LMFDB - Embedded newform 8281.2.a.cu.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8281,2,Mod(1,8281)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8281, 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("8281.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8281 = 7^{2} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8281.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:	$66.1241179138$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 1183)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	8281.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.136454 q^{2} +2.96681 q^{3} -1.98138 q^{4} +3.29030 q^{5} -0.404833 q^{6} +0.543274 q^{8} +5.80198 q^{9} +O(q^{10})$	\(q-0.136454 q^{2} +2.96681 q^{3} -1.98138 q^{4} +3.29030 q^{5} -0.404833 q^{6} +0.543274 q^{8} +5.80198 q^{9} -0.448974 q^{10} -0.874918 q^{11} -5.87839 q^{12} +9.76170 q^{15} +3.88863 q^{16} +5.43856 q^{17} -0.791703 q^{18} +1.86947 q^{19} -6.51933 q^{20} +0.119386 q^{22} -6.86854 q^{23} +1.61179 q^{24} +5.82606 q^{25} +8.31297 q^{27} -4.15579 q^{29} -1.33202 q^{30} +9.04712 q^{31} -1.61717 q^{32} -2.59572 q^{33} -0.742113 q^{34} -11.4959 q^{36} -0.719941 q^{37} -0.255096 q^{38} +1.78753 q^{40} -0.916940 q^{41} +5.76897 q^{43} +1.73354 q^{44} +19.0903 q^{45} +0.937238 q^{46} -3.51803 q^{47} +11.5368 q^{48} -0.794988 q^{50} +16.1352 q^{51} +4.82004 q^{53} -1.13434 q^{54} -2.87874 q^{55} +5.54636 q^{57} +0.567074 q^{58} +4.84944 q^{59} -19.3416 q^{60} -0.968366 q^{61} -1.23451 q^{62} -7.55659 q^{64} +0.354196 q^{66} -6.84691 q^{67} -10.7759 q^{68} -20.3777 q^{69} +6.91393 q^{71} +3.15207 q^{72} -3.29618 q^{73} +0.0982387 q^{74} +17.2848 q^{75} -3.70412 q^{76} +9.00190 q^{79} +12.7947 q^{80} +7.25707 q^{81} +0.125120 q^{82} +10.1044 q^{83} +17.8945 q^{85} -0.787198 q^{86} -12.3295 q^{87} -0.475320 q^{88} +9.67789 q^{89} -2.60494 q^{90} +13.6092 q^{92} +26.8411 q^{93} +0.480048 q^{94} +6.15110 q^{95} -4.79783 q^{96} -15.9432 q^{97} -5.07626 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - q^{2} + 23 q^{4} + 13 q^{5} + 14 q^{6} + 26 q^{9}+O(q^{10}) $ 24 * q - q^2 + 23 * q^4 + 13 * q^5 + 14 * q^6 + 26 * q^9	$ 24 q - q^{2} + 23 q^{4} + 13 q^{5} + 14 q^{6} + 26 q^{9} + 5 q^{10} - q^{11} + 5 q^{12} + 5 q^{15} + 17 q^{16} - 5 q^{17} + 24 q^{19} + 34 q^{20} - 14 q^{22} + 11 q^{23} + 32 q^{24} + 33 q^{25} - 21 q^{27} + 4 q^{29} - 22 q^{30} + 40 q^{31} - 6 q^{32} + 24 q^{33} + 36 q^{34} - 15 q^{36} - 4 q^{37} - 29 q^{38} - 4 q^{40} + 49 q^{41} + 13 q^{43} + 10 q^{44} + 58 q^{45} - 10 q^{46} + 62 q^{47} + 89 q^{48} - 23 q^{50} - 21 q^{51} - 18 q^{53} + 12 q^{54} - 14 q^{55} - 13 q^{57} + 56 q^{58} + 79 q^{59} + 22 q^{60} + 13 q^{61} + 12 q^{62} + 18 q^{64} - 38 q^{66} - 2 q^{67} - 12 q^{68} - 28 q^{69} - 19 q^{71} + 81 q^{72} + 17 q^{73} + 17 q^{74} + 24 q^{75} + 58 q^{76} - 9 q^{79} + 63 q^{80} + 16 q^{81} - 22 q^{82} + 81 q^{83} - 34 q^{85} + 22 q^{86} + 70 q^{87} - 33 q^{88} + 72 q^{89} + q^{90} - 4 q^{92} + 19 q^{93} - 30 q^{94} + 13 q^{95} + 11 q^{96} + 45 q^{97} - 39 q^{99}+O(q^{100}) $ 24 * q - q^2 + 23 * q^4 + 13 * q^5 + 14 * q^6 + 26 * q^9 + 5 * q^10 - q^11 + 5 * q^12 + 5 * q^15 + 17 * q^16 - 5 * q^17 + 24 * q^19 + 34 * q^20 - 14 * q^22 + 11 * q^23 + 32 * q^24 + 33 * q^25 - 21 * q^27 + 4 * q^29 - 22 * q^30 + 40 * q^31 - 6 * q^32 + 24 * q^33 + 36 * q^34 - 15 * q^36 - 4 * q^37 - 29 * q^38 - 4 * q^40 + 49 * q^41 + 13 * q^43 + 10 * q^44 + 58 * q^45 - 10 * q^46 + 62 * q^47 + 89 * q^48 - 23 * q^50 - 21 * q^51 - 18 * q^53 + 12 * q^54 - 14 * q^55 - 13 * q^57 + 56 * q^58 + 79 * q^59 + 22 * q^60 + 13 * q^61 + 12 * q^62 + 18 * q^64 - 38 * q^66 - 2 * q^67 - 12 * q^68 - 28 * q^69 - 19 * q^71 + 81 * q^72 + 17 * q^73 + 17 * q^74 + 24 * q^75 + 58 * q^76 - 9 * q^79 + 63 * q^80 + 16 * q^81 - 22 * q^82 + 81 * q^83 - 34 * q^85 + 22 * q^86 + 70 * q^87 - 33 * q^88 + 72 * q^89 + q^90 - 4 * q^92 + 19 * q^93 - 30 * q^94 + 13 * q^95 + 11 * q^96 + 45 * q^97 - 39 * 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 $

$2$	−0.136454	−0.0964874	−0.0482437	−	0.998836i	$-0.515362\pi$
$2$	−0.136454	−0.0964874	−0.0482437	+	0.998836i	$0.515362\pi$
$3$	2.96681	1.71289	0.856445	−	0.516238i	$-0.172668\pi$
$3$	2.96681	1.71289	0.856445	+	0.516238i	$0.172668\pi$
$4$	−1.98138	−0.990690
$5$	3.29030	1.47147	0.735733	−	0.677272i	$-0.236838\pi$
$5$	3.29030	1.47147	0.735733	+	0.677272i	$0.236838\pi$
$6$	−0.404833	−0.165272
$7$	0	0
$7$	0	0
$8$	0.543274	0.192076
$9$	5.80198	1.93399
$10$	−0.448974	−0.141978
$11$	−0.874918	−0.263798	−0.131899	−	0.991263i	$-0.542107\pi$
$11$	−0.874918	−0.263798	−0.131899	+	0.991263i	$0.542107\pi$
$12$	−5.87839	−1.69694
$13$	0	0
$13$	0	0
$14$	0	0
$15$	9.76170	2.52046
$16$	3.88863	0.972157
$17$	5.43856	1.31905	0.659523	−	0.751685i	$-0.270758\pi$
$17$	5.43856	1.31905	0.659523	+	0.751685i	$0.270758\pi$
$18$	−0.791703	−0.186606
$19$	1.86947	0.428885	0.214442	−	0.976737i	$-0.431207\pi$
$19$	1.86947	0.428885	0.214442	+	0.976737i	$0.431207\pi$
$20$	−6.51933	−1.45777
$21$	0	0
$22$	0.119386	0.0254531
$23$	−6.86854	−1.43219	−0.716095	−	0.698003i	$-0.754072\pi$
$23$	−6.86854	−1.43219	−0.716095	+	0.698003i	$0.754072\pi$
$24$	1.61179	0.329006
$25$	5.82606	1.16521
$26$	0	0
$27$	8.31297	1.59983
$28$	0	0
$29$	−4.15579	−0.771711	−0.385856	−	0.922559i	$-0.626094\pi$
$29$	−4.15579	−0.771711	−0.385856	+	0.922559i	$0.626094\pi$
$30$	−1.33202	−0.243193
$31$	9.04712	1.62491	0.812455	−	0.583023i	$-0.198130\pi$
$31$	9.04712	1.62491	0.812455	+	0.583023i	$0.198130\pi$
$32$	−1.61717	−0.285877
$33$	−2.59572	−0.451857
$34$	−0.742113	−0.127271
$35$	0	0
$36$	−11.4959	−1.91599
$37$	−0.719941	−0.118358	−0.0591788	−	0.998247i	$-0.518848\pi$
$37$	−0.719941	−0.118358	−0.0591788	+	0.998247i	$0.518848\pi$
$38$	−0.255096	−0.0413820
$39$	0	0
$40$	1.78753	0.282634
$41$	−0.916940	−0.143202	−0.0716010	−	0.997433i	$-0.522811\pi$
$41$	−0.916940	−0.143202	−0.0716010	+	0.997433i	$0.522811\pi$
$42$	0	0
$43$	5.76897	0.879760	0.439880	−	0.898057i	$-0.355021\pi$
$43$	5.76897	0.879760	0.439880	+	0.898057i	$0.355021\pi$
$44$	1.73354	0.261342
$45$	19.0903	2.84581
$46$	0.937238	0.138188
$47$	−3.51803	−0.513157	−0.256579	−	0.966523i	$-0.582595\pi$
$47$	−3.51803	−0.513157	−0.256579	+	0.966523i	$0.582595\pi$
$48$	11.5368	1.66520
$49$	0	0
$50$	−0.794988	−0.112428
$51$	16.1352	2.25938
$52$	0	0
$53$	4.82004	0.662083	0.331041	−	0.943616i	$-0.392600\pi$
$53$	4.82004	0.662083	0.331041	+	0.943616i	$0.392600\pi$
$54$	−1.13434	−0.154364
$55$	−2.87874	−0.388169
$56$	0	0
$57$	5.54636	0.734633
$58$	0.567074	0.0744604
$59$	4.84944	0.631343	0.315671	−	0.948869i	$-0.397770\pi$
$59$	4.84944	0.631343	0.315671	+	0.948869i	$0.397770\pi$
$60$	−19.3416	−2.49700
$61$	−0.968366	−0.123987	−0.0619933	−	0.998077i	$-0.519746\pi$
$61$	−0.968366	−0.123987	−0.0619933	+	0.998077i	$0.519746\pi$
$62$	−1.23451	−0.156783
$63$	0	0
$64$	−7.55659	−0.944574
$65$	0	0
$66$	0.354196	0.0435985
$67$	−6.84691	−0.836483	−0.418242	−	0.908336i	$-0.637353\pi$
$67$	−6.84691	−0.836483	−0.418242	+	0.908336i	$0.637353\pi$
$68$	−10.7759	−1.30677
$69$	−20.3777	−2.45318
$70$	0	0
$71$	6.91393	0.820532	0.410266	−	0.911966i	$-0.365436\pi$
$71$	6.91393	0.820532	0.410266	+	0.911966i	$0.365436\pi$
$72$	3.15207	0.371475
$73$	−3.29618	−0.385789	−0.192894	−	0.981220i	$-0.561787\pi$
$73$	−3.29618	−0.385789	−0.192894	+	0.981220i	$0.561787\pi$
$74$	0.0982387	0.0114200
$75$	17.2848	1.99588
$76$	−3.70412	−0.424892
$77$	0	0
$78$	0	0
$79$	9.00190	1.01279	0.506397	−	0.862301i	$-0.330977\pi$
$79$	9.00190	1.01279	0.506397	+	0.862301i	$0.330977\pi$
$80$	12.7947	1.43050
$81$	7.25707	0.806341
$82$	0.125120	0.0138172
$83$	10.1044	1.10910	0.554549	−	0.832151i	$-0.312891\pi$
$83$	10.1044	1.10910	0.554549	+	0.832151i	$0.312891\pi$
$84$	0	0
$85$	17.8945	1.94093
$86$	−0.787198	−0.0848857
$87$	−12.3295	−1.32186
$88$	−0.475320	−0.0506693
$89$	9.67789	1.02585	0.512927	−	0.858432i	$-0.328561\pi$
$89$	9.67789	1.02585	0.512927	+	0.858432i	$0.328561\pi$
$90$	−2.60494	−0.274585
$91$	0	0
$92$	13.6092	1.41886
$93$	26.8411	2.78329
$94$	0.480048	0.0495132
$95$	6.15110	0.631089
$96$	−4.79783	−0.489677
$97$	−15.9432	−1.61879	−0.809395	−	0.587265i	$-0.800205\pi$
$97$	−15.9432	−1.61879	−0.809395	+	0.587265i	$0.800205\pi$
$98$	0	0
$99$	−5.07626	−0.510183
$100$	−11.5436	−1.15436
$101$	2.37023	0.235846	0.117923	−	0.993023i	$-0.462376\pi$
$101$	2.37023	0.235846	0.117923	+	0.993023i	$0.462376\pi$
$102$	−2.20171	−0.218002
$103$	2.17665	0.214472	0.107236	−	0.994234i	$-0.465800\pi$
$103$	2.17665	0.214472	0.107236	+	0.994234i	$0.465800\pi$
$104$	0	0
$105$	0	0
$106$	−0.657712	−0.0638826
$107$	9.09356	0.879107	0.439554	−	0.898216i	$-0.355137\pi$
$107$	9.09356	0.879107	0.439554	+	0.898216i	$0.355137\pi$
$108$	−16.4711	−1.58494
$109$	12.0207	1.15137	0.575685	−	0.817672i	$-0.304736\pi$
$109$	12.0207	1.15137	0.575685	+	0.817672i	$0.304736\pi$
$110$	0.392815	0.0374534
$111$	−2.13593	−0.202734
$112$	0	0
$113$	−0.638453	−0.0600606	−0.0300303	−	0.999549i	$-0.509560\pi$
$113$	−0.638453	−0.0600606	−0.0300303	+	0.999549i	$0.509560\pi$
$114$	−0.756821	−0.0708828
$115$	−22.5995	−2.10742
$116$	8.23421	0.764527
$117$	0	0
$118$	−0.661724	−0.0609166
$119$	0	0
$120$	5.30328	0.484121
$121$	−10.2345	−0.930411
$122$	0.132137	0.0119631
$123$	−2.72039	−0.245289
$124$	−17.9258	−1.60978
$125$	2.71798	0.243103
$126$	0	0
$127$	−18.9130	−1.67826	−0.839128	−	0.543933i	$-0.816934\pi$
$127$	−18.9130	−1.67826	−0.839128	+	0.543933i	$0.816934\pi$
$128$	4.26546	0.377017
$129$	17.1155	1.50693
$130$	0	0
$131$	−12.1156	−1.05855	−0.529274	−	0.848451i	$-0.677536\pi$
$131$	−12.1156	−1.05855	−0.529274	+	0.848451i	$0.677536\pi$
$132$	5.14311	0.447650
$133$	0	0
$134$	0.934287	0.0807101
$135$	27.3521	2.35410
$136$	2.95463	0.253358
$137$	9.52030	0.813374	0.406687	−	0.913568i	$-0.366684\pi$
$137$	9.52030	0.813374	0.406687	+	0.913568i	$0.366684\pi$
$138$	2.78061	0.236701
$139$	−19.2876	−1.63596	−0.817978	−	0.575250i	$-0.804905\pi$
$139$	−19.2876	−1.63596	−0.817978	+	0.575250i	$0.804905\pi$
$140$	0	0
$141$	−10.4373	−0.878982
$142$	−0.943431	−0.0791710
$143$	0	0
$144$	22.5618	1.88015
$145$	−13.6738	−1.13555
$146$	0.449776	0.0372237
$147$	0	0
$148$	1.42648	0.117256
$149$	3.71001	0.303935	0.151968	−	0.988385i	$-0.451439\pi$
$149$	3.71001	0.303935	0.151968	+	0.988385i	$0.451439\pi$
$150$	−2.35858	−0.192577
$151$	16.5840	1.34959	0.674795	−	0.738005i	$-0.264232\pi$
$151$	16.5840	1.34959	0.674795	+	0.738005i	$0.264232\pi$
$152$	1.01563	0.0823787
$153$	31.5545	2.55103
$154$	0	0
$155$	29.7677	2.39100
$156$	0	0
$157$	−5.66389	−0.452028	−0.226014	−	0.974124i	$-0.572570\pi$
$157$	−5.66389	−0.452028	−0.226014	+	0.974124i	$0.572570\pi$
$158$	−1.22834	−0.0977218
$159$	14.3001	1.13408
$160$	−5.32096	−0.420659
$161$	0	0
$162$	−0.990255	−0.0778017
$163$	12.2573	0.960068	0.480034	−	0.877250i	$-0.340624\pi$
$163$	12.2573	0.960068	0.480034	+	0.877250i	$0.340624\pi$
$164$	1.81681	0.141869
$165$	−8.54069	−0.664891
$166$	−1.37878	−0.107014
$167$	4.44819	0.344212	0.172106	−	0.985078i	$-0.444943\pi$
$167$	4.44819	0.344212	0.172106	+	0.985078i	$0.444943\pi$
$168$	0	0
$169$	0	0
$170$	−2.44177	−0.187275
$171$	10.8466	0.829461
$172$	−11.4305	−0.871569
$173$	−24.1401	−1.83534	−0.917670	−	0.397344i	$-0.869932\pi$
$173$	−24.1401	−1.83534	−0.917670	+	0.397344i	$0.869932\pi$
$174$	1.68240	0.127543
$175$	0	0
$176$	−3.40223	−0.256453
$177$	14.3874	1.08142
$178$	−1.32058	−0.0989820
$179$	−5.68045	−0.424577	−0.212288	−	0.977207i	$-0.568092\pi$
$179$	−5.68045	−0.424577	−0.212288	+	0.977207i	$0.568092\pi$
$180$	−37.8251	−2.81931
$181$	8.39175	0.623754	0.311877	−	0.950122i	$-0.399042\pi$
$181$	8.39175	0.623754	0.311877	+	0.950122i	$0.399042\pi$
$182$	0	0
$183$	−2.87296	−0.212375
$184$	−3.73150	−0.275090
$185$	−2.36882	−0.174159
$186$	−3.66257	−0.268553
$187$	−4.75830	−0.347961
$188$	6.97055	0.508380
$189$	0	0
$190$	−0.839341	−0.0608922
$191$	9.18700	0.664748	0.332374	−	0.943148i	$-0.392150\pi$
$191$	9.18700	0.664748	0.332374	+	0.943148i	$0.392150\pi$
$192$	−22.4190	−1.61795
$193$	5.14507	0.370350	0.185175	−	0.982706i	$-0.440715\pi$
$193$	5.14507	0.370350	0.185175	+	0.982706i	$0.440715\pi$
$194$	2.17551	0.156193
$195$	0	0
$196$	0	0
$197$	9.26605	0.660178	0.330089	−	0.943950i	$-0.392921\pi$
$197$	9.26605	0.660178	0.330089	+	0.943950i	$0.392921\pi$
$198$	0.692675	0.0492263
$199$	−15.0967	−1.07018	−0.535090	−	0.844795i	$-0.679722\pi$
$199$	−15.0967	−1.07018	−0.535090	+	0.844795i	$0.679722\pi$
$200$	3.16515	0.223810
$201$	−20.3135	−1.43280
$202$	−0.323426	−0.0227562
$203$	0	0
$204$	−31.9700	−2.23835
$205$	−3.01701	−0.210717
$206$	−0.297012	−0.0206938
$207$	−39.8511	−2.76985
$208$	0	0
$209$	−1.63563	−0.113139
$210$	0	0
$211$	8.34760	0.574673	0.287336	−	0.957830i	$-0.407230\pi$
$211$	8.34760	0.574673	0.287336	+	0.957830i	$0.407230\pi$
$212$	−9.55032	−0.655919
$213$	20.5123	1.40548
$214$	−1.24085	−0.0848228
$215$	18.9816	1.29454
$216$	4.51622	0.307290
$217$	0	0
$218$	−1.64026	−0.111093
$219$	−9.77915	−0.660814
$220$	5.70388	0.384555
$221$	0	0
$222$	0.291456	0.0195612
$223$	−19.1988	−1.28565	−0.642823	−	0.766015i	$-0.722237\pi$
$223$	−19.1988	−1.28565	−0.642823	+	0.766015i	$0.722237\pi$
$224$	0	0
$225$	33.8027	2.25351
$226$	0.0871193	0.00579509
$227$	20.4239	1.35558	0.677792	−	0.735254i	$-0.262937\pi$
$227$	20.4239	1.35558	0.677792	+	0.735254i	$0.262937\pi$
$228$	−10.9894	−0.727794
$229$	18.2761	1.20772	0.603859	−	0.797091i	$-0.293629\pi$
$229$	18.2761	1.20772	0.603859	+	0.797091i	$0.293629\pi$
$230$	3.08379	0.203339
$231$	0	0
$232$	−2.25774	−0.148228
$233$	−7.95222	−0.520967	−0.260484	−	0.965478i	$-0.583882\pi$
$233$	−7.95222	−0.520967	−0.260484	+	0.965478i	$0.583882\pi$
$234$	0	0
$235$	−11.5754	−0.755093
$236$	−9.60858	−0.625465
$237$	26.7070	1.73480
$238$	0	0
$239$	−28.7653	−1.86067	−0.930335	−	0.366711i	$-0.880484\pi$
$239$	−28.7653	−1.86067	−0.930335	+	0.366711i	$0.880484\pi$
$240$	37.9596	2.45028
$241$	−0.159407	−0.0102683	−0.00513414	−	0.999987i	$-0.501634\pi$
$241$	−0.159407	−0.0102683	−0.00513414	+	0.999987i	$0.501634\pi$
$242$	1.39654	0.0897729
$243$	−3.40852	−0.218657
$244$	1.91870	0.122832
$245$	0	0
$246$	0.371208	0.0236673
$247$	0	0
$248$	4.91507	0.312107
$249$	29.9778	1.89976
$250$	−0.370878	−0.0234564
$251$	10.3711	0.654621	0.327310	−	0.944917i	$-0.393858\pi$
$251$	10.3711	0.654621	0.327310	+	0.944917i	$0.393858\pi$
$252$	0	0
$253$	6.00941	0.377808
$254$	2.58075	0.161931
$255$	53.0896	3.32460
$256$	14.5311	0.908196
$257$	−22.5730	−1.40807	−0.704033	−	0.710167i	$-0.748619\pi$
$257$	−22.5730	−1.40807	−0.704033	+	0.710167i	$0.748619\pi$
$258$	−2.33547	−0.145400
$259$	0	0
$260$	0	0
$261$	−24.1118	−1.49249
$262$	1.65322	0.102137
$263$	−21.1607	−1.30483	−0.652414	−	0.757863i	$-0.726243\pi$
$263$	−21.1607	−1.30483	−0.652414	+	0.757863i	$0.726243\pi$
$264$	−1.41019	−0.0867910
$265$	15.8594	0.974232
$266$	0	0
$267$	28.7125	1.75718
$268$	13.5663	0.828696
$269$	21.0444	1.28310	0.641549	−	0.767082i	$-0.278292\pi$
$269$	21.0444	1.28310	0.641549	+	0.767082i	$0.278292\pi$
$270$	−3.73230	−0.227141
$271$	28.0520	1.70404	0.852019	−	0.523510i	$-0.175378\pi$
$271$	28.0520	1.70404	0.852019	+	0.523510i	$0.175378\pi$
$272$	21.1486	1.28232
$273$	0	0
$274$	−1.29908	−0.0784803
$275$	−5.09732	−0.307380
$276$	40.3759	2.43034
$277$	28.0308	1.68421	0.842104	−	0.539315i	$-0.181317\pi$
$277$	28.0308	1.68421	0.842104	+	0.539315i	$0.181317\pi$
$278$	2.63187	0.157849
$279$	52.4912	3.14257
$280$	0	0
$281$	−3.73990	−0.223104	−0.111552	−	0.993759i	$-0.535582\pi$
$281$	−3.73990	−0.223104	−0.111552	+	0.993759i	$0.535582\pi$
$282$	1.42421	0.0848107
$283$	−2.59894	−0.154491	−0.0772455	−	0.997012i	$-0.524613\pi$
$283$	−2.59894	−0.154491	−0.0772455	+	0.997012i	$0.524613\pi$
$284$	−13.6991	−0.812893
$285$	18.2492	1.08099
$286$	0	0
$287$	0	0
$288$	−9.38278	−0.552885
$289$	12.5780	0.739881
$290$	1.86584	0.109566
$291$	−47.3006	−2.77281
$292$	6.53099	0.382197
$293$	−21.1964	−1.23831	−0.619154	−	0.785270i	$-0.712524\pi$
$293$	−21.1964	−1.23831	−0.619154	+	0.785270i	$0.712524\pi$
$294$	0	0
$295$	15.9561	0.928999
$296$	−0.391126	−0.0227337
$297$	−7.27316	−0.422032
$298$	−0.506244	−0.0293259
$299$	0	0
$300$	−34.2478	−1.97730
$301$	0	0
$302$	−2.26295	−0.130218
$303$	7.03202	0.403979
$304$	7.26966	0.416944
$305$	−3.18621	−0.182442
$306$	−4.30573	−0.246142
$307$	5.82988	0.332729	0.166364	−	0.986064i	$-0.446797\pi$
$307$	5.82988	0.332729	0.166364	+	0.986064i	$0.446797\pi$
$308$	0	0
$309$	6.45771	0.367366
$310$	−4.06192	−0.230701
$311$	0.938430	0.0532135	0.0266067	−	0.999646i	$-0.491530\pi$
$311$	0.938430	0.0532135	0.0266067	+	0.999646i	$0.491530\pi$
$312$	0	0
$313$	16.3375	0.923450	0.461725	−	0.887023i	$-0.347231\pi$
$313$	16.3375	0.923450	0.461725	+	0.887023i	$0.347231\pi$
$314$	0.772860	0.0436150
$315$	0	0
$316$	−17.8362	−1.00336
$317$	−2.68669	−0.150900	−0.0754498	−	0.997150i	$-0.524039\pi$
$317$	−2.68669	−0.150900	−0.0754498	+	0.997150i	$0.524039\pi$
$318$	−1.95131	−0.109424
$319$	3.63598	0.203576
$320$	−24.8634	−1.38991
$321$	26.9789	1.50581
$322$	0	0
$323$	10.1672	0.565719
$324$	−14.3790	−0.798834
$325$	0	0
$326$	−1.67256	−0.0926344
$327$	35.6630	1.97217
$328$	−0.498150	−0.0275057
$329$	0	0
$330$	1.16541	0.0641536
$331$	17.1409	0.942151	0.471076	−	0.882093i	$-0.343866\pi$
$331$	17.1409	0.942151	0.471076	+	0.882093i	$0.343866\pi$
$332$	−20.0206	−1.09877
$333$	−4.17709	−0.228903
$334$	−0.606973	−0.0332121
$335$	−22.5284	−1.23086
$336$	0	0
$337$	−10.2932	−0.560704	−0.280352	−	0.959897i	$-0.590451\pi$
$337$	−10.2932	−0.560704	−0.280352	+	0.959897i	$0.590451\pi$
$338$	0	0
$339$	−1.89417	−0.102877
$340$	−35.4558	−1.92286
$341$	−7.91549	−0.428648
$342$	−1.48006	−0.0800325
$343$	0	0
$344$	3.13413	0.168981
$345$	−67.0486	−3.60978
$346$	3.29401	0.177087
$347$	−16.0255	−0.860295	−0.430148	−	0.902759i	$-0.641539\pi$
$347$	−16.0255	−0.860295	−0.430148	+	0.902759i	$0.641539\pi$
$348$	24.4294	1.30955
$349$	−7.61273	−0.407500	−0.203750	−	0.979023i	$-0.565313\pi$
$349$	−7.61273	−0.407500	−0.203750	+	0.979023i	$0.565313\pi$
$350$	0	0
$351$	0	0
$352$	1.41489	0.0754138
$353$	1.15411	0.0614269	0.0307134	−	0.999528i	$-0.490222\pi$
$353$	1.15411	0.0614269	0.0307134	+	0.999528i	$0.490222\pi$
$354$	−1.96321	−0.104343
$355$	22.7489	1.20738
$356$	−19.1756	−1.01630
$357$	0	0
$358$	0.775119	0.0409663
$359$	4.42310	0.233442	0.116721	−	0.993165i	$-0.462762\pi$
$359$	4.42310	0.233442	0.116721	+	0.993165i	$0.462762\pi$
$360$	10.3712	0.546613
$361$	−15.5051	−0.816058
$362$	−1.14509	−0.0601844
$363$	−30.3639	−1.59369
$364$	0	0
$365$	−10.8454	−0.567675
$366$	0.392026	0.0204916
$367$	−15.1442	−0.790523	−0.395261	−	0.918569i	$-0.629346\pi$
$367$	−15.1442	−0.790523	−0.395261	+	0.918569i	$0.629346\pi$
$368$	−26.7092	−1.39231
$369$	−5.32007	−0.276952
$370$	0.323235	0.0168042
$371$	0	0
$372$	−53.1825	−2.75738
$373$	2.47652	0.128229	0.0641147	−	0.997943i	$-0.479578\pi$
$373$	2.47652	0.128229	0.0641147	+	0.997943i	$0.479578\pi$
$374$	0.649287	0.0335739
$375$	8.06374	0.416410
$376$	−1.91126	−0.0985655
$377$	0	0
$378$	0	0
$379$	−28.7790	−1.47828	−0.739140	−	0.673552i	$-0.764768\pi$
$379$	−28.7790	−1.47828	−0.739140	+	0.673552i	$0.764768\pi$
$380$	−12.1877	−0.625214
$381$	−56.1113	−2.87467
$382$	−1.25360	−0.0641398
$383$	24.1588	1.23446	0.617228	−	0.786785i	$-0.288256\pi$
$383$	24.1588	1.23446	0.617228	+	0.786785i	$0.288256\pi$
$384$	12.6548	0.645789
$385$	0	0
$386$	−0.702064	−0.0357341
$387$	33.4715	1.70145
$388$	31.5896	1.60372
$389$	26.5443	1.34585	0.672924	−	0.739711i	$-0.265038\pi$
$389$	26.5443	1.34585	0.672924	+	0.739711i	$0.265038\pi$
$390$	0	0
$391$	−37.3550	−1.88912
$392$	0	0
$393$	−35.9449	−1.81318
$394$	−1.26439	−0.0636989
$395$	29.6189	1.49029
$396$	10.0580	0.505434
$397$	3.61620	0.181492	0.0907458	−	0.995874i	$-0.471075\pi$
$397$	3.61620	0.181492	0.0907458	+	0.995874i	$0.471075\pi$
$398$	2.06001	0.103259
$399$	0	0
$400$	22.6554	1.13277
$401$	−26.5061	−1.32365	−0.661825	−	0.749659i	$-0.730218\pi$
$401$	−26.5061	−1.32365	−0.661825	+	0.749659i	$0.730218\pi$
$402$	2.77186	0.138248
$403$	0	0
$404$	−4.69632	−0.233651
$405$	23.8779	1.18650
$406$	0	0
$407$	0.629889	0.0312225
$408$	8.76584	0.433974
$409$	−23.6953	−1.17166	−0.585828	−	0.810435i	$-0.699231\pi$
$409$	−23.6953	−1.17166	−0.585828	+	0.810435i	$0.699231\pi$
$410$	0.411682	0.0203315
$411$	28.2450	1.39322
$412$	−4.31277	−0.212475
$413$	0	0
$414$	5.43784	0.267255
$415$	33.2464	1.63200
$416$	0	0
$417$	−57.2228	−2.80221
$418$	0.223188	0.0109165
$419$	−13.0737	−0.638693	−0.319347	−	0.947638i	$-0.603463\pi$
$419$	−13.0737	−0.638693	−0.319347	+	0.947638i	$0.603463\pi$
$420$	0	0
$421$	19.2855	0.939920	0.469960	−	0.882688i	$-0.344268\pi$
$421$	19.2855	0.939920	0.469960	+	0.882688i	$0.344268\pi$
$422$	−1.13906	−0.0554487
$423$	−20.4116	−0.992444
$424$	2.61860	0.127171
$425$	31.6854	1.53697
$426$	−2.79899	−0.135611
$427$	0	0
$428$	−18.0178	−0.870923
$429$	0	0
$430$	−2.59012	−0.124906
$431$	6.08723	0.293212	0.146606	−	0.989195i	$-0.453165\pi$
$431$	6.08723	0.293212	0.146606	+	0.989195i	$0.453165\pi$
$432$	32.3260	1.55529
$433$	−27.8249	−1.33718	−0.668589	−	0.743633i	$-0.733101\pi$
$433$	−27.8249	−1.33718	−0.668589	+	0.743633i	$0.733101\pi$
$434$	0	0
$435$	−40.5676	−1.94507
$436$	−23.8175	−1.14065
$437$	−12.8405	−0.614244
$438$	1.33440	0.0637602
$439$	−1.40848	−0.0672230	−0.0336115	−	0.999435i	$-0.510701\pi$
$439$	−1.40848	−0.0672230	−0.0336115	+	0.999435i	$0.510701\pi$
$440$	−1.56395	−0.0745582
$441$	0	0
$442$	0	0
$443$	−22.5545	−1.07160	−0.535799	−	0.844346i	$-0.679989\pi$
$443$	−22.5545	−1.07160	−0.535799	+	0.844346i	$0.679989\pi$
$444$	4.23209	0.200846
$445$	31.8431	1.50951
$446$	2.61975	0.124049
$447$	11.0069	0.520608
$448$	0	0
$449$	−34.1488	−1.61158	−0.805791	−	0.592200i	$-0.798260\pi$
$449$	−34.1488	−1.61158	−0.805791	+	0.592200i	$0.798260\pi$
$450$	−4.61251	−0.217436
$451$	0.802247	0.0377763
$452$	1.26502	0.0595015
$453$	49.2017	2.31170
$454$	−2.78692	−0.130797
$455$	0	0
$456$	3.01319	0.141106
$457$	−22.4990	−1.05246	−0.526228	−	0.850343i	$-0.676394\pi$
$457$	−22.4990	−1.05246	−0.526228	+	0.850343i	$0.676394\pi$
$458$	−2.49384	−0.116530
$459$	45.2106	2.11025
$460$	44.7783	2.08780
$461$	12.9804	0.604558	0.302279	−	0.953219i	$-0.402253\pi$
$461$	12.9804	0.604558	0.302279	+	0.953219i	$0.402253\pi$
$462$	0	0
$463$	30.3212	1.40915	0.704574	−	0.709631i	$-0.251138\pi$
$463$	30.3212	1.40915	0.704574	+	0.709631i	$0.251138\pi$
$464$	−16.1603	−0.750225
$465$	88.3153	4.09552
$466$	1.08511	0.0502668
$467$	−16.5353	−0.765164	−0.382582	−	0.923922i	$-0.624965\pi$
$467$	−16.5353	−0.765164	−0.382582	+	0.923922i	$0.624965\pi$
$468$	0	0
$469$	0	0
$470$	1.57950	0.0728570
$471$	−16.8037	−0.774275
$472$	2.63457	0.121266
$473$	−5.04738	−0.232079
$474$	−3.64427	−0.167387
$475$	10.8916	0.499742
$476$	0	0
$477$	27.9658	1.28046
$478$	3.92513	0.179531
$479$	9.44551	0.431576	0.215788	−	0.976440i	$-0.430768\pi$
$479$	9.44551	0.431576	0.215788	+	0.976440i	$0.430768\pi$
$480$	−15.7863	−0.720543
$481$	0	0
$482$	0.0217516	0.000990760 0
$483$	0	0
$484$	20.2785	0.921749
$485$	−52.4580	−2.38199
$486$	0.465106	0.0210976
$487$	2.82874	0.128182	0.0640912	−	0.997944i	$-0.479585\pi$
$487$	2.82874	0.128182	0.0640912	+	0.997944i	$0.479585\pi$
$488$	−0.526088	−0.0238149
$489$	36.3652	1.64449
$490$	0	0
$491$	37.2871	1.68274	0.841371	−	0.540457i	$-0.181749\pi$
$491$	37.2871	1.68274	0.841371	+	0.540457i	$0.181749\pi$
$492$	5.39013	0.243006
$493$	−22.6015	−1.01792
$494$	0	0
$495$	−16.7024	−0.750717
$496$	35.1809	1.57967
$497$	0	0
$498$	−4.09058	−0.183303
$499$	−18.2471	−0.816851	−0.408426	−	0.912792i	$-0.633922\pi$
$499$	−18.2471	−0.816851	−0.408426	+	0.912792i	$0.633922\pi$
$500$	−5.38535	−0.240840
$501$	13.1970	0.589597
$502$	−1.41518	−0.0631627
$503$	−39.6222	−1.76667	−0.883334	−	0.468745i	$-0.844706\pi$
$503$	−39.6222	−1.76667	−0.883334	+	0.468745i	$0.844706\pi$
$504$	0	0
$505$	7.79875	0.347040
$506$	−0.820006	−0.0364537
$507$	0	0
$508$	37.4738	1.66263
$509$	42.4787	1.88283	0.941417	−	0.337244i	$-0.109495\pi$
$509$	42.4787	1.88283	0.941417	+	0.337244i	$0.109495\pi$
$510$	−7.24428	−0.320782
$511$	0	0
$512$	−10.5137	−0.464646
$513$	15.5408	0.686143
$514$	3.08017	0.135861
$515$	7.16182	0.315588
$516$	−33.9122	−1.49290
$517$	3.07799	0.135370
$518$	0	0
$519$	−71.6193	−3.14374
$520$	0	0
$521$	−20.7345	−0.908393	−0.454197	−	0.890901i	$-0.650074\pi$
$521$	−20.7345	−0.908393	−0.454197	+	0.890901i	$0.650074\pi$
$522$	3.29015	0.144006
$523$	−12.4110	−0.542694	−0.271347	−	0.962482i	$-0.587469\pi$
$523$	−12.4110	−0.542694	−0.271347	+	0.962482i	$0.587469\pi$
$524$	24.0057	1.04869
$525$	0	0
$526$	2.88746	0.125899
$527$	49.2033	2.14333
$528$	−10.0938	−0.439276
$529$	24.1768	1.05117
$530$	−2.16407	−0.0940011
$531$	28.1363	1.22101
$532$	0	0
$533$	0	0
$534$	−3.91793	−0.169545
$535$	29.9205	1.29358
$536$	−3.71975	−0.160669
$537$	−16.8528	−0.727253
$538$	−2.87158	−0.123803
$539$	0	0
$540$	−54.1950	−2.33218
$541$	23.1917	0.997087	0.498544	−	0.866865i	$-0.333868\pi$
$541$	23.1917	0.997087	0.498544	+	0.866865i	$0.333868\pi$
$542$	−3.82780	−0.164418
$543$	24.8968	1.06842
$544$	−8.79506	−0.377085
$545$	39.5515	1.69420
$546$	0	0
$547$	23.3740	0.999401	0.499700	−	0.866198i	$-0.333443\pi$
$547$	23.3740	0.999401	0.499700	+	0.866198i	$0.333443\pi$
$548$	−18.8633	−0.805802
$549$	−5.61845	−0.239789
$550$	0.695549	0.0296583
$551$	−7.76911	−0.330975
$552$	−11.0707	−0.471199
$553$	0	0
$554$	−3.82491	−0.162505
$555$	−7.02785	−0.298316
$556$	38.2161	1.62073
$557$	24.1355	1.02265	0.511327	−	0.859386i	$-0.329154\pi$
$557$	24.1355	1.02265	0.511327	+	0.859386i	$0.329154\pi$
$558$	−7.16263	−0.303218
$559$	0	0
$560$	0	0
$561$	−14.1170	−0.596019
$562$	0.510323	0.0215267
$563$	−14.5788	−0.614421	−0.307211	−	0.951642i	$-0.599396\pi$
$563$	−14.5788	−0.614421	−0.307211	+	0.951642i	$0.599396\pi$
$564$	20.6803	0.870799
$565$	−2.10070	−0.0883771
$566$	0.354635	0.0149064
$567$	0	0
$568$	3.75616	0.157605
$569$	44.7162	1.87460	0.937300	−	0.348523i	$-0.113317\pi$
$569$	44.7162	1.87460	0.937300	+	0.348523i	$0.113317\pi$
$570$	−2.49017	−0.104302
$571$	5.72926	0.239762	0.119881	−	0.992788i	$-0.461749\pi$
$571$	5.72926	0.239762	0.119881	+	0.992788i	$0.461749\pi$
$572$	0	0
$573$	27.2561	1.13864
$574$	0	0
$575$	−40.0165	−1.66880
$576$	−43.8432	−1.82680
$577$	−22.5788	−0.939969	−0.469985	−	0.882675i	$-0.655741\pi$
$577$	−22.5788	−0.939969	−0.469985	+	0.882675i	$0.655741\pi$
$578$	−1.71631	−0.0713892
$579$	15.2645	0.634370
$580$	27.0930	1.12498
$581$	0	0
$582$	6.45435	0.267541
$583$	−4.21714	−0.174656
$584$	−1.79073	−0.0741009
$585$	0	0
$586$	2.89233	0.119481
$587$	34.4761	1.42298	0.711491	−	0.702695i	$-0.248020\pi$
$587$	34.4761	1.42298	0.711491	+	0.702695i	$0.248020\pi$
$588$	0	0
$589$	16.9133	0.696900
$590$	−2.17727	−0.0896367
$591$	27.4906	1.13081
$592$	−2.79958	−0.115062
$593$	−23.1502	−0.950666	−0.475333	−	0.879806i	$-0.657672\pi$
$593$	−23.1502	−0.950666	−0.475333	+	0.879806i	$0.657672\pi$
$594$	0.992450	0.0407207
$595$	0	0
$596$	−7.35093	−0.301106
$597$	−44.7892	−1.83310
$598$	0	0
$599$	−16.5535	−0.676357	−0.338179	−	0.941082i	$-0.609811\pi$
$599$	−16.5535	−0.676357	−0.338179	+	0.941082i	$0.609811\pi$
$600$	9.39041	0.383362
$601$	7.89385	0.321997	0.160999	−	0.986955i	$-0.448529\pi$
$601$	7.89385	0.321997	0.160999	+	0.986955i	$0.448529\pi$
$602$	0	0
$603$	−39.7257	−1.61775
$604$	−32.8593	−1.33703
$605$	−33.6746	−1.36907
$606$	−0.959545	−0.0389789
$607$	38.3412	1.55622	0.778110	−	0.628128i	$-0.216179\pi$
$607$	38.3412	1.55622	0.778110	+	0.628128i	$0.216179\pi$
$608$	−3.02324	−0.122608
$609$	0	0
$610$	0.434771	0.0176034
$611$	0	0
$612$	−62.5214	−2.52728
$613$	−45.1692	−1.82437	−0.912184	−	0.409781i	$-0.865605\pi$
$613$	−45.1692	−1.82437	−0.912184	+	0.409781i	$0.865605\pi$
$614$	−0.795509	−0.0321041
$615$	−8.95090	−0.360935
$616$	0	0
$617$	−40.1763	−1.61744	−0.808718	−	0.588196i	$-0.799838\pi$
$617$	−40.1763	−1.61744	−0.808718	+	0.588196i	$0.799838\pi$
$618$	−0.881179	−0.0354462
$619$	−8.14489	−0.327371	−0.163685	−	0.986513i	$-0.552338\pi$
$619$	−8.14489	−0.327371	−0.163685	+	0.986513i	$0.552338\pi$
$620$	−58.9812	−2.36874
$621$	−57.0979	−2.29126
$622$	−0.128052	−0.00513443
$623$	0	0
$624$	0	0
$625$	−20.1873	−0.807493
$626$	−2.22931	−0.0891013
$627$	−4.85261	−0.193794
$628$	11.2223	0.447820
$629$	−3.91545	−0.156119
$630$	0	0
$631$	−13.6934	−0.545124	−0.272562	−	0.962138i	$-0.587871\pi$
$631$	−13.6934	−0.545124	−0.272562	+	0.962138i	$0.587871\pi$
$632$	4.89050	0.194534
$633$	24.7658	0.984352
$634$	0.366609	0.0145599
$635$	−62.2294	−2.46950
$636$	−28.3340	−1.12352
$637$	0	0
$638$	−0.496143	−0.0196425
$639$	40.1145	1.58690
$640$	14.0346	0.554767
$641$	−3.32843	−0.131465	−0.0657326	−	0.997837i	$-0.520938\pi$
$641$	−3.32843	−0.131465	−0.0657326	+	0.997837i	$0.520938\pi$
$642$	−3.68137	−0.145292
$643$	0.362106	0.0142801	0.00714003	−	0.999975i	$-0.497727\pi$
$643$	0.362106	0.0142801	0.00714003	+	0.999975i	$0.497727\pi$
$644$	0	0
$645$	56.3150	2.21740
$646$	−1.38735	−0.0545847
$647$	−16.4860	−0.648131	−0.324066	−	0.946035i	$-0.605050\pi$
$647$	−16.4860	−0.648131	−0.324066	+	0.946035i	$0.605050\pi$
$648$	3.94258	0.154879
$649$	−4.24286	−0.166547
$650$	0	0
$651$	0	0
$652$	−24.2864	−0.951130
$653$	30.0950	1.17771	0.588853	−	0.808240i	$-0.299580\pi$
$653$	30.0950	1.17771	0.588853	+	0.808240i	$0.299580\pi$
$654$	−4.86636	−0.190290
$655$	−39.8641	−1.55762
$656$	−3.56564	−0.139215
$657$	−19.1244	−0.746113
$658$	0	0
$659$	8.13142	0.316755	0.158378	−	0.987379i	$-0.449374\pi$
$659$	8.13142	0.316755	0.158378	+	0.987379i	$0.449374\pi$
$660$	16.9223	0.658701
$661$	23.9240	0.930534	0.465267	−	0.885170i	$-0.345958\pi$
$661$	23.9240	0.930534	0.465267	+	0.885170i	$0.345958\pi$
$662$	−2.33895	−0.0909057
$663$	0	0
$664$	5.48944	0.213032
$665$	0	0
$666$	0.569979	0.0220863
$667$	28.5442	1.10524
$668$	−8.81357	−0.341007
$669$	−56.9592	−2.20217
$670$	3.07408	0.118762
$671$	0.847241	0.0327074
$672$	0	0
$673$	−19.3113	−0.744395	−0.372197	−	0.928154i	$-0.621396\pi$
$673$	−19.3113	−0.744395	−0.372197	+	0.928154i	$0.621396\pi$
$674$	1.40454	0.0541008
$675$	48.4318	1.86414
$676$	0	0
$677$	−23.1767	−0.890752	−0.445376	−	0.895344i	$-0.646930\pi$
$677$	−23.1767	−0.890752	−0.445376	+	0.895344i	$0.646930\pi$
$678$	0.258467	0.00992636
$679$	0	0
$680$	9.72162	0.372807
$681$	60.5940	2.32197
$682$	1.08010	0.0413591
$683$	35.9572	1.37586	0.687932	−	0.725775i	$-0.258519\pi$
$683$	35.9572	1.37586	0.687932	+	0.725775i	$0.258519\pi$
$684$	−21.4913	−0.821739
$685$	31.3246	1.19685
$686$	0	0
$687$	54.2218	2.06869
$688$	22.4334	0.855265
$689$	0	0
$690$	9.14904	0.348298
$691$	−19.2587	−0.732636	−0.366318	−	0.930490i	$-0.619382\pi$
$691$	−19.2587	−0.732636	−0.366318	+	0.930490i	$0.619382\pi$
$692$	47.8308	1.81825
$693$	0	0
$694$	2.18674	0.0830076
$695$	−63.4621	−2.40725
$696$	−6.69828	−0.253898
$697$	−4.98684	−0.188890
$698$	1.03879	0.0393186
$699$	−23.5928	−0.892360
$700$	0	0
$701$	29.0603	1.09759	0.548797	−	0.835956i	$-0.315086\pi$
$701$	29.0603	1.09759	0.548797	+	0.835956i	$0.315086\pi$
$702$	0	0
$703$	−1.34591	−0.0507618
$704$	6.61139	0.249176
$705$	−34.3420	−1.29339
$706$	−0.157482	−0.00592692
$707$	0	0
$708$	−28.5069	−1.07135
$709$	−31.0355	−1.16556	−0.582781	−	0.812629i	$-0.698036\pi$
$709$	−31.0355	−1.16556	−0.582781	+	0.812629i	$0.698036\pi$
$710$	−3.10417	−0.116497
$711$	52.2289	1.95874
$712$	5.25775	0.197042
$713$	−62.1405	−2.32718
$714$	0	0
$715$	0	0
$716$	11.2551	0.420624
$717$	−85.3412	−3.18712
$718$	−0.603549	−0.0225243
$719$	9.26681	0.345594	0.172797	−	0.984957i	$-0.444720\pi$
$719$	9.26681	0.345594	0.172797	+	0.984957i	$0.444720\pi$
$720$	74.2349	2.76657
$721$	0	0
$722$	2.11573	0.0787393
$723$	−0.472930	−0.0175884
$724$	−16.6273	−0.617947
$725$	−24.2119	−0.899207
$726$	4.14327	0.153771
$727$	13.0885	0.485426	0.242713	−	0.970098i	$-0.421963\pi$
$727$	13.0885	0.485426	0.242713	+	0.970098i	$0.421963\pi$
$728$	0	0
$729$	−31.8837	−1.18088
$730$	1.47990	0.0547735
$731$	31.3749	1.16044
$732$	5.69243	0.210398
$733$	−8.28796	−0.306123	−0.153061	−	0.988217i	$-0.548913\pi$
$733$	−8.28796	−0.306123	−0.153061	+	0.988217i	$0.548913\pi$
$734$	2.06649	0.0762755
$735$	0	0
$736$	11.1076	0.409431
$737$	5.99048	0.220662
$738$	0.725944	0.0267224
$739$	9.11800	0.335411	0.167705	−	0.985837i	$-0.446364\pi$
$739$	9.11800	0.335411	0.167705	+	0.985837i	$0.446364\pi$
$740$	4.69353	0.172538
$741$	0	0
$742$	0	0
$743$	−0.607766	−0.0222968	−0.0111484	−	0.999938i	$-0.503549\pi$
$743$	−0.607766	−0.0222968	−0.0111484	+	0.999938i	$0.503549\pi$
$744$	14.5821	0.534605
$745$	12.2070	0.447231
$746$	−0.337930	−0.0123725
$747$	58.6254	2.14499
$748$	9.42800	0.344722
$749$	0	0
$750$	−1.10033	−0.0401783
$751$	−18.1861	−0.663622	−0.331811	−	0.943346i	$-0.607660\pi$
$751$	−18.1861	−0.663622	−0.331811	+	0.943346i	$0.607660\pi$
$752$	−13.6803	−0.498870
$753$	30.7693	1.12129
$754$	0	0
$755$	54.5664	1.98588
$756$	0	0
$757$	−12.8225	−0.466041	−0.233021	−	0.972472i	$-0.574861\pi$
$757$	−12.8225	−0.466041	−0.233021	+	0.972472i	$0.574861\pi$
$758$	3.92701	0.142635
$759$	17.8288	0.647144
$760$	3.34173	0.121217
$761$	15.8260	0.573691	0.286845	−	0.957977i	$-0.407393\pi$
$761$	15.8260	0.573691	0.286845	+	0.957977i	$0.407393\pi$
$762$	7.65660	0.277369
$763$	0	0
$764$	−18.2029	−0.658560
$765$	103.824	3.75375
$766$	−3.29655	−0.119109
$767$	0	0
$768$	43.1112	1.55564
$769$	−24.6606	−0.889284	−0.444642	−	0.895708i	$-0.646669\pi$
$769$	−24.6606	−0.889284	−0.444642	+	0.895708i	$0.646669\pi$
$770$	0	0
$771$	−66.9699	−2.41186
$772$	−10.1943	−0.366902
$773$	−0.0738456	−0.00265604	−0.00132802	−	0.999999i	$-0.500423\pi$
$773$	−0.0738456	−0.00265604	−0.00132802	+	0.999999i	$0.500423\pi$
$774$	−4.56731	−0.164169
$775$	52.7090	1.89336
$776$	−8.66155	−0.310932
$777$	0	0
$778$	−3.62207	−0.129857
$779$	−1.71419	−0.0614172
$780$	0	0
$781$	−6.04912	−0.216454
$782$	5.09723	0.182277
$783$	−34.5470	−1.23461
$784$	0	0
$785$	−18.6359	−0.665144
$786$	4.90481	0.174949
$787$	0.329950	0.0117614	0.00588072	−	0.999983i	$-0.498128\pi$
$787$	0.329950	0.0117614	0.00588072	+	0.999983i	$0.498128\pi$
$788$	−18.3596	−0.654032
$789$	−62.7800	−2.23503
$790$	−4.04162	−0.143794
$791$	0	0
$792$	−2.75780	−0.0979942
$793$	0	0
$794$	−0.493443	−0.0175117
$795$	47.0517	1.66875
$796$	29.9124	1.06022
$797$	−30.4986	−1.08032	−0.540158	−	0.841563i	$-0.681636\pi$
$797$	−30.4986	−1.08032	−0.540158	+	0.841563i	$0.681636\pi$
$798$	0	0
$799$	−19.1330	−0.676878
$800$	−9.42171	−0.333108
$801$	56.1510	1.98400
$802$	3.61685	0.127715
$803$	2.88389	0.101770
$804$	40.2488	1.41947
$805$	0	0
$806$	0	0
$807$	62.4347	2.19781
$808$	1.28768	0.0453005
$809$	29.6860	1.04370	0.521852	−	0.853036i	$-0.325241\pi$
$809$	29.6860	1.04370	0.521852	+	0.853036i	$0.325241\pi$
$810$	−3.25823	−0.114483
$811$	−38.5645	−1.35418	−0.677091	−	0.735899i	$-0.736760\pi$
$811$	−38.5645	−1.35418	−0.677091	+	0.735899i	$0.736760\pi$
$812$	0	0
$813$	83.2251	2.91883
$814$	−0.0859508	−0.00301257
$815$	40.3302	1.41271
$816$	62.7438	2.19647
$817$	10.7849	0.377316
$818$	3.23331	0.113050
$819$	0	0
$820$	5.97784	0.208755
$821$	−46.9737	−1.63939	−0.819697	−	0.572797i	$-0.805858\pi$
$821$	−46.9737	−1.63939	−0.819697	+	0.572797i	$0.805858\pi$
$822$	−3.85413	−0.134428
$823$	−22.0488	−0.768574	−0.384287	−	0.923214i	$-0.625553\pi$
$823$	−22.0488	−0.768574	−0.384287	+	0.923214i	$0.625553\pi$
$824$	1.18252	0.0411949
$825$	−15.1228	−0.526509
$826$	0	0
$827$	−32.6514	−1.13540	−0.567700	−	0.823235i	$-0.692167\pi$
$827$	−32.6514	−1.13540	−0.567700	+	0.823235i	$0.692167\pi$
$828$	78.9603	2.74406
$829$	−4.38573	−0.152323	−0.0761613	−	0.997096i	$-0.524266\pi$
$829$	−4.38573	−0.152323	−0.0761613	+	0.997096i	$0.524266\pi$
$830$	−4.53659	−0.157467
$831$	83.1622	2.88486
$832$	0	0
$833$	0	0
$834$	7.80827	0.270378
$835$	14.6359	0.506496
$836$	3.24080	0.112086
$837$	75.2084	2.59958
$838$	1.78396	0.0616259
$839$	29.9207	1.03298	0.516488	−	0.856294i	$-0.327239\pi$
$839$	29.9207	1.03298	0.516488	+	0.856294i	$0.327239\pi$
$840$	0	0
$841$	−11.7294	−0.404461
$842$	−2.63158	−0.0906904
$843$	−11.0956	−0.382152
$844$	−16.5398	−0.569323
$845$	0	0
$846$	2.78523	0.0957583
$847$	0	0
$848$	18.7433	0.643649
$849$	−7.71058	−0.264626
$850$	−4.32359	−0.148298
$851$	4.94494	0.169510
$852$	−40.6427	−1.39240
$853$	−44.3926	−1.51997	−0.759987	−	0.649938i	$-0.774795\pi$
$853$	−44.3926	−1.51997	−0.759987	+	0.649938i	$0.774795\pi$
$854$	0	0
$855$	35.6886	1.22052
$856$	4.94030	0.168856
$857$	−8.92234	−0.304781	−0.152391	−	0.988320i	$-0.548697\pi$
$857$	−8.92234	−0.304781	−0.152391	+	0.988320i	$0.548697\pi$
$858$	0	0
$859$	15.3911	0.525138	0.262569	−	0.964913i	$-0.415430\pi$
$859$	15.3911	0.525138	0.262569	+	0.964913i	$0.415430\pi$
$860$	−37.6098	−1.28248
$861$	0	0
$862$	−0.830626	−0.0282912
$863$	−20.5667	−0.700100	−0.350050	−	0.936731i	$-0.613835\pi$
$863$	−20.5667	−0.700100	−0.350050	+	0.936731i	$0.613835\pi$
$864$	−13.4435	−0.457356
$865$	−79.4282	−2.70064
$866$	3.79681	0.129021
$867$	37.3165	1.26734
$868$	0	0
$869$	−7.87593	−0.267172
$870$	5.53560	0.187675
$871$	0	0
$872$	6.53051	0.221151
$873$	−92.5024	−3.13073
$874$	1.75213	0.0592668
$875$	0	0
$876$	19.3762	0.654662
$877$	8.61874	0.291034	0.145517	−	0.989356i	$-0.453515\pi$
$877$	8.61874	0.291034	0.145517	+	0.989356i	$0.453515\pi$
$878$	0.192192	0.00648617
$879$	−62.8858	−2.12109
$880$	−11.1944	−0.377362
$881$	−16.6027	−0.559358	−0.279679	−	0.960094i	$-0.590228\pi$
$881$	−16.6027	−0.559358	−0.279679	+	0.960094i	$0.590228\pi$
$882$	0	0
$883$	40.0699	1.34846	0.674231	−	0.738521i	$-0.264475\pi$
$883$	40.0699	1.34846	0.674231	+	0.738521i	$0.264475\pi$
$884$	0	0
$885$	47.3387	1.59127
$886$	3.07765	0.103396
$887$	14.6818	0.492965	0.246483	−	0.969147i	$-0.420725\pi$
$887$	14.6818	0.492965	0.246483	+	0.969147i	$0.420725\pi$
$888$	−1.16040	−0.0389404
$889$	0	0
$890$	−4.34512	−0.145649
$891$	−6.34934	−0.212711
$892$	38.0401	1.27368
$893$	−6.57684	−0.220085
$894$	−1.50193	−0.0502321
$895$	−18.6904	−0.624750
$896$	0	0
$897$	0	0
$898$	4.65973	0.155497
$899$	−37.5980	−1.25396
$900$	−66.9760	−2.23253
$901$	26.2141	0.873317
$902$	−0.109470	−0.00364494
$903$	0	0
$904$	−0.346855	−0.0115362
$905$	27.6114	0.917833
$906$	−6.71376	−0.223050
$907$	−2.62676	−0.0872201	−0.0436100	−	0.999049i	$-0.513886\pi$
$907$	−2.62676	−0.0872201	−0.0436100	+	0.999049i	$0.513886\pi$
$908$	−40.4676	−1.34296
$909$	13.7520	0.456125
$910$	0	0
$911$	−33.3583	−1.10521	−0.552605	−	0.833443i	$-0.686366\pi$
$911$	−33.3583	−1.10521	−0.552605	+	0.833443i	$0.686366\pi$
$912$	21.5677	0.714179
$913$	−8.84049	−0.292578
$914$	3.07007	0.101549
$915$	−9.45290	−0.312503
$916$	−36.2119	−1.19647
$917$	0	0
$918$	−6.16916	−0.203612
$919$	30.3581	1.00142	0.500710	−	0.865615i	$-0.333072\pi$
$919$	30.3581	1.00142	0.500710	+	0.865615i	$0.333072\pi$
$920$	−12.2777	−0.404785
$921$	17.2962	0.569928
$922$	−1.77123	−0.0583322
$923$	0	0
$924$	0	0
$925$	−4.19442	−0.137912
$926$	−4.13745	−0.135965
$927$	12.6289	0.414787
$928$	6.72061	0.220615
$929$	30.0306	0.985272	0.492636	−	0.870235i	$-0.336033\pi$
$929$	30.0306	0.985272	0.492636	+	0.870235i	$0.336033\pi$
$930$	−12.0510	−0.395166
$931$	0	0
$932$	15.7564	0.516117
$933$	2.78415	0.0911489
$934$	2.25631	0.0738287
$935$	−15.6562	−0.512013
$936$	0	0
$937$	−29.4444	−0.961908	−0.480954	−	0.876746i	$-0.659710\pi$
$937$	−29.4444	−0.961908	−0.480954	+	0.876746i	$0.659710\pi$
$938$	0	0
$939$	48.4703	1.58177
$940$	22.9352	0.748064
$941$	−54.0312	−1.76137	−0.880683	−	0.473706i	$-0.842916\pi$
$941$	−54.0312	−1.76137	−0.880683	+	0.473706i	$0.842916\pi$
$942$	2.29293	0.0747077
$943$	6.29804	0.205092
$944$	18.8577	0.613764
$945$	0	0
$946$	0.688733	0.0223927
$947$	−43.0267	−1.39818	−0.699090	−	0.715034i	$-0.746411\pi$
$947$	−43.0267	−1.39818	−0.699090	+	0.715034i	$0.746411\pi$
$948$	−52.9167	−1.71865
$949$	0	0
$950$	−1.48620	−0.0482188
$951$	−7.97091	−0.258475
$952$	0	0
$953$	−27.1236	−0.878618	−0.439309	−	0.898336i	$-0.644777\pi$
$953$	−27.1236	−0.878618	−0.439309	+	0.898336i	$0.644777\pi$
$954$	−3.81603	−0.123549
$955$	30.2280	0.978154
$956$	56.9949	1.84335
$957$	10.7873	0.348703
$958$	−1.28888	−0.0416417
$959$	0	0
$960$	−73.7652	−2.38076
$961$	50.8504	1.64033
$962$	0	0
$963$	52.7607	1.70019
$964$	0.315845	0.0101727
$965$	16.9288	0.544958
$966$	0	0
$967$	−26.4007	−0.848990	−0.424495	−	0.905430i	$-0.639548\pi$
$967$	−26.4007	−0.848990	−0.424495	+	0.905430i	$0.639548\pi$
$968$	−5.56015	−0.178710
$969$	30.1642	0.969014
$970$	7.15809	0.229832
$971$	5.38602	0.172846	0.0864228	−	0.996259i	$-0.472456\pi$
$971$	5.38602	0.172846	0.0864228	+	0.996259i	$0.472456\pi$
$972$	6.75358	0.216621
$973$	0	0
$974$	−0.385992	−0.0123680
$975$	0	0
$976$	−3.76562	−0.120534
$977$	30.5139	0.976226	0.488113	−	0.872781i	$-0.337685\pi$
$977$	30.5139	0.976226	0.488113	+	0.872781i	$0.337685\pi$
$978$	−4.96217	−0.158673
$979$	−8.46736	−0.270618
$980$	0	0
$981$	69.7436	2.22674
$982$	−5.08796	−0.162363
$983$	−36.0083	−1.14849	−0.574243	−	0.818685i	$-0.694703\pi$
$983$	−36.0083	−1.14849	−0.574243	+	0.818685i	$0.694703\pi$
$984$	−1.47792	−0.0471143
$985$	30.4880	0.971430
$986$	3.08407	0.0982167
$987$	0	0
$988$	0	0
$989$	−39.6244	−1.25998
$990$	2.27911	0.0724347
$991$	50.2430	1.59602	0.798011	−	0.602643i	$-0.205886\pi$
$991$	50.2430	1.59602	0.798011	+	0.602643i	$0.205886\pi$
$992$	−14.6307	−0.464525
$993$	50.8540	1.61380
$994$	0	0
$995$	−49.6728	−1.57473
$996$	−59.3974	−1.88208
$997$	−28.0968	−0.889836	−0.444918	−	0.895571i	$-0.646767\pi$
$997$	−28.0968	−0.889836	−0.444918	+	0.895571i	$0.646767\pi$
$998$	2.48988	0.0788159
$999$	−5.98485	−0.189352

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8281.2.a.cu.1.13		24
7.2	even	3		1183.2.e.l.508.12	yes	48
7.4	even	3		1183.2.e.l.170.12	yes	48
7.6	odd	2		8281.2.a.ct.1.13		24
13.12	even	2		8281.2.a.cv.1.12		24
91.25	even	6		1183.2.e.k.170.13	✓	48
91.51	even	6		1183.2.e.k.508.13	yes	48
91.90	odd	2		8281.2.a.cw.1.12		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.e.k.170.13	✓	48	91.25	even	6
1183.2.e.k.508.13	yes	48	91.51	even	6
1183.2.e.l.170.12	yes	48	7.4	even	3
1183.2.e.l.508.12	yes	48	7.2	even	3
8281.2.a.ct.1.13		24	7.6	odd	2
8281.2.a.cu.1.13		24	1.1	even	1	trivial
8281.2.a.cv.1.12		24	13.12	even	2
8281.2.a.cw.1.12		24	91.90	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:	\( N \)	\(=\)	\( 8281 = 7^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8281.a (trivial)

\(f(q)\)	\(=\)	\(q-0.136454 q^{2} +2.96681 q^{3} -1.98138 q^{4} +3.29030 q^{5} -0.404833 q^{6} +0.543274 q^{8} +5.80198 q^{9} +O(q^{10})\)	\(q-0.136454 q^{2} +2.96681 q^{3} -1.98138 q^{4} +3.29030 q^{5} -0.404833 q^{6} +0.543274 q^{8} +5.80198 q^{9} -0.448974 q^{10} -0.874918 q^{11} -5.87839 q^{12} +9.76170 q^{15} +3.88863 q^{16} +5.43856 q^{17} -0.791703 q^{18} +1.86947 q^{19} -6.51933 q^{20} +0.119386 q^{22} -6.86854 q^{23} +1.61179 q^{24} +5.82606 q^{25} +8.31297 q^{27} -4.15579 q^{29} -1.33202 q^{30} +9.04712 q^{31} -1.61717 q^{32} -2.59572 q^{33} -0.742113 q^{34} -11.4959 q^{36} -0.719941 q^{37} -0.255096 q^{38} +1.78753 q^{40} -0.916940 q^{41} +5.76897 q^{43} +1.73354 q^{44} +19.0903 q^{45} +0.937238 q^{46} -3.51803 q^{47} +11.5368 q^{48} -0.794988 q^{50} +16.1352 q^{51} +4.82004 q^{53} -1.13434 q^{54} -2.87874 q^{55} +5.54636 q^{57} +0.567074 q^{58} +4.84944 q^{59} -19.3416 q^{60} -0.968366 q^{61} -1.23451 q^{62} -7.55659 q^{64} +0.354196 q^{66} -6.84691 q^{67} -10.7759 q^{68} -20.3777 q^{69} +6.91393 q^{71} +3.15207 q^{72} -3.29618 q^{73} +0.0982387 q^{74} +17.2848 q^{75} -3.70412 q^{76} +9.00190 q^{79} +12.7947 q^{80} +7.25707 q^{81} +0.125120 q^{82} +10.1044 q^{83} +17.8945 q^{85} -0.787198 q^{86} -12.3295 q^{87} -0.475320 q^{88} +9.67789 q^{89} -2.60494 q^{90} +13.6092 q^{92} +26.8411 q^{93} +0.480048 q^{94} +6.15110 q^{95} -4.79783 q^{96} -15.9432 q^{97} -5.07626 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - q^{2} + 23 q^{4} + 13 q^{5} + 14 q^{6} + 26 q^{9}+O(q^{10}) \) 24 * q - q^2 + 23 * q^4 + 13 * q^5 + 14 * q^6 + 26 * q^9	\( 24 q - q^{2} + 23 q^{4} + 13 q^{5} + 14 q^{6} + 26 q^{9} + 5 q^{10} - q^{11} + 5 q^{12} + 5 q^{15} + 17 q^{16} - 5 q^{17} + 24 q^{19} + 34 q^{20} - 14 q^{22} + 11 q^{23} + 32 q^{24} + 33 q^{25} - 21 q^{27} + 4 q^{29} - 22 q^{30} + 40 q^{31} - 6 q^{32} + 24 q^{33} + 36 q^{34} - 15 q^{36} - 4 q^{37} - 29 q^{38} - 4 q^{40} + 49 q^{41} + 13 q^{43} + 10 q^{44} + 58 q^{45} - 10 q^{46} + 62 q^{47} + 89 q^{48} - 23 q^{50} - 21 q^{51} - 18 q^{53} + 12 q^{54} - 14 q^{55} - 13 q^{57} + 56 q^{58} + 79 q^{59} + 22 q^{60} + 13 q^{61} + 12 q^{62} + 18 q^{64} - 38 q^{66} - 2 q^{67} - 12 q^{68} - 28 q^{69} - 19 q^{71} + 81 q^{72} + 17 q^{73} + 17 q^{74} + 24 q^{75} + 58 q^{76} - 9 q^{79} + 63 q^{80} + 16 q^{81} - 22 q^{82} + 81 q^{83} - 34 q^{85} + 22 q^{86} + 70 q^{87} - 33 q^{88} + 72 q^{89} + q^{90} - 4 q^{92} + 19 q^{93} - 30 q^{94} + 13 q^{95} + 11 q^{96} + 45 q^{97} - 39 q^{99}+O(q^{100}) \) 24 * q - q^2 + 23 * q^4 + 13 * q^5 + 14 * q^6 + 26 * q^9 + 5 * q^10 - q^11 + 5 * q^12 + 5 * q^15 + 17 * q^16 - 5 * q^17 + 24 * q^19 + 34 * q^20 - 14 * q^22 + 11 * q^23 + 32 * q^24 + 33 * q^25 - 21 * q^27 + 4 * q^29 - 22 * q^30 + 40 * q^31 - 6 * q^32 + 24 * q^33 + 36 * q^34 - 15 * q^36 - 4 * q^37 - 29 * q^38 - 4 * q^40 + 49 * q^41 + 13 * q^43 + 10 * q^44 + 58 * q^45 - 10 * q^46 + 62 * q^47 + 89 * q^48 - 23 * q^50 - 21 * q^51 - 18 * q^53 + 12 * q^54 - 14 * q^55 - 13 * q^57 + 56 * q^58 + 79 * q^59 + 22 * q^60 + 13 * q^61 + 12 * q^62 + 18 * q^64 - 38 * q^66 - 2 * q^67 - 12 * q^68 - 28 * q^69 - 19 * q^71 + 81 * q^72 + 17 * q^73 + 17 * q^74 + 24 * q^75 + 58 * q^76 - 9 * q^79 + 63 * q^80 + 16 * q^81 - 22 * q^82 + 81 * q^83 - 34 * q^85 + 22 * q^86 + 70 * q^87 - 33 * q^88 + 72 * q^89 + q^90 - 4 * q^92 + 19 * q^93 - 30 * q^94 + 13 * q^95 + 11 * q^96 + 45 * q^97 - 39 * q^99

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