LMFDB - Embedded newform 775.2.a.i.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [775,2,Mod(1,775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(775, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("775.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.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:	$6.18840615665$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.205225.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 6x^{3} + 3x^{2} + 7x - 3 $ x^5 - x^4 - 6x^3 + 3x^2 + 7*x - 3
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			1.4
Root			$1.17073$ of defining polynomial
Character	$\chi$	$=$	775.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.170728 q^{2} +0.648789 q^{3} -1.97085 q^{4} +0.110767 q^{6} +2.03774 q^{7} -0.677937 q^{8} -2.57907 q^{9} +O(q^{10})$	\(q+0.170728 q^{2} +0.648789 q^{3} -1.97085 q^{4} +0.110767 q^{6} +2.03774 q^{7} -0.677937 q^{8} -2.57907 q^{9} -1.88641 q^{11} -1.27867 q^{12} -4.03774 q^{13} +0.347900 q^{14} +3.82596 q^{16} -0.781778 q^{17} -0.440321 q^{18} -2.68936 q^{19} +1.32206 q^{21} -0.322063 q^{22} -5.51580 q^{23} -0.439838 q^{24} -0.689357 q^{26} -3.61964 q^{27} -4.01608 q^{28} +3.07831 q^{29} +1.00000 q^{31} +2.00907 q^{32} -1.22388 q^{33} -0.133472 q^{34} +5.08297 q^{36} -6.80823 q^{37} -0.459150 q^{38} -2.61964 q^{39} -0.850446 q^{41} +0.225714 q^{42} +2.82030 q^{43} +3.71782 q^{44} -0.941704 q^{46} -8.52592 q^{47} +2.48224 q^{48} -2.84762 q^{49} -0.507209 q^{51} +7.95779 q^{52} -6.34838 q^{53} -0.617975 q^{54} -1.38146 q^{56} -1.74482 q^{57} +0.525554 q^{58} -4.57986 q^{59} +10.9230 q^{61} +0.170728 q^{62} -5.25548 q^{63} -7.30892 q^{64} -0.208951 q^{66} -7.04633 q^{67} +1.54077 q^{68} -3.57859 q^{69} -10.4136 q^{71} +1.74845 q^{72} -6.57624 q^{73} -1.16236 q^{74} +5.30032 q^{76} -3.84400 q^{77} -0.447247 q^{78} +15.3166 q^{79} +5.38884 q^{81} -0.145195 q^{82} +9.04585 q^{83} -2.60559 q^{84} +0.481506 q^{86} +1.99717 q^{87} +1.27886 q^{88} +7.74414 q^{89} -8.22786 q^{91} +10.8708 q^{92} +0.648789 q^{93} -1.45562 q^{94} +1.30347 q^{96} +3.87328 q^{97} -0.486169 q^{98} +4.86518 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 4 q^{2} - q^{3} + 6 q^{4} - q^{6} - 6 q^{7} - 15 q^{8} + 2 q^{9}+O(q^{10}) $ 5 * q - 4 * q^2 - q^3 + 6 * q^4 - q^6 - 6 * q^7 - 15 * q^8 + 2 * q^9	$ 5 q - 4 q^{2} - q^{3} + 6 q^{4} - q^{6} - 6 q^{7} - 15 q^{8} + 2 q^{9} + 11 q^{12} - 4 q^{13} + 2 q^{14} + 20 q^{16} - 11 q^{17} - 19 q^{18} - 4 q^{19} - 5 q^{21} + 10 q^{22} - 12 q^{23} - 26 q^{24} + 6 q^{26} + 2 q^{27} - 18 q^{28} - 6 q^{29} + 5 q^{31} - 29 q^{32} - 21 q^{33} - 5 q^{34} + 23 q^{36} + 2 q^{37} + 6 q^{38} + 7 q^{39} - 2 q^{41} + 24 q^{42} - 7 q^{43} - 28 q^{44} + 27 q^{46} - 8 q^{47} + 39 q^{48} - q^{49} - 19 q^{51} + 6 q^{52} - 25 q^{53} - 18 q^{54} + 35 q^{56} - 20 q^{57} + q^{58} + 4 q^{59} - 17 q^{61} - 4 q^{62} - 10 q^{63} + 27 q^{64} + 27 q^{66} + 13 q^{67} - 18 q^{68} - 10 q^{69} - 6 q^{71} - 26 q^{72} - 7 q^{73} + 6 q^{74} - 5 q^{76} - 7 q^{77} - 22 q^{78} + 12 q^{79} - 11 q^{81} + 21 q^{82} + 4 q^{83} - 63 q^{84} - 41 q^{86} - q^{87} + 49 q^{88} - 3 q^{89} - 22 q^{91} - 34 q^{92} - q^{93} - 34 q^{94} - 64 q^{96} - 25 q^{97} + 22 q^{98} + 5 q^{99}+O(q^{100}) $ 5 * q - 4 * q^2 - q^3 + 6 * q^4 - q^6 - 6 * q^7 - 15 * q^8 + 2 * q^9 + 11 * q^12 - 4 * q^13 + 2 * q^14 + 20 * q^16 - 11 * q^17 - 19 * q^18 - 4 * q^19 - 5 * q^21 + 10 * q^22 - 12 * q^23 - 26 * q^24 + 6 * q^26 + 2 * q^27 - 18 * q^28 - 6 * q^29 + 5 * q^31 - 29 * q^32 - 21 * q^33 - 5 * q^34 + 23 * q^36 + 2 * q^37 + 6 * q^38 + 7 * q^39 - 2 * q^41 + 24 * q^42 - 7 * q^43 - 28 * q^44 + 27 * q^46 - 8 * q^47 + 39 * q^48 - q^49 - 19 * q^51 + 6 * q^52 - 25 * q^53 - 18 * q^54 + 35 * q^56 - 20 * q^57 + q^58 + 4 * q^59 - 17 * q^61 - 4 * q^62 - 10 * q^63 + 27 * q^64 + 27 * q^66 + 13 * q^67 - 18 * q^68 - 10 * q^69 - 6 * q^71 - 26 * q^72 - 7 * q^73 + 6 * q^74 - 5 * q^76 - 7 * q^77 - 22 * q^78 + 12 * q^79 - 11 * q^81 + 21 * q^82 + 4 * q^83 - 63 * q^84 - 41 * q^86 - q^87 + 49 * q^88 - 3 * q^89 - 22 * q^91 - 34 * q^92 - q^93 - 34 * q^94 - 64 * q^96 - 25 * q^97 + 22 * 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 $

$2$	0.170728	0.120723	0.0603616	−	0.998177i	$-0.480775\pi$
$2$	0.170728	0.120723	0.0603616	+	0.998177i	$0.480775\pi$
$3$	0.648789	0.374578	0.187289	−	0.982305i	$-0.440030\pi$
$3$	0.648789	0.374578	0.187289	+	0.982305i	$0.440030\pi$
$4$	−1.97085	−0.985426
$5$	0	0
$5$	0	0
$6$	0.110767	0.0452203
$7$	2.03774	0.770193	0.385097	−	0.922876i	$-0.374168\pi$
$7$	2.03774	0.770193	0.385097	+	0.922876i	$0.374168\pi$
$8$	−0.677937	−0.239687
$9$	−2.57907	−0.859691
$10$	0	0
$11$	−1.88641	−0.568773	−0.284386	−	0.958710i	$-0.591790\pi$
$11$	−1.88641	−0.568773	−0.284386	+	0.958710i	$0.591790\pi$
$12$	−1.27867	−0.369119
$13$	−4.03774	−1.11987	−0.559934	−	0.828537i	$-0.689173\pi$
$13$	−4.03774	−1.11987	−0.559934	+	0.828537i	$0.689173\pi$
$14$	0.347900	0.0929802
$15$	0	0
$16$	3.82596	0.956490
$17$	−0.781778	−0.189609	−0.0948045	−	0.995496i	$-0.530223\pi$
$17$	−0.781778	−0.189609	−0.0948045	+	0.995496i	$0.530223\pi$
$18$	−0.440321	−0.103785
$19$	−2.68936	−0.616981	−0.308490	−	0.951227i	$-0.599824\pi$
$19$	−2.68936	−0.616981	−0.308490	+	0.951227i	$0.599824\pi$
$20$	0	0
$21$	1.32206	0.288498
$22$	−0.322063	−0.0686640
$23$	−5.51580	−1.15012	−0.575062	−	0.818110i	$-0.695022\pi$
$23$	−5.51580	−1.15012	−0.575062	+	0.818110i	$0.695022\pi$
$24$	−0.439838	−0.0897816
$25$	0	0
$26$	−0.689357	−0.135194
$27$	−3.61964	−0.696600
$28$	−4.01608	−0.758968
$29$	3.07831	0.571627	0.285814	−	0.958285i	$-0.407736\pi$
$29$	3.07831	0.571627	0.285814	+	0.958285i	$0.407736\pi$
$30$	0	0
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	2.00907	0.355158
$33$	−1.22388	−0.213050
$34$	−0.133472	−0.0228902
$35$	0	0
$36$	5.08297	0.847162
$37$	−6.80823	−1.11927	−0.559633	−	0.828740i	$-0.689058\pi$
$37$	−6.80823	−1.11927	−0.559633	+	0.828740i	$0.689058\pi$
$38$	−0.459150	−0.0744839
$39$	−2.61964	−0.419478
$40$	0	0
$41$	−0.850446	−0.132817	−0.0664086	−	0.997793i	$-0.521154\pi$
$41$	−0.850446	−0.132817	−0.0664086	+	0.997793i	$0.521154\pi$
$42$	0.225714	0.0348284
$43$	2.82030	0.430092	0.215046	−	0.976604i	$-0.431010\pi$
$43$	2.82030	0.430092	0.215046	+	0.976604i	$0.431010\pi$
$44$	3.71782	0.560483
$45$	0	0
$46$	−0.941704	−0.138847
$47$	−8.52592	−1.24363	−0.621817	−	0.783163i	$-0.713605\pi$
$47$	−8.52592	−1.24363	−0.621817	+	0.783163i	$0.713605\pi$
$48$	2.48224	0.358281
$49$	−2.84762	−0.406802
$50$	0	0
$51$	−0.507209	−0.0710234
$52$	7.95779	1.10355
$53$	−6.34838	−0.872017	−0.436009	−	0.899942i	$-0.643608\pi$
$53$	−6.34838	−0.872017	−0.436009	+	0.899942i	$0.643608\pi$
$54$	−0.617975	−0.0840958
$55$	0	0
$56$	−1.38146	−0.184605
$57$	−1.74482	−0.231108
$58$	0.525554	0.0690087
$59$	−4.57986	−0.596247	−0.298123	−	0.954527i	$-0.596361\pi$
$59$	−4.57986	−0.596247	−0.298123	+	0.954527i	$0.596361\pi$
$60$	0	0
$61$	10.9230	1.39854	0.699272	−	0.714855i	$-0.253508\pi$
$61$	10.9230	1.39854	0.699272	+	0.714855i	$0.253508\pi$
$62$	0.170728	0.0216825
$63$	−5.25548	−0.662128
$64$	−7.30892	−0.913614
$65$	0	0
$66$	−0.208951	−0.0257201
$67$	−7.04633	−0.860846	−0.430423	−	0.902627i	$-0.641636\pi$
$67$	−7.04633	−0.860846	−0.430423	+	0.902627i	$0.641636\pi$
$68$	1.54077	0.186846
$69$	−3.57859	−0.430812
$70$	0	0
$71$	−10.4136	−1.23587	−0.617935	−	0.786229i	$-0.712030\pi$
$71$	−10.4136	−1.23587	−0.617935	+	0.786229i	$0.712030\pi$
$72$	1.74845	0.206057
$73$	−6.57624	−0.769691	−0.384846	−	0.922981i	$-0.625745\pi$
$73$	−6.57624	−0.769691	−0.384846	+	0.922981i	$0.625745\pi$
$74$	−1.16236	−0.135121
$75$	0	0
$76$	5.30032	0.607989
$77$	−3.84400	−0.438065
$78$	−0.447247	−0.0506408
$79$	15.3166	1.72325	0.861626	−	0.507544i	$-0.169447\pi$
$79$	15.3166	1.72325	0.861626	+	0.507544i	$0.169447\pi$
$80$	0	0
$81$	5.38884	0.598760
$82$	−0.145195	−0.0160341
$83$	9.04585	0.992911	0.496455	−	0.868062i	$-0.334635\pi$
$83$	9.04585	0.992911	0.496455	+	0.868062i	$0.334635\pi$
$84$	−2.60559	−0.284293
$85$	0	0
$86$	0.481506	0.0519221
$87$	1.99717	0.214119
$88$	1.27886	0.136327
$89$	7.74414	0.820878	0.410439	−	0.911888i	$-0.365376\pi$
$89$	7.74414	0.820878	0.410439	+	0.911888i	$0.365376\pi$
$90$	0	0
$91$	−8.22786	−0.862514
$92$	10.8708	1.13336
$93$	0.648789	0.0672763
$94$	−1.45562	−0.150135
$95$	0	0
$96$	1.30347	0.133034
$97$	3.87328	0.393272	0.196636	−	0.980477i	$-0.436998\pi$
$97$	3.87328	0.393272	0.196636	+	0.980477i	$0.436998\pi$
$98$	−0.486169	−0.0491105
$99$	4.86518	0.488969
$100$	0	0
$101$	12.3766	1.23151	0.615757	−	0.787936i	$-0.288850\pi$
$101$	12.3766	1.23151	0.615757	+	0.787936i	$0.288850\pi$
$102$	−0.0865949	−0.00857418
$103$	−0.348268	−0.0343159	−0.0171579	−	0.999853i	$-0.505462\pi$
$103$	−0.348268	−0.0343159	−0.0171579	+	0.999853i	$0.505462\pi$
$104$	2.73733	0.268418
$105$	0	0
$106$	−1.08385	−0.105273
$107$	3.45241	0.333757	0.166879	−	0.985977i	$-0.446631\pi$
$107$	3.45241	0.333757	0.166879	+	0.985977i	$0.446631\pi$
$108$	7.13378	0.686448
$109$	−3.58190	−0.343084	−0.171542	−	0.985177i	$-0.554875\pi$
$109$	−3.58190	−0.343084	−0.171542	+	0.985177i	$0.554875\pi$
$110$	0	0
$111$	−4.41711	−0.419253
$112$	7.79631	0.736682
$113$	16.4466	1.54716	0.773582	−	0.633696i	$-0.218463\pi$
$113$	16.4466	1.54716	0.773582	+	0.633696i	$0.218463\pi$
$114$	−0.297891	−0.0279001
$115$	0	0
$116$	−6.06689	−0.563296
$117$	10.4136	0.962740
$118$	−0.781912	−0.0719808
$119$	−1.59306	−0.146036
$120$	0	0
$121$	−7.44148	−0.676498
$122$	1.86486	0.168837
$123$	−0.551760	−0.0497505
$124$	−1.97085	−0.176988
$125$	0	0
$126$	−0.897259	−0.0799342
$127$	13.7402	1.21925	0.609624	−	0.792690i	$-0.291320\pi$
$127$	13.7402	1.21925	0.609624	+	0.792690i	$0.291320\pi$
$128$	−5.26599	−0.465452
$129$	1.82978	0.161103
$130$	0	0
$131$	−5.19473	−0.453866	−0.226933	−	0.973910i	$-0.572870\pi$
$131$	−5.19473	−0.453866	−0.226933	+	0.973910i	$0.572870\pi$
$132$	2.41208	0.209945
$133$	−5.48021	−0.475194
$134$	−1.20301	−0.103924
$135$	0	0
$136$	0.529996	0.0454468
$137$	−14.6979	−1.25573	−0.627865	−	0.778322i	$-0.716071\pi$
$137$	−14.6979	−1.25573	−0.627865	+	0.778322i	$0.716071\pi$
$138$	−0.610967	−0.0520090
$139$	−0.0509942	−0.00432527	−0.00216263	−	0.999998i	$-0.500688\pi$
$139$	−0.0509942	−0.00432527	−0.00216263	+	0.999998i	$0.500688\pi$
$140$	0	0
$141$	−5.53152	−0.465838
$142$	−1.77790	−0.149198
$143$	7.61681	0.636950
$144$	−9.86743	−0.822286
$145$	0	0
$146$	−1.12275	−0.0929196
$147$	−1.84750	−0.152379
$148$	13.4180	1.10295
$149$	19.6371	1.60874	0.804368	−	0.594131i	$-0.202504\pi$
$149$	19.6371	1.60874	0.804368	+	0.594131i	$0.202504\pi$
$150$	0	0
$151$	−4.83608	−0.393555	−0.196777	−	0.980448i	$-0.563048\pi$
$151$	−4.83608	−0.393555	−0.196777	+	0.980448i	$0.563048\pi$
$152$	1.82321	0.147882
$153$	2.01626	0.163005
$154$	−0.656280	−0.0528846
$155$	0	0
$156$	5.16292	0.413365
$157$	4.95595	0.395528	0.197764	−	0.980250i	$-0.436632\pi$
$157$	4.95595	0.395528	0.197764	+	0.980250i	$0.436632\pi$
$158$	2.61498	0.208036
$159$	−4.11876	−0.326639
$160$	0	0
$161$	−11.2398	−0.885818
$162$	0.920027	0.0722842
$163$	5.58920	0.437780	0.218890	−	0.975750i	$-0.429756\pi$
$163$	5.58920	0.437780	0.218890	+	0.975750i	$0.429756\pi$
$164$	1.67610	0.130882
$165$	0	0
$166$	1.54438	0.119867
$167$	−25.0975	−1.94210	−0.971050	−	0.238877i	$-0.923221\pi$
$167$	−25.0975	−1.94210	−0.971050	+	0.238877i	$0.923221\pi$
$168$	−0.896275	−0.0691492
$169$	3.30334	0.254103
$170$	0	0
$171$	6.93605	0.530413
$172$	−5.55840	−0.423824
$173$	−9.41798	−0.716036	−0.358018	−	0.933715i	$-0.616547\pi$
$173$	−9.41798	−0.716036	−0.358018	+	0.933715i	$0.616547\pi$
$174$	0.340974	0.0258492
$175$	0	0
$176$	−7.21731	−0.544025
$177$	−2.97136	−0.223341
$178$	1.32215	0.0990990
$179$	16.3792	1.22424	0.612119	−	0.790765i	$-0.290317\pi$
$179$	16.3792	1.22424	0.612119	+	0.790765i	$0.290317\pi$
$180$	0	0
$181$	−9.07254	−0.674356	−0.337178	−	0.941441i	$-0.609472\pi$
$181$	−9.07254	−0.674356	−0.337178	+	0.941441i	$0.609472\pi$
$182$	−1.40473	−0.104125
$183$	7.08671	0.523865
$184$	3.73937	0.275670
$185$	0	0
$186$	0.110767	0.00812181
$187$	1.47475	0.107844
$188$	16.8033	1.22551
$189$	−7.37589	−0.536517
$190$	0	0
$191$	−27.5992	−1.99701	−0.998505	−	0.0546664i	$-0.982590\pi$
$191$	−27.5992	−1.99701	−0.998505	+	0.0546664i	$0.982590\pi$
$192$	−4.74194	−0.342220
$193$	17.7402	1.27697	0.638485	−	0.769634i	$-0.279561\pi$
$193$	17.7402	1.27697	0.638485	+	0.769634i	$0.279561\pi$
$194$	0.661280	0.0474771
$195$	0	0
$196$	5.61223	0.400874
$197$	−9.58130	−0.682640	−0.341320	−	0.939947i	$-0.610874\pi$
$197$	−9.58130	−0.682640	−0.341320	+	0.939947i	$0.610874\pi$
$198$	0.830624	0.0590299
$199$	19.7064	1.39695	0.698476	−	0.715634i	$-0.253862\pi$
$199$	19.7064	1.39695	0.698476	+	0.715634i	$0.253862\pi$
$200$	0	0
$201$	−4.57158	−0.322455
$202$	2.11303	0.148672
$203$	6.27279	0.440263
$204$	0.999633	0.0699883
$205$	0	0
$206$	−0.0594593	−0.00414272
$207$	14.2257	0.988751
$208$	−15.4482	−1.07114
$209$	5.07322	0.350922
$210$	0	0
$211$	2.87687	0.198052	0.0990260	−	0.995085i	$-0.468427\pi$
$211$	2.87687	0.198052	0.0990260	+	0.995085i	$0.468427\pi$
$212$	12.5117	0.859309
$213$	−6.75624	−0.462930
$214$	0.589425	0.0402923
$215$	0	0
$216$	2.45389	0.166966
$217$	2.03774	0.138331
$218$	−0.611532	−0.0414182
$219$	−4.26659	−0.288310
$220$	0	0
$221$	3.15661	0.212337
$222$	−0.754125	−0.0506136
$223$	0.0289590	0.00193924	0.000969619	−	1.00000i	$-0.499691\pi$
$223$	0.0289590	0.00193924	0.000969619		1.00000i	$0.499691\pi$
$224$	4.09397	0.273540
$225$	0	0
$226$	2.80790	0.186779
$227$	0.991911	0.0658354	0.0329177	−	0.999458i	$-0.489520\pi$
$227$	0.991911	0.0658354	0.0329177	+	0.999458i	$0.489520\pi$
$228$	3.43879	0.227740
$229$	1.55264	0.102601	0.0513006	−	0.998683i	$-0.483663\pi$
$229$	1.55264	0.102601	0.0513006	+	0.998683i	$0.483663\pi$
$230$	0	0
$231$	−2.49395	−0.164090
$232$	−2.08690	−0.137012
$233$	−15.6572	−1.02574	−0.512868	−	0.858467i	$-0.671417\pi$
$233$	−15.6572	−1.02574	−0.512868	+	0.858467i	$0.671417\pi$
$234$	1.77790	0.116225
$235$	0	0
$236$	9.02622	0.587557
$237$	9.93724	0.645493
$238$	−0.271980	−0.0176299
$239$	3.70029	0.239352	0.119676	−	0.992813i	$-0.461814\pi$
$239$	3.70029	0.239352	0.119676	+	0.992813i	$0.461814\pi$
$240$	0	0
$241$	−13.1219	−0.845257	−0.422629	−	0.906303i	$-0.638893\pi$
$241$	−13.1219	−0.845257	−0.422629	+	0.906303i	$0.638893\pi$
$242$	−1.27047	−0.0816690
$243$	14.3551	0.920883
$244$	−21.5276	−1.37816
$245$	0	0
$246$	−0.0942010	−0.00600604
$247$	10.8589	0.690937
$248$	−0.677937	−0.0430490
$249$	5.86885	0.371923
$250$	0	0
$251$	11.8816	0.749958	0.374979	−	0.927033i	$-0.377650\pi$
$251$	11.8816	0.749958	0.374979	+	0.927033i	$0.377650\pi$
$252$	10.3578	0.652478
$253$	10.4050	0.654159
$254$	2.34585	0.147192
$255$	0	0
$256$	13.7188	0.857424
$257$	−30.8923	−1.92701	−0.963504	−	0.267692i	$-0.913739\pi$
$257$	−30.8923	−1.92701	−0.963504	+	0.267692i	$0.913739\pi$
$258$	0.312396	0.0194489
$259$	−13.8734	−0.862051
$260$	0	0
$261$	−7.93918	−0.491423
$262$	−0.886888	−0.0547921
$263$	−12.8995	−0.795417	−0.397708	−	0.917512i	$-0.630194\pi$
$263$	−12.8995	−0.795417	−0.397708	+	0.917512i	$0.630194\pi$
$264$	0.829713	0.0510653
$265$	0	0
$266$	−0.935627	−0.0573670
$267$	5.02432	0.307483
$268$	13.8873	0.848300
$269$	−15.6382	−0.953480	−0.476740	−	0.879044i	$-0.658182\pi$
$269$	−15.6382	−0.953480	−0.476740	+	0.879044i	$0.658182\pi$
$270$	0	0
$271$	12.2555	0.744467	0.372233	−	0.928139i	$-0.378592\pi$
$271$	12.2555	0.744467	0.372233	+	0.928139i	$0.378592\pi$
$272$	−2.99105	−0.181359
$273$	−5.33815	−0.323079
$274$	−2.50936	−0.151596
$275$	0	0
$276$	7.05287	0.424533
$277$	10.3919	0.624388	0.312194	−	0.950018i	$-0.398936\pi$
$277$	10.3919	0.624388	0.312194	+	0.950018i	$0.398936\pi$
$278$	−0.00870615	−0.000522160 0
$279$	−2.57907	−0.154405
$280$	0	0
$281$	23.5747	1.40635	0.703175	−	0.711017i	$-0.251765\pi$
$281$	23.5747	1.40635	0.703175	+	0.711017i	$0.251765\pi$
$282$	−0.944388	−0.0562375
$283$	18.0609	1.07361	0.536804	−	0.843707i	$-0.319631\pi$
$283$	18.0609	1.07361	0.536804	+	0.843707i	$0.319631\pi$
$284$	20.5237	1.21786
$285$	0	0
$286$	1.30041	0.0768946
$287$	−1.73299	−0.102295
$288$	−5.18155	−0.305326
$289$	−16.3888	−0.964048
$290$	0	0
$291$	2.51294	0.147311
$292$	12.9608	0.758474
$293$	−31.1834	−1.82176	−0.910878	−	0.412676i	$-0.864594\pi$
$293$	−31.1834	−1.82176	−0.910878	+	0.412676i	$0.864594\pi$
$294$	−0.315421	−0.0183957
$295$	0	0
$296$	4.61555	0.268274
$297$	6.82811	0.396207
$298$	3.35262	0.194212
$299$	22.2714	1.28799
$300$	0	0
$301$	5.74705	0.331254
$302$	−0.825657	−0.0475112
$303$	8.02977	0.461298
$304$	−10.2894	−0.590136
$305$	0	0
$306$	0.344233	0.0196785
$307$	6.78955	0.387500	0.193750	−	0.981051i	$-0.437935\pi$
$307$	6.78955	0.387500	0.193750	+	0.981051i	$0.437935\pi$
$308$	7.57596	0.431680
$309$	−0.225952	−0.0128540
$310$	0	0
$311$	3.07342	0.174278	0.0871389	−	0.996196i	$-0.472228\pi$
$311$	3.07342	0.174278	0.0871389	+	0.996196i	$0.472228\pi$
$312$	1.77595	0.100543
$313$	−15.7372	−0.889520	−0.444760	−	0.895650i	$-0.646711\pi$
$313$	−15.7372	−0.889520	−0.444760	+	0.895650i	$0.646711\pi$
$314$	0.846122	0.0477494
$315$	0	0
$316$	−30.1867	−1.69814
$317$	−13.3891	−0.752004	−0.376002	−	0.926619i	$-0.622701\pi$
$317$	−13.3891	−0.752004	−0.376002	+	0.926619i	$0.622701\pi$
$318$	−0.703189	−0.0394329
$319$	−5.80693	−0.325126
$320$	0	0
$321$	2.23989	0.125018
$322$	−1.91895	−0.106939
$323$	2.10248	0.116985
$324$	−10.6206	−0.590033
$325$	0	0
$326$	0.954234	0.0528501
$327$	−2.32390	−0.128512
$328$	0.576549	0.0318346
$329$	−17.3736	−0.957838
$330$	0	0
$331$	8.63988	0.474891	0.237445	−	0.971401i	$-0.423690\pi$
$331$	8.63988	0.474891	0.237445	+	0.971401i	$0.423690\pi$
$332$	−17.8280	−0.978440
$333$	17.5589	0.962223
$334$	−4.28485	−0.234456
$335$	0	0
$336$	5.05816	0.275945
$337$	−9.20097	−0.501209	−0.250604	−	0.968090i	$-0.580629\pi$
$337$	−9.20097	−0.501209	−0.250604	+	0.968090i	$0.580629\pi$
$338$	0.563974	0.0306761
$339$	10.6704	0.579535
$340$	0	0
$341$	−1.88641	−0.102155
$342$	1.18418	0.0640331
$343$	−20.0669	−1.08351
$344$	−1.91199	−0.103088
$345$	0	0
$346$	−1.60792	−0.0864422
$347$	−1.88876	−0.101394	−0.0506970	−	0.998714i	$-0.516144\pi$
$347$	−1.88876	−0.101394	−0.0506970	+	0.998714i	$0.516144\pi$
$348$	−3.93613	−0.210999
$349$	−24.8064	−1.32786	−0.663928	−	0.747797i	$-0.731112\pi$
$349$	−24.8064	−1.32786	−0.663928	+	0.747797i	$0.731112\pi$
$350$	0	0
$351$	14.6152	0.780100
$352$	−3.78993	−0.202004
$353$	−28.4875	−1.51624	−0.758119	−	0.652116i	$-0.773881\pi$
$353$	−28.4875	−1.51624	−0.758119	+	0.652116i	$0.773881\pi$
$354$	−0.507296	−0.0269625
$355$	0	0
$356$	−15.2626	−0.808914
$357$	−1.03356	−0.0547018
$358$	2.79639	0.147794
$359$	−11.6727	−0.616062	−0.308031	−	0.951376i	$-0.599670\pi$
$359$	−11.6727	−0.616062	−0.308031	+	0.951376i	$0.599670\pi$
$360$	0	0
$361$	−11.7674	−0.619335
$362$	−1.54894	−0.0814104
$363$	−4.82795	−0.253402
$364$	16.2159	0.849944
$365$	0	0
$366$	1.20990	0.0632426
$367$	24.3219	1.26959	0.634797	−	0.772679i	$-0.281084\pi$
$367$	24.3219	1.26959	0.634797	+	0.772679i	$0.281084\pi$
$368$	−21.1032	−1.10008
$369$	2.19336	0.114182
$370$	0	0
$371$	−12.9364	−0.671622
$372$	−1.27867	−0.0662958
$373$	−13.1625	−0.681529	−0.340764	−	0.940149i	$-0.610686\pi$
$373$	−13.1625	−0.681529	−0.340764	+	0.940149i	$0.610686\pi$
$374$	0.251782	0.0130193
$375$	0	0
$376$	5.78004	0.298083
$377$	−12.4294	−0.640147
$378$	−1.25927	−0.0647700
$379$	17.5421	0.901076	0.450538	−	0.892757i	$-0.351232\pi$
$379$	17.5421	0.901076	0.450538	+	0.892757i	$0.351232\pi$
$380$	0	0
$381$	8.91451	0.456704
$382$	−4.71197	−0.241085
$383$	−30.7628	−1.57190	−0.785952	−	0.618288i	$-0.787827\pi$
$383$	−30.7628	−1.57190	−0.785952	+	0.618288i	$0.787827\pi$
$384$	−3.41651	−0.174348
$385$	0	0
$386$	3.02876	0.154160
$387$	−7.27377	−0.369747
$388$	−7.63367	−0.387541
$389$	6.78113	0.343817	0.171908	−	0.985113i	$-0.445007\pi$
$389$	6.78113	0.343817	0.171908	+	0.985113i	$0.445007\pi$
$390$	0	0
$391$	4.31213	0.218074
$392$	1.93051	0.0975053
$393$	−3.37028	−0.170008
$394$	−1.63580	−0.0824104
$395$	0	0
$396$	−9.58854	−0.481842
$397$	−29.9329	−1.50229	−0.751146	−	0.660136i	$-0.770498\pi$
$397$	−29.9329	−1.50229	−0.751146	+	0.660136i	$0.770498\pi$
$398$	3.36445	0.168644
$399$	−3.55550	−0.177998
$400$	0	0
$401$	6.22031	0.310627	0.155314	−	0.987865i	$-0.450361\pi$
$401$	6.22031	0.310627	0.155314	+	0.987865i	$0.450361\pi$
$402$	−0.780499	−0.0389277
$403$	−4.03774	−0.201134
$404$	−24.3924	−1.21357
$405$	0	0
$406$	1.07094	0.0531500
$407$	12.8431	0.636608
$408$	0.343856	0.0170234
$409$	−1.61999	−0.0801033	−0.0400517	−	0.999198i	$-0.512752\pi$
$409$	−1.61999	−0.0801033	−0.0400517	+	0.999198i	$0.512752\pi$
$410$	0	0
$411$	−9.53587	−0.470370
$412$	0.686385	0.0338158
$413$	−9.33256	−0.459225
$414$	2.42872	0.119365
$415$	0	0
$416$	−8.11212	−0.397729
$417$	−0.0330844	−0.00162015
$418$	0.866142	0.0423644
$419$	−39.1907	−1.91459	−0.957295	−	0.289111i	$-0.906640\pi$
$419$	−39.1907	−1.91459	−0.957295	+	0.289111i	$0.906640\pi$
$420$	0	0
$421$	39.0788	1.90459	0.952293	−	0.305185i	$-0.0987184\pi$
$421$	39.0788	1.90459	0.952293	+	0.305185i	$0.0987184\pi$
$422$	0.491164	0.0239095
$423$	21.9890	1.06914
$424$	4.30380	0.209011
$425$	0	0
$426$	−1.15348	−0.0558864
$427$	22.2582	1.07715
$428$	−6.80419	−0.328893
$429$	4.94170	0.238588
$430$	0	0
$431$	−20.9501	−1.00913	−0.504566	−	0.863373i	$-0.668347\pi$
$431$	−20.9501	−1.00913	−0.504566	+	0.863373i	$0.668347\pi$
$432$	−13.8486	−0.666291
$433$	5.65398	0.271713	0.135856	−	0.990729i	$-0.456621\pi$
$433$	5.65398	0.271713	0.135856	+	0.990729i	$0.456621\pi$
$434$	0.347900	0.0166997
$435$	0	0
$436$	7.05940	0.338084
$437$	14.8340	0.709604
$438$	−0.728429	−0.0348057
$439$	26.0451	1.24307	0.621533	−	0.783388i	$-0.286510\pi$
$439$	26.0451	1.24307	0.621533	+	0.783388i	$0.286510\pi$
$440$	0	0
$441$	7.34421	0.349724
$442$	0.538924	0.0256340
$443$	−22.8943	−1.08774	−0.543871	−	0.839169i	$-0.683042\pi$
$443$	−22.8943	−1.08774	−0.543871	+	0.839169i	$0.683042\pi$
$444$	8.70546	0.413143
$445$	0	0
$446$	0.00494412	0.000234111 0
$447$	12.7404	0.602598
$448$	−14.8937	−0.703660
$449$	11.8613	0.559769	0.279885	−	0.960034i	$-0.409704\pi$
$449$	11.8613	0.559769	0.279885	+	0.960034i	$0.409704\pi$
$450$	0	0
$451$	1.60428	0.0755428
$452$	−32.4138	−1.52462
$453$	−3.13760	−0.147417
$454$	0.169347	0.00794787
$455$	0	0
$456$	1.18288	0.0553935
$457$	−4.54155	−0.212445	−0.106222	−	0.994342i	$-0.533876\pi$
$457$	−4.54155	−0.212445	−0.106222	+	0.994342i	$0.533876\pi$
$458$	0.265079	0.0123863
$459$	2.82975	0.132082
$460$	0	0
$461$	38.4329	1.79000	0.895000	−	0.446065i	$-0.147175\pi$
$461$	38.4329	1.79000	0.895000	+	0.446065i	$0.147175\pi$
$462$	−0.425787	−0.0198094
$463$	26.5377	1.23331	0.616657	−	0.787232i	$-0.288487\pi$
$463$	26.5377	1.23331	0.616657	+	0.787232i	$0.288487\pi$
$464$	11.7775	0.546756
$465$	0	0
$466$	−2.67313	−0.123830
$467$	−20.2192	−0.935632	−0.467816	−	0.883826i	$-0.654959\pi$
$467$	−20.2192	−0.935632	−0.467816	+	0.883826i	$0.654959\pi$
$468$	−20.5237	−0.948709
$469$	−14.3586	−0.663018
$470$	0	0
$471$	3.21537	0.148156
$472$	3.10486	0.142913
$473$	−5.32024	−0.244625
$474$	1.69657	0.0779260
$475$	0	0
$476$	3.13968	0.143907
$477$	16.3729	0.749666
$478$	0.631745	0.0288953
$479$	−15.3341	−0.700633	−0.350316	−	0.936631i	$-0.613926\pi$
$479$	−15.3341	−0.700633	−0.350316	+	0.936631i	$0.613926\pi$
$480$	0	0
$481$	27.4899	1.25343
$482$	−2.24029	−0.102042
$483$	−7.29223	−0.331808
$484$	14.6660	0.666638
$485$	0	0
$486$	2.45083	0.111172
$487$	−39.1058	−1.77205	−0.886026	−	0.463635i	$-0.846545\pi$
$487$	−39.1058	−1.77205	−0.886026	+	0.463635i	$0.846545\pi$
$488$	−7.40509	−0.335213
$489$	3.62621	0.163983
$490$	0	0
$491$	−24.5487	−1.10787	−0.553934	−	0.832560i	$-0.686874\pi$
$491$	−24.5487	−1.10787	−0.553934	+	0.832560i	$0.686874\pi$
$492$	1.08744	0.0490254
$493$	−2.40655	−0.108386
$494$	1.85393	0.0834121
$495$	0	0
$496$	3.82596	0.171791
$497$	−21.2203	−0.951859
$498$	1.00198	0.0448997
$499$	−6.97517	−0.312251	−0.156126	−	0.987737i	$-0.549900\pi$
$499$	−6.97517	−0.312251	−0.156126	+	0.987737i	$0.549900\pi$
$500$	0	0
$501$	−16.2830	−0.727469
$502$	2.02852	0.0905373
$503$	35.9211	1.60164	0.800822	−	0.598902i	$-0.204396\pi$
$503$	35.9211	1.60164	0.800822	+	0.598902i	$0.204396\pi$
$504$	3.56288	0.158703
$505$	0	0
$506$	1.77643	0.0789721
$507$	2.14317	0.0951816
$508$	−27.0800	−1.20148
$509$	−30.0304	−1.33107	−0.665536	−	0.746366i	$-0.731797\pi$
$509$	−30.0304	−1.33107	−0.665536	+	0.746366i	$0.731797\pi$
$510$	0	0
$511$	−13.4007	−0.592811
$512$	12.8742	0.568963
$513$	9.73451	0.429789
$514$	−5.27419	−0.232635
$515$	0	0
$516$	−3.60623	−0.158755
$517$	16.0833	0.707345
$518$	−2.36858	−0.104070
$519$	−6.11028	−0.268212
$520$	0	0
$521$	−17.3292	−0.759206	−0.379603	−	0.925149i	$-0.623939\pi$
$521$	−17.3292	−0.759206	−0.379603	+	0.925149i	$0.623939\pi$
$522$	−1.35544	−0.0593261
$523$	−12.4723	−0.545374	−0.272687	−	0.962103i	$-0.587912\pi$
$523$	−12.4723	−0.545374	−0.272687	+	0.962103i	$0.587912\pi$
$524$	10.2380	0.447251
$525$	0	0
$526$	−2.20231	−0.0960252
$527$	−0.781778	−0.0340548
$528$	−4.68251	−0.203780
$529$	7.42405	0.322785
$530$	0	0
$531$	11.8118	0.512588
$532$	10.8007	0.468269
$533$	3.43388	0.148738
$534$	0.857793	0.0371203
$535$	0	0
$536$	4.77697	0.206334
$537$	10.6266	0.458573
$538$	−2.66989	−0.115107
$539$	5.37176	0.231378
$540$	0	0
$541$	−8.94919	−0.384756	−0.192378	−	0.981321i	$-0.561620\pi$
$541$	−8.94919	−0.384756	−0.192378	+	0.981321i	$0.561620\pi$
$542$	2.09236	0.0898744
$543$	−5.88616	−0.252599
$544$	−1.57065	−0.0673410
$545$	0	0
$546$	−0.911373	−0.0390032
$547$	29.7772	1.27318	0.636590	−	0.771203i	$-0.280344\pi$
$547$	29.7772	1.27318	0.636590	+	0.771203i	$0.280344\pi$
$548$	28.9675	1.23743
$549$	−28.1712	−1.20232
$550$	0	0
$551$	−8.27867	−0.352683
$552$	2.42606	0.103260
$553$	31.2112	1.32724
$554$	1.77419	0.0753781
$555$	0	0
$556$	0.100502	0.00426223
$557$	−16.5614	−0.701731	−0.350865	−	0.936426i	$-0.614113\pi$
$557$	−16.5614	−0.701731	−0.350865	+	0.936426i	$0.614113\pi$
$558$	−0.440321	−0.0186403
$559$	−11.3877	−0.481646
$560$	0	0
$561$	0.956801	0.0403962
$562$	4.02487	0.169779
$563$	42.9381	1.80963	0.904813	−	0.425810i	$-0.140011\pi$
$563$	42.9381	1.80963	0.904813	+	0.425810i	$0.140011\pi$
$564$	10.9018	0.459049
$565$	0	0
$566$	3.08351	0.129609
$567$	10.9810	0.461161
$568$	7.05978	0.296222
$569$	−38.4203	−1.61066	−0.805332	−	0.592824i	$-0.798013\pi$
$569$	−38.4203	−1.61066	−0.805332	+	0.592824i	$0.798013\pi$
$570$	0	0
$571$	−16.1716	−0.676762	−0.338381	−	0.941009i	$-0.609879\pi$
$571$	−16.1716	−0.676762	−0.338381	+	0.941009i	$0.609879\pi$
$572$	−15.0116	−0.627667
$573$	−17.9061	−0.748037
$574$	−0.295870	−0.0123494
$575$	0	0
$576$	18.8502	0.785426
$577$	−24.8000	−1.03244	−0.516220	−	0.856456i	$-0.672661\pi$
$577$	−24.8000	−1.03244	−0.516220	+	0.856456i	$0.672661\pi$
$578$	−2.79804	−0.116383
$579$	11.5097	0.478326
$580$	0	0
$581$	18.4331	0.764733
$582$	0.429031	0.0177839
$583$	11.9756	0.495980
$584$	4.45828	0.184485
$585$	0	0
$586$	−5.32390	−0.219928
$587$	4.88506	0.201628	0.100814	−	0.994905i	$-0.467855\pi$
$587$	4.88506	0.201628	0.100814	+	0.994905i	$0.467855\pi$
$588$	3.64115	0.150159
$589$	−2.68936	−0.110813
$590$	0	0
$591$	−6.21624	−0.255702
$592$	−26.0480	−1.07057
$593$	−14.1295	−0.580230	−0.290115	−	0.956992i	$-0.593694\pi$
$593$	−14.1295	−0.580230	−0.290115	+	0.956992i	$0.593694\pi$
$594$	1.16575	0.0478314
$595$	0	0
$596$	−38.7019	−1.58529
$597$	12.7853	0.523268
$598$	3.80235	0.155490
$599$	22.6620	0.925945	0.462972	−	0.886373i	$-0.346783\pi$
$599$	22.6620	0.925945	0.462972	+	0.886373i	$0.346783\pi$
$600$	0	0
$601$	25.0849	1.02324	0.511618	−	0.859213i	$-0.329046\pi$
$601$	25.0849	1.02324	0.511618	+	0.859213i	$0.329046\pi$
$602$	0.981184	0.0399901
$603$	18.1730	0.740062
$604$	9.53120	0.387819
$605$	0	0
$606$	1.37091	0.0556894
$607$	35.1819	1.42799	0.713995	−	0.700150i	$-0.246884\pi$
$607$	35.1819	1.42799	0.713995	+	0.700150i	$0.246884\pi$
$608$	−5.40312	−0.219125
$609$	4.06972	0.164913
$610$	0	0
$611$	34.4255	1.39270
$612$	−3.97375	−0.160629
$613$	38.6679	1.56178	0.780891	−	0.624667i	$-0.214765\pi$
$613$	38.6679	1.56178	0.780891	+	0.624667i	$0.214765\pi$
$614$	1.15917	0.0467803
$615$	0	0
$616$	2.60599	0.104998
$617$	28.2507	1.13733	0.568666	−	0.822569i	$-0.307460\pi$
$617$	28.2507	1.13733	0.568666	+	0.822569i	$0.307460\pi$
$618$	−0.0385765	−0.00155177
$619$	−13.1702	−0.529355	−0.264678	−	0.964337i	$-0.585266\pi$
$619$	−13.1702	−0.529355	−0.264678	+	0.964337i	$0.585266\pi$
$620$	0	0
$621$	19.9652	0.801176
$622$	0.524721	0.0210394
$623$	15.7806	0.632234
$624$	−10.0226	−0.401227
$625$	0	0
$626$	−2.68679	−0.107386
$627$	3.29145	0.131448
$628$	−9.76745	−0.389764
$629$	5.32252	0.212223
$630$	0	0
$631$	10.3413	0.411682	0.205841	−	0.978585i	$-0.434007\pi$
$631$	10.3413	0.411682	0.205841	+	0.978585i	$0.434007\pi$
$632$	−10.3837	−0.413041
$633$	1.86648	0.0741860
$634$	−2.28589	−0.0907844
$635$	0	0
$636$	8.11747	0.321878
$637$	11.4979	0.455565
$638$	−0.991409	−0.0392502
$639$	26.8575	1.06247
$640$	0	0
$641$	−19.1986	−0.758300	−0.379150	−	0.925335i	$-0.623784\pi$
$641$	−19.1986	−0.758300	−0.379150	+	0.925335i	$0.623784\pi$
$642$	0.382412	0.0150926
$643$	39.3353	1.55123	0.775617	−	0.631204i	$-0.217439\pi$
$643$	39.3353	1.55123	0.775617	+	0.631204i	$0.217439\pi$
$644$	22.1519	0.872908
$645$	0	0
$646$	0.358953	0.0141228
$647$	5.71624	0.224729	0.112364	−	0.993667i	$-0.464158\pi$
$647$	5.71624	0.224729	0.112364	+	0.993667i	$0.464158\pi$
$648$	−3.65329	−0.143515
$649$	8.63947	0.339129
$650$	0	0
$651$	1.32206	0.0518157
$652$	−11.0155	−0.431399
$653$	−39.1054	−1.53031	−0.765156	−	0.643845i	$-0.777338\pi$
$653$	−39.1054	−1.53031	−0.765156	+	0.643845i	$0.777338\pi$
$654$	−0.396755	−0.0155144
$655$	0	0
$656$	−3.25377	−0.127038
$657$	16.9606	0.661697
$658$	−2.96617	−0.115633
$659$	1.88665	0.0734933	0.0367466	−	0.999325i	$-0.488301\pi$
$659$	1.88665	0.0734933	0.0367466	+	0.999325i	$0.488301\pi$
$660$	0	0
$661$	−9.08025	−0.353181	−0.176590	−	0.984284i	$-0.556507\pi$
$661$	−9.08025	−0.353181	−0.176590	+	0.984284i	$0.556507\pi$
$662$	1.47507	0.0573303
$663$	2.04798	0.0795368
$664$	−6.13252	−0.237988
$665$	0	0
$666$	2.99781	0.116163
$667$	−16.9793	−0.657442
$668$	49.4634	1.91380
$669$	0.0187883	0.000726397 0
$670$	0	0
$671$	−20.6052	−0.795454
$672$	2.65612	0.102462
$673$	−51.0431	−1.96757	−0.983784	−	0.179355i	$-0.942599\pi$
$673$	−51.0431	−1.96757	−0.983784	+	0.179355i	$0.942599\pi$
$674$	−1.57087	−0.0605075
$675$	0	0
$676$	−6.51040	−0.250400
$677$	13.8781	0.533379	0.266690	−	0.963782i	$-0.414070\pi$
$677$	13.8781	0.533379	0.266690	+	0.963782i	$0.414070\pi$
$678$	1.82173	0.0699633
$679$	7.89275	0.302896
$680$	0	0
$681$	0.643541	0.0246605
$682$	−0.322063	−0.0123324
$683$	−41.4889	−1.58753	−0.793765	−	0.608224i	$-0.791882\pi$
$683$	−41.4889	−1.58753	−0.793765	+	0.608224i	$0.791882\pi$
$684$	−13.6699	−0.522683
$685$	0	0
$686$	−3.42599	−0.130805
$687$	1.00733	0.0384322
$688$	10.7904	0.411379
$689$	25.6331	0.976544
$690$	0	0
$691$	−16.1202	−0.613242	−0.306621	−	0.951832i	$-0.599198\pi$
$691$	−16.1202	−0.613242	−0.306621	+	0.951832i	$0.599198\pi$
$692$	18.5615	0.705600
$693$	9.91396	0.376600
$694$	−0.322465	−0.0122406
$695$	0	0
$696$	−1.35396	−0.0513216
$697$	0.664859	0.0251833
$698$	−4.23515	−0.160303
$699$	−10.1582	−0.384219
$700$	0	0
$701$	−6.24252	−0.235777	−0.117888	−	0.993027i	$-0.537613\pi$
$701$	−6.24252	−0.235777	−0.117888	+	0.993027i	$0.537613\pi$
$702$	2.49522	0.0941762
$703$	18.3098	0.690566
$704$	13.7876	0.519639
$705$	0	0
$706$	−4.86363	−0.183045
$707$	25.2202	0.948503
$708$	5.85611	0.220086
$709$	−12.3875	−0.465224	−0.232612	−	0.972570i	$-0.574727\pi$
$709$	−12.3875	−0.465224	−0.232612	+	0.972570i	$0.574727\pi$
$710$	0	0
$711$	−39.5026	−1.48146
$712$	−5.25004	−0.196754
$713$	−5.51580	−0.206568
$714$	−0.176458	−0.00660377
$715$	0	0
$716$	−32.2810	−1.20640
$717$	2.40071	0.0896561
$718$	−1.99286	−0.0743730
$719$	24.2570	0.904634	0.452317	−	0.891857i	$-0.350598\pi$
$719$	24.2570	0.904634	0.452317	+	0.891857i	$0.350598\pi$
$720$	0	0
$721$	−0.709680	−0.0264299
$722$	−2.00902	−0.0747681
$723$	−8.51336	−0.316615
$724$	17.8806	0.664528
$725$	0	0
$726$	−0.824268	−0.0305914
$727$	−11.2543	−0.417398	−0.208699	−	0.977980i	$-0.566923\pi$
$727$	−11.2543	−0.417398	−0.208699	+	0.977980i	$0.566923\pi$
$728$	5.57797	0.206733
$729$	−6.85305	−0.253817
$730$	0	0
$731$	−2.20485	−0.0815494
$732$	−13.9669	−0.516230
$733$	52.7119	1.94696	0.973480	−	0.228774i	$-0.0734717\pi$
$733$	52.7119	1.94696	0.973480	+	0.228774i	$0.0734717\pi$
$734$	4.15245	0.153270
$735$	0	0
$736$	−11.0817	−0.408475
$737$	13.2922	0.489626
$738$	0.374469	0.0137844
$739$	42.0221	1.54581	0.772903	−	0.634524i	$-0.218804\pi$
$739$	42.0221	1.54581	0.772903	+	0.634524i	$0.218804\pi$
$740$	0	0
$741$	7.04515	0.258810
$742$	−2.20860	−0.0810803
$743$	18.0584	0.662499	0.331250	−	0.943543i	$-0.392530\pi$
$743$	18.0584	0.662499	0.331250	+	0.943543i	$0.392530\pi$
$744$	−0.439838	−0.0161252
$745$	0	0
$746$	−2.24721	−0.0822763
$747$	−23.3299	−0.853596
$748$	−2.90651	−0.106273
$749$	7.03512	0.257058
$750$	0	0
$751$	3.30188	0.120487	0.0602437	−	0.998184i	$-0.480812\pi$
$751$	3.30188	0.120487	0.0602437	+	0.998184i	$0.480812\pi$
$752$	−32.6198	−1.18952
$753$	7.70863	0.280918
$754$	−2.12205	−0.0772806
$755$	0	0
$756$	14.5368	0.528697
$757$	4.68080	0.170127	0.0850633	−	0.996376i	$-0.472891\pi$
$757$	4.68080	0.170127	0.0850633	+	0.996376i	$0.472891\pi$
$758$	2.99493	0.108781
$759$	6.75067	0.245034
$760$	0	0
$761$	−49.7822	−1.80460	−0.902302	−	0.431105i	$-0.858124\pi$
$761$	−49.7822	−1.80460	−0.902302	+	0.431105i	$0.858124\pi$
$762$	1.52196	0.0551348
$763$	−7.29898	−0.264241
$764$	54.3940	1.96790
$765$	0	0
$766$	−5.25208	−0.189765
$767$	18.4923	0.667718
$768$	8.90059	0.321172
$769$	−20.2709	−0.730987	−0.365494	−	0.930814i	$-0.619100\pi$
$769$	−20.2709	−0.730987	−0.365494	+	0.930814i	$0.619100\pi$
$770$	0	0
$771$	−20.0426	−0.721816
$772$	−34.9634	−1.25836
$773$	48.1961	1.73349	0.866746	−	0.498750i	$-0.166207\pi$
$773$	48.1961	1.73349	0.866746	+	0.498750i	$0.166207\pi$
$774$	−1.24184	−0.0446370
$775$	0	0
$776$	−2.62584	−0.0942623
$777$	−9.00091	−0.322906
$778$	1.15773	0.0415067
$779$	2.28715	0.0819457
$780$	0	0
$781$	19.6443	0.702929
$782$	0.736203	0.0263266
$783$	−11.1424	−0.398196
$784$	−10.8949	−0.389103
$785$	0	0
$786$	−0.575403	−0.0205239
$787$	9.67720	0.344955	0.172478	−	0.985013i	$-0.444823\pi$
$787$	9.67720	0.344955	0.172478	+	0.985013i	$0.444823\pi$
$788$	18.8833	0.672691
$789$	−8.36905	−0.297946
$790$	0	0
$791$	33.5139	1.19162
$792$	−3.29828	−0.117199
$793$	−44.1042	−1.56618
$794$	−5.11040	−0.181361
$795$	0	0
$796$	−38.8384	−1.37659
$797$	30.0943	1.06599	0.532997	−	0.846117i	$-0.321066\pi$
$797$	30.0943	1.06599	0.532997	+	0.846117i	$0.321066\pi$
$798$	−0.607025	−0.0214884
$799$	6.66538	0.235804
$800$	0	0
$801$	−19.9727	−0.705701
$802$	1.06198	0.0374999
$803$	12.4055	0.437779
$804$	9.00991	0.317755
$805$	0	0
$806$	−0.689357	−0.0242816
$807$	−10.1459	−0.357153
$808$	−8.39053	−0.295178
$809$	−9.22264	−0.324251	−0.162125	−	0.986770i	$-0.551835\pi$
$809$	−9.22264	−0.324251	−0.162125	+	0.986770i	$0.551835\pi$
$810$	0	0
$811$	−15.6129	−0.548243	−0.274121	−	0.961695i	$-0.588387\pi$
$811$	−15.6129	−0.548243	−0.274121	+	0.961695i	$0.588387\pi$
$812$	−12.3627	−0.433847
$813$	7.95121	0.278861
$814$	2.19268	0.0768534
$815$	0	0
$816$	−1.94056	−0.0679332
$817$	−7.58480	−0.265359
$818$	−0.276578	−0.00967033
$819$	21.2203	0.741496
$820$	0	0
$821$	0.136370	0.00475935	0.00237967	−	0.999997i	$-0.499243\pi$
$821$	0.136370	0.00475935	0.00237967	+	0.999997i	$0.499243\pi$
$822$	−1.62804	−0.0567845
$823$	31.7529	1.10684	0.553418	−	0.832904i	$-0.313323\pi$
$823$	31.7529	1.10684	0.553418	+	0.832904i	$0.313323\pi$
$824$	0.236104	0.00822507
$825$	0	0
$826$	−1.59333	−0.0554391
$827$	−24.4033	−0.848587	−0.424294	−	0.905525i	$-0.639478\pi$
$827$	−24.4033	−0.848587	−0.424294	+	0.905525i	$0.639478\pi$
$828$	−28.0366	−0.974341
$829$	−26.4640	−0.919134	−0.459567	−	0.888143i	$-0.651995\pi$
$829$	−26.4640	−0.919134	−0.459567	+	0.888143i	$0.651995\pi$
$830$	0	0
$831$	6.74214	0.233882
$832$	29.5115	1.02313
$833$	2.22620	0.0771334
$834$	−0.00564845	−0.000195590 0
$835$	0	0
$836$	−9.99856	−0.345807
$837$	−3.61964	−0.125113
$838$	−6.69096	−0.231136
$839$	9.24501	0.319173	0.159587	−	0.987184i	$-0.448984\pi$
$839$	9.24501	0.319173	0.159587	+	0.987184i	$0.448984\pi$
$840$	0	0
$841$	−19.5240	−0.673242
$842$	6.67187	0.229928
$843$	15.2950	0.526788
$844$	−5.66989	−0.195166
$845$	0	0
$846$	3.75414	0.129070
$847$	−15.1638	−0.521034
$848$	−24.2887	−0.834076
$849$	11.7177	0.402150
$850$	0	0
$851$	37.5528	1.28730
$852$	13.3156	0.456183
$853$	−51.2430	−1.75453	−0.877263	−	0.480010i	$-0.840633\pi$
$853$	−51.2430	−1.75453	−0.877263	+	0.480010i	$0.840633\pi$
$854$	3.80011	0.130037
$855$	0	0
$856$	−2.34052	−0.0799973
$857$	7.16663	0.244807	0.122404	−	0.992480i	$-0.460940\pi$
$857$	7.16663	0.244807	0.122404	+	0.992480i	$0.460940\pi$
$858$	0.843689	0.0288031
$859$	−41.0720	−1.40136	−0.700678	−	0.713477i	$-0.747119\pi$
$859$	−41.0720	−1.40136	−0.700678	+	0.713477i	$0.747119\pi$
$860$	0	0
$861$	−1.12434	−0.0383175
$862$	−3.57678	−0.121826
$863$	6.52226	0.222020	0.111010	−	0.993819i	$-0.464591\pi$
$863$	6.52226	0.222020	0.111010	+	0.993819i	$0.464591\pi$
$864$	−7.27213	−0.247403
$865$	0	0
$866$	0.965294	0.0328020
$867$	−10.6329	−0.361112
$868$	−4.01608	−0.136315
$869$	−28.8933	−0.980138
$870$	0	0
$871$	28.4512	0.964034
$872$	2.42830	0.0822327
$873$	−9.98948	−0.338093
$874$	2.53258	0.0856657
$875$	0	0
$876$	8.40883	0.284108
$877$	43.6618	1.47435	0.737176	−	0.675700i	$-0.236159\pi$
$877$	43.6618	1.47435	0.737176	+	0.675700i	$0.236159\pi$
$878$	4.44664	0.150067
$879$	−20.2315	−0.682391
$880$	0	0
$881$	35.1074	1.18280	0.591399	−	0.806379i	$-0.298576\pi$
$881$	35.1074	1.18280	0.591399	+	0.806379i	$0.298576\pi$
$882$	1.25387	0.0422198
$883$	49.4037	1.66257	0.831283	−	0.555849i	$-0.187607\pi$
$883$	49.4037	1.66257	0.831283	+	0.555849i	$0.187607\pi$
$884$	−6.22122	−0.209242
$885$	0	0
$886$	−3.90871	−0.131316
$887$	18.4540	0.619623	0.309812	−	0.950798i	$-0.399734\pi$
$887$	18.4540	0.619623	0.309812	+	0.950798i	$0.399734\pi$
$888$	2.99452	0.100490
$889$	27.9990	0.939057
$890$	0	0
$891$	−10.1655	−0.340558
$892$	−0.0570739	−0.00191098
$893$	22.9292	0.767298
$894$	2.17514	0.0727475
$895$	0	0
$896$	−10.7307	−0.358488
$897$	14.4494	0.482452
$898$	2.02506	0.0675771
$899$	3.07831	0.102667
$900$	0	0
$901$	4.96302	0.165342
$902$	0.273897	0.00911977
$903$	3.72862	0.124081
$904$	−11.1498	−0.370835
$905$	0	0
$906$	−0.535677	−0.0177967
$907$	−30.1572	−1.00135	−0.500677	−	0.865634i	$-0.666915\pi$
$907$	−30.1572	−1.00135	−0.500677	+	0.865634i	$0.666915\pi$
$908$	−1.95491	−0.0648760
$909$	−31.9200	−1.05872
$910$	0	0
$911$	22.5492	0.747088	0.373544	−	0.927612i	$-0.378142\pi$
$911$	22.5492	0.747088	0.373544	+	0.927612i	$0.378142\pi$
$912$	−6.67563	−0.221052
$913$	−17.0641	−0.564740
$914$	−0.775372	−0.0256470
$915$	0	0
$916$	−3.06002	−0.101106
$917$	−10.5855	−0.349564
$918$	0.483119	0.0159453
$919$	35.7225	1.17838	0.589188	−	0.807996i	$-0.299448\pi$
$919$	35.7225	1.17838	0.589188	+	0.807996i	$0.299448\pi$
$920$	0	0
$921$	4.40499	0.145149
$922$	6.56159	0.216095
$923$	42.0475	1.38401
$924$	4.91520	0.161698
$925$	0	0
$926$	4.53075	0.148890
$927$	0.898209	0.0295010
$928$	6.18455	0.203018
$929$	24.4206	0.801215	0.400607	−	0.916250i	$-0.368799\pi$
$929$	24.4206	0.801215	0.400607	+	0.916250i	$0.368799\pi$
$930$	0	0
$931$	7.65826	0.250989
$932$	30.8580	1.01079
$933$	1.99400	0.0652807
$934$	−3.45199	−0.112952
$935$	0	0
$936$	−7.05978	−0.230756
$937$	39.5651	1.29253	0.646267	−	0.763111i	$-0.276329\pi$
$937$	39.5651	1.29253	0.646267	+	0.763111i	$0.276329\pi$
$938$	−2.45142	−0.0800417
$939$	−10.2101	−0.333195
$940$	0	0
$941$	34.4739	1.12382	0.561909	−	0.827199i	$-0.310067\pi$
$941$	34.4739	1.12382	0.561909	+	0.827199i	$0.310067\pi$
$942$	0.548954	0.0178859
$943$	4.69089	0.152756
$944$	−17.5224	−0.570304
$945$	0	0
$946$	−0.908315	−0.0295319
$947$	50.8976	1.65395	0.826975	−	0.562239i	$-0.190060\pi$
$947$	50.8976	1.65395	0.826975	+	0.562239i	$0.190060\pi$
$948$	−19.5848	−0.636085
$949$	26.5532	0.861952
$950$	0	0
$951$	−8.68667	−0.281685
$952$	1.07999	0.0350028
$953$	−49.2729	−1.59611	−0.798054	−	0.602586i	$-0.794137\pi$
$953$	−49.2729	−1.59611	−0.798054	+	0.602586i	$0.794137\pi$
$954$	2.79533	0.0905020
$955$	0	0
$956$	−7.29273	−0.235864
$957$	−3.76747	−0.121785
$958$	−2.61797	−0.0845826
$959$	−29.9506	−0.967155
$960$	0	0
$961$	1.00000	0.0322581
$962$	4.69330	0.151318
$963$	−8.90402	−0.286928
$964$	25.8614	0.832939
$965$	0	0
$966$	−1.24499	−0.0400569
$967$	32.0275	1.02994	0.514968	−	0.857209i	$-0.327804\pi$
$967$	32.0275	1.02994	0.514968	+	0.857209i	$0.327804\pi$
$968$	5.04485	0.162148
$969$	1.36407	0.0438201
$970$	0	0
$971$	−6.76487	−0.217095	−0.108548	−	0.994091i	$-0.534620\pi$
$971$	−6.76487	−0.217095	−0.108548	+	0.994091i	$0.534620\pi$
$972$	−28.2919	−0.907462
$973$	−0.103913	−0.00333129
$974$	−6.67647	−0.213928
$975$	0	0
$976$	41.7909	1.33769
$977$	−35.1446	−1.12437	−0.562187	−	0.827010i	$-0.690040\pi$
$977$	−35.1446	−1.12437	−0.562187	+	0.827010i	$0.690040\pi$
$978$	0.619097	0.0197965
$979$	−14.6086	−0.466893
$980$	0	0
$981$	9.23798	0.294946
$982$	−4.19117	−0.133745
$983$	−13.0058	−0.414822	−0.207411	−	0.978254i	$-0.566504\pi$
$983$	−13.0058	−0.414822	−0.207411	+	0.978254i	$0.566504\pi$
$984$	0.374058	0.0119245
$985$	0	0
$986$	−0.410867	−0.0130847
$987$	−11.2718	−0.358786
$988$	−21.4013	−0.680867
$989$	−15.5562	−0.494659
$990$	0	0
$991$	−11.8109	−0.375186	−0.187593	−	0.982247i	$-0.560069\pi$
$991$	−11.8109	−0.375186	−0.187593	+	0.982247i	$0.560069\pi$
$992$	2.00907	0.0637882
$993$	5.60546	0.177884
$994$	−3.62290	−0.114911
$995$	0	0
$996$	−11.5666	−0.366503
$997$	41.3201	1.30862	0.654310	−	0.756227i	$-0.272959\pi$
$997$	41.3201	1.30862	0.654310	+	0.756227i	$0.272959\pi$
$998$	−1.19086	−0.0376960
$999$	24.6434	0.779681

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.a.i.1.4	✓	5
3.2	odd	2		6975.2.a.bx.1.2		5
5.2	odd	4		775.2.b.h.249.6		10
5.3	odd	4		775.2.b.h.249.5		10
5.4	even	2		775.2.a.j.1.2	yes	5
15.14	odd	2		6975.2.a.bq.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
775.2.a.i.1.4	✓	5	1.1	even	1	trivial
775.2.a.j.1.2	yes	5	5.4	even	2
775.2.b.h.249.5		10	5.3	odd	4
775.2.b.h.249.6		10	5.2	odd	4
6975.2.a.bq.1.4		5	15.14	odd	2
6975.2.a.bx.1.2		5	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.a (trivial)

\(f(q)\)	\(=\)	\(q+0.170728 q^{2} +0.648789 q^{3} -1.97085 q^{4} +0.110767 q^{6} +2.03774 q^{7} -0.677937 q^{8} -2.57907 q^{9} +O(q^{10})\)	\(q+0.170728 q^{2} +0.648789 q^{3} -1.97085 q^{4} +0.110767 q^{6} +2.03774 q^{7} -0.677937 q^{8} -2.57907 q^{9} -1.88641 q^{11} -1.27867 q^{12} -4.03774 q^{13} +0.347900 q^{14} +3.82596 q^{16} -0.781778 q^{17} -0.440321 q^{18} -2.68936 q^{19} +1.32206 q^{21} -0.322063 q^{22} -5.51580 q^{23} -0.439838 q^{24} -0.689357 q^{26} -3.61964 q^{27} -4.01608 q^{28} +3.07831 q^{29} +1.00000 q^{31} +2.00907 q^{32} -1.22388 q^{33} -0.133472 q^{34} +5.08297 q^{36} -6.80823 q^{37} -0.459150 q^{38} -2.61964 q^{39} -0.850446 q^{41} +0.225714 q^{42} +2.82030 q^{43} +3.71782 q^{44} -0.941704 q^{46} -8.52592 q^{47} +2.48224 q^{48} -2.84762 q^{49} -0.507209 q^{51} +7.95779 q^{52} -6.34838 q^{53} -0.617975 q^{54} -1.38146 q^{56} -1.74482 q^{57} +0.525554 q^{58} -4.57986 q^{59} +10.9230 q^{61} +0.170728 q^{62} -5.25548 q^{63} -7.30892 q^{64} -0.208951 q^{66} -7.04633 q^{67} +1.54077 q^{68} -3.57859 q^{69} -10.4136 q^{71} +1.74845 q^{72} -6.57624 q^{73} -1.16236 q^{74} +5.30032 q^{76} -3.84400 q^{77} -0.447247 q^{78} +15.3166 q^{79} +5.38884 q^{81} -0.145195 q^{82} +9.04585 q^{83} -2.60559 q^{84} +0.481506 q^{86} +1.99717 q^{87} +1.27886 q^{88} +7.74414 q^{89} -8.22786 q^{91} +10.8708 q^{92} +0.648789 q^{93} -1.45562 q^{94} +1.30347 q^{96} +3.87328 q^{97} -0.486169 q^{98} +4.86518 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 4 q^{2} - q^{3} + 6 q^{4} - q^{6} - 6 q^{7} - 15 q^{8} + 2 q^{9}+O(q^{10}) \) 5 * q - 4 * q^2 - q^3 + 6 * q^4 - q^6 - 6 * q^7 - 15 * q^8 + 2 * q^9	\( 5 q - 4 q^{2} - q^{3} + 6 q^{4} - q^{6} - 6 q^{7} - 15 q^{8} + 2 q^{9} + 11 q^{12} - 4 q^{13} + 2 q^{14} + 20 q^{16} - 11 q^{17} - 19 q^{18} - 4 q^{19} - 5 q^{21} + 10 q^{22} - 12 q^{23} - 26 q^{24} + 6 q^{26} + 2 q^{27} - 18 q^{28} - 6 q^{29} + 5 q^{31} - 29 q^{32} - 21 q^{33} - 5 q^{34} + 23 q^{36} + 2 q^{37} + 6 q^{38} + 7 q^{39} - 2 q^{41} + 24 q^{42} - 7 q^{43} - 28 q^{44} + 27 q^{46} - 8 q^{47} + 39 q^{48} - q^{49} - 19 q^{51} + 6 q^{52} - 25 q^{53} - 18 q^{54} + 35 q^{56} - 20 q^{57} + q^{58} + 4 q^{59} - 17 q^{61} - 4 q^{62} - 10 q^{63} + 27 q^{64} + 27 q^{66} + 13 q^{67} - 18 q^{68} - 10 q^{69} - 6 q^{71} - 26 q^{72} - 7 q^{73} + 6 q^{74} - 5 q^{76} - 7 q^{77} - 22 q^{78} + 12 q^{79} - 11 q^{81} + 21 q^{82} + 4 q^{83} - 63 q^{84} - 41 q^{86} - q^{87} + 49 q^{88} - 3 q^{89} - 22 q^{91} - 34 q^{92} - q^{93} - 34 q^{94} - 64 q^{96} - 25 q^{97} + 22 q^{98} + 5 q^{99}+O(q^{100}) \) 5 * q - 4 * q^2 - q^3 + 6 * q^4 - q^6 - 6 * q^7 - 15 * q^8 + 2 * q^9 + 11 * q^12 - 4 * q^13 + 2 * q^14 + 20 * q^16 - 11 * q^17 - 19 * q^18 - 4 * q^19 - 5 * q^21 + 10 * q^22 - 12 * q^23 - 26 * q^24 + 6 * q^26 + 2 * q^27 - 18 * q^28 - 6 * q^29 + 5 * q^31 - 29 * q^32 - 21 * q^33 - 5 * q^34 + 23 * q^36 + 2 * q^37 + 6 * q^38 + 7 * q^39 - 2 * q^41 + 24 * q^42 - 7 * q^43 - 28 * q^44 + 27 * q^46 - 8 * q^47 + 39 * q^48 - q^49 - 19 * q^51 + 6 * q^52 - 25 * q^53 - 18 * q^54 + 35 * q^56 - 20 * q^57 + q^58 + 4 * q^59 - 17 * q^61 - 4 * q^62 - 10 * q^63 + 27 * q^64 + 27 * q^66 + 13 * q^67 - 18 * q^68 - 10 * q^69 - 6 * q^71 - 26 * q^72 - 7 * q^73 + 6 * q^74 - 5 * q^76 - 7 * q^77 - 22 * q^78 + 12 * q^79 - 11 * q^81 + 21 * q^82 + 4 * q^83 - 63 * q^84 - 41 * q^86 - q^87 + 49 * q^88 - 3 * q^89 - 22 * q^91 - 34 * q^92 - q^93 - 34 * q^94 - 64 * q^96 - 25 * q^97 + 22 * q^98 + 5 * q^99

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