LMFDB - Embedded newform 9525.2.a.j.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9525,2,Mod(1,9525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9525, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("9525.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9525 = 3 \cdot 5^{2} \cdot 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9525.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:	$76.0575079253$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.246832.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 5x^{3} + 6x^{2} + 7x - 2 $ x^5 - 2x^4 - 5x^3 + 6x^2 + 7x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 381)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.71250$ of defining polynomial
Character	$\chi$	$=$	9525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.779856 q^{2} +1.00000 q^{3} -1.39182 q^{4} +0.779856 q^{6} +2.49235 q^{7} -2.64513 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.779856 q^{2} +1.00000 q^{3} -1.39182 q^{4} +0.779856 q^{6} +2.49235 q^{7} -2.64513 q^{8} +1.00000 q^{9} +1.94367 q^{11} -1.39182 q^{12} +3.49235 q^{13} +1.94367 q^{14} +0.720827 q^{16} -4.53628 q^{17} +0.779856 q^{18} +2.24737 q^{19} +2.49235 q^{21} +1.51579 q^{22} -1.85555 q^{23} -2.64513 q^{24} +2.72353 q^{26} +1.00000 q^{27} -3.46892 q^{28} +7.87314 q^{29} -3.36839 q^{31} +5.85241 q^{32} +1.94367 q^{33} -3.53764 q^{34} -1.39182 q^{36} +6.58157 q^{37} +1.75263 q^{38} +3.49235 q^{39} +1.44706 q^{41} +1.94367 q^{42} -11.7328 q^{43} -2.70525 q^{44} -1.44706 q^{46} +5.12509 q^{47} +0.720827 q^{48} -0.788187 q^{49} -4.53628 q^{51} -4.86074 q^{52} -3.51312 q^{53} +0.779856 q^{54} -6.59260 q^{56} +2.24737 q^{57} +6.13991 q^{58} +10.9281 q^{59} +7.59943 q^{61} -2.62686 q^{62} +2.49235 q^{63} +3.12238 q^{64} +1.51579 q^{66} -0.605780 q^{67} +6.31370 q^{68} -1.85555 q^{69} +1.80895 q^{71} -2.64513 q^{72} +4.42816 q^{73} +5.13267 q^{74} -3.12795 q^{76} +4.84432 q^{77} +2.72353 q^{78} -0.536277 q^{79} +1.00000 q^{81} +1.12850 q^{82} -2.30397 q^{83} -3.46892 q^{84} -9.14988 q^{86} +7.87314 q^{87} -5.14128 q^{88} -8.38896 q^{89} +8.70416 q^{91} +2.58260 q^{92} -3.36839 q^{93} +3.99683 q^{94} +5.85241 q^{96} +13.1852 q^{97} -0.614672 q^{98} +1.94367 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 2 q^{2} + 5 q^{3} + 6 q^{4} - 2 q^{6} - 6 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q - 2 * q^2 + 5 * q^3 + 6 * q^4 - 2 * q^6 - 6 * q^8 + 5 * q^9	$ 5 q - 2 q^{2} + 5 q^{3} + 6 q^{4} - 2 q^{6} - 6 q^{8} + 5 q^{9} + 14 q^{11} + 6 q^{12} + 5 q^{13} + 14 q^{14} + 8 q^{16} - 4 q^{17} - 2 q^{18} + 4 q^{19} + 2 q^{22} - 15 q^{23} - 6 q^{24} + 12 q^{26} + 5 q^{27} + 2 q^{28} + 9 q^{29} + 3 q^{31} - 14 q^{32} + 14 q^{33} + 4 q^{34} + 6 q^{36} + 5 q^{37} + 16 q^{38} + 5 q^{39} + 4 q^{41} + 14 q^{42} - 10 q^{43} + 18 q^{44} - 4 q^{46} + 4 q^{47} + 8 q^{48} - 9 q^{49} - 4 q^{51} + 8 q^{52} - 3 q^{53} - 2 q^{54} - 10 q^{56} + 4 q^{57} - 6 q^{58} + 23 q^{59} - 15 q^{61} + 24 q^{62} + 2 q^{66} - 18 q^{67} + 24 q^{68} - 15 q^{69} + 12 q^{71} - 6 q^{72} + 43 q^{73} - 36 q^{74} - 32 q^{76} - 4 q^{77} + 12 q^{78} + 16 q^{79} + 5 q^{81} + 44 q^{82} - 11 q^{83} + 2 q^{84} - 28 q^{86} + 9 q^{87} + 14 q^{88} + 9 q^{89} + 26 q^{91} - 14 q^{92} + 3 q^{93} - 14 q^{94} - 14 q^{96} + 20 q^{97} + 10 q^{98} + 14 q^{99}+O(q^{100}) $ 5 * q - 2 * q^2 + 5 * q^3 + 6 * q^4 - 2 * q^6 - 6 * q^8 + 5 * q^9 + 14 * q^11 + 6 * q^12 + 5 * q^13 + 14 * q^14 + 8 * q^16 - 4 * q^17 - 2 * q^18 + 4 * q^19 + 2 * q^22 - 15 * q^23 - 6 * q^24 + 12 * q^26 + 5 * q^27 + 2 * q^28 + 9 * q^29 + 3 * q^31 - 14 * q^32 + 14 * q^33 + 4 * q^34 + 6 * q^36 + 5 * q^37 + 16 * q^38 + 5 * q^39 + 4 * q^41 + 14 * q^42 - 10 * q^43 + 18 * q^44 - 4 * q^46 + 4 * q^47 + 8 * q^48 - 9 * q^49 - 4 * q^51 + 8 * q^52 - 3 * q^53 - 2 * q^54 - 10 * q^56 + 4 * q^57 - 6 * q^58 + 23 * q^59 - 15 * q^61 + 24 * q^62 + 2 * q^66 - 18 * q^67 + 24 * q^68 - 15 * q^69 + 12 * q^71 - 6 * q^72 + 43 * q^73 - 36 * q^74 - 32 * q^76 - 4 * q^77 + 12 * q^78 + 16 * q^79 + 5 * q^81 + 44 * q^82 - 11 * q^83 + 2 * q^84 - 28 * q^86 + 9 * q^87 + 14 * q^88 + 9 * q^89 + 26 * q^91 - 14 * q^92 + 3 * q^93 - 14 * q^94 - 14 * q^96 + 20 * q^97 + 10 * q^98 + 14 * 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 $

$2$	0.779856	0.551441	0.275721	−	0.961238i	$-0.411084\pi$
$2$	0.779856	0.551441	0.275721	+	0.961238i	$0.411084\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.39182	−0.695912
$5$	0	0
$5$	0	0
$6$	0.779856	0.318375
$7$	2.49235	0.942020	0.471010	−	0.882128i	$-0.343890\pi$
$7$	2.49235	0.942020	0.471010	+	0.882128i	$0.343890\pi$
$8$	−2.64513	−0.935196
$9$	1.00000	0.333333
$10$	0	0
$11$	1.94367	0.586040	0.293020	−	0.956106i	$-0.405340\pi$
$11$	1.94367	0.586040	0.293020	+	0.956106i	$0.405340\pi$
$12$	−1.39182	−0.401785
$13$	3.49235	0.968604	0.484302	−	0.874901i	$-0.339074\pi$
$13$	3.49235	0.968604	0.484302	+	0.874901i	$0.339074\pi$
$14$	1.94367	0.519469
$15$	0	0
$16$	0.720827	0.180207
$17$	−4.53628	−1.10021	−0.550104	−	0.835096i	$-0.685412\pi$
$17$	−4.53628	−1.10021	−0.550104	+	0.835096i	$0.685412\pi$
$18$	0.779856	0.183814
$19$	2.24737	0.515583	0.257791	−	0.966201i	$-0.417005\pi$
$19$	2.24737	0.515583	0.257791	+	0.966201i	$0.417005\pi$
$20$	0	0
$21$	2.49235	0.543876
$22$	1.51579	0.323167
$23$	−1.85555	−0.386909	−0.193454	−	0.981109i	$-0.561969\pi$
$23$	−1.85555	−0.386909	−0.193454	+	0.981109i	$0.561969\pi$
$24$	−2.64513	−0.539936
$25$	0	0
$26$	2.72353	0.534128
$27$	1.00000	0.192450
$28$	−3.46892	−0.655564
$29$	7.87314	1.46201	0.731003	−	0.682374i	$-0.239053\pi$
$29$	7.87314	1.46201	0.731003	+	0.682374i	$0.239053\pi$
$30$	0	0
$31$	−3.36839	−0.604981	−0.302490	−	0.953152i	$-0.597818\pi$
$31$	−3.36839	−0.604981	−0.302490	+	0.953152i	$0.597818\pi$
$32$	5.85241	1.03457
$33$	1.94367	0.338350
$34$	−3.53764	−0.606701
$35$	0	0
$36$	−1.39182	−0.231971
$37$	6.58157	1.08200	0.541002	−	0.841022i	$-0.318045\pi$
$37$	6.58157	1.08200	0.541002	+	0.841022i	$0.318045\pi$
$38$	1.75263	0.284314
$39$	3.49235	0.559224
$40$	0	0
$41$	1.44706	0.225993	0.112996	−	0.993595i	$-0.463955\pi$
$41$	1.44706	0.225993	0.112996	+	0.993595i	$0.463955\pi$
$42$	1.94367	0.299915
$43$	−11.7328	−1.78923	−0.894617	−	0.446834i	$-0.852551\pi$
$43$	−11.7328	−1.78923	−0.894617	+	0.446834i	$0.852551\pi$
$44$	−2.70525	−0.407832
$45$	0	0
$46$	−1.44706	−0.213357
$47$	5.12509	0.747571	0.373785	−	0.927515i	$-0.378060\pi$
$47$	5.12509	0.747571	0.373785	+	0.927515i	$0.378060\pi$
$48$	0.720827	0.104042
$49$	−0.788187	−0.112598
$50$	0	0
$51$	−4.53628	−0.635206
$52$	−4.86074	−0.674064
$53$	−3.51312	−0.482564	−0.241282	−	0.970455i	$-0.577568\pi$
$53$	−3.51312	−0.482564	−0.241282	+	0.970455i	$0.577568\pi$
$54$	0.779856	0.106125
$55$	0	0
$56$	−6.59260	−0.880974
$57$	2.24737	0.297672
$58$	6.13991	0.806210
$59$	10.9281	1.42272	0.711359	−	0.702829i	$-0.248080\pi$
$59$	10.9281	1.42272	0.711359	+	0.702829i	$0.248080\pi$
$60$	0	0
$61$	7.59943	0.973008	0.486504	−	0.873678i	$-0.338272\pi$
$61$	7.59943	0.973008	0.486504	+	0.873678i	$0.338272\pi$
$62$	−2.62686	−0.333611
$63$	2.49235	0.314007
$64$	3.12238	0.390298
$65$	0	0
$66$	1.51579	0.186580
$67$	−0.605780	−0.0740078	−0.0370039	−	0.999315i	$-0.511781\pi$
$67$	−0.605780	−0.0740078	−0.0370039	+	0.999315i	$0.511781\pi$
$68$	6.31370	0.765649
$69$	−1.85555	−0.223382
$70$	0	0
$71$	1.80895	0.214683	0.107342	−	0.994222i	$-0.465766\pi$
$71$	1.80895	0.214683	0.107342	+	0.994222i	$0.465766\pi$
$72$	−2.64513	−0.311732
$73$	4.42816	0.518277	0.259139	−	0.965840i	$-0.416561\pi$
$73$	4.42816	0.518277	0.259139	+	0.965840i	$0.416561\pi$
$74$	5.13267	0.596661
$75$	0	0
$76$	−3.12795	−0.358800
$77$	4.84432	0.552061
$78$	2.72353	0.308379
$79$	−0.536277	−0.0603359	−0.0301679	−	0.999545i	$-0.509604\pi$
$79$	−0.536277	−0.0603359	−0.0301679	+	0.999545i	$0.509604\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	1.12850	0.124622
$83$	−2.30397	−0.252894	−0.126447	−	0.991973i	$-0.540357\pi$
$83$	−2.30397	−0.252894	−0.126447	+	0.991973i	$0.540357\pi$
$84$	−3.46892	−0.378490
$85$	0	0
$86$	−9.14988	−0.986657
$87$	7.87314	0.844089
$88$	−5.14128	−0.548062
$89$	−8.38896	−0.889228	−0.444614	−	0.895722i	$-0.646659\pi$
$89$	−8.38896	−0.889228	−0.444614	+	0.895722i	$0.646659\pi$
$90$	0	0
$91$	8.70416	0.912444
$92$	2.58260	0.269254
$93$	−3.36839	−0.349286
$94$	3.99683	0.412241
$95$	0	0
$96$	5.85241	0.597309
$97$	13.1852	1.33875	0.669377	−	0.742923i	$-0.266561\pi$
$97$	13.1852	1.33875	0.669377	+	0.742923i	$0.266561\pi$
$98$	−0.614672	−0.0620913
$99$	1.94367	0.195347
$100$	0	0
$101$	2.48023	0.246792	0.123396	−	0.992358i	$-0.460622\pi$
$101$	2.48023	0.246792	0.123396	+	0.992358i	$0.460622\pi$
$102$	−3.53764	−0.350279
$103$	−8.99229	−0.886037	−0.443018	−	0.896513i	$-0.646092\pi$
$103$	−8.99229	−0.886037	−0.443018	+	0.896513i	$0.646092\pi$
$104$	−9.23774	−0.905835
$105$	0	0
$106$	−2.73972	−0.266106
$107$	−0.866778	−0.0837946	−0.0418973	−	0.999122i	$-0.513340\pi$
$107$	−0.866778	−0.0837946	−0.0418973	+	0.999122i	$0.513340\pi$
$108$	−1.39182	−0.133928
$109$	9.87287	0.945649	0.472825	−	0.881157i	$-0.343234\pi$
$109$	9.87287	0.945649	0.472825	+	0.881157i	$0.343234\pi$
$110$	0	0
$111$	6.58157	0.624695
$112$	1.79655	0.169758
$113$	−16.0821	−1.51287	−0.756436	−	0.654067i	$-0.773061\pi$
$113$	−16.0821	−1.51287	−0.756436	+	0.654067i	$0.773061\pi$
$114$	1.75263	0.164149
$115$	0	0
$116$	−10.9580	−1.01743
$117$	3.49235	0.322868
$118$	8.52234	0.784545
$119$	−11.3060	−1.03642
$120$	0	0
$121$	−7.22213	−0.656557
$122$	5.92646	0.536557
$123$	1.44706	0.130477
$124$	4.68821	0.421014
$125$	0	0
$126$	1.94367	0.173156
$127$	−1.00000	−0.0887357
$127$	−1.00000	−0.0887357
$128$	−9.26981	−0.819343
$129$	−11.7328	−1.03301
$130$	0	0
$131$	17.6006	1.53777	0.768884	−	0.639388i	$-0.220812\pi$
$131$	17.6006	1.53777	0.768884	+	0.639388i	$0.220812\pi$
$132$	−2.70525	−0.235462
$133$	5.60124	0.485689
$134$	−0.472421	−0.0408109
$135$	0	0
$136$	11.9991	1.02891
$137$	−1.92188	−0.164197	−0.0820986	−	0.996624i	$-0.526162\pi$
$137$	−1.92188	−0.164197	−0.0820986	+	0.996624i	$0.526162\pi$
$138$	−1.44706	−0.123182
$139$	10.8500	0.920283	0.460142	−	0.887846i	$-0.347799\pi$
$139$	10.8500	0.920283	0.460142	+	0.887846i	$0.347799\pi$
$140$	0	0
$141$	5.12509	0.431610
$142$	1.41072	0.118385
$143$	6.78799	0.567640
$144$	0.720827	0.0600689
$145$	0	0
$146$	3.45333	0.285799
$147$	−0.788187	−0.0650086
$148$	−9.16039	−0.752979
$149$	−22.5796	−1.84979	−0.924896	−	0.380219i	$-0.875849\pi$
$149$	−22.5796	−1.84979	−0.924896	+	0.380219i	$0.875849\pi$
$150$	0	0
$151$	22.5109	1.83191	0.915954	−	0.401282i	$-0.131435\pi$
$151$	22.5109	1.83191	0.915954	+	0.401282i	$0.131435\pi$
$152$	−5.94460	−0.482171
$153$	−4.53628	−0.366736
$154$	3.77787	0.304429
$155$	0	0
$156$	−4.86074	−0.389171
$157$	15.7880	1.26002	0.630011	−	0.776586i	$-0.283050\pi$
$157$	15.7880	1.26002	0.630011	+	0.776586i	$0.283050\pi$
$158$	−0.418219	−0.0332717
$159$	−3.51312	−0.278608
$160$	0	0
$161$	−4.62468	−0.364476
$162$	0.779856	0.0612713
$163$	−17.0517	−1.33559	−0.667796	−	0.744345i	$-0.732762\pi$
$163$	−17.0517	−1.33559	−0.667796	+	0.744345i	$0.732762\pi$
$164$	−2.01405	−0.157271
$165$	0	0
$166$	−1.79677	−0.139456
$167$	8.95076	0.692631	0.346315	−	0.938118i	$-0.387433\pi$
$167$	8.95076	0.692631	0.346315	+	0.938118i	$0.387433\pi$
$168$	−6.59260	−0.508630
$169$	−0.803486	−0.0618066
$170$	0	0
$171$	2.24737	0.171861
$172$	16.3300	1.24515
$173$	5.32614	0.404939	0.202469	−	0.979289i	$-0.435103\pi$
$173$	5.32614	0.404939	0.202469	+	0.979289i	$0.435103\pi$
$174$	6.13991	0.465466
$175$	0	0
$176$	1.40105	0.105608
$177$	10.9281	0.821406
$178$	−6.54218	−0.490357
$179$	19.5811	1.46356	0.731780	−	0.681541i	$-0.238690\pi$
$179$	19.5811	1.46356	0.731780	+	0.681541i	$0.238690\pi$
$180$	0	0
$181$	19.1351	1.42230	0.711152	−	0.703038i	$-0.248174\pi$
$181$	19.1351	1.42230	0.711152	+	0.703038i	$0.248174\pi$
$182$	6.78799	0.503159
$183$	7.59943	0.561766
$184$	4.90817	0.361835
$185$	0	0
$186$	−2.62686	−0.192611
$187$	−8.81704	−0.644766
$188$	−7.13322	−0.520244
$189$	2.49235	0.181292
$190$	0	0
$191$	−17.2812	−1.25042	−0.625212	−	0.780455i	$-0.714987\pi$
$191$	−17.2812	−1.25042	−0.625212	+	0.780455i	$0.714987\pi$
$192$	3.12238	0.225339
$193$	−18.8248	−1.35504	−0.677519	−	0.735505i	$-0.736945\pi$
$193$	−18.8248	−1.35504	−0.677519	+	0.735505i	$0.736945\pi$
$194$	10.2826	0.738245
$195$	0	0
$196$	1.09702	0.0783585
$197$	−21.3799	−1.52326	−0.761628	−	0.648015i	$-0.775600\pi$
$197$	−21.3799	−1.52326	−0.761628	+	0.648015i	$0.775600\pi$
$198$	1.51579	0.107722
$199$	26.9170	1.90809	0.954047	−	0.299658i	$-0.0968727\pi$
$199$	26.9170	1.90809	0.954047	+	0.299658i	$0.0968727\pi$
$200$	0	0
$201$	−0.605780	−0.0427284
$202$	1.93422	0.136091
$203$	19.6226	1.37724
$204$	6.31370	0.442048
$205$	0	0
$206$	−7.01269	−0.488597
$207$	−1.85555	−0.128970
$208$	2.51738	0.174549
$209$	4.36816	0.302152
$210$	0	0
$211$	3.54184	0.243831	0.121915	−	0.992541i	$-0.461096\pi$
$211$	3.54184	0.243831	0.121915	+	0.992541i	$0.461096\pi$
$212$	4.88964	0.335822
$213$	1.80895	0.123947
$214$	−0.675962	−0.0462078
$215$	0	0
$216$	−2.64513	−0.179979
$217$	−8.39521	−0.569904
$218$	7.69941	0.521470
$219$	4.42816	0.299228
$220$	0	0
$221$	−15.8423	−1.06567
$222$	5.13267	0.344482
$223$	17.4252	1.16688	0.583438	−	0.812158i	$-0.301707\pi$
$223$	17.4252	1.16688	0.583438	+	0.812158i	$0.301707\pi$
$224$	14.5863	0.974585
$225$	0	0
$226$	−12.5417	−0.834260
$227$	10.8821	0.722267	0.361134	−	0.932514i	$-0.382390\pi$
$227$	10.8821	0.722267	0.361134	+	0.932514i	$0.382390\pi$
$228$	−3.12795	−0.207154
$229$	−12.0378	−0.795480	−0.397740	−	0.917498i	$-0.630205\pi$
$229$	−12.0378	−0.795480	−0.397740	+	0.917498i	$0.630205\pi$
$230$	0	0
$231$	4.84432	0.318733
$232$	−20.8255	−1.36726
$233$	13.3785	0.876452	0.438226	−	0.898865i	$-0.355607\pi$
$233$	13.3785	0.876452	0.438226	+	0.898865i	$0.355607\pi$
$234$	2.72353	0.178043
$235$	0	0
$236$	−15.2100	−0.990087
$237$	−0.536277	−0.0348349
$238$	−8.81704	−0.571524
$239$	30.1290	1.94889	0.974443	−	0.224637i	$-0.0721196\pi$
$239$	30.1290	1.94889	0.974443	+	0.224637i	$0.0721196\pi$
$240$	0	0
$241$	26.4367	1.70294	0.851470	−	0.524403i	$-0.175712\pi$
$241$	26.4367	1.70294	0.851470	+	0.524403i	$0.175712\pi$
$242$	−5.63222	−0.362053
$243$	1.00000	0.0641500
$244$	−10.5771	−0.677128
$245$	0	0
$246$	1.12850	0.0719504
$247$	7.84862	0.499395
$248$	8.90984	0.565776
$249$	−2.30397	−0.146008
$250$	0	0
$251$	−21.4096	−1.35136	−0.675680	−	0.737195i	$-0.736150\pi$
$251$	−21.4096	−1.35136	−0.675680	+	0.737195i	$0.736150\pi$
$252$	−3.46892	−0.218521
$253$	−3.60658	−0.226744
$254$	−0.779856	−0.0489325
$255$	0	0
$256$	−13.4739	−0.842117
$257$	1.84014	0.114785	0.0573923	−	0.998352i	$-0.481721\pi$
$257$	1.84014	0.114785	0.0573923	+	0.998352i	$0.481721\pi$
$258$	−9.14988	−0.569647
$259$	16.4036	1.01927
$260$	0	0
$261$	7.87314	0.487335
$262$	13.7259	0.847989
$263$	−2.13565	−0.131690	−0.0658449	−	0.997830i	$-0.520974\pi$
$263$	−2.13565	−0.131690	−0.0658449	+	0.997830i	$0.520974\pi$
$264$	−5.14128	−0.316424
$265$	0	0
$266$	4.36816	0.267829
$267$	−8.38896	−0.513396
$268$	0.843139	0.0515029
$269$	−22.0930	−1.34703	−0.673517	−	0.739172i	$-0.735217\pi$
$269$	−22.0930	−1.34703	−0.673517	+	0.739172i	$0.735217\pi$
$270$	0	0
$271$	−16.7849	−1.01961	−0.509804	−	0.860291i	$-0.670282\pi$
$271$	−16.7849	−1.01961	−0.509804	+	0.860291i	$0.670282\pi$
$272$	−3.26987	−0.198265
$273$	8.70416	0.526800
$274$	−1.49879	−0.0905451
$275$	0	0
$276$	2.58260	0.155454
$277$	20.6239	1.23917	0.619584	−	0.784931i	$-0.287301\pi$
$277$	20.6239	1.23917	0.619584	+	0.784931i	$0.287301\pi$
$278$	8.46142	0.507482
$279$	−3.36839	−0.201660
$280$	0	0
$281$	12.9127	0.770308	0.385154	−	0.922852i	$-0.374148\pi$
$281$	12.9127	0.770308	0.385154	+	0.922852i	$0.374148\pi$
$282$	3.99683	0.238008
$283$	−5.12835	−0.304849	−0.152424	−	0.988315i	$-0.548708\pi$
$283$	−5.12835	−0.304849	−0.152424	+	0.988315i	$0.548708\pi$
$284$	−2.51775	−0.149401
$285$	0	0
$286$	5.29365	0.313020
$287$	3.60658	0.212890
$288$	5.85241	0.344857
$289$	3.57781	0.210459
$290$	0	0
$291$	13.1852	0.772930
$292$	−6.16323	−0.360676
$293$	−13.8495	−0.809099	−0.404550	−	0.914516i	$-0.632572\pi$
$293$	−13.8495	−0.809099	−0.404550	+	0.914516i	$0.632572\pi$
$294$	−0.614672	−0.0358484
$295$	0	0
$296$	−17.4091	−1.01189
$297$	1.94367	0.112783
$298$	−17.6088	−1.02005
$299$	−6.48023	−0.374761
$300$	0	0
$301$	−29.2422	−1.68549
$302$	17.5552	1.01019
$303$	2.48023	0.142485
$304$	1.61997	0.0929114
$305$	0	0
$306$	−3.53764	−0.202234
$307$	2.97082	0.169554	0.0847769	−	0.996400i	$-0.472982\pi$
$307$	2.97082	0.169554	0.0847769	+	0.996400i	$0.472982\pi$
$308$	−6.74244	−0.384186
$309$	−8.99229	−0.511554
$310$	0	0
$311$	20.8146	1.18029	0.590145	−	0.807297i	$-0.299071\pi$
$311$	20.8146	1.18029	0.590145	+	0.807297i	$0.299071\pi$
$312$	−9.23774	−0.522984
$313$	28.0654	1.58635	0.793175	−	0.608994i	$-0.208427\pi$
$313$	28.0654	1.58635	0.793175	+	0.608994i	$0.208427\pi$
$314$	12.3124	0.694828
$315$	0	0
$316$	0.746403	0.0419885
$317$	−17.9162	−1.00627	−0.503137	−	0.864207i	$-0.667821\pi$
$317$	−17.9162	−1.00627	−0.503137	+	0.864207i	$0.667821\pi$
$318$	−2.73972	−0.153636
$319$	15.3028	0.856793
$320$	0	0
$321$	−0.866778	−0.0483788
$322$	−3.60658	−0.200987
$323$	−10.1947	−0.567249
$324$	−1.39182	−0.0773236
$325$	0	0
$326$	−13.2979	−0.736500
$327$	9.87287	0.545971
$328$	−3.82767	−0.211348
$329$	12.7735	0.704226
$330$	0	0
$331$	−16.8466	−0.925975	−0.462988	−	0.886365i	$-0.653223\pi$
$331$	−16.8466	−0.925975	−0.462988	+	0.886365i	$0.653223\pi$
$332$	3.20673	0.175992
$333$	6.58157	0.360668
$334$	6.98030	0.381945
$335$	0	0
$336$	1.79655	0.0980100
$337$	34.3624	1.87184	0.935920	−	0.352211i	$-0.114570\pi$
$337$	34.3624	1.87184	0.935920	+	0.352211i	$0.114570\pi$
$338$	−0.626603	−0.0340827
$339$	−16.0821	−0.873457
$340$	0	0
$341$	−6.54705	−0.354543
$342$	1.75263	0.0947712
$343$	−19.4109	−1.04809
$344$	31.0348	1.67328
$345$	0	0
$346$	4.15362	0.223300
$347$	−11.7399	−0.630231	−0.315115	−	0.949053i	$-0.602043\pi$
$347$	−11.7399	−0.630231	−0.315115	+	0.949053i	$0.602043\pi$
$348$	−10.9580	−0.587412
$349$	−2.81977	−0.150939	−0.0754695	−	0.997148i	$-0.524046\pi$
$349$	−2.81977	−0.150939	−0.0754695	+	0.997148i	$0.524046\pi$
$350$	0	0
$351$	3.49235	0.186408
$352$	11.3752	0.606299
$353$	15.4602	0.822862	0.411431	−	0.911441i	$-0.365029\pi$
$353$	15.4602	0.822862	0.411431	+	0.911441i	$0.365029\pi$
$354$	8.52234	0.452957
$355$	0	0
$356$	11.6760	0.618825
$357$	−11.3060	−0.598377
$358$	15.2704	0.807067
$359$	22.0346	1.16294	0.581472	−	0.813567i	$-0.302477\pi$
$359$	22.0346	1.16294	0.581472	+	0.813567i	$0.302477\pi$
$360$	0	0
$361$	−13.9493	−0.734174
$362$	14.9227	0.784317
$363$	−7.22213	−0.379064
$364$	−12.1147	−0.634981
$365$	0	0
$366$	5.92646	0.309781
$367$	−16.4982	−0.861199	−0.430599	−	0.902543i	$-0.641698\pi$
$367$	−16.4982	−0.861199	−0.430599	+	0.902543i	$0.641698\pi$
$368$	−1.33753	−0.0697235
$369$	1.44706	0.0753309
$370$	0	0
$371$	−8.75592	−0.454585
$372$	4.68821	0.243072
$373$	35.5556	1.84100	0.920500	−	0.390743i	$-0.127782\pi$
$373$	35.5556	1.84100	0.920500	+	0.390743i	$0.127782\pi$
$374$	−6.87602	−0.355551
$375$	0	0
$376$	−13.5565	−0.699125
$377$	27.4958	1.41610
$378$	1.94367	0.0999718
$379$	−11.0970	−0.570013	−0.285007	−	0.958526i	$-0.591996\pi$
$379$	−11.0970	−0.570013	−0.285007	+	0.958526i	$0.591996\pi$
$380$	0	0
$381$	−1.00000	−0.0512316
$382$	−13.4768	−0.689535
$383$	33.8793	1.73115	0.865576	−	0.500777i	$-0.166952\pi$
$383$	33.8793	1.73115	0.865576	+	0.500777i	$0.166952\pi$
$384$	−9.26981	−0.473048
$385$	0	0
$386$	−14.6806	−0.747224
$387$	−11.7328	−0.596411
$388$	−18.3515	−0.931656
$389$	2.72379	0.138101	0.0690507	−	0.997613i	$-0.478003\pi$
$389$	2.72379	0.138101	0.0690507	+	0.997613i	$0.478003\pi$
$390$	0	0
$391$	8.41728	0.425680
$392$	2.08486	0.105301
$393$	17.6006	0.887831
$394$	−16.6732	−0.839986
$395$	0	0
$396$	−2.70525	−0.135944
$397$	16.6770	0.836994	0.418497	−	0.908218i	$-0.362557\pi$
$397$	16.6770	0.836994	0.418497	+	0.908218i	$0.362557\pi$
$398$	20.9914	1.05220
$399$	5.60124	0.280413
$400$	0	0
$401$	5.90801	0.295032	0.147516	−	0.989060i	$-0.452872\pi$
$401$	5.90801	0.295032	0.147516	+	0.989060i	$0.452872\pi$
$402$	−0.472421	−0.0235622
$403$	−11.7636	−0.585987
$404$	−3.45204	−0.171745
$405$	0	0
$406$	15.3028	0.759466
$407$	12.7924	0.634097
$408$	11.9991	0.594042
$409$	−10.2716	−0.507899	−0.253950	−	0.967217i	$-0.581730\pi$
$409$	−10.2716	−0.507899	−0.253950	+	0.967217i	$0.581730\pi$
$410$	0	0
$411$	−1.92188	−0.0947993
$412$	12.5157	0.616604
$413$	27.2367	1.34023
$414$	−1.44706	−0.0711191
$415$	0	0
$416$	20.4387	1.00209
$417$	10.8500	0.531326
$418$	3.40654	0.166619
$419$	0.982385	0.0479926	0.0239963	−	0.999712i	$-0.492361\pi$
$419$	0.982385	0.0479926	0.0239963	+	0.999712i	$0.492361\pi$
$420$	0	0
$421$	16.2694	0.792924	0.396462	−	0.918051i	$-0.370238\pi$
$421$	16.2694	0.792924	0.396462	+	0.918051i	$0.370238\pi$
$422$	2.76213	0.134458
$423$	5.12509	0.249190
$424$	9.29266	0.451292
$425$	0	0
$426$	1.41072	0.0683497
$427$	18.9405	0.916593
$428$	1.20640	0.0583137
$429$	6.78799	0.327727
$430$	0	0
$431$	−29.4579	−1.41894	−0.709468	−	0.704738i	$-0.751065\pi$
$431$	−29.4579	−1.41894	−0.709468	+	0.704738i	$0.751065\pi$
$432$	0.720827	0.0346808
$433$	−36.8755	−1.77212	−0.886061	−	0.463568i	$-0.846569\pi$
$433$	−36.8755	−1.77212	−0.886061	+	0.463568i	$0.846569\pi$
$434$	−6.54705	−0.314269
$435$	0	0
$436$	−13.7413	−0.658089
$437$	−4.17011	−0.199483
$438$	3.45333	0.165006
$439$	28.1619	1.34410	0.672048	−	0.740507i	$-0.265415\pi$
$439$	28.1619	1.34410	0.672048	+	0.740507i	$0.265415\pi$
$440$	0	0
$441$	−0.788187	−0.0375327
$442$	−12.3547	−0.587652
$443$	−8.90892	−0.423275	−0.211638	−	0.977348i	$-0.567880\pi$
$443$	−8.90892	−0.423275	−0.211638	+	0.977348i	$0.567880\pi$
$444$	−9.16039	−0.434733
$445$	0	0
$446$	13.5891	0.643463
$447$	−22.5796	−1.06798
$448$	7.78207	0.367668
$449$	5.64422	0.266367	0.133184	−	0.991091i	$-0.457480\pi$
$449$	5.64422	0.266367	0.133184	+	0.991091i	$0.457480\pi$
$450$	0	0
$451$	2.81261	0.132441
$452$	22.3834	1.05283
$453$	22.5109	1.05765
$454$	8.48643	0.398288
$455$	0	0
$456$	−5.94460	−0.278382
$457$	−1.69002	−0.0790556	−0.0395278	−	0.999218i	$-0.512585\pi$
$457$	−1.69002	−0.0790556	−0.0395278	+	0.999218i	$0.512585\pi$
$458$	−9.38774	−0.438660
$459$	−4.53628	−0.211735
$460$	0	0
$461$	−2.03146	−0.0946145	−0.0473072	−	0.998880i	$-0.515064\pi$
$461$	−2.03146	−0.0946145	−0.0473072	+	0.998880i	$0.515064\pi$
$462$	3.77787	0.175762
$463$	21.6428	1.00583	0.502913	−	0.864337i	$-0.332261\pi$
$463$	21.6428	1.00583	0.502913	+	0.864337i	$0.332261\pi$
$464$	5.67517	0.263463
$465$	0	0
$466$	10.4333	0.483312
$467$	−11.3847	−0.526819	−0.263410	−	0.964684i	$-0.584847\pi$
$467$	−11.3847	−0.526819	−0.263410	+	0.964684i	$0.584847\pi$
$468$	−4.86074	−0.224688
$469$	−1.50982	−0.0697168
$470$	0	0
$471$	15.7880	0.727474
$472$	−28.9063	−1.33052
$473$	−22.8047	−1.04856
$474$	−0.418219	−0.0192094
$475$	0	0
$476$	15.7360	0.721257
$477$	−3.51312	−0.160855
$478$	23.4963	1.07470
$479$	30.9588	1.41454	0.707272	−	0.706941i	$-0.249925\pi$
$479$	30.9588	1.41454	0.707272	+	0.706941i	$0.249925\pi$
$480$	0	0
$481$	22.9851	1.04803
$482$	20.6168	0.939072
$483$	−4.62468	−0.210430
$484$	10.0519	0.456906
$485$	0	0
$486$	0.779856	0.0353750
$487$	13.8723	0.628614	0.314307	−	0.949321i	$-0.398228\pi$
$487$	13.8723	0.628614	0.314307	+	0.949321i	$0.398228\pi$
$488$	−20.1015	−0.909953
$489$	−17.0517	−0.771104
$490$	0	0
$491$	13.9144	0.627948	0.313974	−	0.949432i	$-0.398340\pi$
$491$	13.9144	0.627948	0.313974	+	0.949432i	$0.398340\pi$
$492$	−2.01405	−0.0908006
$493$	−35.7147	−1.60851
$494$	6.12079	0.275387
$495$	0	0
$496$	−2.42803	−0.109022
$497$	4.50854	0.202236
$498$	−1.79677	−0.0805150
$499$	−5.79082	−0.259233	−0.129616	−	0.991564i	$-0.541375\pi$
$499$	−5.79082	−0.259233	−0.129616	+	0.991564i	$0.541375\pi$
$500$	0	0
$501$	8.95076	0.399890
$502$	−16.6964	−0.745196
$503$	−21.4775	−0.957632	−0.478816	−	0.877915i	$-0.658934\pi$
$503$	−21.4775	−0.957632	−0.478816	+	0.877915i	$0.658934\pi$
$504$	−6.59260	−0.293658
$505$	0	0
$506$	−2.81261	−0.125036
$507$	−0.803486	−0.0356841
$508$	1.39182	0.0617522
$509$	44.5553	1.97488	0.987441	−	0.157991i	$-0.0505018\pi$
$509$	44.5553	1.97488	0.987441	+	0.157991i	$0.0505018\pi$
$510$	0	0
$511$	11.0365	0.488228
$512$	8.03194	0.354965
$513$	2.24737	0.0992239
$514$	1.43504	0.0632970
$515$	0	0
$516$	16.3300	0.718888
$517$	9.96150	0.438106
$518$	12.7924	0.562067
$519$	5.32614	0.233791
$520$	0	0
$521$	−17.8423	−0.781687	−0.390844	−	0.920457i	$-0.627817\pi$
$521$	−17.8423	−0.781687	−0.390844	+	0.920457i	$0.627817\pi$
$522$	6.13991	0.268737
$523$	5.54698	0.242553	0.121276	−	0.992619i	$-0.461301\pi$
$523$	5.54698	0.242553	0.121276	+	0.992619i	$0.461301\pi$
$524$	−24.4969	−1.07015
$525$	0	0
$526$	−1.66550	−0.0726192
$527$	15.2800	0.665605
$528$	1.40105	0.0609730
$529$	−19.5569	−0.850302
$530$	0	0
$531$	10.9281	0.474239
$532$	−7.79595	−0.337997
$533$	5.05364	0.218897
$534$	−6.54218	−0.283108
$535$	0	0
$536$	1.60237	0.0692118
$537$	19.5811	0.844987
$538$	−17.2293	−0.742810
$539$	−1.53198	−0.0659870
$540$	0	0
$541$	23.4622	1.00872	0.504360	−	0.863493i	$-0.331728\pi$
$541$	23.4622	1.00872	0.504360	+	0.863493i	$0.331728\pi$
$542$	−13.0898	−0.562254
$543$	19.1351	0.821168
$544$	−26.5481	−1.13824
$545$	0	0
$546$	6.78799	0.290499
$547$	−14.2196	−0.607985	−0.303992	−	0.952674i	$-0.598320\pi$
$547$	−14.2196	−0.607985	−0.303992	+	0.952674i	$0.598320\pi$
$548$	2.67492	0.114267
$549$	7.59943	0.324336
$550$	0	0
$551$	17.6939	0.753785
$552$	4.90817	0.208906
$553$	−1.33659	−0.0568376
$554$	16.0836	0.683328
$555$	0	0
$556$	−15.1013	−0.640437
$557$	−2.04726	−0.0867452	−0.0433726	−	0.999059i	$-0.513810\pi$
$557$	−2.04726	−0.0867452	−0.0433726	+	0.999059i	$0.513810\pi$
$558$	−2.62686	−0.111204
$559$	−40.9750	−1.73306
$560$	0	0
$561$	−8.81704	−0.372256
$562$	10.0701	0.424779
$563$	−34.9445	−1.47273	−0.736367	−	0.676582i	$-0.763460\pi$
$563$	−34.9445	−1.47273	−0.736367	+	0.676582i	$0.763460\pi$
$564$	−7.13322	−0.300363
$565$	0	0
$566$	−3.99938	−0.168106
$567$	2.49235	0.104669
$568$	−4.78492	−0.200771
$569$	7.52522	0.315474	0.157737	−	0.987481i	$-0.449580\pi$
$569$	7.52522	0.315474	0.157737	+	0.987481i	$0.449580\pi$
$570$	0	0
$571$	−19.0334	−0.796522	−0.398261	−	0.917272i	$-0.630386\pi$
$571$	−19.0334	−0.796522	−0.398261	+	0.917272i	$0.630386\pi$
$572$	−9.44770	−0.395028
$573$	−17.2812	−0.721932
$574$	2.81261	0.117396
$575$	0	0
$576$	3.12238	0.130099
$577$	21.0187	0.875019	0.437510	−	0.899214i	$-0.355861\pi$
$577$	21.0187	0.875019	0.437510	+	0.899214i	$0.355861\pi$
$578$	2.79017	0.116056
$579$	−18.8248	−0.782332
$580$	0	0
$581$	−5.74231	−0.238231
$582$	10.2826	0.426226
$583$	−6.82835	−0.282801
$584$	−11.7131	−0.484691
$585$	0	0
$586$	−10.8006	−0.446171
$587$	−27.1603	−1.12103	−0.560513	−	0.828145i	$-0.689396\pi$
$587$	−27.1603	−1.12103	−0.560513	+	0.828145i	$0.689396\pi$
$588$	1.09702	0.0452403
$589$	−7.57003	−0.311918
$590$	0	0
$591$	−21.3799	−0.879452
$592$	4.74417	0.194984
$593$	3.72771	0.153079	0.0765394	−	0.997067i	$-0.475613\pi$
$593$	3.72771	0.153079	0.0765394	+	0.997067i	$0.475613\pi$
$594$	1.51579	0.0621934
$595$	0	0
$596$	31.4268	1.28729
$597$	26.9170	1.10164
$598$	−5.05364	−0.206659
$599$	6.87209	0.280786	0.140393	−	0.990096i	$-0.455163\pi$
$599$	6.87209	0.280786	0.140393	+	0.990096i	$0.455163\pi$
$600$	0	0
$601$	46.5836	1.90019	0.950093	−	0.311966i	$-0.100988\pi$
$601$	46.5836	1.90019	0.950093	+	0.311966i	$0.100988\pi$
$602$	−22.8047	−0.929451
$603$	−0.605780	−0.0246693
$604$	−31.3312	−1.27485
$605$	0	0
$606$	1.93422	0.0785722
$607$	25.9091	1.05162	0.525808	−	0.850603i	$-0.323763\pi$
$607$	25.9091	1.05162	0.525808	+	0.850603i	$0.323763\pi$
$608$	13.1525	0.533406
$609$	19.6226	0.795149
$610$	0	0
$611$	17.8986	0.724100
$612$	6.31370	0.255216
$613$	−38.0304	−1.53603	−0.768017	−	0.640430i	$-0.778756\pi$
$613$	−38.0304	−1.53603	−0.768017	+	0.640430i	$0.778756\pi$
$614$	2.31681	0.0934990
$615$	0	0
$616$	−12.8139	−0.516286
$617$	−12.4331	−0.500538	−0.250269	−	0.968176i	$-0.580519\pi$
$617$	−12.4331	−0.500538	−0.250269	+	0.968176i	$0.580519\pi$
$618$	−7.01269	−0.282092
$619$	−44.2294	−1.77773	−0.888864	−	0.458171i	$-0.848505\pi$
$619$	−44.2294	−1.77773	−0.888864	+	0.458171i	$0.848505\pi$
$620$	0	0
$621$	−1.85555	−0.0744606
$622$	16.2324	0.650860
$623$	−20.9082	−0.837671
$624$	2.51738	0.100776
$625$	0	0
$626$	21.8870	0.874779
$627$	4.36816	0.174448
$628$	−21.9742	−0.876865
$629$	−29.8558	−1.19043
$630$	0	0
$631$	18.9265	0.753450	0.376725	−	0.926325i	$-0.377050\pi$
$631$	18.9265	0.753450	0.376725	+	0.926325i	$0.377050\pi$
$632$	1.41852	0.0564259
$633$	3.54184	0.140776
$634$	−13.9720	−0.554901
$635$	0	0
$636$	4.88964	0.193887
$637$	−2.75263	−0.109063
$638$	11.9340	0.472471
$639$	1.80895	0.0715611
$640$	0	0
$641$	−30.5891	−1.20820	−0.604099	−	0.796910i	$-0.706467\pi$
$641$	−30.5891	−1.20820	−0.604099	+	0.796910i	$0.706467\pi$
$642$	−0.675962	−0.0266781
$643$	5.97532	0.235644	0.117822	−	0.993035i	$-0.462409\pi$
$643$	5.97532	0.235644	0.117822	+	0.993035i	$0.462409\pi$
$644$	6.43674	0.253643
$645$	0	0
$646$	−7.95040	−0.312804
$647$	−47.5449	−1.86918	−0.934592	−	0.355721i	$-0.884235\pi$
$647$	−47.5449	−1.86918	−0.934592	+	0.355721i	$0.884235\pi$
$648$	−2.64513	−0.103911
$649$	21.2407	0.833769
$650$	0	0
$651$	−8.39521	−0.329034
$652$	23.7330	0.929455
$653$	−34.0921	−1.33413	−0.667063	−	0.745002i	$-0.732449\pi$
$653$	−34.0921	−1.33413	−0.667063	+	0.745002i	$0.732449\pi$
$654$	7.69941	0.301071
$655$	0	0
$656$	1.04308	0.0407254
$657$	4.42816	0.172759
$658$	9.96150	0.388340
$659$	−10.4016	−0.405189	−0.202594	−	0.979263i	$-0.564937\pi$
$659$	−10.4016	−0.405189	−0.202594	+	0.979263i	$0.564937\pi$
$660$	0	0
$661$	13.9384	0.542141	0.271070	−	0.962560i	$-0.412622\pi$
$661$	13.9384	0.542141	0.271070	+	0.962560i	$0.412622\pi$
$662$	−13.1380	−0.510621
$663$	−15.8423	−0.615263
$664$	6.09432	0.236505
$665$	0	0
$666$	5.13267	0.198887
$667$	−14.6090	−0.565662
$668$	−12.4579	−0.482010
$669$	17.4252	0.673696
$670$	0	0
$671$	14.7708	0.570221
$672$	14.5863	0.562677
$673$	−34.4795	−1.32909	−0.664543	−	0.747250i	$-0.731374\pi$
$673$	−34.4795	−1.32909	−0.664543	+	0.747250i	$0.731374\pi$
$674$	26.7977	1.03221
$675$	0	0
$676$	1.11831	0.0430120
$677$	17.9850	0.691219	0.345609	−	0.938379i	$-0.387672\pi$
$677$	17.9850	0.691219	0.345609	+	0.938379i	$0.387672\pi$
$678$	−12.5417	−0.481660
$679$	32.8622	1.26113
$680$	0	0
$681$	10.8821	0.417001
$682$	−5.10576	−0.195510
$683$	10.4054	0.398152	0.199076	−	0.979984i	$-0.436206\pi$
$683$	10.4054	0.398152	0.199076	+	0.979984i	$0.436206\pi$
$684$	−3.12795	−0.119600
$685$	0	0
$686$	−15.1377	−0.577960
$687$	−12.0378	−0.459271
$688$	−8.45731	−0.322432
$689$	−12.2690	−0.467413
$690$	0	0
$691$	−6.48584	−0.246733	−0.123367	−	0.992361i	$-0.539369\pi$
$691$	−6.48584	−0.246733	−0.123367	+	0.992361i	$0.539369\pi$
$692$	−7.41305	−0.281802
$693$	4.84432	0.184020
$694$	−9.15543	−0.347535
$695$	0	0
$696$	−20.8255	−0.789389
$697$	−6.56426	−0.248639
$698$	−2.19902	−0.0832340
$699$	13.3785	0.506020
$700$	0	0
$701$	25.4982	0.963055	0.481528	−	0.876431i	$-0.340082\pi$
$701$	25.4982	0.963055	0.481528	+	0.876431i	$0.340082\pi$
$702$	2.72353	0.102793
$703$	14.7912	0.557862
$704$	6.06889	0.228730
$705$	0	0
$706$	12.0567	0.453760
$707$	6.18159	0.232483
$708$	−15.2100	−0.571627
$709$	41.6178	1.56299	0.781495	−	0.623911i	$-0.214457\pi$
$709$	41.6178	1.56299	0.781495	+	0.623911i	$0.214457\pi$
$710$	0	0
$711$	−0.536277	−0.0201120
$712$	22.1899	0.831603
$713$	6.25021	0.234072
$714$	−8.81704	−0.329970
$715$	0	0
$716$	−27.2535	−1.01851
$717$	30.1290	1.12519
$718$	17.1838	0.641295
$719$	−18.2708	−0.681387	−0.340693	−	0.940174i	$-0.610662\pi$
$719$	−18.2708	−0.681387	−0.340693	+	0.940174i	$0.610662\pi$
$720$	0	0
$721$	−22.4119	−0.834664
$722$	−10.8785	−0.404854
$723$	26.4367	0.983193
$724$	−26.6328	−0.989799
$725$	0	0
$726$	−5.63222	−0.209031
$727$	37.4813	1.39011	0.695053	−	0.718959i	$-0.255381\pi$
$727$	37.4813	1.39011	0.695053	+	0.718959i	$0.255381\pi$
$728$	−23.0237	−0.853314
$729$	1.00000	0.0370370
$730$	0	0
$731$	53.2232	1.96853
$732$	−10.5771	−0.390940
$733$	−15.0688	−0.556579	−0.278289	−	0.960497i	$-0.589767\pi$
$733$	−15.0688	−0.556579	−0.278289	+	0.960497i	$0.589767\pi$
$734$	−12.8662	−0.474901
$735$	0	0
$736$	−10.8594	−0.400284
$737$	−1.17744	−0.0433715
$738$	1.12850	0.0415406
$739$	7.00612	0.257724	0.128862	−	0.991663i	$-0.458868\pi$
$739$	7.00612	0.257724	0.128862	+	0.991663i	$0.458868\pi$
$740$	0	0
$741$	7.84862	0.288326
$742$	−6.82835	−0.250677
$743$	24.6885	0.905733	0.452867	−	0.891578i	$-0.350401\pi$
$743$	24.6885	0.905733	0.452867	+	0.891578i	$0.350401\pi$
$744$	8.90984	0.326651
$745$	0	0
$746$	27.7283	1.01520
$747$	−2.30397	−0.0842980
$748$	12.2718	0.448701
$749$	−2.16032	−0.0789362
$750$	0	0
$751$	25.8423	0.943000	0.471500	−	0.881866i	$-0.343713\pi$
$751$	25.8423	0.943000	0.471500	+	0.881866i	$0.343713\pi$
$752$	3.69430	0.134717
$753$	−21.4096	−0.780208
$754$	21.4427	0.780898
$755$	0	0
$756$	−3.46892	−0.126163
$757$	39.9510	1.45204	0.726022	−	0.687672i	$-0.241367\pi$
$757$	39.9510	1.45204	0.726022	+	0.687672i	$0.241367\pi$
$758$	−8.65404	−0.314329
$759$	−3.60658	−0.130911
$760$	0	0
$761$	−12.6209	−0.457506	−0.228753	−	0.973485i	$-0.573465\pi$
$761$	−12.6209	−0.457506	−0.228753	+	0.973485i	$0.573465\pi$
$762$	−0.779856	−0.0282512
$763$	24.6066	0.890820
$764$	24.0524	0.870185
$765$	0	0
$766$	26.4210	0.954629
$767$	38.1648	1.37805
$768$	−13.4739	−0.486197
$769$	−33.8677	−1.22130	−0.610650	−	0.791901i	$-0.709092\pi$
$769$	−33.8677	−1.22130	−0.610650	+	0.791901i	$0.709092\pi$
$770$	0	0
$771$	1.84014	0.0662709
$772$	26.2008	0.942988
$773$	−10.1726	−0.365884	−0.182942	−	0.983124i	$-0.558562\pi$
$773$	−10.1726	−0.365884	−0.182942	+	0.983124i	$0.558562\pi$
$774$	−9.14988	−0.328886
$775$	0	0
$776$	−34.8766	−1.25200
$777$	16.4036	0.588475
$778$	2.12416	0.0761548
$779$	3.25208	0.116518
$780$	0	0
$781$	3.51601	0.125813
$782$	6.56426	0.234738
$783$	7.87314	0.281363
$784$	−0.568146	−0.0202909
$785$	0	0
$786$	13.7259	0.489587
$787$	6.49794	0.231627	0.115813	−	0.993271i	$-0.463053\pi$
$787$	6.49794	0.231627	0.115813	+	0.993271i	$0.463053\pi$
$788$	29.7571	1.06005
$789$	−2.13565	−0.0760312
$790$	0	0
$791$	−40.0821	−1.42516
$792$	−5.14128	−0.182687
$793$	26.5399	0.942459
$794$	13.0056	0.461553
$795$	0	0
$796$	−37.4637	−1.32787
$797$	−13.4596	−0.476762	−0.238381	−	0.971172i	$-0.576617\pi$
$797$	−13.4596	−0.476762	−0.238381	+	0.971172i	$0.576617\pi$
$798$	4.36816	0.154631
$799$	−23.2488	−0.822484
$800$	0	0
$801$	−8.38896	−0.296409
$802$	4.60740	0.162693
$803$	8.60691	0.303731
$804$	0.843139	0.0297352
$805$	0	0
$806$	−9.17391	−0.323137
$807$	−22.0930	−0.777710
$808$	−6.56053	−0.230799
$809$	−25.6210	−0.900787	−0.450393	−	0.892830i	$-0.648716\pi$
$809$	−25.6210	−0.900787	−0.450393	+	0.892830i	$0.648716\pi$
$810$	0	0
$811$	−23.9897	−0.842391	−0.421196	−	0.906970i	$-0.638389\pi$
$811$	−23.9897	−0.842391	−0.421196	+	0.906970i	$0.638389\pi$
$812$	−27.3113	−0.958438
$813$	−16.7849	−0.588671
$814$	9.97625	0.349667
$815$	0	0
$816$	−3.26987	−0.114468
$817$	−26.3680	−0.922498
$818$	−8.01039	−0.280077
$819$	8.70416	0.304148
$820$	0	0
$821$	0.726367	0.0253504	0.0126752	−	0.999920i	$-0.495965\pi$
$821$	0.726367	0.0253504	0.0126752	+	0.999920i	$0.495965\pi$
$822$	−1.49879	−0.0522762
$823$	3.66517	0.127760	0.0638798	−	0.997958i	$-0.479653\pi$
$823$	3.66517	0.127760	0.0638798	+	0.997958i	$0.479653\pi$
$824$	23.7858	0.828618
$825$	0	0
$826$	21.2407	0.739057
$827$	−32.7090	−1.13740	−0.568702	−	0.822544i	$-0.692554\pi$
$827$	−32.7090	−1.13740	−0.568702	+	0.822544i	$0.692554\pi$
$828$	2.58260	0.0897515
$829$	−19.6772	−0.683418	−0.341709	−	0.939806i	$-0.611006\pi$
$829$	−19.6772	−0.683418	−0.341709	+	0.939806i	$0.611006\pi$
$830$	0	0
$831$	20.6239	0.715434
$832$	10.9045	0.378044
$833$	3.57544	0.123882
$834$	8.46142	0.292995
$835$	0	0
$836$	−6.07972	−0.210271
$837$	−3.36839	−0.116429
$838$	0.766119	0.0264651
$839$	−47.7471	−1.64841	−0.824206	−	0.566290i	$-0.808378\pi$
$839$	−47.7471	−1.64841	−0.824206	+	0.566290i	$0.808378\pi$
$840$	0	0
$841$	32.9863	1.13746
$842$	12.6878	0.437251
$843$	12.9127	0.444737
$844$	−4.92963	−0.169685
$845$	0	0
$846$	3.99683	0.137414
$847$	−18.0001	−0.618490
$848$	−2.53235	−0.0869612
$849$	−5.12835	−0.176005
$850$	0	0
$851$	−12.2124	−0.418636
$852$	−2.51775	−0.0862565
$853$	21.7797	0.745722	0.372861	−	0.927887i	$-0.378377\pi$
$853$	21.7797	0.745722	0.372861	+	0.927887i	$0.378377\pi$
$854$	14.7708	0.505447
$855$	0	0
$856$	2.29275	0.0783644
$857$	−43.0744	−1.47139	−0.735696	−	0.677311i	$-0.763145\pi$
$857$	−43.0744	−1.47139	−0.735696	+	0.677311i	$0.763145\pi$
$858$	5.29365	0.180722
$859$	4.24922	0.144982	0.0724908	−	0.997369i	$-0.476905\pi$
$859$	4.24922	0.144982	0.0724908	+	0.997369i	$0.476905\pi$
$860$	0	0
$861$	3.60658	0.122912
$862$	−22.9729	−0.782459
$863$	−38.2608	−1.30241	−0.651207	−	0.758900i	$-0.725737\pi$
$863$	−38.2608	−1.30241	−0.651207	+	0.758900i	$0.725737\pi$
$864$	5.85241	0.199103
$865$	0	0
$866$	−28.7576	−0.977222
$867$	3.57781	0.121509
$868$	11.6847	0.396603
$869$	−1.04235	−0.0353592
$870$	0	0
$871$	−2.11560	−0.0716842
$872$	−26.1151	−0.884367
$873$	13.1852	0.446252
$874$	−3.25208	−0.110003
$875$	0	0
$876$	−6.16323	−0.208236
$877$	−27.5995	−0.931968	−0.465984	−	0.884793i	$-0.654300\pi$
$877$	−27.5995	−0.931968	−0.465984	+	0.884793i	$0.654300\pi$
$878$	21.9623	0.741190
$879$	−13.8495	−0.467134
$880$	0	0
$881$	16.9324	0.570466	0.285233	−	0.958458i	$-0.407929\pi$
$881$	16.9324	0.570466	0.285233	+	0.958458i	$0.407929\pi$
$882$	−0.614672	−0.0206971
$883$	−37.5631	−1.26410	−0.632049	−	0.774928i	$-0.717786\pi$
$883$	−37.5631	−1.26410	−0.632049	+	0.774928i	$0.717786\pi$
$884$	22.0497	0.741611
$885$	0	0
$886$	−6.94767	−0.233412
$887$	10.4133	0.349644	0.174822	−	0.984600i	$-0.444065\pi$
$887$	10.4133	0.349644	0.174822	+	0.984600i	$0.444065\pi$
$888$	−17.4091	−0.584212
$889$	−2.49235	−0.0835908
$890$	0	0
$891$	1.94367	0.0651155
$892$	−24.2528	−0.812043
$893$	11.5180	0.385434
$894$	−17.6088	−0.588927
$895$	0	0
$896$	−23.1036	−0.771838
$897$	−6.48023	−0.216368
$898$	4.40168	0.146886
$899$	−26.5198	−0.884485
$900$	0	0
$901$	15.9365	0.530921
$902$	2.19343	0.0730333
$903$	−29.2422	−0.973121
$904$	42.5392	1.41483
$905$	0	0
$906$	17.5552	0.583234
$907$	−16.9448	−0.562642	−0.281321	−	0.959614i	$-0.590773\pi$
$907$	−16.9448	−0.562642	−0.281321	+	0.959614i	$0.590773\pi$
$908$	−15.1459	−0.502635
$909$	2.48023	0.0822639
$910$	0	0
$911$	−41.9676	−1.39045	−0.695224	−	0.718793i	$-0.744695\pi$
$911$	−41.9676	−1.39045	−0.695224	+	0.718793i	$0.744695\pi$
$912$	1.61997	0.0536424
$913$	−4.47817	−0.148206
$914$	−1.31797	−0.0435945
$915$	0	0
$916$	16.7545	0.553584
$917$	43.8668	1.44861
$918$	−3.53764	−0.116760
$919$	31.6581	1.04431	0.522153	−	0.852852i	$-0.325129\pi$
$919$	31.6581	1.04431	0.522153	+	0.852852i	$0.325129\pi$
$920$	0	0
$921$	2.97082	0.0978920
$922$	−1.58424	−0.0521743
$923$	6.31750	0.207943
$924$	−6.74244	−0.221810
$925$	0	0
$926$	16.8783	0.554654
$927$	−8.99229	−0.295346
$928$	46.0768	1.51255
$929$	15.9324	0.522724	0.261362	−	0.965241i	$-0.415828\pi$
$929$	15.9324	0.522724	0.261362	+	0.965241i	$0.415828\pi$
$930$	0	0
$931$	−1.77135	−0.0580537
$932$	−18.6205	−0.609934
$933$	20.8146	0.681440
$934$	−8.87840	−0.290510
$935$	0	0
$936$	−9.23774	−0.301945
$937$	26.2574	0.857791	0.428895	−	0.903354i	$-0.358903\pi$
$937$	26.2574	0.857791	0.428895	+	0.903354i	$0.358903\pi$
$938$	−1.17744	−0.0384447
$939$	28.0654	0.915879
$940$	0	0
$941$	−34.8878	−1.13731	−0.568654	−	0.822576i	$-0.692536\pi$
$941$	−34.8878	−1.13731	−0.568654	+	0.822576i	$0.692536\pi$
$942$	12.3124	0.401159
$943$	−2.68509	−0.0874385
$944$	7.87727	0.256383
$945$	0	0
$946$	−17.7844	−0.578221
$947$	−15.3419	−0.498546	−0.249273	−	0.968433i	$-0.580192\pi$
$947$	−15.3419	−0.498546	−0.249273	+	0.968433i	$0.580192\pi$
$948$	0.746403	0.0242421
$949$	15.4647	0.502005
$950$	0	0
$951$	−17.9162	−0.580972
$952$	29.9059	0.969255
$953$	32.2332	1.04414	0.522068	−	0.852904i	$-0.325161\pi$
$953$	32.2332	1.04414	0.522068	+	0.852904i	$0.325161\pi$
$954$	−2.73972	−0.0887018
$955$	0	0
$956$	−41.9343	−1.35625
$957$	15.3028	0.494670
$958$	24.1434	0.780039
$959$	−4.79000	−0.154677
$960$	0	0
$961$	−19.6539	−0.633998
$962$	17.9251	0.577928
$963$	−0.866778	−0.0279315
$964$	−36.7953	−1.18510
$965$	0	0
$966$	−3.60658	−0.116040
$967$	−21.9359	−0.705411	−0.352706	−	0.935734i	$-0.614738\pi$
$967$	−21.9359	−0.705411	−0.352706	+	0.935734i	$0.614738\pi$
$968$	19.1035	0.614010
$969$	−10.1947	−0.327501
$970$	0	0
$971$	55.9118	1.79429	0.897147	−	0.441732i	$-0.145636\pi$
$971$	55.9118	1.79429	0.897147	+	0.441732i	$0.145636\pi$
$972$	−1.39182	−0.0446428
$973$	27.0420	0.866925
$974$	10.8184	0.346644
$975$	0	0
$976$	5.47787	0.175343
$977$	−24.7888	−0.793064	−0.396532	−	0.918021i	$-0.629786\pi$
$977$	−24.7888	−0.793064	−0.396532	+	0.918021i	$0.629786\pi$
$978$	−13.2979	−0.425219
$979$	−16.3054	−0.521123
$980$	0	0
$981$	9.87287	0.315216
$982$	10.8512	0.346276
$983$	−20.3512	−0.649103	−0.324551	−	0.945868i	$-0.605213\pi$
$983$	−20.3512	−0.649103	−0.324551	+	0.945868i	$0.605213\pi$
$984$	−3.82767	−0.122022
$985$	0	0
$986$	−27.8524	−0.887000
$987$	12.7735	0.406585
$988$	−10.9239	−0.347536
$989$	21.7708	0.692270
$990$	0	0
$991$	−40.5877	−1.28931	−0.644656	−	0.764473i	$-0.722999\pi$
$991$	−40.5877	−1.28931	−0.644656	+	0.764473i	$0.722999\pi$
$992$	−19.7132	−0.625895
$993$	−16.8466	−0.534612
$994$	3.51601	0.111521
$995$	0	0
$996$	3.20673	0.101609
$997$	−55.4482	−1.75606	−0.878031	−	0.478605i	$-0.841143\pi$
$997$	−55.4482	−1.75606	−0.878031	+	0.478605i	$0.841143\pi$
$998$	−4.51601	−0.142952
$999$	6.58157	0.208232

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9525.2.a.j.1.4		5
5.4	even	2		381.2.a.d.1.2	✓	5
15.14	odd	2		1143.2.a.g.1.4		5
20.19	odd	2		6096.2.a.bf.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
381.2.a.d.1.2	✓	5	5.4	even	2
1143.2.a.g.1.4		5	15.14	odd	2
6096.2.a.bf.1.1		5	20.19	odd	2
9525.2.a.j.1.4		5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 9525 = 3 \cdot 5^{2} \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9525.a (trivial)

\(f(q)\)	\(=\)	\(q+0.779856 q^{2} +1.00000 q^{3} -1.39182 q^{4} +0.779856 q^{6} +2.49235 q^{7} -2.64513 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.779856 q^{2} +1.00000 q^{3} -1.39182 q^{4} +0.779856 q^{6} +2.49235 q^{7} -2.64513 q^{8} +1.00000 q^{9} +1.94367 q^{11} -1.39182 q^{12} +3.49235 q^{13} +1.94367 q^{14} +0.720827 q^{16} -4.53628 q^{17} +0.779856 q^{18} +2.24737 q^{19} +2.49235 q^{21} +1.51579 q^{22} -1.85555 q^{23} -2.64513 q^{24} +2.72353 q^{26} +1.00000 q^{27} -3.46892 q^{28} +7.87314 q^{29} -3.36839 q^{31} +5.85241 q^{32} +1.94367 q^{33} -3.53764 q^{34} -1.39182 q^{36} +6.58157 q^{37} +1.75263 q^{38} +3.49235 q^{39} +1.44706 q^{41} +1.94367 q^{42} -11.7328 q^{43} -2.70525 q^{44} -1.44706 q^{46} +5.12509 q^{47} +0.720827 q^{48} -0.788187 q^{49} -4.53628 q^{51} -4.86074 q^{52} -3.51312 q^{53} +0.779856 q^{54} -6.59260 q^{56} +2.24737 q^{57} +6.13991 q^{58} +10.9281 q^{59} +7.59943 q^{61} -2.62686 q^{62} +2.49235 q^{63} +3.12238 q^{64} +1.51579 q^{66} -0.605780 q^{67} +6.31370 q^{68} -1.85555 q^{69} +1.80895 q^{71} -2.64513 q^{72} +4.42816 q^{73} +5.13267 q^{74} -3.12795 q^{76} +4.84432 q^{77} +2.72353 q^{78} -0.536277 q^{79} +1.00000 q^{81} +1.12850 q^{82} -2.30397 q^{83} -3.46892 q^{84} -9.14988 q^{86} +7.87314 q^{87} -5.14128 q^{88} -8.38896 q^{89} +8.70416 q^{91} +2.58260 q^{92} -3.36839 q^{93} +3.99683 q^{94} +5.85241 q^{96} +13.1852 q^{97} -0.614672 q^{98} +1.94367 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{2} + 5 q^{3} + 6 q^{4} - 2 q^{6} - 6 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q - 2 * q^2 + 5 * q^3 + 6 * q^4 - 2 * q^6 - 6 * q^8 + 5 * q^9	\( 5 q - 2 q^{2} + 5 q^{3} + 6 q^{4} - 2 q^{6} - 6 q^{8} + 5 q^{9} + 14 q^{11} + 6 q^{12} + 5 q^{13} + 14 q^{14} + 8 q^{16} - 4 q^{17} - 2 q^{18} + 4 q^{19} + 2 q^{22} - 15 q^{23} - 6 q^{24} + 12 q^{26} + 5 q^{27} + 2 q^{28} + 9 q^{29} + 3 q^{31} - 14 q^{32} + 14 q^{33} + 4 q^{34} + 6 q^{36} + 5 q^{37} + 16 q^{38} + 5 q^{39} + 4 q^{41} + 14 q^{42} - 10 q^{43} + 18 q^{44} - 4 q^{46} + 4 q^{47} + 8 q^{48} - 9 q^{49} - 4 q^{51} + 8 q^{52} - 3 q^{53} - 2 q^{54} - 10 q^{56} + 4 q^{57} - 6 q^{58} + 23 q^{59} - 15 q^{61} + 24 q^{62} + 2 q^{66} - 18 q^{67} + 24 q^{68} - 15 q^{69} + 12 q^{71} - 6 q^{72} + 43 q^{73} - 36 q^{74} - 32 q^{76} - 4 q^{77} + 12 q^{78} + 16 q^{79} + 5 q^{81} + 44 q^{82} - 11 q^{83} + 2 q^{84} - 28 q^{86} + 9 q^{87} + 14 q^{88} + 9 q^{89} + 26 q^{91} - 14 q^{92} + 3 q^{93} - 14 q^{94} - 14 q^{96} + 20 q^{97} + 10 q^{98} + 14 q^{99}+O(q^{100}) \) 5 * q - 2 * q^2 + 5 * q^3 + 6 * q^4 - 2 * q^6 - 6 * q^8 + 5 * q^9 + 14 * q^11 + 6 * q^12 + 5 * q^13 + 14 * q^14 + 8 * q^16 - 4 * q^17 - 2 * q^18 + 4 * q^19 + 2 * q^22 - 15 * q^23 - 6 * q^24 + 12 * q^26 + 5 * q^27 + 2 * q^28 + 9 * q^29 + 3 * q^31 - 14 * q^32 + 14 * q^33 + 4 * q^34 + 6 * q^36 + 5 * q^37 + 16 * q^38 + 5 * q^39 + 4 * q^41 + 14 * q^42 - 10 * q^43 + 18 * q^44 - 4 * q^46 + 4 * q^47 + 8 * q^48 - 9 * q^49 - 4 * q^51 + 8 * q^52 - 3 * q^53 - 2 * q^54 - 10 * q^56 + 4 * q^57 - 6 * q^58 + 23 * q^59 - 15 * q^61 + 24 * q^62 + 2 * q^66 - 18 * q^67 + 24 * q^68 - 15 * q^69 + 12 * q^71 - 6 * q^72 + 43 * q^73 - 36 * q^74 - 32 * q^76 - 4 * q^77 + 12 * q^78 + 16 * q^79 + 5 * q^81 + 44 * q^82 - 11 * q^83 + 2 * q^84 - 28 * q^86 + 9 * q^87 + 14 * q^88 + 9 * q^89 + 26 * q^91 - 14 * q^92 + 3 * q^93 - 14 * q^94 - 14 * q^96 + 20 * q^97 + 10 * q^98 + 14 * q^99

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