LMFDB - Embedded newform 6025.2.a.f.1.2

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			1.2
Root			$1.48734$ 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)

$f(q)$	$=$	$q-0.487343 q^{2} +0.815004 q^{3} -1.76250 q^{4} -0.397187 q^{6} +4.61392 q^{7} +1.83363 q^{8} -2.33577 q^{9} +O(q^{10})$	\(q-0.487343 q^{2} +0.815004 q^{3} -1.76250 q^{4} -0.397187 q^{6} +4.61392 q^{7} +1.83363 q^{8} -2.33577 q^{9} +1.93974 q^{11} -1.43644 q^{12} +3.85571 q^{13} -2.24856 q^{14} +2.63139 q^{16} -5.40289 q^{17} +1.13832 q^{18} -4.17145 q^{19} +3.76036 q^{21} -0.945321 q^{22} +1.42545 q^{23} +1.49441 q^{24} -1.87905 q^{26} -4.34867 q^{27} -8.13202 q^{28} -4.85744 q^{29} -7.24699 q^{31} -4.94964 q^{32} +1.58090 q^{33} +2.63306 q^{34} +4.11678 q^{36} -7.12597 q^{37} +2.03293 q^{38} +3.14242 q^{39} +9.18955 q^{41} -1.83259 q^{42} -2.93624 q^{43} -3.41879 q^{44} -0.694685 q^{46} -2.48170 q^{47} +2.14459 q^{48} +14.2883 q^{49} -4.40338 q^{51} -6.79568 q^{52} -5.64997 q^{53} +2.11930 q^{54} +8.46022 q^{56} -3.39975 q^{57} +2.36724 q^{58} -11.9783 q^{59} -13.9214 q^{61} +3.53177 q^{62} -10.7771 q^{63} -2.85060 q^{64} -0.770440 q^{66} +7.30682 q^{67} +9.52258 q^{68} +1.16175 q^{69} -14.8844 q^{71} -4.28293 q^{72} -0.240264 q^{73} +3.47279 q^{74} +7.35217 q^{76} +8.94983 q^{77} -1.53144 q^{78} -3.15128 q^{79} +3.46313 q^{81} -4.47847 q^{82} +2.46821 q^{83} -6.62763 q^{84} +1.43096 q^{86} -3.95883 q^{87} +3.55677 q^{88} +5.55181 q^{89} +17.7900 q^{91} -2.51235 q^{92} -5.90632 q^{93} +1.20944 q^{94} -4.03398 q^{96} -5.27964 q^{97} -6.96330 q^{98} -4.53079 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.487343	−0.344604	−0.172302	−	0.985044i	$-0.555120\pi$
$2$	−0.487343	−0.344604	−0.172302	+	0.985044i	$0.555120\pi$
$3$	0.815004	0.470543	0.235271	−	0.971930i	$-0.424402\pi$
$3$	0.815004	0.470543	0.235271	+	0.971930i	$0.424402\pi$
$4$	−1.76250	−0.881248
$5$	0	0
$5$	0	0
$6$	−0.397187	−0.162151
$7$	4.61392	1.74390	0.871950	−	0.489596i	$-0.162856\pi$
$7$	4.61392	1.74390	0.871950	+	0.489596i	$0.162856\pi$
$8$	1.83363	0.648285
$9$	−2.33577	−0.778590
$10$	0	0
$11$	1.93974	0.584855	0.292427	−	0.956288i	$-0.405537\pi$
$11$	1.93974	0.584855	0.292427	+	0.956288i	$0.405537\pi$
$12$	−1.43644	−0.414665
$13$	3.85571	1.06938	0.534691	−	0.845048i	$-0.320428\pi$
$13$	3.85571	1.06938	0.534691	+	0.845048i	$0.320428\pi$
$14$	−2.24856	−0.600954
$15$	0	0
$16$	2.63139	0.657847
$17$	−5.40289	−1.31039	−0.655197	−	0.755458i	$-0.727414\pi$
$17$	−5.40289	−1.31039	−0.655197	+	0.755458i	$0.727414\pi$
$18$	1.13832	0.268305
$19$	−4.17145	−0.956997	−0.478498	−	0.878088i	$-0.658819\pi$
$19$	−4.17145	−0.956997	−0.478498	+	0.878088i	$0.658819\pi$
$20$	0	0
$21$	3.76036	0.820579
$22$	−0.945321	−0.201543
$23$	1.42545	0.297227	0.148614	−	0.988895i	$-0.452519\pi$
$23$	1.42545	0.297227	0.148614	+	0.988895i	$0.452519\pi$
$24$	1.49441	0.305046
$25$	0	0
$26$	−1.87905	−0.368513
$27$	−4.34867	−0.836902
$28$	−8.13202	−1.53681
$29$	−4.85744	−0.902003	−0.451002	−	0.892523i	$-0.648933\pi$
$29$	−4.85744	−0.902003	−0.451002	+	0.892523i	$0.648933\pi$
$30$	0	0
$31$	−7.24699	−1.30160	−0.650799	−	0.759250i	$-0.725566\pi$
$31$	−7.24699	−1.30160	−0.650799	+	0.759250i	$0.725566\pi$
$32$	−4.94964	−0.874982
$33$	1.58090	0.275199
$34$	2.63306	0.451567
$35$	0	0
$36$	4.11678	0.686131
$37$	−7.12597	−1.17150	−0.585751	−	0.810491i	$-0.699200\pi$
$37$	−7.12597	−1.17150	−0.585751	+	0.810491i	$0.699200\pi$
$38$	2.03293	0.329785
$39$	3.14242	0.503190
$40$	0	0
$41$	9.18955	1.43517	0.717583	−	0.696473i	$-0.245248\pi$
$41$	9.18955	1.43517	0.717583	+	0.696473i	$0.245248\pi$
$42$	−1.83259	−0.282775
$43$	−2.93624	−0.447772	−0.223886	−	0.974615i	$-0.571874\pi$
$43$	−2.93624	−0.447772	−0.223886	+	0.974615i	$0.571874\pi$
$44$	−3.41879	−0.515402
$45$	0	0
$46$	−0.694685	−0.102426
$47$	−2.48170	−0.361994	−0.180997	−	0.983484i	$-0.557932\pi$
$47$	−2.48170	−0.361994	−0.180997	+	0.983484i	$0.557932\pi$
$48$	2.14459	0.309545
$49$	14.2883	2.04118
$50$	0	0
$51$	−4.40338	−0.616596
$52$	−6.79568	−0.942391
$53$	−5.64997	−0.776083	−0.388041	−	0.921642i	$-0.626848\pi$
$53$	−5.64997	−0.776083	−0.388041	+	0.921642i	$0.626848\pi$
$54$	2.11930	0.288400
$55$	0	0
$56$	8.46022	1.13054
$57$	−3.39975	−0.450308
$58$	2.36724	0.310834
$59$	−11.9783	−1.55944	−0.779718	−	0.626131i	$-0.784638\pi$
$59$	−11.9783	−1.55944	−0.779718	+	0.626131i	$0.784638\pi$
$60$	0	0
$61$	−13.9214	−1.78245	−0.891223	−	0.453565i	$-0.850152\pi$
$61$	−13.9214	−1.78245	−0.891223	+	0.453565i	$0.850152\pi$
$62$	3.53177	0.448535
$63$	−10.7771	−1.35778
$64$	−2.85060	−0.356325
$65$	0	0
$66$	−0.770440	−0.0948346
$67$	7.30682	0.892670	0.446335	−	0.894866i	$-0.352729\pi$
$67$	7.30682	0.892670	0.446335	+	0.894866i	$0.352729\pi$
$68$	9.52258	1.15478
$69$	1.16175	0.139858
$70$	0	0
$71$	−14.8844	−1.76645	−0.883226	−	0.468948i	$-0.844633\pi$
$71$	−14.8844	−1.76645	−0.883226	+	0.468948i	$0.844633\pi$
$72$	−4.28293	−0.504748
$73$	−0.240264	−0.0281208	−0.0140604	−	0.999901i	$-0.504476\pi$
$73$	−0.240264	−0.0281208	−0.0140604	+	0.999901i	$0.504476\pi$
$74$	3.47279	0.403704
$75$	0	0
$76$	7.35217	0.843352
$77$	8.94983	1.01993
$78$	−1.53144	−0.173401
$79$	−3.15128	−0.354546	−0.177273	−	0.984162i	$-0.556728\pi$
$79$	−3.15128	−0.354546	−0.177273	+	0.984162i	$0.556728\pi$
$80$	0	0
$81$	3.46313	0.384792
$82$	−4.47847	−0.494564
$83$	2.46821	0.270922	0.135461	−	0.990783i	$-0.456749\pi$
$83$	2.46821	0.270922	0.135461	+	0.990783i	$0.456749\pi$
$84$	−6.62763	−0.723134
$85$	0	0
$86$	1.43096	0.154304
$87$	−3.95883	−0.424431
$88$	3.55677	0.379153
$89$	5.55181	0.588491	0.294246	−	0.955730i	$-0.404932\pi$
$89$	5.55181	0.588491	0.294246	+	0.955730i	$0.404932\pi$
$90$	0	0
$91$	17.7900	1.86489
$92$	−2.51235	−0.261931
$93$	−5.90632	−0.612457
$94$	1.20944	0.124744
$95$	0	0
$96$	−4.03398	−0.411716
$97$	−5.27964	−0.536067	−0.268033	−	0.963410i	$-0.586374\pi$
$97$	−5.27964	−0.536067	−0.268033	+	0.963410i	$0.586374\pi$
$98$	−6.96330	−0.703400
$99$	−4.53079	−0.455362
$100$	0	0
$101$	−12.4239	−1.23623	−0.618113	−	0.786089i	$-0.712103\pi$
$101$	−12.4239	−1.23623	−0.618113	+	0.786089i	$0.712103\pi$
$102$	2.14596	0.212481
$103$	9.80533	0.966148	0.483074	−	0.875580i	$-0.339520\pi$
$103$	9.80533	0.966148	0.483074	+	0.875580i	$0.339520\pi$
$104$	7.06994	0.693264
$105$	0	0
$106$	2.75347	0.267441
$107$	9.15031	0.884593	0.442297	−	0.896869i	$-0.354164\pi$
$107$	9.15031	0.884593	0.442297	+	0.896869i	$0.354164\pi$
$108$	7.66452	0.737519
$109$	3.24534	0.310847	0.155424	−	0.987848i	$-0.450326\pi$
$109$	3.24534	0.310847	0.155424	+	0.987848i	$0.450326\pi$
$110$	0	0
$111$	−5.80769	−0.551241
$112$	12.1410	1.14722
$113$	0.842874	0.0792909	0.0396455	−	0.999214i	$-0.487377\pi$
$113$	0.842874	0.0792909	0.0396455	+	0.999214i	$0.487377\pi$
$114$	1.65684	0.155178
$115$	0	0
$116$	8.56121	0.794889
$117$	−9.00605	−0.832610
$118$	5.83752	0.537387
$119$	−24.9285	−2.28520
$120$	0	0
$121$	−7.23740	−0.657945
$122$	6.78448	0.614238
$123$	7.48952	0.675307
$124$	12.7728	1.14703
$125$	0	0
$126$	5.25213	0.467897
$127$	−11.3416	−1.00641	−0.503203	−	0.864168i	$-0.667845\pi$
$127$	−11.3416	−1.00641	−0.503203	+	0.864168i	$0.667845\pi$
$128$	11.2885	0.997773
$129$	−2.39305	−0.210696
$130$	0	0
$131$	14.1261	1.23421	0.617103	−	0.786882i	$-0.288306\pi$
$131$	14.1261	1.23421	0.617103	+	0.786882i	$0.288306\pi$
$132$	−2.78633	−0.242519
$133$	−19.2468	−1.66891
$134$	−3.56093	−0.307617
$135$	0	0
$136$	−9.90689	−0.849509
$137$	12.9555	1.10686	0.553430	−	0.832896i	$-0.313319\pi$
$137$	12.9555	1.10686	0.553430	+	0.832896i	$0.313319\pi$
$138$	−0.566170	−0.0481956
$139$	8.23606	0.698574	0.349287	−	0.937016i	$-0.386424\pi$
$139$	8.23606	0.698574	0.349287	+	0.937016i	$0.386424\pi$
$140$	0	0
$141$	−2.02260	−0.170333
$142$	7.25380	0.608726
$143$	7.47909	0.625433
$144$	−6.14631	−0.512193
$145$	0	0
$146$	0.117091	0.00969054
$147$	11.6450	0.960464
$148$	12.5595	1.03238
$149$	4.48606	0.367513	0.183756	−	0.982972i	$-0.441174\pi$
$149$	4.48606	0.367513	0.183756	+	0.982972i	$0.441174\pi$
$150$	0	0
$151$	0.0933624	0.00759773	0.00379886	−	0.999993i	$-0.498791\pi$
$151$	0.0933624	0.00759773	0.00379886	+	0.999993i	$0.498791\pi$
$152$	−7.64889	−0.620407
$153$	12.6199	1.02026
$154$	−4.36164	−0.351471
$155$	0	0
$156$	−5.53850	−0.443435
$157$	10.1337	0.808760	0.404380	−	0.914591i	$-0.367487\pi$
$157$	10.1337	0.808760	0.404380	+	0.914591i	$0.367487\pi$
$158$	1.53575	0.122178
$159$	−4.60474	−0.365180
$160$	0	0
$161$	6.57693	0.518334
$162$	−1.68773	−0.132601
$163$	−7.49804	−0.587292	−0.293646	−	0.955914i	$-0.594869\pi$
$163$	−7.49804	−0.587292	−0.293646	+	0.955914i	$0.594869\pi$
$164$	−16.1965	−1.26474
$165$	0	0
$166$	−1.20287	−0.0933606
$167$	−17.7922	−1.37680	−0.688399	−	0.725332i	$-0.741686\pi$
$167$	−17.7922	−1.37680	−0.688399	+	0.725332i	$0.741686\pi$
$168$	6.89511	0.531969
$169$	1.86650	0.143577
$170$	0	0
$171$	9.74355	0.745108
$172$	5.17511	0.394599
$173$	−18.4927	−1.40597	−0.702987	−	0.711203i	$-0.748151\pi$
$173$	−18.4927	−1.40597	−0.702987	+	0.711203i	$0.748151\pi$
$174$	1.92931	0.146260
$175$	0	0
$176$	5.10421	0.384745
$177$	−9.76232	−0.733781
$178$	−2.70564	−0.202796
$179$	−17.3387	−1.29595	−0.647977	−	0.761660i	$-0.724385\pi$
$179$	−17.3387	−1.29595	−0.647977	+	0.761660i	$0.724385\pi$
$180$	0	0
$181$	17.7124	1.31655	0.658275	−	0.752778i	$-0.271287\pi$
$181$	17.7124	1.31655	0.658275	+	0.752778i	$0.271287\pi$
$182$	−8.66981	−0.642649
$183$	−11.3460	−0.838717
$184$	2.61375	0.192688
$185$	0	0
$186$	2.87841	0.211055
$187$	−10.4802	−0.766390
$188$	4.37400	0.319006
$189$	−20.0644	−1.45947
$190$	0	0
$191$	13.2440	0.958303	0.479151	−	0.877732i	$-0.340944\pi$
$191$	13.2440	0.958303	0.479151	+	0.877732i	$0.340944\pi$
$192$	−2.32325	−0.167666
$193$	25.5030	1.83574	0.917872	−	0.396877i	$-0.129906\pi$
$193$	25.5030	1.83574	0.917872	+	0.396877i	$0.129906\pi$
$194$	2.57300	0.184731
$195$	0	0
$196$	−25.1831	−1.79879
$197$	15.0303	1.07087	0.535433	−	0.844578i	$-0.320149\pi$
$197$	15.0303	1.07087	0.535433	+	0.844578i	$0.320149\pi$
$198$	2.20805	0.156919
$199$	−19.3801	−1.37382	−0.686911	−	0.726742i	$-0.741034\pi$
$199$	−19.3801	−1.37382	−0.686911	+	0.726742i	$0.741034\pi$
$200$	0	0
$201$	5.95508	0.420039
$202$	6.05472	0.426008
$203$	−22.4118	−1.57300
$204$	7.76094	0.543374
$205$	0	0
$206$	−4.77856	−0.332938
$207$	−3.32953	−0.231418
$208$	10.1459	0.703489
$209$	−8.09154	−0.559704
$210$	0	0
$211$	27.9383	1.92335	0.961675	−	0.274192i	$-0.0884105\pi$
$211$	27.9383	1.92335	0.961675	+	0.274192i	$0.0884105\pi$
$212$	9.95805	0.683922
$213$	−12.1308	−0.831191
$214$	−4.45934	−0.304834
$215$	0	0
$216$	−7.97384	−0.542551
$217$	−33.4370	−2.26985
$218$	−1.58160	−0.107119
$219$	−0.195816	−0.0132320
$220$	0	0
$221$	−20.8320	−1.40131
$222$	2.83034	0.189960
$223$	0.387500	0.0259489	0.0129745	−	0.999916i	$-0.495870\pi$
$223$	0.387500	0.0259489	0.0129745	+	0.999916i	$0.495870\pi$
$224$	−22.8373	−1.52588
$225$	0	0
$226$	−0.410769	−0.0273240
$227$	−10.2778	−0.682161	−0.341081	−	0.940034i	$-0.610793\pi$
$227$	−10.2778	−0.682161	−0.341081	+	0.940034i	$0.610793\pi$
$228$	5.99204	0.396833
$229$	−10.5346	−0.696147	−0.348074	−	0.937467i	$-0.613164\pi$
$229$	−10.5346	−0.696147	−0.348074	+	0.937467i	$0.613164\pi$
$230$	0	0
$231$	7.29414	0.479919
$232$	−8.90673	−0.584755
$233$	−25.6725	−1.68186	−0.840932	−	0.541141i	$-0.817993\pi$
$233$	−25.6725	−1.68186	−0.840932	+	0.541141i	$0.817993\pi$
$234$	4.38904	0.286920
$235$	0	0
$236$	21.1116	1.37425
$237$	−2.56830	−0.166829
$238$	12.1488	0.787487
$239$	−25.1312	−1.62560	−0.812801	−	0.582542i	$-0.802058\pi$
$239$	−25.1312	−1.62560	−0.812801	+	0.582542i	$0.802058\pi$
$240$	0	0
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	3.52710	0.226730
$243$	15.8685	1.01796
$244$	24.5363	1.57078
$245$	0	0
$246$	−3.64997	−0.232713
$247$	−16.0839	−1.02339
$248$	−13.2883	−0.843806
$249$	2.01160	0.127480
$250$	0	0
$251$	2.52238	0.159211	0.0796055	−	0.996826i	$-0.474634\pi$
$251$	2.52238	0.159211	0.0796055	+	0.996826i	$0.474634\pi$
$252$	18.9945	1.19654
$253$	2.76501	0.173835
$254$	5.52726	0.346811
$255$	0	0
$256$	0.199817	0.0124886
$257$	−3.92348	−0.244740	−0.122370	−	0.992485i	$-0.539049\pi$
$257$	−3.92348	−0.244740	−0.122370	+	0.992485i	$0.539049\pi$
$258$	1.16623	0.0726066
$259$	−32.8787	−2.04298
$260$	0	0
$261$	11.3458	0.702290
$262$	−6.88428	−0.425312
$263$	−6.24984	−0.385382	−0.192691	−	0.981260i	$-0.561721\pi$
$263$	−6.24984	−0.385382	−0.192691	+	0.981260i	$0.561721\pi$
$264$	2.89878	0.178407
$265$	0	0
$266$	9.37978	0.575111
$267$	4.52475	0.276910
$268$	−12.8782	−0.786664
$269$	20.4943	1.24956	0.624780	−	0.780801i	$-0.285189\pi$
$269$	20.4943	1.24956	0.624780	+	0.780801i	$0.285189\pi$
$270$	0	0
$271$	15.3179	0.930499	0.465249	−	0.885180i	$-0.345965\pi$
$271$	15.3179	0.930499	0.465249	+	0.885180i	$0.345965\pi$
$272$	−14.2171	−0.862039
$273$	14.4989	0.877512
$274$	−6.31376	−0.381428
$275$	0	0
$276$	−2.04758	−0.123250
$277$	−3.26388	−0.196108	−0.0980539	−	0.995181i	$-0.531262\pi$
$277$	−3.26388	−0.196108	−0.0980539	+	0.995181i	$0.531262\pi$
$278$	−4.01379	−0.240731
$279$	16.9273	1.01341
$280$	0	0
$281$	−12.4791	−0.744442	−0.372221	−	0.928144i	$-0.621404\pi$
$281$	−12.4791	−0.744442	−0.372221	+	0.928144i	$0.621404\pi$
$282$	0.985700	0.0586976
$283$	15.8115	0.939899	0.469949	−	0.882693i	$-0.344272\pi$
$283$	15.8115	0.939899	0.469949	+	0.882693i	$0.344272\pi$
$284$	26.2337	1.55668
$285$	0	0
$286$	−3.64488	−0.215526
$287$	42.3999	2.50279
$288$	11.5612	0.681252
$289$	12.1913	0.717133
$290$	0	0
$291$	−4.30293	−0.252242
$292$	0.423465	0.0247814
$293$	−18.7147	−1.09333	−0.546663	−	0.837353i	$-0.684102\pi$
$293$	−18.7147	−1.09333	−0.546663	+	0.837353i	$0.684102\pi$
$294$	−5.67512	−0.330979
$295$	0	0
$296$	−13.0664	−0.759467
$297$	−8.43530	−0.489466
$298$	−2.18625	−0.126646
$299$	5.49613	0.317849
$300$	0	0
$301$	−13.5476	−0.780870
$302$	−0.0454995	−0.00261820
$303$	−10.1255	−0.581697
$304$	−10.9767	−0.629557
$305$	0	0
$306$	−6.15023	−0.351585
$307$	−5.23477	−0.298764	−0.149382	−	0.988780i	$-0.547728\pi$
$307$	−5.23477	−0.298764	−0.149382	+	0.988780i	$0.547728\pi$
$308$	−15.7740	−0.898809
$309$	7.99138	0.454614
$310$	0	0
$311$	−26.6878	−1.51332	−0.756662	−	0.653806i	$-0.773171\pi$
$311$	−26.6878	−1.51332	−0.756662	+	0.653806i	$0.773171\pi$
$312$	5.76202	0.326210
$313$	−6.24141	−0.352786	−0.176393	−	0.984320i	$-0.556443\pi$
$313$	−6.24141	−0.352786	−0.176393	+	0.984320i	$0.556443\pi$
$314$	−4.93861	−0.278702
$315$	0	0
$316$	5.55412	0.312443
$317$	−6.89526	−0.387276	−0.193638	−	0.981073i	$-0.562029\pi$
$317$	−6.89526	−0.387276	−0.193638	+	0.981073i	$0.562029\pi$
$318$	2.24409	0.125842
$319$	−9.42218	−0.527541
$320$	0	0
$321$	7.45753	0.416239
$322$	−3.20522	−0.178620
$323$	22.5379	1.25404
$324$	−6.10375	−0.339097
$325$	0	0
$326$	3.65412	0.202383
$327$	2.64497	0.146267
$328$	16.8502	0.930397
$329$	−11.4504	−0.631281
$330$	0	0
$331$	−13.5697	−0.745860	−0.372930	−	0.927859i	$-0.621647\pi$
$331$	−13.5697	−0.745860	−0.372930	+	0.927859i	$0.621647\pi$
$332$	−4.35022	−0.238749
$333$	16.6446	0.912119
$334$	8.67089	0.474450
$335$	0	0
$336$	9.89497	0.539815
$337$	20.2288	1.10193	0.550966	−	0.834528i	$-0.314260\pi$
$337$	20.2288	1.10193	0.550966	+	0.834528i	$0.314260\pi$
$338$	−0.909627	−0.0494772
$339$	0.686946	0.0373098
$340$	0	0
$341$	−14.0573	−0.761245
$342$	−4.74845	−0.256767
$343$	33.6276	1.81572
$344$	−5.38397	−0.290284
$345$	0	0
$346$	9.01229	0.484504
$347$	−1.52458	−0.0818437	−0.0409219	−	0.999162i	$-0.513029\pi$
$347$	−1.52458	−0.0818437	−0.0409219	+	0.999162i	$0.513029\pi$
$348$	6.97742	0.374029
$349$	16.5585	0.886358	0.443179	−	0.896433i	$-0.353851\pi$
$349$	16.5585	0.886358	0.443179	+	0.896433i	$0.353851\pi$
$350$	0	0
$351$	−16.7672	−0.894968
$352$	−9.60104	−0.511737
$353$	−34.6802	−1.84584	−0.922920	−	0.384992i	$-0.874204\pi$
$353$	−34.6802	−1.84584	−0.922920	+	0.384992i	$0.874204\pi$
$354$	4.75760	0.252864
$355$	0	0
$356$	−9.78505	−0.518607
$357$	−20.3168	−1.07528
$358$	8.44989	0.446590
$359$	18.1341	0.957084	0.478542	−	0.878065i	$-0.341165\pi$
$359$	18.1341	0.957084	0.478542	+	0.878065i	$0.341165\pi$
$360$	0	0
$361$	−1.59899	−0.0841573
$362$	−8.63200	−0.453688
$363$	−5.89850	−0.309591
$364$	−31.3547	−1.64343
$365$	0	0
$366$	5.52937	0.289025
$367$	10.9879	0.573566	0.286783	−	0.957996i	$-0.407414\pi$
$367$	10.9879	0.573566	0.286783	+	0.957996i	$0.407414\pi$
$368$	3.75092	0.195530
$369$	−21.4647	−1.11741
$370$	0	0
$371$	−26.0685	−1.35341
$372$	10.4099	0.539727
$373$	−5.23646	−0.271134	−0.135567	−	0.990768i	$-0.543286\pi$
$373$	−5.23646	−0.271134	−0.135567	+	0.990768i	$0.543286\pi$
$374$	5.10747	0.264101
$375$	0	0
$376$	−4.55052	−0.234675
$377$	−18.7289	−0.964586
$378$	9.77827	0.502940
$379$	8.07101	0.414580	0.207290	−	0.978280i	$-0.433536\pi$
$379$	8.07101	0.414580	0.207290	+	0.978280i	$0.433536\pi$
$380$	0	0
$381$	−9.24346	−0.473557
$382$	−6.45438	−0.330235
$383$	−2.46503	−0.125957	−0.0629785	−	0.998015i	$-0.520060\pi$
$383$	−2.46503	−0.125957	−0.0629785	+	0.998015i	$0.520060\pi$
$384$	9.20017	0.469494
$385$	0	0
$386$	−12.4287	−0.632604
$387$	6.85838	0.348631
$388$	9.30535	0.472408
$389$	−28.7159	−1.45595	−0.727977	−	0.685601i	$-0.759539\pi$
$389$	−28.7159	−1.45595	−0.727977	+	0.685601i	$0.759539\pi$
$390$	0	0
$391$	−7.70157	−0.389485
$392$	26.1994	1.32327
$393$	11.5128	0.580746
$394$	−7.32492	−0.369024
$395$	0	0
$396$	7.98550	0.401287
$397$	−12.0605	−0.605301	−0.302651	−	0.953102i	$-0.597871\pi$
$397$	−12.0605	−0.605301	−0.302651	+	0.953102i	$0.597871\pi$
$398$	9.44478	0.473424
$399$	−15.6862	−0.785291
$400$	0	0
$401$	−31.7082	−1.58343	−0.791716	−	0.610890i	$-0.790812\pi$
$401$	−31.7082	−1.58343	−0.791716	+	0.610890i	$0.790812\pi$
$402$	−2.90217	−0.144747
$403$	−27.9423	−1.39190
$404$	21.8971	1.08942
$405$	0	0
$406$	10.9223	0.542063
$407$	−13.8225	−0.685158
$408$	−8.07415	−0.399730
$409$	−14.1893	−0.701617	−0.350809	−	0.936447i	$-0.614093\pi$
$409$	−14.1893	−0.701617	−0.350809	+	0.936447i	$0.614093\pi$
$410$	0	0
$411$	10.5587	0.520825
$412$	−17.2819	−0.851416
$413$	−55.2668	−2.71950
$414$	1.62262	0.0797476
$415$	0	0
$416$	−19.0844	−0.935689
$417$	6.71242	0.328709
$418$	3.94336	0.192876
$419$	31.1014	1.51941	0.759703	−	0.650271i	$-0.225345\pi$
$419$	31.1014	1.51941	0.759703	+	0.650271i	$0.225345\pi$
$420$	0	0
$421$	−27.4415	−1.33742	−0.668709	−	0.743524i	$-0.733153\pi$
$421$	−27.4415	−1.33742	−0.668709	+	0.743524i	$0.733153\pi$
$422$	−13.6155	−0.662794
$423$	5.79669	0.281845
$424$	−10.3599	−0.503123
$425$	0	0
$426$	5.91188	0.286431
$427$	−64.2321	−3.10841
$428$	−16.1274	−0.779546
$429$	6.09548	0.294293
$430$	0	0
$431$	−14.1005	−0.679199	−0.339599	−	0.940570i	$-0.610291\pi$
$431$	−14.1005	−0.679199	−0.339599	+	0.940570i	$0.610291\pi$
$432$	−11.4430	−0.550553
$433$	17.7403	0.852546	0.426273	−	0.904595i	$-0.359826\pi$
$433$	17.7403	0.852546	0.426273	+	0.904595i	$0.359826\pi$
$434$	16.2953	0.782200
$435$	0	0
$436$	−5.71991	−0.273934
$437$	−5.94621	−0.284446
$438$	0.0954297	0.00455981
$439$	−2.52447	−0.120486	−0.0602431	−	0.998184i	$-0.519188\pi$
$439$	−2.52447	−0.120486	−0.0602431	+	0.998184i	$0.519188\pi$
$440$	0	0
$441$	−33.3741	−1.58924
$442$	10.1523	0.482897
$443$	16.8382	0.800008	0.400004	−	0.916513i	$-0.369009\pi$
$443$	16.8382	0.800008	0.400004	+	0.916513i	$0.369009\pi$
$444$	10.2360	0.485780
$445$	0	0
$446$	−0.188846	−0.00894211
$447$	3.65616	0.172930
$448$	−13.1524	−0.621394
$449$	−30.5688	−1.44263	−0.721314	−	0.692608i	$-0.756462\pi$
$449$	−30.5688	−1.44263	−0.721314	+	0.692608i	$0.756462\pi$
$450$	0	0
$451$	17.8254	0.839364
$452$	−1.48556	−0.0698750
$453$	0.0760907	0.00357505
$454$	5.00882	0.235075
$455$	0	0
$456$	−6.23387	−0.291928
$457$	32.7043	1.52984	0.764922	−	0.644123i	$-0.222777\pi$
$457$	32.7043	1.52984	0.764922	+	0.644123i	$0.222777\pi$
$458$	5.13398	0.239895
$459$	23.4954	1.09667
$460$	0	0
$461$	12.3932	0.577210	0.288605	−	0.957448i	$-0.406809\pi$
$461$	12.3932	0.577210	0.288605	+	0.957448i	$0.406809\pi$
$462$	−3.55475	−0.165382
$463$	−12.1379	−0.564094	−0.282047	−	0.959401i	$-0.591013\pi$
$463$	−12.1379	−0.564094	−0.282047	+	0.959401i	$0.591013\pi$
$464$	−12.7818	−0.593380
$465$	0	0
$466$	12.5113	0.579577
$467$	−5.38203	−0.249051	−0.124525	−	0.992216i	$-0.539741\pi$
$467$	−5.38203	−0.249051	−0.124525	+	0.992216i	$0.539741\pi$
$468$	15.8731	0.733736
$469$	33.7131	1.55673
$470$	0	0
$471$	8.25903	0.380556
$472$	−21.9637	−1.01096
$473$	−5.69555	−0.261882
$474$	1.25165	0.0574900
$475$	0	0
$476$	43.9365	2.01382
$477$	13.1970	0.604250
$478$	12.2475	0.560188
$479$	−25.3752	−1.15942	−0.579711	−	0.814822i	$-0.696834\pi$
$479$	−25.3752	−1.15942	−0.579711	+	0.814822i	$0.696834\pi$
$480$	0	0
$481$	−27.4757	−1.25278
$482$	0.487343	0.0221979
$483$	5.36022	0.243898
$484$	12.7559	0.579813
$485$	0	0
$486$	−7.73339	−0.350794
$487$	10.4243	0.472369	0.236185	−	0.971708i	$-0.424103\pi$
$487$	10.4243	0.472369	0.236185	+	0.971708i	$0.424103\pi$
$488$	−25.5266	−1.15553
$489$	−6.11093	−0.276346
$490$	0	0
$491$	34.2858	1.54730	0.773649	−	0.633614i	$-0.218429\pi$
$491$	34.2858	1.54730	0.773649	+	0.633614i	$0.218429\pi$
$492$	−13.2002	−0.595113
$493$	26.2442	1.18198
$494$	7.83839	0.352666
$495$	0	0
$496$	−19.0696	−0.856252
$497$	−68.6754	−3.08051
$498$	−0.980341	−0.0439301
$499$	15.9672	0.714792	0.357396	−	0.933953i	$-0.383665\pi$
$499$	15.9672	0.714792	0.357396	+	0.933953i	$0.383665\pi$
$500$	0	0
$501$	−14.5007	−0.647842
$502$	−1.22926	−0.0548647
$503$	4.53174	0.202060	0.101030	−	0.994883i	$-0.467786\pi$
$503$	4.53174	0.202060	0.101030	+	0.994883i	$0.467786\pi$
$504$	−19.7611	−0.880230
$505$	0	0
$506$	−1.34751	−0.0599041
$507$	1.52121	0.0675591
$508$	19.9896	0.886893
$509$	−4.08798	−0.181197	−0.0905983	−	0.995888i	$-0.528878\pi$
$509$	−4.08798	−0.181197	−0.0905983	+	0.995888i	$0.528878\pi$
$510$	0	0
$511$	−1.10856	−0.0490398
$512$	−22.6744	−1.00208
$513$	18.1403	0.800913
$514$	1.91208	0.0843384
$515$	0	0
$516$	4.21774	0.185675
$517$	−4.81387	−0.211714
$518$	16.0232	0.704019
$519$	−15.0716	−0.661571
$520$	0	0
$521$	34.2884	1.50220	0.751102	−	0.660186i	$-0.229523\pi$
$521$	34.2884	1.50220	0.751102	+	0.660186i	$0.229523\pi$
$522$	−5.52932	−0.242012
$523$	−33.7724	−1.47676	−0.738382	−	0.674382i	$-0.764410\pi$
$523$	−33.7724	−1.47676	−0.738382	+	0.674382i	$0.764410\pi$
$524$	−24.8973	−1.08764
$525$	0	0
$526$	3.04582	0.132804
$527$	39.1547	1.70561
$528$	4.15995	0.181039
$529$	−20.9681	−0.911656
$530$	0	0
$531$	27.9784	1.21416
$532$	33.9223	1.47072
$533$	35.4322	1.53474
$534$	−2.20511	−0.0954243
$535$	0	0
$536$	13.3980	0.578705
$537$	−14.1311	−0.609801
$538$	−9.98777	−0.430603
$539$	27.7156	1.19380
$540$	0	0
$541$	−31.0330	−1.33421	−0.667106	−	0.744963i	$-0.732467\pi$
$541$	−31.0330	−1.33421	−0.667106	+	0.744963i	$0.732467\pi$
$542$	−7.46510	−0.320653
$543$	14.4356	0.619492
$544$	26.7424	1.14657
$545$	0	0
$546$	−7.06593	−0.302394
$547$	33.0104	1.41142	0.705712	−	0.708499i	$-0.250627\pi$
$547$	33.0104	1.41142	0.705712	+	0.708499i	$0.250627\pi$
$548$	−22.8340	−0.975418
$549$	32.5171	1.38779
$550$	0	0
$551$	20.2626	0.863214
$552$	2.13021	0.0906679
$553$	−14.5398	−0.618293
$554$	1.59063	0.0675795
$555$	0	0
$556$	−14.5160	−0.615617
$557$	−15.4826	−0.656019	−0.328010	−	0.944674i	$-0.606378\pi$
$557$	−15.4826	−0.656019	−0.328010	+	0.944674i	$0.606378\pi$
$558$	−8.24940	−0.349225
$559$	−11.3213	−0.478840
$560$	0	0
$561$	−8.54142	−0.360619
$562$	6.08161	0.256537
$563$	−6.21072	−0.261751	−0.130875	−	0.991399i	$-0.541779\pi$
$563$	−6.21072	−0.261751	−0.130875	+	0.991399i	$0.541779\pi$
$564$	3.56482	0.150106
$565$	0	0
$566$	−7.70565	−0.323893
$567$	15.9786	0.671038
$568$	−27.2924	−1.14516
$569$	−20.3014	−0.851078	−0.425539	−	0.904940i	$-0.639916\pi$
$569$	−20.3014	−0.851078	−0.425539	+	0.904940i	$0.639916\pi$
$570$	0	0
$571$	−38.5209	−1.61205	−0.806024	−	0.591882i	$-0.798385\pi$
$571$	−38.5209	−1.61205	−0.806024	+	0.591882i	$0.798385\pi$
$572$	−13.1819	−0.551161
$573$	10.7939	0.450922
$574$	−20.6633	−0.862469
$575$	0	0
$576$	6.65834	0.277431
$577$	−19.3481	−0.805472	−0.402736	−	0.915316i	$-0.631941\pi$
$577$	−19.3481	−0.805472	−0.402736	+	0.915316i	$0.631941\pi$
$578$	−5.94133	−0.247127
$579$	20.7850	0.863795
$580$	0	0
$581$	11.3881	0.472460
$582$	2.09700	0.0869236
$583$	−10.9595	−0.453896
$584$	−0.440555	−0.0182303
$585$	0	0
$586$	9.12050	0.376764
$587$	20.0183	0.826243	0.413122	−	0.910676i	$-0.364438\pi$
$587$	20.0183	0.826243	0.413122	+	0.910676i	$0.364438\pi$
$588$	−20.5243	−0.846407
$589$	30.2305	1.24562
$590$	0	0
$591$	12.2498	0.503888
$592$	−18.7512	−0.770668
$593$	−12.5904	−0.517027	−0.258513	−	0.966008i	$-0.583233\pi$
$593$	−12.5904	−0.517027	−0.258513	+	0.966008i	$0.583233\pi$
$594$	4.11089	0.168672
$595$	0	0
$596$	−7.90667	−0.323870
$597$	−15.7949	−0.646441
$598$	−2.67850	−0.109532
$599$	24.4282	0.998107	0.499054	−	0.866571i	$-0.333681\pi$
$599$	24.4282	0.998107	0.499054	+	0.866571i	$0.333681\pi$
$600$	0	0
$601$	9.02256	0.368038	0.184019	−	0.982923i	$-0.441089\pi$
$601$	9.02256	0.368038	0.184019	+	0.982923i	$0.441089\pi$
$602$	6.60233	0.269091
$603$	−17.0670	−0.695024
$604$	−0.164551	−0.00669548
$605$	0	0
$606$	4.93462	0.200455
$607$	19.0044	0.771364	0.385682	−	0.922632i	$-0.373966\pi$
$607$	19.0044	0.771364	0.385682	+	0.922632i	$0.373966\pi$
$608$	20.6472	0.837355
$609$	−18.2657	−0.740165
$610$	0	0
$611$	−9.56873	−0.387110
$612$	−22.2426	−0.899102
$613$	−3.38617	−0.136766	−0.0683831	−	0.997659i	$-0.521784\pi$
$613$	−3.38617	−0.136766	−0.0683831	+	0.997659i	$0.521784\pi$
$614$	2.55113	0.102955
$615$	0	0
$616$	16.4106	0.661204
$617$	33.9920	1.36847	0.684234	−	0.729263i	$-0.260137\pi$
$617$	33.9920	1.36847	0.684234	+	0.729263i	$0.260137\pi$
$618$	−3.89455	−0.156662
$619$	29.6477	1.19164	0.595822	−	0.803117i	$-0.296826\pi$
$619$	29.6477	1.19164	0.595822	+	0.803117i	$0.296826\pi$
$620$	0	0
$621$	−6.19882	−0.248750
$622$	13.0061	0.521497
$623$	25.6156	1.02627
$624$	8.26892	0.331022
$625$	0	0
$626$	3.04171	0.121571
$627$	−6.59464	−0.263364
$628$	−17.8607	−0.712718
$629$	38.5008	1.53513
$630$	0	0
$631$	14.6241	0.582176	0.291088	−	0.956696i	$-0.405983\pi$
$631$	14.6241	0.582176	0.291088	+	0.956696i	$0.405983\pi$
$632$	−5.77827	−0.229847
$633$	22.7698	0.905018
$634$	3.36036	0.133457
$635$	0	0
$636$	8.11585	0.321814
$637$	55.0915	2.18280
$638$	4.59184	0.181793
$639$	34.7665	1.37534
$640$	0	0
$641$	4.17547	0.164921	0.0824606	−	0.996594i	$-0.473722\pi$
$641$	4.17547	0.164921	0.0824606	+	0.996594i	$0.473722\pi$
$642$	−3.63438	−0.143437
$643$	−23.1928	−0.914635	−0.457317	−	0.889304i	$-0.651190\pi$
$643$	−23.1928	−0.914635	−0.457317	+	0.889304i	$0.651190\pi$
$644$	−11.5918	−0.456781
$645$	0	0
$646$	−10.9837	−0.432148
$647$	31.0975	1.22257	0.611284	−	0.791411i	$-0.290653\pi$
$647$	31.0975	1.22257	0.611284	+	0.791411i	$0.290653\pi$
$648$	6.35008	0.249455
$649$	−23.2347	−0.912043
$650$	0	0
$651$	−27.2513	−1.06806
$652$	13.2153	0.517550
$653$	31.5439	1.23441	0.617204	−	0.786803i	$-0.288265\pi$
$653$	31.5439	1.23441	0.617204	+	0.786803i	$0.288265\pi$
$654$	−1.28901	−0.0504041
$655$	0	0
$656$	24.1813	0.944120
$657$	0.561202	0.0218946
$658$	5.58027	0.217542
$659$	25.2754	0.984590	0.492295	−	0.870428i	$-0.336158\pi$
$659$	25.2754	0.984590	0.492295	+	0.870428i	$0.336158\pi$
$660$	0	0
$661$	−21.7628	−0.846476	−0.423238	−	0.906018i	$-0.639107\pi$
$661$	−21.7628	−0.846476	−0.423238	+	0.906018i	$0.639107\pi$
$662$	6.61312	0.257026
$663$	−16.9781	−0.659377
$664$	4.52578	0.175634
$665$	0	0
$666$	−8.11164	−0.314320
$667$	−6.92404	−0.268100
$668$	31.3586	1.21330
$669$	0.315814	0.0122101
$670$	0	0
$671$	−27.0038	−1.04247
$672$	−18.6125	−0.717991
$673$	37.2710	1.43669	0.718346	−	0.695686i	$-0.244899\pi$
$673$	37.2710	1.43669	0.718346	+	0.695686i	$0.244899\pi$
$674$	−9.85835	−0.379730
$675$	0	0
$676$	−3.28970	−0.126527
$677$	33.5515	1.28949	0.644745	−	0.764398i	$-0.276964\pi$
$677$	33.5515	1.28949	0.644745	+	0.764398i	$0.276964\pi$
$678$	−0.334778	−0.0128571
$679$	−24.3599	−0.934846
$680$	0	0
$681$	−8.37644	−0.320986
$682$	6.85073	0.262328
$683$	−8.94737	−0.342362	−0.171181	−	0.985240i	$-0.554758\pi$
$683$	−8.94737	−0.342362	−0.171181	+	0.985240i	$0.554758\pi$
$684$	−17.1730	−0.656625
$685$	0	0
$686$	−16.3882	−0.625704
$687$	−8.58575	−0.327567
$688$	−7.72638	−0.294566
$689$	−21.7846	−0.829929
$690$	0	0
$691$	7.04969	0.268183	0.134092	−	0.990969i	$-0.457188\pi$
$691$	7.04969	0.268183	0.134092	+	0.990969i	$0.457188\pi$
$692$	32.5933	1.23901
$693$	−20.9047	−0.794105
$694$	0.742994	0.0282036
$695$	0	0
$696$	−7.25902	−0.275152
$697$	−49.6502	−1.88063
$698$	−8.06969	−0.305442
$699$	−20.9232	−0.791389
$700$	0	0
$701$	−5.19179	−0.196091	−0.0980456	−	0.995182i	$-0.531259\pi$
$701$	−5.19179	−0.196091	−0.0980456	+	0.995182i	$0.531259\pi$
$702$	8.17139	0.308409
$703$	29.7256	1.12112
$704$	−5.52943	−0.208398
$705$	0	0
$706$	16.9012	0.636083
$707$	−57.3230	−2.15586
$708$	17.2061	0.646643
$709$	−16.3067	−0.612410	−0.306205	−	0.951966i	$-0.599059\pi$
$709$	−16.3067	−0.612410	−0.306205	+	0.951966i	$0.599059\pi$
$710$	0	0
$711$	7.36066	0.276046
$712$	10.1800	0.381510
$713$	−10.3302	−0.386870
$714$	9.90128	0.370546
$715$	0	0
$716$	30.5594	1.14206
$717$	−20.4820	−0.764915
$718$	−8.83756	−0.329815
$719$	−27.4968	−1.02546	−0.512729	−	0.858551i	$-0.671365\pi$
$719$	−27.4968	−1.02546	−0.512729	+	0.858551i	$0.671365\pi$
$720$	0	0
$721$	45.2410	1.68486
$722$	0.779256	0.0290009
$723$	−0.815004	−0.0303103
$724$	−31.2180	−1.16021
$725$	0	0
$726$	2.87460	0.106686
$727$	15.2319	0.564919	0.282460	−	0.959279i	$-0.408850\pi$
$727$	15.2319	0.564919	0.282460	+	0.959279i	$0.408850\pi$
$728$	32.6201	1.20898
$729$	2.54349	0.0942032
$730$	0	0
$731$	15.8642	0.586758
$732$	19.9972	0.739118
$733$	−6.76475	−0.249862	−0.124931	−	0.992165i	$-0.539871\pi$
$733$	−6.76475	−0.249862	−0.124931	+	0.992165i	$0.539871\pi$
$734$	−5.35490	−0.197653
$735$	0	0
$736$	−7.05548	−0.260068
$737$	14.1734	0.522082
$738$	10.4607	0.385062
$739$	17.9519	0.660372	0.330186	−	0.943916i	$-0.392889\pi$
$739$	17.9519	0.660372	0.330186	+	0.943916i	$0.392889\pi$
$740$	0	0
$741$	−13.1084	−0.481551
$742$	12.7043	0.466390
$743$	17.2096	0.631357	0.315679	−	0.948866i	$-0.397768\pi$
$743$	17.2096	0.631357	0.315679	+	0.948866i	$0.397768\pi$
$744$	−10.8300	−0.397047
$745$	0	0
$746$	2.55195	0.0934336
$747$	−5.76518	−0.210937
$748$	18.4714	0.675380
$749$	42.2188	1.54264
$750$	0	0
$751$	4.98853	0.182034	0.0910170	−	0.995849i	$-0.470988\pi$
$751$	4.98853	0.182034	0.0910170	+	0.995849i	$0.470988\pi$
$752$	−6.53032	−0.238136
$753$	2.05575	0.0749156
$754$	9.12739	0.332400
$755$	0	0
$756$	35.3635	1.28616
$757$	19.5585	0.710864	0.355432	−	0.934702i	$-0.384334\pi$
$757$	19.5585	0.710864	0.355432	+	0.934702i	$0.384334\pi$
$758$	−3.93335	−0.142866
$759$	2.25349	0.0817966
$760$	0	0
$761$	−41.0235	−1.48710	−0.743550	−	0.668681i	$-0.766859\pi$
$761$	−41.0235	−1.48710	−0.743550	+	0.668681i	$0.766859\pi$
$762$	4.50474	0.163189
$763$	14.9738	0.542087
$764$	−23.3425	−0.844503
$765$	0	0
$766$	1.20131	0.0434053
$767$	−46.1847	−1.66763
$768$	0.162852	0.00587641
$769$	11.7068	0.422159	0.211079	−	0.977469i	$-0.432302\pi$
$769$	11.7068	0.422159	0.211079	+	0.977469i	$0.432302\pi$
$770$	0	0
$771$	−3.19765	−0.115161
$772$	−44.9489	−1.61775
$773$	6.66278	0.239643	0.119822	−	0.992795i	$-0.461768\pi$
$773$	6.66278	0.239643	0.119822	+	0.992795i	$0.461768\pi$
$774$	−3.34238	−0.120140
$775$	0	0
$776$	−9.68090	−0.347524
$777$	−26.7962	−0.961309
$778$	13.9945	0.501727
$779$	−38.3338	−1.37345
$780$	0	0
$781$	−28.8719	−1.03312
$782$	3.75331	0.134218
$783$	21.1234	0.754888
$784$	37.5980	1.34279
$785$	0	0
$786$	−5.61071	−0.200127
$787$	−2.88890	−0.102978	−0.0514891	−	0.998674i	$-0.516397\pi$
$787$	−2.88890	−0.102978	−0.0514891	+	0.998674i	$0.516397\pi$
$788$	−26.4909	−0.943698
$789$	−5.09364	−0.181338
$790$	0	0
$791$	3.88896	0.138275
$792$	−8.30778	−0.295204
$793$	−53.6767	−1.90612
$794$	5.87762	0.208589
$795$	0	0
$796$	34.1574	1.21068
$797$	−18.0912	−0.640824	−0.320412	−	0.947278i	$-0.603821\pi$
$797$	−18.0912	−0.640824	−0.320412	+	0.947278i	$0.603821\pi$
$798$	7.64455	0.270614
$799$	13.4084	0.474355
$800$	0	0
$801$	−12.9678	−0.458193
$802$	15.4528	0.545656
$803$	−0.466051	−0.0164466
$804$	−10.4958	−0.370159
$805$	0	0
$806$	13.6175	0.479655
$807$	16.7029	0.587971
$808$	−22.7809	−0.801428
$809$	8.04121	0.282714	0.141357	−	0.989959i	$-0.454853\pi$
$809$	8.04121	0.282714	0.141357	+	0.989959i	$0.454853\pi$
$810$	0	0
$811$	24.5111	0.860701	0.430350	−	0.902662i	$-0.358390\pi$
$811$	24.5111	0.860701	0.430350	+	0.902662i	$0.358390\pi$
$812$	39.5008	1.38621
$813$	12.4842	0.437839
$814$	6.73632	0.236108
$815$	0	0
$816$	−11.5870	−0.405626
$817$	12.2484	0.428517
$818$	6.91507	0.241780
$819$	−41.5532	−1.45199
$820$	0	0
$821$	−10.6539	−0.371823	−0.185912	−	0.982566i	$-0.559524\pi$
$821$	−10.6539	−0.371823	−0.185912	+	0.982566i	$0.559524\pi$
$822$	−5.14574	−0.179478
$823$	−25.6473	−0.894009	−0.447004	−	0.894532i	$-0.647509\pi$
$823$	−25.6473	−0.894009	−0.447004	+	0.894532i	$0.647509\pi$
$824$	17.9793	0.626339
$825$	0	0
$826$	26.9339	0.937150
$827$	−18.0150	−0.626442	−0.313221	−	0.949680i	$-0.601408\pi$
$827$	−18.0150	−0.626442	−0.313221	+	0.949680i	$0.601408\pi$
$828$	5.86828	0.203937
$829$	10.1189	0.351444	0.175722	−	0.984440i	$-0.443774\pi$
$829$	10.1189	0.351444	0.175722	+	0.984440i	$0.443774\pi$
$830$	0	0
$831$	−2.66008	−0.0922771
$832$	−10.9911	−0.381047
$833$	−77.1981	−2.67476
$834$	−3.27125	−0.113274
$835$	0	0
$836$	14.2613	0.493238
$837$	31.5148	1.08931
$838$	−15.1571	−0.523593
$839$	−46.0365	−1.58936	−0.794679	−	0.607030i	$-0.792361\pi$
$839$	−46.0365	−1.58936	−0.794679	+	0.607030i	$0.792361\pi$
$840$	0	0
$841$	−5.40531	−0.186390
$842$	13.3734	0.460879
$843$	−10.1705	−0.350292
$844$	−49.2411	−1.69495
$845$	0	0
$846$	−2.82498	−0.0971247
$847$	−33.3928	−1.14739
$848$	−14.8673	−0.510544
$849$	12.8865	0.442262
$850$	0	0
$851$	−10.1577	−0.348202
$852$	21.3805	0.732485
$853$	55.0001	1.88317	0.941584	−	0.336780i	$-0.109338\pi$
$853$	55.0001	1.88317	0.941584	+	0.336780i	$0.109338\pi$
$854$	31.3031	1.07117
$855$	0	0
$856$	16.7783	0.573469
$857$	31.5202	1.07671	0.538354	−	0.842719i	$-0.319046\pi$
$857$	31.5202	1.07671	0.538354	+	0.842719i	$0.319046\pi$
$858$	−2.97059	−0.101414
$859$	−37.2208	−1.26996	−0.634979	−	0.772529i	$-0.718991\pi$
$859$	−37.2208	−1.26996	−0.634979	+	0.772529i	$0.718991\pi$
$860$	0	0
$861$	34.5561	1.17767
$862$	6.87180	0.234054
$863$	−30.3224	−1.03218	−0.516092	−	0.856533i	$-0.672614\pi$
$863$	−30.3224	−1.03218	−0.516092	+	0.856533i	$0.672614\pi$
$864$	21.5244	0.732274
$865$	0	0
$866$	−8.64563	−0.293791
$867$	9.93592	0.337442
$868$	58.9327	2.00031
$869$	−6.11267	−0.207358
$870$	0	0
$871$	28.1730	0.954605
$872$	5.95075	0.201518
$873$	12.3320	0.417376
$874$	2.89784	0.0980210
$875$	0	0
$876$	0.345125	0.0116607
$877$	−27.0037	−0.911849	−0.455925	−	0.890018i	$-0.650691\pi$
$877$	−27.0037	−0.911849	−0.455925	+	0.890018i	$0.650691\pi$
$878$	1.23028	0.0415200
$879$	−15.2526	−0.514457
$880$	0	0
$881$	−0.565506	−0.0190524	−0.00952619	−	0.999955i	$-0.503032\pi$
$881$	−0.565506	−0.0190524	−0.00952619	+	0.999955i	$0.503032\pi$
$882$	16.2647	0.547660
$883$	−23.8838	−0.803752	−0.401876	−	0.915694i	$-0.631642\pi$
$883$	−23.8838	−0.803752	−0.401876	+	0.915694i	$0.631642\pi$
$884$	36.7163	1.23490
$885$	0	0
$886$	−8.20600	−0.275686
$887$	10.1717	0.341533	0.170767	−	0.985311i	$-0.445376\pi$
$887$	10.1717	0.341533	0.170767	+	0.985311i	$0.445376\pi$
$888$	−10.6491	−0.357362
$889$	−52.3294	−1.75507
$890$	0	0
$891$	6.71757	0.225047
$892$	−0.682968	−0.0228675
$893$	10.3523	0.346427
$894$	−1.78180	−0.0595924
$895$	0	0
$896$	52.0843	1.74001
$897$	4.47937	0.149562
$898$	14.8975	0.497135
$899$	35.2018	1.17405
$900$	0	0
$901$	30.5262	1.01697
$902$	−8.68707	−0.289248
$903$	−11.0413	−0.367432
$904$	1.54552	0.0514031
$905$	0	0
$906$	−0.0370823	−0.00123198
$907$	44.1661	1.46651	0.733255	−	0.679954i	$-0.238000\pi$
$907$	44.1661	1.46651	0.733255	+	0.679954i	$0.238000\pi$
$908$	18.1146	0.601154
$909$	29.0194	0.962514
$910$	0	0
$911$	−7.07316	−0.234344	−0.117172	−	0.993112i	$-0.537383\pi$
$911$	−7.07316	−0.234344	−0.117172	+	0.993112i	$0.537383\pi$
$912$	−8.94605	−0.296233
$913$	4.78770	0.158450
$914$	−15.9382	−0.527190
$915$	0	0
$916$	18.5672	0.613479
$917$	65.1769	2.15233
$918$	−11.4503	−0.377917
$919$	23.6016	0.778544	0.389272	−	0.921123i	$-0.372727\pi$
$919$	23.6016	0.778544	0.389272	+	0.921123i	$0.372727\pi$
$920$	0	0
$921$	−4.26636	−0.140581
$922$	−6.03976	−0.198909
$923$	−57.3899	−1.88901
$924$	−12.8559	−0.422928
$925$	0	0
$926$	5.91530	0.194389
$927$	−22.9030	−0.752233
$928$	24.0426	0.789236
$929$	31.8496	1.04495	0.522475	−	0.852654i	$-0.325009\pi$
$929$	31.8496	1.04495	0.522475	+	0.852654i	$0.325009\pi$
$930$	0	0
$931$	−59.6029	−1.95341
$932$	45.2478	1.48214
$933$	−21.7506	−0.712083
$934$	2.62290	0.0858238
$935$	0	0
$936$	−16.5137	−0.539768
$937$	−44.1729	−1.44307	−0.721533	−	0.692380i	$-0.756562\pi$
$937$	−44.1729	−1.44307	−0.721533	+	0.692380i	$0.756562\pi$
$938$	−16.4299	−0.536454
$939$	−5.08677	−0.166001
$940$	0	0
$941$	−34.5303	−1.12566	−0.562828	−	0.826574i	$-0.690287\pi$
$941$	−34.5303	−1.12566	−0.562828	+	0.826574i	$0.690287\pi$
$942$	−4.02498	−0.131141
$943$	13.0993	0.426571
$944$	−31.5194	−1.02587
$945$	0	0
$946$	2.77569	0.0902454
$947$	3.46191	0.112497	0.0562485	−	0.998417i	$-0.482086\pi$
$947$	3.46191	0.112497	0.0562485	+	0.998417i	$0.482086\pi$
$948$	4.52662	0.147018
$949$	−0.926389	−0.0300719
$950$	0	0
$951$	−5.61966	−0.182230
$952$	−45.7097	−1.48146
$953$	−60.2596	−1.95200	−0.976000	−	0.217771i	$-0.930122\pi$
$953$	−60.2596	−1.95200	−0.976000	+	0.217771i	$0.930122\pi$
$954$	−6.43148	−0.208227
$955$	0	0
$956$	44.2936	1.43256
$957$	−7.67911	−0.248230
$958$	12.3664	0.399541
$959$	59.7755	1.93025
$960$	0	0
$961$	21.5188	0.694156
$962$	13.3901	0.431713
$963$	−21.3730	−0.688735
$964$	1.76250	0.0567662
$965$	0	0
$966$	−2.61227	−0.0840483
$967$	39.9168	1.28364	0.641819	−	0.766856i	$-0.278180\pi$
$967$	39.9168	1.28364	0.641819	+	0.766856i	$0.278180\pi$
$968$	−13.2707	−0.426536
$969$	18.3685	0.590081
$970$	0	0
$971$	43.7104	1.40273	0.701366	−	0.712801i	$-0.252574\pi$
$971$	43.7104	1.40273	0.701366	+	0.712801i	$0.252574\pi$
$972$	−27.9681	−0.897078
$973$	38.0006	1.21824
$974$	−5.08020	−0.162780
$975$	0	0
$976$	−36.6325	−1.17258
$977$	0.955388	0.0305656	0.0152828	−	0.999883i	$-0.495135\pi$
$977$	0.955388	0.0305656	0.0152828	+	0.999883i	$0.495135\pi$
$978$	2.97812	0.0952298
$979$	10.7691	0.344182
$980$	0	0
$981$	−7.58037	−0.242023
$982$	−16.7090	−0.533205
$983$	48.7488	1.55485	0.777423	−	0.628978i	$-0.216526\pi$
$983$	48.7488	1.55485	0.777423	+	0.628978i	$0.216526\pi$
$984$	13.7330	0.437792
$985$	0	0
$986$	−12.7899	−0.407315
$987$	−9.33211	−0.297044
$988$	28.3478	0.901865
$989$	−4.18547	−0.133090
$990$	0	0
$991$	0.488986	0.0155332	0.00776658	−	0.999970i	$-0.497528\pi$
$991$	0.488986	0.0155332	0.00776658	+	0.999970i	$0.497528\pi$
$992$	35.8700	1.13887
$993$	−11.0594	−0.350959
$994$	33.4685	1.06156
$995$	0	0
$996$	−3.54544	−0.112342
$997$	−39.5339	−1.25205	−0.626026	−	0.779802i	$-0.715320\pi$
$997$	−39.5339	−1.25205	−0.626026	+	0.779802i	$0.715320\pi$
$998$	−7.78153	−0.246320
$999$	30.9885	0.980432

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.f.1.2		7
5.4	even	2		241.2.a.a.1.6	✓	7
15.14	odd	2		2169.2.a.e.1.2		7
20.19	odd	2		3856.2.a.j.1.5		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
241.2.a.a.1.6	✓	7	5.4	even	2
2169.2.a.e.1.2		7	15.14	odd	2
3856.2.a.j.1.5		7	20.19	odd	2
6025.2.a.f.1.2		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)

\(f(q)\)	\(=\)	\(q-0.487343 q^{2} +0.815004 q^{3} -1.76250 q^{4} -0.397187 q^{6} +4.61392 q^{7} +1.83363 q^{8} -2.33577 q^{9} +O(q^{10})\)	\(q-0.487343 q^{2} +0.815004 q^{3} -1.76250 q^{4} -0.397187 q^{6} +4.61392 q^{7} +1.83363 q^{8} -2.33577 q^{9} +1.93974 q^{11} -1.43644 q^{12} +3.85571 q^{13} -2.24856 q^{14} +2.63139 q^{16} -5.40289 q^{17} +1.13832 q^{18} -4.17145 q^{19} +3.76036 q^{21} -0.945321 q^{22} +1.42545 q^{23} +1.49441 q^{24} -1.87905 q^{26} -4.34867 q^{27} -8.13202 q^{28} -4.85744 q^{29} -7.24699 q^{31} -4.94964 q^{32} +1.58090 q^{33} +2.63306 q^{34} +4.11678 q^{36} -7.12597 q^{37} +2.03293 q^{38} +3.14242 q^{39} +9.18955 q^{41} -1.83259 q^{42} -2.93624 q^{43} -3.41879 q^{44} -0.694685 q^{46} -2.48170 q^{47} +2.14459 q^{48} +14.2883 q^{49} -4.40338 q^{51} -6.79568 q^{52} -5.64997 q^{53} +2.11930 q^{54} +8.46022 q^{56} -3.39975 q^{57} +2.36724 q^{58} -11.9783 q^{59} -13.9214 q^{61} +3.53177 q^{62} -10.7771 q^{63} -2.85060 q^{64} -0.770440 q^{66} +7.30682 q^{67} +9.52258 q^{68} +1.16175 q^{69} -14.8844 q^{71} -4.28293 q^{72} -0.240264 q^{73} +3.47279 q^{74} +7.35217 q^{76} +8.94983 q^{77} -1.53144 q^{78} -3.15128 q^{79} +3.46313 q^{81} -4.47847 q^{82} +2.46821 q^{83} -6.62763 q^{84} +1.43096 q^{86} -3.95883 q^{87} +3.55677 q^{88} +5.55181 q^{89} +17.7900 q^{91} -2.51235 q^{92} -5.90632 q^{93} +1.20944 q^{94} -4.03398 q^{96} -5.27964 q^{97} -6.96330 q^{98} -4.53079 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 4 q^{2} + 3 q^{3} + 2 q^{4} - 5 q^{6} + 7 q^{7} + 6 q^{8} - 2 q^{9}+O(q^{10}) \) 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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