LMFDB - Embedded newform 6025.2.a.n.1.13

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:	$0$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
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)

$f(q)$	$=$	$q-0.785880 q^{2} -0.0947217 q^{3} -1.38239 q^{4} +0.0744399 q^{6} +3.94418 q^{7} +2.65816 q^{8} -2.99103 q^{9} +O(q^{10})$	\(q-0.785880 q^{2} -0.0947217 q^{3} -1.38239 q^{4} +0.0744399 q^{6} +3.94418 q^{7} +2.65816 q^{8} -2.99103 q^{9} +4.77418 q^{11} +0.130943 q^{12} -2.97479 q^{13} -3.09965 q^{14} +0.675793 q^{16} -1.89018 q^{17} +2.35059 q^{18} +1.88768 q^{19} -0.373599 q^{21} -3.75193 q^{22} +6.71720 q^{23} -0.251785 q^{24} +2.33783 q^{26} +0.567481 q^{27} -5.45240 q^{28} +1.28288 q^{29} +8.34597 q^{31} -5.84740 q^{32} -0.452219 q^{33} +1.48545 q^{34} +4.13477 q^{36} -11.1334 q^{37} -1.48349 q^{38} +0.281777 q^{39} -2.55001 q^{41} +0.293604 q^{42} +5.94817 q^{43} -6.59979 q^{44} -5.27892 q^{46} +9.04414 q^{47} -0.0640123 q^{48} +8.55653 q^{49} +0.179041 q^{51} +4.11232 q^{52} +7.50001 q^{53} -0.445972 q^{54} +10.4842 q^{56} -0.178805 q^{57} -1.00819 q^{58} -8.85114 q^{59} +5.77279 q^{61} -6.55894 q^{62} -11.7971 q^{63} +3.24377 q^{64} +0.355390 q^{66} -9.08208 q^{67} +2.61297 q^{68} -0.636265 q^{69} -2.61889 q^{71} -7.95062 q^{72} +14.8088 q^{73} +8.74951 q^{74} -2.60952 q^{76} +18.8302 q^{77} -0.221443 q^{78} +3.20544 q^{79} +8.91933 q^{81} +2.00400 q^{82} -9.12458 q^{83} +0.516461 q^{84} -4.67455 q^{86} -0.121517 q^{87} +12.6905 q^{88} -13.4880 q^{89} -11.7331 q^{91} -9.28581 q^{92} -0.790545 q^{93} -7.10761 q^{94} +0.553876 q^{96} +1.34999 q^{97} -6.72440 q^{98} -14.2797 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 9 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 20 q^{7} + 27 q^{8} + 38 q^{9}+O(q^{10}) $ 40 * q + 9 * q^2 + 8 * q^3 + 41 * q^4 + 3 * q^6 + 20 * q^7 + 27 * q^8 + 38 * q^9	$ 40 q + 9 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 20 q^{7} + 27 q^{8} + 38 q^{9} + q^{11} + 26 q^{12} + 11 q^{13} - q^{14} + 43 q^{16} + 20 q^{17} + 18 q^{18} + 2 q^{21} + 23 q^{22} + 79 q^{23} - 2 q^{24} + 2 q^{26} + 26 q^{27} + 30 q^{28} + 2 q^{29} + q^{31} + 68 q^{32} + 20 q^{33} + 5 q^{34} + 32 q^{36} + 16 q^{37} + 45 q^{38} - 2 q^{39} - 2 q^{41} + 19 q^{42} + 25 q^{43} + 3 q^{44} + 14 q^{46} + 88 q^{47} + 75 q^{48} + 40 q^{49} - 10 q^{51} + 18 q^{52} + 34 q^{53} + 4 q^{54} - 15 q^{56} + 51 q^{57} + 53 q^{58} + q^{59} + 9 q^{61} + 39 q^{62} + 110 q^{63} + 17 q^{64} + 26 q^{66} + 30 q^{67} + 44 q^{68} - 7 q^{69} + 5 q^{71} + 18 q^{72} + 23 q^{73} - 18 q^{74} + 43 q^{76} + 30 q^{77} + 46 q^{78} + 5 q^{79} + 44 q^{81} + 5 q^{82} + 65 q^{83} - 65 q^{84} + 40 q^{86} + 33 q^{87} + 71 q^{88} - 9 q^{89} + q^{91} + 117 q^{92} + 68 q^{93} - 72 q^{94} + 83 q^{96} - 8 q^{97} + 76 q^{98} - 40 q^{99}+O(q^{100}) $ 40 * q + 9 * q^2 + 8 * q^3 + 41 * q^4 + 3 * q^6 + 20 * q^7 + 27 * q^8 + 38 * q^9 + q^11 + 26 * q^12 + 11 * q^13 - q^14 + 43 * q^16 + 20 * q^17 + 18 * q^18 + 2 * q^21 + 23 * q^22 + 79 * q^23 - 2 * q^24 + 2 * q^26 + 26 * q^27 + 30 * q^28 + 2 * q^29 + q^31 + 68 * q^32 + 20 * q^33 + 5 * q^34 + 32 * q^36 + 16 * q^37 + 45 * q^38 - 2 * q^39 - 2 * q^41 + 19 * q^42 + 25 * q^43 + 3 * q^44 + 14 * q^46 + 88 * q^47 + 75 * q^48 + 40 * q^49 - 10 * q^51 + 18 * q^52 + 34 * q^53 + 4 * q^54 - 15 * q^56 + 51 * q^57 + 53 * q^58 + q^59 + 9 * q^61 + 39 * q^62 + 110 * q^63 + 17 * q^64 + 26 * q^66 + 30 * q^67 + 44 * q^68 - 7 * q^69 + 5 * q^71 + 18 * q^72 + 23 * q^73 - 18 * q^74 + 43 * q^76 + 30 * q^77 + 46 * q^78 + 5 * q^79 + 44 * q^81 + 5 * q^82 + 65 * q^83 - 65 * q^84 + 40 * q^86 + 33 * q^87 + 71 * q^88 - 9 * q^89 + q^91 + 117 * q^92 + 68 * q^93 - 72 * q^94 + 83 * q^96 - 8 * q^97 + 76 * q^98 - 40 * 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 $

$2$	−0.785880	−0.555701	−0.277851	−	0.960624i	$-0.589622\pi$
$2$	−0.785880	−0.555701	−0.277851	+	0.960624i	$0.589622\pi$
$3$	−0.0947217	−0.0546876	−0.0273438	−	0.999626i	$-0.508705\pi$
$3$	−0.0947217	−0.0546876	−0.0273438	+	0.999626i	$0.508705\pi$
$4$	−1.38239	−0.691196
$5$	0	0
$5$	0	0
$6$	0.0744399	0.0303900
$7$	3.94418	1.49076	0.745379	−	0.666641i	$-0.232268\pi$
$7$	3.94418	1.49076	0.745379	+	0.666641i	$0.232268\pi$
$8$	2.65816	0.939800
$9$	−2.99103	−0.997009
$10$	0	0
$11$	4.77418	1.43947	0.719735	−	0.694249i	$-0.244263\pi$
$11$	4.77418	1.43947	0.719735	+	0.694249i	$0.244263\pi$
$12$	0.130943	0.0377999
$13$	−2.97479	−0.825057	−0.412529	−	0.910945i	$-0.635354\pi$
$13$	−2.97479	−0.825057	−0.412529	+	0.910945i	$0.635354\pi$
$14$	−3.09965	−0.828416
$15$	0	0
$16$	0.675793	0.168948
$17$	−1.89018	−0.458436	−0.229218	−	0.973375i	$-0.573617\pi$
$17$	−1.89018	−0.458436	−0.229218	+	0.973375i	$0.573617\pi$
$18$	2.35059	0.554039
$19$	1.88768	0.433064	0.216532	−	0.976275i	$-0.430525\pi$
$19$	1.88768	0.433064	0.216532	+	0.976275i	$0.430525\pi$
$20$	0	0
$21$	−0.373599	−0.0815260
$22$	−3.75193	−0.799915
$23$	6.71720	1.40063	0.700317	−	0.713832i	$-0.253042\pi$
$23$	6.71720	1.40063	0.700317	+	0.713832i	$0.253042\pi$
$24$	−0.251785	−0.0513954
$25$	0	0
$26$	2.33783	0.458485
$27$	0.567481	0.109212
$28$	−5.45240	−1.03041
$29$	1.28288	0.238225	0.119113	−	0.992881i	$-0.461995\pi$
$29$	1.28288	0.238225	0.119113	+	0.992881i	$0.461995\pi$
$30$	0	0
$31$	8.34597	1.49898	0.749491	−	0.662015i	$-0.230299\pi$
$31$	8.34597	1.49898	0.749491	+	0.662015i	$0.230299\pi$
$32$	−5.84740	−1.03368
$33$	−0.452219	−0.0787212
$34$	1.48545	0.254753
$35$	0	0
$36$	4.13477	0.689129
$37$	−11.1334	−1.83032	−0.915159	−	0.403093i	$-0.867935\pi$
$37$	−11.1334	−1.83032	−0.915159	+	0.403093i	$0.867935\pi$
$38$	−1.48349	−0.240654
$39$	0.281777	0.0451204
$40$	0	0
$41$	−2.55001	−0.398245	−0.199122	−	0.979975i	$-0.563809\pi$
$41$	−2.55001	−0.398245	−0.199122	+	0.979975i	$0.563809\pi$
$42$	0.293604	0.0453041
$43$	5.94817	0.907087	0.453543	−	0.891234i	$-0.350160\pi$
$43$	5.94817	0.907087	0.453543	+	0.891234i	$0.350160\pi$
$44$	−6.59979	−0.994956
$45$	0	0
$46$	−5.27892	−0.778334
$47$	9.04414	1.31922	0.659612	−	0.751607i	$-0.270721\pi$
$47$	9.04414	1.31922	0.659612	+	0.751607i	$0.270721\pi$
$48$	−0.0640123	−0.00923938
$49$	8.55653	1.22236
$50$	0	0
$51$	0.179041	0.0250708
$52$	4.11232	0.570276
$53$	7.50001	1.03021	0.515103	−	0.857128i	$-0.327754\pi$
$53$	7.50001	1.03021	0.515103	+	0.857128i	$0.327754\pi$
$54$	−0.445972	−0.0606891
$55$	0	0
$56$	10.4842	1.40101
$57$	−0.178805	−0.0236833
$58$	−1.00819	−0.132382
$59$	−8.85114	−1.15232	−0.576160	−	0.817337i	$-0.695450\pi$
$59$	−8.85114	−1.15232	−0.576160	+	0.817337i	$0.695450\pi$
$60$	0	0
$61$	5.77279	0.739130	0.369565	−	0.929205i	$-0.379507\pi$
$61$	5.77279	0.739130	0.369565	+	0.929205i	$0.379507\pi$
$62$	−6.55894	−0.832986
$63$	−11.7971	−1.48630
$64$	3.24377	0.405472
$65$	0	0
$66$	0.355390	0.0437454
$67$	−9.08208	−1.10955	−0.554776	−	0.832000i	$-0.687196\pi$
$67$	−9.08208	−1.10955	−0.554776	+	0.832000i	$0.687196\pi$
$68$	2.61297	0.316869
$69$	−0.636265	−0.0765973
$70$	0	0
$71$	−2.61889	−0.310805	−0.155402	−	0.987851i	$-0.549667\pi$
$71$	−2.61889	−0.310805	−0.155402	+	0.987851i	$0.549667\pi$
$72$	−7.95062	−0.936989
$73$	14.8088	1.73323	0.866617	−	0.498974i	$-0.166290\pi$
$73$	14.8088	1.73323	0.866617	+	0.498974i	$0.166290\pi$
$74$	8.74951	1.01711
$75$	0	0
$76$	−2.60952	−0.299332
$77$	18.8302	2.14590
$78$	−0.221443	−0.0250735
$79$	3.20544	0.360640	0.180320	−	0.983608i	$-0.442287\pi$
$79$	3.20544	0.360640	0.180320	+	0.983608i	$0.442287\pi$
$80$	0	0
$81$	8.91933	0.991037
$82$	2.00400	0.221305
$83$	−9.12458	−1.00155	−0.500777	−	0.865577i	$-0.666952\pi$
$83$	−9.12458	−1.00155	−0.500777	+	0.865577i	$0.666952\pi$
$84$	0.516461	0.0563505
$85$	0	0
$86$	−4.67455	−0.504069
$87$	−0.121517	−0.0130280
$88$	12.6905	1.35281
$89$	−13.4880	−1.42973	−0.714865	−	0.699263i	$-0.753512\pi$
$89$	−13.4880	−1.42973	−0.714865	+	0.699263i	$0.753512\pi$
$90$	0	0
$91$	−11.7331	−1.22996
$92$	−9.28581	−0.968112
$93$	−0.790545	−0.0819757
$94$	−7.10761	−0.733094
$95$	0	0
$96$	0.553876	0.0565298
$97$	1.34999	0.137071	0.0685356	−	0.997649i	$-0.478167\pi$
$97$	1.34999	0.137071	0.0685356	+	0.997649i	$0.478167\pi$
$98$	−6.72440	−0.679267
$99$	−14.2797	−1.43516
$100$	0	0
$101$	−6.69479	−0.666156	−0.333078	−	0.942899i	$-0.608087\pi$
$101$	−6.69479	−0.666156	−0.333078	+	0.942899i	$0.608087\pi$
$102$	−0.140705	−0.0139318
$103$	−13.2883	−1.30934	−0.654668	−	0.755917i	$-0.727191\pi$
$103$	−13.2883	−1.30934	−0.654668	+	0.755917i	$0.727191\pi$
$104$	−7.90744	−0.775389
$105$	0	0
$106$	−5.89411	−0.572487
$107$	15.9719	1.54407	0.772033	−	0.635583i	$-0.219240\pi$
$107$	15.9719	1.54407	0.772033	+	0.635583i	$0.219240\pi$
$108$	−0.784481	−0.0754867
$109$	12.1047	1.15942	0.579710	−	0.814823i	$-0.303166\pi$
$109$	12.1047	1.15942	0.579710	+	0.814823i	$0.303166\pi$
$110$	0	0
$111$	1.05457	0.100096
$112$	2.66545	0.251861
$113$	−3.72907	−0.350801	−0.175401	−	0.984497i	$-0.556122\pi$
$113$	−3.72907	−0.350801	−0.175401	+	0.984497i	$0.556122\pi$
$114$	0.140519	0.0131608
$115$	0	0
$116$	−1.77345	−0.164660
$117$	8.89767	0.822590
$118$	6.95594	0.640346
$119$	−7.45520	−0.683417
$120$	0	0
$121$	11.7928	1.07207
$122$	−4.53672	−0.410735
$123$	0.241542	0.0217791
$124$	−11.5374	−1.03609
$125$	0	0
$126$	9.27114	0.825939
$127$	16.4291	1.45785	0.728923	−	0.684596i	$-0.240021\pi$
$127$	16.4291	1.45785	0.728923	+	0.684596i	$0.240021\pi$
$128$	9.14559	0.808363
$129$	−0.563421	−0.0496064
$130$	0	0
$131$	−6.80888	−0.594895	−0.297447	−	0.954738i	$-0.596135\pi$
$131$	−6.80888	−0.594895	−0.297447	+	0.954738i	$0.596135\pi$
$132$	0.625144	0.0544118
$133$	7.44536	0.645594
$134$	7.13743	0.616580
$135$	0	0
$136$	−5.02439	−0.430838
$137$	23.0751	1.97144	0.985721	−	0.168388i	$-0.0538560\pi$
$137$	23.0751	1.97144	0.985721	+	0.168388i	$0.0538560\pi$
$138$	0.500028	0.0425652
$139$	11.4953	0.975018	0.487509	−	0.873118i	$-0.337906\pi$
$139$	11.4953	0.975018	0.487509	+	0.873118i	$0.337906\pi$
$140$	0	0
$141$	−0.856677	−0.0721452
$142$	2.05813	0.172715
$143$	−14.2022	−1.18764
$144$	−2.02132	−0.168443
$145$	0	0
$146$	−11.6379	−0.963160
$147$	−0.810489	−0.0668480
$148$	15.3907	1.26511
$149$	−14.0701	−1.15267	−0.576335	−	0.817213i	$-0.695518\pi$
$149$	−14.0701	−1.15267	−0.576335	+	0.817213i	$0.695518\pi$
$150$	0	0
$151$	−16.6665	−1.35630	−0.678150	−	0.734924i	$-0.737218\pi$
$151$	−16.6665	−1.35630	−0.678150	+	0.734924i	$0.737218\pi$
$152$	5.01776	0.406994
$153$	5.65358	0.457065
$154$	−14.7983	−1.19248
$155$	0	0
$156$	−0.389526	−0.0311871
$157$	−13.6474	−1.08918	−0.544590	−	0.838702i	$-0.683315\pi$
$157$	−13.6474	−1.08918	−0.544590	+	0.838702i	$0.683315\pi$
$158$	−2.51909	−0.200408
$159$	−0.710414	−0.0563395
$160$	0	0
$161$	26.4938	2.08801
$162$	−7.00953	−0.550720
$163$	−5.98126	−0.468488	−0.234244	−	0.972178i	$-0.575262\pi$
$163$	−5.98126	−0.468488	−0.234244	+	0.972178i	$0.575262\pi$
$164$	3.52512	0.275265
$165$	0	0
$166$	7.17083	0.556564
$167$	10.2728	0.794935	0.397467	−	0.917616i	$-0.369889\pi$
$167$	10.2728	0.794935	0.397467	+	0.917616i	$0.369889\pi$
$168$	−0.993085	−0.0766182
$169$	−4.15065	−0.319281
$170$	0	0
$171$	−5.64611	−0.431769
$172$	−8.22270	−0.626975
$173$	−9.24449	−0.702845	−0.351423	−	0.936217i	$-0.614302\pi$
$173$	−9.24449	−0.702845	−0.351423	+	0.936217i	$0.614302\pi$
$174$	0.0954977	0.00723966
$175$	0	0
$176$	3.22636	0.243196
$177$	0.838396	0.0630177
$178$	10.6000	0.794503
$179$	−17.0601	−1.27513	−0.637564	−	0.770397i	$-0.720058\pi$
$179$	−17.0601	−1.27513	−0.637564	+	0.770397i	$0.720058\pi$
$180$	0	0
$181$	2.61252	0.194187	0.0970937	−	0.995275i	$-0.469045\pi$
$181$	2.61252	0.194187	0.0970937	+	0.995275i	$0.469045\pi$
$182$	9.22080	0.683491
$183$	−0.546809	−0.0404212
$184$	17.8554	1.31631
$185$	0	0
$186$	0.621274	0.0455540
$187$	−9.02405	−0.659904
$188$	−12.5025	−0.911842
$189$	2.23824	0.162808
$190$	0	0
$191$	−19.8681	−1.43761	−0.718804	−	0.695213i	$-0.755310\pi$
$191$	−19.8681	−1.43761	−0.718804	+	0.695213i	$0.755310\pi$
$192$	−0.307256	−0.0221743
$193$	−2.56469	−0.184611	−0.0923054	−	0.995731i	$-0.529424\pi$
$193$	−2.56469	−0.184611	−0.0923054	+	0.995731i	$0.529424\pi$
$194$	−1.06093	−0.0761706
$195$	0	0
$196$	−11.8285	−0.844891
$197$	1.98908	0.141716	0.0708580	−	0.997486i	$-0.477426\pi$
$197$	1.98908	0.141716	0.0708580	+	0.997486i	$0.477426\pi$
$198$	11.2221	0.797523
$199$	−13.5931	−0.963593	−0.481796	−	0.876283i	$-0.660015\pi$
$199$	−13.5931	−0.963593	−0.481796	+	0.876283i	$0.660015\pi$
$200$	0	0
$201$	0.860270	0.0606788
$202$	5.26130	0.370184
$203$	5.05991	0.355136
$204$	−0.247505	−0.0173288
$205$	0	0
$206$	10.4430	0.727599
$207$	−20.0913	−1.39644
$208$	−2.01034	−0.139392
$209$	9.01214	0.623383
$210$	0	0
$211$	−0.0185957	−0.00128018	−0.000640090	−	1.00000i	$-0.500204\pi$
$211$	−0.0185957	−0.00128018	−0.000640090		1.00000i	$0.500204\pi$
$212$	−10.3680	−0.712074
$213$	0.248065	0.0169972
$214$	−12.5520	−0.858039
$215$	0	0
$216$	1.50845	0.102637
$217$	32.9180	2.23462
$218$	−9.51285	−0.644292
$219$	−1.40271	−0.0947864
$220$	0	0
$221$	5.62288	0.378236
$222$	−0.828769	−0.0556233
$223$	3.05658	0.204684	0.102342	−	0.994749i	$-0.467366\pi$
$223$	3.05658	0.204684	0.102342	+	0.994749i	$0.467366\pi$
$224$	−23.0632	−1.54097
$225$	0	0
$226$	2.93060	0.194941
$227$	13.8550	0.919590	0.459795	−	0.888025i	$-0.347923\pi$
$227$	13.8550	0.919590	0.459795	+	0.888025i	$0.347923\pi$
$228$	0.247178	0.0163698
$229$	21.2563	1.40466	0.702328	−	0.711854i	$-0.252144\pi$
$229$	21.2563	1.40466	0.702328	+	0.711854i	$0.252144\pi$
$230$	0	0
$231$	−1.78363	−0.117354
$232$	3.41010	0.223884
$233$	−10.0579	−0.658916	−0.329458	−	0.944170i	$-0.606866\pi$
$233$	−10.0579	−0.658916	−0.329458	+	0.944170i	$0.606866\pi$
$234$	−6.99250	−0.457114
$235$	0	0
$236$	12.2358	0.796480
$237$	−0.303625	−0.0197225
$238$	5.85889	0.379776
$239$	20.9852	1.35742	0.678709	−	0.734408i	$-0.262540\pi$
$239$	20.9852	1.35742	0.678709	+	0.734408i	$0.262540\pi$
$240$	0	0
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	−9.26772	−0.595752
$243$	−2.54730	−0.163409
$244$	−7.98026	−0.510884
$245$	0	0
$246$	−0.189823	−0.0121027
$247$	−5.61546	−0.357303
$248$	22.1849	1.40874
$249$	0.864296	0.0547726
$250$	0	0
$251$	−1.56099	−0.0985291	−0.0492646	−	0.998786i	$-0.515688\pi$
$251$	−1.56099	−0.0985291	−0.0492646	+	0.998786i	$0.515688\pi$
$252$	16.3083	1.02732
$253$	32.0691	2.01617
$254$	−12.9113	−0.810127
$255$	0	0
$256$	−13.6749	−0.854680
$257$	26.0663	1.62597	0.812984	−	0.582286i	$-0.197842\pi$
$257$	26.0663	1.62597	0.812984	+	0.582286i	$0.197842\pi$
$258$	0.442781	0.0275664
$259$	−43.9121	−2.72856
$260$	0	0
$261$	−3.83714	−0.237513
$262$	5.35096	0.330584
$263$	27.7812	1.71307	0.856533	−	0.516093i	$-0.172614\pi$
$263$	27.7812	1.71307	0.856533	+	0.516093i	$0.172614\pi$
$264$	−1.20207	−0.0739821
$265$	0	0
$266$	−5.85116	−0.358758
$267$	1.27761	0.0781885
$268$	12.5550	0.766918
$269$	−17.9277	−1.09307	−0.546537	−	0.837435i	$-0.684054\pi$
$269$	−17.9277	−1.09307	−0.546537	+	0.837435i	$0.684054\pi$
$270$	0	0
$271$	−16.6947	−1.01413	−0.507065	−	0.861908i	$-0.669270\pi$
$271$	−16.6947	−1.01413	−0.507065	+	0.861908i	$0.669270\pi$
$272$	−1.27737	−0.0774519
$273$	1.11138	0.0672636
$274$	−18.1343	−1.09553
$275$	0	0
$276$	0.879568	0.0529438
$277$	−1.15417	−0.0693475	−0.0346738	−	0.999399i	$-0.511039\pi$
$277$	−1.15417	−0.0693475	−0.0346738	+	0.999399i	$0.511039\pi$
$278$	−9.03392	−0.541819
$279$	−24.9630	−1.49450
$280$	0	0
$281$	22.6631	1.35197	0.675983	−	0.736917i	$-0.263719\pi$
$281$	22.6631	1.35197	0.675983	+	0.736917i	$0.263719\pi$
$282$	0.673245	0.0400912
$283$	2.03929	0.121223	0.0606115	−	0.998161i	$-0.480695\pi$
$283$	2.03929	0.121223	0.0606115	+	0.998161i	$0.480695\pi$
$284$	3.62033	0.214827
$285$	0	0
$286$	11.1612	0.659976
$287$	−10.0577	−0.593687
$288$	17.4897	1.03059
$289$	−13.4272	−0.789837
$290$	0	0
$291$	−0.127874	−0.00749609
$292$	−20.4715	−1.19800
$293$	7.61161	0.444675	0.222338	−	0.974970i	$-0.428631\pi$
$293$	7.61161	0.444675	0.222338	+	0.974970i	$0.428631\pi$
$294$	0.636947	0.0371475
$295$	0	0
$296$	−29.5943	−1.72013
$297$	2.70925	0.157207
$298$	11.0574	0.640541
$299$	−19.9822	−1.15560
$300$	0	0
$301$	23.4606	1.35225
$302$	13.0979	0.753697
$303$	0.634142	0.0364305
$304$	1.27568	0.0731655
$305$	0	0
$306$	−4.44303	−0.253991
$307$	−11.8364	−0.675540	−0.337770	−	0.941229i	$-0.609673\pi$
$307$	−11.8364	−0.675540	−0.337770	+	0.941229i	$0.609673\pi$
$308$	−26.0307	−1.48324
$309$	1.25869	0.0716044
$310$	0	0
$311$	10.5015	0.595486	0.297743	−	0.954646i	$-0.403766\pi$
$311$	10.5015	0.595486	0.297743	+	0.954646i	$0.403766\pi$
$312$	0.749007	0.0424042
$313$	20.5624	1.16226	0.581129	−	0.813811i	$-0.302611\pi$
$313$	20.5624	1.16226	0.581129	+	0.813811i	$0.302611\pi$
$314$	10.7252	0.605259
$315$	0	0
$316$	−4.43117	−0.249273
$317$	−15.1637	−0.851676	−0.425838	−	0.904799i	$-0.640021\pi$
$317$	−15.1637	−0.851676	−0.425838	+	0.904799i	$0.640021\pi$
$318$	0.558300	0.0313079
$319$	6.12471	0.342918
$320$	0	0
$321$	−1.51289	−0.0844413
$322$	−20.8210	−1.16031
$323$	−3.56806	−0.198532
$324$	−12.3300	−0.685001
$325$	0	0
$326$	4.70055	0.260340
$327$	−1.14658	−0.0634060
$328$	−6.77833	−0.374271
$329$	35.6717	1.96664
$330$	0	0
$331$	16.4058	0.901743	0.450871	−	0.892589i	$-0.351113\pi$
$331$	16.4058	0.901743	0.450871	+	0.892589i	$0.351113\pi$
$332$	12.6138	0.692270
$333$	33.3003	1.82484
$334$	−8.07321	−0.441746
$335$	0	0
$336$	−0.252476	−0.0137737
$337$	25.8491	1.40809	0.704046	−	0.710155i	$-0.251375\pi$
$337$	25.8491	1.40809	0.704046	+	0.710155i	$0.251375\pi$
$338$	3.26191	0.177425
$339$	0.353224	0.0191845
$340$	0	0
$341$	39.8452	2.15774
$342$	4.43717	0.239935
$343$	6.13921	0.331486
$344$	15.8111	0.852480
$345$	0	0
$346$	7.26506	0.390572
$347$	15.3559	0.824349	0.412174	−	0.911105i	$-0.364769\pi$
$347$	15.3559	0.824349	0.412174	+	0.911105i	$0.364769\pi$
$348$	0.167984	0.00900488
$349$	36.2909	1.94261	0.971304	−	0.237843i	$-0.0764404\pi$
$349$	36.2909	1.94261	0.971304	+	0.237843i	$0.0764404\pi$
$350$	0	0
$351$	−1.68813	−0.0901059
$352$	−27.9166	−1.48796
$353$	−6.94726	−0.369765	−0.184883	−	0.982761i	$-0.559191\pi$
$353$	−6.94726	−0.369765	−0.184883	+	0.982761i	$0.559191\pi$
$354$	−0.658879	−0.0350190
$355$	0	0
$356$	18.6458	0.988224
$357$	0.706169	0.0373744
$358$	13.4072	0.708590
$359$	6.17571	0.325942	0.162971	−	0.986631i	$-0.447892\pi$
$359$	6.17571	0.325942	0.162971	+	0.986631i	$0.447892\pi$
$360$	0	0
$361$	−15.4366	−0.812455
$362$	−2.05313	−0.107910
$363$	−1.11703	−0.0586291
$364$	16.2197	0.850144
$365$	0	0
$366$	0.429726	0.0224621
$367$	20.4909	1.06962	0.534809	−	0.844973i	$-0.320384\pi$
$367$	20.4909	1.06962	0.534809	+	0.844973i	$0.320384\pi$
$368$	4.53944	0.236634
$369$	7.62716	0.397054
$370$	0	0
$371$	29.5814	1.53579
$372$	1.09284	0.0566613
$373$	21.0490	1.08988	0.544938	−	0.838476i	$-0.316553\pi$
$373$	21.0490	1.08988	0.544938	+	0.838476i	$0.316553\pi$
$374$	7.09182	0.366709
$375$	0	0
$376$	24.0407	1.23981
$377$	−3.81630	−0.196549
$378$	−1.75899	−0.0904728
$379$	12.7929	0.657129	0.328564	−	0.944482i	$-0.393435\pi$
$379$	12.7929	0.657129	0.328564	+	0.944482i	$0.393435\pi$
$380$	0	0
$381$	−1.55619	−0.0797261
$382$	15.6140	0.798880
$383$	20.5921	1.05221	0.526105	−	0.850420i	$-0.323652\pi$
$383$	20.5921	1.05221	0.526105	+	0.850420i	$0.323652\pi$
$384$	−0.866286	−0.0442075
$385$	0	0
$386$	2.01554	0.102588
$387$	−17.7911	−0.904374
$388$	−1.86622	−0.0947430
$389$	22.7221	1.15206	0.576028	−	0.817430i	$-0.304602\pi$
$389$	22.7221	1.15206	0.576028	+	0.817430i	$0.304602\pi$
$390$	0	0
$391$	−12.6967	−0.642100
$392$	22.7446	1.14877
$393$	0.644949	0.0325334
$394$	−1.56318	−0.0787518
$395$	0	0
$396$	19.7402	0.991980
$397$	9.75915	0.489798	0.244899	−	0.969549i	$-0.421245\pi$
$397$	9.75915	0.489798	0.244899	+	0.969549i	$0.421245\pi$
$398$	10.6826	0.535470
$399$	−0.705237	−0.0353060
$400$	0	0
$401$	14.2635	0.712285	0.356142	−	0.934432i	$-0.384092\pi$
$401$	14.2635	0.712285	0.356142	+	0.934432i	$0.384092\pi$
$402$	−0.676070	−0.0337193
$403$	−24.8275	−1.23675
$404$	9.25483	0.460445
$405$	0	0
$406$	−3.97649	−0.197350
$407$	−53.1528	−2.63469
$408$	0.475919	0.0235615
$409$	17.3235	0.856590	0.428295	−	0.903639i	$-0.359114\pi$
$409$	17.3235	0.856590	0.428295	+	0.903639i	$0.359114\pi$
$410$	0	0
$411$	−2.18572	−0.107813
$412$	18.3696	0.905008
$413$	−34.9105	−1.71783
$414$	15.7894	0.776006
$415$	0	0
$416$	17.3948	0.852849
$417$	−1.08885	−0.0533214
$418$	−7.08246	−0.346415
$419$	22.5211	1.10023	0.550113	−	0.835090i	$-0.314585\pi$
$419$	22.5211	1.10023	0.550113	+	0.835090i	$0.314585\pi$
$420$	0	0
$421$	−15.7692	−0.768546	−0.384273	−	0.923220i	$-0.625548\pi$
$421$	−15.7692	−0.768546	−0.384273	+	0.923220i	$0.625548\pi$
$422$	0.0146140	0.000711398 0
$423$	−27.0513	−1.31528
$424$	19.9362	0.968187
$425$	0	0
$426$	−0.194950	−0.00944535
$427$	22.7689	1.10186
$428$	−22.0795	−1.06725
$429$	1.34525	0.0649495
$430$	0	0
$431$	22.4732	1.08250	0.541248	−	0.840863i	$-0.317952\pi$
$431$	22.4732	1.08250	0.541248	+	0.840863i	$0.317952\pi$
$432$	0.383499	0.0184511
$433$	−23.8154	−1.14449	−0.572247	−	0.820081i	$-0.693928\pi$
$433$	−23.8154	−1.14449	−0.572247	+	0.820081i	$0.693928\pi$
$434$	−25.8696	−1.24178
$435$	0	0
$436$	−16.7335	−0.801387
$437$	12.6800	0.606564
$438$	1.10236	0.0526729
$439$	11.0509	0.527433	0.263717	−	0.964600i	$-0.415052\pi$
$439$	11.0509	0.527433	0.263717	+	0.964600i	$0.415052\pi$
$440$	0	0
$441$	−25.5928	−1.21871
$442$	−4.41891	−0.210186
$443$	−10.0320	−0.476635	−0.238317	−	0.971187i	$-0.576596\pi$
$443$	−10.0320	−0.476635	−0.238317	+	0.971187i	$0.576596\pi$
$444$	−1.45784	−0.0691858
$445$	0	0
$446$	−2.40210	−0.113743
$447$	1.33275	0.0630368
$448$	12.7940	0.604460
$449$	32.8521	1.55039	0.775194	−	0.631724i	$-0.217652\pi$
$449$	32.8521	1.55039	0.775194	+	0.631724i	$0.217652\pi$
$450$	0	0
$451$	−12.1742	−0.573261
$452$	5.15504	0.242473
$453$	1.57868	0.0741728
$454$	−10.8884	−0.511017
$455$	0	0
$456$	−0.475291	−0.0222575
$457$	−15.7918	−0.738711	−0.369356	−	0.929288i	$-0.620422\pi$
$457$	−15.7918	−0.738711	−0.369356	+	0.929288i	$0.620422\pi$
$458$	−16.7049	−0.780569
$459$	−1.07264	−0.0500665
$460$	0	0
$461$	−35.2659	−1.64250	−0.821248	−	0.570572i	$-0.806721\pi$
$461$	−35.2659	−1.64250	−0.821248	+	0.570572i	$0.806721\pi$
$462$	1.40172	0.0652139
$463$	26.3296	1.22364	0.611820	−	0.790997i	$-0.290438\pi$
$463$	26.3296	1.22364	0.611820	+	0.790997i	$0.290438\pi$
$464$	0.866963	0.0402477
$465$	0	0
$466$	7.90432	0.366160
$467$	35.8558	1.65921	0.829603	−	0.558353i	$-0.188567\pi$
$467$	35.8558	1.65921	0.829603	+	0.558353i	$0.188567\pi$
$468$	−12.3001	−0.568571
$469$	−35.8213	−1.65408
$470$	0	0
$471$	1.29271	0.0595647
$472$	−23.5277	−1.08295
$473$	28.3976	1.30572
$474$	0.238613	0.0109598
$475$	0	0
$476$	10.3060	0.472375
$477$	−22.4327	−1.02712
$478$	−16.4918	−0.754318
$479$	−19.7490	−0.902353	−0.451177	−	0.892435i	$-0.648996\pi$
$479$	−19.7490	−0.902353	−0.451177	+	0.892435i	$0.648996\pi$
$480$	0	0
$481$	33.1195	1.51012
$482$	−0.785880	−0.0357959
$483$	−2.50954	−0.114188
$484$	−16.3023	−0.741012
$485$	0	0
$486$	2.00187	0.0908067
$487$	15.6806	0.710557	0.355278	−	0.934760i	$-0.384386\pi$
$487$	15.6806	0.710557	0.355278	+	0.934760i	$0.384386\pi$
$488$	15.3450	0.694634
$489$	0.566555	0.0256205
$490$	0	0
$491$	−3.46320	−0.156292	−0.0781461	−	0.996942i	$-0.524900\pi$
$491$	−3.46320	−0.156292	−0.0781461	+	0.996942i	$0.524900\pi$
$492$	−0.333905	−0.0150536
$493$	−2.42488	−0.109211
$494$	4.41308	0.198554
$495$	0	0
$496$	5.64015	0.253250
$497$	−10.3293	−0.463335
$498$	−0.679234	−0.0304372
$499$	11.2720	0.504602	0.252301	−	0.967649i	$-0.418813\pi$
$499$	11.2720	0.504602	0.252301	+	0.967649i	$0.418813\pi$
$500$	0	0
$501$	−0.973059	−0.0434731
$502$	1.22676	0.0547528
$503$	3.89674	0.173747	0.0868735	−	0.996219i	$-0.472312\pi$
$503$	3.89674	0.173747	0.0868735	+	0.996219i	$0.472312\pi$
$504$	−31.3586	−1.39682
$505$	0	0
$506$	−25.2025	−1.12039
$507$	0.393157	0.0174607
$508$	−22.7114	−1.00766
$509$	−33.8130	−1.49873	−0.749367	−	0.662155i	$-0.769642\pi$
$509$	−33.8130	−1.49873	−0.749367	+	0.662155i	$0.769642\pi$
$510$	0	0
$511$	58.4083	2.58383
$512$	−7.54436	−0.333417
$513$	1.07122	0.0472957
$514$	−20.4850	−0.903552
$515$	0	0
$516$	0.778868	0.0342878
$517$	43.1784	1.89898
$518$	34.5096	1.51627
$519$	0.875654	0.0384369
$520$	0	0
$521$	22.6424	0.991981	0.495990	−	0.868328i	$-0.334805\pi$
$521$	22.6424	0.991981	0.495990	+	0.868328i	$0.334805\pi$
$522$	3.01553	0.131986
$523$	−0.518040	−0.0226523	−0.0113261	−	0.999936i	$-0.503605\pi$
$523$	−0.518040	−0.0226523	−0.0113261	+	0.999936i	$0.503605\pi$
$524$	9.41254	0.411189
$525$	0	0
$526$	−21.8327	−0.951952
$527$	−15.7754	−0.687186
$528$	−0.305606	−0.0132998
$529$	22.1208	0.961773
$530$	0	0
$531$	26.4740	1.14887
$532$	−10.2924	−0.446232
$533$	7.58574	0.328575
$534$	−1.00405	−0.0434495
$535$	0	0
$536$	−24.1416	−1.04276
$537$	1.61596	0.0697337
$538$	14.0891	0.607422
$539$	40.8504	1.75955
$540$	0	0
$541$	−8.08102	−0.347430	−0.173715	−	0.984796i	$-0.555577\pi$
$541$	−8.08102	−0.347430	−0.173715	+	0.984796i	$0.555577\pi$
$542$	13.1200	0.563553
$543$	−0.247463	−0.0106196
$544$	11.0526	0.473878
$545$	0	0
$546$	−0.873410	−0.0373785
$547$	−24.0365	−1.02773	−0.513864	−	0.857872i	$-0.671786\pi$
$547$	−24.0365	−1.02773	−0.513864	+	0.857872i	$0.671786\pi$
$548$	−31.8989	−1.36265
$549$	−17.2666	−0.736919
$550$	0	0
$551$	2.42168	0.103167
$552$	−1.69129	−0.0719861
$553$	12.6428	0.537627
$554$	0.907041	0.0385365
$555$	0	0
$556$	−15.8910	−0.673929
$557$	−8.12226	−0.344151	−0.172076	−	0.985084i	$-0.555047\pi$
$557$	−8.12226	−0.344151	−0.172076	+	0.985084i	$0.555047\pi$
$558$	19.6180	0.830494
$559$	−17.6945	−0.748399
$560$	0	0
$561$	0.854774	0.0360886
$562$	−17.8105	−0.751289
$563$	34.9647	1.47359	0.736793	−	0.676119i	$-0.236339\pi$
$563$	34.9647	1.47359	0.736793	+	0.676119i	$0.236339\pi$
$564$	1.18426	0.0498665
$565$	0	0
$566$	−1.60264	−0.0673638
$567$	35.1794	1.47740
$568$	−6.96141	−0.292094
$569$	39.8914	1.67234	0.836168	−	0.548474i	$-0.184791\pi$
$569$	39.8914	1.67234	0.836168	+	0.548474i	$0.184791\pi$
$570$	0	0
$571$	−12.2576	−0.512965	−0.256482	−	0.966549i	$-0.582564\pi$
$571$	−12.2576	−0.512965	−0.256482	+	0.966549i	$0.582564\pi$
$572$	19.6330	0.820895
$573$	1.88194	0.0786194
$574$	7.90414	0.329913
$575$	0	0
$576$	−9.70221	−0.404259
$577$	16.4961	0.686741	0.343370	−	0.939200i	$-0.388431\pi$
$577$	16.4961	0.686741	0.343370	+	0.939200i	$0.388431\pi$
$578$	10.5522	0.438913
$579$	0.242932	0.0100959
$580$	0	0
$581$	−35.9890	−1.49307
$582$	0.100493	0.00416559
$583$	35.8064	1.48295
$584$	39.3640	1.62889
$585$	0	0
$586$	−5.98181	−0.247106
$587$	−26.4654	−1.09234	−0.546171	−	0.837673i	$-0.683915\pi$
$587$	−26.4654	−1.09234	−0.546171	+	0.837673i	$0.683915\pi$
$588$	1.12041	0.0462051
$589$	15.7546	0.649155
$590$	0	0
$591$	−0.188409	−0.00775011
$592$	−7.52387	−0.309229
$593$	16.4292	0.674667	0.337333	−	0.941385i	$-0.390475\pi$
$593$	16.4292	0.674667	0.337333	+	0.941385i	$0.390475\pi$
$594$	−2.12915	−0.0873601
$595$	0	0
$596$	19.4505	0.796722
$597$	1.28757	0.0526966
$598$	15.7036	0.642170
$599$	11.6088	0.474324	0.237162	−	0.971470i	$-0.423783\pi$
$599$	11.6088	0.474324	0.237162	+	0.971470i	$0.423783\pi$
$600$	0	0
$601$	−21.8422	−0.890964	−0.445482	−	0.895291i	$-0.646968\pi$
$601$	−21.8422	−0.890964	−0.445482	+	0.895291i	$0.646968\pi$
$602$	−18.4372	−0.751446
$603$	27.1648	1.10623
$604$	23.0396	0.937469
$605$	0	0
$606$	−0.498360	−0.0202445
$607$	−41.0605	−1.66660	−0.833298	−	0.552824i	$-0.813550\pi$
$607$	−41.0605	−1.66660	−0.833298	+	0.552824i	$0.813550\pi$
$608$	−11.0380	−0.447652
$609$	−0.479284	−0.0194216
$610$	0	0
$611$	−26.9044	−1.08843
$612$	−7.81546	−0.315921
$613$	−13.1510	−0.531164	−0.265582	−	0.964088i	$-0.585564\pi$
$613$	−13.1510	−0.531164	−0.265582	+	0.964088i	$0.585564\pi$
$614$	9.30201	0.375399
$615$	0	0
$616$	50.0536	2.01672
$617$	−7.65124	−0.308027	−0.154014	−	0.988069i	$-0.549220\pi$
$617$	−7.65124	−0.308027	−0.154014	+	0.988069i	$0.549220\pi$
$618$	−0.989181	−0.0397907
$619$	21.0286	0.845210	0.422605	−	0.906314i	$-0.361116\pi$
$619$	21.0286	0.845210	0.422605	+	0.906314i	$0.361116\pi$
$620$	0	0
$621$	3.81188	0.152966
$622$	−8.25293	−0.330912
$623$	−53.1992	−2.13138
$624$	0.190423	0.00762301
$625$	0	0
$626$	−16.1596	−0.645868
$627$	−0.853646	−0.0340913
$628$	18.8661	0.752837
$629$	21.0441	0.839083
$630$	0	0
$631$	−14.6505	−0.583226	−0.291613	−	0.956536i	$-0.594192\pi$
$631$	−14.6505	−0.583226	−0.291613	+	0.956536i	$0.594192\pi$
$632$	8.52055	0.338929
$633$	0.00176142	7.00100e−5 0
$634$	11.9168	0.473277
$635$	0	0
$636$	0.982071	0.0389417
$637$	−25.4538	−1.00852
$638$	−4.81329	−0.190560
$639$	7.83316	0.309875
$640$	0	0
$641$	25.0706	0.990228	0.495114	−	0.868828i	$-0.335126\pi$
$641$	25.0706	0.990228	0.495114	+	0.868828i	$0.335126\pi$
$642$	1.18895	0.0469241
$643$	13.7576	0.542546	0.271273	−	0.962502i	$-0.412555\pi$
$643$	13.7576	0.542546	0.271273	+	0.962502i	$0.412555\pi$
$644$	−36.6249	−1.44322
$645$	0	0
$646$	2.80407	0.110325
$647$	11.8715	0.466715	0.233358	−	0.972391i	$-0.425029\pi$
$647$	11.8715	0.466715	0.233358	+	0.972391i	$0.425029\pi$
$648$	23.7090	0.931376
$649$	−42.2570	−1.65873
$650$	0	0
$651$	−3.11805	−0.122206
$652$	8.26844	0.323817
$653$	13.9865	0.547335	0.273667	−	0.961824i	$-0.411763\pi$
$653$	13.9865	0.547335	0.273667	+	0.961824i	$0.411763\pi$
$654$	0.901074	0.0352348
$655$	0	0
$656$	−1.72328	−0.0672828
$657$	−44.2934	−1.72805
$658$	−28.0337	−1.09287
$659$	−27.2262	−1.06058	−0.530291	−	0.847816i	$-0.677917\pi$
$659$	−27.2262	−1.06058	−0.530291	+	0.847816i	$0.677917\pi$
$660$	0	0
$661$	−50.6362	−1.96952	−0.984760	−	0.173917i	$-0.944357\pi$
$661$	−50.6362	−1.96952	−0.984760	+	0.173917i	$0.944357\pi$
$662$	−12.8930	−0.501100
$663$	−0.532609	−0.0206848
$664$	−24.2546	−0.941259
$665$	0	0
$666$	−26.1700	−1.01407
$667$	8.61738	0.333666
$668$	−14.2011	−0.549456
$669$	−0.289524	−0.0111937
$670$	0	0
$671$	27.5603	1.06395
$672$	2.18459	0.0842722
$673$	−21.7241	−0.837403	−0.418701	−	0.908124i	$-0.637515\pi$
$673$	−21.7241	−0.837403	−0.418701	+	0.908124i	$0.637515\pi$
$674$	−20.3143	−0.782478
$675$	0	0
$676$	5.73782	0.220686
$677$	39.0942	1.50251	0.751255	−	0.660012i	$-0.229449\pi$
$677$	39.0942	1.50251	0.751255	+	0.660012i	$0.229449\pi$
$678$	−0.277592	−0.0106608
$679$	5.32461	0.204340
$680$	0	0
$681$	−1.31237	−0.0502902
$682$	−31.3135	−1.19906
$683$	15.1936	0.581366	0.290683	−	0.956819i	$-0.406117\pi$
$683$	15.1936	0.581366	0.290683	+	0.956819i	$0.406117\pi$
$684$	7.80515	0.298437
$685$	0	0
$686$	−4.82469	−0.184207
$687$	−2.01343	−0.0768173
$688$	4.01973	0.153251
$689$	−22.3109	−0.849979
$690$	0	0
$691$	32.0022	1.21742	0.608711	−	0.793392i	$-0.291687\pi$
$691$	32.0022	1.21742	0.608711	+	0.793392i	$0.291687\pi$
$692$	12.7795	0.485804
$693$	−56.3217	−2.13948
$694$	−12.0679	−0.458092
$695$	0	0
$696$	−0.323011	−0.0122437
$697$	4.81998	0.182570
$698$	−28.5203	−1.07951
$699$	0.952703	0.0360345
$700$	0	0
$701$	7.32583	0.276693	0.138346	−	0.990384i	$-0.455821\pi$
$701$	7.32583	0.276693	0.138346	+	0.990384i	$0.455821\pi$
$702$	1.32667	0.0500720
$703$	−21.0163	−0.792646
$704$	15.4864	0.583664
$705$	0	0
$706$	5.45972	0.205479
$707$	−26.4054	−0.993078
$708$	−1.15899	−0.0435576
$709$	−38.5230	−1.44676	−0.723381	−	0.690449i	$-0.757413\pi$
$709$	−38.5230	−1.44676	−0.723381	+	0.690449i	$0.757413\pi$
$710$	0	0
$711$	−9.58755	−0.359561
$712$	−35.8533	−1.34366
$713$	56.0616	2.09952
$714$	−0.554964	−0.0207690
$715$	0	0
$716$	23.5837	0.881364
$717$	−1.98775	−0.0742339
$718$	−4.85337	−0.181126
$719$	0.163363	0.00609241	0.00304621	−	0.999995i	$-0.499030\pi$
$719$	0.163363	0.00609241	0.00304621	+	0.999995i	$0.499030\pi$
$720$	0	0
$721$	−52.4114	−1.95190
$722$	12.1314	0.451482
$723$	−0.0947217	−0.00352274
$724$	−3.61153	−0.134222
$725$	0	0
$726$	0.877855	0.0325803
$727$	−33.0490	−1.22572	−0.612859	−	0.790192i	$-0.709981\pi$
$727$	−33.0490	−1.22572	−0.612859	+	0.790192i	$0.709981\pi$
$728$	−31.1883	−1.15592
$729$	−26.5167	−0.982100
$730$	0	0
$731$	−11.2431	−0.415841
$732$	0.755904	0.0279390
$733$	48.5149	1.79194	0.895969	−	0.444118i	$-0.146483\pi$
$733$	48.5149	1.79194	0.895969	+	0.444118i	$0.146483\pi$
$734$	−16.1034	−0.594388
$735$	0	0
$736$	−39.2782	−1.44781
$737$	−43.3595	−1.59717
$738$	−5.99403	−0.220643
$739$	−22.1407	−0.814457	−0.407229	−	0.913326i	$-0.633505\pi$
$739$	−22.1407	−0.814457	−0.407229	+	0.913326i	$0.633505\pi$
$740$	0	0
$741$	0.531906	0.0195400
$742$	−23.2474	−0.853439
$743$	−17.8667	−0.655466	−0.327733	−	0.944770i	$-0.606285\pi$
$743$	−17.8667	−0.655466	−0.327733	+	0.944770i	$0.606285\pi$
$744$	−2.10139	−0.0770408
$745$	0	0
$746$	−16.5420	−0.605645
$747$	27.2919	0.998558
$748$	12.4748	0.456123
$749$	62.9961	2.30183
$750$	0	0
$751$	52.5154	1.91632	0.958158	−	0.286241i	$-0.0924056\pi$
$751$	52.5154	1.91632	0.958158	+	0.286241i	$0.0924056\pi$
$752$	6.11197	0.222880
$753$	0.147860	0.00538832
$754$	2.99915	0.109223
$755$	0	0
$756$	−3.09413	−0.112532
$757$	−19.4586	−0.707234	−0.353617	−	0.935390i	$-0.615048\pi$
$757$	−19.4586	−0.707234	−0.353617	+	0.935390i	$0.615048\pi$
$758$	−10.0537	−0.365167
$759$	−3.03764	−0.110259
$760$	0	0
$761$	−0.328442	−0.0119060	−0.00595300	−	0.999982i	$-0.501895\pi$
$761$	−0.328442	−0.0119060	−0.00595300	+	0.999982i	$0.501895\pi$
$762$	1.22298	0.0443039
$763$	47.7431	1.72842
$764$	27.4656	0.993669
$765$	0	0
$766$	−16.1830	−0.584714
$767$	26.3303	0.950730
$768$	1.29531	0.0467404
$769$	−47.0765	−1.69762	−0.848811	−	0.528696i	$-0.822681\pi$
$769$	−47.0765	−1.69762	−0.848811	+	0.528696i	$0.822681\pi$
$770$	0	0
$771$	−2.46904	−0.0889203
$772$	3.54541	0.127602
$773$	−15.0465	−0.541185	−0.270593	−	0.962694i	$-0.587220\pi$
$773$	−15.0465	−0.541185	−0.270593	+	0.962694i	$0.587220\pi$
$774$	13.9817	0.502562
$775$	0	0
$776$	3.58849	0.128819
$777$	4.15943	0.149219
$778$	−17.8568	−0.640198
$779$	−4.81362	−0.172466
$780$	0	0
$781$	−12.5030	−0.447394
$782$	9.97809	0.356816
$783$	0.728011	0.0260170
$784$	5.78244	0.206516
$785$	0	0
$786$	−0.506853	−0.0180788
$787$	35.7418	1.27406	0.637028	−	0.770841i	$-0.280164\pi$
$787$	35.7418	1.27406	0.637028	+	0.770841i	$0.280164\pi$
$788$	−2.74969	−0.0979536
$789$	−2.63149	−0.0936835
$790$	0	0
$791$	−14.7081	−0.522960
$792$	−37.9577	−1.34877
$793$	−17.1728	−0.609824
$794$	−7.66952	−0.272181
$795$	0	0
$796$	18.7911	0.666031
$797$	30.0089	1.06297	0.531485	−	0.847067i	$-0.321634\pi$
$797$	30.0089	1.06297	0.531485	+	0.847067i	$0.321634\pi$
$798$	0.554232	0.0196196
$799$	−17.0950	−0.604779
$800$	0	0
$801$	40.3431	1.42545
$802$	−11.2094	−0.395818
$803$	70.6997	2.49494
$804$	−1.18923	−0.0419410
$805$	0	0
$806$	19.5114	0.687261
$807$	1.69815	0.0597776
$808$	−17.7958	−0.626054
$809$	8.00982	0.281610	0.140805	−	0.990037i	$-0.455031\pi$
$809$	8.00982	0.281610	0.140805	+	0.990037i	$0.455031\pi$
$810$	0	0
$811$	23.9072	0.839494	0.419747	−	0.907641i	$-0.362119\pi$
$811$	23.9072	0.839494	0.419747	+	0.907641i	$0.362119\pi$
$812$	−6.99479	−0.245469
$813$	1.58135	0.0554604
$814$	41.7717	1.46410
$815$	0	0
$816$	0.120995	0.00423566
$817$	11.2283	0.392827
$818$	−13.6142	−0.476008
$819$	35.0940	1.22628
$820$	0	0
$821$	−36.2302	−1.26444	−0.632222	−	0.774787i	$-0.717857\pi$
$821$	−36.2302	−1.26444	−0.632222	+	0.774787i	$0.717857\pi$
$822$	1.71771	0.0599121
$823$	26.1441	0.911327	0.455664	−	0.890152i	$-0.349402\pi$
$823$	26.1441	0.911327	0.455664	+	0.890152i	$0.349402\pi$
$824$	−35.3224	−1.23051
$825$	0	0
$826$	27.4354	0.954601
$827$	47.0363	1.63561	0.817806	−	0.575494i	$-0.195190\pi$
$827$	47.0363	1.63561	0.817806	+	0.575494i	$0.195190\pi$
$828$	27.7741	0.965217
$829$	−45.5031	−1.58039	−0.790194	−	0.612857i	$-0.790020\pi$
$829$	−45.5031	−1.58039	−0.790194	+	0.612857i	$0.790020\pi$
$830$	0	0
$831$	0.109325	0.00379245
$832$	−9.64953	−0.334537
$833$	−16.1734	−0.560374
$834$	0.855709	0.0296308
$835$	0	0
$836$	−12.4583	−0.430880
$837$	4.73618	0.163706
$838$	−17.6989	−0.611397
$839$	−12.3759	−0.427263	−0.213632	−	0.976914i	$-0.568529\pi$
$839$	−12.3759	−0.427263	−0.213632	+	0.976914i	$0.568529\pi$
$840$	0	0
$841$	−27.3542	−0.943249
$842$	12.3927	0.427082
$843$	−2.14669	−0.0739358
$844$	0.0257065	0.000884856 0
$845$	0	0
$846$	21.2591	0.730902
$847$	46.5129	1.59820
$848$	5.06845	0.174051
$849$	−0.193165	−0.00662940
$850$	0	0
$851$	−74.7852	−2.56360
$852$	−0.342924	−0.0117484
$853$	−15.4307	−0.528339	−0.264169	−	0.964476i	$-0.585098\pi$
$853$	−15.4307	−0.528339	−0.264169	+	0.964476i	$0.585098\pi$
$854$	−17.8936	−0.612307
$855$	0	0
$856$	42.4559	1.45111
$857$	4.18668	0.143014	0.0715072	−	0.997440i	$-0.477219\pi$
$857$	4.18668	0.143014	0.0715072	+	0.997440i	$0.477219\pi$
$858$	−1.05721	−0.0360925
$859$	−50.5816	−1.72582	−0.862910	−	0.505357i	$-0.831361\pi$
$859$	−50.5816	−1.72582	−0.862910	+	0.505357i	$0.831361\pi$
$860$	0	0
$861$	0.952683	0.0324673
$862$	−17.6613	−0.601545
$863$	−32.8605	−1.11858	−0.559291	−	0.828971i	$-0.688927\pi$
$863$	−32.8605	−1.11858	−0.559291	+	0.828971i	$0.688927\pi$
$864$	−3.31829	−0.112890
$865$	0	0
$866$	18.7160	0.635996
$867$	1.27185	0.0431943
$868$	−45.5056	−1.54456
$869$	15.3033	0.519130
$870$	0	0
$871$	27.0172	0.915444
$872$	32.1762	1.08962
$873$	−4.03787	−0.136661
$874$	−9.96492	−0.337069
$875$	0	0
$876$	1.93910	0.0655160
$877$	−23.8855	−0.806557	−0.403279	−	0.915077i	$-0.632129\pi$
$877$	−23.8855	−0.806557	−0.403279	+	0.915077i	$0.632129\pi$
$878$	−8.68472	−0.293095
$879$	−0.720985	−0.0243182
$880$	0	0
$881$	−39.5749	−1.33331	−0.666656	−	0.745366i	$-0.732275\pi$
$881$	−39.5749	−1.33331	−0.666656	+	0.745366i	$0.732275\pi$
$882$	20.1129	0.677236
$883$	−47.5311	−1.59955	−0.799775	−	0.600300i	$-0.795048\pi$
$883$	−47.5311	−1.59955	−0.799775	+	0.600300i	$0.795048\pi$
$884$	−7.77302	−0.261435
$885$	0	0
$886$	7.88395	0.264867
$887$	−43.3675	−1.45614	−0.728069	−	0.685504i	$-0.759582\pi$
$887$	−43.3675	−1.45614	−0.728069	+	0.685504i	$0.759582\pi$
$888$	2.80322	0.0940700
$889$	64.7992	2.17330
$890$	0	0
$891$	42.5825	1.42657
$892$	−4.22539	−0.141477
$893$	17.0725	0.571309
$894$	−1.04738	−0.0350297
$895$	0	0
$896$	36.0718	1.20507
$897$	1.89275	0.0631972
$898$	−25.8178	−0.861552
$899$	10.7069	0.357095
$900$	0	0
$901$	−14.1764	−0.472283
$902$	9.56748	0.318562
$903$	−2.22223	−0.0739512
$904$	−9.91245	−0.329683
$905$	0	0
$906$	−1.24065	−0.0412179
$907$	−26.8742	−0.892344	−0.446172	−	0.894947i	$-0.647213\pi$
$907$	−26.8742	−0.892344	−0.446172	+	0.894947i	$0.647213\pi$
$908$	−19.1531	−0.635617
$909$	20.0243	0.664164
$910$	0	0
$911$	4.67105	0.154759	0.0773794	−	0.997002i	$-0.475345\pi$
$911$	4.67105	0.154759	0.0773794	+	0.997002i	$0.475345\pi$
$912$	−0.120835	−0.00400124
$913$	−43.5624	−1.44171
$914$	12.4105	0.410503
$915$	0	0
$916$	−29.3845	−0.970892
$917$	−26.8554	−0.886844
$918$	0.842966	0.0278220
$919$	−41.7886	−1.37848	−0.689239	−	0.724534i	$-0.742055\pi$
$919$	−41.7886	−1.37848	−0.689239	+	0.724534i	$0.742055\pi$
$920$	0	0
$921$	1.12117	0.0369437
$922$	27.7147	0.912737
$923$	7.79063	0.256432
$924$	2.46568	0.0811148
$925$	0	0
$926$	−20.6919	−0.679978
$927$	39.7457	1.30542
$928$	−7.50153	−0.246250
$929$	39.7684	1.30476	0.652380	−	0.757892i	$-0.273771\pi$
$929$	39.7684	1.30476	0.652380	+	0.757892i	$0.273771\pi$
$930$	0	0
$931$	16.1520	0.529361
$932$	13.9040	0.455440
$933$	−0.994722	−0.0325657
$934$	−28.1783	−0.922023
$935$	0	0
$936$	23.6514	0.773070
$937$	1.57005	0.0512914	0.0256457	−	0.999671i	$-0.491836\pi$
$937$	1.57005	0.0512914	0.0256457	+	0.999671i	$0.491836\pi$
$938$	28.1513	0.919172
$939$	−1.94771	−0.0635612
$940$	0	0
$941$	−5.85856	−0.190984	−0.0954919	−	0.995430i	$-0.530442\pi$
$941$	−5.85856	−0.190984	−0.0954919	+	0.995430i	$0.530442\pi$
$942$	−1.01591	−0.0331002
$943$	−17.1289	−0.557795
$944$	−5.98154	−0.194683
$945$	0	0
$946$	−22.3171	−0.725592
$947$	25.7158	0.835650	0.417825	−	0.908528i	$-0.362793\pi$
$947$	25.7158	0.835650	0.417825	+	0.908528i	$0.362793\pi$
$948$	0.419728	0.0136321
$949$	−44.0529	−1.43002
$950$	0	0
$951$	1.43633	0.0465761
$952$	−19.8171	−0.642275
$953$	−31.7965	−1.02999	−0.514995	−	0.857193i	$-0.672206\pi$
$953$	−31.7965	−1.02999	−0.514995	+	0.857193i	$0.672206\pi$
$954$	17.6294	0.570774
$955$	0	0
$956$	−29.0097	−0.938242
$957$	−0.580143	−0.0187534
$958$	15.5203	0.501439
$959$	91.0124	2.93894
$960$	0	0
$961$	38.6553	1.24694
$962$	−26.0279	−0.839174
$963$	−47.7725	−1.53945
$964$	−1.38239	−0.0445239
$965$	0	0
$966$	1.97220	0.0634545
$967$	52.0863	1.67498	0.837492	−	0.546450i	$-0.184021\pi$
$967$	52.0863	1.67498	0.837492	+	0.546450i	$0.184021\pi$
$968$	31.3471	1.00753
$969$	0.337973	0.0108572
$970$	0	0
$971$	−33.4795	−1.07441	−0.537204	−	0.843452i	$-0.680520\pi$
$971$	−33.4795	−1.07441	−0.537204	+	0.843452i	$0.680520\pi$
$972$	3.52136	0.112948
$973$	45.3395	1.45352
$974$	−12.3231	−0.394857
$975$	0	0
$976$	3.90121	0.124875
$977$	−19.4336	−0.621736	−0.310868	−	0.950453i	$-0.600620\pi$
$977$	−19.4336	−0.621736	−0.310868	+	0.950453i	$0.600620\pi$
$978$	−0.445245	−0.0142374
$979$	−64.3943	−2.05805
$980$	0	0
$981$	−36.2055	−1.15595
$982$	2.72166	0.0868517
$983$	−9.36848	−0.298808	−0.149404	−	0.988776i	$-0.547736\pi$
$983$	−9.36848	−0.298808	−0.149404	+	0.988776i	$0.547736\pi$
$984$	0.642055	0.0204680
$985$	0	0
$986$	1.90566	0.0606886
$987$	−3.37888	−0.107551
$988$	7.76276	0.246966
$989$	39.9550	1.27050
$990$	0	0
$991$	−34.5316	−1.09693	−0.548466	−	0.836173i	$-0.684788\pi$
$991$	−34.5316	−1.09693	−0.548466	+	0.836173i	$0.684788\pi$
$992$	−48.8023	−1.54947
$993$	−1.55398	−0.0493142
$994$	8.11763	0.257476
$995$	0	0
$996$	−1.19480	−0.0378586
$997$	29.6123	0.937833	0.468916	−	0.883243i	$-0.344645\pi$
$997$	29.6123	0.937833	0.468916	+	0.883243i	$0.344645\pi$
$998$	−8.85840	−0.280408
$999$	−6.31798	−0.199892

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.n.1.13	yes	40
5.4	even	2		6025.2.a.m.1.28	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6025.2.a.m.1.28	✓	40	5.4	even	2
6025.2.a.n.1.13	yes	40	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)

\(f(q)\)	\(=\)	\(q-0.785880 q^{2} -0.0947217 q^{3} -1.38239 q^{4} +0.0744399 q^{6} +3.94418 q^{7} +2.65816 q^{8} -2.99103 q^{9} +O(q^{10})\)	\(q-0.785880 q^{2} -0.0947217 q^{3} -1.38239 q^{4} +0.0744399 q^{6} +3.94418 q^{7} +2.65816 q^{8} -2.99103 q^{9} +4.77418 q^{11} +0.130943 q^{12} -2.97479 q^{13} -3.09965 q^{14} +0.675793 q^{16} -1.89018 q^{17} +2.35059 q^{18} +1.88768 q^{19} -0.373599 q^{21} -3.75193 q^{22} +6.71720 q^{23} -0.251785 q^{24} +2.33783 q^{26} +0.567481 q^{27} -5.45240 q^{28} +1.28288 q^{29} +8.34597 q^{31} -5.84740 q^{32} -0.452219 q^{33} +1.48545 q^{34} +4.13477 q^{36} -11.1334 q^{37} -1.48349 q^{38} +0.281777 q^{39} -2.55001 q^{41} +0.293604 q^{42} +5.94817 q^{43} -6.59979 q^{44} -5.27892 q^{46} +9.04414 q^{47} -0.0640123 q^{48} +8.55653 q^{49} +0.179041 q^{51} +4.11232 q^{52} +7.50001 q^{53} -0.445972 q^{54} +10.4842 q^{56} -0.178805 q^{57} -1.00819 q^{58} -8.85114 q^{59} +5.77279 q^{61} -6.55894 q^{62} -11.7971 q^{63} +3.24377 q^{64} +0.355390 q^{66} -9.08208 q^{67} +2.61297 q^{68} -0.636265 q^{69} -2.61889 q^{71} -7.95062 q^{72} +14.8088 q^{73} +8.74951 q^{74} -2.60952 q^{76} +18.8302 q^{77} -0.221443 q^{78} +3.20544 q^{79} +8.91933 q^{81} +2.00400 q^{82} -9.12458 q^{83} +0.516461 q^{84} -4.67455 q^{86} -0.121517 q^{87} +12.6905 q^{88} -13.4880 q^{89} -11.7331 q^{91} -9.28581 q^{92} -0.790545 q^{93} -7.10761 q^{94} +0.553876 q^{96} +1.34999 q^{97} -6.72440 q^{98} -14.2797 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 9 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 20 q^{7} + 27 q^{8} + 38 q^{9}+O(q^{10}) \) 40 * q + 9 * q^2 + 8 * q^3 + 41 * q^4 + 3 * q^6 + 20 * q^7 + 27 * q^8 + 38 * q^9	\( 40 q + 9 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 20 q^{7} + 27 q^{8} + 38 q^{9} + q^{11} + 26 q^{12} + 11 q^{13} - q^{14} + 43 q^{16} + 20 q^{17} + 18 q^{18} + 2 q^{21} + 23 q^{22} + 79 q^{23} - 2 q^{24} + 2 q^{26} + 26 q^{27} + 30 q^{28} + 2 q^{29} + q^{31} + 68 q^{32} + 20 q^{33} + 5 q^{34} + 32 q^{36} + 16 q^{37} + 45 q^{38} - 2 q^{39} - 2 q^{41} + 19 q^{42} + 25 q^{43} + 3 q^{44} + 14 q^{46} + 88 q^{47} + 75 q^{48} + 40 q^{49} - 10 q^{51} + 18 q^{52} + 34 q^{53} + 4 q^{54} - 15 q^{56} + 51 q^{57} + 53 q^{58} + q^{59} + 9 q^{61} + 39 q^{62} + 110 q^{63} + 17 q^{64} + 26 q^{66} + 30 q^{67} + 44 q^{68} - 7 q^{69} + 5 q^{71} + 18 q^{72} + 23 q^{73} - 18 q^{74} + 43 q^{76} + 30 q^{77} + 46 q^{78} + 5 q^{79} + 44 q^{81} + 5 q^{82} + 65 q^{83} - 65 q^{84} + 40 q^{86} + 33 q^{87} + 71 q^{88} - 9 q^{89} + q^{91} + 117 q^{92} + 68 q^{93} - 72 q^{94} + 83 q^{96} - 8 q^{97} + 76 q^{98} - 40 q^{99}+O(q^{100}) \) 40 * q + 9 * q^2 + 8 * q^3 + 41 * q^4 + 3 * q^6 + 20 * q^7 + 27 * q^8 + 38 * q^9 + q^11 + 26 * q^12 + 11 * q^13 - q^14 + 43 * q^16 + 20 * q^17 + 18 * q^18 + 2 * q^21 + 23 * q^22 + 79 * q^23 - 2 * q^24 + 2 * q^26 + 26 * q^27 + 30 * q^28 + 2 * q^29 + q^31 + 68 * q^32 + 20 * q^33 + 5 * q^34 + 32 * q^36 + 16 * q^37 + 45 * q^38 - 2 * q^39 - 2 * q^41 + 19 * q^42 + 25 * q^43 + 3 * q^44 + 14 * q^46 + 88 * q^47 + 75 * q^48 + 40 * q^49 - 10 * q^51 + 18 * q^52 + 34 * q^53 + 4 * q^54 - 15 * q^56 + 51 * q^57 + 53 * q^58 + q^59 + 9 * q^61 + 39 * q^62 + 110 * q^63 + 17 * q^64 + 26 * q^66 + 30 * q^67 + 44 * q^68 - 7 * q^69 + 5 * q^71 + 18 * q^72 + 23 * q^73 - 18 * q^74 + 43 * q^76 + 30 * q^77 + 46 * q^78 + 5 * q^79 + 44 * q^81 + 5 * q^82 + 65 * q^83 - 65 * q^84 + 40 * q^86 + 33 * q^87 + 71 * q^88 - 9 * q^89 + q^91 + 117 * q^92 + 68 * q^93 - 72 * q^94 + 83 * q^96 - 8 * q^97 + 76 * q^98 - 40 * q^99

Introduction

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