LMFDB - Embedded newform 9025.2.a.n.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9025,2,Mod(1,9025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9025, 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("9025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9025 = 5^{2} \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9025.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:	$72.0649878242$
Analytic rank:	$2$
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:	no (minimal twist has level 361)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	9025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.618034 q^{2} -2.61803 q^{3} -1.61803 q^{4} -1.61803 q^{6} -3.00000 q^{7} -2.23607 q^{8} +3.85410 q^{9} +O(q^{10})$	\(q+0.618034 q^{2} -2.61803 q^{3} -1.61803 q^{4} -1.61803 q^{6} -3.00000 q^{7} -2.23607 q^{8} +3.85410 q^{9} +0.618034 q^{11} +4.23607 q^{12} +1.00000 q^{13} -1.85410 q^{14} +1.85410 q^{16} -5.23607 q^{17} +2.38197 q^{18} +7.85410 q^{21} +0.381966 q^{22} -7.61803 q^{23} +5.85410 q^{24} +0.618034 q^{26} -2.23607 q^{27} +4.85410 q^{28} -1.38197 q^{29} -2.14590 q^{31} +5.61803 q^{32} -1.61803 q^{33} -3.23607 q^{34} -6.23607 q^{36} -2.14590 q^{37} -2.61803 q^{39} -3.00000 q^{41} +4.85410 q^{42} +6.85410 q^{43} -1.00000 q^{44} -4.70820 q^{46} -3.00000 q^{47} -4.85410 q^{48} +2.00000 q^{49} +13.7082 q^{51} -1.61803 q^{52} -9.32624 q^{53} -1.38197 q^{54} +6.70820 q^{56} -0.854102 q^{58} -15.3262 q^{59} -5.76393 q^{61} -1.32624 q^{62} -11.5623 q^{63} -0.236068 q^{64} -1.00000 q^{66} +7.00000 q^{67} +8.47214 q^{68} +19.9443 q^{69} +1.47214 q^{71} -8.61803 q^{72} -10.7082 q^{73} -1.32624 q^{74} -1.85410 q^{77} -1.61803 q^{78} -13.4164 q^{79} -5.70820 q^{81} -1.85410 q^{82} +0.472136 q^{83} -12.7082 q^{84} +4.23607 q^{86} +3.61803 q^{87} -1.38197 q^{88} -12.2361 q^{89} -3.00000 q^{91} +12.3262 q^{92} +5.61803 q^{93} -1.85410 q^{94} -14.7082 q^{96} -7.14590 q^{97} +1.23607 q^{98} +2.38197 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - q^{11} + 4 q^{12} + 2 q^{13} + 3 q^{14} - 3 q^{16} - 6 q^{17} + 7 q^{18} + 9 q^{21} + 3 q^{22} - 13 q^{23} + 5 q^{24} - q^{26} + 3 q^{28} - 5 q^{29} - 11 q^{31} + 9 q^{32} - q^{33} - 2 q^{34} - 8 q^{36} - 11 q^{37} - 3 q^{39} - 6 q^{41} + 3 q^{42} + 7 q^{43} - 2 q^{44} + 4 q^{46} - 6 q^{47} - 3 q^{48} + 4 q^{49} + 14 q^{51} - q^{52} - 3 q^{53} - 5 q^{54} + 5 q^{58} - 15 q^{59} - 16 q^{61} + 13 q^{62} - 3 q^{63} + 4 q^{64} - 2 q^{66} + 14 q^{67} + 8 q^{68} + 22 q^{69} - 6 q^{71} - 15 q^{72} - 8 q^{73} + 13 q^{74} + 3 q^{77} - q^{78} + 2 q^{81} + 3 q^{82} - 8 q^{83} - 12 q^{84} + 4 q^{86} + 5 q^{87} - 5 q^{88} - 20 q^{89} - 6 q^{91} + 9 q^{92} + 9 q^{93} + 3 q^{94} - 16 q^{96} - 21 q^{97} - 2 q^{98} + 7 q^{99}+O(q^{100}) $ 2 * q - q^2 - 3 * q^3 - q^4 - q^6 - 6 * q^7 + q^9 - q^11 + 4 * q^12 + 2 * q^13 + 3 * q^14 - 3 * q^16 - 6 * q^17 + 7 * q^18 + 9 * q^21 + 3 * q^22 - 13 * q^23 + 5 * q^24 - q^26 + 3 * q^28 - 5 * q^29 - 11 * q^31 + 9 * q^32 - q^33 - 2 * q^34 - 8 * q^36 - 11 * q^37 - 3 * q^39 - 6 * q^41 + 3 * q^42 + 7 * q^43 - 2 * q^44 + 4 * q^46 - 6 * q^47 - 3 * q^48 + 4 * q^49 + 14 * q^51 - q^52 - 3 * q^53 - 5 * q^54 + 5 * q^58 - 15 * q^59 - 16 * q^61 + 13 * q^62 - 3 * q^63 + 4 * q^64 - 2 * q^66 + 14 * q^67 + 8 * q^68 + 22 * q^69 - 6 * q^71 - 15 * q^72 - 8 * q^73 + 13 * q^74 + 3 * q^77 - q^78 + 2 * q^81 + 3 * q^82 - 8 * q^83 - 12 * q^84 + 4 * q^86 + 5 * q^87 - 5 * q^88 - 20 * q^89 - 6 * q^91 + 9 * q^92 + 9 * q^93 + 3 * q^94 - 16 * q^96 - 21 * q^97 - 2 * q^98 + 7 * 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	$-0.429881\pi$
$2$	0.618034	0.437016	0.218508	+	0.975835i	$0.429881\pi$
$3$	−2.61803	−1.51152	−0.755761	−	0.654847i	$-0.772733\pi$
$3$	−2.61803	−1.51152	−0.755761	+	0.654847i	$0.772733\pi$
$4$	−1.61803	−0.809017
$5$	0	0
$5$	0	0
$6$	−1.61803	−0.660560
$7$	−3.00000	−1.13389	−0.566947	−	0.823754i	$-0.691875\pi$
$7$	−3.00000	−1.13389	−0.566947	+	0.823754i	$0.691875\pi$
$8$	−2.23607	−0.790569
$9$	3.85410	1.28470
$10$	0	0
$11$	0.618034	0.186344	0.0931721	−	0.995650i	$-0.470299\pi$
$11$	0.618034	0.186344	0.0931721	+	0.995650i	$0.470299\pi$
$12$	4.23607	1.22285
$13$	1.00000	0.277350	0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000	0.277350	0.138675	+	0.990338i	$0.455716\pi$
$14$	−1.85410	−0.495530
$15$	0	0
$16$	1.85410	0.463525
$17$	−5.23607	−1.26993	−0.634967	−	0.772540i	$-0.718986\pi$
$17$	−5.23607	−1.26993	−0.634967	+	0.772540i	$0.718986\pi$
$18$	2.38197	0.561435
$19$	0	0
$19$	0	0
$20$	0	0
$21$	7.85410	1.71391
$22$	0.381966	0.0814354
$23$	−7.61803	−1.58847	−0.794235	−	0.607611i	$-0.792128\pi$
$23$	−7.61803	−1.58847	−0.794235	+	0.607611i	$0.792128\pi$
$24$	5.85410	1.19496
$25$	0	0
$26$	0.618034	0.121206
$27$	−2.23607	−0.430331
$28$	4.85410	0.917339
$29$	−1.38197	−0.256625	−0.128312	−	0.991734i	$-0.540956\pi$
$29$	−1.38197	−0.256625	−0.128312	+	0.991734i	$0.540956\pi$
$30$	0	0
$31$	−2.14590	−0.385415	−0.192707	−	0.981256i	$-0.561727\pi$
$31$	−2.14590	−0.385415	−0.192707	+	0.981256i	$0.561727\pi$
$32$	5.61803	0.993137
$33$	−1.61803	−0.281664
$34$	−3.23607	−0.554981
$35$	0	0
$36$	−6.23607	−1.03934
$37$	−2.14590	−0.352783	−0.176392	−	0.984320i	$-0.556443\pi$
$37$	−2.14590	−0.352783	−0.176392	+	0.984320i	$0.556443\pi$
$38$	0	0
$39$	−2.61803	−0.419221
$40$	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
$43$	6.85410	1.04524	0.522620	−	0.852566i	$-0.324955\pi$
$43$	6.85410	1.04524	0.522620	+	0.852566i	$0.324955\pi$
$44$	−1.00000	−0.150756
$45$	0	0
$46$	−4.70820	−0.694187
$47$	−3.00000	−0.437595	−0.218797	−	0.975770i	$-0.570213\pi$
$47$	−3.00000	−0.437595	−0.218797	+	0.975770i	$0.570213\pi$
$48$	−4.85410	−0.700629
$49$	2.00000	0.285714
$50$	0	0
$51$	13.7082	1.91953
$52$	−1.61803	−0.224381
$53$	−9.32624	−1.28106	−0.640529	−	0.767934i	$-0.721285\pi$
$53$	−9.32624	−1.28106	−0.640529	+	0.767934i	$0.721285\pi$
$54$	−1.38197	−0.188062
$55$	0	0
$56$	6.70820	0.896421
$57$	0	0
$58$	−0.854102	−0.112149
$59$	−15.3262	−1.99531	−0.997653	−	0.0684709i	$-0.978188\pi$
$59$	−15.3262	−1.99531	−0.997653	+	0.0684709i	$0.978188\pi$
$60$	0	0
$61$	−5.76393	−0.737996	−0.368998	−	0.929430i	$-0.620299\pi$
$61$	−5.76393	−0.737996	−0.368998	+	0.929430i	$0.620299\pi$
$62$	−1.32624	−0.168432
$63$	−11.5623	−1.45671
$64$	−0.236068	−0.0295085
$65$	0	0
$66$	−1.00000	−0.123091
$67$	7.00000	0.855186	0.427593	−	0.903971i	$-0.359362\pi$
$67$	7.00000	0.855186	0.427593	+	0.903971i	$0.359362\pi$
$68$	8.47214	1.02740
$69$	19.9443	2.40101
$70$	0	0
$71$	1.47214	0.174710	0.0873552	−	0.996177i	$-0.472158\pi$
$71$	1.47214	0.174710	0.0873552	+	0.996177i	$0.472158\pi$
$72$	−8.61803	−1.01565
$73$	−10.7082	−1.25330	−0.626650	−	0.779301i	$-0.715575\pi$
$73$	−10.7082	−1.25330	−0.626650	+	0.779301i	$0.715575\pi$
$74$	−1.32624	−0.154172
$75$	0	0
$76$	0	0
$77$	−1.85410	−0.211295
$78$	−1.61803	−0.183206
$79$	−13.4164	−1.50946	−0.754732	−	0.656033i	$-0.772233\pi$
$79$	−13.4164	−1.50946	−0.754732	+	0.656033i	$0.772233\pi$
$80$	0	0
$81$	−5.70820	−0.634245
$82$	−1.85410	−0.204751
$83$	0.472136	0.0518237	0.0259118	−	0.999664i	$-0.491751\pi$
$83$	0.472136	0.0518237	0.0259118	+	0.999664i	$0.491751\pi$
$84$	−12.7082	−1.38658
$85$	0	0
$86$	4.23607	0.456787
$87$	3.61803	0.387894
$88$	−1.38197	−0.147318
$89$	−12.2361	−1.29702	−0.648510	−	0.761206i	$-0.724608\pi$
$89$	−12.2361	−1.29702	−0.648510	+	0.761206i	$0.724608\pi$
$90$	0	0
$91$	−3.00000	−0.314485
$92$	12.3262	1.28510
$93$	5.61803	0.582563
$94$	−1.85410	−0.191236
$95$	0	0
$96$	−14.7082	−1.50115
$97$	−7.14590	−0.725556	−0.362778	−	0.931876i	$-0.618172\pi$
$97$	−7.14590	−0.725556	−0.362778	+	0.931876i	$0.618172\pi$
$98$	1.23607	0.124862
$99$	2.38197	0.239397
$100$	0	0
$101$	13.1803	1.31149	0.655746	−	0.754981i	$-0.272354\pi$
$101$	13.1803	1.31149	0.655746	+	0.754981i	$0.272354\pi$
$102$	8.47214	0.838866
$103$	1.32624	0.130678	0.0653391	−	0.997863i	$-0.479187\pi$
$103$	1.32624	0.130678	0.0653391	+	0.997863i	$0.479187\pi$
$104$	−2.23607	−0.219265
$105$	0	0
$106$	−5.76393	−0.559843
$107$	10.4164	1.00699	0.503496	−	0.863998i	$-0.332047\pi$
$107$	10.4164	1.00699	0.503496	+	0.863998i	$0.332047\pi$
$108$	3.61803	0.348145
$109$	−16.7082	−1.60036	−0.800178	−	0.599763i	$-0.795262\pi$
$109$	−16.7082	−1.60036	−0.800178	+	0.599763i	$0.795262\pi$
$110$	0	0
$111$	5.61803	0.533240
$112$	−5.56231	−0.525589
$113$	−11.2361	−1.05700	−0.528500	−	0.848933i	$-0.677245\pi$
$113$	−11.2361	−1.05700	−0.528500	+	0.848933i	$0.677245\pi$
$114$	0	0
$115$	0	0
$116$	2.23607	0.207614
$117$	3.85410	0.356312
$118$	−9.47214	−0.871981
$119$	15.7082	1.43997
$120$	0	0
$121$	−10.6180	−0.965276
$122$	−3.56231	−0.322516
$123$	7.85410	0.708181
$124$	3.47214	0.311807
$125$	0	0
$126$	−7.14590	−0.636607
$127$	−10.2361	−0.908304	−0.454152	−	0.890924i	$-0.650058\pi$
$127$	−10.2361	−0.908304	−0.454152	+	0.890924i	$0.650058\pi$
$128$	−11.3820	−1.00603
$129$	−17.9443	−1.57991
$130$	0	0
$131$	3.90983	0.341603	0.170802	−	0.985305i	$-0.445364\pi$
$131$	3.90983	0.341603	0.170802	+	0.985305i	$0.445364\pi$
$132$	2.61803	0.227871
$133$	0	0
$134$	4.32624	0.373730
$135$	0	0
$136$	11.7082	1.00397
$137$	1.47214	0.125773	0.0628865	−	0.998021i	$-0.479969\pi$
$137$	1.47214	0.125773	0.0628865	+	0.998021i	$0.479969\pi$
$138$	12.3262	1.04928
$139$	−9.79837	−0.831087	−0.415544	−	0.909573i	$-0.636409\pi$
$139$	−9.79837	−0.831087	−0.415544	+	0.909573i	$0.636409\pi$
$140$	0	0
$141$	7.85410	0.661435
$142$	0.909830	0.0763512
$143$	0.618034	0.0516826
$144$	7.14590	0.595492
$145$	0	0
$146$	−6.61803	−0.547712
$147$	−5.23607	−0.431864
$148$	3.47214	0.285408
$149$	−13.0902	−1.07239	−0.536194	−	0.844095i	$-0.680139\pi$
$149$	−13.0902	−1.07239	−0.536194	+	0.844095i	$0.680139\pi$
$150$	0	0
$151$	−9.90983	−0.806451	−0.403225	−	0.915101i	$-0.632111\pi$
$151$	−9.90983	−0.806451	−0.403225	+	0.915101i	$0.632111\pi$
$152$	0	0
$153$	−20.1803	−1.63148
$154$	−1.14590	−0.0923391
$155$	0	0
$156$	4.23607	0.339157
$157$	11.1459	0.889540	0.444770	−	0.895645i	$-0.353286\pi$
$157$	11.1459	0.889540	0.444770	+	0.895645i	$0.353286\pi$
$158$	−8.29180	−0.659660
$159$	24.4164	1.93635
$160$	0	0
$161$	22.8541	1.80116
$162$	−3.52786	−0.277175
$163$	−6.23607	−0.488447	−0.244223	−	0.969719i	$-0.578533\pi$
$163$	−6.23607	−0.488447	−0.244223	+	0.969719i	$0.578533\pi$
$164$	4.85410	0.379042
$165$	0	0
$166$	0.291796	0.0226478
$167$	−15.7639	−1.21985	−0.609925	−	0.792459i	$-0.708800\pi$
$167$	−15.7639	−1.21985	−0.609925	+	0.792459i	$0.708800\pi$
$168$	−17.5623	−1.35496
$169$	−12.0000	−0.923077
$170$	0	0
$171$	0	0
$172$	−11.0902	−0.845618
$173$	−8.47214	−0.644125	−0.322062	−	0.946718i	$-0.604376\pi$
$173$	−8.47214	−0.644125	−0.322062	+	0.946718i	$0.604376\pi$
$174$	2.23607	0.169516
$175$	0	0
$176$	1.14590	0.0863753
$177$	40.1246	3.01595
$178$	−7.56231	−0.566819
$179$	7.76393	0.580304	0.290152	−	0.956981i	$-0.406294\pi$
$179$	7.76393	0.580304	0.290152	+	0.956981i	$0.406294\pi$
$180$	0	0
$181$	12.0000	0.891953	0.445976	−	0.895045i	$-0.352856\pi$
$181$	12.0000	0.891953	0.445976	+	0.895045i	$0.352856\pi$
$182$	−1.85410	−0.137435
$183$	15.0902	1.11550
$184$	17.0344	1.25580
$185$	0	0
$186$	3.47214	0.254589
$187$	−3.23607	−0.236645
$188$	4.85410	0.354022
$189$	6.70820	0.487950
$190$	0	0
$191$	9.76393	0.706493	0.353247	−	0.935530i	$-0.385078\pi$
$191$	9.76393	0.706493	0.353247	+	0.935530i	$0.385078\pi$
$192$	0.618034	0.0446028
$193$	−22.9443	−1.65156	−0.825782	−	0.563989i	$-0.809266\pi$
$193$	−22.9443	−1.65156	−0.825782	+	0.563989i	$0.809266\pi$
$194$	−4.41641	−0.317080
$195$	0	0
$196$	−3.23607	−0.231148
$197$	−3.00000	−0.213741	−0.106871	−	0.994273i	$-0.534083\pi$
$197$	−3.00000	−0.213741	−0.106871	+	0.994273i	$0.534083\pi$
$198$	1.47214	0.104620
$199$	13.4164	0.951064	0.475532	−	0.879698i	$-0.342256\pi$
$199$	13.4164	0.951064	0.475532	+	0.879698i	$0.342256\pi$
$200$	0	0
$201$	−18.3262	−1.29263
$202$	8.14590	0.573143
$203$	4.14590	0.290985
$204$	−22.1803	−1.55293
$205$	0	0
$206$	0.819660	0.0571084
$207$	−29.3607	−2.04071
$208$	1.85410	0.128559
$209$	0	0
$210$	0	0
$211$	2.85410	0.196484	0.0982422	−	0.995163i	$-0.468678\pi$
$211$	2.85410	0.196484	0.0982422	+	0.995163i	$0.468678\pi$
$212$	15.0902	1.03640
$213$	−3.85410	−0.264079
$214$	6.43769	0.440072
$215$	0	0
$216$	5.00000	0.340207
$217$	6.43769	0.437019
$218$	−10.3262	−0.699381
$219$	28.0344	1.89439
$220$	0	0
$221$	−5.23607	−0.352216
$222$	3.47214	0.233035
$223$	−19.6525	−1.31603	−0.658014	−	0.753006i	$-0.728603\pi$
$223$	−19.6525	−1.31603	−0.658014	+	0.753006i	$0.728603\pi$
$224$	−16.8541	−1.12611
$225$	0	0
$226$	−6.94427	−0.461926
$227$	10.4164	0.691361	0.345681	−	0.938352i	$-0.387648\pi$
$227$	10.4164	0.691361	0.345681	+	0.938352i	$0.387648\pi$
$228$	0	0
$229$	−11.3820	−0.752141	−0.376071	−	0.926591i	$-0.622725\pi$
$229$	−11.3820	−0.752141	−0.376071	+	0.926591i	$0.622725\pi$
$230$	0	0
$231$	4.85410	0.319376
$232$	3.09017	0.202880
$233$	−13.4721	−0.882589	−0.441294	−	0.897362i	$-0.645481\pi$
$233$	−13.4721	−0.882589	−0.441294	+	0.897362i	$0.645481\pi$
$234$	2.38197	0.155714
$235$	0	0
$236$	24.7984	1.61424
$237$	35.1246	2.28159
$238$	9.70820	0.629289
$239$	15.3262	0.991372	0.495686	−	0.868502i	$-0.334917\pi$
$239$	15.3262	0.991372	0.495686	+	0.868502i	$0.334917\pi$
$240$	0	0
$241$	−19.1803	−1.23551	−0.617757	−	0.786369i	$-0.711959\pi$
$241$	−19.1803	−1.23551	−0.617757	+	0.786369i	$0.711959\pi$
$242$	−6.56231	−0.421841
$243$	21.6525	1.38901
$244$	9.32624	0.597051
$245$	0	0
$246$	4.85410	0.309486
$247$	0	0
$248$	4.79837	0.304697
$249$	−1.23607	−0.0783326
$250$	0	0
$251$	19.3607	1.22204	0.611018	−	0.791617i	$-0.290760\pi$
$251$	19.3607	1.22204	0.611018	+	0.791617i	$0.290760\pi$
$252$	18.7082	1.17851
$253$	−4.70820	−0.296002
$254$	−6.32624	−0.396943
$255$	0	0
$256$	−6.56231	−0.410144
$257$	24.3607	1.51958	0.759789	−	0.650170i	$-0.225302\pi$
$257$	24.3607	1.51958	0.759789	+	0.650170i	$0.225302\pi$
$258$	−11.0902	−0.690444
$259$	6.43769	0.400019
$260$	0	0
$261$	−5.32624	−0.329686
$262$	2.41641	0.149286
$263$	−2.94427	−0.181552	−0.0907758	−	0.995871i	$-0.528935\pi$
$263$	−2.94427	−0.181552	−0.0907758	+	0.995871i	$0.528935\pi$
$264$	3.61803	0.222675
$265$	0	0
$266$	0	0
$267$	32.0344	1.96048
$268$	−11.3262	−0.691860
$269$	14.6738	0.894675	0.447338	−	0.894365i	$-0.352372\pi$
$269$	14.6738	0.894675	0.447338	+	0.894365i	$0.352372\pi$
$270$	0	0
$271$	7.85410	0.477103	0.238551	−	0.971130i	$-0.423327\pi$
$271$	7.85410	0.477103	0.238551	+	0.971130i	$0.423327\pi$
$272$	−9.70820	−0.588646
$273$	7.85410	0.475352
$274$	0.909830	0.0549648
$275$	0	0
$276$	−32.2705	−1.94246
$277$	15.4164	0.926282	0.463141	−	0.886285i	$-0.346722\pi$
$277$	15.4164	0.926282	0.463141	+	0.886285i	$0.346722\pi$
$278$	−6.05573	−0.363198
$279$	−8.27051	−0.495142
$280$	0	0
$281$	8.50658	0.507460	0.253730	−	0.967275i	$-0.418343\pi$
$281$	8.50658	0.507460	0.253730	+	0.967275i	$0.418343\pi$
$282$	4.85410	0.289058
$283$	3.03444	0.180379	0.0901894	−	0.995925i	$-0.471253\pi$
$283$	3.03444	0.180379	0.0901894	+	0.995925i	$0.471253\pi$
$284$	−2.38197	−0.141344
$285$	0	0
$286$	0.381966	0.0225861
$287$	9.00000	0.531253
$288$	21.6525	1.27588
$289$	10.4164	0.612730
$290$	0	0
$291$	18.7082	1.09669
$292$	17.3262	1.01394
$293$	16.8541	0.984627	0.492314	−	0.870418i	$-0.336151\pi$
$293$	16.8541	0.984627	0.492314	+	0.870418i	$0.336151\pi$
$294$	−3.23607	−0.188731
$295$	0	0
$296$	4.79837	0.278900
$297$	−1.38197	−0.0801898
$298$	−8.09017	−0.468651
$299$	−7.61803	−0.440562
$300$	0	0
$301$	−20.5623	−1.18519
$302$	−6.12461	−0.352432
$303$	−34.5066	−1.98235
$304$	0	0
$305$	0	0
$306$	−12.4721	−0.712985
$307$	1.67376	0.0955266	0.0477633	−	0.998859i	$-0.484791\pi$
$307$	1.67376	0.0955266	0.0477633	+	0.998859i	$0.484791\pi$
$308$	3.00000	0.170941
$309$	−3.47214	−0.197523
$310$	0	0
$311$	−18.6525	−1.05768	−0.528842	−	0.848720i	$-0.677374\pi$
$311$	−18.6525	−1.05768	−0.528842	+	0.848720i	$0.677374\pi$
$312$	5.85410	0.331423
$313$	−4.32624	−0.244533	−0.122267	−	0.992497i	$-0.539016\pi$
$313$	−4.32624	−0.244533	−0.122267	+	0.992497i	$0.539016\pi$
$314$	6.88854	0.388743
$315$	0	0
$316$	21.7082	1.22118
$317$	−18.0000	−1.01098	−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000	−1.01098	−0.505490	+	0.862832i	$0.668688\pi$
$318$	15.0902	0.846215
$319$	−0.854102	−0.0478205
$320$	0	0
$321$	−27.2705	−1.52209
$322$	14.1246	0.787134
$323$	0	0
$324$	9.23607	0.513115
$325$	0	0
$326$	−3.85410	−0.213459
$327$	43.7426	2.41897
$328$	6.70820	0.370399
$329$	9.00000	0.496186
$330$	0	0
$331$	−6.94427	−0.381692	−0.190846	−	0.981620i	$-0.561123\pi$
$331$	−6.94427	−0.381692	−0.190846	+	0.981620i	$0.561123\pi$
$332$	−0.763932	−0.0419262
$333$	−8.27051	−0.453221
$334$	−9.74265	−0.533094
$335$	0	0
$336$	14.5623	0.794439
$337$	−23.1246	−1.25968	−0.629839	−	0.776726i	$-0.716879\pi$
$337$	−23.1246	−1.25968	−0.629839	+	0.776726i	$0.716879\pi$
$338$	−7.41641	−0.403399
$339$	29.4164	1.59768
$340$	0	0
$341$	−1.32624	−0.0718198
$342$	0	0
$343$	15.0000	0.809924
$344$	−15.3262	−0.826335
$345$	0	0
$346$	−5.23607	−0.281493
$347$	−1.41641	−0.0760368	−0.0380184	−	0.999277i	$-0.512105\pi$
$347$	−1.41641	−0.0760368	−0.0380184	+	0.999277i	$0.512105\pi$
$348$	−5.85410	−0.313813
$349$	25.9787	1.39061	0.695304	−	0.718715i	$-0.255270\pi$
$349$	25.9787	1.39061	0.695304	+	0.718715i	$0.255270\pi$
$350$	0	0
$351$	−2.23607	−0.119352
$352$	3.47214	0.185065
$353$	31.4508	1.67396	0.836980	−	0.547234i	$-0.184319\pi$
$353$	31.4508	1.67396	0.836980	+	0.547234i	$0.184319\pi$
$354$	24.7984	1.31802
$355$	0	0
$356$	19.7984	1.04931
$357$	−41.1246	−2.17655
$358$	4.79837	0.253602
$359$	−22.0344	−1.16293	−0.581467	−	0.813570i	$-0.697521\pi$
$359$	−22.0344	−1.16293	−0.581467	+	0.813570i	$0.697521\pi$
$360$	0	0
$361$	0	0
$362$	7.41641	0.389798
$363$	27.7984	1.45904
$364$	4.85410	0.254424
$365$	0	0
$366$	9.32624	0.487490
$367$	−1.94427	−0.101490	−0.0507451	−	0.998712i	$-0.516160\pi$
$367$	−1.94427	−0.101490	−0.0507451	+	0.998712i	$0.516160\pi$
$368$	−14.1246	−0.736296
$369$	−11.5623	−0.601910
$370$	0	0
$371$	27.9787	1.45258
$372$	−9.09017	−0.471303
$373$	−3.47214	−0.179780	−0.0898902	−	0.995952i	$-0.528652\pi$
$373$	−3.47214	−0.179780	−0.0898902	+	0.995952i	$0.528652\pi$
$374$	−2.00000	−0.103418
$375$	0	0
$376$	6.70820	0.345949
$377$	−1.38197	−0.0711749
$378$	4.14590	0.213242
$379$	25.1246	1.29056	0.645282	−	0.763944i	$-0.276740\pi$
$379$	25.1246	1.29056	0.645282	+	0.763944i	$0.276740\pi$
$380$	0	0
$381$	26.7984	1.37292
$382$	6.03444	0.308749
$383$	−2.61803	−0.133775	−0.0668876	−	0.997761i	$-0.521307\pi$
$383$	−2.61803	−0.133775	−0.0668876	+	0.997761i	$0.521307\pi$
$384$	29.7984	1.52064
$385$	0	0
$386$	−14.1803	−0.721760
$387$	26.4164	1.34282
$388$	11.5623	0.586987
$389$	−24.2705	−1.23056	−0.615282	−	0.788307i	$-0.710958\pi$
$389$	−24.2705	−1.23056	−0.615282	+	0.788307i	$0.710958\pi$
$390$	0	0
$391$	39.8885	2.01725
$392$	−4.47214	−0.225877
$393$	−10.2361	−0.516341
$394$	−1.85410	−0.0934083
$395$	0	0
$396$	−3.85410	−0.193676
$397$	2.52786	0.126870	0.0634349	−	0.997986i	$-0.479794\pi$
$397$	2.52786	0.126870	0.0634349	+	0.997986i	$0.479794\pi$
$398$	8.29180	0.415630
$399$	0	0
$400$	0	0
$401$	−0.111456	−0.00556586	−0.00278293	−	0.999996i	$-0.500886\pi$
$401$	−0.111456	−0.00556586	−0.00278293	+	0.999996i	$0.500886\pi$
$402$	−11.3262	−0.564901
$403$	−2.14590	−0.106895
$404$	−21.3262	−1.06102
$405$	0	0
$406$	2.56231	0.127165
$407$	−1.32624	−0.0657392
$408$	−30.6525	−1.51752
$409$	−21.7082	−1.07340	−0.536701	−	0.843773i	$-0.680330\pi$
$409$	−21.7082	−1.07340	−0.536701	+	0.843773i	$0.680330\pi$
$410$	0	0
$411$	−3.85410	−0.190109
$412$	−2.14590	−0.105721
$413$	45.9787	2.26246
$414$	−18.1459	−0.891822
$415$	0	0
$416$	5.61803	0.275447
$417$	25.6525	1.25621
$418$	0	0
$419$	8.94427	0.436956	0.218478	−	0.975842i	$-0.429891\pi$
$419$	8.94427	0.436956	0.218478	+	0.975842i	$0.429891\pi$
$420$	0	0
$421$	−18.5279	−0.902993	−0.451496	−	0.892273i	$-0.649110\pi$
$421$	−18.5279	−0.902993	−0.451496	+	0.892273i	$0.649110\pi$
$422$	1.76393	0.0858669
$423$	−11.5623	−0.562179
$424$	20.8541	1.01276
$425$	0	0
$426$	−2.38197	−0.115407
$427$	17.2918	0.836809
$428$	−16.8541	−0.814674
$429$	−1.61803	−0.0781194
$430$	0	0
$431$	−3.65248	−0.175934	−0.0879668	−	0.996123i	$-0.528037\pi$
$431$	−3.65248	−0.175934	−0.0879668	+	0.996123i	$0.528037\pi$
$432$	−4.14590	−0.199470
$433$	23.5623	1.13233	0.566166	−	0.824291i	$-0.308426\pi$
$433$	23.5623	1.13233	0.566166	+	0.824291i	$0.308426\pi$
$434$	3.97871	0.190984
$435$	0	0
$436$	27.0344	1.29471
$437$	0	0
$438$	17.3262	0.827880
$439$	14.5967	0.696665	0.348332	−	0.937371i	$-0.386748\pi$
$439$	14.5967	0.696665	0.348332	+	0.937371i	$0.386748\pi$
$440$	0	0
$441$	7.70820	0.367057
$442$	−3.23607	−0.153924
$443$	34.4164	1.63517	0.817586	−	0.575806i	$-0.195312\pi$
$443$	34.4164	1.63517	0.817586	+	0.575806i	$0.195312\pi$
$444$	−9.09017	−0.431400
$445$	0	0
$446$	−12.1459	−0.575125
$447$	34.2705	1.62094
$448$	0.708204	0.0334595
$449$	−32.8885	−1.55211	−0.776053	−	0.630667i	$-0.782781\pi$
$449$	−32.8885	−1.55211	−0.776053	+	0.630667i	$0.782781\pi$
$450$	0	0
$451$	−1.85410	−0.0873063
$452$	18.1803	0.855131
$453$	25.9443	1.21897
$454$	6.43769	0.302136
$455$	0	0
$456$	0	0
$457$	−6.29180	−0.294318	−0.147159	−	0.989113i	$-0.547013\pi$
$457$	−6.29180	−0.294318	−0.147159	+	0.989113i	$0.547013\pi$
$458$	−7.03444	−0.328698
$459$	11.7082	0.546492
$460$	0	0
$461$	3.05573	0.142319	0.0711597	−	0.997465i	$-0.477330\pi$
$461$	3.05573	0.142319	0.0711597	+	0.997465i	$0.477330\pi$
$462$	3.00000	0.139573
$463$	5.27051	0.244941	0.122471	−	0.992472i	$-0.460918\pi$
$463$	5.27051	0.244941	0.122471	+	0.992472i	$0.460918\pi$
$464$	−2.56231	−0.118952
$465$	0	0
$466$	−8.32624	−0.385706
$467$	−1.94427	−0.0899702	−0.0449851	−	0.998988i	$-0.514324\pi$
$467$	−1.94427	−0.0899702	−0.0449851	+	0.998988i	$0.514324\pi$
$468$	−6.23607	−0.288262
$469$	−21.0000	−0.969690
$470$	0	0
$471$	−29.1803	−1.34456
$472$	34.2705	1.57743
$473$	4.23607	0.194775
$474$	21.7082	0.997091
$475$	0	0
$476$	−25.4164	−1.16496
$477$	−35.9443	−1.64578
$478$	9.47214	0.433245
$479$	11.9098	0.544174	0.272087	−	0.962273i	$-0.412286\pi$
$479$	11.9098	0.544174	0.272087	+	0.962273i	$0.412286\pi$
$480$	0	0
$481$	−2.14590	−0.0978445
$482$	−11.8541	−0.539940
$483$	−59.8328	−2.72249
$484$	17.1803	0.780925
$485$	0	0
$486$	13.3820	0.607018
$487$	18.1803	0.823830	0.411915	−	0.911222i	$-0.364860\pi$
$487$	18.1803	0.823830	0.411915	+	0.911222i	$0.364860\pi$
$488$	12.8885	0.583437
$489$	16.3262	0.738298
$490$	0	0
$491$	30.2148	1.36357	0.681787	−	0.731551i	$-0.261203\pi$
$491$	30.2148	1.36357	0.681787	+	0.731551i	$0.261203\pi$
$492$	−12.7082	−0.572930
$493$	7.23607	0.325896
$494$	0	0
$495$	0	0
$496$	−3.97871	−0.178650
$497$	−4.41641	−0.198103
$498$	−0.763932	−0.0342326
$499$	−15.1246	−0.677071	−0.338535	−	0.940954i	$-0.609931\pi$
$499$	−15.1246	−0.677071	−0.338535	+	0.940954i	$0.609931\pi$
$500$	0	0
$501$	41.2705	1.84383
$502$	11.9656	0.534049
$503$	17.8328	0.795126	0.397563	−	0.917575i	$-0.369856\pi$
$503$	17.8328	0.795126	0.397563	+	0.917575i	$0.369856\pi$
$504$	25.8541	1.15163
$505$	0	0
$506$	−2.90983	−0.129358
$507$	31.4164	1.39525
$508$	16.5623	0.734833
$509$	−27.0344	−1.19828	−0.599140	−	0.800644i	$-0.704491\pi$
$509$	−27.0344	−1.19828	−0.599140	+	0.800644i	$0.704491\pi$
$510$	0	0
$511$	32.1246	1.42111
$512$	18.7082	0.826794
$513$	0	0
$514$	15.0557	0.664080
$515$	0	0
$516$	29.0344	1.27817
$517$	−1.85410	−0.0815433
$518$	3.97871	0.174815
$519$	22.1803	0.973609
$520$	0	0
$521$	−27.2705	−1.19474	−0.597371	−	0.801965i	$-0.703788\pi$
$521$	−27.2705	−1.19474	−0.597371	+	0.801965i	$0.703788\pi$
$522$	−3.29180	−0.144078
$523$	−22.4164	−0.980201	−0.490101	−	0.871666i	$-0.663040\pi$
$523$	−22.4164	−0.980201	−0.490101	+	0.871666i	$0.663040\pi$
$524$	−6.32624	−0.276363
$525$	0	0
$526$	−1.81966	−0.0793410
$527$	11.2361	0.489451
$528$	−3.00000	−0.130558
$529$	35.0344	1.52324
$530$	0	0
$531$	−59.0689	−2.56337
$532$	0	0
$533$	−3.00000	−0.129944
$534$	19.7984	0.856759
$535$	0	0
$536$	−15.6525	−0.676084
$537$	−20.3262	−0.877142
$538$	9.06888	0.390987
$539$	1.23607	0.0532412
$540$	0	0
$541$	23.8328	1.02465	0.512326	−	0.858791i	$-0.328784\pi$
$541$	23.8328	1.02465	0.512326	+	0.858791i	$0.328784\pi$
$542$	4.85410	0.208502
$543$	−31.4164	−1.34821
$544$	−29.4164	−1.26122
$545$	0	0
$546$	4.85410	0.207736
$547$	−37.9230	−1.62147	−0.810735	−	0.585413i	$-0.800932\pi$
$547$	−37.9230	−1.62147	−0.810735	+	0.585413i	$0.800932\pi$
$548$	−2.38197	−0.101753
$549$	−22.2148	−0.948104
$550$	0	0
$551$	0	0
$552$	−44.5967	−1.89816
$553$	40.2492	1.71157
$554$	9.52786	0.404800
$555$	0	0
$556$	15.8541	0.672364
$557$	23.1803	0.982183	0.491091	−	0.871108i	$-0.336598\pi$
$557$	23.1803	0.982183	0.491091	+	0.871108i	$0.336598\pi$
$558$	−5.11146	−0.216385
$559$	6.85410	0.289898
$560$	0	0
$561$	8.47214	0.357694
$562$	5.25735	0.221768
$563$	−20.8328	−0.877999	−0.438999	−	0.898487i	$-0.644667\pi$
$563$	−20.8328	−0.877999	−0.438999	+	0.898487i	$0.644667\pi$
$564$	−12.7082	−0.535112
$565$	0	0
$566$	1.87539	0.0788284
$567$	17.1246	0.719166
$568$	−3.29180	−0.138121
$569$	28.0902	1.17760	0.588801	−	0.808278i	$-0.299600\pi$
$569$	28.0902	1.17760	0.588801	+	0.808278i	$0.299600\pi$
$570$	0	0
$571$	22.3262	0.934324	0.467162	−	0.884172i	$-0.345276\pi$
$571$	22.3262	0.934324	0.467162	+	0.884172i	$0.345276\pi$
$572$	−1.00000	−0.0418121
$573$	−25.5623	−1.06788
$574$	5.56231	0.232166
$575$	0	0
$576$	−0.909830	−0.0379096
$577$	−28.1246	−1.17084	−0.585421	−	0.810729i	$-0.699071\pi$
$577$	−28.1246	−1.17084	−0.585421	+	0.810729i	$0.699071\pi$
$578$	6.43769	0.267773
$579$	60.0689	2.49638
$580$	0	0
$581$	−1.41641	−0.0587625
$582$	11.5623	0.479273
$583$	−5.76393	−0.238718
$584$	23.9443	0.990821
$585$	0	0
$586$	10.4164	0.430298
$587$	−38.1246	−1.57357	−0.786786	−	0.617226i	$-0.788256\pi$
$587$	−38.1246	−1.57357	−0.786786	+	0.617226i	$0.788256\pi$
$588$	8.47214	0.349385
$589$	0	0
$590$	0	0
$591$	7.85410	0.323075
$592$	−3.97871	−0.163524
$593$	12.7082	0.521863	0.260932	−	0.965357i	$-0.415970\pi$
$593$	12.7082	0.521863	0.260932	+	0.965357i	$0.415970\pi$
$594$	−0.854102	−0.0350442
$595$	0	0
$596$	21.1803	0.867581
$597$	−35.1246	−1.43755
$598$	−4.70820	−0.192533
$599$	1.58359	0.0647038	0.0323519	−	0.999477i	$-0.489700\pi$
$599$	1.58359	0.0647038	0.0323519	+	0.999477i	$0.489700\pi$
$600$	0	0
$601$	33.7082	1.37499	0.687493	−	0.726191i	$-0.258711\pi$
$601$	33.7082	1.37499	0.687493	+	0.726191i	$0.258711\pi$
$602$	−12.7082	−0.517948
$603$	26.9787	1.09866
$604$	16.0344	0.652432
$605$	0	0
$606$	−21.3262	−0.866319
$607$	−27.2705	−1.10688	−0.553438	−	0.832890i	$-0.686684\pi$
$607$	−27.2705	−1.10688	−0.553438	+	0.832890i	$0.686684\pi$
$608$	0	0
$609$	−10.8541	−0.439830
$610$	0	0
$611$	−3.00000	−0.121367
$612$	32.6525	1.31990
$613$	2.05573	0.0830301	0.0415150	−	0.999138i	$-0.486782\pi$
$613$	2.05573	0.0830301	0.0415150	+	0.999138i	$0.486782\pi$
$614$	1.03444	0.0417467
$615$	0	0
$616$	4.14590	0.167043
$617$	−23.3262	−0.939079	−0.469539	−	0.882911i	$-0.655580\pi$
$617$	−23.3262	−0.939079	−0.469539	+	0.882911i	$0.655580\pi$
$618$	−2.14590	−0.0863207
$619$	−30.1246	−1.21081	−0.605405	−	0.795917i	$-0.706989\pi$
$619$	−30.1246	−1.21081	−0.605405	+	0.795917i	$0.706989\pi$
$620$	0	0
$621$	17.0344	0.683569
$622$	−11.5279	−0.462225
$623$	36.7082	1.47068
$624$	−4.85410	−0.194320
$625$	0	0
$626$	−2.67376	−0.106865
$627$	0	0
$628$	−18.0344	−0.719653
$629$	11.2361	0.448011
$630$	0	0
$631$	−15.3607	−0.611499	−0.305750	−	0.952112i	$-0.598907\pi$
$631$	−15.3607	−0.611499	−0.305750	+	0.952112i	$0.598907\pi$
$632$	30.0000	1.19334
$633$	−7.47214	−0.296991
$634$	−11.1246	−0.441815
$635$	0	0
$636$	−39.5066	−1.56654
$637$	2.00000	0.0792429
$638$	−0.527864	−0.0208983
$639$	5.67376	0.224451
$640$	0	0
$641$	−1.49342	−0.0589866	−0.0294933	−	0.999565i	$-0.509389\pi$
$641$	−1.49342	−0.0589866	−0.0294933	+	0.999565i	$0.509389\pi$
$642$	−16.8541	−0.665178
$643$	37.7082	1.48707	0.743533	−	0.668699i	$-0.233149\pi$
$643$	37.7082	1.48707	0.743533	+	0.668699i	$0.233149\pi$
$644$	−36.9787	−1.45717
$645$	0	0
$646$	0	0
$647$	1.47214	0.0578756	0.0289378	−	0.999581i	$-0.490788\pi$
$647$	1.47214	0.0578756	0.0289378	+	0.999581i	$0.490788\pi$
$648$	12.7639	0.501415
$649$	−9.47214	−0.371814
$650$	0	0
$651$	−16.8541	−0.660564
$652$	10.0902	0.395162
$653$	3.43769	0.134527	0.0672637	−	0.997735i	$-0.478573\pi$
$653$	3.43769	0.134527	0.0672637	+	0.997735i	$0.478573\pi$
$654$	27.0344	1.05713
$655$	0	0
$656$	−5.56231	−0.217172
$657$	−41.2705	−1.61012
$658$	5.56231	0.216841
$659$	45.7771	1.78322	0.891611	−	0.452802i	$-0.149576\pi$
$659$	45.7771	1.78322	0.891611	+	0.452802i	$0.149576\pi$
$660$	0	0
$661$	−21.4164	−0.833002	−0.416501	−	0.909135i	$-0.636744\pi$
$661$	−21.4164	−0.833002	−0.416501	+	0.909135i	$0.636744\pi$
$662$	−4.29180	−0.166805
$663$	13.7082	0.532383
$664$	−1.05573	−0.0409702
$665$	0	0
$666$	−5.11146	−0.198065
$667$	10.5279	0.407641
$668$	25.5066	0.986879
$669$	51.4508	1.98920
$670$	0	0
$671$	−3.56231	−0.137521
$672$	44.1246	1.70214
$673$	6.12461	0.236086	0.118043	−	0.993008i	$-0.462338\pi$
$673$	6.12461	0.236086	0.118043	+	0.993008i	$0.462338\pi$
$674$	−14.2918	−0.550499
$675$	0	0
$676$	19.4164	0.746785
$677$	−11.7426	−0.451307	−0.225653	−	0.974208i	$-0.572452\pi$
$677$	−11.7426	−0.451307	−0.225653	+	0.974208i	$0.572452\pi$
$678$	18.1803	0.698212
$679$	21.4377	0.822703
$680$	0	0
$681$	−27.2705	−1.04501
$682$	−0.819660	−0.0313864
$683$	21.6525	0.828509	0.414254	−	0.910161i	$-0.364042\pi$
$683$	21.6525	0.828509	0.414254	+	0.910161i	$0.364042\pi$
$684$	0	0
$685$	0	0
$686$	9.27051	0.353950
$687$	29.7984	1.13688
$688$	12.7082	0.484496
$689$	−9.32624	−0.355301
$690$	0	0
$691$	−16.8197	−0.639850	−0.319925	−	0.947443i	$-0.603658\pi$
$691$	−16.8197	−0.639850	−0.319925	+	0.947443i	$0.603658\pi$
$692$	13.7082	0.521108
$693$	−7.14590	−0.271450
$694$	−0.875388	−0.0332293
$695$	0	0
$696$	−8.09017	−0.306657
$697$	15.7082	0.594991
$698$	16.0557	0.607718
$699$	35.2705	1.33405
$700$	0	0
$701$	38.6312	1.45908	0.729540	−	0.683938i	$-0.239734\pi$
$701$	38.6312	1.45908	0.729540	+	0.683938i	$0.239734\pi$
$702$	−1.38197	−0.0521589
$703$	0	0
$704$	−0.145898	−0.00549874
$705$	0	0
$706$	19.4377	0.731547
$707$	−39.5410	−1.48709
$708$	−64.9230	−2.43996
$709$	43.4164	1.63054	0.815269	−	0.579083i	$-0.196589\pi$
$709$	43.4164	1.63054	0.815269	+	0.579083i	$0.196589\pi$
$710$	0	0
$711$	−51.7082	−1.93921
$712$	27.3607	1.02538
$713$	16.3475	0.612220
$714$	−25.4164	−0.951185
$715$	0	0
$716$	−12.5623	−0.469475
$717$	−40.1246	−1.49848
$718$	−13.6180	−0.508221
$719$	17.9656	0.670002	0.335001	−	0.942218i	$-0.391263\pi$
$719$	17.9656	0.670002	0.335001	+	0.942218i	$0.391263\pi$
$720$	0	0
$721$	−3.97871	−0.148175
$722$	0	0
$723$	50.2148	1.86751
$724$	−19.4164	−0.721605
$725$	0	0
$726$	17.1803	0.637622
$727$	−42.0689	−1.56025	−0.780124	−	0.625625i	$-0.784844\pi$
$727$	−42.0689	−1.56025	−0.780124	+	0.625625i	$0.784844\pi$
$728$	6.70820	0.248623
$729$	−39.5623	−1.46527
$730$	0	0
$731$	−35.8885	−1.32739
$732$	−24.4164	−0.902456
$733$	−40.9574	−1.51280	−0.756399	−	0.654111i	$-0.773043\pi$
$733$	−40.9574	−1.51280	−0.756399	+	0.654111i	$0.773043\pi$
$734$	−1.20163	−0.0443528
$735$	0	0
$736$	−42.7984	−1.57757
$737$	4.32624	0.159359
$738$	−7.14590	−0.263044
$739$	−25.0000	−0.919640	−0.459820	−	0.888012i	$-0.652086\pi$
$739$	−25.0000	−0.919640	−0.459820	+	0.888012i	$0.652086\pi$
$740$	0	0
$741$	0	0
$742$	17.2918	0.634802
$743$	−41.3607	−1.51738	−0.758688	−	0.651454i	$-0.774159\pi$
$743$	−41.3607	−1.51738	−0.758688	+	0.651454i	$0.774159\pi$
$744$	−12.5623	−0.460556
$745$	0	0
$746$	−2.14590	−0.0785669
$747$	1.81966	0.0665779
$748$	5.23607	0.191450
$749$	−31.2492	−1.14182
$750$	0	0
$751$	−23.8541	−0.870449	−0.435224	−	0.900322i	$-0.643331\pi$
$751$	−23.8541	−0.870449	−0.435224	+	0.900322i	$0.643331\pi$
$752$	−5.56231	−0.202836
$753$	−50.6869	−1.84713
$754$	−0.854102	−0.0311046
$755$	0	0
$756$	−10.8541	−0.394760
$757$	15.7426	0.572176	0.286088	−	0.958203i	$-0.407645\pi$
$757$	15.7426	0.572176	0.286088	+	0.958203i	$0.407645\pi$
$758$	15.5279	0.563997
$759$	12.3262	0.447414
$760$	0	0
$761$	−30.8885	−1.11971	−0.559854	−	0.828591i	$-0.689143\pi$
$761$	−30.8885	−1.11971	−0.559854	+	0.828591i	$0.689143\pi$
$762$	16.5623	0.599989
$763$	50.1246	1.81463
$764$	−15.7984	−0.571565
$765$	0	0
$766$	−1.61803	−0.0584619
$767$	−15.3262	−0.553398
$768$	17.1803	0.619942
$769$	−41.6312	−1.50126	−0.750630	−	0.660723i	$-0.770250\pi$
$769$	−41.6312	−1.50126	−0.750630	+	0.660723i	$0.770250\pi$
$770$	0	0
$771$	−63.7771	−2.29688
$772$	37.1246	1.33614
$773$	−28.9230	−1.04029	−0.520144	−	0.854079i	$-0.674122\pi$
$773$	−28.9230	−1.04029	−0.520144	+	0.854079i	$0.674122\pi$
$774$	16.3262	0.586835
$775$	0	0
$776$	15.9787	0.573602
$777$	−16.8541	−0.604638
$778$	−15.0000	−0.537776
$779$	0	0
$780$	0	0
$781$	0.909830	0.0325563
$782$	24.6525	0.881571
$783$	3.09017	0.110434
$784$	3.70820	0.132436
$785$	0	0
$786$	−6.32624	−0.225649
$787$	−38.0000	−1.35455	−0.677277	−	0.735728i	$-0.736840\pi$
$787$	−38.0000	−1.35455	−0.677277	+	0.735728i	$0.736840\pi$
$788$	4.85410	0.172920
$789$	7.70820	0.274419
$790$	0	0
$791$	33.7082	1.19853
$792$	−5.32624	−0.189260
$793$	−5.76393	−0.204683
$794$	1.56231	0.0554442
$795$	0	0
$796$	−21.7082	−0.769427
$797$	33.7082	1.19401	0.597003	−	0.802239i	$-0.296358\pi$
$797$	33.7082	1.19401	0.597003	+	0.802239i	$0.296358\pi$
$798$	0	0
$799$	15.7082	0.555716
$800$	0	0
$801$	−47.1591	−1.66628
$802$	−0.0688837	−0.00243237
$803$	−6.61803	−0.233545
$804$	29.6525	1.04576
$805$	0	0
$806$	−1.32624	−0.0467147
$807$	−38.4164	−1.35232
$808$	−29.4721	−1.03683
$809$	−0.201626	−0.00708880	−0.00354440	−	0.999994i	$-0.501128\pi$
$809$	−0.201626	−0.00708880	−0.00354440	+	0.999994i	$0.501128\pi$
$810$	0	0
$811$	−23.9787	−0.842007	−0.421003	−	0.907059i	$-0.638322\pi$
$811$	−23.9787	−0.842007	−0.421003	+	0.907059i	$0.638322\pi$
$812$	−6.70820	−0.235412
$813$	−20.5623	−0.721152
$814$	−0.819660	−0.0287291
$815$	0	0
$816$	25.4164	0.889752
$817$	0	0
$818$	−13.4164	−0.469094
$819$	−11.5623	−0.404020
$820$	0	0
$821$	−53.0476	−1.85137	−0.925687	−	0.378290i	$-0.876512\pi$
$821$	−53.0476	−1.85137	−0.925687	+	0.378290i	$0.876512\pi$
$822$	−2.38197	−0.0830806
$823$	−23.5967	−0.822531	−0.411265	−	0.911516i	$-0.634913\pi$
$823$	−23.5967	−0.822531	−0.411265	+	0.911516i	$0.634913\pi$
$824$	−2.96556	−0.103310
$825$	0	0
$826$	28.4164	0.988733
$827$	16.5967	0.577125	0.288563	−	0.957461i	$-0.406823\pi$
$827$	16.5967	0.577125	0.288563	+	0.957461i	$0.406823\pi$
$828$	47.5066	1.65097
$829$	20.3262	0.705959	0.352980	−	0.935631i	$-0.385168\pi$
$829$	20.3262	0.705959	0.352980	+	0.935631i	$0.385168\pi$
$830$	0	0
$831$	−40.3607	−1.40010
$832$	−0.236068	−0.00818418
$833$	−10.4721	−0.362838
$834$	15.8541	0.548983
$835$	0	0
$836$	0	0
$837$	4.79837	0.165856
$838$	5.52786	0.190957
$839$	39.7984	1.37399	0.686996	−	0.726661i	$-0.258929\pi$
$839$	39.7984	1.37399	0.686996	+	0.726661i	$0.258929\pi$
$840$	0	0
$841$	−27.0902	−0.934144
$842$	−11.4508	−0.394622
$843$	−22.2705	−0.767037
$844$	−4.61803	−0.158959
$845$	0	0
$846$	−7.14590	−0.245681
$847$	31.8541	1.09452
$848$	−17.2918	−0.593803
$849$	−7.94427	−0.272647
$850$	0	0
$851$	16.3475	0.560386
$852$	6.23607	0.213644
$853$	−17.2918	−0.592060	−0.296030	−	0.955179i	$-0.595663\pi$
$853$	−17.2918	−0.592060	−0.296030	+	0.955179i	$0.595663\pi$
$854$	10.6869	0.365699
$855$	0	0
$856$	−23.2918	−0.796097
$857$	8.38197	0.286323	0.143161	−	0.989699i	$-0.454273\pi$
$857$	8.38197	0.286323	0.143161	+	0.989699i	$0.454273\pi$
$858$	−1.00000	−0.0341394
$859$	18.5410	0.632611	0.316306	−	0.948657i	$-0.397557\pi$
$859$	18.5410	0.632611	0.316306	+	0.948657i	$0.397557\pi$
$860$	0	0
$861$	−23.5623	−0.803001
$862$	−2.25735	−0.0768858
$863$	44.9443	1.52992	0.764960	−	0.644077i	$-0.222759\pi$
$863$	44.9443	1.52992	0.764960	+	0.644077i	$0.222759\pi$
$864$	−12.5623	−0.427378
$865$	0	0
$866$	14.5623	0.494847
$867$	−27.2705	−0.926155
$868$	−10.4164	−0.353556
$869$	−8.29180	−0.281280
$870$	0	0
$871$	7.00000	0.237186
$872$	37.3607	1.26519
$873$	−27.5410	−0.932122
$874$	0	0
$875$	0	0
$876$	−45.3607	−1.53260
$877$	−34.1803	−1.15419	−0.577094	−	0.816678i	$-0.695813\pi$
$877$	−34.1803	−1.15419	−0.577094	+	0.816678i	$0.695813\pi$
$878$	9.02129	0.304454
$879$	−44.1246	−1.48829
$880$	0	0
$881$	−23.4508	−0.790079	−0.395040	−	0.918664i	$-0.629269\pi$
$881$	−23.4508	−0.790079	−0.395040	+	0.918664i	$0.629269\pi$
$882$	4.76393	0.160410
$883$	−13.9230	−0.468546	−0.234273	−	0.972171i	$-0.575271\pi$
$883$	−13.9230	−0.468546	−0.234273	+	0.972171i	$0.575271\pi$
$884$	8.47214	0.284949
$885$	0	0
$886$	21.2705	0.714597
$887$	−58.6525	−1.96936	−0.984679	−	0.174378i	$-0.944208\pi$
$887$	−58.6525	−1.96936	−0.984679	+	0.174378i	$0.944208\pi$
$888$	−12.5623	−0.421563
$889$	30.7082	1.02992
$890$	0	0
$891$	−3.52786	−0.118188
$892$	31.7984	1.06469
$893$	0	0
$894$	21.1803	0.708377
$895$	0	0
$896$	34.1459	1.14073
$897$	19.9443	0.665920
$898$	−20.3262	−0.678295
$899$	2.96556	0.0989069
$900$	0	0
$901$	48.8328	1.62686
$902$	−1.14590	−0.0381542
$903$	53.8328	1.79144
$904$	25.1246	0.835632
$905$	0	0
$906$	16.0344	0.532709
$907$	17.5279	0.582003	0.291002	−	0.956723i	$-0.406012\pi$
$907$	17.5279	0.582003	0.291002	+	0.956723i	$0.406012\pi$
$908$	−16.8541	−0.559323
$909$	50.7984	1.68488
$910$	0	0
$911$	5.61803	0.186134	0.0930669	−	0.995660i	$-0.470333\pi$
$911$	5.61803	0.186134	0.0930669	+	0.995660i	$0.470333\pi$
$912$	0	0
$913$	0.291796	0.00965704
$914$	−3.88854	−0.128622
$915$	0	0
$916$	18.4164	0.608495
$917$	−11.7295	−0.387342
$918$	7.23607	0.238826
$919$	36.7082	1.21089	0.605446	−	0.795886i	$-0.292995\pi$
$919$	36.7082	1.21089	0.605446	+	0.795886i	$0.292995\pi$
$920$	0	0
$921$	−4.38197	−0.144391
$922$	1.88854	0.0621959
$923$	1.47214	0.0484559
$924$	−7.85410	−0.258381
$925$	0	0
$926$	3.25735	0.107043
$927$	5.11146	0.167882
$928$	−7.76393	−0.254864
$929$	18.6180	0.610838	0.305419	−	0.952218i	$-0.401203\pi$
$929$	18.6180	0.610838	0.305419	+	0.952218i	$0.401203\pi$
$930$	0	0
$931$	0	0
$932$	21.7984	0.714029
$933$	48.8328	1.59871
$934$	−1.20163	−0.0393184
$935$	0	0
$936$	−8.61803	−0.281689
$937$	−20.4377	−0.667670	−0.333835	−	0.942631i	$-0.608343\pi$
$937$	−20.4377	−0.667670	−0.333835	+	0.942631i	$0.608343\pi$
$938$	−12.9787	−0.423770
$939$	11.3262	0.369618
$940$	0	0
$941$	49.6869	1.61975	0.809874	−	0.586604i	$-0.199536\pi$
$941$	49.6869	1.61975	0.809874	+	0.586604i	$0.199536\pi$
$942$	−18.0344	−0.587594
$943$	22.8541	0.744232
$944$	−28.4164	−0.924875
$945$	0	0
$946$	2.61803	0.0851196
$947$	1.34752	0.0437887	0.0218943	−	0.999760i	$-0.493030\pi$
$947$	1.34752	0.0437887	0.0218943	+	0.999760i	$0.493030\pi$
$948$	−56.8328	−1.84584
$949$	−10.7082	−0.347603
$950$	0	0
$951$	47.1246	1.52812
$952$	−35.1246	−1.13840
$953$	−30.7082	−0.994736	−0.497368	−	0.867540i	$-0.665700\pi$
$953$	−30.7082	−0.994736	−0.497368	+	0.867540i	$0.665700\pi$
$954$	−22.2148	−0.719230
$955$	0	0
$956$	−24.7984	−0.802037
$957$	2.23607	0.0722818
$958$	7.36068	0.237813
$959$	−4.41641	−0.142613
$960$	0	0
$961$	−26.3951	−0.851456
$962$	−1.32624	−0.0427596
$963$	40.1459	1.29368
$964$	31.0344	0.999552
$965$	0	0
$966$	−36.9787	−1.18977
$967$	60.5410	1.94687	0.973434	−	0.228968i	$-0.0735351\pi$
$967$	60.5410	1.94687	0.973434	+	0.228968i	$0.0735351\pi$
$968$	23.7426	0.763118
$969$	0	0
$970$	0	0
$971$	−14.5066	−0.465538	−0.232769	−	0.972532i	$-0.574779\pi$
$971$	−14.5066	−0.465538	−0.232769	+	0.972532i	$0.574779\pi$
$972$	−35.0344	−1.12373
$973$	29.3951	0.942364
$974$	11.2361	0.360027
$975$	0	0
$976$	−10.6869	−0.342080
$977$	−55.3607	−1.77115	−0.885573	−	0.464501i	$-0.846234\pi$
$977$	−55.3607	−1.77115	−0.885573	+	0.464501i	$0.846234\pi$
$978$	10.0902	0.322648
$979$	−7.56231	−0.241692
$980$	0	0
$981$	−64.3951	−2.05598
$982$	18.6738	0.595904
$983$	−30.3820	−0.969034	−0.484517	−	0.874782i	$-0.661005\pi$
$983$	−30.3820	−0.969034	−0.484517	+	0.874782i	$0.661005\pi$
$984$	−17.5623	−0.559866
$985$	0	0
$986$	4.47214	0.142422
$987$	−23.5623	−0.749996
$988$	0	0
$989$	−52.2148	−1.66033
$990$	0	0
$991$	−48.4508	−1.53909	−0.769546	−	0.638591i	$-0.779517\pi$
$991$	−48.4508	−1.53909	−0.769546	+	0.638591i	$0.779517\pi$
$992$	−12.0557	−0.382770
$993$	18.1803	0.576936
$994$	−2.72949	−0.0865742
$995$	0	0
$996$	2.00000	0.0633724
$997$	−26.2918	−0.832670	−0.416335	−	0.909211i	$-0.636686\pi$
$997$	−26.2918	−0.832670	−0.416335	+	0.909211i	$0.636686\pi$
$998$	−9.34752	−0.295891
$999$	4.79837	0.151814

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9025.2.a.n.1.2		2
5.4	even	2		361.2.a.f.1.1	yes	2
15.14	odd	2		3249.2.a.i.1.2		2
19.18	odd	2		9025.2.a.s.1.1		2
20.19	odd	2		5776.2.a.s.1.1		2
95.4	even	18		361.2.e.j.54.1		12
95.9	even	18		361.2.e.j.62.2		12
95.14	odd	18		361.2.e.i.234.2		12
95.24	even	18		361.2.e.j.234.1		12
95.29	odd	18		361.2.e.i.62.1		12
95.34	odd	18		361.2.e.i.54.2		12
95.44	even	18		361.2.e.j.245.1		12
95.49	even	6		361.2.c.d.292.2		4
95.54	even	18		361.2.e.j.28.1		12
95.59	odd	18		361.2.e.i.99.1		12
95.64	even	6		361.2.c.d.68.2		4
95.69	odd	6		361.2.c.g.68.1		4
95.74	even	18		361.2.e.j.99.2		12
95.79	odd	18		361.2.e.i.28.2		12
95.84	odd	6		361.2.c.g.292.1		4
95.89	odd	18		361.2.e.i.245.2		12
95.94	odd	2		361.2.a.c.1.2	✓	2
285.284	even	2		3249.2.a.o.1.1		2
380.379	even	2		5776.2.a.bg.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
361.2.a.c.1.2	✓	2	95.94	odd	2
361.2.a.f.1.1	yes	2	5.4	even	2
361.2.c.d.68.2		4	95.64	even	6
361.2.c.d.292.2		4	95.49	even	6
361.2.c.g.68.1		4	95.69	odd	6
361.2.c.g.292.1		4	95.84	odd	6
361.2.e.i.28.2		12	95.79	odd	18
361.2.e.i.54.2		12	95.34	odd	18
361.2.e.i.62.1		12	95.29	odd	18
361.2.e.i.99.1		12	95.59	odd	18
361.2.e.i.234.2		12	95.14	odd	18
361.2.e.i.245.2		12	95.89	odd	18
361.2.e.j.28.1		12	95.54	even	18
361.2.e.j.54.1		12	95.4	even	18
361.2.e.j.62.2		12	95.9	even	18
361.2.e.j.99.2		12	95.74	even	18
361.2.e.j.234.1		12	95.24	even	18
361.2.e.j.245.1		12	95.44	even	18
3249.2.a.i.1.2		2	15.14	odd	2
3249.2.a.o.1.1		2	285.284	even	2
5776.2.a.s.1.1		2	20.19	odd	2
5776.2.a.bg.1.2		2	380.379	even	2
9025.2.a.n.1.2		2	1.1	even	1	trivial
9025.2.a.s.1.1		2	19.18	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 9025 = 5^{2} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9025.a (trivial)

\(f(q)\)	\(=\)	\(q+0.618034 q^{2} -2.61803 q^{3} -1.61803 q^{4} -1.61803 q^{6} -3.00000 q^{7} -2.23607 q^{8} +3.85410 q^{9} +O(q^{10})\)	\(q+0.618034 q^{2} -2.61803 q^{3} -1.61803 q^{4} -1.61803 q^{6} -3.00000 q^{7} -2.23607 q^{8} +3.85410 q^{9} +0.618034 q^{11} +4.23607 q^{12} +1.00000 q^{13} -1.85410 q^{14} +1.85410 q^{16} -5.23607 q^{17} +2.38197 q^{18} +7.85410 q^{21} +0.381966 q^{22} -7.61803 q^{23} +5.85410 q^{24} +0.618034 q^{26} -2.23607 q^{27} +4.85410 q^{28} -1.38197 q^{29} -2.14590 q^{31} +5.61803 q^{32} -1.61803 q^{33} -3.23607 q^{34} -6.23607 q^{36} -2.14590 q^{37} -2.61803 q^{39} -3.00000 q^{41} +4.85410 q^{42} +6.85410 q^{43} -1.00000 q^{44} -4.70820 q^{46} -3.00000 q^{47} -4.85410 q^{48} +2.00000 q^{49} +13.7082 q^{51} -1.61803 q^{52} -9.32624 q^{53} -1.38197 q^{54} +6.70820 q^{56} -0.854102 q^{58} -15.3262 q^{59} -5.76393 q^{61} -1.32624 q^{62} -11.5623 q^{63} -0.236068 q^{64} -1.00000 q^{66} +7.00000 q^{67} +8.47214 q^{68} +19.9443 q^{69} +1.47214 q^{71} -8.61803 q^{72} -10.7082 q^{73} -1.32624 q^{74} -1.85410 q^{77} -1.61803 q^{78} -13.4164 q^{79} -5.70820 q^{81} -1.85410 q^{82} +0.472136 q^{83} -12.7082 q^{84} +4.23607 q^{86} +3.61803 q^{87} -1.38197 q^{88} -12.2361 q^{89} -3.00000 q^{91} +12.3262 q^{92} +5.61803 q^{93} -1.85410 q^{94} -14.7082 q^{96} -7.14590 q^{97} +1.23607 q^{98} +2.38197 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - 3 q^{3} - q^{4} - q^{6} - 6 q^{7} + q^{9}+O(q^{10}) \) 2 * q - q^2 - 3 * q^3 - q^4 - q^6 - 6 * q^7 + q^9	\( 2 q - q^{2} - 3 q^{3} - q^{4} - q^{6} - 6 q^{7} + q^{9} - q^{11} + 4 q^{12} + 2 q^{13} + 3 q^{14} - 3 q^{16} - 6 q^{17} + 7 q^{18} + 9 q^{21} + 3 q^{22} - 13 q^{23} + 5 q^{24} - q^{26} + 3 q^{28} - 5 q^{29} - 11 q^{31} + 9 q^{32} - q^{33} - 2 q^{34} - 8 q^{36} - 11 q^{37} - 3 q^{39} - 6 q^{41} + 3 q^{42} + 7 q^{43} - 2 q^{44} + 4 q^{46} - 6 q^{47} - 3 q^{48} + 4 q^{49} + 14 q^{51} - q^{52} - 3 q^{53} - 5 q^{54} + 5 q^{58} - 15 q^{59} - 16 q^{61} + 13 q^{62} - 3 q^{63} + 4 q^{64} - 2 q^{66} + 14 q^{67} + 8 q^{68} + 22 q^{69} - 6 q^{71} - 15 q^{72} - 8 q^{73} + 13 q^{74} + 3 q^{77} - q^{78} + 2 q^{81} + 3 q^{82} - 8 q^{83} - 12 q^{84} + 4 q^{86} + 5 q^{87} - 5 q^{88} - 20 q^{89} - 6 q^{91} + 9 q^{92} + 9 q^{93} + 3 q^{94} - 16 q^{96} - 21 q^{97} - 2 q^{98} + 7 q^{99}+O(q^{100}) \) 2 * q - q^2 - 3 * q^3 - q^4 - q^6 - 6 * q^7 + q^9 - q^11 + 4 * q^12 + 2 * q^13 + 3 * q^14 - 3 * q^16 - 6 * q^17 + 7 * q^18 + 9 * q^21 + 3 * q^22 - 13 * q^23 + 5 * q^24 - q^26 + 3 * q^28 - 5 * q^29 - 11 * q^31 + 9 * q^32 - q^33 - 2 * q^34 - 8 * q^36 - 11 * q^37 - 3 * q^39 - 6 * q^41 + 3 * q^42 + 7 * q^43 - 2 * q^44 + 4 * q^46 - 6 * q^47 - 3 * q^48 + 4 * q^49 + 14 * q^51 - q^52 - 3 * q^53 - 5 * q^54 + 5 * q^58 - 15 * q^59 - 16 * q^61 + 13 * q^62 - 3 * q^63 + 4 * q^64 - 2 * q^66 + 14 * q^67 + 8 * q^68 + 22 * q^69 - 6 * q^71 - 15 * q^72 - 8 * q^73 + 13 * q^74 + 3 * q^77 - q^78 + 2 * q^81 + 3 * q^82 - 8 * q^83 - 12 * q^84 + 4 * q^86 + 5 * q^87 - 5 * q^88 - 20 * q^89 - 6 * q^91 + 9 * q^92 + 9 * q^93 + 3 * q^94 - 16 * q^96 - 21 * q^97 - 2 * q^98 + 7 * q^99

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