LMFDB - Embedded newform 6025.2.a.f.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6025,2,Mod(1,6025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6025, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6025 = 5^{2} \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6025.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:	$48.1098672178$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	7.7.31056073.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 3x^{5} + 11x^{4} + x^{3} - 9x^{2} + 1 $ x^7 - 3x^6 - 3x^5 + 11x^4 + x^3 - 9x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 241)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$0.369356$ of defining polynomial
Character	$\chi$	$=$	6025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.630644 q^{2} -2.33806 q^{3} -1.60229 q^{4} -1.47449 q^{6} +3.68231 q^{7} -2.27176 q^{8} +2.46654 q^{9} +O(q^{10})$	\(q+0.630644 q^{2} -2.33806 q^{3} -1.60229 q^{4} -1.47449 q^{6} +3.68231 q^{7} -2.27176 q^{8} +2.46654 q^{9} -4.96431 q^{11} +3.74625 q^{12} +1.69048 q^{13} +2.32223 q^{14} +1.77190 q^{16} -5.52260 q^{17} +1.55551 q^{18} +4.21489 q^{19} -8.60948 q^{21} -3.13071 q^{22} +2.77495 q^{23} +5.31152 q^{24} +1.06609 q^{26} +1.24727 q^{27} -5.90013 q^{28} -2.31253 q^{29} -0.199515 q^{31} +5.66096 q^{32} +11.6069 q^{33} -3.48280 q^{34} -3.95210 q^{36} -1.79089 q^{37} +2.65809 q^{38} -3.95245 q^{39} -12.1960 q^{41} -5.42952 q^{42} +5.34523 q^{43} +7.95425 q^{44} +1.75001 q^{46} +10.7345 q^{47} -4.14282 q^{48} +6.55944 q^{49} +12.9122 q^{51} -2.70864 q^{52} -1.32229 q^{53} +0.786587 q^{54} -8.36534 q^{56} -9.85467 q^{57} -1.45838 q^{58} +5.78578 q^{59} -0.0766435 q^{61} -0.125823 q^{62} +9.08256 q^{63} +0.0262532 q^{64} +7.31980 q^{66} -12.6166 q^{67} +8.84880 q^{68} -6.48800 q^{69} -5.20391 q^{71} -5.60338 q^{72} +14.0733 q^{73} -1.12941 q^{74} -6.75346 q^{76} -18.2801 q^{77} -2.49259 q^{78} +7.82844 q^{79} -10.3158 q^{81} -7.69137 q^{82} -2.55372 q^{83} +13.7949 q^{84} +3.37094 q^{86} +5.40683 q^{87} +11.2777 q^{88} -4.35327 q^{89} +6.22489 q^{91} -4.44627 q^{92} +0.466479 q^{93} +6.76964 q^{94} -13.2357 q^{96} -9.02693 q^{97} +4.13668 q^{98} -12.2446 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 4 q^{2} + 3 q^{3} + 2 q^{4} - 5 q^{6} + 7 q^{7} + 6 q^{8} - 2 q^{9}+O(q^{10}) $ 7 * q + 4 * q^2 + 3 * q^3 + 2 * q^4 - 5 * q^6 + 7 * q^7 + 6 * q^8 - 2 * q^9	$ 7 q + 4 q^{2} + 3 q^{3} + 2 q^{4} - 5 q^{6} + 7 q^{7} + 6 q^{8} - 2 q^{9} - 18 q^{11} - q^{12} + q^{13} - 6 q^{14} + 4 q^{16} + 2 q^{17} - 8 q^{18} - 6 q^{19} - 2 q^{21} - 10 q^{22} + 22 q^{23} - 3 q^{24} + 8 q^{26} - 3 q^{27} - 9 q^{28} - 16 q^{29} - 18 q^{31} + 6 q^{32} - 4 q^{33} + 11 q^{34} - 7 q^{36} - 8 q^{37} - 16 q^{38} - 9 q^{39} - 15 q^{41} - 19 q^{42} - 14 q^{43} - 4 q^{44} + 11 q^{46} + 10 q^{47} - 31 q^{48} + 6 q^{49} + 13 q^{51} - 27 q^{52} - 15 q^{53} + 16 q^{54} + 13 q^{56} - 14 q^{57} - 17 q^{58} - 18 q^{59} + 4 q^{61} - 13 q^{62} + 16 q^{63} + 2 q^{64} + 16 q^{66} - 18 q^{67} + 15 q^{68} + 26 q^{69} - 50 q^{71} - 30 q^{72} + 10 q^{74} - 20 q^{76} - 17 q^{77} + 32 q^{78} - 15 q^{79} - 9 q^{81} - 45 q^{82} + 24 q^{83} + 6 q^{84} - 23 q^{86} - 12 q^{87} - 8 q^{88} - 13 q^{89} - 12 q^{91} + 10 q^{92} - 14 q^{93} - 32 q^{94} - 15 q^{96} - q^{97} - 9 q^{98} - 20 q^{99}+O(q^{100}) $ 7 * q + 4 * q^2 + 3 * q^3 + 2 * q^4 - 5 * q^6 + 7 * q^7 + 6 * q^8 - 2 * q^9 - 18 * q^11 - q^12 + q^13 - 6 * q^14 + 4 * q^16 + 2 * q^17 - 8 * q^18 - 6 * q^19 - 2 * q^21 - 10 * q^22 + 22 * q^23 - 3 * q^24 + 8 * q^26 - 3 * q^27 - 9 * q^28 - 16 * q^29 - 18 * q^31 + 6 * q^32 - 4 * q^33 + 11 * q^34 - 7 * q^36 - 8 * q^37 - 16 * q^38 - 9 * q^39 - 15 * q^41 - 19 * q^42 - 14 * q^43 - 4 * q^44 + 11 * q^46 + 10 * q^47 - 31 * q^48 + 6 * q^49 + 13 * q^51 - 27 * q^52 - 15 * q^53 + 16 * q^54 + 13 * q^56 - 14 * q^57 - 17 * q^58 - 18 * q^59 + 4 * q^61 - 13 * q^62 + 16 * q^63 + 2 * q^64 + 16 * q^66 - 18 * q^67 + 15 * q^68 + 26 * q^69 - 50 * q^71 - 30 * q^72 + 10 * q^74 - 20 * q^76 - 17 * q^77 + 32 * q^78 - 15 * q^79 - 9 * q^81 - 45 * q^82 + 24 * q^83 + 6 * q^84 - 23 * q^86 - 12 * q^87 - 8 * q^88 - 13 * q^89 - 12 * q^91 + 10 * q^92 - 14 * q^93 - 32 * q^94 - 15 * q^96 - q^97 - 9 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0.630644	0.445933	0.222966	−	0.974826i	$-0.428426\pi$
$2$	0.630644	0.445933	0.222966	+	0.974826i	$0.428426\pi$
$3$	−2.33806	−1.34988	−0.674940	−	0.737872i	$-0.735831\pi$
$3$	−2.33806	−1.34988	−0.674940	+	0.737872i	$0.735831\pi$
$4$	−1.60229	−0.801144
$5$	0	0
$5$	0	0
$6$	−1.47449	−0.601956
$7$	3.68231	1.39178	0.695892	−	0.718146i	$-0.255009\pi$
$7$	3.68231	1.39178	0.695892	+	0.718146i	$0.255009\pi$
$8$	−2.27176	−0.803189
$9$	2.46654	0.822178
$10$	0	0
$11$	−4.96431	−1.49679	−0.748397	−	0.663250i	$-0.769176\pi$
$11$	−4.96431	−1.49679	−0.748397	+	0.663250i	$0.769176\pi$
$12$	3.74625	1.08145
$13$	1.69048	0.468855	0.234428	−	0.972134i	$-0.424678\pi$
$13$	1.69048	0.468855	0.234428	+	0.972134i	$0.424678\pi$
$14$	2.32223	0.620642
$15$	0	0
$16$	1.77190	0.442975
$17$	−5.52260	−1.33943	−0.669714	−	0.742619i	$-0.733583\pi$
$17$	−5.52260	−1.33943	−0.669714	+	0.742619i	$0.733583\pi$
$18$	1.55551	0.366636
$19$	4.21489	0.966961	0.483481	−	0.875355i	$-0.339372\pi$
$19$	4.21489	0.966961	0.483481	+	0.875355i	$0.339372\pi$
$20$	0	0
$21$	−8.60948	−1.87874
$22$	−3.13071	−0.667470
$23$	2.77495	0.578617	0.289308	−	0.957236i	$-0.406575\pi$
$23$	2.77495	0.578617	0.289308	+	0.957236i	$0.406575\pi$
$24$	5.31152	1.08421
$25$	0	0
$26$	1.06609	0.209078
$27$	1.24727	0.240038
$28$	−5.90013	−1.11502
$29$	−2.31253	−0.429425	−0.214713	−	0.976677i	$-0.568881\pi$
$29$	−2.31253	−0.429425	−0.214713	+	0.976677i	$0.568881\pi$
$30$	0	0
$31$	−0.199515	−0.0358340	−0.0179170	−	0.999839i	$-0.505703\pi$
$31$	−0.199515	−0.0358340	−0.0179170	+	0.999839i	$0.505703\pi$
$32$	5.66096	1.00073
$33$	11.6069	2.02049
$34$	−3.48280	−0.597295
$35$	0	0
$36$	−3.95210	−0.658683
$37$	−1.79089	−0.294420	−0.147210	−	0.989105i	$-0.547029\pi$
$37$	−1.79089	−0.294420	−0.147210	+	0.989105i	$0.547029\pi$
$38$	2.65809	0.431200
$39$	−3.95245	−0.632899
$40$	0	0
$41$	−12.1960	−1.90470	−0.952351	−	0.305003i	$-0.901343\pi$
$41$	−12.1960	−1.90470	−0.952351	+	0.305003i	$0.901343\pi$
$42$	−5.42952	−0.837793
$43$	5.34523	0.815139	0.407570	−	0.913174i	$-0.366376\pi$
$43$	5.34523	0.815139	0.407570	+	0.913174i	$0.366376\pi$
$44$	7.95425	1.19915
$45$	0	0
$46$	1.75001	0.258024
$47$	10.7345	1.56579	0.782893	−	0.622157i	$-0.213743\pi$
$47$	10.7345	1.56579	0.782893	+	0.622157i	$0.213743\pi$
$48$	−4.14282	−0.597964
$49$	6.55944	0.937063
$50$	0	0
$51$	12.9122	1.80807
$52$	−2.70864	−0.375621
$53$	−1.32229	−0.181631	−0.0908154	−	0.995868i	$-0.528947\pi$
$53$	−1.32229	−0.181631	−0.0908154	+	0.995868i	$0.528947\pi$
$54$	0.786587	0.107041
$55$	0	0
$56$	−8.36534	−1.11787
$57$	−9.85467	−1.30528
$58$	−1.45838	−0.191495
$59$	5.78578	0.753244	0.376622	−	0.926367i	$-0.377086\pi$
$59$	5.78578	0.753244	0.376622	+	0.926367i	$0.377086\pi$
$60$	0	0
$61$	−0.0766435	−0.00981320	−0.00490660	−	0.999988i	$-0.501562\pi$
$61$	−0.0766435	−0.00981320	−0.00490660	+	0.999988i	$0.501562\pi$
$62$	−0.125823	−0.0159795
$63$	9.08256	1.14429
$64$	0.0262532	0.00328165
$65$	0	0
$66$	7.31980	0.901005
$67$	−12.6166	−1.54136	−0.770681	−	0.637221i	$-0.780084\pi$
$67$	−12.6166	−1.54136	−0.770681	+	0.637221i	$0.780084\pi$
$68$	8.84880	1.07307
$69$	−6.48800	−0.781064
$70$	0	0
$71$	−5.20391	−0.617591	−0.308796	−	0.951128i	$-0.599926\pi$
$71$	−5.20391	−0.617591	−0.308796	+	0.951128i	$0.599926\pi$
$72$	−5.60338	−0.660365
$73$	14.0733	1.64715	0.823577	−	0.567204i	$-0.191975\pi$
$73$	14.0733	1.64715	0.823577	+	0.567204i	$0.191975\pi$
$74$	−1.12941	−0.131291
$75$	0	0
$76$	−6.75346	−0.774675
$77$	−18.2801	−2.08322
$78$	−2.49259	−0.282230
$79$	7.82844	0.880769	0.440384	−	0.897809i	$-0.354842\pi$
$79$	7.82844	0.880769	0.440384	+	0.897809i	$0.354842\pi$
$80$	0	0
$81$	−10.3158	−1.14620
$82$	−7.69137	−0.849370
$83$	−2.55372	−0.280307	−0.140153	−	0.990130i	$-0.544760\pi$
$83$	−2.55372	−0.280307	−0.140153	+	0.990130i	$0.544760\pi$
$84$	13.7949	1.50514
$85$	0	0
$86$	3.37094	0.363497
$87$	5.40683	0.579673
$88$	11.2777	1.20221
$89$	−4.35327	−0.461446	−0.230723	−	0.973019i	$-0.574109\pi$
$89$	−4.35327	−0.461446	−0.230723	+	0.973019i	$0.574109\pi$
$90$	0	0
$91$	6.22489	0.652546
$92$	−4.44627	−0.463555
$93$	0.466479	0.0483716
$94$	6.76964	0.698235
$95$	0	0
$96$	−13.2357	−1.35086
$97$	−9.02693	−0.916546	−0.458273	−	0.888811i	$-0.651532\pi$
$97$	−9.02693	−0.916546	−0.458273	+	0.888811i	$0.651532\pi$
$98$	4.13668	0.417867
$99$	−12.2446	−1.23063
$100$	0	0
$101$	6.94323	0.690877	0.345439	−	0.938441i	$-0.387730\pi$
$101$	6.94323	0.690877	0.345439	+	0.938441i	$0.387730\pi$
$102$	8.14300	0.806277
$103$	0.105009	0.0103469	0.00517343	−	0.999987i	$-0.498353\pi$
$103$	0.105009	0.0103469	0.00517343	+	0.999987i	$0.498353\pi$
$104$	−3.84037	−0.376580
$105$	0	0
$106$	−0.833897	−0.0809952
$107$	18.1842	1.75793	0.878966	−	0.476885i	$-0.158234\pi$
$107$	18.1842	1.75793	0.878966	+	0.476885i	$0.158234\pi$
$108$	−1.99849	−0.192305
$109$	14.6576	1.40394	0.701972	−	0.712205i	$-0.252303\pi$
$109$	14.6576	1.40394	0.701972	+	0.712205i	$0.252303\pi$
$110$	0	0
$111$	4.18720	0.397432
$112$	6.52470	0.616526
$113$	−1.08836	−0.102384	−0.0511922	−	0.998689i	$-0.516302\pi$
$113$	−1.08836	−0.102384	−0.0511922	+	0.998689i	$0.516302\pi$
$114$	−6.21479	−0.582068
$115$	0	0
$116$	3.70533	0.344031
$117$	4.16963	0.385483
$118$	3.64877	0.335896
$119$	−20.3360	−1.86420
$120$	0	0
$121$	13.6443	1.24040
$122$	−0.0483348	−0.00437603
$123$	28.5151	2.57112
$124$	0.319681	0.0287082
$125$	0	0
$126$	5.72786	0.510279
$127$	−0.364538	−0.0323475	−0.0161737	−	0.999869i	$-0.505148\pi$
$127$	−0.364538	−0.0323475	−0.0161737	+	0.999869i	$0.505148\pi$
$128$	−11.3054	−0.999263
$129$	−12.4975	−1.10034
$130$	0	0
$131$	5.48865	0.479546	0.239773	−	0.970829i	$-0.422927\pi$
$131$	5.48865	0.479546	0.239773	+	0.970829i	$0.422927\pi$
$132$	−18.5975	−1.61871
$133$	15.5205	1.34580
$134$	−7.95658	−0.687344
$135$	0	0
$136$	12.5460	1.07581
$137$	17.1533	1.46551	0.732754	−	0.680493i	$-0.238234\pi$
$137$	17.1533	1.46551	0.732754	+	0.680493i	$0.238234\pi$
$138$	−4.09162	−0.348302
$139$	−19.6074	−1.66308	−0.831539	−	0.555467i	$-0.812540\pi$
$139$	−19.6074	−1.66308	−0.831539	+	0.555467i	$0.812540\pi$
$140$	0	0
$141$	−25.0979	−2.11362
$142$	−3.28182	−0.275404
$143$	−8.39207	−0.701780
$144$	4.37046	0.364205
$145$	0	0
$146$	8.87525	0.734521
$147$	−15.3364	−1.26492
$148$	2.86951	0.235873
$149$	19.0508	1.56070	0.780350	−	0.625343i	$-0.215041\pi$
$149$	19.0508	1.56070	0.780350	+	0.625343i	$0.215041\pi$
$150$	0	0
$151$	−4.76802	−0.388016	−0.194008	−	0.981000i	$-0.562149\pi$
$151$	−4.76802	−0.388016	−0.194008	+	0.981000i	$0.562149\pi$
$152$	−9.57522	−0.776653
$153$	−13.6217	−1.10125
$154$	−11.5283	−0.928974
$155$	0	0
$156$	6.33297	0.507043
$157$	−6.12724	−0.489007	−0.244503	−	0.969648i	$-0.578625\pi$
$157$	−6.12724	−0.489007	−0.244503	+	0.969648i	$0.578625\pi$
$158$	4.93696	0.392764
$159$	3.09160	0.245180
$160$	0	0
$161$	10.2182	0.805310
$162$	−6.50561	−0.511129
$163$	1.20414	0.0943159	0.0471579	−	0.998887i	$-0.484984\pi$
$163$	1.20414	0.0943159	0.0471579	+	0.998887i	$0.484984\pi$
$164$	19.5416	1.52594
$165$	0	0
$166$	−1.61049	−0.124998
$167$	0.900391	0.0696744	0.0348372	−	0.999393i	$-0.488909\pi$
$167$	0.900391	0.0696744	0.0348372	+	0.999393i	$0.488909\pi$
$168$	19.5587	1.50899
$169$	−10.1423	−0.780175
$170$	0	0
$171$	10.3962	0.795015
$172$	−8.56459	−0.653044
$173$	−12.3564	−0.939436	−0.469718	−	0.882817i	$-0.655644\pi$
$173$	−12.3564	−0.939436	−0.469718	+	0.882817i	$0.655644\pi$
$174$	3.40979	0.258495
$175$	0	0
$176$	−8.79626	−0.663043
$177$	−13.5275	−1.01679
$178$	−2.74537	−0.205774
$179$	−10.0258	−0.749367	−0.374683	−	0.927153i	$-0.622249\pi$
$179$	−10.0258	−0.749367	−0.374683	+	0.927153i	$0.622249\pi$
$180$	0	0
$181$	−17.0491	−1.26725	−0.633623	−	0.773642i	$-0.718433\pi$
$181$	−17.0491	−1.26725	−0.633623	+	0.773642i	$0.718433\pi$
$182$	3.92569	0.290992
$183$	0.179197	0.0132467
$184$	−6.30402	−0.464739
$185$	0	0
$186$	0.294182	0.0215705
$187$	27.4159	2.00485
$188$	−17.1997	−1.25442
$189$	4.59286	0.334081
$190$	0	0
$191$	−23.7744	−1.72026	−0.860129	−	0.510077i	$-0.829617\pi$
$191$	−23.7744	−1.72026	−0.860129	+	0.510077i	$0.829617\pi$
$192$	−0.0613816	−0.00442984
$193$	−7.49373	−0.539411	−0.269705	−	0.962943i	$-0.586926\pi$
$193$	−7.49373	−0.539411	−0.269705	+	0.962943i	$0.586926\pi$
$194$	−5.69278	−0.408718
$195$	0	0
$196$	−10.5101	−0.750723
$197$	−1.85647	−0.132268	−0.0661339	−	0.997811i	$-0.521066\pi$
$197$	−1.85647	−0.132268	−0.0661339	+	0.997811i	$0.521066\pi$
$198$	−7.72201	−0.548779
$199$	3.46667	0.245746	0.122873	−	0.992422i	$-0.460789\pi$
$199$	3.46667	0.245746	0.122873	+	0.992422i	$0.460789\pi$
$200$	0	0
$201$	29.4984	2.08066
$202$	4.37871	0.308085
$203$	−8.51545	−0.597667
$204$	−20.6890	−1.44852
$205$	0	0
$206$	0.0662234	0.00461400
$207$	6.84451	0.475726
$208$	2.99537	0.207691
$209$	−20.9240	−1.44734
$210$	0	0
$211$	−2.33201	−0.160542	−0.0802711	−	0.996773i	$-0.525579\pi$
$211$	−2.33201	−0.160542	−0.0802711	+	0.996773i	$0.525579\pi$
$212$	2.11869	0.145512
$213$	12.1671	0.833674
$214$	11.4678	0.783919
$215$	0	0
$216$	−2.83351	−0.192796
$217$	−0.734678	−0.0498732
$218$	9.24373	0.626065
$219$	−32.9042	−2.22346
$220$	0	0
$221$	−9.33587	−0.627998
$222$	2.64063	0.177228
$223$	1.75535	0.117547	0.0587734	−	0.998271i	$-0.481281\pi$
$223$	1.75535	0.117547	0.0587734	+	0.998271i	$0.481281\pi$
$224$	20.8455	1.39280
$225$	0	0
$226$	−0.686369	−0.0456566
$227$	−4.35631	−0.289139	−0.144569	−	0.989495i	$-0.546180\pi$
$227$	−4.35631	−0.289139	−0.144569	+	0.989495i	$0.546180\pi$
$228$	15.7900	1.04572
$229$	6.24160	0.412457	0.206228	−	0.978504i	$-0.433881\pi$
$229$	6.24160	0.412457	0.206228	+	0.978504i	$0.433881\pi$
$230$	0	0
$231$	42.7401	2.81209
$232$	5.25351	0.344910
$233$	−13.8315	−0.906135	−0.453067	−	0.891476i	$-0.649670\pi$
$233$	−13.8315	−0.906135	−0.453067	+	0.891476i	$0.649670\pi$
$234$	2.62956	0.171899
$235$	0	0
$236$	−9.27048	−0.603457
$237$	−18.3034	−1.18893
$238$	−12.8248	−0.831306
$239$	−19.3924	−1.25439	−0.627194	−	0.778863i	$-0.715797\pi$
$239$	−19.3924	−1.25439	−0.627194	+	0.778863i	$0.715797\pi$
$240$	0	0
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	8.60473	0.553133
$243$	20.3772	1.30720
$244$	0.122805	0.00786178
$245$	0	0
$246$	17.9829	1.14655
$247$	7.12519	0.453365
$248$	0.453251	0.0287815
$249$	5.97075	0.378381
$250$	0	0
$251$	−14.4441	−0.911705	−0.455852	−	0.890055i	$-0.650666\pi$
$251$	−14.4441	−0.911705	−0.455852	+	0.890055i	$0.650666\pi$
$252$	−14.5529	−0.916745
$253$	−13.7757	−0.866071
$254$	−0.229894	−0.0144248
$255$	0	0
$256$	−7.18218	−0.448886
$257$	−28.9004	−1.80276	−0.901379	−	0.433031i	$-0.857444\pi$
$257$	−28.9004	−1.80276	−0.901379	+	0.433031i	$0.857444\pi$
$258$	−7.88146	−0.490678
$259$	−6.59460	−0.409769
$260$	0	0
$261$	−5.70393	−0.353064
$262$	3.46139	0.213845
$263$	−26.3078	−1.62221	−0.811103	−	0.584903i	$-0.801133\pi$
$263$	−26.3078	−1.62221	−0.811103	+	0.584903i	$0.801133\pi$
$264$	−26.3680	−1.62284
$265$	0	0
$266$	9.78794	0.600137
$267$	10.1782	0.622897
$268$	20.2154	1.23485
$269$	−9.42450	−0.574622	−0.287311	−	0.957837i	$-0.592761\pi$
$269$	−9.42450	−0.574622	−0.287311	+	0.957837i	$0.592761\pi$
$270$	0	0
$271$	−5.86519	−0.356285	−0.178142	−	0.984005i	$-0.557009\pi$
$271$	−5.86519	−0.356285	−0.178142	+	0.984005i	$0.557009\pi$
$272$	−9.78551	−0.593334
$273$	−14.5542	−0.880859
$274$	10.8177	0.653519
$275$	0	0
$276$	10.3956	0.625744
$277$	−5.60395	−0.336708	−0.168354	−	0.985727i	$-0.553845\pi$
$277$	−5.60395	−0.336708	−0.168354	+	0.985727i	$0.553845\pi$
$278$	−12.3653	−0.741621
$279$	−0.492111	−0.0294619
$280$	0	0
$281$	−4.71669	−0.281374	−0.140687	−	0.990054i	$-0.544931\pi$
$281$	−4.71669	−0.281374	−0.140687	+	0.990054i	$0.544931\pi$
$282$	−15.8278	−0.942534
$283$	−19.2068	−1.14173	−0.570864	−	0.821044i	$-0.693392\pi$
$283$	−19.2068	−1.14173	−0.570864	+	0.821044i	$0.693392\pi$
$284$	8.33817	0.494779
$285$	0	0
$286$	−5.29241	−0.312947
$287$	−44.9097	−2.65094
$288$	13.9630	0.822776
$289$	13.4992	0.794069
$290$	0	0
$291$	21.1055	1.23723
$292$	−22.5495	−1.31961
$293$	−13.0140	−0.760289	−0.380144	−	0.924927i	$-0.624126\pi$
$293$	−13.0140	−0.760289	−0.380144	+	0.924927i	$0.624126\pi$
$294$	−9.67181	−0.564071
$295$	0	0
$296$	4.06847	0.236475
$297$	−6.19185	−0.359288
$298$	12.0143	0.695968
$299$	4.69100	0.271288
$300$	0	0
$301$	19.6828	1.13450
$302$	−3.00692	−0.173029
$303$	−16.2337	−0.932602
$304$	7.46836	0.428340
$305$	0	0
$306$	−8.59045	−0.491083
$307$	11.5372	0.658463	0.329232	−	0.944249i	$-0.393210\pi$
$307$	11.5372	0.658463	0.329232	+	0.944249i	$0.393210\pi$
$308$	29.2900	1.66896
$309$	−0.245518	−0.0139670
$310$	0	0
$311$	−23.1542	−1.31296	−0.656478	−	0.754345i	$-0.727955\pi$
$311$	−23.1542	−1.31296	−0.656478	+	0.754345i	$0.727955\pi$
$312$	8.97903	0.508338
$313$	7.88902	0.445914	0.222957	−	0.974828i	$-0.428429\pi$
$313$	7.88902	0.445914	0.222957	+	0.974828i	$0.428429\pi$
$314$	−3.86411	−0.218064
$315$	0	0
$316$	−12.5434	−0.705623
$317$	2.38325	0.133857	0.0669283	−	0.997758i	$-0.478680\pi$
$317$	2.38325	0.133857	0.0669283	+	0.997758i	$0.478680\pi$
$318$	1.94970	0.109334
$319$	11.4801	0.642761
$320$	0	0
$321$	−42.5157	−2.37300
$322$	6.44407	0.359114
$323$	−23.2772	−1.29518
$324$	16.5289	0.918272
$325$	0	0
$326$	0.759387	0.0420585
$327$	−34.2704	−1.89516
$328$	27.7065	1.52984
$329$	39.5278	2.17924
$330$	0	0
$331$	−3.05598	−0.167972	−0.0839860	−	0.996467i	$-0.526765\pi$
$331$	−3.05598	−0.167972	−0.0839860	+	0.996467i	$0.526765\pi$
$332$	4.09179	0.224566
$333$	−4.41728	−0.242066
$334$	0.567827	0.0310701
$335$	0	0
$336$	−15.2551	−0.832237
$337$	16.1755	0.881134	0.440567	−	0.897720i	$-0.354777\pi$
$337$	16.1755	0.881134	0.440567	+	0.897720i	$0.354777\pi$
$338$	−6.39617	−0.347906
$339$	2.54466	0.138207
$340$	0	0
$341$	0.990454	0.0536361
$342$	6.55628	0.354523
$343$	−1.62227	−0.0875943
$344$	−12.1431	−0.654711
$345$	0	0
$346$	−7.79246	−0.418925
$347$	−24.4716	−1.31370	−0.656851	−	0.754020i	$-0.728112\pi$
$347$	−24.4716	−1.31370	−0.656851	+	0.754020i	$0.728112\pi$
$348$	−8.66329	−0.464401
$349$	−13.0468	−0.698380	−0.349190	−	0.937052i	$-0.613543\pi$
$349$	−13.0468	−0.698380	−0.349190	+	0.937052i	$0.613543\pi$
$350$	0	0
$351$	2.10849	0.112543
$352$	−28.1028	−1.49788
$353$	−23.6788	−1.26029	−0.630147	−	0.776476i	$-0.717005\pi$
$353$	−23.6788	−1.26029	−0.630147	+	0.776476i	$0.717005\pi$
$354$	−8.53104	−0.453420
$355$	0	0
$356$	6.97519	0.369685
$357$	47.5468	2.51644
$358$	−6.32274	−0.334167
$359$	−25.5499	−1.34847	−0.674236	−	0.738516i	$-0.735527\pi$
$359$	−25.5499	−1.34847	−0.674236	+	0.738516i	$0.735527\pi$
$360$	0	0
$361$	−1.23473	−0.0649857
$362$	−10.7519	−0.565107
$363$	−31.9013	−1.67439
$364$	−9.97406	−0.522783
$365$	0	0
$366$	0.113010	0.00590712
$367$	−8.35766	−0.436266	−0.218133	−	0.975919i	$-0.569997\pi$
$367$	−8.35766	−0.436266	−0.218133	+	0.975919i	$0.569997\pi$
$368$	4.91693	0.256313
$369$	−30.0820	−1.56601
$370$	0	0
$371$	−4.86910	−0.252791
$372$	−0.747433	−0.0387526
$373$	24.6934	1.27858	0.639288	−	0.768968i	$-0.279229\pi$
$373$	24.6934	1.27858	0.639288	+	0.768968i	$0.279229\pi$
$374$	17.2897	0.894028
$375$	0	0
$376$	−24.3862	−1.25762
$377$	−3.90928	−0.201338
$378$	2.89646	0.148978
$379$	18.6593	0.958465	0.479232	−	0.877688i	$-0.340915\pi$
$379$	18.6593	0.958465	0.479232	+	0.877688i	$0.340915\pi$
$380$	0	0
$381$	0.852312	0.0436652
$382$	−14.9932	−0.767119
$383$	−11.9780	−0.612049	−0.306025	−	0.952024i	$-0.598999\pi$
$383$	−11.9780	−0.612049	−0.306025	+	0.952024i	$0.598999\pi$
$384$	26.4327	1.34889
$385$	0	0
$386$	−4.72588	−0.240541
$387$	13.1842	0.670190
$388$	14.4637	0.734285
$389$	−7.62670	−0.386689	−0.193344	−	0.981131i	$-0.561933\pi$
$389$	−7.62670	−0.386689	−0.193344	+	0.981131i	$0.561933\pi$
$390$	0	0
$391$	−15.3249	−0.775016
$392$	−14.9015	−0.752639
$393$	−12.8328	−0.647330
$394$	−1.17077	−0.0589826
$395$	0	0
$396$	19.6194	0.985914
$397$	33.4013	1.67636	0.838181	−	0.545392i	$-0.183619\pi$
$397$	33.4013	1.67636	0.838181	+	0.545392i	$0.183619\pi$
$398$	2.18624	0.109586
$399$	−36.2880	−1.81667
$400$	0	0
$401$	−1.73530	−0.0866566	−0.0433283	−	0.999061i	$-0.513796\pi$
$401$	−1.73530	−0.0866566	−0.0433283	+	0.999061i	$0.513796\pi$
$402$	18.6030	0.927833
$403$	−0.337277	−0.0168010
$404$	−11.1251	−0.553492
$405$	0	0
$406$	−5.37022	−0.266519
$407$	8.89050	0.440686
$408$	−29.3334	−1.45222
$409$	−3.81908	−0.188841	−0.0944207	−	0.995532i	$-0.530100\pi$
$409$	−3.81908	−0.188841	−0.0944207	+	0.995532i	$0.530100\pi$
$410$	0	0
$411$	−40.1056	−1.97826
$412$	−0.168255	−0.00828932
$413$	21.3050	1.04835
$414$	4.31645	0.212142
$415$	0	0
$416$	9.56976	0.469196
$417$	45.8433	2.24496
$418$	−13.1956	−0.645418
$419$	0.640088	0.0312703	0.0156352	−	0.999878i	$-0.495023\pi$
$419$	0.640088	0.0312703	0.0156352	+	0.999878i	$0.495023\pi$
$420$	0	0
$421$	13.2765	0.647057	0.323528	−	0.946218i	$-0.395131\pi$
$421$	13.2765	0.647057	0.323528	+	0.946218i	$0.395131\pi$
$422$	−1.47067	−0.0715910
$423$	26.4770	1.28735
$424$	3.00394	0.145884
$425$	0	0
$426$	7.67310	0.371763
$427$	−0.282226	−0.0136579
$428$	−29.1363	−1.40836
$429$	19.6212	0.947320
$430$	0	0
$431$	−26.8180	−1.29178	−0.645888	−	0.763432i	$-0.723513\pi$
$431$	−26.8180	−1.29178	−0.645888	+	0.763432i	$0.723513\pi$
$432$	2.21005	0.106331
$433$	20.7392	0.996664	0.498332	−	0.866986i	$-0.333946\pi$
$433$	20.7392	0.996664	0.498332	+	0.866986i	$0.333946\pi$
$434$	−0.463320	−0.0222401
$435$	0	0
$436$	−23.4857	−1.12476
$437$	11.6961	0.559500
$438$	−20.7509	−0.991515
$439$	−12.7382	−0.607960	−0.303980	−	0.952678i	$-0.598316\pi$
$439$	−12.7382	−0.607960	−0.303980	+	0.952678i	$0.598316\pi$
$440$	0	0
$441$	16.1791	0.770433
$442$	−5.88761	−0.280045
$443$	−23.4058	−1.11204	−0.556022	−	0.831167i	$-0.687673\pi$
$443$	−23.4058	−1.11204	−0.556022	+	0.831167i	$0.687673\pi$
$444$	−6.70910	−0.318400
$445$	0	0
$446$	1.10700	0.0524180
$447$	−44.5419	−2.10676
$448$	0.0966726	0.00456735
$449$	35.8887	1.69369	0.846846	−	0.531838i	$-0.178498\pi$
$449$	35.8887	1.69369	0.846846	+	0.531838i	$0.178498\pi$
$450$	0	0
$451$	60.5449	2.85095
$452$	1.74387	0.0820247
$453$	11.1479	0.523775
$454$	−2.74728	−0.128936
$455$	0	0
$456$	22.3875	1.04839
$457$	23.4014	1.09467	0.547336	−	0.836913i	$-0.315642\pi$
$457$	23.4014	1.09467	0.547336	+	0.836913i	$0.315642\pi$
$458$	3.93623	0.183928
$459$	−6.88820	−0.321514
$460$	0	0
$461$	17.9146	0.834366	0.417183	−	0.908822i	$-0.363017\pi$
$461$	17.9146	0.834366	0.417183	+	0.908822i	$0.363017\pi$
$462$	26.9538	1.25400
$463$	32.0159	1.48790	0.743952	−	0.668233i	$-0.232949\pi$
$463$	32.0159	1.48790	0.743952	+	0.668233i	$0.232949\pi$
$464$	−4.09757	−0.190225
$465$	0	0
$466$	−8.72279	−0.404075
$467$	12.2949	0.568940	0.284470	−	0.958685i	$-0.408182\pi$
$467$	12.2949	0.568940	0.284470	+	0.958685i	$0.408182\pi$
$468$	−6.68095	−0.308827
$469$	−46.4583	−2.14524
$470$	0	0
$471$	14.3259	0.660101
$472$	−13.1439	−0.604997
$473$	−26.5353	−1.22010
$474$	−11.5429	−0.530184
$475$	0	0
$476$	32.5841	1.49349
$477$	−3.26148	−0.149333
$478$	−12.2297	−0.559373
$479$	15.1555	0.692472	0.346236	−	0.938148i	$-0.387460\pi$
$479$	15.1555	0.692472	0.346236	+	0.938148i	$0.387460\pi$
$480$	0	0
$481$	−3.02746	−0.138040
$482$	−0.630644	−0.0287251
$483$	−23.8909	−1.08707
$484$	−21.8622	−0.993735
$485$	0	0
$486$	12.8508	0.582922
$487$	15.5008	0.702407	0.351204	−	0.936299i	$-0.385773\pi$
$487$	15.5008	0.702407	0.351204	+	0.936299i	$0.385773\pi$
$488$	0.174116	0.00788186
$489$	−2.81536	−0.127315
$490$	0	0
$491$	12.5838	0.567901	0.283950	−	0.958839i	$-0.408355\pi$
$491$	12.5838	0.567901	0.283950	+	0.958839i	$0.408355\pi$
$492$	−45.6894	−2.05984
$493$	12.7712	0.575184
$494$	4.49346	0.202170
$495$	0	0
$496$	−0.353521	−0.0158736
$497$	−19.1625	−0.859553
$498$	3.76542	0.168732
$499$	−41.9638	−1.87856	−0.939280	−	0.343152i	$-0.888505\pi$
$499$	−41.9638	−1.87856	−0.939280	+	0.343152i	$0.888505\pi$
$500$	0	0
$501$	−2.10517	−0.0940521
$502$	−9.10910	−0.406559
$503$	−7.23458	−0.322574	−0.161287	−	0.986908i	$-0.551564\pi$
$503$	−7.23458	−0.322574	−0.161287	+	0.986908i	$0.551564\pi$
$504$	−20.6334	−0.919085
$505$	0	0
$506$	−8.68756	−0.386209
$507$	23.7133	1.05314
$508$	0.584094	0.0259150
$509$	43.2945	1.91899	0.959497	−	0.281718i	$-0.0909041\pi$
$509$	43.2945	1.91899	0.959497	+	0.281718i	$0.0909041\pi$
$510$	0	0
$511$	51.8223	2.29248
$512$	18.0813	0.799090
$513$	5.25712	0.232108
$514$	−18.2259	−0.803909
$515$	0	0
$516$	20.0245	0.881531
$517$	−53.2893	−2.34366
$518$	−4.15885	−0.182729
$519$	28.8899	1.26813
$520$	0	0
$521$	−22.7560	−0.996961	−0.498480	−	0.866901i	$-0.666108\pi$
$521$	−22.7560	−0.996961	−0.498480	+	0.866901i	$0.666108\pi$
$522$	−3.59715	−0.157443
$523$	−36.7529	−1.60709	−0.803547	−	0.595241i	$-0.797056\pi$
$523$	−36.7529	−1.60709	−0.803547	+	0.595241i	$0.797056\pi$
$524$	−8.79440	−0.384185
$525$	0	0
$526$	−16.5908	−0.723395
$527$	1.10184	0.0479970
$528$	20.5662	0.895029
$529$	−15.2997	−0.665203
$530$	0	0
$531$	14.2708	0.619301
$532$	−24.8684	−1.07818
$533$	−20.6172	−0.893030
$534$	6.41884	0.277770
$535$	0	0
$536$	28.6619	1.23801
$537$	23.4410	1.01156
$538$	−5.94351	−0.256243
$539$	−32.5631	−1.40259
$540$	0	0
$541$	−19.7726	−0.850089	−0.425045	−	0.905172i	$-0.639742\pi$
$541$	−19.7726	−0.850089	−0.425045	+	0.905172i	$0.639742\pi$
$542$	−3.69885	−0.158879
$543$	39.8617	1.71063
$544$	−31.2633	−1.34040
$545$	0	0
$546$	−9.17851	−0.392804
$547$	9.94319	0.425140	0.212570	−	0.977146i	$-0.431817\pi$
$547$	9.94319	0.425140	0.212570	+	0.977146i	$0.431817\pi$
$548$	−27.4846	−1.17408
$549$	−0.189044	−0.00806820
$550$	0	0
$551$	−9.74703	−0.415238
$552$	14.7392	0.627342
$553$	28.8268	1.22584
$554$	−3.53410	−0.150149
$555$	0	0
$556$	31.4167	1.33236
$557$	7.84163	0.332260	0.166130	−	0.986104i	$-0.446873\pi$
$557$	7.84163	0.332260	0.166130	+	0.986104i	$0.446873\pi$
$558$	−0.310347	−0.0131380
$559$	9.03601	0.382182
$560$	0	0
$561$	−64.1001	−2.70631
$562$	−2.97455	−0.125474
$563$	19.2105	0.809625	0.404813	−	0.914400i	$-0.367337\pi$
$563$	19.2105	0.809625	0.404813	+	0.914400i	$0.367337\pi$
$564$	40.2140	1.69332
$565$	0	0
$566$	−12.1127	−0.509134
$567$	−37.9861	−1.59526
$568$	11.8221	0.496043
$569$	25.1338	1.05366	0.526831	−	0.849970i	$-0.323380\pi$
$569$	25.1338	1.05366	0.526831	+	0.849970i	$0.323380\pi$
$570$	0	0
$571$	−18.1912	−0.761277	−0.380638	−	0.924724i	$-0.624296\pi$
$571$	−18.1912	−0.761277	−0.380638	+	0.924724i	$0.624296\pi$
$572$	13.4465	0.562227
$573$	55.5861	2.32214
$574$	−28.3220	−1.18214
$575$	0	0
$576$	0.0647545	0.00269810
$577$	−28.9417	−1.20486	−0.602429	−	0.798172i	$-0.705800\pi$
$577$	−28.9417	−1.20486	−0.602429	+	0.798172i	$0.705800\pi$
$578$	8.51317	0.354101
$579$	17.5208	0.728140
$580$	0	0
$581$	−9.40358	−0.390126
$582$	13.3101	0.551721
$583$	6.56427	0.271864
$584$	−31.9712	−1.32298
$585$	0	0
$586$	−8.20724	−0.339038
$587$	21.9772	0.907098	0.453549	−	0.891231i	$-0.350158\pi$
$587$	21.9772	0.907098	0.453549	+	0.891231i	$0.350158\pi$
$588$	24.5733	1.01339
$589$	−0.840934	−0.0346501
$590$	0	0
$591$	4.34054	0.178546
$592$	−3.17327	−0.130421
$593$	−15.0138	−0.616544	−0.308272	−	0.951298i	$-0.599751\pi$
$593$	−15.0138	−0.616544	−0.308272	+	0.951298i	$0.599751\pi$
$594$	−3.90486	−0.160218
$595$	0	0
$596$	−30.5248	−1.25035
$597$	−8.10529	−0.331728
$598$	2.95835	0.120976
$599$	−31.7086	−1.29558	−0.647789	−	0.761820i	$-0.724306\pi$
$599$	−31.7086	−1.29558	−0.647789	+	0.761820i	$0.724306\pi$
$600$	0	0
$601$	5.63682	0.229931	0.114965	−	0.993369i	$-0.463324\pi$
$601$	5.63682	0.229931	0.114965	+	0.993369i	$0.463324\pi$
$602$	12.4129	0.505910
$603$	−31.1193	−1.26727
$604$	7.63973	0.310856
$605$	0	0
$606$	−10.2377	−0.415878
$607$	−39.7534	−1.61354	−0.806770	−	0.590866i	$-0.798786\pi$
$607$	−39.7534	−1.61354	−0.806770	+	0.590866i	$0.798786\pi$
$608$	23.8603	0.967664
$609$	19.9096	0.806780
$610$	0	0
$611$	18.1465	0.734127
$612$	21.8259	0.882259
$613$	−30.3066	−1.22407	−0.612035	−	0.790831i	$-0.709649\pi$
$613$	−30.3066	−1.22407	−0.612035	+	0.790831i	$0.709649\pi$
$614$	7.27588	0.293631
$615$	0	0
$616$	41.5281	1.67322
$617$	−18.2240	−0.733670	−0.366835	−	0.930286i	$-0.619559\pi$
$617$	−18.2240	−0.733670	−0.366835	+	0.930286i	$0.619559\pi$
$618$	−0.154834	−0.00622836
$619$	−26.3431	−1.05882	−0.529409	−	0.848366i	$-0.677586\pi$
$619$	−26.3431	−1.05882	−0.529409	+	0.848366i	$0.677586\pi$
$620$	0	0
$621$	3.46112	0.138890
$622$	−14.6021	−0.585491
$623$	−16.0301	−0.642233
$624$	−7.00335	−0.280359
$625$	0	0
$626$	4.97516	0.198848
$627$	48.9216	1.95374
$628$	9.81759	0.391765
$629$	9.89035	0.394354
$630$	0	0
$631$	18.4187	0.733236	0.366618	−	0.930372i	$-0.380516\pi$
$631$	18.4187	0.733236	0.366618	+	0.930372i	$0.380516\pi$
$632$	−17.7844	−0.707424
$633$	5.45238	0.216713
$634$	1.50298	0.0596910
$635$	0	0
$636$	−4.95364	−0.196425
$637$	11.0886	0.439347
$638$	7.23985	0.286629
$639$	−12.8356	−0.507770
$640$	0	0
$641$	−12.6956	−0.501446	−0.250723	−	0.968059i	$-0.580668\pi$
$641$	−12.6956	−0.501446	−0.250723	+	0.968059i	$0.580668\pi$
$642$	−26.8123	−1.05820
$643$	35.1591	1.38654	0.693270	−	0.720678i	$-0.256169\pi$
$643$	35.1591	1.38654	0.693270	+	0.720678i	$0.256169\pi$
$644$	−16.3725	−0.645169
$645$	0	0
$646$	−14.6796	−0.577561
$647$	−19.7535	−0.776588	−0.388294	−	0.921535i	$-0.626936\pi$
$647$	−19.7535	−0.776588	−0.388294	+	0.921535i	$0.626936\pi$
$648$	23.4351	0.920616
$649$	−28.7224	−1.12745
$650$	0	0
$651$	1.71772	0.0673228
$652$	−1.92939	−0.0755606
$653$	44.0129	1.72236	0.861178	−	0.508303i	$-0.169727\pi$
$653$	44.0129	1.72236	0.861178	+	0.508303i	$0.169727\pi$
$654$	−21.6124	−0.845113
$655$	0	0
$656$	−21.6102	−0.843736
$657$	34.7123	1.35426
$658$	24.9280	0.971793
$659$	−32.2032	−1.25446	−0.627229	−	0.778835i	$-0.715811\pi$
$659$	−32.2032	−1.25446	−0.627229	+	0.778835i	$0.715811\pi$
$660$	0	0
$661$	29.5485	1.14930	0.574651	−	0.818398i	$-0.305138\pi$
$661$	29.5485	1.14930	0.574651	+	0.818398i	$0.305138\pi$
$662$	−1.92724	−0.0749043
$663$	21.8278	0.847723
$664$	5.80143	0.225139
$665$	0	0
$666$	−2.78573	−0.107945
$667$	−6.41714	−0.248473
$668$	−1.44269	−0.0558192
$669$	−4.10412	−0.158674
$670$	0	0
$671$	0.380482	0.0146883
$672$	−48.7380	−1.88011
$673$	−28.4424	−1.09637	−0.548186	−	0.836356i	$-0.684681\pi$
$673$	−28.4424	−1.09637	−0.548186	+	0.836356i	$0.684681\pi$
$674$	10.2010	0.392927
$675$	0	0
$676$	16.2508	0.625032
$677$	−16.9259	−0.650514	−0.325257	−	0.945626i	$-0.605451\pi$
$677$	−16.9259	−0.650514	−0.325257	+	0.945626i	$0.605451\pi$
$678$	1.60477	0.0616310
$679$	−33.2400	−1.27563
$680$	0	0
$681$	10.1853	0.390303
$682$	0.624625	0.0239181
$683$	29.0324	1.11090	0.555448	−	0.831551i	$-0.312547\pi$
$683$	29.0324	1.11090	0.555448	+	0.831551i	$0.312547\pi$
$684$	−16.6576	−0.636921
$685$	0	0
$686$	−1.02307	−0.0390612
$687$	−14.5933	−0.556767
$688$	9.47121	0.361087
$689$	−2.23531	−0.0851586
$690$	0	0
$691$	−21.5798	−0.820935	−0.410467	−	0.911875i	$-0.634634\pi$
$691$	−21.5798	−0.820935	−0.410467	+	0.911875i	$0.634634\pi$
$692$	19.7984	0.752623
$693$	−45.0886	−1.71277
$694$	−15.4329	−0.585823
$695$	0	0
$696$	−12.2830	−0.465587
$697$	67.3540	2.55121
$698$	−8.22790	−0.311431
$699$	32.3390	1.22317
$700$	0	0
$701$	−13.2247	−0.499489	−0.249744	−	0.968312i	$-0.580347\pi$
$701$	−13.2247	−0.499489	−0.249744	+	0.968312i	$0.580347\pi$
$702$	1.32971	0.0501867
$703$	−7.54838	−0.284692
$704$	−0.130329	−0.00491196
$705$	0	0
$706$	−14.9329	−0.562006
$707$	25.5672	0.961552
$708$	21.6750	0.814595
$709$	18.8314	0.707228	0.353614	−	0.935391i	$-0.384953\pi$
$709$	18.8314	0.707228	0.353614	+	0.935391i	$0.384953\pi$
$710$	0	0
$711$	19.3091	0.724149
$712$	9.88960	0.370628
$713$	−0.553644	−0.0207341
$714$	29.9851	1.12216
$715$	0	0
$716$	16.0643	0.600351
$717$	45.3406	1.69328
$718$	−16.1129	−0.601328
$719$	−37.7936	−1.40946	−0.704731	−	0.709475i	$-0.748932\pi$
$719$	−37.7936	−1.40946	−0.704731	+	0.709475i	$0.748932\pi$
$720$	0	0
$721$	0.386677	0.0144006
$722$	−0.778675	−0.0289793
$723$	2.33806	0.0869535
$724$	27.3175	1.01525
$725$	0	0
$726$	−20.1184	−0.746664
$727$	9.96692	0.369653	0.184826	−	0.982771i	$-0.440828\pi$
$727$	9.96692	0.369653	0.184826	+	0.982771i	$0.440828\pi$
$728$	−14.1415	−0.524118
$729$	−16.6957	−0.618359
$730$	0	0
$731$	−29.5196	−1.09182
$732$	−0.287126	−0.0106125
$733$	−46.8282	−1.72964	−0.864819	−	0.502083i	$-0.832567\pi$
$733$	−46.8282	−1.72964	−0.864819	+	0.502083i	$0.832567\pi$
$734$	−5.27071	−0.194546
$735$	0	0
$736$	15.7089	0.579037
$737$	62.6326	2.30710
$738$	−18.9710	−0.698333
$739$	31.1213	1.14482	0.572408	−	0.819969i	$-0.306009\pi$
$739$	31.1213	1.14482	0.572408	+	0.819969i	$0.306009\pi$
$740$	0	0
$741$	−16.6591	−0.611989
$742$	−3.07067	−0.112728
$743$	22.3465	0.819815	0.409907	−	0.912127i	$-0.365561\pi$
$743$	22.3465	0.819815	0.409907	+	0.912127i	$0.365561\pi$
$744$	−1.05973	−0.0388516
$745$	0	0
$746$	15.5728	0.570159
$747$	−6.29883	−0.230462
$748$	−43.9282	−1.60617
$749$	66.9599	2.44666
$750$	0	0
$751$	−41.3430	−1.50863	−0.754313	−	0.656515i	$-0.772030\pi$
$751$	−41.3430	−1.50863	−0.754313	+	0.656515i	$0.772030\pi$
$752$	19.0204	0.693604
$753$	33.7713	1.23069
$754$	−2.46537	−0.0897834
$755$	0	0
$756$	−7.35908	−0.267647
$757$	5.70532	0.207364	0.103682	−	0.994611i	$-0.466938\pi$
$757$	5.70532	0.207364	0.103682	+	0.994611i	$0.466938\pi$
$758$	11.7674	0.427411
$759$	32.2084	1.16909
$760$	0	0
$761$	15.1656	0.549754	0.274877	−	0.961479i	$-0.411363\pi$
$761$	15.1656	0.549754	0.274877	+	0.961479i	$0.411363\pi$
$762$	0.537505	0.0194718
$763$	53.9739	1.95399
$764$	38.0935	1.37817
$765$	0	0
$766$	−7.55388	−0.272933
$767$	9.78075	0.353162
$768$	16.7924	0.605943
$769$	5.23538	0.188793	0.0943964	−	0.995535i	$-0.469908\pi$
$769$	5.23538	0.188793	0.0943964	+	0.995535i	$0.469908\pi$
$770$	0	0
$771$	67.5710	2.43351
$772$	12.0071	0.432145
$773$	27.0422	0.972641	0.486321	−	0.873780i	$-0.338339\pi$
$773$	27.0422	0.972641	0.486321	+	0.873780i	$0.338339\pi$
$774$	8.31453	0.298860
$775$	0	0
$776$	20.5070	0.736160
$777$	15.4186	0.553139
$778$	−4.80973	−0.172437
$779$	−51.4050	−1.84177
$780$	0	0
$781$	25.8338	0.924407
$782$	−9.66459	−0.345605
$783$	−2.88435	−0.103078
$784$	11.6227	0.415096
$785$	0	0
$786$	−8.09294	−0.288666
$787$	25.6221	0.913329	0.456665	−	0.889639i	$-0.349044\pi$
$787$	25.6221	0.913329	0.456665	+	0.889639i	$0.349044\pi$
$788$	2.97459	0.105966
$789$	61.5092	2.18979
$790$	0	0
$791$	−4.00769	−0.142497
$792$	27.8169	0.988431
$793$	−0.129565	−0.00460097
$794$	21.0643	0.747545
$795$	0	0
$796$	−5.55460	−0.196878
$797$	−28.8151	−1.02068	−0.510341	−	0.859972i	$-0.670481\pi$
$797$	−28.8151	−1.02068	−0.510341	+	0.859972i	$0.670481\pi$
$798$	−22.8848	−0.810114
$799$	−59.2823	−2.09726
$800$	0	0
$801$	−10.7375	−0.379391
$802$	−1.09436	−0.0386430
$803$	−69.8642	−2.46545
$804$	−47.2649	−1.66690
$805$	0	0
$806$	−0.212702	−0.00749210
$807$	22.0351	0.775671
$808$	−15.7734	−0.554905
$809$	20.6265	0.725188	0.362594	−	0.931947i	$-0.381891\pi$
$809$	20.6265	0.725188	0.362594	+	0.931947i	$0.381891\pi$
$810$	0	0
$811$	45.2088	1.58749	0.793747	−	0.608248i	$-0.208127\pi$
$811$	45.2088	1.58749	0.793747	+	0.608248i	$0.208127\pi$
$812$	13.6442	0.478817
$813$	13.7132	0.480942
$814$	5.60675	0.196516
$815$	0	0
$816$	22.8791	0.800930
$817$	22.5295	0.788208
$818$	−2.40848	−0.0842106
$819$	15.3539	0.536509
$820$	0	0
$821$	23.2674	0.812039	0.406019	−	0.913864i	$-0.366917\pi$
$821$	23.2674	0.812039	0.406019	+	0.913864i	$0.366917\pi$
$822$	−25.2924	−0.882172
$823$	−2.12031	−0.0739095	−0.0369547	−	0.999317i	$-0.511766\pi$
$823$	−2.12031	−0.0739095	−0.0369547	+	0.999317i	$0.511766\pi$
$824$	−0.238556	−0.00831049
$825$	0	0
$826$	13.4359	0.467495
$827$	16.5417	0.575213	0.287606	−	0.957749i	$-0.407141\pi$
$827$	16.5417	0.575213	0.287606	+	0.957749i	$0.407141\pi$
$828$	−10.9669	−0.381125
$829$	2.61675	0.0908835	0.0454418	−	0.998967i	$-0.485530\pi$
$829$	2.61675	0.0908835	0.0454418	+	0.998967i	$0.485530\pi$
$830$	0	0
$831$	13.1024	0.454516
$832$	0.0443806	0.00153862
$833$	−36.2252	−1.25513
$834$	28.9108	1.00110
$835$	0	0
$836$	33.5263	1.15953
$837$	−0.248850	−0.00860152
$838$	0.403668	0.0139445
$839$	40.9480	1.41368	0.706841	−	0.707373i	$-0.250120\pi$
$839$	40.9480	1.41368	0.706841	+	0.707373i	$0.250120\pi$
$840$	0	0
$841$	−23.6522	−0.815594
$842$	8.37275	0.288544
$843$	11.0279	0.379821
$844$	3.73655	0.128617
$845$	0	0
$846$	16.6976	0.574074
$847$	50.2428	1.72636
$848$	−2.34297	−0.0804580
$849$	44.9068	1.54120
$850$	0	0
$851$	−4.96961	−0.170356
$852$	−19.4952	−0.667893
$853$	−17.3933	−0.595537	−0.297768	−	0.954638i	$-0.596242\pi$
$853$	−17.3933	−0.595537	−0.297768	+	0.954638i	$0.596242\pi$
$854$	−0.177984	−0.00609049
$855$	0	0
$856$	−41.3101	−1.41195
$857$	−16.7101	−0.570805	−0.285402	−	0.958408i	$-0.592127\pi$
$857$	−16.7101	−0.570805	−0.285402	+	0.958408i	$0.592127\pi$
$858$	12.3740	0.422441
$859$	13.9877	0.477255	0.238628	−	0.971111i	$-0.423302\pi$
$859$	13.9877	0.477255	0.238628	+	0.971111i	$0.423302\pi$
$860$	0	0
$861$	105.002	3.57845
$862$	−16.9126	−0.576045
$863$	23.1575	0.788290	0.394145	−	0.919048i	$-0.371041\pi$
$863$	23.1575	0.788290	0.394145	+	0.919048i	$0.371041\pi$
$864$	7.06078	0.240212
$865$	0	0
$866$	13.0791	0.444445
$867$	−31.5619	−1.07190
$868$	1.17716	0.0399556
$869$	−38.8628	−1.31833
$870$	0	0
$871$	−21.3281	−0.722676
$872$	−33.2986	−1.12763
$873$	−22.2652	−0.753564
$874$	7.37608	0.249499
$875$	0	0
$876$	52.7221	1.78131
$877$	−40.3104	−1.36119	−0.680594	−	0.732661i	$-0.738278\pi$
$877$	−40.3104	−1.36119	−0.680594	+	0.732661i	$0.738278\pi$
$878$	−8.03326	−0.271110
$879$	30.4276	1.02630
$880$	0	0
$881$	−23.2156	−0.782152	−0.391076	−	0.920358i	$-0.627897\pi$
$881$	−23.2156	−0.782152	−0.391076	+	0.920358i	$0.627897\pi$
$882$	10.2033	0.343562
$883$	0.920055	0.0309623	0.0154812	−	0.999880i	$-0.495072\pi$
$883$	0.920055	0.0309623	0.0154812	+	0.999880i	$0.495072\pi$
$884$	14.9587	0.503117
$885$	0	0
$886$	−14.7608	−0.495897
$887$	28.9082	0.970643	0.485321	−	0.874336i	$-0.338703\pi$
$887$	28.9082	0.970643	0.485321	+	0.874336i	$0.338703\pi$
$888$	−9.51233	−0.319213
$889$	−1.34234	−0.0450207
$890$	0	0
$891$	51.2109	1.71563
$892$	−2.81257	−0.0941720
$893$	45.2446	1.51405
$894$	−28.0901	−0.939473
$895$	0	0
$896$	−41.6299	−1.39076
$897$	−10.9679	−0.366206
$898$	22.6330	0.755273
$899$	0.461384	0.0153880
$900$	0	0
$901$	7.30250	0.243282
$902$	38.1823	1.27133
$903$	−46.0196	−1.53144
$904$	2.47250	0.0822341
$905$	0	0
$906$	7.03037	0.233568
$907$	−36.3884	−1.20826	−0.604128	−	0.796887i	$-0.706478\pi$
$907$	−36.3884	−1.20826	−0.604128	+	0.796887i	$0.706478\pi$
$908$	6.98007	0.231642
$909$	17.1257	0.568024
$910$	0	0
$911$	−10.8289	−0.358776	−0.179388	−	0.983778i	$-0.557412\pi$
$911$	−10.8289	−0.358776	−0.179388	+	0.983778i	$0.557412\pi$
$912$	−17.4615	−0.578208
$913$	12.6774	0.419562
$914$	14.7580	0.488150
$915$	0	0
$916$	−10.0008	−0.330437
$917$	20.2110	0.667424
$918$	−4.34401	−0.143374
$919$	28.3998	0.936823	0.468412	−	0.883510i	$-0.344826\pi$
$919$	28.3998	0.936823	0.468412	+	0.883510i	$0.344826\pi$
$920$	0	0
$921$	−26.9747	−0.888847
$922$	11.2977	0.372071
$923$	−8.79712	−0.289561
$924$	−68.4820	−2.25289
$925$	0	0
$926$	20.1906	0.663505
$927$	0.259009	0.00850696
$928$	−13.0911	−0.429737
$929$	−32.8431	−1.07755	−0.538774	−	0.842451i	$-0.681112\pi$
$929$	−32.8431	−1.07755	−0.538774	+	0.842451i	$0.681112\pi$
$930$	0	0
$931$	27.6473	0.906104
$932$	22.1621	0.725944
$933$	54.1361	1.77233
$934$	7.75371	0.253709
$935$	0	0
$936$	−9.47242	−0.309616
$937$	−4.11911	−0.134566	−0.0672828	−	0.997734i	$-0.521433\pi$
$937$	−4.11911	−0.134566	−0.0672828	+	0.997734i	$0.521433\pi$
$938$	−29.2986	−0.956635
$939$	−18.4450	−0.601930
$940$	0	0
$941$	−8.26409	−0.269402	−0.134701	−	0.990886i	$-0.543007\pi$
$941$	−8.26409	−0.269402	−0.134701	+	0.990886i	$0.543007\pi$
$942$	9.03452	0.294361
$943$	−33.8434	−1.10209
$944$	10.2518	0.333668
$945$	0	0
$946$	−16.7344	−0.544081
$947$	−43.3860	−1.40986	−0.704928	−	0.709279i	$-0.749021\pi$
$947$	−43.3860	−1.40986	−0.704928	+	0.709279i	$0.749021\pi$
$948$	29.3273	0.952506
$949$	23.7907	0.772277
$950$	0	0
$951$	−5.57218	−0.180690
$952$	46.1985	1.49730
$953$	26.7790	0.867457	0.433728	−	0.901044i	$-0.357198\pi$
$953$	26.7790	0.867457	0.433728	+	0.901044i	$0.357198\pi$
$954$	−2.05684	−0.0665925
$955$	0	0
$956$	31.0722	1.00495
$957$	−26.8412	−0.867651
$958$	9.55772	0.308796
$959$	63.1640	2.03967
$960$	0	0
$961$	−30.9602	−0.998716
$962$	−1.90925	−0.0615567
$963$	44.8519	1.44533
$964$	1.60229	0.0516062
$965$	0	0
$966$	−15.0666	−0.484761
$967$	−7.46107	−0.239932	−0.119966	−	0.992778i	$-0.538279\pi$
$967$	−7.46107	−0.239932	−0.119966	+	0.992778i	$0.538279\pi$
$968$	−30.9967	−0.996272
$969$	54.4234	1.74833
$970$	0	0
$971$	−21.4365	−0.687931	−0.343966	−	0.938982i	$-0.611770\pi$
$971$	−21.4365	−0.687931	−0.343966	+	0.938982i	$0.611770\pi$
$972$	−32.6501	−1.04725
$973$	−72.2006	−2.31465
$974$	9.77548	0.313226
$975$	0	0
$976$	−0.135805	−0.00434700
$977$	30.9584	0.990446	0.495223	−	0.868766i	$-0.335086\pi$
$977$	30.9584	0.990446	0.495223	+	0.868766i	$0.335086\pi$
$978$	−1.77549	−0.0567740
$979$	21.6110	0.690690
$980$	0	0
$981$	36.1535	1.15429
$982$	7.93592	0.253246
$983$	−13.6397	−0.435040	−0.217520	−	0.976056i	$-0.569797\pi$
$983$	−13.6397	−0.435040	−0.217520	+	0.976056i	$0.569797\pi$
$984$	−64.7796	−2.06510
$985$	0	0
$986$	8.05406	0.256494
$987$	−92.4183	−2.94171
$988$	−11.4166	−0.363211
$989$	14.8327	0.471653
$990$	0	0
$991$	−46.0458	−1.46269	−0.731347	−	0.682006i	$-0.761108\pi$
$991$	−46.0458	−1.46269	−0.731347	+	0.682006i	$0.761108\pi$
$992$	−1.12945	−0.0358600
$993$	7.14508	0.226742
$994$	−12.0847	−0.383303
$995$	0	0
$996$	−9.56685	−0.303137
$997$	−57.1775	−1.81083	−0.905415	−	0.424527i	$-0.860440\pi$
$997$	−57.1775	−1.81083	−0.905415	+	0.424527i	$0.860440\pi$
$998$	−26.4643	−0.837711
$999$	−2.23373	−0.0706719

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.f.1.4		7
5.4	even	2		241.2.a.a.1.4	✓	7
15.14	odd	2		2169.2.a.e.1.4		7
20.19	odd	2		3856.2.a.j.1.1		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
241.2.a.a.1.4	✓	7	5.4	even	2
2169.2.a.e.1.4		7	15.14	odd	2
3856.2.a.j.1.1		7	20.19	odd	2
6025.2.a.f.1.4		7	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6025 = 5^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6025.a (trivial)

\(f(q)\)	\(=\)	\(q+0.630644 q^{2} -2.33806 q^{3} -1.60229 q^{4} -1.47449 q^{6} +3.68231 q^{7} -2.27176 q^{8} +2.46654 q^{9} +O(q^{10})\)	\(q+0.630644 q^{2} -2.33806 q^{3} -1.60229 q^{4} -1.47449 q^{6} +3.68231 q^{7} -2.27176 q^{8} +2.46654 q^{9} -4.96431 q^{11} +3.74625 q^{12} +1.69048 q^{13} +2.32223 q^{14} +1.77190 q^{16} -5.52260 q^{17} +1.55551 q^{18} +4.21489 q^{19} -8.60948 q^{21} -3.13071 q^{22} +2.77495 q^{23} +5.31152 q^{24} +1.06609 q^{26} +1.24727 q^{27} -5.90013 q^{28} -2.31253 q^{29} -0.199515 q^{31} +5.66096 q^{32} +11.6069 q^{33} -3.48280 q^{34} -3.95210 q^{36} -1.79089 q^{37} +2.65809 q^{38} -3.95245 q^{39} -12.1960 q^{41} -5.42952 q^{42} +5.34523 q^{43} +7.95425 q^{44} +1.75001 q^{46} +10.7345 q^{47} -4.14282 q^{48} +6.55944 q^{49} +12.9122 q^{51} -2.70864 q^{52} -1.32229 q^{53} +0.786587 q^{54} -8.36534 q^{56} -9.85467 q^{57} -1.45838 q^{58} +5.78578 q^{59} -0.0766435 q^{61} -0.125823 q^{62} +9.08256 q^{63} +0.0262532 q^{64} +7.31980 q^{66} -12.6166 q^{67} +8.84880 q^{68} -6.48800 q^{69} -5.20391 q^{71} -5.60338 q^{72} +14.0733 q^{73} -1.12941 q^{74} -6.75346 q^{76} -18.2801 q^{77} -2.49259 q^{78} +7.82844 q^{79} -10.3158 q^{81} -7.69137 q^{82} -2.55372 q^{83} +13.7949 q^{84} +3.37094 q^{86} +5.40683 q^{87} +11.2777 q^{88} -4.35327 q^{89} +6.22489 q^{91} -4.44627 q^{92} +0.466479 q^{93} +6.76964 q^{94} -13.2357 q^{96} -9.02693 q^{97} +4.13668 q^{98} -12.2446 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 4 q^{2} + 3 q^{3} + 2 q^{4} - 5 q^{6} + 7 q^{7} + 6 q^{8} - 2 q^{9}+O(q^{10}) \) 7 * q + 4 * q^2 + 3 * q^3 + 2 * q^4 - 5 * q^6 + 7 * q^7 + 6 * q^8 - 2 * q^9	\( 7 q + 4 q^{2} + 3 q^{3} + 2 q^{4} - 5 q^{6} + 7 q^{7} + 6 q^{8} - 2 q^{9} - 18 q^{11} - q^{12} + q^{13} - 6 q^{14} + 4 q^{16} + 2 q^{17} - 8 q^{18} - 6 q^{19} - 2 q^{21} - 10 q^{22} + 22 q^{23} - 3 q^{24} + 8 q^{26} - 3 q^{27} - 9 q^{28} - 16 q^{29} - 18 q^{31} + 6 q^{32} - 4 q^{33} + 11 q^{34} - 7 q^{36} - 8 q^{37} - 16 q^{38} - 9 q^{39} - 15 q^{41} - 19 q^{42} - 14 q^{43} - 4 q^{44} + 11 q^{46} + 10 q^{47} - 31 q^{48} + 6 q^{49} + 13 q^{51} - 27 q^{52} - 15 q^{53} + 16 q^{54} + 13 q^{56} - 14 q^{57} - 17 q^{58} - 18 q^{59} + 4 q^{61} - 13 q^{62} + 16 q^{63} + 2 q^{64} + 16 q^{66} - 18 q^{67} + 15 q^{68} + 26 q^{69} - 50 q^{71} - 30 q^{72} + 10 q^{74} - 20 q^{76} - 17 q^{77} + 32 q^{78} - 15 q^{79} - 9 q^{81} - 45 q^{82} + 24 q^{83} + 6 q^{84} - 23 q^{86} - 12 q^{87} - 8 q^{88} - 13 q^{89} - 12 q^{91} + 10 q^{92} - 14 q^{93} - 32 q^{94} - 15 q^{96} - q^{97} - 9 q^{98} - 20 q^{99}+O(q^{100}) \) 7 * q + 4 * q^2 + 3 * q^3 + 2 * q^4 - 5 * q^6 + 7 * q^7 + 6 * q^8 - 2 * q^9 - 18 * q^11 - q^12 + q^13 - 6 * q^14 + 4 * q^16 + 2 * q^17 - 8 * q^18 - 6 * q^19 - 2 * q^21 - 10 * q^22 + 22 * q^23 - 3 * q^24 + 8 * q^26 - 3 * q^27 - 9 * q^28 - 16 * q^29 - 18 * q^31 + 6 * q^32 - 4 * q^33 + 11 * q^34 - 7 * q^36 - 8 * q^37 - 16 * q^38 - 9 * q^39 - 15 * q^41 - 19 * q^42 - 14 * q^43 - 4 * q^44 + 11 * q^46 + 10 * q^47 - 31 * q^48 + 6 * q^49 + 13 * q^51 - 27 * q^52 - 15 * q^53 + 16 * q^54 + 13 * q^56 - 14 * q^57 - 17 * q^58 - 18 * q^59 + 4 * q^61 - 13 * q^62 + 16 * q^63 + 2 * q^64 + 16 * q^66 - 18 * q^67 + 15 * q^68 + 26 * q^69 - 50 * q^71 - 30 * q^72 + 10 * q^74 - 20 * q^76 - 17 * q^77 + 32 * q^78 - 15 * q^79 - 9 * q^81 - 45 * q^82 + 24 * q^83 + 6 * q^84 - 23 * q^86 - 12 * q^87 - 8 * q^88 - 13 * q^89 - 12 * q^91 + 10 * q^92 - 14 * q^93 - 32 * q^94 - 15 * q^96 - q^97 - 9 * q^98 - 20 * q^99

Introduction

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