LMFDB - Embedded newform 6027.2.a.bj.1.7

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:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} - 19 x^{12} + 36 x^{11} + 134 x^{10} - 237 x^{9} - 438 x^{8} + 716 x^{7} + 662 x^{6} + \cdots + 16 $ x^14 - 2x^13 - 19x^12 + 36x^11 + 134x^10 - 237x^9 - 438x^8 + 716x^7 + 662x^6 - 1007x^5 - 384x^4 + 579x^3 + 44x^2 - 112*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 861)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$0.442251$ 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)

$f(q)$	$=$	$q-0.442251 q^{2} -1.00000 q^{3} -1.80441 q^{4} +4.29274 q^{5} +0.442251 q^{6} +1.68250 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.442251 q^{2} -1.00000 q^{3} -1.80441 q^{4} +4.29274 q^{5} +0.442251 q^{6} +1.68250 q^{8} +1.00000 q^{9} -1.89847 q^{10} -2.21212 q^{11} +1.80441 q^{12} +3.11687 q^{13} -4.29274 q^{15} +2.86474 q^{16} +6.92396 q^{17} -0.442251 q^{18} -7.72487 q^{19} -7.74589 q^{20} +0.978311 q^{22} +0.0381692 q^{23} -1.68250 q^{24} +13.4277 q^{25} -1.37844 q^{26} -1.00000 q^{27} +2.66709 q^{29} +1.89847 q^{30} -4.69959 q^{31} -4.63194 q^{32} +2.21212 q^{33} -3.06213 q^{34} -1.80441 q^{36} -0.0300718 q^{37} +3.41633 q^{38} -3.11687 q^{39} +7.22256 q^{40} +1.00000 q^{41} +11.0093 q^{43} +3.99158 q^{44} +4.29274 q^{45} -0.0168804 q^{46} +3.78108 q^{47} -2.86474 q^{48} -5.93839 q^{50} -6.92396 q^{51} -5.62412 q^{52} -0.546137 q^{53} +0.442251 q^{54} -9.49606 q^{55} +7.72487 q^{57} -1.17952 q^{58} +9.55909 q^{59} +7.74589 q^{60} -6.02077 q^{61} +2.07840 q^{62} -3.68100 q^{64} +13.3799 q^{65} -0.978311 q^{66} -8.97673 q^{67} -12.4937 q^{68} -0.0381692 q^{69} +15.6199 q^{71} +1.68250 q^{72} +2.42299 q^{73} +0.0132993 q^{74} -13.4277 q^{75} +13.9389 q^{76} +1.37844 q^{78} +2.16136 q^{79} +12.2976 q^{80} +1.00000 q^{81} -0.442251 q^{82} -17.0488 q^{83} +29.7228 q^{85} -4.86886 q^{86} -2.66709 q^{87} -3.72190 q^{88} +8.69193 q^{89} -1.89847 q^{90} -0.0688730 q^{92} +4.69959 q^{93} -1.67218 q^{94} -33.1609 q^{95} +4.63194 q^{96} -0.216724 q^{97} -2.21212 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{2} - 14 q^{3} + 14 q^{4} + 10 q^{5} + 2 q^{6} - 6 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q - 2 * q^2 - 14 * q^3 + 14 * q^4 + 10 * q^5 + 2 * q^6 - 6 * q^8 + 14 * q^9	$ 14 q - 2 q^{2} - 14 q^{3} + 14 q^{4} + 10 q^{5} + 2 q^{6} - 6 q^{8} + 14 q^{9} + 3 q^{10} - 16 q^{11} - 14 q^{12} + 21 q^{13} - 10 q^{15} + 22 q^{16} + 12 q^{17} - 2 q^{18} + 2 q^{19} + 40 q^{20} + q^{22} - 7 q^{23} + 6 q^{24} + 22 q^{25} + 2 q^{26} - 14 q^{27} - 16 q^{29} - 3 q^{30} + 8 q^{31} - 19 q^{32} + 16 q^{33} + 33 q^{34} + 14 q^{36} + q^{37} + 32 q^{38} - 21 q^{39} - 13 q^{40} + 14 q^{41} + 14 q^{43} - 36 q^{44} + 10 q^{45} - 12 q^{46} + 12 q^{47} - 22 q^{48} - q^{50} - 12 q^{51} + 60 q^{52} - 20 q^{53} + 2 q^{54} - 11 q^{55} - 2 q^{57} + 21 q^{58} + 25 q^{59} - 40 q^{60} + 26 q^{61} - 33 q^{62} + 42 q^{64} - 8 q^{65} - q^{66} - 22 q^{67} + 15 q^{68} + 7 q^{69} - 36 q^{71} - 6 q^{72} + 31 q^{73} - 65 q^{74} - 22 q^{75} - 2 q^{76} - 2 q^{78} + 12 q^{79} + 112 q^{80} + 14 q^{81} - 2 q^{82} + 20 q^{83} + 40 q^{85} - 9 q^{86} + 16 q^{87} - 54 q^{88} + 39 q^{89} + 3 q^{90} + 63 q^{92} - 8 q^{93} + 14 q^{94} - 55 q^{95} + 19 q^{96} + 18 q^{97} - 16 q^{99}+O(q^{100}) $ 14 * q - 2 * q^2 - 14 * q^3 + 14 * q^4 + 10 * q^5 + 2 * q^6 - 6 * q^8 + 14 * q^9 + 3 * q^10 - 16 * q^11 - 14 * q^12 + 21 * q^13 - 10 * q^15 + 22 * q^16 + 12 * q^17 - 2 * q^18 + 2 * q^19 + 40 * q^20 + q^22 - 7 * q^23 + 6 * q^24 + 22 * q^25 + 2 * q^26 - 14 * q^27 - 16 * q^29 - 3 * q^30 + 8 * q^31 - 19 * q^32 + 16 * q^33 + 33 * q^34 + 14 * q^36 + q^37 + 32 * q^38 - 21 * q^39 - 13 * q^40 + 14 * q^41 + 14 * q^43 - 36 * q^44 + 10 * q^45 - 12 * q^46 + 12 * q^47 - 22 * q^48 - q^50 - 12 * q^51 + 60 * q^52 - 20 * q^53 + 2 * q^54 - 11 * q^55 - 2 * q^57 + 21 * q^58 + 25 * q^59 - 40 * q^60 + 26 * q^61 - 33 * q^62 + 42 * q^64 - 8 * q^65 - q^66 - 22 * q^67 + 15 * q^68 + 7 * q^69 - 36 * q^71 - 6 * q^72 + 31 * q^73 - 65 * q^74 - 22 * q^75 - 2 * q^76 - 2 * q^78 + 12 * q^79 + 112 * q^80 + 14 * q^81 - 2 * q^82 + 20 * q^83 + 40 * q^85 - 9 * q^86 + 16 * q^87 - 54 * q^88 + 39 * q^89 + 3 * q^90 + 63 * q^92 - 8 * q^93 + 14 * q^94 - 55 * q^95 + 19 * q^96 + 18 * q^97 - 16 * 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 $

$2$	−0.442251	−0.312718	−0.156359	−	0.987700i	$-0.549976\pi$
$2$	−0.442251	−0.312718	−0.156359	+	0.987700i	$0.549976\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.80441	−0.902207
$5$	4.29274	1.91977	0.959887	−	0.280387i	$-0.0904629\pi$
$5$	4.29274	1.91977	0.959887	+	0.280387i	$0.0904629\pi$
$6$	0.442251	0.180548
$7$	0	0
$7$	0	0
$8$	1.68250	0.594855
$9$	1.00000	0.333333
$10$	−1.89847	−0.600349
$11$	−2.21212	−0.666979	−0.333489	−	0.942754i	$-0.608226\pi$
$11$	−2.21212	−0.666979	−0.333489	+	0.942754i	$0.608226\pi$
$12$	1.80441	0.520890
$13$	3.11687	0.864463	0.432231	−	0.901763i	$-0.357726\pi$
$13$	3.11687	0.864463	0.432231	+	0.901763i	$0.357726\pi$
$14$	0	0
$15$	−4.29274	−1.10838
$16$	2.86474	0.716185
$17$	6.92396	1.67931	0.839654	−	0.543122i	$-0.182758\pi$
$17$	6.92396	1.67931	0.839654	+	0.543122i	$0.182758\pi$
$18$	−0.442251	−0.104239
$19$	−7.72487	−1.77221	−0.886104	−	0.463487i	$-0.846598\pi$
$19$	−7.72487	−1.77221	−0.886104	+	0.463487i	$0.846598\pi$
$20$	−7.74589	−1.73203
$21$	0	0
$22$	0.978311	0.208577
$23$	0.0381692	0.00795883	0.00397941	−	0.999992i	$-0.498733\pi$
$23$	0.0381692	0.00795883	0.00397941	+	0.999992i	$0.498733\pi$
$24$	−1.68250	−0.343440
$25$	13.4277	2.68553
$26$	−1.37844	−0.270334
$27$	−1.00000	−0.192450
$28$	0	0
$29$	2.66709	0.495266	0.247633	−	0.968854i	$-0.420347\pi$
$29$	2.66709	0.495266	0.247633	+	0.968854i	$0.420347\pi$
$30$	1.89847	0.346612
$31$	−4.69959	−0.844072	−0.422036	−	0.906579i	$-0.638684\pi$
$31$	−4.69959	−0.844072	−0.422036	+	0.906579i	$0.638684\pi$
$32$	−4.63194	−0.818820
$33$	2.21212	0.385080
$34$	−3.06213	−0.525151
$35$	0	0
$36$	−1.80441	−0.300736
$37$	−0.0300718	−0.00494377	−0.00247189	−	0.999997i	$-0.500787\pi$
$37$	−0.0300718	−0.00494377	−0.00247189	+	0.999997i	$0.500787\pi$
$38$	3.41633	0.554202
$39$	−3.11687	−0.499098
$40$	7.22256	1.14199
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	11.0093	1.67890	0.839449	−	0.543438i	$-0.182878\pi$
$43$	11.0093	1.67890	0.839449	+	0.543438i	$0.182878\pi$
$44$	3.99158	0.601753
$45$	4.29274	0.639925
$46$	−0.0168804	−0.00248887
$47$	3.78108	0.551527	0.275763	−	0.961226i	$-0.411069\pi$
$47$	3.78108	0.551527	0.275763	+	0.961226i	$0.411069\pi$
$48$	−2.86474	−0.413490
$49$	0	0
$50$	−5.93839	−0.839815
$51$	−6.92396	−0.969549
$52$	−5.62412	−0.779925
$53$	−0.546137	−0.0750176	−0.0375088	−	0.999296i	$-0.511942\pi$
$53$	−0.546137	−0.0750176	−0.0375088	+	0.999296i	$0.511942\pi$
$54$	0.442251	0.0601827
$55$	−9.49606	−1.28045
$56$	0	0
$57$	7.72487	1.02318
$58$	−1.17952	−0.154879
$59$	9.55909	1.24449	0.622243	−	0.782824i	$-0.286221\pi$
$59$	9.55909	1.24449	0.622243	+	0.782824i	$0.286221\pi$
$60$	7.74589	0.999990
$61$	−6.02077	−0.770881	−0.385441	−	0.922733i	$-0.625951\pi$
$61$	−6.02077	−0.770881	−0.385441	+	0.922733i	$0.625951\pi$
$62$	2.07840	0.263957
$63$	0	0
$64$	−3.68100	−0.460125
$65$	13.3799	1.65957
$66$	−0.978311	−0.120422
$67$	−8.97673	−1.09668	−0.548341	−	0.836255i	$-0.684741\pi$
$67$	−8.97673	−1.09668	−0.548341	+	0.836255i	$0.684741\pi$
$68$	−12.4937	−1.51508
$69$	−0.0381692	−0.00459503
$70$	0	0
$71$	15.6199	1.85374	0.926868	−	0.375386i	$-0.122490\pi$
$71$	15.6199	1.85374	0.926868	+	0.375386i	$0.122490\pi$
$72$	1.68250	0.198285
$73$	2.42299	0.283590	0.141795	−	0.989896i	$-0.454713\pi$
$73$	2.42299	0.283590	0.141795	+	0.989896i	$0.454713\pi$
$74$	0.0132993	0.00154601
$75$	−13.4277	−1.55049
$76$	13.9389	1.59890
$77$	0	0
$78$	1.37844	0.156077
$79$	2.16136	0.243172	0.121586	−	0.992581i	$-0.461202\pi$
$79$	2.16136	0.243172	0.121586	+	0.992581i	$0.461202\pi$
$80$	12.2976	1.37491
$81$	1.00000	0.111111
$82$	−0.442251	−0.0488384
$83$	−17.0488	−1.87135	−0.935675	−	0.352862i	$-0.885208\pi$
$83$	−17.0488	−1.87135	−0.935675	+	0.352862i	$0.885208\pi$
$84$	0	0
$85$	29.7228	3.22389
$86$	−4.86886	−0.525023
$87$	−2.66709	−0.285942
$88$	−3.72190	−0.396756
$89$	8.69193	0.921343	0.460672	−	0.887571i	$-0.347609\pi$
$89$	8.69193	0.921343	0.460672	+	0.887571i	$0.347609\pi$
$90$	−1.89847	−0.200116
$91$	0	0
$92$	−0.0688730	−0.00718051
$93$	4.69959	0.487325
$94$	−1.67218	−0.172473
$95$	−33.1609	−3.40224
$96$	4.63194	0.472746
$97$	−0.216724	−0.0220050	−0.0110025	−	0.999939i	$-0.503502\pi$
$97$	−0.216724	−0.0220050	−0.0110025	+	0.999939i	$0.503502\pi$
$98$	0	0
$99$	−2.21212	−0.222326
$100$	−24.2291	−2.42291
$101$	2.53326	0.252069	0.126034	−	0.992026i	$-0.459775\pi$
$101$	2.53326	0.252069	0.126034	+	0.992026i	$0.459775\pi$
$102$	3.06213	0.303196
$103$	0.709634	0.0699223	0.0349612	−	0.999389i	$-0.488869\pi$
$103$	0.709634	0.0699223	0.0349612	+	0.999389i	$0.488869\pi$
$104$	5.24414	0.514230
$105$	0	0
$106$	0.241529	0.0234594
$107$	6.42089	0.620731	0.310366	−	0.950617i	$-0.399549\pi$
$107$	6.42089	0.620731	0.310366	+	0.950617i	$0.399549\pi$
$108$	1.80441	0.173630
$109$	−2.52449	−0.241802	−0.120901	−	0.992665i	$-0.538578\pi$
$109$	−2.52449	−0.241802	−0.120901	+	0.992665i	$0.538578\pi$
$110$	4.19964	0.400420
$111$	0.0300718	0.00285429
$112$	0	0
$113$	1.71911	0.161721	0.0808603	−	0.996725i	$-0.474233\pi$
$113$	1.71911	0.161721	0.0808603	+	0.996725i	$0.474233\pi$
$114$	−3.41633	−0.319969
$115$	0.163851	0.0152791
$116$	−4.81253	−0.446832
$117$	3.11687	0.288154
$118$	−4.22751	−0.389174
$119$	0	0
$120$	−7.22256	−0.659327
$121$	−6.10653	−0.555139
$122$	2.66269	0.241069
$123$	−1.00000	−0.0901670
$124$	8.48001	0.761527
$125$	36.1778	3.23584
$126$	0	0
$127$	−18.8770	−1.67506	−0.837529	−	0.546392i	$-0.816001\pi$
$127$	−18.8770	−1.67506	−0.837529	+	0.546392i	$0.816001\pi$
$128$	10.8918	0.962709
$129$	−11.0093	−0.969313
$130$	−5.91727	−0.518979
$131$	9.69220	0.846811	0.423406	−	0.905940i	$-0.360834\pi$
$131$	9.69220	0.846811	0.423406	+	0.905940i	$0.360834\pi$
$132$	−3.99158	−0.347422
$133$	0	0
$134$	3.96997	0.342953
$135$	−4.29274	−0.369461
$136$	11.6496	0.998945
$137$	6.05845	0.517608	0.258804	−	0.965930i	$-0.416672\pi$
$137$	6.05845	0.517608	0.258804	+	0.965930i	$0.416672\pi$
$138$	0.0168804	0.00143695
$139$	−1.67013	−0.141658	−0.0708291	−	0.997488i	$-0.522565\pi$
$139$	−1.67013	−0.141658	−0.0708291	+	0.997488i	$0.522565\pi$
$140$	0	0
$141$	−3.78108	−0.318424
$142$	−6.90790	−0.579698
$143$	−6.89487	−0.576578
$144$	2.86474	0.238728
$145$	11.4491	0.950798
$146$	−1.07157	−0.0886837
$147$	0	0
$148$	0.0542620	0.00446031
$149$	2.69542	0.220817	0.110409	−	0.993886i	$-0.464784\pi$
$149$	2.69542	0.220817	0.110409	+	0.993886i	$0.464784\pi$
$150$	5.93839	0.484868
$151$	−1.70580	−0.138816	−0.0694082	−	0.997588i	$-0.522111\pi$
$151$	−1.70580	−0.138816	−0.0694082	+	0.997588i	$0.522111\pi$
$152$	−12.9971	−1.05421
$153$	6.92396	0.559769
$154$	0	0
$155$	−20.1741	−1.62043
$156$	5.62412	0.450290
$157$	11.6850	0.932562	0.466281	−	0.884637i	$-0.345594\pi$
$157$	11.6850	0.932562	0.466281	+	0.884637i	$0.345594\pi$
$158$	−0.955865	−0.0760445
$159$	0.546137	0.0433114
$160$	−19.8837	−1.57195
$161$	0	0
$162$	−0.442251	−0.0347465
$163$	−12.3332	−0.966009	−0.483005	−	0.875618i	$-0.660455\pi$
$163$	−12.3332	−0.966009	−0.483005	+	0.875618i	$0.660455\pi$
$164$	−1.80441	−0.140901
$165$	9.49606	0.739267
$166$	7.53985	0.585206
$167$	6.35364	0.491659	0.245830	−	0.969313i	$-0.420940\pi$
$167$	6.35364	0.491659	0.245830	+	0.969313i	$0.420940\pi$
$168$	0	0
$169$	−3.28515	−0.252704
$170$	−13.1449	−1.00817
$171$	−7.72487	−0.590736
$172$	−19.8653	−1.51471
$173$	−0.579038	−0.0440235	−0.0220117	−	0.999758i	$-0.507007\pi$
$173$	−0.579038	−0.0440235	−0.0220117	+	0.999758i	$0.507007\pi$
$174$	1.17952	0.0894193
$175$	0	0
$176$	−6.33714	−0.477680
$177$	−9.55909	−0.718505
$178$	−3.84401	−0.288121
$179$	21.2907	1.59134	0.795672	−	0.605727i	$-0.207118\pi$
$179$	21.2907	1.59134	0.795672	+	0.605727i	$0.207118\pi$
$180$	−7.74589	−0.577345
$181$	−21.3004	−1.58325	−0.791623	−	0.611010i	$-0.790763\pi$
$181$	−21.3004	−1.58325	−0.791623	+	0.611010i	$0.790763\pi$
$182$	0	0
$183$	6.02077	0.445068
$184$	0.0642198	0.00473435
$185$	−0.129091	−0.00949093
$186$	−2.07840	−0.152396
$187$	−15.3166	−1.12006
$188$	−6.82263	−0.497591
$189$	0	0
$190$	14.6654	1.06394
$191$	−2.25947	−0.163490	−0.0817448	−	0.996653i	$-0.526049\pi$
$191$	−2.25947	−0.163490	−0.0817448	+	0.996653i	$0.526049\pi$
$192$	3.68100	0.265653
$193$	−19.8775	−1.43081	−0.715406	−	0.698709i	$-0.753758\pi$
$193$	−19.8775	−1.43081	−0.715406	+	0.698709i	$0.753758\pi$
$194$	0.0958464	0.00688137
$195$	−13.3799	−0.958155
$196$	0	0
$197$	−7.13650	−0.508455	−0.254227	−	0.967144i	$-0.581821\pi$
$197$	−7.13650	−0.508455	−0.254227	+	0.967144i	$0.581821\pi$
$198$	0.978311	0.0695255
$199$	−13.9705	−0.990343	−0.495172	−	0.868795i	$-0.664895\pi$
$199$	−13.9705	−0.990343	−0.495172	+	0.868795i	$0.664895\pi$
$200$	22.5921	1.59750
$201$	8.97673	0.633170
$202$	−1.12034	−0.0788265
$203$	0	0
$204$	12.4937	0.874734
$205$	4.29274	0.299818
$206$	−0.313836	−0.0218660
$207$	0.0381692	0.00265294
$208$	8.92901	0.619115
$209$	17.0883	1.18202
$210$	0	0
$211$	23.3091	1.60466	0.802332	−	0.596878i	$-0.203592\pi$
$211$	23.3091	1.60466	0.802332	+	0.596878i	$0.203592\pi$
$212$	0.985457	0.0676814
$213$	−15.6199	−1.07026
$214$	−2.83964	−0.194114
$215$	47.2600	3.22311
$216$	−1.68250	−0.114480
$217$	0	0
$218$	1.11646	0.0756159
$219$	−2.42299	−0.163731
$220$	17.1348	1.15523
$221$	21.5811	1.45170
$222$	−0.0132993	−0.000892589 0
$223$	24.6795	1.65266	0.826330	−	0.563186i	$-0.190425\pi$
$223$	24.6795	1.65266	0.826330	+	0.563186i	$0.190425\pi$
$224$	0	0
$225$	13.4277	0.895177
$226$	−0.760279	−0.0505730
$227$	11.7407	0.779259	0.389630	−	0.920972i	$-0.372603\pi$
$227$	11.7407	0.779259	0.389630	+	0.920972i	$0.372603\pi$
$228$	−13.9389	−0.923124
$229$	−15.4411	−1.02037	−0.510187	−	0.860063i	$-0.670424\pi$
$229$	−15.4411	−1.02037	−0.510187	+	0.860063i	$0.670424\pi$
$230$	−0.0724630	−0.00477807
$231$	0	0
$232$	4.48739	0.294611
$233$	−7.24116	−0.474384	−0.237192	−	0.971463i	$-0.576227\pi$
$233$	−7.24116	−0.474384	−0.237192	+	0.971463i	$0.576227\pi$
$234$	−1.37844	−0.0901112
$235$	16.2312	1.05881
$236$	−17.2486	−1.12279
$237$	−2.16136	−0.140396
$238$	0	0
$239$	−13.7858	−0.891726	−0.445863	−	0.895101i	$-0.647103\pi$
$239$	−13.7858	−0.891726	−0.445863	+	0.895101i	$0.647103\pi$
$240$	−12.2976	−0.793806
$241$	3.50900	0.226035	0.113017	−	0.993593i	$-0.463948\pi$
$241$	3.50900	0.226035	0.113017	+	0.993593i	$0.463948\pi$
$242$	2.70062	0.173602
$243$	−1.00000	−0.0641500
$244$	10.8640	0.695494
$245$	0	0
$246$	0.442251	0.0281969
$247$	−24.0774	−1.53201
$248$	−7.90709	−0.502100
$249$	17.0488	1.08042
$250$	−15.9997	−1.01191
$251$	14.8746	0.938876	0.469438	−	0.882965i	$-0.344457\pi$
$251$	14.8746	0.938876	0.469438	+	0.882965i	$0.344457\pi$
$252$	0	0
$253$	−0.0844348	−0.00530837
$254$	8.34835	0.523822
$255$	−29.7228	−1.86131
$256$	2.54509	0.159068
$257$	−21.7559	−1.35709	−0.678547	−	0.734557i	$-0.737390\pi$
$257$	−21.7559	−1.35709	−0.678547	+	0.734557i	$0.737390\pi$
$258$	4.86886	0.303122
$259$	0	0
$260$	−24.1429	−1.49728
$261$	2.66709	0.165089
$262$	−4.28638	−0.264814
$263$	2.27801	0.140468	0.0702340	−	0.997531i	$-0.477625\pi$
$263$	2.27801	0.140468	0.0702340	+	0.997531i	$0.477625\pi$
$264$	3.72190	0.229067
$265$	−2.34442	−0.144017
$266$	0	0
$267$	−8.69193	−0.531938
$268$	16.1977	0.989435
$269$	2.03093	0.123828	0.0619141	−	0.998081i	$-0.480280\pi$
$269$	2.03093	0.123828	0.0619141	+	0.998081i	$0.480280\pi$
$270$	1.89847	0.115537
$271$	15.8435	0.962427	0.481214	−	0.876603i	$-0.340196\pi$
$271$	15.8435	0.962427	0.481214	+	0.876603i	$0.340196\pi$
$272$	19.8354	1.20269
$273$	0	0
$274$	−2.67935	−0.161866
$275$	−29.7036	−1.79119
$276$	0.0688730	0.00414567
$277$	−3.50000	−0.210294	−0.105147	−	0.994457i	$-0.533531\pi$
$277$	−3.50000	−0.210294	−0.105147	+	0.994457i	$0.533531\pi$
$278$	0.738614	0.0442992
$279$	−4.69959	−0.281357
$280$	0	0
$281$	26.7164	1.59377	0.796883	−	0.604134i	$-0.206481\pi$
$281$	26.7164	1.59377	0.796883	+	0.604134i	$0.206481\pi$
$282$	1.67218	0.0995771
$283$	15.6917	0.932774	0.466387	−	0.884581i	$-0.345555\pi$
$283$	15.6917	0.932774	0.466387	+	0.884581i	$0.345555\pi$
$284$	−28.1847	−1.67245
$285$	33.1609	1.96428
$286$	3.04926	0.180307
$287$	0	0
$288$	−4.63194	−0.272940
$289$	30.9413	1.82007
$290$	−5.06338	−0.297332
$291$	0.216724	0.0127046
$292$	−4.37208	−0.255857
$293$	14.4844	0.846189	0.423095	−	0.906085i	$-0.360944\pi$
$293$	14.4844	0.846189	0.423095	+	0.906085i	$0.360944\pi$
$294$	0	0
$295$	41.0347	2.38913
$296$	−0.0505959	−0.00294083
$297$	2.21212	0.128360
$298$	−1.19205	−0.0690537
$299$	0.118968	0.00688011
$300$	24.2291	1.39887
$301$	0	0
$302$	0.754393	0.0434105
$303$	−2.53326	−0.145532
$304$	−22.1297	−1.26923
$305$	−25.8456	−1.47992
$306$	−3.06213	−0.175050
$307$	−19.7492	−1.12715	−0.563573	−	0.826066i	$-0.690574\pi$
$307$	−19.7492	−1.12715	−0.563573	+	0.826066i	$0.690574\pi$
$308$	0	0
$309$	−0.709634	−0.0403697
$310$	8.92203	0.506737
$311$	18.1355	1.02837	0.514184	−	0.857680i	$-0.328095\pi$
$311$	18.1355	1.02837	0.514184	+	0.857680i	$0.328095\pi$
$312$	−5.24414	−0.296891
$313$	−3.28237	−0.185531	−0.0927653	−	0.995688i	$-0.529571\pi$
$313$	−3.28237	−0.185531	−0.0927653	+	0.995688i	$0.529571\pi$
$314$	−5.16769	−0.291629
$315$	0	0
$316$	−3.90000	−0.219392
$317$	−0.440700	−0.0247522	−0.0123761	−	0.999923i	$-0.503940\pi$
$317$	−0.440700	−0.0247522	−0.0123761	+	0.999923i	$0.503940\pi$
$318$	−0.241529	−0.0135443
$319$	−5.89991	−0.330332
$320$	−15.8016	−0.883336
$321$	−6.42089	−0.358379
$322$	0	0
$323$	−53.4867	−2.97608
$324$	−1.80441	−0.100245
$325$	41.8522	2.32154
$326$	5.45436	0.302089
$327$	2.52449	0.139604
$328$	1.68250	0.0929008
$329$	0	0
$330$	−4.19964	−0.231183
$331$	−3.26805	−0.179628	−0.0898141	−	0.995959i	$-0.528627\pi$
$331$	−3.26805	−0.179628	−0.0898141	+	0.995959i	$0.528627\pi$
$332$	30.7631	1.68835
$333$	−0.0300718	−0.00164792
$334$	−2.80990	−0.153751
$335$	−38.5348	−2.10538
$336$	0	0
$337$	−18.8129	−1.02481	−0.512403	−	0.858745i	$-0.671244\pi$
$337$	−18.8129	−1.02481	−0.512403	+	0.858745i	$0.671244\pi$
$338$	1.45286	0.0790252
$339$	−1.71911	−0.0933694
$340$	−53.6323	−2.90862
$341$	10.3961	0.562978
$342$	3.41633	0.184734
$343$	0	0
$344$	18.5232	0.998702
$345$	−0.163851	−0.00882142
$346$	0.256080	0.0137669
$347$	−24.8798	−1.33562	−0.667809	−	0.744332i	$-0.732768\pi$
$347$	−24.8798	−1.33562	−0.667809	+	0.744332i	$0.732768\pi$
$348$	4.81253	0.257979
$349$	34.7651	1.86094	0.930468	−	0.366374i	$-0.119401\pi$
$349$	34.7651	1.86094	0.930468	+	0.366374i	$0.119401\pi$
$350$	0	0
$351$	−3.11687	−0.166366
$352$	10.2464	0.546135
$353$	−16.6295	−0.885098	−0.442549	−	0.896744i	$-0.645926\pi$
$353$	−16.6295	−0.885098	−0.442549	+	0.896744i	$0.645926\pi$
$354$	4.22751	0.224690
$355$	67.0521	3.55876
$356$	−15.6839	−0.831242
$357$	0	0
$358$	−9.41584	−0.497643
$359$	−25.2772	−1.33408	−0.667041	−	0.745021i	$-0.732439\pi$
$359$	−25.2772	−1.33408	−0.667041	+	0.745021i	$0.732439\pi$
$360$	7.22256	0.380663
$361$	40.6736	2.14072
$362$	9.42011	0.495110
$363$	6.10653	0.320510
$364$	0	0
$365$	10.4013	0.544428
$366$	−2.66269	−0.139181
$367$	33.2183	1.73398	0.866992	−	0.498322i	$-0.166050\pi$
$367$	33.2183	1.73398	0.866992	+	0.498322i	$0.166050\pi$
$368$	0.109345	0.00569999
$369$	1.00000	0.0520579
$370$	0.0570904	0.00296799
$371$	0	0
$372$	−8.48001	−0.439668
$373$	25.9809	1.34524	0.672619	−	0.739989i	$-0.265169\pi$
$373$	25.9809	1.34524	0.672619	+	0.739989i	$0.265169\pi$
$374$	6.77379	0.350264
$375$	−36.1778	−1.86821
$376$	6.36168	0.328079
$377$	8.31295	0.428139
$378$	0	0
$379$	10.2601	0.527028	0.263514	−	0.964656i	$-0.415118\pi$
$379$	10.2601	0.527028	0.263514	+	0.964656i	$0.415118\pi$
$380$	59.8360	3.06952
$381$	18.8770	0.967096
$382$	0.999253	0.0511262
$383$	−2.59188	−0.132439	−0.0662194	−	0.997805i	$-0.521094\pi$
$383$	−2.59188	−0.132439	−0.0662194	+	0.997805i	$0.521094\pi$
$384$	−10.8918	−0.555820
$385$	0	0
$386$	8.79083	0.447441
$387$	11.0093	0.559633
$388$	0.391060	0.0198531
$389$	−8.65407	−0.438779	−0.219390	−	0.975637i	$-0.570407\pi$
$389$	−8.65407	−0.438779	−0.219390	+	0.975637i	$0.570407\pi$
$390$	5.91727	0.299633
$391$	0.264282	0.0133653
$392$	0	0
$393$	−9.69220	−0.488907
$394$	3.15612	0.159003
$395$	9.27818	0.466836
$396$	3.99158	0.200584
$397$	30.0428	1.50780	0.753902	−	0.656987i	$-0.228170\pi$
$397$	30.0428	1.50780	0.753902	+	0.656987i	$0.228170\pi$
$398$	6.17847	0.309699
$399$	0	0
$400$	38.4667	1.92334
$401$	12.0942	0.603955	0.301978	−	0.953315i	$-0.402353\pi$
$401$	12.0942	0.603955	0.301978	+	0.953315i	$0.402353\pi$
$402$	−3.96997	−0.198004
$403$	−14.6480	−0.729669
$404$	−4.57105	−0.227418
$405$	4.29274	0.213308
$406$	0	0
$407$	0.0665224	0.00329739
$408$	−11.6496	−0.576741
$409$	−13.5140	−0.668222	−0.334111	−	0.942534i	$-0.608436\pi$
$409$	−13.5140	−0.668222	−0.334111	+	0.942534i	$0.608436\pi$
$410$	−1.89847	−0.0937587
$411$	−6.05845	−0.298841
$412$	−1.28047	−0.0630844
$413$	0	0
$414$	−0.0168804	−0.000829624 0
$415$	−73.1862	−3.59257
$416$	−14.4371	−0.707839
$417$	1.67013	0.0817864
$418$	−7.55733	−0.369641
$419$	32.1763	1.57191	0.785957	−	0.618281i	$-0.212171\pi$
$419$	32.1763	1.57191	0.785957	+	0.618281i	$0.212171\pi$
$420$	0	0
$421$	−32.2673	−1.57261	−0.786307	−	0.617836i	$-0.788010\pi$
$421$	−32.2673	−1.57261	−0.786307	+	0.617836i	$0.788010\pi$
$422$	−10.3085	−0.501808
$423$	3.78108	0.183842
$424$	−0.918877	−0.0446246
$425$	92.9726	4.50983
$426$	6.90790	0.334689
$427$	0	0
$428$	−11.5859	−0.560028
$429$	6.89487	0.332888
$430$	−20.9008	−1.00792
$431$	10.4482	0.503271	0.251635	−	0.967822i	$-0.419032\pi$
$431$	10.4482	0.503271	0.251635	+	0.967822i	$0.419032\pi$
$432$	−2.86474	−0.137830
$433$	3.79123	0.182195	0.0910975	−	0.995842i	$-0.470963\pi$
$433$	3.79123	0.182195	0.0910975	+	0.995842i	$0.470963\pi$
$434$	0	0
$435$	−11.4491	−0.548943
$436$	4.55522	0.218155
$437$	−0.294852	−0.0141047
$438$	1.07157	0.0512016
$439$	−4.49268	−0.214424	−0.107212	−	0.994236i	$-0.534192\pi$
$439$	−4.49268	−0.214424	−0.107212	+	0.994236i	$0.534192\pi$
$440$	−15.9772	−0.761682
$441$	0	0
$442$	−9.54424	−0.453973
$443$	−8.19908	−0.389550	−0.194775	−	0.980848i	$-0.562398\pi$
$443$	−8.19908	−0.389550	−0.194775	+	0.980848i	$0.562398\pi$
$444$	−0.0542620	−0.00257516
$445$	37.3123	1.76877
$446$	−10.9145	−0.516817
$447$	−2.69542	−0.127489
$448$	0	0
$449$	32.0190	1.51107	0.755535	−	0.655109i	$-0.227377\pi$
$449$	32.0190	1.51107	0.755535	+	0.655109i	$0.227377\pi$
$450$	−5.93839	−0.279938
$451$	−2.21212	−0.104165
$452$	−3.10199	−0.145906
$453$	1.70580	0.0801457
$454$	−5.19234	−0.243689
$455$	0	0
$456$	12.9971	0.608647
$457$	3.92379	0.183547	0.0917736	−	0.995780i	$-0.470746\pi$
$457$	3.92379	0.183547	0.0917736	+	0.995780i	$0.470746\pi$
$458$	6.82882	0.319090
$459$	−6.92396	−0.323183
$460$	−0.295654	−0.0137850
$461$	26.4099	1.23003	0.615016	−	0.788514i	$-0.289149\pi$
$461$	26.4099	1.23003	0.615016	+	0.788514i	$0.289149\pi$
$462$	0	0
$463$	5.27988	0.245377	0.122688	−	0.992445i	$-0.460848\pi$
$463$	5.27988	0.245377	0.122688	+	0.992445i	$0.460848\pi$
$464$	7.64051	0.354702
$465$	20.1741	0.935554
$466$	3.20241	0.148349
$467$	20.1035	0.930280	0.465140	−	0.885237i	$-0.346004\pi$
$467$	20.1035	0.930280	0.465140	+	0.885237i	$0.346004\pi$
$468$	−5.62412	−0.259975
$469$	0	0
$470$	−7.17826	−0.331108
$471$	−11.6850	−0.538415
$472$	16.0832	0.740290
$473$	−24.3538	−1.11979
$474$	0.955865	0.0439043
$475$	−103.727	−4.75932
$476$	0	0
$477$	−0.546137	−0.0250059
$478$	6.09676	0.278859
$479$	−23.4552	−1.07170	−0.535848	−	0.844315i	$-0.680008\pi$
$479$	−23.4552	−1.07170	−0.535848	+	0.844315i	$0.680008\pi$
$480$	19.8837	0.907565
$481$	−0.0937297	−0.00427371
$482$	−1.55186	−0.0706852
$483$	0	0
$484$	11.0187	0.500851
$485$	−0.930341	−0.0422446
$486$	0.442251	0.0200609
$487$	39.6797	1.79806	0.899030	−	0.437886i	$-0.144273\pi$
$487$	39.6797	1.79806	0.899030	+	0.437886i	$0.144273\pi$
$488$	−10.1300	−0.458563
$489$	12.3332	0.557726
$490$	0	0
$491$	42.0432	1.89738	0.948691	−	0.316204i	$-0.102408\pi$
$491$	42.0432	1.89738	0.948691	+	0.316204i	$0.102408\pi$
$492$	1.80441	0.0813493
$493$	18.4668	0.831703
$494$	10.6482	0.479087
$495$	−9.49606	−0.426816
$496$	−13.4631	−0.604511
$497$	0	0
$498$	−7.53985	−0.337869
$499$	−5.70934	−0.255585	−0.127793	−	0.991801i	$-0.540789\pi$
$499$	−5.70934	−0.255585	−0.127793	+	0.991801i	$0.540789\pi$
$500$	−65.2797	−2.91940
$501$	−6.35364	−0.283860
$502$	−6.57830	−0.293604
$503$	5.71736	0.254924	0.127462	−	0.991843i	$-0.459317\pi$
$503$	5.71736	0.254924	0.127462	+	0.991843i	$0.459317\pi$
$504$	0	0
$505$	10.8746	0.483915
$506$	0.0373413	0.00166002
$507$	3.28515	0.145899
$508$	34.0618	1.51125
$509$	35.4392	1.57081	0.785407	−	0.618980i	$-0.212454\pi$
$509$	35.4392	1.57081	0.785407	+	0.618980i	$0.212454\pi$
$510$	13.1449	0.582067
$511$	0	0
$512$	−22.9092	−1.01245
$513$	7.72487	0.341061
$514$	9.62155	0.424388
$515$	3.04628	0.134235
$516$	19.8653	0.874521
$517$	−8.36419	−0.367857
$518$	0	0
$519$	0.579038	0.0254170
$520$	22.5118	0.987206
$521$	−4.21069	−0.184474	−0.0922368	−	0.995737i	$-0.529402\pi$
$521$	−4.21069	−0.184474	−0.0922368	+	0.995737i	$0.529402\pi$
$522$	−1.17952	−0.0516262
$523$	12.4112	0.542703	0.271352	−	0.962480i	$-0.412529\pi$
$523$	12.4112	0.542703	0.271352	+	0.962480i	$0.412529\pi$
$524$	−17.4887	−0.763999
$525$	0	0
$526$	−1.00745	−0.0439269
$527$	−32.5398	−1.41746
$528$	6.33714	0.275789
$529$	−22.9985	−0.999937
$530$	1.03682	0.0450367
$531$	9.55909	0.414829
$532$	0	0
$533$	3.11687	0.135006
$534$	3.84401	0.166347
$535$	27.5632	1.19166
$536$	−15.1034	−0.652367
$537$	−21.2907	−0.918763
$538$	−0.898182	−0.0387234
$539$	0	0
$540$	7.74589	0.333330
$541$	29.7330	1.27832	0.639162	−	0.769072i	$-0.279282\pi$
$541$	29.7330	1.27832	0.639162	+	0.769072i	$0.279282\pi$
$542$	−7.00682	−0.300969
$543$	21.3004	0.914087
$544$	−32.0714	−1.37505
$545$	−10.8370	−0.464205
$546$	0	0
$547$	−1.76774	−0.0755829	−0.0377915	−	0.999286i	$-0.512032\pi$
$547$	−1.76774	−0.0755829	−0.0377915	+	0.999286i	$0.512032\pi$
$548$	−10.9320	−0.466990
$549$	−6.02077	−0.256960
$550$	13.1364	0.560139
$551$	−20.6029	−0.877713
$552$	−0.0642198	−0.00273338
$553$	0	0
$554$	1.54788	0.0657630
$555$	0.129091	0.00547959
$556$	3.01360	0.127805
$557$	−37.5462	−1.59088	−0.795442	−	0.606029i	$-0.792761\pi$
$557$	−37.5462	−1.59088	−0.795442	+	0.606029i	$0.792761\pi$
$558$	2.07840	0.0879856
$559$	34.3144	1.45135
$560$	0	0
$561$	15.3166	0.646668
$562$	−11.8153	−0.498400
$563$	−7.50392	−0.316253	−0.158126	−	0.987419i	$-0.550545\pi$
$563$	−7.50392	−0.316253	−0.158126	+	0.987419i	$0.550545\pi$
$564$	6.82263	0.287284
$565$	7.37972	0.310467
$566$	−6.93966	−0.291696
$567$	0	0
$568$	26.2805	1.10271
$569$	−2.92823	−0.122758	−0.0613790	−	0.998115i	$-0.519550\pi$
$569$	−2.92823	−0.122758	−0.0613790	+	0.998115i	$0.519550\pi$
$570$	−14.6654	−0.614267
$571$	14.3396	0.600095	0.300047	−	0.953924i	$-0.402997\pi$
$571$	14.3396	0.600095	0.300047	+	0.953924i	$0.402997\pi$
$572$	12.4412	0.520193
$573$	2.25947	0.0943908
$574$	0	0
$575$	0.512523	0.0213737
$576$	−3.68100	−0.153375
$577$	−15.3261	−0.638036	−0.319018	−	0.947749i	$-0.603353\pi$
$577$	−15.3261	−0.638036	−0.319018	+	0.947749i	$0.603353\pi$
$578$	−13.6838	−0.569171
$579$	19.8775	0.826080
$580$	−20.6590	−0.857817
$581$	0	0
$582$	−0.0958464	−0.00397296
$583$	1.20812	0.0500352
$584$	4.07670	0.168695
$585$	13.3799	0.553191
$586$	−6.40575	−0.264619
$587$	−18.1300	−0.748306	−0.374153	−	0.927367i	$-0.622066\pi$
$587$	−18.1300	−0.748306	−0.374153	+	0.927367i	$0.622066\pi$
$588$	0	0
$589$	36.3037	1.49587
$590$	−18.1476	−0.747126
$591$	7.13650	0.293556
$592$	−0.0861479	−0.00354066
$593$	−14.6521	−0.601691	−0.300845	−	0.953673i	$-0.597269\pi$
$593$	−14.6521	−0.601691	−0.300845	+	0.953673i	$0.597269\pi$
$594$	−0.978311	−0.0401406
$595$	0	0
$596$	−4.86366	−0.199223
$597$	13.9705	0.571775
$598$	−0.0526138	−0.00215154
$599$	4.58262	0.187241	0.0936205	−	0.995608i	$-0.470156\pi$
$599$	4.58262	0.187241	0.0936205	+	0.995608i	$0.470156\pi$
$600$	−22.5921	−0.922319
$601$	0.579777	0.0236496	0.0118248	−	0.999930i	$-0.496236\pi$
$601$	0.579777	0.0236496	0.0118248	+	0.999930i	$0.496236\pi$
$602$	0	0
$603$	−8.97673	−0.365561
$604$	3.07798	0.125241
$605$	−26.2138	−1.06574
$606$	1.12034	0.0455105
$607$	11.2678	0.457345	0.228672	−	0.973503i	$-0.426562\pi$
$607$	11.2678	0.457345	0.228672	+	0.973503i	$0.426562\pi$
$608$	35.7812	1.45112
$609$	0	0
$610$	11.4303	0.462798
$611$	11.7851	0.476774
$612$	−12.4937	−0.505028
$613$	41.6317	1.68149	0.840745	−	0.541431i	$-0.182117\pi$
$613$	41.6317	1.68149	0.840745	+	0.541431i	$0.182117\pi$
$614$	8.73410	0.352479
$615$	−4.29274	−0.173100
$616$	0	0
$617$	−14.5914	−0.587427	−0.293713	−	0.955894i	$-0.594891\pi$
$617$	−14.5914	−0.587427	−0.293713	+	0.955894i	$0.594891\pi$
$618$	0.313836	0.0126243
$619$	20.3756	0.818965	0.409482	−	0.912318i	$-0.365709\pi$
$619$	20.3756	0.818965	0.409482	+	0.912318i	$0.365709\pi$
$620$	36.4025	1.46196
$621$	−0.0381692	−0.00153168
$622$	−8.02043	−0.321590
$623$	0	0
$624$	−8.92901	−0.357446
$625$	88.1637	3.52655
$626$	1.45163	0.0580189
$627$	−17.0883	−0.682442
$628$	−21.0845	−0.841364
$629$	−0.208216	−0.00830212
$630$	0	0
$631$	9.23277	0.367551	0.183775	−	0.982968i	$-0.441168\pi$
$631$	9.23277	0.367551	0.183775	+	0.982968i	$0.441168\pi$
$632$	3.63651	0.144652
$633$	−23.3091	−0.926453
$634$	0.194900	0.00774047
$635$	−81.0339	−3.21573
$636$	−0.985457	−0.0390759
$637$	0	0
$638$	2.60924	0.103301
$639$	15.6199	0.617912
$640$	46.7558	1.84818
$641$	5.12329	0.202358	0.101179	−	0.994868i	$-0.467739\pi$
$641$	5.12329	0.202358	0.101179	+	0.994868i	$0.467739\pi$
$642$	2.83964	0.112072
$643$	15.5518	0.613302	0.306651	−	0.951822i	$-0.400792\pi$
$643$	15.5518	0.613302	0.306651	+	0.951822i	$0.400792\pi$
$644$	0	0
$645$	−47.2600	−1.86086
$646$	23.6545	0.930675
$647$	20.5466	0.807768	0.403884	−	0.914810i	$-0.367660\pi$
$647$	20.5466	0.807768	0.403884	+	0.914810i	$0.367660\pi$
$648$	1.68250	0.0660950
$649$	−21.1458	−0.830046
$650$	−18.5092	−0.725989
$651$	0	0
$652$	22.2542	0.871540
$653$	22.6686	0.887091	0.443546	−	0.896252i	$-0.353720\pi$
$653$	22.6686	0.887091	0.443546	+	0.896252i	$0.353720\pi$
$654$	−1.11646	−0.0436569
$655$	41.6061	1.62569
$656$	2.86474	0.111849
$657$	2.42299	0.0945299
$658$	0	0
$659$	−38.2328	−1.48934	−0.744669	−	0.667434i	$-0.767393\pi$
$659$	−38.2328	−1.48934	−0.744669	+	0.667434i	$0.767393\pi$
$660$	−17.1348	−0.666972
$661$	25.8102	1.00390	0.501951	−	0.864896i	$-0.332616\pi$
$661$	25.8102	1.00390	0.501951	+	0.864896i	$0.332616\pi$
$662$	1.44530	0.0561731
$663$	−21.5811	−0.838139
$664$	−28.6847	−1.11318
$665$	0	0
$666$	0.0132993	0.000515336 0
$667$	0.101801	0.00394173
$668$	−11.4646	−0.443579
$669$	−24.6795	−0.954164
$670$	17.0421	0.658392
$671$	13.3187	0.514161
$672$	0	0
$673$	−7.21950	−0.278291	−0.139146	−	0.990272i	$-0.544436\pi$
$673$	−7.21950	−0.278291	−0.139146	+	0.990272i	$0.544436\pi$
$674$	8.32003	0.320476
$675$	−13.4277	−0.516831
$676$	5.92777	0.227991
$677$	11.7898	0.453119	0.226560	−	0.973997i	$-0.427252\pi$
$677$	11.7898	0.453119	0.226560	+	0.973997i	$0.427252\pi$
$678$	0.760279	0.0291983
$679$	0	0
$680$	50.0088	1.91775
$681$	−11.7407	−0.449906
$682$	−4.59766	−0.176054
$683$	27.1434	1.03861	0.519307	−	0.854588i	$-0.326190\pi$
$683$	27.1434	1.03861	0.519307	+	0.854588i	$0.326190\pi$
$684$	13.9389	0.532966
$685$	26.0074	0.993691
$686$	0	0
$687$	15.4411	0.589114
$688$	31.5387	1.20240
$689$	−1.70223	−0.0648500
$690$	0.0724630	0.00275862
$691$	−2.26956	−0.0863380	−0.0431690	−	0.999068i	$-0.513745\pi$
$691$	−2.26956	−0.0863380	−0.0431690	+	0.999068i	$0.513745\pi$
$692$	1.04482	0.0397183
$693$	0	0
$694$	11.0031	0.417673
$695$	−7.16943	−0.271952
$696$	−4.48739	−0.170094
$697$	6.92396	0.262264
$698$	−15.3749	−0.581949
$699$	7.24116	0.273886
$700$	0	0
$701$	31.9632	1.20723	0.603616	−	0.797275i	$-0.293726\pi$
$701$	31.9632	1.20723	0.603616	+	0.797275i	$0.293726\pi$
$702$	1.37844	0.0520257
$703$	0.232301	0.00876139
$704$	8.14281	0.306894
$705$	−16.2312	−0.611302
$706$	7.35440	0.276786
$707$	0	0
$708$	17.2486	0.648240
$709$	−17.4623	−0.655812	−0.327906	−	0.944710i	$-0.606343\pi$
$709$	−17.4623	−0.655812	−0.327906	+	0.944710i	$0.606343\pi$
$710$	−29.6538	−1.11289
$711$	2.16136	0.0810575
$712$	14.6242	0.548066
$713$	−0.179380	−0.00671782
$714$	0	0
$715$	−29.5979	−1.10690
$716$	−38.4173	−1.43572
$717$	13.7858	0.514838
$718$	11.1789	0.417192
$719$	−15.8378	−0.590649	−0.295325	−	0.955397i	$-0.595428\pi$
$719$	−15.8378	−0.590649	−0.295325	+	0.955397i	$0.595428\pi$
$720$	12.2976	0.458304
$721$	0	0
$722$	−17.9879	−0.669442
$723$	−3.50900	−0.130501
$724$	38.4347	1.42842
$725$	35.8127	1.33005
$726$	−2.70062	−0.100229
$727$	−14.3866	−0.533568	−0.266784	−	0.963756i	$-0.585961\pi$
$727$	−14.3866	−0.533568	−0.266784	+	0.963756i	$0.585961\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−4.59998	−0.170253
$731$	76.2278	2.81939
$732$	−10.8640	−0.401544
$733$	43.3409	1.60083	0.800416	−	0.599444i	$-0.204612\pi$
$733$	43.3409	1.60083	0.800416	+	0.599444i	$0.204612\pi$
$734$	−14.6908	−0.542249
$735$	0	0
$736$	−0.176798	−0.00651684
$737$	19.8576	0.731464
$738$	−0.442251	−0.0162795
$739$	7.73562	0.284560	0.142280	−	0.989826i	$-0.454557\pi$
$739$	7.73562	0.284560	0.142280	+	0.989826i	$0.454557\pi$
$740$	0.232933	0.00856278
$741$	24.0774	0.884505
$742$	0	0
$743$	29.4859	1.08173	0.540867	−	0.841108i	$-0.318096\pi$
$743$	29.4859	1.08173	0.540867	+	0.841108i	$0.318096\pi$
$744$	7.90709	0.289888
$745$	11.5708	0.423920
$746$	−11.4901	−0.420681
$747$	−17.0488	−0.623783
$748$	27.6375	1.01053
$749$	0	0
$750$	15.9997	0.584225
$751$	−16.3584	−0.596926	−0.298463	−	0.954421i	$-0.596474\pi$
$751$	−16.3584	−0.596926	−0.298463	+	0.954421i	$0.596474\pi$
$752$	10.8318	0.394995
$753$	−14.8746	−0.542060
$754$	−3.67641	−0.133887
$755$	−7.32259	−0.266496
$756$	0	0
$757$	−47.1225	−1.71270	−0.856349	−	0.516397i	$-0.827273\pi$
$757$	−47.1225	−1.71270	−0.856349	+	0.516397i	$0.827273\pi$
$758$	−4.53755	−0.164811
$759$	0.0844348	0.00306479
$760$	−55.7934	−2.02384
$761$	−39.2835	−1.42403	−0.712013	−	0.702166i	$-0.752216\pi$
$761$	−39.2835	−1.42403	−0.712013	+	0.702166i	$0.752216\pi$
$762$	−8.34835	−0.302429
$763$	0	0
$764$	4.07702	0.147502
$765$	29.7228	1.07463
$766$	1.14626	0.0414161
$767$	29.7944	1.07581
$768$	−2.54509	−0.0918380
$769$	−25.4482	−0.917687	−0.458843	−	0.888517i	$-0.651736\pi$
$769$	−25.4482	−0.917687	−0.458843	+	0.888517i	$0.651736\pi$
$770$	0	0
$771$	21.7559	0.783519
$772$	35.8672	1.29089
$773$	1.77505	0.0638440	0.0319220	−	0.999490i	$-0.489837\pi$
$773$	1.77505	0.0638440	0.0319220	+	0.999490i	$0.489837\pi$
$774$	−4.86886	−0.175008
$775$	−63.1045	−2.26678
$776$	−0.364639	−0.0130898
$777$	0	0
$778$	3.82727	0.137214
$779$	−7.72487	−0.276772
$780$	24.1429	0.864454
$781$	−34.5530	−1.23640
$782$	−0.116879	−0.00417958
$783$	−2.66709	−0.0953139
$784$	0	0
$785$	50.1606	1.79031
$786$	4.28638	0.152890
$787$	48.7760	1.73868	0.869338	−	0.494218i	$-0.164545\pi$
$787$	48.7760	1.73868	0.869338	+	0.494218i	$0.164545\pi$
$788$	12.8772	0.458731
$789$	−2.27801	−0.0810992
$790$	−4.10328	−0.145988
$791$	0	0
$792$	−3.72190	−0.132252
$793$	−18.7659	−0.666398
$794$	−13.2864	−0.471518
$795$	2.34442	0.0831482
$796$	25.2086	0.893495
$797$	12.9486	0.458665	0.229332	−	0.973348i	$-0.426346\pi$
$797$	12.9486	0.458665	0.229332	+	0.973348i	$0.426346\pi$
$798$	0	0
$799$	26.1800	0.926183
$800$	−62.1961	−2.19897
$801$	8.69193	0.307114
$802$	−5.34866	−0.188868
$803$	−5.35994	−0.189148
$804$	−16.1977	−0.571251
$805$	0	0
$806$	6.47809	0.228181
$807$	−2.03093	−0.0714923
$808$	4.26222	0.149944
$809$	−34.2717	−1.20493	−0.602464	−	0.798146i	$-0.705814\pi$
$809$	−34.2717	−1.20493	−0.602464	+	0.798146i	$0.705814\pi$
$810$	−1.89847	−0.0667054
$811$	39.7411	1.39550	0.697749	−	0.716342i	$-0.254185\pi$
$811$	39.7411	1.39550	0.697749	+	0.716342i	$0.254185\pi$
$812$	0	0
$813$	−15.8435	−0.555657
$814$	−0.0294196	−0.00103116
$815$	−52.9432	−1.85452
$816$	−19.8354	−0.694376
$817$	−85.0452	−2.97536
$818$	5.97656	0.208965
$819$	0	0
$820$	−7.74589	−0.270498
$821$	−42.6305	−1.48782	−0.743908	−	0.668282i	$-0.767030\pi$
$821$	−42.6305	−1.48782	−0.743908	+	0.668282i	$0.767030\pi$
$822$	2.67935	0.0934532
$823$	11.8760	0.413973	0.206986	−	0.978344i	$-0.433634\pi$
$823$	11.8760	0.413973	0.206986	+	0.978344i	$0.433634\pi$
$824$	1.19396	0.0415937
$825$	29.7036	1.03415
$826$	0	0
$827$	−18.5702	−0.645751	−0.322875	−	0.946442i	$-0.604649\pi$
$827$	−18.5702	−0.645751	−0.322875	+	0.946442i	$0.604649\pi$
$828$	−0.0688730	−0.00239350
$829$	−45.5475	−1.58193	−0.790966	−	0.611860i	$-0.790421\pi$
$829$	−45.5475	−1.58193	−0.790966	+	0.611860i	$0.790421\pi$
$830$	32.3667	1.12346
$831$	3.50000	0.121414
$832$	−11.4732	−0.397761
$833$	0	0
$834$	−0.738614	−0.0255761
$835$	27.2745	0.943875
$836$	−30.8344	−1.06643
$837$	4.69959	0.162442
$838$	−14.2300	−0.491566
$839$	−0.520222	−0.0179601	−0.00898004	−	0.999960i	$-0.502858\pi$
$839$	−0.520222	−0.0179601	−0.00898004	+	0.999960i	$0.502858\pi$
$840$	0	0
$841$	−21.8866	−0.754712
$842$	14.2703	0.491785
$843$	−26.7164	−0.920161
$844$	−42.0593	−1.44774
$845$	−14.1023	−0.485134
$846$	−1.67218	−0.0574909
$847$	0	0
$848$	−1.56454	−0.0537265
$849$	−15.6917	−0.538537
$850$	−41.1172	−1.41031
$851$	−0.00114782	−3.93466e−5 0
$852$	28.1847	0.965592
$853$	−26.2375	−0.898356	−0.449178	−	0.893442i	$-0.648283\pi$
$853$	−26.2375	−0.898356	−0.449178	+	0.893442i	$0.648283\pi$
$854$	0	0
$855$	−33.1609	−1.13408
$856$	10.8032	0.369245
$857$	−37.6320	−1.28548	−0.642742	−	0.766083i	$-0.722203\pi$
$857$	−37.6320	−1.28548	−0.642742	+	0.766083i	$0.722203\pi$
$858$	−3.04926	−0.104100
$859$	−21.6450	−0.738518	−0.369259	−	0.929327i	$-0.620388\pi$
$859$	−21.6450	−0.738518	−0.369259	+	0.929327i	$0.620388\pi$
$860$	−85.2766	−2.90791
$861$	0	0
$862$	−4.62071	−0.157382
$863$	−33.1370	−1.12800	−0.563998	−	0.825776i	$-0.690737\pi$
$863$	−33.1370	−1.12800	−0.563998	+	0.825776i	$0.690737\pi$
$864$	4.63194	0.157582
$865$	−2.48566	−0.0845151
$866$	−1.67668	−0.0569757
$867$	−30.9413	−1.05082
$868$	0	0
$869$	−4.78119	−0.162191
$870$	5.06338	0.171665
$871$	−27.9793	−0.948041
$872$	−4.24746	−0.143837
$873$	−0.216724	−0.00733500
$874$	0.130399	0.00441080
$875$	0	0
$876$	4.37208	0.147719
$877$	2.91954	0.0985857	0.0492929	−	0.998784i	$-0.484303\pi$
$877$	2.91954	0.0985857	0.0492929	+	0.998784i	$0.484303\pi$
$878$	1.98689	0.0670544
$879$	−14.4844	−0.488548
$880$	−27.2037	−0.917038
$881$	−24.7028	−0.832258	−0.416129	−	0.909306i	$-0.636613\pi$
$881$	−24.7028	−0.832258	−0.416129	+	0.909306i	$0.636613\pi$
$882$	0	0
$883$	6.69015	0.225141	0.112571	−	0.993644i	$-0.464092\pi$
$883$	6.69015	0.225141	0.112571	+	0.993644i	$0.464092\pi$
$884$	−38.9412	−1.30973
$885$	−41.0347	−1.37937
$886$	3.62605	0.121819
$887$	−9.40760	−0.315876	−0.157938	−	0.987449i	$-0.550485\pi$
$887$	−9.40760	−0.315876	−0.157938	+	0.987449i	$0.550485\pi$
$888$	0.0505959	0.00169789
$889$	0	0
$890$	−16.5014	−0.553127
$891$	−2.21212	−0.0741088
$892$	−44.5320	−1.49104
$893$	−29.2083	−0.977419
$894$	1.19205	0.0398682
$895$	91.3957	3.05502
$896$	0	0
$897$	−0.118968	−0.00397223
$898$	−14.1604	−0.472539
$899$	−12.5342	−0.418040
$900$	−24.2291	−0.807635
$901$	−3.78143	−0.125978
$902$	0.978311	0.0325742
$903$	0	0
$904$	2.89242	0.0962004
$905$	−91.4371	−3.03947
$906$	−0.754393	−0.0250630
$907$	21.7567	0.722421	0.361210	−	0.932484i	$-0.382364\pi$
$907$	21.7567	0.722421	0.361210	+	0.932484i	$0.382364\pi$
$908$	−21.1851	−0.703053
$909$	2.53326	0.0840229
$910$	0	0
$911$	−38.9801	−1.29147	−0.645734	−	0.763562i	$-0.723449\pi$
$911$	−38.9801	−1.29147	−0.645734	+	0.763562i	$0.723449\pi$
$912$	22.1297	0.732789
$913$	37.7140	1.24815
$914$	−1.73530	−0.0573986
$915$	25.8456	0.854431
$916$	27.8621	0.920589
$917$	0	0
$918$	3.06213	0.101065
$919$	−57.3909	−1.89315	−0.946576	−	0.322480i	$-0.895483\pi$
$919$	−57.3909	−1.89315	−0.946576	+	0.322480i	$0.895483\pi$
$920$	0.275679	0.00908888
$921$	19.7492	0.650758
$922$	−11.6798	−0.384654
$923$	48.6850	1.60249
$924$	0	0
$925$	−0.403794	−0.0132767
$926$	−2.33503	−0.0767338
$927$	0.709634	0.0233074
$928$	−12.3538	−0.405533
$929$	−35.3944	−1.16125	−0.580627	−	0.814170i	$-0.697192\pi$
$929$	−35.3944	−1.16125	−0.580627	+	0.814170i	$0.697192\pi$
$930$	−8.92203	−0.292565
$931$	0	0
$932$	13.0661	0.427993
$933$	−18.1355	−0.593729
$934$	−8.89079	−0.290916
$935$	−65.7504	−2.15027
$936$	5.24414	0.171410
$937$	−33.9294	−1.10842	−0.554212	−	0.832376i	$-0.686980\pi$
$937$	−33.9294	−1.10842	−0.554212	+	0.832376i	$0.686980\pi$
$938$	0	0
$939$	3.28237	0.107116
$940$	−29.2878	−0.955263
$941$	−18.0053	−0.586955	−0.293477	−	0.955966i	$-0.594813\pi$
$941$	−18.0053	−0.586955	−0.293477	+	0.955966i	$0.594813\pi$
$942$	5.16769	0.168372
$943$	0.0381692	0.00124296
$944$	27.3843	0.891283
$945$	0	0
$946$	10.7705	0.350179
$947$	−28.6412	−0.930714	−0.465357	−	0.885123i	$-0.654074\pi$
$947$	−28.6412	−0.930714	−0.465357	+	0.885123i	$0.654074\pi$
$948$	3.90000	0.126666
$949$	7.55214	0.245153
$950$	45.8733	1.48833
$951$	0.440700	0.0142907
$952$	0	0
$953$	10.2041	0.330544	0.165272	−	0.986248i	$-0.447150\pi$
$953$	10.2041	0.330544	0.165272	+	0.986248i	$0.447150\pi$
$954$	0.241529	0.00781980
$955$	−9.69934	−0.313863
$956$	24.8752	0.804522
$957$	5.89991	0.190717
$958$	10.3731	0.335139
$959$	0	0
$960$	15.8016	0.509994
$961$	−8.91384	−0.287543
$962$	0.0414520	0.00133647
$963$	6.42089	0.206910
$964$	−6.33169	−0.203930
$965$	−85.3289	−2.74684
$966$	0	0
$967$	−49.6045	−1.59517	−0.797587	−	0.603204i	$-0.793891\pi$
$967$	−49.6045	−1.59517	−0.797587	+	0.603204i	$0.793891\pi$
$968$	−10.2743	−0.330228
$969$	53.4867	1.71824
$970$	0.411444	0.0132107
$971$	26.3030	0.844102	0.422051	−	0.906572i	$-0.361310\pi$
$971$	26.3030	0.844102	0.422051	+	0.906572i	$0.361310\pi$
$972$	1.80441	0.0578766
$973$	0	0
$974$	−17.5484	−0.562287
$975$	−41.8522	−1.34034
$976$	−17.2480	−0.552093
$977$	32.8265	1.05021	0.525106	−	0.851037i	$-0.324026\pi$
$977$	32.8265	1.05021	0.525106	+	0.851037i	$0.324026\pi$
$978$	−5.45436	−0.174411
$979$	−19.2276	−0.614516
$980$	0	0
$981$	−2.52449	−0.0806006
$982$	−18.5936	−0.593347
$983$	−12.6918	−0.404805	−0.202403	−	0.979302i	$-0.564875\pi$
$983$	−12.6918	−0.404805	−0.202403	+	0.979302i	$0.564875\pi$
$984$	−1.68250	−0.0536363
$985$	−30.6352	−0.976118
$986$	−8.16696	−0.260089
$987$	0	0
$988$	43.4456	1.38219
$989$	0.420215	0.0133621
$990$	4.19964	0.133473
$991$	−52.5027	−1.66780	−0.833902	−	0.551912i	$-0.813898\pi$
$991$	−52.5027	−1.66780	−0.833902	+	0.551912i	$0.813898\pi$
$992$	21.7682	0.691142
$993$	3.26805	0.103708
$994$	0	0
$995$	−59.9718	−1.90123
$996$	−30.7631	−0.974767
$997$	24.7134	0.782683	0.391341	−	0.920246i	$-0.372011\pi$
$997$	24.7134	0.782683	0.391341	+	0.920246i	$0.372011\pi$
$998$	2.52496	0.0799262
$999$	0.0300718	0.000951430 0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bj.1.7		14
7.2	even	3		861.2.i.g.739.8	yes	28
7.4	even	3		861.2.i.g.247.8	✓	28
7.6	odd	2		6027.2.a.bk.1.7		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.i.g.247.8	✓	28	7.4	even	3
861.2.i.g.739.8	yes	28	7.2	even	3
6027.2.a.bj.1.7		14	1.1	even	1	trivial
6027.2.a.bk.1.7		14	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-0.442251 q^{2} -1.00000 q^{3} -1.80441 q^{4} +4.29274 q^{5} +0.442251 q^{6} +1.68250 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.442251 q^{2} -1.00000 q^{3} -1.80441 q^{4} +4.29274 q^{5} +0.442251 q^{6} +1.68250 q^{8} +1.00000 q^{9} -1.89847 q^{10} -2.21212 q^{11} +1.80441 q^{12} +3.11687 q^{13} -4.29274 q^{15} +2.86474 q^{16} +6.92396 q^{17} -0.442251 q^{18} -7.72487 q^{19} -7.74589 q^{20} +0.978311 q^{22} +0.0381692 q^{23} -1.68250 q^{24} +13.4277 q^{25} -1.37844 q^{26} -1.00000 q^{27} +2.66709 q^{29} +1.89847 q^{30} -4.69959 q^{31} -4.63194 q^{32} +2.21212 q^{33} -3.06213 q^{34} -1.80441 q^{36} -0.0300718 q^{37} +3.41633 q^{38} -3.11687 q^{39} +7.22256 q^{40} +1.00000 q^{41} +11.0093 q^{43} +3.99158 q^{44} +4.29274 q^{45} -0.0168804 q^{46} +3.78108 q^{47} -2.86474 q^{48} -5.93839 q^{50} -6.92396 q^{51} -5.62412 q^{52} -0.546137 q^{53} +0.442251 q^{54} -9.49606 q^{55} +7.72487 q^{57} -1.17952 q^{58} +9.55909 q^{59} +7.74589 q^{60} -6.02077 q^{61} +2.07840 q^{62} -3.68100 q^{64} +13.3799 q^{65} -0.978311 q^{66} -8.97673 q^{67} -12.4937 q^{68} -0.0381692 q^{69} +15.6199 q^{71} +1.68250 q^{72} +2.42299 q^{73} +0.0132993 q^{74} -13.4277 q^{75} +13.9389 q^{76} +1.37844 q^{78} +2.16136 q^{79} +12.2976 q^{80} +1.00000 q^{81} -0.442251 q^{82} -17.0488 q^{83} +29.7228 q^{85} -4.86886 q^{86} -2.66709 q^{87} -3.72190 q^{88} +8.69193 q^{89} -1.89847 q^{90} -0.0688730 q^{92} +4.69959 q^{93} -1.67218 q^{94} -33.1609 q^{95} +4.63194 q^{96} -0.216724 q^{97} -2.21212 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} - 14 q^{3} + 14 q^{4} + 10 q^{5} + 2 q^{6} - 6 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - 2 * q^2 - 14 * q^3 + 14 * q^4 + 10 * q^5 + 2 * q^6 - 6 * q^8 + 14 * q^9	\( 14 q - 2 q^{2} - 14 q^{3} + 14 q^{4} + 10 q^{5} + 2 q^{6} - 6 q^{8} + 14 q^{9} + 3 q^{10} - 16 q^{11} - 14 q^{12} + 21 q^{13} - 10 q^{15} + 22 q^{16} + 12 q^{17} - 2 q^{18} + 2 q^{19} + 40 q^{20} + q^{22} - 7 q^{23} + 6 q^{24} + 22 q^{25} + 2 q^{26} - 14 q^{27} - 16 q^{29} - 3 q^{30} + 8 q^{31} - 19 q^{32} + 16 q^{33} + 33 q^{34} + 14 q^{36} + q^{37} + 32 q^{38} - 21 q^{39} - 13 q^{40} + 14 q^{41} + 14 q^{43} - 36 q^{44} + 10 q^{45} - 12 q^{46} + 12 q^{47} - 22 q^{48} - q^{50} - 12 q^{51} + 60 q^{52} - 20 q^{53} + 2 q^{54} - 11 q^{55} - 2 q^{57} + 21 q^{58} + 25 q^{59} - 40 q^{60} + 26 q^{61} - 33 q^{62} + 42 q^{64} - 8 q^{65} - q^{66} - 22 q^{67} + 15 q^{68} + 7 q^{69} - 36 q^{71} - 6 q^{72} + 31 q^{73} - 65 q^{74} - 22 q^{75} - 2 q^{76} - 2 q^{78} + 12 q^{79} + 112 q^{80} + 14 q^{81} - 2 q^{82} + 20 q^{83} + 40 q^{85} - 9 q^{86} + 16 q^{87} - 54 q^{88} + 39 q^{89} + 3 q^{90} + 63 q^{92} - 8 q^{93} + 14 q^{94} - 55 q^{95} + 19 q^{96} + 18 q^{97} - 16 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 - 14 * q^3 + 14 * q^4 + 10 * q^5 + 2 * q^6 - 6 * q^8 + 14 * q^9 + 3 * q^10 - 16 * q^11 - 14 * q^12 + 21 * q^13 - 10 * q^15 + 22 * q^16 + 12 * q^17 - 2 * q^18 + 2 * q^19 + 40 * q^20 + q^22 - 7 * q^23 + 6 * q^24 + 22 * q^25 + 2 * q^26 - 14 * q^27 - 16 * q^29 - 3 * q^30 + 8 * q^31 - 19 * q^32 + 16 * q^33 + 33 * q^34 + 14 * q^36 + q^37 + 32 * q^38 - 21 * q^39 - 13 * q^40 + 14 * q^41 + 14 * q^43 - 36 * q^44 + 10 * q^45 - 12 * q^46 + 12 * q^47 - 22 * q^48 - q^50 - 12 * q^51 + 60 * q^52 - 20 * q^53 + 2 * q^54 - 11 * q^55 - 2 * q^57 + 21 * q^58 + 25 * q^59 - 40 * q^60 + 26 * q^61 - 33 * q^62 + 42 * q^64 - 8 * q^65 - q^66 - 22 * q^67 + 15 * q^68 + 7 * q^69 - 36 * q^71 - 6 * q^72 + 31 * q^73 - 65 * q^74 - 22 * q^75 - 2 * q^76 - 2 * q^78 + 12 * q^79 + 112 * q^80 + 14 * q^81 - 2 * q^82 + 20 * q^83 + 40 * q^85 - 9 * q^86 + 16 * q^87 - 54 * q^88 + 39 * q^89 + 3 * q^90 + 63 * q^92 - 8 * q^93 + 14 * q^94 - 55 * q^95 + 19 * q^96 + 18 * q^97 - 16 * q^99

Introduction

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