LMFDB - Embedded newform 7225.2.a.bs.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7225,2,Mod(1,7225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7225, 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("7225.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7225 = 5^{2} \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7225.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:	$57.6919154604$
Analytic rank:	$0$
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} - 4 x^{11} - 10 x^{10} + 52 x^{9} + 21 x^{8} - 232 x^{7} + 44 x^{6} + 424 x^{5} - 137 x^{4} + \cdots + 17 $ x^12 - 4x^11 - 10x^10 + 52x^9 + 21x^8 - 232x^7 + 44x^6 + 424x^5 - 137x^4 - 316x^3 + 46x^2 + 92*x + 17
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 85)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.43840$ of defining polynomial
Character	$\chi$	$=$	7225.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.43840 q^{2} -0.109907 q^{3} +0.0689897 q^{4} +0.158090 q^{6} +0.695085 q^{7} +2.77756 q^{8} -2.98792 q^{9} +O(q^{10})$	\(q-1.43840 q^{2} -0.109907 q^{3} +0.0689897 q^{4} +0.158090 q^{6} +0.695085 q^{7} +2.77756 q^{8} -2.98792 q^{9} -4.85089 q^{11} -0.00758244 q^{12} -5.63906 q^{13} -0.999809 q^{14} -4.13322 q^{16} +4.29782 q^{18} -2.32272 q^{19} -0.0763945 q^{21} +6.97750 q^{22} +4.63686 q^{23} -0.305273 q^{24} +8.11121 q^{26} +0.658113 q^{27} +0.0479537 q^{28} -6.50618 q^{29} -6.63194 q^{31} +0.390093 q^{32} +0.533145 q^{33} -0.206136 q^{36} +0.118625 q^{37} +3.34100 q^{38} +0.619770 q^{39} -1.07877 q^{41} +0.109886 q^{42} +0.641108 q^{43} -0.334661 q^{44} -6.66965 q^{46} -4.93703 q^{47} +0.454269 q^{48} -6.51686 q^{49} -0.389037 q^{52} -11.9864 q^{53} -0.946629 q^{54} +1.93064 q^{56} +0.255283 q^{57} +9.35848 q^{58} -9.91829 q^{59} -1.60292 q^{61} +9.53937 q^{62} -2.07686 q^{63} +7.70533 q^{64} -0.766875 q^{66} +2.99411 q^{67} -0.509622 q^{69} +4.68852 q^{71} -8.29913 q^{72} +5.49911 q^{73} -0.170630 q^{74} -0.160244 q^{76} -3.37178 q^{77} -0.891477 q^{78} -14.8439 q^{79} +8.89143 q^{81} +1.55170 q^{82} -5.03506 q^{83} -0.00527044 q^{84} -0.922169 q^{86} +0.715073 q^{87} -13.4736 q^{88} -2.35657 q^{89} -3.91962 q^{91} +0.319896 q^{92} +0.728895 q^{93} +7.10141 q^{94} -0.0428738 q^{96} -2.70080 q^{97} +9.37384 q^{98} +14.4941 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} + 8 q^{3} + 12 q^{4} - 8 q^{6} + 16 q^{7} + 12 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q + 4 * q^2 + 8 * q^3 + 12 * q^4 - 8 * q^6 + 16 * q^7 + 12 * q^8 + 12 * q^9	$ 12 q + 4 q^{2} + 8 q^{3} + 12 q^{4} - 8 q^{6} + 16 q^{7} + 12 q^{8} + 12 q^{9} - 16 q^{11} + 16 q^{12} + 8 q^{13} + 16 q^{14} + 12 q^{16} - 4 q^{18} + 16 q^{21} + 16 q^{22} + 16 q^{23} + 16 q^{26} + 32 q^{27} + 40 q^{28} - 16 q^{29} - 24 q^{31} + 28 q^{32} + 12 q^{36} + 24 q^{37} + 24 q^{38} - 8 q^{39} - 8 q^{41} + 16 q^{43} - 8 q^{44} - 40 q^{46} + 32 q^{47} - 24 q^{48} + 20 q^{49} + 24 q^{52} - 8 q^{54} + 24 q^{56} + 32 q^{57} - 16 q^{58} + 8 q^{59} - 24 q^{61} + 8 q^{62} + 48 q^{63} + 36 q^{64} + 40 q^{66} + 8 q^{67} + 48 q^{69} + 16 q^{71} - 12 q^{72} + 16 q^{73} + 16 q^{76} - 24 q^{77} - 24 q^{78} - 40 q^{79} + 36 q^{81} - 16 q^{82} + 40 q^{83} + 32 q^{84} - 8 q^{86} + 32 q^{87} + 48 q^{88} + 8 q^{89} - 72 q^{91} - 8 q^{92} - 24 q^{93} - 16 q^{94} - 8 q^{96} + 32 q^{97} + 60 q^{98} - 56 q^{99}+O(q^{100}) $ 12 * q + 4 * q^2 + 8 * q^3 + 12 * q^4 - 8 * q^6 + 16 * q^7 + 12 * q^8 + 12 * q^9 - 16 * q^11 + 16 * q^12 + 8 * q^13 + 16 * q^14 + 12 * q^16 - 4 * q^18 + 16 * q^21 + 16 * q^22 + 16 * q^23 + 16 * q^26 + 32 * q^27 + 40 * q^28 - 16 * q^29 - 24 * q^31 + 28 * q^32 + 12 * q^36 + 24 * q^37 + 24 * q^38 - 8 * q^39 - 8 * q^41 + 16 * q^43 - 8 * q^44 - 40 * q^46 + 32 * q^47 - 24 * q^48 + 20 * q^49 + 24 * q^52 - 8 * q^54 + 24 * q^56 + 32 * q^57 - 16 * q^58 + 8 * q^59 - 24 * q^61 + 8 * q^62 + 48 * q^63 + 36 * q^64 + 40 * q^66 + 8 * q^67 + 48 * q^69 + 16 * q^71 - 12 * q^72 + 16 * q^73 + 16 * q^76 - 24 * q^77 - 24 * q^78 - 40 * q^79 + 36 * q^81 - 16 * q^82 + 40 * q^83 + 32 * q^84 - 8 * q^86 + 32 * q^87 + 48 * q^88 + 8 * q^89 - 72 * q^91 - 8 * q^92 - 24 * q^93 - 16 * q^94 - 8 * q^96 + 32 * q^97 + 60 * 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 $

$2$	−1.43840	−1.01710	−0.508551	−	0.861032i	$-0.669819\pi$
$2$	−1.43840	−1.01710	−0.508551	+	0.861032i	$0.669819\pi$
$3$	−0.109907	−0.0634547	−0.0317274	−	0.999497i	$-0.510101\pi$
$3$	−0.109907	−0.0634547	−0.0317274	+	0.999497i	$0.510101\pi$
$4$	0.0689897	0.0344949
$5$	0	0
$5$	0	0
$6$	0.158090	0.0645399
$7$	0.695085	0.262717	0.131359	−	0.991335i	$-0.458066\pi$
$7$	0.695085	0.262717	0.131359	+	0.991335i	$0.458066\pi$
$8$	2.77756	0.982016
$9$	−2.98792	−0.995974
$10$	0	0
$11$	−4.85089	−1.46260	−0.731298	−	0.682058i	$-0.761085\pi$
$11$	−4.85089	−1.46260	−0.731298	+	0.682058i	$0.761085\pi$
$12$	−0.00758244	−0.00218886
$13$	−5.63906	−1.56399	−0.781996	−	0.623283i	$-0.785798\pi$
$13$	−5.63906	−1.56399	−0.781996	+	0.623283i	$0.785798\pi$
$14$	−0.999809	−0.267210
$15$	0	0
$16$	−4.13322	−1.03330
$17$	0	0
$17$	0	0
$18$	4.29782	1.01301
$19$	−2.32272	−0.532869	−0.266434	−	0.963853i	$-0.585846\pi$
$19$	−2.32272	−0.532869	−0.266434	+	0.963853i	$0.585846\pi$
$20$	0	0
$21$	−0.0763945	−0.0166706
$22$	6.97750	1.48761
$23$	4.63686	0.966852	0.483426	−	0.875385i	$-0.339392\pi$
$23$	4.63686	0.966852	0.483426	+	0.875385i	$0.339392\pi$
$24$	−0.305273	−0.0623136
$25$	0	0
$26$	8.11121	1.59074
$27$	0.658113	0.126654
$28$	0.0479537	0.00906240
$29$	−6.50618	−1.20817	−0.604084	−	0.796921i	$-0.706461\pi$
$29$	−6.50618	−1.20817	−0.604084	+	0.796921i	$0.706461\pi$
$30$	0	0
$31$	−6.63194	−1.19113	−0.595565	−	0.803307i	$-0.703072\pi$
$31$	−6.63194	−1.19113	−0.595565	+	0.803307i	$0.703072\pi$
$32$	0.390093	0.0689593
$33$	0.533145	0.0928087
$34$	0	0
$35$	0	0
$36$	−0.206136	−0.0343560
$37$	0.118625	0.0195018	0.00975091	−	0.999952i	$-0.496896\pi$
$37$	0.118625	0.0195018	0.00975091	+	0.999952i	$0.496896\pi$
$38$	3.34100	0.541981
$39$	0.619770	0.0992427
$40$	0	0
$41$	−1.07877	−0.168475	−0.0842375	−	0.996446i	$-0.526845\pi$
$41$	−1.07877	−0.168475	−0.0842375	+	0.996446i	$0.526845\pi$
$42$	0.109886	0.0169557
$43$	0.641108	0.0977681	0.0488840	−	0.998804i	$-0.484434\pi$
$43$	0.641108	0.0977681	0.0488840	+	0.998804i	$0.484434\pi$
$44$	−0.334661	−0.0504521
$45$	0	0
$46$	−6.66965	−0.983386
$47$	−4.93703	−0.720139	−0.360070	−	0.932925i	$-0.617247\pi$
$47$	−4.93703	−0.720139	−0.360070	+	0.932925i	$0.617247\pi$
$48$	0.454269	0.0655681
$49$	−6.51686	−0.930980
$50$	0	0
$51$	0	0
$52$	−0.389037	−0.0539497
$53$	−11.9864	−1.64646	−0.823228	−	0.567711i	$-0.807829\pi$
$53$	−11.9864	−1.64646	−0.823228	+	0.567711i	$0.807829\pi$
$54$	−0.946629	−0.128820
$55$	0	0
$56$	1.93064	0.257993
$57$	0.255283	0.0338130
$58$	9.35848	1.22883
$59$	−9.91829	−1.29125	−0.645626	−	0.763654i	$-0.723403\pi$
$59$	−9.91829	−1.29125	−0.645626	+	0.763654i	$0.723403\pi$
$60$	0	0
$61$	−1.60292	−0.205233	−0.102617	−	0.994721i	$-0.532722\pi$
$61$	−1.60292	−0.205233	−0.102617	+	0.994721i	$0.532722\pi$
$62$	9.53937	1.21150
$63$	−2.07686	−0.261659
$64$	7.70533	0.963166
$65$	0	0
$66$	−0.766875	−0.0943958
$67$	2.99411	0.365789	0.182894	−	0.983133i	$-0.441453\pi$
$67$	2.99411	0.365789	0.182894	+	0.983133i	$0.441453\pi$
$68$	0	0
$69$	−0.509622	−0.0613513
$70$	0	0
$71$	4.68852	0.556425	0.278213	−	0.960520i	$-0.410258\pi$
$71$	4.68852	0.556425	0.278213	+	0.960520i	$0.410258\pi$
$72$	−8.29913	−0.978062
$73$	5.49911	0.643622	0.321811	−	0.946804i	$-0.395708\pi$
$73$	5.49911	0.643622	0.321811	+	0.946804i	$0.395708\pi$
$74$	−0.170630	−0.0198353
$75$	0	0
$76$	−0.160244	−0.0183812
$77$	−3.37178	−0.384250
$78$	−0.891477	−0.100940
$79$	−14.8439	−1.67007	−0.835037	−	0.550193i	$-0.814554\pi$
$79$	−14.8439	−1.67007	−0.835037	+	0.550193i	$0.814554\pi$
$80$	0	0
$81$	8.89143	0.987937
$82$	1.55170	0.171356
$83$	−5.03506	−0.552670	−0.276335	−	0.961061i	$-0.589120\pi$
$83$	−5.03506	−0.552670	−0.276335	+	0.961061i	$0.589120\pi$
$84$	−0.00527044	−0.000575052 0
$85$	0	0
$86$	−0.922169	−0.0994400
$87$	0.715073	0.0766639
$88$	−13.4736	−1.43629
$89$	−2.35657	−0.249796	−0.124898	−	0.992170i	$-0.539860\pi$
$89$	−2.35657	−0.249796	−0.124898	+	0.992170i	$0.539860\pi$
$90$	0	0
$91$	−3.91962	−0.410888
$92$	0.319896	0.0333514
$93$	0.728895	0.0755829
$94$	7.10141	0.732454
$95$	0	0
$96$	−0.0428738	−0.00437579
$97$	−2.70080	−0.274225	−0.137113	−	0.990555i	$-0.543782\pi$
$97$	−2.70080	−0.274225	−0.137113	+	0.990555i	$0.543782\pi$
$98$	9.37384	0.946900
$99$	14.4941	1.45671
$100$	0	0
$101$	14.3025	1.42315	0.711575	−	0.702610i	$-0.247982\pi$
$101$	14.3025	1.42315	0.711575	+	0.702610i	$0.247982\pi$
$102$	0	0
$103$	10.8963	1.07365	0.536824	−	0.843694i	$-0.319624\pi$
$103$	10.8963	1.07365	0.536824	+	0.843694i	$0.319624\pi$
$104$	−15.6628	−1.53587
$105$	0	0
$106$	17.2412	1.67461
$107$	−16.6273	−1.60742	−0.803712	−	0.595019i	$-0.797145\pi$
$107$	−16.6273	−1.60742	−0.803712	+	0.595019i	$0.797145\pi$
$108$	0.0454030	0.00436891
$109$	10.5999	1.01529	0.507643	−	0.861568i	$-0.330517\pi$
$109$	10.5999	1.01529	0.507643	+	0.861568i	$0.330517\pi$
$110$	0	0
$111$	−0.0130377	−0.00123748
$112$	−2.87294	−0.271467
$113$	−11.5397	−1.08556	−0.542780	−	0.839875i	$-0.682628\pi$
$113$	−11.5397	−1.08556	−0.542780	+	0.839875i	$0.682628\pi$
$114$	−0.367198	−0.0343913
$115$	0	0
$116$	−0.448860	−0.0416756
$117$	16.8490	1.55770
$118$	14.2665	1.31333
$119$	0	0
$120$	0	0
$121$	12.5311	1.13919
$122$	2.30564	0.208743
$123$	0.118564	0.0106905
$124$	−0.457535	−0.0410879
$125$	0	0
$126$	2.98735	0.266134
$127$	0.498539	0.0442381	0.0221191	−	0.999755i	$-0.492959\pi$
$127$	0.498539	0.0442381	0.0221191	+	0.999755i	$0.492959\pi$
$128$	−11.8635	−1.04860
$129$	−0.0704621	−0.00620384
$130$	0	0
$131$	19.5341	1.70670	0.853350	−	0.521338i	$-0.174567\pi$
$131$	19.5341	1.70670	0.853350	+	0.521338i	$0.174567\pi$
$132$	0.0367815	0.00320142
$133$	−1.61449	−0.139994
$134$	−4.30672	−0.372044
$135$	0	0
$136$	0	0
$137$	3.81724	0.326129	0.163065	−	0.986615i	$-0.447862\pi$
$137$	3.81724	0.326129	0.163065	+	0.986615i	$0.447862\pi$
$138$	0.733040	0.0624005
$139$	−13.2525	−1.12406	−0.562030	−	0.827117i	$-0.689980\pi$
$139$	−13.2525	−1.12406	−0.562030	+	0.827117i	$0.689980\pi$
$140$	0	0
$141$	0.542613	0.0456962
$142$	−6.74396	−0.565941
$143$	27.3544	2.28749
$144$	12.3497	1.02914
$145$	0	0
$146$	−7.90991	−0.654629
$147$	0.716247	0.0590750
$148$	0.00818390	0.000672712 0
$149$	−17.4543	−1.42991	−0.714955	−	0.699171i	$-0.753553\pi$
$149$	−17.4543	−1.42991	−0.714955	+	0.699171i	$0.753553\pi$
$150$	0	0
$151$	−11.2715	−0.917262	−0.458631	−	0.888627i	$-0.651660\pi$
$151$	−11.2715	−0.917262	−0.458631	+	0.888627i	$0.651660\pi$
$152$	−6.45150	−0.523286
$153$	0	0
$154$	4.84996	0.390821
$155$	0	0
$156$	0.0427578	0.00342336
$157$	6.14541	0.490457	0.245229	−	0.969465i	$-0.421137\pi$
$157$	6.14541	0.490457	0.245229	+	0.969465i	$0.421137\pi$
$158$	21.3515	1.69863
$159$	1.31738	0.104475
$160$	0	0
$161$	3.22301	0.254009
$162$	−12.7894	−1.00483
$163$	11.2012	0.877344	0.438672	−	0.898647i	$-0.355449\pi$
$163$	11.2012	0.877344	0.438672	+	0.898647i	$0.355449\pi$
$164$	−0.0744238	−0.00581152
$165$	0	0
$166$	7.24243	0.562121
$167$	5.70603	0.441546	0.220773	−	0.975325i	$-0.429142\pi$
$167$	5.70603	0.441546	0.220773	+	0.975325i	$0.429142\pi$
$168$	−0.212190	−0.0163709
$169$	18.7989	1.44607
$170$	0	0
$171$	6.94010	0.530723
$172$	0.0442299	0.00337250
$173$	−4.53754	−0.344983	−0.172491	−	0.985011i	$-0.555182\pi$
$173$	−4.53754	−0.344983	−0.172491	+	0.985011i	$0.555182\pi$
$174$	−1.02856	−0.0779750
$175$	0	0
$176$	20.0498	1.51131
$177$	1.09009	0.0819360
$178$	3.38969	0.254068
$179$	−18.3756	−1.37345	−0.686727	−	0.726915i	$-0.740953\pi$
$179$	−18.3756	−1.37345	−0.686727	+	0.726915i	$0.740953\pi$
$180$	0	0
$181$	−10.7182	−0.796679	−0.398339	−	0.917238i	$-0.630413\pi$
$181$	−10.7182	−0.796679	−0.398339	+	0.917238i	$0.630413\pi$
$182$	5.63798	0.417915
$183$	0.176172	0.0130230
$184$	12.8792	0.949465
$185$	0	0
$186$	−1.04844	−0.0768754
$187$	0	0
$188$	−0.340604	−0.0248411
$189$	0.457444	0.0332742
$190$	0	0
$191$	18.5397	1.34149	0.670743	−	0.741690i	$-0.265976\pi$
$191$	18.5397	1.34149	0.670743	+	0.741690i	$0.265976\pi$
$192$	−0.846868	−0.0611174
$193$	9.88591	0.711603	0.355802	−	0.934562i	$-0.384208\pi$
$193$	9.88591	0.711603	0.355802	+	0.934562i	$0.384208\pi$
$194$	3.88483	0.278915
$195$	0	0
$196$	−0.449596	−0.0321140
$197$	13.9534	0.994138	0.497069	−	0.867711i	$-0.334410\pi$
$197$	13.9534	0.994138	0.497069	+	0.867711i	$0.334410\pi$
$198$	−20.8482	−1.48162
$199$	−12.7366	−0.902876	−0.451438	−	0.892303i	$-0.649089\pi$
$199$	−12.7366	−0.902876	−0.451438	+	0.892303i	$0.649089\pi$
$200$	0	0
$201$	−0.329073	−0.0232110
$202$	−20.5727	−1.44749
$203$	−4.52235	−0.317407
$204$	0	0
$205$	0	0
$206$	−15.6733	−1.09201
$207$	−13.8546	−0.962959
$208$	23.3075	1.61608
$209$	11.2672	0.779372
$210$	0	0
$211$	12.8778	0.886545	0.443273	−	0.896387i	$-0.353817\pi$
$211$	12.8778	0.886545	0.443273	+	0.896387i	$0.353817\pi$
$212$	−0.826937	−0.0567943
$213$	−0.515300	−0.0353078
$214$	23.9167	1.63491
$215$	0	0
$216$	1.82795	0.124376
$217$	−4.60976	−0.312931
$218$	−15.2469	−1.03265
$219$	−0.604389	−0.0408409
$220$	0	0
$221$	0	0
$222$	0.0187534	0.00125864
$223$	−20.4208	−1.36748	−0.683738	−	0.729728i	$-0.739647\pi$
$223$	−20.4208	−1.36748	−0.683738	+	0.729728i	$0.739647\pi$
$224$	0.271147	0.0181168
$225$	0	0
$226$	16.5986	1.10412
$227$	1.22029	0.0809935	0.0404968	−	0.999180i	$-0.487106\pi$
$227$	1.22029	0.0809935	0.0404968	+	0.999180i	$0.487106\pi$
$228$	0.0176119	0.00116638
$229$	3.51944	0.232571	0.116286	−	0.993216i	$-0.462901\pi$
$229$	3.51944	0.232571	0.116286	+	0.993216i	$0.462901\pi$
$230$	0	0
$231$	0.370581	0.0243824
$232$	−18.0713	−1.18644
$233$	−29.0026	−1.90002	−0.950011	−	0.312218i	$-0.898928\pi$
$233$	−29.0026	−1.90002	−0.950011	+	0.312218i	$0.898928\pi$
$234$	−24.2356	−1.58433
$235$	0	0
$236$	−0.684260	−0.0445415
$237$	1.63145	0.105974
$238$	0	0
$239$	7.87133	0.509154	0.254577	−	0.967053i	$-0.418064\pi$
$239$	7.87133	0.509154	0.254577	+	0.967053i	$0.418064\pi$
$240$	0	0
$241$	−11.6270	−0.748959	−0.374479	−	0.927235i	$-0.622179\pi$
$241$	−11.6270	−0.748959	−0.374479	+	0.927235i	$0.622179\pi$
$242$	−18.0247	−1.15867
$243$	−2.95157	−0.189343
$244$	−0.110585	−0.00707950
$245$	0	0
$246$	−0.170542	−0.0108734
$247$	13.0979	0.833403
$248$	−18.4206	−1.16971
$249$	0.553388	0.0350695
$250$	0	0
$251$	−7.94692	−0.501605	−0.250803	−	0.968038i	$-0.580694\pi$
$251$	−7.94692	−0.501605	−0.250803	+	0.968038i	$0.580694\pi$
$252$	−0.143282	−0.00902591
$253$	−22.4929	−1.41411
$254$	−0.717097	−0.0449947
$255$	0	0
$256$	1.65381	0.103363
$257$	7.92727	0.494489	0.247245	−	0.968953i	$-0.420475\pi$
$257$	7.92727	0.494489	0.247245	+	0.968953i	$0.420475\pi$
$258$	0.101353	0.00630994
$259$	0.0824544	0.00512347
$260$	0	0
$261$	19.4400	1.20330
$262$	−28.0978	−1.73589
$263$	−8.53622	−0.526366	−0.263183	−	0.964746i	$-0.584772\pi$
$263$	−8.53622	−0.526366	−0.263183	+	0.964746i	$0.584772\pi$
$264$	1.48084	0.0911396
$265$	0	0
$266$	2.32228	0.142388
$267$	0.259003	0.0158507
$268$	0.206563	0.0126178
$269$	−15.9828	−0.974490	−0.487245	−	0.873265i	$-0.661998\pi$
$269$	−15.9828	−0.974490	−0.487245	+	0.873265i	$0.661998\pi$
$270$	0	0
$271$	−22.5289	−1.36853	−0.684266	−	0.729232i	$-0.739877\pi$
$271$	−22.5289	−1.36853	−0.684266	+	0.729232i	$0.739877\pi$
$272$	0	0
$273$	0.430793	0.0260728
$274$	−5.49072	−0.331706
$275$	0	0
$276$	−0.0351587	−0.00211630
$277$	−6.90211	−0.414708	−0.207354	−	0.978266i	$-0.566485\pi$
$277$	−6.90211	−0.414708	−0.207354	+	0.978266i	$0.566485\pi$
$278$	19.0623	1.14328
$279$	19.8157	1.18633
$280$	0	0
$281$	9.38062	0.559601	0.279801	−	0.960058i	$-0.409732\pi$
$281$	9.38062	0.559601	0.279801	+	0.960058i	$0.409732\pi$
$282$	−0.780493	−0.0464777
$283$	−20.5769	−1.22317	−0.611584	−	0.791179i	$-0.709468\pi$
$283$	−20.5769	−1.22317	−0.611584	+	0.791179i	$0.709468\pi$
$284$	0.323460	0.0191938
$285$	0	0
$286$	−39.3465	−2.32661
$287$	−0.749834	−0.0442613
$288$	−1.16557	−0.0686816
$289$	0	0
$290$	0	0
$291$	0.296837	0.0174009
$292$	0.379382	0.0222017
$293$	23.4539	1.37019	0.685097	−	0.728452i	$-0.259760\pi$
$293$	23.4539	1.37019	0.685097	+	0.728452i	$0.259760\pi$
$294$	−1.03025	−0.0600853
$295$	0	0
$296$	0.329488	0.0191511
$297$	−3.19243	−0.185244
$298$	25.1062	1.45436
$299$	−26.1475	−1.51215
$300$	0	0
$301$	0.445624	0.0256854
$302$	16.2129	0.932948
$303$	−1.57194	−0.0903056
$304$	9.60031	0.550616
$305$	0	0
$306$	0	0
$307$	−30.4260	−1.73650	−0.868251	−	0.496126i	$-0.834756\pi$
$307$	−30.4260	−1.73650	−0.868251	+	0.496126i	$0.834756\pi$
$308$	−0.232618	−0.0132546
$309$	−1.19758	−0.0681280
$310$	0	0
$311$	1.07989	0.0612348	0.0306174	−	0.999531i	$-0.490253\pi$
$311$	1.07989	0.0612348	0.0306174	+	0.999531i	$0.490253\pi$
$312$	1.72145	0.0974580
$313$	−3.62554	−0.204928	−0.102464	−	0.994737i	$-0.532673\pi$
$313$	−3.62554	−0.204928	−0.102464	+	0.994737i	$0.532673\pi$
$314$	−8.83955	−0.498845
$315$	0	0
$316$	−1.02408	−0.0576090
$317$	8.79483	0.493967	0.246984	−	0.969020i	$-0.420561\pi$
$317$	8.79483	0.493967	0.246984	+	0.969020i	$0.420561\pi$
$318$	−1.89492	−0.106262
$319$	31.5607	1.76706
$320$	0	0
$321$	1.82746	0.101999
$322$	−4.63597	−0.258353
$323$	0	0
$324$	0.613417	0.0340787
$325$	0	0
$326$	−16.1117	−0.892347
$327$	−1.16500	−0.0644246
$328$	−2.99634	−0.165445
$329$	−3.43165	−0.189193
$330$	0	0
$331$	35.1634	1.93275	0.966377	−	0.257128i	$-0.0827760\pi$
$331$	35.1634	1.93275	0.966377	+	0.257128i	$0.0827760\pi$
$332$	−0.347368	−0.0190643
$333$	−0.354442	−0.0194233
$334$	−8.20754	−0.449097
$335$	0	0
$336$	0.315755	0.0172259
$337$	31.5152	1.71674	0.858370	−	0.513031i	$-0.171477\pi$
$337$	31.5152	1.71674	0.858370	+	0.513031i	$0.171477\pi$
$338$	−27.0404	−1.47080
$339$	1.26829	0.0688839
$340$	0	0
$341$	32.1708	1.74214
$342$	−9.98263	−0.539799
$343$	−9.39536	−0.507302
$344$	1.78072	0.0960098
$345$	0	0
$346$	6.52679	0.350882
$347$	0.440312	0.0236372	0.0118186	−	0.999930i	$-0.496238\pi$
$347$	0.440312	0.0236372	0.0118186	+	0.999930i	$0.496238\pi$
$348$	0.0493327	0.00264451
$349$	−12.4222	−0.664944	−0.332472	−	0.943113i	$-0.607883\pi$
$349$	−12.4222	−0.664944	−0.332472	+	0.943113i	$0.607883\pi$
$350$	0	0
$351$	−3.71114	−0.198086
$352$	−1.89229	−0.100860
$353$	7.38055	0.392827	0.196414	−	0.980521i	$-0.437071\pi$
$353$	7.38055	0.392827	0.196414	+	0.980521i	$0.437071\pi$
$354$	−1.56798	−0.0833372
$355$	0	0
$356$	−0.162579	−0.00861668
$357$	0	0
$358$	26.4314	1.39694
$359$	−7.05177	−0.372178	−0.186089	−	0.982533i	$-0.559581\pi$
$359$	−7.05177	−0.372178	−0.186089	+	0.982533i	$0.559581\pi$
$360$	0	0
$361$	−13.6050	−0.716051
$362$	15.4171	0.810303
$363$	−1.37725	−0.0722869
$364$	−0.270414	−0.0141735
$365$	0	0
$366$	−0.253406	−0.0132457
$367$	−16.3167	−0.851725	−0.425862	−	0.904788i	$-0.640029\pi$
$367$	−16.3167	−0.851725	−0.425862	+	0.904788i	$0.640029\pi$
$368$	−19.1652	−0.999053
$369$	3.22327	0.167797
$370$	0	0
$371$	−8.33155	−0.432552
$372$	0.0502862	0.00260722
$373$	18.3821	0.951787	0.475893	−	0.879503i	$-0.342125\pi$
$373$	18.3821	0.951787	0.475893	+	0.879503i	$0.342125\pi$
$374$	0	0
$375$	0	0
$376$	−13.7129	−0.707189
$377$	36.6887	1.88957
$378$	−0.657987	−0.0338432
$379$	−16.4955	−0.847315	−0.423657	−	0.905822i	$-0.639254\pi$
$379$	−16.4955	−0.847315	−0.423657	+	0.905822i	$0.639254\pi$
$380$	0	0
$381$	−0.0547928	−0.00280712
$382$	−26.6675	−1.36443
$383$	36.3426	1.85702	0.928510	−	0.371307i	$-0.121090\pi$
$383$	36.3426	1.85702	0.928510	+	0.371307i	$0.121090\pi$
$384$	1.30388	0.0665384
$385$	0	0
$386$	−14.2199	−0.723772
$387$	−1.91558	−0.0973744
$388$	−0.186328	−0.00945935
$389$	6.36837	0.322889	0.161445	−	0.986882i	$-0.448385\pi$
$389$	6.36837	0.322889	0.161445	+	0.986882i	$0.448385\pi$
$390$	0	0
$391$	0	0
$392$	−18.1010	−0.914237
$393$	−2.14693	−0.108298
$394$	−20.0705	−1.01114
$395$	0	0
$396$	0.999941	0.0502489
$397$	−33.3778	−1.67518	−0.837591	−	0.546298i	$-0.816037\pi$
$397$	−33.3778	−1.67518	−0.837591	+	0.546298i	$0.816037\pi$
$398$	18.3203	0.918316
$399$	0.177443	0.00888327
$400$	0	0
$401$	11.7500	0.586769	0.293384	−	0.955995i	$-0.405218\pi$
$401$	11.7500	0.586769	0.293384	+	0.955995i	$0.405218\pi$
$402$	0.473338	0.0236080
$403$	37.3979	1.86292
$404$	0.986724	0.0490914
$405$	0	0
$406$	6.50494	0.322835
$407$	−0.575436	−0.0285233
$408$	0	0
$409$	12.6834	0.627154	0.313577	−	0.949563i	$-0.398473\pi$
$409$	12.6834	0.627154	0.313577	+	0.949563i	$0.398473\pi$
$410$	0	0
$411$	−0.419541	−0.0206944
$412$	0.751735	0.0370353
$413$	−6.89405	−0.339234
$414$	19.9284	0.979427
$415$	0	0
$416$	−2.19975	−0.107852
$417$	1.45654	0.0713269
$418$	−16.2068	−0.792700
$419$	35.0224	1.71095	0.855477	−	0.517840i	$-0.173264\pi$
$419$	35.0224	1.71095	0.855477	+	0.517840i	$0.173264\pi$
$420$	0	0
$421$	−10.0231	−0.488497	−0.244248	−	0.969713i	$-0.578541\pi$
$421$	−10.0231	−0.488497	−0.244248	+	0.969713i	$0.578541\pi$
$422$	−18.5234	−0.901706
$423$	14.7514	0.717240
$424$	−33.2929	−1.61685
$425$	0	0
$426$	0.741207	0.0359116
$427$	−1.11417	−0.0539184
$428$	−1.14711	−0.0554479
$429$	−3.00643	−0.145152
$430$	0	0
$431$	−23.7461	−1.14381	−0.571905	−	0.820320i	$-0.693795\pi$
$431$	−23.7461	−1.14381	−0.571905	+	0.820320i	$0.693795\pi$
$432$	−2.72013	−0.130872
$433$	32.2917	1.55184	0.775919	−	0.630832i	$-0.217286\pi$
$433$	32.2917	1.55184	0.775919	+	0.630832i	$0.217286\pi$
$434$	6.63067	0.318282
$435$	0	0
$436$	0.731283	0.0350221
$437$	−10.7701	−0.515205
$438$	0.869353	0.0415393
$439$	−21.3269	−1.01788	−0.508939	−	0.860803i	$-0.669962\pi$
$439$	−21.3269	−1.01788	−0.508939	+	0.860803i	$0.669962\pi$
$440$	0	0
$441$	19.4719	0.927231
$442$	0	0
$443$	13.8187	0.656546	0.328273	−	0.944583i	$-0.393533\pi$
$443$	13.8187	0.656546	0.328273	+	0.944583i	$0.393533\pi$
$444$	−0.000899466 0	−4.26868e−5 0
$445$	0	0
$446$	29.3732	1.39086
$447$	1.91834	0.0907345
$448$	5.35586	0.253040
$449$	−6.61380	−0.312125	−0.156062	−	0.987747i	$-0.549880\pi$
$449$	−6.61380	−0.312125	−0.156062	+	0.987747i	$0.549880\pi$
$450$	0	0
$451$	5.23297	0.246411
$452$	−0.796118	−0.0374462
$453$	1.23881	0.0582046
$454$	−1.75526	−0.0823786
$455$	0	0
$456$	0.709063	0.0332049
$457$	−5.01039	−0.234376	−0.117188	−	0.993110i	$-0.537388\pi$
$457$	−5.01039	−0.234376	−0.117188	+	0.993110i	$0.537388\pi$
$458$	−5.06236	−0.236548
$459$	0	0
$460$	0	0
$461$	16.3822	0.762994	0.381497	−	0.924370i	$-0.375409\pi$
$461$	16.3822	0.762994	0.381497	+	0.924370i	$0.375409\pi$
$462$	−0.533043	−0.0247994
$463$	27.3768	1.27231	0.636153	−	0.771563i	$-0.280525\pi$
$463$	27.3768	1.27231	0.636153	+	0.771563i	$0.280525\pi$
$464$	26.8915	1.24841
$465$	0	0
$466$	41.7172	1.93251
$467$	0.646341	0.0299091	0.0149545	−	0.999888i	$-0.495240\pi$
$467$	0.646341	0.0299091	0.0149545	+	0.999888i	$0.495240\pi$
$468$	1.16241	0.0537325
$469$	2.08116	0.0960991
$470$	0	0
$471$	−0.675423	−0.0311218
$472$	−27.5487	−1.26803
$473$	−3.10994	−0.142995
$474$	−2.34668	−0.107786
$475$	0	0
$476$	0	0
$477$	35.8144	1.63983
$478$	−11.3221	−0.517861
$479$	13.5649	0.619795	0.309898	−	0.950770i	$-0.399705\pi$
$479$	13.5649	0.619795	0.309898	+	0.950770i	$0.399705\pi$
$480$	0	0
$481$	−0.668933	−0.0305007
$482$	16.7242	0.761767
$483$	−0.354231	−0.0161181
$484$	0.864516	0.0392962
$485$	0	0
$486$	4.24553	0.192581
$487$	29.0339	1.31565	0.657826	−	0.753170i	$-0.271476\pi$
$487$	29.0339	1.31565	0.657826	+	0.753170i	$0.271476\pi$
$488$	−4.45222	−0.201543
$489$	−1.23108	−0.0556716
$490$	0	0
$491$	13.1298	0.592541	0.296271	−	0.955104i	$-0.404257\pi$
$491$	13.1298	0.592541	0.296271	+	0.955104i	$0.404257\pi$
$492$	0.00817968	0.000368768 0
$493$	0	0
$494$	−18.8401	−0.847655
$495$	0	0
$496$	27.4113	1.23080
$497$	3.25892	0.146183
$498$	−0.795992	−0.0356692
$499$	−11.3410	−0.507691	−0.253846	−	0.967245i	$-0.581695\pi$
$499$	−11.3410	−0.507691	−0.253846	+	0.967245i	$0.581695\pi$
$500$	0	0
$501$	−0.627131	−0.0280182
$502$	11.4308	0.510183
$503$	20.5436	0.915995	0.457998	−	0.888953i	$-0.348567\pi$
$503$	20.5436	0.915995	0.457998	+	0.888953i	$0.348567\pi$
$504$	−5.76860	−0.256954
$505$	0	0
$506$	32.3537	1.43830
$507$	−2.06613	−0.0917601
$508$	0.0343940	0.00152599
$509$	8.40900	0.372722	0.186361	−	0.982481i	$-0.440331\pi$
$509$	8.40900	0.372722	0.186361	+	0.982481i	$0.440331\pi$
$510$	0	0
$511$	3.82235	0.169091
$512$	21.3482	0.943467
$513$	−1.52861	−0.0674899
$514$	−11.4026	−0.502946
$515$	0	0
$516$	−0.00486116	−0.000214001 0
$517$	23.9489	1.05327
$518$	−0.118602	−0.00521108
$519$	0.498706	0.0218908
$520$	0	0
$521$	−21.3561	−0.935627	−0.467813	−	0.883827i	$-0.654958\pi$
$521$	−21.3561	−0.935627	−0.467813	+	0.883827i	$0.654958\pi$
$522$	−27.9624	−1.22388
$523$	24.4644	1.06975	0.534877	−	0.844930i	$-0.320358\pi$
$523$	24.4644	1.06975	0.534877	+	0.844930i	$0.320358\pi$
$524$	1.34765	0.0588724
$525$	0	0
$526$	12.2785	0.535367
$527$	0	0
$528$	−2.20361	−0.0958996
$529$	−1.49953	−0.0651969
$530$	0	0
$531$	29.6351	1.28605
$532$	−0.111383	−0.00482907
$533$	6.08323	0.263494
$534$	−0.372550	−0.0161218
$535$	0	0
$536$	8.31633	0.359211
$537$	2.01960	0.0871521
$538$	22.9897	0.991155
$539$	31.6125	1.36165
$540$	0	0
$541$	1.92406	0.0827219	0.0413610	−	0.999144i	$-0.486831\pi$
$541$	1.92406	0.0827219	0.0413610	+	0.999144i	$0.486831\pi$
$542$	32.4055	1.39194
$543$	1.17800	0.0505530
$544$	0	0
$545$	0	0
$546$	−0.619652	−0.0265186
$547$	14.7222	0.629475	0.314737	−	0.949179i	$-0.398084\pi$
$547$	14.7222	0.629475	0.314737	+	0.949179i	$0.398084\pi$
$548$	0.263350	0.0112498
$549$	4.78941	0.204407
$550$	0	0
$551$	15.1120	0.643794
$552$	−1.41551	−0.0602480
$553$	−10.3178	−0.438757
$554$	9.92798	0.421800
$555$	0	0
$556$	−0.914285	−0.0387743
$557$	24.3617	1.03224	0.516119	−	0.856517i	$-0.327376\pi$
$557$	24.3617	1.03224	0.516119	+	0.856517i	$0.327376\pi$
$558$	−28.5029	−1.20662
$559$	−3.61524	−0.152909
$560$	0	0
$561$	0	0
$562$	−13.4931	−0.569171
$563$	30.7200	1.29470	0.647348	−	0.762195i	$-0.275878\pi$
$563$	30.7200	1.29470	0.647348	+	0.762195i	$0.275878\pi$
$564$	0.0374347	0.00157628
$565$	0	0
$566$	29.5978	1.24409
$567$	6.18030	0.259548
$568$	13.0227	0.546419
$569$	5.35732	0.224590	0.112295	−	0.993675i	$-0.464180\pi$
$569$	5.35732	0.224590	0.112295	+	0.993675i	$0.464180\pi$
$570$	0	0
$571$	−36.0360	−1.50806	−0.754031	−	0.656839i	$-0.771893\pi$
$571$	−36.0360	−1.50806	−0.754031	+	0.656839i	$0.771893\pi$
$572$	1.88717	0.0789067
$573$	−2.03764	−0.0851235
$574$	1.07856	0.0450182
$575$	0	0
$576$	−23.0229	−0.959288
$577$	39.5472	1.64637	0.823186	−	0.567772i	$-0.192194\pi$
$577$	39.5472	1.64637	0.823186	+	0.567772i	$0.192194\pi$
$578$	0	0
$579$	−1.08653	−0.0451546
$580$	0	0
$581$	−3.49979	−0.145196
$582$	−0.426969	−0.0176984
$583$	58.1446	2.40810
$584$	15.2741	0.632048
$585$	0	0
$586$	−33.7361	−1.39363
$587$	−17.9282	−0.739975	−0.369988	−	0.929037i	$-0.620638\pi$
$587$	−17.9282	−0.739975	−0.369988	+	0.929037i	$0.620638\pi$
$588$	0.0494137	0.00203778
$589$	15.4041	0.634716
$590$	0	0
$591$	−1.53357	−0.0630827
$592$	−0.490303	−0.0201513
$593$	15.2975	0.628192	0.314096	−	0.949391i	$-0.398299\pi$
$593$	15.2975	0.628192	0.314096	+	0.949391i	$0.398299\pi$
$594$	4.59199	0.188412
$595$	0	0
$596$	−1.20416	−0.0493245
$597$	1.39984	0.0572917
$598$	37.6105	1.53801
$599$	34.6498	1.41575	0.707877	−	0.706336i	$-0.249653\pi$
$599$	34.6498	1.41575	0.707877	+	0.706336i	$0.249653\pi$
$600$	0	0
$601$	16.0361	0.654126	0.327063	−	0.945003i	$-0.393941\pi$
$601$	16.0361	0.654126	0.327063	+	0.945003i	$0.393941\pi$
$602$	−0.640985	−0.0261246
$603$	−8.94617	−0.364316
$604$	−0.777618	−0.0316408
$605$	0	0
$606$	2.26108	0.0918499
$607$	36.5119	1.48197	0.740986	−	0.671521i	$-0.234359\pi$
$607$	36.5119	1.48197	0.740986	+	0.671521i	$0.234359\pi$
$608$	−0.906076	−0.0367462
$609$	0.497037	0.0201409
$610$	0	0
$611$	27.8402	1.12629
$612$	0	0
$613$	−33.2758	−1.34400	−0.671998	−	0.740553i	$-0.734564\pi$
$613$	−33.2758	−1.34400	−0.671998	+	0.740553i	$0.734564\pi$
$614$	43.7647	1.76620
$615$	0	0
$616$	−9.36532	−0.377339
$617$	−31.7084	−1.27653	−0.638267	−	0.769815i	$-0.720348\pi$
$617$	−31.7084	−1.27653	−0.638267	+	0.769815i	$0.720348\pi$
$618$	1.72260	0.0692931
$619$	−40.8302	−1.64110	−0.820552	−	0.571572i	$-0.806334\pi$
$619$	−40.8302	−1.64110	−0.820552	+	0.571572i	$0.806334\pi$
$620$	0	0
$621$	3.05158	0.122456
$622$	−1.55331	−0.0622820
$623$	−1.63802	−0.0656258
$624$	−2.56165	−0.102548
$625$	0	0
$626$	5.21497	0.208432
$627$	−1.23835	−0.0494548
$628$	0.423970	0.0169183
$629$	0	0
$630$	0	0
$631$	−15.8001	−0.628992	−0.314496	−	0.949259i	$-0.601835\pi$
$631$	−15.8001	−0.628992	−0.314496	+	0.949259i	$0.601835\pi$
$632$	−41.2300	−1.64004
$633$	−1.41536	−0.0562555
$634$	−12.6505	−0.502415
$635$	0	0
$636$	0.0908860	0.00360386
$637$	36.7489	1.45605
$638$	−45.3969	−1.79728
$639$	−14.0089	−0.554185
$640$	0	0
$641$	−24.9339	−0.984831	−0.492415	−	0.870360i	$-0.663886\pi$
$641$	−24.9339	−0.984831	−0.492415	+	0.870360i	$0.663886\pi$
$642$	−2.62861	−0.103743
$643$	−24.0161	−0.947103	−0.473552	−	0.880766i	$-0.657028\pi$
$643$	−24.0161	−0.947103	−0.473552	+	0.880766i	$0.657028\pi$
$644$	0.222355	0.00876200
$645$	0	0
$646$	0	0
$647$	23.8307	0.936882	0.468441	−	0.883495i	$-0.344816\pi$
$647$	23.8307	0.936882	0.468441	+	0.883495i	$0.344816\pi$
$648$	24.6965	0.970170
$649$	48.1125	1.88858
$650$	0	0
$651$	0.506644	0.0198569
$652$	0.772766	0.0302638
$653$	−16.5191	−0.646441	−0.323221	−	0.946324i	$-0.604766\pi$
$653$	−16.5191	−0.646441	−0.323221	+	0.946324i	$0.604766\pi$
$654$	1.67573	0.0655264
$655$	0	0
$656$	4.45878	0.174086
$657$	−16.4309	−0.641031
$658$	4.93608	0.192428
$659$	10.2510	0.399324	0.199662	−	0.979865i	$-0.436016\pi$
$659$	10.2510	0.399324	0.199662	+	0.979865i	$0.436016\pi$
$660$	0	0
$661$	−21.3416	−0.830090	−0.415045	−	0.909801i	$-0.636234\pi$
$661$	−21.3416	−0.830090	−0.415045	+	0.909801i	$0.636234\pi$
$662$	−50.5790	−1.96581
$663$	0	0
$664$	−13.9852	−0.542731
$665$	0	0
$666$	0.509829	0.0197555
$667$	−30.1683	−1.16812
$668$	0.393657	0.0152311
$669$	2.24438	0.0867728
$670$	0	0
$671$	7.77560	0.300174
$672$	−0.0298009	−0.00114960
$673$	−27.5159	−1.06066	−0.530331	−	0.847791i	$-0.677932\pi$
$673$	−27.5159	−1.06066	−0.530331	+	0.847791i	$0.677932\pi$
$674$	−45.3314	−1.74610
$675$	0	0
$676$	1.29693	0.0498821
$677$	−17.0437	−0.655042	−0.327521	−	0.944844i	$-0.606213\pi$
$677$	−17.0437	−0.655042	−0.327521	+	0.944844i	$0.606213\pi$
$678$	−1.82430	−0.0700619
$679$	−1.87729	−0.0720437
$680$	0	0
$681$	−0.134118	−0.00513942
$682$	−46.2744	−1.77194
$683$	−3.12281	−0.119491	−0.0597456	−	0.998214i	$-0.519029\pi$
$683$	−3.12281	−0.119491	−0.0597456	+	0.998214i	$0.519029\pi$
$684$	0.478796	0.0183072
$685$	0	0
$686$	13.5143	0.515977
$687$	−0.386810	−0.0147577
$688$	−2.64984	−0.101024
$689$	67.5919	2.57505
$690$	0	0
$691$	−36.1278	−1.37437	−0.687184	−	0.726484i	$-0.741153\pi$
$691$	−36.1278	−1.37437	−0.687184	+	0.726484i	$0.741153\pi$
$692$	−0.313044	−0.0119001
$693$	10.0746	0.382702
$694$	−0.633344	−0.0240414
$695$	0	0
$696$	1.98616	0.0752852
$697$	0	0
$698$	17.8680	0.676315
$699$	3.18758	0.120565
$700$	0	0
$701$	−18.1677	−0.686185	−0.343093	−	0.939302i	$-0.611474\pi$
$701$	−18.1677	−0.686185	−0.343093	+	0.939302i	$0.611474\pi$
$702$	5.33809	0.201473
$703$	−0.275533	−0.0103919
$704$	−37.3777	−1.40872
$705$	0	0
$706$	−10.6162	−0.399545
$707$	9.94144	0.373886
$708$	0.0752048	0.00282637
$709$	−11.6045	−0.435817	−0.217909	−	0.975969i	$-0.569923\pi$
$709$	−11.6045	−0.435817	−0.217909	+	0.975969i	$0.569923\pi$
$710$	0	0
$711$	44.3525	1.66335
$712$	−6.54553	−0.245304
$713$	−30.7514	−1.15165
$714$	0	0
$715$	0	0
$716$	−1.26772	−0.0473771
$717$	−0.865112	−0.0323082
$718$	10.1433	0.378543
$719$	−25.7861	−0.961658	−0.480829	−	0.876814i	$-0.659664\pi$
$719$	−25.7861	−0.961658	−0.480829	+	0.876814i	$0.659664\pi$
$720$	0	0
$721$	7.57388	0.282066
$722$	19.5694	0.728296
$723$	1.27788	0.0475249
$724$	−0.739447	−0.0274813
$725$	0	0
$726$	1.98104	0.0735231
$727$	−17.7430	−0.658051	−0.329025	−	0.944321i	$-0.606720\pi$
$727$	−17.7430	−0.658051	−0.329025	+	0.944321i	$0.606720\pi$
$728$	−10.8870	−0.403499
$729$	−26.3499	−0.975922
$730$	0	0
$731$	0	0
$732$	0.0121541	0.000449227 0
$733$	26.8221	0.990695	0.495348	−	0.868695i	$-0.335041\pi$
$733$	26.8221	0.990695	0.495348	+	0.868695i	$0.335041\pi$
$734$	23.4699	0.866290
$735$	0	0
$736$	1.80880	0.0666734
$737$	−14.5241	−0.535002
$738$	−4.63634	−0.170666
$739$	0.451458	0.0166071	0.00830357	−	0.999966i	$-0.497357\pi$
$739$	0.451458	0.0166071	0.00830357	+	0.999966i	$0.497357\pi$
$740$	0	0
$741$	−1.43955	−0.0528833
$742$	11.9841	0.439950
$743$	20.6466	0.757450	0.378725	−	0.925509i	$-0.376363\pi$
$743$	20.6466	0.757450	0.378725	+	0.925509i	$0.376363\pi$
$744$	2.02455	0.0742236
$745$	0	0
$746$	−26.4407	−0.968063
$747$	15.0444	0.550445
$748$	0	0
$749$	−11.5574	−0.422298
$750$	0	0
$751$	−26.7059	−0.974514	−0.487257	−	0.873259i	$-0.662002\pi$
$751$	−26.7059	−0.974514	−0.487257	+	0.873259i	$0.662002\pi$
$752$	20.4058	0.744123
$753$	0.873420	0.0318292
$754$	−52.7730	−1.92188
$755$	0	0
$756$	0.0315589	0.00114779
$757$	−19.3283	−0.702499	−0.351250	−	0.936282i	$-0.614243\pi$
$757$	−19.3283	−0.702499	−0.351250	+	0.936282i	$0.614243\pi$
$758$	23.7270	0.861805
$759$	2.47212	0.0897322
$760$	0	0
$761$	−9.52382	−0.345238	−0.172619	−	0.984989i	$-0.555223\pi$
$761$	−9.52382	−0.345238	−0.172619	+	0.984989i	$0.555223\pi$
$762$	0.0788138	0.00285512
$763$	7.36782	0.266733
$764$	1.27905	0.0462743
$765$	0	0
$766$	−52.2751	−1.88878
$767$	55.9298	2.01951
$768$	−0.181764	−0.00655886
$769$	21.8393	0.787544	0.393772	−	0.919208i	$-0.371170\pi$
$769$	21.8393	0.787544	0.393772	+	0.919208i	$0.371170\pi$
$770$	0	0
$771$	−0.871260	−0.0313777
$772$	0.682026	0.0245466
$773$	18.2320	0.655760	0.327880	−	0.944719i	$-0.393666\pi$
$773$	18.2320	0.655760	0.327880	+	0.944719i	$0.393666\pi$
$774$	2.75537	0.0990396
$775$	0	0
$776$	−7.50165	−0.269294
$777$	−0.00906229	−0.000325108 0
$778$	−9.16025	−0.328411
$779$	2.50567	0.0897751
$780$	0	0
$781$	−22.7435	−0.813826
$782$	0	0
$783$	−4.28180	−0.153019
$784$	26.9356	0.961986
$785$	0	0
$786$	3.08814	0.110150
$787$	−10.0983	−0.359967	−0.179983	−	0.983670i	$-0.557604\pi$
$787$	−10.0983	−0.359967	−0.179983	+	0.983670i	$0.557604\pi$
$788$	0.962641	0.0342927
$789$	0.938188	0.0334004
$790$	0	0
$791$	−8.02104	−0.285195
$792$	40.2581	1.43051
$793$	9.03898	0.320984
$794$	48.0105	1.70383
$795$	0	0
$796$	−0.878696	−0.0311446
$797$	30.2149	1.07027	0.535133	−	0.844768i	$-0.320262\pi$
$797$	30.2149	1.07027	0.535133	+	0.844768i	$0.320262\pi$
$798$	−0.255234	−0.00903518
$799$	0	0
$800$	0	0
$801$	7.04125	0.248790
$802$	−16.9012	−0.596803
$803$	−26.6756	−0.941360
$804$	−0.0227027	−0.000800661 0
$805$	0	0
$806$	−53.7930	−1.89478
$807$	1.75662	0.0618360
$808$	39.7260	1.39756
$809$	−25.8073	−0.907337	−0.453669	−	0.891170i	$-0.649885\pi$
$809$	−25.8073	−0.907337	−0.453669	+	0.891170i	$0.649885\pi$
$810$	0	0
$811$	47.1759	1.65657	0.828284	−	0.560308i	$-0.189317\pi$
$811$	47.1759	1.65657	0.828284	+	0.560308i	$0.189317\pi$
$812$	−0.311995	−0.0109489
$813$	2.47608	0.0868399
$814$	0.827706	0.0290111
$815$	0	0
$816$	0	0
$817$	−1.48911	−0.0520975
$818$	−18.2438	−0.637880
$819$	11.7115	0.409233
$820$	0	0
$821$	−34.8152	−1.21506	−0.607530	−	0.794297i	$-0.707839\pi$
$821$	−34.8152	−1.21506	−0.607530	+	0.794297i	$0.707839\pi$
$822$	0.603467	0.0210483
$823$	−11.9291	−0.415823	−0.207912	−	0.978148i	$-0.566667\pi$
$823$	−11.9291	−0.415823	−0.207912	+	0.978148i	$0.566667\pi$
$824$	30.2652	1.05434
$825$	0	0
$826$	9.91639	0.345035
$827$	7.58265	0.263674	0.131837	−	0.991271i	$-0.457912\pi$
$827$	7.58265	0.263674	0.131837	+	0.991271i	$0.457912\pi$
$828$	−0.955823	−0.0332171
$829$	24.5064	0.851141	0.425570	−	0.904925i	$-0.360073\pi$
$829$	24.5064	0.851141	0.425570	+	0.904925i	$0.360073\pi$
$830$	0	0
$831$	0.758589	0.0263152
$832$	−43.4508	−1.50639
$833$	0	0
$834$	−2.09508	−0.0725467
$835$	0	0
$836$	0.777324	0.0268843
$837$	−4.36456	−0.150861
$838$	−50.3761	−1.74021
$839$	13.9747	0.482462	0.241231	−	0.970468i	$-0.422449\pi$
$839$	13.9747	0.482462	0.241231	+	0.970468i	$0.422449\pi$
$840$	0	0
$841$	13.3304	0.459669
$842$	14.4172	0.496850
$843$	−1.03099	−0.0355093
$844$	0.888437	0.0305813
$845$	0	0
$846$	−21.2184	−0.729505
$847$	8.71017	0.299285
$848$	49.5423	1.70129
$849$	2.26154	0.0776158
$850$	0	0
$851$	0.550047	0.0188554
$852$	−0.0355504	−0.00121794
$853$	−7.40009	−0.253374	−0.126687	−	0.991943i	$-0.540434\pi$
$853$	−7.40009	−0.253374	−0.126687	+	0.991943i	$0.540434\pi$
$854$	1.60262	0.0548404
$855$	0	0
$856$	−46.1834	−1.57852
$857$	−48.3185	−1.65053	−0.825264	−	0.564748i	$-0.808973\pi$
$857$	−48.3185	−1.65053	−0.825264	+	0.564748i	$0.808973\pi$
$858$	4.32445	0.147634
$859$	−5.21085	−0.177792	−0.0888959	−	0.996041i	$-0.528334\pi$
$859$	−5.21085	−0.177792	−0.0888959	+	0.996041i	$0.528334\pi$
$860$	0	0
$861$	0.0824119	0.00280859
$862$	34.1563	1.16337
$863$	−7.90307	−0.269024	−0.134512	−	0.990912i	$-0.542947\pi$
$863$	−7.90307	−0.269024	−0.134512	+	0.990912i	$0.542947\pi$
$864$	0.256725	0.00873396
$865$	0	0
$866$	−46.4483	−1.57838
$867$	0	0
$868$	−0.318026	−0.0107945
$869$	72.0063	2.44265
$870$	0	0
$871$	−16.8840	−0.572091
$872$	29.4419	0.997027
$873$	8.06979	0.273121
$874$	15.4917	0.524016
$875$	0	0
$876$	−0.0416967	−0.00140880
$877$	−27.5064	−0.928824	−0.464412	−	0.885619i	$-0.653734\pi$
$877$	−27.5064	−0.928824	−0.464412	+	0.885619i	$0.653734\pi$
$878$	30.6766	1.03528
$879$	−2.57775	−0.0869452
$880$	0	0
$881$	19.7314	0.664769	0.332384	−	0.943144i	$-0.392147\pi$
$881$	19.7314	0.664769	0.332384	+	0.943144i	$0.392147\pi$
$882$	−28.0083	−0.943088
$883$	−21.8566	−0.735534	−0.367767	−	0.929918i	$-0.619878\pi$
$883$	−21.8566	−0.735534	−0.367767	+	0.929918i	$0.619878\pi$
$884$	0	0
$885$	0	0
$886$	−19.8768	−0.667774
$887$	2.77874	0.0933011	0.0466505	−	0.998911i	$-0.485145\pi$
$887$	2.77874	0.0933011	0.0466505	+	0.998911i	$0.485145\pi$
$888$	−0.0362130	−0.00121523
$889$	0.346526	0.0116221
$890$	0	0
$891$	−43.1313	−1.44495
$892$	−1.40882	−0.0471709
$893$	11.4673	0.383740
$894$	−2.75934	−0.0922861
$895$	0	0
$896$	−8.24615	−0.275485
$897$	2.87379	0.0959530
$898$	9.51328	0.317462
$899$	43.1486	1.43909
$900$	0	0
$901$	0	0
$902$	−7.52710	−0.250625
$903$	−0.0489771	−0.00162986
$904$	−32.0521	−1.06604
$905$	0	0
$906$	−1.78191	−0.0592000
$907$	42.4769	1.41042	0.705210	−	0.708998i	$-0.250853\pi$
$907$	42.4769	1.41042	0.705210	+	0.708998i	$0.250853\pi$
$908$	0.0841875	0.00279386
$909$	−42.7347	−1.41742
$910$	0	0
$911$	59.0680	1.95701	0.978505	−	0.206223i	$-0.0661171\pi$
$911$	59.0680	1.95701	0.978505	+	0.206223i	$0.0661171\pi$
$912$	−1.05514	−0.0349392
$913$	24.4245	0.808333
$914$	7.20694	0.238384
$915$	0	0
$916$	0.242805	0.00802251
$917$	13.5778	0.448380
$918$	0	0
$919$	26.5657	0.876323	0.438161	−	0.898896i	$-0.355630\pi$
$919$	26.5657	0.876323	0.438161	+	0.898896i	$0.355630\pi$
$920$	0	0
$921$	3.34402	0.110189
$922$	−23.5641	−0.776042
$923$	−26.4388	−0.870245
$924$	0.0255663	0.000841069 0
$925$	0	0
$926$	−39.3787	−1.29406
$927$	−32.5574	−1.06932
$928$	−2.53801	−0.0833144
$929$	38.9968	1.27944	0.639722	−	0.768606i	$-0.279049\pi$
$929$	38.9968	1.27944	0.639722	+	0.768606i	$0.279049\pi$
$930$	0	0
$931$	15.1368	0.496090
$932$	−2.00088	−0.0655410
$933$	−0.118687	−0.00388563
$934$	−0.929695	−0.0304206
$935$	0	0
$936$	46.7993	1.52968
$937$	−9.80514	−0.320320	−0.160160	−	0.987091i	$-0.551201\pi$
$937$	−9.80514	−0.320320	−0.160160	+	0.987091i	$0.551201\pi$
$938$	−2.99354	−0.0977425
$939$	0.398471	0.0130036
$940$	0	0
$941$	49.2240	1.60466	0.802328	−	0.596884i	$-0.203595\pi$
$941$	49.2240	1.60466	0.802328	+	0.596884i	$0.203595\pi$
$942$	0.971527	0.0316540
$943$	−5.00209	−0.162890
$944$	40.9945	1.33426
$945$	0	0
$946$	4.47333	0.145441
$947$	18.1975	0.591339	0.295669	−	0.955290i	$-0.404457\pi$
$947$	18.1975	0.591339	0.295669	+	0.955290i	$0.404457\pi$
$948$	0.112553	0.00365556
$949$	−31.0098	−1.00662
$950$	0	0
$951$	−0.966612	−0.0313445
$952$	0	0
$953$	5.23591	0.169608	0.0848039	−	0.996398i	$-0.472974\pi$
$953$	5.23591	0.169608	0.0848039	+	0.996398i	$0.472974\pi$
$954$	−51.5153	−1.66787
$955$	0	0
$956$	0.543041	0.0175632
$957$	−3.46874	−0.112128
$958$	−19.5117	−0.630395
$959$	2.65331	0.0856797
$960$	0	0
$961$	12.9826	0.418793
$962$	0.962191	0.0310223
$963$	49.6811	1.60095
$964$	−0.802141	−0.0258352
$965$	0	0
$966$	0.509525	0.0163937
$967$	−3.19462	−0.102732	−0.0513661	−	0.998680i	$-0.516358\pi$
$967$	−3.19462	−0.102732	−0.0513661	+	0.998680i	$0.516358\pi$
$968$	34.8059	1.11870
$969$	0	0
$970$	0	0
$971$	−27.2613	−0.874856	−0.437428	−	0.899253i	$-0.644110\pi$
$971$	−27.2613	−0.874856	−0.437428	+	0.899253i	$0.644110\pi$
$972$	−0.203628	−0.00653136
$973$	−9.21160	−0.295310
$974$	−41.7623	−1.33815
$975$	0	0
$976$	6.62524	0.212069
$977$	−8.00610	−0.256138	−0.128069	−	0.991765i	$-0.540878\pi$
$977$	−8.00610	−0.256138	−0.128069	+	0.991765i	$0.540878\pi$
$978$	1.77079	0.0566236
$979$	11.4315	0.365351
$980$	0	0
$981$	−31.6716	−1.01120
$982$	−18.8859	−0.602674
$983$	−10.9464	−0.349137	−0.174569	−	0.984645i	$-0.555853\pi$
$983$	−10.9464	−0.349137	−0.174569	+	0.984645i	$0.555853\pi$
$984$	0.329318	0.0104983
$985$	0	0
$986$	0	0
$987$	0.377162	0.0120052
$988$	0.903624	0.0287481
$989$	2.97273	0.0945273
$990$	0	0
$991$	−29.0834	−0.923863	−0.461932	−	0.886915i	$-0.652843\pi$
$991$	−29.0834	−0.923863	−0.461932	+	0.886915i	$0.652843\pi$
$992$	−2.58707	−0.0821395
$993$	−3.86470	−0.122642
$994$	−4.68762	−0.148682
$995$	0	0
$996$	0.0381780	0.00120972
$997$	−13.6956	−0.433745	−0.216873	−	0.976200i	$-0.569586\pi$
$997$	−13.6956	−0.433745	−0.216873	+	0.976200i	$0.569586\pi$
$998$	16.3128	0.516373
$999$	0.0780686	0.00246998

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7225.2.a.bs.1.3		12
5.4	even	2		1445.2.a.p.1.10		12
17.11	odd	16		425.2.m.b.376.2		24
17.14	odd	16		425.2.m.b.26.2		24
17.16	even	2		7225.2.a.bq.1.3		12
85.4	even	4		1445.2.d.j.866.5		24
85.14	odd	16		85.2.l.a.26.5	✓	24
85.28	even	16		425.2.n.c.274.2		24
85.48	even	16		425.2.n.f.349.5		24
85.62	even	16		425.2.n.f.274.5		24
85.64	even	4		1445.2.d.j.866.6		24
85.79	odd	16		85.2.l.a.36.5	yes	24
85.82	even	16		425.2.n.c.349.2		24
85.84	even	2		1445.2.a.q.1.10		12
255.14	even	16		765.2.be.b.451.2		24
255.164	even	16		765.2.be.b.631.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.26.5	✓	24	85.14	odd	16
85.2.l.a.36.5	yes	24	85.79	odd	16
425.2.m.b.26.2		24	17.14	odd	16
425.2.m.b.376.2		24	17.11	odd	16
425.2.n.c.274.2		24	85.28	even	16
425.2.n.c.349.2		24	85.82	even	16
425.2.n.f.274.5		24	85.62	even	16
425.2.n.f.349.5		24	85.48	even	16
765.2.be.b.451.2		24	255.14	even	16
765.2.be.b.631.2		24	255.164	even	16
1445.2.a.p.1.10		12	5.4	even	2
1445.2.a.q.1.10		12	85.84	even	2
1445.2.d.j.866.5		24	85.4	even	4
1445.2.d.j.866.6		24	85.64	even	4
7225.2.a.bq.1.3		12	17.16	even	2
7225.2.a.bs.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:	\( N \)	\(=\)	\( 7225 = 5^{2} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7225.a (trivial)

\(f(q)\)	\(=\)	\(q-1.43840 q^{2} -0.109907 q^{3} +0.0689897 q^{4} +0.158090 q^{6} +0.695085 q^{7} +2.77756 q^{8} -2.98792 q^{9} +O(q^{10})\)	\(q-1.43840 q^{2} -0.109907 q^{3} +0.0689897 q^{4} +0.158090 q^{6} +0.695085 q^{7} +2.77756 q^{8} -2.98792 q^{9} -4.85089 q^{11} -0.00758244 q^{12} -5.63906 q^{13} -0.999809 q^{14} -4.13322 q^{16} +4.29782 q^{18} -2.32272 q^{19} -0.0763945 q^{21} +6.97750 q^{22} +4.63686 q^{23} -0.305273 q^{24} +8.11121 q^{26} +0.658113 q^{27} +0.0479537 q^{28} -6.50618 q^{29} -6.63194 q^{31} +0.390093 q^{32} +0.533145 q^{33} -0.206136 q^{36} +0.118625 q^{37} +3.34100 q^{38} +0.619770 q^{39} -1.07877 q^{41} +0.109886 q^{42} +0.641108 q^{43} -0.334661 q^{44} -6.66965 q^{46} -4.93703 q^{47} +0.454269 q^{48} -6.51686 q^{49} -0.389037 q^{52} -11.9864 q^{53} -0.946629 q^{54} +1.93064 q^{56} +0.255283 q^{57} +9.35848 q^{58} -9.91829 q^{59} -1.60292 q^{61} +9.53937 q^{62} -2.07686 q^{63} +7.70533 q^{64} -0.766875 q^{66} +2.99411 q^{67} -0.509622 q^{69} +4.68852 q^{71} -8.29913 q^{72} +5.49911 q^{73} -0.170630 q^{74} -0.160244 q^{76} -3.37178 q^{77} -0.891477 q^{78} -14.8439 q^{79} +8.89143 q^{81} +1.55170 q^{82} -5.03506 q^{83} -0.00527044 q^{84} -0.922169 q^{86} +0.715073 q^{87} -13.4736 q^{88} -2.35657 q^{89} -3.91962 q^{91} +0.319896 q^{92} +0.728895 q^{93} +7.10141 q^{94} -0.0428738 q^{96} -2.70080 q^{97} +9.37384 q^{98} +14.4941 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + 8 q^{3} + 12 q^{4} - 8 q^{6} + 16 q^{7} + 12 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q + 4 * q^2 + 8 * q^3 + 12 * q^4 - 8 * q^6 + 16 * q^7 + 12 * q^8 + 12 * q^9	\( 12 q + 4 q^{2} + 8 q^{3} + 12 q^{4} - 8 q^{6} + 16 q^{7} + 12 q^{8} + 12 q^{9} - 16 q^{11} + 16 q^{12} + 8 q^{13} + 16 q^{14} + 12 q^{16} - 4 q^{18} + 16 q^{21} + 16 q^{22} + 16 q^{23} + 16 q^{26} + 32 q^{27} + 40 q^{28} - 16 q^{29} - 24 q^{31} + 28 q^{32} + 12 q^{36} + 24 q^{37} + 24 q^{38} - 8 q^{39} - 8 q^{41} + 16 q^{43} - 8 q^{44} - 40 q^{46} + 32 q^{47} - 24 q^{48} + 20 q^{49} + 24 q^{52} - 8 q^{54} + 24 q^{56} + 32 q^{57} - 16 q^{58} + 8 q^{59} - 24 q^{61} + 8 q^{62} + 48 q^{63} + 36 q^{64} + 40 q^{66} + 8 q^{67} + 48 q^{69} + 16 q^{71} - 12 q^{72} + 16 q^{73} + 16 q^{76} - 24 q^{77} - 24 q^{78} - 40 q^{79} + 36 q^{81} - 16 q^{82} + 40 q^{83} + 32 q^{84} - 8 q^{86} + 32 q^{87} + 48 q^{88} + 8 q^{89} - 72 q^{91} - 8 q^{92} - 24 q^{93} - 16 q^{94} - 8 q^{96} + 32 q^{97} + 60 q^{98} - 56 q^{99}+O(q^{100}) \) 12 * q + 4 * q^2 + 8 * q^3 + 12 * q^4 - 8 * q^6 + 16 * q^7 + 12 * q^8 + 12 * q^9 - 16 * q^11 + 16 * q^12 + 8 * q^13 + 16 * q^14 + 12 * q^16 - 4 * q^18 + 16 * q^21 + 16 * q^22 + 16 * q^23 + 16 * q^26 + 32 * q^27 + 40 * q^28 - 16 * q^29 - 24 * q^31 + 28 * q^32 + 12 * q^36 + 24 * q^37 + 24 * q^38 - 8 * q^39 - 8 * q^41 + 16 * q^43 - 8 * q^44 - 40 * q^46 + 32 * q^47 - 24 * q^48 + 20 * q^49 + 24 * q^52 - 8 * q^54 + 24 * q^56 + 32 * q^57 - 16 * q^58 + 8 * q^59 - 24 * q^61 + 8 * q^62 + 48 * q^63 + 36 * q^64 + 40 * q^66 + 8 * q^67 + 48 * q^69 + 16 * q^71 - 12 * q^72 + 16 * q^73 + 16 * q^76 - 24 * q^77 - 24 * q^78 - 40 * q^79 + 36 * q^81 - 16 * q^82 + 40 * q^83 + 32 * q^84 - 8 * q^86 + 32 * q^87 + 48 * q^88 + 8 * q^89 - 72 * q^91 - 8 * q^92 - 24 * q^93 - 16 * q^94 - 8 * q^96 + 32 * q^97 + 60 * q^98 - 56 * q^99

Introduction

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