LMFDB - Embedded newform 4025.2.a.y.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4025,2,Mod(1,4025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4025, 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("4025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4025 = 5^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4025.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:	$32.1397868136$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 14 x^{10} + 26 x^{9} + 71 x^{8} - 120 x^{7} - 162 x^{6} + 244 x^{5} + 170 x^{4} + \cdots + 17 $ x^12 - 2x^11 - 14x^10 + 26x^9 + 71x^8 - 120x^7 - 162x^6 + 244x^5 + 170x^4 - 210x^3 - 81x^2 + 58*x + 17
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 805)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.69164$ of defining polynomial
Character	$\chi$	$=$	4025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.69164 q^{2} +0.285164 q^{3} +0.861643 q^{4} -0.482394 q^{6} -1.00000 q^{7} +1.92569 q^{8} -2.91868 q^{9} +O(q^{10})$	\(q-1.69164 q^{2} +0.285164 q^{3} +0.861643 q^{4} -0.482394 q^{6} -1.00000 q^{7} +1.92569 q^{8} -2.91868 q^{9} +3.30777 q^{11} +0.245710 q^{12} +2.44160 q^{13} +1.69164 q^{14} -4.98086 q^{16} -2.66169 q^{17} +4.93736 q^{18} +0.468614 q^{19} -0.285164 q^{21} -5.59556 q^{22} +1.00000 q^{23} +0.549137 q^{24} -4.13031 q^{26} -1.68779 q^{27} -0.861643 q^{28} +3.18616 q^{29} -9.56481 q^{31} +4.57444 q^{32} +0.943258 q^{33} +4.50262 q^{34} -2.51486 q^{36} +7.09019 q^{37} -0.792725 q^{38} +0.696256 q^{39} -8.90225 q^{41} +0.482394 q^{42} +2.71642 q^{43} +2.85012 q^{44} -1.69164 q^{46} -10.1450 q^{47} -1.42036 q^{48} +1.00000 q^{49} -0.759018 q^{51} +2.10379 q^{52} +9.81614 q^{53} +2.85514 q^{54} -1.92569 q^{56} +0.133632 q^{57} -5.38983 q^{58} -9.47940 q^{59} +5.42588 q^{61} +16.1802 q^{62} +2.91868 q^{63} +2.22342 q^{64} -1.59565 q^{66} +4.04113 q^{67} -2.29343 q^{68} +0.285164 q^{69} +5.14273 q^{71} -5.62047 q^{72} +1.26345 q^{73} -11.9940 q^{74} +0.403778 q^{76} -3.30777 q^{77} -1.17781 q^{78} -4.09504 q^{79} +8.27475 q^{81} +15.0594 q^{82} +3.98793 q^{83} -0.245710 q^{84} -4.59521 q^{86} +0.908577 q^{87} +6.36974 q^{88} -17.8497 q^{89} -2.44160 q^{91} +0.861643 q^{92} -2.72754 q^{93} +17.1616 q^{94} +1.30446 q^{96} +5.66233 q^{97} -1.69164 q^{98} -9.65434 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + 8 q^{4} - 6 q^{6} - 12 q^{7} + 6 q^{8} + 8 q^{9}+O(q^{10}) $ 12 * q + 2 * q^2 + 8 * q^4 - 6 * q^6 - 12 * q^7 + 6 * q^8 + 8 * q^9	$ 12 q + 2 q^{2} + 8 q^{4} - 6 q^{6} - 12 q^{7} + 6 q^{8} + 8 q^{9} - 8 q^{11} - 12 q^{12} + 2 q^{13} - 2 q^{14} - 4 q^{16} - 8 q^{17} + 20 q^{18} - 26 q^{19} + 4 q^{22} + 12 q^{23} - 12 q^{24} - 22 q^{26} + 12 q^{27} - 8 q^{28} - 12 q^{29} - 50 q^{31} + 14 q^{32} + 4 q^{33} - 28 q^{34} - 18 q^{36} + 8 q^{37} - 4 q^{38} - 26 q^{39} - 4 q^{41} + 6 q^{42} + 26 q^{43} - 10 q^{44} + 2 q^{46} + 16 q^{47} - 40 q^{48} + 12 q^{49} - 32 q^{51} + 10 q^{52} - 18 q^{53} - 10 q^{54} - 6 q^{56} - 10 q^{57} - 18 q^{58} - 18 q^{59} + 8 q^{61} - 54 q^{62} - 8 q^{63} + 12 q^{64} - 2 q^{66} + 38 q^{67} - 36 q^{68} - 24 q^{71} + 18 q^{72} - 14 q^{73} + 36 q^{74} - 56 q^{76} + 8 q^{77} - 26 q^{78} - 44 q^{79} - 16 q^{81} - 44 q^{82} - 14 q^{83} + 12 q^{84} - 32 q^{86} + 16 q^{87} + 32 q^{88} - 10 q^{89} - 2 q^{91} + 8 q^{92} + 26 q^{93} + 18 q^{94} - 38 q^{96} - 4 q^{97} + 2 q^{98} - 56 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 + 8 * q^4 - 6 * q^6 - 12 * q^7 + 6 * q^8 + 8 * q^9 - 8 * q^11 - 12 * q^12 + 2 * q^13 - 2 * q^14 - 4 * q^16 - 8 * q^17 + 20 * q^18 - 26 * q^19 + 4 * q^22 + 12 * q^23 - 12 * q^24 - 22 * q^26 + 12 * q^27 - 8 * q^28 - 12 * q^29 - 50 * q^31 + 14 * q^32 + 4 * q^33 - 28 * q^34 - 18 * q^36 + 8 * q^37 - 4 * q^38 - 26 * q^39 - 4 * q^41 + 6 * q^42 + 26 * q^43 - 10 * q^44 + 2 * q^46 + 16 * q^47 - 40 * q^48 + 12 * q^49 - 32 * q^51 + 10 * q^52 - 18 * q^53 - 10 * q^54 - 6 * q^56 - 10 * q^57 - 18 * q^58 - 18 * q^59 + 8 * q^61 - 54 * q^62 - 8 * q^63 + 12 * q^64 - 2 * q^66 + 38 * q^67 - 36 * q^68 - 24 * q^71 + 18 * q^72 - 14 * q^73 + 36 * q^74 - 56 * q^76 + 8 * q^77 - 26 * q^78 - 44 * q^79 - 16 * q^81 - 44 * q^82 - 14 * q^83 + 12 * q^84 - 32 * q^86 + 16 * q^87 + 32 * q^88 - 10 * q^89 - 2 * q^91 + 8 * q^92 + 26 * q^93 + 18 * q^94 - 38 * q^96 - 4 * q^97 + 2 * q^98 - 56 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.69164	−1.19617	−0.598085	−	0.801433i	$-0.704071\pi$
$2$	−1.69164	−1.19617	−0.598085	+	0.801433i	$0.704071\pi$
$3$	0.285164	0.164639	0.0823197	−	0.996606i	$-0.473767\pi$
$3$	0.285164	0.164639	0.0823197	+	0.996606i	$0.473767\pi$
$4$	0.861643	0.430822
$5$	0	0
$5$	0	0
$6$	−0.482394	−0.196937
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.92569	0.680834
$9$	−2.91868	−0.972894
$10$	0	0
$11$	3.30777	0.997332	0.498666	−	0.866794i	$-0.333824\pi$
$11$	3.30777	0.997332	0.498666	+	0.866794i	$0.333824\pi$
$12$	0.245710	0.0709302
$13$	2.44160	0.677178	0.338589	−	0.940934i	$-0.390050\pi$
$13$	2.44160	0.677178	0.338589	+	0.940934i	$0.390050\pi$
$14$	1.69164	0.452110
$15$	0	0
$16$	−4.98086	−1.24521
$17$	−2.66169	−0.645555	−0.322778	−	0.946475i	$-0.604617\pi$
$17$	−2.66169	−0.645555	−0.322778	+	0.946475i	$0.604617\pi$
$18$	4.93736	1.16375
$19$	0.468614	0.107507	0.0537537	−	0.998554i	$-0.482881\pi$
$19$	0.468614	0.107507	0.0537537	+	0.998554i	$0.482881\pi$
$20$	0	0
$21$	−0.285164	−0.0622279
$22$	−5.59556	−1.19298
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	0.549137	0.112092
$25$	0	0
$26$	−4.13031	−0.810020
$27$	−1.68779	−0.324816
$28$	−0.861643	−0.162835
$29$	3.18616	0.591655	0.295827	−	0.955241i	$-0.404405\pi$
$29$	3.18616	0.591655	0.295827	+	0.955241i	$0.404405\pi$
$30$	0	0
$31$	−9.56481	−1.71789	−0.858945	−	0.512067i	$-0.828880\pi$
$31$	−9.56481	−1.71789	−0.858945	+	0.512067i	$0.828880\pi$
$32$	4.57444	0.808654
$33$	0.943258	0.164200
$34$	4.50262	0.772193
$35$	0	0
$36$	−2.51486	−0.419144
$37$	7.09019	1.16562	0.582810	−	0.812608i	$-0.301953\pi$
$37$	7.09019	1.16562	0.582810	+	0.812608i	$0.301953\pi$
$38$	−0.792725	−0.128597
$39$	0.696256	0.111490
$40$	0	0
$41$	−8.90225	−1.39030	−0.695149	−	0.718866i	$-0.744662\pi$
$41$	−8.90225	−1.39030	−0.695149	+	0.718866i	$0.744662\pi$
$42$	0.482394	0.0744351
$43$	2.71642	0.414251	0.207125	−	0.978314i	$-0.433589\pi$
$43$	2.71642	0.414251	0.207125	+	0.978314i	$0.433589\pi$
$44$	2.85012	0.429672
$45$	0	0
$46$	−1.69164	−0.249419
$47$	−10.1450	−1.47980	−0.739899	−	0.672718i	$-0.765127\pi$
$47$	−10.1450	−1.47980	−0.739899	+	0.672718i	$0.765127\pi$
$48$	−1.42036	−0.205011
$49$	1.00000	0.142857
$50$	0	0
$51$	−0.759018	−0.106284
$52$	2.10379	0.291743
$53$	9.81614	1.34835	0.674175	−	0.738572i	$-0.264499\pi$
$53$	9.81614	1.34835	0.674175	+	0.738572i	$0.264499\pi$
$54$	2.85514	0.388535
$55$	0	0
$56$	−1.92569	−0.257331
$57$	0.133632	0.0176999
$58$	−5.38983	−0.707719
$59$	−9.47940	−1.23411	−0.617056	−	0.786919i	$-0.711675\pi$
$59$	−9.47940	−1.23411	−0.617056	+	0.786919i	$0.711675\pi$
$60$	0	0
$61$	5.42588	0.694712	0.347356	−	0.937733i	$-0.387080\pi$
$61$	5.42588	0.694712	0.347356	+	0.937733i	$0.387080\pi$
$62$	16.1802	2.05489
$63$	2.91868	0.367719
$64$	2.22342	0.277927
$65$	0	0
$66$	−1.59565	−0.196411
$67$	4.04113	0.493703	0.246851	−	0.969053i	$-0.420604\pi$
$67$	4.04113	0.493703	0.246851	+	0.969053i	$0.420604\pi$
$68$	−2.29343	−0.278119
$69$	0.285164	0.0343297
$70$	0	0
$71$	5.14273	0.610330	0.305165	−	0.952299i	$-0.401288\pi$
$71$	5.14273	0.610330	0.305165	+	0.952299i	$0.401288\pi$
$72$	−5.62047	−0.662379
$73$	1.26345	0.147876	0.0739379	−	0.997263i	$-0.476443\pi$
$73$	1.26345	0.147876	0.0739379	+	0.997263i	$0.476443\pi$
$74$	−11.9940	−1.39428
$75$	0	0
$76$	0.403778	0.0463165
$77$	−3.30777	−0.376956
$78$	−1.17781	−0.133361
$79$	−4.09504	−0.460728	−0.230364	−	0.973105i	$-0.573992\pi$
$79$	−4.09504	−0.460728	−0.230364	+	0.973105i	$0.573992\pi$
$80$	0	0
$81$	8.27475	0.919416
$82$	15.0594	1.66303
$83$	3.98793	0.437733	0.218866	−	0.975755i	$-0.429764\pi$
$83$	3.98793	0.437733	0.218866	+	0.975755i	$0.429764\pi$
$84$	−0.245710	−0.0268091
$85$	0	0
$86$	−4.59521	−0.495514
$87$	0.908577	0.0974097
$88$	6.36974	0.679017
$89$	−17.8497	−1.89207	−0.946035	−	0.324065i	$-0.894950\pi$
$89$	−17.8497	−1.89207	−0.946035	+	0.324065i	$0.894950\pi$
$90$	0	0
$91$	−2.44160	−0.255949
$92$	0.861643	0.0898325
$93$	−2.72754	−0.282833
$94$	17.1616	1.77009
$95$	0	0
$96$	1.30446	0.133136
$97$	5.66233	0.574922	0.287461	−	0.957792i	$-0.407189\pi$
$97$	5.66233	0.574922	0.287461	+	0.957792i	$0.407189\pi$
$98$	−1.69164	−0.170881
$99$	−9.65434	−0.970298
$100$	0	0
$101$	−8.10097	−0.806076	−0.403038	−	0.915183i	$-0.632046\pi$
$101$	−8.10097	−0.806076	−0.403038	+	0.915183i	$0.632046\pi$
$102$	1.28399	0.127133
$103$	−12.2183	−1.20391	−0.601954	−	0.798531i	$-0.705611\pi$
$103$	−12.2183	−1.20391	−0.601954	+	0.798531i	$0.705611\pi$
$104$	4.70176	0.461046
$105$	0	0
$106$	−16.6054	−1.61286
$107$	9.74740	0.942317	0.471158	−	0.882049i	$-0.343836\pi$
$107$	9.74740	0.942317	0.471158	+	0.882049i	$0.343836\pi$
$108$	−1.45428	−0.139938
$109$	−0.864235	−0.0827787	−0.0413893	−	0.999143i	$-0.513178\pi$
$109$	−0.864235	−0.0827787	−0.0413893	+	0.999143i	$0.513178\pi$
$110$	0	0
$111$	2.02187	0.191907
$112$	4.98086	0.470647
$113$	18.1377	1.70625	0.853126	−	0.521704i	$-0.174704\pi$
$113$	18.1377	1.70625	0.853126	+	0.521704i	$0.174704\pi$
$114$	−0.226057	−0.0211721
$115$	0	0
$116$	2.74533	0.254898
$117$	−7.12626	−0.658823
$118$	16.0357	1.47621
$119$	2.66169	0.243997
$120$	0	0
$121$	−0.0586268	−0.00532971
$122$	−9.17863	−0.830994
$123$	−2.53860	−0.228898
$124$	−8.24146	−0.740105
$125$	0	0
$126$	−4.93736	−0.439855
$127$	1.20260	0.106713	0.0533566	−	0.998576i	$-0.483008\pi$
$127$	1.20260	0.106713	0.0533566	+	0.998576i	$0.483008\pi$
$128$	−12.9101	−1.14110
$129$	0.774626	0.0682020
$130$	0	0
$131$	5.31147	0.464065	0.232033	−	0.972708i	$-0.425462\pi$
$131$	5.31147	0.464065	0.232033	+	0.972708i	$0.425462\pi$
$132$	0.812752	0.0707410
$133$	−0.468614	−0.0406340
$134$	−6.83614	−0.590552
$135$	0	0
$136$	−5.12559	−0.439516
$137$	10.0521	0.858807	0.429403	−	0.903113i	$-0.358724\pi$
$137$	10.0521	0.858807	0.429403	+	0.903113i	$0.358724\pi$
$138$	−0.482394	−0.0410641
$139$	−6.02117	−0.510709	−0.255355	−	0.966847i	$-0.582192\pi$
$139$	−6.02117	−0.510709	−0.255355	+	0.966847i	$0.582192\pi$
$140$	0	0
$141$	−2.89298	−0.243633
$142$	−8.69965	−0.730058
$143$	8.07627	0.675371
$144$	14.5375	1.21146
$145$	0	0
$146$	−2.13730	−0.176884
$147$	0.285164	0.0235199
$148$	6.10922	0.502174
$149$	−17.3340	−1.42006	−0.710028	−	0.704174i	$-0.751318\pi$
$149$	−17.3340	−1.42006	−0.710028	+	0.704174i	$0.751318\pi$
$150$	0	0
$151$	4.04869	0.329478	0.164739	−	0.986337i	$-0.447322\pi$
$151$	4.04869	0.329478	0.164739	+	0.986337i	$0.447322\pi$
$152$	0.902404	0.0731946
$153$	7.76863	0.628057
$154$	5.59556	0.450903
$155$	0	0
$156$	0.599925	0.0480324
$157$	−13.9110	−1.11022	−0.555108	−	0.831778i	$-0.687323\pi$
$157$	−13.9110	−1.11022	−0.555108	+	0.831778i	$0.687323\pi$
$158$	6.92733	0.551109
$159$	2.79921	0.221992
$160$	0	0
$161$	−1.00000	−0.0788110
$162$	−13.9979	−1.09978
$163$	−19.6377	−1.53814	−0.769072	−	0.639162i	$-0.779281\pi$
$163$	−19.6377	−1.53814	−0.769072	+	0.639162i	$0.779281\pi$
$164$	−7.67056	−0.598970
$165$	0	0
$166$	−6.74615	−0.523603
$167$	2.30164	0.178106	0.0890531	−	0.996027i	$-0.471616\pi$
$167$	2.30164	0.178106	0.0890531	+	0.996027i	$0.471616\pi$
$168$	−0.549137	−0.0423668
$169$	−7.03859	−0.541430
$170$	0	0
$171$	−1.36773	−0.104593
$172$	2.34059	0.178468
$173$	−13.9796	−1.06285	−0.531424	−	0.847106i	$-0.678343\pi$
$173$	−13.9796	−1.06285	−0.531424	+	0.847106i	$0.678343\pi$
$174$	−1.53698	−0.116519
$175$	0	0
$176$	−16.4756	−1.24189
$177$	−2.70318	−0.203184
$178$	30.1953	2.26324
$179$	−10.7300	−0.802002	−0.401001	−	0.916078i	$-0.631338\pi$
$179$	−10.7300	−0.802002	−0.401001	+	0.916078i	$0.631338\pi$
$180$	0	0
$181$	16.4964	1.22617	0.613084	−	0.790018i	$-0.289929\pi$
$181$	16.4964	1.22617	0.613084	+	0.790018i	$0.289929\pi$
$182$	4.13031	0.306159
$183$	1.54726	0.114377
$184$	1.92569	0.141964
$185$	0	0
$186$	4.61401	0.338316
$187$	−8.80428	−0.643832
$188$	−8.74136	−0.637529
$189$	1.68779	0.122769
$190$	0	0
$191$	1.65601	0.119825	0.0599125	−	0.998204i	$-0.480918\pi$
$191$	1.65601	0.119825	0.0599125	+	0.998204i	$0.480918\pi$
$192$	0.634039	0.0457578
$193$	−23.2499	−1.67356	−0.836781	−	0.547537i	$-0.815565\pi$
$193$	−23.2499	−1.67356	−0.836781	+	0.547537i	$0.815565\pi$
$194$	−9.57861	−0.687704
$195$	0	0
$196$	0.861643	0.0615460
$197$	−21.3143	−1.51858	−0.759292	−	0.650750i	$-0.774455\pi$
$197$	−21.3143	−1.51858	−0.759292	+	0.650750i	$0.774455\pi$
$198$	16.3317	1.16064
$199$	15.7924	1.11949	0.559746	−	0.828664i	$-0.310899\pi$
$199$	15.7924	1.11949	0.559746	+	0.828664i	$0.310899\pi$
$200$	0	0
$201$	1.15238	0.0812829
$202$	13.7039	0.964204
$203$	−3.18616	−0.223624
$204$	−0.654003	−0.0457894
$205$	0	0
$206$	20.6690	1.44008
$207$	−2.91868	−0.202862
$208$	−12.1613	−0.843232
$209$	1.55007	0.107220
$210$	0	0
$211$	−22.0687	−1.51927	−0.759637	−	0.650347i	$-0.774624\pi$
$211$	−22.0687	−1.51927	−0.759637	+	0.650347i	$0.774624\pi$
$212$	8.45801	0.580898
$213$	1.46652	0.100484
$214$	−16.4891	−1.12717
$215$	0	0
$216$	−3.25017	−0.221146
$217$	9.56481	0.649302
$218$	1.46197	0.0990173
$219$	0.360290	0.0243462
$220$	0	0
$221$	−6.49879	−0.437156
$222$	−3.42027	−0.229553
$223$	1.01366	0.0678794	0.0339397	−	0.999424i	$-0.489195\pi$
$223$	1.01366	0.0678794	0.0339397	+	0.999424i	$0.489195\pi$
$224$	−4.57444	−0.305642
$225$	0	0
$226$	−30.6825	−2.04097
$227$	−1.41300	−0.0937838	−0.0468919	−	0.998900i	$-0.514932\pi$
$227$	−1.41300	−0.0937838	−0.0468919	+	0.998900i	$0.514932\pi$
$228$	0.115143	0.00762552
$229$	−8.92555	−0.589817	−0.294909	−	0.955525i	$-0.595289\pi$
$229$	−8.92555	−0.589817	−0.294909	+	0.955525i	$0.595289\pi$
$230$	0	0
$231$	−0.943258	−0.0620618
$232$	6.13555	0.402819
$233$	22.3221	1.46237	0.731185	−	0.682179i	$-0.238968\pi$
$233$	22.3221	1.46237	0.731185	+	0.682179i	$0.238968\pi$
$234$	12.0551	0.788063
$235$	0	0
$236$	−8.16786	−0.531683
$237$	−1.16776	−0.0758540
$238$	−4.50262	−0.291862
$239$	22.0526	1.42647	0.713233	−	0.700927i	$-0.247230\pi$
$239$	22.0526	1.42647	0.713233	+	0.700927i	$0.247230\pi$
$240$	0	0
$241$	12.8098	0.825151	0.412576	−	0.910923i	$-0.364629\pi$
$241$	12.8098	0.825151	0.412576	+	0.910923i	$0.364629\pi$
$242$	0.0991755	0.00637524
$243$	7.42304	0.476188
$244$	4.67517	0.299297
$245$	0	0
$246$	4.29439	0.273801
$247$	1.14417	0.0728016
$248$	−18.4189	−1.16960
$249$	1.13721	0.0720681
$250$	0	0
$251$	21.8144	1.37691	0.688457	−	0.725277i	$-0.258288\pi$
$251$	21.8144	1.37691	0.688457	+	0.725277i	$0.258288\pi$
$252$	2.51486	0.158421
$253$	3.30777	0.207958
$254$	−2.03436	−0.127647
$255$	0	0
$256$	17.3924	1.08702
$257$	3.86334	0.240989	0.120494	−	0.992714i	$-0.461552\pi$
$257$	3.86334	0.240989	0.120494	+	0.992714i	$0.461552\pi$
$258$	−1.31039	−0.0815812
$259$	−7.09019	−0.440563
$260$	0	0
$261$	−9.29938	−0.575617
$262$	−8.98509	−0.555101
$263$	24.7313	1.52500	0.762500	−	0.646988i	$-0.223972\pi$
$263$	24.7313	1.52500	0.762500	+	0.646988i	$0.223972\pi$
$264$	1.81642	0.111793
$265$	0	0
$266$	0.792725	0.0486051
$267$	−5.09010	−0.311509
$268$	3.48201	0.212698
$269$	−16.6699	−1.01638	−0.508191	−	0.861244i	$-0.669686\pi$
$269$	−16.6699	−1.01638	−0.508191	+	0.861244i	$0.669686\pi$
$270$	0	0
$271$	−23.2737	−1.41378	−0.706889	−	0.707325i	$-0.749902\pi$
$271$	−23.2737	−1.41378	−0.706889	+	0.707325i	$0.749902\pi$
$272$	13.2575	0.803854
$273$	−0.696256	−0.0421393
$274$	−17.0045	−1.02728
$275$	0	0
$276$	0.245710	0.0147900
$277$	1.14510	0.0688025	0.0344013	−	0.999408i	$-0.489048\pi$
$277$	1.14510	0.0688025	0.0344013	+	0.999408i	$0.489048\pi$
$278$	10.1857	0.610895
$279$	27.9166	1.67133
$280$	0	0
$281$	−0.753762	−0.0449657	−0.0224828	−	0.999747i	$-0.507157\pi$
$281$	−0.753762	−0.0449657	−0.0224828	+	0.999747i	$0.507157\pi$
$282$	4.89388	0.291426
$283$	−17.3276	−1.03002	−0.515011	−	0.857184i	$-0.672212\pi$
$283$	−17.3276	−1.03002	−0.515011	+	0.857184i	$0.672212\pi$
$284$	4.43120	0.262943
$285$	0	0
$286$	−13.6621	−0.807859
$287$	8.90225	0.525483
$288$	−13.3513	−0.786734
$289$	−9.91540	−0.583259
$290$	0	0
$291$	1.61469	0.0946548
$292$	1.08864	0.0637081
$293$	−7.18575	−0.419796	−0.209898	−	0.977723i	$-0.567313\pi$
$293$	−7.18575	−0.419796	−0.209898	+	0.977723i	$0.567313\pi$
$294$	−0.482394	−0.0281338
$295$	0	0
$296$	13.6535	0.793594
$297$	−5.58284	−0.323949
$298$	29.3228	1.69863
$299$	2.44160	0.141201
$300$	0	0
$301$	−2.71642	−0.156572
$302$	−6.84892	−0.394111
$303$	−2.31010	−0.132712
$304$	−2.33410	−0.133870
$305$	0	0
$306$	−13.1417	−0.751262
$307$	−29.8637	−1.70441	−0.852205	−	0.523207i	$-0.824735\pi$
$307$	−29.8637	−1.70441	−0.852205	+	0.523207i	$0.824735\pi$
$308$	−2.85012	−0.162401
$309$	−3.48422	−0.198211
$310$	0	0
$311$	−0.301925	−0.0171206	−0.00856030	−	0.999963i	$-0.502725\pi$
$311$	−0.301925	−0.0171206	−0.00856030	+	0.999963i	$0.502725\pi$
$312$	1.34077	0.0759063
$313$	−16.8957	−0.955000	−0.477500	−	0.878632i	$-0.658457\pi$
$313$	−16.8957	−0.955000	−0.477500	+	0.878632i	$0.658457\pi$
$314$	23.5323	1.32801
$315$	0	0
$316$	−3.52846	−0.198492
$317$	9.18396	0.515823	0.257911	−	0.966169i	$-0.416966\pi$
$317$	9.18396	0.515823	0.257911	+	0.966169i	$0.416966\pi$
$318$	−4.73525	−0.265540
$319$	10.5391	0.590076
$320$	0	0
$321$	2.77961	0.155142
$322$	1.69164	0.0942714
$323$	−1.24730	−0.0694019
$324$	7.12988	0.396104
$325$	0	0
$326$	33.2199	1.83988
$327$	−0.246449	−0.0136286
$328$	−17.1430	−0.946562
$329$	10.1450	0.559311
$330$	0	0
$331$	0.725140	0.0398573	0.0199286	−	0.999801i	$-0.493656\pi$
$331$	0.725140	0.0398573	0.0199286	+	0.999801i	$0.493656\pi$
$332$	3.43618	0.188585
$333$	−20.6940	−1.13402
$334$	−3.89354	−0.213045
$335$	0	0
$336$	1.42036	0.0774870
$337$	−18.1165	−0.986868	−0.493434	−	0.869783i	$-0.664259\pi$
$337$	−18.1165	−0.986868	−0.493434	+	0.869783i	$0.664259\pi$
$338$	11.9067	0.647642
$339$	5.17222	0.280916
$340$	0	0
$341$	−31.6382	−1.71331
$342$	2.31371	0.125111
$343$	−1.00000	−0.0539949
$344$	5.23099	0.282036
$345$	0	0
$346$	23.6484	1.27135
$347$	−22.7652	−1.22210	−0.611051	−	0.791591i	$-0.709253\pi$
$347$	−22.7652	−1.22210	−0.611051	+	0.791591i	$0.709253\pi$
$348$	0.782870	0.0419662
$349$	−34.3192	−1.83706	−0.918531	−	0.395348i	$-0.870624\pi$
$349$	−34.3192	−1.83706	−0.918531	+	0.395348i	$0.870624\pi$
$350$	0	0
$351$	−4.12092	−0.219958
$352$	15.1312	0.806496
$353$	−31.9345	−1.69970	−0.849852	−	0.527021i	$-0.823309\pi$
$353$	−31.9345	−1.69970	−0.849852	+	0.527021i	$0.823309\pi$
$354$	4.57281	0.243042
$355$	0	0
$356$	−15.3801	−0.815144
$357$	0.759018	0.0401715
$358$	18.1514	0.959330
$359$	6.69496	0.353347	0.176673	−	0.984270i	$-0.443466\pi$
$359$	6.69496	0.353347	0.176673	+	0.984270i	$0.443466\pi$
$360$	0	0
$361$	−18.7804	−0.988442
$362$	−27.9060	−1.46670
$363$	−0.0167183	−0.000877481 0
$364$	−2.10379	−0.110269
$365$	0	0
$366$	−2.61741	−0.136814
$367$	19.7440	1.03063	0.515315	−	0.857001i	$-0.327675\pi$
$367$	19.7440	1.03063	0.515315	+	0.857001i	$0.327675\pi$
$368$	−4.98086	−0.259645
$369$	25.9828	1.35261
$370$	0	0
$371$	−9.81614	−0.509628
$372$	−2.35017	−0.121850
$373$	−22.8686	−1.18409	−0.592046	−	0.805904i	$-0.701680\pi$
$373$	−22.8686	−1.18409	−0.592046	+	0.805904i	$0.701680\pi$
$374$	14.8937	0.770133
$375$	0	0
$376$	−19.5361	−1.00750
$377$	7.77933	0.400656
$378$	−2.85514	−0.146852
$379$	−23.1640	−1.18985	−0.594927	−	0.803780i	$-0.702819\pi$
$379$	−23.1640	−1.18985	−0.594927	+	0.803780i	$0.702819\pi$
$380$	0	0
$381$	0.342937	0.0175692
$382$	−2.80138	−0.143331
$383$	−23.3601	−1.19364	−0.596822	−	0.802373i	$-0.703570\pi$
$383$	−23.3601	−1.19364	−0.596822	+	0.802373i	$0.703570\pi$
$384$	−3.68149	−0.187870
$385$	0	0
$386$	39.3304	2.00186
$387$	−7.92838	−0.403022
$388$	4.87890	0.247689
$389$	−25.9091	−1.31364	−0.656822	−	0.754046i	$-0.728100\pi$
$389$	−25.9091	−1.31364	−0.656822	+	0.754046i	$0.728100\pi$
$390$	0	0
$391$	−2.66169	−0.134608
$392$	1.92569	0.0972620
$393$	1.51464	0.0764035
$394$	36.0562	1.81648
$395$	0	0
$396$	−8.31860	−0.418025
$397$	28.3916	1.42493	0.712466	−	0.701706i	$-0.247578\pi$
$397$	28.3916	1.42493	0.712466	+	0.701706i	$0.247578\pi$
$398$	−26.7150	−1.33910
$399$	−0.133632	−0.00668995
$400$	0	0
$401$	5.43750	0.271536	0.135768	−	0.990741i	$-0.456650\pi$
$401$	5.43750	0.271536	0.135768	+	0.990741i	$0.456650\pi$
$402$	−1.94942	−0.0972282
$403$	−23.3535	−1.16332
$404$	−6.98014	−0.347275
$405$	0	0
$406$	5.38983	0.267493
$407$	23.4528	1.16251
$408$	−1.46163	−0.0723616
$409$	2.01786	0.0997766	0.0498883	−	0.998755i	$-0.484113\pi$
$409$	2.01786	0.0997766	0.0498883	+	0.998755i	$0.484113\pi$
$410$	0	0
$411$	2.86649	0.141393
$412$	−10.5278	−0.518669
$413$	9.47940	0.466451
$414$	4.93736	0.242658
$415$	0	0
$416$	11.1689	0.547603
$417$	−1.71702	−0.0840829
$418$	−2.62216	−0.128254
$419$	11.4962	0.561627	0.280813	−	0.959762i	$-0.409396\pi$
$419$	11.4962	0.561627	0.280813	+	0.959762i	$0.409396\pi$
$420$	0	0
$421$	3.02374	0.147368	0.0736840	−	0.997282i	$-0.476524\pi$
$421$	3.02374	0.147368	0.0736840	+	0.997282i	$0.476524\pi$
$422$	37.3324	1.81731
$423$	29.6100	1.43969
$424$	18.9028	0.918002
$425$	0	0
$426$	−2.48083	−0.120196
$427$	−5.42588	−0.262577
$428$	8.39878	0.405970
$429$	2.30306	0.111193
$430$	0	0
$431$	−34.1764	−1.64622	−0.823110	−	0.567882i	$-0.807763\pi$
$431$	−34.1764	−1.64622	−0.823110	+	0.567882i	$0.807763\pi$
$432$	8.40666	0.404466
$433$	−10.0210	−0.481579	−0.240789	−	0.970577i	$-0.577406\pi$
$433$	−10.0210	−0.481579	−0.240789	+	0.970577i	$0.577406\pi$
$434$	−16.1802	−0.776675
$435$	0	0
$436$	−0.744662	−0.0356629
$437$	0.468614	0.0224168
$438$	−0.609482	−0.0291222
$439$	−13.6281	−0.650431	−0.325216	−	0.945640i	$-0.605437\pi$
$439$	−13.6281	−0.650431	−0.325216	+	0.945640i	$0.605437\pi$
$440$	0	0
$441$	−2.91868	−0.138985
$442$	10.9936	0.522912
$443$	−5.82640	−0.276821	−0.138410	−	0.990375i	$-0.544199\pi$
$443$	−5.82640	−0.276821	−0.138410	+	0.990375i	$0.544199\pi$
$444$	1.74213	0.0826777
$445$	0	0
$446$	−1.71474	−0.0811952
$447$	−4.94303	−0.233797
$448$	−2.22342	−0.105047
$449$	−11.0290	−0.520489	−0.260244	−	0.965543i	$-0.583803\pi$
$449$	−11.0290	−0.520489	−0.260244	+	0.965543i	$0.583803\pi$
$450$	0	0
$451$	−29.4466	−1.38659
$452$	15.6282	0.735091
$453$	1.15454	0.0542450
$454$	2.39028	0.112181
$455$	0	0
$456$	0.257333	0.0120507
$457$	−2.56697	−0.120078	−0.0600389	−	0.998196i	$-0.519122\pi$
$457$	−2.56697	−0.120078	−0.0600389	+	0.998196i	$0.519122\pi$
$458$	15.0988	0.705521
$459$	4.49239	0.209687
$460$	0	0
$461$	29.8761	1.39147	0.695734	−	0.718299i	$-0.255079\pi$
$461$	29.8761	1.39147	0.695734	+	0.718299i	$0.255079\pi$
$462$	1.59565	0.0742364
$463$	18.8439	0.875751	0.437876	−	0.899036i	$-0.355731\pi$
$463$	18.8439	0.875751	0.437876	+	0.899036i	$0.355731\pi$
$464$	−15.8698	−0.736737
$465$	0	0
$466$	−37.7610	−1.74924
$467$	−10.6078	−0.490871	−0.245436	−	0.969413i	$-0.578931\pi$
$467$	−10.6078	−0.490871	−0.245436	+	0.969413i	$0.578931\pi$
$468$	−6.14029	−0.283835
$469$	−4.04113	−0.186602
$470$	0	0
$471$	−3.96690	−0.182785
$472$	−18.2544	−0.840226
$473$	8.98532	0.413145
$474$	1.97542	0.0907342
$475$	0	0
$476$	2.29343	0.105119
$477$	−28.6502	−1.31180
$478$	−37.3051	−1.70630
$479$	−12.8774	−0.588383	−0.294191	−	0.955747i	$-0.595050\pi$
$479$	−12.8774	−0.588383	−0.294191	+	0.955747i	$0.595050\pi$
$480$	0	0
$481$	17.3114	0.789333
$482$	−21.6696	−0.987021
$483$	−0.285164	−0.0129754
$484$	−0.0505154	−0.00229616
$485$	0	0
$486$	−12.5571	−0.569602
$487$	−0.0165578	−0.000750304 0	−0.000375152	−	1.00000i	$-0.500119\pi$
$487$	−0.0165578	−0.000750304 0	−0.000375152		1.00000i	$0.500119\pi$
$488$	10.4485	0.472984
$489$	−5.59997	−0.253239
$490$	0	0
$491$	−4.51705	−0.203851	−0.101926	−	0.994792i	$-0.532500\pi$
$491$	−4.51705	−0.203851	−0.101926	+	0.994792i	$0.532500\pi$
$492$	−2.18737	−0.0986141
$493$	−8.48057	−0.381946
$494$	−1.93552	−0.0870831
$495$	0	0
$496$	47.6410	2.13914
$497$	−5.14273	−0.230683
$498$	−1.92376	−0.0862056
$499$	1.16067	0.0519588	0.0259794	−	0.999662i	$-0.491730\pi$
$499$	1.16067	0.0519588	0.0259794	+	0.999662i	$0.491730\pi$
$500$	0	0
$501$	0.656344	0.0293233
$502$	−36.9022	−1.64702
$503$	−40.8076	−1.81952	−0.909761	−	0.415133i	$-0.863735\pi$
$503$	−40.8076	−1.81952	−0.909761	+	0.415133i	$0.863735\pi$
$504$	5.62047	0.250356
$505$	0	0
$506$	−5.59556	−0.248753
$507$	−2.00715	−0.0891407
$508$	1.03621	0.0459744
$509$	21.5140	0.953589	0.476795	−	0.879015i	$-0.341799\pi$
$509$	21.5140	0.953589	0.476795	+	0.879015i	$0.341799\pi$
$510$	0	0
$511$	−1.26345	−0.0558918
$512$	−3.60145	−0.159163
$513$	−0.790923	−0.0349201
$514$	−6.53539	−0.288263
$515$	0	0
$516$	0.667451	0.0293829
$517$	−33.5573	−1.47585
$518$	11.9940	0.526988
$519$	−3.98647	−0.174987
$520$	0	0
$521$	−5.08358	−0.222716	−0.111358	−	0.993780i	$-0.535520\pi$
$521$	−5.08358	−0.222716	−0.111358	+	0.993780i	$0.535520\pi$
$522$	15.7312	0.688536
$523$	−5.89233	−0.257654	−0.128827	−	0.991667i	$-0.541121\pi$
$523$	−5.89233	−0.257654	−0.128827	+	0.991667i	$0.541121\pi$
$524$	4.57659	0.199929
$525$	0	0
$526$	−41.8365	−1.82416
$527$	25.4586	1.10899
$528$	−4.69823	−0.204464
$529$	1.00000	0.0434783
$530$	0	0
$531$	27.6674	1.20066
$532$	−0.403778	−0.0175060
$533$	−21.7357	−0.941479
$534$	8.61062	0.372618
$535$	0	0
$536$	7.78196	0.336129
$537$	−3.05982	−0.132041
$538$	28.1995	1.21576
$539$	3.30777	0.142476
$540$	0	0
$541$	−35.5894	−1.53011	−0.765053	−	0.643967i	$-0.777287\pi$
$541$	−35.5894	−1.53011	−0.765053	+	0.643967i	$0.777287\pi$
$542$	39.3707	1.69112
$543$	4.70418	0.201876
$544$	−12.1757	−0.522031
$545$	0	0
$546$	1.17781	0.0504058
$547$	−13.0320	−0.557209	−0.278604	−	0.960406i	$-0.589872\pi$
$547$	−13.0320	−0.557209	−0.278604	+	0.960406i	$0.589872\pi$
$548$	8.66130	0.369993
$549$	−15.8364	−0.675881
$550$	0	0
$551$	1.49308	0.0636072
$552$	0.549137	0.0233728
$553$	4.09504	0.174139
$554$	−1.93710	−0.0822995
$555$	0	0
$556$	−5.18810	−0.220025
$557$	44.3953	1.88109	0.940546	−	0.339668i	$-0.110315\pi$
$557$	44.3953	1.88109	0.940546	+	0.339668i	$0.110315\pi$
$558$	−47.2249	−1.99919
$559$	6.63242	0.280522
$560$	0	0
$561$	−2.51066	−0.106000
$562$	1.27509	0.0537866
$563$	8.23011	0.346858	0.173429	−	0.984846i	$-0.444515\pi$
$563$	8.23011	0.346858	0.173429	+	0.984846i	$0.444515\pi$
$564$	−2.49272	−0.104962
$565$	0	0
$566$	29.3121	1.23208
$567$	−8.27475	−0.347507
$568$	9.90330	0.415533
$569$	−15.6315	−0.655306	−0.327653	−	0.944798i	$-0.606258\pi$
$569$	−15.6315	−0.655306	−0.327653	+	0.944798i	$0.606258\pi$
$570$	0	0
$571$	−4.43621	−0.185650	−0.0928248	−	0.995682i	$-0.529590\pi$
$571$	−4.43621	−0.185650	−0.0928248	+	0.995682i	$0.529590\pi$
$572$	6.95886	0.290965
$573$	0.472235	0.0197279
$574$	−15.0594	−0.628567
$575$	0	0
$576$	−6.48945	−0.270394
$577$	6.94474	0.289113	0.144557	−	0.989497i	$-0.453824\pi$
$577$	6.94474	0.289113	0.144557	+	0.989497i	$0.453824\pi$
$578$	16.7733	0.697676
$579$	−6.63002	−0.275534
$580$	0	0
$581$	−3.98793	−0.165447
$582$	−2.73147	−0.113223
$583$	32.4696	1.34475
$584$	2.43301	0.100679
$585$	0	0
$586$	12.1557	0.502147
$587$	−12.9945	−0.536339	−0.268169	−	0.963372i	$-0.586419\pi$
$587$	−12.9945	−0.536339	−0.268169	+	0.963372i	$0.586419\pi$
$588$	0.245710	0.0101329
$589$	−4.48220	−0.184686
$590$	0	0
$591$	−6.07808	−0.250019
$592$	−35.3152	−1.45145
$593$	−16.9008	−0.694033	−0.347017	−	0.937859i	$-0.612805\pi$
$593$	−16.9008	−0.694033	−0.347017	+	0.937859i	$0.612805\pi$
$594$	9.44416	0.387498
$595$	0	0
$596$	−14.9357	−0.611791
$597$	4.50342	0.184313
$598$	−4.13031	−0.168901
$599$	42.1045	1.72034	0.860172	−	0.510004i	$-0.170356\pi$
$599$	42.1045	1.72034	0.860172	+	0.510004i	$0.170356\pi$
$600$	0	0
$601$	23.7925	0.970517	0.485259	−	0.874371i	$-0.338725\pi$
$601$	23.7925	0.970517	0.485259	+	0.874371i	$0.338725\pi$
$602$	4.59521	0.187287
$603$	−11.7948	−0.480320
$604$	3.48853	0.141946
$605$	0	0
$606$	3.90786	0.158746
$607$	−25.0177	−1.01544	−0.507719	−	0.861523i	$-0.669511\pi$
$607$	−25.0177	−1.01544	−0.507719	+	0.861523i	$0.669511\pi$
$608$	2.14364	0.0869362
$609$	−0.908577	−0.0368174
$610$	0	0
$611$	−24.7700	−1.00209
$612$	6.69379	0.270580
$613$	8.36891	0.338017	0.169009	−	0.985615i	$-0.445943\pi$
$613$	8.36891	0.338017	0.169009	+	0.985615i	$0.445943\pi$
$614$	50.5186	2.03876
$615$	0	0
$616$	−6.36974	−0.256644
$617$	−44.4235	−1.78842	−0.894212	−	0.447644i	$-0.852263\pi$
$617$	−44.4235	−1.78842	−0.894212	+	0.447644i	$0.852263\pi$
$618$	5.89405	0.237093
$619$	−28.0958	−1.12927	−0.564633	−	0.825342i	$-0.690982\pi$
$619$	−28.0958	−1.12927	−0.564633	+	0.825342i	$0.690982\pi$
$620$	0	0
$621$	−1.68779	−0.0677288
$622$	0.510748	0.0204791
$623$	17.8497	0.715135
$624$	−3.46795	−0.138829
$625$	0	0
$626$	28.5814	1.14234
$627$	0.442023	0.0176527
$628$	−11.9863	−0.478305
$629$	−18.8719	−0.752472
$630$	0	0
$631$	−24.5600	−0.977716	−0.488858	−	0.872363i	$-0.662586\pi$
$631$	−24.5600	−0.977716	−0.488858	+	0.872363i	$0.662586\pi$
$632$	−7.88577	−0.313679
$633$	−6.29321	−0.250133
$634$	−15.5359	−0.617011
$635$	0	0
$636$	2.41192	0.0956388
$637$	2.44160	0.0967397
$638$	−17.8283	−0.705831
$639$	−15.0100	−0.593786
$640$	0	0
$641$	21.5775	0.852258	0.426129	−	0.904662i	$-0.359877\pi$
$641$	21.5775	0.852258	0.426129	+	0.904662i	$0.359877\pi$
$642$	−4.70209	−0.185577
$643$	−2.69053	−0.106104	−0.0530520	−	0.998592i	$-0.516895\pi$
$643$	−2.69053	−0.106104	−0.0530520	+	0.998592i	$0.516895\pi$
$644$	−0.861643	−0.0339535
$645$	0	0
$646$	2.10999	0.0830164
$647$	−25.8199	−1.01509	−0.507543	−	0.861626i	$-0.669446\pi$
$647$	−25.8199	−1.01509	−0.507543	+	0.861626i	$0.669446\pi$
$648$	15.9346	0.625970
$649$	−31.3557	−1.23082
$650$	0	0
$651$	2.72754	0.106901
$652$	−16.9207	−0.662666
$653$	14.7895	0.578759	0.289380	−	0.957214i	$-0.406551\pi$
$653$	14.7895	0.578759	0.289380	+	0.957214i	$0.406551\pi$
$654$	0.416902	0.0163022
$655$	0	0
$656$	44.3408	1.73122
$657$	−3.68761	−0.143867
$658$	−17.1616	−0.669031
$659$	9.76538	0.380405	0.190203	−	0.981745i	$-0.439086\pi$
$659$	9.76538	0.380405	0.190203	+	0.981745i	$0.439086\pi$
$660$	0	0
$661$	28.5883	1.11196	0.555978	−	0.831197i	$-0.312344\pi$
$661$	28.5883	1.11196	0.555978	+	0.831197i	$0.312344\pi$
$662$	−1.22667	−0.0476761
$663$	−1.85322	−0.0719731
$664$	7.67952	0.298023
$665$	0	0
$666$	35.0068	1.35649
$667$	3.18616	0.123369
$668$	1.98319	0.0767320
$669$	0.289058	0.0111756
$670$	0	0
$671$	17.9476	0.692858
$672$	−1.30446	−0.0503208
$673$	23.0768	0.889545	0.444773	−	0.895644i	$-0.353284\pi$
$673$	23.0768	0.889545	0.444773	+	0.895644i	$0.353284\pi$
$674$	30.6466	1.18046
$675$	0	0
$676$	−6.06475	−0.233260
$677$	−4.19697	−0.161303	−0.0806514	−	0.996742i	$-0.525700\pi$
$677$	−4.19697	−0.161303	−0.0806514	+	0.996742i	$0.525700\pi$
$678$	−8.74953	−0.336024
$679$	−5.66233	−0.217300
$680$	0	0
$681$	−0.402935	−0.0154405
$682$	53.5205	2.04941
$683$	−24.5425	−0.939095	−0.469547	−	0.882907i	$-0.655583\pi$
$683$	−24.5425	−0.939095	−0.469547	+	0.882907i	$0.655583\pi$
$684$	−1.17850	−0.0450610
$685$	0	0
$686$	1.69164	0.0645871
$687$	−2.54525	−0.0971072
$688$	−13.5301	−0.515831
$689$	23.9671	0.913073
$690$	0	0
$691$	−23.2939	−0.886141	−0.443071	−	0.896487i	$-0.646111\pi$
$691$	−23.2939	−0.886141	−0.443071	+	0.896487i	$0.646111\pi$
$692$	−12.0454	−0.457898
$693$	9.65434	0.366738
$694$	38.5106	1.46184
$695$	0	0
$696$	1.74964	0.0663198
$697$	23.6950	0.897514
$698$	58.0556	2.19744
$699$	6.36546	0.240764
$700$	0	0
$701$	45.0694	1.70225	0.851123	−	0.524966i	$-0.175922\pi$
$701$	45.0694	1.70225	0.851123	+	0.524966i	$0.175922\pi$
$702$	6.97111	0.263108
$703$	3.32256	0.125313
$704$	7.35457	0.277186
$705$	0	0
$706$	54.0217	2.03313
$707$	8.10097	0.304668
$708$	−2.32918	−0.0875359
$709$	−31.7819	−1.19359	−0.596796	−	0.802393i	$-0.703560\pi$
$709$	−31.7819	−1.19359	−0.596796	+	0.802393i	$0.703560\pi$
$710$	0	0
$711$	11.9521	0.448239
$712$	−34.3731	−1.28818
$713$	−9.56481	−0.358205
$714$	−1.28399	−0.0480519
$715$	0	0
$716$	−9.24548	−0.345520
$717$	6.28862	0.234853
$718$	−11.3255	−0.422662
$719$	48.3844	1.80443	0.902216	−	0.431284i	$-0.141939\pi$
$719$	48.3844	1.80443	0.902216	+	0.431284i	$0.141939\pi$
$720$	0	0
$721$	12.2183	0.455034
$722$	31.7697	1.18234
$723$	3.65289	0.135852
$724$	14.2140	0.528260
$725$	0	0
$726$	0.0282813	0.00104962
$727$	−19.8794	−0.737286	−0.368643	−	0.929571i	$-0.620177\pi$
$727$	−19.8794	−0.737286	−0.368643	+	0.929571i	$0.620177\pi$
$728$	−4.70176	−0.174259
$729$	−22.7075	−0.841017
$730$	0	0
$731$	−7.23028	−0.267422
$732$	1.33319	0.0492761
$733$	41.9597	1.54982	0.774909	−	0.632072i	$-0.217795\pi$
$733$	41.9597	1.54982	0.774909	+	0.632072i	$0.217795\pi$
$734$	−33.3998	−1.23281
$735$	0	0
$736$	4.57444	0.168616
$737$	13.3671	0.492385
$738$	−43.9536	−1.61795
$739$	−0.433331	−0.0159403	−0.00797017	−	0.999968i	$-0.502537\pi$
$739$	−0.433331	−0.0159403	−0.00797017	+	0.999968i	$0.502537\pi$
$740$	0	0
$741$	0.326275	0.0119860
$742$	16.6054	0.609602
$743$	−46.0817	−1.69057	−0.845287	−	0.534313i	$-0.820571\pi$
$743$	−46.0817	−1.69057	−0.845287	+	0.534313i	$0.820571\pi$
$744$	−5.25239	−0.192562
$745$	0	0
$746$	38.6855	1.41638
$747$	−11.6395	−0.425867
$748$	−7.58615	−0.277377
$749$	−9.74740	−0.356162
$750$	0	0
$751$	−11.6510	−0.425151	−0.212576	−	0.977145i	$-0.568185\pi$
$751$	−11.6510	−0.425151	−0.212576	+	0.977145i	$0.568185\pi$
$752$	50.5307	1.84267
$753$	6.22069	0.226694
$754$	−13.1598	−0.479252
$755$	0	0
$756$	1.45428	0.0528915
$757$	−41.5605	−1.51054	−0.755271	−	0.655413i	$-0.772495\pi$
$757$	−41.5605	−1.51054	−0.755271	+	0.655413i	$0.772495\pi$
$758$	39.1851	1.42327
$759$	0.943258	0.0342381
$760$	0	0
$761$	−7.26981	−0.263530	−0.131765	−	0.991281i	$-0.542064\pi$
$761$	−7.26981	−0.263530	−0.131765	+	0.991281i	$0.542064\pi$
$762$	−0.580126	−0.0210157
$763$	0.864235	0.0312874
$764$	1.42689	0.0516232
$765$	0	0
$766$	39.5168	1.42780
$767$	−23.1449	−0.835714
$768$	4.95968	0.178967
$769$	44.5441	1.60630	0.803151	−	0.595776i	$-0.203155\pi$
$769$	44.5441	1.60630	0.803151	+	0.595776i	$0.203155\pi$
$770$	0	0
$771$	1.10169	0.0396763
$772$	−20.0331	−0.721007
$773$	6.46275	0.232449	0.116225	−	0.993223i	$-0.462921\pi$
$773$	6.46275	0.232449	0.116225	+	0.993223i	$0.462921\pi$
$774$	13.4120	0.482083
$775$	0	0
$776$	10.9039	0.391426
$777$	−2.02187	−0.0725340
$778$	43.8288	1.57134
$779$	−4.17171	−0.149467
$780$	0	0
$781$	17.0110	0.608702
$782$	4.50262	0.161013
$783$	−5.37758	−0.192179
$784$	−4.98086	−0.177888
$785$	0	0
$786$	−2.56222	−0.0913915
$787$	4.38339	0.156251	0.0781254	−	0.996944i	$-0.475107\pi$
$787$	4.38339	0.156251	0.0781254	+	0.996944i	$0.475107\pi$
$788$	−18.3654	−0.654239
$789$	7.05249	0.251075
$790$	0	0
$791$	−18.1377	−0.644903
$792$	−18.5913	−0.660612
$793$	13.2478	0.470444
$794$	−48.0283	−1.70446
$795$	0	0
$796$	13.6074	0.482302
$797$	32.0825	1.13642	0.568211	−	0.822883i	$-0.307636\pi$
$797$	32.0825	1.13642	0.568211	+	0.822883i	$0.307636\pi$
$798$	0.226057	0.00800232
$799$	27.0028	0.955291
$800$	0	0
$801$	52.0977	1.84078
$802$	−9.19828	−0.324803
$803$	4.17921	0.147481
$804$	0.992944	0.0350184
$805$	0	0
$806$	39.5056	1.39153
$807$	−4.75365	−0.167337
$808$	−15.5999	−0.548804
$809$	41.8738	1.47220	0.736101	−	0.676871i	$-0.236665\pi$
$809$	41.8738	1.47220	0.736101	+	0.676871i	$0.236665\pi$
$810$	0	0
$811$	19.0881	0.670274	0.335137	−	0.942169i	$-0.391217\pi$
$811$	19.0881	0.670274	0.335137	+	0.942169i	$0.391217\pi$
$812$	−2.74533	−0.0963423
$813$	−6.63682	−0.232764
$814$	−39.6736	−1.39056
$815$	0	0
$816$	3.78056	0.132346
$817$	1.27295	0.0445350
$818$	−3.41349	−0.119350
$819$	7.12626	0.249012
$820$	0	0
$821$	3.20974	0.112021	0.0560103	−	0.998430i	$-0.482162\pi$
$821$	3.20974	0.112021	0.0560103	+	0.998430i	$0.482162\pi$
$822$	−4.84906	−0.169131
$823$	37.9347	1.32232	0.661161	−	0.750244i	$-0.270064\pi$
$823$	37.9347	1.32232	0.661161	+	0.750244i	$0.270064\pi$
$824$	−23.5287	−0.819661
$825$	0	0
$826$	−16.0357	−0.557954
$827$	49.1061	1.70759	0.853794	−	0.520611i	$-0.174296\pi$
$827$	49.1061	1.70759	0.853794	+	0.520611i	$0.174296\pi$
$828$	−2.51486	−0.0873975
$829$	−13.8473	−0.480937	−0.240469	−	0.970657i	$-0.577301\pi$
$829$	−13.8473	−0.480937	−0.240469	+	0.970657i	$0.577301\pi$
$830$	0	0
$831$	0.326542	0.0113276
$832$	5.42870	0.188206
$833$	−2.66169	−0.0922221
$834$	2.90458	0.100577
$835$	0	0
$836$	1.33561	0.0461929
$837$	16.1434	0.557999
$838$	−19.4474	−0.671801
$839$	−2.87702	−0.0993259	−0.0496629	−	0.998766i	$-0.515815\pi$
$839$	−2.87702	−0.0993259	−0.0496629	+	0.998766i	$0.515815\pi$
$840$	0	0
$841$	−18.8484	−0.649945
$842$	−5.11508	−0.176277
$843$	−0.214946	−0.00740312
$844$	−19.0154	−0.654537
$845$	0	0
$846$	−50.0894	−1.72211
$847$	0.0586268	0.00201444
$848$	−48.8928	−1.67899
$849$	−4.94122	−0.169582
$850$	0	0
$851$	7.09019	0.243049
$852$	1.26362	0.0432909
$853$	38.8788	1.33118	0.665592	−	0.746316i	$-0.268179\pi$
$853$	38.8788	1.33118	0.665592	+	0.746316i	$0.268179\pi$
$854$	9.17863	0.314086
$855$	0	0
$856$	18.7705	0.641561
$857$	−1.65595	−0.0565660	−0.0282830	−	0.999600i	$-0.509004\pi$
$857$	−1.65595	−0.0565660	−0.0282830	+	0.999600i	$0.509004\pi$
$858$	−3.89594	−0.133005
$859$	11.1426	0.380181	0.190090	−	0.981767i	$-0.439122\pi$
$859$	11.1426	0.380181	0.190090	+	0.981767i	$0.439122\pi$
$860$	0	0
$861$	2.53860	0.0865152
$862$	57.8142	1.96916
$863$	−30.1212	−1.02534	−0.512669	−	0.858586i	$-0.671343\pi$
$863$	−30.1212	−1.02534	−0.512669	+	0.858586i	$0.671343\pi$
$864$	−7.72071	−0.262664
$865$	0	0
$866$	16.9519	0.576050
$867$	−2.82751	−0.0960274
$868$	8.24146	0.279733
$869$	−13.5455	−0.459498
$870$	0	0
$871$	9.86683	0.334325
$872$	−1.66425	−0.0563585
$873$	−16.5265	−0.559338
$874$	−0.792725	−0.0268143
$875$	0	0
$876$	0.310442	0.0104889
$877$	−0.492495	−0.0166304	−0.00831519	−	0.999965i	$-0.502647\pi$
$877$	−0.492495	−0.0166304	−0.00831519	+	0.999965i	$0.502647\pi$
$878$	23.0537	0.778026
$879$	−2.04912	−0.0691150
$880$	0	0
$881$	28.4430	0.958269	0.479135	−	0.877741i	$-0.340951\pi$
$881$	28.4430	0.958269	0.479135	+	0.877741i	$0.340951\pi$
$882$	4.93736	0.166249
$883$	−22.4699	−0.756173	−0.378087	−	0.925770i	$-0.623418\pi$
$883$	−22.4699	−0.756173	−0.378087	+	0.925770i	$0.623418\pi$
$884$	−5.59964	−0.188336
$885$	0	0
$886$	9.85617	0.331125
$887$	−32.9763	−1.10724	−0.553619	−	0.832770i	$-0.686753\pi$
$887$	−32.9763	−1.10724	−0.553619	+	0.832770i	$0.686753\pi$
$888$	3.89348	0.130657
$889$	−1.20260	−0.0403338
$890$	0	0
$891$	27.3710	0.916963
$892$	0.873409	0.0292439
$893$	−4.75408	−0.159089
$894$	8.36182	0.279661
$895$	0	0
$896$	12.9101	0.431296
$897$	0.696256	0.0232473
$898$	18.6570	0.622593
$899$	−30.4750	−1.01640
$900$	0	0
$901$	−26.1275	−0.870434
$902$	49.8131	1.65859
$903$	−0.774626	−0.0257779
$904$	34.9276	1.16167
$905$	0	0
$906$	−1.95307	−0.0648863
$907$	8.66021	0.287557	0.143779	−	0.989610i	$-0.454075\pi$
$907$	8.66021	0.287557	0.143779	+	0.989610i	$0.454075\pi$
$908$	−1.21750	−0.0404041
$909$	23.6441	0.784227
$910$	0	0
$911$	−14.3443	−0.475248	−0.237624	−	0.971357i	$-0.576369\pi$
$911$	−14.3443	−0.475248	−0.237624	+	0.971357i	$0.576369\pi$
$912$	−0.665600	−0.0220402
$913$	13.1912	0.436565
$914$	4.34239	0.143633
$915$	0	0
$916$	−7.69064	−0.254106
$917$	−5.31147	−0.175400
$918$	−7.59950	−0.250821
$919$	−34.8003	−1.14796	−0.573978	−	0.818871i	$-0.694600\pi$
$919$	−34.8003	−1.14796	−0.573978	+	0.818871i	$0.694600\pi$
$920$	0	0
$921$	−8.51604	−0.280613
$922$	−50.5396	−1.66443
$923$	12.5565	0.413302
$924$	−0.812752	−0.0267376
$925$	0	0
$926$	−31.8771	−1.04755
$927$	35.6614	1.17127
$928$	14.5749	0.478444
$929$	−20.5979	−0.675795	−0.337897	−	0.941183i	$-0.609716\pi$
$929$	−20.5979	−0.675795	−0.337897	+	0.941183i	$0.609716\pi$
$930$	0	0
$931$	0.468614	0.0153582
$932$	19.2337	0.630021
$933$	−0.0860981	−0.00281873
$934$	17.9446	0.587166
$935$	0	0
$936$	−13.7229	−0.448549
$937$	11.8669	0.387676	0.193838	−	0.981034i	$-0.437906\pi$
$937$	11.8669	0.387676	0.193838	+	0.981034i	$0.437906\pi$
$938$	6.83614	0.223208
$939$	−4.81804	−0.157231
$940$	0	0
$941$	−35.7620	−1.16581	−0.582904	−	0.812541i	$-0.698083\pi$
$941$	−35.7620	−1.16581	−0.582904	+	0.812541i	$0.698083\pi$
$942$	6.71057	0.218642
$943$	−8.90225	−0.289897
$944$	47.2155	1.53674
$945$	0	0
$946$	−15.1999	−0.494192
$947$	49.6114	1.61215	0.806077	−	0.591811i	$-0.201587\pi$
$947$	49.6114	1.61215	0.806077	+	0.591811i	$0.201587\pi$
$948$	−1.00619	−0.0326795
$949$	3.08484	0.100138
$950$	0	0
$951$	2.61893	0.0849247
$952$	5.12559	0.166121
$953$	39.7672	1.28819	0.644094	−	0.764947i	$-0.277235\pi$
$953$	39.7672	1.28819	0.644094	+	0.764947i	$0.277235\pi$
$954$	48.4658	1.56914
$955$	0	0
$956$	19.0015	0.614553
$957$	3.00537	0.0971498
$958$	21.7839	0.703806
$959$	−10.0521	−0.324598
$960$	0	0
$961$	60.4856	1.95115
$962$	−29.2847	−0.944176
$963$	−28.4496	−0.916774
$964$	11.0375	0.355493
$965$	0	0
$966$	0.482394	0.0155208
$967$	4.50254	0.144792	0.0723959	−	0.997376i	$-0.476935\pi$
$967$	4.50254	0.144792	0.0723959	+	0.997376i	$0.476935\pi$
$968$	−0.112897	−0.00362865
$969$	−0.355686	−0.0114263
$970$	0	0
$971$	−9.71827	−0.311874	−0.155937	−	0.987767i	$-0.549840\pi$
$971$	−9.71827	−0.311874	−0.155937	+	0.987767i	$0.549840\pi$
$972$	6.39601	0.205152
$973$	6.02117	0.193030
$974$	0.0280098	0.000897491 0
$975$	0	0
$976$	−27.0255	−0.865066
$977$	11.7309	0.375304	0.187652	−	0.982236i	$-0.439912\pi$
$977$	11.7309	0.375304	0.187652	+	0.982236i	$0.439912\pi$
$978$	9.47312	0.302917
$979$	−59.0429	−1.88702
$980$	0	0
$981$	2.52243	0.0805349
$982$	7.64121	0.243841
$983$	58.1985	1.85624	0.928121	−	0.372277i	$-0.121423\pi$
$983$	58.1985	1.85624	0.928121	+	0.372277i	$0.121423\pi$
$984$	−4.88855	−0.155841
$985$	0	0
$986$	14.3461	0.456872
$987$	2.89298	0.0920846
$988$	0.985864	0.0313645
$989$	2.71642	0.0863773
$990$	0	0
$991$	−48.0872	−1.52754	−0.763771	−	0.645488i	$-0.776654\pi$
$991$	−48.0872	−1.52754	−0.763771	+	0.645488i	$0.776654\pi$
$992$	−43.7536	−1.38918
$993$	0.206784	0.00656208
$994$	8.69965	0.275936
$995$	0	0
$996$	0.979874	0.0310485
$997$	−6.34479	−0.200942	−0.100471	−	0.994940i	$-0.532035\pi$
$997$	−6.34479	−0.200942	−0.100471	+	0.994940i	$0.532035\pi$
$998$	−1.96344	−0.0621516
$999$	−11.9668	−0.378612

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.y.1.3		12
5.2	odd	4		805.2.c.b.484.5	✓	24
5.3	odd	4		805.2.c.b.484.20	yes	24
5.4	even	2		4025.2.a.x.1.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.c.b.484.5	✓	24	5.2	odd	4
805.2.c.b.484.20	yes	24	5.3	odd	4
4025.2.a.x.1.10		12	5.4	even	2
4025.2.a.y.1.3		12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4025.a (trivial)

\(f(q)\)	\(=\)	\(q-1.69164 q^{2} +0.285164 q^{3} +0.861643 q^{4} -0.482394 q^{6} -1.00000 q^{7} +1.92569 q^{8} -2.91868 q^{9} +O(q^{10})\)	\(q-1.69164 q^{2} +0.285164 q^{3} +0.861643 q^{4} -0.482394 q^{6} -1.00000 q^{7} +1.92569 q^{8} -2.91868 q^{9} +3.30777 q^{11} +0.245710 q^{12} +2.44160 q^{13} +1.69164 q^{14} -4.98086 q^{16} -2.66169 q^{17} +4.93736 q^{18} +0.468614 q^{19} -0.285164 q^{21} -5.59556 q^{22} +1.00000 q^{23} +0.549137 q^{24} -4.13031 q^{26} -1.68779 q^{27} -0.861643 q^{28} +3.18616 q^{29} -9.56481 q^{31} +4.57444 q^{32} +0.943258 q^{33} +4.50262 q^{34} -2.51486 q^{36} +7.09019 q^{37} -0.792725 q^{38} +0.696256 q^{39} -8.90225 q^{41} +0.482394 q^{42} +2.71642 q^{43} +2.85012 q^{44} -1.69164 q^{46} -10.1450 q^{47} -1.42036 q^{48} +1.00000 q^{49} -0.759018 q^{51} +2.10379 q^{52} +9.81614 q^{53} +2.85514 q^{54} -1.92569 q^{56} +0.133632 q^{57} -5.38983 q^{58} -9.47940 q^{59} +5.42588 q^{61} +16.1802 q^{62} +2.91868 q^{63} +2.22342 q^{64} -1.59565 q^{66} +4.04113 q^{67} -2.29343 q^{68} +0.285164 q^{69} +5.14273 q^{71} -5.62047 q^{72} +1.26345 q^{73} -11.9940 q^{74} +0.403778 q^{76} -3.30777 q^{77} -1.17781 q^{78} -4.09504 q^{79} +8.27475 q^{81} +15.0594 q^{82} +3.98793 q^{83} -0.245710 q^{84} -4.59521 q^{86} +0.908577 q^{87} +6.36974 q^{88} -17.8497 q^{89} -2.44160 q^{91} +0.861643 q^{92} -2.72754 q^{93} +17.1616 q^{94} +1.30446 q^{96} +5.66233 q^{97} -1.69164 q^{98} -9.65434 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + 8 q^{4} - 6 q^{6} - 12 q^{7} + 6 q^{8} + 8 q^{9}+O(q^{10}) \) 12 * q + 2 * q^2 + 8 * q^4 - 6 * q^6 - 12 * q^7 + 6 * q^8 + 8 * q^9	\( 12 q + 2 q^{2} + 8 q^{4} - 6 q^{6} - 12 q^{7} + 6 q^{8} + 8 q^{9} - 8 q^{11} - 12 q^{12} + 2 q^{13} - 2 q^{14} - 4 q^{16} - 8 q^{17} + 20 q^{18} - 26 q^{19} + 4 q^{22} + 12 q^{23} - 12 q^{24} - 22 q^{26} + 12 q^{27} - 8 q^{28} - 12 q^{29} - 50 q^{31} + 14 q^{32} + 4 q^{33} - 28 q^{34} - 18 q^{36} + 8 q^{37} - 4 q^{38} - 26 q^{39} - 4 q^{41} + 6 q^{42} + 26 q^{43} - 10 q^{44} + 2 q^{46} + 16 q^{47} - 40 q^{48} + 12 q^{49} - 32 q^{51} + 10 q^{52} - 18 q^{53} - 10 q^{54} - 6 q^{56} - 10 q^{57} - 18 q^{58} - 18 q^{59} + 8 q^{61} - 54 q^{62} - 8 q^{63} + 12 q^{64} - 2 q^{66} + 38 q^{67} - 36 q^{68} - 24 q^{71} + 18 q^{72} - 14 q^{73} + 36 q^{74} - 56 q^{76} + 8 q^{77} - 26 q^{78} - 44 q^{79} - 16 q^{81} - 44 q^{82} - 14 q^{83} + 12 q^{84} - 32 q^{86} + 16 q^{87} + 32 q^{88} - 10 q^{89} - 2 q^{91} + 8 q^{92} + 26 q^{93} + 18 q^{94} - 38 q^{96} - 4 q^{97} + 2 q^{98} - 56 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 + 8 * q^4 - 6 * q^6 - 12 * q^7 + 6 * q^8 + 8 * q^9 - 8 * q^11 - 12 * q^12 + 2 * q^13 - 2 * q^14 - 4 * q^16 - 8 * q^17 + 20 * q^18 - 26 * q^19 + 4 * q^22 + 12 * q^23 - 12 * q^24 - 22 * q^26 + 12 * q^27 - 8 * q^28 - 12 * q^29 - 50 * q^31 + 14 * q^32 + 4 * q^33 - 28 * q^34 - 18 * q^36 + 8 * q^37 - 4 * q^38 - 26 * q^39 - 4 * q^41 + 6 * q^42 + 26 * q^43 - 10 * q^44 + 2 * q^46 + 16 * q^47 - 40 * q^48 + 12 * q^49 - 32 * q^51 + 10 * q^52 - 18 * q^53 - 10 * q^54 - 6 * q^56 - 10 * q^57 - 18 * q^58 - 18 * q^59 + 8 * q^61 - 54 * q^62 - 8 * q^63 + 12 * q^64 - 2 * q^66 + 38 * q^67 - 36 * q^68 - 24 * q^71 + 18 * q^72 - 14 * q^73 + 36 * q^74 - 56 * q^76 + 8 * q^77 - 26 * q^78 - 44 * q^79 - 16 * q^81 - 44 * q^82 - 14 * q^83 + 12 * q^84 - 32 * q^86 + 16 * q^87 + 32 * q^88 - 10 * q^89 - 2 * q^91 + 8 * q^92 + 26 * q^93 + 18 * q^94 - 38 * q^96 - 4 * q^97 + 2 * q^98 - 56 * q^99

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