LMFDB - Embedded newform 125.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [125,2,Mod(1,125)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(125, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("125.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 125 = 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	125.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:	$0.998130025266$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	125.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.618034 q^{2} +2.61803 q^{3} -1.61803 q^{4} -1.61803 q^{6} +3.00000 q^{7} +2.23607 q^{8} +3.85410 q^{9} +O(q^{10})$	\(q-0.618034 q^{2} +2.61803 q^{3} -1.61803 q^{4} -1.61803 q^{6} +3.00000 q^{7} +2.23607 q^{8} +3.85410 q^{9} -3.00000 q^{11} -4.23607 q^{12} -1.85410 q^{13} -1.85410 q^{14} +1.85410 q^{16} +0.236068 q^{17} -2.38197 q^{18} -1.38197 q^{19} +7.85410 q^{21} +1.85410 q^{22} -3.23607 q^{23} +5.85410 q^{24} +1.14590 q^{26} +2.23607 q^{27} -4.85410 q^{28} -6.70820 q^{29} -6.09017 q^{31} -5.61803 q^{32} -7.85410 q^{33} -0.145898 q^{34} -6.23607 q^{36} +9.70820 q^{37} +0.854102 q^{38} -4.85410 q^{39} -3.00000 q^{41} -4.85410 q^{42} +9.00000 q^{43} +4.85410 q^{44} +2.00000 q^{46} -7.32624 q^{47} +4.85410 q^{48} +2.00000 q^{49} +0.618034 q^{51} +3.00000 q^{52} -2.38197 q^{53} -1.38197 q^{54} +6.70820 q^{56} -3.61803 q^{57} +4.14590 q^{58} +10.8541 q^{59} +5.09017 q^{61} +3.76393 q^{62} +11.5623 q^{63} -0.236068 q^{64} +4.85410 q^{66} +7.14590 q^{67} -0.381966 q^{68} -8.47214 q^{69} -3.00000 q^{71} +8.61803 q^{72} +4.85410 q^{73} -6.00000 q^{74} +2.23607 q^{76} -9.00000 q^{77} +3.00000 q^{78} +9.47214 q^{79} -5.70820 q^{81} +1.85410 q^{82} +8.47214 q^{83} -12.7082 q^{84} -5.56231 q^{86} -17.5623 q^{87} -6.70820 q^{88} +13.4164 q^{89} -5.56231 q^{91} +5.23607 q^{92} -15.9443 q^{93} +4.52786 q^{94} -14.7082 q^{96} -1.14590 q^{97} -1.23607 q^{98} -11.5623 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + 3 q^{3} - q^{4} - q^{6} + 6 q^{7} + q^{9}+O(q^{10}) $ 2 * q + q^2 + 3 * q^3 - q^4 - q^6 + 6 * q^7 + q^9	$ 2 q + q^{2} + 3 q^{3} - q^{4} - q^{6} + 6 q^{7} + q^{9} - 6 q^{11} - 4 q^{12} + 3 q^{13} + 3 q^{14} - 3 q^{16} - 4 q^{17} - 7 q^{18} - 5 q^{19} + 9 q^{21} - 3 q^{22} - 2 q^{23} + 5 q^{24} + 9 q^{26} - 3 q^{28} - q^{31} - 9 q^{32} - 9 q^{33} - 7 q^{34} - 8 q^{36} + 6 q^{37} - 5 q^{38} - 3 q^{39} - 6 q^{41} - 3 q^{42} + 18 q^{43} + 3 q^{44} + 4 q^{46} + q^{47} + 3 q^{48} + 4 q^{49} - q^{51} + 6 q^{52} - 7 q^{53} - 5 q^{54} - 5 q^{57} + 15 q^{58} + 15 q^{59} - q^{61} + 12 q^{62} + 3 q^{63} + 4 q^{64} + 3 q^{66} + 21 q^{67} - 3 q^{68} - 8 q^{69} - 6 q^{71} + 15 q^{72} + 3 q^{73} - 12 q^{74} - 18 q^{77} + 6 q^{78} + 10 q^{79} + 2 q^{81} - 3 q^{82} + 8 q^{83} - 12 q^{84} + 9 q^{86} - 15 q^{87} + 9 q^{91} + 6 q^{92} - 14 q^{93} + 18 q^{94} - 16 q^{96} - 9 q^{97} + 2 q^{98} - 3 q^{99}+O(q^{100}) $ 2 * q + q^2 + 3 * q^3 - q^4 - q^6 + 6 * q^7 + q^9 - 6 * q^11 - 4 * q^12 + 3 * q^13 + 3 * q^14 - 3 * q^16 - 4 * q^17 - 7 * q^18 - 5 * q^19 + 9 * q^21 - 3 * q^22 - 2 * q^23 + 5 * q^24 + 9 * q^26 - 3 * q^28 - q^31 - 9 * q^32 - 9 * q^33 - 7 * q^34 - 8 * q^36 + 6 * q^37 - 5 * q^38 - 3 * q^39 - 6 * q^41 - 3 * q^42 + 18 * q^43 + 3 * q^44 + 4 * q^46 + q^47 + 3 * q^48 + 4 * q^49 - q^51 + 6 * q^52 - 7 * q^53 - 5 * q^54 - 5 * q^57 + 15 * q^58 + 15 * q^59 - q^61 + 12 * q^62 + 3 * q^63 + 4 * q^64 + 3 * q^66 + 21 * q^67 - 3 * q^68 - 8 * q^69 - 6 * q^71 + 15 * q^72 + 3 * q^73 - 12 * q^74 - 18 * q^77 + 6 * q^78 + 10 * q^79 + 2 * q^81 - 3 * q^82 + 8 * q^83 - 12 * q^84 + 9 * q^86 - 15 * q^87 + 9 * q^91 + 6 * q^92 - 14 * q^93 + 18 * q^94 - 16 * q^96 - 9 * q^97 + 2 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.618034	−0.437016	−0.218508	−	0.975835i	$-0.570119\pi$
$2$	−0.618034	−0.437016	−0.218508	+	0.975835i	$0.570119\pi$
$3$	2.61803	1.51152	0.755761	−	0.654847i	$-0.227267\pi$
$3$	2.61803	1.51152	0.755761	+	0.654847i	$0.227267\pi$
$4$	−1.61803	−0.809017
$5$	0	0
$5$	0	0
$6$	−1.61803	−0.660560
$7$	3.00000	1.13389	0.566947	−	0.823754i	$-0.308125\pi$
$7$	3.00000	1.13389	0.566947	+	0.823754i	$0.308125\pi$
$8$	2.23607	0.790569
$9$	3.85410	1.28470
$10$	0	0
$11$	−3.00000	−0.904534	−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000	−0.904534	−0.452267	+	0.891883i	$0.649385\pi$
$12$	−4.23607	−1.22285
$13$	−1.85410	−0.514235	−0.257118	−	0.966380i	$-0.582773\pi$
$13$	−1.85410	−0.514235	−0.257118	+	0.966380i	$0.582773\pi$
$14$	−1.85410	−0.495530
$15$	0	0
$16$	1.85410	0.463525
$17$	0.236068	0.0572549	0.0286274	−	0.999590i	$-0.490886\pi$
$17$	0.236068	0.0572549	0.0286274	+	0.999590i	$0.490886\pi$
$18$	−2.38197	−0.561435
$19$	−1.38197	−0.317045	−0.158522	−	0.987355i	$-0.550673\pi$
$19$	−1.38197	−0.317045	−0.158522	+	0.987355i	$0.550673\pi$
$20$	0	0
$21$	7.85410	1.71391
$22$	1.85410	0.395296
$23$	−3.23607	−0.674767	−0.337383	−	0.941367i	$-0.609542\pi$
$23$	−3.23607	−0.674767	−0.337383	+	0.941367i	$0.609542\pi$
$24$	5.85410	1.19496
$25$	0	0
$26$	1.14590	0.224729
$27$	2.23607	0.430331
$28$	−4.85410	−0.917339
$29$	−6.70820	−1.24568	−0.622841	−	0.782348i	$-0.714022\pi$
$29$	−6.70820	−1.24568	−0.622841	+	0.782348i	$0.714022\pi$
$30$	0	0
$31$	−6.09017	−1.09383	−0.546913	−	0.837189i	$-0.684197\pi$
$31$	−6.09017	−1.09383	−0.546913	+	0.837189i	$0.684197\pi$
$32$	−5.61803	−0.993137
$33$	−7.85410	−1.36722
$34$	−0.145898	−0.0250213
$35$	0	0
$36$	−6.23607	−1.03934
$37$	9.70820	1.59602	0.798009	−	0.602645i	$-0.205886\pi$
$37$	9.70820	1.59602	0.798009	+	0.602645i	$0.205886\pi$
$38$	0.854102	0.138554
$39$	−4.85410	−0.777278
$40$	0	0
$41$	−3.00000	−0.468521	−0.234261	−	0.972174i	$-0.575267\pi$
$41$	−3.00000	−0.468521	−0.234261	+	0.972174i	$0.575267\pi$
$42$	−4.85410	−0.749004
$43$	9.00000	1.37249	0.686244	−	0.727372i	$-0.259258\pi$
$43$	9.00000	1.37249	0.686244	+	0.727372i	$0.259258\pi$
$44$	4.85410	0.731783
$45$	0	0
$46$	2.00000	0.294884
$47$	−7.32624	−1.06864	−0.534321	−	0.845282i	$-0.679433\pi$
$47$	−7.32624	−1.06864	−0.534321	+	0.845282i	$0.679433\pi$
$48$	4.85410	0.700629
$49$	2.00000	0.285714
$50$	0	0
$51$	0.618034	0.0865421
$52$	3.00000	0.416025
$53$	−2.38197	−0.327188	−0.163594	−	0.986528i	$-0.552309\pi$
$53$	−2.38197	−0.327188	−0.163594	+	0.986528i	$0.552309\pi$
$54$	−1.38197	−0.188062
$55$	0	0
$56$	6.70820	0.896421
$57$	−3.61803	−0.479220
$58$	4.14590	0.544383
$59$	10.8541	1.41308	0.706542	−	0.707671i	$-0.250254\pi$
$59$	10.8541	1.41308	0.706542	+	0.707671i	$0.250254\pi$
$60$	0	0
$61$	5.09017	0.651729	0.325865	−	0.945416i	$-0.394345\pi$
$61$	5.09017	0.651729	0.325865	+	0.945416i	$0.394345\pi$
$62$	3.76393	0.478020
$63$	11.5623	1.45671
$64$	−0.236068	−0.0295085
$65$	0	0
$66$	4.85410	0.597499
$67$	7.14590	0.873010	0.436505	−	0.899702i	$-0.356216\pi$
$67$	7.14590	0.873010	0.436505	+	0.899702i	$0.356216\pi$
$68$	−0.381966	−0.0463202
$69$	−8.47214	−1.01993
$70$	0	0
$71$	−3.00000	−0.356034	−0.178017	−	0.984027i	$-0.556968\pi$
$71$	−3.00000	−0.356034	−0.178017	+	0.984027i	$0.556968\pi$
$72$	8.61803	1.01565
$73$	4.85410	0.568130	0.284065	−	0.958805i	$-0.408317\pi$
$73$	4.85410	0.568130	0.284065	+	0.958805i	$0.408317\pi$
$74$	−6.00000	−0.697486
$75$	0	0
$76$	2.23607	0.256495
$77$	−9.00000	−1.02565
$78$	3.00000	0.339683
$79$	9.47214	1.06570	0.532849	−	0.846210i	$-0.321121\pi$
$79$	9.47214	1.06570	0.532849	+	0.846210i	$0.321121\pi$
$80$	0	0
$81$	−5.70820	−0.634245
$82$	1.85410	0.204751
$83$	8.47214	0.929938	0.464969	−	0.885327i	$-0.346066\pi$
$83$	8.47214	0.929938	0.464969	+	0.885327i	$0.346066\pi$
$84$	−12.7082	−1.38658
$85$	0	0
$86$	−5.56231	−0.599799
$87$	−17.5623	−1.88288
$88$	−6.70820	−0.715097
$89$	13.4164	1.42214	0.711068	−	0.703123i	$-0.248212\pi$
$89$	13.4164	1.42214	0.711068	+	0.703123i	$0.248212\pi$
$90$	0	0
$91$	−5.56231	−0.583088
$92$	5.23607	0.545898
$93$	−15.9443	−1.65334
$94$	4.52786	0.467014
$95$	0	0
$96$	−14.7082	−1.50115
$97$	−1.14590	−0.116348	−0.0581742	−	0.998306i	$-0.518528\pi$
$97$	−1.14590	−0.116348	−0.0581742	+	0.998306i	$0.518528\pi$
$98$	−1.23607	−0.124862
$99$	−11.5623	−1.16206
$100$	0	0
$101$	−3.00000	−0.298511	−0.149256	−	0.988799i	$-0.547688\pi$
$101$	−3.00000	−0.298511	−0.149256	+	0.988799i	$0.547688\pi$
$102$	−0.381966	−0.0378203
$103$	0.708204	0.0697814	0.0348907	−	0.999391i	$-0.488892\pi$
$103$	0.708204	0.0697814	0.0348907	+	0.999391i	$0.488892\pi$
$104$	−4.14590	−0.406539
$105$	0	0
$106$	1.47214	0.142986
$107$	11.0902	1.07213	0.536064	−	0.844178i	$-0.319911\pi$
$107$	11.0902	1.07213	0.536064	+	0.844178i	$0.319911\pi$
$108$	−3.61803	−0.348145
$109$	−10.3262	−0.989074	−0.494537	−	0.869157i	$-0.664662\pi$
$109$	−10.3262	−0.989074	−0.494537	+	0.869157i	$0.664662\pi$
$110$	0	0
$111$	25.4164	2.41242
$112$	5.56231	0.525589
$113$	−19.9443	−1.87620	−0.938100	−	0.346366i	$-0.887416\pi$
$113$	−19.9443	−1.87620	−0.938100	+	0.346366i	$0.887416\pi$
$114$	2.23607	0.209427
$115$	0	0
$116$	10.8541	1.00778
$117$	−7.14590	−0.660639
$118$	−6.70820	−0.617540
$119$	0.708204	0.0649209
$120$	0	0
$121$	−2.00000	−0.181818
$122$	−3.14590	−0.284816
$123$	−7.85410	−0.708181
$124$	9.85410	0.884924
$125$	0	0
$126$	−7.14590	−0.636607
$127$	−3.70820	−0.329050	−0.164525	−	0.986373i	$-0.552609\pi$
$127$	−3.70820	−0.329050	−0.164525	+	0.986373i	$0.552609\pi$
$128$	11.3820	1.00603
$129$	23.5623	2.07455
$130$	0	0
$131$	21.2705	1.85841	0.929207	−	0.369561i	$-0.120492\pi$
$131$	21.2705	1.85841	0.929207	+	0.369561i	$0.120492\pi$
$132$	12.7082	1.10611
$133$	−4.14590	−0.359495
$134$	−4.41641	−0.381520
$135$	0	0
$136$	0.527864	0.0452640
$137$	−3.38197	−0.288941	−0.144470	−	0.989509i	$-0.546148\pi$
$137$	−3.38197	−0.288941	−0.144470	+	0.989509i	$0.546148\pi$
$138$	5.23607	0.445724
$139$	−7.76393	−0.658528	−0.329264	−	0.944238i	$-0.606801\pi$
$139$	−7.76393	−0.658528	−0.329264	+	0.944238i	$0.606801\pi$
$140$	0	0
$141$	−19.1803	−1.61528
$142$	1.85410	0.155593
$143$	5.56231	0.465143
$144$	7.14590	0.595492
$145$	0	0
$146$	−3.00000	−0.248282
$147$	5.23607	0.431864
$148$	−15.7082	−1.29121
$149$	−15.0000	−1.22885	−0.614424	−	0.788976i	$-0.710612\pi$
$149$	−15.0000	−1.22885	−0.614424	+	0.788976i	$0.710612\pi$
$150$	0	0
$151$	−9.90983	−0.806451	−0.403225	−	0.915101i	$-0.632111\pi$
$151$	−9.90983	−0.806451	−0.403225	+	0.915101i	$0.632111\pi$
$152$	−3.09017	−0.250646
$153$	0.909830	0.0735554
$154$	5.56231	0.448223
$155$	0	0
$156$	7.85410	0.628831
$157$	−21.2705	−1.69757	−0.848786	−	0.528737i	$-0.822666\pi$
$157$	−21.2705	−1.69757	−0.848786	+	0.528737i	$0.822666\pi$
$158$	−5.85410	−0.465727
$159$	−6.23607	−0.494552
$160$	0	0
$161$	−9.70820	−0.765114
$162$	3.52786	0.277175
$163$	13.1459	1.02967	0.514833	−	0.857290i	$-0.327854\pi$
$163$	13.1459	1.02967	0.514833	+	0.857290i	$0.327854\pi$
$164$	4.85410	0.379042
$165$	0	0
$166$	−5.23607	−0.406398
$167$	−4.76393	−0.368644	−0.184322	−	0.982866i	$-0.559009\pi$
$167$	−4.76393	−0.368644	−0.184322	+	0.982866i	$0.559009\pi$
$168$	17.5623	1.35496
$169$	−9.56231	−0.735562
$170$	0	0
$171$	−5.32624	−0.407308
$172$	−14.5623	−1.11037
$173$	17.9443	1.36428	0.682139	−	0.731223i	$-0.261050\pi$
$173$	17.9443	1.36428	0.682139	+	0.731223i	$0.261050\pi$
$174$	10.8541	0.822847
$175$	0	0
$176$	−5.56231	−0.419275
$177$	28.4164	2.13591
$178$	−8.29180	−0.621496
$179$	−6.70820	−0.501395	−0.250697	−	0.968066i	$-0.580660\pi$
$179$	−6.70820	−0.501395	−0.250697	+	0.968066i	$0.580660\pi$
$180$	0	0
$181$	−4.18034	−0.310722	−0.155361	−	0.987858i	$-0.549654\pi$
$181$	−4.18034	−0.310722	−0.155361	+	0.987858i	$0.549654\pi$
$182$	3.43769	0.254819
$183$	13.3262	0.985104
$184$	−7.23607	−0.533450
$185$	0	0
$186$	9.85410	0.722538
$187$	−0.708204	−0.0517890
$188$	11.8541	0.864549
$189$	6.70820	0.487950
$190$	0	0
$191$	12.0000	0.868290	0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000	0.868290	0.434145	+	0.900843i	$0.357051\pi$
$192$	−0.618034	−0.0446028
$193$	18.2705	1.31514	0.657570	−	0.753393i	$-0.271584\pi$
$193$	18.2705	1.31514	0.657570	+	0.753393i	$0.271584\pi$
$194$	0.708204	0.0508461
$195$	0	0
$196$	−3.23607	−0.231148
$197$	21.9443	1.56346	0.781732	−	0.623614i	$-0.214336\pi$
$197$	21.9443	1.56346	0.781732	+	0.623614i	$0.214336\pi$
$198$	7.14590	0.507837
$199$	−6.18034	−0.438113	−0.219056	−	0.975712i	$-0.570298\pi$
$199$	−6.18034	−0.438113	−0.219056	+	0.975712i	$0.570298\pi$
$200$	0	0
$201$	18.7082	1.31957
$202$	1.85410	0.130454
$203$	−20.1246	−1.41247
$204$	−1.00000	−0.0700140
$205$	0	0
$206$	−0.437694	−0.0304956
$207$	−12.4721	−0.866873
$208$	−3.43769	−0.238361
$209$	4.14590	0.286778
$210$	0	0
$211$	18.1803	1.25159	0.625793	−	0.779989i	$-0.284775\pi$
$211$	18.1803	1.25159	0.625793	+	0.779989i	$0.284775\pi$
$212$	3.85410	0.264701
$213$	−7.85410	−0.538154
$214$	−6.85410	−0.468537
$215$	0	0
$216$	5.00000	0.340207
$217$	−18.2705	−1.24028
$218$	6.38197	0.432241
$219$	12.7082	0.858741
$220$	0	0
$221$	−0.437694	−0.0294425
$222$	−15.7082	−1.05427
$223$	4.85410	0.325055	0.162527	−	0.986704i	$-0.448035\pi$
$223$	4.85410	0.325055	0.162527	+	0.986704i	$0.448035\pi$
$224$	−16.8541	−1.12611
$225$	0	0
$226$	12.3262	0.819929
$227$	4.38197	0.290841	0.145421	−	0.989370i	$-0.453546\pi$
$227$	4.38197	0.290841	0.145421	+	0.989370i	$0.453546\pi$
$228$	5.85410	0.387697
$229$	−3.61803	−0.239086	−0.119543	−	0.992829i	$-0.538143\pi$
$229$	−3.61803	−0.239086	−0.119543	+	0.992829i	$0.538143\pi$
$230$	0	0
$231$	−23.5623	−1.55029
$232$	−15.0000	−0.984798
$233$	−8.88854	−0.582308	−0.291154	−	0.956676i	$-0.594039\pi$
$233$	−8.88854	−0.582308	−0.291154	+	0.956676i	$0.594039\pi$
$234$	4.41641	0.288710
$235$	0	0
$236$	−17.5623	−1.14321
$237$	24.7984	1.61083
$238$	−0.437694	−0.0283715
$239$	19.1459	1.23845	0.619223	−	0.785215i	$-0.287448\pi$
$239$	19.1459	1.23845	0.619223	+	0.785215i	$0.287448\pi$
$240$	0	0
$241$	3.18034	0.204864	0.102432	−	0.994740i	$-0.467338\pi$
$241$	3.18034	0.204864	0.102432	+	0.994740i	$0.467338\pi$
$242$	1.23607	0.0794575
$243$	−21.6525	−1.38901
$244$	−8.23607	−0.527260
$245$	0	0
$246$	4.85410	0.309486
$247$	2.56231	0.163036
$248$	−13.6180	−0.864746
$249$	22.1803	1.40562
$250$	0	0
$251$	−27.2705	−1.72130	−0.860650	−	0.509198i	$-0.829942\pi$
$251$	−27.2705	−1.72130	−0.860650	+	0.509198i	$0.829942\pi$
$252$	−18.7082	−1.17851
$253$	9.70820	0.610350
$254$	2.29180	0.143800
$255$	0	0
$256$	−6.56231	−0.410144
$257$	15.3607	0.958173	0.479086	−	0.877768i	$-0.340968\pi$
$257$	15.3607	0.958173	0.479086	+	0.877768i	$0.340968\pi$
$258$	−14.5623	−0.906610
$259$	29.1246	1.80972
$260$	0	0
$261$	−25.8541	−1.60033
$262$	−13.1459	−0.812156
$263$	−0.673762	−0.0415459	−0.0207730	−	0.999784i	$-0.506613\pi$
$263$	−0.673762	−0.0415459	−0.0207730	+	0.999784i	$0.506613\pi$
$264$	−17.5623	−1.08089
$265$	0	0
$266$	2.56231	0.157105
$267$	35.1246	2.14959
$268$	−11.5623	−0.706280
$269$	−17.5623	−1.07079	−0.535396	−	0.844601i	$-0.679838\pi$
$269$	−17.5623	−1.07079	−0.535396	+	0.844601i	$0.679838\pi$
$270$	0	0
$271$	8.90983	0.541234	0.270617	−	0.962687i	$-0.412772\pi$
$271$	8.90983	0.541234	0.270617	+	0.962687i	$0.412772\pi$
$272$	0.437694	0.0265391
$273$	−14.5623	−0.881351
$274$	2.09017	0.126272
$275$	0	0
$276$	13.7082	0.825137
$277$	−18.7082	−1.12407	−0.562034	−	0.827114i	$-0.689981\pi$
$277$	−18.7082	−1.12407	−0.562034	+	0.827114i	$0.689981\pi$
$278$	4.79837	0.287787
$279$	−23.4721	−1.40524
$280$	0	0
$281$	12.0000	0.715860	0.357930	−	0.933748i	$-0.383483\pi$
$281$	12.0000	0.715860	0.357930	+	0.933748i	$0.383483\pi$
$282$	11.8541	0.705901
$283$	2.29180	0.136233	0.0681166	−	0.997677i	$-0.478301\pi$
$283$	2.29180	0.136233	0.0681166	+	0.997677i	$0.478301\pi$
$284$	4.85410	0.288038
$285$	0	0
$286$	−3.43769	−0.203275
$287$	−9.00000	−0.531253
$288$	−21.6525	−1.27588
$289$	−16.9443	−0.996722
$290$	0	0
$291$	−3.00000	−0.175863
$292$	−7.85410	−0.459627
$293$	−23.3607	−1.36475	−0.682373	−	0.731004i	$-0.739052\pi$
$293$	−23.3607	−1.36475	−0.682373	+	0.731004i	$0.739052\pi$
$294$	−3.23607	−0.188731
$295$	0	0
$296$	21.7082	1.26176
$297$	−6.70820	−0.389249
$298$	9.27051	0.537026
$299$	6.00000	0.346989
$300$	0	0
$301$	27.0000	1.55625
$302$	6.12461	0.352432
$303$	−7.85410	−0.451206
$304$	−2.56231	−0.146958
$305$	0	0
$306$	−0.562306	−0.0321449
$307$	27.2705	1.55641	0.778205	−	0.628010i	$-0.216130\pi$
$307$	27.2705	1.55641	0.778205	+	0.628010i	$0.216130\pi$
$308$	14.5623	0.829764
$309$	1.85410	0.105476
$310$	0	0
$311$	−12.2705	−0.695797	−0.347898	−	0.937532i	$-0.613105\pi$
$311$	−12.2705	−0.695797	−0.347898	+	0.937532i	$0.613105\pi$
$312$	−10.8541	−0.614493
$313$	7.41641	0.419200	0.209600	−	0.977787i	$-0.432784\pi$
$313$	7.41641	0.419200	0.209600	+	0.977787i	$0.432784\pi$
$314$	13.1459	0.741866
$315$	0	0
$316$	−15.3262	−0.862168
$317$	9.05573	0.508620	0.254310	−	0.967123i	$-0.418152\pi$
$317$	9.05573	0.508620	0.254310	+	0.967123i	$0.418152\pi$
$318$	3.85410	0.216127
$319$	20.1246	1.12676
$320$	0	0
$321$	29.0344	1.62054
$322$	6.00000	0.334367
$323$	−0.326238	−0.0181524
$324$	9.23607	0.513115
$325$	0	0
$326$	−8.12461	−0.449981
$327$	−27.0344	−1.49501
$328$	−6.70820	−0.370399
$329$	−21.9787	−1.21173
$330$	0	0
$331$	−9.90983	−0.544694	−0.272347	−	0.962199i	$-0.587800\pi$
$331$	−9.90983	−0.544694	−0.272347	+	0.962199i	$0.587800\pi$
$332$	−13.7082	−0.752335
$333$	37.4164	2.05041
$334$	2.94427	0.161103
$335$	0	0
$336$	14.5623	0.794439
$337$	−23.8328	−1.29826	−0.649128	−	0.760679i	$-0.724866\pi$
$337$	−23.8328	−1.29826	−0.649128	+	0.760679i	$0.724866\pi$
$338$	5.90983	0.321452
$339$	−52.2148	−2.83592
$340$	0	0
$341$	18.2705	0.989404
$342$	3.29180	0.178000
$343$	−15.0000	−0.809924
$344$	20.1246	1.08505
$345$	0	0
$346$	−11.0902	−0.596211
$347$	1.94427	0.104374	0.0521870	−	0.998637i	$-0.483381\pi$
$347$	1.94427	0.104374	0.0521870	+	0.998637i	$0.483381\pi$
$348$	28.4164	1.52328
$349$	27.3607	1.46458	0.732292	−	0.680991i	$-0.238451\pi$
$349$	27.3607	1.46458	0.732292	+	0.680991i	$0.238451\pi$
$350$	0	0
$351$	−4.14590	−0.221292
$352$	16.8541	0.898327
$353$	31.8885	1.69726	0.848628	−	0.528990i	$-0.177429\pi$
$353$	31.8885	1.69726	0.848628	+	0.528990i	$0.177429\pi$
$354$	−17.5623	−0.933426
$355$	0	0
$356$	−21.7082	−1.15053
$357$	1.85410	0.0981295
$358$	4.14590	0.219118
$359$	−4.14590	−0.218812	−0.109406	−	0.993997i	$-0.534895\pi$
$359$	−4.14590	−0.218812	−0.109406	+	0.993997i	$0.534895\pi$
$360$	0	0
$361$	−17.0902	−0.899483
$362$	2.58359	0.135791
$363$	−5.23607	−0.274822
$364$	9.00000	0.471728
$365$	0	0
$366$	−8.23607	−0.430506
$367$	−7.85410	−0.409981	−0.204990	−	0.978764i	$-0.565716\pi$
$367$	−7.85410	−0.409981	−0.204990	+	0.978764i	$0.565716\pi$
$368$	−6.00000	−0.312772
$369$	−11.5623	−0.601910
$370$	0	0
$371$	−7.14590	−0.370997
$372$	25.7984	1.33758
$373$	4.85410	0.251336	0.125668	−	0.992072i	$-0.459893\pi$
$373$	4.85410	0.251336	0.125668	+	0.992072i	$0.459893\pi$
$374$	0.437694	0.0226326
$375$	0	0
$376$	−16.3820	−0.844835
$377$	12.4377	0.640574
$378$	−4.14590	−0.213242
$379$	12.5623	0.645282	0.322641	−	0.946521i	$-0.395429\pi$
$379$	12.5623	0.645282	0.322641	+	0.946521i	$0.395429\pi$
$380$	0	0
$381$	−9.70820	−0.497366
$382$	−7.41641	−0.379456
$383$	−26.5279	−1.35551	−0.677755	−	0.735288i	$-0.737047\pi$
$383$	−26.5279	−1.35551	−0.677755	+	0.735288i	$0.737047\pi$
$384$	29.7984	1.52064
$385$	0	0
$386$	−11.2918	−0.574737
$387$	34.6869	1.76324
$388$	1.85410	0.0941278
$389$	28.4164	1.44077	0.720385	−	0.693575i	$-0.243965\pi$
$389$	28.4164	1.44077	0.720385	+	0.693575i	$0.243965\pi$
$390$	0	0
$391$	−0.763932	−0.0386337
$392$	4.47214	0.225877
$393$	55.6869	2.80903
$394$	−13.5623	−0.683259
$395$	0	0
$396$	18.7082	0.940123
$397$	−10.4164	−0.522785	−0.261392	−	0.965233i	$-0.584182\pi$
$397$	−10.4164	−0.522785	−0.261392	+	0.965233i	$0.584182\pi$
$398$	3.81966	0.191462
$399$	−10.8541	−0.543385
$400$	0	0
$401$	12.0000	0.599251	0.299626	−	0.954057i	$-0.403138\pi$
$401$	12.0000	0.599251	0.299626	+	0.954057i	$0.403138\pi$
$402$	−11.5623	−0.576675
$403$	11.2918	0.562484
$404$	4.85410	0.241501
$405$	0	0
$406$	12.4377	0.617272
$407$	−29.1246	−1.44365
$408$	1.38197	0.0684175
$409$	−27.2361	−1.34674	−0.673368	−	0.739307i	$-0.735153\pi$
$409$	−27.2361	−1.34674	−0.673368	+	0.739307i	$0.735153\pi$
$410$	0	0
$411$	−8.85410	−0.436741
$412$	−1.14590	−0.0564543
$413$	32.5623	1.60229
$414$	7.70820	0.378838
$415$	0	0
$416$	10.4164	0.510706
$417$	−20.3262	−0.995380
$418$	−2.56231	−0.125326
$419$	6.70820	0.327717	0.163859	−	0.986484i	$-0.447606\pi$
$419$	6.70820	0.327717	0.163859	+	0.986484i	$0.447606\pi$
$420$	0	0
$421$	20.0902	0.979135	0.489567	−	0.871965i	$-0.337155\pi$
$421$	20.0902	0.979135	0.489567	+	0.871965i	$0.337155\pi$
$422$	−11.2361	−0.546963
$423$	−28.2361	−1.37288
$424$	−5.32624	−0.258665
$425$	0	0
$426$	4.85410	0.235182
$427$	15.2705	0.738992
$428$	−17.9443	−0.867369
$429$	14.5623	0.703075
$430$	0	0
$431$	21.2705	1.02456	0.512282	−	0.858817i	$-0.328800\pi$
$431$	21.2705	1.02456	0.512282	+	0.858817i	$0.328800\pi$
$432$	4.14590	0.199470
$433$	−27.7082	−1.33157	−0.665786	−	0.746143i	$-0.731903\pi$
$433$	−27.7082	−1.33157	−0.665786	+	0.746143i	$0.731903\pi$
$434$	11.2918	0.542024
$435$	0	0
$436$	16.7082	0.800178
$437$	4.47214	0.213931
$438$	−7.85410	−0.375284
$439$	−10.1246	−0.483221	−0.241611	−	0.970373i	$-0.577676\pi$
$439$	−10.1246	−0.483221	−0.241611	+	0.970373i	$0.577676\pi$
$440$	0	0
$441$	7.70820	0.367057
$442$	0.270510	0.0128668
$443$	15.1803	0.721240	0.360620	−	0.932713i	$-0.382565\pi$
$443$	15.1803	0.721240	0.360620	+	0.932713i	$0.382565\pi$
$444$	−41.1246	−1.95169
$445$	0	0
$446$	−3.00000	−0.142054
$447$	−39.2705	−1.85743
$448$	−0.708204	−0.0334595
$449$	−5.72949	−0.270391	−0.135196	−	0.990819i	$-0.543166\pi$
$449$	−5.72949	−0.270391	−0.135196	+	0.990819i	$0.543166\pi$
$450$	0	0
$451$	9.00000	0.423793
$452$	32.2705	1.51788
$453$	−25.9443	−1.21897
$454$	−2.70820	−0.127102
$455$	0	0
$456$	−8.09017	−0.378857
$457$	18.0000	0.842004	0.421002	−	0.907060i	$-0.361678\pi$
$457$	18.0000	0.842004	0.421002	+	0.907060i	$0.361678\pi$
$458$	2.23607	0.104485
$459$	0.527864	0.0246386
$460$	0	0
$461$	2.72949	0.127125	0.0635625	−	0.997978i	$-0.479754\pi$
$461$	2.72949	0.127125	0.0635625	+	0.997978i	$0.479754\pi$
$462$	14.5623	0.677500
$463$	−26.1246	−1.21411	−0.607057	−	0.794658i	$-0.707650\pi$
$463$	−26.1246	−1.21411	−0.607057	+	0.794658i	$0.707650\pi$
$464$	−12.4377	−0.577405
$465$	0	0
$466$	5.49342	0.254478
$467$	−34.7639	−1.60868	−0.804341	−	0.594167i	$-0.797482\pi$
$467$	−34.7639	−1.60868	−0.804341	+	0.594167i	$0.797482\pi$
$468$	11.5623	0.534468
$469$	21.4377	0.989901
$470$	0	0
$471$	−55.6869	−2.56592
$472$	24.2705	1.11714
$473$	−27.0000	−1.24146
$474$	−15.3262	−0.703957
$475$	0	0
$476$	−1.14590	−0.0525222
$477$	−9.18034	−0.420339
$478$	−11.8328	−0.541220
$479$	−12.4377	−0.568293	−0.284146	−	0.958781i	$-0.591710\pi$
$479$	−12.4377	−0.568293	−0.284146	+	0.958781i	$0.591710\pi$
$480$	0	0
$481$	−18.0000	−0.820729
$482$	−1.96556	−0.0895287
$483$	−25.4164	−1.15649
$484$	3.23607	0.147094
$485$	0	0
$486$	13.3820	0.607018
$487$	9.70820	0.439921	0.219960	−	0.975509i	$-0.429407\pi$
$487$	9.70820	0.439921	0.219960	+	0.975509i	$0.429407\pi$
$488$	11.3820	0.515237
$489$	34.4164	1.55636
$490$	0	0
$491$	2.72949	0.123180	0.0615901	−	0.998102i	$-0.480383\pi$
$491$	2.72949	0.123180	0.0615901	+	0.998102i	$0.480383\pi$
$492$	12.7082	0.572930
$493$	−1.58359	−0.0713214
$494$	−1.58359	−0.0712492
$495$	0	0
$496$	−11.2918	−0.507017
$497$	−9.00000	−0.403705
$498$	−13.7082	−0.614279
$499$	−2.36068	−0.105679	−0.0528393	−	0.998603i	$-0.516827\pi$
$499$	−2.36068	−0.105679	−0.0528393	+	0.998603i	$0.516827\pi$
$500$	0	0
$501$	−12.4721	−0.557214
$502$	16.8541	0.752235
$503$	−1.20163	−0.0535779	−0.0267889	−	0.999641i	$-0.508528\pi$
$503$	−1.20163	−0.0535779	−0.0267889	+	0.999641i	$0.508528\pi$
$504$	25.8541	1.15163
$505$	0	0
$506$	−6.00000	−0.266733
$507$	−25.0344	−1.11182
$508$	6.00000	0.266207
$509$	−13.4164	−0.594672	−0.297336	−	0.954773i	$-0.596098\pi$
$509$	−13.4164	−0.594672	−0.297336	+	0.954773i	$0.596098\pi$
$510$	0	0
$511$	14.5623	0.644198
$512$	−18.7082	−0.826794
$513$	−3.09017	−0.136434
$514$	−9.49342	−0.418737
$515$	0	0
$516$	−38.1246	−1.67834
$517$	21.9787	0.966623
$518$	−18.0000	−0.790875
$519$	46.9787	2.06214
$520$	0	0
$521$	−27.2705	−1.19474	−0.597371	−	0.801965i	$-0.703788\pi$
$521$	−27.2705	−1.19474	−0.597371	+	0.801965i	$0.703788\pi$
$522$	15.9787	0.699369
$523$	10.5836	0.462788	0.231394	−	0.972860i	$-0.425671\pi$
$523$	10.5836	0.462788	0.231394	+	0.972860i	$0.425671\pi$
$524$	−34.4164	−1.50349
$525$	0	0
$526$	0.416408	0.0181562
$527$	−1.43769	−0.0626269
$528$	−14.5623	−0.633743
$529$	−12.5279	−0.544690
$530$	0	0
$531$	41.8328	1.81539
$532$	6.70820	0.290838
$533$	5.56231	0.240930
$534$	−21.7082	−0.939406
$535$	0	0
$536$	15.9787	0.690175
$537$	−17.5623	−0.757869
$538$	10.8541	0.467954
$539$	−6.00000	−0.258438
$540$	0	0
$541$	−11.8197	−0.508167	−0.254083	−	0.967182i	$-0.581774\pi$
$541$	−11.8197	−0.508167	−0.254083	+	0.967182i	$0.581774\pi$
$542$	−5.50658	−0.236528
$543$	−10.9443	−0.469664
$544$	−1.32624	−0.0568620
$545$	0	0
$546$	9.00000	0.385164
$547$	28.8541	1.23371	0.616856	−	0.787076i	$-0.288406\pi$
$547$	28.8541	1.23371	0.616856	+	0.787076i	$0.288406\pi$
$548$	5.47214	0.233758
$549$	19.6180	0.837277
$550$	0	0
$551$	9.27051	0.394937
$552$	−18.9443	−0.806322
$553$	28.4164	1.20839
$554$	11.5623	0.491235
$555$	0	0
$556$	12.5623	0.532760
$557$	−4.36068	−0.184768	−0.0923840	−	0.995723i	$-0.529449\pi$
$557$	−4.36068	−0.184768	−0.0923840	+	0.995723i	$0.529449\pi$
$558$	14.5066	0.614112
$559$	−16.6869	−0.705781
$560$	0	0
$561$	−1.85410	−0.0782802
$562$	−7.41641	−0.312842
$563$	−24.9443	−1.05128	−0.525638	−	0.850708i	$-0.676173\pi$
$563$	−24.9443	−1.05128	−0.525638	+	0.850708i	$0.676173\pi$
$564$	31.0344	1.30679
$565$	0	0
$566$	−1.41641	−0.0595361
$567$	−17.1246	−0.719166
$568$	−6.70820	−0.281470
$569$	−26.8328	−1.12489	−0.562445	−	0.826835i	$-0.690139\pi$
$569$	−26.8328	−1.12489	−0.562445	+	0.826835i	$0.690139\pi$
$570$	0	0
$571$	−13.0000	−0.544033	−0.272017	−	0.962293i	$-0.587691\pi$
$571$	−13.0000	−0.544033	−0.272017	+	0.962293i	$0.587691\pi$
$572$	−9.00000	−0.376309
$573$	31.4164	1.31244
$574$	5.56231	0.232166
$575$	0	0
$576$	−0.909830	−0.0379096
$577$	−9.43769	−0.392896	−0.196448	−	0.980514i	$-0.562941\pi$
$577$	−9.43769	−0.392896	−0.196448	+	0.980514i	$0.562941\pi$
$578$	10.4721	0.435583
$579$	47.8328	1.98786
$580$	0	0
$581$	25.4164	1.05445
$582$	1.85410	0.0768550
$583$	7.14590	0.295953
$584$	10.8541	0.449146
$585$	0	0
$586$	14.4377	0.596416
$587$	−6.47214	−0.267134	−0.133567	−	0.991040i	$-0.542643\pi$
$587$	−6.47214	−0.267134	−0.133567	+	0.991040i	$0.542643\pi$
$588$	−8.47214	−0.349385
$589$	8.41641	0.346792
$590$	0	0
$591$	57.4508	2.36321
$592$	18.0000	0.739795
$593$	−3.36068	−0.138007	−0.0690033	−	0.997616i	$-0.521982\pi$
$593$	−3.36068	−0.138007	−0.0690033	+	0.997616i	$0.521982\pi$
$594$	4.14590	0.170108
$595$	0	0
$596$	24.2705	0.994159
$597$	−16.1803	−0.662217
$598$	−3.70820	−0.151640
$599$	9.27051	0.378783	0.189391	−	0.981902i	$-0.439349\pi$
$599$	9.27051	0.378783	0.189391	+	0.981902i	$0.439349\pi$
$600$	0	0
$601$	−45.3607	−1.85030	−0.925150	−	0.379601i	$-0.876061\pi$
$601$	−45.3607	−1.85030	−0.925150	+	0.379601i	$0.876061\pi$
$602$	−16.6869	−0.680108
$603$	27.5410	1.12156
$604$	16.0344	0.652432
$605$	0	0
$606$	4.85410	0.197184
$607$	36.5410	1.48315	0.741577	−	0.670868i	$-0.234078\pi$
$607$	36.5410	1.48315	0.741577	+	0.670868i	$0.234078\pi$
$608$	7.76393	0.314869
$609$	−52.6869	−2.13498
$610$	0	0
$611$	13.5836	0.549533
$612$	−1.47214	−0.0595076
$613$	22.4164	0.905390	0.452695	−	0.891665i	$-0.350463\pi$
$613$	22.4164	0.905390	0.452695	+	0.891665i	$0.350463\pi$
$614$	−16.8541	−0.680176
$615$	0	0
$616$	−20.1246	−0.810844
$617$	30.2361	1.21726	0.608629	−	0.793455i	$-0.291720\pi$
$617$	30.2361	1.21726	0.608629	+	0.793455i	$0.291720\pi$
$618$	−1.14590	−0.0460948
$619$	−29.4721	−1.18459	−0.592293	−	0.805723i	$-0.701777\pi$
$619$	−29.4721	−1.18459	−0.592293	+	0.805723i	$0.701777\pi$
$620$	0	0
$621$	−7.23607	−0.290373
$622$	7.58359	0.304074
$623$	40.2492	1.61255
$624$	−9.00000	−0.360288
$625$	0	0
$626$	−4.58359	−0.183197
$627$	10.8541	0.433471
$628$	34.4164	1.37336
$629$	2.29180	0.0913799
$630$	0	0
$631$	2.00000	0.0796187	0.0398094	−	0.999207i	$-0.487325\pi$
$631$	2.00000	0.0796187	0.0398094	+	0.999207i	$0.487325\pi$
$632$	21.1803	0.842509
$633$	47.5967	1.89180
$634$	−5.59675	−0.222275
$635$	0	0
$636$	10.0902	0.400101
$637$	−3.70820	−0.146924
$638$	−12.4377	−0.492413
$639$	−11.5623	−0.457398
$640$	0	0
$641$	−42.2705	−1.66958	−0.834792	−	0.550565i	$-0.814412\pi$
$641$	−42.2705	−1.66958	−0.834792	+	0.550565i	$0.814412\pi$
$642$	−17.9443	−0.708204
$643$	−15.2705	−0.602210	−0.301105	−	0.953591i	$-0.597355\pi$
$643$	−15.2705	−0.602210	−0.301105	+	0.953591i	$0.597355\pi$
$644$	15.7082	0.618990
$645$	0	0
$646$	0.201626	0.00793287
$647$	15.7639	0.619744	0.309872	−	0.950778i	$-0.399714\pi$
$647$	15.7639	0.619744	0.309872	+	0.950778i	$0.399714\pi$
$648$	−12.7639	−0.501415
$649$	−32.5623	−1.27818
$650$	0	0
$651$	−47.8328	−1.87472
$652$	−21.2705	−0.833017
$653$	−26.6525	−1.04299	−0.521496	−	0.853254i	$-0.674626\pi$
$653$	−26.6525	−1.04299	−0.521496	+	0.853254i	$0.674626\pi$
$654$	16.7082	0.653342
$655$	0	0
$656$	−5.56231	−0.217172
$657$	18.7082	0.729877
$658$	13.5836	0.529544
$659$	−19.1459	−0.745818	−0.372909	−	0.927868i	$-0.621640\pi$
$659$	−19.1459	−0.745818	−0.372909	+	0.927868i	$0.621640\pi$
$660$	0	0
$661$	−30.3607	−1.18089	−0.590447	−	0.807077i	$-0.701048\pi$
$661$	−30.3607	−1.18089	−0.590447	+	0.807077i	$0.701048\pi$
$662$	6.12461	0.238040
$663$	−1.14590	−0.0445030
$664$	18.9443	0.735180
$665$	0	0
$666$	−23.1246	−0.896061
$667$	21.7082	0.840545
$668$	7.70820	0.298239
$669$	12.7082	0.491328
$670$	0	0
$671$	−15.2705	−0.589511
$672$	−44.1246	−1.70214
$673$	−28.6869	−1.10580	−0.552900	−	0.833248i	$-0.686479\pi$
$673$	−28.6869	−1.10580	−0.552900	+	0.833248i	$0.686479\pi$
$674$	14.7295	0.567359
$675$	0	0
$676$	15.4721	0.595082
$677$	−39.8885	−1.53304	−0.766521	−	0.642220i	$-0.778014\pi$
$677$	−39.8885	−1.53304	−0.766521	+	0.642220i	$0.778014\pi$
$678$	32.2705	1.23934
$679$	−3.43769	−0.131927
$680$	0	0
$681$	11.4721	0.439613
$682$	−11.2918	−0.432385
$683$	−15.0689	−0.576595	−0.288297	−	0.957541i	$-0.593089\pi$
$683$	−15.0689	−0.576595	−0.288297	+	0.957541i	$0.593089\pi$
$684$	8.61803	0.329519
$685$	0	0
$686$	9.27051	0.353950
$687$	−9.47214	−0.361385
$688$	16.6869	0.636183
$689$	4.41641	0.168252
$690$	0	0
$691$	48.1803	1.83287	0.916433	−	0.400188i	$-0.131055\pi$
$691$	48.1803	1.83287	0.916433	+	0.400188i	$0.131055\pi$
$692$	−29.0344	−1.10372
$693$	−34.6869	−1.31765
$694$	−1.20163	−0.0456131
$695$	0	0
$696$	−39.2705	−1.48854
$697$	−0.708204	−0.0268251
$698$	−16.9098	−0.640047
$699$	−23.2705	−0.880172
$700$	0	0
$701$	36.2705	1.36992	0.684959	−	0.728581i	$-0.259820\pi$
$701$	36.2705	1.36992	0.684959	+	0.728581i	$0.259820\pi$
$702$	2.56231	0.0967080
$703$	−13.4164	−0.506009
$704$	0.708204	0.0266914
$705$	0	0
$706$	−19.7082	−0.741728
$707$	−9.00000	−0.338480
$708$	−45.9787	−1.72799
$709$	12.0344	0.451963	0.225981	−	0.974132i	$-0.427441\pi$
$709$	12.0344	0.451963	0.225981	+	0.974132i	$0.427441\pi$
$710$	0	0
$711$	36.5066	1.36910
$712$	30.0000	1.12430
$713$	19.7082	0.738078
$714$	−1.14590	−0.0428842
$715$	0	0
$716$	10.8541	0.405637
$717$	50.1246	1.87194
$718$	2.56231	0.0956244
$719$	27.4377	1.02325	0.511627	−	0.859208i	$-0.329043\pi$
$719$	27.4377	1.02325	0.511627	+	0.859208i	$0.329043\pi$
$720$	0	0
$721$	2.12461	0.0791247
$722$	10.5623	0.393088
$723$	8.32624	0.309656
$724$	6.76393	0.251380
$725$	0	0
$726$	3.23607	0.120102
$727$	14.8328	0.550119	0.275059	−	0.961427i	$-0.411302\pi$
$727$	14.8328	0.550119	0.275059	+	0.961427i	$0.411302\pi$
$728$	−12.4377	−0.460972
$729$	−39.5623	−1.46527
$730$	0	0
$731$	2.12461	0.0785816
$732$	−21.5623	−0.796966
$733$	−3.43769	−0.126974	−0.0634871	−	0.997983i	$-0.520222\pi$
$733$	−3.43769	−0.126974	−0.0634871	+	0.997983i	$0.520222\pi$
$734$	4.85410	0.179168
$735$	0	0
$736$	18.1803	0.670136
$737$	−21.4377	−0.789668
$738$	7.14590	0.263044
$739$	22.2361	0.817967	0.408983	−	0.912542i	$-0.365883\pi$
$739$	22.2361	0.817967	0.408983	+	0.912542i	$0.365883\pi$
$740$	0	0
$741$	6.70820	0.246432
$742$	4.41641	0.162131
$743$	37.0902	1.36071	0.680353	−	0.732884i	$-0.261826\pi$
$743$	37.0902	1.36071	0.680353	+	0.732884i	$0.261826\pi$
$744$	−35.6525	−1.30708
$745$	0	0
$746$	−3.00000	−0.109838
$747$	32.6525	1.19469
$748$	1.14590	0.0418982
$749$	33.2705	1.21568
$750$	0	0
$751$	29.3607	1.07139	0.535693	−	0.844413i	$-0.320050\pi$
$751$	29.3607	1.07139	0.535693	+	0.844413i	$0.320050\pi$
$752$	−13.5836	−0.495343
$753$	−71.3951	−2.60178
$754$	−7.68692	−0.279941
$755$	0	0
$756$	−10.8541	−0.394760
$757$	−27.0000	−0.981332	−0.490666	−	0.871348i	$-0.663246\pi$
$757$	−27.0000	−0.981332	−0.490666	+	0.871348i	$0.663246\pi$
$758$	−7.76393	−0.281999
$759$	25.4164	0.922557
$760$	0	0
$761$	−18.0000	−0.652499	−0.326250	−	0.945284i	$-0.605785\pi$
$761$	−18.0000	−0.652499	−0.326250	+	0.945284i	$0.605785\pi$
$762$	6.00000	0.217357
$763$	−30.9787	−1.12150
$764$	−19.4164	−0.702461
$765$	0	0
$766$	16.3951	0.592380
$767$	−20.1246	−0.726658
$768$	−17.1803	−0.619942
$769$	22.8885	0.825382	0.412691	−	0.910871i	$-0.364589\pi$
$769$	22.8885	0.825382	0.412691	+	0.910871i	$0.364589\pi$
$770$	0	0
$771$	40.2148	1.44830
$772$	−29.5623	−1.06397
$773$	16.7639	0.602957	0.301478	−	0.953473i	$-0.402520\pi$
$773$	16.7639	0.602957	0.301478	+	0.953473i	$0.402520\pi$
$774$	−21.4377	−0.770562
$775$	0	0
$776$	−2.56231	−0.0919814
$777$	76.2492	2.73543
$778$	−17.5623	−0.629639
$779$	4.14590	0.148542
$780$	0	0
$781$	9.00000	0.322045
$782$	0.472136	0.0168835
$783$	−15.0000	−0.536056
$784$	3.70820	0.132436
$785$	0	0
$786$	−34.4164	−1.22759
$787$	24.7082	0.880752	0.440376	−	0.897813i	$-0.354845\pi$
$787$	24.7082	0.880752	0.440376	+	0.897813i	$0.354845\pi$
$788$	−35.5066	−1.26487
$789$	−1.76393	−0.0627976
$790$	0	0
$791$	−59.8328	−2.12741
$792$	−25.8541	−0.918686
$793$	−9.43769	−0.335142
$794$	6.43769	0.228465
$795$	0	0
$796$	10.0000	0.354441
$797$	16.2148	0.574357	0.287179	−	0.957877i	$-0.407283\pi$
$797$	16.2148	0.574357	0.287179	+	0.957877i	$0.407283\pi$
$798$	6.70820	0.237468
$799$	−1.72949	−0.0611850
$800$	0	0
$801$	51.7082	1.82702
$802$	−7.41641	−0.261882
$803$	−14.5623	−0.513893
$804$	−30.2705	−1.06756
$805$	0	0
$806$	−6.97871	−0.245815
$807$	−45.9787	−1.61853
$808$	−6.70820	−0.235994
$809$	35.1246	1.23492	0.617458	−	0.786604i	$-0.288163\pi$
$809$	35.1246	1.23492	0.617458	+	0.786604i	$0.288163\pi$
$810$	0	0
$811$	−34.1803	−1.20023	−0.600117	−	0.799912i	$-0.704879\pi$
$811$	−34.1803	−1.20023	−0.600117	+	0.799912i	$0.704879\pi$
$812$	32.5623	1.14271
$813$	23.3262	0.818087
$814$	18.0000	0.630900
$815$	0	0
$816$	1.14590	0.0401145
$817$	−12.4377	−0.435140
$818$	16.8328	0.588546
$819$	−21.4377	−0.749094
$820$	0	0
$821$	−12.2705	−0.428244	−0.214122	−	0.976807i	$-0.568689\pi$
$821$	−12.2705	−0.428244	−0.214122	+	0.976807i	$0.568689\pi$
$822$	5.47214	0.190863
$823$	−4.41641	−0.153946	−0.0769732	−	0.997033i	$-0.524526\pi$
$823$	−4.41641	−0.153946	−0.0769732	+	0.997033i	$0.524526\pi$
$824$	1.58359	0.0551670
$825$	0	0
$826$	−20.1246	−0.700225
$827$	29.3820	1.02171	0.510856	−	0.859667i	$-0.329329\pi$
$827$	29.3820	1.02171	0.510856	+	0.859667i	$0.329329\pi$
$828$	20.1803	0.701315
$829$	48.7426	1.69290	0.846451	−	0.532467i	$-0.178735\pi$
$829$	48.7426	1.69290	0.846451	+	0.532467i	$0.178735\pi$
$830$	0	0
$831$	−48.9787	−1.69905
$832$	0.437694	0.0151743
$833$	0.472136	0.0163585
$834$	12.5623	0.434997
$835$	0	0
$836$	−6.70820	−0.232008
$837$	−13.6180	−0.470708
$838$	−4.14590	−0.143218
$839$	−44.3951	−1.53269	−0.766345	−	0.642429i	$-0.777927\pi$
$839$	−44.3951	−1.53269	−0.766345	+	0.642429i	$0.777927\pi$
$840$	0	0
$841$	16.0000	0.551724
$842$	−12.4164	−0.427898
$843$	31.4164	1.08204
$844$	−29.4164	−1.01255
$845$	0	0
$846$	17.4508	0.599973
$847$	−6.00000	−0.206162
$848$	−4.41641	−0.151660
$849$	6.00000	0.205919
$850$	0	0
$851$	−31.4164	−1.07694
$852$	12.7082	0.435376
$853$	−47.8328	−1.63776	−0.818882	−	0.573962i	$-0.805406\pi$
$853$	−47.8328	−1.63776	−0.818882	+	0.573962i	$0.805406\pi$
$854$	−9.43769	−0.322951
$855$	0	0
$856$	24.7984	0.847591
$857$	11.8197	0.403752	0.201876	−	0.979411i	$-0.435296\pi$
$857$	11.8197	0.403752	0.201876	+	0.979411i	$0.435296\pi$
$858$	−9.00000	−0.307255
$859$	15.1246	0.516045	0.258023	−	0.966139i	$-0.416929\pi$
$859$	15.1246	0.516045	0.258023	+	0.966139i	$0.416929\pi$
$860$	0	0
$861$	−23.5623	−0.803001
$862$	−13.1459	−0.447751
$863$	11.2361	0.382480	0.191240	−	0.981543i	$-0.438749\pi$
$863$	11.2361	0.382480	0.191240	+	0.981543i	$0.438749\pi$
$864$	−12.5623	−0.427378
$865$	0	0
$866$	17.1246	0.581918
$867$	−44.3607	−1.50657
$868$	29.5623	1.00341
$869$	−28.4164	−0.963961
$870$	0	0
$871$	−13.2492	−0.448933
$872$	−23.0902	−0.781932
$873$	−4.41641	−0.149473
$874$	−2.76393	−0.0934914
$875$	0	0
$876$	−20.5623	−0.694736
$877$	−27.9787	−0.944774	−0.472387	−	0.881391i	$-0.656608\pi$
$877$	−27.9787	−0.944774	−0.472387	+	0.881391i	$0.656608\pi$
$878$	6.25735	0.211175
$879$	−61.1591	−2.06284
$880$	0	0
$881$	−21.5410	−0.725735	−0.362868	−	0.931841i	$-0.618202\pi$
$881$	−21.5410	−0.725735	−0.362868	+	0.931841i	$0.618202\pi$
$882$	−4.76393	−0.160410
$883$	35.8328	1.20587	0.602935	−	0.797790i	$-0.293998\pi$
$883$	35.8328	1.20587	0.602935	+	0.797790i	$0.293998\pi$
$884$	0.708204	0.0238195
$885$	0	0
$886$	−9.38197	−0.315193
$887$	33.5279	1.12576	0.562878	−	0.826540i	$-0.309694\pi$
$887$	33.5279	1.12576	0.562878	+	0.826540i	$0.309694\pi$
$888$	56.8328	1.90718
$889$	−11.1246	−0.373108
$890$	0	0
$891$	17.1246	0.573696
$892$	−7.85410	−0.262975
$893$	10.1246	0.338807
$894$	24.2705	0.811727
$895$	0	0
$896$	34.1459	1.14073
$897$	15.7082	0.524482
$898$	3.54102	0.118165
$899$	40.8541	1.36256
$900$	0	0
$901$	−0.562306	−0.0187331
$902$	−5.56231	−0.185205
$903$	70.6869	2.35231
$904$	−44.5967	−1.48327
$905$	0	0
$906$	16.0344	0.532709
$907$	8.72949	0.289858	0.144929	−	0.989442i	$-0.453705\pi$
$907$	8.72949	0.289858	0.144929	+	0.989442i	$0.453705\pi$
$908$	−7.09017	−0.235296
$909$	−11.5623	−0.383497
$910$	0	0
$911$	30.5410	1.01187	0.505935	−	0.862572i	$-0.331148\pi$
$911$	30.5410	1.01187	0.505935	+	0.862572i	$0.331148\pi$
$912$	−6.70820	−0.222131
$913$	−25.4164	−0.841160
$914$	−11.1246	−0.367969
$915$	0	0
$916$	5.85410	0.193425
$917$	63.8115	2.10724
$918$	−0.326238	−0.0107675
$919$	34.0689	1.12383	0.561914	−	0.827195i	$-0.310065\pi$
$919$	34.0689	1.12383	0.561914	+	0.827195i	$0.310065\pi$
$920$	0	0
$921$	71.3951	2.35255
$922$	−1.68692	−0.0555557
$923$	5.56231	0.183086
$924$	38.1246	1.25421
$925$	0	0
$926$	16.1459	0.530587
$927$	2.72949	0.0896482
$928$	37.6869	1.23713
$929$	23.2918	0.764179	0.382090	−	0.924125i	$-0.375205\pi$
$929$	23.2918	0.764179	0.382090	+	0.924125i	$0.375205\pi$
$930$	0	0
$931$	−2.76393	−0.0905842
$932$	14.3820	0.471097
$933$	−32.1246	−1.05171
$934$	21.4853	0.703020
$935$	0	0
$936$	−15.9787	−0.522281
$937$	−29.5623	−0.965758	−0.482879	−	0.875687i	$-0.660409\pi$
$937$	−29.5623	−0.965758	−0.482879	+	0.875687i	$0.660409\pi$
$938$	−13.2492	−0.432602
$939$	19.4164	0.633631
$940$	0	0
$941$	6.27051	0.204413	0.102206	−	0.994763i	$-0.467410\pi$
$941$	6.27051	0.204413	0.102206	+	0.994763i	$0.467410\pi$
$942$	34.4164	1.12135
$943$	9.70820	0.316143
$944$	20.1246	0.655000
$945$	0	0
$946$	16.6869	0.542538
$947$	−26.5967	−0.864278	−0.432139	−	0.901807i	$-0.642241\pi$
$947$	−26.5967	−0.864278	−0.432139	+	0.901807i	$0.642241\pi$
$948$	−40.1246	−1.30319
$949$	−9.00000	−0.292152
$950$	0	0
$951$	23.7082	0.768791
$952$	1.58359	0.0513245
$953$	56.1591	1.81917	0.909585	−	0.415518i	$-0.136400\pi$
$953$	56.1591	1.81917	0.909585	+	0.415518i	$0.136400\pi$
$954$	5.67376	0.183695
$955$	0	0
$956$	−30.9787	−1.00192
$957$	52.6869	1.70313
$958$	7.68692	0.248353
$959$	−10.1459	−0.327628
$960$	0	0
$961$	6.09017	0.196457
$962$	11.1246	0.358672
$963$	42.7426	1.37736
$964$	−5.14590	−0.165738
$965$	0	0
$966$	15.7082	0.505403
$967$	−22.8541	−0.734938	−0.367469	−	0.930036i	$-0.619776\pi$
$967$	−22.8541	−0.734938	−0.367469	+	0.930036i	$0.619776\pi$
$968$	−4.47214	−0.143740
$969$	−0.854102	−0.0274377
$970$	0	0
$971$	15.5410	0.498735	0.249368	−	0.968409i	$-0.419777\pi$
$971$	15.5410	0.498735	0.249368	+	0.968409i	$0.419777\pi$
$972$	35.0344	1.12373
$973$	−23.2918	−0.746701
$974$	−6.00000	−0.192252
$975$	0	0
$976$	9.43769	0.302093
$977$	−25.6180	−0.819594	−0.409797	−	0.912177i	$-0.634400\pi$
$977$	−25.6180	−0.819594	−0.409797	+	0.912177i	$0.634400\pi$
$978$	−21.2705	−0.680156
$979$	−40.2492	−1.28637
$980$	0	0
$981$	−39.7984	−1.27066
$982$	−1.68692	−0.0538317
$983$	47.7426	1.52275	0.761377	−	0.648309i	$-0.224524\pi$
$983$	47.7426	1.52275	0.761377	+	0.648309i	$0.224524\pi$
$984$	−17.5623	−0.559866
$985$	0	0
$986$	0.978714	0.0311686
$987$	−57.5410	−1.83155
$988$	−4.14590	−0.131899
$989$	−29.1246	−0.926109
$990$	0	0
$991$	−49.1803	−1.56226	−0.781132	−	0.624365i	$-0.785358\pi$
$991$	−49.1803	−1.56226	−0.781132	+	0.624365i	$0.785358\pi$
$992$	34.2148	1.08632
$993$	−25.9443	−0.823317
$994$	5.56231	0.176426
$995$	0	0
$996$	−35.8885	−1.13717
$997$	−46.1459	−1.46146	−0.730728	−	0.682669i	$-0.760819\pi$
$997$	−46.1459	−1.46146	−0.730728	+	0.682669i	$0.760819\pi$
$998$	1.45898	0.0461832
$999$	21.7082	0.686817

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	125.2.a.b.1.1	yes	2
3.2	odd	2		1125.2.a.c.1.2		2
4.3	odd	2		2000.2.a.a.1.1		2
5.2	odd	4		125.2.b.b.124.2		4
5.3	odd	4		125.2.b.b.124.3		4
5.4	even	2		125.2.a.a.1.2	✓	2
7.6	odd	2		6125.2.a.g.1.1		2
8.3	odd	2		8000.2.a.u.1.2		2
8.5	even	2		8000.2.a.d.1.1		2
15.2	even	4		1125.2.b.f.874.3		4
15.8	even	4		1125.2.b.f.874.2		4
15.14	odd	2		1125.2.a.d.1.1		2
20.3	even	4		2000.2.c.e.1249.1		4
20.7	even	4		2000.2.c.e.1249.4		4
20.19	odd	2		2000.2.a.l.1.2		2
25.2	odd	20		625.2.e.d.124.1		8
25.3	odd	20		625.2.e.g.249.2		8
25.4	even	10		625.2.d.d.376.1		4
25.6	even	5		625.2.d.g.251.1		4
25.8	odd	20		625.2.e.g.374.1		8
25.9	even	10		625.2.d.j.126.1		4
25.11	even	5		625.2.d.a.501.1		4
25.12	odd	20		625.2.e.d.499.2		8
25.13	odd	20		625.2.e.d.499.1		8
25.14	even	10		625.2.d.j.501.1		4
25.16	even	5		625.2.d.a.126.1		4
25.17	odd	20		625.2.e.g.374.2		8
25.19	even	10		625.2.d.d.251.1		4
25.21	even	5		625.2.d.g.376.1		4
25.22	odd	20		625.2.e.g.249.1		8
25.23	odd	20		625.2.e.d.124.2		8
35.34	odd	2		6125.2.a.d.1.2		2
40.19	odd	2		8000.2.a.c.1.1		2
40.29	even	2		8000.2.a.v.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
125.2.a.a.1.2	✓	2	5.4	even	2
125.2.a.b.1.1	yes	2	1.1	even	1	trivial
125.2.b.b.124.2		4	5.2	odd	4
125.2.b.b.124.3		4	5.3	odd	4
625.2.d.a.126.1		4	25.16	even	5
625.2.d.a.501.1		4	25.11	even	5
625.2.d.d.251.1		4	25.19	even	10
625.2.d.d.376.1		4	25.4	even	10
625.2.d.g.251.1		4	25.6	even	5
625.2.d.g.376.1		4	25.21	even	5
625.2.d.j.126.1		4	25.9	even	10
625.2.d.j.501.1		4	25.14	even	10
625.2.e.d.124.1		8	25.2	odd	20
625.2.e.d.124.2		8	25.23	odd	20
625.2.e.d.499.1		8	25.13	odd	20
625.2.e.d.499.2		8	25.12	odd	20
625.2.e.g.249.1		8	25.22	odd	20
625.2.e.g.249.2		8	25.3	odd	20
625.2.e.g.374.1		8	25.8	odd	20
625.2.e.g.374.2		8	25.17	odd	20
1125.2.a.c.1.2		2	3.2	odd	2
1125.2.a.d.1.1		2	15.14	odd	2
1125.2.b.f.874.2		4	15.8	even	4
1125.2.b.f.874.3		4	15.2	even	4
2000.2.a.a.1.1		2	4.3	odd	2
2000.2.a.l.1.2		2	20.19	odd	2
2000.2.c.e.1249.1		4	20.3	even	4
2000.2.c.e.1249.4		4	20.7	even	4
6125.2.a.d.1.2		2	35.34	odd	2
6125.2.a.g.1.1		2	7.6	odd	2
8000.2.a.c.1.1		2	40.19	odd	2
8000.2.a.d.1.1		2	8.5	even	2
8000.2.a.u.1.2		2	8.3	odd	2
8000.2.a.v.1.2		2	40.29	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:	\( N \)	\(=\)	\( 125 = 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	125.a (trivial)

\(f(q)\)	\(=\)	\(q-0.618034 q^{2} +2.61803 q^{3} -1.61803 q^{4} -1.61803 q^{6} +3.00000 q^{7} +2.23607 q^{8} +3.85410 q^{9} +O(q^{10})\)	\(q-0.618034 q^{2} +2.61803 q^{3} -1.61803 q^{4} -1.61803 q^{6} +3.00000 q^{7} +2.23607 q^{8} +3.85410 q^{9} -3.00000 q^{11} -4.23607 q^{12} -1.85410 q^{13} -1.85410 q^{14} +1.85410 q^{16} +0.236068 q^{17} -2.38197 q^{18} -1.38197 q^{19} +7.85410 q^{21} +1.85410 q^{22} -3.23607 q^{23} +5.85410 q^{24} +1.14590 q^{26} +2.23607 q^{27} -4.85410 q^{28} -6.70820 q^{29} -6.09017 q^{31} -5.61803 q^{32} -7.85410 q^{33} -0.145898 q^{34} -6.23607 q^{36} +9.70820 q^{37} +0.854102 q^{38} -4.85410 q^{39} -3.00000 q^{41} -4.85410 q^{42} +9.00000 q^{43} +4.85410 q^{44} +2.00000 q^{46} -7.32624 q^{47} +4.85410 q^{48} +2.00000 q^{49} +0.618034 q^{51} +3.00000 q^{52} -2.38197 q^{53} -1.38197 q^{54} +6.70820 q^{56} -3.61803 q^{57} +4.14590 q^{58} +10.8541 q^{59} +5.09017 q^{61} +3.76393 q^{62} +11.5623 q^{63} -0.236068 q^{64} +4.85410 q^{66} +7.14590 q^{67} -0.381966 q^{68} -8.47214 q^{69} -3.00000 q^{71} +8.61803 q^{72} +4.85410 q^{73} -6.00000 q^{74} +2.23607 q^{76} -9.00000 q^{77} +3.00000 q^{78} +9.47214 q^{79} -5.70820 q^{81} +1.85410 q^{82} +8.47214 q^{83} -12.7082 q^{84} -5.56231 q^{86} -17.5623 q^{87} -6.70820 q^{88} +13.4164 q^{89} -5.56231 q^{91} +5.23607 q^{92} -15.9443 q^{93} +4.52786 q^{94} -14.7082 q^{96} -1.14590 q^{97} -1.23607 q^{98} -11.5623 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 3 q^{3} - q^{4} - q^{6} + 6 q^{7} + q^{9}+O(q^{10}) \) 2 * q + q^2 + 3 * q^3 - q^4 - q^6 + 6 * q^7 + q^9	\( 2 q + q^{2} + 3 q^{3} - q^{4} - q^{6} + 6 q^{7} + q^{9} - 6 q^{11} - 4 q^{12} + 3 q^{13} + 3 q^{14} - 3 q^{16} - 4 q^{17} - 7 q^{18} - 5 q^{19} + 9 q^{21} - 3 q^{22} - 2 q^{23} + 5 q^{24} + 9 q^{26} - 3 q^{28} - q^{31} - 9 q^{32} - 9 q^{33} - 7 q^{34} - 8 q^{36} + 6 q^{37} - 5 q^{38} - 3 q^{39} - 6 q^{41} - 3 q^{42} + 18 q^{43} + 3 q^{44} + 4 q^{46} + q^{47} + 3 q^{48} + 4 q^{49} - q^{51} + 6 q^{52} - 7 q^{53} - 5 q^{54} - 5 q^{57} + 15 q^{58} + 15 q^{59} - q^{61} + 12 q^{62} + 3 q^{63} + 4 q^{64} + 3 q^{66} + 21 q^{67} - 3 q^{68} - 8 q^{69} - 6 q^{71} + 15 q^{72} + 3 q^{73} - 12 q^{74} - 18 q^{77} + 6 q^{78} + 10 q^{79} + 2 q^{81} - 3 q^{82} + 8 q^{83} - 12 q^{84} + 9 q^{86} - 15 q^{87} + 9 q^{91} + 6 q^{92} - 14 q^{93} + 18 q^{94} - 16 q^{96} - 9 q^{97} + 2 q^{98} - 3 q^{99}+O(q^{100}) \) 2 * q + q^2 + 3 * q^3 - q^4 - q^6 + 6 * q^7 + q^9 - 6 * q^11 - 4 * q^12 + 3 * q^13 + 3 * q^14 - 3 * q^16 - 4 * q^17 - 7 * q^18 - 5 * q^19 + 9 * q^21 - 3 * q^22 - 2 * q^23 + 5 * q^24 + 9 * q^26 - 3 * q^28 - q^31 - 9 * q^32 - 9 * q^33 - 7 * q^34 - 8 * q^36 + 6 * q^37 - 5 * q^38 - 3 * q^39 - 6 * q^41 - 3 * q^42 + 18 * q^43 + 3 * q^44 + 4 * q^46 + q^47 + 3 * q^48 + 4 * q^49 - q^51 + 6 * q^52 - 7 * q^53 - 5 * q^54 - 5 * q^57 + 15 * q^58 + 15 * q^59 - q^61 + 12 * q^62 + 3 * q^63 + 4 * q^64 + 3 * q^66 + 21 * q^67 - 3 * q^68 - 8 * q^69 - 6 * q^71 + 15 * q^72 + 3 * q^73 - 12 * q^74 - 18 * q^77 + 6 * q^78 + 10 * q^79 + 2 * q^81 - 3 * q^82 + 8 * q^83 - 12 * q^84 + 9 * q^86 - 15 * q^87 + 9 * q^91 + 6 * q^92 - 14 * q^93 + 18 * q^94 - 16 * q^96 - 9 * q^97 + 2 * q^98 - 3 * q^99

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