LMFDB - Embedded newform 6027.2.a.bn.1.21

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			1.21
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.48810 q^{2} -1.00000 q^{3} +4.19062 q^{4} -2.36641 q^{5} -2.48810 q^{6} +5.45047 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.48810 q^{2} -1.00000 q^{3} +4.19062 q^{4} -2.36641 q^{5} -2.48810 q^{6} +5.45047 q^{8} +1.00000 q^{9} -5.88785 q^{10} +4.46600 q^{11} -4.19062 q^{12} +5.01637 q^{13} +2.36641 q^{15} +5.18004 q^{16} -4.88608 q^{17} +2.48810 q^{18} +3.64438 q^{19} -9.91672 q^{20} +11.1118 q^{22} -2.22001 q^{23} -5.45047 q^{24} +0.599893 q^{25} +12.4812 q^{26} -1.00000 q^{27} +2.88239 q^{29} +5.88785 q^{30} -1.18084 q^{31} +1.98751 q^{32} -4.46600 q^{33} -12.1570 q^{34} +4.19062 q^{36} -0.748295 q^{37} +9.06756 q^{38} -5.01637 q^{39} -12.8980 q^{40} +1.00000 q^{41} +6.98238 q^{43} +18.7153 q^{44} -2.36641 q^{45} -5.52359 q^{46} +7.64313 q^{47} -5.18004 q^{48} +1.49259 q^{50} +4.88608 q^{51} +21.0217 q^{52} +10.3267 q^{53} -2.48810 q^{54} -10.5684 q^{55} -3.64438 q^{57} +7.17166 q^{58} -8.70177 q^{59} +9.91672 q^{60} -8.35367 q^{61} -2.93804 q^{62} -5.41498 q^{64} -11.8708 q^{65} -11.1118 q^{66} -0.0922892 q^{67} -20.4757 q^{68} +2.22001 q^{69} +3.08552 q^{71} +5.45047 q^{72} +9.88365 q^{73} -1.86183 q^{74} -0.599893 q^{75} +15.2722 q^{76} -12.4812 q^{78} +7.87830 q^{79} -12.2581 q^{80} +1.00000 q^{81} +2.48810 q^{82} +6.26355 q^{83} +11.5625 q^{85} +17.3728 q^{86} -2.88239 q^{87} +24.3418 q^{88} +10.3142 q^{89} -5.88785 q^{90} -9.30321 q^{92} +1.18084 q^{93} +19.0168 q^{94} -8.62409 q^{95} -1.98751 q^{96} +4.64324 q^{97} +4.46600 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.48810	1.75935	0.879675	−	0.475576i	$-0.157760\pi$
$2$	2.48810	1.75935	0.879675	+	0.475576i	$0.157760\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.19062	2.09531
$5$	−2.36641	−1.05829	−0.529145	−	0.848531i	$-0.677487\pi$
$5$	−2.36641	−1.05829	−0.529145	+	0.848531i	$0.677487\pi$
$6$	−2.48810	−1.01576
$7$	0	0
$7$	0	0
$8$	5.45047	1.92703
$9$	1.00000	0.333333
$10$	−5.88785	−1.86190
$11$	4.46600	1.34655	0.673275	−	0.739392i	$-0.264887\pi$
$11$	4.46600	1.34655	0.673275	+	0.739392i	$0.264887\pi$
$12$	−4.19062	−1.20973
$13$	5.01637	1.39129	0.695645	−	0.718385i	$-0.255118\pi$
$13$	5.01637	1.39129	0.695645	+	0.718385i	$0.255118\pi$
$14$	0	0
$15$	2.36641	0.611004
$16$	5.18004	1.29501
$17$	−4.88608	−1.18505	−0.592524	−	0.805552i	$-0.701869\pi$
$17$	−4.88608	−1.18505	−0.592524	+	0.805552i	$0.701869\pi$
$18$	2.48810	0.586450
$19$	3.64438	0.836078	0.418039	−	0.908429i	$-0.362718\pi$
$19$	3.64438	0.836078	0.418039	+	0.908429i	$0.362718\pi$
$20$	−9.91672	−2.21745
$21$	0	0
$22$	11.1118	2.36905
$23$	−2.22001	−0.462904	−0.231452	−	0.972846i	$-0.574348\pi$
$23$	−2.22001	−0.462904	−0.231452	+	0.972846i	$0.574348\pi$
$24$	−5.45047	−1.11257
$25$	0.599893	0.119979
$26$	12.4812	2.44777
$27$	−1.00000	−0.192450
$28$	0	0
$29$	2.88239	0.535246	0.267623	−	0.963524i	$-0.413762\pi$
$29$	2.88239	0.535246	0.267623	+	0.963524i	$0.413762\pi$
$30$	5.88785	1.07497
$31$	−1.18084	−0.212085	−0.106043	−	0.994362i	$-0.533818\pi$
$31$	−1.18084	−0.212085	−0.106043	+	0.994362i	$0.533818\pi$
$32$	1.98751	0.351345
$33$	−4.46600	−0.777431
$34$	−12.1570	−2.08491
$35$	0	0
$36$	4.19062	0.698436
$37$	−0.748295	−0.123019	−0.0615095	−	0.998107i	$-0.519591\pi$
$37$	−0.748295	−0.123019	−0.0615095	+	0.998107i	$0.519591\pi$
$38$	9.06756	1.47095
$39$	−5.01637	−0.803262
$40$	−12.8980	−2.03936
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	6.98238	1.06480	0.532402	−	0.846492i	$-0.321290\pi$
$43$	6.98238	1.06480	0.532402	+	0.846492i	$0.321290\pi$
$44$	18.7153	2.82144
$45$	−2.36641	−0.352763
$46$	−5.52359	−0.814409
$47$	7.64313	1.11486	0.557432	−	0.830222i	$-0.311787\pi$
$47$	7.64313	1.11486	0.557432	+	0.830222i	$0.311787\pi$
$48$	−5.18004	−0.747675
$49$	0	0
$50$	1.49259	0.211084
$51$	4.88608	0.684188
$52$	21.0217	2.91518
$53$	10.3267	1.41848	0.709238	−	0.704969i	$-0.249039\pi$
$53$	10.3267	1.41848	0.709238	+	0.704969i	$0.249039\pi$
$54$	−2.48810	−0.338587
$55$	−10.5684	−1.42504
$56$	0	0
$57$	−3.64438	−0.482710
$58$	7.17166	0.941685
$59$	−8.70177	−1.13287	−0.566437	−	0.824105i	$-0.691679\pi$
$59$	−8.70177	−1.13287	−0.566437	+	0.824105i	$0.691679\pi$
$60$	9.91672	1.28024
$61$	−8.35367	−1.06958	−0.534789	−	0.844986i	$-0.679609\pi$
$61$	−8.35367	−1.06958	−0.534789	+	0.844986i	$0.679609\pi$
$62$	−2.93804	−0.373132
$63$	0	0
$64$	−5.41498	−0.676872
$65$	−11.8708	−1.47239
$66$	−11.1118	−1.36777
$67$	−0.0922892	−0.0112749	−0.00563746	−	0.999984i	$-0.501794\pi$
$67$	−0.0922892	−0.0112749	−0.00563746	+	0.999984i	$0.501794\pi$
$68$	−20.4757	−2.48304
$69$	2.22001	0.267258
$70$	0	0
$71$	3.08552	0.366184	0.183092	−	0.983096i	$-0.441389\pi$
$71$	3.08552	0.366184	0.183092	+	0.983096i	$0.441389\pi$
$72$	5.45047	0.642344
$73$	9.88365	1.15679	0.578397	−	0.815755i	$-0.303678\pi$
$73$	9.88365	1.15679	0.578397	+	0.815755i	$0.303678\pi$
$74$	−1.86183	−0.216433
$75$	−0.599893	−0.0692696
$76$	15.2722	1.75184
$77$	0	0
$78$	−12.4812	−1.41322
$79$	7.87830	0.886378	0.443189	−	0.896428i	$-0.353847\pi$
$79$	7.87830	0.886378	0.443189	+	0.896428i	$0.353847\pi$
$80$	−12.2581	−1.37050
$81$	1.00000	0.111111
$82$	2.48810	0.274764
$83$	6.26355	0.687514	0.343757	−	0.939059i	$-0.388300\pi$
$83$	6.26355	0.687514	0.343757	+	0.939059i	$0.388300\pi$
$84$	0	0
$85$	11.5625	1.25413
$86$	17.3728	1.87336
$87$	−2.88239	−0.309024
$88$	24.3418	2.59484
$89$	10.3142	1.09330	0.546652	−	0.837360i	$-0.315902\pi$
$89$	10.3142	1.09330	0.546652	+	0.837360i	$0.315902\pi$
$90$	−5.88785	−0.620634
$91$	0	0
$92$	−9.30321	−0.969926
$93$	1.18084	0.122447
$94$	19.0168	1.96144
$95$	−8.62409	−0.884813
$96$	−1.98751	−0.202849
$97$	4.64324	0.471449	0.235725	−	0.971820i	$-0.424254\pi$
$97$	4.64324	0.471449	0.235725	+	0.971820i	$0.424254\pi$
$98$	0	0
$99$	4.46600	0.448850
$100$	2.51392	0.251392
$101$	13.8197	1.37511	0.687555	−	0.726133i	$-0.258684\pi$
$101$	13.8197	1.37511	0.687555	+	0.726133i	$0.258684\pi$
$102$	12.1570	1.20373
$103$	13.0191	1.28281	0.641403	−	0.767204i	$-0.278353\pi$
$103$	13.0191	1.28281	0.641403	+	0.767204i	$0.278353\pi$
$104$	27.3416	2.68106
$105$	0	0
$106$	25.6937	2.49560
$107$	−19.9762	−1.93117	−0.965586	−	0.260083i	$-0.916250\pi$
$107$	−19.9762	−1.93117	−0.965586	+	0.260083i	$0.916250\pi$
$108$	−4.19062	−0.403242
$109$	4.41695	0.423067	0.211533	−	0.977371i	$-0.432154\pi$
$109$	4.41695	0.423067	0.211533	+	0.977371i	$0.432154\pi$
$110$	−26.2952	−2.50714
$111$	0.748295	0.0710250
$112$	0	0
$113$	−14.4815	−1.36230	−0.681151	−	0.732143i	$-0.738520\pi$
$113$	−14.4815	−1.36230	−0.681151	+	0.732143i	$0.738520\pi$
$114$	−9.06756	−0.849255
$115$	5.25345	0.489887
$116$	12.0790	1.12151
$117$	5.01637	0.463764
$118$	−21.6508	−1.99312
$119$	0	0
$120$	12.8980	1.17742
$121$	8.94517	0.813197
$122$	−20.7847	−1.88176
$123$	−1.00000	−0.0901670
$124$	−4.94845	−0.444384
$125$	10.4125	0.931318
$126$	0	0
$127$	17.9357	1.59154	0.795769	−	0.605600i	$-0.207067\pi$
$127$	17.9357	1.59154	0.795769	+	0.605600i	$0.207067\pi$
$128$	−17.4480	−1.54220
$129$	−6.98238	−0.614765
$130$	−29.5356	−2.59045
$131$	−1.81416	−0.158504	−0.0792518	−	0.996855i	$-0.525253\pi$
$131$	−1.81416	−0.158504	−0.0792518	+	0.996855i	$0.525253\pi$
$132$	−18.7153	−1.62896
$133$	0	0
$134$	−0.229624	−0.0198365
$135$	2.36641	0.203668
$136$	−26.6314	−2.28363
$137$	10.3191	0.881623	0.440811	−	0.897600i	$-0.354691\pi$
$137$	10.3191	0.881623	0.440811	+	0.897600i	$0.354691\pi$
$138$	5.52359	0.470199
$139$	12.1318	1.02901	0.514504	−	0.857488i	$-0.327976\pi$
$139$	12.1318	1.02901	0.514504	+	0.857488i	$0.327976\pi$
$140$	0	0
$141$	−7.64313	−0.643667
$142$	7.67708	0.644246
$143$	22.4031	1.87344
$144$	5.18004	0.431670
$145$	−6.82091	−0.566446
$146$	24.5915	2.03520
$147$	0	0
$148$	−3.13582	−0.257763
$149$	−16.8170	−1.37771	−0.688853	−	0.724901i	$-0.741886\pi$
$149$	−16.8170	−1.37771	−0.688853	+	0.724901i	$0.741886\pi$
$150$	−1.49259	−0.121869
$151$	−16.1017	−1.31034	−0.655168	−	0.755483i	$-0.727402\pi$
$151$	−16.1017	−1.31034	−0.655168	+	0.755483i	$0.727402\pi$
$152$	19.8636	1.61115
$153$	−4.88608	−0.395016
$154$	0	0
$155$	2.79435	0.224448
$156$	−21.0217	−1.68308
$157$	−7.43656	−0.593502	−0.296751	−	0.954955i	$-0.595903\pi$
$157$	−7.43656	−0.593502	−0.296751	+	0.954955i	$0.595903\pi$
$158$	19.6020	1.55945
$159$	−10.3267	−0.818958
$160$	−4.70326	−0.371825
$161$	0	0
$162$	2.48810	0.195483
$163$	19.1144	1.49715	0.748576	−	0.663049i	$-0.230738\pi$
$163$	19.1144	1.49715	0.748576	+	0.663049i	$0.230738\pi$
$164$	4.19062	0.327232
$165$	10.5684	0.822748
$166$	15.5843	1.20958
$167$	3.05717	0.236571	0.118285	−	0.992980i	$-0.462260\pi$
$167$	3.05717	0.236571	0.118285	+	0.992980i	$0.462260\pi$
$168$	0	0
$169$	12.1640	0.935690
$170$	28.7685	2.20645
$171$	3.64438	0.278693
$172$	29.2605	2.23109
$173$	−12.6063	−0.958439	−0.479219	−	0.877695i	$-0.659080\pi$
$173$	−12.6063	−0.958439	−0.479219	+	0.877695i	$0.659080\pi$
$174$	−7.17166	−0.543682
$175$	0	0
$176$	23.1341	1.74380
$177$	8.70177	0.654065
$178$	25.6627	1.92350
$179$	−6.53673	−0.488578	−0.244289	−	0.969702i	$-0.578555\pi$
$179$	−6.53673	−0.488578	−0.244289	+	0.969702i	$0.578555\pi$
$180$	−9.91672	−0.739148
$181$	−1.75566	−0.130497	−0.0652487	−	0.997869i	$-0.520784\pi$
$181$	−1.75566	−0.130497	−0.0652487	+	0.997869i	$0.520784\pi$
$182$	0	0
$183$	8.35367	0.617521
$184$	−12.1001	−0.892030
$185$	1.77077	0.130190
$186$	2.93804	0.215428
$187$	−21.8212	−1.59573
$188$	32.0294	2.33599
$189$	0	0
$190$	−21.4576	−1.55669
$191$	3.79254	0.274418	0.137209	−	0.990542i	$-0.456187\pi$
$191$	3.79254	0.274418	0.137209	+	0.990542i	$0.456187\pi$
$192$	5.41498	0.390792
$193$	−0.179574	−0.0129260	−0.00646302	−	0.999979i	$-0.502057\pi$
$193$	−0.179574	−0.0129260	−0.00646302	+	0.999979i	$0.502057\pi$
$194$	11.5528	0.829444
$195$	11.8708	0.850085
$196$	0	0
$197$	−13.2115	−0.941280	−0.470640	−	0.882325i	$-0.655977\pi$
$197$	−13.2115	−0.941280	−0.470640	+	0.882325i	$0.655977\pi$
$198$	11.1118	0.789684
$199$	−5.46727	−0.387564	−0.193782	−	0.981045i	$-0.562075\pi$
$199$	−5.46727	−0.387564	−0.193782	+	0.981045i	$0.562075\pi$
$200$	3.26969	0.231202
$201$	0.0922892	0.00650958
$202$	34.3847	2.41930
$203$	0	0
$204$	20.4757	1.43359
$205$	−2.36641	−0.165277
$206$	32.3926	2.25690
$207$	−2.22001	−0.154301
$208$	25.9850	1.80174
$209$	16.2758	1.12582
$210$	0	0
$211$	12.8035	0.881430	0.440715	−	0.897647i	$-0.354725\pi$
$211$	12.8035	0.881430	0.440715	+	0.897647i	$0.354725\pi$
$212$	43.2751	2.97215
$213$	−3.08552	−0.211417
$214$	−49.7027	−3.39761
$215$	−16.5232	−1.12687
$216$	−5.45047	−0.370857
$217$	0	0
$218$	10.9898	0.744322
$219$	−9.88365	−0.667875
$220$	−44.2881	−2.98590
$221$	−24.5104	−1.64875
$222$	1.86183	0.124958
$223$	1.61990	0.108477	0.0542383	−	0.998528i	$-0.482727\pi$
$223$	1.61990	0.108477	0.0542383	+	0.998528i	$0.482727\pi$
$224$	0	0
$225$	0.599893	0.0399928
$226$	−36.0313	−2.39676
$227$	7.09352	0.470813	0.235407	−	0.971897i	$-0.424358\pi$
$227$	7.09352	0.470813	0.235407	+	0.971897i	$0.424358\pi$
$228$	−15.2722	−1.01143
$229$	−10.2801	−0.679326	−0.339663	−	0.940547i	$-0.610313\pi$
$229$	−10.2801	−0.679326	−0.339663	+	0.940547i	$0.610313\pi$
$230$	13.0711	0.861882
$231$	0	0
$232$	15.7104	1.03144
$233$	26.2441	1.71931	0.859656	−	0.510874i	$-0.170678\pi$
$233$	26.2441	1.71931	0.859656	+	0.510874i	$0.170678\pi$
$234$	12.4812	0.815922
$235$	−18.0868	−1.17985
$236$	−36.4658	−2.37372
$237$	−7.87830	−0.511750
$238$	0	0
$239$	9.99590	0.646581	0.323290	−	0.946300i	$-0.395211\pi$
$239$	9.99590	0.646581	0.323290	+	0.946300i	$0.395211\pi$
$240$	12.2581	0.791257
$241$	2.67886	0.172560	0.0862801	−	0.996271i	$-0.472502\pi$
$241$	2.67886	0.172560	0.0862801	+	0.996271i	$0.472502\pi$
$242$	22.2564	1.43070
$243$	−1.00000	−0.0641500
$244$	−35.0071	−2.24110
$245$	0	0
$246$	−2.48810	−0.158635
$247$	18.2815	1.16323
$248$	−6.43613	−0.408695
$249$	−6.26355	−0.396936
$250$	25.9072	1.63851
$251$	23.4644	1.48106	0.740529	−	0.672024i	$-0.234575\pi$
$251$	23.4644	1.48106	0.740529	+	0.672024i	$0.234575\pi$
$252$	0	0
$253$	−9.91456	−0.623323
$254$	44.6258	2.80007
$255$	−11.5625	−0.724070
$256$	−32.5823	−2.03639
$257$	−20.6351	−1.28718	−0.643590	−	0.765370i	$-0.722556\pi$
$257$	−20.6351	−1.28718	−0.643590	+	0.765370i	$0.722556\pi$
$258$	−17.3728	−1.08159
$259$	0	0
$260$	−49.7459	−3.08511
$261$	2.88239	0.178415
$262$	−4.51380	−0.278863
$263$	10.4139	0.642152	0.321076	−	0.947054i	$-0.395956\pi$
$263$	10.4139	0.642152	0.321076	+	0.947054i	$0.395956\pi$
$264$	−24.3418	−1.49813
$265$	−24.4371	−1.50116
$266$	0	0
$267$	−10.3142	−0.631219
$268$	−0.386749	−0.0236244
$269$	−18.0405	−1.09995	−0.549973	−	0.835182i	$-0.685362\pi$
$269$	−18.0405	−1.09995	−0.549973	+	0.835182i	$0.685362\pi$
$270$	5.88785	0.358323
$271$	30.1360	1.83063	0.915315	−	0.402739i	$-0.131942\pi$
$271$	30.1360	1.83063	0.915315	+	0.402739i	$0.131942\pi$
$272$	−25.3101	−1.53465
$273$	0	0
$274$	25.6750	1.55108
$275$	2.67912	0.161557
$276$	9.30321	0.559987
$277$	−15.2878	−0.918558	−0.459279	−	0.888292i	$-0.651892\pi$
$277$	−15.2878	−0.918558	−0.459279	+	0.888292i	$0.651892\pi$
$278$	30.1851	1.81038
$279$	−1.18084	−0.0706950
$280$	0	0
$281$	4.02679	0.240218	0.120109	−	0.992761i	$-0.461676\pi$
$281$	4.02679	0.240218	0.120109	+	0.992761i	$0.461676\pi$
$282$	−19.0168	−1.13244
$283$	−18.0462	−1.07274	−0.536368	−	0.843984i	$-0.680204\pi$
$283$	−18.0462	−1.07274	−0.536368	+	0.843984i	$0.680204\pi$
$284$	12.9303	0.767269
$285$	8.62409	0.510847
$286$	55.7411	3.29604
$287$	0	0
$288$	1.98751	0.117115
$289$	6.87380	0.404341
$290$	−16.9711	−0.996576
$291$	−4.64324	−0.272191
$292$	41.4186	2.42384
$293$	−5.56871	−0.325327	−0.162664	−	0.986682i	$-0.552009\pi$
$293$	−5.56871	−0.325327	−0.162664	+	0.986682i	$0.552009\pi$
$294$	0	0
$295$	20.5920	1.19891
$296$	−4.07856	−0.237061
$297$	−4.46600	−0.259144
$298$	−41.8424	−2.42387
$299$	−11.1364	−0.644034
$300$	−2.51392	−0.145141
$301$	0	0
$302$	−40.0625	−2.30534
$303$	−13.8197	−0.793920
$304$	18.8780	1.08273
$305$	19.7682	1.13192
$306$	−12.1570	−0.694972
$307$	20.3285	1.16021	0.580106	−	0.814541i	$-0.303011\pi$
$307$	20.3285	1.16021	0.580106	+	0.814541i	$0.303011\pi$
$308$	0	0
$309$	−13.0191	−0.740628
$310$	6.95261	0.394882
$311$	24.9893	1.41701	0.708505	−	0.705705i	$-0.249370\pi$
$311$	24.9893	1.41701	0.708505	+	0.705705i	$0.249370\pi$
$312$	−27.3416	−1.54791
$313$	19.0197	1.07506	0.537529	−	0.843245i	$-0.319358\pi$
$313$	19.0197	1.07506	0.537529	+	0.843245i	$0.319358\pi$
$314$	−18.5029	−1.04418
$315$	0	0
$316$	33.0149	1.85724
$317$	−26.7130	−1.50035	−0.750177	−	0.661237i	$-0.770032\pi$
$317$	−26.7130	−1.50035	−0.750177	+	0.661237i	$0.770032\pi$
$318$	−25.6937	−1.44083
$319$	12.8728	0.720736
$320$	12.8140	0.716327
$321$	19.9762	1.11496
$322$	0	0
$323$	−17.8067	−0.990793
$324$	4.19062	0.232812
$325$	3.00928	0.166925
$326$	47.5583	2.63401
$327$	−4.41695	−0.244258
$328$	5.45047	0.300952
$329$	0	0
$330$	26.2952	1.44750
$331$	−28.7281	−1.57904	−0.789519	−	0.613726i	$-0.789670\pi$
$331$	−28.7281	−1.57904	−0.789519	+	0.613726i	$0.789670\pi$
$332$	26.2481	1.44055
$333$	−0.748295	−0.0410063
$334$	7.60652	0.416210
$335$	0.218394	0.0119321
$336$	0	0
$337$	5.39749	0.294020	0.147010	−	0.989135i	$-0.453035\pi$
$337$	5.39749	0.294020	0.147010	+	0.989135i	$0.453035\pi$
$338$	30.2651	1.64621
$339$	14.4815	0.786525
$340$	48.4539	2.62778
$341$	−5.27363	−0.285583
$342$	9.06756	0.490317
$343$	0	0
$344$	38.0573	2.05191
$345$	−5.25345	−0.282836
$346$	−31.3657	−1.68623
$347$	−11.2384	−0.603308	−0.301654	−	0.953418i	$-0.597539\pi$
$347$	−11.2384	−0.603308	−0.301654	+	0.953418i	$0.597539\pi$
$348$	−12.0790	−0.647502
$349$	32.7910	1.75526	0.877631	−	0.479337i	$-0.159123\pi$
$349$	32.7910	1.75526	0.877631	+	0.479337i	$0.159123\pi$
$350$	0	0
$351$	−5.01637	−0.267754
$352$	8.87622	0.473104
$353$	−37.0316	−1.97099	−0.985496	−	0.169699i	$-0.945720\pi$
$353$	−37.0316	−1.97099	−0.985496	+	0.169699i	$0.945720\pi$
$354$	21.6508	1.15073
$355$	−7.30161	−0.387529
$356$	43.2229	2.29081
$357$	0	0
$358$	−16.2640	−0.859579
$359$	−28.8297	−1.52157	−0.760786	−	0.649003i	$-0.775186\pi$
$359$	−28.8297	−1.52157	−0.760786	+	0.649003i	$0.775186\pi$
$360$	−12.8980	−0.679786
$361$	−5.71851	−0.300974
$362$	−4.36826	−0.229590
$363$	−8.94517	−0.469499
$364$	0	0
$365$	−23.3888	−1.22422
$366$	20.7847	1.08644
$367$	−30.4855	−1.59133	−0.795664	−	0.605738i	$-0.792878\pi$
$367$	−30.4855	−1.59133	−0.795664	+	0.605738i	$0.792878\pi$
$368$	−11.4997	−0.599465
$369$	1.00000	0.0520579
$370$	4.40585	0.229049
$371$	0	0
$372$	4.94845	0.256565
$373$	11.0618	0.572758	0.286379	−	0.958116i	$-0.407548\pi$
$373$	11.0618	0.572758	0.286379	+	0.958116i	$0.407548\pi$
$374$	−54.2933	−2.80744
$375$	−10.4125	−0.537697
$376$	41.6586	2.14838
$377$	14.4591	0.744683
$378$	0	0
$379$	18.5413	0.952404	0.476202	−	0.879336i	$-0.342013\pi$
$379$	18.5413	0.952404	0.476202	+	0.879336i	$0.342013\pi$
$380$	−36.1403	−1.85396
$381$	−17.9357	−0.918875
$382$	9.43620	0.482798
$383$	−25.7669	−1.31663	−0.658313	−	0.752745i	$-0.728729\pi$
$383$	−25.7669	−1.31663	−0.658313	+	0.752745i	$0.728729\pi$
$384$	17.4480	0.890389
$385$	0	0
$386$	−0.446798	−0.0227414
$387$	6.98238	0.354935
$388$	19.4580	0.987832
$389$	8.98025	0.455317	0.227658	−	0.973741i	$-0.426893\pi$
$389$	8.98025	0.455317	0.227658	+	0.973741i	$0.426893\pi$
$390$	29.5356	1.49560
$391$	10.8471	0.548564
$392$	0	0
$393$	1.81416	0.0915121
$394$	−32.8715	−1.65604
$395$	−18.6433	−0.938045
$396$	18.7153	0.940479
$397$	−29.8142	−1.49633	−0.748165	−	0.663513i	$-0.769065\pi$
$397$	−29.8142	−1.49633	−0.748165	+	0.663513i	$0.769065\pi$
$398$	−13.6031	−0.681861
$399$	0	0
$400$	3.10747	0.155373
$401$	30.6347	1.52983	0.764913	−	0.644134i	$-0.222782\pi$
$401$	30.6347	1.52983	0.764913	+	0.644134i	$0.222782\pi$
$402$	0.229624	0.0114526
$403$	−5.92353	−0.295072
$404$	57.9130	2.88128
$405$	−2.36641	−0.117588
$406$	0	0
$407$	−3.34189	−0.165651
$408$	26.6314	1.31845
$409$	−9.88842	−0.488951	−0.244475	−	0.969656i	$-0.578616\pi$
$409$	−9.88842	−0.488951	−0.244475	+	0.969656i	$0.578616\pi$
$410$	−5.88785	−0.290780
$411$	−10.3191	−0.509005
$412$	54.5579	2.68787
$413$	0	0
$414$	−5.52359	−0.271470
$415$	−14.8221	−0.727589
$416$	9.97008	0.488823
$417$	−12.1318	−0.594098
$418$	40.4957	1.98071
$419$	7.68415	0.375395	0.187698	−	0.982227i	$-0.439897\pi$
$419$	7.68415	0.375395	0.187698	+	0.982227i	$0.439897\pi$
$420$	0	0
$421$	−5.53541	−0.269780	−0.134890	−	0.990861i	$-0.543068\pi$
$421$	−5.53541	−0.269780	−0.134890	+	0.990861i	$0.543068\pi$
$422$	31.8563	1.55074
$423$	7.64313	0.371622
$424$	56.2851	2.73345
$425$	−2.93112	−0.142180
$426$	−7.67708	−0.371956
$427$	0	0
$428$	−83.7126	−4.04640
$429$	−22.4031	−1.08163
$430$	−41.1112	−1.98256
$431$	−34.5461	−1.66403	−0.832014	−	0.554755i	$-0.812812\pi$
$431$	−34.5461	−1.66403	−0.832014	+	0.554755i	$0.812812\pi$
$432$	−5.18004	−0.249225
$433$	1.93996	0.0932284	0.0466142	−	0.998913i	$-0.485157\pi$
$433$	1.93996	0.0932284	0.0466142	+	0.998913i	$0.485157\pi$
$434$	0	0
$435$	6.82091	0.327038
$436$	18.5097	0.886455
$437$	−8.09055	−0.387023
$438$	−24.5915	−1.17503
$439$	−36.9625	−1.76412	−0.882062	−	0.471134i	$-0.843845\pi$
$439$	−36.9625	−1.76412	−0.882062	+	0.471134i	$0.843845\pi$
$440$	−57.6026	−2.74610
$441$	0	0
$442$	−60.9842	−2.90072
$443$	−28.9153	−1.37381	−0.686903	−	0.726749i	$-0.741030\pi$
$443$	−28.9153	−1.37381	−0.686903	+	0.726749i	$0.741030\pi$
$444$	3.13582	0.148819
$445$	−24.4076	−1.15703
$446$	4.03047	0.190848
$447$	16.8170	0.795419
$448$	0	0
$449$	−8.04865	−0.379839	−0.189920	−	0.981800i	$-0.560823\pi$
$449$	−8.04865	−0.379839	−0.189920	+	0.981800i	$0.560823\pi$
$450$	1.49259	0.0703614
$451$	4.46600	0.210296
$452$	−60.6863	−2.85444
$453$	16.1017	0.756523
$454$	17.6493	0.828325
$455$	0	0
$456$	−19.8636	−0.930196
$457$	4.73364	0.221430	0.110715	−	0.993852i	$-0.464686\pi$
$457$	4.73364	0.221430	0.110715	+	0.993852i	$0.464686\pi$
$458$	−25.5778	−1.19517
$459$	4.88608	0.228063
$460$	22.0152	1.02646
$461$	−36.8719	−1.71730	−0.858648	−	0.512567i	$-0.828695\pi$
$461$	−36.8719	−1.71730	−0.858648	+	0.512567i	$0.828695\pi$
$462$	0	0
$463$	11.4447	0.531880	0.265940	−	0.963990i	$-0.414318\pi$
$463$	11.4447	0.531880	0.265940	+	0.963990i	$0.414318\pi$
$464$	14.9309	0.693150
$465$	−2.79435	−0.129585
$466$	65.2979	3.02487
$467$	−9.31809	−0.431190	−0.215595	−	0.976483i	$-0.569169\pi$
$467$	−9.31809	−0.431190	−0.215595	+	0.976483i	$0.569169\pi$
$468$	21.0217	0.971728
$469$	0	0
$470$	−45.0016	−2.07577
$471$	7.43656	0.342658
$472$	−47.4287	−2.18308
$473$	31.1833	1.43381
$474$	−19.6020	−0.900348
$475$	2.18624	0.100311
$476$	0	0
$477$	10.3267	0.472826
$478$	24.8707	1.13756
$479$	−39.5784	−1.80838	−0.904191	−	0.427128i	$-0.859525\pi$
$479$	−39.5784	−1.80838	−0.904191	+	0.427128i	$0.859525\pi$
$480$	4.70326	0.214673
$481$	−3.75372	−0.171155
$482$	6.66525	0.303594
$483$	0	0
$484$	37.4858	1.70390
$485$	−10.9878	−0.498930
$486$	−2.48810	−0.112862
$487$	25.9347	1.17521	0.587607	−	0.809147i	$-0.300070\pi$
$487$	25.9347	1.17521	0.587607	+	0.809147i	$0.300070\pi$
$488$	−45.5314	−2.06111
$489$	−19.1144	−0.864381
$490$	0	0
$491$	−11.5856	−0.522851	−0.261426	−	0.965224i	$-0.584193\pi$
$491$	−11.5856	−0.522851	−0.261426	+	0.965224i	$0.584193\pi$
$492$	−4.19062	−0.188928
$493$	−14.0836	−0.634293
$494$	45.4862	2.04652
$495$	−10.5684	−0.475014
$496$	−6.11680	−0.274653
$497$	0	0
$498$	−15.5843	−0.698349
$499$	22.5754	1.01061	0.505306	−	0.862940i	$-0.331380\pi$
$499$	22.5754	1.01061	0.505306	+	0.862940i	$0.331380\pi$
$500$	43.6346	1.95140
$501$	−3.05717	−0.136584
$502$	58.3816	2.60570
$503$	−23.5474	−1.04993	−0.524963	−	0.851125i	$-0.675921\pi$
$503$	−23.5474	−1.04993	−0.524963	+	0.851125i	$0.675921\pi$
$504$	0	0
$505$	−32.7030	−1.45527
$506$	−24.6684	−1.09664
$507$	−12.1640	−0.540221
$508$	75.1618	3.33476
$509$	−27.1606	−1.20387	−0.601937	−	0.798543i	$-0.705604\pi$
$509$	−27.1606	−1.20387	−0.601937	+	0.798543i	$0.705604\pi$
$510$	−28.7685	−1.27389
$511$	0	0
$512$	−46.1719	−2.04053
$513$	−3.64438	−0.160903
$514$	−51.3420	−2.26460
$515$	−30.8084	−1.35758
$516$	−29.2605	−1.28812
$517$	34.1342	1.50122
$518$	0	0
$519$	12.6063	0.553355
$520$	−64.7013	−2.83734
$521$	19.8395	0.869183	0.434592	−	0.900628i	$-0.356893\pi$
$521$	19.8395	0.869183	0.434592	+	0.900628i	$0.356893\pi$
$522$	7.17166	0.313895
$523$	3.17412	0.138795	0.0693974	−	0.997589i	$-0.477892\pi$
$523$	3.17412	0.138795	0.0693974	+	0.997589i	$0.477892\pi$
$524$	−7.60244	−0.332114
$525$	0	0
$526$	25.9109	1.12977
$527$	5.76968	0.251331
$528$	−23.1341	−1.00678
$529$	−18.0716	−0.785720
$530$	−60.8019	−2.64106
$531$	−8.70177	−0.377625
$532$	0	0
$533$	5.01637	0.217283
$534$	−25.6627	−1.11054
$535$	47.2719	2.04374
$536$	−0.503019	−0.0217271
$537$	6.53673	0.282081
$538$	−44.8864	−1.93519
$539$	0	0
$540$	9.91672	0.426748
$541$	−25.4484	−1.09411	−0.547057	−	0.837096i	$-0.684252\pi$
$541$	−25.4484	−1.09411	−0.547057	+	0.837096i	$0.684252\pi$
$542$	74.9812	3.22072
$543$	1.75566	0.0753427
$544$	−9.71113	−0.416361
$545$	−10.4523	−0.447727
$546$	0	0
$547$	−41.5789	−1.77779	−0.888893	−	0.458116i	$-0.848525\pi$
$547$	−41.5789	−1.77779	−0.888893	+	0.458116i	$0.848525\pi$
$548$	43.2435	1.84727
$549$	−8.35367	−0.356526
$550$	6.66591	0.284235
$551$	10.5045	0.447507
$552$	12.1001	0.515014
$553$	0	0
$554$	−38.0376	−1.61606
$555$	−1.77077	−0.0751651
$556$	50.8398	2.15609
$557$	40.8397	1.73043	0.865217	−	0.501398i	$-0.167181\pi$
$557$	40.8397	1.73043	0.865217	+	0.501398i	$0.167181\pi$
$558$	−2.93804	−0.124377
$559$	35.0262	1.48145
$560$	0	0
$561$	21.8212	0.921294
$562$	10.0190	0.422627
$563$	−7.56052	−0.318638	−0.159319	−	0.987227i	$-0.550930\pi$
$563$	−7.56052	−0.318638	−0.159319	+	0.987227i	$0.550930\pi$
$564$	−32.0294	−1.34868
$565$	34.2691	1.44171
$566$	−44.9007	−1.88732
$567$	0	0
$568$	16.8175	0.705649
$569$	−20.8842	−0.875513	−0.437756	−	0.899094i	$-0.644227\pi$
$569$	−20.8842	−0.875513	−0.437756	+	0.899094i	$0.644227\pi$
$570$	21.4576	0.898758
$571$	−29.6774	−1.24196	−0.620980	−	0.783827i	$-0.713265\pi$
$571$	−29.6774	−1.24196	−0.620980	+	0.783827i	$0.713265\pi$
$572$	93.8829	3.92544
$573$	−3.79254	−0.158436
$574$	0	0
$575$	−1.33177	−0.0555385
$576$	−5.41498	−0.225624
$577$	0.394080	0.0164057	0.00820287	−	0.999966i	$-0.497389\pi$
$577$	0.394080	0.0164057	0.00820287	+	0.999966i	$0.497389\pi$
$578$	17.1027	0.711377
$579$	0.179574	0.00746285
$580$	−28.5838	−1.18688
$581$	0	0
$582$	−11.5528	−0.478879
$583$	46.1189	1.91005
$584$	53.8705	2.22918
$585$	−11.8708	−0.490797
$586$	−13.8555	−0.572364
$587$	12.0519	0.497435	0.248717	−	0.968576i	$-0.419991\pi$
$587$	12.0519	0.497435	0.248717	+	0.968576i	$0.419991\pi$
$588$	0	0
$589$	−4.30343	−0.177320
$590$	51.2348	2.10930
$591$	13.2115	0.543448
$592$	−3.87620	−0.159311
$593$	34.1529	1.40249	0.701246	−	0.712919i	$-0.252627\pi$
$593$	34.1529	1.40249	0.701246	+	0.712919i	$0.252627\pi$
$594$	−11.1118	−0.455924
$595$	0	0
$596$	−70.4738	−2.88672
$597$	5.46727	0.223760
$598$	−27.7084	−1.13308
$599$	−2.14962	−0.0878312	−0.0439156	−	0.999035i	$-0.513983\pi$
$599$	−2.14962	−0.0878312	−0.0439156	+	0.999035i	$0.513983\pi$
$600$	−3.26969	−0.133485
$601$	15.3782	0.627291	0.313646	−	0.949540i	$-0.398450\pi$
$601$	15.3782	0.627291	0.313646	+	0.949540i	$0.398450\pi$
$602$	0	0
$603$	−0.0922892	−0.00375831
$604$	−67.4760	−2.74556
$605$	−21.1679	−0.860598
$606$	−34.3847	−1.39678
$607$	−31.2239	−1.26734	−0.633669	−	0.773604i	$-0.718452\pi$
$607$	−31.2239	−1.26734	−0.633669	+	0.773604i	$0.718452\pi$
$608$	7.24323	0.293752
$609$	0	0
$610$	49.1852	1.99145
$611$	38.3408	1.55110
$612$	−20.4757	−0.827681
$613$	32.6293	1.31789	0.658943	−	0.752193i	$-0.271004\pi$
$613$	32.6293	1.31789	0.658943	+	0.752193i	$0.271004\pi$
$614$	50.5794	2.04122
$615$	2.36641	0.0954228
$616$	0	0
$617$	−33.6100	−1.35309	−0.676544	−	0.736402i	$-0.736523\pi$
$617$	−33.6100	−1.35309	−0.676544	+	0.736402i	$0.736523\pi$
$618$	−32.3926	−1.30302
$619$	24.9576	1.00313	0.501566	−	0.865119i	$-0.332757\pi$
$619$	24.9576	1.00313	0.501566	+	0.865119i	$0.332757\pi$
$620$	11.7101	0.470287
$621$	2.22001	0.0890859
$622$	62.1757	2.49302
$623$	0	0
$624$	−25.9850	−1.04023
$625$	−27.6396	−1.10558
$626$	47.3229	1.89140
$627$	−16.2758	−0.649993
$628$	−31.1638	−1.24357
$629$	3.65623	0.145783
$630$	0	0
$631$	−25.2251	−1.00420	−0.502099	−	0.864810i	$-0.667439\pi$
$631$	−25.2251	−1.00420	−0.502099	+	0.864810i	$0.667439\pi$
$632$	42.9404	1.70808
$633$	−12.8035	−0.508894
$634$	−66.4646	−2.63965
$635$	−42.4433	−1.68431
$636$	−43.2751	−1.71597
$637$	0	0
$638$	32.0286	1.26803
$639$	3.08552	0.122061
$640$	41.2891	1.63209
$641$	0.428767	0.0169353	0.00846764	−	0.999964i	$-0.497305\pi$
$641$	0.428767	0.0169353	0.00846764	+	0.999964i	$0.497305\pi$
$642$	49.7027	1.96161
$643$	−35.6986	−1.40781	−0.703907	−	0.710292i	$-0.748563\pi$
$643$	−35.6986	−1.40781	−0.703907	+	0.710292i	$0.748563\pi$
$644$	0	0
$645$	16.5232	0.650600
$646$	−44.3048	−1.74315
$647$	1.15325	0.0453389	0.0226695	−	0.999743i	$-0.492783\pi$
$647$	1.15325	0.0453389	0.0226695	+	0.999743i	$0.492783\pi$
$648$	5.45047	0.214115
$649$	−38.8621	−1.52547
$650$	7.48738	0.293679
$651$	0	0
$652$	80.1010	3.13700
$653$	−10.8046	−0.422815	−0.211408	−	0.977398i	$-0.567805\pi$
$653$	−10.8046	−0.422815	−0.211408	+	0.977398i	$0.567805\pi$
$654$	−10.9898	−0.429734
$655$	4.29304	0.167743
$656$	5.18004	0.202247
$657$	9.88365	0.385598
$658$	0	0
$659$	−21.9857	−0.856441	−0.428220	−	0.903674i	$-0.640859\pi$
$659$	−21.9857	−0.856441	−0.428220	+	0.903674i	$0.640859\pi$
$660$	44.2881	1.72391
$661$	12.5178	0.486885	0.243443	−	0.969915i	$-0.421723\pi$
$661$	12.5178	0.486885	0.243443	+	0.969915i	$0.421723\pi$
$662$	−71.4782	−2.77808
$663$	24.5104	0.951905
$664$	34.1393	1.32486
$665$	0	0
$666$	−1.86183	−0.0721444
$667$	−6.39893	−0.247767
$668$	12.8114	0.495689
$669$	−1.61990	−0.0626290
$670$	0.543385	0.0209928
$671$	−37.3075	−1.44024
$672$	0	0
$673$	−31.4333	−1.21166	−0.605832	−	0.795593i	$-0.707160\pi$
$673$	−31.4333	−1.21166	−0.605832	+	0.795593i	$0.707160\pi$
$674$	13.4295	0.517284
$675$	−0.599893	−0.0230899
$676$	50.9746	1.96056
$677$	35.2655	1.35536	0.677682	−	0.735355i	$-0.262985\pi$
$677$	35.2655	1.35536	0.677682	+	0.735355i	$0.262985\pi$
$678$	36.0313	1.38377
$679$	0	0
$680$	63.0208	2.41674
$681$	−7.09352	−0.271824
$682$	−13.1213	−0.502441
$683$	9.57717	0.366460	0.183230	−	0.983070i	$-0.441345\pi$
$683$	9.57717	0.366460	0.183230	+	0.983070i	$0.441345\pi$
$684$	15.2722	0.583947
$685$	−24.4193	−0.933013
$686$	0	0
$687$	10.2801	0.392209
$688$	36.1691	1.37893
$689$	51.8024	1.97351
$690$	−13.0711	−0.497608
$691$	−37.0205	−1.40832	−0.704162	−	0.710039i	$-0.748677\pi$
$691$	−37.0205	−1.40832	−0.704162	+	0.710039i	$0.748677\pi$
$692$	−52.8282	−2.00823
$693$	0	0
$694$	−27.9622	−1.06143
$695$	−28.7089	−1.08899
$696$	−15.7104	−0.595500
$697$	−4.88608	−0.185074
$698$	81.5871	3.08812
$699$	−26.2441	−0.992645
$700$	0	0
$701$	−23.3692	−0.882641	−0.441320	−	0.897350i	$-0.645490\pi$
$701$	−23.3692	−0.882641	−0.441320	+	0.897350i	$0.645490\pi$
$702$	−12.4812	−0.471073
$703$	−2.72707	−0.102853
$704$	−24.1833	−0.911442
$705$	18.0868	0.681187
$706$	−92.1381	−3.46766
$707$	0	0
$708$	36.4658	1.37047
$709$	−14.6548	−0.550371	−0.275185	−	0.961391i	$-0.588739\pi$
$709$	−14.6548	−0.550371	−0.275185	+	0.961391i	$0.588739\pi$
$710$	−18.1671	−0.681799
$711$	7.87830	0.295459
$712$	56.2173	2.10683
$713$	2.62148	0.0981750
$714$	0	0
$715$	−53.0149	−1.98265
$716$	−27.3929	−1.02372
$717$	−9.99590	−0.373304
$718$	−71.7309	−2.67697
$719$	−30.4680	−1.13626	−0.568132	−	0.822937i	$-0.692334\pi$
$719$	−30.4680	−1.13626	−0.568132	+	0.822937i	$0.692334\pi$
$720$	−12.2581	−0.456833
$721$	0	0
$722$	−14.2282	−0.529519
$723$	−2.67886	−0.0996277
$724$	−7.35731	−0.273432
$725$	1.72912	0.0642180
$726$	−22.2564	−0.826013
$727$	15.9546	0.591723	0.295861	−	0.955231i	$-0.404393\pi$
$727$	15.9546	0.591723	0.295861	+	0.955231i	$0.404393\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−58.1935	−2.15384
$731$	−34.1165	−1.26184
$732$	35.0071	1.29390
$733$	−0.380394	−0.0140502	−0.00702509	−	0.999975i	$-0.502236\pi$
$733$	−0.380394	−0.0140502	−0.00702509	+	0.999975i	$0.502236\pi$
$734$	−75.8507	−2.79970
$735$	0	0
$736$	−4.41229	−0.162639
$737$	−0.412163	−0.0151822
$738$	2.48810	0.0915881
$739$	2.04392	0.0751868	0.0375934	−	0.999293i	$-0.488031\pi$
$739$	2.04392	0.0751868	0.0375934	+	0.999293i	$0.488031\pi$
$740$	7.42063	0.272788
$741$	−18.2815	−0.671589
$742$	0	0
$743$	10.1113	0.370948	0.185474	−	0.982649i	$-0.440618\pi$
$743$	10.1113	0.370948	0.185474	+	0.982649i	$0.440618\pi$
$744$	6.43613	0.235960
$745$	39.7960	1.45801
$746$	27.5228	1.00768
$747$	6.26355	0.229171
$748$	−91.4445	−3.34354
$749$	0	0
$750$	−25.9072	−0.945996
$751$	35.9620	1.31227	0.656136	−	0.754643i	$-0.272190\pi$
$751$	35.9620	1.31227	0.656136	+	0.754643i	$0.272190\pi$
$752$	39.5917	1.44376
$753$	−23.4644	−0.855090
$754$	35.9757	1.31016
$755$	38.1032	1.38672
$756$	0	0
$757$	6.05727	0.220155	0.110078	−	0.993923i	$-0.464890\pi$
$757$	6.05727	0.220155	0.110078	+	0.993923i	$0.464890\pi$
$758$	46.1326	1.67561
$759$	9.91456	0.359876
$760$	−47.0053	−1.70506
$761$	−51.1971	−1.85589	−0.927947	−	0.372712i	$-0.878428\pi$
$761$	−51.1971	−1.85589	−0.927947	+	0.372712i	$0.878428\pi$
$762$	−44.6258	−1.61662
$763$	0	0
$764$	15.8931	0.574991
$765$	11.5625	0.418042
$766$	−64.1104	−2.31640
$767$	−43.6513	−1.57616
$768$	32.5823	1.17571
$769$	−24.5528	−0.885396	−0.442698	−	0.896671i	$-0.645979\pi$
$769$	−24.5528	−0.885396	−0.442698	+	0.896671i	$0.645979\pi$
$770$	0	0
$771$	20.6351	0.743154
$772$	−0.752527	−0.0270840
$773$	51.3061	1.84535	0.922676	−	0.385577i	$-0.125998\pi$
$773$	51.3061	1.84535	0.922676	+	0.385577i	$0.125998\pi$
$774$	17.3728	0.624454
$775$	−0.708377	−0.0254457
$776$	25.3078	0.908497
$777$	0	0
$778$	22.3437	0.801061
$779$	3.64438	0.130573
$780$	49.7459	1.78119
$781$	13.7800	0.493086
$782$	26.9887	0.965115
$783$	−2.88239	−0.103008
$784$	0	0
$785$	17.5979	0.628097
$786$	4.51380	0.161002
$787$	−8.42945	−0.300478	−0.150239	−	0.988650i	$-0.548004\pi$
$787$	−8.42945	−0.300478	−0.150239	+	0.988650i	$0.548004\pi$
$788$	−55.3643	−1.97227
$789$	−10.4139	−0.370746
$790$	−46.3862	−1.65035
$791$	0	0
$792$	24.3418	0.864948
$793$	−41.9051	−1.48809
$794$	−74.1805	−2.63257
$795$	24.4371	0.866695
$796$	−22.9112	−0.812067
$797$	43.9602	1.55715	0.778575	−	0.627551i	$-0.215943\pi$
$797$	43.9602	1.55715	0.778575	+	0.627551i	$0.215943\pi$
$798$	0	0
$799$	−37.3449	−1.32117
$800$	1.19229	0.0421539
$801$	10.3142	0.364435
$802$	76.2222	2.69150
$803$	44.1404	1.55768
$804$	0.386749	0.0136396
$805$	0	0
$806$	−14.7383	−0.519135
$807$	18.0405	0.635054
$808$	75.3237	2.64988
$809$	41.9373	1.47444	0.737218	−	0.675655i	$-0.236139\pi$
$809$	41.9373	1.47444	0.737218	+	0.675655i	$0.236139\pi$
$810$	−5.88785	−0.206878
$811$	1.50049	0.0526892	0.0263446	−	0.999653i	$-0.491613\pi$
$811$	1.50049	0.0526892	0.0263446	+	0.999653i	$0.491613\pi$
$812$	0	0
$813$	−30.1360	−1.05691
$814$	−8.31493	−0.291438
$815$	−45.2324	−1.58442
$816$	25.3101	0.886031
$817$	25.4464	0.890259
$818$	−24.6033	−0.860235
$819$	0	0
$820$	−9.91672	−0.346307
$821$	46.6313	1.62744	0.813722	−	0.581255i	$-0.197438\pi$
$821$	46.6313	1.62744	0.813722	+	0.581255i	$0.197438\pi$
$822$	−25.6750	−0.895518
$823$	12.4390	0.433595	0.216797	−	0.976217i	$-0.430439\pi$
$823$	12.4390	0.433595	0.216797	+	0.976217i	$0.430439\pi$
$824$	70.9599	2.47201
$825$	−2.67912	−0.0932750
$826$	0	0
$827$	25.6272	0.891147	0.445573	−	0.895245i	$-0.353000\pi$
$827$	25.6272	0.891147	0.445573	+	0.895245i	$0.353000\pi$
$828$	−9.30321	−0.323309
$829$	8.98335	0.312005	0.156002	−	0.987757i	$-0.450139\pi$
$829$	8.98335	0.312005	0.156002	+	0.987757i	$0.450139\pi$
$830$	−36.8788	−1.28008
$831$	15.2878	0.530329
$832$	−27.1635	−0.941726
$833$	0	0
$834$	−30.1851	−1.04523
$835$	−7.23451	−0.250360
$836$	68.2056	2.35894
$837$	1.18084	0.0408158
$838$	19.1189	0.660451
$839$	−14.9267	−0.515326	−0.257663	−	0.966235i	$-0.582952\pi$
$839$	−14.9267	−0.515326	−0.257663	+	0.966235i	$0.582952\pi$
$840$	0	0
$841$	−20.6918	−0.713512
$842$	−13.7726	−0.474636
$843$	−4.02679	−0.138690
$844$	53.6546	1.84687
$845$	−28.7849	−0.990232
$846$	19.0168	0.653812
$847$	0	0
$848$	53.4926	1.83694
$849$	18.0462	0.619345
$850$	−7.29292	−0.250145
$851$	1.66122	0.0569459
$852$	−12.9303	−0.442983
$853$	−29.3002	−1.00322	−0.501610	−	0.865094i	$-0.667259\pi$
$853$	−29.3002	−1.00322	−0.501610	+	0.865094i	$0.667259\pi$
$854$	0	0
$855$	−8.62409	−0.294938
$856$	−108.880	−3.72143
$857$	−0.206054	−0.00703868	−0.00351934	−	0.999994i	$-0.501120\pi$
$857$	−0.206054	−0.00703868	−0.00351934	+	0.999994i	$0.501120\pi$
$858$	−55.7411	−1.90297
$859$	10.3195	0.352096	0.176048	−	0.984382i	$-0.443669\pi$
$859$	10.3195	0.352096	0.176048	+	0.984382i	$0.443669\pi$
$860$	−69.2423	−2.36114
$861$	0	0
$862$	−85.9540	−2.92761
$863$	2.67563	0.0910796	0.0455398	−	0.998963i	$-0.485499\pi$
$863$	2.67563	0.0910796	0.0455398	+	0.998963i	$0.485499\pi$
$864$	−1.98751	−0.0676164
$865$	29.8317	1.01431
$866$	4.82680	0.164021
$867$	−6.87380	−0.233446
$868$	0	0
$869$	35.1845	1.19355
$870$	16.9711	0.575373
$871$	−0.462957	−0.0156867
$872$	24.0744	0.815263
$873$	4.64324	0.157150
$874$	−20.1301	−0.680909
$875$	0	0
$876$	−41.4186	−1.39941
$877$	28.0493	0.947158	0.473579	−	0.880751i	$-0.342962\pi$
$877$	28.0493	0.947158	0.473579	+	0.880751i	$0.342962\pi$
$878$	−91.9662	−3.10371
$879$	5.56871	0.187828
$880$	−54.7447	−1.84544
$881$	−2.95290	−0.0994856	−0.0497428	−	0.998762i	$-0.515840\pi$
$881$	−2.95290	−0.0994856	−0.0497428	+	0.998762i	$0.515840\pi$
$882$	0	0
$883$	12.2203	0.411246	0.205623	−	0.978631i	$-0.434078\pi$
$883$	12.2203	0.411246	0.205623	+	0.978631i	$0.434078\pi$
$884$	−102.714	−3.45464
$885$	−20.5920	−0.692191
$886$	−71.9440	−2.41700
$887$	−10.3073	−0.346084	−0.173042	−	0.984914i	$-0.555360\pi$
$887$	−10.3073	−0.346084	−0.173042	+	0.984914i	$0.555360\pi$
$888$	4.07856	0.136867
$889$	0	0
$890$	−60.7285	−2.03563
$891$	4.46600	0.149617
$892$	6.78838	0.227292
$893$	27.8544	0.932113
$894$	41.8424	1.39942
$895$	15.4686	0.517057
$896$	0	0
$897$	11.1364	0.371833
$898$	−20.0258	−0.668270
$899$	−3.40364	−0.113518
$900$	2.51392	0.0837974
$901$	−50.4569	−1.68096
$902$	11.1118	0.369984
$903$	0	0
$904$	−78.9308	−2.62520
$905$	4.15462	0.138104
$906$	40.0625	1.33099
$907$	29.2512	0.971269	0.485635	−	0.874162i	$-0.338589\pi$
$907$	29.2512	0.971269	0.485635	+	0.874162i	$0.338589\pi$
$908$	29.7262	0.986499
$909$	13.8197	0.458370
$910$	0	0
$911$	14.2520	0.472190	0.236095	−	0.971730i	$-0.424132\pi$
$911$	14.2520	0.472190	0.236095	+	0.971730i	$0.424132\pi$
$912$	−18.8780	−0.625114
$913$	27.9730	0.925772
$914$	11.7777	0.389573
$915$	−19.7682	−0.653517
$916$	−43.0799	−1.42340
$917$	0	0
$918$	12.1570	0.401242
$919$	21.2445	0.700791	0.350395	−	0.936602i	$-0.386047\pi$
$919$	21.2445	0.700791	0.350395	+	0.936602i	$0.386047\pi$
$920$	28.6337	0.944027
$921$	−20.3285	−0.669848
$922$	−91.7408	−3.02132
$923$	15.4781	0.509469
$924$	0	0
$925$	−0.448897	−0.0147596
$926$	28.4755	0.935763
$927$	13.0191	0.427602
$928$	5.72877	0.188056
$929$	−32.1903	−1.05613	−0.528064	−	0.849204i	$-0.677082\pi$
$929$	−32.1903	−1.05613	−0.528064	+	0.849204i	$0.677082\pi$
$930$	−6.95261	−0.227985
$931$	0	0
$932$	109.979	3.60249
$933$	−24.9893	−0.818112
$934$	−23.1843	−0.758613
$935$	51.6380	1.68874
$936$	27.3416	0.893687
$937$	30.2630	0.988649	0.494324	−	0.869278i	$-0.335415\pi$
$937$	30.2630	0.988649	0.494324	+	0.869278i	$0.335415\pi$
$938$	0	0
$939$	−19.0197	−0.620685
$940$	−75.7947	−2.47215
$941$	21.1631	0.689897	0.344948	−	0.938622i	$-0.387896\pi$
$941$	21.1631	0.689897	0.344948	+	0.938622i	$0.387896\pi$
$942$	18.5029	0.602856
$943$	−2.22001	−0.0722934
$944$	−45.0756	−1.46708
$945$	0	0
$946$	77.5871	2.52257
$947$	49.3799	1.60463	0.802316	−	0.596900i	$-0.203601\pi$
$947$	49.3799	1.60463	0.802316	+	0.596900i	$0.203601\pi$
$948$	−33.0149	−1.07228
$949$	49.5801	1.60944
$950$	5.43956	0.176483
$951$	26.7130	0.866230
$952$	0	0
$953$	42.6273	1.38083	0.690417	−	0.723412i	$-0.257427\pi$
$953$	42.6273	1.38083	0.690417	+	0.723412i	$0.257427\pi$
$954$	25.6937	0.831865
$955$	−8.97470	−0.290414
$956$	41.8890	1.35479
$957$	−12.8728	−0.416117
$958$	−98.4748	−3.18158
$959$	0	0
$960$	−12.8140	−0.413572
$961$	−29.6056	−0.955020
$962$	−9.33962	−0.301122
$963$	−19.9762	−0.643724
$964$	11.2261	0.361567
$965$	0.424946	0.0136795
$966$	0	0
$967$	40.3526	1.29765	0.648826	−	0.760937i	$-0.275260\pi$
$967$	40.3526	1.29765	0.648826	+	0.760937i	$0.275260\pi$
$968$	48.7553	1.56706
$969$	17.8067	0.572035
$970$	−27.3387	−0.877792
$971$	58.4250	1.87495	0.937474	−	0.348057i	$-0.113158\pi$
$971$	58.4250	1.87495	0.937474	+	0.348057i	$0.113158\pi$
$972$	−4.19062	−0.134414
$973$	0	0
$974$	64.5280	2.06761
$975$	−3.00928	−0.0963742
$976$	−43.2724	−1.38512
$977$	−0.829520	−0.0265387	−0.0132694	−	0.999912i	$-0.504224\pi$
$977$	−0.829520	−0.0265387	−0.0132694	+	0.999912i	$0.504224\pi$
$978$	−47.5583	−1.52075
$979$	46.0633	1.47219
$980$	0	0
$981$	4.41695	0.141022
$982$	−28.8261	−0.919877
$983$	2.32545	0.0741703	0.0370852	−	0.999312i	$-0.488193\pi$
$983$	2.32545	0.0741703	0.0370852	+	0.999312i	$0.488193\pi$
$984$	−5.45047	−0.173755
$985$	31.2638	0.996148
$986$	−35.0413	−1.11594
$987$	0	0
$988$	76.6110	2.43732
$989$	−15.5010	−0.492902
$990$	−26.2952	−0.835715
$991$	−16.1129	−0.511843	−0.255921	−	0.966698i	$-0.582379\pi$
$991$	−16.1129	−0.511843	−0.255921	+	0.966698i	$0.582379\pi$
$992$	−2.34693	−0.0745151
$993$	28.7281	0.911659
$994$	0	0
$995$	12.9378	0.410156
$996$	−26.2481	−0.831704
$997$	0.484528	0.0153452	0.00767258	−	0.999971i	$-0.497558\pi$
$997$	0.484528	0.0153452	0.00767258	+	0.999971i	$0.497558\pi$
$998$	56.1697	1.77802
$999$	0.748295	0.0236750

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bn.1.21	✓	24
7.6	odd	2		6027.2.a.bo.1.21	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6027.2.a.bn.1.21	✓	24	1.1	even	1	trivial
6027.2.a.bo.1.21	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)

\(f(q)\)	\(=\)	\(q+2.48810 q^{2} -1.00000 q^{3} +4.19062 q^{4} -2.36641 q^{5} -2.48810 q^{6} +5.45047 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.48810 q^{2} -1.00000 q^{3} +4.19062 q^{4} -2.36641 q^{5} -2.48810 q^{6} +5.45047 q^{8} +1.00000 q^{9} -5.88785 q^{10} +4.46600 q^{11} -4.19062 q^{12} +5.01637 q^{13} +2.36641 q^{15} +5.18004 q^{16} -4.88608 q^{17} +2.48810 q^{18} +3.64438 q^{19} -9.91672 q^{20} +11.1118 q^{22} -2.22001 q^{23} -5.45047 q^{24} +0.599893 q^{25} +12.4812 q^{26} -1.00000 q^{27} +2.88239 q^{29} +5.88785 q^{30} -1.18084 q^{31} +1.98751 q^{32} -4.46600 q^{33} -12.1570 q^{34} +4.19062 q^{36} -0.748295 q^{37} +9.06756 q^{38} -5.01637 q^{39} -12.8980 q^{40} +1.00000 q^{41} +6.98238 q^{43} +18.7153 q^{44} -2.36641 q^{45} -5.52359 q^{46} +7.64313 q^{47} -5.18004 q^{48} +1.49259 q^{50} +4.88608 q^{51} +21.0217 q^{52} +10.3267 q^{53} -2.48810 q^{54} -10.5684 q^{55} -3.64438 q^{57} +7.17166 q^{58} -8.70177 q^{59} +9.91672 q^{60} -8.35367 q^{61} -2.93804 q^{62} -5.41498 q^{64} -11.8708 q^{65} -11.1118 q^{66} -0.0922892 q^{67} -20.4757 q^{68} +2.22001 q^{69} +3.08552 q^{71} +5.45047 q^{72} +9.88365 q^{73} -1.86183 q^{74} -0.599893 q^{75} +15.2722 q^{76} -12.4812 q^{78} +7.87830 q^{79} -12.2581 q^{80} +1.00000 q^{81} +2.48810 q^{82} +6.26355 q^{83} +11.5625 q^{85} +17.3728 q^{86} -2.88239 q^{87} +24.3418 q^{88} +10.3142 q^{89} -5.88785 q^{90} -9.30321 q^{92} +1.18084 q^{93} +19.0168 q^{94} -8.62409 q^{95} -1.98751 q^{96} +4.64324 q^{97} +4.46600 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} - 24 q^{3} + 32 q^{4} - 4 q^{5} - 8 q^{6} + 24 q^{8} + 24 q^{9}+O(q^{10}) \) 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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