LMFDB - Embedded newform 1014.4.a.be.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,4,Mod(1,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, 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("1014.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1014.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:	$59.8279367458$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 422x^{4} + 85x^{3} + 54852x^{2} + 14112x - 2044224 $ x^6 - x^5 - 422x^4 + 85x^3 + 54852x^2 + 14112x - 2044224
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 13^{2} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$14.7697$ of defining polynomial
Character	$\chi$	$=$	1014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +9.80890 q^{5} +6.00000 q^{6} +11.4763 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +9.80890 q^{5} +6.00000 q^{6} +11.4763 q^{7} +8.00000 q^{8} +9.00000 q^{9} +19.6178 q^{10} +19.6826 q^{11} +12.0000 q^{12} +22.9525 q^{14} +29.4267 q^{15} +16.0000 q^{16} +25.5010 q^{17} +18.0000 q^{18} -4.32083 q^{19} +39.2356 q^{20} +34.4288 q^{21} +39.3653 q^{22} -33.5416 q^{23} +24.0000 q^{24} -28.7854 q^{25} +27.0000 q^{27} +45.9051 q^{28} +116.838 q^{29} +58.8534 q^{30} +288.350 q^{31} +32.0000 q^{32} +59.0479 q^{33} +51.0020 q^{34} +112.570 q^{35} +36.0000 q^{36} +124.747 q^{37} -8.64165 q^{38} +78.4712 q^{40} -142.268 q^{41} +68.8576 q^{42} -228.871 q^{43} +78.7305 q^{44} +88.2801 q^{45} -67.0831 q^{46} -598.729 q^{47} +48.0000 q^{48} -211.295 q^{49} -57.5708 q^{50} +76.5030 q^{51} +119.901 q^{53} +54.0000 q^{54} +193.065 q^{55} +91.8101 q^{56} -12.9625 q^{57} +233.676 q^{58} +499.881 q^{59} +117.707 q^{60} +696.612 q^{61} +576.701 q^{62} +103.286 q^{63} +64.0000 q^{64} +118.096 q^{66} -67.8564 q^{67} +102.004 q^{68} -100.625 q^{69} +225.139 q^{70} +538.072 q^{71} +72.0000 q^{72} -1214.82 q^{73} +249.495 q^{74} -86.3562 q^{75} -17.2833 q^{76} +225.883 q^{77} +345.554 q^{79} +156.942 q^{80} +81.0000 q^{81} -284.536 q^{82} -1160.79 q^{83} +137.715 q^{84} +250.137 q^{85} -457.741 q^{86} +350.514 q^{87} +157.461 q^{88} -726.029 q^{89} +176.560 q^{90} -134.166 q^{92} +865.051 q^{93} -1197.46 q^{94} -42.3826 q^{95} +96.0000 q^{96} +598.944 q^{97} -422.591 q^{98} +177.144 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 12 q^{2} + 18 q^{3} + 24 q^{4} - 3 q^{5} + 36 q^{6} - q^{7} + 48 q^{8} + 54 q^{9}+O(q^{10}) $ 6 * q + 12 * q^2 + 18 * q^3 + 24 * q^4 - 3 * q^5 + 36 * q^6 - q^7 + 48 * q^8 + 54 * q^9	\( 6 q + 12 q^{2} + 18 q^{3} + 24 q^{4} - 3 q^{5} + 36 q^{6} - q^{7} + 48 q^{8} + 54 q^{9} - 6 q^{10} + 64 q^{11} + 72 q^{12} - 2 q^{14} - 9 q^{15} + 96 q^{16} + 51 q^{17} + 108 q^{18} + 213 q^{19} - 12 q^{20} - 3 q^{21} + 128 q^{22} + 222 q^{23} + 144 q^{24} + 185 q^{25} + 162 q^{27} - 4 q^{28} + 329 q^{29} - 18 q^{30} + 289 q^{31} + 192 q^{32} + 192 q^{33} + 102 q^{34} + 844 q^{35} + 216 q^{36} + 470 q^{37} + 426 q^{38} - 24 q^{40} - 321 q^{41} - 6 q^{42} + 491 q^{43} + 256 q^{44} - 27 q^{45} + 444 q^{46} - 641 q^{47} + 288 q^{48} + 1133 q^{49} + 370 q^{50} + 153 q^{51} + 2302 q^{53} + 324 q^{54} - 329 q^{55} - 8 q^{56} + 639 q^{57} + 658 q^{58} - 139 q^{59} - 36 q^{60} + 345 q^{61} + 578 q^{62} - 9 q^{63} + 384 q^{64} + 384 q^{66} + 855 q^{67} + 204 q^{68} + 666 q^{69} + 1688 q^{70} - 1362 q^{71} + 432 q^{72} - 831 q^{73} + 940 q^{74} + 555 q^{75} + 852 q^{76} + 3291 q^{77} + 3100 q^{79} - 48 q^{80} + 486 q^{81} - 642 q^{82} + 447 q^{83} - 12 q^{84} + 847 q^{85} + 982 q^{86} + 987 q^{87} + 512 q^{88} - 1241 q^{89} - 54 q^{90} + 888 q^{92} + 867 q^{93} - 1282 q^{94} - 665 q^{95} + 576 q^{96} - 1554 q^{97} + 2266 q^{98} + 576 q^{99}+O(q^{100}) \) 6 * q + 12 * q^2 + 18 * q^3 + 24 * q^4 - 3 * q^5 + 36 * q^6 - q^7 + 48 * q^8 + 54 * q^9 - 6 * q^10 + 64 * q^11 + 72 * q^12 - 2 * q^14 - 9 * q^15 + 96 * q^16 + 51 * q^17 + 108 * q^18 + 213 * q^19 - 12 * q^20 - 3 * q^21 + 128 * q^22 + 222 * q^23 + 144 * q^24 + 185 * q^25 + 162 * q^27 - 4 * q^28 + 329 * q^29 - 18 * q^30 + 289 * q^31 + 192 * q^32 + 192 * q^33 + 102 * q^34 + 844 * q^35 + 216 * q^36 + 470 * q^37 + 426 * q^38 - 24 * q^40 - 321 * q^41 - 6 * q^42 + 491 * q^43 + 256 * q^44 - 27 * q^45 + 444 * q^46 - 641 * q^47 + 288 * q^48 + 1133 * q^49 + 370 * q^50 + 153 * q^51 + 2302 * q^53 + 324 * q^54 - 329 * q^55 - 8 * q^56 + 639 * q^57 + 658 * q^58 - 139 * q^59 - 36 * q^60 + 345 * q^61 + 578 * q^62 - 9 * q^63 + 384 * q^64 + 384 * q^66 + 855 * q^67 + 204 * q^68 + 666 * q^69 + 1688 * q^70 - 1362 * q^71 + 432 * q^72 - 831 * q^73 + 940 * q^74 + 555 * q^75 + 852 * q^76 + 3291 * q^77 + 3100 * q^79 - 48 * q^80 + 486 * q^81 - 642 * q^82 + 447 * q^83 - 12 * q^84 + 847 * q^85 + 982 * q^86 + 987 * q^87 + 512 * q^88 - 1241 * q^89 - 54 * q^90 + 888 * q^92 + 867 * q^93 - 1282 * q^94 - 665 * q^95 + 576 * q^96 - 1554 * q^97 + 2266 * q^98 + 576 * 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 $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	4.00000	0.500000
$5$	9.80890	0.877335	0.438667	−	0.898649i	$-0.355451\pi$
$5$	9.80890	0.877335	0.438667	+	0.898649i	$0.355451\pi$
$6$	6.00000	0.408248
$7$	11.4763	0.619660	0.309830	−	0.950792i	$-0.399728\pi$
$7$	11.4763	0.619660	0.309830	+	0.950792i	$0.399728\pi$
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	19.6178	0.620370
$11$	19.6826	0.539503	0.269752	−	0.962930i	$-0.413058\pi$
$11$	19.6826	0.539503	0.269752	+	0.962930i	$0.413058\pi$
$12$	12.0000	0.288675
$13$	0	0
$13$	0	0
$14$	22.9525	0.438166
$15$	29.4267	0.506530
$16$	16.0000	0.250000
$17$	25.5010	0.363818	0.181909	−	0.983315i	$-0.441772\pi$
$17$	25.5010	0.363818	0.181909	+	0.983315i	$0.441772\pi$
$18$	18.0000	0.235702
$19$	−4.32083	−0.0521719	−0.0260859	−	0.999660i	$-0.508304\pi$
$19$	−4.32083	−0.0521719	−0.0260859	+	0.999660i	$0.508304\pi$
$20$	39.2356	0.438667
$21$	34.4288	0.357761
$22$	39.3653	0.381487
$23$	−33.5416	−0.304083	−0.152041	−	0.988374i	$-0.548585\pi$
$23$	−33.5416	−0.304083	−0.152041	+	0.988374i	$0.548585\pi$
$24$	24.0000	0.204124
$25$	−28.7854	−0.230283
$26$	0	0
$27$	27.0000	0.192450
$28$	45.9051	0.309830
$29$	116.838	0.748147	0.374074	−	0.927399i	$-0.377961\pi$
$29$	116.838	0.748147	0.374074	+	0.927399i	$0.377961\pi$
$30$	58.8534	0.358171
$31$	288.350	1.67062	0.835311	−	0.549778i	$-0.185288\pi$
$31$	288.350	1.67062	0.835311	+	0.549778i	$0.185288\pi$
$32$	32.0000	0.176777
$33$	59.0479	0.311482
$34$	51.0020	0.257258
$35$	112.570	0.543649
$36$	36.0000	0.166667
$37$	124.747	0.554279	0.277140	−	0.960830i	$-0.410614\pi$
$37$	124.747	0.554279	0.277140	+	0.960830i	$0.410614\pi$
$38$	−8.64165	−0.0368911
$39$	0	0
$40$	78.4712	0.310185
$41$	−142.268	−0.541916	−0.270958	−	0.962591i	$-0.587340\pi$
$41$	−142.268	−0.541916	−0.270958	+	0.962591i	$0.587340\pi$
$42$	68.8576	0.252975
$43$	−228.871	−0.811685	−0.405842	−	0.913943i	$-0.633022\pi$
$43$	−228.871	−0.811685	−0.405842	+	0.913943i	$0.633022\pi$
$44$	78.7305	0.269752
$45$	88.2801	0.292445
$46$	−67.0831	−0.215019
$47$	−598.729	−1.85816	−0.929081	−	0.369877i	$-0.879400\pi$
$47$	−598.729	−1.85816	−0.929081	+	0.369877i	$0.879400\pi$
$48$	48.0000	0.144338
$49$	−211.295	−0.616021
$50$	−57.5708	−0.162835
$51$	76.5030	0.210050
$52$	0	0
$53$	119.901	0.310750	0.155375	−	0.987856i	$-0.450341\pi$
$53$	119.901	0.310750	0.155375	+	0.987856i	$0.450341\pi$
$54$	54.0000	0.136083
$55$	193.065	0.473325
$56$	91.8101	0.219083
$57$	−12.9625	−0.0301214
$58$	233.676	0.529020
$59$	499.881	1.10303	0.551517	−	0.834164i	$-0.314049\pi$
$59$	499.881	1.10303	0.551517	+	0.834164i	$0.314049\pi$
$60$	117.707	0.253265
$61$	696.612	1.46216	0.731082	−	0.682290i	$-0.239016\pi$
$61$	696.612	1.46216	0.731082	+	0.682290i	$0.239016\pi$
$62$	576.701	1.18131
$63$	103.286	0.206553
$64$	64.0000	0.125000
$65$	0	0
$66$	118.096	0.220251
$67$	−67.8564	−0.123731	−0.0618655	−	0.998084i	$-0.519705\pi$
$67$	−67.8564	−0.123731	−0.0618655	+	0.998084i	$0.519705\pi$
$68$	102.004	0.181909
$69$	−100.625	−0.175562
$70$	225.139	0.384418
$71$	538.072	0.899399	0.449700	−	0.893180i	$-0.351531\pi$
$71$	538.072	0.899399	0.449700	+	0.893180i	$0.351531\pi$
$72$	72.0000	0.117851
$73$	−1214.82	−1.94773	−0.973866	−	0.227124i	$-0.927068\pi$
$73$	−1214.82	−1.94773	−0.973866	+	0.227124i	$0.927068\pi$
$74$	249.495	0.391935
$75$	−86.3562	−0.132954
$76$	−17.2833	−0.0260859
$77$	225.883	0.334309
$78$	0	0
$79$	345.554	0.492124	0.246062	−	0.969254i	$-0.420863\pi$
$79$	345.554	0.492124	0.246062	+	0.969254i	$0.420863\pi$
$80$	156.942	0.219334
$81$	81.0000	0.111111
$82$	−284.536	−0.383192
$83$	−1160.79	−1.53510	−0.767550	−	0.640989i	$-0.778524\pi$
$83$	−1160.79	−1.53510	−0.767550	+	0.640989i	$0.778524\pi$
$84$	137.715	0.178880
$85$	250.137	0.319190
$86$	−457.741	−0.573948
$87$	350.514	0.431943
$88$	157.461	0.190743
$89$	−726.029	−0.864707	−0.432353	−	0.901704i	$-0.642317\pi$
$89$	−726.029	−0.864707	−0.432353	+	0.901704i	$0.642317\pi$
$90$	176.560	0.206790
$91$	0	0
$92$	−134.166	−0.152041
$93$	865.051	0.964534
$94$	−1197.46	−1.31392
$95$	−42.3826	−0.0457722
$96$	96.0000	0.102062
$97$	598.944	0.626944	0.313472	−	0.949598i	$-0.398508\pi$
$97$	598.944	0.626944	0.313472	+	0.949598i	$0.398508\pi$
$98$	−422.591	−0.435593
$99$	177.144	0.179834
$100$	−115.142	−0.115142
$101$	1769.08	1.74287	0.871437	−	0.490508i	$-0.163189\pi$
$101$	1769.08	1.74287	0.871437	+	0.490508i	$0.163189\pi$
$102$	153.006	0.148528
$103$	973.249	0.931040	0.465520	−	0.885037i	$-0.345867\pi$
$103$	973.249	0.931040	0.465520	+	0.885037i	$0.345867\pi$
$104$	0	0
$105$	337.709	0.313876
$106$	239.803	0.219733
$107$	−1318.13	−1.19092	−0.595460	−	0.803385i	$-0.703030\pi$
$107$	−1318.13	−1.19092	−0.595460	+	0.803385i	$0.703030\pi$
$108$	108.000	0.0962250
$109$	325.349	0.285897	0.142949	−	0.989730i	$-0.454342\pi$
$109$	325.349	0.285897	0.142949	+	0.989730i	$0.454342\pi$
$110$	386.130	0.334691
$111$	374.242	0.320013
$112$	183.620	0.154915
$113$	732.485	0.609791	0.304895	−	0.952386i	$-0.401378\pi$
$113$	732.485	0.609791	0.304895	+	0.952386i	$0.401378\pi$
$114$	−25.9250	−0.0212991
$115$	−329.006	−0.266782
$116$	467.352	0.374074
$117$	0	0
$118$	999.763	0.779963
$119$	292.656	0.225443
$120$	235.414	0.179085
$121$	−943.594	−0.708936
$122$	1393.22	1.03391
$123$	−426.805	−0.312875
$124$	1153.40	0.835311
$125$	−1508.47	−1.07937
$126$	206.573	0.146055
$127$	−2259.84	−1.57896	−0.789480	−	0.613776i	$-0.789650\pi$
$127$	−2259.84	−1.57896	−0.789480	+	0.613776i	$0.789650\pi$
$128$	128.000	0.0883883
$129$	−686.612	−0.468627
$130$	0	0
$131$	1615.48	1.07745	0.538723	−	0.842483i	$-0.318907\pi$
$131$	1615.48	1.07745	0.538723	+	0.842483i	$0.318907\pi$
$132$	236.192	0.155741
$133$	−49.5869	−0.0323288
$134$	−135.713	−0.0874911
$135$	264.840	0.168843
$136$	204.008	0.128629
$137$	389.403	0.242839	0.121420	−	0.992601i	$-0.461255\pi$
$137$	389.403	0.242839	0.121420	+	0.992601i	$0.461255\pi$
$138$	−201.249	−0.124141
$139$	1727.37	1.05405	0.527027	−	0.849848i	$-0.323307\pi$
$139$	1727.37	1.05405	0.527027	+	0.849848i	$0.323307\pi$
$140$	450.278	0.271825
$141$	−1796.19	−1.07281
$142$	1076.14	0.635971
$143$	0	0
$144$	144.000	0.0833333
$145$	1146.05	0.656376
$146$	−2429.65	−1.37725
$147$	−633.886	−0.355660
$148$	498.989	0.277140
$149$	278.594	0.153177	0.0765883	−	0.997063i	$-0.475597\pi$
$149$	278.594	0.153177	0.0765883	+	0.997063i	$0.475597\pi$
$150$	−172.712	−0.0940128
$151$	−776.493	−0.418477	−0.209239	−	0.977865i	$-0.567099\pi$
$151$	−776.493	−0.418477	−0.209239	+	0.977865i	$0.567099\pi$
$152$	−34.5666	−0.0184455
$153$	229.509	0.121273
$154$	451.766	0.236392
$155$	2828.40	1.46569
$156$	0	0
$157$	398.605	0.202625	0.101313	−	0.994855i	$-0.467696\pi$
$157$	398.605	0.202625	0.101313	+	0.994855i	$0.467696\pi$
$158$	691.107	0.347984
$159$	359.704	0.179411
$160$	313.885	0.155092
$161$	−384.932	−0.188428
$162$	162.000	0.0785674
$163$	2777.81	1.33482	0.667408	−	0.744693i	$-0.267404\pi$
$163$	2777.81	1.33482	0.667408	+	0.744693i	$0.267404\pi$
$164$	−569.073	−0.270958
$165$	579.195	0.273274
$166$	−2321.58	−1.08548
$167$	−3774.00	−1.74875	−0.874374	−	0.485253i	$-0.838728\pi$
$167$	−3774.00	−1.74875	−0.874374	+	0.485253i	$0.838728\pi$
$168$	275.430	0.126488
$169$	0	0
$170$	500.274	0.225701
$171$	−38.8874	−0.0173906
$172$	−915.483	−0.405842
$173$	−1692.90	−0.743982	−0.371991	−	0.928236i	$-0.621325\pi$
$173$	−1692.90	−0.743982	−0.371991	+	0.928236i	$0.621325\pi$
$174$	701.028	0.305430
$175$	−330.349	−0.142697
$176$	314.922	0.134876
$177$	1499.64	0.636837
$178$	−1452.06	−0.611440
$179$	−367.052	−0.153267	−0.0766333	−	0.997059i	$-0.524417\pi$
$179$	−367.052	−0.153267	−0.0766333	+	0.997059i	$0.524417\pi$
$180$	353.121	0.146222
$181$	999.648	0.410515	0.205258	−	0.978708i	$-0.434197\pi$
$181$	999.648	0.410515	0.205258	+	0.978708i	$0.434197\pi$
$182$	0	0
$183$	2089.84	0.844181
$184$	−268.333	−0.107509
$185$	1223.63	0.486289
$186$	1730.10	0.682028
$187$	501.927	0.196281
$188$	−2394.92	−0.929081
$189$	309.859	0.119254
$190$	−84.7651	−0.0323658
$191$	1562.34	0.591870	0.295935	−	0.955208i	$-0.404369\pi$
$191$	1562.34	0.591870	0.295935	+	0.955208i	$0.404369\pi$
$192$	192.000	0.0721688
$193$	−4656.25	−1.73660	−0.868301	−	0.496038i	$-0.834787\pi$
$193$	−4656.25	−1.73660	−0.868301	+	0.496038i	$0.834787\pi$
$194$	1197.89	0.443316
$195$	0	0
$196$	−845.181	−0.308011
$197$	1181.41	0.427269	0.213634	−	0.976914i	$-0.431470\pi$
$197$	1181.41	0.427269	0.213634	+	0.976914i	$0.431470\pi$
$198$	354.287	0.127162
$199$	3341.44	1.19029	0.595147	−	0.803617i	$-0.297094\pi$
$199$	3341.44	1.19029	0.595147	+	0.803617i	$0.297094\pi$
$200$	−230.283	−0.0814174
$201$	−203.569	−0.0714362
$202$	3538.16	1.23240
$203$	1340.86	0.463597
$204$	306.012	0.105025
$205$	−1395.49	−0.475442
$206$	1946.50	0.658344
$207$	−301.874	−0.101361
$208$	0	0
$209$	−85.0452	−0.0281469
$210$	675.417	0.221944
$211$	1395.08	0.455172	0.227586	−	0.973758i	$-0.426917\pi$
$211$	1395.08	0.455172	0.227586	+	0.973758i	$0.426917\pi$
$212$	479.606	0.155375
$213$	1614.22	0.519269
$214$	−2636.26	−0.842107
$215$	−2244.97	−0.712120
$216$	216.000	0.0680414
$217$	3309.19	1.03522
$218$	650.698	0.202160
$219$	−3644.47	−1.12452
$220$	772.260	0.236663
$221$	0	0
$222$	748.484	0.226284
$223$	−3511.30	−1.05441	−0.527207	−	0.849737i	$-0.676761\pi$
$223$	−3511.30	−1.05441	−0.527207	+	0.849737i	$0.676761\pi$
$224$	367.240	0.109541
$225$	−259.069	−0.0767611
$226$	1464.97	0.431187
$227$	−590.297	−0.172596	−0.0862982	−	0.996269i	$-0.527504\pi$
$227$	−590.297	−0.172596	−0.0862982	+	0.996269i	$0.527504\pi$
$228$	−51.8499	−0.0150607
$229$	−3432.98	−0.990645	−0.495322	−	0.868709i	$-0.664950\pi$
$229$	−3432.98	−0.990645	−0.495322	+	0.868709i	$0.664950\pi$
$230$	−658.012	−0.188644
$231$	677.649	0.193013
$232$	934.704	0.264510
$233$	5376.00	1.51156	0.755780	−	0.654826i	$-0.227258\pi$
$233$	5376.00	1.51156	0.755780	+	0.654826i	$0.227258\pi$
$234$	0	0
$235$	−5872.87	−1.63023
$236$	1999.53	0.551517
$237$	1036.66	0.284128
$238$	585.312	0.159412
$239$	−4342.72	−1.17534	−0.587672	−	0.809099i	$-0.699955\pi$
$239$	−4342.72	−1.17534	−0.587672	+	0.809099i	$0.699955\pi$
$240$	470.827	0.126632
$241$	493.464	0.131895	0.0659477	−	0.997823i	$-0.478993\pi$
$241$	493.464	0.131895	0.0659477	+	0.997823i	$0.478993\pi$
$242$	−1887.19	−0.501293
$243$	243.000	0.0641500
$244$	2786.45	0.731082
$245$	−2072.58	−0.540457
$246$	−853.609	−0.221236
$247$	0	0
$248$	2306.80	0.590654
$249$	−3482.37	−0.886291
$250$	−3016.93	−0.763230
$251$	−1116.07	−0.280661	−0.140331	−	0.990105i	$-0.544817\pi$
$251$	−1116.07	−0.280661	−0.140331	+	0.990105i	$0.544817\pi$
$252$	413.145	0.103277
$253$	−660.186	−0.164054
$254$	−4519.67	−1.11649
$255$	750.410	0.184284
$256$	256.000	0.0625000
$257$	2998.66	0.727825	0.363913	−	0.931433i	$-0.381441\pi$
$257$	2998.66	0.727825	0.363913	+	0.931433i	$0.381441\pi$
$258$	−1373.22	−0.331369
$259$	1431.63	0.343465
$260$	0	0
$261$	1051.54	0.249382
$262$	3230.97	0.761870
$263$	2234.09	0.523802	0.261901	−	0.965095i	$-0.415651\pi$
$263$	2234.09	0.523802	0.261901	+	0.965095i	$0.415651\pi$
$264$	472.383	0.110126
$265$	1176.10	0.272632
$266$	−99.1739	−0.0228599
$267$	−2178.09	−0.499239
$268$	−271.426	−0.0618655
$269$	−1476.38	−0.334635	−0.167317	−	0.985903i	$-0.553510\pi$
$269$	−1476.38	−0.334635	−0.167317	+	0.985903i	$0.553510\pi$
$270$	529.681	0.119390
$271$	2073.87	0.464866	0.232433	−	0.972612i	$-0.425331\pi$
$271$	2073.87	0.464866	0.232433	+	0.972612i	$0.425331\pi$
$272$	408.016	0.0909544
$273$	0	0
$274$	778.807	0.171713
$275$	−566.573	−0.124239
$276$	−402.499	−0.0877811
$277$	−385.634	−0.0836481	−0.0418240	−	0.999125i	$-0.513317\pi$
$277$	−385.634	−0.0836481	−0.0418240	+	0.999125i	$0.513317\pi$
$278$	3454.74	0.745329
$279$	2595.15	0.556874
$280$	900.556	0.192209
$281$	−50.9106	−0.0108081	−0.00540405	−	0.999985i	$-0.501720\pi$
$281$	−50.9106	−0.0108081	−0.00540405	+	0.999985i	$0.501720\pi$
$282$	−3592.37	−0.758591
$283$	−7079.05	−1.48695	−0.743474	−	0.668765i	$-0.766823\pi$
$283$	−7079.05	−1.48695	−0.743474	+	0.668765i	$0.766823\pi$
$284$	2152.29	0.449700
$285$	−127.148	−0.0264266
$286$	0	0
$287$	−1632.71	−0.335804
$288$	288.000	0.0589256
$289$	−4262.70	−0.867637
$290$	2292.11	0.464128
$291$	1796.83	0.361966
$292$	−4859.30	−0.973866
$293$	−7424.87	−1.48043	−0.740214	−	0.672371i	$-0.765276\pi$
$293$	−7424.87	−1.48043	−0.740214	+	0.672371i	$0.765276\pi$
$294$	−1267.77	−0.251490
$295$	4903.29	0.967730
$296$	997.979	0.195967
$297$	531.431	0.103827
$298$	557.188	0.108312
$299$	0	0
$300$	−345.425	−0.0664771
$301$	−2626.58	−0.502969
$302$	−1552.99	−0.295908
$303$	5307.24	1.00625
$304$	−69.1332	−0.0130430
$305$	6833.00	1.28281
$306$	459.018	0.0857526
$307$	−1513.08	−0.281290	−0.140645	−	0.990060i	$-0.544918\pi$
$307$	−1513.08	−0.281290	−0.140645	+	0.990060i	$0.544918\pi$
$308$	903.532	0.167154
$309$	2919.75	0.537536
$310$	5656.80	1.03640
$311$	4122.14	0.751592	0.375796	−	0.926702i	$-0.377369\pi$
$311$	4122.14	0.751592	0.375796	+	0.926702i	$0.377369\pi$
$312$	0	0
$313$	−9089.64	−1.64146	−0.820730	−	0.571316i	$-0.806433\pi$
$313$	−9089.64	−1.64146	−0.820730	+	0.571316i	$0.806433\pi$
$314$	797.211	0.143278
$315$	1013.13	0.181216
$316$	1382.21	0.246062
$317$	−5598.11	−0.991864	−0.495932	−	0.868361i	$-0.665174\pi$
$317$	−5598.11	−0.991864	−0.495932	+	0.868361i	$0.665174\pi$
$318$	719.409	0.126863
$319$	2299.68	0.403628
$320$	627.770	0.109667
$321$	−3954.39	−0.687578
$322$	−769.864	−0.133239
$323$	−110.185	−0.0189810
$324$	324.000	0.0555556
$325$	0	0
$326$	5555.62	0.943857
$327$	976.047	0.165063
$328$	−1138.15	−0.191596
$329$	−6871.17	−1.15143
$330$	1158.39	0.193234
$331$	−4375.60	−0.726601	−0.363301	−	0.931672i	$-0.618350\pi$
$331$	−4375.60	−0.726601	−0.363301	+	0.931672i	$0.618350\pi$
$332$	−4643.16	−0.767550
$333$	1122.73	0.184760
$334$	−7548.00	−1.23655
$335$	−665.597	−0.108554
$336$	550.861	0.0894402
$337$	−9930.42	−1.60518	−0.802588	−	0.596534i	$-0.796544\pi$
$337$	−9930.42	−1.60518	−0.802588	+	0.596534i	$0.796544\pi$
$338$	0	0
$339$	2197.45	0.352063
$340$	1000.55	0.159595
$341$	5675.50	0.901306
$342$	−77.7749	−0.0122970
$343$	−6361.24	−1.00138
$344$	−1830.97	−0.286974
$345$	−987.018	−0.154027
$346$	−3385.80	−0.526074
$347$	−2527.04	−0.390947	−0.195474	−	0.980709i	$-0.562624\pi$
$347$	−2527.04	−0.390947	−0.195474	+	0.980709i	$0.562624\pi$
$348$	1402.06	0.215972
$349$	9477.40	1.45362	0.726810	−	0.686838i	$-0.241002\pi$
$349$	9477.40	1.45362	0.726810	+	0.686838i	$0.241002\pi$
$350$	−660.698	−0.100902
$351$	0	0
$352$	629.844	0.0953716
$353$	4890.71	0.737411	0.368706	−	0.929546i	$-0.379801\pi$
$353$	4890.71	0.737411	0.368706	+	0.929546i	$0.379801\pi$
$354$	2999.29	0.450312
$355$	5277.89	0.789075
$356$	−2904.11	−0.432353
$357$	877.968	0.130160
$358$	−734.103	−0.108376
$359$	6750.73	0.992451	0.496226	−	0.868194i	$-0.334719\pi$
$359$	6750.73	0.992451	0.496226	+	0.868194i	$0.334719\pi$
$360$	706.241	0.103395
$361$	−6840.33	−0.997278
$362$	1999.30	0.290278
$363$	−2830.78	−0.409304
$364$	0	0
$365$	−11916.1	−1.70881
$366$	4179.67	0.596926
$367$	−1226.22	−0.174409	−0.0872046	−	0.996190i	$-0.527793\pi$
$367$	−1226.22	−0.174409	−0.0872046	+	0.996190i	$0.527793\pi$
$368$	−536.665	−0.0760207
$369$	−1280.41	−0.180639
$370$	2447.27	0.343858
$371$	1376.02	0.192559
$372$	3460.21	0.482267
$373$	10148.0	1.40870	0.704349	−	0.709854i	$-0.251239\pi$
$373$	10148.0	1.40870	0.704349	+	0.709854i	$0.251239\pi$
$374$	1003.85	0.138792
$375$	−4525.40	−0.623175
$376$	−4789.83	−0.656959
$377$	0	0
$378$	619.718	0.0843250
$379$	−9857.27	−1.33597	−0.667987	−	0.744173i	$-0.732844\pi$
$379$	−9857.27	−1.33597	−0.667987	+	0.744173i	$0.732844\pi$
$380$	−169.530	−0.0228861
$381$	−6779.51	−0.911613
$382$	3124.69	0.418515
$383$	6761.43	0.902070	0.451035	−	0.892506i	$-0.351055\pi$
$383$	6761.43	0.902070	0.451035	+	0.892506i	$0.351055\pi$
$384$	384.000	0.0510310
$385$	2215.67	0.293301
$386$	−9312.49	−1.22796
$387$	−2059.84	−0.270562
$388$	2395.77	0.313472
$389$	−13560.8	−1.76750	−0.883750	−	0.467960i	$-0.844989\pi$
$389$	−13560.8	−1.76750	−0.883750	+	0.467960i	$0.844989\pi$
$390$	0	0
$391$	−855.343	−0.110631
$392$	−1690.36	−0.217796
$393$	4846.45	0.622064
$394$	2362.82	0.302125
$395$	3389.50	0.431758
$396$	708.575	0.0899172
$397$	8154.41	1.03088	0.515439	−	0.856926i	$-0.327629\pi$
$397$	8154.41	1.03088	0.515439	+	0.856926i	$0.327629\pi$
$398$	6682.89	0.841665
$399$	−148.761	−0.0186651
$400$	−460.567	−0.0575708
$401$	820.960	0.102236	0.0511182	−	0.998693i	$-0.483721\pi$
$401$	820.960	0.102236	0.0511182	+	0.998693i	$0.483721\pi$
$402$	−407.139	−0.0505130
$403$	0	0
$404$	7076.33	0.871437
$405$	794.521	0.0974817
$406$	2681.73	0.327813
$407$	2455.36	0.299036
$408$	612.024	0.0742640
$409$	−4598.95	−0.555999	−0.278000	−	0.960581i	$-0.589671\pi$
$409$	−4598.95	−0.555999	−0.278000	+	0.960581i	$0.589671\pi$
$410$	−2790.99	−0.336188
$411$	1168.21	0.140203
$412$	3893.00	0.465520
$413$	5736.77	0.683506
$414$	−603.748	−0.0716730
$415$	−11386.1	−1.34680
$416$	0	0
$417$	5182.11	0.608559
$418$	−170.090	−0.0199029
$419$	10274.3	1.19793	0.598965	−	0.800775i	$-0.295579\pi$
$419$	10274.3	1.19793	0.598965	+	0.800775i	$0.295579\pi$
$420$	1350.83	0.156938
$421$	−12730.1	−1.47370	−0.736852	−	0.676054i	$-0.763689\pi$
$421$	−12730.1	−1.47370	−0.736852	+	0.676054i	$0.763689\pi$
$422$	2790.16	0.321855
$423$	−5388.56	−0.619387
$424$	959.212	0.109867
$425$	−734.057	−0.0837811
$426$	3228.43	0.367178
$427$	7994.50	0.906045
$428$	−5272.52	−0.595460
$429$	0	0
$430$	−4489.94	−0.503545
$431$	−960.330	−0.107326	−0.0536630	−	0.998559i	$-0.517090\pi$
$431$	−960.330	−0.107326	−0.0536630	+	0.998559i	$0.517090\pi$
$432$	432.000	0.0481125
$433$	−13800.9	−1.53171	−0.765853	−	0.643016i	$-0.777683\pi$
$433$	−13800.9	−1.53171	−0.765853	+	0.643016i	$0.777683\pi$
$434$	6618.37	0.732009
$435$	3438.16	0.378959
$436$	1301.40	0.142949
$437$	144.927	0.0158646
$438$	−7288.95	−0.795158
$439$	−5932.37	−0.644958	−0.322479	−	0.946577i	$-0.604516\pi$
$439$	−5932.37	−0.644958	−0.322479	+	0.946577i	$0.604516\pi$
$440$	1544.52	0.167346
$441$	−1901.66	−0.205340
$442$	0	0
$443$	−3164.11	−0.339349	−0.169674	−	0.985500i	$-0.554272\pi$
$443$	−3164.11	−0.339349	−0.169674	+	0.985500i	$0.554272\pi$
$444$	1496.97	0.160007
$445$	−7121.54	−0.758637
$446$	−7022.60	−0.745583
$447$	835.782	0.0884365
$448$	734.481	0.0774575
$449$	4040.22	0.424654	0.212327	−	0.977199i	$-0.431896\pi$
$449$	4040.22	0.424654	0.212327	+	0.977199i	$0.431896\pi$
$450$	−518.137	−0.0542783
$451$	−2800.21	−0.292366
$452$	2929.94	0.304895
$453$	−2329.48	−0.241608
$454$	−1180.59	−0.122044
$455$	0	0
$456$	−103.700	−0.0106495
$457$	−10702.3	−1.09548	−0.547740	−	0.836649i	$-0.684512\pi$
$457$	−10702.3	−1.09548	−0.547740	+	0.836649i	$0.684512\pi$
$458$	−6865.96	−0.700492
$459$	688.527	0.0700167
$460$	−1316.02	−0.133391
$461$	6301.39	0.636627	0.318314	−	0.947985i	$-0.396884\pi$
$461$	6301.39	0.636627	0.318314	+	0.947985i	$0.396884\pi$
$462$	1355.30	0.136481
$463$	12433.2	1.24799	0.623995	−	0.781429i	$-0.285509\pi$
$463$	12433.2	1.24799	0.623995	+	0.781429i	$0.285509\pi$
$464$	1869.41	0.187037
$465$	8485.21	0.846219
$466$	10752.0	1.06883
$467$	−16155.0	−1.60078	−0.800390	−	0.599479i	$-0.795374\pi$
$467$	−16155.0	−1.60078	−0.800390	+	0.599479i	$0.795374\pi$
$468$	0	0
$469$	−778.738	−0.0766712
$470$	−11745.7	−1.15275
$471$	1195.82	0.116986
$472$	3999.05	0.389981
$473$	−4504.78	−0.437907
$474$	2073.32	0.200909
$475$	124.377	0.0120143
$476$	1170.62	0.112722
$477$	1079.11	0.103583
$478$	−8685.44	−0.831093
$479$	−12044.8	−1.14894	−0.574468	−	0.818527i	$-0.694791\pi$
$479$	−12044.8	−1.14894	−0.574468	+	0.818527i	$0.694791\pi$
$480$	941.655	0.0895426
$481$	0	0
$482$	986.928	0.0932642
$483$	−1154.80	−0.108789
$484$	−3774.38	−0.354468
$485$	5874.98	0.550039
$486$	486.000	0.0453609
$487$	−9695.94	−0.902187	−0.451093	−	0.892477i	$-0.648966\pi$
$487$	−9695.94	−0.902187	−0.451093	+	0.892477i	$0.648966\pi$
$488$	5572.89	0.516953
$489$	8333.43	0.770656
$490$	−4145.15	−0.382161
$491$	6776.62	0.622861	0.311431	−	0.950269i	$-0.399192\pi$
$491$	6776.62	0.622861	0.311431	+	0.950269i	$0.399192\pi$
$492$	−1707.22	−0.156438
$493$	2979.48	0.272189
$494$	0	0
$495$	1737.59	0.157775
$496$	4613.61	0.417655
$497$	6175.05	0.557322
$498$	−6964.74	−0.626702
$499$	7886.70	0.707530	0.353765	−	0.935334i	$-0.384901\pi$
$499$	7886.70	0.707530	0.353765	+	0.935334i	$0.384901\pi$
$500$	−6033.87	−0.539685
$501$	−11322.0	−1.00964
$502$	−2232.15	−0.198458
$503$	−22143.4	−1.96288	−0.981439	−	0.191775i	$-0.938576\pi$
$503$	−22143.4	−1.96288	−0.981439	+	0.191775i	$0.938576\pi$
$504$	826.291	0.0730276
$505$	17352.7	1.52908
$506$	−1320.37	−0.116003
$507$	0	0
$508$	−9039.34	−0.789480
$509$	−11807.8	−1.02823	−0.514116	−	0.857720i	$-0.671880\pi$
$509$	−11807.8	−1.02823	−0.514116	+	0.857720i	$0.671880\pi$
$510$	1500.82	0.130309
$511$	−13941.6	−1.20693
$512$	512.000	0.0441942
$513$	−116.662	−0.0100405
$514$	5997.31	0.514650
$515$	9546.51	0.816834
$516$	−2746.45	−0.234313
$517$	−11784.6	−1.00248
$518$	2863.27	0.242866
$519$	−5078.70	−0.429538
$520$	0	0
$521$	5614.28	0.472104	0.236052	−	0.971740i	$-0.424147\pi$
$521$	5614.28	0.472104	0.236052	+	0.971740i	$0.424147\pi$
$522$	2103.08	0.176340
$523$	8738.77	0.730630	0.365315	−	0.930884i	$-0.380961\pi$
$523$	8738.77	0.730630	0.365315	+	0.930884i	$0.380961\pi$
$524$	6461.94	0.538723
$525$	−991.047	−0.0823864
$526$	4468.18	0.370384
$527$	7353.22	0.607802
$528$	944.766	0.0778706
$529$	−11042.0	−0.907534
$530$	2352.20	0.192780
$531$	4498.93	0.367678
$532$	−198.348	−0.0161644
$533$	0	0
$534$	−4356.17	−0.353015
$535$	−12929.4	−1.04484
$536$	−542.851	−0.0437455
$537$	−1101.15	−0.0884885
$538$	−2952.77	−0.236623
$539$	−4158.85	−0.332346
$540$	1059.36	0.0844216
$541$	−10863.1	−0.863291	−0.431645	−	0.902043i	$-0.642067\pi$
$541$	−10863.1	−0.863291	−0.431645	+	0.902043i	$0.642067\pi$
$542$	4147.74	0.328710
$543$	2998.94	0.237011
$544$	816.032	0.0643145
$545$	3191.32	0.250828
$546$	0	0
$547$	−12943.4	−1.01174	−0.505868	−	0.862611i	$-0.668828\pi$
$547$	−12943.4	−1.01174	−0.505868	+	0.862611i	$0.668828\pi$
$548$	1557.61	0.121420
$549$	6269.51	0.487388
$550$	−1133.15	−0.0878500
$551$	−504.837	−0.0390322
$552$	−804.998	−0.0620706
$553$	3965.66	0.304950
$554$	−771.268	−0.0591481
$555$	3670.90	0.280759
$556$	6909.48	0.527027
$557$	17075.0	1.29891	0.649453	−	0.760402i	$-0.274998\pi$
$557$	17075.0	1.29891	0.649453	+	0.760402i	$0.274998\pi$
$558$	5190.31	0.393769
$559$	0	0
$560$	1801.11	0.135912
$561$	1505.78	0.113323
$562$	−101.821	−0.00764247
$563$	4614.20	0.345409	0.172704	−	0.984974i	$-0.444749\pi$
$563$	4614.20	0.345409	0.172704	+	0.984974i	$0.444749\pi$
$564$	−7184.75	−0.536405
$565$	7184.87	0.534991
$566$	−14158.1	−1.05143
$567$	929.577	0.0688511
$568$	4304.57	0.317986
$569$	18131.4	1.33586	0.667932	−	0.744222i	$-0.267180\pi$
$569$	18131.4	1.33586	0.667932	+	0.744222i	$0.267180\pi$
$570$	−254.295	−0.0186864
$571$	1526.19	0.111855	0.0559274	−	0.998435i	$-0.482188\pi$
$571$	1526.19	0.111855	0.0559274	+	0.998435i	$0.482188\pi$
$572$	0	0
$573$	4687.03	0.341716
$574$	−3265.41	−0.237449
$575$	965.508	0.0700252
$576$	576.000	0.0416667
$577$	−23094.3	−1.66625	−0.833127	−	0.553082i	$-0.813452\pi$
$577$	−23094.3	−1.66625	−0.833127	+	0.553082i	$0.813452\pi$
$578$	−8525.40	−0.613512
$579$	−13968.7	−1.00263
$580$	4584.21	0.328188
$581$	−13321.5	−0.951240
$582$	3593.66	0.255949
$583$	2359.98	0.167651
$584$	−9718.59	−0.688627
$585$	0	0
$586$	−14849.7	−1.04682
$587$	22084.0	1.55282	0.776410	−	0.630228i	$-0.217039\pi$
$587$	22084.0	1.55282	0.776410	+	0.630228i	$0.217039\pi$
$588$	−2535.54	−0.177830
$589$	−1245.91	−0.0871594
$590$	9806.58	0.684289
$591$	3544.23	0.246684
$592$	1995.96	0.138570
$593$	−4484.19	−0.310529	−0.155265	−	0.987873i	$-0.549623\pi$
$593$	−4484.19	−0.310529	−0.155265	+	0.987873i	$0.549623\pi$
$594$	1062.86	0.0734171
$595$	2870.64	0.197789
$596$	1114.38	0.0765883
$597$	10024.3	0.687217
$598$	0	0
$599$	12402.2	0.845978	0.422989	−	0.906135i	$-0.360981\pi$
$599$	12402.2	0.845978	0.422989	+	0.906135i	$0.360981\pi$
$600$	−690.850	−0.0470064
$601$	−25204.8	−1.71069	−0.855344	−	0.518060i	$-0.826655\pi$
$601$	−25204.8	−1.71069	−0.855344	+	0.518060i	$0.826655\pi$
$602$	−5253.16	−0.355653
$603$	−610.708	−0.0412437
$604$	−3105.97	−0.209239
$605$	−9255.62	−0.621974
$606$	10614.5	0.711525
$607$	−1715.02	−0.114680	−0.0573399	−	0.998355i	$-0.518262\pi$
$607$	−1715.02	−0.114680	−0.0573399	+	0.998355i	$0.518262\pi$
$608$	−138.266	−0.00922277
$609$	4022.59	0.267658
$610$	13666.0	0.907082
$611$	0	0
$612$	918.036	0.0606363
$613$	11803.0	0.777679	0.388840	−	0.921305i	$-0.372876\pi$
$613$	11803.0	0.777679	0.388840	+	0.921305i	$0.372876\pi$
$614$	−3026.16	−0.198902
$615$	−4186.48	−0.274497
$616$	1807.06	0.118196
$617$	−4891.04	−0.319134	−0.159567	−	0.987187i	$-0.551010\pi$
$617$	−4891.04	−0.319134	−0.159567	+	0.987187i	$0.551010\pi$
$618$	5839.49	0.380095
$619$	−11692.6	−0.759235	−0.379618	−	0.925144i	$-0.623944\pi$
$619$	−11692.6	−0.759235	−0.379618	+	0.925144i	$0.623944\pi$
$620$	11313.6	0.732847
$621$	−905.622	−0.0585207
$622$	8244.28	0.531456
$623$	−8332.10	−0.535824
$624$	0	0
$625$	−11198.2	−0.716686
$626$	−18179.3	−1.16069
$627$	−255.136	−0.0162506
$628$	1594.42	0.101313
$629$	3181.18	0.201657
$630$	2026.25	0.128139
$631$	1559.27	0.0983731	0.0491866	−	0.998790i	$-0.484337\pi$
$631$	1559.27	0.0983731	0.0491866	+	0.998790i	$0.484337\pi$
$632$	2764.43	0.173992
$633$	4185.24	0.262794
$634$	−11196.2	−0.701354
$635$	−22166.5	−1.38528
$636$	1438.82	0.0897057
$637$	0	0
$638$	4599.36	0.285408
$639$	4842.65	0.299800
$640$	1255.54	0.0775462
$641$	15946.8	0.982621	0.491310	−	0.870985i	$-0.336518\pi$
$641$	15946.8	0.982621	0.491310	+	0.870985i	$0.336518\pi$
$642$	−7908.78	−0.486191
$643$	−24409.1	−1.49705	−0.748524	−	0.663108i	$-0.769237\pi$
$643$	−24409.1	−1.49705	−0.748524	+	0.663108i	$0.769237\pi$
$644$	−1539.73	−0.0942139
$645$	−6734.91	−0.411142
$646$	−220.371	−0.0134216
$647$	−17248.1	−1.04805	−0.524027	−	0.851701i	$-0.675571\pi$
$647$	−17248.1	−1.04805	−0.524027	+	0.851701i	$0.675571\pi$
$648$	648.000	0.0392837
$649$	9838.98	0.595091
$650$	0	0
$651$	9927.56	0.597683
$652$	11111.2	0.667408
$653$	31685.0	1.89882	0.949410	−	0.314039i	$-0.101682\pi$
$653$	31685.0	1.89882	0.949410	+	0.314039i	$0.101682\pi$
$654$	1952.09	0.116717
$655$	15846.1	0.945282
$656$	−2276.29	−0.135479
$657$	−10933.4	−0.649244
$658$	−13742.3	−0.814183
$659$	−43.1572	−0.00255109	−0.00127554	−	0.999999i	$-0.500406\pi$
$659$	−43.1572	−0.00255109	−0.00127554	+	0.999999i	$0.500406\pi$
$660$	2316.78	0.136637
$661$	−1356.07	−0.0797960	−0.0398980	−	0.999204i	$-0.512703\pi$
$661$	−1356.07	−0.0797960	−0.0398980	+	0.999204i	$0.512703\pi$
$662$	−8751.21	−0.513785
$663$	0	0
$664$	−9286.33	−0.542740
$665$	−486.393	−0.0283632
$666$	2245.45	0.130645
$667$	−3918.93	−0.227499
$668$	−15096.0	−0.874374
$669$	−10533.9	−0.608766
$670$	−1331.19	−0.0767590
$671$	13711.2	0.788843
$672$	1101.72	0.0632438
$673$	−7091.49	−0.406177	−0.203088	−	0.979160i	$-0.565098\pi$
$673$	−7091.49	−0.406177	−0.203088	+	0.979160i	$0.565098\pi$
$674$	−19860.8	−1.13503
$675$	−777.206	−0.0443180
$676$	0	0
$677$	2245.58	0.127481	0.0637405	−	0.997967i	$-0.479697\pi$
$677$	2245.58	0.127481	0.0637405	+	0.997967i	$0.479697\pi$
$678$	4394.91	0.248946
$679$	6873.64	0.388492
$680$	2001.09	0.112851
$681$	−1770.89	−0.0996486
$682$	11351.0	0.637320
$683$	8548.77	0.478931	0.239465	−	0.970905i	$-0.423028\pi$
$683$	8548.77	0.478931	0.239465	+	0.970905i	$0.423028\pi$
$684$	−155.550	−0.00869531
$685$	3819.62	0.213051
$686$	−12722.5	−0.708085
$687$	−10298.9	−0.571949
$688$	−3661.93	−0.202921
$689$	0	0
$690$	−1974.04	−0.108913
$691$	6392.96	0.351953	0.175977	−	0.984394i	$-0.443692\pi$
$691$	6392.96	0.351953	0.175977	+	0.984394i	$0.443692\pi$
$692$	−6771.60	−0.371991
$693$	2032.95	0.111436
$694$	−5054.08	−0.276441
$695$	16943.6	0.924759
$696$	2804.11	0.152715
$697$	−3627.98	−0.197159
$698$	18954.8	1.02786
$699$	16128.0	0.872699
$700$	−1321.40	−0.0713487
$701$	22777.7	1.22725	0.613625	−	0.789597i	$-0.289711\pi$
$701$	22777.7	1.22725	0.613625	+	0.789597i	$0.289711\pi$
$702$	0	0
$703$	−539.011	−0.0289178
$704$	1259.69	0.0674379
$705$	−17618.6	−0.941214
$706$	9781.42	0.521429
$707$	20302.4	1.07999
$708$	5998.58	0.318419
$709$	−35220.3	−1.86562	−0.932812	−	0.360365i	$-0.882652\pi$
$709$	−35220.3	−1.86562	−0.932812	+	0.360365i	$0.882652\pi$
$710$	10555.8	0.557960
$711$	3109.98	0.164041
$712$	−5808.23	−0.305720
$713$	−9671.73	−0.508007
$714$	1755.94	0.0920368
$715$	0	0
$716$	−1468.21	−0.0766333
$717$	−13028.2	−0.678585
$718$	13501.5	0.701769
$719$	25790.8	1.33774	0.668869	−	0.743381i	$-0.266779\pi$
$719$	25790.8	1.33774	0.668869	+	0.743381i	$0.266779\pi$
$720$	1412.48	0.0731112
$721$	11169.3	0.576928
$722$	−13680.7	−0.705182
$723$	1480.39	0.0761499
$724$	3998.59	0.205258
$725$	−3363.23	−0.172286
$726$	−5661.56	−0.289422
$727$	12236.4	0.624239	0.312119	−	0.950043i	$-0.398961\pi$
$727$	12236.4	0.624239	0.312119	+	0.950043i	$0.398961\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	−23832.2	−1.20831
$731$	−5836.43	−0.295305
$732$	8359.34	0.422090
$733$	6703.90	0.337809	0.168905	−	0.985632i	$-0.445977\pi$
$733$	6703.90	0.337809	0.168905	+	0.985632i	$0.445977\pi$
$734$	−2452.44	−0.123326
$735$	−6217.73	−0.312033
$736$	−1073.33	−0.0537547
$737$	−1335.59	−0.0667533
$738$	−2560.83	−0.127731
$739$	−6779.55	−0.337469	−0.168735	−	0.985662i	$-0.553968\pi$
$739$	−6779.55	−0.337469	−0.168735	+	0.985662i	$0.553968\pi$
$740$	4894.54	0.243144
$741$	0	0
$742$	2752.04	0.136160
$743$	25938.1	1.28072	0.640361	−	0.768074i	$-0.278785\pi$
$743$	25938.1	1.28072	0.640361	+	0.768074i	$0.278785\pi$
$744$	6920.41	0.341014
$745$	2732.70	0.134387
$746$	20296.0	0.996100
$747$	−10447.1	−0.511700
$748$	2007.71	0.0981404
$749$	−15127.2	−0.737965
$750$	−9050.80	−0.440651
$751$	−35204.5	−1.71056	−0.855279	−	0.518168i	$-0.826614\pi$
$751$	−35204.5	−1.71056	−0.855279	+	0.518168i	$0.826614\pi$
$752$	−9579.66	−0.464540
$753$	−3348.22	−0.162040
$754$	0	0
$755$	−7616.54	−0.367145
$756$	1239.44	0.0596268
$757$	−23447.7	−1.12579	−0.562895	−	0.826529i	$-0.690312\pi$
$757$	−23447.7	−1.12579	−0.562895	+	0.826529i	$0.690312\pi$
$758$	−19714.5	−0.944676
$759$	−1980.56	−0.0947164
$760$	−339.060	−0.0161829
$761$	25158.2	1.19840	0.599200	−	0.800599i	$-0.295485\pi$
$761$	25158.2	1.19840	0.599200	+	0.800599i	$0.295485\pi$
$762$	−13559.0	−0.644608
$763$	3733.79	0.177159
$764$	6249.37	0.295935
$765$	2251.23	0.106397
$766$	13522.9	0.637860
$767$	0	0
$768$	768.000	0.0360844
$769$	3708.37	0.173898	0.0869488	−	0.996213i	$-0.472288\pi$
$769$	3708.37	0.173898	0.0869488	+	0.996213i	$0.472288\pi$
$770$	4431.33	0.207395
$771$	8995.97	0.420210
$772$	−18625.0	−0.868301
$773$	3567.51	0.165995	0.0829976	−	0.996550i	$-0.473551\pi$
$773$	3567.51	0.165995	0.0829976	+	0.996550i	$0.473551\pi$
$774$	−4119.67	−0.191316
$775$	−8300.29	−0.384716
$776$	4791.55	0.221658
$777$	4294.90	0.198299
$778$	−27121.5	−1.24981
$779$	614.716	0.0282728
$780$	0	0
$781$	10590.7	0.485229
$782$	−1710.69	−0.0782277
$783$	3154.63	0.143981
$784$	−3380.73	−0.154005
$785$	3909.88	0.177770
$786$	9692.91	0.439866
$787$	34978.8	1.58432	0.792160	−	0.610313i	$-0.208956\pi$
$787$	34978.8	1.58432	0.792160	+	0.610313i	$0.208956\pi$
$788$	4725.64	0.213634
$789$	6702.27	0.302417
$790$	6779.00	0.305299
$791$	8406.19	0.377863
$792$	1417.15	0.0635811
$793$	0	0
$794$	16308.8	0.728940
$795$	3528.31	0.157404
$796$	13365.8	0.595147
$797$	27780.2	1.23466	0.617330	−	0.786704i	$-0.288214\pi$
$797$	27780.2	1.23466	0.617330	+	0.786704i	$0.288214\pi$
$798$	−297.522	−0.0131982
$799$	−15268.2	−0.676032
$800$	−921.133	−0.0407087
$801$	−6534.26	−0.288236
$802$	1641.92	0.0722920
$803$	−23910.9	−1.05081
$804$	−814.277	−0.0357181
$805$	−3775.76	−0.165314
$806$	0	0
$807$	−4429.15	−0.193202
$808$	14152.7	0.616199
$809$	−19900.8	−0.864865	−0.432433	−	0.901666i	$-0.642345\pi$
$809$	−19900.8	−0.864865	−0.432433	+	0.901666i	$0.642345\pi$
$810$	1589.04	0.0689299
$811$	43420.9	1.88004	0.940022	−	0.341114i	$-0.110804\pi$
$811$	43420.9	1.88004	0.940022	+	0.341114i	$0.110804\pi$
$812$	5363.45	0.231798
$813$	6221.61	0.268390
$814$	4910.71	0.211450
$815$	27247.3	1.17108
$816$	1224.05	0.0525125
$817$	988.910	0.0423471
$818$	−9197.91	−0.393151
$819$	0	0
$820$	−5581.98	−0.237721
$821$	20320.2	0.863799	0.431899	−	0.901922i	$-0.357844\pi$
$821$	20320.2	0.863799	0.431899	+	0.901922i	$0.357844\pi$
$822$	2336.42	0.0991387
$823$	31446.2	1.33189	0.665944	−	0.746002i	$-0.268029\pi$
$823$	31446.2	1.33189	0.665944	+	0.746002i	$0.268029\pi$
$824$	7785.99	0.329172
$825$	−1699.72	−0.0717292
$826$	11473.5	0.483312
$827$	18625.1	0.783143	0.391572	−	0.920148i	$-0.371932\pi$
$827$	18625.1	0.783143	0.391572	+	0.920148i	$0.371932\pi$
$828$	−1207.50	−0.0506804
$829$	27595.2	1.15612	0.578058	−	0.815996i	$-0.303811\pi$
$829$	27595.2	1.15612	0.578058	+	0.815996i	$0.303811\pi$
$830$	−22772.2	−0.952330
$831$	−1156.90	−0.0482942
$832$	0	0
$833$	−5388.24	−0.224119
$834$	10364.2	0.430316
$835$	−37018.8	−1.53424
$836$	−340.181	−0.0140734
$837$	7785.46	0.321511
$838$	20548.6	0.847064
$839$	34829.9	1.43321	0.716605	−	0.697479i	$-0.245695\pi$
$839$	34829.9	1.43321	0.716605	+	0.697479i	$0.245695\pi$
$840$	2701.67	0.110972
$841$	−10737.9	−0.440276
$842$	−25460.3	−1.04207
$843$	−152.732	−0.00624005
$844$	5580.32	0.227586
$845$	0	0
$846$	−10777.1	−0.437973
$847$	−10828.9	−0.439299
$848$	1918.42	0.0776874
$849$	−21237.2	−0.858489
$850$	−1468.11	−0.0592422
$851$	−4184.22	−0.168547
$852$	6456.86	0.259634
$853$	−35675.7	−1.43202	−0.716010	−	0.698090i	$-0.754034\pi$
$853$	−35675.7	−1.43202	−0.716010	+	0.698090i	$0.754034\pi$
$854$	15989.0	0.640670
$855$	−381.443	−0.0152574
$856$	−10545.0	−0.421054
$857$	48343.4	1.92693	0.963465	−	0.267833i	$-0.0863076\pi$
$857$	48343.4	1.92693	0.963465	+	0.267833i	$0.0863076\pi$
$858$	0	0
$859$	34409.4	1.36674	0.683372	−	0.730070i	$-0.260513\pi$
$859$	34409.4	1.36674	0.683372	+	0.730070i	$0.260513\pi$
$860$	−8979.88	−0.356060
$861$	−4898.12	−0.193876
$862$	−1920.66	−0.0758909
$863$	7065.25	0.278684	0.139342	−	0.990244i	$-0.455501\pi$
$863$	7065.25	0.278684	0.139342	+	0.990244i	$0.455501\pi$
$864$	864.000	0.0340207
$865$	−16605.5	−0.652721
$866$	−27601.8	−1.08308
$867$	−12788.1	−0.500930
$868$	13236.7	0.517609
$869$	6801.40	0.265503
$870$	6876.32	0.267964
$871$	0	0
$872$	2602.79	0.101080
$873$	5390.49	0.208981
$874$	289.855	0.0112179
$875$	−17311.6	−0.668843
$876$	−14577.9	−0.562262
$877$	−18998.8	−0.731521	−0.365760	−	0.930709i	$-0.619191\pi$
$877$	−18998.8	−0.731521	−0.365760	+	0.930709i	$0.619191\pi$
$878$	−11864.7	−0.456054
$879$	−22274.6	−0.854726
$880$	3089.04	0.118331
$881$	12897.2	0.493211	0.246605	−	0.969116i	$-0.420685\pi$
$881$	12897.2	0.493211	0.246605	+	0.969116i	$0.420685\pi$
$882$	−3803.32	−0.145198
$883$	−2504.93	−0.0954672	−0.0477336	−	0.998860i	$-0.515200\pi$
$883$	−2504.93	−0.0954672	−0.0477336	+	0.998860i	$0.515200\pi$
$884$	0	0
$885$	14709.9	0.558719
$886$	−6328.22	−0.239956
$887$	11715.5	0.443481	0.221740	−	0.975106i	$-0.428826\pi$
$887$	11715.5	0.443481	0.221740	+	0.975106i	$0.428826\pi$
$888$	2993.94	0.113142
$889$	−25934.5	−0.978418
$890$	−14243.1	−0.536438
$891$	1594.29	0.0599448
$892$	−14045.2	−0.527207
$893$	2587.00	0.0969438
$894$	1671.56	0.0625340
$895$	−3600.37	−0.134466
$896$	1468.96	0.0547707
$897$	0	0
$898$	8080.44	0.300276
$899$	33690.3	1.24987
$900$	−1036.27	−0.0383806
$901$	3057.61	0.113056
$902$	−5600.43	−0.206734
$903$	−7879.74	−0.290389
$904$	5859.88	0.215594
$905$	9805.45	0.360159
$906$	−4658.96	−0.170843
$907$	32397.6	1.18605	0.593023	−	0.805185i	$-0.297934\pi$
$907$	32397.6	1.18605	0.593023	+	0.805185i	$0.297934\pi$
$908$	−2361.19	−0.0862982
$909$	15921.7	0.580958
$910$	0	0
$911$	6809.26	0.247641	0.123820	−	0.992305i	$-0.460485\pi$
$911$	6809.26	0.247641	0.123820	+	0.992305i	$0.460485\pi$
$912$	−207.400	−0.00753036
$913$	−22847.4	−0.828192
$914$	−21404.7	−0.774621
$915$	20499.0	0.740629
$916$	−13731.9	−0.495322
$917$	18539.7	0.667651
$918$	1377.05	0.0495093
$919$	50361.8	1.80771	0.903854	−	0.427841i	$-0.140726\pi$
$919$	50361.8	1.80771	0.903854	+	0.427841i	$0.140726\pi$
$920$	−2632.05	−0.0943218
$921$	−4539.24	−0.162403
$922$	12602.8	0.450163
$923$	0	0
$924$	2710.60	0.0965066
$925$	−3590.90	−0.127641
$926$	24866.4	0.882462
$927$	8759.24	0.310347
$928$	3738.82	0.132255
$929$	3689.36	0.130295	0.0651475	−	0.997876i	$-0.479248\pi$
$929$	3689.36	0.130295	0.0651475	+	0.997876i	$0.479248\pi$
$930$	16970.4	0.598367
$931$	912.970	0.0321390
$932$	21504.0	0.755780
$933$	12366.4	0.433932
$934$	−32310.0	−1.13192
$935$	4923.35	0.172204
$936$	0	0
$937$	43698.7	1.52356	0.761779	−	0.647837i	$-0.224326\pi$
$937$	43698.7	1.52356	0.761779	+	0.647837i	$0.224326\pi$
$938$	−1557.48	−0.0542147
$939$	−27268.9	−0.947697
$940$	−23491.5	−0.815115
$941$	−7298.16	−0.252830	−0.126415	−	0.991977i	$-0.540347\pi$
$941$	−7298.16	−0.252830	−0.126415	+	0.991977i	$0.540347\pi$
$942$	2391.63	0.0827214
$943$	4771.90	0.164787
$944$	7998.10	0.275759
$945$	3039.38	0.104625
$946$	−9009.56	−0.309647
$947$	12875.6	0.441818	0.220909	−	0.975294i	$-0.429098\pi$
$947$	12875.6	0.441818	0.220909	+	0.975294i	$0.429098\pi$
$948$	4146.64	0.142064
$949$	0	0
$950$	248.754	0.00849540
$951$	−16794.3	−0.572653
$952$	2341.25	0.0797062
$953$	−34020.0	−1.15636	−0.578182	−	0.815908i	$-0.696238\pi$
$953$	−34020.0	−1.15636	−0.578182	+	0.815908i	$0.696238\pi$
$954$	2158.23	0.0732444
$955$	15324.9	0.519268
$956$	−17370.9	−0.587672
$957$	6899.04	0.233035
$958$	−24089.6	−0.812421
$959$	4468.90	0.150478
$960$	1883.31	0.0633162
$961$	53355.0	1.79098
$962$	0	0
$963$	−11863.2	−0.396973
$964$	1973.86	0.0659477
$965$	−45672.7	−1.52358
$966$	−2309.59	−0.0769253
$967$	26847.5	0.892820	0.446410	−	0.894829i	$-0.352702\pi$
$967$	26847.5	0.892820	0.446410	+	0.894829i	$0.352702\pi$
$968$	−7548.75	−0.250647
$969$	−330.556	−0.0109587
$970$	11750.0	0.388937
$971$	−30144.5	−0.996275	−0.498138	−	0.867098i	$-0.665983\pi$
$971$	−30144.5	−0.996275	−0.498138	+	0.867098i	$0.665983\pi$
$972$	972.000	0.0320750
$973$	19823.7	0.653155
$974$	−19391.9	−0.637942
$975$	0	0
$976$	11145.8	0.365541
$977$	2834.23	0.0928097	0.0464049	−	0.998923i	$-0.485224\pi$
$977$	2834.23	0.0928097	0.0464049	+	0.998923i	$0.485224\pi$
$978$	16666.9	0.544936
$979$	−14290.2	−0.466512
$980$	−8290.30	−0.270229
$981$	2928.14	0.0952991
$982$	13553.2	0.440429
$983$	−15556.3	−0.504749	−0.252374	−	0.967630i	$-0.581211\pi$
$983$	−15556.3	−0.504749	−0.252374	+	0.967630i	$0.581211\pi$
$984$	−3414.44	−0.110618
$985$	11588.3	0.374858
$986$	5958.97	0.192467
$987$	−20613.5	−0.664778
$988$	0	0
$989$	7676.68	0.246819
$990$	3475.17	0.111564
$991$	19781.4	0.634084	0.317042	−	0.948412i	$-0.397310\pi$
$991$	19781.4	0.634084	0.317042	+	0.948412i	$0.397310\pi$
$992$	9227.22	0.295327
$993$	−13126.8	−0.419503
$994$	12350.1	0.394086
$995$	32775.9	1.04429
$996$	−13929.5	−0.443145
$997$	20397.3	0.647932	0.323966	−	0.946069i	$-0.394984\pi$
$997$	20397.3	0.647932	0.323966	+	0.946069i	$0.394984\pi$
$998$	15773.4	0.500299
$999$	3368.18	0.106671

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.4.a.be.1.4	yes	6
13.5	odd	4		1014.4.b.q.337.3		12
13.8	odd	4		1014.4.b.q.337.10		12
13.12	even	2		1014.4.a.bc.1.3	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1014.4.a.bc.1.3	✓	6	13.12	even	2
1014.4.a.be.1.4	yes	6	1.1	even	1	trivial
1014.4.b.q.337.3		12	13.5	odd	4
1014.4.b.q.337.10		12	13.8	odd	4

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:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1014.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +9.80890 q^{5} +6.00000 q^{6} +11.4763 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +9.80890 q^{5} +6.00000 q^{6} +11.4763 q^{7} +8.00000 q^{8} +9.00000 q^{9} +19.6178 q^{10} +19.6826 q^{11} +12.0000 q^{12} +22.9525 q^{14} +29.4267 q^{15} +16.0000 q^{16} +25.5010 q^{17} +18.0000 q^{18} -4.32083 q^{19} +39.2356 q^{20} +34.4288 q^{21} +39.3653 q^{22} -33.5416 q^{23} +24.0000 q^{24} -28.7854 q^{25} +27.0000 q^{27} +45.9051 q^{28} +116.838 q^{29} +58.8534 q^{30} +288.350 q^{31} +32.0000 q^{32} +59.0479 q^{33} +51.0020 q^{34} +112.570 q^{35} +36.0000 q^{36} +124.747 q^{37} -8.64165 q^{38} +78.4712 q^{40} -142.268 q^{41} +68.8576 q^{42} -228.871 q^{43} +78.7305 q^{44} +88.2801 q^{45} -67.0831 q^{46} -598.729 q^{47} +48.0000 q^{48} -211.295 q^{49} -57.5708 q^{50} +76.5030 q^{51} +119.901 q^{53} +54.0000 q^{54} +193.065 q^{55} +91.8101 q^{56} -12.9625 q^{57} +233.676 q^{58} +499.881 q^{59} +117.707 q^{60} +696.612 q^{61} +576.701 q^{62} +103.286 q^{63} +64.0000 q^{64} +118.096 q^{66} -67.8564 q^{67} +102.004 q^{68} -100.625 q^{69} +225.139 q^{70} +538.072 q^{71} +72.0000 q^{72} -1214.82 q^{73} +249.495 q^{74} -86.3562 q^{75} -17.2833 q^{76} +225.883 q^{77} +345.554 q^{79} +156.942 q^{80} +81.0000 q^{81} -284.536 q^{82} -1160.79 q^{83} +137.715 q^{84} +250.137 q^{85} -457.741 q^{86} +350.514 q^{87} +157.461 q^{88} -726.029 q^{89} +176.560 q^{90} -134.166 q^{92} +865.051 q^{93} -1197.46 q^{94} -42.3826 q^{95} +96.0000 q^{96} +598.944 q^{97} -422.591 q^{98} +177.144 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 12 q^{2} + 18 q^{3} + 24 q^{4} - 3 q^{5} + 36 q^{6} - q^{7} + 48 q^{8} + 54 q^{9}+O(q^{10}) \) 6 * q + 12 * q^2 + 18 * q^3 + 24 * q^4 - 3 * q^5 + 36 * q^6 - q^7 + 48 * q^8 + 54 * q^9	\( 6 q + 12 q^{2} + 18 q^{3} + 24 q^{4} - 3 q^{5} + 36 q^{6} - q^{7} + 48 q^{8} + 54 q^{9} - 6 q^{10} + 64 q^{11} + 72 q^{12} - 2 q^{14} - 9 q^{15} + 96 q^{16} + 51 q^{17} + 108 q^{18} + 213 q^{19} - 12 q^{20} - 3 q^{21} + 128 q^{22} + 222 q^{23} + 144 q^{24} + 185 q^{25} + 162 q^{27} - 4 q^{28} + 329 q^{29} - 18 q^{30} + 289 q^{31} + 192 q^{32} + 192 q^{33} + 102 q^{34} + 844 q^{35} + 216 q^{36} + 470 q^{37} + 426 q^{38} - 24 q^{40} - 321 q^{41} - 6 q^{42} + 491 q^{43} + 256 q^{44} - 27 q^{45} + 444 q^{46} - 641 q^{47} + 288 q^{48} + 1133 q^{49} + 370 q^{50} + 153 q^{51} + 2302 q^{53} + 324 q^{54} - 329 q^{55} - 8 q^{56} + 639 q^{57} + 658 q^{58} - 139 q^{59} - 36 q^{60} + 345 q^{61} + 578 q^{62} - 9 q^{63} + 384 q^{64} + 384 q^{66} + 855 q^{67} + 204 q^{68} + 666 q^{69} + 1688 q^{70} - 1362 q^{71} + 432 q^{72} - 831 q^{73} + 940 q^{74} + 555 q^{75} + 852 q^{76} + 3291 q^{77} + 3100 q^{79} - 48 q^{80} + 486 q^{81} - 642 q^{82} + 447 q^{83} - 12 q^{84} + 847 q^{85} + 982 q^{86} + 987 q^{87} + 512 q^{88} - 1241 q^{89} - 54 q^{90} + 888 q^{92} + 867 q^{93} - 1282 q^{94} - 665 q^{95} + 576 q^{96} - 1554 q^{97} + 2266 q^{98} + 576 q^{99}+O(q^{100}) \) 6 * q + 12 * q^2 + 18 * q^3 + 24 * q^4 - 3 * q^5 + 36 * q^6 - q^7 + 48 * q^8 + 54 * q^9 - 6 * q^10 + 64 * q^11 + 72 * q^12 - 2 * q^14 - 9 * q^15 + 96 * q^16 + 51 * q^17 + 108 * q^18 + 213 * q^19 - 12 * q^20 - 3 * q^21 + 128 * q^22 + 222 * q^23 + 144 * q^24 + 185 * q^25 + 162 * q^27 - 4 * q^28 + 329 * q^29 - 18 * q^30 + 289 * q^31 + 192 * q^32 + 192 * q^33 + 102 * q^34 + 844 * q^35 + 216 * q^36 + 470 * q^37 + 426 * q^38 - 24 * q^40 - 321 * q^41 - 6 * q^42 + 491 * q^43 + 256 * q^44 - 27 * q^45 + 444 * q^46 - 641 * q^47 + 288 * q^48 + 1133 * q^49 + 370 * q^50 + 153 * q^51 + 2302 * q^53 + 324 * q^54 - 329 * q^55 - 8 * q^56 + 639 * q^57 + 658 * q^58 - 139 * q^59 - 36 * q^60 + 345 * q^61 + 578 * q^62 - 9 * q^63 + 384 * q^64 + 384 * q^66 + 855 * q^67 + 204 * q^68 + 666 * q^69 + 1688 * q^70 - 1362 * q^71 + 432 * q^72 - 831 * q^73 + 940 * q^74 + 555 * q^75 + 852 * q^76 + 3291 * q^77 + 3100 * q^79 - 48 * q^80 + 486 * q^81 - 642 * q^82 + 447 * q^83 - 12 * q^84 + 847 * q^85 + 982 * q^86 + 987 * q^87 + 512 * q^88 - 1241 * q^89 - 54 * q^90 + 888 * q^92 + 867 * q^93 - 1282 * q^94 - 665 * q^95 + 576 * q^96 - 1554 * q^97 + 2266 * q^98 + 576 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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