LMFDB - Embedded newform 6027.2.a.be.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6027,2,Mod(1,6027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6027, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("6027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6027 = 3 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6027.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:	$48.1258372982$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} - 11x^{8} + 56x^{7} + 26x^{6} - 266x^{5} + 52x^{4} + 526x^{3} - 255x^{2} - 372x + 239 $ x^10 - 4x^9 - 11x^8 + 56x^7 + 26x^6 - 266x^5 + 52x^4 + 526x^3 - 255x^2 - 372*x + 239
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$2.13183$ of defining polynomial
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.13183 q^{2} +1.00000 q^{3} +2.54468 q^{4} +2.36072 q^{5} +2.13183 q^{6} +1.16116 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.13183 q^{2} +1.00000 q^{3} +2.54468 q^{4} +2.36072 q^{5} +2.13183 q^{6} +1.16116 q^{8} +1.00000 q^{9} +5.03264 q^{10} +4.44436 q^{11} +2.54468 q^{12} -0.290057 q^{13} +2.36072 q^{15} -2.61397 q^{16} +1.80941 q^{17} +2.13183 q^{18} +4.99859 q^{19} +6.00727 q^{20} +9.47459 q^{22} -1.55849 q^{23} +1.16116 q^{24} +0.572989 q^{25} -0.618352 q^{26} +1.00000 q^{27} +8.05686 q^{29} +5.03264 q^{30} -9.92711 q^{31} -7.89484 q^{32} +4.44436 q^{33} +3.85735 q^{34} +2.54468 q^{36} +6.77139 q^{37} +10.6561 q^{38} -0.290057 q^{39} +2.74117 q^{40} +1.00000 q^{41} -6.70057 q^{43} +11.3095 q^{44} +2.36072 q^{45} -3.32244 q^{46} +0.0265330 q^{47} -2.61397 q^{48} +1.22151 q^{50} +1.80941 q^{51} -0.738103 q^{52} -2.59306 q^{53} +2.13183 q^{54} +10.4919 q^{55} +4.99859 q^{57} +17.1758 q^{58} -12.0597 q^{59} +6.00727 q^{60} +1.73842 q^{61} -21.1629 q^{62} -11.6025 q^{64} -0.684744 q^{65} +9.47459 q^{66} +13.8400 q^{67} +4.60437 q^{68} -1.55849 q^{69} -10.2484 q^{71} +1.16116 q^{72} -7.01139 q^{73} +14.4354 q^{74} +0.572989 q^{75} +12.7198 q^{76} -0.618352 q^{78} +14.8949 q^{79} -6.17084 q^{80} +1.00000 q^{81} +2.13183 q^{82} +6.61380 q^{83} +4.27151 q^{85} -14.2844 q^{86} +8.05686 q^{87} +5.16061 q^{88} -13.1333 q^{89} +5.03264 q^{90} -3.96587 q^{92} -9.92711 q^{93} +0.0565637 q^{94} +11.8003 q^{95} -7.89484 q^{96} -4.50954 q^{97} +4.44436 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} + 10 q^{3} + 18 q^{4} + 6 q^{5} + 4 q^{6} + 12 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 4 * q^2 + 10 * q^3 + 18 * q^4 + 6 * q^5 + 4 * q^6 + 12 * q^8 + 10 * q^9	$ 10 q + 4 q^{2} + 10 q^{3} + 18 q^{4} + 6 q^{5} + 4 q^{6} + 12 q^{8} + 10 q^{9} + 2 q^{10} - 2 q^{11} + 18 q^{12} + 6 q^{15} + 14 q^{16} + 8 q^{17} + 4 q^{18} + 6 q^{19} + 20 q^{20} + 2 q^{22} + 12 q^{24} + 10 q^{25} + 16 q^{26} + 10 q^{27} + 16 q^{29} + 2 q^{30} + 2 q^{31} + 38 q^{32} - 2 q^{33} - 4 q^{34} + 18 q^{36} + 24 q^{37} - 26 q^{38} + 40 q^{40} + 10 q^{41} + 8 q^{43} - 8 q^{44} + 6 q^{45} + 4 q^{46} - 8 q^{47} + 14 q^{48} + 44 q^{50} + 8 q^{51} - 30 q^{52} + 24 q^{53} + 4 q^{54} + 6 q^{57} - 14 q^{58} + 6 q^{59} + 20 q^{60} - 14 q^{61} - 2 q^{62} + 86 q^{64} + 28 q^{65} + 2 q^{66} + 26 q^{67} - 6 q^{68} + 14 q^{71} + 12 q^{72} - 36 q^{73} + 18 q^{74} + 10 q^{75} - 32 q^{76} + 16 q^{78} + 20 q^{79} + 70 q^{80} + 10 q^{81} + 4 q^{82} + 40 q^{83} + 24 q^{85} - 36 q^{86} + 16 q^{87} + 14 q^{88} + 2 q^{89} + 2 q^{90} + 8 q^{92} + 2 q^{93} - 54 q^{94} - 24 q^{95} + 38 q^{96} + 16 q^{97} - 2 q^{99}+O(q^{100}) $ 10 * q + 4 * q^2 + 10 * q^3 + 18 * q^4 + 6 * q^5 + 4 * q^6 + 12 * q^8 + 10 * q^9 + 2 * q^10 - 2 * q^11 + 18 * q^12 + 6 * q^15 + 14 * q^16 + 8 * q^17 + 4 * q^18 + 6 * q^19 + 20 * q^20 + 2 * q^22 + 12 * q^24 + 10 * q^25 + 16 * q^26 + 10 * q^27 + 16 * q^29 + 2 * q^30 + 2 * q^31 + 38 * q^32 - 2 * q^33 - 4 * q^34 + 18 * q^36 + 24 * q^37 - 26 * q^38 + 40 * q^40 + 10 * q^41 + 8 * q^43 - 8 * q^44 + 6 * q^45 + 4 * q^46 - 8 * q^47 + 14 * q^48 + 44 * q^50 + 8 * q^51 - 30 * q^52 + 24 * q^53 + 4 * q^54 + 6 * q^57 - 14 * q^58 + 6 * q^59 + 20 * q^60 - 14 * q^61 - 2 * q^62 + 86 * q^64 + 28 * q^65 + 2 * q^66 + 26 * q^67 - 6 * q^68 + 14 * q^71 + 12 * q^72 - 36 * q^73 + 18 * q^74 + 10 * q^75 - 32 * q^76 + 16 * q^78 + 20 * q^79 + 70 * q^80 + 10 * q^81 + 4 * q^82 + 40 * q^83 + 24 * q^85 - 36 * q^86 + 16 * q^87 + 14 * q^88 + 2 * q^89 + 2 * q^90 + 8 * q^92 + 2 * q^93 - 54 * q^94 - 24 * q^95 + 38 * q^96 + 16 * q^97 - 2 * 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 $

$2$	2.13183	1.50743	0.753714	−	0.657203i	$-0.228260\pi$
$2$	2.13183	1.50743	0.753714	+	0.657203i	$0.228260\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.54468	1.27234
$5$	2.36072	1.05575	0.527873	−	0.849324i	$-0.322990\pi$
$5$	2.36072	1.05575	0.527873	+	0.849324i	$0.322990\pi$
$6$	2.13183	0.870314
$7$	0	0
$7$	0	0
$8$	1.16116	0.410532
$9$	1.00000	0.333333
$10$	5.03264	1.59146
$11$	4.44436	1.34002	0.670012	−	0.742350i	$-0.266289\pi$
$11$	4.44436	1.34002	0.670012	+	0.742350i	$0.266289\pi$
$12$	2.54468	0.734586
$13$	−0.290057	−0.0804475	−0.0402237	−	0.999191i	$-0.512807\pi$
$13$	−0.290057	−0.0804475	−0.0402237	+	0.999191i	$0.512807\pi$
$14$	0	0
$15$	2.36072	0.609535
$16$	−2.61397	−0.653492
$17$	1.80941	0.438847	0.219423	−	0.975630i	$-0.429582\pi$
$17$	1.80941	0.438847	0.219423	+	0.975630i	$0.429582\pi$
$18$	2.13183	0.502476
$19$	4.99859	1.14675	0.573377	−	0.819291i	$-0.305633\pi$
$19$	4.99859	1.14675	0.573377	+	0.819291i	$0.305633\pi$
$20$	6.00727	1.34327
$21$	0	0
$22$	9.47459	2.01999
$23$	−1.55849	−0.324968	−0.162484	−	0.986711i	$-0.551951\pi$
$23$	−1.55849	−0.324968	−0.162484	+	0.986711i	$0.551951\pi$
$24$	1.16116	0.237021
$25$	0.572989	0.114598
$26$	−0.618352	−0.121269
$27$	1.00000	0.192450
$28$	0	0
$29$	8.05686	1.49612	0.748060	−	0.663631i	$-0.230985\pi$
$29$	8.05686	1.49612	0.748060	+	0.663631i	$0.230985\pi$
$30$	5.03264	0.918830
$31$	−9.92711	−1.78296	−0.891481	−	0.453058i	$-0.850333\pi$
$31$	−9.92711	−1.78296	−0.891481	+	0.453058i	$0.850333\pi$
$32$	−7.89484	−1.39562
$33$	4.44436	0.773663
$34$	3.85735	0.661530
$35$	0	0
$36$	2.54468	0.424113
$37$	6.77139	1.11321	0.556605	−	0.830777i	$-0.312104\pi$
$37$	6.77139	1.11321	0.556605	+	0.830777i	$0.312104\pi$
$38$	10.6561	1.72865
$39$	−0.290057	−0.0464464
$40$	2.74117	0.433417
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−6.70057	−1.02183	−0.510914	−	0.859632i	$-0.670693\pi$
$43$	−6.70057	−1.02183	−0.510914	+	0.859632i	$0.670693\pi$
$44$	11.3095	1.70497
$45$	2.36072	0.351915
$46$	−3.32244	−0.489866
$47$	0.0265330	0.00387024	0.00193512	−	0.999998i	$-0.499384\pi$
$47$	0.0265330	0.00387024	0.00193512	+	0.999998i	$0.499384\pi$
$48$	−2.61397	−0.377294
$49$	0	0
$50$	1.22151	0.172748
$51$	1.80941	0.253368
$52$	−0.738103	−0.102356
$53$	−2.59306	−0.356185	−0.178092	−	0.984014i	$-0.556993\pi$
$53$	−2.59306	−0.356185	−0.178092	+	0.984014i	$0.556993\pi$
$54$	2.13183	0.290105
$55$	10.4919	1.41472
$56$	0	0
$57$	4.99859	0.662079
$58$	17.1758	2.25529
$59$	−12.0597	−1.57004	−0.785020	−	0.619470i	$-0.787347\pi$
$59$	−12.0597	−1.57004	−0.785020	+	0.619470i	$0.787347\pi$
$60$	6.00727	0.775535
$61$	1.73842	0.222582	0.111291	−	0.993788i	$-0.464501\pi$
$61$	1.73842	0.222582	0.111291	+	0.993788i	$0.464501\pi$
$62$	−21.1629	−2.68769
$63$	0	0
$64$	−11.6025	−1.45031
$65$	−0.684744	−0.0849320
$66$	9.47459	1.16624
$67$	13.8400	1.69082	0.845412	−	0.534115i	$-0.179355\pi$
$67$	13.8400	1.69082	0.845412	+	0.534115i	$0.179355\pi$
$68$	4.60437	0.558362
$69$	−1.55849	−0.187621
$70$	0	0
$71$	−10.2484	−1.21626	−0.608131	−	0.793837i	$-0.708080\pi$
$71$	−10.2484	−1.21626	−0.608131	+	0.793837i	$0.708080\pi$
$72$	1.16116	0.136844
$73$	−7.01139	−0.820621	−0.410310	−	0.911946i	$-0.634580\pi$
$73$	−7.01139	−0.820621	−0.410310	+	0.911946i	$0.634580\pi$
$74$	14.4354	1.67808
$75$	0.572989	0.0661631
$76$	12.7198	1.45906
$77$	0	0
$78$	−0.618352	−0.0700146
$79$	14.8949	1.67580	0.837901	−	0.545822i	$-0.183783\pi$
$79$	14.8949	1.67580	0.837901	+	0.545822i	$0.183783\pi$
$80$	−6.17084	−0.689921
$81$	1.00000	0.111111
$82$	2.13183	0.235421
$83$	6.61380	0.725959	0.362979	−	0.931797i	$-0.381760\pi$
$83$	6.61380	0.725959	0.362979	+	0.931797i	$0.381760\pi$
$84$	0	0
$85$	4.27151	0.463310
$86$	−14.2844	−1.54033
$87$	8.05686	0.863786
$88$	5.16061	0.550123
$89$	−13.1333	−1.39213	−0.696066	−	0.717978i	$-0.745068\pi$
$89$	−13.1333	−1.39213	−0.696066	+	0.717978i	$0.745068\pi$
$90$	5.03264	0.530487
$91$	0	0
$92$	−3.96587	−0.413470
$93$	−9.92711	−1.02939
$94$	0.0565637	0.00583410
$95$	11.8003	1.21068
$96$	−7.89484	−0.805764
$97$	−4.50954	−0.457874	−0.228937	−	0.973441i	$-0.573525\pi$
$97$	−4.50954	−0.457874	−0.228937	+	0.973441i	$0.573525\pi$
$98$	0	0
$99$	4.44436	0.446675
$100$	1.45807	0.145807
$101$	14.8611	1.47873	0.739366	−	0.673304i	$-0.235125\pi$
$101$	14.8611	1.47873	0.739366	+	0.673304i	$0.235125\pi$
$102$	3.85735	0.381934
$103$	−2.74435	−0.270409	−0.135205	−	0.990818i	$-0.543169\pi$
$103$	−2.74435	−0.270409	−0.135205	+	0.990818i	$0.543169\pi$
$104$	−0.336803	−0.0330263
$105$	0	0
$106$	−5.52796	−0.536923
$107$	3.07941	0.297698	0.148849	−	0.988860i	$-0.452443\pi$
$107$	3.07941	0.297698	0.148849	+	0.988860i	$0.452443\pi$
$108$	2.54468	0.244862
$109$	−10.8608	−1.04027	−0.520137	−	0.854083i	$-0.674119\pi$
$109$	−10.8608	−1.04027	−0.520137	+	0.854083i	$0.674119\pi$
$110$	22.3668	2.13259
$111$	6.77139	0.642712
$112$	0	0
$113$	5.65327	0.531815	0.265907	−	0.963999i	$-0.414328\pi$
$113$	5.65327	0.531815	0.265907	+	0.963999i	$0.414328\pi$
$114$	10.6561	0.998036
$115$	−3.67916	−0.343084
$116$	20.5021	1.90357
$117$	−0.290057	−0.0268158
$118$	−25.7092	−2.36672
$119$	0	0
$120$	2.74117	0.250234
$121$	8.75230	0.795664
$122$	3.70601	0.335527
$123$	1.00000	0.0901670
$124$	−25.2613	−2.26853
$125$	−10.4509	−0.934759
$126$	0	0
$127$	1.66494	0.147739	0.0738697	−	0.997268i	$-0.476465\pi$
$127$	1.66494	0.147739	0.0738697	+	0.997268i	$0.476465\pi$
$128$	−8.94479	−0.790616
$129$	−6.70057	−0.589952
$130$	−1.45975	−0.128029
$131$	−20.1673	−1.76202	−0.881012	−	0.473094i	$-0.843137\pi$
$131$	−20.1673	−1.76202	−0.881012	+	0.473094i	$0.843137\pi$
$132$	11.3095	0.984362
$133$	0	0
$134$	29.5044	2.54879
$135$	2.36072	0.203178
$136$	2.10102	0.180161
$137$	14.2458	1.21710	0.608551	−	0.793515i	$-0.291751\pi$
$137$	14.2458	1.21710	0.608551	+	0.793515i	$0.291751\pi$
$138$	−3.32244	−0.282825
$139$	11.5913	0.983159	0.491580	−	0.870833i	$-0.336420\pi$
$139$	11.5913	0.983159	0.491580	+	0.870833i	$0.336420\pi$
$140$	0	0
$141$	0.0265330	0.00223448
$142$	−21.8478	−1.83343
$143$	−1.28912	−0.107802
$144$	−2.61397	−0.217831
$145$	19.0200	1.57952
$146$	−14.9471	−1.23703
$147$	0	0
$148$	17.2310	1.41638
$149$	17.0799	1.39924	0.699619	−	0.714516i	$-0.253353\pi$
$149$	17.0799	1.39924	0.699619	+	0.714516i	$0.253353\pi$
$150$	1.22151	0.0997361
$151$	4.28647	0.348828	0.174414	−	0.984672i	$-0.444197\pi$
$151$	4.28647	0.348828	0.174414	+	0.984672i	$0.444197\pi$
$152$	5.80416	0.470780
$153$	1.80941	0.146282
$154$	0	0
$155$	−23.4351	−1.88235
$156$	−0.738103	−0.0590955
$157$	−5.53484	−0.441728	−0.220864	−	0.975305i	$-0.570888\pi$
$157$	−5.53484	−0.441728	−0.220864	+	0.975305i	$0.570888\pi$
$158$	31.7532	2.52615
$159$	−2.59306	−0.205643
$160$	−18.6375	−1.47342
$161$	0	0
$162$	2.13183	0.167492
$163$	4.92782	0.385977	0.192988	−	0.981201i	$-0.438182\pi$
$163$	4.92782	0.385977	0.192988	+	0.981201i	$0.438182\pi$
$164$	2.54468	0.198706
$165$	10.4919	0.816791
$166$	14.0995	1.09433
$167$	−11.0874	−0.857966	−0.428983	−	0.903313i	$-0.641128\pi$
$167$	−11.0874	−0.857966	−0.428983	+	0.903313i	$0.641128\pi$
$168$	0	0
$169$	−12.9159	−0.993528
$170$	9.10611	0.698407
$171$	4.99859	0.382251
$172$	−17.0508	−1.30011
$173$	−15.4355	−1.17354	−0.586768	−	0.809755i	$-0.699600\pi$
$173$	−15.4355	−1.17354	−0.586768	+	0.809755i	$0.699600\pi$
$174$	17.1758	1.30209
$175$	0	0
$176$	−11.6174	−0.875695
$177$	−12.0597	−0.906463
$178$	−27.9980	−2.09854
$179$	3.64551	0.272478	0.136239	−	0.990676i	$-0.456498\pi$
$179$	3.64551	0.272478	0.136239	+	0.990676i	$0.456498\pi$
$180$	6.00727	0.447755
$181$	3.63738	0.270364	0.135182	−	0.990821i	$-0.456838\pi$
$181$	3.63738	0.270364	0.135182	+	0.990821i	$0.456838\pi$
$182$	0	0
$183$	1.73842	0.128508
$184$	−1.80966	−0.133410
$185$	15.9853	1.17527
$186$	−21.1629	−1.55174
$187$	8.04167	0.588065
$188$	0.0675180	0.00492426
$189$	0	0
$190$	25.1561	1.82501
$191$	−10.3820	−0.751212	−0.375606	−	0.926779i	$-0.622565\pi$
$191$	−10.3820	−0.751212	−0.375606	+	0.926779i	$0.622565\pi$
$192$	−11.6025	−0.837337
$193$	19.0283	1.36969	0.684844	−	0.728690i	$-0.259870\pi$
$193$	19.0283	1.36969	0.684844	+	0.728690i	$0.259870\pi$
$194$	−9.61354	−0.690212
$195$	−0.684744	−0.0490355
$196$	0	0
$197$	7.16377	0.510398	0.255199	−	0.966889i	$-0.417859\pi$
$197$	7.16377	0.510398	0.255199	+	0.966889i	$0.417859\pi$
$198$	9.47459	0.673330
$199$	−4.63169	−0.328332	−0.164166	−	0.986433i	$-0.552493\pi$
$199$	−4.63169	−0.328332	−0.164166	+	0.986433i	$0.552493\pi$
$200$	0.665332	0.0470461
$201$	13.8400	0.976197
$202$	31.6812	2.22908
$203$	0	0
$204$	4.60437	0.322370
$205$	2.36072	0.164880
$206$	−5.85048	−0.407622
$207$	−1.55849	−0.108323
$208$	0.758201	0.0525718
$209$	22.2155	1.53668
$210$	0	0
$211$	−1.15161	−0.0792801	−0.0396401	−	0.999214i	$-0.512621\pi$
$211$	−1.15161	−0.0792801	−0.0396401	+	0.999214i	$0.512621\pi$
$212$	−6.59852	−0.453188
$213$	−10.2484	−0.702209
$214$	6.56477	0.448759
$215$	−15.8182	−1.07879
$216$	1.16116	0.0790069
$217$	0	0
$218$	−23.1533	−1.56814
$219$	−7.01139	−0.473786
$220$	26.6984	1.80001
$221$	−0.524833	−0.0353041
$222$	14.4354	0.968842
$223$	−21.3568	−1.43016	−0.715080	−	0.699043i	$-0.753610\pi$
$223$	−21.3568	−1.43016	−0.715080	+	0.699043i	$0.753610\pi$
$224$	0	0
$225$	0.572989	0.0381993
$226$	12.0518	0.801672
$227$	−0.453953	−0.0301299	−0.0150650	−	0.999887i	$-0.504796\pi$
$227$	−0.453953	−0.0301299	−0.0150650	+	0.999887i	$0.504796\pi$
$228$	12.7198	0.842389
$229$	18.5024	1.22268	0.611338	−	0.791370i	$-0.290632\pi$
$229$	18.5024	1.22268	0.611338	+	0.791370i	$0.290632\pi$
$230$	−7.84333	−0.517174
$231$	0	0
$232$	9.35530	0.614206
$233$	−0.886114	−0.0580513	−0.0290256	−	0.999579i	$-0.509240\pi$
$233$	−0.886114	−0.0580513	−0.0290256	+	0.999579i	$0.509240\pi$
$234$	−0.618352	−0.0404229
$235$	0.0626370	0.00408598
$236$	−30.6881	−1.99762
$237$	14.8949	0.967525
$238$	0	0
$239$	−10.3105	−0.666930	−0.333465	−	0.942763i	$-0.608218\pi$
$239$	−10.3105	−0.666930	−0.333465	+	0.942763i	$0.608218\pi$
$240$	−6.17084	−0.398326
$241$	−10.7928	−0.695227	−0.347614	−	0.937638i	$-0.613008\pi$
$241$	−10.7928	−0.695227	−0.347614	+	0.937638i	$0.613008\pi$
$242$	18.6584	1.19941
$243$	1.00000	0.0641500
$244$	4.42373	0.283200
$245$	0	0
$246$	2.13183	0.135920
$247$	−1.44988	−0.0922535
$248$	−11.5270	−0.731963
$249$	6.61380	0.419133
$250$	−22.2795	−1.40908
$251$	−13.9975	−0.883513	−0.441756	−	0.897135i	$-0.645644\pi$
$251$	−13.9975	−0.883513	−0.441756	+	0.897135i	$0.645644\pi$
$252$	0	0
$253$	−6.92650	−0.435465
$254$	3.54936	0.222707
$255$	4.27151	0.267492
$256$	4.13624	0.258515
$257$	8.45313	0.527292	0.263646	−	0.964620i	$-0.415075\pi$
$257$	8.45313	0.527292	0.263646	+	0.964620i	$0.415075\pi$
$258$	−14.2844	−0.889311
$259$	0	0
$260$	−1.74245	−0.108062
$261$	8.05686	0.498707
$262$	−42.9931	−2.65612
$263$	−29.3309	−1.80862	−0.904310	−	0.426875i	$-0.859614\pi$
$263$	−29.3309	−1.80862	−0.904310	+	0.426875i	$0.859614\pi$
$264$	5.16061	0.317614
$265$	−6.12149	−0.376040
$266$	0	0
$267$	−13.1333	−0.803748
$268$	35.2183	2.15130
$269$	1.45573	0.0887573	0.0443787	−	0.999015i	$-0.485869\pi$
$269$	1.45573	0.0887573	0.0443787	+	0.999015i	$0.485869\pi$
$270$	5.03264	0.306277
$271$	30.5158	1.85370	0.926850	−	0.375432i	$-0.122506\pi$
$271$	30.5158	1.85370	0.926850	+	0.375432i	$0.122506\pi$
$272$	−4.72974	−0.286783
$273$	0	0
$274$	30.3696	1.83469
$275$	2.54657	0.153564
$276$	−3.96587	−0.238717
$277$	29.2660	1.75842	0.879211	−	0.476433i	$-0.158071\pi$
$277$	29.2660	1.75842	0.879211	+	0.476433i	$0.158071\pi$
$278$	24.7106	1.48204
$279$	−9.92711	−0.594321
$280$	0	0
$281$	−12.6815	−0.756512	−0.378256	−	0.925701i	$-0.623476\pi$
$281$	−12.6815	−0.756512	−0.378256	+	0.925701i	$0.623476\pi$
$282$	0.0565637	0.00336832
$283$	−26.4622	−1.57301	−0.786506	−	0.617583i	$-0.788112\pi$
$283$	−26.4622	−1.57301	−0.786506	+	0.617583i	$0.788112\pi$
$284$	−26.0789	−1.54750
$285$	11.8003	0.698987
$286$	−2.74818	−0.162503
$287$	0	0
$288$	−7.89484	−0.465208
$289$	−13.7260	−0.807414
$290$	40.5472	2.38102
$291$	−4.50954	−0.264354
$292$	−17.8417	−1.04411
$293$	2.35974	0.137857	0.0689287	−	0.997622i	$-0.478042\pi$
$293$	2.35974	0.137857	0.0689287	+	0.997622i	$0.478042\pi$
$294$	0	0
$295$	−28.4696	−1.65756
$296$	7.86267	0.457008
$297$	4.44436	0.257888
$298$	36.4113	2.10925
$299$	0.452053	0.0261429
$300$	1.45807	0.0841819
$301$	0	0
$302$	9.13800	0.525833
$303$	14.8611	0.853747
$304$	−13.0661	−0.749395
$305$	4.10393	0.234990
$306$	3.85735	0.220510
$307$	−10.3588	−0.591205	−0.295603	−	0.955311i	$-0.595520\pi$
$307$	−10.3588	−0.591205	−0.295603	+	0.955311i	$0.595520\pi$
$308$	0	0
$309$	−2.74435	−0.156121
$310$	−49.9596	−2.83751
$311$	−4.07018	−0.230799	−0.115399	−	0.993319i	$-0.536815\pi$
$311$	−4.07018	−0.230799	−0.115399	+	0.993319i	$0.536815\pi$
$312$	−0.336803	−0.0190677
$313$	−17.4202	−0.984649	−0.492324	−	0.870412i	$-0.663853\pi$
$313$	−17.4202	−0.984649	−0.492324	+	0.870412i	$0.663853\pi$
$314$	−11.7993	−0.665874
$315$	0	0
$316$	37.9026	2.13219
$317$	−28.1622	−1.58175	−0.790873	−	0.611980i	$-0.790373\pi$
$317$	−28.1622	−1.58175	−0.790873	+	0.611980i	$0.790373\pi$
$318$	−5.52796	−0.309993
$319$	35.8075	2.00484
$320$	−27.3902	−1.53116
$321$	3.07941	0.171876
$322$	0	0
$323$	9.04450	0.503249
$324$	2.54468	0.141371
$325$	−0.166200	−0.00921911
$326$	10.5052	0.581832
$327$	−10.8608	−0.600602
$328$	1.16116	0.0641143
$329$	0	0
$330$	22.3668	1.23125
$331$	−9.65052	−0.530441	−0.265220	−	0.964188i	$-0.585445\pi$
$331$	−9.65052	−0.530441	−0.265220	+	0.964188i	$0.585445\pi$
$332$	16.8300	0.923666
$333$	6.77139	0.371070
$334$	−23.6363	−1.29332
$335$	32.6723	1.78508
$336$	0	0
$337$	8.72939	0.475520	0.237760	−	0.971324i	$-0.423587\pi$
$337$	8.72939	0.475520	0.237760	+	0.971324i	$0.423587\pi$
$338$	−27.5344	−1.49767
$339$	5.65327	0.307043
$340$	10.8696	0.589488
$341$	−44.1196	−2.38921
$342$	10.6561	0.576217
$343$	0	0
$344$	−7.78044	−0.419493
$345$	−3.67916	−0.198080
$346$	−32.9057	−1.76902
$347$	31.1565	1.67257	0.836284	−	0.548296i	$-0.184723\pi$
$347$	31.1565	1.67257	0.836284	+	0.548296i	$0.184723\pi$
$348$	20.5021	1.09903
$349$	5.77148	0.308940	0.154470	−	0.987997i	$-0.450633\pi$
$349$	5.77148	0.308940	0.154470	+	0.987997i	$0.450633\pi$
$350$	0	0
$351$	−0.290057	−0.0154821
$352$	−35.0875	−1.87017
$353$	−5.70652	−0.303727	−0.151864	−	0.988401i	$-0.548527\pi$
$353$	−5.70652	−0.303727	−0.151864	+	0.988401i	$0.548527\pi$
$354$	−25.7092	−1.36643
$355$	−24.1936	−1.28406
$356$	−33.4201	−1.77126
$357$	0	0
$358$	7.77159	0.410741
$359$	14.2254	0.750789	0.375394	−	0.926865i	$-0.377507\pi$
$359$	14.2254	0.750789	0.375394	+	0.926865i	$0.377507\pi$
$360$	2.74117	0.144472
$361$	5.98587	0.315046
$362$	7.75426	0.407555
$363$	8.75230	0.459377
$364$	0	0
$365$	−16.5519	−0.866367
$366$	3.70601	0.193716
$367$	−13.5717	−0.708438	−0.354219	−	0.935163i	$-0.615253\pi$
$367$	−13.5717	−0.708438	−0.354219	+	0.935163i	$0.615253\pi$
$368$	4.07385	0.212364
$369$	1.00000	0.0520579
$370$	34.0779	1.77163
$371$	0	0
$372$	−25.2613	−1.30974
$373$	−5.56422	−0.288104	−0.144052	−	0.989570i	$-0.546013\pi$
$373$	−5.56422	−0.288104	−0.144052	+	0.989570i	$0.546013\pi$
$374$	17.1434	0.886466
$375$	−10.4509	−0.539683
$376$	0.0308091	0.00158886
$377$	−2.33695	−0.120359
$378$	0	0
$379$	−24.0210	−1.23388	−0.616939	−	0.787011i	$-0.711627\pi$
$379$	−24.0210	−1.23388	−0.616939	+	0.787011i	$0.711627\pi$
$380$	30.0279	1.54040
$381$	1.66494	0.0852974
$382$	−22.1325	−1.13240
$383$	22.6618	1.15797	0.578983	−	0.815340i	$-0.303450\pi$
$383$	22.6618	1.15797	0.578983	+	0.815340i	$0.303450\pi$
$384$	−8.94479	−0.456462
$385$	0	0
$386$	40.5650	2.06471
$387$	−6.70057	−0.340609
$388$	−11.4753	−0.582571
$389$	14.8536	0.753106	0.376553	−	0.926395i	$-0.377109\pi$
$389$	14.8536	0.753106	0.376553	+	0.926395i	$0.377109\pi$
$390$	−1.45975	−0.0739175
$391$	−2.81996	−0.142611
$392$	0	0
$393$	−20.1673	−1.01731
$394$	15.2719	0.769388
$395$	35.1625	1.76922
$396$	11.3095	0.568322
$397$	−31.7430	−1.59313	−0.796567	−	0.604551i	$-0.793353\pi$
$397$	−31.7430	−1.59313	−0.796567	+	0.604551i	$0.793353\pi$
$398$	−9.87395	−0.494936
$399$	0	0
$400$	−1.49778	−0.0748888
$401$	−14.5053	−0.724360	−0.362180	−	0.932108i	$-0.617968\pi$
$401$	−14.5053	−0.724360	−0.362180	+	0.932108i	$0.617968\pi$
$402$	29.5044	1.47155
$403$	2.87943	0.143435
$404$	37.8167	1.88145
$405$	2.36072	0.117305
$406$	0	0
$407$	30.0945	1.49173
$408$	2.10102	0.104016
$409$	14.3986	0.711965	0.355982	−	0.934493i	$-0.384146\pi$
$409$	14.3986	0.711965	0.355982	+	0.934493i	$0.384146\pi$
$410$	5.03264	0.248544
$411$	14.2458	0.702694
$412$	−6.98350	−0.344052
$413$	0	0
$414$	−3.32244	−0.163289
$415$	15.6133	0.766428
$416$	2.28996	0.112274
$417$	11.5913	0.567627
$418$	47.3596	2.31643
$419$	30.8227	1.50579	0.752893	−	0.658143i	$-0.228658\pi$
$419$	30.8227	1.50579	0.752893	+	0.658143i	$0.228658\pi$
$420$	0	0
$421$	−0.694209	−0.0338337	−0.0169168	−	0.999857i	$-0.505385\pi$
$421$	−0.694209	−0.0338337	−0.0169168	+	0.999857i	$0.505385\pi$
$422$	−2.45503	−0.119509
$423$	0.0265330	0.00129008
$424$	−3.01096	−0.146225
$425$	1.03677	0.0502909
$426$	−21.8478	−1.05853
$427$	0	0
$428$	7.83612	0.378773
$429$	−1.28912	−0.0622392
$430$	−33.7215	−1.62620
$431$	−19.6946	−0.948657	−0.474328	−	0.880348i	$-0.657309\pi$
$431$	−19.6946	−0.948657	−0.474328	+	0.880348i	$0.657309\pi$
$432$	−2.61397	−0.125765
$433$	21.8904	1.05199	0.525993	−	0.850489i	$-0.323694\pi$
$433$	21.8904	1.05199	0.525993	+	0.850489i	$0.323694\pi$
$434$	0	0
$435$	19.0200	0.911938
$436$	−27.6372	−1.32358
$437$	−7.79027	−0.372659
$438$	−14.9471	−0.714198
$439$	3.09324	0.147632	0.0738161	−	0.997272i	$-0.476482\pi$
$439$	3.09324	0.147632	0.0738161	+	0.997272i	$0.476482\pi$
$440$	12.1827	0.580790
$441$	0	0
$442$	−1.11885	−0.0532184
$443$	−28.9415	−1.37505	−0.687526	−	0.726159i	$-0.741303\pi$
$443$	−28.9415	−1.37505	−0.687526	+	0.726159i	$0.741303\pi$
$444$	17.2310	0.817748
$445$	−31.0041	−1.46974
$446$	−45.5290	−2.15586
$447$	17.0799	0.807851
$448$	0	0
$449$	−25.2696	−1.19255	−0.596274	−	0.802781i	$-0.703353\pi$
$449$	−25.2696	−1.19255	−0.596274	+	0.802781i	$0.703353\pi$
$450$	1.22151	0.0575827
$451$	4.44436	0.209277
$452$	14.3857	0.676649
$453$	4.28647	0.201396
$454$	−0.967749	−0.0454187
$455$	0	0
$456$	5.80416	0.271805
$457$	−10.0789	−0.471473	−0.235736	−	0.971817i	$-0.575750\pi$
$457$	−10.0789	−0.471473	−0.235736	+	0.971817i	$0.575750\pi$
$458$	39.4440	1.84310
$459$	1.80941	0.0844561
$460$	−9.36229	−0.436519
$461$	0.973232	0.0453279	0.0226640	−	0.999743i	$-0.492785\pi$
$461$	0.973232	0.0453279	0.0226640	+	0.999743i	$0.492785\pi$
$462$	0	0
$463$	13.9337	0.647553	0.323776	−	0.946134i	$-0.395047\pi$
$463$	13.9337	0.647553	0.323776	+	0.946134i	$0.395047\pi$
$464$	−21.0604	−0.977702
$465$	−23.4351	−1.08678
$466$	−1.88904	−0.0875081
$467$	2.67442	0.123758	0.0618788	−	0.998084i	$-0.480291\pi$
$467$	2.67442	0.123758	0.0618788	+	0.998084i	$0.480291\pi$
$468$	−0.738103	−0.0341188
$469$	0	0
$470$	0.133531	0.00615933
$471$	−5.53484	−0.255032
$472$	−14.0033	−0.644552
$473$	−29.7797	−1.36927
$474$	31.7532	1.45847
$475$	2.86414	0.131416
$476$	0	0
$477$	−2.59306	−0.118728
$478$	−21.9801	−1.00535
$479$	7.15536	0.326937	0.163468	−	0.986549i	$-0.447732\pi$
$479$	7.15536	0.326937	0.163468	+	0.986549i	$0.447732\pi$
$480$	−18.6375	−0.850681
$481$	−1.96409	−0.0895549
$482$	−23.0084	−1.04801
$483$	0	0
$484$	22.2718	1.01235
$485$	−10.6457	−0.483398
$486$	2.13183	0.0967016
$487$	38.5585	1.74725	0.873625	−	0.486599i	$-0.161763\pi$
$487$	38.5585	1.74725	0.873625	+	0.486599i	$0.161763\pi$
$488$	2.01859	0.0913772
$489$	4.92782	0.222844
$490$	0	0
$491$	−40.3676	−1.82176	−0.910882	−	0.412667i	$-0.864597\pi$
$491$	−40.3676	−1.82176	−0.910882	+	0.412667i	$0.864597\pi$
$492$	2.54468	0.114723
$493$	14.5782	0.656568
$494$	−3.09089	−0.139066
$495$	10.4919	0.471575
$496$	25.9491	1.16515
$497$	0	0
$498$	14.0995	0.631812
$499$	12.9878	0.581414	0.290707	−	0.956812i	$-0.406110\pi$
$499$	12.9878	0.581414	0.290707	+	0.956812i	$0.406110\pi$
$500$	−26.5942	−1.18933
$501$	−11.0874	−0.495347
$502$	−29.8402	−1.33183
$503$	−28.4964	−1.27059	−0.635296	−	0.772269i	$-0.719122\pi$
$503$	−28.4964	−1.27059	−0.635296	+	0.772269i	$0.719122\pi$
$504$	0	0
$505$	35.0828	1.56116
$506$	−14.7661	−0.656433
$507$	−12.9159	−0.573614
$508$	4.23674	0.187975
$509$	−3.91314	−0.173447	−0.0867235	−	0.996232i	$-0.527640\pi$
$509$	−3.91314	−0.173447	−0.0867235	+	0.996232i	$0.527640\pi$
$510$	9.10611	0.403225
$511$	0	0
$512$	26.7073	1.18031
$513$	4.99859	0.220693
$514$	18.0206	0.794854
$515$	−6.47864	−0.285483
$516$	−17.0508	−0.750620
$517$	0.117922	0.00518621
$518$	0	0
$519$	−15.4355	−0.677542
$520$	−0.795097	−0.0348673
$521$	29.5289	1.29369	0.646843	−	0.762624i	$-0.276089\pi$
$521$	29.5289	1.29369	0.646843	+	0.762624i	$0.276089\pi$
$522$	17.1758	0.751765
$523$	−38.8288	−1.69786	−0.848932	−	0.528502i	$-0.822754\pi$
$523$	−38.8288	−1.69786	−0.848932	+	0.528502i	$0.822754\pi$
$524$	−51.3193	−2.24189
$525$	0	0
$526$	−62.5284	−2.72637
$527$	−17.9622	−0.782447
$528$	−11.6174	−0.505582
$529$	−20.5711	−0.894396
$530$	−13.0500	−0.566854
$531$	−12.0597	−0.523347
$532$	0	0
$533$	−0.290057	−0.0125638
$534$	−27.9980	−1.21159
$535$	7.26963	0.314293
$536$	16.0704	0.694137
$537$	3.64551	0.157315
$538$	3.10336	0.133795
$539$	0	0
$540$	6.00727	0.258512
$541$	−23.2651	−1.00025	−0.500123	−	0.865954i	$-0.666712\pi$
$541$	−23.2651	−1.00025	−0.500123	+	0.865954i	$0.666712\pi$
$542$	65.0543	2.79432
$543$	3.63738	0.156095
$544$	−14.2850	−0.612465
$545$	−25.6392	−1.09826
$546$	0	0
$547$	−8.34737	−0.356908	−0.178454	−	0.983948i	$-0.557110\pi$
$547$	−8.34737	−0.356908	−0.178454	+	0.983948i	$0.557110\pi$
$548$	36.2510	1.54857
$549$	1.73842	0.0741941
$550$	5.42884	0.231486
$551$	40.2729	1.71568
$552$	−1.80966	−0.0770243
$553$	0	0
$554$	62.3899	2.65069
$555$	15.9853	0.678540
$556$	29.4961	1.25091
$557$	−8.69009	−0.368211	−0.184106	−	0.982906i	$-0.558939\pi$
$557$	−8.69009	−0.368211	−0.184106	+	0.982906i	$0.558939\pi$
$558$	−21.1629	−0.895896
$559$	1.94355	0.0822034
$560$	0	0
$561$	8.04167	0.339519
$562$	−27.0347	−1.14039
$563$	35.6405	1.50207	0.751034	−	0.660263i	$-0.229555\pi$
$563$	35.6405	1.50207	0.751034	+	0.660263i	$0.229555\pi$
$564$	0.0675180	0.00284302
$565$	13.3458	0.561461
$566$	−56.4127	−2.37120
$567$	0	0
$568$	−11.9000	−0.499315
$569$	−2.01831	−0.0846120	−0.0423060	−	0.999105i	$-0.513470\pi$
$569$	−2.01831	−0.0846120	−0.0423060	+	0.999105i	$0.513470\pi$
$570$	25.1561	1.05367
$571$	45.5386	1.90573	0.952866	−	0.303392i	$-0.0981193\pi$
$571$	45.5386	1.90573	0.952866	+	0.303392i	$0.0981193\pi$
$572$	−3.28039	−0.137160
$573$	−10.3820	−0.433713
$574$	0	0
$575$	−0.893000	−0.0372407
$576$	−11.6025	−0.483437
$577$	12.2375	0.509454	0.254727	−	0.967013i	$-0.418014\pi$
$577$	12.2375	0.509454	0.254727	+	0.967013i	$0.418014\pi$
$578$	−29.2615	−1.21712
$579$	19.0283	0.790789
$580$	48.3997	2.00969
$581$	0	0
$582$	−9.61354	−0.398494
$583$	−11.5245	−0.477296
$584$	−8.14134	−0.336891
$585$	−0.684744	−0.0283107
$586$	5.03055	0.207810
$587$	−19.8859	−0.820777	−0.410389	−	0.911911i	$-0.634607\pi$
$587$	−19.8859	−0.820777	−0.410389	+	0.911911i	$0.634607\pi$
$588$	0	0
$589$	−49.6215	−2.04462
$590$	−60.6921	−2.49866
$591$	7.16377	0.294678
$592$	−17.7002	−0.727473
$593$	−9.29758	−0.381806	−0.190903	−	0.981609i	$-0.561142\pi$
$593$	−9.29758	−0.381806	−0.190903	+	0.981609i	$0.561142\pi$
$594$	9.47459	0.388747
$595$	0	0
$596$	43.4628	1.78031
$597$	−4.63169	−0.189562
$598$	0.963698	0.0394085
$599$	−14.3452	−0.586127	−0.293063	−	0.956093i	$-0.594675\pi$
$599$	−14.3452	−0.586127	−0.293063	+	0.956093i	$0.594675\pi$
$600$	0.665332	0.0271621
$601$	24.4136	0.995851	0.497925	−	0.867220i	$-0.334095\pi$
$601$	24.4136	0.995851	0.497925	+	0.867220i	$0.334095\pi$
$602$	0	0
$603$	13.8400	0.563608
$604$	10.9077	0.443827
$605$	20.6617	0.840018
$606$	31.6812	1.28696
$607$	−6.54301	−0.265573	−0.132786	−	0.991145i	$-0.542392\pi$
$607$	−6.54301	−0.265573	−0.132786	+	0.991145i	$0.542392\pi$
$608$	−39.4631	−1.60044
$609$	0	0
$610$	8.74886	0.354231
$611$	−0.00769610	−0.000311351 0
$612$	4.60437	0.186121
$613$	−4.74967	−0.191837	−0.0959186	−	0.995389i	$-0.530579\pi$
$613$	−4.74967	−0.191837	−0.0959186	+	0.995389i	$0.530579\pi$
$614$	−22.0830	−0.891199
$615$	2.36072	0.0951933
$616$	0	0
$617$	−40.3997	−1.62643	−0.813216	−	0.581962i	$-0.802285\pi$
$617$	−40.3997	−1.62643	−0.813216	+	0.581962i	$0.802285\pi$
$618$	−5.85048	−0.235341
$619$	26.1618	1.05153	0.525766	−	0.850629i	$-0.323779\pi$
$619$	26.1618	1.05153	0.525766	+	0.850629i	$0.323779\pi$
$620$	−59.6348	−2.39499
$621$	−1.55849	−0.0625402
$622$	−8.67691	−0.347913
$623$	0	0
$624$	0.758201	0.0303523
$625$	−27.5366	−1.10147
$626$	−37.1369	−1.48429
$627$	22.2155	0.887202
$628$	−14.0844	−0.562028
$629$	12.2522	0.488528
$630$	0	0
$631$	−28.0225	−1.11556	−0.557778	−	0.829990i	$-0.688346\pi$
$631$	−28.0225	−1.11556	−0.557778	+	0.829990i	$0.688346\pi$
$632$	17.2953	0.687970
$633$	−1.15161	−0.0457724
$634$	−60.0369	−2.38437
$635$	3.93045	0.155975
$636$	−6.59852	−0.261648
$637$	0	0
$638$	76.3354	3.02215
$639$	−10.2484	−0.405421
$640$	−21.1161	−0.834689
$641$	0.737870	0.0291441	0.0145721	−	0.999894i	$-0.495361\pi$
$641$	0.737870	0.0291441	0.0145721	+	0.999894i	$0.495361\pi$
$642$	6.56477	0.259091
$643$	−34.8978	−1.37624	−0.688118	−	0.725599i	$-0.741563\pi$
$643$	−34.8978	−1.37624	−0.688118	+	0.725599i	$0.741563\pi$
$644$	0	0
$645$	−15.8182	−0.622839
$646$	19.2813	0.758612
$647$	11.0952	0.436197	0.218098	−	0.975927i	$-0.430015\pi$
$647$	11.0952	0.436197	0.218098	+	0.975927i	$0.430015\pi$
$648$	1.16116	0.0456147
$649$	−53.5976	−2.10389
$650$	−0.354309	−0.0138971
$651$	0	0
$652$	12.5397	0.491093
$653$	−5.40616	−0.211559	−0.105780	−	0.994390i	$-0.533734\pi$
$653$	−5.40616	−0.211559	−0.105780	+	0.994390i	$0.533734\pi$
$654$	−23.1533	−0.905365
$655$	−47.6093	−1.86025
$656$	−2.61397	−0.102058
$657$	−7.01139	−0.273540
$658$	0	0
$659$	−27.2471	−1.06140	−0.530698	−	0.847561i	$-0.678070\pi$
$659$	−27.2471	−1.06140	−0.530698	+	0.847561i	$0.678070\pi$
$660$	26.6984	1.03924
$661$	−37.0310	−1.44034	−0.720169	−	0.693799i	$-0.755936\pi$
$661$	−37.0310	−1.44034	−0.720169	+	0.693799i	$0.755936\pi$
$662$	−20.5732	−0.799601
$663$	−0.524833	−0.0203828
$664$	7.67968	0.298029
$665$	0	0
$666$	14.4354	0.559361
$667$	−12.5566	−0.486192
$668$	−28.2138	−1.09162
$669$	−21.3568	−0.825703
$670$	69.6516	2.69088
$671$	7.72617	0.298266
$672$	0	0
$673$	37.1780	1.43311	0.716554	−	0.697532i	$-0.245719\pi$
$673$	37.1780	1.43311	0.716554	+	0.697532i	$0.245719\pi$
$674$	18.6095	0.716813
$675$	0.572989	0.0220544
$676$	−32.8667	−1.26411
$677$	−13.6605	−0.525017	−0.262508	−	0.964930i	$-0.584550\pi$
$677$	−13.6605	−0.525017	−0.262508	+	0.964930i	$0.584550\pi$
$678$	12.0518	0.462846
$679$	0	0
$680$	4.95991	0.190204
$681$	−0.453953	−0.0173955
$682$	−94.0553	−3.60156
$683$	−24.8142	−0.949489	−0.474744	−	0.880124i	$-0.657459\pi$
$683$	−24.8142	−0.949489	−0.474744	+	0.880124i	$0.657459\pi$
$684$	12.7198	0.486354
$685$	33.6303	1.28495
$686$	0	0
$687$	18.5024	0.705912
$688$	17.5151	0.667756
$689$	0.752138	0.0286542
$690$	−7.84333	−0.298591
$691$	−4.35305	−0.165598	−0.0827989	−	0.996566i	$-0.526386\pi$
$691$	−4.35305	−0.165598	−0.0827989	+	0.996566i	$0.526386\pi$
$692$	−39.2783	−1.49314
$693$	0	0
$694$	66.4202	2.52128
$695$	27.3637	1.03797
$696$	9.35530	0.354612
$697$	1.80941	0.0685363
$698$	12.3038	0.465705
$699$	−0.886114	−0.0335159
$700$	0	0
$701$	0.411635	0.0155472	0.00777361	−	0.999970i	$-0.497526\pi$
$701$	0.411635	0.0155472	0.00777361	+	0.999970i	$0.497526\pi$
$702$	−0.618352	−0.0233382
$703$	33.8474	1.27658
$704$	−51.5656	−1.94345
$705$	0.0626370	0.00235904
$706$	−12.1653	−0.457847
$707$	0	0
$708$	−30.6881	−1.15333
$709$	−15.0664	−0.565831	−0.282915	−	0.959145i	$-0.591302\pi$
$709$	−15.0664	−0.565831	−0.282915	+	0.959145i	$0.591302\pi$
$710$	−51.5765	−1.93563
$711$	14.8949	0.558601
$712$	−15.2499	−0.571515
$713$	15.4713	0.579406
$714$	0	0
$715$	−3.04325	−0.113811
$716$	9.27665	0.346685
$717$	−10.3105	−0.385052
$718$	30.3261	1.13176
$719$	35.8607	1.33738	0.668688	−	0.743543i	$-0.266856\pi$
$719$	35.8607	1.33738	0.668688	+	0.743543i	$0.266856\pi$
$720$	−6.17084	−0.229974
$721$	0	0
$722$	12.7608	0.474909
$723$	−10.7928	−0.401390
$724$	9.25596	0.343995
$725$	4.61649	0.171452
$726$	18.6584	0.692477
$727$	−27.2538	−1.01079	−0.505394	−	0.862889i	$-0.668653\pi$
$727$	−27.2538	−1.01079	−0.505394	+	0.862889i	$0.668653\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−35.2858	−1.30599
$731$	−12.1241	−0.448426
$732$	4.42373	0.163506
$733$	50.8127	1.87681	0.938405	−	0.345538i	$-0.112303\pi$
$733$	50.8127	1.87681	0.938405	+	0.345538i	$0.112303\pi$
$734$	−28.9325	−1.06792
$735$	0	0
$736$	12.3041	0.453534
$737$	61.5098	2.26574
$738$	2.13183	0.0784736
$739$	6.60828	0.243090	0.121545	−	0.992586i	$-0.461215\pi$
$739$	6.60828	0.243090	0.121545	+	0.992586i	$0.461215\pi$
$740$	40.6776	1.49534
$741$	−1.44988	−0.0532626
$742$	0	0
$743$	26.8065	0.983434	0.491717	−	0.870755i	$-0.336369\pi$
$743$	26.8065	0.983434	0.491717	+	0.870755i	$0.336369\pi$
$744$	−11.5270	−0.422599
$745$	40.3208	1.47724
$746$	−11.8619	−0.434297
$747$	6.61380	0.241986
$748$	20.4635	0.748218
$749$	0	0
$750$	−22.2795	−0.813534
$751$	20.8690	0.761522	0.380761	−	0.924674i	$-0.375662\pi$
$751$	20.8690	0.761522	0.380761	+	0.924674i	$0.375662\pi$
$752$	−0.0693564	−0.00252917
$753$	−13.9975	−0.510096
$754$	−4.98197	−0.181433
$755$	10.1191	0.368273
$756$	0	0
$757$	−12.8198	−0.465942	−0.232971	−	0.972484i	$-0.574845\pi$
$757$	−12.8198	−0.465942	−0.232971	+	0.972484i	$0.574845\pi$
$758$	−51.2086	−1.85998
$759$	−6.92650	−0.251416
$760$	13.7020	0.497023
$761$	36.2182	1.31291	0.656454	−	0.754366i	$-0.272056\pi$
$761$	36.2182	1.31291	0.656454	+	0.754366i	$0.272056\pi$
$762$	3.54936	0.128580
$763$	0	0
$764$	−26.4188	−0.955797
$765$	4.27151	0.154437
$766$	48.3111	1.74555
$767$	3.49801	0.126306
$768$	4.13624	0.149254
$769$	−14.7160	−0.530671	−0.265336	−	0.964156i	$-0.585483\pi$
$769$	−14.7160	−0.530671	−0.265336	+	0.964156i	$0.585483\pi$
$770$	0	0
$771$	8.45313	0.304432
$772$	48.4209	1.74271
$773$	33.6972	1.21200	0.606002	−	0.795463i	$-0.292772\pi$
$773$	33.6972	1.21200	0.606002	+	0.795463i	$0.292772\pi$
$774$	−14.2844	−0.513444
$775$	−5.68813	−0.204324
$776$	−5.23629	−0.187972
$777$	0	0
$778$	31.6652	1.13525
$779$	4.99859	0.179093
$780$	−1.74245	−0.0623898
$781$	−45.5476	−1.62982
$782$	−6.01165	−0.214976
$783$	8.05686	0.287929
$784$	0	0
$785$	−13.0662	−0.466353
$786$	−42.9931	−1.53351
$787$	44.9121	1.60094	0.800472	−	0.599370i	$-0.204582\pi$
$787$	44.9121	1.60094	0.800472	+	0.599370i	$0.204582\pi$
$788$	18.2295	0.649399
$789$	−29.3309	−1.04421
$790$	74.9604	2.66697
$791$	0	0
$792$	5.16061	0.183374
$793$	−0.504243	−0.0179062
$794$	−67.6704	−2.40153
$795$	−6.12149	−0.217107
$796$	−11.7862	−0.417749
$797$	22.6417	0.802009	0.401004	−	0.916076i	$-0.368661\pi$
$797$	22.6417	0.802009	0.401004	+	0.916076i	$0.368661\pi$
$798$	0	0
$799$	0.0480091	0.00169844
$800$	−4.52366	−0.159936
$801$	−13.1333	−0.464044
$802$	−30.9228	−1.09192
$803$	−31.1611	−1.09965
$804$	35.2183	1.24205
$805$	0	0
$806$	6.13845	0.216218
$807$	1.45573	0.0512441
$808$	17.2561	0.607067
$809$	21.5559	0.757864	0.378932	−	0.925425i	$-0.376291\pi$
$809$	21.5559	0.757864	0.378932	+	0.925425i	$0.376291\pi$
$810$	5.03264	0.176829
$811$	21.0625	0.739603	0.369801	−	0.929111i	$-0.379426\pi$
$811$	21.0625	0.739603	0.369801	+	0.929111i	$0.379426\pi$
$812$	0	0
$813$	30.5158	1.07023
$814$	64.1561	2.24867
$815$	11.6332	0.407493
$816$	−4.72974	−0.165574
$817$	−33.4934	−1.17179
$818$	30.6953	1.07324
$819$	0	0
$820$	6.00727	0.209783
$821$	31.9922	1.11653	0.558267	−	0.829661i	$-0.311467\pi$
$821$	31.9922	1.11653	0.558267	+	0.829661i	$0.311467\pi$
$822$	30.3696	1.05926
$823$	30.9541	1.07899	0.539495	−	0.841989i	$-0.318615\pi$
$823$	30.9541	1.07899	0.539495	+	0.841989i	$0.318615\pi$
$824$	−3.18663	−0.111012
$825$	2.54657	0.0886601
$826$	0	0
$827$	−5.33182	−0.185405	−0.0927027	−	0.995694i	$-0.529551\pi$
$827$	−5.33182	−0.185405	−0.0927027	+	0.995694i	$0.529551\pi$
$828$	−3.96587	−0.137823
$829$	−25.4635	−0.884383	−0.442191	−	0.896921i	$-0.645799\pi$
$829$	−25.4635	−0.884383	−0.442191	+	0.896921i	$0.645799\pi$
$830$	33.2849	1.15533
$831$	29.2660	1.01523
$832$	3.36539	0.116674
$833$	0	0
$834$	24.7106	0.855657
$835$	−26.1741	−0.905793
$836$	56.5313	1.95518
$837$	−9.92711	−0.343131
$838$	65.7086	2.26987
$839$	20.2282	0.698356	0.349178	−	0.937056i	$-0.386461\pi$
$839$	20.2282	0.698356	0.349178	+	0.937056i	$0.386461\pi$
$840$	0	0
$841$	35.9129	1.23838
$842$	−1.47993	−0.0510018
$843$	−12.6815	−0.436773
$844$	−2.93048	−0.100871
$845$	−30.4907	−1.04891
$846$	0.0565637	0.00194470
$847$	0	0
$848$	6.77819	0.232764
$849$	−26.4622	−0.908179
$850$	2.21022	0.0758099
$851$	−10.5532	−0.361758
$852$	−26.0789	−0.893448
$853$	−4.47575	−0.153247	−0.0766233	−	0.997060i	$-0.524414\pi$
$853$	−4.47575	−0.153247	−0.0766233	+	0.997060i	$0.524414\pi$
$854$	0	0
$855$	11.8003	0.403560
$856$	3.57569	0.122215
$857$	−6.14745	−0.209993	−0.104997	−	0.994473i	$-0.533483\pi$
$857$	−6.14745	−0.209993	−0.104997	+	0.994473i	$0.533483\pi$
$858$	−2.74818	−0.0938212
$859$	8.71423	0.297326	0.148663	−	0.988888i	$-0.452503\pi$
$859$	8.71423	0.297326	0.148663	+	0.988888i	$0.452503\pi$
$860$	−40.2521	−1.37259
$861$	0	0
$862$	−41.9855	−1.43003
$863$	43.6551	1.48604	0.743019	−	0.669270i	$-0.233393\pi$
$863$	43.6551	1.48604	0.743019	+	0.669270i	$0.233393\pi$
$864$	−7.89484	−0.268588
$865$	−36.4388	−1.23896
$866$	46.6665	1.58579
$867$	−13.7260	−0.466160
$868$	0	0
$869$	66.1980	2.24561
$870$	40.5472	1.37468
$871$	−4.01439	−0.136022
$872$	−12.6111	−0.427066
$873$	−4.50954	−0.152625
$874$	−16.6075	−0.561757
$875$	0	0
$876$	−17.8417	−0.602816
$877$	−8.85811	−0.299117	−0.149559	−	0.988753i	$-0.547785\pi$
$877$	−8.85811	−0.299117	−0.149559	+	0.988753i	$0.547785\pi$
$878$	6.59425	0.222545
$879$	2.35974	0.0795920
$880$	−27.4254	−0.924510
$881$	−17.2141	−0.579957	−0.289978	−	0.957033i	$-0.593648\pi$
$881$	−17.2141	−0.579957	−0.289978	+	0.957033i	$0.593648\pi$
$882$	0	0
$883$	29.4313	0.990441	0.495221	−	0.868767i	$-0.335087\pi$
$883$	29.4313	0.990441	0.495221	+	0.868767i	$0.335087\pi$
$884$	−1.33553	−0.0449188
$885$	−28.4696	−0.956994
$886$	−61.6983	−2.07279
$887$	48.1948	1.61822	0.809111	−	0.587656i	$-0.199949\pi$
$887$	48.1948	1.61822	0.809111	+	0.587656i	$0.199949\pi$
$888$	7.86267	0.263854
$889$	0	0
$890$	−66.0954	−2.21552
$891$	4.44436	0.148892
$892$	−54.3463	−1.81965
$893$	0.132628	0.00443821
$894$	36.4113	1.21778
$895$	8.60602	0.287667
$896$	0	0
$897$	0.452053	0.0150936
$898$	−53.8704	−1.79768
$899$	−79.9813	−2.66753
$900$	1.45807	0.0486025
$901$	−4.69192	−0.156311
$902$	9.47459	0.315469
$903$	0	0
$904$	6.56435	0.218327
$905$	8.58683	0.285436
$906$	9.13800	0.303590
$907$	4.87399	0.161838	0.0809190	−	0.996721i	$-0.474214\pi$
$907$	4.87399	0.161838	0.0809190	+	0.996721i	$0.474214\pi$
$908$	−1.15517	−0.0383355
$909$	14.8611	0.492911
$910$	0	0
$911$	3.16921	0.105001	0.0525003	−	0.998621i	$-0.483281\pi$
$911$	3.16921	0.105001	0.0525003	+	0.998621i	$0.483281\pi$
$912$	−13.0661	−0.432663
$913$	29.3941	0.972802
$914$	−21.4865	−0.710711
$915$	4.10393	0.135672
$916$	47.0828	1.55566
$917$	0	0
$918$	3.85735	0.127311
$919$	5.06669	0.167135	0.0835673	−	0.996502i	$-0.473369\pi$
$919$	5.06669	0.167135	0.0835673	+	0.996502i	$0.473369\pi$
$920$	−4.27210	−0.140847
$921$	−10.3588	−0.341332
$922$	2.07476	0.0683286
$923$	2.97263	0.0978452
$924$	0	0
$925$	3.87993	0.127571
$926$	29.7042	0.976139
$927$	−2.74435	−0.0901364
$928$	−63.6076	−2.08802
$929$	−28.7365	−0.942814	−0.471407	−	0.881916i	$-0.656254\pi$
$929$	−28.7365	−0.942814	−0.471407	+	0.881916i	$0.656254\pi$
$930$	−49.9596	−1.63824
$931$	0	0
$932$	−2.25488	−0.0738609
$933$	−4.07018	−0.133252
$934$	5.70140	0.186556
$935$	18.9841	0.620847
$936$	−0.336803	−0.0110088
$937$	−8.98878	−0.293651	−0.146825	−	0.989162i	$-0.546906\pi$
$937$	−8.98878	−0.293651	−0.146825	+	0.989162i	$0.546906\pi$
$938$	0	0
$939$	−17.4202	−0.568487
$940$	0.159391	0.00519876
$941$	41.6826	1.35881	0.679406	−	0.733762i	$-0.262237\pi$
$941$	41.6826	1.35881	0.679406	+	0.733762i	$0.262237\pi$
$942$	−11.7993	−0.384442
$943$	−1.55849	−0.0507515
$944$	31.5237	1.02601
$945$	0	0
$946$	−63.4852	−2.06408
$947$	−49.3593	−1.60396	−0.801981	−	0.597349i	$-0.796221\pi$
$947$	−49.3593	−1.60396	−0.801981	+	0.597349i	$0.796221\pi$
$948$	37.9026	1.23102
$949$	2.03371	0.0660169
$950$	6.10584	0.198100
$951$	−28.1622	−0.913222
$952$	0	0
$953$	7.39228	0.239460	0.119730	−	0.992807i	$-0.461797\pi$
$953$	7.39228	0.239460	0.119730	+	0.992807i	$0.461797\pi$
$954$	−5.52796	−0.178974
$955$	−24.5089	−0.793089
$956$	−26.2369	−0.848561
$957$	35.8075	1.15749
$958$	15.2540	0.492834
$959$	0	0
$960$	−27.3902	−0.884015
$961$	67.5475	2.17895
$962$	−4.18710	−0.134998
$963$	3.07941	0.0992327
$964$	−27.4643	−0.884565
$965$	44.9205	1.44604
$966$	0	0
$967$	−42.9143	−1.38003	−0.690016	−	0.723795i	$-0.742396\pi$
$967$	−42.9143	−1.38003	−0.690016	+	0.723795i	$0.742396\pi$
$968$	10.1628	0.326646
$969$	9.04450	0.290551
$970$	−22.6949	−0.728688
$971$	−28.9224	−0.928165	−0.464083	−	0.885792i	$-0.653616\pi$
$971$	−28.9224	−0.928165	−0.464083	+	0.885792i	$0.653616\pi$
$972$	2.54468	0.0816206
$973$	0	0
$974$	82.1999	2.63385
$975$	−0.166200	−0.00532265
$976$	−4.54418	−0.145456
$977$	22.2031	0.710339	0.355169	−	0.934802i	$-0.384423\pi$
$977$	22.2031	0.710339	0.355169	+	0.934802i	$0.384423\pi$
$978$	10.5052	0.335921
$979$	−58.3693	−1.86549
$980$	0	0
$981$	−10.8608	−0.346758
$982$	−86.0566	−2.74618
$983$	−32.9506	−1.05096	−0.525480	−	0.850806i	$-0.676114\pi$
$983$	−32.9506	−1.05096	−0.525480	+	0.850806i	$0.676114\pi$
$984$	1.16116	0.0370164
$985$	16.9117	0.538850
$986$	31.0781	0.989728
$987$	0	0
$988$	−3.68947	−0.117378
$989$	10.4428	0.332062
$990$	22.3668	0.710865
$991$	−24.4004	−0.775104	−0.387552	−	0.921848i	$-0.626679\pi$
$991$	−24.4004	−0.775104	−0.387552	+	0.921848i	$0.626679\pi$
$992$	78.3730	2.48834
$993$	−9.65052	−0.306250
$994$	0	0
$995$	−10.9341	−0.346635
$996$	16.8300	0.533279
$997$	4.47325	0.141669	0.0708346	−	0.997488i	$-0.477434\pi$
$997$	4.47325	0.141669	0.0708346	+	0.997488i	$0.477434\pi$
$998$	27.6877	0.876440
$999$	6.77139	0.214237

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.be.1.8	yes	10
7.6	odd	2		6027.2.a.bd.1.8	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6027.2.a.bd.1.8	✓	10	7.6	odd	2
6027.2.a.be.1.8	yes	10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q+2.13183 q^{2} +1.00000 q^{3} +2.54468 q^{4} +2.36072 q^{5} +2.13183 q^{6} +1.16116 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.13183 q^{2} +1.00000 q^{3} +2.54468 q^{4} +2.36072 q^{5} +2.13183 q^{6} +1.16116 q^{8} +1.00000 q^{9} +5.03264 q^{10} +4.44436 q^{11} +2.54468 q^{12} -0.290057 q^{13} +2.36072 q^{15} -2.61397 q^{16} +1.80941 q^{17} +2.13183 q^{18} +4.99859 q^{19} +6.00727 q^{20} +9.47459 q^{22} -1.55849 q^{23} +1.16116 q^{24} +0.572989 q^{25} -0.618352 q^{26} +1.00000 q^{27} +8.05686 q^{29} +5.03264 q^{30} -9.92711 q^{31} -7.89484 q^{32} +4.44436 q^{33} +3.85735 q^{34} +2.54468 q^{36} +6.77139 q^{37} +10.6561 q^{38} -0.290057 q^{39} +2.74117 q^{40} +1.00000 q^{41} -6.70057 q^{43} +11.3095 q^{44} +2.36072 q^{45} -3.32244 q^{46} +0.0265330 q^{47} -2.61397 q^{48} +1.22151 q^{50} +1.80941 q^{51} -0.738103 q^{52} -2.59306 q^{53} +2.13183 q^{54} +10.4919 q^{55} +4.99859 q^{57} +17.1758 q^{58} -12.0597 q^{59} +6.00727 q^{60} +1.73842 q^{61} -21.1629 q^{62} -11.6025 q^{64} -0.684744 q^{65} +9.47459 q^{66} +13.8400 q^{67} +4.60437 q^{68} -1.55849 q^{69} -10.2484 q^{71} +1.16116 q^{72} -7.01139 q^{73} +14.4354 q^{74} +0.572989 q^{75} +12.7198 q^{76} -0.618352 q^{78} +14.8949 q^{79} -6.17084 q^{80} +1.00000 q^{81} +2.13183 q^{82} +6.61380 q^{83} +4.27151 q^{85} -14.2844 q^{86} +8.05686 q^{87} +5.16061 q^{88} -13.1333 q^{89} +5.03264 q^{90} -3.96587 q^{92} -9.92711 q^{93} +0.0565637 q^{94} +11.8003 q^{95} -7.89484 q^{96} -4.50954 q^{97} +4.44436 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} + 10 q^{3} + 18 q^{4} + 6 q^{5} + 4 q^{6} + 12 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 4 * q^2 + 10 * q^3 + 18 * q^4 + 6 * q^5 + 4 * q^6 + 12 * q^8 + 10 * q^9	\( 10 q + 4 q^{2} + 10 q^{3} + 18 q^{4} + 6 q^{5} + 4 q^{6} + 12 q^{8} + 10 q^{9} + 2 q^{10} - 2 q^{11} + 18 q^{12} + 6 q^{15} + 14 q^{16} + 8 q^{17} + 4 q^{18} + 6 q^{19} + 20 q^{20} + 2 q^{22} + 12 q^{24} + 10 q^{25} + 16 q^{26} + 10 q^{27} + 16 q^{29} + 2 q^{30} + 2 q^{31} + 38 q^{32} - 2 q^{33} - 4 q^{34} + 18 q^{36} + 24 q^{37} - 26 q^{38} + 40 q^{40} + 10 q^{41} + 8 q^{43} - 8 q^{44} + 6 q^{45} + 4 q^{46} - 8 q^{47} + 14 q^{48} + 44 q^{50} + 8 q^{51} - 30 q^{52} + 24 q^{53} + 4 q^{54} + 6 q^{57} - 14 q^{58} + 6 q^{59} + 20 q^{60} - 14 q^{61} - 2 q^{62} + 86 q^{64} + 28 q^{65} + 2 q^{66} + 26 q^{67} - 6 q^{68} + 14 q^{71} + 12 q^{72} - 36 q^{73} + 18 q^{74} + 10 q^{75} - 32 q^{76} + 16 q^{78} + 20 q^{79} + 70 q^{80} + 10 q^{81} + 4 q^{82} + 40 q^{83} + 24 q^{85} - 36 q^{86} + 16 q^{87} + 14 q^{88} + 2 q^{89} + 2 q^{90} + 8 q^{92} + 2 q^{93} - 54 q^{94} - 24 q^{95} + 38 q^{96} + 16 q^{97} - 2 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 + 10 * q^3 + 18 * q^4 + 6 * q^5 + 4 * q^6 + 12 * q^8 + 10 * q^9 + 2 * q^10 - 2 * q^11 + 18 * q^12 + 6 * q^15 + 14 * q^16 + 8 * q^17 + 4 * q^18 + 6 * q^19 + 20 * q^20 + 2 * q^22 + 12 * q^24 + 10 * q^25 + 16 * q^26 + 10 * q^27 + 16 * q^29 + 2 * q^30 + 2 * q^31 + 38 * q^32 - 2 * q^33 - 4 * q^34 + 18 * q^36 + 24 * q^37 - 26 * q^38 + 40 * q^40 + 10 * q^41 + 8 * q^43 - 8 * q^44 + 6 * q^45 + 4 * q^46 - 8 * q^47 + 14 * q^48 + 44 * q^50 + 8 * q^51 - 30 * q^52 + 24 * q^53 + 4 * q^54 + 6 * q^57 - 14 * q^58 + 6 * q^59 + 20 * q^60 - 14 * q^61 - 2 * q^62 + 86 * q^64 + 28 * q^65 + 2 * q^66 + 26 * q^67 - 6 * q^68 + 14 * q^71 + 12 * q^72 - 36 * q^73 + 18 * q^74 + 10 * q^75 - 32 * q^76 + 16 * q^78 + 20 * q^79 + 70 * q^80 + 10 * q^81 + 4 * q^82 + 40 * q^83 + 24 * q^85 - 36 * q^86 + 16 * q^87 + 14 * q^88 + 2 * q^89 + 2 * q^90 + 8 * q^92 + 2 * q^93 - 54 * q^94 - 24 * q^95 + 38 * q^96 + 16 * q^97 - 2 * q^99

Introduction

L-functions

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Database

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