LMFDB - Embedded newform 6027.2.a.bf.1.4

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:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 15 x^{10} + 30 x^{9} + 74 x^{8} - 149 x^{7} - 140 x^{6} + 278 x^{5} + 126 x^{4} + \cdots + 18 $ x^12 - 2x^11 - 15x^10 + 30x^9 + 74x^8 - 149x^7 - 140x^6 + 278x^5 + 126x^4 - 211x^3 - 64x^2 + 53*x + 18
Coefficient ring:	$\Z[a_1, a_2]$
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			1.4
Root			$1.22157$ 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)

$f(q)$	$=$	$q-1.22157 q^{2} -1.00000 q^{3} -0.507765 q^{4} -0.145411 q^{5} +1.22157 q^{6} +3.06341 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.22157 q^{2} -1.00000 q^{3} -0.507765 q^{4} -0.145411 q^{5} +1.22157 q^{6} +3.06341 q^{8} +1.00000 q^{9} +0.177630 q^{10} +1.83208 q^{11} +0.507765 q^{12} +2.53359 q^{13} +0.145411 q^{15} -2.72665 q^{16} +5.73593 q^{17} -1.22157 q^{18} +5.97791 q^{19} +0.0738345 q^{20} -2.23802 q^{22} -7.46090 q^{23} -3.06341 q^{24} -4.97886 q^{25} -3.09496 q^{26} -1.00000 q^{27} -0.614905 q^{29} -0.177630 q^{30} -9.81881 q^{31} -2.79603 q^{32} -1.83208 q^{33} -7.00685 q^{34} -0.507765 q^{36} -1.76699 q^{37} -7.30244 q^{38} -2.53359 q^{39} -0.445453 q^{40} +1.00000 q^{41} +2.38271 q^{43} -0.930267 q^{44} -0.145411 q^{45} +9.11402 q^{46} -8.27179 q^{47} +2.72665 q^{48} +6.08202 q^{50} -5.73593 q^{51} -1.28647 q^{52} -6.25111 q^{53} +1.22157 q^{54} -0.266405 q^{55} -5.97791 q^{57} +0.751150 q^{58} -8.36107 q^{59} -0.0738345 q^{60} -2.56376 q^{61} +11.9944 q^{62} +8.86884 q^{64} -0.368412 q^{65} +2.23802 q^{66} +11.2446 q^{67} -2.91250 q^{68} +7.46090 q^{69} +8.94583 q^{71} +3.06341 q^{72} -6.60634 q^{73} +2.15851 q^{74} +4.97886 q^{75} -3.03537 q^{76} +3.09496 q^{78} +7.02241 q^{79} +0.396484 q^{80} +1.00000 q^{81} -1.22157 q^{82} +1.70262 q^{83} -0.834067 q^{85} -2.91065 q^{86} +0.614905 q^{87} +5.61243 q^{88} -15.4305 q^{89} +0.177630 q^{90} +3.78838 q^{92} +9.81881 q^{93} +10.1046 q^{94} -0.869254 q^{95} +2.79603 q^{96} -6.11958 q^{97} +1.83208 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - 12 q^{3} + 10 q^{4} - 12 q^{5} + 2 q^{6} + 12 q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 - 12 * q^3 + 10 * q^4 - 12 * q^5 + 2 * q^6 + 12 * q^9	$ 12 q - 2 q^{2} - 12 q^{3} + 10 q^{4} - 12 q^{5} + 2 q^{6} + 12 q^{9} - 11 q^{10} + 10 q^{11} - 10 q^{12} - 15 q^{13} + 12 q^{15} + 14 q^{16} - 8 q^{17} - 2 q^{18} - 2 q^{19} - 16 q^{20} - 7 q^{22} + 5 q^{23} + 20 q^{25} - 12 q^{27} + 20 q^{29} + 11 q^{30} - 10 q^{31} + 3 q^{32} - 10 q^{33} + 23 q^{34} + 10 q^{36} - 17 q^{37} - 6 q^{38} + 15 q^{39} - 39 q^{40} + 12 q^{41} + 12 q^{43} + 20 q^{44} - 12 q^{45} - 36 q^{46} - 34 q^{47} - 14 q^{48} + 59 q^{50} + 8 q^{51} - 26 q^{52} + 6 q^{53} + 2 q^{54} + q^{55} + 2 q^{57} - 11 q^{58} - 27 q^{59} + 16 q^{60} - 22 q^{61} + 45 q^{62} + 26 q^{64} + 7 q^{66} - 26 q^{67} - 33 q^{68} - 5 q^{69} + 50 q^{71} - 21 q^{73} - 35 q^{74} - 20 q^{75} + 24 q^{76} - 10 q^{79} - 22 q^{80} + 12 q^{81} - 2 q^{82} - 8 q^{83} + 8 q^{85} - 17 q^{86} - 20 q^{87} - 46 q^{88} - 11 q^{89} - 11 q^{90} + 63 q^{92} + 10 q^{93} - 10 q^{94} + 35 q^{95} - 3 q^{96} - 32 q^{97} + 10 q^{99}+O(q^{100}) $ 12 * q - 2 * q^2 - 12 * q^3 + 10 * q^4 - 12 * q^5 + 2 * q^6 + 12 * q^9 - 11 * q^10 + 10 * q^11 - 10 * q^12 - 15 * q^13 + 12 * q^15 + 14 * q^16 - 8 * q^17 - 2 * q^18 - 2 * q^19 - 16 * q^20 - 7 * q^22 + 5 * q^23 + 20 * q^25 - 12 * q^27 + 20 * q^29 + 11 * q^30 - 10 * q^31 + 3 * q^32 - 10 * q^33 + 23 * q^34 + 10 * q^36 - 17 * q^37 - 6 * q^38 + 15 * q^39 - 39 * q^40 + 12 * q^41 + 12 * q^43 + 20 * q^44 - 12 * q^45 - 36 * q^46 - 34 * q^47 - 14 * q^48 + 59 * q^50 + 8 * q^51 - 26 * q^52 + 6 * q^53 + 2 * q^54 + q^55 + 2 * q^57 - 11 * q^58 - 27 * q^59 + 16 * q^60 - 22 * q^61 + 45 * q^62 + 26 * q^64 + 7 * q^66 - 26 * q^67 - 33 * q^68 - 5 * q^69 + 50 * q^71 - 21 * q^73 - 35 * q^74 - 20 * q^75 + 24 * q^76 - 10 * q^79 - 22 * q^80 + 12 * q^81 - 2 * q^82 - 8 * q^83 + 8 * q^85 - 17 * q^86 - 20 * q^87 - 46 * q^88 - 11 * q^89 - 11 * q^90 + 63 * q^92 + 10 * q^93 - 10 * q^94 + 35 * q^95 - 3 * q^96 - 32 * q^97 + 10 * 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 $

$2$	−1.22157	−0.863781	−0.431891	−	0.901926i	$-0.642153\pi$
$2$	−1.22157	−0.863781	−0.431891	+	0.901926i	$0.642153\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.507765	−0.253882
$5$	−0.145411	−0.0650297	−0.0325149	−	0.999471i	$-0.510352\pi$
$5$	−0.145411	−0.0650297	−0.0325149	+	0.999471i	$0.510352\pi$
$6$	1.22157	0.498704
$7$	0	0
$7$	0	0
$8$	3.06341	1.08308
$9$	1.00000	0.333333
$10$	0.177630	0.0561714
$11$	1.83208	0.552394	0.276197	−	0.961101i	$-0.410926\pi$
$11$	1.83208	0.552394	0.276197	+	0.961101i	$0.410926\pi$
$12$	0.507765	0.146579
$13$	2.53359	0.702692	0.351346	−	0.936246i	$-0.385724\pi$
$13$	2.53359	0.702692	0.351346	+	0.936246i	$0.385724\pi$
$14$	0	0
$15$	0.145411	0.0375449
$16$	−2.72665	−0.681661
$17$	5.73593	1.39117	0.695584	−	0.718445i	$-0.255146\pi$
$17$	5.73593	1.39117	0.695584	+	0.718445i	$0.255146\pi$
$18$	−1.22157	−0.287927
$19$	5.97791	1.37143	0.685714	−	0.727871i	$-0.259490\pi$
$19$	5.97791	1.37143	0.685714	+	0.727871i	$0.259490\pi$
$20$	0.0738345	0.0165099
$21$	0	0
$22$	−2.23802	−0.477147
$23$	−7.46090	−1.55571	−0.777853	−	0.628447i	$-0.783691\pi$
$23$	−7.46090	−1.55571	−0.777853	+	0.628447i	$0.783691\pi$
$24$	−3.06341	−0.625316
$25$	−4.97886	−0.995771
$26$	−3.09496	−0.606972
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−0.614905	−0.114185	−0.0570925	−	0.998369i	$-0.518183\pi$
$29$	−0.614905	−0.114185	−0.0570925	+	0.998369i	$0.518183\pi$
$30$	−0.177630	−0.0324306
$31$	−9.81881	−1.76351	−0.881756	−	0.471707i	$-0.843638\pi$
$31$	−9.81881	−1.76351	−0.881756	+	0.471707i	$0.843638\pi$
$32$	−2.79603	−0.494274
$33$	−1.83208	−0.318925
$34$	−7.00685	−1.20166
$35$	0	0
$36$	−0.507765	−0.0846275
$37$	−1.76699	−0.290492	−0.145246	−	0.989396i	$-0.546397\pi$
$37$	−1.76699	−0.290492	−0.145246	+	0.989396i	$0.546397\pi$
$38$	−7.30244	−1.18461
$39$	−2.53359	−0.405700
$40$	−0.445453	−0.0704324
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	2.38271	0.363361	0.181680	−	0.983358i	$-0.441846\pi$
$43$	2.38271	0.363361	0.181680	+	0.983358i	$0.441846\pi$
$44$	−0.930267	−0.140243
$45$	−0.145411	−0.0216766
$46$	9.11402	1.34379
$47$	−8.27179	−1.20656	−0.603282	−	0.797528i	$-0.706141\pi$
$47$	−8.27179	−1.20656	−0.603282	+	0.797528i	$0.706141\pi$
$48$	2.72665	0.393557
$49$	0	0
$50$	6.08202	0.860128
$51$	−5.73593	−0.803191
$52$	−1.28647	−0.178401
$53$	−6.25111	−0.858656	−0.429328	−	0.903149i	$-0.641249\pi$
$53$	−6.25111	−0.858656	−0.429328	+	0.903149i	$0.641249\pi$
$54$	1.22157	0.166235
$55$	−0.266405	−0.0359220
$56$	0	0
$57$	−5.97791	−0.791794
$58$	0.751150	0.0986308
$59$	−8.36107	−1.08852	−0.544259	−	0.838917i	$-0.683189\pi$
$59$	−8.36107	−1.08852	−0.544259	+	0.838917i	$0.683189\pi$
$60$	−0.0738345	−0.00953199
$61$	−2.56376	−0.328256	−0.164128	−	0.986439i	$-0.552481\pi$
$61$	−2.56376	−0.328256	−0.164128	+	0.986439i	$0.552481\pi$
$62$	11.9944	1.52329
$63$	0	0
$64$	8.86884	1.10861
$65$	−0.368412	−0.0456959
$66$	2.23802	0.275481
$67$	11.2446	1.37374	0.686872	−	0.726779i	$-0.258983\pi$
$67$	11.2446	1.37374	0.686872	+	0.726779i	$0.258983\pi$
$68$	−2.91250	−0.353193
$69$	7.46090	0.898187
$70$	0	0
$71$	8.94583	1.06167	0.530837	−	0.847474i	$-0.321878\pi$
$71$	8.94583	1.06167	0.530837	+	0.847474i	$0.321878\pi$
$72$	3.06341	0.361027
$73$	−6.60634	−0.773213	−0.386607	−	0.922245i	$-0.626353\pi$
$73$	−6.60634	−0.773213	−0.386607	+	0.922245i	$0.626353\pi$
$74$	2.15851	0.250921
$75$	4.97886	0.574909
$76$	−3.03537	−0.348181
$77$	0	0
$78$	3.09496	0.350436
$79$	7.02241	0.790083	0.395041	−	0.918663i	$-0.370730\pi$
$79$	7.02241	0.790083	0.395041	+	0.918663i	$0.370730\pi$
$80$	0.396484	0.0443283
$81$	1.00000	0.111111
$82$	−1.22157	−0.134900
$83$	1.70262	0.186887	0.0934435	−	0.995625i	$-0.470213\pi$
$83$	1.70262	0.186887	0.0934435	+	0.995625i	$0.470213\pi$
$84$	0	0
$85$	−0.834067	−0.0904672
$86$	−2.91065	−0.313864
$87$	0.614905	0.0659247
$88$	5.61243	0.598287
$89$	−15.4305	−1.63563	−0.817815	−	0.575482i	$-0.804815\pi$
$89$	−15.4305	−1.63563	−0.817815	+	0.575482i	$0.804815\pi$
$90$	0.177630	0.0187238
$91$	0	0
$92$	3.78838	0.394966
$93$	9.81881	1.01816
$94$	10.1046	1.04221
$95$	−0.869254	−0.0891835
$96$	2.79603	0.285369
$97$	−6.11958	−0.621350	−0.310675	−	0.950516i	$-0.600555\pi$
$97$	−6.11958	−0.621350	−0.310675	+	0.950516i	$0.600555\pi$
$98$	0	0
$99$	1.83208	0.184131
$100$	2.52809	0.252809
$101$	19.1023	1.90075	0.950376	−	0.311105i	$-0.100699\pi$
$101$	19.1023	1.90075	0.950376	+	0.311105i	$0.100699\pi$
$102$	7.00685	0.693781
$103$	−6.61906	−0.652196	−0.326098	−	0.945336i	$-0.605734\pi$
$103$	−6.61906	−0.652196	−0.326098	+	0.945336i	$0.605734\pi$
$104$	7.76144	0.761072
$105$	0	0
$106$	7.63617	0.741690
$107$	18.2368	1.76302	0.881508	−	0.472169i	$-0.156529\pi$
$107$	18.2368	1.76302	0.881508	+	0.472169i	$0.156529\pi$
$108$	0.507765	0.0488597
$109$	−10.2908	−0.985678	−0.492839	−	0.870121i	$-0.664041\pi$
$109$	−10.2908	−0.985678	−0.492839	+	0.870121i	$0.664041\pi$
$110$	0.325432	0.0310288
$111$	1.76699	0.167715
$112$	0	0
$113$	4.53348	0.426474	0.213237	−	0.977001i	$-0.431599\pi$
$113$	4.53348	0.426474	0.213237	+	0.977001i	$0.431599\pi$
$114$	7.30244	0.683937
$115$	1.08490	0.101167
$116$	0.312227	0.0289896
$117$	2.53359	0.234231
$118$	10.2136	0.940242
$119$	0	0
$120$	0.445453	0.0406642
$121$	−7.64347	−0.694861
$122$	3.13181	0.283541
$123$	−1.00000	−0.0901670
$124$	4.98565	0.447724
$125$	1.45103	0.129784
$126$	0	0
$127$	5.61309	0.498081	0.249041	−	0.968493i	$-0.419885\pi$
$127$	5.61309	0.498081	0.249041	+	0.968493i	$0.419885\pi$
$128$	−5.24185	−0.463319
$129$	−2.38271	−0.209786
$130$	0.450041	0.0394712
$131$	−9.82271	−0.858215	−0.429107	−	0.903254i	$-0.641172\pi$
$131$	−9.82271	−0.858215	−0.429107	+	0.903254i	$0.641172\pi$
$132$	0.930267	0.0809694
$133$	0	0
$134$	−13.7360	−1.18661
$135$	0.145411	0.0125150
$136$	17.5715	1.50675
$137$	−5.11311	−0.436843	−0.218421	−	0.975855i	$-0.570091\pi$
$137$	−5.11311	−0.436843	−0.218421	+	0.975855i	$0.570091\pi$
$138$	−9.11402	−0.775837
$139$	16.0072	1.35771	0.678855	−	0.734272i	$-0.262476\pi$
$139$	16.0072	1.35771	0.678855	+	0.734272i	$0.262476\pi$
$140$	0	0
$141$	8.27179	0.696610
$142$	−10.9280	−0.917054
$143$	4.64175	0.388163
$144$	−2.72665	−0.227220
$145$	0.0894139	0.00742542
$146$	8.07011	0.667887
$147$	0	0
$148$	0.897216	0.0737507
$149$	−2.17399	−0.178100	−0.0890500	−	0.996027i	$-0.528383\pi$
$149$	−2.17399	−0.178100	−0.0890500	+	0.996027i	$0.528383\pi$
$150$	−6.08202	−0.496595
$151$	−21.3530	−1.73768	−0.868842	−	0.495090i	$-0.835135\pi$
$151$	−21.3530	−1.73768	−0.868842	+	0.495090i	$0.835135\pi$
$152$	18.3128	1.48537
$153$	5.73593	0.463723
$154$	0	0
$155$	1.42776	0.114681
$156$	1.28647	0.103000
$157$	−20.2632	−1.61718	−0.808589	−	0.588374i	$-0.799768\pi$
$157$	−20.2632	−1.61718	−0.808589	+	0.588374i	$0.799768\pi$
$158$	−8.57837	−0.682458
$159$	6.25111	0.495745
$160$	0.406574	0.0321425
$161$	0	0
$162$	−1.22157	−0.0959757
$163$	−0.815935	−0.0639089	−0.0319545	−	0.999489i	$-0.510173\pi$
$163$	−0.815935	−0.0639089	−0.0319545	+	0.999489i	$0.510173\pi$
$164$	−0.507765	−0.0396498
$165$	0.266405	0.0207396
$166$	−2.07987	−0.161430
$167$	−20.3307	−1.57324	−0.786620	−	0.617437i	$-0.788171\pi$
$167$	−20.3307	−1.57324	−0.786620	+	0.617437i	$0.788171\pi$
$168$	0	0
$169$	−6.58091	−0.506224
$170$	1.01887	0.0781439
$171$	5.97791	0.457142
$172$	−1.20986	−0.0922508
$173$	4.52494	0.344025	0.172013	−	0.985095i	$-0.444973\pi$
$173$	4.52494	0.344025	0.172013	+	0.985095i	$0.444973\pi$
$174$	−0.751150	−0.0569445
$175$	0	0
$176$	−4.99544	−0.376546
$177$	8.36107	0.628457
$178$	18.8494	1.41283
$179$	5.05117	0.377542	0.188771	−	0.982021i	$-0.439550\pi$
$179$	5.05117	0.377542	0.188771	+	0.982021i	$0.439550\pi$
$180$	0.0738345	0.00550330
$181$	−15.3431	−1.14044	−0.570221	−	0.821491i	$-0.693142\pi$
$181$	−15.3431	−1.14044	−0.570221	+	0.821491i	$0.693142\pi$
$182$	0	0
$183$	2.56376	0.189519
$184$	−22.8558	−1.68495
$185$	0.256940	0.0188906
$186$	−11.9944	−0.879470
$187$	10.5087	0.768473
$188$	4.20012	0.306325
$189$	0	0
$190$	1.06185	0.0770351
$191$	17.5078	1.26682	0.633411	−	0.773815i	$-0.281654\pi$
$191$	17.5078	1.26682	0.633411	+	0.773815i	$0.281654\pi$
$192$	−8.86884	−0.640054
$193$	−23.7353	−1.70850	−0.854252	−	0.519859i	$-0.825984\pi$
$193$	−23.7353	−1.70850	−0.854252	+	0.519859i	$0.825984\pi$
$194$	7.47551	0.536710
$195$	0.368412	0.0263825
$196$	0	0
$197$	2.92277	0.208239	0.104119	−	0.994565i	$-0.466798\pi$
$197$	2.92277	0.208239	0.104119	+	0.994565i	$0.466798\pi$
$198$	−2.23802	−0.159049
$199$	4.31321	0.305756	0.152878	−	0.988245i	$-0.451146\pi$
$199$	4.31321	0.305756	0.152878	+	0.988245i	$0.451146\pi$
$200$	−15.2523	−1.07850
$201$	−11.2446	−0.793131
$202$	−23.3348	−1.64183
$203$	0	0
$204$	2.91250	0.203916
$205$	−0.145411	−0.0101559
$206$	8.08565	0.563354
$207$	−7.46090	−0.518568
$208$	−6.90821	−0.478998
$209$	10.9520	0.757568
$210$	0	0
$211$	23.9810	1.65092	0.825459	−	0.564462i	$-0.190916\pi$
$211$	23.9810	1.65092	0.825459	+	0.564462i	$0.190916\pi$
$212$	3.17409	0.217997
$213$	−8.94583	−0.612958
$214$	−22.2775	−1.52286
$215$	−0.346473	−0.0236292
$216$	−3.06341	−0.208439
$217$	0	0
$218$	12.5709	0.851410
$219$	6.60634	0.446415
$220$	0.135271	0.00911997
$221$	14.5325	0.977562
$222$	−2.15851	−0.144869
$223$	−1.56949	−0.105101	−0.0525503	−	0.998618i	$-0.516735\pi$
$223$	−1.56949	−0.105101	−0.0525503	+	0.998618i	$0.516735\pi$
$224$	0	0
$225$	−4.97886	−0.331924
$226$	−5.53797	−0.368380
$227$	−13.1290	−0.871404	−0.435702	−	0.900091i	$-0.643500\pi$
$227$	−13.1290	−0.871404	−0.435702	+	0.900091i	$0.643500\pi$
$228$	3.03537	0.201023
$229$	−14.7066	−0.971837	−0.485918	−	0.874004i	$-0.661515\pi$
$229$	−14.7066	−0.971837	−0.485918	+	0.874004i	$0.661515\pi$
$230$	−1.32528	−0.0873862
$231$	0	0
$232$	−1.88371	−0.123671
$233$	11.0589	0.724492	0.362246	−	0.932083i	$-0.382010\pi$
$233$	11.0589	0.724492	0.362246	+	0.932083i	$0.382010\pi$
$234$	−3.09496	−0.202324
$235$	1.20281	0.0784625
$236$	4.24546	0.276356
$237$	−7.02241	−0.456154
$238$	0	0
$239$	−20.8795	−1.35058	−0.675290	−	0.737552i	$-0.735982\pi$
$239$	−20.8795	−1.35058	−0.675290	+	0.737552i	$0.735982\pi$
$240$	−0.396484	−0.0255929
$241$	12.4691	0.803203	0.401602	−	0.915815i	$-0.368454\pi$
$241$	12.4691	0.803203	0.401602	+	0.915815i	$0.368454\pi$
$242$	9.33704	0.600208
$243$	−1.00000	−0.0641500
$244$	1.30179	0.0833383
$245$	0	0
$246$	1.22157	0.0778845
$247$	15.1456	0.963691
$248$	−30.0791	−1.91002
$249$	−1.70262	−0.107899
$250$	−1.77254	−0.112105
$251$	4.61513	0.291304	0.145652	−	0.989336i	$-0.453472\pi$
$251$	4.61513	0.291304	0.145652	+	0.989336i	$0.453472\pi$
$252$	0	0
$253$	−13.6690	−0.859362
$254$	−6.85679	−0.430233
$255$	0.834067	0.0522313
$256$	−11.3344	−0.708400
$257$	−21.5623	−1.34502	−0.672510	−	0.740088i	$-0.734784\pi$
$257$	−21.5623	−1.34502	−0.672510	+	0.740088i	$0.734784\pi$
$258$	2.91065	0.181209
$259$	0	0
$260$	0.187067	0.0116014
$261$	−0.614905	−0.0380617
$262$	11.9991	0.741309
$263$	18.8906	1.16485	0.582424	−	0.812885i	$-0.302105\pi$
$263$	18.8906	1.16485	0.582424	+	0.812885i	$0.302105\pi$
$264$	−5.61243	−0.345421
$265$	0.908979	0.0558381
$266$	0	0
$267$	15.4305	0.944331
$268$	−5.70960	−0.348769
$269$	−8.84262	−0.539144	−0.269572	−	0.962980i	$-0.586882\pi$
$269$	−8.84262	−0.539144	−0.269572	+	0.962980i	$0.586882\pi$
$270$	−0.177630	−0.0108102
$271$	−14.2444	−0.865288	−0.432644	−	0.901565i	$-0.642419\pi$
$271$	−14.2444	−0.865288	−0.432644	+	0.901565i	$0.642419\pi$
$272$	−15.6398	−0.948305
$273$	0	0
$274$	6.24603	0.377337
$275$	−9.12168	−0.550058
$276$	−3.78838	−0.228034
$277$	20.0564	1.20508	0.602538	−	0.798091i	$-0.294156\pi$
$277$	20.0564	1.20508	0.602538	+	0.798091i	$0.294156\pi$
$278$	−19.5539	−1.17276
$279$	−9.81881	−0.587837
$280$	0	0
$281$	1.96455	0.117195	0.0585977	−	0.998282i	$-0.481337\pi$
$281$	1.96455	0.117195	0.0585977	+	0.998282i	$0.481337\pi$
$282$	−10.1046	−0.601718
$283$	−16.1770	−0.961622	−0.480811	−	0.876824i	$-0.659658\pi$
$283$	−16.1770	−0.961622	−0.480811	+	0.876824i	$0.659658\pi$
$284$	−4.54238	−0.269540
$285$	0.869254	0.0514901
$286$	−5.67023	−0.335288
$287$	0	0
$288$	−2.79603	−0.164758
$289$	15.9009	0.935347
$290$	−0.109225	−0.00641394
$291$	6.11958	0.358736
$292$	3.35447	0.196305
$293$	2.71850	0.158817	0.0794083	−	0.996842i	$-0.474697\pi$
$293$	2.71850	0.158817	0.0794083	+	0.996842i	$0.474697\pi$
$294$	0	0
$295$	1.21579	0.0707861
$296$	−5.41302	−0.314626
$297$	−1.83208	−0.106308
$298$	2.65568	0.153839
$299$	−18.9029	−1.09318
$300$	−2.52809	−0.145959
$301$	0	0
$302$	26.0842	1.50098
$303$	−19.1023	−1.09740
$304$	−16.2997	−0.934849
$305$	0.372798	0.0213464
$306$	−7.00685	−0.400555
$307$	19.5124	1.11363	0.556817	−	0.830635i	$-0.312023\pi$
$307$	19.5124	1.11363	0.556817	+	0.830635i	$0.312023\pi$
$308$	0	0
$309$	6.61906	0.376545
$310$	−1.74411	−0.0990590
$311$	26.1930	1.48527	0.742634	−	0.669697i	$-0.233576\pi$
$311$	26.1930	1.48527	0.742634	+	0.669697i	$0.233576\pi$
$312$	−7.76144	−0.439405
$313$	23.4271	1.32418	0.662088	−	0.749426i	$-0.269670\pi$
$313$	23.4271	1.32418	0.662088	+	0.749426i	$0.269670\pi$
$314$	24.7529	1.39689
$315$	0	0
$316$	−3.56573	−0.200588
$317$	29.6646	1.66613	0.833064	−	0.553177i	$-0.186585\pi$
$317$	29.6646	1.66613	0.833064	+	0.553177i	$0.186585\pi$
$318$	−7.63617	−0.428215
$319$	−1.12656	−0.0630751
$320$	−1.28963	−0.0720923
$321$	−18.2368	−1.01788
$322$	0	0
$323$	34.2889	1.90789
$324$	−0.507765	−0.0282092
$325$	−12.6144	−0.699721
$326$	0.996722	0.0552033
$327$	10.2908	0.569081
$328$	3.06341	0.169149
$329$	0	0
$330$	−0.325432	−0.0179145
$331$	−21.4288	−1.17784	−0.588918	−	0.808193i	$-0.700446\pi$
$331$	−21.4288	−1.17784	−0.588918	+	0.808193i	$0.700446\pi$
$332$	−0.864532	−0.0474473
$333$	−1.76699	−0.0968305
$334$	24.8354	1.35894
$335$	−1.63508	−0.0893342
$336$	0	0
$337$	−35.3061	−1.92324	−0.961622	−	0.274377i	$-0.911529\pi$
$337$	−35.3061	−1.92324	−0.961622	+	0.274377i	$0.911529\pi$
$338$	8.03905	0.437266
$339$	−4.53348	−0.246225
$340$	0.423510	0.0229680
$341$	−17.9889	−0.974153
$342$	−7.30244	−0.394871
$343$	0	0
$344$	7.29924	0.393548
$345$	−1.08490	−0.0584088
$346$	−5.52754	−0.297162
$347$	14.2038	0.762498	0.381249	−	0.924472i	$-0.375494\pi$
$347$	14.2038	0.762498	0.381249	+	0.924472i	$0.375494\pi$
$348$	−0.312227	−0.0167371
$349$	0.124695	0.00667474	0.00333737	−	0.999994i	$-0.498938\pi$
$349$	0.124695	0.00667474	0.00333737	+	0.999994i	$0.498938\pi$
$350$	0	0
$351$	−2.53359	−0.135233
$352$	−5.12257	−0.273034
$353$	−32.3815	−1.72349	−0.861745	−	0.507341i	$-0.830628\pi$
$353$	−32.3815	−1.72349	−0.861745	+	0.507341i	$0.830628\pi$
$354$	−10.2136	−0.542849
$355$	−1.30082	−0.0690404
$356$	7.83506	0.415257
$357$	0	0
$358$	−6.17037	−0.326114
$359$	−0.756964	−0.0399510	−0.0199755	−	0.999800i	$-0.506359\pi$
$359$	−0.756964	−0.0399510	−0.0199755	+	0.999800i	$0.506359\pi$
$360$	−0.445453	−0.0234775
$361$	16.7355	0.880813
$362$	18.7427	0.985092
$363$	7.64347	0.401178
$364$	0	0
$365$	0.960634	0.0502819
$366$	−3.13181	−0.163702
$367$	−4.65793	−0.243142	−0.121571	−	0.992583i	$-0.538793\pi$
$367$	−4.65793	−0.243142	−0.121571	+	0.992583i	$0.538793\pi$
$368$	20.3432	1.06046
$369$	1.00000	0.0520579
$370$	−0.313870	−0.0163173
$371$	0	0
$372$	−4.98565	−0.258494
$373$	19.9680	1.03390	0.516951	−	0.856015i	$-0.327067\pi$
$373$	19.9680	1.03390	0.516951	+	0.856015i	$0.327067\pi$
$374$	−12.8371	−0.663792
$375$	−1.45103	−0.0749311
$376$	−25.3399	−1.30680
$377$	−1.55792	−0.0802369
$378$	0	0
$379$	−0.324794	−0.0166835	−0.00834176	−	0.999965i	$-0.502655\pi$
$379$	−0.324794	−0.0166835	−0.00834176	+	0.999965i	$0.502655\pi$
$380$	0.441376	0.0226421
$381$	−5.61309	−0.287567
$382$	−21.3871	−1.09426
$383$	−2.02355	−0.103398	−0.0516992	−	0.998663i	$-0.516464\pi$
$383$	−2.02355	−0.103398	−0.0516992	+	0.998663i	$0.516464\pi$
$384$	5.24185	0.267497
$385$	0	0
$386$	28.9943	1.47577
$387$	2.38271	0.121120
$388$	3.10731	0.157750
$389$	5.64751	0.286340	0.143170	−	0.989698i	$-0.454270\pi$
$389$	5.64751	0.286340	0.143170	+	0.989698i	$0.454270\pi$
$390$	−0.450041	−0.0227887
$391$	−42.7952	−2.16425
$392$	0	0
$393$	9.82271	0.495490
$394$	−3.57037	−0.179873
$395$	−1.02113	−0.0513789
$396$	−0.930267	−0.0467477
$397$	−22.8333	−1.14597	−0.572985	−	0.819566i	$-0.694214\pi$
$397$	−22.8333	−1.14597	−0.572985	+	0.819566i	$0.694214\pi$
$398$	−5.26890	−0.264106
$399$	0	0
$400$	13.5756	0.678779
$401$	−24.2797	−1.21247	−0.606235	−	0.795286i	$-0.707321\pi$
$401$	−24.2797	−1.21247	−0.606235	+	0.795286i	$0.707321\pi$
$402$	13.7360	0.685092
$403$	−24.8769	−1.23921
$404$	−9.69948	−0.482567
$405$	−0.145411	−0.00722552
$406$	0	0
$407$	−3.23728	−0.160466
$408$	−17.5715	−0.869920
$409$	26.1903	1.29503	0.647514	−	0.762053i	$-0.275809\pi$
$409$	26.1903	1.29503	0.647514	+	0.762053i	$0.275809\pi$
$410$	0.177630	0.00877251
$411$	5.11311	0.252211
$412$	3.36093	0.165581
$413$	0	0
$414$	9.11402	0.447930
$415$	−0.247580	−0.0121532
$416$	−7.08401	−0.347322
$417$	−16.0072	−0.783874
$418$	−13.3787	−0.654373
$419$	−3.85993	−0.188570	−0.0942849	−	0.995545i	$-0.530056\pi$
$419$	−3.85993	−0.188570	−0.0942849	+	0.995545i	$0.530056\pi$
$420$	0	0
$421$	−23.8277	−1.16129	−0.580645	−	0.814157i	$-0.697200\pi$
$421$	−23.8277	−1.16129	−0.580645	+	0.814157i	$0.697200\pi$
$422$	−29.2945	−1.42603
$423$	−8.27179	−0.402188
$424$	−19.1497	−0.929992
$425$	−28.5584	−1.38528
$426$	10.9280	0.529462
$427$	0	0
$428$	−9.25999	−0.447599
$429$	−4.64175	−0.224106
$430$	0.423241	0.0204105
$431$	3.21741	0.154977	0.0774887	−	0.996993i	$-0.475310\pi$
$431$	3.21741	0.154977	0.0774887	+	0.996993i	$0.475310\pi$
$432$	2.72665	0.131186
$433$	−20.6425	−0.992016	−0.496008	−	0.868318i	$-0.665201\pi$
$433$	−20.6425	−0.992016	−0.496008	+	0.868318i	$0.665201\pi$
$434$	0	0
$435$	−0.0894139	−0.00428707
$436$	5.22529	0.250246
$437$	−44.6006	−2.13354
$438$	−8.07011	−0.385605
$439$	−6.84739	−0.326808	−0.163404	−	0.986559i	$-0.552247\pi$
$439$	−6.84739	−0.326808	−0.163404	+	0.986559i	$0.552247\pi$
$440$	−0.816108	−0.0389064
$441$	0	0
$442$	−17.7525	−0.844400
$443$	11.4657	0.544752	0.272376	−	0.962191i	$-0.412190\pi$
$443$	11.4657	0.544752	0.272376	+	0.962191i	$0.412190\pi$
$444$	−0.897216	−0.0425800
$445$	2.24376	0.106365
$446$	1.91724	0.0907840
$447$	2.17399	0.102826
$448$	0	0
$449$	16.6274	0.784693	0.392347	−	0.919817i	$-0.371663\pi$
$449$	16.6274	0.784693	0.392347	+	0.919817i	$0.371663\pi$
$450$	6.08202	0.286709
$451$	1.83208	0.0862694
$452$	−2.30194	−0.108274
$453$	21.3530	1.00325
$454$	16.0380	0.752702
$455$	0	0
$456$	−18.3128	−0.857576
$457$	−34.4178	−1.61000	−0.804999	−	0.593276i	$-0.797834\pi$
$457$	−34.4178	−1.61000	−0.804999	+	0.593276i	$0.797834\pi$
$458$	17.9651	0.839454
$459$	−5.73593	−0.267730
$460$	−0.550872	−0.0256845
$461$	−0.543006	−0.0252903	−0.0126452	−	0.999920i	$-0.504025\pi$
$461$	−0.543006	−0.0252903	−0.0126452	+	0.999920i	$0.504025\pi$
$462$	0	0
$463$	−40.1255	−1.86479	−0.932395	−	0.361441i	$-0.882285\pi$
$463$	−40.1255	−1.86479	−0.932395	+	0.361441i	$0.882285\pi$
$464$	1.67663	0.0778355
$465$	−1.42776	−0.0662109
$466$	−13.5092	−0.625802
$467$	15.0788	0.697763	0.348882	−	0.937167i	$-0.386562\pi$
$467$	15.0788	0.697763	0.348882	+	0.937167i	$0.386562\pi$
$468$	−1.28647	−0.0594670
$469$	0	0
$470$	−1.46931	−0.0677744
$471$	20.2632	0.933678
$472$	−25.6134	−1.17895
$473$	4.36533	0.200718
$474$	8.57837	0.394018
$475$	−29.7632	−1.36563
$476$	0	0
$477$	−6.25111	−0.286219
$478$	25.5058	1.16661
$479$	1.28093	0.0585273	0.0292636	−	0.999572i	$-0.490684\pi$
$479$	1.28093	0.0585273	0.0292636	+	0.999572i	$0.490684\pi$
$480$	−0.406574	−0.0185575
$481$	−4.47684	−0.204126
$482$	−15.2318	−0.693792
$483$	0	0
$484$	3.88108	0.176413
$485$	0.889854	0.0404062
$486$	1.22157	0.0554116
$487$	6.08770	0.275860	0.137930	−	0.990442i	$-0.455955\pi$
$487$	6.08770	0.275860	0.137930	+	0.990442i	$0.455955\pi$
$488$	−7.85385	−0.355527
$489$	0.815935	0.0368978
$490$	0	0
$491$	15.6046	0.704225	0.352112	−	0.935958i	$-0.385463\pi$
$491$	15.6046	0.704225	0.352112	+	0.935958i	$0.385463\pi$
$492$	0.507765	0.0228918
$493$	−3.52705	−0.158850
$494$	−18.5014	−0.832418
$495$	−0.266405	−0.0119740
$496$	26.7724	1.20212
$497$	0	0
$498$	2.07987	0.0932014
$499$	−9.97737	−0.446649	−0.223324	−	0.974744i	$-0.571691\pi$
$499$	−9.97737	−0.446649	−0.223324	+	0.974744i	$0.571691\pi$
$500$	−0.736784	−0.0329500
$501$	20.3307	0.908311
$502$	−5.63771	−0.251623
$503$	−8.37434	−0.373394	−0.186697	−	0.982418i	$-0.559778\pi$
$503$	−8.37434	−0.373394	−0.186697	+	0.982418i	$0.559778\pi$
$504$	0	0
$505$	−2.77768	−0.123605
$506$	16.6976	0.742301
$507$	6.58091	0.292268
$508$	−2.85013	−0.126454
$509$	38.6361	1.71251	0.856257	−	0.516550i	$-0.172784\pi$
$509$	38.6361	1.71251	0.856257	+	0.516550i	$0.172784\pi$
$510$	−1.01887	−0.0451164
$511$	0	0
$512$	24.3295	1.07522
$513$	−5.97791	−0.263931
$514$	26.3399	1.16180
$515$	0.962484	0.0424121
$516$	1.20986	0.0532610
$517$	−15.1546	−0.666499
$518$	0	0
$519$	−4.52494	−0.198623
$520$	−1.12860	−0.0494923
$521$	−3.67649	−0.161070	−0.0805351	−	0.996752i	$-0.525663\pi$
$521$	−3.67649	−0.161070	−0.0805351	+	0.996752i	$0.525663\pi$
$522$	0.751150	0.0328769
$523$	−9.99389	−0.437002	−0.218501	−	0.975837i	$-0.570117\pi$
$523$	−9.99389	−0.437002	−0.218501	+	0.975837i	$0.570117\pi$
$524$	4.98763	0.217886
$525$	0	0
$526$	−23.0763	−1.00617
$527$	−56.3200	−2.45334
$528$	4.99544	0.217399
$529$	32.6650	1.42022
$530$	−1.11038	−0.0482319
$531$	−8.36107	−0.362840
$532$	0	0
$533$	2.53359	0.109742
$534$	−18.8494	−0.815695
$535$	−2.65183	−0.114648
$536$	34.4468	1.48787
$537$	−5.05117	−0.217974
$538$	10.8019	0.465703
$539$	0	0
$540$	−0.0738345	−0.00317733
$541$	−38.7654	−1.66665	−0.833327	−	0.552780i	$-0.813567\pi$
$541$	−38.7654	−1.66665	−0.833327	+	0.552780i	$0.813567\pi$
$542$	17.4006	0.747419
$543$	15.3431	0.658435
$544$	−16.0379	−0.687617
$545$	1.49639	0.0640984
$546$	0	0
$547$	−7.03480	−0.300786	−0.150393	−	0.988626i	$-0.548054\pi$
$547$	−7.03480	−0.300786	−0.150393	+	0.988626i	$0.548054\pi$
$548$	2.59626	0.110907
$549$	−2.56376	−0.109419
$550$	11.1428	0.475130
$551$	−3.67585	−0.156596
$552$	22.8558	0.972808
$553$	0	0
$554$	−24.5004	−1.04092
$555$	−0.256940	−0.0109065
$556$	−8.12787	−0.344699
$557$	17.5813	0.744946	0.372473	−	0.928043i	$-0.378510\pi$
$557$	17.5813	0.744946	0.372473	+	0.928043i	$0.378510\pi$
$558$	11.9944	0.507762
$559$	6.03683	0.255331
$560$	0	0
$561$	−10.5087	−0.443678
$562$	−2.39984	−0.101231
$563$	19.6243	0.827068	0.413534	−	0.910489i	$-0.364294\pi$
$563$	19.6243	0.827068	0.413534	+	0.910489i	$0.364294\pi$
$564$	−4.20012	−0.176857
$565$	−0.659217	−0.0277335
$566$	19.7613	0.830631
$567$	0	0
$568$	27.4048	1.14988
$569$	5.77853	0.242249	0.121124	−	0.992637i	$-0.461350\pi$
$569$	5.77853	0.242249	0.121124	+	0.992637i	$0.461350\pi$
$570$	−1.06185	−0.0444762
$571$	14.1340	0.591491	0.295746	−	0.955267i	$-0.404432\pi$
$571$	14.1340	0.591491	0.295746	+	0.955267i	$0.404432\pi$
$572$	−2.35692	−0.0985477
$573$	−17.5078	−0.731400
$574$	0	0
$575$	37.1467	1.54913
$576$	8.86884	0.369535
$577$	−11.5054	−0.478977	−0.239488	−	0.970899i	$-0.576980\pi$
$577$	−11.5054	−0.478977	−0.239488	+	0.970899i	$0.576980\pi$
$578$	−19.4241	−0.807935
$579$	23.7353	0.986405
$580$	−0.0454012	−0.00188518
$581$	0	0
$582$	−7.47551	−0.309870
$583$	−11.4525	−0.474316
$584$	−20.2379	−0.837452
$585$	−0.368412	−0.0152320
$586$	−3.32084	−0.137183
$587$	−33.8814	−1.39844	−0.699218	−	0.714909i	$-0.746468\pi$
$587$	−33.8814	−1.39844	−0.699218	+	0.714909i	$0.746468\pi$
$588$	0	0
$589$	−58.6960	−2.41853
$590$	−1.48517	−0.0611437
$591$	−2.92277	−0.120227
$592$	4.81796	0.198017
$593$	32.9905	1.35476	0.677379	−	0.735634i	$-0.263116\pi$
$593$	32.9905	1.35476	0.677379	+	0.735634i	$0.263116\pi$
$594$	2.23802	0.0918271
$595$	0	0
$596$	1.10387	0.0452165
$597$	−4.31321	−0.176528
$598$	23.0912	0.944270
$599$	−25.7136	−1.05063	−0.525314	−	0.850908i	$-0.676052\pi$
$599$	−25.7136	−1.05063	−0.525314	+	0.850908i	$0.676052\pi$
$600$	15.2523	0.622672
$601$	−24.8386	−1.01319	−0.506594	−	0.862185i	$-0.669096\pi$
$601$	−24.8386	−1.01319	−0.506594	+	0.862185i	$0.669096\pi$
$602$	0	0
$603$	11.2446	0.457915
$604$	10.8423	0.441167
$605$	1.11144	0.0451866
$606$	23.3348	0.947913
$607$	−17.4325	−0.707564	−0.353782	−	0.935328i	$-0.615105\pi$
$607$	−17.4325	−0.707564	−0.353782	+	0.935328i	$0.615105\pi$
$608$	−16.7144	−0.677860
$609$	0	0
$610$	−0.455400	−0.0184386
$611$	−20.9573	−0.847843
$612$	−2.91250	−0.117731
$613$	−25.8187	−1.04281	−0.521404	−	0.853310i	$-0.674592\pi$
$613$	−25.8187	−1.04281	−0.521404	+	0.853310i	$0.674592\pi$
$614$	−23.8358	−0.961935
$615$	0.145411	0.00586353
$616$	0	0
$617$	39.0849	1.57350	0.786749	−	0.617273i	$-0.211763\pi$
$617$	39.0849	1.57350	0.786749	+	0.617273i	$0.211763\pi$
$618$	−8.08565	−0.325253
$619$	−41.5165	−1.66869	−0.834344	−	0.551244i	$-0.814153\pi$
$619$	−41.5165	−1.66869	−0.834344	+	0.551244i	$0.814153\pi$
$620$	−0.724967	−0.0291154
$621$	7.46090	0.299396
$622$	−31.9966	−1.28295
$623$	0	0
$624$	6.90821	0.276550
$625$	24.6833	0.987331
$626$	−28.6178	−1.14380
$627$	−10.9520	−0.437382
$628$	10.2889	0.410573
$629$	−10.1353	−0.404122
$630$	0	0
$631$	2.92451	0.116423	0.0582114	−	0.998304i	$-0.481460\pi$
$631$	2.92451	0.116423	0.0582114	+	0.998304i	$0.481460\pi$
$632$	21.5125	0.855723
$633$	−23.9810	−0.953158
$634$	−36.2374	−1.43917
$635$	−0.816205	−0.0323901
$636$	−3.17409	−0.125861
$637$	0	0
$638$	1.37617	0.0544831
$639$	8.94583	0.353892
$640$	0.762223	0.0301295
$641$	−3.78728	−0.149589	−0.0747943	−	0.997199i	$-0.523830\pi$
$641$	−3.78728	−0.149589	−0.0747943	+	0.997199i	$0.523830\pi$
$642$	22.2775	0.879223
$643$	25.9242	1.02235	0.511175	−	0.859477i	$-0.329210\pi$
$643$	25.9242	1.02235	0.511175	+	0.859477i	$0.329210\pi$
$644$	0	0
$645$	0.346473	0.0136423
$646$	−41.8863	−1.64800
$647$	−4.48166	−0.176192	−0.0880962	−	0.996112i	$-0.528078\pi$
$647$	−4.48166	−0.176192	−0.0880962	+	0.996112i	$0.528078\pi$
$648$	3.06341	0.120342
$649$	−15.3182	−0.601291
$650$	15.4094	0.604405
$651$	0	0
$652$	0.414303	0.0162253
$653$	−7.04571	−0.275720	−0.137860	−	0.990452i	$-0.544022\pi$
$653$	−7.04571	−0.275720	−0.137860	+	0.990452i	$0.544022\pi$
$654$	−12.5709	−0.491562
$655$	1.42833	0.0558095
$656$	−2.72665	−0.106458
$657$	−6.60634	−0.257738
$658$	0	0
$659$	22.4833	0.875823	0.437912	−	0.899018i	$-0.355718\pi$
$659$	22.4833	0.875823	0.437912	+	0.899018i	$0.355718\pi$
$660$	−0.135271	−0.00526542
$661$	23.7682	0.924474	0.462237	−	0.886756i	$-0.347047\pi$
$661$	23.7682	0.924474	0.462237	+	0.886756i	$0.347047\pi$
$662$	26.1768	1.01739
$663$	−14.5325	−0.564396
$664$	5.21583	0.202414
$665$	0	0
$666$	2.15851	0.0836404
$667$	4.58775	0.177638
$668$	10.3232	0.399418
$669$	1.56949	0.0606799
$670$	1.99737	0.0771652
$671$	−4.69702	−0.181326
$672$	0	0
$673$	−22.7110	−0.875444	−0.437722	−	0.899110i	$-0.644215\pi$
$673$	−22.7110	−0.875444	−0.437722	+	0.899110i	$0.644215\pi$
$674$	43.1289	1.66126
$675$	4.97886	0.191636
$676$	3.34155	0.128521
$677$	38.3529	1.47402	0.737012	−	0.675880i	$-0.236236\pi$
$677$	38.3529	1.47402	0.737012	+	0.675880i	$0.236236\pi$
$678$	5.53797	0.212684
$679$	0	0
$680$	−2.55509	−0.0979832
$681$	13.1290	0.503105
$682$	21.9747	0.841455
$683$	−14.6031	−0.558773	−0.279386	−	0.960179i	$-0.590131\pi$
$683$	−14.6031	−0.558773	−0.279386	+	0.960179i	$0.590131\pi$
$684$	−3.03537	−0.116060
$685$	0.743503	0.0284078
$686$	0	0
$687$	14.7066	0.561090
$688$	−6.49682	−0.247689
$689$	−15.8378	−0.603370
$690$	1.32528	0.0504525
$691$	−2.45208	−0.0932816	−0.0466408	−	0.998912i	$-0.514852\pi$
$691$	−2.45208	−0.0932816	−0.0466408	+	0.998912i	$0.514852\pi$
$692$	−2.29761	−0.0873419
$693$	0	0
$694$	−17.3509	−0.658631
$695$	−2.32762	−0.0882915
$696$	1.88371	0.0714018
$697$	5.73593	0.217264
$698$	−0.152323	−0.00576552
$699$	−11.0589	−0.418286
$700$	0	0
$701$	−15.6409	−0.590747	−0.295374	−	0.955382i	$-0.595444\pi$
$701$	−15.6409	−0.590747	−0.295374	+	0.955382i	$0.595444\pi$
$702$	3.09496	0.116812
$703$	−10.5629	−0.398388
$704$	16.2485	0.612387
$705$	−1.20281	−0.0453004
$706$	39.5562	1.48872
$707$	0	0
$708$	−4.24546	−0.159554
$709$	20.7676	0.779944	0.389972	−	0.920827i	$-0.372485\pi$
$709$	20.7676	0.779944	0.389972	+	0.920827i	$0.372485\pi$
$710$	1.58904	0.0596358
$711$	7.02241	0.263361
$712$	−47.2700	−1.77152
$713$	73.2572	2.74350
$714$	0	0
$715$	−0.674961	−0.0252421
$716$	−2.56481	−0.0958513
$717$	20.8795	0.779758
$718$	0.924685	0.0345089
$719$	−34.4833	−1.28601	−0.643006	−	0.765861i	$-0.722313\pi$
$719$	−34.4833	−1.28601	−0.643006	+	0.765861i	$0.722313\pi$
$720$	0.396484	0.0147761
$721$	0	0
$722$	−20.4435	−0.760830
$723$	−12.4691	−0.463729
$724$	7.79067	0.289538
$725$	3.06152	0.113702
$726$	−9.33704	−0.346530
$727$	−2.24989	−0.0834439	−0.0417220	−	0.999129i	$-0.513284\pi$
$727$	−2.24989	−0.0834439	−0.0417220	+	0.999129i	$0.513284\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−1.17348	−0.0434325
$731$	13.6671	0.505495
$732$	−1.30179	−0.0481154
$733$	−27.2936	−1.00811	−0.504055	−	0.863671i	$-0.668159\pi$
$733$	−27.2936	−1.00811	−0.504055	+	0.863671i	$0.668159\pi$
$734$	5.68999	0.210021
$735$	0	0
$736$	20.8609	0.768944
$737$	20.6010	0.758848
$738$	−1.22157	−0.0449666
$739$	22.0409	0.810786	0.405393	−	0.914142i	$-0.367135\pi$
$739$	22.0409	0.810786	0.405393	+	0.914142i	$0.367135\pi$
$740$	−0.130465	−0.00479599
$741$	−15.1456	−0.556387
$742$	0	0
$743$	−17.1279	−0.628362	−0.314181	−	0.949363i	$-0.601730\pi$
$743$	−17.1279	−0.628362	−0.314181	+	0.949363i	$0.601730\pi$
$744$	30.0791	1.10275
$745$	0.316122	0.0115818
$746$	−24.3923	−0.893065
$747$	1.70262	0.0622957
$748$	−5.33595	−0.195102
$749$	0	0
$750$	1.77254	0.0647240
$751$	−38.5946	−1.40834	−0.704168	−	0.710033i	$-0.748680\pi$
$751$	−38.5946	−1.40834	−0.704168	+	0.710033i	$0.748680\pi$
$752$	22.5542	0.822468
$753$	−4.61513	−0.168185
$754$	1.90311	0.0693071
$755$	3.10496	0.113001
$756$	0	0
$757$	8.61206	0.313011	0.156505	−	0.987677i	$-0.449977\pi$
$757$	8.61206	0.313011	0.156505	+	0.987677i	$0.449977\pi$
$758$	0.396758	0.0144109
$759$	13.6690	0.496153
$760$	−2.66288	−0.0965929
$761$	15.4289	0.559298	0.279649	−	0.960102i	$-0.409782\pi$
$761$	15.4289	0.559298	0.279649	+	0.960102i	$0.409782\pi$
$762$	6.85679	0.248395
$763$	0	0
$764$	−8.88986	−0.321624
$765$	−0.834067	−0.0301557
$766$	2.47191	0.0893136
$767$	−21.1835	−0.764893
$768$	11.3344	0.408995
$769$	13.7338	0.495253	0.247627	−	0.968856i	$-0.420349\pi$
$769$	13.7338	0.495253	0.247627	+	0.968856i	$0.420349\pi$
$770$	0	0
$771$	21.5623	0.776548
$772$	12.0519	0.433759
$773$	−16.6513	−0.598905	−0.299453	−	0.954111i	$-0.596804\pi$
$773$	−16.6513	−0.598905	−0.299453	+	0.954111i	$0.596804\pi$
$774$	−2.91065	−0.104621
$775$	48.8865	1.75605
$776$	−18.7468	−0.672971
$777$	0	0
$778$	−6.89883	−0.247335
$779$	5.97791	0.214181
$780$	−0.187067	−0.00669806
$781$	16.3895	0.586463
$782$	52.2774	1.86944
$783$	0.614905	0.0219749
$784$	0	0
$785$	2.94649	0.105165
$786$	−11.9991	−0.427995
$787$	40.0103	1.42621	0.713106	−	0.701056i	$-0.247288\pi$
$787$	40.0103	1.42621	0.713106	+	0.701056i	$0.247288\pi$
$788$	−1.48408	−0.0528681
$789$	−18.8906	−0.672525
$790$	1.24739	0.0443801
$791$	0	0
$792$	5.61243	0.199429
$793$	−6.49552	−0.230663
$794$	27.8925	0.989866
$795$	−0.908979	−0.0322382
$796$	−2.19010	−0.0776260
$797$	−24.9693	−0.884458	−0.442229	−	0.896902i	$-0.645812\pi$
$797$	−24.9693	−0.884458	−0.442229	+	0.896902i	$0.645812\pi$
$798$	0	0
$799$	−47.4464	−1.67853
$800$	13.9210	0.492183
$801$	−15.4305	−0.545210
$802$	29.6594	1.04731
$803$	−12.1034	−0.427118
$804$	5.70960	0.201362
$805$	0	0
$806$	30.3889	1.07040
$807$	8.84262	0.311275
$808$	58.5183	2.05867
$809$	36.7819	1.29318	0.646591	−	0.762837i	$-0.276194\pi$
$809$	36.7819	1.29318	0.646591	+	0.762837i	$0.276194\pi$
$810$	0.177630	0.00624127
$811$	−24.7568	−0.869330	−0.434665	−	0.900592i	$-0.643133\pi$
$811$	−24.7568	−0.869330	−0.434665	+	0.900592i	$0.643133\pi$
$812$	0	0
$813$	14.2444	0.499574
$814$	3.95456	0.138607
$815$	0.118646	0.00415598
$816$	15.6398	0.547504
$817$	14.2437	0.498323
$818$	−31.9933	−1.11862
$819$	0	0
$820$	0.0738345	0.00257841
$821$	−33.2744	−1.16128	−0.580642	−	0.814159i	$-0.697198\pi$
$821$	−33.2744	−1.16128	−0.580642	+	0.814159i	$0.697198\pi$
$822$	−6.24603	−0.217855
$823$	46.1529	1.60879	0.804395	−	0.594095i	$-0.202490\pi$
$823$	46.1529	1.60879	0.804395	+	0.594095i	$0.202490\pi$
$824$	−20.2769	−0.706380
$825$	9.12168	0.317576
$826$	0	0
$827$	−37.4274	−1.30148	−0.650738	−	0.759302i	$-0.725541\pi$
$827$	−37.4274	−1.30148	−0.650738	+	0.759302i	$0.725541\pi$
$828$	3.78838	0.131655
$829$	47.2630	1.64151	0.820756	−	0.571279i	$-0.193552\pi$
$829$	47.2630	1.64151	0.820756	+	0.571279i	$0.193552\pi$
$830$	0.302436	0.0104977
$831$	−20.0564	−0.695750
$832$	22.4700	0.779008
$833$	0	0
$834$	19.5539	0.677096
$835$	2.95631	0.102307
$836$	−5.56106	−0.192333
$837$	9.81881	0.339388
$838$	4.71517	0.162883
$839$	−41.6062	−1.43640	−0.718202	−	0.695834i	$-0.755035\pi$
$839$	−41.6062	−1.43640	−0.718202	+	0.695834i	$0.755035\pi$
$840$	0	0
$841$	−28.6219	−0.986962
$842$	29.1072	1.00310
$843$	−1.96455	−0.0676628
$844$	−12.1767	−0.419139
$845$	0.956936	0.0329196
$846$	10.1046	0.347402
$847$	0	0
$848$	17.0446	0.585312
$849$	16.1770	0.555193
$850$	34.8861	1.19658
$851$	13.1833	0.451919
$852$	4.54238	0.155619
$853$	−24.1153	−0.825693	−0.412846	−	0.910801i	$-0.635465\pi$
$853$	−24.1153	−0.825693	−0.412846	+	0.910801i	$0.635465\pi$
$854$	0	0
$855$	−0.869254	−0.0297278
$856$	55.8668	1.90949
$857$	1.66574	0.0569005	0.0284503	−	0.999595i	$-0.490943\pi$
$857$	1.66574	0.0569005	0.0284503	+	0.999595i	$0.490943\pi$
$858$	5.67023	0.193578
$859$	8.70390	0.296973	0.148487	−	0.988914i	$-0.452560\pi$
$859$	8.70390	0.296973	0.148487	+	0.988914i	$0.452560\pi$
$860$	0.175927	0.00599905
$861$	0	0
$862$	−3.93030	−0.133866
$863$	11.2956	0.384508	0.192254	−	0.981345i	$-0.438420\pi$
$863$	11.2956	0.384508	0.192254	+	0.981345i	$0.438420\pi$
$864$	2.79603	0.0951230
$865$	−0.657976	−0.0223719
$866$	25.2163	0.856885
$867$	−15.9009	−0.540023
$868$	0	0
$869$	12.8656	0.436437
$870$	0.109225	0.00370309
$871$	28.4892	0.965319
$872$	−31.5249	−1.06757
$873$	−6.11958	−0.207117
$874$	54.4828	1.84291
$875$	0	0
$876$	−3.35447	−0.113337
$877$	−54.4976	−1.84025	−0.920126	−	0.391622i	$-0.871914\pi$
$877$	−54.4976	−1.84025	−0.920126	+	0.391622i	$0.871914\pi$
$878$	8.36458	0.282291
$879$	−2.71850	−0.0916928
$880$	0.726392	0.0244867
$881$	−46.1184	−1.55377	−0.776884	−	0.629644i	$-0.783201\pi$
$881$	−46.1184	−1.55377	−0.776884	+	0.629644i	$0.783201\pi$
$882$	0	0
$883$	−51.8443	−1.74470	−0.872350	−	0.488882i	$-0.837405\pi$
$883$	−51.8443	−1.74470	−0.872350	+	0.488882i	$0.837405\pi$
$884$	−7.37910	−0.248186
$885$	−1.21579	−0.0408684
$886$	−14.0062	−0.470547
$887$	−55.2996	−1.85678	−0.928389	−	0.371610i	$-0.878806\pi$
$887$	−55.2996	−1.85678	−0.928389	+	0.371610i	$0.878806\pi$
$888$	5.41302	0.181649
$889$	0	0
$890$	−2.74091	−0.0918756
$891$	1.83208	0.0613771
$892$	0.796930	0.0266832
$893$	−49.4480	−1.65471
$894$	−2.65568	−0.0888193
$895$	−0.734495	−0.0245515
$896$	0	0
$897$	18.9029	0.631149
$898$	−20.3115	−0.677803
$899$	6.03764	0.201367
$900$	2.52809	0.0842696
$901$	−35.8559	−1.19453
$902$	−2.23802	−0.0745179
$903$	0	0
$904$	13.8879	0.461905
$905$	2.23105	0.0741626
$906$	−26.0842	−0.866590
$907$	9.79733	0.325315	0.162657	−	0.986683i	$-0.447993\pi$
$907$	9.79733	0.325315	0.162657	+	0.986683i	$0.447993\pi$
$908$	6.66646	0.221234
$909$	19.1023	0.633584
$910$	0	0
$911$	−20.9578	−0.694362	−0.347181	−	0.937798i	$-0.612861\pi$
$911$	−20.9578	−0.694362	−0.347181	+	0.937798i	$0.612861\pi$
$912$	16.2997	0.539735
$913$	3.11935	0.103235
$914$	42.0438	1.39069
$915$	−0.372798	−0.0123243
$916$	7.46747	0.246732
$917$	0	0
$918$	7.00685	0.231260
$919$	37.2158	1.22764	0.613819	−	0.789447i	$-0.289633\pi$
$919$	37.2158	1.22764	0.613819	+	0.789447i	$0.289633\pi$
$920$	3.32348	0.109572
$921$	−19.5124	−0.642956
$922$	0.663320	0.0218453
$923$	22.6651	0.746030
$924$	0	0
$925$	8.79760	0.289263
$926$	49.0161	1.61077
$927$	−6.61906	−0.217399
$928$	1.71930	0.0564386
$929$	−53.6954	−1.76169	−0.880844	−	0.473406i	$-0.843024\pi$
$929$	−53.6954	−1.76169	−0.880844	+	0.473406i	$0.843024\pi$
$930$	1.74411	0.0571917
$931$	0	0
$932$	−5.61531	−0.183936
$933$	−26.1930	−0.857520
$934$	−18.4198	−0.602715
$935$	−1.52808	−0.0499736
$936$	7.76144	0.253691
$937$	−54.2183	−1.77124	−0.885618	−	0.464415i	$-0.846265\pi$
$937$	−54.2183	−1.77124	−0.885618	+	0.464415i	$0.846265\pi$
$938$	0	0
$939$	−23.4271	−0.764514
$940$	−0.610743	−0.0199202
$941$	−29.9105	−0.975055	−0.487527	−	0.873108i	$-0.662101\pi$
$941$	−29.9105	−0.975055	−0.487527	+	0.873108i	$0.662101\pi$
$942$	−24.7529	−0.806493
$943$	−7.46090	−0.242960
$944$	22.7977	0.742001
$945$	0	0
$946$	−5.33256	−0.173377
$947$	29.3581	0.954009	0.477005	−	0.878901i	$-0.341722\pi$
$947$	29.3581	0.954009	0.477005	+	0.878901i	$0.341722\pi$
$948$	3.56573	0.115810
$949$	−16.7378	−0.543331
$950$	36.3578	1.17960
$951$	−29.6646	−0.961939
$952$	0	0
$953$	−27.0697	−0.876875	−0.438437	−	0.898762i	$-0.644468\pi$
$953$	−27.0697	−0.876875	−0.438437	+	0.898762i	$0.644468\pi$
$954$	7.63617	0.247230
$955$	−2.54583	−0.0823811
$956$	10.6019	0.342889
$957$	1.12656	0.0364164
$958$	−1.56475	−0.0505548
$959$	0	0
$960$	1.28963	0.0416225
$961$	65.4091	2.10997
$962$	5.46877	0.176320
$963$	18.2368	0.587672
$964$	−6.33135	−0.203919
$965$	3.45137	0.111104
$966$	0	0
$967$	15.8570	0.509927	0.254964	−	0.966951i	$-0.417936\pi$
$967$	15.8570	0.509927	0.254964	+	0.966951i	$0.417936\pi$
$968$	−23.4151	−0.752590
$969$	−34.2889	−1.10152
$970$	−1.08702	−0.0349021
$971$	−2.48639	−0.0797919	−0.0398960	−	0.999204i	$-0.512703\pi$
$971$	−2.48639	−0.0797919	−0.0398960	+	0.999204i	$0.512703\pi$
$972$	0.507765	0.0162866
$973$	0	0
$974$	−7.43656	−0.238283
$975$	12.6144	0.403984
$976$	6.99046	0.223759
$977$	43.8787	1.40380	0.701902	−	0.712273i	$-0.252334\pi$
$977$	43.8787	1.40380	0.701902	+	0.712273i	$0.252334\pi$
$978$	−0.996722	−0.0318716
$979$	−28.2700	−0.903512
$980$	0	0
$981$	−10.2908	−0.328559
$982$	−19.0621	−0.608296
$983$	41.2449	1.31551	0.657754	−	0.753232i	$-0.271506\pi$
$983$	41.2449	1.31551	0.657754	+	0.753232i	$0.271506\pi$
$984$	−3.06341	−0.0976580
$985$	−0.425003	−0.0135417
$986$	4.30854	0.137212
$987$	0	0
$988$	−7.69040	−0.244664
$989$	−17.7772	−0.565282
$990$	0.325432	0.0103429
$991$	−41.8266	−1.32867	−0.664334	−	0.747436i	$-0.731285\pi$
$991$	−41.8266	−1.32867	−0.664334	+	0.747436i	$0.731285\pi$
$992$	27.4537	0.871657
$993$	21.4288	0.680024
$994$	0	0
$995$	−0.627188	−0.0198832
$996$	0.864532	0.0273937
$997$	−58.2706	−1.84545	−0.922725	−	0.385460i	$-0.874043\pi$
$997$	−58.2706	−1.84545	−0.922725	+	0.385460i	$0.874043\pi$
$998$	12.1881	0.385807
$999$	1.76699	0.0559051

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bf.1.4		12
7.3	odd	6		861.2.i.e.247.9	✓	24
7.5	odd	6		861.2.i.e.739.9	yes	24
7.6	odd	2		6027.2.a.bg.1.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.i.e.247.9	✓	24	7.3	odd	6
861.2.i.e.739.9	yes	24	7.5	odd	6
6027.2.a.bf.1.4		12	1.1	even	1	trivial
6027.2.a.bg.1.4		12	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)

\(f(q)\)	\(=\)	\(q-1.22157 q^{2} -1.00000 q^{3} -0.507765 q^{4} -0.145411 q^{5} +1.22157 q^{6} +3.06341 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.22157 q^{2} -1.00000 q^{3} -0.507765 q^{4} -0.145411 q^{5} +1.22157 q^{6} +3.06341 q^{8} +1.00000 q^{9} +0.177630 q^{10} +1.83208 q^{11} +0.507765 q^{12} +2.53359 q^{13} +0.145411 q^{15} -2.72665 q^{16} +5.73593 q^{17} -1.22157 q^{18} +5.97791 q^{19} +0.0738345 q^{20} -2.23802 q^{22} -7.46090 q^{23} -3.06341 q^{24} -4.97886 q^{25} -3.09496 q^{26} -1.00000 q^{27} -0.614905 q^{29} -0.177630 q^{30} -9.81881 q^{31} -2.79603 q^{32} -1.83208 q^{33} -7.00685 q^{34} -0.507765 q^{36} -1.76699 q^{37} -7.30244 q^{38} -2.53359 q^{39} -0.445453 q^{40} +1.00000 q^{41} +2.38271 q^{43} -0.930267 q^{44} -0.145411 q^{45} +9.11402 q^{46} -8.27179 q^{47} +2.72665 q^{48} +6.08202 q^{50} -5.73593 q^{51} -1.28647 q^{52} -6.25111 q^{53} +1.22157 q^{54} -0.266405 q^{55} -5.97791 q^{57} +0.751150 q^{58} -8.36107 q^{59} -0.0738345 q^{60} -2.56376 q^{61} +11.9944 q^{62} +8.86884 q^{64} -0.368412 q^{65} +2.23802 q^{66} +11.2446 q^{67} -2.91250 q^{68} +7.46090 q^{69} +8.94583 q^{71} +3.06341 q^{72} -6.60634 q^{73} +2.15851 q^{74} +4.97886 q^{75} -3.03537 q^{76} +3.09496 q^{78} +7.02241 q^{79} +0.396484 q^{80} +1.00000 q^{81} -1.22157 q^{82} +1.70262 q^{83} -0.834067 q^{85} -2.91065 q^{86} +0.614905 q^{87} +5.61243 q^{88} -15.4305 q^{89} +0.177630 q^{90} +3.78838 q^{92} +9.81881 q^{93} +10.1046 q^{94} -0.869254 q^{95} +2.79603 q^{96} -6.11958 q^{97} +1.83208 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - 12 q^{3} + 10 q^{4} - 12 q^{5} + 2 q^{6} + 12 q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 - 12 * q^3 + 10 * q^4 - 12 * q^5 + 2 * q^6 + 12 * q^9	\( 12 q - 2 q^{2} - 12 q^{3} + 10 q^{4} - 12 q^{5} + 2 q^{6} + 12 q^{9} - 11 q^{10} + 10 q^{11} - 10 q^{12} - 15 q^{13} + 12 q^{15} + 14 q^{16} - 8 q^{17} - 2 q^{18} - 2 q^{19} - 16 q^{20} - 7 q^{22} + 5 q^{23} + 20 q^{25} - 12 q^{27} + 20 q^{29} + 11 q^{30} - 10 q^{31} + 3 q^{32} - 10 q^{33} + 23 q^{34} + 10 q^{36} - 17 q^{37} - 6 q^{38} + 15 q^{39} - 39 q^{40} + 12 q^{41} + 12 q^{43} + 20 q^{44} - 12 q^{45} - 36 q^{46} - 34 q^{47} - 14 q^{48} + 59 q^{50} + 8 q^{51} - 26 q^{52} + 6 q^{53} + 2 q^{54} + q^{55} + 2 q^{57} - 11 q^{58} - 27 q^{59} + 16 q^{60} - 22 q^{61} + 45 q^{62} + 26 q^{64} + 7 q^{66} - 26 q^{67} - 33 q^{68} - 5 q^{69} + 50 q^{71} - 21 q^{73} - 35 q^{74} - 20 q^{75} + 24 q^{76} - 10 q^{79} - 22 q^{80} + 12 q^{81} - 2 q^{82} - 8 q^{83} + 8 q^{85} - 17 q^{86} - 20 q^{87} - 46 q^{88} - 11 q^{89} - 11 q^{90} + 63 q^{92} + 10 q^{93} - 10 q^{94} + 35 q^{95} - 3 q^{96} - 32 q^{97} + 10 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - 12 * q^3 + 10 * q^4 - 12 * q^5 + 2 * q^6 + 12 * q^9 - 11 * q^10 + 10 * q^11 - 10 * q^12 - 15 * q^13 + 12 * q^15 + 14 * q^16 - 8 * q^17 - 2 * q^18 - 2 * q^19 - 16 * q^20 - 7 * q^22 + 5 * q^23 + 20 * q^25 - 12 * q^27 + 20 * q^29 + 11 * q^30 - 10 * q^31 + 3 * q^32 - 10 * q^33 + 23 * q^34 + 10 * q^36 - 17 * q^37 - 6 * q^38 + 15 * q^39 - 39 * q^40 + 12 * q^41 + 12 * q^43 + 20 * q^44 - 12 * q^45 - 36 * q^46 - 34 * q^47 - 14 * q^48 + 59 * q^50 + 8 * q^51 - 26 * q^52 + 6 * q^53 + 2 * q^54 + q^55 + 2 * q^57 - 11 * q^58 - 27 * q^59 + 16 * q^60 - 22 * q^61 + 45 * q^62 + 26 * q^64 + 7 * q^66 - 26 * q^67 - 33 * q^68 - 5 * q^69 + 50 * q^71 - 21 * q^73 - 35 * q^74 - 20 * q^75 + 24 * q^76 - 10 * q^79 - 22 * q^80 + 12 * q^81 - 2 * q^82 - 8 * q^83 + 8 * q^85 - 17 * q^86 - 20 * q^87 - 46 * q^88 - 11 * q^89 - 11 * q^90 + 63 * q^92 + 10 * q^93 - 10 * q^94 + 35 * q^95 - 3 * q^96 - 32 * q^97 + 10 * q^99

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