LMFDB - Embedded newform 4375.2.a.o.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4375,2,Mod(1,4375)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4375, 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("4375.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4375 = 5^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4375.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:	$34.9345508843$
Analytic rank:	$1$
Dimension:	$28$
Twist minimal:	no (minimal twist has level 175)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	4375.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.25752 q^{2} +0.637250 q^{3} -0.418653 q^{4} -0.801353 q^{6} +1.00000 q^{7} +3.04150 q^{8} -2.59391 q^{9} +O(q^{10})$	\(q-1.25752 q^{2} +0.637250 q^{3} -0.418653 q^{4} -0.801353 q^{6} +1.00000 q^{7} +3.04150 q^{8} -2.59391 q^{9} -1.82131 q^{11} -0.266787 q^{12} +2.00117 q^{13} -1.25752 q^{14} -2.98742 q^{16} +6.79685 q^{17} +3.26189 q^{18} -1.83012 q^{19} +0.637250 q^{21} +2.29032 q^{22} -4.34226 q^{23} +1.93819 q^{24} -2.51650 q^{26} -3.56472 q^{27} -0.418653 q^{28} -6.68402 q^{29} +4.95292 q^{31} -2.32626 q^{32} -1.16063 q^{33} -8.54715 q^{34} +1.08595 q^{36} -2.60245 q^{37} +2.30140 q^{38} +1.27525 q^{39} +7.38250 q^{41} -0.801353 q^{42} -7.31612 q^{43} +0.762495 q^{44} +5.46047 q^{46} -10.4778 q^{47} -1.90374 q^{48} +1.00000 q^{49} +4.33130 q^{51} -0.837795 q^{52} +5.34810 q^{53} +4.48270 q^{54} +3.04150 q^{56} -1.16624 q^{57} +8.40527 q^{58} +0.0247636 q^{59} -3.95171 q^{61} -6.22838 q^{62} -2.59391 q^{63} +8.90015 q^{64} +1.45951 q^{66} +4.63844 q^{67} -2.84552 q^{68} -2.76711 q^{69} +11.9566 q^{71} -7.88937 q^{72} +9.51486 q^{73} +3.27262 q^{74} +0.766183 q^{76} -1.82131 q^{77} -1.60364 q^{78} +4.98284 q^{79} +5.51011 q^{81} -9.28362 q^{82} -2.66740 q^{83} -0.266787 q^{84} +9.20014 q^{86} -4.25940 q^{87} -5.53950 q^{88} -15.3752 q^{89} +2.00117 q^{91} +1.81790 q^{92} +3.15625 q^{93} +13.1760 q^{94} -1.48241 q^{96} -12.1483 q^{97} -1.25752 q^{98} +4.72431 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 8 q^{2} - 8 q^{3} + 24 q^{4} + 28 q^{7} - 24 q^{8} + 22 q^{9}+O(q^{10}) $ 28 * q - 8 * q^2 - 8 * q^3 + 24 * q^4 + 28 * q^7 - 24 * q^8 + 22 * q^9	$ 28 q - 8 q^{2} - 8 q^{3} + 24 q^{4} + 28 q^{7} - 24 q^{8} + 22 q^{9} - 16 q^{11} - 24 q^{12} - 16 q^{13} - 8 q^{14} + 24 q^{16} - 40 q^{17} - 24 q^{18} + 4 q^{19} - 8 q^{21} - 16 q^{22} - 32 q^{23} + 14 q^{24} + 6 q^{26} - 32 q^{27} + 24 q^{28} - 24 q^{29} + 6 q^{31} - 56 q^{32} - 28 q^{33} + 18 q^{36} - 32 q^{37} - 40 q^{38} - 28 q^{39} + 2 q^{41} - 16 q^{43} - 26 q^{44} - 12 q^{46} - 26 q^{47} - 46 q^{48} + 28 q^{49} - 22 q^{51} - 28 q^{52} - 60 q^{53} + 38 q^{54} - 24 q^{56} - 76 q^{57} - 16 q^{58} + 8 q^{59} + 18 q^{61} - 34 q^{62} + 22 q^{63} + 28 q^{64} + 38 q^{66} - 24 q^{67} - 62 q^{68} + 14 q^{69} - 54 q^{71} - 40 q^{72} - 46 q^{73} - 30 q^{74} + 26 q^{76} - 16 q^{77} - 32 q^{78} - 30 q^{79} + 4 q^{81} - 22 q^{82} - 60 q^{83} - 24 q^{84} - 10 q^{86} - 18 q^{87} - 16 q^{88} + 6 q^{89} - 16 q^{91} - 72 q^{92} - 48 q^{93} + 86 q^{94} + 106 q^{96} - 70 q^{97} - 8 q^{98} - 30 q^{99}+O(q^{100}) $ 28 * q - 8 * q^2 - 8 * q^3 + 24 * q^4 + 28 * q^7 - 24 * q^8 + 22 * q^9 - 16 * q^11 - 24 * q^12 - 16 * q^13 - 8 * q^14 + 24 * q^16 - 40 * q^17 - 24 * q^18 + 4 * q^19 - 8 * q^21 - 16 * q^22 - 32 * q^23 + 14 * q^24 + 6 * q^26 - 32 * q^27 + 24 * q^28 - 24 * q^29 + 6 * q^31 - 56 * q^32 - 28 * q^33 + 18 * q^36 - 32 * q^37 - 40 * q^38 - 28 * q^39 + 2 * q^41 - 16 * q^43 - 26 * q^44 - 12 * q^46 - 26 * q^47 - 46 * q^48 + 28 * q^49 - 22 * q^51 - 28 * q^52 - 60 * q^53 + 38 * q^54 - 24 * q^56 - 76 * q^57 - 16 * q^58 + 8 * q^59 + 18 * q^61 - 34 * q^62 + 22 * q^63 + 28 * q^64 + 38 * q^66 - 24 * q^67 - 62 * q^68 + 14 * q^69 - 54 * q^71 - 40 * q^72 - 46 * q^73 - 30 * q^74 + 26 * q^76 - 16 * q^77 - 32 * q^78 - 30 * q^79 + 4 * q^81 - 22 * q^82 - 60 * q^83 - 24 * q^84 - 10 * q^86 - 18 * q^87 - 16 * q^88 + 6 * q^89 - 16 * q^91 - 72 * q^92 - 48 * q^93 + 86 * q^94 + 106 * q^96 - 70 * q^97 - 8 * q^98 - 30 * 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 $

$2$	−1.25752	−0.889198	−0.444599	−	0.895730i	$-0.646654\pi$
$2$	−1.25752	−0.889198	−0.444599	+	0.895730i	$0.646654\pi$
$3$	0.637250	0.367917	0.183958	−	0.982934i	$-0.441109\pi$
$3$	0.637250	0.367917	0.183958	+	0.982934i	$0.441109\pi$
$4$	−0.418653	−0.209326
$5$	0	0
$5$	0	0
$6$	−0.801353	−0.327151
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	3.04150	1.07533
$9$	−2.59391	−0.864637
$10$	0	0
$11$	−1.82131	−0.549145	−0.274572	−	0.961566i	$-0.588536\pi$
$11$	−1.82131	−0.549145	−0.274572	+	0.961566i	$0.588536\pi$
$12$	−0.266787	−0.0770147
$13$	2.00117	0.555025	0.277512	−	0.960722i	$-0.410490\pi$
$13$	2.00117	0.555025	0.277512	+	0.960722i	$0.410490\pi$
$14$	−1.25752	−0.336085
$15$	0	0
$16$	−2.98742	−0.746856
$17$	6.79685	1.64848	0.824239	−	0.566242i	$-0.191603\pi$
$17$	6.79685	1.64848	0.824239	+	0.566242i	$0.191603\pi$
$18$	3.26189	0.768834
$19$	−1.83012	−0.419857	−0.209929	−	0.977717i	$-0.567323\pi$
$19$	−1.83012	−0.419857	−0.209929	+	0.977717i	$0.567323\pi$
$20$	0	0
$21$	0.637250	0.139059
$22$	2.29032	0.488298
$23$	−4.34226	−0.905425	−0.452712	−	0.891657i	$-0.649544\pi$
$23$	−4.34226	−0.905425	−0.452712	+	0.891657i	$0.649544\pi$
$24$	1.93819	0.395632
$25$	0	0
$26$	−2.51650	−0.493527
$27$	−3.56472	−0.686031
$28$	−0.418653	−0.0791179
$29$	−6.68402	−1.24119	−0.620596	−	0.784130i	$-0.713109\pi$
$29$	−6.68402	−1.24119	−0.620596	+	0.784130i	$0.713109\pi$
$30$	0	0
$31$	4.95292	0.889571	0.444785	−	0.895637i	$-0.353280\pi$
$31$	4.95292	0.889571	0.444785	+	0.895637i	$0.353280\pi$
$32$	−2.32626	−0.411228
$33$	−1.16063	−0.202039
$34$	−8.54715	−1.46582
$35$	0	0
$36$	1.08595	0.180991
$37$	−2.60245	−0.427840	−0.213920	−	0.976851i	$-0.568623\pi$
$37$	−2.60245	−0.427840	−0.213920	+	0.976851i	$0.568623\pi$
$38$	2.30140	0.373336
$39$	1.27525	0.204203
$40$	0	0
$41$	7.38250	1.15295	0.576477	−	0.817114i	$-0.304427\pi$
$41$	7.38250	1.15295	0.576477	+	0.817114i	$0.304427\pi$
$42$	−0.801353	−0.123651
$43$	−7.31612	−1.11570	−0.557849	−	0.829942i	$-0.688373\pi$
$43$	−7.31612	−1.11570	−0.557849	+	0.829942i	$0.688373\pi$
$44$	0.762495	0.114950
$45$	0	0
$46$	5.46047	0.805102
$47$	−10.4778	−1.52834	−0.764170	−	0.645014i	$-0.776851\pi$
$47$	−10.4778	−1.52834	−0.764170	+	0.645014i	$0.776851\pi$
$48$	−1.90374	−0.274781
$49$	1.00000	0.142857
$50$	0	0
$51$	4.33130	0.606503
$52$	−0.837795	−0.116181
$53$	5.34810	0.734618	0.367309	−	0.930099i	$-0.380279\pi$
$53$	5.34810	0.734618	0.367309	+	0.930099i	$0.380279\pi$
$54$	4.48270	0.610018
$55$	0	0
$56$	3.04150	0.406437
$57$	−1.16624	−0.154472
$58$	8.40527	1.10367
$59$	0.0247636	0.00322394	0.00161197	−	0.999999i	$-0.499487\pi$
$59$	0.0247636	0.00322394	0.00161197	+	0.999999i	$0.499487\pi$
$60$	0	0
$61$	−3.95171	−0.505965	−0.252982	−	0.967471i	$-0.581411\pi$
$61$	−3.95171	−0.505965	−0.252982	+	0.967471i	$0.581411\pi$
$62$	−6.22838	−0.791005
$63$	−2.59391	−0.326802
$64$	8.90015	1.11252
$65$	0	0
$66$	1.45951	0.179653
$67$	4.63844	0.566676	0.283338	−	0.959020i	$-0.408558\pi$
$67$	4.63844	0.566676	0.283338	+	0.959020i	$0.408558\pi$
$68$	−2.84552	−0.345070
$69$	−2.76711	−0.333121
$70$	0	0
$71$	11.9566	1.41898	0.709492	−	0.704714i	$-0.248925\pi$
$71$	11.9566	1.41898	0.709492	+	0.704714i	$0.248925\pi$
$72$	−7.88937	−0.929771
$73$	9.51486	1.11363	0.556815	−	0.830637i	$-0.312023\pi$
$73$	9.51486	1.11363	0.556815	+	0.830637i	$0.312023\pi$
$74$	3.27262	0.380434
$75$	0	0
$76$	0.766183	0.0878872
$77$	−1.82131	−0.207557
$78$	−1.60364	−0.181577
$79$	4.98284	0.560613	0.280307	−	0.959911i	$-0.409564\pi$
$79$	4.98284	0.560613	0.280307	+	0.959911i	$0.409564\pi$
$80$	0	0
$81$	5.51011	0.612235
$82$	−9.28362	−1.02520
$83$	−2.66740	−0.292785	−0.146392	−	0.989227i	$-0.546766\pi$
$83$	−2.66740	−0.292785	−0.146392	+	0.989227i	$0.546766\pi$
$84$	−0.266787	−0.0291088
$85$	0	0
$86$	9.20014	0.992077
$87$	−4.25940	−0.456655
$88$	−5.53950	−0.590512
$89$	−15.3752	−1.62977	−0.814886	−	0.579621i	$-0.803201\pi$
$89$	−15.3752	−1.62977	−0.814886	+	0.579621i	$0.803201\pi$
$90$	0	0
$91$	2.00117	0.209780
$92$	1.81790	0.189529
$93$	3.15625	0.327288
$94$	13.1760	1.35900
$95$	0	0
$96$	−1.48241	−0.151298
$97$	−12.1483	−1.23348	−0.616738	−	0.787168i	$-0.711546\pi$
$97$	−12.1483	−1.23348	−0.616738	+	0.787168i	$0.711546\pi$
$98$	−1.25752	−0.127028
$99$	4.72431	0.474811
$100$	0	0
$101$	−13.7082	−1.36402	−0.682008	−	0.731345i	$-0.738893\pi$
$101$	−13.7082	−1.36402	−0.682008	+	0.731345i	$0.738893\pi$
$102$	−5.44668	−0.539301
$103$	−5.63505	−0.555238	−0.277619	−	0.960691i	$-0.589545\pi$
$103$	−5.63505	−0.555238	−0.277619	+	0.960691i	$0.589545\pi$
$104$	6.08655	0.596835
$105$	0	0
$106$	−6.72532	−0.653221
$107$	17.1093	1.65402	0.827011	−	0.562186i	$-0.190039\pi$
$107$	17.1093	1.65402	0.827011	+	0.562186i	$0.190039\pi$
$108$	1.49238	0.143604
$109$	−12.7763	−1.22375	−0.611873	−	0.790956i	$-0.709584\pi$
$109$	−12.7763	−1.22375	−0.611873	+	0.790956i	$0.709584\pi$
$110$	0	0
$111$	−1.65841	−0.157409
$112$	−2.98742	−0.282285
$113$	−15.8300	−1.48916	−0.744578	−	0.667535i	$-0.767349\pi$
$113$	−15.8300	−1.48916	−0.744578	+	0.667535i	$0.767349\pi$
$114$	1.46657	0.137357
$115$	0	0
$116$	2.79829	0.259814
$117$	−5.19086	−0.479895
$118$	−0.0311406	−0.00286673
$119$	6.79685	0.623066
$120$	0	0
$121$	−7.68284	−0.698440
$122$	4.96934	0.449903
$123$	4.70450	0.424191
$124$	−2.07355	−0.186211
$125$	0	0
$126$	3.26189	0.290592
$127$	5.03690	0.446952	0.223476	−	0.974709i	$-0.428260\pi$
$127$	5.03690	0.446952	0.223476	+	0.974709i	$0.428260\pi$
$128$	−6.53958	−0.578022
$129$	−4.66220	−0.410484
$130$	0	0
$131$	4.85501	0.424184	0.212092	−	0.977250i	$-0.431972\pi$
$131$	4.85501	0.424184	0.212092	+	0.977250i	$0.431972\pi$
$132$	0.485900	0.0422922
$133$	−1.83012	−0.158691
$134$	−5.83291	−0.503887
$135$	0	0
$136$	20.6726	1.77266
$137$	−11.6879	−0.998566	−0.499283	−	0.866439i	$-0.666403\pi$
$137$	−11.6879	−0.998566	−0.499283	+	0.866439i	$0.666403\pi$
$138$	3.47969	0.296211
$139$	−9.79638	−0.830918	−0.415459	−	0.909612i	$-0.636379\pi$
$139$	−9.79638	−0.830918	−0.415459	+	0.909612i	$0.636379\pi$
$140$	0	0
$141$	−6.67697	−0.562302
$142$	−15.0356	−1.26176
$143$	−3.64474	−0.304789
$144$	7.74912	0.645760
$145$	0	0
$146$	−11.9651	−0.990238
$147$	0.637250	0.0525595
$148$	1.08952	0.0895581
$149$	21.3913	1.75245	0.876223	−	0.481907i	$-0.160056\pi$
$149$	21.3913	1.75245	0.876223	+	0.481907i	$0.160056\pi$
$150$	0	0
$151$	14.2060	1.15607	0.578034	−	0.816013i	$-0.303820\pi$
$151$	14.2060	1.15607	0.578034	+	0.816013i	$0.303820\pi$
$152$	−5.56629	−0.451485
$153$	−17.6304	−1.42534
$154$	2.29032	0.184559
$155$	0	0
$156$	−0.533885	−0.0427450
$157$	−11.5228	−0.919617	−0.459809	−	0.888018i	$-0.652082\pi$
$157$	−11.5228	−0.919617	−0.459809	+	0.888018i	$0.652082\pi$
$158$	−6.26600	−0.498496
$159$	3.40808	0.270278
$160$	0	0
$161$	−4.34226	−0.342218
$162$	−6.92906	−0.544398
$163$	21.6099	1.69262	0.846308	−	0.532694i	$-0.178820\pi$
$163$	21.6099	1.69262	0.846308	+	0.532694i	$0.178820\pi$
$164$	−3.09070	−0.241343
$165$	0	0
$166$	3.35429	0.260344
$167$	−13.5870	−1.05140	−0.525698	−	0.850671i	$-0.676196\pi$
$167$	−13.5870	−1.05140	−0.525698	+	0.850671i	$0.676196\pi$
$168$	1.93819	0.149535
$169$	−8.99532	−0.691948
$170$	0	0
$171$	4.74716	0.363024
$172$	3.06291	0.233545
$173$	10.4496	0.794467	0.397233	−	0.917718i	$-0.369970\pi$
$173$	10.4496	0.794467	0.397233	+	0.917718i	$0.369970\pi$
$174$	5.35626	0.406057
$175$	0	0
$176$	5.44102	0.410132
$177$	0.0157806	0.00118614
$178$	19.3346	1.44919
$179$	−20.3686	−1.52242	−0.761210	−	0.648506i	$-0.775394\pi$
$179$	−20.3686	−1.52242	−0.761210	+	0.648506i	$0.775394\pi$
$180$	0	0
$181$	−10.9986	−0.817522	−0.408761	−	0.912641i	$-0.634039\pi$
$181$	−10.9986	−0.817522	−0.408761	+	0.912641i	$0.634039\pi$
$182$	−2.51650	−0.186536
$183$	−2.51823	−0.186153
$184$	−13.2070	−0.973631
$185$	0	0
$186$	−3.96904	−0.291024
$187$	−12.3791	−0.905253
$188$	4.38655	0.319922
$189$	−3.56472	−0.259295
$190$	0	0
$191$	12.2086	0.883380	0.441690	−	0.897168i	$-0.354379\pi$
$191$	12.2086	0.883380	0.441690	+	0.897168i	$0.354379\pi$
$192$	5.67163	0.409314
$193$	0.109074	0.00785131	0.00392565	−	0.999992i	$-0.498750\pi$
$193$	0.109074	0.00785131	0.00392565	+	0.999992i	$0.498750\pi$
$194$	15.2767	1.09681
$195$	0	0
$196$	−0.418653	−0.0299038
$197$	−10.1526	−0.723346	−0.361673	−	0.932305i	$-0.617794\pi$
$197$	−10.1526	−0.723346	−0.361673	+	0.932305i	$0.617794\pi$
$198$	−5.94090	−0.422201
$199$	12.7337	0.902665	0.451332	−	0.892356i	$-0.350949\pi$
$199$	12.7337	0.902665	0.451332	+	0.892356i	$0.350949\pi$
$200$	0	0
$201$	2.95585	0.208489
$202$	17.2383	1.21288
$203$	−6.68402	−0.469127
$204$	−1.81331	−0.126957
$205$	0	0
$206$	7.08617	0.493717
$207$	11.2634	0.782864
$208$	−5.97834	−0.414523
$209$	3.33320	0.230562
$210$	0	0
$211$	−7.84309	−0.539941	−0.269970	−	0.962869i	$-0.587014\pi$
$211$	−7.84309	−0.539941	−0.269970	+	0.962869i	$0.587014\pi$
$212$	−2.23900	−0.153775
$213$	7.61933	0.522068
$214$	−21.5153	−1.47075
$215$	0	0
$216$	−10.8421	−0.737711
$217$	4.95292	0.336226
$218$	16.0664	1.08815
$219$	6.06335	0.409723
$220$	0	0
$221$	13.6017	0.914946
$222$	2.08548	0.139968
$223$	−11.1471	−0.746468	−0.373234	−	0.927737i	$-0.621751\pi$
$223$	−11.1471	−0.746468	−0.373234	+	0.927737i	$0.621751\pi$
$224$	−2.32626	−0.155429
$225$	0	0
$226$	19.9064	1.32416
$227$	−12.6449	−0.839272	−0.419636	−	0.907692i	$-0.637842\pi$
$227$	−12.6449	−0.839272	−0.419636	+	0.907692i	$0.637842\pi$
$228$	0.488250	0.0323352
$229$	9.35348	0.618095	0.309048	−	0.951047i	$-0.399990\pi$
$229$	9.35348	0.618095	0.309048	+	0.951047i	$0.399990\pi$
$230$	0	0
$231$	−1.16063	−0.0763637
$232$	−20.3294	−1.33469
$233$	−8.80049	−0.576540	−0.288270	−	0.957549i	$-0.593080\pi$
$233$	−8.80049	−0.576540	−0.288270	+	0.957549i	$0.593080\pi$
$234$	6.52759	0.426722
$235$	0	0
$236$	−0.0103673	−0.000674857 0
$237$	3.17532	0.206259
$238$	−8.54715	−0.554030
$239$	−14.2625	−0.922567	−0.461284	−	0.887253i	$-0.652611\pi$
$239$	−14.2625	−0.922567	−0.461284	+	0.887253i	$0.652611\pi$
$240$	0	0
$241$	4.82042	0.310511	0.155255	−	0.987874i	$-0.450380\pi$
$241$	4.82042	0.310511	0.155255	+	0.987874i	$0.450380\pi$
$242$	9.66130	0.621052
$243$	14.2055	0.911283
$244$	1.65439	0.105912
$245$	0	0
$246$	−5.91599	−0.377190
$247$	−3.66237	−0.233031
$248$	15.0643	0.956583
$249$	−1.69980	−0.107720
$250$	0	0
$251$	12.7306	0.803549	0.401774	−	0.915739i	$-0.368394\pi$
$251$	12.7306	0.803549	0.401774	+	0.915739i	$0.368394\pi$
$252$	1.08595	0.0684083
$253$	7.90859	0.497209
$254$	−6.33398	−0.397429
$255$	0	0
$256$	−9.57668	−0.598543
$257$	−24.5321	−1.53027	−0.765136	−	0.643869i	$-0.777328\pi$
$257$	−24.5321	−1.53027	−0.765136	+	0.643869i	$0.777328\pi$
$258$	5.86279	0.365002
$259$	−2.60245	−0.161708
$260$	0	0
$261$	17.3378	1.07318
$262$	−6.10526	−0.377184
$263$	−15.4336	−0.951675	−0.475838	−	0.879533i	$-0.657855\pi$
$263$	−15.4336	−0.951675	−0.475838	+	0.879533i	$0.657855\pi$
$264$	−3.53005	−0.217259
$265$	0	0
$266$	2.30140	0.141108
$267$	−9.79788	−0.599621
$268$	−1.94190	−0.118620
$269$	19.6081	1.19553	0.597763	−	0.801673i	$-0.296056\pi$
$269$	19.6081	1.19553	0.597763	+	0.801673i	$0.296056\pi$
$270$	0	0
$271$	−19.1010	−1.16031	−0.580153	−	0.814508i	$-0.697007\pi$
$271$	−19.1010	−1.16031	−0.580153	+	0.814508i	$0.697007\pi$
$272$	−20.3051	−1.23118
$273$	1.27525	0.0771814
$274$	14.6977	0.887923
$275$	0	0
$276$	1.15846	0.0697310
$277$	2.57722	0.154850	0.0774250	−	0.996998i	$-0.475330\pi$
$277$	2.57722	0.154850	0.0774250	+	0.996998i	$0.475330\pi$
$278$	12.3191	0.738851
$279$	−12.8474	−0.769156
$280$	0	0
$281$	−14.1961	−0.846866	−0.423433	−	0.905927i	$-0.639175\pi$
$281$	−14.1961	−0.846866	−0.423433	+	0.905927i	$0.639175\pi$
$282$	8.39640	0.499998
$283$	−20.4604	−1.21624	−0.608121	−	0.793844i	$-0.708077\pi$
$283$	−20.4604	−1.21624	−0.608121	+	0.793844i	$0.708077\pi$
$284$	−5.00565	−0.297031
$285$	0	0
$286$	4.58332	0.271018
$287$	7.38250	0.435775
$288$	6.03410	0.355563
$289$	29.1972	1.71748
$290$	0	0
$291$	−7.74153	−0.453817
$292$	−3.98342	−0.233112
$293$	−8.06270	−0.471028	−0.235514	−	0.971871i	$-0.575677\pi$
$293$	−8.06270	−0.471028	−0.235514	+	0.971871i	$0.575677\pi$
$294$	−0.801353	−0.0467358
$295$	0	0
$296$	−7.91533	−0.460069
$297$	6.49245	0.376730
$298$	−26.8999	−1.55827
$299$	−8.68961	−0.502533
$300$	0	0
$301$	−7.31612	−0.421694
$302$	−17.8643	−1.02797
$303$	−8.73555	−0.501844
$304$	5.46733	0.313573
$305$	0	0
$306$	22.1706	1.26741
$307$	9.08866	0.518717	0.259359	−	0.965781i	$-0.416489\pi$
$307$	9.08866	0.518717	0.259359	+	0.965781i	$0.416489\pi$
$308$	0.762495	0.0434472
$309$	−3.59094	−0.204281
$310$	0	0
$311$	−26.5743	−1.50689	−0.753445	−	0.657510i	$-0.771610\pi$
$311$	−26.5743	−1.50689	−0.753445	+	0.657510i	$0.771610\pi$
$312$	3.87866	0.219586
$313$	−8.57706	−0.484804	−0.242402	−	0.970176i	$-0.577935\pi$
$313$	−8.57706	−0.484804	−0.242402	+	0.970176i	$0.577935\pi$
$314$	14.4901	0.817722
$315$	0	0
$316$	−2.08608	−0.117351
$317$	−5.93456	−0.333318	−0.166659	−	0.986015i	$-0.553298\pi$
$317$	−5.93456	−0.333318	−0.166659	+	0.986015i	$0.553298\pi$
$318$	−4.28572	−0.240331
$319$	12.1737	0.681594
$320$	0	0
$321$	10.9029	0.608542
$322$	5.46047	0.304300
$323$	−12.4390	−0.692126
$324$	−2.30682	−0.128157
$325$	0	0
$326$	−27.1748	−1.50507
$327$	−8.14169	−0.450237
$328$	22.4538	1.23981
$329$	−10.4778	−0.577659
$330$	0	0
$331$	−15.4604	−0.849778	−0.424889	−	0.905245i	$-0.639687\pi$
$331$	−15.4604	−0.849778	−0.424889	+	0.905245i	$0.639687\pi$
$332$	1.11671	0.0612876
$333$	6.75052	0.369926
$334$	17.0859	0.934899
$335$	0	0
$336$	−1.90374	−0.103857
$337$	−14.8938	−0.811317	−0.405658	−	0.914025i	$-0.632958\pi$
$337$	−14.8938	−0.811317	−0.405658	+	0.914025i	$0.632958\pi$
$338$	11.3118	0.615279
$339$	−10.0876	−0.547886
$340$	0	0
$341$	−9.02078	−0.488503
$342$	−5.96963	−0.322800
$343$	1.00000	0.0539949
$344$	−22.2519	−1.19974
$345$	0	0
$346$	−13.1405	−0.706439
$347$	14.3113	0.768269	0.384135	−	0.923277i	$-0.374500\pi$
$347$	14.3113	0.768269	0.384135	+	0.923277i	$0.374500\pi$
$348$	1.78321	0.0955900
$349$	−3.94565	−0.211206	−0.105603	−	0.994408i	$-0.533677\pi$
$349$	−3.94565	−0.211206	−0.105603	+	0.994408i	$0.533677\pi$
$350$	0	0
$351$	−7.13361	−0.380764
$352$	4.23682	0.225824
$353$	−9.05336	−0.481862	−0.240931	−	0.970542i	$-0.577453\pi$
$353$	−9.05336	−0.481862	−0.240931	+	0.970542i	$0.577453\pi$
$354$	−0.0198444	−0.00105472
$355$	0	0
$356$	6.43689	0.341154
$357$	4.33130	0.229237
$358$	25.6138	1.35373
$359$	−36.7204	−1.93803	−0.969016	−	0.247000i	$-0.920555\pi$
$359$	−36.7204	−1.93803	−0.969016	+	0.247000i	$0.920555\pi$
$360$	0	0
$361$	−15.6507	−0.823720
$362$	13.8310	0.726940
$363$	−4.89590	−0.256968
$364$	−0.837795	−0.0439124
$365$	0	0
$366$	3.16672	0.165527
$367$	−15.7081	−0.819956	−0.409978	−	0.912095i	$-0.634464\pi$
$367$	−15.7081	−0.819956	−0.409978	+	0.912095i	$0.634464\pi$
$368$	12.9722	0.676222
$369$	−19.1496	−0.996886
$370$	0	0
$371$	5.34810	0.277660
$372$	−1.32137	−0.0685100
$373$	−9.41464	−0.487472	−0.243736	−	0.969842i	$-0.578373\pi$
$373$	−9.41464	−0.487472	−0.243736	+	0.969842i	$0.578373\pi$
$374$	15.5670	0.804949
$375$	0	0
$376$	−31.8681	−1.64347
$377$	−13.3759	−0.688892
$378$	4.48270	0.230565
$379$	31.3435	1.61001	0.805004	−	0.593270i	$-0.202163\pi$
$379$	31.3435	1.61001	0.805004	+	0.593270i	$0.202163\pi$
$380$	0	0
$381$	3.20977	0.164441
$382$	−15.3525	−0.785500
$383$	−17.9813	−0.918801	−0.459401	−	0.888229i	$-0.651936\pi$
$383$	−17.9813	−0.918801	−0.459401	+	0.888229i	$0.651936\pi$
$384$	−4.16735	−0.212664
$385$	0	0
$386$	−0.137162	−0.00698137
$387$	18.9774	0.964674
$388$	5.08593	0.258199
$389$	−9.30160	−0.471610	−0.235805	−	0.971800i	$-0.575773\pi$
$389$	−9.30160	−0.471610	−0.235805	+	0.971800i	$0.575773\pi$
$390$	0	0
$391$	−29.5137	−1.49257
$392$	3.04150	0.153619
$393$	3.09386	0.156065
$394$	12.7671	0.643198
$395$	0	0
$396$	−1.97784	−0.0993904
$397$	1.44966	0.0727566	0.0363783	−	0.999338i	$-0.488418\pi$
$397$	1.44966	0.0727566	0.0363783	+	0.999338i	$0.488418\pi$
$398$	−16.0128	−0.802648
$399$	−1.16624	−0.0583851
$400$	0	0
$401$	−6.92538	−0.345837	−0.172919	−	0.984936i	$-0.555320\pi$
$401$	−6.92538	−0.345837	−0.172919	+	0.984936i	$0.555320\pi$
$402$	−3.71703	−0.185388
$403$	9.91163	0.493733
$404$	5.73897	0.285524
$405$	0	0
$406$	8.40527	0.417147
$407$	4.73985	0.234946
$408$	13.1736	0.652191
$409$	−10.9318	−0.540542	−0.270271	−	0.962784i	$-0.587113\pi$
$409$	−10.9318	−0.540542	−0.270271	+	0.962784i	$0.587113\pi$
$410$	0	0
$411$	−7.44813	−0.367389
$412$	2.35913	0.116226
$413$	0.0247636	0.00121854
$414$	−14.1640	−0.696121
$415$	0	0
$416$	−4.65523	−0.228242
$417$	−6.24275	−0.305709
$418$	−4.19155	−0.205016
$419$	−10.8595	−0.530523	−0.265261	−	0.964177i	$-0.585458\pi$
$419$	−10.8595	−0.530523	−0.265261	+	0.964177i	$0.585458\pi$
$420$	0	0
$421$	19.4546	0.948158	0.474079	−	0.880482i	$-0.342781\pi$
$421$	19.4546	0.948158	0.474079	+	0.880482i	$0.342781\pi$
$422$	9.86281	0.480114
$423$	27.1784	1.32146
$424$	16.2662	0.789958
$425$	0	0
$426$	−9.58143	−0.464222
$427$	−3.95171	−0.191237
$428$	−7.16287	−0.346230
$429$	−2.32261	−0.112137
$430$	0	0
$431$	5.12070	0.246655	0.123328	−	0.992366i	$-0.460643\pi$
$431$	5.12070	0.246655	0.123328	+	0.992366i	$0.460643\pi$
$432$	10.6493	0.512367
$433$	13.9352	0.669683	0.334842	−	0.942274i	$-0.391317\pi$
$433$	13.9352	0.669683	0.334842	+	0.942274i	$0.391317\pi$
$434$	−6.22838	−0.298972
$435$	0	0
$436$	5.34883	0.256162
$437$	7.94684	0.380149
$438$	−7.62476	−0.364325
$439$	27.3812	1.30683	0.653417	−	0.756998i	$-0.273335\pi$
$439$	27.3812	1.30683	0.653417	+	0.756998i	$0.273335\pi$
$440$	0	0
$441$	−2.59391	−0.123520
$442$	−17.1043	−0.813568
$443$	−39.3336	−1.86880	−0.934399	−	0.356228i	$-0.884063\pi$
$443$	−39.3336	−1.86880	−0.934399	+	0.356228i	$0.884063\pi$
$444$	0.694298	0.0329499
$445$	0	0
$446$	14.0177	0.663758
$447$	13.6316	0.644754
$448$	8.90015	0.420493
$449$	−28.2960	−1.33537	−0.667685	−	0.744444i	$-0.732715\pi$
$449$	−28.2960	−1.33537	−0.667685	+	0.744444i	$0.732715\pi$
$450$	0	0
$451$	−13.4458	−0.633138
$452$	6.62725	0.311720
$453$	9.05278	0.425337
$454$	15.9012	0.746279
$455$	0	0
$456$	−3.54712	−0.166109
$457$	−7.27936	−0.340514	−0.170257	−	0.985400i	$-0.554460\pi$
$457$	−7.27936	−0.340514	−0.170257	+	0.985400i	$0.554460\pi$
$458$	−11.7621	−0.549609
$459$	−24.2289	−1.13091
$460$	0	0
$461$	5.93149	0.276257	0.138129	−	0.990414i	$-0.455891\pi$
$461$	5.93149	0.276257	0.138129	+	0.990414i	$0.455891\pi$
$462$	1.45951	0.0679025
$463$	13.9974	0.650513	0.325257	−	0.945626i	$-0.394549\pi$
$463$	13.9974	0.650513	0.325257	+	0.945626i	$0.394549\pi$
$464$	19.9680	0.926992
$465$	0	0
$466$	11.0668	0.512658
$467$	−4.64605	−0.214994	−0.107497	−	0.994205i	$-0.534284\pi$
$467$	−4.64605	−0.214994	−0.107497	+	0.994205i	$0.534284\pi$
$468$	2.17317	0.100455
$469$	4.63844	0.214183
$470$	0	0
$471$	−7.34289	−0.338343
$472$	0.0753183	0.00346681
$473$	13.3249	0.612680
$474$	−3.99301	−0.183405
$475$	0	0
$476$	−2.84552	−0.130424
$477$	−13.8725	−0.635178
$478$	17.9354	0.820345
$479$	13.7905	0.630104	0.315052	−	0.949074i	$-0.397978\pi$
$479$	13.7905	0.630104	0.315052	+	0.949074i	$0.397978\pi$
$480$	0	0
$481$	−5.20794	−0.237461
$482$	−6.06176	−0.276106
$483$	−2.76711	−0.125908
$484$	3.21644	0.146202
$485$	0	0
$486$	−17.8636	−0.810311
$487$	27.7215	1.25618	0.628091	−	0.778140i	$-0.283837\pi$
$487$	27.7215	1.25618	0.628091	+	0.778140i	$0.283837\pi$
$488$	−12.0191	−0.544080
$489$	13.7709	0.622742
$490$	0	0
$491$	29.9543	1.35182	0.675910	−	0.736985i	$-0.263751\pi$
$491$	29.9543	1.35182	0.675910	+	0.736985i	$0.263751\pi$
$492$	−1.96955	−0.0887943
$493$	−45.4303	−2.04608
$494$	4.60549	0.207211
$495$	0	0
$496$	−14.7965	−0.664381
$497$	11.9566	0.536325
$498$	2.13752	0.0957848
$499$	13.0499	0.584196	0.292098	−	0.956388i	$-0.405647\pi$
$499$	13.0499	0.584196	0.292098	+	0.956388i	$0.405647\pi$
$500$	0	0
$501$	−8.65834	−0.386826
$502$	−16.0089	−0.714514
$503$	−37.6867	−1.68037	−0.840184	−	0.542301i	$-0.817553\pi$
$503$	−37.6867	−1.68037	−0.840184	+	0.542301i	$0.817553\pi$
$504$	−7.88937	−0.351420
$505$	0	0
$506$	−9.94519	−0.442117
$507$	−5.73227	−0.254579
$508$	−2.10871	−0.0935589
$509$	42.2419	1.87234	0.936170	−	0.351547i	$-0.114344\pi$
$509$	42.2419	1.87234	0.936170	+	0.351547i	$0.114344\pi$
$510$	0	0
$511$	9.51486	0.420912
$512$	25.1220	1.11025
$513$	6.52385	0.288035
$514$	30.8495	1.36072
$515$	0	0
$516$	1.95184	0.0859251
$517$	19.0832	0.839280
$518$	3.27262	0.143791
$519$	6.65900	0.292298
$520$	0	0
$521$	23.5292	1.03083	0.515417	−	0.856939i	$-0.327637\pi$
$521$	23.5292	1.03083	0.515417	+	0.856939i	$0.327637\pi$
$522$	−21.8025	−0.954271
$523$	−19.6481	−0.859150	−0.429575	−	0.903031i	$-0.641337\pi$
$523$	−19.6481	−0.859150	−0.429575	+	0.903031i	$0.641337\pi$
$524$	−2.03256	−0.0887930
$525$	0	0
$526$	19.4080	0.846228
$527$	33.6643	1.46644
$528$	3.46729	0.150894
$529$	−4.14474	−0.180206
$530$	0	0
$531$	−0.0642346	−0.00278754
$532$	0.766183	0.0332182
$533$	14.7736	0.639917
$534$	12.3210	0.533182
$535$	0	0
$536$	14.1078	0.609364
$537$	−12.9799	−0.560124
$538$	−24.6575	−1.06306
$539$	−1.82131	−0.0784492
$540$	0	0
$541$	−35.7670	−1.53774	−0.768872	−	0.639403i	$-0.779182\pi$
$541$	−35.7670	−1.53774	−0.768872	+	0.639403i	$0.779182\pi$
$542$	24.0199	1.03174
$543$	−7.00889	−0.300780
$544$	−15.8112	−0.677900
$545$	0	0
$546$	−1.60364	−0.0686296
$547$	−20.0913	−0.859041	−0.429520	−	0.903057i	$-0.641317\pi$
$547$	−20.0913	−0.859041	−0.429520	+	0.903057i	$0.641317\pi$
$548$	4.89318	0.209026
$549$	10.2504	0.437476
$550$	0	0
$551$	12.2325	0.521123
$552$	−8.41615	−0.358215
$553$	4.98284	0.211892
$554$	−3.24089	−0.137692
$555$	0	0
$556$	4.10128	0.173933
$557$	−10.2545	−0.434498	−0.217249	−	0.976116i	$-0.569708\pi$
$557$	−10.2545	−0.434498	−0.217249	+	0.976116i	$0.569708\pi$
$558$	16.1559	0.683932
$559$	−14.6408	−0.619240
$560$	0	0
$561$	−7.88862	−0.333058
$562$	17.8518	0.753032
$563$	37.8120	1.59359	0.796793	−	0.604253i	$-0.206528\pi$
$563$	37.8120	1.59359	0.796793	+	0.604253i	$0.206528\pi$
$564$	2.79533	0.117705
$565$	0	0
$566$	25.7292	1.08148
$567$	5.51011	0.231403
$568$	36.3658	1.52588
$569$	−23.0532	−0.966439	−0.483220	−	0.875499i	$-0.660533\pi$
$569$	−23.0532	−0.966439	−0.483220	+	0.875499i	$0.660533\pi$
$570$	0	0
$571$	−40.0234	−1.67493	−0.837464	−	0.546492i	$-0.815963\pi$
$571$	−40.0234	−1.67493	−0.837464	+	0.546492i	$0.815963\pi$
$572$	1.52588	0.0638003
$573$	7.77991	0.325010
$574$	−9.28362	−0.387491
$575$	0	0
$576$	−23.0862	−0.961926
$577$	21.5960	0.899053	0.449526	−	0.893267i	$-0.351593\pi$
$577$	21.5960	0.899053	0.449526	+	0.893267i	$0.351593\pi$
$578$	−36.7159	−1.52718
$579$	0.0695074	0.00288863
$580$	0	0
$581$	−2.66740	−0.110662
$582$	9.73510	0.403533
$583$	−9.74053	−0.403412
$584$	28.9394	1.19752
$585$	0	0
$586$	10.1390	0.418837
$587$	−1.80802	−0.0746251	−0.0373126	−	0.999304i	$-0.511880\pi$
$587$	−1.80802	−0.0746251	−0.0373126	+	0.999304i	$0.511880\pi$
$588$	−0.266787	−0.0110021
$589$	−9.06441	−0.373493
$590$	0	0
$591$	−6.46978	−0.266131
$592$	7.77461	0.319535
$593$	−38.4929	−1.58071	−0.790356	−	0.612648i	$-0.790104\pi$
$593$	−38.4929	−1.58071	−0.790356	+	0.612648i	$0.790104\pi$
$594$	−8.16437	−0.334988
$595$	0	0
$596$	−8.95553	−0.366833
$597$	8.11453	0.332105
$598$	10.9273	0.446851
$599$	−31.7681	−1.29801	−0.649005	−	0.760784i	$-0.724815\pi$
$599$	−31.7681	−1.29801	−0.649005	+	0.760784i	$0.724815\pi$
$600$	0	0
$601$	19.1855	0.782592	0.391296	−	0.920265i	$-0.372027\pi$
$601$	19.1855	0.782592	0.391296	+	0.920265i	$0.372027\pi$
$602$	9.20014	0.374970
$603$	−12.0317	−0.489969
$604$	−5.94738	−0.241995
$605$	0	0
$606$	10.9851	0.446239
$607$	−35.5410	−1.44256	−0.721282	−	0.692641i	$-0.756447\pi$
$607$	−35.5410	−1.44256	−0.721282	+	0.692641i	$0.756447\pi$
$608$	4.25732	0.172657
$609$	−4.25940	−0.172600
$610$	0	0
$611$	−20.9678	−0.848267
$612$	7.38103	0.298360
$613$	−4.03171	−0.162839	−0.0814196	−	0.996680i	$-0.525945\pi$
$613$	−4.03171	−0.162839	−0.0814196	+	0.996680i	$0.525945\pi$
$614$	−11.4291	−0.461242
$615$	0	0
$616$	−5.53950	−0.223193
$617$	−32.7317	−1.31773	−0.658864	−	0.752262i	$-0.728963\pi$
$617$	−32.7317	−1.31773	−0.658864	+	0.752262i	$0.728963\pi$
$618$	4.51566	0.181647
$619$	48.2035	1.93746	0.968731	−	0.248114i	$-0.0798106\pi$
$619$	48.2035	1.93746	0.968731	+	0.248114i	$0.0798106\pi$
$620$	0	0
$621$	15.4790	0.621150
$622$	33.4176	1.33992
$623$	−15.3752	−0.615996
$624$	−3.80970	−0.152510
$625$	0	0
$626$	10.7858	0.431087
$627$	2.12408	0.0848277
$628$	4.82404	0.192500
$629$	−17.6884	−0.705284
$630$	0	0
$631$	14.7102	0.585604	0.292802	−	0.956173i	$-0.405412\pi$
$631$	14.7102	0.585604	0.292802	+	0.956173i	$0.405412\pi$
$632$	15.1553	0.602845
$633$	−4.99801	−0.198653
$634$	7.46281	0.296386
$635$	0	0
$636$	−1.42680	−0.0565764
$637$	2.00117	0.0792892
$638$	−15.3086	−0.606072
$639$	−31.0143	−1.22691
$640$	0	0
$641$	−5.42208	−0.214159	−0.107080	−	0.994250i	$-0.534150\pi$
$641$	−5.42208	−0.214159	−0.107080	+	0.994250i	$0.534150\pi$
$642$	−13.7106	−0.541115
$643$	41.4190	1.63341	0.816703	−	0.577058i	$-0.195799\pi$
$643$	41.4190	1.63341	0.816703	+	0.577058i	$0.195799\pi$
$644$	1.81790	0.0716353
$645$	0	0
$646$	15.6423	0.615437
$647$	−5.67887	−0.223259	−0.111630	−	0.993750i	$-0.535607\pi$
$647$	−5.67887	−0.223259	−0.111630	+	0.993750i	$0.535607\pi$
$648$	16.7590	0.658355
$649$	−0.0451021	−0.00177041
$650$	0	0
$651$	3.15625	0.123703
$652$	−9.04704	−0.354309
$653$	−1.46373	−0.0572802	−0.0286401	−	0.999590i	$-0.509118\pi$
$653$	−1.46373	−0.0572802	−0.0286401	+	0.999590i	$0.509118\pi$
$654$	10.2383	0.400350
$655$	0	0
$656$	−22.0547	−0.861090
$657$	−24.6807	−0.962886
$658$	13.1760	0.513653
$659$	3.23169	0.125889	0.0629443	−	0.998017i	$-0.479951\pi$
$659$	3.23169	0.125889	0.0629443	+	0.998017i	$0.479951\pi$
$660$	0	0
$661$	−18.3454	−0.713552	−0.356776	−	0.934190i	$-0.616124\pi$
$661$	−18.3454	−0.713552	−0.356776	+	0.934190i	$0.616124\pi$
$662$	19.4416	0.755621
$663$	8.66766	0.336624
$664$	−8.11287	−0.314840
$665$	0	0
$666$	−8.48889	−0.328938
$667$	29.0238	1.12381
$668$	5.68824	0.220085
$669$	−7.10353	−0.274638
$670$	0	0
$671$	7.19728	0.277848
$672$	−1.48241	−0.0571851
$673$	−7.72432	−0.297750	−0.148875	−	0.988856i	$-0.547565\pi$
$673$	−7.72432	−0.297750	−0.148875	+	0.988856i	$0.547565\pi$
$674$	18.7292	0.721421
$675$	0	0
$676$	3.76592	0.144843
$677$	−23.0312	−0.885160	−0.442580	−	0.896729i	$-0.645937\pi$
$677$	−23.0312	−0.885160	−0.442580	+	0.896729i	$0.645937\pi$
$678$	12.6854	0.487179
$679$	−12.1483	−0.466210
$680$	0	0
$681$	−8.05797	−0.308782
$682$	11.3438	0.434376
$683$	35.4273	1.35559	0.677793	−	0.735253i	$-0.262936\pi$
$683$	35.4273	1.35559	0.677793	+	0.735253i	$0.262936\pi$
$684$	−1.98741	−0.0759905
$685$	0	0
$686$	−1.25752	−0.0480122
$687$	5.96051	0.227408
$688$	21.8564	0.833266
$689$	10.7025	0.407731
$690$	0	0
$691$	9.67149	0.367921	0.183960	−	0.982934i	$-0.441108\pi$
$691$	9.67149	0.367921	0.183960	+	0.982934i	$0.441108\pi$
$692$	−4.37475	−0.166303
$693$	4.72431	0.179462
$694$	−17.9967	−0.683144
$695$	0	0
$696$	−12.9549	−0.491056
$697$	50.1778	1.90062
$698$	4.96172	0.187804
$699$	−5.60812	−0.212119
$700$	0	0
$701$	−4.79790	−0.181214	−0.0906071	−	0.995887i	$-0.528881\pi$
$701$	−4.79790	−0.181214	−0.0906071	+	0.995887i	$0.528881\pi$
$702$	8.97064	0.338575
$703$	4.76278	0.179632
$704$	−16.2099	−0.610934
$705$	0	0
$706$	11.3847	0.428471
$707$	−13.7082	−0.515549
$708$	−0.00660659	−0.000248291 0
$709$	42.4152	1.59294	0.796469	−	0.604679i	$-0.206699\pi$
$709$	42.4152	1.59294	0.796469	+	0.604679i	$0.206699\pi$
$710$	0	0
$711$	−12.9250	−0.484727
$712$	−46.7637	−1.75255
$713$	−21.5069	−0.805439
$714$	−5.44668	−0.203837
$715$	0	0
$716$	8.52737	0.318683
$717$	−9.08881	−0.339428
$718$	46.1766	1.72329
$719$	−43.3185	−1.61551	−0.807754	−	0.589519i	$-0.799317\pi$
$719$	−43.3185	−1.61551	−0.807754	+	0.589519i	$0.799317\pi$
$720$	0	0
$721$	−5.63505	−0.209860
$722$	19.6810	0.732450
$723$	3.07182	0.114242
$724$	4.60461	0.171129
$725$	0	0
$726$	6.15667	0.228495
$727$	0.248871	0.00923012	0.00461506	−	0.999989i	$-0.498531\pi$
$727$	0.248871	0.00923012	0.00461506	+	0.999989i	$0.498531\pi$
$728$	6.08655	0.225582
$729$	−7.47789	−0.276959
$730$	0	0
$731$	−49.7266	−1.83920
$732$	1.05426	0.0389667
$733$	−30.0870	−1.11129	−0.555645	−	0.831420i	$-0.687529\pi$
$733$	−30.0870	−1.11129	−0.555645	+	0.831420i	$0.687529\pi$
$734$	19.7532	0.729103
$735$	0	0
$736$	10.1012	0.372336
$737$	−8.44802	−0.311187
$738$	24.0809	0.886430
$739$	10.0368	0.369211	0.184605	−	0.982813i	$-0.440899\pi$
$739$	10.0368	0.369211	0.184605	+	0.982813i	$0.440899\pi$
$740$	0	0
$741$	−2.33385	−0.0857360
$742$	−6.72532	−0.246894
$743$	12.7497	0.467740	0.233870	−	0.972268i	$-0.424861\pi$
$743$	12.7497	0.467740	0.233870	+	0.972268i	$0.424861\pi$
$744$	9.59972	0.351943
$745$	0	0
$746$	11.8391	0.433459
$747$	6.91899	0.253153
$748$	5.18256	0.189493
$749$	17.1093	0.625162
$750$	0	0
$751$	31.5166	1.15006	0.575028	−	0.818133i	$-0.304991\pi$
$751$	31.5166	1.15006	0.575028	+	0.818133i	$0.304991\pi$
$752$	31.3016	1.14145
$753$	8.11259	0.295639
$754$	16.8204	0.612562
$755$	0	0
$756$	1.49238	0.0542774
$757$	37.1340	1.34966	0.674829	−	0.737974i	$-0.264217\pi$
$757$	37.1340	1.34966	0.674829	+	0.737974i	$0.264217\pi$
$758$	−39.4150	−1.43162
$759$	5.03976	0.182932
$760$	0	0
$761$	34.7049	1.25805	0.629026	−	0.777384i	$-0.283454\pi$
$761$	34.7049	1.25805	0.629026	+	0.777384i	$0.283454\pi$
$762$	−4.03633	−0.146221
$763$	−12.7763	−0.462533
$764$	−5.11114	−0.184915
$765$	0	0
$766$	22.6118	0.816997
$767$	0.0495561	0.00178937
$768$	−6.10275	−0.220214
$769$	−38.1521	−1.37580	−0.687900	−	0.725805i	$-0.741467\pi$
$769$	−38.1521	−1.37580	−0.687900	+	0.725805i	$0.741467\pi$
$770$	0	0
$771$	−15.6331	−0.563013
$772$	−0.0456641	−0.00164349
$773$	−24.8055	−0.892192	−0.446096	−	0.894985i	$-0.647186\pi$
$773$	−24.8055	−0.892192	−0.446096	+	0.894985i	$0.647186\pi$
$774$	−23.8644	−0.857787
$775$	0	0
$776$	−36.9491	−1.32640
$777$	−1.65841	−0.0594951
$778$	11.6969	0.419354
$779$	−13.5108	−0.484076
$780$	0	0
$781$	−21.7766	−0.779227
$782$	37.1140	1.32719
$783$	23.8267	0.851497
$784$	−2.98742	−0.106694
$785$	0	0
$786$	−3.89058	−0.138772
$787$	27.2546	0.971522	0.485761	−	0.874092i	$-0.338542\pi$
$787$	27.2546	0.971522	0.485761	+	0.874092i	$0.338542\pi$
$788$	4.25043	0.151415
$789$	−9.83506	−0.350137
$790$	0	0
$791$	−15.8300	−0.562848
$792$	14.3690	0.510579
$793$	−7.90804	−0.280823
$794$	−1.82298	−0.0646950
$795$	0	0
$796$	−5.33098	−0.188952
$797$	−15.0974	−0.534777	−0.267389	−	0.963589i	$-0.586161\pi$
$797$	−15.0974	−0.534777	−0.267389	+	0.963589i	$0.586161\pi$
$798$	1.46657	0.0519159
$799$	−71.2159	−2.51944
$800$	0	0
$801$	39.8820	1.40916
$802$	8.70878	0.307518
$803$	−17.3295	−0.611544
$804$	−1.23747	−0.0436423
$805$	0	0
$806$	−12.4640	−0.439027
$807$	12.4953	0.439854
$808$	−41.6934	−1.46677
$809$	−27.8081	−0.977679	−0.488840	−	0.872374i	$-0.662580\pi$
$809$	−27.8081	−0.977679	−0.488840	+	0.872374i	$0.662580\pi$
$810$	0	0
$811$	−23.7140	−0.832710	−0.416355	−	0.909202i	$-0.636693\pi$
$811$	−23.7140	−0.832710	−0.416355	+	0.909202i	$0.636693\pi$
$812$	2.79829	0.0982006
$813$	−12.1721	−0.426896
$814$	−5.96044	−0.208913
$815$	0	0
$816$	−12.9394	−0.452970
$817$	13.3893	0.468434
$818$	13.7469	0.480649
$819$	−5.19086	−0.181383
$820$	0	0
$821$	3.52569	0.123048	0.0615238	−	0.998106i	$-0.480404\pi$
$821$	3.52569	0.123048	0.0615238	+	0.998106i	$0.480404\pi$
$822$	9.36615	0.326682
$823$	−12.1598	−0.423863	−0.211931	−	0.977285i	$-0.567975\pi$
$823$	−12.1598	−0.423863	−0.211931	+	0.977285i	$0.567975\pi$
$824$	−17.1390	−0.597064
$825$	0	0
$826$	−0.0311406	−0.00108352
$827$	45.0501	1.56655	0.783273	−	0.621678i	$-0.213549\pi$
$827$	45.0501	1.56655	0.783273	+	0.621678i	$0.213549\pi$
$828$	−4.71547	−0.163874
$829$	21.1372	0.734126	0.367063	−	0.930196i	$-0.380363\pi$
$829$	21.1372	0.734126	0.367063	+	0.930196i	$0.380363\pi$
$830$	0	0
$831$	1.64233	0.0569719
$832$	17.8107	0.617475
$833$	6.79685	0.235497
$834$	7.85036	0.271836
$835$	0	0
$836$	−1.39545	−0.0482628
$837$	−17.6558	−0.610273
$838$	13.6560	0.471740
$839$	−27.9220	−0.963975	−0.481988	−	0.876178i	$-0.660085\pi$
$839$	−27.9220	−0.963975	−0.481988	+	0.876178i	$0.660085\pi$
$840$	0	0
$841$	15.6762	0.540558
$842$	−24.4644	−0.843101
$843$	−9.04645	−0.311576
$844$	3.28353	0.113024
$845$	0	0
$846$	−34.1773	−1.17504
$847$	−7.68284	−0.263986
$848$	−15.9770	−0.548654
$849$	−13.0384	−0.447476
$850$	0	0
$851$	11.3005	0.387377
$852$	−3.18985	−0.109283
$853$	27.4479	0.939799	0.469899	−	0.882720i	$-0.344290\pi$
$853$	27.4479	0.939799	0.469899	+	0.882720i	$0.344290\pi$
$854$	4.96934	0.170047
$855$	0	0
$856$	52.0380	1.77862
$857$	25.1788	0.860093	0.430047	−	0.902807i	$-0.358497\pi$
$857$	25.1788	0.860093	0.430047	+	0.902807i	$0.358497\pi$
$858$	2.92073	0.0997119
$859$	53.6735	1.83132	0.915659	−	0.401957i	$-0.131670\pi$
$859$	53.6735	1.83132	0.915659	+	0.401957i	$0.131670\pi$
$860$	0	0
$861$	4.70450	0.160329
$862$	−6.43936	−0.219326
$863$	−40.8609	−1.39092	−0.695460	−	0.718565i	$-0.744799\pi$
$863$	−40.8609	−1.39092	−0.695460	+	0.718565i	$0.744799\pi$
$864$	8.29246	0.282115
$865$	0	0
$866$	−17.5237	−0.595481
$867$	18.6059	0.631890
$868$	−2.07355	−0.0703810
$869$	−9.07528	−0.307858
$870$	0	0
$871$	9.28230	0.314519
$872$	−38.8590	−1.31593
$873$	31.5117	1.06651
$874$	−9.99328	−0.338028
$875$	0	0
$876$	−2.53844	−0.0857658
$877$	−33.3974	−1.12775	−0.563876	−	0.825860i	$-0.690690\pi$
$877$	−33.3974	−1.12775	−0.563876	+	0.825860i	$0.690690\pi$
$878$	−34.4323	−1.16203
$879$	−5.13796	−0.173299
$880$	0	0
$881$	−16.5238	−0.556700	−0.278350	−	0.960480i	$-0.589787\pi$
$881$	−16.5238	−0.556700	−0.278350	+	0.960480i	$0.589787\pi$
$882$	3.26189	0.109833
$883$	2.11684	0.0712372	0.0356186	−	0.999365i	$-0.488660\pi$
$883$	2.11684	0.0712372	0.0356186	+	0.999365i	$0.488660\pi$
$884$	−5.69437	−0.191522
$885$	0	0
$886$	49.4627	1.66173
$887$	−2.28850	−0.0768403	−0.0384201	−	0.999262i	$-0.512233\pi$
$887$	−2.28850	−0.0768403	−0.0384201	+	0.999262i	$0.512233\pi$
$888$	−5.04405	−0.169267
$889$	5.03690	0.168932
$890$	0	0
$891$	−10.0356	−0.336205
$892$	4.66678	0.156255
$893$	19.1755	0.641685
$894$	−17.1420	−0.573314
$895$	0	0
$896$	−6.53958	−0.218472
$897$	−5.53746	−0.184890
$898$	35.5826	1.18741
$899$	−33.1054	−1.10413
$900$	0	0
$901$	36.3502	1.21100
$902$	16.9083	0.562985
$903$	−4.66220	−0.155148
$904$	−48.1467	−1.60134
$905$	0	0
$906$	−11.3840	−0.378209
$907$	53.0301	1.76084	0.880418	−	0.474199i	$-0.157262\pi$
$907$	53.0301	1.76084	0.880418	+	0.474199i	$0.157262\pi$
$908$	5.29383	0.175682
$909$	35.5578	1.17938
$910$	0	0
$911$	−0.854969	−0.0283264	−0.0141632	−	0.999900i	$-0.504508\pi$
$911$	−0.854969	−0.0283264	−0.0141632	+	0.999900i	$0.504508\pi$
$912$	3.48406	0.115369
$913$	4.85814	0.160781
$914$	9.15391	0.302784
$915$	0	0
$916$	−3.91586	−0.129384
$917$	4.85501	0.160327
$918$	30.4682	1.00560
$919$	48.5039	1.60000	0.799999	−	0.600002i	$-0.204833\pi$
$919$	48.5039	1.60000	0.799999	+	0.600002i	$0.204833\pi$
$920$	0	0
$921$	5.79175	0.190845
$922$	−7.45895	−0.245647
$923$	23.9271	0.787571
$924$	0.485900	0.0159849
$925$	0	0
$926$	−17.6019	−0.578436
$927$	14.6168	0.480079
$928$	15.5488	0.510413
$929$	53.4455	1.75349	0.876745	−	0.480955i	$-0.159710\pi$
$929$	53.4455	1.75349	0.876745	+	0.480955i	$0.159710\pi$
$930$	0	0
$931$	−1.83012	−0.0599796
$932$	3.68435	0.120685
$933$	−16.9345	−0.554410
$934$	5.84249	0.191172
$935$	0	0
$936$	−15.7880	−0.516046
$937$	−9.30436	−0.303960	−0.151980	−	0.988384i	$-0.548565\pi$
$937$	−9.30436	−0.303960	−0.151980	+	0.988384i	$0.548565\pi$
$938$	−5.83291	−0.190451
$939$	−5.46574	−0.178368
$940$	0	0
$941$	−10.9094	−0.355638	−0.177819	−	0.984063i	$-0.556904\pi$
$941$	−10.9094	−0.355638	−0.177819	+	0.984063i	$0.556904\pi$
$942$	9.23380	0.300854
$943$	−32.0568	−1.04391
$944$	−0.0739793	−0.00240782
$945$	0	0
$946$	−16.7563	−0.544794
$947$	33.9581	1.10349	0.551745	−	0.834013i	$-0.313962\pi$
$947$	33.9581	1.10349	0.551745	+	0.834013i	$0.313962\pi$
$948$	−1.32935	−0.0431754
$949$	19.0408	0.618092
$950$	0	0
$951$	−3.78180	−0.122633
$952$	20.6726	0.670002
$953$	−1.14239	−0.0370055	−0.0185028	−	0.999829i	$-0.505890\pi$
$953$	−1.14239	−0.0370055	−0.0185028	+	0.999829i	$0.505890\pi$
$954$	17.4449	0.564799
$955$	0	0
$956$	5.97105	0.193118
$957$	7.75767	0.250770
$958$	−17.3418	−0.560287
$959$	−11.6879	−0.377423
$960$	0	0
$961$	−6.46859	−0.208664
$962$	6.54907	0.211150
$963$	−44.3801	−1.43013
$964$	−2.01808	−0.0649981
$965$	0	0
$966$	3.47969	0.111957
$967$	25.7773	0.828943	0.414472	−	0.910062i	$-0.363966\pi$
$967$	25.7773	0.828943	0.414472	+	0.910062i	$0.363966\pi$
$968$	−23.3673	−0.751054
$969$	−7.92677	−0.254645
$970$	0	0
$971$	36.5809	1.17394	0.586968	−	0.809610i	$-0.300321\pi$
$971$	36.5809	1.17394	0.586968	+	0.809610i	$0.300321\pi$
$972$	−5.94717	−0.190756
$973$	−9.79638	−0.314058
$974$	−34.8603	−1.11699
$975$	0	0
$976$	11.8054	0.377883
$977$	56.6204	1.81145	0.905723	−	0.423869i	$-0.139328\pi$
$977$	56.6204	1.81145	0.905723	+	0.423869i	$0.139328\pi$
$978$	−17.3171	−0.553741
$979$	28.0030	0.894981
$980$	0	0
$981$	33.1406	1.05810
$982$	−37.6680	−1.20204
$983$	−15.3682	−0.490168	−0.245084	−	0.969502i	$-0.578816\pi$
$983$	−15.3682	−0.490168	−0.245084	+	0.969502i	$0.578816\pi$
$984$	14.3087	0.456145
$985$	0	0
$986$	57.1294	1.81937
$987$	−6.67697	−0.212530
$988$	1.53326	0.0487795
$989$	31.7685	1.01018
$990$	0	0
$991$	33.4163	1.06150	0.530752	−	0.847527i	$-0.321909\pi$
$991$	33.4163	1.06150	0.530752	+	0.847527i	$0.321909\pi$
$992$	−11.5218	−0.365816
$993$	−9.85212	−0.312647
$994$	−15.0356	−0.476900
$995$	0	0
$996$	0.711626	0.0225487
$997$	6.53609	0.207000	0.103500	−	0.994629i	$-0.466996\pi$
$997$	6.53609	0.207000	0.103500	+	0.994629i	$0.466996\pi$
$998$	−16.4105	−0.519466
$999$	9.27700	0.293511

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4375.2.a.o.1.9		28
5.4	even	2		4375.2.a.p.1.20		28
25.2	odd	20		875.2.n.c.274.4		56
25.9	even	10		875.2.h.d.526.10		56
25.11	even	5		875.2.h.e.351.5		56
25.12	odd	20		175.2.n.a.169.11	yes	56
25.13	odd	20		875.2.n.c.99.4		56
25.14	even	10		875.2.h.d.351.10		56
25.16	even	5		875.2.h.e.526.5		56
25.23	odd	20		175.2.n.a.29.11	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.n.a.29.11	✓	56	25.23	odd	20
175.2.n.a.169.11	yes	56	25.12	odd	20
875.2.h.d.351.10		56	25.14	even	10
875.2.h.d.526.10		56	25.9	even	10
875.2.h.e.351.5		56	25.11	even	5
875.2.h.e.526.5		56	25.16	even	5
875.2.n.c.99.4		56	25.13	odd	20
875.2.n.c.274.4		56	25.2	odd	20
4375.2.a.o.1.9		28	1.1	even	1	trivial
4375.2.a.p.1.20		28	5.4	even	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:	\( N \)	\(=\)	\( 4375 = 5^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4375.a (trivial)

\(f(q)\)	\(=\)	\(q-1.25752 q^{2} +0.637250 q^{3} -0.418653 q^{4} -0.801353 q^{6} +1.00000 q^{7} +3.04150 q^{8} -2.59391 q^{9} +O(q^{10})\)	\(q-1.25752 q^{2} +0.637250 q^{3} -0.418653 q^{4} -0.801353 q^{6} +1.00000 q^{7} +3.04150 q^{8} -2.59391 q^{9} -1.82131 q^{11} -0.266787 q^{12} +2.00117 q^{13} -1.25752 q^{14} -2.98742 q^{16} +6.79685 q^{17} +3.26189 q^{18} -1.83012 q^{19} +0.637250 q^{21} +2.29032 q^{22} -4.34226 q^{23} +1.93819 q^{24} -2.51650 q^{26} -3.56472 q^{27} -0.418653 q^{28} -6.68402 q^{29} +4.95292 q^{31} -2.32626 q^{32} -1.16063 q^{33} -8.54715 q^{34} +1.08595 q^{36} -2.60245 q^{37} +2.30140 q^{38} +1.27525 q^{39} +7.38250 q^{41} -0.801353 q^{42} -7.31612 q^{43} +0.762495 q^{44} +5.46047 q^{46} -10.4778 q^{47} -1.90374 q^{48} +1.00000 q^{49} +4.33130 q^{51} -0.837795 q^{52} +5.34810 q^{53} +4.48270 q^{54} +3.04150 q^{56} -1.16624 q^{57} +8.40527 q^{58} +0.0247636 q^{59} -3.95171 q^{61} -6.22838 q^{62} -2.59391 q^{63} +8.90015 q^{64} +1.45951 q^{66} +4.63844 q^{67} -2.84552 q^{68} -2.76711 q^{69} +11.9566 q^{71} -7.88937 q^{72} +9.51486 q^{73} +3.27262 q^{74} +0.766183 q^{76} -1.82131 q^{77} -1.60364 q^{78} +4.98284 q^{79} +5.51011 q^{81} -9.28362 q^{82} -2.66740 q^{83} -0.266787 q^{84} +9.20014 q^{86} -4.25940 q^{87} -5.53950 q^{88} -15.3752 q^{89} +2.00117 q^{91} +1.81790 q^{92} +3.15625 q^{93} +13.1760 q^{94} -1.48241 q^{96} -12.1483 q^{97} -1.25752 q^{98} +4.72431 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 8 q^{2} - 8 q^{3} + 24 q^{4} + 28 q^{7} - 24 q^{8} + 22 q^{9}+O(q^{10}) \) 28 * q - 8 * q^2 - 8 * q^3 + 24 * q^4 + 28 * q^7 - 24 * q^8 + 22 * q^9	\( 28 q - 8 q^{2} - 8 q^{3} + 24 q^{4} + 28 q^{7} - 24 q^{8} + 22 q^{9} - 16 q^{11} - 24 q^{12} - 16 q^{13} - 8 q^{14} + 24 q^{16} - 40 q^{17} - 24 q^{18} + 4 q^{19} - 8 q^{21} - 16 q^{22} - 32 q^{23} + 14 q^{24} + 6 q^{26} - 32 q^{27} + 24 q^{28} - 24 q^{29} + 6 q^{31} - 56 q^{32} - 28 q^{33} + 18 q^{36} - 32 q^{37} - 40 q^{38} - 28 q^{39} + 2 q^{41} - 16 q^{43} - 26 q^{44} - 12 q^{46} - 26 q^{47} - 46 q^{48} + 28 q^{49} - 22 q^{51} - 28 q^{52} - 60 q^{53} + 38 q^{54} - 24 q^{56} - 76 q^{57} - 16 q^{58} + 8 q^{59} + 18 q^{61} - 34 q^{62} + 22 q^{63} + 28 q^{64} + 38 q^{66} - 24 q^{67} - 62 q^{68} + 14 q^{69} - 54 q^{71} - 40 q^{72} - 46 q^{73} - 30 q^{74} + 26 q^{76} - 16 q^{77} - 32 q^{78} - 30 q^{79} + 4 q^{81} - 22 q^{82} - 60 q^{83} - 24 q^{84} - 10 q^{86} - 18 q^{87} - 16 q^{88} + 6 q^{89} - 16 q^{91} - 72 q^{92} - 48 q^{93} + 86 q^{94} + 106 q^{96} - 70 q^{97} - 8 q^{98} - 30 q^{99}+O(q^{100}) \) 28 * q - 8 * q^2 - 8 * q^3 + 24 * q^4 + 28 * q^7 - 24 * q^8 + 22 * q^9 - 16 * q^11 - 24 * q^12 - 16 * q^13 - 8 * q^14 + 24 * q^16 - 40 * q^17 - 24 * q^18 + 4 * q^19 - 8 * q^21 - 16 * q^22 - 32 * q^23 + 14 * q^24 + 6 * q^26 - 32 * q^27 + 24 * q^28 - 24 * q^29 + 6 * q^31 - 56 * q^32 - 28 * q^33 + 18 * q^36 - 32 * q^37 - 40 * q^38 - 28 * q^39 + 2 * q^41 - 16 * q^43 - 26 * q^44 - 12 * q^46 - 26 * q^47 - 46 * q^48 + 28 * q^49 - 22 * q^51 - 28 * q^52 - 60 * q^53 + 38 * q^54 - 24 * q^56 - 76 * q^57 - 16 * q^58 + 8 * q^59 + 18 * q^61 - 34 * q^62 + 22 * q^63 + 28 * q^64 + 38 * q^66 - 24 * q^67 - 62 * q^68 + 14 * q^69 - 54 * q^71 - 40 * q^72 - 46 * q^73 - 30 * q^74 + 26 * q^76 - 16 * q^77 - 32 * q^78 - 30 * q^79 + 4 * q^81 - 22 * q^82 - 60 * q^83 - 24 * q^84 - 10 * q^86 - 18 * q^87 - 16 * q^88 + 6 * q^89 - 16 * q^91 - 72 * q^92 - 48 * q^93 + 86 * q^94 + 106 * q^96 - 70 * q^97 - 8 * q^98 - 30 * q^99

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