LMFDB - Embedded newform 8925.2.a.cu.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8925,2,Mod(1,8925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8925, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8925.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8925 = 3 \cdot 5^{2} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8925.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:	$71.2664838040$
Analytic rank:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 3 x^{13} - 18 x^{12} + 54 x^{11} + 124 x^{10} - 366 x^{9} - 416 x^{8} + 1164 x^{7} + 727 x^{6} + \cdots - 40 $ x^14 - 3x^13 - 18x^12 + 54x^11 + 124x^10 - 366x^9 - 416x^8 + 1164x^7 + 727x^6 - 1783x^5 - 662x^4 + 1242x^3 + 284x^2 - 300*x - 40
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 1785)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.53468$ of defining polynomial
Character	$\chi$	$=$	8925.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.53468 q^{2} -1.00000 q^{3} +4.42458 q^{4} +2.53468 q^{6} -1.00000 q^{7} -6.14554 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.53468 q^{2} -1.00000 q^{3} +4.42458 q^{4} +2.53468 q^{6} -1.00000 q^{7} -6.14554 q^{8} +1.00000 q^{9} +2.67562 q^{11} -4.42458 q^{12} -2.82990 q^{13} +2.53468 q^{14} +6.72778 q^{16} +1.00000 q^{17} -2.53468 q^{18} +6.17364 q^{19} +1.00000 q^{21} -6.78182 q^{22} +2.83634 q^{23} +6.14554 q^{24} +7.17288 q^{26} -1.00000 q^{27} -4.42458 q^{28} -3.59961 q^{29} +0.268975 q^{31} -4.76167 q^{32} -2.67562 q^{33} -2.53468 q^{34} +4.42458 q^{36} -0.972382 q^{37} -15.6482 q^{38} +2.82990 q^{39} -9.16460 q^{41} -2.53468 q^{42} -4.71924 q^{43} +11.8385 q^{44} -7.18921 q^{46} +13.4273 q^{47} -6.72778 q^{48} +1.00000 q^{49} -1.00000 q^{51} -12.5211 q^{52} -10.3318 q^{53} +2.53468 q^{54} +6.14554 q^{56} -6.17364 q^{57} +9.12383 q^{58} +7.82368 q^{59} -12.2096 q^{61} -0.681766 q^{62} -1.00000 q^{63} -1.38627 q^{64} +6.78182 q^{66} +0.100710 q^{67} +4.42458 q^{68} -2.83634 q^{69} +13.9605 q^{71} -6.14554 q^{72} -12.9290 q^{73} +2.46467 q^{74} +27.3158 q^{76} -2.67562 q^{77} -7.17288 q^{78} -13.0779 q^{79} +1.00000 q^{81} +23.2293 q^{82} -8.22428 q^{83} +4.42458 q^{84} +11.9617 q^{86} +3.59961 q^{87} -16.4431 q^{88} +9.68583 q^{89} +2.82990 q^{91} +12.5496 q^{92} -0.268975 q^{93} -34.0339 q^{94} +4.76167 q^{96} +5.84462 q^{97} -2.53468 q^{98} +2.67562 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 3 q^{2} - 14 q^{3} + 17 q^{4} + 3 q^{6} - 14 q^{7} - 15 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q - 3 * q^2 - 14 * q^3 + 17 * q^4 + 3 * q^6 - 14 * q^7 - 15 * q^8 + 14 * q^9	$ 14 q - 3 q^{2} - 14 q^{3} + 17 q^{4} + 3 q^{6} - 14 q^{7} - 15 q^{8} + 14 q^{9} + 4 q^{11} - 17 q^{12} + q^{13} + 3 q^{14} + 19 q^{16} + 14 q^{17} - 3 q^{18} - 6 q^{19} + 14 q^{21} - 12 q^{22} - 7 q^{23} + 15 q^{24} - 2 q^{26} - 14 q^{27} - 17 q^{28} + 20 q^{29} - 7 q^{31} - 33 q^{32} - 4 q^{33} - 3 q^{34} + 17 q^{36} - 9 q^{37} - 18 q^{38} - q^{39} + 25 q^{41} - 3 q^{42} - 28 q^{43} + 24 q^{44} - 10 q^{46} - 29 q^{47} - 19 q^{48} + 14 q^{49} - 14 q^{51} - 4 q^{52} - 26 q^{53} + 3 q^{54} + 15 q^{56} + 6 q^{57} - 2 q^{58} + 14 q^{59} - 9 q^{61} - 28 q^{62} - 14 q^{63} + 27 q^{64} + 12 q^{66} - 32 q^{67} + 17 q^{68} + 7 q^{69} + 2 q^{71} - 15 q^{72} - 18 q^{73} + 64 q^{74} - 42 q^{76} - 4 q^{77} + 2 q^{78} - 4 q^{79} + 14 q^{81} - 42 q^{82} - 51 q^{83} + 17 q^{84} + 44 q^{86} - 20 q^{87} - 32 q^{88} + 38 q^{89} - q^{91} + 16 q^{92} + 7 q^{93} + 8 q^{94} + 33 q^{96} - 14 q^{97} - 3 q^{98} + 4 q^{99}+O(q^{100}) $ 14 * q - 3 * q^2 - 14 * q^3 + 17 * q^4 + 3 * q^6 - 14 * q^7 - 15 * q^8 + 14 * q^9 + 4 * q^11 - 17 * q^12 + q^13 + 3 * q^14 + 19 * q^16 + 14 * q^17 - 3 * q^18 - 6 * q^19 + 14 * q^21 - 12 * q^22 - 7 * q^23 + 15 * q^24 - 2 * q^26 - 14 * q^27 - 17 * q^28 + 20 * q^29 - 7 * q^31 - 33 * q^32 - 4 * q^33 - 3 * q^34 + 17 * q^36 - 9 * q^37 - 18 * q^38 - q^39 + 25 * q^41 - 3 * q^42 - 28 * q^43 + 24 * q^44 - 10 * q^46 - 29 * q^47 - 19 * q^48 + 14 * q^49 - 14 * q^51 - 4 * q^52 - 26 * q^53 + 3 * q^54 + 15 * q^56 + 6 * q^57 - 2 * q^58 + 14 * q^59 - 9 * q^61 - 28 * q^62 - 14 * q^63 + 27 * q^64 + 12 * q^66 - 32 * q^67 + 17 * q^68 + 7 * q^69 + 2 * q^71 - 15 * q^72 - 18 * q^73 + 64 * q^74 - 42 * q^76 - 4 * q^77 + 2 * q^78 - 4 * q^79 + 14 * q^81 - 42 * q^82 - 51 * q^83 + 17 * q^84 + 44 * q^86 - 20 * q^87 - 32 * q^88 + 38 * q^89 - q^91 + 16 * q^92 + 7 * q^93 + 8 * q^94 + 33 * q^96 - 14 * q^97 - 3 * q^98 + 4 * 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 $

$2$	−2.53468	−1.79229	−0.896143	−	0.443765i	$-0.853643\pi$
$2$	−2.53468	−1.79229	−0.896143	+	0.443765i	$0.853643\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.42458	2.21229
$5$	0	0
$5$	0	0
$6$	2.53468	1.03478
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−6.14554	−2.17278
$9$	1.00000	0.333333
$10$	0	0
$11$	2.67562	0.806729	0.403364	−	0.915039i	$-0.367841\pi$
$11$	2.67562	0.806729	0.403364	+	0.915039i	$0.367841\pi$
$12$	−4.42458	−1.27727
$13$	−2.82990	−0.784873	−0.392436	−	0.919779i	$-0.628368\pi$
$13$	−2.82990	−0.784873	−0.392436	+	0.919779i	$0.628368\pi$
$14$	2.53468	0.677421
$15$	0	0
$16$	6.72778	1.68194
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.53468	−0.597429
$19$	6.17364	1.41633	0.708165	−	0.706047i	$-0.249523\pi$
$19$	6.17364	1.41633	0.708165	+	0.706047i	$0.249523\pi$
$20$	0	0
$21$	1.00000	0.218218
$22$	−6.78182	−1.44589
$23$	2.83634	0.591418	0.295709	−	0.955278i	$-0.404444\pi$
$23$	2.83634	0.591418	0.295709	+	0.955278i	$0.404444\pi$
$24$	6.14554	1.25445
$25$	0	0
$26$	7.17288	1.40672
$27$	−1.00000	−0.192450
$28$	−4.42458	−0.836168
$29$	−3.59961	−0.668430	−0.334215	−	0.942497i	$-0.608471\pi$
$29$	−3.59961	−0.668430	−0.334215	+	0.942497i	$0.608471\pi$
$30$	0	0
$31$	0.268975	0.0483094	0.0241547	−	0.999708i	$-0.492311\pi$
$31$	0.268975	0.0483094	0.0241547	+	0.999708i	$0.492311\pi$
$32$	−4.76167	−0.841751
$33$	−2.67562	−0.465765
$34$	−2.53468	−0.434693
$35$	0	0
$36$	4.42458	0.737431
$37$	−0.972382	−0.159859	−0.0799293	−	0.996801i	$-0.525469\pi$
$37$	−0.972382	−0.159859	−0.0799293	+	0.996801i	$0.525469\pi$
$38$	−15.6482	−2.53847
$39$	2.82990	0.453146
$40$	0	0
$41$	−9.16460	−1.43127	−0.715635	−	0.698475i	$-0.753862\pi$
$41$	−9.16460	−1.43127	−0.715635	+	0.698475i	$0.753862\pi$
$42$	−2.53468	−0.391109
$43$	−4.71924	−0.719677	−0.359839	−	0.933015i	$-0.617168\pi$
$43$	−4.71924	−0.719677	−0.359839	+	0.933015i	$0.617168\pi$
$44$	11.8385	1.78472
$45$	0	0
$46$	−7.18921	−1.05999
$47$	13.4273	1.95857	0.979287	−	0.202479i	$-0.0648998\pi$
$47$	13.4273	1.95857	0.979287	+	0.202479i	$0.0648998\pi$
$48$	−6.72778	−0.971071
$49$	1.00000	0.142857
$50$	0	0
$51$	−1.00000	−0.140028
$52$	−12.5211	−1.73637
$53$	−10.3318	−1.41919	−0.709593	−	0.704612i	$-0.751121\pi$
$53$	−10.3318	−1.41919	−0.709593	+	0.704612i	$0.751121\pi$
$54$	2.53468	0.344926
$55$	0	0
$56$	6.14554	0.821232
$57$	−6.17364	−0.817718
$58$	9.12383	1.19802
$59$	7.82368	1.01856	0.509278	−	0.860602i	$-0.329912\pi$
$59$	7.82368	1.01856	0.509278	+	0.860602i	$0.329912\pi$
$60$	0	0
$61$	−12.2096	−1.56328	−0.781642	−	0.623727i	$-0.785618\pi$
$61$	−12.2096	−1.56328	−0.781642	+	0.623727i	$0.785618\pi$
$62$	−0.681766	−0.0865843
$63$	−1.00000	−0.125988
$64$	−1.38627	−0.173284
$65$	0	0
$66$	6.78182	0.834785
$67$	0.100710	0.0123036	0.00615182	−	0.999981i	$-0.498042\pi$
$67$	0.100710	0.0123036	0.00615182	+	0.999981i	$0.498042\pi$
$68$	4.42458	0.536560
$69$	−2.83634	−0.341455
$70$	0	0
$71$	13.9605	1.65680	0.828401	−	0.560136i	$-0.189251\pi$
$71$	13.9605	1.65680	0.828401	+	0.560136i	$0.189251\pi$
$72$	−6.14554	−0.724258
$73$	−12.9290	−1.51323	−0.756614	−	0.653861i	$-0.773148\pi$
$73$	−12.9290	−1.51323	−0.756614	+	0.653861i	$0.773148\pi$
$74$	2.46467	0.286513
$75$	0	0
$76$	27.3158	3.13334
$77$	−2.67562	−0.304915
$78$	−7.17288	−0.812168
$79$	−13.0779	−1.47138	−0.735691	−	0.677317i	$-0.763142\pi$
$79$	−13.0779	−1.47138	−0.735691	+	0.677317i	$0.763142\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	23.2293	2.56525
$83$	−8.22428	−0.902732	−0.451366	−	0.892339i	$-0.649063\pi$
$83$	−8.22428	−0.902732	−0.451366	+	0.892339i	$0.649063\pi$
$84$	4.42458	0.482762
$85$	0	0
$86$	11.9617	1.28987
$87$	3.59961	0.385918
$88$	−16.4431	−1.75284
$89$	9.68583	1.02670	0.513348	−	0.858181i	$-0.328405\pi$
$89$	9.68583	1.02670	0.513348	+	0.858181i	$0.328405\pi$
$90$	0	0
$91$	2.82990	0.296654
$92$	12.5496	1.30839
$93$	−0.268975	−0.0278914
$94$	−34.0339	−3.51032
$95$	0	0
$96$	4.76167	0.485985
$97$	5.84462	0.593431	0.296715	−	0.954966i	$-0.404109\pi$
$97$	5.84462	0.593431	0.296715	+	0.954966i	$0.404109\pi$
$98$	−2.53468	−0.256041
$99$	2.67562	0.268910
$100$	0	0
$101$	3.76952	0.375081	0.187541	−	0.982257i	$-0.439948\pi$
$101$	3.76952	0.375081	0.187541	+	0.982257i	$0.439948\pi$
$102$	2.53468	0.250970
$103$	15.3905	1.51648	0.758238	−	0.651978i	$-0.226061\pi$
$103$	15.3905	1.51648	0.758238	+	0.651978i	$0.226061\pi$
$104$	17.3912	1.70535
$105$	0	0
$106$	26.1878	2.54359
$107$	−10.4289	−1.00820	−0.504098	−	0.863647i	$-0.668175\pi$
$107$	−10.4289	−1.00820	−0.504098	+	0.863647i	$0.668175\pi$
$108$	−4.42458	−0.425756
$109$	−12.1216	−1.16104	−0.580519	−	0.814247i	$-0.697150\pi$
$109$	−12.1216	−1.16104	−0.580519	+	0.814247i	$0.697150\pi$
$110$	0	0
$111$	0.972382	0.0922944
$112$	−6.72778	−0.635715
$113$	6.13424	0.577061	0.288531	−	0.957471i	$-0.406833\pi$
$113$	6.13424	0.577061	0.288531	+	0.957471i	$0.406833\pi$
$114$	15.6482	1.46559
$115$	0	0
$116$	−15.9268	−1.47876
$117$	−2.82990	−0.261624
$118$	−19.8305	−1.82555
$119$	−1.00000	−0.0916698
$120$	0	0
$121$	−3.84107	−0.349189
$122$	30.9475	2.80185
$123$	9.16460	0.826344
$124$	1.19010	0.106875
$125$	0	0
$126$	2.53468	0.225807
$127$	18.9227	1.67912	0.839560	−	0.543267i	$-0.182813\pi$
$127$	18.9227	1.67912	0.839560	+	0.543267i	$0.182813\pi$
$128$	13.0371	1.15233
$129$	4.71924	0.415506
$130$	0	0
$131$	−8.60741	−0.752033	−0.376017	−	0.926613i	$-0.622706\pi$
$131$	−8.60741	−0.752033	−0.376017	+	0.926613i	$0.622706\pi$
$132$	−11.8385	−1.03041
$133$	−6.17364	−0.535322
$134$	−0.255266	−0.0220517
$135$	0	0
$136$	−6.14554	−0.526975
$137$	−9.20549	−0.786478	−0.393239	−	0.919436i	$-0.628646\pi$
$137$	−9.20549	−0.786478	−0.393239	+	0.919436i	$0.628646\pi$
$138$	7.18921	0.611986
$139$	−16.3493	−1.38673	−0.693363	−	0.720589i	$-0.743872\pi$
$139$	−16.3493	−1.38673	−0.693363	+	0.720589i	$0.743872\pi$
$140$	0	0
$141$	−13.4273	−1.13078
$142$	−35.3852	−2.96946
$143$	−7.57172	−0.633179
$144$	6.72778	0.560648
$145$	0	0
$146$	32.7709	2.71214
$147$	−1.00000	−0.0824786
$148$	−4.30239	−0.353654
$149$	5.64922	0.462802	0.231401	−	0.972858i	$-0.425669\pi$
$149$	5.64922	0.462802	0.231401	+	0.972858i	$0.425669\pi$
$150$	0	0
$151$	−0.979344	−0.0796979	−0.0398489	−	0.999206i	$-0.512688\pi$
$151$	−0.979344	−0.0796979	−0.0398489	+	0.999206i	$0.512688\pi$
$152$	−37.9403	−3.07737
$153$	1.00000	0.0808452
$154$	6.78182	0.546495
$155$	0	0
$156$	12.5211	1.00249
$157$	13.5350	1.08021	0.540104	−	0.841598i	$-0.318385\pi$
$157$	13.5350	1.08021	0.540104	+	0.841598i	$0.318385\pi$
$158$	33.1483	2.63714
$159$	10.3318	0.819367
$160$	0	0
$161$	−2.83634	−0.223535
$162$	−2.53468	−0.199143
$163$	−1.69805	−0.133001	−0.0665007	−	0.997786i	$-0.521183\pi$
$163$	−1.69805	−0.133001	−0.0665007	+	0.997786i	$0.521183\pi$
$164$	−40.5495	−3.16639
$165$	0	0
$166$	20.8459	1.61795
$167$	−5.93222	−0.459049	−0.229525	−	0.973303i	$-0.573717\pi$
$167$	−5.93222	−0.459049	−0.229525	+	0.973303i	$0.573717\pi$
$168$	−6.14554	−0.474138
$169$	−4.99167	−0.383975
$170$	0	0
$171$	6.17364	0.472110
$172$	−20.8807	−1.59214
$173$	−11.0062	−0.836786	−0.418393	−	0.908266i	$-0.637407\pi$
$173$	−11.0062	−0.836786	−0.418393	+	0.908266i	$0.637407\pi$
$174$	−9.12383	−0.691676
$175$	0	0
$176$	18.0010	1.35687
$177$	−7.82368	−0.588064
$178$	−24.5504	−1.84013
$179$	18.2252	1.36221	0.681106	−	0.732185i	$-0.261499\pi$
$179$	18.2252	1.36221	0.681106	+	0.732185i	$0.261499\pi$
$180$	0	0
$181$	−4.89359	−0.363738	−0.181869	−	0.983323i	$-0.558215\pi$
$181$	−4.89359	−0.363738	−0.181869	+	0.983323i	$0.558215\pi$
$182$	−7.17288	−0.531689
$183$	12.2096	0.902563
$184$	−17.4308	−1.28502
$185$	0	0
$186$	0.681766	0.0499895
$187$	2.67562	0.195660
$188$	59.4102	4.33294
$189$	1.00000	0.0727393
$190$	0	0
$191$	3.22202	0.233137	0.116569	−	0.993183i	$-0.462811\pi$
$191$	3.22202	0.233137	0.116569	+	0.993183i	$0.462811\pi$
$192$	1.38627	0.100046
$193$	−7.47523	−0.538079	−0.269040	−	0.963129i	$-0.586706\pi$
$193$	−7.47523	−0.538079	−0.269040	+	0.963129i	$0.586706\pi$
$194$	−14.8142	−1.06360
$195$	0	0
$196$	4.42458	0.316042
$197$	−1.31764	−0.0938780	−0.0469390	−	0.998898i	$-0.514947\pi$
$197$	−1.31764	−0.0938780	−0.0469390	+	0.998898i	$0.514947\pi$
$198$	−6.78182	−0.481963
$199$	−3.75784	−0.266386	−0.133193	−	0.991090i	$-0.542523\pi$
$199$	−3.75784	−0.266386	−0.133193	+	0.991090i	$0.542523\pi$
$200$	0	0
$201$	−0.100710	−0.00710351
$202$	−9.55451	−0.672253
$203$	3.59961	0.252643
$204$	−4.42458	−0.309783
$205$	0	0
$206$	−39.0101	−2.71796
$207$	2.83634	0.197139
$208$	−19.0389	−1.32011
$209$	16.5183	1.14259
$210$	0	0
$211$	3.94059	0.271281	0.135641	−	0.990758i	$-0.456691\pi$
$211$	3.94059	0.271281	0.135641	+	0.990758i	$0.456691\pi$
$212$	−45.7140	−3.13965
$213$	−13.9605	−0.956555
$214$	26.4338	1.80698
$215$	0	0
$216$	6.14554	0.418151
$217$	−0.268975	−0.0182592
$218$	30.7243	2.08091
$219$	12.9290	0.873663
$220$	0	0
$221$	−2.82990	−0.190360
$222$	−2.46467	−0.165418
$223$	−12.3046	−0.823976	−0.411988	−	0.911189i	$-0.635165\pi$
$223$	−12.3046	−0.823976	−0.411988	+	0.911189i	$0.635165\pi$
$224$	4.76167	0.318152
$225$	0	0
$226$	−15.5483	−1.03426
$227$	10.7792	0.715441	0.357720	−	0.933829i	$-0.383554\pi$
$227$	10.7792	0.715441	0.357720	+	0.933829i	$0.383554\pi$
$228$	−27.3158	−1.80903
$229$	−16.8801	−1.11547	−0.557734	−	0.830020i	$-0.688329\pi$
$229$	−16.8801	−1.11547	−0.557734	+	0.830020i	$0.688329\pi$
$230$	0	0
$231$	2.67562	0.176043
$232$	22.1215	1.45235
$233$	−14.4278	−0.945194	−0.472597	−	0.881279i	$-0.656683\pi$
$233$	−14.4278	−0.945194	−0.472597	+	0.881279i	$0.656683\pi$
$234$	7.17288	0.468906
$235$	0	0
$236$	34.6165	2.25334
$237$	13.0779	0.849503
$238$	2.53468	0.164299
$239$	6.81210	0.440638	0.220319	−	0.975428i	$-0.429290\pi$
$239$	6.81210	0.440638	0.220319	+	0.975428i	$0.429290\pi$
$240$	0	0
$241$	0.719989	0.0463786	0.0231893	−	0.999731i	$-0.492618\pi$
$241$	0.719989	0.0463786	0.0231893	+	0.999731i	$0.492618\pi$
$242$	9.73588	0.625846
$243$	−1.00000	−0.0641500
$244$	−54.0226	−3.45844
$245$	0	0
$246$	−23.2293	−1.48105
$247$	−17.4708	−1.11164
$248$	−1.65300	−0.104965
$249$	8.22428	0.521192
$250$	0	0
$251$	−24.1847	−1.52653	−0.763263	−	0.646088i	$-0.776404\pi$
$251$	−24.1847	−1.52653	−0.763263	+	0.646088i	$0.776404\pi$
$252$	−4.42458	−0.278723
$253$	7.58896	0.477114
$254$	−47.9630	−3.00946
$255$	0	0
$256$	−30.2722	−1.89202
$257$	−21.4316	−1.33687	−0.668433	−	0.743773i	$-0.733035\pi$
$257$	−21.4316	−1.33687	−0.668433	+	0.743773i	$0.733035\pi$
$258$	−11.9617	−0.744706
$259$	0.972382	0.0604209
$260$	0	0
$261$	−3.59961	−0.222810
$262$	21.8170	1.34786
$263$	−8.00460	−0.493585	−0.246793	−	0.969068i	$-0.579377\pi$
$263$	−8.00460	−0.493585	−0.246793	+	0.969068i	$0.579377\pi$
$264$	16.4431	1.01200
$265$	0	0
$266$	15.6482	0.959451
$267$	−9.68583	−0.592763
$268$	0.445598	0.0272193
$269$	15.2324	0.928735	0.464367	−	0.885643i	$-0.346282\pi$
$269$	15.2324	0.928735	0.464367	+	0.885643i	$0.346282\pi$
$270$	0	0
$271$	12.3967	0.753048	0.376524	−	0.926407i	$-0.377119\pi$
$271$	12.3967	0.753048	0.376524	+	0.926407i	$0.377119\pi$
$272$	6.72778	0.407931
$273$	−2.82990	−0.171273
$274$	23.3329	1.40959
$275$	0	0
$276$	−12.5496	−0.755399
$277$	−22.2410	−1.33633	−0.668166	−	0.744013i	$-0.732920\pi$
$277$	−22.2410	−1.33633	−0.668166	+	0.744013i	$0.732920\pi$
$278$	41.4401	2.48541
$279$	0.268975	0.0161031
$280$	0	0
$281$	30.3105	1.80817	0.904086	−	0.427350i	$-0.140553\pi$
$281$	30.3105	1.80817	0.904086	+	0.427350i	$0.140553\pi$
$282$	34.0339	2.02669
$283$	7.53626	0.447984	0.223992	−	0.974591i	$-0.428091\pi$
$283$	7.53626	0.447984	0.223992	+	0.974591i	$0.428091\pi$
$284$	61.7692	3.66533
$285$	0	0
$286$	19.1919	1.13484
$287$	9.16460	0.540969
$288$	−4.76167	−0.280584
$289$	1.00000	0.0588235
$290$	0	0
$291$	−5.84462	−0.342618
$292$	−57.2056	−3.34770
$293$	27.8572	1.62743	0.813717	−	0.581261i	$-0.197441\pi$
$293$	27.8572	1.62743	0.813717	+	0.581261i	$0.197441\pi$
$294$	2.53468	0.147825
$295$	0	0
$296$	5.97581	0.347337
$297$	−2.67562	−0.155255
$298$	−14.3190	−0.829475
$299$	−8.02656	−0.464188
$300$	0	0
$301$	4.71924	0.272012
$302$	2.48232	0.142841
$303$	−3.76952	−0.216553
$304$	41.5349	2.38219
$305$	0	0
$306$	−2.53468	−0.144898
$307$	−14.2241	−0.811814	−0.405907	−	0.913914i	$-0.633044\pi$
$307$	−14.2241	−0.811814	−0.405907	+	0.913914i	$0.633044\pi$
$308$	−11.8385	−0.674561
$309$	−15.3905	−0.875538
$310$	0	0
$311$	−18.4183	−1.04440	−0.522202	−	0.852822i	$-0.674889\pi$
$311$	−18.4183	−1.04440	−0.522202	+	0.852822i	$0.674889\pi$
$312$	−17.3912	−0.984585
$313$	9.24130	0.522349	0.261175	−	0.965292i	$-0.415890\pi$
$313$	9.24130	0.522349	0.261175	+	0.965292i	$0.415890\pi$
$314$	−34.3068	−1.93604
$315$	0	0
$316$	−57.8644	−3.25513
$317$	10.1457	0.569839	0.284920	−	0.958551i	$-0.408033\pi$
$317$	10.1457	0.569839	0.284920	+	0.958551i	$0.408033\pi$
$318$	−26.1878	−1.46854
$319$	−9.63116	−0.539242
$320$	0	0
$321$	10.4289	0.582082
$322$	7.18921	0.400639
$323$	6.17364	0.343510
$324$	4.42458	0.245810
$325$	0	0
$326$	4.30400	0.238377
$327$	12.1216	0.670326
$328$	56.3214	3.10983
$329$	−13.4273	−0.740271
$330$	0	0
$331$	8.09315	0.444840	0.222420	−	0.974951i	$-0.428604\pi$
$331$	8.09315	0.444840	0.222420	+	0.974951i	$0.428604\pi$
$332$	−36.3890	−1.99711
$333$	−0.972382	−0.0532862
$334$	15.0363	0.822748
$335$	0	0
$336$	6.72778	0.367030
$337$	6.19090	0.337240	0.168620	−	0.985681i	$-0.446069\pi$
$337$	6.19090	0.337240	0.168620	+	0.985681i	$0.446069\pi$
$338$	12.6523	0.688193
$339$	−6.13424	−0.333166
$340$	0	0
$341$	0.719675	0.0389726
$342$	−15.6482	−0.846156
$343$	−1.00000	−0.0539949
$344$	29.0023	1.56370
$345$	0	0
$346$	27.8972	1.49976
$347$	25.4722	1.36742	0.683710	−	0.729754i	$-0.260365\pi$
$347$	25.4722	1.36742	0.683710	+	0.729754i	$0.260365\pi$
$348$	15.9268	0.853764
$349$	11.6109	0.621519	0.310759	−	0.950489i	$-0.399417\pi$
$349$	11.6109	0.621519	0.310759	+	0.950489i	$0.399417\pi$
$350$	0	0
$351$	2.82990	0.151049
$352$	−12.7404	−0.679065
$353$	27.4324	1.46008	0.730040	−	0.683404i	$-0.239501\pi$
$353$	27.4324	1.46008	0.730040	+	0.683404i	$0.239501\pi$
$354$	19.8305	1.05398
$355$	0	0
$356$	42.8558	2.27135
$357$	1.00000	0.0529256
$358$	−46.1949	−2.44148
$359$	−9.01857	−0.475982	−0.237991	−	0.971267i	$-0.576489\pi$
$359$	−9.01857	−0.475982	−0.237991	+	0.971267i	$0.576489\pi$
$360$	0	0
$361$	19.1138	1.00599
$362$	12.4037	0.651923
$363$	3.84107	0.201604
$364$	12.5211	0.656285
$365$	0	0
$366$	−30.9475	−1.61765
$367$	0.540557	0.0282168	0.0141084	−	0.999900i	$-0.495509\pi$
$367$	0.540557	0.0282168	0.0141084	+	0.999900i	$0.495509\pi$
$368$	19.0823	0.994732
$369$	−9.16460	−0.477090
$370$	0	0
$371$	10.3318	0.536402
$372$	−1.19010	−0.0617040
$373$	−6.14299	−0.318072	−0.159036	−	0.987273i	$-0.550839\pi$
$373$	−6.14299	−0.318072	−0.159036	+	0.987273i	$0.550839\pi$
$374$	−6.78182	−0.350680
$375$	0	0
$376$	−82.5180	−4.25554
$377$	10.1865	0.524632
$378$	−2.53468	−0.130370
$379$	−5.98190	−0.307269	−0.153635	−	0.988128i	$-0.549098\pi$
$379$	−5.98190	−0.307269	−0.153635	+	0.988128i	$0.549098\pi$
$380$	0	0
$381$	−18.9227	−0.969440
$382$	−8.16678	−0.417849
$383$	16.7998	0.858427	0.429214	−	0.903203i	$-0.358791\pi$
$383$	16.7998	0.858427	0.429214	+	0.903203i	$0.358791\pi$
$384$	−13.0371	−0.665296
$385$	0	0
$386$	18.9473	0.964392
$387$	−4.71924	−0.239892
$388$	25.8600	1.31284
$389$	6.62924	0.336116	0.168058	−	0.985777i	$-0.446250\pi$
$389$	6.62924	0.336116	0.168058	+	0.985777i	$0.446250\pi$
$390$	0	0
$391$	2.83634	0.143440
$392$	−6.14554	−0.310396
$393$	8.60741	0.434187
$394$	3.33979	0.168256
$395$	0	0
$396$	11.8385	0.594907
$397$	−11.0069	−0.552421	−0.276211	−	0.961097i	$-0.589079\pi$
$397$	−11.0069	−0.552421	−0.276211	+	0.961097i	$0.589079\pi$
$398$	9.52490	0.477440
$399$	6.17364	0.309068
$400$	0	0
$401$	11.8228	0.590405	0.295202	−	0.955435i	$-0.404613\pi$
$401$	11.8228	0.590405	0.295202	+	0.955435i	$0.404613\pi$
$402$	0.255266	0.0127315
$403$	−0.761173	−0.0379167
$404$	16.6786	0.829789
$405$	0	0
$406$	−9.12383	−0.452808
$407$	−2.60172	−0.128963
$408$	6.14554	0.304249
$409$	−16.2239	−0.802222	−0.401111	−	0.916029i	$-0.631376\pi$
$409$	−16.2239	−0.802222	−0.401111	+	0.916029i	$0.631376\pi$
$410$	0	0
$411$	9.20549	0.454074
$412$	68.0968	3.35489
$413$	−7.82368	−0.384978
$414$	−7.18921	−0.353330
$415$	0	0
$416$	13.4750	0.660668
$417$	16.3493	0.800627
$418$	−41.8685	−2.04786
$419$	10.0431	0.490637	0.245318	−	0.969443i	$-0.421108\pi$
$419$	10.0431	0.490637	0.245318	+	0.969443i	$0.421108\pi$
$420$	0	0
$421$	−0.327910	−0.0159814	−0.00799069	−	0.999968i	$-0.502544\pi$
$421$	−0.327910	−0.0159814	−0.00799069	+	0.999968i	$0.502544\pi$
$422$	−9.98812	−0.486214
$423$	13.4273	0.652858
$424$	63.4946	3.08357
$425$	0	0
$426$	35.3852	1.71442
$427$	12.2096	0.590866
$428$	−46.1434	−2.23042
$429$	7.57172	0.365566
$430$	0	0
$431$	30.6790	1.47775	0.738877	−	0.673840i	$-0.235356\pi$
$431$	30.6790	1.47775	0.738877	+	0.673840i	$0.235356\pi$
$432$	−6.72778	−0.323690
$433$	−22.8410	−1.09767	−0.548834	−	0.835931i	$-0.684928\pi$
$433$	−22.8410	−1.09767	−0.548834	+	0.835931i	$0.684928\pi$
$434$	0.681766	0.0327258
$435$	0	0
$436$	−53.6330	−2.56856
$437$	17.5105	0.837643
$438$	−32.7709	−1.56585
$439$	−3.59112	−0.171395	−0.0856975	−	0.996321i	$-0.527312\pi$
$439$	−3.59112	−0.171395	−0.0856975	+	0.996321i	$0.527312\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	7.17288	0.341179
$443$	−11.0622	−0.525583	−0.262792	−	0.964853i	$-0.584643\pi$
$443$	−11.0622	−0.525583	−0.262792	+	0.964853i	$0.584643\pi$
$444$	4.30239	0.204182
$445$	0	0
$446$	31.1881	1.47680
$447$	−5.64922	−0.267199
$448$	1.38627	0.0654953
$449$	31.5468	1.48878	0.744392	−	0.667742i	$-0.232739\pi$
$449$	31.5468	1.48878	0.744392	+	0.667742i	$0.232739\pi$
$450$	0	0
$451$	−24.5209	−1.15465
$452$	27.1415	1.27663
$453$	0.979344	0.0460136
$454$	−27.3218	−1.28228
$455$	0	0
$456$	37.9403	1.77672
$457$	−17.7329	−0.829512	−0.414756	−	0.909933i	$-0.636133\pi$
$457$	−17.7329	−0.829512	−0.414756	+	0.909933i	$0.636133\pi$
$458$	42.7856	1.99924
$459$	−1.00000	−0.0466760
$460$	0	0
$461$	−42.3347	−1.97173	−0.985863	−	0.167556i	$-0.946413\pi$
$461$	−42.3347	−1.97173	−0.985863	+	0.167556i	$0.946413\pi$
$462$	−6.78182	−0.315519
$463$	13.1494	0.611105	0.305553	−	0.952175i	$-0.401159\pi$
$463$	13.1494	0.611105	0.305553	+	0.952175i	$0.401159\pi$
$464$	−24.2173	−1.12426
$465$	0	0
$466$	36.5697	1.69406
$467$	23.4306	1.08424	0.542119	−	0.840302i	$-0.317622\pi$
$467$	23.4306	1.08424	0.542119	+	0.840302i	$0.317622\pi$
$468$	−12.5211	−0.578789
$469$	−0.100710	−0.00465034
$470$	0	0
$471$	−13.5350	−0.623659
$472$	−48.0807	−2.21309
$473$	−12.6269	−0.580584
$474$	−33.1483	−1.52255
$475$	0	0
$476$	−4.42458	−0.202800
$477$	−10.3318	−0.473062
$478$	−17.2665	−0.789750
$479$	−34.2130	−1.56323	−0.781617	−	0.623759i	$-0.785605\pi$
$479$	−34.2130	−1.56323	−0.781617	+	0.623759i	$0.785605\pi$
$480$	0	0
$481$	2.75174	0.125469
$482$	−1.82494	−0.0831237
$483$	2.83634	0.129058
$484$	−16.9952	−0.772507
$485$	0	0
$486$	2.53468	0.114975
$487$	23.0901	1.04631	0.523157	−	0.852236i	$-0.324754\pi$
$487$	23.0901	1.04631	0.523157	+	0.852236i	$0.324754\pi$
$488$	75.0348	3.39667
$489$	1.69805	0.0767884
$490$	0	0
$491$	−13.7848	−0.622099	−0.311049	−	0.950394i	$-0.600680\pi$
$491$	−13.7848	−0.622099	−0.311049	+	0.950394i	$0.600680\pi$
$492$	40.5495	1.82811
$493$	−3.59961	−0.162118
$494$	44.2828	1.99238
$495$	0	0
$496$	1.80961	0.0812537
$497$	−13.9605	−0.626212
$498$	−20.8459	−0.934126
$499$	−35.6592	−1.59632	−0.798162	−	0.602443i	$-0.794194\pi$
$499$	−35.6592	−1.59632	−0.798162	+	0.602443i	$0.794194\pi$
$500$	0	0
$501$	5.93222	0.265032
$502$	61.3005	2.73597
$503$	19.4662	0.867955	0.433978	−	0.900924i	$-0.357110\pi$
$503$	19.4662	0.867955	0.433978	+	0.900924i	$0.357110\pi$
$504$	6.14554	0.273744
$505$	0	0
$506$	−19.2356	−0.855125
$507$	4.99167	0.221688
$508$	83.7251	3.71470
$509$	−37.2678	−1.65187	−0.825934	−	0.563767i	$-0.809351\pi$
$509$	−37.2678	−1.65187	−0.825934	+	0.563767i	$0.809351\pi$
$510$	0	0
$511$	12.9290	0.571947
$512$	50.6562	2.23871
$513$	−6.17364	−0.272573
$514$	54.3221	2.39605
$515$	0	0
$516$	20.8807	0.919220
$517$	35.9263	1.58004
$518$	−2.46467	−0.108292
$519$	11.0062	0.483119
$520$	0	0
$521$	20.1590	0.883182	0.441591	−	0.897216i	$-0.354414\pi$
$521$	20.1590	0.883182	0.441591	+	0.897216i	$0.354414\pi$
$522$	9.12383	0.399339
$523$	1.53917	0.0673031	0.0336516	−	0.999434i	$-0.489286\pi$
$523$	1.53917	0.0673031	0.0336516	+	0.999434i	$0.489286\pi$
$524$	−38.0842	−1.66372
$525$	0	0
$526$	20.2891	0.884646
$527$	0.268975	0.0117168
$528$	−18.0010	−0.783391
$529$	−14.9552	−0.650225
$530$	0	0
$531$	7.82368	0.339519
$532$	−27.3158	−1.18429
$533$	25.9349	1.12336
$534$	24.5504	1.06240
$535$	0	0
$536$	−0.618915	−0.0267331
$537$	−18.2252	−0.786474
$538$	−38.6092	−1.66456
$539$	2.67562	0.115247
$540$	0	0
$541$	−40.9976	−1.76262	−0.881311	−	0.472536i	$-0.843339\pi$
$541$	−40.9976	−1.76262	−0.881311	+	0.472536i	$0.843339\pi$
$542$	−31.4217	−1.34968
$543$	4.89359	0.210004
$544$	−4.76167	−0.204155
$545$	0	0
$546$	7.17288	0.306971
$547$	−20.3683	−0.870885	−0.435442	−	0.900217i	$-0.643408\pi$
$547$	−20.3683	−0.870885	−0.435442	+	0.900217i	$0.643408\pi$
$548$	−40.7305	−1.73992
$549$	−12.2096	−0.521095
$550$	0	0
$551$	−22.2227	−0.946717
$552$	17.4308	0.741906
$553$	13.0779	0.556130
$554$	56.3737	2.39509
$555$	0	0
$556$	−72.3387	−3.06784
$557$	17.9048	0.758650	0.379325	−	0.925263i	$-0.376156\pi$
$557$	17.9048	0.758650	0.379325	+	0.925263i	$0.376156\pi$
$558$	−0.681766	−0.0288614
$559$	13.3550	0.564855
$560$	0	0
$561$	−2.67562	−0.112965
$562$	−76.8273	−3.24076
$563$	−43.4886	−1.83283	−0.916413	−	0.400233i	$-0.868929\pi$
$563$	−43.4886	−1.83283	−0.916413	+	0.400233i	$0.868929\pi$
$564$	−59.4102	−2.50162
$565$	0	0
$566$	−19.1020	−0.802916
$567$	−1.00000	−0.0419961
$568$	−85.7945	−3.59986
$569$	36.2315	1.51890	0.759452	−	0.650564i	$-0.225467\pi$
$569$	36.2315	1.51890	0.759452	+	0.650564i	$0.225467\pi$
$570$	0	0
$571$	26.4307	1.10609	0.553045	−	0.833152i	$-0.313466\pi$
$571$	26.4307	1.10609	0.553045	+	0.833152i	$0.313466\pi$
$572$	−33.5017	−1.40078
$573$	−3.22202	−0.134602
$574$	−23.2293	−0.969572
$575$	0	0
$576$	−1.38627	−0.0577614
$577$	7.24749	0.301717	0.150859	−	0.988555i	$-0.451796\pi$
$577$	7.24749	0.301717	0.150859	+	0.988555i	$0.451796\pi$
$578$	−2.53468	−0.105429
$579$	7.47523	0.310660
$580$	0	0
$581$	8.22428	0.341200
$582$	14.8142	0.614069
$583$	−27.6440	−1.14490
$584$	79.4558	3.28791
$585$	0	0
$586$	−70.6090	−2.91683
$587$	−44.9985	−1.85729	−0.928644	−	0.370972i	$-0.879025\pi$
$587$	−44.9985	−1.85729	−0.928644	+	0.370972i	$0.879025\pi$
$588$	−4.42458	−0.182467
$589$	1.66056	0.0684220
$590$	0	0
$591$	1.31764	0.0542005
$592$	−6.54197	−0.268873
$593$	38.0682	1.56328	0.781638	−	0.623733i	$-0.214385\pi$
$593$	38.0682	1.56328	0.781638	+	0.623733i	$0.214385\pi$
$594$	6.78182	0.278262
$595$	0	0
$596$	24.9955	1.02385
$597$	3.75784	0.153798
$598$	20.3447	0.831958
$599$	−11.6339	−0.475350	−0.237675	−	0.971345i	$-0.576385\pi$
$599$	−11.6339	−0.475350	−0.237675	+	0.971345i	$0.576385\pi$
$600$	0	0
$601$	7.59027	0.309614	0.154807	−	0.987945i	$-0.450524\pi$
$601$	7.59027	0.309614	0.154807	+	0.987945i	$0.450524\pi$
$602$	−11.9617	−0.487524
$603$	0.100710	0.00410121
$604$	−4.33319	−0.176315
$605$	0	0
$606$	9.55451	0.388125
$607$	−28.0706	−1.13935	−0.569675	−	0.821870i	$-0.692931\pi$
$607$	−28.0706	−1.13935	−0.569675	+	0.821870i	$0.692931\pi$
$608$	−29.3968	−1.19220
$609$	−3.59961	−0.145863
$610$	0	0
$611$	−37.9979	−1.53723
$612$	4.42458	0.178853
$613$	35.9949	1.45382	0.726911	−	0.686732i	$-0.240955\pi$
$613$	35.9949	1.45382	0.726911	+	0.686732i	$0.240955\pi$
$614$	36.0536	1.45500
$615$	0	0
$616$	16.4431	0.662511
$617$	−11.5231	−0.463903	−0.231951	−	0.972727i	$-0.574511\pi$
$617$	−11.5231	−0.463903	−0.231951	+	0.972727i	$0.574511\pi$
$618$	39.0101	1.56921
$619$	−43.6477	−1.75435	−0.877176	−	0.480170i	$-0.840575\pi$
$619$	−43.6477	−1.75435	−0.877176	+	0.480170i	$0.840575\pi$
$620$	0	0
$621$	−2.83634	−0.113818
$622$	46.6844	1.87187
$623$	−9.68583	−0.388055
$624$	19.0389	0.762167
$625$	0	0
$626$	−23.4237	−0.936200
$627$	−16.5183	−0.659677
$628$	59.8866	2.38974
$629$	−0.972382	−0.0387714
$630$	0	0
$631$	28.5906	1.13817	0.569086	−	0.822278i	$-0.307297\pi$
$631$	28.5906	1.13817	0.569086	+	0.822278i	$0.307297\pi$
$632$	80.3709	3.19698
$633$	−3.94059	−0.156624
$634$	−25.7161	−1.02132
$635$	0	0
$636$	45.7140	1.81268
$637$	−2.82990	−0.112125
$638$	24.4119	0.966476
$639$	13.9605	0.552267
$640$	0	0
$641$	23.7289	0.937236	0.468618	−	0.883401i	$-0.344752\pi$
$641$	23.7289	0.937236	0.468618	+	0.883401i	$0.344752\pi$
$642$	−26.4338	−1.04326
$643$	42.9662	1.69442	0.847211	−	0.531257i	$-0.178280\pi$
$643$	42.9662	1.69442	0.847211	+	0.531257i	$0.178280\pi$
$644$	−12.5496	−0.494525
$645$	0	0
$646$	−15.6482	−0.615669
$647$	−42.7951	−1.68245	−0.841225	−	0.540686i	$-0.818165\pi$
$647$	−42.7951	−1.68245	−0.841225	+	0.540686i	$0.818165\pi$
$648$	−6.14554	−0.241419
$649$	20.9332	0.821699
$650$	0	0
$651$	0.268975	0.0105420
$652$	−7.51316	−0.294238
$653$	7.30739	0.285960	0.142980	−	0.989726i	$-0.454332\pi$
$653$	7.30739	0.285960	0.142980	+	0.989726i	$0.454332\pi$
$654$	−30.7243	−1.20142
$655$	0	0
$656$	−61.6574	−2.40732
$657$	−12.9290	−0.504410
$658$	34.0339	1.32678
$659$	8.24440	0.321156	0.160578	−	0.987023i	$-0.448664\pi$
$659$	8.24440	0.321156	0.160578	+	0.987023i	$0.448664\pi$
$660$	0	0
$661$	−8.85399	−0.344380	−0.172190	−	0.985064i	$-0.555084\pi$
$661$	−8.85399	−0.344380	−0.172190	+	0.985064i	$0.555084\pi$
$662$	−20.5135	−0.797280
$663$	2.82990	0.109904
$664$	50.5426	1.96143
$665$	0	0
$666$	2.46467	0.0955042
$667$	−10.2097	−0.395322
$668$	−26.2476	−1.01555
$669$	12.3046	0.475723
$670$	0	0
$671$	−32.6683	−1.26115
$672$	−4.76167	−0.183685
$673$	40.6122	1.56549	0.782743	−	0.622345i	$-0.213820\pi$
$673$	40.6122	1.56549	0.782743	+	0.622345i	$0.213820\pi$
$674$	−15.6919	−0.604431
$675$	0	0
$676$	−22.0861	−0.849464
$677$	−10.6023	−0.407478	−0.203739	−	0.979025i	$-0.565309\pi$
$677$	−10.6023	−0.407478	−0.203739	+	0.979025i	$0.565309\pi$
$678$	15.5483	0.597130
$679$	−5.84462	−0.224296
$680$	0	0
$681$	−10.7792	−0.413060
$682$	−1.82414	−0.0698501
$683$	−16.1464	−0.617827	−0.308913	−	0.951090i	$-0.599965\pi$
$683$	−16.1464	−0.617827	−0.308913	+	0.951090i	$0.599965\pi$
$684$	27.3158	1.04445
$685$	0	0
$686$	2.53468	0.0967744
$687$	16.8801	0.644016
$688$	−31.7500	−1.21046
$689$	29.2380	1.11388
$690$	0	0
$691$	−31.5928	−1.20185	−0.600923	−	0.799307i	$-0.705200\pi$
$691$	−31.5928	−1.20185	−0.600923	+	0.799307i	$0.705200\pi$
$692$	−48.6979	−1.85122
$693$	−2.67562	−0.101638
$694$	−64.5638	−2.45081
$695$	0	0
$696$	−22.1215	−0.838514
$697$	−9.16460	−0.347134
$698$	−29.4299	−1.11394
$699$	14.4278	0.545708
$700$	0	0
$701$	−15.0683	−0.569122	−0.284561	−	0.958658i	$-0.591848\pi$
$701$	−15.0683	−0.569122	−0.284561	+	0.958658i	$0.591848\pi$
$702$	−7.17288	−0.270723
$703$	−6.00314	−0.226413
$704$	−3.70914	−0.139793
$705$	0	0
$706$	−69.5323	−2.61688
$707$	−3.76952	−0.141767
$708$	−34.6165	−1.30097
$709$	32.9168	1.23622	0.618108	−	0.786093i	$-0.287899\pi$
$709$	32.9168	1.23622	0.618108	+	0.786093i	$0.287899\pi$
$710$	0	0
$711$	−13.0779	−0.490461
$712$	−59.5246	−2.23078
$713$	0.762906	0.0285711
$714$	−2.53468	−0.0948579
$715$	0	0
$716$	80.6387	3.01361
$717$	−6.81210	−0.254402
$718$	22.8592	0.853097
$719$	−50.5233	−1.88420	−0.942101	−	0.335330i	$-0.891152\pi$
$719$	−50.5233	−1.88420	−0.942101	+	0.335330i	$0.891152\pi$
$720$	0	0
$721$	−15.3905	−0.573174
$722$	−48.4473	−1.80302
$723$	−0.719989	−0.0267767
$724$	−21.6521	−0.804694
$725$	0	0
$726$	−9.73588	−0.361332
$727$	39.0916	1.44983	0.724914	−	0.688839i	$-0.241879\pi$
$727$	39.0916	1.44983	0.724914	+	0.688839i	$0.241879\pi$
$728$	−17.3912	−0.644562
$729$	1.00000	0.0370370
$730$	0	0
$731$	−4.71924	−0.174547
$732$	54.0226	1.99673
$733$	15.1802	0.560695	0.280347	−	0.959899i	$-0.409550\pi$
$733$	15.1802	0.560695	0.280347	+	0.959899i	$0.409550\pi$
$734$	−1.37014	−0.0505727
$735$	0	0
$736$	−13.5057	−0.497827
$737$	0.269460	0.00992570
$738$	23.2293	0.855082
$739$	−33.2452	−1.22294	−0.611472	−	0.791266i	$-0.709422\pi$
$739$	−33.2452	−1.22294	−0.611472	+	0.791266i	$0.709422\pi$
$740$	0	0
$741$	17.4708	0.641805
$742$	−26.1878	−0.961386
$743$	13.0619	0.479194	0.239597	−	0.970872i	$-0.422985\pi$
$743$	13.0619	0.479194	0.239597	+	0.970872i	$0.422985\pi$
$744$	1.65300	0.0606018
$745$	0	0
$746$	15.5705	0.570077
$747$	−8.22428	−0.300911
$748$	11.8385	0.432858
$749$	10.4289	0.381062
$750$	0	0
$751$	0.708627	0.0258582	0.0129291	−	0.999916i	$-0.495884\pi$
$751$	0.708627	0.0258582	0.0129291	+	0.999916i	$0.495884\pi$
$752$	90.3359	3.29421
$753$	24.1847	0.881340
$754$	−25.8195	−0.940292
$755$	0	0
$756$	4.42458	0.160921
$757$	22.8545	0.830663	0.415331	−	0.909670i	$-0.363666\pi$
$757$	22.8545	0.830663	0.415331	+	0.909670i	$0.363666\pi$
$758$	15.1622	0.550715
$759$	−7.58896	−0.275462
$760$	0	0
$761$	−19.0731	−0.691399	−0.345700	−	0.938345i	$-0.612358\pi$
$761$	−19.0731	−0.691399	−0.345700	+	0.938345i	$0.612358\pi$
$762$	47.9630	1.73751
$763$	12.1216	0.438831
$764$	14.2561	0.515767
$765$	0	0
$766$	−42.5819	−1.53855
$767$	−22.1402	−0.799437
$768$	30.2722	1.09236
$769$	24.5762	0.886239	0.443120	−	0.896463i	$-0.353872\pi$
$769$	24.5762	0.886239	0.443120	+	0.896463i	$0.353872\pi$
$770$	0	0
$771$	21.4316	0.771840
$772$	−33.0748	−1.19039
$773$	−38.3443	−1.37915	−0.689575	−	0.724214i	$-0.742203\pi$
$773$	−38.3443	−1.37915	−0.689575	+	0.724214i	$0.742203\pi$
$774$	11.9617	0.429956
$775$	0	0
$776$	−35.9183	−1.28939
$777$	−0.972382	−0.0348840
$778$	−16.8030	−0.602416
$779$	−56.5789	−2.02715
$780$	0	0
$781$	37.3528	1.33659
$782$	−7.18921	−0.257086
$783$	3.59961	0.128639
$784$	6.72778	0.240278
$785$	0	0
$786$	−21.8170	−0.778187
$787$	45.5389	1.62329	0.811643	−	0.584154i	$-0.198574\pi$
$787$	45.5389	1.62329	0.811643	+	0.584154i	$0.198574\pi$
$788$	−5.83001	−0.207686
$789$	8.00460	0.284971
$790$	0	0
$791$	−6.13424	−0.218109
$792$	−16.4431	−0.584280
$793$	34.5520	1.22698
$794$	27.8990	0.990097
$795$	0	0
$796$	−16.6269	−0.589324
$797$	19.1640	0.678825	0.339412	−	0.940638i	$-0.389772\pi$
$797$	19.1640	0.678825	0.339412	+	0.940638i	$0.389772\pi$
$798$	−15.6482	−0.553939
$799$	13.4273	0.475024
$800$	0	0
$801$	9.68583	0.342232
$802$	−29.9671	−1.05817
$803$	−34.5931	−1.22077
$804$	−0.445598	−0.0157150
$805$	0	0
$806$	1.92933	0.0679577
$807$	−15.2324	−0.536205
$808$	−23.1657	−0.814967
$809$	−22.3419	−0.785500	−0.392750	−	0.919645i	$-0.628476\pi$
$809$	−22.3419	−0.785500	−0.392750	+	0.919645i	$0.628476\pi$
$810$	0	0
$811$	21.2903	0.747604	0.373802	−	0.927509i	$-0.378054\pi$
$811$	21.2903	0.747604	0.373802	+	0.927509i	$0.378054\pi$
$812$	15.9268	0.558920
$813$	−12.3967	−0.434772
$814$	6.59452	0.231138
$815$	0	0
$816$	−6.72778	−0.235519
$817$	−29.1349	−1.01930
$818$	41.1224	1.43781
$819$	2.82990	0.0988847
$820$	0	0
$821$	−9.71416	−0.339027	−0.169513	−	0.985528i	$-0.554220\pi$
$821$	−9.71416	−0.339027	−0.169513	+	0.985528i	$0.554220\pi$
$822$	−23.3329	−0.813830
$823$	10.8097	0.376803	0.188401	−	0.982092i	$-0.439669\pi$
$823$	10.8097	0.376803	0.188401	+	0.982092i	$0.439669\pi$
$824$	−94.5832	−3.29496
$825$	0	0
$826$	19.8305	0.689991
$827$	1.59735	0.0555454	0.0277727	−	0.999614i	$-0.491159\pi$
$827$	1.59735	0.0555454	0.0277727	+	0.999614i	$0.491159\pi$
$828$	12.5496	0.436130
$829$	−13.4929	−0.468629	−0.234315	−	0.972161i	$-0.575285\pi$
$829$	−13.4929	−0.468629	−0.234315	+	0.972161i	$0.575285\pi$
$830$	0	0
$831$	22.2410	0.771531
$832$	3.92301	0.136006
$833$	1.00000	0.0346479
$834$	−41.4401	−1.43495
$835$	0	0
$836$	73.0866	2.52775
$837$	−0.268975	−0.00929715
$838$	−25.4560	−0.879362
$839$	2.17356	0.0750397	0.0375198	−	0.999296i	$-0.488054\pi$
$839$	2.17356	0.0750397	0.0375198	+	0.999296i	$0.488054\pi$
$840$	0	0
$841$	−16.0428	−0.553201
$842$	0.831147	0.0286432
$843$	−30.3105	−1.04395
$844$	17.4355	0.600154
$845$	0	0
$846$	−34.0339	−1.17011
$847$	3.84107	0.131981
$848$	−69.5102	−2.38699
$849$	−7.53626	−0.258644
$850$	0	0
$851$	−2.75801	−0.0945433
$852$	−61.7692	−2.11618
$853$	−40.4215	−1.38400	−0.692002	−	0.721895i	$-0.743271\pi$
$853$	−40.4215	−1.38400	−0.692002	+	0.721895i	$0.743271\pi$
$854$	−30.9475	−1.05900
$855$	0	0
$856$	64.0909	2.19058
$857$	−31.2983	−1.06913	−0.534564	−	0.845128i	$-0.679524\pi$
$857$	−31.2983	−1.06913	−0.534564	+	0.845128i	$0.679524\pi$
$858$	−19.1919	−0.655200
$859$	−35.0656	−1.19642	−0.598211	−	0.801339i	$-0.704122\pi$
$859$	−35.0656	−1.19642	−0.598211	+	0.801339i	$0.704122\pi$
$860$	0	0
$861$	−9.16460	−0.312329
$862$	−77.7613	−2.64856
$863$	−42.9879	−1.46333	−0.731663	−	0.681666i	$-0.761256\pi$
$863$	−42.9879	−1.46333	−0.731663	+	0.681666i	$0.761256\pi$
$864$	4.76167	0.161995
$865$	0	0
$866$	57.8945	1.96734
$867$	−1.00000	−0.0339618
$868$	−1.19010	−0.0403948
$869$	−34.9915	−1.18701
$870$	0	0
$871$	−0.284998	−0.00965679
$872$	74.4937	2.52267
$873$	5.84462	0.197810
$874$	−44.3836	−1.50130
$875$	0	0
$876$	57.2056	1.93280
$877$	3.94069	0.133068	0.0665338	−	0.997784i	$-0.478806\pi$
$877$	3.94069	0.133068	0.0665338	+	0.997784i	$0.478806\pi$
$878$	9.10233	0.307189
$879$	−27.8572	−0.939600
$880$	0	0
$881$	−25.2993	−0.852355	−0.426177	−	0.904640i	$-0.640140\pi$
$881$	−25.2993	−0.852355	−0.426177	+	0.904640i	$0.640140\pi$
$882$	−2.53468	−0.0853470
$883$	−50.1801	−1.68869	−0.844347	−	0.535797i	$-0.820011\pi$
$883$	−50.1801	−1.68869	−0.844347	+	0.535797i	$0.820011\pi$
$884$	−12.5211	−0.421131
$885$	0	0
$886$	28.0392	0.941996
$887$	−46.5689	−1.56363	−0.781815	−	0.623510i	$-0.785706\pi$
$887$	−46.5689	−1.56363	−0.781815	+	0.623510i	$0.785706\pi$
$888$	−5.97581	−0.200535
$889$	−18.9227	−0.634648
$890$	0	0
$891$	2.67562	0.0896365
$892$	−54.4427	−1.82288
$893$	82.8953	2.77399
$894$	14.3190	0.478897
$895$	0	0
$896$	−13.0371	−0.435538
$897$	8.02656	0.267999
$898$	−79.9609	−2.66833
$899$	−0.968205	−0.0322915
$900$	0	0
$901$	−10.3318	−0.344203
$902$	62.1527	2.06946
$903$	−4.71924	−0.157046
$904$	−37.6982	−1.25382
$905$	0	0
$906$	−2.48232	−0.0824695
$907$	5.67017	0.188275	0.0941375	−	0.995559i	$-0.469991\pi$
$907$	5.67017	0.188275	0.0941375	+	0.995559i	$0.469991\pi$
$908$	47.6935	1.58276
$909$	3.76952	0.125027
$910$	0	0
$911$	14.3073	0.474022	0.237011	−	0.971507i	$-0.423832\pi$
$911$	14.3073	0.474022	0.237011	+	0.971507i	$0.423832\pi$
$912$	−41.5349	−1.37536
$913$	−22.0050	−0.728260
$914$	44.9473	1.48672
$915$	0	0
$916$	−74.6874	−2.46774
$917$	8.60741	0.284242
$918$	2.53468	0.0836568
$919$	7.39494	0.243936	0.121968	−	0.992534i	$-0.461079\pi$
$919$	7.39494	0.243936	0.121968	+	0.992534i	$0.461079\pi$
$920$	0	0
$921$	14.2241	0.468701
$922$	107.305	3.53390
$923$	−39.5067	−1.30038
$924$	11.8385	0.389458
$925$	0	0
$926$	−33.3295	−1.09528
$927$	15.3905	0.505492
$928$	17.1401	0.562652
$929$	−53.4925	−1.75503	−0.877516	−	0.479547i	$-0.840801\pi$
$929$	−53.4925	−1.75503	−0.877516	+	0.479547i	$0.840801\pi$
$930$	0	0
$931$	6.17364	0.202333
$932$	−63.8369	−2.09105
$933$	18.4183	0.602987
$934$	−59.3890	−1.94327
$935$	0	0
$936$	17.3912	0.568451
$937$	−15.9601	−0.521394	−0.260697	−	0.965421i	$-0.583952\pi$
$937$	−15.9601	−0.521394	−0.260697	+	0.965421i	$0.583952\pi$
$938$	0.255266	0.00833474
$939$	−9.24130	−0.301579
$940$	0	0
$941$	−29.6449	−0.966396	−0.483198	−	0.875511i	$-0.660525\pi$
$941$	−29.6449	−0.966396	−0.483198	+	0.875511i	$0.660525\pi$
$942$	34.3068	1.11778
$943$	−25.9939	−0.846479
$944$	52.6360	1.71316
$945$	0	0
$946$	32.0050	1.04057
$947$	34.8186	1.13145	0.565727	−	0.824593i	$-0.308596\pi$
$947$	34.8186	1.13145	0.565727	+	0.824593i	$0.308596\pi$
$948$	57.8644	1.87935
$949$	36.5879	1.18769
$950$	0	0
$951$	−10.1457	−0.328997
$952$	6.14554	0.199178
$953$	−44.3859	−1.43780	−0.718901	−	0.695113i	$-0.755354\pi$
$953$	−44.3859	−1.43780	−0.718901	+	0.695113i	$0.755354\pi$
$954$	26.1878	0.847863
$955$	0	0
$956$	30.1407	0.974820
$957$	9.63116	0.311331
$958$	86.7189	2.80176
$959$	9.20549	0.297261
$960$	0	0
$961$	−30.9277	−0.997666
$962$	−6.97478	−0.224876
$963$	−10.4289	−0.336065
$964$	3.18565	0.102603
$965$	0	0
$966$	−7.18921	−0.231309
$967$	13.5056	0.434312	0.217156	−	0.976137i	$-0.430322\pi$
$967$	13.5056	0.434312	0.217156	+	0.976137i	$0.430322\pi$
$968$	23.6055	0.758708
$969$	−6.17364	−0.198326
$970$	0	0
$971$	51.2881	1.64591	0.822956	−	0.568105i	$-0.192323\pi$
$971$	51.2881	1.64591	0.822956	+	0.568105i	$0.192323\pi$
$972$	−4.42458	−0.141919
$973$	16.3493	0.524133
$974$	−58.5260	−1.87530
$975$	0	0
$976$	−82.1437	−2.62936
$977$	−54.6359	−1.74796	−0.873979	−	0.485964i	$-0.838469\pi$
$977$	−54.6359	−1.74796	−0.873979	+	0.485964i	$0.838469\pi$
$978$	−4.30400	−0.137627
$979$	25.9156	0.828265
$980$	0	0
$981$	−12.1216	−0.387013
$982$	34.9400	1.11498
$983$	21.4549	0.684305	0.342152	−	0.939645i	$-0.388844\pi$
$983$	21.4549	0.684305	0.342152	+	0.939645i	$0.388844\pi$
$984$	−56.3214	−1.79546
$985$	0	0
$986$	9.12383	0.290562
$987$	13.4273	0.427396
$988$	−77.3009	−2.45927
$989$	−13.3854	−0.425630
$990$	0	0
$991$	−44.8117	−1.42349	−0.711745	−	0.702438i	$-0.752095\pi$
$991$	−44.8117	−1.42349	−0.711745	+	0.702438i	$0.752095\pi$
$992$	−1.28077	−0.0406645
$993$	−8.09315	−0.256828
$994$	35.3852	1.12235
$995$	0	0
$996$	36.3890	1.15303
$997$	−45.3790	−1.43717	−0.718584	−	0.695440i	$-0.755209\pi$
$997$	−45.3790	−1.43717	−0.718584	+	0.695440i	$0.755209\pi$
$998$	90.3845	2.86107
$999$	0.972382	0.0307648

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8925.2.a.cu.1.2		14
5.2	odd	4		1785.2.g.g.1429.2	✓	28
5.3	odd	4		1785.2.g.g.1429.27	yes	28
5.4	even	2		8925.2.a.cx.1.13		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1785.2.g.g.1429.2	✓	28	5.2	odd	4
1785.2.g.g.1429.27	yes	28	5.3	odd	4
8925.2.a.cu.1.2		14	1.1	even	1	trivial
8925.2.a.cx.1.13		14	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8925 = 3 \cdot 5^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8925.a (trivial)

\(f(q)\)	\(=\)	\(q-2.53468 q^{2} -1.00000 q^{3} +4.42458 q^{4} +2.53468 q^{6} -1.00000 q^{7} -6.14554 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.53468 q^{2} -1.00000 q^{3} +4.42458 q^{4} +2.53468 q^{6} -1.00000 q^{7} -6.14554 q^{8} +1.00000 q^{9} +2.67562 q^{11} -4.42458 q^{12} -2.82990 q^{13} +2.53468 q^{14} +6.72778 q^{16} +1.00000 q^{17} -2.53468 q^{18} +6.17364 q^{19} +1.00000 q^{21} -6.78182 q^{22} +2.83634 q^{23} +6.14554 q^{24} +7.17288 q^{26} -1.00000 q^{27} -4.42458 q^{28} -3.59961 q^{29} +0.268975 q^{31} -4.76167 q^{32} -2.67562 q^{33} -2.53468 q^{34} +4.42458 q^{36} -0.972382 q^{37} -15.6482 q^{38} +2.82990 q^{39} -9.16460 q^{41} -2.53468 q^{42} -4.71924 q^{43} +11.8385 q^{44} -7.18921 q^{46} +13.4273 q^{47} -6.72778 q^{48} +1.00000 q^{49} -1.00000 q^{51} -12.5211 q^{52} -10.3318 q^{53} +2.53468 q^{54} +6.14554 q^{56} -6.17364 q^{57} +9.12383 q^{58} +7.82368 q^{59} -12.2096 q^{61} -0.681766 q^{62} -1.00000 q^{63} -1.38627 q^{64} +6.78182 q^{66} +0.100710 q^{67} +4.42458 q^{68} -2.83634 q^{69} +13.9605 q^{71} -6.14554 q^{72} -12.9290 q^{73} +2.46467 q^{74} +27.3158 q^{76} -2.67562 q^{77} -7.17288 q^{78} -13.0779 q^{79} +1.00000 q^{81} +23.2293 q^{82} -8.22428 q^{83} +4.42458 q^{84} +11.9617 q^{86} +3.59961 q^{87} -16.4431 q^{88} +9.68583 q^{89} +2.82990 q^{91} +12.5496 q^{92} -0.268975 q^{93} -34.0339 q^{94} +4.76167 q^{96} +5.84462 q^{97} -2.53468 q^{98} +2.67562 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 3 q^{2} - 14 q^{3} + 17 q^{4} + 3 q^{6} - 14 q^{7} - 15 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - 3 * q^2 - 14 * q^3 + 17 * q^4 + 3 * q^6 - 14 * q^7 - 15 * q^8 + 14 * q^9	\( 14 q - 3 q^{2} - 14 q^{3} + 17 q^{4} + 3 q^{6} - 14 q^{7} - 15 q^{8} + 14 q^{9} + 4 q^{11} - 17 q^{12} + q^{13} + 3 q^{14} + 19 q^{16} + 14 q^{17} - 3 q^{18} - 6 q^{19} + 14 q^{21} - 12 q^{22} - 7 q^{23} + 15 q^{24} - 2 q^{26} - 14 q^{27} - 17 q^{28} + 20 q^{29} - 7 q^{31} - 33 q^{32} - 4 q^{33} - 3 q^{34} + 17 q^{36} - 9 q^{37} - 18 q^{38} - q^{39} + 25 q^{41} - 3 q^{42} - 28 q^{43} + 24 q^{44} - 10 q^{46} - 29 q^{47} - 19 q^{48} + 14 q^{49} - 14 q^{51} - 4 q^{52} - 26 q^{53} + 3 q^{54} + 15 q^{56} + 6 q^{57} - 2 q^{58} + 14 q^{59} - 9 q^{61} - 28 q^{62} - 14 q^{63} + 27 q^{64} + 12 q^{66} - 32 q^{67} + 17 q^{68} + 7 q^{69} + 2 q^{71} - 15 q^{72} - 18 q^{73} + 64 q^{74} - 42 q^{76} - 4 q^{77} + 2 q^{78} - 4 q^{79} + 14 q^{81} - 42 q^{82} - 51 q^{83} + 17 q^{84} + 44 q^{86} - 20 q^{87} - 32 q^{88} + 38 q^{89} - q^{91} + 16 q^{92} + 7 q^{93} + 8 q^{94} + 33 q^{96} - 14 q^{97} - 3 q^{98} + 4 q^{99}+O(q^{100}) \) 14 * q - 3 * q^2 - 14 * q^3 + 17 * q^4 + 3 * q^6 - 14 * q^7 - 15 * q^8 + 14 * q^9 + 4 * q^11 - 17 * q^12 + q^13 + 3 * q^14 + 19 * q^16 + 14 * q^17 - 3 * q^18 - 6 * q^19 + 14 * q^21 - 12 * q^22 - 7 * q^23 + 15 * q^24 - 2 * q^26 - 14 * q^27 - 17 * q^28 + 20 * q^29 - 7 * q^31 - 33 * q^32 - 4 * q^33 - 3 * q^34 + 17 * q^36 - 9 * q^37 - 18 * q^38 - q^39 + 25 * q^41 - 3 * q^42 - 28 * q^43 + 24 * q^44 - 10 * q^46 - 29 * q^47 - 19 * q^48 + 14 * q^49 - 14 * q^51 - 4 * q^52 - 26 * q^53 + 3 * q^54 + 15 * q^56 + 6 * q^57 - 2 * q^58 + 14 * q^59 - 9 * q^61 - 28 * q^62 - 14 * q^63 + 27 * q^64 + 12 * q^66 - 32 * q^67 + 17 * q^68 + 7 * q^69 + 2 * q^71 - 15 * q^72 - 18 * q^73 + 64 * q^74 - 42 * q^76 - 4 * q^77 + 2 * q^78 - 4 * q^79 + 14 * q^81 - 42 * q^82 - 51 * q^83 + 17 * q^84 + 44 * q^86 - 20 * q^87 - 32 * q^88 + 38 * q^89 - q^91 + 16 * q^92 + 7 * q^93 + 8 * q^94 + 33 * q^96 - 14 * q^97 - 3 * q^98 + 4 * q^99

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