LMFDB - Embedded newform 6025.2.a.l.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:	$40$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
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)

$f(q)$	$=$	$q-2.74359 q^{2} -0.0877195 q^{3} +5.52727 q^{4} +0.240666 q^{6} -1.38863 q^{7} -9.67736 q^{8} -2.99231 q^{9} +O(q^{10})$	\(q-2.74359 q^{2} -0.0877195 q^{3} +5.52727 q^{4} +0.240666 q^{6} -1.38863 q^{7} -9.67736 q^{8} -2.99231 q^{9} -1.68686 q^{11} -0.484849 q^{12} -1.34511 q^{13} +3.80984 q^{14} +15.4962 q^{16} -3.06688 q^{17} +8.20965 q^{18} +8.07490 q^{19} +0.121810 q^{21} +4.62806 q^{22} -2.18428 q^{23} +0.848894 q^{24} +3.69042 q^{26} +0.525642 q^{27} -7.67535 q^{28} -8.72354 q^{29} +7.09750 q^{31} -23.1603 q^{32} +0.147971 q^{33} +8.41424 q^{34} -16.5393 q^{36} -0.976988 q^{37} -22.1542 q^{38} +0.117992 q^{39} +3.27244 q^{41} -0.334197 q^{42} +8.18683 q^{43} -9.32375 q^{44} +5.99275 q^{46} +8.16516 q^{47} -1.35931 q^{48} -5.07170 q^{49} +0.269025 q^{51} -7.43476 q^{52} -2.61978 q^{53} -1.44214 q^{54} +13.4383 q^{56} -0.708326 q^{57} +23.9338 q^{58} +2.45879 q^{59} -3.69058 q^{61} -19.4726 q^{62} +4.15522 q^{63} +32.5500 q^{64} -0.405971 q^{66} +5.99654 q^{67} -16.9514 q^{68} +0.191604 q^{69} +9.10030 q^{71} +28.9576 q^{72} +4.03560 q^{73} +2.68045 q^{74} +44.6321 q^{76} +2.34244 q^{77} -0.323721 q^{78} -0.0889430 q^{79} +8.93081 q^{81} -8.97823 q^{82} +10.5321 q^{83} +0.673278 q^{84} -22.4613 q^{86} +0.765225 q^{87} +16.3244 q^{88} +0.520962 q^{89} +1.86786 q^{91} -12.0731 q^{92} -0.622590 q^{93} -22.4018 q^{94} +2.03161 q^{96} -13.5274 q^{97} +13.9146 q^{98} +5.04761 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 11 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 16 q^{7} - 33 q^{8} + 38 q^{9}+O(q^{10}) $ 40 * q - 11 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 16 * q^7 - 33 * q^8 + 38 * q^9	$ 40 q - 11 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 16 q^{7} - 33 q^{8} + 38 q^{9} + q^{11} - 14 q^{12} - 9 q^{13} - q^{14} + 43 q^{16} - 12 q^{17} - 42 q^{18} + 2 q^{21} - 5 q^{22} - 77 q^{23} - 2 q^{24} + 2 q^{26} - 38 q^{27} - 42 q^{28} + 2 q^{29} + q^{31} - 72 q^{32} - 20 q^{33} + 5 q^{34} + 32 q^{36} - 28 q^{37} - 23 q^{38} - 2 q^{39} - 2 q^{41} - 37 q^{42} - 31 q^{43} + 3 q^{44} + 14 q^{46} - 96 q^{47} - 13 q^{48} + 40 q^{49} - 10 q^{51} - 42 q^{52} - 54 q^{53} + 4 q^{54} - 15 q^{56} - 37 q^{57} - 27 q^{58} + q^{59} + 5 q^{61} - 39 q^{62} - 70 q^{63} + 65 q^{64} - 52 q^{66} - 34 q^{67} - 52 q^{68} + 21 q^{69} - 9 q^{71} - 70 q^{72} - 25 q^{73} + 22 q^{74} - 47 q^{76} - 54 q^{77} - 58 q^{78} + 13 q^{79} + 12 q^{81} + 5 q^{82} - 63 q^{83} + 95 q^{84} - 18 q^{86} - 47 q^{87} - 13 q^{88} + 19 q^{89} - 31 q^{91} - 137 q^{92} - 52 q^{93} + 120 q^{94} - 49 q^{96} - 36 q^{97} - 64 q^{98} + 16 q^{99}+O(q^{100}) $ 40 * q - 11 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 16 * q^7 - 33 * q^8 + 38 * q^9 + q^11 - 14 * q^12 - 9 * q^13 - q^14 + 43 * q^16 - 12 * q^17 - 42 * q^18 + 2 * q^21 - 5 * q^22 - 77 * q^23 - 2 * q^24 + 2 * q^26 - 38 * q^27 - 42 * q^28 + 2 * q^29 + q^31 - 72 * q^32 - 20 * q^33 + 5 * q^34 + 32 * q^36 - 28 * q^37 - 23 * q^38 - 2 * q^39 - 2 * q^41 - 37 * q^42 - 31 * q^43 + 3 * q^44 + 14 * q^46 - 96 * q^47 - 13 * q^48 + 40 * q^49 - 10 * q^51 - 42 * q^52 - 54 * q^53 + 4 * q^54 - 15 * q^56 - 37 * q^57 - 27 * q^58 + q^59 + 5 * q^61 - 39 * q^62 - 70 * q^63 + 65 * q^64 - 52 * q^66 - 34 * q^67 - 52 * q^68 + 21 * q^69 - 9 * q^71 - 70 * q^72 - 25 * q^73 + 22 * q^74 - 47 * q^76 - 54 * q^77 - 58 * q^78 + 13 * q^79 + 12 * q^81 + 5 * q^82 - 63 * q^83 + 95 * q^84 - 18 * q^86 - 47 * q^87 - 13 * q^88 + 19 * q^89 - 31 * q^91 - 137 * q^92 - 52 * q^93 + 120 * q^94 - 49 * q^96 - 36 * q^97 - 64 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.74359	−1.94001	−0.970004	−	0.243088i	$-0.921840\pi$
$2$	−2.74359	−1.94001	−0.970004	+	0.243088i	$0.921840\pi$
$3$	−0.0877195	−0.0506449	−0.0253224	−	0.999679i	$-0.508061\pi$
$3$	−0.0877195	−0.0506449	−0.0253224	+	0.999679i	$0.508061\pi$
$4$	5.52727	2.76363
$5$	0	0
$5$	0	0
$6$	0.240666	0.0982515
$7$	−1.38863	−0.524854	−0.262427	−	0.964952i	$-0.584523\pi$
$7$	−1.38863	−0.524854	−0.262427	+	0.964952i	$0.584523\pi$
$8$	−9.67736	−3.42146
$9$	−2.99231	−0.997435
$10$	0	0
$11$	−1.68686	−0.508609	−0.254304	−	0.967124i	$-0.581847\pi$
$11$	−1.68686	−0.508609	−0.254304	+	0.967124i	$0.581847\pi$
$12$	−0.484849	−0.139964
$13$	−1.34511	−0.373065	−0.186533	−	0.982449i	$-0.559725\pi$
$13$	−1.34511	−0.373065	−0.186533	+	0.982449i	$0.559725\pi$
$14$	3.80984	1.01822
$15$	0	0
$16$	15.4962	3.87404
$17$	−3.06688	−0.743826	−0.371913	−	0.928267i	$-0.621298\pi$
$17$	−3.06688	−0.743826	−0.371913	+	0.928267i	$0.621298\pi$
$18$	8.20965	1.93503
$19$	8.07490	1.85251	0.926255	−	0.376898i	$-0.123009\pi$
$19$	8.07490	1.85251	0.926255	+	0.376898i	$0.123009\pi$
$20$	0	0
$21$	0.121810	0.0265812
$22$	4.62806	0.986706
$23$	−2.18428	−0.455453	−0.227727	−	0.973725i	$-0.573129\pi$
$23$	−2.18428	−0.455453	−0.227727	+	0.973725i	$0.573129\pi$
$24$	0.848894	0.173280
$25$	0	0
$26$	3.69042	0.723750
$27$	0.525642	0.101160
$28$	−7.67535	−1.45051
$29$	−8.72354	−1.61992	−0.809961	−	0.586484i	$-0.800512\pi$
$29$	−8.72354	−1.61992	−0.809961	+	0.586484i	$0.800512\pi$
$30$	0	0
$31$	7.09750	1.27475	0.637375	−	0.770554i	$-0.280020\pi$
$31$	7.09750	1.27475	0.637375	+	0.770554i	$0.280020\pi$
$32$	−23.1603	−4.09420
$33$	0.147971	0.0257584
$34$	8.41424	1.44303
$35$	0	0
$36$	−16.5393	−2.75655
$37$	−0.976988	−0.160616	−0.0803079	−	0.996770i	$-0.525590\pi$
$37$	−0.976988	−0.160616	−0.0803079	+	0.996770i	$0.525590\pi$
$38$	−22.1542	−3.59388
$39$	0.117992	0.0188939
$40$	0	0
$41$	3.27244	0.511070	0.255535	−	0.966800i	$-0.417748\pi$
$41$	3.27244	0.511070	0.255535	+	0.966800i	$0.417748\pi$
$42$	−0.334197	−0.0515677
$43$	8.18683	1.24848	0.624240	−	0.781233i	$-0.285409\pi$
$43$	8.18683	1.24848	0.624240	+	0.781233i	$0.285409\pi$
$44$	−9.32375	−1.40561
$45$	0	0
$46$	5.99275	0.883583
$47$	8.16516	1.19101	0.595505	−	0.803351i	$-0.296952\pi$
$47$	8.16516	1.19101	0.595505	+	0.803351i	$0.296952\pi$
$48$	−1.35931	−0.196200
$49$	−5.07170	−0.724528
$50$	0	0
$51$	0.269025	0.0376710
$52$	−7.43476	−1.03102
$53$	−2.61978	−0.359854	−0.179927	−	0.983680i	$-0.557586\pi$
$53$	−2.61978	−0.359854	−0.179927	+	0.983680i	$0.557586\pi$
$54$	−1.44214	−0.196251
$55$	0	0
$56$	13.4383	1.79577
$57$	−0.708326	−0.0938201
$58$	23.9338	3.14266
$59$	2.45879	0.320107	0.160054	−	0.987108i	$-0.448833\pi$
$59$	2.45879	0.320107	0.160054	+	0.987108i	$0.448833\pi$
$60$	0	0
$61$	−3.69058	−0.472531	−0.236265	−	0.971689i	$-0.575923\pi$
$61$	−3.69058	−0.472531	−0.236265	+	0.971689i	$0.575923\pi$
$62$	−19.4726	−2.47302
$63$	4.15522	0.523508
$64$	32.5500	4.06875
$65$	0	0
$66$	−0.405971	−0.0499716
$67$	5.99654	0.732594	0.366297	−	0.930498i	$-0.380625\pi$
$67$	5.99654	0.732594	0.366297	+	0.930498i	$0.380625\pi$
$68$	−16.9514	−2.05566
$69$	0.191604	0.0230664
$70$	0	0
$71$	9.10030	1.08001	0.540003	−	0.841663i	$-0.318423\pi$
$71$	9.10030	1.08001	0.540003	+	0.841663i	$0.318423\pi$
$72$	28.9576	3.41269
$73$	4.03560	0.472331	0.236165	−	0.971713i	$-0.424109\pi$
$73$	4.03560	0.472331	0.236165	+	0.971713i	$0.424109\pi$
$74$	2.68045	0.311596
$75$	0	0
$76$	44.6321	5.11966
$77$	2.34244	0.266946
$78$	−0.323721	−0.0366542
$79$	−0.0889430	−0.0100069	−0.00500344	−	0.999987i	$-0.501593\pi$
$79$	−0.0889430	−0.0100069	−0.00500344	+	0.999987i	$0.501593\pi$
$80$	0	0
$81$	8.93081	0.992312
$82$	−8.97823	−0.991480
$83$	10.5321	1.15604	0.578022	−	0.816021i	$-0.303825\pi$
$83$	10.5321	1.15604	0.578022	+	0.816021i	$0.303825\pi$
$84$	0.673278	0.0734607
$85$	0	0
$86$	−22.4613	−2.42206
$87$	0.765225	0.0820407
$88$	16.3244	1.74019
$89$	0.520962	0.0552219	0.0276110	−	0.999619i	$-0.491210\pi$
$89$	0.520962	0.0552219	0.0276110	+	0.999619i	$0.491210\pi$
$90$	0	0
$91$	1.86786	0.195805
$92$	−12.0731	−1.25871
$93$	−0.622590	−0.0645595
$94$	−22.4018	−2.31057
$95$	0	0
$96$	2.03161	0.207350
$97$	−13.5274	−1.37350	−0.686748	−	0.726896i	$-0.740962\pi$
$97$	−13.5274	−1.37350	−0.686748	+	0.726896i	$0.740962\pi$
$98$	13.9146	1.40559
$99$	5.04761	0.507304
$100$	0	0
$101$	11.6091	1.15514	0.577572	−	0.816340i	$-0.304000\pi$
$101$	11.6091	1.15514	0.577572	+	0.816340i	$0.304000\pi$
$102$	−0.738093	−0.0730821
$103$	−4.00226	−0.394354	−0.197177	−	0.980368i	$-0.563177\pi$
$103$	−4.00226	−0.394354	−0.197177	+	0.980368i	$0.563177\pi$
$104$	13.0171	1.27643
$105$	0	0
$106$	7.18759	0.698121
$107$	−16.4448	−1.58978	−0.794890	−	0.606753i	$-0.792472\pi$
$107$	−16.4448	−1.58978	−0.794890	+	0.606753i	$0.792472\pi$
$108$	2.90536	0.279569
$109$	16.3031	1.56155	0.780775	−	0.624812i	$-0.214825\pi$
$109$	16.3031	1.56155	0.780775	+	0.624812i	$0.214825\pi$
$110$	0	0
$111$	0.0857009	0.00813437
$112$	−21.5185	−2.03331
$113$	3.75354	0.353103	0.176552	−	0.984291i	$-0.443506\pi$
$113$	3.75354	0.353103	0.176552	+	0.984291i	$0.443506\pi$
$114$	1.94335	0.182012
$115$	0	0
$116$	−48.2174	−4.47687
$117$	4.02497	0.372109
$118$	−6.74591	−0.621011
$119$	4.25877	0.390401
$120$	0	0
$121$	−8.15449	−0.741317
$122$	10.1254	0.916714
$123$	−0.287057	−0.0258831
$124$	39.2298	3.52294
$125$	0	0
$126$	−11.4002	−1.01561
$127$	12.7182	1.12856	0.564278	−	0.825585i	$-0.309155\pi$
$127$	12.7182	1.12856	0.564278	+	0.825585i	$0.309155\pi$
$128$	−42.9831	−3.79921
$129$	−0.718145	−0.0632291
$130$	0	0
$131$	6.42086	0.560993	0.280497	−	0.959855i	$-0.409501\pi$
$131$	6.42086	0.560993	0.280497	+	0.959855i	$0.409501\pi$
$132$	0.817875	0.0711869
$133$	−11.2131	−0.972298
$134$	−16.4520	−1.42124
$135$	0	0
$136$	29.6793	2.54498
$137$	−23.0808	−1.97193	−0.985964	−	0.166957i	$-0.946606\pi$
$137$	−23.0808	−1.97193	−0.985964	+	0.166957i	$0.946606\pi$
$138$	−0.525681	−0.0447490
$139$	−3.88549	−0.329563	−0.164781	−	0.986330i	$-0.552692\pi$
$139$	−3.88549	−0.329563	−0.164781	+	0.986330i	$0.552692\pi$
$140$	0	0
$141$	−0.716244	−0.0603186
$142$	−24.9675	−2.09522
$143$	2.26901	0.189744
$144$	−46.3692	−3.86410
$145$	0	0
$146$	−11.0720	−0.916326
$147$	0.444887	0.0366936
$148$	−5.40008	−0.443883
$149$	−11.7040	−0.958828	−0.479414	−	0.877589i	$-0.659151\pi$
$149$	−11.7040	−0.958828	−0.479414	+	0.877589i	$0.659151\pi$
$150$	0	0
$151$	−14.8733	−1.21037	−0.605184	−	0.796085i	$-0.706901\pi$
$151$	−14.8733	−1.21037	−0.605184	+	0.796085i	$0.706901\pi$
$152$	−78.1438	−6.33830
$153$	9.17703	0.741919
$154$	−6.42668	−0.517877
$155$	0	0
$156$	0.652174	0.0522157
$157$	−21.8491	−1.74375	−0.871873	−	0.489732i	$-0.837095\pi$
$157$	−21.8491	−1.74375	−0.871873	+	0.489732i	$0.837095\pi$
$158$	0.244023	0.0194134
$159$	0.229806	0.0182248
$160$	0	0
$161$	3.03316	0.239047
$162$	−24.5024	−1.92509
$163$	6.68221	0.523391	0.261695	−	0.965150i	$-0.415718\pi$
$163$	6.68221	0.523391	0.261695	+	0.965150i	$0.415718\pi$
$164$	18.0877	1.41241
$165$	0	0
$166$	−28.8956	−2.24274
$167$	7.44352	0.575997	0.287999	−	0.957631i	$-0.407010\pi$
$167$	7.44352	0.575997	0.287999	+	0.957631i	$0.407010\pi$
$168$	−1.17880	−0.0909466
$169$	−11.1907	−0.860822
$170$	0	0
$171$	−24.1626	−1.84776
$172$	45.2508	3.45034
$173$	6.18003	0.469859	0.234930	−	0.972012i	$-0.424514\pi$
$173$	6.18003	0.469859	0.234930	+	0.972012i	$0.424514\pi$
$174$	−2.09946	−0.159160
$175$	0	0
$176$	−26.1399	−1.97037
$177$	−0.215684	−0.0162118
$178$	−1.42931	−0.107131
$179$	11.7335	0.877002	0.438501	−	0.898731i	$-0.355510\pi$
$179$	11.7335	0.877002	0.438501	+	0.898731i	$0.355510\pi$
$180$	0	0
$181$	−18.7826	−1.39610	−0.698049	−	0.716050i	$-0.745948\pi$
$181$	−18.7826	−1.39610	−0.698049	+	0.716050i	$0.745948\pi$
$182$	−5.12464	−0.379863
$183$	0.323736	0.0239313
$184$	21.1380	1.55832
$185$	0	0
$186$	1.70813	0.125246
$187$	5.17340	0.378317
$188$	45.1310	3.29152
$189$	−0.729924	−0.0530942
$190$	0	0
$191$	−10.1789	−0.736523	−0.368261	−	0.929722i	$-0.620047\pi$
$191$	−10.1789	−0.736523	−0.368261	+	0.929722i	$0.620047\pi$
$192$	−2.85527	−0.206061
$193$	−2.40830	−0.173354	−0.0866768	−	0.996236i	$-0.527625\pi$
$193$	−2.40830	−0.173354	−0.0866768	+	0.996236i	$0.527625\pi$
$194$	37.1135	2.66459
$195$	0	0
$196$	−28.0326	−2.00233
$197$	2.10597	0.150044	0.0750220	−	0.997182i	$-0.476097\pi$
$197$	2.10597	0.150044	0.0750220	+	0.997182i	$0.476097\pi$
$198$	−13.8486	−0.984175
$199$	−7.70654	−0.546302	−0.273151	−	0.961971i	$-0.588066\pi$
$199$	−7.70654	−0.546302	−0.273151	+	0.961971i	$0.588066\pi$
$200$	0	0
$201$	−0.526013	−0.0371021
$202$	−31.8505	−2.24099
$203$	12.1138	0.850223
$204$	1.48697	0.104109
$205$	0	0
$206$	10.9805	0.765051
$207$	6.53602	0.454285
$208$	−20.8440	−1.44527
$209$	−13.6213	−0.942203
$210$	0	0
$211$	−16.1242	−1.11004	−0.555019	−	0.831838i	$-0.687289\pi$
$211$	−16.1242	−1.11004	−0.555019	+	0.831838i	$0.687289\pi$
$212$	−14.4802	−0.994506
$213$	−0.798274	−0.0546968
$214$	45.1178	3.08419
$215$	0	0
$216$	−5.08683	−0.346115
$217$	−9.85584	−0.669058
$218$	−44.7289	−3.02942
$219$	−0.354001	−0.0239211
$220$	0	0
$221$	4.12527	0.277496
$222$	−0.235128	−0.0157808
$223$	22.9109	1.53423	0.767115	−	0.641509i	$-0.221691\pi$
$223$	22.9109	1.53423	0.767115	+	0.641509i	$0.221691\pi$
$224$	32.1612	2.14886
$225$	0	0
$226$	−10.2982	−0.685024
$227$	4.59387	0.304906	0.152453	−	0.988311i	$-0.451283\pi$
$227$	4.59387	0.304906	0.152453	+	0.988311i	$0.451283\pi$
$228$	−3.91511	−0.259284
$229$	−6.48905	−0.428808	−0.214404	−	0.976745i	$-0.568781\pi$
$229$	−6.48905	−0.428808	−0.214404	+	0.976745i	$0.568781\pi$
$230$	0	0
$231$	−0.205478	−0.0135194
$232$	84.4209	5.54250
$233$	23.7129	1.55348	0.776740	−	0.629821i	$-0.216872\pi$
$233$	23.7129	1.55348	0.776740	+	0.629821i	$0.216872\pi$
$234$	−11.0429	−0.721894
$235$	0	0
$236$	13.5904	0.884660
$237$	0.00780204	0.000506797 0
$238$	−11.6843	−0.757380
$239$	16.1211	1.04279	0.521395	−	0.853316i	$-0.325412\pi$
$239$	16.1211	1.04279	0.521395	+	0.853316i	$0.325412\pi$
$240$	0	0
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	22.3725	1.43816
$243$	−2.36033	−0.151415
$244$	−20.3988	−1.30590
$245$	0	0
$246$	0.787566	0.0502134
$247$	−10.8616	−0.691107
$248$	−68.6851	−4.36151
$249$	−0.923868	−0.0585477
$250$	0	0
$251$	−14.6940	−0.927475	−0.463737	−	0.885973i	$-0.653492\pi$
$251$	−14.6940	−0.927475	−0.463737	+	0.885973i	$0.653492\pi$
$252$	22.9670	1.44678
$253$	3.68458	0.231648
$254$	−34.8934	−2.18941
$255$	0	0
$256$	52.8280	3.30175
$257$	−23.6089	−1.47269	−0.736343	−	0.676609i	$-0.763449\pi$
$257$	−23.6089	−1.47269	−0.736343	+	0.676609i	$0.763449\pi$
$258$	1.97029	0.122665
$259$	1.35668	0.0842999
$260$	0	0
$261$	26.1035	1.61577
$262$	−17.6162	−1.08833
$263$	−18.7533	−1.15638	−0.578189	−	0.815903i	$-0.696240\pi$
$263$	−18.7533	−1.15638	−0.578189	+	0.815903i	$0.696240\pi$
$264$	−1.43197	−0.0881316
$265$	0	0
$266$	30.7641	1.88627
$267$	−0.0456986	−0.00279671
$268$	33.1445	2.02462
$269$	−23.4769	−1.43141	−0.715705	−	0.698402i	$-0.753895\pi$
$269$	−23.4769	−1.43141	−0.715705	+	0.698402i	$0.753895\pi$
$270$	0	0
$271$	1.41297	0.0858319	0.0429159	−	0.999079i	$-0.486335\pi$
$271$	1.41297	0.0858319	0.0429159	+	0.999079i	$0.486335\pi$
$272$	−47.5248	−2.88161
$273$	−0.163848	−0.00991652
$274$	63.3243	3.82556
$275$	0	0
$276$	1.05904	0.0637470
$277$	30.7273	1.84622	0.923112	−	0.384530i	$-0.125637\pi$
$277$	30.7273	1.84622	0.923112	+	0.384530i	$0.125637\pi$
$278$	10.6602	0.639355
$279$	−21.2379	−1.27148
$280$	0	0
$281$	3.71354	0.221532	0.110766	−	0.993847i	$-0.464670\pi$
$281$	3.71354	0.221532	0.110766	+	0.993847i	$0.464670\pi$
$282$	1.96508	0.117019
$283$	13.2718	0.788924	0.394462	−	0.918912i	$-0.370931\pi$
$283$	13.2718	0.788924	0.394462	+	0.918912i	$0.370931\pi$
$284$	50.2998	2.98474
$285$	0	0
$286$	−6.22523	−0.368106
$287$	−4.54423	−0.268237
$288$	69.3027	4.08370
$289$	−7.59428	−0.446722
$290$	0	0
$291$	1.18661	0.0695605
$292$	22.3058	1.30535
$293$	−22.8056	−1.33232	−0.666158	−	0.745810i	$-0.732062\pi$
$293$	−22.8056	−1.33232	−0.666158	+	0.745810i	$0.732062\pi$
$294$	−1.22058	−0.0711860
$295$	0	0
$296$	9.45467	0.549542
$297$	−0.886687	−0.0514508
$298$	32.1109	1.86014
$299$	2.93809	0.169914
$300$	0	0
$301$	−11.3685	−0.655270
$302$	40.8061	2.34813
$303$	−1.01834	−0.0585022
$304$	125.130	7.17669
$305$	0	0
$306$	−25.1780	−1.43933
$307$	7.76735	0.443306	0.221653	−	0.975126i	$-0.428855\pi$
$307$	7.76735	0.443306	0.221653	+	0.975126i	$0.428855\pi$
$308$	12.9473	0.737740
$309$	0.351076	0.0199720
$310$	0	0
$311$	3.90820	0.221614	0.110807	−	0.993842i	$-0.464657\pi$
$311$	3.90820	0.221614	0.110807	+	0.993842i	$0.464657\pi$
$312$	−1.14185	−0.0646447
$313$	18.9001	1.06830	0.534148	−	0.845391i	$-0.320633\pi$
$313$	18.9001	1.06830	0.534148	+	0.845391i	$0.320633\pi$
$314$	59.9448	3.38288
$315$	0	0
$316$	−0.491612	−0.0276553
$317$	−13.1540	−0.738801	−0.369400	−	0.929270i	$-0.620437\pi$
$317$	−13.1540	−0.738801	−0.369400	+	0.929270i	$0.620437\pi$
$318$	−0.630492	−0.0353562
$319$	14.7154	0.823907
$320$	0	0
$321$	1.44253	0.0805142
$322$	−8.32174	−0.463752
$323$	−24.7647	−1.37795
$324$	49.3630	2.74239
$325$	0	0
$326$	−18.3332	−1.01538
$327$	−1.43010	−0.0790845
$328$	−31.6686	−1.74861
$329$	−11.3384	−0.625107
$330$	0	0
$331$	−17.8857	−0.983089	−0.491544	−	0.870852i	$-0.663567\pi$
$331$	−17.8857	−0.983089	−0.491544	+	0.870852i	$0.663567\pi$
$332$	58.2136	3.19488
$333$	2.92345	0.160204
$334$	−20.4219	−1.11744
$335$	0	0
$336$	1.88759	0.102977
$337$	18.4814	1.00675	0.503374	−	0.864069i	$-0.332092\pi$
$337$	18.4814	1.00675	0.503374	+	0.864069i	$0.332092\pi$
$338$	30.7026	1.67000
$339$	−0.329259	−0.0178829
$340$	0	0
$341$	−11.9725	−0.648349
$342$	66.2921	3.58467
$343$	16.7632	0.905126
$344$	−79.2269	−4.27163
$345$	0	0
$346$	−16.9554	−0.911531
$347$	12.4603	0.668906	0.334453	−	0.942412i	$-0.391448\pi$
$347$	12.4603	0.668906	0.334453	+	0.942412i	$0.391448\pi$
$348$	4.22960	0.226731
$349$	−25.0759	−1.34228	−0.671140	−	0.741331i	$-0.734195\pi$
$349$	−25.0759	−1.34228	−0.671140	+	0.741331i	$0.734195\pi$
$350$	0	0
$351$	−0.707045	−0.0377392
$352$	39.0683	2.08235
$353$	−24.0369	−1.27935	−0.639677	−	0.768644i	$-0.720932\pi$
$353$	−24.0369	−1.27935	−0.639677	+	0.768644i	$0.720932\pi$
$354$	0.591748	0.0314510
$355$	0	0
$356$	2.87950	0.152613
$357$	−0.373577	−0.0197718
$358$	−32.1918	−1.70139
$359$	−25.8489	−1.36425	−0.682127	−	0.731234i	$-0.738945\pi$
$359$	−25.8489	−1.36425	−0.682127	+	0.731234i	$0.738945\pi$
$360$	0	0
$361$	46.2040	2.43179
$362$	51.5316	2.70844
$363$	0.715307	0.0375439
$364$	10.3242	0.541133
$365$	0	0
$366$	−0.888198	−0.0464269
$367$	13.7562	0.718068	0.359034	−	0.933324i	$-0.383106\pi$
$367$	13.7562	0.718068	0.359034	+	0.933324i	$0.383106\pi$
$368$	−33.8479	−1.76444
$369$	−9.79215	−0.509759
$370$	0	0
$371$	3.63792	0.188871
$372$	−3.44122	−0.178419
$373$	−4.09173	−0.211862	−0.105931	−	0.994373i	$-0.533782\pi$
$373$	−4.09173	−0.211862	−0.105931	+	0.994373i	$0.533782\pi$
$374$	−14.1937	−0.733938
$375$	0	0
$376$	−79.0172	−4.07500
$377$	11.7341	0.604337
$378$	2.00261	0.103003
$379$	−33.6065	−1.72625	−0.863124	−	0.504992i	$-0.831495\pi$
$379$	−33.6065	−1.72625	−0.863124	+	0.504992i	$0.831495\pi$
$380$	0	0
$381$	−1.11563	−0.0571556
$382$	27.9268	1.42886
$383$	20.9590	1.07096	0.535478	−	0.844549i	$-0.320132\pi$
$383$	20.9590	1.07096	0.535478	+	0.844549i	$0.320132\pi$
$384$	3.77046	0.192410
$385$	0	0
$386$	6.60739	0.336307
$387$	−24.4975	−1.24528
$388$	−74.7694	−3.79584
$389$	6.32158	0.320517	0.160258	−	0.987075i	$-0.448767\pi$
$389$	6.32158	0.320517	0.160258	+	0.987075i	$0.448767\pi$
$390$	0	0
$391$	6.69890	0.338778
$392$	49.0806	2.47895
$393$	−0.563235	−0.0284114
$394$	−5.77790	−0.291087
$395$	0	0
$396$	27.8995	1.40200
$397$	−3.36213	−0.168741	−0.0843703	−	0.996434i	$-0.526888\pi$
$397$	−3.36213	−0.168741	−0.0843703	+	0.996434i	$0.526888\pi$
$398$	21.1436	1.05983
$399$	0.983606	0.0492419
$400$	0	0
$401$	−21.5665	−1.07698	−0.538490	−	0.842632i	$-0.681005\pi$
$401$	−21.5665	−1.07698	−0.538490	+	0.842632i	$0.681005\pi$
$402$	1.44316	0.0719785
$403$	−9.54690	−0.475565
$404$	64.1664	3.19240
$405$	0	0
$406$	−33.2353	−1.64944
$407$	1.64805	0.0816907
$408$	−2.60345	−0.128890
$409$	9.59465	0.474425	0.237212	−	0.971458i	$-0.423766\pi$
$409$	9.59465	0.474425	0.237212	+	0.971458i	$0.423766\pi$
$410$	0	0
$411$	2.02464	0.0998681
$412$	−22.1216	−1.08985
$413$	−3.41436	−0.168010
$414$	−17.9321	−0.881317
$415$	0	0
$416$	31.1531	1.52741
$417$	0.340833	0.0166907
$418$	37.3711	1.82788
$419$	10.9416	0.534534	0.267267	−	0.963623i	$-0.413879\pi$
$419$	10.9416	0.534534	0.267267	+	0.963623i	$0.413879\pi$
$420$	0	0
$421$	−0.843741	−0.0411214	−0.0205607	−	0.999789i	$-0.506545\pi$
$421$	−0.843741	−0.0411214	−0.0205607	+	0.999789i	$0.506545\pi$
$422$	44.2382	2.15348
$423$	−24.4326	−1.18796
$424$	25.3526	1.23123
$425$	0	0
$426$	2.19013	0.106112
$427$	5.12487	0.248010
$428$	−90.8949	−4.39357
$429$	−0.199037	−0.00960958
$430$	0	0
$431$	−9.19126	−0.442727	−0.221364	−	0.975191i	$-0.571051\pi$
$431$	−9.19126	−0.442727	−0.221364	+	0.975191i	$0.571051\pi$
$432$	8.14543	0.391897
$433$	34.5448	1.66012	0.830059	−	0.557676i	$-0.188307\pi$
$433$	34.5448	1.66012	0.830059	+	0.557676i	$0.188307\pi$
$434$	27.0403	1.29798
$435$	0	0
$436$	90.1114	4.31555
$437$	−17.6378	−0.843731
$438$	0.971231	0.0464072
$439$	−34.4428	−1.64387	−0.821934	−	0.569583i	$-0.807105\pi$
$439$	−34.4428	−1.64387	−0.821934	+	0.569583i	$0.807105\pi$
$440$	0	0
$441$	15.1761	0.722670
$442$	−11.3180	−0.538345
$443$	2.65568	0.126175	0.0630875	−	0.998008i	$-0.479905\pi$
$443$	2.65568	0.126175	0.0630875	+	0.998008i	$0.479905\pi$
$444$	0.473692	0.0224804
$445$	0	0
$446$	−62.8582	−2.97642
$447$	1.02667	0.0485597
$448$	−45.2000	−2.13550
$449$	2.75802	0.130159	0.0650794	−	0.997880i	$-0.479270\pi$
$449$	2.75802	0.130159	0.0650794	+	0.997880i	$0.479270\pi$
$450$	0	0
$451$	−5.52017	−0.259935
$452$	20.7468	0.975848
$453$	1.30467	0.0612990
$454$	−12.6037	−0.591521
$455$	0	0
$456$	6.85473	0.321002
$457$	−8.49913	−0.397572	−0.198786	−	0.980043i	$-0.563700\pi$
$457$	−8.49913	−0.397572	−0.198786	+	0.980043i	$0.563700\pi$
$458$	17.8033	0.831892
$459$	−1.61208	−0.0752454
$460$	0	0
$461$	−32.3259	−1.50557	−0.752783	−	0.658269i	$-0.771289\pi$
$461$	−32.3259	−1.50557	−0.752783	+	0.658269i	$0.771289\pi$
$462$	0.563745	0.0262278
$463$	−30.8997	−1.43603	−0.718016	−	0.696026i	$-0.754950\pi$
$463$	−30.8997	−1.43603	−0.718016	+	0.696026i	$0.754950\pi$
$464$	−135.181	−6.27564
$465$	0	0
$466$	−65.0583	−3.01377
$467$	−0.328063	−0.0151810	−0.00759048	−	0.999971i	$-0.502416\pi$
$467$	−0.328063	−0.0151810	−0.00759048	+	0.999971i	$0.502416\pi$
$468$	22.2471	1.02837
$469$	−8.32700	−0.384505
$470$	0	0
$471$	1.91659	0.0883118
$472$	−23.7946	−1.09524
$473$	−13.8101	−0.634988
$474$	−0.0214056	−0.000983190 0
$475$	0	0
$476$	23.5393	1.07892
$477$	7.83918	0.358931
$478$	−44.2297	−2.02302
$479$	25.2532	1.15385	0.576924	−	0.816798i	$-0.304253\pi$
$479$	25.2532	1.15385	0.576924	+	0.816798i	$0.304253\pi$
$480$	0	0
$481$	1.31415	0.0599202
$482$	2.74359	0.124967
$483$	−0.266067	−0.0121065
$484$	−45.0720	−2.04873
$485$	0	0
$486$	6.47578	0.293747
$487$	−39.4297	−1.78673	−0.893365	−	0.449333i	$-0.851662\pi$
$487$	−39.4297	−1.78673	−0.893365	+	0.449333i	$0.851662\pi$
$488$	35.7151	1.61675
$489$	−0.586160	−0.0265071
$490$	0	0
$491$	12.0485	0.543739	0.271870	−	0.962334i	$-0.412358\pi$
$491$	12.0485	0.543739	0.271870	+	0.962334i	$0.412358\pi$
$492$	−1.58664	−0.0715313
$493$	26.7540	1.20494
$494$	29.7997	1.34075
$495$	0	0
$496$	109.984	4.93843
$497$	−12.6370	−0.566846
$498$	2.53471	0.113583
$499$	−14.5964	−0.653426	−0.326713	−	0.945124i	$-0.605941\pi$
$499$	−14.5964	−0.653426	−0.326713	+	0.945124i	$0.605941\pi$
$500$	0	0
$501$	−0.652942	−0.0291713
$502$	40.3142	1.79931
$503$	−33.6921	−1.50226	−0.751129	−	0.660156i	$-0.770490\pi$
$503$	−33.6921	−1.50226	−0.751129	+	0.660156i	$0.770490\pi$
$504$	−40.2115	−1.79116
$505$	0	0
$506$	−10.1090	−0.449398
$507$	0.981642	0.0435962
$508$	70.2968	3.11891
$509$	−2.82042	−0.125013	−0.0625066	−	0.998045i	$-0.519909\pi$
$509$	−2.82042	−0.125013	−0.0625066	+	0.998045i	$0.519909\pi$
$510$	0	0
$511$	−5.60397	−0.247905
$512$	−58.9718	−2.60621
$513$	4.24451	0.187400
$514$	64.7732	2.85702
$515$	0	0
$516$	−3.96938	−0.174742
$517$	−13.7735	−0.605759
$518$	−3.72217	−0.163543
$519$	−0.542109	−0.0237960
$520$	0	0
$521$	33.3228	1.45990	0.729948	−	0.683502i	$-0.239544\pi$
$521$	33.3228	1.45990	0.729948	+	0.683502i	$0.239544\pi$
$522$	−71.6172	−3.13460
$523$	34.1620	1.49380	0.746900	−	0.664936i	$-0.231541\pi$
$523$	34.1620	1.49380	0.746900	+	0.664936i	$0.231541\pi$
$524$	35.4898	1.55038
$525$	0	0
$526$	51.4513	2.24338
$527$	−21.7672	−0.948192
$528$	2.29298	0.0997892
$529$	−18.2289	−0.792562
$530$	0	0
$531$	−7.35746	−0.319286
$532$	−61.9777	−2.68707
$533$	−4.40178	−0.190662
$534$	0.125378	0.00542563
$535$	0	0
$536$	−58.0307	−2.50654
$537$	−1.02926	−0.0444157
$538$	64.4109	2.77695
$539$	8.55527	0.368501
$540$	0	0
$541$	23.1983	0.997372	0.498686	−	0.866783i	$-0.333816\pi$
$541$	23.1983	0.997372	0.498686	+	0.866783i	$0.333816\pi$
$542$	−3.87661	−0.166515
$543$	1.64760	0.0707052
$544$	71.0298	3.04538
$545$	0	0
$546$	0.449531	0.0192381
$547$	−0.251587	−0.0107571	−0.00537854	−	0.999986i	$-0.501712\pi$
$547$	−0.251587	−0.0107571	−0.00537854	+	0.999986i	$0.501712\pi$
$548$	−127.574	−5.44969
$549$	11.0434	0.471319
$550$	0	0
$551$	−70.4418	−3.00092
$552$	−1.85422	−0.0789208
$553$	0.123509	0.00525215
$554$	−84.3030	−3.58169
$555$	0	0
$556$	−21.4761	−0.910791
$557$	5.86433	0.248480	0.124240	−	0.992252i	$-0.460351\pi$
$557$	5.86433	0.248480	0.124240	+	0.992252i	$0.460351\pi$
$558$	58.2680	2.46668
$559$	−11.0122	−0.465765
$560$	0	0
$561$	−0.453808	−0.0191598
$562$	−10.1884	−0.429773
$563$	2.00215	0.0843807	0.0421904	−	0.999110i	$-0.486566\pi$
$563$	2.00215	0.0843807	0.0421904	+	0.999110i	$0.486566\pi$
$564$	−3.95887	−0.166699
$565$	0	0
$566$	−36.4122	−1.53052
$567$	−12.4016	−0.520819
$568$	−88.0669	−3.69521
$569$	40.0230	1.67785	0.838926	−	0.544246i	$-0.183184\pi$
$569$	40.0230	1.67785	0.838926	+	0.544246i	$0.183184\pi$
$570$	0	0
$571$	−12.3124	−0.515260	−0.257630	−	0.966244i	$-0.582942\pi$
$571$	−12.3124	−0.515260	−0.257630	+	0.966244i	$0.582942\pi$
$572$	12.5414	0.524384
$573$	0.892892	0.0373011
$574$	12.4675	0.520382
$575$	0	0
$576$	−97.3995	−4.05831
$577$	−21.4137	−0.891464	−0.445732	−	0.895166i	$-0.647057\pi$
$577$	−21.4137	−0.891464	−0.445732	+	0.895166i	$0.647057\pi$
$578$	20.8356	0.866645
$579$	0.211255	0.00877947
$580$	0	0
$581$	−14.6252	−0.606755
$582$	−3.25558	−0.134948
$583$	4.41922	0.183025
$584$	−39.0539	−1.61606
$585$	0	0
$586$	62.5691	2.58471
$587$	−6.14344	−0.253567	−0.126783	−	0.991930i	$-0.540465\pi$
$587$	−6.14344	−0.253567	−0.126783	+	0.991930i	$0.540465\pi$
$588$	2.45901	0.101408
$589$	57.3116	2.36149
$590$	0	0
$591$	−0.184734	−0.00759896
$592$	−15.1396	−0.622232
$593$	40.7560	1.67365	0.836825	−	0.547471i	$-0.184409\pi$
$593$	40.7560	1.67365	0.836825	+	0.547471i	$0.184409\pi$
$594$	2.43270	0.0998150
$595$	0	0
$596$	−64.6911	−2.64985
$597$	0.676014	0.0276674
$598$	−8.06089	−0.329634
$599$	34.7912	1.42153	0.710766	−	0.703429i	$-0.248349\pi$
$599$	34.7912	1.42153	0.710766	+	0.703429i	$0.248349\pi$
$600$	0	0
$601$	−30.9358	−1.26190	−0.630950	−	0.775824i	$-0.717335\pi$
$601$	−30.9358	−1.26190	−0.630950	+	0.775824i	$0.717335\pi$
$602$	31.1905	1.27123
$603$	−17.9435	−0.730715
$604$	−82.2085	−3.34502
$605$	0	0
$606$	2.79391	0.113495
$607$	−38.0624	−1.54491	−0.772453	−	0.635071i	$-0.780971\pi$
$607$	−38.0624	−1.54491	−0.772453	+	0.635071i	$0.780971\pi$
$608$	−187.017	−7.58455
$609$	−1.06262	−0.0430594
$610$	0	0
$611$	−10.9830	−0.444325
$612$	50.7239	2.05039
$613$	26.3263	1.06331	0.531655	−	0.846961i	$-0.321570\pi$
$613$	26.3263	1.06331	0.531655	+	0.846961i	$0.321570\pi$
$614$	−21.3104	−0.860017
$615$	0	0
$616$	−22.6686	−0.913345
$617$	−37.6152	−1.51433	−0.757166	−	0.653222i	$-0.773417\pi$
$617$	−37.6152	−1.51433	−0.757166	+	0.653222i	$0.773417\pi$
$618$	−0.963208	−0.0387459
$619$	23.5018	0.944616	0.472308	−	0.881433i	$-0.343421\pi$
$619$	23.5018	0.944616	0.472308	+	0.881433i	$0.343421\pi$
$620$	0	0
$621$	−1.14815	−0.0460736
$622$	−10.7225	−0.429932
$623$	−0.723426	−0.0289835
$624$	1.82842	0.0731955
$625$	0	0
$626$	−51.8540	−2.07250
$627$	1.19485	0.0477177
$628$	−120.766	−4.81908
$629$	2.99630	0.119470
$630$	0	0
$631$	10.8128	0.430451	0.215225	−	0.976564i	$-0.430951\pi$
$631$	10.8128	0.430451	0.215225	+	0.976564i	$0.430951\pi$
$632$	0.860734	0.0342382
$633$	1.41441	0.0562177
$634$	36.0891	1.43328
$635$	0	0
$636$	1.27020	0.0503666
$637$	6.82197	0.270296
$638$	−40.3731	−1.59839
$639$	−27.2309	−1.07724
$640$	0	0
$641$	33.1211	1.30820	0.654101	−	0.756407i	$-0.273047\pi$
$641$	33.1211	1.30820	0.654101	+	0.756407i	$0.273047\pi$
$642$	−3.95771	−0.156198
$643$	−15.2022	−0.599516	−0.299758	−	0.954015i	$-0.596906\pi$
$643$	−15.2022	−0.599516	−0.299758	+	0.954015i	$0.596906\pi$
$644$	16.7651	0.660637
$645$	0	0
$646$	67.9441	2.67323
$647$	−3.61671	−0.142188	−0.0710938	−	0.997470i	$-0.522649\pi$
$647$	−3.61671	−0.142188	−0.0710938	+	0.997470i	$0.522649\pi$
$648$	−86.4267	−3.39516
$649$	−4.14765	−0.162810
$650$	0	0
$651$	0.864549	0.0338843
$652$	36.9344	1.44646
$653$	6.11369	0.239247	0.119624	−	0.992819i	$-0.461831\pi$
$653$	6.11369	0.239247	0.119624	+	0.992819i	$0.461831\pi$
$654$	3.92359	0.153425
$655$	0	0
$656$	50.7103	1.97990
$657$	−12.0757	−0.471120
$658$	31.1079	1.21271
$659$	−7.30750	−0.284660	−0.142330	−	0.989819i	$-0.545459\pi$
$659$	−7.30750	−0.284660	−0.142330	+	0.989819i	$0.545459\pi$
$660$	0	0
$661$	−26.9475	−1.04814	−0.524068	−	0.851677i	$-0.675586\pi$
$661$	−26.9475	−1.04814	−0.524068	+	0.851677i	$0.675586\pi$
$662$	49.0711	1.90720
$663$	−0.361867	−0.0140537
$664$	−101.923	−3.95537
$665$	0	0
$666$	−8.02073	−0.310797
$667$	19.0546	0.737798
$668$	41.1423	1.59184
$669$	−2.00974	−0.0777009
$670$	0	0
$671$	6.22552	0.240333
$672$	−2.82116	−0.108829
$673$	−8.91441	−0.343625	−0.171813	−	0.985130i	$-0.554962\pi$
$673$	−8.91441	−0.343625	−0.171813	+	0.985130i	$0.554962\pi$
$674$	−50.7054	−1.95310
$675$	0	0
$676$	−61.8539	−2.37900
$677$	−16.2141	−0.623158	−0.311579	−	0.950220i	$-0.600858\pi$
$677$	−16.2141	−0.623158	−0.311579	+	0.950220i	$0.600858\pi$
$678$	0.903350	0.0346929
$679$	18.7846	0.720885
$680$	0	0
$681$	−0.402972	−0.0154419
$682$	32.8477	1.25780
$683$	1.03326	0.0395366	0.0197683	−	0.999805i	$-0.493707\pi$
$683$	1.03326	0.0395366	0.0197683	+	0.999805i	$0.493707\pi$
$684$	−133.553	−5.10653
$685$	0	0
$686$	−45.9912	−1.75595
$687$	0.569216	0.0217169
$688$	126.864	4.83666
$689$	3.52388	0.134249
$690$	0	0
$691$	24.6967	0.939505	0.469753	−	0.882798i	$-0.344343\pi$
$691$	24.6967	0.939505	0.469753	+	0.882798i	$0.344343\pi$
$692$	34.1587	1.29852
$693$	−7.00929	−0.266261
$694$	−34.1860	−1.29768
$695$	0	0
$696$	−7.40536	−0.280699
$697$	−10.0362	−0.380147
$698$	68.7978	2.60404
$699$	−2.08008	−0.0786758
$700$	0	0
$701$	−19.9544	−0.753668	−0.376834	−	0.926281i	$-0.622987\pi$
$701$	−19.9544	−0.753668	−0.376834	+	0.926281i	$0.622987\pi$
$702$	1.93984	0.0732145
$703$	−7.88908	−0.297542
$704$	−54.9075	−2.06940
$705$	0	0
$706$	65.9473	2.48196
$707$	−16.1207	−0.606283
$708$	−1.19214	−0.0448035
$709$	35.3959	1.32932	0.664660	−	0.747146i	$-0.268577\pi$
$709$	35.3959	1.32932	0.664660	+	0.747146i	$0.268577\pi$
$710$	0	0
$711$	0.266145	0.00998121
$712$	−5.04154	−0.188940
$713$	−15.5029	−0.580589
$714$	1.02494	0.0383574
$715$	0	0
$716$	64.8541	2.42371
$717$	−1.41414	−0.0528120
$718$	70.9187	2.64666
$719$	17.5408	0.654161	0.327080	−	0.944997i	$-0.393935\pi$
$719$	17.5408	0.654161	0.327080	+	0.944997i	$0.393935\pi$
$720$	0	0
$721$	5.55767	0.206979
$722$	−126.765	−4.71770
$723$	0.0877195	0.00326232
$724$	−103.816	−3.85830
$725$	0	0
$726$	−1.96251	−0.0728355
$727$	−33.7229	−1.25071	−0.625357	−	0.780339i	$-0.715047\pi$
$727$	−33.7229	−1.25071	−0.625357	+	0.780339i	$0.715047\pi$
$728$	−18.0760	−0.669940
$729$	−26.5854	−0.984643
$730$	0	0
$731$	−25.1080	−0.928652
$732$	1.78938	0.0661372
$733$	1.47790	0.0545876	0.0272938	−	0.999627i	$-0.491311\pi$
$733$	1.47790	0.0545876	0.0272938	+	0.999627i	$0.491311\pi$
$734$	−37.7414	−1.39306
$735$	0	0
$736$	50.5885	1.86472
$737$	−10.1154	−0.372604
$738$	26.8656	0.988937
$739$	−0.339380	−0.0124843	−0.00624214	−	0.999981i	$-0.501987\pi$
$739$	−0.339380	−0.0124843	−0.00624214	+	0.999981i	$0.501987\pi$
$740$	0	0
$741$	0.952774	0.0350010
$742$	−9.98094	−0.366412
$743$	−18.6620	−0.684643	−0.342322	−	0.939583i	$-0.611213\pi$
$743$	−18.6620	−0.684643	−0.342322	+	0.939583i	$0.611213\pi$
$744$	6.02503	0.220888
$745$	0	0
$746$	11.2260	0.411014
$747$	−31.5152	−1.15308
$748$	28.5948	1.04553
$749$	22.8358	0.834403
$750$	0	0
$751$	19.0954	0.696803	0.348401	−	0.937345i	$-0.386725\pi$
$751$	19.0954	0.696803	0.348401	+	0.937345i	$0.386725\pi$
$752$	126.529	4.61402
$753$	1.28895	0.0469718
$754$	−32.1935	−1.17242
$755$	0	0
$756$	−4.03449	−0.146733
$757$	6.62264	0.240704	0.120352	−	0.992731i	$-0.461598\pi$
$757$	6.62264	0.240704	0.120352	+	0.992731i	$0.461598\pi$
$758$	92.2022	3.34894
$759$	−0.323210	−0.0117318
$760$	0	0
$761$	−36.3808	−1.31880	−0.659401	−	0.751791i	$-0.729190\pi$
$761$	−36.3808	−1.31880	−0.659401	+	0.751791i	$0.729190\pi$
$762$	3.06083	0.110882
$763$	−22.6390	−0.819586
$764$	−56.2618	−2.03548
$765$	0	0
$766$	−57.5029	−2.07766
$767$	−3.30734	−0.119421
$768$	−4.63404	−0.167217
$769$	−45.9984	−1.65875	−0.829373	−	0.558696i	$-0.811302\pi$
$769$	−45.9984	−1.65875	−0.829373	+	0.558696i	$0.811302\pi$
$770$	0	0
$771$	2.07097	0.0745840
$772$	−13.3113	−0.479086
$773$	−23.3465	−0.839714	−0.419857	−	0.907590i	$-0.637920\pi$
$773$	−23.3465	−0.839714	−0.419857	+	0.907590i	$0.637920\pi$
$774$	67.2110	2.41585
$775$	0	0
$776$	130.909	4.69937
$777$	−0.119007	−0.00426936
$778$	−17.3438	−0.621806
$779$	26.4247	0.946761
$780$	0	0
$781$	−15.3510	−0.549301
$782$	−18.3790	−0.657233
$783$	−4.58546	−0.163871
$784$	−78.5918	−2.80685
$785$	0	0
$786$	1.54528	0.0551184
$787$	−10.6585	−0.379933	−0.189967	−	0.981791i	$-0.560838\pi$
$787$	−10.6585	−0.379933	−0.189967	+	0.981791i	$0.560838\pi$
$788$	11.6402	0.414667
$789$	1.64503	0.0585646
$790$	0	0
$791$	−5.21229	−0.185328
$792$	−48.8476	−1.73572
$793$	4.96423	0.176285
$794$	9.22430	0.327358
$795$	0	0
$796$	−42.5961	−1.50978
$797$	−18.7371	−0.663703	−0.331852	−	0.943332i	$-0.607673\pi$
$797$	−18.7371	−0.663703	−0.331852	+	0.943332i	$0.607673\pi$
$798$	−2.69861	−0.0955297
$799$	−25.0415	−0.885905
$800$	0	0
$801$	−1.55888	−0.0550803
$802$	59.1696	2.08935
$803$	−6.80751	−0.240232
$804$	−2.90742	−0.102537
$805$	0	0
$806$	26.1927	0.922600
$807$	2.05938	0.0724936
$808$	−112.345	−3.95229
$809$	−34.8006	−1.22352	−0.611762	−	0.791042i	$-0.709539\pi$
$809$	−34.8006	−1.22352	−0.611762	+	0.791042i	$0.709539\pi$
$810$	0	0
$811$	7.12783	0.250292	0.125146	−	0.992138i	$-0.460060\pi$
$811$	7.12783	0.250292	0.125146	+	0.992138i	$0.460060\pi$
$812$	66.9563	2.34970
$813$	−0.123945	−0.00434694
$814$	−4.52156	−0.158481
$815$	0	0
$816$	4.16885	0.145939
$817$	66.1078	2.31282
$818$	−26.3237	−0.920388
$819$	−5.58921	−0.195303
$820$	0	0
$821$	−29.3699	−1.02502	−0.512508	−	0.858682i	$-0.671284\pi$
$821$	−29.3699	−1.02502	−0.512508	+	0.858682i	$0.671284\pi$
$822$	−5.55477	−0.193745
$823$	4.23749	0.147710	0.0738548	−	0.997269i	$-0.476470\pi$
$823$	4.23749	0.147710	0.0738548	+	0.997269i	$0.476470\pi$
$824$	38.7313	1.34927
$825$	0	0
$826$	9.36760	0.325940
$827$	−10.2062	−0.354904	−0.177452	−	0.984129i	$-0.556785\pi$
$827$	−10.2062	−0.354904	−0.177452	+	0.984129i	$0.556785\pi$
$828$	36.1263	1.25548
$829$	−52.2071	−1.81323	−0.906614	−	0.421962i	$-0.861342\pi$
$829$	−52.2071	−1.81323	−0.906614	+	0.421962i	$0.861342\pi$
$830$	0	0
$831$	−2.69538	−0.0935018
$832$	−43.7832	−1.51791
$833$	15.5543	0.538923
$834$	−0.935105	−0.0323801
$835$	0	0
$836$	−75.2884	−2.60390
$837$	3.73075	0.128953
$838$	−30.0193	−1.03700
$839$	−54.1448	−1.86929	−0.934644	−	0.355586i	$-0.884281\pi$
$839$	−54.1448	−1.86929	−0.934644	+	0.355586i	$0.884281\pi$
$840$	0	0
$841$	47.1002	1.62415
$842$	2.31488	0.0797759
$843$	−0.325750	−0.0112194
$844$	−89.1229	−3.06774
$845$	0	0
$846$	67.0331	2.30465
$847$	11.3236	0.389083
$848$	−40.5965	−1.39409
$849$	−1.16419	−0.0399550
$850$	0	0
$851$	2.13401	0.0731530
$852$	−4.41227	−0.151162
$853$	15.4892	0.530340	0.265170	−	0.964202i	$-0.414572\pi$
$853$	15.4892	0.530340	0.265170	+	0.964202i	$0.414572\pi$
$854$	−14.0605	−0.481141
$855$	0	0
$856$	159.142	5.43938
$857$	−32.9960	−1.12712	−0.563561	−	0.826075i	$-0.690569\pi$
$857$	−32.9960	−1.12712	−0.563561	+	0.826075i	$0.690569\pi$
$858$	0.546074	0.0186427
$859$	22.7095	0.774837	0.387418	−	0.921904i	$-0.373367\pi$
$859$	22.7095	0.774837	0.387418	+	0.921904i	$0.373367\pi$
$860$	0	0
$861$	0.398617	0.0135848
$862$	25.2170	0.858895
$863$	−6.11570	−0.208181	−0.104090	−	0.994568i	$-0.533193\pi$
$863$	−6.11570	−0.208181	−0.104090	+	0.994568i	$0.533193\pi$
$864$	−12.1740	−0.414169
$865$	0	0
$866$	−94.7767	−3.22064
$867$	0.666166	0.0226242
$868$	−54.4758	−1.84903
$869$	0.150035	0.00508958
$870$	0	0
$871$	−8.06599	−0.273305
$872$	−157.771	−5.34279
$873$	40.4780	1.36997
$874$	48.3909	1.63685
$875$	0	0
$876$	−1.95666	−0.0661093
$877$	−32.6597	−1.10284	−0.551420	−	0.834228i	$-0.685914\pi$
$877$	−32.6597	−1.10284	−0.551420	+	0.834228i	$0.685914\pi$
$878$	94.4969	3.18912
$879$	2.00049	0.0674750
$880$	0	0
$881$	44.6175	1.50320	0.751600	−	0.659619i	$-0.229282\pi$
$881$	44.6175	1.50320	0.751600	+	0.659619i	$0.229282\pi$
$882$	−41.6368	−1.40199
$883$	−19.5029	−0.656324	−0.328162	−	0.944621i	$-0.606429\pi$
$883$	−19.5029	−0.656324	−0.328162	+	0.944621i	$0.606429\pi$
$884$	22.8015	0.766897
$885$	0	0
$886$	−7.28608	−0.244781
$887$	9.73987	0.327033	0.163516	−	0.986541i	$-0.447716\pi$
$887$	9.73987	0.327033	0.163516	+	0.986541i	$0.447716\pi$
$888$	−0.829359	−0.0278315
$889$	−17.6609	−0.592327
$890$	0	0
$891$	−15.0651	−0.504699
$892$	126.635	4.24005
$893$	65.9329	2.20636
$894$	−2.81675	−0.0942063
$895$	0	0
$896$	59.6878	1.99403
$897$	−0.257727	−0.00860527
$898$	−7.56686	−0.252509
$899$	−61.9154	−2.06499
$900$	0	0
$901$	8.03454	0.267669
$902$	15.1451	0.504275
$903$	0.997240	0.0331861
$904$	−36.3244	−1.20813
$905$	0	0
$906$	−3.57949	−0.118921
$907$	−7.48693	−0.248599	−0.124300	−	0.992245i	$-0.539668\pi$
$907$	−7.48693	−0.248599	−0.124300	+	0.992245i	$0.539668\pi$
$908$	25.3916	0.842649
$909$	−34.7379	−1.15218
$910$	0	0
$911$	19.5726	0.648470	0.324235	−	0.945977i	$-0.394893\pi$
$911$	19.5726	0.648470	0.324235	+	0.945977i	$0.394893\pi$
$912$	−10.9763	−0.363463
$913$	−17.7662	−0.587975
$914$	23.3181	0.771294
$915$	0	0
$916$	−35.8667	−1.18507
$917$	−8.91623	−0.294440
$918$	4.42288	0.145977
$919$	3.51244	0.115865	0.0579323	−	0.998321i	$-0.481549\pi$
$919$	3.51244	0.115865	0.0579323	+	0.998321i	$0.481549\pi$
$920$	0	0
$921$	−0.681348	−0.0224512
$922$	88.6888	2.92081
$923$	−12.2409	−0.402913
$924$	−1.13573	−0.0373627
$925$	0	0
$926$	84.7761	2.78592
$927$	11.9760	0.393343
$928$	202.040	6.63229
$929$	−13.2440	−0.434521	−0.217261	−	0.976114i	$-0.569712\pi$
$929$	−13.2440	−0.434521	−0.217261	+	0.976114i	$0.569712\pi$
$930$	0	0
$931$	−40.9534	−1.34219
$932$	131.067	4.29325
$933$	−0.342825	−0.0112236
$934$	0.900070	0.0294512
$935$	0	0
$936$	−38.9511	−1.27316
$937$	19.4083	0.634042	0.317021	−	0.948419i	$-0.397317\pi$
$937$	19.4083	0.634042	0.317021	+	0.948419i	$0.397317\pi$
$938$	22.8458	0.745943
$939$	−1.65791	−0.0541037
$940$	0	0
$941$	−40.5608	−1.32224	−0.661122	−	0.750279i	$-0.729919\pi$
$941$	−40.5608	−1.32224	−0.661122	+	0.750279i	$0.729919\pi$
$942$	−5.25833	−0.171326
$943$	−7.14792	−0.232768
$944$	38.1018	1.24011
$945$	0	0
$946$	37.8891	1.23188
$947$	−58.6415	−1.90559	−0.952797	−	0.303609i	$-0.901808\pi$
$947$	−58.6415	−1.90559	−0.952797	+	0.303609i	$0.901808\pi$
$948$	0.0431239	0.00140060
$949$	−5.42831	−0.176210
$950$	0	0
$951$	1.15386	0.0374165
$952$	−41.2136	−1.33574
$953$	−26.5555	−0.860217	−0.430109	−	0.902777i	$-0.641525\pi$
$953$	−26.5555	−0.860217	−0.430109	+	0.902777i	$0.641525\pi$
$954$	−21.5075	−0.696330
$955$	0	0
$956$	89.1058	2.88189
$957$	−1.29083	−0.0417266
$958$	−69.2843	−2.23847
$959$	32.0508	1.03498
$960$	0	0
$961$	19.3746	0.624986
$962$	−3.60549	−0.116246
$963$	49.2079	1.58570
$964$	−5.52727	−0.178021
$965$	0	0
$966$	0.729979	0.0234867
$967$	58.4290	1.87895	0.939474	−	0.342619i	$-0.111314\pi$
$967$	58.4290	1.87895	0.939474	+	0.342619i	$0.111314\pi$
$968$	78.9139	2.53639
$969$	2.17235	0.0697859
$970$	0	0
$971$	30.4483	0.977134	0.488567	−	0.872526i	$-0.337520\pi$
$971$	30.4483	0.977134	0.488567	+	0.872526i	$0.337520\pi$
$972$	−13.0462	−0.418457
$973$	5.39552	0.172973
$974$	108.179	3.46627
$975$	0	0
$976$	−57.1898	−1.83060
$977$	−4.89196	−0.156508	−0.0782539	−	0.996933i	$-0.524934\pi$
$977$	−4.89196	−0.156508	−0.0782539	+	0.996933i	$0.524934\pi$
$978$	1.60818	0.0514239
$979$	−0.878793	−0.0280864
$980$	0	0
$981$	−48.7837	−1.55754
$982$	−33.0560	−1.05486
$983$	10.1994	0.325310	0.162655	−	0.986683i	$-0.447994\pi$
$983$	10.1994	0.325310	0.162655	+	0.986683i	$0.447994\pi$
$984$	2.77796	0.0885580
$985$	0	0
$986$	−73.4020	−2.33759
$987$	0.994600	0.0316585
$988$	−60.0350	−1.90997
$989$	−17.8823	−0.568624
$990$	0	0
$991$	61.2312	1.94507	0.972536	−	0.232753i	$-0.0747734\pi$
$991$	61.2312	1.94507	0.972536	+	0.232753i	$0.0747734\pi$
$992$	−164.380	−5.21908
$993$	1.56893	0.0497884
$994$	34.6707	1.09969
$995$	0	0
$996$	−5.10647	−0.161805
$997$	−19.4529	−0.616081	−0.308040	−	0.951373i	$-0.599673\pi$
$997$	−19.4529	−0.616081	−0.308040	+	0.951373i	$0.599673\pi$
$998$	40.0466	1.26765
$999$	−0.513546	−0.0162479

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.l.1.2	✓	40
5.4	even	2		6025.2.a.o.1.39	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6025.2.a.l.1.2	✓	40	1.1	even	1	trivial
6025.2.a.o.1.39	yes	40	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.74359 q^{2} -0.0877195 q^{3} +5.52727 q^{4} +0.240666 q^{6} -1.38863 q^{7} -9.67736 q^{8} -2.99231 q^{9} +O(q^{10})\)	\(q-2.74359 q^{2} -0.0877195 q^{3} +5.52727 q^{4} +0.240666 q^{6} -1.38863 q^{7} -9.67736 q^{8} -2.99231 q^{9} -1.68686 q^{11} -0.484849 q^{12} -1.34511 q^{13} +3.80984 q^{14} +15.4962 q^{16} -3.06688 q^{17} +8.20965 q^{18} +8.07490 q^{19} +0.121810 q^{21} +4.62806 q^{22} -2.18428 q^{23} +0.848894 q^{24} +3.69042 q^{26} +0.525642 q^{27} -7.67535 q^{28} -8.72354 q^{29} +7.09750 q^{31} -23.1603 q^{32} +0.147971 q^{33} +8.41424 q^{34} -16.5393 q^{36} -0.976988 q^{37} -22.1542 q^{38} +0.117992 q^{39} +3.27244 q^{41} -0.334197 q^{42} +8.18683 q^{43} -9.32375 q^{44} +5.99275 q^{46} +8.16516 q^{47} -1.35931 q^{48} -5.07170 q^{49} +0.269025 q^{51} -7.43476 q^{52} -2.61978 q^{53} -1.44214 q^{54} +13.4383 q^{56} -0.708326 q^{57} +23.9338 q^{58} +2.45879 q^{59} -3.69058 q^{61} -19.4726 q^{62} +4.15522 q^{63} +32.5500 q^{64} -0.405971 q^{66} +5.99654 q^{67} -16.9514 q^{68} +0.191604 q^{69} +9.10030 q^{71} +28.9576 q^{72} +4.03560 q^{73} +2.68045 q^{74} +44.6321 q^{76} +2.34244 q^{77} -0.323721 q^{78} -0.0889430 q^{79} +8.93081 q^{81} -8.97823 q^{82} +10.5321 q^{83} +0.673278 q^{84} -22.4613 q^{86} +0.765225 q^{87} +16.3244 q^{88} +0.520962 q^{89} +1.86786 q^{91} -12.0731 q^{92} -0.622590 q^{93} -22.4018 q^{94} +2.03161 q^{96} -13.5274 q^{97} +13.9146 q^{98} +5.04761 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 11 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 16 q^{7} - 33 q^{8} + 38 q^{9}+O(q^{10}) \) 40 * q - 11 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 16 * q^7 - 33 * q^8 + 38 * q^9	\( 40 q - 11 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 16 q^{7} - 33 q^{8} + 38 q^{9} + q^{11} - 14 q^{12} - 9 q^{13} - q^{14} + 43 q^{16} - 12 q^{17} - 42 q^{18} + 2 q^{21} - 5 q^{22} - 77 q^{23} - 2 q^{24} + 2 q^{26} - 38 q^{27} - 42 q^{28} + 2 q^{29} + q^{31} - 72 q^{32} - 20 q^{33} + 5 q^{34} + 32 q^{36} - 28 q^{37} - 23 q^{38} - 2 q^{39} - 2 q^{41} - 37 q^{42} - 31 q^{43} + 3 q^{44} + 14 q^{46} - 96 q^{47} - 13 q^{48} + 40 q^{49} - 10 q^{51} - 42 q^{52} - 54 q^{53} + 4 q^{54} - 15 q^{56} - 37 q^{57} - 27 q^{58} + q^{59} + 5 q^{61} - 39 q^{62} - 70 q^{63} + 65 q^{64} - 52 q^{66} - 34 q^{67} - 52 q^{68} + 21 q^{69} - 9 q^{71} - 70 q^{72} - 25 q^{73} + 22 q^{74} - 47 q^{76} - 54 q^{77} - 58 q^{78} + 13 q^{79} + 12 q^{81} + 5 q^{82} - 63 q^{83} + 95 q^{84} - 18 q^{86} - 47 q^{87} - 13 q^{88} + 19 q^{89} - 31 q^{91} - 137 q^{92} - 52 q^{93} + 120 q^{94} - 49 q^{96} - 36 q^{97} - 64 q^{98} + 16 q^{99}+O(q^{100}) \) 40 * q - 11 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 16 * q^7 - 33 * q^8 + 38 * q^9 + q^11 - 14 * q^12 - 9 * q^13 - q^14 + 43 * q^16 - 12 * q^17 - 42 * q^18 + 2 * q^21 - 5 * q^22 - 77 * q^23 - 2 * q^24 + 2 * q^26 - 38 * q^27 - 42 * q^28 + 2 * q^29 + q^31 - 72 * q^32 - 20 * q^33 + 5 * q^34 + 32 * q^36 - 28 * q^37 - 23 * q^38 - 2 * q^39 - 2 * q^41 - 37 * q^42 - 31 * q^43 + 3 * q^44 + 14 * q^46 - 96 * q^47 - 13 * q^48 + 40 * q^49 - 10 * q^51 - 42 * q^52 - 54 * q^53 + 4 * q^54 - 15 * q^56 - 37 * q^57 - 27 * q^58 + q^59 + 5 * q^61 - 39 * q^62 - 70 * q^63 + 65 * q^64 - 52 * q^66 - 34 * q^67 - 52 * q^68 + 21 * q^69 - 9 * q^71 - 70 * q^72 - 25 * q^73 + 22 * q^74 - 47 * q^76 - 54 * q^77 - 58 * q^78 + 13 * q^79 + 12 * q^81 + 5 * q^82 - 63 * q^83 + 95 * q^84 - 18 * q^86 - 47 * q^87 - 13 * q^88 + 19 * q^89 - 31 * q^91 - 137 * q^92 - 52 * q^93 + 120 * q^94 - 49 * q^96 - 36 * q^97 - 64 * q^98 + 16 * q^99

Introduction

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