LMFDB - Embedded newform 6027.2.a.bn.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("6027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1258372982$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
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)

$f(q)$	$=$	$q-0.844195 q^{2} -1.00000 q^{3} -1.28734 q^{4} +1.91229 q^{5} +0.844195 q^{6} +2.77515 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.844195 q^{2} -1.00000 q^{3} -1.28734 q^{4} +1.91229 q^{5} +0.844195 q^{6} +2.77515 q^{8} +1.00000 q^{9} -1.61434 q^{10} +2.68119 q^{11} +1.28734 q^{12} -1.87964 q^{13} -1.91229 q^{15} +0.231902 q^{16} -6.09325 q^{17} -0.844195 q^{18} -7.23586 q^{19} -2.46175 q^{20} -2.26345 q^{22} -3.42494 q^{23} -2.77515 q^{24} -1.34316 q^{25} +1.58678 q^{26} -1.00000 q^{27} +10.5168 q^{29} +1.61434 q^{30} -7.41515 q^{31} -5.74607 q^{32} -2.68119 q^{33} +5.14389 q^{34} -1.28734 q^{36} +1.51750 q^{37} +6.10847 q^{38} +1.87964 q^{39} +5.30689 q^{40} +1.00000 q^{41} -4.03715 q^{43} -3.45159 q^{44} +1.91229 q^{45} +2.89131 q^{46} +12.2199 q^{47} -0.231902 q^{48} +1.13389 q^{50} +6.09325 q^{51} +2.41973 q^{52} +11.8762 q^{53} +0.844195 q^{54} +5.12720 q^{55} +7.23586 q^{57} -8.87821 q^{58} -1.76036 q^{59} +2.46175 q^{60} +10.2265 q^{61} +6.25983 q^{62} +4.38700 q^{64} -3.59441 q^{65} +2.26345 q^{66} -3.15832 q^{67} +7.84405 q^{68} +3.42494 q^{69} -4.62953 q^{71} +2.77515 q^{72} -4.04568 q^{73} -1.28107 q^{74} +1.34316 q^{75} +9.31497 q^{76} -1.58678 q^{78} +1.99326 q^{79} +0.443463 q^{80} +1.00000 q^{81} -0.844195 q^{82} +7.18385 q^{83} -11.6520 q^{85} +3.40814 q^{86} -10.5168 q^{87} +7.44070 q^{88} -4.71625 q^{89} -1.61434 q^{90} +4.40904 q^{92} +7.41515 q^{93} -10.3159 q^{94} -13.8370 q^{95} +5.74607 q^{96} +4.66151 q^{97} +2.68119 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{2} - 24 q^{3} + 32 q^{4} - 4 q^{5} - 8 q^{6} + 24 q^{8} + 24 q^{9}+O(q^{10}) $ 24 * q + 8 * q^2 - 24 * q^3 + 32 * q^4 - 4 * q^5 - 8 * q^6 + 24 * q^8 + 24 * q^9	$ 24 q + 8 q^{2} - 24 q^{3} + 32 q^{4} - 4 q^{5} - 8 q^{6} + 24 q^{8} + 24 q^{9} + 4 q^{10} + 12 q^{11} - 32 q^{12} + 4 q^{15} + 44 q^{16} - 8 q^{17} + 8 q^{18} + 4 q^{19} - 28 q^{20} + 16 q^{22} + 20 q^{23} - 24 q^{24} + 48 q^{25} - 32 q^{26} - 24 q^{27} + 24 q^{29} - 4 q^{30} + 4 q^{31} + 36 q^{32} - 12 q^{33} - 16 q^{34} + 32 q^{36} + 64 q^{37} - 20 q^{38} + 48 q^{40} + 24 q^{41} + 20 q^{43} + 48 q^{44} - 4 q^{45} + 28 q^{46} - 32 q^{47} - 44 q^{48} - 20 q^{50} + 8 q^{51} + 76 q^{53} - 8 q^{54} + 24 q^{55} - 4 q^{57} + 28 q^{58} - 28 q^{59} + 28 q^{60} + 28 q^{61} + 4 q^{62} + 48 q^{64} + 28 q^{65} - 16 q^{66} + 44 q^{67} + 32 q^{68} - 20 q^{69} + 20 q^{71} + 24 q^{72} + 16 q^{73} + 44 q^{74} - 48 q^{75} + 16 q^{76} + 32 q^{78} + 4 q^{79} - 44 q^{80} + 24 q^{81} + 8 q^{82} - 8 q^{83} + 28 q^{85} + 56 q^{86} - 24 q^{87} + 60 q^{88} - 60 q^{89} + 4 q^{90} + 60 q^{92} - 4 q^{93} - 24 q^{94} + 28 q^{95} - 36 q^{96} + 48 q^{97} + 12 q^{99}+O(q^{100}) $ 24 * q + 8 * q^2 - 24 * q^3 + 32 * q^4 - 4 * q^5 - 8 * q^6 + 24 * q^8 + 24 * q^9 + 4 * q^10 + 12 * q^11 - 32 * q^12 + 4 * q^15 + 44 * q^16 - 8 * q^17 + 8 * q^18 + 4 * q^19 - 28 * q^20 + 16 * q^22 + 20 * q^23 - 24 * q^24 + 48 * q^25 - 32 * q^26 - 24 * q^27 + 24 * q^29 - 4 * q^30 + 4 * q^31 + 36 * q^32 - 12 * q^33 - 16 * q^34 + 32 * q^36 + 64 * q^37 - 20 * q^38 + 48 * q^40 + 24 * q^41 + 20 * q^43 + 48 * q^44 - 4 * q^45 + 28 * q^46 - 32 * q^47 - 44 * q^48 - 20 * q^50 + 8 * q^51 + 76 * q^53 - 8 * q^54 + 24 * q^55 - 4 * q^57 + 28 * q^58 - 28 * q^59 + 28 * q^60 + 28 * q^61 + 4 * q^62 + 48 * q^64 + 28 * q^65 - 16 * q^66 + 44 * q^67 + 32 * q^68 - 20 * q^69 + 20 * q^71 + 24 * q^72 + 16 * q^73 + 44 * q^74 - 48 * q^75 + 16 * q^76 + 32 * q^78 + 4 * q^79 - 44 * q^80 + 24 * q^81 + 8 * q^82 - 8 * q^83 + 28 * q^85 + 56 * q^86 - 24 * q^87 + 60 * q^88 - 60 * q^89 + 4 * q^90 + 60 * q^92 - 4 * q^93 - 24 * q^94 + 28 * q^95 - 36 * q^96 + 48 * q^97 + 12 * 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 $

$2$	−0.844195	−0.596936	−0.298468	−	0.954420i	$-0.596476\pi$
$2$	−0.844195	−0.596936	−0.298468	+	0.954420i	$0.596476\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.28734	−0.643668
$5$	1.91229	0.855201	0.427600	−	0.903968i	$-0.359359\pi$
$5$	1.91229	0.855201	0.427600	+	0.903968i	$0.359359\pi$
$6$	0.844195	0.344641
$7$	0	0
$7$	0	0
$8$	2.77515	0.981164
$9$	1.00000	0.333333
$10$	−1.61434	−0.510500
$11$	2.68119	0.808409	0.404204	−	0.914669i	$-0.367548\pi$
$11$	2.68119	0.808409	0.404204	+	0.914669i	$0.367548\pi$
$12$	1.28734	0.371622
$13$	−1.87964	−0.521319	−0.260659	−	0.965431i	$-0.583940\pi$
$13$	−1.87964	−0.521319	−0.260659	+	0.965431i	$0.583940\pi$
$14$	0	0
$15$	−1.91229	−0.493750
$16$	0.231902	0.0579755
$17$	−6.09325	−1.47783	−0.738915	−	0.673799i	$-0.764661\pi$
$17$	−6.09325	−1.47783	−0.738915	+	0.673799i	$0.764661\pi$
$18$	−0.844195	−0.198979
$19$	−7.23586	−1.66002	−0.830010	−	0.557749i	$-0.811665\pi$
$19$	−7.23586	−1.66002	−0.830010	+	0.557749i	$0.811665\pi$
$20$	−2.46175	−0.550465
$21$	0	0
$22$	−2.26345	−0.482568
$23$	−3.42494	−0.714149	−0.357074	−	0.934076i	$-0.616226\pi$
$23$	−3.42494	−0.714149	−0.357074	+	0.934076i	$0.616226\pi$
$24$	−2.77515	−0.566475
$25$	−1.34316	−0.268631
$26$	1.58678	0.311194
$27$	−1.00000	−0.192450
$28$	0	0
$29$	10.5168	1.95292	0.976458	−	0.215705i	$-0.0692051\pi$
$29$	10.5168	1.95292	0.976458	+	0.215705i	$0.0692051\pi$
$30$	1.61434	0.294737
$31$	−7.41515	−1.33180	−0.665900	−	0.746041i	$-0.731952\pi$
$31$	−7.41515	−1.33180	−0.665900	+	0.746041i	$0.731952\pi$
$32$	−5.74607	−1.01577
$33$	−2.68119	−0.466735
$34$	5.14389	0.882170
$35$	0	0
$36$	−1.28734	−0.214556
$37$	1.51750	0.249476	0.124738	−	0.992190i	$-0.460191\pi$
$37$	1.51750	0.249476	0.124738	+	0.992190i	$0.460191\pi$
$38$	6.10847	0.990925
$39$	1.87964	0.300984
$40$	5.30689	0.839092
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−4.03715	−0.615660	−0.307830	−	0.951441i	$-0.599603\pi$
$43$	−4.03715	−0.615660	−0.307830	+	0.951441i	$0.599603\pi$
$44$	−3.45159	−0.520346
$45$	1.91229	0.285067
$46$	2.89131	0.426301
$47$	12.2199	1.78245	0.891225	−	0.453561i	$-0.149846\pi$
$47$	12.2199	1.78245	0.891225	+	0.453561i	$0.149846\pi$
$48$	−0.231902	−0.0334721
$49$	0	0
$50$	1.13389	0.160356
$51$	6.09325	0.853226
$52$	2.41973	0.335556
$53$	11.8762	1.63132	0.815659	−	0.578533i	$-0.196374\pi$
$53$	11.8762	1.63132	0.815659	+	0.578533i	$0.196374\pi$
$54$	0.844195	0.114880
$55$	5.12720	0.691352
$56$	0	0
$57$	7.23586	0.958412
$58$	−8.87821	−1.16577
$59$	−1.76036	−0.229179	−0.114590	−	0.993413i	$-0.536555\pi$
$59$	−1.76036	−0.229179	−0.114590	+	0.993413i	$0.536555\pi$
$60$	2.46175	0.317811
$61$	10.2265	1.30937	0.654686	−	0.755901i	$-0.272801\pi$
$61$	10.2265	1.30937	0.654686	+	0.755901i	$0.272801\pi$
$62$	6.25983	0.794999
$63$	0	0
$64$	4.38700	0.548375
$65$	−3.59441	−0.445832
$66$	2.26345	0.278611
$67$	−3.15832	−0.385850	−0.192925	−	0.981214i	$-0.561797\pi$
$67$	−3.15832	−0.385850	−0.192925	+	0.981214i	$0.561797\pi$
$68$	7.84405	0.951231
$69$	3.42494	0.412314
$70$	0	0
$71$	−4.62953	−0.549424	−0.274712	−	0.961527i	$-0.588583\pi$
$71$	−4.62953	−0.549424	−0.274712	+	0.961527i	$0.588583\pi$
$72$	2.77515	0.327055
$73$	−4.04568	−0.473511	−0.236755	−	0.971569i	$-0.576084\pi$
$73$	−4.04568	−0.473511	−0.236755	+	0.971569i	$0.576084\pi$
$74$	−1.28107	−0.148921
$75$	1.34316	0.155094
$76$	9.31497	1.06850
$77$	0	0
$78$	−1.58678	−0.179668
$79$	1.99326	0.224260	0.112130	−	0.993694i	$-0.464233\pi$
$79$	1.99326	0.224260	0.112130	+	0.993694i	$0.464233\pi$
$80$	0.443463	0.0495807
$81$	1.00000	0.111111
$82$	−0.844195	−0.0932257
$83$	7.18385	0.788529	0.394265	−	0.918997i	$-0.370999\pi$
$83$	7.18385	0.788529	0.394265	+	0.918997i	$0.370999\pi$
$84$	0	0
$85$	−11.6520	−1.26384
$86$	3.40814	0.367509
$87$	−10.5168	−1.12752
$88$	7.44070	0.793182
$89$	−4.71625	−0.499921	−0.249961	−	0.968256i	$-0.580418\pi$
$89$	−4.71625	−0.499921	−0.249961	+	0.968256i	$0.580418\pi$
$90$	−1.61434	−0.170167
$91$	0	0
$92$	4.40904	0.459675
$93$	7.41515	0.768915
$94$	−10.3159	−1.06401
$95$	−13.8370	−1.41965
$96$	5.74607	0.586456
$97$	4.66151	0.473304	0.236652	−	0.971594i	$-0.423950\pi$
$97$	4.66151	0.473304	0.236652	+	0.971594i	$0.423950\pi$
$98$	0	0
$99$	2.68119	0.269470
$100$	1.72909	0.172909
$101$	−4.23382	−0.421281	−0.210641	−	0.977564i	$-0.567555\pi$
$101$	−4.23382	−0.421281	−0.210641	+	0.977564i	$0.567555\pi$
$102$	−5.14389	−0.509321
$103$	−9.73645	−0.959361	−0.479680	−	0.877443i	$-0.659247\pi$
$103$	−9.73645	−0.959361	−0.479680	+	0.877443i	$0.659247\pi$
$104$	−5.21629	−0.511499
$105$	0	0
$106$	−10.0258	−0.973793
$107$	2.13975	0.206858	0.103429	−	0.994637i	$-0.467019\pi$
$107$	2.13975	0.206858	0.103429	+	0.994637i	$0.467019\pi$
$108$	1.28734	0.123874
$109$	−8.76924	−0.839941	−0.419970	−	0.907538i	$-0.637960\pi$
$109$	−8.76924	−0.839941	−0.419970	+	0.907538i	$0.637960\pi$
$110$	−4.32836	−0.412693
$111$	−1.51750	−0.144035
$112$	0	0
$113$	1.79145	0.168526	0.0842628	−	0.996444i	$-0.473146\pi$
$113$	1.79145	0.168526	0.0842628	+	0.996444i	$0.473146\pi$
$114$	−6.10847	−0.572111
$115$	−6.54947	−0.610741
$116$	−13.5386	−1.25703
$117$	−1.87964	−0.173773
$118$	1.48608	0.136805
$119$	0	0
$120$	−5.30689	−0.484450
$121$	−3.81123	−0.346476
$122$	−8.63317	−0.781611
$123$	−1.00000	−0.0901670
$124$	9.54578	0.857237
$125$	−12.1299	−1.08493
$126$	0	0
$127$	13.5946	1.20632	0.603162	−	0.797619i	$-0.293907\pi$
$127$	13.5946	1.20632	0.603162	+	0.797619i	$0.293907\pi$
$128$	7.78866	0.688427
$129$	4.03715	0.355451
$130$	3.03439	0.266133
$131$	18.4781	1.61444	0.807219	−	0.590252i	$-0.200972\pi$
$131$	18.4781	1.61444	0.807219	+	0.590252i	$0.200972\pi$
$132$	3.45159	0.300422
$133$	0	0
$134$	2.66624	0.230328
$135$	−1.91229	−0.164583
$136$	−16.9097	−1.44999
$137$	10.6875	0.913097	0.456548	−	0.889699i	$-0.349085\pi$
$137$	10.6875	0.913097	0.456548	+	0.889699i	$0.349085\pi$
$138$	−2.89131	−0.246125
$139$	3.38677	0.287262	0.143631	−	0.989631i	$-0.454122\pi$
$139$	3.38677	0.287262	0.143631	+	0.989631i	$0.454122\pi$
$140$	0	0
$141$	−12.2199	−1.02910
$142$	3.90823	0.327971
$143$	−5.03967	−0.421439
$144$	0.231902	0.0193252
$145$	20.1111	1.67014
$146$	3.41534	0.282655
$147$	0	0
$148$	−1.95353	−0.160579
$149$	7.62042	0.624289	0.312145	−	0.950035i	$-0.398953\pi$
$149$	7.62042	0.624289	0.312145	+	0.950035i	$0.398953\pi$
$150$	−1.13389	−0.0925814
$151$	7.06209	0.574705	0.287352	−	0.957825i	$-0.407225\pi$
$151$	7.06209	0.574705	0.287352	+	0.957825i	$0.407225\pi$
$152$	−20.0806	−1.62875
$153$	−6.09325	−0.492610
$154$	0	0
$155$	−14.1799	−1.13896
$156$	−2.41973	−0.193733
$157$	−10.5957	−0.845625	−0.422813	−	0.906217i	$-0.638957\pi$
$157$	−10.5957	−0.845625	−0.422813	+	0.906217i	$0.638957\pi$
$158$	−1.68270	−0.133869
$159$	−11.8762	−0.941842
$160$	−10.9881	−0.868689
$161$	0	0
$162$	−0.844195	−0.0663262
$163$	−21.4964	−1.68373	−0.841865	−	0.539688i	$-0.818542\pi$
$163$	−21.4964	−1.68373	−0.841865	+	0.539688i	$0.818542\pi$
$164$	−1.28734	−0.100524
$165$	−5.12720	−0.399152
$166$	−6.06456	−0.470702
$167$	−5.80772	−0.449415	−0.224707	−	0.974426i	$-0.572143\pi$
$167$	−5.80772	−0.449415	−0.224707	+	0.974426i	$0.572143\pi$
$168$	0	0
$169$	−9.46695	−0.728227
$170$	9.83659	0.754432
$171$	−7.23586	−0.553340
$172$	5.19717	0.396280
$173$	21.1101	1.60497	0.802487	−	0.596670i	$-0.203510\pi$
$173$	21.1101	1.60497	0.802487	+	0.596670i	$0.203510\pi$
$174$	8.87821	0.673055
$175$	0	0
$176$	0.621772	0.0468679
$177$	1.76036	0.132317
$178$	3.98143	0.298421
$179$	−4.84198	−0.361907	−0.180953	−	0.983492i	$-0.557918\pi$
$179$	−4.84198	−0.361907	−0.180953	+	0.983492i	$0.557918\pi$
$180$	−2.46175	−0.183488
$181$	−24.0285	−1.78602	−0.893012	−	0.450032i	$-0.851413\pi$
$181$	−24.0285	−1.78602	−0.893012	+	0.450032i	$0.851413\pi$
$182$	0	0
$183$	−10.2265	−0.755966
$184$	−9.50472	−0.700697
$185$	2.90190	0.213352
$186$	−6.25983	−0.458993
$187$	−16.3371	−1.19469
$188$	−15.7311	−1.14731
$189$	0	0
$190$	11.6812	0.847440
$191$	17.0408	1.23303	0.616516	−	0.787343i	$-0.288544\pi$
$191$	17.0408	1.23303	0.616516	+	0.787343i	$0.288544\pi$
$192$	−4.38700	−0.316605
$193$	26.2654	1.89062	0.945311	−	0.326171i	$-0.105759\pi$
$193$	26.2654	1.89062	0.945311	+	0.326171i	$0.105759\pi$
$194$	−3.93522	−0.282532
$195$	3.59441	0.257401
$196$	0	0
$197$	23.0071	1.63919	0.819595	−	0.572943i	$-0.194198\pi$
$197$	23.0071	1.63919	0.819595	+	0.572943i	$0.194198\pi$
$198$	−2.26345	−0.160856
$199$	24.8226	1.75963	0.879814	−	0.475317i	$-0.157667\pi$
$199$	24.8226	1.75963	0.879814	+	0.475317i	$0.157667\pi$
$200$	−3.72746	−0.263572
$201$	3.15832	0.222771
$202$	3.57417	0.251478
$203$	0	0
$204$	−7.84405	−0.549194
$205$	1.91229	0.133560
$206$	8.21946	0.572677
$207$	−3.42494	−0.238050
$208$	−0.435892	−0.0302237
$209$	−19.4007	−1.34197
$210$	0	0
$211$	−10.6322	−0.731949	−0.365974	−	0.930625i	$-0.619264\pi$
$211$	−10.6322	−0.731949	−0.365974	+	0.930625i	$0.619264\pi$
$212$	−15.2886	−1.05003
$213$	4.62953	0.317210
$214$	−1.80637	−0.123481
$215$	−7.72019	−0.526513
$216$	−2.77515	−0.188825
$217$	0	0
$218$	7.40295	0.501391
$219$	4.04568	0.273381
$220$	−6.60043	−0.445001
$221$	11.4531	0.770420
$222$	1.28107	0.0859796
$223$	15.6888	1.05060	0.525300	−	0.850917i	$-0.323953\pi$
$223$	15.6888	1.05060	0.525300	+	0.850917i	$0.323953\pi$
$224$	0	0
$225$	−1.34316	−0.0895438
$226$	−1.51233	−0.100599
$227$	−14.8416	−0.985073	−0.492536	−	0.870292i	$-0.663930\pi$
$227$	−14.8416	−0.985073	−0.492536	+	0.870292i	$0.663930\pi$
$228$	−9.31497	−0.616899
$229$	7.51697	0.496735	0.248368	−	0.968666i	$-0.420106\pi$
$229$	7.51697	0.496735	0.248368	+	0.968666i	$0.420106\pi$
$230$	5.52902	0.364573
$231$	0	0
$232$	29.1857	1.91613
$233$	17.2580	1.13061	0.565305	−	0.824882i	$-0.308758\pi$
$233$	17.2580	1.13061	0.565305	+	0.824882i	$0.308758\pi$
$234$	1.58678	0.103731
$235$	23.3679	1.52435
$236$	2.26617	0.147515
$237$	−1.99326	−0.129476
$238$	0	0
$239$	−26.4633	−1.71177	−0.855885	−	0.517166i	$-0.826987\pi$
$239$	−26.4633	−1.71177	−0.855885	+	0.517166i	$0.826987\pi$
$240$	−0.443463	−0.0286254
$241$	27.6180	1.77903	0.889515	−	0.456906i	$-0.151043\pi$
$241$	27.6180	1.77903	0.889515	+	0.456906i	$0.151043\pi$
$242$	3.21742	0.206824
$243$	−1.00000	−0.0641500
$244$	−13.1650	−0.842800
$245$	0	0
$246$	0.844195	0.0538239
$247$	13.6008	0.865399
$248$	−20.5782	−1.30671
$249$	−7.18385	−0.455258
$250$	10.2400	0.647636
$251$	19.4790	1.22951	0.614753	−	0.788719i	$-0.289256\pi$
$251$	19.4790	1.22951	0.614753	+	0.788719i	$0.289256\pi$
$252$	0	0
$253$	−9.18290	−0.577324
$254$	−11.4765	−0.720098
$255$	11.6520	0.729679
$256$	−15.3492	−0.959322
$257$	18.4487	1.15080	0.575400	−	0.817872i	$-0.304846\pi$
$257$	18.4487	1.15080	0.575400	+	0.817872i	$0.304846\pi$
$258$	−3.40814	−0.212182
$259$	0	0
$260$	4.62722	0.286968
$261$	10.5168	0.650972
$262$	−15.5991	−0.963716
$263$	29.0590	1.79185	0.895926	−	0.444203i	$-0.146513\pi$
$263$	29.0590	1.79185	0.895926	+	0.444203i	$0.146513\pi$
$264$	−7.44070	−0.457944
$265$	22.7107	1.39510
$266$	0	0
$267$	4.71625	0.288630
$268$	4.06581	0.248359
$269$	−19.1863	−1.16981	−0.584904	−	0.811103i	$-0.698868\pi$
$269$	−19.1863	−1.16981	−0.584904	+	0.811103i	$0.698868\pi$
$270$	1.61434	0.0982458
$271$	−13.5358	−0.822243	−0.411121	−	0.911581i	$-0.634863\pi$
$271$	−13.5358	−0.822243	−0.411121	+	0.911581i	$0.634863\pi$
$272$	−1.41304	−0.0856779
$273$	0	0
$274$	−9.02235	−0.545060
$275$	−3.60126	−0.217164
$276$	−4.40904	−0.265393
$277$	−15.0702	−0.905478	−0.452739	−	0.891643i	$-0.649553\pi$
$277$	−15.0702	−0.905478	−0.452739	+	0.891643i	$0.649553\pi$
$278$	−2.85910	−0.171477
$279$	−7.41515	−0.443933
$280$	0	0
$281$	10.9228	0.651602	0.325801	−	0.945438i	$-0.394366\pi$
$281$	10.9228	0.651602	0.325801	+	0.945438i	$0.394366\pi$
$282$	10.3159	0.614306
$283$	−5.60619	−0.333253	−0.166627	−	0.986020i	$-0.553287\pi$
$283$	−5.60619	−0.333253	−0.166627	+	0.986020i	$0.553287\pi$
$284$	5.95976	0.353646
$285$	13.8370	0.819635
$286$	4.25447	0.251572
$287$	0	0
$288$	−5.74607	−0.338591
$289$	20.1277	1.18398
$290$	−16.9777	−0.996964
$291$	−4.66151	−0.273262
$292$	5.20814	0.304783
$293$	−3.69810	−0.216045	−0.108023	−	0.994148i	$-0.534452\pi$
$293$	−3.69810	−0.216045	−0.108023	+	0.994148i	$0.534452\pi$
$294$	0	0
$295$	−3.36631	−0.195994
$296$	4.21130	0.244777
$297$	−2.68119	−0.155578
$298$	−6.43312	−0.372661
$299$	6.43766	0.372299
$300$	−1.72909	−0.0998293
$301$	0	0
$302$	−5.96178	−0.343062
$303$	4.23382	0.243227
$304$	−1.67801	−0.0962404
$305$	19.5560	1.11978
$306$	5.14389	0.294057
$307$	−2.67275	−0.152542	−0.0762709	−	0.997087i	$-0.524301\pi$
$307$	−2.67275	−0.152542	−0.0762709	+	0.997087i	$0.524301\pi$
$308$	0	0
$309$	9.73645	0.553887
$310$	11.9706	0.679884
$311$	−14.9516	−0.847827	−0.423914	−	0.905703i	$-0.639344\pi$
$311$	−14.9516	−0.847827	−0.423914	+	0.905703i	$0.639344\pi$
$312$	5.21629	0.295314
$313$	17.4503	0.986349	0.493174	−	0.869930i	$-0.335836\pi$
$313$	17.4503	0.986349	0.493174	+	0.869930i	$0.335836\pi$
$314$	8.94480	0.504784
$315$	0	0
$316$	−2.56600	−0.144349
$317$	29.2867	1.64491	0.822454	−	0.568832i	$-0.192605\pi$
$317$	29.2867	1.64491	0.822454	+	0.568832i	$0.192605\pi$
$318$	10.0258	0.562219
$319$	28.1975	1.57875
$320$	8.38921	0.468971
$321$	−2.13975	−0.119429
$322$	0	0
$323$	44.0899	2.45323
$324$	−1.28734	−0.0715186
$325$	2.52465	0.140043
$326$	18.1472	1.00508
$327$	8.76924	0.484940
$328$	2.77515	0.153232
$329$	0	0
$330$	4.32836	0.238268
$331$	9.52575	0.523583	0.261791	−	0.965125i	$-0.415687\pi$
$331$	9.52575	0.523583	0.261791	+	0.965125i	$0.415687\pi$
$332$	−9.24802	−0.507551
$333$	1.51750	0.0831586
$334$	4.90285	0.268272
$335$	−6.03961	−0.329979
$336$	0	0
$337$	26.0785	1.42059	0.710294	−	0.703905i	$-0.248562\pi$
$337$	26.0785	1.42059	0.710294	+	0.703905i	$0.248562\pi$
$338$	7.99195	0.434705
$339$	−1.79145	−0.0972983
$340$	15.0001	0.813494
$341$	−19.8814	−1.07664
$342$	6.10847	0.330308
$343$	0	0
$344$	−11.2037	−0.604063
$345$	6.54947	0.352611
$346$	−17.8211	−0.958067
$347$	7.69389	0.413030	0.206515	−	0.978443i	$-0.433788\pi$
$347$	7.69389	0.413030	0.206515	+	0.978443i	$0.433788\pi$
$348$	13.5386	0.725746
$349$	13.3724	0.715806	0.357903	−	0.933759i	$-0.383492\pi$
$349$	13.3724	0.715806	0.357903	+	0.933759i	$0.383492\pi$
$350$	0	0
$351$	1.87964	0.100328
$352$	−15.4063	−0.821159
$353$	−14.2898	−0.760572	−0.380286	−	0.924869i	$-0.624174\pi$
$353$	−14.2898	−0.760572	−0.380286	+	0.924869i	$0.624174\pi$
$354$	−1.48608	−0.0789845
$355$	−8.85299	−0.469868
$356$	6.07139	0.321783
$357$	0	0
$358$	4.08758	0.216035
$359$	−2.49554	−0.131709	−0.0658547	−	0.997829i	$-0.520977\pi$
$359$	−2.49554	−0.131709	−0.0658547	+	0.997829i	$0.520977\pi$
$360$	5.30689	0.279697
$361$	33.3576	1.75566
$362$	20.2847	1.06614
$363$	3.81123	0.200038
$364$	0	0
$365$	−7.73650	−0.404947
$366$	8.63317	0.451263
$367$	36.6391	1.91255	0.956273	−	0.292477i	$-0.0944793\pi$
$367$	36.6391	1.91255	0.956273	+	0.292477i	$0.0944793\pi$
$368$	−0.794249	−0.0414031
$369$	1.00000	0.0520579
$370$	−2.44977	−0.127357
$371$	0	0
$372$	−9.54578	−0.494926
$373$	−6.74704	−0.349349	−0.174674	−	0.984626i	$-0.555887\pi$
$373$	−6.74704	−0.349349	−0.174674	+	0.984626i	$0.555887\pi$
$374$	13.7917	0.713154
$375$	12.1299	0.626387
$376$	33.9120	1.74888
$377$	−19.7678	−1.01809
$378$	0	0
$379$	8.45609	0.434360	0.217180	−	0.976132i	$-0.430314\pi$
$379$	8.45609	0.434360	0.217180	+	0.976132i	$0.430314\pi$
$380$	17.8129	0.913783
$381$	−13.5946	−0.696471
$382$	−14.3858	−0.736041
$383$	−34.7954	−1.77796	−0.888981	−	0.457945i	$-0.848586\pi$
$383$	−34.7954	−1.77796	−0.888981	+	0.457945i	$0.848586\pi$
$384$	−7.78866	−0.397463
$385$	0	0
$386$	−22.1731	−1.12858
$387$	−4.03715	−0.205220
$388$	−6.00092	−0.304651
$389$	−38.2428	−1.93899	−0.969494	−	0.245117i	$-0.921174\pi$
$389$	−38.2428	−1.93899	−0.969494	+	0.245117i	$0.921174\pi$
$390$	−3.03439	−0.153652
$391$	20.8690	1.05539
$392$	0	0
$393$	−18.4781	−0.932096
$394$	−19.4225	−0.978492
$395$	3.81169	0.191787
$396$	−3.45159	−0.173449
$397$	−15.8180	−0.793883	−0.396941	−	0.917844i	$-0.629928\pi$
$397$	−15.8180	−0.793883	−0.396941	+	0.917844i	$0.629928\pi$
$398$	−20.9551	−1.05039
$399$	0	0
$400$	−0.311481	−0.0155740
$401$	2.58004	0.128841	0.0644205	−	0.997923i	$-0.479480\pi$
$401$	2.58004	0.128841	0.0644205	+	0.997923i	$0.479480\pi$
$402$	−2.66624	−0.132980
$403$	13.9378	0.694293
$404$	5.45035	0.271165
$405$	1.91229	0.0950223
$406$	0	0
$407$	4.06871	0.201678
$408$	16.9097	0.837154
$409$	−11.4726	−0.567283	−0.283641	−	0.958930i	$-0.591543\pi$
$409$	−11.4726	−0.567283	−0.283641	+	0.958930i	$0.591543\pi$
$410$	−1.61434	−0.0797267
$411$	−10.6875	−0.527177
$412$	12.5341	0.617510
$413$	0	0
$414$	2.89131	0.142100
$415$	13.7376	0.674351
$416$	10.8006	0.529541
$417$	−3.38677	−0.165851
$418$	16.3780	0.801072
$419$	−13.6522	−0.666953	−0.333476	−	0.942758i	$-0.608222\pi$
$419$	−13.6522	−0.666953	−0.333476	+	0.942758i	$0.608222\pi$
$420$	0	0
$421$	−22.5347	−1.09828	−0.549138	−	0.835732i	$-0.685044\pi$
$421$	−22.5347	−1.09828	−0.549138	+	0.835732i	$0.685044\pi$
$422$	8.97562	0.436926
$423$	12.2199	0.594150
$424$	32.9582	1.60059
$425$	8.18419	0.396992
$426$	−3.90823	−0.189354
$427$	0	0
$428$	−2.75458	−0.133148
$429$	5.03967	0.243318
$430$	6.51735	0.314294
$431$	−6.38263	−0.307441	−0.153720	−	0.988114i	$-0.549125\pi$
$431$	−6.38263	−0.307441	−0.153720	+	0.988114i	$0.549125\pi$
$432$	−0.231902	−0.0111574
$433$	35.0047	1.68222	0.841109	−	0.540866i	$-0.181903\pi$
$433$	35.0047	1.68222	0.841109	+	0.540866i	$0.181903\pi$
$434$	0	0
$435$	−20.1111	−0.964254
$436$	11.2890	0.540643
$437$	24.7824	1.18550
$438$	−3.41534	−0.163191
$439$	−8.35908	−0.398957	−0.199479	−	0.979902i	$-0.563925\pi$
$439$	−8.35908	−0.398957	−0.199479	+	0.979902i	$0.563925\pi$
$440$	14.2288	0.678330
$441$	0	0
$442$	−9.66867	−0.459892
$443$	−26.8933	−1.27774	−0.638869	−	0.769316i	$-0.720597\pi$
$443$	−26.8933	−1.27774	−0.638869	+	0.769316i	$0.720597\pi$
$444$	1.95353	0.0927106
$445$	−9.01882	−0.427533
$446$	−13.2444	−0.627141
$447$	−7.62042	−0.360433
$448$	0	0
$449$	−0.624983	−0.0294948	−0.0147474	−	0.999891i	$-0.504694\pi$
$449$	−0.624983	−0.0294948	−0.0147474	+	0.999891i	$0.504694\pi$
$450$	1.13389	0.0534519
$451$	2.68119	0.126252
$452$	−2.30620	−0.108474
$453$	−7.06209	−0.331806
$454$	12.5292	0.588025
$455$	0	0
$456$	20.0806	0.940360
$457$	−12.4788	−0.583736	−0.291868	−	0.956459i	$-0.594277\pi$
$457$	−12.4788	−0.583736	−0.291868	+	0.956459i	$0.594277\pi$
$458$	−6.34578	−0.296519
$459$	6.09325	0.284409
$460$	8.43136	0.393114
$461$	0.841829	0.0392079	0.0196039	−	0.999808i	$-0.493759\pi$
$461$	0.841829	0.0392079	0.0196039	+	0.999808i	$0.493759\pi$
$462$	0	0
$463$	28.2428	1.31255	0.656277	−	0.754520i	$-0.272130\pi$
$463$	28.2428	1.31255	0.656277	+	0.754520i	$0.272130\pi$
$464$	2.43886	0.113221
$465$	14.1799	0.657577
$466$	−14.5691	−0.674902
$467$	1.71415	0.0793213	0.0396606	−	0.999213i	$-0.487372\pi$
$467$	1.71415	0.0793213	0.0396606	+	0.999213i	$0.487372\pi$
$468$	2.41973	0.111852
$469$	0	0
$470$	−19.7271	−0.909941
$471$	10.5957	0.488222
$472$	−4.88526	−0.224862
$473$	−10.8244	−0.497705
$474$	1.68270	0.0772891
$475$	9.71889	0.445933
$476$	0	0
$477$	11.8762	0.543773
$478$	22.3402	1.02182
$479$	−21.3898	−0.977326	−0.488663	−	0.872473i	$-0.662515\pi$
$479$	−21.3898	−0.977326	−0.488663	+	0.872473i	$0.662515\pi$
$480$	10.9881	0.501538
$481$	−2.85236	−0.130056
$482$	−23.3149	−1.06197
$483$	0	0
$484$	4.90633	0.223015
$485$	8.91414	0.404770
$486$	0.844195	0.0382935
$487$	9.09761	0.412252	0.206126	−	0.978525i	$-0.433914\pi$
$487$	9.09761	0.412252	0.206126	+	0.978525i	$0.433914\pi$
$488$	28.3801	1.28471
$489$	21.4964	0.972102
$490$	0	0
$491$	14.2219	0.641826	0.320913	−	0.947109i	$-0.396010\pi$
$491$	14.2219	0.641826	0.320913	+	0.947109i	$0.396010\pi$
$492$	1.28734	0.0580375
$493$	−64.0814	−2.88608
$494$	−11.4817	−0.516588
$495$	5.12720	0.230451
$496$	−1.71959	−0.0772117
$497$	0	0
$498$	6.06456	0.271760
$499$	−13.5848	−0.608138	−0.304069	−	0.952650i	$-0.598345\pi$
$499$	−13.5848	−0.608138	−0.304069	+	0.952650i	$0.598345\pi$
$500$	15.6153	0.698337
$501$	5.80772	0.259470
$502$	−16.4441	−0.733937
$503$	−16.7950	−0.748853	−0.374427	−	0.927257i	$-0.622160\pi$
$503$	−16.7950	−0.748853	−0.374427	+	0.927257i	$0.622160\pi$
$504$	0	0
$505$	−8.09629	−0.360280
$506$	7.75216	0.344626
$507$	9.46695	0.420442
$508$	−17.5008	−0.776471
$509$	−10.7163	−0.474991	−0.237496	−	0.971389i	$-0.576327\pi$
$509$	−10.7163	−0.474991	−0.237496	+	0.971389i	$0.576327\pi$
$510$	−9.83659	−0.435572
$511$	0	0
$512$	−2.61965	−0.115773
$513$	7.23586	0.319471
$514$	−15.5743	−0.686954
$515$	−18.6189	−0.820446
$516$	−5.19717	−0.228793
$517$	32.7638	1.44095
$518$	0	0
$519$	−21.1101	−0.926632
$520$	−9.97504	−0.437435
$521$	29.4211	1.28896	0.644482	−	0.764620i	$-0.277073\pi$
$521$	29.4211	1.28896	0.644482	+	0.764620i	$0.277073\pi$
$522$	−8.87821	−0.388589
$523$	19.6952	0.861213	0.430606	−	0.902540i	$-0.358300\pi$
$523$	19.6952	0.861213	0.430606	+	0.902540i	$0.358300\pi$
$524$	−23.7875	−1.03916
$525$	0	0
$526$	−24.5314	−1.06962
$527$	45.1824	1.96817
$528$	−0.621772	−0.0270592
$529$	−11.2698	−0.489991
$530$	−19.1722	−0.832788
$531$	−1.76036	−0.0763930
$532$	0	0
$533$	−1.87964	−0.0814163
$534$	−3.98143	−0.172293
$535$	4.09183	0.176905
$536$	−8.76481	−0.378582
$537$	4.84198	0.208947
$538$	16.1969	0.698300
$539$	0	0
$540$	2.46175	0.105937
$541$	14.2318	0.611874	0.305937	−	0.952052i	$-0.401030\pi$
$541$	14.2318	0.611874	0.305937	+	0.952052i	$0.401030\pi$
$542$	11.4269	0.490826
$543$	24.0285	1.03116
$544$	35.0123	1.50114
$545$	−16.7693	−0.718318
$546$	0	0
$547$	20.5026	0.876629	0.438314	−	0.898822i	$-0.355576\pi$
$547$	20.5026	0.876629	0.438314	+	0.898822i	$0.355576\pi$
$548$	−13.7584	−0.587731
$549$	10.2265	0.436457
$550$	3.04016	0.129633
$551$	−76.0979	−3.24188
$552$	9.50472	0.404548
$553$	0	0
$554$	12.7222	0.540512
$555$	−2.90190	−0.123179
$556$	−4.35991	−0.184902
$557$	−10.6502	−0.451265	−0.225632	−	0.974213i	$-0.572445\pi$
$557$	−10.6502	−0.451265	−0.225632	+	0.974213i	$0.572445\pi$
$558$	6.25983	0.265000
$559$	7.58840	0.320955
$560$	0	0
$561$	16.3371	0.689755
$562$	−9.22101	−0.388965
$563$	−6.50690	−0.274233	−0.137117	−	0.990555i	$-0.543783\pi$
$563$	−6.50690	−0.274233	−0.137117	+	0.990555i	$0.543783\pi$
$564$	15.7311	0.662397
$565$	3.42577	0.144123
$566$	4.73271	0.198931
$567$	0	0
$568$	−12.8476	−0.539075
$569$	25.3805	1.06401	0.532003	−	0.846742i	$-0.321439\pi$
$569$	25.3805	1.06401	0.532003	+	0.846742i	$0.321439\pi$
$570$	−11.6812	−0.489270
$571$	−0.483855	−0.0202487	−0.0101243	−	0.999949i	$-0.503223\pi$
$571$	−0.483855	−0.0202487	−0.0101243	+	0.999949i	$0.503223\pi$
$572$	6.48775	0.271266
$573$	−17.0408	−0.711891
$574$	0	0
$575$	4.60023	0.191843
$576$	4.38700	0.182792
$577$	33.2621	1.38472	0.692360	−	0.721552i	$-0.256571\pi$
$577$	33.2621	1.38472	0.692360	+	0.721552i	$0.256571\pi$
$578$	−16.9917	−0.706761
$579$	−26.2654	−1.09155
$580$	−25.8897	−1.07501
$581$	0	0
$582$	3.93522	0.163120
$583$	31.8423	1.31877
$584$	−11.2274	−0.464592
$585$	−3.59441	−0.148611
$586$	3.12192	0.128965
$587$	32.2902	1.33276	0.666379	−	0.745613i	$-0.267843\pi$
$587$	32.2902	1.33276	0.666379	+	0.745613i	$0.267843\pi$
$588$	0	0
$589$	53.6550	2.21081
$590$	2.84182	0.116996
$591$	−23.0071	−0.946387
$592$	0.351911	0.0144635
$593$	−7.39899	−0.303840	−0.151920	−	0.988393i	$-0.548546\pi$
$593$	−7.39899	−0.303840	−0.151920	+	0.988393i	$0.548546\pi$
$594$	2.26345	0.0928703
$595$	0	0
$596$	−9.81003	−0.401835
$597$	−24.8226	−1.01592
$598$	−5.43464	−0.222239
$599$	−42.5119	−1.73699	−0.868495	−	0.495698i	$-0.834912\pi$
$599$	−42.5119	−1.73699	−0.868495	+	0.495698i	$0.834912\pi$
$600$	3.72746	0.152173
$601$	24.7770	1.01067	0.505337	−	0.862922i	$-0.331368\pi$
$601$	24.7770	1.01067	0.505337	+	0.862922i	$0.331368\pi$
$602$	0	0
$603$	−3.15832	−0.128617
$604$	−9.09128	−0.369919
$605$	−7.28817	−0.296306
$606$	−3.57417	−0.145191
$607$	−14.7307	−0.597902	−0.298951	−	0.954268i	$-0.596637\pi$
$607$	−14.7307	−0.597902	−0.298951	+	0.954268i	$0.596637\pi$
$608$	41.5778	1.68620
$609$	0	0
$610$	−16.5091	−0.668434
$611$	−22.9690	−0.929225
$612$	7.84405	0.317077
$613$	25.1379	1.01531	0.507655	−	0.861560i	$-0.330512\pi$
$613$	25.1379	1.01531	0.507655	+	0.861560i	$0.330512\pi$
$614$	2.25632	0.0910576
$615$	−1.91229	−0.0771109
$616$	0	0
$617$	20.2465	0.815094	0.407547	−	0.913184i	$-0.366384\pi$
$617$	20.2465	0.815094	0.407547	+	0.913184i	$0.366384\pi$
$618$	−8.21946	−0.330635
$619$	21.8666	0.878892	0.439446	−	0.898269i	$-0.355175\pi$
$619$	21.8666	0.878892	0.439446	+	0.898269i	$0.355175\pi$
$620$	18.2543	0.733110
$621$	3.42494	0.137438
$622$	12.6221	0.506099
$623$	0	0
$624$	0.435892	0.0174497
$625$	−16.4801	−0.659206
$626$	−14.7314	−0.588787
$627$	19.4007	0.774789
$628$	13.6402	0.544302
$629$	−9.24652	−0.368683
$630$	0	0
$631$	25.8901	1.03067	0.515334	−	0.856989i	$-0.327668\pi$
$631$	25.8901	1.03067	0.515334	+	0.856989i	$0.327668\pi$
$632$	5.53161	0.220035
$633$	10.6322	0.422591
$634$	−24.7237	−0.981904
$635$	25.9967	1.03165
$636$	15.2886	0.606233
$637$	0	0
$638$	−23.8042	−0.942415
$639$	−4.62953	−0.183141
$640$	14.8942	0.588743
$641$	23.2803	0.919516	0.459758	−	0.888044i	$-0.347936\pi$
$641$	23.2803	0.919516	0.459758	+	0.888044i	$0.347936\pi$
$642$	1.80637	0.0712917
$643$	35.9954	1.41952	0.709759	−	0.704444i	$-0.248804\pi$
$643$	35.9954	1.41952	0.709759	+	0.704444i	$0.248804\pi$
$644$	0	0
$645$	7.72019	0.303982
$646$	−37.2204	−1.46442
$647$	−9.20528	−0.361897	−0.180948	−	0.983493i	$-0.557917\pi$
$647$	−9.20528	−0.361897	−0.180948	+	0.983493i	$0.557917\pi$
$648$	2.77515	0.109018
$649$	−4.71985	−0.185270
$650$	−2.13130	−0.0835965
$651$	0	0
$652$	27.6731	1.08376
$653$	−32.8249	−1.28454	−0.642269	−	0.766480i	$-0.722007\pi$
$653$	−32.8249	−1.28454	−0.642269	+	0.766480i	$0.722007\pi$
$654$	−7.40295	−0.289478
$655$	35.3354	1.38067
$656$	0.231902	0.00905424
$657$	−4.04568	−0.157837
$658$	0	0
$659$	21.5406	0.839102	0.419551	−	0.907732i	$-0.362187\pi$
$659$	21.5406	0.839102	0.419551	+	0.907732i	$0.362187\pi$
$660$	6.60043	0.256921
$661$	11.7865	0.458441	0.229220	−	0.973375i	$-0.426382\pi$
$661$	11.7865	0.458441	0.229220	+	0.973375i	$0.426382\pi$
$662$	−8.04159	−0.312545
$663$	−11.4531	−0.444802
$664$	19.9363	0.773677
$665$	0	0
$666$	−1.28107	−0.0496403
$667$	−36.0193	−1.39467
$668$	7.47648	0.289274
$669$	−15.6888	−0.606564
$670$	5.09861	0.196976
$671$	27.4192	1.05851
$672$	0	0
$673$	−34.5436	−1.33156	−0.665778	−	0.746150i	$-0.731900\pi$
$673$	−34.5436	−1.33156	−0.665778	+	0.746150i	$0.731900\pi$
$674$	−22.0154	−0.848000
$675$	1.34316	0.0516981
$676$	12.1871	0.468736
$677$	−27.2133	−1.04589	−0.522945	−	0.852366i	$-0.675167\pi$
$677$	−27.2133	−1.04589	−0.522945	+	0.852366i	$0.675167\pi$
$678$	1.51233	0.0580808
$679$	0	0
$680$	−32.3362	−1.24004
$681$	14.8416	0.568732
$682$	16.7838	0.642684
$683$	6.92911	0.265135	0.132567	−	0.991174i	$-0.457678\pi$
$683$	6.92911	0.265135	0.132567	+	0.991174i	$0.457678\pi$
$684$	9.31497	0.356167
$685$	20.4376	0.780881
$686$	0	0
$687$	−7.51697	−0.286790
$688$	−0.936223	−0.0356932
$689$	−22.3230	−0.850437
$690$	−5.52902	−0.210486
$691$	37.1434	1.41300	0.706500	−	0.707713i	$-0.250273\pi$
$691$	37.1434	1.41300	0.706500	+	0.707713i	$0.250273\pi$
$692$	−27.1758	−1.03307
$693$	0	0
$694$	−6.49514	−0.246552
$695$	6.47649	0.245667
$696$	−29.1857	−1.10628
$697$	−6.09325	−0.230798
$698$	−11.2889	−0.427290
$699$	−17.2580	−0.652759
$700$	0	0
$701$	29.7764	1.12464	0.562319	−	0.826921i	$-0.309909\pi$
$701$	29.7764	1.12464	0.562319	+	0.826921i	$0.309909\pi$
$702$	−1.58678	−0.0598893
$703$	−10.9804	−0.414134
$704$	11.7624	0.443311
$705$	−23.3679	−0.880086
$706$	12.0634	0.454013
$707$	0	0
$708$	−2.26617	−0.0851679
$709$	−27.4792	−1.03200	−0.516002	−	0.856587i	$-0.672580\pi$
$709$	−27.4792	−1.03200	−0.516002	+	0.856587i	$0.672580\pi$
$710$	7.47365	0.280481
$711$	1.99326	0.0747532
$712$	−13.0883	−0.490505
$713$	25.3964	0.951104
$714$	0	0
$715$	−9.63730	−0.360415
$716$	6.23325	0.232948
$717$	26.4633	0.988291
$718$	2.10672	0.0786221
$719$	4.88656	0.182238	0.0911189	−	0.995840i	$-0.470956\pi$
$719$	4.88656	0.182238	0.0911189	+	0.995840i	$0.470956\pi$
$720$	0.443463	0.0165269
$721$	0	0
$722$	−28.1603	−1.04802
$723$	−27.6180	−1.02712
$724$	30.9327	1.14961
$725$	−14.1257	−0.524615
$726$	−3.21742	−0.119410
$727$	−35.7363	−1.32539	−0.662694	−	0.748890i	$-0.730587\pi$
$727$	−35.7363	−1.32539	−0.662694	+	0.748890i	$0.730587\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	6.53111	0.241727
$731$	24.5994	0.909841
$732$	13.1650	0.486591
$733$	19.1607	0.707715	0.353858	−	0.935299i	$-0.384870\pi$
$733$	19.1607	0.707715	0.353858	+	0.935299i	$0.384870\pi$
$734$	−30.9305	−1.14167
$735$	0	0
$736$	19.6799	0.725412
$737$	−8.46805	−0.311924
$738$	−0.844195	−0.0310752
$739$	42.7261	1.57170	0.785852	−	0.618414i	$-0.212225\pi$
$739$	42.7261	1.57170	0.785852	+	0.618414i	$0.212225\pi$
$740$	−3.73572	−0.137328
$741$	−13.6008	−0.499638
$742$	0	0
$743$	13.5962	0.498795	0.249397	−	0.968401i	$-0.419767\pi$
$743$	13.5962	0.498795	0.249397	+	0.968401i	$0.419767\pi$
$744$	20.5782	0.754432
$745$	14.5724	0.533893
$746$	5.69582	0.208539
$747$	7.18385	0.262843
$748$	21.0314	0.768983
$749$	0	0
$750$	−10.2400	−0.373913
$751$	−44.5097	−1.62418	−0.812091	−	0.583531i	$-0.801671\pi$
$751$	−44.5097	−1.62418	−0.812091	+	0.583531i	$0.801671\pi$
$752$	2.83381	0.103338
$753$	−19.4790	−0.709856
$754$	16.6879	0.607736
$755$	13.5047	0.491488
$756$	0	0
$757$	25.8209	0.938478	0.469239	−	0.883071i	$-0.344528\pi$
$757$	25.8209	0.938478	0.469239	+	0.883071i	$0.344528\pi$
$758$	−7.13859	−0.259285
$759$	9.18290	0.333318
$760$	−38.3999	−1.39291
$761$	11.2451	0.407635	0.203818	−	0.979009i	$-0.434665\pi$
$761$	11.2451	0.407635	0.203818	+	0.979009i	$0.434665\pi$
$762$	11.4765	0.415749
$763$	0	0
$764$	−21.9373	−0.793662
$765$	−11.6520	−0.421280
$766$	29.3741	1.06133
$767$	3.30884	0.119475
$768$	15.3492	0.553865
$769$	−30.9246	−1.11517	−0.557585	−	0.830120i	$-0.688272\pi$
$769$	−30.9246	−1.11517	−0.557585	+	0.830120i	$0.688272\pi$
$770$	0	0
$771$	−18.4487	−0.664415
$772$	−33.8123	−1.21693
$773$	28.6555	1.03067	0.515333	−	0.856990i	$-0.327668\pi$
$773$	28.6555	1.03067	0.515333	+	0.856990i	$0.327668\pi$
$774$	3.40814	0.122503
$775$	9.95971	0.357763
$776$	12.9364	0.464389
$777$	0	0
$778$	32.2844	1.15745
$779$	−7.23586	−0.259251
$780$	−4.62722	−0.165681
$781$	−12.4126	−0.444159
$782$	−17.6175	−0.630001
$783$	−10.5168	−0.375839
$784$	0	0
$785$	−20.2619	−0.723179
$786$	15.5991	0.556402
$787$	39.6962	1.41502	0.707508	−	0.706705i	$-0.249819\pi$
$787$	39.6962	1.41502	0.707508	+	0.706705i	$0.249819\pi$
$788$	−29.6179	−1.05509
$789$	−29.0590	−1.03453
$790$	−3.21781	−0.114485
$791$	0	0
$792$	7.44070	0.264394
$793$	−19.2222	−0.682600
$794$	13.3535	0.473897
$795$	−22.7107	−0.805464
$796$	−31.9550	−1.13262
$797$	−24.4338	−0.865488	−0.432744	−	0.901517i	$-0.642455\pi$
$797$	−24.4338	−0.865488	−0.432744	+	0.901517i	$0.642455\pi$
$798$	0	0
$799$	−74.4587	−2.63416
$800$	7.71788	0.272868
$801$	−4.71625	−0.166640
$802$	−2.17805	−0.0769098
$803$	−10.8472	−0.382790
$804$	−4.06581	−0.143390
$805$	0	0
$806$	−11.7662	−0.414448
$807$	19.1863	0.675389
$808$	−11.7495	−0.413346
$809$	44.1172	1.55108	0.775539	−	0.631300i	$-0.217478\pi$
$809$	44.1172	1.55108	0.775539	+	0.631300i	$0.217478\pi$
$810$	−1.61434	−0.0567222
$811$	−1.98405	−0.0696693	−0.0348347	−	0.999393i	$-0.511090\pi$
$811$	−1.98405	−0.0696693	−0.0348347	+	0.999393i	$0.511090\pi$
$812$	0	0
$813$	13.5358	0.474722
$814$	−3.43478	−0.120389
$815$	−41.1073	−1.43993
$816$	1.41304	0.0494661
$817$	29.2122	1.02201
$818$	9.68510	0.338631
$819$	0	0
$820$	−2.46175	−0.0859682
$821$	20.8561	0.727883	0.363942	−	0.931422i	$-0.381431\pi$
$821$	20.8561	0.727883	0.363942	+	0.931422i	$0.381431\pi$
$822$	9.02235	0.314691
$823$	−1.26248	−0.0440073	−0.0220036	−	0.999758i	$-0.507005\pi$
$823$	−1.26248	−0.0440073	−0.0220036	+	0.999758i	$0.507005\pi$
$824$	−27.0201	−0.941291
$825$	3.60126	0.125380
$826$	0	0
$827$	−19.6810	−0.684376	−0.342188	−	0.939631i	$-0.611168\pi$
$827$	−19.6810	−0.684376	−0.342188	+	0.939631i	$0.611168\pi$
$828$	4.40904	0.153225
$829$	44.4105	1.54244	0.771220	−	0.636569i	$-0.219647\pi$
$829$	44.4105	1.54244	0.771220	+	0.636569i	$0.219647\pi$
$830$	−11.5972	−0.402544
$831$	15.0702	0.522778
$832$	−8.24599	−0.285878
$833$	0	0
$834$	2.85910	0.0990025
$835$	−11.1060	−0.384340
$836$	24.9752	0.863785
$837$	7.41515	0.256305
$838$	11.5251	0.398128
$839$	28.4176	0.981084	0.490542	−	0.871417i	$-0.336799\pi$
$839$	28.4176	0.981084	0.490542	+	0.871417i	$0.336799\pi$
$840$	0	0
$841$	81.6027	2.81388
$842$	19.0237	0.655600
$843$	−10.9228	−0.376203
$844$	13.6872	0.471132
$845$	−18.1035	−0.622780
$846$	−10.3159	−0.354670
$847$	0	0
$848$	2.75411	0.0945764
$849$	5.60619	0.192404
$850$	−6.90905	−0.236979
$851$	−5.19735	−0.178163
$852$	−5.95976	−0.204178
$853$	−46.6971	−1.59888	−0.799439	−	0.600747i	$-0.794870\pi$
$853$	−46.6971	−1.59888	−0.799439	+	0.600747i	$0.794870\pi$
$854$	0	0
$855$	−13.8370	−0.473217
$856$	5.93814	0.202962
$857$	−25.5591	−0.873081	−0.436541	−	0.899685i	$-0.643796\pi$
$857$	−25.5591	−0.873081	−0.436541	+	0.899685i	$0.643796\pi$
$858$	−4.25447	−0.145245
$859$	−36.7538	−1.25402	−0.627012	−	0.779009i	$-0.715722\pi$
$859$	−36.7538	−1.25402	−0.627012	+	0.779009i	$0.715722\pi$
$860$	9.93848	0.338899
$861$	0	0
$862$	5.38819	0.183522
$863$	39.4980	1.34453	0.672263	−	0.740312i	$-0.265322\pi$
$863$	39.4980	1.34453	0.672263	+	0.740312i	$0.265322\pi$
$864$	5.74607	0.195485
$865$	40.3686	1.37258
$866$	−29.5508	−1.00418
$867$	−20.1277	−0.683572
$868$	0	0
$869$	5.34431	0.181293
$870$	16.9777	0.575598
$871$	5.93651	0.201151
$872$	−24.3360	−0.824120
$873$	4.66151	0.157768
$874$	−20.9211	−0.707668
$875$	0	0
$876$	−5.20814	−0.175967
$877$	23.7836	0.803114	0.401557	−	0.915834i	$-0.368469\pi$
$877$	23.7836	0.803114	0.401557	+	0.915834i	$0.368469\pi$
$878$	7.05669	0.238152
$879$	3.69810	0.124734
$880$	1.18901	0.0400814
$881$	24.4349	0.823233	0.411616	−	0.911357i	$-0.364964\pi$
$881$	24.4349	0.823233	0.411616	+	0.911357i	$0.364964\pi$
$882$	0	0
$883$	6.20562	0.208836	0.104418	−	0.994534i	$-0.466702\pi$
$883$	6.20562	0.208836	0.104418	+	0.994534i	$0.466702\pi$
$884$	−14.7440	−0.495895
$885$	3.36631	0.113157
$886$	22.7031	0.762727
$887$	−13.6868	−0.459557	−0.229779	−	0.973243i	$-0.573800\pi$
$887$	−13.6868	−0.459557	−0.229779	+	0.973243i	$0.573800\pi$
$888$	−4.21130	−0.141322
$889$	0	0
$890$	7.61364	0.255210
$891$	2.68119	0.0898232
$892$	−20.1967	−0.676237
$893$	−88.4212	−2.95890
$894$	6.43312	0.215156
$895$	−9.25926	−0.309503
$896$	0	0
$897$	−6.43766	−0.214947
$898$	0.527607	0.0176065
$899$	−77.9835	−2.60090
$900$	1.72909	0.0576364
$901$	−72.3645	−2.41081
$902$	−2.26345	−0.0753645
$903$	0	0
$904$	4.97155	0.165351
$905$	−45.9494	−1.52741
$906$	5.96178	0.198067
$907$	−40.4953	−1.34462	−0.672312	−	0.740268i	$-0.734699\pi$
$907$	−40.4953	−1.34462	−0.672312	+	0.740268i	$0.734699\pi$
$908$	19.1061	0.634059
$909$	−4.23382	−0.140427
$910$	0	0
$911$	42.8087	1.41832	0.709158	−	0.705050i	$-0.249075\pi$
$911$	42.8087	1.41832	0.709158	+	0.705050i	$0.249075\pi$
$912$	1.67801	0.0555644
$913$	19.2612	0.637454
$914$	10.5346	0.348453
$915$	−19.5560	−0.646503
$916$	−9.67685	−0.319732
$917$	0	0
$918$	−5.14389	−0.169774
$919$	−16.0982	−0.531030	−0.265515	−	0.964107i	$-0.585542\pi$
$919$	−16.0982	−0.531030	−0.265515	+	0.964107i	$0.585542\pi$
$920$	−18.1758	−0.599237
$921$	2.67275	0.0880700
$922$	−0.710668	−0.0234046
$923$	8.70186	0.286425
$924$	0	0
$925$	−2.03824	−0.0670170
$926$	−23.8424	−0.783511
$927$	−9.73645	−0.319787
$928$	−60.4302	−1.98372
$929$	8.85492	0.290520	0.145260	−	0.989393i	$-0.453598\pi$
$929$	8.85492	0.290520	0.145260	+	0.989393i	$0.453598\pi$
$930$	−11.9706	−0.392531
$931$	0	0
$932$	−22.2169	−0.727738
$933$	14.9516	0.489493
$934$	−1.44707	−0.0473497
$935$	−31.2413	−1.02170
$936$	−5.21629	−0.170500
$937$	−15.4981	−0.506301	−0.253150	−	0.967427i	$-0.581467\pi$
$937$	−15.4981	−0.506301	−0.253150	+	0.967427i	$0.581467\pi$
$938$	0	0
$939$	−17.4503	−0.569469
$940$	−30.0823	−0.981177
$941$	4.30488	0.140335	0.0701675	−	0.997535i	$-0.477647\pi$
$941$	4.30488	0.140335	0.0701675	+	0.997535i	$0.477647\pi$
$942$	−8.94480	−0.291437
$943$	−3.42494	−0.111531
$944$	−0.408230	−0.0132868
$945$	0	0
$946$	9.13787	0.297098
$947$	18.6177	0.604992	0.302496	−	0.953151i	$-0.402180\pi$
$947$	18.6177	0.604992	0.302496	+	0.953151i	$0.402180\pi$
$948$	2.56600	0.0833397
$949$	7.60442	0.246850
$950$	−8.20464	−0.266194
$951$	−29.2867	−0.949688
$952$	0	0
$953$	16.2926	0.527768	0.263884	−	0.964554i	$-0.414996\pi$
$953$	16.2926	0.527768	0.263884	+	0.964554i	$0.414996\pi$
$954$	−10.0258	−0.324598
$955$	32.5870	1.05449
$956$	34.0672	1.10181
$957$	−28.1975	−0.911495
$958$	18.0572	0.583401
$959$	0	0
$960$	−8.38921	−0.270760
$961$	23.9845	0.773692
$962$	2.40795	0.0776353
$963$	2.13975	0.0689526
$964$	−35.5536	−1.14510
$965$	50.2269	1.61686
$966$	0	0
$967$	42.0786	1.35316	0.676578	−	0.736371i	$-0.263462\pi$
$967$	42.0786	1.35316	0.676578	+	0.736371i	$0.263462\pi$
$968$	−10.5767	−0.339949
$969$	−44.0899	−1.41637
$970$	−7.52527	−0.241622
$971$	−11.6017	−0.372317	−0.186159	−	0.982520i	$-0.559604\pi$
$971$	−11.6017	−0.372317	−0.186159	+	0.982520i	$0.559604\pi$
$972$	1.28734	0.0412913
$973$	0	0
$974$	−7.68016	−0.246088
$975$	−2.52465	−0.0808536
$976$	2.37155	0.0759114
$977$	36.0348	1.15286	0.576428	−	0.817148i	$-0.304446\pi$
$977$	36.0348	1.15286	0.576428	+	0.817148i	$0.304446\pi$
$978$	−18.1472	−0.580282
$979$	−12.6451	−0.404141
$980$	0	0
$981$	−8.76924	−0.279980
$982$	−12.0061	−0.383129
$983$	40.3590	1.28725	0.643625	−	0.765341i	$-0.277429\pi$
$983$	40.3590	1.28725	0.643625	+	0.765341i	$0.277429\pi$
$984$	−2.77515	−0.0884686
$985$	43.9962	1.40184
$986$	54.0972	1.72280
$987$	0	0
$988$	−17.5088	−0.557029
$989$	13.8270	0.439673
$990$	−4.32836	−0.137564
$991$	−24.9144	−0.791431	−0.395715	−	0.918373i	$-0.629503\pi$
$991$	−24.9144	−0.791431	−0.395715	+	0.918373i	$0.629503\pi$
$992$	42.6080	1.35281
$993$	−9.52575	−0.302291
$994$	0	0
$995$	47.4680	1.50484
$996$	9.24802	0.293035
$997$	−45.1066	−1.42854	−0.714269	−	0.699871i	$-0.753241\pi$
$997$	−45.1066	−1.42854	−0.714269	+	0.699871i	$0.753241\pi$
$998$	11.4682	0.363020
$999$	−1.51750	−0.0480116

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bn.1.8	✓	24
7.6	odd	2		6027.2.a.bo.1.8	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6027.2.a.bn.1.8	✓	24	1.1	even	1	trivial
6027.2.a.bo.1.8	yes	24	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)

\(f(q)\)	\(=\)	\(q-0.844195 q^{2} -1.00000 q^{3} -1.28734 q^{4} +1.91229 q^{5} +0.844195 q^{6} +2.77515 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.844195 q^{2} -1.00000 q^{3} -1.28734 q^{4} +1.91229 q^{5} +0.844195 q^{6} +2.77515 q^{8} +1.00000 q^{9} -1.61434 q^{10} +2.68119 q^{11} +1.28734 q^{12} -1.87964 q^{13} -1.91229 q^{15} +0.231902 q^{16} -6.09325 q^{17} -0.844195 q^{18} -7.23586 q^{19} -2.46175 q^{20} -2.26345 q^{22} -3.42494 q^{23} -2.77515 q^{24} -1.34316 q^{25} +1.58678 q^{26} -1.00000 q^{27} +10.5168 q^{29} +1.61434 q^{30} -7.41515 q^{31} -5.74607 q^{32} -2.68119 q^{33} +5.14389 q^{34} -1.28734 q^{36} +1.51750 q^{37} +6.10847 q^{38} +1.87964 q^{39} +5.30689 q^{40} +1.00000 q^{41} -4.03715 q^{43} -3.45159 q^{44} +1.91229 q^{45} +2.89131 q^{46} +12.2199 q^{47} -0.231902 q^{48} +1.13389 q^{50} +6.09325 q^{51} +2.41973 q^{52} +11.8762 q^{53} +0.844195 q^{54} +5.12720 q^{55} +7.23586 q^{57} -8.87821 q^{58} -1.76036 q^{59} +2.46175 q^{60} +10.2265 q^{61} +6.25983 q^{62} +4.38700 q^{64} -3.59441 q^{65} +2.26345 q^{66} -3.15832 q^{67} +7.84405 q^{68} +3.42494 q^{69} -4.62953 q^{71} +2.77515 q^{72} -4.04568 q^{73} -1.28107 q^{74} +1.34316 q^{75} +9.31497 q^{76} -1.58678 q^{78} +1.99326 q^{79} +0.443463 q^{80} +1.00000 q^{81} -0.844195 q^{82} +7.18385 q^{83} -11.6520 q^{85} +3.40814 q^{86} -10.5168 q^{87} +7.44070 q^{88} -4.71625 q^{89} -1.61434 q^{90} +4.40904 q^{92} +7.41515 q^{93} -10.3159 q^{94} -13.8370 q^{95} +5.74607 q^{96} +4.66151 q^{97} +2.68119 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} - 24 q^{3} + 32 q^{4} - 4 q^{5} - 8 q^{6} + 24 q^{8} + 24 q^{9}+O(q^{10}) \) 24 * q + 8 * q^2 - 24 * q^3 + 32 * q^4 - 4 * q^5 - 8 * q^6 + 24 * q^8 + 24 * q^9	\( 24 q + 8 q^{2} - 24 q^{3} + 32 q^{4} - 4 q^{5} - 8 q^{6} + 24 q^{8} + 24 q^{9} + 4 q^{10} + 12 q^{11} - 32 q^{12} + 4 q^{15} + 44 q^{16} - 8 q^{17} + 8 q^{18} + 4 q^{19} - 28 q^{20} + 16 q^{22} + 20 q^{23} - 24 q^{24} + 48 q^{25} - 32 q^{26} - 24 q^{27} + 24 q^{29} - 4 q^{30} + 4 q^{31} + 36 q^{32} - 12 q^{33} - 16 q^{34} + 32 q^{36} + 64 q^{37} - 20 q^{38} + 48 q^{40} + 24 q^{41} + 20 q^{43} + 48 q^{44} - 4 q^{45} + 28 q^{46} - 32 q^{47} - 44 q^{48} - 20 q^{50} + 8 q^{51} + 76 q^{53} - 8 q^{54} + 24 q^{55} - 4 q^{57} + 28 q^{58} - 28 q^{59} + 28 q^{60} + 28 q^{61} + 4 q^{62} + 48 q^{64} + 28 q^{65} - 16 q^{66} + 44 q^{67} + 32 q^{68} - 20 q^{69} + 20 q^{71} + 24 q^{72} + 16 q^{73} + 44 q^{74} - 48 q^{75} + 16 q^{76} + 32 q^{78} + 4 q^{79} - 44 q^{80} + 24 q^{81} + 8 q^{82} - 8 q^{83} + 28 q^{85} + 56 q^{86} - 24 q^{87} + 60 q^{88} - 60 q^{89} + 4 q^{90} + 60 q^{92} - 4 q^{93} - 24 q^{94} + 28 q^{95} - 36 q^{96} + 48 q^{97} + 12 q^{99}+O(q^{100}) \) 24 * q + 8 * q^2 - 24 * q^3 + 32 * q^4 - 4 * q^5 - 8 * q^6 + 24 * q^8 + 24 * q^9 + 4 * q^10 + 12 * q^11 - 32 * q^12 + 4 * q^15 + 44 * q^16 - 8 * q^17 + 8 * q^18 + 4 * q^19 - 28 * q^20 + 16 * q^22 + 20 * q^23 - 24 * q^24 + 48 * q^25 - 32 * q^26 - 24 * q^27 + 24 * q^29 - 4 * q^30 + 4 * q^31 + 36 * q^32 - 12 * q^33 - 16 * q^34 + 32 * q^36 + 64 * q^37 - 20 * q^38 + 48 * q^40 + 24 * q^41 + 20 * q^43 + 48 * q^44 - 4 * q^45 + 28 * q^46 - 32 * q^47 - 44 * q^48 - 20 * q^50 + 8 * q^51 + 76 * q^53 - 8 * q^54 + 24 * q^55 - 4 * q^57 + 28 * q^58 - 28 * q^59 + 28 * q^60 + 28 * q^61 + 4 * q^62 + 48 * q^64 + 28 * q^65 - 16 * q^66 + 44 * q^67 + 32 * q^68 - 20 * q^69 + 20 * q^71 + 24 * q^72 + 16 * q^73 + 44 * q^74 - 48 * q^75 + 16 * q^76 + 32 * q^78 + 4 * q^79 - 44 * q^80 + 24 * q^81 + 8 * q^82 - 8 * q^83 + 28 * q^85 + 56 * q^86 - 24 * q^87 + 60 * q^88 - 60 * q^89 + 4 * q^90 + 60 * q^92 - 4 * q^93 - 24 * q^94 + 28 * q^95 - 36 * q^96 + 48 * q^97 + 12 * q^99

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