889\pi$
$281$	−7122.92	−1.51216	−0.756082	+	0.654477i	$0.772889\pi$
$282$	982.453	0.207462
$283$	2576.18	0.541123	0.270561	−	0.962703i	$-0.412791\pi$
$283$	2576.18	0.541123	0.270561	+	0.962703i	$0.412791\pi$
$284$	2225.60	0.465017
$285$	2541.93	0.528320
$286$	552.998	0.114334
$287$	0	0
$288$	304.187	0.0622375
$289$	5621.12	1.14413
$290$	−10881.0	−2.20329
$291$	−4067.07	−0.819298
$292$	699.162	0.140121
$293$	6955.17	1.38678	0.693388	−	0.720565i	$-0.256117\pi$
$293$	6955.17	1.38678	0.693388	+	0.720565i	$0.256117\pi$
$294$	0	0
$295$	−7553.34	−1.49075
$296$	1705.42	0.334884
$297$	1593.65	0.311357
$298$	−6276.98	−1.22019
$299$	−337.448	−0.0652681
$300$	−109.342	−0.0210428
$301$	0	0
$302$	−5451.06	−1.03865
$303$	−4387.72	−0.831908
$304$	3399.21	0.641310
$305$	−829.407	−0.155710
$306$	−555.356	−0.103750
$307$	−1690.34	−0.314244	−0.157122	−	0.987579i	$-0.550222\pi$
$307$	−1690.34	−0.314244	−0.157122	+	0.987579i	$0.550222\pi$
$308$	0	0
$309$	−4241.21	−0.780822
$310$	4846.61	0.887963
$311$	−7291.22	−1.32941	−0.664706	−	0.747105i	$-0.731443\pi$
$311$	−7291.22	−1.32941	−0.664706	+	0.747105i	$0.731443\pi$
$312$	703.568	0.127666
$313$	4730.37	0.854237	0.427118	−	0.904196i	$-0.359529\pi$
$313$	4730.37	0.854237	0.427118	+	0.904196i	$0.359529\pi$
$314$	−3713.91	−0.667477
$315$	0	0
$316$	1318.21	0.234668
$317$	8225.90	1.45745	0.728726	−	0.684805i	$-0.240113\pi$
$317$	8225.90	1.45745	0.728726	+	0.684805i	$0.240113\pi$
$318$	7730.90	1.36329
$319$	3184.37	0.558904
$320$	1258.27	0.219812
$321$	11290.3	1.96312
$322$	0	0
$323$	−4442.34	−0.765258
$324$	−3996.13	−0.685207
$325$	−51.1137	−0.00872393
$326$	13985.4	2.37601
$327$	7281.25	1.23136
$328$	4575.23	0.770198
$329$	0	0
$330$	−2498.23	−0.416736
$331$	−7168.03	−1.19030	−0.595152	−	0.803613i	$-0.702908\pi$
$331$	−7168.03	−1.19030	−0.595152	+	0.803613i	$0.702908\pi$
$332$	1008.36	0.166690
$333$	250.394	0.0412057
$334$	−1541.54	−0.252542
$335$	3704.96	0.604249
$336$	0	0
$337$	4566.95	0.738213	0.369107	−	0.929387i	$-0.379664\pi$
$337$	4566.95	0.738213	0.369107	+	0.929387i	$0.379664\pi$
$338$	−614.245	−0.0988477
$339$	6817.39	1.09224
$340$	−5883.96	−0.938536
$341$	−1418.38	−0.225248
$342$	234.199	0.0370294
$343$	0	0
$344$	959.531	0.150391
$345$	1524.46	0.237896
$346$	−11330.9	−1.76055
$347$	−4616.95	−0.714267	−0.357134	−	0.934053i	$-0.616246\pi$
$347$	−4616.95	−0.714267	−0.357134	+	0.934053i	$0.616246\pi$
$348$	−7566.41	−1.16552
$349$	7688.68	1.17927	0.589636	−	0.807669i	$-0.299271\pi$
$349$	7688.68	1.17927	0.589636	+	0.807669i	$0.299271\pi$
$350$	0	0
$351$	−1770.16	−0.269185
$352$	−2391.38	−0.362105
$353$	8037.67	1.21190	0.605952	−	0.795501i	$-0.292792\pi$
$353$	8037.67	1.21190	0.605952	+	0.795501i	$0.292792\pi$
$354$	−13317.3	−1.99945
$355$	−4700.09	−0.702690
$356$	5189.37	0.772573
$357$	0	0
$358$	−10766.4	−1.58945
$359$	170.112	0.0250089	0.0125044	−	0.999922i	$-0.496020\pi$
$359$	170.112	0.0250089	0.0125044	+	0.999922i	$0.496020\pi$
$360$	−166.096	−0.0243167
$361$	−4985.62	−0.726873
$362$	−4355.22	−0.632335
$363$	−6373.07	−0.921487
$364$	0	0
$365$	−1476.51	−0.211738
$366$	−1462.33	−0.208844
$367$	−6547.73	−0.931304	−0.465652	−	0.884968i	$-0.654180\pi$
$367$	−6547.73	−0.931304	−0.465652	+	0.884968i	$0.654180\pi$
$368$	2038.59	0.288774
$369$	671.745	0.0947687
$370$	6726.29	0.945089
$371$	0	0
$372$	3370.23	0.469727
$373$	−12845.2	−1.78311	−0.891554	−	0.452915i	$-0.850384\pi$
$373$	−12845.2	−1.78311	−0.891554	+	0.452915i	$0.850384\pi$
$374$	4365.95	0.603631
$375$	7572.02	1.04271
$376$	−513.507	−0.0704312
$377$	−3537.05	−0.483203
$378$	0	0
$379$	9494.88	1.28686	0.643429	−	0.765505i	$-0.277511\pi$
$379$	9494.88	1.28686	0.643429	+	0.765505i	$0.277511\pi$
$380$	2481.32	0.334971
$381$	6825.74	0.917829
$382$	14323.9	1.91851
$383$	−6344.95	−0.846506	−0.423253	−	0.906012i	$-0.639112\pi$
$383$	−6344.95	−0.846506	−0.423253	+	0.906012i	$0.639112\pi$
$384$	−6506.22	−0.864634
$385$	0	0
$386$	7175.16	0.946130
$387$	140.880	0.0185048
$388$	−3970.09	−0.519461
$389$	−13196.7	−1.72005	−0.860026	−	0.510250i	$-0.829553\pi$
$389$	−13196.7	−1.72005	−0.860026	+	0.510250i	$0.829553\pi$
$390$	2774.92	0.360291
$391$	−2664.18	−0.344586
$392$	0	0
$393$	15291.9	1.96278
$394$	−10077.3	−1.28855
$395$	−2783.83	−0.354607
$396$	−90.7817	−0.0115201
$397$	32.4042	0.00409653	0.00204826	−	0.999998i	$-0.499348\pi$
$397$	32.4042	0.00409653	0.00204826	+	0.999998i	$0.499348\pi$
$398$	−3343.35	−0.421072
$399$	0	0
$400$	308.787	0.0385984
$401$	3853.07	0.479834	0.239917	−	0.970793i	$-0.422880\pi$
$401$	3853.07	0.479834	0.239917	+	0.970793i	$0.422880\pi$
$402$	6532.21	0.810440
$403$	1575.47	0.194739
$404$	−4283.10	−0.527455
$405$	8439.15	1.03542
$406$	0	0
$407$	−1968.48	−0.239739
$408$	5554.72	0.674018
$409$	−10221.7	−1.23577	−0.617886	−	0.786268i	$-0.712011\pi$
$409$	−10221.7	−1.23577	−0.617886	+	0.786268i	$0.712011\pi$
$410$	18045.0	2.17361
$411$	7979.31	0.957640
$412$	−4140.08	−0.495065
$413$	0	0
$414$	140.455	0.0166739
$415$	−2129.49	−0.251886
$416$	2656.24	0.313059
$417$	9521.27	1.11813
$418$	−1841.17	−0.215441
$419$	12153.6	1.41704	0.708521	−	0.705689i	$-0.249363\pi$
$419$	12153.6	1.41704	0.708521	+	0.705689i	$0.249363\pi$
$420$	0	0
$421$	13630.9	1.57798	0.788990	−	0.614405i	$-0.210604\pi$
$421$	13630.9	1.57798	0.788990	+	0.614405i	$0.210604\pi$
$422$	−3403.97	−0.392660
$423$	−75.3942	−0.00866618
$424$	−4040.77	−0.462824
$425$	−403.546	−0.0460585
$426$	−8286.72	−0.942472
$427$	0	0
$428$	11021.1	1.24468
$429$	−812.092	−0.0913943
$430$	3784.45	0.424424
$431$	−5959.31	−0.666009	−0.333004	−	0.942925i	$-0.608062\pi$
$431$	−5959.31	−0.666009	−0.333004	+	0.942925i	$0.608062\pi$
$432$	10693.8	1.19099
$433$	−13019.1	−1.44494	−0.722470	−	0.691402i	$-0.756993\pi$
$433$	−13019.1	−1.44494	−0.722470	+	0.691402i	$0.756993\pi$
$434$	0	0
$435$	15979.0	1.76123
$436$	7107.63	0.780720
$437$	1123.51	0.122986
$438$	−2603.24	−0.283990
$439$	892.739	0.0970572	0.0485286	−	0.998822i	$-0.484547\pi$
$439$	892.739	0.0970572	0.0485286	+	0.998822i	$0.484547\pi$
$440$	1305.77	0.141477
$441$	0	0
$442$	−4849.50	−0.521872
$443$	−8779.74	−0.941621	−0.470810	−	0.882234i	$-0.656038\pi$
$443$	−8779.74	−0.941621	−0.470810	+	0.882234i	$0.656038\pi$
$444$	4677.32	0.499946
$445$	−10959.1	−1.16744
$446$	19057.4	2.02330
$447$	9217.91	0.975374
$448$	0	0
$449$	13122.2	1.37923	0.689617	−	0.724174i	$-0.257779\pi$
$449$	13122.2	1.37923	0.689617	+	0.724174i	$0.257779\pi$
$450$	21.2749	0.00222868
$451$	−5280.95	−0.551375
$452$	6654.83	0.692515
$453$	8005.02	0.830262
$454$	−13889.1	−1.43578
$455$	0	0
$456$	−2342.48	−0.240563
$457$	−9100.56	−0.931524	−0.465762	−	0.884910i	$-0.654220\pi$
$457$	−9100.56	−0.931524	−0.465762	+	0.884910i	$0.654220\pi$
$458$	7795.67	0.795345
$459$	−13975.5	−1.42118
$460$	1488.11	0.150833
$461$	11153.6	1.12685	0.563423	−	0.826169i	$-0.309484\pi$
$461$	11153.6	1.12685	0.563423	+	0.826169i	$0.309484\pi$
$462$	0	0
$463$	−10006.3	−1.00439	−0.502197	−	0.864753i	$-0.667475\pi$
$463$	−10006.3	−1.00439	−0.502197	+	0.864753i	$0.667475\pi$
$464$	21368.0	2.13790
$465$	−7117.37	−0.709806
$466$	12623.1	1.25484
$467$	−10455.5	−1.03603	−0.518014	−	0.855372i	$-0.673328\pi$
$467$	−10455.5	−1.03603	−0.518014	+	0.855372i	$0.673328\pi$
$468$	100.836	0.00995973
$469$	0	0
$470$	−2025.30	−0.198767
$471$	5453.97	0.533558
$472$	6960.66	0.678793
$473$	−1107.54	−0.107663
$474$	−4908.17	−0.475611
$475$	170.179	0.0164387
$476$	0	0
$477$	−593.275	−0.0569480
$478$	−13415.3	−1.28368
$479$	11161.0	1.06463	0.532314	−	0.846547i	$-0.321322\pi$
$479$	11161.0	1.06463	0.532314	+	0.846547i	$0.321322\pi$
$480$	−11999.8	−1.14107
$481$	2186.50	0.207267
$482$	−3324.94	−0.314205
$483$	0	0
$484$	−6221.11	−0.584251
$485$	8384.17	0.784959
$486$	1516.57	0.141549
$487$	3941.17	0.366717	0.183359	−	0.983046i	$-0.441303\pi$
$487$	3941.17	0.366717	0.183359	+	0.983046i	$0.441303\pi$
$488$	764.326	0.0709005
$489$	−20537.9	−1.89930
$490$	0	0
$491$	11636.5	1.06955	0.534775	−	0.844995i	$-0.320397\pi$
$491$	11636.5	1.06955	0.534775	+	0.844995i	$0.320397\pi$
$492$	12548.1	1.14982
$493$	−27925.3	−2.55110
$494$	2045.08	0.186260
$495$	191.716	0.0174080
$496$	−9517.72	−0.861610
$497$	0	0
$498$	−3754.51	−0.337838
$499$	2370.55	0.212666	0.106333	−	0.994331i	$-0.466089\pi$
$499$	2370.55	0.212666	0.106333	+	0.994331i	$0.466089\pi$
$500$	7391.46	0.661113
$501$	2263.79	0.201873
$502$	21142.7	1.87977
$503$	−16697.1	−1.48010	−0.740048	−	0.672554i	$-0.765197\pi$
$503$	−16697.1	−1.48010	−0.740048	+	0.672554i	$0.765197\pi$
$504$	0	0
$505$	9045.18	0.797040
$506$	−1104.19	−0.0970104
$507$	902.035	0.0790153
$508$	6662.98	0.581933
$509$	12297.2	1.07085	0.535426	−	0.844582i	$-0.320151\pi$
$509$	12297.2	1.07085	0.535426	+	0.844582i	$0.320151\pi$
$510$	21908.1	1.90217
$511$	0	0
$512$	−9676.19	−0.835217
$513$	5893.61	0.507230
$514$	11144.2	0.956324
$515$	8743.15	0.748096
$516$	2631.63	0.224518
$517$	592.714	0.0504208
$518$	0	0
$519$	16639.7	1.40732
$520$	−1450.39	−0.122315
$521$	−18304.4	−1.53922	−0.769609	−	0.638516i	$-0.779549\pi$
$521$	−18304.4	−1.53922	−0.769609	+	0.638516i	$0.779549\pi$
$522$	1472.21	0.123443
$523$	12673.2	1.05958	0.529788	−	0.848130i	$-0.322271\pi$
$523$	12673.2	1.05958	0.529788	+	0.848130i	$0.322271\pi$
$524$	14927.3	1.24447
$525$	0	0
$526$	−4416.05	−0.366063
$527$	12438.5	1.02814
$528$	4905.99	0.404367
$529$	−11493.2	−0.944621
$530$	−15937.1	−1.30615
$531$	1021.98	0.0835219
$532$	0	0
$533$	5865.84	0.476694
$534$	−19321.9	−1.56581
$535$	−23274.7	−1.88084
$536$	−3414.24	−0.275136
$537$	15810.7	1.27055
$538$	13410.7	1.07468
$539$	0	0
$540$	7806.19	0.622083
$541$	−21283.1	−1.69137	−0.845684	−	0.533684i	$-0.820807\pi$
$541$	−21283.1	−1.69137	−0.845684	+	0.533684i	$0.820807\pi$
$542$	20615.7	1.63380
$543$	6395.75	0.505466
$544$	20971.1	1.65281
$545$	−15010.1	−1.17975
$546$	0	0
$547$	−19081.2	−1.49150	−0.745751	−	0.666225i	$-0.767909\pi$
$547$	−19081.2	−1.49150	−0.745751	+	0.666225i	$0.767909\pi$
$548$	7789.04	0.607174
$549$	112.220	0.00872392
$550$	−167.253	−0.0129667
$551$	11776.4	0.910507
$552$	−1404.84	−0.108322
$553$	0	0
$554$	−22776.5	−1.74672
$555$	−9877.73	−0.755471
$556$	9294.24	0.708927
$557$	−13693.3	−1.04166	−0.520828	−	0.853661i	$-0.674377\pi$
$557$	−13693.3	−1.04166	−0.520828	+	0.853661i	$0.674377\pi$
$558$	−655.753	−0.0497495
$559$	1230.20	0.0930805
$560$	0	0
$561$	−6411.52	−0.482521
$562$	25888.9	1.94316
$563$	15762.2	1.17993	0.589964	−	0.807430i	$-0.299142\pi$
$563$	15762.2	1.17993	0.589964	+	0.807430i	$0.299142\pi$
$564$	−1408.36	−0.105146
$565$	−14053.9	−1.04646
$566$	−9363.33	−0.695354
$567$	0	0
$568$	4331.29	0.319960
$569$	22202.1	1.63578	0.817892	−	0.575372i	$-0.195143\pi$
$569$	22202.1	1.63578	0.817892	+	0.575372i	$0.195143\pi$
$570$	−9238.88	−0.678902
$571$	21989.8	1.61164	0.805819	−	0.592162i	$-0.201725\pi$
$571$	21989.8	1.61164	0.805819	+	0.592162i	$0.201725\pi$
$572$	−792.727	−0.0579468
$573$	−21035.0	−1.53359
$574$	0	0
$575$	102.061	0.00740212
$576$	−170.247	−0.0123153
$577$	18405.1	1.32793	0.663965	−	0.747764i	$-0.268872\pi$
$577$	18405.1	1.32793	0.663965	+	0.747764i	$0.268872\pi$
$578$	−20430.4	−1.47023
$579$	−10536.9	−0.756303
$580$	15598.0	1.11667
$581$	0	0
$582$	14782.1	1.05281
$583$	4664.05	0.331330
$584$	1360.66	0.0964116
$585$	−212.949	−0.0150502
$586$	−25279.1	−1.78203
$587$	13059.4	0.918260	0.459130	−	0.888369i	$-0.348161\pi$
$587$	13059.4	0.918260	0.459130	+	0.888369i	$0.348161\pi$
$588$	0	0
$589$	−5245.42	−0.366951
$590$	27453.3	1.91565
$591$	14798.8	1.03002
$592$	−13209.0	−0.917040
$593$	−11511.8	−0.797189	−0.398595	−	0.917127i	$-0.630502\pi$
$593$	−11511.8	−0.797189	−0.398595	+	0.917127i	$0.630502\pi$
$594$	−5792.27	−0.400100
$595$	0	0
$596$	8998.11	0.618418
$597$	4909.79	0.336590
$598$	1226.49	0.0838708
$599$	7113.35	0.485215	0.242607	−	0.970125i	$-0.421997\pi$
$599$	7113.35	0.485215	0.242607	+	0.970125i	$0.421997\pi$
$600$	−212.793	−0.0144787
$601$	7802.91	0.529596	0.264798	−	0.964304i	$-0.414695\pi$
$601$	7802.91	0.529596	0.264798	+	0.964304i	$0.414695\pi$
$602$	0	0
$603$	−501.287	−0.0338540
$604$	7814.14	0.526412
$605$	13137.9	0.882865
$606$	15947.5	1.06902
$607$	13290.9	0.888732	0.444366	−	0.895845i	$-0.353429\pi$
$607$	13290.9	0.888732	0.444366	+	0.895845i	$0.353429\pi$
$608$	−8843.74	−0.589903
$609$	0	0
$610$	3014.55	0.200091
$611$	−658.360	−0.0435915
$612$	796.108	0.0525830
$613$	−3133.55	−0.206465	−0.103232	−	0.994657i	$-0.532919\pi$
$613$	−3133.55	−0.206465	−0.103232	+	0.994657i	$0.532919\pi$
$614$	6143.69	0.403810
$615$	−26499.5	−1.73750
$616$	0	0
$617$	−126.313	−0.00824175	−0.00412088	−	0.999992i	$-0.501312\pi$
$617$	−126.313	−0.00824175	−0.00412088	+	0.999992i	$0.501312\pi$
$618$	15415.0	1.00337
$619$	−5888.40	−0.382350	−0.191175	−	0.981556i	$-0.561230\pi$
$619$	−5888.40	−0.382350	−0.191175	+	0.981556i	$0.561230\pi$
$620$	−6947.65	−0.450039
$621$	3534.54	0.228400
$622$	26500.6	1.70832
$623$	0	0
$624$	−5449.36	−0.349598
$625$	−15118.1	−0.967556
$626$	−17192.9	−1.09771
$627$	2703.80	0.172216
$628$	5323.92	0.338292
$629$	17262.5	1.09428
$630$	0	0
$631$	−21316.2	−1.34483	−0.672413	−	0.740176i	$-0.734742\pi$
$631$	−21316.2	−1.34483	−0.672413	+	0.740176i	$0.734742\pi$
$632$	2565.40	0.161465
$633$	4998.82	0.313879
$634$	−29897.7	−1.87286
$635$	−14071.1	−0.879361
$636$	−11082.3	−0.690947
$637$	0	0
$638$	−11573.9	−0.718203
$639$	635.930	0.0393693
$640$	13412.4	0.828395
$641$	−11687.9	−0.720193	−0.360097	−	0.932915i	$-0.617256\pi$
$641$	−11687.9	−0.720193	−0.360097	+	0.932915i	$0.617256\pi$
$642$	−41035.5	−2.52265
$643$	20771.5	1.27395	0.636974	−	0.770885i	$-0.280186\pi$
$643$	20771.5	1.27395	0.636974	+	0.770885i	$0.280186\pi$
$644$	0	0
$645$	−5557.56	−0.339270
$646$	16146.1	0.983372
$647$	15685.1	0.953086	0.476543	−	0.879151i	$-0.341890\pi$
$647$	15685.1	0.953086	0.476543	+	0.879151i	$0.341890\pi$
$648$	−7776.96	−0.471463
$649$	−8034.32	−0.485940
$650$	185.777	0.0112104
$651$	0	0
$652$	−20048.2	−1.20422
$653$	5161.91	0.309343	0.154672	−	0.987966i	$-0.450568\pi$
$653$	5161.91	0.309343	0.154672	+	0.987966i	$0.450568\pi$
$654$	−26464.3	−1.58232
$655$	−31523.9	−1.88052
$656$	−35436.6	−2.10910
$657$	199.775	0.0118629
$658$	0	0
$659$	−19647.1	−1.16137	−0.580683	−	0.814130i	$-0.697214\pi$
$659$	−19647.1	−1.16137	−0.580683	+	0.814130i	$0.697214\pi$
$660$	3581.23	0.211211
$661$	−25197.0	−1.48268	−0.741340	−	0.671130i	$-0.765809\pi$
$661$	−25197.0	−1.48268	−0.741340	+	0.671130i	$0.765809\pi$
$662$	26052.8	1.52956
$663$	7121.62	0.417166
$664$	1962.40	0.114693
$665$	0	0
$666$	−910.077	−0.0529501
$667$	7062.56	0.409990
$668$	2209.81	0.127994
$669$	−27986.2	−1.61735
$670$	−13466.0	−0.776473
$671$	−882.222	−0.0507568
$672$	0	0
$673$	31227.3	1.78860	0.894298	−	0.447472i	$-0.147676\pi$
$673$	31227.3	1.78860	0.894298	+	0.447472i	$0.147676\pi$
$674$	−16599.0	−0.948619
$675$	535.381	0.0305286
$676$	880.526	0.0500982
$677$	1846.13	0.104804	0.0524022	−	0.998626i	$-0.483312\pi$
$677$	1846.13	0.104804	0.0524022	+	0.998626i	$0.483312\pi$
$678$	−24778.4	−1.40355
$679$	0	0
$680$	−11450.9	−0.645769
$681$	20396.4	1.14771
$682$	5155.23	0.289448
$683$	−5829.61	−0.326594	−0.163297	−	0.986577i	$-0.552213\pi$
$683$	−5829.61	−0.326594	−0.163297	+	0.986577i	$0.552213\pi$
$684$	−335.727	−0.0187673
$685$	−16449.2	−0.917503
$686$	0	0
$687$	−11448.1	−0.635770
$688$	−7431.87	−0.411828
$689$	−5180.62	−0.286453
$690$	−5540.78	−0.305701
$691$	12829.3	0.706294	0.353147	−	0.935568i	$-0.385112\pi$
$691$	12829.3	0.706294	0.353147	+	0.935568i	$0.385112\pi$
$692$	16242.9	0.892286
$693$	0	0
$694$	16780.7	0.917847
$695$	−19627.9	−1.07126
$696$	−14725.2	−0.801949
$697$	46311.2	2.51673
$698$	−27945.2	−1.51539
$699$	−18537.4	−1.00307
$700$	0	0
$701$	−30321.8	−1.63372	−0.816862	−	0.576834i	$-0.804288\pi$
$701$	−30321.8	−1.63372	−0.816862	+	0.576834i	$0.804288\pi$
$702$	6433.79	0.345908
$703$	−7279.78	−0.390558
$704$	1338.40	0.0716517
$705$	2974.21	0.158887
$706$	−29213.6	−1.55732
$707$	0	0
$708$	19090.5	1.01337
$709$	13767.1	0.729246	0.364623	−	0.931155i	$-0.381198\pi$
$709$	13767.1	0.729246	0.364623	+	0.931155i	$0.381198\pi$
$710$	17082.9	0.902971
$711$	376.657	0.0198674
$712$	10099.2	0.531576
$713$	−3145.81	−0.165233
$714$	0	0
$715$	1674.11	0.0875638
$716$	15433.7	0.805566
$717$	19700.7	1.02613
$718$	−618.288	−0.0321369
$719$	25769.7	1.33664	0.668322	−	0.743872i	$-0.267013\pi$
$719$	25769.7	1.33664	0.668322	+	0.743872i	$0.267013\pi$
$720$	1286.47	0.0665885
$721$	0	0
$722$	18120.7	0.934046
$723$	4882.77	0.251165
$724$	6243.24	0.320481
$725$	1069.77	0.0548006
$726$	23163.5	1.18413
$727$	−20584.7	−1.05013	−0.525064	−	0.851063i	$-0.675959\pi$
$727$	−20584.7	−1.05013	−0.525064	+	0.851063i	$0.675959\pi$
$728$	0	0
$729$	18481.3	0.938949
$730$	5366.52	0.272087
$731$	9712.52	0.491424
$732$	2096.26	0.105847
$733$	−12560.0	−0.632900	−0.316450	−	0.948609i	$-0.602491\pi$
$733$	−12560.0	−0.632900	−0.316450	+	0.948609i	$0.602491\pi$
$734$	23798.3	1.19674
$735$	0	0
$736$	−5303.80	−0.265626
$737$	3940.88	0.196966
$738$	−2441.52	−0.121780
$739$	2247.01	0.111850	0.0559252	−	0.998435i	$-0.482189\pi$
$739$	2247.01	0.111850	0.0559252	+	0.998435i	$0.482189\pi$
$740$	−9642.19	−0.478992
$741$	−3003.26	−0.148890
$742$	0	0
$743$	−17437.7	−0.861006	−0.430503	−	0.902589i	$-0.641664\pi$
$743$	−17437.7	−0.861006	−0.430503	+	0.902589i	$0.641664\pi$
$744$	6558.89	0.323200
$745$	−19002.5	−0.934494
$746$	46687.0	2.29133
$747$	288.124	0.0141123
$748$	−6258.63	−0.305934
$749$	0	0
$750$	−27521.2	−1.33991
$751$	−13096.0	−0.636323	−0.318162	−	0.948036i	$-0.603065\pi$
$751$	−13096.0	−0.636323	−0.318162	+	0.948036i	$0.603065\pi$
$752$	3977.28	0.192867
$753$	−31048.6	−1.50262
$754$	12855.7	0.620925
$755$	−16502.2	−0.795464
$756$	0	0
$757$	29343.6	1.40887	0.704433	−	0.709771i	$-0.251202\pi$
$757$	29343.6	1.40887	0.704433	+	0.709771i	$0.251202\pi$
$758$	−34510.0	−1.65364
$759$	1621.53	0.0775467
$760$	4828.96	0.230480
$761$	23788.7	1.13316	0.566582	−	0.824005i	$-0.308265\pi$
$761$	23788.7	1.13316	0.566582	+	0.824005i	$0.308265\pi$
$762$	−24808.7	−1.17943
$763$	0	0
$764$	−20533.4	−0.972345
$765$	−1681.25	−0.0794584
$766$	23061.3	1.08778
$767$	8924.16	0.420121
$768$	28530.4	1.34050
$769$	−11235.6	−0.526875	−0.263437	−	0.964676i	$-0.584856\pi$
$769$	−11235.6	−0.526875	−0.263437	+	0.964676i	$0.584856\pi$
$770$	0	0
$771$	−16365.6	−0.764452
$772$	−10285.7	−0.479519
$773$	7742.41	0.360252	0.180126	−	0.983644i	$-0.442349\pi$
$773$	7742.41	0.360252	0.180126	+	0.983644i	$0.442349\pi$
$774$	−512.042	−0.0237790
$775$	−476.499	−0.0220856
$776$	−7726.29	−0.357420
$777$	0	0
$778$	47964.6	2.21030
$779$	−19529.9	−0.898242
$780$	−3977.87	−0.182603
$781$	−4999.38	−0.229055
$782$	9683.18	0.442800
$783$	37048.2	1.69092
$784$	0	0
$785$	−11243.2	−0.511195
$786$	−55579.7	−2.52222
$787$	−73.6706	−0.00333681	−0.00166841	−	0.999999i	$-0.500531\pi$
$787$	−73.6706	−0.00333681	−0.00166841	+	0.999999i	$0.500531\pi$
$788$	14445.9	0.653063
$789$	6485.09	0.292618
$790$	10118.1	0.455678
$791$	0	0
$792$	−176.673	−0.00792650
$793$	979.932	0.0438820
$794$	−117.776	−0.00526412
$795$	23404.0	1.04409
$796$	4792.72	0.213409
$797$	−5805.43	−0.258016	−0.129008	−	0.991644i	$-0.541179\pi$
$797$	−5805.43	−0.258016	−0.129008	+	0.991644i	$0.541179\pi$
$798$	0	0
$799$	−5197.80	−0.230144
$800$	−803.373	−0.0355044
$801$	1482.78	0.0654076
$802$	−14004.3	−0.616596
$803$	−1570.53	−0.0690199
$804$	−9363.98	−0.410749
$805$	0	0
$806$	−5726.19	−0.250244
$807$	−19694.0	−0.859059
$808$	−8335.44	−0.362921
$809$	27095.9	1.17755	0.588776	−	0.808296i	$-0.299610\pi$
$809$	27095.9	1.17755	0.588776	+	0.808296i	$0.299610\pi$
$810$	−30672.8	−1.33053
$811$	28006.3	1.21262	0.606309	−	0.795229i	$-0.292650\pi$
$811$	28006.3	1.21262	0.606309	+	0.795229i	$0.292650\pi$
$812$	0	0
$813$	−30274.7	−1.30600
$814$	7154.60	0.308070
$815$	42338.5	1.81970
$816$	−43023.0	−1.84572
$817$	−4095.87	−0.175393
$818$	37151.7	1.58799
$819$	0	0
$820$	−25867.7	−1.10163
$821$	−16408.0	−0.697493	−0.348747	−	0.937217i	$-0.613393\pi$
$821$	−16408.0	−0.697493	−0.348747	+	0.937217i	$0.613393\pi$
$822$	−29001.5	−1.23059
$823$	7614.47	0.322507	0.161254	−	0.986913i	$-0.448446\pi$
$823$	7614.47	0.322507	0.161254	+	0.986913i	$0.448446\pi$
$824$	−8057.11	−0.340634
$825$	245.615	0.0103651
$826$	0	0
$827$	−17850.7	−0.750581	−0.375290	−	0.926907i	$-0.622457\pi$
$827$	−17850.7	−0.750581	−0.375290	+	0.926907i	$0.622457\pi$
$828$	−201.343	−0.00845068
$829$	3802.11	0.159292	0.0796459	−	0.996823i	$-0.474621\pi$
$829$	3802.11	0.159292	0.0796459	+	0.996823i	$0.474621\pi$
$830$	7739.83	0.323679
$831$	33448.0	1.39627
$832$	−1486.63	−0.0619468
$833$	0	0
$834$	−34605.9	−1.43681
$835$	−4666.74	−0.193412
$836$	2639.33	0.109190
$837$	−16502.0	−0.681472
$838$	−44173.2	−1.82093
$839$	3538.68	0.145613	0.0728063	−	0.997346i	$-0.476805\pi$
$839$	3538.68	0.145613	0.0728063	+	0.997346i	$0.476805\pi$
$840$	0	0
$841$	49639.0	2.03530
$842$	−49542.7	−2.02774
$843$	−38018.5	−1.55329
$844$	4879.62	0.199009
$845$	−1859.52	−0.0757036
$846$	274.027	0.0111362
$847$	0	0
$848$	31297.1	1.26739
$849$	13750.3	0.555841
$850$	1466.72	0.0591861
$851$	−4365.86	−0.175863
$852$	11879.1	0.477666
$853$	21190.1	0.850570	0.425285	−	0.905059i	$-0.360174\pi$
$853$	21190.1	0.850570	0.425285	+	0.905059i	$0.360174\pi$
$854$	0	0
$855$	708.999	0.0283594
$856$	21448.4	0.856415
$857$	19184.4	0.764673	0.382337	−	0.924023i	$-0.375119\pi$
$857$	19184.4	0.764673	0.382337	+	0.924023i	$0.375119\pi$
$858$	2951.62	0.117443
$859$	37876.3	1.50445	0.752226	−	0.658905i	$-0.228980\pi$
$859$	37876.3	1.50445	0.752226	+	0.658905i	$0.228980\pi$
$860$	−5425.04	−0.215108
$861$	0	0
$862$	21659.6	0.855834
$863$	9543.13	0.376422	0.188211	−	0.982129i	$-0.439731\pi$
$863$	9543.13	0.376422	0.188211	+	0.982129i	$0.439731\pi$
$864$	−27822.2	−1.09552
$865$	−34302.3	−1.34834
$866$	47319.1	1.85678
$867$	30002.6	1.17525
$868$	0	0
$869$	−2961.10	−0.115591
$870$	−58077.0	−2.26321
$871$	−4377.35	−0.170288
$872$	13832.3	0.537181
$873$	−1134.39	−0.0439786
$874$	−4083.49	−0.158039
$875$	0	0
$876$	3731.77	0.143932
$877$	27017.4	1.04027	0.520133	−	0.854085i	$-0.325882\pi$
$877$	27017.4	1.04027	0.520133	+	0.854085i	$0.325882\pi$
$878$	−3244.74	−0.124720
$879$	37123.1	1.42449
$880$	−10113.6	−0.387419
$881$	31954.5	1.22199	0.610996	−	0.791634i	$-0.290769\pi$
$881$	31954.5	1.22199	0.610996	+	0.791634i	$0.290769\pi$
$882$	0	0
$883$	42055.4	1.60280	0.801402	−	0.598126i	$-0.204088\pi$
$883$	42055.4	1.60280	0.801402	+	0.598126i	$0.204088\pi$
$884$	6951.81	0.264496
$885$	−40315.8	−1.53130
$886$	31910.7	1.21000
$887$	−34830.5	−1.31848	−0.659242	−	0.751931i	$-0.729123\pi$
$887$	−34830.5	−1.31848	−0.659242	+	0.751931i	$0.729123\pi$
$888$	9102.66	0.343992
$889$	0	0
$890$	39831.7	1.50018
$891$	8976.54	0.337514
$892$	−27318.9	−1.02545
$893$	2191.96	0.0821403
$894$	−33503.3	−1.25338
$895$	−32593.4	−1.21729
$896$	0	0
$897$	−1801.13	−0.0670433
$898$	−47693.9	−1.77234
$899$	−32973.6	−1.22328
$900$	−30.4977	−0.00112954
$901$	−40901.3	−1.51234
$902$	19194.1	0.708528
$903$	0	0
$904$	12951.1	0.476492
$905$	−13184.7	−0.484281
$906$	−29094.9	−1.06690
$907$	28035.7	1.02636	0.513180	−	0.858281i	$-0.328467\pi$
$907$	28035.7	1.02636	0.513180	+	0.858281i	$0.328467\pi$
$908$	19910.1	0.727686
$909$	−1223.83	−0.0446554
$910$	0	0
$911$	19163.8	0.696954	0.348477	−	0.937317i	$-0.386699\pi$
$911$	19163.8	0.696954	0.348477	+	0.937317i	$0.386699\pi$
$912$	18143.2	0.658753
$913$	−2265.10	−0.0821070
$914$	33076.8	1.19703
$915$	−4426.95	−0.159946
$916$	−11175.2	−0.403098
$917$	0	0
$918$	50795.2	1.82624
$919$	−34654.1	−1.24389	−0.621945	−	0.783061i	$-0.713657\pi$
$919$	−34654.1	−1.24389	−0.621945	+	0.783061i	$0.713657\pi$
$920$	2896.04	0.103782
$921$	−9022.18	−0.322791
$922$	−40538.8	−1.44802
$923$	5553.09	0.198031
$924$	0	0
$925$	−661.301	−0.0235064
$926$	36368.9	1.29067
$927$	−1182.96	−0.0419132
$928$	−55593.1	−1.96652
$929$	−42110.2	−1.48718	−0.743591	−	0.668635i	$-0.766879\pi$
$929$	−42110.2	−1.48718	−0.743591	+	0.668635i	$0.766879\pi$
$930$	25868.7	0.912115
$931$	0	0
$932$	−18095.4	−0.635980
$933$	−38916.8	−1.36557
$934$	38001.6	1.33132
$935$	13217.2	0.462298
$936$	196.240	0.00685289
$937$	18514.6	0.645514	0.322757	−	0.946482i	$-0.395390\pi$
$937$	18514.6	0.645514	0.322757	+	0.946482i	$0.395390\pi$
$938$	0	0
$939$	25248.3	0.877471
$940$	2903.29	0.100739
$941$	8119.45	0.281282	0.140641	−	0.990061i	$-0.455084\pi$
$941$	8119.45	0.281282	0.140641	+	0.990061i	$0.455084\pi$
$942$	−19822.9	−0.685632
$943$	−11712.5	−0.404467
$944$	−53912.5	−1.85880
$945$	0	0
$946$	4025.44	0.138349
$947$	49354.7	1.69357	0.846786	−	0.531934i	$-0.178534\pi$
$947$	49354.7	1.69357	0.846786	+	0.531934i	$0.178534\pi$
$948$	7035.91	0.241050
$949$	1744.48	0.0596714
$950$	−618.531	−0.0211240
$951$	43905.6	1.49709
$952$	0	0
$953$	−300.006	−0.0101974	−0.00509872	−	0.999987i	$-0.501623\pi$
$953$	−300.006	−0.0101974	−0.00509872	+	0.999987i	$0.501623\pi$
$954$	2156.31	0.0731793
$955$	43363.1	1.46932
$956$	19230.9	0.650598
$957$	16996.5	0.574106
$958$	−40565.4	−1.36807
$959$	0	0
$960$	6716.02	0.225790
$961$	−15103.9	−0.506996
$962$	−7947.01	−0.266343
$963$	3149.10	0.105377
$964$	4766.34	0.159246
$965$	21721.6	0.724604
$966$	0	0
$967$	−20103.3	−0.668539	−0.334270	−	0.942477i	$-0.608490\pi$
$967$	−20103.3	−0.668539	−0.334270	+	0.942477i	$0.608490\pi$
$968$	−12107.1	−0.402000
$969$	−23710.9	−0.786073
$970$	−30473.0	−1.00869
$971$	−39115.5	−1.29277	−0.646383	−	0.763013i	$-0.723719\pi$
$971$	−39115.5	−1.29277	−0.646383	+	0.763013i	$0.723719\pi$
$972$	−2174.01	−0.0717402
$973$	0	0
$974$	−14324.5	−0.471239
$975$	−272.819	−0.00896122
$976$	−5919.95	−0.194153
$977$	21590.6	0.707005	0.353502	−	0.935434i	$-0.384991\pi$
$977$	21590.6	0.707005	0.353502	+	0.935434i	$0.384991\pi$
$978$	74646.9	2.44064
$979$	−11656.9	−0.380549
$980$	0	0
$981$	2030.89	0.0660973
$982$	−42293.9	−1.37439
$983$	7689.51	0.249499	0.124749	−	0.992188i	$-0.460187\pi$
$983$	7689.51	0.249499	0.124749	+	0.992188i	$0.460187\pi$
$984$	24420.2	0.791147
$985$	−30507.3	−0.986847
$986$	101497.	3.27821
$987$	0	0
$988$	−2931.65	−0.0944009
$989$	−2456.39	−0.0789774
$990$	−696.807	−0.0223697
$991$	23913.5	0.766537	0.383269	−	0.923637i	$-0.374798\pi$
$991$	23913.5	0.766537	0.383269	+	0.923637i	$0.374798\pi$
$992$	24762.3	0.792544
$993$	−38259.3	−1.22268
$994$	0	0
$995$	−10121.4	−0.322483
$996$	5382.12	0.171224
$997$	33.8007	0.00107370	0.000536851	−	1.00000i	$-0.499829\pi$
$997$	33.8007	0.00107370	0.000536851		1.00000i	$0.499829\pi$
$998$	−8615.97	−0.273280
$999$	−22902.0	−0.725314

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.4.a.d.1.2		4
7.6	odd	2		91.4.a.b.1.2	✓	4
21.20	even	2		819.4.a.h.1.3		4
28.27	even	2		1456.4.a.s.1.3		4
35.34	odd	2		2275.4.a.h.1.3		4
91.90	odd	2		1183.4.a.e.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.4.a.b.1.2	✓	4	7.6	odd	2
637.4.a.d.1.2		4	1.1	even	1	trivial
819.4.a.h.1.3		4	21.20	even	2
1183.4.a.e.1.3		4	91.90	odd	2
1456.4.a.s.1.3		4	28.27	even	2
2275.4.a.h.1.3		4	35.34	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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	637.a (trivial)

\(f(q)\)	\(=\)	\(q-3.63459 q^{2} +5.33748 q^{3} +5.21021 q^{4} -11.0031 q^{5} -19.3995 q^{6} +10.1397 q^{8} +1.48874 q^{9} +O(q^{10})\)	\(q-3.63459 q^{2} +5.33748 q^{3} +5.21021 q^{4} -11.0031 q^{5} -19.3995 q^{6} +10.1397 q^{8} +1.48874 q^{9} +39.9917 q^{10} -11.7038 q^{11} +27.8094 q^{12} +13.0000 q^{13} -58.7289 q^{15} -78.5354 q^{16} +102.636 q^{17} -5.41094 q^{18} -43.2825 q^{19} -57.3285 q^{20} +42.5383 q^{22} -25.9576 q^{23} +54.1206 q^{24} -3.93182 q^{25} -47.2496 q^{26} -136.166 q^{27} -272.081 q^{29} +213.455 q^{30} +121.190 q^{31} +204.326 q^{32} -62.4686 q^{33} -373.039 q^{34} +7.75663 q^{36} +168.192 q^{37} +157.314 q^{38} +69.3873 q^{39} -111.568 q^{40} +451.218 q^{41} +94.6309 q^{43} -60.9790 q^{44} -16.3807 q^{45} +94.3450 q^{46} -50.6431 q^{47} -419.181 q^{48} +14.2905 q^{50} +547.817 q^{51} +67.7327 q^{52} -398.509 q^{53} +494.907 q^{54} +128.778 q^{55} -231.020 q^{57} +988.901 q^{58} +686.474 q^{59} -305.990 q^{60} +75.3794 q^{61} -440.476 q^{62} -114.356 q^{64} -143.040 q^{65} +227.047 q^{66} -336.720 q^{67} +534.754 q^{68} -138.548 q^{69} +427.161 q^{71} +15.0954 q^{72} +134.191 q^{73} -611.308 q^{74} -20.9860 q^{75} -225.511 q^{76} -252.194 q^{78} +253.005 q^{79} +864.133 q^{80} -766.980 q^{81} -1639.99 q^{82} +193.536 q^{83} -1129.31 q^{85} -343.944 q^{86} -1452.23 q^{87} -118.673 q^{88} +996.000 q^{89} +59.5371 q^{90} -135.244 q^{92} +646.851 q^{93} +184.067 q^{94} +476.242 q^{95} +1090.59 q^{96} -761.982 q^{97} -17.4238 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 5 q^{3} + 26 q^{4} + 36 q^{5} + 45 q^{6} - 30 q^{8} + 21 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 5 * q^3 + 26 * q^4 + 36 * q^5 + 45 * q^6 - 30 * q^8 + 21 * q^9	\( 4 q - 4 q^{2} + 5 q^{3} + 26 q^{4} + 36 q^{5} + 45 q^{6} - 30 q^{8} + 21 q^{9} + 44 q^{10} - 95 q^{11} + 17 q^{12} + 52 q^{13} - 16 q^{15} + 58 q^{16} + 146 q^{17} + 65 q^{18} + 48 q^{19} + 474 q^{20} - 143 q^{22} - 121 q^{23} + 469 q^{24} + 506 q^{25} - 52 q^{26} + 83 q^{27} - 440 q^{29} + 1548 q^{30} + 283 q^{31} - 114 q^{32} - 227 q^{33} - 1234 q^{34} + 755 q^{36} - 209 q^{37} - 440 q^{38} + 65 q^{39} - 754 q^{40} + 93 q^{41} + 526 q^{43} + 217 q^{44} + 768 q^{45} - 841 q^{46} + 783 q^{47} - 1407 q^{48} + 446 q^{50} - 672 q^{51} + 338 q^{52} - 340 q^{53} + 199 q^{54} - 756 q^{55} - 1014 q^{57} + 1916 q^{58} + 922 q^{59} - 396 q^{60} + 141 q^{61} - 1745 q^{62} - 1510 q^{64} + 468 q^{65} - 503 q^{66} - 523 q^{67} + 1710 q^{68} - 1595 q^{69} + 1468 q^{71} - 9 q^{72} + 47 q^{73} - 2249 q^{74} + 1547 q^{75} + 1382 q^{76} + 585 q^{78} + 1025 q^{79} + 2538 q^{80} - 1772 q^{81} + 1561 q^{82} + 1190 q^{83} - 568 q^{85} + 738 q^{86} - 720 q^{87} - 555 q^{88} + 2962 q^{89} + 1960 q^{90} - 599 q^{92} - 763 q^{93} - 317 q^{94} + 2082 q^{95} + 45 q^{96} - 2715 q^{97} + 586 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 5 * q^3 + 26 * q^4 + 36 * q^5 + 45 * q^6 - 30 * q^8 + 21 * q^9 + 44 * q^10 - 95 * q^11 + 17 * q^12 + 52 * q^13 - 16 * q^15 + 58 * q^16 + 146 * q^17 + 65 * q^18 + 48 * q^19 + 474 * q^20 - 143 * q^22 - 121 * q^23 + 469 * q^24 + 506 * q^25 - 52 * q^26 + 83 * q^27 - 440 * q^29 + 1548 * q^30 + 283 * q^31 - 114 * q^32 - 227 * q^33 - 1234 * q^34 + 755 * q^36 - 209 * q^37 - 440 * q^38 + 65 * q^39 - 754 * q^40 + 93 * q^41 + 526 * q^43 + 217 * q^44 + 768 * q^45 - 841 * q^46 + 783 * q^47 - 1407 * q^48 + 446 * q^50 - 672 * q^51 + 338 * q^52 - 340 * q^53 + 199 * q^54 - 756 * q^55 - 1014 * q^57 + 1916 * q^58 + 922 * q^59 - 396 * q^60 + 141 * q^61 - 1745 * q^62 - 1510 * q^64 + 468 * q^65 - 503 * q^66 - 523 * q^67 + 1710 * q^68 - 1595 * q^69 + 1468 * q^71 - 9 * q^72 + 47 * q^73 - 2249 * q^74 + 1547 * q^75 + 1382 * q^76 + 585 * q^78 + 1025 * q^79 + 2538 * q^80 - 1772 * q^81 + 1561 * q^82 + 1190 * q^83 - 568 * q^85 + 738 * q^86 - 720 * q^87 - 555 * q^88 + 2962 * q^89 + 1960 * q^90 - 599 * q^92 - 763 * q^93 - 317 * q^94 + 2082 * q^95 + 45 * q^96 - 2715 * q^97 + 586 * q^99

Introduction

L-functions

Modular forms

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Database

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