LMFDB - Embedded newform 975.2.a.q.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(1,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, 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("975.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.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:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.48119$ of defining polynomial
Character	$\chi$	$=$	975.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.67513 q^{2} +1.00000 q^{3} +5.15633 q^{4} +2.67513 q^{6} -2.28726 q^{7} +8.44358 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.67513 q^{2} +1.00000 q^{3} +5.15633 q^{4} +2.67513 q^{6} -2.28726 q^{7} +8.44358 q^{8} +1.00000 q^{9} -0.130933 q^{11} +5.15633 q^{12} -1.00000 q^{13} -6.11871 q^{14} +12.2750 q^{16} +7.96239 q^{17} +2.67513 q^{18} -5.11871 q^{19} -2.28726 q^{21} -0.350262 q^{22} -5.50659 q^{23} +8.44358 q^{24} -2.67513 q^{26} +1.00000 q^{27} -11.7938 q^{28} -3.00000 q^{29} -7.79384 q^{31} +15.9502 q^{32} -0.130933 q^{33} +21.3004 q^{34} +5.15633 q^{36} +4.80606 q^{37} -13.6932 q^{38} -1.00000 q^{39} +11.4314 q^{41} -6.11871 q^{42} -2.93207 q^{43} -0.675131 q^{44} -14.7308 q^{46} +2.67513 q^{47} +12.2750 q^{48} -1.76845 q^{49} +7.96239 q^{51} -5.15633 q^{52} -8.50659 q^{53} +2.67513 q^{54} -19.3127 q^{56} -5.11871 q^{57} -8.02539 q^{58} -10.4133 q^{59} +5.18664 q^{61} -20.8496 q^{62} -2.28726 q^{63} +18.1187 q^{64} -0.350262 q^{66} -6.05571 q^{67} +41.0567 q^{68} -5.50659 q^{69} -15.0435 q^{71} +8.44358 q^{72} -0.932071 q^{73} +12.8568 q^{74} -26.3938 q^{76} +0.299477 q^{77} -2.67513 q^{78} +8.85685 q^{79} +1.00000 q^{81} +30.5804 q^{82} +6.80114 q^{83} -11.7938 q^{84} -7.84367 q^{86} -3.00000 q^{87} -1.10554 q^{88} -8.12601 q^{89} +2.28726 q^{91} -28.3938 q^{92} -7.79384 q^{93} +7.15633 q^{94} +15.9502 q^{96} +18.9624 q^{97} -4.73084 q^{98} -0.130933 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 3 q^{3} + 5 q^{4} + 3 q^{6} - q^{7} + 9 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + 3 * q^3 + 5 * q^4 + 3 * q^6 - q^7 + 9 * q^8 + 3 * q^9	$ 3 q + 3 q^{2} + 3 q^{3} + 5 q^{4} + 3 q^{6} - q^{7} + 9 q^{8} + 3 q^{9} - 5 q^{11} + 5 q^{12} - 3 q^{13} + 3 q^{14} + 5 q^{16} + 13 q^{17} + 3 q^{18} + 6 q^{19} - q^{21} + 9 q^{22} + 4 q^{23} + 9 q^{24} - 3 q^{26} + 3 q^{27} - 9 q^{28} - 9 q^{29} + 3 q^{31} + 11 q^{32} - 5 q^{33} + 17 q^{34} + 5 q^{36} + 14 q^{37} - 8 q^{38} - 3 q^{39} - 8 q^{41} + 3 q^{42} + 3 q^{44} - 22 q^{46} + 3 q^{47} + 5 q^{48} + 6 q^{49} + 13 q^{51} - 5 q^{52} - 5 q^{53} + 3 q^{54} - 37 q^{56} + 6 q^{57} - 9 q^{58} - 17 q^{59} + 3 q^{61} - 19 q^{62} - q^{63} + 33 q^{64} + 9 q^{66} - q^{67} + 39 q^{68} + 4 q^{69} - 2 q^{71} + 9 q^{72} + 6 q^{73} + 8 q^{74} - 26 q^{76} + 21 q^{77} - 3 q^{78} - 4 q^{79} + 3 q^{81} + 26 q^{82} + 7 q^{83} - 9 q^{84} - 34 q^{86} - 9 q^{87} - 23 q^{88} - 16 q^{89} + q^{91} - 32 q^{92} + 3 q^{93} + 11 q^{94} + 11 q^{96} + 46 q^{97} + 8 q^{98} - 5 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 + 3 * q^3 + 5 * q^4 + 3 * q^6 - q^7 + 9 * q^8 + 3 * q^9 - 5 * q^11 + 5 * q^12 - 3 * q^13 + 3 * q^14 + 5 * q^16 + 13 * q^17 + 3 * q^18 + 6 * q^19 - q^21 + 9 * q^22 + 4 * q^23 + 9 * q^24 - 3 * q^26 + 3 * q^27 - 9 * q^28 - 9 * q^29 + 3 * q^31 + 11 * q^32 - 5 * q^33 + 17 * q^34 + 5 * q^36 + 14 * q^37 - 8 * q^38 - 3 * q^39 - 8 * q^41 + 3 * q^42 + 3 * q^44 - 22 * q^46 + 3 * q^47 + 5 * q^48 + 6 * q^49 + 13 * q^51 - 5 * q^52 - 5 * q^53 + 3 * q^54 - 37 * q^56 + 6 * q^57 - 9 * q^58 - 17 * q^59 + 3 * q^61 - 19 * q^62 - q^63 + 33 * q^64 + 9 * q^66 - q^67 + 39 * q^68 + 4 * q^69 - 2 * q^71 + 9 * q^72 + 6 * q^73 + 8 * q^74 - 26 * q^76 + 21 * q^77 - 3 * q^78 - 4 * q^79 + 3 * q^81 + 26 * q^82 + 7 * q^83 - 9 * q^84 - 34 * q^86 - 9 * q^87 - 23 * q^88 - 16 * q^89 + q^91 - 32 * q^92 + 3 * q^93 + 11 * q^94 + 11 * q^96 + 46 * q^97 + 8 * q^98 - 5 * 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 $

$2$	2.67513	1.89160	0.945802	−	0.324745i	$-0.105279\pi$
$2$	2.67513	1.89160	0.945802	+	0.324745i	$0.105279\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.15633	2.57816
$5$	0	0
$5$	0	0
$6$	2.67513	1.09212
$7$	−2.28726	−0.864502	−0.432251	−	0.901753i	$-0.642281\pi$
$7$	−2.28726	−0.864502	−0.432251	+	0.901753i	$0.642281\pi$
$8$	8.44358	2.98526
$9$	1.00000	0.333333
$10$	0	0
$11$	−0.130933	−0.0394777	−0.0197388	−	0.999805i	$-0.506283\pi$
$11$	−0.130933	−0.0394777	−0.0197388	+	0.999805i	$0.506283\pi$
$12$	5.15633	1.48850
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−6.11871	−1.63530
$15$	0	0
$16$	12.2750	3.06876
$17$	7.96239	1.93116	0.965581	−	0.260101i	$-0.0837558\pi$
$17$	7.96239	1.93116	0.965581	+	0.260101i	$0.0837558\pi$
$18$	2.67513	0.630534
$19$	−5.11871	−1.17431	−0.587157	−	0.809473i	$-0.699753\pi$
$19$	−5.11871	−1.17431	−0.587157	+	0.809473i	$0.699753\pi$
$20$	0	0
$21$	−2.28726	−0.499121
$22$	−0.350262	−0.0746761
$23$	−5.50659	−1.14820	−0.574101	−	0.818784i	$-0.694648\pi$
$23$	−5.50659	−1.14820	−0.574101	+	0.818784i	$0.694648\pi$
$24$	8.44358	1.72354
$25$	0	0
$26$	−2.67513	−0.524636
$27$	1.00000	0.192450
$28$	−11.7938	−2.22883
$29$	−3.00000	−0.557086	−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000	−0.557086	−0.278543	+	0.960424i	$0.589851\pi$
$30$	0	0
$31$	−7.79384	−1.39982	−0.699908	−	0.714233i	$-0.746776\pi$
$31$	−7.79384	−1.39982	−0.699908	+	0.714233i	$0.746776\pi$
$32$	15.9502	2.81962
$33$	−0.130933	−0.0227924
$34$	21.3004	3.65299
$35$	0	0
$36$	5.15633	0.859388
$37$	4.80606	0.790112	0.395056	−	0.918657i	$-0.370725\pi$
$37$	4.80606	0.790112	0.395056	+	0.918657i	$0.370725\pi$
$38$	−13.6932	−2.22134
$39$	−1.00000	−0.160128
$40$	0	0
$41$	11.4314	1.78528	0.892640	−	0.450771i	$-0.148851\pi$
$41$	11.4314	1.78528	0.892640	+	0.450771i	$0.148851\pi$
$42$	−6.11871	−0.944138
$43$	−2.93207	−0.447137	−0.223568	−	0.974688i	$-0.571771\pi$
$43$	−2.93207	−0.447137	−0.223568	+	0.974688i	$0.571771\pi$
$44$	−0.675131	−0.101780
$45$	0	0
$46$	−14.7308	−2.17194
$47$	2.67513	0.390208	0.195104	−	0.980783i	$-0.437496\pi$
$47$	2.67513	0.390208	0.195104	+	0.980783i	$0.437496\pi$
$48$	12.2750	1.77175
$49$	−1.76845	−0.252636
$50$	0	0
$51$	7.96239	1.11496
$52$	−5.15633	−0.715054
$53$	−8.50659	−1.16847	−0.584235	−	0.811585i	$-0.698605\pi$
$53$	−8.50659	−1.16847	−0.584235	+	0.811585i	$0.698605\pi$
$54$	2.67513	0.364039
$55$	0	0
$56$	−19.3127	−2.58076
$57$	−5.11871	−0.677990
$58$	−8.02539	−1.05379
$59$	−10.4133	−1.35569	−0.677846	−	0.735204i	$-0.737086\pi$
$59$	−10.4133	−1.35569	−0.677846	+	0.735204i	$0.737086\pi$
$60$	0	0
$61$	5.18664	0.664082	0.332041	−	0.943265i	$-0.392263\pi$
$61$	5.18664	0.664082	0.332041	+	0.943265i	$0.392263\pi$
$62$	−20.8496	−2.64790
$63$	−2.28726	−0.288167
$64$	18.1187	2.26484
$65$	0	0
$66$	−0.350262	−0.0431142
$67$	−6.05571	−0.739823	−0.369911	−	0.929067i	$-0.620612\pi$
$67$	−6.05571	−0.739823	−0.369911	+	0.929067i	$0.620612\pi$
$68$	41.0567	4.97885
$69$	−5.50659	−0.662915
$70$	0	0
$71$	−15.0435	−1.78533	−0.892667	−	0.450717i	$-0.851168\pi$
$71$	−15.0435	−1.78533	−0.892667	+	0.450717i	$0.851168\pi$
$72$	8.44358	0.995086
$73$	−0.932071	−0.109091	−0.0545454	−	0.998511i	$-0.517371\pi$
$73$	−0.932071	−0.109091	−0.0545454	+	0.998511i	$0.517371\pi$
$74$	12.8568	1.49458
$75$	0	0
$76$	−26.3938	−3.02757
$77$	0.299477	0.0341285
$78$	−2.67513	−0.302899
$79$	8.85685	0.996473	0.498237	−	0.867041i	$-0.333981\pi$
$79$	8.85685	0.996473	0.498237	+	0.867041i	$0.333981\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	30.5804	3.37704
$83$	6.80114	0.746522	0.373261	−	0.927726i	$-0.378240\pi$
$83$	6.80114	0.746522	0.373261	+	0.927726i	$0.378240\pi$
$84$	−11.7938	−1.28681
$85$	0	0
$86$	−7.84367	−0.845805
$87$	−3.00000	−0.321634
$88$	−1.10554	−0.117851
$89$	−8.12601	−0.861355	−0.430678	−	0.902506i	$-0.641725\pi$
$89$	−8.12601	−0.861355	−0.430678	+	0.902506i	$0.641725\pi$
$90$	0	0
$91$	2.28726	0.239770
$92$	−28.3938	−2.96025
$93$	−7.79384	−0.808184
$94$	7.15633	0.738119
$95$	0	0
$96$	15.9502	1.62791
$97$	18.9624	1.92534	0.962669	−	0.270680i	$-0.0872485\pi$
$97$	18.9624	1.92534	0.962669	+	0.270680i	$0.0872485\pi$
$98$	−4.73084	−0.477887
$99$	−0.130933	−0.0131592
$100$	0	0
$101$	−3.54420	−0.352661	−0.176330	−	0.984331i	$-0.556423\pi$
$101$	−3.54420	−0.352661	−0.176330	+	0.984331i	$0.556423\pi$
$102$	21.3004	2.10906
$103$	14.0811	1.38745	0.693726	−	0.720239i	$-0.255968\pi$
$103$	14.0811	1.38745	0.693726	+	0.720239i	$0.255968\pi$
$104$	−8.44358	−0.827961
$105$	0	0
$106$	−22.7562	−2.21028
$107$	−2.64974	−0.256160	−0.128080	−	0.991764i	$-0.540881\pi$
$107$	−2.64974	−0.256160	−0.128080	+	0.991764i	$0.540881\pi$
$108$	5.15633	0.496168
$109$	−9.31994	−0.892689	−0.446344	−	0.894861i	$-0.647274\pi$
$109$	−9.31994	−0.892689	−0.446344	+	0.894861i	$0.647274\pi$
$110$	0	0
$111$	4.80606	0.456171
$112$	−28.0762	−2.65295
$113$	13.3503	1.25589	0.627943	−	0.778259i	$-0.283897\pi$
$113$	13.3503	1.25589	0.627943	+	0.778259i	$0.283897\pi$
$114$	−13.6932	−1.28249
$115$	0	0
$116$	−15.4690	−1.43626
$117$	−1.00000	−0.0924500
$118$	−27.8568	−2.56443
$119$	−18.2120	−1.66949
$120$	0	0
$121$	−10.9829	−0.998442
$122$	13.8749	1.25618
$123$	11.4314	1.03073
$124$	−40.1876	−3.60895
$125$	0	0
$126$	−6.11871	−0.545098
$127$	8.73084	0.774737	0.387368	−	0.921925i	$-0.373384\pi$
$127$	8.73084	0.774737	0.387368	+	0.921925i	$0.373384\pi$
$128$	16.5696	1.46456
$129$	−2.93207	−0.258154
$130$	0	0
$131$	19.0435	1.66384	0.831919	−	0.554897i	$-0.187243\pi$
$131$	19.0435	1.66384	0.831919	+	0.554897i	$0.187243\pi$
$132$	−0.675131	−0.0587626
$133$	11.7078	1.01520
$134$	−16.1998	−1.39945
$135$	0	0
$136$	67.2311	5.76502
$137$	7.66291	0.654687	0.327343	−	0.944905i	$-0.393847\pi$
$137$	7.66291	0.654687	0.327343	+	0.944905i	$0.393847\pi$
$138$	−14.7308	−1.25397
$139$	7.61213	0.645652	0.322826	−	0.946458i	$-0.395367\pi$
$139$	7.61213	0.645652	0.322826	+	0.946458i	$0.395367\pi$
$140$	0	0
$141$	2.67513	0.225287
$142$	−40.2433	−3.37714
$143$	0.130933	0.0109491
$144$	12.2750	1.02292
$145$	0	0
$146$	−2.49341	−0.206356
$147$	−1.76845	−0.145859
$148$	24.7816	2.03704
$149$	0.887166	0.0726795	0.0363397	−	0.999339i	$-0.488430\pi$
$149$	0.887166	0.0726795	0.0363397	+	0.999339i	$0.488430\pi$
$150$	0	0
$151$	2.93700	0.239009	0.119505	−	0.992834i	$-0.461869\pi$
$151$	2.93700	0.239009	0.119505	+	0.992834i	$0.461869\pi$
$152$	−43.2203	−3.50563
$153$	7.96239	0.643721
$154$	0.801139	0.0645576
$155$	0	0
$156$	−5.15633	−0.412836
$157$	15.7816	1.25951	0.629755	−	0.776793i	$-0.283155\pi$
$157$	15.7816	1.25951	0.629755	+	0.776793i	$0.283155\pi$
$158$	23.6932	1.88493
$159$	−8.50659	−0.674616
$160$	0	0
$161$	12.5950	0.992624
$162$	2.67513	0.210178
$163$	−17.4314	−1.36533	−0.682665	−	0.730732i	$-0.739179\pi$
$163$	−17.4314	−1.36533	−0.682665	+	0.730732i	$0.739179\pi$
$164$	58.9438	4.60274
$165$	0	0
$166$	18.1939	1.41212
$167$	−1.91890	−0.148489	−0.0742444	−	0.997240i	$-0.523654\pi$
$167$	−1.91890	−0.148489	−0.0742444	+	0.997240i	$0.523654\pi$
$168$	−19.3127	−1.49000
$169$	1.00000	0.0769231
$170$	0	0
$171$	−5.11871	−0.391438
$172$	−15.1187	−1.15279
$173$	−7.93207	−0.603064	−0.301532	−	0.953456i	$-0.597498\pi$
$173$	−7.93207	−0.603064	−0.301532	+	0.953456i	$0.597498\pi$
$174$	−8.02539	−0.608403
$175$	0	0
$176$	−1.60720	−0.121147
$177$	−10.4133	−0.782709
$178$	−21.7381	−1.62934
$179$	14.9175	1.11499	0.557493	−	0.830182i	$-0.311764\pi$
$179$	14.9175	1.11499	0.557493	+	0.830182i	$0.311764\pi$
$180$	0	0
$181$	−23.5804	−1.75272	−0.876358	−	0.481659i	$-0.840034\pi$
$181$	−23.5804	−1.75272	−0.876358	+	0.481659i	$0.840034\pi$
$182$	6.11871	0.453549
$183$	5.18664	0.383408
$184$	−46.4953	−3.42768
$185$	0	0
$186$	−20.8496	−1.52876
$187$	−1.04254	−0.0762378
$188$	13.7938	1.00602
$189$	−2.28726	−0.166374
$190$	0	0
$191$	8.38787	0.606925	0.303463	−	0.952843i	$-0.401857\pi$
$191$	8.38787	0.606925	0.303463	+	0.952843i	$0.401857\pi$
$192$	18.1187	1.30761
$193$	18.1563	1.30692	0.653460	−	0.756961i	$-0.273317\pi$
$193$	18.1563	1.30692	0.653460	+	0.756961i	$0.273317\pi$
$194$	50.7269	3.64198
$195$	0	0
$196$	−9.11871	−0.651337
$197$	−1.19394	−0.0850645	−0.0425322	−	0.999095i	$-0.513543\pi$
$197$	−1.19394	−0.0850645	−0.0425322	+	0.999095i	$0.513543\pi$
$198$	−0.350262	−0.0248920
$199$	0.700523	0.0496588	0.0248294	−	0.999692i	$-0.492096\pi$
$199$	0.700523	0.0496588	0.0248294	+	0.999692i	$0.492096\pi$
$200$	0	0
$201$	−6.05571	−0.427137
$202$	−9.48119	−0.667095
$203$	6.86177	0.481602
$204$	41.0567	2.87454
$205$	0	0
$206$	37.6688	2.62451
$207$	−5.50659	−0.382734
$208$	−12.2750	−0.851121
$209$	0.670206	0.0463591
$210$	0	0
$211$	16.9829	1.16915	0.584574	−	0.811340i	$-0.301262\pi$
$211$	16.9829	1.16915	0.584574	+	0.811340i	$0.301262\pi$
$212$	−43.8627	−3.01250
$213$	−15.0435	−1.03076
$214$	−7.08840	−0.484553
$215$	0	0
$216$	8.44358	0.574513
$217$	17.8265	1.21014
$218$	−24.9321	−1.68861
$219$	−0.932071	−0.0629836
$220$	0	0
$221$	−7.96239	−0.535608
$222$	12.8568	0.862895
$223$	−0.806063	−0.0539780	−0.0269890	−	0.999636i	$-0.508592\pi$
$223$	−0.806063	−0.0539780	−0.0269890	+	0.999636i	$0.508592\pi$
$224$	−36.4821	−2.43757
$225$	0	0
$226$	35.7137	2.37564
$227$	7.68243	0.509900	0.254950	−	0.966954i	$-0.417941\pi$
$227$	7.68243	0.509900	0.254950	+	0.966954i	$0.417941\pi$
$228$	−26.3938	−1.74797
$229$	−4.44851	−0.293966	−0.146983	−	0.989139i	$-0.546956\pi$
$229$	−4.44851	−0.293966	−0.146983	+	0.989139i	$0.546956\pi$
$230$	0	0
$231$	0.299477	0.0197041
$232$	−25.3307	−1.66305
$233$	−10.1260	−0.663377	−0.331688	−	0.943389i	$-0.607618\pi$
$233$	−10.1260	−0.663377	−0.331688	+	0.943389i	$0.607618\pi$
$234$	−2.67513	−0.174879
$235$	0	0
$236$	−53.6942	−3.49519
$237$	8.85685	0.575314
$238$	−48.7196	−3.15802
$239$	−19.4363	−1.25723	−0.628615	−	0.777717i	$-0.716378\pi$
$239$	−19.4363	−1.25723	−0.628615	+	0.777717i	$0.716378\pi$
$240$	0	0
$241$	−6.46898	−0.416703	−0.208352	−	0.978054i	$-0.566810\pi$
$241$	−6.46898	−0.416703	−0.208352	+	0.978054i	$0.566810\pi$
$242$	−29.3806	−1.88866
$243$	1.00000	0.0641500
$244$	26.7440	1.71211
$245$	0	0
$246$	30.5804	1.94973
$247$	5.11871	0.325696
$248$	−65.8080	−4.17881
$249$	6.80114	0.431005
$250$	0	0
$251$	−17.7685	−1.12153	−0.560767	−	0.827973i	$-0.689494\pi$
$251$	−17.7685	−1.12153	−0.560767	+	0.827973i	$0.689494\pi$
$252$	−11.7938	−0.742942
$253$	0.720992	0.0453283
$254$	23.3561	1.46549
$255$	0	0
$256$	8.08840	0.505525
$257$	−4.81924	−0.300616	−0.150308	−	0.988639i	$-0.548026\pi$
$257$	−4.81924	−0.300616	−0.150308	+	0.988639i	$0.548026\pi$
$258$	−7.84367	−0.488326
$259$	−10.9927	−0.683054
$260$	0	0
$261$	−3.00000	−0.185695
$262$	50.9438	3.14732
$263$	−1.30536	−0.0804917	−0.0402459	−	0.999190i	$-0.512814\pi$
$263$	−1.30536	−0.0804917	−0.0402459	+	0.999190i	$0.512814\pi$
$264$	−1.10554	−0.0680413
$265$	0	0
$266$	31.3199	1.92035
$267$	−8.12601	−0.497304
$268$	−31.2252	−1.90738
$269$	−8.79877	−0.536470	−0.268235	−	0.963353i	$-0.586440\pi$
$269$	−8.79877	−0.536470	−0.268235	+	0.963353i	$0.586440\pi$
$270$	0	0
$271$	17.4264	1.05858	0.529290	−	0.848441i	$-0.322458\pi$
$271$	17.4264	1.05858	0.529290	+	0.848441i	$0.322458\pi$
$272$	97.7386	5.92627
$273$	2.28726	0.138431
$274$	20.4993	1.23841
$275$	0	0
$276$	−28.3938	−1.70910
$277$	11.7381	0.705276	0.352638	−	0.935760i	$-0.385285\pi$
$277$	11.7381	0.705276	0.352638	+	0.935760i	$0.385285\pi$
$278$	20.3634	1.22132
$279$	−7.79384	−0.466605
$280$	0	0
$281$	−14.5647	−0.868855	−0.434428	−	0.900707i	$-0.643049\pi$
$281$	−14.5647	−0.868855	−0.434428	+	0.900707i	$0.643049\pi$
$282$	7.15633	0.426153
$283$	26.1016	1.55158	0.775789	−	0.630993i	$-0.217352\pi$
$283$	26.1016	1.55158	0.775789	+	0.630993i	$0.217352\pi$
$284$	−77.5691	−4.60288
$285$	0	0
$286$	0.350262	0.0207114
$287$	−26.1465	−1.54338
$288$	15.9502	0.939873
$289$	46.3996	2.72939
$290$	0	0
$291$	18.9624	1.11159
$292$	−4.80606	−0.281254
$293$	9.07381	0.530098	0.265049	−	0.964235i	$-0.414612\pi$
$293$	9.07381	0.530098	0.265049	+	0.964235i	$0.414612\pi$
$294$	−4.73084	−0.275908
$295$	0	0
$296$	40.5804	2.35869
$297$	−0.130933	−0.00759748
$298$	2.37328	0.137481
$299$	5.50659	0.318454
$300$	0	0
$301$	6.70640	0.386551
$302$	7.85685	0.452111
$303$	−3.54420	−0.203609
$304$	−62.8324	−3.60369
$305$	0	0
$306$	21.3004	1.21766
$307$	−11.3806	−0.649524	−0.324762	−	0.945796i	$-0.605284\pi$
$307$	−11.3806	−0.649524	−0.324762	+	0.945796i	$0.605284\pi$
$308$	1.54420	0.0879889
$309$	14.0811	0.801046
$310$	0	0
$311$	9.22425	0.523059	0.261530	−	0.965195i	$-0.415773\pi$
$311$	9.22425	0.523059	0.261530	+	0.965195i	$0.415773\pi$
$312$	−8.44358	−0.478024
$313$	18.7685	1.06086	0.530428	−	0.847730i	$-0.322031\pi$
$313$	18.7685	1.06086	0.530428	+	0.847730i	$0.322031\pi$
$314$	42.2179	2.38249
$315$	0	0
$316$	45.6688	2.56907
$317$	10.5442	0.592221	0.296111	−	0.955154i	$-0.404310\pi$
$317$	10.5442	0.592221	0.296111	+	0.955154i	$0.404310\pi$
$318$	−22.7562	−1.27611
$319$	0.392798	0.0219924
$320$	0	0
$321$	−2.64974	−0.147894
$322$	33.6932	1.87765
$323$	−40.7572	−2.26779
$324$	5.15633	0.286463
$325$	0	0
$326$	−46.6312	−2.58266
$327$	−9.31994	−0.515394
$328$	96.5217	5.32952
$329$	−6.11871	−0.337336
$330$	0	0
$331$	4.95651	0.272434	0.136217	−	0.990679i	$-0.456506\pi$
$331$	4.95651	0.272434	0.136217	+	0.990679i	$0.456506\pi$
$332$	35.0689	1.92466
$333$	4.80606	0.263371
$334$	−5.13330	−0.280882
$335$	0	0
$336$	−28.0762	−1.53168
$337$	−32.6082	−1.77628	−0.888140	−	0.459573i	$-0.848002\pi$
$337$	−32.6082	−1.77628	−0.888140	+	0.459573i	$0.848002\pi$
$338$	2.67513	0.145508
$339$	13.3503	0.725087
$340$	0	0
$341$	1.02047	0.0552614
$342$	−13.6932	−0.740445
$343$	20.0557	1.08291
$344$	−24.7572	−1.33482
$345$	0	0
$346$	−21.2193	−1.14076
$347$	−22.1622	−1.18973	−0.594865	−	0.803826i	$-0.702794\pi$
$347$	−22.1622	−1.18973	−0.594865	+	0.803826i	$0.702794\pi$
$348$	−15.4690	−0.829224
$349$	−4.34297	−0.232474	−0.116237	−	0.993222i	$-0.537083\pi$
$349$	−4.34297	−0.232474	−0.116237	+	0.993222i	$0.537083\pi$
$350$	0	0
$351$	−1.00000	−0.0533761
$352$	−2.08840	−0.111312
$353$	−6.96827	−0.370883	−0.185442	−	0.982655i	$-0.559372\pi$
$353$	−6.96827	−0.370883	−0.185442	+	0.982655i	$0.559372\pi$
$354$	−27.8568	−1.48057
$355$	0	0
$356$	−41.9003	−2.22071
$357$	−18.2120	−0.963883
$358$	39.9062	2.10911
$359$	−15.0122	−0.792315	−0.396157	−	0.918183i	$-0.629657\pi$
$359$	−15.0122	−0.792315	−0.396157	+	0.918183i	$0.629657\pi$
$360$	0	0
$361$	7.20123	0.379012
$362$	−63.0806	−3.31544
$363$	−10.9829	−0.576450
$364$	11.7938	0.618165
$365$	0	0
$366$	13.8749	0.725255
$367$	27.0738	1.41324	0.706621	−	0.707593i	$-0.250219\pi$
$367$	27.0738	1.41324	0.706621	+	0.707593i	$0.250219\pi$
$368$	−67.5936	−3.52356
$369$	11.4314	0.595093
$370$	0	0
$371$	19.4568	1.01014
$372$	−40.1876	−2.08363
$373$	3.49341	0.180882	0.0904410	−	0.995902i	$-0.471172\pi$
$373$	3.49341	0.180882	0.0904410	+	0.995902i	$0.471172\pi$
$374$	−2.78892	−0.144212
$375$	0	0
$376$	22.5877	1.16487
$377$	3.00000	0.154508
$378$	−6.11871	−0.314713
$379$	26.9937	1.38657	0.693286	−	0.720663i	$-0.256162\pi$
$379$	26.9937	1.38657	0.693286	+	0.720663i	$0.256162\pi$
$380$	0	0
$381$	8.73084	0.447295
$382$	22.4387	1.14806
$383$	5.52118	0.282119	0.141059	−	0.990001i	$-0.454949\pi$
$383$	5.52118	0.282119	0.141059	+	0.990001i	$0.454949\pi$
$384$	16.5696	0.845563
$385$	0	0
$386$	48.5705	2.47218
$387$	−2.93207	−0.149046
$388$	97.7762	4.96384
$389$	−15.9003	−0.806179	−0.403090	−	0.915161i	$-0.632064\pi$
$389$	−15.9003	−0.806179	−0.403090	+	0.915161i	$0.632064\pi$
$390$	0	0
$391$	−43.8456	−2.21737
$392$	−14.9321	−0.754183
$393$	19.0435	0.960617
$394$	−3.19394	−0.160908
$395$	0	0
$396$	−0.675131	−0.0339266
$397$	−17.1998	−0.863234	−0.431617	−	0.902057i	$-0.642057\pi$
$397$	−17.1998	−0.863234	−0.431617	+	0.902057i	$0.642057\pi$
$398$	1.87399	0.0939347
$399$	11.7078	0.586124
$400$	0	0
$401$	19.0435	0.950987	0.475493	−	0.879719i	$-0.342270\pi$
$401$	19.0435	0.950987	0.475493	+	0.879719i	$0.342270\pi$
$402$	−16.1998	−0.807973
$403$	7.79384	0.388239
$404$	−18.2750	−0.909217
$405$	0	0
$406$	18.3561	0.911000
$407$	−0.629270	−0.0311918
$408$	67.2311	3.32843
$409$	12.4182	0.614040	0.307020	−	0.951703i	$-0.400668\pi$
$409$	12.4182	0.614040	0.307020	+	0.951703i	$0.400668\pi$
$410$	0	0
$411$	7.66291	0.377984
$412$	72.6067	3.57708
$413$	23.8178	1.17200
$414$	−14.7308	−0.723981
$415$	0	0
$416$	−15.9502	−0.782021
$417$	7.61213	0.372767
$418$	1.79289	0.0876931
$419$	6.14174	0.300043	0.150022	−	0.988683i	$-0.452066\pi$
$419$	6.14174	0.300043	0.150022	+	0.988683i	$0.452066\pi$
$420$	0	0
$421$	−17.6121	−0.858363	−0.429181	−	0.903218i	$-0.641198\pi$
$421$	−17.6121	−0.858363	−0.429181	+	0.903218i	$0.641198\pi$
$422$	45.4314	2.21156
$423$	2.67513	0.130069
$424$	−71.8261	−3.48818
$425$	0	0
$426$	−40.2433	−1.94979
$427$	−11.8632	−0.574100
$428$	−13.6629	−0.660422
$429$	0.130933	0.00632148
$430$	0	0
$431$	−3.65703	−0.176153	−0.0880765	−	0.996114i	$-0.528072\pi$
$431$	−3.65703	−0.176153	−0.0880765	+	0.996114i	$0.528072\pi$
$432$	12.2750	0.590583
$433$	9.28963	0.446431	0.223216	−	0.974769i	$-0.428345\pi$
$433$	9.28963	0.446431	0.223216	+	0.974769i	$0.428345\pi$
$434$	47.6883	2.28911
$435$	0	0
$436$	−48.0567	−2.30150
$437$	28.1866	1.34835
$438$	−2.49341	−0.119140
$439$	27.0581	1.29141	0.645706	−	0.763586i	$-0.276563\pi$
$439$	27.0581	1.29141	0.645706	+	0.763586i	$0.276563\pi$
$440$	0	0
$441$	−1.76845	−0.0842120
$442$	−21.3004	−1.01316
$443$	7.09428	0.337059	0.168530	−	0.985697i	$-0.446098\pi$
$443$	7.09428	0.337059	0.168530	+	0.985697i	$0.446098\pi$
$444$	24.7816	1.17608
$445$	0	0
$446$	−2.15633	−0.102105
$447$	0.887166	0.0419615
$448$	−41.4422	−1.95796
$449$	−14.7612	−0.696622	−0.348311	−	0.937379i	$-0.613245\pi$
$449$	−14.7612	−0.696622	−0.348311	+	0.937379i	$0.613245\pi$
$450$	0	0
$451$	−1.49674	−0.0704786
$452$	68.8383	3.23788
$453$	2.93700	0.137992
$454$	20.5515	0.964529
$455$	0	0
$456$	−43.2203	−2.02398
$457$	2.28233	0.106763	0.0533815	−	0.998574i	$-0.483000\pi$
$457$	2.28233	0.106763	0.0533815	+	0.998574i	$0.483000\pi$
$458$	−11.9003	−0.556066
$459$	7.96239	0.371652
$460$	0	0
$461$	−10.5647	−0.492046	−0.246023	−	0.969264i	$-0.579124\pi$
$461$	−10.5647	−0.492046	−0.246023	+	0.969264i	$0.579124\pi$
$462$	0.801139	0.0372724
$463$	−6.18172	−0.287289	−0.143644	−	0.989629i	$-0.545882\pi$
$463$	−6.18172	−0.287289	−0.143644	+	0.989629i	$0.545882\pi$
$464$	−36.8251	−1.70956
$465$	0	0
$466$	−27.0884	−1.25485
$467$	6.32250	0.292570	0.146285	−	0.989242i	$-0.453268\pi$
$467$	6.32250	0.292570	0.146285	+	0.989242i	$0.453268\pi$
$468$	−5.15633	−0.238351
$469$	13.8510	0.639578
$470$	0	0
$471$	15.7816	0.727179
$472$	−87.9253	−4.04709
$473$	0.383904	0.0176519
$474$	23.6932	1.08827
$475$	0	0
$476$	−93.9072	−4.30423
$477$	−8.50659	−0.389490
$478$	−51.9946	−2.37818
$479$	3.33075	0.152186	0.0760929	−	0.997101i	$-0.475755\pi$
$479$	3.33075	0.152186	0.0760929	+	0.997101i	$0.475755\pi$
$480$	0	0
$481$	−4.80606	−0.219138
$482$	−17.3054	−0.788237
$483$	12.5950	0.573092
$484$	−56.6312	−2.57414
$485$	0	0
$486$	2.67513	0.121346
$487$	8.44358	0.382615	0.191308	−	0.981530i	$-0.438727\pi$
$487$	8.44358	0.382615	0.191308	+	0.981530i	$0.438727\pi$
$488$	43.7938	1.98245
$489$	−17.4314	−0.788274
$490$	0	0
$491$	−23.3112	−1.05202	−0.526011	−	0.850478i	$-0.676313\pi$
$491$	−23.3112	−1.05202	−0.526011	+	0.850478i	$0.676313\pi$
$492$	58.9438	2.65739
$493$	−23.8872	−1.07582
$494$	13.6932	0.616088
$495$	0	0
$496$	−95.6697	−4.29570
$497$	34.4083	1.54343
$498$	18.1939	0.815290
$499$	−31.8651	−1.42648	−0.713239	−	0.700921i	$-0.752773\pi$
$499$	−31.8651	−1.42648	−0.713239	+	0.700921i	$0.752773\pi$
$500$	0	0
$501$	−1.91890	−0.0857300
$502$	−47.5329	−2.12150
$503$	−9.43136	−0.420524	−0.210262	−	0.977645i	$-0.567432\pi$
$503$	−9.43136	−0.420524	−0.210262	+	0.977645i	$0.567432\pi$
$504$	−19.3127	−0.860254
$505$	0	0
$506$	1.92875	0.0857433
$507$	1.00000	0.0444116
$508$	45.0191	1.99740
$509$	37.4821	1.66137	0.830684	−	0.556745i	$-0.187950\pi$
$509$	37.4821	1.66137	0.830684	+	0.556745i	$0.187950\pi$
$510$	0	0
$511$	2.13189	0.0943092
$512$	−11.5017	−0.508306
$513$	−5.11871	−0.225997
$514$	−12.8921	−0.568646
$515$	0	0
$516$	−15.1187	−0.665564
$517$	−0.350262	−0.0154045
$518$	−29.4069	−1.29207
$519$	−7.93207	−0.348179
$520$	0	0
$521$	15.9248	0.697677	0.348839	−	0.937183i	$-0.386576\pi$
$521$	15.9248	0.697677	0.348839	+	0.937183i	$0.386576\pi$
$522$	−8.02539	−0.351262
$523$	2.27645	0.0995424	0.0497712	−	0.998761i	$-0.484151\pi$
$523$	2.27645	0.0995424	0.0497712	+	0.998761i	$0.484151\pi$
$524$	98.1944	4.28964
$525$	0	0
$526$	−3.49200	−0.152258
$527$	−62.0576	−2.70327
$528$	−1.60720	−0.0699445
$529$	7.32250	0.318370
$530$	0	0
$531$	−10.4133	−0.451897
$532$	60.3693	2.61734
$533$	−11.4314	−0.495147
$534$	−21.7381	−0.940701
$535$	0	0
$536$	−51.1319	−2.20856
$537$	14.9175	0.643737
$538$	−23.5379	−1.01479
$539$	0.231548	0.00997348
$540$	0	0
$541$	19.3317	0.831135	0.415567	−	0.909562i	$-0.363583\pi$
$541$	19.3317	0.831135	0.415567	+	0.909562i	$0.363583\pi$
$542$	46.6180	2.00241
$543$	−23.5804	−1.01193
$544$	127.001	5.44514
$545$	0	0
$546$	6.11871	0.261857
$547$	−40.9438	−1.75063	−0.875316	−	0.483552i	$-0.839347\pi$
$547$	−40.9438	−1.75063	−0.875316	+	0.483552i	$0.839347\pi$
$548$	39.5125	1.68789
$549$	5.18664	0.221361
$550$	0	0
$551$	15.3561	0.654194
$552$	−46.4953	−1.97897
$553$	−20.2579	−0.861453
$554$	31.4010	1.33410
$555$	0	0
$556$	39.2506	1.66460
$557$	−36.4953	−1.54636	−0.773178	−	0.634189i	$-0.781334\pi$
$557$	−36.4953	−1.54636	−0.773178	+	0.634189i	$0.781334\pi$
$558$	−20.8496	−0.882632
$559$	2.93207	0.124013
$560$	0	0
$561$	−1.04254	−0.0440159
$562$	−38.9624	−1.64353
$563$	1.04349	0.0439779	0.0219890	−	0.999758i	$-0.493000\pi$
$563$	1.04349	0.0439779	0.0219890	+	0.999758i	$0.493000\pi$
$564$	13.7938	0.580826
$565$	0	0
$566$	69.8251	2.93497
$567$	−2.28726	−0.0960558
$568$	−127.021	−5.32968
$569$	−39.4807	−1.65512	−0.827559	−	0.561378i	$-0.810271\pi$
$569$	−39.4807	−1.65512	−0.827559	+	0.561378i	$0.810271\pi$
$570$	0	0
$571$	35.4920	1.48529	0.742647	−	0.669683i	$-0.233570\pi$
$571$	35.4920	1.48529	0.742647	+	0.669683i	$0.233570\pi$
$572$	0.675131	0.0282286
$573$	8.38787	0.350408
$574$	−69.9452	−2.91946
$575$	0	0
$576$	18.1187	0.754946
$577$	−36.0625	−1.50130	−0.750652	−	0.660698i	$-0.770260\pi$
$577$	−36.0625	−1.50130	−0.750652	+	0.660698i	$0.770260\pi$
$578$	124.125	5.16292
$579$	18.1563	0.754551
$580$	0	0
$581$	−15.5560	−0.645370
$582$	50.7269	2.10270
$583$	1.11379	0.0461284
$584$	−7.87002	−0.325664
$585$	0	0
$586$	24.2736	1.00273
$587$	−22.4944	−0.928442	−0.464221	−	0.885719i	$-0.653666\pi$
$587$	−22.4944	−0.928442	−0.464221	+	0.885719i	$0.653666\pi$
$588$	−9.11871	−0.376049
$589$	39.8945	1.64382
$590$	0	0
$591$	−1.19394	−0.0491120
$592$	58.9946	2.42466
$593$	−28.8627	−1.18525	−0.592625	−	0.805478i	$-0.701908\pi$
$593$	−28.8627	−1.18525	−0.592625	+	0.805478i	$0.701908\pi$
$594$	−0.350262	−0.0143714
$595$	0	0
$596$	4.57452	0.187379
$597$	0.700523	0.0286705
$598$	14.7308	0.602389
$599$	2.62927	0.107429	0.0537145	−	0.998556i	$-0.482894\pi$
$599$	2.62927	0.107429	0.0537145	+	0.998556i	$0.482894\pi$
$600$	0	0
$601$	−31.6048	−1.28919	−0.644594	−	0.764525i	$-0.722974\pi$
$601$	−31.6048	−1.28919	−0.644594	+	0.764525i	$0.722974\pi$
$602$	17.9405	0.731200
$603$	−6.05571	−0.246608
$604$	15.1441	0.616205
$605$	0	0
$606$	−9.48119	−0.385147
$607$	13.9149	0.564790	0.282395	−	0.959298i	$-0.408871\pi$
$607$	13.9149	0.564790	0.282395	+	0.959298i	$0.408871\pi$
$608$	−81.6444	−3.31112
$609$	6.86177	0.278053
$610$	0	0
$611$	−2.67513	−0.108224
$612$	41.0567	1.65962
$613$	25.4471	1.02780	0.513899	−	0.857851i	$-0.328201\pi$
$613$	25.4471	1.02780	0.513899	+	0.857851i	$0.328201\pi$
$614$	−30.4445	−1.22864
$615$	0	0
$616$	2.52865	0.101882
$617$	30.6497	1.23391	0.616956	−	0.786998i	$-0.288366\pi$
$617$	30.6497	1.23391	0.616956	+	0.786998i	$0.288366\pi$
$618$	37.6688	1.51526
$619$	−7.99412	−0.321311	−0.160655	−	0.987011i	$-0.551361\pi$
$619$	−7.99412	−0.321311	−0.160655	+	0.987011i	$0.551361\pi$
$620$	0	0
$621$	−5.50659	−0.220972
$622$	24.6761	0.989421
$623$	18.5863	0.744643
$624$	−12.2750	−0.491395
$625$	0	0
$626$	50.2081	2.00672
$627$	0.670206	0.0267655
$628$	81.3752	3.24722
$629$	38.2677	1.52583
$630$	0	0
$631$	41.3463	1.64597	0.822985	−	0.568063i	$-0.192307\pi$
$631$	41.3463	1.64597	0.822985	+	0.568063i	$0.192307\pi$
$632$	74.7835	2.97473
$633$	16.9829	0.675008
$634$	28.2071	1.12025
$635$	0	0
$636$	−43.8627	−1.73927
$637$	1.76845	0.0700686
$638$	1.05079	0.0416010
$639$	−15.0435	−0.595111
$640$	0	0
$641$	3.26187	0.128836	0.0644180	−	0.997923i	$-0.479481\pi$
$641$	3.26187	0.128836	0.0644180	+	0.997923i	$0.479481\pi$
$642$	−7.08840	−0.279757
$643$	−6.82065	−0.268980	−0.134490	−	0.990915i	$-0.542940\pi$
$643$	−6.82065	−0.268980	−0.134490	+	0.990915i	$0.542940\pi$
$644$	64.9438	2.55915
$645$	0	0
$646$	−109.031	−4.28976
$647$	−30.9478	−1.21668	−0.608342	−	0.793675i	$-0.708165\pi$
$647$	−30.9478	−1.21668	−0.608342	+	0.793675i	$0.708165\pi$
$648$	8.44358	0.331695
$649$	1.36344	0.0535195
$650$	0	0
$651$	17.8265	0.698677
$652$	−89.8818	−3.52004
$653$	16.9003	0.661361	0.330681	−	0.943743i	$-0.392722\pi$
$653$	16.9003	0.661361	0.330681	+	0.943743i	$0.392722\pi$
$654$	−24.9321	−0.974921
$655$	0	0
$656$	140.320	5.47859
$657$	−0.932071	−0.0363636
$658$	−16.3684	−0.638105
$659$	4.79621	0.186834	0.0934170	−	0.995627i	$-0.470221\pi$
$659$	4.79621	0.186834	0.0934170	+	0.995627i	$0.470221\pi$
$660$	0	0
$661$	−0.105540	−0.00410503	−0.00205251	−	0.999998i	$-0.500653\pi$
$661$	−0.105540	−0.00410503	−0.00205251	+	0.999998i	$0.500653\pi$
$662$	13.2593	0.515338
$663$	−7.96239	−0.309234
$664$	57.4260	2.22856
$665$	0	0
$666$	12.8568	0.498193
$667$	16.5198	0.639648
$668$	−9.89446	−0.382828
$669$	−0.806063	−0.0311642
$670$	0	0
$671$	−0.679100	−0.0262164
$672$	−36.4821	−1.40733
$673$	3.86670	0.149050	0.0745251	−	0.997219i	$-0.476256\pi$
$673$	3.86670	0.149050	0.0745251	+	0.997219i	$0.476256\pi$
$674$	−87.2311	−3.36002
$675$	0	0
$676$	5.15633	0.198320
$677$	30.1622	1.15923	0.579614	−	0.814891i	$-0.303203\pi$
$677$	30.1622	1.15923	0.579614	+	0.814891i	$0.303203\pi$
$678$	35.7137	1.37158
$679$	−43.3719	−1.66446
$680$	0	0
$681$	7.68243	0.294391
$682$	2.72989	0.104533
$683$	−17.9805	−0.688004	−0.344002	−	0.938969i	$-0.611783\pi$
$683$	−17.9805	−0.688004	−0.344002	+	0.938969i	$0.611783\pi$
$684$	−26.3938	−1.00919
$685$	0	0
$686$	53.6516	2.04843
$687$	−4.44851	−0.169721
$688$	−35.9913	−1.37216
$689$	8.50659	0.324075
$690$	0	0
$691$	31.4363	1.19589	0.597946	−	0.801536i	$-0.295984\pi$
$691$	31.4363	1.19589	0.597946	+	0.801536i	$0.295984\pi$
$692$	−40.9003	−1.55480
$693$	0.299477	0.0113762
$694$	−59.2868	−2.25050
$695$	0	0
$696$	−25.3307	−0.960160
$697$	91.0210	3.44766
$698$	−11.6180	−0.439748
$699$	−10.1260	−0.383001
$700$	0	0
$701$	5.32724	0.201207	0.100604	−	0.994927i	$-0.467923\pi$
$701$	5.32724	0.201207	0.100604	+	0.994927i	$0.467923\pi$
$702$	−2.67513	−0.100966
$703$	−24.6009	−0.927839
$704$	−2.37233	−0.0894105
$705$	0	0
$706$	−18.6410	−0.701564
$707$	8.10650	0.304876
$708$	−53.6942	−2.01795
$709$	27.8046	1.04423	0.522113	−	0.852876i	$-0.325144\pi$
$709$	27.8046	1.04423	0.522113	+	0.852876i	$0.325144\pi$
$710$	0	0
$711$	8.85685	0.332158
$712$	−68.6126	−2.57137
$713$	42.9175	1.60727
$714$	−48.7196	−1.82328
$715$	0	0
$716$	76.9194	2.87461
$717$	−19.4363	−0.725862
$718$	−40.1596	−1.49874
$719$	−0.992706	−0.0370217	−0.0185108	−	0.999829i	$-0.505893\pi$
$719$	−0.992706	−0.0370217	−0.0185108	+	0.999829i	$0.505893\pi$
$720$	0	0
$721$	−32.2071	−1.19946
$722$	19.2642	0.716941
$723$	−6.46898	−0.240584
$724$	−121.588	−4.51879
$725$	0	0
$726$	−29.3806	−1.09042
$727$	−40.0468	−1.48525	−0.742627	−	0.669705i	$-0.766420\pi$
$727$	−40.0468	−1.48525	−0.742627	+	0.669705i	$0.766420\pi$
$728$	19.3127	0.715774
$729$	1.00000	0.0370370
$730$	0	0
$731$	−23.3463	−0.863494
$732$	26.7440	0.988487
$733$	−30.8627	−1.13994	−0.569970	−	0.821665i	$-0.693045\pi$
$733$	−30.8627	−1.13994	−0.569970	+	0.821665i	$0.693045\pi$
$734$	72.4260	2.67329
$735$	0	0
$736$	−87.8310	−3.23749
$737$	0.792890	0.0292065
$738$	30.5804	1.12568
$739$	34.1309	1.25553	0.627763	−	0.778404i	$-0.283971\pi$
$739$	34.1309	1.25553	0.627763	+	0.778404i	$0.283971\pi$
$740$	0	0
$741$	5.11871	0.188041
$742$	52.0494	1.91079
$743$	−14.1916	−0.520638	−0.260319	−	0.965523i	$-0.583828\pi$
$743$	−14.1916	−0.520638	−0.260319	+	0.965523i	$0.583828\pi$
$744$	−65.8080	−2.41264
$745$	0	0
$746$	9.34534	0.342157
$747$	6.80114	0.248841
$748$	−5.37565	−0.196553
$749$	6.06063	0.221451
$750$	0	0
$751$	13.4050	0.489156	0.244578	−	0.969630i	$-0.421351\pi$
$751$	13.4050	0.489156	0.244578	+	0.969630i	$0.421351\pi$
$752$	32.8373	1.19745
$753$	−17.7685	−0.647518
$754$	8.02539	0.292268
$755$	0	0
$756$	−11.7938	−0.428938
$757$	5.76116	0.209393	0.104696	−	0.994504i	$-0.466613\pi$
$757$	5.76116	0.209393	0.104696	+	0.994504i	$0.466613\pi$
$758$	72.2116	2.62284
$759$	0.720992	0.0261703
$760$	0	0
$761$	−9.05334	−0.328183	−0.164092	−	0.986445i	$-0.552469\pi$
$761$	−9.05334	−0.328183	−0.164092	+	0.986445i	$0.552469\pi$
$762$	23.3561	0.846104
$763$	21.3171	0.771731
$764$	43.2506	1.56475
$765$	0	0
$766$	14.7699	0.533657
$767$	10.4133	0.376001
$768$	8.08840	0.291865
$769$	−38.8383	−1.40054	−0.700272	−	0.713876i	$-0.746938\pi$
$769$	−38.8383	−1.40054	−0.700272	+	0.713876i	$0.746938\pi$
$770$	0	0
$771$	−4.81924	−0.173561
$772$	93.6199	3.36945
$773$	−23.7381	−0.853801	−0.426901	−	0.904299i	$-0.640395\pi$
$773$	−23.7381	−0.853801	−0.426901	+	0.904299i	$0.640395\pi$
$774$	−7.84367	−0.281935
$775$	0	0
$776$	160.111	5.74763
$777$	−10.9927	−0.394361
$778$	−42.5355	−1.52497
$779$	−58.5139	−2.09648
$780$	0	0
$781$	1.96968	0.0704808
$782$	−117.293	−4.19438
$783$	−3.00000	−0.107211
$784$	−21.7078	−0.775279
$785$	0	0
$786$	50.9438	1.81711
$787$	19.1803	0.683704	0.341852	−	0.939754i	$-0.388946\pi$
$787$	19.1803	0.683704	0.341852	+	0.939754i	$0.388946\pi$
$788$	−6.15633	−0.219310
$789$	−1.30536	−0.0464719
$790$	0	0
$791$	−30.5355	−1.08572
$792$	−1.10554	−0.0392837
$793$	−5.18664	−0.184183
$794$	−46.0118	−1.63290
$795$	0	0
$796$	3.61213	0.128028
$797$	51.8627	1.83707	0.918536	−	0.395337i	$-0.129372\pi$
$797$	51.8627	1.83707	0.918536	+	0.395337i	$0.129372\pi$
$798$	31.3199	1.10871
$799$	21.3004	0.753555
$800$	0	0
$801$	−8.12601	−0.287118
$802$	50.9438	1.79889
$803$	0.122039	0.00430665
$804$	−31.2252	−1.10123
$805$	0	0
$806$	20.8496	0.734394
$807$	−8.79877	−0.309731
$808$	−29.9257	−1.05278
$809$	−18.1866	−0.639408	−0.319704	−	0.947517i	$-0.603584\pi$
$809$	−18.1866	−0.639408	−0.319704	+	0.947517i	$0.603584\pi$
$810$	0	0
$811$	4.71133	0.165437	0.0827185	−	0.996573i	$-0.473640\pi$
$811$	4.71133	0.165437	0.0827185	+	0.996573i	$0.473640\pi$
$812$	35.3815	1.24165
$813$	17.4264	0.611172
$814$	−1.68338	−0.0590024
$815$	0	0
$816$	97.7386	3.42154
$817$	15.0084	0.525079
$818$	33.2203	1.16152
$819$	2.28726	0.0799233
$820$	0	0
$821$	−33.8046	−1.17979	−0.589895	−	0.807480i	$-0.700831\pi$
$821$	−33.8046	−1.17979	−0.589895	+	0.807480i	$0.700831\pi$
$822$	20.4993	0.714995
$823$	−2.82653	−0.0985267	−0.0492633	−	0.998786i	$-0.515687\pi$
$823$	−2.82653	−0.0985267	−0.0492633	+	0.998786i	$0.515687\pi$
$824$	118.895	4.14190
$825$	0	0
$826$	63.7158	2.21696
$827$	39.9560	1.38941	0.694704	−	0.719296i	$-0.255535\pi$
$827$	39.9560	1.38941	0.694704	+	0.719296i	$0.255535\pi$
$828$	−28.3938	−0.986751
$829$	1.30280	0.0452482	0.0226241	−	0.999744i	$-0.492798\pi$
$829$	1.30280	0.0452482	0.0226241	+	0.999744i	$0.492798\pi$
$830$	0	0
$831$	11.7381	0.407191
$832$	−18.1187	−0.628153
$833$	−14.0811	−0.487881
$834$	20.3634	0.705128
$835$	0	0
$836$	3.45580	0.119521
$837$	−7.79384	−0.269395
$838$	16.4299	0.567563
$839$	−17.9551	−0.619879	−0.309939	−	0.950756i	$-0.600309\pi$
$839$	−17.9551	−0.619879	−0.309939	+	0.950756i	$0.600309\pi$
$840$	0	0
$841$	−20.0000	−0.689655
$842$	−47.1147	−1.62368
$843$	−14.5647	−0.501634
$844$	87.5691	3.01425
$845$	0	0
$846$	7.15633	0.246040
$847$	25.1206	0.863155
$848$	−104.419	−3.58575
$849$	26.1016	0.895804
$850$	0	0
$851$	−26.4650	−0.907209
$852$	−77.5691	−2.65747
$853$	−43.3258	−1.48345	−0.741724	−	0.670705i	$-0.765992\pi$
$853$	−43.3258	−1.48345	−0.741724	+	0.670705i	$0.765992\pi$
$854$	−31.7356	−1.08597
$855$	0	0
$856$	−22.3733	−0.764703
$857$	−15.5223	−0.530232	−0.265116	−	0.964216i	$-0.585410\pi$
$857$	−15.5223	−0.530232	−0.265116	+	0.964216i	$0.585410\pi$
$858$	0.350262	0.0119577
$859$	14.0957	0.480939	0.240469	−	0.970657i	$-0.422699\pi$
$859$	14.0957	0.480939	0.240469	+	0.970657i	$0.422699\pi$
$860$	0	0
$861$	−26.1465	−0.891070
$862$	−9.78304	−0.333212
$863$	−46.6105	−1.58664	−0.793320	−	0.608804i	$-0.791649\pi$
$863$	−46.6105	−1.58664	−0.793320	+	0.608804i	$0.791649\pi$
$864$	15.9502	0.542636
$865$	0	0
$866$	24.8510	0.844470
$867$	46.3996	1.57581
$868$	91.9194	3.11995
$869$	−1.15965	−0.0393384
$870$	0	0
$871$	6.05571	0.205190
$872$	−78.6937	−2.66491
$873$	18.9624	0.641780
$874$	75.4030	2.55054
$875$	0	0
$876$	−4.80606	−0.162382
$877$	−33.3357	−1.12567	−0.562833	−	0.826571i	$-0.690289\pi$
$877$	−33.3357	−1.12567	−0.562833	+	0.826571i	$0.690289\pi$
$878$	72.3839	2.44284
$879$	9.07381	0.306052
$880$	0	0
$881$	22.1793	0.747241	0.373621	−	0.927582i	$-0.378116\pi$
$881$	22.1793	0.747241	0.373621	+	0.927582i	$0.378116\pi$
$882$	−4.73084	−0.159296
$883$	−27.4109	−0.922450	−0.461225	−	0.887283i	$-0.652590\pi$
$883$	−27.4109	−0.922450	−0.461225	+	0.887283i	$0.652590\pi$
$884$	−41.0567	−1.38089
$885$	0	0
$886$	18.9781	0.637582
$887$	1.33170	0.0447142	0.0223571	−	0.999750i	$-0.492883\pi$
$887$	1.33170	0.0447142	0.0223571	+	0.999750i	$0.492883\pi$
$888$	40.5804	1.36179
$889$	−19.9697	−0.669762
$890$	0	0
$891$	−0.130933	−0.00438641
$892$	−4.15633	−0.139164
$893$	−13.6932	−0.458226
$894$	2.37328	0.0793745
$895$	0	0
$896$	−37.8989	−1.26611
$897$	5.50659	0.183860
$898$	−39.4880	−1.31773
$899$	23.3815	0.779818
$900$	0	0
$901$	−67.7328	−2.25651
$902$	−4.00397	−0.133318
$903$	6.70640	0.223175
$904$	112.724	3.74915
$905$	0	0
$906$	7.85685	0.261026
$907$	−31.1754	−1.03516	−0.517581	−	0.855634i	$-0.673167\pi$
$907$	−31.1754	−1.03516	−0.517581	+	0.855634i	$0.673167\pi$
$908$	39.6131	1.31461
$909$	−3.54420	−0.117554
$910$	0	0
$911$	9.56722	0.316976	0.158488	−	0.987361i	$-0.449338\pi$
$911$	9.56722	0.316976	0.158488	+	0.987361i	$0.449338\pi$
$912$	−62.8324	−2.08059
$913$	−0.890491	−0.0294709
$914$	6.10554	0.201953
$915$	0	0
$916$	−22.9380	−0.757891
$917$	−43.5574	−1.43839
$918$	21.3004	0.703019
$919$	−35.8397	−1.18224	−0.591121	−	0.806583i	$-0.701315\pi$
$919$	−35.8397	−1.18224	−0.591121	+	0.806583i	$0.701315\pi$
$920$	0	0
$921$	−11.3806	−0.375003
$922$	−28.2619	−0.930755
$923$	15.0435	0.495163
$924$	1.54420	0.0508004
$925$	0	0
$926$	−16.5369	−0.543436
$927$	14.0811	0.462484
$928$	−47.8505	−1.57077
$929$	19.7137	0.646785	0.323393	−	0.946265i	$-0.395177\pi$
$929$	19.7137	0.646785	0.323393	+	0.946265i	$0.395177\pi$
$930$	0	0
$931$	9.05220	0.296674
$932$	−52.2130	−1.71029
$933$	9.22425	0.301989
$934$	16.9135	0.553427
$935$	0	0
$936$	−8.44358	−0.275987
$937$	−57.2736	−1.87105	−0.935524	−	0.353263i	$-0.885072\pi$
$937$	−57.2736	−1.87105	−0.935524	+	0.353263i	$0.885072\pi$
$938$	37.0532	1.20983
$939$	18.7685	0.612485
$940$	0	0
$941$	−25.2447	−0.822954	−0.411477	−	0.911420i	$-0.634987\pi$
$941$	−25.2447	−0.822954	−0.411477	+	0.911420i	$0.634987\pi$
$942$	42.2179	1.37553
$943$	−62.9478	−2.04986
$944$	−127.823	−4.16029
$945$	0	0
$946$	1.02699	0.0333904
$947$	−5.04254	−0.163860	−0.0819302	−	0.996638i	$-0.526108\pi$
$947$	−5.04254	−0.163860	−0.0819302	+	0.996638i	$0.526108\pi$
$948$	45.6688	1.48325
$949$	0.932071	0.0302563
$950$	0	0
$951$	10.5442	0.341919
$952$	−153.775	−4.98387
$953$	−15.4426	−0.500236	−0.250118	−	0.968215i	$-0.580469\pi$
$953$	−15.4426	−0.500236	−0.250118	+	0.968215i	$0.580469\pi$
$954$	−22.7562	−0.736760
$955$	0	0
$956$	−100.220	−3.24134
$957$	0.392798	0.0126973
$958$	8.91019	0.287875
$959$	−17.5271	−0.565978
$960$	0	0
$961$	29.7440	0.959484
$962$	−12.8568	−0.414521
$963$	−2.64974	−0.0853866
$964$	−33.3561	−1.07433
$965$	0	0
$966$	33.6932	1.08406
$967$	−30.2979	−0.974314	−0.487157	−	0.873314i	$-0.661966\pi$
$967$	−30.2979	−0.974314	−0.487157	+	0.873314i	$0.661966\pi$
$968$	−92.7347	−2.98060
$969$	−40.7572	−1.30931
$970$	0	0
$971$	−40.7367	−1.30730	−0.653652	−	0.756795i	$-0.726764\pi$
$971$	−40.7367	−1.30730	−0.653652	+	0.756795i	$0.726764\pi$
$972$	5.15633	0.165389
$973$	−17.4109	−0.558168
$974$	22.5877	0.723756
$975$	0	0
$976$	63.6662	2.03791
$977$	53.1608	1.70076	0.850382	−	0.526166i	$-0.176371\pi$
$977$	53.1608	1.70076	0.850382	+	0.526166i	$0.176371\pi$
$978$	−46.6312	−1.49110
$979$	1.06396	0.0340043
$980$	0	0
$981$	−9.31994	−0.297563
$982$	−62.3606	−1.99001
$983$	11.1831	0.356687	0.178343	−	0.983968i	$-0.442926\pi$
$983$	11.1831	0.356687	0.178343	+	0.983968i	$0.442926\pi$
$984$	96.5217	3.07700
$985$	0	0
$986$	−63.9013	−2.03503
$987$	−6.11871	−0.194761
$988$	26.3938	0.839697
$989$	16.1457	0.513404
$990$	0	0
$991$	−57.9208	−1.83992	−0.919958	−	0.392018i	$-0.871777\pi$
$991$	−57.9208	−1.83992	−0.919958	+	0.392018i	$0.871777\pi$
$992$	−124.313	−3.94695
$993$	4.95651	0.157290
$994$	92.0468	2.91955
$995$	0	0
$996$	35.0689	1.11120
$997$	−27.4241	−0.868529	−0.434265	−	0.900785i	$-0.642992\pi$
$997$	−27.4241	−0.868529	−0.434265	+	0.900785i	$0.642992\pi$
$998$	−85.2433	−2.69833
$999$	4.80606	0.152057

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.a.q.1.3	yes	3
3.2	odd	2		2925.2.a.be.1.1		3
5.2	odd	4		975.2.c.k.274.6		6
5.3	odd	4		975.2.c.k.274.1		6
5.4	even	2		975.2.a.m.1.1	✓	3
15.2	even	4		2925.2.c.y.2224.1		6
15.8	even	4		2925.2.c.y.2224.6		6
15.14	odd	2		2925.2.a.bk.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
975.2.a.m.1.1	✓	3	5.4	even	2
975.2.a.q.1.3	yes	3	1.1	even	1	trivial
975.2.c.k.274.1		6	5.3	odd	4
975.2.c.k.274.6		6	5.2	odd	4
2925.2.a.be.1.1		3	3.2	odd	2
2925.2.a.bk.1.3		3	15.14	odd	2
2925.2.c.y.2224.1		6	15.2	even	4
2925.2.c.y.2224.6		6	15.8	even	4

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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.a (trivial)

\(f(q)\)	\(=\)	\(q+2.67513 q^{2} +1.00000 q^{3} +5.15633 q^{4} +2.67513 q^{6} -2.28726 q^{7} +8.44358 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.67513 q^{2} +1.00000 q^{3} +5.15633 q^{4} +2.67513 q^{6} -2.28726 q^{7} +8.44358 q^{8} +1.00000 q^{9} -0.130933 q^{11} +5.15633 q^{12} -1.00000 q^{13} -6.11871 q^{14} +12.2750 q^{16} +7.96239 q^{17} +2.67513 q^{18} -5.11871 q^{19} -2.28726 q^{21} -0.350262 q^{22} -5.50659 q^{23} +8.44358 q^{24} -2.67513 q^{26} +1.00000 q^{27} -11.7938 q^{28} -3.00000 q^{29} -7.79384 q^{31} +15.9502 q^{32} -0.130933 q^{33} +21.3004 q^{34} +5.15633 q^{36} +4.80606 q^{37} -13.6932 q^{38} -1.00000 q^{39} +11.4314 q^{41} -6.11871 q^{42} -2.93207 q^{43} -0.675131 q^{44} -14.7308 q^{46} +2.67513 q^{47} +12.2750 q^{48} -1.76845 q^{49} +7.96239 q^{51} -5.15633 q^{52} -8.50659 q^{53} +2.67513 q^{54} -19.3127 q^{56} -5.11871 q^{57} -8.02539 q^{58} -10.4133 q^{59} +5.18664 q^{61} -20.8496 q^{62} -2.28726 q^{63} +18.1187 q^{64} -0.350262 q^{66} -6.05571 q^{67} +41.0567 q^{68} -5.50659 q^{69} -15.0435 q^{71} +8.44358 q^{72} -0.932071 q^{73} +12.8568 q^{74} -26.3938 q^{76} +0.299477 q^{77} -2.67513 q^{78} +8.85685 q^{79} +1.00000 q^{81} +30.5804 q^{82} +6.80114 q^{83} -11.7938 q^{84} -7.84367 q^{86} -3.00000 q^{87} -1.10554 q^{88} -8.12601 q^{89} +2.28726 q^{91} -28.3938 q^{92} -7.79384 q^{93} +7.15633 q^{94} +15.9502 q^{96} +18.9624 q^{97} -4.73084 q^{98} -0.130933 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{3} + 5 q^{4} + 3 q^{6} - q^{7} + 9 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + 3 * q^3 + 5 * q^4 + 3 * q^6 - q^7 + 9 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} + 3 q^{3} + 5 q^{4} + 3 q^{6} - q^{7} + 9 q^{8} + 3 q^{9} - 5 q^{11} + 5 q^{12} - 3 q^{13} + 3 q^{14} + 5 q^{16} + 13 q^{17} + 3 q^{18} + 6 q^{19} - q^{21} + 9 q^{22} + 4 q^{23} + 9 q^{24} - 3 q^{26} + 3 q^{27} - 9 q^{28} - 9 q^{29} + 3 q^{31} + 11 q^{32} - 5 q^{33} + 17 q^{34} + 5 q^{36} + 14 q^{37} - 8 q^{38} - 3 q^{39} - 8 q^{41} + 3 q^{42} + 3 q^{44} - 22 q^{46} + 3 q^{47} + 5 q^{48} + 6 q^{49} + 13 q^{51} - 5 q^{52} - 5 q^{53} + 3 q^{54} - 37 q^{56} + 6 q^{57} - 9 q^{58} - 17 q^{59} + 3 q^{61} - 19 q^{62} - q^{63} + 33 q^{64} + 9 q^{66} - q^{67} + 39 q^{68} + 4 q^{69} - 2 q^{71} + 9 q^{72} + 6 q^{73} + 8 q^{74} - 26 q^{76} + 21 q^{77} - 3 q^{78} - 4 q^{79} + 3 q^{81} + 26 q^{82} + 7 q^{83} - 9 q^{84} - 34 q^{86} - 9 q^{87} - 23 q^{88} - 16 q^{89} + q^{91} - 32 q^{92} + 3 q^{93} + 11 q^{94} + 11 q^{96} + 46 q^{97} + 8 q^{98} - 5 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^3 + 5 * q^4 + 3 * q^6 - q^7 + 9 * q^8 + 3 * q^9 - 5 * q^11 + 5 * q^12 - 3 * q^13 + 3 * q^14 + 5 * q^16 + 13 * q^17 + 3 * q^18 + 6 * q^19 - q^21 + 9 * q^22 + 4 * q^23 + 9 * q^24 - 3 * q^26 + 3 * q^27 - 9 * q^28 - 9 * q^29 + 3 * q^31 + 11 * q^32 - 5 * q^33 + 17 * q^34 + 5 * q^36 + 14 * q^37 - 8 * q^38 - 3 * q^39 - 8 * q^41 + 3 * q^42 + 3 * q^44 - 22 * q^46 + 3 * q^47 + 5 * q^48 + 6 * q^49 + 13 * q^51 - 5 * q^52 - 5 * q^53 + 3 * q^54 - 37 * q^56 + 6 * q^57 - 9 * q^58 - 17 * q^59 + 3 * q^61 - 19 * q^62 - q^63 + 33 * q^64 + 9 * q^66 - q^67 + 39 * q^68 + 4 * q^69 - 2 * q^71 + 9 * q^72 + 6 * q^73 + 8 * q^74 - 26 * q^76 + 21 * q^77 - 3 * q^78 - 4 * q^79 + 3 * q^81 + 26 * q^82 + 7 * q^83 - 9 * q^84 - 34 * q^86 - 9 * q^87 - 23 * q^88 - 16 * q^89 + q^91 - 32 * q^92 + 3 * q^93 + 11 * q^94 + 11 * q^96 + 46 * q^97 + 8 * q^98 - 5 * q^99

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