LMFDB - Embedded newform 1875.2.a.o.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1875,2,Mod(1,1875)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1875, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1875.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1875 = 3 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1875.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:	$14.9719503790$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.8.13366265625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 12x^{6} + 10x^{5} + 41x^{4} - 20x^{3} - 48x^{2} + 8x + 16 $ x^8 - x^7 - 12x^6 + 10x^5 + 41x^4 - 20x^3 - 48x^2 + 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$0.741379$ of defining polynomial
Character	$\chi$	$=$	1875.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.741379 q^{2} +1.00000 q^{3} -1.45036 q^{4} +0.741379 q^{6} +1.03586 q^{7} -2.55802 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.741379 q^{2} +1.00000 q^{3} -1.45036 q^{4} +0.741379 q^{6} +1.03586 q^{7} -2.55802 q^{8} +1.00000 q^{9} -0.513903 q^{11} -1.45036 q^{12} +3.54391 q^{13} +0.767968 q^{14} +1.00425 q^{16} -1.36691 q^{17} +0.741379 q^{18} +0.894573 q^{19} +1.03586 q^{21} -0.380997 q^{22} +5.45465 q^{23} -2.55802 q^{24} +2.62738 q^{26} +1.00000 q^{27} -1.50237 q^{28} -9.65038 q^{29} +10.4630 q^{31} +5.86057 q^{32} -0.513903 q^{33} -1.01340 q^{34} -1.45036 q^{36} -2.19473 q^{37} +0.663218 q^{38} +3.54391 q^{39} +3.12460 q^{41} +0.767968 q^{42} +10.2866 q^{43} +0.745343 q^{44} +4.04396 q^{46} +7.65509 q^{47} +1.00425 q^{48} -5.92699 q^{49} -1.36691 q^{51} -5.13993 q^{52} -10.5524 q^{53} +0.741379 q^{54} -2.64976 q^{56} +0.894573 q^{57} -7.15459 q^{58} +11.9238 q^{59} +7.85170 q^{61} +7.75704 q^{62} +1.03586 q^{63} +2.33641 q^{64} -0.380997 q^{66} +8.80731 q^{67} +1.98251 q^{68} +5.45465 q^{69} +5.00948 q^{71} -2.55802 q^{72} +5.82505 q^{73} -1.62713 q^{74} -1.29745 q^{76} -0.532334 q^{77} +2.62738 q^{78} -6.74036 q^{79} +1.00000 q^{81} +2.31651 q^{82} -7.99598 q^{83} -1.50237 q^{84} +7.62626 q^{86} -9.65038 q^{87} +1.31458 q^{88} +12.9917 q^{89} +3.67101 q^{91} -7.91118 q^{92} +10.4630 q^{93} +5.67533 q^{94} +5.86057 q^{96} -7.27747 q^{97} -4.39414 q^{98} -0.513903 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 8 q^{3} + 9 q^{4} + q^{6} + 12 q^{7} + 3 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + q^2 + 8 * q^3 + 9 * q^4 + q^6 + 12 * q^7 + 3 * q^8 + 8 * q^9	$ 8 q + q^{2} + 8 q^{3} + 9 q^{4} + q^{6} + 12 q^{7} + 3 q^{8} + 8 q^{9} + 12 q^{11} + 9 q^{12} + 14 q^{13} + 16 q^{14} + 15 q^{16} - q^{17} + q^{18} + 16 q^{19} + 12 q^{21} + 18 q^{22} - 4 q^{23} + 3 q^{24} - 34 q^{26} + 8 q^{27} - 21 q^{28} + 2 q^{29} + 13 q^{31} - 18 q^{32} + 12 q^{33} - 37 q^{34} + 9 q^{36} - 8 q^{37} - 24 q^{38} + 14 q^{39} - 12 q^{41} + 16 q^{42} + 20 q^{43} + 47 q^{44} + 33 q^{46} - 15 q^{47} + 15 q^{48} + 30 q^{49} - q^{51} - q^{52} - 4 q^{53} + q^{54} + 60 q^{56} + 16 q^{57} + 2 q^{58} + 14 q^{59} + 10 q^{61} + 4 q^{62} + 12 q^{63} + 41 q^{64} + 18 q^{66} + 19 q^{67} - 33 q^{68} - 4 q^{69} + 21 q^{71} + 3 q^{72} - 19 q^{73} - 9 q^{74} - q^{76} - 11 q^{77} - 34 q^{78} + 10 q^{79} + 8 q^{81} + 24 q^{82} - 27 q^{83} - 21 q^{84} + 42 q^{86} + 2 q^{87} + 53 q^{88} - 9 q^{89} - 12 q^{91} - 63 q^{92} + 13 q^{93} + 14 q^{94} - 18 q^{96} + 24 q^{97} - 24 q^{98} + 12 q^{99}+O(q^{100}) $ 8 * q + q^2 + 8 * q^3 + 9 * q^4 + q^6 + 12 * q^7 + 3 * q^8 + 8 * q^9 + 12 * q^11 + 9 * q^12 + 14 * q^13 + 16 * q^14 + 15 * q^16 - q^17 + q^18 + 16 * q^19 + 12 * q^21 + 18 * q^22 - 4 * q^23 + 3 * q^24 - 34 * q^26 + 8 * q^27 - 21 * q^28 + 2 * q^29 + 13 * q^31 - 18 * q^32 + 12 * q^33 - 37 * q^34 + 9 * q^36 - 8 * q^37 - 24 * q^38 + 14 * q^39 - 12 * q^41 + 16 * q^42 + 20 * q^43 + 47 * q^44 + 33 * q^46 - 15 * q^47 + 15 * q^48 + 30 * q^49 - q^51 - q^52 - 4 * q^53 + q^54 + 60 * q^56 + 16 * q^57 + 2 * q^58 + 14 * q^59 + 10 * q^61 + 4 * q^62 + 12 * q^63 + 41 * q^64 + 18 * q^66 + 19 * q^67 - 33 * q^68 - 4 * q^69 + 21 * q^71 + 3 * q^72 - 19 * q^73 - 9 * q^74 - q^76 - 11 * q^77 - 34 * q^78 + 10 * q^79 + 8 * q^81 + 24 * q^82 - 27 * q^83 - 21 * q^84 + 42 * q^86 + 2 * q^87 + 53 * q^88 - 9 * q^89 - 12 * q^91 - 63 * q^92 + 13 * q^93 + 14 * q^94 - 18 * q^96 + 24 * q^97 - 24 * q^98 + 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 $

$2$	0.741379	0.524234	0.262117	−	0.965036i	$-0.415579\pi$
$2$	0.741379	0.524234	0.262117	+	0.965036i	$0.415579\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.45036	−0.725178
$5$	0	0
$5$	0	0
$6$	0.741379	0.302667
$7$	1.03586	0.391520	0.195760	−	0.980652i	$-0.437283\pi$
$7$	1.03586	0.391520	0.195760	+	0.980652i	$0.437283\pi$
$8$	−2.55802	−0.904398
$9$	1.00000	0.333333
$10$	0	0
$11$	−0.513903	−0.154948	−0.0774738	−	0.996994i	$-0.524685\pi$
$11$	−0.513903	−0.154948	−0.0774738	+	0.996994i	$0.524685\pi$
$12$	−1.45036	−0.418682
$13$	3.54391	0.982904	0.491452	−	0.870905i	$-0.336466\pi$
$13$	3.54391	0.982904	0.491452	+	0.870905i	$0.336466\pi$
$14$	0.767968	0.205248
$15$	0	0
$16$	1.00425	0.251062
$17$	−1.36691	−0.331525	−0.165762	−	0.986166i	$-0.553008\pi$
$17$	−1.36691	−0.331525	−0.165762	+	0.986166i	$0.553008\pi$
$18$	0.741379	0.174745
$19$	0.894573	0.205229	0.102615	−	0.994721i	$-0.467279\pi$
$19$	0.894573	0.205229	0.102615	+	0.994721i	$0.467279\pi$
$20$	0	0
$21$	1.03586	0.226044
$22$	−0.380997	−0.0812289
$23$	5.45465	1.13737	0.568686	−	0.822554i	$-0.307452\pi$
$23$	5.45465	1.13737	0.568686	+	0.822554i	$0.307452\pi$
$24$	−2.55802	−0.522154
$25$	0	0
$26$	2.62738	0.515272
$27$	1.00000	0.192450
$28$	−1.50237	−0.283922
$29$	−9.65038	−1.79203	−0.896015	−	0.444024i	$-0.853550\pi$
$29$	−9.65038	−1.79203	−0.896015	+	0.444024i	$0.853550\pi$
$30$	0	0
$31$	10.4630	1.87921	0.939604	−	0.342265i	$-0.111194\pi$
$31$	10.4630	1.87921	0.939604	+	0.342265i	$0.111194\pi$
$32$	5.86057	1.03601
$33$	−0.513903	−0.0894591
$34$	−1.01340	−0.173797
$35$	0	0
$36$	−1.45036	−0.241726
$37$	−2.19473	−0.360812	−0.180406	−	0.983592i	$-0.557741\pi$
$37$	−2.19473	−0.360812	−0.180406	+	0.983592i	$0.557741\pi$
$38$	0.663218	0.107588
$39$	3.54391	0.567480
$40$	0	0
$41$	3.12460	0.487980	0.243990	−	0.969778i	$-0.421544\pi$
$41$	3.12460	0.487980	0.243990	+	0.969778i	$0.421544\pi$
$42$	0.767968	0.118500
$43$	10.2866	1.56869	0.784345	−	0.620325i	$-0.212999\pi$
$43$	10.2866	1.56869	0.784345	+	0.620325i	$0.212999\pi$
$44$	0.745343	0.112365
$45$	0	0
$46$	4.04396	0.596250
$47$	7.65509	1.11661	0.558305	−	0.829636i	$-0.311452\pi$
$47$	7.65509	1.11661	0.558305	+	0.829636i	$0.311452\pi$
$48$	1.00425	0.144951
$49$	−5.92699	−0.846712
$50$	0	0
$51$	−1.36691	−0.191406
$52$	−5.13993	−0.712780
$53$	−10.5524	−1.44948	−0.724742	−	0.689020i	$-0.758041\pi$
$53$	−10.5524	−1.44948	−0.724742	+	0.689020i	$0.758041\pi$
$54$	0.741379	0.100889
$55$	0	0
$56$	−2.64976	−0.354090
$57$	0.894573	0.118489
$58$	−7.15459	−0.939443
$59$	11.9238	1.55234	0.776172	−	0.630521i	$-0.217159\pi$
$59$	11.9238	1.55234	0.776172	+	0.630521i	$0.217159\pi$
$60$	0	0
$61$	7.85170	1.00531	0.502653	−	0.864488i	$-0.332357\pi$
$61$	7.85170	1.00531	0.502653	+	0.864488i	$0.332357\pi$
$62$	7.75704	0.985145
$63$	1.03586	0.130507
$64$	2.33641	0.292052
$65$	0	0
$66$	−0.380997	−0.0468975
$67$	8.80731	1.07598	0.537992	−	0.842950i	$-0.319183\pi$
$67$	8.80731	1.07598	0.537992	+	0.842950i	$0.319183\pi$
$68$	1.98251	0.240414
$69$	5.45465	0.656662
$70$	0	0
$71$	5.00948	0.594516	0.297258	−	0.954797i	$-0.403928\pi$
$71$	5.00948	0.594516	0.297258	+	0.954797i	$0.403928\pi$
$72$	−2.55802	−0.301466
$73$	5.82505	0.681770	0.340885	−	0.940105i	$-0.389273\pi$
$73$	5.82505	0.681770	0.340885	+	0.940105i	$0.389273\pi$
$74$	−1.62713	−0.189150
$75$	0	0
$76$	−1.29745	−0.148828
$77$	−0.532334	−0.0606651
$78$	2.62738	0.297492
$79$	−6.74036	−0.758350	−0.379175	−	0.925325i	$-0.623792\pi$
$79$	−6.74036	−0.758350	−0.379175	+	0.925325i	$0.623792\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	2.31651	0.255816
$83$	−7.99598	−0.877673	−0.438837	−	0.898567i	$-0.644609\pi$
$83$	−7.99598	−0.877673	−0.438837	+	0.898567i	$0.644609\pi$
$84$	−1.50237	−0.163922
$85$	0	0
$86$	7.62626	0.822361
$87$	−9.65038	−1.03463
$88$	1.31458	0.140134
$89$	12.9917	1.37711	0.688557	−	0.725182i	$-0.258244\pi$
$89$	12.9917	1.37711	0.688557	+	0.725182i	$0.258244\pi$
$90$	0	0
$91$	3.67101	0.384826
$92$	−7.91118	−0.824798
$93$	10.4630	1.08496
$94$	5.67533	0.585365
$95$	0	0
$96$	5.86057	0.598142
$97$	−7.27747	−0.738916	−0.369458	−	0.929248i	$-0.620457\pi$
$97$	−7.27747	−0.738916	−0.369458	+	0.929248i	$0.620457\pi$
$98$	−4.39414	−0.443876
$99$	−0.513903	−0.0516492
$100$	0	0
$101$	11.5323	1.14751	0.573753	−	0.819028i	$-0.305487\pi$
$101$	11.5323	1.14751	0.573753	+	0.819028i	$0.305487\pi$
$102$	−1.01340	−0.100341
$103$	−1.95586	−0.192717	−0.0963585	−	0.995347i	$-0.530720\pi$
$103$	−1.95586	−0.192717	−0.0963585	+	0.995347i	$0.530720\pi$
$104$	−9.06540	−0.888936
$105$	0	0
$106$	−7.82333	−0.759869
$107$	−15.2874	−1.47789	−0.738945	−	0.673766i	$-0.764676\pi$
$107$	−15.2874	−1.47789	−0.738945	+	0.673766i	$0.764676\pi$
$108$	−1.45036	−0.139561
$109$	−0.346596	−0.0331979	−0.0165989	−	0.999862i	$-0.505284\pi$
$109$	−0.346596	−0.0331979	−0.0165989	+	0.999862i	$0.505284\pi$
$110$	0	0
$111$	−2.19473	−0.208315
$112$	1.04026	0.0982958
$113$	−3.91425	−0.368222	−0.184111	−	0.982905i	$-0.558941\pi$
$113$	−3.91425	−0.368222	−0.184111	+	0.982905i	$0.558941\pi$
$114$	0.663218	0.0621161
$115$	0	0
$116$	13.9965	1.29954
$117$	3.54391	0.327635
$118$	8.84004	0.813792
$119$	−1.41593	−0.129798
$120$	0	0
$121$	−10.7359	−0.975991
$122$	5.82108	0.527016
$123$	3.12460	0.281735
$124$	−15.1751	−1.36276
$125$	0	0
$126$	0.767968	0.0684160
$127$	−6.02350	−0.534499	−0.267249	−	0.963627i	$-0.586115\pi$
$127$	−6.02350	−0.534499	−0.267249	+	0.963627i	$0.586115\pi$
$128$	−9.98898	−0.882910
$129$	10.2866	0.905683
$130$	0	0
$131$	1.26444	0.110474	0.0552372	−	0.998473i	$-0.482408\pi$
$131$	1.26444	0.110474	0.0552372	+	0.998473i	$0.482408\pi$
$132$	0.745343	0.0648738
$133$	0.926656	0.0803513
$134$	6.52956	0.564068
$135$	0	0
$136$	3.49659	0.299830
$137$	1.85695	0.158650	0.0793249	−	0.996849i	$-0.474724\pi$
$137$	1.85695	0.158650	0.0793249	+	0.996849i	$0.474724\pi$
$138$	4.04396	0.344245
$139$	17.4734	1.48207	0.741037	−	0.671464i	$-0.234334\pi$
$139$	17.4734	1.48207	0.741037	+	0.671464i	$0.234334\pi$
$140$	0	0
$141$	7.65509	0.644675
$142$	3.71392	0.311666
$143$	−1.82123	−0.152299
$144$	1.00425	0.0836873
$145$	0	0
$146$	4.31857	0.357407
$147$	−5.92699	−0.488850
$148$	3.18314	0.261653
$149$	20.5555	1.68397	0.841985	−	0.539502i	$-0.181387\pi$
$149$	20.5555	1.68397	0.841985	+	0.539502i	$0.181387\pi$
$150$	0	0
$151$	2.86944	0.233512	0.116756	−	0.993161i	$-0.462750\pi$
$151$	2.86944	0.233512	0.116756	+	0.993161i	$0.462750\pi$
$152$	−2.28834	−0.185609
$153$	−1.36691	−0.110508
$154$	−0.394661	−0.0318027
$155$	0	0
$156$	−5.13993	−0.411524
$157$	−14.3887	−1.14834	−0.574172	−	0.818735i	$-0.694676\pi$
$157$	−14.3887	−1.14834	−0.574172	+	0.818735i	$0.694676\pi$
$158$	−4.99716	−0.397553
$159$	−10.5524	−0.836860
$160$	0	0
$161$	5.65027	0.445304
$162$	0.741379	0.0582483
$163$	−7.90445	−0.619125	−0.309562	−	0.950879i	$-0.600183\pi$
$163$	−7.90445	−0.619125	−0.309562	+	0.950879i	$0.600183\pi$
$164$	−4.53178	−0.353873
$165$	0	0
$166$	−5.92806	−0.460106
$167$	−18.9057	−1.46297	−0.731483	−	0.681859i	$-0.761172\pi$
$167$	−18.9057	−1.46297	−0.731483	+	0.681859i	$0.761172\pi$
$168$	−2.64976	−0.204434
$169$	−0.440707	−0.0339006
$170$	0	0
$171$	0.894573	0.0684097
$172$	−14.9192	−1.13758
$173$	−4.41184	−0.335426	−0.167713	−	0.985836i	$-0.553638\pi$
$173$	−4.41184	−0.335426	−0.167713	+	0.985836i	$0.553638\pi$
$174$	−7.15459	−0.542388
$175$	0	0
$176$	−0.516086	−0.0389015
$177$	11.9238	0.896246
$178$	9.63175	0.721931
$179$	−11.6515	−0.870876	−0.435438	−	0.900219i	$-0.643407\pi$
$179$	−11.6515	−0.870876	−0.435438	+	0.900219i	$0.643407\pi$
$180$	0	0
$181$	15.5625	1.15675	0.578375	−	0.815771i	$-0.303687\pi$
$181$	15.5625	1.15675	0.578375	+	0.815771i	$0.303687\pi$
$182$	2.72161	0.201739
$183$	7.85170	0.580414
$184$	−13.9531	−1.02864
$185$	0	0
$186$	7.75704	0.568774
$187$	0.702460	0.0513690
$188$	−11.1026	−0.809741
$189$	1.03586	0.0753480
$190$	0	0
$191$	−21.4213	−1.54999	−0.774996	−	0.631966i	$-0.782248\pi$
$191$	−21.4213	−1.54999	−0.774996	+	0.631966i	$0.782248\pi$
$192$	2.33641	0.168616
$193$	−3.32583	−0.239398	−0.119699	−	0.992810i	$-0.538193\pi$
$193$	−3.32583	−0.239398	−0.119699	+	0.992810i	$0.538193\pi$
$194$	−5.39537	−0.387365
$195$	0	0
$196$	8.59624	0.614017
$197$	14.8102	1.05518	0.527591	−	0.849498i	$-0.323095\pi$
$197$	14.8102	1.05518	0.527591	+	0.849498i	$0.323095\pi$
$198$	−0.380997	−0.0270763
$199$	−15.3279	−1.08657	−0.543285	−	0.839549i	$-0.682820\pi$
$199$	−15.3279	−1.08657	−0.543285	+	0.839549i	$0.682820\pi$
$200$	0	0
$201$	8.80731	0.621220
$202$	8.54981	0.601562
$203$	−9.99648	−0.701615
$204$	1.98251	0.138803
$205$	0	0
$206$	−1.45004	−0.101029
$207$	5.45465	0.379124
$208$	3.55896	0.246770
$209$	−0.459724	−0.0317998
$210$	0	0
$211$	−0.377050	−0.0259572	−0.0129786	−	0.999916i	$-0.504131\pi$
$211$	−0.377050	−0.0259572	−0.0129786	+	0.999916i	$0.504131\pi$
$212$	15.3047	1.05113
$213$	5.00948	0.343244
$214$	−11.3338	−0.774761
$215$	0	0
$216$	−2.55802	−0.174051
$217$	10.8382	0.735747
$218$	−0.256959	−0.0174035
$219$	5.82505	0.393620
$220$	0	0
$221$	−4.84421	−0.325857
$222$	−1.62713	−0.109206
$223$	0.270144	0.0180902	0.00904509	−	0.999959i	$-0.497121\pi$
$223$	0.270144	0.0180902	0.00904509	+	0.999959i	$0.497121\pi$
$224$	6.07076	0.405620
$225$	0	0
$226$	−2.90194	−0.193034
$227$	7.14071	0.473946	0.236973	−	0.971516i	$-0.423845\pi$
$227$	7.14071	0.473946	0.236973	+	0.971516i	$0.423845\pi$
$228$	−1.29745	−0.0859258
$229$	24.8881	1.64465	0.822325	−	0.569018i	$-0.192677\pi$
$229$	24.8881	1.64465	0.822325	+	0.569018i	$0.192677\pi$
$230$	0	0
$231$	−0.532334	−0.0350250
$232$	24.6859	1.62071
$233$	−16.9547	−1.11074	−0.555368	−	0.831604i	$-0.687423\pi$
$233$	−16.9547	−1.11074	−0.555368	+	0.831604i	$0.687423\pi$
$234$	2.62738	0.171757
$235$	0	0
$236$	−17.2937	−1.12573
$237$	−6.74036	−0.437833
$238$	−1.04974	−0.0680448
$239$	−4.12456	−0.266796	−0.133398	−	0.991063i	$-0.542589\pi$
$239$	−4.12456	−0.266796	−0.133398	+	0.991063i	$0.542589\pi$
$240$	0	0
$241$	−5.94241	−0.382784	−0.191392	−	0.981514i	$-0.561300\pi$
$241$	−5.94241	−0.382784	−0.191392	+	0.981514i	$0.561300\pi$
$242$	−7.95938	−0.511648
$243$	1.00000	0.0641500
$244$	−11.3878	−0.729027
$245$	0	0
$246$	2.31651	0.147695
$247$	3.17029	0.201721
$248$	−26.7646	−1.69955
$249$	−7.99598	−0.506725
$250$	0	0
$251$	−18.1052	−1.14279	−0.571394	−	0.820676i	$-0.693597\pi$
$251$	−18.1052	−1.14279	−0.571394	+	0.820676i	$0.693597\pi$
$252$	−1.50237	−0.0946406
$253$	−2.80316	−0.176233
$254$	−4.46570	−0.280203
$255$	0	0
$256$	−12.0784	−0.754903
$257$	−23.9627	−1.49475	−0.747375	−	0.664402i	$-0.768686\pi$
$257$	−23.9627	−1.49475	−0.747375	+	0.664402i	$0.768686\pi$
$258$	7.62626	0.474790
$259$	−2.27344	−0.141265
$260$	0	0
$261$	−9.65038	−0.597343
$262$	0.937428	0.0579145
$263$	−13.2525	−0.817184	−0.408592	−	0.912717i	$-0.633980\pi$
$263$	−13.2525	−0.817184	−0.408592	+	0.912717i	$0.633980\pi$
$264$	1.31458	0.0809066
$265$	0	0
$266$	0.687004	0.0421229
$267$	12.9917	0.795077
$268$	−12.7737	−0.780281
$269$	−0.728075	−0.0443915	−0.0221958	−	0.999754i	$-0.507066\pi$
$269$	−0.728075	−0.0443915	−0.0221958	+	0.999754i	$0.507066\pi$
$270$	0	0
$271$	−16.9085	−1.02712	−0.513558	−	0.858055i	$-0.671673\pi$
$271$	−16.9085	−1.02712	−0.513558	+	0.858055i	$0.671673\pi$
$272$	−1.37272	−0.0832332
$273$	3.67101	0.222179
$274$	1.37670	0.0831697
$275$	0	0
$276$	−7.91118	−0.476197
$277$	10.0386	0.603160	0.301580	−	0.953441i	$-0.402486\pi$
$277$	10.0386	0.603160	0.301580	+	0.953441i	$0.402486\pi$
$278$	12.9544	0.776954
$279$	10.4630	0.626402
$280$	0	0
$281$	20.5358	1.22507	0.612533	−	0.790445i	$-0.290151\pi$
$281$	20.5358	1.22507	0.612533	+	0.790445i	$0.290151\pi$
$282$	5.67533	0.337961
$283$	21.2483	1.26308	0.631541	−	0.775343i	$-0.282423\pi$
$283$	21.2483	1.26308	0.631541	+	0.775343i	$0.282423\pi$
$284$	−7.26553	−0.431130
$285$	0	0
$286$	−1.35022	−0.0798402
$287$	3.23666	0.191054
$288$	5.86057	0.345338
$289$	−15.1316	−0.890091
$290$	0	0
$291$	−7.27747	−0.426613
$292$	−8.44840	−0.494405
$293$	−29.8828	−1.74577	−0.872885	−	0.487927i	$-0.837753\pi$
$293$	−29.8828	−1.74577	−0.872885	+	0.487927i	$0.837753\pi$
$294$	−4.39414	−0.256272
$295$	0	0
$296$	5.61417	0.326317
$297$	−0.513903	−0.0298197
$298$	15.2394	0.882794
$299$	19.3308	1.11793
$300$	0	0
$301$	10.6555	0.614173
$302$	2.12735	0.122415
$303$	11.5323	0.662513
$304$	0.898374	0.0515253
$305$	0	0
$306$	−1.01340	−0.0579322
$307$	−0.531050	−0.0303086	−0.0151543	−	0.999885i	$-0.504824\pi$
$307$	−0.531050	−0.0303086	−0.0151543	+	0.999885i	$0.504824\pi$
$308$	0.772074	0.0439930
$309$	−1.95586	−0.111265
$310$	0	0
$311$	−18.2322	−1.03385	−0.516927	−	0.856030i	$-0.672924\pi$
$311$	−18.2322	−1.03385	−0.516927	+	0.856030i	$0.672924\pi$
$312$	−9.06540	−0.513227
$313$	29.3523	1.65909	0.829546	−	0.558439i	$-0.188599\pi$
$313$	29.3523	1.65909	0.829546	+	0.558439i	$0.188599\pi$
$314$	−10.6675	−0.602001
$315$	0	0
$316$	9.77593	0.549939
$317$	−32.8989	−1.84778	−0.923892	−	0.382653i	$-0.875011\pi$
$317$	−32.8989	−1.84778	−0.923892	+	0.382653i	$0.875011\pi$
$318$	−7.82333	−0.438711
$319$	4.95936	0.277671
$320$	0	0
$321$	−15.2874	−0.853260
$322$	4.18899	0.233444
$323$	−1.22280	−0.0680385
$324$	−1.45036	−0.0805754
$325$	0	0
$326$	−5.86020	−0.324566
$327$	−0.346596	−0.0191668
$328$	−7.99279	−0.441328
$329$	7.92963	0.437175
$330$	0	0
$331$	−3.75461	−0.206372	−0.103186	−	0.994662i	$-0.532904\pi$
$331$	−3.75461	−0.206372	−0.103186	+	0.994662i	$0.532904\pi$
$332$	11.5970	0.636470
$333$	−2.19473	−0.120271
$334$	−14.0163	−0.766937
$335$	0	0
$336$	1.04026	0.0567511
$337$	−14.3206	−0.780095	−0.390047	−	0.920795i	$-0.627541\pi$
$337$	−14.3206	−0.780095	−0.390047	+	0.920795i	$0.627541\pi$
$338$	−0.326731	−0.0177718
$339$	−3.91425	−0.212593
$340$	0	0
$341$	−5.37696	−0.291179
$342$	0.663218	0.0358627
$343$	−13.3906	−0.723024
$344$	−26.3133	−1.41872
$345$	0	0
$346$	−3.27085	−0.175842
$347$	5.91568	0.317571	0.158785	−	0.987313i	$-0.449242\pi$
$347$	5.91568	0.317571	0.158785	+	0.987313i	$0.449242\pi$
$348$	13.9965	0.750290
$349$	26.2468	1.40496	0.702479	−	0.711705i	$-0.252077\pi$
$349$	26.2468	1.40496	0.702479	+	0.711705i	$0.252077\pi$
$350$	0	0
$351$	3.54391	0.189160
$352$	−3.01177	−0.160528
$353$	14.3082	0.761546	0.380773	−	0.924669i	$-0.375658\pi$
$353$	14.3082	0.761546	0.380773	+	0.924669i	$0.375658\pi$
$354$	8.84004	0.469843
$355$	0	0
$356$	−18.8426	−0.998653
$357$	−1.41593	−0.0749392
$358$	−8.63820	−0.456543
$359$	36.3183	1.91681	0.958404	−	0.285416i	$-0.0921318\pi$
$359$	36.3183	1.91681	0.958404	+	0.285416i	$0.0921318\pi$
$360$	0	0
$361$	−18.1997	−0.957881
$362$	11.5377	0.606408
$363$	−10.7359	−0.563489
$364$	−5.32427	−0.279068
$365$	0	0
$366$	5.82108	0.304273
$367$	27.3604	1.42820	0.714100	−	0.700043i	$-0.246836\pi$
$367$	27.3604	1.42820	0.714100	+	0.700043i	$0.246836\pi$
$368$	5.47782	0.285551
$369$	3.12460	0.162660
$370$	0	0
$371$	−10.9309	−0.567502
$372$	−15.1751	−0.786790
$373$	−30.3763	−1.57283	−0.786413	−	0.617702i	$-0.788064\pi$
$373$	−30.3763	−1.57283	−0.786413	+	0.617702i	$0.788064\pi$
$374$	0.520789	0.0269294
$375$	0	0
$376$	−19.5819	−1.00986
$377$	−34.2001	−1.76139
$378$	0.767968	0.0395000
$379$	27.5797	1.41668	0.708338	−	0.705873i	$-0.249445\pi$
$379$	27.5797	1.41668	0.708338	+	0.705873i	$0.249445\pi$
$380$	0	0
$381$	−6.02350	−0.308593
$382$	−15.8813	−0.812559
$383$	14.6341	0.747765	0.373883	−	0.927476i	$-0.378026\pi$
$383$	14.6341	0.747765	0.373883	+	0.927476i	$0.378026\pi$
$384$	−9.98898	−0.509748
$385$	0	0
$386$	−2.46570	−0.125501
$387$	10.2866	0.522896
$388$	10.5549	0.535846
$389$	−22.0844	−1.11972	−0.559862	−	0.828586i	$-0.689146\pi$
$389$	−22.0844	−1.11972	−0.559862	+	0.828586i	$0.689146\pi$
$390$	0	0
$391$	−7.45602	−0.377067
$392$	15.1614	0.765765
$393$	1.26444	0.0637824
$394$	10.9800	0.553163
$395$	0	0
$396$	0.745343	0.0374549
$397$	10.3527	0.519589	0.259794	−	0.965664i	$-0.416345\pi$
$397$	10.3527	0.519589	0.259794	+	0.965664i	$0.416345\pi$
$398$	−11.3638	−0.569617
$399$	0.926656	0.0463908
$400$	0	0
$401$	−19.8832	−0.992919	−0.496460	−	0.868060i	$-0.665367\pi$
$401$	−19.8832	−0.992919	−0.496460	+	0.868060i	$0.665367\pi$
$402$	6.52956	0.325665
$403$	37.0799	1.84708
$404$	−16.7259	−0.832147
$405$	0	0
$406$	−7.41118	−0.367811
$407$	1.12788	0.0559069
$408$	3.49659	0.173107
$409$	−7.05843	−0.349017	−0.174509	−	0.984656i	$-0.555834\pi$
$409$	−7.05843	−0.349017	−0.174509	+	0.984656i	$0.555834\pi$
$410$	0	0
$411$	1.85695	0.0915966
$412$	2.83670	0.139754
$413$	12.3514	0.607773
$414$	4.04396	0.198750
$415$	0	0
$416$	20.7693	1.01830
$417$	17.4734	0.855676
$418$	−0.340830	−0.0166705
$419$	−9.67801	−0.472802	−0.236401	−	0.971656i	$-0.575968\pi$
$419$	−9.67801	−0.472802	−0.236401	+	0.971656i	$0.575968\pi$
$420$	0	0
$421$	4.30464	0.209795	0.104898	−	0.994483i	$-0.466548\pi$
$421$	4.30464	0.209795	0.104898	+	0.994483i	$0.466548\pi$
$422$	−0.279537	−0.0136076
$423$	7.65509	0.372203
$424$	26.9933	1.31091
$425$	0	0
$426$	3.71392	0.179940
$427$	8.13329	0.393597
$428$	22.1722	1.07173
$429$	−1.82123	−0.0879296
$430$	0	0
$431$	−5.53549	−0.266635	−0.133318	−	0.991073i	$-0.542563\pi$
$431$	−5.53549	−0.266635	−0.133318	+	0.991073i	$0.542563\pi$
$432$	1.00425	0.0483169
$433$	28.1770	1.35410	0.677051	−	0.735936i	$-0.263258\pi$
$433$	28.1770	1.35410	0.677051	+	0.735936i	$0.263258\pi$
$434$	8.03524	0.385704
$435$	0	0
$436$	0.502688	0.0240744
$437$	4.87958	0.233422
$438$	4.31857	0.206349
$439$	−10.5674	−0.504353	−0.252176	−	0.967681i	$-0.581146\pi$
$439$	−10.5674	−0.504353	−0.252176	+	0.967681i	$0.581146\pi$
$440$	0	0
$441$	−5.92699	−0.282237
$442$	−3.59140	−0.170825
$443$	−36.7964	−1.74825	−0.874126	−	0.485699i	$-0.838565\pi$
$443$	−36.7964	−1.74825	−0.874126	+	0.485699i	$0.838565\pi$
$444$	3.18314	0.151065
$445$	0	0
$446$	0.200279	0.00948350
$447$	20.5555	0.972240
$448$	2.42021	0.114344
$449$	26.9341	1.27110	0.635549	−	0.772060i	$-0.280774\pi$
$449$	26.9341	1.27110	0.635549	+	0.772060i	$0.280774\pi$
$450$	0	0
$451$	−1.60574	−0.0756114
$452$	5.67706	0.267026
$453$	2.86944	0.134818
$454$	5.29398	0.248459
$455$	0	0
$456$	−2.28834	−0.107161
$457$	24.6289	1.15209	0.576046	−	0.817417i	$-0.304595\pi$
$457$	24.6289	1.15209	0.576046	+	0.817417i	$0.304595\pi$
$458$	18.4515	0.862182
$459$	−1.36691	−0.0638019
$460$	0	0
$461$	24.6914	1.14999	0.574996	−	0.818156i	$-0.305004\pi$
$461$	24.6914	1.14999	0.574996	+	0.818156i	$0.305004\pi$
$462$	−0.394661	−0.0183613
$463$	−22.7190	−1.05584	−0.527921	−	0.849293i	$-0.677028\pi$
$463$	−22.7190	−1.05584	−0.527921	+	0.849293i	$0.677028\pi$
$464$	−9.69137	−0.449911
$465$	0	0
$466$	−12.5698	−0.582286
$467$	10.8747	0.503222	0.251611	−	0.967829i	$-0.419040\pi$
$467$	10.8747	0.503222	0.251611	+	0.967829i	$0.419040\pi$
$468$	−5.13993	−0.237593
$469$	9.12318	0.421269
$470$	0	0
$471$	−14.3887	−0.662996
$472$	−30.5013	−1.40394
$473$	−5.28631	−0.243065
$474$	−4.99716	−0.229527
$475$	0	0
$476$	2.05361	0.0941270
$477$	−10.5524	−0.483161
$478$	−3.05786	−0.139863
$479$	0.739002	0.0337659	0.0168829	−	0.999857i	$-0.494626\pi$
$479$	0.739002	0.0337659	0.0168829	+	0.999857i	$0.494626\pi$
$480$	0	0
$481$	−7.77793	−0.354643
$482$	−4.40558	−0.200669
$483$	5.65027	0.257096
$484$	15.5709	0.707768
$485$	0	0
$486$	0.741379	0.0336296
$487$	−29.1699	−1.32181	−0.660907	−	0.750468i	$-0.729828\pi$
$487$	−29.1699	−1.32181	−0.660907	+	0.750468i	$0.729828\pi$
$488$	−20.0848	−0.909197
$489$	−7.90445	−0.357452
$490$	0	0
$491$	−31.6811	−1.42975	−0.714875	−	0.699252i	$-0.753516\pi$
$491$	−31.6811	−1.42975	−0.714875	+	0.699252i	$0.753516\pi$
$492$	−4.53178	−0.204308
$493$	13.1912	0.594102
$494$	2.35038	0.105749
$495$	0	0
$496$	10.5074	0.471798
$497$	5.18914	0.232765
$498$	−5.92806	−0.265643
$499$	−8.89261	−0.398088	−0.199044	−	0.979991i	$-0.563784\pi$
$499$	−8.89261	−0.398088	−0.199044	+	0.979991i	$0.563784\pi$
$500$	0	0
$501$	−18.9057	−0.844644
$502$	−13.4228	−0.599088
$503$	−17.0282	−0.759248	−0.379624	−	0.925141i	$-0.623947\pi$
$503$	−17.0282	−0.759248	−0.379624	+	0.925141i	$0.623947\pi$
$504$	−2.64976	−0.118030
$505$	0	0
$506$	−2.07821	−0.0923875
$507$	−0.440707	−0.0195725
$508$	8.73622	0.387607
$509$	−18.6709	−0.827571	−0.413786	−	0.910374i	$-0.635794\pi$
$509$	−18.6709	−0.827571	−0.413786	+	0.910374i	$0.635794\pi$
$510$	0	0
$511$	6.03396	0.266927
$512$	11.0233	0.487164
$513$	0.894573	0.0394964
$514$	−17.7654	−0.783600
$515$	0	0
$516$	−14.9192	−0.656782
$517$	−3.93398	−0.173016
$518$	−1.68548	−0.0740559
$519$	−4.41184	−0.193658
$520$	0	0
$521$	4.44863	0.194898	0.0974489	−	0.995241i	$-0.468932\pi$
$521$	4.44863	0.194898	0.0974489	+	0.995241i	$0.468932\pi$
$522$	−7.15459	−0.313148
$523$	20.4791	0.895490	0.447745	−	0.894161i	$-0.352227\pi$
$523$	20.4791	0.895490	0.447745	+	0.894161i	$0.352227\pi$
$524$	−1.83389	−0.0801137
$525$	0	0
$526$	−9.82513	−0.428396
$527$	−14.3020	−0.623003
$528$	−0.516086	−0.0224598
$529$	6.75318	0.293616
$530$	0	0
$531$	11.9238	0.517448
$532$	−1.34398	−0.0582690
$533$	11.0733	0.479637
$534$	9.63175	0.416807
$535$	0	0
$536$	−22.5293	−0.973118
$537$	−11.6515	−0.502801
$538$	−0.539780	−0.0232716
$539$	3.04590	0.131196
$540$	0	0
$541$	19.4764	0.837355	0.418678	−	0.908135i	$-0.362494\pi$
$541$	19.4764	0.837355	0.418678	+	0.908135i	$0.362494\pi$
$542$	−12.5356	−0.538450
$543$	15.5625	0.667850
$544$	−8.01088	−0.343464
$545$	0	0
$546$	2.72161	0.116474
$547$	40.3751	1.72631	0.863157	−	0.504936i	$-0.168484\pi$
$547$	40.3751	1.72631	0.863157	+	0.504936i	$0.168484\pi$
$548$	−2.69324	−0.115049
$549$	7.85170	0.335102
$550$	0	0
$551$	−8.63297	−0.367777
$552$	−13.9531	−0.593884
$553$	−6.98210	−0.296909
$554$	7.44240	0.316197
$555$	0	0
$556$	−25.3427	−1.07477
$557$	−1.34777	−0.0571067	−0.0285534	−	0.999592i	$-0.509090\pi$
$557$	−1.34777	−0.0571067	−0.0285534	+	0.999592i	$0.509090\pi$
$558$	7.75704	0.328382
$559$	36.4547	1.54187
$560$	0	0
$561$	0.702460	0.0296579
$562$	15.2249	0.642222
$563$	−9.88833	−0.416744	−0.208372	−	0.978050i	$-0.566816\pi$
$563$	−9.88833	−0.416744	−0.208372	+	0.978050i	$0.566816\pi$
$564$	−11.1026	−0.467504
$565$	0	0
$566$	15.7531	0.662150
$567$	1.03586	0.0435022
$568$	−12.8144	−0.537679
$569$	9.70429	0.406825	0.203413	−	0.979093i	$-0.434797\pi$
$569$	9.70429	0.406825	0.203413	+	0.979093i	$0.434797\pi$
$570$	0	0
$571$	4.61768	0.193244	0.0966219	−	0.995321i	$-0.469196\pi$
$571$	4.61768	0.193244	0.0966219	+	0.995321i	$0.469196\pi$
$572$	2.64143	0.110444
$573$	−21.4213	−0.894888
$574$	2.39959	0.100157
$575$	0	0
$576$	2.33641	0.0973505
$577$	2.05700	0.0856338	0.0428169	−	0.999083i	$-0.486367\pi$
$577$	2.05700	0.0856338	0.0428169	+	0.999083i	$0.486367\pi$
$578$	−11.2182	−0.466616
$579$	−3.32583	−0.138217
$580$	0	0
$581$	−8.28275	−0.343626
$582$	−5.39537	−0.223645
$583$	5.42291	0.224594
$584$	−14.9006	−0.616592
$585$	0	0
$586$	−22.1545	−0.915192
$587$	−18.7955	−0.775774	−0.387887	−	0.921707i	$-0.626795\pi$
$587$	−18.7955	−0.775774	−0.387887	+	0.921707i	$0.626795\pi$
$588$	8.59624	0.354503
$589$	9.35990	0.385668
$590$	0	0
$591$	14.8102	0.609210
$592$	−2.20405	−0.0905861
$593$	23.8873	0.980934	0.490467	−	0.871460i	$-0.336826\pi$
$593$	23.8873	0.980934	0.490467	+	0.871460i	$0.336826\pi$
$594$	−0.380997	−0.0156325
$595$	0	0
$596$	−29.8128	−1.22118
$597$	−15.3279	−0.627331
$598$	14.3314	0.586056
$599$	−0.641179	−0.0261979	−0.0130989	−	0.999914i	$-0.504170\pi$
$599$	−0.641179	−0.0261979	−0.0130989	+	0.999914i	$0.504170\pi$
$600$	0	0
$601$	28.1316	1.14751	0.573755	−	0.819027i	$-0.305486\pi$
$601$	28.1316	1.14751	0.573755	+	0.819027i	$0.305486\pi$
$602$	7.89977	0.321971
$603$	8.80731	0.358661
$604$	−4.16172	−0.169338
$605$	0	0
$606$	8.54981	0.347312
$607$	0.0458025	0.00185907	0.000929533	−	1.00000i	$-0.499704\pi$
$607$	0.0458025	0.00185907	0.000929533		1.00000i	$0.499704\pi$
$608$	5.24271	0.212620
$609$	−9.99648	−0.405078
$610$	0	0
$611$	27.1289	1.09752
$612$	1.98251	0.0801382
$613$	−23.3986	−0.945062	−0.472531	−	0.881314i	$-0.656660\pi$
$613$	−23.3986	−0.945062	−0.472531	+	0.881314i	$0.656660\pi$
$614$	−0.393710	−0.0158888
$615$	0	0
$616$	1.36172	0.0548654
$617$	5.62099	0.226292	0.113146	−	0.993578i	$-0.463907\pi$
$617$	5.62099	0.226292	0.113146	+	0.993578i	$0.463907\pi$
$618$	−1.45004	−0.0583290
$619$	−9.38706	−0.377298	−0.188649	−	0.982045i	$-0.560411\pi$
$619$	−9.38706	−0.377298	−0.188649	+	0.982045i	$0.560411\pi$
$620$	0	0
$621$	5.45465	0.218887
$622$	−13.5170	−0.541981
$623$	13.4576	0.539167
$624$	3.55896	0.142473
$625$	0	0
$626$	21.7612	0.869753
$627$	−0.459724	−0.0183596
$628$	20.8687	0.832754
$629$	3.00000	0.119618
$630$	0	0
$631$	−0.494043	−0.0196675	−0.00983376	−	0.999952i	$-0.503130\pi$
$631$	−0.494043	−0.0196675	−0.00983376	+	0.999952i	$0.503130\pi$
$632$	17.2420	0.685850
$633$	−0.377050	−0.0149864
$634$	−24.3905	−0.968672
$635$	0	0
$636$	15.3047	0.606873
$637$	−21.0047	−0.832237
$638$	3.67677	0.145565
$639$	5.00948	0.198172
$640$	0	0
$641$	−29.9045	−1.18116	−0.590578	−	0.806981i	$-0.701100\pi$
$641$	−29.9045	−1.18116	−0.590578	+	0.806981i	$0.701100\pi$
$642$	−11.3338	−0.447308
$643$	−17.8273	−0.703039	−0.351519	−	0.936181i	$-0.614335\pi$
$643$	−17.8273	−0.703039	−0.351519	+	0.936181i	$0.614335\pi$
$644$	−8.19491	−0.322925
$645$	0	0
$646$	−0.906560	−0.0356681
$647$	−6.25123	−0.245761	−0.122881	−	0.992421i	$-0.539213\pi$
$647$	−6.25123	−0.245761	−0.122881	+	0.992421i	$0.539213\pi$
$648$	−2.55802	−0.100489
$649$	−6.12767	−0.240532
$650$	0	0
$651$	10.8382	0.424784
$652$	11.4643	0.448976
$653$	−3.40836	−0.133379	−0.0666897	−	0.997774i	$-0.521244\pi$
$653$	−3.40836	−0.133379	−0.0666897	+	0.997774i	$0.521244\pi$
$654$	−0.256959	−0.0100479
$655$	0	0
$656$	3.13787	0.122513
$657$	5.82505	0.227257
$658$	5.87886	0.229182
$659$	−8.85617	−0.344988	−0.172494	−	0.985011i	$-0.555182\pi$
$659$	−8.85617	−0.344988	−0.172494	+	0.985011i	$0.555182\pi$
$660$	0	0
$661$	−16.5504	−0.643735	−0.321867	−	0.946785i	$-0.604311\pi$
$661$	−16.5504	−0.643735	−0.321867	+	0.946785i	$0.604311\pi$
$662$	−2.78359	−0.108187
$663$	−4.84421	−0.188133
$664$	20.4539	0.793766
$665$	0	0
$666$	−1.62713	−0.0630499
$667$	−52.6394	−2.03821
$668$	27.4200	1.06091
$669$	0.270144	0.0104444
$670$	0	0
$671$	−4.03501	−0.155770
$672$	6.07076	0.234185
$673$	−50.3337	−1.94022	−0.970110	−	0.242665i	$-0.921979\pi$
$673$	−50.3337	−1.94022	−0.970110	+	0.242665i	$0.921979\pi$
$674$	−10.6170	−0.408952
$675$	0	0
$676$	0.639183	0.0245840
$677$	−0.624178	−0.0239891	−0.0119946	−	0.999928i	$-0.503818\pi$
$677$	−0.624178	−0.0239891	−0.0119946	+	0.999928i	$0.503818\pi$
$678$	−2.90194	−0.111448
$679$	−7.53847	−0.289300
$680$	0	0
$681$	7.14071	0.273633
$682$	−3.98637	−0.152646
$683$	−41.3608	−1.58263	−0.791313	−	0.611411i	$-0.790602\pi$
$683$	−41.3608	−1.58263	−0.791313	+	0.611411i	$0.790602\pi$
$684$	−1.29745	−0.0496093
$685$	0	0
$686$	−9.92751	−0.379034
$687$	24.8881	0.949539
$688$	10.3303	0.393838
$689$	−37.3968	−1.42470
$690$	0	0
$691$	−40.0489	−1.52353	−0.761767	−	0.647851i	$-0.775668\pi$
$691$	−40.0489	−1.52353	−0.761767	+	0.647851i	$0.775668\pi$
$692$	6.39874	0.243244
$693$	−0.532334	−0.0202217
$694$	4.38577	0.166481
$695$	0	0
$696$	24.6859	0.935716
$697$	−4.27105	−0.161777
$698$	19.4588	0.736527
$699$	−16.9547	−0.641284
$700$	0	0
$701$	39.8261	1.50421	0.752106	−	0.659043i	$-0.229038\pi$
$701$	39.8261	1.50421	0.752106	+	0.659043i	$0.229038\pi$
$702$	2.62738	0.0991641
$703$	−1.96335	−0.0740491
$704$	−1.20069	−0.0452527
$705$	0	0
$706$	10.6078	0.399229
$707$	11.9459	0.449272
$708$	−17.2937	−0.649938
$709$	25.1649	0.945087	0.472543	−	0.881307i	$-0.343336\pi$
$709$	25.1649	0.945087	0.472543	+	0.881307i	$0.343336\pi$
$710$	0	0
$711$	−6.74036	−0.252783
$712$	−33.2330	−1.24546
$713$	57.0719	2.13736
$714$	−1.04974	−0.0392857
$715$	0	0
$716$	16.8989	0.631541
$717$	−4.12456	−0.154034
$718$	26.9256	1.00486
$719$	19.1076	0.712593	0.356297	−	0.934373i	$-0.384039\pi$
$719$	19.1076	0.712593	0.356297	+	0.934373i	$0.384039\pi$
$720$	0	0
$721$	−2.02601	−0.0754525
$722$	−13.4929	−0.502154
$723$	−5.94241	−0.221001
$724$	−22.5711	−0.838850
$725$	0	0
$726$	−7.95938	−0.295400
$727$	22.4025	0.830862	0.415431	−	0.909625i	$-0.363631\pi$
$727$	22.4025	0.830862	0.415431	+	0.909625i	$0.363631\pi$
$728$	−9.39052	−0.348036
$729$	1.00000	0.0370370
$730$	0	0
$731$	−14.0608	−0.520059
$732$	−11.3878	−0.420904
$733$	−45.4058	−1.67710	−0.838551	−	0.544823i	$-0.816597\pi$
$733$	−45.4058	−1.67710	−0.838551	+	0.544823i	$0.816597\pi$
$734$	20.2844	0.748712
$735$	0	0
$736$	31.9674	1.17833
$737$	−4.52611	−0.166721
$738$	2.31651	0.0852720
$739$	41.4109	1.52332	0.761662	−	0.647974i	$-0.224384\pi$
$739$	41.4109	1.52332	0.761662	+	0.647974i	$0.224384\pi$
$740$	0	0
$741$	3.17029	0.116463
$742$	−8.10391	−0.297504
$743$	−12.1759	−0.446689	−0.223344	−	0.974740i	$-0.571697\pi$
$743$	−12.1759	−0.446689	−0.223344	+	0.974740i	$0.571697\pi$
$744$	−26.7646	−0.981236
$745$	0	0
$746$	−22.5204	−0.824529
$747$	−7.99598	−0.292558
$748$	−1.01882	−0.0372517
$749$	−15.8357	−0.578623
$750$	0	0
$751$	−31.1833	−1.13789	−0.568947	−	0.822374i	$-0.692649\pi$
$751$	−31.1833	−1.13789	−0.568947	+	0.822374i	$0.692649\pi$
$752$	7.68761	0.280338
$753$	−18.1052	−0.659789
$754$	−25.3552	−0.923382
$755$	0	0
$756$	−1.50237	−0.0546408
$757$	−25.8685	−0.940207	−0.470104	−	0.882611i	$-0.655783\pi$
$757$	−25.8685	−0.940207	−0.470104	+	0.882611i	$0.655783\pi$
$758$	20.4471	0.742670
$759$	−2.80316	−0.101748
$760$	0	0
$761$	31.2246	1.13189	0.565945	−	0.824443i	$-0.308511\pi$
$761$	31.2246	1.13189	0.565945	+	0.824443i	$0.308511\pi$
$762$	−4.46570	−0.161775
$763$	−0.359026	−0.0129976
$764$	31.0686	1.12402
$765$	0	0
$766$	10.8494	0.392004
$767$	42.2568	1.52580
$768$	−12.0784	−0.435843
$769$	−1.72556	−0.0622253	−0.0311127	−	0.999516i	$-0.509905\pi$
$769$	−1.72556	−0.0622253	−0.0311127	+	0.999516i	$0.509905\pi$
$770$	0	0
$771$	−23.9627	−0.862995
$772$	4.82363	0.173606
$773$	39.2992	1.41349	0.706747	−	0.707466i	$-0.250162\pi$
$773$	39.2992	1.41349	0.706747	+	0.707466i	$0.250162\pi$
$774$	7.62626	0.274120
$775$	0	0
$776$	18.6159	0.668274
$777$	−2.27344	−0.0815593
$778$	−16.3729	−0.586998
$779$	2.79518	0.100148
$780$	0	0
$781$	−2.57439	−0.0921188
$782$	−5.52774	−0.197671
$783$	−9.65038	−0.344876
$784$	−5.95216	−0.212577
$785$	0	0
$786$	0.937428	0.0334369
$787$	50.7384	1.80863	0.904315	−	0.426866i	$-0.140383\pi$
$787$	50.7384	1.80863	0.904315	+	0.426866i	$0.140383\pi$
$788$	−21.4801	−0.765195
$789$	−13.2525	−0.471802
$790$	0	0
$791$	−4.05463	−0.144166
$792$	1.31458	0.0467114
$793$	27.8257	0.988120
$794$	7.67530	0.272386
$795$	0	0
$796$	22.2310	0.787957
$797$	1.77689	0.0629405	0.0314703	−	0.999505i	$-0.489981\pi$
$797$	1.77689	0.0629405	0.0314703	+	0.999505i	$0.489981\pi$
$798$	0.687004	0.0243197
$799$	−10.4638	−0.370184
$800$	0	0
$801$	12.9917	0.459038
$802$	−14.7410	−0.520522
$803$	−2.99351	−0.105639
$804$	−12.7737	−0.450495
$805$	0	0
$806$	27.4902	0.968302
$807$	−0.728075	−0.0256295
$808$	−29.4999	−1.03780
$809$	−50.7926	−1.78577	−0.892887	−	0.450281i	$-0.851324\pi$
$809$	−50.7926	−1.78577	−0.892887	+	0.450281i	$0.851324\pi$
$810$	0	0
$811$	−26.4748	−0.929655	−0.464827	−	0.885401i	$-0.653884\pi$
$811$	−26.4748	−0.929655	−0.464827	+	0.885401i	$0.653884\pi$
$812$	14.4985	0.508796
$813$	−16.9085	−0.593006
$814$	0.836186	0.0293083
$815$	0	0
$816$	−1.37272	−0.0480547
$817$	9.20210	0.321941
$818$	−5.23298	−0.182967
$819$	3.67101	0.128275
$820$	0	0
$821$	30.1888	1.05359	0.526797	−	0.849991i	$-0.323393\pi$
$821$	30.1888	1.05359	0.526797	+	0.849991i	$0.323393\pi$
$822$	1.37670	0.0480181
$823$	10.5256	0.366901	0.183450	−	0.983029i	$-0.441273\pi$
$823$	10.5256	0.366901	0.183450	+	0.983029i	$0.441273\pi$
$824$	5.00314	0.174293
$825$	0	0
$826$	9.15708	0.318616
$827$	48.0149	1.66964	0.834820	−	0.550523i	$-0.185572\pi$
$827$	48.0149	1.66964	0.834820	+	0.550523i	$0.185572\pi$
$828$	−7.91118	−0.274933
$829$	−27.0527	−0.939581	−0.469790	−	0.882778i	$-0.655671\pi$
$829$	−27.0527	−0.939581	−0.469790	+	0.882778i	$0.655671\pi$
$830$	0	0
$831$	10.0386	0.348235
$832$	8.28003	0.287059
$833$	8.10166	0.280706
$834$	12.9544	0.448575
$835$	0	0
$836$	0.666764	0.0230605
$837$	10.4630	0.361654
$838$	−7.17508	−0.247859
$839$	48.1448	1.66214	0.831072	−	0.556165i	$-0.187728\pi$
$839$	48.1448	1.66214	0.831072	+	0.556165i	$0.187728\pi$
$840$	0	0
$841$	64.1297	2.21137
$842$	3.19137	0.109982
$843$	20.5358	0.707292
$844$	0.546856	0.0188236
$845$	0	0
$846$	5.67533	0.195122
$847$	−11.1209	−0.382120
$848$	−10.5972	−0.363910
$849$	21.2483	0.729240
$850$	0	0
$851$	−11.9715	−0.410377
$852$	−7.26553	−0.248913
$853$	6.56698	0.224849	0.112425	−	0.993660i	$-0.464138\pi$
$853$	6.56698	0.224849	0.112425	+	0.993660i	$0.464138\pi$
$854$	6.02985	0.206337
$855$	0	0
$856$	39.1056	1.33660
$857$	−26.7026	−0.912143	−0.456072	−	0.889943i	$-0.650744\pi$
$857$	−26.7026	−0.912143	−0.456072	+	0.889943i	$0.650744\pi$
$858$	−1.35022	−0.0460957
$859$	−12.6095	−0.430231	−0.215116	−	0.976589i	$-0.569013\pi$
$859$	−12.6095	−0.430231	−0.215116	+	0.976589i	$0.569013\pi$
$860$	0	0
$861$	3.23666	0.110305
$862$	−4.10390	−0.139779
$863$	−7.76101	−0.264188	−0.132094	−	0.991237i	$-0.542170\pi$
$863$	−7.76101	−0.264188	−0.132094	+	0.991237i	$0.542170\pi$
$864$	5.86057	0.199381
$865$	0	0
$866$	20.8899	0.709867
$867$	−15.1316	−0.513895
$868$	−15.7193	−0.533548
$869$	3.46389	0.117505
$870$	0	0
$871$	31.2123	1.05759
$872$	0.886601	0.0300241
$873$	−7.27747	−0.246305
$874$	3.61762	0.122368
$875$	0	0
$876$	−8.44840	−0.285445
$877$	15.3303	0.517667	0.258834	−	0.965922i	$-0.416662\pi$
$877$	15.3303	0.517667	0.258834	+	0.965922i	$0.416662\pi$
$878$	−7.83443	−0.264399
$879$	−29.8828	−1.00792
$880$	0	0
$881$	37.4961	1.26328	0.631638	−	0.775263i	$-0.282383\pi$
$881$	37.4961	1.26328	0.631638	+	0.775263i	$0.282383\pi$
$882$	−4.39414	−0.147959
$883$	−1.99657	−0.0671899	−0.0335950	−	0.999436i	$-0.510696\pi$
$883$	−1.99657	−0.0671899	−0.0335950	+	0.999436i	$0.510696\pi$
$884$	7.02583	0.236304
$885$	0	0
$886$	−27.2801	−0.916494
$887$	−13.0003	−0.436506	−0.218253	−	0.975892i	$-0.570036\pi$
$887$	−13.0003	−0.436506	−0.218253	+	0.975892i	$0.570036\pi$
$888$	5.61417	0.188399
$889$	−6.23952	−0.209267
$890$	0	0
$891$	−0.513903	−0.0172164
$892$	−0.391805	−0.0131186
$893$	6.84804	0.229161
$894$	15.2394	0.509682
$895$	0	0
$896$	−10.3472	−0.345677
$897$	19.3308	0.645436
$898$	19.9684	0.666354
$899$	−100.972	−3.36760
$900$	0	0
$901$	14.4242	0.480539
$902$	−1.19046	−0.0396381
$903$	10.6555	0.354593
$904$	10.0127	0.333019
$905$	0	0
$906$	2.12735	0.0706764
$907$	15.3852	0.510857	0.255429	−	0.966828i	$-0.417783\pi$
$907$	15.3852	0.510857	0.255429	+	0.966828i	$0.417783\pi$
$908$	−10.3566	−0.343695
$909$	11.5323	0.382502
$910$	0	0
$911$	−0.397650	−0.0131747	−0.00658736	−	0.999978i	$-0.502097\pi$
$911$	−0.397650	−0.0131747	−0.00658736	+	0.999978i	$0.502097\pi$
$912$	0.898374	0.0297481
$913$	4.10916	0.135993
$914$	18.2594	0.603966
$915$	0	0
$916$	−36.0966	−1.19266
$917$	1.30979	0.0432529
$918$	−1.01340	−0.0334472
$919$	4.87620	0.160851	0.0804255	−	0.996761i	$-0.474372\pi$
$919$	4.87620	0.160851	0.0804255	+	0.996761i	$0.474372\pi$
$920$	0	0
$921$	−0.531050	−0.0174987
$922$	18.3057	0.602865
$923$	17.7531	0.584352
$924$	0.772074	0.0253994
$925$	0	0
$926$	−16.8434	−0.553509
$927$	−1.95586	−0.0642390
$928$	−56.5567	−1.85657
$929$	25.0861	0.823048	0.411524	−	0.911399i	$-0.364997\pi$
$929$	25.0861	0.823048	0.411524	+	0.911399i	$0.364997\pi$
$930$	0	0
$931$	−5.30212	−0.173770
$932$	24.5903	0.805482
$933$	−18.2322	−0.596895
$934$	8.06229	0.263806
$935$	0	0
$936$	−9.06540	−0.296312
$937$	39.6519	1.29537	0.647686	−	0.761907i	$-0.275737\pi$
$937$	39.6519	1.29537	0.647686	+	0.761907i	$0.275737\pi$
$938$	6.76373	0.220844
$939$	29.3523	0.957877
$940$	0	0
$941$	10.8852	0.354847	0.177424	−	0.984135i	$-0.443224\pi$
$941$	10.8852	0.354847	0.177424	+	0.984135i	$0.443224\pi$
$942$	−10.6675	−0.347565
$943$	17.0436	0.555015
$944$	11.9744	0.389735
$945$	0	0
$946$	−3.91916	−0.127423
$947$	−34.0211	−1.10554	−0.552768	−	0.833335i	$-0.686429\pi$
$947$	−34.0211	−1.10554	−0.552768	+	0.833335i	$0.686429\pi$
$948$	9.77593	0.317507
$949$	20.6434	0.670115
$950$	0	0
$951$	−32.8989	−1.06682
$952$	3.62199	0.117389
$953$	−40.0497	−1.29734	−0.648669	−	0.761071i	$-0.724674\pi$
$953$	−40.0497	−1.29734	−0.648669	+	0.761071i	$0.724674\pi$
$954$	−7.82333	−0.253290
$955$	0	0
$956$	5.98208	0.193474
$957$	4.95936	0.160313
$958$	0.547881	0.0177012
$959$	1.92355	0.0621146
$960$	0	0
$961$	78.4740	2.53142
$962$	−5.76639	−0.185916
$963$	−15.2874	−0.492630
$964$	8.61862	0.277587
$965$	0	0
$966$	4.18899	0.134779
$967$	−1.82683	−0.0587469	−0.0293734	−	0.999569i	$-0.509351\pi$
$967$	−1.82683	−0.0587469	−0.0293734	+	0.999569i	$0.509351\pi$
$968$	27.4627	0.882684
$969$	−1.22280	−0.0392821
$970$	0	0
$971$	40.4775	1.29899	0.649493	−	0.760368i	$-0.274981\pi$
$971$	40.4775	1.29899	0.649493	+	0.760368i	$0.274981\pi$
$972$	−1.45036	−0.0465202
$973$	18.1001	0.580261
$974$	−21.6259	−0.692940
$975$	0	0
$976$	7.88505	0.252394
$977$	−20.8782	−0.667954	−0.333977	−	0.942581i	$-0.608391\pi$
$977$	−20.8782	−0.667954	−0.333977	+	0.942581i	$0.608391\pi$
$978$	−5.86020	−0.187388
$979$	−6.67646	−0.213381
$980$	0	0
$981$	−0.346596	−0.0110660
$982$	−23.4877	−0.749524
$983$	−21.0491	−0.671361	−0.335680	−	0.941976i	$-0.608966\pi$
$983$	−21.0491	−0.671361	−0.335680	+	0.941976i	$0.608966\pi$
$984$	−7.99279	−0.254801
$985$	0	0
$986$	9.77968	0.311449
$987$	7.92963	0.252403
$988$	−4.59805	−0.146283
$989$	56.1097	1.78418
$990$	0	0
$991$	42.2138	1.34097	0.670483	−	0.741925i	$-0.266087\pi$
$991$	42.2138	1.34097	0.670483	+	0.741925i	$0.266087\pi$
$992$	61.3191	1.94688
$993$	−3.75461	−0.119149
$994$	3.84712	0.122023
$995$	0	0
$996$	11.5970	0.367466
$997$	32.3301	1.02390	0.511952	−	0.859014i	$-0.328923\pi$
$997$	32.3301	1.02390	0.511952	+	0.859014i	$0.328923\pi$
$998$	−6.59280	−0.208691
$999$	−2.19473	−0.0694382

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1875.2.a.o.1.5	yes	8
3.2	odd	2		5625.2.a.u.1.4		8
5.2	odd	4		1875.2.b.g.1249.9		16
5.3	odd	4		1875.2.b.g.1249.8		16
5.4	even	2		1875.2.a.n.1.4	✓	8
15.14	odd	2		5625.2.a.bc.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1875.2.a.n.1.4	✓	8	5.4	even	2
1875.2.a.o.1.5	yes	8	1.1	even	1	trivial
1875.2.b.g.1249.8		16	5.3	odd	4
1875.2.b.g.1249.9		16	5.2	odd	4
5625.2.a.u.1.4		8	3.2	odd	2
5625.2.a.bc.1.5		8	15.14	odd	2

Overview	Random
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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:	\( N \)	\(=\)	\( 1875 = 3 \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1875.a (trivial)

\(f(q)\)	\(=\)	\(q+0.741379 q^{2} +1.00000 q^{3} -1.45036 q^{4} +0.741379 q^{6} +1.03586 q^{7} -2.55802 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.741379 q^{2} +1.00000 q^{3} -1.45036 q^{4} +0.741379 q^{6} +1.03586 q^{7} -2.55802 q^{8} +1.00000 q^{9} -0.513903 q^{11} -1.45036 q^{12} +3.54391 q^{13} +0.767968 q^{14} +1.00425 q^{16} -1.36691 q^{17} +0.741379 q^{18} +0.894573 q^{19} +1.03586 q^{21} -0.380997 q^{22} +5.45465 q^{23} -2.55802 q^{24} +2.62738 q^{26} +1.00000 q^{27} -1.50237 q^{28} -9.65038 q^{29} +10.4630 q^{31} +5.86057 q^{32} -0.513903 q^{33} -1.01340 q^{34} -1.45036 q^{36} -2.19473 q^{37} +0.663218 q^{38} +3.54391 q^{39} +3.12460 q^{41} +0.767968 q^{42} +10.2866 q^{43} +0.745343 q^{44} +4.04396 q^{46} +7.65509 q^{47} +1.00425 q^{48} -5.92699 q^{49} -1.36691 q^{51} -5.13993 q^{52} -10.5524 q^{53} +0.741379 q^{54} -2.64976 q^{56} +0.894573 q^{57} -7.15459 q^{58} +11.9238 q^{59} +7.85170 q^{61} +7.75704 q^{62} +1.03586 q^{63} +2.33641 q^{64} -0.380997 q^{66} +8.80731 q^{67} +1.98251 q^{68} +5.45465 q^{69} +5.00948 q^{71} -2.55802 q^{72} +5.82505 q^{73} -1.62713 q^{74} -1.29745 q^{76} -0.532334 q^{77} +2.62738 q^{78} -6.74036 q^{79} +1.00000 q^{81} +2.31651 q^{82} -7.99598 q^{83} -1.50237 q^{84} +7.62626 q^{86} -9.65038 q^{87} +1.31458 q^{88} +12.9917 q^{89} +3.67101 q^{91} -7.91118 q^{92} +10.4630 q^{93} +5.67533 q^{94} +5.86057 q^{96} -7.27747 q^{97} -4.39414 q^{98} -0.513903 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 8 q^{3} + 9 q^{4} + q^{6} + 12 q^{7} + 3 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + q^2 + 8 * q^3 + 9 * q^4 + q^6 + 12 * q^7 + 3 * q^8 + 8 * q^9	\( 8 q + q^{2} + 8 q^{3} + 9 q^{4} + q^{6} + 12 q^{7} + 3 q^{8} + 8 q^{9} + 12 q^{11} + 9 q^{12} + 14 q^{13} + 16 q^{14} + 15 q^{16} - q^{17} + q^{18} + 16 q^{19} + 12 q^{21} + 18 q^{22} - 4 q^{23} + 3 q^{24} - 34 q^{26} + 8 q^{27} - 21 q^{28} + 2 q^{29} + 13 q^{31} - 18 q^{32} + 12 q^{33} - 37 q^{34} + 9 q^{36} - 8 q^{37} - 24 q^{38} + 14 q^{39} - 12 q^{41} + 16 q^{42} + 20 q^{43} + 47 q^{44} + 33 q^{46} - 15 q^{47} + 15 q^{48} + 30 q^{49} - q^{51} - q^{52} - 4 q^{53} + q^{54} + 60 q^{56} + 16 q^{57} + 2 q^{58} + 14 q^{59} + 10 q^{61} + 4 q^{62} + 12 q^{63} + 41 q^{64} + 18 q^{66} + 19 q^{67} - 33 q^{68} - 4 q^{69} + 21 q^{71} + 3 q^{72} - 19 q^{73} - 9 q^{74} - q^{76} - 11 q^{77} - 34 q^{78} + 10 q^{79} + 8 q^{81} + 24 q^{82} - 27 q^{83} - 21 q^{84} + 42 q^{86} + 2 q^{87} + 53 q^{88} - 9 q^{89} - 12 q^{91} - 63 q^{92} + 13 q^{93} + 14 q^{94} - 18 q^{96} + 24 q^{97} - 24 q^{98} + 12 q^{99}+O(q^{100}) \) 8 * q + q^2 + 8 * q^3 + 9 * q^4 + q^6 + 12 * q^7 + 3 * q^8 + 8 * q^9 + 12 * q^11 + 9 * q^12 + 14 * q^13 + 16 * q^14 + 15 * q^16 - q^17 + q^18 + 16 * q^19 + 12 * q^21 + 18 * q^22 - 4 * q^23 + 3 * q^24 - 34 * q^26 + 8 * q^27 - 21 * q^28 + 2 * q^29 + 13 * q^31 - 18 * q^32 + 12 * q^33 - 37 * q^34 + 9 * q^36 - 8 * q^37 - 24 * q^38 + 14 * q^39 - 12 * q^41 + 16 * q^42 + 20 * q^43 + 47 * q^44 + 33 * q^46 - 15 * q^47 + 15 * q^48 + 30 * q^49 - q^51 - q^52 - 4 * q^53 + q^54 + 60 * q^56 + 16 * q^57 + 2 * q^58 + 14 * q^59 + 10 * q^61 + 4 * q^62 + 12 * q^63 + 41 * q^64 + 18 * q^66 + 19 * q^67 - 33 * q^68 - 4 * q^69 + 21 * q^71 + 3 * q^72 - 19 * q^73 - 9 * q^74 - q^76 - 11 * q^77 - 34 * q^78 + 10 * q^79 + 8 * q^81 + 24 * q^82 - 27 * q^83 - 21 * q^84 + 42 * q^86 + 2 * q^87 + 53 * q^88 - 9 * q^89 - 12 * q^91 - 63 * q^92 + 13 * q^93 + 14 * q^94 - 18 * q^96 + 24 * q^97 - 24 * q^98 + 12 * q^99

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