LMFDB - Embedded newform 1925.2.a.x.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1925,2,Mod(1,1925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1925, 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("1925.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1925 = 5^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1925.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:	$15.3712023891$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.11348.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 5x^{2} + x + 2 $ x^4 - x^3 - 5*x^2 + x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 385)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.64119$ of defining polynomial
Character	$\chi$	$=$	1925.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.88395 q^{2} -2.33468 q^{3} +1.54927 q^{4} +4.39842 q^{6} +1.00000 q^{7} +0.849150 q^{8} +2.45073 q^{9} +O(q^{10})$	\(q-1.88395 q^{2} -2.33468 q^{3} +1.54927 q^{4} +4.39842 q^{6} +1.00000 q^{7} +0.849150 q^{8} +2.45073 q^{9} -1.00000 q^{11} -3.61705 q^{12} +4.94769 q^{13} -1.88395 q^{14} -4.69830 q^{16} -0.334680 q^{17} -4.61705 q^{18} +3.51447 q^{19} -2.33468 q^{21} +1.88395 q^{22} +4.50100 q^{23} -1.98249 q^{24} -9.32121 q^{26} +1.28237 q^{27} +1.54927 q^{28} +8.56475 q^{29} +6.65185 q^{31} +7.15307 q^{32} +2.33468 q^{33} +0.630520 q^{34} +3.79684 q^{36} -4.73310 q^{37} -6.62109 q^{38} -11.5513 q^{39} -7.55331 q^{41} +4.39842 q^{42} +1.93626 q^{43} -1.54927 q^{44} -8.47967 q^{46} -8.75061 q^{47} +10.9690 q^{48} +1.00000 q^{49} +0.781369 q^{51} +7.66532 q^{52} -8.86059 q^{53} -2.41593 q^{54} +0.849150 q^{56} -8.20516 q^{57} -16.1356 q^{58} -8.11806 q^{59} -6.39842 q^{61} -12.5318 q^{62} +2.45073 q^{63} -4.07943 q^{64} -4.39842 q^{66} -7.36745 q^{67} -0.518509 q^{68} -10.5084 q^{69} +8.00000 q^{71} +2.08104 q^{72} +14.8994 q^{73} +8.91693 q^{74} +5.44487 q^{76} -1.00000 q^{77} +21.7620 q^{78} +11.3461 q^{79} -10.3461 q^{81} +14.2301 q^{82} +8.18383 q^{83} -3.61705 q^{84} -3.64781 q^{86} -19.9959 q^{87} -0.849150 q^{88} -7.28237 q^{89} +4.94769 q^{91} +6.97328 q^{92} -15.5299 q^{93} +16.4857 q^{94} -16.7001 q^{96} -13.8471 q^{97} -1.88395 q^{98} -2.45073 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{3} + 8 q^{4} + 4 q^{6} + 4 q^{7} - 12 q^{8} + 8 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^3 + 8 * q^4 + 4 * q^6 + 4 * q^7 - 12 * q^8 + 8 * q^9	$ 4 q - 2 q^{2} - 2 q^{3} + 8 q^{4} + 4 q^{6} + 4 q^{7} - 12 q^{8} + 8 q^{9} - 4 q^{11} + 12 q^{12} + 8 q^{13} - 2 q^{14} + 12 q^{16} + 6 q^{17} + 8 q^{18} + 6 q^{19} - 2 q^{21} + 2 q^{22} - 14 q^{23} - 6 q^{24} - 6 q^{26} - 14 q^{27} + 8 q^{28} - 4 q^{29} + 10 q^{31} - 26 q^{32} + 2 q^{33} - 12 q^{36} + 2 q^{37} + 22 q^{38} + 16 q^{39} - 10 q^{41} + 4 q^{42} + 14 q^{43} - 8 q^{44} - 16 q^{46} - 16 q^{47} + 18 q^{48} + 4 q^{49} + 16 q^{51} + 38 q^{52} - 2 q^{53} + 2 q^{54} - 12 q^{56} + 4 q^{57} - 8 q^{58} + 26 q^{59} - 12 q^{61} - 50 q^{62} + 8 q^{63} + 36 q^{64} - 4 q^{66} + 10 q^{67} + 28 q^{68} - 14 q^{69} + 32 q^{71} + 10 q^{72} + 14 q^{73} - 8 q^{74} - 6 q^{76} - 4 q^{77} + 50 q^{78} + 20 q^{79} - 16 q^{81} + 26 q^{82} + 10 q^{83} + 12 q^{84} - 20 q^{86} + 4 q^{87} + 12 q^{88} - 10 q^{89} + 8 q^{91} - 26 q^{92} - 14 q^{93} - 38 q^{94} - 84 q^{96} + 2 q^{97} - 2 q^{98} - 8 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^3 + 8 * q^4 + 4 * q^6 + 4 * q^7 - 12 * q^8 + 8 * q^9 - 4 * q^11 + 12 * q^12 + 8 * q^13 - 2 * q^14 + 12 * q^16 + 6 * q^17 + 8 * q^18 + 6 * q^19 - 2 * q^21 + 2 * q^22 - 14 * q^23 - 6 * q^24 - 6 * q^26 - 14 * q^27 + 8 * q^28 - 4 * q^29 + 10 * q^31 - 26 * q^32 + 2 * q^33 - 12 * q^36 + 2 * q^37 + 22 * q^38 + 16 * q^39 - 10 * q^41 + 4 * q^42 + 14 * q^43 - 8 * q^44 - 16 * q^46 - 16 * q^47 + 18 * q^48 + 4 * q^49 + 16 * q^51 + 38 * q^52 - 2 * q^53 + 2 * q^54 - 12 * q^56 + 4 * q^57 - 8 * q^58 + 26 * q^59 - 12 * q^61 - 50 * q^62 + 8 * q^63 + 36 * q^64 - 4 * q^66 + 10 * q^67 + 28 * q^68 - 14 * q^69 + 32 * q^71 + 10 * q^72 + 14 * q^73 - 8 * q^74 - 6 * q^76 - 4 * q^77 + 50 * q^78 + 20 * q^79 - 16 * q^81 + 26 * q^82 + 10 * q^83 + 12 * q^84 - 20 * q^86 + 4 * q^87 + 12 * q^88 - 10 * q^89 + 8 * q^91 - 26 * q^92 - 14 * q^93 - 38 * q^94 - 84 * q^96 + 2 * q^97 - 2 * q^98 - 8 * 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 $

$2$	−1.88395	−1.33215	−0.666077	−	0.745883i	$-0.732028\pi$
$2$	−1.88395	−1.33215	−0.666077	+	0.745883i	$0.732028\pi$
$3$	−2.33468	−1.34793	−0.673964	−	0.738764i	$-0.735410\pi$
$3$	−2.33468	−1.34793	−0.673964	+	0.738764i	$0.735410\pi$
$4$	1.54927	0.774636
$5$	0	0
$5$	0	0
$6$	4.39842	1.79565
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	0.849150	0.300220
$9$	2.45073	0.816909
$10$	0	0
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−3.61705	−1.04415
$13$	4.94769	1.37224	0.686122	−	0.727487i	$-0.259312\pi$
$13$	4.94769	1.37224	0.686122	+	0.727487i	$0.259312\pi$
$14$	−1.88395	−0.503507
$15$	0	0
$16$	−4.69830	−1.17458
$17$	−0.334680	−0.0811717	−0.0405859	−	0.999176i	$-0.512922\pi$
$17$	−0.334680	−0.0811717	−0.0405859	+	0.999176i	$0.512922\pi$
$18$	−4.61705	−1.08825
$19$	3.51447	0.806275	0.403137	−	0.915139i	$-0.367920\pi$
$19$	3.51447	0.806275	0.403137	+	0.915139i	$0.367920\pi$
$20$	0	0
$21$	−2.33468	−0.509469
$22$	1.88395	0.401660
$23$	4.50100	0.938524	0.469262	−	0.883059i	$-0.344520\pi$
$23$	4.50100	0.938524	0.469262	+	0.883059i	$0.344520\pi$
$24$	−1.98249	−0.404675
$25$	0	0
$26$	−9.32121	−1.82804
$27$	1.28237	0.246793
$28$	1.54927	0.292785
$29$	8.56475	1.59043	0.795217	−	0.606325i	$-0.207357\pi$
$29$	8.56475	1.59043	0.795217	+	0.606325i	$0.207357\pi$
$30$	0	0
$31$	6.65185	1.19471	0.597354	−	0.801978i	$-0.296219\pi$
$31$	6.65185	1.19471	0.597354	+	0.801978i	$0.296219\pi$
$32$	7.15307	1.26450
$33$	2.33468	0.406416
$34$	0.630520	0.108133
$35$	0	0
$36$	3.79684	0.632807
$37$	−4.73310	−0.778117	−0.389059	−	0.921213i	$-0.627200\pi$
$37$	−4.73310	−0.778117	−0.389059	+	0.921213i	$0.627200\pi$
$38$	−6.62109	−1.07408
$39$	−11.5513	−1.84968
$40$	0	0
$41$	−7.55331	−1.17963	−0.589814	−	0.807539i	$-0.700799\pi$
$41$	−7.55331	−1.17963	−0.589814	+	0.807539i	$0.700799\pi$
$42$	4.39842	0.678691
$43$	1.93626	0.295277	0.147638	−	0.989041i	$-0.452833\pi$
$43$	1.93626	0.295277	0.147638	+	0.989041i	$0.452833\pi$
$44$	−1.54927	−0.233561
$45$	0	0
$46$	−8.47967	−1.25026
$47$	−8.75061	−1.27641	−0.638204	−	0.769868i	$-0.720322\pi$
$47$	−8.75061	−1.27641	−0.638204	+	0.769868i	$0.720322\pi$
$48$	10.9690	1.58324
$49$	1.00000	0.142857
$50$	0	0
$51$	0.781369	0.109414
$52$	7.66532	1.06299
$53$	−8.86059	−1.21710	−0.608548	−	0.793517i	$-0.708248\pi$
$53$	−8.86059	−1.21710	−0.608548	+	0.793517i	$0.708248\pi$
$54$	−2.41593	−0.328766
$55$	0	0
$56$	0.849150	0.113472
$57$	−8.20516	−1.08680
$58$	−16.1356	−2.11870
$59$	−8.11806	−1.05688	−0.528440	−	0.848970i	$-0.677223\pi$
$59$	−8.11806	−1.05688	−0.528440	+	0.848970i	$0.677223\pi$
$60$	0	0
$61$	−6.39842	−0.819234	−0.409617	−	0.912258i	$-0.634338\pi$
$61$	−6.39842	−0.819234	−0.409617	+	0.912258i	$0.634338\pi$
$62$	−12.5318	−1.59154
$63$	2.45073	0.308763
$64$	−4.07943	−0.509929
$65$	0	0
$66$	−4.39842	−0.541408
$67$	−7.36745	−0.900077	−0.450039	−	0.893009i	$-0.648590\pi$
$67$	−7.36745	−0.900077	−0.450039	+	0.893009i	$0.648590\pi$
$68$	−0.518509	−0.0628785
$69$	−10.5084	−1.26506
$70$	0	0
$71$	8.00000	0.949425	0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000	0.949425	0.474713	+	0.880141i	$0.342552\pi$
$72$	2.08104	0.245253
$73$	14.8994	1.74385	0.871923	−	0.489643i	$-0.162873\pi$
$73$	14.8994	1.74385	0.871923	+	0.489643i	$0.162873\pi$
$74$	8.91693	1.03657
$75$	0	0
$76$	5.44487	0.624569
$77$	−1.00000	−0.113961
$78$	21.7620	2.46407
$79$	11.3461	1.27654	0.638269	−	0.769814i	$-0.279651\pi$
$79$	11.3461	1.27654	0.638269	+	0.769814i	$0.279651\pi$
$80$	0	0
$81$	−10.3461	−1.14957
$82$	14.2301	1.57145
$83$	8.18383	0.898292	0.449146	−	0.893458i	$-0.351728\pi$
$83$	8.18383	0.898292	0.449146	+	0.893458i	$0.351728\pi$
$84$	−3.61705	−0.394653
$85$	0	0
$86$	−3.64781	−0.393354
$87$	−19.9959	−2.14379
$88$	−0.849150	−0.0905197
$89$	−7.28237	−0.771930	−0.385965	−	0.922513i	$-0.626131\pi$
$89$	−7.28237	−0.771930	−0.385965	+	0.922513i	$0.626131\pi$
$90$	0	0
$91$	4.94769	0.518659
$92$	6.97328	0.727014
$93$	−15.5299	−1.61038
$94$	16.4857	1.70037
$95$	0	0
$96$	−16.7001	−1.70445
$97$	−13.8471	−1.40596	−0.702981	−	0.711209i	$-0.748148\pi$
$97$	−13.8471	−1.40596	−0.702981	+	0.711209i	$0.748148\pi$
$98$	−1.88395	−0.190308
$99$	−2.45073	−0.246307
$100$	0	0
$101$	8.18766	0.814702	0.407351	−	0.913272i	$-0.366453\pi$
$101$	8.18766	0.814702	0.407351	+	0.913272i	$0.366453\pi$
$102$	−1.47206	−0.145756
$103$	14.5398	1.43265	0.716327	−	0.697765i	$-0.245822\pi$
$103$	14.5398	1.43265	0.716327	+	0.697765i	$0.245822\pi$
$104$	4.20134	0.411975
$105$	0	0
$106$	16.6929	1.62136
$107$	10.4373	1.00901	0.504504	−	0.863409i	$-0.331675\pi$
$107$	10.4373	1.00901	0.504504	+	0.863409i	$0.331675\pi$
$108$	1.98674	0.191175
$109$	−6.66936	−0.638809	−0.319404	−	0.947619i	$-0.603483\pi$
$109$	−6.66936	−0.638809	−0.319404	+	0.947619i	$0.603483\pi$
$110$	0	0
$111$	11.0503	1.04885
$112$	−4.69830	−0.443948
$113$	−5.33064	−0.501465	−0.250732	−	0.968056i	$-0.580671\pi$
$113$	−5.33064	−0.501465	−0.250732	+	0.968056i	$0.580671\pi$
$114$	15.4581	1.44779
$115$	0	0
$116$	13.2691	1.23201
$117$	12.1255	1.12100
$118$	15.2940	1.40793
$119$	−0.334680	−0.0306800
$120$	0	0
$121$	1.00000	0.0909091
$122$	12.0543	1.09135
$123$	17.6346	1.59005
$124$	10.3055	0.925464
$125$	0	0
$126$	−4.61705	−0.411320
$127$	1.76790	0.156876	0.0784380	−	0.996919i	$-0.475007\pi$
$127$	1.76790	0.156876	0.0784380	+	0.996919i	$0.475007\pi$
$128$	−6.62069	−0.585192
$129$	−4.52054	−0.398011
$130$	0	0
$131$	−13.5937	−1.18769	−0.593843	−	0.804581i	$-0.702390\pi$
$131$	−13.5937	−1.18769	−0.593843	+	0.804581i	$0.702390\pi$
$132$	3.61705	0.314824
$133$	3.51447	0.304743
$134$	13.8799	1.19904
$135$	0	0
$136$	−0.284193	−0.0243694
$137$	0.605617	0.0517413	0.0258707	−	0.999665i	$-0.491764\pi$
$137$	0.605617	0.0517413	0.0258707	+	0.999665i	$0.491764\pi$
$138$	19.7973	1.68526
$139$	13.4312	1.13922	0.569609	−	0.821916i	$-0.307094\pi$
$139$	13.4312	1.13922	0.569609	+	0.821916i	$0.307094\pi$
$140$	0	0
$141$	20.4299	1.72050
$142$	−15.0716	−1.26478
$143$	−4.94769	−0.413747
$144$	−11.5143	−0.959522
$145$	0	0
$146$	−28.0698	−2.32307
$147$	−2.33468	−0.192561
$148$	−7.33286	−0.602757
$149$	2.03501	0.166715	0.0833573	−	0.996520i	$-0.473436\pi$
$149$	2.03501	0.166715	0.0833573	+	0.996520i	$0.473436\pi$
$150$	0	0
$151$	−10.2126	−0.831086	−0.415543	−	0.909573i	$-0.636408\pi$
$151$	−10.2126	−0.831086	−0.415543	+	0.909573i	$0.636408\pi$
$152$	2.98431	0.242060
$153$	−0.820209	−0.0663099
$154$	1.88395	0.151813
$155$	0	0
$156$	−17.8961	−1.43283
$157$	17.2905	1.37993	0.689964	−	0.723844i	$-0.257626\pi$
$157$	17.2905	1.37993	0.689964	+	0.723844i	$0.257626\pi$
$158$	−21.3755	−1.70055
$159$	20.6866	1.64056
$160$	0	0
$161$	4.50100	0.354729
$162$	19.4916	1.53140
$163$	7.06981	0.553750	0.276875	−	0.960906i	$-0.410701\pi$
$163$	7.06981	0.553750	0.276875	+	0.960906i	$0.410701\pi$
$164$	−11.7021	−0.913783
$165$	0	0
$166$	−15.4179	−1.19666
$167$	−4.35804	−0.337236	−0.168618	−	0.985682i	$-0.553930\pi$
$167$	−4.35804	−0.337236	−0.168618	+	0.985682i	$0.553930\pi$
$168$	−1.98249	−0.152953
$169$	11.4797	0.883052
$170$	0	0
$171$	8.61301	0.658654
$172$	2.99979	0.228732
$173$	−3.90550	−0.296929	−0.148465	−	0.988918i	$-0.547433\pi$
$173$	−3.90550	−0.296929	−0.148465	+	0.988918i	$0.547433\pi$
$174$	37.6714	2.85586
$175$	0	0
$176$	4.69830	0.354148
$177$	18.9531	1.42460
$178$	13.7196	1.02833
$179$	8.24018	0.615900	0.307950	−	0.951403i	$-0.400357\pi$
$179$	8.24018	0.615900	0.307950	+	0.951403i	$0.400357\pi$
$180$	0	0
$181$	7.71156	0.573196	0.286598	−	0.958051i	$-0.407476\pi$
$181$	7.71156	0.573196	0.286598	+	0.958051i	$0.407476\pi$
$182$	−9.32121	−0.690934
$183$	14.9383	1.10427
$184$	3.82203	0.281764
$185$	0	0
$186$	29.2577	2.14528
$187$	0.334680	0.0244742
$188$	−13.5571	−0.988751
$189$	1.28237	0.0932789
$190$	0	0
$191$	16.2052	1.17256	0.586282	−	0.810107i	$-0.300591\pi$
$191$	16.2052	1.17256	0.586282	+	0.810107i	$0.300591\pi$
$192$	9.52416	0.687347
$193$	22.8337	1.64360	0.821801	−	0.569774i	$-0.192969\pi$
$193$	22.8337	1.64360	0.821801	+	0.569774i	$0.192969\pi$
$194$	26.0873	1.87296
$195$	0	0
$196$	1.54927	0.110662
$197$	−1.06981	−0.0762210	−0.0381105	−	0.999274i	$-0.512134\pi$
$197$	−1.06981	−0.0762210	−0.0381105	+	0.999274i	$0.512134\pi$
$198$	4.61705	0.328120
$199$	−5.73714	−0.406695	−0.203348	−	0.979107i	$-0.565182\pi$
$199$	−5.73714	−0.406695	−0.203348	+	0.979107i	$0.565182\pi$
$200$	0	0
$201$	17.2006	1.21324
$202$	−15.4251	−1.08531
$203$	8.56475	0.601127
$204$	1.21055	0.0847557
$205$	0	0
$206$	−27.3924	−1.90852
$207$	11.0307	0.766689
$208$	−23.2458	−1.61180
$209$	−3.51447	−0.243101
$210$	0	0
$211$	23.1066	1.59073	0.795363	−	0.606134i	$-0.207280\pi$
$211$	23.1066	1.59073	0.795363	+	0.606134i	$0.207280\pi$
$212$	−13.7275	−0.942805
$213$	−18.6774	−1.27976
$214$	−19.6633	−1.34415
$215$	0	0
$216$	1.08893	0.0740921
$217$	6.65185	0.451557
$218$	12.5647	0.850992
$219$	−34.7854	−2.35058
$220$	0	0
$221$	−1.65589	−0.111387
$222$	−20.8182	−1.39722
$223$	−13.4763	−0.902441	−0.451220	−	0.892413i	$-0.649011\pi$
$223$	−13.4763	−0.902441	−0.451220	+	0.892413i	$0.649011\pi$
$224$	7.15307	0.477934
$225$	0	0
$226$	10.0427	0.668028
$227$	−10.1006	−0.670397	−0.335199	−	0.942148i	$-0.608803\pi$
$227$	−10.1006	−0.670397	−0.335199	+	0.942148i	$0.608803\pi$
$228$	−12.7120	−0.841874
$229$	18.4453	1.21890	0.609451	−	0.792824i	$-0.291390\pi$
$229$	18.4453	1.21890	0.609451	+	0.792824i	$0.291390\pi$
$230$	0	0
$231$	2.33468	0.153611
$232$	7.27276	0.477480
$233$	−25.0657	−1.64211	−0.821056	−	0.570848i	$-0.806615\pi$
$233$	−25.0657	−1.64211	−0.821056	+	0.570848i	$0.806615\pi$
$234$	−22.8438	−1.49334
$235$	0	0
$236$	−12.5771	−0.818698
$237$	−26.4895	−1.72068
$238$	0.630520	0.0408705
$239$	26.4332	1.70982	0.854911	−	0.518775i	$-0.173612\pi$
$239$	26.4332	1.70982	0.854911	+	0.518775i	$0.173612\pi$
$240$	0	0
$241$	−23.2166	−1.49551	−0.747756	−	0.663973i	$-0.768869\pi$
$241$	−23.2166	−1.49551	−0.747756	+	0.663973i	$0.768869\pi$
$242$	−1.88395	−0.121105
$243$	20.3077	1.30274
$244$	−9.91289	−0.634608
$245$	0	0
$246$	−33.2226	−2.11820
$247$	17.3885	1.10641
$248$	5.64842	0.358675
$249$	−19.1066	−1.21083
$250$	0	0
$251$	10.3852	0.655506	0.327753	−	0.944763i	$-0.393709\pi$
$251$	10.3852	0.655506	0.327753	+	0.944763i	$0.393709\pi$
$252$	3.79684	0.239179
$253$	−4.50100	−0.282976
$254$	−3.33064	−0.208983
$255$	0	0
$256$	20.6319	1.28949
$257$	2.94972	0.183999	0.0919994	−	0.995759i	$-0.470674\pi$
$257$	2.94972	0.183999	0.0919994	+	0.995759i	$0.470674\pi$
$258$	8.51648	0.530213
$259$	−4.73310	−0.294101
$260$	0	0
$261$	20.9899	1.29924
$262$	25.6098	1.58218
$263$	−0.429184	−0.0264646	−0.0132323	−	0.999912i	$-0.504212\pi$
$263$	−0.429184	−0.0264646	−0.0132323	+	0.999912i	$0.504212\pi$
$264$	1.98249	0.122014
$265$	0	0
$266$	−6.62109	−0.405965
$267$	17.0020	1.04051
$268$	−11.4142	−0.697232
$269$	−13.7546	−0.838636	−0.419318	−	0.907840i	$-0.637731\pi$
$269$	−13.7546	−0.838636	−0.419318	+	0.907840i	$0.637731\pi$
$270$	0	0
$271$	−2.40225	−0.145926	−0.0729631	−	0.997335i	$-0.523246\pi$
$271$	−2.40225	−0.145926	−0.0729631	+	0.997335i	$0.523246\pi$
$272$	1.57243	0.0953423
$273$	−11.5513	−0.699115
$274$	−1.14095	−0.0689274
$275$	0	0
$276$	−16.2804	−0.979963
$277$	31.8397	1.91306	0.956532	−	0.291628i	$-0.0941970\pi$
$277$	31.8397	1.91306	0.956532	+	0.291628i	$0.0941970\pi$
$278$	−25.3037	−1.51762
$279$	16.3019	0.975968
$280$	0	0
$281$	4.53380	0.270464	0.135232	−	0.990814i	$-0.456822\pi$
$281$	4.53380	0.270464	0.135232	+	0.990814i	$0.456822\pi$
$282$	−38.4889	−2.29198
$283$	−11.7333	−0.697473	−0.348737	−	0.937221i	$-0.613389\pi$
$283$	−11.7333	−0.697473	−0.348737	+	0.937221i	$0.613389\pi$
$284$	12.3942	0.735459
$285$	0	0
$286$	9.32121	0.551175
$287$	−7.55331	−0.445858
$288$	17.5302	1.03298
$289$	−16.8880	−0.993411
$290$	0	0
$291$	32.3286	1.89514
$292$	23.0833	1.35085
$293$	−16.8298	−0.983209	−0.491604	−	0.870819i	$-0.663589\pi$
$293$	−16.8298	−0.983209	−0.491604	+	0.870819i	$0.663589\pi$
$294$	4.39842	0.256521
$295$	0	0
$296$	−4.01911	−0.233606
$297$	−1.28237	−0.0744108
$298$	−3.83386	−0.222090
$299$	22.2696	1.28788
$300$	0	0
$301$	1.93626	0.111604
$302$	19.2400	1.10714
$303$	−19.1156	−1.09816
$304$	−16.5120	−0.947031
$305$	0	0
$306$	1.54523	0.0883351
$307$	−10.5861	−0.604179	−0.302090	−	0.953279i	$-0.597684\pi$
$307$	−10.5861	−0.604179	−0.302090	+	0.953279i	$0.597684\pi$
$308$	−1.54927	−0.0882779
$309$	−33.9459	−1.93111
$310$	0	0
$311$	1.29180	0.0732514	0.0366257	−	0.999329i	$-0.488339\pi$
$311$	1.29180	0.0732514	0.0366257	+	0.999329i	$0.488339\pi$
$312$	−9.80877	−0.555312
$313$	12.6922	0.717407	0.358704	−	0.933451i	$-0.383219\pi$
$313$	12.6922	0.717407	0.358704	+	0.933451i	$0.383219\pi$
$314$	−32.5744	−1.83828
$315$	0	0
$316$	17.5782	0.988852
$317$	29.2300	1.64172	0.820861	−	0.571128i	$-0.193494\pi$
$317$	29.2300	1.64172	0.820861	+	0.571128i	$0.193494\pi$
$318$	−38.9726	−2.18547
$319$	−8.56475	−0.479534
$320$	0	0
$321$	−24.3677	−1.36007
$322$	−8.47967	−0.472554
$323$	−1.17622	−0.0654467
$324$	−16.0289	−0.890497
$325$	0	0
$326$	−13.3192	−0.737681
$327$	15.5708	0.861068
$328$	−6.41390	−0.354148
$329$	−8.75061	−0.482437
$330$	0	0
$331$	23.7292	1.30428	0.652139	−	0.758100i	$-0.273872\pi$
$331$	23.7292	1.30428	0.652139	+	0.758100i	$0.273872\pi$
$332$	12.6790	0.695849
$333$	−11.5995	−0.635651
$334$	8.21034	0.449250
$335$	0	0
$336$	10.9690	0.598409
$337$	16.1414	0.879279	0.439640	−	0.898174i	$-0.355106\pi$
$337$	16.1414	0.879279	0.439640	+	0.898174i	$0.355106\pi$
$338$	−21.6271	−1.17636
$339$	12.4453	0.675938
$340$	0	0
$341$	−6.65185	−0.360218
$342$	−16.2265	−0.877428
$343$	1.00000	0.0539949
$344$	1.64417	0.0886479
$345$	0	0
$346$	7.35776	0.395556
$347$	−10.8956	−0.584906	−0.292453	−	0.956280i	$-0.594472\pi$
$347$	−10.8956	−0.584906	−0.292453	+	0.956280i	$0.594472\pi$
$348$	−30.9791	−1.66066
$349$	−17.2999	−0.926041	−0.463021	−	0.886347i	$-0.653234\pi$
$349$	−17.2999	−0.926041	−0.463021	+	0.886347i	$0.653234\pi$
$350$	0	0
$351$	6.34479	0.338660
$352$	−7.15307	−0.381260
$353$	−22.5378	−1.19957	−0.599783	−	0.800162i	$-0.704747\pi$
$353$	−22.5378	−1.19957	−0.599783	+	0.800162i	$0.704747\pi$
$354$	−35.7066	−1.89779
$355$	0	0
$356$	−11.2824	−0.597965
$357$	0.781369	0.0413545
$358$	−15.5241	−0.820473
$359$	−6.99461	−0.369161	−0.184581	−	0.982817i	$-0.559093\pi$
$359$	−6.99461	−0.369161	−0.184581	+	0.982817i	$0.559093\pi$
$360$	0	0
$361$	−6.64849	−0.349921
$362$	−14.5282	−0.763585
$363$	−2.33468	−0.122539
$364$	7.66532	0.401772
$365$	0	0
$366$	−28.1430	−1.47106
$367$	31.5353	1.64613	0.823065	−	0.567947i	$-0.192262\pi$
$367$	31.5353	1.64613	0.823065	+	0.567947i	$0.192262\pi$
$368$	−21.1471	−1.10237
$369$	−18.5111	−0.963650
$370$	0	0
$371$	−8.86059	−0.460019
$372$	−24.0601	−1.24746
$373$	31.8195	1.64755	0.823776	−	0.566916i	$-0.191864\pi$
$373$	31.8195	1.64755	0.823776	+	0.566916i	$0.191864\pi$
$374$	−0.630520	−0.0326034
$375$	0	0
$376$	−7.43058	−0.383203
$377$	42.3757	2.18246
$378$	−2.41593	−0.124262
$379$	−32.5688	−1.67294	−0.836472	−	0.548009i	$-0.815386\pi$
$379$	−32.5688	−1.67294	−0.836472	+	0.548009i	$0.815386\pi$
$380$	0	0
$381$	−4.12748	−0.211457
$382$	−30.5297	−1.56204
$383$	32.9304	1.68266	0.841332	−	0.540519i	$-0.181772\pi$
$383$	32.9304	1.68266	0.841332	+	0.540519i	$0.181772\pi$
$384$	15.4572	0.788797
$385$	0	0
$386$	−43.0175	−2.18953
$387$	4.74524	0.241214
$388$	−21.4529	−1.08911
$389$	26.1086	1.32376	0.661880	−	0.749610i	$-0.269759\pi$
$389$	26.1086	1.32376	0.661880	+	0.749610i	$0.269759\pi$
$390$	0	0
$391$	−1.50639	−0.0761816
$392$	0.849150	0.0428886
$393$	31.7369	1.60092
$394$	2.01547	0.101538
$395$	0	0
$396$	−3.79684	−0.190799
$397$	−10.6440	−0.534205	−0.267103	−	0.963668i	$-0.586066\pi$
$397$	−10.6440	−0.534205	−0.267103	+	0.963668i	$0.586066\pi$
$398$	10.8085	0.541781
$399$	−8.20516	−0.410772
$400$	0	0
$401$	−36.8359	−1.83950	−0.919748	−	0.392510i	$-0.871607\pi$
$401$	−36.8359	−1.83950	−0.919748	+	0.392510i	$0.871607\pi$
$402$	−32.4051	−1.61622
$403$	32.9113	1.63943
$404$	12.6849	0.631098
$405$	0	0
$406$	−16.1356	−0.800794
$407$	4.73310	0.234611
$408$	0.663500	0.0328482
$409$	−28.5767	−1.41302	−0.706512	−	0.707701i	$-0.749732\pi$
$409$	−28.5767	−1.41302	−0.706512	+	0.707701i	$0.749732\pi$
$410$	0	0
$411$	−1.41392	−0.0697436
$412$	22.5262	1.10978
$413$	−8.11806	−0.399463
$414$	−20.7814	−1.02135
$415$	0	0
$416$	35.3912	1.73520
$417$	−31.3575	−1.53558
$418$	6.62109	0.323848
$419$	−10.3715	−0.506680	−0.253340	−	0.967377i	$-0.581529\pi$
$419$	−10.3715	−0.506680	−0.253340	+	0.967377i	$0.581529\pi$
$420$	0	0
$421$	−6.95152	−0.338796	−0.169398	−	0.985548i	$-0.554182\pi$
$421$	−6.95152	−0.338796	−0.169398	+	0.985548i	$0.554182\pi$
$422$	−43.5317	−2.11909
$423$	−21.4454	−1.04271
$424$	−7.52397	−0.365396
$425$	0	0
$426$	35.1874	1.70483
$427$	−6.39842	−0.309641
$428$	16.1702	0.781614
$429$	11.5513	0.557701
$430$	0	0
$431$	14.5843	0.702500	0.351250	−	0.936282i	$-0.385757\pi$
$431$	14.5843	0.702500	0.351250	+	0.936282i	$0.385757\pi$
$432$	−6.02497	−0.289877
$433$	35.4473	1.70349	0.851745	−	0.523956i	$-0.175544\pi$
$433$	35.4473	1.70349	0.851745	+	0.523956i	$0.175544\pi$
$434$	−12.5318	−0.601544
$435$	0	0
$436$	−10.3326	−0.494844
$437$	15.8186	0.756708
$438$	65.5340	3.13133
$439$	−0.174214	−0.00831480	−0.00415740	−	0.999991i	$-0.501323\pi$
$439$	−0.174214	−0.00831480	−0.00415740	+	0.999991i	$0.501323\pi$
$440$	0	0
$441$	2.45073	0.116701
$442$	3.11962	0.148385
$443$	−19.4451	−0.923866	−0.461933	−	0.886915i	$-0.652844\pi$
$443$	−19.4451	−0.923866	−0.461933	+	0.886915i	$0.652844\pi$
$444$	17.1199	0.812473
$445$	0	0
$446$	25.3887	1.20219
$447$	−4.75110	−0.224719
$448$	−4.07943	−0.192735
$449$	33.2496	1.56914	0.784572	−	0.620037i	$-0.212883\pi$
$449$	33.2496	1.56914	0.784572	+	0.620037i	$0.212883\pi$
$450$	0	0
$451$	7.55331	0.355671
$452$	−8.25861	−0.388452
$453$	23.8431	1.12024
$454$	19.0289	0.893072
$455$	0	0
$456$	−6.96742	−0.326279
$457$	−6.33851	−0.296503	−0.148251	−	0.988950i	$-0.547364\pi$
$457$	−6.33851	−0.296503	−0.148251	+	0.988950i	$0.547364\pi$
$458$	−34.7501	−1.62377
$459$	−0.429184	−0.0200326
$460$	0	0
$461$	−25.3989	−1.18294	−0.591472	−	0.806325i	$-0.701453\pi$
$461$	−25.3989	−1.18294	−0.591472	+	0.806325i	$0.701453\pi$
$462$	−4.39842	−0.204633
$463$	23.9753	1.11423	0.557113	−	0.830437i	$-0.311909\pi$
$463$	23.9753	1.11423	0.557113	+	0.830437i	$0.311909\pi$
$464$	−40.2398	−1.86808
$465$	0	0
$466$	47.2226	2.18755
$467$	−20.0909	−0.929694	−0.464847	−	0.885391i	$-0.653891\pi$
$467$	−20.0909	−0.929694	−0.464847	+	0.885391i	$0.653891\pi$
$468$	18.7856	0.868366
$469$	−7.36745	−0.340197
$470$	0	0
$471$	−40.3677	−1.86004
$472$	−6.89345	−0.317297
$473$	−1.93626	−0.0890292
$474$	49.9050	2.29221
$475$	0	0
$476$	−0.518509	−0.0237658
$477$	−21.7149	−0.994257
$478$	−49.7989	−2.27775
$479$	18.0483	0.824646	0.412323	−	0.911038i	$-0.364717\pi$
$479$	18.0483	0.824646	0.412323	+	0.911038i	$0.364717\pi$
$480$	0	0
$481$	−23.4179	−1.06777
$482$	43.7389	1.99225
$483$	−10.5084	−0.478149
$484$	1.54927	0.0704214
$485$	0	0
$486$	−38.2588	−1.73545
$487$	−11.1932	−0.507214	−0.253607	−	0.967307i	$-0.581617\pi$
$487$	−11.1932	−0.507214	−0.253607	+	0.967307i	$0.581617\pi$
$488$	−5.43322	−0.245950
$489$	−16.5057	−0.746416
$490$	0	0
$491$	31.9805	1.44326	0.721629	−	0.692280i	$-0.243394\pi$
$491$	31.9805	1.44326	0.721629	+	0.692280i	$0.243394\pi$
$492$	27.3207	1.23171
$493$	−2.86645	−0.129098
$494$	−32.7591	−1.47390
$495$	0	0
$496$	−31.2524	−1.40327
$497$	8.00000	0.358849
$498$	35.9959	1.61302
$499$	22.3407	1.00011	0.500054	−	0.865994i	$-0.333313\pi$
$499$	22.3407	1.00011	0.500054	+	0.865994i	$0.333313\pi$
$500$	0	0
$501$	10.1746	0.454569
$502$	−19.5651	−0.873235
$503$	−32.3849	−1.44397	−0.721986	−	0.691907i	$-0.756771\pi$
$503$	−32.3849	−1.44397	−0.721986	+	0.691907i	$0.756771\pi$
$504$	2.08104	0.0926968
$505$	0	0
$506$	8.47967	0.376967
$507$	−26.8014	−1.19029
$508$	2.73896	0.121522
$509$	−19.4312	−0.861272	−0.430636	−	0.902526i	$-0.641711\pi$
$509$	−19.4312	−0.861272	−0.430636	+	0.902526i	$0.641711\pi$
$510$	0	0
$511$	14.8994	0.659112
$512$	−25.6281	−1.13261
$513$	4.50686	0.198983
$514$	−5.55714	−0.245115
$515$	0	0
$516$	−7.00355	−0.308314
$517$	8.75061	0.384851
$518$	8.91693	0.391787
$519$	9.11808	0.400239
$520$	0	0
$521$	−15.7816	−0.691404	−0.345702	−	0.938344i	$-0.612359\pi$
$521$	−15.7816	−0.691404	−0.345702	+	0.938344i	$0.612359\pi$
$522$	−39.5439	−1.73079
$523$	41.7277	1.82463	0.912313	−	0.409494i	$-0.134295\pi$
$523$	41.7277	1.82463	0.912313	+	0.409494i	$0.134295\pi$
$524$	−21.0603	−0.920024
$525$	0	0
$526$	0.808562	0.0352550
$527$	−2.22624	−0.0969765
$528$	−10.9690	−0.477366
$529$	−2.74097	−0.119172
$530$	0	0
$531$	−19.8952	−0.863376
$532$	5.44487	0.236065
$533$	−37.3715	−1.61874
$534$	−32.0309	−1.38611
$535$	0	0
$536$	−6.25607	−0.270221
$537$	−19.2382	−0.830188
$538$	25.9131	1.11719
$539$	−1.00000	−0.0430730
$540$	0	0
$541$	36.6424	1.57538	0.787690	−	0.616071i	$-0.211277\pi$
$541$	36.6424	1.57538	0.787690	+	0.616071i	$0.211277\pi$
$542$	4.52572	0.194396
$543$	−18.0040	−0.772626
$544$	−2.39399	−0.102641
$545$	0	0
$546$	21.7620	0.931329
$547$	25.3347	1.08323	0.541616	−	0.840626i	$-0.317813\pi$
$547$	25.3347	1.08323	0.541616	+	0.840626i	$0.317813\pi$
$548$	0.938265	0.0400807
$549$	−15.6808	−0.669240
$550$	0	0
$551$	30.1006	1.28233
$552$	−8.92321	−0.379797
$553$	11.3461	0.482486
$554$	−59.9845	−2.54850
$555$	0	0
$556$	20.8086	0.882480
$557$	9.65743	0.409198	0.204599	−	0.978846i	$-0.434411\pi$
$557$	9.65743	0.409198	0.204599	+	0.978846i	$0.434411\pi$
$558$	−30.7120	−1.30014
$559$	9.58001	0.405191
$560$	0	0
$561$	−0.781369	−0.0329894
$562$	−8.54145	−0.360299
$563$	−13.1645	−0.554818	−0.277409	−	0.960752i	$-0.589476\pi$
$563$	−13.1645	−0.554818	−0.277409	+	0.960752i	$0.589476\pi$
$564$	31.6514	1.33276
$565$	0	0
$566$	22.1050	0.929142
$567$	−10.3461	−0.434496
$568$	6.79320	0.285036
$569$	−2.30170	−0.0964922	−0.0482461	−	0.998835i	$-0.515363\pi$
$569$	−2.30170	−0.0964922	−0.0482461	+	0.998835i	$0.515363\pi$
$570$	0	0
$571$	−21.0945	−0.882777	−0.441388	−	0.897316i	$-0.645514\pi$
$571$	−21.0945	−0.882777	−0.441388	+	0.897316i	$0.645514\pi$
$572$	−7.66532	−0.320503
$573$	−37.8339	−1.58053
$574$	14.2301	0.593951
$575$	0	0
$576$	−9.99757	−0.416565
$577$	−22.4815	−0.935916	−0.467958	−	0.883751i	$-0.655010\pi$
$577$	−22.4815	−0.935916	−0.467958	+	0.883751i	$0.655010\pi$
$578$	31.8161	1.32338
$579$	−53.3093	−2.21546
$580$	0	0
$581$	8.18383	0.339522
$582$	−60.9055	−2.52461
$583$	8.86059	0.366968
$584$	12.6519	0.523537
$585$	0	0
$586$	31.7066	1.30979
$587$	−28.7679	−1.18738	−0.593689	−	0.804695i	$-0.702329\pi$
$587$	−28.7679	−1.18738	−0.593689	+	0.804695i	$0.702329\pi$
$588$	−3.61705	−0.149165
$589$	23.3777	0.963263
$590$	0	0
$591$	2.49767	0.102740
$592$	22.2375	0.913957
$593$	−9.87202	−0.405395	−0.202698	−	0.979241i	$-0.564971\pi$
$593$	−9.87202	−0.405395	−0.202698	+	0.979241i	$0.564971\pi$
$594$	2.41593	0.0991267
$595$	0	0
$596$	3.15279	0.129143
$597$	13.3944	0.548196
$598$	−41.9548	−1.71566
$599$	39.8186	1.62695	0.813473	−	0.581603i	$-0.197574\pi$
$599$	39.8186	1.62695	0.813473	+	0.581603i	$0.197574\pi$
$600$	0	0
$601$	15.2516	0.622126	0.311063	−	0.950389i	$-0.399315\pi$
$601$	15.2516	0.622126	0.311063	+	0.950389i	$0.399315\pi$
$602$	−3.64781	−0.148674
$603$	−18.0556	−0.735282
$604$	−15.8220	−0.643789
$605$	0	0
$606$	36.0128	1.46292
$607$	−20.6130	−0.836656	−0.418328	−	0.908296i	$-0.637384\pi$
$607$	−20.6130	−0.836656	−0.418328	+	0.908296i	$0.637384\pi$
$608$	25.1392	1.01953
$609$	−19.9959	−0.810276
$610$	0	0
$611$	−43.2953	−1.75154
$612$	−1.27073	−0.0513660
$613$	−9.57261	−0.386634	−0.193317	−	0.981136i	$-0.561925\pi$
$613$	−9.57261	−0.386634	−0.193317	+	0.981136i	$0.561925\pi$
$614$	19.9437	0.804860
$615$	0	0
$616$	−0.849150	−0.0342132
$617$	−9.70416	−0.390675	−0.195337	−	0.980736i	$-0.562580\pi$
$617$	−9.70416	−0.390675	−0.195337	+	0.980736i	$0.562580\pi$
$618$	63.9524	2.57254
$619$	36.4146	1.46363	0.731813	−	0.681506i	$-0.238675\pi$
$619$	36.4146	1.46363	0.731813	+	0.681506i	$0.238675\pi$
$620$	0	0
$621$	5.77197	0.231621
$622$	−2.43369	−0.0975821
$623$	−7.28237	−0.291762
$624$	54.2714	2.17259
$625$	0	0
$626$	−23.9115	−0.955697
$627$	8.20516	0.327683
$628$	26.7876	1.06894
$629$	1.58407	0.0631611
$630$	0	0
$631$	33.2879	1.32517	0.662586	−	0.748986i	$-0.269459\pi$
$631$	33.2879	1.32517	0.662586	+	0.748986i	$0.269459\pi$
$632$	9.63456	0.383242
$633$	−53.9466	−2.14418
$634$	−55.0680	−2.18703
$635$	0	0
$636$	32.0492	1.27083
$637$	4.94769	0.196035
$638$	16.1356	0.638813
$639$	19.6058	0.775595
$640$	0	0
$641$	7.87991	0.311238	0.155619	−	0.987817i	$-0.450263\pi$
$641$	7.87991	0.311238	0.155619	+	0.987817i	$0.450263\pi$
$642$	45.9075	1.81182
$643$	−8.60291	−0.339265	−0.169633	−	0.985507i	$-0.554258\pi$
$643$	−8.60291	−0.339265	−0.169633	+	0.985507i	$0.554258\pi$
$644$	6.97328	0.274786
$645$	0	0
$646$	2.21594	0.0871851
$647$	15.1879	0.597097	0.298548	−	0.954395i	$-0.403498\pi$
$647$	15.1879	0.597097	0.298548	+	0.954395i	$0.403498\pi$
$648$	−8.78541	−0.345123
$649$	8.11806	0.318662
$650$	0	0
$651$	−15.5299	−0.608667
$652$	10.9531	0.428955
$653$	15.2920	0.598422	0.299211	−	0.954187i	$-0.403277\pi$
$653$	15.2920	0.598422	0.299211	+	0.954187i	$0.403277\pi$
$654$	−29.3347	−1.14708
$655$	0	0
$656$	35.4877	1.38556
$657$	36.5144	1.42456
$658$	16.4857	0.642680
$659$	−16.9717	−0.661125	−0.330563	−	0.943784i	$-0.607238\pi$
$659$	−16.9717	−0.661125	−0.330563	+	0.943784i	$0.607238\pi$
$660$	0	0
$661$	29.0035	1.12811	0.564054	−	0.825738i	$-0.309241\pi$
$661$	29.0035	1.12811	0.564054	+	0.825738i	$0.309241\pi$
$662$	−44.7047	−1.73750
$663$	3.86598	0.150142
$664$	6.94930	0.269685
$665$	0	0
$666$	21.8530	0.846786
$667$	38.5500	1.49266
$668$	−6.75179	−0.261235
$669$	31.4629	1.21642
$670$	0	0
$671$	6.39842	0.247008
$672$	−16.7001	−0.644221
$673$	−29.1434	−1.12340	−0.561698	−	0.827342i	$-0.689852\pi$
$673$	−29.1434	−1.12340	−0.561698	+	0.827342i	$0.689852\pi$
$674$	−30.4096	−1.17134
$675$	0	0
$676$	17.7851	0.684043
$677$	15.0334	0.577782	0.288891	−	0.957362i	$-0.406713\pi$
$677$	15.0334	0.577782	0.288891	+	0.957362i	$0.406713\pi$
$678$	−23.4464	−0.900454
$679$	−13.8471	−0.531404
$680$	0	0
$681$	23.5815	0.903647
$682$	12.5318	0.479866
$683$	28.7910	1.10166	0.550828	−	0.834619i	$-0.314312\pi$
$683$	28.7910	1.10166	0.550828	+	0.834619i	$0.314312\pi$
$684$	13.3439	0.510217
$685$	0	0
$686$	−1.88395	−0.0719296
$687$	−43.0640	−1.64299
$688$	−9.09712	−0.346824
$689$	−43.8395	−1.67015
$690$	0	0
$691$	−35.3308	−1.34405	−0.672024	−	0.740529i	$-0.734575\pi$
$691$	−35.3308	−1.34405	−0.672024	+	0.740529i	$0.734575\pi$
$692$	−6.05067	−0.230012
$693$	−2.45073	−0.0930955
$694$	20.5268	0.779186
$695$	0	0
$696$	−16.9796	−0.643608
$697$	2.52794	0.0957525
$698$	32.5921	1.23363
$699$	58.5205	2.21345
$700$	0	0
$701$	−32.2940	−1.21973	−0.609864	−	0.792506i	$-0.708776\pi$
$701$	−32.2940	−1.21973	−0.609864	+	0.792506i	$0.708776\pi$
$702$	−11.9533	−0.451147
$703$	−16.6343	−0.627376
$704$	4.07943	0.153749
$705$	0	0
$706$	42.4601	1.59801
$707$	8.18766	0.307929
$708$	29.3634	1.10355
$709$	35.9075	1.34853	0.674267	−	0.738488i	$-0.264460\pi$
$709$	35.9075	1.34853	0.674267	+	0.738488i	$0.264460\pi$
$710$	0	0
$711$	27.8062	1.04282
$712$	−6.18383	−0.231749
$713$	29.9400	1.12126
$714$	−1.47206	−0.0550905
$715$	0	0
$716$	12.7663	0.477098
$717$	−61.7130	−2.30472
$718$	13.1775	0.491780
$719$	−39.1683	−1.46073	−0.730366	−	0.683056i	$-0.760651\pi$
$719$	−39.1683	−1.46073	−0.730366	+	0.683056i	$0.760651\pi$
$720$	0	0
$721$	14.5398	0.541492
$722$	12.5254	0.466149
$723$	54.2033	2.01584
$724$	11.9473	0.444018
$725$	0	0
$726$	4.39842	0.163241
$727$	2.49829	0.0926565	0.0463283	−	0.998926i	$-0.485248\pi$
$727$	2.49829	0.0926565	0.0463283	+	0.998926i	$0.485248\pi$
$728$	4.20134	0.155712
$729$	−16.3737	−0.606434
$730$	0	0
$731$	−0.648026	−0.0239681
$732$	23.1434	0.855406
$733$	−35.9863	−1.32918	−0.664591	−	0.747207i	$-0.731394\pi$
$733$	−35.9863	−1.32918	−0.664591	+	0.747207i	$0.731394\pi$
$734$	−59.4110	−2.19290
$735$	0	0
$736$	32.1960	1.18676
$737$	7.36745	0.271383
$738$	34.8740	1.28373
$739$	9.80291	0.360606	0.180303	−	0.983611i	$-0.442292\pi$
$739$	9.80291	0.360606	0.180303	+	0.983611i	$0.442292\pi$
$740$	0	0
$741$	−40.5966	−1.49135
$742$	16.6929	0.612816
$743$	−17.5627	−0.644314	−0.322157	−	0.946686i	$-0.604408\pi$
$743$	−17.5627	−0.644314	−0.322157	+	0.946686i	$0.604408\pi$
$744$	−13.1873	−0.483468
$745$	0	0
$746$	−59.9464	−2.19479
$747$	20.0563	0.733823
$748$	0.518509	0.0189586
$749$	10.4373	0.381369
$750$	0	0
$751$	0.921252	0.0336170	0.0168085	−	0.999859i	$-0.494649\pi$
$751$	0.921252	0.0336170	0.0168085	+	0.999859i	$0.494649\pi$
$752$	41.1130	1.49924
$753$	−24.2460	−0.883575
$754$	−79.8338	−2.90738
$755$	0	0
$756$	1.98674	0.0722572
$757$	12.9939	0.472272	0.236136	−	0.971720i	$-0.424119\pi$
$757$	12.9939	0.472272	0.236136	+	0.971720i	$0.424119\pi$
$758$	61.3579	2.22862
$759$	10.5084	0.381431
$760$	0	0
$761$	44.2323	1.60342	0.801710	−	0.597714i	$-0.203924\pi$
$761$	44.2323	1.60342	0.801710	+	0.597714i	$0.203924\pi$
$762$	7.77598	0.281694
$763$	−6.66936	−0.241447
$764$	25.1062	0.908310
$765$	0	0
$766$	−62.0392	−2.24157
$767$	−40.1657	−1.45030
$768$	−48.1689	−1.73815
$769$	−39.1977	−1.41351	−0.706753	−	0.707460i	$-0.749841\pi$
$769$	−39.1977	−1.41351	−0.706753	+	0.707460i	$0.749841\pi$
$770$	0	0
$771$	−6.88666	−0.248017
$772$	35.3755	1.27319
$773$	47.2477	1.69938	0.849691	−	0.527280i	$-0.176788\pi$
$773$	47.2477	1.69938	0.849691	+	0.527280i	$0.176788\pi$
$774$	−8.93980	−0.321335
$775$	0	0
$776$	−11.7583	−0.422098
$777$	11.0503	0.396426
$778$	−49.1874	−1.76345
$779$	−26.5459	−0.951105
$780$	0	0
$781$	−8.00000	−0.286263
$782$	2.83797	0.101486
$783$	10.9832	0.392507
$784$	−4.69830	−0.167796
$785$	0	0
$786$	−59.7908	−2.13267
$787$	4.42918	0.157883	0.0789417	−	0.996879i	$-0.474846\pi$
$787$	4.42918	0.157883	0.0789417	+	0.996879i	$0.474846\pi$
$788$	−1.65743	−0.0590435
$789$	1.00201	0.0356724
$790$	0	0
$791$	−5.33064	−0.189536
$792$	−2.08104	−0.0739464
$793$	−31.6574	−1.12419
$794$	20.0527	0.711644
$795$	0	0
$796$	−8.88839	−0.315041
$797$	54.4199	1.92765	0.963827	−	0.266530i	$-0.0858771\pi$
$797$	54.4199	1.92765	0.963827	+	0.266530i	$0.0858771\pi$
$798$	15.4581	0.547212
$799$	2.92865	0.103608
$800$	0	0
$801$	−17.8471	−0.630597
$802$	69.3970	2.45049
$803$	−14.8994	−0.525789
$804$	26.6484	0.939818
$805$	0	0
$806$	−62.0033	−2.18397
$807$	32.1127	1.13042
$808$	6.95255	0.244590
$809$	−9.08640	−0.319461	−0.159730	−	0.987161i	$-0.551063\pi$
$809$	−9.08640	−0.319461	−0.159730	+	0.987161i	$0.551063\pi$
$810$	0	0
$811$	43.6083	1.53129	0.765647	−	0.643261i	$-0.222419\pi$
$811$	43.6083	1.53129	0.765647	+	0.643261i	$0.222419\pi$
$812$	13.2691	0.465655
$813$	5.60848	0.196698
$814$	−8.91693	−0.312538
$815$	0	0
$816$	−3.67111	−0.128515
$817$	6.80492	0.238074
$818$	53.8370	1.88237
$819$	12.1255	0.423698
$820$	0	0
$821$	39.2381	1.36942	0.684710	−	0.728816i	$-0.259929\pi$
$821$	39.2381	1.36942	0.684710	+	0.728816i	$0.259929\pi$
$822$	2.66376	0.0929092
$823$	0.872726	0.0304213	0.0152107	−	0.999884i	$-0.495158\pi$
$823$	0.872726	0.0304213	0.0152107	+	0.999884i	$0.495158\pi$
$824$	12.3465	0.430111
$825$	0	0
$826$	15.2940	0.532147
$827$	15.5447	0.540544	0.270272	−	0.962784i	$-0.412886\pi$
$827$	15.5447	0.540544	0.270272	+	0.962784i	$0.412886\pi$
$828$	17.0896	0.593905
$829$	−1.14163	−0.0396505	−0.0198253	−	0.999803i	$-0.506311\pi$
$829$	−1.14163	−0.0396505	−0.0198253	+	0.999803i	$0.506311\pi$
$830$	0	0
$831$	−74.3355	−2.57867
$832$	−20.1838	−0.699746
$833$	−0.334680	−0.0115960
$834$	59.0760	2.04564
$835$	0	0
$836$	−5.44487	−0.188315
$837$	8.53016	0.294845
$838$	19.5394	0.674976
$839$	49.4970	1.70883	0.854413	−	0.519595i	$-0.173917\pi$
$839$	49.4970	1.70883	0.854413	+	0.519595i	$0.173917\pi$
$840$	0	0
$841$	44.3549	1.52948
$842$	13.0963	0.451329
$843$	−10.5850	−0.364566
$844$	35.7984	1.23223
$845$	0	0
$846$	40.4020	1.38905
$847$	1.00000	0.0343604
$848$	41.6297	1.42957
$849$	27.3935	0.940143
$850$	0	0
$851$	−21.3037	−0.730282
$852$	−28.9364	−0.991345
$853$	3.00558	0.102909	0.0514545	−	0.998675i	$-0.483614\pi$
$853$	3.00558	0.102909	0.0514545	+	0.998675i	$0.483614\pi$
$854$	12.0543	0.412490
$855$	0	0
$856$	8.86280	0.302924
$857$	11.9279	0.407451	0.203725	−	0.979028i	$-0.434695\pi$
$857$	11.9279	0.407451	0.203725	+	0.979028i	$0.434695\pi$
$858$	−21.7620	−0.742944
$859$	4.84894	0.165444	0.0827218	−	0.996573i	$-0.473639\pi$
$859$	4.84894	0.165444	0.0827218	+	0.996573i	$0.473639\pi$
$860$	0	0
$861$	17.6346	0.600984
$862$	−27.4761	−0.935839
$863$	−39.7275	−1.35234	−0.676169	−	0.736746i	$-0.736361\pi$
$863$	−39.7275	−1.35234	−0.676169	+	0.736746i	$0.736361\pi$
$864$	9.17290	0.312068
$865$	0	0
$866$	−66.7811	−2.26931
$867$	39.4280	1.33905
$868$	10.3055	0.349792
$869$	−11.3461	−0.384891
$870$	0	0
$871$	−36.4519	−1.23512
$872$	−5.66329	−0.191783
$873$	−33.9355	−1.14854
$874$	−29.8016	−1.00805
$875$	0	0
$876$	−53.8920	−1.82084
$877$	5.61169	0.189493	0.0947466	−	0.995501i	$-0.469796\pi$
$877$	5.61169	0.189493	0.0947466	+	0.995501i	$0.469796\pi$
$878$	0.328211	0.0110766
$879$	39.2922	1.32529
$880$	0	0
$881$	−43.9127	−1.47946	−0.739728	−	0.672907i	$-0.765046\pi$
$881$	−43.9127	−1.47946	−0.739728	+	0.672907i	$0.765046\pi$
$882$	−4.61705	−0.155464
$883$	−9.34051	−0.314333	−0.157167	−	0.987572i	$-0.550236\pi$
$883$	−9.34051	−0.314333	−0.157167	+	0.987572i	$0.550236\pi$
$884$	−2.56543	−0.0862846
$885$	0	0
$886$	36.6337	1.23073
$887$	−15.7248	−0.527988	−0.263994	−	0.964524i	$-0.585040\pi$
$887$	−15.7248	−0.527988	−0.263994	+	0.964524i	$0.585040\pi$
$888$	9.38335	0.314884
$889$	1.76790	0.0592935
$890$	0	0
$891$	10.3461	0.346608
$892$	−20.8785	−0.699063
$893$	−30.7538	−1.02914
$894$	8.95084	0.299361
$895$	0	0
$896$	−6.62069	−0.221182
$897$	−51.9923	−1.73597
$898$	−62.6406	−2.09034
$899$	56.9714	1.90010
$900$	0	0
$901$	2.96546	0.0987937
$902$	−14.2301	−0.473809
$903$	−4.52054	−0.150434
$904$	−4.52652	−0.150550
$905$	0	0
$906$	−44.9191	−1.49234
$907$	−6.38566	−0.212032	−0.106016	−	0.994364i	$-0.533810\pi$
$907$	−6.38566	−0.212032	−0.106016	+	0.994364i	$0.533810\pi$
$908$	−15.6485	−0.519314
$909$	20.0657	0.665538
$910$	0	0
$911$	−13.8029	−0.457311	−0.228655	−	0.973507i	$-0.573433\pi$
$911$	−13.8029	−0.457311	−0.228655	+	0.973507i	$0.573433\pi$
$912$	38.5503	1.27653
$913$	−8.18383	−0.270845
$914$	11.9414	0.394988
$915$	0	0
$916$	28.5768	0.944205
$917$	−13.5937	−0.448903
$918$	0.808562	0.0266865
$919$	−19.5870	−0.646115	−0.323057	−	0.946379i	$-0.604711\pi$
$919$	−19.5870	−0.646115	−0.323057	+	0.946379i	$0.604711\pi$
$920$	0	0
$921$	24.7151	0.814390
$922$	47.8503	1.57586
$923$	39.5815	1.30284
$924$	3.61705	0.118992
$925$	0	0
$926$	−45.1683	−1.48432
$927$	35.6332	1.17035
$928$	61.2642	2.01110
$929$	6.27630	0.205919	0.102959	−	0.994686i	$-0.467169\pi$
$929$	6.27630	0.205919	0.102959	+	0.994686i	$0.467169\pi$
$930$	0	0
$931$	3.51447	0.115182
$932$	−38.8337	−1.27204
$933$	−3.01594	−0.0987375
$934$	37.8502	1.23850
$935$	0	0
$936$	10.2963	0.336546
$937$	−22.1239	−0.722757	−0.361378	−	0.932419i	$-0.617694\pi$
$937$	−22.1239	−0.722757	−0.361378	+	0.932419i	$0.617694\pi$
$938$	13.8799	0.453195
$939$	−29.6323	−0.967013
$940$	0	0
$941$	33.1027	1.07912	0.539559	−	0.841948i	$-0.318591\pi$
$941$	33.1027	1.07912	0.539559	+	0.841948i	$0.318591\pi$
$942$	76.0507	2.47787
$943$	−33.9975	−1.10711
$944$	38.1411	1.24139
$945$	0	0
$946$	3.64781	0.118601
$947$	24.2070	0.786620	0.393310	−	0.919406i	$-0.371330\pi$
$947$	24.2070	0.786620	0.393310	+	0.919406i	$0.371330\pi$
$948$	−41.0395	−1.33290
$949$	73.7178	2.39298
$950$	0	0
$951$	−68.2428	−2.21292
$952$	−0.284193	−0.00921076
$953$	−18.7838	−0.608468	−0.304234	−	0.952597i	$-0.598401\pi$
$953$	−18.7838	−0.608468	−0.304234	+	0.952597i	$0.598401\pi$
$954$	40.9098	1.32450
$955$	0	0
$956$	40.9522	1.32449
$957$	19.9959	0.646377
$958$	−34.0021	−1.09856
$959$	0.605617	0.0195564
$960$	0	0
$961$	13.2471	0.427327
$962$	44.1182	1.42243
$963$	25.5789	0.824268
$964$	−35.9688	−1.15848
$965$	0	0
$966$	19.7973	0.636968
$967$	−46.8152	−1.50548	−0.752738	−	0.658320i	$-0.771267\pi$
$967$	−46.8152	−1.50548	−0.752738	+	0.658320i	$0.771267\pi$
$968$	0.849150	0.0272927
$969$	2.74610	0.0882174
$970$	0	0
$971$	−36.1394	−1.15977	−0.579884	−	0.814699i	$-0.696902\pi$
$971$	−36.1394	−1.15977	−0.579884	+	0.814699i	$0.696902\pi$
$972$	31.4622	1.00915
$973$	13.4312	0.430584
$974$	21.0875	0.675687
$975$	0	0
$976$	30.0617	0.962252
$977$	−19.2889	−0.617107	−0.308553	−	0.951207i	$-0.599845\pi$
$977$	−19.2889	−0.617107	−0.308553	+	0.951207i	$0.599845\pi$
$978$	31.0960	0.994341
$979$	7.28237	0.232746
$980$	0	0
$981$	−16.3448	−0.521849
$982$	−60.2496	−1.92264
$983$	14.5037	0.462597	0.231298	−	0.972883i	$-0.425703\pi$
$983$	14.5037	0.462597	0.231298	+	0.972883i	$0.425703\pi$
$984$	14.9744	0.477366
$985$	0	0
$986$	5.40024	0.171979
$987$	20.4299	0.650290
$988$	26.9395	0.857061
$989$	8.71510	0.277124
$990$	0	0
$991$	1.88059	0.0597390	0.0298695	−	0.999554i	$-0.490491\pi$
$991$	1.88059	0.0597390	0.0298695	+	0.999554i	$0.490491\pi$
$992$	47.5812	1.51070
$993$	−55.4002	−1.75807
$994$	−15.0716	−0.478042
$995$	0	0
$996$	−29.6013	−0.937954
$997$	−5.10057	−0.161537	−0.0807684	−	0.996733i	$-0.525737\pi$
$997$	−5.10057	−0.161537	−0.0807684	+	0.996733i	$0.525737\pi$
$998$	−42.0888	−1.33230
$999$	−6.06960	−0.192034

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1925.2.a.x.1.2		4
5.2	odd	4		1925.2.b.p.1849.3		8
5.3	odd	4		1925.2.b.p.1849.6		8
5.4	even	2		385.2.a.h.1.3	✓	4
15.14	odd	2		3465.2.a.bk.1.2		4
20.19	odd	2		6160.2.a.br.1.2		4
35.34	odd	2		2695.2.a.l.1.3		4
55.54	odd	2		4235.2.a.r.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.a.h.1.3	✓	4	5.4	even	2
1925.2.a.x.1.2		4	1.1	even	1	trivial
1925.2.b.p.1849.3		8	5.2	odd	4
1925.2.b.p.1849.6		8	5.3	odd	4
2695.2.a.l.1.3		4	35.34	odd	2
3465.2.a.bk.1.2		4	15.14	odd	2
4235.2.a.r.1.2		4	55.54	odd	2
6160.2.a.br.1.2		4	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1925 = 5^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1925.a (trivial)

\(f(q)\)	\(=\)	\(q-1.88395 q^{2} -2.33468 q^{3} +1.54927 q^{4} +4.39842 q^{6} +1.00000 q^{7} +0.849150 q^{8} +2.45073 q^{9} +O(q^{10})\)	\(q-1.88395 q^{2} -2.33468 q^{3} +1.54927 q^{4} +4.39842 q^{6} +1.00000 q^{7} +0.849150 q^{8} +2.45073 q^{9} -1.00000 q^{11} -3.61705 q^{12} +4.94769 q^{13} -1.88395 q^{14} -4.69830 q^{16} -0.334680 q^{17} -4.61705 q^{18} +3.51447 q^{19} -2.33468 q^{21} +1.88395 q^{22} +4.50100 q^{23} -1.98249 q^{24} -9.32121 q^{26} +1.28237 q^{27} +1.54927 q^{28} +8.56475 q^{29} +6.65185 q^{31} +7.15307 q^{32} +2.33468 q^{33} +0.630520 q^{34} +3.79684 q^{36} -4.73310 q^{37} -6.62109 q^{38} -11.5513 q^{39} -7.55331 q^{41} +4.39842 q^{42} +1.93626 q^{43} -1.54927 q^{44} -8.47967 q^{46} -8.75061 q^{47} +10.9690 q^{48} +1.00000 q^{49} +0.781369 q^{51} +7.66532 q^{52} -8.86059 q^{53} -2.41593 q^{54} +0.849150 q^{56} -8.20516 q^{57} -16.1356 q^{58} -8.11806 q^{59} -6.39842 q^{61} -12.5318 q^{62} +2.45073 q^{63} -4.07943 q^{64} -4.39842 q^{66} -7.36745 q^{67} -0.518509 q^{68} -10.5084 q^{69} +8.00000 q^{71} +2.08104 q^{72} +14.8994 q^{73} +8.91693 q^{74} +5.44487 q^{76} -1.00000 q^{77} +21.7620 q^{78} +11.3461 q^{79} -10.3461 q^{81} +14.2301 q^{82} +8.18383 q^{83} -3.61705 q^{84} -3.64781 q^{86} -19.9959 q^{87} -0.849150 q^{88} -7.28237 q^{89} +4.94769 q^{91} +6.97328 q^{92} -15.5299 q^{93} +16.4857 q^{94} -16.7001 q^{96} -13.8471 q^{97} -1.88395 q^{98} -2.45073 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{3} + 8 q^{4} + 4 q^{6} + 4 q^{7} - 12 q^{8} + 8 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^3 + 8 * q^4 + 4 * q^6 + 4 * q^7 - 12 * q^8 + 8 * q^9	\( 4 q - 2 q^{2} - 2 q^{3} + 8 q^{4} + 4 q^{6} + 4 q^{7} - 12 q^{8} + 8 q^{9} - 4 q^{11} + 12 q^{12} + 8 q^{13} - 2 q^{14} + 12 q^{16} + 6 q^{17} + 8 q^{18} + 6 q^{19} - 2 q^{21} + 2 q^{22} - 14 q^{23} - 6 q^{24} - 6 q^{26} - 14 q^{27} + 8 q^{28} - 4 q^{29} + 10 q^{31} - 26 q^{32} + 2 q^{33} - 12 q^{36} + 2 q^{37} + 22 q^{38} + 16 q^{39} - 10 q^{41} + 4 q^{42} + 14 q^{43} - 8 q^{44} - 16 q^{46} - 16 q^{47} + 18 q^{48} + 4 q^{49} + 16 q^{51} + 38 q^{52} - 2 q^{53} + 2 q^{54} - 12 q^{56} + 4 q^{57} - 8 q^{58} + 26 q^{59} - 12 q^{61} - 50 q^{62} + 8 q^{63} + 36 q^{64} - 4 q^{66} + 10 q^{67} + 28 q^{68} - 14 q^{69} + 32 q^{71} + 10 q^{72} + 14 q^{73} - 8 q^{74} - 6 q^{76} - 4 q^{77} + 50 q^{78} + 20 q^{79} - 16 q^{81} + 26 q^{82} + 10 q^{83} + 12 q^{84} - 20 q^{86} + 4 q^{87} + 12 q^{88} - 10 q^{89} + 8 q^{91} - 26 q^{92} - 14 q^{93} - 38 q^{94} - 84 q^{96} + 2 q^{97} - 2 q^{98} - 8 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^3 + 8 * q^4 + 4 * q^6 + 4 * q^7 - 12 * q^8 + 8 * q^9 - 4 * q^11 + 12 * q^12 + 8 * q^13 - 2 * q^14 + 12 * q^16 + 6 * q^17 + 8 * q^18 + 6 * q^19 - 2 * q^21 + 2 * q^22 - 14 * q^23 - 6 * q^24 - 6 * q^26 - 14 * q^27 + 8 * q^28 - 4 * q^29 + 10 * q^31 - 26 * q^32 + 2 * q^33 - 12 * q^36 + 2 * q^37 + 22 * q^38 + 16 * q^39 - 10 * q^41 + 4 * q^42 + 14 * q^43 - 8 * q^44 - 16 * q^46 - 16 * q^47 + 18 * q^48 + 4 * q^49 + 16 * q^51 + 38 * q^52 - 2 * q^53 + 2 * q^54 - 12 * q^56 + 4 * q^57 - 8 * q^58 + 26 * q^59 - 12 * q^61 - 50 * q^62 + 8 * q^63 + 36 * q^64 - 4 * q^66 + 10 * q^67 + 28 * q^68 - 14 * q^69 + 32 * q^71 + 10 * q^72 + 14 * q^73 - 8 * q^74 - 6 * q^76 - 4 * q^77 + 50 * q^78 + 20 * q^79 - 16 * q^81 + 26 * q^82 + 10 * q^83 + 12 * q^84 - 20 * q^86 + 4 * q^87 + 12 * q^88 - 10 * q^89 + 8 * q^91 - 26 * q^92 - 14 * q^93 - 38 * q^94 - 84 * q^96 + 2 * q^97 - 2 * q^98 - 8 * q^99

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